notebooks/StateLearning.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<img align=\"right\" src=\"https://i.imgur.com/cHp1Owf.gif\">\n",
    "\n",
    "# Quantum state learning\n",
    "\n",
    "This notebook works through the process used to produce the state preparation results presented in [*\"Machine learning method for state preparation and gate synthesis on photonic quantum computers\"*](https://iopscience.iop.org/article/10.1088/2058-9565/aaf59e/pdf).\n",
    "\n",
    "We use the continuous-variable (CV) quantum optical circuit package [Strawberry Fields](https://github.com/XanaduAI/strawberryfields), and in particular its TensorFlow backend, to perform quantum circuit optimization. By leveraging Tensorflow, we have access to a number of additional funtionalities, including GPU integration, automatic gradient computation, built-in optimization algorithms, and other machine learning tools."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Variational quantum circuits"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A key element of machine learning is optimization. We can use Tensorflow’s automatic differentiation tools to optimize the parameters of variational quantum circuits constructed using Strawberry Fields. In this approach, we fix a circuit architecture where the states, gates, and/or measurements may have learnable parameters $\\vec{\\theta}$ associated with them. We then define a loss function based on the output state of this circuit. In this case, we define a loss function such that the fidelity of the output state of the variational circuit is maximized with respect to some target state. For more details on the TensorFlow backend in Strawberry Fields, please see the [Strawberry Fields documentation](http://strawberryfields.readthedocs.io/en/stable/tutorials/tutorial_machine_learning.html).\n",
    "\n",
    "For arbitrary state preparation using optimization, we need to make use of a quantum circuit with a layer structure that is **universal** - that is, by 'stacking' the layers, we can guarantee that we can produce *any* CV state with at-most polynomial overhead. Therefore, the architecture we choose must consist of layers with each layer containing parameterized Gaussian *and* non-Gaussian gates. **The non-Gaussian gates provide both the nonlinearity and the universality of the model.** To this end, we employ the CV quantum neural network architecture described below:\n",
    "\n",
    "![layer](https://i.imgur.com/NEsaVIX.png)\n",
    "\n",
    "Here,\n",
    "\n",
    "\n",
    "* $\\mathcal{U}_i(\\theta_i,\\phi_i)$ is an N-mode linear optical interferometer composed of two-mode beamsplitters $BS(\\theta,\\phi)$ and single-mode rotation gates $R(\\phi)=e^{i\\phi\\hat{n}}$,\n",
    "\n",
    "* $\\mathcal{D}(\\alpha_i)$ are single mode displacements in the phase space by complex value $\\alpha_i$,\n",
    "\n",
    "* $\\mathcal{S}(r_i, \\phi_i)$ are single mode squeezing operations of magnitude $r_i$ and phase $\\phi_i$, and\n",
    "\n",
    "* $\\Phi(\\lambda_i)$ is a single mode non-Gaussian operation, in this case chosen to be the Kerr interaction $\\mathcal{K}(\\kappa_i)=e^{i\\kappa_i\\hat{n}^2}$ of strength $\\kappa_i$.\n",
    "\n",
    "<br/>\n",
    "\n",
    "<div class=\"alert alert-success\" style=\"border: 0px; border-left: 3px solid #119a68; color: black; background-color: #daf0e9\">\n",
    "<p style=\"color: #119a68;\"><strong>Reference</strong></p>Killoran, N., Bromley, T. R., Arrazola, J. M., Schuld, M., Quesada, N., & Lloyd, S. (2018). \"Continuous-variable quantum neural networks.\" <a href=https://arxiv.org/abs/1806.06871>arXiv:1806.06871</a>.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hyperparameters\n",
    "\n",
    "\n",
    "First, we must define the **hyperparameters** of our layer structure:\n",
    "\n",
    "* `cutoff`: the simulation Fock space truncation we will use in the optimization. The TensorFlow backend will perform numerical operations in this truncated Fock space when performing the optimization.\n",
    "\n",
    "\n",
    "* `depth`: The number of layer ansatz in our variational quantum circuit. As a general rule, increasing the number of layers (and thus, the number of parameters we are optimizing over) increases the optimizers chance of finding a reasonable local minimum in the optimization landscape.\n",
    "\n",
    "\n",
    "* `reps`: the number of steps in the optimization routine performing gradient descent\n",
    "\n",
    "Some other optional hyperparameters include:\n",
    "\n",
    "* The standard deviation of initial parameters. Note that we make a distinction between the standard deviation of *passive* parameters (those that preserve photon number when changed, such as phase parameters), and *active* parameters (those that introduce or remove energy from the system when changed)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Cutoff dimension\n",
    "cutoff = 10\n",
    "\n",
    "# Number of layers\n",
    "depth = 20\n",
    "\n",
    "# Number of steps in optimization routine performing gradient descent\n",
    "reps = 1000\n",
    "\n",
    "# Standard deviation of initial parameters\n",
    "passive_sd = 0.1\n",
    "active_sd = 0.001"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The layer parameters $\\vec{\\theta}$\n",
    "\n",
    "We use TensorFlow to create the variables corresponding to the gate parameters. Note that each variable has shape `[depth]`, with each individual element representing the gate parameter in layer $i$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import tensorflow as tf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# squeeze gate\n",
    "sq_r = tf.Variable(tf.random_normal(shape=[depth], stddev=active_sd))\n",
    "sq_phi = tf.Variable(tf.random_normal(shape=[depth], stddev=passive_sd))\n",
    "\n",
    "# displacement gate\n",
    "d_r = tf.Variable(tf.random_normal(shape=[depth], stddev=active_sd))\n",
    "d_phi = tf.Variable(tf.random_normal(shape=[depth], stddev=passive_sd))\n",
    "\n",
    "# rotation gates\n",
    "r1 = tf.Variable(tf.random_normal(shape=[depth], stddev=passive_sd))\n",
    "r2 = tf.Variable(tf.random_normal(shape=[depth], stddev=passive_sd))\n",
    "\n",
    "# kerr gate\n",
    "kappa = tf.Variable(tf.random_normal(shape=[depth], stddev=active_sd))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For convenience, we store the TensorFlow variables representing the parameters in a list:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "params = [r1, sq_r, sq_phi, r2, d_r, d_phi, kappa]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can create a function to define the $i$th layer, acting on qumode `q`. This allows us to simply call this function in a loop later on when we build our circuit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# layer architecture\n",
