Reinforcement_learning.ipynb

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   "source": [
    "# Reinforcement learning"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "## Goal and perspectives\n",
    "\n",
    "This tutorial is mainly adapted from this article https://arxiv.org/pdf/2103.06294.pdf and inspired by the work done during the 2022 LOQCathon."
   ]
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    "### Reinforcement learning\n",
    "\n",
    "Reinforcement learning is a machine learning framework where an agent tries to find the right actions to perform by interacting with an environment. This is modelled by an agent who is taking actions and receiving percepts from the environment which can be used to choose the next actions. At the end of an epoch (or a series of epochs), the environment rewards (or not) the agent according to the string of actions taken. From the reward, the agent learns and adapts their strategy for the next epochs.\n",
    "\n",
    "![reinforcement_learning.png](../_static/img/reinforcement-learning_reinforcement_learning.png)"
   ]
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   "source": [
    "In Quantum Reinforcement learning, the exchanged actions, percepts and rewards are now quantum states being exchanged between the environment and the agent. In their paper, the authors claimed to have found a quantum advantage in the time for training by making use of Grover's amplification method to reach good actions quicker, and the goal of this tutorial is to reproduce the main results of their paper:\n",
    "\n",
    "![results_paper.png](../_static/img/reinforcement-learning_results_paper.png)\n"
   ]
  },
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   "source": [
    "## Imports of packages and configuration of display"
   ]
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  {
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   "source": [
    "from typing import Union\n",
    "import math\n",
    "\n",
    "from ipywidgets import FloatProgress\n",
    "from IPython.display import display\n",
    "\n",
    "import perceval as pcvl\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from perceval.components.unitary_components import Unitary, BS, PS\n",
    "from perceval.rendering.circuit import DisplayConfig, SymbSkin\n",
    "\n",
    "DisplayConfig.select_skin(SymbSkin)"
   ]
  },
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   "source": [
    "## Grover's algorithm"
   ]
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   "source": [
    "We will now implement Grover's algorithm, firstly from a high-level picture (using unitaries) and then photonically (using Mach-Zehnder interferometers) in the same way that was done in the article."
   ]
  },
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   "cell_type": "markdown",
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   "metadata": {},
   "source": [
    "### Grover's algorithm in high-level picture"
   ]
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    "# Let's create a function that generates our circuit, given an angle xi\n",
    "\n",
    "def grover_circuit_unitaries(xi:float) -> pcvl.Circuit:\n",
    "    # Unitary to go from |00> to cos(xi)|10> + sin(xi)|01>\n",
    "    unitary_p = pcvl.Matrix(\n",
    "        np.array([[math.cos(xi), -math.sin(xi)], [math.sin(xi), math.cos(xi)]])\n",
    "    )\n",
    "    # Unitary for Hadamard gate\n",
    "    unitary_hadamard = pcvl.Matrix(1 / math.sqrt(2) * np.array([[1, 1], [1, -1]]))\n",
    "    # Unitary for environment interaction, that switches the phase of the good state\n",
    "    unitary_env = pcvl.Matrix(np.array([[0, -1], [-1, 0]]))\n",
    "    # Unitary of the reflection\n",
    "    unitary_reflection = pcvl.Matrix(\n",
    "        np.array(\n",
    "            [\n",
    "                [math.cos(2 * xi), math.sin(2 * xi)],\n",
    "                [math.sin(2 * xi), -math.cos(2 * xi)],\n",
    "            ]\n",
    "        )\n",
    "    )\n",
    "    \n",
    "    # We can now assemble our circuit\n",
    "    hadamard_component = Unitary(unitary_hadamard, \"H\")\n",
    "    circuit = pcvl.Circuit(4) // (1, Unitary(unitary_p, \"P\")) // (0, hadamard_component) // (2, hadamard_component) // (2, Unitary(unitary_env, \"env\"))\\\n",
    "              // (0, hadamard_component) // (2, hadamard_component) // (1, Unitary(unitary_reflection, \"reflection\"))\n",
    "    return circuit"
   ]
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    "pcvl.pdisplay(grover_circuit_unitaries(math.pi/3))"
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    "One step of amplitude amplification in Grover's algorithm should rotate our state from a $\\xi$ angle to a $3\\xi$ angle from the loosing state to the winning state. Hence we can check the validity of our Grover's amplification algorithm by inputting a photon in the spatial mode 1 and detecting at spatial mode 2. This should follow a $\\sin(3\\xi)^2$ distribution."
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   "source": [
    "xis = np.linspace(0, math.pi/2, 100)\n",
    "results = []\n",
    "for xi in xis:\n",
    "    circuit = grover_circuit_unitaries(xi)\n",
    "    backend = pcvl.BackendFactory.get_backend()\n",
    "    backend.set_circuit(circuit)\n",
    "    input_state = pcvl.BasicState([0, 1, 0, 0])\n",
    "    backend.set_input_state(input_state)\n",
    "    results.append(backend.probability(pcvl.BasicState([0, 0, 1, 0])))"
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(xis, results, \"-o\", label=\"Simulation\")\n",
    "plt.plot(xis, np.sin((3*xis)) ** 2, \"--\", label=\"Theoritical\")\n",
    "plt.title(\"Probability after Grover's amplification\")\n",
    "plt.xlabel(\"$\\\\xi$\")\n",
    "plt.ylabel(\"Probability\")\n",
    "plt.grid()\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ebd4183",
   "metadata": {},
   "source": [
    "### Designing the circuit with Mach-Zehnder interferometers"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "a46700fb",
   "metadata": {},
   "source": [
    "In the article they have used Mach-Zehnder interferometers (see below) to realize all the circuits.\n",
    "\n",
    "![mzi.png](../_static/img/reinforcement-learning_mzi.png)\n",
    "\n",
    "\n",
    "We want to perform the following unitary transformation (equation A.19 in the paper)\n",
    "\n",
    "$$U_{\\theta,\\varphi} = \\begin{pmatrix}e^{i\\varphi}\\sin\\left(\\frac{\\theta}{2}\\right) & e^{i\\varphi}\\cos\\left(\\frac{\\theta}{2}\\right)\\\\ \\cos\\left(\\frac{\\theta}{2}\\right) & -\\sin\\left(\\frac{\\theta}{2}\\right) \\end{pmatrix}$$\n",
    "\n",
    "However taking the MZI as shown and using the Rx convention for beam splitters yields the following matrix (see documentation [here](https://perceval.quandela.net/docs/components.html#beam-splitter)).\n",
    "\n",
    "\n",
    "$$ie^{i\\frac{\\theta}{2}}\\begin{pmatrix}e^{i\\varphi}\\sin\\left(\\frac{\\theta}{2}\\right) & e^{i\\varphi}\\cos\\left(\\frac{\\theta}{2}\\right)\\\\ \\cos\\left(\\frac{\\theta}{2}\\right) & -\\sin\\left(\\frac{\\theta}{2}\\right) \\end{pmatrix}$$\n",
    "\n",
    "To remove this global phase effect, we use phase shifters with angle $\\theta_2$ to be $-\\frac \\pi 2 - \\frac \\theta 2$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "9cc0419f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def mzi(name:str, theta:Union[float, pcvl.Parameter], phi:Union[float, pcvl.Parameter],theta_2:Union[float, pcvl.Parameter]) -> pcvl.Circuit:\n",
    "    # For the mzi to be in the right shape:\n",
    "    #   theta_2 should be set to '- pi/2 - theta/2'\n",
    "    #   however we cannot pass a symbolic expression to the input of PS\n",
    "    #   so we need to define a third angle theta_2 that we will set to '- pi/2 - theta/2' later on\n",
    "    return (\n",
    "        pcvl.Circuit(2, name=name)\n",
    "        .add(0, BS())\n",
    "        .add(0, PS(theta))\n",
    "        .add(0, BS())\n",
    "        .add(0, PS(phi))\n",
    "        .add(0, PS(theta_2))\n",
    "        .add(1, PS(theta_2))\n",
    "    )\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "79a8d2a1",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<defs>\n",
       "</defs>\n",
       "<path d=\"M10,25 L25,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M10,75 L25,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M37.9442,25.0002 C51.653800000000004,25.0002,51.5923,50.0,65.3019,50.0 M65.3038,50.0 C51.59219999999999,50.0,51.6538,74.9998,37.94409999999999,74.9998 M65.3038,49.99999999999999 L87.1884,49.99999999999999 M87.1884,49.99999999999999 C100.9,49.99999999999999,100.83840000000001,25.000199999999992,114.5481,25.000199999999992 M87.1884,49.99999999999999 C100.9,49.99999999999999,100.83840000000001,74.9998,114.5481,74.9998 M25.0,24.999999999999993 L38.0,24.999999999999993 M38.0019,74.9998 L25.0,74.9998 M112.6453,74.9998 L125.0,74.9998 M112.1944,24.999799999999993 L125.0,24.999799999999993\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
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       "<text x=\"102\" y=\"60\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M125,25 L145,25 M155,25 L175,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M140,35 L160,35 L160,15 L140,15 L140,35\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"150\" y=\"44\" font-size=\"7\" text-anchor=\"middle\">Φ=theta_t</text>\n",
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       "<path d=\"M187.9442,25.0002 C201.6538,25.0002,201.5923,50.0,215.3019,50.0 M215.3038,50.0 C201.5922,50.0,201.6538,74.9998,187.9441,74.9998 M215.3038,49.99999999999999 L237.1884,49.99999999999999 M237.1884,49.99999999999999 C250.9,49.99999999999999,250.8384,25.000199999999992,264.5481,25.000199999999992 M237.18839999999997,49.99999999999999 C250.89999999999998,49.99999999999999,250.83839999999998,74.9998,264.5481,74.9998 M174.99999999999997,24.999999999999993 L187.99999999999997,24.999999999999993 M188.00189999999998,74.9998 L174.99999999999997,74.9998 M262.64529999999996,74.9998 L274.99999999999994,74.9998 M262.1944,24.999799999999993 L275.0,24.999799999999993\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
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      ],
      "text/plain": [
       "<drawsvg.drawing.Drawing at 0x7fcd74680e80>"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_t = pcvl.P(\"theta_t\")\n",
    "phi_t = pcvl.P(\"phi_t\")\n",
    "theta_2 = pcvl.P(\"theta_2\")\n",
    "\n",
    "pcvl.pdisplay(mzi(\"test\", theta_t, phi_t, theta_2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f282446",
   "metadata": {},
   "source": [
    "#### Implementing the gates with MZI"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1227b4b9",
   "metadata": {},
   "source": [
    "##### Hadamard\n",
    "\n",
    "For the Hadamard, we want $\\theta$ and $\\varphi$ such that\n",
    "\n",
    "$$\\begin{pmatrix}e^{i\\varphi}\\sin\\left(\\frac{\\theta}{2}\\right) & e^{i\\varphi}\\cos\\left(\\frac{\\theta}{2}\\right)\\\\ \\cos\\left(\\frac{\\theta}{2}\\right) & -\\sin\\left(\\frac{\\theta}{2}\\right) \\end{pmatrix} = \\frac{1}{\\sqrt{2}}\\begin{pmatrix}1 & 1\\\\ 1 & -1 \\end{pmatrix}$$\n",
    "\n",
    "so we set $\\theta = \\frac{\\pi}{2}$ and $\\varphi = 0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "5edc592f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "$\\left[\\begin{matrix}0.707106781186547 - 1.11022302462516 \\cdot 10^{-16} i & \\frac{i \\left(-3.33066907387547 \\cdot 10^{-16} - 1.4142135623731 i\\right)}{2}\\\\\\frac{i \\left(-3.33066907387547 \\cdot 10^{-16} - 1.4142135623731 i\\right)}{2} & -0.707106781186547 + 1.11022302462516 \\cdot 10^{-16} i\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hadamard = mzi(\"H\", math.pi/2, 0, -math.pi/2 - math.pi/4)\n",
    "\n",
    "pcvl.pdisplay(hadamard.U)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5ce938e",
   "metadata": {},
   "source": [
    "##### Environnement\n",
    "For the environnement, we want a matrix of the form\n",
    "\n",
    "$$\\begin{pmatrix}e^{i\\varphi}\\sin\\left(\\frac{\\theta}{2}\\right) & e^{i\\varphi}\\cos\\left(\\frac{\\theta}{2}\\right)\\\\ \\cos\\left(\\frac{\\theta}{2}\\right) & -\\sin\\left(\\frac{\\theta}{2}\\right) \\end{pmatrix} = \\begin{pmatrix}0 & -1\\\\ -1 & 0 \\end{pmatrix}$$\n",
    "\n",
    "which gives $\\theta = -2\\pi$ and $\\varphi=0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "5a76c917",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "$\\left[\\begin{matrix}1.22464679914735 \\cdot 10^{-16} & \\frac{i \\left(3.67394039744206 \\cdot 10^{-16} + 2.0 i\\right)}{2}\\\\\\frac{i \\left(3.67394039744206 \\cdot 10^{-16} + 2.0 i\\right)}{2} & -1.22464679914735 \\cdot 10^{-16}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "env = mzi(\"U_E\", -2 * math.pi, 0, -math.pi/2 + math.pi)\n",
    "\n",
    "pcvl.pdisplay(env.U)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c740108",
   "metadata": {},
   "source": [
    "##### Preparation of state\n",
    "\n",
    "For the preparation of the state, we want a matrix of the form\n",
    "\n",
    "\n",
    "$$\\begin{pmatrix}e^{i\\varphi}\\sin\\left(\\frac{\\theta}{2}\\right) & e^{i\\varphi}\\cos\\left(\\frac{\\theta}{2}\\right)\\\\ \\cos\\left(\\frac{\\theta}{2}\\right) & -\\sin\\left(\\frac{\\theta}{2}\\right) \\end{pmatrix} = \\begin{pmatrix}\\cos(\\xi) & -\\sin(\\xi)\\\\ \\sin(\\xi) & \\cos(\\xi) \\end{pmatrix}$$\n",
    "\n",
    "which gives $\\theta = \\pi - 2\\xi$ and $\\varphi=0$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "30243876",
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_prep = pcvl.P(\"theta_prep\") # We will set it to pi - 2*xi later\n",
    "theta2_prep = pcvl.P(\"theta2_prep\") # We will set it to -pi/2 - pi/2 + xi = -pi + xi later as we cannot pass symbolic expression to the function mzi\n",
    "state_prep = mzi(\"U_p\", theta_prep, 0, theta2_prep)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6905688f",
   "metadata": {},
   "source": [
    "##### Reflection\n",
    "\n",
    "For the reflection, we want a matrix of the form \n",
    "\n",
    "$$\\begin{pmatrix}e^{i\\varphi}\\sin\\left(\\frac{\\theta}{2}\\right) & e^{i\\varphi}\\cos\\left(\\frac{\\theta}{2}\\right)\\\\ \\cos\\left(\\frac{\\theta}{2}\\right) & -\\sin\\left(\\frac{\\theta}{2}\\right) \\end{pmatrix} = \\begin{pmatrix}\\cos(2\\xi) & \\sin(2\\xi)\\\\ \\sin(2\\xi) & -\\cos(2\\xi) \\end{pmatrix}$$\n",
    "\n",
    "which gives $\\theta = \\pi - 4\\xi$ and $\\varphi=0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "a640d216",
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_ref = pcvl.P(\"theta_ref\") # We will set it to pi - 4*xi later\n",
    "theta2_ref = pcvl.P(\"theta2_ref\") # We will set it to -pi/2 - pi/2 + 2xi = -pi + 2xi later as we cannot pass symbolic expression to the function mzi\n",
    "ref = mzi(\"U_ref\", theta_ref, 0, theta2_ref)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f0e532b8",
   "metadata": {},
   "source": [
    "### Grover's algorithm with MZI"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3acb6e44",
   "metadata": {},
   "source": [
    "We now implement again Grover's algorithm with MZI implementation as a sanity check for the definitions of the gates we chose."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "5029c0f7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n",
       "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"\n",
       "     width=\"2320.0\" height=\"281.25\" viewBox=\"-28.0 0 1856.0 225.0\">\n",
       "<defs>\n",
       "</defs>\n",
       "<path d=\"M10,25 L25,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M10,75 L25,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M10,125 L25,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M10,175 L25,175\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M27,52 L373,52 L373,148 L27,148 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"29\" y=\"155\" font-size=\"8\" text-anchor=\"start\">U_P</text>\n",
       "<path d=\"M37.9442,75.0002 C51.653800000000004,75.0002,51.5923,100.0,65.3019,100.0 M65.3038,100.0 C51.59219999999999,100.0,51.6538,124.9998,37.94409999999999,124.9998 M65.3038,100.0 L87.1884,100.0 M87.1884,100.0 C100.9,100.0,100.83840000000001,75.0002,114.5481,75.0002 M87.1884,100.0 C100.9,100.0,100.83840000000001,124.9998,114.5481,124.9998 M25.0,75.0 L38.0,75.0 M38.0019,124.9998 L25.0,124.9998 M112.6453,124.9998 L125.0,124.9998 M112.1944,74.9998 L125.0,74.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"75\" y=\"88\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M97,103 L107,103 L107,113 L97,113 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"102\" y=\"110\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M125,75 L145,75 M155,75 L175,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M140,85 L160,85 L160,65 L140,65 L140,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"150\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=theta_prep</text>\n",
       "<path d=\"M125,125 L175,125\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M187.9442,75.0002 C201.6538,75.0002,201.5923,100.0,215.3019,100.0 M215.3038,100.0 C201.5922,100.0,201.6538,124.9998,187.9441,124.9998 M215.3038,100.0 L237.1884,100.0 M237.1884,100.0 C250.9,100.0,250.8384,75.0002,264.5481,75.0002 M237.18839999999997,100.0 C250.89999999999998,100.0,250.83839999999998,124.9998,264.5481,124.9998 M174.99999999999997,75.0 L187.99999999999997,75.0 M188.00189999999998,124.9998 L174.99999999999997,124.9998 M262.64529999999996,124.9998 L274.99999999999994,124.9998 M262.1944,74.9998 L275.0,74.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"225\" y=\"88\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M247,103 L257,103 L257,113 L247,113 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"252\" y=\"110\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M275,75 L295,75 M305,75 L325,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M290,85 L310,85 L310,65 L290,65 L290,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"300\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M325,75 L345,75 M355,75 L375,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M340,85 L360,85 L360,65 L340,65 L340,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"350\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=theta2_prep</text>\n",
       "<path d=\"M275,125 L295,125 M305,125 L325,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M290,135 L310,135 L310,115 L290,115 L290,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"300\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=theta2_prep</text>\n",
       "<path d=\"M25,25 L375,25\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M325,125 L375,125\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M377,2 L723,2 L723,98 L377,98 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"379\" y=\"105\" font-size=\"8\" text-anchor=\"start\">H</text>\n",
       "<path d=\"M387.9442,25.0002 C401.65380000000005,25.0002,401.5923,50.0,415.30190000000005,50.0 M415.3038,50.0 C401.59220000000005,50.0,401.65380000000005,74.9998,387.94410000000005,74.9998 M415.3038,49.99999999999999 L437.1884,49.99999999999999 M437.1884,49.99999999999999 C450.9,49.99999999999999,450.8384,25.000199999999992,464.5481,25.000199999999992 M437.1884,49.99999999999999 C450.9,49.99999999999999,450.8384,74.9998,464.5481,74.9998 M375.0,24.999999999999993 L388.0,24.999999999999993 M388.0019,74.9998 L375.0,74.9998 M462.6453,74.9998 L475.0,74.9998 M462.1944,24.999799999999993 L475.0,24.999799999999993\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"425\" y=\"38\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M447,53 L457,53 L457,63 L447,63 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"452\" y=\"60\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M475,25 L495,25 M505,25 L525,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M490,35 L510,35 L510,15 L490,15 L490,35\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"500\" y=\"44\" font-size=\"7\" text-anchor=\"middle\">Φ=pi/2</text>\n",
