{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Particle swarm optimization of a polarization beam splitter\n",
        "\n",
        "**Note: the cost of running the entire notebook is larger than 10\n",
        "FlexCredits.**\n",
        "\n",
        "[Particle Swarm\n",
        "Optimization](https://en.wikipedia.org/wiki/Particle_swarm_optimization)\n",
        "(PSO) is a powerful and versatile optimization technique. PSO has since\n",
        "emerged as a popular metaheuristic algorithm for solving complex\n",
        "optimization problems across a wide range of domains, including\n",
        "integrated photonic device design. At its core, PSO embodies the\n",
        "principles of collaboration and information sharing within a population\n",
        "of simple entities known as “particles.” These particles navigate\n",
        "through a multi-dimensional search space, seeking optimal solutions to a\n",
        "given problem. They learn from their own experiences, as well as the\n",
        "experiences of other particles, to adapt their positions and velocities\n",
        "over time.\n",
        "\n",
        "In this notebook, we demonstrate the PSO of a compact polarization beam\n",
        "splitter (PBS) using `Tidy3D` and the\n",
        "[PySwarms](https://pyswarms.readthedocs.io/en/latest/index.html) library\n",
        "implemented in the `Tidy3D` Design plugin. The coupling region is\n",
        "segmented into 10 sections with varying widths $W_1$, $W_2$, …,\n",
        "$W_{10}$. Since performing the traditional parameter sweep is\n",
        "unrealistic in this case due to the large parameter space dimension, we\n",
        "use PSO to optimize all the widths to maximize the beam splitting of the\n",
        "TE0 mode and the TM0 mode. The device is inspired by the work\n",
        "`Weiwei Chen, et al., \"Ultra-compact and low-loss silicon polarization beam splitter using a particle-swarm-optimized counter-tapered coupler,\" Opt. Express 28, 30701-30709 (2020)`[DOI:10.1364/OE.408432](https://doi.org/10.1364/OE.408432).\n",
        "In the original work, the authors employed a more complex PSO scheme of\n",
        "changing objective functions. For the sake of simplicity, we will use a\n",
        "simpler PSO scheme in this notebook, only aiming to demonstrate the idea\n",
        "and workflow. Tidy3D users can draw inspiration from this notebook, as\n",
        "well as from the wealth of PSO research in the literature. By harnessing\n",
        "the versatility of PSO in combination with the exceptional speed of\n",
        "`Tidy3D`, we anticipate that users can design many novel and\n",
        "high-performance photonic devices.\n",
        "\n",
        "<img src=\"img/particle_swarm_optimization_pbs.png\" width=\"500\" alt=\"Schematic of the polarization beam splitter\">\n",
        "\n",
        "Besides the PSO introduced in this notebook, Tidy3D also provides\n",
        "built-in automatic differentiation support for adjoint optimization.\n",
        "Unlike PSO, adjoint optimization is gradient-based and thus more\n",
        "efficient. To learn more, please refer to the adjoint optimizations of a\n",
        "[wavelength division\n",
        "multiplexer](https://www.flexcompute.com/tidy3d/examples/notebooks/Autograd9WDM/),\n",
        "a [mode\n",
        "converter](https://www.flexcompute.com/tidy3d/examples/notebooks/Autograd3InverseDesign/),\n",
        "and a [waveguide\n",
        "taper](https://www.flexcompute.com/tidy3d/examples/notebooks/Autograd5BoundaryGradients/).\n",
        "If you are new to adjoint optimization, please start with the\n",
        "[tutorial](https://www.flexcompute.com/tidy3d/examples/notebooks/Autograd1Intro/)\n",
        "on adjoint basis and our [video\n",
        "lectures](https://www.flexcompute.com/tidy3d/learning-center/inverse-design/)\n",
        "on inverse design."
      ],
      "id": "068fba38-f29a-4998-932a-807e588ac736"
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {},
      "outputs": [],
      "source": [
        "# uncomment the following line to install pyswarms if it's not installed in your environment already\n",
        "# pip install pyswarms\n",
        "\n",
        "import gdstk\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import tidy3d as td\n",
        "import tidy3d.plugins.design as tdd\n",
        "import tidy3d.web as web"
      ],
      "id": "3eebd881"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Preparation Work Before the PSO\n",
        "\n",
        "### Define Fixed Simulation Settings\n",
        "\n",
        "Before we can perform the PSO, we need to prepare a few things. First of\n",
        "all, we will define parts that are unchanged in the optimization\n",
        "procedure. The wavelength range of interest in this case is 1500 nm to\n",
        "1600 nm."
      ],
      "id": "4d1b9143-228b-41ca-8d04-6d44936cece1"
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {},
      "outputs": [],
      "source": [
        "lda0 = 1.55  # central wavelength\n",
        "freq0 = td.C_0 / lda0  # central frequency\n",
        "ldas = np.linspace(1.5, 1.6, 31)  # wavelength range\n",
        "freqs = td.C_0 / ldas  # frequency range\n",
        "fwidth = 0.5 * (freqs[0] - freqs[-1])  # width of the source frequency range"
      ],
      "id": "d32dfa6e"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "For simplicity, we use a constant refractive index for silicon and\n",
        "silicon oxide. Dispersive models can certainly be used instead if\n",
        "needed."
      ],
      "id": "b7482645-afcc-47a1-b4e1-edee052654ed"
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {},
      "outputs": [],
      "source": [
        "n_si = 3.48  # silicon refractive index\n",
        "si = td.Medium(permittivity=n_si**2)\n",
        "\n",
        "n_sio2 = 1.44  # silicon oxide refractive index\n",
        "sio2 = td.Medium(permittivity=n_sio2**2)"
      ],
      "id": "502190b2"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Define geometric parameters outside of the optimization region."
      ],
      "id": "932bdd70-45dc-4c96-8df1-60ab3e936af3"
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {},
      "outputs": [],
      "source": [
        "Ls = 0.5  # length of each segment\n",
        "W0 = 0.45  # width of the input waveguide\n",
        "Wa = 0.2  # width of the taper tip\n",
        "Wt = 0.45  # width of the taper end\n",
        "Hc = 0.22  # thickness of the Si layer\n",
        "G0 = 0.27  # size of the gap\n",
        "buffer = 8  # buffer spacing\n",
        "M = 10  # number of segments to be optimized"
      ],
      "id": "ed76faa6"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Next, we define the device geometry outside the optimization region.\n",
        "These geometries will stay unchanged in the optimization process. After\n",
        "each part is defined, we can perform a union operation (+) to combine\n",
        "them together."
      ],
      "id": "9e474e16-9745-4a4e-a991-e6f4caec923a"
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {},
      "outputs": [],
      "source": [
        "# Define the input straight waveguide geometry\n",
        "input_waveguide_geo = td.Box.from_bounds(rmin=(-buffer, 0, -Hc / 2), rmax=(0, W0, Hc / 2))\n",
        "\n",
        "# Define the bar port straight waveguide geometry\n",
        "bar_waveguide_geo = td.Box.from_bounds(\n",
        "    rmin=((M + 1) * Ls, 0, -Hc / 2), rmax=((M + 1) * Ls + buffer, W0, Hc / 2)\n",
        ")\n",
        "\n",
        "# Define the lower waveguide geometry with the help of gdstk\n",
        "cell = gdstk.Cell(\"lower_waveguide\")\n",
        "path = gdstk.RobustPath(\n",
        "    initial_point=(0, -G0 - Wa / 2), width=Wa, tolerance=1e-4, layer=1, datatype=0\n",
        ")\n",
        "path.segment(xy=((M + 1) * Ls, -G0 - Wt / 2), width=Wt, offset=-(Wt - Wa))\n",
        "bend_length = 6\n",
        "bend_height = 1\n",
        "path.segment(\n",
        "    xy=((M + 1) * Ls + bend_length, -G0 - Wt / 2),\n",
        "    offset=lambda u: bend_height * np.cos(np.pi * (u)) / 2 - bend_height / 2,\n",
        ")\n",
        "path.horizontal(x=(M + 1) * Ls + bend_length + buffer)\n",
        "cell.add(path)\n",
        "lower_waveguide_geo = td.Geometry.from_gds(cell, gds_layer=1, axis=2, slab_bounds=(-Hc / 2, Hc / 2))\n",
        "\n",
        "# Perform a union operation to combine all the geometries\n",
        "unchanged_geo = input_waveguide_geo + bar_waveguide_geo + lower_waveguide_geo"
      ],
      "id": "0dd5925d"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "To visually inspect if the above-defined geometries are correct, we can\n",
        "simply use the `plot()` method. The geometries do look correct. The\n",
        "missing design region will be optimized by PSO later."
      ],
      "id": "bfdb98d5-6c52-4cd4-a58b-0fc11c92c9b7"
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
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E/eQnP9Hvfvc7xcXFxaBK67LijQUAQDiFCkJPdKh8RwhC7S6H5LQT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\nHgsvg0PJm1uJXJIGDBigsWPHaty4cRo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          }
        }
      ],
      "source": [
        "ax = unchanged_geo.plot(z=0)\n",
        "ax.set_xlim(-2, 12)\n",
        "plt.show()"
      ],
      "id": "e3c8ed5a"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Define Design Region\n",
        "\n",
        "Next we define a function that creates the geometry of the design\n",
        "region. This region is parameterized by 10 parameters $W_1$, $W_2$, …,\n",
        "$W_{10}$. We will define an array `Ws` to store these 10 values. The\n",
        "geometry of the design region is defined as a\n",
        "[PolySlab](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.PolySlab.html),\n",
        "whose vertices can be easily calculated from `Ws`."
      ],
      "id": "77432f4c-f361-44af-a315-94a49d57c9a7"
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {},
      "outputs": [],
      "source": [
        "def define_optimize_region(Ws: np.array) -> td.PolySlab:\n",
        "    \"\"\"Calculate the vertices of the design region and return a PolySlab.\"\"\"\n",
        "    vertices = [(0, 0), (0, W0)]\n",
        "    for i, Wi in enumerate(Ws):\n",
        "        vertices.append(((i + 1) * Ls, Wi))\n",
        "\n",
        "    vertices.append(((M + 1) * Ls, W0))\n",
        "    vertices.append(((M + 1) * Ls, 0))\n",
        "\n",
        "    optimize_region_geo = td.PolySlab(vertices=vertices, axis=2, slab_bounds=(-Hc / 2, Hc / 2))\n",
        "\n",
        "    return optimize_region_geo"
      ],
      "id": "74b63df3"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Again, we want to visually inspect if the `define_optimize_region`\n",
        "function works correctly. To do so, we define `Ws` with some random\n",
        "values and plot the design region geometry together with the unchanged\n",
        "region geometries. From the plot, we can confirm that the geometries are\n",
        "generated correctly."
      ],
      "id": "918e0202-5f61-4de8-8c13-38499309c6aa"
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
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FZZZwRJcdLywAAIDOOjEIjeaEST09CHUkRAJMZ6JbjkSP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\nADh9Nd4Dc8mSJVq6dKlWrFjR5iQ+Do9Tnn5p8g7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          }
        }
      ],
      "source": [
        "np.random.seed(1)  # use a fixed random seed for reproducibility of the notebook\n",
        "Ws = np.random.uniform(0.3, 0.45, M)\n",
        "optimize_region_geo = define_optimize_region(Ws)\n",
        "\n",
        "device = td.Structure(geometry=unchanged_geo + optimize_region_geo, medium=si)\n",
        "ax = device.plot(z=0)\n",
        "ax.set_xlim(-1, 12)\n",
        "plt.show()"
      ],
      "id": "e20d938b"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Define Source and Monitors\n",
        "\n",
        "To characterize the performance of the PBS, we need to perform two\n",
        "simulations: 1. excite the input waveguide with a TE0\n",
        "[ModeSource](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.ModeSource.html)\n",
        "and calculate the TE0 mode transmission at the bar port using a\n",
        "[ModeMonitor](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.ModeMonitor.html);\n",
        "2. Excite the input waveguide with a TM0\n",
        "[ModeSource](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.ModeSource.html)\n",
        "and calculate the TM0 mode transmission at the cross port using a\n",
        "[ModeMonitor](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.ModeMonitor.html).\n",
        "Since the PBS is surrounded by SiO$_2$, there is a symmetry that can be\n",
        "exploited in the $z$ direction. We can use this symmetry to\n",
        "strategically select TE0 mode or the TM0 mode at the\n",
        "[ModeSource](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.ModeSource.html)\n",
        "(more on it later). Therefore, here we set `num_modes=1` in the\n",
        "[ModeSpec](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.ModeSpec.html).\n",
        "If no symmetry is used, `num_modes=2` should be used."
      ],
      "id": "4f7b4e26-45a3-415e-8f30-b8020cb7a277"
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {},
      "outputs": [],
      "source": [
        "# Add a mode source as excitation\n",
        "mode_spec = td.ModeSpec(num_modes=1, target_neff=n_si)\n",
        "mode_source = td.ModeSource(\n",
        "    center=(-lda0 / 2, W0 / 2, 0),\n",
        "    size=(0, 4 * W0, 6 * Hc),\n",
        "    source_time=td.GaussianPulse(freq0=freq0, fwidth=fwidth),\n",
        "    direction=\"+\",\n",
        "    mode_spec=mode_spec,\n",
        "    mode_index=0,\n",
        ")\n",
        "\n",
        "# Add a mode monitor at the bar port\n",
        "mode_monitor_bar = td.ModeMonitor(\n",
        "    center=((M + 1) * Ls + bend_length + lda0 / 2, W0 / 2, 0),\n",
        "    size=mode_source.size,\n",
        "    freqs=freqs,\n",
        "    mode_spec=mode_spec,\n",
        "    name=\"bar\",\n",
        ")\n",
        "\n",
        "# Add a mode monitor at the cross port\n",
        "mode_monitor_cross = td.ModeMonitor(\n",
        "    center=((M + 1) * Ls + bend_length + lda0 / 2, -G0 - Wt / 2 - bend_height, 0),\n",
        "    size=mode_source.size,\n",
        "    freqs=freqs,\n",
        "    mode_spec=mode_spec,\n",
        "    name=\"cross\",\n",
        ")\n",
        "\n",
        "# Simulation domain box\n",
        "sim_box = td.Box.from_bounds(rmin=(-1, -3.5, -1), rmax=(12.5, 1.5, 1))\n",
        "\n",
        "# Simulation run time\n",
        "run_time = 5e-13"
      ],
      "id": "04e2ac29"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Define Tidy3D Simulation\n",
        "\n",
        "Next, we define a function `make_sim` that takes the design parameters\n",
        "and polarization and returns a Tidy3D\n",
        "[Simulation](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.Simulation.html).\n",
        "If we want to define a TE0 mode excitation, we set `symmetry` to\n",
        "`(0,0,1)` while for TM0 excitation, we have `symmetry=(0,0,-1)`. Note\n",
        "again that we can use symmetry because the PBS is surrounded by silicon\n",
        "oxide. If no cladding is used, this symmetry will be broken and we need\n",
        "to define the excitation mode at the source differently."
