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{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "2fa8b1fa",
   "metadata": {},
   "source": [
    "# The Quantum Autoencoder"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1764d89",
   "metadata": {},
   "source": [
    "The goal of this tutorial is to build an Quantum Autoencoder, a circuit which can compress a quantum state onto a smaller amount of qubits, while retaining the information from the initial state.\n",
    "\n",
    "Throughout this tutorial, we explain the architecture of a Quantum Autoencoder and how one can design and train such a system to compress and encode information. Following this discussion, we give two examples to demonstrate the capabilities of such a system to compress different quantum states, as well as the ability to compress images of zeros and ones. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29f13968",
   "metadata": {},
   "source": [
    "## Contents\n",
    "\n",
    "The following tutorial is broken down as follows:\n",
    "\n",
    "1. What is an Autoencoder?\n",
    "1. The Quantum Autoencoder \n",
    "3. Components of a Quantum Autoencoder\n",
    "4. Choosing a Loss Function\n",
    "5. Building our Autoencoder\n",
    "6. A Simple Example: The Domain Wall\n",
    "7. A Quantum Autoencoder for Noisy Images of Digits\n",
    "8. Applications of a Quantum Autoencoder\n",
    "9. References "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2af97494",
   "metadata": {},
   "source": [
    "## 1. What is an Autoencoder?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9246a6a6",
   "metadata": {},
   "source": [
    "A classical autoencoder (CAE) is a type of neural network architecture that is commonly used to efficiently compress and encode information from the input using of representation learning. Following compression, one can then uncompress the data through the use of a decoder. \n",
    "\n",
    "Typical autoencoders are commonly divided into three layers, as seen in Figure 1. "
   ]
  },
  {
   "attachments": {
    "qae_fig1_wide.png": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "9b1f9027",
   "metadata": {},
   "source": [
    "![qae_fig1_wide.png](attachment:qae_fig1_wide.png)\n",
    "Figure 1: Example of a Classical Autoencoder which includes the input, bottleneck and output layer."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6c4123a",
   "metadata": {},
   "source": [
    "The first layer is called the Input Layer (1) and is the layer of which we input our data of length $n$. \n",
    "\n",
    "The input data then passes through an encoder and travels to the next layer, which has less nodes or is reduced in dimensions and is known as the Bottleneck Layer (2). The input layer is compressed through this process. Common CAEs may have several layers.\n",
    "\n",
    "The final layer is called the Output Layer (3). Here the compressed data is reconstructed to its original size, $n$, from the compressed data through the process of a decoder. \n",
    "\n",
    "By passing our input data through a CAE, we are therefore able to reduce the dimensionality of our input data, as seen in the bottleneck layer, while retaining as much information as possible from the input data. Because of this feature, common uses of CAE are Image Denoising, Anomaly Detection and Facial Recognition devices. For more information on classical autoencoders, see [1]."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1ff37d8",
   "metadata": {},
   "source": [
    "## 2. The Quantum Autoencoder "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66031d83",
   "metadata": {},
   "source": [
    "We can also define a quantum counterpart to the CAE, the Quantum Autoencoder. Much like the CAE, the Quantum Autoencoder aims to reduce the dimensionality of the input of the neural network, in this case a quantum state. A pictorial representation of this can be seen in Figure 2."
   ]
  },
  {
   "attachments": {
    "qae_fig2_wide.png": {
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    }
   },
   "cell_type": "markdown",
   "id": "31f6a05e",
   "metadata": {},
   "source": [
    "![qae_fig2_wide.png](attachment:qae_fig2_wide.png)\n",
    "Figure 2: Pictorial Representation of a Quantum Autoencoder. Here one can see the similarities with the CAE, with the circuit having an input state, bottleneck state and an output state."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1110c76f",
   "metadata": {},
   "source": [
    " \n",
    "\n",
    "Much like its classical counterpart, our circuit contains three layers. We first input our state $|\\psi>$ (which contains $n$ qubits), of which we wish to compress. This is our input layer (1). \n",
    "\n",
    "We then apply our parametrized circuit on our input state, which will act as our encoder and 'compresses' our quantum state, reducing the dimensionality of our state to $n-k$ qubits. Our new compressed state is of the form $|\\psi_{comp}> \\otimes |0>^{\\otimes k}$, where $|\\psi_{comp}>$ contains $n-k$ qubits. \n",
    "\n",
    "This parametrized circuit will depend on a set of parameters, which will be the nodes of our Quantum Autoencoder. Throughout the training process, these parameters will be updated to optimize the loss function. \n",
    "\n",
    "We disregard the remaining $k$ qubits for the remainder of the circuit. This is our bottleneck layer (2) and our input state is now compressed. \n",
    "\n",
    "The final layer consists of the addition of $k$ qubits (all in the state $|0\\rangle$) and applying another parametrized circuit between the compressed state and the new qubits. This parametrized circuit acts as our decoder and reconstructs the input state from the compressed state using the new qubits. After the decoder, we retain the original state as the state travels to the output layer (3)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38ef78c0",
   "metadata": {},
   "source": [
    "## 3. Components of a Quantum Autoencoder"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f4aae55",
   "metadata": {},
   "source": [
    "Before building our Quantum Autoencoder, we must note a few subtleties.\n",
    "\n",
    "We first note that we cannot introduce or disregard qubits in the middle of a Quantum Circuit when implementing an autoencoder using Qiskit. \n",
    "\n",
    "Because of this we must include our reference state as well as our auxiliary qubits (whose role will be described in later sections) at the beginning of the circuit. \n",
    "\n",
    "Therefore our input state will consist of our input state, reference state and one auxiliary qubit, as well as a classical register to perform measurements (which will be described in the next section). A pictorial representation of this can be seen in Figure 3. "
   ]
  },
  {
   "attachments": {
    "qae_fig3_wide.png": {
     "image/png": 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    }
   },
   "cell_type": "markdown",
   "id": "premium-inspector",
   "metadata": {},
   "source": [
    "![qae_fig3_wide.png](attachment:qae_fig3_wide.png)\n",
    "Figure 3: Pictorial Representation of input state of Quantum Autoencoder. Note that we must also include an auxiliary qubit, the reference state and classical register at the beginning of the circuit, even though they are not used until later in the circuit."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5faba1fc",
   "metadata": {},
   "source": [
    "## 4. Choosing a Loss Function "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6186d9a",
   "metadata": {},
   "source": [
    "We now define our cost function, which we will use to train our Quantum Autoencoder, to return the input state. There's a bit of math involved here, so skip this section if you're not interested! \n",
    "\n",
    "We take the cost function as defined in [2], which tries to maximize the fidelity between the input and output state of our Quantum Autoencoder. \n",
    "\n",
    "We first define subsystems $A$ and $B$ to contain $n$ and $k$ qubits respectively, while $B'$ is the space which will contain our reference space. We call the subsystem $A$ our latent space, which will contain the compressed qubit state, and $B$ our trash space, which contain the qubits of which we disregard throughout compression. \n",
    "\n",
    "Our input state therefore $|\\psi_{AB}>$ contains $n + k$ qubits. We define the reference space $B'$ which contains the reference state $|a>_{B'}$. This space will contain the additional $k$ qubits we use in the decoder. All of these subsystems can be seen in Figure 3. \n",
    "\n",
    "We define the parameterized circuit as $U(\\theta)$ which we will use as our encoder. However the structure and parameters of our parametrized circuit is currently unknown to us and may vary for different input states. To determine the parameters to compress our input state, we must train our device to maximally compress the state by adjusting the values of the parameters $\\theta$. For the decoder we will use $U^{\\dagger}(\\theta)$.\n",
    "\n",
    "Our goal therefore is to maximize the fidelity between the input and output states, i.e.\n",
    "\n",
    "$$\\text{max }F(\\psi_{AB}, \\rho_{out})$$\n",
    "\n",
    "where\n",
    "\n",
    "$$\\rho_{out} = U^{\\dagger}(\\theta)_{AB'} \\text{Tr}_{B} [U(\\theta)_{AB}[\\psi_{AB} \\otimes a_{B'}]U^{\\dagger}(\\theta)_{AB}]U(\\theta)_{AB'}$$\n",
    "\n",
    "We can maximize this fidelity by tuning the parameters $\\theta$ in our parametrized circuit. However, this fidelity can at times be complicated to determine and may require a large amount of gates needed to calculate the fidelity between two states, i.e. the larger the number of qubits, the more gates required which results to deeper circuits.  Therefore we look for alternative means of comparing the input and output states. \n",
    "\n",
    "As shown in [2] a simpler way of determining an optimally compressed state is to perform a swap gate between the trash state and reference state. These states usually have a smaller number of qubits and are therefore easier to compare, due to the smaller amount of gates required. As shown in [2] maximizing the fidelity of such these two states is equivalent to maximizing the fidelity of the input and output state and thus determining an optimal compression of our input circuit. \n",
