{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How to optimize controls using arbitrary basis functions\n",
    "**Create optimized controls from superpositions of basis functions**\n",
    "\n",
    "Boulder Opal exposes a highly flexible [optimization engine](https://docs.q-ctrl.com/references/boulder-opal/boulderopal/graph/run_optimization) for general-purpose optimization.\n",
    "The controls can be described in terms of optimizable linear combinations from a set of built in or user-defined basis functions, which can greatly reduce the dimensionality of the optimization search space.\n",
    "\n",
    "In this user guide, you'll learn how to optimize controls using a Fourier basis, a Hann series basis, or define your own custom basis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary workflow\n",
    "\n",
    "### 1. Define basis function for signal composition in the graph\n",
    "\n",
    "Define the graph that creates a signal as a superposition of basis functions with [optimizable coefficients](https://docs.q-ctrl.com/references/boulder-opal/boulderopal/graph/Graph/optimization_variable) and use it to define [your system's Hamiltonian](https://docs.q-ctrl.com/boulder-opal/toolkit/design/design-model-based-controls/how-to-optimize-controls-in-arbitrary-quantum-systems-using-graphs).\n",
    "Traditionally, a [randomized Fourier basis](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.190501) is used, although the same technique has also seen success with other bases, for example [Slepian functions](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.062346) or [Hann functions](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.93.012324).\n",
    "\n",
    "The operations that you can use to build the optimizable signal depend on the basis you want to use:\n",
    "\n",
    "- The Boulder Opal optimization engine provides a convenience graph operation, `graph.real_fourier_pwc_signal`, for creating optimizable signals in a Fourier basis, suitable for use in a **c**hopped **ra**ndom **b**asis (CRAB) optimization.\n",
    "\n",
    "- The [`signals` attribute](https://docs.q-ctrl.com/boulder-opal/toolkit/design/represent-time-varying-signals/leverage-predefined-signals-in-graphs) of a graph object provides convenience operations to create optimizable signals in a Hann series basis, as either piecewise-constant functions (`graph.signals.hann_series_pwc`) or as a sampleable function (`graph.signals.hann_series_stf`).\n",
    "These operations take some potentially optimizable `coefficients`, allowing you to easily create an optimizable signal in a Hann series basis.\n",
    "\n",
    "- You can also define a custom basis using the [library of graph operations](https://docs.q-ctrl.com/references/boulder-opal/boulderopal/graph/nodes).\n",
    "In particular, you can create an analytical pulse by creating a node with the `graph.identity_stf` operation, which returns an STF representing the function $f(t) = t$, and then apply [arithmetic](https://docs.q-ctrl.com/references/boulder-opal/boulderopal/graph/nodes#arithmetic) and [mathematical](https://docs.q-ctrl.com/references/boulder-opal/boulderopal/graph/nodes#basic-mathematical-functions) operations to it in order to generate more complex functions.\n",
    "\n",
    "### 2. Run graph-based optimization\n",
    "\n",
    "With the graph object created, you can run an optimization using the `boulderopal.run_optimization` function, providing the graph, the cost node, and the desired output nodes.\n",
    "The function returns the results of the optimization."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Fourier-basis optimization on a qutrit\n",
    "\n",
    "In this example, we perform a CRAB optimization (in the Fourier basis) for a robust single qubit Hadamard gate of a qutrit system while [minimizing leakage out of the computational subspace](https://docs.q-ctrl.com/boulder-opal/toolkit/design/design-error-robust-quantum-logic-gates/how-to-create-leakage-robust-single-qubit-gates), using [Hann window functions](https://en.wikipedia.org/wiki/Hann_function).\n",
    "\n",
    "The system is described by the following Hamiltonian:\n",
    "$$\n",
    "H(t) = \\frac{\\chi}{2} (a^\\dagger)^2 a^2 + (1+\\beta(t)) \\left(\\gamma(t) a + \\gamma^*(t) a^\\dagger \\right) ,\n",
    "$$\n",
    "where $\\chi$ is the anharmonicity, $\\gamma(t)$ is a complex time-dependent pulse, $\\beta(t)$ is a small, slowly-varying stochastic amplitude noise process, and $a = |0 \\rangle \\langle 1 | + \\sqrt{2} |1 \\rangle \\langle 2 |$.\n",
    "We will parametrize the optimizable pulses, $\\gamma(t)$, as a sum of Fourier components."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "import qctrlvisualizer as qv\n",
    "import boulderopal as bo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define target and projector matrices.\n",
    "hadamard = np.array([[1.0, 1.0, 0], [1.0, -1.0, 0], [0, 0, np.sqrt(2)]]) / np.sqrt(2)\n",
    "qubit_projector = np.diag([1.0, 1.0, 0.0])\n",
    "\n",
    "# Define physical constraints.\n",
    "chi = 2 * np.pi * -300e6  # Hz\n",
    "segment_count = 200\n",
    "duration = 100e-9  # s\n",
    "gamma_max = 2 * np.pi * 30e6  # Hz\n",
    "\n",
    "\n",
    "def create_infidelity(graph, gamma):\n",
    "    \"\"\"\n",
    "    Define a qutrit Hamiltonian with a drive control given by the input gamma\n",
    "    and calculate the infidelity with respect to the target operation.\n",
    "    \"\"\"\n",
    "    # Define standard matrices.\n",
    "    a = graph.annihilation_operator(3)\n",
    "    ada = graph.number_operator(3)\n",
    "\n",
    "    # Create Hamiltonian.\n",
    "    anharmonicity = (ada @ ada - ada) * chi / 2\n",
    "    drive = graph.hermitian_part(2 * gamma * a)\n",
    "    hamiltonian = anharmonicity + drive\n",
    "\n",
    "    # Create target operator in the qubit subspace\n",