    "def layer(i, q):\n",
    "    Rgate(r1[i]) | q\n",
    "    Sgate(sq_r[i], sq_phi[i]) | q\n",
    "    Rgate(r2[i]) | q\n",
    "    Dgate(d_r[i], d_phi[i]) | q\n",
    "    Kgate(kappa[i]) | q\n",
    "    \n",
    "    return q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Constructing the circuit\n",
    "\n",
    "Now that we have defined our gate parameters and our layer structure, we can import Strawberry Fields and construct our variational quantum circuit. Note that, to ensure the TensorFlow backend computes the circuit symbolically, we specify `eval=False`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import strawberryfields as sf\n",
    "from strawberryfields.ops import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Start SF program\n",
    "prog = sf.Program(1)\n",
    "\n",
    "# Apply circuit of layers with corresponding depth\n",
    "with prog.context as q:\n",
    "    for k in range(depth):\n",
    "        layer(k, q[0])\n",
    "\n",
    "# Run engine\n",
    "eng = sf.Engine('tf', backend_options={\"cutoff_dim\": cutoff})\n",
    "state = eng.run(prog, run_options={\"eval\": False}).state\n",
    "ket = state.ket()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the output state vector is an unevaluated tensor:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor 'ket:0' shape=(10,) dtype=complex64>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ket"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Performing the optimization\n",
    "\n",
    "$\\newcommand{ket}[1]{\\left|#1\\right\\rangle}$ With the Strawberry Fields TensorFlow backend calculating the resulting state of the circuit symbolically, we can use TensorFlow to optimize the gate parameters to minimize the cost function we specify. With state learning, the measure of distance between two quantum states is given by the **fidelity of the output state $\\ket{\\psi}$ with some target state $\\ket{\\psi_t}$**. This is defined as the overlap between the two states:\n",
    "\n",
    "$$ F = \\left|\\left\\langle{\\psi}\\mid{\\psi_t}\\right\\rangle\\right|^2$$\n",
    "\n",
    "where the output state can be written $\\ket{\\psi}=U(\\vec{\\theta})\\ket{\\psi_0}$, with $U(\\vec{\\theta})$ the unitary operation applied by the variational quantum circuit, and $\\ket{\\psi_0}=\\ket{0}$ the initial state.\n",
    "\n",
    "Let's define the target state as the single photon state $\\ket{\\psi_t}=\\ket{1}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "target_state = np.zeros([cutoff])\n",
    "target_state[1] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 1., 0., 0., 0., 0., 0., 0., 0., 0.])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "target_state"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using this target state, we calculate the fidelity with the state exiting the variational circuit. We must use TensorFlow functions to manipulate this data, as were are working with symbolic variables!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "fidelity = tf.abs(tf.reduce_sum(tf.conj(ket) * target_state)) ** 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We choose the following cost function:\n",
    "\n",
    "$$C(\\vec{\\theta}) = \\left| \\langle \\psi_t \\mid U(\\vec{\\theta})\\mid 0\\rangle - 1\\right|$$\n",
    "\n",
    "By minimizing this cost function, the variational quantum circuit will prepare a state with high fidelity to the target state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Objective function to minimize\n",
    "cost = tf.abs(tf.reduce_sum(tf.conj(ket) * target_state) - 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that the cost function is defined, we can define and run the optimization. Below, we choose the Adam optimizer that is built into TensorFlow."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Using Adam algorithm for optimization\n",
    "optimiser = tf.train.AdamOptimizer()\n",
    "min_cost = optimiser.minimize(cost)\n",
    "\n",
    "# Begin Tensorflow session\n",
    "session = tf.Session()\n",
    "session.run(tf.global_variables_initializer())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We then loop over all repetitions, storing the best predicted fidelity value. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rep: 0 Cost: 0.9953 Fidelity: 0.0000\n",
      "Rep: 100 Cost: 0.0404 Fidelity: 0.9209\n",
      "Rep: 200 Cost: 0.0111 Fidelity: 0.9793\n",
      "Rep: 300 Cost: 0.0068 Fidelity: 0.9889\n",
      "Rep: 400 Cost: 0.0051 Fidelity: 0.9932\n",
      "Rep: 500 Cost: 0.0042 Fidelity: 0.9954\n",
      "Rep: 600 Cost: 0.0037 Fidelity: 0.9967\n",
      "Rep: 700 Cost: 0.0033 Fidelity: 0.9975\n",
      "Rep: 800 Cost: 0.0031 Fidelity: 0.9980\n",
      "Rep: 900 Cost: 0.0029 Fidelity: 0.9984\n"
     ]
    }
   ],
   "source": [
    "fid_progress = []\n",
    "best_fid = 0\n",
    "\n",
    "# Run optimization\n",
    "for i in range(reps):\n",
    "\n",
    "    # one repitition of the optimization\n",
    "    _, cost_val, fid_val, ket_val = session.run([min_cost, cost, fidelity, ket])\n",
    "\n",
    "    # Stores fidelity at each step\n",
    "    fid_progress.append(fid_val)\n",
    "    \n",
    "    if fid_val > best_fid:\n",
    "        # store the new best fidelity and best state\n",
    "        best_fid = fid_val\n",
    "        learnt_state = ket_val\n",
    "\n",
    "    # Prints progress at every 10 reps\n",
    "    if i % 100 == 0:\n",
    "        print(\"Rep: {} Cost: {:.4f} Fidelity: {:.4f}\".format(i, cost_val, fid_val))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Results and visualisation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting the fidelity vs. optimization step:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.rcParams['font.family'] = 'serif'\n",
    "plt.rcParams['font.sans-serif'] = ['Computer Modern Roman']\n",
    "plt.style.use('default')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f50e8473b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(fid_progress)\n",
    "plt.ylabel('Fidelity')\n",
    "plt.xlabel('Step');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use the following function to plot the Wigner function of our target and learnt state:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "\n",
    "def wigner(rho):\n",
    "    \"\"\"This code is a modified version of the ‘iterative’ method\n",