    "\n",
    "Keeping our reference state fixed, our cost function will now be a function of the trash state and is denoted as; \n",
    "\n",
    "$$\\text{max }F(\\text{Tr}_{A} [ U(\\theta)_{AB}\\psi_{AB} U^{\\dagger}(\\theta)_{AB}], a_{B'})$$\n",
    "\n",
    "Throughout the training process, we adjust the parameters $\\theta$ in our encoder and perform a swap test (as described below) to determine the fidelity between these trash and reference states. In doing so, we must include an additional qubit, our auxiliary qubit, which will be used throughout the swap test and measured to determine the overall fidelity of the trash and reference states. This is the reason why we included both an auxiliary qubit and classical register in the previous section when initializing our circuit.  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af4f5611",
   "metadata": {},
   "source": [
    "### The SWAP Test"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "721636a1",
   "metadata": {},
   "source": [
    "The SWAP Test is a procedure commonly used to compare two states by applying CNOT gates to each qubit (for further information see [3]). By running the circuit $M$ times, and applying the SWAP test, we then measure the auxiliary qubit. We use the number of states in the state $|1\\rangle$ to compute:\n",
    "\n",
    "$$S = 1 - \\frac{2}{M}L$$\n",
    "\n",
    "where $L$ is the count for the states in the $|1\\rangle$ state. As shown in [3], maximizing this function corresponds to the two states of which we are comparing being identical. We therefore aim to maximize this function, i.e. minimize  $\\frac{2}{M}L$. This value will be therefore be our cost function."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24563883",
   "metadata": {},
   "source": [
    "## 5. Building the Quantum Autoencoder Ansatz"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa17e37a",
   "metadata": {},
   "source": [
    "First, we implement IBM's Qiskit to build our Quantum Autoencoder. We first begin by importing in the necessary libraries and fixing the seed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "6497cb31",
   "metadata": {},
   "outputs": [],
   "source": [
    "import json\n",
    "import time\n",
    "import warnings\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from IPython.display import clear_output\n",
    "from qiskit import ClassicalRegister, QuantumRegister\n",
    "from qiskit import QuantumCircuit\n",
    "from qiskit.algorithms.optimizers import COBYLA\n",
    "from qiskit.circuit.library import RealAmplitudes\n",
    "from qiskit.quantum_info import Statevector\n",
    "from qiskit.utils import algorithm_globals\n",
    "\n",
    "from qiskit_machine_learning.circuit.library import RawFeatureVector\n",
    "from qiskit_machine_learning.neural_networks import SamplerQNN\n",
    "\n",
    "algorithm_globals.random_seed = 42"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5793bc10",
   "metadata": {},
   "source": [
    "We begin by defining our parametrized ansatz for the Quantum Autoencoder. This will be our parametrized circuit where we can tune the parameters to maximize the fidelity between the trash and reference states. \n",
    "\n",
    "### The Parametrized Circuit \n",
    "\n",
    "The parametrized circuit we will use below for our encoder is the RealAmplitude Ansatz available in Qiskit. One of the reasons why we have chosen this ansatz is because it is a 2-local circuit, the prepared quantum states will only have real amplitudes, and does not rely on full connectivity between each qubits, which is hard to implement or can lead to deep circuits. \n",
    "\n",
    "We define our parametrized circuit for our Encoder below, where we set the repetition parameter to `reps=5`, to increase the number of parameters in our circuit allowing greater flexibility. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "78152563",
   "metadata": {},
   "outputs": [],
   "source": [
    "def ansatz(num_qubits):\n",
    "    return RealAmplitudes(num_qubits, reps=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "seasonal-atmosphere",
   "metadata": {},
   "source": [
    "Let's draw this ansatz with $5$ qubits and see what it looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "expanded-consensus",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1123.61x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num_qubits = 5\n",
    "circ = ansatz(num_qubits)\n",
    "circ.decompose().draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8925b02",
   "metadata": {},
   "source": [
    "We now apply this Encoder to the state we wish to compress. In this example, we divide our initial $5$ qubit state into a $3$ qubit latent state ($n = 3$) and $2$ qubit trash space ($k = 2$). \n",
    "\n",
    "As explained in the previous section, we must also include a $2$ qubit reference space in our circuit, as well as an auxiliary qubit to perform the swap test between the reference and trash states. We will therefore have a total of $2 + 3 + 2 + 1 = 8$ qubits and $1$ classical register in our circuit.\n",
    "\n",
    "After initializing our state, we apply our parametrized circuit.\n",
    "\n",
    "Following this, we then split our initial state into the latent space (the compressed state) and trash space (the part of the state we will disregard) and perform the swap test between the reference state and the trash space. The last qubit is then measured to determine the fidelity between the reference and trash states.  A pictorial representation of this is given below in Figure 4. "
   ]
  },
  {
   "attachments": {
    "qae_fig4_wide.png": {
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    }
   },
   "cell_type": "markdown",
   "id": "bound-blond",
   "metadata": {},
   "source": [
    "![qae_fig4_wide.png](attachment:qae_fig4_wide.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "31edf744",
   "metadata": {},
   "source": [
    "Figure 4: Example of a Quantum Autoencoder in the training process. We use the swap test to determine the fidelity between the trash and reference space. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d24d20fb",
   "metadata": {},
   "source": [
    "We define a function below to implement the above circuit configuration to the $5$ qubit domain wall state $|00111\\rangle$ and plot an example below. Here qubits $5$ and $6$ are the reference state, $0, 1, 2, 3, 4$ are the initial state we wish to compress and qubit $7$ is our auxiliary qubit which is used in the swap test. We also include a classical register to measure the results of qubit $7$ in the swap test. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "1d415550",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1374.44x785.944 with 1 Axes>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def auto_encoder_circuit(num_latent, num_trash):\n",
    "    qr = QuantumRegister(num_latent + 2 * num_trash + 1, \"q\")\n",
    "    cr = ClassicalRegister(1, \"c\")\n",
    "    circuit = QuantumCircuit(qr, cr)\n",
    "    circuit.compose(ansatz(num_latent + num_trash), range(0, num_latent + num_trash), inplace=True)\n",
    "    circuit.barrier()\n",
    "    auxiliary_qubit = num_latent + 2 * num_trash\n",
    "    # swap test\n",
    "    circuit.h(auxiliary_qubit)\n",
    "    for i in range(num_trash):\n",
    "        circuit.cswap(auxiliary_qubit, num_latent + i, num_latent + num_trash + i)\n",
    "\n",
    "    circuit.h(auxiliary_qubit)\n",
    "    circuit.measure(auxiliary_qubit, cr[0])\n",
    "    return circuit\n",
    "\n",
    "\n",
    "num_latent = 3\n",
    "num_trash = 2\n",
    "circuit = auto_encoder_circuit(num_latent, num_trash)\n",
    "circuit.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c0bc911",
   "metadata": {},
   "source": [
    "In order to reconstruct the original input state, we must apply the adjoint of our parametrized circuit after the swap test. However, during training, we are only interested in the trash state and the reference state. We can therefore exclude the gates following compression until we wish to reconstruct our initial input. \n",
    "\n",
    "After building our Quantum Autoencoder, the next step is to train our Quantum Autoencoder to compress the state and maximize the cost function and determine the parameters $\\theta$. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a578973",
   "metadata": {},
   "source": [
    "## 6. A Simple Example: The Domain Wall Autoencoder"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc886404",
   "metadata": {},
   "source": [
    "Let's first begin with a simple example, a state known as the Domain Wall, which for $5$ qubits is given by $|00111\\rangle$. Here we will try and compress this state from $5$ qubits to $3$ qubits, with the remaining qubits in the trash space, in the state $|00\\rangle$. We can create a function to build the domain wall state below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "2787d73c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 203.885x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def domain_wall(circuit, a, b):\n",
    "    # Here we place the Domain Wall to qubits a - b in our circuit\n",
    "    for i in np.arange(int(b / 2), int(b)):\n",
    "        circuit.x(i)\n",
    "    return circuit\n",
    "\n",
    "\n",
    "domain_wall_circuit = domain_wall(QuantumCircuit(5), 0, 5)\n",
    "domain_wall_circuit.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dcc66776",
   "metadata": {},
   "source": [
    "Now let's train our Autoencoder to compress this state from 5 qubits to 3 qubits (qubits 0,1 and 2), with the remaining qubits in the trash space (qubits 3 and 4) being in the |00> state. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a8442b1",
   "metadata": {},
   "source": [
