{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Inverse design optimization of a plasmonic nanoantenna metasurface\n",
        "\n",
        "In this notebook we perform inverse design of an antenna using a medium\n",
        "ranging between air and an experimentally measured gold from `tidy3d`’s\n",
        "material library.\n",
        "\n",
        "We use topology optimization to design the patterning on this sheet of\n",
        "gold to maximizes the intensity enhancement in a central location, while\n",
        "respecting fabrication penalties.\n",
        "\n",
        "<img src=\"img/adjoint_15.png\" width=400 alt=\"Schematic of the nanoantenna \">\n",
        "\n",
        "## Set up\n",
        "\n",
        "We start by importing the packages we need, including `autograd` and the\n",
        "`autograd` wrapper for `numpy`."
      ],
      "id": "d9c08ab1-9663-427b-9f83-dda807b75a35"
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {},
      "outputs": [],
      "source": [
        "import autograd\n",
        "import autograd.numpy as np\n",
        "import matplotlib.pylab as plt\n",
        "import tidy3d as td\n",
        "import tidy3d.web as web"
      ],
      "id": "4f878f3c"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "We’ll set a few helper constants for the notebook."
      ],
      "id": "667e275f-2efb-4cba-9ca6-646c42ac41e3"
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {},
      "outputs": [],
      "source": [
        "# whether to run checks for setting up sim and normalization enhancement\n",
        "run_pre_sims = True\n",
        "\n",
        "um = 1e0\n",
        "nm = 1e-3"
      ],
      "id": "d3d59c89"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Then we define the parameters setting our source spectrum and FDTD\n",
        "spatial resolution."
      ],
      "id": "e0536a09-d428-418b-8a9e-ee15c68180d7"
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {},
      "outputs": [],
      "source": [
        "wavelength = 0.910\n",
        "\n",
        "freq = td.C_0 / wavelength\n",
        "fwidth = freq / 10\n",
        "run_time = 20 / fwidth\n",
        "\n",
        "dl = 3 * nm\n",
        "\n",
        "# min_steps_per_wvl = 30"
      ],
      "id": "d361d314"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Next we define our material parameters.\n",
        "\n",
        "We import the gold model from our material library, which is a\n",
        "`td.PoleResidue` medium from a fit to measured data."
      ],
      "id": "9ac9d08d-8e42-4d16-b62a-82b8fc7cfd56"
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {},
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "('Olmon2012crystal', 'Olmon2012stripped', 'Olmon2012evaporated', 'Olmon2012Drude', 'JohnsonChristy1972', 'RakicLorentzDrude1998')"
          ]
        }
      ],
      "source": [
        "# select one of the material library variants\n",
        "print(tuple(td.material_library[\"Au\"].variants.keys()))"
      ],
      "id": "40c23dcf"
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {},
      "outputs": [],
      "source": [
        "medium_SiO2 = td.Medium(permittivity=1.44**2)\n",
        "medium_gold = td.material_library[\"Au\"][\"JohnsonChristy1972\"]\n",
        "eps_background = 1.0"
      ],
      "id": "67ae1999"
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
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KGydCKgC+kl1YotdXJOutVXtUUOL+rK5ndYrT/ef11ID2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          }
        }
      ],
      "source": [
        "wvls = np.linspace(0.5, 1.0, 101)\n",
        "freqs = td.C_0 / wvls\n",
        "eps_complex = medium_gold.eps_model(freqs)\n",
        "eps_real, sigma = medium_gold.eps_complex_to_eps_sigma(eps_complex, freq=freq)\n",
        "plt.plot(wvls, eps_real, label=\"permittivity (real)\")\n",
        "plt.plot(wvls, np.imag(eps_complex), label=\"permittivity (imag)\")\n",
        "plt.plot(wvls, sigma, label=\"conductivity\")\n",
        "plt.plot(wvls, np.ones_like(eps_real), label=\"1\", linestyle=\"--\")\n",
        "plt.plot(wvls, np.zeros_like(eps_real), label=\"0\", linestyle=\"--\")\n",
        "plt.xlabel(\"wavelength (um)\")\n",
        "plt.ylabel(\"relative permittivity\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "id": "cae33be3"
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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BAAAAAFyLkAqAg5AAH70/pKU+vKelQgK8HWrp2Vb9a/ZWPfDVep1MyTSoQwAA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5cuXcr16/Hjx8V0ZlSSPH78GDNmzMCQIUNw69YtxMTE4Pnz51iyZAlkMhlevnyJfv36KRV6FM6f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          }
        }
      ],
      "source": [
        "density_values = np.linspace(0, 1, 101)\n",
        "eps_complex = 0j * np.zeros_like(density_values)\n",
        "for i, d in enumerate(density_values):\n",
        "    new_eps_inf = 1.0 + d * (medium_gold.eps_inf - 1)\n",
        "    new_poles = [(a, c * d) for (a, c) in medium_gold.poles]\n",
        "    new_medium = medium_gold.updated_copy(eps_inf=new_eps_inf, poles=new_poles)\n",
        "    eps_complex[i] = new_medium.eps_model(freq)\n",
        "\n",
        "eps_real, sigma = medium_gold.eps_complex_to_eps_sigma(eps_complex, freq=freq)\n",
        "plt.plot(density_values, eps_real, label=\"permittivity (real)\")\n",
        "plt.plot(wvls, eps_complex.imag, label=\"permittivity (imag)\")\n",
        "plt.plot(density_values, sigma, label=\"conductivity\")\n",
        "plt.plot(density_values, np.ones_like(eps_real), label=\"1\", linestyle=\"--\")\n",
        "plt.plot(density_values, np.zeros_like(eps_real), label=\"0\", linestyle=\"--\")\n",
        "plt.xlabel(\"density value\")\n",
        "plt.ylabel(\"relative permittivity\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "id": "8d10d3ad"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Next we define the geometric parameters describing our device.\n",
        "\n",
        "We have a rectangular metal slab sitting on top of a SiO2 substrate with\n",
        "air on top.\n",
        "\n",
        "The rectangular slab has a hole in the center, where we’ll be measuring\n",
        "the field intensity enhancement."
      ],
      "id": "bb852fe7-41c8-4140-aa40-d34f25d93181"
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {},
      "outputs": [],
      "source": [
        "size_design_x = 500 * nm\n",
        "size_design_y = 500 * nm\n",
        "thick_metal = 50 * nm\n",
        "thick_sub = 0.8 * wavelength\n",
        "thick_air = 0.8 * wavelength\n",
        "buffer_xy = 0.0 * wavelength\n",
        "\n",
        "hole_radius = 12 * nm"
      ],
      "id": "00ebff92"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "We derive the total sizes needed for our simulation in all dimensions."
      ],
      "id": "71d8a3ec-69f7-4327-b24b-dceb68025b5b"
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {},
      "outputs": [],
      "source": [
        "size_x = size_design_x + 2 * buffer_xy\n",
        "size_y = size_design_y + 2 * buffer_xy\n",
        "size_z = thick_sub + thick_metal + thick_air"
      ],
      "id": "042e14f8"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "As well as set some variables to help us keep track of location within\n",
        "the simulation."
      ],
      "id": "7afe3b55-e7d4-4ff9-b8a9-597cc5a38d0b"
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {},
      "outputs": [],
      "source": [
        "top_z = size_z / 2.0\n",
        "\n",
        "center_air_z = top_z - thick_air / 2.0\n",
        "center_metal_z = top_z - thick_air - thick_metal / 2.0\n",
        "center_sub_z = top_z - thick_air - thick_metal - thick_sub / 2.0"
      ],
      "id": "048f463a"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Next, we define our static components, such as the substrate, source,\n",
        "and monitors.\n",
        "\n",
        "We will include the pattern gold film later on, but we set the geometry\n",
        "as a `td.Box` here so we can use it later.\n",
        "\n",
        "All of these components will be combined into our base `td.Simulation`,\n",
        "which defines our setup without any gold film."
      ],
      "id": "23a77d2f-d0b8-4e22-ac4e-2b92e34c9fb5"
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {},
      "outputs": [],
      "source": [
        "design_region_geometry = td.Box(\n",
        "    center=(0, 0, center_metal_z),\n",
        "    size=(td.inf, td.inf, thick_metal),\n",
        ")\n",
        "\n",
        "substrate = td.Structure(\n",
        "    geometry=td.Box(\n",
        "        center=(0, 0, -size_z + thick_sub),\n",
        "        size=(td.inf, td.inf, size_z),\n",
        "    ),\n",
        "    medium=medium_SiO2,\n",
        ")\n",
        "\n",
        "plane_wave = td.PlaneWave(\n",
        "    center=(0, 0, center_air_z),\n",
        "    size=(td.inf, td.inf, 0),\n",
        "    source_time=td.GaussianPulse(freq0=freq, fwidth=fwidth),\n",
        "    pol_angle=0,\n",
        "    direction=\"-\",\n",
        ")\n",
        "\n",
        "point_monitor = td.FieldMonitor(\n",
        "    size=(0, 0, 0),\n",
        "    center=(0, 0, center_metal_z),\n",
        "    freqs=[freq],\n",
        "    name=\"point\",\n",
        ")\n",
        "\n",
        "field_monitor_xy = td.FieldMonitor(\n",
        "    center=(0, 0, center_metal_z),\n",
        "    size=(td.inf, td.inf, 0),\n",
        "    freqs=[freq],\n",
        "    name=\"field_xy\",\n",
        ")\n",
        "\n",
        "eps_monitor_xy = td.PermittivityMonitor(\n",
        "    center=(0, 0, center_metal_z),\n",
        "    size=(td.inf, td.inf, 0),\n",
        "    freqs=[freq],\n",
        "    name=\"eps_xy\",\n",
        ")\n",
        "\n",
        "field_monitor_xz = td.FieldMonitor(\n",
        "    center=(0, 0, 0),\n",
        "    size=(td.inf, 0, td.inf),\n",
        "    freqs=[freq],\n",
        "    name=\"field_xz\",\n",
        ")\n",
        "\n",
        "sim_no_antenna = td.Simulation(\n",
        "    size=(size_x, size_y, size_z),\n",
        "    run_time=run_time,\n",
        "    structures=[substrate],\n",
        "    sources=[plane_wave],\n",
        "    monitors=[point_monitor, field_monitor_xy, field_monitor_xz, eps_monitor_xy],\n",
        "    grid_spec=td.GridSpec.uniform(dl=dl),\n",
        "    boundary_spec=td.BoundarySpec.pml(x=False, y=False, z=True),\n",
        "    # grid_spec=td.GridSpec.auto(wavelength=wavelength, min_steps_per_wvl=min_steps_per_wvl),\n",
        ")"
      ],
      "id": "a0366dd1"
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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ZtVlS1r9nwsPDjT///LNQmcOHDxsNGjRwqS+1detWs/+3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\nZKRatGih4cOHm69Bu3btzGkTCjqr9hT39S7K+vX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5g8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\nREREREREREREREQm5f8Bs6KPNVacxHUAAAAASUVORK5CYII=\n"
          }
        }
      ],
      "source": [
        "# shift the plot positions a little so the field monitors don't overlap plots\n",
        "shift_plot = 0.01\n",
        "\n",
        "f, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(10, 4), tight_layout=True)\n",
        "sim_no_antenna.plot(x=0.0 + shift_plot, ax=ax1)\n",
        "sim_no_antenna.plot(y=0.0 + shift_plot, ax=ax2)\n",
        "sim_no_antenna.plot(z=center_metal_z + shift_plot, ax=ax3)\n",
        "plt.show()"
      ],
      "id": "fa2ff7a2"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Antenna Parameterization\n",
        "\n",
        "Next, we’ll define our antenna as a `td.Structure`, which we add to the\n",
        "simulation.\n",
        "\n",
        "We will be optimizing this pattern with respect to an array of\n",
        "parameters. So it makes sense to write our components from here on as\n",
        "functions so we can update them as they change.\n",
        "\n",
        "We start by defining some variables to define our design\n",
        "parameterization, such as the pixel size, feature size, and projection\n",
        "(binarization) strength."