    "    of the wigner function provided in QuTiP, which is released\n",
    "    under the BSD license, with the following copyright notice:\n",
    "\n",
    "    Copyright (C) 2011 and later, P.D. Nation, J.R. Johansson,\n",
    "    A.J.G. Pitchford, C. Granade, and A.L. Grimsmo.\n",
    "    \n",
    "    All rights reserved.\"\"\"\n",
    "    import copy\n",
    "    # Domain parameter for Wigner function plots\n",
    "    l = 5.0\n",
    "    cutoff = rho.shape[0]\n",
    "\n",
    "    # Creates 2D grid for Wigner function plots\n",
    "    x = np.linspace(-l, l, 100)\n",
    "    p = np.linspace(-l, l, 100)\n",
    "\n",
    "    Q, P = np.meshgrid(x, p)\n",
    "    A = (Q + P * 1.0j) / (2 * np.sqrt(2 / 2))\n",
    "\n",
    "    Wlist = np.array([np.zeros(np.shape(A), dtype=complex) for k in range(cutoff)])\n",
    "\n",
    "    # Wigner function for |0><0|\n",
    "    Wlist[0] = np.exp(-2.0 * np.abs(A) ** 2) / np.pi\n",
    "\n",
    "    # W = rho(0,0)W(|0><0|)\n",
    "    W = np.real(rho[0, 0]) * np.real(Wlist[0])\n",
    "\n",
    "    for n in range(1, cutoff):\n",
    "        Wlist[n] = (2.0 * A * Wlist[n - 1]) / np.sqrt(n)\n",
    "        W += 2 * np.real(rho[0, n] * Wlist[n])\n",
    "\n",
    "    for m in range(1, cutoff):\n",
    "        temp = copy.copy(Wlist[m])\n",
    "        # Wlist[m] = Wigner function for |m><m|\n",
    "        Wlist[m] = (2 * np.conj(A) * temp - np.sqrt(m)\n",
    "                    * Wlist[m - 1]) / np.sqrt(m)\n",
    "\n",
    "        # W += rho(m,m)W(|m><m|)\n",
    "        W += np.real(rho[m, m] * Wlist[m])\n",
    "\n",
    "        for n in range(m + 1, cutoff):\n",
    "            temp2 = (2 * A * Wlist[n - 1] - np.sqrt(m) * temp) / np.sqrt(n)\n",
    "            temp = copy.copy(Wlist[n])\n",
    "            # Wlist[n] = Wigner function for |m><n|\n",
    "            Wlist[n] = temp2\n",
    "\n",
    "            # W += rho(m,n)W(|m><n|) + rho(n,m)W(|n><m|)\n",
    "            W += 2 * np.real(rho[m, n] * Wlist[n])\n",
    "\n",
    "    return Q, P, W / 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Computing the density matrices $\\rho = \\left|\\psi\\right\\rangle \\left\\langle\\psi\\right|$ of the target and learnt state,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "rho_target = np.outer(target_state, target_state.conj())\n",
    "rho_learnt = np.outer(learnt_state, learnt_state.conj())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting the Wigner function of the target state:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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pu8CDkyZlk2MkxjThN2gfIUS8DelSjkOGmGRhxJCm60wh8T4iRBrIkFoiIqd7j4WAOEzhWZf85OAjxkj6PqBN+qDeB5SWuD4kq8SlhUcwjHoLEErg+8D2VkmhFQeLjp2xYTopWTSOpnPJkjEpRVKVyRPXMvnpSmvGVc1v/tt/ne16+v1/cjOPkyzIme+ezq34cP4l9pv3gTQsoYRO483RJxGMYrAXIlJofvOD9/m177xLCJEYgBCwLqCFoO8dhdE8PFmDj1ya1QQibe95eLSm0opzk5LbB0tCAG0k1nqI6dduEGIhQJA+p+19WoUJw+MEwQ8VdoggB1EWAudCaln7iNQSJQUhRryLpx9fqTTKHX2kqDS296diPJS56c0iRHShcL2nrDWVVvTWc36rRirBveOG2ahAKsG41NjI4H2D1oogBEJCpQuiUPzstc/xN//lv/j4nuzM4yALcuYPpvcNH5z8I/abDxBCEkJq1MUYkFLx8fUhiYMwE8GGwH/9O19iYd0w/BGIIWJdQJFywfiAloJ173k4bxhpxValETGmPRES5l3Pycol4RXgXQQi3geCiygtk0DCx9VvDPihuvU+Cazt09cmhugaIRLhVFBhqLCHJiGCU2HfVOBKCXxI04VSpCyx7TxFrXF9oCjTcEshBbO6BAnLzjGtDU3nGFWGk85R6I2vnFRZSIExEqUVSkm0FvzST/w4P375eSb6HLXZYbu4wtjsIUQOPv2QkgU580/H+oYPF1/lweptEIHgA0pqQvRIoYBIiMkRFUIgEEQ8Eo2Ljv/5jTf4+v4BLghkjKw7S+8DNZL9dUetFKVREAIygnWeQkvmrWNWFyxby/685dy44Li1qSImVbgb+yD4kCyHGLFdirEFl+wHqZL1MOwnQhmJjNB7DwFMoYgh4nxIFbZMlbAyMmlwiKAk0QWESu64UkMVbQPlyNA3jmpi6FuPLiRKpWGXWWUwSpBO7IODRceFnQpESldY54kI6lIjVbJRQggg0ufWRnJhXPGXfvqnkFIghCKG9AZYqBFKFMyKy4zNeWblZWo9exyXSOaPljypl/n9WN/y4fzLPFy/A4PIKjTISIieVEICMYmwEBIfeqTUp+/GN4+OePfkhEKlZl/jAqOyoA4B5zznpxW9DxwsOmZGMR0XlFGxbBzz1hFi5Fxd0Jaak7WlKFI16fqALCTeg3fJy3U2gBSYKlkRNg62hlY4EVFKYHufbBNADhWodQGlJMZIvEvNOFMIepcE2pQSayOq0gQ7CL+A6KEaGZyPmErjI5gynVDtY+TCtKLrPXWl6XrPwbzlmYtbeAHzxrJqLJe2azASD3ggOI+UEi0FSqc43HHb8Zs3bvDzTz9DIICIaTLQrwnhhLU9xIe0sEgKSW120KJiWpxnWlxiVlzCqPpxXEKZP0ZyhfwjggsdH5x8mYfNu6lhhhuaYwEpNT54lFAgIi6k8WQRBVIMy3dQhJDOq/vlr3+Nh21H5/zp1jYRobOeQgpcCGnBvBLcX7UsG8duoZkU+lT4QogYKXn/YJl8XynoBo9YS4ntXZrUG3zlqjR01lEUiuA8IQh8GMpjCSoKnPeAQBcK2zmMlsnLlaTKWgsKqeh7B0ogAjBE5yQSJwK+T6PdwQbKymCdHxIWMCo1i3XPCxe3OFj3HK16Xrq8xXHn2F+0jI3m8k5NFwM+pp+DIEXllEoWiFKSwiiMgJFW/NIrr7Jdj4hEpEg/YykVCIn3HVJoIgEpNAGXfP2QnjuJojbb1GqbUbHDrLjCtLiAEubxXGSZfxbZssgkIb45f417qzeJeEJM1kTyg3XyfocKTUQ1eK4pGxyG/0ciShhCdPy9G+/x+oMHuAg2JC/Zh8B+YzlXaB6seraNQg6399Z62s4xqQoaH9kuau7MV5ys17xy8VnW1vLWwxuUhSGEkFZumjR0sUGSUhObzLI2Eh9i2rjWpVNBiGCMpF1ZVJnsCqMlfedRhcIISR88MSTLI/rkFXufkiRFqbHWo0pFsGnwY3O0UwiBqjQsli3/4nNf4J3jW9w+fshPXrnGh8sDjtYNV6cjJpXiftuzGnzkSkkmVRoLZ0hqGClxpN+OlOTqdMK/9/LnBvMjQowIqYbESbKPfEinYhMjQhh87JO9FBxCSGIMKGkIwSOkQIuKQtVMi0uM9M5gf5zL/vTjJVsWP8q40HNj/hXurd5KVSl+qLZiqnQJiNOkrwBk8o+jHNINiohn+Md4PA8Wx7x18BAlk8UggG7weZ8YF8z7wPmR4dh61quea+MtLm7vEILhvaM7HK4W7O1d4sVzF3i9eYsPjx7w2YvPsj865qA5oS5TRepdwBQK23uUVqnBqFUS0M6jVPJkdZGaZNamKtZHGE1Lus4lQRUwqgta5/AiDt+XQBqJEJGi0PiYrAIhBToMey+MpDQKGyN975iMSjrneGK2xzyuuTV/yM88+TILv6Z1kZ+6+mOU2vCVh99mr5xyeWxAOIyOLILDD5E8LQWeiBaCkVIEIvvNiq/du81PXn6SGB0AcVP5b/x7kV7Lqf+Y7l5Sk3XIa0eIw38SRe8ber9iaQ8QpOdKSkWpRigKZuUVJsUes+IKld76fl6WmT+AXCH/kOGC5cb8yzxYvwMx4mIayog+WRMhepRMIheGSTsZJUJKXHDJoog+ZY+JCBQIsNbxa+9+k8Oux3pP6wIBUr5WSHqv2ComCGpaF5nomtcevsVI1jw5vUj0MZ0OPZpRGsOyX/P6vbd58dw1SlXwjXvvUGpF8AEZJY2z+M6nSltLnB9ywTFCiEmE1bBjWYCIgt56ylLjvKeQiqZ31KWm6x1KKVwMSAFhM70RUva5GvzgTaLDaJkah1KgI8hSs1h2/PzzP8Xfu/k6r55/nmk54rUH3+HVi8+z6NbcbQ54evsyWmh619PSceyWVLJECIePPTF6jIJaK5SESkqMkoyk4BdefIXtukzpjqGhKoVCIIYIosIFd/pmqITG45BoQrDJlxEBhcFHP1hNgVR1gxRqePEOWeyQqu+P/emCaZm86WlxCSOrx3MB//CSLYsfJXyw3Fy8zt3lN4mE9IKWQ8pBGkKww5MXEWJzY5SUKXnDmzpZE4iEOPiUQgGCv3/jTT44PqaL6bSPgMZ6ybn6PDfmB1yfXubW4hF79S6l0rTecndxyP7yhM9deBYvAsu+4fcevs+5covntq/yxsP3WduWz1/6FF+/9x264BgXhlVvU0NORKJP4tF0ATksuEcICBE/CHDv0l7lvnNoleyMUW1YLjrq2tB7n/Q3gC4lvgsILam1YrXuUaVMnnepCS5QKIU2gvnasjstOW4slydbNDEy02O2ywnvzm/z6sXneffgNhemO2xXUw6aE5q+YzYaMSlrjDL4EAghcn48xUiBcw0rf4wNa6zrUVJQKsH5quLPPv9ZtJKDhsbTib/NG2OIdhDWMLxxJm/ZR4uWCjf0ATwBLQw+2BRljOnx6eMMgzAxDbGk5VCKQEAJjfM9Siqk0NR6h1JNmJg9ZmXyp6XIN9V/SLIg/yjgo+Wj+evcWb4BMRCFR4oC790wlvxxZZzEFXz0w9Uh0gs62NMsrhQq+ceEIb8r+fbDO3xz/zZRaISoiLFGygItK+6vDrg42uOd41tslzvcWtxBi5KL4/PslGPurw/45qMP2at3eHJyiXvLAz48vsendp+kkJp//OBdntq6xEiXfHv/BqMiVbg2QmUUrfUUSiBipGkcdaVpbGBca5xLlbJ3aTxZSoEKYH0SXELA+5iyw6WiazyqlNRKs7YWEEyMZmkdIyNZ29SEM0biY6QSEisEwQde2nuC908e8mN7z6QdFlLw3sEdPrP3JFEJ3j+6S2d7Xr74FEIKHq6PeLA+5lO71yFaGt+gpURJxdiUbBUjwBL9irVboIXnqa0ZX7z24jAVmQwlsXleEPjoEDI19dTgVUiZ7JvU7OsRG3Fl0wQ0+OggDokaYYY3a3HqU2+0QgqdRF8qvHdDsiagRIGPqcGoMFR6i0mxx0