      ],
      "id": "95c7bb80-9bcb-4f3b-ac2a-7c8daeee4b4e"
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {},
      "outputs": [],
      "source": [
        "def make_sim(Ws: np.array, pol: str) -> td.Simulation:\n",
        "    \"\"\"Build a Simulation object from design region widths and desired polarization.\"\"\"\n",
        "    optimize_region_geo = define_optimize_region(Ws)\n",
        "\n",
        "    # Define the structure for the entire PBS\n",
        "    device = td.Structure(geometry=unchanged_geo + optimize_region_geo, medium=si)\n",
        "\n",
        "    # Define symmetry according to excitation polarization\n",
        "    pol_to_symmetry = {\"TE\": (0, 0, 1), \"TM\": (0, 0, -1)}\n",
        "\n",
        "    try:\n",
        "        symmetry = pol_to_symmetry[pol]\n",
        "    except KeyError:\n",
        "        raise ValueError(\"Polarization can either be TE or TM\")\n",
        "\n",
        "    # Add mode monitor according to excitation polarization\n",
        "    if pol == \"TE\":\n",
        "        monitor = [mode_monitor_bar]\n",
        "    elif pol == \"TM\":\n",
        "        monitor = [mode_monitor_cross]\n",
        "\n",
        "    # Define simulation\n",
        "    sim = td.Simulation(\n",
        "        center=sim_box.center,\n",
        "        size=sim_box.size,\n",
        "        grid_spec=td.GridSpec.auto(min_steps_per_wvl=10, wavelength=lda0),\n",
        "        structures=[device],\n",
        "        sources=[mode_source],\n",
        "        monitors=monitor,\n",
        "        run_time=run_time,\n",
        "        boundary_spec=td.BoundarySpec.all_sides(boundary=td.PML()),\n",
        "        medium=sio2,\n",
        "        symmetry=symmetry,\n",
        "    )\n",
        "\n",
        "    return sim"
      ],
      "id": "e61849c6"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "We again inspect the simulation setup by plotting it. For the TM\n",
        "simulation, we see the\n",
        "[ModeMonitor](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.ModeMonitor.html)\n",
        "at the cross port. For TE simulation, we should see the monitor at the\n",
        "bar port."
      ],
      "id": "ec256ef5-0851-4c91-b7f2-15615f371a94"
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
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DBspFIYrQgTPFU4QCADAW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          }
        }
      ],
      "source": [
        "sim = make_sim(Ws, \"TM\")\n",
        "sim.plot(z=0)\n",
        "plt.show()"
      ],
      "id": "d80e9982"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Preparing the DesignSpace\n",
        "\n",
        "The `Design` plugin requires a pre and post function that define the\n",
        "simulation(s) to be run and how to postprocess the result.\n",
        "\n",
        "We can define a short pre function which will create the both TE and TM\n",
        "simulations based on the parameter widths that the PSO will suggest.\n",
        "Outputting this as a dictionary of `Simulations` will allow the Design\n",
        "plugin to efficiently parallelize this problem and correctly format the\n",
        "task names."
      ],
      "id": "7dc40d12-2ac3-404c-a751-c47f4ca7eda0"
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {},
      "outputs": [],
      "source": [
        "def fn_pre(**params: dict) -> dict[td.Simulation, td.Simulation]:\n",
        "    \"\"\"Take parameter widths suggested by the PSO and output a dictionary of Simulations.\"\"\"\n",
        "    widths = np.array(list(params.values()))\n",
        "    sim_te = make_sim(widths, \"TE\")\n",
        "    sim_tm = make_sim(widths, \"TM\")\n",
        "\n",
        "    return {\"TE\": sim_te, \"TM\": sim_tm}"
      ],
      "id": "f149824b"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Define the Figure of Merit (FOM)\n",
        "\n",
        "We need to define a function that acts as post function for our\n",
        "`DesignSpace` and calculates the FOM from our simulation output. In the\n",
        "case of the PBS, we define the FOM as the sum of $P_{TE,bar}$ and\n",
        "$P_{TM,cross}$, where $P_{TE,bar}$ is the transmission of TE0 mode at\n",
        "the bar port and $P_{TM,cross}$ is the transmission of TM0 mode at the\n",
        "cross port. In this particular case, we only optimize the transmission\n",
        "at the central frequency. If broadband operation is desired, the FOM can\n",
        "be defined with respect to the entire frequency range.\n",
        "\n",
        "The input for this function is a dictionary with the same keys as the\n",
        "output of `fn_pre`. The optimizer replaces the `Simulation` objects it\n",
        "receives with `SimulationData` objects, meaning we can easily access the\n",
        "appropriate TE or TM simulation.\n",
        "\n",
        "Note that this FOM is a maximizing function; all the optimizers in the\n",
        "`Design` plugin are maximizing by default so the sign does not need to\n",
        "be changed."
      ],
      "id": "fc5c01b6-6646-429f-b548-4b635e326975"
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {},
      "outputs": [],
      "source": [
        "def fn_post(sim_data_dict: dict[td.SimulationData, td.SimulationData]) -> float:\n",
        "    \"\"\"Calculate the power for TE and TM polarizations in different regions of the PBS.\"\"\"\n",
        "    # Extract te power at the bar at the central frequency\n",
        "    P_TE_bar = (\n",
        "        np.abs(sim_data_dict[\"TE\"][\"bar\"].amps.sel(mode_index=0, direction=\"+\", f=freq0)) ** 2\n",
        "    )\n",
        "\n",
        "    # Extract tm transmission at cross port at the central frequency\n",
        "    P_TM_cross = (\n",
        "        np.abs(sim_data_dict[\"TM\"][\"cross\"].amps.sel(mode_index=0, direction=\"+\", f=freq0)) ** 2\n",
        "    )\n",
        "\n",
        "    return float(P_TE_bar + P_TM_cross)"
      ],
      "id": "7e07a47f"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Performing PSO\n",
        "\n",
        "With all the preparation work done, we are finally ready to perform the\n",
        "PSO. Defining the hyper-parameters within the `Method` lets the\n",
        "`DesignSpace` manage the PSO run using the\n",
        "[PySwarms](https://pyswarms.readthedocs.io/en/latest/index.html)\n",
        "library.\n",
        "\n",
        "In this optimization, we put an upper and lower bound for the $W_i$ to\n",
        "be 450 nm and 300 nm. 5 particles are used for a total of 40 iterations.\n",
        "As discussed above, this means the entire optimization will run 400\n",
        "simulations and cost 10 FlexCredits. Since this notebook is mainly for\n",
        "demonstration purposes, the numbers of particles and iterations are kept\n",
        "small. To really achieve a design with high performance, larger numbers\n",
        "should be used. To ensure the final result is reproducible every time we\n",
        "run the notebook, the initial positions of the particles are fixed with\n",
        "a random seed.\n",
        "\n",
        "There are three hyperparameters in PSO, namely the inertia weight, the\n",
        "cognitive coefficient, and the social coefficient. Their values can\n",
        "significantly impact the performance of the algorithm. The best values\n",
        "of them depend on the specific problem so it can take some\n",
        "experimentation to determine.\n",
        "\n",
        "We also include a very low `ftol` value that must be maintained for 8\n",
        "consecutive iterations as an early-stop criterion. This means that if\n",
        "the fitness stops improving, the optimization will finish early."
      ],
      "id": "14b3828b-ecb1-415b-93d0-674bd58dec18"
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {},
      "outputs": [],
      "source": [
        "W_max = 0.45  # upper bound\n",
        "W_min = 0.3  # lower bound\n",
        "\n",
        "n_particles = 5  # number of particles\n",
        "\n",
        "# Set initial positions\n",
        "init_pos = np.random.uniform(W_min, W_max, (n_particles, M))\n",
        "\n",
        "particle_swarm = tdd.MethodParticleSwarm(\n",
        "    n_particles=n_particles,\n",
        "    n_iter=75,\n",
        "    cognitive_coeff=1,\n",
        "    social_coeff=1,\n",
        "    weight=0.7,\n",
        "    init_pos=init_pos,\n",
        "    seed=1,\n",
        "    ftol=1e-4,\n",
        "    ftol_iter=8,\n",
        ")\n",
        "\n",
        "parameters = [tdd.ParameterFloat(name=str(i), span=(W_min, W_max)) for i in range(M)]\n",
        "\n",
        "design_space = tdd.DesignSpace(\n",
        "    method=particle_swarm, parameters=parameters, task_name=\"PSO_Notebook\", path_dir=\"./data\"\n",
        ")"
      ],