    "We create a circuit to be used in the loss function, as described in Section 4, which determines the fidelity between the two states below using the swap test for our particular AutoEncoder function. For further information on the swap test, see [1]. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "602efbb0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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OHs9SU/9gXdL5Oo0dPE3Nm1xQuX123gEt/vYFbdn9lQ7l7lVJaZFaBbXXoJ536pYrn5CX2atWOY4eP6gfU1Zo9MC/6eJOQ9WsyQVa/fPbiu9w+hUPb38uUiHNI/Xg9f/S3E8nKmXfj7L4NNZVPcbonqGJKreV6d+rp2rd1oU6VnhEnSJ665Gb56ptyB/zp32etECzPr5Lifes0a/p3+nzpH/r6PEshbfsqNuuekr940edNfOpc+xMfL2ffvn9G0nSoEl/jDQ6OadQTXPjZOWka8z0dhoz6JkqI32OFx7VWysTtOHX/+pEaZFiInrpvmEv1Jjnt/0btfCr/9P2tPUqKjmukKBIDexxh0b1m1zlNLv0rB16d82zSk7/XscKstXEr7nahHTWLVc+oYs7X3vW+w3ANfj4+CgoKMjoGAAAJ3LbYkeqmOx4xYoVp92en5+v9PR0mc1mde3atcoym82m0aNH66uvvtKqVavUu3fvhorrdKY2beSz8pMzruN1263yuu3WBkrkuIRRC5QwaoHRMQCPZD2yR5LUtHHFC4BDR/dpwpw+Kis/ocG9x6l1iyhlZqdqxQ+va+uedXptwkb5+wVKktKsv2jD9qXq2/VGtWoRpXJbqZJ2rtbbq6Yo68jvenTE3FplWLPpXdns5RrU4w55eXnrqgtHa8WPb6igKK/yWH+WnZehKW8O0pXxt+ryuBHatOsLLfn2RXmZvbX34A6VlBZpVP8pyivI1uJvZunZd27Q20+knHaK57xVk1V8okDDLn1QkvRF0r/13Ae36URpscMTPP/lqqdlt9u0PW29Jo96r/L22MhLHdqPJJWVl+rJedfot/1JGnjRGHVue4n2HNiqyW8OVNPGLU5b/6eUlfrHOzepdXAHjbhyogL8gpS89we9+/nftefAVv19zH8kSccKjmjS3IqRrNddcr9CmrdVXkG2dmVsVMq+nyh2ADeyb98+zZgxQ1OmTFGbP43mBgC4LrcudmqyY8cO2e12xcTEnDZp3EMPPaT//Oc/mjJliho3bqwff/yxcllUVFS1l0MHAFdXXFqovIJs2e0Vc+x8+sMbSs3cok4RvRXesmK4/pxlD6u8vFSvP7pFLZuFV257RdwtmjDnEi1Z/1LlyJK4qCv17pO/V5kL56bLH9WMhWP02c/zNObqZ9Wi6dlPcV2dNF/d2l2h0KBISdKgnndqyfqXtHbLhxp26QOnrX/gyB5Nvf1jXdn9FknSsD7368GXe+g/3zyvSzoP08x7v6zM1NS/hV775BFt2r1GvTpeU2U/eQXZevPxXyrLo2GX3K97X4zT3E8fV7/4W9XIp3YTv0tSj5hB+mrzB9qetl4De9xe6+2q83nSv/Xb/iTdPvDvuvOaf1Te3jaki15f/phCmretvO1EabFe+HicOrW5WM/ft7ZydM51fe5TVOvueuPTx7Vtz9fqHtVPv6ZvUG7+IU29fZGu7D7ynDICOL8dP35c69at00MPPWR0FACAk7jtHDtnsn37dknVn4b12WefSZJmzJihPn36VPm3cuXKBs0JAA3l3S+e0YhnW+qWf1yge1+M06c/vKbLut6kf4ytGPVXUJSnn1JW6JLY4fL1sSivILvyX2hQpMJadNCmXV9U7q+Rj19lgVJadkLHCnOUV5CtnjHXyGa3aVfG2SeV35H+vfYf2qlBPf84DTOqdXdFtY7X6qTqJ7QPDgyrLHVOim13mex2u27o+3CVoqlbu8slSZnZu0/bz7A+D1QZEeTvF6jr+tyv40VHDZ3jZ8OOZTKbvTTiyolVbr+uzwNqbGla5bZNu9foaP5BXd3rLuUX51Z5znp3GipJ2vi/58zfUnFff975mQqKjzXAPQEAAICzeOSInTMVO+np6Q2cBgCMd+3F9+qKuFtUZitVmnW7Fn2dqOy8jMpJgPcf/k02u02rf35bq39+u9p9tApqX/l5eXmZPlo3Q2s2vasDR1JPm6A9v/DoWTOt/vlteXv5qEPrC5WZnVp5e8+O12jRukT9fuAXtW8dV2Wb0KB2p+0nwK95tcua/O/24wVHTtumzQWdT7ut7QUV861Zj/x+1uz1JevI72oR0Er+p5Q4vt6N1CqovfKL/nhc9x1MkSS98PFfa9xf7vGDkqTuUVdqUI879MXGBVq75QPFhPfSRdED1S/+VrUNcc155gAAADwFxQ4AQGHB0booZqAkqXenIera7jI99tpl+teS+/X07R/Jropi5qqLbtfVPU6fyFySfP90etIbnz6uZRteUb/ut+ovVz2tZk0ukLfZR7szN2veqsmy2W1nzFNUkq9vfvlYZeWleuDlC6tdZ3XSfD14/ctVbjObap6U2VzDhM0n75tRarp0e7mt7Jz2e/J+3Xvt84pqHV/tOi0CW1d+njDqHd3Sb5KSdn6m7WnrtfjbF/Th2v/TA8Nf1g19x59TFgAAANQfjyx21q5da3QEADivxUZeqoEXjdGaTe/qhssmKKJlR5lMJpWVn6gsgM7ky83vqVv7K/T07R9VuT3zSGoNW1T1zbaPVVSSr78OeU5hwdGnLV/23Wx9tfl93XPtTPl4+9buTjlg36EUXaqqVwrceyhZktSqRfvqNjmjmsobSQrwC9Luwk2n3V7dyKDQFu21adcXKig+VmXUzomyEllzfq8cnSSp8nGz+PrX6jmTpHahXdUutKtG9puk/KJcPfzKxXp71RRdf+lDZ7wPAFxHSEiIJk+erJCQEKOjAACcxCPn2AEAnN3ogX+T2eyldz7/u5r6t1DvTkP13falSt7742nr2u125eYfrvzabPKSTjn9quhEgZauf6lWx/7s57cV0DhII6+cpCviRpz2b3DvcTpWeETf7zjzlf/q6tMfXldBUV7l1wVFeVrxwxtq4tdMce2vdHh/fo2aSJKOFeactiy8ZYwKS45r576fK2+z2WzVPlaXdrleNlu5Fn9T9fLmK354XYWnzI3Ts+M1atbkAn20bka1xy0pLVJh8fHKXDZb1VFUTfyaKbR5O5WUFupEWXEt7ymA811wcLDGjh2r4OBgo6MAAJzEI0fsAADOLiy4g/p3H6Wvtnyg7b+v14SbXtdjr16mia9foYE97lCH1hfKbrfJmvO7vt/xiQb1uKPyqliXx43Qyh/natr7t+qi6IE6evygVifNr/aS3Kfad2inkvd+r6t7jq28ktOp+nQZLm8vH63++e3TJkt2hkD/YD38ysW6utddkioud34od58ev2WeLL6Nz7L16Tq3uUSfbJijV5Y+qN6dr5W3l486tblYrYLaaegl92rxty/o2Xdu1I2XPSIfb199+8viak/FuqbXXVr105t6/8t/KisnTV3a9lHqgS369pf/qHWLqCrb+Pn6K2HUu3p2wQ3668yOuqbXXxUW3EH5Rbnaf2invvt1qZ6987/qHtVPX256V0u+fUl9u96o1sEd5G320S+/f6ONuz7Xld1HOnQVMADnt7y8PP3www/q06ePAgMDz74BAOC8R7EDAKjRbVc9rXVbF+qdL/6uWfev02uPbtKidYn6fscn+mrz+/L1tqhlswhd0mVYlctk3z/sRTVuFKBvtn2s73d8opbNInTtxfcqJqKXJr955tOCTk7OfFm3m2pcJ6Bxc3WP6q/Nu9foUO5+XdAswjl3+H/uHpqo7Wnrtfz7V5V7/KDCWsboyb98oAEX/qVO++sff5tSM7fo620f6dtf/iOb3aYnRv5brYLaqVVQOz175zLN/+wpvfP53xTg30IDLxqjwb3+qr8+36nKfny8fTXj3jV6a8UkbdixTN9tX6KYiF6acc8avbniCR08ml5l/V4dr9GcR5K0aO0MfbX5feUVHFYTv+Zq3SJKN1/+uNq1qph8Oq59P6VmbtFPKSuUc8wqs9lLoUHtdO91s3Q98+sAbiUjI0OPPfaYFi9eTLEDAG7CZD/1UiU4LxSUl6n52jVGx6i1owMGyb+Gd9bPpPyEtG52PQQCgDr4PGmBZn18l2bdv07do/oZHQeAm+g/QfJy/nRglXbu3FnrdXfs2KERI0Zo8eLFio2NrfV2nTp1OvtKAABDMMcOAAAAAACAi6LYAQAAAAAAcFEUOwAAAICHsFgs6ty5sywWi9FRAABOwuTJAAD8zzW9xuqaXmONjgEA9SYqKkpLly41OgYAwIkYsQMAAAAAAOCiKHYAAAAAD5GcnKy4uDglJycbHQUA4CQUOwAAAICHsNvtKi0tld1uNzoKAMBJmGPnPNXY7KWjAwYZHaPWGpu9jI4AAAAAAIDHodg5T5lMJvl78fQAAAAAAICacSoWAAAAAACAi2JICAAAAOAhoqKitHz5ckVERBgdBQDgJBQ7AAAAgIewWCyKjo42OgYAwIk4FQsAAADwEJmZmZo6daoyMzONjgIAcBKKHQAAAMBD5ObmasmSJcrNzTU6CgDASSh2AAAAAAAAXBTFDgAAAAAAgIui2AEAAAAAAHBRFDsAAACAhzCbzerVq5fMZl4GAIC74Dc6AAAA4CFsNpuSkpJks9mMjgIAcBKKHQAAAAAAABdFsQMAAAAAAOCiKHYAAAAAAABcFMUOAAAA4CECAwM1bNgwBQYGGh0FAOAk3kYHAAAAANAwwsPDNXPmTKNjAACciBE7AAAAgIcoKSnR3r17VVJSYnQUAICTUOwAAAAAHiI1NVWDBw9Wamqq0VEAAE5CsQMAAAAAAOCimGPnPGW321VoKzc6Rq01NnvJZDIZHQMAAAAAAI9CsXOeKrSVq/naNUbHqLWjAwbJ34tvJwAAAAAAGhKnYgEAAAAAALgohlgAAAAAHiI2NlYpKSlGxwAAOBEjdgAAAAAAAFwUxQ4AAADgIdLS0jRq1CilpaUZHQUA4CQUOwAAAICHKCws1LZt21RYWGh0FACAk1DsAAAAAAAAuCiKHQAAAAAAABdFsQMAAAAAAOCiKHYAAAAADxEWFqbExESFhYUZHQUA4CTeRgcAAAAA0DCaNWum4cOHGx0DAOBEjNgBAAAAPEROTo4++OAD5eTkGB0F9cBmk3Z+KRUcqfs+Sgqk5M+lshPOywWgflHsAAAAAB7CarVq2rRpslqtRkeBk9ls0o6VUsZWadOiupU7JQXS5kXSge3S1qWUO4Cr8IhiJzs7WwkJCerQoYMsFosiIiL0yCOPqKCgQOPGjZPJZNKcOXOMjgkAAAAAdWIrlQpzKz4/Ueh4uXOy1Cn432Cu4mNSWbHTYwKoB24/x87WrVs1ZMgQZWVlyd/fX126dNGBAwc0e/Zs7dmzp3IYanx8vLFB60n5/AWyffSxvB5/VObBV1dZZrfbVT5piuwpKfKeM1umdpHGhDyD/Yd+0/tf/lO7MzfryLEDKi8v1QXN2qh3p6G6pd8ktWjayuiIAAAAgOG8G0kX3SJt/o90/OAf5U6PWyX/Fmfe9tRSx9K0YjtL0/rPDeDcufWInezsbA0bNkxZWVmaOHGirFarNm/erKysLCUmJmrlypVKSkqSyWRSXFyc0XHrhXnMaCmyrcrnviX74ewqy2xLl8n+y3aZx9x+XpY6knQ4L0M5x6zq2/VGjRsyXQ8Mf1kXxQzSyp/e1IP/6qGj+YeMjggAAACcF3wsFeVOQEjF17UZuVNTqeMXWP95ATiHWxc7EyZMUEZGhsaPH69Zs2YpICCgcllCQoK6d++usrIyRUZGqmlT96yjTT4+8p40USouVvmLL1febt+fIduCd2Xq1FHmW242LuBZXBR9lZ6/f63GDXlOwy99UNdecq/G3/CKnhj5b+Ucs+qLpAVGRwQAAHAZ/v7+6tu3r/z9/Y2OgnriSLlDqQO4B7ctdlJSUrRo0SIFBwdr+vTp1a7To0cPSVL37t0rb1u/fr0GDhyoVq1aqVGjRgoPD9ett96qlJSUBsldH0zRHWQeNVL2TZtlW/mZ7OXlKp85S7Lb5TVpokxeXkZHdFhI87aSpPyiowYnAQAAcB2RkZGaN2+eIiMjjY6CelSbcodSB3AfbjvHzsKFC2Wz2TR69Gg1adKk2nX8/PwkVS12jh49qm7duum+++7TBRdcoIyMDE2fPl19+vTRr7/+qvDw8AbJ72zm0bfJ9sNPKn9rnsx7fpf9t10y33u3TBGucX9OlBar6ES+TpQWa+/BZM1bNVmS1LvTUIOTAQAAuI7y8nIVFRXJz89PXi745h5q72S5U92cO94WSh3AnbhtsbN27VpJUv/+/WtcJyMjQ1LVYmf48OEaPnx4lfV69eqljh07asmSJXrkkUfqIW39M3l7y3vS4yp7+FHZVqyUqWuszDfdYHSsWlv18zy9uuzhyq9Dm0dqym3vq1v7yw1MBQAA4Fp27typESNGaPHixYqNjTU6DupZdeXOxo8kb1+pKK9iHUodwPW5bbGzd+9eSVLbtm2rXV5WVqYNGzZIqlrsVKdFi4pp5L296/Zw9ezZU1lZWQ5tY/f1lea+Wqfj1cjfX/LxkcrKZOrVUyaz887Ei4mOkenECYe38/X205vjd591vb6xN6hNy04qOpGv1Mwt+iF5ufIKss+6HQAAgNGiY6J1oqyo3vY/duzYWq9rtVolSatWrdKWLVtqvd2CBQscTIXzSeNGgUq4aaEiQ+JUWiSV/u/bMfvYfs2Yf4uy/5lhbEAACg0N1caNG+u0rdsWOwUFBZKkoqLq/4guWrRI2dnZCggIULt27U5bXl5eLpvNpr179+rJJ59UaGioRo4cWacsWVlZyszMdGwjSyP51Olo1bPb7Sp/4SWprFRqEyHbhx/JfOUVMrV2zuXCD1gPSMUlDm9n8Wlcq/VaNgtXy2YVp4317XqDLu92s8bP7qWS0kLdNuBJh48LAADQUKwHDqi4tLDe9l9YWPt9FxcXV350ZDuH/y+L80ym/vHOLXrjsa1q5FMxHYXdbtfMhWO1LfUng7MBOFduW+yEhobq6NGj2rx5s/r06VNlmdVq1aRJkyRJcXFxMplMp21/5ZVXVo7o6dChg9auXauWLVvWOYuj7L6+Olyno1XPtmy57Nt+kfmuO2Xuc4nKHnpY5S+8JK9ZidXef0e1btW6ziN26qJ96zhFhV2oT79/rc7Fzp4D2/TS4ntUWHJcIc3aavJt76lZk5batudrPTVviMJbdtSMe79Q8yYXqPhEoV74zzjt2p8kk8msvw55TlfEjZAkvblikr7etkjRYRfpH2OXnfW4S759SSt/nCu77BrY4w6NvuppSdLMj8Zq8+41uqTLMD168xuSpH++O0I79n6vnGNW/fefR9XEr5kkqaS0SBNe6aMDR1I15bb31bfrDWc8Zn5RrmZ+dKcyDv8mXx8/PXrzXHVq01uSNGiSSZGhXXX30ERd3Hmo1m39SB+tnSGbrUySdHWvu3TLlRMlSdt/X685yx7W79ZtVfI44zGe/9nT+iF5ucymivP9Rw2Yov7xo+r9MT7pnc+f0ftf/lOvP7pFHcLiJUlPvNFfvx/YptsH/V03Xf7oGY9ZWnZCLy+5Tyl7f5DZ7KV7rp2piztfK0m6/blI+Xg30i1XTtLQi++ucv9Pmv3wD2rk41evj7EkLf/+NS3b8Iq8zN4ym8x65eGf5OtjqbfHOM26XTMWjqncrqA4V4XFx7T0nzn1+hjbbDa9ueIJJf22Wl5mbzX1b6HHRrylsOAOOpC9R/9492btO5SsVx7+ufL5rsmho/s0c9GdyjmepQC/ICWMekdhwR2UlZOuO2dEKTK0mybdukAdwuJ19PhB/WvpAzqQnaoyW6muu+S+yvv19dZFem/NP3Tk2AEt+3+5Z32Mt6Su1eufPKrS8hJ1CLtIT4ycr0Y+fvo8aYFeW/6IwoKj9dojFe/qfPjVc1qz6R1lZu/WM3csrfI74Wj+Ic1ceIcO5OyRr1cjPXzTa4prf4UkafqHo7Vl91fqFz9KD17/8hnz2O12zVs1Rd/vWCaTTBrZL0GDe/9VkjTx9X46dHSvru51l8YM+ruKSvL1j3dv1u6MTSq3lVW5v2daVp/PzU8pK/XO539Xetavuq7PA1Xu73+/m61VP74pmUyV921gj9slGfe8Pb/oLu3O2CSTySxvLx+NGzpDF0VfJcmY5+3PZn40Vms2vVP5O6o+/yb9tj9Jr33yiPYc2KoeMVdX+f108jENbV7xBl1A4+aadf86SY4/b/WtVevW9Tpip3Hj2r1RJkkWi6XyoyPbhYWFOZwL54/Axi2VcPOiylJHkkwmk56+faFmLB4p69FUA9MBkOrWG5zktsXOwIEDlZKSosTERA0aNEgxMTGSpKSkJI0ZM0bZ2RWn8cTHx1e7/dtvv63c3FylpaXp+eef19VXX60NGzaoTZs2Dmepy3CqgvIyNV+7xuHtqmPPzJRt/gKZOsbIPHKETF5eMt8+WrZ/vyPbsuXyuvH6cz7Grt275O/l+LdT+Qlp3ey6HfNEaZGOF+bUbWNJzy8aqydG/lsdwuK1+uf5enPFE0oY9Y4kKbxlR819fGvluv/5ZpZ8vBrpnSmpsuakacLsixUf1V9N/Vvo3uueV9uQWH2/Y9lZj/nb/iSt375Ebzy+TWaTWU/NG6LYtpcqvkPFXFAj+02q8uL2ukvu18M3vaaR/wipsp9GPn6a+/hWTXy9X63u679XT9VFMYP0z7s+0d6DyfrnuyP01sRfZf7f6XgvPbi+skBoGRih6XevVlDTUBUU5enBf/VQTHgPdY/qp27tL9fcx7dq0KTalYGOPMYj+03SX4f8nyQpOy9T457vrIuiByrQP7heH2NJ2rnvZ/2WkVR5tbWTZt2/TjM/Glur+7rsu9lq2riF5ifs1JFjVk18/Up1bXe5/C1NJUlPj15U5UXqqff/pPp8jL//9RN9tfkDvTL+R/n7BSo3/7C8vCrGBtbXY9yuVbcqGV757/gqZXJ9PcY/JC/XjvQNmvv4Nnl7+eiDL6dp/mdP6W9jPlbr4CjNfXyrbn8uslbHnf3fBzXiiom6pMt12pK6Vi/+52698MDXkiS/RgFV7t8bnz6utiFd9OydS1V0okCPzumr2Mi+6hjRS/3ib1WnNhfr/pfiz3rME6XF+teS+zXzvq90QbMILfj87/po7Qzdec0/JEnxUf2rvMC9KHqg+seP0qyP/3ravt5eNUWd216i6fes1m/7k/TsOzfqvSfT5O3loyf/8oHe/eJZ5RflnjXT+u1LlJWTprefSFHRiXw9/trlimt/pVoHR0mS7h/+UuULei8vH93af7IC/IL0xBv9quznTMvq87kJC47WxJHz9e0v/1FRSX6V/bQNidXLD22Qv1+gDuXu1wMvXagubfuodXCUYc/bA8Nfqvy9nJq5RQlzr9LiZ7NlNpsNed7+2N9SeXtVHVNcn3+TggJa6YHhLys1c4uSfvvstH2d+pie5Mjz1hB279otL9/62//OnTtrve6OHTs0f/58DR061KE5dqZNm1aXaDgPnHr1qz8L9L9ALzzwtXrcKvm3aPhsAJzDbS93npCQoBYtWmj//v2KjY1Vt27dFB0drd69e6t9+/YaMGCApJrn1+nYsaMuvvhijRo1Sl999ZWOHz+umTNnNuRdcAq7zaby51+UbDZ5TXq88tLm5pEjZIqJlm3+AtkPWA1OWbOcY9XPTbQ1dZ3Ss35Vp7aX1Gm/qZlb5NeoSeWLwEE979QPyctVWlb9qKNvti3SdX3ulyS1CmqnuKh++u7X/zp83C83v69ret0lX+9G8vby0eDe4/TFxndqXP+imIGVIy3OxddbP9LQi++RJLUN6aKWzSK0Pe3batft2q6vgppWtMX+foGKuKCTsnLSHT6mo4/xn0emFJXkyy67bHabw8d19DEuPlGoOcvG69Gb5zp8rKrHfU/D+jwgSWrRtJXio/rru+1Lz2mfZ+PoY/zxN89rzKBn5P+/2RGbNWkpL7PjV0Rx9DE+6URpsdZu+UCDe41z+JgVx639Y2ySSSfKSnSitFh2u12FxcfUMtDxqwAeKziiNOt2XdLlOknShR0GKOe4tcafid8PbKu8Wp+fr7/i2l+hLze95/Bxf975mTq1uVgXNIuQJA3r84DWbKr5Me