       "<path d=\"M475,75 L525,75\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M537.9442,25.0002 C551.6538,25.0002,551.5923,50.0,565.3019,50.0 M565.3038,50.0 C551.5922,50.0,551.6538,74.9998,537.9441,74.9998 M565.3038,49.99999999999999 L587.1884,49.99999999999999 M587.1884,49.99999999999999 C600.9,49.99999999999999,600.8384,25.000199999999992,614.5481,25.000199999999992 M587.1884,49.99999999999999 C600.9,49.99999999999999,600.8384,74.9998,614.5481,74.9998 M525.0,24.999999999999993 L538.0,24.999999999999993 M538.0019,74.9998 L525.0,74.9998 M612.6453,74.9998 L625.0,74.9998 M612.1944,24.999799999999993 L625.0,24.999799999999993\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"575\" y=\"38\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M597,53 L607,53 L607,63 L597,63 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"602\" y=\"60\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M625,25 L645,25 M655,25 L675,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M640,35 L660,35 L660,15 L640,15 L640,35\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"650\" y=\"44\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M675,25 L695,25 M705,25 L725,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M690,35 L710,35 L710,15 L690,15 L690,35\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"700\" y=\"44\" font-size=\"7\" text-anchor=\"middle\">Φ=5*pi/4</text>\n",
       "<path d=\"M625,75 L645,75 M655,75 L675,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M640,85 L660,85 L660,65 L640,65 L640,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"650\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=5*pi/4</text>\n",
       "<path d=\"M675,75 L725,75\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M25,175 L375,175\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M377,102 L723,102 L723,198 L377,198 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"379\" y=\"205\" font-size=\"8\" text-anchor=\"start\">H</text>\n",
       "<path d=\"M387.9442,125.0002 C401.65380000000005,125.0002,401.5923,150.0,415.30190000000005,150.0 M415.3038,150.0 C401.59220000000005,150.0,401.65380000000005,174.9998,387.94410000000005,174.9998 M415.3038,150.0 L437.1884,150.0 M437.1884,150.0 C450.9,150.0,450.8384,125.0002,464.5481,125.0002 M437.1884,150.0 C450.9,150.0,450.8384,174.9998,464.5481,174.9998 M375.0,125.0 L388.0,125.0 M388.0019,174.9998 L375.0,174.9998 M462.6453,174.9998 L475.0,174.9998 M462.1944,124.9998 L475.0,124.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"425\" y=\"138\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M447,153 L457,153 L457,163 L447,163 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"452\" y=\"160\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M475,125 L495,125 M505,125 L525,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M490,135 L510,135 L510,115 L490,115 L490,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"500\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=pi/2</text>\n",
       "<path d=\"M475,175 L525,175\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M537.9442,125.0002 C551.6538,125.0002,551.5923,150.0,565.3019,150.0 M565.3038,150.0 C551.5922,150.0,551.6538,174.9998,537.9441,174.9998 M565.3038,150.0 L587.1884,150.0 M587.1884,150.0 C600.9,150.0,600.8384,125.0002,614.5481,125.0002 M587.1884,150.0 C600.9,150.0,600.8384,174.9998,614.5481,174.9998 M525.0,125.0 L538.0,125.0 M538.0019,174.9998 L525.0,174.9998 M612.6453,174.9998 L625.0,174.9998 M612.1944,124.9998 L625.0,124.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"575\" y=\"138\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M597,153 L607,153 L607,163 L597,163 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"602\" y=\"160\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M625,125 L645,125 M655,125 L675,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M640,135 L660,135 L660,115 L640,115 L640,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"650\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M675,125 L695,125 M705,125 L725,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M690,135 L710,135 L710,115 L690,115 L690,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"700\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=5*pi/4</text>\n",
       "<path d=\"M625,175 L645,175 M655,175 L675,175\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M640,185 L660,185 L660,165 L640,165 L640,185\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"650\" y=\"194\" font-size=\"7\" text-anchor=\"middle\">Φ=5*pi/4</text>\n",
       "<path d=\"M675,175 L725,175\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M727,102 L1073,102 L1073,198 L727,198 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"729\" y=\"205\" font-size=\"8\" text-anchor=\"start\">U_E</text>\n",
       "<path d=\"M737.9442,125.0002 C751.6538,125.0002,751.5923,150.0,765.3019,150.0 M765.3038,150.0 C751.5922,150.0,751.6538,174.9998,737.9441,174.9998 M765.3038,150.0 L787.1884,150.0 M787.1884,150.0 C800.9,150.0,800.8384,125.0002,814.5481,125.0002 M787.1884,150.0 C800.9,150.0,800.8384,174.9998,814.5481,174.9998 M725.0,125.0 L738.0,125.0 M738.0019,174.9998 L725.0,174.9998 M812.6453,174.9998 L825.0,174.9998 M812.1944,124.9998 L825.0,124.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"775\" y=\"138\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M797,153 L807,153 L807,163 L797,163 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"802\" y=\"160\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M825,125 L845,125 M855,125 L875,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M840,135 L860,135 L860,115 L840,115 L840,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"850\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=2*pi</text>\n",
       "<path d=\"M825,175 L875,175\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M887.9442,125.0002 C901.6538,125.0002,901.5923,150.0,915.3019,150.0 M915.3038,150.0 C901.5922,150.0,901.6538,174.9998,887.9441,174.9998 M915.3038,150.0 L937.1884,150.0 M937.1884,150.0 C950.9,150.0,950.8384,125.0002,964.5481,125.0002 M937.1884,150.0 C950.9,150.0,950.8384,174.9998,964.5481,174.9998 M875.0,125.0 L888.0,125.0 M888.0019,174.9998 L875.0,174.9998 M962.6453,174.9998 L975.0,174.9998 M962.1944,124.9998 L975.0,124.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"925\" y=\"138\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M947,153 L957,153 L957,163 L947,163 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"952\" y=\"160\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M975,125 L995,125 M1005,125 L1025,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M990,135 L1010,135 L1010,115 L990,115 L990,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1000\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M1025,125 L1045,125 M1055,125 L1075,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1040,135 L1060,135 L1060,115 L1040,115 L1040,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1050\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=pi/2</text>\n",
       "<path d=\"M975,175 L995,175 M1005,175 L1025,175\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M990,185 L1010,185 L1010,165 L990,165 L990,185\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1000\" y=\"194\" font-size=\"7\" text-anchor=\"middle\">Φ=pi/2</text>\n",
       "<path d=\"M1025,175 L1075,175\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M727,2 L1073,2 L1073,98 L727,98 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"729\" y=\"105\" font-size=\"8\" text-anchor=\"start\">H</text>\n",
       "<path d=\"M737.9442,25.0002 C751.6538,25.0002,751.5923,50.0,765.3019,50.0 M765.3038,50.0 C751.5922,50.0,751.6538,74.9998,737.9441,74.9998 M765.3038,49.99999999999999 L787.1884,49.99999999999999 M787.1884,49.99999999999999 C800.9,49.99999999999999,800.8384,25.000199999999992,814.5481,25.000199999999992 M787.1884,49.99999999999999 C800.9,49.99999999999999,800.8384,74.9998,814.5481,74.9998 M725.0,24.999999999999993 L738.0,24.999999999999993 M738.0019,74.9998 L725.0,74.9998 M812.6453,74.9998 L825.0,74.9998 M812.1944,24.999799999999993 L825.0,24.999799999999993\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"775\" y=\"38\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M797,53 L807,53 L807,63 L797,63 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"802\" y=\"60\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M825,25 L845,25 M855,25 L875,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M840,35 L860,35 L860,15 L840,15 L840,35\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"850\" y=\"44\" font-size=\"7\" text-anchor=\"middle\">Φ=pi/2</text>\n",
       "<path d=\"M825,75 L875,75\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M887.9442,25.0002 C901.6538,25.0002,901.5923,50.0,915.3019,50.0 M915.3038,50.0 C901.5922,50.0,901.6538,74.9998,887.9441,74.9998 M915.3038,49.99999999999999 L937.1884,49.99999999999999 M937.1884,49.99999999999999 C950.9,49.99999999999999,950.8384,25.000199999999992,964.5481,25.000199999999992 M937.1884,49.99999999999999 C950.9,49.99999999999999,950.8384,74.9998,964.5481,74.9998 M875.0,24.999999999999993 L888.0,24.999999999999993 M888.0019,74.9998 L875.0,74.9998 M962.6453,74.9998 L975.0,74.9998 M962.1944,24.999799999999993 L975.0,24.999799999999993\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"925\" y=\"38\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M947,53 L957,53 L957,63 L947,63 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"952\" y=\"60\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M975,25 L995,25 M1005,25 L1025,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M990,35 L1010,35 L1010,15 L990,15 L990,35\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1000\" y=\"44\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M1025,25 L1045,25 M1055,25 L1075,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1040,35 L1060,35 L1060,15 L1040,15 L1040,35\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1050\" y=\"44\" font-size=\"7\" text-anchor=\"middle\">Φ=5*pi/4</text>\n",
       "<path d=\"M975,75 L995,75 M1005,75 L1025,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M990,85 L1010,85 L1010,65 L990,65 L990,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1000\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=5*pi/4</text>\n",
       "<path d=\"M1025,75 L1075,75\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1077,102 L1423,102 L1423,198 L1077,198 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"1079\" y=\"205\" font-size=\"8\" text-anchor=\"start\">H</text>\n",
       "<path d=\"M1087.9442,125.0002 C1101.6537999999998,125.0002,1101.5922999999998,150.0,1115.3019,150.0 M1115.3038,150.0 C1101.5921999999998,150.0,1101.6537999999998,174.9998,1087.9441,174.9998 M1115.3038,150.0 L1137.1884,150.0 M1137.1884,150.0 C1150.9,150.0,1150.8384,125.0002,1164.5481,125.0002 M1137.1884,150.0 C1150.9,150.0,1150.8384,174.9998,1164.5481,174.9998 M1075.0,125.0 L1088.0,125.0 M1088.0019,174.9998 L1075.0,174.9998 M1162.6453,174.9998 L1175.0,174.9998 M1162.1944,124.9998 L1175.0,124.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"1125\" y=\"138\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M1147,153 L1157,153 L1157,163 L1147,163 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"1152\" y=\"160\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M1175,125 L1195,125 M1205,125 L1225,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1190,135 L1210,135 L1210,115 L1190,115 L1190,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1200\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=pi/2</text>\n",
       "<path d=\"M1175,175 L1225,175\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1237.9442,125.0002 C1251.6537999999998,125.0002,1251.5922999999998,150.0,1265.3019,150.0 M1265.3038,150.0 C1251.5921999999998,150.0,1251.6537999999998,174.9998,1237.9441,174.9998 M1265.3038,150.0 L1287.1884,150.0 M1287.1884,150.0 C1300.9,150.0,1300.8384,125.0002,1314.5481,125.0002 M1287.1884,150.0 C1300.9,150.0,1300.8384,174.9998,1314.5481,174.9998 M1225.0,125.0 L1238.0,125.0 M1238.0019,174.9998 L1225.0,174.9998 M1312.6453,174.9998 L1325.0,174.9998 M1312.1944,124.9998 L1325.0,124.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"1275\" y=\"138\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M1297,153 L1307,153 L1307,163 L1297,163 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"1302\" y=\"160\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M1325,125 L1345,125 M1355,125 L1375,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1340,135 L1360,135 L1360,115 L1340,115 L1340,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1350\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M1375,125 L1395,125 M1405,125 L1425,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1390,135 L1410,135 L1410,115 L1390,115 L1390,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1400\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=5*pi/4</text>\n",
       "<path d=\"M1325,175 L1345,175 M1355,175 L1375,175\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1340,185 L1360,185 L1360,165 L1340,165 L1340,185\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1350\" y=\"194\" font-size=\"7\" text-anchor=\"middle\">Φ=5*pi/4</text>\n",
       "<path d=\"M1375,175 L1425,175\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1075,75 L1425,75\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1427,52 L1773,52 L1773,148 L1427,148 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"1429\" y=\"155\" font-size=\"8\" text-anchor=\"start\">U_REF</text>\n",
       "<path d=\"M1437.9442,75.0002 C1451.6537999999998,75.0002,1451.5922999999998,100.0,1465.3019,100.0 M1465.3038,100.0 C1451.5921999999998,100.0,1451.6537999999998,124.9998,1437.9441,124.9998 M1465.3038,100.0 L1487.1884,100.0 M1487.1884,100.0 C1500.9,100.0,1500.8384,75.0002,1514.5481,75.0002 M1487.1884,100.0 C1500.9,100.0,1500.8384,124.9998,1514.5481,124.9998 M1425.0,75.0 L1438.0,75.0 M1438.0019,124.9998 L1425.0,124.9998 M1512.6453,124.9998 L1525.0,124.9998 M1512.1944,74.9998 L1525.0,74.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"1475\" y=\"88\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M1497,103 L1507,103 L1507,113 L1497,113 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"1502\" y=\"110\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M1525,75 L1545,75 M1555,75 L1575,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1540,85 L1560,85 L1560,65 L1540,65 L1540,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1550\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=theta_ref</text>\n",
       "<path d=\"M1525,125 L1575,125\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1587.9442,75.0002 C1601.6537999999998,75.0002,1601.5922999999998,100.0,1615.3019,100.0 M1615.3038,100.0 C1601.5921999999998,100.0,1601.6537999999998,124.9998,1587.9441,124.9998 M1615.3038,100.0 L1637.1884,100.0 M1637.1884,100.0 C1650.9,100.0,1650.8384,75.0002,1664.5481,75.0002 M1637.1884,100.0 C1650.9,100.0,1650.8384,124.9998,1664.5481,124.9998 M1575.0,75.0 L1588.0,75.0 M1588.0019,124.9998 L1575.0,124.9998 M1662.6453,124.9998 L1675.0,124.9998 M1662.1944,74.9998 L1675.0,74.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"1625\" y=\"88\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M1647,103 L1657,103 L1657,113 L1647,113 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"1652\" y=\"110\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M1675,75 L1695,75 M1705,75 L1725,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1690,85 L1710,85 L1710,65 L1690,65 L1690,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1700\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M1725,75 L1745,75 M1755,75 L1775,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1740,85 L1760,85 L1760,65 L1740,65 L1740,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1750\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=theta2_ref</text>\n",
       "<path d=\"M1675,125 L1695,125 M1705,125 L1725,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1690,135 L1710,135 L1710,115 L1690,115 L1690,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1700\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=theta2_ref</text>\n",
       "<path d=\"M1075,25 L1775,25\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1725,125 L1775,125\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1425,175 L1775,175\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1775,25 L1790,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1775,75 L1790,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1775,125 L1790,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1775,175 L1790,175\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"1800\" y=\"28\" font-size=\"6\" text-anchor=\"end\">0</text>\n",
       "<text x=\"1800\" y=\"78\" font-size=\"6\" text-anchor=\"end\">1</text>\n",
       "<text x=\"1800\" y=\"128\" font-size=\"6\" text-anchor=\"end\">2</text>\n",
       "<text x=\"1800\" y=\"178\" font-size=\"6\" text-anchor=\"end\">3</text>\n",
       "<text x=\"0\" y=\"28\" font-size=\"6\" text-anchor=\"start\">0</text>\n",
       "<text x=\"0\" y=\"78\" font-size=\"6\" text-anchor=\"start\">1</text>\n",
       "<text x=\"0\" y=\"128\" font-size=\"6\" text-anchor=\"start\">2</text>\n",
       "<text x=\"0\" y=\"178\" font-size=\"6\" text-anchor=\"start\">3</text>\n",
       "</svg>"
      ],
      "text/plain": [
       "<drawsvg.drawing.Drawing at 0x7fcd744e7d90>"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit = pcvl.Circuit(4)\n",
    "circuit.add(1, state_prep).add(0, hadamard).add(2, hadamard).add(2, env).add(0, hadamard).add(2, hadamard).add(1, ref)\n",
    "\n",
    "pcvl.pdisplay(circuit, recursive=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "3d002e05",
   "metadata": {},
   "outputs": [],
   "source": [
    "results_mzis = []\n",
    "\n",
    "for xi in xis:\n",
    "    # Update values in the circuit\n",
    "    theta1 = math.pi - 2*xi #set the angle as explained above in 'Preparation of state'\n",
    "    theta_prep.set_value(theta1)\n",
    "    theta2_prep.set_value(-math.pi/2 - theta1/2)\n",
    "    \n",
    "    theta2 = math.pi - 4*xi #set the angle as explained above in 'Reflection'\n",
    "    theta_ref.set_value(theta2)\n",
    "    theta2_ref.set_value(-math.pi/2 - theta2/2)\n",
    "    \n",
    "    backend = pcvl.BackendFactory.get_backend()\n",
    "    backend.set_circuit(circuit)\n",
    "    input_state = pcvl.BasicState([0, 1, 0, 0])\n",
    "    backend.set_input_state(input_state)\n",
    "    results_mzis.append(backend.probability(pcvl.BasicState([0, 0, 1, 0])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "68692596",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fcd744bf0d0>"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(xis, results, \"-o\", label=\"Simulation (Unitaries)\")\n",
    "plt.plot(xis, results_mzis, \"-o\", label=\"Simulation (MZIs)\")\n",
    "plt.plot(xis, np.sin((3*xis)) ** 2, \"--\", label=\"Theoritical\")\n",
    "plt.title(\"Probability after Grover's amplification\")\n",
    "plt.xlabel(\"$\\\\xi$\")\n",
    "plt.ylabel(\"Probability\")\n",
    "plt.grid()\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f746dd6f",
   "metadata": {},
   "source": [
    "## Reproducing the results of the paper"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "630086db",
   "metadata": {},
   "source": [
    "### Classical circuit"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "8e07dd70",
   "metadata": {},
   "source": [
    "The classical circuit emulates the agent choosing a good action with probability $\\varepsilon = \\sin^2(\\xi)$. To this end, the operation $U_p |0_A0_R\\rangle = \\cos(\\xi)|0_A0_R\\rangle + \\sin(\\xi)|1_A0_R\\rangle$ is implemented putting the action state in a superposition with the corresponding amplitude. Then the interaction with the environment will make the second qubit switch only if the first qubit is in the state $|1_A\\rangle$, hence putting the reward qubit in the $|1_R\\rangle$ state.\n",