    "    target_operator = graph.target(\n",
    "        hadamard.dot(qubit_projector), filter_function_projector=qubit_projector\n",
    "    )\n",
    "\n",
    "    # Create infidelity\n",
    "    infidelity = graph.infidelity_pwc(\n",
    "        hamiltonian=hamiltonian,\n",
    "        target=target_operator,\n",
    "        noise_operators=[drive],\n",
    "        name=\"infidelity\",\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your task (action_id=\"1828723\") has started.\n",
      "Your task (action_id=\"1828723\") has completed.\n",
      "\n",
      "Optimized cost: 5.799e-07\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Number of Fourier terms in superposition.\n",
    "coefficient_count = 10\n",
    "\n",
    "# Create optimization graph object.\n",
    "graph = bo.Graph()\n",
    "\n",
    "# Create gamma(t) signal in Fourier basis. To demonstrate the full\n",
    "# flexibility, we show how to use both randomized and optimizable\n",
    "# basis elements. Elements with fixed frequencies may be chosen too.\n",
    "gamma_i = graph.real_fourier_pwc_signal(\n",
    "    duration=duration,\n",
    "    segment_count=segment_count,\n",
    "    randomized_frequency_count=coefficient_count,\n",
    ")\n",
    "gamma_q = graph.real_fourier_pwc_signal(\n",
    "    duration=duration,\n",
    "    segment_count=segment_count,\n",
    "    optimizable_frequency_count=coefficient_count,\n",
    ")\n",
    "gamma = gamma_max * (gamma_i + 1j * gamma_q)\n",
    "gamma.name = r\"$\\gamma$\"\n",
    "\n",
    "# Build the rest of the graph.\n",
    "create_infidelity(graph, gamma)\n",
    "\n",
    "# Run the optimization\n",
    "optimization_result = bo.run_optimization(\n",
    "    cost_node_name=\"infidelity\",\n",
    "    output_node_names=[r\"$\\gamma$\"],\n",
    "    graph=graph,\n",
    "    optimization_count=4,\n",
    ")\n",
    "\n",
    "print(f\"\\nOptimized cost: {optimization_result['cost']:.3e}\")\n",
    "qv.plot_controls(optimization_result[\"output\"], smooth=True, polar=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Robust optimization on a qutrit using Hann window functions\n",
    "\n",
    "In this example, we optimize the same gate as in the previous example, but parametrizing the optimizable pulse using [Hann window functions](https://en.wikipedia.org/wiki/Hann_function).\n",
    "The signal $\\gamma(t) = \\gamma_I(t) + i \\gamma_Q(t)$ is then expanded as\n",
    "$$\n",
    "\\gamma_{I(Q)}(t) = \\sum_{n=1}^N{\\frac{c^{I(Q)}_n}{2} \\left[1-\\cos\\left(\\frac{2\\pi nt}{\\tau_g}\\right) \\right]},\n",
    "$$\n",
    "where $c^{I(Q)}_n$ are the different real-valued coefficients describing the parametrization and $\\tau_g$ is the gate duration. \n",
    "This is a good choice for implementation in bandwidth-limited hardware as it is composed of smooth functions that go to zero at the edges. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your task (action_id=\"1828724\") has started.\n",
      "Your task (action_id=\"1828724\") has completed.\n",
      "\n",
      "Optimized cost: 1.759e-04\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Number of terms in Hann superposition.\n",
    "coefficient_count = 10\n",
    "\n",
    "# Create optimization graph object.\n",
    "graph = bo.Graph()\n",
    "\n",
    "# Define the coefficients of the Hann functions for optimization.\n",
    "hann_coefficients_i = graph.optimization_variable(\n",
    "    coefficient_count, lower_bound=-1, upper_bound=1\n",
    ")\n",
    "hann_coefficients_q = graph.optimization_variable(\n",
    "    coefficient_count, lower_bound=-1, upper_bound=1\n",
    ")\n",
    "hann_coefficients = gamma_max * (hann_coefficients_i + 1j * hann_coefficients_q)\n",
    "\n",
    "# Create gamma(t) signal in Hann function basis.\n",
    "gamma = graph.signals.hann_series_pwc(\n",
    "    duration=duration,\n",
    "    segment_count=segment_count,\n",
    "    coefficients=hann_coefficients,\n",
    "    name=r\"$\\gamma$\",\n",
    ")\n",
    "\n",
    "# Build the rest of the graph.\n",
    "create_infidelity(graph, gamma)\n",
    "\n",
    "# Run the optimization and retrieve results.\n",
    "optimization_result = bo.run_optimization(\n",
    "    cost_node_name=\"infidelity\",\n",
    "    output_node_names=r\"$\\gamma$\",\n",
    "    graph=graph,\n",
    "    optimization_count=4,\n",
    ")\n",
    "\n",
    "print(f\"\\nOptimized cost: {optimization_result['cost']:.3e}\")\n",
    "qv.plot_controls(optimization_result[\"output\"], smooth=True, polar=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Robust optimization on a qutrit using a custom function superposition\n",
    "\n",
    "In this example, we optimize the same dynamics as in the previous examples, but with pulses parametrized as a superposition of [Lorentz functions](https://en.wikipedia.org/wiki/Cauchy_distribution).\n",
    "Then, the real and imaginary parts of the optimizable pulse, $\\gamma(t) = \\gamma_I(t) + i \\gamma_Q(t)$, are given by\n",
    "$$\n",
    "\\gamma_{I(Q)}(t) = \\sum_{n=1}^N c^{I(Q)}_n \\frac{\\sigma^2}{(t - t_n)^2 + \\sigma^2} ,\n",
    "$$\n",
    "where $c^{I(Q)}_n$ are the different real-valued coefficients describing the parametrization, $\\{t_n\\}$ are the centers of the Lorentz functions, and $\\sigma$ is their width.\n",
    "This is a good choice for implementation in bandwidth-limited hardware as it is composed of smooth functions that go to zero away from the choice of centers $\\{t_n\\}$.\n",
    "\n",
    "Note that you can create a wide variety of analytical functions and superpositions using the different [mathematical and arithmetic graph operations](https://docs.q-ctrl.com/references/boulder-opal/boulderopal/graph/nodes#basic-mathematical-functions)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the function to generate the pulse components.\n",
