{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Quantum models as Fourier series\n",
    "\n",
    "This demonstration is based on the paper *The effect of data encoding on\n",
    "the expressive power of variational quantum machine learning models* by\n",
    "[Schuld, Sweke, and Meyer (2020)](https://arxiv.org/abs/2008.08605).\n",
    "\n",
    "![](images/scheme_thumb.png)\n",
    "\n",
    "The paper links common quantum machine learning models designed for\n",
    "near-term quantum computers to Fourier series (and, in more general, to\n",
    "Fourier-type sums). With this link, the class of functions a quantum\n",
    "model can learn (i.e., its \\\"expressivity\\\") can be characterized by the\n",
    "model\\'s control of the Fourier series\\' frequencies and coefficients.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Background\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ref. considers quantum machine learning models of the form\n",
    "\n",
    "$$f_{\\boldsymbol \\theta}(x) = \\langle 0| U^{\\dagger}(x,\\boldsymbol \\theta) M U(x, \\boldsymbol \\theta) | 0 \\rangle$$\n",
    "\n",
    "where $M$ is a measurement observable and $U(x, \\boldsymbol \\theta)$ is\n",
    "a variational quantum circuit that encodes a data input $x$ and depends\n",
    "on a set of parameters $\\boldsymbol \\theta$. Here we will restrict\n",
    "ourselves to one-dimensional data inputs, but the paper motivates that\n",
    "higher-dimensional features simply generalize to multi-dimensional\n",
    "Fourier series.\n",
    "\n",
    "The circuit itself repeats $L$ layers, each consisting of a\n",
    "data-encoding circuit block $S(x)$ and a trainable circuit block\n",
    "$W(\\boldsymbol \\theta)$ that is controlled by the parameters\n",
    "$\\boldsymbol \\theta$. The data encoding block consists of gates of the\n",
    "form $\\mathcal{G}(x) = e^{-ix H}$, where $H$ is a Hamiltonian. A\n",
    "prominent example of such gates are Pauli rotations.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The paper shows how such a quantum model can be written as a\n",
    "Fourier-type sum of the form\n",
    "\n",
    "$$f_{ \\boldsymbol \\theta}(x) = \\sum_{\\omega \\in \\Omega} c_{\\omega}( \\boldsymbol \\theta) \\; e^{i  \\omega x}.$$\n",
    "\n",
    "As illustrated in the picture below (which is Figure 1 from the paper),\n",
    "the \\\"encoding Hamiltonians\\\" in $S(x)$ determine the set $\\Omega$ of\n",
    "available \\\"frequencies\\\", and the remainder of the circuit, including\n",
    "the trainable parameters, determines the coefficients $c_{\\omega}$.\n",
    "\n",
    "![](images/scheme.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The paper demonstrates many of its findings for circuits in which\n",
    "$\\mathcal{G}(x)$ is a single-qubit Pauli rotation gate. For example, it\n",
    "shows that $r$ repetitions of a Pauli rotation-encoding gate in\n",
    "\\\"sequence\\\" (on the same qubit, but with multiple layers $r=L$) or in\n",
    "\\\"parallel\\\" (on $r$ different qubits, with $L=1$) creates a quantum\n",
    "model that can be expressed as a *Fourier series* of the form\n",
    "\n",
    "$$f_{ \\boldsymbol \\theta}(x) = \\sum_{n \\in \\Omega} c_{n}(\\boldsymbol \\theta) e^{i  n x},$$\n",
    "\n",
    "where $\\Omega = \\{ -r, \\dots, -1, 0, 1, \\dots, r\\}$ is a spectrum of\n",
    "consecutive integer-valued frequencies up to degree $r$.\n",
    "\n",
    "As a result, we expect quantum models that encode an input $x$ by $r$\n",
    "Pauli rotations to only be able to fit Fourier series of at most degree\n",
    "$r$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Goal of this demonstration\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The experiments below investigate this \\\"Fourier-series\\\"-like nature of quantum models by showing how to reproduce the simulations underlying Figures 3, 4 and 5 in Section II of the paper:\n",
    "\n",
    "-   **Figures 3 and 4** are function-fitting experiments, where quantum\n",
    "    models with different encoding strategies have the task to fit\n",
    "    Fourier series up to a certain degree. As in the paper, we will use\n",
    "    examples of qubit-based quantum circuits where a single data feature\n",
    "    is encoded via Pauli rotations.\n",
    "-   **Figure 5** plots the Fourier coefficients of randomly sampled\n",
    "    instances from a family of quantum models which is defined by some\n",
    "    parametrized ansatz.\n",
    "\n",
    "The code is presented so you can easily modify it in order to play around with other settings and models. The settings used in the paper are given in the various subsections.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First of all, let\\'s make some imports and define a standard loss function for the training.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import pennylane as qml\n",
    "from pennylane import numpy as np\n",
    "\n",
    "np.random.seed(42)\n",
    "\n",
    "def square_loss(targets, predictions):\n",
    "    loss = 0\n",
    "    for t, p in zip(targets, predictions):\n",
    "        loss += (t - p) ** 2\n",
    "    loss = loss / len(targets)\n",
    "    return 0.5*loss"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part I: Fitting Fourier series with serial Pauli-rotation encoding\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we will reproduce Figures 3 and 4 from the paper. These show how quantum models that use Pauli rotations as data-encoding gates can only fit Fourier series up to a certain degree. The degree corresponds to the\n",
    "number of times that the Pauli gate gets repeated in the quantum model.\n",
    "\n",
    "Let us consider circuits where the encoding gate gets repeated sequentially (as in Figure 2a of the paper). For simplicity we will only look at single-qubit circuits:\n",
    "\n",
    "![](images/single_qubit_model.png)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define a target function\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We first define a (classical) target function which will be used as a \\\"ground truth\\\" that the quantum model has to fit. The target function is constructed as a Fourier series of a specific degree.\n",
    "\n",
    "We also allow for a rescaling of the data by a hyperparameter `scaling`, which we will do in the quantum model as well. As shown in, for the quantum model to learn the classical model in the experiment below, the\n",
    "scaling of the quantum model and the target function have to match, which is an important observation for the design of quantum machine learning models.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "degree = 1  # degree of the target function\n",
    "scaling = 1  # scaling of the data\n",
    "coeffs = [0.15 + 0.15j]*degree  # coefficients of non-zero frequencies\n",
    "coeff0 = 0.1  # coefficient of zero frequency\n",
    "\n",
    "def target_function(x):\n",
    "    \"\"\"Generate a truncated Fourier series, where the data gets re-scaled.\"\"\"\n",
    "    res = coeff0\n",
    "    for idx, coeff in enumerate(coeffs):\n",
    "        exponent = np.complex128(scaling * (idx+1) * x * 1j)\n",
    "        conj_coeff = np.conjugate(coeff)\n",
    "        res += coeff * np.exp(exponent) + conj_coeff * np.exp(-exponent)\n",
    "    return np.real(res)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let\\'s have a look at it.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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4WL58uTIOKC4urlB7dOw6wMnq8ePHEhgYKBMnThSRZwtw2INDlDfTwYlxcXGyZcsWs0avffv2cu/ePaX8tGnTxNHR0axMQECAcg8+6/4yMzNzHCPg7e2tNM6PHz+WcePGKa/1799fdu7cKQDk888/t0iDSWTvjBcjs2fPVsbItG3bVv766y8REVm+fHmhH6vG940aNUp5/V//+pfFByDbTIDzLLeoctKlSxfp1q2biDzbLaqsOAaHyFxOjVnZsmWV/x86dKhZUGG83+7v7y9bt24tUOCRtTFNT083614XEfnqq6+UQchubm7ZZmpxdhUVZ3ldjLz77rtmx6Lx1lFBLxLyc6yKiHzzzTdmAdS//vUviw1AtpkAR+TJIONhw4Ypz/V6vTz33HO5DjLOKjMzU2rUqCEjR44Ukf8NMp41a5ZSJjU1lYOMiZ5R1sGJSUlJ0qJFC7MGMzIyMsfu7cIKMkzrYPw7n376qVmQs3HjRs6uomIvp4sR0xmN0dHRYjAYlPKFPfg3p2N1z5490rRpU7NZWkePHrVIHWwqwFmxYoU4OzvL999/L6dOnZKBAweKu7u7MvW7Z8+eMm7cOKX8pEmTZPPmzXLx4kU5dOiQdOvWTVxcXOTkyZNKmRkzZoi7u7usW7dOjh07Jh06dOA0caJnkHVwYlJSkjRp0kS5f9+oUSPx9PTM1qCadm8Xlpwa7hIlSii9NwEBAUU+Y4PIlmS9GLl9+7a8+uqrZsdM1sDDEhcDT7t9VblyZQEgpUuXlvXr1yvvKawByDYV4IiIzJ8/XypXrixOTk4SHBysTFMTEXnllVekd+/eyvMRI0YoZb28vKRNmzZy+PBhs/0ZE/15eXmJs7OztGzZUs6ePZvv+jDAIXrCdHDi7du3pVq1agJAKlSoILt371Yapa1bt1ps0KCpnJKUrVy5UgIDAwWAlC9fXo4dOyYinF1FxUvWixGdTqcM8i1RokSRXowY62PaJixfvlwAyJUrV5SgKzIyUulNKqzJAjYX4NgaBjhETxgHJ965c0deeeUV5QrMmBncmjOYjHVLS0uT5ORkCQ4OFgDi5+cnycnJnF1FxYrpxcjjx4+VaeClS5eWLVu2FPnFSF71++STT8zOsdboweFim0TFmI+PDwCgd+/e+OOPP1C2bFls3LgR1apVAwCcOHHCrJw16nbixAl4enrit99+Q9WqVfH333/j9ddfV9a8skbdiIpaYmIiAKBu3boYOXIk4uLiUKZMGcTFxSE8PBx169YFANy8eROhoaF46623EBoaWmRrubVo0QL+/v6YNm0atFotPvzwQ2WtKIPBgOnTpyMgIAAtWrQokvoAAHtwiIqxzMxMKVeunABPMpP++uuvymvWHueStUteROTMmTNKJuXnn39e/P39OQaHigVjD4lpGoW1a9cqr9vCLdvcBiCrdhaVLWKAQ8WZ6b3zyZMnK3kz6tSpY/HBiQWVU4M5d+5cpc5vv/12jjk8iNQmMzNTvL29ld/+5MmTldesfTFiKqcByIU5DogBTh4Y4FBxldtifPXr1zdbiqGwG6XCrnOFChUEeLLwn4eHB3PkkCqZBu8rVqwQV1dXJZHe7t27bepixJQlLzoY4OSBAQ4VR6a9IevXrxdfX18BIBUrVlRmK9lqT0hODWZERIQATxbpXLp0KXPkkKrkdjHi6empTMW2tYuRolCQ87dGRMQig3tsmE6ng5ubG1JTU5VBUERqptfrUbVqVQQFBSEmJgZhYWE4ePAgatasid27d6NPnz44ceIEzp8/X2SDEv8JvV6PwMBA3L9/H7dv30alSpWwf/9+eHt7w2AwoGPHjnb1eYhMxcbGokuXLoiMjMT48eMxe/ZsrF69Gk5OTnj8+DFWrlwJDw8PJCYmwsfHBy1atCg2v/MCnb8tHm7ZIPbgUHFjOoVz0KBBym2eCxcuiIhtDFAsCOPn2bx5s7JA50svvaT0Otnb5yEyyjq4furUqQJAHB0dZceOHTYz1sZaOE2ciMwYp5gmJibi66+/BgD89NNPCAwMBABliqmxnK0z1rN58+bYsGEDypYti127dmHOnDkA7O/zEBnFx8fj8uXLmDBhAnbu3ImJEycCAL788ku88sorGD9+PC5duoT4+Hgr19T2McAhKgaMuWIGDhwIABg+fDhatmypvG7NfDfPwjRHTrVq1TB37lwAwMSJE3Hy5Em7+zxERsag3N/fH3379oWIoF+/fhg0aBAABu8FwTE4HINDxYBer4ebmxvu37+P6tWr488//0SpUqUAwC7HrJiOKVq7di00Gg3atWuHjRs3omHDhvDx8cGpU6fs5vMQGe3YsQNhYWHo1KkTYmNj4efnh+PHj6Ns2bIAgISEBDRv3hxxcXEIDQ21bmWtoCDnb/bgEBUDa9euxf379wEAnp6eOHr0KNLS0pCQkICOHTtiw4YNmDVrlt0EA1qtFrNnz8aGDRvQsWNH7N27F59//jnKli2Lw4cPY+PGjXb1eYiMWrRoAS8vL8TGxgIAFi9erAQ3VssIbKccrV0BIip8er0e8fHxSExMhLOzs9K93blzZxw6dAjNmzdXygYEBGDVqlXo1KmTtar7TDp16oRVq1YhKirK7PMATwIgf39/61SM6B94+PAhjDdW/Pz8UKpUKaSlpeHEiROYPn06NmzYgFWrVjF4zwfeouItKlKZ2NhYREVF4fLly2bb/f39cfbsWWi1WiX4UcMUU9NgztvbGwsWLMDq1atRp04dzJkzB3fu3FHF56TiYejQofjqq6/g4eGBkiVL4sqVK8prAQEBmDVrlt1djBSmgpy/GeAwwCEVMc2fMWHCBBw9ehSDBw+GRqOBiGD16tWqbxxv3bqFatWqITU11Wy7v78/Zs+erfrPT/bFNEBPTExEVFQUAGDr1q0IDQ1V1cVIYWCAkwcGOKRGWQfeXrt2DUFBQdDpdJg2bRoSEhLsaiDxs4qNjUXnzp0BAA4ODvj9999RunRpTJs2TeneZ5BDtiC33tZWrVph8+bN1qmUjWOivzww0R+pkWkyP4PBIOHh4QJAmjVrJpmZmcUi+Z1pkrSePXsKAKlWrZrcv3/fphYkJDJdOiUhIUH69+8vAKRkyZICoNgsvVBQTPRHVAwZ82LUrVsXP/30E7Zu3YqSJUti6dKl0Gq1xSJ/hmmStHnz5uG5557D+fPnMWXKFDg4ODBJGtkEvV6PqKgoREZGYu3atXjw4AG+/fZbAMD69evRrl07jB49Gnq93so1tW8McIhUwpjU7sCBAxg9ejQAYMKECahWrRoA+0vm9yxMgzx3d3d89dVXAIDZs2fj4sWLxSLII9tnGohnZGQosxyHDBmC8PBwBuKFhAEOkUq0aNEC/v7+GDhwIK5fv46AgAAl0Cku+TNMMxwDQLt27dC6dWs8fvwYo0aNKhZBHtk+00D8iy++wIULF+Dt7Y1PP/1U2W5ajp4NAxwildBqtRg9ejQuXLgAABg0aBAyMjLsNpnfszAGedOmTYPBYIBGo8HcuXPh6OiI9evXY+TIkaoP8sj2GQPsP/74A5MnTwYAzJgxQ0nox0C8kBTBmCCbw0HGpFbt2rUTAOLi4iIAlEdAQECxGbRoOnhzz549otPp5K233lK+ixUrVli7ilTMGQfDV6pUSQBIcHCw6PV6EREOhs9DQc7fzGRMpBK//fYbfvnlFzg6OuLgwYO4detWscyfkVuGY61WC71ej2vXrlmxdkRPfotDhgzB2LFjAQD9+/fH/fv3ma24kDEPDvPgkJ0yTRBWoUIFDBs2DOfPn8fo0aMxc+ZMa1fP6ky/Hx8fH/z111/o168fypYti3PnzsHb29vaVaRiSkTQvHlz7N27F6VLl1bWiQOYrTgvTPSXBwY4ZO9ySxDm7u6Ov//+m7/rHBgMBjRr1gz79+9H79690adPn2LZw0XW98MPP+Dtt99G6dKlcfr0aVy8eJG/xXxigJMHSwU4Wa8Y+UMlS8i6HEOFChVQv359PHjwAACKxXIMz2r//v0ICQnJtp3LOJClGc8Ply5dwgcffIDbt29j2rRpGD9+vLWrZlcKcv7mLKpCEhsbi6pVqyIsLAzdu3dHWFgYqlatqix5T1QYsiYIa9q0KSZNmoQHDx6gadOmiIyMZIKwpzAdf1OrVi2kpqYiISEBQUFB6NKlC49XsgjT88M777yD27dvw9HREQEBAdaumrpZcrSzrSrsWVRZU26npaVJQkKCtGvXTjQaTbGZvUKWZ7ocg4jIrl27BIBoNBo5ePBgsViO4VkZZ660atVKXF1dBYAsXrxYRDhzhSzH9PywevVqcXZ2FgDSuHFjnh+eQUHO3wxw/iHTtW/0er1kZmbK48ePRYSNJhW+mJgYASBpaWliMBikadOmAkD69+8vIiI6nU4ASExMjJVrantMg8PZs2cLAPH09JS0tDQREQaHVOiynh86d+4sAKRly5aSmZnJ88Mz4FpURcg05fbmzZsRFBSEr7/+GgC49g0VOtNMvevXr8fevXtRqlQpfPLJJ8p203L0P6bZY4cNG4aqVavi5s2b+OKLL5TtpuWI/inT88OuXbuwevVqODg4YO7cudBqtTw/WBgDnH/ItNH8+++/cfr0aUyZMkWZ9sdGkwqTMVPv1KlTMWHCBADAiBEj4OPjU2yWY3hWpsGhk5OTEhR+9tlnuHPnDoNDKnTGdr9OnToYN24cAGDgwIHKeYHnB8tigPMPmTaa77zzDqpUqYLk5GTMnz9f2W5ajuif0Gq1mD17NjZs2IBTp06hbNmyGDx4cLFajuFZZV3G4c0330S9evWg0+kwffp0BodU6Izt/tdff42EhASULFkSH330kfI6zw8WVgS3zGyOJcfgLF++XACIu7u73Llzh/dYqdA9evRIKlasaLYUA4rZcgzPKusyDqtWrRIA4uDgIAD4/VGhyszMFD8/P2VQ+9ixY5XXOEbz2XCphiJkvKLu0qULOnbsiA8++AC1a9fGqVOnEBISgosXLzLlNhWqhQsX4vbt2/D19cV3332Hu3fvMu9SPuW2jIPBYEB4eDjz4FCh0mq1eP3115UFX8PCwpCWlsYlGYoIE/0VUqK/nDLLajQafPvtt3jnnXcK5W8QpaWloUqVKrh9+za++eYbDBgwwNpVskumSTlv376N4cOHQ6vV4tSpU6hevbq1q0cqkZGRgVq1auHixYtwd3dHSkqK8hqXZHg2BTl/swenkHTq1AkdOnRAfHw8bty4gcmTJ+PMmTM4evSotatGKjJnzhzcvn0b1atXR9++fa1dHbul1WoRGhqqPN+yZQt++eUXfPjhh/jpp5+sVzFSle+++w4XL16Ep6cnzp07hz///JOZ7osQe3AstGbPtm3bEB4eDicnJ5w7dw5+fn4W+TukfsbehrNnz2LkyJF4+PAhVq5ciTfeeMPaVVON48ePo169ehARfP311yhbtixPQvSPPHz4EFWrVsWNGzfwxRdfYPjw4daukirY3FINCxYsgL+/P1xcXBASEoL9+/fnWnbRokVo0aIFypUrh3LlyiE8PDxb+T59+kCj0Zg9IiIiLP0xCqRly5Zo2bIlHj9+jEmTJlm7OmSnTFO8Dx48GA8fPoSTkxM0Go21q6YqQUFByuypQYMGcbkVeiZ6vR47duzAjz/+iFGjRuHGjRuoXLkyBg0aZO2qFUsWD3B++uknjBo1CtHR0Th8+DDq1auH1q1b4+bNmzmW37FjB9566y3ExcUhISEBlSpVQqtWrXD9+nWzchEREUhMTFQeP/74o6U/SoFNnToVALB06VIsW7YMP/74I3bs2MF1gihfjItqBgUFITY2Fk5OTgCAhg0bomvXrjzxFqLY2Fjs3LlTCRx//fVXrlFFBZJ1PcKFCxcCANq1awdnZ2cr166YsuyELpHg4GAZOnSo8lyv14uvr69Mnz49X+/PzMyUsmXLytKlS5VtvXv3lg4dOuS7Do8ePZLU1FTlcfXq1UJdi+ppmjRpkm06r7+/P6ej0lNlTT/Qp08fASCvvvoqU7wXMtPv+t133xUA0rRpUzEYDJzKS/mSdT3CcePGCQApU6YM0w8UMptZiyo9PV20Wq2sWbPGbHuvXr2kffv2+dqHTqcTFxcX+eWXX5RtvXv3Fjc3N/Hw8JDq1avL4MGD5fbt27nuIzo6OluQURQBzurVq83+Xnx8PBfhpHwxXTfp9OnTSp6Wffv2iQjXTSpMpt91YmKilCpVSgDI2rVrRYTfNT1d1ouRmzdvKoHNypUrGSAXMpsJcK5fvy4AZM+ePWbbx4wZI8HBwfnax5AhQ6RKlSry8OFDZduPP/4o69atk2PHjsmaNWukVq1a0qRJk1x/QNbowTH90Xfv3l0AyGuvvSYiTPBEeTNdVLNHjx4CwOyigItqFh7T71pEZMKECQJA6tevLwaDgd81PZVpgCwiMnLkSAEgjRo1EoPBwAC5kKkmwJk+fbqUK1dOjh49+tRyFy9eFACydevWfNWrMDMZ58b0R3/hwgVxdHQUALJr1y4R4VUhPZ3x97NixQql9+bQoUPK6/z9FJ6sJ6jbt28rV+Br167ld01PZRog37hxQ1xcXASAbNq0SUR4MVLYbGY18YoVK0Kr1SI5Odlse3JyMry9vZ/63lmzZmHGjBn4/fff8cILLzy1bJUqVVCxYkVcuHDhH9e5sJguwhkYGKjkLDEu8MdF1uhpjOsmRUVFwWAwoH379mjYsCEAcFHNQpZ1jaoKFSrgvffeAwBMmjQJ06ZN43dNuTJdj3DmzJl49OgRmjdvjlatWinbTctREbJ0tBUcHCzDhg1Tnuv1ennuueeeOsj4008/FVdXV+WKKi9Xr14VjUYj69aty1f5ou7BERG5dOmS0ouTkJDAq0LK0/z585XxW999953odDrZs2cPx3BZQNY1qi5duiQlS5ZUvn9+15Qb43CEVq1aKb8ZY+8NhyMUPpu5RSUismLFCnF2dpbvv/9eTp06JQMHDhR3d3dJSkoSEZGePXvKuHHjlPIzZswQJycnWbVqlSQmJioP4/3xtLQ0GT16tCQkJMilS5dk69at0rBhQ6lWrZo8evQoX3UqigAn68AzEZF33nlHAEhERAR/9JSnnj17CgCzEy24qKbFrF69Wvz9/bNNRggMDBSDwWDt6pENM51QUqdOHUlNTeXFiIXYVIAj8uRKtHLlyuLk5CTBwcGyd+9e5bVXXnlFevfurTz38/PLccZTdHS0iIg8ePBAWrVqJR4eHlKiRAnx8/OTAQMGKAFTfhRFgCOS/arwyJEjotVqeVVIeTp37pzZzKm4uDiJiYmRuLg4BsUWlJmZqXzXa9euldKlSwsAs1mcRFklJyeLs7NztvMWL0YKX0HO31yqwUJLNRjltAgnADRq1AgHDx606N8m+9WnTx8sXboUbdu2xYYNG6xdnWJr7Nix+Oyzz9C4cWPs37+fGaQpR6a/k88++wxJSUlc6sNCCnL+ZoBj4QAHMF+5WK/Xo3fv3jAYDDh48CAaNWpk8b9P9uXChQuoWbMm9Ho99u/fjyZNmli7SsXWrVu34O/vjwcPHmDjxo1o06aNtatENub27dvw9/fH/fv38csvvyAyMtLaVVI1riZuY7KuXLx582YsX74cn3zyCdatW2e9ipHNMA2Cly1bBr1ejzZt2jC4sTIPDw8MHToUM2fORHR0NEqWLMmrczIzZ84c3L9/Hw0bNkTbtm2tXR0ywR6cIujByers2bOoVasWRASHDx9GgwYNirwOZDtyu405Y8YMjB071jqVIsXNmzdRuXJlpKenm2339/fH7Nmz0alTJyvVjKztzp078Pf3x71797B27Vp06NDB2lVSPZtbTZzM1ahRA926dQPwJC+OcfVZLsRZ/JguqJmQkIC3334bAODp6Ynx48dzkUcbsGvXLiW4qVOnDnQ6HRfiLOaMq4b3798f9+7dQ7169dC+fXtrV4uysuRoZ1tVVLOonubUqVOi0Wi4EGcxljWVwMWLF5VZdsYppkwlYF055Tj57bffRIQ5ToqrnNIJeHh4sN0uIjaTyZhyd/r0acj/vzsYFhaGtLQ0XhUWM/Hx8bh8+TImTJgABwcHTJs2DXq9HhEREWjWrBnGjx+PS5cuIT4+3tpVLbaM/0aTJk3CkCFDADzJbiwicHBw4L9RMWPa4/rOO+8AAAIDAxESEsJ22xZZPNyyQdbuwTFeFb7yyivKFcDx48dFhFeFxYnpGjZ///23lChRwmztNq5hY32m/0aJiYnKOkPGde/4b1R8mPa43rlzR9zc3ASA/Pzzz2y3ixB7cGyc8apwxowZ6NKlCwBgypQpAMCrwmIk6xo2GRkZePXVV9GsWTNlu2k5Knqm/0be3t4YMGAAgP8dr/w3Kj5Me1wXLFiA1NRU1KlTB506dWK7bauKIOCyOdbuwTG9Kjxy5IgAEI1GI2fPnhURXhUWF8Yrwn/9619Kz8C2bdtEhD15tiLrOKkrV64oPW3x8fH8NypGjO12YmKilC9fPlsbzXa7aLAHx8aZXhXWq1cP7dq1g4hgxowZynbTcqROWq0Ws2fPxpYtW/Do0SPUqVMHjRs3RkJCAjp27IgNGzZg1qxZzLViRcZ/ow0bNqBjx464du0aunfvDgDo3Lkz/42KEWN7PG3aNNy9exdVq1ZF165dldfZbtsgy8dbtsfaPThZrwr37t0rAMTR0VH++usvXhUWI7dv31Z6b0wfXMPGtuS2EOfMmTOtXTUqIpmZmVK5cmVlzalvv/1WeY09rkWHPTg2LutVocFgQGhoKDIzM/Hqq6/yqrAYmTdvHh49eoT69etj+/btiImJQVxcHM6fP88EcjakU6dOuHDhAuLi4hATE4Pw8HAAwN69e61cMyoqWq0WrVu3Rnp6OlxcXFCtWjVl9it7XG0TMxlbIZOxUU4ZbDUaDRYtWoR+/fpZrV5UNHQ6Hfz8/JCSkoKff/5ZGXBOtu/kyZOoW7cuNBoNTp48iVq1alm7SmRhGRkZqFatGv7++2+UL18ed+/eVV4LCAjArFmzeFFSBJjJ2E6YXhX+8MMPqFOnDkQEZ86csXbVqAj85z//QUpKCmrWrMmG0c7UqVMHr7/+OkQE06dPt3Z1qAj88MMP+Pvvv+Hl5YW///5b6c1jj6vtYg+OFXtwstq4cSMiIyNRunRp/P3336hQoYK1q0SFzLio5uXLlzFy5EikpKRg2bJl6Nmzp7WrRgV06NAhNG7cGFqtFufOnUOVKlWsXSWyEL1ej9q1a+PcuXP49NNP8cEHH1i7SsUWe3DsVJs2bVC/fn3cv38f8+bNs3Z1qJDFxsaiatWqCAsLQ9++fZGSkgJHR0e4uLhYu2r0DBo1aoSIiAjo9XrMmDGDa8qp2OrVq3Hu3DmUK1dOyWhNto8Bjg3RaDSYMGECgCeDT3U6nZVrRIXFNMX7H3/8AV9fXwBA7dq18eabbzLFu53697//DQBYtGgRwsLC0L17d4SFhaFq1ar8N7VzxgU1Y2JilHb5/fffR9myZa1cM8ovBjg2plOnTqhRowZSUlIwZswYXhGqgF6vR1RUFCIjI7F27VqcPXsWN27cwHPPPYe9e/ciMjISo0eP5r+xHbp586by/2+++SbXlFMJ097WHj164OLFi9BoNPD397d21aggLDph3UZZOw9OXt577z2uMq4icXFxAkASEhIkIyNDqlSpIgBk7ty5IiKyZ88eASBxcXHWrSgViDGfVdOmTQWAlCxZUpKTk0WEeVHs2erVq0Wj0Ui7du1kz5490rhxYwEggYGBotFo2A5bGfPg2LHY2FjMnz8fJUuWBAB89tlnvCK0c4mJiQCAunXrYsWKFfjrr7/g4eGhrGtUt25ds3JkH4yDxefMmYMmTZrg4cOHmDt3LgCuKWevsva2PnjwAAcPHoSLiwvi4+PZ22pnGODYEOPB1a5dO8yaNQvAk7E4DRs2xNq1a3lw2Slj6vZjx44pU4pHjhyJUqVKAWCKd3tlDEiDgoKUsThffvkl/vvf/wJg4GqPTBfUdHBwwNSpUwEAAwYMgI+PD4NWO8MAx4aYHlzvvPMOfHx8cO3aNSxbtoxXhHasRYsW8Pf3x/vvv49Tp07Bzc0N7777LgDAYDBg+vTpCAgIQIsWLaxcUyoI0zXl2rVrh6CgIKSlpeHLL79UtpuWI9tn2tuakJCAuLg4lChRAmPGjFG2m5Yj28YAx4aYHlwuLi4YPXo0AGDGjBnIzMzkwWWntFotZs2ahYMHDwJ4MpDcwcGBKd7tnDFwnTZtGgAoM23mzp0LnU7HwNUOmQatxt6bXr16oVKlSsp203Jk44pgTJDNsdVBxqaDUUVE7t27JxUqVBAAsnz5cg5GtWO//vqrABCNRsNFNVXEdEBqfHy8BAYGCgCpXbs2B6TaIePA8ZdfflkAiIODg5w/f15EOHDcVhTk/M0Ax4ZkXWVcRGTq1KlKgxkZGcmDyw4ZDAZ58cUXBYCMHDlS4uLiJCYmRuLi4vhvqQI5rTSu1Wrlxx9/tHbV6BmsXr1a+Xds1aqV6HQ62bNnj7Rr145Bqw1ggJMHWw1wRLJPUbx69aqUKVNGOeB4cNmfHTt2CABxdnaWGzduWLs6ZAGZmZkSFxcny5YtE09PTwEgCxYssHa16BmcOnUqW08re1ttR0HO345FcRuM8q9Tp05YtWoVoqKi0Lx5c7PXAgIC8Prrr1upZvSsjPfyjQPHSX20Wi1CQ0MBPFkrZ9iwYfj0008xYMAAlChRwrqVowKZPn06RAQdO3bE+++/j8TERPj4+KBFixYcJ2dnuNimDS22acq4KGNiYiJKlSqF7t2748GDB/j111/x2muvWbt6lE/79+9HSEgItFotLly4wEyoxcDDhw8REBCA5ORkfPfdd+jbt6+1q0T59Ndff6F69erQ6/U4ePAgGjVqZO0qURYFOX+zB8dGmV4RAsCQIUMwe/ZsTJkyBREREdBoNNarHD2VaXBqnDLcs2dPBjfFRMmSJREVFYUPPvgA06dPR+XKlXHz5k32AtiBTz/9FHq9HhEREQxuVIA9ODbag5NVYmIiAgICkJ6ejri4OLPgh2xHbGwsoqKicPnyZbPt8+bNw3vvvWedSlGRS0tLg6+vL+7du2e23d/fH7Nnz0anTp2sVDPKzbVr11ClShVkZGRg165dePHFF61dJcpBQc7fzINjJ3x8fNCvXz8AwOTJk7Fjxw4uxGljTFcMT0hIQJcuXQAAvr6+eP/997nMRjGyZcsWJbgJDAxEamoql1yxUcZVwwcMGICMjAy8/PLLDG7UwrLjnW2TLc+ieprLly+LVqvlQpw2KOsU/7Nnz4qDg4MAkMOHDzN/RjFi/C20bt1aypYtKwBk3bp1IsJcKrYmpyn+Xl5ebE9tGBfbVKlDhw4pvTUvvvgi0tLSeFVoI7KuYTNjxgwYDAZERkaiQYMGXGajGDH+Fj7++GNlSY4pU6ZARLjkig0x7XHt2bMnAKB27dpo0qQJ21O1sHy8ZXvssQfHeFUYFham9Az8+eefIsKrQlsQExMjACQtLU0uXryo9LTt3btXRER0Op0AkJiYGCvXlCzN9LeQlJQkJUuWFACyadMmEeFvwRaY9rjevn1b6Wlbv34921Mbxx4cFTJeFU6bNg1du3YF8L/8KrwqtD7TNWymTZsGvV6P1q1bIyQkRNluWo7Uy/S34OXlhUGDBgEAJk2aBBHhb8EGmPa4zp8/H2lpaXjhhRcQGRnJ9lRNLB9viXz55Zfi5+cnzs7OEhwcLPv27Xtq+ZUrV0qNGjXE2dlZ6tatKxs3bjR73WAwyIcffije3t7i4uIiLVu2lHPnzuW7PvbYg2N6VXj8+HFlXaPjx4+LCK8Krc14RdiyZUtxdHQUALJnzx4RYQ9bcZN1PNaNGzfExcVF6cXhb8H6jO3p1atXxc3NTQDIypUrldfZntoum1qqYcWKFeLk5CTfffednDx5UgYMGCDu7u6SnJycY/ndu3eLVquVzz77TE6dOiUTJ06UEiVKKCdyEZEZM2aIm5ubrF27Vo4ePSrt27eXgIAAefjwYb7qZI8BTtaFOLt06SIApGvXriIiXIjTBpiuYdOkSROuYVOMZV1yZfDgwQJAypUrxyVXbICxPe3fv78AkLp16yrr/4mwPbVlNhXgBAcHy9ChQ5Xner1efH19Zfr06TmW79q1q7Rt29ZsW0hIiAwaNEhEnvTeeHt7y8yZM5XXU1JSxNnZOdfF7R49eiSpqanK4+rVq3YX4GS9Kjx27JjSi3P06FFeFdqAy5cvK703pg+uYVM85TRDB4BER0dbu2rFXmZmplSqVEk5Xk17b9jjattsZgzO48ePcejQIYSHhyvbHBwcEB4ejoSEhBzfk5CQYFYeAFq3bq2Uv3TpEpKSkszKuLm5ISQkJNd9Tp8+HW5ubsqjUqVK//SjFTmtVovZs2djw4YN6NixI+7du4cOHTpARPDaa69hw4YNmDVrFrOkWtGMGTOQmZmJsLAwxMXFISYmBnFxcTh//jwTuxVDnTp1woULF5TfgnEdue3bt0OKX35Vm6LVatG8eXNkZmaibNmy8PX1VWalduzYke2pWlgy0rp+/brZWASjMWPGSHBwcI7vKVGiRLb7ngsWLBBPT08ReXILC0C2VZnfeOMN5XZNVmrowTHK7arw888/t3bVirUrV65IiRIlBID88ccf1q4O2aBr166Jk5OTAJDt27dbuzrFWkpKiri7uwsA8fDwYI+rHbGZHhxb4ezsDFdXV7OHvcp6Vfjyyy8DAPbu3WvlmhVvM2bMQEZGBkJDQ5V/EyJTzz33HAYMGADgyYwqsp558+YhJSUFtWvXxvXr19njqlIWDXAqVqwIrVaL5ORks+3Jycnw9vbO8T3e3t5PLW/8b0H2qTbGhTjfeustzJ8/HwCwcuVKnDx50so1K16MKd6//PJLLFq0CAAQHR1t5VqRLRs3bhycnJzwxx9/4I8//rB2dYql1NRUzJkzBwDw0UcfoUSJEkp7GhoayttSKmLRAMfJyQmNGjXCtm3blG0GgwHbtm1Ds2bNcnxPs2bNzMoDT9Z1MZYPCAiAt7e3WRmdTod9+/bluk81e+GFF9C5c2eICCZPnmzt6hQbsbGxqFq1KsLCwvDee+8hIyMDzs7OuHv3rrWrRjbs+eefV9aU+/jjj7mmnBWY9t4Y14sjlbL0/bIVK1aIs7OzfP/993Lq1CkZOHCguLu7S1JSkoiI9OzZU8aNG6eU3717tzg6OsqsWbPk9OnTEh0dneM0cXd3d1m3bp0cO3ZMOnTooPpp4k9z9OhRZUbVkiVLJCYmRuLi4jgDwEJMpwCvX79enJ2dBYA0a9aM08EpT3///XeOs+24ppzlZGZmSlxcnHz77bdK1uLcZt2SbbOpaeIiIvPnz5fKlSuLk5OTBAcHK+nrRUReeeUV6d27t1n5lStXSvXq1cXJyUnq1KmTa6I/Ly8vcXZ2lpYtW8rZs2fzXR+1BTgiT6bSs8G0vKzT9YcPHy4A5MUXX5TMzExOL6U8meZLaty4saSlpUlCQgLzJVlIThMzSpQoYTY1nOyHzQU4tkZtAY5pg6nRaOTAgQNsMC3ENOGiaYba33//XUSYIIyezjTjtXHW3a5du0SE+VcswbS3devWrUqixYYNG7JttFMMcPKgpgDHtEfh9ddfFwDSrVs3EWGDaQmmS2a8++67AkCaN28uBoNBRJjinZ7ONEAeOHCgAJCwsDDl98MAufBk7W2dMmWKAJCaNWvK48eP2TbaKQY4eVBTgGPaYB45ckTpxTl58qSIsMEsbMbve9WqVco4CtPvlt83PY1pgPz3338reXGMPYAMkAuPadv43//+V+m9MX63PFbtE/PgFCOJiYkAgLp166JevXro1KkTRAQTJ05UtpuWo3+mRYsW8Pf3x/vvv4/MzEy0atUKoaGhAJ7MEJw+fToCAgLQokUL61aUbJLpSuOVK1fGu+++CwAYP348VxovZKZt48yZM/Hf//4XtWvXRteuXZXtpuVIfRjg2DnTBhMAJk+eDAcHB6xZswZ79+5lg1nItFothg8fjuvXrwMAunXrxhTvlG/GAHnatGkwGAyYMGECypQpg0OHDuHnn39mgFyIjG3ejh078PnnnwMApk2bphybbBuLAYv3J9kgNd2iynqfWUSkb9++AkBeeeUViYyM5H3mQta+fXsBIKVKlWKKdyqwrCuNjxs3TgBI6dKludJ4ITK2jX5+fkoaB+NYJ45PtF8cg5MHNQU4ItkbzFOnTin39tlgFi7jfXsHBwc5ceKExMXFMe8QFVhua8q9++671q6aqnz55ZfKd7tgwQLR6XSyZ88ezjC1YwU5f2tEit+ytjqdDm5ubkhNTbXrdalMxcbGIioqCpcvXzbb7u/vj4sXL8LBgXcj/ykRwauvvoodO3bgnXfeweLFi61dJbJjer0e8fHxSExMRHx8PP7zn/+gUqVKOHfuHFxcXKxdPVV46623sGLFCpQsWRIPHz5UtgcEBGDWrFlcc8oOFeT8zQBHJQEOYN5glipVCr169YJOp8MPP/yA7t27W7t6du/3339H69at4eTkhPPnz6Ny5crWrhKpxKNHj1CtWjVcu3YNc+bMwciRI61dJbv3559/omHDhgCAgwcPIi0tDYmJifDx8UGLFi04Ts5OFeT87VhEdaIiYFyE0+iDDz7AxIkT8eGHH6JLly5wcnKyXuXslDFovHHjhrIC9LvvvsvghgqVi4sLPv74Y/Tv3x/Tpk1DjRo1kJqaypPxPzBhwgQAQPfu3dGoUSMr14asgT04KurByer+/fuoWrUqkpKSMG/ePAQFBfEKpgByuu2n0WiwePFi9O3b13oVI1XKzMyEn58fbty4Ybbd398fs2fP5u2UfDBekGzbtg1TpkyBo6Mjzpw5g8DAQGtXjQpJQc7fHJihYqVLl8ZHH30EABgxYgTCwsLQvXt3hIWFoWrVqoiNjbVyDW1XbGwsunTpgqCgIMTHx6NatWoAgGrVqqFfv3787qjQrV+/XgluSpUqhb/++gsJCQkICgpCly5d+JvLQ2xsLKpWrYqwsDBMmTIFAFCyZEkcPXrUyjUja2GAo3IVKlQA8CQJ3YABA5ScLWw0c6fX6xEVFYXIyEisXbsW58+fx/nz51GhQgXs27cPkZGRGD16NPR6vbWrSiph+ptr2LAhHjx4gPnz56Np06ZYu3Ytf3N5ML0gmTFjBoAnt/2aNm3Kdq44s+R0LlultmniuTHmgWjYsKEAkLJly8rNmzdFhHkgnsY0xfu9e/fkueeeEwAya9YsEWGKdyp8pr+5zZs3CwBxcnKSS5cuiQh/c09jmgvs8ePHUqtWLQEg//73v9nOqRCXaiAAQHx8PC5fvoz58+ejQYMGSEtLw7Rp0wAADg4OGD9+PC5duoT4+Hgr19S2mKZ4nz59Oq5fv46AgAAMHTpU2W5ajuifMv3N/etf/0LLli3x+PFjjB49WtluWo7+x9jOTZgwAf/3f/+H06dPo3z58hgzZgzbuWKOAY6KGRvDF154Qem2XbBgAc6ePQuAjWZujKnbN2/ejFmzZgEAZs+ereQmYYp3KmymS65oNBrMnTsXWq0Wq1evxvbt2/mbewpj+1WpUiWMHz8eAPDvf/8bbm5uANjOFWcMcFTMtNFs1aoV2rZti4yMDAwfPpwL+z2Fcb2gYcOGIT09HS1btkTHjh0BcEFNsoysa1TVrVsXQ4YMAQAMHz4cU6dO5W8uF8b2KyoqCjdv3kSNGjUwbNgw5XW2c8WY5e+Y2Z7iNgbHuE7V+fPnlSUcVq9ezXvTTxEdHS0ARKPRyPLly5ninSwu65Irly9fFjc3Ny65kofMzEzx9fUVjUYjAGTz5s3KaxyDoz5ciyoPxSXAEcneaI4ePVoASMmSJdlo5iIjI0Pq1KmjDMwGuKAmFY3c1qgqXbq03Lp1y9rVs0kGg0Hq1q0rAMTb21v27NnDCxIV41pUeSguif6MclunqmvXrvjpp5+sUykbNn/+fAwfPhwVKlTAmTNncOLECSZIpCJjuuSKp6cnoqKicPToUQwaNAgLFy60dvVszs8//4yuXbvCyckJHh4euH79uvIa15xSH65FlYfiFuAA5o3m2bNnMWnSJDg7O+P06dMICAiwdvWszvj9nD17FqNHj8a9e/fwn//8B4MHD7Z21aiYi4+Px8svvwyNRoP9+/fj3r17DLj/v/v376NWrVq4evUqoqOj8eGHHyrtHL8fdWKAk4fiGOCYEhGEh4dj+/bt6NChA0aMGFGsG4ScerhKlCiBH374AW+88Yb1Kkb0/xlXxXZ2dkZ6erqyvTgu42B6sfbrr79i+fLl8Pf3x6lTp1CyZElrV48sjEs10FNpNBrMmzcPDg4OWLduXbFewsE0A+qyZcvg4PDkkGjcuDHefPPNYvVdkO0KCwsDAKSnp+OTTz4pthnJTZdj6N69O5YvXw7gye12BjeUjSUHA9mq4jTIODerV69WBjBWqlRJbt++LQkJCcVqUJ7pLLPMzEx5+eWXBYC88cYbnH1BNsP4O61Ro4YAkOeee07u3bsnIsVrlpDphImEhAR57bXXBIBUrFiREyaKEc6iykNxD3CMDWZERIR4eXkJAJkxY4aIFK8G0zQ9/rJlywSAuLi4yOXLl0WE6fHJNhh/p3FxccoMq/HjxyuvF4ffadaUFxs3bhQA4ujoKCdPniw2bRZxqQbKgzG1eXR0ND777DMAwOTJk3Ht2rVildrcmNm0QoUKGD58OABg4sSJ8PPzA8AMqGQbjL+/xo0b4/PPPwcAfPbZZzh48CCA4vE7NV2OIT09He+//z4AYMSIEahdu3axabOoYBjgFEOm6968/fbbaN68Oe7fv4+BAwdCRIpFgwn8L7Npnz59kJKSgkaNGmHs2LHK68yASrbANCN5x44d8eabb0Kv16N379549OhRsfidmrZZ48ePx4ULF+Dr64sPP/xQ2W5ajghggFMsmTaYDg4OWLRoEZydnfHbb7/h66+/LhYNJvAkPX6FChWwZ88eODk5YenSpXB0dATAJRnIdmRdxmHBggXw8vLCqVOn8NFHHxWL36mxLfr+++/xxRdfAAC+/fZbZRZNcWmzqIAsf8fM9nAMjvn9bBGROXPmCAApVaqUhIWFFYv72VevXpVSpUoJAKlZsyYzoJLNypqR/McffzTLdKz232lmZqZUrlxZycA+aNAg5bXiNG6QOMg4T8U9wBHJ3mCmpKRIw4YNlQZz5cqV1q5iocvMzJS4uDiJiYmR7du3S+vWrQWAVKtWTfz8/LgkA9m03JZx8PHxkfv371u7ehYXFhamXIRt3bqVFyPFVEHO345F2l1ENqNTp05YtWoVoqKi0Lx5c2W7RqOBiOD8+fNWrF3hy225ihIlSmDdunWoXr06M6CSTevUqRM6dOig/E7LlCmDwYMH48aNGxg/fjxef/111f5+161bh7i4OGg0Gri6uiI8PFx5LSAgAKtWrSpWyQ4pf5jJuBhmMjZlmhXUx8cHly9fRt++feHo6IiEhARVpIU3JvOLjIzEhAkT4ObmhsaNG+PBgwcAgNWrV7NxJLu0adMmvPbaa9m223uGY9N2ycXFBYMGDcKtW7fwwQcfYNq0abwYKcYKdP62dHeSLeItqtwZDAZ5/fXXBYCUKFHCrCvc39/f7rqBs443MhgMEh4eLgCkWbNmEhkZyXv3ZLdME3Y+99xzkpiYaPcJO3O7FVe5cmV59OiRtatHVsY8OPTMNBoN2rVrBwDIyMjAW2+9Zddp4U3zZzg4OOCbb77B1q1b4eLigu+//x4TJkxg/gyyS3q9HlFRUYiIiEDlypVx/fp1TJ48GU2bNsXatWsRGRmJ0aNHQ6/XW7uq+Wa6dEpCQgK+/vprAE/apStXrmDjxo1WriHZlSIIuGwOe3ByZ+zxCA4OFgCi0Whkx44dImKfsxViYmIEgKSlpcn+/fvFxcVFAMicOXNERESn0wkAiYmJsXJNiQrGNBP31q1bs82osrcMx1l7W69cuSKurq4CQKZMmWJ3bQ9ZBntw6JkZezy++OIL9O/fHyKCt99+G0lJSXaZ5diYFyMuLg4dO3bEo0eP0LZtWyVzMfNnkL0yTX7XsmVLjBo1CgDQs2dPHDlyxO6S35n2tj569AidO3eGTqdD06ZNMXbsWLtre8j6LBrg3L17Fz169ICrqyvc3d3Rr18/3Lt376nl33vvPdSoUQMlS5ZE5cqVMXz4cKSmppqV02g02R4rVqyw5EcpNkwbzTlz5qB69eq4du0a2rdvjwcPHthdo9miRQtUrlwZvXr1wo0bN1C7dm3ExMRAq9UymR/ZNdOEnQDw6aefonXr1njw4AHat2+PnTt3mpWzdcY2pXbt2ujVqxcOHDiA8uXLY/ny5XB0dLS7toesz6IBTo8ePXDy5Els2bIFGzZswM6dOzFw4MBcy9+4cQM3btzArFmzcOLECXz//ffYtGkT+vXrl63skiVLkJiYqDw6duxowU9SfJg2mmXLlsWGDRtQvnx5HDhwAD179sSxY8fMytkivV6PHTt24Mcff8TOnTvh5+eHlJQUlChRAh9//DE0Gg0SEhLQsWNHbNiwAbNmzeIsDLI7WTMcOzo6YsWKFahRowauXr2Knj17ws/Pz26Cd2Ob8t5772H16tUoUaIE1qxZg8DAQADsbaVnYKn7ZKdOnRIAcuDAAWXbb7/9JhqNRq5fv57v/axcuVKcnJwkIyND2QZA1qxZ88x14xic3OWU5Xjnzp3i5OQkACQwMNCm74PnNgNDo9EoK6cbH0zmR/Yua8JOnU4nP/30kzIDMjQ0VDIyMpQEl3FxcTZ17Jom39y6datUqFBBOT6XLl2qlLPH8X9kGTaRyXjx4sXi7u5uti0jI0O0Wq3Exsbmez+LFi2SihUrmm0DIL6+vlKhQgVp0qSJLF68WAwGQ677ePTokaSmpiqPq1evMsB5ipwazejoaKXhGThwoE02mKb1TkhIkJUrV4pGozHLzmyL9Sb6J3IK6r29vcXBwUEASLly5Wwy3UNuFyP4/9nFuXQK5cQmApypU6dK9erVs2338PCQr776Kl/7uHXrllSuXFkmTJhgtv2TTz6RXbt2yeHDh2XGjBni7OwsX3zxRa77MT05mz4Y4OQup8bH3d09x+/RFhrMrD1PJ0+elLJlyyoBGfPdkJqZ9oQYg/f+/fsrx+hnn30maWlpNpMjJ+vFyOHDh5XjFYB4enqyt5VyZNEAZ+zYsTme5Ewfp0+f/scBTmpqqgQHB0tERIQ8fvz4qWU//PBDef7553N9nT04zyZro7ly5Url37h06dKyb98+m2kwTafMJicnS2BgoACQl19+WdLT0+1uyizRP5GZmSl+fn7KGmtlypSRY8eOiYj1b/dkvRi5c+eOVKtWTQBISEiItGnTRvz9/WXr1q3sbaVsLBrg3Lx5U06fPv3UR3p6+j+6RaXT6aRZs2bSsmVLefjwYZ512rBhgwDId5ZLjsEpOGOj1KZNG2nRooUAED8/P7l+/brVG0yR/+W7OX78uFStWlXpWbp586aIMN8NFS/GgD8+Pl5ZpNLDw0P2798vItbNkWN6MaLT6eTll19W2pOkpCRejNBTWXSxTQ8PD3h4eORZrlmzZkhJScGhQ4fQqFEjAMD27dthMBgQEhKS6/t0Oh1at24NZ2dnrF+/Hi4uLnn+rSNHjqBcuXJwdnbO/wehAjHmqPjxxx9RrVo1NG3aFBcuXECzZs2wYcMGjB8/Hs2bN0d8fDxCQ0MtXp+sa2h5enoCAEJDQ3Hnzh34+/tj8+bNym+VMzCoODFOpa5fvz5WrVqFf/3rXzh8+DBCQ0OxatUqvPTSSwCAbdu2FfmaTsa6lS9fHi+//DKOHDmizNj08vJCqVKlzMoRPTNLRloRERHSoEED2bdvn+zatUuqVasmb731lvL6tWvXpEaNGrJv3z4ReRKZhYSESFBQkFy4cEESExOVh7FnYP369bJo0SI5fvy4nD9/Xr766ispVaqUfPTRR/muF3twCs40I7CIyMWLF6V69eoCQMqWLSurVq0SALJ8+XKLD+TNaXyQl5eXMqD4hRdekBs3bijlbaGHiagomfaSiDzpwWzVqpUAEK1WK507dxZHR8ciGUuX9Va3Meuyh4eHMt7GeA4Qsb8MzFS0bGKQsYjInTt35K233pIyZcqIq6ur9O3bVzlBiohcunTJ7IdsPChzely6dElEnkw1r1+/vpQpU0ZKly4t9erVk4ULFypTmvODAU7BZW0wRZ78+4aGhgoAZcaGj4+PRRvNrIMT09LSZOrUqcrfByARERGcgUHFWk7pHtLT06Vnz57KcVKjRg3Zs2ePRQcf53Qx4unpqVyM1KpVS2nbRXgxQnmzmQDHVjHAKbicGkyRJ41mnz59zGY77Nq1yyKNZk51WLBggdJY+vj4iIeHR7YGlTMwqDjKKd3Dzp07lRw5AGTIkCFKIFHYwUVOFyNjxowxOzZ5MUIFxQAnDwxwnk1ODeaePXukbdu2Zj0obdu2FZ1OJyLmjWZ6enqBb1+Zdm9//vnnZoMTR44cadZQx8fHCwDZunUr890QSe65ZkaNGqVcGHTo0EEZjG+8PfQsx1DWpH2mFyN6vV6ioqKUv1+pUiVejNAzYYCTBwY4zy63pGIAZOrUqcpq3dWrV5eVK1eKXq9XGs3cbl/llMMjt78FQL788kvlbwKQTz75RAwGA2dKEeXA9PiaOHGiMpbu559/FmdnZwEgrq6uMmPGDLl582aOeWie9Vjds2eP/P7779KkSRNl25QpU2T37t28GKFnwgAnDwxw/pmsjdzy5cuVRnPfvn1mwccLL7wgI0aMEAASGRmpdFUbb18ZBwhnbUzHjBmTrXt7+PDhZuUCAwNl3bp1Sr04OJHo6bKOpUtISJAGDRoox5Qxmec/PVYnTZokAJSUEgCkVKlS8sMPP4gI0zbQs2OAkwcGOIUra6OZkpIi0dHR4urqqjRubm5usn79erMlNX7++WfRaDTZGtPIyEhxdHSUyMhI0ev1cvbsWWnfvr2yL0dHR5k1a5akp6cr++LgRKK85TSOTa/Xy7Jly+T5559XjrFGjRrJjh07lPfl91gVETl8+LCEhIQo+3JycpLhw4dLUlKSsj9ejNCzYoCTBwY4hSu3Ach37tyRHj16mF3xBQcHy8SJE2Xp0qXi4+MjERERZu/JyMiQb775RgBI+/bt5YUXXlDG92i1WnnttdeUcT4cnEhUcLmNpQsODlZ6WozHa926daV3795Svnx5efHFF81mwYo8mdVqvE384YcfSkREhNnxXqlSJbNZUiK8GKF/hgFOHhjgFL7cGs2GDRsKABkxYoRZw5l1DM8rr7wiL774opQsWTLHMm3atJFTp06JiMjy5cuz5fDg4ESi/MtpzIwxL81ff/0lQ4YMEa1Wm+04dHBwkDp16shrr70m1apVM1vM1vjQaDTSvXt3mT9/vmg0Gl6MUKEqyPlbIyKCYkan08HNzQ2pqalwdXW1dnVUIzY2FlFRUbh8+bKyzdvbG0lJSUhISEBAQAB+/PFHnDp1CvHx8Thz5kyO+yldujTu37+Pnj174vXXX0eTJk3w/PPPK68nJCSgefPm+Pzzz+Hl5VWkWViJ1CJrNnC9Xo/w8HAkJCSgadOmSEpKwr59+7Bs2TLExsbCy8sLycnJOe4rKCgIISEhqF27Nlq1aoU6deoAAKZPn46PPvoImZmZStmAgADMmjULnTp1KpLPSepSkPM3AxwGOIUqa6PZvHlz1KhRA0FBQVi7di0cHBwAADt27EBYWBh+//13uLm54ezZswCAJk2aIDAwEP7+/mjQoAHWr1+vvAcADAYDOnbsiBMnTuD8+fMMaogKiV6vR9WqVXM9VhMSElC5cmUcOnQIN27cQLVq1VCjRg00adIEDRs2zPVYPX78OL799lvcvHmTFyP0jxXo/G3h3iSbxFtURSun21fx8fFSpkwZadu2bbYs1Hq9Xho3biwAst3yYvc2keXwWCVbxzE4eWCAU/SelrI9t4ZxzJgxTARGVMR4rJIt4xicPPAWlXVkvX3VokULrFu3Ltu4HdN79Dm9h93bRJbFY5VsFcfg5IEBjm1hw0hkH3iskrUxwMkDAxwiIiL7U5Dzt8NTXyUiIiKyQwxwiIiISHUY4BAREZHqMMAhIiIi1WGAQ0RERKrDAIeIiIhUhwEOERERqQ4DHCIiIlIdBjhERESkOgxwiIiISHUY4BAREZHqMMAhIiIi1WGAQ0RERKrDAIeIiIhUhwEOERERqQ4DHCIiIlIdBjhERESkOgxwiIiISHUY4BAREZHqMMAhIiIi1WGAQ0RERKrDAIeIiIhUx6IBzt27d9GjRw+4urrC3d0d/fr1w7179576ntDQUGg0GrPH4MGDzcpcuXIFbdu2RalSpeDp6YkxY8YgMzPTkh+FiIiI7IijJXfeo0cPJCYmYsuWLcjIyEDfvn0xcOBAxMTEPPV9AwYMwCeffKI8L1WqlPL/er0ebdu2hbe3N/bs2YPExET06tULJUqUwLRp0yz2WYiIiMh+aERELLHj06dPo3bt2jhw4AAaN24MANi0aRPatGmDa9euwdfXN8f3hYaGon79+pg7d26Or//222+IjIzEjRs34OXlBQBYuHAhxo4di1u3bsHJySnPuul0Ori5uSE1NRWurq7P9gGJiIioSBXk/G2xW1QJCQlwd3dXghsACA8Ph4ODA/bt2/fU9/7www+oWLEi6tati/Hjx+PBgwdm+w0KClKCGwBo3bo1dDodTp48meP+0tPTodPpzB5ERESkXha7RZWUlARPT0/zP+boiPLlyyMpKSnX93Xv3h1+fn7w9fXFsWPHMHbsWJw9exaxsbHKfk2DGwDK89z2O336dEyaNOmffBwiIiKyIwUOcMaNG4dPP/30qWVOnz79zBUaOHCg8v9BQUHw8fFBy5YtcfHiRQQGBj7TPsePH49Ro0Ypz3U6HSpVqvTMdSQiIiLbVuAAJyoqCn369HlqmSpVqsDb2xs3b940256ZmYm7d+/C29s7338vJCQEAHDhwgUEBgbC29sb+/fvNyuTnJwMALnu19nZGc7Ozvn+m0RERGTfChzgeHh4wMPDI89yzZo1Q0pKCg4dOoRGjRoBALZv3w6DwaAELflx5MgRAICPj4+y36lTp+LmzZvKLbAtW7bA1dUVtWvXLuCnISIiIjWy2CDjWrVqISIiAgMGDMD+/fuxe/duDBs2DN26dVNmUF2/fh01a9ZUemQuXryIyZMn49ChQ7h8+TLWr1+PXr164eWXX8YLL7wAAGjVqhVq166Nnj174ujRo9i8eTMmTpyIoUOHspeGiIiIAFg40d8PP/yAmjVromXLlmjTpg1eeuklfPPNN8rrGRkZOHv2rDJLysnJCVu3bkWrVq1Qs2ZNREVFoXPnzvjll1+U92i1WmzYsAFarRbNmjXD22+/jV69epnlzSEiIqLizWJ5cGwZ8+AQERHZH5vIg0NERERkLQxwiIiISHUY4BAREZHqMMAhIiIi1WGAQ0RERKrDAIeIiIhUhwEOERERqQ4DHCIiIlIdBjhERESkOgxwiIiISHUY4BAREZHqMMAhIiIi1WGAQ0RERKrDAIeIiIhUhwEOERERqQ4DHCIiIlIdBjhERESkOgxwiIiISHUY4BAREZHqMMAhIiIi1WGAQ0RERKrDAIeIiIhUhwEOERERqQ4DHCIiIlIdBjhERESkOgxwiIiISHUY4BAREZHqMMAhIiIi1WGAQ0RERKrDAIeIiIhUhwEOERERqQ4DHCIiIlIdBjhERESkOgxwiIiISHUY4BAREZHqWDTAuXv3Lnr06AFXV1e4u7ujX79+uHfvXq7lL1++DI1Gk+Pj559/Vsrl9PqKFSss+VGIiIjIjjhacuc9evRAYmIitmzZgoyMDPTt2xcDBw5ETExMjuUrVaqExMREs23ffPMNZs6ciddee81s+5IlSxAREaE8d3d3L/T6ExERkX2yWIBz+vRpbNq0CQcOHEDjxo0BAPPnz0ebNm0wa9Ys+Pr6ZnuPVquFt7e32bY1a9aga9euKFOmjNl2d3f3bGWJiIiIAAveokpISIC7u7sS3ABAeHg4HBwcsG/fvnzt49ChQzhy5Aj69euX7bWhQ4eiYsWKCA4OxnfffQcRyXU/6enp0Ol0Zg8iIiJSL4v14CQlJcHT09P8jzk6onz58khKSsrXPhYvXoxatWqhefPmZts/+eQTvPrqqyhVqhR+//13vPvuu7h37x6GDx+e436mT5+OSZMmPdsHISIiIrtT4B6ccePG5ToQ2Pg4c+bMP67Yw4cPERMTk2PvzYcffogXX3wRDRo0wNixY/HBBx9g5syZue5r/PjxSE1NVR5Xr179x/UjIiIi21XgHpyoqCj06dPnqWWqVKkCb29v3Lx502x7ZmYm7t69m6+xM6tWrcKDBw/Qq1evPMuGhIRg8uTJSE9Ph7Ozc7bXnZ2dc9xORERE6lTgAMfDwwMeHh55lmvWrBlSUlJw6NAhNGrUCACwfft2GAwGhISE5Pn+xYsXo3379vn6W0eOHEG5cuUYxBAREREAC47BqVWrFiIiIjBgwAAsXLgQGRkZGDZsGLp166bMoLp+/TpatmyJZcuWITg4WHnvhQsXsHPnTvz666/Z9vvLL78gOTkZTZs2hYuLC7Zs2YJp06Zh9OjRlvooREREZGcsmgfnhx9+wLBhw9CyZUs4ODigc+fOmDdvnvJ6RkYGzp49iwcPHpi977vvvsPzzz+PVq1aZdtniRIlsGDBAowcORIigqpVq2LOnDkYMGCAJT8KERER2RGNPG1+tUrpdDq4ubkhNTUVrq6u1q4OERER5UNBzt9ci4qIiIhUhwEOERERqQ4DHCIiIlIdBjhERESkOgxwiIiISHUY4BAREZHqMMAhIiIi1WGAQ0RERKrDAIeIiIhUhwEOERERqQ4DHCIiIlIdBjhERESkOgxwiIiISHUY4BAREZHqMMAhIiIi1WGAQ0RERKrDAIeIiIhUhwEOERERqQ4DHCIiIlIdBjhERESkOgxwiIiISHUY4BAREZHqMMAhIiIi1WGAQ0RERKrDAIeIiIhUhwEOERERqQ4DHCIiIlIdBjhERESkOgxwiIiISHUY4BAREZHqMMAhIiIi1WGAQ0RERKrDAIeIiIhUhwEOERERqQ4DHCIiIlIdBjhERESkOhYLcKZOnYrmzZujVKlScHd3z9d7RAQfffQRfHx8ULJkSYSHh+P8+fNmZe7evYsePXrA1dUV7u7u6NevH+7du2eBT0BERET2ymIBzuPHj/HGG29gyJAh+X7PZ599hnnz5mHhwoXYt28fSpcujdatW+PRo0dKmR49euDkyZPYsmULNmzYgJ07d2LgwIGW+AhERERkpzQiIpb8A99//z1GjBiBlJSUp5YTEfj6+iIqKgqjR48GAKSmpsLLywvff/89unXrhtOnT6N27do4cOAAGjduDADYtGkT2rRpg2vXrsHX1zfHfaenpyM9PV15npqaisqVK+Pq1atwdXUtnA9KREREFqXT6VCpUiWkpKTAzc3t6YXFwpYsWSJubm55lrt48aIAkD///NNs+8svvyzDhw8XEZHFixeLu7u72esZGRmi1WolNjY2131HR0cLAD744IMPPvjgQwWPq1ev5hlXOMJGJCUlAQC8vLzMtnt5eSmvJSUlwdPT0+x1R0dHlC9fXimTk/Hjx2PUqFHKc4PBgLt376JChQrQaDSF9REA/C+6ZO9Q3vhd5R+/q/zjd5V//K7yj99VwVjq+xIRpKWl5XrHxlSBApxx48bh008/fWqZ06dPo2bNmgXZrcU5OzvD2dnZbFt+Bz4/K1dXVx4E+cTvKv/4XeUfv6v843eVf/yuCsYS31eet6b+vwIFOFFRUejTp89Ty1SpUqUgu1R4e3sDAJKTk+Hj46NsT05ORv369ZUyN2/eNHtfZmYm7t69q7yfiIiIqEABjoeHBzw8PCxSkYCAAHh7e2Pbtm1KQKPT6bBv3z5lJlazZs2QkpKCQ4cOoVGjRgCA7du3w2AwICQkxCL1IiIiIvtjsWniV65cwZEjR3DlyhXo9XocOXIER44cMctZU7NmTaxZswYAoNFoMGLECEyZMgXr16/H8ePH0atXL/j6+qJjx44AgFq1aiEiIgIDBgzA/v37sXv3bgwbNgzdunXL1/24ouDs7Izo6Ohst8QoO35X+cfvKv/4XeUfv6v843dVMLbwfVlsmnifPn2wdOnSbNvj4uIQGhr65I9rNFiyZIly20tEEB0djW+++QYpKSl46aWX8NVXX6F69erK++/evYthw4bhl19+gYODAzp37ox58+ahTJkylvgYREREZIcsngeHiIiIqKhxLSoiIiJSHQY4REREpDoMcIiIiEh1GOAQERGR6jDAsbCNGzciJCQEJUuWRLly5ZQp75Sz9PR01K9fHxqNBkeOHLF2dWzO5cuX0a9fPwQEBKBkyZIIDAxEdHQ0Hj9+bO2q2YwFCxbA398fLi4uCAkJwf79+61dJZszffp0NGnSBGXLloWnpyc6duyIs2fPWrtadmHGjBlKWhPK7vr163j77bdRoUIFlCxZEkFBQTh48KBV6sIAx4JWr16Nnj17om/fvjh69Ch2796N7t27W7taNu2DDz6wmZxGtujMmTMwGAz4+uuvcfLkSXz++edYuHAhJkyYYO2q2YSffvoJo0aNQnR0NA4fPox69eqhdevW2TKgF3d//PEHhg4dir1792LLli3IyMhAq1atcP/+fWtXzaYdOHAAX3/9NV544QVrV8Um/fe//8WLL76IEiVK4LfffsOpU6cwe/ZslCtXzjoVynM5TnomGRkZ8txzz8m3335r7arYjV9//VVq1qwpJ0+eFCD7yvKUs88++0wCAgKsXQ2bEBwcLEOHDlWe6/V68fX1lenTp1uxVrbv5s2bAkD++OMPa1fFZqWlpUm1atVky5Yt8sorr8j7779v7SrZnLFjx8pLL71k7Woo2INjIYcPH8b169fh4OCABg0awMfHB6+99hpOnDhh7arZpOTkZAwYMAD/93//h1KlSlm7OnYlNTUV5cuXt3Y1rO7x48c4dOgQwsPDlW0ODg4IDw9HQkKCFWtm+1JTUwGAv6OnGDp0KNq2bWv2+yJz69evR+PGjfHGG2/A09MTDRo0wKJFi6xWHwY4FvLXX38BAD7++GNMnDgRGzZsQLly5RAaGoq7d+9auXa2RUTQp08fDB48GI0bN7Z2dezKhQsXMH/+fAwaNMjaVbG627dvQ6/Xw8vLy2y7l5cXkpKSrFQr22cwGDBixAi8+OKLqFu3rrWrY5NWrFiBw4cPY/r06dauik3766+/8J///AfVqlXD5s2bMWTIEAwfPjzHVQ2KAgOcAho3bhw0Gs1TH8ZxEgDw73//G507d0ajRo2wZMkSaDQa/Pzzz1b+FEUjv9/V/PnzkZaWhvHjx1u7ylaT3+/K1PXr1xEREYE33ngDAwYMsFLNyd4NHToUJ06cwIoVK6xdFZt09epVvP/++/jhhx/g4uJi7erYNIPBgIYNG2LatGlo0KABBg4ciAEDBmDhwoVWqU+BVhMnICoqSlk7KzdVqlRBYmIiAKB27drKdmdnZ1SpUgVXrlyxZBVtRn6/q+3btyMhISHbomyNGzdGjx49rBb9F6X8fldGN27cQFhYGJo3b45vvvnGwrWzDxUrVoRWq0VycrLZ9uTkZHh7e1upVrZt2LBh2LBhA3bu3Innn3/e2tWxSYcOHcLNmzfRsGFDZZter8fOnTvx5ZdfIj09HVqt1oo1tB0+Pj5m5zzgySLZq1evtkp9GOAUkIeHBzw8PPIs16hRIzg7O+Ps2bN46aWXAAAZGRm4fPky/Pz8LF1Nm5Df72revHmYMmWK8vzGjRto3bo1fvrpJ4SEhFiyijYjv98V8KTnJiwsTOkVdHBgRywAODk5oVGjRti2bZuSjsFgMGDbtm0YNmyYdStnY0QE7733HtasWYMdO3YgICDA2lWyWS1btsTx48fNtvXt2xc1a9bE2LFjGdyYePHFF7OlGzh37pzVznkMcCzE1dUVgwcPRnR0NCpVqgQ/Pz/MnDkTAPDGG29YuXa2pXLlymbPjSvDBwYG8qoyi+vXryM0NBR+fn6YNWsWbt26pbzGXgpg1KhR6N27Nxo3bozg4GDMnTsX9+/fR9++fa1dNZsydOhQxMTEYN26dShbtqwyRsnNzQ0lS5a0cu1sS9myZbONTSpdujQqVKjAMUtZjBw5Es2bN8e0adPQtWtX7N+/H998843VepkZ4FjQzJkz4ejoiJ49e+Lhw4cICQnB9u3brZcTgOzeli1bcOHCBVy4cCFb8CciVqqV7XjzzTdx69YtfPTRR0hKSkL9+vWxadOmbAOPi7v//Oc/AIDQ0FCz7UuWLMnzVilRbpo0aYI1a9Zg/Pjx+OSTTxAQEIC5c+eiR48eVqmPRtgqEhERkcrw5j0RERGpDgMcIiIiUh0GOERERKQ6DHCIiIhIdRjgEBERkeowwCEiIiLVYYBDREREqsMAh4iIiFSHAQ4RERGpDgMcIiIiUh0GOERERKQ6/w9EL0oJCi0PfAAAAABJRU5ErkJggg==\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-6, 6, 70, requires_grad=False)\n",
    "target_y = np.array([target_function(x_) for x_ in x], requires_grad=False)\n",
    "\n",
    "plt.plot(x, target_y, c='black')\n",
    "plt.scatter(x, target_y, facecolor='white', edgecolor='black')\n",
    "plt.ylim(-1, 1)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Send it after class\n",
    "\n",
    "To reproduce the figures in the paper, you can use the following settings in the cells above:\n",
    "\n",
    "-   For the settings\n",
    "\n",
    "        degree = 1\n",
    "        coeffs = (0.15 + 0.15j) * degree \n",
    "        coeff0 = 0.1\n",
    "\n",
    "    this function is the ground truth\n",
    "    $g(x) = \\sum_{n=-1}^1 c_{n} e^{-nix}$ from Figure 3 in the paper.\n",
    "\n",
    "-   To get the ground truth $g'(x) = \\sum_{n=-2}^2 c_{n} e^{-nix}$ with\n",
    "    $c_0=0.1$, $c_1 = c_2 = 0.15 - 0.15i$ from Figure 3, you need to\n",
    "    increase the degree to two:\n",
    "\n",
    "        degree = 2\n",
    "\n",
    "-   The ground truth from Figure 4 can be reproduced by changing the\n",
    "    settings to:\n",
    "\n",
    "        degree = 5 \n",
    "        coeffs = (0.05 + 0.05j) * degree \n",
    "        coeff0 = 0.0 \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define the serial quantum model\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now define the quantum model itself.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "scaling = 1\n",
    "\n",
    "dev = qml.device('default.qubit', wires=1)\n",
    "\n",
    "def S(x):\n",
    "    \"\"\"Data-encoding circuit block.\"\"\"\n",
    "    qml.RX(scaling * x, wires=0)\n",
    "\n",
    "def W(theta):\n",
    "    \"\"\"Trainable circuit block.\"\"\"\n",
    "    qml.Rot(theta[0], theta[1], theta[2], wires=0)\n",
    "\n",
    "    \n",
    "@qml.qnode(dev)\n",
    "def serial_quantum_model(weights, x):\n",
    "    \n",
    "    for theta in weights[:-1]:\n",
    "        W(theta)\n",
    "        S(x)\n",
    "        \n",
    "    # (L+1)'th unitary\n",
    "    W(weights[-1])\n",
    "    \n",
    "    return qml.expval(qml.PauliZ(wires=0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can run the following cell multiple times, each time sampling\n",
    "different weights, and therefore different quantum models.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = 1 # number of times the encoding gets repeated (here equal to the number of layers)\n",
    "weights = 2 * np.pi * np.random.random(size=(r+1, 3), requires_grad=True) # some random initial weights\n",
    "\n",
    "x = np.linspace(-6, 6, 70, requires_grad=False)\n",
    "random_quantum_model_y = [serial_quantum_model(weights, x_) for x_ in x]\n",
    "\n",
    "plt.plot(x, random_quantum_model_y, c='blue')\n",
    "plt.ylim(-1,1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "No matter what weights are picked, the single qubit model for\n",
    "[L=1]{.title-ref} will always be a sine function of a fixed frequency.\n",
    "The weights merely influence the amplitude, y-shift, and phase of the\n",
    "sine.\n",
    "\n",
    "This observation is formally derived in Section II.A of the paper.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Send it after class\n",
    "\n",
    "Increase the number of layers. Figure 4 from the paper, for example, uses the settings `L=1`, `L=3` and `L=5`. What is the difference?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, let\\'s look at the circuit we just created:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0: ──Rot(2.35,5.97,4.60)──RX(6.00)──Rot(3.76,0.98,0.98)─┤  <Z>\n"
     ]
    }
   ],
   "source": [
    "print(qml.draw(serial_quantum_model)(weights, x[-1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fit the model to the target"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next step is to optimize the weights in order to fit the ground\n",
    "truth.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost at step  10: 0.03212041720004567\n",
      "Cost at step  20: 0.01385356188302468\n",
      "Cost at step  30: 0.004049396436389442\n",
      "Cost at step  40: 0.0005624933894468399\n",
      "Cost at step  50: 8.145777333271303e-05\n"
     ]
    }
   ],
   "source": [
    "def cost(weights, x, y):\n",
    "    predictions = [serial_quantum_model(weights, x_) for x_ in x]\n",
    "    return square_loss(y, predictions)\n",
    "\n",
    "max_steps = 50\n",
    "opt = qml.AdamOptimizer(0.3)\n",
    "batch_size = 25\n",
    "cst = [cost(weights, x, target_y)]  # initial cost\n",
    "\n",
    "for step in range(max_steps):\n",
    "\n",
    "    # Select batch of data\n",
    "    batch_index = np.random.randint(0, len(x), (batch_size,))\n",
    "    x_batch = x[batch_index]\n",
    "    y_batch = target_y[batch_index]\n",
    "\n",
    "    # Update the weights by one optimizer step\n",
    "    weights, _, _ = opt.step(cost, weights, x_batch, y_batch)\n",
    "\n",
    "    # Save, and possibly print, the current cost\n",
    "    c = cost(weights, x, target_y)\n",
    "    cst.append(c)\n",
    "    if (step + 1) % 10 == 0:\n",
    "        print(\"Cost at step {0:3}: {1}\".format(step + 1, c))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To continue training, you may just run the above cell again. Once you are happy, you can use the trained model to predict function values, and compare them with the ground truth.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "predictions = [serial_quantum_model(weights, x_) for x_ in x]\n",
    "\n",
    "plt.plot(x, target_y, c='black')\n",
    "plt.scatter(x, target_y, facecolor='white', edgecolor='black')\n",
    "plt.plot(x, predictions, c='blue')\n",
    "plt.ylim(-1,1)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let\\'s also have a look at the cost during training.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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IQCGCMUAAAJiHABQi6AIDAMA8BKAQER15cjsMAhAAAB2OABQiYlgHCAAA0xCAQkSMqzEAsRI0AAAdjwAUImLoAgMAwDQEoBBBFxgAAOYhAIUIVoIGAMA8BKAQEWwBqicAAQDQ0QhAIaJpJWhagAAA6HgEoBDR1ALk8TIGCACAjkYAChF0gQEAYB4CUIhgEDQAAOY5pwD06KOPqqam5rTjtbW1evTRR9tcVDhqGgPEXmAAAHS8cwpA8+bNU3V19WnHa2pqNG/evDYXFY5O7QbfIMMwLK4GAICu7ZwCkGEYstlspx3fsmWLunfv3uaiwlFTAAoYkrchYHE1AAB0bRGtOTkpKUk2m002m02DBg1qFoL8fr+qq6t1++23t3uR4aCpC0xqHAcUFemwsBoAALq2VgWgBQsWyDAM3XzzzZo3b54SEhKCzzmdTmVlZSk3N7fdiwwHDrtNzgi7fA0B1fga1D3WaXVJAAB0Wa0KQDNmzJAkZWdn66KLLlJERKtejq8R43TI1xBgIDQAAB3snMYAdevWTbt27Qp+/8Ybb2jq1Kl68MEH5fP52q24cBMTyVR4AADMcE4B6Ic//KE+/fRTSdLnn3+uadOmKSYmRkuXLtX999/frgWGkxhXY4uahx3hAQDoUOcUgD799FONGjVKkrR06VJNnDhRr776qhYvXqy//vWv7VlfWAmuBk0LEAAAHeqcp8EHAo1Ttd99911dccUVkqTMzEyVlpa2X3VhJpouMAAATHFOAWjs2LF67LHH9Pvf/16rVq3SlVdeKUkqLCxUSkpKuxYYTmgBAgDAHOcUgBYsWKBNmzbprrvu0k9/+lMNGDBAkvSXv/xFF154YbsWGE6a1gKqYQwQAAAd6pzmsY8YMULbtm077fhTTz0lh4MF/M5VUwuQhxYgAAA6VJsW8tm4cWNwOvywYcM0evTodikqXNEFBgCAOc4pAJWUlGjatGlatWqVEhMTJUnl5eX61re+pSVLlqhnz57tWWPYiA52gRGAAADoSOc0Bujuu+9WdXW1duzYoePHj+v48ePavn27Kisr9V//9V/tXWPYCLYA1TMGCACAjnROLUDLly/Xu+++q6FDhwaPDRs2TAsXLtTkyZPbrbhw0xSAaAECAKBjnVMLUCAQUGRk5GnHIyMjg+sDofVi6AIDAMAU5xSALr30Us2cOVNHjx4NHjty5Ih+/OMfa9KkSe1WXLg51QJEFxgAAB3pnALQ888/r8rKSmVlZal///7q37+/srOzVVlZqeeee669awwb0XSBAQBginMaA5SZmalNmzbp3Xff1e7duyVJQ4cOVV5eXrsWF26YBg8AgDla1QL03nvvadiwYaqsrJTNZtNll12mu+++W3fffbfGjRun4cOH68MPP+yoWrs8BkEDAGCOVgWgBQsW6NZbb1V8fPxpzyUkJOiHP/yhnnnmmXYrLtxERzIIGgAAM7QqAG3ZskVTpkw54/OTJ0/Wxo0b21xUuIp1MQgaAAAztCoAFRcXtzj9vUlERISOHTvW5qLCVXRwIUS/DMOwuBoAALquVgWgjIwMbd++/YzPb926VWlpaW0uKlw1rQNkGFJdPespAQDQUVoVgK644go9/PDDqqurO+252tpazZ07V1dddVW7FRduoiMdwa/pBgMAoOO0ahr8Qw89pP/7v//ToEGDdNddd2nw4MGSpN27d2vhwoXy+/366U9/2iGFhgOH3SZXhF3ehoBqfH71sLogAAC6qFYFoJSUFH388ce64447NHv27OA4FZvNpvz8fC1cuFApKSkdUmi4iHVFyNvgYyYYAAAdqNULIfbt21dvvfWWTpw4ob1798owDA0cOFBJSUkdUV/YaeoGowsMAICOc04rQUtSUlKSxo0b1561QKwGDQCAGc5pLzB0HFaDBgCg4xGAQkxwQ9R6AhAAAB3F8gC0cOFCZWVlKSoqSjk5OVq3bt0Zz92xY4euueYaZWVlyWazacGCBW2+ZqiJPbkWUI2XMUAAAHQUSwPQa6+9plmzZmnu3LnatGmTRo4cqfz8fJWUlLR4fk1Njfr166fHH39cqamp7XLNUBNNFxgAAB3O0gD0zDPP6NZbb9VNN92kYcOGadGiRYqJidHLL7/c4vnjxo3TU089peuuu04ul6tdrhlqYr6wHQYAAOgYlgUgn8+njRs3Ki8v71Qxdrvy8vK0evVqU6/p9XpVWVnZ7GGVpu0wmAYPAEDHsSwAlZaWyu/3n7ZwYkpKitxut6nXnD9/vhISEoKPzMzMc/r57YEuMAAAOp7lg6BDwezZs1VRURF8HDp0yLJaYpsCkJcABABARznnhRDbKjk5WQ6HQ8XFxc2OFxcXn3GAc0dd0+VynXFMkdl6dmuso7DMY3ElAAB0XZa1ADmdTo0ZM0YFBQXBY4FAQAUFBcrNzQ2Za5ptbFZ3SdLmQ+WqYyA0AAAdwrIWIEmaNWuWZsyYobFjx2r8+PFasGCBPB6PbrrpJknS9OnTlZGRofnz50tqHOS8c+fO4NdHjhzR5s2bFRcXpwEDBpzVNUNdv+RYJce5VFrt1dbDFRqf3d3qkgAA6HIsDUDTpk3TsWPHNGfOHLndbo0aNUrLly8PDmI+ePCg7PZTjVRHjx7VBRdcEPz+6aef1tNPP62JEydq5cqVZ3XNUGez2ZST3V3/2FakdYVlBCAAADqAzTAMw+oiQk1lZaUSEhJUUVGh+Ph403/+Kx/v19y/7dAlA5P1+x/kmP7zAQDojFrz+c0ssBDU1Oqz8cAJ1fsDFlcDAEDXQwAKQYNTuikhOlI1Pr92HLVuUUYAALoqAlAIstttGndyNti6wjKLqwEAoOshAIWonOymAHTc4koAAOh6CEAhavwXApA/wDh1AADaEwEoRA1Pj1es06HKugbtcVdZXQ4AAF0KAShERTjsGsM4IAAAOgQBKIQFxwHtZxwQAADtiQAUwr44Doj1KgEAaD8EoBA2oneCXBF2lVb7tO8Yu8MDANBeCEAhzBXh0AV9EiUxHR4AgPZEAApx47N7SGIgNAAA7YkAFOKaBkKvZRwQAADthgAU4i7ok6gIu01FFXU6fKLW6nIAAOgSCEAhLsYZoRG9EyQ1tgIBAIC2IwB1AowDAgCgfRGAOgE2RgUAoH0RgDqBMVlJstuk/WU1Kq6ss7ocAAA6PQJQJxAfFalh6fGSGAcEAEB7IAB1EuOzGAcEAEB7IQB1EuMZBwQAQLshAHUSTQHo0+JqHff4LK4GAIDOjQDUSXSPdWpQSpwkWoEAAGgrAlAnQjcYAADtgwDUiQQXRNzPQGgAANqCANSJNC2IuPNopSrr6i2uBgCAzosA1ImkxEcpq0eMAoa0cf8Jq8sBAKDTIgB1Mk3jgFgQEQCAc0cA6mTYGBUAgLYjAHUyTeOAth6uUK3Pb3E1AAB0TgSgTqZ3UrTSE6LUEDC06SDjgAAAOBcEoE7GZrOdGgf0Od1gAACcCwJQJ3TRgGRJ0pL1h+gGAwDgHBCAOqF/G5Wu3knRKqny6uWPCq0uBwCATocA1Am5Ihy6d/IgSdKiVftUXsPmqAAAtAYBqJO6emSGhqbFq6quQS+s3Gd1OQAAdCoEoE7Kbrfp/imDJUmLP96vI+W1FlcEAEDnQQDqxL45qKdysrvL1xDQghWfWl0OAACdBgGoE7PZbPrvy4dIkv666bA+K66yuCIAADoHAlAnN7pPkvKHpyhgSE/+c4/V5QAA0CkQgLqAn+QPlt0mrdhZrI0H2CQVAICvQwDqAgb06qbvjc2UJD3+9m4ZhmFxRQAAhDYCUBdxT94guSLsWr//hN7bXWJ1OQAAhDQCUBeRmhClGy/KkiQ9uXyP/AFagQAAOBMCUBfyo4kDFB8VoT3FVVr2yRGrywEAIGQRgLqQhJhI3fHNAZKkZ1Z8Km8DG6UCANASAlAXc+OFWUqJd+lIea3+sOag1eUAABCSCEBdTLTToR/nNW6U+vx7n6myrt7iigAACD0EoC7ou2N6q3/PWJ2oqddv/7Xf6nIAAAg5BKAuKMJh1w+/0V+S9OFnxyyuBgCA0EMA6qJGZiZKkna7qxRgSjwAAM0QgLqofj1j5XTYVe1t0OETtVaXAwBASCEAdVGRDrsGpsRJkna5Ky2uBgCA0EIA6sKGpMZLknYVEYAAAPgiAlAXNjStmyQCEAAAX0YA6sKGpTW1AFVZXAkAAKGFANSFDTkZgA4er1G1t8HiagAACB0EoC6se6xTKfEuSdIeBkIDABBEAOrihp5sBdpJNxgAAEEEoC5uaBozwQAA+DICUBfXFIB2E4AAAAgiAHVxQ1Mbp8KzJQYAAKcQgLq47ORYOSPsqvH5dfB4jdXlAAAQEghAXVyEw67BKSyICADAFxGAwkBwRWg3M8EAAJAIQGGBPcEAAGiOABQGmAoPAEBzBKAw0LQn2OETtaqsq7e4GgAArEcACgMJMZFKT4iSJO1hHBAAAASgcDGEbjAAAIJCIgAtXLhQWVlZioqKUk5OjtatW/eV5y9dulRDhgxRVFSUzj//fL311lvNnr/xxhtls9maPaZMmdKRbyHkBWeCEYAAALA+AL322muaNWuW5s6dq02bNmnkyJHKz89XSUlJi+d//PHHuv766/WDH/xAn3zyiaZOnaqpU6dq+/btzc6bMmWKioqKgo8//elPZrydkHVqIDRdYAAA2AzDsHR/hJycHI0bN07PP/+8JCkQCCgzM1N33323HnjggdPOnzZtmjwej958883gsQkTJmjUqFFatGiRpMYWoPLyci1btuysavB6vfJ6vcHvKysrlZmZqYqKCsXHx7fh3YWOfceqNekXqxQd6dD2efly2G1WlwQAQLuqrKxUQkLCWX1+W9oC5PP5tHHjRuXl5QWP2e125eXlafXq1S2+ZvXq1c3Ol6T8/PzTzl+5cqV69eqlwYMH64477lBZWdkZ65g/f74SEhKCj8zMzDa8q9CU1SNWUZF21db7daDMY3U5AABYytIAVFpaKr/fr5SUlGbHU1JS5Ha7W3yN2+3+2vOnTJmi3/3udyooKNATTzyhVatW6fLLL5ff72/xmrNnz1ZFRUXwcejQoTa+s9DjsNu+sCUG3WAAgPAWYXUBHeG6664Lfn3++edrxIgR6t+/v1auXKlJkyaddr7L5ZLL5TKzREsMTYvXlsMV2u2u1JUj0qwuBwAAy1jaApScnCyHw6Hi4uJmx4uLi5Wamtria1JTU1t1viT169dPycnJ2rt3b9uL7sSGpDITDAAAyeIA5HQ6NWbMGBUUFASPBQIBFRQUKDc3t8XX5ObmNjtfklasWHHG8yXp8OHDKisrU1paeLd6MBMMAIBGlk+DnzVrll566SW98sor2rVrl+644w55PB7ddNNNkqTp06dr9uzZwfNnzpyp5cuX6xe/+IV2796tRx55RBs2bNBdd90lSaqurtZPfvITrVmzRvv371dBQYGuvvpqDRgwQPn5+Za8x1DRtBjikfJaVdSwJQYAIHxZPgZo2rRpOnbsmObMmSO3261Ro0Zp+fLlwYHOBw8elN1+KqddeOGFevXVV/XQQw/pwQcf1MCBA7Vs2TKdd955kiSHw6GtW7fqlVdeUXl5udLT0zV58mT97Gc/C4txPl8lITpSGYnROlJeq93uSuX062F1SQAAWMLydYBCUWvWEehsbnllvd7dVaJHvj1MN16UbXU5AAC0m06zDhDMxzggAAAIQGGnKQDtdjMTDAAQvghAYaYpAO0prpI/QO8nACA8EYDCTJ/uMYqOdKiuPqDCUrbEAACEJwJQmHHYbRrMgogAgDBHAApDoToOqN4f0B/XHtCKncWqq2953zYAANqD5esAwXzD0kJvU1TDMPTQ69v12obGjWhjnQ5dOjRFl5+Xqm8O7qkYJ7+qAID2w6dKGBoSnAofOi1Av/6wUK9tOCS7TerVLUruyjr9fctR/X3LUUVF2jVxUE9dfl6aLh3aS/FRkVaXCwDo5AhAYahpU9SiijqV1/iUGOO0tJ53dxbrf97eJUn66ZXDdNOFWdpyuFxvb3fr7e1FOnS8Vv/cUax/7iiW02HXxQOTdfelA3RBnyRL6wYAdF6MAQpD3aIildk9WpL13WC7iio1c8knMgzp+vF9dPNFWbLbbbqgT5IevGKoPvjJt/Tm3Rfrrm8NUP+esfL5A3pvd4mmv7xO+5nFBgA4RwSgMDU01fpusGNVXt3yygZ5fH5d2L+HHr16uGw2W7NzbDabzstI0H35g1Vw7ze14sff0Og+iaqqa9Dtf9ioWh+DpQEArUcAClNWjwOqq/frh7/foCPltcpOjtULN4xWpOPrfx0HpnTTCzeMUXKcU7vdVXpo2XaxnR0AoLUIQGEqOBPMgqnwhmHov/+6VZsOlis+KkK/mTG2VeOQUhOi9Oz1F8huk/666bD+tO5QB1YLAOiKCEBhqmktoE+Lq9XgD5j6s59/b6/e2HxUDrtNL35/jPr1jGv1NS7sn6z7pwyRJD3ytx3acqi8nasEAHRlBKAwlZkUo1inQ74Gc7fEeGtbkX6x4lNJ0qNXD9dFA5LP+Vo//EY/TR6WIp8/oB/9cZNOeHztVSYAoIsjAIUp+xe2xNhp0jigrYfLNevPmyVJN12UpRty+rbpejabTU9/b6SyesToSHmtZr62mQ1eAQBnhQAUxk5tidHxU+GPVXl16+82qK4+oG8O7qmHrhzWLteNj4rUi98fo6hIuz749JieLfisXa4LAOjaCEBh7LyMBEnS+7tLOnwm1f9791MVV3o1sFecnrv+Ajnstq9/0Vkamhav//n38yVJz773md7fU9Ju1wYAdE0EoDB2xXlpinNFaLe7SgW7Oi407C/16M/rG2dqPTb1PHXrgK0svjO6t74/oY8MQ7pnyWYdOl7T7j8DANB1EIDCWEJMpL4/oXEczvPv7+2wVqBnVnyqhoChiYN6Kqdfjw75GZL08FXDNDIzURW19frRHzexozwA4IwIQGHuBxdnyxVh1+ZD5Vq9r6zdr7/zaKX+tuWoJOkn+YPb/fpf5Ipw6IUbRispJlLbjlTof97a1aE/DwDQeRGAwlzPbi5dNy5TUmMrUHt7+p09kqQrR6QFxxx1pIzEaC247gJJ0h/WHNC+Y9Ud/jMBAJ0PAQi6bWJ/Rdht+nhfmTYdPNFu192w/7je210ih92mey8b1G7X/ToTB/VU3tAUBYzG7jcAAL6MAARlJEbrO6MzJEkvtFMrkGEYenJ5Y+vPtWN6n9Nqz21x7+RBstmkf2wt0vYjFab+bABA6CMAQZJ0+8T+stukd3eVtMsGqSs/PaZ1+4/LGWHXzLyB7VBh6wxNi9e/jUyXJP3iZDccAABNCECQJPXrGacrzk+TJL2wcl+brhUIGHrqZOvP9Al9lZYQ3eb6zsWP8wbJYbfp/T3HtH7/cUtqAACEJgIQgn70zQGSpH9sPdqm/cH+sa1IO4sqFeeK0I++NaC9ymu1rORYfW9s4wDvp5bv6fDFHgEAnQcBCEHD0uM1aUgvBQxp0Tm2AtX7A8GBx7dckq3usc72LLHV/mvSADkj7Fq3/7g++KzU0loAAKGDAIRm7ry0scXm/z45rKPlta1+/V82HlZhqUfdY5265ZJ+7V1eq6UlRGv6ycUen/rnblqBAACSCED4ktF9kpTbr4fq/YZ+9cHnrXptXb1f//tu42akP/pmf8W5IjqixFa745v9Fet0aPuRSi3f7ra6HABACCAA4TR3nWwF+tO6gyqt9p71636/+oDclXVKT4gKbrERCnrEufSDk61RT7+zR/4ArUAAEO4IQDjNhf17aGRmorwNAf3mX4Vn9Zqqunq9sLJxDaGZeQMVFenoyBJb7dZLspUYE6l9xzx6/ZMjVpcDALAYAQinsdlsuuvk7K3frz6gitr6r33NSx8W6kRNvfr1jNU1o3t3dImt1i0qUj/6Zn9J0v9b8am8DWyUCgDhjACEFk0a0ktDUrup2tug3328v8Vz6ur92njghH77UaF+82HjeKF7LxusCEdo/lpNz81SSrxLR8prtWTdIavLAQBYKDRGqSLk2O023fHN/pq5ZLNe/qhQN16UpaKKOm0+VK4th8q15XC5dhdVqeEL42lG9E7Q5eelWlj1V4uKdOjuSwfqoWXb9dx7e3Xt2N6KcfJXAADCkc1gXvBpKisrlZCQoIqKCsXHx1tdjmX8AUOTfrFS+8tqFOmwqd5/+q9Kj1inRmYmamTvRE3P7aski9f9+Tq+hoDynlmlg8drdP+UwcHFHwEAnV9rPr/55y/OyGG36a5LB+q+pVtU7zcU43TovIwEjToZeEZmJigjMVo2m83qUs+aM8KuH182UD9+bYsWrdynG3L6KiE60uqyAAAmIwDhK10zOkN9uscoITpSA3rFyWHvPGHnTP5tZIZeXLlPnxZX61cf7NNP8odYXRIAwGShOVoVIcNms2l8dncNTu3WJcKP1Niyde/kwZKkX39YqMMnaiyuCABgNgIQwtLkYSnKye4ub0NA89/abXU5AACTEYAQlmw2mx75t+Gy2xp3r1+9r8zqkgAAJiIAIWwNTYvXDTmNW3bM+/sONfgDFlcEADALAQhhbdZlg5QQHand7ir9aT2LIwJAuCAAIawlxTp17+RBkqRfvLNH5TU+iysCAJiBAISw9x/j+2hIajeV19TrmRWfWl0OAMAEBCCEvQiHXXO+PUyS9Ic1B7TbXWlxRQCAjkYAAiRd2D9ZV5yfqoAhzfvbTrFDDAB0bQQg4KQHrxgqV4Rdqz8v09vb3VaXAwDoQAQg4KTeSTH64cT+kqSf/2OX6ur9FlcEAOgo7AUGfMEdE/vrLxsO6Uh5rX656nPNzBtodUkhpa7eryPltTp0vEaHTtTqyIlapSdG6epRGWwqC6BTsRkMdjhNZWWlEhISVFFRofj4eKvLgcn+vuWo7v7TJ4qKtKvg3m8qIzHa6pJM5w8Yem93ibYdLtehE02Bp0bFld4Wz4+OdGjqBen6zwlZGpbO3xkA1mjN5zcBqAUEoPBmGIam/WqN1hUe15Uj0rTwP0ZbXZJp6v0BLfvkiF5ctU+fH/O0eE6M06HMpBhldo9WemK01n5+XHuKq4LPj+2bpP/M7asp56XKFeEwq3QAIAC1FQEIO45W6NvP/UsBQ1py2wRN6NfD6pI6VF29X0s3HNKiVZ/rSHmtJCkhOlJThqeqb3LMycATo8ykaHWPdcpmswVfaxiG1u8/od+t3q/l291qCDT+LyU5zqlp4zL1Hzl9w7IVDYD5CEBtRACCJP309W3649qD6p0UrSW3TVDvpBirS2p31d4G/XHNAb30YaFKqxu7t5LjnLrlkn76/oS+inO1bphgSWWdlqw/pFfXHpS7sk6SZLdJ14zurZ//+/lyRjDvAkDHIQC1EQEIknTC49PUFz7SgbIaZSRG69Vbc9S3R6zVZZ2m2tugnUcrtf1IhbYfrdDOo5XyBwwlx7nUI86p5DiXkuOc6hHnCh6Lj4rUm1uP6rcf7VdFbb0kKT0hSj+c2F/TxmUqKrJtXVf1/oDe3Vms360+oNWfl0mS8ob20sIbRtMtBqDDEIDaiACEJu6KOv3Hr9fo82MepcZH6Y+35qh/zzjL6qmsq9f2IxXacaRS204GnsJSj9rytzg7OVZ3TOyvqRdkdEgLzapPj+m2322QtyGgS4f00ovfJwQB6BgEoDYiAOGLSqrqdMNLa/VZSbWS41z60605GpjSzZSfXVFbr/WFx7Xm8zKtKSzTjqOVLYadtIQoDU9P0HkZ8RqenqAYp0Ol1V6VVvtUWu1VWbVXZSe/Lq32qczjVf+ecbp9Yn9dcX6aHHbb6RdtRx/tLdUPXlmvuvqAvjW4p178/pg2tzIBwJcRgNqIAIQvK6v26vu/WaddRZXqEevUH27J0dC09v/dqKip17r9JwPP52XaWXR64MlIjNb5GQk6v3eChqc3Bp6e3VztXkt7+3hvqW4+GYImDuqpX/4nIQhA+yIAtREBCC0pr/HpP3+zTtuOVCgxJlK/vzlH5/dOaPN1D5R59I9tRVq+3a1tRypOCzz9esYqJ7uHJvTrrgn9eiglPqrNP9Mqq/eV6ebF61Vb79clA5P10vSxhCAA7YYA1EYEIJxJRW29Zry8TpsPlatbVIReuXm8RvdJavV19pc2hp63thVpx9Hmu8/36xmrCf16ND6yu6tXJw48LVnzeWMIqvH5dfGAxhAU7SQEAWg7AlAbEYDwVarq6nXz4vVav/+EYp0OLb55vMZldf/a1xWWevTWtiL9Y2uRdhadCj0Ou00X9u+hK85P06Qhvbpc4GnJusLjuvG361Tj8+vC/j30mxnjOlUIqqip1253pY5Ve9XgN9QQMNTgD6g+YMjvD6ghYKjeb8gfCCjWFaHBqd00NDVeSbFOq0sHujQCUBsRgPB1PN4G3fLKBq3+vEzRkQ7NuDBLDf6Aaur9qvX5VeNrUI2v6Wu/qrz1OnS8Nvj6ptBz5flpmjw8Vd3D8INx/f7juvHldfL4/JrQr7tevnGcYpyhtT1hvT+gz495tNtdqd3uKu0uavyzqKLunK6XEu/SkNR4DUlrDERD0rqpX3Ic6yMB7YQA1EYEIJyNWp9ft/1+gz78rPSszif0nG7jgeOa8fJ6VXsbdEGfRP2/741SVrJ1ay01+ANaV3hcb20v0sYD5dpXUi2fP9DiuRmJ0cpIilakw6YIuz34p8NhU6TdpghH47Gyap92u6t08HhNi9eJdNg0PD1Bl5+XqitHpHXJBTcBsxCA2ogAhLNVV+/Xyx8Vqqi8TjFOh6KdjpN/Rigm0vGFYxEa2CuOLpAWbDxwQje+vE5V3ga5Iuy6d/Ig3XxRtiIc5rSKNPgDWlt4XP/YVqR/bnerzONr9nzcyS6sIandNCQtXkNTu2lQajfFR0W26udUexu0x13V2JpUdOrPKm9Ds/NGZSbqqhFpuuL8NKWzhQjQKgSgNiIAAeY6WFaj2a9v1Ud7G1eNPj8jQU9cM6LDdpZv8Ae0+vMyvbXNrX/ucOv4F0JPUkyk8oen6ltDemlYWrx6J0U32/usPRmGocMnarXq02P6x9YirSksazYLcEzfpGAY6syz/wCzEIDaiAAEmM8wDC3deFiPvblTlXUNirDbdPvE/rrr0gHtMlW+rt6vj/eV6p0dxXpnZ/FpoWfKeam64vw0TejXQ5EmtT59WUlVnZZvd+vNrUVav/94MAzZbNLYvkmacl6appyXyuaywBkQgNqIAARYp6SyTnPe2KHlO9ySpP49Y/XENSM09ixm2n1ZRW29Vu4p0Ts7irVyT4k8Pn/wue6xTuUPT9WV56dpQr/upnW5nS13RZ3e3t44a3DDgRPNnhvRO0FTzkvVlOGp6mfh1ixAqCEAtREBCLDe29uK9PAbO1Ra7ZXNJv3nhL66J2+QYpwORdhtcthtLXZNuSvqtGJXsd7Z4dbqfWVqCJz6X1xqfJQmD09R/vBU5WSHXug5k6PltfrnDrfe3u5u1jIkSYNTujWGofNSNSS1W4d117VWXb1fR8prdcLj03GPTydqfDruqdeJGp/Kqpu+98lzcgxUU9k22Zp9L0muSIf6do9RVnKsspNjlNUjVtnJsUqMYUwdmiMAtREBCAgNFTX1+vlbO/XnDYdbfD7S0RiEIu12RThsctjtKq32NjtnYK845Q9P1eThKTo/IyFkAsK5Olbl1YqdxXp7e9FpAS8jMVpjs5I0uk+SLuiTqKFp8R3enVdRU6+9x6q0t6T61ONYtQ6fqG3TJr1nIzEmMhiGsnrEKutkOMpKjlVCdOsGqXcWhmGo2tug8pp6VdQ2Pqq9DbLbbHLYdfJPmxw2m+wn/6Fgt9nkirCrR5xTyXEuy7p4zdDpAtDChQv11FNPye12a+TIkXruuec0fvz4M56/dOlSPfzww9q/f78GDhyoJ554QldccUXwecMwNHfuXL300ksqLy/XRRddpBdffFEDBw48q3oIQEBo+ddnpXr4je0qLPV87bk2m3RBZqLyh6fqsmEpXbqLqKKmXu/uKtbyHW598OkxeRuaT9mPirRrREaiLuiTqAv6JGl030T16ta6wdT+gKGSqjodPlGrIydqdfhEjY6U16qw1KO9JZ7TAucXxbki1CPOqaQYp7rHNv0ZqaRYp7rHOJUU61Q3V4Rkk3Tyk6jpA+mLn0zV3nrtL6vR/lKPCks92l/mUXHlmX+u1DiuK6spGJ0MR326xyg9MVrJca4O3wD4bNX7Azru8elYlVdlHp/Kqr0nNzD26Vi1V8c9PpXX1Kuytl7lJwOPP3DuH9s2m9Q9xqme3Vzq2c2lXt2i1CvepV7dXEqJj1LvpGj16R6jhOjITvmPhU4VgF577TVNnz5dixYtUk5OjhYsWKClS5dqz5496tWr12nnf/zxx/rGN76h+fPn66qrrtKrr76qJ554Qps2bdJ5550nSXriiSc0f/58vfLKK8rOztbDDz+sbdu2aefOnYqK+vq//AQgIPQYhiFvQ+DUqst+Q/6AoXp/82NN/2MPNx5vgzYdPKFNB8q16eAJfXLwhCrrGk47r3uss3F5hsjGJRqiIhu/bjoW5XSoviGgI+W1OnyiVkUVtar3f/XHRFpClAb0ilP/nnEa0OvUo0ess8M+RGt8DdpfWqP9ZSdDUalHB8pqVFjm0bGqrw5HEXabUuKjlJYQpdSExj/TEqKVltAYBmKcEafdn0hHy12uUmNI9DUEVFfvl7chIG+DXx6vX8c9PpV5GkNM49c+Ha9uPFZ28lh5Tf05vX9nhF2J0ZFKiI5UXFSEDEMKGI1/J/wBI/h1wGisz9vgV1m1r1mL4Vfp5opQ7+4x6tM9WplJMerTI0aZSTHqnRStHnEuJURHhkyI/KJOFYBycnI0btw4Pf/885KkQCCgzMxM3X333XrggQdOO3/atGnyeDx68803g8cmTJigUaNGadGiRTIMQ+np6br33nt13333SZIqKiqUkpKixYsX67rrrvvamghAADq7QMDQ56Wek2GoXJ8cPKE9xVXn1C0VYbcpLTFKvRNjlJEUrd5JjR+KA3rFqX+vOMW5QmsFb4+3QQfKGsPR/rLGcLS/rEaHjteouLJO59KA4rDbGgNipENOh00+f0B19Y1h5+sC4tex26TusS4ln+yiSo5zqkecS8lxLvWIdSoxpjHoJMY4T/4ZeU4zIwMBQydqfCqp8jY+KutUUuXVsSqvSqrq5K6o06ETtV8bIKXGlqTE6OateU1/JsZEynEWwXdkZqLGZ7d+csNXac3nt6W/tT6fTxs3btTs2bODx+x2u/Ly8rR69eoWX7N69WrNmjWr2bH8/HwtW7ZMklRYWCi32628vLzg8wkJCcrJydHq1atbDEBer1de76n/4BUVFZIabyQAdFa9oqQpgxI0ZVCCpL6qqqtXUUWtan1+1dUHVNfgV50voBpfg7wNftXW+1XnM2SzSemJUUpPjFZGYrR6xUed8V/7AW+NvqY3yhK946TecbG6uG/zlcUb/AGVVnvlrqxTcYVX7spauSu9Kq5o/LPM41Wdr/He1Pr8wbAUkFRfK33dp0KE3SZnRGNYSoxp7PbrEdsYDJJinOoeF6mkmFPdgo0Bxyn7WbWmGJJ88tX65Kv92pNbFCkpI1bKiHVJqS23lNb6/DpaXqPD5Y3dnodO1OrIiRodPlGroxW1qq5rnE1ZVieVnWjxEmfllouzNaRH+8aQps/ts2nbsTQAlZaWyu/3KyUlpdnxlJQU7d69u8XXuN3uFs93u93B55uOnemcL5s/f77mzZt32vHMzMyzeyMAAKBV5i6Q5nbQtauqqpSQkPCV54RWu6VFZs+e3axVKRAI6Pjx4+rRo0e7919XVlYqMzNThw4donutA3GfzcF9Ngf32RzcZ3N05H02DENVVVVKT0//2nMtDUDJyclyOBwqLi5udry4uFipqaktviY1NfUrz2/6s7i4WGlpac3OGTVqVIvXdLlccrmaNwUmJia25q20Wnx8PH/BTMB9Ngf32RzcZ3Nwn83RUff561p+mli6GIDT6dSYMWNUUFAQPBYIBFRQUKDc3NwWX5Obm9vsfElasWJF8Pzs7GylpqY2O6eyslJr16494zUBAEB4sbwLbNasWZoxY4bGjh2r8ePHa8GCBfJ4PLrpppskSdOnT1dGRobmz58vSZo5c6YmTpyoX/ziF7ryyiu1ZMkSbdiwQb/61a8kSTabTffcc48ee+wxDRw4MDgNPj09XVOnTrXqbQIAgBBieQCaNm2ajh07pjlz5sjtdmvUqFFavnx5cBDzwYMHZbefaqi68MIL9eqrr+qhhx7Sgw8+qIEDB2rZsmXBNYAk6f7775fH49Ftt92m8vJyXXzxxVq+fPlZrQHU0Vwul+bOnXtalxvaF/fZHNxnc3CfzcF9Nkeo3GfL1wECAAAwW9fdEAQAAOAMCEAAACDsEIAAAEDYIQABAICwQwAy0cKFC5WVlaWoqCjl5ORo3bp1VpfU6X3wwQf69re/rfT0dNlstuCecE0Mw9CcOXOUlpam6Oho5eXl6bPPPrOm2E5q/vz5GjdunLp166ZevXpp6tSp2rNnT7Nz6urqdOedd6pHjx6Ki4vTNddcc9qCpfhqL774okaMGBFcHC43N1dvv/128Hnuccd4/PHHg8unNOFet49HHnlENput2WPIkCHB562+zwQgk7z22muaNWuW5s6dq02bNmnkyJHKz89XSUmJ1aV1ah6PRyNHjtTChQtbfP7JJ5/Us88+q0WLFmnt2rWKjY1Vfn6+6urqTK6081q1apXuvPNOrVmzRitWrFB9fb0mT54sj8cTPOfHP/6x/v73v2vp0qVatWqVjh49qu985zsWVt359O7dW48//rg2btyoDRs26NJLL9XVV1+tHTt2SOIed4T169frl7/8pUaMGNHsOPe6/QwfPlxFRUXBx7/+9a/gc5bfZwOmGD9+vHHnnXcGv/f7/UZ6eroxf/58C6vqWiQZr7/+evD7QCBgpKamGk899VTwWHl5ueFyuYw//elPFlTYNZSUlBiSjFWrVhmG0XhPIyMjjaVLlwbP2bVrlyHJWL16tVVldglJSUnGr3/9a+5xB6iqqjIGDhxorFixwpg4caIxc+ZMwzD4fW5Pc+fONUaOHNnic6Fwn2kBMoHP59PGjRuVl5cXPGa325WXl6fVq1dbWFnXVlhYKLfb3ey+JyQkKCcnh/veBhUVFZKk7t27S5I2btyo+vr6Zvd5yJAh6tOnD/f5HPn9fi1ZskQej0e5ubnc4w5w55136sorr2x2TyV+n9vbZ599pvT0dPXr10833HCDDh48KCk07rPlK0GHg9LSUvn9/uDq1k1SUlK0e/dui6rq+txutyS1eN+bnkPrBAIB3XPPPbrooouCq6+73W45nc7TNhDmPrfetm3blJubq7q6OsXFxen111/XsGHDtHnzZu5xO1qyZIk2bdqk9evXn/Ycv8/tJycnR4sXL9bgwYNVVFSkefPm6ZJLLtH27dtD4j4TgACctTvvvFPbt29v1o+P9jN48GBt3rxZFRUV+stf/qIZM2Zo1apVVpfVpRw6dEgzZ87UihUrQmJ7pK7s8ssvD349YsQI5eTkqG/fvvrzn/+s6OhoCytrRBeYCZKTk+VwOE4b3V5cXKzU1FSLqur6mu4t97193HXXXXrzzTf1/vvvq3fv3sHjqamp8vl8Ki8vb3Y+97n1nE6nBgwYoDFjxmj+/PkaOXKk/vd//5d73I42btyokpISjR49WhEREYqIiNCqVav07LPPKiIiQikpKdzrDpKYmKhBgwZp7969IfE7TQAygdPp1JgxY1RQUBA8FggEVFBQoNzcXAsr69qys7OVmpra7L5XVlZq7dq13PdWMAxDd911l15//XW99957ys7Obvb8mDFjFBkZ2ew+79mzRwcPHuQ+t1EgEJDX6+Uet6NJkyZp27Zt2rx5c/AxduxY3XDDDcGvudcdo7q6Wvv27VNaWlpo/E6bMtQaxpIlSwyXy2UsXrzY2Llzp3HbbbcZiYmJhtvttrq0Tq2qqsr45JNPjE8++cSQZDzzzDPGJ598Yhw4cMAwDMN4/PHHjcTEROONN94wtm7dalx99dVGdna2UVtba3Hlnccdd9xhJCQkGCtXrjSKioqCj5qamuA5t99+u9GnTx/jvffeMzZs2GDk5uYaubm5Flbd+TzwwAPGqlWrjMLCQmPr1q3GAw88YNhsNuOdd94xDIN73JG+OAvMMLjX7eXee+81Vq5caRQWFhofffSRkZeXZyQnJxslJSWGYVh/nwlAJnruueeMPn36GE6n0xg/fryxZs0aq0vq9N5//31D0mmPGTNmGIbROBX+4YcfNlJSUgyXy2VMmjTJ2LNnj7VFdzIt3V9Jxm9/+9vgObW1tcaPfvQjIykpyYiJiTH+/d//3SgqKrKu6E7o5ptvNvr27Ws4nU6jZ8+exqRJk4LhxzC4xx3pywGIe90+pk2bZqSlpRlOp9PIyMgwpk2bZuzduzf4vNX32WYYhmFOWxMAAEBoYAwQAAAIOwQgAAAQdghAAAAg7BCAAABA2CEAAQCAsEMAAgAAYYcABAAAwg4BCAAAhB0CEAAACDsEIACd1rFjx3THHXeoT58+crlcSk1NVX5+vj766CNJks1m07Jly6wtEkBIirC6AAA4V9dcc418Pp9eeeUV9evXT8XFxSooKFBZWZnVpQEIcewFBqBTKi8vV1JSklauXKmJEyee9nxWVpYOHDgQ/L5v377av3+/JOmNN97QvHnztHPnTqWnp2vGjBn66U9/qoiIxn8T2mw2vfDCC/rb3/6mlStXKi0tTU8++aS++93vmvLeAHQ8usAAdEpxcXGKi4vTsmXL5PV6T3t+/fr1kqTf/va3KioqCn7/4Ycfavr06Zo5c6Z27typX/7yl1q8eLF+/vOfN3v9ww8/rGuuuUZbtmzRDTfcoOuuu067du3q+DcGwBS0AAHotP7617/q1ltvVW1trUaPHq2JEyfquuuu04gRIyQ1tuS8/vrrmjp1avA1eXl5mjRpkmbPnh089oc//EH333+/jh49Gnzd7bffrhdffDF4zoQJEzR69Gi98MIL5rw5AB2KFiAAndY111yjo0eP6m9/+5umTJmilStXavTo0Vq8ePEZX7NlyxY9+uijwRakuLg43XrrrSoqKlJNTU3wvNzc3Gavy83NpQUI6EIYBA2gU4uKitJll12myy67TA8//LBuueUWzZ07VzfeeGOL51dXV2vevHn6zne+0+K1AIQHWoAAdCnDhg2Tx+ORJEVGRsrv9zd7fvTo0dqzZ48GDBhw2sNuP/W/xDVr1jR73Zo1azR06NCOfwMATEELEIBOqaysTNdee61uvvlmjRgxQt26ddOGDRv05JNP6uqrr5bUOBOsoKBAF110kVwul5KSkjRnzhxdddVV6tOnj7773e/Kbrdry5Yt2r59ux577LHg9ZcuXaqxY8fq4osv1h//+EetW7dOv/nNb6x6uwDaGYOgAXRKXq9XjzzyiN555x3t27dP9fX1yszM1LXXXqsHH3xQ0dHR+vvf/65Zs2Zp//79ysjICE6D/+c//6lHH31Un3zyiSIjIzVkyBDdcsstuvXWWyU1DoJeuHChli1bpg8++EBpaWl64okn9L3vfc/CdwygPRGAAOBLWpo9BqBrYQwQAAAIOwQgAAAQdhgEDQBfwsgAoOujBQgAAIQdAhAAAAg7BCAAABB2CEAAACDsEIAAAEDYIQABAICwQwACAABhhwAEAADCzv8HRwk57Q2irm0AAAAASUVORK5CYII=\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(len(cst)), cst)\n",