    "\n",
    "![classical_circuit.png](../_static/img/reinforcement-learning_classical_circuit.png)\n",
    "\n",
    "The detector D1, corresponding to $|0_A0_R\\rangle$, will click with probability $\\cos^2(\\xi) = 1-\\varepsilon$ and corresponds to no reward, whereas detector D2, corresponding to $|1_A1_R\\rangle$, will click with probability $\\sin^2(\\xi) = \\varepsilon$ and correspond to a rewarded action.\n",
    "\n",
    "Both operations $U_p$ and $U_e$ were already implemented as part of the Grover's algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "4fe0e455",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "     width=\"1007.5\" height=\"281.25\" viewBox=\"-28.0 0 806.0 225.0\">\n",
       "<defs>\n",
       "</defs>\n",
       "<path d=\"M10,25 L25,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M10,75 L25,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M10,125 L25,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M10,175 L25,175\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M27,52 L373,52 L373,148 L27,148 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"29\" y=\"155\" font-size=\"8\" text-anchor=\"start\">U_P</text>\n",
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       "<text x=\"75\" y=\"88\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M97,103 L107,103 L107,113 L97,113 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"102\" y=\"110\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M125,75 L145,75 M155,75 L175,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M140,85 L160,85 L160,65 L140,65 L140,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"150\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M125,125 L175,125\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M187.9442,75.0002 C201.6538,75.0002,201.5923,100.0,215.3019,100.0 M215.3038,100.0 C201.5922,100.0,201.6538,124.9998,187.9441,124.9998 M215.3038,100.0 L237.1884,100.0 M237.1884,100.0 C250.9,100.0,250.8384,75.0002,264.5481,75.0002 M237.18839999999997,100.0 C250.89999999999998,100.0,250.83839999999998,124.9998,264.5481,124.9998 M174.99999999999997,75.0 L187.99999999999997,75.0 M188.00189999999998,124.9998 L174.99999999999997,124.9998 M262.64529999999996,124.9998 L274.99999999999994,124.9998 M262.1944,74.9998 L275.0,74.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
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       "<path d=\"M290,85 L310,85 L310,65 L290,65 L290,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"300\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
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       "<path d=\"M340,85 L360,85 L360,65 L340,65 L340,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"350\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=3*pi/2</text>\n",
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       "<path d=\"M290,135 L310,135 L310,115 L290,115 L290,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"300\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=3*pi/2</text>\n",
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       "<path d=\"M377,102 L723,102 L723,198 L377,198 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"379\" y=\"205\" font-size=\"8\" text-anchor=\"start\">U_E</text>\n",
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       "<text x=\"452\" y=\"160\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M475,125 L495,125 M505,125 L525,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M490,135 L510,135 L510,115 L490,115 L490,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"500\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=2*pi</text>\n",
       "<path d=\"M475,175 L525,175\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M537.9442,125.0002 C551.6538,125.0002,551.5923,150.0,565.3019,150.0 M565.3038,150.0 C551.5922,150.0,551.6538,174.9998,537.9441,174.9998 M565.3038,150.0 L587.1884,150.0 M587.1884,150.0 C600.9,150.0,600.8384,125.0002,614.5481,125.0002 M587.1884,150.0 C600.9,150.0,600.8384,174.9998,614.5481,174.9998 M525.0,125.0 L538.0,125.0 M538.0019,174.9998 L525.0,174.9998 M612.6453,174.9998 L625.0,174.9998 M612.1944,124.9998 L625.0,124.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"575\" y=\"138\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M597,153 L607,153 L607,163 L597,163 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"602\" y=\"160\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M625,125 L645,125 M655,125 L675,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M640,135 L660,135 L660,115 L640,115 L640,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"650\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M675,125 L695,125 M705,125 L725,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M690,135 L710,135 L710,115 L690,115 L690,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"700\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=pi/2</text>\n",
       "<path d=\"M625,175 L645,175 M655,175 L675,175\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M640,185 L660,185 L660,165 L640,165 L640,185\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"650\" y=\"194\" font-size=\"7\" text-anchor=\"middle\">Φ=pi/2</text>\n",
       "<path d=\"M675,175 L725,175\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M375,25 L725,25\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M375,75 L725,75\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M725,25 L740,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M725,75 L740,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M725,125 L740,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M725,175 L740,175\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"750\" y=\"28\" font-size=\"6\" text-anchor=\"end\">0</text>\n",
       "<text x=\"750\" y=\"78\" font-size=\"6\" text-anchor=\"end\">1</text>\n",
       "<text x=\"750\" y=\"128\" font-size=\"6\" text-anchor=\"end\">2</text>\n",
       "<text x=\"750\" y=\"178\" font-size=\"6\" text-anchor=\"end\">3</text>\n",
       "<text x=\"0\" y=\"28\" font-size=\"6\" text-anchor=\"start\">0</text>\n",
       "<text x=\"0\" y=\"78\" font-size=\"6\" text-anchor=\"start\">1</text>\n",
       "<text x=\"0\" y=\"128\" font-size=\"6\" text-anchor=\"start\">2</text>\n",
       "<text x=\"0\" y=\"178\" font-size=\"6\" text-anchor=\"start\">3</text>\n",
       "</svg>"
      ],
      "text/plain": [
       "<drawsvg.drawing.Drawing at 0x7fcd73cae440>"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "classical_circuit = pcvl.Circuit(4)\n",
    "classical_circuit.add(1, state_prep).add(2, env) # circuit for classical strategy\n",
    "pcvl.pdisplay(classical_circuit, recursive=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d288dabc",
   "metadata": {},
   "source": [
    "### Quantum circuit"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "6fad7238",
   "metadata": {},
   "source": [
    "The quantum circuit performs a Grover's amplification step in order to get the state closer to a rewarded state. However, during this step, no reward is ever perceived and a classical round is still needed afterward to check if the state is rewarded or not.\n",
    "\n",
    "![quantum_circuit.png](../_static/img/reinforcement-learning_quantum_circuit.png)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "c3f95a3e",
   "metadata": {},
   "source": [
    "We will here, directly append the classical circuit (without state preparation) to the quantum circuit, so that the whole operation is done with one circuits. Note that we will count this as being 2 epochs to have a fair comparison with the classical strategy.\n",
    "\n",
    "![classical_quantum.png](../_static/img/reinforcement-learning_classical_quantum.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "c1a8c795",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n",
       "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"\n",
       "     width=\"2757.5\" height=\"281.25\" viewBox=\"-28.0 0 2206.0 225.0\">\n",
       "<defs>\n",
       "</defs>\n",
       "<path d=\"M10,25 L25,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M10,75 L25,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M10,125 L25,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M10,175 L25,175\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M27,52 L373,52 L373,148 L27,148 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"29\" y=\"155\" font-size=\"8\" text-anchor=\"start\">U_P</text>\n",
       "<path d=\"M37.9442,75.0002 C51.653800000000004,75.0002,51.5923,100.0,65.3019,100.0 M65.3038,100.0 C51.59219999999999,100.0,51.6538,124.9998,37.94409999999999,124.9998 M65.3038,100.0 L87.1884,100.0 M87.1884,100.0 C100.9,100.0,100.83840000000001,75.0002,114.5481,75.0002 M87.1884,100.0 C100.9,100.0,100.83840000000001,124.9998,114.5481,124.9998 M25.0,75.0 L38.0,75.0 M38.0019,124.9998 L25.0,124.9998 M112.6453,124.9998 L125.0,124.9998 M112.1944,74.9998 L125.0,74.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"75\" y=\"88\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M97,103 L107,103 L107,113 L97,113 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"102\" y=\"110\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M125,75 L145,75 M155,75 L175,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M140,85 L160,85 L160,65 L140,65 L140,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"150\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M125,125 L175,125\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M187.9442,75.0002 C201.6538,75.0002,201.5923,100.0,215.3019,100.0 M215.3038,100.0 C201.5922,100.0,201.6538,124.9998,187.9441,124.9998 M215.3038,100.0 L237.1884,100.0 M237.1884,100.0 C250.9,100.0,250.8384,75.0002,264.5481,75.0002 M237.18839999999997,100.0 C250.89999999999998,100.0,250.83839999999998,124.9998,264.5481,124.9998 M174.99999999999997,75.0 L187.99999999999997,75.0 M188.00189999999998,124.9998 L174.99999999999997,124.9998 M262.64529999999996,124.9998 L274.99999999999994,124.9998 M262.1944,74.9998 L275.0,74.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"225\" y=\"88\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M247,103 L257,103 L257,113 L247,113 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"252\" y=\"110\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M275,75 L295,75 M305,75 L325,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M290,85 L310,85 L310,65 L290,65 L290,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"300\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M325,75 L345,75 M355,75 L375,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M340,85 L360,85 L360,65 L340,65 L340,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"350\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=3*pi/2</text>\n",
       "<path d=\"M275,125 L295,125 M305,125 L325,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M290,135 L310,135 L310,115 L290,115 L290,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"300\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=3*pi/2</text>\n",
       "<path d=\"M25,25 L375,25\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M325,125 L375,125\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M377,2 L723,2 L723,98 L377,98 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"379\" y=\"105\" font-size=\"8\" text-anchor=\"start\">H</text>\n",
       "<path d=\"M387.9442,25.0002 C401.65380000000005,25.0002,401.5923,50.0,415.30190000000005,50.0 M415.3038,50.0 C401.59220000000005,50.0,401.65380000000005,74.9998,387.94410000000005,74.9998 M415.3038,49.99999999999999 L437.1884,49.99999999999999 M437.1884,49.99999999999999 C450.9,49.99999999999999,450.8384,25.000199999999992,464.5481,25.000199999999992 M437.1884,49.99999999999999 C450.9,49.99999999999999,450.8384,74.9998,464.5481,74.9998 M375.0,24.999999999999993 L388.0,24.999999999999993 M388.0019,74.9998 L375.0,74.9998 M462.6453,74.9998 L475.0,74.9998 M462.1944,24.999799999999993 L475.0,24.999799999999993\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"425\" y=\"38\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M447,53 L457,53 L457,63 L447,63 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"452\" y=\"60\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M475,25 L495,25 M505,25 L525,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M490,35 L510,35 L510,15 L490,15 L490,35\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"500\" y=\"44\" font-size=\"7\" text-anchor=\"middle\">Φ=pi/2</text>\n",
       "<path d=\"M475,75 L525,75\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M537.9442,25.0002 C551.6538,25.0002,551.5923,50.0,565.3019,50.0 M565.3038,50.0 C551.5922,50.0,551.6538,74.9998,537.9441,74.9998 M565.3038,49.99999999999999 L587.1884,49.99999999999999 M587.1884,49.99999999999999 C600.9,49.99999999999999,600.8384,25.000199999999992,614.5481,25.000199999999992 M587.1884,49.99999999999999 C600.9,49.99999999999999,600.8384,74.9998,614.5481,74.9998 M525.0,24.999999999999993 L538.0,24.999999999999993 M538.0019,74.9998 L525.0,74.9998 M612.6453,74.9998 L625.0,74.9998 M612.1944,24.999799999999993 L625.0,24.999799999999993\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"575\" y=\"38\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M597,53 L607,53 L607,63 L597,63 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"602\" y=\"60\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M625,25 L645,25 M655,25 L675,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M640,35 L660,35 L660,15 L640,15 L640,35\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"650\" y=\"44\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M675,25 L695,25 M705,25 L725,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M690,35 L710,35 L710,15 L690,15 L690,35\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"700\" y=\"44\" font-size=\"7\" text-anchor=\"middle\">Φ=5*pi/4</text>\n",
       "<path d=\"M625,75 L645,75 M655,75 L675,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M640,85 L660,85 L660,65 L640,65 L640,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"650\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=5*pi/4</text>\n",
       "<path d=\"M675,75 L725,75\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M25,175 L375,175\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M377,102 L723,102 L723,198 L377,198 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"379\" y=\"205\" font-size=\"8\" text-anchor=\"start\">H</text>\n",
       "<path d=\"M387.9442,125.0002 C401.65380000000005,125.0002,401.5923,150.0,415.30190000000005,150.0 M415.3038,150.0 C401.59220000000005,150.0,401.65380000000005,174.9998,387.94410000000005,174.9998 M415.3038,150.0 L437.1884,150.0 M437.1884,150.0 C450.9,150.0,450.8384,125.0002,464.5481,125.0002 M437.1884,150.0 C450.9,150.0,450.8384,174.9998,464.5481,174.9998 M375.0,125.0 L388.0,125.0 M388.0019,174.9998 L375.0,174.9998 M462.6453,174.9998 L475.0,174.9998 M462.1944,124.9998 L475.0,124.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"425\" y=\"138\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M447,153 L457,153 L457,163 L447,163 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"452\" y=\"160\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M475,125 L495,125 M505,125 L525,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M490,135 L510,135 L510,115 L490,115 L490,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"500\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=pi/2</text>\n",
       "<path d=\"M475,175 L525,175\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M537.9442,125.0002 C551.6538,125.0002,551.5923,150.0,565.3019,150.0 M565.3038,150.0 C551.5922,150.0,551.6538,174.9998,537.9441,174.9998 M565.3038,150.0 L587.1884,150.0 M587.1884,150.0 C600.9,150.0,600.8384,125.0002,614.5481,125.0002 M587.1884,150.0 C600.9,150.0,600.8384,174.9998,614.5481,174.9998 M525.0,125.0 L538.0,125.0 M538.0019,174.9998 L525.0,174.9998 M612.6453,174.9998 L625.0,174.9998 M612.1944,124.9998 L625.0,124.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"575\" y=\"138\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M597,153 L607,153 L607,163 L597,163 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"602\" y=\"160\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M625,125 L645,125 M655,125 L675,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M640,135 L660,135 L660,115 L640,115 L640,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"650\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M675,125 L695,125 M705,125 L725,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M690,135 L710,135 L710,115 L690,115 L690,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"700\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=5*pi/4</text>\n",
       "<path d=\"M625,175 L645,175 M655,175 L675,175\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M640,185 L660,185 L660,165 L640,165 L640,185\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"650\" y=\"194\" font-size=\"7\" text-anchor=\"middle\">Φ=5*pi/4</text>\n",
       "<path d=\"M675,175 L725,175\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M727,102 L1073,102 L1073,198 L727,198 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"729\" y=\"205\" font-size=\"8\" text-anchor=\"start\">U_E</text>\n",
       "<path d=\"M737.9442,125.0002 C751.6538,125.0002,751.5923,150.0,765.3019,150.0 M765.3038,150.0 C751.5922,150.0,751.6538,174.9998,737.9441,174.9998 M765.3038,150.0 L787.1884,150.0 M787.1884,150.0 C800.9,150.0,800.8384,125.0002,814.5481,125.0002 M787.1884,150.0 C800.9,150.0,800.8384,174.9998,814.5481,174.9998 M725.0,125.0 L738.0,125.0 M738.0019,174.9998 L725.0,174.9998 M812.6453,174.9998 L825.0,174.9998 M812.1944,124.9998 L825.0,124.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"775\" y=\"138\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M797,153 L807,153 L807,163 L797,163 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"802\" y=\"160\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M825,125 L845,125 M855,125 L875,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M840,135 L860,135 L860,115 L840,115 L840,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"850\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=2*pi</text>\n",
       "<path d=\"M825,175 L875,175\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M887.9442,125.0002 C901.6538,125.0002,901.5923,150.0,915.3019,150.0 M915.3038,150.0 C901.5922,150.0,901.6538,174.9998,887.9441,174.9998 M915.3038,150.0 L937.1884,150.0 M937.1884,150.0 C950.9,150.0,950.8384,125.0002,964.5481,125.0002 M937.1884,150.0 C950.9,150.0,950.8384,174.9998,964.5481,174.9998 M875.0,125.0 L888.0,125.0 M888.0019,174.9998 L875.0,174.9998 M962.6453,174.9998 L975.0,174.9998 M962.1944,124.9998 L975.0,124.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"925\" y=\"138\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M947,153 L957,153 L957,163 L947,163 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"952\" y=\"160\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M975,125 L995,125 M1005,125 L1025,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M990,135 L1010,135 L1010,115 L990,115 L990,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1000\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M1025,125 L1045,125 M1055,125 L1075,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1040,135 L1060,135 L1060,115 L1040,115 L1040,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1050\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=pi/2</text>\n",
       "<path d=\"M975,175 L995,175 M1005,175 L1025,175\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M990,185 L1010,185 L1010,165 L990,165 L990,185\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1000\" y=\"194\" font-size=\"7\" text-anchor=\"middle\">Φ=pi/2</text>\n",