    "def custom_optimizable_superposition(graph, duration, coefficient_count, name):\n",
    "    \"\"\"\n",
    "    Create an STF optimizable superposition of Lorentzian functions.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    graph : The graph where the signal will belong.\n",
    "    duration : The duration of the signal.\n",
    "    coefficient_count : The number of terms in the superposition.\n",
    "    name : The name of the Tensor node with the optimizable coefficients.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    Stf\n",
    "        An optimizable superposition of Lorentzian functions.\n",
    "    \"\"\"\n",
    "\n",
    "    # Define optimizable coefficients.\n",
    "    coefficients = graph.optimization_variable(\n",
    "        coefficient_count, lower_bound=-1, upper_bound=1, name=name\n",
    "    )\n",
    "\n",
    "    # Define Lorentz function parameters.\n",
    "    width = 0.1 * duration\n",
    "    centers = np.linspace(0.3, 0.7, coefficient_count) * duration\n",
    "\n",
    "    # Create Lorentz function superposition.\n",
    "    time = graph.identity_stf()\n",
    "    return graph.stf_sum(\n",
    "        [\n",
    "            coefficients[index] * width**2 / ((time - center) ** 2 + width**2)\n",
    "            for index, center in zip(range(coefficient_count), centers)\n",
    "        ]\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "pycharm": {
     "is_executing": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your task (action_id=\"1828725\") has started.\n",
      "Your task (action_id=\"1828725\") has completed.\n",
      "\n",
      "Optimized cost: 8.332e-05\n",
      "Optimized coefficients:\n",
      "\tI: [ 7.927e+07  3.302e+07 -1.078e+08 -5.857e+07  1.337e+08]\n",
      "\tQ: [-1.385e+08  7.739e+07  1.745e+08 -9.236e+07 -5.986e+07]\n"
     ]
    },
    {
     "data": {
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t9Bhjlm72BkgCZ5SSwCm2LvIy/d92di0Pdk0l5+gYeGUMzRv57NiTVbjFz4z/OPA6ofMIE5M+TJDwII5JDWg8OrCM/A0BBl1loetoc7hLikr7t/lZ+Lab4h3BMedtTzdywcM2cnvJUKCGRAJnlJLA2XjtWu7jm8kONs4LzrKOSVDod4mFdmcYZfzhKSreEeC7xxy4qzU6DTfxt08SpKVTHNXST91M+WsVthSFS5+Lk+Erp0BVNTbO87L0Ew8eRzB+9LzAzJj7YmnWRj5ENwQSOKOUBM7GZ99aH99OdrDm+2DQNMZA19HBLSlNMfJGV1dK9wT45uFg6Oxxvplrp8iYTnE4v1fjwV6llO5SOfNvMbSX7RvrhMeusfJrN2tneQl4QaeHQVdZGH13LInpsoxSNJPAGaUkcDYeO5f5mPOsk9+/Dc48N5ihy0gz3c8zyWzYECneGeCbh+14ndBvooUrX5PZ66KmBW86+fR2O4kZOi7+rw2dXv4+6pK9VGX5F242/eRDU4OvewMuj2H4rVZSciV4RiMJnFFKAmfDpmka6+d4mfOsk62LfADojdBpmIke55uxJkrQDLXCLX6+nRycSDT4GgsTn4uTiQwCAI9D4/5upVTtVxl+u5VW/WSsYaiU7wvw21Q3O37zgxZs8ex9kZkRt8eS0UG62qOJBM4oJYGzYfK6NFZMczPvJSd564MD6E1W6DTMTNfRJgma9SxvfXAiUcAHQ2+KYfxjsji8gNnPOPjqAQepLfWMfyxW/ibqQfm+AKu+8bBlYbDFE6DLKBNnXB8cziA9EJFPAmeUksDZsBRt97PwbReLP3DjrAieetYmCl1Hm+l0tgmTVV5Mw2X3Kh+z/htcHP68f8cy+q7YcJckwshZoXJfl1KcFRrn3muVTRXqWVWRyurvPGyc7yUQ7PyhaWs9QybFMOBSCzEJ8qE8UkngjFISOKOf36uxbpaXhe+62PCD9+Dx1JZ6Og830eY0o8x6jRDbl/qY+5wTTYUrX4tjwGWydWFj9fVDdmb910lGRz1j7pfWzXBxVqpsnO9l/VwvjtJgXDHFQt8JFgZcFkOLvgZ5biJMgwqcqqqydeN2tm3aTllJGT6vD1ucjazcTNp3aUeT5CbhLrHOSOCMTpqmsXuFn18/cbP8czeO8uBppjdC64FGOg830bS1jEuKROtme1j4jhudAW7+MpH2Z8is5Mamcn+A+7uW4nXCBY/EktZWztVwUwMau5b7WTvbQ/6BYUgQbPXsf6mFfhMtJDWXSUaRoEEETq/Xy48zF7Bw3iKcdieZOZkkJMZjNBlx2p0U5BVSWV5F+85tGXnBcFq0zg13yadMAmd0KdzsZ+XXHpZ95qZwy6EXxaRsHe2HmGg3xCgzzqPA4g9crP7OiyVO4f9+aEJmRwkcjcln/1fNT6+7yO1tYNQ/ZWhFpCnbF2DTT162LvQdHJqkKNBmsJFe4yx0P89MfFN5nQ2XUw6cM7+czdnnDsVoDN8L7323PERu61z6nd6HDp3boTcc/mmmrKSM5YtX8sv8JYw4/2wGnTkgDJXWHQmckU3TNPI3Blj1lZuVX3ko2HgoZMYkKLQ5zUi7002yvEeU0VSNOc852bHUT5PmOu6c30TWBmwkSncHeKBHKQE/THjSRnK2PO+RSg1o7F3jZ8sCHzuX+w6O9VQUaD3ISM+xZrqPMcu5W89OOXDecuUdXPbXS2jZNpfUZqk1Ltu4ZhMduravm0qPIX9vARlZ6bW6rt/vp6yknKZpqce/cgSTwBl5fG6NrYu8rJvjZd1sL8XbD4VMUyy06G2kVX8jzbsaZCHxKOb3anzziIP9WwJkdTNw+6xELDZpNWno3ru+il8/dtPmNCNn32wNdzmiljwOjV3LfWz/1cfeNX5U/6HLsroZ6DTcROfhZlr0MchaqiFWJ4HTaDLi8/owmU2kN08jMzuDpOQm/DhrAf955ZE6L1pI4IwEmqaxf2uAzQuCA9c3L/DidR663BKn0KKvgZZ9jWR2lpDZkLiqVL68z0FloUqXkSb+9lmCLMvSgBVs8vNIvzIUBS55xkZCmrSMRSOPU2P3imD43LfGj//QXE1imyh0GGqi3ZDgV0quTiYd1bGj5ZYT6h9/4Ol78bjd5O3JZ9/ufPJ257F90w7adGxTZ4XW1oO3T6ZNh9Zc/JcLMRgO/TPs1Xb++8BzPPjMv+u9JtEwaJpGyS6VrQu9bP7Zy+YFPioL1RrXScnVkd3DSE4PA01b6+UTcwMVE6/jnH9ZmXavg7WzvHz/uINz77GFuywRIt9OdqCp0HGYScJmFDNbFdoONtF2sAm/VyN/g589v/vZvdJP1X6V5V94WP5FcEe3pGwd7U430XawkZb9jKS21EsADZETCpwKkNosldRmqXTv0y1EJdVOWUk5WzZs44XHXmHSbddgiwu+CaiqRllJeVhrE9HF49DYvdLHzt987PjNx85lPqqLazb8W+IVmncykNnFQHYPA7Yk6VptLBLS9Az7Rwwz/uNkxn+cZHU10u1cc7jLEnVs90ofq772oDdBr3Hy/DYUBpNCdncj2d2NDLpKo6JAJW+tn33r/OSvD1C2R2XJh26WfOgGwJas0KKPkRZ9g1+5vQwylKaOnFDg3Lcnn1ZtW2AyR8YyITfdfT3TPvyap+5/lutvv67W4ztF4+V1aRRs9LNvbfAT747ffOSv96MGal7PEqeQ3l5PZicDmZ0NNGku3S6NWVZXI/0usfDrx26mTKrirh+bkNZOZq43JF8/7ACgywgTsfKBskFSFIUmGXqaZOjpPMKMpmqU7FbJW+enYJOfwi0B7KUaa2d5WTsr2A+v6CCjo4GcngayugbfD5p3NsjC8yfhhF4xX33qDRRFIblpMplZ6WRmZ5CRlUFGVjopTZNDVeNRWSwWrr/9Wr7+9FuefeRFrvr7ZWS3zK73OkTk0TSNqv3BF5K9a4KfZvPW+tm/NXBYuFR0kNJCR1pbA83a6GnWRk98MwmYoqbuY0wU7wiw/Vcfr02s5K6fmhATL286DcGWhV42zvNiioEe50vrZmOh6BRSW+hJbaGn+3lmNE2jukijcKuf/VsC7N8aoHR3gLx1fvLW+WvcNjlXR1YXI5ldggE0vb2elBZ6GcN/DLUOnGkZzbju1r9QVVlN/p588vfms371Rn6Y8SNej5cX3n86lHUelaIojJ04hvTm6bz78gcMHjooLHWI8PB7NYp3BF8Y9m8JfkIt3BIMlq7Kw+fDKTpokqkjOUdPSm4wXKa21GO0yIuEODZFUTjz7zGU5wX/3t6bVMWkj2USUbTTNI2vH7QD0O08s6yT24gpikJ8M4X4ZibanhY85vME32NKdgXDZ8muAOX7VEp3qZTu8vD7t56Dt9cbgzvIpbU10KytnrS2wZ+bttZjTZS/q1oHznsevxOApmmptG7X8uBxTdMoKSqp+8pOUL/BfUhtlsJbL0wJdymiDmmaRlWRSulu9eDJXrYnQMnuwMFj/9ti+QeTFZKz9STn6A8ETB1JWXoMJgkI4uQYLQoj/8/KtHvsrJ7hZdZTTtlzPcqtm+Vlx29+YuIVuo6W1k1Rk9GskNHBQEaHQ3Ep4NeoyD/wnrQ7QNlulfL8APYSjcLNAQo3H/6mFJOokPLHe1GOjuRcPcnZwYaP5Gw9JmvDf1+Kqp2G/qyspIzEpER0upqfGqoqq9mfv582HVqHqbK61ZCXRdI0DWd5cBB3ZUGAigL1wM/qoVC5J4DPdYw7USAuNTguJzFTF/yeoSMxQ0dMgiLd4iIkdq/y8f0TThQFbv0ukbaDI2Ncuzgxqqrx2KBy8tb5GXilhW7nSOAUJ8/nDr6fVeQHKM9TqcxXKc8LULlfxe859m3jm+pIytaR+Md7WFrwfSwhQ3/w52hpfT+ldTidDhc7tu7Eao2hRZvcGm/iHreH+TN/YtQFI+q2YgFEX+BUVQ1XhUZ1iYq9RMVeqmEvUYO/lwbDZEWBSmVhgMoCFZ/7+PdptinEN9URl6oQ11RHfKquxndpsRThsPRTNyu/9JCQruPfi5OwpUTHm4E4ZNnnbt65pgpbssLE5+LktUSEhKZpuKo0qotUqorU4PdileqiYA+evUQ9ak/dn1niFBLSdCSk64hLPfCVosOWoiMuRTnwPXg8JlEJ23Cfk16Hs2BfIS89/ir2ageaptE8N5PrbrmapJTgnXk8XmZ+OafeAucLj71McIGmY7vlnhtCX0wDpmka7moNV6WGs0LFWRlsjXRVqjgrNJyVKo6yP4XJEhV7iYa9tHYnzh9MVohtoiM2SYe1iRL8uUnwxAmGTF2j6GoQ0afPRWbyN/gp3Bzgvb9VccPnCdKiHkUCPo1vHw3OTO99oUXCpggZRVGwJihYE3Q0O8Ky5aqqHXw/dZQF31sd5f/zvUzFXa3hrg6OIT8enR5syTpsKQpxqTostuD3Cx6xhW086XED5zdTZ5DbJpcrr78Ut9vDtA++5NmHX+Tme24Iy7aR6c1rLn20+Mcl9OjXgxirpd5raQgWv+9ixZceAr7gJzBnhYqrQsNZqaGpx7/9kZhiwBKvIyZewRKvEBOvEBOvwxKnYG2iYPtTuJTJOiJa6fQKZ99i5fM77ayb7WX+yy6G3iRbIUaLxR+4Kd4eICFdR7shxnCXIxoxnU4hLkUh7hi9JJqm4XWAvUzFWa7iqtIOfrmr1APf/zim4nVCVZFKVRHAoYDadoiJPheGJy8dN3Du2rabW+65AbPFjNli5pqbr2L6R1/zwmMvc8u/bsBijamPOg+66MpxNX5funAZo8eNCMuyTA3BN5MdVBYcOVkazMHubLNVwRyrYIo98LNNwWRVsNj+J1DGK8TEKeiNEiJF4xCXouPMv8cw679OvrzfTuuBRnJ6SniJdF6XxvdPBFs3+04wy05hIuIpioLZBmZbcJLR8QR8Gq7qP0Koyqz/OvF7QPWFb9rOcQOn3+8/rAd73GXno2kazz/2ClffcHmoamtwHHYHH7/1GZvWbiE2LpYxE0bTe2CvsNak+oN/fENviiExXRcMlbHBQCnriQlxfC36GOky0sTaWV7e/ksV/1oo63NGup/fdFGRr5KSq6NVf/mAIBoevVHBlqRgSwLQ07KvkS0LfWGt6biBs2l6Knt27CU9M63G8fGXj0XTNN549p0TesDXn3m7Vte7/vZrT+h+o8HU96ajNxh47OWH2Lc7j9eefovM7EzSm6cd/8Yh1ryLQdYJE+Ik9b/MQsEmP8U7Anx8azXXvpMQ7pLEUdhLVb5/6kDr5iUWFFlHVYh6cdyE0a13V1b8uuqIl114xQX0OcEWulibtVZfDY3H7WH1sjWcO34kZouZVu1a0qVnJ35btDzcpQkhTpHBpDDsH1YMZlj+uYdlX9Ri+QURFjOfcuCq0GjexUB2d9meVIj6ctyzzV5lZ/h5Q1FV9bA1LwEmXD2eCVePr/UDXj5p4olV+D9+X7amxu+aqrFxzSbiEuJqHO/ep+spPU5dKyosRqfX0TS96cFjmVkZbNu0PYxVHWK2KVji5JO+ECcrrZ2BIZNimPeii09uraZ5Fz2J6ccfayXqT/HOAAvecIECZ1wfI0MfRKOhi4DPVsctwef1MeWVDwj4A3Ts1pGuvTrToWs7TKbwLHT8zovvHXbs8/enH3YsXFttHo3H48USU3NmmMVqwe0+fDXYRfOXsOinJQAMv2Qcm73+w65TV+JzwJQISk4VWmLIHkaIRqHzJNj+O+xaqPHq5eX0vxFkpaTIsexNCPig41hIOaOaqNz1RIiTYGsJyfugzFvN5t3VIX0ss+nI0bLWOw3t2r6btSvXs3bFOkqLy2jbqQ1de3Wmc49OxMXb6rTYhmjvrn08+8iLPPP2EwePzfv+J7Zt3Mb1d1x31NtF28LvQjR2lYUBHulXhqNMY/A1FjqPkN1rIkHBJj9fPeDAZIWHViWTmCGtz0KEwkkv/P6H3FY55LbK4byLRlO8v5g1K9azdOEypk75guyW2XTt2ZleA3qQmJRYl3U3GE3TUlEDKkWFxQfXL83bk09aBEwYEkLUnYQ0PZc+H8ebV1Sx5EM3zbsYJNyEmaZqLP4gOK727Fus8nwIEQa1Dpyfvvs55100mlhbLKnNUhk6+gyGjj4De7U92PK5cj0AQ885M2TFQrClsDaycpuHtI4TZbaY6da7CzOmzeLSayeQtyeftSvXcfv9t4S7NCFEHes51kLfSzz89qmHeS+7uODhWFnrMYy2LfFRtC1AfDMdw/7R8CalChENat2l/vKTr7Nnxx5Gjh3O6cNOQ68PzyfEW668o1bXi7QxnBBch/OjNz9j87otxMZZGTPhnOOuwyld6kJEJ2eFyuT+ZZTnqfSZYKb3eNkNLRz8Xo1Pb6+muljjshfjOO3q+t2sRIjG5mi5pdaBE2DtyvV89ck3oCiMu3QMnbp3rNMia+P2a+4kLiGOfoP70rNfd0zmIy/a+8de79FOAqcQ0WvTT16eP68CnR7GP2YjJVe6cuvbqq89/Pqxm4yOeu5dnCQtzUKEWJ0EToCAP8BPs39m9jdzyW2Vw7jLx5KW0azOCj0ep8PF8sUrWLJgKaXFpfTo250BZ/Qjt1VOvdVQnyRwChHdPr2jmgVvuEjJ1THuUZvs4FWP7KUqn9xWjd8DN3+ZQMezZQKXEKFWZ4HzD9VVdr77/HuWLVrOwDMH0Pe03qRnpmE01d82YXt37WPJgqWs+HUVCQnx9B/SjzNGDD7ieqHRSgKnENHNbVd5pF8ZZXtU+l5sptc46VqvL3OedbL9Vx/dzzNz/cey+5MQ9eGUA6fX42Xrxm3sLyiiqKCI/QXF7C8owl5lR9EpaKqGolNompbKvY/fVef/gGOpqqxmyssfsG3Tdv7zysPE2mLr9fFDSQKnENFv449eXhhTgc4AFz1uIylLutZDbe9qH9895sRkhQeWJ8v/uRD15JSXRXr+sZcp3Lef5rmZNEtvSqfuHThr1BBS01JJbZqC3+8nb08++3bn1Wnhx7Jlw1Z+/fk3Vi9fS/OcTC697mKssTIDUQgRWTqcaeK0qy38MsXNj6/JrPVQC/g0Fr4bXAZp9F2xEjaFiAC1Dpxej5c7HryFjKyMI16uN+hp2bYFLdu2qLPijqS8rIKlP//G0oXL8Pl89BnUm7seub3GlpFCCBFpxk22sX6ul6JtAVbP8NJjjIwnDJXfv/FQWaCS1k7P0JukEUKISHDSYzjD5R9X/x+JTRLoN7gPHbt1OOryTJG2DufJki51IRqO9XM9vDSuEr0RLnrSRhNZgLzOVRWpfHp7NQEf3DojkXanh2cbZiEaq1PuUo8UmqpRXlrBrK/mMuuruUe9XiSuwymEaNw6DTMz4DILSz5y89OrLs5/KBadTrrW69IvU1wEfNBnglnCphARJOoC54PP3BvuEoQQ4qSN/4+NDfO8FG4JsG6Wl66jpWu9ruxa4WP3Cj+WeIXxj9rCXY4Q4k+iKnCWFJWS0jS5VtfVNI2KsgqaJDcJcVVCCFF7sU10THwujtcuqWTpJ25yehpISJOu9VPldWosfNsFwHn3xsr/qRARJqoWrHzm4Rf46M1P2bl111Gv43Q4WfjDIh69+wnWrFxXf8UJIUQtdTvHTJ8JZvxe+Ol1F5oaVUPpI9KSj93YSzVyehkYMkm2rxQi0kTVpCGnw8Wcb+ayZMFSFEVHVovmJCTGYzQacTqcFObvpzB/Pzktsxk1djgdurYPd8mnTCYNCdEw2UtVHu5TSnWxxuBrLXQeLl3rJ2vfOj/fPuJAb4R//ZJEZseo6rwTokGp852Gwsnr9bL+943s2LKDspJyfF4fsXGxNM9pTocu7cjISg93iXVGAqcQDdfKr928eXkVRgtc/N844lKjqtMpIvjcGp/9s5rqIo3z/h3L6LsazsYfQkSjBhU4GxMJnEI0bG9eUcnKrzw072rg3HusKIrMWj8RC950seEHL827GLh7QRP0Rvn/EyKcjpZb5OO0EEKE0cXPxBGbpLBvjZ+N833hLieq7F7pY8MPXgwmuOqNeAmbQkQwCZxCCBFG8ak6Lv5vHABLPnBhL1HDXFF0cFWp/PhacFb6mPttNO8s4zaFiGQSOIUQIsx6X2im27kmvC746Q0XMtLp2DRN46fXXbgqNdoONjL0ZpmVLkSkk8AphBBhpigKE5+LI7aJwt7V0rV+PGtnetm13E9MgsKVr8XLbk1CRAEJnEIIEQESmum5+Jlg1/riD1xUF0vX+pEUbfOz5CM3AFe8HEdytizwLkQ0kMAphBARovd4M93HmPG54MfXnNK1/j88Do05zztR/XDG9TH0ON8S7pKEELUkgVMIISLEH13rtmSFvHUBNvzgDXdJEUNTNea95KS6SCOru4Fxsle6EFFFAqcQQkSQ+FQdlzz7R9e6m6oi6VoHWPaFh90r/VgTFf76fgJGs4zbFCKaSOAUQogI0+sCCz0vMOP3wI+vOhv9Xus7l/lYMc2DooPr3ksgtYWM2xQi2kjgFEKICHTJ03HYUhTyNwRYPaPxdq2X7Arww4tOAMY+GEuHs0xhrkgIcTIkcAohRASKS9VxxcvxACz91E3xjkCYK6p/9jKV759w4PdA34vNDLvVGu6ShBAnSQKnEEJEqK6jzQyZFIPqh7kvOPG5G0/Xus+tMfMJB44yjVYDjFz+crzsMy9EFJPAKYQQEWzcZBvpHfRUFqgses8V7nLqRcCvMftpJyW7VFJb6vnbxzJJSIhoJ4FTCCEimClG4dp3EzCYYeN8H9t/bdi7EGmqxvyXXexd48eWonDTtARsKfJWJUS0k7NYCCEiXGYnA+MPrDu54A0n9pKGuVSSpmksfNfNtsU+LHEKN3+ZSNPWhnCXJYSoAxI4hRAiCgyZFEPnESY8DvjhJSdqA1sqSdM0Fr3nZv0cLwYz/P2zBLK7G8NdlhCijkjgFEKIKKAoCle+Gk98Mx0FGwP89pkn3CXVGU3TWPKBm7UzveiNMOnDBNoOluWPhGhIJHAKIUSUiEvVce278ej0sOorDzuXRf94Tk0NtmyunnEobHYZaQ53WUKIOiaBUwghokjbwSbGPhQczznvZSfl+dG7Pqeqavz0uutgy+Zf30+g62gJm0I0RDIau44smLuQpQuXUbC3gJ79e3LF9RNrXL55/Ramvjed8tJycltlc/mkiSSlJIWpWiFENDv7lhh2rfCx8ksPs55yMu4RG2ZbdC0b5PdqzHvJyY6lfowx8LdPEug4VMKmEA2VtHDWkYTEBEaMGUb/0/sddpm92s5bz0/h3PEjeeLVyWS3yOLdl94PQ5VCiIZAURSueDmOzE56KvJVZj/rIOCPnklEbrvKt4862LHUjyVe4R9fJ0rYFKKBk8BZR7r36Uq33l2ItR2+9drqZWtJz0yjR7/uGE1GRl0wgrw9+RTm7w9DpUKIhsASp+OGzxOJb6qQty7Az2+50LTID51V+1W+vM9B4aYAiRk67pjdhFYDZIKQEA2ddKnXg4K8QjKzMw7+braYSWmaQmFeIWkZzQ67/qL5S1j00xIARl92IaRL17sQ4nBJWXr+PjWRZ0aVs+lHH7FJOvpOsIS7rKPat8bPnOedeOwamZ0N3PhFAk0y9eEuSwhRDyRw1gOP24Mt3lbjmMVqwe068rImg84awKCzBgCwq6As5PUJIaJXbi8j17ydwJtXVLJimgdTjEL38yKre1rTNNZ872XJh240FTqPMHHNO/HExEsnmxCNhQTOWnj+0ZfZtmn7ES9r2bYFt9138zFvb7aYcbvcNY65XW4sMZH1piCEiE7dzzNz5atxTJlUzZIP3RjM0Hl4ZLy+eBwaP77mZOdvfgBG/p+V8/4di04fXZOchBCnRgJnLfzj3htP6fbpmWks/WXZwd89bg8lRaWkZaadamlCCAFAv4