jvsl1cYWTOndoqmX8qWZB/mAnBcXPxu9xdvUk6OsgOL043+L/ptjbEQIx+8B8lUkp82OR7AxJFiGFo+KSJOIaqKiK58fA+b548oDAzjJzReo9WaTlP6z0SReN6Kl1y3C540JxwrtzhzvI+u/U2paq4NX/Eg+aYz1/4FCNdcNQtOOkWXByd48H6CBscT00v8/q9N2hdOgpp0TlKLXE+EkgJBxcCKkSWrcMU6c0lCiijYNU76kJiI+gYaV1kXKUK1buAl4KJUSw6hx5GqnsbmI4Lluueca2RUdJZjy4lTefZHRmOGsduVeCl4TPnnuH+4oC6Klj2LbjI03uXePPgJuuu44vXXuZRe8j7J3epVcVPXHwRHztijMPPOCVIIL2Rlloz0QW10RA61vYh18oRrzzxbDpkVUSQmyo23ckoqYfKN1XKkHoAqflnh79P1tPHYtoPYutOK2Y9NAGTTGymY4axdCTBp+spDlV4iA4pzfCxxWkj0QeHlgYlSko9ZmtoIG4Vl6mzP/1JsiD/MBKi59YiVcQ+euLmxSkGX9G7YTdE8iDD4CGKYWF6qmTEcOubJuwQEWI6CTrETU4M9hdL7rYdymzROkfvA52zRCQPmyMkkqNuzU45ZWk7RnpMpTX3V4e8d3QHG+EnL36aQii+c/wh91aHfHr3WVwMvLH/PtcmFzlXzfjaw7d5cusSq37OfrtmrBXOpWxx7yOdC0zqVBkLKSiINL3HaIkNUOkUmauNZGUjo1Kybhyj0tD4QK0Eq96zVRuCT+LYAypEnJSY1L5ECclYS06cp0RgZaCIillVUhUzTroVL86u4qTja/ff4888+eN86+B95l3LF69+lg/nH3Fveciz29e4vnWBR80jDpoTOucoteHK+Dx79YQYHVrBSFfp7L/oMRK2iooQGi7qkr2tEm3kYDCktaUMNtTGIz4V3s1EIPG0yhXDnwshIXqUKLCxS/aE9ymVEQeBj354I04nbcdNjnHIqaepmjjcTfWnbwqbQSItSmy0w9fi084TAkqWFGKMUQXb5TUmxR5b5jJG/Uj60zll8cNEiJ7bi29wa/l1QnSpyhGGIDdCGgh4kBGBhtNdvKnyFVEhxDC1BsMLTOBPbzUjPkKMaZBi1UfWoqIuSpro8XHY5iYi95b3OFfvcXe1z/nRlHcOP+L61jUeru8yLraYmDFfuPxpHq73efPgLZ6eXefyeI/7q0M+OLnDS7tPs1NtcWN+n/OjHXarKTfn93lm6wL77ZrWe+pC0zjPbiU5XltaFyiNoPNpCk8qmfZVEHEIhFEYJRDW0wWo6wI/eMdOQmkkXYx4IoUUxABFKXE2UhUFNqRGZVVqTnxgXBmOe0tdKCyRJ8czJCnG9qV77/Bz11/l1vIOS7vmn7vyY9xe3eKkW/DqxRfYKka8sf8mSmgujc8xK6bMypo+rAGLkik5sXIrJDAuSgpV4KOn0BWt1iysYBLTBjyt0srP1OCDjZchNss+0hVCSsqkGJ8UahDm1CfYeNKCzfFUQ0t2mB/fNHOjiEQRBmsj2RmCmLLjMaCkAiSIYQ8IkiAigvT1xeHjBRGR0bNyhyivmHcPhuEXKFRNqaYYVbFdXGViLrBVXjy11H6UyRXyGSfGwK3l17m9+AYh+uFEjc2LTRCIKMzp7WgcBnrTOXZ8Yj/FxidUw2a1OFRR6QgjISQuRFyQtCHS9IF1cPTO4aLAB1j2DT6ClBrrIxBYW0upK+6tHnJ3+Ygnt65jfUetRyxtw1sHN1Cy4KXdZxAx4mJgZCqUkJx0KwqVzqm7tzqktR23V/dYWc9OZZj3jlKKtMzHO1yARR+YFpLWRwoJBMHKB0aD7ysjND4yLRSC9H14CYWM+CCJREZasug8o1KhhaCQksb7tCeDFFGrjESQquZZucWN+QFfvPJZvnX4LgLDKxee5st33+CV8y9hlOCdwxu8tPs0LkZunHzAE5PLTIrxEEnrOGgPMFKjpUYJiZGaaVEPXnJAK8nEFIx0gVaCWihqragMFCKilUCIjahuPGaXKmKftu9toojIzc4PP+wjGapcYhoC8v0/MSYfhgraxX74vTvNnaeopB90Ow2vECGKiIgCL/xQVQ8V9JCRTh5pnuGVAAAgAElEQVS0IUSLFiX+tGr3qacxDMBscvBCSApZU+sdClXz9OxnKNX4+/1y++MkV8g/yIQQuL36erImQn+aeghhSBsgECgEjhDd6TSXiAI3dNcjKbYFm10Ucbi9TcId0x4ffOruYIddEL2P2BiQgFIa69LCIaUka7ukjGMO2keMzRYRx9p6zte7PDE5z3tHN7i3PmKv2uPq5DI/+8Qr3Fs/5KR/xJXxBd49us3crvjM7vMctvs8bA757PmXOOr26VzLpXHF0no6ZymHU6FLDY0XjIYBkD7EdP6dEGyPNKVL03xrHyi1oNQpAtZ62Ko1R52jUIqqVPQuYCNcmlYcdZYYA1qCi7BbKk76wKxUzK2nUhIj0y6Nq5MLtH5J4zp+9sqnef3h7/Hy3rNoKXj/5ANePv8891aHaBn4zN5zNK5jbddEOqbFmKe2riYPWSimRZ2eN9JdhxCBsSkpZWq4+RAJRmKjRdh0N4CIKDGsJiU1XQVpN0YqmFPjM4rBgSJ+3BeA1CjkYx8ahjdi0sh5EBER0xs4QQz+dBL+EFO+OQifxsujT0WA8OlA12E3dgguJXvi8FFjqtoZApJSKFzY7EjxCPRpGijEQB8aoo9cHv/sD5sYf9fk0Z0zRoyR24tv8NUHf4ub89fo3Hq4vRRI9OkLIGy26iCQUiFJE10bf1EKPSRY3emLcTMkEGKEmEaPfYyEKLA+0jtwmy1pIkWjvO8xUrDoT/CxZ2amrN2CvXqXxh3z0eI2Y1OytEe0ruXi+CKfO/8Se/WY4/4RgfRm8qg5ZN6vuDa9TIiRO8uHXJmcB+Du8hFPz64M0SuFFoFSSy6PS0ZGYkNMQxUR9sYFe7Vhp0rjwUamHRfj4Zw9JQVSBjZL37QUnB8ZpBC0PjAd9lIoGZkYybTUjI0ePn6qnkstOT8q0FIwLQwH7QmfPf8k7518xKvnn+eoP+DSaI8QLfP+iM/uvcD7xze5Mt7m2vQCD5sDFt2K3armickFBHBn9YBSKlb2kAfru+w3Bxx3c5Z2jQsBHz1NWKcI2zDS3vuAJ9DFgI0RFyW9i7g49AVIFT+nIj34/yKeVp3EtNToVCT5+LpRUqWKWwDR8ckVeJteQxxsDUFazJ/EPiRrI6aR+lPXRCThJgaU0sNnYRB3uQnyDX/28dcuhEJIyZXJy/zUxX+X86Pn/mhfVD9AZMvijBBj5N7qW9yYfxUf+6ERl6JLqbJJWdKNv/dxxvTjKNPmAt9kS+Mw4JGqFXH66zA0gUJI+9u8T1WjD6la7kNgbVsQihglXXD4YdnQ2lkKaWh9TwjJC721uMOj5oRP7byIjxaQ3F7e58H6iCvjK0zMmAerA7bKKRfqHVa2pfOWiRlx3C15/+Quz+9c41uP3iWKwLRQzHvHVqFYWY+RyTKZ955ztea488zKFFNL1gmnAtz6yMgMy4pCWgNaDrf7axcpRZpRVDJ9P0ZGGg+7peGws0y0ovUOLSVjo2hcYFaco9CBedvy/M513jp6l5d2nh0GKwIfLe5zfesJxlryzvFNBIZP7V5jaZfcXjxgbMY8t32ViCMQ8cETY6DUBVvFCC0kqQhOy5KIASE8pdJUSiNF2vtRKIEebGM5TP9tJi7l6bWQ0hcRhsafP7UnNnulhRKnFsPpQilgk7JJmWU5pDPUMOk3ROJIlodUekhrFPjQnVodYkj26MHyiGyeH0WIIFIZfnptAmyXV3l++5+n0j/US/uzZfGDQBLib3Nz/ru42JOqk+QRg09TWVITRRjGmONQ9aZNbCKCi+609lAYHD2np31sxmzxp5WKjw6Bxg3VkP/EC9IGiw+BUpc0rkNJSduviAg65/AxsG/XXBxd4cTN0aLkqek1Lo8v8O7xe/gouTi6yPXJFa5NrrD2azSR67Md3j76gN4vuDA6z3eO32ermHB9eoVi1aGE5U9e/Sy35nc56g4RwNJ6tgrN2gUmhcAoQT/sWG5dZGwkUUPnIzZEJkYzk4HeQ+sC52vDUWepdGqKbZekf6cE/dDPGhtF4z1GBQqVvOPapL3GI6NYWM9Lu1d57eE3eXnvRZb9klfOv8h3Dm/yzNYljvoFENkuDG8dvo8Wmpf3nuXD+Q0W/Ypnt59ipxyz3z3iqJmjhOLi+Dy71YTOr1i741NPuFCKigIlBUZI1One5iTiQSq8EB/vm96Mv4vUUoukGOCgfMNd1DAOFIcBIRwyfuLvTqf+hqRFDDB4u0ro08RFiI5N5iOe9oHj6d2bQA27N4bg9KYJOOSg05vE0O8IHiEkRta8sPMvsFs9+cf5EvuBIlfIj5G7y29xa/k1rG9TxbsJ+ws1NO/0UKXI39+821S/Q0UshDi1K4Ahh5oWvWup057f4fbV+zQy7YepOxtSxKn3aY+vDZZlv6bSU/rg8CF9LW2w+GHZ+93VfWqdPOQQJaWqaZ2lVCXH3REjUwOS945uEBE8PXuK/fUhd1ePeH77GZZ2ze3lPV7aeZZH6wMOumNe3nuJb+2/Ta3SCRuHjWOrVBx3PlW5gFEC6wPzPnCuMqxdqqCPWsdulWJupYTjzrNbpd0dnYu4CJNCMm8940Kmqnv43ksFnYd6yD0n6yIJ9dTMGBuDURVGGjq/5qRf8dzsKbqw5K3Dm/zM5Vf5ztHbSAyf2n2Wd0/eRomSa5MrlFrx3sk7TM2MnXKHnWqLxi9ofYv3acBDizR2PjY1aqh+k98cEcIP37ekkBIt0/J8JWJq8g0b+ZQQhJiiaJtERYzxtLewGRJxoUfLgvCJLLP+xOCHjy75xXiULIZc+8cxyuR5D1X4psoV6e7LR3u6jW5zuIEaGn2pmWiRskCIyNXxqzy59fkfpYVHuUI+q9xbvclH89fowmqoKvSwt0Dh6YfmWyCKZFMIFCJaovAp9yl1qk6G4Y7ToQ8hhxePH1IWEoRP+yxQIMTpeXg+pM67CxYpNDb0w/9TZVToEh97XLDJxvBrajPGhoZSTXhq6ymWdsGj9ZxSTyikxBQFvbccd4fst5Grk2tcm17lpFughODp2VV2y20Qkp3yEiF47q0ecm16mYPumOP2hCcml7i3us+20UyKQKUksyKytIFZqWlcYGzUabMJ0qGqF0eahfUUKgnWhZFk7UI63aNUzHuPC5HzY83KelqfmniHnWdSKGKXmntGSua9Z1pqmibw9OwKbx+9y9XJZZSM1GbM0jaMjeDtR7f46Uuf5dbiQ4xQPL19jQ8X77FdztgutjEK7q9v89zsGXwI1Kbgo8W71HrM2IypzBaTooboCFg8LW5Y/KSFICqDEakuFXHwdAeRDSIdDDDcBg3XAgSGOGNI14kLqTLdeL/JJvjEEEhk2HkBCIWIbjB5P24GSjRu2BS42Z/9seWRphs3meY4zJikpiLpOhv8aCEE2+VlXtj50z+yTbs/iFwhfx95uH6H94+/hI0riGmMNp0kwTDxpIespxmEctjAJjTw8d6CdKeZfD2iwIU+VSSEofrxaVGQHCJKg6cYSZ8vxABCYYNFYmhcgxQFfeghKgKSzqdKam0btCpY2zXzfsFOucdHi48o1YSLo8uEGDhsD7izuo8WFU+Mr6JlEviVWzItphw2R9xvHnJtcp0QAx/OP+L69CoRwZ3FHV7cfRHnIsf9ilrXvLH/FmOTYlo2wFaR8sfWR1aDyAqRjlJaWkdEsF2m06FdhMYFdkpJ4yOSVP1OjeCg82wVKc626AOlghBFsiqURErBynq0SIuIRlqzN7rMWI846Zacqyd849F3+PzFz/HW4VvMih0uT87xztH7PDt7Bh97Ot9RqJKRrmjdgrGZst8ecK6eIYgUqqR1LdNiwqI/wEdHITVaSKRU1HrESJcUUg0+MWgh0skjgBQBiRisgRTV00oNFfLHC+1dsBhV4nyHVkW6RoaTYFJVu/GY3VClDkmK6E6jcVJu/OACF9phMs/+EyPVLgzDJmEYNgnudFT/dNhEaEo14fntP8V2efWxvf4eM99Vhfwjc7/wOHm4foev3vtbvH30/+BiiySF7kP0Q9MjiTMxeZ2bBkxKSgx96uHxafxZI2Ta/hXxwzKYdCK08za9WIYO+ua2MiUs3KnHl7Kmij40FKqk90sKVbDuj9EisuyPEDEQ6XGhY8tMuVDvEWPgyelTjI3hg/lbHLSP2C63efncZ3hico6D7hZRdAQsD9b3uL96wHa1Q6Uqbi1uU+masR5xe3mXiR4BcOPkQ6T0PGpvUWnPC9vnUUJQ683lmeyFaamYGpXWbGqJi5GdUlNIgRIi2RJ6WJIkBCKmFAak9MVupSmGKN1OlZbAz0pNYIjMyXQ46aVxSmKMlOGo3ef28ha71Zg7q9tcn17hqHtAoTRXpxd59/gdXtp5DiXB01FqnVIGIi1Iurm4ydXxBUa6YG0XPFo/ZKccIbHMihlbxRZjM+VcdY6xNsS4Zu1OWLkTWr9KdhYuZckH0VQyCWoqYkNKzgwebYjD2+/wd1KkqKAahi4inF5f6dgulYby4uATC3U6ETjY0wRSZlgMSYlNfHJjjaRkRVoCFTeCP1gcEs2T08/zkxf+nR9lMf6uyRXyHyMPm3e5Mf8qnV0MCQhBjOnUh3Rnp4bjkeTQANHp4sfgYo8SycvTosT7HiHlaVh/M32VfOK0T2ATdQrRE4NAK5UiVSF5dylr3ANpXDaEgJIFNtjUHQ9ggx/8wEjrGowasd88YG1bLo6vcNwdU+gxIqYtcCu7ZGlP2Ckv4GLg1uIWCM1T06dxweFCoNIVEsHKtWkwAsVhd4IQEhscN+Y3eW72LHdX97Ch4/rkMrdWd6mVZNU7Gh+ZFYq1D8yMZGXTno2ldczKNKnYeU/vh6EOlSrd1ChLW95cWguBkbB2sFVKGhvYLg2d9wiRIn9q8N7HRlGrCbv1Re6vjrg0mvHm0Xt8/sIr/N7BN3lh+wVO+kO2i23ur/bZrsYIIXi0PuL57es8ah4w79d8ZvdFDrtHPGr2uT59iqkpOe4OWfRzSj3mifFlfGxO12XGGBnpUbIs8BAtUjJYV2lQpVRmSJWE01NEtNTEmA6LVULjgk3WVjIUkr0wLLAPMQ1zhOGOyg8TnalvsdmBoYdR+5RXlsMQ0cfrQTf9io/9YyHUqQUXCZyvnuG5nT+FkfmoKfIui8fHo/V7fLR4jcae4IfY2mZ/RBhObvbeopQZmiXpFAghFCE4lDQM4axhTeIQaRrsCCE+PoA0fcy0LCj925IQPH6IQAU+4TPGNFDQuxYpCqTUuBjSaRzRI4XhsH1Irbdw3jPv5+zUl4gx0nvLyq3TUpoIa7dkpGf03nKw3mdvdIna1ITguXHyHkJqLo2u8Kh5xGF3zJPTp1naJY+ahzy99QxH7TEH3SEvzF5i7Rq0KEEIvnXwJs/OnuajxQ0iMCsU/bCx7bC1TE2a0psaTeMsjYetQtL5iBGCkz7ZFSHGlL6IMNGwdDAeqmotBK2PlCpiPdgIMwMnFi7Viv027b+YFFscdHNe3v0x3jz6Ni9uv8SHi3e5OnkSLRRdWHPYHnF1fBUbWm4sbvG5vZe5ufgAgeTZ2bN8OH8bI0uujK/ShiX76/vsVnvslLuE2HHYPkQIqPWEc+U5EJ4QUzUMESMLSmnSn5OSNwJBqdIejHQX49CyGDxbm2yrYTJu4+9qWeCjS8uGQjcc2+Uw0gzZ5/K0CHAhfbxAsrQ2R0ZFPFqWpzZH+EQTeTN4FKJnZLZ5cefn2CouPaZX4JkkC/L3m/3mA27Mv0rjDgcN3Nxyq3Q+mkyTVYq0DAiGc9OUgWEDlw0fj69KMQi2TMIsohiql03ueDPSKlFS40KPGhp2aYpP4KJNX4EscL7DRY8WBXEQaOt7Gr+k1FOs6+mCo1ZTEILOdxw0jxjpKVqV9L5DyZJ1vyYKQaFGiOjxRO6v7tL4nsujq/gY+Wh+g0kxY6+6yIfzDxFCcH3yFB/OP0AKwbXpU7xz/A6zYpudcsat5U2e3nqG1vUUasSD9Yfstx17dRqhrqREicBRF1I+2UV2yhR/A1i6yJYRNA60TOPTEw0nfWBq1OnE38JG9krBfpuidKXSnHQ+bVYjUkhJpdPPbmT2WPY9pQosreXp2XXure6ipKYUKeFSqTGVVmla79znuDH/DqWacHl8hQ9Ovs3F0VUqVTHv9yl0xdhMKaTh0fojtsodKl1TyorGHdH5hlKVVHrMSI+IWHzoCASM1JSyTtbIkFMvVIkUELAokYaD4rC0fjM5p9Ww41ililcPMTQtDS50Hy8ZEkl40+P64drzw3XTnvY10uM3az3TfmYfHVoUCATXt77Atekr3/8X39knC/L3i4PmJh/M/xFre3hqJ6TSJODxKNLtvRBquLUDYvLeogifsC5SE8XI1IRJVcggzMPoaQibsH3KfgJDlEkPJ0ukSJMNDqMKNs/vMDZCCJu1FpLONzR2xajYhpg+1tqvWPcrxsU2IfrUpY8SG3oKVdH5bvjsmv12n6U94fLoGUpVD4kMh5YlITgetQ8YmwmFrHmwvses3GWkxjSupdQjrHfcWt3h4ugCH81vIoXgiclVbi4+5Hw1YmVb2hBQCNY+MDWCzgVqrXnUutNmX60ix31EieQZV0oxtw4lBCMN8z5ZEWOTBLlUYITExkAfYK807HeWWZGSGSEK9sqC/a7nc3uf41sHv8dzsxe4Of+AS5MrFLJCYLkxv8Wnd17kreM3eX72KQ66OyhRMCu2edTc4fL4Kst+iZIiNTe7A/bKPRBponJtV+yWuyD8aSNuZEa07gQjC5QsqFQJ0dOFJVJAKWsKVRJiS4iBQv1/7L15lGXXXd/72Xuf4Y41V3X1PKpb1mAZyRaeJFuOGQzGCQl5WXmBAAEewRBMBhLCCyGE5OUBgYRn3koIySIG8giBYOPYDgTDAkue5UmjJXWr1UN1zcOdz7CH98fe90odD3HjodXy+a7lZfW9Vafuqbr3d37n9/sOtSB/L0hU4v/SjlA4SyJRQwdK29jg3t9OCYITqKdSIkNHLcOoJLAywiJQElHafCIyUSH0QAYByFLzNKemX0Mkk6/cB+/GQlWQv9zYzS7x1N6fkOnehPc7JsDLsEizwfDFuBKlIs+7Dx2wV8sZPwbAIp3yt41hHqhkbcKgMLYMs+egyrI2jD/8QkUKRWEzotBtC6Ew1mBMSRSlOAuFGSBUikSRmx44QaJaOMBYR+ly9vJtGtEMiapjnaN0JbvZBjXVJhJ1cpOFYhGBUwx0lyuDS0ynC7TjWdaHK4xMzoHmUfplj+1sg/3No+Q6ZzNb41DzGN28w16xw4mp0zzTO8difR8zySKb2TaJSrjcu4QSlnoEg1Izk8Rs5ppYOgoDqZIk0tIpoRXUdIm0DDVMp5JBCamCfumYSQXaeP/jobZMxYJu6agp33F3Sy8UQXglnBL+olU6mE0PsJevs9w8hBISJRRrww0Otfbx5N4T3DZ3B4/vfoqDzePEUjDQPWLlZ/XtpM3qcIUDjWW001wZXOam6VsobJ/N4RWWG0epRTF7xRaFzlhuHkYIw8j00SZntraETzUs0aakETdRQgSesPAXW7ziL5YJjjIUYt/hRtI/L4km6s1x8MCYAjf+GoHEMFbO+XmzC8KRCe/YjeXUflGM8LP7ZjzP6Zn7aCWL1/GTeEOgKshfLuxml3i68wBD3Qmzs2cZEEKoUICDNwBjhzU76YJ8wR3zOH0nbKzxBVd4EYZ2/jbUe+Um/vuERFuDVH4zLoLqbsw5HZuJFy5HBV7zeM6njU+TwEkKlyGJ/O0rFuOsl/PiF43dYpvSFLTTJT/ewDHQffbyTabiRYSQbA7XECJisXYQJxyl8bezERGZLdDOUFcNSptTWktdNRjoAYUpqak6T+49TituM1ub4/LgAkdax1kfXqEZN1msH+J85xyRzOkUpReK4MUdQghG2tGOvTdFPYrYzQ3NyCvVlPBdcC1k1w20pjCCuVSwm1tasb9wJjKiU2hmU8lubmlGvhMcastiLWYjK7ll7lae6Z5jOp0FZ9jJtzg1/SLOdR/nSPsUO6PLNONZGlGLTrmFFIqZeBYpLc90n+bM7K1sZysMy4zjU6e5MjiLkin7G4fYzi4DjrnaMlLATnaFZjxNO5kl130y06UZeQZGZnpom9OIp4iQ5LZPLGt+2cuIWCaMDeojkXq5fYjk8uOIsTAkDWMtn1g9fjySNU9rExFlMJy36JDP9+xYIhapH50Fit7JqVez3HzR9foY3mioCvKXGnvZZc53P0i/2Aqy/3EWnQyFeczxlRPnrDHFaNxpELpn48oJXzMSCYbSd9RW+w/MWKkXRhk+Ny0NSz3hmRMi8sYx4TZV24JYpWGLHoWxh6fPaVd4elIo4hO/Amt8d+R8990rd7BOU1MzFCanMAWNZAYlYrzqbUhhC1LZpJNv0y13mKsdQImYK4NnqEVtZtMlVvoXUFKxVD/Epf55Ihmz3DjEhd5TTCdzNKNpSlvSTubYy/dYH61yqHmEi/2zHGweZWO4Si3yCdl7hWG2FtEpDC3lU0FyYzDOsyYkkBloxIrSGBpRxF6haceem62toLSWZiQYlH5mM5tGbI00jVjQjCNAMdAFNSnpacOhxgE2sw2WGgfASQa6Sz2aoldsImXCUm2RvWKbWKZYVwCCVjyDFJrL/Wc4M/NiLvY/TSueZaG2jwu9x1luHiURCdvZJeZq+wEobJ9G1KKwBfWohnUl1jlSWQujDAJ9L0VTIJwjUX4MIZDEMqYwQxJVx7kSUEQqjBWIA384obS574iDnNkyXiKPC3bI1BvPla1BqSSMJRSlCawN4djXuIWTM69Cifg6fRJvSFQF+UuFTn6F890P0ivWJy5rV9sMGpwQYUzhf+86FNKxF8U4LscaTaSSYPauMJPFig3zOR1myuWkY1bCL/tUmEFHIg3jChk8L+SEcuQAY7wowIVoJm1zrIMkqpGXQwyGVDXRtggz3zrWaUa6RyTrCBTb2RUQkna8SG5GZHpEO5knkgmZyZBCkYgECxQmQ0qFImakh0ipiESN3IyACCUjeoX3cdDOcGXwDAebx9jNt8jMiMOtE6wNVzjUOs6wHHK5f5GDrWNc6p9lJonIje/yPd3NUY/GMVSCgXZMJ165CNApDVOxxKEQWLqlYbGWsD3KaSdxYJ9I+towFSs6hVf3TceKjaxkXz1lryg50DyGQDDSI9pJk3Ods5yePsMz/XMcbp1gc3SZmqrTiqbJbR/rYCptsdK/wMnpWznfeYT9reMkMqFThMWoiBHSMig6TCfzSOHYKzaZSReJpKSTr9OO56hFdbrFBqlq0Yha9MpNUtmiFtXJdIc0avnxhS2IRBqyEw1SJpR2SCLrE4n0RDrtfMitcCCkDPS2MGJzQWofjOHA3+GpoO4cJ1834wVunv16mvHsV/oj+EJAVZC/WHSLVZ7ufJBuvoLDK6cEYzctG8YOvjD7NAQ7+QB4DoVAmxKpPIdzzDMWiBCBk4TImwgbZsXPurd583DvrBWWesRhlCEDvWlcmD2bwl8SVPDKBW1Cxxz+bM76mWQkU3I9xNiCRE1RuozCDKlF01in6Ze7pGoKKRRbo8vEqkE7nqdbbDIyQ2bTgxQmZyu7wly6n1jWuDI4TyuepRXPsdo/Rz2eZiqZ53L/HDPpIomqsz68yP7GMT9XF4p61GZtuAL4FWWn2OBI+ya2RussN45wqfcUmc1oRjEDrZlNE4alRUnng0mVwiEog4ewd+AUDLUlVoK6UvRKjQIflCokQ22YSsLcWUki4f1Delqzv9FgdThkNq1T6IjMjjjWPs353uOcmbmDs51PcbB5gl6xSy2qe68P06WTdznYOsxK/zyHWidYHZ5nX+NIoBsauvk2C41DaDtka7TK0fbNbOcXkcTM1/azPjzHdLJII27TyVdpxbNEMqGwAyIRE8s4jMU0qWpSmL4v7kJibEGsGmibh2gkO3n/2jDeGntKjLnJYzXduFsem8cbWxLL1IfgivGdlCKWCSen72WpcdNX+BP4gkJVkP+s6BbrPN25n052BSn9bZmPSdLhK3xYqLM+7mZsvEKQpLoQLCpFFH5jEkM58TJW4cPA/8xHvkqy6jmjFh28jgtE6JgjkaDNs8u+SKWT4FLjSgTKd9NBCFDqjDiq+dc7MQr3F4Rc9yltTk1NkZkhpRvRiGYxtmSoO9SjOayzdIpNWvEsUsRsjVZoxFPUozYbw0skqsVUPM9OvkqimrTjWQZlj1pUR4nUd9AiYVD0WB9d4mDrFCv9p6lFDaaSWfplh+XGMTrZDj3dJVEpu/k6S7U5hqZHJCSbWU5d+Vl8M46wCHbzgrk0prCWRCh2ioKp0C1LIdkrSqZiiXaCSAhyY2nGMTt5znQSTcyF6kow0IaaUjSiBOMkUtRpRnOsDs+x3DjObn6FxfrBoFIr6ZdD2nGdjdE6R9s3cXlwjsXafjLToxG3MAZqUcTK8BzH27ezMTpHI5qhFU+zk11irnYgyJn9WySWMeDDautRk26xTSuaQUpHpnu0k3ky0yORDX9BdiVKpFjKEH8XUqWfM5bwY4o4XJiTQINL0SZDygTrCpSs+Zw8EaNNjlRjpaE/9nLjVk5Ov8rL9Ct8MagK8rUi0z0e3/19uvk6kYwnoaDjQEc/GvC3hxNLnzAXniQkCIFwMgSNuvC9ceim5WTZ53BEY3OW0J34Qu1vPbXJJ2GSnujvC7y2WSDtG6RIQgFXk58zzl7zM2kRZNreUKgwIxJRxwYrTini0DUl5HpAYYfU1DSZGWBcSTOao7QZxmlSNTUZccSqibVlmDvWKG3uSXgipld0EFKiRMrK4AlmkiUimbA+usT+xgm6xTb1qE0rnmNQdgHJbrZBYTP2N46wm6+x3DjFTrbJyHSwriAzmpkkobAOJQR7Rc58LUWgyHRBr9S0Ym/InxmfDdiKvbFOES5UrShiNy9pRhGR8nFVudFMxzE7RcFSvcGgLEQiu9oAACAASURBVImkpBG12M4GLNQWGOohM+k84ChsQU2mXBk+w5H2KVYH5znYPMlmdpF61PajAjcikjUkjr18k4PNU1wefJp99WNY/ELNR1zVyUyPmmwhpKCbbbDYOEInX6URz/iO1uUkoo6QDm1y3x3bAbFMJsIgP5bwC7jCegZMGUYZCPPsgjhw3ISTPn4JGWhwEd7fQmEZvzcts8khTs++jlqVHP2lQlWQ/ywo7