       "<path d=\"M1025,175 L1075,175\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M727,2 L1073,2 L1073,98 L727,98 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"729\" y=\"105\" font-size=\"8\" text-anchor=\"start\">H</text>\n",
       "<path d=\"M737.9442,25.0002 C751.6538,25.0002,751.5923,50.0,765.3019,50.0 M765.3038,50.0 C751.5922,50.0,751.6538,74.9998,737.9441,74.9998 M765.3038,49.99999999999999 L787.1884,49.99999999999999 M787.1884,49.99999999999999 C800.9,49.99999999999999,800.8384,25.000199999999992,814.5481,25.000199999999992 M787.1884,49.99999999999999 C800.9,49.99999999999999,800.8384,74.9998,814.5481,74.9998 M725.0,24.999999999999993 L738.0,24.999999999999993 M738.0019,74.9998 L725.0,74.9998 M812.6453,74.9998 L825.0,74.9998 M812.1944,24.999799999999993 L825.0,24.999799999999993\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"775\" y=\"38\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M797,53 L807,53 L807,63 L797,63 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"802\" y=\"60\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M825,25 L845,25 M855,25 L875,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M840,35 L860,35 L860,15 L840,15 L840,35\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"850\" y=\"44\" font-size=\"7\" text-anchor=\"middle\">Φ=pi/2</text>\n",
       "<path d=\"M825,75 L875,75\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M887.9442,25.0002 C901.6538,25.0002,901.5923,50.0,915.3019,50.0 M915.3038,50.0 C901.5922,50.0,901.6538,74.9998,887.9441,74.9998 M915.3038,49.99999999999999 L937.1884,49.99999999999999 M937.1884,49.99999999999999 C950.9,49.99999999999999,950.8384,25.000199999999992,964.5481,25.000199999999992 M937.1884,49.99999999999999 C950.9,49.99999999999999,950.8384,74.9998,964.5481,74.9998 M875.0,24.999999999999993 L888.0,24.999999999999993 M888.0019,74.9998 L875.0,74.9998 M962.6453,74.9998 L975.0,74.9998 M962.1944,24.999799999999993 L975.0,24.999799999999993\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"925\" y=\"38\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M947,53 L957,53 L957,63 L947,63 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"952\" y=\"60\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M975,25 L995,25 M1005,25 L1025,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M990,35 L1010,35 L1010,15 L990,15 L990,35\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1000\" y=\"44\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M1025,25 L1045,25 M1055,25 L1075,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1040,35 L1060,35 L1060,15 L1040,15 L1040,35\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1050\" y=\"44\" font-size=\"7\" text-anchor=\"middle\">Φ=5*pi/4</text>\n",
       "<path d=\"M975,75 L995,75 M1005,75 L1025,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M990,85 L1010,85 L1010,65 L990,65 L990,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1000\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=5*pi/4</text>\n",
       "<path d=\"M1025,75 L1075,75\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1077,102 L1423,102 L1423,198 L1077,198 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"1079\" y=\"205\" font-size=\"8\" text-anchor=\"start\">H</text>\n",
       "<path d=\"M1087.9442,125.0002 C1101.6537999999998,125.0002,1101.5922999999998,150.0,1115.3019,150.0 M1115.3038,150.0 C1101.5921999999998,150.0,1101.6537999999998,174.9998,1087.9441,174.9998 M1115.3038,150.0 L1137.1884,150.0 M1137.1884,150.0 C1150.9,150.0,1150.8384,125.0002,1164.5481,125.0002 M1137.1884,150.0 C1150.9,150.0,1150.8384,174.9998,1164.5481,174.9998 M1075.0,125.0 L1088.0,125.0 M1088.0019,174.9998 L1075.0,174.9998 M1162.6453,174.9998 L1175.0,174.9998 M1162.1944,124.9998 L1175.0,124.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"1125\" y=\"138\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M1147,153 L1157,153 L1157,163 L1147,163 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"1152\" y=\"160\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M1175,125 L1195,125 M1205,125 L1225,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1190,135 L1210,135 L1210,115 L1190,115 L1190,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1200\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=pi/2</text>\n",
       "<path d=\"M1175,175 L1225,175\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1237.9442,125.0002 C1251.6537999999998,125.0002,1251.5922999999998,150.0,1265.3019,150.0 M1265.3038,150.0 C1251.5921999999998,150.0,1251.6537999999998,174.9998,1237.9441,174.9998 M1265.3038,150.0 L1287.1884,150.0 M1287.1884,150.0 C1300.9,150.0,1300.8384,125.0002,1314.5481,125.0002 M1287.1884,150.0 C1300.9,150.0,1300.8384,174.9998,1314.5481,174.9998 M1225.0,125.0 L1238.0,125.0 M1238.0019,174.9998 L1225.0,174.9998 M1312.6453,174.9998 L1325.0,174.9998 M1312.1944,124.9998 L1325.0,124.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"1275\" y=\"138\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M1297,153 L1307,153 L1307,163 L1297,163 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"1302\" y=\"160\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M1325,125 L1345,125 M1355,125 L1375,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1340,135 L1360,135 L1360,115 L1340,115 L1340,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1350\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M1375,125 L1395,125 M1405,125 L1425,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1390,135 L1410,135 L1410,115 L1390,115 L1390,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1400\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=5*pi/4</text>\n",
       "<path d=\"M1325,175 L1345,175 M1355,175 L1375,175\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1340,185 L1360,185 L1360,165 L1340,165 L1340,185\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1350\" y=\"194\" font-size=\"7\" text-anchor=\"middle\">Φ=5*pi/4</text>\n",
       "<path d=\"M1375,175 L1425,175\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1075,75 L1425,75\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1427,52 L1773,52 L1773,148 L1427,148 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"1429\" y=\"155\" font-size=\"8\" text-anchor=\"start\">U_REF</text>\n",
       "<path d=\"M1437.9442,75.0002 C1451.6537999999998,75.0002,1451.5922999999998,100.0,1465.3019,100.0 M1465.3038,100.0 C1451.5921999999998,100.0,1451.6537999999998,124.9998,1437.9441,124.9998 M1465.3038,100.0 L1487.1884,100.0 M1487.1884,100.0 C1500.9,100.0,1500.8384,75.0002,1514.5481,75.0002 M1487.1884,100.0 C1500.9,100.0,1500.8384,124.9998,1514.5481,124.9998 M1425.0,75.0 L1438.0,75.0 M1438.0019,124.9998 L1425.0,124.9998 M1512.6453,124.9998 L1525.0,124.9998 M1512.1944,74.9998 L1525.0,74.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"1475\" y=\"88\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M1497,103 L1507,103 L1507,113 L1497,113 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"1502\" y=\"110\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M1525,75 L1545,75 M1555,75 L1575,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1540,85 L1560,85 L1560,65 L1540,65 L1540,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1550\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=pi</text>\n",
       "<path d=\"M1525,125 L1575,125\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1587.9442,75.0002 C1601.6537999999998,75.0002,1601.5922999999998,100.0,1615.3019,100.0 M1615.3038,100.0 C1601.5921999999998,100.0,1601.6537999999998,124.9998,1587.9441,124.9998 M1615.3038,100.0 L1637.1884,100.0 M1637.1884,100.0 C1650.9,100.0,1650.8384,75.0002,1664.5481,75.0002 M1637.1884,100.0 C1650.9,100.0,1650.8384,124.9998,1664.5481,124.9998 M1575.0,75.0 L1588.0,75.0 M1588.0019,124.9998 L1575.0,124.9998 M1662.6453,124.9998 L1675.0,124.9998 M1662.1944,74.9998 L1675.0,74.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"1625\" y=\"88\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M1647,103 L1657,103 L1657,113 L1647,113 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"1652\" y=\"110\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M1675,75 L1695,75 M1705,75 L1725,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1690,85 L1710,85 L1710,65 L1690,65 L1690,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1700\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M1725,75 L1745,75 M1755,75 L1775,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1740,85 L1760,85 L1760,65 L1740,65 L1740,85\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1750\" y=\"94\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M1675,125 L1695,125 M1705,125 L1725,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1690,135 L1710,135 L1710,115 L1690,115 L1690,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1700\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M1075,25 L1775,25\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1725,125 L1775,125\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1425,175 L1775,175\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1777,102 L2123,102 L2123,198 L1777,198 Z\" stroke=\"black\" fill=\"lightblue\" stroke-dasharray=\"1,2\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"1779\" y=\"205\" font-size=\"8\" text-anchor=\"start\">U_E</text>\n",
       "<path d=\"M1787.9442,125.0002 C1801.6537999999998,125.0002,1801.5922999999998,150.0,1815.3019,150.0 M1815.3038,150.0 C1801.5921999999998,150.0,1801.6537999999998,174.9998,1787.9441,174.9998 M1815.3038,150.0 L1837.1884,150.0 M1837.1884,150.0 C1850.9,150.0,1850.8384,125.0002,1864.5481,125.0002 M1837.1884,150.0 C1850.9,150.0,1850.8384,174.9998,1864.5481,174.9998 M1775.0,125.0 L1788.0,125.0 M1788.0019,174.9998 L1775.0,174.9998 M1862.6453,174.9998 L1875.0,174.9998 M1862.1944,124.9998 L1875.0,124.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"1825\" y=\"138\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M1847,153 L1857,153 L1857,163 L1847,163 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"1852\" y=\"160\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M1875,125 L1895,125 M1905,125 L1925,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M1890,135 L1910,135 L1910,115 L1890,115 L1890,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"1900\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=2*pi</text>\n",
       "<path d=\"M1875,175 L1925,175\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1937.9442,125.0002 C1951.6537999999998,125.0002,1951.5922999999998,150.0,1965.3019,150.0 M1965.3038,150.0 C1951.5921999999998,150.0,1951.6537999999998,174.9998,1937.9441,174.9998 M1965.3038,150.0 L1987.1884,150.0 M1987.1884,150.0 C2000.9,150.0,2000.8384,125.0002,2014.5481,125.0002 M1987.1884,150.0 C2000.9,150.0,2000.8384,174.9998,2014.5481,174.9998 M1925.0,125.0 L1938.0,125.0 M1938.0019,174.9998 L1925.0,174.9998 M2012.6453,174.9998 L2025.0,174.9998 M2012.1944,124.9998 L2025.0,124.9998\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"1975\" y=\"138\" font-size=\"7\" text-anchor=\"middle\"></text>\n",
       "<path d=\"M1997,153 L2007,153 L2007,163 L1997,163 Z\" stroke=\"black\" fill=\"thistle\" stroke-linejoin=\"miter\" />\n",
       "<text x=\"2002\" y=\"160\" font-size=\"6\" text-anchor=\"middle\">Rx</text>\n",
       "<path d=\"M2025,125 L2045,125 M2055,125 L2075,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M2040,135 L2060,135 L2060,115 L2040,115 L2040,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"2050\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=0</text>\n",
       "<path d=\"M2075,125 L2095,125 M2105,125 L2125,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M2090,135 L2110,135 L2110,115 L2090,115 L2090,135\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"2100\" y=\"144\" font-size=\"7\" text-anchor=\"middle\">Φ=pi/2</text>\n",
       "<path d=\"M2025,175 L2045,175 M2055,175 L2075,175\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M2040,185 L2060,185 L2060,165 L2040,165 L2040,185\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"lightgray\" />\n",
       "<text x=\"2050\" y=\"194\" font-size=\"7\" text-anchor=\"middle\">Φ=pi/2</text>\n",
       "<path d=\"M2075,175 L2125,175\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1775,25 L2125,25\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M1775,75 L2125,75\" stroke=\"black\" stroke-width=\"1\" fill=\"none\" />\n",
       "<path d=\"M2125,25 L2140,25\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M2125,75 L2140,75\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M2125,125 L2140,125\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<path d=\"M2125,175 L2140,175\" stroke-width=\"1\" stroke=\"black\" stroke-linejoin=\"miter\" fill=\"none\" />\n",
       "<text x=\"2150\" y=\"28\" font-size=\"6\" text-anchor=\"end\">0</text>\n",
       "<text x=\"2150\" y=\"78\" font-size=\"6\" text-anchor=\"end\">1</text>\n",
       "<text x=\"2150\" y=\"128\" font-size=\"6\" text-anchor=\"end\">2</text>\n",
       "<text x=\"2150\" y=\"178\" font-size=\"6\" text-anchor=\"end\">3</text>\n",
       "<text x=\"0\" y=\"28\" font-size=\"6\" text-anchor=\"start\">0</text>\n",
       "<text x=\"0\" y=\"78\" font-size=\"6\" text-anchor=\"start\">1</text>\n",
       "<text x=\"0\" y=\"128\" font-size=\"6\" text-anchor=\"start\">2</text>\n",
       "<text x=\"0\" y=\"178\" font-size=\"6\" text-anchor=\"start\">3</text>\n",
       "</svg>"
      ],
      "text/plain": [
       "<drawsvg.drawing.Drawing at 0x7fcd743937f0>"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "quantum_circuit = pcvl.Circuit(4)\n",
    "quantum_circuit.add(1, state_prep).add(0, hadamard).add(2, hadamard).add(2, env).add(0, hadamard).add(2, hadamard).add(1, ref) #circuit for quantum strategy\n",
    "quantum_circuit.add(2,env) #appending directly the classical round (without preparation) at the end\n",
    "pcvl.pdisplay(quantum_circuit, recursive=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "367229cf",
   "metadata": {},
   "source": [
    "### Simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "318570c5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Simulation parameters\n",
    "N_AGENTS = 100 #number of agents that we simulate and average over\n",
    "N_EPOCH = 1000\n",
    "H_0 = 99\n",
    "H_1 = 1\n",
    "EPS0 = H_1 / (H_0+H_1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46ff0d04",
   "metadata": {},
   "source": [
    "#### Reward function\n",
    "First we define a reward function that takes as an input a circuit, output a sample state and returns True if it corresponds to a rewarded state (False otherwise)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "2369c08f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_reward(circuit: pcvl.Circuit) -> bool:\n",
    "    proc = pcvl.Processor(\"SLOS\", circuit)\n",
    "    proc.with_input(pcvl.BasicState([0, 1, 0, 0]))\n",
    "    sampler = pcvl.algorithm.Sampler(proc)\n",
    "    samples = sampler.samples(1)\n",
    "\n",
    "    # Take a random sample and check if it's the rewarded state or not\n",
    "    return samples[\"results\"][0] == pcvl.BasicState([0, 0, 0, 1])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae5b5de3",
   "metadata": {},
   "source": [
    "#### Classical strategy"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2aa85433",
   "metadata": {},
   "source": [
    "Below we gather everything defined above to run the purely classical strategy from the article."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5cdf619c",
   "metadata": {},
   "outputs": [],
   "source": [
    "eta_classical = []\n",
    "\n",
    "# Percentage bar\n",
    "f = FloatProgress(min=0, max=N_AGENTS)\n",
    "display(f)\n",
    "\n",
    "for agent in range(N_AGENTS): #Loop and average over all agents\n",
    "    f.value = agent\n",
    "    # Initialize initial score\n",
    "    h_0 = H_0\n",
    "    h_1 = H_1\n",
    "    eps = h_1 / (h_0 + h_1)\n",
    "\n",
    "    # Initialize circuit with initial probability and corresponding angles\n",
    "    xi = math.asin(eps**0.5)\n",
    "    \n",
    "    theta1 = math.pi - 2*xi\n",
    "    theta_prep.set_value(theta1)\n",
    "    theta2_prep.set_value(-math.pi/2 - theta1/2)\n",
    "\n",
    "    # Arrays of epsilon\n",
    "    eps_array = []\n",
    "    for i in range(N_EPOCH):\n",
    "        if get_reward(classical_circuit): #update policy if output state corresponds to a rewarded state\n",
    "            h_1 = h_1 + 2\n",
    "            eps = h_1 / (h_0 + h_1)\n",
    "            xi = math.asin(eps**0.5)\n",
    "            theta1 = math.pi - 2*xi\n",
    "            theta_prep.set_value(theta1)\n",
    "            theta2_prep.set_value(-math.pi/2 - theta1/2)\n",
    "            eps_array.append(1)\n",
    "        else:\n",
    "            eps_array.append(0)\n",
    "\n",
    "    eta_classical.append(eps_array)\n",
    "\n",
    "eta_classical = np.array(eta_classical)\n",
    "f.value = N_AGENTS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "413721c6",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.mean(eta_classical, axis=0)[::2], \".\", label=\"Fully classical strategy\")\n",
    "plt.xlabel(\"Even epochs\")\n",
    "plt.ylabel(\"$\\eta$\")\n",
    "plt.legend()\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ab3f4c9",
   "metadata": {},
   "source": [
    "Here we plot the proportion of agents that gets a reward. In the first epochs, the probability of getting a reward is small and few agents get some. However, once an agent gets a reward, they are more likely to get a reward in the future."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4e33516",
   "metadata": {},
   "source": [
    "#### Quantum strategy"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3235182e",
   "metadata": {},
   "source": [
    "Below we run the purely quantum strategy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "63cdbf11",
   "metadata": {},
   "outputs": [],
   "source": [
    "eta_quantum = []\n",
    "\n",
    "# Percentage bar\n",
    "f = FloatProgress(min=0, max=N_AGENTS)\n",
    "display(f)\n",
    "\n",
    "for agent in range(N_AGENTS):\n",
    "    f.value = agent\n",
    "    # Initialize initial scores\n",
    "    h_0 = H_0\n",
    "    h_1 = H_1\n",
    "    eps = h_1 / (h_0 + h_1)\n",
    "\n",
    "    # Initialize circuit with initial probability\n",
    "    xi = math.asin(eps**0.5)\n",
    "    \n",
    "    theta1 = math.pi - 2*xi\n",
    "    theta_prep.set_value(theta1)\n",
    "    theta2_prep.set_value(-math.pi/2 - theta1/2)\n",
    "    \n",
    "    theta2 = math.pi - 4*xi\n",
    "    theta_ref.set_value(theta2)\n",
    "    theta2_ref.set_value(-math.pi/2 - theta2/2)\n",
    "\n",
    "    # Arrays of epsilon\n",
    "    eps_array = []\n",
    "    for i in range(N_EPOCH//2):\n",
    "        if get_reward(quantum_circuit):\n",
    "            h_1 = h_1 + 2\n",
    "            eps = h_1 / (h_0 + h_1)\n",
    "            xi = math.asin(eps**0.5)\n",
    "            \n",
    "            theta1 = math.pi - 2*xi\n",
    "            theta_prep.set_value(theta1)\n",
    "            theta2_prep.set_value(-math.pi/2 - theta1/2)\n",
    "            \n",
    "            theta2 = math.pi - 4*xi\n",
    "            theta_ref.set_value(theta2)\n",
    "            theta2_ref.set_value(-math.pi/2 - theta2/2)\n",
    "            \n",
    "            eps_array.append(0.5)\n",
    "            eps_array.append(0.5)\n",
    "        else:\n",
    "            eps_array.append(0)\n",
    "            eps_array.append(0)\n",
    "\n",
    "    eta_quantum.append(eps_array)\n",
    "\n",
    "eta_quantum = np.array(eta_quantum)\n",
    "f.value=N_AGENTS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "6678e44f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.mean(eta_quantum, axis=0)[::2], \".\", label=\"Fully quantum strategy\")\n",
    "plt.xlabel(\"Even epochs\")\n",
    "plt.ylabel(\"$\\eta$\")\n",
    "plt.legend()\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc7ac058",