      "id": "3b92f729"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Running the PSO optimization is easily managed by supplying the `fn_pre`\n",
        "and `fn_post` functions to the `DesignSpace.run` method."
      ],
      "id": "fc19b7c5-2b81-4ce6-a45e-c87b1cab4e52"
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {},
      "outputs": [
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              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">06:42:36 UTC </span>Running <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">10</span> Simulations                                             \n",
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              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">06:44:42 UTC </span>Running <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">10</span> Simulations                                             \n",
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              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">06:45:14 UTC </span>Running <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">10</span> Simulations                                             \n",
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              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">06:45:47 UTC </span>Running <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">10</span> Simulations                                             \n",
              "</pre>"
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              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">06:46:26 UTC </span>Running <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">10</span> Simulations                                             \n",
              "</pre>"
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              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">06:46:59 UTC </span>Running <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">10</span> Simulations                                             \n",
              "</pre>"
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        {
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          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">06:47:39 UTC </span>Running <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">10</span> Simulations                                             \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">06:49:26 UTC </span>Running <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">10</span> Simulations                                             \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">06:50:11 UTC </span>Best Result: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">-1.6447994633909997</span>                                   \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>Best Parameters: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span>: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.36569514953861787</span> <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1</span>: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.3122289105981696</span> <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span>:   \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.4091189543637529</span> <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">3</span>: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.4282830732962929</span> <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">4</span>: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.3880362943864307</span> <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">5</span>:  \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.32239727328670414</span> <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">6</span>: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.3373365173571663</span> <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">7</span>: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.32336518513529305</span> <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">8</span>:\n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.34003640122419787</span> <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">9</span>: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.44988811607034884</span>                         \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>                                                                   \n",
              "</pre>"
            ]
          }
        }
      ],
      "source": [
        "results = design_space.run(fn_pre, fn_post, verbose=True)\n",
        "df = results.to_dataframe()"
      ],
      "id": "72be9938"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "After the optimization is complete, plot the FOM as a function of\n",
        "iteration. We can use the optimizer object from the `results` to access\n",
        "the cost history."
      ],
      "id": "796597fa-465f-4a24-a6c0-5713df6782ef"
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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AWUMZBgAAAEDWUIbBUdi9b09MmDslvvvEL2PP/r1JxwEAAACOUn7SAaC2+M8/\nfDeefuNf6RJsbP8RMab/iIRTAQAAAEfDlWFQQXm5uRlXg42fOyXBNAAAAMCxUIZBBY3tPzJjPHH+\ntISSAAAAAMdKGQYVdFa/4ZGTk5Mez1mxMNZv25RgIgAAAOBoKcOgglo3bRGndu2bse0VV4cBAABA\nraIMg6MwbkDmVMkJ86YmlAQAAAA4FsowOAql7x45cd7USKVSCaUBAAAAjpYyDI7C8J6nRqP6DdPj\nd7asj4XvLEsuEAAAAHBUlGFwFBrUqx+jew/J2DbRVEkAAACoNZRhcJTGlpoqOX7elISSAAAAAEdL\nGQZHaWypRfQnFc6IfUX7E0oDAAAAHA1lGBylvp1OjI4t2qXHu/bujjeWzE4wEQAAAFBRyjA4Sjk5\nOXFW/+EZ2ybMNVUSAAAAagNlGByDcaXWDZswb1pCSQAAAICjoQyDYzCm1JVhM9+eF5t3bk0oDQAA\nAFBRyjA4Bu2at4kBXXqlx6lUKl6Z/0aCiQAAAICKUIbBMSp9V8mJ86YmlAQAAACoKGUYHKOxpdYN\nGz93SqRSqYTSAAAAABWhDINjNLLXoGiQXz89XrlpTSxdtyLBRAAAAMCRKMPgGDWq3zBG9hqUsW2C\nqZIAAABQoynD4DiMKTVVcuK8aQklAQAAACpCGQbHYVypRfRfXfBGFBUXJZQGAAAAOBJlGByHAV16\nRZtmrdLj7Xt2xoxlcxNMBAAAAByOMgyOQ25ubozpNzxj2/i5UxJKAwAAAByJMgyO09gy64ZZRB8A\nAABqKmUYHKfSZdj0ZXNj2+4dCaUBAAAADkcZBsepU6v20btjj/S4uKQ4XlvwZnKBAAAAgENShkEl\nKH1XyQmmSgIAAECNpAyDSjDGumEAAABQKyjDoBKc3ntI1MvLT4+XrFsRb29YnWAiAAAAoDzKMKgE\nTRo2jmE9T83Y5uowAAAAqHmUYVBJSt9VcsK8aQklAQAAAA5FGQaVpPS6Ya/MnxbFJcUJpQEAAADK\nowyDSjKoe79o2bh5erxl17aY9faCBBMBAAAApSnDoJLk5ebFmf2GZWyzbhgAAADULPlHPoSjsXfv\n3igoKIipU6dGYWFhlJSURJs2beLb3/52pZz/8ccfj5dffvmIxzVv3jx+8IMfVOice/bsiX/+85/x\n1ltvxYYNG6J9+/bRu3fvOP/886Np06bHGzmrjOs/Ip6b/lJ6PH7ulPjP93wsuUAAAABABmVYJXnq\nqafiBz/4QcycOTP27duXsa979+6VVoa98sor8atf/eqIx3Xo0OGIZVhRUVH8/Oc/j+985zuxffv2\nMvsbN24cX/jCF+J73/veMefNNqXXDXtjyezYuWdXNGnYOKFEAAAAwMGUYZWkoKAgpk2bFvXr14/h\nw4fHiBEj4vnnn4+lS5dWyeu1bNkyvvvd7x5yf5MmTQ77/H379sX73ve+eO655yIiol+/fnHxxRdH\nly5dYvfu3TFnzpx4/vnnY/LkyZWau67r1rZznNjuhFi6fmVEROwvLorXC2fE+aeekXAyAAAAIEIZ\nVmmuvPLKuPjii2Pw4MFRv379iIg488wzq6wMa9KkSdxyyy3H/PzPfOYz8dxzz0VOTk787Gc/i//8\nz/+MnJycjGP27NkTs2bNOt6oWWfsgJGxdMLK9HjivKnKMAAAAKghLKBfSQYNGhQjRoxIF2E12YQJ\nE+Kee+6JiIhvfOMb8fnPf75MERYR0bBhwxgxYkSZ7Rze2FJTJSdYRB8AAABqDGVYFrrzzjsjIqJt\n27bxX//1XwmnqXvO6Hta5OXmpccL31kaqzevSzARAAAA8C5lWJbZvHlzPP/88xER8aEPfSgaNGiQ\ncKK6p3mjpjG0x4CMbRNdHQYAAAA1gjXDaql9+/bFgw8+GPPmzYvdu3dH69atY/DgwTFu3LjDLp4/\nZcqUKC4ujoiIs846KyIi5s+fH88//3ysXr06GjduHCeffHJceOGF0bJly+p4K3XSmP4jYtqS2enx\nxHlT48OnX5pgIgAAACBCGVZrrV+/Pq677roy21u2bBm33npr3H777ZGXl1dm/5w5c9KPu3TpEtdd\nd108+OCDZY5r1qxZ/Pd//3d8+ctfPupsmzdvPuS+LVu2HPX5aqOx/UfEnX+9Nz2eMH9alJSURG6u\nizEBAAAgScqwWqhx48YxZsyY6N27d3Tt2jX27dsXBQUF8dxzz8WWLVvi61//ekybNi0ef/zxMoXY\npk2b0o8/+9nPRkFBQXTr1i0++MEPRqdOnWLZsmXx8MMPx4YNG+K2226LtWvXxk9/+tOjyte6detK\neZ+12ZATT45mDZvE9j07IyJi4/bNMXfVojila5+EkwEAAEB2U4bVMp/85Cfj+9//frlTIVetWhUf\n+MAHYtKkSfH000/HnXfeGbfddlvGMbt27Uo/LigoiAsvvDCefPLJaNSoUXr7N7/5zTjvvPOioKAg\n7rzzzrjqqqvi9NNPr7o3VQfVy8uPM/qeFi/MnJjeNmHeVGUYAAAAJCyryrCHHnooXn/99eM6x803\n3xwnn3xyJSU6eqeccsoh93Xp0iWef/756NevX6xduzbuuOOOuPXWWzOm5h1cejVs2DAeeOCBjG0R\nEW3atIk//OEPMWjQoIiI+NWvfnVUZdjBV5+VtmXLlujZs2eFz1Wbjek/IrMMmzslPnNB2amtAAAA\nQPXJqjLspZdeinvvvffIBx7GRRddlGgZdiQtW7aMj3/84/HDH/4wNmzYEAUFBTF06ND0/ubNm6cf\nn3POOdG+fftyzzNw4MAYMGBAzJ07N1555ZWjytCqVatjC1/HjOs/ImM8ZdHM2L1vTzSq3zChRAAA\nAEBWlWHXXnttDB48+LjOcbgrs2qKU089Nf145cqVGWXYSSedVO7j8vTs2TPmzp0ba9asqfyQWeDE\n9l3jhNYdY+WmA5/f3qJ9MXXRzBg7YGTCyQAAACB7ZVUZdvbZZ8fZZ5+ddIwqV1RUlH5cegH9g4uy\n4uLiw57n3f3l3ZWSI8vJyYmx/UfEg689k942ft5UZRgAAAAkKPfIh1DbTJs2Lf34xBNPzNjXv3//\n6NGjR0REzJ0797DneXf/u8dz9EoXXxPnTU0oCQAAABChDKtzli9fHvfff39ERHTv3j0GDBhQ5pjr\nrjuwiPsrr7wShYWF5Z7nxRdfjOXLl0dExIUXXlhFaeu+M/sOi5ycnPT4rZWFsX7bxgQTAQAAQHZT\nhtUgjz32WNxyyy1xyy23xNtvv11m/5tvvhnPPPNM7N69u9znT5o0Kc4999zYsWNHRER85zvfKfe4\nW2+9Ndq1axfFxcXx/ve/P1auXJmx/6233orrr78+IiIaN24cX/ziF4/nbWW11k1bxKBu/TO2TZw3\n7RBHAwAAAFUtq9YMq0qbNm2Kb3zjGxnblixZkt53yy23ZOy79dZby0w/nDBhQvzqV7+KiIiPfexj\n0a1bt4z9M2bMiE996lPRqFGjOPXUU6Njx47RoUOH2Lt3bxQUFMSsWbPSx375y1+Oj3zkI+VmbdGi\nRTz++ONxwQUXxKxZs6JPnz5x/vnnR8eOHWPZsmXx0ksvRVFRUdSrVy8eeOCBMjk4OmP7D4+C5f+e\nkjph3tR438iLEkwEAAAA2UsZVkm2bduWLrJK2759e5l911133VGvxTV8+PC46qqr4sUXX4ypU8tf\ne2rEiBHx3//933HppZce9lxnnXVWTJ48OW6++eaYNGlSPPPMMxn7hw8fHj//+c/j9NNPP