    "plt.ylabel(\"Cost\")\n",
    "plt.xlabel(\"Step\")\n",
    "plt.ylim(0, 0.23)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the initial settings and enough training steps, the quantum model\n",
    "learns to fit the ground truth perfectly. This is expected, since the\n",
    "number of Pauli-rotation-encoding gates and the degree of the ground\n",
    "truth Fourier series are both one.\n",
    "\n",
    "If the ground truth\\'s degree is larger than the number of layers in the\n",
    "quantum model, the fit will look much less accurate. And finally, we\n",
    "also need to have the correct scaling of the data: if one of the models\n",
    "changes the `scaling` parameter (which effectively scales the\n",
    "frequencies), fitting does not work even with enough encoding\n",
    "repetitions.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Send it after class\n",
    "\n",
    "What happens for larger L?\n",
    "\n",
    "Tip: It is an open research question whether for asymptotically large L, the\n",
    "single qubit model can fit *any* function by constructing arbitrary\n",
    "Fourier coefficients.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part II: Fitting Fourier series with parallel Pauli-rotation encoding\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our next task is to repeat the function-fitting experiment for a circuit\n",
    "where the Pauli rotation gate gets repeated $r$ times on *different*\n",
    "qubits, using a single layer $L=1$.\n",
    "\n",
    "As shown in the paper, we expect similar results to the serial model: a\n",
    "Fourier series of degree $r$ can only be fitted if there are at least\n",
    "$r$ repetitions of the encoding gate in the quantum model. However, in\n",
    "practice this experiment is a bit harder, since the dimension of the\n",
    "trainable unitaries $W$ grows quickly with the number of qubits.\n",
    "\n",
    "In the paper, the investigations are made with the assumption that the\n",
    "purple trainable blocks $W$ are arbitrary unitaries. We could use the\n",
    "`~.pennylane.templates.ArbitraryUnitary`{.interpreted-text role=\"class\"}\n",
    "template, but since this template requires a number of parameters that\n",
    "grows exponentially with the number of qubits ($4^L-1$ to be precise),\n",
    "this quickly becomes cumbersome to train.\n",
    "\n",
    "We therefore follow Figure 4 in the paper and use an ansatz for $W$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](images/parallel_model.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define the parallel quantum model\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The ansatz is PennyLane\\'s layer structure called\n",
    "`~.pennylane.templates.StronglyEntanglingLayers`, and as the name suggests, it has itself a user-defined\n",
    "number of layers (which we will call \\\"ansatz layers\\\" to avoid\n",
    "confusion).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from pennylane.templates import StronglyEntanglingLayers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let\\'s have a quick look at the ansatz itself for 3 qubits by making a\n",
    "dummy circuit of 2 ansatz layers:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0: ──Rot(1.38,4.29,0.48)─╭●────╭X──Rot(4.26,3.55,1.68)─╭●─╭X────┤  <I>\n",
      "1: ──Rot(5.35,3.11,3.02)─╰X─╭●─│───Rot(5.52,5.01,4.14)─│──╰●─╭X─┤     \n",
      "2: ──Rot(3.72,5.18,2.19)────╰X─╰●──Rot(5.34,5.45,4.45)─╰X────╰●─┤     \n"
     ]
    }
   ],
   "source": [
    "n_ansatz_layers = 2\n",
    "n_qubits = 3\n",
    "\n",
    "dev = qml.device('default.qubit', wires=4)\n",
    "\n",
    "@qml.qnode(dev)\n",
    "def ansatz(weights):\n",
    "    StronglyEntanglingLayers(weights, wires=range(n_qubits))\n",
    "    return qml.expval(qml.Identity(wires=0))\n",
    "\n",
    "weights_ansatz = 2 * np.pi * np.random.random(size=(n_ansatz_layers, n_qubits, 3))\n",
    "print(qml.draw(ansatz, expansion_strategy=\"device\")(weights_ansatz))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we define the actual quantum model.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "scaling = 1\n",
    "r = 3\n",
    "\n",
    "dev = qml.device('default.qubit', wires=r)\n",
    "\n",
    "def S(x):\n",
    "    \"\"\"Data-encoding circuit block.\"\"\"\n",
    "    for w in range(r):\n",
    "        qml.RX(scaling * x, wires=w)\n",
    "\n",
    "def W(theta):\n",
    "    \"\"\"Trainable circuit block.\"\"\"\n",
    "    StronglyEntanglingLayers(theta, wires=range(r))\n",
    "\n",
    "    \n",
    "@qml.qnode(dev)\n",
    "def parallel_quantum_model(weights, x):\n",
    "    \n",
    "    W(weights[0])\n",
    "    S(x)        \n",
    "    W(weights[1])\n",
    "    \n",
    "    return qml.expval(qml.PauliZ(wires=0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, you can sample random weights and plot the model function:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "trainable_block_layers = 3\n",
    "weights = 2 * np.pi * np.random.random(size=(2, trainable_block_layers, r, 3), requires_grad=True)\n",
    "\n",
    "x = np.linspace(-6, 6, 70, requires_grad=False)\n",
    "random_quantum_model_y = [parallel_quantum_model(weights, x_) for x_ in x]\n",
    "\n",
    "plt.plot(x, random_quantum_model_y, c='blue')\n",
    "plt.ylim(-1,1)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Send it after class: Training the model\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Training the model is done exactly as before, but it may take a lot\n",
    "longer this time. We set a default of 25 steps, which you should\n",
    "increase if necessary. Small models of \\<6 qubits usually converge after\n",
    "a few hundred steps at most---but this depends on your settings.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid syntax (3349130107.py, line 2)",
     "output_type": "error",
     "traceback": [
      "\u001B[0;36m  Input \u001B[0;32mIn [15]\u001B[0;36m\u001B[0m\n\u001B[0;31m    predictions =  #fill me\u001B[0m\n\u001B[0m                   ^\u001B[0m\n\u001B[0;31mSyntaxError\u001B[0m\u001B[0;31m:\u001B[0m invalid syntax\n"
     ]
    }
   ],
   "source": [
    "def cost(weights, x, y):\n",
    "    predictions =  #fill me\n",
    "    return square_loss(y, predictions)\n",
    "\n",
    "max_steps = 50\n",
    "opt = qml.AdamOptimizer(0.3)\n",
    "batch_size = # fill me\n",
    "cst = ##fill me  # initial cost\n",
    "\n",
    "for step in range(max_steps):\n",
    "\n",
    "    # select batch of data\n",
    "    batch_index = ## fill me\n",
    "    x_batch = x[batch_index]\n",
    "    y_batch = target_y[batch_index]\n",
    "\n",
    "    # update the weights by one optimizer step\n",
    "    weights, _, _ = opt.step(cost, weights, x_batch, y_batch)\n",
    "    \n",
    "    # save, and possibly print, the current cost\n",
    "    c = cost(weights, x, target_y)\n",
    "    cst.append(c)\n",
    "    if (step + 1) % 10 == 0:\n",
    "        print(\"Cost at step {0:3}: {1}\".format(step + 1, c))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "predictions = [parallel_quantum_model(weights, x_) for x_ in x]\n",
    "\n",
    "plt.plot(x, target_y, c='black')\n",
    "plt.scatter(x, target_y, facecolor='white', edgecolor='black')\n",
    "plt.plot(x, predictions, c='blue')\n",
    "plt.ylim(-1,1)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.plot(range(len(cst)), cst)\n",
    "plt.ylabel(\"Cost\")\n",
    "plt.xlabel(\"Step\")\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "To reproduce the right column in Figure 4 from the paper, use the\n",
    "correct ground truth, $r=3$ and `trainable_block_layers=3`, as well as\n",
    "sufficiently many training steps. The amount of steps depends on the\n",
    "initial weights and other hyperparameters, and in some settings training\n",
    "may not converge to zero error at all.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part III: Sampling Fourier coefficients\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When we use a trainable ansatz above, it is possible that even with\n",
    "enough repetitions of the data-encoding Pauli rotation, the quantum\n",
    "model cannot fit the circuit, since the expressivity of quantum models\n",
    "also depends on the Fourier coefficients the model can create.\n",
    "\n",
    "Figure 5 in shows Fourier coefficients from quantum models sampled from\n",
    "a model family defined by an ansatz for the trainable circuit block. For\n",
    "this we need a function that numerically computes the Fourier\n",
    "coefficients of a periodic function f with period $2 \\pi$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def fourier_coefficients(f, K):\n",
    "    \"\"\"\n",
    "    Computes the first 2*K+1 Fourier coefficients of a 2*pi periodic function.\n",
    "    \"\"\"\n",
    "    n_coeffs = 2 * K + 1\n",
    "    t = np.linspace(0, 2 * np.pi, n_coeffs, endpoint=False)\n",
    "    y = np.fft.rfft(f(t)) / t.size\n",
    "    return y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define your quantum model\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we need to define a quantum model. This could be any model, using a\n",
    "qubit or continuous-variable circuit, or one of the quantum models from\n",
    "above. We will use a slight derivation of the `parallel_qubit_model()`\n",
    "from above, this time using the\n",
    "`~.pennylane.templates.BasicEntanglerLayers` ansatz:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from pennylane.templates import BasicEntanglerLayers\n",
    "\n",
    "scaling = 1\n",
    "n_qubits = 4\n",
    "\n",
    "dev = qml.device('default.qubit', wires=n_qubits)\n",
    "\n",
    "def S(x):\n",
    "    \"\"\"Data encoding circuit block.\"\"\"\n",
    "    for w in range(n_qubits):\n",
    "        qml.RX(scaling * x, wires=w)\n",
    "\n",
    "def W(theta):\n",
    "    \"\"\"Trainable circuit block.\"\"\"\n",
    "    BasicEntanglerLayers(theta, wires=range(n_qubits))\n",
    "\n",
    "    \n",
    "@qml.qnode(dev)\n",
    "def quantum_model(weights, x):\n",
    "    \n",
    "    W(weights[0])\n",
    "    S(x)\n",
    "    W(weights[1])\n",
    "    \n",
    "    return qml.expval(qml.PauliZ(wires=0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It will also be handy to define a function that samples different random\n",
    "weights of the correct size for the model.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "n_ansatz_layers = 1\n",
    "\n",
    "def random_weights():\n",
    "    return 2 * np.pi * np.random.random(size=(2, n_ansatz_layers, n_qubits))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can compute the first few Fourier coefficients for samples from\n",
    "this model. The samples are created by randomly sampling different\n",
    "parameters using the `random_weights()` function.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "n_coeffs = 5\n",
    "n_samples = 100\n",
    "\n",
    "\n",
    "coeffs = []\n",
    "for i in range(n_samples):\n",
    "\n",
    "    weights = random_weights()\n",
    "\n",
    "    def f(x):\n",
    "        return np.array([quantum_model(weights, x_) for x_ in x])\n",
    "\n",
    "    coeffs_sample = fourier_coefficients(f, n_coeffs)\n",
    "    coeffs.append(coeffs_sample)\n",
    "\n",
    "coeffs = np.array(coeffs)\n",
    "coeffs_real = np.real(coeffs)\n",
    "coeffs_imag = np.imag(coeffs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let\\'s plot the real vs. the imaginary part of the coefficients. As a\n",
    "sanity check, the $c_0$ coefficient should be real, and therefore have\n",
    "no contribution on the y-axis.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 1500x400 with 6 Axes>",
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "<Figure size 1500x400 with 6 Axes>",
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_coeffs = len(coeffs_real[0])\n",
    "\n",
    "fig, ax = plt.subplots(1, n_coeffs, figsize=(15, 4))\n",
    "\n",
    "for idx, ax_ in enumerate(ax):\n",
    "    ax_.set_title(r\"$c_{}$\".format(idx))\n",
    "    ax_.scatter(coeffs_real[:, idx], coeffs_imag[:, idx], s=20, \n",
    "                facecolor='white', edgecolor='red')\n",
    "    ax_.set_aspect(\"equal\")\n",
    "    ax_.set_ylim(-1, 1)\n",
    "    ax_.set_xlim(-1, 1)\n",
    "\n",
    "\n",
    "plt.tight_layout(pad=0.5)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Playing around with different quantum models, you will find that some\n",
    "quantum models create different distributions over the coefficients than\n",
    "others. For example `BasicEntanglingLayers` (with the default Pauli-X\n",
    "rotation) seems to have a structure that forces the even Fourier\n",
    "coefficients to zero, while `StronglyEntanglingLayers` will have a\n",
    "non-zero variance for all supported coefficients.\n",
    "\n",
    "Note also how the variance of the distribution decreases for growing\n",
    "orders of the coefficients---an effect linked to the convergence of a\n",
    "Fourier series.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Send it after class\n",
    "\n",
    "To reproduce the results from Figure 5 you have to change the ansatz (no\n",
    "unitary, `BasicEntanglerLayers` or `StronglyEntanglingLayers`, and set\n",
    "`n_ansatz_layers` either to $1$ or $5$). The `StronglyEntanglingLayers`\n",
    "requires weights of shape `size=(2, n_ansatz_layers, n_qubits, 3)`.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Continuous-variable model\n",
    "\n",
    "\n",
    "Ref. mentions that a phase rotation in continuous-variable quantum\n",
    "computing has a spectrum that supports *all* Fourier frequecies. To play\n",
    "with this model, we finally show you the code for a continuous-variable\n",
    "circuit. For example, to see its Fourier coefficients run the cell\n",
    "below, and then re-run the two cells above.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "var = 2\n",
    "n_ansatz_layers = 1\n",
    "dev_cv = qml.device('default.gaussian', wires=1)\n",
    "\n",
    "def S(x):\n",
    "    qml.Rotation(x, wires=0)\n",
    "\n",
    "def W(theta):\n",
    "    \"\"\"Trainable circuit block.\"\"\"\n",
    "    for r_ in range(n_ansatz_layers):\n",
    "        qml.Displacement(theta[0], theta[1], wires=0)\n",
    "        qml.Squeezing(theta[2], theta[3], wires=0)\n",
    "\n",
    "@qml.qnode(dev_cv)\n",
    "def quantum_model(weights, x):\n",
    "    W(weights[0])\n",
    "    S(x)\n",
    "    W(weights[1])\n",
    "    return qml.expval(qml.X(wires=0))\n",
    "\n",
    "def random_weights():\n",
    "    return np.random.normal(size=(2, 5 * n_ansatz_layers), loc=0, scale=var)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Send it after class\n",
    "To find out what effect so-called \\\"non-Gaussian\\\" gates like the `Kerr`\n",
    "gate have, you need to install the [strawberryfields\n",
    "plugin](https://pennylane-sf.readthedocs.io/en/latest/) and change the\n",
    "device to\n",
    "\n",
    "``` {.python}\n",
    "dev_cv = qml.device('strawberryfields.fock', wires=1, cutoff_dim=50)\n",
    "```\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data-reuploading classifier\n",
    "\n",
    "\n",
    "A single-qubit quantum circuit which can implement arbitrary unitary\n",
    "operations can be used as a universal classifier much like a single\n",
    "hidden-layered Neural Network. As surprising as it sounds,\n",
    "[Pérez-Salinas et al. (2019)](https://arxiv.org/abs/1907.02085) discuss\n",
    "this with their idea of \\'data reuploading\\'. It is possible to load a\n",
    "single qubit with arbitrary dimensional data and then use it as a\n",
    "universal classifier.\n",
    "\n",
    "In this example, we will implement this idea with Pennylane - a python\n",
    "based tool for quantum machine learning, automatic differentiation, and\n",
    "optimization of hybrid quantum-classical computations.\n",
    "\n",
    "## Background\n",
    "\n",
    "\n",
    "We consider a simple classification problem and will train a\n",
    "single-qubit variational quantum circuit to achieve this goal. The data\n",
    "is generated as a set of random points in a plane $(x_1, x_2)$ and\n",
    "labeled as 1 (blue) or 0 (red) depending on whether they lie inside or\n",
    "outside a circle. The goal is to train a quantum circuit to predict the\n",
    "label (red or blue) given an input point\\'s coordinate.\n",
    "\n",
    "![](images/universal_circles.png)\n",
    "\n",
    "## Transforming quantum states using unitary operations\n",
    "\n",
    "A single-qubit quantum state is characterized by a two-dimensional state\n",
    "vector and can be visualized as a point in the so-called Bloch sphere.\n",
    "Instead of just being a 0 (up) or 1 (down), it can exist in a\n",
    "superposition with say 30% chance of being in the $|0 \\rangle$ and 70%\n",
    "chance of being in the $|1 \\rangle$ state. This is represented by a\n",
    "state vector\n",
    "$|\\psi \\rangle = \\sqrt{0.3}|0 \\rangle + \\sqrt{0.7}|1 \\rangle$ -the\n",
    "probability \\\"amplitude\\\" of the quantum state. In general we can take a\n",
    "vector $(\\alpha, \\beta)$ to represent the probabilities of a qubit being\n",
    "in a particular state and visualize it on the Bloch sphere as an arrow.\n",
    "\n",
    "![](../demonstrations/data_reuploading/universal_bloch.png)\n",
    "\n",
    "## Data loading using unitaries\n",
    "\n",
    "In order to load data onto a single qubit, we use a unitary operation\n",
    "$U(x_1, x_2, x_3)$ which is just a parameterized matrix multiplication\n",
    "representing the rotation of the state vector in the Bloch sphere. E.g.,\n",
    "to load $(x_1, x_2)$ into the qubit, we just start from some initial\n",
    "state vector, $|0 \\rangle$, apply the unitary operation $U(x_1, x_2, 0)$\n",
    "and end up at a new point on the Bloch sphere. Here we have padded 0\n",
    "since our data is only 2D. Pérez-Salinas et al. (2019) discuss how to\n",
    "load a higher dimensional data point ($[x_1, x_2, x_3, x_4, x_5, x_6]$)\n",
    "by breaking it down in sets of three parameters\n",
    "($U(x_1, x_2, x_3), U(x_4, x_5, x_6)$).\n",
    "\n",
    "## Model parameters with data re-uploading\n",
    "\n",
    "Once we load the data onto the quantum circuit, we want to have some\n",
    "trainable nonlinear model similar to a neural network as well as a way\n",
    "of learning the weights of the model from data. This is again done with\n",
    "unitaries, $U(\\theta_1, \\theta_2, \\theta_3)$, such that we load the data\n",
    "first and then apply the weights to form a single layer\n",
    "$L(\\vec \\theta, \\vec x) = U(\\vec \\theta)U(\\vec x)$. In principle, this\n",
    "is just application of two matrix multiplications on an input vector\n",
    "initialized to some value. In order to increase the number of trainable\n",
    "parameters (similar to increasing neurons in a single layer of a neural\n",
    "network), we can reapply this layer again and again with new sets of\n",
    "weights,\n",
    "$L(\\vec \\theta_1, \\vec x) L(\\vec \\theta_2, , \\vec x) ... L(\\vec \\theta_L, \\vec x)$\n",
    "for $L$ layers. The quantum circuit would look like the following:\n",
    "\n",
    "![](images/universal_layers.png)\n",
    "\n",
    "## The cost function and \\\"nonlinear collapse\\\"\n",
    "\n",
    "So far, we have only performed linear operations (matrix\n",
    "multiplications) and we know that we need to have some nonlinear\n",
    "squashing similar to activation functions in neural networks to really\n",
    "make a universal classifier (Cybenko 1989). Here is where things gets a\n",
    "bit quantum. After the application of the layers, we will end up at some\n",
    "point on the Bloch sphere due to the sequence of unitaries implementing\n",
    "rotations of the input. These are still just linear transformations of\n",
    "the input state. Now, the output of the model should be a class label\n",
    "which can be encoded as fixed vectors (Blue = $[1, 0]$, Red = $[0, 1]$)\n",
    "on the Bloch sphere. We want to end up at either of them after\n",
    "transforming our input state through alternate applications of data\n",
    "layer and weights.\n",
    "\n",
    "We can use the idea of the \\\"collapse\\\" of our quantum state into one or\n",
    "other class. This happens when we measure the quantum state which leads\n",
    "to its projection as either the state 0 or 1. We can compute the\n",
    "fidelity (or closeness) of the output state to the class label making\n",
    "the output state jump to either $| 0 \\rangle$ or $|1\\rangle$. By\n",
    "repeating this process several times, we can compute the probability or\n",
    "overlap of our output to both labels and assign a class based on the\n",
    "label our output has a higher overlap. This is much like having a set of\n",
    "output neurons and selecting the one which has the highest value as the\n",
    "label.\n",
    "\n",
    "We can encode the output label as a particular quantum state that we\n",
    "want to end up in and use Pennylane to find the probability of ending up\n",
    "in that state after running the circuit. We construct an observable\n",
    "corresponding to the output label using the\n",
    "[Hermitian](https://pennylane.readthedocs.io/en/latest/code/ops/qubit.html#pennylane.ops.qubit.Hermitian)\n",
    "operator. The expectation value of the observable gives the overlap or\n",
    "fidelity. We can then define the cost function as the sum of the\n",
    "fidelities for all the data points after passing through the circuit and\n",
    "optimize the parameters $(\\vec \\theta)$ to minimize the cost.\n",
    "\n",
    "$$\\texttt{Cost} = \\sum_{\\texttt{data points}} (1 - \\texttt{fidelity}(\\psi_{\\texttt{output}}(\\vec x, \\vec \\theta), \\psi_{\\texttt{label}}))$$\n",
    "\n",
    "Now, we can use our favorite optimizer to maximize the sum of the\n",
    "fidelities over all data points (or batches of datapoints) and find the\n",
    "optimal weights for classification. Gradient-based optimizers such as\n",
    "Adam (Kingma et. al., 2014) can be used if we have a good model of the\n",
    "circuit and how noise might affect it. Or, we can use some gradient-free\n",
    "method such as L-BFGS (Liu, Dong C., and Nocedal, J., 1989) to evaluate\n",
    "the gradient and find the optimal weights where we can treat the quantum\n",
    "circuit as a black-box and the gradients are computed numerically using\n",
    "a fixed number of function evaluations and iterations. The L-BFGS method\n",
    "can be used with the PyTorch interface for Pennylane.\n",
    "\n",
    "## Multiple qubits, entanglement and Deep Neural Networks\n",
    "\n",
    "The Universal Approximation Theorem declares that a neural network with\n",
    "two or more hidden layers can serve as a universal function\n",
    "approximator. Recently, we have witnessed remarkable progress of\n",
    "learning algorithms using Deep Neural Networks.\n",
    "\n",
    "Pérez-Salinas et al. (2019) make a connection to Deep Neural Networks by\n",
    "describing that in their approach the \\\"layers\\\"\n",
    "$L_i(\\vec \\theta_i, \\vec x )$ are analogous to the size of the\n",
    "intermediate hidden layer of a neural network. And the concept of deep\n",
    "(multiple layers of the neural network) relates to the number of qubits.\n",
    "So, multiple qubits with entanglement between them could provide some\n",
    "quantum advantage over classical neural networks. But here, we will only\n",
    "implement a single qubit classifier.\n",
    "\n",
    "![](images/universal_dnn.png)\n",
    "\n",
    "## \\\"Talk is cheap. Show me the code.\\\" - Linus Torvalds\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 400x400 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pennylane as qml\n",
    "from pennylane import numpy as np\n",
    "from pennylane.optimize import AdamOptimizer, GradientDescentOptimizer\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "# Set a random seed\n",
    "np.random.seed(42)\n",
    "\n",
    "\n",
    "# Make a dataset of points inside and outside of a circle\n",
    "def circle(samples, center=[0.0, 0.0], radius=np.sqrt(2 / np.pi)):\n",
    "    \"\"\"\n",
    "    Generates a dataset of points with 1/0 labels inside a given radius.\n",
    "\n",
    "    Args:\n",
    "        samples (int): number of samples to generate\n",
    "        center (tuple): center of the circle\n",
    "        radius (float: radius of the circle\n",
    "\n",
    "    Returns:\n",
    "        Xvals (array[tuple]): coordinates of points\n",
    "        yvals (array[int]): classification labels\n",
    "    \"\"\"\n",
    "    Xvals, yvals = [], []\n",
    "\n",
    "    for i in range(samples):\n",
    "        x = 2 * (np.random.rand(2)) - 1\n",
    "        y = 0\n",
    "        if np.linalg.norm(x - center) < radius:\n",
    "            y = 1\n",
    "        Xvals.append(x)\n",
    "        yvals.append(y)\n",
    "    return np.array(Xvals, requires_grad=False), np.array(yvals, requires_grad=False)\n",
    "\n",
    "\n",
    "def plot_data(x, y, fig=None, ax=None):\n",
    "    \"\"\"\n",
    "    Plot data with red/blue values for a binary classification.\n",
    "\n",
    "    Args:\n",
    "        x (array[tuple]): array of data points as tuples\n",
    "        y (array[int]): array of data points as tuples\n",
    "    \"\"\"\n",
    "    if fig == None:\n",
    "        fig, ax = plt.subplots(1, 1, figsize=(5, 5))\n",
    "    reds = y == 0\n",
    "    blues = y == 1\n",
    "    ax.scatter(x[reds, 0], x[reds, 1], c=\"red\", s=20, edgecolor=\"k\")\n",
    "    ax.scatter(x[blues, 0], x[blues, 1], c=\"blue\", s=20, edgecolor=\"k\")\n",
    "    ax.set_xlabel(\"$x_1$\")\n",
    "    ax.set_ylabel(\"$x_2$\")\n",
    "\n",
    "\n",
    "Xdata, ydata = circle(500)\n",
    "fig, ax = plt.subplots(1, 1, figsize=(4, 4))\n",
    "plot_data(Xdata, ydata, fig=fig, ax=ax)\n",
    "plt.show()\n",
    "\n",
    "\n",
    "# Define output labels as quantum state vectors\n",
    "def density_matrix(state):\n",
    "    \"\"\"Calculates the density matrix representation of a state.\n",
    "\n",
    "    Args:\n",
    "        state (array[complex]): array representing a quantum state vector\n",
    "\n",
    "    Returns:\n",
    "        dm: (array[complex]): array representing the density matrix\n",
    "    \"\"\"\n",
    "    return state * np.conj(state).T\n",
    "\n",
    "\n",
    "label_0 = [[1], [0]]\n",
    "label_1 = [[0], [1]]\n",
    "state_labels = np.array([label_0, label_1], requires_grad=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simple classifier with data reloading and fidelity loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "dev = qml.device(\"default.qubit\", wires=1)\n",
    "# Install any pennylane-plugin to run on some particular backend\n",
    "\n",
    "\n",