      ],
      "id": "fa106955-0371-4fa2-a515-f1dc428e1054"
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {},
      "outputs": [],
      "source": [
        "# resolution of the design region pixels\n",
        "# pixel_size = 10 * nm\n",
        "pixel_size = dl\n",
        "\n",
        "# radius of the circular filter (um) (higher = larger features)\n",
        "radius = 24 * nm\n",
        "\n",
        "# projection strengths (higher = more binarized)\n",
        "beta_project = 10\n",
        "beta_penalty = 10"
      ],
      "id": "baf2d9fd"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Next, we write a function to get the density (between 0 and 1) of gold\n",
        "on our film as a function of our optimization parameters.\n",
        "\n",
        "> Note: there are many helper functions in `tidy3d.plugins.autograd`\n",
        "> that are used for inverse design. These have very close analogues in\n",
        "> the `adjoint` plugin, but are compatible with `autograd` and have\n",
        "> extra features added."
      ],
      "id": "279e9f75-ad85-4f28-bd5f-d00c5a6dbd1f"
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {},
      "outputs": [],
      "source": [
        "from tidy3d.plugins.autograd import make_filter_and_project\n",
        "\n",
        "\n",
        "def get_density(params: np.ndarray, beta: float = beta_project) -> np.ndarray:\n",
        "    \"\"\"Generic function to get the etch density as a function of design parameters, using filter and projection.\"\"\"\n",
        "    filter_project = make_filter_and_project(radius, pixel_size, beta=beta)\n",
        "    return filter_project(params)"
      ],
      "id": "fe4e2892"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Next, we need to generate the `td.Structure` containing the gold film by\n",
        "modifying the material properties of the gold model from our material\n",
        "library.\n",
        "\n",
        "We use a `td.CustomPoleResidue` to define a spatially-varying dispersive\n",
        "medium. The relative permittivity at infinite frequency (`eps_inf`) is\n",
        "set between that of air (1) and that of the gold `eps_inf` linearly,\n",
        "depending on the density value at each point. The numerator of the\n",
        "`poles` are also multiplied by the density so that they interpolate\n",
        "between values of 0 for density of 0 and the values for gold when\n",
        "density is 1.\n",
        "\n",
        "We apply the mask over the central region to set it to air and combine\n",
        "everything together into a `td.Structure`."
      ],
      "id": "5207c855-4b4b-430b-96e0-8aa39d17ea98"
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {},
      "outputs": [],
      "source": [
        "def make_antenna_from_density(density: np.ndarray) -> td.Structure:\n",
        "    \"\"\"Make a `td.Structure` containing a `td.CustomPoleResidue` corresponding to a density array.\"\"\"\n",
        "\n",
        "    rmin, rmax = sim_no_antenna.bounds\n",
        "    coords = {}\n",
        "    for key, pt_min, pt_max, num_pts in zip(\"xyz\", rmin, rmax, density.shape):\n",
        "        coord_edges = np.linspace(pt_min, pt_max, num_pts + 1)\n",
        "        coord_centers = (coord_edges[1:] + coord_edges[:-1]) / 2.0\n",
        "        coords[key] = coord_centers\n",
        "\n",
        "    mask = td.ScalarFieldDataArray(\n",
        "        np.ones_like(density),\n",
        "        coords=coords,\n",
        "    )\n",
        "    is_in_hole = mask.x**2 + mask.y**2 >= hole_radius**2\n",
        "    mask = mask.where(is_in_hole, 0)\n",
        "\n",
        "    density_masked = density * mask.values\n",
        "\n",
        "    eps_inf_scaled_array = eps_background + density_masked * (medium_gold.eps_inf - eps_background)\n",
        "\n",
        "    poles_arrays_scaled = [\n",
        "        (a * np.ones_like(density_masked), c * density_masked) for (a, c) in medium_gold.poles\n",
        "    ]\n",
        "\n",
        "    eps_inf_scaled = td.ScalarFieldDataArray(\n",
        "        eps_inf_scaled_array,\n",
        "        coords=coords,\n",
        "    )\n",
        "\n",
        "    poles_scaled = []\n",
        "    for a_array, c_array in poles_arrays_scaled:\n",
        "        a_scaled = td.ScalarFieldDataArray(a_array, coords=coords)\n",
        "        c_scaled = td.ScalarFieldDataArray(c_array, coords=coords)\n",
        "        poles_scaled.append((a_scaled, c_scaled))\n",
        "\n",
        "    medium_gold_scaled = td.CustomPoleResidue(\n",
        "        eps_inf=eps_inf_scaled, poles=poles_scaled, interp_method=\"linear\"\n",
        "    )\n",
        "\n",
        "    return td.Structure(geometry=design_region_geometry, medium=medium_gold_scaled)"
      ],
      "id": "063ea668"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Next we write a quick helper function to create the `td.Structure` as a\n",
        "function of the optimization parameters."
      ],
      "id": "2bfc408a-ed64-411f-bd91-a0088448ef97"
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {},
      "outputs": [],
      "source": [
        "def make_antenna(params: np.ndarray, beta: float = beta_project) -> td.Structure:\n",
        "    \"\"\"Make the antenna structure.\"\"\"\n",
        "    density = get_density(params, beta=beta)\n",
        "    return make_antenna_from_density(density)"
      ],
      "id": "d02bf64b"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "We also write a function that generates a `td.Simulation` with the\n",
        "structure added to our original simulation."
      ],
      "id": "e3d9870c-a9ea-4248-99ae-704304f5e619"
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {},
      "outputs": [],
      "source": [
        "def make_sim_with_antenna(\n",
        "    params: np.ndarray, include_field_mnts: bool = True, beta: float = beta_project\n",
        ") -> td.Simulation:\n",
        "    \"\"\"Make a simulation as a function of the density parameters for the antenna regions.\"\"\"\n",
        "\n",
        "    antenna = make_antenna(params, beta=beta)\n",
        "\n",
        "    sim = sim_no_antenna.updated_copy(\n",
        "        structures=list(sim_no_antenna.structures) + [antenna],\n",
        "    )\n",
        "\n",
        "    if not include_field_mnts:\n",
        "        sim = sim.updated_copy(monitors=[point_monitor])\n",
        "\n",
        "    return sim"
      ],
      "id": "3b2c47da"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Let’s test this out by generating a set of initial parameters for the\n",
        "optimization and calling our code."
      ],
      "id": "803e7ce9-30bd-4349-b4e4-567da87d9a2f"
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {},
      "outputs": [],
      "source": [
        "# some variables we might need later\n",
        "\n",
        "nx = int(size_design_x // pixel_size)\n",
        "ny = int(size_design_y // pixel_size)\n",
        "\n",
        "\n",
        "# some initial parameters to test with\n",
        "def make_symmetric_x(arr: np.ndarray) -> np.ndarray:\n",
        "    \"\"\"make an array symmetric in x.\"\"\"\n",
        "    return (arr + np.flipud(arr)) / 2.0\n",
        "\n",
        "\n",
        "params0 = make_symmetric_x(0.5 * np.ones((nx, ny, 1)))"
      ],
      "id": "6bc66dc0"
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {},
      "outputs": [],
      "source": [
        "sim_antenna_params0 = make_sim_with_antenna(params0)"
      ],
      "id": "8d516237"
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
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9/PLLNhdLSqIs23V3EnPatGlm/c6sbeXOJKbFYil0XvquXbvanBfjxo1zWPbd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\n2LF2y5bk+S6pu+++26bfkf945syZbmu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tcY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\nQmCC\n"
          }
        }
      ],
      "source": [
        "f, axes = f, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(10, 4), tight_layout=True)\n",
        "sim_antenna_params0.plot(x=0.0 + shift_plot, monitor_alpha=0.0, ax=ax1)\n",
        "sim_antenna_params0.plot(y=0.0 + shift_plot, monitor_alpha=0.0, ax=ax2)\n",
        "sim_antenna_params0.plot(z=center_metal_z + shift_plot, monitor_alpha=0.0, ax=ax3)\n",
        "\n",
        "for ax in axes:\n",
        "    ax.set_aspect(\"equal\")\n",
        "\n",
        "plt.show()"
      ],
      "id": "5d845c11"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "If we want, we can also visualize the initial fields."
      ],
      "id": "517be470-4f03-4926-acd2-dc61bbcd16d5"
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {},
      "outputs": [
        {
          "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\">10:24:29 UTC </span>Created task <span style=\"color: #008000; text-decoration-color: #008000\">'check fields'</span> with resource_id                       \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #008000; text-decoration-color: #008000\">'fdve-09a7f718-e978-4ca0-877e-c7a5d7f36a6b'</span> and task_type <span style=\"color: #008000; text-decoration-color: #008000\">'FDTD'</span>.  \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>View task using web UI at                                          \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-09a7f718-e978-4ca0-877e-c7a5d7f36a6b\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">'https://tidy3d.simulation.cloud/workbench?taskId=fdve-09a7f718-e97</span></a>\n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-09a7f718-e978-4ca0-877e-c7a5d7f36a6b\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">8-4ca0-877e-c7a5d7f36a6b'</span></a>.                                         \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>Task folder: <a href=\"https://tidy3d.simulation.cloud/folders/9b36e144-ddb6-41f8-8dd8-30b62b26a870\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">'default'</span></a>.                                            \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"a60cc5b004c74f6a95f39fff86e53439\",\"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\">10:24:31 UTC </span>Estimated FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.563</span>. This assumes the FDTD solver runs\n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>for the full simulation time; if early shutoff is reached, the     \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>billed cost can be lower. Use <span style=\"color: #008000; text-decoration-color: #008000\">'web.real_cost(task_id)'</span> to get the  \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>billed FlexCredit cost after a simulation run.                     \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\">10:24:32 UTC </span>status = success                                                   \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"8dbb754ba2d143a6abfd9168230788d6\",\"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\">10:24:34 UTC </span>Loading results from simulation_data.hdf5                          \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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s3rwZGRkZuP322zF48GCUL19evWOpXLlyuP76673aZ1YfM8FQvHhx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A+fn5Scm/NWnSJNx8880AgIMOOgjTp083XuHfkGMloszh+Hn+/kc/o0ePxg033JCUNquqqnDJ\nJZcgFArhggsuwODBg+Nuo3nz5uHHFRUVhppqGFd5uXRpg+rGCS4iIiIiIiIiImo0/va3v6G4uDhq\nmZznZO+994ZlWRBCYNmyZcY2v/vuu/Aytp4oOU4vvfQSRo4cCQDYd999MWPGDLRq1cq4TEONlYio\nLvn5+Um7A/Thhx/Gd999h7Zt22LChAkJtdGqVSvYtg3HcYyhVwEoucPkdUiXNqhunOAiIiIiIqIY\nRJx3utWvJyIiomQYPXq0p3otWrTAoYceis8//xz//e9/IYRwRTIAau6I+vHHHwEAxx57bL3G9uab\nb+KSSy6BEAJ77bUXZs2ahbZt26blWIkoE/l3/p4Kv/zyS/jxCSecELXOTz/9BKAmHOvBBx8MADj0\n0EPxxBNPAABycnKw2267YeXKlVi1apWxP7m8V69e4cfp0gbVjRNcRERERERERETUJA0bNgyff/45\nVq5ciY8++ggnnniiq85TTz0Vfnzuuecm3Nf777+Pv/zlLwiFQujRowdmz56NDh06pOVYiYga0tat\nW7F161ZjnVAohMWLFwMAWrdurZQdcMABWLlyJb7++msEg8GY+Q2/+OILADWTUb17907LNsiME1yU\nRDbMGYES4zm3VZQrlyIMOaGsFNyu72oz+dslUfoVXvL6x5OrS889pZbFzqWl9K3nqzGMRc2lpebV\nsZQ8PvHk2ZJzA+k5fuQcRvo2k/Nlafm5pOcBPReRYTeQy1wZzeJox/g2kOjZY+RcSHpeKDUHl7rt\ng9WRluxy9QohKytSFkC12r+cs8nRcgNVSzmycquUMuREYhIjoG0pU8LOkJT/KKStfZXUX6U6TlEu\n5dkq1cpKIsvp+ceC5dL2rNa2mbQNTdtaaPtdPBl/TPuBsq/p+1aMeoCaQUovk/d1fdxyKjFHfy9J\nu4z+3pXfk/rVZ0J5f+rvXSdqvZqyyLYXWrI5Ncch1DIhj0XbX6XlbO0iOUeqq6+fnpFLaROxxyLv\nCXq+PP/pG8qQ1yvRHoz5wAw5seQ3gWFDxZcrLFbfdREwv+LpzYH/MfyJiIj8dPnll+PBBx/EunXr\nMHLkSMybNw+77rpruHzOnDl4+OGHAQBDhw7FQQcd5Grj559/xrRp0wAARx11FPr16+eq89///hdn\nn302qqursdtuu2H27Nno0qWL72MlosbN1xxcKWhzzJgx+Nvf/masc80112DBggVo0aIF5syZAwBo\n2bKlUueUU07BtGnTUFpaitmzZ+P44493tVNZWYmZM2cCqLnjNT8/Py3bIDNOcBERERERERERUZOU\nn5+PV155BccffzxWrVqF/fffH8OGDUOXLl2wdOlSvP322wgGg+jatSsmTZoUtY1ly5bh73//OwDg\nvvvuc01wrV69GqeddhoqKioAACeddBLefPNN47jOOeccdOvWLeljJSJKZ7vttht22203Y53ayaxA\nIBAOUag788wzcdNNN6G4uBj33nsvjjvuONdF/0899VT4LrFLL700bdsgM05wERERERFRTH7dWMUb\nuIiIqKEcffTRmDlzJi6++GKsXLnSNTl01FFH4cUXX0Tnzp0Tan/9+vUoKSkJP5fDCMZy4IEHuia4\n/BgrEWU2AZ5XAzUhC8eMGYMbb7wR8+bNw2WXXYYJEyagZcuWcBwHL7/8MkaNGgUA6N+/P84888y0\nbYPMOMFFacdzSMIGkIxwhuawfLHDB/7xDx7b0criCqWkLhlp3xD+zRQC0jAW07hs13Kx9wulTWEK\nNRi7Tde2V8IX6mOTt4s+FtOY5dCGeptSLdeq6mMThrre6GGgQtLzkB5KzYk8rw6p2zArKIVnq9K2\nb7kckksNH2Y7kXB/VlAL+VYRCf1n5agfU1aO9Gq4YkAa9nM5DGJIC3dXFZIeB9WySqmsTA0x5kgh\nGYPlShGC0rYIBtVxydtQ3raAuu21YSYcusu9jwrlmVo3UqaH21P2WaHvk7HaV/u3teUCUl09nKD5\n/SmHLNVeT+kYIK9PTR+R19AdslR6XfQwhB6PW3r4QlMIPfmYKkRi4euMx3b92KDvT5YjVdXakUMB\n6p9DQn6YWBhC/bPNHXqw4cj7RSYnZiYiIqL4DRw4ED/99BPmzJmDJUuWoLi4GB06dMCAAQPQt29f\n47I9e/bEjTfeCAA49NBDXeWdO3cOl3tluoOhPmMlImoqbrjhBixduhQvvvgi/vWvf+HVV1/FHnvs\ngY0bN2LLli0AgB49euCtt95K+zYoNk5wERERERFRVL7G8OecIhERNbBAIIDBgwdj8ODBcS3Xp08f\njB8/PmZ5t27djOWJSHSsRNS48fxd9cILL2DgwIF4+OGH8d133+G7774DALRt2xbnn38+xo4d68rf\nla5tUHSc4CIiIiIiIiIiIiIiorT3z3/+E9u3b0dWlrepjYsvvhgXX3wxNm/ejI0bN6Jly5bo0qUL\nAgFTtKr0bIPcOMFFRERERERERERERERpr2fPngkt165dO7Rr165efadLGxTBCS5KCwnn3TImIDLk\nhTLm0vKWr8o15iTk5/KDvu5KbhnDOtiGHDh19eF5OWMurYBUT8+d4y3Plr4OtqFMyf9j6XmKordR\n8zx6PUDNYWRq07RcPBxtbI6Ine9IvqtczwsVtOScUVo+qWrpdTG+JdQcQwEpwZQdVPNe2bmRfDwi\nV13OkjdGQNuXTG9BOcVPSM33I+R79yvVMkd67lSoTYaqIo+DFerVNtVVkY9XeRvVdC/l59K2p7zt\n9Tv95ddMDzegv9Ze6fuWaT+U91lby20l7zKu3F3yuLXllPeZYTn9fSaUPEmm/Fzaa620qb4uQnp/\nuHJEIXa+KqXMla8q9nLy2PQMXEo7+o4grW6iubt8oX/WSNvCnNtKfyPH3r5q7q7Yy7l2Zo9xNPTP\nmiabk0tkRugRIiIiIiKqOXfn+Ts1JZnxizwRERERERERERERERHRH3gHFxERERERRSUA7V7I1PGr\nHyIiIiKixsrP83feKEbpgBNc5JuEwxAqjSShjbi6S/QmR+/h/FLBFaYvwe1mWaYkh3IYMO8hCU0h\nEeV2TPuLq00hjyX2ttfbVMKjGUINmsMXamOTQ7XpoQaVNvwnn+A4Qh1BSHoe0sJDBqUwYNUh7TWT\n9hGrWu3PkmLOCe3sSgQj/xDQ4u05VZEyWwsZKIcotLL0jY/YpC5EUO1PDlHoVEEtk6Inhiq00I1V\nUqhBLQyhHJawOqSVSdsw6HodpHCQWpn8mjXEj8DyaPR3vLyvO4aXxRKm95n2uhjen+p7Vz+OSPud\n0I+FcphOLfylEr5QC4VnCBko9y+0V0Zux/2ayaH39HCJQb1yVK5ju4g9llQwhWuM56uO/Fkg9INF\nKsjbLY7YHabPpSYbvpCIiIiIiIioAXGCi4iIiIiIonLgzvuXKswVQERERERUP47w8fzdn26IjJiD\ni4iIiIiIiIiIiIiIiDIK7+AiIiIiIqLoBO+sIiIiIiLKFMLP83d+T6A0wAkuSiIrOXm2XM16bdOQ\nB8qYS8v7jYzJWD99LGo+J1uvrNWNnb8q0Txfajve817FbkPPe+U9P5eJmh/He54t27icaX0NY5EK\n9Xpqm973l2S9c+STGNd5hpLDSS1Vc3CpZUEnsn2rtYEGQpG6cn4jALCkPFRC6LmCIjmGHC0nViBH\nypNUpbUZkJ5r/Rl3J0NqICGlYnKCWk6sKmmbhdSy6urIR2gwqHau5NnS8pZVO5HtIm9bAJA2pzsH\nlzJotUx/rZNxMhvfPmlFeVT7XN5HtEL55TS2Hvt9LaBvC1N+LidqvbqY8mwZj3dyFyL2ctDygSnb\nUzu+es1RZRwLoOalswxj0/tLQr4s/fU056+S10Mbp3EssZfTGlGfJ/jmMefnIiIiIiIiIqJU4AQX\nERERERFFJWCcIkx6X0RERERElDgHPH+npoU5uIiIiIiIiIiIiIiIiCij8A4uSj+eQxICic/RJhrO\nUK6o10tBeMYkkdcpnrCAekg/tSyx0IOm7WuJSJmNgFomhwETib3upjBnepllySHC1HZM28XzWAxN\nxNO6K5qWFbssKD3O0socKeRdUAt/F5C2d1BrtFoOsRdETHqIQrmZQEC9tsgJRZ5b6m4A25bC3dmJ\nXSskHC30n/RcaJHiQlJ4wZAWajAYjAyuWg9DKJdpYQiDSjjI2GWOHqJQyPXUcZqiqsUTcc1raM5E\n6e8dRwoz6XoPSuPWl4snvKDaphzmVd0w8jFH6BtNCuFnChmoH/vkcIb6MdNRyrTQmFFHH6UPV3Q9\n05J+0wZnGcIeytWMIRn1Y7/X6xLjWM4yHESbKAH/NgU3ORERERFR/fG8mpoS3sFFRERERERERERE\nREREGYV3cBERERERUVTMwUVERERElDmYg4uaGt7BRURERERERERERERERBmFd3BRw0g4mYv3OVnP\nubRMbSSa50Ubp5oDKzm5ulx9yDmq4tq+cq6pgKFegjm3DGV6TppEt42aS8t7m3KZaW8xteHKxCZV\ntfXcXT6kaXNiPNbpOZyylLxQWj4gKXhz0NG3r+F6HSknl56DS857pefgkp/bWp4tJQeXlWAOLsNY\nHC0/lzEHl7QtgnoOLqmsSs/BJT0PaasQMuTg0l8zmf5ap/pqLde+Lfetl0nj1selvrf0nFhyibf3\ncc1zOZef2qbXDFXufH3Sa6athdyfiKNM22rqcpacD8x7Xi3l2F9HrkL3eDz2IW8b/XNWyA+9ty+3\nKRK8BtCcu0sXe9trjcYua0JB7YUQ7rx0KevLl26IiIiIiBotP8/feQ8XpQPewUVERERERERERERE\nREQZhXdwERERERFRVEIAjk8XZvL6TyIiIiKi+nH8PH/nCTylAU5wUeokHIZQ5+1GQ3NIQkMIvXhC\nGSYh7KGxfyt2qC1X3Xj6UMIXxhHmMcHt5jVkoWUIoeUOEeYtDKFtXM77Pqm3o/TnQ6hBr/RzCfnk\nQj/RcJTwZWpZUKpsu0LjSdtQi+Zleq2VvvXnUpsBrb+AFO7PHaIw0lLyQhTa0mM9PKMUutEVajB2\nmRyWUA/rKC8X1Mci5DJ94FL4Qm3/1F9rZT9A+nC9d6TB6e85xzBy03teKOHuTOEL1b3SGAZRxD6G\nyqH49PeDUuYK5xd7OVMwRaUd/XWPJyygqR3LsE7G0H9eO4+9LVxVpbruvk1hHk3LxWrD3Y5hYLHL\n+C2PiIiIiIiIyBec4CIiIiIioqgE/Jso59QgEREREVH9+Hn+TpQOOMHlwbZt2zBr1iysWbMGubm5\n6NmzJwYNGoSsrORtvlAohOXLl2PRokVYv349AKBv3744+eST026sREREREREREREREREDYmzHgaV\nlZUYM2YMJk6ciKqqKqWsffv2eOyxx3DuuefWq4/HHnsMU6dOxZdffonS0lKl7NJLL/U8weXHWImI\niIioaRFgDH8iIiIiokzBHLrU1HCCKwbHcXDuuefinXfeAQAceOCBGDhwIEpLS/Huu+9i06ZNGDZs\nGIqLi3HFFVck3M/kyZPx2WefwbZt9OnTBwcddBBeeumltBxr3awkJSeKI0dUKnJiec7TZM6X5TdL\n2vZx5dmyAuHHprxTtse8Wu72vY/FRmQsfmxPS8nPZahnKNTL7CS8Beo6QVBzBQmtLFY9wJF+OQxq\nbcqprhw9B5eUM8r1cjreXqcsoeeMiuS5ceW9kgZja2dl8v5kJ3gq5c5fJeW2cuXnkvJsubaLlGfL\nUFat5+CS82w5+mskj0Udd1B5jdQy/bU2bRlTrqlknJzq7wEn9u6qvn/0MuVx6hPfqfm5AkpZyPWO\nkZYz5HqS29TzY8nHVMdVJu0HljoWIbyNRc8l5ffEgSkfmWlP019rkYS90pU3zXNOrgTzjekfDPzW\nR0RERERERJQSDfuLfBp74oknwhNGt99+O5YsWYJHH30Uzz77LH766ScceeSRAICrrroKP/74Y8L9\nXHvttZgzZw62b9+OZcuW4emnn07bsRIRERFR01J7Bagff5wLJCIiIiKqH7/O3Xn+TumCE1xRVFVV\n4e677wYAHHrooeHHtVq2bIlXX30VOTk5CAaDGDt2bMJ9nX322Tj66KPRokWLtB8rERERERERERER\nERFROmCIwihmzZqFzZs3AwCuvPJKJfRbrV133RWnnXYa3nzzTUybNg0VFRXIy8vze6gZNVazVMy1\nJiFsXoIhEPX2lVB4eptyaEFtzO527Jh14xhdHHUTDEtoKLOVdfA+FkvI4cNih4fU25Sfm0Iwuvoz\nhSX03EpyuGInW7HL5HBwekgyxzBwOTRe0BXLTNpHTZfnOHpIsshywlZDfTmhSFmWVib3YVt66Lao\nw4qPvl3kx0IPZRZ5HNTWLyQNQC+TQw+6whdKz11hDw2hImONWR+nXm6Kve1XXO5acYUCNYxNfi/r\nIRfV0KPq6yKHtRRCPxaHYo9NOY7o+4Ej1Ysdls8css8V+zPmWBLd8Y2fGYZtL6zYYRehh/ozhGs0\nD87QplzNGGownm3oVSraJCIiIiIiIqJk4R1cUXz88cfhx0OGDIlZr7astLQU8+fPT/m4osmksRIR\nERFRZhGoyYXm139ERERERJQ4P8/fidIBJ7ii+O677wAA7dq1Q8eOHWPW23///V3L+C2TxkpERERE\nRERERERERJQMDFEYxapVqwDUhPYzkctXrlyZyiHF5MdYt23bFrOsuLg4rraIiIiIKHMI4V84U1eE\nXCIiIiIiiovD83dqYjjBFcWOHTsAAAUFBcZ6cvnOnTtTOqZY/BhrmzZt4h9YnZKT28prm6bl4skD\n5X/2pcTUlcvL63Je20g0H5e7bmL5shIljyxa/rpktp9MjpKjSi2TTy70jEK2XKavr7yg6wRFel20\nsqBxoHLzWu4cKe9WyAkoZQFpALY2TtuQBMz0EppOuuRcV3reKznPlt6GnHfLnUsrdg4ux1Am5+AK\nav2ZxhLSnptezlSc6MqvbrKyFMnvSVtb4VRkQjLl9TKRj3ECsfNVucoMeafU46YhN5h+XFZe93TO\nF+U94ZqlvC5qPcuY8yv2XmleziQVezoRERERERERJYoTXFGUl5cDAHJycoz1cnNzXcv4LZPGSkRE\nRESZRcDHKzN5BSgRERERUf0I3llFTQsnuKLIz8/Hjh07UFVVZaxXWVmpLNMQ/BhrUVFRzLLi4mLs\nsccecbVHRERERERERERERERUH01mguvLL7/ERx99FLVsr732wtlnnx1+XlBQgI0bN6KkpMTYphzq\nr64Qganix1gLCws91rSRihB+XsPrJa/DxML5+T1OPaReov2bQgHaKQglaYkE25TGooeVtA2hDeW6\n8YWjjN6+e1x+hK0U2rPYoerkiHfu0HSRwpDQQ33JYfq05aSW9JB68oeIKVyhPhYhhSXUww6GlBCF\n+jilxwle6q+Hn5M3hR6iUK7rCl8oh3w0hCjUl1PL1LEp4RIRuz/3OBHzuWsfMS6ZfOp7RO1Pfm85\ncYzF9L42hRoUynJa2EyPIedcxzArspx+7PMa/k4/1jrSWPTjT+yAhdqwXMdhdSypvqIv4fCJruVS\nGwow0dcsviC0mX35pICI6/1Zv76IiIiIiKg+HJ6/UxPTZCa4Pv/8c4wZMyZq2WmnnaZMcO2+++74\n+eef8fvvvxvblMt33333pIwzXpk0ViIiIiIiIiIiIiIiomRoMhNchxxyCG6//faoZfvss4/yvE+f\nPpg1axY2bdqETZs2oX379lGXW7ZsWcw2/JJJYyUiIiKiDONjDH9eAUpEREREVD++5tAlSgNNZoLr\n0EMPxaGHHuqp7uDBgzFx4kQAwKxZs3DeeedFrTdr1iwAQLNmzXDEEUckZ6BxyqSxEhERERERERER\nERERJUOTmeCKx5AhQ9C2bVts3boVTz75ZNRJo3Xr1uHtt98GAJx66qlo1qyZ38MEkFlj9Sq+XFKG\nXE+mPFCe8yYlll9Jb18Zi547S84tpY3ZlecrwZxY8npYVsBQL54WvY3FlMfLhjqWxNcv+fzJrRVh\nyplkGoqeY8iRFna05eTMMrYhd5c7B5ecM0otDEpl+geKnJPLnSMq8i+Wlk8qYMXuz0rByyKU3ECx\n817p6xBScprpr0PkuZ63TN6+ei4tx9CfkitMK3M9N6yTiTD0n2ru91zDXXKmH4vkY1VIyzYnH+NC\nhtxSieb8crUjHcOF8JqRq+7xaIURrmOFlHNMb0PKXyXiev0MHSq19Jxq0nHEmEvLnI9M6UNqx3s+\nrsbNgWmLJRcvNCUiIiIiqh+ev1NTkz6/JqeR3Nxc3HbbbQCAzz77DOPGjVPKS0tLcf7556OyshKB\nQAD/+Mc/orYzadIkjBs3DuPHj0/7sRIREREREREREREREWUK3sEVw7XXXotZs2bhww8/xJgxYzB9\n+nQcffTRKC0txdSpU7F27VoAwIQJE7D33ntHbePRRx/FDz/8gFatWuGmm26KWufrr7/G+++/H34e\nDAaVMnnCKicnBzfffHNKxkpEREREFI3wKYi/X/0QERERETVWQgj/zqt5/k5pgBNcMQQCAUyZMgU3\n33wznnrqKXz++ef4/PPPw+WFhYV45JFHcNFFF9Wrny+//BJjxoyJWrZ48WIsXrw4/Lx58+ZRJ7j8\nGisREREREREREREREVE64ASXQX5+Pv75z39izJgxmDFjBn7//Xfk5uaiV69eOO6445Cbm2tcfsSI\nEdi8eTPy8/Nj1unbty9uv/12T+Mx9VffsfotvjxbshRE1YxjLOmUI8okFdvXtO7xbBevua0soefA\nSW1OrFS0r8c8ltconjxbek4s25iTK3Yf8lPHlWtKzmWjlgUNiZnkD5Gg1qac50tLNQUh9WFZaqNy\n3it9XeWqib5i7nxgEXpOLHV7xs7P5crBpeQtU/sLiuiP9eVCepnUh+u1NbzWOnV9DRX15Qx1UxHf\nW35POimI7K2/54V8zLFi57Zy54GKTT426jm3TGXq0cL71s2U/FFx5SOTP8+Stk7etq/pszSdt2+y\nCRHfsaJeffnTDRERERFRo8Xzd2pqOMHlQfv27XHBBRfEvdy1115bZ52DDjoIBx10UCLDiirRsRIR\nEREREREREREREWUKTnAREREREVFUDkRK7qKMhleAEhERERHVj5/n70TpgBNclDKJh8nTeWvH1J/X\nsHi1tRPpL74+6s/dv7ftpIflMoYeNG7T+ocsTHSb6e3L7eht2oYyf18x7+oKXyjfaq4HyZKr6mEB\nQzHqAYAlDOHgpHCCQVcktUhd/QNFDYOoh3WTQiLG7g62thJ6OEOlLGZJHSH7lHXXy+Q2tDCE0nJ6\nqEGZXhZ05P70NqO3r49ND6DnCruotKOWmUIVpGt+WNf+Kv2LK9Sg8T0vhwWMHYbQ3b/HzwVD6D1j\nmX6sFbGXs6XlTGvgOg7rYUKF9/VPhGubeQ6fqG9r03teCtup1fMerlH/vPIWepDhC4mIiIiIiIga\nHie4iIiIiIgoOuHf5He6TrITEREREWUK4ef5uz/dEBkl6xYbIiIiIiIiIiIiIiIiIl/wDi4iIiIi\nIopK+JqDi9eAEhERERHVB3NwUVPDCS5KGsuyYVnJyGrk/cbChPN8eVzOay4p13J6+5acE8aOWded\nW0qvm2DOKivgqZ6dgps6LeG9TT2XTlOi3D6u58oxLed6LuV30u5JV/JzGdoxZubR9kElJ5c2blvK\nlxXUmrENOZTkjWHraXwMG8P09jDdnq9uM1erkTKtxDHmuYqdn8sx9BeSc35pZcJQprcjlNxEsZlz\nkxkKGzl9nzTmupKPcVZyci/Jx2LHkBNKP7YLob/TYlM+T0zHaUNKLKGtr5LjLI48VGpuNMNyhlxl\nxva15bzn5Ers9XSfm4gm/X4iIiIiIiIiShVOcBERERERUVQCjOFPRERERJQpfM3BxRN4SgPMwUVE\nREREREREREREREQZhXdwUZpIQWi8FIS7Szgkou/iWff6h2uMZ7vY8BYuMdHwkOlMDiOnh95T6mnP\n3VtCSI/Uhkx9GMMQSoV6KEw5drM+bDncXlC7dCdLCe+nl8ltqGwrdgg/YxhL46VDsZczBSFzhyyM\nUEIPCitmmaP1LS+m9y2/niE9fGGMNqI9l8ftXoXYK+U1IJtpu2Qqr2Hy9GNYyBWAU2rTih2yz3NY\nPtcRwFQ3M8K8xhcy0GObrvdZMnbSeLY9EREREREREfmNE1xERERERBSVgPsihdT11Qhnz4mIKCOF\nQiHs3LkTrVq1SlKucbNt27ahsrISAJCfn49WrVp5XtbvsRJRehMQvp2/M8g4pYPGd4sEERERERER\nERFRHEKhEP75z3+ib9++yM3NRWFhIfLy8jB48GC89957Kev3119/RdeuXdGpUyd06tQJV1xxRdqO\nlYiIKN3wDi4iIiIiIopKCAHHp+zRTFJNREQNpaysDCeeeCLmzZsHoCZse8uWLbFjxw7Mnj0bs2fP\nxnXXXYdHHnkkqf0KIXDppZeirKws7cdKRJnB8fP83ZdeiMx4Bxc1EFv788aybOVPKdP+Uwtt9U9b\nUv3zOBZTfz6wYKt/MbZLXct5rRtPmS39l7yxRP7T1ty4XKoJ7T/vy6l/jvTnqivUP8fw53U5vUwe\nS0iof46wwn96mboOlvIXFAj/yW04wkLQkf6kekEBBJ3In75+rrrKn2X4i72c0r6j/SnjUsetrI/e\nprQd9Nc61rbVt6++nGkf0F9PmWl/MS6n/cljiUci749UkY8b8RzDvR6nbO2/WG3o7STruKzU0z4v\n4+kjFRL/vDR8Psf8XDf35/Xz0i3+8xYiIiLKDJdeeinmzZsHy7IwZswYbN++Hdu3b8fq1atxxhln\nAAAeffRRPPnkk0ntd9KkSZg7dy7222+/tB8rERFROuI3dCIiIiIiiqpmYtu//4iIiPy2YMECvP76\n6wCA66+/HmPHjkVBQQEAoFu3bnjzzTdx+OGHA0B4QikZfvvtN9xyyy2wbRvPPPNMWo+ViDKHn+fv\nROmAE1xERERERERERNQkPfXUUwCAvLw83H777a5y27bxj3/8AwBQVFSEyZMnJ6Xfyy67DDt37sSI\nESNw2GGHpfVYiYiI0hVzcFES2YgnxJ9X8YcQqmd/Cc77KuO01O3gtU1X2Cq9nQS3hdcwfqnY1n6E\nb2zoMIUyOUygneCw9Gtg9NBxwtCuUB5bWpmIWg9QQyNaWmFIeaZ3Hqns2nvk/VdbCbk/0+vnxHFF\nkGnvjRb6MSpt48rL6SEg1XrackIu0+pKfYSihJWMtZyI8bjmuf5ax6a0o/dvWM4r03bym75vhVJw\nhZl8jEtW68qxWMTee93rl2Af+t4mImXC8O7RP7OE5cQuM6yHsU3v796E6J97XscZ3zViafSmSEBN\nCFr/+iIiIvKTEALvv/8+AODoo49GmzZtotYbMmRIOM/Vu+++i8suu6xe/f7rX//CzJkz0blzZ9x7\n771pPVYiyiyx0l+kAs/fKR3wDi4iIiIiIiIiImpyVq5ciW3btgEA+vXrF7NeIBDAQQcdBAD46quv\n6tXn2rVrceONNwIAHn/8cbRs2TJtx0pERJTuOMFFRERERERRORC+/fEKUCIi8tsPP/wQfrzHHnsY\n63bv3h0AsG7dOuzcuTPhPv/2t79h+/btOO2003D66ad7Xq4hxkpEmUf4ev7OM3hqeAxRSERERERE\nRERETU5RUVH48S677GKsK5dv27YNBQUFcff38ssv4/3330dBQQEef/zxuJb1Y6y1d4hFU1xc7KkN\nIiIiP3GCi9JOPHmgjPmdjO00YE4qrc1Ec36Z+wgkv03DOJO1Dpaofzt+5PzySs9FZCspqdRCJYdS\nXKsQux29f7lZYzxmrf+A1I47d5c87tgJnYQrL51cL3Z+Lj0nlimvWaIxpr3mjNLzbJlyWam5u7Tl\nRPTHgJpDSR+XY1hOr6vvFYlw5efS/8HQf0NSc2IlNjDXsciKJ7uVPJbYuaxMZYmSj/1CBJPTpn58\nV45jyRq3tC2MbcbOAej6zBdyPrDY+QgTH0tTIozv/+R2lUYHEyIiahJKS0vDj/Py8ox18/Pzw49L\nSkri7mvjxo249tprAQD33HMPunbtGtfyfow1Vl4vIsocQvh4/k6UBhiikIiIiIiIiIiImhxLuhCv\nrh+E5XLbjv/ntJEjR6KoqAj9+vXDlVdeGffyfo6ViIgoU/AOLiIiIiIiikqgJg+XH1LVjxACy5cv\nx9y5czF//nz8/vvvWL9+PYLBIDp27Ih+/frhoosuwv/93//FbOOpp57CXXfdFVe/M2bMwAEHHBC1\nbOfOnXjuuefw3nvv4bfffkNWVhZ69OiBs88+G+effz6ysvg1jYioPjZv3oxQKPpd+G3btkV2djYA\noEWLFuF/Ly8vN7ZZVlYWfiwv58XkyZMxdepUZGVl4Zlnnklo0smPscphEHXFxcV15v4iooZXmx/L\nD7xPjNIBvzlRWvAaCjAV4efiCa+XTuHv3BIbm+3zjZxet6GdpG2d3q9ZdK7wc9oqyJEAjcG8tOXU\n8IWGEF36eKR/CGmLycEw3SH8IpX1NuW9zhi+UJeC2+z1cSvdGbp2DGXytnaFITSEfJTrGkMUGsIl\n6nVd4QsN+08mRjFwv8cTWwn5mGMKSOj3MUU/Rjuewxmm77EvrpCBqQjl6DGMpX5uwpCFmevmm2/G\n+PHjo5atWrUKn3/+OR577DFceumlePLJJ5GTk+OqV1paio0bN3ru07ZttGvXLmrZ0qVLcdppp2HV\nqlXKv//www/44IMP8NRTT+Hdd99Fhw4dPPdHRESqvn37Yu3atVHLFixYgMMOOwwA0L59+/C/b9iw\nwdhmbblt23XmwNKNHj0aAPDXv/4VHTp0MPZVUVERLm/ZsiWaNWvm21gLCws91yUiIkoHvE+ZiIiI\niIiiqr0C1I+/VM2xV1dXAwBatWqFK6+8Eu+//z5++OEH/Prrr3jrrbdw0EEHAQD+9a9/4ZJLLona\nxsiRI7F+/Xrj39y5c8P1jz32WHTu3NnVzsaNG3HSSSdh1apVaNmyJZ544gn8+OOP+PbbbzF69GgE\nAgEsWrQIQ4cODY+biIji1759e3To0CHqn3whw9577x1+/PPPPxvb/OWXXwAAu+++e505sHS1d1Q9\n99xz6NSpU9S/Wu+8807435588knfx0pEmc3f8/cMvEqWGh3ewUVERERERI1WixYtcPfdd+O6665z\nhWnq3r07hg4diuOPPx7/3959h0dR7X8c/+ymUELvEBCkiiioFAUVVIoooHCxgOIFEdsF9ad4bXDp\nWNCrcrEXEBsiKAJKbFzgCqIgIIqCNKWF0AOEhJLs/P4IWWbbZHezNXm/eOZ5dpkz53xndjI7s2fm\nexYvXqwPPvhA9957ry699FKXcmXLlnXeQe/L5MmTna99dZSNHj1au3btUkJCgtLS0tShQwfnvPPO\nO0/169fXnXfeqZUrV+qNN94IaowWAIC0evVqv8rVqVNH9erV044dO7Rs2TKf5Y4fP+6s8+KLLw44\nnho1aig3N9eyTMGTwqVLl1bFihUlSSkpKRGPFQCAeMITXAAAAAB8MCJ2D2i4sviPHz9eI0eO9DkG\nSXJysp599lnn+zlz5gTchsPh0Pvvvy9JqlSpknr37u1R5vDhw5o6daok6aabbnLp3CowZMgQnX/+\n+ZKk559/PuA4AACB69Onj6T81IXu6WMLfPLJJzpx4oRL+UCsXr1aGRkZllOB66+/3vl/9957b8Rj\nBRDvIvcMFxAL6OBCxNhsdp+T5XKmf9YF7a6TWy2uk39xBrI+stnOTGFik/3MFMA2dGV3m/xrz2Oe\nRds2w+6cEDiH22S4T4Zpcptnfuc+z2GcmQzZ3CYv7Zye8owzk9U898lh2JyTS8wWy+QZ7nG6tSdb\nyCdf28hRSJzm9TGvq8OwWS9nsf2sPgfz5+UeZyD7gdX+Y97vEDjzsc/9+Gd1zHY5thd6aubf8dsj\nNvfvXr/bC5L5O9FmC/671bq0fH6v+zwfcK/B9V8gsQX3HYxosPlxbnbBBRc4X2/bti3gNr755hvt\n3LlTktS/f3+v6aA+//xzZ9rBW265xWdd/fv3lyRt3bpVv/zyS8CxAAACM2zYMCUmJsrhcGj48OEy\n3AamPXLkiEaNGiVJatiwodebGE6cOOHslDp27FhMxwoAQHHCFTkAAAAAryL3/Fb+FC0HDhxwvi5T\npkzAy0+fPt35+vbbb/da5scff3S+dk+BaGaeZ14GABAeTZo00aOPPipJ+vTTT9WnTx8tW7ZMf/31\nl+bNm6fLLrtMW7duld1u13/+8x8lJSV51JGWluYcN2vKlCkxHSuA4i3/plXG4ELJwRhcAAAAAEo0\nc1rCNm3aBLTs4cOH9dlnn0mSWrRoobZt23ott379eklSlSpVVLlyZZ/1NWrUyGMZAEB4jR8/XpmZ\nmXr55Zc1d+5czZ0712V+6dKl9fLLL6tHjx5RivCMeIoVAIBwo4MLIWM7nYIoso0G156/KZkKTYvo\nZ/3m7eIxz/TePYVOqLan/+sb2c/PHsD2jXRsoeF6J4vDvL5uN7mYP/pA9jq3jBSWqeXMbTjc2ze9\nznNbLsE0M8/wPc99nRwu89z3bfM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          }
        }
      ],
      "source": [
        "if run_pre_sims:\n",
        "    sim_data = web.run(sim_antenna_params0, task_name=\"check fields\")\n",
        "    f, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 4), tight_layout=True)\n",
        "    sim_data.plot_field(\"field_xy\", field_name=\"E\", val=\"abs^2\", ax=ax1)\n",
        "    sim_data.plot_field(\"field_xz\", field_name=\"E\", val=\"abs^2\", ax=ax2)\n",
        "    plt.show()"
      ],
      "id": "1cf39d0e"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Next, we are ready to put everything together into an objective function\n",
        "to optimize.\n",
        "\n",
        "We start by writing functions to compute the intensity at our\n",
        "measurement point through a `tidy3d` simulation."