   "metadata": {},
   "source": [
    "Here we see a different behavior. With Grover's amplification, getting a reward is more likely in the first epochs. However, as the probability gets updated, one of Grover's amplification feature will manifest itself: we start to \"overshoot\" or rotate too much and we get past the winning state, and once we got past it, it is not possible to recover the winning state. We converge to a state with zero probability of getting a reward and nothing will get updated. This is why we need to consider an hybrid strategy."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eee6f816",
   "metadata": {},
   "source": [
    "#### Classical-quantum strategy"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dfe8e73e",
   "metadata": {},
   "source": [
    "We want to start with a quantum strategy, and then switch to a classical strategy when e start to overshoot. This happens when the probability of winning in the quantum strategy gets lower than the classical one.\n",
    "\n",
    "Due to normalization (and the fact that the quantum strategy takes twice as many epochs than the classical one), this corresponds to solve the equation\n",
    "\n",
    "$$\\frac{1}{2}\\sin^2(3\\xi) = \\sin^2(\\xi)$$\n",
    "\n",
    "The solution can be found numerically and gives a value of $\\xi = 0.6811$ which corresponds to $\\varepsilon=\\sin^2(\\xi)=0.396$.\n",
    "\n",
    "We then choose $Q_L$ to be the value where we switch from quantum to classical and the only requirement is $Q_L<0.396$. To follow [1] we will choose, $Q_L = 0.37$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "90a4acc1",
   "metadata": {},
   "outputs": [],
   "source": [
    "QL = 0.37\n",
    "eta_classical_quantum = []\n",
    "\n",
    "# Percentage bar\n",
    "f = FloatProgress(min=0, max=N_AGENTS)\n",
    "display(f)\n",
    "\n",
    "for agent in range(N_AGENTS):\n",
    "    f.value = agent\n",
    "    # Initialize initial scores\n",
    "    h_0 = H_0\n",
    "    h_1 = H_1\n",
    "    eps = h_1 / (h_0 + h_1)\n",
    "\n",
    "    # Initialize circuit with initial probability\n",
    "    xi = math.asin(eps**0.5)\n",
    "    \n",
    "    theta1 = math.pi - 2*xi\n",
    "    theta_prep.set_value(theta1)\n",
    "    theta2_prep.set_value(-math.pi/2 - theta1/2)\n",
    "    \n",
    "    theta2 = math.pi - 4*xi\n",
    "    theta_ref.set_value(theta2)\n",
    "    theta2_ref.set_value(-math.pi/2 - theta2/2)\n",
    "\n",
    "    # Arrays of epsilon\n",
    "    eps_array = []\n",
    "    i = 0\n",
    "    while i < N_EPOCH:\n",
    "        if eps < QL:\n",
    "            # Perform a quantum round\n",
    "            if get_reward(quantum_circuit):\n",
    "                h_1 = h_1 + 2\n",
    "                eps = h_1 / (h_0 + h_1)\n",
    "                xi = math.asin(eps**0.5)\n",
    "                theta1 = math.pi - 2*xi\n",
    "                theta_prep.set_value(theta1)\n",
    "                theta2_prep.set_value(-math.pi/2 - theta1/2)\n",
    "    \n",
    "                theta2 = math.pi - 4*xi\n",
    "                theta_ref.set_value(theta2)\n",
    "                theta2_ref.set_value(-math.pi/2 - theta2/2)\n",
    "                eps_array.append(0.5)\n",
    "                eps_array.append(0.5)\n",
    "            else:\n",
    "                eps_array.append(0)\n",
    "                eps_array.append(0)\n",
    "\n",
    "            # Update epoch by 2\n",
    "            i = i + 2\n",
    "        else:\n",
    "            # Perform a classical round\n",
    "            if get_reward(classical_circuit):\n",
    "                h_1 = h_1 + 2\n",
    "                eps = h_1 / (h_0 + h_1)\n",
    "                xi = math.asin(eps**0.5)\n",
    "                theta1 = math.pi - 2*xi\n",
    "                theta_prep.set_value(theta1)\n",
    "                theta2_prep.set_value(-math.pi/2 - theta1/2)\n",
    "\n",
    "                eps_array.append(1)\n",
    "            else:\n",
    "                eps_array.append(0)\n",
    "            # Update epoch by 1\n",
    "            i = i + 1\n",
    "\n",
    "    eta_classical_quantum.append(eps_array)\n",
    "\n",
    "eta_classical_quantum = np.array(eta_classical_quantum)\n",
    "f.value=N_AGENTS"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20a92f86",
   "metadata": {},
   "source": [
    "#### Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "957d52f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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nWZaLXaFAoSwzHhX3YkQy6b/z/ha1NxcTdKL8BLYe2Sp5jwKFWYdmwQCD5GmKc/BGlGdWwFDYg40rkYpVomkK//7tLhbqD4hk3UJXJZe6PcEBnAMOsH8HgG/Sga+vUSjPHginQAmDRmI+v2asglvraik4k4XZ6K5i3GxG99VmUOiY7ozn2j9XN4syAZGJEwiEhwZrSK1r2ofGTYPE2EReNl0KlCh+JdA10Kz82dwc5O6fyzlX6/VLFYkUSqMZpCTIpiTLcoG5NIxSccpex5NJZxVnIelUkqj99K7TZU+mskuysbV0q8kgYCaQmIkr4cJIoGcP1bAnSUJZNjcGRSjrzirOkjVuKKhQpesqGlMKmhbPzRw8VxMlkHUH7kb53cES65Ueh9kHlfMtXhZmRlLOvGYKm9ZlOgM5yAkOgUB4aLCG1Lo2fTDSXSYGIzIgUjbrrin5s7k5yN0/ffd0rdcvVSTSlDRaKEE2J1mWgys7ZmTSdq7S/XT26yzbj/a+tKtwUuQktFK3MiuPZuYS1VLPu8a8Z7sunce/f7vLk3lzZd1yrkoAWPr4x+ji3Qe/XtyOry7/W3T/X5H/wr37zlhzOBv60hYAAAevY3DyPyC7XqVQFA1DWTDKbo+GS/MNgnvyz9i5ZMjmw2FoqOKzxMAhEJooDZHSv7FjTmqtZM9qK9c2l/E4uyQbd0ruINQzFDGamBrNQUpqTYGCh4OHpJInrzQPWcVZbGyIqT0QSq4BgKr0E40nnBe3xIKLvYusZFkOmgYou2JjbIfeC25u93Hh3nXJ9ey7ehbX8jLROSCcje1hxg/1ELsKVZQKI9uMNP5dJFF/0KvgS/xoRgac4I8umjD2msZNg4Gt1VioPwAaYONQGIl7pq4UOQUeEEqwq8eikVtxDW0CPaC6LJakx7cxngp9s/MA8CDAt6qoAxz9/hDNz1KY/UWltyirsim3Ga13Mdu+oQp2EgOHQGiCNERKf1tATvbMSGSV7JmpPmrLifITmL9lPgyo3RxS7qRIZs2df3Q+7xrjLnvn8DtQUSoMaTkE269vN7kHQsm1HUXhg2GPwcHLWTIGR25/uWOZx2gQuDTfAJqm0MXrCby0Z3Z1Zl3OF6qBpvHT9STgevXT3LUEugZiuMtwbCvbJvkZ4O4b42oCAKegzTzp9teX/42vLlEY0uwNLBnwGvvM4Ss5oGnw4lIoUFh+rBg//9EMBhpwUMfz+mPgnh4x+Ya41cyZ9/f5fnew/c5KyZgXsWQbUFHi2Cau4ca4oIwnNxQq73H7M+7334V/SL5Xzs1+FUnEjWUd0kDDKK+f22Nug/ySRWTiRCZuk5B9lqemslw5muJeCyXONdkza8u1/9H9I5It12QOUmuRw1xCOlPjZ+pKkZFbgjA/VzYWhZkPNxuwqf39YdAPuFN8B+8cekc0j7k956Kjb0fcKb7DBv3WBik5fmZppsk5UqBQdG02aBpwa71E8pSEpilsGLgNXTRhyNSV4tElB0Db6UTtaZpC8bXZrOvKzu0iXEK+MxlQzJWam3p/hfJvlaoC7w3qApWqCl2DWyPAwxlpmdcw9YfzgEM+AGMCQQrAuyOc8fnfiSLDjukPFX74851nQNnrcCbnDGYemik7X5oGprZbjuEde4Gy1+FGwQ1cTb2KF4e8SGTiBAKh9jRESv/GgFKXHFfKrC3UAqjZnplyNVniHmTaXs0Xy3QNtAGbr2zGyLYjee4jrqya68bKKs7C3oy9il0/5rLtGmgD9mbsxYCwAQD4VbSD1C6i3DTMWhmZd4hHiOycmJggB3hJzqOlV0tE+EegtKq01sYNdy1PNH/C+LpSjcpiZ2RX2uF6Vi509FXJoGfKIRcqu2JZFxBF0Th1+xoAYH3qCdB2FUa3lCguxRivQuvdYajwe9DG9Jxp0PBx8QEANkuz1GeVomhQqgroS1oZ1wagg08EerXyZdvoKwpAqypgKA1jjSwawJ38StH+c/uj7HX4+dwfGBXdFd5OpiXfFAU4OxoefC5c4Ovoi7uqu6YXWYcQA4dAaGI0REr/hkape4nbjsGUlLkme2aJe1BqPkJWn12NL89+iaGthopcOnLyb2uy9MRSfHLiEwDguUvk9leoEDJ1SrT0xFJetl0GUTyRhfE6ptby6YlP0alyON761J4XR2TnoINba3Fsjp3zbTgG7JTtk6aBLdd/wSfnjoKiaKN8OnugZFyKc/BG1u1TnvO4WUm4VAVzqc8qtywCANhRFK80QvLVZCSmJsK1BS2o9A1sOJ0ikocz/TFutm/SaXybTuGtbm+ZfD9pmkLX4NbyC6pniEycQGhiWFJluSmgVLYtbMcgJ2WuyZ5ZIiGXm48UNGhsS98mOXcp+bcSuHJ1JeMzX2qm9ldK/mzulKg6rqW6cjd376U+z5X3+FLq6r9TkpJm7jUDDDhrvwW0nY7XRl+pRllmvEjO7hy4y7QbiQKuFafwZNJGyfUgTnVwsPfYNv6HUFUYwd4Tzluugrnws8qVpANG4+bD+M48t6GwOjtT6Zuy18EpcLeovEP53UEAwJN/06CRdCqJNXKEe0vTxngkbtB1Q0NOcAiEJojSKssNTW2VXqbcH0L3kiXVlC3dM2Yd+WX5knM5k3NGtM6aSKXl5r712lbJvmbFzIK/i79I+gyYNzzMjSm1v0r6HBr2LP6b8SvvGkUBpf+8AAB488k2iG0WC6B6X2ObxWLPyD04k3MGJ2/9gzV3MlBV+iBxnt4VhkpvTH+qBfq1a45vTm7HgWzTMmeu5JxLxb0YJA0bBZVjHvQVvsYyBArWJNU/aApT2ibB2cmAD3anSkivaVTeewQV+X1g55JhPIGhHbFwWFe00TjBCf44eVvsNjPQBgQ5t2E/q07wR3GxB1wdVSipMPBiogDgdOZVyersKsfc6rkK1mIoC5Z0szFjL47ZhPv0NRRW6nAztwjuDmo83a5XozJuAGLgEAhNFnNy5IamtkovUy4ZKfeSKVcHV8ps6Z6Zcw1xM+Ny12lN18umK5tE11SUCv1b9Gf/Lqx3JCV9Vorc/poLWqZpCj//EQjXcH47mqZAOejgFLALX12m8c0VsaJrSMsh+G/6f0GDhktQ9TrKM0eCKg+Fu4cOL+2aDQMtzkAsfs136TDYURRu5Trio106GGidpNtKCTQNOGt2YPXVXXgzag7oshYSLiuKLWtgKAthx+8X3g2Hr+RgTvI52HkdknAfAVO+0+LDYaEYFSOdRoBhU6oW7227BZdW0mPbe6SZ3BvhnCmoMOU7LfSVOjioT/KyF+vK30AXTbWarDFAXFQEAqHeqW1GYVPuHTn3ktDVYa59befBhfkNmrtOufkAlmeolYLJ5iudZXek0a1BK3dTMW4JU/srzNTMfY5xpVSVhaDsTjzHffOgTEDALvbL1EAbeC455rU4GNboRpky0BHLzyxm23Oz70rHuYg32I6iMGtgO3y06xIbmyPlthK6x0Q9cyXrMGD5mcWYPag9KrIEa+a4lRhmDWoHAJiTfA60nQ5OMu4xYXZkKZiM0/pKNe+9ZqqzD47QiNxTAFB5d5BxXlVqlHPmTEGFssxnoK801pkSZi/efmclzmZlyG9MA0BOcAgEQr1TW6WXnHtnVsws9G/RX7YPrutOKGW21jqESCmjmHVy52MPe+w4vAPuwW2xYl8+7N0vSmaonRUzC1H+UTh99zSWnlgqOy43m298m3g4VXbAtF/38So9VxW3RcIzAXB2y8UHxz4wuY6ljy+Fj7OPyf2SytR88maBaNwKXQwqi9uyxRml3CFKoSgafn53YMgQF62syO8JR59jEs+A56Ka93QHDO4SJJmlmXFb+fsU4W6+O6asvw77ovYilxO3by4G2oColnoc6vQuTt8ehWsFGfjPrgKRcQMAXYK92DnYyais2LmXqNnsyFJw11Kpi0HVg/1+o/cjGPVMBG6VnMPhveI9Xx4/FGqqw4Mg5Sdw+na1y27KemNyITmV2Knb1xqVm4oYOARCI8EWMw/XdM61VXpJPU+BMmncMCh1Q2UVZ7Fy56iAKF4eErbatXuwWTeTXObgcznneFLvyspKaJ20iG73BFZsP4zKKk9RhloKFKL8oxDhHwF/V398evJTRS66s1kZuJp/A6j0432xqvReiGv9KCh7HRYfXyy7DhWlQqR/JADgj4zjyLlfjr5hMZJfZho3DegqNW7kFoOuckPXYDXo0lbVgbb2Otg55sJQ6ceTNQvdIUpRUSqEuHUEBRWvojcFFfS67qC9j0kUkKx2w9hRFAZ3CUKQ2gV3C8tEtZfsKArRwWEIUrsg06UUKuo69KUtFBfFpEDhWl4m7lLu6BochujgMPznv2LDVUWBVT6pKBgNQokxmLmrAJ5SSogw4zRdZaz+3a91G1D2OuSX5YuyNqsoFaKCWkPjVi0vD1J3QKauFCcy8tn+jHMTu726Brfm/UzwdazupyEgBg6B0AiwxczDtZlzbbMBM88LVTspd1Kssm9CuTMFComxiQAgus6Vb7PuGKEr5YGRw80czMCsfWjYUABAkNqZzRRcnhkvUrK8tOsldq+5eyjsj9nL2Xu/ZrPeurSiUJ4Vj8p7MQK1jYtkX8zcE3olIOVOChJSEtjrX10ChjSbxsviC0hXGmfWo/I8zovbYOTKdJWat1YKKgxtNQT/Td8OGgY2O66D12lAYCwO0kzFhC+zYef5DK/vssxnQDmJXZ7GcZ8BXaXm7QEzb6Fxw1UkcbM4l2eOlMhGLMwCbHzPPjzxPusaWvjkq1gyMgKzN59jV0I92CdmHjSNB3syUpBBme/aOnwlh1elnIsw4zRgNCSf+3E5nIOqMzYzhgpNUxgUNFX0b5D7fjJLFb5fjILq2v1TeHlv9b/puT3mwhGOkvOrD0gmY5LJ2CZpSvts7czD1kZqr60159pkA84qzkLcr3Gi30Bru29ZxVkY8OsASSMFEBsvTEZext2VU5KDMTvHiE5t3u/5Pj489qFsvaYdw3fg5MGT7D4zmYLL7G7gzUOvymY4lsseDBhPbkbvHib6Tfu9zt+jX5u2IvcGt687xXdYNxMAyT3hZvEFwGbyNQiMhD9n90NOaTZe2jOcd8oizO7Lrd20+f8GIf6rXYBDLuvesnfQYdELHqDsSuDl5IUgl3YYsfxvdjzmeeZ0RpxNGCjJmAJDWXMsfz4SPVr5GU9mJOatAvDblFhEhoiT2zHvjZvbfVzIO4cb+TnwcVHj463lbIyKnUsGm/eGu96y9Nn438xnAAAnMwpAUUDXFt6y87Cz12HWCGfkFZXjm/00DJXVJ3DM3sq5qQDgzK0CjFiVYjwNspfKsAyU3R4NfWkLqPRevP6k5sOFOY376sU4dGymlvyZ8LbH2ySTMYHwsGKLmYfl5nwm54yiLMKMS0uJu0jODaYt1IqMBe6+CV1MzDPCfoT9y8md5ZQ0TEZeJtvv6bunJXPBlOvLTVbcTstKx1UdhUxdGUL9HNhMwccz003G8XBl58K1nbx9VTJWooLKQU6pGpvOXYC/czCeeGDscPuL8I9g92dvxl7J9VMUjYPXLqKo2B3ubkU4efuqMb8Mx2CBYy4OXAlGheouz7hhnufGwtBVavbvqRkFRmOBNsZ8GABUVarRwvkRNkNvSnou78uX+7yda7qkBJpSVQCg4OvuiJzSbOy+dhWOdIDoS5y21yH54iHklXWAs8oX4X5urBFyI7cYbo52KCp2x+PNn8ILnVyQkp4LfeUxdh603l1y72mHXGTklqBXK18Miaw2JFLSc5FfXCGah75KjS7ej4D2pvHVg/65hpypOBwAKK7Qs6dS0rEzAK13M+4daJzMKGDnJRWTxNujKjWqqtRwUflBW5gu+TMhT58n30EdQwwcAqGBscXMw3IS51mHZqG4sthsFmGlLi1Tz5jaN1MZdeWy/zLXY5vFSsqd5U5wAHG2XyEqSoXogGiT8Toztu5ERX4frLp4GIvjI1jXw995f0v2x3w+TO1RoeGGpAz46O00fHJuButeSNwXj0VPvSpyd5iTwNM0haTdBbBz+4x1V7i15haoNF5b/Pc3RqVUoLRcWYgdRSEmzBuOXqlw1PBdWmdvt2cNnHA/N5m63PJxIoYKP1CgsenyZvyRt5rt20Fdnd2XyeCbnElj8x3juPrCGDwTHYzfTt/mn/Q8cC/1aevPi3mRG5+pLM4gdAEJ18PNSqyiADvPVJ5r6GKRCr3wguT7w+yRudgZ7nswbeNpFFdUYVRMqGTleCHM/Ch76X+PvnYNF4dDZOIEQgNji5mHmTkLJcEGKMsirEQWbu4ZuX0DYDKjrlz2X+Y6AJHcmYnBkZJBc/uXM24SeiUgwj9CVhYOAI4Bu0DZ63gS4KziLCSdShK1ZSTgpvYoqzgLay5+Lsqh0t1rJI7kr+dn1Q1Kxnvb/uTJjqUk8PzswQ/iQQCRZNgpaLP4mii7b3U8yeAIDeweTJSJewn0KYezqN9kLN13zKQ82rjnxtOFiqx4UOBn/KX0avRvUcAaN9y+2ey+EuPSdjpsPnVb9GXPvF+A0dBh1sHEqQjX+07/njwXEGPcANWGjerBe8aNAQpSu2DO0CDR3JafWWzy3xETi2NHUaI9oaBChUCuzv38Bald8O7A9rJ9c+cn9e9xbo+5UKvEarH6gpzgEAiNAFvJPMwlvk08XO1dRVlylWYRNueGU/KM1L4dzzyuqIjk6bunZfuXkjszYzLXrxVcw+qzq02OI5StM/3uzdgrknhz3TV6mkZGbgnsXKVl6IwE3NQe0TQtDhimgHDvAJzUiV0neOA6Yb58pYs6AmV3nwBdoTEqiarUsq4g4bkKRdEwlAWj+Nps1r3CfLG+/EgY5g3pyKtOLvU+cl08QWoXo1JLtDvAihei4evuhDC/J0DZT+Jl/A1WO2L5jm9BSfQtn91XOvMxA/N+jYoJRZ+2/sjILcG1u/cxbytYeTaz3i7BXuxzUi4gGsBKdv78rMSR4VWgrsq7K+Xgzou7JyEeITiRbsDUDacl1xOkdkFEc+k1M9J67vyE/x59HX2x87J8Ha+6hhg4BEIjwRL5cmORk0cFREnKtfNK89hkdoBpd5JwPdyK2VJ9M64Z7nPcitpKMurKuYxUlArOds7YfWM3uz6phHYaNw0i/SPx1bmvTEqrpWTrGjcNBoQNEEm8aRqgDUbFicljf6jgBH9kFWchvyxfUoZ+LS8TdKWPpAw4QtMKv9wQuykgcJ1IvWc0DZ5xQ9nrQNkVSWS8FbvzuJl7uYaCvYMO9+gLoOzboFer6r0K9QwVzZ+mKaDCD9dy7iOvuBwuDiqRrFsFIMTHBZEh3sjUleJ6lj3cHFvjZn4JKKocwWpHhDv7gC6Vd9WYc+MI4bqRmNOWMD9XJGz7GwZuXBBFwdVRhZT0XIT7uUm6gLjzF1Ibdza/+rsL+7ns1qJUNAfueuTmKDRuGLg/xyorK83Oqy4hKiqiorJJHtZ9bgg5ubm9fv/P97EtfZvounB+wnbDWg1Dt8BuvPWYSs8P8OXapvZBKgaHgekjvk28aE6R/pE4m3NWNF5NqoEPazUMHzwmnzxP6lmulJiJh+G2Y90sFFipL7/sAivkZaXVjl5poCHeXyY2h6aN0vFFT5qLwaFA0zT7TJWOL4dm5lAt6T7FW1d5ZjwMhT0wIroZtpy+Az1Nw9ErlV2H/Pu4gJWKc6tgm0JFQTJeBg92aFRLPejQTOzI+pwnc668F4PNp26zMTjc2B/h3BkYN41w7zalakVS8HjOnJjYHQA8KTczf24cltx7Yq2fAZtStewcpNYjWguAJSOl58elLn5OW/L9TQwcYuDYJA/jPjeUnNzUXkvNiQszPwCidtSD/+SURUwbAKITCuFzUvuQVZyFQ/8cwgd/fSB6fu+zeyXnZGoNcnucVZyFMzln2HpTSp8DgHM550SScqnnzmZlIP7rbdCXy8ufy7JGwFmzVSxLzpiMz17qjGC1Gi/tekmwXmNByOEde8kqceTWJ4SRGxsqveEatkp0orMkZlN1wjxdKU7fzsCc1BcUvY9pmdeQV+CBuZv/qUWJUO6qaRya+TjuVeXh1O1r6BrcmpW6n7lVgBMZBfDyLMb9qmyEeobAReXHuosYibhccUtAWl5N4UEhSwkJ/d3CMlbKLbwn9b7UJr2CHMy6lK5HiUS9oQ0c4qIiEGyExignN1eqwFQ8iFxQrrCN1DVTsmmu6yrcM1wy2FhuTqbWILfHjLTclGRdjtKqUsm1pGVew8DWnBimu46oKjZm/ZWVP1OV0rJkVQXUVAeUVollvACNbuEekl9S1XJoJ9zJU5k0bpg50Ho3UKoK0Txo0PD3KeIlzDuTf1NyzzadPoVWnlEI8XZBcYUe4X5qDGz9GFLSc0HjH5NzUAIjsT6TGYahEZ3RRRPGyrTD/dwQGeLNcQ9FiJ7nu3qkkYutER4nMLEu1Sdx4nvm3EAMtXVdm1qX1HpMza+xQAwcAsFGaIxycnMVsbnzk2pnLlZGySkP046Rh3OP76d3nW5yz5RU81ayxzV9b6TjXKgH1aK1GBUTyroHGKSlvgDsSiSvq5xv4+ztexjeTfkcudJlgEkQZ7qUAjNWVWGkaB7CcRgXorgPCkm774GuOs151uiuuVdS+3gOruvp/VPfotI5AZX3uosyL5tzvZhDLm4FJmJdTMXBmKOuXddS67Fkfg0FkYkTCDZCY5STy8nFGbgVrad3nS7ZhrueYa2G8V4nxiZiejfp54TklOSIJNNJp5JYI4fpk9kzqf0c1mqYSB6uZI9r+t5IV/qOh75SjfeSz+PMrQJj+QDOM3SVGhV3B/L6oSjAye8gynP78k4CKApwCtiFpfuOga5SK5qjULrMjGmUPMuvhRkLAE8eLRyHkZ9LZUWWqrBtoIE5m8/ho92X5AeXgCs9ByCSf9MPUhq8t+3P6tw1tPkq3UrgSrMBozGweGSE6BpXAi53zxw1ScFgjfUonV9DQk5wCAQbor7l5FnFWTiZeRLnKs6hW0k3NFc3l5yTlFwc4Fe07uTbSXSfBo2lffhVql9o9wJO3z2NUI9QuDq4wtXe/G+JNGhsvbZV0oXXzL0ZPur9EShQPLk3M3dudfHSqlK80O4FXpkCpj3jsmEy2krtg/C94boNAOlClXKVvvU0jf0X70omWZsS2xffpO/iXaMoGtC7ioozMtLqkxkF6BU2CB927wA7x7wHRRWr94JZn1Q2XcBYkZo2OMlW0WbGUjnm8qpXT+39CHoFVLt6TmdelTw1K7v9AqruR0r2awAks/ktHN4J5VUGLNpxUXSPKz13dVTh4M2j+CZd7A6EQy7woPwBk3n59O1wBKk7yK6TwdRngi/NdgVlr4O2UIvf3uyI4mIPUayLsL1S46G+XNc1nV9DQgwcAsHGUConry1CJdLPW36WVRRJycWFbgk5N06kf7URIaUsYtxU5uJ1Nl3ZJHn9nUPvyKp0AON+ptxJMXnEL1VAUsqNwX1vuGsRzl9YqLJrcBiv4rZx3cDKA9dEY9hRFPq17og118WuLX1pmKzE+Y2fjG4fGswaKjAqRrw+qWy6DPrSFibfC8ZNpS9pxcrBl+/Jwcq9B1jF0Lw//gvHAHF2ZX1pmGSfgLx756mOgQCAD3delHSfcONKAn264tt0oaReBVQaA7e57qvZqd+gzEFePQco+0ww40u5kHqpxX0rie8RUp+u65rMryEhLioCgSAiqzhLJLOmQcsefStx0ZhrI5U5lxmXac/8n+vKMocwg7GlWZaFLhslbgxhn+KEdcD2OytxNisDgPGLY9HwjmzyOWZlQjNCRQEfxhsDY7l7SUGFiqx4GMpCUJEVz/bAdfvQnP64a5DKpitnStJVapRlxsvuPeOmoux1vOuMm+m9bX/CMWC3KLty+d1BItcUg7XcO8zcuZmFyzKfwaTHukq4r+Q/64Bln4m6diE1Rtd1Y4Gc4BAIBBFyBSdNHX0rcZ+ZamNKkSXlynoj+g3JjMCmqEmW5ZooSMypywCjO+fU7Wusq+q5bs1RqT2LVlGP4F6ZXpRdFjBm6B0S2QyAeC/pKjUvU+3Paafxn10FsoYDV8FjqtaQkIp7MUgaNgr+PkXIK80TuSYpisa4Pm5Yd4D/nAGAnYN0sUdDWTDv2rQnWuPJDgEiGbaci0SJ++RGbjEq7sWgsoifWdjb1VGyCKWpz7oln4n6cCHZYib0+oAYOARCA2GprFOqvakswKVVpez/LZWOymUDZjL9Hs88LtmnEveZXBupzLUMFChE+hvjM7SFWrYfqYzAppA6upcal9vOlIJE7j00py4DjCcIXYNb8655OQE9w32QW1IlOWa3MG9eNeviCnuE+3WGxq1afm3EBc917ouk7QdkT2NMKXgAJgmg+DkVgGAPDSI13sgqzpJ0j/QJb4/vqGuiDMN0pflij3YUhSc7BKC4Qg83RzvcyC1m12bKRWLOfcK+j4LMwjFh3oDEvEy5eSxRFdWFC0kq9of778pcvNjDAjFwCIQGwFJZp1R7ALJZgIVYKh3VuGmMxSU5bioKFIa0HMImi7O2HDXlTorJOJuVp1fyshwzYyf0SpDNJsxNFCh3dC8cV6icYlwgwkyvR+/ukn0PGbeBXAwOkzmXOb0RIjfm4Ss5IoWTqfgPbh+UcXGgabEbZ3F8BC9TrXGO0kaOAcAzq1LYMRN6JfCyDZfceQYTvr3G68uOojAiuhmSTxkVVsIswdCree2eWZWiaI2WwOwHN27mw/jOiAzxxofDHsO8/fFs5XIKpt08cu+PXM4a7mehti4kc7E/SuPFHgZIJmOSydgmseV9tjQjsVR7pflhuNQk63FWcRZOZZ7CqdOn8HTvpzF+7/g6yaRsLiOyFNyxmcyuznbOKNOXsf9nfkuWO7qX29u9z+6VlE9zFTFK3kNuxlkAOJiRipz75Xg8rLvIuJH6THPHBCDKJstgKqussA8pN06mrhSxi8WnPRSAz0ZHw9lBhYnrT0pm2gWAxz75DXDgF9Bk9wXA1+O64bX1J3l5dbhuIhWAlaOj0dzbRWTcKFmjJWhz7+PnnX/g+cH9EOrnwduD07czoJJQmMlhKvuvEGtkHzaXUbimGYfrCpLJmEB4yLDUJy/VXkkWYCFK/f5Ct0v/Fv1R+XclSqtKTc7blLvsdtFtANLFK+XWaMl65Nxe5tyAaXfTJPdWap9yK67hatlpuFdEo7TE9F4wCOf1QqehAMBmzjW6mfQI93ODnyv/x7HQzbD97B3ZWBlTMUFC141cfIpU1zQAHzcnk5l2adDQV6pZqbUQA4A/LuWI8upwC24aHoxTXKGv0RotIUjtjDZqGkFqZ8F1F0XScPEzyuZTU/Vjpq4UJzLyQT0IojYV+2OrGYfrCmLgEAj1jKU+ean2NT3BMef3l3KFDQ0zfimHekjHlZzPPY9b928pcpfJFa9UErMixfnc87xK4ubWIlWQU4jUPgmLcvZv0b/GcRXCLMHGZ4FFwzvCTaINUzgy+dRtk/2evX0PvVr5mh1finA/N0lpuIqC2Uy729LumO3/h2Nak/fNxQMJ2zwsCItcAmIJv7nK3w/jvjEQmTiBUM9YKuuUap8Ym4iEWHEWXjn5rhK/v5ycNbskGwAQ6BoomY34Pyf/gwUp/Oe2pW+TNFbk5LdyWYW5r/u36C/qL+lUkqTc1pw0Vy6brtQ+ncs5J6qWvu/mPkzoPMFiaa5UlmDj/IC5Wy/gXjmQqSsTSZA3n7pt9rzu412Xa5yBN0jtgiUjI3j5qKkH8RumpNgAJDMMS+e15t9npOKmJN8MtpI515pk6kpFxg2DSmLvANvNOFxXkBMcAqEBsFTWKddeeO2N6DdkY1HMjWHKdcYgl43YEneZnKtMao3MekI8QqAt1GLfzX2K+jLnBpRziX3c52PEhcXxrp2+K5ZrA4C3szf2jNxjUVyFlAuhen5AThmFm3klFsm2GWrrimCk1iczCkBRQNcW3mal2CnpuZJzXfliNLIKyyQzDM97ugMGdwkCIB0PxB3HVMXupo4pt+HKF6Lh6+4kuS+2mHG4riAGDoHQQJjyyUvFjki1F15j/i4Xd2IqJkXOdeZs74zrldeRXZINF3sXSfm4kkzD3LZCqTl3XjGaGGQVZ7H3uS4opW4h2bU8GNfF3kU2q7KoLw9pBUpz1w64nmWUadNVYKtRC79QeNXN/dSyLhgVBfg702jh6yrbhm0LiDL7qgCUVFTy5qFULsxtx+TZMdWG6cvN0U6ktGLk7HcLyyTvDe4SxDtxkMLWMubWBabcht3CvE3uD9k/I8TAIRAaGbWpDGzqWXP9SslZh7QcgvF7xsMAA9ZuWQuAn5WXK8PmXjNl7NCgMWbnGFa6zY3XkXrNzNMSua3cWrgSd6lxhH0xeyYkQv0kJnyZDQOdzbpjqksgVMtypfZ8cXx3Vl7MYEdRWDi8A9yyzyJI7cyTIAvhuoe4bQwAJnx3EkB13M5vp2+blQsrkRVLtQFgLAQqMGC4cnape+SLVxmM25DrpuK6DQnmITJxIhO3SZrqPlsqIVf6LADF/XIl14xBIEdtT3OUIJynJXJbU2tRUSr8MOgHWReenHR9wSOfYua6StkTFkaWa0pKzmQd5rpg/FzteZ/pM7cKMGJViihZ3m9TYhEZ4g0Akm3kkJILK5EVS7WRO0H6bUosAjydJdtz592Q2NrPjkxdqazbsLFDZOIEAoGlNmnd5Z49k3MGVwvEFZyF/QrdRLtv7DarapIyZKxp3AjnaXST8LP3moJx4R3PPC65/jJ9mawKSy5OR1ekMuk+0tM0TmYUICDgH8kx0zKvwZNqz3P1ZOpK8df1fNwrr25bXKGXTLJXUmEw2cbUvJgYHVOVw4WxPFJxQ1LVvZm5ybXnztsWaajswEFqFwyJtB2jpjFBDBwCoREhJ5c2JYc29SwFiq2mLYQbvyJ0pQxpOQT/Tf+vyfGkpOo1ka+bg5lnbTK01iRdvtQzNE0h/54HVFS5SSNn2sbTmDM0SOL9UGHKd1roK3UiV4+xkrcdHEL/wehHwhVJfqXayME8KyVTF8KVnEuNIVfd25yk3FYh2YFtEyITJxAaERo3jaQUW04OLXyWX2GaklU4cWNOpCTV29K3SbqemJgbOam68JrUs8J+hHJw4euEXgmgq9QWV/Q2tTdKZN0aNw3ejJzDqz5dnhmPVb/n4d1B7VkprpQk2kADS/6bhTcj5/DGLMt8xpgUD9UVtvmVvCnM3XoBmbpSRZJfOVm1EG7cjjnjBuBLzqXmYY3q3rZCTarJExoHjeIE5/PPP8fSpUuRlZWFyMhIrFy5Ej169JBtn5SUhC+++AJarRZ+fn549tlnsXjxYjg7O8s+QyBYE0sLZVrSj5QUW4mbKqs4C83dm7NxJVKVnhn+L+L/ENssFoDyLMJLHl2CrkFdeaUHtIVayTgWRu4tVzKB+3ehHFzqtZQcWcrlIuc+yNSVQqPqg+8HbEU5chTLutu7P4XiawbYuWQAoKAvbQGaptEl2At/zu7HSnFP3iwQVf/W0zQMhT3YMa/844j3L/zDayPp6qHBrkuJ5Jdps+NspllZtqlsyMK57zibiacfKJ7k5lGb6t62AskObLs0uIGzadMmzJgxA6tXr0bPnj2RlJSEuLg4XL58GQEBAaL2GzZswOzZs7FmzRrExsbiypUrGD9+PCiKwrJlyxpgBYSHjdqonJT0UxN3ilRfsc1iZQN+V59dja/OfYWEXgnQlevMzpUChS7+XdiYFqnxuC40OQm8lKRdqr3wtSl3TU2KD8bEKDNKw/3c4OB+hS3CSNMUKrLiEeb3BE+Ke7tAOpvvoh0XOZmI/5FsI3L/cLIHA8okv0FqFzzdJQgf7rwo2qPBXYIki3SaY9GOi/hw50V2P6XmUZvq3rYCyQ5suzS4iqpnz56IiYnBZ599BgAwGAwICQnBG2+8gdmzZ4vaT506FRcvXsT+/fvZa2+//TaOHTuGP//8U3KM8vJylJdXR+8VFhYiJCQEubm5daKi2rdvH/r3728TEfq2SkPtc3ZJNp7e8jQvxkRFqbBj+A4EugZarZ8t6Vuw6Pgi1oCY22MuRrQaYXFfRzOP4t/H/i07DymZNwA8FfIUDvxzgB1/mPMwzBkyBw4ODlbbA0v55eQ/mLv1AmuoLBreEY+19kPfTw+LDISDb/dBkNoZmboyk/fNkV2SjcFbBgtk8CrsHFG9VqkxlEJRwDsD2uCTvVcfxODQ+PfQ9nihRwvLO4PyPapeC9gK43JYsl+2QE1+dkjt63PdmtfxTG2fuvg5XVhYCD8/P0UqqgY1cCoqKuDq6opff/0VI0aMYK+PGzcO9+7dw9atW0XPbNiwAZMnT8bevXvRo0cPXL9+HU8//TRefvllvPfee5LjJCYmYsECcS6LDRs2wNWVWOEE5VyvvI41xWtE1191exUtHVpatR+dQYc8fR587XyhVkkXMlTS17mKc9hUsknx3Jhnfe18Jce31h7UhHvlxmy//s40vJyAqzoKn12wE7Wb2lGPNmra7H1zKFmr3BhKmdpRD39nmreu2qB0j0a00CPa17gHOWUUHFU0rt+nsOVmzferKSPcV0LDUFJSgtGjRzd+mXhubi70ej0CA/m/9QUGBuLSJXF9EwAYPXo0cnNz8dhjj4GmaVRVVWHSpEmyxg0AzJkzBzNmzGBfMyc4AwYMICc4NkpDnuCs27JOdHrxXP/nRKcX2SXZ0N7XItQjVPKe0n5qO6duJd3wy5ZfZJVNQjcWBQpduneBi70LnvB4Aj4OPvh1z68Iiw5DS++W6IZuVpu7cB1y+yVHpq4Mqy6KT2ieH9yPPcExd/9mXgla+LryTiiY6y50W1DH1oEWrPXxnsNQXOIOF0c7oKAUqotna3SCo6KAvr1jUVqhR2+1A84d+5+iz7TcvOXaSu3BjOf6iZ7N1JVhm8SJF7NfTQHyM7r+qKsTHKU0eAyOpRw8eBAffvghVq1ahZ49e+LatWt48803sXDhQsybN0/yGScnJzg5iU1uBweHOvuA12XfhGrqe5+bq5sjIVacTbe5mn9cbS5OR2k/1piT8L4QGjTPyKFBY/qh6QCMX+ZPhz2N7YXbQR+i2b6tNXeGmsY1hfo58LL+MoqdUD8Ps/flYneEMmoH9TNwCjLG4KgoFQZppuLZVZd4RgBTPJKmjfEZI6KbIVlQIFOqbMGI6GZ4/qtj7ByeD6cw2Mxn2lLJsrk9qmlbW4f8jK4/rLnXlvRjcy6q3r1745FHHsHSpUvZaz/88AP+7//+D0VFRVCpzCvfSSZj26eh99lUNl1LshFbkpW3NnNi7p/JOYOZh2ZKPq80AzE3O7I15l6b7M0MmbpSk4od4X25DL7Jk3vhmVUpotMYyl4He6c8fPnCAExcc026lhSAlaOj0bWFMVuvVDbflaOj0dzbBSUVBrg6qkRjUaBxaObjsgaFkszDNd2jmra1NRr6Z8fDRENnMm7QPDiOjo7o1q0bL2DYYDBg//796NWrl+QzJSUlIiPGzs7oM34Iq04Q6hmmCCQAxGhieFmAj2ceZ2Xf5qpyM2jcNLx+