6qMlDWm\n/4j43xf+kB5PmDc1UqlUxvRJAAAAoHoowypJmzZt4he/+EWFjy+9sH1ExAc/+MHo169fRBxY76u0\nQYMGxeOPPx5FRUUxZ86cWLVqVaxZsyZyc3OjXbt2MXTo0OjcuXOFMwwaNChef/31WLRoURQUFMSm\nTZuiRYsWMXTo0Ojdu3eFz8PhDet5ajRu0Ch27T0wvXXt1g2x4J2l0a9zz4STAQAAQPbJSaVSqaRD\nkD02b94crVu3jogD00dbtWqVcKLqce0vvxgvznk9Pf7OBz4fN5z74QQTAQAAQM1XFT2CBfShGozt\nPyJjPH7ulISSAAAAQHZThkE1GNt/ZMZ4UuGM2Lt/X0JpAAAAIHspw6Aa9OnUIzq2aJce7963J95Y\nMjvBRAAAAJCdlGFQDXJycmJM/+EZ2ybMK/+OoAAAAEDVUYZBNRk3IHOqpDIMAAAAqp8yDKrJWf0y\nrwyb9fb82LRja0JpAAAAIDspw6CatGveOk4+oXd6nEql4pX50xJMBAAAANlHGQbVaGz/ERnjiaZK\nAgAAQLVShkE1Kl2GjZ83NVKpVEJpAAAAIPsow6Aajeg1KBrWa5Aer9q0JpasW5FgIgAAAMguyjCo\nRo3qN4yRvQZlbHNXSQAAAKg+yjCoZmNKTZWcMHdKQkkAAAAg+yjDoJqNGzAyY/zawjdjf3FRQmkA\nAAAguyjDoJr173xStG3WKj3esWdXzFj6VoKJAAAAIHsow6Ca5ebmxph+wzO2jbduGAAAAFQLZRgk\nYGypqZITlWEAAABQLZRhkIDSV4bNWDY3tu7anlAaAAAAyB7KMEhAp1bto0+nE9Pj4pLieG3Bmwkm\nAgAAgOygDIOEjOufOVVygqmSAAAAUOWUYZCQMf1HZIytGwYAAABVTxkGCRndZ0jUy8tPj5euXxnL\nN6xOMBEAAADUfcowSEiTBo1i+EkDM7a5OgwAAACqljIMEjS21FTJ8XOnJJQEAAAAsoMyDBI0dkDm\nIvqvLXgzikuKE0oDAAAAdZ8yDBJ0atc+0apJ8/R4y65tMXP5/AQTAQAAQN2mDIME5eXmxZl9h2ds\nmzDPVEkAAACoKsowSNi4AZnrhk2YNy2hJAAAAFD3KcMgYWNKLaL/5pLZsWPPzoTSAAAAQN2mDIOE\ndW3TKXq275oe7y8uitcXzkgwEQAAANRdyjCoAcb2z7yr5MR5UxNKAgAAAHWbMgxqgLH9S68bpgwD\nAACAqqAMgxrg9L5DIy83Lz0uXLMsVm9el2AiAAAAqJuUYVADNG/UNE478eSMba4OAwAAgMqnDIMa\novRdJa0bBgAAAJVPGQY1RHnrhpWUlCSUBgAAAOomZRjUEEN6DIhmDZukx5t2bIm3VhYmmAgAAADq\nHmUY1BD5eflxZt9hGdvGz5uSUBoAAACom5RhUIOMHWDdMAAAAKhKyjCoQUqvGzZ10azYtW9PQmkA\nAACg7lGGQQ3So90J0bVNp/R4b9G+mFJYkFwgAAAAqGOUYVCD5OTkxLgBIzO2TTBVEgAAACqNMgxq\nmDH9rBsGAAAAVUUZBjXMmf1Oi5ycnPR47qpFsW7rxgQTAQAAQN2hDIMaplWTFjG4e/+MbRPnuzoM\nAAAAKoMyDGqg0neVnDBvWkJJAAAAoG5RhkENNKZ/2XXDUqlUQmkAAACg7lCGQQ00rOep0bhBo/R4\n7dYNMX/1kgQTAQAAQN2gDIMaqH5+vTi9z9CMbe4qCQAAAMdPGQY11Nh+mVMlx8+bklASAAAAqDuU\nYVBDjR2QWYZNXjgj9u7fl1AaAAAAqBuUYVBD9e7YIzq1bJce796/N6YtnpVgIgAAAKj9lGFQQ+Xk\n5MTYASMztk2wbhgAAAAcF2UY1GBj+2dOlVSGAQAAwPFRhkENdmbfYRnj2SsWxMYdW5IJAwAAAHWA\nMgxqsHbNW8epXfukx6lUKl6ZPy3BRAAAAFC7KcOghhtTaqrkRFMlAQAA4Jgpw6CGK7Nu2NypkUql\nEkoDAAAAtZsyDGq4Eb0GRcN6DdLjVZvXxuK1byeYCAAAAGovZRjUcA3rNYhRvQdnbHNXSQAAADg2\nyjCoBcb0KzVVct6UhJIAAABA7aYMg1pg3IDMMuz1hdNjf3FRQmkAAACg9lKGQS3Qv0uvaNe8dXq8\nY8+umL50ToKJAAAAoHZShkEtkJOTE2P6Dc/YNn6udcMAAADgaCnDoJYYO2BkxniiRfQBAADgqCnD\noJYofWXYjGVzY8vObQmlAQAAgNpJGQa1RMeW7aJf55PS45JUSby28M0EEwEAAEDtowyDWmRs/8yr\nwyaYKgkAAABHRRkGtciY/iMyxhMsog8AAABHRRkGtcio3kOifn699Hj5hlWxfP2qBBMBAABA7aIM\ng1qkSYNGMfykgRnbTJUEAACAilOGQS0ztvRUyXlTEkoCAAAAtY8yDGqZsf1HZoxfXfBmFJcUJ5QG\nAAAAahdlGNQyp3btE62btEiPt+7aHjOXz0swEQAAANQeyjCoZXJzc+PMfsMyto13V0kAAACoEGUY\n1ELjBmROlZxoEX0AAACoEGUY1EJjSi2i/8aS2bFjz86E0gAAAEDtoQyDWuiE1h3jpA7d0uOikuJ4\nfeH0BBMBAABA7aAMg1pqbKmrwyaYKgkAAABHpAyDWqpMGWYRfQAAADgiZRjUUqf3OS3ycvPS40Vr\nl8eqTWsTTAQAAAA1nzIMaqlmjZrEsJ6nZGwzVRIAAAAOTxkGtVjpu0pOmDcloSQAAABQOyjDoBYb\n139kxviV+W9ESUlJQmkAAACg5lOGQS02qHu/aN6oaXq8aceWmLNyYYKJAAAAoGZThkEtlp+XH2f2\nPS1jm7tKAgAAwKEpw6CWGzsgc6qkRfQBAADg0JRhUMuNLbWI/tTFM2PXvj0JpQEAAICaTRkGtVyP\ndidEt7ad0+N9RftjcuGMBBMBAABAzaUMgzqg9F0lTZUEAACA8inDoA4Y0394xtgi+gAAAFA+ZRjU\nAWf2HRa5Of/+dZ6/enGs3bohwUQAAABQMynDoA5o2aR5DO7RP2PbxHnTEkoDAAAANZcyDOqI0neV\nnDBvSkJJAAAAoOZShkEdMaZUGTZx3rRIpVIJpQEAAICaSRkGdcRpJ54STRo0To/XbdsY81cvTjAR\nAAAA1DzKMKgj6ufXi9P7DMnYNn6uqZIAAABwMGUY1CFjB4zMGFtEHwAAADIpw6AOKb2I/uTCGbFn\n/96E0gAAAEDNowyDOqRXh+7RuVX79Hj3/r0xbfGsBBMBAABAzaIMgzokJycnxvbPnCo5Yd7UhNIA\nAABAzaMMgzqm9FTJicowAAAASFOGQR1zZr9hGeNZby+IDds3J5QGAAAAahZlGNQxbZu1ioHd+mZs\ne3X+GwmlAQAAgJpFGQZ10JhSUyXHz5uSUBIAAACoWZRhUAeVt25YKpVKKA0AAADUHMowqIOGnzQw\nGtVrkB6v3rwuFq1dnmAiAAAAqBmUYVAHNazXIEb1HpKxbcJcUyUBAABAGQZ11Jj+wzPGE+ZNTSgJ\nAAAA1BzKMKijxg0YmTF+feGM2Fe0P6E0AAAAUDMow6CO6tf5pGjfvE16vHPvrnhz6ZwEEwEAAEDy\nlGFQR+Xk5MSYcu4qCQAAANlMGQZ12NhSZZh1wwAAAMh2yjCow0ovol+wbF5s2bktoTQAAACQPGUY\n1GEdWrSN/l1OSo9LUiXx6oI3EkwEAAAAyVKGQR1Xdt2waQklAQAAgOQpw6COK71u2Ph5UxJKAgAA\nAMlThkEdN6r3kKifXy89fnvD6li2fmWCiQAAACA5yjCo4xrXbxgjThqUsW38XFeHAQAAkJ2UYZAF\nSk+VnDhvakJJAAAAIFnKMMgCYwdklmGvLngzioqLEkoDAAAAyVGGQRY45YQ+0bppy/R42+4dUbB8\nXnKBAAAAICHKMMgCubm5cVa/YRnbJpgqCQAAQBZShkGWGNt/ZMbYumEAAABkI2UYZInSi+i/sWRO\nbN+9M6E0AAAAkAxlGGSJLq07RO+O3dPj4pLieH3hmwkmAgAAgOqnDIMsMqbU1WHWDQMAACDb5Ccd\noC4qKiqK2bNnR2FhYZSUlESTJk3isssuq5Rzz5gxIxYsWHDE4xo1ahSXX375EY/bvXt3zJ49O9as\nWRPFxcXRpk2bOOWUU6J169aVEZcaZmz/EXHvy4+lx8owAAAAso0yrJJMnz49/vSnP8XUqVNj+vTp\nsXv37vS+7t27V1oZ9oc//CH+93//94jHdejQ4bBl2KpVq+KrX/1qPPbYYxlZIyJycnLinHPOiR/8\n4AcxYsSIQ5yB2uj0PkMjPzcvikqKIyJi8dq3Y+WmNXFC644JJwMAAIDqoQyrJM8880z8z//8T0RE\n5Ofnx6BBg2LlypWxcePGKnm9Ro0axXvf+95D7m/ZsuUh9y1YsCDGjBkT69ati4iIjh07xsknnxwN\nGjSIBQsWxOLFi+PFF1+MM888M/785z/HFVdcUcnpSUrThk1iWM9TY/KigvS2ifOmxjVnHPpnCQAA\nAOoSZVglOe200+LOO++MESNGxGmnnRaNGjWKM888M1577bUqeb3WrVvHI488ckzP/fSnP50uwr73\nve/FbbfdFvXq1Uvvf/LJJ+Pqq6+OvXv3xic+8Yk4//zzo0mTJpWSm+SN6T8iowwbP3eKMgwAAICs\nYQH9SnLZZZfFF7/4xTjzzDOjUaNGScc5pM2bN8fLL78cERHnnXdefO1rX8sowiIirrzyyrj99tsj\nImLTpk0xfvz46o5JFRo3IHPq6yvzp0Xx/582CQAAAHWdMizLbN68OVKpVEREjBw58pDHHbyvqqZ6\nkoxB3ftHi8bN0uPNO7fF7BULE0wEAAAA1UcZlmW6desW9evXj4iIlStXHvK4g/f17t27ynNRffJy\n8+LMvqdlbJvorpIAAABkCWVYLbZ8+fJ44YUX4sknn4wJEybE5s2bj/ic/Pz8uPHGGyMi4s9//nPM\nnDmzzDGbN2+OH//4xxERMWzYsMNeQUbtNLZ/5nc6QRkGAABAlrCAfi21atWq6NGjR8a2nJycGDt2\nbHzjG9+Is88++5DP/dGPfhRr1qyJxx57LEaOHBnXXXddDBkyJOrXrx8LFy6M+++/PzZu3BgDBw6M\nxx57LHJzdaZ1zdj+meuGTV00M3bu3R1NGtTc9e4AAACgMijDaqkWLVpEz549o2vXrrFv376YNWtW\nrF69OsaPHx8TJkyIH/zgB+lF8Etr3Lhx/PnPf45nn302Pv7xj8e9996bsT8/Pz9+/OMfxxe+8IUy\ni+tXxOGuUNuyZctRn4/K171dl+jetkss37AqIiL2FxfF5MIZce4ppyecDAAAAKqWMqyWOeecc+J9\n73tfnHHGGRlXbKVSqXjmmWfixhtvjLVr18Z//dd/Rd++fePKK68sc45UKhVf+9rX4mc/+1ns3bs3\nOnToEKeddlrUr18/5s2bFwsWLIivfOUr8frrr8cf//jHaNasWZlzHE7r1q2P+31S9cYOGBEPTHwy\nPZ44b6oyDAAAgDovq8qwadOmxeLFi4/rHGPGjInOnTtXUqKj9973vrfc7Tk5OXH55ZdHr169Ytiw\nYbFnz5746le/Wm4Z9qlPfSruvffeyMnJiZ/97Gfx2c9+NvLz//2j8MILL8Q111wTTz/9dIwbNy5e\nf/31aNCgQZW9J5Ixtn9mGTbeumEAAABkgawqw37729+WmRJ4tJ599tlEy7AjOfnkk+M//uM/4u67\n74758+dHYWFhxt0gp0yZkv4MPvvZz8YXvvCFMue46KKL4ne/+1184AMfiOnTp8dvf/vb+NznPlfh\nDJs2bTrkvi1btkTPnj2P4h1RVc7sOyxyc3KjJFUSERELVi+JNVvWR8eW7RJOBgAAAFUnq8qwESNG\nxI4dO47rHF26dKmkNFXnjDPOiLvvvjsiIhYtWpRRhj3zzDPpxx//+McPeY6rrroqWrZsGVu2bIln\nn332qMqwVq1aHUNqqluLxs1iSI8B8ebSOeltE+dPiw+OujjBVAAAAFC1sqoMu+GGG+KGG25IOkaV\nO3hK4759+zL2rV69Ov24e/fuhzxHbm5udOvWLbZs2RKrVq2q/JDUCGP6j8gowybMnaIMAwAAoE7L\nPfIh1Dbz589PP+7UqVPGvoMXwz/SnR3fvSvk0S6gT+0xbsCIjPHE+dMilUollAYAAACqnjKsjtm9\ne3fcf//9ERHRokWLGDJkSMb+U089Nf34b3/72yHPM2fOnFixYkWZ51C3DD3xlGjasHF6vH7bppi3\nalGCiQAAAKBqKcNqkOnTp8cjjzwSjzzySPqqrIOtXLkyNmzYcMjnb926Nd73vvfF22+/HRERn/vc\n56JevXoZx1xxxRXRpEmTiIj4xje+EXPnzi1zni1btsQnPvGJ9Pjaa689pvdDzVcvLz9O7zM0Y9v4\nue4qCQAAQN2VVWuGVaWdO3fGs88+m7Ht3eJq586d8cgjj2TsO//886NNmzYZ2+6777741a9+FRER\n06ZNi2HDhmXsf+GFF+LGG2+M008/PUaMGBEdO3aMDh06xN69e6OgoCAeeeSR9J0czz777Pja175W\nJme7du3ipz/9adx8882xYcOGGDZsWFxzzTUxatSoqFevXsybNy/+8Ic/xJo1ayIi4qMf/WicffbZ\nx/HJUNON7T8y/jHr1fR44vyp8ekLFKAAAADUTcqwSrJ+/fq4+uqry923YcOGMvsmTZpUpgw7kq5d\nu0b79u3j1VdfjVdffbXcYxo3bhyf/exn49vf/nbGQvoHu+mmm6Jx48bxxS9+MTZu3Bj33ntv3Hvv\nvRnHNGjQIL70pS/Ft7/97aPKSO0ztn/mumGTCwtiz/690bBe+T8/AAAAUJspwypJkyZN4kMf+lCF\nj2/btm2Zbaeddlr6HK1bty6z/8ILL4zVq1dHQUFBvPbaa7Fq1apYs2ZN5ObmRrt27WLo0KFx4YUX\nRosWLY74+h/5yEfigx/8YPztb3+LqVOnxtq1a6O4uDjatGkTgwYNiksuuaTcjNQ9J3XoFl1adYhV\nm9dGRMSe/Xtj6qKZMaZUSQYAAAB1QU7KreOoRps3b04XfZs2bYpWrVolnIiIiC/+8fvx0Gv/nub7\nmQuui/++6pYEEwEAAEDV9AgW0AfKXAU2YZ5F9AEAAKiblGFAnNVveOTk5KTHc1YsjPXbNiWYCAAA\nAKqGMgyINk1bxqld+2Zse3XBGwmlAQAAgKqjDAMiouxdJcfPnZJQEgAAAKg6yjAgIiLGDhiZMZ44\nb2q4vwYAAAB1jTIMiIiI4T1PjUb1G6bH72xZH4VrliUXCAAAAKqAMgyIiIgG9erHqN6DM7ZNmOuu\nkgAAANQtyjAgbVz/zKmSE+YrwwAAAKhblGFA2phSi+i/vnB67Cvan1AaAAAAqHzKMCCtX+ee0aFF\n2/R4197d8caS2QkmAgAAgMqlDAPScnJyylwdNnGeqZIAAADUHcowIMPY/sMzxuMtog8AAEAdogwD\nMozpl3ll2My358XmnVsTSgMAAACVSxkGZGjfok0M6NIrPU6lUvHq/DcTTAQAAACVRxkGlFF63bAJ\n86YklAQAAAAqlzIMKGNsmTJsaqRSqYTSAAAAQOVRhgFljOw9OBrk10+PV2x8J5atX5lgIgAAAKgc\nyjCgjMb1G8aIXgMzto2fa6okAAAAtZ8yDChX6XXDJs6bllASAAAAqDzKMKBc4/qPzBi/uuCNKCou\nSigNAAAAVA5lGFCuk0/oHW2atUqPt+/ZGTOWzU0wEQAAABw/ZRhQrtzc3BjTb3jGtgnzpiaUBgAA\nACqHMgw4pLLrhinDAAAAqN2UYcAhjS1Vhr259K3YtntHQmkAAADg+CnDgEPq3Kp99O7YIz0uLimO\n1xdMTy4QAAAAHCdlGHBYpa8OGz9vSkJJAAAA4Pgpw4DDsm4YAAAAdYkyDDisM/oMjXp5+enxknUr\n4u0NqxNMBAAAAMdOGQYcVpOGjeO0nqdmbHN1GAAAALWVMgw4orH9h2eMJ8ybllASAAAAOD7KMOCI\nxvYfmTF+dcG0KC4pTigNAAAAHDtlGHBEg7r3i5aNm6fHm3dui1lvL0gwEQAAABwbZRhwRHm5eXFG\n39Mytlk3DAAAgNpIGQZUyLgBmVMlJyjDAAAAqIWUYUCFjOk/ImM8bfGs2LlnV0JpAAAA4Ngow4AK\n6d62c5zY7oT0eH9xUUwqLEguEAAAABwDZRhQYaWvDrNuGAAAALWNMgyosLGlyrDx86YklAQAAACO\njTIMqLAz+p4Webl56fHCd5bGO5vXJZgIAAAAjo4yDKiwFo2bxZAeAzK2uaskAAAAtYkyDDgq1g0D\nAACgNlOGAUdlXOkybP60KCkpSSgNAAAAHB1lGHBUhpx4cjRt2Dg93rB9c8xdtSjBRAAAAFBxyjDg\nqNTLy48z+pyWsc26YQAAANQWyjDgqI0dMDJjbN0wAAAAagtlGHDUxpZaN2xyYUHs3rcnoTQAAABQ\nccow4Kj1bN81urTumB7vLdoXUxfNTDARAAAAVIwyDDhqOTk5Ze4qad0wAAAAagNlGHBMxijDAAAA\nqIWUYcAxOavf8MjJyUmP31pZGOu3bUwwEQAAAByZMgw4Jq2btoiB3fplbHtl/hsJpQEAAICKUYYB\nx6z0XSXHz52SUBIAAACoGGUYcMxKl2ET502LVCqVUBoAAAA4MmUYcMyG9Tw1GtVvmB6v2bo+Fryz\nNMFEAAAAcHjKMOCYNahXP0b3HpKxbaK7SgIAAFCDKcOA4zJuwMiM8QRlGAAAADWYMgw4LmNKrRv2\n+sLpsXf/voTSAAAAwOEpw4Dj0rfTidGxRbv0ePe+PfHGktkJJgIAAIBDU4YBxyUnJyfG9B+esc26\nYQAAANRUyjDguI0tNVVyvDIMAACAGkoZBhy30leGzXp7fmzasTWhNAAAAHBoyjDguLVr3iZOPqF3\nepxKpeLVBW8kmAgAAADKpwwDKkXpu0pOmDsloSQAAABwaMowoFKMK12GzZsaqVQqoTQAAABQPmUY\nUClG9BoUDfLrp8crN62JpetWJJgIAAAAylKGAZWiUf2GMbLXoIxt7ioJAABATaMMAyrN2AEjM8YT\nlWEAAADUMMowoNKMLbVu2KsL3oj9xUUJpQEAAICylGFApRnQpVe0adYqPd6xZ1fMWPpWgokAAAAg\nkzIMqDS5ubkxtt/wjG0TTJUEAACgBlGGAZVqTKmpksowAAAAahJlGFCpSq8bNmPZ3Ni2e0dCaQAA\nACCTMgyoVJ1atY8+nU5Mj4tLiuO1BW8mmAgAAAD+TRkGVLrSV4eNnzsloSQAAACQSRkGVLrS64ZN\ntG4YAAAANYQyDKh0p/ceEvXy8tPjpetXxvINqxNMBAAAAAcow4BK16Rh4xjW89SMba4OAwAAoCZQ\nhgFVYtyAkRnjCcowAAAAagBlGFAlSq8b9ur8N6K4pDihNAAAAHCAMgyoEgO79Y2WjZunx1t2bYuZ\ny+cnmAgAAACUYUAVycvNi7P6Dc/YZt0wAAAAkqYMA6rM2P6ZZdh4ZRgAAAAJU4YBVab0umFvLpkd\nO/fsSigNAAAAKMOAKtStbefo2b5rery/uCheL5yRYCIAAACynTIMqFKlrw6bMHdKQkkAAABAGQZU\nsbGlyzDrhgEAAJAgZRhQpc7oe1rk5ealx4VrlsXqzesSTAQAAEA2U4YBVap5o6YxtMeAjG2uDgMA\nACApyjCgypVeN2yiMgwAAICEKMOAKjduwMiM8cT506KkpCShNAAAAGQzZRhQ5Yb0GBDNGjZJjzdu\n3xxvrSxMMBEAAADZShkGVLn8vPw4s++wjG3WDQMAACAJyjCgWozpPzxjPGHelISSAAAAkM2UYUC1\nGFtqEf2pi2bF7n17EkoDAABAtlKGAdXixPZdo2ubTunx3qJ9MWXRzAQTAQAAkI2UYUC1yMnJKXN1\n2Pi5pkoCAABQvZRhQLUZU6oMm2gRfQAAAKqZMgyoNmf1GxY5OTnp8dxVi2Ld1o0JJgIAACDbKMOA\natOqSYsY1K1/xraJ810dBgAAQPVRhgHVamz/4RnjCfOmJZQEAACAbKQMA6rV2AEjM8YT502NVCqV\nUBoAAACyjTIMqFbDep4ajRs0So/Xbt0Q81cvSTARAAAA2UQZBlSr+vn1YnTvIRnb3FUSAACA6lLl\nZdjDDz8c1113XTz//PNV+hyg9hjXP3Oq5ARlGAAAANWkysuwN998Mx588MGYO3dulT4HqD3G9B+R\nMZ60cHrs3b8voTQAAABkkxo9TTInJyfpCEAV6NOpR3Rq2S493r1/b0xbMjvBRAAAAGSLGlmG7dix\nIyIiGjVqdIQjgdooJyenzNVhE+ZOSSgNAAAA2aTGlWF79+6N8ePHR0REp06dkg0DVJmxpcsw64YB\nAABQDfIr+4QPP/xw/PWvf02Pp0+fnt5eUFBw2Odu37493njjjVi9enXk5eXF6NGjKzseUEOc1W94\nxnj2igWxcceWaNO0ZTKBAAAAyAqVXoa9u/h9adOnT08XYxXx+c9/Pjp27FiZ0YAapF3z1nFK1z4x\nZ8XCiIhIpVLxyvxpccWw8xNOBgAAQF1W6WVY165d47TTTkuPV65cGWvXro0TTjghOnTocMjn5ebm\nRpMmTeKkk06KK664Ii699NLKjgbUMGP6DU+XYRERE+dNVYYBAABQpXJSqVSqKl/g1ltvjTvvvDPu\nuOOOuPXWW6vypagFNm/eHK1bt46IiE2bNkWrVq0STkSSJs6bGh/838+lx11ad4w3vv+kO8kCAAAQ\nEVXTI1T6lWGlnXnmmbFnz54YMmRIVb8UUMuM6DUoGtZrEHv2742IiFWb1sSPn/ltNGnQOOFkdUdu\nbm6c2XdYDOreL+koAAAANUKVXxkGB3NlGKV96H8/506S1eCBT/80Lhh4ZtIxAAAAjkpV9Ai5x32G\nSvDOO+/EH/7wh7jrrrtiypQpSccBqtHY/iOTjpAVfvWPPyYdAQAAoEaoljLs//7v/+LDH/5wTJ48\nucy+p556Kk466aT42Mc+Fp/5zGdi1KhRcc0110RxcXF1RAMS9oFR74nWTVsmHaPOm7Fsbno6KgAA\nQDar8mmSRUVF0bFjx9i2bVusWbMmfWlbRMTGjRujZ8+esW3btjLP+853vhP//d//XZXRSIBpkpRn\n+fpV8cz0F2Prru1JR6lTHnn9udiwfXN6/OSXfh2je1u/EQAAqD1q5QL6EydOjI0bN8b555+fUYRF\nRNx///2xbdu2qFevXvzhD3+Is846K372s5/F//zP/8T//M//xFe+8pWoX79+VUcEEta9XZf47IUf\nSTpGnbN268Z4bPLz6fGkhTOUYQAAQNar8mmSixcvjoiIk046qcy+Z599NiIiPvShD8XVV18dJ5xw\nQvz0pz+NLl26xObNm2PqVItqAxyr0b0HZ4wnF85IJggAAEANUuVl2DvvvBMREV26dMnYvm/fvvRi\n+Zdddtm/A+XmxtixYyMiorCwsKrjAdRZo3oNzhhPWzI79hcXJRMGAACghqjyMmzv3gMLNu/Zsydj\n+7Rp09L7zjzzzIx9bdq0iYgody0xACrmxPZdo33zNunx7n17Yvbb8xNMBAAAkLwqL8PatWsXEWWv\n8vr73/8eERE9e/aMzp07Z+zbvPnAgs8WVwc4djk5OTGq1FTJ1xeaKgkAAGS3Ki/Dhg0bFhERzz33\nXCxZsiQiDlzxdf/990dExHnnnVfmOWvWrImIKFOSAXB0Si+YP3lRQTJBAAAAaogqL8NOP/306NOn\nT+zatSuGDx8eV155ZQwaNChWrlwZERHXX399mefMn39gGs/JJ59c1fEA6rRRpcqwqYtmRnFJcUJp\nAAAAklflZVhubm78/ve/jyZNmsSmTZviqaeeimXLlkVExC233BKjRo3KOH7OnDmxcuXKGDhwYHTq\n1Kmq4wHUaX07nRitmjRPj7ft3hHzVi1OMBEAAECy8qvjRUaPHh2zZ8+Ou+66K+bNmxcdOnSISy+9\nNK688soyx86cOTNOPvnkuPrqq6sjGkCdlpubGyN7DY4XZk5Mb5tcOCNO6donwVQAAADJyUmlUqmk\nQ9RFJSUlsWbNmigpKYn8/Pzo2LFjlb5ecXFxbN68OVq1ahV5eXlH/fydO3fGvn37qvymBZs3b47W\nrVtHRMSmTZvcJAGqwW//9XB88y//mx5fMmRc3Hvjj5ILBAAAUEFV0SNU+TTJbLFhw4Z44okn4vbb\nb4+zzz47WrZsGV26dImuXbuWmQpaWTZt2hTf+MY34uSTT4769etHu3btomHDhtG3b9+47bbbYs6c\nOUfM/PnPfz46d+4cTZs2jdatW0ezZs3iwx/+cMyePbtKMgPVr/S6YZMKC8J/BwEAALJVtUyTzAa/\n/OUv49vf/nZ6nJubG/Xq1Yv9+/dXyev9/e9/j//4j/+I9evXp1+vXbt2sXv37li4cGHccccdMX36\n9PjXv/5V7vPfeuutOPfcc2Pt2rUREdGwYcOoX79+bNu2LR599NF46qmn4oEHHogPfvCDVZIfqD4n\nn9ArmjZsHDv27IqIiE07tkThmmXRp9OJCScDAACoftV+Zdj8+fPjzjvvjOuuuy7e8573xMUXXxwf\n/ehH4xe/+EUsX768uuNUmnbt2sWVV14ZP/zhD+PFF1+MLVu2xIgRI6rktf71r3/F5ZdfHuvXr4++\nffvGE088ETt37ox169bF9u3bY9myZXHnnXfGwIEDy33+jh074uKLL461a9dGy5Yt4y9/+Uvs2rUr\ntm7dGtOmTYsBAwbE3r174yMf+UgUFBRUyXsAqk9+Xn4MPynz74PJhQXJhAEAAEhYta0ZtmHDhrjp\nppviiSeeOOT0nLy8vPjYxz4WP//5z6Np06bVEatKnXnmmfHaa69F9+7d03fQPF5bt26NAQMGxOrV\nq2Pw4MExfvz4aNGixVGd49vf/nZ861vfiogDV5hdcMEFGftXr14dAwYMiK1bt8Z5550X//znPysl\ne4Q1wyAp//fCH+IHT/06Pb5q+AVx1ye+k2AiAACAI6u1a4atW7cuRo0aFY8//ni6CGvatGn06tUr\nevbsGY0bN46IA4vA33vvvXH22WfHzp07qyNarfOzn/0sVq9eHTk5OfH73//+qIuwVCoVv/vd7yIi\n4owzzihThEVEdO7cOW644YaIOHAV2pIlS44/OJCo0WXWDZth3TAAACArVUsZdvPNN8fixYsjIuIj\nH/lITJ8+PbZt2xaFhYWxePHi2LZtW0yaNCmuvPLKiIh444034r/+67+qI1qtUlJSEvfcc09ERJxz\nzjkxaNCgoz7HG2+8EatXr46IiKuuuuqQx73vfe9LP37mmWeO+nWAmmVQ9/7RsF6D9PidLevj7Q2r\nE0wEAACQjCovw5YsWRJPPPFERET8+te/jj/84Q8xZMiQyMnJSR+Tl5cXo0aNiieeeCK+8Y1vRETE\nb3/729i2bVtVx6tV5syZky6yLrnkkvT2VCoVGzZsiF27dh3xHDNmzEg/PtyaZkOHDo38/PwyzwFq\np/r59eK0nqdkbJtU6HcbAADIPlVehr344osRcWBK3k033XTE47/5zW9G7969Y9++ffHKK69Udbxa\nZdq0aenHp512WsyYMSOuuOKKaNSoUbRr1y6aNGkSPXv2jC9/+cuxbt26cs+xYMGC9OMTTzz0neTq\n1asXnTt3jogDNz0Aar9RvQZnjCcvKkgkBwAAQJKqvAxbuXJlRESce+65FTo+Nzc3xo0bFxERK1as\nqKpYtdKqVavSj1977bUYMWJEPP3001FSUhLt2rWLvLy8WLp0afz0pz+NQYMGlXtF16ZNm9KP27Zt\ne9jXe3f/5s2bjyrn5s2bD/lny5YtR3UuoPKUXjfMHSUBAIBsVOVl2LsLNOfmVvyl3j3W4s6Ztm7d\nmn789a9/PerXrx/33HNPbNu2LdatWxebN2+OH/3oR5GXlxdr1qyJ9773vRnPiYjYsWNHRETk5ORE\ngwYN4nAaNWqU8ZyKat269SH/9OzZ86jOBVSeoT1PiXp5+enxsvUr453N5V9FCgAAUFflH/mQ4/Pu\nVLtXX321ws95/fXXM55bWTZv3nzcd6ls27ZtNGzYsJISHbuSkpL405/+lL7pQEREs2bN4itf+UrU\nq1cvvvSlL8XKlSvjrrvuyrgZwcFFYyqVyli7rbzXOPg5QO3WuH7DGNy9f0xbMju9bfKigrhyeNm7\nygIAANRVVd5ynH322RER8a9//Ssef/zxIx5/1113xezZsyMvLy/GjBlTqVm+/OUvR9euXY/rz7/+\n9a9KzXQ0mjZtmn7cv3//jCLsYJ/5zGeiRYsWERHx1FNPHfIcu3fvPuzrvbv/4OdUxKZNmw75Z8mS\nJUd1LqByjSo1VdIi+gAAQLap8ivD+vbtGxdddFG88MILcfXVV8eXvvSl+OxnP1vmqq9317r69a9/\nHRERH/vYx6JVq1aVmqV169bRpUuX4zrHu1MHk9CxY8f049GjRx/yuAYNGsTQoUPj5Zdfjnnz5mXs\n69ChQ/rxmjVrDjtt8Z133inznIqo7O8NqDyjeg+OX/z9gfTYumEAAEC2qfIyLCLit7/9bYwaNSre\neeed+NGPfhQ/+tGPokePHtGpU6dIpVKxatWqjMXy+/fvH3fccUel5/jJT34SP/nJTyr9vNVlwIAB\n6cfNmzc/7LHv7i89LbR///7px4sWLTpkGbZjx470HSkPfg5Qu404aVDk5uRGSerANOiF7yyNDds3\nR9tmSmwAACA7VMtiUN26dYtJkybF2LFj09uWLVsWkyZNismTJ2cUYVdccUVMnDjR1UXlGDp0aHrR\n+3eLqkNZu3ZtRBy4Gu5go0aNSj9+7bXXDvn8119/PX0Dg5EjRx5TXqDmadaoSZzStU/GtimLCpIJ\nAwAAkIBqWxm9e/fuMX78+Hj99dfjq1/9alx88cUxcuTIGDVqVFx22WXxrW99K2bOnBlPPvlktG3b\ntrpi1SrNmjWL888/PyIiXn755SgqKir3uI0bN8aMGQfWARoxYkTGvt69e8fJJ58cEREPP/zwIe/Y\n+dBDD0VERF5eXlx22WWVkh+oGUb3HpwxNlUSAADIJtUyTfJgo0ePPux6V9lsy5YtsWPHjog4sE5X\nvXr1yhzz5S9/OZ577rl455134sc//nF87WtfK3PM7bffHnv37o2IiOuvv77M/i9+8YvxiU98IgoL\nC+MXv/hFfO5zn8vYP2XKlHjwwQcjIuKjH/2ochLqmFG9h8RvX3wkPZ5sEX0AACCLVNuVYXVdcXFx\nrFy5MuPPvn37jrjvYF//+tfTd62cOXNmua8zZsyY+OQnP5k+/oYbbohJkybF0qVL4+WXX46rrroq\n7rnnnoiIuOSSS+J973tfmXN89KMfjbPOOisiIr7whS/EbbfdFgUFBTFv3rz45S9/GRdeeGEUFRVF\np06d4rvf/W6lfD5AzTGi16CM8ZyVhbFt946E0gAAAFSvKrkybPv27emF21u0aFGhOzDu2LEjfVVU\ns2bNokmTJlURrcqsWLEiTjzxxHL3rVy5Mrp27ZqxbdKkSRnrdx2NX//611FUVBS///3v4+677467\n7767zDFXXXVV/OEPf4icnJwy+/Ly8uKpp56KK664Il555ZW44447ytywoHv37vHUU0+VuesnUPu1\nadoy+nbuGQtWL4mIiFQqFVMWzYzzTz0j4WQAAABVr9LLsF27dsXAgQNj2bJlMXDgwBg/fnyFyrAt\nW7bEWWedFcuWLYuhQ4fGtGnTIje39ly4lp+fH126dKnw8e8uhH+wVq1apc9Rv379w77W/fffH9df\nf3088MADUVBQEJs2bYoWLVrE0KFD49prr41zzjnnsK/funXrGD9+fDz66KPx5z//OQoLC2P//v3R\ntWvXuOSSS+KTn/xkNGvWrMLvB6hdRvceki7DIg5MlVSGAQAA2SAndagV1I/R97///fj6178ebdu2\njTlz5kSHDh0q/NyFCxfG4MGDY/fu3XHfffeVu94VtdvmzZvTd7jctGmTu4ZCQp56459x0z3/nR6f\nduIp8dev3JNgIgAAgLKqokeo1EuviouL4ze/+U1ERPz0pz89qiIsIqJPnz7pBeF/+ctfVmY0AA4y\nqtfgjPHM5fNi597dyYQBAACoRpVahhUUFMTKlSujXbt2ce211x7TOT796U9HgwYNYvr06bF69erK\njAfA/9exZbs4sd0J6XFRSXFMXzonwUQAAADVo1LLsGnTpkVExEUXXRT5+ce2HFmrVq3Sdzp893wA\nVL7RfYZkjF9fOCOhJAAAANWnUsuwNWvWREREjx49jus87z5/7dq1x5kIgEMZ1TuzDJtcqAwDAADq\nvkotw/bv3x8REfXq1Tuu87z7/H379h13JgDKV3rdsOlL34q9+/29CwAA1G2VWoa1adMmIv59hdix\neueddyIiom3btsedCYDydW3TKbq0+veNTvYW7YuC5XMTTAQAAFD1KrUMO/HEEyMiYuLEicd8jlQq\nFa+++mpEHP90SwAOLScnJ0b1HpyxbXJhQSJZAAAAqkullmHjxo2L3NzcmDNnTrz22mvHdI7HHnss\nNmzYEM2bN49hw4ZVZjwAShldat2wSdYNAwAA6rhKLcNatWoVF110UURE3HTTTbF169ajev6qVavi\n1ltvjYiID37wg8d8R0oAKqb0IvpTF8+KouKihNIAAABUvUotwyIivvWtb0VOTk7MmTMnzjnnnJg3\nb16FnjdlypQYN25crFixIho0aBBf//rXKzsaAKWc1KFbtG3WKj3etXd3zF6xMMFEAAAAVavSy7Dh\nw4fH9773vYiImD59egwcODCuvPLK+P3vfx+zZ8+OdevWxc6dO2Pt2rVRUFAQd999d1xwwQUxevTo\nWLRoUURE/O53v4vu3btXdjQASjmwbljm1WGTTZUEAADqsCqZh/jVr3419u3bF9/97nejqKgonnrq\nqXjqqaeO+Lz69evHz3/+8/jIRz5SFbEAKMeo3oPjuekvpceTCwvi5vOvTTARAABA1an0K8Pe9a1v\nfSv+9a9/xRlnnFGh4y+88MJ4/fXX4+abb66qSACU4/RSV4ZNWTQzSkpKEkoDAABQtap0hfqzzz47\nXn311Zg1a1a89NJLMX369NiwYUNs3749mjdvHu3bt48RI0bEueeeG3369KnKKAAcQr/OJ0WLxs1i\n667tERGxZde2mL96cQw4oXfCyQAAACpftdyuceDAgTFw4MDqeCkAjlJubm6M7DUo/jHr1fS2SYUF\nyjAAAKBOqrJpkgDUHqN6lV5EvyCZIAAAAFVMGQZAjOo9OGM8edGMSKVSyYQBAACoQsowAGJgt77R\nuEGj9Hj9tk2xeO3bCSYCAACoGsowACI/Lz9GnJS5tuPkwhkJpQEAAKg6yjAAIiJiVK/BGePJiwoS\nyQEAAFCVlGEARETEqN6Zi+hPsog+AABQBynDAIiIiME9+keD/Prp8apNa+LtDasTTAQAAFD5lGEA\nREREw3oNYuiJJ2dsM1USAACoa5RhAKSVnippEX0AAKCuUYYBkDa69