    "@qml.qnode(dev)\n",
    "def qcircuit(params, x, y):\n",
    "    \"\"\"A variational quantum circuit representing the Universal classifier.\n",
    "\n",
    "    Args:\n",
    "        params (array[float]): array of parameters\n",
    "        x (array[float]): single input vector\n",
    "        y (array[float]): single output state density matrix\n",
    "\n",
    "    Returns:\n",
    "        float: fidelity between output state and input\n",
    "    \"\"\"\n",
    "    for p in params:\n",
    "        qml.Rot(*x, wires=0)\n",
    "        qml.Rot(*p, wires=0)\n",
    "    return qml.expval(qml.Hermitian(y, wires=[0]))\n",
    "\n",
    "\n",
    "def cost(params, x, y, state_labels=None):\n",
    "    \"\"\"Cost function to be minimized.\n",
    "\n",
    "    Args:\n",
    "        params (array[float]): array of parameters\n",
    "        x (array[float]): 2-d array of input vectors\n",
    "        y (array[float]): 1-d array of targets\n",
    "        state_labels (array[float]): array of state representations for labels\n",
    "\n",
    "    Returns:\n",
    "        float: loss value to be minimized\n",
    "    \"\"\"\n",
    "    # Compute prediction for each input in data batch\n",
    "    loss = 0.0\n",
    "    dm_labels = [density_matrix(s) for s in state_labels]\n",
    "    for i in range(len(x)):\n",
    "        f = qcircuit(params, x[i], dm_labels[y[i]])\n",
    "        loss = loss + (1 - f) ** 2\n",
    "    return loss / len(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Utility functions for testing and creating batches\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def test(params, x, y, state_labels=None):\n",
    "    \"\"\"\n",
    "    Tests on a given set of data.\n",
    "\n",
    "    Args:\n",
    "        params (array[float]): array of parameters\n",
    "        x (array[float]): 2-d array of input vectors\n",
    "        y (array[float]): 1-d array of targets\n",
    "        state_labels (array[float]): 1-d array of state representations for labels\n",
    "\n",
    "    Returns:\n",
    "        predicted (array([int]): predicted labels for test data\n",
    "        output_states (array[float]): output quantum states from the circuit\n",
    "    \"\"\"\n",
    "    fidelity_values = []\n",
    "    dm_labels = [density_matrix(s) for s in state_labels]\n",
    "    predicted = []\n",
    "\n",
    "    for i in range(len(x)):\n",
    "        fidel_function = lambda y: qcircuit(params, x[i], y)\n",
    "        fidelities = [fidel_function(dm) for dm in dm_labels]\n",
    "        best_fidel = np.argmax(fidelities)\n",
    "\n",
    "        predicted.append(best_fidel)\n",
    "        fidelity_values.append(fidelities)\n",
    "\n",
    "    return np.array(predicted), np.array(fidelity_values)\n",
    "\n",
    "\n",
    "def accuracy_score(y_true, y_pred):\n",
    "    \"\"\"Accuracy score.\n",
    "\n",
    "    Args:\n",
    "        y_true (array[float]): 1-d array of targets\n",
    "        y_predicted (array[float]): 1-d array of predictions\n",
    "        state_labels (array[float]): 1-d array of state representations for labels\n",
    "\n",
    "    Returns:\n",
    "        score (float): the fraction of correctly classified samples\n",
    "    \"\"\"\n",
    "    score = y_true == y_pred\n",
    "    return score.sum() / len(y_true)\n",
    "\n",
    "\n",
    "def iterate_minibatches(inputs, targets, batch_size):\n",
    "    \"\"\"\n",
    "    A generator for batches of the input data\n",
    "\n",
    "    Args:\n",
    "        inputs (array[float]): input data\n",
    "        targets (array[float]): targets\n",
    "\n",
    "    Returns:\n",
    "        inputs (array[float]): one batch of input data of length `batch_size`\n",
    "        targets (array[float]): one batch of targets of length `batch_size`\n",
    "    \"\"\"\n",
    "    for start_idx in range(0, inputs.shape[0] - batch_size + 1, batch_size):\n",
    "        idxs = slice(start_idx, start_idx + batch_size)\n",
    "        yield inputs[idxs], targets[idxs]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train a quantum classifier on the circle dataset\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch:  0 | Cost: 0.415535 | Train accuracy: 0.460000 | Test Accuracy: 0.448500\n",
      "Epoch:  1 | Loss: 0.125417 | Train accuracy: 0.840000 | Test accuracy: 0.804000\n",
      "Epoch:  2 | Loss: 0.154322 | Train accuracy: 0.775000 | Test accuracy: 0.756000\n",
      "Epoch:  3 | Loss: 0.145234 | Train accuracy: 0.810000 | Test accuracy: 0.799000\n",
      "Epoch:  4 | Loss: 0.126142 | Train accuracy: 0.805000 | Test accuracy: 0.781500\n",
      "Epoch:  5 | Loss: 0.127102 | Train accuracy: 0.845000 | Test accuracy: 0.794500\n",
      "Epoch:  6 | Loss: 0.128556 | Train accuracy: 0.825000 | Test accuracy: 0.807000\n",
      "Epoch:  7 | Loss: 0.113327 | Train accuracy: 0.810000 | Test accuracy: 0.794500\n",
      "Epoch:  8 | Loss: 0.109549 | Train accuracy: 0.895000 | Test accuracy: 0.857000\n",
      "Epoch:  9 | Loss: 0.147936 | Train accuracy: 0.750000 | Test accuracy: 0.750000\n",
      "Epoch: 10 | Loss: 0.104038 | Train accuracy: 0.890000 | Test accuracy: 0.847000\n"
     ]
    }
   ],
   "source": [
    "# Generate training and test data\n",
    "num_training = 200\n",
    "num_test = 2000\n",
    "\n",
    "Xdata, y_train = circle(num_training)\n",
    "X_train = np.hstack((Xdata, np.zeros((Xdata.shape[0], 1), requires_grad=False)))\n",
    "\n",
    "Xtest, y_test = circle(num_test)\n",
    "X_test = np.hstack((Xtest, np.zeros((Xtest.shape[0], 1), requires_grad=False)))\n",
    "\n",
    "\n",
    "# Train using Adam optimizer and evaluate the classifier\n",
    "num_layers = 3\n",
    "learning_rate = 0.6\n",
    "epochs = 10\n",
    "batch_size = 32\n",
    "\n",
    "opt = AdamOptimizer(learning_rate, beta1=0.9, beta2=0.999)\n",
    "\n",
    "# initialize random weights\n",
    "params = np.random.uniform(size=(num_layers, 3), requires_grad=True)\n",
    "\n",
    "predicted_train, fidel_train = test(params, X_train, y_train, state_labels)\n",
    "accuracy_train = accuracy_score(y_train, predicted_train)\n",
    "\n",
    "predicted_test, fidel_test = test(params, X_test, y_test, state_labels)\n",
    "accuracy_test = accuracy_score(y_test, predicted_test)\n",
    "\n",
    "# save predictions with random weights for comparison\n",
    "initial_predictions = predicted_test\n",
    "\n",
    "loss = cost(params, X_test, y_test, state_labels)\n",
    "\n",
    "print(\n",
    "    \"Epoch: {:2d} | Cost: {:3f} | Train accuracy: {:3f} | Test Accuracy: {:3f}\".format(\n",
    "        0, loss, accuracy_train, accuracy_test\n",
    "    )\n",
    ")\n",
    "\n",
    "for it in range(epochs):\n",
    "    for Xbatch, ybatch in iterate_minibatches(X_train, y_train, batch_size=batch_size):\n",
    "        params, _, _, _ = opt.step(cost, params, Xbatch, ybatch, state_labels)\n",
    "\n",
    "    predicted_train, fidel_train = test(params, X_train, y_train, state_labels)\n",
    "    accuracy_train = accuracy_score(y_train, predicted_train)\n",
    "    loss = cost(params, X_train, y_train, state_labels)\n",
    "\n",
    "    predicted_test, fidel_test = test(params, X_test, y_test, state_labels)\n",
    "    accuracy_test = accuracy_score(y_test, predicted_test)\n",
    "    res = [it + 1, loss, accuracy_train, accuracy_test]\n",
    "    print(\n",
    "        \"Epoch: {:2d} | Loss: {:3f} | Train accuracy: {:3f} | Test accuracy: {:3f}\".format(\n",
    "            *res\n",
    "        )\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost: 0.104038 | Train accuracy 0.890000 | Test Accuracy : 0.847000\n",
      "Learned weights\n",
      "Layer 0: [-0.23838965  1.17081693 -0.19781887]\n",
      "Layer 1: [0.64850867 0.71778245 0.46408056]\n",
      "Layer 2: [ 2.39560597 -1.21404538  0.32099705]\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 1000x300 with 3 Axes>",
      "image/png": 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U09FMOkwMW6MmLDnllFN8GH3jjTfSzJkzqVAo+M5bu3YtVVVV0aFDh0L7tXDhQh8PUmq7H/nIR6i+vj4Ur+69994A/xJG6XSajjvuuCKmExENDg4SgADfpmLZiy++SIsWLaJcLuc7PnPmTN+4ma4n0vO3MZVGsXs5gFWrVmH27Nk46aSTcMkll6C2thZf/epXccIJJ/jO+8AHPuD7fu+99yKZTKK7uxu/+93vip+2tjbU1tYWrXC7d+/Giy++WHSdZrrmmmusfXv00Ufx85//HNdcc00gTq4cd7LDhw9jcHAQb3rTm3D66acXjx933HF45zvfie985zv44x//6Lvmiiuu8N2rq6sLhw8fxtNPPw3Ai9+7//778X//93+R+zJ79mycddZZ+M///E8AwHe/+11UVVVhzZo1+PWvf40nnngCgLCiZjKZcbnP/dVf/RUaGhp8zwAIF+0o9P73vx9VVVW+Y9OnTy/+/3//938YHR3FGWecgVQqhR/+8IeBNmzjWMo8GRgYwLJly5DJZIrHamtrccUVV+Cpp57CT3/6U9/57373u32WlnPOOQdEFHAtPeecc/CLX/wCL730knEsHMfB8uXLi+/tZz/7GUZHR7F27VoQEb7//e8DEO9t0aJFxfkRdb3o6IEHHsAJJ5yAiy66qHhs2rRpeP/73689v7a21hcjNnXqVCxbtizS+2ZL9q5du/D8889bz49pcijG6SOD04Af65577jn87ne/Q1dXF55//nk8/vjjpT4eAGBsbAz/8R//gbe//e3FNn/3u99hdHQU+XweTzzxBH75y1/6rtHhcDlUU1OD9773vYHj433O8ewzq1atKlqZAOENUF9fX7z28OHD2L17N970pjfh+OOPL553xhln4Pzzz7e2H1NMryQyrdGodO+996KrqwsNDQ0+3F+1ahUOHz5c5F8mqt1UKoU//elPePDBB8t+Bpl+9atf4Uc/+hEuvfRSn7ddd3c3WlpaAufLWPb73/8ezz77LLq6urS8qY5K5W9jikaxezmA2267DWeeeSamTJmCuXPnYv78+XAcvz5iypQpAReOJ554As8++yzmzJmjbZeTyjDTM2/ePN/vs2fP9m3QOmIXykrVHf7tb3+L559/HvPnzw/8tmDBArz88sv4xS9+gYULFxaPn3zyyb7zuM8cD5nNZnHxxRejt7cXt9xyC8477zy86U1vwjvf+U7U1NSE9qerqwsDAwMAhJDW3t6O9vZ2NDY24uGHH8bcuXPx4x//GO985zvH9dy2Z7DRaaedFjj2wgsv4KabbsLWrVvxy1/+0hebrov9tfWhlHny9NNPB9xLAc816emnn/bNGfXeDNonnXRS4PjLL7+MZ5991ue2q1JXVxeuv/56vPDCC3j44Ydx3HHHobW1FUuXLsXDDz+M7u5ufOc738Hb3/724jVR14uOnn76aTQ3NwcEGM6QrNKJJ54YOLehoQH79+833oPptNNOw8c+9jF87nOfw913342uri5cdNFFeNe73hW7lh9BinFa0JHA6cceewyf+MQn8B//8R8BYb/cPAdPPvkkiAj/+I//iH/8x3/UnvOb3/zGp1TR4XA5dMIJJ2iTNY73Ocezz6jX8vV87W9+8xu88MILWswz4WBMMb1SybRGo9ITTzyB/fv3G0MvwviNSrT7wQ9+EP/2b/+G888/HyeccAJe//rX4+1vfzve8IY3lHVf0/4EAPPnzw8Iwvfffz/WrVuHH/3oR748PVGVwKXytzFFo1joBrBs2bJiVlwT1dTUBBi8l19+GXPmzMHdd9+tveZYibMyWRZ4ESYSCezcuROPPPIIvvnNb2LXrl143/veh89+9rN45JFHUFtba2w7k8mgr68PBw8exMMPP4yuri4kEglkMhk8/PDDOP744/Hyyy8XLQYT9Qw2krV+TFdddRW2bt2Ka665Bq997WuRTCaRSCRwySWXaBN1jLcP4yHTvcvtUyaTwf/93//h+9//fvG9AUIYf/jhh/H444/jt7/9re+9TeZ6Ge9Yf/azn8V73vMefP3rX8fg4CCuvvpq3HTTTXjkkUeMCZximliKcTqcJgqn//CHPyCbzaK+vh433HADmpubMW3aNPzwhz/EddddV3bpLL5u9erVyOfz2nNUYVKHw+WQrp1KPOd4cOdI7g8xxXS0UalrXU12+PLLL6O7uxvXXnut9vwzzzyzrH5FbXfOnDn40Y9+hF27duFb3/oWvvWtb2Hr1q1497vfjW3btpV176j08MMP46KLLsKKFSvwpS99Cccddxyqq6uxdetWfPnLX47URqn8bUzRKBa6x0HNzc3YvXs3zj333FCAOOWUUwAIDZnsKvjb3/7WqgFnd7Of/OQnWLVqlfG8qNqr2bNnY8aMGRgZGQn89vjjj8NxnID1Myp1dnais7MT//RP/4Qvf/nL+Ou//mvcc889uPzyy43XsFD24IMPYnh4uFi/dMWKFbj99ttx/PHHY+bMmWhrawu995HI3Lpz505ceuml+OxnP1s89uc//9mX1bsUKmWenHLKKcZ3KLc1UbRs2TJMnToVDz/8MB5++GGsWbMGgHhvfX19eOihh4rfmaKuFx2dcsop+OlPfwoi8r3rJ598suxnsM2ZxYsXY/HixfjEJz6B733vezj33HOxadMmrFu3rux7xjT5FOO0n0rF6T179mB0dBRf+cpXfOuZs8bbyPTMPMbV1dWhY1YOlbMfjPc5J5rmzJmDadOmaTFvPDgYU0yvJGpoaAjwWC+++CJ+9atf+Y41Nzfjf//3f8vGFhOGlNLu1KlT8cY3vhFvfOMb8fLLL+ODH/wgNm/ejH/8x3/EGWecURJOyfuTSuo+cd9992HatGnYtWuXz4tp69atgWtNfag0fxuToDimexz09re/HYcPH8aNN94Y+O2ll14qTs5Vq1ahuroat956q09rHZY9kam1tRWnnXYaNm7cGJjscltcr9S2IKqqqvD6178eX//6132p/3/961/jy1/+MjKZDOrr6639kun3v/99QBufTqcBwFp+6rTTTsMJJ5yAW265Bf/3f/+Hc889F4AQxg8cOICdO3eis7PTWtc06vNXkqqqqgLPfeuttwY0rlGplHnS09ODoaGhYvw0IDJ8b9myBaeeeqo2xqeSNG3aNHR0dOBf//VfcejQIZ+l+4UXXsAXvvAFNDc347jjjiteE3W96Cifz+OXv/ylr5TQn//8Z/T19ZX9DKY588c//jEQ07548WI4jmOdzzEdfRTjtKBycZotsPK1L774Ir70pS9Fui9nuVWfec6cOTjvvPOwefPmAMMMIFDurBQqZz8Y73NONFVVVWHVqlX42te+hmeeeaZ4/Mknn8S3vvWtI9izmGKaPGpubg7EY2/ZsiXAd7397W/H97//fezatSvQxh/+8IfQvDWAwBAdfkRtd3R01Peb4zjFqg2Mt6Xg1HHHHYd0Oo1t27b53LsffPDBQA6fqqoqJBIJ35g89dRT+NrXvhb5OSvN38YkKLZ0j4Oy2SyuvPJK3HTTTfjRj36E17/+9aiursYTTzyBe++9F5///Ofx1re+FbNnz8bq1atx00034cILL0RPTw8effRRfOtb38KsWbNC7+E4Dm6//Xa88Y1vRDqdxnvf+14cd9xxePzxx/HYY48VFz5bgq+++mrk83lUVVXhkksu0ba5bt06PPjgg8hkMvjgBz+IKVOmYPPmzfjLX/7iq2UclbZt24YvfelLePOb34zm5mY899xz6OvrQ319PXp6eqzXd3V14Z577sHixYuLMXCtra2YOXMmCoVCpHjuUp6/UnThhRdi+/btSCaTaGlpwfe//33s3r07NBY6jEqZJ2vXrsW//uu/4vzzz8fVV1+NxsZGbNu2DT//+c9x3333BVxsJ4K6urrw//7f/0MymcTixYsBCEZ6/vz5GBkZCdTMjLpedHTllVfii1/8It7xjnfgIx/5CI477jjcfffdmDZtGoDyLFvNzc1IpVLYtGkT6urqMHPmTJxzzjn48Y9/jA9/+MN429vehjPPPBMvvfQStm/fjqqqKlx88cUl3yemI0sxTgsqF6eXL1+OhoYGXHrppbj66quRSCSwffv2kkJzWlpa0N/fjzPPPBONjY1YtGgRFi1ahNtuuw2ZTAaLFy/G+9//fpx++un49a9/je9///v47//+b/z4xz8u+TkB89oOiwkf73NOBl1//fUYHBzEueeeiw984AM4fPgwvvjFL2LRokX40Y9+dKS7F1NME06XX345/vZv/xYXX3wxuru78eMf/xi7du0KYPSaNWvwjW98AxdeeCHe8573oK2tDX/605/w//1//x927tyJp556KhTX29racPvtt2PdunU444wzMGfOHORyucjtXn755RgbG0Mul8OJJ56Ip59+GrfeeivS6XQx9046nUZVVRU+85nP4Nlnn0VNTQ1yuZwx/8hNN92ECy64AJlMBu973/swNjaGW2+9FQsXLsT//u//Fs+74IIL8LnPfQ5veMMb8M53vhO/+c1vcNttt+GMM84I5LVpa2vD7t278bnPfQ7HH388TjvtNJxzzjkV529jcmmSsqQflcRlSGwlVC699FKaOXOm8fctW7ZQW1sbTZ8+nerq6mjx4sV07bXX0jPPPFM85/Dhw9Tb20vHHXccTZ8+nc477zz6yU9+EihzoJaiYfrOd75D3d3dVFdXRzNnzqQlS5b4Som89NJLdNVVV9Hs2bMpkUj4SjBAU2Lhhz/8IeXzeaqtraUZM2bQypUr6Xvf+16k8VH7+MMf/pDe8Y530Mknn0w1NTU0Z84cuvDCC+m//uu/woa1SLfddhsBoA984AO+46tWrSIA9NBDD/mO60qGmZ6fz12/fn3gvrpxUSlsjvz+97+n9773vTRr1iyqra2lfD5Pjz/+eOCdRh1HoujzhIjowIED9Na3vpVSqRRNmzaNli1bRvfff7/2Hmr5K1OfdCV/TPTv//7vBCBQduzyyy8nAHTHHXdor4uyXtSSYUREBw8epAsuuICmT59Os2fPpr/7u7+j++67jwDQI4884rt24cKFgfuqZX6IREmflpaWYsmdrVu30sGDB+l973sfNTc307Rp06ixsZFWrlxJu3fvto5JTJWnGKePPE5/97vfpc7OTpo+fTodf/zxdO2119KuXbsCY2DCj+9973vU1tZGU6dODTzngQMH6N3vfje95jWvoerqajrhhBPowgsvpJ07d1qfMYx0a5vIjA+lPKepZFiUfcZUMuxDH/pQ4Fod7j/00EN09tln09SpU6m5uZn++Z//mf7u7/6Opk2bFj4gMcV0FJKpZJhpjR4+fJiuu+46mjVrFs2YMYPy+Tw9+eST2rXy3HPP0d///d/TGWecQVOnTqVZs2bR8uXLacOGDb4Sqjr6n//5H7rggguorq6OAPj4kSjt7ty5k17/+tfTnDlzaOrUqXTyySfTlVdeSb/61a989+nr66PTTz+dqqqqIpUPu++++2jBggVUU1NDLS0t9JWvfEXL29xxxx00b948qqmpobPOOou2bt2qxZ7HH3+cVqxYQdOnT/eVxozK38ZUGiWIjiI1bkwxxRRTCbRx40Z89KMfxX//938HSkfFFFNMMb0a6E1vehMee+wxbbxnTDHFFFNMRwfFMd0xxRTTK4JeeOEF3/c///nP2Lx5M+bNmxcL3DHFFNOrglQcfOKJJzAwMIDzzjvvyHQopphiiimmSBTHdMcUU0yvCHrLW96Ck08+Gel0Gs8++yx27NiBxx9/3FgKKqaYYorpWKPTTz8d73nPe3D66afj6aefxu23346pU6caSxjFFFNMMcV0dFAsdMcUU0yvCMrn8/jnf/5n3H333Th8+DBaWlpwzz334K/+6q+OdNdiiimmmCaF3vCGN+Bf//Vf8T//8z+oqanBa1/7Wnz605/GvHnzjnTXYooppphiCqE4pjummGKKKaaYYooppphiiimmmCaI4pjumGKKKaaYYooppphiiimmmGKaIIqF7phiiimmmGKKKaaYYooppphimiCKY7ot9PLLL+OZZ55BXV0dEonEke5OTDHFNAFERHjuuedw/PHHw3FiXWQpFGNkTDEd2xTjY/kU42NMMR3bVAo+xkK3hZ555hmcdNJJR7obMcUU0yTQL37xC5x44olHuhuvKIoxMqaYXh0U42PpFONjTDG9OigKPsZCt4Xq6uoAiMGsr68/wr2JKaaYJoL++Mc/4qSTTiqu95iiU4yRMcV0bFOMj+VTjI8xxXRsUyn4GAvdFmJ3oPr6+hgwY4rpGKfY/a90ijEyppheHRTjY+kU42NMMb06KAo+xsE5McUUU0wxxRRTTDHFFFNMMcU0QRQL3THFFFNMMcUUU0wxxRRTTDHFNEH0ihK6//M//xNvfOMbcfzxxyORSOBrX/ua9Zo9e/agtbUVNTU1OOOMM3DXXXdNeD9jiimmmCabYnyMKaaYYjJTjJExxRTTkaRXVEz3n/70JyxduhTve9/78Ja3vMV6/s9//nNccMEF+Nu//VvcfffdeOihh3D55ZfjuOOOQz6fn9C+FgoFHDhwAGeccQbmzZtXsXMnmo6mvtgorK+VeI5Kt3Hw4EHs27cPr33ta9Hd3V1We+XSZL9X9X6m+5fyDl9Jc/NIUIyPE09HU1+iUDnrbrxtl9vGqwkf1XsS0bjx8Ug9xyuJXikYGePj5NDRzkOqGLF3714kEglks9lJH98jyUOa8NHWr6OSh6RXKAGgr371q6HnXHvttbRw4ULfsb/6q7+ifD4f+T7PPvssAaBnn3020vmjo6OUz/cQgOInn++hsbExIiIaGRmhgYEBKhQKNDo6Sj35vO/cnnyexsbGfOdNBoX15WijsL5W4jl0bWQzGV8btvczOjpKKzKZ4vVVUlsAaG5TEx08eHDcY2Hry759+6ijtXXC3yv3YWhoKDB2c5uaAmN5xx13UFYaH3mMdeOvtlHpZyh1nR/tNFn4SFTa2NnWZ4yPlSFTfw8cODAh+Nje2krDw8PFc6Lgo9zGkcLH0dHRAA5NJD7q5rWjPHtPPk8PPvggtSu4zWOsG//uXI66c7kJe45jDR+Jjk4eslL4qJ470XSs4ONk8ZCl4qOKEY675isxvra+HGkeUoePQ0ND1N/ff9TwkKWs8WNa6O7q6qKPfOQjvmN33nkn1dfXR75PqZtNPt9DVVWNBOwg4BABO6iqqpFWrlwVEMZnNc2hlOPQDoAOAbQDoJTjjHty8OTdtWtXYDGZFlhPPk+NVVW+vjRWVVFPiQz4ZFBYX23PoXt+9VhPPk8px6G0hhGMwrSOjo763mEVQEm3L9ynpNveeCjKxuFo7l3ue9WNna4PNQBtdu+XNjw7A2lKM8bduVzgHSbdtiZqbh5rTOVk4SNRaWNnWp+rVq7UbpITgY9EYi5v2bKF+vr6jjl8JDL3d25TU8n4qB7ntjcBlFPWb1Thb9XKlVRzBPGRf5/b1DTp+CjP6xxADcr9U4mEj9GcrcFI9R2mEgmqqdBz6OhYw0eio5OHHC8+ms6tFA95rOPjRPOQsxsbS8ZHHQ/XAMFnjWd8o+BjJXlI09wJ4yGj4OPRwEPGQrdL8+bNo09/+tO+Y//+7/9OAOj555/XXvPnP/+Znn322eLnF7/4ReTBHBkZcV/8DgJI+txMgEOO0+ATxoEkLYYjn6gVUkyTQ2UcdRopnpyrVq40Lnbu9w5/p2m7e14UTWmYtqySGldbX8N+y3Z1+Z6/Zf58Orez03eMNWdpgBoRZARnpVLWzSWbyRTf4XZLnwYHB8seC9PmsCKTofbWVqpNJMb9XonCLVu6PjQA1APQiOXZWzRzvdZyTaHMZ7DRscZUThQ+EpWPkaa1e7OLUw0KA8mb5HjwUWYcd+3aRf39/YE177jrfiLxUe5PmEBbCbL1d0NEfFzW1iY8UpTjDgRD1GPASJvwNzIyIt43QNceIXwcGBigjra2CcPHFZlM0RJjYv5s+LhXM9/XR8THSmPksYaPREcfD1kJfNzunhtFANYJ1mE8pEnZeazhYyk85NlLlpTMQ5aCj7b1Pp71HaZcGBkZqRgPGYaPshJX5SFXlIGPR4qHjIVul8oBzE996lO+ycGfKIM5MDDgnr+HgAEChgiQrduqML7dNwlsmzBPjtHRUVq1cqVP2+NArxFrdCdmNUAzIRgudYFxvw8p9z3ktj0wMGB85vG66YRZ5cPG2NRX02+6TatGM14NjkMJy3swMa2FQiEA6L0hfQJAvb292ue0bTS6jWPUfdfq3C3nvcoUZtliBlw3Hn2W++vGeLWtz2U+g42ONaZyovCRqHyM5LW7x32PQxCCm43RKQcfGXcYI+W/gTUPYW2dCHxU+yPjYBSvmVLxUR5nU3+3aY6bmHqTFboz4jvTvZ8tW7YUry0XH+WxMSl6JxsfdwC0X3OPNEBjmvGw4eMWzRgP2Po8jucIo2MNH4mOPh5SXrcjAPUDlJWuj7LW9tjOVdzSo/KQKQhhZg2EsHO04SPzXhPNQ6pjUy4PGRUfbes9bHxLxUcC6HYE3bnHi5E2fAzjIUvFR8KR4SFjodulclyDxmPp3rdvHwGONKEcAlIErHG/HyL/PDjkmwTyAhtxvxc0k6Mnn6caeG4XOYDqDRNQt4h6IJgAnti7du2yArWOWBuW1Lg42dx0dEDL/QxzhbJpKROaBXyzZmxsDHypTCsA6u/vDwD6P1vuc+edd/qA0aYVZNJtHCsgNkYWHKxWkYgeDNyGybKVM4yHCRTDxtjKNJTxDFHoWGMqJwoficrHyH379gWYvBQEIxdlk7QKHBI+NlZVFS0N/Fe3HnSCWCXxcWBgQGvttLl6l4uPfN+w/t6gHNfhY9jxKBipE/76+/uJyGMqDwH0gOUeKj4SRYsp1+FjDwReseBQaXzke6gY2egeLxUfdUK5VfFU5nPY6FjDR6Kjj4fkucR4xEJeVHwkRBA4BgYC+FguD7kJRyc+jpeHjIqF4+EhdfjY3tpKY2NjPnyMcg81RKpcfCQIZeoMVI6HjIKPSZh5yFLxkXBkeMhY6Hbp2muvpUWLFvmOveMd75iwJBj5fA8lEikSFu097qTZQYDJ7VxYunvdicMLe7FPcPe+y5ZUnlTMtJiAOQe95rIHeiDe7h7fDgFwHa2tkWIwOgDa6YLJetgXjBZo4TLIGncb2dqT7eoK9hWeq0mNe4x/m+Hec6/UjygaxFIt3dlMpvh+NsGz4vHmKfepDqDp1dW+MezJ532xKDqtoOrStR5CI96hngchOKQ1905CuEmZxlcn3EcFMvnYXsP9GxHuOqQbryS8eByemyZ3uXJA9FhjKicLH4mij11PPk+pRIJ2KPPJxlio+Gg6b3h42LcuAL/7sm7NhwlJsrBowses66psY3qaARqGp0y1uVWXgo9EwVAjHmu5vxwHGAUfCUK5WC5G6vAgm8kU+ypjZCn4ODY2Fup5o3N5HQHoFqBofZIxcrHm3g1un3QxmypGqtbJUpi99fBiFtX7h4Xn6DA1pXmvlcTIYw0fiY5OHpJzDMjCjm1eLYDgFbYDlHSc0HNZQJbbL5eH5LVXCXxcAMHH7EL5+Njg9kkWzpl0PKQJH1Pu8/FvN7vH1bEZDw+pw8ek4xRdu234mARoCvTYVw4+ThQPWQ4+ysc6UTo+Hgke8pgVup977jl69NFH6dFHHyUA9LnPfY4effRRevrpp4mIaO3atfQ3f/M3xfMPHjxIM2bMoDVr1tDPfvYzuu2226iqqooeeOCByPeMOpjBeG52NWfrdg8BjSQE7UPu3xQBUwlIFCf61OppBCRJjf2e1TSHiGQXdv+C0gmEtknOwFsoFGhsbCyQCdCkOdRZsJPwMzX8fzmAxP2SsxiqmtZZqZQWILYr5+k0tGMRxka3aBsBmmU4nnav27hxI2W7unyeCDrheXp1tVaL60h90goEkqZXjbFKu/fiTbEboC7NGDgQG2UUaxrPa5u2fbU0HmqiC1M/TczjVIDOUvo8bcoU/3vUJPww/V7JdX4005HAR6JoY6dqvFWGhee6urlWK/NgblMTpTTncVIZxsfblHmv2/Sj4iNnRFXnWEN9vXbOmfBRXYfjxUd2FVVDjQDQOe3todYpGz4S7EoOE2MTEP7gx8dCoUDduVwRIzlhThR85D3K5HkjM1JyMiITRjZpxqDL/TswMGDFyKGhoWJ/bEz4NnjMnoyJ6v1r3Pd0CHqMrIdQSsjXNCWTlF6yZMIw8ljAR6JXBg+pm0smfGyGUJolpHc6p7FRuy7nNjUV8ZEVavK626NZ71EsrUcbPhak/8N4yCrlu4yPWcPaTMPDx3J4yBT0+NgjXdfX10fndnaG4mOV29ZE4+N4echS8NHEQ5aKjykIvuF09bqqqqMCH19RQve3v/3twKIEQJdeeikREV166aWUzWYD16TTaZo6dSqdfvrptHXr1pLuGXUwPWGYhWxVCB8jf3w3yHNFV13S30VAHwEF99rtxcV4xx13FM+tBeiqwPWgM5Gg/bC7GtW6E1oGJtUakHMXvZxgQQUanYvmVNjBOow5AUAdra0BN6iiVtONm9kGv4aM29gIobkLXOc+03Z48Ti+Betmgd2sWbQ9AN2hAYEeCKBSx099dmaWb7rpptCx2QsP0NfAYDVyrf0mN0Y+r979ba/bVj08K47W/R9Ba1pPPm/VoKtgNTw87NMYFgoFbYkHdWNOQFif5GMLlO+LFi70uUrZso1Wcp0fzXQk8JEo2tip7mwqwzIGf3y3utny/61Ll2rXH8cGf/rTnyZAMKNJBN3jZObVZsmthYdrUTFyhcT0hOEjz+nx4CN7KMkKPpWJ3QsvTKlUfGyEYGBMGPlGBLGwVTM+OnxML10aeP4CvD3LNjZ7EI6PLNizZ0UYRm6Ah49J6V1FxUg+J4o7PuPj2NgYFQqFIkby/5ycMgwjU4a5xJ/FLS1F5QbTeDHyWMBHolcGD6lTEEbFR95fT1LO5Tm9bt06AkCXuWtRTdalCvc2HpJ5pKMJHwek/8N4yCSEJVWHjxxPr8PVNDwsDOMhr0IQH7sBOls5xorOQ8rxowUfx8tDloqPjJEyD1kKPqrKlA54/MHRgI+vKKH7SFD5lm4iIWQ3kN+6XU3ADAI2kGfJbiAgR8AmAmqUCXgeAZwx0VF+c0hYyesISCu/eVod0yTnZDjtIcCk08KpgKfTqHFyIpPLUVi/ZPd0W0yJydX7dMt1AGgREND0OfBiwmW3KzWZ0wb4wVpulzc806bQ29sb+vuHYXb1iarp5fPWGM6xxWGpXhAMdDUQrl+qBl0Vsk2kq4ubdWPW+/r6ROZVBOegA9BSdUwUTap2LCK6CR0rTOWRoHIs3YwbqutYLcSmntTMgTSEhU9lZOZKa1c+nnbXTDdQtI7vR5DBM7owwhMWS8HIKPhoEmhLwUdewxOFj2n3XaSU8WKMfEC6B2NhFHyUhUQTBtp+a1b6pOKjnIzIhpEDmt/lUCHbe1AZQR1GzkqlAnk5dGSq7zs8PEy9vb2h+Hgb9OFIlcDIGB/Lp6hjJ3IC6RWEMj7ORGn4eA487w0dRh6AwNAkoHVJDps738TRh48F5V7lZPyPgo+AMC4llWOMjyPSMZmH1PGVcttLDeN0pPBxvDxkFHysFA+5ZOHC0FCIwLgcAXyMhW4LlTKYTU1zSbiGs5CtE6JBpthu4FzSuZaLNtIk3NPl3xpICN6635LUDIfmQTBOqltSFqUB017DYrW52CxuaQlMctnFSOeG2FhVRe1u2QqbNWqG8mzcRhRgkjehjRs3ahUKvBnJ96jWHJMXNsdI7oA/IV5UsKpGUMNq27jkZxtQ3pvunKuuuir0dx73LVu20Oc///mAezdrE9MQtZOjagR1Lk01EKDZbinho4Jp0nFoXnNz+FhEzEwZM5XlU9Sx43hFXjebEFR62bK+6gTyJLw4PN2a6dbcpxpC+FsCfcxYVrlvKRhZCj4GrMIR8VF2pZ8MfOxoby8qxuTrysHHWgRjVlWMDBuzplTKmKeEz2GLXhSM1HlK3XLLLVblKGPk2rVrqaOtLWBhKQcje/Lm+r5na7wD5HFRPRfWA1TrOMU9eDwYGeNj+VRKzguOKTYpCMvFxxroS1g1ums4pblXCqD74HkNqetZ5UeOND76vHRK4CFXY+Lwsccde3mPWe1epypUWHl2tOHjeHnI3t5e+spXvjLhPKStBGQCRwc+xkK3hUq3dC/wTQZh7R4mYLV0TJ/FXHxMAnkpv40o9wPJVvIcBMPLidKiAhPgdynZDqFdD7vuoosuoq1btwY0WLoYIAYwWftkA/IwV8aw6wDQ6+Elr5DfoXzNQQQtPXUzZoTGS24AaBWCjH4NQN25HBGRnqmuqirWfDT1uy6RoCY3nj1Mw9jgOL74cP6EZbOX2+iVznOg38inKdfw+w2rt+kgqFBgr4ha14XdNJdY4zqKoKtdGqIElbo5xZbuiadSLN2qK2wPRIKx1crxMGanVKsuX1Nw58cu6X69mnWahpeYqByMlBM9RklGds011wQy0NrwUc63MFH4+FZ3TXICNPk98nUH4XkalIKPhHCMDEvMZMNHOV46DCOTCNY51uFjGvqSX/JcNmHkLOWasNJGcvZqVThKwkucZFsbOnx0IOa6zvsgtnRPLJWCj5sBWqa8uyyEu7PsAVgOPkbBzgJEVv3LpHVSj6DL7nh4yInGR8bIqDzkROIje1qpmMLrXPf9aMHH8fKQUfCxkjwk96lcfGTvhHJ4yFjoriCVF9OdJWAmAevJcytvIOFaDgoXnsME8rDf9hDQ795bnlBLCdhMDpI0XXFPLwWYZOFUBjyb5pU/c5ua6ODBg4Fx41iNwcHBwCJbkclQrePQAmi0ghLAmFwZl7W1hSY94zGQkyWYwOzspUuLVlVepHUQG8leeJpWBwK05xhApjuXo9HRUerO5YLxPrkc9ff3hwJHsra26MaVVO6fhJ8x50zo8rPUAIE4HllD3OCOD59nmxe3Sn3jLKbqHOPxZS+J9Yb3dZ3lXqxRNZWdkMezGqCzly6Nhe5JoFJjurMQLpLrpXnJydDqZ8604kmY5dG02e5BsO4tr+NFENaFhdAoBcrASB1DaMNHB2L9q4lbwvCRSGDkVASt9alEYkLwkUiPkbWJBM2cPj0SPh6CYHx0GJkC6LyurnHj4w6I8Cm2GnE/ZZyY29REKcex4mMSStZbeK6vO2Cv7DAo9Y8FFN34yp4LJtfTKGsjCj6eBdBMd45Uao3HpKdycl40QXipqHO3bhz4aMPOfQC1I4hLi9x7t0OT5+YowUc57rcUHtLB5OBj0nFowVln0SLXqspC6Hp37NdDYMpE42PtjBmR8XE8PGQp+FgODzkR+DgF/vEshYeMhe4KUnkx3WMEdPteoBd/7ZDfBX27+z2KQG76TY31ThOw3z2/kYS1XZzLpRgGBweLfeeECmkEgYkXIYOrDGo7d+4kAMbrWpRJPbepKdKY22ow8kI8cOBAwGWVwZQX6pzGRt91aQjNbau7mFSNmm5DkMGHF+pmBLWQzLBz5m3T4pfLXRQT+DgOdbS2Wl3PAaFh7lbu7QDUmk774gbHxsaKiUvCNriboR/nHbBnnJwGKeOnLrmblIzilltuCU1Ctw36ODaeg+xqFTY+34S5zFol1nlMQSo1ppu1/+r8TUj/q2s6CbuCz2TpVudcGl6GVi4/UtRqw2MeGSO5UkASZqxz4MWV8fobHh6mRS0tRc286grpQKx/7gdnYI9CKkbqGLCJwEciPUayABsFH3cgvGQgIPBwPPhoSjqV7eoqvqNy8FFui8+zYeRat3+OO/YmfFTr2DM+yrGY7EKuzj8eW5vgE+Pj5FM5OS90HiRsbS4XH8N+a1HulYNYw1Hwkag8HrJQKBR5gonGRxMPeZ6mdFgqkSgK+LrKK/UQybs4mWs5POR+zTpkvDxa8JGIaGhoqOimXyoPGRUfo/KQo6OjwXBV+PFxqWH+nYxo+LjB8G5sGBkL3RWkUut0V1XJZcHWUyIxg2bOrCPHSZIQgvdTMOmZQ0Av6QXyFPljuuXfGt3zuW2O52ZBWxbM9xLgz3zLxOVbdMDU0dpKu3fv1oIIa9X2GxZxv2ZS33nnndZkCaa4toa6uiIgjIyMUEdrq/a8uU1NRXBf3tkZKDtUA6EtVBkueWHJWlNbQp2NGzcWrUqyO2eYxjkMFGe5MTmqhrUZ3oao09R1tLYWx1C36cybN8/XL5Ob9sxEonhelJIh1YA2K6l8XqFQoGwmY0wAw4DHSV1876uqihLwLPthY9uuGZsoWShjprJ8KiVmUdaarwdoRiJBdTNnFpkIk8DmSH9VBi2JYG1VXjN10CcdUjO0cryhnPmWMVLFIxUjW5cupeVuWIiKJWzByinX5KT7qetJdaXUkS6urRqgBfPnR8JHdk8/e+nSgIaf8dFWQoUx0sboyfjoQFhXbBhpSt4zHnxcsnBhse/l4mMLhJeGfJ4NI0+CvX4yh22Z5iqftxt6fOSx5XwiMT4ePVQuPsoeJLWSZTEMHxfAXKYqDT1GcjKwsHkXho9E4+chK42PjNmq55LKQ569ZInRhXtkZIT6+/spVVfn+z0NEYO8auXKcfOQLATed9991JPPTxg+NsBL0FYuPnLWbxtGMg5HxUfeu2w8ZFjFHj7nBugV+lHxcQD2UmvjWeNEsdBtpVIGc2xsjPJ5f1mwTGaF+79qpV7jHr/c/XuIhGCtWq27yZy9PGFomwXtAnku6G8hSIucgUBOjMYxj4PQx3Crk1BdJHx98R5Sp/ZDr2lUtUcMTosRrEOYhKg/K4OBeu9ezX3SEHGj7EJ0O4IxSgykuoWlun4FFqq7+RQKBVq7dm2gbzqQCQPTpFLnGi4QDEnfw5g3IrPiQr7WlDVULddhsj7PltpUwVh9Llu2zMZksug2n0LQzbcxmaSzpTq05WjzwzbqmKksn6KOnc4CYNtoARE7B/iZBrkNnofqmrFZfuQMre9z/w5Kv+/atSswbxlnZI+hsHIjMrPF1xaUPpSCj0ReXFsSQXx0AF9mVxM2Z7u6fPfKQihJuW8JhOekkKkUfOzv76dFCxda16opOc/RiI98rk4ZxPvMIkuyHhs+1sETnHT4OCuVojvuuMOaTCjGx8mnycLHHIRCSF0bXGu5HIxkYVuHj5XmISuJj4DfxVnGyHM7OwM8pHxvXcxyCzx8JEwcDzk8POwLYywXH9W+VQofG1wFhA0jHUTDx1J4SBs+zmlsLPKQdQiGQqRqa63JKHdFHJ9y1zhRLHRbqZzNRtZwBet382ebe3yP+3cHAUPu/xsIGCAhNMtJ0d5KgND0DQ4OFrOrmmO9+0m1qk+BiIVWlQNZOL5kMVGZAZ1WLYlggpo0NNpUjfZIjmszuYsmHYfWuP+rCzSnuw88y5axL/Asrrt27fJZ43VayhH4NxUmNRmOOi7LLEyRmqFSrUO+1PDcMniHJeThupLsDmTqRwIikcZ26N1t5gL0Wem7bZ7oMsPL/b7zzjuLG7Cu30kIQaFQKBRrb6qaXC6zZtvYKrXOYxJU6tjp8DFso93j/r1BmrO6pGjMfKr4GKbV1jFYNQDNbmjwHcsBZeFjoVDQuniz22ap+EhEdOONN4bi44xEwoiPh9znbZA8C3TWfwfmZDWq23kp+Ehkx0iVYTva8fEQ9Jn4U9L/48XHsyVvijB8JCLKdnX5+hbj45GlycLHzfDcktUyfqul8zmxbRSM/BD0+JjNZAIKgnIx0mSZLRcfJ5qHHIHnUVAuD8kJu2QjGFOl8DGPoIDebnjmqPiYhFA2RMHIWqnvOnwslYcM63d7aysdPHgwEg+pw8eke43NFd6EkbHQXUEa72ajr99NBNwsHe8hz3U8RyLp2u3u//JEdaihYXZRu2dumy3dC0h1PU8kUtTYOMd1g/eOO0hSHo6RGdgDf7IJGfRVrXsK/jJltsXJgKOrvydnReR7Xga9y4rNjWUI9lgZkzaVNbW3I2hpkzWuUdw6Of5JdQHr1oyt2s/eCGMpbzrqeZuUZwzbzOefcYav/9UAvRGgu+G5pqWl+5qS0PXk8/TAAw9Q2CbI8bCmfsvPp7MI1AB0fcR5NhHr/NVM4xk7W+gG/8Ya9TQEQ6Zbhw6EsKzio6nt9fCELHVzrlGOqUxgVHzksioqRta4a7FUfAy4aCKIj2+FGQtt98oq4647Z4lkqWb843jFKPg4MDBA2a4uI0Zq4yxx9OGjOg41AF0N0McgPCFKwUeeq6YEQTE+vnJpMvFxO0SCrBTMGCknJLO1z+X/ZCxMJRJFq2IpGKkqyPZI/aoEPhIJjGTDRhhGrkF5PGQUfAzjIcP4Qvmdh/GQuuRmSQghVo5v1vVzSHOsFHzk8zql9k0YqVbOmAXQdIDegtJ5SBamw/BRDucK67taNxwQMfr1Jc61ctd4LHRbqBKbjT/Wew8Bq8lxktTUNNc9von8ArZDXny3Wpe7hvL5HkPbcmI2dkU3CeQbtMc50ywzA7rkLt0QGS11AJMF6Dua42GLk7VrbMEMs8AAoM+431W359WW+yyFFy9zCP7yAGwBSkKvTWXQ1J3T4DgBl6XAuLigwHGUujhzZirlDW+GCzSc4bKxqormNjVpgamjtdVneQobixst4MJlyfizHCKbpnwsDc+diuOfzlViWxOANlnTfvhBV85Gb5srTLxBDA8P+2JGk9Kc4A2JrUATuc5frTTesVM32pvhlWLh3zbBYyAdw1rVJdvRZpJV1meY1UA9Vio+6rBgOTx3z6j4SESUzWSsFuowfNyOYDyyeq9aeOWCTBgZ6ENVVbGMTVR8ZAZSxcihoaFXBD4u7+wMKIinK32Ogo8OvGzE8vEc3JJMiPHxlU6TjY+VxkjTGjAp0GWMXLVyZWCddMMfd1spfGQeMgpGqpVQovKQtYDPQl4qD8leTyo+Zru6rMkxGR/7+/sD/FkaQtEixzdfB5GRewb8VSRY0aziYzaT8eXoCB1z2F2xG5RY+G5UjofU4aOsvIwyX2SPkqGhoUCJXJ1ytBJrPBa6LVSJzWZsbIxWrlxFakz2ihUrKZfzZzlvbp5Ht956q/vdnMlczpSouop3dWWl2GKT6/k2w3HxYZBYkcnQTAiAVS1BNhcbQACUbXHKSYjCrFLs3ngZBMiNIZjEIawNbocXu3yNLeO4Lr5TPadOGYuk41C7y+jprFRZ+OMouX8pBJPlMCDMbWqiRx99NDQzZ08+XxzTMIEiB7GJyICcBGh6dbUvEzFv1l0IaqS7czkfw5iAYD4vc9tMa+ZILTwtKGuhuV+2mMQwa0w2k6GZiUSgj6omeaLW+auVxjt2smUuIMAq8wtAMeYtbJ2HZZLlDK02l94BzbFS8HEHhEXAhpG2Unm7d++2xnbK+Hid2/dhBPExSgZ4tvaUipHs9h4VH2VGb2ho6KjDR2bIb4Yn1Cfhtzb5LIDuM5aCjzsQLMGzHoJRTiDGx2OBjgQ+Mg9ZLkZ2tLZaY2zDSjTyOuvO5Yqu3DzfU6gsPi7v7PSNQRhGJt0xZItpqTzkdfDwcbHCz5+J8GSJd9xxRxFjdb83pVIBTGEeUoePapy5jLMmfDQp+VQFKAv1NoV0KTxkI4QyWlWo6jBypvuObDxkFn58LBQKkZL66qgnn6ek49CH4bfky/t9JdZ4LHRbqFKbjWeR9izXVVWNlM/30NDQELW2digL3yGR6VwvGMvaPV0dV7tb+3XKcSHQc2bIMFdv1bVJN7GZQWPA7oEAW1l7xFrXGiA0BpHvNUVZCKztSsJLmuBAn6HTkdqfq1nEtqyG8sd0jimjpDGRCDwNrHyfudAnp0jDK2dBJDR17a2tvszPsuXJlOW3ByLr5GLluRyITMy2zVoujSRr2lWgUl35dZku50KUR+Hnv+WWW6ihvr5kTSORQcByPQwma52/GqlSY8exVupcXrVyZSDxlwPhLWFaqzZ85N90c51dzAY1878UfLQpG2WMDMPHuU1NVOtmvw7Dp6kIYmQagglrh2fBzsEcK8jt62rERsXIVzI+yi6yB+CPywZA06ZMod27d4e+1462tkj4KCc32gE9Ps5CjI+vdJpofORSXGoN+CgYKedmUOtc2/DxOsP8Z4w0lcDj8lCl4qOOr+M1H5WHrE4kfP0plYdkRcMsrSdqkgAncP/9YH7eu29eyqEk98/o1h6SuVt9zgaY8TEJT8nG71suYVtUIDoOTZsyJRQfy+Uhs5kMDQ8PF+eaye1exUe+p4qR3fDKzm7ZsoX6+/v1vK8FI3X42N7aWiwNV6k1HgvdFqoEYNpir7u6sgGBXCzgtPZ8APTxj3+cWloW+SZIV1fWt4F2dp5LXgkyXamytHt8e1EBwNSTzxvddGSQMAHcRmWxDEET64LoAAzotV2A0J59UzpPXbzyd1PMny2WYwO8GCTTOaaMkhzXGaY15P/vtNxDzT5vGzN1zNPwEqOp45mEF6doeq99fX3FjVouFcTZKXe447QGov6i3JYu02USgolWE1qp/VZrIIeRyjxEoZipLJ8qiZG6uewg6NKcRDBZozzvP/7xjxczRvOnQ9lAR0ZGqHXp0uLmzOtCx5SlEomAS6YNHxlromCkDR9t1h4gmK13vbsG6yCs3oxfm2Gu07oDoH2Ge9kwcofl91cCPsqxpCaMXHjWWaHvlYUZ2TNKxkd+N7UAzUNQsCgHH9UayGEU4+Pk0kTjIyAStJaKkfOUnC3l4CPzEzqhpqO1VWvFzqF0fByDP56a8bEUJedMzXoulYfcAA8fTfy8aslerBHQq6QcSvI7CVMYmCzkqqU7Cj5mM5lI82oi8VHmIdPwY58OHwl6jExBCP9qX2cpLvhReciJxsdY6LZQJQDTC+7fQ15WciK/S7fJlXw9ebHaDQRM8U0koUHrImAzASJO/MCBA5LLuSP99S98Ofb7jDPOpI0bN0ZiVtbDvrhl97zt8OqD74U+4dCAcv4eCJeVJDxtmqztWqVZZAmILK+NVVW03r3nGvjjn9gSpAMEZu5VC5C8celKH7AWVB6LUQSBuxN+dyB+9tXwtLWrQ/oHaRw3btxozWy6xv3/793+qYktwpjRMC0llHb2uH83wWPmHaUtW4KSavhdLNm16uylS4sulTJ4hllnZO39ZK7zVytVEiP3wI8P37DMm/XSOmxA0NLrQIRFbIZnzV21cqXPnc2R/iYRZCJ47fzDP/xDSfhoLT8Cz8LN696Ej9tgxscO5V4mfDzT/Zt0MW4vRCmgGYmELz6ULT5RMVK2fhwt+Lho4cJi4jEbPvZK80Yds0pg5B74340OI9db2jThY3trK917770BK2eYO2SMj5NLE4mP+2EPGZExkvGs0vgICIW9XAPbtn5KwUeZh1QTsqk8JOMPY2Q9QMukNV9w1+FKJMgru8ufhI+H/AyEh1DScYq5Ik4tXqMP3ayV8PHmYrt6/n49BD5mNWMhLMl+C3kGThEjZczb7uJDGH8r42MCKFqbbedPND7K55vwMQoPaQpf6u/vn3AeMha6K0iVAMx9+/ZRsMZ2D4kEauEL2P+pIqCegsnVphKQLS7kVGoWOU6DdN51oQvf/3Fo/vwFxAygbiHOhFczlJlAGdRnQTBPwwjGAIcB7Bj0zGKrAiQ9EK6UXIJAPZ/jU9Tj50aIHbe5sY5Bk50XwsVFZjbTCN+gZCsWIOJaosa2A6DFLS3WjY03Jt6I2P3qY8p4qu83gSDj3OAen5FIFONXuS/cbg5SYgu3Xzn3WhuzHPYcM6EpWaaJQ9Rmd7bE4lRynb9aqVIYGbDeAXRKhHnDnyoIBktecw0QWJGV5pMuYzm7TocxEYwHC+bPD+0T4+N2CIY2iSBGngvBJO5EtKRuG2DGx24IvOU+qfiow0KdEq47l6PXloGROXjZgScSH6PGbQKg+kTCHtsHPT7uhd0KdzqCe18tQPUzZxbd2ffAj4/8bnQYaUtwZ5ubUWqqx/h4ZGgi8XERvAR+UTCyBkLAtuGjquApBR8Be136Ke61zB+YeEgVH23reQwiEZt6Tb3CfzfAIb8By/97Y+NsUgXyFStW+vDRxE/rhUozf88We8ZEHgudhVw2lJ2p9Lk7l7PWoWZ8rIXwbOCqMjbFB3vp3IZoPKQOH5MQydVqHSfAQ9rwMQU7D2kKX2pKpagOE8tDxkJ3BalUwNRpSPL5HkokUqTLRG5bwMAgAX0EXGw5DwSYAMFUK5wX/hr3/01Kn0AZJALJbOTEFVXKRE4p3zlpwjYIYNcxKlPgaWN1zBgnCJK1XQkIBltenLKGa1YqFXC3anAccmCOaWyorycioqGhIWqXLAcmQJqRSBT7ratDGMZAc7xmkcl0F3Y2k6GpCMZ3ykDE4JHNZIzZaHPuPWXtIP9vs6oAQcZ5tvJd3ihqpePrlfv1I1qZjSgArjLoasZdbVxohFjHctZ5TB6VMnYmDXJPPh9g9FjREzZvBgHqA+jiCPNLjqlVz4tiQVXXuOleMj4mEMQFnTX+mxAWaxWX6hMJStXVFa3TzKSqLpus3OT1x/i4w3BNEsGyaJzhm9e/DiM7WlsD8eyTiY+FQoGSM2dqc1UwPsoZfMvBxyhWlW/C76KvE4g4SVO98m7kv5zwrsNyv7C5yUpS3Z4pr7MYH48MTSQ+OrAnOByEKCM40fi4A4JvSYW0I2Mkn2PjIRkfB6DnIesQzkMGhdf1JATqGSSq+HCZXlW4rSE1B5OXeylHXplfr2pQa2sHjY6OUldX1vcMJr79Wuk5Uq41Pcp1ot+eAC6HljbU1dEM+D0cTPhowkg+T8XBqDykio+698wYeZbSpo6HXCZdZ7qnyUgI6OWEJCrHQ8ZCdwUp6mCOjo4GsohzkrTwxQN34TQoC7jBPc6u6Nvcc8ME5xR5Gjv5PFs9b75HjwQ+wRjwKaii5Z2dxWfmeIwN8AOiznqxA8FMkSqjYmOwawFqVq5xIDS3uvNNMTA3aACB+6Im9TFpYh1N/3vyeRoeHqYrrrgiFAQG4AcnXthszUlo2pYtQPt5PByHNkNfi3MzBGCpFhtOIscg5APaqqpijcsNEIqWAQiGcDpAl8PLQNoo9cWR3h27L6l96oSZAZ5lyZQZ9tuuXbsC8eW682xuQjFTWT5FGbswDXKUuDKd54UDz1rJ8y5MC56S5ql63h7LPFM1/kYLtgYfd0hrKQu9AJzG+PGRrVbyNdkIz6Vbb6a47y9+8YtHFB95DqkMnIyPcq3aq1AaPsrurLpnY8Ut7y0FiPAnEz6y5d+BZy28TTc27r10cyo5c2bZ+HjjjTfG+HiEaaLxETB7HWYxefhI8Au8JoyUEx1y3gMbD5l22y8VI0eKvzHvO0rAYt81gmfeLD8WBXljlWffTIJf9rfzxS9+UZM0OU1ebiW1rK9nreb3PTQ0RCeddIp7fK/SL+b3B0gWwKuqGimX6w7IINy+CR/XwByrPwS9x08YD6nDxy0AvQYiv4hc5UPmIavg4aOJh2yAMOKZ9hubF4bpd078Z/UcDcHIWOiuIEUdTFN2ck8zZnMfzxm+D7jnc9bxMMH5Zul69TzTwu9077FLua6HhCbPe55EIkWdncuLmlg5HsRkGeCYllppoayHYA6T8INrrZtZ0rQxNGiuScKzWqjnm0pazHD7shdeXCQvcHaL4ufQlZRIu0CxA/6yYPv27QvG1sFzvZQ3KJnBlH9j18S9AF3kHuMSQGrCDFmpUICnjV7e2am1KqmlgNQNS008sQigs5VzHAhXUXb9vNb9yyVK1sMTknRWy1maex48eNBaK1SdE/uhV0zsN7xzuX7teNZ5TEGKMnZhGmRbXJluA+bvvH5sSb4KkOPr9Oc50DARCMZMk7sGdC69yzs7tfhIsGMkWz2M+GjJYN6quYaVE6ZrdGXREtI4yBjJ601WdB4pfDwE0EfgCd8cq6l771HxkRBMaGdSfkbFx0GpL/PdxFWmUpstCCoTqgB66KGHjPjIHg4xPh69NBn4uF+zDh0IK2FUfJSFFJ3BIgwfCwjimw4jqyHy7rAAUwoPKVuFawGaWVPjc1WWecg9ENixsXhv5r9lw5Js1c6R/7aycKseS5Bn5d5LwGqSrc5BIX6MgkmMcwRsLsoILPT19/dTKjVLObfHbUPl94MCuOMkSeXZAceKjwTPwnz20qVGfLTxkCo+vlbzezf8CfCYh1y8SCSGDuMhdcrcc13PMhUfWQHA58nrZxRBnoL3JuNeGYKRsdBdQYoymLbs5GG/tbV1SL8XyEu0xtfuJc4u3tQ0111EsuDcSEA3BbVuNSTcxfm8ehJgI5+jxpkzOOmeZzQAHJlMtrggB5SJrUvtry4WeSEPwIt9K0ejrwMUk6VbjWWU4wfrEwktk7pDaZP7XMwG2dWlTTTS4C5u2WVH7sugsrDVuJQ0gtpiBhMj8710qc8VjduQXcTY8jYIT7NYq7jj62Jf2e1TBiyOjeE6h2HvaS8EyHJmc7ZUDw8Pa2vrcvZKtb20pm9JmLO1xpaciSPb2Nk0yDYrHP/Gc1ZmELk2aGNVFc1taqJUIhFwk+tGEIvkLKwswKQRzJCrYpbKHHKfhhC0FmSVmOJSMVIejxGIpGfl4qMt863ajvosaamdJIKKziOFjywM6BJgmpSxJnzcDn3Cz4J0nJOvlYKPcny1rc72AoDuBugtEMrhbFdXkRnX5RsxVeOI8fHoocnCR4KHR7zuouBjD/RCSBpSZnIIAapDOUfGq3aYMVINMwO8jPvl8ZBqgjERBnmV5jdPCI7q8Wk7BtJXAgJ5bt+qEL/H/X2N1OYICYEdkju6Lo67wW2P+f0epT+D5Pd4DT5bssL4aOIho+Jjj3Q/mYfMdnVRvas4Mc33uyGS202H4OV37dqlxUfef3XhF7LXmqzkckLuG1u6J4miDKaXnVxvzW5tbXet4J6wzCW6xsbGqKlpLgWt0CkfeOTzPXTw4EHK5bqVxd5DQujWlRyTNW/yNVM0i3s9eYCke56g5buqqpFmNc2hVCIR0KRyQgR1wVUDNG3qVAL02tkqiBg4FSBsiWZWS+fzBhPQfLn363HbfB9EdkrOICnHuqhMKgusxj5bgEK3iTkIWnJUl8tvIsj4q9Z43b3k3zj2WvebfN0GeMxylBJu/KmGYCrHxsaKsfBhWnlAuJ6pyo8VmQxt3Lix6O7D9RtT8CsebFp7OZZJrts73nUek55sY2ez1AwMDGgteexSPLepKaB4Sinroiefp4MHD/qSbQFeEi8Vi5LwW27V+TwdwprC18hxZipzaMI7ldHdo8xb3TVJgKZIHj86xlOnMLDho+xpxOuiRjkm42Oj+8zF7L0ICsSywH6k8JHHlEsd8icBEUZUDj6G9XMXysPH89zYQVtGdfnjAHT2kiW+Y4taWopVRnjNLIY/B0iMj0cXHe34yN4qurAXbiOlzM0pEJgjn8+5C3QYacLHnny+GK8ehYesA0hYmmvJFAYpDE6bKRifvZqCfK3Hp4vfBf8tjFs1FPQMTZPHC68n4DMEXOb+pgrDssAu33uU/EYy5sVlHlynFADJZX5FHxzyu5qr7uh7irhxtOGjnESNFZPj5SE72tpo7dq1NDg4SESk5SHVfVjtm7pXxjHdk0yVsHQPDw8b473ZyqcmXsjne3wF5OV79fX10XHHnUACeGxu5yeSOQOiyQVdbTP8+XjisyXDtunLTJaO6azXnGdb7L6NxN1gVMtpzgWQAxAbjPzbXIAOSgu7VtUMuhZcZnBUZlzOUKsDipMMzyRromUtm47Zrp0+3fddZb4bq6qsgHU69JbzBIKabhvwyYBXBTHPbVr7PghmPQ1PC7ofQVBX36EqGEUBZRnMK7HOY9LTeC05hUKh6Ckhvzsu9zE8PBzQYnN8sAkf582bR3WwY9GJ0FsEdRpvnrNqm7akW/I6cSDwIwpG7oBZMJfXQxR81GUqVxlwxsewLOlyPKCs6Dwa8HHB/PnU4taIldvZj+j4+DHoc0/UIZhMMqwddbyj4uMgPEul4/Z5EzQZ4WN8fMXQROEjW4r7+/tpWXt7WfgYVQjRYWRac76OB7Th486dOwNlyVR8FJZ4XQUgncGpgTwBWBVaQVGq+ORy3RoDl0NC4B0jYBUFjVnd7m9BIV64ffO9u0kY1XaQZwE3GbtkpcBJyv3S7t/1rlFP5ulVwR60dOnZdNppzb5ji+GUhI+9EPl5khg/Pk6Hh1s17rEosdWV4iHDeGT5PF2W81LXuEyx0G2h0mO6g9Zszkg5ODhIAwMDNDQ0pBXCdSDJpEvUJkqI8f9hMeMmkFG1YvvJbx1PuufakrgJlw/Vhcg0qbchWsZNdttkhkPHDCUhEs3cd9992rErFAoBy7DJCp9FOJPKGTflPrNGN8rGxbXD10NYGFRNtByXknP7pGO4cvDX1eTj2a4un7uWrh+9CILP4paWQAyNLTsla0rlTXjJwoVERFrNexICFHWWmDAt+OjoqK/Um/yxzR3ZDTl2n5w4KiVmUadBljP2FgoF4SqmlF0xMZFMukREDfX1ViwKm0eqVXU/EGAOVZc70z0+A8EsDMMvLIZt/FwVwMZ8cL/C8HF4eLgYZy6Pnw4feU2mEI6RKmNyjsv4H2l8TEOKKZfeWRR8ZNxrUdqsQmn4WAvQfJSHj7ISw6R4kfFRVUjF+Hh00XjxkYi0PKRJSVkOPpaLkQXN+ex1wni02tL+KScJYTKMh8zDoYTWeBTG37Kl2cTXehbs+voG7f5SKBSotbWdEola5V662PAGkkv3yp+mprm0YsVKRfgm8gvaNvf3WhLW8G3u32TxufL5HsrluiUZJEdhSZE5plxuI5vJWPGxAIG5Kg9ZDj7Ww8Npjtfu6+sjosnhIcOeUQ3TqCQ+xkK3haIO5tjYWEAoXrlyVUBb5l8cwaRrupc7MjJCra0dgWuEC0y1ZaGGCcv6+I+dO3fSkiVpCmrywjWEeTg0BrtrCcf4hAExuxXKbk/7Eaz7zYtf1kbJTDxrzdLuomSLiynGsdr9bIBgutdAMEA9+Txt3Lgx0GdZi8sLXwUKB5pyCRohQtVmGxkuBMs+mJjT4gYujUEP/ImFTCCUhr6URFp6j+r4cfxZWmlb9V7gcbRpwbOZjLZUyhQgEJ+WhDlOKU4UNHEUZex0lppVK1cG3R2l+atuoB1uQi6VRkZGqKO1VXtNTVVV6PwKwyBT3c+dO3dSesmSyPVjfc8HYS2+1nLNMDyNuw0jeZ1uhr/sTzn4eDOEgiCsb9UQid42QAjJG9yx1tUvP5L4qHsHUfGR4Hd/LAUfZWxWk19GxcdUXR0BdmVFNpMJznsgEJIT4+ORo3LxsSefpwMHDmiPl4qR2UwmUEK1saqKpk2ZUsyvUg5GDmjOLxQKNDQ0FMDIUvBR5iGDGcj5Y3MX5yRoafK8Pb9JQLNyX8HnNjXNDWAkr1dxLbuVr3GPbVDuy/xwNQFT3d+3kZxdvKVlkdJnVdDme4RnOgdEHLisZAnKIOakyF5suMLD53v0SckQzL2h8pCVwMd169b59iS5b42a+VIuD8nx5kcCH2Oh20KlbjZsTdi1axctXdpK0V27vcnPsd5B67bpmgTpM5MnLNfVSdfcTI5TS5lMVsnEvtcFmRrDPdLFZ0sgSVkIt+waBIUimaGxLZSL4U+spnMnbIbfonFuZ2dgg+KMhA9DuJDrAF5eXDMQLK/AfbrmmmtCwUVndUnOnEmf/vSni1a8LVu2FGOWTbRu3TqKwnDtdf+eCv9G+trOzkCWYLbc6575Y9BvrLJlTx6z/e7/vfBAk9vq7e0ttsUbp6ooaZaeSxcfK7cX9vxq3xyYy8fFlpyJo1LGTsbH1qVLI7t2ywwal1ZRrTema6ZWVWk32CglCvmamyFCTrKZjC/TMCvmdJt4Cppa2HCFO0PeCRkjbet/DTyM3IQgPiYAuh/l42MOHlboMFLGEtUtPio+OgC1ptPU399ftOJxckXTmo2KjwWpz1xH2IaPWQTx8WKUho+yC36f0lYUfJS/29zyw55fp6CO8XHyqRx8ZIVYJTByhZLQUT2/oa7O6CVjw0g5P0AdUKxUoGJks6Z9xkf2cNkAv3DHPKQn2KnC9R4K52/fS8Dl7v+bKJhsOEHAR0jmzTs7zzWU3dpPwAEC5iq/yZnFWdif4V4TzDrOPKS/z2w13046q3R9fQPdcccdkXnIvr4+abxs1vO97t+FxMa/XK67OGdUfDTxkJXCx76+vmKOA8b3D8Oc4LRcHlJnrZ8sfIyFbguVutlEF5RN9ffWFN3SPeGXNWthLuSqVZrdR0zCsqw5U691yF/yYISAD2vOS0ug4lccdOdydJ7i9paWFus+COtGEkGgV60eOeiTIXHiH3lxJDXaXAf6+HGdRYStGxuk33nxXnXVVdqawbo+JyBK2sguLqY6nPLckcHOxnDJWsaCO6anK/3gGq86wCxaXxC+sZpKlsltcvZ3OdPqALwyI+q4V0HEkrOb0PqQe4SBaV9fX3ETYquPyUWvkus8Jo9KGbuogrKphvMa6Z0yYxdFMFE32BzEBmvSeMvWV9vmPALBGJSyiWczGfrhD39Ic5uatOtzFEJoMjHDjnKfLs06S0JkGy4XH2V81WFkUvqdx7oUfNws9SEKRqq/X2Z573K970F3TM9S+nHW/PlGxjAqPvK8NGWCl/HxzjvvjISPDoRChN3My8FHDnu46qqrYnw8glQOD1lJjLSVGiwXI6tCrlWxbwiesl3GgBaFp1wsffd4SJPx6HoSIZYm/lbmZ7tIn2y4Q2pPX3YrmEBNZzGW+V9OiJaUfjtUXIuiPyxkHyKhEKjxjQOwwP17XVEe0IWYsoFOnjttbRzfv4HsceKrpfYK7pgmfPeor/dXPWKPVnkuVgofBwcHi5Zu3tdz0O9tDfX1vv0/7B5hc3+y8TEWui1UKmBGF5T1rt3+cmF8nlpDW71mAQHfkM6XsyZuIp1bCrvutbcvI8cx1S0MJmMQyRzWhj7bySefWtR2Jh1RI7ATfmasGcKlLu1r2xPE5QUmZ8XULWrZomFyCQXMLuVy9nIdw8ZM5q5duygBfX3eRfDXtGVmlIXKjra24ljshZ/ZJBJgqTLg1ZbnroVXemuR0qccRFIjdSxZk3wzhMXqTPdZswi6frJ7bhLBDTettFkD1/olub7ZSsCdvXQpJRBkyNMApVyrog3M1XjGgBCjKDYqtc5j8qiUsYsqKJvWcQHBzdwmFC0A6BvS+fLGrNN4d7S2FnNELGtvD7hlJt01pPO+SUCUremzPF9vby9lu7qosaqKNgC0FP6qDWl4LuOqdbjGPc79scV+D0YY1zB8LCYzgx8jWeknv5Mo+FgPv8cTt9PR1haouytj5KqVKwNthz33enjCwUYELflpCIxVMbIRQjif4f4dgVBe6PCxJ5+nhvr6YHJK972p+MgYlXL3grD+33XXXTS7oaFsfNTl74jxcfKp1LGrNEaycipsH81B5GiJipHZri4aHh6mvr4+WrJwYcDVPQwjXwOun+1QleIJWuUKzFdffTUVCgWJn05T0O16KolSuGkFE9Ts5Wo8tso/D7rfTbz5zVLbpjbWkyeAqwKtx9MLo0SCgkJ2DQHzyIvX5ra8smKZTNZVCKwhYbTbURTIiQQPKSohye1yYsmwOPFp7v+LlGtzBCwm1VvXcT1aZR6ykvjIPCQrHMPmbkN9vVZZtMm9vw0j1dxNk4GPsdBtoVIG05/F3JLxO1GvAIisMZMTP/BnLgVBRwYj1m6ZhPzLCEAxlX6wv7oFmSW9dnCB5joPHHQMEZel0P3GSQtMTAgzZabNpx2epkzW/upqT5pcY1TrhizI17ox3URE3blcgPGbornHAeV5ddYU2Tq8qKXFV6JoB4T7lckbgK1T3F69cm3SMJa3S31R+1SrfGfASivH0/C7nfKY3QCvjImsqTe9t0UtLTQV+lIlcu1vNUyBQZrdc1XLXbarK9Q9dbzrPCY/RR07OSupLbykPiQ0Zb9m7s6FZtOHZ8Ftt8zFPkhCpDtvbFlUs9Br4GsQxDK1bnUp+MgY+T7DmNnwUV7D5eKjDiM5vGU1PAYrCj7mEA0f5XvdcccdlEAQ58I8FeTnPhX6DMzqeI7Cj3eqR4HKkHHiIRUjdR5F34SHUTJzZ9zXWluFi62m3zI+muLT2T03xscjS+XwkJXGSAf+snLs3s2CTxSMZOFdx0OWipGnF/smV8gZIM9KLH92kPCoVA1A8vUFArYox/hji/2G2/Ym93/2QtUZnXLk9+5U2xijoOv2ap9wLPI8qUL3FOX7KhJZzuVjVcp3r8+7du1y48W5lJrMr4d5A6Sl9uo11+rG0zMKqpU5KoWPzENy+6Y5WQ09PrIBKIyHnIIjg4+x0G2hUgYzWK9blxShgQAnUCLMH/+RpmAseIrM8SSyZTw8doMTAoyMjBTjy8rLfM5x5LeTACK5XwlaZlgse6Xz1N9MWYD3wLL5wNOUyefISdhkK4bqUn4t9BuX7ArK2i5TwpOdO3cS4NW6Zs3fDniZdtV+dMHMbMr3D1jiIBItyUxxVEY8B89SrdsMExDMHntCcBsFCMuJ2uaI9N564c/2KLua696bqe/bpTbGxsYCybYcgF6rySSvXjtR6zwmP0UdO7UerS6xFmcxDZQIk9ZFGkEBKgVzzoYoLnCykm1gYMCHj2HCbNjcZkZXZTgcgC40rM9y8JHvydizBUKJIIfKJCEUeOXg4wz4Yzf5HJ+LoMvgmPBxeHiYtmzZUhyzrHRvEz5y/ogwjNRa4SASdcrvNCpGyonZdP2qhcBI3hPkOc3eDaZa4u+G3wopu5qPBx/V8XYiXjsRazymIJXDQ1YaI9lNXF0npbgJMzYxPg4MDBTjh8vFSGFg0sVaf4jYUOTnTwvkVdNRfzO5Uu9xj5t42Q0k+PIa8udb0rmTm8qRXUtBA1owTxORPulyPt9T5CFFf7Lkz46ukwkaSbjNqwa6YCx58JwOAoYpnNePoqwAzXfLjlUaHwuFQnFMwuaQDeNMPOSRwkeU1PKrkMq3dBPptXM1lMt1E5FXjkC4jHgJzcIBYgYBS8nvQs6LoIP8sSJBAPj85z9PJ510CnngFnYv84K74ooryIsLZzD4BgGn+553sRT/YVssahkA+RoH+kQc3VKbyzs7i1r/PSFtAZ5Luc7lcL97XoPjULarS/uudeV3Vq1cWXQJ53vbtNWqdVtmelVL02XwygSpYxlFUcF9sZVz4GztqhZbfhad25gj/V3U0kLduZz+vSUSPmugacOWM0YWCgXq6+srJhBRmZOwayu9zmPyUzmWboLeuivXDS4UCtTuxrXy/AnDCEAIiEvhd4/kOdGBYLyxTsg884wzfH0K2/BN84+TfaXgMb/fQDDnQinMhPrsoxDxdf79xW8NaXLxV17bKj6yFV5meBgfuzXvKAfPfc+ULVmHj0QCI9nyzUqCsHFYAL37twkjr0X02GcVI+W+2Pqlw0j1Gh1GVsHLMH/HHXdoS+M0VlVRQ309zbDMMRUf5ZJSNmEoxsfJo3It3ROFkdPcOaibF82wZ5yW8dGWaC1sDopPmjzBNsg/2vlT1dvSdL5DwnClWnvnkmy46uxc7rqz2/jwveTx16oxLEfAptCKRPzuVIxcuXIVeVZvzo4epZSYKc78kNK3ywjoI09+COP190QYA2ERb0JVYJ8ZLz6mlywx8pBJeB5UUTFO5iFt+Njf3z9hazwWui1Ufky3vLhriQVcNfHB2NhYoKyYfgHw4klQMMnZ+9zfrqag24oAAMdJ0ZQp0yhYr3CxBoxSBJwZuuAKhQJlMivcc3SZITmRW5IWwwnEeZjc4phJVTW7s6GPFexWFoqq9Q8DfNYMc/mexYv8MS1R4zmIRDzNnMZG3/U52EujRYnLStbVaeP66uHFQ0dRVLBlx1ZXWHazVd9TGuGWcn5/7Lqji0l1IDTvNsY2TNuognmpdWdVipnK8qmcmG55fbN2XLfmdFrqsLnLCbr4uBwz/C4EMSQNT8lWn0j4XKEdiNJYKh4lATo3wtzlpIi6zOI5eDkXVIFLxseb4dWuVvFxeSA2UFaAei6CeRd/AeHFIvcjqwjt8nfZcnaV0v9S8ZFIj5E2l9bQMZb+r3acgBs7YySX37JhpIyLtoy4Joxk67j8v4qRU9z7NqVSlHKcgCfErFSKALtyNCo+8joope6sSjE+lk/lxnRPJka+z/1tJoJxraxk0+FjEgLHUggaRM60zN+2tg6y84/BRMDBRMMy72pKHLyIgsJxmgSv68Vh9/f3K1bocCuvZ1W+KjD+Kq9vo9HRUWpsnKNpv9/SF3t+KMeppqB7epqESzkfNykr1PHUW/szSFQUH6sRzkPeYJlf48HHbCYT+b0RxUJ3RalUwNS5jqj19JjYRSeTkRMk7AhZACKZggCa20m4lsiT0aGGhtn0ta99jVpb232/VVdPdwGpgby4mR0k4kZ0SR2E24pIshYEPCKi/n4GgxxFrQPItSdZg+X7DaCDCLpjsuZrB7z4b9UqIy8yLqsQtiCvhWC21Xtlu7q078pG2UxGm7RshQUYTBlIV7sANL26usj4q+DEAkQCCGzSSfe4uoFGYeZkNzKd++JMy/WsxJATMxXgz7Ye5j6XSiR8GSPlusLyMVPSJgeg4eHhkt5fzFSWT6WMnW4+dbS3G9fcyMgItbe2Um0iQWvcORc29zgD6e3Qb9SA8Ii58847izkL+DNFWmd73GOLDHNsObxQDZ3QTOThYw76DNXd0MS6uQz1gQMHqCHlX7uz4NCjvmsc8lwQ90iYHtw3ZIz08NEhRxHSE26s3wz3efbDn1EYALW2dpS8voj0GJm0vE8ZK3QYmUokqDGZLAoAatuslOSkdSpGzm5oCAgsUSzdYRjpKG2Znkv+nfc1Oeb/EMy1zdWMuipGjoyMFMdEnWNVAD300EMlvbsYH8uncnhIFSNNfAm/92wmU0zUWgpGdilzwwHovK4ueuihhwIKOh0+7oDAMR1Gcvhcg2SFlzEyGv8YTAScz/fQgQMHXGOV6unTTcFYaIdEfW6Ql9FbtfSuL+IjESn1uXUCbZV7zX5SE7mVi4+ZTJb0LuQrLH0xVUJaTUBSMrbpEiZXkahb7mgUGEkCEprkbOa4dsavSuMjQc9DlouPRGI/qjPgYwKl8ZCx0F1BGn/JMH1a/2AtwDQBQy4gZEl1E2dh1xPqdVYNEZfCQjG7r/zTP/2TdJ8d5MW+yIxaQQIjT1BWY8/lZ/Hc6W2A4Gcq1ezW29wFxdqmvfAvApsbcq0ipBERPfDAA8XEO7p4KF78SSjMcMQSATLZkomomdvZdd2xgE5DfX1kcFLrzna4cdlEYgMRpSo8CzX/DXMjkwGqUCgUY1w/Znkf/Ps2w+/y8+jc57pzOW0dZp4/HCtkYrSnus9fCsVMZflUDkYG4hE15fPUd78CwnMkq1lPvG55g9eubZ730hpnAfTd7363b14OwD9Xdco+XXZo+TlkfDSt38VKeRYZ49WqEg5qqRWJIlPtx93w0jByMkgigY8eE6rDbWZWg/uMrHiNSmEY6WjeZ4Pj0LK2Niv2nevmdrCdp/OCynZ10djYGI2MjFBfXx/deOONvr7kNP0Kw0h2WdwL0BUIx0hE+H0H9Ph4bmensYwaz0EWaKZp1kESYm8phWJ8LJ/GWzIsKj6mIUpzcTWScjCSk5TK+DgwMEAf/ehHCfAU6YyPe6S5qsNIXme6Z4nGP+7wXcsYmct1K1WCtpHgXTkh293ucR6j8GpCjlPrw7SRkREpMZkuebGMkZXDx/AKRUlfX8T+4IRco5b7CnPTF8oC9buOhwxrpzYEH2Ue8p1HGB/Hxsaov79fWy2J10ApPGQsdFeQyncvX+8CwQZynAbq6spqzuGFqqvTNzsANEFmzjz5BwcHDcJ9joRwbwei1tZ2IjLH5xGRZFE3ub6IZAxLIVyauAyAbE3QuV8yM8vWpDCmqqO9PXSRyYwxW7/eammzFEu3Lb5Y7QMv/HPa27Wuq4sgNrcGx7Fmb4TUX/U96cZiKoQ7mK5P7EZmUjzwvLONnc7SLf9+Tnt7IJtkLUAt8+f7xp3dknRKERYawhjtODvv5FA57pNh5fP4HH73Oo+U2Zr1pOKjaW5c5v4dGhoKrI8cxEY+Ih0zKvtcQTYMH9lapLaxHyCdu5/jpKSwHcZ3XRZdtvAw7obvCZzYRr8nyIl3PJdF4X1lbrOSGKnDx927d1Oqro5qEVScNkPsJbKyMQwjZS8oflc6fGysr6ep0vdSMJLn3Xp4sfulWHLk38/t7PRh5HqIfAXLOzsDa0lbwUHy4jDdQ85CbaMYH8unct3L10MorpkXkPPLqO99E4LW5vFgpMxDBoQWCOEesBtE2l3BxYSRZv5xPwWt2MLl3I9LjHs6F3WHgPvd4+FYlslkQ/BR7keP2zeQV2qrcvgY5s6eSs3yY1Gum+rrG0nv/r2UWPbwrgl3lTfxkMHxqHHHO6iI6AzBR3nezRknPqo8ZKn4WGkeMha6K0jlJVJLK5M0XVzYnELfv1B7KOj60UBAopg4Sib9Ah0lNYt4U9NcRbiXsy/2EFAXChpR3Cv0zyMrAJIEOEUNGLuHyO7FNdDHdjgQgnoP9InUkhDxbzJpFxlEEiVZA7tR6Qd/eLMoJdGMbQNb1NLiAzRm9k3u0d2axW9qmzNF6ki3eacSCR8jeSZApyh9YAuQTPv27fMxuKwhVN8Hv8spmt9Zgzi7oUH/3G5ymChjGiVrainvMGYqy6dSxm7fvn2h5fOGh4cD717OKC1roxPuPDDhozw3dOWxGurrA1jRAC9JV5Nl7clVDUzE+Ki2cabWU0m1ojC+m7LoqlYO3kf8LoLhCl818Q7j9jDZsteWg5HroU901tHW5sPHMMZ3LoJZ6cPeU0dbm7ZP8l6xB0KASDoOTa+u9rV7KjRlIRXL48jICPX39xfjsR0JC1WMnOL+Nr26Wouhc5uatKXXSsXIU046KRQje3t7I7+/GB/Lp3J4yLTy7vl7NpPRYoquEkElMFJbltO931x4ZUZNc9DGQ5r5x7QBH3s0uNRDXuik6j6dJi+hsS4+OQo+NpBIUqy6pOuyq48PH018dFtbBxGRDyOF27euTjknh5P7GsajC9lERzojoldujNtd4PbDO6bbG2Ue0oaPaejLQR6tPGQsdFeQSi/34JA+PsUhx6mVXDhUC8Ua8mckN2vLggt0hESdbrnO3noKX2ibye8+6Aeizs5zI4+R5wpprgN4putGqcYbDSEctNnKcT+EdUPdEA4ePBgYF1Nb66VFa4u1LjWmuzuXCyQTSQLUmEwGYrGWtbVRnXR/nVuWXO5GJ8AyOM1uaNAy/rbNW/4k3H7Kx7hsGGu6ZVe0PYa20lJ7ixct8tVwBITLG5cdMz63O042y5gtZj/Khi9TzFSWT6WMXUdrq9btm5m99tZW37tni/Ma+DOSh61TXZKUdvhrPNvyGjBOJQ1rry2djjw+Pfm8L67x+uIcDXf381tywjLXMu4GPaZyue4SPKTWk1c6p4dsceKlYOTo6CjNavInCVoMh2ZCJDqT12omk6VEws9AVyFJrXC82HQJCxa1tBiVgNOmTAnFR5OXVX1tre+YKoir+MjXJaW5tdnQNgBKL11KgMjOLv8ufx8vRv793/996By/7777Ir+/GB/Lp1J5SAf6HBAOhHdNh+I984D7Pk2eZTaM5LC+LPyCuw0jAeGVp1t7DUo4SxgF+Udb5nA175HN8LPebbeXAP86Lg0fOWN5koRgW1l8FEK0yovXUl1dKsDLLFy4WLk3h4cy38+yBFuzp2jaThIwlZqa5oZipMmIKH8aGmZTe/s5vmOtre1aHjIKPjJGvlJ4yFjoriCVMphenJxp0V4rTaAdJKzT/jgKz9UvXFsmLAE6LRdfb3dXEZ920iVSW7LkbN/9dIkImIaGhgLxIMK9pZfYelPlCuGr3YXFSW1smbTVRdfR3k5r167VusZFcfNulxYtl6MxJUKK8uxMOsuEah05r6urGKdtLZcF0O3wx5+r4LRcil3RjUXY5r1GOlYDYQHfBL2muz7hKUwI/sy+Muhx3+crJZfkvi81PDcD3bp164pjHgaIhUKhmJhJpwmV49KiUMxUlk/llgzTbXIAiklsNkF4qMi/cUZtm0dKTz6vzQzN19uyU/OnC3pvlLOXLAk8mwkjxsbGipnMxYfjuM3Y3NXFCTNttVKX+vvblaWNGzeW4CGl7gntLm4zsxpMsKPGLEbBxyghVblcN7W3L6OwPZSVIX3w4yOAQIWHpmTSp5TVjUUO+ioMU6VjafeYCR9TjuMTUNS5xRjJuUpUfJyltKkLKXoAXq4MnvO29bRr1y5qqK83KmxjfJwcKoeHtIVuMT6qQotcccCGkatWrtRWc+Dro2BkDiJTuYqzDfX1Ad7EhBNjY2NuEjEon7CQRRmXtlnOryQ+goRlt/L46DgpCsaLe/fN53voBz/4AaV8CTZNfR1wv98utaO66zvU2bk8lIcMMyIKQyEfq6FEIkUC1/0et7Oa5vh4SBs+XnHFFYE8ADYeslx8ZCPAeHnIY17o/uIXv0innHIK1dTU0LJly2jfvn3Gc7du3RpYeDU1NZHvVbqlO2whCHBobW13F2qagi4x7EKzvTgxTEAlygskDdeHa+1e97rXSWOiT6TGcW+mxHC636ZP91sIPCWAaLM2kaDuXE5hQu2xRWpmVt2YRGXqeRHPQDC7t+w2GCWhiXpfBpAs9C7zXMd7j+W518Nzr+E2NkAkxqmbOdOqRbVt3oPudzlLr86NNwnPw+CQ5hq1bVaoqG5uOff/euXaJxGslc4eDNqyclVV1J3L0aqVKykBvTKiG5678kTE5BztNJn4SBR97GxKsaXwNs2efF4bdsKujfLGacJHroGsu96WnbpTSdBl0qjbEmfqY+JY6DbHFwpFplyBIsyK43chteGj3cIuGLJEYiblct0l4b+uTI7+vsGQKsG0sSXKHuOZgOPzXtgBUVnBgdmlPNinEMUeouFjGn5GslR85Db4u+yyq8PHWalUUZlgwkje13QYOQegz0pzOArF+Djx+Ehkx0g2UrS3tobiozyPTRjJ3nmm620Yqa4fNQN/WFywGUPkxJJ6nHKcJHV2Lg9U6AnDtVcWPhZIGOMUb5+qRrcK0YwIz8xWeS6hxu1sIGAazZxZF5mHNN9j0P0u918XCpWkU13stuEj4FWaiMJDTgQ+lsNDHtNC9z333ENTp06lO++8kx577DF6//vfT6lUin79619rz9+6dSvV19fTr371q+Lnf/7nfyLfr7yY7nAGaXh4WJMsJwgsaqr+TCZbgitMgby4GNbC3U5Bq7aOwfGs7LoYl6qqRspkVlBra7ub1ELKsOuIWHTgMwT0kermwgXv5ftXQZ9lvMZdgExRhGDdIku6bcmJm5Lu4hwbGzMm+QhLwiCTulFG2axkJk6uxZtUQEB2kZU3NFsSHNvmPQC/NntPxD7zcY4hU5Oh2ZhYZjyTjvB6aIQ+u+7cpiZt6RTOfi8zHHvdd1sLoezwPecExOQczTTZ+EhUOUs3e6AUCgVjLDSfm3ScgMJMjiOzekrAs2DKczilade4hiz4yOUggzGCSRKMSTAkp7Y25ZbCkfG5ioKuga4HkWRVicLk6WvbJknsC2tIMGuij6nUrOK1Oow0PbuauTeojI7C3Kq/nUWC2dzgG8fFcLT4GIVZMiW5kzEyKj7uUn7XlbKJgo/8PQHhSlwfgo9E+vJSbH1Pw1MSMEYm3b7F+Hj04SNRtBA5ALRz507rebJwofJLUfCRNBh5O4KeP2H4SKTHCcdJUmtruwEfa0l4cepDFlW+uKVlMQmeU8VIESrDMdvHDj6yx2yaxD6wnYSr+2p37FSLNocp+Y1qUXlIuzVdVw1Jj+th+JiE5+Vj4yEnCh/rUR4PeUwL3cuWLaMPfehDxe+HDx+m448/nm666Sbt+Vu3bqVkMln2/crPXh7OINkmdF1dihKJoPs4x1/YF8RqcpyUAlAOASkJBMLjvvW1CkcDffJnv5XdWeTfNxEzxqogm0LQFdtBMF45ihCsW2SqJktO3GRizKK4N5vOtblltbuL/bPuX7lvswC6A8J9EhBZjnVxL2vXrtX2mYE/6qYqx8xG6TODpC5bqi3T+oD7POr7MFrj3U1B3tCiWqhKjc0/VpjKycZHotLGTqcUa0CwlJdNaZSqq6P6RCLg1sjKGtv1q6EXsGc3NhatP3s082wEXjLI6PiYlvBR/l3v7hdkQlMkYvL856pMYxQmzys5GWxLh9c2fIwSzxg817Z3tZPHTO4n4CRN/zzvqS7NOJqYJRkjbYod2dIdJRxIZiT3I+hyu9TSRj/0yaxs+EjkYSTPSVs8rmqNrOQaP5rpaMdHIoN1Dn6MjBJKF5ZsKopFXaeEdIDI+Ojfr8MqMUTHx3S6VYtxwutTNSg51NAw+xjEx21uH1IELNL071wC+kkYvUCquzd/1yVS1PGQ4YY9WUkQXg1J5iF1+CjjXhhGTgY+lspDHrNC91/+8heqqqqir371q77j7373u+miiy7SXrN161aqqqqik08+mU488US66KKL6Cc/+Unke5YKmGGLNp/voaGhId/LD9f2p0nnqtHVlY3kCsN19rgWrf78NOkSLDQ1zS3W+vQvIp37CLu0k7ugk8rvQuOYyWRDJ7r8UbMfliIEE4k483aldnUOInlDo7RwTVosq6VYum5kZITaW1sp6SZL0m1Gcl/vA2gVvAyOgU0RHrOXht6lcVl7e/H+Jg8AroeuahOnuqDDx2oAX2I3uc83u8ev1oBdD0DDCFqYolgXd8Be71u3KXjzOFygKrXe+rHAVB4JfCQqbezClGI9+XwAH8OwwrQ2sl1dkUJNuJa9uiGrHh31AH0IoGUKc6Mvd2PDR/X3DSSsE9VW7yf13nKSl1KYPCLBhPT395PjVCttp0kwc7lI+Bglc+/IyIjkFcVWmbDnvI88xjxYVk30r8e9l0NOYL9JEuD4nrlUjKyBp2BMw26lvgygbyLISGYhGMUCPCw1ulXCn4V6PPj4Gcu1at12G8X4ODn4SBQNI21JoO68885izXnVTdcBIuEr4FUykXnIqPiYz/doeMiJw8dMJuu7fyYT3TP0SOIjEVEms4Icp5aEIcyGj9eRUFKsIiFbBHMyAd0khGGH9JWRHJ9QavIC8OqhBxOweQnq2I3dVA1JJMbT8ZBZCR9NXpXyvMxOEj6WykMes0L3L3/5SwJA3/ve93zH16xZQ8uWLdNe873vfY+2bdtGjz76KO3Zs4cuvPBCqq+vp1/84hfa8//85z/Ts88+W/z84he/iDyYMjEjx/HIujIoXkkvfxIGf1IyM0j4F6q43nEaqb6+wXefTGYFrV271gACwVg5c71Ym6AfrkjYuHFj6ES/+uqrtQkuiEoTgom8jMFh8aA6sGXieJawjKBhNcEd6LPp8u+8+Zk2xQJAZ1kAiPtu8gBY3tnpK/Ml90/+vzuXo+WdncX+mDSRfH4KCNTObayqohWZjK8N2ZLpwEsCw8/zAMKfT90U1LCENLykL/J1zJzYyjnJdCwwlZOBj0SVwUgdPurcwHTxWPKcDlsbKzIZqnWTXBWvd5xiMkP+rMhkqL+/n9atW+fDGGF1ZGx0SFUmButYVwYfTYxaFHwspXxNW9uywDOpZcts+CiYYv3+FF7zlsdTV/ECBHQSMNPSP7as2BlpHUYmHYfOXrrUV9NaxfDiXp1KBbBN52rrALQcogyjDiNnpVLB5J3wY22l8NGBUDLrro1S7k6mGB8nFx+J7BjpAL5axXIi2BtvvDF07vT19enx0Z2jOnxUSyzZ8JHDbLw1OrH42NvbG8j/w3Q04iORKeeHEwEfFxDQRmFCtW08o7jCL1lyNnV1ZTX98/+fy3VTZ+dyqT/spZTWXjvT/ZTKQ04WPpbKQ8ZCdwi9+OKL1NzcTJ/4xCe0v3/qU59SJgkiD2YY6eNaVPdvefLyMT1IBLOFi8nc1DTXzYK4wzDpw6wovaTWIvSy6EbJEvmW0N+jpOg3TfbxuHur53KWxHnNzYH3NDo6GkjyloYQQuVNjUifiCTpggkQ1OqlIawhayCszWF9vAygmW7GR1nRMAIvmcrAwEDk5HGpujqqSyT8Ar7jFGPm5Wy+DEhJ5dlSAHVCKCLUcIC5TU306U9/Wvvc6nf5eeZCr5zgmBymnnyeUkr/k/ASEPF1Ha2tJZd7I3r1MpUq2fCRaGIwUicU6dy/WUGkm0sETwlnUjbNSqUo5SrjdIoleS3l4bhVF8LCcErJovuxSPhoxmiBB9GTlekZrCjnA6Dm5nmB9zQ6Oiox0vxJk9hr/Jl79TVvk+S5yqtuj2kCvklCmJ5h7V8iMU0zniPF92DKYjvqvlv53g2pJpqZSNAG+BWXjCcqPvKcUvGfQyXqE4lAmbFZqRT97d/+rTbcab/0vZL4WKNcK2N+KRTjo6AjhY9EQYzcjKDSpzuX8wkXJnxcsnCh77qJw0fBQ4okiatD8e9YwcegEK3HRyJy83cwvy5jZIKC+NhCHj7KCYtNfXy9YTz3ECAUL1GfNZPJ0tKlZ2tzOHHMvKfY4H5rFNVI0plwjPh4zTXXkI2HnEh8lDG/FDpmhe5y3IN09Na3vpUuueQS7W+V0lLKZJvUsnbOX4xevoYTIchlCoIudeKz2b1GddVZQKaEPOJecp1wAXT9/f2acg4290czsPHk1yVNy8GcrIzInIlQPZddmsJcR4BgndLR0dEAk5+GcJ+S3buiJCLha+W21CyLYX0EUBT+d0Awimpsd7ary+o9sA1+AVXXVzUGXE0KpJ6fgNCwb3Db74V/898BfbbnO++8M9DuQQjG1TdOJdZflxmOUqw3Mh0LTOVk4CNR5THS9n5lfGQMUGOy5ERaDvQZonkNpyE8JNRs1HxtAzxXYMHgcGycnhkUiXwqg49hOUH4byIhkq2ppLtWl7hndHTU4BovM8B6fFSVxKJf9aTGmEfLBJxW2lLbDu9fW1uHdI9grGhXl8gC39vb68NIT1jw75+clM2GjwWAtijzT72mKZWixqoq2gDQbQjW494ADx9VLJsofJT3r1IpxkePJhsfiezvmD1gJhIfd8CrqFIKPt5yyy3kt44em/hIRLRy5SrSu3sHFQJ2jOwlf0lh1SPVXnrS334QIzOZbIgXLLezxh03J/Td+J8n3Mpuw0cTDxkFH+Xs5VHWzmTj4ytK6CYSiTA+/OEPF78fPnyYTjjhBGMiDJVeeuklmj9/Pn30ox+NdH65m42ckMDm2tLb22tIXMDJElTmRBas1YU6g0TtVt2kH3Pb0zFNKfKSWfgXk9f/bQRkyUtyI4DLcRqotbXDCIoysA0NDYUnNoPeek2kj3XSLZKOtrbQRVYLscFkMxm65ZZbihsW131WXdLT8Jh/Jta6moTdBPyW4rTy3ZbIYd26db5NNI3gBphKJCJle9R9l/vKFiF+flZKhCkE1LgudpPPIegalIQ/G7mqOEkl5DIhwXcqhxYw81CAFzvPTMd46FhgKokmHx+Jyhs7HT6GxWbpkgP2QF8jNsxt7Dp3/XP9b3XdLAJ7oagMjhlz2e0yDB+7urI0MDCgeA4F8VFfs9afOIwVsjp8jFKiJpPJukk6wxi+BGUyWR8+in6pwqqntJXx0Z7oM6G0lVa+h1vP5s2br2SHZ6bb65uwrnnvcTEcGiqOjYF5jICP2+F5G0XBSFV4WQxN1ny3lOZE4SOvoXIpxkdBk4WPRNEwkt9xX19fRfBxgzs3FxnwcRNYOC8HH/eSECKPDXzM53vo3nvvLbq1i/E3u3ur2cI9y70JI6eQZwXPadqtDe3junXrJHzcbmgjSbYSlnLGc/EOg31ljBTvJkl2rwYvdHO8+NhYVUWpujqS36uMkSZ8lLH66quvnjR8fMUJ3ffccw/V1NTQXXfdRT/96U/piiuuoFQqVSzj8Dd/8ze+zM69vb20a9cuOnDgAP3gBz+gSy65hKZNm0aPPfZYpPuVCpg695JMhkFCntTBLLeeyzhP1DES2n+V0Um6C0iezPspCIS6Sa87jwXvNOmAzq8MGCOTRWFgYICGh4cDz9/VlQ0sgL3wa/qLDA6CzI5KphJfsmt4GuaSBEsBugF+7a5NeFX7E8VVXtYy685NK+CiixHszuXota47relenQgKuo3w6m2q46tez+PY39+vLVemnp+AcD0jeHE1DKBjCFr00xCuwgyEquKkBoIJkN06Ze8Fnn865oH/54Qv5dKxwlRONj4SlTZ2ujwIWcmjg+faqOZ9dyglnniuJREM8cgpc1e47wYZxf3G81TMTZGwWASZwUriIxEpSs6g9xG7T5sUTWH46I+xZE8o2WrE5XpuIH8MoY0xCyZPs51vj4VnQVzuXx0lEn63xFRqluVeXpmfUy3WoVLw0Yb/hzT4SBCJMk1ZpWN8nFg62vGRKBpG6jzfxoOPxbAcpU29Uqny+MjeMf39/YEYYk4IzHRk8TFJQnC9itTyXDNnmhKJbdf2x+4uz7+FYSm/C+5jsCyw3zvJdK8W0nvBcoI7z+qtu17GyGheDQKH29y/48FHLgGm5jRijDThY0r5Xq6Vm+gYF7qJiG699VY6+eSTaerUqbRs2TJ65JFHir9ls1m69NJLi9+vueaa4rlz586lnp4e+uEPfxj5XuWXDPMnJAgmTWOGwh8f4XfhiJqynzTtyZYCuUbfze7xDdIxdaF7GkBPiaAu7vXkOLV0zjnLA0xkLtfti7vkDWH37t0+l2n5ocpN1S9TTz5PtY5Y8PsR3JRqle+8CDdIv4VZLnbt2uUrp8CuqKaED9yWqYTYfgQTmyWBAHiom6nat37Ns6ahTzKmJk3RMW8bIDZfVWnBVv8khCZcvWcPULQkmdwn+Z0WCgXX7SxanP7cpqbA2DTAHpIQlY4VppJocvGRqLySYeocV5Om8TxTcxA4sCuzdF4di7WMonAplrXfntukzQXSj5GCsYmOj/68HUIx29/fT0NDQxGymAtsL9W7I5/vcRNvstCpMsA6ZSzvFfJ1QWFVxUciORGRysg1K22ZrOJBBbHj1Lj7pG7fNPWN68nqBH7/2F4GoRC24eMARCbdFIL4XwOhmFSZPBkfTe6TMj7aFLsxPpZHRzM+EkXDSPYoU88pFx+3w3U7d8/fo1zLGMml8yqFj5lMVmuo6uxcTkuXnu071traQbt37z6C+AgCZinfHQLud/uiyzHh4dCNN97ow0e/ZVzGSMYzbsvmNeQo/fHvc1VVjbRw4RJLG/0UXgpYjK1XgSJonPOeifeMoFeD5xmVItXrNi95IkXBx4GBAbr33nvD57h7vg4fk/ByAo0XI495oXsyqZTBtGn3Mxm/Bs8MGrUULTHPavf/mw3tLaJgfEl1aJtr1641ZDXcTGpiB39JAb9b3xQEY4aqINxE0i643wzhprceHoPAFulSk73w2Ktu2wWImGN5Q5Fdxx13YdvKuagZPXvyeTqvq0urkZuitCVvfjKDz23/wz/8A81rbg69f9hvu9w273a/L25pCboouuMv91WNgR4dHaXZjY2UhHAj61TO74EQ5HmDDmz68DTle2DwZJCsYe0WZYIpEVIAWFG+oobpWGIqJ5uijp3tPapZpMPCQ6K4+K52/zcL0rdTUNCsCsXHlpZF1N/fH8BIkbzSz7Q0Nc014qPAZX1ODvF7mjw3vb3kZ1gEU1bKXPf2Jp3bdh/p3SIb3eMDZN5jxJ7lWZu9veHgwYNUXT1dGd80iazkclvyvikriEXbt956KzU3z5PaMO2b+kzBItRqwB1HUHPzmZq40BSpzGsYPm6HSIppCpXSKlBLxMeoFTtifDy6qRweMgpGVgofmedS2+xxjy/WupLvV9ZaefjILt/RMbJKwsdGF5e2kcC1icRHkKio0KjpU4d7ngkjg/sMKyREIjVdDPgUqS1VrpDzO4G2bt1KGzdulDAyineRDiOFvNHcPE8rXIta6P7nyOW6fRj55JNPupifJFHL3G988wR53t8k5QCS1Oq2b3IFV71fo/CQUfDR932CE/HGQreFShnMKGUJCoVCMbGLWZg+3f1rd+nzf9T2ugIT22PuzAkRmPRKhAJxvMYdd9xBYcyOqkkFhJXgAIIuyLJAyPG/JpJjndSxPwQvRoSFTtbOrjH0adA9jxkl1SV9enW1VvPcctZZtGD+fN9zOACdvWQJndvZ6RN8F0HvMpNwn1eXqVwGj/bWVmqsqgooKtRxdAB66KGHjC6Ke91xSGrqtPbk8zRV089tyrjtQfimn1Cu98Xs+7S8wXZG4MWU+12WQoAVZlCOSjFTWT5FHbsoQoSMj6bzTlfmWZQEKXp8zI0LH4l0GFkgmSEKw0e/p5KM6ZtI1FlVGV3eD2q0iYLUfskY6d+bVLdJLr21xtCnQfc81dtJuFtWV0/Xene1tXXQNddcI7ldik8qNYsWLlyiCL46BbFIQORV5OB+6vdNYaWSmfAGCiZnc+ihhx7SZBiuIaFY9vqvJlgy4aMaKlUJfCTyyg6p7bASaevWrdHWVYyPR5TK4SHDMFIt3aWes7QMfGRMldscAyhp8BASQtP48dHGQ+rxaAMBBzRrmxWmlcbHm6V7hPXThJE1pGYoF+XURM6M+fMXBDBqyZKzqbPzXCUem8c9+MxNTXMpkWBlph4fW1vbXWFaVeT6x7Gz81xXGeAd81dF2kvAGnKcZAAjhUcD54iS+ymHAthDj9LK/OTvevkknIeMgo++72VgZCx0V5AqY+kWi5YTKdjj3QrkZRpPk+qiwQzB8PCwlGVRbm+EAFu8iB8YdBkfzUqEoNuf3xXlkG8yyxP6YxBuearVOQkvuZlJ4NbFOumyiXPmTT5HZ40YUxbddsO5DW6CBlu86cKzzqKNGzcWQUGNPdFZPpIAtbh/edMzbZC7d+8OZFavgsisrrbJJQ9KcVGUAYy9BS4z9MmWaG2G0id2uZSFfLkETyNEPHtOfU/5PA0NDdGilpbwZ9A8z0Su85j8VClLNyfsiqKZXgDPPSwQBuG6iRUKBerv7y8mVhwPPgJJLSOnx8hRCpZ7CeKj5/YsHwOZLSoCc3XJf5h0rpr5fA8NDQ1Jz2tzK+e+yv3crj23rq5BM47BfCX19Q10zTXXFPfAYFIjE3PPsYYLrO8slfLjo2BI6wNtctJPGR9tSpbJxkeeW+yhtR36Ek4r3GSgMT4evVQJSzcrWryEXeHvOwsviZoNH3XW830AtViNPutJxke2XMs0Xh7Sj5F73GOfoWBlHg8jJw8f1X7yuJytnK8bw6D1+6yzFgZ4SH88tgkjF7t/TzfcS/RLDWkS7bGA7A/X6erKFgXWXbui1fv2apOzwnkD6TE73Dhp4pXVMmBReMio+Oj7Hlu6jyyVH9O9nXR1shkQ8vke101GjXfIKhPVnHiCqVAoUGtrh9aFx2xNb1fOC2oHzcqBtGbxN5KXdMFv6dYJqVHi1FQyxToxs6JmNuyFEEzVBdwIIXjLcc4NEFmLVcsxa4tlBkpXSiOVSASYJh4/E3Mm318GG1+MoGuR1j17EuYyYIBg4qxWYler522Ofrc01WtgO7z4d9PzbDAcl5Oh8Nhsdu+hAu0m+C1K2rGBF5LA80DnBRGFYqayfConpjsseWBPPk/duVygtGAjBDMpl2tSFWyAPmmUqBWbHAc+TtUK3XqM7CG9q7YfHz3Nf1BINTE4bN00kSmnSD7fo6kssZ5EuJEJy2XmuoGAqRS0LukSk+kZ4qamuYaxuyz0mf1eAw4JJtGvhPZypkSzyPFezPgY5p1GVBo+1lcAH+Xx4b1TxkhVAI/x8eilcmO6TYqWMHzsgZe8rxR8LBQK1NHaSinHce/nkKiEE4aR8qeZHCcVsHyOl4cUGBksdRWGF2Fzu7L4qGJUkoDZhr7avawSiVRIfLRNScwYGbS0O05DCD6avboyGSFnRPHgJSLJg1cNizV5Dpgt3VHkgzAeMgo+JuHFdI8XI2Ohu4JUKmD6NfhBzRQvcKFZUzVoKkMjT/JCcTLr3B88rRjfb49lYhekhTpIMmDJky4IRLYFs74Y061LimSLM1q0cKFWS2nV7hYK2syGYddw6TBelE0ICtOqgGlNTqJxef+M5Zn59y8huMFmu7qKWtgoCVG4zTUuiFgT14VYckybtuN+UgiCmBPynOq8ZeZCjacfhZd1dRM87aXqhSB/787lqDvnty6Wko0yZirLp1LGTucBkkokAoq0czs7A+9bVYjJ86wAD1sqh49eKI1chkbdlP0YaWt3vRSvqEuqacvjYbZ02zyodJnTw/sqZ+d1CGiioDCtlq0J74O+rNhnLM/MbuXbSLiA+93QM5lshHcZbFO4eIYnZRoPPiYVfEyViI9EHkZeq2Bkt9tejI9HP5XDQzJG6qx+Jnxc7M4LGz729/cb7zu3qUlKOBtetk/wjYyPXg4GNaFiuTykh5E58isxw8NMFi5cNEn4yII2Y+RsAlaSHyN1YxjeD73Lu628GGPol0hV4IqElmHPoS8D5ji1muzz5v4GLd18vi4hXRUFvcm8BHLj5SEZH1kAX6TBxybl+3gwMha6K0jlbjY2lwx/7cJ2Eho1BpZwxk2ngQm3uKgTO0emkgB+d3WRKEGN77Axhblcd2DyRhVa6zUWYyIPgPbAi597AMJdHfDXIWW3GFvs06KFwp3nxhtv9PVTTXYmM1A2pYGubI7N0n2S+5eFZ2bqOtraaHR01J4sQtNmFl6cYLarS1vbUBfTXQNhIUm7z7waImZxAYRb5Aa3jc0IWigZ1KJ6MagCGD/fCqkd1auAM80vcM9hl2SbF4SNYqayfCpn7KKEPsCde+0AVcNL3LenxHlGVAo+JkkunehhpMfQyXOeE4YFmbVwfAxiajShFdigjTcm0pXSeYCAXgLu9mGkio9hzKuKj15iHznZmWxdCVca9Pb2at6JzdIN9x7DvuMtLYtoaGhI2rNMYz6gaTNLInYe1trATCo+NsJLBnotRALNWugtLYCXmLKUeavDSHkPNeFjFt4+Mjg4GOPjEaTx8pA2fORM+jw31WSy6nXZTEZ7P16PXobyQ6QvmxXOQ0bDx1IxMrrQmkjUR8RHDjP6TBGbSsFHANTevoze//73u99NFYPS5BcwV4e2qyZIFO3ZLN0nuX9ZwSj60tbWYfXmMZUBE3sHDMY3PUZ6iu00BRPdVZNIormBdF7AckjWeHhIVcaQMbKY0wgePleCh4yF7gpSuYBpc8lYt26dtIjkeBIGFYdMpQR0m7P+fmMUjC2UresrSJQK8LSUQB3JWjou68DxP21tHRS2+GVLxvDwcDEr9yF4tSV1VgDV5Vt9xn379vk0VWombv4ua6Zs1nHZnY/jhtWYEP7erByPYjkeGBigbCZDSbfUkam8WC2EFY/bYmG6v7+fevJ5Srpl0MLc0+VxTLttdyrtyP3XafDGxsaoO5ejBPRWk82G+/fB2+iXtbVRg+NYBXx5jO68887i841I99xjGet5Z5wRLQY4gptQzFSWT+PFSJMyid/pkDIPRoDQ9TQ+fKxXvjNGMkNVq8VHIqKhoSFqaVkcGR8LhQKtXbtW6dcoCY8nmUlTmdug8lXUmM1K/a4i/3N439lSHsXyw+QJtup48fdm5Xj48/Paz2SybnIf834nmLQUqcx9f3+/mxk5GXpPf+xpI3kM4VJfO3L/dd4EjI+MjeoepMPIouALqepDifhYKBR8AhiHV9jwcUYiQdlMJsbHI0wTjY+kwcgs9DxWOuSdq555XkJH1SPTxkNuIC8+OEmtre1UKBRcBVmHdK0dIzdu3EhBfNSVsJUxMgo+6p4p4Vv7Nny87777iu37y42pGNmluZ+5XZmH9JKfraFwjKwlsW/45Yz+/v4IJdZqNW3WEOPjwMCAJgeHHiMPHjwoxaGre5BDwlNJ7kPQ27ajrY1qHSe0vC2PTxg+6gRw/jD2dbS1FdsaD0bGQncFqVzAtCdLkzMCqpovZhD1DI7qYiEAxbawTnIX13oCFpKIz5PbrnFBZwcB+0gkZ/B+7+rKSuVvmGkJ13qNjIz4rFmscdoMz1LJn0ByM0nbx8Iru6HOhj7RQkqzOHvyea0b9BQId5LR0dGiCzYz8mqSGweCaVoPEePNGmWf66Brodcle5vb1FS8Tj5eA+EGY0roIAOJLnYwCdBMwzjKmXKZeWYNrg1Asl1d1KC4/CYhFBDy5OJ3tRpeHVEeR1+fFAHfNEYpxykmIQI8jXsY0wGAzl66NPS8KNkoY6ayfBovRoZZcmoA+rAyD7juvUlBpnvf+/bts+DjZeTF7y0goZFXs8pWkWAa9pEoE1M5fPT61UNCwEwr99YkqnTLobDw6sXszSZ9wp3ZJIc4EZHLSKXIz3QlCZhSjGHft28fnXba6aQvK8ZM3yAxA1Vf30C6RHRNTXO1iYwEk5YgffbybuU9+d1YvbHTWeSSFFSi8Dh6+zDnSImKj4VCgZYsXEj1iQStgbCeRMXI2Q0NAXzUlSbTKUm7czlqrKqi98X4+IqiicbHTQh64PVDn0B2v+GdB4VSkChbxTiyl0SiLhsPucjtZpCH9GfAZpdxM0aa8bGRBA6r+OxPACnzkJ7wyvdW8ZEFzXQAH4O5l4SSkBPH7du3T6opHoaRlxMAam/vcO/lf36O6dZhpKcUMGGkGkqjYmRwTxLPUU1eXg55HDcVv8s5pKJiZHv7Mnfc1D0oJ0/l4rsCVhdzcwSf289DRsXHHfB4hTCM7M7lxo2RsdBdQRrPZpPLdWsWbIpEdtodmkmmczHkEgses3H11Vf7tIGe64duYTUQcCYB95HHyLGWUJdUoUv7u+MwcHByt2BJG67Zp1sULHBugj8GzlTGa2hoKNBGGqB7pQVFmus49o0toLfccktg80nDiz9uUupvGzMrSwvw7CVLjIyTzkUllUhorceqomEb/Fo9WdOtix2sVb5n3fNksJgOUW5MV8pDB5733ntv6Djwu5LLMgCe0Oxzc3QcrSubyY1Hzs7O7yisL8zs1lnOUxMUVXqdv9qp3LEbHR2luU1NxgRQvHbUsAVZe11AsO69io9ELFwGGR2Bx8tIuNJdTZ5FgmPOVIxstOBnNHzUl6y63v1/E/lj4PRlajIZlUlOE3Av+fcSVbngWRR27drlZnZVrTDp4vME72Fqt4+YgbrjjjsCzFNT09yim6m+Jm9C048sBbMEry4yxX7vBV3c4KkEtCrH1Mzsl/m8FZhM+Mh7SqDuLhyv7Be8EKX10jkyRtpKN+rwsTuX88X62hK2xfh4dFCl8TEF4cWm4qMOIzdI+Ci/czUho25dem7CHKYShYc8mzzruO73tDv9giW/GCNKx0d9qcOhoSFNOzbjFIiVh2Z8zJEQ+pOUSs1SfgtrW7ix9/f3u67z/nZ5fzC/Cx1Gqni2jWQFhoeR+ymIjwkCXqMcy1IUfCTSY6SHj2HjIJcOW128t18p48kdXV3+e0fFxwYgEOvNHzmpZSqRoOpxYmQsdFeQxit0BzVTvGg8bdLg4CC1tnYoMRPM+AQ1bPIk3b17tzTBdYyHvEhnRwCGGZbfOelCj9ufNe4xz4JiyrTtwEvvv8P9X7UYs8CpXVgAzXP7b9JIcYx3R6uf2VoAof1VN59piJbgrQ9+V5NCoUB9fX3FeBAiu2baZN3frh7XlEHjtgoQwq7OKs8u+gSRFVpncT5w4IBWS7h79+5i7HjYOHwIQQvjMrckUxSXe1sc75133knzmpupFkLw1oUiNEjPydc60HsC6ErxVHqdv9qp3LHryecp5Ti0WJlPDoQHiLw2Fre0+PISpJV5sQEg1Z2NmTjP62izBh/NbtjhjFn5+GgWPBmrc+Ql49FbhPTZaBsJmOe2cUjpHzNRvaQv17OAPDdR73kSiRkULcFbX/EaXu+Dg4PU29tbQqnMTQQcp/QraJkOd/+Uk9/pSq+xC2qwZE9XV5YOHDigdaM8cOCA5E2WoECCVCQp67Z3ujKfG+rraefOnRQFI021uWXvp76+Pmo+7TSqifHxFUHjxce0Bh+Zf2BFT19fXyB3i4qRcrJTQCiB/PiorssNFMTHKDzkTMvvBfIs1htcbNlQUXw0teMlfjThGAi4LYANYs1fRea64YfIluCNc1fIuYdMPKR57E5W+hXEx3CMZCPeetJb5cPx0aQ0zuW6NSXJTOPwIVK9eG3J3qLiI7uan37qqUVBOiycVb42q8FIUznH8azxWOi20Pjdy9eQsDTPIDnWRUxuMfFMMRNBV4saEoyjp/2qq0tpJniBhFudHH8oW2PCFsTFlt/XUJTi9mEuUfybznrb0dpqtbaG/XYtvLg5k0BK8ITIy9zvttiP9bAnVQiLweKFr/aJN0YHwiKtatTUEkvbgUgx3jXwsjeq1mRZmaGW5rKNb8Lt73oIRcUGd6wdw3MD+phy9dz9MGffVY/n4Fn0CV5s46ma69k1uZIxOTH5qZyxk5P2ZCGsdrKrLq/XsDnkr1uvt0w3Nc3VJJJhxqNBe40dI8ePj+G/yb+PkWedicaghP82SELAVp+bmS0do0gRnmm9McEbky3Pid46xh5cSaqvbwjgoynBD6w1hqtJV59Wp8xwnBRVV09X3k+aPCu8f+xrFXxsrKoqKoGjYmQUfOSY8hgfj24aLz4WIDKTy4lMGSPlkBpd9RY/Rgp+Yz88Q8jcpqaQRFumMJXx8pC2pGCl4qOfb25pWRxibbWXqxL5KXTPnTM8DydqfCC0bcdJhuIjkQ0jw/ERcKi1tT0SRtrzYOjxUa/M2ERB42JY2wkSsomnkPY8afVzxoaPjKOqsc3EQ7LBS772Cnedyed1wFNshWFkLHRXkMoBzNHRUSVhRPgmLb9MNWaiUChI2WOjglT44g//bYfl91qyZV+UFwW72e2VxoJ/48Rq8jjNkty9t0FfDisFvQY3CVjdRFRL916EJ3hLSgvWVj7AZOm2ubh0QsS564R63UYqJ6fTAU/Ccj+5TmwPghbzGsM4nAxv41Y3crVd+X7ZTIYaq6poE8wZfNPQx+k3u+9sF0BXKdfq5o/jttUrvV9mSiq9zmMSVOrYjY6OBjbHNPyCgqxAkjGyHHxctEiX3Gw8GDl+fPR+4yy3e93jp0m/B+vTTp9eJ33fQ17okdx+ivReUk0EnGXpf0H5vpfCkxd5TLiplBlTlDwn5t8WaOsA65TVra0dNH8+x3uGvQPTvVR3fmZq1TjNrLZdEz6GYXI2k6GU49BZhvNM+NgCsb/eiRgfj1aqBD46MCcytfGQd9xxB4Xtz5XHRxsPeVmEtRkFH4n0NbxlCy1nKpfvocMxjulmfLXho3xsSOqDGSNt+EgUhpE2ZUEnAZu1ik8dRnpVOMrBR/U3rgIi42ONYRwWkN5FnmPI9aFUNnwsevNoPGybIfjHGxHkU0cRxGsHoFN4XSFaXHcsdFeQytls9G4tektCa2u7tT2v6Ly6QPa4xxPkd7F5S+iCmjZtphEYRF/1SWlmzvQYLNuiVGO3eTLLk14td8KLRI1V1rlh67KXJ+AlFjMJpBw3nXT7oyZ4U12ns11d1N/fH4hbMSWT0FmmZ1j6xCW/ZBcZ9R733ntvUdi2MXB1CK8Hu839brLub4Le6vwpeG6KqsXegYjhVkMFslKdcB7nNPxuPDalxOlKP5LubxyeoCa+q3E/YdnwK7HOYxJU6tiZQkd0nii1mphXlcz4KDMQCxRMC8fIqVOnGzAybcBH1tRHw8dgXCIzbB+VruX7qBaX08iW/EbvNp8gL3zINFa3kXk/2EyqW2B7+7KS8FFndRH3Ot3Sr4Hi+Jnwsbl5HvmfOewdJELutU06ZlMUZEl176xF0CLJnky60o2MkYyLMT4eW1QJfEzCnKSvvbU1tD3GRxM/ID5pGj8+ynl/TIkNo4bvRMFHIj1GpsgTnmV8lNepKvgxdtvw8cNk3g92kK4UVmtrR8D6XDpG2vrF1nY9Ru7bt0+qrDFefJT7YcLHTYYxnkd6a73YV0QGeL/XUiaTpTB8jOL9qcNHOQRDh5FzlTZiS/ckUamAadfm+y0JUZKYeEXnuU2ddq8x8oK67777qKsrq1kQi0gA1iYKZk6vIuGyvoOE1pFdcLwFkkCSOuDQ6fDX1ZU3DhbmwjRW8n3TEJZtXhyd8BKDDMKL4b7qqqsIsNeo9C2+urqiQCxrvzhuWl1