lI4vzInDjGvK2NC4aeDtJJ8qX2kGYq5k3ZK5y2HJfskRpHZBr1a+vMzAKem5vFwu3Pty0t/UjAJJ44WuUqOyuCWOXMsD5ZIOyl6sPDMA8HFzQpDaRTabr4+bEyJDvNGrlS+KK/SiNjQoaPNLZNcpN++TGQWyzwDVWXiVGizC/SIQbJEGd1HNmDED48aNQ/fu3dGjRw8kJSWhuLgYr7zyCgBg7NixCA4OxuLFiwEAQ4cOxbJlyxAdHc26qObNm4ehQ4eyhg6BUBfIuVGE16d3nW6xzNua45ty74R6hsqe1FhyglPbtQjnZM39UuLCkcsAXFBSIZsZ2EGdik3ZyXBtQbNJ/yp11dJ4rnS4plmIKdAI9ZEXPsjNe9rG0yiuqKpxMU0CoSnS4JmMR40ahU8++QTz589HVFQU0tLSsHv3bjbwWKvVIjMzk20/d+5cvP3225g7dy46duyICRMmIC4uDl9++WVDLYHwECCV7XfB0QU4l3NOdD3pVBJr5ADKsuZac/wFRxfIZj3WuGmQGJsoO44wA7GKUmFo+FBe5uHarkVqTpZmGZZDadbZILUL3h3YXvT86oPXeVmKGezsdWwcDgBQFG18/eAkR5ittyZZiFUUMKqlwWQwL/OM8Ae33DpJFl7Cw0yDn+AAxtw2U6dOlbx38OBB3mt7e3skJCQgISGhHmZGIBiRc6Ocvnta8npnv87YM3KP1eJrLB3fVNbj+DbxcLV3FWU5pkFjaZ+l8HH24WUg9nX0Rfu89mgT0wbh3uFWNW64c2KyH9dmvyzJOhvRXCy91wuyFDPVvo9nHcM31wSlKygaE/t54ImwRyRdP5ZkIc7ILUGw2hGnjxwwu8ZRMaFwc7KXzJwsXCfJwkt4mGkUBg6B0FAoKbmQVZyF/LJ8qKASSaOjA6Jl3StMf9pCLQDw4nVMjSl1X86NY2p8U0QFREk+F+kfKZpTZWUl1Co1ugd2t2pQpnCdzJ9MXSn+e+Y2KIpCtxbekqUYzmZl4OTtq2jhGQpnlS973ZKss26OdpLKJsYY4cbzpOc3A01T7AkOYKxNNbRTBLpofHn9CueqJAtxkNoFlZWVOG2yZTXdWngrWifJwkt4mCEGDuGhRUnsCrcNUySSRrVcOsI/Agm9xJJpuXIGAEyOKTcnxo0jvGdqfFPI9VcXpzNSyK1zU6oWszefYyOBKADxXYPx2+nbbAxJTMRV/F2xhi2dUJ4ZD31hDFuZm2uwUBQkCz0ycSlC40bYlhu/4qCOZ91UNE1hSLM30EUTJtlvXce7MK4qoZxbqpSCknYEQlOkwUs1NAREJm771HaflUiTpdpQoLC0z1JEBvBPOoQSbblnKVCiUyBmTKVzknLj1FRuruQ5a3+m5db5/YCtGJ70t8kwZ8peB7fWS0QnKcXXZoOqUgPCuk4Ajsx5gveFLiW1VgH4bUosIkO8Tbazs9fhzUHe6Nuqg8i4qY2EG6jZPiuVczdl2belkJ/R9UdDy8TJCQ7hocSUNJnrWhK2oUHDx8VHZAwIi0PKPStUKXHl0Hsz9krO6UzOGZErB5B28TBYUu28vn/HOZ15VXKdB9MvmtVwqRxzecYNYIyFUTnmQl+lFlfmBkQVx/OLKyQl3KkZBQjwdGYNgJM3xZJxfZUaMZoeIrcUYFrC7eMuX+m8NigtaNlUCl8SCJZADBzCQ4kSaXJt5MtSz0qholQ4n3seE/dOlGxLgcKsQ7NggHJpuFLZuLWqolvCplQt3tt2Cy6t+PEsFFRI2lUAQL7mFgAYKvwkY2EMFX5GZZGCiuOUsZnImOJWzwaA2ZvPicY3Fb8iLfs2SriJRJtAqH8aXCZOIDQESqTJtZEvM88y8mopmJw5SaeSZI0bAKxLS4k0XE5OLpUY0BJ5uTVgJMv6SjXKM+NB0w/k0VChLPMZGKrExg1FASO7BldLqfVe6OT4KvssE4Oj0nth8cgISWk2AJ5UmrE/VBJvjYEG5mw+Z4zPEdxTycTzMIhk35w+mf8TiTaBUH+QExzCQ4uUNFno2qmNfFlOjg0As2JmoX+L/pKuLOa+v4u/6Flz0nCaphXJxpW46IRkl2TjTskdRW4vKbgunEpdDKqK20LlmIupvR/B8os5ovbTnmiNF3uGIkjtgplx7dgYEqAf9l/pi/yKTHQOaAkXlR8vtkQozU5Jz5XIGAy80a81KApYvv8afx+YBgJWvBCNIZHNRCopLlzZd15xuUkpt6l+CARC7SEGDuGhhhu7YkrBVFN1UWZxpuT1KkMVNG4a7LqxS3RPRanQv0V/9u+WSsOVuNUsdb+dKD+B+Vvmi1xlliB04dBVakDvhSdat8HKvTki1xJj3ADVMSRilZILRsXw42GE8SZy2X9XHLgm6a6Sc3V1C/NWpJJixs/UlUqOe/b2PWjzi0X9xEcFKd5LAoFgHuKiIhBQNy6brOIs/OfkfyTvJZ1Kwrmcc0g6lSS6N73rdNaoknKRMdJwKdeZUreaJe637JJsbC3dKnKVWbo3ctl9I0O8zWb9BWqelVc4Lhehu8qOohS7usyNL5ct+aOdl2T6KTO5DgKBYBnkBIdAQM1cNkr6lKvtJOdqAoDOfp3Zv8u5yEy5zpS61ZS2094Xr6OmeyOX3VdJ1t/aZOVl+t9xNhOLdlzk3aMBrHwhGr7uTha7usyNL5UtWcoFpqdpk0U2CQSC5RADh/DQkVWchbS7abhXfg9eTl6ICoiyesFHwHRhSzlXEwUKeaV5yCrOYo0HOReZKdeZUreaknahHuJ11GZv5CTLwuvCGJXaZuUNUrsgJsxb1iUlNKyUuLrsKAqujiqkpOci3M8NAMzOWc4FFurjijyZtRMIBMshBg7hoSL5ajISUxJ5X9YUKCTGJlo9sy9T2FJqPKksxIxq6p3D79SbbFsJga6BGO4yHNvKttVb1mO5WJfaZOUVZklmoAFM3XDarIxbKivwiOhmeGZVCis/Z/ozN2cAEutwxmkAv5z8B3O3XiDScgKhlpBMxiSTsU1Sk33OKs7CgF8HyJ6o7Bm5BwCsViCTO+6ZnDO4V2Y8MZLKgnwm5wyb70Y4p/oqnyAHs9fd+nZDZmmmVfdGCnMZgWuSlTdTV4rYxQfMJhJUknmYGd/VUcUaN+b6kpqz8FplZSU2/LYTC07b1zgbMsE85Gd0/UEyGRMI9YS5mJhb928hRhPDfnmfyzmH03dPIzogGhH+EYrHkSsiaaqNtlDLM264czJnTFiStbg2BLoGorm6eZ31z2AqI/CQSJcaZeW9kVts1rhhxjEX08OMLxWTI9eX1JylruWUUaT6N4FgJYiBQ3hoMBcTw40pef/P97EtfRv7elirYfjgsQ/MjmFpAU+mTWyz2BrFADVENuK6Rk7WPW3jaRRXVNXIXRPu5yaZvViIJTE9cvOsSV8M/s40qf5NIFgJIhMnPDQwMTHC7MJMTAz35IZr3ADAtvRtOJcjTt3PRYnUXK4NAIuzJjdENuL6gIl1Ef5wqk0m4CC1C5aMjOC988IsyZbG9Ajl59SDPmvSF4OXE7BoeMcaz4lAIFRDTnAIDxWMNNpUTMzpu6cln03LSTPpqqppAU+mjaVZk+tC2t5YGBUTCjcne5OZgGvSZ5+2/jiZUQCKArq28BZlSba0X6G8HUCtq3Y/1605+nXQkOrfBEItIQYO4aHDnDQ61EPaBRLlH2WyX2sU8LQka7K1pO31FcNjKd1aeCty13Al1QBMyquD1C4YEmk6FsZSibbweSaomJGO18RAIdW/CYTaQwwcAoEDE9MiZFirYWYDjZnswKak5kraKMUafTXmGB4pWbbQXSOsEg6IZdqWoKQUQ330QSAQag8xcAiEBwhjWhhW9luJvqF9FfWhxM1UmwKe1uxLLoYntllsoznJMZXhWFi6gRvry8Tr9Gnrb5GUXKqEQn33QSAQrAMxcAgPPYyLJr8sX7J0gpujm8V9mXP3KHVFMf252LugtKpUst+aFgOt7xgeJa4kKfeQnLtGSk7OhYnXkRtLSX+WxvxYow8CgWAdiIFDeKjhumioB//VtCSBtd093P6487GWG6kuylPIocSVZKlrR4lM++ztexjzzV+K+qxtKQhr9UEgEKwDkYkTHlqELhrGsLFEqi3XV20l23LuMmtKwS2pKF4bpFxJzPc/48I5c6vA4krhcnJyhkl9W+KjXZcsqv6tpKq5KazRB4FAsA7kBIfw0CLloqFBY2mfpfBx9uHFtDAFOgEgKiAKGjcNe01bqMWNwhu1dvdw3VtSc+P2u/nKZrTyasXOpSZk6kqhUfXB9wO2ohw5dVaCQYkrKTWjoEauHTk5OWA0Lizt01zMjxJXl5LK6KbI1JXhH52OFNokEGoJMXAIDy1SLhoAuFN0B3FhcexrYYFOChSGthqK/6b/V7b0A1A799b0rtMl58aw+uxqdi6JsYkWu6yk3EExMXUTWKzElRQTpkwSLoWUnJwCsOLANcmxzPUpFfNjqfuspjLvo9kU3vr0MFFgEQhWgLioCA8tGjcNpnedLrqedCqJdQFlFWeJqoHToLEtfZtZ46Y27q2kU0mskWMKGrTFLis5pU9NMgQrQUnG38gQ7xq7doT9qyBfkuFffVvW4ESlfvYrU1eGTddV9fa+EAhNHXKCQ3io6eTbSXSN61oyVaBTjhfavYAJERMUu3vk1Eyd/Tpjz8g9uHX/FpztnHH67mksPbHU5HyV0BBKHyUZf2vj2uE+m1dcLumyAgBvV0eL515f+3UzrwS0oIwIUWARCDWHGDiEhxo5JZGznTOOZx6Hi72LbIFOOR5t9qhFsSym1ExcCbi/qz8+OfGJaC6WKp/qWukjF6silfFXiCnXjrBf4Wvmj6kTj+5h3havp76UUS18XR980qqNHKLAIhBqDnFRER5qpJREQ1oOwUu7XsKEvRPw0q6XMLTVUF6BTgoUhrUaJirayfDmwTeRfDW5VnOQcm9JFQsVFgpVQl0qfTalavHokgMY/fUxPLrkADalamvdp1S/b/+cJjtOkNoFH40UZ50e2TUYkSGWGzj1pYwKUjtjVEsDVLUs2EkgEIyQExzCQw83G7CznTNe2vUSLx5m+/Xt+HHwj7hTfAegwRbnfCP6DZzJOYO/c/7Gugvr2JOVmmQEVpqRmFsslDsXS6mt0keKusriK9Xv5lO32ftS4zDr+/1CNnKLyvFE+4AaGTcMdbFfUvQKpDE5vg9u6ypIoU0CoZYQA4fQZLCkaKSwLfPneOZxyXiYMn0ZT1kFVGcQ9nbyxtoLa0XPSMXFmJqj0ozENc1cLMTaBR0tjVVhXExujnYortBLyqIzdaXYfvaOSZm53DhBahe83CtM8fzNycDrqwBmkNoZoX4edT4OgdDUIQYOoUlgSRZhU21rkt1X6TONubClNbAkVoUru2YQyqKl2shBAbWKVSEFMgmEpgeJwSHYPJZkETbXtibZfZU8Y+1Mx40RpbEqQpcTA1cWLdcGkPmhJR0OpYj6ls0TCIT6gZzgEGweS4pGKmlbkwrd5p6p78KWDYWSWBVTmY0ZVxMNWrLNvKc7IFDtLJKB0zRqLKcmBTIJhKYJMXAINo85FxE37kWpO8lUnItcHI2pZ+qzsGV9kqkrxYmMfFAUhW4tvHlybTlMZTbmurSk3F2DuwTJ3qupi4oUyCQQmibERUWweUy5iJKvJiNucxwm7J2AuM1xSLmTUqsCk8L+lMrB66uwZX2yKVWL2MUH8MZPaZi64TRiFyuThQtdWQxcl5Ypd5e1ZdukQCaB0DQhJziEJoGUi0gu7mXPyD1shmBLCkzK9adUDl4T11djJVNXitmbz/FSDtIA5iSfUyQL57qyXB1VKKkwiFxaptxd1pZt15cMnEAg1B/EwCHYHFnFWbhecB06g453Teg2kot7OZNzBnFhcRZJuE31Z0kcjbUk3vXNvXLgr+v5aK3xRJDaBTdyiyVzOxsEsTBSLiwGriuLkWgz16XaCLG2bJvpS2oeBALB9iAGDsGm4EqtKVBwSXeBnZ2dpPz677y/JfuYdWgWiiuLeRJtJRLuphpHY45fTv6DxFN2oE+dYCXUfdr6g4J0Ucuzt++hVytfbErV8k55KABLRorl141Fot1Y5kEgEKwDicEh2AxCFxENGguPLcSCFLHb6FzOOSSdSpLsxwC+RFuphLspxtGYI1NXirlbL7D1kRgJNWA0VqT4eNdlnLlVIOvC4sqvG4tEu7HMg0AgWA9ygkOwGaRcRPSD/7gYaANO3z0taitsw60YLud6YsZl3FZK42gsyarcmBBm8zUloR4VEwo3J3uRZFtP00jNKJB1Ye04m4mnuwSZ7b8+XUSNZR4EAsF6EAOHYDNIuYioB/8ZwHcbRQdEi9py4bqW5FxP53PPY+LeiSK3lbk4GlvNWCzlounT1t+khLpbC2/J+zFh3rIurEU7LuLDnRcV9V9fEKk4gdD0IC4qgs0gdBFRoDCv5zwkxIrdRhH+EUjolSBb8Xt61+mskSLlepredTqSTiVZnHnYVjMWy7loAGDR8I6gHpgqQgm1nMQ6MsQbS0ZGyCYY5vbfGCTaRCpOIDQ9yAkOwaZgXEQ3Cm7gaupVjGg1Ag4ODpJuo/g28XC1d8U7h98R9dPZr7Nkv0wfNVVM2WrGYlMumue6NUel9ixaRT2CVoGeoi99OYk1c/1kRgGu3r2P5fuvSfbfWCTajWUeBALBOhADh9BoEMatmMoYXFVVhb/0fyG7JBvN1c15bqNzOedw+u5pRAdEIyogSrHySeh6qoliylaVVuZcNF5OQM9wHzg4OEg+LyfZDlK7YEikC87cKsCKA9dAC/p3dVQhJT0X4X5u6NXK16prqgn1VTGcQCDUPcTAITQKhHErQ1oOwfbr2yXjWJKvJhuVUzBg3ZZ1SIitvvf+n+9jW/o2tt9hrYYhoVeCKCbG3GkK47aqr+caGsZF817yeehpmueiqaysrFXfTGwPLTghigxR45lVKUSWTSAQ6gRi4BAaHKm4Fa6Rws0YDMDY9kFQMSP5jm0Wi5ySHN5zALAtfRteaPdCjTIX1zTzsK1mLK4LF42pquCntPfYvzMxOUqyIBMIBIISiIFDaHCk4laEMHEsNE3LxrhczLso+WxaThpe7vhyjQyNmmYettWMxUpdNEI5uTBjMQCcyMjH1btFspXDhTAxOQB4fRMIBEJNIAYOocGRilsRwo1jkWp7Pvc8ugd2l3w2yj/KanMliOXkz0QHI/nUbUlJuCXYURTO3r6HMd/8RdxWBAKh1hCZOKHBkZJpD2s1TDJjsMZNg+ldp4v6SDqVBH9XfwxrNYx3fVirYYjwl864S7AcKTn55hoYN3YUhZFdg3my7FkD2+GjXZdINmECgWAVyAkOoVEgjFsBgN7BvUGBQmRAJOvuySrOgh1lJ3qecVN98NgHeKHdC0jLSUOUf5TIuLHVDMNSCN1EzDW54pY16f9ERj70egN05UCmrgx7Lt5V7HISMu/pDuge5s2rHD4zrh0b80OyCRMIBGtCDBxCo4E5oZHLBMy9LoTrworwj5A8tbHVDMNSSGUdBqCouKXS/vm1pOyQeOpwjd1QKgoY/KA8AxdhzA/JJkwgEKwFcVERGhVymYDP5ZwzadyYk2LbaoZhKaTcRHM2n1NU3FJp/8K+wOYy5sO4mkxBPTDAzJ3CkGzCBALBmpATHEKjQi4TsFzxzLe7vo2BLQeadTfZaoZhKaRcOXLh2QYaFrt4buQWKzqpmfd0B/ZUpl/7AFHRTQCY9kRrvNgzVPH4JJswgUCwFsTAITQqXOxdQIHiVQinQMHRzlHy+lOhTykyUGw1w7AUUlmHVTCe2AgNExUF1sUjFbMj179coUzueEzcDCBfdNMS44aBZBMmEAjWgLioCI2G5KvJGLNzDM+IYfjg2Aci42a4y3AEugYq6ltKqWULGYalkHLlLB4ZISpuyXUNbUrV4tElBzD662N4dMkBbErVmuzfVKFMwHhiNOG7k2x/h6/kEPcSgUBoVJATHEKjIKs4C4kpiZLGjdQ1AGjj0MaiMWw1w7AUcq4cprglRQFdH6io5CqFm8oaPComFO01HhjxeYpZdxXT35+z++HP2f2Ie4lAIDQKGsUJzueff46wsDA4OzujZ8+eOH78uMn29+7dw5QpUxAUFAQnJye0bdsWO3furKfZEiwlqzgLxzOPmwzo1RZqZQ0ZKWjQyNPnIbskW7JvuTE1bhrEaGJs2rjJ1JUiJT0XANCrlS/PkDAWt2yGp7s0Y6/Lya9PZhSwfUkFIhdX6BW/I1w5t3BOBAKB0BA0+AnOpk2bMGPGDKxevRo9e/ZEUlIS4uLicPnyZQQEBIjaV1RUoH///ggICMCvv/6K4OBg3Lx5E15eXvU/eYJZlEqzQz1DRTE2plBRKtzW38bTW56GAfJycluXgwuRkoebk4FLxewAwBs/GYOCaUj3JfecFETOTSAQGhsNbuAsW7YMr732Gl555RUAwOrVq7Fjxw6sWbMGs2fPFrVfs2YN8vPzkZKSAgcHBwBAWFiYyTHKy8tRXl7Ovi4sLAQAVFZW1rpSshCmP2v3a4tkl2SzVb+Baml2j4AeotgZX0dfzOs5DwuPLWSNHAoUhoQPwY6MHaLg4CkRU/DZ2c/Ytkzf4R7hise0NTJ1ZWJ5ePI59Ar3RpDaWfY5P1d7LBreEe9vuSCSkTNI9cU8N3frBdagGhEZhC1nMvkBzhSwcHgH+Lnak899LSA/O+oHss/1R13stSV9UTRN17aETI2pqKiAq6srfv31V4wYMYK9Pm7cONy7dw9bt24VPTN48GD4+PjA1dUVW7duhb+/P0aPHo13330XdnbiDLcAkJiYiAULFoiub9iwAa6u5LfOuuJ65XWsKV4juv6q26to6dBS8hmdQQdtpRaggFD7UKhVaugMOuTp8+BIOaKCroCvnS/y9HmSfQ9yHoRdZbssGtNWuKqj8NkF8Wd8akc92qjN/zM+nUth3VXpfyOm+rpXDuSUUfB3puHlVP3aUUWjwlB9nUAgEOqakpISjB49GjqdDp6enibbNugJTm5uLvR6PQID+b9ZBwYG4tKlS5LPXL9+HQcOHMCYMWOwc+dOXLt2DZMnT0ZlZSUSEhIkn5kzZw5mzJjBvi4sLERISAgGDBhgdoMspbKyEvv27UP//v3ZE6aHleySbKzbso49TQGMpy/P9X8Oga6ByC7Jhva+FqEeRreI9r4W3Ty6SZ60cNsGugbiH90/WLtjLc+lpaJUePHxF7Fnzx7emBQodkxbJlNXhlUXD4tOT/r2jkVphR4tfF1lT3IydWWA9h7WXzsr63KiYOwrsrmad93WP9N6vR5VVVVowN/lFFFVVYWUlBTExsbC3r7BD9ebLGSf64+a7DVFUXBwcIBKJR0izHhglGBz767BYEBAQAC++uor2NnZoVu3brh9+zaWLl0qa+A4OTnByUn8K6aDg0Od/cCuy75thebq5kiITRDFwzRXN+fFyVAPBMk0aMmYGamYmqFhQzHcZTi2lW3jXY/WRCMhNkGkyDp+97jNx+GE+jlgcXwE3ks+Dz1Nw46iMCK6GZ7/6pjJmBxu3A4Fo3ycfvB3PPg7YHRZPf/VMdm4Hlv7TNM0jaysLNy7d6+hp6IImqah0WiQmZkJijIl0ifUBrLP9UdN91qlUiE8PByOjo6ie5b8DGpQA8fPzw92dnbIzs7mXc/OzoZGI61yCQoKgoODA88d1aFDB2RlZaGiokJyQwgNh5Q0W1g2gWuIMDEzsc1iJdtyY2q6O3XH63GvI7M0kyf7jm0WywtYpkHz+rRluPJwV0cVnlmVYlL+LZSI0wBUNPDZ6Gh0beGNu4VlGLEqhTVylEjIbQXGuAkICICrq2uj/zIzGAwoKiqCu7u77G+vhNpD9rn+qMleGwwG3LlzB5mZmQgNDa3Vv9sGNXAcHR3RrVs37N+/n43BMRgM2L9/P6ZOnSr5zKOPPooNGzbAYDCwG3blyhUEBQUR46aRwhTRZJAqm8CFW0LBVIkFAAh0DURzdXPefW2hlueiEvZp6zCZflPSc81W35Yr6+Dj5oQgtYuxLEMTrOCt1+tZ48bX17ehp6MIg8GAiooKODs7ky/eOoTsc/1R07329/fHnTt3UFVVVatT4wZ/d2fMmIGvv/4a3333HS5evIh//etfKC4uZlVVY8eOxZw5c9j2//rXv5Cfn48333wTV65cwY4dO/Dhhx9iypQpDbUEgoUwZRPk4JZQkGprrsRCTZ6xRRgZNxehXNtcGyV92CKM0oKICAgE24M5rNDr9bXqp8ENnFGjRuGTTz7B/PnzERUVhbS0NOzevZsNPNZqtcjMzGTbh4SEYM+ePUhNTUWXLl0wbdo0vPnmm5KSckLjRFg2gXrwHyAuoSBXYsFUwHBTKstgCiXVt821aeoVvBu7W4pAIIix1r/bBpWJNxSFhYVQq9WKZGaWUllZiZ07d2Lw4ME2FZDZEGQVZ7GxOQBMllDgttW4aRTts/AZW0RJgcxMXSkbk1NcoUe4nxsA8J5j2ghLKDD9uznaoaTCwJ7ccJ+1xc90WVkZbty4gfDwcDg7y+cIakwYDAYUFhbC09OTuE7qELLP9UdN99rUv19Lvr9tTkVFaDoIY3NMGSHCtjXp39ZQmrU4SO2Cw1dyeEopQJyhWGggSfWvzS8WXYuPCqr7xRIIBIKVIeYrwWKk6jwpqTdFUI5cgUypmlFSSinmWFbuOan+52w+JzNmmfUXSKgT+vbti+nTp7Ovw8LCkJSUVG/j1SUURWHLli1W669ly5Z1ujeEhoec4BAsQionDYAmW/upoZArkCmlbpJqa+45OXWVsBSYnqahzS+xfAGEGjF58mT89NNPoutXr15F69atG2BGjYfMzEx4e3s39DQAGLPjb9myBWlpaVbpb/z48bh3755VDTgCMXAIFiCVkyYhJYGXc0aYx4b7rLZQi1DPUEXXpe4DYP/u62gb0l85zMXWSBW6lFM3mSuKSQFwdVSZfUb1oLFwzFAfV+QpX1qTQ0kclDWJi4vDunXreNf8/f3rfNzGjlxutMZMZWWlzcStNUWIi4qgGLn8NcIK4Nw8NYDx1Cducxwm7J2AuM1xSL6abPK61HMDfh2AAb8OYNtuSd9i/QXWE5tStXh0yQGM/voYHl1yAJtStaI2lqibhG2F+gMawIjPU3jjSPW/eGSEzJi2EaRbFyh5r6yNk5MTNBoN74+dnR3Gjx/Pq9kHANOnT0ffvn0V9fvqq69iyJAhvGuVlZUICAjAt99+K/vckSNH0LdvX7i6usLb2xtxcXEoKCiQbPv999+je/fu8PDwgEajwejRo3H37l32fkFBAcaMGQN/f3+4uLigTZs2WLt2LQBjbcKpU6ciKCgIzs7OaNGiBRYvXsw+K3RR/fPPP3jxxRfh4+MDNzc3dO/eHceOHQMApKenY/jw4QgMDIS7uztiYmLw+++/K9onhoMHD6JHjx5wc3ODl5cXHn30Udy8eRPr1q3DggULcObMGVAUBYqiWIOUoih88cUXGDZsGNzc3PDBBx9Ar9djwoQJCA8Ph4uLC9q1a4fly5ez4yQmJuK7777D1q1b2f4OHjwIALh16xaef/55eHl5wcfHB8OHD0dGRgb7bFVVFaZNmwYvLy/4+vri3Xffxbhx49jPyfr16+Hr68srNg0AI0aMwMsvv2zRftgi5ASHIIvwdIXJL2MqSR/Azzkjl4m4jVcbyetyGYyF2Y4XHV+Etz3erotl1ylysTVSmYO5WYuF6ichwgzHIz5PEVUOn5N8jjeOXP/Caw9r1WVL3itbYOLEiejTpw8yMzMRFGQMHN++fTtKSkowatQoyWfS0tLw5JNP4tVXX8Xy5cthb2+PP/74QzY/SWVlJRYuXIh27drh7t27mDFjBsaPH4+dO3cCAObNm4cLFy5g165d8PPzw7Vr11BaaowPW7FiBbZt24aff/4ZoaGhuHXrFm7duiU5TlFRER5//HEEBwdj27Zt0Gg0OHXqFAwGA3t/8ODB+OCDD+Dk5IT169dj6NChuHz5Mpo3by7ZJ5eqqiqMGDECr732Gn766SdUVFTg+PHjoCgKo0aNwvnz57F7927WaFKrq+u3JSYmYsmSJUhKSoK9vT0MBgOaN2+OX375Bb6+vkhJScH//d//ISgoCM8//zxmzpyJixcvorCwkDX2fHx8UFlZibi4OPTq1Qv/+9//YG9vj0WLFmHgwIE4e/YsHB0d8dFHH+HHH3/E2rVr0aFDByxfvhxbtmxBv379AADPPfccpk2bhm3btuG5554DANy9exc7duzA3r17ze6DrUMMHIIkUrE28W3ikdBLXOeJizDnTNrdNMlMxKfvnpbNUCyXwVjYNk9ve44TS2JrgOqsxQym3CXcDMdS746BhmgcbsZj4XjMNT/X6h8T9e2uaUgsfa+sxY4dO+Du7s6+HjRoEH755Zda9xsbG4t27drh+++/x6xZswAAa9euxXPPPccbj8vHH3+M7t27Y9WqVey1Tp06yY7x6quvsn9v2bIlVqxYgZiYGDZdv1arRXR0NLp37w7AGATNoNVq0aZNGzz22GOgKAotWrSQHWfDhg3IyclBamoqfHx8AIAXoxQZGYnIyEj29cKFC/Hbb79h27ZtmDx5smy/DIWFhdDpdBgyZAhatWoFwFgSiMHd3R329vaSbrPRo0eziWoZFixYwP49PDwcR48exc8//4znn38e7u7ucHFxQXl5Oa+/H374AQaDAd988w2bF2bt2rXw8vLCwYMHMWDAAKxcuRJz5szBM888AwD47LPPWGMSAFxcXDB69Gj2fWb6DQ0NVXzyZ8sQA4cgQu7UJbZZLOLbxKONVxuM2TmGZ+RQoLC0z1JEBkSyxk3y1WQkpiSK+ldRKkQHRItOg6QyGMsZOSpKBV8724vDsSS2RohS2fi5f3SSz6soiMaR6hMA79qi4R3hBuCXk/9g7tYLZsdvKtTmvaoNffv2xerVq9nXbm5uVut74sSJ+OqrrzBr1ixkZ2dj165dOHDggGz7tLQ09otRCSdPnkRiYiLOnDmDgoIC9kRFq9WiY8eO+Ne//oWRI0fi1KlTGDBgAEaMGIHY2FgAxkDb/v37o127dhg4cCCGDBmCAQMGyM4rOjqaNW6EFBUVITExETt27EBmZiaqqqpQWloKrVaZi9HHxwfjx49HXFwc+vfvj6eeegrPP/88e/JlCsZ44/L5559jzZo10Gq1KC0tRUVFBaKiokz2c+bMGVy7dg0eHh6862VlZUhPT4dOp0N2djZ69OjB3mMKUDP7DgCvvfYaYmJicPv2bQQHB2PdunUYP378Q5EEk8TgEESYq/8U4R+BxNhEXqbgxNhExIXHscYNYyQJT3qYE54I/wiT2YbNZTue22Mu1Co1bI2aZg5WKhvP1JXio92XRM9TMBokwtMgJVLxuVsv4OZ9sMaNqfGbEg2V5dnNzQ2tW7dm/zBfqiqVCsK8rJa6D8eOHYvr16/j6NGj+OGHHxAeHo7evXvLtndxUb7W4uJixMXFwdPTEz/++CNSU1Px22+/ATDG1wDG06ibN2/irbfewp07d/Dkk09i5syZAICuXbvixo0bWLhwIUpLS/H888/j2WefrdG8Zs6cid9++w0ffvgh/ve//yEtLQ0RERHsPJSwdu1aHD16FLGxsdi0aRPatm2Lv/76y+xzQoN048aNmDlzJiZMmIC9e/ciLS0Nr7zyitm5FBUVoVu3bkhLS+P9uXLlCkaPHq14HdHR0YiMjMT69etx8uRJ/P333xg/frzi520ZcoJDECF1eiKs5SRVJZyLnIvp4z4fIy4sTlEfwvtAdbZjX0df7Ly8U9S/LWBJbA2DUneJnGR85YvRGBLZzGyfUlJxAw1cv081iLumoanJe1VX+Pv74/z587xraWlpFql0fH19MWLECPbLW+hKEdKlSxfs37+f52KR49KlS8jLy8OSJUsQEmL893rixAnJdYwbNw7jxo1D79698c477+CTTz4BAHh6emLUqFEYNWoUnn32WQwcOBD5+fmik5ouXbrgm2++kbwHGAOjx48fz7puioqKeMG5SomOjkZ0dDTmzJmDXr16YcOGDXjkkUfg6OiouE7SkSNHEBsby3ONpaen89pI9de1a1ds2rQJAQEBshl7AwMDkZqaij59+gAw1m46deqU6HRo4sSJSEpKwu3bt/HUU0+x709Th5zgEEQoreWkcdMgRhMjKe+WK3gZ6R/Ju2aqD+F9c20B20k4GKR2Qa9Wvoq/MJUWxZRr1y1MnD9Eqi0FQHhyTQFwoNAki3IqwdL3qq544okncOLECaxfvx5Xr15FQkKCyOBRwsSJE9nixuPGjTPZds6cOUhNTcXkyZNx9uxZXLp0CV988QVyc3NFbUNDQ+Ho6IiVK1fi+vXr2LZtGxYuXMhrM3/+fGzduhXXrl3D33//je3bt7OxLcuWLcNPP/2ES5cu4cqVK/jll1+g0Wjg5eUlGuvFF1+ERqPBiBEjcOTIEVy/fh2bN2/G0aNHAQBt2rRBcnIy0tLScObMGYwePZrntjHHjRs3MGfOHBw9ehQ3b97E3r17cfXqVXauYWFhuHHjBtLS0pCbmytSKXFp06YNTpw4gT179uDKlSuYN28eUlNTeW3CwsJw9uxZXL58Gbm5uaisrMSYMWPg5+eH4cOH43//+x9u3LiBgwcPYtq0afjnn38AAG+88QYWL16MrVu34vLly3jzzTdRUFAgcj+NHj0a//zzD77++mtenFRThxg4BEni28Rjz8g9WBO3BntG7rE4cZ/GTYMhLfmS1CEth9Rp6QRzsnNbRqm7pDbycuDB4Q1dbeQwd37JsAPNud7UinLaAnFxcZg3bx5mzZqFmJgY3L9/H2PHjrW4n6eeegpBQUGIi4tDs2bNTLZt27Yt9u7dizNnzqBHjx7o1asXtm7dCnt78eG/v78/1q1bh19++QUdO3bEkiVL2JMZBkdHR8yZMwddunRBnz59YGdnh40bNwIAPDw82KDmmJgYZGRkYOfOnZI1jBwdHbF3714EBARg8ODBiIiIwJIlS2BnZwfAaCx5e3sjNjYWQ4cORVxcHLp27ap4j1xdXXHp0iWMHDkSbdu2xf/93/9hypQpeP311wEAI0eOxMCBA9GvXz/4+/tLJmdkeP311xEfH49Ro0ahZ8+eyMvLEwU6v/baa2jXrh26d+8Of39/HDlyBK6urjh8+DBCQ0MRHx+PDh06YMKECSgrK2NPdN599128+OKLGDt2LHr16gV3d3fExcWJ6jep1WqMHDkS7u7uolQDTRlSbJMU26wTsoqzELc5TuTm2jNyj1WMHOE+1/V4jQW5opk1bQcAZ24VYMSqFHB/EqgA/HtEJ8zf+rcoGeDK0dHo2sK7URs3pNimPEVFRQgODsbatWsRH//wZRxvysU2DQYDOnTogOeff150evbkk0+iU6dOWLFiRb3OhxTbJDQ5zAUqp91NAwBEBUSxeW9MZTSuzXi2aODIybGVysa57bhtALDVw5nK48UVegh/zTEAKKs0SMbo+Lg5NWrjhiCNwWBAbm4uPv30U3h5eWHYsGENPSVCLWHcZ48//jjKy8vx2Wef4caNG7wg5IKCAhw8eBAHDx7kyf0fBoiBQ6gT5AKVz+eex4Q9E1h1FQUKQ1sNxfbr22tVy0pJYLStoFQOrqQdtw23yjiDigLeHdheUg4dE+bdIDJpQt2g1WoRHh6O5s2bY926dZJuJoJtoVKpsG7dOsycORM0TaNz5874/fffeTl7oqOjUVBQgI8++gjt2rVrwNnWP03rfI5gEXUZkCsVqDy963T85+R/eNJxGjS2pW8T5dyxdE5KA6MbO5bIwc21M1VlnMFAAx/vvox3B7UXxe1EhnhjcXwEG1ysokDibmyYsLAw0DSNW7du4cknn2zo6RCsQEhICI4cOQKdTofCwkKkpKSwiiqGjIwM6HQ6Vo7/MEFM+IcUuUzFlmDOrSSUeWsLtbIZkLnU1LVkTnbeEFia+bc2cnBhO3NVxrnPdQn2wp+z+4nidkbFhKJXuDd+3vkHnh/cD6F+HmZ6IxAIhMYBMXAeQkxlKlZqFCg1kBh5NwDsurFLUd+1cS1xx2tolLqauCjNnquknbkq48LnhPE9DEFqZ7RR0w910U0CgWB7EBfVQ4i5AGBzyBlIptxKWcVZSDqVJLpOgcKwVsNs3rUkRKmrSYg15eBSVcaFOW6I3JtAIDRVyAnOQ0htA3JroliSy2y89PGliAuLwxvRbzQq11JtqU2hRqXZc5W0E7YBwFYcL6kwNHh2XgKBQKgriIHzEMIE5ApdTEoNCzkDydnOGcczj0vG5Mg9w2Q2bkyuJWtQk0KNwngdoeEhJfcO93NDr1a+yNSVIiU912SVce5rAoFAaOoQA+chpTYBuVIG0pCWQ/DSrpdkY3Jqa1TZGox76L3k89DTtFlXkLl4HTm5t4oCnokOxm+nbz80Vb4JBAJBCcTAeYipzakJ10BytnNmjRtAPmi5Maqc6hKlria5eJ0+bf0RpHaRlHszGGhg86nbvNfcZwkPF3379kVUVBSSkpIAGKXh06dPx/Tp0xt0XgRCQ0CCjAk8LMmNwxS/LK0qlYzJOZNzRtSXkoKZdTnn+iZI7YIwP1fcyC2WDTA+ebNANl5H7r4puM8SbIvJkyfDzs4OFEXx/ly7dq2hp9bgrFu3TrLwZmMgIyMDFEUhLS3NKv0dPHgQFEXh3r17VunvYYWc4BBYapobRyq+hgKFWYdmwYCa59lRwpb0LVh0fFGt8vnUJUpcT7M3nxM9x8TryN03Bck2bGV0t4H8dMCnFaAOrvPh4uLisG7dOt41f3//Oh+XUPdUVFTA0dGxoafx0GDxCU5paSny8vLwENbobNKcyzmHxJREWem38JSE+1qYRZh6ECViQO2yE5tDZ9Bh0bFFtc6CXFeYk4oz94X/kpiMwQAk73Pl3nYUhZFdgxVVDyfUgFPrgaTOwHdDjf8/tb7Oh3RycoJGo+H9sbOzw/jx40WVoKdPn46+ffsq6vfVV1/FkCFDeNcqKysREBCAb7/9Vva5devWITQ0FK6urnjmmWfYWlYMSua1e/duPPbYY/Dy8oKvry+GDBmC9PR09j5zApKcnIx+/frB1dUVkZGROHr0KADjicYrr7wCnU7HnmolJiYCACiKwpYtW3jje3l5sUYi0/fPP/+M3r17w83NDU888QSuXLmC1NRUdO/eHe7u7hg0aBBycnJk96GgoABjxoyBv78/XFxc0KZNG6xduxYAEB4eDsBYFoGiKHbtzN588MEHaNasGVsq4fvvv0f37t3h4eEBjUaD0aNH4+7du+x8+/XrBwDw9vYGRVEYP348AGM9scWLFyM8PBwuLi6IjIzEr7/+ypvntm3b0KZNGzg7O6Nfv3747rvv2NOg4uJieHp6ip7ZsmUL3NzccP/+fdn12yIWneAsX74cs2fPZq3Qzp07IyoqClFRUYiOjkZkZCTc3Nzqaq6EOiL5ajISUxJFWYYZ6XfKnRRRQLFU7SgmviavNA/vHH5Hsi9ruqby9HmsEVWX49QUc1JxuUzDK16IxpDIZkhJz5W8v/LFaHQL8+bF9syMa6e4ejhBIbrbwH/fBJiTSdoA/Hc60OrJejnJsTYTJ05Enz59kJmZiaCgIADA9u3bUVJSglGjRkk+c+zYMUyYMAGLFy/GiBEjsHv3biQkJFg8dnFxMWbMmIEuXbqgqKgI8+fPxzPPPIO0tDRelen3338fn3zyCdq0aYP3338fL774Iq5du4bY2FgkJSVh/vz5uHz5MgDA3d3dojkkJCQgKSkJzZs3xyuvvIKXXnoJHh4eWL58OVxdXfH8889j/vz5+OKLLySfnzdvHi5cuIBdu3bBz88P165dQ2mp8ZeV48ePo0ePHvj999/RqVMn3inN/v374enpiX379rHXKisrsXDhQrRr1w53797FjBkzMH78eOzcuRMhISHYvHkzRo4cicuXL8PT0xMuLsZ/04sXL8YPP/yA1atXo02bNjh8+DBeeukl+Pv74/HHH8eNGzfw7LPP4s0338TEiRNx+vRpXokGNzc3vPDCC1i7di2effZZ9jrz2sOjaWUqt8jAWbJkCaZMmYLx48cjJycHaWlpSEtLw5dffolLly7BYDCgZcuWiIqKws8//1xXcyZYESZpn1QJBUb6LUzqty19G9vGQBuQmJIIV3tXRAVEIUYTg6ziLItl5DXB184XKqh4Rk5jKrBpTioudV8FoFuYt9n7UtJvYthYmfz0auOGgdYD+dfr1MDZsWMH78t70KBB+OWXX2rdb2xsLNq1a4fvv/8es2bNAmD8YnvuuedkjYXly5dj4MCBbPu2bdsiJSUFu3fvtmjskSNH8l6vWbMG/v7+uHDhAjp37sxenzlzJp5++mkAwIIFC9CpUydcu3YN7du3h1qtBkVR0Ghq9rNj5syZiIuLg8FgwOuvv46JEydi//79ePTRRwEAEyZMELkGuWi1WkRHR6N79+4AjAHcDIwL0dfXVzQ/Nzc3fPPNNzyj59VXX2X/3rJlS6xYsQIxMTEoKiqCu7s7fHx8AAABAQHsaVl5eTk+/PBD/P777+jVqxf77J9//okvv/wSjz/+OL788ku0a9cOS5cuBQC0a9cO58+fxwcffMCON3HiRMTGxrKG7t27d7Fz5078/vvvlmynTWCRi6q8vByTJ09G586d0a9fP7z11lv47rvvcPbsWRQVFeH48eOYNWsWAgMD62q+BCsjl4BPBePJjFQAsRAaNN45/A7iNsch+WqyZOFLRkY+Ye8Etl1tUavUmNtzbqPNgmwu2zBzn5tcmAZw+EqOovuEOsanFUAJfkRSdoBPyzodtm/fvuwvj2lpaVixYoXV+p44cSLrVsnOzsauXbt4X7ZCLl68iJ49e/KuMV+ulnD16lW8+OKLaNmyJTw9PVnjQKvV8tp16dKF/TtzysS4bmoLt++AgAAAQEREBHstMDDQ5Fj/+te/sHHjRkRFRWHWrFlISUlRNG5ERIQo7ubkyZMYOnQoQkND4eHhgccffxyAeD+4XLt2DSUlJejfvz/c3d3ZP+vXr2fdfZcvX0ZMTAzvuR49eohed+rUCd999x0A4IcffkCLFi1ERTqbAhad4IwaNQqpqalo2VL8D9zR0RFdu3ZF165drTY5Qt0jFyD8w+AfEOEfIXkaIwdXHl4TGXlNGNFqBHqH9G600nNzUvE+bf1BUQDNkYBzZd7m7hPqEHUwMHS50S1F643GzdCkOndPubm5oXXr1qLrKpVKFPtYWVlpUd9jx47F7NmzcfToUaSkpCA8PBy9e/eu1XyVzGvo0KFo0aIFvv76azRr1gwGgwGdO3dGRUUFr52DgwP7d+rBLwYGg+mfPRRFKdoXqb6F10yNNWjQINy8eRM7d+7Evn378OSTT2LKlCn45JNPTM5PGLZRXFyMuLg4xMXF4ccff4S/vz+0Wi3i4uJE+8GlqKgIgPGELziY/xl0cnIyOQchEydOxOeff47Zs2dj7dq1eOWVV9g9aUpYdILTvHlzJCQk8HyJBNtG6rQlMTYREf4Rsve5taOEcGtamZORK619pWQN1paeW5MgtQt6tfJlDRIm6zCTmVguTidTV4rtZ++YlJAT6piuY4Hp54Bx243/7zq2wabi7++PzMxM3jVLZcm+vr4YMWIE1q5di3Xr1uGVV14x2b5Dhw44duwY79pff/1l0bzy8vJw+fJlzJ07F08++SQ6dOiAgoICi+YNGH+J1uv1ouvC8a9evYqSkrr59+Hv749x48bhhx9+QFJSEr766it2bgAk5yfk0qVLyMvLw5IlS9C7d2+0b99edHIk1V/Hjh3h5OQErVaL1q1b8/6EhBjd8u3atcOJEyd4faWmporm8NJLL+HmzZtYsWIFLly4gHHjxlmwC7aDRSc4GzduxPXr1xEXF4egoCB0796dDTKOiopiI8kJtoW5BHxS99+IfgNncs6wUnAGqRiY2ta+akoIZePvDmwvGadz9vY9jPnmL8kgYyIDr2fUwY0iqPiJJ57A0qVLsX79evTq1Qs//PADzp8/j+joaIv6mThxIoYMGQK9Xm/2i23atGl49NFH8cknn2D48OHYs2ePKP7G3Ly8vb3h6+uLr776CkFBQdBqtZg9e7