+CM8WTrhgEAAHWMMgyAtNN6\nnhr5uXnp8ZJ1K2Lt1g0JJgIAAKhcyjAA0po0aBSDuvfP2DbJVEkAAKAOUYYBkGGUqZIAAEAdpgwD\nIEPZRfQLkgkCAABQBZRhAGQYcdLAyMnJSY/nr14cm3ZsTTARAABA5VGGAZChReNmcfIJvTO2TV00\nM6E0AAAAlUsZBkAZo0tNlZxUOD2hJAAAAJVLGQZAGaUX0Z9k3TAAAKCOUIYBUMbIXoMzxnNWLIzt\nu3cmEwYAAKASKcMAKKNts1bRu2OP9LgkVRLTlsxKLhAAAEAlUYYBUK7S64ZNNlUSAACoA5RhAJRr\ndJ9Si+gvtIg+AABQ+ynDAChX6XXDCpbPi1379iQTBgAAoJIowwAoV+dW7aN72y7p8f7iopi+9K0E\nEwEAABw/ZRgAhzSq9+CM8eTCGckEAQAAqCTKMAAOaZRF9AEAgDpGGQbAIZ1eqgx7c8ns2Fe0P6E0\nAAAAx08ZBsAhdWvbOTq1bJce796/N2Yun5dgIgAAgOOjDAPgkHJyckyVBAAA6hRlGACHVXoR/UkW\n0QcAAGoxZRgAhzWqV+aVYVMXz4yi4qKE0gAAABwfZRgAh9WnU49o3bRlerxjz654a+Wi5AIBAAAc\nB2UYAIeVk5MTo0tNlZxsqiQAAFBLKcMAOKLSUyUtog8AANRWyjAAjqj0IvpTFhVESUlJMmEAAACO\ngzIMgCMacEKvaN6oaXq8aefWWPDO0gQTAQAAHBtlGABHlJebFyN6DcrYZt0wAACgNlKGAVAho3oN\nzhhPXlSQSA4AAIDjoQwDoEJG9y67iH4qlUooDQAAwLFRhgFQIQO794tG9Rumx2u3bohl61cmmAgA\nAODoKcMAqJB6efkxvOepGdsmWTcMAACoZZRhAFTYqFJTJScVFiQTBAAA4BgpwwCosFG9B2eM3VES\nAACobZRhAFTYkB4Don5+vfR4xcZ3YuWmNQkmAgAAODrKMAAqrFH9hjGkx4CMbVNMlQQAAGoRZRgA\nR2V0mXXDTJUEAABqD2UYAEel9CL6k10ZBgAA1CLKMACOyrCep0Rebl56vGjt8li/bWOCiQAAACpO\nGQbAUWnasEmc2rVvxrbJhTMTSgMAAHB0lGEAHLVRvQdnjCcvsm4YAABQOyjDADhqp/cptYj+QmUY\nAABQOyjDADhqI04aFDk5OenxvNWLY/POrQkmAgAAqBhlGABHrWWT5tG/80npcSqVimmLZyWYCAAA\noGKUYQAck9Lrhk0qLEgkBwAAwNFQhgFwTEb1tm4YAABQ+yjDADgmo0tdGTZ7xYLYsWdnMmEAAAAq\nSBkGwDFp17xN9OrQPT0uLimON5bMSTARAADAkSnDADhmpdcNm1xoqiQAAFCzKcMAOGZly7CCRHIA\nAABUlDIMgGM2uvfQjPH0ZW/F7n17EkoDAABwZMowAI5Zl9YdomubTunxvqL9MWPZ3AQTAQAAHJ4y\nDIDjMqr3kIyxqZIAAEBNpgwD4LiMtog+AABQiyjDADguo3oNzhhPWzI79hcXJRMGAADgCJRhAByX\nE9t3jQ4t2qbHu/ftiVnL5yeYCAAA4NCUYQAcl5ycnBhVaqrkJFMlAQCAGkoZBsBxKz1VcvKigkRy\nAAAAHIkyDIDjVvqOklMXzYzikuKE0gAAAByaMgyA49a304nRqknz9Hjb7h0xb9XiBBMBAACUTxkG\nwHHLzc2NUb0yrw6btNC6YQAAQM2jDAOgUpReRH/yImUYAABQ8yjDAKgUpdcNm1RYEKlUKqE0AAAA\n5VOGAVApTj6hVzRt2Dg93rRjSxSuWZZcIAAAgHIowwCoFPl5+TH8pIEZ2yYXFiQTBgAA4BCUYQBU\nmtN7D80YTyq0bhgAAFCzKMMAqDRlFtEvnGHdMAAAoEZRhgFQaQZ17x8N6zVIj9/Zsj7e3rA6wUQA\nAACZlGEAVJr6+fXitJ6nZGwzVRIAAKhJlGEAVKpRvQZnjJVhAABATaIMA6BSje6TuYi+O0oCAAA1\niTIMgEo19MSTo15efnq8fMOqWL15XYKJAAAA/k0ZBkClaly/YQzu3j9j25RFBcmEAQAAKEUZBkCl\nG9V7SMbYumEAAEBNoQwDoNKN7lOqDFuoDAMAAGoGZRgAlW54z4GRm/Pv/4kpXLMs1m/blGAiAACA\nA5RhAFS6Zo2axCld+2Rsm7p4ZkJpAAAA/k0ZBkCVGN17cMZ4cmFBIjkAAAAOpgwDoEqUXkR/skX0\nAQCAGkAZBkCVGNlrcMZ4zsrC2LprezJhAAAA/j9lGABVonXTFtGv80npcSqViqmLZyWYCAAAQBkG\nQBUaVWbdMFMlAQCAZCnDAKgyZcuwgkRyAAAAvEsZBkCVGV1qEf2Zy+fFzr27E0oDAACgDAOgCnVo\n0TZ6tu+aHheVFMebS2YnmAgAAMh2yjAAqlTpqZKTTJUEAAASpAwDoEqNKjVV0iL6AABAkpRhAFSp\nUb0GZ4ynL30r9u7fl0wYAAAg6ynDAKhSXdt0ii6tOqTHe4v2RcHyuQkmAgAAspkyDIAqlZOTE6P7\nZE6VnLTQVEkAACAZyjAAqlzpqZKTFxUkkgMAAEAZBkCVK72I/tTFs6KouCihNAAAQDZThgFQ5U7q\n0C3aNmuVHu/auztmr1iYYCIAACBbKcMAqHI5OTllrg6zbhgAAJAEZRgA1WJ0qTJs8iJlGAAAUP2U\nYQBUi9G9B2eMpyyaGSUlJcmEAQAAspYyDIBq0a/zSdGicbP0eOuu7TF/9eIEEwEAANlIGQZAtcjN\nzY2RvQZlbJtUWJBMGAAAIGspwwCoNqXXDZtUaN0wAACgeinDAKg2pe8oOblwRqRSqYTSAAAA2UgZ\nBkC1ObVrn2jcoFF6vGH75li89u0EEwEAANlGGQZAtcnPy48RJw3M2DbZVEkAAKAaKcMAqFajeg3O\nGE9eVJBIDgAAIDvlJx2gLlm3bl1MnTo1pkyZElOnTo3CwsIoKSmJE044IV599dUqec1//OMf8fjj\nj8dbb70VGzZsiPbt20fv3r3j8ssvj4suuijq169f5jlr166NCRMmxCuvvBJLly6Nd955J3bs2BGt\nW7eOIUOGxAc+8IE4++yzqyQvwOg+pRbRX3hg3bCcnJyEEgEAANkkJ2Xl4krxk5/8JL7yla+Uu697\n9+6xbNmySn29ZcuWxfXXXx/jx48/5DHvec974vnnn8/Y9pe//CU+8IEPHPH8F154YfzpT3+Ktm3b\nHm/UDJs3b47WrVtHRMSmTZuiVatWlXp+oObbu39f9PnCebG3aF9629TvPRHd2nZOMBUAAFATVUWP\nYJpkJdm1a1e0b98+Lrnkkvj2t78df/vb32Lo0KFV8lpLliyJMWPGxPjx46Nhw4bxxS9+MV566aVY\nsGBBFBQUxJ/+9Ke48sory73KYs+ePRERkZeXF1dccUXcd9998cYbb8SCBQviueeeiwsvvDAiIv7+\n97/HRRddFPv376+S9wBkrwb16sfQE0/O2GaqJAAAUF1cGVZJdu/eHY0aNcrYduaZZ8Zrr71WqVeG\nFRcXx+jRo2PatGnRrl27eOmll+KUU04p99j9+/dHvXr1MrY99NBD8be//S2+973vRffu3ct93s03\n3xy/+c1vIiLiF7/4Rdxyyy2Vkj3ClWHAAT9+5nfxP8/flx5fc8Zl8bP/+FqCiQAAgJrIlWE1WOki\nrKrce++9MW3atIiIuPvuuw9ZhEVEmSIsIuJDH/pQ/PGPfzxkERYRcccdd6TfzxNPPHGciQHKGt17\ncMZ4cmFBIjkAAIDsowyrZX71q19FRMQpp5wSl19++VE/Py8v74jHNG3aNPr06RMREUuXLj3q1wA4\nktN6nhr5uf/++2jJuhWxduuGBBMBAADZQhlWiyxdujRmzZoVERHvf//7q/S1Nm/eHBERDRs2rNLX\nAbJTkwaNYlD3/hnbJhXOSCgNAACQTZRhtciUKVPSj0eOHBnbtm2Ln/70p3HOOedEv379YujQofEf\n//Ef8fTTT8fxLAVXUFAQb7/9dkREnHbaacedG6A8o0yVBAAAEpCfdAAqbsmSJenH27Zti1NOOSVW\nrFiRccyMGTPiT3/6U4wdOzb+8pe/RNu2bY/6db785S+nH3/iE5846ue/e1VZebZs2XLU5wPqplG9\nh8Sv/vGn9FgZBgAAVAdXhtUiBxdJN9xwQ6xYsSI+9rGPxfjx42PBggXx97//PS677LKIiJgwYUJc\nccUVUVRUdFSv8dOf/jT+9a9/RUTEVVddFWefffZR52zduvUh//Ts2fOozwfUTSNOGhg5OTnp8fzV\ni2PTjq0JJgIAALKBMqwW2b9/f/rx1q1b49vf/nbcf//9MXbs2OjTp09ccMEF8cwzz8T1118fERGv\nvfZaPPjggxU+/9/+9re4/fbbIyKiW7ducffdd1fuGwA4SIvGzeKUE3pnbJuyqCCZMAAAQNbIqmmS\nt99+ezzyyCPHdY777rsvzjnnnEpKdHSaNGmSftyxY8f46le/Wu5xd9xxRzz00EOxd+/eePDBB+Oj\nH/3oEc89adKkeP/73x/FxcXRpk2beOGFF6J169bHlHPTpk2H3LdlyxZXhwFpo3oPidkrFqbHkwtn\nxHsGj00wEQAAUNdlVRm2YcOGWL58+XGdY9euXZWU5ui1adMm/fjss8+O/Pzyv742bdrEkCFDYvLk\nyTF9+vQjnregoCAuvvji2LVrVzRv3jxeeOGF6N+//xGfdyitWrU65ucC2WVU78Fx90uPpseTrBsG\nAABUsawqw3784x/H17/+9eM6R4cOHSopzdHr169f+nH79u0Pe+y7OQ+3mH1ExLx58+KCCy6ILVu2\nROPGjeOvf/1rDBs27PjDAlTAyF6DM8ZzViyM7bt3RrNGTcp/AgAAwHHKqjKsTZs2GVdX1TZDhgyJ\nnJycSKVSsX379sMeu23btoiIaNq06SGPWbJkSZx33nmxfv36aNiwYTzzzDNx5plnVmpmgMNp26xV\n9O7YIwrXLIuIiJJUSUxdPDPOPeX0ZIMBAAB1lgX0a5GOHTvGyJEjIyJi8uTJhzxu3759MWPGjIiI\nOOWUU8o9ZsWKFXHOOefE6tWro379+vH444/HueeeW/mhAY5gdJ8hGePJpkoCAABVSBlWy9x8880R\nETF37tx4+umnyz3m17/+dWzZsiUiIj7wgQ+U2b927do477zzYvny5ZGfnx+PPvpoXHzxxVWWGeBw\nRvcuXYbNSCgJAACQDZRhNcg3v/nN6NGjR/To0SNmz55d7jHXXXddjB49Ov34gQceiH379kVExM6d\nO+NnP/tZ3HrrrRER0bdv37jxxhsznr9p06Y4//zzY+HChZGXlxcPPvhgXHHFFVX3pgCOoPS6YQXL\n58WufXuSCQMAANR5WbVmWFVauXJlmfW21qxZk97Xo0ePjH1PPvlkDBmSeTXExo0b03e73Lt3b7mv\nk5ubG08//XScc845MWfOnPjoRz8aN954Y7Ru3TrWr18f+/fvj4iIXr16xXPPPReNGjXKeP5vfvOb\ndNGWn58ft912W9x2222HfW/Lli077H6A49G5Vfvo3rZLLN+wKiIi9hcXxfSlb8WZfU9LOBkAAFAX\nKcMqSVFRUbrIKq24uLjMvkOVXRXRrl27eOONN+LOO++MBx54IBYsWBCrV6+OiIg+ffrEtddeG5//\n/OejefPmZZ5bUlKSkeFQmQGq0+g+Q9JlWETEpIXTlWEAAECVyEmlUqmkQ9QFRUVFsXLlygof36lT\np2jQoEHGtk2bNqXvAtm5c+eoX79+hc61Z8+e2LRpU7Ro0SKaNGly2GO3bt0amzdvrnDOiChzVdvx\n2Lx5c7Ru3ToiDrzfVq1aVdq5gdrrkdefi88/8L30+Iy+p8XjX/hVgokAAICaoCp6BFeGVZL8/Pzj\nLo1at26d/oKPRsOGDaNz584VOrZFixbRokWLo34NgKpUehH9N5fMiX1F+6N+fr2EEgEAAHWVBfQB\nSFy3tp2jU8t26fGe/Xtj5vJ5CSYCAADqKmUYAInLycmJUaWuDptcWJBMGAAAoE5ThgFQI5SeKvl6\n4fSEkgAAAHWZMgyAGmFU78EZ42mLZ0VRcVEyYQAAgDpLGQZAjdC7Y49o3bRlerxjz654a+Wi5AIB\nAAB1kjIMgBohJycnRpe6Omxy4YxkwgAAAHWWMgyAGmNUL4voAwAAVUsZBkCNMbpPqTJs0YwoKSlJ\nKA0AAFAXKcMAqDH6dzkpmjdqmh5v3rktFryzNMFEAABAXaMMA6DGyMvNixG9BmVss24YAABQmZRh\nANQoo3oNzhhPXlSQSA4AAKBuUoYBUKOM7l12Ef1UKpVQGgAAoK5RhgFQowzs3i8a1W+YHq/duiGW\nrluRYCIAAKAuUYYBUKPUy8uP4T1PzdhmqiQAAFBZlGEA1DijSk2VnFRYkEwQAACgzlGGAVDjjOo9\nOGPsjpIAAEBlUYYBUOMM6TEg6ufXS49XbHwnVm5ak2AiAACgrlCGAVDjNKrfMIb2ODljm6vDAACA\nyqAMA6BGKjtVsiCRHAAAQN2iDAOgRiq9iL4yDAAAqAzKMABqpGE9T4m83Lz0eNHa5bF+28YEEwEA\nAHWBMgyAGqlpwyYxsFvfjG2TXB0GAAAcJ2UYADVW2amSFtEHAACOjzIMgBprtEX0AQCASqYMA6DG\nGnHSoMjJyUmP561eHJt3bk0wEQAAUNspwwCosVo2aR79O5+UHqdSqZi2eFaCiQAAgNpOGQZAjTa6\nT+a6Ya8vtG4YAABw7JRhANRoo3qVXkS/IJkgAABAnaAMA6BGG9V7UMZ49ooFsWPPzoTSAAAAtZ0y\nDIAarV3zNtGrQ/f0uLikON5YMifBRAAAQG2mDAOgxhvVe3DGeHKhdcMAAIBjowwDoMYb3Ttz3bBJ\nyjAAAOAYKcMAqPFGlSrDZiybG7v37UkoDQAAUJspwwCo8bq07hBd23RKj/cV7Y8Zy+YmmAgAAKit\nlGEA1Aqlrw6bXFiQTBAAAKBWU4YBUCuMtog+AABQCZRhANQKpRfRn7ZkduwvLkooDQAAUFspwwCo\nFXq0OyE6tGibHu/etydmLZ+fYCIAAKA2UoYBUCvk5OTEqFJTJSeZKgkAABwlZRgAtcaoXoMzxpMX\nFSSSAwAAqL2UYQDUGqXvKDmlsCCKS4oTSgMAANRGyjAAao2+nU6M1k1apMfb9+yMuSsXJZgIAACo\nbZRhANQaubm5MbL0VMnCgkSyAAAAtZMyDIBapfQi+pMXWUQfAACoOGUYALVK6XXDJhUWRCqVSigN\nAABQ2yjDAKhVTunaO5o2bJweb9qxJRa+syy5QAAAQK2iDAOgVsnLzYsRJw3K2GaqJAAAUFHKMABq\nndGlpkpaRB8AAKgoZRgAtU6ZRfQLZ1g3DAAAqBBlGAC1zqDu/aNRvQbp8Ttb1sfbG1YnmAgAAKgt\nlGEA1Dr18+vFaT1Pzdj2eqF1wwAAgCNThgFQK5U3VRIAAOBIlGEA1EqjLKIPAAAcA2UYALXS0BNP\njnp5+enx8g2rYvXmdQkmAgAAagNlGAC1UuP6DWNw9/4Z26YsKkgmDAAAUGsowwCotUb3GZoxnrTQ\numEAAMDhKcMAqLVKL6I/ySL6AADAESjDAKi1hvccGLk5//6fssI1y2L9tk0JJgIAAGo6ZRgAtVaz\nRk3ilK59MrZNXTwzoTQAAEBtoAwDoFYbXWqq5OTCgkRyAAAAtYMyDIBabXTvUovoWzcMAAA4DGUY\nALXaiF6DMsZvrSyMrbu2J5QGAACo6ZRhANRqrZu2iH6dT0qPU6lUTF08K8FEAABATaYMA6DWG1Vm\n3TBTJQEAgPIpwwCo9UqXYdYNAwAADkUZBkCtN7r3kIzxrOXzY+eeXQmlAQAAajJlGAC1XocWbaNn\n+67pcVFJcby5dE6CiQAAgJpKGQZAnVB2qmRBIjkAAICaTRkGQJ0wqtRUSYvoAwAA5VGGAVAnlF43\nbPrSt2LP/r0JpQEAAGoqZRgAdULXNp2iS+uO6fHeon1RsGxegokAAICaSBkGQJ0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          }
        }
      ],
      "source": [
        "cost_history = results.optimizer.cost_history\n",
        "plt.plot(cost_history)\n",
        "plt.xlabel(\"Iteration\")\n",
        "plt.ylabel(\"Cost\")\n",
        "plt.title(\"Cost history of optimization\")\n",
        "plt.show()"
      ],
      "id": "95b86f23"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Final Optimized Design\n",
        "\n",
        "Finally, we will run two simulations again with the optimized\n",
        "parameters. We will add a\n",
        "[FieldMonitor](https://docs.flexcompute.com/projects/tidy3d/en/latest/api/_autosummary/tidy3d.FieldMonitor.html)\n",
        "to help visualize the mode splitting."