7UprdatWhf7bJvtn2s6y6p+P3VMaKXWjRtrV/2fONwpi83vadrL7lPZrNZ/pam6hc/Sl9urv6++Xo30oUdBlQ74uxMyxzh6HMT3jJGUa27y8t8+psQF0VfVflzcUGzCAUFhOpw3n6HMznzefvz41NQnOdwlpOc9bxJ0tHjB7Vw7XO6f9iLdc4jOfY3qWWzcHVq01s+3o3O6Zj4Q0xMjDZs2FD5pifcW3WXND9VdZdCB+Ba3HbETnh4uNavX69Jkybpm2++UXp6urp06aK5c+fqnnvuUVRUxTtVZ5s4WZKaNWumDh06KDXV9YYo2hYvlT05Rea775LpT6ONTF5e8nricaefkuVss5c+oCPHrYrvMEAhzdrqRFmxdmds0tfbPpJfowDdd90LddqvNSdNadbtuu/F+MrbSk4UKvtY9eePH8rdV2U0R2jzSB3K3efwcbNy0vRj8qda9t0rkqTi0gK1aNra4f044lhhjvKLc/Xw7Isrbzuct1/WnDR1j+p3xm33HkxW8t4f9MhNb5xxveo4+hhLFadDLP/+VWXnZuixW+bVqdRy9DF+a2WCruvzQOULsbrKyknTs+/cKJOpoi/PzT+o5gE1D6e05uzRAy9fJLPJS9f0ukvDL33Q4WM6+hjvO5isXRkb9d6af6i0vESDetyhGy+b4PBx6/p9/N2vS9UqqP1ZT68503Fr+xhf0mWYtu5Zp1v/GSq/RgEKDgzTCw84XmYcPLpXeQWHqzzGR44dUFZOmkKDTp+fLTq8h9Zu+VCd21yiY4VHtHHX51VOuautrJw0bfrt8yrHPZyXofLyMof2c6zgiMrLSyvLWkkKOYffX3P++5B8vCtO48gvOnrW3yH1ydHnprY27/pSx4uOKiail8PbOut5O2neqin6dtt/lF90VH+/Y0nliBZHMznreXtx8T2659qZamwJqNP20rn9TarOr2nf6b4X42XxbaybLn9MV3a/pc7ZPIWPj4+CgoKMjoEGUF2p0+NWacM8SfaK2wJCTr8UOiN3ANfjtsWOJHXu3FkrVqw47fb8/Hylp6fLbDara9euZ93PoUOH9Ntvv+niiy8+67rnE/u+fbK9855MnTvJfPNNpy03RbZ1+ilZztb/wtu0ZtO7+mrTe8otOCyTTApp3lbXXnKfRl45SRc0d/zUuJM6tblYM+75vPLrEc/WbQ4lR901+P804MLbJEk/pazUoq/rfySYl8mryikJ/3zv7P/xPZybob8vuF6P3PRG5cTVjnL0Mb7xsgm68bIJ2nNgm2YsvF09Y65W0zr876K2j/GmXWt06OhePXzjHIePUZ3p93yuFk0rJiR/c8WkGtfrEHaRFj6dIX+/QB3OzdDTbw9VoH+wruzu+ATtjjzG5bYyZeWk6cUHv1V+0VFNfP1KtQpqXzniwRF1+T7+7Oe3Nbh33UbrnFTbx3hXxkalZ/2qhX/LVONGTfX2qin615L7NeUv7zt8zJbNIqr8/Dz0r5pf8N837AXN/fQJPfDyhWrW5AJ1b99PuQV1mzGtb9cb9eiIipFkRScKdMPUat5mbWBPjPy3ukRWzFv3yYZX9dv+nw3N48hzUxtp1u2a9fFdmnr7Ivn5+tdpH8583u4eOkN3D52hzbu+1FsrE/TyQxvk4+34+TzOeN5W/TRPFzRrows7DHB421PV5W9SdS7pcp2u7D5SFt/G2nswRU++dbVaNotQlzqO5vUU+/bt04wZMzRlypQ6TTEA11BTqVPlkuam0y+FTrkDuCa3PRXrTHbs2CG73a7o6OjTJo27/fbb9eyzz2rZsmX6+uuv9dZbb6lfv37y9vbWY489ZlDiujG1aSOflZ/I+18vVp6CdSqv226VzxerzstSR5Ku7D5S0/66Qh9O3a9V04u1cnqR5ifs1PgbXjmnUqdVUPsq71gXFB9T8YkCBTetfmLAC5q10cGjeyu/zjqarguaOX78U4+blZOuVkHVD8N3lqaNg+Tr46ejxw9W3nbwLMfNzjugyW8O1Oirptb53U9HH+M/i2rdXcFNw7Rtz9fnfNwzPcZbU9dqd+Zm3f5cpG5/LlKH8zL09Pyh+iH5U4ePG3rqcY+m13iKhb+laeVpHy2bhav/hbdpe9p6h49Zl+/j/hfeJi+zlwL9g9W701Cl7PvxnI9bm+9ja06adu79UQMu/IvDxzvJkcd4zaZ3Ff+/U0rMZrMG9bxTW/esc/iYIUGRyjmeVTniwm6361DuvhqPG+gfrIRRCzT38W1KvHeNZDIpMqT2c1ic1KpF1ft6MKfid46Xg3OZNfVvIS+zd5XTWg/W9ffXqZmO1v/vrzNx9Lk5m70HkzV1/nWaOHK+ura7rE77cNbzdqqLYgaqqOS40rK2n3umOj5v2/as0w87Pqn8fSlJ974Yp9TM2l8uW6rb36SaBPoHy+Jb8f+4tiGd1bvTUO1I3+DwfjzN8ePHtW7dOh0/ftzoKKgntSp1/sfHUlHuBPxvOkdOywJck0cWO9u3V/zHqLrTsC655BKtWrVKd911l4YMGaLnn39el19+ubZu3aoOHTo0dFTUkw5h8fI2+2jTrooJqj/9/jVd2f3WGt8JvSLuFq34oeJ0JGtOmn7Z83WNV/3IzsvUX2d2qnbZwB5jtGbjOyosPq6S0iJ99vM8Xd1z7DnfH0latmGO3l5V/RXCBvYYo2UbKk6b2ZH+vfKLc9Wt3eXVrnvkmFUJb16lkf0n6+qed571uIkL79B320+fb8jRx3jvweTKzw9k71HqgS1qE9Kl2nWd9RiPGzpdH/0tU+8/la73n0pXy8Bw/d9fV6lPl2HVrv/d9v8qceEdNR73k/+dmpRxeLdS9v6gvl1vrHbdI8esstkq5g8qLD6uH5NXqEPrC6tdV3LeY9z/wr9o487VkiqurLZtz9dq36r601Gd/X38+c/z1bfrjWedV8VZj3GroPbamrq2cr6hH1NWKDK05hGab696Uss2nD5yq2njIMW1u0Kfb1wgSfp62yK1Dely2kTbJx0rOKKy8lJJFXMgff/rMg07w2l2k+ZepZ37Th890avjYKUf3KG0rF8lScs2vFLn3xWXx92iFT9W/P76bX+SsvMyFRd1ZbXr7tz3sybNvaraZQMvGqMVP76h8vIy5eYf1re//EcDe4ypdl1nctZzcyZ7D6bo6beH6tERb6pHzKCzrl/fz1tZeakys/84/Xvnvp+Vm3+oxvKjIZ63J//ygT6cur/y96Ukvfn4L+oQVv3vLmf9TTqT7Lw/Tjs9evygtuxZW2MeqebnDXAnjpQ6J1HuAK7PrU/FqsmZip3x48dr/PjxDR0JBnjyLx/o+Y/v0uylD6h1iw5nPEXjln6T9MLHf9Ud06NkNntp/I1zFOgfXO262XmZ1U7OKUkx4T107SX36f6X4mWXXUMvvkfda3iBJUlPv32tfrdukyTdPStWYcHRlVd8OdW+g8k1/qf/rmumKfGjO3TnjA6y+Prrqb8srHGuhnc+/7sOH92n/67/l/67/l+SpBsvf0SDe91V7fq7MjbqhhrmaXHkMX5rZYKyctLkZfaRl5e3xt8wR21DOle7rjMfY0dkZu9W4+pmHVTFaWQvL7lPd0yPkreXjx4b8Vbl1ZpOtX77Eq344XV5mb1VbivTFXG36JoaHl/JeY/xiCse18tL7tO457vIZDLpsm431zgiy5mPsc1m0xcbFyhh1Ls1rnOSsx7j4X0f0r5DKbrvpe7yNvuoeUDoaZe4/7M91m2KDu9R7bKHb3pNiQvHaNHXiQpsHKwpt9X8GO/c/7Ne/WSCvMzeatwoQFPHfFx56tipym3l+v3ANgVXM6mzr49FCbe+o/97/1adKC1WpzYX68HhL9d43A++nKYVP76hvPzDejHrV81ZNl6vP7pFzZq01D3XJmrGwjG6MzFaPl6+mnLb+6dd1eikg0fTq1wK988uj7tZv2Uk6a6ZHWUymTRm0LNnHB1z7wtxyis4rMKSY7ptWri6R/XXlNveO+uyUznrudm8+ys9v+hOFRYfk112rd++WA/f+JoujR2u1z6ZoILiPM1bOVnzVk6WJN19baJ6dbzmtP00xPNm8fXXzI/uVGFxnsxmb1l8/fW3OxYroHHzavfTUM+bI5z1N2n/od+U8OZVKjlRqJLSIt02LVy3DXhKwy99UJ98/6p+2PGJvMw+stttuvnyx2o8VexMz5skPfX2UN159T/VMaKnftu/Ue988Xc9N26VJGnB539Xi6atNex/F1EAzlelxY6XOiedLHdOPS2r51+kxs3qNTYAJ6DYgcdq16qbXnukdpei9/P119TbF9Vq3V9+/0a39p9S4/KbLn9EN13+SK329X/jVtZqPUn63fqL7h6aWO0yf79A/fOuT2q1n8dveUuP3/JWrdbNzT+s4MAwdYzoWe1yRx7jaX89fT6smjjzMf6zk+9C1yR57/d6oIYXad5ePnpi5PxaHeeGvuN1Q9/aFcjOfIx9fSyVl0I/G2c+xmazWR9Ord0Vhpz1GPt6N6r193G5rVx5+Yd1WdfT5yKTKq6SVFOheqrenYaod6fdtVo3NXOzLu16g4IDq594Or5Df817Yket9jV64FSNHji12mXNA0KUeO8XtdrPtj3faNQZnveTc77UxpsTf6nTsj9z5nNzUfRVWjg1o9plifeuqdU+pIZ73v41vvanFDXU8/Zna563n3G5s/4mRVzQscbnbdyQ5zRuyHO12s/ZnreTJY4kdYzoWeXrsdf8s1bHAIzm3UhqFl5R7DhS6px0arkTECI1alJ/eQE4j0eeirV27VrZ7XZde+21RkfBecjby1fHC4/ovhfjdTT/0FnXf3PFJH20brqa+FW8kzqy3yQN7HG7w8f19wvU8u9f08tLzv6OYElpke57MV7WnN/l+78rnbz80Hd1ulJJ8yYhmvj6lfopZdVZ193++3rd92K8mjcJkclkVrMmLR16QXSSKzzGkvTEG/21/fdvZPnfJKr/GLtMoUGRDh830L+lEhferlU/zTvrujzG9f8YH8jeo/tejFdZeam8vXzkZfbSq48kOXzFIbPZS418G+u+F+OVmrn1rOt/vXWR/vbvYWr+v7HuHSN6aeItZ897qkY+ftpzYKse/Ff1ZZ8jpn84Wl9tfr9ylNSEm16t0/wyAY2D9PZnT+q9Nef2Atio5+ZMeN7Ozqi/SWfirOfNHYWEhGjy5MkKCQkxOgqczGSSOg2S2l3ieKlz0slyp01PKe566RynCAPQQEx2u/3Mb7nAEAXlZWq+1vEXc0Y5OmCQ/Ovwm7/8hLRudj0EAgAAOE/0nyB5OX5Bs1rbuXNn/e38fzp1qn7eNbieL19QxeXOTdLAiUanAeAMHjliBwAAAPBEeXl5Wr16tfLy8oyOAgBwEoodAAAAwENkZGToscceU0ZG9XMXAQBcD8UOAAAAAACAi6LYAQAAAAAAcFEUOwAAAAAAAC6KYgcAAADwEBaLRZ07d5bFYjE6CgDASRy/PjUAAAAAlxQVFaWlS5caHQMA4ESM2AEAAAAAAHBRFDsAAACAh0hOTlZcXJySk5ONjgIAcBKKHQAAAMBD2O12lZaWym63Gx0FAOAkzLFznmps9tLRAYOMjlFrjc1eRkcAAAAAAMDjUOycp0wmk/y9eHoAAAAAAEDNOBULAAAAAADARTEkBAAAAPAQUVFRWr58uSIiIoyOAgBwEoodAAAAwENYLBZFR0cbHQMA4EScigUAAAB4iMzMTE2dOlWZmZlGRwEAOAnFDgAAAOAhcnNztWTJEuXm5hodBQDgJBQ7AAAAAAAALopiBwAAAAAAwEVR7AAAAAAAALgoih0AAADAQwQHB+uee+5RcHCw0VEAAE5CsQMAAAB4CJPJJF9fX5lMJqOjAACchGIHAAAA8BCHDx/Wq6++qsOHDxsdBQDgJBQ7AAAAAAAALopiBwAAAAAAwEVR7AAAAAAAALgoih0AAADAQwQGBmrYsGEKDAw0OgoAwEm8jQ4AAAAAoGGEh4dr5syZRscAADgRI3YAAAAAD1FSUqK9e/eqpKTE6CgAACeh2AEAAAA8RGpqqgYPHqzU1FSjowAAnIRTsc5TdrtdhbZyo2PUWmOzl0wmk9ExAAAAAADwKBQ756lCW7mar11jdIxaOzpgkPy9+HYCAAAAAKAhcSoWAAAAAACAi6LYAQAAAAAAcFGcOwMAAAB4iNjYWKWkpBgdAwDgRIzYAQAAAAAAcFEUOwAAAICHSEtL06hRo5SWlmZ0FACAk1DsAAAAAB6isLBQ27ZtU2FhodFRAABOQrEDAAAAAADgoih2AAAAAAAAXBTFDgAAAAAAgIui2AEAAAA8RFhYmBITExUWFmZ0FACAk3gbHQAAAABAw2jWrJmGDx9udAyg3pwokEpLJP+guu/j2EGpcXPJ29d5uYD6xIgdAAAAwEPk5OTogw8+UE5OjtFRAKc7USBt+o+06SOp4Ejd9pGbKW1aJG1dKpWdcG4+oL5Q7AAAAAAewmq1atq0abJarUZHAZxu1zdSQbZ0orCinHG03MnNlLYskcpPSLkZUtqP9ZMTcDa3L3ays7OVkJCgDh06yGKxKCIiQo888ogKCgo0btw4mUwmzZkzx+iY9aZ8/gKVXj1UttVfnLbMbrer7InJKr12uOxp6Q0frg6KTxRqzPT2GjTJpFf+O97oOAAAAADOEx37SwEhFZ87Wu78udSRpKC2Uvs+9ZMTcDa3Lna2bt2qbt266fnnn1dWVpa6dOmi0tJSzZ49W7feeqtSUlIkSfHx8cYGrUfmMaOlyLYqn/uW7IezqyyzLV0m+y/bZR5zu0ztIo0J6KB3Pv+78goOGx0DAAAAwHnGx0+6aITj5U51pU73GyQvn3qNCziN2xY72dnZGjZsmLKysjRx4kRZrVZt3rxZWVlZSkxM1MqVK5WUlCSTyaS4uDij49Ybk4+PvCdNlIqLVf7iy5W32/dnyLbgXZk6dZT5lpuNC+iA3RmbtfS7l3XHoH8YHQUAAADAecjRcodSB+7AbYudCRMmKCMjQ+PHj9esWbMUEBBQuSwhIUHdu3dXWVmZIiMj1bRpUwOT1j9TdAeZR42UfdNm2VZ+Jnt5ucpnzpLsdnlNmiiTl5fREc+q3Faulxbfo14dB+uybjcZHQcAAMAl+fv7q2/fvvL39zc6ClBvalvuUOrAXbhlsZOSkqJFixYpODhY06dPr3adHj16SJK6d+9e436GDBkik8mkZ599tj5iNijz6Nuk9u1V/tY82V59Q/bfdsk89g6ZIsKNjlYrS799SfsP7dT4G9x3PiQAAID6FhkZqXnz5ikyMtLoKEC9Olu5Q6kDd+KWxc7ChQtls9k0evRoNWnSpNp1/Pz8JNVc7Hz88cfaunVrfUVscCZvb3lPelw6USrbipUydY2V+aYbjI5VK9acNL37xTMaPejvCg2KNDoOAACAyyovL1d+fr7Ky8uNjgLUu5rKHWsypQ7ci1sWO2vXrpUk9e/fv8Z1MjIyJFVf7Bw7dkyPPvqoZs2aVT8BjeLvL/lU/LYy9eopk9k1nv5/LblfoS3aa8QVjxsdBQAAwKXt3LlTvXr10s6dO42OAjSI6sqdHasodeBevI0OUB/27t0rSWrbtm21y8vKyrRhwwZJ1Rc7Tz/9tGJiYjR69Gjdfvvt55ynZ8+eysrKcmgbu6+vNPfVcz525f7sdpW/8JJUViq1iZDtw49kvvIKmVq3csr+Y6JjZDpxwuHtfL399Ob43TUu/3LT+9q8e41efOBbefPbFgAAuKDomGidKCuqt/2PHTu21utarVZJ0qpVq7Rly5Zab7dgwQIHU+F8NX/CXpnNXrKVlys8vPrXS+7Iv1EzTb11mVoFdai8bXdmkma+cptKHys2MBlQITQ0VBs3bqzTtm5Z7BQUFEiSioqq/wO6aNEiZWdnKyAgQO3atauybOPGjXrrrbe0adMmp+XJyspSZmamYxtZGsmZNYZt2XLZt/0i8113ytznEpU99LDKX3hJXrMSZTKZznn/B6wHpOISh7ez+DSucdmJshLN/fRx9e40VM0DQpWZnSpJys6reCwLivOUmZ2qQP9gNfFrVqfcAAAA9c164ICKSwvrbf+FhbXfd3FxceVHR7Zz+P+yOG/ZZa/86EnPa5e2bdS08QVVbgtuGiFbsY8yD+0xKBXgHG5Z7ISGhuro0aPavHmz+vTpU2WZ1WrVpEmTJElxcXFVSo3y8nLdd999Gj9+vGJjY52ax1F2X18ddtLx7ZmZss1fIFPHGJlHjpDJy0vm20fL9u93ZFu2XF43Xn/Ox2jdqnWdR+zU5ERpkXILDuunlJX6KWXlacu/2vy+vtr8vu699nnd0u8Jh48NAADQEFq1bl2vI3YaN675jbJTWSyWyo+ObBcWFuZwLpyfTDJVfvSU57VDqx6aeMP78msUUOX25gGhevHBbzRj8UhZj6YalA6oUJfe4CS3LHYGDhyolJQUJSYmatCgQYqJiZEkJSUlacyYMcrOzpYkxcfHV9luzpw5OnjwoNOvglWX4VQF5WVqvnbNOR/bbrOp/PkXJZtNXpMer7y0uXnkCNk3fC/b/AUyX9z7nE/J2rV7l/y9HP92Kj8hrZtd/TKLr7/+NuY/p92el39Ys//7oHp1HKzBvcepfas4h48LAADQUHbv2i0v3/rbvyPz5ezYsUPz58/X0KFDHXojc9q0aXWJhvPQly9IsktmL6/KeUfd2alXvzpVoP8FeuGBr9XjVsm/RcNmA5zFLYudhIQEffjhh9q/f79iY2PVqVMnFRcXKzU1VUOGDFFkZKQ+//zzKvPrZGdn629/+5tmzZqlsrIy5ebmVi4rLi5Wbm6umjZtKrOLTDh8km3xUtmTU2S++y6Z2rSpvN3k5SWvJx53+ilZzuTt5aMr4kacdntWTrokqVWLqGqXAwAAoHoxMTHasGGDAgICzr4y4OKqu6R5zt4/lgeESMcP/nG1LModuCrXailqKTw8XOvXr9e1114ri8Wi9PR0BQUFae7cuVq5cqV27dolqerEyRkZGTp+/Ljuu+8+NW/evPKfJCUmJqp58+bat2+fIfenruz79sn2znsyde4k8803nbbcFNlW5ttHy779V9mWLTcgIQAAABqSj4+PgoKC5OPDRSng3qordbrfIOnke9mm6i+FXnDEgLDAOXLLETuS1LlzZ61YseK02/Pz85Weni6z2ayuXbtW3t6hQwetW7futPX79++vO++8U2PHjj2nc96MYGrTRj4rPznjOl633Sqv225toETOERoUqTXP242OAQAA4HL27dunGTNmaMqUKWrzp9HcgDupqdQ59SK7Jy+FvnkxI3fg2ty22KnJjh07ZLfbFRMTU2XCuCZNmqhfv37VbhMZGVnjMgAAAMBVHD9+XOvWrdNDDz1kdBSgXtS21DmJcgfuwC1PxTqT7du3S6p6GhYAAAAAwLU5WuqcdLLc4bQsuCqPG7HjaLFjt3PKDwAAAACc7w7ucrzUOam6kTvZvzNqB66BYgcAAAAA4PJi+km2Uqkoz7FS56Q/lzvB7aW2veojJeB8HlfsrF271ugIAAAAgCFCQkI0efJkhYSEGB0FcDqTSeo0SLKVS151fKXr4yf1HOV4KQQYyeOKHQAAAMBTBQcHa+zYsUbHAOqNyVT3UuckSh24Go+bPBkAAADwVHl5eVq9erXy8vKMjgIAcBKKHQAAAMBDZGRk6LHHHlNGRobRUQAATkKxAwAAAAAA4KIodgAAAAAAAFwUxQ4AAAAAAICLotgBAAAAPITFYlHnzp1lsViMjgIAcBIudw4AAAB4iKioKC1dutToGAAAJ2LEDgAAAAAAgIui2AEAAAA8RHJysuLi4pScnGx0FACAk1DsAAAAAB7CbrertLRUdrvd6CgAACdhjp3zVGOzl44OGGR0jFprbPaq03ZmH6n/BCeHAQAAOI+YfYxOAABwZxQ75ymTySR/L/d/ekwmycvX6BQAAAAAALgmTsUCAAAAAABwUe4/JAQAAACApIrLnS9fvlwRERFGRwEAOAnFDgAAAOAhLBaLoqOjjY4BAHAiTsUCAAAAPERmZqamTp2qzMxMo6MAAJyEYgcAAADwELm5uVqyZIlyc3ONjgIAcBKKHQAAAAAAABdFsQMAAAAAAOCiKHYAAAAAAABcFMUOAAAA4CHMZrN69eols5mXAQDgLviNDgAAAHgIm82mpKQk2Ww2o6MAAJyEYgcAAAAAAMBFUewAAAAAAAC4KIodAAAAAAAAF0WxAwAAAHiIwMBADRs2TIGBgUZHAQA4ibfRAQAAAAA0jPDwcM2cOdPoGAAAJ2LEDgAAAOAhSkpKtHfvXpWUlBgdBQDgJBQ7AAAAgIdITU3V4MGDlZqaanQUAICTUOwAAAAAAAC4KIodAAAAAAAAF0WxAwAAAAAA4KIodgAAAAAAAFwUlzsHAAAAPERsbKxSUlKMjgEAcCJG7AAAAAAAALgoih0AAADAQ6SlpWnUqFFKS0szOgoAwEkodgAAAAAPUVhYqG3btqmwsNDoKAAAJ6HYAQAAAAAAcFEUOwAAAAAAAC6KYgcAAAAAAMBFUewAAAAAHiIsLEyJiYkKCwszOgoAwEm8jQ4AAAAAoGE0a9ZMw4cPNzoG6pHdJpnO8e17Z+wDQMPhxxUAAADwEDk5Ofrggw+Uk5NjdBTUgxMF0s/vSwd31X0fuZnSDwukAr5FAJdBsQMAAAB4CKvVqmnTpslqtRodBU5WWixt+o90/JD066d1K3dyM6UtS6TCHGnTIqko1+kxAdQDjyh2srOzlZCQoA4dOshisSgiIkKPPPKICgoKNG7cOJlMJs2ZM8fomAAAAABQJ96NpKahFZ/b7Y6XOydLnfITFV83CZZ8/Z2fE4Dzuf0cO1u3btWQIUOUlZUlf39/denSRQcOHNDs2bO1Z8+eymGo8fHxxgYFAAAAgDoymaQu11R8bv31j3JHw6SQmDNve2qpE9RW6n6D5OVTn4kBOItbj9jJzs7WsGHDlJWVpYkTJ8pqtWrz5s3KyspSYmKiVq5cqaSkJJlMJsXFxRkdFwAAAADq7GS506prxde1GblDqQO4PrcudiZMmKCMjAyNHz9es2bNUkBAQOWyhIQEde/eXWVlZYqMjFTTpk0NTAoAAADUP39/f/Xt21f+/pxj464cKXcodQD34LbFTkpKihYtWqTg4GBNnz692nV69OghSerevXvlbV9//bVMJtNp/zhVCwAAAK4uMjJS8+bNU2RkpNFRUI9qVe7YKXUAd+G2c+wsXLhQNptNo0ePVpMmTapdx8/PT1LVYuekV199VRdddFHl17yrAQAAAFdXXl6uoqIi+fn5ycvLy+g4qEc1zrlj/2MdSh3APbhtsbN27VpJUv/+/WtcJyMjQ1L1xU6XLl10ySWX1E84AAAAwAA7d+7UiBEjtHjxYsXGxhodB/WsunLnVJQ6gOtz22Jn7969kqS2bdtWu7ysrEwbNmyQVH2x40w9e/ZUVlZWvR4DAAAAnmns2LG1XtdqtUqSVq1apS1bttR6uwULFjiYCucTk0y6a9DzuiJ2VJXbf937rf71yl9V+lixQcka3vwJe2U2e8lWXq7w8OpfKwJGCA0N1caNG+u0rdsWOwUFBZKkoqKiapcvWrRI2dnZCggIULt27U5bfuuttyo7O1stWrTQ8OHDNWPGDAUHB9cpS1ZWljIzM+u0LQAAAHAmhYWFtV63uLi48qMj2/F/Wde3dN0r6tPxJvl4+0qS7Ha7Pln/utL37TE4WcOy/+9cNLvsfF/DbbhtsRMaGqqjR49q8+bN6tOnT5VlVqtVkyZNkiTFxcXJZDJVLgsMDNSkSZN0xRVXqEmTJvrhhx80ffp0/fjjj9q4caMsFkudsgAAAAD1oXHjxrVe9+T/ZS0Wi0PbhYWFOZwL548OrXpo4g3vV5Y6kmQymTTlL+8psFmANqauMjBdwzLJVPmR72ucT86lNzDZ7dWdaen6JkyYoFdeeUURERH68ssvFRMTI0lKSkrSmDFj9Pvvv6u0tFQPPfSQ5syZc8Z9ffrppxo+fLjmz5+vu+66qyHiAwAAALWyc+fOWq+7Y8eOOs2x06lTp7pEw3ng1EuayyzJ9sdyk0nqOkwKiTEiXcP78gVVTCBtkgZONDoN4Bxue7nzhIQEtWjRQvv371dsbKy6deum6Oho9e7dW+3bt9eAAQMk1W5+neuuu07+/v51Pt8NAAAAOB/ExMRow4YNlW96wr2dWuoEtZV8Ky4MLPP/zt2o9lLoAFyK2xY74eHhWr9+va699lpZLBalp6crKChIc+fO1cqVK7VrV8VvLkcmTv7zKVsAAACAq/Hx8VFQUJB8fLgEkrurrtTpfkPFCB1J8m4ktepa8TnlDuDa3HaOHUnq3LmzVqxYcdrt+fn5Sk9Pl9lsVteuXc+6n+XLl6ugoEC9e/euj5gAAABAg9i3b59mzJihKVOmqE2bNkbHQT2pqdT58yXNq7sU+q+fSvKg07IAd+HWxU5NduzYIbvdrpiYmNMmjbv99tvVvn17XXTRRZWTJ8+cOVPx8fEaNWpUDXsEAAAAzn/Hjx/XunXr9NBDDxkdBfWkNqXOSZQ7gHvwyGJn+/btkqo/DSs2NlYffvihXn75ZRUVFSk8PFz33HOPnnnmGfn6+p62PgAAAACcDxwpdU6i3AFcH8XOKZ588kk9+eSTDR0JAAAAAOrsRJG0daljpc5JNZU7/ndKTYLrLTIAJ3HbyZPP5EzFDgAAAAC4Gl8/KaZ/xeeOlDonnSx3Tk6oHHkJpQ7gKjxyxM7atWuNjgAAAAA0uJCQEE2ePFkhISFGR0E9aN1V8m0sNY9wrNQ56WS507KDdEEH5+cDUD88stgBAAAAPFFwcLDGjh1rdAzUo+D257a9yUSpA7gajzwVCwAAAPBEeXl5Wr16tfLy8oyOAgBwEoodAAAAwENkZGToscceU0ZGhtFRAABOQrEDAAAAAADgoih2AAAAAAAAXBTFDgAAAAAAgIui2AEAAAA8hMViUefOnWWxWIyOAgBwEi53DgAAAHiIqKgoLV261OgYAAAnYsQOAAAAAACAi6LYAQAAADxEcnKy4uLilJycbHQUAICTUOwAAAAAHsJut6u0tFR2u93oKAAAJ6HYAQAAAAAAcFEUOwAAAAAAAC6KYgcAAAAAAMBFcblzAAAAwENERUVp+fLlioiIMDoKAMBJKHYAAAAAD2GxWBQdHW10DACAE3EqFgAAAOAhMjMzNXXqVGVmZhodBQDgJBQ7AAAAgIfIzc3VkiVLlJuba3QUAICTUOwAAAAAAAC4KIodAAAAAAAAF0WxAwAAAAAA4KIodgAAAAAPYTab1atXL5nNvAwAAHfBb3QAAADAQ9hsNiUlJclmsxkdBQDgJBQ7AAAAAAAALopiBwAAAAAAwEVR7AAAAAAAALgoih0AAADAQwQGBmrYsGEKDAw0OgoAwEm8jQ4AAAAAoGGEh4dr5syZRscAADgRI3YAAAAAD1FSUqK9e/eqpKTE6CgAACeh2AEAAAA8RGpqqgYPHqzU1FSjowAAnIRiBwAAAAAAwEVR7AAAAAAAALgoih0AAAAAAAAXRbEDAAAAAADgorjcOQAAAOAhYmNjlZKSYnQMAIATMWIHAAAAAADARVHsAAAAAB4iLS1No0aNUlpamtFRAABOQrEDAAAAeIjCwkJt27ZNhYWFRkcBADgJxQ4AAAAAAICLotgBAAAAAABwURQ7AAAAAAAALopiBwAAAPAQYWFhSkxMVFhYmNFRAABO4m10AAAAAAANo1mzZho+fLjRMQAATsSIHQAAAMBD5OTk6IMPPlBOTo7RUYB6kWeVDu0+t30c2C4V8CMCF0KxAwAAAHgIq9WqadOmyWq1Gh0FcLo8q7RlsbT9U+ngrrrtY/8WKflzafPHlDtwHW5f7GRnZyshIUEdOnSQxWJRRESEHnnkERUUFGjcuHEymUyaM2eO0TEBAAAAAOcgK1kqK5HsNunXFY6XO/u3SL99VfF5Sb50+BxH/gANxa3n2Nm6dauGDBmirKws+fv7q0uXLjpw4IBmz56tPXv2VA5BjY+PNzYoAAAAAOCcxPSXyk5I1h1/lDu6TgqJOfu2fy51JCnyYqlt73qLCjiV247Yyc7O1rBhw5SVlaWJEyfKarVq8+bNysrKUmJiolauXKmkpCSZTCbFxcUZHRcAAAAAcA5MZqnLNVKr2Iqvaztyp7pSJ+oyyWSqv6yAM7ltsTNhwgRlZGRo/PjxmjVrlgICAiqXJSQkqHv37iorK1NkZKSaNm1qYFIAAACgYfj7+6tv377y9/c3OgpQLxwtdyh14A7csthJSUnRokWLFBwcrOnTp1e7To8ePSRJ3bt3P23Zf//7X1166aXy9/dXYGCg+vbtqx07dtRrZgAAAKC+RUZGat68eYqMjDQ6ClBvalvuUOrAXbhlsbNw4ULZbDaNHj1aTZo0qXYdPz8/SacXO7Nnz9bIkSN12WWXafny5Vq4cKEGDhyooqKies8NAAAA1Kfy8nLl5+ervLzc6ChAvaqp3JH9fyvYKXXgPtxy8uS1a9dKkvr371/jOhkZGZKqFjt79uzRpEmT9NJLL2n8+PGVtw8dOrSekgIAAAANZ+fOnRoxYoQWL16s2NhYo+MA9epkuSP9MaFydSh14OrccsTO3r17JUlt27atdnlZWZk2bNggqWqxM3/+fPn4+Oiee+6p/5AAAAAAgHp16sidU1HqwB245YidgoICSarx9KlFixYpOztbAQEBateuXeXt33//vTp27Kj3339f06ZN0/79+xUdHa2///3vuu222+qcp2fPnsrKyqrz9gAAAEBNxo4dW+t1rVarJGnVqlXasmVLrbdbsGCBg6lwvnpxXJKCAlrJarUqPLyX0XEajMlk1tMj/6sOrXpU3rZx9yqNffleA1MBfwgNDdXGjRvrtK1bFjuhoaE6evSoNm/erD59+lRZZrVaNWnSJElSXFycTH+qZq1WqzIzM/Xkk08qMTFRERERevvtt/WXv/xFLVu21MCBA+uUJysrS5mZmXW/QwAAAEANCgsLa71ucXFx5UdHtuP/su7j5PxK5eXlHvW8DuvzQJVSR5Li2w9Su6CL9d32pQalApzDLYudgQMHKiUlRYmJiRo0aJBiYmIkSUlJSRozZoyys7MlSfHx8VW2s9lsys/P13vvvacbbrhBknTVVVcpOTlZ/+///b86FzuhoaF1vi8AAADAmTRu3LjW61oslsqPjmwXFhbmcC6cn7y8vCo/esrzOiDuDt0x4LnTbvf28tHToz/SG589pI2pqwxIBvzhXHoDk91ut599NdeSkZGh+Ph4HTlyRN7e3urUqZOKi4uVmpqqIUOGyGaz6fPPP9ebb75ZZT6dSy65RD/99JOOHz9e5WpaEydO1IIFC3TkyBEj7g4AAABQo507d9Z63dLSUh0/flwBAQHy8fGp9XadOnWqSzSch9a/IZXkS42aSJffb3Sa+nfqJc29fKTyUsnsLdnKKm4zmaWu10khMcZkBM6VW06eHB4ervXr1+vaa6+VxWJRenq6goKCNHfuXK1cuVK7du2SdPqlzs90ZYCTw1YBAAAAV+Xj46OgoCCHSh3AVZ1a6kReLHn5Vnzu3ej0S6Ef3NXwGQFncMtiR5I6d+6sFStW6Pjx4zp+/Lh++ukn3XvvvSooKFB6errMZrO6du1aZZvrr79ekvTFF19U3maz2bRmzRr16uU5E4sBAADAPe3bt08PPvig9u3bZ3QUoF5VV+r8+epXJlPVq2VR7sCVueUcO2eyY8cO2e12xcTEnHZe8bBhw3T55Zfr3nvv1ZEjR9SmTRvNmzdPO3bs0Jo1awxKDAAAADjH8ePHtW7dOj300ENGRwHqzdlKnZNOXgpdkqw7/ih3xGlZcDFuO2KnJtu3b5d0+mlYkmQymbR8+XLdfPPNeuqppzR8+HDt3btXq1at0oABAxo6KgAAAADAAbUtdU46We4wcgeuzONG7Jyp2JGkZs2aae7cuZo7d25DxgIAAAAAnANHS52Tahq5Y7pOuoCRO3ABjNgBAAAAALg8rz8NW6htqXPSqSN3ZJLMXk6PCNQLjxuxs3btWqMjAAAAAIYICQnR5MmTFRISYnQUwOlad6v4WJjrWKlz0slyx+wltYySgqOcHhGoFx5X7AAAAACeKjg4WGPHjjU6BlBvTpY7dWUyS52vdk4WoKF43KlYAAAAgKfKy8vT6tWrlZeXZ3QUAICTUOwAAAAAHiIjI0OPPfaYMjIyjI4CAHASih0AAAAAAAAXRbEDAAAAAADgoih2AAAAAAAAXBTFDgAAAOAhLBaLOnfuLIvFYnQUAICTcLlzAAAAwENERUVp6dKlRscAADgRI3YAAAAAAABcFMUOAAAA4CGSk5MVFxen5ORko6MAAJyEYgcAAADwEHa7XaWlpbLb7UZHAQA4CcUOAAAAAACAi6LYAQAAAAAAcFEUOwAAAAAAAC6Ky50DAAAAHiIqKkrLly9XRESE0VEAAE5CsQMAAAB4CIvFoujoaKNjAACciFOxAAAAAA+RmZmpqVOnKjMz0+goAAAnodgBAAAAPERubq6WLFmi3Nxco6MAAJyEYgcAAAAAAMBFUewAAAAAAAC4KIodAAAAAAAAF0WxAwAAAHiI4OBg3XPPPQoODjY6CgDASSh2AAAAAA9hMpnk6+srk8lkdBQAgJNQ7AAAAAAe4vDhw3r11Vd1+PBho6MAAJyEYgcAAAAAAMBFUewAAAAAAAC4KIodAAAAAAAAF0WxAwAAAHiIwMBADRs2TIGBgUZHAQA4ibfRAQAAAAA0jPDwcM2cOdPoGAAAJ2LEDgAAAOAhSkpKtHfvXpWUlBgdBQDgJBQ7AAAAgIdITU3V4MGDlZqaanQUAICTcCoWAAAAgPOO3S6dKDc6hWN8vSSTyegUcBee/jNgt9tVWFjonJ01kMaNG8tkwC8Bih0AAAAA550T5dLkRUancEzirVIjXmHBSTz9Z6CwsFBNmjRxzs4aSH5+vvz9/Rv8uJyKBQAAAAAA4KIodgAAAAAAAFwUAwUBAAAADxEbG6uUlBSjYwAAnIgROwAAAAAAAC6KYgcAAADwEGlpaRo1apTS0tKMjgIAcBKKHQAAAMBDFBYWatu2bS53CWEAQM0odgAAAAAAAFwUxQ4AAAAAAICLotgBAAAAAABwURQ7AAAAgIcICwtTYmKiwsLCjI4CAHASih0AAADAQzRr1kzDhw9Xs2bNjI4CAC6nVatW8vHxMTrGabyNDgAAAACgYeTk5Oizzz7TkCFDFBQUZHQcAKh3wcHBuvjii9WzZ091795dzZs3l5eXl4qKirR7925t2rRJGzdu1Pbt28+4nzZt2ujrr7/Wli1bNGrUKJWWljbQPTg7ih0AAADAQ1itVk2bNk3x8fEUOwDc2oABA/Tggw/q+uuvl7d39dXH1VdfXfn5zp079frrr+udd95RXl5elfVOljrt2rVTu3btlJiYqMcff7xe8zvCI07Fys7OVkJCgjp06CCLxaKIiAg98sgjKigo0Lhx42QymTRnzhyjYwIAAABwsozkr/Wv203atHJWjev863aTPpl1XQOmMkZ+tlReVvG5rVyy243N09BOFEm2k/e/TCo7YWyehuJpPwOxsbH6+eef9dVXX+nmm2+usdQ5VadOnfSvf/1LGRkZGj9+vEwmk6SqpY5UUQDNnDmz3vLXhduP2Nm6dauGDBmirKws+fv7q0uXLjpw4IBmz56tPXv2KCcnR5IUHx9vbFAAAAAAcDKbTcpKljK2Ssey/ri9tEj68d9SWLwU1lXy8jUqYf07dlDav1k6uLOi0JKk0mJp/etSq1gp4iLJnwFsLs9sNmvy5Ml69tln5ev7xzf0gQMHtHDhQv3000/avHmzMjMzVV5eroCAAMXFxalHjx669tpr1b9/f0lSkyZN9Morr+jmm2/W1KlT9d5771Updfr376+srKxqMxjFrYud7OxsDRs2TFlZWZo4caKeeeYZBQQESJJmzpypyZMny9vbWyaTSXFxcQanBQAAAADnKT8h/fKpdCSt+uUFOdKutZJ1hxR/k9TIv2HzNYTMX6SUNZKqGZ1UXlpReB34Vep2ndSyQ0Ong7N4e3vr3Xff1W233VZ5W3Jysp555hktW7ZMZWVlp22Tk5Ojr7/+Wl9//bVeeOEFde7cWRMnTtS4ceMkSf369dPXX39dOeLnfC11JDc/FWvChAmVw6hmzZpVWepIUkJCgrp3766ysjJFRkaqadOmBiYFAAAA6p+/v7/69u0rf383fAWPKuw2afuKmkudPzt+UNq61P1OTcraKaV8oWpLnT+zlUm/LJdy9jVILDiZ2WzWe++9V1nqlJeXa/r06brooou0ePHiakud6qSkpOjuu+/WgAEDtH//fkmqLHV+//3387bUkdy42ElJSdGiRYsUHBys6dOnV7tOjx49JEndu3evvK1fv34ymUzV/rv//vsbJDsAAABQHyIjIzVv3jxFRkYaHaXBlZ0oVNHx7Gr/uaNDqVL277Vf//jBitEr7qK8TPrtq9qvb7dJv33p3vMOuevPwNSpUzVq1ChJUlFRkYYPH66nnnpKJSUlddrfnj17ZLPZqtzm5eWl48ePn3PW+uK2p2ItXLhQNptNo0ePVpMmTapdx8/PT1LVYue1117TsWPHqqy3cuVKTZs2Tddd5x6TSQEAAMAzlZeXq6ioSH5+fvLy8jI6ToP6cckz+nHJM0bHaDB1KWkyt0lte0n/mzPWpR3aVTGPkCMKcqSj+6WgNvWTyWju+DPQvXt3TZ06VZJUVlamm2++WZ999lmd93dyouS2bdtKkoqLi2WxWNS2bVvNmDFDDz/8sFNyO5vbFjtr166VpMoJkKqTkZEhqWqx06VLl9PW+7//+z+1bNlSgwcPdnJKAAAAoOHs3LlTI0aM0OLFixUbG2t0nAbVtf+9ir74lmqX/XfGoAZOU7+Kj0lH63BaUVGelJshNY9wfqaGZt1R9+3ctdhxt58Bs9msBQsWyMfHR5I0ffp0p5Q6f54o+a677tJXX32lxo0ba/z48fr444+1fv16p+R3Jrctdvbu3StJlU3bqcrKyrRhwwZJVYudUx0+fFirV6/Wgw8+WOvLpJ2qZ8+e5+25eAAAAHBtY8eOrfW6VqtVkrRq1Spt2bKl1tstWLDAwVTnzsvHTzdO2+20/TULjVabrgOdtr/qxERHq9zRYSL1oEOrHpp66yd12vbesQ/rh9/+6+REDW/6HV+rVZDjsyF/9dl3uuaeUfWQyHGe/jNw6ulQpxoyZEjl1a1/+eUX/b//9//qfKzqSp2Tc+pMmTJFs2fPliRNmTLljMVOdHS0zOa6zXgTGhqqjRs31mlbty12CgoKJFWcY1edRYsWKTs7WwEBAZVPXnUWLlyosrIyjRkzps5ZsrKylJmZWeftAQAAgJoUFhbWet3i4uLKj45sZ8T/Zb0bNW7wY56rA9YDKiup/eNaX5p6133IzZGcI27x2qW0lhPmnqq4pPi8uf/8DJzZgw8+WPn5008/rdLS0jrt50yljiS9+uqrevzxxxUZGanBgwerXbt2Skurflbyk+V5Q3PbYic0NFRHjx7V5s2b1adPnyrLrFarJk2aJEmKi4uT6Qwnkb733nvq3LmzevbseU5ZAAAAgPrQuHHtX/xZLJbKj45sFxYW5nCuc+Xl49fgxzxXrVu1Pi9G7HhbKkoNu91+xtc6f1a5rk+xIc+3sx0rOiipk8PbFZw4ct7cf0//GbDZbDUWJeHh4ZVTpaSnp2vVqlV1OsbZSp2TOd544w3NmDFDZrNZ48aNq5zX51StWrU6pxE7deW2xc7AgQOVkpKixMREDRo0SDExMZKkpKQkjRkzRtnZFTN/nxy6VZ2dO3dq48aNeu65584pS12HUwEAAABns3Pnzlqvu2PHDs2fP19Dhw51aI6dadOm1SXaOSkpkyYvavDDnpNdu3er0XnyCmvzf6ScvbWfBdlkMsmvmfTVT0vdYvLkrBTp15WOb/foP2/VP/59q/MD1YGn/wwUFBTUeCGkvn37VhYo77777llP26pObUqdkxYsWKAZM2ZIki6//PIa97l79275+/s7nOVcue3lzhMSEtSiRQvt379fsbGx6tatm6Kjo9W7d2+1b99eAwYMkHTm+XXee+89mUwmjR49uqFiAwAAAPUmJiZGGzZsqHzTE+4rPL4O23R3jytiSdIF0ZKjA178W0jNwusnD5yrR48elZ//+OOPDm/vSKkjSQcPHlR6erok6cILL6zzqJz6cn6lcaLw8HCtX79e1157rSwWi9LT0xUUFKS5c+dq5cqV2rVrl6Saix273a4PPvhA/fr1U5s2bjotOgAAADyKj4+PgoKCKq8iA/fVMkpq6cDcwU1DK4odd2H2ljo5cKEnk1fF+u5SbLm7Cy+8sPLzTZs2ObSto6XOqccJCAhQhw6OT8xdn86TgYL1o3PnzlqxYsVpt+fn5ys9PV1ms1ldu3atdttvv/1We/fu1TPPPFPfMQEAAIAGsW/fPs2YMUNTpkzxmDcvw7v00yPv28+4ztmWuyKTWep6rbR9hZS958zrNm0lxd8oefk2TLaGEhIjlQ+WUr6Q7Gc4U8fLR+o2TGrupqN13PFnICgoSJJ04sQJHTp0qNbb1bXUkaT9+/dXft68eXMHE9cvty52arJjxw7Z7XbFxMTUOGnce++9Jz8/P40YMaKB0wEAAAD14/jx41q3bp0eeugho6OgAXj5SN2vlw7+JmVslXJPudhTk2Ap/EKpVZeKdd1R665SQIi0f3PFvDu2P10sy7uR1CpWirhQanx+vU7HWdx99911Gn14yy231KnUkaQ333xTn332mYqLi5WcnOxw5vrkkcXO9u3bJdV8GlZxcbEWL16sG264QQEBAQ0ZDQAAAACcxmSWQjtX/CvIkYqPVYxeadREatLSM049CmgpdblGir5SOn5IKi+VvH2lpiHuN0rJU2zZsqVO273wwgsKCgrSTTfd5FCpI0kpKSlKSUmp03HrG8VONSwWi3JzcxswEQAAAADUL/+gin+eysciBXnGGYg4g6efflozZszQ8ePHjY7iNG47efKZnK3YAQAAAAAA7smdSh3JQ0fsrF271ugIAAAAQIMLCQnR5MmTFRISYnQUAICTeGSxAwAAAHii4OBgjR071ugYAAAn8shTsQAAAABPlJeXp9WrVysvL8/oKAAAJ6HYAQAAADxERkaGHnvsMWVkZBgdBQDgJBQ7AAAAAAAALopiBwAAAAAAwEVR7AAAAAAAALgoih0AAADAQ1gsFnXu3FkWi8XoKAAAJ+Fy5wAAAICHiIqK0tKlS42OAQBwIkbsAAAAAAAAuCiKHQAAAMBDJCcnKy4uTsnJyUZHAQA4CcUOAAAA4CHsdrtKS0tlt9uNjgIAcBLm2AEAAABw3vH1khJvNTqFY3y9jE4Ad+LpPwONGzdWfn6+0/b3/NyPdKygUE39G2vSfaNO+9oZGjdu7JT9OIpiBwAAAMB5x2SSGvFqBR7M038GTCaT/P39nbY/30YW+ZaWy7eRRf7+/qd97co4FQsAAAAAAMBFeXD/BwAAAHiWqKgoLV++XBEREUZHAQA4CcUOAAAA4CEsFouio6ONjgEAcCJOxQIAAAA8RGZmpqZOnarMzEyjowAAnIRiBwAAAPAQubm5WrJkiXJzc42OAgBwEoodAAAAAAAAF0WxAwAAAAAA4KIodgAAAAAAAFwUV8UCAAAAXFinTp1qvW5gYKCeeeYZXXrppWrVqlU9pgIANBSKHQAAAMBDtGrVSs8++6zRMQAATsSpWAAAAAAAAC6KYgcAAAAAAMBFUewAAAAAAAC4KIodAAAAAAAAF0WxAwAAAAAA4KIodgAAAAAAAFwUxQ4AAAAAAICLotgBAAAAAABwURQ7AAAAAAAALopiBwAAAAAAwEVR7AAAAAAAALgoip3zxLfffqvrr7/+/7d3f7FZlQcYwJ+W0iq2hY2h/JO6uGVSjDADGoYb4AYW0DGXTXflkhEXb6bBi2nwxkQTnVu4YcuMsSTgskQukBuZiJlNFmdGZNQ4OqYsUweWLiZIW/nbr92FSECsQvno11N/v5sv5z3nvOf5bp+85z1pampKVVVVHn300UpHAgAAAAaxdevWzJkzJ3V1dbnqqquydu3aiuRQ7IwQvb29aW5uzhNPPJHJkydXOg4AAAAwiNdeey0rV67MsmXL0t7enocffjhr1qzJk08+OexZaob9iXyq5cuXZ/ny5UmSBx54oMJpAAAAgMGsXbs28+bNy2OPPZYkmTlzZnbv3p3HH38899xzz7BmsWIHAAAA4Dy88soraWlpOWOspaUl77zzTvbt2zesWazYAQAAAEaFUqk//373vbPG+0qlU79v/mffWcenm/ilxkyc0PiZz+ns7DxrG5WPjzs7OzN9+vQh/4fzpdgBAAAARoUxY6rT3vFW/v6Ptz71/OEjR7N+09ZBjy+pq83qn/3ooucsJ69iAQAAAKPG97+3IBMa64d07w+W3pTx53DvlClTcuDAgTPGurq6Tp0bToodAAAAYNS4pK42P16xKFXned/smVdnTvPXzunaBQsWZNu2bWeMvfDCC2lqahrW17ASxc6I0dvbm/b29rS3t+f48eM5cOBA2tvbs3fv3kpHAwAAgEK5esbU3DTvunO+vrF+XFYuWXDO169evTo7duzIQw89lD179mTDhg1Zt25dHnzwwaHEvSBVAwMDA8P+VM7S1taWxYsXnzW+cOHCtLW1DX8gAAAAKLATfX357Ybn0vX+wc+9dtUdy/P1r57fSpvnn38+a9asyZ49ezJ58uTcd999uf/++4cad8gUOwAAAMCo9F7X+/ndxi0p9fcPes3862ed12qdkcarWAXz387/5fDRY5WOAQAAACPe1Cu+kiXfnjvo+UlfHp9li24cxkTlp9gpkL5SKX94bnt+9fs/5t39XZWOAwAAACPed264Lk3TrjhrvLqqKnfcuji1Y2sqkKp8FDufUCqV8swzz2Tp0qWZNGlS6urqMmPGjLS0tOTpp59OqVSqWLadb/wrh3o+TG3t2Ey5fGLFcgAAAEBRVFdXf1Tg1I49Y/zmBdfnyimXVyhV+Sh2TtPd3Z0lS5bkrrvuyvbt21NbW5vZs2env78/L774Yu6+++709PRUJFtfqZQ//3VXkmTRjXMytuCNIgAAAAyXiRMac9vN808dXzllUhbP/2YFE5WPduA0q1atyssvv5zp06dn48aNZ3ylqqurK62trRk7duxnzHDxfLxap6F+XG6YfU1FMgAAAEBRzb3uG+nY+3b2vr0/d9y6OGOqR8daF1/FOmnnzp2ZO3duampqsmvXrlx77bVlm3vdhs3p6T1yATMMpOfDIxkYGMgldbWprVC5BAAAAEXW3z+QUqk04t6Caai/NL/46Q+HdO/I+icVtGXLliTJihUrylrqJElP75F0935YlrmOHjueo8eOl2UuAAAA+CI6cmz0fG1asXNSR0dHkmT+/Pmfc+X5a6i/9ALutloHAAAARrML6Q0UOyd1d3cnScaPH1/2uYe6nCpJ/tb+zzy37S9pqB+XX/78JyNuuRgAAABQOVqCkxobG5Mkhw4dKvvcQ99j56PVOkly4kRffv3Us+UNBgAAAFScPXbKYNasWdm8eXNeffXVss9djj127K0DAAAAfJJi56Tbb789jzzySLZu3ZqOjo40NzeXbe6hvStnbx0AAAD4IriQPXZ87vw0d955ZzZt2pQZM2Zk48aNWbhw4alzXV1dWb9+fe69995cdtllFz2LvXUAAACAz6PYOU13d3dWrlyZtra2JMm0adMyderUdHZ2Zv/+/RkYGMjBgwczYcKEi5qjr1TKb556Nh909+a2734rC+aW9/PrAAAAwOhQXekAI0ljY2NeeumltLa2ZtGiRTl8+HBef/31VFdX55Zbbklra2saGhoueo6db7yZD7p701A/LjfMvuaiPw8AAAAoJit2RqBdu9/Kn9p2ZOGNs63WAQAAAAal2BmhTvT1pSpVqakZU+koAAAAwAil2AEAAAAoKHvsAAAAABSUYgcAAACgoBQ7AAAAAAWl2AEAAAAoKMUOAAAAQEEpdgAAAAAKSrEDAAAAUFCKHQAAAICCUuwAAAAAFJRiBwAAAKCgFDsAAAAABaXYAQAAACgoxQ4AAABAQSl2AAAAAApKsQMAAABQUIodAAAAgIJS7AAAAAAUlGIHAAAAoKAUOwAAAAAFpdgBAAAAKCjFDgAAAEBBKXYAAAAACkqxAwAAAFBQih0AAACAglLsAAAAABSUYgcAAACgoBQ7AAAAAAWl2AEAAAAoKMUOAAAAQEEpdgAAAAAKSrEDAAAAUFCKHQAAAICCUuwAAAAAFJRiBwAAAKCgFDsAAAAABaXYAQAAACgoxQ4AAABAQSl2AAAAAApKsQMAAABQUP8HJPt1+yB7BdUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1458.05x785.944 with 1 Axes>"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ae = auto_encoder_circuit(num_latent, num_trash)\n",
    "qc = QuantumCircuit(num_latent + 2 * num_trash + 1, 1)\n",
    "qc = qc.compose(domain_wall_circuit, range(num_latent + num_trash))\n",
    "qc = qc.compose(ae)\n",
    "qc.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "reasonable-distributor",
   "metadata": {},
   "source": [
    "Then, we create a quantum neural network and pass the circuit as a parameter. We note that this network must take an interpret function, which determines how we map the output of the network to the output shape. Since we measure only one qubit, the output of the network is a bit string either $0$ or $1$, so the output shape is $2$, the number of possible outcomes. Then, we introduce an identity mapping. The output of the network is a vector of probabilities of getting interpret-mapped bit strings. Thus, we get probabilities of getting $0$ or $1$ and this is exactly what we are looking for. In the cost function we make use of the probability of getting $1$ and penalize the outcomes that lead to $1$, therefore maximizing the fidelity between the trash space and the reference space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "varying-township",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Here we define our interpret for our SamplerQNN\n",
    "def identity_interpret(x):\n",
    "    return x\n",
    "\n",
    "\n",
    "qnn = SamplerQNN(\n",
    "    circuit=qc,\n",
    "    input_params=[],\n",
    "    weight_params=ae.parameters,\n",
    "    interpret=identity_interpret,\n",
    "    output_shape=2,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa0fea32",
   "metadata": {},
   "source": [
    "Next we create our cost function. As described in the previous section, our aim is to minimize $\\frac{2}{M}L$, which is the twice the probability of getting the final qubit in the $|1\\rangle$ state. We therefore wish to minimize the of getting a $|1\\rangle$ on qubit 7.\n",
    "\n",
    "The cost function will also plot out the objective value at each cost function evaluation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "28abf03b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def cost_func_domain(params_values):\n",
    "    probabilities = qnn.forward([], params_values)\n",
    "    # we pick a probability of getting 1 as the output of the network\n",
    "    cost = np.sum(probabilities[:, 1])\n",
    "\n",
    "    # plotting part\n",
    "    clear_output(wait=True)\n",
    "    objective_func_vals.append(cost)\n",
    "    plt.title(\"Objective function value against iteration\")\n",
    "    plt.xlabel(\"Iteration\")\n",
    "    plt.ylabel(\"Objective function value\")\n",
    "    plt.plot(range(len(objective_func_vals)), objective_func_vals)\n",
    "    plt.show()\n",
    "    return cost"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c97545c2",
   "metadata": {},
   "source": [
    "Now we will train our Autoencoder to reduce the dimension of the Hilbert space from $5$ qubits to $3$, while leaving the trash space in the state $|00\\rangle$.  We initially set the parameters $\\theta$ to random values and tune these parameters to minimize our cost function through the use of the COBYLA optimizer. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "71344086",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fit in 50.21 seconds\n"
     ]
    }
   ],
   "source": [
    "opt = COBYLA(maxiter=150, rhobeg=0.8)\n",
    "initial_point = algorithm_globals.random.random(ae.num_parameters)\n",
    "\n",
    "objective_func_vals = []\n",
    "# make the plot nicer\n",
    "plt.rcParams[\"figure.figsize\"] = (12, 6)\n",
    "\n",
    "start = time.time()\n",
    "opt_result = opt.minimize(cost_func_domain, initial_point)\n",
    "elapsed = time.time() - start\n",
    "\n",
    "print(f\"Fit in {elapsed:0.2f} seconds\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0242ad6d",
   "metadata": {},
   "source": [
    "Looks like it has converged! After training our Quantum Autoencoder, let's build it and see how well it compresses the state! \n",
    "\n",
    "To do this, we first apply our Autoencoder to a $5$ qubit Domain Wall state. After applying this state, the compressed state should be of the form $|00\\rangle$. Therefore resetting the last two qubits should not effect our over all state. \n",
    "\n",
    "After resetting we apply our decoder (the hermitian conjugate of our encoder) and compare it to the initial state by determining the fidelity. If our fidelity is one, then our Autoencoder has encoded all the information of the domain wall efficiently into a smaller set of qubits and when decoding, we retain the original state! "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c88b086",
   "metadata": {},
   "source": [
    "Let's first apply our circuit to the Domain Wall State, using the parameters we obtained when training our Quantum Autoencoder. (Note we have included barriers in our circuit below, however these are not necessary for the implementation of the Quantum Autoencoder and are used to determine between different sections of our circuit). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "749338a0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1959.72x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_qc = QuantumCircuit(num_latent + num_trash)\n",
    "test_qc = test_qc.compose(domain_wall_circuit)\n",
    "ansatz_qc = ansatz(num_latent + num_trash)\n",
    "test_qc = test_qc.compose(ansatz_qc)\n",
    "test_qc.barrier()\n",
    "test_qc.reset(4)\n",
    "test_qc.reset(3)\n",
    "test_qc.barrier()\n",
    "test_qc = test_qc.compose(ansatz_qc.inverse())\n",
    "\n",
    "test_qc.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "grand-canal",
   "metadata": {},
   "source": [
    "Now we assign the parameter values obtained in the training."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "shaped-marina",
   "metadata": {},
   "outputs": [],
   "source": [
    "test_qc = test_qc.assign_parameters(opt_result.x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8dce4200",
   "metadata": {},
   "source": [