Yi9bIVeucHO6AIWTW4GjP0kBL7YiqB6c2FpJ6QCK0BYrHXBRHxcrMVkuz2e102WfUEq7YRFOh/bEyk/c45ChDthpDEpxETPbssD71cbr77yj6chTdqLBvwoY5yR5vnHsaqHrD1v/uLFAAm56VLakpqaJrcDpFCkqo02GUJEXu4cjIdKWzAyA2qyTa/cYaB3WawfZWt0BSkEs+l++uUe7WQegSI3GZGocan/aWpRi0bcZie7wpHWLZSmwOLo5Nv0yz0ONI8z0LsoUbCdDUhVRG5KGpGXDe/lJdNpGh6L2MkKmkEA0o5jNrOM6SRCSYm1jm5ZMl9L2M1K6rEikRGFMYx0wUxSo1t6k/WpOGErH3Fq+sVc6H2apfohrCvoFNscaB7jfPfTnJq5nUv9J1isHSIzPYzTzKX72MmvMBUvUtg+CEkrmmGod5Eioqbq5GZATdZ9Ac63WGocZXN0ntnU/wwpPLdcSkGm+7TiWQblFo14DhMuxOO9QSRSSuuLv98rJD7FI/DMx6MsEeh6diyDtgalookc2loDEFgZiljVODF9D4v1E9f1c/gCRFWQv1QwrqSbr7NXXGJY7tEr1ihthjfcVkE1F/jHgReM9Ll4hMfGy75yUpjdhH7kl31+q+2cDzHVLp8U8LEKz2/FQ8ENY5LxbalxmljWJu5b2hTPzpiRaFcgkH6O7TRCKHI9IImaYRQThCsmR8mEQbGDEJJGMkOh/QffWzX6Gfew3ENjiUWdzewZppNFIpmS6SHtZJFxgokkYiu7TKoawQFul+XGSQo9oh5NMdRDtvMVFuqHWR2c43DrDNZ5Kl632KFf7jId15BSYIxjtxgxncZo62jECdujIakKRkpAHgzsm1FCX+c4B7Uo0P2sJhKSWEo6RcFivcFIayI57hElnXLEoeZpLvefYr5+gEgotvMrHGvdytO9hzjWvo214Tna8SyxTNkt1tnfOMnq4AmW6sfp6Q3a8YJf7wro5FvM1/azNjzLgdYZNodPM1c7hBuLNJwIWYW7TCVL7OWrzKTL5KZPIhvB57ogEok3gpK14G8Sh5GXV9eVJgt/73CBDstiz0lOfRGXKWVQ3RlXEsv65N8Ow5H2XRxt3/3V5FH8lURVkL+ccM7SL7foFKvsZBco7Yhce77oWLzx7EzZTDjCBBcy73EBzongOeGXMWMvi/GIYyx7Hdtyjg3D9ZitETrm0mREKvEfSJEGdVY8+aCOjYe08Yb346WO96kYUYuagWPqLzA+riemX+7QiKcniiwpYrKyi1R+NrlXrLFYPx7moTGRrJHrAZFM6eSbZLbHfO0wO9kK87XD4GRYQCpWhk+wVD9Gv9hlOl1AiYTN0QoztX1cGTzF4dYZ+sUVtCsZ6RKHF3SM+dK9MmcmSTHOd4QDrdlXb9Mth8QyZlDmzKUt1kddFmpNf+tOwm4xYLHWYLcY0YxqODSZtighSGWKFSk11SCRdTZGFzjcOsPF/sMcbJ6hU2zhnGW+tp/V4VMcbL6Iy/2HWW6eIdN7xLJGoupkpkNELdwxGRpxm8KOUEISyZS9bJ35+kF2sxVm0mUK2ydRnuGibU4iU3IzJFZ179InYxReOBTJhKIcksQNPx+WngangqVqomqT99FEXWef62chKW1JHARJs+kRTs/eR6pa1/Mj9UJHVZCvB4Z6j738MoNym738YpjBmkDSfzZlQYSCbV0ZlNYi+NHa4DwWHNwCk2P8wXLPLczIMKLwklk54ZEmIT1ivMDxvgVRGGUIISldhiIK3rYOZ40vBKqBdv7DXJiBf63Od+y1qB34zBG5HdLJN5irHaE0Q2LV8N7MLkeJhPXRWdrxPLGshUI6zbDsIGREr9iitDkLtaNhPt1gY/gMsfLKxFS1aMQz7GZXSCRs5zvMpU2MtRS2JDOaRpSiBPR1iUIihCWRKX09IlURsVA4JN1yRDuOiGXCsPR+IqmMGegRqYypRymbWY+5tEZpoR7VUHKGSKRsZc+wVD/J2vBJ5muHcc7RLTbY3zjF5cHDHGrdxuboGaaSBSIZsZets9g4ypXBk+xvnKZbXKEZLyCFQNuMRDbITJdENSCwaJQcp3SMQ0jd5P3hF3L+71mYAWnU8rsCYpy0YAlL3wgpBc4KhPSjNYSc0DDH/HgfFRV79oeEWNQ5M/vnmK0dvr4fmq8OVAX5+YLCDOkUV9jNL5GVXYZ6l9z2GSdB4wROjJVyMA5/BCaxOP4zJNFhWcfYrwBf7EtbkgTKkhLjW1jfMSuZ+ogeGaF1jlJpoNspCpMTh9kwQqBNgUWTyOZEpTUod0lVM8zEvSKuMANi2WCod6hHM4EO6FNINkcXmE2XMcE6VImIke55T4vROeZrh4lEihNgrWN99BRL9ZOMdI92ssig7DDS3SAJLkiUoZOPaCYp/SKjGSdk2osmRqZkOq7TL3MSFWGc9V4WRU4axaQiQjvNUJe04sQnqQiBdjqwJLos1WYY6hGJSlAiIRKz7BVXWKgfZS9fJ5V1GvEUq8OnONK6lbXhWRbrRynMkMwMmU4W2RqdZ1/jFN1inVYyj3UluRnSimfYzdaYqx9gVO5Sj2YwrsTY0nfSuks9mqa0mZ/rBxtLYwtikU68TrxZkH9Ou5JYJD7Wa0yNDF4mXtWZI0USuMgpjhLJs2byAjg6dTeHW3dN5NAVvuyoCvLzGcYWdIpVesUGO9kzgQs8wjrtBR1hpjsJbw+CESHCQlGMzcCv7qxN6KxNmDFrM54xGyKVTNKqtSmJZYLBIFGUZoSSKQKfRFLYDOFAyRTvu2vJdZ96ND3hUA/LPS8QUU3GmW2DYpckapKbrucyE/vxCRFroydZbpwOjJGYQvfZKzaYqx3COO8yt1uskcgGg3KP2doyhR7SK9eIAkugEdXZyXs0opjClqQyol+WTKdNtDUkUrGV9ZhKasGcXbBbDFiqT9MvR9RUjHEOKSydImOpPkdhtE/GkBG4hKEZMpseoLAZw7LDYv0wa4MnWW6eZqQ7RDJBCcWo7JMEOqGQ0ne8QlHaAbFsMtI7NKK5IN6BRNXpFRu0kyWG5S6NaBbLsz+7DIs78IvWMtDVCj0iUQ0/S5YppRn5NBBbEsvaJB1am4IoSrEm3B3ZDKXiYLPpxxWztaOcmXmd79IrfCVRFeQbDc5ZesUGe8VlhuUuneIKpRlNCq91Dhf8lcemQi4IUvxjIRWYMQ96zKH2I5CxAZKfB/tO24SZsw3mMmVgYJhgsViaIUqFIoGitAUI630N0GAFQ71HK5kP6q6Igd5FCkUtmvJzZxTbo4vM1A5Mlo+ZGZKbAUnIVqupFv1yi1R6ZdpMepDCjNA2Z6g3acR+kVkYn5DiVYiWkS5pxU0cEEnF5qjDVJyiZIQA9oo+c0mLYpL9ZmlEDbayXWbTVpAFeyFEJCIGuqAZLxDLlI3ReZYbpxjoHerRtKc1gucaRzMMyk1a8SJg6Zc7TCXLdPIVZmsHKMwISYyQDmO9VWosEm8ohSURCSPTpRZNUeghadRC2xwhIrQdkcjGZBxhMYDPxXuWD+zCKExcJU4amwc9u5jz3tm1aIqbZ1/PdHrgK/BOrvBZUBXkFwqGepdOvspufoFCDxiaPb88DPPlSbBkWJZJ6TvDcUSUECJ45bqg+GLiRoewQeDiRQUm0KC8L0bNe+SGwpyoeuji6mg7ejaVeJIN6CZcaYlXmtWjad99q4RhsUs9ngq5fSWlKTAUtKJFSjtAiZSt7DyL9RNoWwCKnewyrdgXttKUlNYQy5halJLpPCRYQCwVvWJALYox1lJTdbbzXWbSFtb6My+snz1nRhNJgRISrCB3mnbcQtuS3CqmkyX6xR61qI4gQgrBIBTc3fwCs7UjaJuFHDnlY5OcJlZ1hJAUuk8tmqJfbNFK5v3oQCQY/Hy9CPPksc0lgaY2ZuOIIKn3rmuBfWMMQo6l9mGZK0LGXZDUx0HkIaTyLn+BJne4dRdHpu66ju/gClQF+YWNXA/oFCv0iw22M8+XLu3QU9NCJJMQBKpcORZPe5Mg5znKOhgZ+SLgVYOel+xVY845P8Me2zQ65WedMqW0ObGqh2VhTK4HpKoVbqsTRrpPLNPgsSsobekXg6odaHeSfrFFO1kMs84avXyNRjwLQkw6bZAkQmNFQalzCmdoRQ0/f3aWzBS0ogaFzXHWodEkIqJw3mzeOkckJJ1ywGw6Q2FzFBGl08RSkZuSZtRACkmhS5BtUtlEU2JsEQyFtmnG0xOmjO+QZ+mVG7TjRU8pdAKHnqS/xLKOEIJS+4vROJ3DhuVroUckkf/9xaJOaUeT32uiamF3kFCaUVBilkSqNjGLf1ah6XcMhcm8TD6wKbTLWWic4sz0fUSqdl3fqxWAqiB/9WE8l97LLzPSe3TyVT+jtCZE9vj5sZfQJhjjk6nHHdyzCq4CkF6oIHzUDwKEc959JgRc+qBLgtrLd+PeD6EefBC8wKERTwf70JhhuUs9np64i43KDknUAHwYZ2EGKBn7qCFXBO5zDykMpSn80lMIIhkz1COaUcPHTwHdokczroODSCb0dZ9mVKc05bO39lhGVjOlahTOn39pDU3VILMliVrCu+dZCptRV9M4NKUpSKJaEOAoRAjwzEyPmmqh7YhYNjDOp6qMyh71qD0x+SnMyN9xuIJI1CajJxPYMOPILhvokP6TphDi2R2CIvbuQEgcOnTXXhnqc0W9NL6VLHB65j7ayb6v/JuwwudCVZArPHcuvcJefhltcwblFoRiEMual9oGSa/fyodFn80npviRTIKIIArLJM/okEJS2gwV5qPCCbTLgp+G510bW4TFVRoENGBd4M/awsfJu5xYpmRlj1o05TtwmTIod/wizvaRStHPezSSGoRl5rAcUk9qaGMQWHJb0ooaZKYMyjdJJKFXjJhK25POdFgMSaMIbR1pVMNYSyRrDEtNK1kI9MGUXPeoxW0volEtvBG8P8dUNgNlTU7YLg4XaIgO7bSf+wrJ2JtaSRlCReOJks7YwtPTBN6D2GqklBOWxMRoypU+/issXv24QvpFrvJBskemvpZDrRdf1/dchc+KqiBX+NwYLw07xRW6+SrWWXLTD8ZDxXMKrqI0GYlK0U7722rj58dewFAP4ZhjLwVfdH1BH6GEt4BUIiE3o0kApw/b1Eg1ZoIkQeAoKewoMBZihIDSDLC2O/Fj0Lb0fhl431/GDF5nMEBdJliB74yFJBYSM0lRyYlUCsZ6SllIx3AIItFAyqmgplSTGf04EbywQ5RMkWG5NmammOdcXHw3PAyJK/ozxw7BDN5n2vmCa0ISeWmCihMTzORHYa5fEMn6c6iLwSzIaU9vo2B/4xZOTd8TLgYVnof4ggpyZeH0VYpGPEsjnmV/89bJY7nus1es0CvW6RXrDPTOhO/sEBMXO0/HC4tDnl0cqmBU4zs8hRRJELWUSGFRUoWOzvnJhzBEJDghvceGHpGoOpGMvfjEDEhVEyVSb7JuMpLIG7VHQqGNIVKKTOfEKsI5QV0mPoxVJSgksaoF6XeEQ5CIBO0ciVKMypIkigER5rCGmhLhXHxhVVHs5eoiDv/zF5o0iGqkEBgLXtCBP1YwefKGUw6l4pBR55eqUo6dAcXEXxsHSgXmDAB24jTon9aBWSNRaqzslDTiWU7Pvo5WvPCVeNtU+DKj6pArfF4YW9At1tjJLjLUOwzLXTLbRRAFiYgMFDrJ2BHCm9w4EDYsCMOYwpZImSBCMfEiiOBwR4wTGufExI/BBTm5tgURA0xIvyj0CBn5AqwcWOl/nnGaWlAGGuEwuiBNmkHV6F8tVmOFIEJ6177QdSsnQC3Cc7jcvqCKyevwc3QVTHqeNWYaO6TZ59DQxhl0JpyjhInHMCGKSoYxhi/M40RoGy5aZSjcTBJmPCvGIYmRUnFi6lVVhNKNg2pkUeHLA2stvXKdXrHGdnaB0g7JTR8b8v18IXmWuSFCBwwC5zTj3aAUUaDLjT08fJH1AhevPhvzq7XexrnMd6XWUAJSysnPc9YQOTAyZBgKUFqjo3jCy5UIdDlERjHWWpRzWISfx+oCmRycCGP0hHamgwS9CPPznCgY/CjUc+bnwc7U+IuGcSWxqIVxzthrpIZz2nONTRGUlppIjCOWfABBImuUZmwOlE9Mg6TwMusDrds5Mf3KKkLpxkI1sqjw5YGUkul0P9Ppfg61v2by+KDYZq9YYVBusp1dBDy/eeLFIWJfKGWCNiOQ0hckEqzwyc/a5CQqnTAZSh1sJ5HeXMd6EYx0GuFU0Jo7nDFI5Y3rpRDkWqOcG7Ot0UaHAg/SeVMngcPpHCG8eY8UktLkxIEPLJ3P4lPS+W4Yf6EheH8IGXnusAAd/i3C91prscrPt31r7b/P4ohCwME41dl7Uwchh/O+E1KOX7kIznnQSpY4PXOfpwZWeEGiKsgVvmRoJvM0k/mrHst0n05+mU5xhaHepVdsQEgt8bfiFif8rFWOAwDw6rZYSs+TFoLSQgxIKRDOYS1ErkRiiIynrjkVeRmzUqjgDWKsQTrhkzmcxViLVP443o89iNODX8g4INThw5C8o54F57DCoMYJMkJ6x74gz/ZzYz057ziqTbyGLSYsLf0YwyeNK4Tz9L3x6AaYiHEArPCjGyUjTkzfw77G6S/vH7DCdUc1sqjwFYe2