Zli4cx5qWoqAj79+9HZGQkXF1d4erqiieeeAKfffYZevXqBb1ej3fffZd3MmMt5s+fj27duqFTp04oLy/H9u3b0aFDBwBGl5eLiwt2796N5s2bw9nZGWq1WrKf0NBQODo6YuXKlZg0aRLOnz+PhQsX8tq0aNECFEVh+/btGDx4MFxcXODh4YGZM2firbfegsFgwGOPPQadTocjR47A09MT48aNw+uvv45ly5bh3XffxYQJE5CWlsbGFXFPaLy9vREfH4933nkHAwYMQPPmza2+X40Bi05wzp07h6KiIpw4cQKLFi1CWFgYDh06hFdffVXySJVgO3BPQbgScObvAHinJBo3DeLC4pAQmyCKgQHAk5RLnQI1pliZ+kJKNv7x7st4d1B7XpzOrIHt8NGuS7LGDZGBP5zExcVh3rx5mDVrFmJiYnD//n2MHWv5idJTTz2FoKAgxMXFoVmzZibbPvLII/j666+xfPlyREZGYu/evZg7d65F81KpVNi4cSNOnjyJzp0746233mKDYC0hNjYWkyZNwqhRo+Dv74+PP/4YAPDpp58iJCQEvXv3xujRozFz5ky4ulr/FwBHR0fMmTMHXbp0QZ8+fWBnZ4eNGzcCAOzt7bFixQp8+eWXaNasGYYPHy7bj7+/P9atW4dffvkFHTt2xJIlS0RuruDgYCxYsACzZ89GYGAgpk6dCgBYuHAh5s2bh8WLF6NDhw4YOHAgduzYwR4uhIeH49dff0VycjK6dOmCL774Au+//z4AsRtrwoQJqKioMBmDZetQtJUS2ty8eRMtWrSwRld1TmFhIdRqNXQ6HTw9Pa3ad2VlJXbu3InBgwfXyW8RdQ032R+Tz4YGbTKJXlZxFnu6I5SUc5/htuMaN1nFWdAWai1SV9naPjPupg92XBLd++m1RxDm54qTGQUoKK3A9ZxirD2SIWo37+kOGNwlqN6NG1vbawAoKyvDjRs3EB4eDmdn54aejiIMBgMKCwvh6enJk05bm6KiIgQHB2Pt2rWIj7c8Kea6deswffp0m82yW1/73Fj44IMPsHr1aty6xQ8J+P777/HWW2/hzp07dZZ8sKZ7berfryXf31bLZGwrxg1BHkYyzriSuNJxU4HBTE0r4fPCZ6RqX9U0e7ItwXVLCWHcTYev5GD2ZnFSP267hjBuCE0Hg8GA3NxcNlHfsGHDGnpKhDpg1apViImJga+vL44cOYKlS5eyJ0AAUFJSgszMTCxZsgSvv/56k86s3PTNVwIPxuV0LuecqH6TnGScwVxgsNTzpp6RM4gaSyZiayB0SwmZNciY2dSUccNkNibGDaE2aLVaBAYGYsOGDVizZg3s7UmlnqbI1atXMXz4cHTs2BELFy7E22+/zWZ9BoCPP/4Y7du3h0ajwZw5cxpuovUA+YQ/RHBPSxi4pyZSwcBczAUGWxpMbMogairxOXLZihm6BHvhRm6xrHEDVGc2JhBqQ1hYmFVK7IwfP54tHUBofPznP//Bf/7zH9n7iYmJPIOnKUNOcB4ShKclDNxTE6maUkwcjpLAYI2bBtO7TocKyoKJGYOIS1NTVzHZiKVg3FPhfm6Qy0ChoqozGzNwZeYEAoFAkIac4DwkmHI/cU9NhJJwADiTcwY0TSMqIMrkGMlXk5F0KgkGGAOUp3edbjKehjGohDE4TeX0BqjORix0QVECt9OSkdJtFsdH8FxT5qqTEwgEAsEIMXAeEky5n4SnJtxgYKVBwFIBykmnkjAofJBJg8VcDp6mgDAbMQBQtPE6A5Px+GRGAe6VVsDb1RFdW3jzjBu56uQkqzGBQCCIIQbOQ4LwtITB1KmJOVUU00ZbqEV+WX6N42mk1FWNASbTcLifW60MCKk4HAPAVhVnCFK7YEik/DjmqpMTCAQCoRpi4DxECOtDlenLTJ6amAsCFubMoUDxpOW2HE9jTVeQuari9d0PgUAgPAyQIOMmBDcDMXS3gfPJwPFvjP/X3QZQnbE4wj/CbP0mU0HAcjlzmkK2YjlXUE2Des1VFa/vfggEAuFhgJzgNBF4sTKgkJCTh/gH1WeNUMCwFRYVCzQVBHw887jodIcGjaV9lsLH2cem42nqwhVkrqp4ffdDIDQVEhMTsWXLFosLj9aEvn37IioqCklJSVbpb/z48bh37x62bNlilf4IfIiB0wQQxcqAxgI/b7SpKEepSoXQyipo9Hpg2zRkQQ+tZyBCg7qaNECY2JrYZrHYM3KPKAhYLudNpH+kzRo2DLV1BcnF7gSpXUQGSU3ifKT6ITQdbt26hQULFmD37t3Izc1FUFAQRowYgfnz58PX17fe52PtL3VbJjk5udGUKzl48CD69euHgoICeHl51bo/Wy/BIQUxcGwYkwG+FIUxzTSgKQoqmkZCbj4AYMHZT2GgKOMpT2yipCJKiXKqKUu8GVfQe8nnoadpi1xBlsTuEMm3bVCTWmk1JSMjA3FxcWjbti1++uknhIeH4++//8Y777yDXbt24a+//oKPj0+dzoEgjy3ufUVFRZMux2AKEoNjoyRfTUbc5jhM2DsBsw7PYhPycaEfxGoYKAqJfj5Y4OcDA3MNtGRZBEvKJ8S3iceekXuwJm4N9ozc06RqSI2KCcWfs/vhp9cewZ+z+ykyPCyJ3bF2nA+hbuD+O4vbHIfkq8l1Ot7MmTPh6OiIvXv34vHHH0doaCgGDRqE33//Hbdv32YrQwMARVEi14aXlxfWrVvHvn733XfRtm1buLq6omXLlpg3bx4qKyvZ+4mJiYiKisL333+PsLAwqNVqvPDCC7h//z4Aowvl0KFDWL58OSiKAkVRyMjIwLp160SnBlu2bAFFUaK+16xZg9DQULi7u2Py5MnQ6/X4+OOPodFoEBAQgA8++MDsvvzzzz948cUX4ePjAzc3N3Tv3h3Hjh2TbJuamor+/fvDz88ParUajz/+OE6dOsXep2kaS5YsQVhYGJycnNCsWTNMmzaNvb9q1Sq0adMGzs7OCAwMxLPPPsve69u3L6ZPn86+Li8vx7vvvouQkBA4OTmhdevW+PbbbwEAer0eEyZMQHh4OFxcXNCuXTssX77c7Fq53Lx5E0OHDoW3tzfc3NzQqVMn7Ny5ExkZGejXrx8AwNvbGxRFsdml+/bti6lTp2L69Onw8/NDXFwcAGDZsmWIiIiAm5sbQkJCMHnyZBQ9CGM4ePAgXnnlFeh0OvZ9ZrIdl5eXY+bMmQgODoabmxt69uyJgwcP8ub59ddfIyQkBK6urnjmmWewbNky9vOh1Wphb2+PEydO8J5JSkpCixYtYDDIlweqLeQExwaRCvClAFA0zRo1QmiKEpUDkJJxW1o+obFKvK2BUlcQ42bKL66Qjd0BwHNFEcl340dJmgRrkp+fjwMHDmDRokVwceF/BjQaDcaMGYNNmzZh1apVPEPCFB4eHli3bh2aNWuGc+fO4bXXXoOHhwdmzZrFtklPT8eWLVuwfft2FBQU4Pnnn8eSJUvwwQcfYPny5bhy5Qo6d+6Mf//73wAAf39/ueFEpKenY9euXdi9ezfS09Px7LPP4vr162jbti0OHTqElJQUvPrqq3jqqafQs2dPyT6Kiorw+OOPIzg4GNu2bYNGo8GpU6dkvxjv37+PcePGYeXKlaBpGp9++ikGDx6Mq1evwsPDA5s3b8aqVavw008/ISIiAllZWThz5gwA4MSJE5g2bRq+//57xMbGIj8/H//73/9k1zd27FgcPXoUK1asQGRkJG7cuIHc3FwAxuKmzZs3xy+//AJfX1+kpKTg//7v/xAUFITnn39e0f5NmTIFFRUVOHz4MNzc3HDhwgW4u7sjJCQEmzdvxsiRI3H58mV4enryPjPfffcd/vWvf+HIkSPsNZVKhRUrViA8PBzXr1/H5MmTMWvWLKxatQqxsbFISkrC/PnzcfnyZQCAu7s7AGDq1Km4cOECNm7ciGbNmuG3337DwIEDce7cObRp0wZHjhzBpEmT8NFHH2HYsGH4/fffMW/ePHbc0NBQPPnkk1i7di26d+/OXl+7di3Gjx9fpxXdiYFjg0gZITSASQU6rPbxkn6IyTLH+cEoJeO2tJ7Uww7XzUTB+Idrt9hRFM7evocx3/zFc0X1aetPJN+NnPqulXb16lXQNI327dtL3u/QoQMKCgqQk5ODgIAARX3OnTuX/XtYWBhmzpyJjRs38gwcg8GAdevWwcPDAwDw8ssvY//+/fjggw+gVqvh6OgIV1dXaDSWr9lgMGDNmjXw8PBAx44d0a9fP1y+fBk7d+6ESqVCu3bt8NFHH+GPP/6QNXA2bNiAnJwcpKamsi6i1q1by475xBNP8F5/9dVX8PLywqFDhzBkyBDcunULgYGBeOqpp+Dk5ITQ0FD06NEDgPG0wc3NDUOGDIGHhwdatGiB6OhoyXGuXLmCn3/+Gfv27cNTTz0FAGjZsiV738HBAQsWLGBfh4eH4+jRo/j5558VGzharRYjR45ERESEqH9mLwICAkSnaW3atMHHH3/Mu8Y9eQoLC8OiRYswadIkrFq1Co6OjlCr1aAoivc+a7VarF27FlqtFs2aGevhzZw5E7t378batWvx4YcfYuXKlRg0aBBmzpwJAGjbti1SUlKwfft2tp8JEyZg8uTJWLZsGZycnHDq1CmcO3cOW7duVbQPNYW4qGwQSfk2TaNPaSlUEsX0KNp4wgPBb33Tu04X/aAW1qNqSrE11kboZmJ2nqk9ZUdRmDWwHT7adUnkigJAJN+NnIaqlWauIKYl8RSbNm3Co48+Co1GA3d3d8ydOxdarZbXJiwsjDVuACAoKAh37961bNIyCPsODAxEx44deb+1BwYGsuNNmjQJ7u7u7B8ASEtLQ3R0tOL4l+zsbLz22mto06YN1Go1PD09UVRUxK772WefRWlpKVq3bo3XXnsNv/32G6qqqgAA/fv3R4sWLdCyZUu8/PLL+PHHH1FSUiI5TlpaGuzs7PD444/LzuXzzz9Ht27d4O/vD3d3d3z11Vei/TfFtGnTsGjRIjz66KNISEjA2bNnFT3XrVs30bXff/8dTz75JIKDg+Hh4YGXX34ZeXl5susDgHPnzkGv16Nt27a89+XQoUNIT08HAFy+fJk1EBmEr0eMGAE7Ozv89ttvAIwBzf369UNYWJii9dQUYuDYIKwRwhS1fBBEHFFRiYTcfNbIoWga491a4eO7uZKuq85+nfm5cx5gjdgaqX6bGlJuJhrG6t9M7E5Ec7WsK6omcT6E+qO+jf3WrVuDoihcunRJ8v7Fixfh7+/P/rZOUZTIGOLG1xw9ehRjxozB4MGDsX37dpw+fRrvv/8+KioqeM8IVUEURZmNi1CpVCbHNtW3qfH+/e9/Iy0tjf0DQOSuM8e4ceOQlpaG5cuXIyUlBWlpafD19WXXHRISgtTUVHz22WdwcXHB5MmT0adPH1RWVsLDwwOnTp3CTz/9hKCgIMyfPx+RkZGSyiJz89q4cSNmzpyJCRMmYO/evUhLS8Mrr7wi2n9TTJw4EdevX8fLL7+Mc+fOoXv37li5cqXZ59zc3HivMzIyMGTIEHTp0gWbN2/GyZMn8fnnnwOAyfkUFRXBzs4OJ0+e5L0vFy9etCieyNHREWPHjsXatWtRUVGBDRs24NVXX1X8fE0hLiobJb5NPGI9WuLWdwMRUlFhlIEDiC8qRmxpGW452COksgoa/W1k2dtBRdNsgDFg/GF9Pvc8Ju6dKKmWqk1sjdL6VbaOnJy8Wxi/hpQpVxSRfDdu6rNWmq+vL/r164cvvvgCM2bM4H2BZmVl4ccff8SUKVPYa/7+/sjMzGRfX716lffbeEpKClq0aMELTL5586bF83J0dIT+wc8X7tj3799HcXEx+2VqjTw0AQEBIvdbly5d8M033yA/P1/RKc6RI0ewatUqDB48GIBRds/ExTC4uLhg6NChGD58OKZMmYL27dvj3Llz6Nq1K+zt7fHUU0/hqaeeQkJCAry8vHDgwAHEx/N/hkVERMBgMODQoUOsi0o4j9jYWEyePJm9xpx6WEJISAgmTZqESZMmYc6cOfj666/xxhtvsCd5wvdGipMnT8JgMODTTz9lT89+/vlnXhup9zk6Ohp6vR53795F7969Jftu164dUlNTedeErwGjsda5c2esWrUKVVVVov2sC8gJjg2j0UQhpv/H0Oj5v0lp9HrElJU/MHoM0PT4FxLy7rEnO6oHlb6TTiUpUktxMXcyY4kKy9ZRklmYZB+2fZjs3/Xhpv34449RXl6OuLg4HD58GLdu3cLu3bvRv39/tG3bFvPnz2fbPvHEE/jss89w+vRpnDhxApMmTeKdjrRp0wZarRYbN25Eeno6VqxYwboILCEsLAzHjh1DRkYGcnNzYTAY0LNnT7i6uuK9995Deno6NmzYwFNvWZMXX3wRGo0GI0aMwJEjR3D9+nVs3rwZR48elWzfpk0bfP/997h48SKOHTuGMWPG8IzFdevW4fvvv8f58+dx/fp1/PDDD3BxcUGLFi2wfft2rFixAmlpabh58ybWr18Pg8GAdu3aSe7LuHHj8Oqrr2LLli24ceMGDh48yBoObdq0wYkTJ7Bnzx5cuXIF8+bNk/ziN8X06dOxZ88e3LhxA6dOncIff/yBDh06AABatGgBiqKwfft25OTksIooKVq3bo3KykqsXLkS169fx/fff4/Vq1eL1lNUVIT9+/cjNzcXJSUlaNu2LcaMGYOxY8ciOTkZN27cwPHjx7F48WLs2LEDAPDGG29g586dWLZsGa5evYovv/wSu3btEgXCd+jQAY888gjeffddvPjiixafzNUEYuDYOl3HAr1nyN+n7ICekxA/8Rj2PPIh1jz6EfY8uxedfDvJBlDKoUQyayowsymixM1EXFEEpbRq1QrHjh1Dy5Yt8fzzz6NFixYYNGgQ2rZtiyNHjrBxKQDw6aefIiQkBL1798bo0aMxc+ZMuLpWB6kPGzYMb731FqZOnYqoqCikpKTw1C1KmTlzJuzs7NCxY0f4+/tDq9XCx8cHP/zwA3bu3ImIiAj89NNPrKzY2jCy+YCAAAwePBgRERFYsmQJ7OzsJNt/++23KCgoQNeuXfHyyy9j2rRpvFMhLy8vrF+/Hr1790aXLl3w+++/47///S98fX3h5eWF5ORkPPHEE+jQoQNWr16Nn376CZ06dZIc64svvsCzzz6LyZMno3379njttddQXFwMAHj99dcRHx+PUaNGoWfPnsjLy+Od5ihBr9djypQp6NChAwYOHIi2bdti1apVAIDg4GAsWLAAs2fPRmBgIKZOnSrbT2RkJJYtW4aPPvoInTt3xo8//ojFixfz2sTGxmLSpEkYNWoU/P392SDltWvXYuzYsXj77bfRrl07jBgxAqmpqQgNNf4ce/TRR7F69WosW7YMkZGR2L17N9566y04OzuL5jFhwgRUVFTUi3sKACjaXERbE6SwsBBqtRo6nQ6enp5W7buyshI7d+7E4MGD6zTjJZN8zKW8CKWbRiP0gZsqy84OWgd7Y/ZiA4ChSfzyDLrbQH46slw8Ebd3HM8YoUBh77N7ZSuLx22OE6mr9ozcw2uvtF1tqa99rinWqkTeGGjsey1FWVkZbty4gfDwcMkftI0Rg8GAwsJCeHp68oJwExISsGzZMuzbtw+PPPJIA86waSC3zwTr8dprr+HSpUs4dOgQb68XLlyIX375xWywtKl/v5Z8f5MYHBuEG+MCAND4AzSNbqXlOO3iVJ2pOOpNxEdyjJtT64Ft0wDQ0IBCwmMTkXh7L68CeMqdFMl4GaWS2aac4VgpJEMxwZosWLAAYWFh+Ouvv9CjRw/ypUxodHzyySfo378/3NzcsGvXLnz33XfsSRMAVsX22WefYdGiRfU2L2Lg2BjCGBcWisJJ12pL1wAaC86sQGzrp43Ghe42a9wYoRF7dC2o0GDOFVo2kZkl+XHqMzCzsSGXobhPW3+bP8khNByvvPJKQ0+BQJDl+PHj+Pjjj3H//n20bNkSK1aswMSJE1l13BtvvIGNGzdixIgR9eaeAhpRDM7nn3+OsLAwODs7o2fPnjh+/Lii5zZu3AiKojBixIi6nWAjQeokRQ4DbcCZnDNG4+bkOkCQy1jrYAeD4JpcvIylktn6DMysDzJ1pUhJzzVbSsFUhmICgUBoivz888+4e/cuSktL8ffff2PSpEm8+2vXrkV5eTk2bdokGztVFzSKE5xNmzZhxowZWL16NXr27ImkpCTExcXh8uXLJjN2ZmRkYObMmbLytaaI1EmKKWYdegfFuXmIvy+OsA+trIIKALcnU4nMHtaTGUtcTrWtRE4gEAgE69AoDJxly5bhtddeY49hV69ejR07dmDNmjWYPXu25DN6vR5jxozBggUL8L///c9kiffy8nKUl5ezrwsLCwEYgyelklPVBqY/a/fLUFVVhTHtx+DHiz8YT19oWpShmIsBNBJ9veGq1yOqvDpfDmCUk8/Pyce//X1hAA0VpcLcHnPh6+iLf/45iVtZJxCi6Y7AwC7sM76OvvD19a3TNSqhrveZIVNXJnI5zUk+h17h3ghSi4NX/VztsWh4R8zdeoE1iBYO7wA/V/sG3a/aUF97bU2qqqpA0zSqqqrqtJifNWH0HjRN28ycbRGyz/VHTfdar9ez/36FP3cs+TnU4CqqiooKuLq64tdff+W5mcaNG4d79+7J1qpg0lb/9ttvGD9+PO7duyeqrMuQmJjIqwnCsGHDBp6ssrFzovwEtpZuNRbXpGmM0xXCgabxtZfapJHDwGQ8ji8q5l03Kq8ccD9gJIp843AjfwPWUn8bg5VpGq/QnRDuM7qultWouaqj8NkF8ZHq1I56tFHL/9O5Vw7klFHwd6bh5VSXMyTIERgYCHd3d/j4+MDevlH8LkcgEMxA0zQKCwuRn5+P7OxsUcbskpISjB492jZUVLm5udDr9QgMDORdDwwMlE1Z/ueff+Lbb79VnDlzzpw5mDGjOldMYWEhQkJCMGDAgDqRie/btw/9+/e3qqQ2uyQb87fMZxVPNEXhO7Un9t66g74lZXgpOIinhpLCQFFY4OeD2NIy0UmORq8HfWsjbnd9FPML/mazHhsoCmvxN3Z0aw54BEJ7X4tQj1AEugbKDVMv1GafM3VluJlXgha+rpKnMMK2qy4e5rmcKADPD+4HALiZVwIXRzuUVugV9WeL1NVnuq6prKxEdna2ydPdxgRN0ygrK4Ozs7PiauEEyyH7XH/UdK8pikK7du3QtWtX0T3GA6OEBjdwLOX+/ft4+eWX8fXXX8PPz0/RM05OTnByEv8a7eDgUGc/sK3d952SOzCAf8RHUxR+9HTH2wU6JKojsaDwLAy0AZSxtKakwWOgKNxydISmVBwsm60CDhyYBYOvj+iZTZd/wPrbBxpd+QVL99lSCXeonwMWx0dg9uZzvN1cfiAdv52+zTN8mrokvC7/vdQFDg4OCAsLQ1VVlaJ09g1NZWUlDh8+jD59+tjUPtsaZJ/rj5rutYODg2wwsiX9NLiB4+fnBzs7O2RnZ/OuZ2dn88q2M6SnpyMjIwNDhw5lrzG+PXt7e1y+fBmtWrWq20k3AH/n/S15fb3aE2MKixB/ZjtiX/8Dt1CJEI8Q5JTkYPROsVtJRakQMm43kLoOOLmWvZ7s7oYFfj7GkxtBXA9F01j/z35WccWUX5CSkzdmairh7tPWH8y2AEYt2uZTt0XtiCS88cEUd7SFLzI7OztUVVXB2dnZJuZrq5B9rj8aeq8bXCbu6OiIbt26Yf/+/ew1g8GA/fv3o1evXqL2TFE0bmXTYcOGoV+/fkhLS0NIiLQCyJbJKs5C0skkyXsGisItB3uANkBTep+VZpdWScuZR7YZCY2LP3Dqu+r+7eyqjRsA3G9zFU1jnH+MYjl5Y8YSCTdXFi71nBx6msbJjAJFbZVKzwkEAoFgOQ1+ggMAM2bMwLhx49C9e3f06NEDSUlJKC4uZlVVY8eORXBwMBYvXgxnZ2d07tyZ97yXlxcAiK43FX68+KPIPcWgommEVFYZa075tGSvy8nJN1/ZjM60I+I517UO9rxK4wAAisKsvHvoP2wNEBSB9RLlF+Tk5I0VpRJuoRvr3YHtRc+ZYtrG0yiuqDLpqiLZjgkEAqFuafATHAAYNWoUPvnkE8yfPx9RUVFIS0vD7t272cBjrVaLzMzMBp5lw5BVnIXv/v5O8h6jimJrTqmD2XtMYj4mHofBAAMWXPsJWfbVx4WhlVVspXFu3/0fnQ2Nf0do7l5BQuQ0xUn+GitKKntLubE+3n0Z7w5qz3tuZNdg9rUQxlUldzIj5yojJzkEAoFgPRrFCQ4ATJ06VbYa6sGDB00+u27dOutPqJGgLdRKBgvHFRVhZr4OmvbDgQGLeMYNQ3ybeLjau+Kdw+/wrhtoA/ZGjcCAtC3QVFVCo9cjITefdVOpoEJC9DRo9A5AUmeANiAeFGL7zcKtdv1tOsnfqJhQ9Gnrj4zcEoT5uYpiZeTcWMFqF/w5ux/vuZlx7ZCRW4Jrd+9j3ta/Rc9k5JZIxuKYcpWR2B0CgUCwDo3GwCFII+VqomjaaNzo9cCFLUYDR4aogChJV9XSvGP4tLkGCbkFiI9+HfEt+yHWxYMNUtZU6VnjxggNzR8fQWPvDjwaUwcrrT+C1C6yhoSUGwswup2EbiSmnzA/VyRs+1tx9mKS7ZhAIBDqnkbhoiLII6oBRdNIzM2vzmNDG4D864qf52LMi+ONrKMrAJ+W0GiiqutH5adzjBsOvycYa1s1URg3lnC3TLmRlLi+atOeQCAQCJZDTnBsALYGVOYphGwcC00VJ1W1ILjY1PN7M/Zi6YmlvHsGisItexU0+df5bi6fVjCmtBMcZTAGlYRLrKkwKiYUbk72mLrhNO+6KTeSOddXbdsTCAQCwTLICY4NkFWcBW2hFiHuzaDpMQlgTmMoO1FwsRwaNw0GhA2AShB0rKJphFQZAAdX4Mbh6tMZdTDQX1zeAlCZNaiaAt1aeEMliCE250YKUrugVytf1lgxJwMXticQCASC9SAnOI2c5KvJWHB0gTFDMU3jrfx7eIWmgdhpQM9JFp2kaNw0SIhNxIKURGNxTZpGQt49aDo9B3z7lPF0hlIBTyUC6hDjn94zgf99iuqTHBpI3w90HVsXy200MG6k95LPQ0/TFruRiAycQCAQGhZi4DRisoqzWOMGMJZmWObjBQB45ejnRgPHQnjurqoqaNyDq40bwPj/ffMFT3GPMmjgv9OBVk82aTcVUHM3Uk0zJhMIBALBehADpxGjLdSK1E+gKCT5eGFQcYk4bkYhGjcNNK0HG1/cOCwdTMxDGIejb7JxOEzm4nA/N1YlJTRKMnWlOJGRD4qiEOLtguIKPdwc7VBcoUe4nxuRgRMIBEIjgBg4jZhQz1BQoER5cNiCmdaIhfFpZXRLmTVyOCgIbLZFlLiVNqVqRYU3uchlPiYycAKBQKhfSJBxI0bjpsFb3d4SXVfRNEL6zrPOCYo62BhzYxJKOrBZd5sfmGzDKMkunKkrNWncMM9JZT4mMnACgUCoX8gJTiPnlc6vALdPIinzoDHLME0jIbAPND2nWG+QZtHy9ygKGLrCGHOTf914cqMOBk6tB/77ZnVg8tDlNh14rMStdCO32KRxw32uS7CXKPMxgUAgEOoPYuA0crKy0tAp7Vf8oK9CmUqFkMoqaG5uBGLft14MjKSbigIGfwq0G1g9DvN/3e1q4wYw/t/GA4+lsgurAJ5bKdzPTSozkAjGHWUqYzKBQCAQ6hbiomrEJF9NRtyelzFB44+Xmmlwy97emMGYCfK1Fupg4wkMZWd8TdkBw1YAPSZIGyxSWY6tPad6hpGFC/RiOHwlh9dmycgISJfYNELcUQQCgdA4ICc4jZSs4qwH+WqMGMsq+CC2tMxo5DhYOWC161ixG0oOqROfJhB43KetPygKYAqr0xDLuxnp+MmMAlAU0NzbBSUVBrg6qlBSYSDuKAKBQGgkEAOnkaIt1MIgpZ5yeHCKU1li/UHVwcpcTMyJz3+nG09uLMio3JiRi8M5mVEAH3e+dHxIJDFiCAQCoTFDDJxGSqhnKFSgeEaOiqYRUlllPD1p6NMSS058bASpOBwKxkriJCMxgUAg2BYkBqeRwpRVYGpHqWgaCbn50BgMxtOT+jAozMnA1cFAeO8mYdwA4irfzD8OU9JxAoFAIDROyAlOIya2WSw+6j4bVN41RNp5QtO9BRDSo34MCjkZuO62McjYp5VNGzZMxmI3Rzto80tAURS6tfDmlWfIKy6XrCi+42wmnu4SJBlrI8yETCAQCISGgRg4jZTkq8mCopgFiO+3uP5ObqRk4KX3gN8TbD73DTdjMRcKwJKRRhdUkNoFmbpSkcsKABbtuIgPd14UuatIgU0CgUBoPBAXVSOkWkFl/GY1UBQW+Hoja+eM+skaLCcD3zefb/RsmwYc/8amMhkLMxZzoQHMST7HuqCELisuQneVkkzIBAKBQKg/iIHTCJFVUNmr6ifXDCMDFyG0Cmhg59vAfzoZXVo2gJRSiouBBjJyqxVqo2JC8efsfpj7dAdRWybTsVy/3PsEAoFAqF+IgdMIYRRUXFQ0jZAqQ/2op4SJ/8x+TGijS0t4ktMIa1UxSik5KACujvz1Bqld8HSXINFz3AKaUv2SApsEAoHQcBADp5GRVZwFbaEW0zu9yldQ5d2DZvCy+gvs7ToWmH4OGLcdePZb8+1pA/906dR6IKkz8N1Q4/8byQmPKbcTYDyjemZVCjalak0+J8xYbO4+gUAgEOoXEmTciEi+mowFRxfAQBugomlMz7+HzhWVCIl8GZpn3qp/1RKT+E93W6JWlQBubp5GXquKq5RydVTh7D86zN/6N+uAY+JnuBmMhc9JZSw2d59AIBAI9Qc5wWkkZBVnscYNYIy5SfLxQkhlJTTHFJyg1CWMy8rUx6UXp7p5I6tVlakrRUp6Li/gN0jtgl6tfBEZ4o1WAe6i6CK5+BnmOTnjxdx9AoFAINQPxMBpJGgLtaxxw8CUZgAMwLHVDTMxhq5jTbiqKCBlZbUrSipIuYFqVW1K1eLRJQcw+utjeHTJAZHrCSDxMwQCgdAUIQZOIyHUMxQqgVFAMaUZAODoZw0frBvS07S6inFF3c8ynugwbRuoVpVS6TaJnyEQCISmB4nBaSRo3DRI6JWAxJRE0ByHSYqLM+KLiquDeBsyhkVYZFMKWg98+2R1Se6I54F2g4zGUT3AzVD8+8Vsk9JtbsbhPm39kfRCJFQUha4tvIlxQyAQCDYOMXAaEbHNYkGBYg0cmqKwwM8HsaVl0BjQ8AU2geoim7eOA7++AnFuHFQbNwBw7mfjn3rIfCyXoZiLHUXh7O17GPPNX2zG4Weig/Hb6dskAzGBQCA0IYiLqhFhTPAnEYfj6NggLh5Z1MGAmy8kjRs5GPdVHbnZTGUoZlBRwKyB7fDRrks8t9XmU7dJBmICgUBoYhADpxEhFYcDAOefnN34aj7JZjs2QR0qqcxlKAaAFS9EI6K52mw7koGYQCAQbB9i4DQSmAR/EzpPEN1LurAWWcVZDTArE4iyHSugDpRUmboypKTnorSiCjK5+4xDAygorcApbQFMNANAFFQEAoHQFCAxOI0AboI/SuLr10AbcOv+LWjcNA0wOxMw8Th/bwH2vme6bR0oqY5mU3jr08NmT2QAozNt3pa/RdftKAojopthy+k70NM0UVARCARCE4EYOA2MMMEfLRHXoqJUCPEIqe+pKUMdDHQaAeybK0jupwKeXQN4hQKVJcaTGyYrcn660cVVC2MnU1eGTddVklFAKgBfj+uG0goD7pVWYN6WvyXbUQCSJ/dCZIg3Zsa1IxmICQQCoQlBDJwGRirBH2CsP2WgKKhAIaFXQuM7veEiko+rgP6JQOdnjPcZo+b8ZuD3BKMhVEtV1c28EtAyziYDgBu5JXi6SxBu5BbLhkLTAFIzChDg6YwgtYvIsGEk54yU/P/bO/O4qOr9/7/ODIuAsokwgOCupSYpLl8s7Rq4ZJvaYmY3M+v+Kr1qtqmVQN2u5q1uaWbfe23R+7XslmiLSyFuFeQCuJspqRA4qJGAgGzn8/vjzJk5Z+acWWA2hvfz8aDknM/5nM/5MDDveb9f7/ebIAiCaDuQgeNhRGGx1MjRMIb/K9PjmkaDhCYeumj31JBpFUMeBuquADuWCAbMjgwgKEI4J+1LJdLK/lTdOgcbEuqVjZy/bTmJv289iRcmXAcO6vle4jjz1HBpyjmljhMEQbQ9SGTsYXQhOswfMh8aw49CwxjSL1fghoZGDLtWD11To8d6ODlEZanBOyOpavzVPGXjRqQVWVWxYR0wtSdv0WJBCs+A5dtPYeHE66wKi81Tw+2tgEwQBEF4L+TB8TBZp7PwdsHb4MGDAzC/4opQuVjEQz2cHEapwSZ426VyygqBHqNadMuUGIanpoxGaWUDggM0OHDuD/xty0nZmGbGMCg+HLmLbkX+uT9wpa4Bl6rr8U7OGYtx5y7XIjYsSDHlXHqeIAiC8H7Ig+NBLAXGwD8jw3E0wN80KC3Dewr8WUOxLo7Gdq2cHRmqxf/ELuCHS/6w6AZ+ofIaTlcKfhmxK/jtg2JVm2bGhgXhjqQ4PPQ/3fHA8ESrzTWp+SZBEETbhwwcD6IkMGYch+lxOmR1DBEOxA32wMpagHldHE4L3PWOWa0chZcbawby1wK/5QNn9xqNHWkX8LtX5cq6gX92oBh/enMv3j2hxZ/e3GvsEB4bFoTJg+XG4KTBcRZeF1vNNan5JkEQRNuHQlQeRElgDEh6UF1rgK4thKdExLo4Fb+a0sIB0zH/YOCDNMtQ1t7XhS8A4DS4kvYGFn2jswgT8QxYtPEowMFCHzO6bxcAwKZCuTdoc2EZnh3fz8I4mTosEaP7dlFNDbd1niAIgvBuyIPjQcQO4orF/TgOJaPnt43wlJSweEFTI123eKyTDkiZDViT/DIeYTueRTT7XfE0D6jqY9S0M1uOXFAUCMeGBSGlV2dV48XWeYIgCMJ7IQPHw0zpMwXrJ663MHI0nAYJyY95aFUuoGAd8PZAIHclbCmPOcajh6bcoemPlF5R1M4AQiq4GN4iCIIg2gdk4HgBN3S5ARk3zjOlinMa7y/uZ05lqUxDY3HOWrq4BRrM/FN/owbGdFTd97N82ykAkGlnpFCqN0EQRPuCNDieprIU2LcaU/JWYaSGQ4m/PxJS5kHXZ4qnV2Y/BetMBoxShWLFFHIAqiX4eIzLewj5d7yBk7pJCA7QoKSiDmUlZ7Ar9yec5XXQo7PsCjFMJWpnthy5oJgyTqneBEEQ7QMycDxJwTrgq7kQ3+R1zYCuuRnY9Trg1xG4aa5n12cP5t4ZpQrFYgq51MjhtMCsbOCKIWzkHwRseEBWKDB8x3NImT8Bn/3SjMLNK/Ca3xr8JYChmXFY1PQY/ts8xjidNI07NiwItw+Kxd+3npRpcijVmyAIov1AISpPIRoGanqUHemq9WG8CiXvjHmFYqUU8jvfBromC/2qBk4GAoJNxo1knt9LTuKdrN14zW8NtJxwXssx/N3vA+hw2fC9ZRo3pXoTBEG0b8iD4ylUwzYGGC8YCd6eRaXmnTFPb1dLIbcxz1k+Bt24AqNxI+LH8Xiu5wXE/GkCesWEKhoulOpNEATRfiEPjqdQrPwroa20aFDzzigZZtIUcoko+UJlHXIvB+JK2hsW88R3643zTIdmJhcOM06LjhExGNEj0qrhQqneBEEQ7RPy4HgK0TD4er4Q0jHmBzHrRoI3Yss7Y45ElMygwTuNs7CheQw0nA5v37YddyXUG+eJBTBvyp+wePNjeM3vA/hxPJqYBgcHvoRr/pFueTyCIAii7UEGjicRDYOS/QAYEN4NaKy1z0jwNsLi7VuzmSiZA4+/+a1BFeuAAr4vnt7GYdjCMYhFheDhieyF0X27YBE/BnvqB6G7phzn+BhczO+M9MFNLn4ogiAIoq1CBo6nKcqxTLFuYXftNoGC9siPY3gvYKUxO+ri7jPQFaaDAw/GaVAz4jXwrBv06Aw93xk6/I4R3HHUXY2WzXOhsg5nL9egR1QIhaQIgiDaOWTgeBJ7Uqx9DSUxsQEhO2oNuAKAM4iKOcaj508vIo57B2WsM+7X7sJSQ0YVX8yBP8SAYTPx2YFiLMo6Cp4BGk4o+Dd1WKK7n44gCILwEkhk7EnsSbH2FURRMWDWYVyOH8csMqY04PFOv6O4kSsyGjfCcQbt1mdw6VQuvty0wdi/Kpr9jq82fYby34qsr6UtpOETBEEQLYI8OJ7E3hTrto5SpeP5RwXt0cZHZc/fzAwtGcy6LQw79y9sCrRs1cCxZkR9OhGfGAoAZjXfjCnaH6DlGNiavwN3mVVVtlV1mSAIgvAJyIPjScLigbRMU7p4W8uesge1MBwgFPiTeHMYNODAWRg3IkqHGQAOpgKA92q/N3p4OPDAV/OA3/Ktr4U8OQRBED4HGTiepGAd9Ltewf5Af+i1fkBauu95E2yF4YY8LHhz7v0Y3OhnoeFUKjsrwFv0YLf0/AA88EGq4LlpTyFBgiCIdo7XGDirVq1C9+7d0aFDB4wYMQL79+9XHfvvf/8bo0aNQkREBCIiIpCWlmZ1vFdSWYqsXYswvqsOs2JjMD4hFlk//cP3vAlKBQ3Nw3BFOUKoau9yu6dl4LCz63zLAoBK9hFjgqfGP8T2WgiCIAifwCsMnM8++wwLFixAeno6CgoKkJSUhPHjx+PixYuK43fv3o1p06Zh165dyMvLQ0JCAsaNG4fS0rZjHOgvHERm5wjwBpcDz3HI7BwO/YV8D6/MBaTMVg/DmYeNZKjEqiCEpbS15VjbNFZm1HCcSncv1izUGLK36jJBEATRpvEKkfFbb72Fxx9/HDNnzgQAvP/++9iyZQs+/PBDLFy40GL8+vXrZd+vWbMGGzduRE5ODh5+uG2EeIpLco3GjQjPcSjx84POQ2tyOlJBLzhg5FxgxBNyg0KtJ9eAKcC4vwHVemDNrRanGYAxFZ/gT36WYSlFs0j01PQY5VjVZYIgCKJN4nEDp6GhAfn5+Vi0aJHxmEajQVpaGvLy8uyao7a2Fo2NjYiMVC7dX19fj/r6euP3VVVVAIDGxkY0Nja2YvWWiPNZnbeqDAn7PoCmq05m5GjAIbbLIKevySNUlcHv63ngjMYLA8tbhabkxwDp84V2gx84o1BYhJ3YjKZbM4CYQeBufxvaLfNlhov4bzVBsnBHYRzjtGie+CZYcLRw7+Bo4QuQr4VQxK7XNNFqaJ/dA+2z+3DFXjsyl8cNnMuXL6O5uRkxMTGy4zExMfj555/tmuOFF15AXFwc0tLSFM8vXboUmZmZFse/++47BAcHO75oO8jOzlY9F1V9AuUdAmRv6RxjeFAzAvm7fSNEFVV9AjeZeWY41oysLzagPOQ6NPAcAjQMDTyHCZETMLBim9lYHoVf/y8a/TrhaqAOkd1nY9i5VQ6tgQNwNO5B/N6xL/xP6XH13P/hWgD1r2op1l7ThPOgfXYPtM/uw5l7XVtba/dYjxs4rWXZsmXYsGEDdu/ejQ4dOiiOWbRoERYsWGD8vqqqyqjbCQ0Ndep6GhsbkZ2djbFjx8Lf319xTHl5Vzy1Yz2Ymfth+q1PIiZmkFPX4zGqbgR7d7nEgwM0MQ3+eTYWerOXXRY3ET8EbodGYvI1Mw7Dzq02tmtoHrME7LxGNp8tGKfB9df1hXbXK+CYYZ6Jb4Hd+FDrn68dYc9rmmg9tM/ugfbZfbhir8UIjD143MCJioqCVqtFeXm57Hh5eTl0OutqlDfeeAPLli3Djh07MGiQumEQGBiIwMBAi+P+/v4ue4Fbm7tM22yhv2Echwt+PLr6yi9c526ybulNTIPFTbOgR2eLoWWsMxY2Poa/G7uFc0KxPxgacjIefrteFWoG7cgAWLMp/AR1KTI3ZAb8dr1iauzJePhtfQboO460Ny3Alb8vhAnaZ/dA++w+nLnXjszjcQMnICAAycnJyMnJwaRJkwAAPM8jJycHc+bMUb1u+fLleO211/Dtt99i6NChblqtc0gMTYSG04CXeCM0nAYJnRI8uCoXYOiWfuxYIR77ukLRuBH5b/MY7G0WuoVHohLvBayUD2DNQNxgoWZOxa9o0gRg3/e7MGLUGPhXl1lURAY0QI/RQP5HlvNU/EoGDkEQhI/jFWniCxYswL///W+sXbsWJ0+exJNPPomamhpjVtXDDz8sEyG//vrrePnll/Hhhx+ie/fu0Ov10Ov1uHr1qqcewSF0ITqkp6RDY0id5sBh/pD50IX4TP6UibB4dB6YioucunEjokdn/MT3RwHf17K+jSEL6gIikctfjwsh/fF7p+uBuCEWFZHBaYUWDQkjLOveQAP4u0Z3RRAEQXgPHvfgAMDUqVNx6dIlLFmyBHq9HjfeeCO2b99uFB4XFxdDozG9Ua1evRoNDQ249957ZfOkp6cjIyPDnUtvMVP6TEFlfSX+mf9PMDC8XfA2wgLDMKXPFE8vzenEhgVh6ZQbsDjrGJoVKvFpOQ6TBschq6AUDIKhs7jpMSz1/wAa8GhiGrzU+Cgav72ETYWHjB3D7+/BYaI4icFbZJH+LQmTCfDAB2nUg4ogCMLH8QoDBwDmzJmjGpLavXu37Ptz5865fkEuRl+jx9sFb4MZhLU845GZl4mRcSN90pMzdVgiRvftgnOXaxEcoEFtA2/8f/eoYMSGBeHZ8f2Qf+4PcBzQNWIkbn5vEBK5cpzjY4TwVoGpkCPPgD2//oGK4zmI6XGDYNCIX1KGPAxEDwDWpMJYApAZelT1SqVQFUEQhI/iNQZOe0Jfo8d3576TaXAAwcgpqS7xSQMHEDw5sWFBsmMXKutw9nINLlZdQ01DM5K7RyA2LAi5RZdRxjqjjCmHtu7X7sJSvzXQbma2u4Kf2ATL+sY8sO99YNyrrX8wgiAIwusgA8fNZJ3OQmZepoVxA/io0NgKnx0oxqKso+AltoeGA5ZOuQGj+3aBhoPsnIgOvwvGDSfxyHw9X9kjU1kK5L6rvIC8dy0rKxMEQRA+gVeIjNsL+hq9VeMmPSXdZ7035lyorLMwbgDBoFmcdQyAYOhoDen0Wo7DPUPioeU49NDoTcaNiFpX8IoiqHSnEgwj6iROEAThk5AHx40UVxUrGjfPD3seY7uNbTfGDQCcvVyj6J0BgGbGcO5yrUy3I9XplJ1PBNu0VF70T60ruNjNXKlAIHUSJwiC8FnIg+NGxPo3Ujhw7cK4uVBZh9yiyzhc8gdyiy4jJEALjUqFPi3HoXuUkModGxaElF6djdqd2LAgJA8aiOaJb4GHSodyc6TdzEXEawDg7F4hlNUaKkudMw9BEAThFMiD40bE+jcZuemmoAnjkZv3BqakveHJpbkUNa3N5MHx2FxYZpE6PmlwnIUY2Rx240PIPgekDu4Ovy595cZNZakQmio7BOxIl3cz7z8JaKwVPDdFOcDbA4XztoTK1pB2TW/NPObrj+xF+iCCIIgWQh4cNzOy7Gdwkjd0xnHI/G079PpDnluUC7GmtdlcWIZ/PTzEoiP45sIyXKisszn3tYBIsG43y42AgnWC0bL2TiD7ZUloigF5q4BOOqDHKOGQaJQAJqGyox6YylLnzKO0/rcHCt8TBEEQDkMGjjupLMWhfSst+lDxHIeSC22ri7gYclIyRKThqG+OlFnV2py9XAvz2n+iBseRewKwNDbMkQqRK4osx7FmoGS/cqhJLQSlNk9LxMu/5QNfz3WesUQQBNGOoRCVG8k6/h9kRFvWddEwhoTYZA+sqGVIQ05iWvfUYYkW52yh5TgM6x5hkQ4u1eCo3fNvd/dHiPmESsaGFKmoWFF8zJl6WklDTdZCUErztES8XLAO+GouLDK+qHcWQRBEiyAPjpvQ6w8h8/QnYGbeGw1jSI8ZDZ3uRs8szEHMQ05iWveFyjrVcJQSWo7D36cMRFJChEU6+N+nDJRpcJTu+dKXJ3Cl3mxS0dhQQkmIPGSGZLzh/+bek9/yrYegwuKFLuecnYJnEalHSPQ8KaWzU6YXQRBEiyAPjjsoWIfi7OfB67pYnFquuxXjJ6zwwKJahlJ6txhS+r2m3qpxM/fW3ki9PlrWngGAYjq4rXvyDLh0zUy