      ],
      "id": "348fa4bf-63aa-4183-94fb-f266618da5a8"
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"9d6239bf98184b1f914c582f16a68d07\",\"version_major\":2,\"version_minor\":0,\"quarto_mimetype\":\"application/vnd.jupyter.widget-view+json\"}\n",
              "</script>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">06:50:14 UTC </span>Started working on Batch containing <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span> tasks.                       \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">06:50:16 UTC </span>Maximum FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.050</span> for the whole batch.                \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>Use <span style=\"color: #008000; text-decoration-color: #008000\">'Batch.real_cost()'</span> to get the billed FlexCredit cost after    \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>completion.                                                        \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"e745116a13d24b46afc4e3e812958a32\",\"version_major\":2,\"version_minor\":0,\"quarto_mimetype\":\"application/vnd.jupyter.widget-view+json\"}\n",
              "</script>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">06:50:34 UTC </span>Batch complete.                                                    \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>"
            ]
          }
        }
      ],
      "source": [
        "# Get the best parameters from the optimizer\n",
        "W_opt = results.optimizer.swarm.best_pos\n",
        "\n",
        "# Define a field monitor to help visualize the field distribution\n",
        "field_monitor = td.FieldMonitor(\n",
        "    center=(0, 0, 0), size=(td.inf, td.inf, 0), freqs=[freq0], name=\"field\"\n",
        ")\n",
        "\n",
        "# Define simulations with the optimal design\n",
        "sims = {\n",
        "    \"TE\": make_sim(W_opt, \"TE\").copy(\n",
        "        update={\"monitors\": [mode_monitor_bar, mode_monitor_cross, field_monitor]}\n",
        "    ),\n",
        "    \"TM\": make_sim(W_opt, \"TM\").copy(\n",
        "        update={\"monitors\": [mode_monitor_bar, mode_monitor_cross, field_monitor]}\n",
        "    ),\n",
        "}\n",
        "\n",
        "# Define and submit the batch\n",
        "batch = web.Batch(simulations=sims, verbose=True)\n",
        "batch_results = batch.run(path_dir=\"data\")"
      ],
      "id": "820dac62"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Plot the field intensity distribution for the TE and TM simulations. As\n",
        "expected, the TE mode mainly transmits to the bar port while the TM mode\n",
        "mainly transmits to the cross port."
      ],
      "id": "f050c70a-2e2e-4806-815c-6ced67c7d0e5"
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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DPcMwDMMwTC6QklLOhnqGYRiGYRiG2SfQUtiPih1yDmjY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Rdc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\nnEKNVeTWPff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          }
        }
      ],
      "source": [
        "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(8, 2), tight_layout=True)\n",
        "batch_results[\"TE\"].plot_field(\"field\", \"E\", \"abs^2\", ax=ax1)\n",
        "batch_results[\"TM\"].plot_field(\"field\", \"E\", \"abs^2\", ax=ax2)\n",
        "plt.show()"
      ],
      "id": "5295d640"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Plot the transmission spectra."
      ],
      "id": "084ee3ff-c31e-4e87-b6f9-ed20537b663a"
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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acFWCrkHnTZM8lghskvzNBwAAVNf6rOQa2IB+ydy+AGtVx8HB1kDgVW0De2/N\nf3Ltrmua2BdaNU/pD7Gm9H8mL39sntIXgNU1jMxvAKgSIRUAALDhGLwBfbZZu2t7e5au1lp2dday\nx0rY1dr3qfYeXAMry+b+Y82vaRzfF1Y1T17zYKu+acR+AsDaElIBAACbhprapY/WrY3K6q3W/gBr\n0HFFbYOPvT0j81tWpGNh32dt9tsaeByxsmJrcJA1te+8cuwPvWrrR+43AJs0IRUAAMCqDF69NWnb\nNb+uXO7bpH1IqDU3aVtNuFXNjeXX5XHEpolLA6tlg6yBMKt5SjJ2at+xcYI3IwJrREgFAAAwEkql\nvkCnaWKSHdf8ut6evscOl7T2BVqLn+8PuFZ0fH7piq5y70j9kqEGHkV8/tE1G19bPyjAWmZVVvPU\n5QOvsVPsrwWbKCEVAADAaFJTu3Q10prq7U065vcFWkOCrZWFW/3HajyO2NOVLHym77OmGif0/xls\n1h9kDfqMnZKM628f299mby3YKAipAAAANnQ1NX1vAxzTsubXDDyOOCTY6g+wKiHXnP7zOUvHVeNR\nxI4FfZ/Wx9ZsfMO45cOswaFW89S+YGsg1GoYO7L1A+tESAUAALApGvI44vQ1u6byKOLzyeI5S48D\nAVel7fmljyN2Lh7JX9Gnc1HfZ03fhlg/dumjhsuu1ho7NRk3tb99s75wq37MiJYP9BFSAQAAsGYG\nP4q42QvW7JqutqGrsVYUZi3bP9L7a3UtSeY90fdZE4NXao3bbFCANRBqDQq0vAER1pmQCgAAgJFT\nPyaZtE3fZ0309ibtc/sCq8Vz+j+zB50PegRx0ez+vbW6R/Y3rO1KrTEt/aHWZkv3zxpYsbVsyNXU\n0ve4JiCkAgAAYBSpqVn6lr81Wa1VLift85aGVysMtfpXbi2a3Rdu9XSN7G9om9v3mfPQ6sfW1Pbv\nmzUouGreLBm3+dKQq7JSa3OPHrJRE1IBAACw4SqVlm4aP3WX1Y+vbBg/aFXWkFBr0Hk1Qq3enmTR\nc32fNTHw6OG4zYc+ZriiYMsqLTYwQioAAAA2HYM3jJ+y0+rHl8tJ+/y+8GrRQIg1e2mgNbht0eyR\nfwPi2jx6WFPbv2fW5ksfNawEWYPamvvP65tGrm5YA0IqAAAAWJlSKRkzqe+zJiu1enuSJa1LQ6vB\nodaQkGt23yqu9vkjV3tvT7Lo2b7PmmicsEyQ1X8++DPQ3jCu788GhpGQCgAAAIZLTe3Sx+22WIPx\n3R2DVmU9N+hRw+f6Q67nhoZbI/noYceCvs/zj6x+bP2YvhVYg4OsymOIgz+bJU2TBFqsESEVAAAA\nFKWuMZm4dd9ndQY2iV/UH2JVgq3ZywRb/au4OhaMXN1dbcm8x/s+q1Nbv/QRw4HHC4fsqTUo1Bo7\nuS/oY5MkpAIAAIANweBN4jdbg0cPu9r7V2b1h1eDHz+sBFr94daSOX2PB46Enq5kwcy+z+qUaoYG\nWpUAa4vlvwu0NjpCKgAAANgY1Tclk7bp+6xOb2/SNnfpmwYHB1mLnusPugYePXyu7zHFkVDuXfN9\ntEo1Sx8xbN4sGb/FMntnbb60bewUgdYGQEgFAAAAm7qamqR5St9ni91WPbZc7nuUcHCIVQm2Bn0f\naOtcPDI1l3uX3md1SjV9QdX4LZZ/xHDwZ/wWAq0CCakAAACANVcqJU0T+z5r8sbDzsWDNoFfNsSa\nM+j77L49t0ZCuXfpo46rU1mhNfCI4RZLA6zKiq3+tjEtfQEfw0JIBQAAAIychuZkcnMyeYfVj+3u\nGBpiVUKtZ5d/9LBt3sjUuzYrtGrqBgVXgwKtIXtpbZ6M39xbDteAkGqUefzxx3PzzTfntttuy9NP\nP51Zs2alXC5n2rRpeclLXpKTTjop22+/fdFlAgAAwPCra0wmbdv3WZ3ujkErtJYNtJZZtdU2d2Tq\n7e1OFs7q+6xObcMKAqzBe2lt0feo5ZiWkal1A1Aql8vloougz+mnn54LL7xwlWPq6uryiU98Ip/6\n1KdSGuYEdu7cuZk8eXKSpLW1NS0tm+7/YQAAALAR6e4ctBn8QID17NDvi59LFj47coHWmnjrD5Pd\nXlvc/dfScOcIVlKNIgsXLkySNDc3501velOOPPLI7LzzzimVSrnjjjty/vnn57HHHstnPvOZdHR0\n5Itf/GLBFQMAAMAGoK4hmbh132d1KoFWf4i18LllAq1Bjx+2zx/eOsdtPrzzbWCspBpF3ve+92XK\nlCn50Ic+tML0cf78+Tn44INz//33p7a2Ng888EBmzJgxbPe3kgoAAADWQlfbMuFV/2qsxSsIt9bk\nLYdn3pe0bDhb/FhJtRH7z//8z9TX16+0f+LEiTnvvPPy2te+Nj09PbniiivysY99rIoVAgAAABX1\nY/pCpTUJljoW9W/8PrsvyBq8UmvgUcNNfCWVkGoUWVVANWD//fevnD/66KMjWQ4AAAAwXBrH9X2m\nTC+6klGrpugCWDvz5s2rnDc2NhZXCAAAAMAwElJtYH7+859Xzvfee+/iCgEAAAAYRh7324DMmzcv\n//7v/56kb3+q4447bq3nmDt35a/SHLxKCwAAAKCahFQbiHK5nFNPPTXPPfdckuSzn/3sOu2aP7Dr\nPgAAAMBo4nG/DcQ555yTK6+8Mkny2te+NqeffnqxBQEAAAAMIyup1sFhhx2Wp59+er3m+POf/5yG\nhoY1Gvv1r389n/vc55Ik++67b374wx+mVCqt031bW1tX2jdv3rxMn+4tAwAAAED1CanWwSOPPJLH\nH398vebo7e1do3Hf+973Kqumdt9991x33XUZP378Ot93XR4RBAAAABhpQqp1cOONN6arq2u95mhs\nbFztmJ/+9Kc59dRTUy6Xs/POO+eGG27I1KlT1+u+AAAAAKORkGod7LTTTiN+j2uvvTYnnnhienp6\nsv322+fGG2/MlltuOeL3BQAAACiCjdNHoZtuuinHH398urq6svXWW+emm27KdtttV3RZAAAAACNG\nSDXK3HbbbXn961+f9vb2bLHFFrnxxhttZg4AAABs9IRUo8g999yT17zmNVm8eHGmTp2aG2+8MTNm\nzCi6LAAAAIARZ0+qUeTDH/5w5s2bl6Tv7X/HH3/8Kse/9KUvzaWXXlqFygAAAABGlpBqFOnp6amc\nt7a2prW1dZXjt9lmm5EuCQAAAKAqhFSjyGWXXZYlS5as8fjm5uYRrAYAAACgeoRUo4g3+AEAAACb\nKhunAwAAAFA4IRUAAAAAhRNSAQAAAFA4IRUAAAAAhRNSAQAAAFA4IRUAAAAAhRNSAQAAAFA4IRUA\nAAAAhRNSAQAAAFA4IRUAAAAAhRNSAQAAAFA4IRUAAAAAhRNSAQAAAFA4IRUAAAAAhRNSAQAAAFA4\nIRUAAAAAhRNSAQAAAFA4IRUAAAAAhRNSAQAAAFA4IRUAAAAAhRNSAQAAAFA4IRUAAAAAhRNSAQAA\nAFA4IRUAAAAAhRNSAQAAAFA4IRUAAAAAhRNSAQAAAFA4IRUAAAAAhRNSAQAAAFA4IRUAAAAAhRNS\nAQAAAFA4IRUAAAAAhRNSAQAAAFA4IRUAAAAAhRNSAQAAAFA4IRUAAAAAhRNSAQAAAFA4IRUAAAAA\nhRNSAQAAAFA4IRUAAAAAhRNSAQAAAFA4IRUAAAAAhRNSAQAAAFA4IRUAAAAAhRNSAQAAAFA4IRUA\nAAAAhRNSAQAAAFA4IRUAAAAAhRNSAQAAAFA4IRUAAAAAhRNSAQAAAFA4IRUAAAAAhRNSAQAAAFA4\nIRUAAAAAhRNSAQAAAFA4IRUAAAAAhRNSAQAAAFA4IRUAAAAAhRNSAQAAAFA4IRUAAAAAhRNSAQAA\nAFA4IRUAAAAAhRNSAQAAAFA4IRUAAAAAhRNSAQAAAFA4IRUAAAAAhRNSAQAAAFA4IRUAAAAAhRNS\nAQAAAFA4IRUAAAAAhRNSAQAAAFA4IRUAAAAAhRNSAQAAAFA4IRUAAAAAhRNSAQAAAFA4IRUAAAAA\nhRNSAQAAAFA4IRUAAAAAhRNSAQAAAFA4IRUAAAAAhRNSAQAAAFA4IRUAAAAAhRNSAQAAAFA4IRUA\nAAAAhRNSAQAAAFA4IRUAAAAAhRNSAQAAAFA4IRUAAAAAhRNSAQAAAFA4IRUAAAAAhRNSAQAAAFC4\numrcZOHChbnlllty880356677spzzz2X2bNnp729PZtttlk222yz7LLLLjnkkENyyCGHZKeddqpG\nWQAAAACMEqVyuVweqclvvvnmfOMb38gVV1yRrq6uNb5ujz32yHvf+968/e1vz4QJE0aqPJYxd+7c\nTJ48OUnS2tqalpaWgisCAAAARqvhzhFGJKS66qqrctZZZ+XBBx8c0j527NjMmDEjkydPzpQpU9LY\n2Jjnn38+ra2teeKJJzJz5swh45ubm/Pe9743Z599diZOnDjcZbIMIRUAAACwpkZ1SHXPPffkQx/6\nUG6++eYkSU1NTV7xilfk2GOPzYEHHpi99tordXUrf8LwySefzB/+8IfceOON+fGPf5zW1tYkyWab\nbZbPfOYzefe7353a2trhKpdlCKkAAACANTWqQ6p99903d999d7baaqucccYZedvb3patt956nebq\n7OzMNddck4suuii//vWvkyR33nln9t133+Eql2UIqQAAAIA1Ndw5wrC+3W/LLbfMV77ylTzyyCP5\n6Ec/us4BVZI0NDTk2GOPza9+9avccssteeUrX5lSqTSM1QIAAAAwWgzrSqre3t7U1Axr7lXV+Td1\nVlIBAAAAa2pUr6Qa6QBJQAUAAACwcZL6AAAAAFA4IRUAAAAAhasruoA5c+bk7rvvzvz587PZZptl\n//33T3Nzc9FlAQAAAFBFIxZSdXV15dprr82f/vSnNDQ0ZM8998xrX/vayr5SCxcuzBlnnJHvf//7\n6e7urlzX2NiY008/PZ///OfT0NAwUuUBAAAAMIqMSEj11FNP5aijjsr9998/pH3vvffOTTfdlObm\n5hxzzDG56aablru2o6MjX/rSl/LQQw/lyiuvHInyAAAAABhlhj2kKpfLOf7445cLqJLkT3/6U844\n44wccMABuemmm1JTU5Mjjzwy++23XxobG/OPf/wjV1xxRebMmZOrrroql19+ed7ylrcMd4kAAAAA\njDKlcrlcHs4Jf/3rX+fII49MkrzxjW/M+973vrS0tOS3v/1tPv7xj6dUKmWHHXbIww8/nF/96lc5\n5JBDhlw/f/78vOY1r8mtt96agw46KLfccstwlscqzJ07N5MnT06StLa2pqWlpeCKAAAAgNFquHOE\nYV9Jdd111yVJDj744Pz4xz+utO+9996ZPHly3v72t+eBBx7I6aefvlxAlSQTJ07MxRdfnBe+8IW5\n44470tHRkcbGxuEuEwAAAIBRpGa4J/zLX/6SJDn11FOX63vzm9+cMWPGJEkOP/zwlc6x5557Ztq0\naenq6spTTz013CUCAAAAMMoMe0g1b968JMkOO+ywXF9dXV222WabJMnmm2++ynmmTZuWJFmwYMGw\n1gcAAADA6DPsIVV3d3eSZMKECSvsH2ivra1d5TwD/T09PcNYHQAAAACj0bCHVAAAAACwtoRUAAAA\nABRu2N/uN2DRokWV/akGG3h8b2X9y44DAAAAYOM3YiHVK17xivXqBwAAAGDT4XE/AAAAAAo37Cup\njj/++Oy7777DNt/mm28+bHMBAAAAMDoNe0j18Y9/fLinBAAAAGAj53E/AAAAAAonpAIAAACgcEIq\nAAAAAAo3rHtS/fCHP8yzzz47nFPmLW95i83TAQAAADZywxpSffnLX87dd989nFPm4IMPFlIBAAAA\nbOSGNaSqq6tLbW3tKsf09PQM+V4qlVIul4e0DZ6jVCoNX4EAAAAAjErDuifVH/7wh3R3d6/ws2jR\nonzwgx9MfX19Tj311Nx0001pbW1NT09P2tracv/99+fLX/5yttpqq7zoRS/KPffck+7u7uyzzz7D\nWSIAAAAAo1CpvOwyphHQ29ubN77xjbnmmmvy85//PEccccRKx86bNy9HHHFEHn744dx2222ZMWPG\nSJdHv7lz52by5MlJktbW1rS0tBRcEQAAADBaDXeOUJW3+1199dW54oor8v73v3+VAVWSTJo0Kd/9\n7nczd+7cnHnmmdUoDwAAAICCVSWk+slPfpIkOeqoo9Zo/G677ZYdd9wx1157bRYuXDiSpW0wPvjB\nD6ZUKlU+//jHP4ouCQAAAGDYVCWkevzxx5MkTU1Na3xNU1NTyuVynnzyyZEqa4Px+9//PhdeeGHR\nZQAAAACMmKqEVM3NzUmS22+/fY3Gt7a25uGHHx5y7aaqvb0973jHO9Lb25vp06cXXQ4AAADAiKhK\nSHXAAQckSc4///zVrowql8v5//6//y9dXV3Zaqutsu2221ajxFHrnHPOyd///vccdthhedOb3lR0\nOQAAAAAjoioh1WmnnZZx48blueeey0te8pJ897vfzZIlS5Ybd9ddd+V1r3tdLrvssiTJGWeckZqa\nqpQ4Kt155535j//4jzQ1NeWiiy4quhwAAACAEVNXjZtss802ufTSS3PiiSdm5syZOeWUU3Laaafl\nBS94QVpaWtLe3p7HHnsszz//fOWa1772tfnQhz5UjfJGpc7Ozpx66qnp6enJZz/72ey8885FlwQA\nAAAwYqoSUiXJm970pmy22WZ597vfnYceeihdXV154IEHlhvX1NSUM888M+ecc07q6+urVd6o89nP\nfjYPPPBA9txzz3zkIx8puhwAAACAEVW1kCpJDj300Pz1r3/NDTfckBtvvDF/+9vfMn/+/DQ1NWWr\nrbbKS17ykhx//PGZPHlyNcsadf70pz/lvPPOS6lUyn//939v0mEdAAAAsGmoakiVJDU1NTniiCNy\nxBFHVPvWG4Tu7u6ceuqp6e7uznvf+94ceOCBwzr/3LlzV9o3b968Yb0XAAAAwJqqekjFqn3xi1/M\nn/70p2y11Vb593//92Gff1NfpQYAAACMTpvuq/NGoQceeCCf+9znkiRf+9rXMmHChIIrAgAAAKiO\nYV1J1dPTk9ra2uGcsqrzr6kddtghjz/++HrN0dbWlqampsr3np6enHrqqens7MzRRx+d448/fn3L\nXKHW1taV9s2bNy/Tp08fkfsCAAAArMqwrqR63etel/PPPz9LliwZzmnzf//3fzn44INzzz33DOu8\no8kPf/jD3HnnnRk3bly+/vWvj9h9WlpaVvqZNGnSiN0XAAAAYFWGNaSaM2dO/u3f/i3Tp0/P5z//\n+fVabdTe3p7//d//zaGHHppXvvKV+f3vf59SqTSM1a67f/zjHymXy+v1GbyKKlm6afmiRYuy3Xbb\npVQqLfc577zzKuN33HHHlEqlTJ06tZo/HQAAAGBEDGtI9Z3vfCdHHnlknn322Zx99tnZcccdc+ih\nh+Y///M/c/vtt6ezs3OV1z/22GP5n//5n7zrXe/KtGnT8s///M/5zW9+k6222iqXXHJJ/umf/mk4\nywUAAABglCiVy+XycE/6y1/+Mp/4xCfyxz/+cUh7Q0NDdt5550yZMiWTJ09OY2NjWltb09ramiee\neCJz5swZMr6lpSVnnHFGPvKRj6S5uXm4y9zgfOxjH6uspnrssceyww47DOv8c+fOrbz9r7W1NS0t\nLcM6PwAAALDxGO4cYVg3Th/w6le/Oq9+9atz22235Rvf+EZ+/OMfp729PZ2dnXnwwQdXe/0BBxyQ\n97znPfnnf/7njBkzZiRKBAAAAGAUGZGQasCBBx6YAw88MBdffHH+8Ic/5Le//W3uvvvuPPvss5k9\ne3Y6OzszderUbLbZZtlll11yyCGH5JBDDsm0adNGsiwAAAAARpkRDakGjBkzJq94xSvyile8ohq3\nAwAAAGADM6wbpwMAAADAuhiRjdPZMNk4HQAAAFhTw50jWEkFAAAAQOGEVAAAAAAUTkgFAAAAQOGE\nVAAAAAAUTkgFAAAAQOGEVAAAAAAUTkgFAAAAQOGEVAAAAAAUTkgFAAAAQOGEVAAAAAAUrq7aN3zq\nqafym9/8Jg8//HAWLFiQnp6eVY4/88wzs+2221apOgAAAACKULWQavbs2fnABz6Qn/zkJ+nt7V3j\n6972trcJqQAAAAA2clUJqTo6OnLYYYflvvvuq7RNmDAhkydPTm1t7SqvbWpqGunyAAAAAChYVUKq\nSy65pBJQvfOd78xHPvKRzJgxoxq3BgAAAGADUJWQ6te//nWS5KSTTsq3vvWtatwSAAAAgA1IVd7u\nN3v27CTJW9/61mrcDgAAAIANTFVCqi222CJJMnbs2GrcDgAAAIANTFVCqiOOOCJJcu+991bjdgAA\nAABsYKoSUp188snZY4898pWvfCULFy6sxi0BAAAA2IBUJaQaM2ZMrrnmmowdOzaHHXaYFVUAAAAA\nDFGVt/udc845efTRR/OCF7wgV155Zfbee+/stttu2XXXXVe7T9W5556bHXfcsRplAgAAAFCQUrlc\nLo/0Tfbdd9/cfffd63TtnXfemX333XeYK2JF5s6dm8mTJydJWltb09LSUnBFAAAAwGg13DlCVVZS\n7b777ut8bXNz8zBWAgAAAMBoVJWQ6rLLLqvGbQAAAADYQFVl43QAAAAAWBUhFQAAAACFE1IBAAAA\nULiq7Ek1WG9vb6677rrceOON+etf/5p58+ZlzJgx2WqrrXLggQfmhBNOyNSpU6tdFgAAAAAFKpXL\n5XK1bnbbbbfl5JNPzkMPPbTSMU1NTTnrrLPyiU98IjU1FnpV03C/OhIAAADYeA13jlC1lVQ33nhj\njjrqqHR1dSVJSqVStt9++0yZMiXt7e157LHHsmTJkrS3t+ecc87Jww8/nO9+97vVKg8AAACAAlVl\nqdLixYvz1re+NV1dXZkwYUK+9KUvZfbs2Xnsscdy11135f7778+CBQty/fXX54ADDkiSXHbZZfmf\n//mfapQHAAAAQMGqElJdfvnlefbZZzN+/PjceuutOfPMMzNlypQhY2pra/OqV70qt9xyS44++ugk\nyZe//OVqlAcAAABAwaoSUt10001JkjPPPDN77LHHKsfW1dXloosuSk1NTe6+++7Mnz+/GiUCAAAA\nUKCqhFRPP/10kuSQQw5Zo/FbbbVVdtlll5TL5cycOXMkSwMAAABgFBi1r88beOlgqVQquBIAAAAA\nRlpVQqptttkmSXLzzTev0fiZM2fm4YcfTqlUylZbbTWClQEAAAAwGlQlpDrssMOSJP/xH/+RBx54\nYJVju7u78773vS+9vb3Zb7/9MmHChGqUCAAAAECBqhJSnXjiidlyyy2zcOHCHHTQQfmP//iPzJkz\nZ8iY7u7u3HDDDXn5y1+eq666Kkny4Q9/uBrlAQAAAFCwUnlg86cRdvPNN+fII49MZ2dnpW277bZL\nS0tLOjo68o9//CPt7e2Vvne84x255JJLqlEa/ebOnZvJkycnSVpbW9PS0lJwRQAAAMBoNdw5QtU2\nTj/00EPz29/+Nrvttlul7Yknnsi9996bv/71r5WAqrm5OV/4whfyzW9+s1qlAQAAAFCwumre7IAD\nDsgDDzyQG2+8MTfccEP++te/Zv78+WlqaspWW22VAw88MMcff7wVPAAAAACbmKqGVElSKpXyqle9\nKq961auqfWsAAAAARqmqPe4HAAAAACsjpAIAAACgcEIqAAAAAAo3rHtSnXHGGfn73/+eJLnggguy\nyy67LNe+tgbPAwAAAMDGaVhDqltvvTV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NWd2Kp+9+97urreGGG27I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\niIiIiMjg/h/9r4mGHIQH8gAAAABJRU5ErkJggg==\n"
          }
        }
      ],
      "source": [
        "# Extract transmission spectra to the bar and cross ports\n",
        "P_TE_bar = np.abs(batch_results[\"TE\"][\"bar\"].amps.sel(mode_index=0, direction=\"+\")) ** 2\n",
        "P_TM_cross = np.abs(batch_results[\"TM\"][\"cross\"].amps.sel(mode_index=0, direction=\"+\")) ** 2\n",
        "\n",
        "# Plot the spectra\n",
        "plt.plot(ldas * 1e3, 10 * np.log10(P_TE_bar), label=\"TE bar port\")\n",
        "plt.plot(ldas * 1e3, 10 * np.log10(P_TM_cross), label=\"TM cross port\")\n",
        "plt.legend()\n",
        "plt.ylabel(\"Transmission (dB)\")\n",
        "plt.xlabel(\"Wavelength (nm)\")\n",
        "plt.ylim(-10, 0)\n",
        "plt.show()"
      ],
      "id": "c6b6b142"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Closing Remark\n",
        "\n",
        "The final design in this notebook achieves reasonable performance but is\n",
        "by no means the best design. A more intricate optimization scheme can be\n",
        "used to enhance the final result as demonstrated in the\n",
        "[publication](https://doi.org/10.1364/OE.408432).\n",
        "\n",
        "Using the PSO optimizer from the `Design` plugin is a convenient\n",
        "plug-and-play tool for managing parallelized PSO runs within `Tidy3D`.\n",
        "Advanced users may wish to develop their own optimizer that supports\n",
        "advanced options like dynamic hyperparameters.\n",
        "\n",
        "Due to the large number of simulation runs, a PSO task can take a\n",
        "significant amount of time and FlexCredits. Users should have a good\n",
        "familiarity with Tidy3D before attempting to perform PSO to avoid making\n",
        "mistakes in the optimization and wasting credits. Running a smaller PSO\n",
        "task as a test and practice before a large PSO task is also highly\n",
        "recommended."
      ],
      "id": "363490b6-a1db-4524-9426-25cdc7601b5a"
    }
  ],
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