      ],
      "id": "c0652a94-ef18-436f-8e85-825ae03483c5"
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {},
      "outputs": [
        {
          "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\">10:24:36 UTC </span>Created task <span style=\"color: #008000; text-decoration-color: #008000\">'antenna_normalize'</span> with resource_id                  \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #008000; text-decoration-color: #008000\">'fdve-5da6b635-6108-41d5-9c22-46f996dc907f'</span> and task_type <span style=\"color: #008000; text-decoration-color: #008000\">'FDTD'</span>.  \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>View task using web UI at                                          \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-5da6b635-6108-41d5-9c22-46f996dc907f\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">'https://tidy3d.simulation.cloud/workbench?taskId=fdve-5da6b635-610</span></a>\n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-5da6b635-6108-41d5-9c22-46f996dc907f\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">8-41d5-9c22-46f996dc907f'</span></a>.                                         \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>Task folder: <a href=\"https://tidy3d.simulation.cloud/folders/9b36e144-ddb6-41f8-8dd8-30b62b26a870\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">'default'</span></a>.                                            \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"c58d6c7ead0849b59169f4536819d202\",\"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\">10:24:38 UTC </span>Estimated FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.563</span>. This assumes the FDTD solver runs\n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>for the full simulation time; if early shutoff is reached, the     \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>billed cost can be lower. Use <span style=\"color: #008000; text-decoration-color: #008000\">'web.real_cost(task_id)'</span> to get the  \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>billed FlexCredit cost after a simulation run.                     \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\">10:24:39 UTC </span>status = success                                                   \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"37cc098c7f764ad794b486b39bcb61ea\",\"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\">10:24:40 UTC </span>Loading results from simulation_data.hdf5                          \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Intensity without structure = 2083.5806 (au)"
          ]
        }
      ],
      "source": [
        "def extract_intensity(sim_data: td.SimulationData) -> float:\n",
        "    \"\"\"Grab the intensity from a simulation data.\"\"\"\n",
        "    return np.sum(sim_data.get_intensity(\"point\").values)\n",
        "\n",
        "\n",
        "def measure_intensity(\n",
        "    params: np.ndarray,\n",
        "    task_name: str = \"antenna_intensity\",\n",
        "    verbose=False,\n",
        "    beta: float = beta_project,\n",
        ") -> float:\n",
        "    \"\"\"Measure intensity as a function of design parameters.\"\"\"\n",
        "    sim = make_sim_with_antenna(params, beta=beta, include_field_mnts=False)\n",
        "    sim_data = web.run(sim, task_name=task_name, verbose=verbose)\n",
        "    return extract_intensity(sim_data)\n",
        "\n",
        "\n",
        "if run_pre_sims:\n",
        "    intensity0 = measure_intensity(\n",
        "        0 * np.ones_like(params0), task_name=\"antenna_normalize\", verbose=True\n",
        "    )\n",
        "else:\n",
        "    intensity0 = 2083.6917\n",
        "\n",
        "print(f\"Intensity without structure = {intensity0:.4f} (au)\")"
      ],
      "id": "082961ce"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "We then define a penalty function to discourage density patterns that\n",
        "have small feature sizes below the `radius` we defined."
      ],
      "id": "f1755b03-23ca-40e5-970f-0e670d57183a"
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {},
      "outputs": [],
      "source": [
        "from tidy3d.plugins.autograd import make_erosion_dilation_penalty\n",
        "\n",
        "penalty_fn = make_erosion_dilation_penalty(radius, pixel_size, beta=beta_penalty)\n",
        "\n",
        "\n",
        "def penalty(params: np.ndarray, beta: float = None) -> float:\n",
        "    \"\"\"Define the erosion dilation invariance penalty for Si density parameters.\"\"\"\n",
        "    beta_kwargs = {}\n",
        "    if beta is not None:\n",
        "        beta_kwargs[\"beta\"] = beta\n",
        "    density = get_density(params, **beta_kwargs)\n",
        "    pen_val = penalty_fn(density)\n",
        "    return pen_val"
      ],
      "id": "62ad656b"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Objective Function\n",
        "\n",
        "Finally, we define our objective function as the ratio of our measured\n",
        "intensity compared to the intensity with no gold film minus the\n",
        "fabrication penalty, which is normalized between 0 and 1."
      ],
      "id": "4a1408ed-b7a4-4726-bdf2-81d9c74079de"
    },
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {},
      "outputs": [],
      "source": [
        "# let's us grab and print autograd values while they're in the objective function\n",
        "from autograd.tracer import getval\n",
        "\n",
        "\n",
        "def intensity_enhancement(\n",
        "    params: np.ndarray, task_name: str = \"antenna_intensity\", verbose=False\n",
        ") -> float:\n",
        "    intensity_with_params = measure_intensity(params, task_name=task_name, verbose=verbose)\n",
        "    return intensity_with_params / intensity0\n",
        "\n",
        "\n",
        "def objective(\n",
        "    params,\n",
        "    beta: float = beta_project,\n",
        "    verbose: bool = False,\n",
        "    penalty_only: bool = False,\n",
        ") -> float:\n",
        "    if penalty_only:\n",
        "        enhancement_factor = 0.0\n",
        "    else:\n",
        "        enhancement_factor = intensity_enhancement(params, verbose=verbose, task_name=\"antenna\")\n",
        "        print(f\"\\tenhancement = {getval(enhancement_factor):.2e}\")\n",
        "\n",
        "    # penalty_value = 0\n",
        "    penalty_value = penalty(params, beta=beta)\n",
        "    print(f\"\\tpenalty val = {getval(penalty_value):.2e}\")\n",
        "    objective_value = enhancement_factor * (1.0 - penalty_value)\n",
        "    print(f\"\\tobjective = {getval(objective_value):.2e}\")\n",
        "    return objective_value"
      ],
      "id": "7b6e2dcc"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "We can use `autograd` to simply compute a function that returns the\n",
        "value of our objective along with the gradient, to feed to our\n",
        "optimizer."
      ],
      "id": "595219cf-8b76-4dbf-9922-64015a1bab35"
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {},
      "outputs": [],
      "source": [
        "val_grad_fn = autograd.value_and_grad(objective)"
      ],
      "id": "5bac9db8"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "We can take this opportunity to run through the function to verify\n",
        "everything, see our initial objective function value, and visualize the\n",
        "gradients of our objective w.r.t. the initial parameters."
      ],
      "id": "ec12451a-173d-4bea-9c70-f6759149fe87"
    },
    {
      "cell_type": "code",
      "execution_count": 26,
      "metadata": {},
      "outputs": [
        {
          "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\">10:24:42 UTC </span>Created task <span style=\"color: #008000; text-decoration-color: #008000\">'antenna'</span> with resource_id                            \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #008000; text-decoration-color: #008000\">'fdve-238557bb-c0cb-4b52-8065-8c822b24efb4'</span> and task_type <span style=\"color: #008000; text-decoration-color: #008000\">'FDTD'</span>.  \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>View task using web UI at                                          \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-238557bb-c0cb-4b52-8065-8c822b24efb4\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">'https://tidy3d.simulation.cloud/workbench?taskId=fdve-238557bb-c0c</span></a>\n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-238557bb-c0cb-4b52-8065-8c822b24efb4\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">b-4b52-8065-8c822b24efb4'</span></a>.                                         \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>Task folder: <a href=\"https://tidy3d.simulation.cloud/folders/9b36e144-ddb6-41f8-8dd8-30b62b26a870\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">'default'</span></a>.                                            \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"c12d8241a6e84c1a9196fdcd31d4765d\",\"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": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"c23ec72f9e484d969ddc9c7aa7067bd4\",\"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\">10:24:45 UTC </span>status = success                                                   \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"550e4be330394a7bb7a9a9090d7fdd03\",\"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\">10:24:46 UTC </span>Loading results from simulation_data.hdf5                          \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "    enhancement = 1.20e+00\n",
            "    penalty val = 9.98e-01\n",
            "    objective = 2.17e-03"
          ]
        },
        {
          "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\">10:24:48 UTC </span>Started working on Batch containing <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1</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\">10:24:51 UTC </span>Maximum FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.563</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\":\"00634bd8b8634e729c4b8ab98d653c8d\",\"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\">10:24:52 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>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"c8ce159877db42eea18899cc1e478e59\",\"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": "stream",
          "name": "stdout",
          "text": [
            "starting objective function value = 0.0021721132071279422"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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sWKFt27apffv22m233fxBizfffFOnnXaaJOnqq6/WI4884lr/p59+0p9//imp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\nPK7phhtu0PTp0yVJH374oT94IUlNmzZVQUGBduzYEbStmst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VrDhw/XGWecUQ6tt7eTJ09q0aJF2rx5s44cOaLw8HDV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\nRpmZmYqLi1N8fLxq1qypp59+Wvfff3+h4+njsvH2M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          }
        }
      ],
      "source": [
        "if run_pre_sims:\n",
        "    val, grad = val_grad_fn(params0, verbose=True)\n",
        "    print(f\"starting objective function value = {val}\")\n",
        "    vmag1 = np.max(abs(grad))\n",
        "    im1 = plt.imshow(np.flipud(np.squeeze(grad)).T, cmap=\"PiYG\", vmax=vmag1, vmin=-vmag1)\n",
        "    plt.colorbar(im1)\n",
        "    plt.title(\"gradient w.r.t. parameters\")"
      ],
      "id": "52bef49a"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Optimization\n",
        "\n",
        "Next, we will use Tidy3D’s built-in Adam helper to optimize this\n",
        "objective function with respect to our parameter array.\n",
        "\n",
        "Note that the parameters are clipped between 0 and 1.\n",
        "\n",
        "We will also visualize the density of the gold regions as we go."