opqyJsvaSy8rI59gsz2x9N7nIzG1qCrinL4A5TkVn0SbNcVtmx8shGMhq9xmYuQsrv6CODbuufUa6VhdWYGcKxGcR/O7wYe+5FxNTZzEmP5UydtbSHOqcam+3WgeC+MgYmVbmT0NgPpWGkakQfKwhkc3XjI9efduzSGQGZjyVBWpmVKpD++d9ciSEYbbUdJJn/R4k4GMEQPIGWG9pl4V5h/xCumyB8OKm+/r6iu9BF+unWnfGxsY0NcodAr5h6VeBPEW134tMhGGxhYnHc737PtR30CjNC71VxX/c5hJf67ZXR9MVRUcGCeqHtyfdd9992v3Dc4WN8fFYpInAR/mYjYfUxcEGLXz7SQ1jKR0f0ySSqJkwcgoJrDLhIwuxnWTHxxriOtLhGMn4yOs+SaIUVsH99BEnOCsNH0GCJ+awExVLRDvr1q3zvYsoGHngwAFNaKktXMbv7eTHSFYoVAof5X7Y8PFyEhhZTXYvgmBy0Hy+Rwp/ELyrDh8XzJ9PUTByEUBTlWNhGBklrLTUNR4L3RYqdbOxx61to1JcTlhblUo1SQskR0F3DhmQlrgTPAhqTU1zi23LbkgCCOpJLfMgPlwOQV4sY6QytQ2KZisNvcvoBtitv9vgj3sGhOBnrBXd11dsT1deKwVP4P8MhDVXXXy6OA+57ESHa6lQ46R5Qaq1udfAc+NLa/qUBGiWdE+di0wanuV/B/wug6Y4FdlKqFpVOKZ7O7xYv/XQZzjdBU/50JhMWt8ZW7x4To2OjhatOPyR4w0L7nuO4g4vW41kZsEGsraQgHLXeUwelTJ2ttqzqidKlHc4MjLi5raQteTMYOkwcjEB7yIvDtyOkZlM1sVHP+b5GRuuQTpCIimZWtJmFQWzmsulwGShz2bZ2EZ+Dyq+9gbl/O0+fBTXmyz1/GxvI8GEq3tBsGwZC92iLE9HwMNLVwaotbWdEgmO6WPrfJh1bC55VipHuUeavORIOyiokFatLT3us8Htg9+q4sV083F269RnSAauJQBUVcXl5vTWLsCh/v5+35zSVejQ4aONOYzx8eimSuLjagRD36LgY6qujmoRtPB52fXV+XoymVylTfgokp1tIlEBR26LBUYbPi6i6PiYlNo1YeQaCuJjgoK1omVhMgo+goBPUan4ODAwQF1d2VCM9Jc320DC8+gk6R3p8HGWMkYyRubIK5s4fnz0x3RvJ8/bdj35Q514THeRUNDavazq6lKB0o26UnZ5ODSm4OPilhYKw0g5Vwzj49VXX02VwshY6K4gVd7SzZ+lpIvB4MWpK3fgT+YSFo8mACmRqPZdz9l8deS3QKgLkbVmJnCroSQSWrdjncvoAOwuc6oACIAWKRmM5WznsoZYpwnrlP4vQCRvSoX0l++rMkZhMXny/RZDZGAGvPIuMjMEeHHoOehdZNj9W67Hqrrkb4Bwqc9K17CgrPapJ5+ngwcP+p5HddNPu32dqxx3ALrBMgYd7f5QCZ2bnJxZdwQo1lRMQ6+UaDHcy/Y+AATKRlVyncfkUSUtOfxphpfwR9U0h2FkNPfu2uJ5aoIsE0aG4+MS9+9+0pdlAQnrjs4VkplCGU8HyB7DpzI3wlqjc8/L53uUfUlX5SJLzGwBG93vpsy23n2D70DfX/276iZ/eSGddWwxcd3yYPIfOVmpyjDL/a4joN0dM69MTSajMHP5nmJZM/18gtu/TW6fVGtUWhpbtQ9JWrhwic9zKgo+MpY7CFb6aHCP66yfMT4ePTQR+AiAlkKfC0bGR1Wp42jmRpOxPGJikvBxirS2ouJjlNjyAqn42Nrark286FUmiIKPIFFmshx8NPc3k8kq5zE+8pjqlL5J8pK8qQnSKo+PY2NjmhhxNZQp7fZVxcfwfCKJRH2gPJguVLcKScrDIYInRwBmHjJrWEe2SjqlYGQsdFeQxhfTrbptZMlLsuNnmoKLU3UHERqxefPOlBaQTgD2AMlxktTW1uEr26IjOfZDZMZVAViO1dGBWyJ08qoCNCcncACqTyRoNYQmSk3lTwhqndRsnLIWqiefpwbJursewkqcle7dANAKhDMk6+Fl9uzO5aixqson+JKmf7VKtvQUhJvfDoDaEbSqV0MI5fICb1cy3LL79x6pX2H97lTu0ZPP0/DwsDZ2qFAoCMu90u8kRG1vVYGShFAOZKF3a0+791zc0kLDw8NW5kHt637ocwB8yTDegIi3TyUSZZV4qMQ6j0lQuTGL6hzKQgrr0MyZKBjpOA30mtecYMFIxmBRpsaGkdHxMU36GGyH7G6LBeX/QwQ4lEjUu/3dS94+ossyLj5q3VjZkyq4L60noYDIKn1JWfq6vvhcnmU4vFyOx+yqsZdckaPR128R411HspWqpUVN/sNeZXukfoX1uzMwNmH4qLPce+9zruZdN1KUOsAdra3WEmIqPgLBfCP8fQAxPh7NVCl87IES+qbBR1nIVkPSdkBUGjnhNaI28yF4in3TfC2Vh2xvX0aJhCqMhuNjfb0c9lMKPopM5ULRuJ78vLYqqLvrqvPcQHgLY2R0fLSF/ujwcQfZyi6K59Dh4w4SQvFUBROqSQjlHra0trZL95g4fCTyMNJxdBg5XfOuG8nDTVU2knF+sY+HNPVXLcFr4iH7DfhYKBREWb4KYGQsdFeQytlsdNkCPQ25nmnyb/B7QiebHZz8zKUpAYAuviS87Zm+xZJwgWWR69phcxmVBWpdHWkHIuZC55JedA+pqqKOtrbAJjA6OkrduVygzS4IV/Kku5AS8Ny1w9xK0hAKAUAIu1sQLvCa4qc7lP60AzSsPBcA2rhxI62Qko4R/InOeiL0ewaCJcIYOB544AFtzdxSM63/g+a99UAAHvfBQVCBIPdVZgb2SPcbgaiH3gdPwRCWEV0XP+8A1J3LRXKZHO86j0lQqWOny8ifk9ZpzjC/K4eRnAnXn5xLpdLx0fybqHdtZrgEVst7Q7BOqpd3Q1cFw6sFbmKS9bGCKQK+Q56rYj3ZXdt5P5NjKseT7Vit9JElf9Ij8b48oVu1dLNruq0G7wwKc+vcsmVLsWbu+DKtm/uwBv7QCRs+svKY9yHGxwKCSm1CjI9HI1UCH9MQe2yYYUIOf5P3VdLMD/5tAOHztTweMsw4o3ftDirUysVHkN4l3cPHfL6Hdu3aFcDIaPg4hbw47lLwcYTspdJMMdQqPrYTMEwqPm7cuFGx2E8cPvIx/fPYvLTmK8/D70vuh6MoEIL9ZX6X5zqHSQ66f4uVTwz4yGutEhgZC90VpPFsNsPDw9LE4U+aTKXDvEVnqpuoCug6bVGQuTSlug+6boRbK2YqIJd1v19xxRVkA3h146gBKJVIBKypNQi60PEGo0vvz5Zu2VVvLwRzUwuPuUnDY3Z4MXINTLW/g+73D8GLN+bFmFL7Z6lRXSsBAzNccv1h1lovammhpOMEEqRxv8PKbdkEf7kMGyAs+FxGRO03x8iox/fDL2xvgD4OnMe2NqH3ftAJ9asQrBVeA9DshoZgjXL3eWRALBQKdM0119BFF11EW7dunfR1/mqncsdueHi4qJyR15iat+Fm39zguLTwDTkcI4MKSh1GloqPYRlfvczaYYJamoQL43YSFo4UyUyQYPpqlGdqIA/3g8nj9JbuDSSsLhyKxLhe4z4DW0RMccyD7ne2pCwlj+lN+vrnOA20cCG7l5rGjS08e9x7Jt1n4t/fRwDHGKbJX6kjTZ5rOltqSmNqzzlnOakM/NKlPC/DGGv1t/1kS3gkC8tR8XEUYt9R99J6BPfLJEAN9fW+5FoxPh5ZKnfsCoUC9ff3B8LE0tAbJnhfHoVQ7uv2cVVA97A1XEEZjYcMt+QKYSqn/e3jH/+4pR86fExSafhIpBPWg5ZuEz6mSSgl2U26VHxkjEyRipFhNart+CgUIy0ti1z38gUUzP9UPj62t3cExiyX6w6p726aB/uVdkzjJ/Yfgffm/jK/O4pgOGQp+EhEtGvXLvqbv/kbeve7311S2E05azwWui1Uic1GTjbhZwRvp2BR+R4ClodOtuHhYY12UQakRhJubmYtpV5LZdfusxZJZR5YO6+Lye2HcB2F8okStyQnltGVGFPLUunaG1S+q657bGVTBfxG5Txd5kMH/gRvXJechc8boHd54QRrqrDZohmD6ZZxDhP8HQjBfw08b4EkPEHcxPSpCok0POtLp9vmeqkPrH2XlQmO+37kvta6cet74M2jbgTj61OJBK1cscIYk8bKlieffDIQcjC3qcmYu2Ai1/mrlcY7dnLiFNm1cj9Ai7Uxtd0kmIpSMZK9jVIuxg4Qb/AqRpaLj2EZX1OpWS6DpSbCOY2EdVdd+2H3kZ+JlbjBeD19TLeuzUHp/07NPTaRFztIJAR8tc9dFEwu5Eh/N5NXd1d2F72B9OWBrqOgNetc8sqL8We6cl1Q8A9naqtJMLYbyM/AO5Z3oDKNafe6s9z2PJdXOQ6RMfJ0BLFch4+m0ppzGhu1Vhr+vyefpx/84AcxPh5hqiQPmc1kfHvq7QjyEHMhyoaG8UTDw8PS3sox3aqCslQe0oYxrMzTCVoiXly4Kk8UPpL73S+sy2WpwvFRL7RHx8ccAZ+jIM/vkOcFUAo+siVdbe8M5XuVcp36rhnrTPg4hVR8TCRSIWNmSj7J+LiehCKinoJzTlUmOAHlOeP5tgrg44EDB2JL99FGldxsgm7njpvxUY17cMiUqXDhwiXF9jKZLCUSMymYBXKa73smkw3UUjVnWV+qWZSNxAluPgy/UJ12v2/WgL8DwThz42o2VpMWtq+vr1hGRedqLV+zPUJ7A9J3tlbrSpm1wBPwswjGQzW61+qE2CkIxphUQWicdaXTqt3fddZ+BoYOgM5173sdRHm0j2jGuaG+Xjs210PvCr6J229vp6TjFGPqdRt4zm0HCK+9rtZSZ7d5tfzZa885J9CnsPdaKBRo+Tnn0BTl/BoIYJzb1BR4T0kIxvJIrfNXG1UaIz1mkBkEU34Jfbbr1taOYnudncvJS9TDH//3VGpWxfBR4LFqacmRiDdPadwXHRLKUiLBoAyQV8JGzwTJ+BiV4fVnL9cxVgPEceR6C7tD/gztYUnhFpCwaslCbJ3mPTCzuFTTVtI9X33/3BeQKDt0rnvtdSTKo32EVCbUixlVx0bHQLOroxfTKpjIbSSYxRR5Me8yM329+39a835BC92MuyRh2zc1+FwOPg4NDVGqzl+XOA1QynFoenV1jI9HmCYOH11+RsNDpKGv4pKE2JOZurqylEgkNfPWz0Pqak3rMbKH/J4oJmFqsvExilLAho96ob10fEyTEGLXELu9m/ExQUIJqqtWVE1AlUaG4P60ENDq3neDO27vIi8mnT8cK146PmYyWRcjV7vPojMk2vFR1zZ7WaglIuvrVfwNx8dCoUDpJUuoWrmmBkIwV9dPHNN9hGkiNptCoVDMnGcGgPtJp936+Mc/TgMDA7Rr1y7legYkdi3RMyrsSmO2fFxvWGiitIvsbp2G3s2pr6+vWLPZFlNkWig9+TzVwMvYanJ7PhShvazbT1u8ctJNwrbHcp7OjVuNw5MF6HLGYAOEewyPs8pQAf7YZwfBDXaqpk+N8BLwnHLiib52q9x7mpQAOeg1iicjaPHm59i1axf19fVRX18fDQ0NBYRkW4K6LVu2FDP3qsBoKzUWZ+edHJqIsQvim4qPe0mfZdahjRs3auJyGR+zFFZu0Y6POuurh4+itKOOSfH6Pjg4KJXN0t0jPCbOK/FYQx6DG+7aad9vhq33zWTYU8sWs6f7LXxfKj0ucAN5MYoqI8ff+8izrjkUVNDoXFT9AkJNzUyl7ekUrpRQGW2hJLosBCPXrVtXNj4WS1QiiPOnx/h4VNBE85BGazb0SnI9PkbjIeVwFT1GHiCvRJVJmLLj48DAALW1dWjaLxcfD5GXQNMkWNvwMVxoz2QmEx+j5Jbg3BybSG8p/wfyLOo6C7gdH886a6HSbhWZ66ub8RG4jIJKGk9hPDg4SP39/dSQavTd71R3fMLwcWRkRMtDMn8dxp+bchmMZ43HQreFKgWYcgZcoij1vNeQHwh7KcjsyVpAIn+JAJ0LzwZfcgR9lvUkzUAVCYaGtVfCPY5dPW317XgzSEOvaT0ZetdjtfzXZgQ3DaNgrbhdyVm1+a+tzrQaX2o6b5t0bBT2WOu90rERRLP2D0By0UaQoXLcc2SlQ1oZK8Ac521SEqQN59vGnz/sqp9ynIBbY5PGpd3mwXDjjTcWf2fXfTW0wTSGvb29k77OX41UibErHx8ZIz9EXjyt+Hgacm6jEvhYQ8Iy4MdHwSgIYW/dunVue3u1ffcLwDprfQMJxsXPBAVdxTdTkJkKZ0SFVUS9Vw35613rx7y/v1/x1ApjXvm3UYqS0dv/juzWLHGOcD/UW5Qc8qz3qjAuf8LiCpkRVRnIdMhz2F1ecwB9FkGvIrZWl4KPrJyK8fHopYnmIW0efgUE89P4+R15jYVjpOMkfSVuc7luBVMYRxKkhliwgGXDRxaUvDUb5FFFUt9y8DFcaDbjY45sQvvk4CO/o20R7vMW92+O9J5EHcr5qnxxZPBR9PezpFrM6+p4X5RCA1yBPsyAJyunZIzkfEphhjxTLoPxrHGUs/hfTTRewNRld8zne2hoaEiavLqi8v56q+bEOml3EfaTVw+RP2pWQH+23rGxMZrVNMd3zWI4dIdmAebhFDNUv+td7yLALNCxK+N+mN2RAXP5L3UzKbgLpROaclWuoD42NkbLXOt6sT34Ldz8sbmi2DTI8nNHySq+BqB98JKbROqL9L/pnHXwLN3Zri5qrKqiXoj6nbpxUAEl7N7qM5x+2mmhzzivudl3z9kNDQGmkl3E1TZyIe+V30VOaUv+HltyjiyNZ+xGR0cDcfs9+bwVH0UprXCtvBCYHbeN8vAx6O4IAq4ivbV7P8n4aIrv9rt66631QLCGOFuZggoJVsx2kokRJSK69957Df3e5LtvmOBOFMULQf4tStZcuH1YQcGxNt1Djnk0nXMnMaPc1cVWqPUE3EbAyZa5MC3C/cOYaf9vGzdu9Cl1HYh9o1l5XjUkiyz4yHMhxsejlyrBQ4ZhJGdt1iU15flSA42S3eH1zhg7RMFM2eq68Md4i/JbqjsxJ5zMKcfFd1akC+tmUKDj+HVxzn4y4aMpIZoZH/cS4ATyajBGivEMw8dwTJpYfNxBwD7yEohGwcgdEc7xvIG6uthV/EMUDFmdeHz0J512SAjYaj/q3X48QMIQeS0BAkt1+EhERh7SZiyT32kl13gsdFtovICpLe5e1UgrV67SMHRpcpwU5XLdZZSqcSgYJ+J301Cz9bJGcAO8xF6H4GnX1QzVujJfiyGVslAs1TyZCxACp+q6bCr/ZSpntUlzf06GoG5KWYAOICj0N9TXGy3sMulqZSbh1bCW3dBt9bPVWJIcvBh4tUYgux4ShHaa34nc7iGlPU6M05PPay3YcpulxMDL53/hC18IfUZWWAwMDNC9995LVZp+JKF3tze9V3bzNbmXOxAJ4WoBX633JOKYxcmk8YydXHVAxoVVK1dOAD4mSTAYnJk2Gj6KcwdIMCggr1wZH2cGQxcDt5g4wWV4UrMsqclqTOW/zK7vmwL3z+d76MCBA5rxaifhMjlKfubYCVh7ZMGdyeQl5dWwbiDPzdJWH3YZBeMZ0wRM1Vie+J0RCebQxqy6mJvrlurz6iw06lw4ydL2AAWfw86QFwoFuuWWW8hBdG+j8eDjtClTYnw8wjTesQvDSNVwkYbey0y3d98OUDDJlo2H9LKZB8N3OLHXHuW4mhhMxcguAjYFSlT511OBBGb5LZ2JRC01N8+LiI/i/l1dWd/9GSPV2GGByQdoYvCxkUrDR12c9GbylM06jIwSqy4+TU1z6eDBg+4+EQUfbe2Wj4+eJ1hK048kBfeKKuW7h488H0wYWQUE8DGO6T7CNB7ADF/8jraofFPT3OJkYSHGngTnXRSuoUuSWk5M1ibKgjYDsy4Jh1ZbimBGaSK/0LpHA/qjCCYeM12vCsdytmP53B3wl+aaC00MciJRTDymuy+TrlZmC0AHERTkDxnGK2kYMxaCdcxUGp4Sg4X1MLd13oB1yg71/PVuX2yx0GsgXODXw2PeAH3mdJ3CYrFbt93UvqyV1CVv4xqz8hpSXS7ZNeicdr/m14GwssfZeSePyh278PlaSXy8zP2bVjCSvzM+jpBsyQlaTNS6pypTZSpjI7BZX75rO+lrjo+SquU3X+9n/lR89Ct+95C/7AwnPuI+MyOnvy9TMCkoSCQ2GyZhiZAZ20OG8Uq592rUjFsjiZrk6r6WJq9KBycECov79hQYXJ83/Jpa9566dyKfdxl5oQX8jplZDWfIO1pbi95RYVhdCXxsP/ts37UxPk4+VYKH1M0TB6BGx9EmyRsbGwvgo6pkz/qEq29o1prKQ2ZpfPjIApM+p4aKM+EYGcwOHhUfiagEjJxLlcNHh0QmctW7KQwfpxIwh8xCcFDRytnUq6oaKZlsVMZNxTF//XJ7lYtacpyp0r0qj49iXoWXXhR7ozd/Eoogrgrd8hpiF/NeBPlvB4I/jrOXH0EaD2Ca4xLDN/Ro5WvkCbjEsChZQ3c6eYyKWAA9+Tw9+OCDvskoC477oY8RjuKqNjo6St25XGBCM+hzXb0kgpZvFuB0Qq9OOOaxMWXWVmv+ypbeRS0txaQiJjKV6lgvLdgdEO7bJlf6MKEZAF0O0G0IKiEAfVy8XNpMbs+0ucqWcSek3SQQyBI+DZ4gvh/Cs0F9RhmgvLlq7oda+zxsHsiKoVFljHXXNjhOSRpKppipLJ/KHTtTTOKe4juuFD72UXjs76kkrC1+Rorx0d8uC6mbKOg+ae6Dio/C6qoySxzjOEqC2fNjusyg6Jg6HfPnjY0pmY65z2ecMS8yPmYyajnM7eRZIHZQmBt9+LsDAZeTcAlXXQ1B5pjPtLY9u4JGZvZMgoPcb2Ym309ijw2WTMvlugP4eLEFI2N8PHaoEjykCSPDPM+YTIoZ/7rrCOCNn4f0GyrKw0dLDXupz2aMPESVxEd5fMwYuVnb35aWRbRz506f8K6SLNwHFQHXSuNRLj7udf/+DfnrgYMyGQ7X0WGkWr88Kj6eJN3DhL3l4yMR0T//8z8r71vXD5AacnadBSPVcFcTPma7ukpep7HQXUGaGEt3eEIGXfC+2V3FVvDe/8nCoc3upJzb1OTLEK4TtLOZDK1du7b43eiSLPW5J5+nlONos26PAbQC0TcMBq1du3ZpwU2OaQtYtd3juv6yNVxnpdeRTgnAzyQLr+shErY1w55xna0Rg9Jv7KrOyUZUoOBnHdO0Jycd043rUglsUpp3HZa9vA9eTcR6gC4D6DMQIQgMcKOjo764xbBYmXUAbYkwD2SGQa7HWArTEYViprJ8qrSle3VxnlQCH3Mk4r9sGBlk4IR7u5oBdxOplo7m5nnSd3ufvb5uomBN7B4SNcSjMacyU6cmWiKSFb850ifTcYx9Ftlvg1Z6HektOzrGbL3bbrP7neM/w5irPvIYLOGK6SVj2k96ZnW/tr2rrroqwlxgBY1OcKghwYTzGDaQsEYtcvvYQ0JAWeP+vqaYfGp0dDTgwrpYKiVGCkb+TYyPxwRNhKXblgRKxUjVc5BD18Q8jlJKq5bKxcfW1nbauHGjdCwaRjpOivTeSZXDR6IoGJnT9lckc/MEzPIw0lHGbz15iej2kh0fWZYYdI8Xisc8AVqHkTny1y+Pio9nSdfr3o8OH2tIKHW4eogZH4PjEzYn+3x977VgZPoowcdY6LZQ5WK6PWZQJCswTyhdghPzguVFEqa5F5lg+zST6wYEhboE/GUlvJqH9kmqm+CyAHeWdB/ThtHb21tsb3R0lLKZjK9/OteR0L4ZjsmJ0XRu0jpSXbZ0QrEDUD/smWdrEaxzzWPAcS06C34afqFbjrXXuoC718hlttJKm6db+io/2yLlGL/Tjra2YnIWfv+qJV32fjjbMg94E+7J54vtcv8GIl4blWKmsnyqREy3b54UE/zo8bGvry+wKZrxcTOJzd4m2Jk29xtIJ9Tdd999RWWgjI82RtCviGVLqszkyRYlfX9lfCQi2rdvX0CYC5Y+C3tGfcI3L9Zwg9YNUEdBl3+TUNzv3svG8MsZ6b1kdf4M8EFXU8EMMlM5Sn7m0CF9HGSazGXITqTwfsptf1bzzAmaP3+Bu/f7mfrFcIwYGePjK58qFdOtw8ioSfKCRgPZ6mzDx0TIvLfjY39/v1T+qxSMTFMQH2uldvT93bJli0+4DsNH//3C1rcpgzdIddG2URAjVcUefx8gOz5yOAzjo5fszMNInQW/XHzk/am0zPD+z2ICupVjMj7yuPL7D7OkeyEQsvFKxbkVrgxxNOBjLHRbaLyAaXJzyeW6QxItiHI3w8PDvrZGR0cpk5GZi7R7jW2yi0msy0rN5a84Qzi7PPf39wcsu1PgWcUZ/FOJhE9Y9bSGwRiK9fAvPpuAt2rlSprT2BjqXjc6OlostRJmUZYF0B7l9wGUruHSJYuTn5HH2hTr7cCL35bjvOV+ZDOZoieC/Py1EEIyJ36Q48Z13gos0HPbixYupKTj0Hp4sdu2cmrb4ClOatxrdC7xaYC6obek10C4+/Nz1FnmAXs3DA8PFy3o3D+bQqOUzLxEMVM5HhrP2JnCSHT4KBLYeBuuipF6fGykaHVTTQznNve7nAFXVx4G5MUr+vssM2IePu5R+sSlsi6T2gtnYFauXCW5YPqFOWYAR0dHqa4uZXnGGRRksHqk3/1Z3aOQuQYwM1QyE5ujIJOXdMdTtpow4wfFXdPEnJ/uvi/eJ81xmR7DejMBCYn520aedd42T9gyNtv9u4aAb1JQgOd7Bd+pjJG2BJ3jwUed4iqMYnwsnyrBQ+owsjuX0yZ7ZaVNR2trAB/9ScQmGx9TFLSMh2Hk+PARgGuNN+Mjj4sdI1dTOD4GlQc2CiaiUxPOMUaa8NEhL8dFMNlZoVBw90Me80rj43b3+tXkZTM3jd8a6d48D7iShC5TejeVYkmvRVUoRrKnRVR8XLdu3YThYyx0W6hSm42auEFvmZEXkFhU+uQQ7HLCVgSdZkquvyq06fLk4jJa1xkmHZegkoW9eggXZLnP53Z2+lxqZK3hN6G3orNwphNGW6T72RKJFQoFrZZfPc+3WcGzEstW73I0XKYM52mpD2MICp8OhIeBrq9Jx6HuXM63yfJzqTF73Jbu2ZlhG5SuzRmuBUBnuiW/bN4Cugz2afiVB92afpra1lrm3dAH+VpZU8lKnCyCSqAkoocMyBQzleVTJcYuGj6qG64fI834CANGJkkwKjoGjhnR65TjgqHxSlCpVmqOYxafzs5zDfh4saaP6l6gU8q2SPerIaDO0H+vnzbPqoULTaXUZOZPME/9/f2R36nZ5T+t9EOXDIi9FIL9zWSyUsynGic6qhlPc1vCC6wQcp3437PU2Sxhugz26rxl5thjSpsMGJkuAx/Jxch2iD07zNsoKkbG+Fg+TSQPqQrj8l7M75rf8ZHHx0YSCin/+lBjeh944AHp91LxsUa6Z5o8y7jZui5c2cMx0o6P3louhYfUY6Qab23Cxxu0fXWcpKbCx9GCjyaMTJNfedBteO/69mdGwMgo+JiaBHyMhW4LTfRm42VT1bv4cbyDXyumWhGGCWjVLAjBkMxqmlOcXDpLKAM1T1Z1A+dPUQsEEc+rAoyunmQNQFfBy7SdhBc7rPYjBU8gHpGOm6yvi6Qs2apF+WaAah2HOtraqK+vr2jdNZXnMlm6TXFAREQHDhwILOyaqioto5NwF/NUyzO1t7YWNdhrlHPlmD015trU3hb4BVQ1acSShQuLzza3qUnrmi4nbcshWkmygvt5S4T32NHqn7uzUilKKVlZG6uqKFlXZ6z9zZ8qgO6XromaNChmKsuniRw7fwkR/YbrOEnJwq3DxwIBd5CaDMgTkGWGcz/p4wj3E2db9RLUmBiMdcQhPSo+6q0/HOPGZXpq3GNqP1LkWUj5GaPEROuSgt1MjlNLmUyWRkZGqKVlMTlOLQnrg2rR8Qu8KpkwcmxsTCrTJY+5WmM9ScyEzZhRSwDXJ9c/E1vR/AIEn6tz2U+SOS7zMvJiDf3XOU4DNTefWfSayed7LCXMiDyrlHx/fdIi2arF+6mKkfsRVHKa8LGhvp7qoFfyyvvxfOW6KBgZ42P5NFk85AZl7siK/BXFEL3y8NGb95XAx0Eqhjz29RWfY/z4WEWe8BgNH1taFkl9lTFyDwGri3uLHh/167pUHjJYGrOGhKAdxEfxl7OH65+ptbVd8hQ70vioa1uHkcG9RsxL9mz4TOgzt0fgIWuASPiYQLAykI1iobuCNNGAac5wLru16LIKBjOrOk6SWloWUV9fHw0ODhYX+tDQUCDmVye4AaLcxJ133klhQpLJHVtXT1Jum8tk8eSWJ34CgsHgew1Iv5mE/xmJRLGfcvZwlUmRn00+noanbOB4Z3a70ykQVK0XP+8GCPfrDRAlyWqmTPFdl4NwGUxCKBvCnok3ULbo6v7XXWfacOWP6VouQXPw4EHtGKmKkDBruOyO7o/PNV83NDQUiNuXLdocf6+buymAzoXetb+UkIGYqSyfjhaMtOGjWveaLUc7d+4kP1OjMgR+pmfp0rMt/dG7Y/vL0ujahtvvz1LQEpAgf3Iwk5u6yuByP+XsuDqrie64x0yLsRRJdJjJ0jHJurI/worETLPOdZHvw+PB7ob6Z/KX/QpTRuuEXN34wHKdeK6DBw9qlAhpCipCbPf35q2YD47Vlbyjrc13Xx0+AkLpmERQKdqhnFcqRsb4WD5NFj6GhdeNBx+Hh4clpebRiY/NzWcq94yGj4mEHDYyRsCqQNtmfFSF43oCEiXjo3jmDSRc9W8gOz6ycuSVgI+qFT1KHzx89DwQwmuZ63jI9RI+EoTscTTgYyx0W2iiAdNe7kbEyAStPcESA6bsiQzKOxC+sb8Vfq2o6bz1CGqAbDWiN7iTm12ceSNgazUgMorzZGcBLw29G3oWnou8fM8shCCmLqq022euId2pAMps5fvcpiatNYGf2fa86vPIv3VonolLufT395O8gbJ125attBbBMapx+2fLoj4jkaD21tYisAwODlJvby/NP+MMn+XbmjEVQWE/m8lQdy7ny5Kv5gOQlTXcV9UVnt9XFIF/QO1XBHevmKksn44WjBwvPoprw+6zhoANEVwR1weS6kR7Btb454p99iwxfH9mjGw1cT0h2X/PLAnrkWqJzZGwXiTptNOayZ/ADCRK9PjH0rOm6GMlzc98s9SWKYlbNvBMjtNAuVw3tba2k8coywLEauW4yuzLcZkp8lxRt1muu6zoFUAkvC/6+vpcRj8p9dF2f3/sJyA8B9izSbfXsZukDR/l7xOBkTE+lk+ThY+m977XN1dKx0ciU5y1umY3ELCGEolwl+5K4uPGjRuVPB6MJ1HwsYeC8ew6S7AfH71qFTnpvn6BfHz4KAu8JnzsCDzT0YaPopoOK2lKwUg/PnrjmA48M4+nzEPehqDhrQegbxwl+BgL3RaajM1GH9fBoOCPPdFlQm9unheaOIoX92USCMuT7pAyQRMALTzrrICrcRL+JB0yQLNS4P9n793j67qqO/F1j2TLD0n3SrKjAE0AOy8/dSNLjuJc+caX6CcqZvqGKS2PlgCdGZKQDxOTDFOaOjFtE7vEH5iUxBoneGIG1DjQB6ixkhS7QIslIMUtpFJjMzVtgX5G+jSkD+gMWb8/9ln3rL332mefe3X1sLPX53M/0j33PPbze9Z7ZRXI6EXQAnYyrgoorVQLyG7o3aCsryfjtrbF9z7p2VQ8kdsxSJKflcF2vc6DHputbc5YA0z95RYHPpausXhj/Ezep/LgIM7NzVkKD7P+t6tvphIhgqRGuc9CzT+UfGV6ehrvuusuC7x849vZ1ITrCgXt/KFKBW8cHLTuNVSp4OTkpHbP6bjtUvK4tDEdhfq1lIiBqZwPLRZGRpGegMfEyFKJ4gjvR0qAlcu1ZsbHxJXtFOrL7Dzqe2ATumMgFfPV29sv4mMtApn6rEaV8IYfqyCV5lHufFJpqxEE+ANUwnMbJi6TaUzeDNoMn+xaSBbatFhJPWkcJQlCTJi4tPE4hKZQMDioGDBb6WEKEFniMrkFJgvzqz5btmyvJqdSWetN61fafU5Z6wRAxbQOVdT8mRhZFmK1JXzklSkyeajViJEBH+unxRi7keFh7HCEz9EcJ3HWifs0wBovPiKaGb59+AioXL0XHh+vvvoaVAkX+bOLmLjB59GNjxSXncNcrh39CeVMfKQEaCQA14uP5zFJFMctvWnj8W5cjvi4Y8dOHBsbM8LCOoX7uxUyEj4mFnRbuWHykGWQrdmXefBxPjzkggvd//Iv/4J/+7d/ax3/y7/8y3put6ypVsDk8RtpsRyc/viP/xgjIwEPMVZcM3b27Flc13WJsDnU/66g/9nZWcttWEooxj/ta9ZYDMBOALzFWISmG3YWLVIR3HHl3CV9qFKpMiNVJgQAz4JK1sWP87bSpiJhmAR8shLkQFlZswjqUsb38fFxrTQabwdXIPiE3E0AuDaXw3KpVF07dM88AL4DVKzfAVBCZ37tWitxW2dTE0agKxFGjXHAeL4tSzMk1nAzHICP5wrQxzkPbmVMmocAaUB55lzTNc6lIJC8GswxbQFVzoyPzVLFdAeMlKkefHz++eexvb1gvXABBjWMtOPj7Be0Cx/tuDp3hunk3mZ7tiPAWyx8lBPaSAwdZ6peLdy/gooRUkyJzozQpw8Bnka7JAu/F2fkpjERgserz29rKzAFRlq7ZQZ8fHwcT58+LfShDwFuSxkPbgWvIMA+LfY8uWY3qoziNyMJs1GUx/b2DkEx3RG3g5QIZqgWomwNK6CemClxd9XXC/cKSFfGqI+eWI3WLzHiPDQsKz5yHHT9tgkSJXatGBnwsX5aaHycnZ3Fa4tFK8ntegD8bTbHc3NzuGcPd5/Ojo92rLUPH1cKe39x8REABFzfgCoH0vNoeu8k+3hx8FEvjcbbwbN514uPI6iSyP0MAnwC0/AxURA0Dh/19WXOUyH+uDAyOz4iomUAqxcf58NDLqjQ/fjjj+OrXvUq7OnpwW3btuGXv/zl6m/XXnttrbdb9pR1MG3w8APa9PQ0jo2NYTMoweUeANxquPXx63aXStgaRXgnAPbEL1BJuDHBemR4GDsNQagDlEX5flDlolaAcofmCc/yra0WkLeAEoaJuFvHAMg1os0kW1dBxmRccftnZmawr7e3mgitIlzfAYlwKNW2jgBwX/z/fwU7pjxN+2VuTp54TErMsBpUNlo+Fh8TntkCgOs7OqrzS+AxAHJc+kc+8hErzry7qwtzxrMkAXUObI8Cbg03+9gej3PRGOt9QtvKkChj0kBNYh7oRUGu+Gn1E30CPyXBoHYsVfbygJE2mco5y/3LMVenT5/GpqYWTOIIT6Fys07qkxJGlkq742Q3B1ExJHqZFHp5m/iorOi6pSJxKbwflXC3AvVkPnlcu7YdlSX6Mq0vXV3dQsWJYwgwgHKVCSnJ1kp0J5vR4yFnZmawt7ePlXGpCNd2xH0gpkzKRltGqnkKsNZgWF0Wl59FKRaQPLPclqZVcR/Je4EsU/ycFgTIVec3sQwNos3IRbh9+7V47tw5lsiJv4tzbOxPsnGgds8Jz+fWHnN+WuPzzXW2T2jbSHzcxUjLCZgQE3yk+ERJoYqQvK/ICi5hZAsArjLyjSxF9vKAjzbNBx8LbW3Vd6OWXwb07OXT09MMJ4ooWWdd+GjHWhM+PhbvhWYEeD8qAfVg/Hsu3sNZ8ZH2UmPw8fbbb0fEJOt7qcQt/euF67lb/MLjIyJie3sHKk8kE3tWoT/Bpwsfv4AApnGuCTdv3ibio+pHo/GR1sB6tMuVrUUbI8sIcAu7Nhs+Iuo85HzwcT485IIK3T09Pfjd734XERG/8pWv4JYtW/ATn/gEIiIWi8Vab1cX/ff//t/x1a9+Nba0tODOnTvx9OnTqef/7u/+Ll599dXY0tKCW7duxc997nOZn5V1MGXwkGM5pCRdXFCZgSR+9tFHH8XZ2VkrSUCacMM/rvhsqfQTfb8JALcZv1VACWiFXK4qdJuxRGPCPYuQJCvLswWdxSLex1zYzfIYruuJuZDcxVviD3e5UnEn6WM5AEqQl/peBDmjeKsxFvRSNBUFESRgMj09ndr+GwYGxOzwHwY7xo/iACVwWQNJqIELnHjyFT42JBSfAj1JRRa3ejMuRtoHvtht1/ri41lrDdpa9nkWWmqMXEx8RMw2dlw5VxHWt6lRzm4BUUlUSqWyhX1Z3OHcmXalsib0/SYE2Gb8VkRKdsOZV/3eY8I9pUy1Zhkss/0qhr23t0/Dx2zjFaXUtqYyk1RqEqpJNf1jOYDc60DvexltxquAygWVW0MkRUGk4aM6T6o7m8eBgRtSysyZTGtkZdqNog5sayNhwVd39g6Ux5oY31Oou9T7XUaluEHJS833vlppnEvvbsJH01LUqD2elQI+2lQPPqbxkHxNHD9+XNgX88XHBE9kjCwYx7Pg4xwqV+3G4COAbrTKhpFR7BmzMPiYyxWwUhlCRDQs3eaz8qh7U2XFRxp789w85vOd1jooFNZhFBVQYSRXjM4XH8fR7QVA2OnCyKPiPV34aO6DtL1wbU+PZfxqBA+5oEL35s2brU7v3r0b9+3btyhayk996lO4cuVKfOSRR/Ab3/gGvutd78JCoYDf+973xPO/9KUvYVNTE95///34zW9+E3/1V38VV6xYgX/xF3+R6XlZBjO9nJetrSGLNWklAdyCyqsuvRSHKhXsYJZqs5SUec1eYLGwcfZo81zJWtwZL8AWkJORcWGVu76dBCWAnYh/OwhKAC8bi1tyATfbzuPO8nFyMU6Uxd11vW/TXRn/JZfz8fFxsd42eQKQwNsEipkhoTuJV3E/6574OTd7zqOyGTxuynVuXvBYIA8BrqyZmprKJKBnSb7CxzqL+46ZNdJl6XZlu6cMk6Yb/RWvfS0CAG5g6yxtPGuhRjKVS4mRi42PiP6x48o5bwb82K0yscj4SmLlsKenN2aUiMnwXbMXiRlRlnHpXMlaTMJqC9rJyMjKkmC9XnFiGgEIM8iNbwplN/BXeNqvmBYqJ8nJrnJhXgu4eTMpDFyM4l3Vc8fHxz31tjmT2IQdHetxbm6O4eOA51n3xL+5z5Hw0XWuWjMmY8otZSoL7hNPPOFhQH3t5sn7+FhniX88gDqz6bbkSBjZ4sDHzdeoxHmvhYQPkBJ5Bny8sPEREWviIdesbjUs1Y3Ax/MoC4KdKAt9WfBxHAFOsDZMYVptaL9C7KCVsA0R8bbbbku9/rLLXuPZw1dW21ArPgKsxEplCKenp3HfPr/3Sy34iIi4Y0df6rk2PlI76byZ6vgNDpa1sa8NH2fQnYDtpOfag6jHuDcGH28YGMANr3mNJoc0iodcUKH7xhtvxK9//evasR/+8If48z//89jU1FTr7WqmnTt34nve857q9x/96Ef4yle+En/zN39TPP9Nb3oTvuENb9COXXfddfgrv/IrmZ6XZTD1hAjp5W14tm4AFSedNvlrBRDOUrqJjkmuxvOJe+DC6unTpy3LYzfo7hubQFlWD8bffaVRDsQbZjvIwlqWrOFpLyCyQN/B7m1a0QHkmHdyzyavA1/imr74e5rLNN/gPENomkIlbc65Vdn0kKCX+jgATgDgRnCHA6SthaJ0XVMT3rRnj1hyrCAoT3zz6PLCAAD8sYzjWQs1kqlcSoxcbHxE9I8dj7ny7YXeXtPSQS9+nrmbv6Cp5At/gddSGkXSxmcRnNLurbA+ETyL7DruMng+/q0Vddf1Ns8zWlHFR9rMSJaMuH7BvKd6LuGjbSkrYhLTye+fM8oLpTHtgCrGO/2dKeFjusCQNueJ1WR2dlbwkOACcRnt2EPdhVUe6yKaYQRNTZ24Z89NQoxpEaOoYAkGfC5NjHxIwEfJGh7w0aYLHR/HxsYsr0cfD9l4fKzneFZ8BEyEdto/m1Dh/MH4e3r5KIU5W7RjHCOffPLJ1Ov379+P6RiThDbVjo+bjPOkOPL68BER8a677vLcz4ePybljY2PzwEffWjDfgwojOzrWo10yraXqHcBpPvh4qWefLQuh+/vf/z4iIn7729/G73znO+I5X/ziF7Peri764Q9/iE1NTfiZz3xGO/62t70Nf+InfkK85rLLLsMHHnhAO/Zrv/ZruH37dvH8H/zgB/jCCy9UP9/+9re9g1mLpbs9l7OyMpPwVgTdFbsPEivpUdCFabJUm+7DFWERRaAs11lLP6X99o7478TEBI4MD2Mh7s9JUAJhGwA2Gws+i9CWZxslAsBDoAuQnOi50vVdceZsXwbzVQBOK7ovu3trFFmZ0KVnQTxnWbXXWSzdrraNC/ckLSB5Rpgu6INgg1MFFGh1gMobEIFdxqYAYMX6jwwPY29PT3U9cMt1d1eXFRfjqy36swDYmsthoa3Nsu5TJvM0z4GlcC9faoxcDHxErB0jJUuObIWLhNjBAuqJqiqo3A07USXT+pn4+FHUGQeyVJvWh4qBy9xiQ+eSpcRtLXb/drh6/czMTCxk5VExK1SHdaW2d9xMiWQ9IZfDQ8gFSE7DwyOWayBPAEbZXn0ukaVSWbvvzMwMs864x0bVviXG2McgAybWrfRY5yyWbndm5XHrnnpI2INou8oOoYof58do/eURYKNjngoIRmLU4eER7OnpjedFtzTxGFdOPoxcBSoEq1wqadYen2I74ONntOPLER9d3mLlUknzevTxkOTZ5/bkqQcfKY5buq+vvJQPHw8iQDs2N5P7smu/Fx3t5/iYPNfEyOS5+vUrVqzOgI8K03bs6NfumRUf1WcvJhbfxuAjol+h4MfH5NxSqVwHPhZRhRFQPH5BGOdOlPJyDA+P4NatPWh6SXCXfE4+fPz/QJXD7SoULGu4i4ckI6Uvm79JCyJ09/T0OIFysejv/u7vEADwT//0T7Xje/fuxZ07d4rXrFixAv/X//pf2rEHH3wQL7nkEvH8u+++21hEkGkwdReTCpoJIShDIE3yLNjJvijWgAtCplC0G5TrtpTQKgJ3YiyzpFTaS9n3G3/eh4V+ULveF/81N8UZoe3UPlIyaIXqDQZhbm7OympOcWudUYTdXV1i+YwyJK5YAICd+TyeO3euel+f9ZVebAch0Uj3gGwtJgGXhOGicF4e9KR0iEqhINW0zsdjliaM82yL5os8ArnMDM1Doa0NpTmkFzkI3/fv34+jo6P41FNPeZUd5hxm9VhwnRMZ4yklqlvsRGpLjZGLgY+I9WHkyPAwFqLIWkuk5MlH9ALmzMIsysljAJPMsyYjsBtV7LSU0CpCd+IX81wfI5QlHrKMCSPCf9sY/31f/NfFoJlW/wgp+2+a293c3JyQ1byCAA9jFCl3S+VRIDFDPdVrWlvz+Mwzz2j3zlZb9mbUrTOuZxGGj6OyjphJlFScNidlUWoRz00r0UMZzt3xpGV0hxMAmnXLdYu1Ob/qO8fHQqEL08ZNYvKyYKQrR8q2gI8WLXd87Gxqwo+Byjpuvm8LUWSVj8vKQ9rrbhpV0qr54KMr1ttn6c6Cj/y7CyPPONrP8VEWTBERz507hytWrLaem8vlcXCwnFKisoykWFi1ak2d+EjtI4wkQXP++IjoViik4+MB5LJKMjdZ8REYxvH5kNZOkljy0UcfxfHx8UwYuZA85Bmw+dyFwsfMQvcv/dIv4eWXX47PPfecdvzZZ5/FH//xH896m3nRYoBmPZZuRMXo6OW89IW2Zct2BEgE0BGwE3B1gLIgknBUYf9Li6KjvR2npqaqSVGk2OR8fM+HIckOfQLkLH4khK0EWUCUykutF/qRj+9DGndXbNkEJNpcOtYKygLLBUiTpqenq65JrnvvKOpA3m2MHb2UVq9YoW2scqkkCtFF1q9TkGikJeXHCChBAiARhtvBtg6btc5pHQ1VKtY9qZSBZHXm5xJQ1FJGgRg+itM/ceJEtbRXeXAQO5ua8AAohcU+sJm31StW4Jr4f6ervdBX13otQrbcBVcZ82la2Re7ZNhSY+RiMZX1YOTc3Bx2d3VZeSRoT23dsgVt5orKlJgxuk3shU+/n0GTeWtv79Dw0RV7Vyisi6+hWOsTMX5LmXQjTDLnmkyNXj5FMW3UVjsBTmIFdrnOz2DCnNG5raisBI+J8YqIOj667v3xj38c3UmQALmQaVbe2LFjp9B/SjIUoSpRw5nPSeFZI5hkAj6FVHfcbM/Y2Ji1jpRCQb9fe3sn6tnQTWZT74tdI9fN7G3evA1nZmY0fKTSNb29/fGaIkvdPqsfirlfw54nKVjkCidS/WWeb8SFu6ZiO+Dj8sfHkeFhMeFqHhSvd+jQIW2us/KQzRBhBHlUySF1Y8XWrdurdZXdsclkPb4HE9diSmooYWSTgA+14GMn27PvxwSbJWFxAm183IZcgJQwMrEI34lSfoWBgV04MHCDgUdmaEgk7ls/PvbEzyLccVU8qB0fEZVCwQxjURgk42Nnp57pfHh4BMfGxrBWfETEan3u0dHRasLGwcFyHEt+BwL8IZrv6eHhkbgN6RjJE4cSzZeHfAXDx7yxlxYKHzML3YjKraarqwu/8IUv4PT0NL7xjW/EKIrw3/27f1fLbeqmxXIP4pR1MEnrQlbQGdATW9EnS7KMg8I5IsAasbLE2PLnXQOqhNUKUK4TRyGxJpvuxj3x31eD24pOMcEz4K+dbLqZV61acXvugEQozYNdH9rUNEmZCiuQxF7zzURud61RhFeCXK5ra/zcnX192hjm167VzqX4burXO405Kcb34f0p5HJaX8gS3waAr4mPpbn4UU3rD3zgA9UxngNbs72uUNAEC3M9HoNscWKu8TVrpZvMGylWfC6NUlI8KZa+yObTt08OgFJmgOe8LK6UjYpZXEqMXAp8RKwt2aRfK00vdp/F4P3G77aAHkUdGsM1NzcnxtTmcm3Y1laIGYP7MbGuVIxze6rX2NnLyUrEE8D4rD7Nxj0qmLgur0DFpJxCm/mVhTS5nm4F9djChIFR1pw8qtq1Utma9ais4/o4PvDAA5jOJL7TmBPy/mp39CmZC1VOpoBkCXHtXcLHQ4cO4Y4d5BHwMEqJl5544gknPqq5SY+ZfOSRR5zja9dKjwwX8qxu9nLSp7m5OSuGl+cb8b2DWyHJgRHwcfniI2J2jKyVh3wYAIer2JFHF0bKsckVVML22hiT7kelXLqZ/S5hZKtxvB58NO9RxMR1uRUVbulYYuJ7NozkNcfVno+iVhweHsFSqYy5XCuq5Gl2rDHA1jrw8a2sr2TBLsZ9SPBR4Qi/D5+Lq7x7d2JiAvft24cf+chHMA0fBwZ2VRWKdiiPHx97eq7Fubk5cWyHh0fw3Llz7Li0BvOYBSOlxKHz5SHzkCTmXSx8rEnoRkT80Ic+hKtWrcIVK1bg61//em+5hUbTzp078ZZbbql+/9GPfoSvetWrUhNhmIB+/fXXNzSRGqI/vmAvxFnBczlvTPVR0AWlWmOCpezhLiF6ElTsOP+NXL23GUnfTLenHqEfs2AL8yRw5iHRKJltuXb7dpyamtI2v1hv3IjN4Nm7+ZgAqAzeu0ulVNdqEhb5xiKNshlHz2PpTJcUc3x37tiBAEpAlyzx5VKpOmdp5Vv6enutMZ4B3U3eVd+Vapv7GDNqizS+pO0jDaZ5H75OSQmRlphNauvMzAxeuXGjuCcqkB7/z8MmXPtJKjVR7z7PQkuJkYuNj4i1JZtMw8dmaGKxyL7YQO526K8YgcgZCbJoT6LOhJiMUhEBnkaVzIYfLyPAF9F0OVZCqsSA8j7Mos2oVlAxRCSE5o3fVQ1qEx+pT7YlPy17d+LmODU1xUoCFVEuW1O2xjGxortKvqyOrzG9D1zuoKNoWpqIwfLho4pfNy0k5B2gMoxLSXH0DPnpzH+pVK4+yxxfEpQ5Pur34QwrV0JwN1I9q7PUV0rAKuX0iAAsa3g+Pj4CgHcHfKzScsVHxMXhIbNj5F704yMJ0pNoY6T5vZH4aLfjmms249TUFCJiKg8pY6S9B0kAnJqairOZk1Xf7bFUOz6eR92CrfdLWcwBlRLT9lYqlcrVOUvDyN5emgsZHyXMqQUfCavT8BER8cQJV2w6z6GShpFufKyXh1wKfMwsdH/3u9/F2267DVevXo29vb24Zs0a/NSnPpX18obRpz71KWxpacGPf/zj+M1vfhPf/e53Y6FQqNZ9fOtb34p33XVX9fwvfelL2NzcjAcPHsTnnnsO77777oaXDEP0aymnwM6ql6alfJKdczj+35lEK14UHLS5ZZy7qZMwVcjlsAXkOtPkosQFsCK460zzfowIzzIFL/M+eVAWW9JIShZXV71xHtN8PyjNPgli+/bt89bhvi/+y910ssZ206dcKuHY2BhOTEyI2UW5ZYLm7MiRI3bGdMOynyWxGoDKAkqgK40deRCYwENWegCoAqLrOSdOnMBbb73VAieuEJoDwH5jbKjvPgCj5CVZMlGWAfAI2CXpltqSsxwwcrHxEbExlm7CR5uhymLp5kyOLaCb+JgwH9w6XkGp9rOyukpMWgF1jX0R7Zg3Ysp4H0aE5+hMhVRjtVBYl8FikzZep1AxT61I5V727dvHMpn7rk3G0R+3OKC1qVQqV11YZ2ZmcGxsjJUtow9ZmxLriRmXblqtknbcnNqee++9V8NHe9y4FdBk9orI8TFNaKF3jS5E8LGaQ9vSZFvZJIx04WNVcTqoJzTqB8CnQfeMCvi4fPERceF4yAOgwsLstenDyHR8VApSqlktKey4O/nC4iNApOGDtM/9Ncf3osLHMlKSs9HRUXzve9/rue4+bQxrxcfh4ZGqtyLxkKVS2YsTR44cES3LLh4yLc583759deKjr5KDDx8R9RJiUq12/d3QCB5yKfExs9C9evVqLBaL+NnPfhYREf/oj/4I29vb8f777896i4bRRz/6Ubz88stx5cqVuHPnTvzyl79c/a1cLuPb3/527fzf/d3fxauuugpXrlyJW7Zswc997nOZn1XLYErxwB2gtJMjoKej7+3pcWpfyBU6B0LyE7BLWZlaSu7qO5/yYFSCwuuiEWvZT3rOo3JjrrJXaRZXV71xGlNTEDY3meu6m41nE90wMICtYLiMg0pQAwDVeJUstadJ6WD2lc47GY+J6YJNL8ABSBeY+ae7qwsLRnbTPMghA7sB8MH4/7WrV2vjRGEENGd8fM35LbL20RpwxdqnAZgUn8Mt7X29vdgWHzcVSbwN1b0XRVgeHGz4PnfRcsHIxcRHxOxjNzI8nBkfx8fH45i6AtqxgStRMXQ5tF3+OHPisuIcQ10YcjFJPvdHijNMZ7KUteAx9NcnJcuDXNalVCpXx9K2KvjrmduMlIkfrmuTbMNESiBuRd1dvIAqo+1j1XmU9nu6tSnpa3LOSQTYa7kXJgLCSUyPwU/62NXVHdeaNZn2VwtjshtV1l7A1asp5IjGiNxk1Zy1tRXYdeb8ksBBbaO5kuNUXRiZho+IytpTaGvDVgEj6f+Aj8sXHxEbw0OuhIRvNPPIZLd0c1ff+ZZQXBx85PggYUx6zXFznBIs2Lx5q+e6m619q/Axj4k7/gFsDD7q74PsGDmAaUpFPz5uQVWm0nzXTmLilWaO0XT1t3R8fAx1oZ7WgZyPZCF4SAkfO5uasL+3d+mE7k9+8pPWsa9+9av4ile8Av/zf/7PWW9zwVEtg/nAAw+ISbV+Pf7//ZAIHlIsQgUAN0NiCR4E2bpcAfuFSzQyPKwJqL543rTfjsbfzXuYAhm5QPvuRy5RaSW5XBZXn4t0m2OcvLHGkAivtLlmZ2fxhgFdGxmBigGXak4T+TTVB+I5I0v4Q2DHaOcA8IknntDu9zDYieCKoOKZpeR2RcfzAeTQAwAVY+9qU8TGVwKnQhTh6hUrtPPzYAOYLymFWC+dWf/NrPV8nOfAVkJEwj0asc9dFDAyfewmJydTkw6SAoz2oSsGW8UW5lHFVZsMQgcqq4ycRCdhaLhLmytmzefifjT+bl6vC2SJe1824dZd1gWqLpM28+JjjNsc43QsHs+0a9sRINLw0U4yFKFK8PaQM3kRot8KFEV5ZuV5CG3LcM7CR3WvIZRjLleizUAWHf0EVILwGCb14elDYyS1KUIVZ8ktgglzG0UFK1PyihWrraRVaeNG+8HnHXXu3DktrwthpJQPJODj4tBC8pBmDp8iqHd5Hmwvxm2O2sgSRuoCanpMb/pv48L1C4WP6ne3V0oWJaqNj0nMcTZ8RER86qmnsL29w+jXegT47XnhI8ABI7u4jJHkap/c72G0E8EV47YXMRs+0rhKoQeEgw+jChEwf1sZ/2bjY1NTJw4O3mi867OtVZPq5SHT8DELRi5oTLdJ3/rWt/Caa66Z722WLdUymBTLcQqUUDopTCSvWUwbgqyC3KL8pLEo6POYsSiGKhVtMczNzVVjsRtt6XYJZBRrKMX88vu1QnrZKwCo1jmUBHdJmMt77jkDdvkUM6bjTHzu4cOHcWxsDNcVCs4sy2mbzxeTRZuXMkNWQL0UHwI7Dp6eMzI8jPkowlsgiaHnY+8qESfFom8AJTCbL2MeUkDlylyCvARO1FZK3PHEE09kcp13xSGZcasmkUvsfQA4yvp6HpTSojVeu1VPgwwCfyNjFk0KGKmI9gfh4wzIOSBordgx2NxqYiZSkwSoCCuVIQsfVbksYNc3ytItC2QmPqYnDjLdLfU+jY+PC27y9Klg7aViZuJ2uzIOR0gxluPj43j69OmYmcyj5OIJIGfhNtdAWobaJHNuBZU15iE04zzpGYkS5deRlzvTmUBXv02mfQMmSY1MS1MhHiMqV+YS5G0Xcmor4ePExISYtIqP23zwERHx9ttvR8JI/i4YAJXxPODj4tFC8ZBS8l7i1Ug453zRWQBsNerHd3V1a2VTERVGJuEfjbR0LzQ+Kjfv9FrZkpt0mqBJpRld19n4qJQIdH66G7xJPnwknNAxsoBS5Q56RpIw8xa0MbKIeqLNNHy8AxOLuYSReXSHG1BuETc+IqLGQ2Zxna8XI3nYKe0djPddDmwjng8jF1XoRsTMtcwuRKplME1Lp5RxnNdRNgVMsihzJtQlwN2Xshimp6dVlmnQ3Sgky6PLHaO7q0s7XgS3QMaf70rhHwHgDQMD2L5mTWpiLEpA5hKiebZqAMCNnnEaB7kueD+oGCkEVcPU/L2W+A7a/L64aCrNZcZqu9bJTXv2WPXIzU9av83nA7jruqYpYcjLYIIdIy8HV5Iiik8ygU+KOa+lHqLLC2EIkri1emJzFpKpRAwYiSh7gog5IJqacHep5GCexlB3A3YxJ1ejmcjFbIeql03WRlkD39XVLVok7eNFdAlkg4Pl6rPTyvJUKkPY1pZHN3MHODhYrsau2cznQ2i7SG/0jNN49f8rrrjauLYfAaaQGLHBwTL7TWZ8XfWmeWKjtOv1c+g8OzM9zevZs2cFbwj+Seu3JDzkMK196b/xhHDKinfbbbc594KEkY3AR/OdQfg4GfBxSWiheEguoNNcjoHOy3D+YBgibII8KmXhUXRlzE/aEWES3iPjo55AK/ktifduLD6q0oAmPhaQ416SgMy1T+3SWyrpYzo+2nko0vAxHePMsc6KjxIP6RKABwfLODs7a+XGmB8+1ouRpMCewPngI6Icr5+myODkynkE8V6rl4dcdKH7YqZaXzZDlQoWcrlqfThz8iQBrwjKgjgNSf1sn1v0hGcxDFUqWjy4+cy+3l6cmppyumOcO3cO+w238bT2kDvL5OSkdV1vTw/uYoKSGWe0CQB/B5TGlgv8VOLsACjBfFN8vqTZTbN0c6GXMnpzoX8FJNp/ygruFGZZEofZ2VkraZqprOAKDg6u5JJ/MqX9UXytZAm/KuU6iMdMiml561vfmto//tss2Fp2UlZI6y4Lw5iWIf3JJ5+sWoJcNDI8bNWbpZi35hrmbr77PFBCtYwdzf/9kCQx5Gt4FqRcBfwFXkbFdPlKMAEmVgobH5X2v4Bp2bVLpbJR7iR5wZ87d86wmKczWqVSGefm5nBubs5KktPb249PP/00e06Tcc9NCPA7yJnkxHrBY6ophlnyDEizRCVjVCqVY9fSA8iZ67a2jrh0DiUtk5k1Ex/Nvg4Pj2ClMiQqMkqlchUfE5fTk6ntVzVgzXkEVO70af3W+0cZyAkf02Pj+W9StuV+pJJnJpb5GMY0fKT6665YULrehY8bAj4uCdXDQ7YB4DsEfESQeUjK9VMGxSuZ/GPW7OWclLDGBVQdH3t7+6o8pFRKb/v2a4190Sh8NBWLLfF+SxQJiVLUjKkmSzll8E5PkJgVHwuFrhgfSaHhx8j54CMiGm75bnxU97K9hdI9gWR8TLwR0jCS/ya5mtePj4jpVSR8PKQr51Ixxsl6ecggdDeQagXMs2fPanE25uRVQM7eXQRbAHOVYIogsWS6FoMkTO+67jrs7enRjpFQRO4YJ06csLRue0G58aYtxm1btljPI8HeXOgPs8W9CUC7phj/7cznteNNoGqOm22Yjcckb4yTK/bdHBfz5bXbmAP6kJC5bbMqTTE7O4vdXV3WXBaiyIqzMmtdA0DVWkvKmfOg10Dna0HSdufjMTT7nQfAQlub9iwu+D755JOp/ZPWn+Rm3wKqzBt/WacxjIjumPeDYCtiuru6LLc3niiQuwQ9Zly7HC05FzPVMnYmPpr72VxzehyiKYC5yovQXkusFBI+mi/3667bZcUq0wtfKkOTxA7uRWXlTGNE1uLg4I1CRt2y4SZ9DJXVZUN8zibtfBIu+/p2GscjVPF5Zhtm4zGhMaRxkmPfpXFpbl5lPMvN5G3evK2Kj8oCnUeTOapUhqxnmNbqZB54gjhe45czeEWUXR2bULmk6lYzPamP7dad1j/14QnQpGzLeQSIsKmppaqMJkpjGM1wM3qIJGRJoWUBH5cn1TJ2kqdCFh6yA5KqLRL/mJQY9SvLiFwY2dOjG1VMjCQecuHw8TyqetWknCwa2KS+5/OdxnE637RqD6LsXTSIWfDRfk56lvTNm7fh008/PS98HB4ewaeffpodS8NH2VsoSUqaHR8REXfs6MO0/snvaBsfm5tXVataEPnKjhH/mv5smYf04eMBdm2wdC8h1fqyIcFDslRnia/mICvFzxZp8uP73eFZDBwI+3t7RaGoXCrhAw88gFu3bNGeNTI8jEOVStUy5Wt73siazZOGmdfdAbElFwzXqfj4WrBfKi2gx2/PQpJgzGRKuBAnuefNzMxgf2+v9fLqjO9pKjvykCS5iwCwq1BIHQ/uFuMSRru7ujAfJ70rGu0nq8RJBggSUJjCKh+H/ljpwWl8fLw67pIyZ2VTE+bBn7iulT1rZHjYW9JmcnJSqznOFQzrwWYiWkEpD/i6HhsbEzX8Z9j3y6S+LXHM4sVO9Vi6j4GtZJTwcQ5I8ObzToybqwTTQ/H/J1DKvM2JC9OlUhmjSBegyMJw+PBhPHTokGWZSLK9+uK/lWVeWaft+9vXjqMSpE2GpRP1xF10vAOVxSdi95nFJHmOOYaJNV1yzaNxKRTWoR2b2IJyVvnNSAxVoUCKFbdljZ5RKpVFRkuNLSlfZcZaZ/I406nH9kv/9/b2W/iIiLh1aw/KmX5JGFqDshLInHMVg0rj6xPoTffVXohwCmQhqx2U0pVX3Qj4uDypUfiIDoxE0PmwNP7R5fab5l3Gecje3n5xr/b29uPjjz9uJUXLjo8qR0d2fERU2F4PRhbZPWaREqHp47QSyY06DR+VS7mJj52ocNdUCFO+iDx7Xv34ODw8wsqgpeEj4dQB1OuG09jzyhZ+fFTx5DTuJkZG8f3yGea8tfq84eGRlLCpxBvC5gF05c3eeP0fAOW92lUoaO1Ow8f3xX97wB2O24g9HoRuDzUiHocm7z0GKNLnvLEQTEAlAf79oF6+28B2Ny6XSmJMg+ny6xP4Ib73w/FCG6pUqtdH4E5IFgHgrSn3NvtMv7nacyc7xpULwNowACrhQdFof1v8N80Nz5dp3LTAd4N6ibkUJOZcmjUbXc8pl0rYBLLQCQB4C8iuZAQUraBcyvqEe7ji/UEYM/r+xBNP4M6+Pm//aD4oJIAL1NL55NYvPZuPj+TSTkoTKqeieRbEH36+qYhYrOy8L1dqREz3Y5CUr/Pho/1SJlfzT2DC3KzXrimVys41oNz8fDVcTYbmDHLhMGFYTGGNGCwS2ORyNzYj4dPo32kcv5/dh9owgMrN2mTIlCdMGj4iplkVpNjxblRKEHO80i1rPkG0VCpjkuRNTtymPqbrJB/vznhN2Ay9FM+qmD+zf4kyZ+tWs3SOy3qnFD5UxseXJEm5rcp9TMPH8uBgwMdlTI3Cx6w8pIt/3A4RRlVsOGPhgisu1nb5zYKRFQR4uAZ8pN9vTbm3uW/otywYOY1J9nPAxH36KrRjvFcggCoTlqaM8HvFmF5KlEiMY/X88HFqaiqujJCGj7egjGdn4v9bsRZ8TNpkvlfU949+9KP4ilf8mLePyXwcjBU3fannJ2797vGQEg/u7OurCR8jsEsQL6vs5Rc7ZR3M2dlZS/AwNY1Zkli1gFuwBQBcVyhUs+sVjYXBM6MTkeaUuzHzZxNYk4aIrL0jrF2kdXvXu95lCYAkoOdBCcHSvaU+k9Dmas99IJe2Mp9fBLcLtOQyRa6hlAHb9fw1bL76IamNbgoALgs0MbO+jOY8i6K5JiJQNTdNoOhkc3+ghraYa+IA6DHz3HL9kY98JHWtUiK1cdDXr89tvdvoj7kuXYljdjs8JorC+HREEe7s6/Nm+K1nnweyKcvYSfhIGLkesuNjMzTFSXrMpD2cqSC3Yp0p6OrqFl+cdokciUHYi7olQ6+ZOjExgWNjY0IyMsV8JvHW7nJgtqU7rT33xee4SrdwRkh273PFpxFG3nbbbZ42rEJl1ejHJAPueaMtsgXaxEfXM2699VZhbDhjuxGTGt2mVStC3ep9J0qWHletXDtmXo3b8PAIHj9+3DFvvG1UV1gxl+5SRnS+XLfbh48dURTwcRlTo/AxC0bmwOYfC7kc45sIG3IoldirVIastiUuvzzUIytG+vCxiKTAVPtrwHFvad+Q0OZqz/vQj49p2JGNh3Q/f008zlejSrhGv/O61guNj5tRWe1NobwTk/cjCbK14aNaEwcwiZlP8DGxWmfBx3HUlSs+fJTCyvJYhkjEx0IuVzM+lgcHM1WJqGWPEwWh20NZB5NKO5nCD7kDUQ3ajQIodkJiuZYsmzcMDODY2BieOHECH3jgAQRQ7sfmYsmD0noTcc1ploRj5rGqYMW0bgT6ZtxZ2n3KpZKY0dzHYJNlXRKo+fi47kH1XBFti3+WlxewZ1GiEt6+NqMdRVBuf645cPXTfNEipCssquPKzkuzho+Pj2tJ3KR4f7q+CEktcopZN9eqppBhbaDwBdMtpz8laRxfl/S/a22Z4+Rd0xkZylr2eSCbsowdx0ea63EAPBHP1Z2QDR8VjuqJxrq6uvGZZ57Bw4cP4/79++Pj16ASvHntVT1TLiLX2vsSs804jumWicQ6vNdxjSxYlUrkQkiMhM81jzONBUy3Asv32LGjX1NC2BYtX5baHDuHrDi8fVeixNgPDOwSxt/XTxdj+6EM83YG0yw9Jj4iqthNO+tvhABbMYoK1WR2SUZm081yBE3mcnx8XMzOrEIaopQ+Bny8kKkR+HgQAA9nxEiTF1hXKOAzzzxTdRH/wAc+EO9bEx/VOuTrQt+fWZIyyoKVbbl1Y6F0n1LJxEdSgvmwo358BADNvbo+fKQ2DGGimCTlxWLg4wOe68tYLz6acefJPVpYXHoWfEzeo0n4Qho+SmFlUTXzeKPwUXKtn88eJwpCt4eyDCZtjIcgiTGmD5W0okQWfyiAYjm+FiARdO+LF08rAK7v6BDLJAEkwiBfLC4rq5SYLQ8KrPmiIyHqHfFf7mJzbZyILc3t2IyDkIS8IgAOgh07kQeVTZyYcNeGeD/IG4m3pa+3t9puHitVAb1etaYVBmVdHgTdqtwJgFsBtIzw1I8zkCgEVq9YYVnTdpdK2BpFWkZxSvTmK1GQ1r8xSCzieXBbw80M6zQn/Tt2VLO2n4zXW55d98wzz1hJryqg1ioJ3yZISdnLn3rqqSoYSv2pgFJgbAR9bGltuxQQ4477mS7+jdrngWTyjR1XPN0k7KEIVPUCFz72s31ybdVFMSl7A9CO+by+TnUmQhcIOVOpWxJkDbqyVksMzWE0Y8azuRDrWWl5zWm9D+vRZljyqNwfD6I/pjidIYuiVs19UE9iU0G9ZrXZhhZUFvxOds5WlJhIdV7C8JrWtFJpt5UROKkF6+vj1tQ+KitKEdMsPaVSWWszzYc63oqKST4W/81Xr5uamooFc5NhraByRdeZS1J4mvOcJI2T+0hhVAEfL0xqBD6eYfPp4yEBAN8Jiuc8COqdrvOQkoCV4CMvA2rjWa0Y+TPVtU/U03OtcU/zmjswGz4WUSU7kzByY7yf0rDj5zztaKoTHwuorMuDqMeSD6Ltku3HR7fXTRZ89Fnjx7BefFTrlitvTqLCSBUjnx0fk/ZOTU3VgI9KUT4Bil9f0WB85PLDfPc4pyB0eyjLYBIwVcDt6kxuwHsBcJewQFpA1dLkFkSKZU4TqvKg4nm5xdEVT0wlJUxAf9hYdFKcNwlqvoRZ0jVEJ06cwLvuugv741rc9HyzPfy7k2GAJJt5Wlt4FnbT4i8lGiGX7iHjXgdS5kESPqenp3FsbAzLg4Ni/0bY86n+ual88JUFeycksd+uc7oKBTGJG7nbPCSMAVn5aR396q/+KnZ1dGjnFEExAlKSCdMtZ2R4GFsgqbFutvUhADGu3bSq0/jTOPmSvaXFY9WzzwPJ5Bs7rvwbAqXYMjGScigcAIVnayFJJkifrur/9PIlt7xNaDMNlJ2bLBt9aFpdEE1LgqxBd5dVcTEibiaor69fvI7acujQIdy8eavxfLM99H96DFwikLoYsgMWRtoWLWlM2uPPiHEvUoiY8zBiPfvEiRM4NjYm1Lal/hUxsQxRll+Tsc6z69ITNLl+LxS6xCRFSYz/Q0L/c9o6OnHiBL7pTW/CV7ziVcZ5irmUYiM5RrosQjnI4zBEAR8vcGoEPhZB93Rw8ZBbQecfx0HnXa4S96iOj1zotvFsDpV1tDaM5DjnS5jlug4x4SF37Og3nu/CyDR8POxphyprVTs+RqiE7iHjftnx8fjx4zg+Po6Tk5NOjxs/Pq5DgHs9fXxn6u8ufBweHqmGRrow8tChQ9U5k/GxiMqa/piFkbXgI4LKc5VvMD7S3Ddij3MKQreHarF0p00gB0hJeCvEC6cTlLbTFITM+7rqfZsLhSy8HwM7+VpXoYArQRb4WswFzAQruqcr7rzPyJot1W9eF2f/pk+hrQ3bWX1RX53yGVBCHzEjLler8fFx7aVmaremQZVDo5rBo8YzSMiXagqb7aFzqWSXyz2+B3TXsYeF+Y7YX8k7gX5vNvpDH5d2zwSVCqi1VzSe3wSAn/70py1Ld761VUu0BpCeZIL2BvXRBL7HADS3OqmdrZAI+VI7pfmPIFhyFouyWnJ8e5qHa0h7Z3X19zNov+TT3Od0hsVdxuljaCfkakaZoWlBzohEUUfVdV1yIeYujaVSWSuVItUmHRi4wahzSxYFzrD5alFPobKWm+0nC4NiPjlGqmP8f1JsTGASi8hj8Cgu7z5PW8hlNHGZlpjQJD7/JOp1dIvGvPDvFZStbxEmDLiL8U5rM7+3Xed2YOCG2AqkM/mtrXntuytBFd8bSmiRXSaz4GNLjLHmOz4NH7lwNd89HshNjcJHntzVxVuQl56dtZznf6H1LtVQrhUfKemYZG0uooSP+j1ljKQa4EQSRqrKCsn31atbUcfILCFDrnJhQ1g/Po4az8iCNRI+qvlQmGgqSQYwOz5G6MZHcoGvFx8JIwtWG9aubRfxcevW7TgwsEs75sJIHz5+FrJV2qkVH7n80Ig9zikI3R7KOpi+7M1r4kVxMgOwDkFiMSe3dMklNw826HZ3dWntItdu0Urb1ISrmptFa7PL+j01NeV0Fz8DtoCOKNdvzsfXpAnYBWFD5EG58PM2mdlYuwHwt+P/XZZuycIbAeAUmzOeJIxi8tMs73yTS32aBVtoJNcxBCW4j4MeYgDCNXysfZbutDbz+0keGquam51r7MiRI/iWt7wFH330UUREK+aHyAxxmALlLsyf79s7GyAJoUA2tneCLIjT9xCzuDiUNWaxNRYe6sXId1TnuIhJcjBidCSmIUKphrJpdUxcF11WID2GPM2yUyqV8dy5cw5XyDMoZYWVapMqRosE+5MoMz9FlGPmCphYTw4K7e9GgHPVNrstOS5GjjOSlMzo5pR5AFQMImfYXBboj6FsuToTP1eq5WLVpQAAm8hJREFUQysxZJX4eKvjOZxxTGM46VpXvdlmNNdYLlfAHTt24q233or79+/Xaru78DFpA/XxVPX5PnzMgf6+noEkUelnU/AxCN2LQ4uFj/TOvwr09zmFddm1uuU1XRs+FlBXbnGsmGPNS/Bxbm4uxV08O0bqgr1LwC6gLFR34+Lgo5kkLCs+usKHZoXnpuEjKUPNawgf2x3jxuPSzzjafDPqfc+Oj8PDI5l4yCz46ONza8XHMiShGsHSvQSUdTB9btcH4+++OIJVBqBKwf61Jkih5D4HHecfBCXo7QXANblcavt4nANlY3Xd1xR4xXMcY0J9dDEMB0BlGezu6sJCLod3gqqzdycoy/1K0GuYcut8BRKXbtPbgLujHIDEjZ+scK5+0LlRfI7UJymzYj6+v2tsqGTIO411xM+VrMdSXXPz/uSKlmXd0kfysFi9YoX2nVu+XfNPgvPExIR3jZwy1gUxD/tAlYjYbbSnBQB3DQwsyD4PZFOWsZubm3NmEM2KkYrZNJPXuNy50xORuTDSndznTlQCPrnjycwTj5NOslXL97SZOem5xGSYz0y3AAB8Nr5HSyzAH0TFgN2MihnahFHUiqVSuToGuvWJLOQmE0XMKrVPMb5JPW1XP8xYRFfse8Xx3KLjvmVUTB0lJ5IS2JGwwBlvqa65eW9yz5eYX5NB5sddigP1vxlSkHbvLPgovTtJYXvIgY85YQ/Md48Hkmmx8NHl3Ua8lG7pTl93tePjwXiP/6xjX9v4iLhYGGkKnPT9AC48Ph5AhTXEI2XFR3T0yaX8c+HjTHwNCddZ8bETk1jvtHtzr8f68VGVPUu+Zw3XGh0dra6hWvDR5CHNULZaecggdDeQahnMNLdr7s6ctkDa1q61FomZAI20NE6ra+wSIbl188Rr3EpL96glzsFXDst07ebnnIzPGXWMCX+xkGDOXbgBoBobXjQ2DP9OAqBknU9zR+Hu3QCAQ5UKXtLZmVrOrYO12eyT9J3ireiFyN1bKE58DnSXGNdYm4LwblCZ8AGUe6KUPG8yw32PGsddHhYF9t3l6cBjaVqjSFOKSMnmuBKD16flfTX7XQQVOz5UqSzYPg+kUy1jVx4cxA5hPdaCkW5GhDMN6SXAOEbaMXOUWCg5P7FE+BjAJE7al1TNdlvk55CgN+p4ZnYLgBxzZwuBtvUprY955Bau4eER3L17j1XOzc4UTFYZqU/mMXLdPMCey5lCmifu8uqyJJlC8AhSzGYupye3SxJDUeypr1TSUeO4S3FQwXQrXtIGVbe2v/qudeFjme2VWVChaVnw8ZLOzgXb44F0Wgp8dHlGboMImyCPvnJbHB9ti3Rj8BHRn3iycRjp8pJZaHxU96pUhjLiYxMCfNExlvXgI8Zz1ZM6zjI+TrJ1Yia5rMTX89Jg88XHQvU7x8hG4uNC8ZBB6G4g1TKYkmA3YADkNKhEQe0guE13deHHP/5x7XwEJXgVjYWRBro8gZWVRAvsxF88vf55kC2nPM5hbGwMEfVYJFd9aFNLzxc+fUZAWV35M33C/7YtW3B8fLwa82z2MQJluecC4PT0NI6Ojlbrz6a5oxRBuaQAJG54c3NzVmK0zaAyLx8EJXRzyzJXlpBm7YzQf2nTc3dq/jJNe9GeArm2eUd7u/U8crfZ7bkvt3T7XvYTwvyb+8Ls60179uBQpWK1j9YFhVoUjb/HIMlCb8497ZXR0dFQh3YRqFaMNPMEUKxiFozMx0pJneGZQ9uacY1wXsIY0boYHh4RYuY4w2LG3HGmwR0nPTY2ZpQjk+uf2pp8Kc5yBFWMIXcjT7fkb9x4JasjW0HZOtKDnMEh976k7Fqa23WEAFuq+4zmVnYZ/SzyrLZJm01lCTF4Z4QxkJhCYvy5+2aaG/kpzFbbPMIkfGAE/aWJuCUni1VOX4Pp5XfA2i8cHykZJ+Ee9+AK+Lg8aDF5SMqVIyUrTd69fK378dF2624MPiJyTw+5xGJtGLnVeG46Rl5++auxFnyk9hL/6MfHK6r7jObW3uctCHAPJpU48qhblkcwwX0KpcqCj0XU3fuzlqA8irXhIyLAbs+9a8HHCWv+G4mPtfKQWZNNBqG7gVTry4YAgteKK8cAWQQQFwdAUh+5r7dXTJ7VCUoYfB8oIbcFBJfiuL4yb0eaO3Qe3K7NpnA0AkmcQ/+OHTg+Po6PP/64JdBRP1yWTmmRkzt4u/HMFbmcaFmmslzk8pQmBNL/Ztks33X8u8mYUNZGl1t9ey6Hj4E73lhyMd8JSnExIMwrKQ5Wr1iBeVAKiaNsDnlIguTC3tnUhOXBQTx8+DCOjo5i/44d1WecATl2vrOpqfq8rB4W+0B33TGTUJAWn7etBQALLIEeufmXIVE4UZZ6HiefzRoar92URG/17vNACdUydoRLByFR1E2DKofUJuwXEyPX5nIIEGEkxultQsU0HEDFRHWgaQE3Gah0BoAsFkXj94fQLQSqa3fs6MexsTFsb+8wzitW6zwT6Zr8Ctpx6J0IsA3Ncly53AqU4hVXrFhtuOZlEwLtj+ua/SgJj0RJVlvZZTSXa4//P4O2soQYRokJ3onKnVHvM81pVxdl8b2frYM8qrhCSdhP7t/U1ImbN2/D0dFRoyYwtdF2wVTKGopZNBUHLob8MBLzbOLjzMwM9vX2Yp5hZBFkz6LN7OYcIwM+Lj+aLw85DSoPSj4DPhaiCDva21ONJu8DVXK1SVjTi42PO3bsNM6roJTx34+RFC7Sqd1PuS3LGJlkUc+Gj6VS2WhrffiYKEN9Y3s+HkuzDGMaPo6jSrJmz2uCj4+h8hK4A5UitAVVpnNqj42PUdSBvb39eOLECezt7YvDiej+D6GccLQefNyHSjC3MbIR+FgPD9lofAxCt4dqBUxyhTkJutUxEhZHRwympoWYANQU1vj3XaCsgPxYeXCwujhMt25yZz7Fzm8CXVt6PyjX6k2Q1Mv+GQD8RPzbauAZhJUSoFVY8N1dXVrMmlk6KwsjcFn8N7Fsqc+6QgHPnTsn9pE+JASOs/9bHcKeKdAXwRZ2TTp8+HDqc19z+eX6vMRrgRKIpcW36xrpZNPTC8Ks4dnCnpGvYXzN5HPrhGc+++yzlhYx7f47jfP4epSUQD7QOxX/TwlmeFLBLHFtp0B2d2/EPg+UUC1j58LHrBhJHjDbLKbOTIYzgioZjq4h5/G0utsiueqZ7odNqBgTm1FZu5YYlvdjYllZHX8A5Yzjeezq6rbwUS+d5WLEzL2Yw7a2gnasUFhXxUdExN5eirlzMTnj7P+9rJ0tDlfIIkoMOifCR9czL7/8NUY/+lHVi51BxTCmjcEUmoI6zemnP/1pYR2sxqRsDgnkafdPxlG/zy4E6NWOVSpDODh4I9oChnR/O45xcLCsMXMmRvrwkbtSEkYGfFx+VC8P+WAd+JjFaEKfIQCsGGtyfvhIGNiKSgHaikrouhmVl0k2fASItJje8fFxoX6zz2Kr7v/ggw9aik+OkbXgYxTxthZRTtDmx0ddGZpmLafPACrcG0eFlWn9n0FJ6TE8PIJPP/10POYmXuXjv2X0e/XwD7/PEALcoP1eGz7S/XUlDMfIRuBjrTzkwQXAxyB0e6hWwDx9+nQV8HKgC0lpwhafbNJUHoDEotkGtiW4Asq6aMbHIiYL1JWl+7b4/5XsGD+Hl6fICb/z7zxOnPp0/Phxy02KMwXSIt8b//8Q2MLllRs34hNPPCH2MW1cTTdpUj7sE/pkljEjYdfMqJglsQ2NG4By4R4DldQmrf8bIPESMGtd+1zpHwTAV2ccX1KODIAeFkAKGTOr7cTEBO7btw8nJiawu6tL9D5okdrGwEpSkGQBPQCoJpipRUtZltZDiitlYCrrp1rGjuNjBLZ1OwtGEvPJ8bEZmlAxcBvQZIaiKI+9vX3W/CfMT9HAKP79NpQZlauM75FwDn23XaGPHz9uucxdeukr4/9djBhn+mwLSF9fv6WR99fEnTH+J+Z6n9UfUxAdHh5JxUc/45Zj//ehYixv8YzBLXEd7bL13N7efrRjBTsxifnegv4SOUeRLDuq/0dRd3u1axnPzMzg6Oho1UouZ5RvQWX50a3rnCk3MTIrPgIk+U0CPi4/qmXsZmdnq1559eIjXdsKyjvtFKgEqCZPVQHFa+VjD8va8ZEqEKxEHe/os9HY6/PDx82bt7Lvrv1LikMbHzduvNLiIWvDx4OY4KOt/MuKj4iIpZLPJdvEx92oFJOHPP3fUPWkknhIuaJHZ3z8QQR4dcbx5S742fFxZmbGsLhzhQV5KsgYOR98nA8P2Wh8DEK3h2p92YwMD2Mhl8MDMfB1QFKyIc0iyye3PZezLNvkam1alSOws0WTG3F5cFDM0p0HBcAjoMrwRI5ziDluFn7vAAXaZpw4X/ArQdUeNzeA78UxIjyvs6kJd5dKFoC5hMD1kLjcR+COpd509dXKEm+4n98wMGDFGvNxHqpUNEv5/aBKemxibS7En6z9bwXdS4CTz5UeIBHyfePrOkZWxLQ4lnPnzlnW75bm5vTnOrLY+0CPQHp6ehqv3LixWq+bQi8oVEGaex4TX91nKTUXA1NZP9WabJLwEdh81oqRm409taq5ORa8bebPzBZN+KgzAKa1pRkVM3gYXaXHkucUUDGeEjNTRD0GklsyWhDgw2jXvs0SGzdiPc+lXHAzOevZ/4MoxfFdffUmHBsbs1wrBwZusBLQ8XGuVIYESzkpRU6xMVxvPNOX5Tcn1nTNJuhHCLDGc94MuscckSzlLoycm5uLxyW7dYfmq1ZLzsTEBI6Pj+OJEydw3759VSU/YWLAx+VB9STjnS8+3gN6AlbJSp4HmX+kNTU+Ph4LkhI+FjDBtXdgOkYWMFFENQIfs+zfxuFjooAz26G+33XXXTXj49zcnPBc8hIYwMRlfhDlEBxX/1s1TypO/+N//A/PtbWMr+tYOj4iKh5S9T15XnNzS+pzJR6yFnwcHx/HbZs3V71ZfTxkNwgJpxuEj0Ho9lA98YrHAPAwWxBZ3WjzoCfioqzd7/dcf/z4cRwbG8NdAwOW9TbtumsznON79ozj/4MQu3CDDvRSLHo+XvyujSTVtx4ZHsbHH38cQfhtA/ufrNe00aSXTnlw0Eo4V8jlsAVswZ8st2nJwUYgKUNgut+7+t8NupBqks+VntoROe5fBN2qTde9A5SVnHs20PimxbFw67cvlIHAylRUPMbWiBTDLmXfjyBRLkhjH4G7xnyw5CwMZR07jo/jbM5qxcgiuPGRjk1AkoOgf8cOPHLkCA4M7MLaXN02ZTjnIPprQVN2WdNq0oGqxAzX7hdRZgAjTKwP/sRCZGVJXL1Nxo33rSn+LsUJRjg4WPbUEbetEnbyG3PcRxDgSlRC8EG0FR5S7fGicx/7siDrbYiEMe5A5bo5Y1y3ClVIwR9aYygJ/0TcupPEcMpt48yciZFFcOf4kPAxH/Bx2dFS4SPGePgOz7WEj0mIi7lX0/BxV4bzfIquWvBRhb4oPDAxsoJZ8XFwsJwZHxP3dCmOPMK+vp014yOiwkj3mFN1hRzaSo8WlOOnR9BU5HHat28fpuHQ+vXdrC3SO6iIekJQwsh3oLKS83dKOj4iyjyk/o5LqnG4eMha8ZHCKjkumhi5GeRExsHSvUhUT7zieUiEbhJEzLJfj4ESNviE08vyDw1wPGrciz7n2XUR2LWnSTt6EmSBCyARUF333uf5ncdN3wGJ1dv1kpBiljkjUEt964idOwlJzDR9Lgflrk1x4WZb7mfn1mQdZptvXaGgaZAl13jufi/1nwTeT9CYCho1n0t7Lh6Th0HXcEugMgKAvy0cL4LyCMga52e2zRXKMDU1hYgKMM2xWQmqfI3Wvljgl7Lv50El3fpEvN7ycWgFeUBIZftCzOLCUtax4/g4zea7Vow8YOxLHz6uAWIkTGsLLwXlilkEdo4kzI2jPzkMZZ29A3WrjhRfLGViX2mcZzIortqtnJE7gypmj983QoC3sHPTLCCu+rxyxmGiUqmMSZIdat8+1ifOZM6x+0quqIpBTsPHNAt50oYzwhhHRlt+W2hDC6qsvTIT7SJf28qlkuZBZWJks/Hdh4+bQNXpvjng47KgCwcfSbAiLCHc8uHjBnaehH8/4/m9FnxElBO1RZhk1G4sPiaW7sbjIyLi2rV51PFRSp7GXfBd/X+iOqYSRia11uV+qASXWfAxDSOL8fXZ8RGRY6Rcvi2Nh6wFH8mYdgfIPGS5VFpwfAxCt4fqtXSbQielrueLowiAnwXA90C6oOYqn3W/cY15zmlIT6hxEPzJt054fufWbd7urPEW5VIJhyqV6kI/aTwvS4bBY+DI2g26FZzaIpUtq4Cu3aJ2jAptJ0AzXb5nQVms80I7TPf7d4KygncZ7eBCqknkmmtasWmO+RjNQGLpo7mm9nSAAqpCSjtNBQO5nbm0fSPDw2IoQyGXw5HhYW1v8LrrpiuQy9VSmncAFaszNjYmliczQbhR+zyQTvVYchDscnUSRlZAKf7Wgp3TgrDGh4/v1K7jDIcvZvEUJlaYNHe7k55zDrB7c+aJM7USM6o+w8MjODBwA+qZZ+l5PmHzGOuTxHiW2bmn2PWzaLtT8rZTG0atdhM+2tnTyeJEDL7papqUFFIKkTwqC47MgJmUlH+TvASkMeLzwq3tHagUBQWjjR2YCAQ2E52GkWKtWcjjNoiqTJ0PI3mJr4CPFw5dOPhoYl0WfCQcyYJBC4OPpVL5gsRHREkQnkVl3XfhI+//OxFgLeqx32puXHya25VeUirQvFDsfhaM5O3Mjo+IGHtG2WEIuVyhWtKy0fhoYqSEj1wpOt89jhiEbi/VE9NNAuQg2K4PrfFE8gzXEdgCEMVMk6alid3rDLhLR5gWYum+FM9NizACuUQZnVMU+sHbR/Wpa6npzDeIudBpPB4Dv5a2D7Jn7abfJQG9Iz7uqiM+J7Sd3HWobb6a12mu+KaQKtHc3JwVZ16B5KXpGqPLQPd08NVAn2HXjo2NZWLSKCFJ2nxTG6dZe0xFBlEWd3op8d3Zs2cDU7nIVE/MIuFYAWxsWQu6iyyAUma5lGqEj4QZEj4mH5OBW49yzGI3O6eI7rqzxFxEaLtEd8bXkqVEjg92MYQmRupxcCS4+qzs4+ivo3oq/ruX/WbHRKr+DKFcIzexUlMMnV4a5zxmq3ntcjXVGTCJknhq3rYKKuY0bYwuQ91t0pfhXHevHBsbs5I+ma6Vc3NzVtznMETWewXA7ZnGMTLg44VDjcbH9jrwkTzy0vFREnJdOS84Pqbh34jn95cvPnIeMmmfry1m4kveRjU3XV3dzvUlxVOr+uZpY7QGlet4rRiZHR8R/UntauEhs+Bjb08P7hoY0NpFGMmrLWXByCB0N5BqfdlIAiSfvPXGd3ItThMY+3t7tXtF4E6KkdVCPGUsQtM1uwgKnAnkm4zftQUJgFvBfjmsAOW6xFP3p7lqTE1NYZ/RV/qk9aMv/j9tg+0aGMBCLucVOAdASOIWj0chl9Pa1RdnjOWeDWnt4O73/Pi40A5JGzg7O1vNwsjrwPuEfXOuHvS0c5xdu23zZstFR5pDH8hR7JT5sqfvrsyprj6Rl0bRaFd3V1em9s53nwdKqJaxkzTJBfa/ue97APC4Z31v27y5unclfDyg3VOydPuEqzPodqNTloLm5lXCOWSBKKNibHTBXVllI1RMzYHqcZdbni248eel9WEM05kqYkzb0LYUSfckN0TObBZZLVjpPUHCNHfpl9rSirZFZ9xqgwsfk6zAe9n8ZckUzBnkBz1tHNeu37x5mxXTKc0hYeRR0N1/CSMfeOCBVM+0WipoBHxcPtRIfASweUgq1elaC+VSCY8cOeLkHxN8dFm6symfknJW9KmgchfOo1zdgT4vD3yMIhsfd+zoY/fKUkrMdMGXMcllTZYx0oePkmt5FoysDx9d96yFh8yCj668TfVgZBC6G0j1vmwef/xxuyQVCO63MQi6hJXR0dHqAipCYil3LSaqu+2zEJvZLqks2bU9PVYm7/LgID799NO4fcsWJNA2F317LqdltTbPoe9ZtOpU6mBiYgIPHz5cza5uWtpJePWm/o/dQ/jLLE1Ad92nCQA/bGxEyip/R4briYkyy6tJDJgUkzMyPFytN3gynkNy/y+C7a2QBxUzbSoQrvG08wC43da1dtcAcjMzM9VM86ayqLurS1wHYvwhCC7w8XdSqHCFhKu9JgWmsn6qZ+xmZmYsIUNSJlId2rQ9Sy/jY+xccx1u02K6ibHLYgXhzMda7Om51rJYDg6W8ezZs0atbZNRacGODj1Tty2gqmt8CWh4KZgTJ06gbEXirtDpzHMU5bFSGbKsEe5x2Svep7m5hcUFEsPZgsoNkZIp+RjWMprlg/S4SNtFk2h4eCSupUttn0aKA0/cR023ypVoM8jXeNp4il3vcl23mV9fBYpyqYSFXE72TBMYvoCPFwY1Ch9dPCR5Gjp5vfHx6vt5Qyo+5o194nPvNvHxAAKsxba2gtbm3t5+nJqawsnJSdyyZTsuJj7OzMzg5s3bUE6cuLj4qJSwK9HMC5HLrUDdKp+GPST0ujDSjY+IJkaeRD8+NqHs6u7DyANYLz6mnVsLDynhYwcIpcDYw+rFyCB0N5BqBUyKWzBfoLw+HAqTedBxnCZ5ZHgYC1HkTXxmuh25nmdmTCeml+LlzBp/tIBJuJMW/dzcHJ44cQKv2rgRO6JIfzFEEZYHB61xSnvRE0nJE1pAWQBoMzmzghsluBSTmi4Yu8a2FRKGhm/QIruWxkeKu85HkXW86Jl3Pl4AgFeCrdAAcJdEu9Vxfx6uYLaTxvdWz3gQsFOWyIjd8yQkSSrMeMUs/UWU3ekjABwCpbjgCqRZUFZRfu6IeV4oibMgVGveC57UiTDyJKTjlW/tED7d4lizZ4CYHsnaklW4ipz4mMTsHkNl4bHj0iqVIZyZmcHDhw/jli3bLe1/FHXg4GDZGicfKZdqM/FOCyorEzFQUsZb1S/OxFL7/OMiMZtrUDFv/Ddyn+RMGiU2MtvSIhwz7ydbcpL4cXpe0RiPMygl6AG41dFHYjZd8eE0xrdiGgM+Pj6uZdEljLwfkhrznU1NVUW306NLiGMP+HhhUCPwsVE85Nqc8r6R8ZHWtomRtSifFEaa+IjIMZIEvMXBR9v1fKnwcS/aeSHITZvjlSwAr17dhlFktjE9z4S5ttT9rxTm2IWPaf30YWR2fEwUGpF1T7KK18pDSl4jVeNfdc0nBsj5YGQQuhtIWQdTSk9fhMSq6UsstgbstPe8LrW5gNKY070AeBW4y0dxoa0MgGNgl3fiRIvdB/rcQu46Z3JysuaYMrPv94AtYObiPvNjO3fs0JLIUF/6e3udGrC0tlP/SQPG3bRn4ue3g+3+Qu5gvT092vEmSDwTfO734+Pj1Qz1rfEcnxLmhBJM0PFTjvV2OdjJ+1oAsG3Nmur9fB4EpkLmYVB5DEylwFClgmNjY6nr3wVm5VIJ23O5an95wjeuqRRru5vnBUvOglCWsXOVf0urWsDXB2Xnd2Hk1NRUZny8GwA/UP0uMzg6U9KPAJ/14mOWxD2lUpndN8s5fsuOXZ7LZOIAlfumzmj19vbj8ePHrQSG4+PjrEyYyeBFznYn7qlT7Dfuhrg9HtuH0E5CFOH27dcax5pQuWraDJhJiWtiJb6OSpGdNMZ6BpWFjtrqYpAvR0mR0d7egbkcL4GUPt9cIXQMAL8Atrtwd1cXHjlyBAM+XpzUCHzEDBiZhYfc7VHuqM9RBDjOMMOnfCqjctHWyztxOn36tIERi4ePiJLr+VLgoxmPbeLjKBtvs31NeOTIESFnha48SMsYrjCSPL5aUSkBzCR3Jj5S27Jj5Jo1beyefnzUFdZnhL5HdfOQ09PTeNXGjbgG9NxJncDc0uP7zAcjg9DdQMo6mFQ/TpowBL8AYyXGYK7aAIlgeuLECVGYJje0CJT7cCso4bRi3JcErVrcJ3gsWtqib42iapky1zmFtrbUeIk0DebMzAz29vRgKxgp/yFJ9kbj2NHWpvX7pj17NKuAKRiS5bwCtis7zSP1oQ+UMsV0054U7luGJCavXCphPorwZlAlXe4BIWu9QwFBrjfm/V3x9J2gx/ib80ztlrJA8vmTypSY88XHQMwin8GSY843j18/AHpiIbqmNZ73k8Y8mPcma3sj9nkgm7KMnYSP+Xi/ZcFHae1LGHn8+HEvPh6I93AzRJiDduEl34QA96CeOMZtQdBj0dLj0pRr3y0ZzpHj33z4ODY2hoXCOlRM1c0IcB8qBqoDFYOUZLo1rT++7+r6rWgrKSjGkJixAibuj9zCPYm2haUPyTo9MzODpVI57v/7EeB3EGCzdr6LwU4UH1L84RDKSZzSGGRqMzGhnGE2E7PZlnuXdWYh8JEUpCaOB3xcHpRl7Fzl3ypsvhrBQ05OTjrxcYW27mlNP4y2gowELZ43IR0je3spdjndZV3t/fS8D/XiI6LCyJ6eXrTxkSzwrUgY2Xh85AJrHyqM5Pjoyha/qTquyj08H7f91zErPiJy920TI6WM5p0IcANrW60YWRs+ujKnf6JOjDSVWC4ecgUknpnzwcggdDeQsgym1+0h/l4UwC4POjPZ19uLNwwMOAVTYvAk4esh4xgdn4Ik5tgs0eWzsCImmzWLe9OT7H/pnLTrzVhyUwCdnZ21ajpHkLxsipDUmc6DnkSmBcBm+qMI+3p7cdfAgCb8SmPLs8y2QpIArwiKiSJ3wU3x73dA4sLPAaNo3Ju+80ycEpGlOw+2Jk6yLneDiueWFAh98TkuxQifI6lMCc3L9PS0lsE9S2y9b91VwzMGB3GtkbiO5oLcggqGYsXVn77e3pCddwHJN3ZZ8ZE0zXx9FMDOwpyGkWbSSR8+rhOSnw0M7LLLO6VYEPRYNF/yofdjki3WdY5c87VUKmttlRisPXtuQtv6EKEUT5hYVM5jkqFdZ2ZLpTKOj4/jwMAuTGprS4Itr7ENCDCAuutkHlXM4gAq6/UdSO6pNgMmM50TExOp67C9vcPqQ5JR2BQcRjDJXG8ymyQguCw89xnzN4ema+bw8AhOTk4uKD5Sfg9TsU7fAz4uD2oUPiLIPKSV4HVe+BihEjxNfJpBijkulcpYqQxlxki9dKCvBONBBHiS/d9YfJydncXOzksMLCB8JOw5g/XhYwu7n4SPvA+tSLhm42NHPE5HEeBAw/AxsXRLGLke7TZT2JKksPRhZG346HQ/rxEjOT5SuFkaD3mt4X1aL0YGobuBlGUwKcbDNWFH48XRDoCXGAugBZQLERcE0wC4P86YDaCEOqm0yF7QhTJupR0fH0+t1SlpCkngI5cM0/JJoD8Aet+KkGRA7wR/QqRWIw7cZDjKpZKYaCmClHgmyF7rm5KSHQRloW4FPfM6Petn2HX/Kz7O+91kfB8ZHsaxsbHqGJpCcwTp8XSI/iQ89NnL+nEPJAI2Z8j2ecZjkzDHraCUG/19fWLZmSKoMIW0+b22p8eKQaR1J7nXbQJZyVCkuY0TpfBEWuIayBD3FZjK+sk3dj58vCP+/yGwPT+aALBg4IIPI2vFx3J8HoXYpJU4ceGjYmaICa2gyaioTLxN2j3tuEJyT6zdwoNIzG2EdimbAqZbdU9gGiNMeTD0DOT9qBjHJKuw6r8p3AImSgb66ONAY6uPo8kURqkY6baYmK7vN6MSIOj8DUbbKpjEhacJBlJceiuuXduOTz/9dMPwsTw46MTHAwDVJKPSOzHg4/Ig39j5Kn8QPpISstvYX7XykD58jKpCo0MQinnIrBiph36QRVnfO0mmchM/iphUiZgfPiJiLJibQqerZFmt+HiMnXsnKsHUVOrRs36G9bEP9T43Hh8R/YnKZHy8R2hfFozcZM0xQCuuXt2KTz/9tBAOtQkTxURyH3NtunhIiSc9BurdnoeF5yGD0N1AqkXo9oFcBCq+dwqUe7F0DVmk0wRTX/ZpyW28Go/MYlNGR0erFlbppU7uSGaqflNzRNbmfPyco5CULKFzRwDwcU+770xZ8MRUudziXbHL4+CPhQJIEpGRNZlczU3GiX9vYuebbmE7+/q0F48pNJM7IM1LNi1luiaOXNTeI8yRpBiQLPId7e1iXPoAqMRq7bkcru/oEOPBr/TMbz6KnGET3L3uKPs9zSpENDs7W81qmdV7o559HkimrEK3Dx8JS3ZBki+hHoz8Mc/aEcNqwMabLPg4NzfHmJki+920dlB8MlkwDqIdG7kT0xmZO8XjhDFJgh/Z7dMdv5xubUisERVMLCVSXPZIfDzGhJY1KFtWFONpevfYHgO6y2IaRvrKzQCsxa6u7tg69zEE6DHa3iHMVx6VtT6xOCXW9IfQtg4VMZfLY2fn+rrxcahSET2+yDuN4+NJ3zqPxzbg49LSfC3dJj4Owfx4SB8+3ll9njsOlwTriYmJKp+jJ8RSn+HhEXz88cfj7w9jYvE08ZGszeRentSdTs6dHz4mirmFwsczcf/SMLJofCecsZWkjcRHRD9GtrUVmPfCg8IcSRjZitxrKYo64uOF+MPPvwYB1mChsA6jqCCMRQFJwRJBHochysxD1oOPxENKiYBrxcggdDeQsrqXk8bZdB1fCaAlOcmDsvgOOYDRt1AOgnL57RYWSB70GCAEXVgfGR52Mo980ZLwyN2Wovg7CdXvB8C1oGIiSHAsahso+T4Rt2U8vo9pRSVr71FH28fGxqpuUdU2g55VcC+7bhqSF88oJJbftJdaMW7Hw2AL2z2grMN50F3WfeXbbGuYO8v4kSNHUteh78U8NTVVFV4lRUAnAG6Mz/3gBz9oJXWLQCU8e/rppzWB/RZIEszxc13WFRG4QE9GoSW0iJO98L7xmucnQdbGj42NVceGMvub68/MXD/ffR5IpixMpYSPHZBk0TcxcgObx1oxcgpqx8c74rV405492fExinBdF7kqEqOVuAWquq7NqFzKJYaLvo9iEhfHLebcghzF97WZJcoAq0rj8PuTWyMxj1TKhhg2atcjmMbM6mXJpBjPDQjwh5hYcirxvSQ3VZsZJtItYvz+lWo/XeSzdA8M7MJz587FQoHLxbKMAO9AAMD77rsvFrCTdnR1deNnPvMZ1JnRgyjF/rdD/fiY93h2ED5S/hQXRtJ4BXxcWsoyduTFZ66LAuiJUwkf+wDwZ6Hx+BjF34chwibDShtFHbhnz01OC7eeEEvtq8SCTXvuMVQC2h0IsBYVPh5EgD9AW8jjSrwJnC8+9vaadcRd+EgYSSW89qdiS2LpLqI7Dr4HlfCex8RlPd3VvlZ85DyRRD6MfOaZZ4Qs4iZGbkTiIVVsPG9HFLvZAyax6gdRJdkrG+fSWPH7JwqWZmjSqhOl8ZD14iONF08EbPL+WUocZ93jREHo9lAtidRM7XYEevbJWZAF0znQgVFkUKNIq8U4B7IwxJ9H9wPQa1VbCTs87kin4vu6+seFacl1mtyjaBNIY0AbiTYNtwJTfIZ57xFIynatAcCPsU1jWnqbwZ0pXMroOQN67W1prnwaZc4k8lrr5jjlQcWtmsTdtJzWCiPBA2UJTVMwkALFdOUfqlSqQvuq+NwBUC99ArmbIf2F/mOvelW1nnsVuMAuYSO1i4/j9cIc8rhcU3tN7TGzt2dxnaxlnweyKWsiNcn6x+duFmSFlIRpkvCSh0SorhUf6QUrCdcufNymMSZnUMq6qhiwdLdAxdydxySBkHkf+s7dHxOm0M4AawqSxDyuZfcyGdwCujKFy8zaDOp1ZU1GFtFXB90Uot3u8coyLpUJ495EKrOvLigA5HFg4IbqNUkW5TQXSzU+SmDQ3VWVkiVCgFWpfdsL8jrLgo/mtdJ7ZgQA28CPkQEfl56yjN3c3JxlwaO8MfXio2QE8uEjPW8OlODNfx8c5LHcZmzzbs+++kN04yOiCleRhDwSMI/iwuNjKyovGHqmiZHuTOFy/yWMLGKCj+mW51rxsVQqW+dzfJydnY2Tv5nKFN0NP/FMSMNIGx+jqDO+f4SqegT1bXc8tgcxSaTnvv8TTzzhNbJxHrKR+Iig8/4LgY9B6PZQ1sGU4qSlhSAJXEXQNTpDYIOrK3MfvTzfD25G9IaBAUR0W0u9wiPojMNtt92G+/fvr15DydN8gh5AYtkiiznVKe3u6hK18V1xEqUsrldNkJTsMse5AGAlYSMtlq8UwSsd43PS029zw1I8vut8cg+SvBHWd3TgSrBB5JLOTpycnKyCa18MVq6+uFzSuJXlHlCukGY21BEAPORZKwCAv/Ebv4HEPEquvBOO63ibhsC21lMGaq5k8Lnd++Kcat3ngWzKylSaa5qs2TR3LnxsAdsCNAS28k5iQE18lBjRjvZ2nJqaqgkfE28MOevq2972NkyYjiyxdBH7m0duMc/lCtjZeQlzjdYtHX6GV31yuRUI1WzttpVhxYrV2vl6LKGbOQR4dfzXdM88mdouEx99MYccH01r2549N8VZ221GeWDg+io+JlmUXX3Z6233PQC4rZp4ST7HFe6UBR8/YVwrvWfmQL3T8pCOkQEfl55q4SHN0IL54GMWAZ3jIwDg1fG6ovsdAOXRuGtgIEPehLR9NR5/l/Axy31pvy0cPiqrew4Ta7TbEsvxERGrPKS7/68UfveX0+KUZfzT3PwHB29ElQxTx8h8vlMrrevHSDORpNmOezAJ39lojHHZu1Zuu+22agnFLDzkhYaPkOmOL2Oq9WUzMzOD4+PjVQGLFo2UzIu7QdOHNDoISWIf2kxkpTYBthgvrnUg114eqlQQ0b3ApEXLF/gMKC2r6XrBLd1pC/eqK6/EjligLoDNLHd3deG5c+eqlly+SShDq+vePClSHuwyXtZmZTFIRD7X7WMp9yQLv+aVkMvh9i1bLNC86667Uvuyb98+RETcXSphaxThwXhu9oIKU6CxORUfawc7aVsupa0Ayt0+rQ0bjPsVIckI3wmAu4X7Sx4cTaC/vHkYgWTpJm+GxwDwDzx9mJqayjx3wZKz8FTL2BE+lkslbM0pRuogZMdHjpFckJmYmPDi42awkxAVQbmJ88oQWfBxvHoPF2NCn2Pos2hceeVVcSzcMQQYRKn26eDgjU7XaJVAKK0tRzFhGnmJGpthSsNHN5N1LOV32x00ijpw48arrBhEXyZbwsdSaXfc54OYuGmuZONyCpXwnEc7rjBdWE7c/N3t6Kvei7vMJpZ1gGhe+ChZySMAbW3/urAm6VyOkQEfl57q4SH7enur+MiTo5rzSJ5+WXhI/o6V8LEAgDeCm4f0K998+2oW5RjndIG1pWXNIuJjhD63b6nSjD9JmQsjiyKGXH75ay18zDL+4+PjrKwYxcYfiMeAW8kJI+m4ur5UKmeYy1FPO8zEa0VMMsJ3IkCX5/6185AXEj5CpjsuE5qdncVf+IVfwLa2Nszn8/iOd7wDX3zxxdRryuWysQAAf+VXfiXzM+t52czOzuKNg4PaM3sgEXZcbkL3OCaeNpNkLSLLJ9VYPAZy7WWXKwVftHljgXdAUmdcKhxfyOWwBRLgT7NGm+XGTDc3iosx77HXc29JCyYxzsSgm3EvaUkUzJh28/c8qBrZkjKC/t81MFDVIvoykB8/ftzSdPN78ZgVPnY3gx7vtR7kuPkR8GdyzxtzTNfxc64yxqIoXJcHBZi8L8R48ozw5OI/NzdXdfP3zaGpfRSFrRqSBNW7z5cbLQU+ItY+dhI+bmRz7sLHW8G933342AKAO+L/D4Jcs9OFQRI+Jsyu29KZuJ/fn3pu8hsXbu3ap3qWXH6fvZ77zwjPkxkmCR91ZlbKOAzi7+r7VrQZ7YTJKxS68JFHHtHw0dWP48ePW2WBVI1ZaS54TObNqCdmWo92XGg+bidd625HPl4jZ6pznLRnG0TVpKL14mM+iiwsG6pUNHwk5WoWjAz4qOhCwUdExLNnz4rlUc9AosiplYccGxtz4mMRlDtuGg/pxh/CFQkDOjCpUT2Ctmt0Hn2KwMXHR7Lk+jFStyrXg5HtaCsGk+zlHB+zWLqVa7jp7cO/07WU14MUDPchwMFYuRFhkmnejJ0fQb9nQt6YY7qOn9PuWCuRxstm5SEpNNLcq8sRHy8oofv1r3899vT04Je//GX8whe+gFdccQW++c1vTr2mXC7ju971LvzOd75T/dQCfvUA5sjwsPiSjeL/a3ETokVmxrDuBeViQcCYNb5YWmAdoGo907Po0wIq/uEkpAtqBN55sIVSil8jt+Y0Ky//nb9UXPeuOO6V1lae9ZqPhyuJwtTUFI6Pj+PU1JTt8m2cH4GKfyaGzBzPkeFhvKSzU+xLd1cXlkslK9a6AxKFzRmQX7TV+0MSr1I2zitCov2W6iHT+uTn8XGbYeO7NpfD1StWaPd3jff7wQ4jMMfkqaeeshK7pd3T1D6mlcBbyH2+3Ggp8BGx9rFbCnzMopAbHx8X8TEPsnJNYqJ41tU5ALzKI5Ru2bIdEwYv3ZJhW4JnUc8GbN6fMzvJfdIYplKprM1VEgtpJwcaHh7R8NEuA6Nn925qWokqrlyOgR8eHolr6Nrj1NXVjaVS2YojVOduYOPCx8RkOnliJlOYijCJL+UCgm3FNjGyWoGCraWWJr3sT1Z8lJjHXdddZ8WB+zyaOEYGfFR0oeAjolweNR/jHc4TI0k4vRN05WMWHjLBA3NfFMU9ncRBn0zFnWz4eJj9v5D4eHNqW0ulcnWe9FhxGdPSMdLMCL4ixiH5XpXKUIyBprDagqXSbty48SqUq0UQf3UG3fgI7Jn3COcVMYlHd+Ojfp6p3KAxXoPKnV9fKxXILToPudj4eMEI3d/85jcRQHct/aM/+iPM5XL4d3/3d87ryuUyvve97637ubUCpi+R1VrPYuCfIiSuj5QUYXRUuXZkcYGUFpm4wCBhIoiBWAu20Gg+8wzoQl9knN/d1YVPPfWUaK0122damfhLRRJgI3AnRZLqTKcx6LUkUTh+/DheuXGj2F/eJuml2NnUhDcODlqgsb6zE3d64r1pPZj37AAlDJBVmgSDO0BZ2+4A5QVRyOWq43EQVGI5rQ0A+GHQLdsIelw/V1ycO3dOs8q7XtQSkJGL8eTkpDPbegvYrkV5AOzv7bXmxCxfcuLECctFttH7fLnRUuEjYm1jt1T4mEUhNzMzI+JjERJ85PhwDwCWDatCGaLquUlITg4BVqOqRZqc29XVjU899VT83bTk2MyebcmhWtGuRG4u5keqodpZvd4usSMnB3Lh48aNV6LNzNF3Emx52xVz2NTUiYODN8bJeJLrOjvX444dvnJB9Jt9X702MCkO7kDKohxFeVZOjMbkITTdWHdBhA9nxMhnnnmmbnxEVC7GY2NjWC6VnGUpJY+mfApGUgm8gI+KliM+zs7OioldOU75vP8kjCyXStU5rzvMMMZHW3A0cYasp+9F28vFFJjPoG4J1vFxcnKSPYPv84XER1IipGOk2/Ks+i+V8JqensZDhw7h1VdfY/U3Cz5WKkNxwkh+XQ47OriCMw0ji9Z99YoTnQgQxe7oPNP8Cibsn0HlwWS2fzBuv0uZMV5ty8DALqsf/N2JHoxcCB5ysfDxghG6jxw5ggUjw/P//b//F5uamvDTn/6087pyuYzr1q3Drq4u3LJlC9511134z//8z5mfW+vL5tpY2+J6yZKg5vp96+bN2iK7YWDAKgbvAkbJIuxykyDm9BjI6fQprmwGAA87nlkUFnpr3A6eLZ2Sm/naR1Yml7s6KQTuhESoNTfUamOcq5sVlPAOkFj9a0miYCY3czFCFfC7cJcN19quQgHXxvFbrrZs89zTtObxz1Cloq0havtBSGqqEyNpuu3T9wOganRvNWLV01xyAQD7d+zQknRwGhkedmaGfkiYwwiUuz4xplLCuY72dhGkG73PlxstFT4i1jZ2vkR/C4mPfO37MHJmZqZqOTkJjpJMkGDkO4TnkkfJw2AL56VSuYqPzdVarY+hYn50C4KeJbccuwC6XNaJ4e1H2YWakqWZDNMIKmbKxscs2XXt5D1kWTKt0hX0KRcGB8ta2wqFLszl1qa2Jcl+nMZ0HkBznQAoC1JSTiw5vg0i/ENQ78I82GE2Lozs6+21rIppAlJfb68mDBKl4WP1XWL0JQtGat5RAR+XFT6ODA9789jQJytGmkr+tISu9eCjP3naDFIpPndMM+HEQQRYg83NLdV1qQRKUoDZFuvG4mOESchKOkYuFT5OTk5aGKks5Ld65mNb6n25q/6OHXp5NV3Y523n+TNMF3LTbf8A5nIduGXL9io+zszM4OHDh53rcSl4yIXGxwtG6P7Qhz6EV111lXV8/fr1+Du/8zvO6x5++GF88skn8cyZM3js2DF81atehT/90z/tPP8HP/gBvvDCC9XPt7/97cyDmWi+UhaQ5/fJyUkrrrcFFOOWpsHpbGrCXQMDdqr94WEtuzXR6dOnU9Ppm9lXB0CV5aJYCl8c98TERDVGjyzPaXXwZmdncahS0drkeqmsyuVwH9ju3cV4XHrj76b7lGn1ryWJAi+1dtLT97RkZREA5nM5y3Lf7rnnIc+YjLP/iekz5zwLwFHilaOQKDJyICgx2LyJpczi+XApfbgbcFq/7gNlWcwL9xPL34FeSz1rbM6FzlQuFj4i1o+Ri4mP1nqM18HU1JSFkeVSSXyp+zCSx5efj/dJay6HBxwYwa3kHB+vAsBmjcHTmb3h4RE8e/YsYw747y4G69+hYip5+4uo4gep/3eiVGM63dJtn4doulmeTL0uPRFPhLlcHm2rVLvnnlOYJPBxjYkqV9Pb2yfiI2IiJB8Eef3xMJssGHn27FkRHzUPJQGjsuIj92jKipG+Z0sU8HHx8NHMf2OuQR+G+vAxD4CrV6wQ41glHjINH9P35Aw7dh4BcpjLtaISfM+jL9dFgpG5eP+7XbjPnj1rxFZnwccBA2MqmFhqX4M+jFw4fNyf2vbe3n6MooI1DgDrPPc95BmTceQKAwkj/XH93IX8KOrKDH1uCB9dOZWWiodcaHxccqH7zjvvNBaO/XnuuefqBk2TnnnmGQQAfP7558Xf7777brENWQaTBJoKyFbYYvx9k7TAmpqwXCphX28v5qPIWgTcnU3S4Jiuadz1QjpvZHhYjB9uie99AJQgNwnpccSuhU4u2PQpguyiSRuaL/5jkO2lQ8yRJFivADtuuZDLaa6oR44cwSs3bsRW5notaXZN4XzM0/fLHO0nRcUGkK3k64R1QwDgU3JwS/czzzwjrs/Z2VmvpfFmY3zLAPhaob00RiPDw2Kpt+54vl1x2KQlPplxrkeM+/ksSC5Fi4uWK1O53PARsX6MpDlfanxE1N13XeelYWQRkoSGkyCHv9SKj1OQYFk1Tjh2UTSZgzur1/rK4BxEiWlUlhHdop7LFap1uQkfN268MmaUZcsSoiSc+8rnXOZoOzHh12BS15VbgdahbJ0qYhYmnqxc88HHUbCxqQxujHSVwiR8dGFUrfhYL0YGfFx++HgeZE8+4gUOQFLNxMTIjvZ2Lz7SnK+Ly7FK2JcVH5uhCSMxgWIRk2RdkyjX6Kb/ZZxIwlToM4KJO7jay/v370dEU6g9j0pYzoKPgMpSOyOck46Rhw8fxiuuuBJzuTWYKBKy4GOWLPDc1Vxq+waULeUSRpL7uA8fE0u3hAezs7MZyontQ9ujqIwAtyCA4tdNfHTmVIKl5yEXAh+XXOj+h3/4B3zuuedSPz/84Q/rdg8y6Z/+6Z8QAPDJJ58Uf5+PpZuE7ofBFlSbjO+my4+VHACElzIoRu9o/H3//v2psQeSFqezqckbM9SZz1fb4XKjptrVrnuYwE/uy3Qed+E2hdpZUExJHtyMuU+7daswBzlQ7qjSfPDvJoNuuqFLZbN431shqUdO7f8YqBelb47LxjlceOgGW5FAL2L636xjba4Hn7sigLK6r43Hi+p3pp1Pv5kZ6blVyMw4zufcFSpAfS/H48TX/hvf+MbU+R83v3vqLS5XpnK54SPi/C05i4WPAHJ5FyIXPpJiLm3drwB9j5oYWYAkMdxC4KMaP9vVMmF4j2I6c3Qr2olycjgwcEP8f5PxW/Kd16dFlNzQfXVxW+P76W1XLuSSS+ccu7Zs/G5a89cLY6JiMXOQx2ZwWy6y4mMLqHrGa0AlufQpRMlqLuGjC6NqwcceUAobUgKR0vrd7343+jAy4OPyw8djoLAtzdhhhoyZv2fFR6lEIFEWfHwYAIfF2OQW47skIF6SihOq7JUrC7bCsdHRUUGopQRqafh4HpOs5rVhZF/fTgGnIqRyhH589GX/Phi3s0VrexQVsL3dTLzGFREujORtlfCRhPIkaaVESSmytLbTpx1V0swcKiE8j9viBKP0MfERwTDIpeCjuV/SMLLdwEfy5szCQy4EPi650J2VKBHGV77yleqxEydOeBNhmPTFL34RAQC//vWvZzq/lsGcnp7GCBLBiNy+2uPJNwGO16y1wA0SJowmnlwv6bN9yxZnvIGPaUxbbK0xQ3gS0pkJszQKX+i1WCBNoXYE5Hre14CyMrvqnvP7kns8MTqn4nZ1RBEWQFYk5NeuFV8+fCzpuUXHJi+zNvT3JfUKJcZcmuMeANwHSnDfFB8bBWVNGwI5RoW/aKuur0Y/fABlJmQzx961VnyglaYppJf6Q2BrOYuQ1AcvgF1fmfp9sVu6s9JS4SNibWNHWXk5PubZeuNC8nzxMQK7BBaRDx99CdnWxtf6MLIVFgYfO0GOFU+SA/kYu1Pxdyq9cwpVAp0OVC7oNpO8dm0+FR/1ZHBFlK3S5Wobtm6lzMTqUyisE55LjDZ3WTyASnBP7qVc1mdQJUCTGGIlHDQCHwugsNi0pLjWylHH8TEPRmXFxzy48dGHkQEfly8+ngeloNF4AUOJSDW905R4i4GPnM/SheyTHhzKoavWfVaLrC3UUhIyu+KCshBPxefVh5FKGDZxSmUQ7+vb6RxLvVxXhHb2byrXNYO2EKsSy0VRJ/oUEaqPbajCbcjqPIrK40BKgMa/F0U80PtA4+tSZvDklckzzjQYHxHTMbIC6h2ZX2b4eMEI3Yiq5MO1116Lp0+fxi9+8Yt45ZVXaiUf/vZv/xavvvpqPH36NCIiPv/883jPPffgV77yFfzWt76Fv//7v48bNmzA3bt3Z35mrS+boUpFs4IAKM34UKUinm+Cm1mDeTT+n4R5SesokS9JGD2TnscXGGmexiGdmXgQhDJjcamUkwBi8iGKg+Nt52Nw2tgIM6BcKU1hcwRUmbM8KEsDLykgMbVkjfBZbvt37BAVGbS5SQt3BmRN9BjrKylYfHHUfOwpEV0RlLKG6qD3sPk/BYA/G59/yjHOpmaOrwdJi94PtmYcAPD2229PbXvabzQfrjUqZYrm648+RZAVFgVI94aQQgVcdKEzlYhLg4+ItY3d3NycZbUuQpKF3KT54GMeVNJCiXz4yPfsfDByA9gYkQOFH/y+WfFRUjZOAuCl1Wdwq43NHCkXTImhJdfD92MaI+rCx8S9k2pjn0G5NM0YSnGD/lhB02WxgkrA5syeYv62QVQtUfkJWDh8JIvJvffem4qDrvjwAWGuzb0yH3wsgpz/hXtHBXwM+ChRvfh4f7XdWV2pb0WzSkBTE30/iXpoDF1zB+ZyBaxUhrQxcFeAmESAVxj7iCzEFVQKPKpmkAUj03AqSZLJSS+1Rl5IpkKAviex1aOjoxnxkQvqrags2hwfTyLARkyUBVSL/BTqNc8TbJbWg/p9Dm1s34hyJng/D1kvPtJ+MTFyL+j5ViR8JAyk3xYTHy8ooXt2dhbf/OY3Y2trK7a3t+Mv//Iv44svvlj9/Vvf+hYCAH7+859HRMTz58/j7t27sbOzE1taWvCKK67AvXv3LlidbkoGZjJZQ5UKzs3NVWPlpNgtU4iTLJquElmSC6VPU7lrYABbjGe0gGIICWh91mRa2DyreEcUWa6i3AJbPWa4cJNQS0wqB/uysGk6QWl/JbfUGwcHrSQha+Lf3yfcHyF5mazK5bCfZZ8lMl+G9LIZheTFRmNizovvBXYH2NnDIZ6LZvadz4N3bjKsB8mVh7eL7lMulbAjivT4sXj8uWcHBy1av77sj7xUw1vf+lZrnHz9vAz0+bfW3sskOy/i0uAjYuMwUkr4uFT4ODMzgzft2dMQjCRs+AQkzG7BuG/Rs25NpR/fIyPxPW2mbA7NWMp1XZfg4OCNQq3dNfE578OEubKZ5FW5nFZ+iGhubg7XdV3CnkXtIIaOhOaEOeTz4ssEHMEaHIAIXxO7cCYf3Q1+W1x2ZjHwkX47ceIE9vf2isxbM7gTBGXBqPni41vA4x0V8LH6e8DHhOrFx4RfyepKzYXF+xDgYOxtY4a3jKASItX3SmVIW7e20s9UPnagbSG+CZOM3vSJqpm63RjpxikAwChqxd7efgsf7VJrxxDgBKo46AlxTEwe0v3cOzCxenMreYS6JZtb293zkm7ppnOT8pGJV4A9Hmk8ZPs88ZHaNjo6irfddhvWio+HIPEiWSx8vKCE7qWgWss9SDEwQ5WKM6EZLeYiJDWYKyBrJSts0SQ1YPV7cmCm9mgLOtbcDFUqVpKgPNiuj1T2xtwUUvwhTzLDEyZ0gIqBvAwA18RMm0lzc3PVWHO+SdI2TQRy8hppvAfivz5L9/tB3nA0TwcB8FoAkRkfBBW7bf7mi6EHSGKwaCzvi/tXAHf8egVswCrkcnjDwIAYp0VzLlmGpXbt7OurjqPkaUAJ5cx12EPrYXRU3CfT09NikhapVrnPkkifK0G55dN3VxmeRuzzQDrNGyOjyI7ZXmJ8RMSGYSTHR76/OEa2gip3mIaPHNMkfByGCJsEV82rIJeUBozx0WQA+6vCbLqlm+OjNE8HAbAXIiG5UhI3qOq9RmjOS9pzS5DT8HEfKEzPx8+UlKmSm3ghl8OhSkVUgNeKj3lj3UoY+U7heBkAf4fWhICRC4GP20DhNSmAtm7eHPBxkejlhI9t1fvxfUxCr5lnwXSLHtX2vJ5IsQNVYrNLMZdr1RKVIUpCbRbh0o41pyRoc3Nz2NXVjaCN0TXC/U0lAiD3yuHx3YnguhcBdqFp4VffBxHgY9ZvpZIvTwZgYr2n8bwv7mMB5fh12xOKPAgkfKxUhlit7myhAH19O1N5yCN14CONpYSRpnIpKz7mAPCuRcLHIHR7KOtg+jSDVswNAy8ulGW1LhOjx+9ZMBawlGyjPDhYZXCyxCE+BLYQWQTQithz4ZGAnBJZzYKc2Vda0FJ2Y0r6YW6ak55xIncc7mpCY1YA2S25m23GvcYccWv1DSDHhEfxx3wR8SyN5jM3QhKjzt3CSNBOWxNSluaVoADEfDkjqpekpJluF8aiq1DAa3t6tHV7MF4bZbAZ/kkA7DPuXR4c1LSEUk3EIiSxiZ1NTbi6uVmbG1+SolOQKHZaAEQvhUbu80A2NQojzcymjcZH2qM+fOTMbL0YKSUyouNnIMHIJCmaHx8REUdHRzECGR/nwE5qRJbfLPg4XBWWCyjFWXZBk+YGz+eJ4+MkALanxA02Q5NWwojuobtgxkwg5HEQIgsfTxjrQFoXcyCEPwHg+g49GRFhZC34mAPAQlsbtglKmT42pvSeOghK6C0b9+cYudD4WATlieZyKW7EHg9k08WEj/2xMju9rWYCs4fQFjClBGB0/Ez8P9X5nkUp+7mEkSrWPMJEmHQllDwZH5eFxcSd26z+UMQkpttUKragnn9ir5bJXLdW34BycjllmVbCra4M6OrqFqzveVSu3TOYZIs/UH1+0kdJ+WB7QgG0xHXRk2OkOFB1um1FQUfHerFd7e0duGtgQFMiuXjILPiI6MfIQi6HLXXgYx6UxXsx8DEI3R7KOpg+F+K9LhCMSzMAqBc0Wetc97kD/AInLaTOpia8ac8eSxvkK4vChTZgG2Fv/L9pPeBJZsi1mIM7aWA5uPf39lpjmJbd2Oyr5GbJ+7Bv3z7r9zlIlAKWWzoAngP95cTniNp2jWfs034rDw5qz2wGBUAbjbYUQCVq4u13ZWfcCnLG88+C/nLmL0lKejIDgL8OtuBulRIBORMqQhITsxVk6z/PZSBq8eP7T7M57TKeL9UUdZVBeeKJJxZ0nweyqVEYOS7M50Lg4x9COj6ODA9Xn5kVIyMAvAeUwJUHNz52QiIIzkBt+IiImmXLhY8zAPgznnFy4WOSmE137+yCJgsf+ZgSk8rbxcs5cldtVwzf1NSUZYGPIMLXGH1dD4C3CP1zYWSXY664AFNmgosPHzva27XvafhIHlmdTU1ejFwMfOzv68vkLlnvHg9k02Lh43kAPAwJD9gIfCTrd59Ru9vHQ9rJusrx3w3ozp5tJuAiQZcssrqA2tvbb41hYk0uGs83hWvJDR2RBGbCR/v3M6iSv0lKxSHUKy3oCd+StpHFPM1qLf82OFg2ntuMKoZ7o3G8gCp7OO+DKwFaF9p9uQe5wF8q0XOPoR4Drtq1Zct24R7q/yLIRrqF5CH5pwnkvBYSPm6r0cJd6x5HDEK3lxqlpXSB4Pj4OJ4+fdp6sbsWKv/4wLnqgh1FuBeYVidDWZR3gnKHNDeGlCWQMx2kWZqA2uPqEFFzaaLsxi0Alttfey6Xem+zBt80KE2aGb/RAsplsuo+BbZbKCWV6O7qqsaGp7mrpDG6ExMT+MADD6gNDrKLfD5uB2+/q4TIIDiYdmM8zGyjkoWtr7cXbzA0kxzUeF/eB8rqVIgi7CoUqqUZ+DqrKmDYCydtzdGnv7cXn3jiCdy3bx/+xm/8Bt511124k2WCB1BrkO8PPv5Z43Dq2eeBbGoURkpxswuBj33sGgkfs5RVNDGSLEdZ8XEj1IePiAlGHgBlcZbqmvswXsLHcVBKDa5QSMNHc566u7owD/5yjq5stfv27cOZmRmcmZnB/fv3Yw7c+EjrwWfZXg/p+GjOaaPxkdz5d5dKqRjpqxnrwsdHHnkEH3jgAdy+ZUvAx2VKC42PLkWcy9umFnwEUMkTW6NIs7Rn4SFlK3E72gIxt3pTsrKN8ffaYo8ReXz3AVSW7k1oCvq+0ldy4rJpBHgP2gL3KuR1uiXXeeIhlcs6xYa748Jdv1GMN/GQKibddpNX3zuNPkgJ0NajpNAA6LfGxN9m5f3jK4d5Mj73vni9LAQPuX3LFjx06BDee++9+IEPfKAmfKwHI4PQ3UCqJx7HjIGJUhYKxc4UwGYMisZ9RoaHq8JT2uKbiL//AchxFOSWLLXVjB2qxOcXosiygAIkygSJSemBdHCnFwaPHZGyEbpqUkZgC+Pc7apcKmEbJC8jk4F7GLK5hfINT+6N9Vi66dPR3l5tS9r5ObA1dK2ggO348ePe5/GsyGYGddHC5niRkqBwHOwXe3dXF/7qr/6qc50BAL71rW8Vk1zwtbCXtaOzqQlvHBy01mIEgCVPnyluNUvGyXr3eSCd5ouRhHWNwMeZmRm89dZbvftwBtLxEUB5pmTFyN8GG0t8+EgeLrXgI6KMkdJeIYzJio8mRp4R9nsRZGUHFxp9ygSXpZszPIXWVmz13EfCxzwoS/ChQ4cy4SMf73rxke53CGylbndXF547dw4feOCB1LV23XXX1YSPQ5UK3rRnj3VPX58DPi4+LTQ+IiJe0tnpzNBcLz6eARkf50D34JDx0XQxV3WmVVlAfk9KwEW1tflvRQT4nfh