8ExYveFfMPSEj58oL+il5S5IfBvI/ls/HmoG9y9VDWRgO7P2H4ToGgAPS0m0LjM09QimzVdLYNfYZSwRBEIQFZOC4GsOn80QNBw1jMv2NhtMgadRiDy7OcXpEhSiGlI6UXsGyrT9bvfbdXWcQHxFkDGdJUWrjYO2eGg7o0kHBmuqVCnAcZMKevFWCgQMIPw+lUJC5cSPyy3bl41/MtJwDDNiRCQy8V90oURIl565SCJdpgFk7gK5tJ3RJEAThTVCIytVIdCH3VF01ZlBp0DYrF4udwaUhpecn9MPr235WqxdsRBrOau09/3Z3f4QHKgy2Jfq1VtnYIdSqI4veHRUUdUI8kDJHCEcBwv/vesdx44Zq8RAEQRghD46rieyFrE4dkdE5wqS/YQzzB8zElD5TPLu2FmIeUlKrSjxzZHd8lHtOdkwMZ9mqc2PrnlHBfti69YjlQFui38heADg4x8hRYeOjQEO1cqhKbX0jnhC+Kn4V1upoWMrZtXgIgiDaOOTBcTF6Py0yoiLl4mKOw9snP4K+Ru+5hbWS2LAgo3GjVJVYy3GYNDhO8Xj3qGDbKd8q95RWNVZE1OFIvSFSHUtYPHDXCghGjhSVssotQSm9W/SuAOrrC4sXavQ4atw4uxYPQRCED0AeHBdTXFWs6CvgGY+S6pI2F6ISMU/bllYlNs+QWpx1THZ87y+XVNPMncKQhwUtjpo3ZMjDQPQA4PS3QEgM0G8CcGyjvOoxB4OORwOMehroOQYoKwR2ZAhhKFteIGlYbN9qQQck9a7MP9pyb4051sJyJFAmCKKdQgaOi0kMTQQHDszszVDDGBLO7wd0wzy0spajlLa9ubAMWU+l2MyQAoCblu20SDMf3beLw2Erq4geESXMwzmlB4EjG0zGzdhM4f87lgjHfvgnENEduGkuMPAek2ECCHqb2gpg27OWRsaBNcCJLyEzhETvyvyjporKrcVZtXgIgiB8CApRuRhdiA4ZIzPASUIgHGNIv1wB3faX22QYQS1VvLaBtwghXaisw9nLNUajx1qauVtQCucc/kTe0iE7w+DNYaYxYk2ciiLAP9ggVgYwcLLgARoyw/JeJzZD0ctjS4jsKLbCcgRBEO0Q8uC4gSl9pmBksxaHv/p/AICk+gbompuFk20wjNAjKsQiQMMBNqsPL51yA0b37WJX5WKXYavaMQCAV8gAbwY+SJWnn3MaYNADEu+PA1gTIrcEW2E5giCIdgZ5cNyELnYoxtfVY3xtncm48aUwgplGV63iMQCblYtdirVqx0Y4KIqOzZtmWXh/HKAlQmDzNHDzasgVRWTcEARBGCAPjrsQwwhfzxe8AW04jHD2co2lg4NBlv5tLRRlq3KxS1H6OQyaChz5TCIeBlqdRs5pgZ5/Aopy1Mc4IgQ21w3JPEeSNVOKOEEQBAAycNyD+Om6V6pzs2dciKid6REVYmGAKFUW5gD8XlOPC5V1iA0LUq14LIairFUudjlK4ZxbXxJ0MWKzzRajAe79EEgYDlTrgaKdUDWWOI2g5zm7V/AsOVL9+PAnkgEKIuZeqV79+iIIgnA1ZOC4Guknb3DAyDnAiCe9+s3HWrdwwFRZeOHGo8a3VgZgzieFsvFKKeIeM2rMkWZZiQYoWOuMG9ErN3Cy6eduzROUmAJ8kKZcnK+yFCjZZxrryLrMKzdLjSdjKMuKQUUQBOEDkIHjSsw/eYMBuSuFmiheGkZQ086Yp3GP7tvFouWT+XiPhqLsxdwAtVrfhgMmvqmQEi7x2oTFK/zcVTj/o+nfUs9LUY5CvywHqi9zWqFmz7q75MYTQNWOCYJoN5DI2JWoZex4caVZe9O41doziOPzz/0BwM7qw55CyQAFoFrVeORfgeGzLFOy73pH8NqIHhHVTC0b1ZLF9HGlZqBit3JFOKHBqLiem+ebavgAwv+/mit8UbVjgiDaCeTBcSVKBdhEvLTSrC3tjLVxUuZuKERNQ5NzKxQ7G0VDhAET3wK2PWPmntKYOpLbSslWK7x323Jg6zPq6+G0wv1VPTWikWO2rsd2AJ10wnrKCoHsJQpzqNTj8cLXIEEQhDMgD44rETN2lLbZS1PElTp3K2lnYsOC8MKE61TnaWnncLeilDLOaYXCfXeusPTSSA0BW32jUmab5ha1Of1us5KirgHS0oGEEbDp6ZHOK3YdD4sXXk870uFQKMue12BVGaKqTwBVZaZj9nYupw7nBEF4CPLguJpeqcC9Hwh/5AvWGvQP7kkRt5YJZY2pwxJxna4TDpz7A8O6RyApIUJxvhu6hlmdRwxVRXZ0fA1uwVrqfksL51mIyucKnh/xeun9ZPBAdrrwz7tWqISpIBy75yMgJMpyXXYVMRThhFBWyT6gBAbDCpYC5IJ18Pt6Hm5iPNjK1wWRfEi0qW8XpwHSMoC4wabrRCFz2SH5ONL8CJDQmyDcAhk4rsS8dklaBhA3xC0p4rYyoRy9FoBdVYmlcBBCVS5rqukMrBky1vpZKaGk6clbZQptifeLHmBZFVkcn70EGPsq8PRxobHn0f/Kh3Bak5jZHNWQqJJAmQHfv6k8TjRGeqUCX88DZ5iPE0Xysml4Q0gM1is7U/q6gPnfBDL6CMJlUIjKVVSVGf+Q6bVa7A/0h37Xq24xbtQyoewJFyldu2jjUbuqEnMwaV3FF1ZL1uB2bIWb7MVaV29pqKaxRsG4kZC9RKihc+wLy3M3P23ykpzdK/THOpYlfAGCEa2EzerNgNEIYjzw1TzBmHEoPd1GZWfWDJzarh6yUgpn+VKIS6meka8KvX3p50a0WciD4yI4w5tdVscQZEZFguc4aBhD+vH/YMrIhS69t7VMKFthIqVrecDCAaBWlRgQKhr/XlOPOZ8UtmgNbRY1D8qBNcDJr+SePDXxOQDB86NiXPzwpmA8K/a/MtRZUprvno+E675bbOfD8MC+1XaOdYCtC4T/m3svlDwbgG95O6wZwL7k1SIvFeElkAfHRbDIXtD7+RuNGwDgOQ6ZZz6FvkbvlHtcqKxDbtFlC6+ImOEkRZoJJV53uOQPi+uVrlXqzGRelVhMBRf/nRARZPTmKF3jk4TFK3tQTmyWf2rfkQmkZZpEzEoc36TsdWHMipeEAbnvKlynAcITgQGTYFPA7C6k3gslz8ZX82x7O6x5CVzhQWith0lN1O6FyQYtpj15qQivhzw4Tqa8thy/Nv6Kcr9kHBs0GfwfP8nO84xHSXUJdCG6Vt3HmsZGzIRSqiIsvU5Eev3eXy4pRk+kh2xVJRbvIZ3H6yoZu4q4wbbHsGZhnNi2o2CdpdYGAHqOAYp2weBDsxMGpPxV0P4Yhcy8UDH5zncED4+5jsb+mQXziNMC199h8EpJ+3WY9/XSWF+7seKyUgVpXkE21AzkrwWirwMqf1MXMLvCg6A0Z90VQ70hO3uAtbQfXVsSJbcXLxXRJiADx4lknc5CZm4mePD4aPOHYIzB3I2h4TRI6JTQqvvYU21YqYqw+XUi4vXX6ToJhonZ/cyqriDrqRRjZpWttdlzjU9hrfaRiPipXRQxR/YEjn4Oi3f0X3cB0z4FNjxgXbMjm9tQr6f/JLmQWfwkPSvbYPw43pJCeCVrgAc+ATZMs1zTzU8DqS8Lfb0qfhX6bK1JtXwu44SGfVDSGqmx93XLY1IBM6DsQWiNuFnRw/RX9TVYu4+j2XltLdyjVgPKl7xURJuBQlROQl+jR2aeYNwAhj/p5sYNOKSnpLfae6OmsRGrB4uYVxG2VX34wLk/VM+L8ABqG9TfHNU0PNau8SnET+nSGjpJD8q/N//UHhavrJ1hPBAQIq/JYw2OE0JkFUXAlfOWBghrBhpr1Wsz2QUPnP5ORR/0liB6rigSjJsr54HkR6AYFhP3ARCyxVqL6CVQ8yCU7G/53Pam30t7gFlDKmq3FWazN9zjLaJepde/G0piEIQS5MFxEsVVxeBt/BG8J+w6TOkzpdX3UqsibKt68NHfKlXn1HIc/qhtsHlvWzoaeysh+zRq3cqtfWof8aSlZ0X85NtjlDCfYrdzQ3+s4EigssQUtlHqqyWdL6Aj8MXMlj3fwQ+UjzNeJf0dQLebgPO5MAa60tKFfTq7t0XeJAukXgIlD9rGR4GG6pZ5P+zxyon3dcRTYead4Sa+BSDSdN7ecI+3eXlaWkOKIJwMeXCcRGJoIjQ2UnE3Vv7sFIGxqLExv5u1VOwLlXV4ffvPivNpOQ7PT+iH1buLrN5Xw8GmjsbeSsg+j3nqua1UdFuffMPihX5XaZlmlYxXCP2xEoZLjBvAaNgYX5OGSsnifAkjFMTInHx8SwTJaqG08z+a1gQmFDU8lgX4h9iZwm4F6V6pVQ8Xhcst8X4Y57SxHzcvEIwSe7woCt4Z7dZn0KGhwjTGHlGyt4p6nVV6gSBaAXlwnIQuRIf0uLHI/G27MWvKHB7MKQJjQNDYhAT62Z2KrRaeevn26zFxUKzV8JXIigcG446kOLvW5vVdxL0RW598C9bJPTSiFwRQ76vFRGkwL4SCgiKEa9QEr9L7F+UIRoFVkbMDXc7N1/bFTElxQFGYbO98HDA2U7lw5pCHVTxUPLDvfWDcq6ZDDnk/1NbFAf3vEkJ0379hnxdF4efFsWaE1JebDtgjSiZRL0GoQgaOs6gsxZQf1mCkVoPDgQF4LjoKzAUCY8DUMiEhIsjucJBS6EgDYGh3Qfj7+9V6q1WJtRyH5O4Rdrd/EFPGCQdRq56sVCV5RyYw8F6DUNlaGMVMaCwKYUWDqmS/MCZhhLwjeq9U4LEdYGtShSrGFmgcF0FbLI0HDm8QGoY21grGSrVePdQlMm2DML7mknJYyNjTy2yO3JVCBpvYmsIeQbK494qIezDNfmFzZSlQc9ni58U4LWoCY+RjbRm9/iGC9so8m80bRL32ZH95a4aYN63Lm9bSxiADx1lUFAFg0DU3Q1dbh5rLFciIijQaOZyTBMbm6eGTB8djc2GZRTq4OUrp3zyASatyAZhSgMW/lUI6sPBvcd69v1xqcfsHopXY+qQuftq35XEx/3RflCP3YEhbLRg8Ec23/xOaLQugsZiXAed/sG3ccBzQ81bhXorwQq2gca8Kf8yvnAcG3qecWQYIb/ifPiA/N/YV4CaJEVKUo3yt6DkCB3RLsc/7oSoy5oRmpwHB1ueRvkFJ9xucxDjRoDllLjpe1AsFGTt3M80lNTrF7ytLhUKMeassjZu0dKHH2KkKQZslNVzdhT2eMcVWNoNb90buDGPAnrW7y+jwNn1VG4MMHGcR2QvST4xTrtZgZN01HO7QAbj9TSR1G9Nq40YpPXxzYRmynkpBbQOvGg4Sr1P5cy/7t4YB7z44GEO6CZ4daYXim5bttJqaTrgQe9Jvrfa5UrhGSb9x+BPTWIMngs0pRPaAt5DatyP8Nv9F7kXKfVf5Pne/J2RSAYI+CAD+OQCqYZ68d4GQLoa+VtYMJg4o2mk5JnuJcO6muTY8LsaHM4ieFSgrFPQjIma/2zLE1HS1n41581Xx3uL/mSgG56HN/SduAsDeXW69rs+gB4DDnyqsRyOk6menm53jBK2Wu94Y1XRBUo+W0hhpT7OWvJE7wxiwZ+3uMjrsWQthFRIZO4uweOCuFWDgoNdqsT04CIc6BCJp9IsY33+aXcaNWmViEbX08NoG3pgOrlSl2B59jQgP4b1RDDF1jwrG2cs12HGiXLX9A+EG7E2/7ZpsllbOmcoVmF9jT/ozawb3x6+4FhAJBHdW1vkoEZ4oiKIHTjZ5mBTbSIjT8ED2y+rziesfOUd9TPYS0yfr1mRmZafLRbqqa2dCeC8sXi7+hsbUqd08rKhYZUo4Jpo/HOOFbvLHsoS0e0UjVGkPeEEDpHSPr+cJc1kTU1eWmvqatUakbM3baG2McWwLhNLOElvbWrs7Rd327CNhFfLgOJMhD+MLrh6vHF5h/GvF/fy/yIiMtZkebk/3b6U0b6nmRq1K8QsTrrOqrzHnr58K6eYAFAsDSjlSegUpvTrbNzHROuxNvzUfByhfY2dRQhbRE8AhMMXxGoNzw2wOcy8IoJwKby/j/y4ULwQMXiMVf+S+94VCh/akdauiIEZWW/vGR4W6QLLeYLxCp3ZHkYTSWiTiNp+ON3n2lLwOBesEo8p4r1Z4fezxNtp67TkqlN632r5wY2vX7k5RNxVNbDXkwXEi+ho9Xj2yUpZNysCQmZdpNT3cnu7famnez9/Wz2aV4uXbT+GF266Tdf22BgOw0KyDuBrLt53yzg7hvoq96bfScWrX2FuUMNSQORcaZzn+rneU+2/tyLD8VGt+P3vhNIJxIz7LXSvUx+auAE5tE1K2W0Peu5brT5kNi98e0aPSYmPKnt9GJ2Fe1Vp8vspSM+PGcN+v58nHSL0/0m725scrisx6rWkEQ+nUNpNXqqJI+BmplgjQmEKctqgsVQ6VOlqXCLDtKXWkn5janlnzoEnPt/WiiZWl4M59Ly994GbIg+NEiquKwRT+INnqP2Wr+/eFyjp8c6RM0dgYFB+uOod0Li3HIeupFJRU1AEc8EdNA17+8rjqszDY1o6ar5Nog9hTlLCx0fr4s3st51X7VCu9Xq0HlxSOE/7IS+fplQrc+5HQl+rsbstrtj5j9+Orwnjg1HagSx+g7JBZjSFn4YB3plUeKQVYs+n5ai4rr4Pxws9JJowG0G0kUPyTmWdBA1x/p7w/2Q33AeCEn3H+Rw4ukDf1T+uVaqiOHQI01pj+H9lLGHp8k/L6U+ZYZsOV7APX3IwODVflx6WC4V6pwD1rhLUnDLd8DafMNnnz1IwOc52OdG9ED5r4XObic6mHzRlFE10piFab2/D8fozHOHBo7g5gWAsLi7YCMnCcSGJoouKfLA1jSIC/6nXWqv8qhZ3MxwDWqxQDwN+2nJRJHBXq3MoQM6pseXDaXZViX8Q8NV0tVV3tvKOudPHao58rnDRUZgYMGUDDFf9wqlZrdiZbW+kFsolcCMyM/1UaKj6vvc/KAf3uAE59o36N8flUvEicwYsi0xFBWZzNeODEl/Jjij9fBxC1SBynYtyZi7alaIRQpYgkBOcHmN50tVqbWYSKYm9wwMi5wj3Mf1eUdDrSvbF4LrPnMBcT2/p9tIYrBdFqc5s9PwcG7dZngL7j3O59ohCVE9GF6PByrwfASVwfHGNIv1wBXV216nVq1X8BdQ2MNCXcWpViKVKJo/h/jcLfNo4Dlt1zg2xNxnMwaVbbbZXitoqr+hW1xJVuKKtgwci/CpWZh88yCZRFlGoBucq4sUVrqy9bwMB6j7PxNA54e8ZmAr9ssfMahTGi5+zKeRd4rhyBWbm/ys9fDJ0CpjCaWQiOA4N2y9PKAm7p918ZxNlKr728VcrLskvkzqy/jm2JidVChOZjLJrEzgX2vKEsJHckpKY4t2GvSvZZPD/nIXE0eXCczKTrH8LNu97CkUDBY5NU3wAdD5uxYKXqv7lFl61WH7bVRPPPIxLxn33FqvdkAFY+MBidOwYiOECDkoo6cBwwpFuEcW5xTcEBGmMqOgCqUtzWcHVqq6OudDXBsvRTtzktzY4aOku9f1ZL4LRCV/YrxQq9wVqO5sy3zpgFmLVDCOG0Zl1pmcL/v3jUCWtyI6IYvSgHeHugVc8XZ6z0bQ2DODtljv3i4rLCVjyAuDgrHlCZJ0kcr/A7rSS8BgN2ieJ5iZBcqRSBmicLUPld5IE1tyoumXFacB4QR5OB42xC46CPn4FxJR8LVqvKp1mlisDm1X/VQlcTB8UCAHKLLiMkQIvfr9ZbFDPVchzuHdoV6/cX26xOLN4zKSHCYoxaRWIybNoQ7qqn4Ygr3Z42BOY4ksUlwmmBG6cLGhBnGCKcRlhn12Thq6Ha9AzQwOVeJWtaHLFYnqhTaU34Ljvd4Kr1kIesJXBawbip1pt5bJSfQQgJ2vGMjAkVsJWa1/oHC14OUYNSWSoI7Fv7HEq/CwYNkYVxA5i8M00NQL/bhGNqNapMFwlzRQ+wXQ/rq3lASLRQ1DKyl/0NaAEwcGie+Cb8PCCOJgPHBRR3vgUD754H/6pixU+z9qSEA6bQ1eKsY7JKxdKKwmpMGhyHn/XVqh9QKLzUjvDWfkWOen3UjCJAYmQAxjci8XzXZPl10ECx2nPyTCD/Y1h9wxsyQ/5JVvoMxzYqi2n7TADOfGdFR+KArsbaG8qQGcKbq/ipu9etVqpH28Ie74YjcILouN9EoPyYoV6PE+YEYFQVDvmz8DPIftmBqx15RulYDdA7VVJUkxNqJYV3b50hfcsLQJfrTK1ERHJeNZQesLZeJgjstz5rvV6U7BIe2P8vO9bMA59ONfybA5IfEdrE2EoSAHCg+1MYfONDttfiAjjGnPoqbhNUVVUhLCwMlZWVCA0NdercjY2N2Lp1KyZOnAh/f0th8YXKOllFYEAwNn5YOEbV2LhQWadaUVgNayJhDYBNs0cqemzaCrb2mZBQWSpx1xvgtMD8o3YZOF6315WllkaR9BigbDSJY/yDhQwdpf0AgL3/UM/64TTA/GPKn66VKjWL4xX7a2ks+1gBYNCAS55hZmzZMoSUPFlq3i03eGYmviWIxMMTTT3GRA+HtYrW7RrOJDyWhoU+mwGc3OzpxbUIBuB43APoN/Ndp/3tcOT9mzw4LuBKPbD1qB5VDc2ICA5AQkQQiitqcaWuEb9eUk4J33GiHL2iOyIkQGscCwARwQFI7haBlF6draaLm8Og/gGMB1Db4EnhIOFWWhIO8maUQmFKmWDWrlPbj8pSoGCt+r3F1Gnz+dVE02KqckWRwi8kDwSEyNbCQwP+1iXw2/WK2XxWfuk5jZC6nLvScv4hM5WNNWennUsZOVcQiSuhtk/eRvxQoPSgG24kGpsGb5S5IJjTtlnjBhCeqn/Zf9FctVjeX81NkIHjZD7P/w3pBVqg4IhD11mrScMBmDIkHpsKS+2uRmwNSu1uhzijnoYvobYftoTMauJPW6Jpa6n0PUYBvVLRdOkX5BSeQ2psNweMD4OouJPOstIypwV6jFYwcAzhp5FzBc3KlWKgtkI4deY74Jftdt5bZT3WhOLW+nqJ149+Dtj7eivW4ATcYtwAABNeh0r91cCAL59y0zpchwY8+D9+9YiBQ2niTuRCZR1e3HwCtquTOgYDsLHAecYNaW/aKfZWQW4vKO2HUqVaEWueL6VU+bskBQptpdKHxYN1uxnXAiJNLTHkN7c8Jt6ja7L6/Akj1J8nb5VgGA2cLHhc+k0AfrGWyaWB1b9t5s+sxsg5yvOI1yfPsH6fVuJ1/qOiHLRsVTZ+Hk6jdffgoTG0e3E/5MFxImcv17j1l+fl26/H0O4RqG3gERygQc7Ji1ix84zVcZTaTRBWUArnpaUDcUNse75secns9aKJLTHMQ2jitf7Bcl2LrfnvfEfIgjEXVpsLzdXCRzfcL8wd2dNQcXe+Saw9co7gBVJajznmhfKSZwI9brHU6QBC+rJ5b6ykacCRzyRicivc8gJw9aKlaJzj0DwmHcWH96BHxR6hsanVgoHGCwVhbWRPOzreK5A803BtOhQF7g7DAWMzgKAI5Z+t0nhReH/9HfKK0zZx5Fnl3jnGaXE44REMFNu9uBkycJxIj6gQd8j3AJjSxaXGSnRoB7y764xiWjkZNQRhJ60J5zlaBdrRNdiTaaZkWEUPsBQ529UA05B6Ls7Z0r1RKpRXsE4IRynNId6nZL/wvVjRWmwj4h9sCK39Dmx7zjI0N2SGMH70c8IctRXGytgsOBpH/+iJhAffMWW6VutVarhwQluQhOHCtyX7YFGTwyoa4LEdgpcNALrdpCA2bwkM2JEpCOMf26Faf0a2hsZaicDe7P5jlgBBYZZ7aYsxS4CgcOHf2561eO00PbINxYf0GGj/jE6FDBwnsveXS265D8dBMcykllZOxg1BOEhryuN74xq6JgN3rrAuNLdXjN6SdbWkVEFYPBA2Wfne5t4g0ehQCP1ZzCH2VguNM+lCKoqU1zDyr0IIT6m4ni3ETCjRuAEsfw6tgTUDxzcDAyYJ67QQmQNCMT/JGs7uVX6GXa/CoY/m4j6LJRMU5+XBNdbaP6cL8BoDZ9WqVfjHP/4BvV6PpKQkrFy5EsOHD1cd//nnn+Pll1/GuXPn0KdPH7z++uuYOHGiG1csR+zmbeslYkNeh3/PSEZdA4/zFTV449tfFMdyTKgwrIRSRWSCIAi7vC+uEqM72q/MGkreIKYxeVpasmZrInGL+5mjFOIyiL+lxo2IuMentiv3O5v2mVDPx44aM/huMZD9kuBlU3t36ZVq+reqyNsRj5JGqOQtfTaVn6+gvTnkwNzOxStExp999hkWLFiA9PR0FBQUICkpCePHj8fFixcVx+fm5mLatGmYNWsWCgsLMWnSJEyaNAnHjh1z88pNWOvmLcXaEB5AcIA/7kiKw+DECNWxPIRWCWrEhgUhpVdnMm4IgpBjj9DcFWL0lvQrU0OtTUBIVMvXbE0kbi2zjtMKeqG7Vlheq2TcSO/XVKd8rqwAOPaF5fH+k0z3kMJ4IVyV/IjCZEzeAyos3iDybg28EO6Sovbz9ZD2RsQrPDhvvfUWHn/8ccycORMA8P7772PLli348MMPsXDhQovx77zzDiZMmIDnnnsOAPDqq68iOzsb7777Lt5//323rl1Eqa2COdaK74kcKb2ClF6drc7HcaA0b4Ig2hbO8g450xtkz/rUvDv3fij3GDn6bIkpysdDopUNqmGPCb22jm8WPDdSWLMg2C5Ya3tfRjxpWVLAEdT2Wmn/xHCgh/C4gdPQ0ID8/HwsWrTIeEyj0SAtLQ15eXmK1+Tl5WHBArlrb/z48di8ebPi+Pr6etTX1xu/r6qqAiBUaG100g8gKtgPf7u7P1768gR4ZukE5Djgtbv7A4BxjBKvb/sZt/WPRmxYB/zt7v54cfMJS08OAxobm5y29raI+OzteQ/cBe21e2gX+xwcLXwBLX/zC44GN/EtaLc+A441g3FaNE98Eyw42q45re6z0vrU7tfvDotxDj1bzCBobngAmqMbjO8X/A0PgO81Fn6cxpDhJcA4LZpCE4X5+90Bv+yXLM/HDrFvX8yfx3B3pWRwxmnAD7wfmmOf27fXZnvgite0I3N5vFVDWVkZ4uPjkZubi5QUk0X7/PPPY8+ePdi3b5/FNQEBAVi7di2mTZtmPPbee+8hMzMT5eXlFuMzMjKQmZlpcfyTTz5BcLBzPSFX6oFL1zh06SBs69lq4WXToxNDeKB8zNVG4OPTli7HOf2b0SdMuL7wMmdzDEEQRHujQ0MFQurLURMYg2sBkW32fmE1v6Lz1V/we8e+qAwRPCOJv+9BUvFHQpE8aHA4cSaKO99ivMbaeXvXKR0HAD0vfYfeF7eBAwMPDkXRt+HXLuNwLSDS7XttjdraWjz44IPUqkFk0aJFMo9PVVUVEhISMG7cOJf0osrOzsbYsWNt9t64UHkN697cK/PmaDjg/oljEBvWAQAw2I4x7RFH9ploHbTX7oH22T20jX2eiOaqeeD/+BUsoicGhsaZpVrbOt8SHkJTVRk4w5zdQ+PQvZUzumKvxQiMPXjcwImKioJWq7XwvJSXl0On0yleo9PpHBofGBiIwMBAi+P+/v4ue4HbM3dilL9iWndiVCeHxrRnXPkzJOTQXrsH2mf34PX73Lmb9fYGts674p4txJl77cg8HjdwAgICkJycjJycHEyaNAkAwPM8cnJyMGeOsto7JSUFOTk5mD9/vvFYdna2LMTVVrAnrZtSvwmCIAjCMTxu4ADAggULMGPGDAwdOhTDhw/H22+/jZqaGmNW1cMPP4z4+HgsXboUADBv3jzccsstePPNN3H77bdjw4YNOHjwIP71r3958jFaTGxYkE2jxZ4xBEEQBEEIeIWBM3XqVFy6dAlLliyBXq/HjTfeiO3btyMmRhA/FRcXQ6MxlewZOXIkPvnkE7z00ktYvHgx+vTpg82bN2PgQE8VhCYIgiAIwpvwCgMHAObMmaMaktq9e7fFsfvuuw/33Xefi1dFEARBEERbxCsqGRMEQRAEQTgTMnAIgiAIgvA5yMAhCIIgCMLnIAOHIAiCIAifgwwcgiAIgiB8DjJwCIIgCILwOcjAIQiCIAjC5yADhyAIgiAIn4MMHIIgCIIgfA6vqWTsThhjABxru24vjY2NqK2tRVVVlXd3qm3j0D67D9pr90D77B5on92HK/ZafN8W38et0S4NnOrqagBAQkKCh1dCEARBEISjVFdXIywszOoYjtljBvkYPM+jrKwMnTp1AsdxTp27qqoKCQkJKCkpQWhoqFPnJkzQPrsP2mv3QPvsHmif3Ycr9poxhurqasTFxcmacCvRLj04Go0GXbt2dek9QkND6ZfHDdA+uw/aa/dA++weaJ/dh7P32pbnRoRExgRBEARB+Bxk4BAEQRAE4XOQgeNkAgMDkZ6ejsDAQE8vxaehfXYftNfugfbZPdA+uw9P73W7FBkTBEEQBOHbkAeHIAiCIAifgwwcgiAIgiB8DjJwCIIgCILwOcjAIQiCIAjC5yADx4msWrUK3bt3R4cOHTBixAjs37/f00tqc+zduxd33nkn4uLiwHEcNm/eLDvPGMOSJUsQGxuLoKAgpKWl4fTp07IxFRUVmD59OkJDQxEeHo5Zs2bh6tWrbnwK72bp0qUYNmwYOnXqhOjoaEyaNAmnTp2Sjbl27Rpmz56Nzp07o2PHjrjnnntQXl4uG1NcXIzbb78dwcHBiI6OxnPPPYempiZ3PorXs3r1agwaNMhY6CwlJQXbtm0znqd9dg3Lli0Dx3GYP3++8RjttXPIyMgAx3Gyr+uuu8543qv2mRFOYcOGDSwgIIB9+OGH7Pjx4+zxxx9n4eHhrLy83NNLa1Ns3bqVvfjiiywrK4sBYJs2bZKdX7ZsGQsLC2ObN29mhw8fZnfddRfr0aMHq6urM46ZMGECS0pKYj/99BP7/vvvWe/evdm0adPc/CTey/jx49lHH33Ejh07xg4dOsQmTpzIEhMT2dWrV41jnnjiCZaQkMBycnLYwYMH2f/8z/+wkSNHGs83NTWxgQMHsrS0NFZYWMi2bt3KoqKi2KJFizzxSF7LV199xbZs2cJ++eUXdurUKbZ48WLm7+/Pjh07xhijfXYF+/fvZ927d2eDBg1i8+bNMx6nvXYO6enpbMCAAezChQvGr0uXLhnPe9M+k4HjJIYPH85mz55t/L65uZnFxcWxpUuXenBVbRtzA4fneabT6dg//vEP47ErV66wwMBA9umnnzLGGDtx4gQDwA4cOGAcs23bNsZxHCstLXXb2tsSFy9eZADYnj17GGPCnvr7+7PPP//cOObkyZMMAMvLy2OMCYaoRqNher3eOGb16tUsNDSU1dfXu/cB2hgRERFszZo1tM8uoLq6mvXp04dlZ2ezW265xWjg0F47j/T0dJaUlKR4ztv2mUJUTqChoQH5+flIS0szHtNoNEhLS0NeXp4HV+ZbnD17Fnq9XrbPYWFhGDFihHGf8/LyEB4ejqFDhxrHpKWlQaPRYN++fW5fc1ugsrISABAZGQkAyM/PR2Njo2yfr7vuOiQmJsr2+YYbbkBMTIxxzPjx41FVVYXjx4+7cfVth+bmZmzYsAE1NTVISUmhfXYBs2fPxu233y7bU4Be087m9OnTiIuLQ8+ePTF9+nQUFxcD8L59bpfNNp3N5cuX0dzcLPuBAUBMTAx+/vlnD63K99Dr9QCguM/iOb1ej+joaNl5Pz8/REZGGscQJniex/z583HTTTdh4MCBAIQ9DAgIQHh4uGys+T4r/RzEc4SJo0ePIiUlBdeuXUPHjh2xadMm9O/fH4cOHaJ9diIbNmxAQUEBDhw4YHGOXtPOY8SIEfj444/Rr18/XLhwAZmZmRg1ahSOHTvmdftMBg5BtGNmz56NY8eO4YcffvD0UnyWfv364dChQ6isrMQXX3yBGTNmYM+ePZ5elk9RUlKCefPmITs7Gx06dPD0cnya2267zfjvQYMGYcSIEejWrRv++9//IigoyIMrs4RCVE4gKioKWq3WQileXl4OnU7noVX5HuJeWttnnU6Hixcvys43NTWhoqKCfhZmzJkzB9988w127dqFrl27Go/rdDo0NDTgypUrsvHm+6z0cxDPESYCAgLQu3dvJCcnY+nSpUhKSsI777xD++xE8vPzcfHiRQwZMgR+fn7w8/PDnj17sGLFCvj5+SEmJob22kWEh4ejb9++OHPmjNe9psnAcQIBAQFITk5GTk6O8RjP88jJyUFKSooHV+Zb9OjRAzqdTrbPVVVV2Ldvn3GfU1JScOXKFeTn5xvH7Ny5EzzPY8SIEW5fszfCGMOcOXOwadMm7Ny5Ez169JCdT05Ohr+/v2yfT506heLiYtk+Hz16VGZMZmdnIzQ0FP3793fPg7RReJ5HfX097bMTSU1NxdGjR3Ho0CHj19ChQzF9+nTjv2mvXcPVq1dRVFSE2NhY73tNO1Wy3I7ZsGEDCwwMZB9//DE7ceIE+8tf/sLCw8NlSnHCNtXV1aywsJAVFhYyAOytt95ihYWF7Pz584wxIU08PDycffnll+zIkSPs7rvvVkwTHzx4MNu3bx/74YcfWJ8+fShNXMKTTz7JwsLC2O7du2WpnrW1tcYxTzzxBEtMTGQ7d+5kBw8eZCkpKSwlJcV4Xkz1HDduHDt06BDbvn0769KlC6XUmrFw4UK2Z88edvbsWXbkyBG2cOFCxnEc++677xhjtM+uRJpFxRjttbN45pln2O7du9nZs2fZjz/+yNLS0lhUVBS7ePEiY8y79pkMHCeycuVKlpiYyAICAtjw4cPZTz/95OkltTl27drFAFh8zZgxgzEmpIq//PLLLCYmhgUGBrLU1FR26tQp2Ry///47mzZtGuvYsSMLDQ1lM2fOZNXV1R54Gu9EaX8BsI8++sg4pq6ujj311FMsIiKCBQcHs8mTJ7MLFy7I5jl37hy77bbbWFBQEIuKimLPPPMMa2xsdPPTeDePPvoo69atGwsICGBdunRhqampRuOGMdpnV2Ju4NBeO4epU6ey2NhYFhAQwOLj49nUqVPZmTNnjOe9aZ85xhhzrk+IIAiCIAjCs5AGhyAIgiAIn4MMHIIgCIIgfA4ycAiCIAiC8DnIwCEIgiAIwucgA4cgCIIgCJ+DDByCIAiCIHwOMnAIgiAIgvA5yMAhCIIgCMLnIAOHIAjCCTzyyCOYNGmSp5dBEIQBMnAIgrCLRx55BBzHWXxNmDDB00sjCIKwwM/TCyAIou0wYcIEfPTRR7JjgYGBHloNQRCEOuTBIQjCbgIDA6HT6WRfERERAIAHH3wQU6dOlY1vbGxEVFQU1q1bBwDgeR5Lly5Fjx49EBQUhKSkJHzxxRfG8bt37wbHccjJycHQoUMRHByMkSNH4tSpU1bXVVJSgvvvvx/h4eGIjIzE3XffjXPnzhnPi+GjzMxMdOnSBaGhoXjiiSfQ0NBgHFNfX4+5c+ciOjoaHTp0wM0334wDBw7I7nP8+HHccccdCA0NRadOnTBq1CgUFRXJxrzxxhuIjY1F586dMXv2bDQ2NhrPvffee+jTpw86dOiAmJgY3HvvvXbsOkEQLYEMHIIgnML06dPx9ddf4+rVq8Zj3377LWprazF58mQAwNKlS7Fu3Tq8//77OH78OJ5++mk89NBD2LNnj2yuF198EW+++SYOHjwIPz8/PProo6r3bWxsxPjx49GpUyd8//33+PHHH9GxY0dMmDBBZsDk5OTg5MmT2L17Nz799FNkZWUhMzPTeP7555/Hxo0bsXbtWhQUFKB3794YP348KioqAAClpaUYPXo0AgMDsXPnTuTn5+PRRx9FU1OTcY5du3ahqKgIu3btwtq1a/Hxxx/j448/BgAcPHgQc+fOxSuvvIJTp05h+/btGD16dMs3nCAI6zi9PzlBED7JjBkzmFarZSEhIbKv1157jTHGWGNjI4uKimLr1q0zXjNt2jQ2depUxhhj165dY8HBwSw3N1c276xZs9i0adMYY4zt2rWLAWA7duwwnt+yZQsDwOrq6hTX9Z///If169eP8TxvPFZfX8+CgoLYt99+a1x7ZGQkq6mpMY5ZvXo169ixI2tubmZXr15l/v7+bP369cbzDQ0NLC4uji1fvpwxxtiiRYtYjx49WENDg+r+dOvWjTU1NRmP3Xfffcbn37hxIwsNDWVVVVWK1xME4VxIg0MQhN2MGTMGq1evlh2LjIwEAPj5+eH+++/H+vXr8ec//xk1NTX48ssvsWHDBgDAmTNnUFtbi7Fjx8qub2howODBg2XHBg0aZPx3bGwsAODixYtITEy0WNPhw4dx5swZdOrUSXb82rVrsvBRUlISgoODjd+npKTg6tWrKCkpQWVlJRobG3HTTTcZz/v7+2P48OE4efIkAODQoUMYNWoU/P39VfdnwIAB0Gq1srUfPXoUADB27Fh069YNPXv2xIQJEzBhwgRMnjxZtiaCIJwHGTgEQdhNSEgIevfurXp++vTpuOWWW3Dx4kVkZ2cjKCjImGUlhq62bNmC+Ph42XXmQmWpEcFxHABBv6PE1atXkZycjPXr11uc69Klix1PZR9BQUE2x5gbPxzHGdfdqVMnFBQUYPfu3fjuu++wZMkSZGRk4MCBAwgPD3faOgmCECANDkEQTmPkyJFISEjAZ599hvXr1+O+++4zvun3798fgYGBKC4uRu/evWVfCQkJLb7nkCFDcPr0aURHR1vMGxYWZhx3+PBh1NXVGb//6aef0LFjRyQkJKBXr14ICAjAjz/+aDzf2NiIAwcOoH///gAEr9L3338vEw07ip+fH9LS0rB8+XIcOXIE586dw86dO1s8H0EQ6pCBQxCE3dTX10Ov18u+Ll++LBvz4IMP4v3330d2djamT59uPN6pUyc8++yzePrpp7F27VoUFRWhoKAAK1euxNq1a1u8punTpyMqKgp33303vv/+e5w9exa7d+/G3Llz8dtvvxnHNTQ0YNasWThx4gS2bt2K9PR0zJkzBxqNBiEhIXjyySfx3HPPYfv27Thx4gQef/xx1NbWYtasWQCAOXPmoKqqCg888AAOHjyI06dP4z//+Y/NDC+Rb775BitWrMChQ4dw/vx5rFu3DjzPo1+/fi1+doIg1KEQFUEQdrN9+3ajJkakX79++Pnnn43fT58+Ha+99hq6desm07QAwKuvvoouXbpg6dKl+PXXXxEeHo4hQ4Zg8eLFLV5TcHAw9u7dixdeeAFTpkxBdXU14uPjkZqaitDQUOO41NRU9OnTB6NHj0Z9fT2mTZuGjIwM4/lly5aB53n8+c9/RnV1NYYOHYpvv/3WmAbfuXNn7Ny5E8899xxuueUWaLVa3HjjjRbPqEZ4eDiysrKQkZGBa9euoU+fPvj0008xYMCAFj87QRDqcIwx5ulFEARBuJJHHnkEV65cwebNmz29FIIg3ASFqAiCIAiC8DnIwCEIgiAIwuegEBVBEARBED4HeXAIgiAIgvA5yMAhCIIgCMLnIAOHIAiCIAifgwwcgiAIgiB8DjJwCIIgCILwOcjAIQiCIAjC5yADhyAIgiAIn4MMHIIgCIIgfI7/D4z59We16YyqAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.mean(eta_classical, axis=0)[::2], \".\", label=\"Fully classical strategy\")\n",
    "plt.plot(np.mean(eta_quantum, axis=0)[::2], \".\", label=\"Fully quantum strategy\")\n",
    "plt.plot(np.mean(eta_classical_quantum,axis=0,)[::2],\".\",label=\"Quantum-classical strategy\",)\n",
    "plt.xlabel(\"Even epochs\")\n",
    "plt.ylabel(\"$\\eta$\")\n",
    "plt.legend()\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4390ce7",
   "metadata": {},
   "source": [
    "## Conclusion"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "34dd02db",
   "metadata": {},
   "source": [
    "Simulating the circuits of [1], we are able to reproduce their results. Data are still noisier than the results due to a smaller number agents. A parallelized version of this code was executed with 10 000 agents and the following results were found:\n",
    "\n",
    "![results_10000.png](../_static/img/reinforcement-learning_results_10000.png)\n",
    "\n",
    "which are very close to the paper results.\n",
    "\n",
    "It's possible to play with the value of $Q_L$ and the number of agents. Remember that the simulation time is linear with the number of agents."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "911dd875",
   "metadata": {},
   "source": [
    "## Acknowledgement"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7721eae9",
   "metadata": {},
   "source": [
    "This work was initially done during the Hackathon on Linear Optical Quantum Communication (LOQCathon) organised by [Quandela](https://www.quandela.com/) and [QICS](https://qics.sorbonne-universite.fr/en) (Quantum Information Center of Sorbonne Université), by the team composed of Luís Bugalho, Laura dos Santos Martins, Paolo Fittipaldi, Yoann Piétri and Verena Yacoub. The supervision was provided by Pierre-Emmanuel Emeriau."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "441c442e",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    ">  [1] V. Saggio, B. E. Asenbeck, A.  Hamann, et al. Experimental quantum speed-up in reinforcement learning agents. [Nature](https://doi.org/10.1038/s41586-021-03242-7), 591(7849), 229-233 (2021).\n",
    "\n",
    " > [2] A. Hamann, S. Wölk. Performance analysis of a hybrid agent for quantum-accessible reinforcement learning. [New Journal of Physics](https://doi.org/10.1088/1367-2630/ac5b56 ), 24(3), 033044 (2022)."
   ]
  }
 ],
 "metadata": {
  "language_info": {
   "name": "python"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}