      ],
      "id": "83ec995e-bb79-4e14-a52c-92abef6d5c58"
    },
    {
      "cell_type": "code",
      "execution_count": 27,
      "metadata": {},
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "step = 1"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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/+to8bbLX7yUjPzqeVfM/a6OOsUorzyRGdHEb5xDkOXHLAzAju9XvgK06AIBI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\nJDnB/xcAAAAASUVORK5CYII=\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "    enhancement = 1.20e+00\n",
            "    penalty val = 9.98e-01\n",
            "    objective = 2.17e-03\n",
            "    beta = 1.0000e+00\n",
            "    grad_norm = 1.0934e-02\n",
            "step = 2"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAU4AAAFOCAYAAADpU/RpAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90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\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "    enhancement = 2.33e+00\n",
            "    penalty val = 9.98e-01\n",
            "    objective = 4.51e-03\n",
            "    beta = 3.7000e+00\n",
            "    grad_norm = 2.4513e-02\n",
            "step = 3"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "    enhancement = 4.20e+00\n",
            "    penalty val = 9.97e-01\n",
            "    objective = 1.36e-02\n",
            "    beta = 6.4000e+00\n",
            "    grad_norm = 7.9026e-02\n",
            "step = 4"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "    enhancement = 7.29e+00\n",
            "    penalty val = 9.90e-01\n",
            "    objective = 7.31e-02\n",
            "    beta = 9.1000e+00\n",
            "    grad_norm = 4.5116e-01\n",
            "step = 5"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "    enhancement = 1.21e+01\n",
            "    penalty val = 9.61e-01\n",
            "    objective = 4.75e-01\n",
            "    beta = 1.1800e+01\n",
            "    grad_norm = 7.0327e+00\n",
            "step = 6"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "    enhancement = 2.01e+01\n",
            "    penalty val = 8.40e-01\n",
            "    objective = 3.22e+00\n",
            "    beta = 1.4500e+01\n",
            "    grad_norm = 2.8692e+01\n",
            "step = 7"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "    enhancement = 3.48e+01\n",
            "    penalty val = 5.08e-01\n",
            "    objective = 1.71e+01\n",
            "    beta = 1.7200e+01\n",
            "    grad_norm = 2.0053e+02\n",
            "step = 8"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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I2vnE+fT01NhfYp2IvI3Hn0xe/xtFokBkk/tik/trU01PwB/CBH8SJwAkUTgB\nIInCCQBJFE4ASNr5wSGR7Q7iAGjGEAaFFIkTAJIonACQROEEgCQKJwAkUTgBIGnvaUhDXQDQAhIn\nACRROAEgicIJAEkUTgBIonACQBKFEwCSKJwAkEThBIAkCicAJFE4ASCJwgkASRROAEiicAJAEoUT\nAJIonACQROEEgCQKJwAkUTgBIOn/zfSUeWo83BoAAAAASUVORK5CYII=\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "    enhancement = 6.64e+01\n",
            "    penalty val = 2.80e-01\n",
            "    objective = 4.78e+01\n",
            "    beta = 1.9900e+01\n",
            "    grad_norm = 4.8808e+02\n",
            "step = 9"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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2faMRfosBIBOFEwAyUTgBIBOFEwAyUTgBIBOFEwAyUTgBIBOFEwAyUTgBINPW\nrhzalOl0Wvlvba9iQj/UXRd11xOaQ+IEgEwUTgDIROEEgEwUTgDIROEEgEwUTgDIROEEgEwUTgDI\nROEEgEwUTgDIROEEgEwUTgDIROEEgEwUTgDI1IvCubOzs+mnAKAFOzs7vfh9Zz/Olu3u9uKzCj3B\n9bQZvOoAkGmQidOift92VO9DEwXt6+t10dfnvQoSJwBkGmTi7KIhf/pi87i+2kXiBIBMa02c8VOv\nb32MAIajyRTeaFO9r4M0m0BTC8/hGlld068VTXUAyNSbwSHSKzBcfUvTJE4AyEThBIBMFE4AyLQz\no9MQALKQOAEgE4UTADJROAEgE4UTADJROAEgE4UTADJROAEgE4UTADJROAEgE4UTADJROAEgE4UT\nADJROAEgE4UTADJROAEgE4UTADJROAEgE4UTADL9H0LHAGiF5WY/AAAAAElFTkSuQmCC\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "    enhancement = 1.16e+02\n",
            "    penalty val = 1.81e-01\n",
            "    objective = 9.50e+01\n",
            "    beta = 2.2600e+01\n",
            "    grad_norm = 9.5010e+02\n",
            "step = 10"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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JEwAykThnoOrKhbEA3s9NcbgHvDjH6QviYwE8V0RtVm87ziaGLb4BxwtwxdvV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\n66Xp0wAAAABJRU5ErkJggg==\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "    enhancement = 2.89e+02\n",
            "    penalty val = 1.09e-01\n",
            "    objective = 2.57e+02\n",
            "    beta = 2.5300e+01\n",
            "    grad_norm = 1.7137e+03\n",
            "step = 11"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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lMtBUB4BIrUuc4zLqUktLEzYA8PDhQy0sLEga3HNznDsfIU1uU91vlVi5sKb6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\ngEj/B66wWoUarDUSAAAAAElFTkSuQmCC\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "    enhancement = 1.64e+02\n",
            "    penalty val = 5.99e-02\n",
            "    objective = 1.54e+02\n",
            "    beta = 2.8000e+01\n",
            "    grad_norm = 1.8395e+03\n",
            "step = 12"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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zXFzZxy5aTZcGBT2sAIRVcv/oo48kDZKlmdvsrqIzi/y5zsXFxey+Wzt4+PCh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\nCQCR/g+vBsPHQaHiQwAAAABJRU5ErkJggg==\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "    enhancement = 2.06e+02\n",
            "    penalty val = 3.36e-02\n",
            "    objective = 1.99e+02\n",
            "    beta = 3.0700e+01\n",
            "    grad_norm = 2.1638e+03\n",
            "step = 13"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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TvPJNetybIIrMobocM009qCaum5YlZBOnH/93/vz5JAzJihVbIeK0mo8QJ27N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\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "    enhancement = 3.45e+02\n",
            "    penalty val = 1.99e-02\n",
            "    objective = 3.38e+02\n",
            "    beta = 3.3400e+01\n",
            "    grad_norm = 1.0689e+04\n",
            "step = 14"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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9Z4ol5Cw52k6ltG2Wy8vLQ81tIn3+ffPnOpeXlzfdd0m6c+eOpM15nbGrw8ee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\nSUVORK5CYII=\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "    enhancement = 5.80e+02\n",
            "    penalty val = 1.40e-02\n",
            "    objective = 5.72e+02\n",
            "    beta = 3.6100e+01\n",
            "    grad_norm = 4.3775e+03\n",
            "step = 15"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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01sqBlYuxsTFJa1sgoZY593sZIXECgKeoE2eqZwdthTvxeWJiIu/TKg4KFf9t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\nEKvxjecBJPIAAAAASUVORK5CYII=\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "    enhancement = 6.01e+02\n",
            "    penalty val = 1.20e-02\n",
            "    objective = 5.93e+02\n",
            "    beta = 3.8800e+01\n",
            "    grad_norm = 4.1281e+03\n",
            "step = 16"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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11dWeZZ3Oqdtq/45us5OmT9WL6vp+4N0HAE+VJE5SZq5bqcnQ0JD3/Zu9/t71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\nHeKy4AAAAABJRU5ErkJggg==\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "    enhancement = 6.31e+02\n",
            "    penalty val = 1.21e-02\n",
            "    objective = 6.23e+02\n",
            "    beta = 4.1500e+01\n",
            "    grad_norm = 2.6477e+03\n",
            "step = 17"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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EuZley5BIntVG4gQATyTOgsXPj+nlLJk8k2OWKTPUbeV85zHTJs807zN5X3Dm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\nRK5CYII=\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "    enhancement = 6.35e+02\n",
            "    penalty val = 1.40e-02\n",
            "    objective = 6.26e+02\n",
            "    beta = 4.4200e+01\n",
            "    grad_norm = 3.8932e+03\n",
            "step = 18"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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0RJ4/DHl1gmUN2RuNxqb/z3obw2UCqFfHl2YYn1fb0mH6g6E6ADgicQ6QXumv\n6K9HRZNjWmmfp1tSTbLyx3UY3+sxJMbBQeIEAEckTk8kLYDvpFsaLOJrUXmlyzzFvaden3G3e5xJ\nJn6azWaqr3UTLYBH+WgJAHBE4qy4fidNH5Oli07vPy7Ndbs3WcTXUB0kTgBwROIsWREbN3RKjMOa\nMpMI/xuj6TPpfc/o1/NKl3EbwqBcdJyeCP9w5b0m25cOsx8bHefxy8f+3a7Dd/t6p8417X6cnf4f\n5eFXFwA4InFWVNblkHFfyythlnmERppd2zvptvQz6wQQk0TVRuIEAEckzpLF7Y6URtadi9Kmzazp\nsogdj5K8RprPutFodJw4Snq8cJrXZXck/5A4AcARidMT/dhWLs/7mmVtOefy3EXcY+w04x73fGwr\nN7hInADgiMRZkrj0UFSiyCtp5r3tXNHy2hYuTrfkmXc79vNaQTJ0nJ7I4wchSceVd4dZ9tHBJunk\nTK/Hu3Z83Yrlo6+b1woilI+hOgA4InGWLOthbS5p0DVtxj133gfA5cW15CjvNebh5JnX7kgc1uYv\nEicAOCJxeqysXXDSbBaS5Ov9lvVEyrKWRbL7kf9oIQBwROIcQGnvbea9LV0ej0+qyFl1l+QZXpbJ\nRh6Di47TE/V6vdQfMNeJIN8miZJ0inGPd5nAKaJGMwk2MPYPLQEAjkicAyJtqisiaZY9SZR1Uqjb\n17IMv8tKrMgfiRMAHJE4K8YlzfXzzKB+7cuZNun1+v48J3KSLMMs4nXRPyROAHBE4hxSLvc2fSpH\n6vT9SRNbXqdUkhSHG4kTAByROAdIljRHHWfvr6WdFSedDh46ziFT9o5F/XzdfnRUdIrDiaE6ADgi\ncXrMylpGRka2fK1bmnMpQxrEAniTJA0WWQDfrSyp2/PkXUaG/JE4AcARidMTjUbDm6TWSdX24zRZ\nk2fZ7L2RRP1B4gQARyROD+VVnN5PPi+5DL9G2YmyW6lTp8fCP3ScQ8SnoXZeuzn5UnLk81Af+WOo\nDgCOSJweYWiGOFwX/iFxAoAjOk4AcETHCQCOak1uoACAExInADii4wQAR3ScAOCIjhMAHNFxAoAj\nOk4AcETHCQCO6DgBwBEdJwA4ouMEAEd0nADgiI4TABzRcQKAIzpOAHBExwkAjug4AcARHScAOKLj\nBABH/w+5sMXnE1FswAAAAABJRU5ErkJggg==\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "    enhancement = 6.47e+02\n",
            "    penalty val = 1.64e-02\n",
            "    objective = 6.37e+02\n",
            "    beta = 4.6900e+01\n",
            "    grad_norm = 5.2340e+03\n",