kxuO0an95uZ+Hbbnwu6HF+eENn4RY/P7zopLpIwxIfnOjUc2zkdvkLIUJH+jPqSCAQwOf1oaoqmqbi8/oIBILr43Xt3YWCfYX8vmw1Pq+PWV/NITMr/YjjN4UQ4mQN+auVS56xoSjw68dulnwYnolEAZ/Gr5+4+eoBB9VFGtk9DNyzsImETSEaMUWLhmmNUeD76bOY+eWcGsdGXTCc0eNGArBp3RY+f3865SVl5LTK4fJJE0lOPf5koF0FZeTKpCEhxAlY9rmbKZOqUP3Qoq+Bs/5uxWStny7sws1+FrzlomyPiqLA2bdYOe++WIxm6UIXojE4Wm6RwBnhJHAKIU7G+rke3rq6CneVRmKGjhF3WElqHroZ4a4qlV8/drPpx+B2m6kt9Vz1WpwseSREIyOBM0pJ4BRCnKyibX5ev6yS/A0B9EboNd5M9/PM6A1119rodWqsnuFh9XcefG7QG2HYrVZG/V9svbWqCiEihwTOKCWBUwhxKjwOjc/+Lzh7HSApW0f/iRayexhQlJMPhI5ylfVzvKyf68VdHXwb6TzcxPj/2EhrK/NRhWisJHBGKQmcQoi6sPFHLx//o4qSnSoAKbk6up5jJre3EXMtWyL9Xo09q/xsW+xj53IfanClI1r1N3L+g7G0GSTd50I0dhI4o5QETiFEXfE6NX5+y8XcF5xU7Q8GT50Bmncx0KyNnqQsPXEpOvQm0OnAVaXhKFcp26tSuNnP/q0B/Af2q1B00O1cM0NvjKHVAOMptZYKIRoOCZxRSgKnEKKu+dwav37sZtnnbrYt9qGptb9tTk8DvcZZ6DXOTFKWbEsphKhJAmeUksAphAilqmKVjT942LcuQP4GP1X7VfweDb9Pw5asIzFDT0qunlb9jLTsbyS+qSzfLIQ4uqPlFhnZLYQQjVh8qo5+E2PoF+5ChBANmnxUFUIIIYQQISWBUwghhBBChJQETiGEEEIIEVISOIUQQgghREjJpKEI5/MH2FVQFtLHsFfZscXbQvoY4sTJ8xJ55DmJPPKcRCZ5XiJPfT0nPn/giMclcEa4NlmpIX+MJ1+dwp0P3x7yxxEnRp6XyCPPSeSR5yQyyfMSecL9nEiXuhBCCCGECCkJnEIIIYQQIqQkcAoGnTEg3CWII5DnJfLIcxJ55DmJTPK8RJ5wPyeytaUQQgghhAgpaeEUQgghhBAhJYFTCCGEEEKElAROIYQQQggRUhI4hRBCCCFESEngFEIIIYQQISWBUwghhBBChJQETiGEEEIIEVISOIUQQgghREhJ4BRCCCGEECElgVMIIYQQQoSUBE4hhBBCCBFSEjiFEEIIIURISeAUQgghhBAhJYFTCCGEEEKElAROIYQQQggRUhI4hRBCCCFESEngFEIIIYQQISWBUwghhBBChJQETiGEEEIIEVKGcBcgjm3r3mKMBn24yxBCCCGEOC6fP0CbrNTDjkvgjHBGg57c9KRwlyGEEEIIcVy7CsqOeFy61IUQQgghREhJ4BRCCCGEECElXepCCBGl1IBGyc4A+RsClO4JEPBpaCrEpepIa28gvb2emHhpVxBChJ8ETiGEiCJuu8q62V5Wf+dh3Rwv7irtqNdVdNBuiJE+F1nocb5ZwqcQImwUTdOO/molwm5XQZlMGhJCULY3wE+vu/jlPReuikMv27HJCslZehLSdOiMoCjgKNUozwtQtldFDQSvZ01UGHVnLEMmxWA0K2H6VwghGrqj5RYJnHXE5/MzdcoXbF6/FafDSUrTZM6bcA6dunUAYPP6LUx9bzrlpeXktsrm8kkTSUo5fpCUwClE41ZVrPL94w4WvuNC9QePNW2tp/VAIy16G4lvdvRWS7ddZcdSP5sXeCncHEyeybk6rng5nnanm+qjfCFEIyOBM8Q8bg/zvv+RfoP70iQ5kQ2rNzLllQ/512P/xGwx8dAdj3HptRPo3KMTM6bNZPvmHdzx4K3HvV8JnEI0TgGfxg8vOpn5lBOPXUPRQasBRrqONtGs9YmNhtI0jT2/+1nyoZvyfSqKDs75Vyyj/mlFp5fWTiFE3TlabpExnHXEbDEzetzIg7937tGJ5NQk9u7ai6PaSXpmGj36dQdg1AUj+NcN91GYv5+0jGZhqlgIEal2r/Tx4U3V7FsbbNLM6Wmg30QLydkntwmEoijk9DCS1dXA8mkeVkz38N2jDnYs9fHXD+Kx2GRspxAitCRwhkhVZTVFhcWkZabxy7zFZGZnHLzMbDGT0jSFwrzCIwbORfOXsOinJQCMvuxCkBZOIRqFgF9j5pMOvn/CGZxt3lRhyHUxZHUz1sn96/QKfSdYSG+vZ96LLjb84OXFsZXc+EUC1kQJnUKI0JHAGQIBf4D3Xv2Qfqf1Ji2jGR63B1u8rcZ1LFYLbpfniLcfdNYABp01ADj6iv1CiIaldE+Ad6+tYvuvPlCg2zkm+kywYLTUfZd3VlcjYx/W8e0jwVbO586r4JYvE7GlSOgUQoSGvLrUMVVVef+1jzDo9Vx05Xgg2KLpdrlrXM/tcmOJMYejRCFEhNkwz8N/Titj+68+YpsonPfvWAZeGROSsPmHxHQ9Yx+ykZCmY+/vfl6ZUIHXJUP6hRChIYGzDmmaxsdvfUZ1VTXX/uNq9IbgeKv0zDTy9uQfvJ7H7aGkqJS0zLRwlSqEiACapjH7GQcvjavEUa6R3cPARU/aaN65fjqf4lJ1nP9ALLYUhZ3L/Ez5axWqKqFTCFH3JHDWoc+mfMH+/P1cf/t1mEyHlhzp2rsLBfsK+X3ZanxeH7O+mkNmVrpMGBKiEfN5NKZMquKrBxxoKvQab2b0ndZ6X5w9NknHOXfHYrLCqq89fPlve70+vhCicZBlkepIWUkZD9w2GYPRgE536A3jkr9cRJ9Bvdi0bgufvz+d8pIyclrlcPmkiSSnyjqcQjRGjjKV1y+tZOsiHwYznH2zlRZ96mZi0Mnat87PjP84UP1w7ZR4eo+3hLUeIUR0knU4o5QETiEalrJ9AV48v4LCLQFimyiMuiuW1BYnt9xRXVs328PCd9xY4hT+9XMTmp7gep9CCHG03CJd6kIIUU8KN/v577ByCrcESMrWMe5RW8SETYBOw0206m/EXa3x5lVV+NzSHiGEqBsSOIUQoh7sXe3j6RHllO9TSWunZ+wDNmzJkfUSrCgKQ66PIb6Zjn1r/Hz5gIznFELUjch6tRNCiAZo9yofz55Tgb1UI7u7gXPvjcVsi8wtJc1WheG3WlF08OMrLrb+4g13SUKIBkACpxBChNCuFT6eP68CV6VGiz4GRv7TitEcmWHzD6kt9fS8ILhO8Ac3VuN1Ste6EOLUSOAUQogQ2bvaxwvnHwibfQ0Mu9WK3hDZYfMPvcaZScrWUbwjwNcPS9e6EOLUSOAUQogQKNjkrxk2/xE9YRNAb1A46++HutZ3LvOFuyQhRBSTwCmEEHWsdHeAF84PjtnM6m5g2C3RFTb/kNpST7dzTWgafHJ7NWpAutaFECdHAqcQQtQhe4nKC+dXUJGvkt5Bz4jbreiN0Rc2/9B7vIXYZIW9v/tZ+K4r3OUIIaKUBE4hhKgjXqfGKxMqKNoeIDlHx+g7YyN+gtDxGC0Kg66KAeDrBx1UFathrkgIEY0kcAohRB1QAxpv/6WSncv82FKUA/uTR3fY/EPLvgayuhlwVWp8LWtzCiFOggROIYSoA1/eZ2fN917MsQrn/iuW2KSG8/KqKAqnXW1Bp4clH7rZt1YmEAkhTkzDeUUUQogwWfSeix9edKHTw8j/s9KkeeRsV1lXEjP0dB4RnED0xT12NE0mEAkhak8CpxBCnIKti7x8cls1AIOvjSGjoyHMFYVOr/FmzLEKm3/ysW627EAkhKg9CZxCCHGSyvMCvHlFJQEfdD3HRMehpnCXFFIWm45e44M7EE2/107AJ62cQojakcAphBAnwe/VePOKSqqLNTI76xlwmSXcJdWLziNMJKTpKNwSYMlH7nCXI4SIEhI4hRDiJHx+tz04Iz1ZYdg/rOj0DWNG+vHoDQp9JgRbOb9/woHPLa2cQojjk8AphBAnaNkXbn5+04XOACNutxIT37heSlsPMJKcraN8n8rCd2QxeCHE8TWuV0khhDhFRdv9fHxLcJLQaVdbaNq64U4SOhpFp9Dn4uAQgln/deBxSCunEOLYJHAKIUQt+Twab/+lCne1Rst+Bjqe3bAnCR1Lbi8DTVvrqS7W+PFVZ7jLEUJEOAmcQghRS18/YGfPKj9xqQpnXG9FURrHuM0jURSFfgdaOec858RZIVteCiGOTgKnEELUwqafvMx72YWig2H/sGKObbxh8w+ZXfRkdNTjqtT44UVp5RRCHJ0ETiGEOA5Hucp7f6sCoPeFZpq1aXzjNo9EURT6XRJs5Zz/iovqYmnlFEIcmQROIYQ4js/+r5qKPJWmrfX0HGsOdzkRJa2dgeweBjx2jdnPOMJdjhAiQsnH9Dq0YO5Cli5cRsHeAnr278kV1088eNnm9VuY+t50ykvLyW2VzeWTJpKUkhTGaoUQtbHiSzfLpnowmGHoTTGNZr3NE9H3Ygt7VtlZ8KaLs2+2kpjR8PaSF0KcGmnhrEMJiQmMGDOM/qf3q3HcXm3nreencO74kTzx6mSyW2Tx7kvvh6lKIURtVRerfHp7cAmkAZdZSEyXIHUkqS30tOxnwO+B2c/KWE4hxOEkcNah7n260q13F2Jt1hrHVy9bS3pmGj36dcdoMjLqghHk7cmnMH9/mCoVQtTG1DursZdoZHTU02lY410CqTZ6Xxgcy/nLuy4q8gNhrkYIEWkkcNaDgrxCMrMzDv5utphJaZpCYV7hEa+/aP4Snrz/GZ68/xnsVfb6KlMI8Se/f+th+RfBrvQz/2ZF0UlX+rEkZ0srpxDi6GQMZz3wuD3Y4m01jlmsFtwuzxGvP+isAQw6awAAuwrKQl6fEKImV5XKp3cEu9L7TbQQ30w+m9dG7wst7Fhq55d3XYy43SpDEIQQB8mraD0wW8y4Xe4ax9wuN5YYme0qRCT69lEHlQXBWeldRkhXem39uZVzjrRyCiH+RAJnPUjPTCNvT/7B3z1uDyVFpaRlpoWxKiHEkexd7eOn14ILvJ9+XYx0pZ+g3uODYzkXvuOiokDGcgohgqKyS11VVbZu3M62TdspKynD5/Vhi7ORlZtJ+y7taJLcJCx1BQIB1ICKqqpomorP60On19G1dxe++vRbfl+2mk7dOjLrqzlkZqWTltEsLHUKIY5MVTU+vrUaTYUuo0yktpAu4ROVnBNs5dyx1M+c55xMeCIu3CUJISKAommaFu4iasvr9fLjzAUsnLcIp91JZk4mCYnxGE1GnHYnBXmFVJZX0b5zW0ZeMJwWrXPrtb7vp89i5pdzahwbdcFwRo8byaZ1W/j8/emUl5SR0yqHyydNJDn1+Otw7iooIzdd1usUoj4sfMfFx/+oJraJwiXPxGGySuvmySjdHWDqnXaMFnhkbTIJaRLchWgsjpZbah04Z345m7PPHYrRGL5G0ftueYjc1rn0O70PHTq3Q284/EWsrKSM5YtX8sv8JYw4/2wGnTkgDJXWHQmcQtSPqmKVB3uU4qrUGHZrDK0HyNjNUzHraQc7f/Nz5g0x0sopRCNytNxS6/Q488s5JKUk0bJtLqnNUmtctnHNJjp0bX/qVR7H3/85iYys9GNeJyklieFjzuas0WdQVlIe8pqEEA3D9HvtuCo1sroaaNXfGO5yol7v8RZ2/mbnl3dcjLjNKq2cQjRyJ9RcOfW9afi8PkxmE+nN08jMziApuQk/zlrAf155JFQ1HnS8sPlnBoOBpmmpx7+iEKLR2/KLl6WfuNEbYfC1FhRFutJPVUqunhZ9DOxcFhzLedHj0sopRGN2QrPUH3j6Xu576m4un3QJ7Tq1pbKskmWLVtCmY5tQ1XdUD94+mY/e/BS/31/juL3azoO3T673eoQQ0Sng1/j0tuCamz3ON0tLXB36Y/ehhW+7qNwvM9aFaMxOqIVTAVKbpZLaLJXufbqFqKTaKSspZ8uGbbzw2CtMuu0abHHBhdVVVZOudCFErS18x0XBpgDxzXT0OF/Wxq1Lf27lnPuskwullVOIRuuEWjj37cnH6/GGqpYTdtPd12ONtfLU/c+Sv7cg3OUIIaKMo1zlu0cdAAy4zILBJF3pde2PVs6fpZVTiEbthFo4X33qDRRFIblpMplZ6WRmZ5CRlUFGVjopTZNDVeNRWSwWrr/9Wr7+9FuefeRFrvr7ZWS3zK73OoQQ0WnmEw4cZRoZHfW06BuVyxJHvBqtnM85ufA/0sopRGNU61fYtIxmXHfrX6iqrCZ/Tz75e/NZv3ojP8z4Ea/HywvvPx3KOo9KURTGThxDevN03n35AwYPHRSWOoQQ0WX/Vj8/vu4CBQZeGSMThUKo13gLO5fZ+fltF8NutZLQTMbJCtHY1Dpw3vP4nQA0TUuldbuWB49rmkZJUUndV3aC+g3uQ2qzFN56YUq4SxFCRIHp/7aj+qH9mUbZUSjEUlvoye1tYNdyaeUUorGKqp2G/qyspIzEpER0uprDUKsqq9mfv582HVqHqbK6JQu/C1H3Nv7o5YUxFRgtcOnzcVgTT2g4uzgJxTsDfHG3HWMMTF6XQnxT+T8XoiE6Wm6p1RnvdLhY9/sGdmzZyf/mU4/bw8wvZ59UUS6niz079pK3Jx+3y31Ct01KSTosbALEJ8Q1mLAphKh7akBj2r+CyyD1HGuWsFlP/mjl9Llg7nOOcJcjhKhnx+1SL9hXyEuPv4q92oGmaTTPzeS6W64mKSWYXj0eLzO/nMOoC0bU+kHLSsr5/L1pbFiz6WCA1et1dO3dlQsvH0tcQrC7xefzH7aV5guPvUxwgaZju+WeG2pdjxCi8Vj0npu89QHiUhW6niPLINWn3uMt7FpuZ8FbLobdGiutnEI0IscNnN9MnUFum1yuvP5S3G4P0z74kmcffpGb77nhpHbyqSir4OmHnkenKIweP5K0jGYAFOYVsnDeIp5+6HnumnwH2zfvoCCvkGHnDq1x+/TmNXcbWvzjEnr060GM1XLCtQghGhd3tcq3k+0A9JdlkOpdass/jeV83sn4R23hLkkIUU+OGzh3bdvNLffcgNlixmwxc83NVzH9o6954bGXueVfN2CxxpzQA878cg7JqUncdPffMJlMB493692FM0cO4eUnX+eNZ95m9449XPG3yw67/UVXjqvx+9KFyxg9bkRYlmUSQkSXuS84qS7WaNZWL/ulh8nBVs43nQy71Up8qrRyCtEYHPdM9/v9h/Vgj7vsfHr07c7zj73C/vz9J/SAG1Zv5LyLRtcIm38wmU2ce+Eotm/ZydiJY+jRN7y7GQkhGo7K/QF+eNEJBBd5l2WQwiO1pZ6cXsGxnD887wx3OUKIenLcwNk0PZU9O/Yednz85WPp0bcbbzz7zgk9oL3aTkqzlKNentIsBUWncPqw007ofoUQ4li+f8KJ1wG5vQ2kt5dF3sOpz4Hdhxa86aSqWA1zNUKI+nDcwNmtd1dW/LrqiJddeMUF9BnY64Qe0BYfR8n+o6/bWVxYTHxC/AndpxBCHEvRNj+/vOtC0UG/S2S8d7ilttST09OA1ymtnEI0Fsf9mG+vsjP8vKGoqnrEZYgmXD2eCVePr/UDduzanu++mMlNd//9sBnoPq+PGdNm0alb+6Pe/vdla2r8rqkaG9dsOjiz/Q/d+3StdU1CiIbt64cdBxd5T8qSRd4jQe8Lzexe6Q+O5fyHlTgZyylEg3bchd8/e/cL1q5aR8AfoGO3jnTt1ZkOXdsdcQxmbVSWV/Lk/c+i0+k4fdggmqX/eZb6YlRV5c6HbyOhScIRb3/LlXfU6nHCtdVmXZOF34U4NbuW+3jizHL0xuAi77ZkCTaR4vsnHOxe6Wf4rVYueERmrAvREBwtt9R6p6Fd23ezduV61q5YR2lxGW07taFrr8507tGJuPgTe6EoLS5j6pQv2Lh2c43jHbq2Z8JV40lOlYD1BwmcQpw8TdN47pwKtiz00eN8M/0vle70SFK0zc+0ex2YrMHdh6SVU4jod8qB88+K9xezZsV61q5cx+7tu8lumU3Xnp3pNaAHiUmJtb4fp8NJUWExENyj3RprPdFSGjwJnEKcvHVzPLw8vhJzrMJlL8RhtsnM9EhzsJXzNisXPCytnEJEu1MOnJ+++znnXTSaWFtsjeP2anuw5XPlelq1bcHQc86sm4qPYu+ufbW6XlZu85DWUV8kcApxctSAxmODyshbH2DA5Ra6nye7CkWig62csTB5rbRyChHtjpZbar02SGlxGQ//32OMHDuc04edhl4fHHhvi7MxYEg/BgzpV3fVHsNT9z9bq+s1lDGcQoiT89tnwS0sbckKnUec3JhzEXpNWxvI7mFgzyo/c551MP6xuOPfSAgRdWodOG+883rWrlzPV598wy/zlzDu0jF06t4xlLUdkcGgJy4hjn6D+9KzX3dMZtktRAhRk8+t8e1kBwB9LpYtLCNd3wkW9qyy89MbLs78u1VWEhCiATrhMZwBf4CfZv/M7G/mktsqh3GXjz24H3p9cDpcLF+8giULllJaXEqPvt0ZcEY/clvl1FsNJ8thd/DxW5+xae0WYuNiGTNhNL2Ps46pdKkLceJ+eNHJtHvsJGXruOgJGzqdBM5IN/cFJ9sW+eg30cLVb8hazEJEqzqdNARQXWXnu8+/Z9mi5Qw8cwB9T+tNemYaRlP9tTju3bWPJQuWsuLXVSQkxNN/SD/OGDH4iOuFRoJ3X/4ATdO47LqL2bc7j9eefovb77+F9OZpR72NBE4hToyzQuX+rqU4yjVG320lp4f0gkSDqiKVT26rRgvAPYua0LyLPG9CRKNTHsPp9XjZunEb+wuKKCooYn9BMfsLivD7Ayyct4if5/6ColNompbKvY/fVafFH01WbnOycpszcuxwprz8AV998g39Bvc+bGJTJPC4PaxetoZ7/vNPzBYzrdq1pEvPTvy2aDnnX3xu2Op659pKXBUaV78VT2yTyAzqQpyIOc86cZRrZHTUk91dtrCMFvFNdXQaZmLtTC9fPuDg5umJ4S5JiAZj7vNOtvzsZegtVtoPCc+Y9lq/Gj//2MsU7ttP89xMmqU3pVP3Dpw1agipaamkNk3B7/eTtyeffbvzQllvDVs2bOXXn39j9fK1NM/J5NLrLo7YpZWKCovR6XU0TW968FhmVgbbNm0/7LqL5i9h0U9LABh+yTg2e/0hq2v9D+Asg4UzSrAcea19IaKGsxR+eDH4c5+bAgTSqsJbkDgh3a+HTT/DhrlePplcRHq3cFckRMOwYhbs/gUyz/Ci5Ib2scymI0fLE2rhvOPBW8jIyjji5XqDnpZtW9CybYuTq7CWyssqWPrzbyxduAyfz0efQb2565HbawS5SOTxeLHE1Fx02mK14HZ7DrvuoLMGMOisAUDou9T1+mJAI1EXh1UvLZwiuq2e7iTg89FzrJmRV8gnqGhkv9vBl/c5WPuhjvZdbegNMv5WiFNlVpyAj/SUONrlxIT0sXYVlB3xeK0DZ311kx/Pg7dPJrFJAv0G96Fjtw7o9Xo8Hu9h63NG2jqcZrMJt8td45jb5cFiiYy1AXcs9ZGQrsMUo2CyHvoymEBR5AVfRL6yfQE2L/Ch08OY+yNvWI2onTP/buWXd90U7wiwYa6XLqMi4zVSiHDQNA2/N7jyhs+l4XOD16UFf3dr+FzB3/1uDe+B3/1ejYAX/L5D38v3qeH+p9Q+cEYKTdUoL61g1ldzmfXV3KNeL9LW4WyalooaUCkqLKZpWioAeXvySTvGhKH6oDcqgMbCd9xHvFynB2OMgskK5gMh1BijYLYqmGMVzDYFS9yfvmw6LPEKFpuCwSxhVdSfpZ+40VQ47doYmrWJupc2cYDRrDD+URuvTaxk2ece2pxmxBInvS8iOmmaht8DHocW/LJrh34+8OX98+8HLvf+KWBqdZQVFQVSW4bvtTHqXpUffObecJdwUswWM916d2HGtFlceu0E8vbks3blOm6//5aw1jX+MRurvvIQ8Gu47RruKg1XpYarSsVdHfxj99g1PHao5sQWNNAbwXIgkJrjgiHUmqjDmqhgbXLge6KO2CYKlnhFlq4RJy1/o59dy/2YrHDOvyJzHLeova7nmGh3hpHNP/n47TMPp18X2i5AIU5EwK/hKNNwVaq4qjRcVX+8dx763VWlHjwe8J3a4xktBBt4/mjUsR1o7LEdavQxxx74PU7BFBNsGDJZFIwWMFiCP8en6UhqHr41bk96WaRwKCkqJaVpcq2uq2kaFWUVNEluEuKqas9hd/DRm5+xed0WYuOsjJlwTsSvw+nzHDiR/jh5qg8FUmeFhqNMxV4a/B780rCXBn/2HbnR9IgUHcQkKAdDqC1ZR1yKQlxTHXEpOuJSgwFVkVAq/oemaUz/t4OibQFG323lvHtlP+6GIH+jn0cHlqEGYPzkWJq2jrr2ERFlNE3D6wB7qYr9wPuZo0zFWa7hKA++r9nLgu+JJ8Jo4VBjy/80ugTf9w6/LCbuUKgM9kRGjzpfhzMc7rnpATp168DAM/rTok3uEa/jdDhZsWQVC+YuZPDZgxgybHD9FlnHwh04T4XXeSh82g8E0eoilcrC4FfV/sCB78HQejw6A8EgmqoQlxoMofFNdSRm6EhM12OyRtdJKerGtsVe5j7vIr6pjodWJ2GxSfdrQzH933bmPu8ktaWecY/GSi+IOGV+r0ZloUp1cfD9qOqP70XB717X8e9D0UFCmo74ZsH3oeD70oFGklQdtpRDDSW2FB3m2Mb1d9sgAqfT4WLON3NZsmApiqIjq0VzEhLjMRqNOB1OCvP3U5i/n5yW2YwaO5wOXduHu+RTFs2B80T4vRpVRSpVB8JoeV6A0t0ByvaqlO4N/mwvOfafqjVRORg+EzOCQTQpW48tWZGxpA1UwKfxye3VVBdpXPp8HIOvka7XhsRtV3m4Txnl+1RO+4uFLiNlApE4Pk3TcJRrVOSrVOQHDnwP/lxdonGs0WHmWIUmzXU13ksS0mu+r8Q31aHTy3vK0TSIwPkHr9fL+t83smPLDspKyvF5fcTGxdI8pzkdurQjIys93CXWmcYSOGvD49Ao2xugbG+A0j0qZXsCFO8IsH+rn6LtgaN24ZtiITlbT0qOnuQcPck5OpKy9LK/dgOweoaHxe+7SWun59+/JskSOg3Q7994eP2ySkwxcPEzcdiSpAVbHOLzaJTtCVC6W6Vk94GGij2Bo7ZU6gyQkqMnpYWe5GwdyTl6UnKD7w0pOXpipYHilDWowNmYSOCsHVXVKN+rsn+rn8KtAfZvDbB/i5+8df4jdtcrCiRm6mjWRk+zNgaatdGT1FwnY0SjiMeu8dEt1XgcGjdMTZDlcxooTdN4dUIla2d5yelpYNSdVgkEjZTPo1G8Pfj6XrwzGC4rC9UjzuKObaLQrK2BtLb64Ot82+DrfGoLfdSNiYw2EjijlATOU6NpwfE6+9b6yVvrZ9/64Pf9WwOogZrXNcVA0wPhM61t8AXKLONCI9biD12s/tZL28FGbp2RKCGkAavID/Bw3zJclRpDb4qh7eDwbM0n6o+maVQXaRRuCb5e798aDJj/+7qt00NaOz3Nuxho3sVI8y4GMrsYiE+VlvBwkcAZpSRwhobPrbF3jZ+dy3zs/M3Hjt98hy2Mq+ggtaWezM4GmncykNZeuuEjRVWRyie3VaP64e6fm5DTwxjukkSILX7fxQc3VmOOVbjkGRvWRAkUDYmmaVQWqOSt95O3LkD+Rj+uyprxRNFBZmcDLfoYye1loHkXA+ntDRgt8rocSSRwRikJnPWnIj/AjmU+di71sWOpj10r/ah/2sZeb4T09gZyega/EtLCt55ZYzf3BSfbFvnoe7GZv7wlW1g2Bpqm8dK4Sjb8IF3rDYW7WmXPaj97V/vJW+/H8T/Dn2zJCi36GmnRx0jLfkZyehpkFYooIIEzSkngDB+3XWXbYh+bF/jYvMDLvjV+/ny2JGboyOlpILeXkbT2elmypZ7s3+pn+r8dGMzw4MpkkrMl+DcWZfsCTO4f7FoffI2FziNk3G400TSNkl0qe1b52L3KT9G2QI3xl7ZkhXZDTLQbYqLtYCNNW+vlQ0UUOlpukZV0hTgKi01H5+FmOg8PvqnZS1U2zPOydpaH9XO9B5bZ8LL6Oy/WJgqt+hlpNcBIWlu9TD4KEVU9tA3r0ButEjYbmaTmei57IY63rqpi8Ydu0jsY5G8gwmmqRuGWADt+C/Yc/Xl5O70RWp9upPNwM+3PNJHRUT64N2TSwhnhpIUzMgX8Gjt+9bFmppdV37gp3XXoY3psE4VWA420H2IiOUfeDOvShnleFrzhIjFDxwMrZJH3xuqDG6pY/IGbpCwd4x61YTRLSIkkmqZRuDnAtsXB8fHO8kMxIyFNR+cRpgMh04glTs7hhka61KOUBM7Ip2kae1b5WTHdw4ov3ZTtORQ+U1vqaX+GkdaDjBKOTpHbrvLJrXbc1RrXTomn93hLuEsSYeJxaDx2WhlF2wK0HWzkrBtjpOs1AlQUBNiy0MeWhV6qiw5Fi6QsHT3ON9PjfAst+hqkFbOBk8AZpSRwRhdN09i13M+vn7hZ9rkbV0Xw9NIZoGVfI11GmmjWVsYlnYyF77hYN1uWQRJBeRv8PHlmGV4nDLraQldZhzUsvC6Nrb942bzAx/6th9YsapKpo89FFnpeYCa7h0HO10ZEAmeUksAZvXxujd+/87DkQzeb5nsPTjhKbamn80gTrQcYZZmlWirZFeCLf9lRFLhnURKZnWT4uYAV0928dVUVig7G3BdLRkf5u6gvxTsDbPjBy9ZfvAd3eTPHQo/zLfSbaKHtYKNs/9hISeCMUhI4G4ayvQEWvuNi4TsuHGXBU84Sr9BpmIkuI03ExEt3+9FomsZXDzoo3BTgzBtimPBEXLhLEhFk2r12fnjBidmmcMEjsTTJkHHToRLwaWxd5GP9HC9F2w+1ZrYeaOS0qy10H2PBHCshs7GTwBmlJHA2LF6XxvIv3Pz4mot9a4KLfBpM0GGoie7nmbElS/D8X1sWepn3kgtbisJDq5JlwW9RQ8Cv8frE4NaXcakK4ybLovB1zVWlsmGul7WzvQcXY49JVOh/qYXBf4khvb20LItDJHBGKQmcDZOmaWxb7GPuc07WzvICwXGe7YYY6THGLIvKH+B1aXxyWzXOco0rXolj4BUx4S5JRCCPQ+PZ0eXsXukntaWeMffHYoqRlrZTVZ4fYM33XrYs8OIPvkyR2dnA0Btj6DXeIv/H4ogkcEYpCZwN3761Pmb918nKLz1oWnD7tvZnGuk93tLoWzz/mCiU29vAP+c1kdmt4qiqilWeGlpGyU6VtHZ6zvmXhM6ToWkaBRsD/P6dh90rDm211nm4iaE3W2k3xCgTgMQxSeCMUhI4G4/9W/3MfsbJ0k/cqAHQm6DLCBM9xpob5ZJK+Rv9fP2gA50B/rUwieadpdtOHFvJrgDPjCqnfJ9KWns95/4rVvbZrqU/lndbPs1D0bbg+EyDGfpPtHDWjVbpNhe1JoEzSkngbHz2b/Xz7WQHK6Z7ADBZofsYM11HmxvNAtd+r8bUO+1UFqiMutPKmPts4S5JRIniHX6eHV1BeZ5Ks7Z6Rt9plcXFj0FTNXYu97NiupuSncE1hGOTFM64PobT/2olPlX+78SJkcAZpSRwNl67V/n4+iEHG+cFB0/ZkhUGXG6h1YCG36X16yduVn3lIa2tnnsWJzWaoC3qRtF2P8+dW0H5PpXEDB3n/CuW+KYSnP5MVYO7pa2Y7qFsbzBoxjfVMewfVgZfGyOzzcVJk8AZpSRwik0LvEy7x35wVntaez2nXRVDasuGObGoYJOfrx9ygAZ3zGlCq/7GcJckolBFfoCXxleSt86PNVFhxB1W0tpKt7Aa0Nj6i4+VX3moyA8GzSaZOobfZmXglTEy7lWcMgmcUUoCp4Dgm8Ti9918/bAde4kGCrQ/w0j/Sy0Nag1Pr1Nj6l3VVBdpjLjdytiHpCtdnDxXpcrrl1WyeYEPnQEGXmGh8whTg+8hOJKAX2PzAh+rvvZQtT8YNJNzdIy4PZb+l1mkF0HUGQmcUUoCp/gzV6XK9084mP+qC9UP5liF/pdZ6HCmEaUBzOCe/4qTzQt8ZHUzcOf8JrITkzhlAZ/G9PvszH/ZBUDrAUYGX2dpNBPx/F6NjfO8/P6tB3tp8O2+aSs9I//PSt+LLeiNco6JuiWBM0pJ4BRHUrjFz9R/VrNxvg+AtHZ6Tr8uhuTs6O1m37rIyw8vuDBagrPSZVasqEvLp7n54MYqvA6wNlE4Y1IMOT0b7nANr1Nj/Vwvq2d4Di7Wnt5ez8h/xtJrnBm9QYKmCA0JnCG2YO5Cli5cRsHeAnr278kV10+scfnm9VuY+t50ykvLyW2VzeWTJpKUcvwgKYFTHI2maSyf5uGLu+xUFano9ND1HBO9x1uibimYsr0Bpt1rx++BS561MeQ6a7hLEg1Q0XY/7/+9mu1Lgh/UWvYzMPCKGOIa0Exsd7XKmple1s7y4HUEj2X3MDDq/2Lpeq5J1rIVISeBM8R+X7YGRVHYtHYzXq+vRuC0V9t56I7HuPTaCXTu0YkZ02ayffMO7njw1uPerwROcTzOCpWvH3aw8C0XmgZxqQqn/SWG3F7R0XrjdWp8cU9wCaS+l5i5+o34RjnGTtQPNaAx/xUX306243UGt5btdp6ZbueYo3pmdnWJytpZHtbP8eIPrqhG64FGRv3TSoehjXPcqgiPo+WWhvOxLsy69+lKt95diLUd3jKzetla0jPT6NGvO0aTkVEXjCBvTz6F+fvDUKloaKyJOiY+E8ed85uQ1c1AdbHGzCedzPqvA3uJGu7yjklVNea/4qSyQCWzk57LnpewKUJLp1c4+2YrD65MpvdFZvxeWDHNw0c3V7H8Czdue2SfM3+maRr5G/zMetrBRzdXs/rbYNjsOMzE7bMSuWN2EzqebZZzSkQEGSRVDwryCsnMzjj4u9liJqVpCoV5haRlNDvs+ovmL2HRT0sAGH3ZhSAtnKIWcnsbueunJix4w8U3jzjYuczP3jXV9J1gocsoEzp9ZL3paJrG4vfc7FzmJyZBYdKHCZiskVWjaLiaZOq59p0Ezvirl28mO9jys49ln3tY9bWHtqeb6DLSRFJWZI6J9jo1ti3xsW6Wh9I9wYCsM0DvC80MvclKTo/o6N0QjYsEznrgcXuwxddc3sViteB2eY54/UFnDWDQWQOAYNO0ELWlNyicdYOVnmPNTL3TzqqvPSz+wM3mn72cfl1MRK1DuPo7L2tneTGY4G+fJNC0deTUJhqPVgNM3DbDxJaFXmY97WTjPC8bfgh+NW2lp90QIy37G7EmhLdDMODX2Lvaz5aFPnYt9xEIDkMlvqmOwddaGHxNDAlpkRmQhQAJnLXy/KMvs23T9iNe1rJtC2677+Zj3t5sMeN2uWscc7vcWGLMdVajEH+WmKFn0ocJrJvt4dM7qindrfLl/Q46DjXRf6IFsy28LYkb53tZ8mHwnLjy9XjaDjaFtR4h2g420XawiYJNfn58zcWyz90UbQ9QtD3AL1PcpLXT06K3keZdDSRl6eqlm9rv1chb72fXCj/bl/jw2A9NuWg90Mhpf4mh5wWNZ8tbEd0kcNbCP+698ZRun56ZxtJflh383eP2UFJUSlpm2qmWJsQxdR5h5v7BJr5/0sHc551s+MHLzmU+Bl5hoc1p4dkic91sDwvfCYbN8Y/a6HOhpd5rEOJo0tsbuPS5OC78j43V33n47VM3m37yUrAxQMHGAAAxCQrp7fU0a2OgaWs9yTl6zHUwHMTj1CjZEaBws5+CTQHyN/oPtmQCZHbS02eChT4XWSK2u1+Io5HAWUcCgQBqQEVVVTRNxef1odPr0Ov1dO3dha8+/Zbfl62mU7eOzPpqDplZ6UccvylEXTNZFcY+aKPvxRY+ubWabYt9zHvJxfq5XgZcbqm3bnZN0/j9Wy+/fhQMmxf+x8bQm2T5IxGZTDEKfS4KhjtXlcq6OV7Wz/Gy6ScvlQUqO5b62bHUf/D6tmSFhHQd8U11xKXoiEnQYYlXMFkU9KbgGEstAGoAvC4Nj13DVaVRVaRSXaRSnheguvjwRWOyexjoNMxEzwssNO8sb9kiesmySHXk++mzmPnlnBrHRl0wnNHjRgKwad0WPn9/OuUlZeS0yuHySRNJTpV1OEX90jSNXz9yM/3f9oO7jrTsZ6DfRAuJ6aFrMfF7NRa84WLLwmBzzSXP2BjyVwmbIvpomsb+LQF2LPWx4zcfe1b7Kdzkx+c+/m2Px2CGjI4GWvYz0nqAkdaDjCQ0k5ZMEV1kHc4oJYFThIKrSmXOc07mveTE5wKdHjqebaLXODPWxLqdHFGeH+CH552U7FIxWeHKV+PpNU660UXDoQY0incEKN4ZoHR3gPJ9KtUlKvYSFY9Dw+cObrGpN4CiV4iJU7AmKdiSdSRl6UnO1tOsjZ6mrfWyA5CIehI4o5QEThFKFfkBvn3UwZIP3Wgq6I3QboiJbueaTrnF0+/VWPlVcJkZ1Q+pLfVc/3ECmZ2kW1AIIRoqCZxRSgKnqA95G/x8+4id1d95Dx7L7Kyn/RkmWvQxntBWmR6Hxsb5XtbO9Bzsth94pYVxk23ENpG9JoQQoiGTwBmlJHCK+lS42c/c550s+9x9cEyazgAZHQw072ogJVdHUnM91kQFRaegaRpeF9hLVAo3+9m7xs/e1f6DW+tldtJzyTNxtB4oyx4JIURjIIEzSkngFOHgrFBZMd3Drx+52LnMz5FeJfRGUHQcDJd/1u4MI0NvtNJpuAmdTsakCSFEYyGBM0pJ4BThVl2ssnG+l22LveRvDFCwyY+z/NDLhska3CYwo6OBDmeZ6HCWiZRcmVkrhBCNkQTOKCWBU0QiVdXwu4Ozc802JSwLyAshhIg8R8stMl1UCHHCdDoFkxVAgqYQQojjkymjQgghhBAipCRwCiGEEEKIkJLAKYQQQgghQkrGcEY4nz/AroKykD6GvcqOLd4W0scQJ06el8gjz0nkkeckMsnzEnnq6znx+QNHPC6BM8K1yUoN+WM8+eoU7nz49pA/jjgx8rxEHnlOIo88J5FJnpfIE+7nRLrUhRBCCCFESEngFEIIIYQQISWBUzDojAHhLkEcgTwvkUeek8gjz0lkkucl8oT7OZGdhoQQQgghREhJC6cQQgghhAgpCZxCCCGEECKkZFmkRsxhd/DxW5+xae0WYuNiGTNhNL0H9gp3WY2Kz+dn6pQv2Lx+K06Hk5SmyZw34Rw6desAwOb1W5j63nTKS8vJbZXN5ZMmkpSSFOaqG4+iwmL+c89TdO/Tlav+fjkAyxev4Jup3+OodtCuc1su++vFxNpiw1xp47FiySpmfjWb8pIK4hPjuGzSRFq3aynnSpiUFpcxdcoX7Ny2G4PRQPc+XRl/+Vj0ej37dufx8VufUZi/n7SMZlx63cU0z8kMd8kNzoK5C1m6cBkFewvo2b8nV1w/8eBlxzov/nj/+f231RjNJs4+50zOGnVGyOqUFs5GbOp709EbDDz28kNc9ffL+GzKNAr2FYa7rEZFDQRokpzIP+69kSdff5RzLxzFuy+9T2lxGfZqO289P4Vzx4/kiVcnk90ii3dfej/cJTcqn783jewWWQd/L9hXyKfvfsGVf7uUx15+CJPZyNQp08JYYeOyae1mvv7sOy776yU89eZj/OPeG0lJTZJzJYymTvkCW3wcj774IHdPvoNtm7az8IdF+P1+3nj2HXoP7MUTrz1K39N688az7+D3+8NdcoOTkJjAiDHD6H96vxrHj3dezJw+i6LCYh567j5u+dcN/DDjRzas2RiyOiVwNlIet4fVy9Zw7viRmC1mWrVrSZeenfht0fJwl9aomC1mRo8bSXJqEjqdjs49OpGcmsTeXXtZvWwt6Zlp9OjXHaPJyKgLRpC3J5/C/P3hLrtRWLFkFTHWGNp1anPw2LLFK+jcoyOt27fCbDFzzvhRrF6+FrfLHcZKG4/vp89m1NhhtGidi06nIzEpkcSkRDlXwqi0pIye/bphNBmJT4ynY9f2FOYVsnXjdlQ1wJkjT8doNHDGiNMBjS0btoa75Aane5+udOvdhVibtcbx450XS39Zzsixw7HGWknLbMbAM/qz9OdlIatTAmcjVVRYjE6vo2l604PHMrMyKJQWzrCqqqymqLCYtMw0CvIKyczOOHiZ2WImpWkKhXnyHIWay+VmxvRZXHDZ+TWOF/7Pc5LaLAW9QU9RYXF9l9joqKrKnp17qa528NAdj3LfLQ8x9b1peL1eOVfC6IwRp7Pi19/xerxUlFWwYfUmOnRtT8G+QjKyMlAU5eB1M7IyKNgnHwLqy7HOC6fDSVVFVY3LM7MzKAjhOSNjOBspj8eLJcZS45jFasHt9oSpIhHwB3jv1Q/pd1pv0jKa4XF7Dtv31mK14HbJcxRqM76YyYAhfWmSlFjjuMftJSYmpsaxGKsFj5w3IVddWU0gEOD3Zau59b6b0et1vPHsO8z++gc5V8KodbtWLP7xV/456R5UVaXvaX3o2qsLs7+eS8z/vMfExFjwuKU3oL4c67z44zXrz89R8PkJ3TkjLZyNlNlsOqwb0O3yYLGYw1RR46aqKu+/9hEGvZ6LrhwPBD+NHv4cubHEyHMUSvt257F5/RbOHDnksMvMliOfN2Y5b0LOaDICMGTYYBIS47HF2Thr1BA2rN4o50qYqKrKK0+9QbfeXfjvW4/z+CuP4HI6+frT7zCZj/ycmC2Wo9ybqGvHOi/+eM368+Vutzukr2USOBuppmmpqAG1Rldg3p580pqnhbGqxknTND5+6zOqq6q59h9XozfoAUjPTCNvT/7B63ncHkqKSknLlOcolLZu3EZZcTn33/oI99z0APO+/4nVy9bwxL+fJu1/npOSolL8Pj9N01LDWHHjYI21kpiUCMqfjwZ/kXMlPJwOJ+Wl5Zw+7DSMRgOxcbH0G9yXDas3kt48jfy9Bfx5b5m8vQWkN28Wxoobl2OdF9ZYK/GJ8TUuz9uTT3oIzxkJnI2U2WKmW+8uzJg2C4/bw44tO1m7ch19B/UOd2mNzmdTvmB//n6uv/06TCbTweNde3ehYF8hvy9bjc/rY9ZXc8jMSictQ16wQ2nQmQN44Ol7uHvyHdw9+Q5OO2sgnbp35IY7r6fPwF6sW7WebZt34HF7mDFtJt16dzlseIoIjf6n9+HnOb9QXVmN0+Hkx1kL6NS9o5wrYWKLs5GcmsTCeYsJBAI4HS5++2UZGdnptOnQCkWnY8Gchfh8fhbMXQhA245tjnOv4kQFAgF8Xh+qqqJpKj6vj0AgcNzzou9pvZn99VycDieF+ftZ/OOv9Du9T8jqlK0tGzGH3cFHb37G5nVbiI2zMmbCObIOZz0rKynjgdsmYzAa0OkOff675C8X0WdQLzat28Ln70+nvKSMnFY5XD5pIsmpsrZgffp++iyK95f8zzqcM3BUO2nXuQ2X/fUSWYezngT8Ab748EtWLFmJwWikZ99unH/JeRhNRjlXwmTf7jymffgVeXvy0el0tO3YmguvHEd8Qhx7d+3jk7enUphXSLMD63Bm5TYPd8kNzvfTZzHzyzk1jo26YDijx4085nlRYx1Ok5Gzzz0rpOtwSuAUQgghhBAhJV3qQgghhBAipCRwCiGEEEKIkJLAKYQQQgghQkoCpxBCCCGECCkJnEIIIYQQIqQkcAohhBBCiJCSwCmEEEIIIUJKAqcQQgghhAgpCZxCCCGEECKkJHAKIYQQQoiQksAphBBCCCFCSgKnEEIIIYQIKQmcQgghhBAipCRwCiGEEEKIkJLAKYQQQgghQkoCpxBCCCGECCkJnEIIIYQQIqQkcAohhBBCiJCSwCmEEBHo159/447r7g7b4zsdTu658X6K95fUyf35fH7uv/Vh9uzYWyf3J4SILoqmaVq4ixBCiMbk5ituP+blfU/rw8V/GY/H5SEuIa6eqqrpq0++wV7t4PJJE+vsPhfMWciaFeu4+V9/r7P7FEJEB0O4CxBCiMbm0RcfPPjzut838MnbU2scM5qMmEwmTCZT/RcHeD1eFv+0lOtvv7ZO77f3wJ589ck3FOwrJL15Wp3etxAiskngFEKIehafGH/w5xhrzGHHINil/vn703n6rccB+H76LH7/bQ1DzzmT76fPwl7loEe/blxyzUUs/mkpc7+dh9frpd9pfRg78Tx0uuCIKb/fz4wvZrJ88UocDifpmWmce+EoOnRtf9T61q/eiKJAy7YtDh7bunEbLzz2Cjfd/Te+nfo9+fsKSMtsxsRrJpCV2xwAl9PF5+9PZ+OazbjdbhIS4xkyfDBnjhwCQKwtlhZtWrBiyUrOvWh0HfxPCiGihQROIYSIEqUlZaxZuY7rb7+OyvJK3nphClUVVcQnxnPjndezv2A/77z0Pi3b5tK9TzcAPnrjU0qKSrjqhstJTEpk/eoNvP7M2/zfQ7fSPCfziI+zffMOsnKzUBTlsMu+mTqD8y8+l/jEeKZ9+BXvvfoh9z5+F4qi8N0XM8nfW8D1d1xLfEIcpcVl2KvsNW6f0yqbrZu21/1/jhAiosmkISGEiBKaqnL5Xy8hIyudDl3b07Fre/bu2scl11xEWmYzuvXuSss2LdiyYRsAxftLWPHrKv5y01W0bt+KlKbJDBk2mI7dOrDoxyVHfZyyknISmsQf8bJzx4+ibcc2pGU0Y9TY4ezPL6KivPLg7bJym5PbKoeklCTadGhNj37da9w+ITGespLyuvkPEUJEDWnhFEKIKNEkucnBLniAuPg4UtNSMRgOvZTHJcQdbFXct2sfmqbx6N1P1Lgfv99P245tjvo4Pp+PeKPtiJdlZGcc/PmPYQD2KjtNkhI5behA3nnhPfbs3Ev7zu3o3KMjbTq0rnF7o8mIz+ur5b9YCNFQSOAUQogoodfrax5QDj+mAOqBxUdUTUNRFP750G3oDTU7tIxG41Efx2aLxelwHaWGQ/fzR5e7pgYfr1O3Djz03L/ZsHoTm9dv5bWn36JH3241Zro7HU5s8bHH/ocKIRoc6VIXQogGKisnE03TqKqsIrVZao2vxKTEo96ueU4mhXn7T+oxbXE2+p7Wmyuun8il113Mb78sx+fzH7y8YF8hWTnNT+q+hRDRSwKnEEI0UE3Tm9J7YE8+fONTVv22mpKiUvbs2Mu8GT/y+7I1R71dh67tKMzfj6PacUKPN2PaTFYvX0tRYTGFeftZvXwtyalJGI2HOtO2b95xzBnyQoiGSbrUhRCiAbv8rxOZ/c1cvv70WyrKKrHarOS0zKZNx9ZHvU1GVgY5rbJZ8esqTh92Wq0fy2Aw8N0X31NaXIbRaCC3VQ7X337dwct3bt2Fy+mme9+up/RvEkJEH9lpSAghxGE2rNnItA++4t4n7jq4puepevuF92iem8mIMWfXyf0JIaKHtHAKIYQ4TMeuHSg6u5iKsgqSUpJO+f58Pj+Z2emcOfL0OqhOCBFtpIVTCCGEEEKElEwaEkIIIYQQISWBUwghhBBChJQETiGEEEIIEVISOIUQQgghREhJ4BRCCCGEECElgVMIIYQQQoTU/wO0dfCYwFrq5wAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Number of terms in superposition.\n",
    "coefficient_count = 5\n",
    "\n",
    "# Create optimization graph object.\n",
    "graph = bo.Graph()\n",
    "\n",
    "# Create gamma(t) signal using custom basis.\n",
    "gamma_i = custom_optimizable_superposition(\n",
    "    graph, duration, coefficient_count, name=\"coef_i\"\n",
    ")\n",
    "gamma_q = custom_optimizable_superposition(\n",
    "    graph, duration, coefficient_count, name=\"coef_q\"\n",
    ")\n",
    "gamma_stf = gamma_max * (gamma_i + 1j * gamma_q)\n",
    "\n",
    "# Discretize gamma into PWC.\n",
    "gamma = graph.discretize_stf(\n",
    "    stf=gamma_stf, duration=duration, segment_count=segment_count, name=r\"$\\gamma$\"\n",
    ")\n",
    "\n",
    "# Build the rest of the graph.\n",
    "create_infidelity(graph, gamma)\n",
    "\n",
    "# Run the optimization.\n",
    "optimization_result = bo.run_optimization(\n",
    "    graph=graph,\n",
    "    cost_node_name=\"infidelity\",\n",
    "    output_node_names=[r\"$\\gamma$\", \"coef_i\", \"coef_q\"],\n",
    "    optimization_count=4,\n",
    ")\n",
    "\n",
    "# Retrieve results and plot optimized pulse.\n",
    "coefficients_i = gamma_max * optimization_result[\"output\"].pop(\"coef_i\")[\"value\"]\n",
    "coefficients_q = gamma_max * optimization_result[\"output\"].pop(\"coef_q\")[\"value\"]\n",
    "\n",
    "print(f\"\\nOptimized cost: {optimization_result['cost']:.3e}\")\n",
    "\n",
    "print(\"Optimized coefficients:\")\n",
    "np.set_printoptions(precision=3)\n",
    "print(\"\\tI:\", coefficients_i)\n",
    "print(\"\\tQ:\", coefficients_q)\n",
    "\n",
    "qv.plot_controls(optimization_result[\"output\"], smooth=True, polar=False)"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
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    "name": "ipython",
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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