/Wdg7fPiwiI+mx4wdnx2JbeTu4KVSOf79Y5hkFjcF3Icxi+u8bukm9+/aLd0Ayt17+/Yia0va+VJJtja8+urNGZ5lZo13n3sK/LzxIZC9MocqFdy/f38qPv7ET/wE7t+/HzNjZBTh+s7OmvGRK95rwcggdDeQai33ICVMG6pUnAkpsmpvzMQZEdiudJ3xcbJ0bwQ56zdZYvoNl6Huri4sGFqqfHxP7nJ5FAA/ZCxel5tkmsJBcusk7RJlbORgWi6VNI2rKDSze4yNjWFT3A4fIGyFdAaVu35Jbowd8SZvFu6Th0RAOAZQZSZ9FqFDhw6llg/xuXiZdbLphe6Kc3kH+AWFlnjcz8dj2hpF2LZ6tbjOBsF+aRch3dWIH2sV1lMTJAnmzDHuhoQh4AxJo/d5IJ3mi5GEO43AR0RlMRIFTtBzTvjwcWxszNlWF0aSsGfiTaPxEdHGSLNmryQ0u/DxGLjdTqkv/SC8c4SYbt5f89xVRkwy7d08H5dYuF0MfDTHuxZ8JIysAFhtOMP60tfbi1dfcYW11gqgLPH14uMKkONyaU4DPi4PWkh8RPRbyOvFxyLI+DjC9pCLh3wYeKhKIiwSD5mUrCIhTnYhT6zKaQJqcn8fPvb29sVW7mOoXMWLznuotnLh3Ccsb8U0IV6P6bZdvaOoAzs716NyGTcF5TySC76y4lPiSylBWiIoX331JpTisCuVIezt7Uu9Nompj5NZlspW7HYEeRyGCBHk0IZG42ME7iz8Eka214GP2j0zYmQQuhtI9bxsTpw4UXUlRsRqkhZz8Wy+5poqk+ZiDACgeh8icn00GSr6fgr8CQRoQZl1UtMs8hzcxyER/H3P4kmH6IVxSWenlXCMMsuaND09XbXUmjX4uPu0uUGefPJJrb1p4zwGtoApZS8/Bm5X7xwkAjb/rQkAp9gz74iPu5hc03rEYyP572Ttdo3JPtBfzmaGeBoLSbgeAcAhsAWFjvi4L+a+6roLNugVQQe7imNOXHkQ3gt6KTVa+wXQGQKz1mSj93kgRbWOHS+DNDMz48THja95Df63//bfasZHRMTrBwZSNee+Kgb8hVsvRnbE63sx8HF8fByPHDlSxQv+HBKazXHi+IiQDSNNbDOVwXQvCSPJU8pVho0wrNH4eMDx+8OgCzC14iP10RR8OyEbRhZhfviYNjbtxrMDPi4dLSQ+PvHEE1XeyLVv9+/fbz1jvvhYLZHq4SF5Lgfd2nsMlQtzHhOXclmYbW3NYxSZscgFVMJkIqTz2t3meHJ8VG7v/DkHRHxM2kpt85XtGkPTWi9nLz+Gsqt3hIllumj81oQAU9q4qM/J1LFLfrPjsBNvyQOohwHQtT0I8JCW0d30IChDhGcFrFtIfOSJ0urlIdPwkV+fFSOD0N1AqrXGoqs02MjwsB1bDUn8XBrzR7FuRFQzOh+D39H4bwFsy6ILiK/t6dHa7k3iES8+01pazPAsMwlH2RMvSX3l4ym9IHgJGcnNiPfJ5/J4ijZwrHmj+3D3TtP16wCohGc9AHizcX9KxkMvp1H2TM5MupL/RJBokWlcKe7yVHy9qWWugHppUibvJkhqxLuyPs6BbIWjWBrXeBEY1ptdnjMPLs3lfSDHsd0a/3Ux25whWIh9HkinrGO3UPjocjHs7urCVlBMX3V/g44lWfERsXaMvCvjsxYSH/lzzHEy++PDSIpRNut0E0ZK7vhtAHh1vFfXsDwcPFlZVXEKjcXHsbEx0RKeB4WPESTujWfPnq0ZH6kMZT0Y6RvrLPhI7y1pTQV8XD60kPgYAWDb2rWpa+nee+9tOD62xt4knLLiYxJz/euox0fLwuzY2JhQ4zpC5dptC5ocH5PrzDhs7gLudlXXrcG+muOnkOLFe3v7RB6yVCrHdchJgXAAVcKzHgS42bg/CcpkYR/V2pucKydIa2+nKg00rpTd/FR1XG23+yIqhUYRlfDfVK2J7uIhXcaZxcBHF0aSfPIJx1pMw0cziXIj9zhiELq91Ig63b6kPCvAdndog8QN2QRgRAWaZjbsvjjByvj4OD7++OOpz9w1MKC13ZvEQ4i5JkumTyvKtaEzMzNezSzV5hsZHsZCFFVLfJnasn5Q1lyL4XRYXyQGrpDLadfTtRLArO/osJ5F37cJwKH1yRiXCNyJlwbifrVGEebic0ytYBOouBXRzRVYXGpc81dam3kA3OCZOxdTRxrE047rSbvtGo8rQU9ARXMi1TnncWQAgPs995YYgkbu80A6ZR27RuJjZ7yGXHsfUcbI/r4+HBsbqxkfEevHSEq+uBT4OBPvKWmcpNKR5n40GXE+viZG5oTnVK8DwF/07Ftex5zeLfXiYwSgkp4JGNkNCT7mY6yoFx/T+rMXlJV8t3APn1dBPfiYtV0BHxeXFhof10DCT5g85ELhY1ehYCWaqgUfdWGYEoulJ0sjjLz33nvj893JxhC5cL8NlSDJXdc7UVnaZ1DFbNuu8HNzc1WMtN3g9drW/Hq6Vhf6gZ0jZT6HuJ3uftl1zFtQZX5/CJOYc/psxlyuHZXlfB9KVvWBgRvi8TFd+ruRZ2EvlcrO9enLu+HDRwSZh/Th42WQCMwcI89A9oSCrnvfASGme0mpUZkn0yb5FtBLWJEGPg9gATCP4xkfH8fjx49bFs/+3l7cNTCALSAzULQoTS2OKxGctPioVMUNAwPVNueNZ7muNZN6mWM1OjpaU4kuHmdsjhPvk7ghh4dxamrK0nCaAFNk83ENqBfdQVBWmb3gj888YMxBZ5xMjbeFrHrm8WZjLfji03kCNYBsmXF9wGheQ8L4SDz+5jrLAsanwK5xHIFQ55yNfzf4taDlUilk511EyjJ2jcRHgMSrx4WRhI+Tk5M2Y1knPiLWjpFHjhzBdXFm1qXCx2awY9vo2WZ/pJrj5cFBHBsbc74vjoESjMmNkOMj4VUrJIk1vd5GAHhdX59lpc6Kj8dACRy+ZxGDBZ5z09am7xmk6C2CrvDNEv6VFR95wqwCyEJ+wMelo4XGxzvivWGuk3rxsVwqYXH7dic+UrLARuDj2NgYDgzcgL6kZpwIH11COsfHbEnLmlFlVdfrYtOzE+H9MXTFgUs8ZHLdMVRCcQd7xmWolA0HUbmI78Ukhj3dkg6Qx4GBG+K62aYAT7He5vEWVJ4BJFy3ecZlBrlF3cVD+owrPnxEkHnILPhIPDXHSGnN14qPJBeE7OVLRI2qsZiFAdi2eTNG4BdYeIId6SWcj49vBeX6wTdfBKqGM4Adr+BKBJe2+Mjt6VZI3EnSrp2dna2WTzEBvQPUy4Pimfi90oRCV829EydO4NjYmPhSkZhIIvMFyIU8+t9lXVkL9kuqUziPnj86OoqvufzyatIwzrzy+Syy/vm0gDyBGoBckzfr2swL/SHlAo2FVFc9AhCTynWCUFIpVnz4hI02APxi/F0qI9cRRVgeHMy4s3UKTGX9lGXsGoGPr7nssurayqLUaTQ+ItaOkcSE3gOJ0DkffIwAqjlDsuKjiR98nCSlrUsRyYljpISPx0COhY5AKQBclnSOj4iIExMT+KpLL60JHxH8zCD9fgr8Y5j6Lga3+ztXjkox7k3QWHwEUB5XpFw27x3wcWlosfDxqo0bG4qPAErJvZD4iKgwsj2Xw9cYguK6rktEfCyVdqMSKrmbNtX7jgx8pIRtLusxCbtF4/ekdNjY2JhVH7tUKmfiIZVQa7ql0/eHUI7rXoumq7guREdVfJyZmYkrw1AsuCTgH4u/UxkzRF+dcuWGnigmXDzkSc862wRufMzCQ5oYJuEjrTGKUa8XHzubmrCfhZbWQkHobiA1ytK9c8cOcQGNsHNIm+TL2toau8z5FnweFFNZNhboxvgvJbYwmSspc3jWPpuJM0wiJnQr2BaVZmHT+V44M8b/fJz4xydoczJfgFzIpf8rIGcjbmlqEvtQBpWIyIynczGvrr5ihvMOQGJd4evKdf4AyBrtFrA9A7q7unDXwAB2RJHF2FKcJjEBbwHbKsVd3ylRDK1Bs5a4ue75p7O93UouU0/9WaLAVNZPjbDklAcHscPM0As6Pk5MTGTGyL2wcPiImA0jG42PKwHwks5O7Vjk6aOEj6491dfbi1NTU5nmnGOkhI/nwZ2xvSuft/pwLTQOHzHj3PO1VS8+Su7v5cFBvHb7dmyNY9j5Gp2BJIax0fj4GuNepqdAwMeloQsVHw/Gz+gy1hXHR2p7o3hIMxeOeX1iPd6KdlbuldjZeYlx7PL4b5pF1yyRxYXP5FMqpQvanPRM5WYCNvpeQSlje1OT2a8IAa5FlajtgDUulBBTFvCl/iL6E7AdiNtWRB8PKSmI86ASZxaiyOIh1xUKeO327Zl4yDR8nJiYqK6x6elpr3HJxEezBPJi4WMQuj3UiDrdJPCtam7WJrkSL6B8POG0UbOAIYLf4kkLOg8247O+s7NmjaRJWRNnEHGAPQu6FjVytDMC2zWPv3C05xnjRGP8MPhjNPiLI4ulO21+zDl+GJRbyzaw3bs4I5XFgk3HiiBbockNtwhJ6RxExKFKxbZ8gJ5lkre7t6fHEmq3bd6MU1NTljbb516ZBz1ZS0fcLiluPuu4NgHgM888U42BNRnUEydOZHrpEwWmsn6qNWZRcj2cnJzEjvZ2Jz52d3UhImbGSHp5Xyz4CAC4MoqwQ4hRLkBt+NhojJTw0RcCQ5+B+NnUD8Ks+eIjMYMSRkZsbVGfa8XHCACv3b5dO3blxo34xBNPIKJeKSLg48ubGoWPrsSpeQBcvWIFIjYWH7nHHIWKEOZ0d3WlJn7LSrVgpJ39+yZM3KlJOM2jHaPchLZVvBMTy69ZIosLnyQcP+x0d+ftM/Ex3dKdJvTyTxGV+3sBo6hQbYOJkbKAbyoReBkw26Vft6oXq8+bnZ3FdYWCiJFSJvIIAI8cOWKtj1p5yHIKPiLKyQeXOz4GodtDjaixyL+vhSQ2jS/QqakpjZFx1YKOGEBlycgN4I7Lbc3l9GyYRuZuRFmLyX/jz6fsscRwmbFjZq3rAuiWVFc/1kISu0iffkjKcPH+EhBUIIkH5tpgsx+uF4dZW70ICQPXA+kvq73AYqiM5++67jpLmKVrTnjGgceFt4Md51qMj5N2kL8AhyoVXGmcXwHFUEpuoOXBwWoiETO7Mt13amoKO9rbbQ+OOMHR3niOXPeWEnNIbuP5+LglbLS1WXMnJXPKwggEprJ+yjp2Ej4OVSrWfjDXKb0gEdGLkXlIyofMFx/zUVStDnEQZHykNkkYKVmvpiER9n342Am2JTXNjc+Hjxw/Go2RFUisHRVI3FtdGHnU8eyOfL4h+FjI5bAJ3OXJTGxIw0cEhZFm+FR5cBCffvppJz4iIt4wMOAU/A+Asu6XhfsGfLx4qNH4aHoEFti+bSQ+8twwksKuXCrZGdUXkIfUrceISmguoB5j7RJiVxiYUkZlOeaW7gOou6pXMEm6NlI9T8JHM7v68PAIVipDLBacXL5JwN1g9MUUjveinvRN9bFQ6MKzZ88K2dzpmhOecUjiwgFy2OxM6pb0g9blWiPpsMlDunCsHh4yD4rnT8NHRHfupeWMj0Ho9lA9LxtyrSmXSnY2yngRjcYfYvzMcjOi25qgOZeyzZqMzCkGZjOgYhrMhWVaVSSwlxYfZdAtGtcXQLe0IiYAS4BajNvqc4XKxyUx6MPbXgRd0ARQmjczW6E5zrz9UsbQoUrF2pCmkJv2sjJfHvT8rZs3V593Bmz37fUgx7GY80OMo6vsAa85aY77zUb7JTdQM9GS9BuinAHVVDRVIMk2TNnUXe50DwlrMwJ32ZxWIx6tBdITEDZynwdSVOvYcddDcX1BUpngE8K+TcNIc63Ug4+EOxuFe3MslMpMmRhJbf2Y0NYWAK3utrlPOePsw0hpz3B8NLFLyug6X4zkbfCVejsBMj4CKMa9Ufh4DBzlyWLLhjTuJj7ydWSOQXdXlxcfzTVy0549VpjAJgBcm8sFfLwIaSHxcYJhQBYeshZ8dPE0LtffheYhZetxEZVQujf+Lguxq1e3affWhcsWtBOPDWFSUowLrDY+6gnTkkRslcqQI3s5/6S5gVOJrwPaNaVSmT3PTuwGsB5tC3YBzbjwevHxIAAehoXlIVev0JUkJj7ydnGMnAP7nbHc8DEI3R6q92XjLZ9gfhfKzdCHx9plyTZLbkedTU2YA9sKUhAWVj5erPS9kMtZ2iHTNXpmZgbn5uaqbifmi4EWv5kVvDVKNr8vVi+Kn8vvza00+bg/DwPgz4KysOwGm4G+Q2hLlhIX9AIkF54/BMA+cLsuDoLsanML+34gbl8Z5JhHk0Gm+SQtMk8y52LCqWzGk08+iW95y1uq594ESY3aPGTLEun6jQT76enpavI7qtUrhQnwF67PrWx0dBQPHz6Ml6xbl3rez7JjXs19iqtQYCrrp4XESGnu0jCyEfhYhCROzYU7aQLXblbHem5uDstxYjQTIykxmgsfT7L17MNI0+2c8Jfw8Qyo0o4toDx1JCXDfDCS4ulOQWKdkDCyAHJyJo6PN8Pi4eP09DTeeuut1bab+PgYZA/3yoKPLkEqD0pZGfDx4qPlxENmwcciKLwgnmYr2NbGJqifh+T4SO3NykMmAu4drD2+WOZIKI3FLdl5VOW6jiHAzyJAKwLsRiXw8izedzjxMa3cGcdHJbiPobK0u9y7B1FOsMa/H4jbV0YpLly51PPzKwiwD6OoFTdv3lY9Xis+cg/VRvGQJE9QjLaLh+T4iOjHyH379uErL7009ZylwMcgdHuoXsD0LYijDNQoXpGTKxGFKzvk7/3e72GhTdfmre/sxFXNzTWXm5K+I8j1Xn1xawC6ZpDHuvHxEV2hosjbVjNew2wfgXY+smuT1hJPRMkqSGB+ApS22Xz2ZlCgZALGSpBdV1x9a83lrPkkoTUBevf1H/rQhyyLcxEAb4REScG14K4x8P1mPiNNqyhpT13tNzWfrvM+wY55Y9SEbKvz3eeBFg4j7wA3PiLKGDlffDwG/sy/HHe4wDULcknCBx54IPV+xOBQ+wkfTet2PRhZddM09mijMdKM8SaMNL0FCiAL0s2glB9Z8fFOsEO1asHHQ4cO4U179ljPuwSUZ4CJj753eVZ8lLzVeLu4oB7w8eKgheYhC7mcsyRXVnycmprCI0eOYJeRXGpVc3NdJUul7y58pFrYWXhIvcY3fbi7uV5DO4ry8TlZEqnRxxRwiwgAGEV5K6bbdnmnz3kRHxMFwTgCPIEAG4Vnb0a7rngekzJfZvvkvuVyrdjWps/n8PAIqz1eOz4OQeJt1Age0rx/VnzkY5oFI5cTPoL3jJc5LZSW0mR4ssbAEJmAShrMg5DEIK4QFlzWZDTmd4w3WB4MBjVm+tI2nJTlsn/HDq1tUrKaa3t6vG2l//eCu5xME8huTRKjaFrXeDyjaWEpAmBbLleNYfIpIHJs/CiDbZrAQSAjrYV1hYKzjmYEgPnWVmdiOt4+X5xk2m+bhfWQhyRmTFoL9KLlMYuaa5tgQSyAO2kcb1uw5CwNLSRGLjY+IvjLTXHc4QKXy8Vu6+bNqffjQjf1rb+vD9vj7NdpGEmxcmmMOQB4S275MJKUjZJ1jTDSrBUM8fddAwOqTwbmm/PNrWc+fORJnrgyj8iHj1ddcUWqtY6eNwPKGpLWbpelW8JHMy+LhJEBHy8uWmgeMgLQqg7Ug4+IC89DuvDRh2ESDzkxMcEstiR0zqFpIe7t7Yv/T0ssxuOopXJbeQRoqsY3S3OkC9OJIE/4qBQFObQzrrfgwMCu6lyocmhpSgKeLO6op2/KMi/xkD583LZ5M64Q8It+5+vhiAdXXL9FIHiT1YCPfM2mYaQUkrSU+BiEbg/N52UjLghQVgfTtW98fLzubJBkhZUWkAlmWcuumN9d1/lcS67cuBEPHTpkaeaHKhVc39EhboYNoKwuPiGWC8g+4dFMWkR00549IqNIsZY0h8V47rTESqC7vBw6dMgabxMwqH1ZkzxJ2jUCeldtQ5+wfCr+TgnUIpBrFlI8Tj4u7UCJ6jpBufBnWUfmc4+xe0tad2nOz0GSLIY+l3R24g0DA1ZSoZb4XHNN+erTBqayfloIjOyHpcFHhGyZf02By7ef03679957RYzs7uqqKur4+LSDsgyXSyUvY87j8HxtlDBydnZW9JjhsZY0h9vivccxspDLVbF0bGzMi49Zx9NcG5yy4GOU4f48waQLI4m5uz/uM5Vr9OGjS1A/CI3Bx9UrVuB1fX0BH5cBLSQPyfmEevFxenparAHfSB5yPviYxkOqEmF55NbtHLRiBJGGj9ks3elJyFw85J49N6EkTFcqQ4jIXeK3obJgH0AlMB/EXK5QPQ8x4SHdgjRvn69vcgx6Fnz05eQ4Bdnw0cVD5j33z4KPiLLnhomR58AOaVq9YgXeMDBg7a3FwMcgdHtoPoApLYgiJAlsNGCamcFyqWTH5qUE8Zsgy4FxnD3TXNhFYYPkIYnHoe8t8f8nQbmVuBgmacPlQWdw8qBrtAq5HO7ZvRt3xtaP6ksiHh8al61btmDeqE9JsZX0nAr4ta+tguskosrqXTCSKRCjKCV+M+eS5g4RxRcXn2OzfZK7aCe4Mwm76rWatQ07PGNxs/F8yZWSEkWZiVCieC2MeZ7xDkiYUFoL5txS37jW3ceY3wDK9X5keBjLpZKVybUJlIWJHzNjgRq9z1/u1GiMlJJ8LSY+khbexDQTd9az/UvW8VMgr9t6MbJn69bUWqWHDh2qJuw0caTInnEe6sNIX/xxLRiZxXIneQ5I+GiuDcTs+NgJgGs8YzEOumXujNC3keFh/NrXvmYpJboB8BHP/dfkchYT2g3zx8efBuV639nUhF35fMDHZUCLhY++hFUmSUJ6I3nIAiQ85H2wMPh4XV8fWhm3IdLwcXCwzLKIm9nJKY66gr5yWy4eslIZwlyugNw6TsJ0IvRTMrSi1lb6bvKQ6aXEePtsl/q0bOtSPWsTHy8FPz7eDNnw0cVDXuu5f2sUaYpMWgv83eeqC+/CSErK+kZIEoGuNxJakpJ7IfExCN0easTLxsxmbmqDbtqzB/s8rneSawOBrBRjQ5rFItiMSzsAtjTpiRak5DZSjF0RZKWBWU6lBVR2TQJbV7+IQToKeuyPKQRGKf8/DH5NKo1RLUmCeNsiEFyj4uM8bicC22WHEiaZz5IyLVZArx+LKL8cfcxr2u+rQPZQmAE9mZL0EqfatVk01/RZD4AfhoRhdlmoELEm7wYaa+4OR+BMz3Zpp00KTGX91CiM7OvttRRsS4GPeQDMt7U5M4LT/x8GZXFqMs6TmOLPCnt9JQDeCgkTkbaXTkHiHSXho5RbAUDFZNK9a8XILEnUKKYxK0aWSyUx+ziNDbdwSPhYhCTJE2FkPfjoi0vd6/idrqPYQlERBH5LtzlXW0EJKY3AR/oe8HF50ELj48jwMD7++ON14+MxkL175stDboMkoWI9+JiVh8yCj+u6LjH2nZnJ+2H0WY7TeEjXNUlSx6Pxc8ykZ50IEBmx3xHadcU7WJv5s+bQFuQrCPCQVle81nrWPnxc6fg9Cz52gB8fzdwCnIekuXXFWNfKQ7YD6GXvILH0LwQ+BqHbQ4182bjKh6wrFKqT7NS8O1xEaGFJVoGWeEGZYFYAwNXx//dB8qI+AYDvY+dI6fPzoGszSQhD0IU2MyOwq1+33367tUFc5Vn649hpYvampqawu6urysRVwF3+QhpHnqhEyuZLWsef8wDE/v37q0A8VKmI7upbHXPU2dSEuwYGUmu9Zq3X2gmJBrEiPCsPCmQ2ZpgXX/KnUyBru6WMpXlQGd/NkjyuusbSSz4P6gXO25jWvttuuy01BsekwFTWT40auyzllRYbHz/BcIHj40pIMoObGMkt4hwfOVPCPz7sz4qP5cFBLQusWV2iVoz04eP4+Hh1nF0YScq9Rx99tDrHkrt6OyRJ1sx939/Xh2NjY9UkOyZGZsXHPABuYWPtqmPcyp7hmpOxsTEvc7cJ6sPH94POuJpr2oePCP4QiYCPi0cLiY+7rrtOsyTWi48cV7JgZBsk+Ru4wYRjZB4SHqEefDSfOW98ZFnTOQ/Z1dWNiYu6WU/7MWyCPA5DlMpDuqzjieX6/fFfWTgnfERUlnPJXR1gK0qW7aamThwY2MXi19WHx6BnrWftw8cCKB7yUs+cZMHHAWG9STkrDoDC5DK7VsJHvq4bwUPu378/894MQncDaT6AaSa0kLRNlNCg3bMAeKIMRDuz5SSoFze/91ClgjcMDOggDYmrePU84dh2T3voUwHd8k2LmRL3POa5z9ve9jbMxecfAD+zYCbNMWv8ubSqksaXb1CTCQQAi8njfT0NqvSOyQSeO3fOmuPuri4sRMrlyfQI4MK1lNzEfDkS87tP6OsGSIRuV7xOLp4jXwy8L/kTfTra261nUPbyWaMN1twY8Wa0ps842j4mrEFX+3hyqiwUmMr6aT6JgrLgYx4Ar/Gs18XGx05QlhwfRrrwcU183Ul2rus+r7z0UlwD2fDxxIkTYsbiejDSh4+Tk5PWfFF/T4Nd3YH2O5VRMzGyPZeznmW69pkYKQkP06BKkJn9zAHgq9n4SYnpmkDhT5YcIVmSiK4zLDZp+EjPd2FkVnxE8CcDDPi4eNQofERUGGnu5Sz4aFrspMzok2DzNBJGrhPw4KywJgueNgEofkjCxxwkXjM+HvKSdesy4+Px48dFfBwcLLO22+7qLh7y9OnT8XnuOHB1vzXxee5YbY6PZob2rq5ujKICAjyESjHA2seE66w85BjYhrEs+LgyXnO+cc6KjyZG8+zlEj52Gt+XCw8ZhO4GUj2A6UpoMVSpWBoc+v0YJDXwTNfklvh6TrSRHnIsrieeeAIRk0VI2kgpg2Q+fgY/Rtp+c0GeNJ7l2nSUuIeEQ8vCC0kWWXPj+zaqtNk42NCGPwC6Bo3GkL/MyFJujUdTk+hafRPoycdMbSo9g7dnbm5OLL+wo1hMdV3h8Td/ALbQEIEqDdZvWMkLbB2dAsWAtUKimU6z/uUBtDh71/xu37JFe2Zfb6+VSI6vNbKwucaLr2l6JsUa0T6pJnKL6yunta8WKw5iYCrnQ7WOXa34yOOFlws+dgLgleDHyCz4CJDumVIPPjYKI6X6uXlQyjZnPVXw46PZHhdGDlUqTozk+HgSkvrg/PpNV1+NvXEVDAkfaZ2tATtTsw8ffS6YO/t0y5OpyDTXWtEzZj585HPpLXsX8HHRqFH4aHp1nGTzTvgo8VlFYe/xtSQJN9u3bKkqMjlGlkHGx4JwPAsPudexPqltWXjIpcTH8uAgNkMTRkK97Y6Cstg+DID9kIufKwvnB+MxpKSTZnvm5uZiCzjvQw53DQyk4iPPcfEg2PgIAHjFa1+bCR9zkChcSF6ZDz6aPGS5VNLisWvFR3NdSxjJc2hs8LRvoTyBgtDtoXpeNq6EFpExwYfZgjsJgA8IIOJKHEDPWQEK3A6yZ/G6jWZZrNRFxo6ZMb8SMK8rFLDd2HSFeHNWjHMLxvdi/DdvxHv4LP5mBmyJXLUoz549W1Psn5RBMcrQRmf8lNHXPOiWHAJJ04KUM9pbAWUtyQNgfu1ae62BrY0mLR8B12MgJ7/o7uqqAp/k/pMHxXBL65u7E/G1VkspBilbayGX0/ZFfu3aap/yQvt6e3oy71WiwFTWT7WOXa34SOWj7oblg48mc+jCyJa4fT583Aq2NT2CxGOI2t7maSPvZ6MwMs1SZf5WhPoFvqFKRUyWxBnR6elp5WrOrH0mPhZBYdsxkEOkGoWP50ExsVYOjyiyXCSPgV5T3VxrWTEyrUSO2Z+Aj8uDGoWPZg1jSnRG+Pg7ALjTWK9pnn6UVXqDtEcEZY9PiDL5pSw85ErQ8bEDknjhrDwkx7ylwMeHQVnDdb4ystoxCBHmDOGcXNez4mMb6PHHWfDRfGfWi4//DRKMz8fzZs7RfPCR85DmWms0D0keRS6M5GOahYLQ3UCqFTB9yWf2gnLjSXO75UkhEOS4nNnZWUuD7wJYWoR3xMddWsBx4xhfkKKlMoosd7gyyPX38qDcWcxshMSA8BrZdL1p0eKxP2nulESuWr3ULkqW4xqPo8bxk2wOU8cxQ/wU78OugQENyGncHwKVQMIEzHw8zlIyNH5f+pAb0fsBcG0uhy1xciWTaSUXtNOnT1uldcxzndadHTuwIy4PQWPky5q8b9++6hxJL7v+3l584okncGxsDLuY5e0PINFW8rEzXY0XYp8HSqiWsfPthYNgWyxNN7jlgo8AqnRXGkYSzmXBxyLonim14CNdL42pVMeaKA0jfbWyzd+IMaoVH7OsC66I9OFjAZRru89FvF58NN3uTYxMq0ceAVj4iJAdI134ODU1hZOTk1hoa6sqagI+Lg9qJD4SXzIJSTIqEx/pHK4kNPfe7OyslVXalRUdUeGCz13Y5Jey8JAmPo4A4K9Ddh6yCDI+0jOz4GO9PKSJj2YWcHOs5gCw3+G6zsdRcmuuBx+PAeAggJhj6FqoHR9PgeI51+ZyuNJIopcD5dkzX3wEUBZwc601gof8+Mc/jn29vdUM5S6MLA8OZkqeVu8eD0K3h2p92UixMnxxACgtSyGe9PVsAZz0bAIe+yi5RXeCnhDH9aJ23f9EvLhPQBITxpPKuK7jyYayZrUmhtjUlNH3jcJxHvtz0vgdIL0mpSv2L62tpuaWxiTrPNWyJsjiz+/dD8qtR9POQgJmV0M6EB2FRPtrKkc2g9KM3wmqPEP/jh3Vl8vI8LBWRu1gvA5WAFQTvqX1hYNsFguiNH+Tk5NWcjmKj3S5DK8F2814ofZ5oIRqGbus+EjYthzxcQYShddaSDxf0q4dhdrwccs119SEjxEo6wW/p4mRvpq9Uuyfr638N2KMasVHxKRUjmtdbN282cpE78NH+jQaHxHRWl8H47Z0FQreNW7iY9ax5nMY8PHCoUbjYxR/CmAncvRZo3nCV6tUKihvG/48jpG+xFgUMmPykBSGkwUfOW759kIOlFAp4aMp6GXBRx9GzhcfkY0JjZd03aFDh6xn14OPT8Zj1A76e5BX08mCj3lI1pyJkXcD4DtB8a+7WaK6+eAjze188BFR5iFJAeHCyGvr8AKqdY8HodtDjbZ0v5NtuCeFhSRlkMyD7obsAz8zQy4txNHRUTE2Jg8g1vNMA61pSDR9GyARiH0aqbe85S04MTGB/Tt2aNrMk6AsJO2QuFXug0SwTHNRqoBy8UlzF3Jt9ArYWtFOUHGJ0jhRW8x4lvtBgUpHW1vNawJAZfQeB/XyARASroFupQNwl20w3WGLILsQlUFOqBFBkuzHvOfx48dTn0kM8D5IhCeu5Za0z9U2sflz1QeOIIl/NX/raG+vWUNZ7z4PlFAjLTlLiY8zMzN41caNdsZpsPExB37GjmMkJXDx4eOtt96Ko6OjuG3LFi8+HgAVp0ea+jSMLAJgwVFnlkiqbypWXIiPl0HHTu55Uws+IiLee++9Xow8AEkMfBZ8/P+E9VMLPo6ASghnKjhMN1/zvidOnEj9/RTY+HgedNd2H0YGfLxwqNGeQGQIoSz35rmudUQY6S0FaOwjjpHbt2wR+aUusC2qtfCQfZDwkD6Po7e85S0WPpLCoRUUNlNy3vdAkhxuIXjINHx0vasIj83rWkG9Z/r7+qxnk9CdFR9NZa3kxVByrB8TH7n3QCN4yCz4eAySCiH14COizEMWIB0j6wm9qXWPB6HbQ/OJ6TYZN6kWtrmJ54QNwxmmpC6gG5TWOBaiKxttG+jaMIkJycd9kLJUrgQVk2gyXtSuWeGZ1HeXxon+tkGizXW6ucf3kCwpFCft2ugPgc08jwDgORCy74LSBHeAHs9iXs/dUygpCoGWCc7muND9Co4+njGe57ovueL7NITc1YbPdQXktTU+Pi6ubwI//jKiY+a88nUt1Xz3gTKAEkC45dF0pZUyvzZ6nwdSVG/M4nLDR0SlHTfX6SVgWwtc5RRdGNke711XSMjHhP0RAeBvC/fi5+XitnAccGEk7UUJH2dmZkRlhVQrmxi4MaHN3VAfPrqwjKwyPG57qfGxI4owgnT3eWmN8xApCR8B7NrHLoz04eMBUDkRyIJo4qM5943e44ESagQ+dkKSxNXEgjPGOjD3gImRPqvpzeAWZiR8HAGlmOL7pCjsmzR8XAnKav0YyHHZLh7yYZCFaMKMheYh0/BxDmyFHfGQ5t73YWS5VKoJH139M2uY+/ARwe950Cge0gwh3Qq2IsdUfrvwMQsPeTPoHhb0bqZSZAuFj0Ho9lA9LxsppoAsp5KbRxaXG1oQ+/fv9750NzkWIrkOkxvKUUji77K6cbSl9IPa1QQq3tvUUGXRylOmxFewTVUAHaDSNGTEWEgZQE3LAjH7UbzR+np7Mc/aTWO+l82DCaQEWiZTRgJAf29vNYOlJCy0g54ZmWei5XGrfG758x4GG5g4EPksa2njKSWOcsUV0st/GpIEWHTfSbAzr+fAZhaoTZSR2GyzxEzQdzO2k5/nc6utd58HUlTr2C1nfERMEgzdEd/DvFc9GEl4J+HjY5DUlTavWQ8yPl4Gyl2YGCwTX9KYjX379onlviJQjE4n2NaE/r4+Jz4ehASr6sXHYyAnLmsBwM72divEYDngo8s91IWRlfi5pgeHhI9XbtzobZfrNxMjc6AskfyYWerRh5EBH+unRuAjCWsSrhQd6/BOY4/Qfr399tu9GMH3iLm2OT6eAluROF8eMgLAGwYGNKHMxUNWQM9yfRISjyCyvi40D9kR77GtW7Zo+PgYJMkT6+Ehqa44VYmQeEgXPh4DO9YdIElslhUfEfyeB43iIQkfTR5yBuTKFI3iIXOgFOv8mFnqsZH4GIRuD9XjXk7aEdK23OlZmOYmJjBBkLV4tDEk5singZcWO1+c82FCboMEtMwyVmkAf8zRz8i4dqunbe8wNo3kfucSzvp7e8Ua28TU8nGmGM6bM/TN/H0G9LieHADew36XrEdkwfGN5X2QlPR4DBQAv8NzTdp43sH6LJXLmJiY0DTA/KXG78tfilmYBRdTIL14O8GOa+NCThH8brX17PNACdXqPrmc8RFRZnr5NfPByE+AjI9p1xx09POVwnU+jOS4Iwn5gyBnUb92+/ZFwUcE3f2fku6QgNtIfDwPttK5FnxsNRhsF0aSZdH06krDRymbv9kuV3UNEwtdXhkRZHOrrXWPB9KpXh7ykUceqc6zT5Dlpa1MTwwXbyUlq6W9tVQ8JO3HsbGxmqoopHlM8msbwUOaCqwIFJ4eOXLEavPu2EK9UDzktrjsFmEBjb0pnGdVyA6AHRa0KsN18+EhXfjow8g8NIaHTMNH4iV8PGQQuhtIWQfTVVtx18BAVZPkWphmyZMIkngIabG1xJu2aFxH2mun1oklGuIlBWhhkZap3g02ajxrcnIys8betano5THNzvcBlDmG5nn9YJcRkmpsU31DE8B64jlrzeVS+/azjvGStG3kklQGWbDkc+163t74HjcZ9ydGzLTw31DDeJYHB8VyGaQB5IkzTrL7ZmUWPgZylk0qJ+Jyy3Udp/u3srFLcxMKTGX9lGXs0mpzr4n30SnHum4UPpL2Ogs+mm0lfMQMa9rHhHB85IleXNccdfSzALoSoVaM5H3i5xAG8dI0i4mP9LtZx3UEAHfB/PGRGLuI/TXxMQ9+fKTYbr6eXRg5VKlgCyjmmyc78q0lbjmTMLII6n3yGMil2nz3bwW3W22tezyQTPPhIbu7urAtl8Of8axt/tkW14OnOZewY6WwllogSXCbhpFSOzkmzwcfbwZ9HWblIStCH/OgKxEayUO2go6PeVA8EqKe8ZziwOvFyPc5xsvFQ06C7F6eRaECcX9NfASQLfydkFifs4xnVnxcTB7Sd+87wR2aVc8eR8QgdPso62CaQfsPCQvAxeQcBMUk5kC5OdO9XAKFFIfcFTOUnIE4CYrJyxtaGlcSlmL8fRPIG2yToz188ZuJDHhtUtemzFL/kWvwuCaOGCTTRXsNKK2dC1xcwhvFcyDqSU0mwY7x7mhrS223qyRDEdxJKdLut8bze2v8fwV00JViY1pAWbTERCBNTThUqVhMpa+2Im8XJREhIcPHLEQgW97MdW7eJ0tZI7qHVKqo1n0eyKYsYycmNYkivKSzU38Bg53wpRH4uGtgAIcqlYbg42NgJ3nJipH8WTzUJ+0aV8Ik0805K0aeBMUw5kGPoVsu+EgWWwtrID3cwFfOkPCRv+OOgbusjgsf86DquLqYRwkjdw0MaG2j+/rwkStlfBi5QbhXFqtjBICfhXSMDPhYPy0GD3knJEnEeBhhLRhJtd4JI++HpDyXN0FVLoctwv6aDz7Ss7LwkL7fj0Ht+NgK7rjkvcZxCR8Rlx8PmfYbxWY/Bop3LsTnVkDOP9ENiRJT4iFpPdWDj4SRC81DZsFH3u9G4GMQuj2UZTClbJC0YCTGrcrsQcL0cE2i6b7jWhCjo6Mq5qNU0uLitgoLbdfAQKbMlfRpMr4XIXHjNcGUL2yyfPLnuBiXKH4OCZOufq6BBNS4Jo5vNldCjTLYTDx/lnQNj9+gF0wRZBfAdYUCdphxPJCAtdl3n2U2bRzW5nK4CWxXpc6mJuzt6dG8F+j+XJM3A3aMzxTYYFoeHLTA0ScYmO02E165ruPuRS5G/2dS7uMbz3sgWWvB0r0w5Bs7F+ZIjEMHqBd+I/GRM6EPgxKy5ouPOagPIyV8lHDiMVAMRFZ8JCVCGkZ+2HF8SujjUuHjYwBeJtvlEXFtT0/VWmI+z8RHun8WfJTGbFccc6q93zMIBzSuc8Z90yyLMzMzIkZOgx6qdFK4l8+SswmUQmsje149ezyQmxrNQ14DTBiGxvOQXwCFY3zNF9ra8JlnnsmMj/XykBxbsvKQpGxz9ZErEeaDjxIG+fARsT6M5PPaSB6yGWR87O/txampKat0pokfhJHED1IeD5OHXFcoYCEug1sPPhJGNoqHpN/qwccCJPxCsHQvAmUZTLOUgGsipQy1Q/Hiok1x2223VSf2yJEj2uI3GYKZmRl88sknEUCP7xoBh2aqq0ssC8M3JYCKOxwDvUY3geYKkK0COdAzLvIMmSaDAfF9qH7jNZ6FT6BK4PkYKNC7A3SG1OWCWYGEib3BYXEwgZC0rVnqU5rMHCkBCDikmNO08Xc+J26HuYY4yJPLJ91/zPM8Em66QJUfAgB829veZrVjPnFa27dssbOxsjE2948rBk1K8tQJemZSOt4Bal1mcZ3Mus8DyeQbO6nUioSRUobarPhI99QYgjiLvflCHgE7sU4t+HgKkuQutWBkJyvZZI6JhBPNkA0fOR5IGEkxeRWQXTB7IGG+TBf8pcDHrbF7rGsOTCtTVUCemqp6M2hrqFKpjvvMzIyWZMeHa0chcd0uAOAfsvuaMdVZLDLmGB2Ix8Niuo0Ya75eXPhIwkQBdCykmEUTN4vsL71f6t3jgdzUKB5SwsduUJVW+Drbv38/IiqhlZfiy8pD0p7nFQjoQ54XrjWeA1XffgLmh4+ItfGQafgDkJRXrQcfN7J9kwfd28aHj4j1YWQREmORJNTWy4vtGhhIxUdEnYfMio950HnIRuFjI3nIIih+ol587N+xY157nCgI3R6qR0vpWqgVkF1CuGBAH2J+qCSMCVA3DAzYSRsA8BBbYBKAUGKaNAH3WLxod4EdTwmgGIVRALw3/ktMbj6K8KY9eyxtGT2DJ4DYBAkgn4ckq6ImOEURXn3FFdUNLGUwjFibfMDbAolbYJrrlekq5KrxTWDB43e4Ve0xkDPy+sbfAgAhnpKSmJmCpLkWd2cYlzKoMh5mOwcgexxrR5xB09SgUm1QVyw4IlZf+sQY9IGc2GKl0Eaaf1OrPgKKaQBIkvsF9/KFoXos3RJGigwMpONjBCobrrkuVjc3440GI1MBwMchwZ/54COCHyPvBZVccoJdXy6VcHZ21smE8SRiWfBxO0ukMw6yZXYF+z8NB4qgXP4pjGQx8PE8yLF4aW3lbuKSgDozM4Ojo6NaeSzXeswSf5qGkWVIMPKk514rhDks5HJOV3Vu8eOKo91g5yTJQxK/OGi0MQeAnfm8hY9mXfOxsbG693ggNzWKh0zDR3PN8uzLtfCQ5P580PE8n7WScqjMFx9r5SFJYDb5jw2vfnX1HqQoLRttyYqPNG7rOzpqwkfE2jCSvA7qxccsPORyxMeVYAvEhVyuioWN4CG3wdLjYxC6PVRrPA5386vFjYHA6jwkMcmbQGmPpMWzqrk5tdRKBHpWbP6snTt2ODU7AEkSIgLcU6CsC6tBTz5jPu+W+G8+inAvKKFNYhQlQVnSZJYHB0XL0wwo6wxZuYugM6gSqPEkb6YbzUlQL7lJqQ2lEk5OTqbO3SOPPKIJwBwgSLPK568FbHAhUJyamrIyG/vKFfCM0NUyPFFUBX+aS/OFtAKSJBRFkIUXittBSNyBzXZzAYhfS/eiceGMN6KdOKbZuF6K7+WfZlAupaSZPQV6iRSa+zuMdsxnnweyqZaYbpeLXL34eAbc2Ueb2TEpPnIzyPGRO4rFVHyUcidwjKT6sPxZ/EXfv2MHtkZRVfA39xMlQqoXHxESRRNd3wd+fORjwPM5nI/nR2JYs+DjxMSEhlEmA1ULRt4wMFAzPiLaGNnb01N1OY3Ancl5DWTHyMcgiUU3sTbtvTk1NYWIfnwE0AUEF3NIn8vi9UilhwCUZYrwkc9/wMeFo0bwkFmSSXWAwqRjoDBqQ4wDeWF/5aF+HjICwTMDdOXoAagfH8uDgzXzkC6X8UOHDjUEH/eBUXorIz72xW7bPrd8zkPOBx8bxUMuJj52RlHVaJKGj4iN5SGXCh8vGKF7//79eP311+Pq1asxn89nuuall17CD37wg3jppZfiqlWr8HWve12mQuecsg7m3NwcDlUq1kahxeVzrdgASlMkuSK7NurPxQtE1EjGbRgBJUyOQwI0d911l7fsCoDtHkLJMYqO520TNk2H8d0EKzNe5QCojI7k6iaBFb2AqLzEGfBbdGfYWJPF8/HHH7fauzLuhwYaXV3VGGeTmbIsrAzcqCSS2SYpiYkJiia4SGQCDr8n//+MsK4isDXQrnkdiPtLVjB+TVc+j+3smoOgXvhlYbxNGhkexkIUWSBdgbiMDSRafC4cmC5yrnGm383kLPPZ58uZljNGmvgI8d4hxsGXEM+Fj7RXXXO/HxKMlOIju8HGxw2veU0qPhbi5DcujGxxPCsS9r2Fj4OD+MADD8wLHxH0WLbzcR99+MjHO60UYMH4noaPUp8J61yxylkwMgs+ImbHyIrxLPpuMnEujNwESQJKU1BuAYVn/Pw+8HvguPCxGK9FbumkebsZ5PrlPoxMcy3PuseXOy1nfERM5yGzJAwdgcXjIa+KM4rzZ/MwoHrx0dyXAIDrjO9pPCS5jLfHFtKlwMetYFtTeRKxrDzkfPARsbE8pAsfzTbUg4+FtjaRhxxgY+2ienhIUqAsFT5eMEL3r/3ar+GHP/xhfN/73pcZMH/rt34L8/k8/t7v/R5+/etfx5/4iZ/A1772tfiv//qvmZ9by2BSpsW9oLKBmgshbVJPgQ18JFSmAa3vvqZmPALAj370o1VA5C9oKeacwJQEXZ8bd6uw4YjxOnToECKi5lrpsuBIiShMBcZJoy1lkDVyUqIRuq+Z7ZA0iGYfJFesgnAud+PhMUnS/O3fvz8T45i23khTzbXK1Ja1xviYSTCkT5obEZV8MLOap2nf+XhzopehBNIElPyFZ778+DiOj49ba4Qz/VksYRcDU7ncMZLj4ylQL0XT+lwLPvI1Ph+MNPGR/jfxsfoCNtzWTYysBx972FrmjGI9+PgYqBrSZltMAf4xUPhF+ChhJC8FSNYM/j0NH4ugmE8Tl5YTRvIyW4SPHG9qwchyqSSWxFkofJTu5Uoyl4aRFAKURgEflwcP6VpLnzD2+GLxkHtBfydn4SHTnkWu0Sa+dMa/j46OImJtPORi4qOLh3QKnI5zX0746Hs3u/q2WDxko/HxghG6iR599NFMgPnSSy/hpZdeigcOHKge+8d//EdsaWnBT37yk5mfl3UwXRo1ehnyUjeSq4wkzPpcishlJ21TSkzets2bRZcRyU2TFi/FGPk0rq4kN62Q1DHkdZ01C04UiRolKZ6DxqUMiTb4DNgvKXJB5e43rvnyjffMzExVI+Yr45OmpaRz6AVSD2WNu+HacprnTtA1l/ex/13zSm3lIH2f55rWFAszufP41jdAkuytmDLW0hqhjJxZ6GJgKomWI0b63OtGR0exPDhYEz4i+DO5ZsHIvZDgXQESJaGkwGsCuZQVx8h68LEd9Az7Q5UKFnI5DR/XgkqEY5K09okp5aV7JHxcCUkdUx9G1oKPBzOev1ww0qoIAYnwcAoAD2eYW864LQY+zhj3ijxjLa0TU4HjooCPipaSh9zZ1+fER9caX448ZNqz0tpK5dAQa+MhFwsfa8XIlxsPaeLjeUjqsruu2bpli7P9i8FDLgQ+Qk2ztAwoK2CePXsWAQCfffZZ7fju3bvxtttuc173gx/8AF944YXq59vf/namwcySKMGVDGDXwICzLExFWPDceuvb5KZ7D9cg8U3jW7wEzD5Lt0vTTtZpDpqWxchjkZSS8TwEgOuNPmwCFWvSwdxAzftL8+XL1Dg+Pq7FfvjOnZ6eTo2HqVc7abbf125J8/wQ6HPudc+PY334OYc912zbvNk5n3SvtHbfwdrY3dWFBU+GX3ON1EIvR6ZyMTFyofDxPMhMQS0YOSMck/BxwHOfvaDvqfniY1riGInMtU+udwWjH4SPvT09qc8w56wWfMyCS8sJIzcaY1QU5tKHkaaL4kLj4zi7V7lUEt1XG4WRAR8TWioecmxszImPeXCHMC43HjLtnLT+c3xErJ2HrAUf1+ZyuPmaa1LvH3jI2nhIyYXbh5HkHSvRcuIhg9CNiF/60pcQAPDv//7vteNvfOMb8U1vepPzurvvvtsCkSyD6bPk8Ak0J3Vubg67jFIt9JFiNyqgJwBygWqUshjpWeQyMupZvACqtEIe5MRcHR5Nuyt+rV4hyWRKzfhkHheTJcs3QjYtJV3nUz5wi5WUOXSoUqmpvybVkmFyAJQl7Y54HjjYmMoLcx2llWWYBtlKVIBsLwRfGY18FGF/b69TC5nFbTwrvRyZysXEyIXCR7p+VXNzzRiZh6RetA8fedbcNIxshiRm0XzWYuIjjRvtGRc+pj2jHkt3Lbi0nDCyHRSmV+sfG/hIlrCCsI7o3MXGxwOg3rvcg2yhMDLgY0JLzUNK+MhzrSx3HtKFj2XPepfwURqPrNRofKwVIy8kHpIyxc+Hh3SVDp2PUmG58JAXjNB95513iuDEP88995x2zUIDZr1aSkQ5dkTSpEg0NzeH6woFG/jil+rExATeeuutmUHVZ5UxyxL43DQnAPC3AZxZBl2JIjohe63keogDYq3gK82XWLPPmEO6rghy9mF+7kJudN7+igBchVzOmZyE2iBlynS1VXrJDIFcjiTLC0FyEeMCijRO8xFC0mi5MpUXE0YuJD4iYs0YGUFSL9qHj4+Bv1zObaCYNyk771ClsiT4iOgvM5hG5pwVa8BHFy4tJ4wkrMmKjwB6OSZ+7mLjo2ucFgIjAz4mtBx5yLm5OSyXSrIrcHz9cuEhpf22Z/fuah+s9oNdCaWR1Eh8vNh4SI41ZhLdWnlIl1Jp6wJi5HLExyUVuv/hH/4Bn3vuudTPD3/4Q+2ahXYNMqmWwZzv5sjiLpMGylNTU9jHSgWkAbDUVqrPamqcKgJ479u3Dx999FFnqSz6VGJAz8pcLyZJ7R2qVPCGgYHUOTBLgmWZ74XY6FnAbmpqKpNSIqvywlx/Uimm+a75WmKxG0XLlam8mDByMfAR0Y2RQ5WKlgQwAtDipn34mKZYLLJrqQ7q/v37tVqoFxo+IsptdgmdrmuWM0ZS2bVa8DGtrYuBj7zNi0UBHxNazjxklnJRy4WHvO2223D//v2Wy7gp3BVBVU65UPBx18AA9vb0XBQ8pIk18+UhpbUnVcW50HjIC0borodqTYJx8ODB6rEXXnhhwZJgcJrv5ki7Pgso0/VmPeq0c13uF1EdG8EE7lo30WKTNN5Z5nA+GtJG0nys/bWSa/1x4b4eWuh2+2i5MpX10HLHyIXER0Q/RtaLj657p1kdJbrQ8BExu9Dpumap9/ditSXg4/Kn5Y6PiC9vHpIs3hcyPrqOua57ufCQaWtvofmChaRa9ngOEREuADp//jzMzc3BH/zBH8CBAwfgC1/4AgAAXHHFFdDa2goAANdccw385m/+Jvz0T/80AADcd9998Fu/9Vtw9OhReO1rXwsf/OAH4cyZM/DNb34TVq1alem53//+9yGfz8MLL7wA7e3tC9O5Ouiv//qv4fnnn4crrrgCrrzyyoada54PADVdO5/nBrpw6GKb2+W6z2uhgJE6ZV2j9axluqa5uRn+3//7fwEfA2l0sc3tct3jtVDAR52WOw95se2hQAldbHNb0x5fcBVAg+jtb3+7ph2hz+c///nqOQCAjz76aPX7Sy+9hB/84Aexu7sbW1pa8HWvex1OT0/X9NyLScMbKFAgmS6GfR4wMlCgQAtBF8MeD/gYKFCghaCL0tK9VLRctZSBAgVqHIV9Xj+FsQsU6OKmsMfrpzB2gQJd3FTLHo8WqU2BAgUKFChQoECBAgUKFCjQy46al7oBy53IEeD73//+ErckUKBAC0W0v4PjT+0UMDJQoIubAj7WTwEfAwW6uKkWfAxCt4defPFFAAC47LLLlrglgQIFWmh68cUXIZ/PL3UzLigKGBko0MuDAj7WTgEfAwV6eVAWfAwx3R566aWX4O///u+hra0Ncrmc9/zvf//7cNlll8G3v/3tizJ+52LvH0Do48VAtfYPEeHFF1+EV77ylRBFIeqmFqoFIy/2dQdw8ffxYu8fQOijSQEf66eAjzqFPl74dLH3D2Dh8DFYuj0URRH82I/9WM3Xtbe3X7SLEeDi7x9A6OPFQLX0L1hw6qN6MPJiX3cAF38fL/b+AYQ+cgr4WB8FfJQp9PHCp4u9fwCNx8egsgwUKFCgQIECBQoUKFCgQIEWiILQHShQoECBAgUKFChQoECBAi0QBaG7wdTS0gJ33303tLS0LHVTFoQu9v4BhD5eDHSx9+9CpZfDvFzsfbzY+wcQ+hhoaejlMCehjxc+Xez9A1i4PoZEaoECBQoUKFCgQIECBQoUKNACUbB0BwoUKFCgQIECBQoUKFCgQAtEQegOFChQoECBAgUKFChQoECBFoiC0B0oUKBAgQIFChQoUKBAgQItEAWhO1CgQIECBQoUKFCgQIECBVogCkL3POlDH/oQ7Nq1C9asWQOFQiHTNYgIv/ZrvwaveMUrYPXq1XDTTTfBX//1Xy9sQ+dBc3Nz8Iu/+IvQ3t4OhUIBbr75Zvinf/qn1GtuvPFGyOVy2uc//sf/uEgt9tODDz4Ir3nNa2DVqlVw3XXXweTkZOr5jz/+OFxzzTWwatUq2LZtG4yPjy9SS+unWvr48Y9/3JqvVatWLWJra6M/+ZM/gX//7/89vPKVr4RcLge/93u/573m5MmT0NvbCy0tLXDFFVfAxz/+8QVvZ6CLHyMDPgZ8XG4U8PHCoYsdHwECRgJceBh5MeMjwNJhZBC650n/9m//Bm984xvhP/2n/5T5mvvvvx8+8pGPwEMPPQSnT5+GtWvXwvDwMPzgBz9YwJbWT7/4i78I3/jGN+Cpp56Cz372s/Anf/In8O53v9t73bve9S74zne+U/3cf//9i9BaP42NjcH73vc+uPvuu+FrX/sa9PT0wPDwMPzDP/yDeP6f/umfwpvf/Ga4+eab4dlnn4Wf+qmfgp/6qZ+Cv/zLv1zklmenWvsIANDe3q7N19/8zd8sYotro3/+53+Gnp4eePDBBzOd/61vfQve8IY3wJ49e+DP//zP4fbbb4d3vvOdcOLEiQVuaaCLHSMDPgZ8XG4U8PHCoYsdHwECRl5oGHmx4yPAEmIkBmoIPfroo5jP573nvfTSS3jppZfigQMHqsf+8R//EVtaWvCTn/zkArawPvrmN7+JAIBTU1PVY3/0R3+EuVwO/+7v/s55Xblcxve+972L0MLaaefOnfie97yn+v1HP/oRvvKVr8Tf/M3fFM9/05vehG94wxu0Y9dddx3+yq/8yoK2cz5Uax+zrt/lSACAn/nMZ1LPef/7349btmzRjv2H//AfcHh4eAFbFojTxYiRAR8DPi53Cvh4YdDFiI+IASMRLzyMfDnhI+LiYmSwdC8yfetb34Lvfve7cNNNN1WP5fN5uO666+DP/uzPlrBlMv3Zn/0ZFAoF6Ovrqx676aabIIoiOH36dOq1n/jEJ2DdunWwdetW+K//9b/Cv/zLvyx0c730b//2b/DVr35VG/8oiuCmm25yjv+f/dmfaecDAAwPDy/L+QKor48AAP/0T/8Er371q+Gyyy6Dn/zJn4RvfOMbi9HcRaELbQ5fznQhYWTAxwtvbwV8tOlCm8OXM11I+AgQMBLgwtpfAR9latQcNjeyUYH89N3vfhcAALq7u7Xj3d3d1d+WE333u9+FSy65RDvW3NwMnZ2dqe39hV/4BXj1q18Nr3zlK+HMmTNw5513wvT0NHz6059e6Can0v/5P/8HfvSjH4nj/1d/9VfiNd/97ncvmPkCqK+PV199NTzyyCOwfft2eOGFF+DgwYOwa9cu+MY3vgE/9mM/thjNXlByzeH3v/99+Nd//VdYvXr1ErUskEkXEkYGfAz4GPAx0GLShYSPAAEjAS4sjAz4KFOjMDJYugW66667rKQA5se1+C4UWug+vvvd74bh4WHYtm0b/OIv/iL8z//5P+Ezn/kMnD17toG9CNQouv766+Ftb3sbFItFKJfL8OlPfxrWr18PDz/88FI3LdAypIsdIwM+BuIU8DFQLXSx4yNAwMhACQV8zE7B0i3Qf/kv/wV+6Zd+KfWcDRs21HXvSy+9FAAAvve978ErXvGK6vHvfe97UCwW67pnPZS1j5deeqmVPOH//b//B3Nzc9W+ZKHrrrsOAACef/552LhxY83tbRStW7cOmpqa4Hvf+552/Hvf+56zP5deemlN5y811dNHk1asWAHXXnstPP/88wvRxEUn1xy2t7cHK04ddLFjZMDHgI9pFPAxUBpd7PgIEDDyYsXIgI8yNQojg9At0Pr162H9+vULcu/Xvva1cOmll8IzzzxTBcjvf//7cPr06ZqyV86Xsvbx+uuvh3/8x3+Er371q7Bjxw4AAPjjP/5jeOmll6ogmIX+/M//HABAe0ksBa1cuRJ27NgBzzzzDPzUT/0UAAC89NJL8Mwzz8Att9wiXnP99dfDM888A7fffnv12FNPPQXXX3/9IrS4dqqnjyb96Ec/gr/4i7+AkZGRBWzp4tH1119vlehYznO43Olix8iAjwEf0yjgY6A0utjxESBg5MWKkQEfZWoYRtaa5S2QTn/zN3+Dzz77LO7btw9bW1vx2WefxWeffRZffPHF6jlXX301fvrTn65+/63f+i0sFAr4+7//+3jmzBn8yZ/8SXzta1+L//qv/7oUXfDS61//erz22mvx9OnT+MUvfhGvvPJKfPOb31z9/W//9m/x6quvxtOnTyMi4vPPP4/33HMPfuUrX8Fvfetb+Pu///u4YcMG3L1791J1QaNPfepT2NLSgh//+Mfxm9/8Jr773e/GQqGA3/3udxER8a1vfSvedddd1fO/9KUvYXNzMx48eBCfe+45vPvuu3HFihX4F3/xF0vVBS/V2sd9+/bhiRMn8OzZs/jVr34Vf/7nfx5XrVqF3/jGN5aqC6n04osvVvcaAOCHP/xhfPbZZ/Fv/uZvEBHxrrvuwre+9a3V88+dO4dr1qzBvXv34nPPPYcPPvggNjU14ZNPPrlUXXjZ0MWOkQEfAz4uNwr4eOHQxY6PiAEjLzSMvNjxEXHpMDII3fOkt7/97QgA1ufzn/989RwAwEcffbT6/aWXXsIPfvCD2N3djS0tLfi6170Op6enF7/xGWl2dhbf/OY3Y2trK7a3t+Mv//Ivay+Eb33rW1qfz58/j7t378bOzk5saWnBK664Avfu3YsvvPDCEvXApo9+9KN4+eWX48qVK3Hnzp345S9/ufpbuVzGt7/97dr5v/u7v4tXXXUVrly5Erds2YKf+9znFrnFtVMtfbz99tur53Z3d+PIyAh+7WtfW4JWZ6PPf/7z4r6jPr397W/HcrlsXVMsFnHlypW4YcMGbU8GWji62DEy4GPAx+VGAR8vHLrY8RExYCTihYeRFzM+Ii4dRuYQEWuzjQcKFChQoECBAgUKFChQoECBslDIXh4oUKBAgQIFChQoUKBAgQItEAWhO1CgQIECBQoUKFCgQIECBVogCkJ3oECBAgUKFChQoECBAgUKtEAUhO5AgQIFChQoUKBAgQIFChRogSgI3YECBQoUKFCgQIECBQoUKNACURC6AwUKFChQoECBAgUKFChQoAWiIHQHChQoUKBAgQIFChQoUKBAC0RB6A4UKFCgQIECBQoUKFCgQIEWiILQHShQoECBAgUKFChQoECBAi0QBaE70MuaPvnJT8Lq1avhO9/5TvXYL//yL8P27dvhhRdeWMKWBQoUKNDSUsDHQIECBXJTwMhAtVAOEXGpGxEo0FIRIkKxWITdu3fDRz/6Ubj77rvhkUcegS9/+cvwqle9aqmbFyhQoEBLRgEfAwUKFMhNASMD1ULNS92AQIGWknK5HHzoQx+Cn/u5n4NLL70UPvrRj8IXvvCFKlj+9E//NJw8eRJe97rXwfHjx5e4tYECBQq0eBTwMVCgQIHcFDAyUC0ULN2BAgFAb28vfOMb34CJiQkol8vV4ydPnoQXX3wRjh49GgAzUKBAL0sK+BgoUKBAbgoYGSgLhZjuQC97evLJJ+Gv/uqv4Ec/+hF0d3drv914443Q1ta2RC0LFChQoKWlgI+BAgUK5KaAkYGyUhC6A72s6Wtf+xq86U1vgiNHjsDrXvc6+OAHP7jUTQoUKFCgZUEBHwMFChTITQEjA9VCIaY70MuW/vf//t/whje8AT7wgQ/Am9/8ZtiwYQNcf/318LWvfQ16e3uXunmBAgUKtGQU8DFQoECB3BQwMlCtFCzdgV6WNDc3B69//evhJ3/yJ+Guu+4CAIDrrrsOfvzHfxw+8IEPLHHrAgUKFGjpKOBjoECBArkpYGSgeihYugO9LKmzsxP+6q/+yjr+uc99bglaEyhQoEDLhwI+BgoUKJCbAkYGqodC9vJAgVLopptugq9//evwz//8z9DZ2QmPP/44XH/99UvdrECBAgVacvr/27dDGwAAGIZh/389WjIYZh9RKaD2EeBnI1miGwAAACI+3QAAABAR3QAAABAR3QAAABAR3QAAABAR3QAAABAR3QAAABAR3QAAABAR3QAAABAR3QAAABAR3QAAABAR3QAAABAR3QAAABA5p6U9pwbc0ioAAAAASUVORK5CYII=\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\n",
    "    \"Cost: {:3f} | Train accuracy {:3f} | Test Accuracy : {:3f}\".format(\n",
    "        loss, accuracy_train, accuracy_test\n",
    "    )\n",
    ")\n",
    "\n",
    "print(\"Learned weights\")\n",
    "for i in range(num_layers):\n",
    "    print(\"Layer {}: {}\".format(i, params[i]))\n",
    "\n",
    "\n",
    "fig, axes = plt.subplots(1, 3, figsize=(10, 3))\n",
    "plot_data(X_test, initial_predictions, fig, axes[0])\n",
    "plot_data(X_test, predicted_test, fig, axes[1])\n",
    "plot_data(X_test, y_test, fig, axes[2])\n",
    "axes[0].set_title(\"Predictions with random weights\")\n",
    "axes[1].set_title(\"Predictions after training\")\n",
    "axes[2].set_title(\"True test data\")\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Send it after class\n",
    "\n",
    "Try improving the accuracy.\n",
    "\n",
    "## References\n",
    "\n",
    "\n",
    "\\[1\\] Pérez-Salinas, Adrián, et al. \\\"Data re-uploading for a universal\n",
    "quantum classifier.\\\" arXiv preprint arXiv:1907.02085 (2019).\n",
    "\n",
    "\\[2\\] Kingma, Diederik P., and Ba, J. \\\"Adam: A method for stochastic\n",
    "optimization.\\\" arXiv preprint arXiv:1412.6980 (2014).\n",
    "\n",
    "\\[3\\] Liu, Dong C., and Nocedal, J. \\\"On the limited memory BFGS method\n",
    "for large scale optimization.\\\" Mathematical programming 45.1-3 (1989):\n",
    "503-528.\n",
    "\n"
   ]
  }
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