OZ1ild3sIoNym8z0yPReGBE4nzFI6WetgCDCoXF6w3fYQoJ1uJBa4qXDIQJLCJAKjEFYA3GKLTOEinwXajU2xG8J6/nL1lqIZ3CqGYQzZpLiMpYqSxTG5YDvyhWBdiblxFPC2hIhx6kuz2Wb5IFtYgJ9MEfJoK4T9eCQ52mHsaph8BJ040oOt+/k2NTLA4e6wg2MamRR4fmJSKbM144xXzs2ecxaTbf07I7t7Bm0zchM15vV23zCOFDOobFI55A4z7aw3lrSCIdCYpxDYDBYImt8RhyCQhfEPk4DZZ3/Pq80QakWpfPyb+M0iawHz2rp01JUDZDeS9h4G0+EX2IKCrwBkyEWKQS3PmP9GMWPNRzaGmQwgRL4JBM/1oBxoR934+10P2dm76silL7KUHXIFZ63cM4FX+nL9MtNdvY+ANJSYpEOtPEZeJ6z4ScQkZAYIMZROosSEm0NsZNo5ZBOeBaF8Nal0gkKDEn9RGCBeFP/WKWBbTG2rYwCE8J3ug43CQOwwXbUp7mMF23B69qvJREob1aPDVRC70HiJn4jfoQTyRqnZu5loYpQeqGh6pAr3NgQQtBKFmglnmPrdAbsMTI5HTei54b09YiBKRHCJ6w4J3CmwCIRkQRtfNeL8UXRGiQOK50fe+B8aKg1uKBZjlUaimSQLEtv6q6CsERIzyv2CsNikp0YBYP9sSl8LHzuoJen58Si5kcrE7/qWhh/eFbGofadHJ2qIpS+mlEV5Ao3DqI5XO8ytaJHfWqJ5agN2uBKg04FHWfYKweMRtv0MVhkmNvG2DJHqMiPMYzFSV/wtTMoKxDSy5ZLW6CE51IrkQQJtQw2pTWc8Oke2nlToHH3W5pRiGAai0xGWBVNxhMwFoYEq1Q/vcY5y0z9EDfNvJY0WJFW+OpFVZAr3DiI94G1oCSu30XMhPmq1cSixoJssJBJUAZXOmxrH931p+lON9nNdzAo+j4lyZsgBWUhqKAu9Is/z3vOkJHybnVOeMaEMIxHEC7k+I3Xjkr5EAAXpnpRSGXxRDcbjOe9DG/M1khUk9Mzr2W2duR6/DYrPA9RFeQKNw4ax0CXEEvo7uHabYR1EGhiaI3bWkHMNgGHLC0zWjCbzHIkG0Eyi3MDBmVBtyzZa8QMjMMkLZz0Hs3gOcpRlAYVnU/P9k5tnldsnSFWtcDG8DQ2KcZBtOPkDx9RFYnU5+KJGCsskfLHPdJ+GUfaVYRShatRFeQKNwyEinxohwOcga1t3PSU75idg+1NhAum71JAfwDG4IwFrWHYR6aSlpa0cseBvgat4O6/Sa5MCKfdYnv0DA5LaYcIMXa58252Eak3TWJsmuT/7TMBNFJ4Jzog0OJqk7xC5wxz9VPcNP0aYlW/jr/JCs9XVAW5wo0F1YJ8B2QEgw4YA7GArR0oSojw6csKXLeLEAI3HHnBSTaCtAm68JSMbAi1NjJtUQcf0wScmnkNAKUdsZut0C1W6Zeb9MtNgEBjE97g38UoGXnPC4cPmZXe30KKZz0o6mqam2ZfW0UoVfi8qApyhRsLahYGa6DCoqy7hzC55/CqFBEpb63pLBSZf4f3e/578xznGmBKXKEBG/jFnx2xrLPUOMVS49TkMeNKesU6u9lFhnqPbrGGtZlnVYTgUc+y8BajTsCx9t0cfo7EvEKFz4WqIFe4sRAtQfEQpJEfW+gy2Es4MBpQoB1kff//kYK8BAUMh1C0/HFCigi1+c/zwz4TSsTMpIeYSQ9NHnPO0i832ctX2CtWKMyAQbnFQv04p2ZeQyTTL9npV3hhoyrIFW4sLNwCK38IRQ4qAvLwhGCskHOlQXT7OJkgagq71UHtm4KsxOX4Qi0EzghE6+AX/ZKEkLSTfbSTfRzmzi/6eBW+elEx0CvcUJD1eZwWuFGJs3IyugDvZwHgej0Y5lCWuNxANsIVDpzFXVmHQvtQUmth+uT1O5kKFf4nVB1yhRsOTitEVoCTvg6PDZYDbY1uzzfMRuMy45kWWeknG/0RJApkhEMhFs9cxzOpUOFqVB1yhRsPUQtnNK7n2RMYCxaEFDjrsFsd/3XWQpb7zjjzow3XzwMVDhD1igdc4XmFqiBXuOEgp496H4rODk5b/9/au6a5bokwwUHNOtxw4Iv2aOTpcNbCqPRMi7Jx/U6iQoXPgqogV7jxsPxinAaMw5xb9wwLwA0K7IoPZnXBYV6YMMbIMpwOtpjP7KEv7EF96fq8/goVPgeqGXKFGw5i4RSutH5EMRhh1kagStzWFrLZ9mMIK7Bdg4gFaIsbaZAWJ5Qfd3QL5MFbrvepVKhwFaoOucINByEE6BhQEMW4fold2UAY50cYgNNg1nbAgCvAZhoKDURgJagIefKl1/U8KlT4n1EV5Ao3Jlr7cFog4gSs9zx2Dux4eZdpyEtsKbG575BdUeB0CB2tt5DJ51bpVahwPVAV5Ao3JFz7kKe0KYXT1nfNUuKKAgC7M0QIgdnaww1KXK7BWOyw8DS55rUp9CpU+EqgKsgVbkjIoy/BDbXXgpS+CCMiz6IAzPYACJ3yaIQtBLqTQekLstx37Pq88AoVPg+qglzhhkR0/HZMbilX9hAyzI0toARmYLCdkX9s4Iu1GWnMzgjhLBiLvOnu6/XSK1T4nKgKcoUbEkIIiJu43YG3Rx7T3KRAb4xAKAB0P9DeDJi9HFcajBZEp15y3V57hQqfC1VBrnDjorGIcI7iSgZIrLHovsHuZbjCF2LTL7AGXF5iC8h3NUVfVAq9Cs9LVAW5wg0Lue8EKIXeHZJvlORrPbKntnFCIazF2giMQw81oiyxTlDsaMRMZRJf4fmJqiBXuGERv/IbsUSIOKbc7FFc3gV8Jh5A2fMSar0z9I9rg84L1Klbr88LrlDhf4GqIFe4YREtH8ZQQ0gBSjHOsrPB1yLf8EkhZlDgENi8QCCo3f3a6/SKK1T4/KgKcoUbGrY+i9MarENIb8VpC43ONcWup77lI4eVCU7GkNZIT56+zq+6QoXPjqogV7ihoU7cTmlibFF4v2MLDkm2V2BGOdYJyt0B2VYfh0DM7bveL7lChc+JqiBXuKFRf903kW30QHqaGyrC5jlFJ8NpizbePyvfG+CMJTrxouv4aitU+Pyo3N4q3HAoTEmn6NMvhvQalmYUUW4OmZpWlAgGT+8Q1xXgGPVHOAfDzYyi1mB4x4vY3b1IO2kylTSpR2lFgavwvIFwwUv2C8Q1fXGFCtcKbQ0r/Q0udte43N9gpb/B2mCb9eE2W6M9trMOg3J01ff87Duf4eTFAQLoNxWtrsbNptScYxS8ke1OzlYa8YM/dHWHnMiYufoUC7UZ9jXmWG4ucKC1yMHWEkfayxyZWqYeVanRFb5ofEFX/aogV7hu6BUDHt1+mse2n+bxnfOc3bvE050VtDWTr0lkzL7mHPsacyzW55ivTzOTtplJ20wlTZpxndlf+y3q7/l99Mjg0hpRPkTOTyGKAm0cIkkoejn54SOM3vpPGZYZnaJPNx+wl/fYyTpsjvZYH2yzNty+quALBAdbi5yaOcyZuWPcMnec2xZOsVyZE1W4NlQFucLzCztZhw+vPsJH1x/jY+uPc27vMi68pZab85yZPcrJmcOcmDrIkallDrf3sVCfYW/Y4/zWKhd311jZ22Sts816b4edQZfdYY/6+iY//SePoa0jHhkasWCURGS5pYGjiARZ7vj9M/t438vPMFNvMdecYrE1y/L0HAenlzgyt49j8/vZ156jr0dc7q9zqbfO050Vnt67zFN7lzjfWcGEZOt9jTnuXLqZly3fysv3387Rqf3X81db4fmPqiBXuP54avcif3Txo/zJ5Qd5eOssAM24zksWT/M1Szfz4oWbuHX+BDO1Nr1swCcuPcknLj3JQytneWz1PE+sX2R32L3qmEoqFlszzDenmW20mao3ectv3c9cnlMbFsSxILeCYmRxQC2Froj4+e96HTuuZG/UZ2fQZbO/R1bmVx27HqfctHSYFy0f4/aDJ3nJodO89OjN7JuaJ9M5T+5e5OGts3xy8wkeXHuMjZEXoxxpL3PvoTv5c0fu5q6lm1HjXY6W0QAAFiBJREFUJWOFCh5VQa5wfbA12uP3zv0p7zz3p5zdu4RAcPvCKe49dCevOnAHt8yfIJKKvWGPP37iQf74iY/xwLlP8fDKOWzoQBdbs9x64Dg37zvKqaVDnFw4xJG5fRyaWWKhNYOUVxOEzv3YT9B59++RigJVS9nZyEhTQZ47kkZM/aZT3Pp777jqe5xzdEZ9VvY2ubS7ztNbK5zdvMyT65d4bPU857evTL722Px+Xn3yDu47cxdfd/PdHJ7bh3OOC91VPrD6EO+7/HE+vPoIhS2Zr03zzSdezV869ec4NXv4y/8Lr3AjoCrIFb6yeGjzKX7tsXfxhxc+jHaGlyye4Y0n7uH1R+5msTELwJW9TX7743/M2z/5Jzxw7iGMNTSSGq88cTuvPPFi7j52C3cduZnl6Wub0Y7OnuPBr3sTaSPCqYThZo/2jGLQt5S55dRP/RjHfuC7r+mY3dGAT15+ko9eeIwPPv0ID5z7FOvdHQBuO3CSv3DHvfzlO1/H7QdPIYRgUI54YOWTvOf8A/zJ5Y+hreHOpZv5jlu+mdcfuRspKpbpVzGqglzhK4OHNp/iFz/xm3xo9WGmkibfeuo+vu306zkxfRAAbTTvfOh+fvn+d/CHn/4IzjluO3CSb7n91bzh1lfw8hO3EasvnoH5obtfx3B1ExFFkI2ozzUYbg8Qs/O85pH7keqLGyM453j0ytP8weMf4l0Pv5/3PfVJrLO8+OApvvdVb+Kvv/ybmK63AD8vf+e59/GfP/0HXOqvc2L6ID/4kv+Nbzj6iopm99WJqiBX+PJiJ+vwcw/+Ou8896fM1ab4ntv+An/59OtpxnUACl3y79//e/zs//gNLuyscXh2H9/1im/mr73sGzizfPTP/HOHRcbZjUuc21rh0s46a90dtgZ7LH7gUV71zo+jMkMSCfYiSd06Lu6b5UM/8k3MN6dZas9yYGaB4/MHOL3vCAutmT/z69js7fLbH/8jfvWD7+bBC4/TrjX4gXv/Ij/6dd8+Oa6xhj+8+GH+zad+h7N7l/iapTP845d/H6dn/+znX+GGRFWQK3z5cP/KJ/jxB36JbjHgu299E993+7dOCjHAf3vofn7kt/81T2+t8IoTt/P3v+7b+ZYXv/qal13OOR65co4/fuJjfOj8I3z84hM8tXkJISGtx8RpRJpGtJoN0iTm7771CQ7t5ZRCoDuOclbxK99xjPP7UwbDjCwrKHNNnml0YVhqz3Ln4TO8/Pht3HvT1/DKE7eTxsk1/z4++sxj/MIf/Sa/9bH30k4b/ONv/hu85b6/QhQ6f2MN7zj3J/yrj/0neuWQv33nX+M7b3lj1S1/9aAqyBW+PPj1x97Nz3z0bdw0e5ifvect3DR7ZPLcIB/x5t/8OX7tw+/hlv3H+fm/9MN8wy0vv6bC45zjwQuP8xsf+X3e/sk/5dLuOnEacWj/AosLM9jEMLTZVd8TS0mqJPuuDPn2f/RpTEOQZI73v2mZD/75AxTGkRlz1fckIqbmUnqdEU9fXmXUy2mmdb7l9lfz17/2DXz9LV97zReQx1bP86O/+1be88gHeNnRW/jP3/PTnFg8OHl+N+vyTz74y7z34kd444l7+OlX/gCJiq/pZ1S4IVEV5ApfevzqI+/kX37s13n9kbv5v+/54atUbBvdHb7xl36ET10+yz96w3fzf77hu0iiL7zYOOd4zyMf4Kfe/R/46IXHqKcpL73lDLINm4Wnl00lKXN1wUwqmEoVU4lirhbTSiISpYiEIPmNp1HvWsHcu4z+wdNoaymsZaQNO6OSTqHp5oa9zNDJJVujEQ6Yipu0dYtPPn6Wzb09js3v5x98/Xfwva9606TT/ULP47c//kd8/3/6GaQUvOcHf4GvPX7bVc//ysNv5xc/8Zu8/sjX8guv+dsVTe6Fj6ogV/jS4oGVT/L97/3nfOOxV/Az97yF6DlFpJ8NefXPfz9Prl/kv/4f/4I33PbKazr2eneb7/n1/4t3P/J+Tiwc5L6Xfg0PD56kX4440p5hqanZ31IsNxrM1SJm0pTptMZifZpG1CRVKZFMUEikG7/7BVY4rHCUtqQwOSM9ZDfvsZP12csLdnPN+mDA6qBkc5hwbq+DAF4yezNPPXGZD517lBcfPMWvfddPcsehm67pnM5uXOIbf+lvs9nb5YN//99zy/7jVz3/tkffxc8++DZ+4I5v44de8leu6dgVbjhUBbnClw6FKXnjO95CqhJ+51t+llRdPWd982/+LL98/zt49w/+PN946yuu6diXdta59xf+JmvdHf7xG7+bR/VZPrH5BHcsHuVgu8tCPeZQu83+ZsxSfY752jxTySz1rEAMu7hsAJ0Obq8DoxynLVgLUoCSiDRGTLVhdhZRb0JjiqLepGu67GY7bIw2WB3kXO5nbI76bA3m+NDqBRbrs3zbodfz07/3H+mM+rzrzT/PfWfuuuZze9nPfDf72nN87B/+x8/otP/hA7/Eu5++n3f8+V+YsFIqvCBRFeQKXzq86+n7+Qf3/z/829f/OPcc/Jqrnru0s87xn/iL/MC938pb/8rfu6bjOud47b96M5+49ATv/eG38u+e+q88uP4433v76+iUD3KkfZTjUwWztQUOtw7SktOIjbO4zg724gZubRu9U5Bd3KbsZJhhiS0t1oIQICOJqkdErZja4QXihQS5OI08fhAxPQXLp8mU5nL/CjvZCiv9Oo/vnmM2uZn/8sTjKCH5N6/9cb713/wD1rrbfPonf4vF9uw1neN//fgf822/8uP8f3/jn/JXX/b1Vz23k3X4ut95M99y8l7+ySu+/5qOW+GGwhdUkCumeoUvCO9f+STztWledeCOz3juXQ8/gLGGt9x37bfdH3nmUd731Cf4F3/+zSTNiA+uPszfueuvkdvHONa+mVvnIhbqR7l59kW01QHEkx/A9ST6vR/H7tTY+MPLrP+P85jj93Gxc5z3v2OHP337Hve/Y4/3vX2PB96xw6OfTDAv+mZ2PtVj9XcfR4+W0X/8MeyWgLMfopY3OTl9ggOtl3BkKufuffewW3yaf/KK72RtuM2frn2M//K9/5ydQZe3feg913yO3/qS13JwZpHf+9T7PuO5udo09x66k/evfOqaj1vhhYeqIFf4grA23ObI1PJnVZtd3F0nkoqTi4eu+bgXd9YBuOfUHZzveKnynUsnycyQkzNnsOTM1U74n9vX4Cx2NwZt0AfvoVjZYubbv4/Gt/0NnvzdD1HkcPqHvoO7f+Wfcfs//WGMkaw9dJnh/BmWfvLnsCPNcLcJ7SXsuVWI2rCzhhCChZqXOR9pe6Og+bpisT7L+c4Ktx44wWxjivNbVz77iXweSCm5ed9RLuysfdbnj00dYHWwdc3HrfDCQ2VQX+ELQj2qsdPf+KzPzTen0daw2dtlaWrumo57ep+nzP3BYx/mTS+9B4D3XvwEU8ksD209yF1LLdaHjzCdnCZp1yCpI2e7uJkpokf/M1N3n6Hztl8iuv+PeOn33sPaR89y5W2/wYoFIWFuKeHAq28l/eR/58qvfpj6sQVajUsw2EG9/HawO7DvINblXBk8gXOOJ3afBgRrg5LN0S4vmjvOR555lN1hl1NL137RAbjS2eLk4mefEfeKAY24hnOu4iV/laMqyBW+INyxeBPvu/xxVvobHGwtXfXc173obgDe9qH38KNf/+3XdNwXHzzFN932Sn7iv/07bjtwgr9w8rX8ysNv53+/+bU48TAfWZ/nzGyMsUP2Nw8xf/JOVGeL6N7bcTtdppfXaJ+5nXJrRHPtInMvF9i7lnDGIaQIM+RN4uaIuW+7GTlTRy6niOW7EDMN3NzNdMwaV3ZW2c23udBLeKb7IO3oNn7i/f+eI+1lXjZ/K2/8f/8e+6cX+J5Xvumaf3cfeeZRHl97hr95z7d+xnPWWT64+hC3L5yqinGFaqlX4QvDlf4mb3j73+JNJ+7lp1/15s94/g1v/REeOPcQD/7Yr16zLHq73+H1v/i3eGjlLD98319GLDj+4OIHOTa1j1OzjoVGyXJjhuWmYl+jxXxtnpl0jpZsEA+HiHwAxQg3HOEGAygKMIFlkcSIeh2aDURah7SJrrcYiIJuscdOts3GqMPaQLMy6LEz0qz2p/jExgVOzx7hvpm7+al3/geMtfz+D/1rXn7itv/1CT0HwyLjlT/3fax2tnjqp36HqXrzquff/fQD/P37f5GfueeHeeOJe67p2BVuKFQsiwpfWvzLB3+dX330nfzCa/4O33DsamrbxZ017voX30UzqfHet7yVU0vXZjvZz4b86O++lX97/9uZb07zLS9/FZfdKleGW7TjGsdnUhYbln2NhPl6nZlUMZUkTCd1ZmttaqpGrBKUiFBC4d//DussxmlKW5LrjL2iRycf0i1KOkXJzihnfZizMXCsDSVX+h2acZ072qf5wCce4bHVZ3jFidt523f+BDctHflfnMXVGOQj/uIv/xh/+OmP8O43//xncLMvdFf5q+/5cQ619vGb3/TPK3HICxtVQa7wpUVhSr77D36KR7fP8a9e+3e57/BLr3r+Yxc+zTe89S04HL/2nT/JN9/+qmv+GR995jH+2X//Vf7bww/gnOPuF72ImaUmq8UWxhkiKVms12glhulU0UokzVgxnUY0I0WiJFIIBAKHwzpHaS3D0tLJNUNt6BWGXmHpFYKtUUmmNQDL6Ty6a/noY08wynPuOPT/t3f3sVWdBRzHv/fc19729va9vVBKKS+1tLyV8eIcA0YYanAZcZszLFMXt5gYE2fiombGaXTx7Z+5aIyime5Fl+BmDEbGBGVvuMIGo7BSWqC0lL7evtzb+3ruPcc/GrsRcJNtbAf3+/x7zn07ufnm5JznPM9CvnHjndy2ctNF8y+/nc7Bs3zmN/fT3n+KHXd8iy9cu/WC7b2xQe7a813SuQxPfPJB6oprLvtYyVVFQZb33mRmiruf/T4dY6f5WusdfK556wUjL7qH+/j0r77J0f5utq/ewg9v/jK1pVVv8Y6X1js2yONtz/CHQ3to7z+FYbgoryimLlKNv9BD0k6RtXMXvc5nGLgNA8MFlg2WbZPN5y/64xoYFBlB8mmLgeExBoai5E2LurIati1bz2dXbWZ1ffNlX9dNZtP89NnHeXD37yjyF/Do579z0ZnxS+df477nHsLCZsfmb7O4vOFyD49cfRRkuTISZor7X/wFe87+i1U1zTyw9h7qw7NmtmfMLD/Y/Qg/2vMohsvgS+u2ce+m26kre2dngefGh9nf9SovnWrnUG8HxwfOkMik8Hjd+AJuPD4PPp+HYMCP3+fFMAxcLhe2bWNZNlkzRyqTIZPJksvmyWZymJk8XreHxZF5rJiziLXzWli3YDlNNfXv6OZaPJ1gx4t/4cd7HmMwFuXW1k08dNu9RMIVb+yTTfCzw3/kiRO7mR+u5eEb7tNafB8eCrJcObZt81T3Pn5y8Pek8hlub9zC3Uu2UVHwxvzCPdHzPLBrB4+1PQPATUuv465rP8WWxWvf1YT0lmXRPzHC6dF++idGGIqPEZ2aZCI1RTydJGflyFsWhsvA43ZT6AsQCgQpLwxTXVxGbUkVDRWzqSurvqxJgy51DA6d7eCRA3/lsbbdxNIJNixq5Xtb72HdwuUz+2XyWXae3Msvj+5kPB1ne9PH+Wrr9gsmZpL/ewqyXHkjqXEePvwkT3fvw2d42bZgI9ubPsG8N83L0Ds2yM/37+S3L+1idGqCssJibl62npuWruOGxpWEAoVv8QnOksvnOHD6GLuOvcDTR/bTNdxHwOvnlhUb+crGW1ld3zyz73g6xs6uvTze8TdGUuOsql7M11fdSXP5/A/wF8gHREGW90/P5Hl+3f40u848T87Ks6amhZsXbGBT3eoLVhDZffwAT77yd3a1v0gsncDr9rCmvpnrFy7n2oalrJnX/K5W8XivJbNpXjl7ggNn2nm++wj7uw4TTyfxGG42Nq7kttZN3NJ6AyXBEAA5K0/b4DH+3P1Pnj37MlnL5KORJXxxyTbW1LRorPGHl4Is77/R1AR/6trLU137ODc1jN/t5bpZy9kw5xqur22duaSRzZm80P0aezpeZl/nK7za10nemp5Avq6shqWz59McaaCxei4Lq2qZVzGLSHHFZY92+F/Yts1YIkZPdIDukT46h3p5feAMR/u76RzqnVkJe1FVHRsWtbK5aTWbm1bPrJ+XNNO0DR5nX99B/tF3kLF0jJA3yNaGddzeuEUrTwsoyPJBsmyLw8OdPNNzgL29bQwmowA0lc1jTU0LK6ubWFHVSGmgGJgeh3yot4ODPR0c7jvJ0f5uTg73YubfGEnhMdzMLqkkEq6gKlRKeWGYkmAR4UARhf4Cgj4/PrcXr9szc1MvZ+Ux8zlSZoZEJkU8k2Q8GWcsEWM4Ps5gLMr5yVESmdTM57hcLurLIrTMamDFnEaumfsR1tQ3zzwWnjTTHIue4tDQ67QNHufIcCemlaPQW8D1s1u5sX4t62tbL5qiVD7UFGRxBtu2OTHWw3P9r3Lg/FGOjJzEtKZDOydUTUv5fBrL6mksncv8kloihRUYLgMzn+NsdIDukXOcGT1P3/gw5yaGGYxFGYqNEU1M38h7c0zfjt/joyRYRFmwmMpQKZHiciLhCuaW1TC3vIYFlbXMr6wl6JueWyKanuTUxDm6Jno5MdbD8ehpuid6sWwbFy4ay+aytmYJH5u9jGuqF2s5JvlvFGRxpkw+y7HRUxwZOUn7aBevR0/TPzUysz3g9jEnVE1tqJrZRZVECiupDpZRWVBKeUGYEn+IYl/hzJNtuXyOZDZDykxj5vNkcyY208H0uN143R4KvH6CvsDMklK2bRM3k4ynY4ylY4ymJhhOjjGQGGUgMUJffIi++BCxbGLme5X6Qywub6ClYgHLKheyvLKRsL/o/T14crVSkOXqEcsm6Brv5fRkP2cm++mND3IuPkT/1AjJXPqSrynyFlDkDRL0BvC7ffjdXrzG9OUKw2VMj0O2LUwrj2mZpHNZUrkMU2aSKTOJdYn/vs/wEimqoLaoijmhGuqLIzSEa1lUWkdFQYluysk7pSDL1e8/Z7JDiSgjqXHG0jEmMnEmM1PEslMkzDRJM00mnyWbN8laJpY9/ci04XJhuFx4DA8+w0PA4yfg8RPyBin0FhD2F1HiD1EeCFMRLJk+Aw+EFV25EhRkERGH0BJOIiJXEwVZRMQhFGQREYdQkEVEHEJBFhFxCAVZRMQhFGQREYdQkEVEHEJBFhFxCAVZRMQhFGQREYdQkEVEHEJBFhFxCAVZRMQhFGQREYdQkEVEHEJBFhFxCAVZRMQhFGQREYdQkEVEHEJBFhFxCAVZRMQhFGQREYdQkEVEHEJBFhFxCAVZRMQhFGQREYdQkEVEHEJBFhFxCAVZRMQhFGQREYdQkEVEHEJBFhFxCAVZRMQhFGQREYdQkEVEHEJBFhFxCAVZRMQhFGQREYfwXOb+rivyLURERGfIIiJOoSCLiDiEgiwi4hAKsoiIQyjIIiIOoSCLiDiEgiwi4hAKsoiIQyjIIiIOoSCLiDjEvwHh8SaTaio29wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f50ba72e6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection=\"3d\")\n",
    "X, P, W = wigner(rho_target)\n",
    "ax.plot_surface(X, P, W, cmap=\"RdYlGn\", lw=0.5, rstride=1, cstride=1)\n",
    "ax.contour(X, P, W, 10, cmap=\"RdYlGn\", linestyles=\"solid\", offset=-0.17)\n",
    "ax.set_axis_off()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting the Wigner function of the learnt state:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f50ba6c4cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection=\"3d\")\n",
    "X, P, W = wigner(rho_learnt)\n",
    "ax.plot_surface(X, P, W, cmap=\"RdYlGn\", lw=0.5, rstride=1, cstride=1)\n",
    "ax.contour(X, P, W, 10, cmap=\"RdYlGn\", linestyles=\"solid\", offset=-0.17)\n",
    "ax.set_axis_off()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "[1] Juan Miguel Arrazola, Thomas R. Bromley, Josh Izaac, Casey R. Myers, Kamil Brádler, and Nathan Killoran. *Machine learning method for state preparation and gate synthesis on photonic quantum computers.* [Quantum Science and Technology. 4 024004](https://iopscience.iop.org/article/10.1088/2058-9565/aaf59e/pdf), 2019.\n",
    "\n",
    "[2] Killoran, N., Bromley, T. R., Arrazola, J. M., Schuld, M., Quesada, N., & Lloyd, S. *Continuous-variable quantum neural networks.* <a href=https://arxiv.org/abs/1806.06871>arXiv:1806.06871</a>, 2018."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
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    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  },
  "toc": {
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