    "Now let's get the statevectors of our Domain Wall state and output circuit and calculate the fidelity! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "756cfa05",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fidelity of our Output State with our Input State:  0.9999874528158202\n"
     ]
    }
   ],
   "source": [
    "domain_wall_state = Statevector(domain_wall_circuit).data\n",
    "output_state = Statevector(test_qc).data\n",
    "\n",
    "fidelity = np.sqrt(np.dot(domain_wall_state.conj(), output_state) ** 2)\n",
    "print(\"Fidelity of our Output State with our Input State: \", fidelity.real)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "618128d3",
   "metadata": {},
   "source": [
    "As you can see our fidelity is quite high and our Autoencoder has thus compressed our dataset while retaining all the information from the input state!\n",
    "\n",
    "Now we will see if we can apply such a Quantum Autoencoder to more complicated datasets containing noise, such as images of the numbers zero and one. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0b5be665",
   "metadata": {},
   "source": [
    "## 7. A Quantum Autoencoder for Digital Compression"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f6f37a6",
   "metadata": {},
   "source": [
    "One can also apply a Quantum Autoencoder to more complicated examples, such as a set of handwritten digits in order to compress the dataset. Below, we will show that we can indeed train an Quantum Autoencoder to compress such an example, giving us the ability to store data more efficiently on a Quantum Computer. \n",
    "\n",
    "For this tutorial, we will build a Quantum Autoencoder for a noisy dataset containing zeros and ones, which can be seen below. \n",
    "\n",
    "Each image contains $32$ pixels of which can be encoded into $5$ qubits by Amplitude Encoding. This can be done using Qiskit's `RawFeatureVector` feature map.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "41d40622",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IBgATogHAhGgAMCEaAEyIBgATogHAhGgAMCEaAEyafQPo8+XxxsvjiXfr8C1iQv/Rbo8QcWs/KnV7hBZRV3HQ7REirs452aTtONMAYEI0AJgQDQAmRAOACdEAYEI0AJgQDQAmRAOACdEAYEI0AJgQDQAmRAOACdEAYEI0AJgQDQAmRAOACdEAYEI0AJgQDQAmRAOACdEAYEI0AJgQDQAmRAOAiSkaCxcuVFZWlhITE5WYmKgRI0Zo3bp1kZoNQBQyRSM9PV1z5szR9u3btW3bNt1444269dZb9cEHH0RqPgBRxnRbxnHjxtV7PHv2bC1cuFBlZWW68sorwzoYgOjU7Hu51tXV6eWXX1Ztba1GjBjR4HaBQECBQCD0uLq6urmHBBAFzBdCd+3apY4dO8rr9erBBx/U6tWrlZmZ2eD2Pp9PSUlJoSUjI+O8BgbgLnM0+vXrp507d+q9997TQw89pPz8fH344YcNbl9UVCS/3x9aKioqzmtgAO4yfzyJj49X3759JUmDBw9WeXm55s2bp0WLFp11e6/XK6/Xe35TAoga5/19GsFgsN41CwBtm+lMo6ioSHl5eerZs6dqampUXFys0tJSrV+/PlLzAYgypmhUVVXp3nvv1VdffaWkpCRlZWVp/fr1Gj16dKTmAxBlTNH4y1/+Eqk5ALQS/OwJABOiAcCEaAAwIRoATIgGABOiAcCEaAAwIRoATIgGABOiAcCEaAAwIRoATIgGABOiAcCEaAAwIRoATIgGABOiAcCEaAAwIRoATIgGABOiAcCk2XeNP19O4IQcj+PW4VtETEKC2yNEXFBBt0doEbHJnd0eIeKc4AmpsvHtONMAYEI0AJgQDQAmRAOACdEAYEI0AJgQDQAmRAOACdEAYEI0AJgQDQAmRAOACdEAYEI0AJgQDQAmRAOACdEAYEI0AJgQDQAmRAOACdEAYEI0AJgQDQAmRAOAyXlFY86cOfJ4PJo6dWqYxgEQ7ZodjfLyci1atEhZWVnhnAdAlGtWNI4dO6ZJkyZp8eLF6ty57d+uDsAPmhWNgoIC3XzzzcrNzW1020AgoOrq6noLgNbLfAPoFStWaMeOHSovL2/S9j6fT7NmzTIPBiA6mc40Kioq9Mgjj2j58uVq165dk/YpKiqS3+8PLRUVFc0aFEB0MJ1pbN++XVVVVbrmmmtC6+rq6rRlyxb96U9/UiAQUGxsbL19vF6vvF5veKYF4DpTNHJycrRr16566yZPnqwrrrhCv/71r88IBoC2xxSNhIQEDRgwoN66iy++WMnJyWesB9A28R2hAEzMXz35X6WlpWEYA0BrwZkGABOiAcCEaAAwIRoATIgGABOiAcCEaAAwIRoATIgGABOiAcCEaAAwIRoATIgGABOiAcCEaAAwIRoATIgGABOiAcCEaAAwIRoATIgGABOiAcDkvG9h0FwxHTsoxhPv1uFbhKfjxW6PEHFez0Vuj9AigtU1bo8QcUHnRJO240wDgAnRAGBCNACYEA0AJkQDgAnRAGBCNACYEA0AJkQDgAnRAGBCNACYEA0AJkQDgAnRAGBCNACYEA0AJkQDgAnRAGBCNACYEA0AJkQDgAnRAGBCNACYmKIxc+ZMeTyeessVV1wRqdkARCHzzZKuvPJKbdiw4YcXiHPtfksAXGD+Fx8XF6fu3btHYhYArYD5msann36qtLQ09enTR5MmTdLnn38eibkARCnTmcbw4cO1dOlS9evXT1999ZVmzZqlkSNHavfu3UpISDjrPoFAQIFAIPS4urr6/CYG4CpTNPLy8kK/zsrK0vDhw9WrVy+99NJL+slPfnLWfXw+n2bNmnV+UwKIGuf1JddOnTrp8ssv1969exvcpqioSH6/P7RUVFSczyEBuOy8onHs2DH9+9//Vo8ePRrcxuv1KjExsd4CoPUyRWP69OnavHmzDhw4oHfffVe33XabYmNjddddd0VqPgBRxnRN44svvtBdd92lI0eOKCUlRdddd53KysqUkpISqfkARBlTNFasWBGpOQC0EvzsCQATogHAhGgAMCEaAEyIBgATogHAhGgAMCEaAEyIBgATogHAhGgAMCEaAEyIBgATogHAhGgAMCEaAEyIBgATogHAhGgAMCEaAEyIBgATogHAxHQLg3DydOwoT4zXrcO3DMdxe4KI23PiO7dHQAvjTAOACdEAYEI0AJgQDQAmRAOACdEAYEI0AJgQDQAmRAOACdEAYEI0AJgQDQAmRAOACdEAYEI0AJgQDQAmRAOACdEAYEI0AJgQDQAmRAOACdEAYEI0AJgQDQAm5mh8+eWXuueee5ScnKz27dtr4MCB2rZtWyRmAxCFTHdY+/bbb5Wdna0bbrhB69atU0pKij799FN17tw5UvMBiDKmaDz55JPKyMjQkiVLQusuueSSsA8FIHqZPp6sXbtWQ4YM0YQJE5Samqqrr75aixcvjtRsAKKQKRr79u3TwoULddlll2n9+vV66KGH9POf/1zPP/98g/sEAgFVV1fXWwC0XqaPJ8FgUEOGDNETTzwhSbr66qu1e/duPfvss8rPzz/rPj6fT7NmzTr/SQFEBdOZRo8ePZSZmVlvXf/+/fX55583uE9RUZH8fn9oqaioaN6kAKKC6UwjOztbH3/8cb11n3zyiXr16tXgPl6vV16vt3nTAYg6pjONX/ziFyorK9MTTzyhvXv3qri4WM8995wKCgoiNR+AKGOKxtChQ7V69Wr9/e9/14ABA/T444/r6aef1qRJkyI1H4AoY/p4Ikljx47V2LFjIzELgFaAnz0BYEI0AJgQDQAmRAOACdEAYEI0AJgQDQAmRAOACdEAYEI0AJgQDQAmRAOACdEAYEI0AJgQDQAmRAOACdEAYEI0AJgQDQAmRAOACdEAYEI0AJiYb2EQNidPSTFtu1l1h4+4PULE/aLfDW6P0CKcwHdujxBxQedkk7Zr2/9qAYQd0QBgQjQAmBANACZEA4AJ0QBgQjQAmBANACZEA4AJ0QBgQjQAmBANACZEA4AJ0QBgQjQAmBANACZEA4AJ0QBgQjQAmBANACZEA4AJ0QBgQjQAmBANACamaPTu3Vsej+eMpaCgIFLzAYgypjuslZeXq66uLvR49+7dGj16tCZMmBD2wQBEJ1M0UlJS6j2eM2eOLr30Uv3f//1fWIcCEL2afS/XEydO6G9/+5umTZsmj8fT4HaBQECBQCD0uLq6urmHBBAFmn0h9NVXX9XRo0d13333nXM7n8+npKSk0JKRkdHcQwKIAh7HcZzm7DhmzBjFx8frtddeO+d2ZzvTyMjIUG63BxQXE9+cQ7caF8Jd4xUb6/YELcL5r7/DbdUp56RKtUZ+v1+JiYkNbtesjyefffaZNmzYoFWrVjW6rdfrldfrbc5hAEShZn08WbJkiVJTU3XzzTeHex4AUc4cjWAwqCVLlig/P19xcc2+jgqglTJHY8OGDfr88891//33R2IeAFHOfKpw0003qZnXTgG0AfzsCQATogHAhGgAMCEaAEyIBgATogHAhGgAMCEaAEyIBgATogHAhGgAMCEaAEyIBgATogHAhGgAMCEaAEyIBgATogHAhGgAMCEaAEyIBgCTFr9xyen/yfxU8ERLH7rF1Tkn3R4h8pyg2xO0COcC+LM8pf+8x8buNtDi0aipqZEklX79fEsfGpFwyu0BEG41NTVKSkpq8Plm3wC6uYLBoA4ePKiEhAR5PJ6IH+/0DacrKirOeVPb1o732ba48T4dx1FNTY3S0tIUE9PwlYsWP9OIiYlRenp6Sx9WiYmJbfov2Wm8z7alpd/nuc4wTuNCKAATogHApM1Hw+v1asaMGfJ6vW6PElG8z7Ylmt9ni18IBdC6tfkzDQDhRTQAmBANACZEA4BJm4/GggUL1Lt3b7Vr107Dhw/X+++/7/ZIYbVlyxaNGzdOaWlp8ng8evXVV90eKSJ8Pp+GDh2qhIQEpaamavz48fr444/dHiusFi5cqKysrNA3dI0YMULr1q1ze6wztOlovPjii5o2bZpmzJihHTt2aNCgQRozZoyqqqrcHi1samtrNWjQIC1YsMDtUSJq8+bNKigoUFlZmUpKSnTy5EnddNNNqq2tdXu0sElPT9ecOXO0fft2bdu2TTfeeKNuvfVWffDBB26PVp/Thg0bNswpKCgIPa6rq3PS0tIcn8/n4lSRI8lZvXq122O0iKqqKkeSs3nzZrdHiajOnTs7f/7zn90eo542e6Zx4sQJbd++Xbm5uaF1MTExys3N1datW12cDOHg9/slSV26dHF5ksioq6vTihUrVFtbqxEjRrg9Tj0t/gNrLeXw4cOqq6tTt27d6q3v1q2bPvroI5emQjgEg0FNnTpV2dnZGjBggNvjhNWuXbs0YsQIHT9+XB07dtTq1auVmZnp9lj1tNlooO0qKCjQ7t279fbbb7s9Stj169dPO3fulN/v18qVK5Wfn6/NmzdHVTjabDS6du2q2NhYVVZW1ltfWVmp7t27uzQVzldhYaFef/11bdmyxZX/YiHS4uPj1bdvX0nS4MGDVV5ernnz5mnRokUuT/aDNntNIz4+XoMHD9bGjRtD64LBoDZu3Bh1nxHROMdxVFhYqNWrV+utt97SJZdc4vZILSIYDCoQCLg9Rj1t9kxDkqZNm6b8/HwNGTJEw4YN09NPP63a2lpNnjzZ7dHC5tixY9q7d2/o8f79+7Vz50516dJFPXv2dHGy8CooKFBxcbHWrFmjhIQEHTp0SNJ//tOY9u3buzxdeBQVFSkvL089e/ZUTU2NiouLVVpaqvXr17s9Wn1uf/km0ubPn+/07NnTiY+Pd4YNG+aUlZW5PVJYbdq0yZF0xpKfn+/2aGF1tvcoyVmyZInbo4XN/fff7/Tq1cuJj493UlJSnJycHOfNN990e6wz8KPxAEza7DUNAJFBNACYEA0AJkQDgAnRAGBCNACYEA0AJkQDgAnRAGBCNACYEA0AJkQDgMn/A/L20dSrpm8gAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def zero_idx(j, i):\n",
    "    # Index for zero pixels\n",
    "    return [\n",
    "        [i, j],\n",
    "        [i - 1, j - 1],\n",
    "        [i - 1, j + 1],\n",
    "        [i - 2, j - 1],\n",
    "        [i - 2, j + 1],\n",
    "        [i - 3, j - 1],\n",
    "        [i - 3, j + 1],\n",
    "        [i - 4, j - 1],\n",
    "        [i - 4, j + 1],\n",
    "        [i - 5, j],\n",
    "    ]\n",
    "\n",
    "\n",
    "def one_idx(i, j):\n",
    "    # Index for one pixels\n",
    "    return [[i, j - 1], [i, j - 2], [i, j - 3], [i, j - 4], [i, j - 5], [i - 1, j - 4], [i, j]]\n",
    "\n",
    "\n",
    "def get_dataset_digits(num, draw=True):\n",
    "    # Create Dataset containing zero and one\n",
    "    train_images = []\n",
    "    train_labels = []\n",
    "    for i in range(int(num / 2)):\n",
    "        # First we introduce background noise\n",
    "        empty = np.array([algorithm_globals.random.uniform(0, 0.1) for i in range(32)]).reshape(\n",
    "            8, 4\n",
    "        )\n",
    "\n",
    "        # Now we insert the pixels for the one\n",
    "        for i, j in one_idx(2, 6):\n",
    "            empty[j][i] = algorithm_globals.random.uniform(0.9, 1)\n",
    "        train_images.append(empty)\n",
    "        train_labels.append(1)\n",
    "        if draw:\n",
    "            plt.title(\"This is a One\")\n",
    "            plt.imshow(train_images[-1])\n",
    "            plt.show()\n",
    "\n",
    "    for i in range(int(num / 2)):\n",
    "        empty = np.array([algorithm_globals.random.uniform(0, 0.1) for i in range(32)]).reshape(\n",
    "            8, 4\n",
    "        )\n",
    "\n",
    "        # Now we insert the pixels for the zero\n",
    "        for k, j in zero_idx(2, 6):\n",
    "            empty[k][j] = algorithm_globals.random.uniform(0.9, 1)\n",
    "\n",
    "        train_images.append(empty)\n",
    "        train_labels.append(0)\n",
    "        if draw:\n",
    "            plt.imshow(train_images[-1])\n",
    "            plt.title(\"This is a Zero\")\n",
    "            plt.show()\n",
    "\n",
    "    train_images = np.array(train_images)\n",
    "    train_images = train_images.reshape(len(train_images), 32)\n",
    "\n",
    "    for i in range(len(train_images)):\n",
    "        sum_sq = np.sum(train_images[i] ** 2)\n",
    "        train_images[i] = train_images[i] / np.sqrt(sum_sq)\n",
    "\n",
    "    return train_images, train_labels\n",
    "\n",
    "\n",
    "train_images, __ = get_dataset_digits(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "646f12b6",
   "metadata": {},
   "source": [
    "After encoding our image into $5$ qubits, we begin to train our Quantum Autoencoder to compress this state into $3$ qubits.\n",
    "\n",
    "We repeat the steps in the previous example and write a cost function, again based on the Swap Test between the trash and latent space. We can also use the same Autoencoder function as given in the previous example, as the input state and trash space contain the same amount of qubits. \n",
    "\n",
    "Let's input one of our digits and see our circuit for the Autoencoder below. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "a11ec8f3",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 2126.94x785.944 with 1 Axes>"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num_latent = 3\n",
    "num_trash = 2\n",
    "\n",
    "fm = RawFeatureVector(2 ** (num_latent + num_trash))\n",
    "\n",
    "ae = auto_encoder_circuit(num_latent, num_trash)\n",
    "\n",
    "qc = QuantumCircuit(num_latent + 2 * num_trash + 1, 1)\n",
    "qc = qc.compose(fm, range(num_latent + num_trash))\n",
    "qc = qc.compose(ae)\n",
    "\n",
    "qc.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "effd4db6",
   "metadata": {},
   "source": [
    "Again, we can see the swap test being performed on the qubits $3$, $4$, $5$ and $6$, which will determine the value of our cost function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "301b80ad",
   "metadata": {},
   "outputs": [],
   "source": [
    "def identity_interpret(x):\n",
    "    return x\n",
    "\n",
    "\n",
    "qnn = SamplerQNN(\n",
    "    circuit=qc,\n",
    "    input_params=fm.parameters,\n",
    "    weight_params=ae.parameters,\n",
    "    interpret=identity_interpret,\n",
    "    output_shape=2,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "inner-second",
   "metadata": {},
   "source": [
    "We build our cost function, based on the swap test between the reference and trash space for the digit dataset. To do this, we again use Qiskit's CircuitQNN network and use the same interpret function as we are measuring the probability of getting the final qubit in the $|1\\rangle$ state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "frequent-negotiation",
   "metadata": {},
   "outputs": [],
   "source": [
    "def cost_func_digits(params_values):\n",
    "    probabilities = qnn.forward(train_images, params_values)\n",
    "    cost = np.sum(probabilities[:, 1]) / train_images.shape[0]\n",
    "\n",
    "    # plotting part\n",
    "    clear_output(wait=True)\n",
    "    objective_func_vals.append(cost)\n",
    "    plt.title(\"Objective function value against iteration\")\n",
    "    plt.xlabel(\"Iteration\")\n",
    "    plt.ylabel(\"Objective function value\")\n",
    "    plt.plot(range(len(objective_func_vals)), objective_func_vals)\n",
    "    plt.show()\n",
    "\n",
    "    return cost"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d868874b",
   "metadata": {},
   "source": [
    "Since model training may take a long time we have already pre-trained the model for some iterations and saved the pre-trained weights. We'll continue training from that point by setting `initial_point` to a vector of pre-trained weights."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "cd34af70",
   "metadata": {},
   "outputs": [],
   "source": [
    "with open(\"12_qae_initial_point.json\", \"r\") as f:\n",
    "    initial_point = json.load(f)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a99a0c03",
   "metadata": {},
   "source": [
    "By minimizing this cost function, we can thus determine the required parameters to compress our noisy images. Let's see if we can encode our images! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "a2e4b67e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Traceback \u001b[1;36m(most recent call last)\u001b[0m:\n",
      "\u001b[0m  Cell \u001b[0;32mIn[54], line 8\u001b[0m\n",
      "    opt_result = opt.minimize(fun=cost_func_digits, x0=initial_point)\u001b[0m\n",
      "\u001b[0m  File \u001b[0;32m/opt/conda/lib/python3.10/site-packages/qiskit/algorithms/optimizers/scipy_optimizer.py:149\u001b[0m in \u001b[0;35mminimize\u001b[0m\n",
      "    raw_result = minimize(\u001b[0m\n",
      "\u001b[0m  File \u001b[0;32m/opt/conda/lib/python3.10/site-packages/scipy/optimize/_minimize.py:705\u001b[0m in \u001b[0;35mminimize\u001b[0m\n",
      "    res = _minimize_cobyla(fun, x0, args, constraints, callback=callback,\u001b[0m\n",
      "\u001b[0m  File \u001b[0;32m/opt/conda/lib/python3.10/site-packages/scipy/optimize/_cobyla_py.py:34\u001b[0m in \u001b[0;35mwrapper\u001b[0m\n",
      "    return func(*args, **kwargs)\u001b[0m\n",
      "\u001b[0m  File \u001b[0;32m/opt/conda/lib/python3.10/site-packages/scipy/optimize/_cobyla_py.py:273\u001b[0m in \u001b[0;35m_minimize_cobyla\u001b[0m\n",
      "    xopt, info = cobyla.minimize(calcfc, m=m, x=np.copy(x0), rhobeg=rhobeg,\u001b[0m\n",
      "\u001b[0m  File \u001b[0;32m/opt/conda/lib/python3.10/site-packages/scipy/optimize/_cobyla_py.py:261\u001b[0m in \u001b[0;35mcalcfc\u001b[0m\n",
      "    f = fun(np.copy(x), *args)\u001b[0m\n",
      "\u001b[0m  Cell \u001b[0;32mIn[52], line 2\u001b[0m in \u001b[0;35mcost_func_digits\u001b[0m\n",
      "    probabilities = qnn.forward(train_images, params_values)\u001b[0m\n",
      "\u001b[0m  File \u001b[0;32m/opt/conda/lib/python3.10/site-packages/qiskit_machine_learning/neural_networks/neural_network.py:225\u001b[0m in \u001b[0;35mforward\u001b[0m\n",
      "    weights_ = self._validate_weights(weights)\u001b[0m\n",
      "\u001b[1;36m  File \u001b[1;32m/opt/conda/lib/python3.10/site-packages/qiskit_machine_learning/neural_networks/neural_network.py:178\u001b[1;36m in \u001b[1;35m_validate_weights\u001b[1;36m\n",
      "\u001b[1;33m    return weights_.reshape(self._num_weights)\u001b[1;36m\n",
      "\u001b[1;31mValueError\u001b[0m\u001b[1;31m:\u001b[0m cannot reshape array of size 30 into shape (20,)\n",
      "\n",
      "Use %tb to get the full traceback.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "capi_return is NULL\n",
      "Call-back cb_calcfc_in__cobyla__user__routines failed.\n"
     ]
    },
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       "<a href=\"https://stackoverflow.com/search?q=ValueError: cannot reshape array of size 30 into shape (20,)\" target='_blank'><button class='button iqx-button'>Search for solution online</button></a>\n"
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   "source": [
    "opt = COBYLA(maxiter=150)\n",
    "\n",
    "objective_func_vals = []\n",
    "# make the plot nicer\n",
    "plt.rcParams[\"figure.figsize\"] = (12, 6)\n",
    "\n",
    "start = time.time()\n",
    "opt_result = opt.minimize(fun=cost_func_digits, x0=initial_point)\n",
    "elapsed = time.time() - start\n",
    "print(f\"Fit in {elapsed:0.2f} seconds\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c92af0a",
   "metadata": {},
   "source": [
    "Looks like it has converged!\n",
    "\n",
    "Now let's build our Encoder and Decoder using the parameters obtained from the training period. After applying this circuit to our new dataset, we can then compare our input and output data and see if we were able to retain the images efficiently throughout the compression! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8d847b99",
   "metadata": {
    "tags": [
     "nbsphinx-thumbnail"
    ]
   },
   "outputs": [],
   "source": [
    "# Test\n",
    "test_qc = QuantumCircuit(num_latent + num_trash)\n",
    "test_qc = test_qc.compose(fm)\n",
    "ansatz_qc = ansatz(num_latent + num_trash)\n",
    "test_qc = test_qc.compose(ansatz_qc)\n",
    "test_qc.barrier()\n",
    "test_qc.reset(4)\n",
    "test_qc.reset(3)\n",
    "test_qc.barrier()\n",
    "test_qc = test_qc.compose(ansatz_qc.inverse())\n",
    "\n",
    "# sample new images\n",
    "test_images, test_labels = get_dataset_digits(2, draw=False)\n",
    "for image, label in zip(test_images, test_labels):\n",
    "    original_qc = fm.assign_parameters(image)\n",
    "    original_sv = Statevector(original_qc).data\n",
    "    original_sv = np.reshape(np.abs(original_sv) ** 2, (8, 4))\n",
    "\n",
    "    param_values = np.concatenate((image, opt_result.x))\n",
    "    output_qc = test_qc.assign_parameters(param_values)\n",
    "    output_sv = Statevector(output_qc).data\n",
    "    output_sv = np.reshape(np.abs(output_sv) ** 2, (8, 4))\n",
    "\n",
    "    fig, (ax1, ax2) = plt.subplots(1, 2)\n",
    "    ax1.imshow(original_sv)\n",
    "    ax1.set_title(\"Input Data\")\n",
    "    ax2.imshow(output_sv)\n",
    "    ax2.set_title(\"Output Data\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ecfe78e",
   "metadata": {},
   "source": [
    "It looks like our Quantum Autoencoder can be trained to encode digits as well! Now it's your turn to build your own Quantum Autoencoder and come up with ideas and datasets to compress!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae71d1a3",
   "metadata": {},
   "source": [
    "## 8. Applications of a Quantum Autoencoder"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c076968",
   "metadata": {},
   "source": [
    "Quantum Autoencoder's can be used for various different applications, including\n",
    "\n",
    "1. Digital Compression: where information can be encoded into a smaller amount of qubits. This can be hugely beneficial for near term quantum devices, as smaller systems of qubits are less prone to noise.\n",
    "2. Denoising: where one can use Quantum Autoencoder to extract relevant features from the initial quantum state or encoded data, while neglecting any additional noise.\n",
    "3. Quantum Chemistry: in which a Quantum Autoencoder can be used as an ansatz for systems, such as the Hubbard Model. This is commonly used to describe electron-electron interactions in molecules. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bfd1eb3c",
   "metadata": {},
   "source": [
    "## 9. References"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c44364ae",
   "metadata": {},
   "source": [
    "1. A wikipedia page on Autoencoder: https://en.wikipedia.org/wiki/Autoencoder\n",
    "\n",
    "2. Romero, Jonathan, Jonathan P. Olson, and Alan Aspuru-Guzik. \"Quantum autoencoders for efficient compression of quantum data.\" Quantum Science and Technology 2.4 (2017): 045001.\n",
    "\n",
    "3. Swap Test Algorithm: https://en.wikipedia.org/wiki/Swap_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "aab7dbd0",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import qiskit.tools.jupyter\n",
    "\n",
    "%qiskit_version_table\n",
    "%qiskit_copyright"
   ]
  }
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