            "step = 19"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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lSSTOcNACAOCJxFmTZI3m2NiY02p6L2UmxjyptKok6cr18y2tZa2cu6TJQcx/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\nJRWlKWEAAAAASUVORK5CYII=\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "    enhancement = 6.25e+02\n",
            "    penalty val = 1.68e-02\n",
            "    objective = 6.14e+02\n",
            "    beta = 4.9600e+01\n",
            "    grad_norm = 8.5529e+03\n",
            "step = 20"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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li3jijF+TPErRonSXVFl0yF40PRZR5L2KJrV4usxLmj4LSXnvlyyEt8TJUL15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\nnADgiY4TADz9H2LwK1DLhnDhAAAAAElFTkSuQmCC\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "    enhancement = 6.30e+02\n",
            "    penalty val = 4.17e-02\n",
            "    objective = 6.04e+02\n",
            "    beta = 5.2300e+01\n",
            "    grad_norm = 6.5192e+03"
          ]
        }
      ],
      "source": [
        "from tidy3d.plugins.autograd import adam, apply_updates\n",
        "\n",
        "# hyperparameters\n",
        "num_steps = 20\n",
        "learning_rate = 0.01\n",
        "\n",
        "beta_min = 1.0\n",
        "beta_max = 55.0\n",
        "\n",
        "\n",
        "def plot_density(density: np.ndarray, ax=None) -> None:\n",
        "    \"\"\"Plot the density of the device.\"\"\"\n",
        "    if ax is None:\n",
        "        _, ax = plt.subplots(figsize=(2, 2))\n",
        "    arr = np.flipud(1 - density.squeeze().T)\n",
        "    plt.imshow(arr, cmap=\"gray\", vmin=0, vmax=1, interpolation=\"none\")\n",
        "    plt.axis(\"off\")\n",
        "    plt.show()\n",
        "\n",
        "\n",
        "# initialize adam optimizer with starting parameters (all combined)\n",
        "params = np.array(params0)\n",
        "optimizer = adam(learning_rate=learning_rate)\n",
        "opt_state = optimizer.init(params)\n",
        "\n",
        "# store history\n",
        "objective_values_history = []\n",
        "params_history = [params.copy()]\n",
        "beta_history = []\n",
        "\n",
        "# optimization loop\n",
        "for i in range(num_steps):\n",
        "    print(f\"step = {i + 1}\")\n",
        "\n",
        "    beta = beta_min + i / num_steps * (beta_max - beta_min)\n",
        "    beta_history.append(beta)\n",
        "\n",
        "    # plot the densities, to monitor\n",
        "    plot_density(get_density(params, beta=beta))\n",
        "\n",
        "    val, grad = val_grad_fn(params, verbose=False, beta=beta)\n",
        "    gradient = np.array(grad)\n",
        "\n",
        "    # outputs\n",
        "    # print(f\"\\tobjective = {val:.4e}\")\n",
        "    print(f\"\\tbeta = {beta:.4e}\")\n",
        "    print(f\"\\tgrad_norm = {np.linalg.norm(gradient):.4e}\")\n",
        "\n",
        "    # compute and apply updates to the optimizer based on gradient (-1 sign to maximize obj_fn)\n",
        "    updates, opt_state = optimizer.update(-gradient, opt_state, params)\n",
        "    params[:] = apply_updates(params, updates)\n",
        "\n",
        "    # clip the parameters between 0 and 1\n",
        "    np.clip(params, 0.0, 1.0, out=params)\n",
        "\n",
        "    # save history\n",
        "    objective_values_history.append(val)\n",
        "    params_history.append(params.copy())"
      ],
      "id": "c86f872a"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Analyze Results\n",
        "\n",
        "Let’s grab and evaluate the final parameters, since we exited the loop\n",
        "without doing this."
      ],
      "id": "5b56d17f-3aec-4cb1-9fdf-0a709655aff5"
    },
    {
      "cell_type": "code",
      "execution_count": 28,
      "metadata": {},
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "    enhancement = 6.57e+02\n",
            "    penalty val = 9.74e-02\n",
            "    objective = 5.93e+02"
          ]
        }
      ],
      "source": [
        "params_final = params_history[-1]\n",
        "beta_final = beta_history[-1]\n",
        "objective_value_final = objective(params_final, beta=beta_final)\n",
        "objective_values_history.append(objective_value_final)"
      ],
      "id": "e86f1690"
    },
    {
      "cell_type": "code",
      "execution_count": 29,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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vzv1C362dpxJ7SblrGtYL0/3Dfq9xg36nekF1Ta4QAFBTEEYBAAAAuGgpGel6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\nSk5OrvD6wIEDNW3aNPXr10+tW7dWt27dFBYWpsLCQu3fv1/r1q3T6dO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6dOdxPHfsAQAA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          }
        }
      ],
      "source": [
        "plt.plot(objective_values_history)\n",
        "plt.xlabel(\"iterations\")\n",
        "plt.ylabel(\"objective function\")\n",
        "plt.show()"
      ],
      "id": "73706792"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "We can also generate a figure looking at the final fields and density\n",
        "pattern."
      ],
      "id": "1fac2ed0-6e24-4a25-a0e6-2b817b02ce95"
    },
    {
      "cell_type": "code",
      "execution_count": 30,
      "metadata": {},
      "outputs": [
        {
          "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\">10:56:25 UTC </span>Created task <span style=\"color: #008000; text-decoration-color: #008000\">'antenna final'</span> with resource_id                      \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #008000; text-decoration-color: #008000\">'fdve-4cb20098-92d2-43fd-931d-c901da303c96'</span> and task_type <span style=\"color: #008000; text-decoration-color: #008000\">'FDTD'</span>.  \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>View task using web UI at                                          \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-4cb20098-92d2-43fd-931d-c901da303c96\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">'https://tidy3d.simulation.cloud/workbench?taskId=fdve-4cb20098-92d</span></a>\n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-4cb20098-92d2-43fd-931d-c901da303c96\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">2-43fd-931d-c901da303c96'</span></a>.                                         \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>Task folder: <a href=\"https://tidy3d.simulation.cloud/folders/9b36e144-ddb6-41f8-8dd8-30b62b26a870\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">'default'</span></a>.                                            \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"24d2317b52ad4f71ace8b0fe1349d3eb\",\"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\">10:56:28 UTC </span>Estimated FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.563</span>. This assumes the FDTD solver runs\n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>for the full simulation time; if early shutoff is reached, the     \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>billed cost can be lower. Use <span style=\"color: #008000; text-decoration-color: #008000\">'web.real_cost(task_id)'</span> to get the  \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>billed FlexCredit cost after a simulation run.                     \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\">10:56:29 UTC </span>status = success                                                   \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"cb08d8b4ef404d228746e7064310bb8e\",\"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\">10:56:30 UTC </span>Loading results from simulation_data.hdf5                          \n",
              "</pre>"
            ]
          }
        }
      ],
      "source": [
        "sim_final = make_sim_with_antenna(params_final)\n",
        "sim_data_final = web.run(sim_final, task_name=\"antenna final\")"
      ],
      "id": "29cb1fa5"
    },
    {
      "cell_type": "code",
      "execution_count": 31,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
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ZM0mpUf32hjGU8r5N6Yf+HDhwoN2yvLy8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\n/PHHzfdfffWVqlSpoqZNm+o///mPpNRtGjFihN2hetNzZVvZt2+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EEEJIC7FW462TFAnlS5OO1157DYcddhgeeOABKKVw1FFH4aKLLsK8efOyfR566CF85zvf\nwa233jqGPSWEEELIaPPd734XV1xxBQDg2WefxbPPPtvvMRtssAFFMhOESCrQyWSfXACTTxLyBTIa\ncNxk0jKlAiiYGreZVDQToOSJZdLHBxvFZBCoEBC7DiBXaCSuMhqBjfcxAq1VJtywziYCk0QuFaOW\ntLsMG7ek4TvJlIMYpVKMUluMoEMQdGrotewfhdXsaXnE0ngUyKRobfsXxVBRDFWNoCtWIBJUehH0\nGZQqMUrVGOUoRiXW2Rjk45IPli483hnJo5ZEfFcZwF6XVETjCmTiRKSS+sTEKkaMKItUipGKZHJx\nTIxqjSjG7mOFMakgxhTKvclrdVxksuNkcjvJGFEwLXo+b+U7B9I6brjhBhx33HFYsWIF5syZg69/\n/es45ZRTvH3+v//v/8PChQtx1FFHjVEvcyiSIWSK8z//8z+4//77oZTCf/zHf+BTn/oUNthgg7Hu\nFiGEEEIIIYSQCcinP/1pPPDAA9hwww2xfPlyXHPNNfjDH/6A3/zmN9h+++3HunuEEEIIaRGnn346\nLrzwwmx9xowZmD9/PkqlUtPjXGEtGd94ooFkWalcDGLgxC6JFcSkshmT7KsSgYKGzgQz6bqIlUME\nqpQ5y+R1a2ilE/cYW78rYdCiYJRClDjKKAUYKM81xhVr1ENDoAsuMqG2B4TaIExFMu0G4XRAd4ZQ\na7Xbg+fMBNaeA1lvvfErkEnRGrLeelDVKtBXgeq1jim6N0LYU4HpMyj1xQgrMUIdZGOQjomNXRKk\nQVn18KKtEuEMACtXEUEkJhPSJHKYpDwXyERJtJLACmIAZM4xsVQzcYzrFiMSZ8IXQZzdQ8Ypz/ro\nOczUimUmu0iGkOGwbNkyfOxjH0NfXx8222wz/OMf/8Cpp56Ke++9F1dddRXK5fJYd7EGimQImeLc\neeedAICTTjoJ3/jGN8a4N4QQQgghhJCxRKDo7kKGzPLly3Hdddfh8ssvx/HHH4/ly5fj05/+NH72\ns59hn332wf/93/8xYokQQgiZAvztb3/Dd7/7XQA2PulrX/sadtxxxzHuFSGEkEa08l0A3zlMPq6+\n+mrMmjUL99xzDzbZZBPce++9+PjHP45rrrkGK1euxK9+9au68UtjCUUyhExxVq5cCQA45JBDxrYj\nZMLgfn1pIrQfG4p5xs2mAkxgpshptgR36Ib31VzqLgK110c5vqNSKDQmn6XQJJ7bErs7FDNxK06D\n3V5JoN/01kvBkmz5VZnllT22Ip+9tcO1b3hl6+w9xBtvGANdHK9mZe76kmtXeGWPrZiTLb9aXemV\nrYqWeOvdffl49VX8saxU83GuVv1rEMd+dnFsHJtX489GcWenNDtHABDjlo/ODz9/pYwM/f4MTxbG\n+YmO794RMvl49tlnscUWW+D4448HYKN8f/rTn+Jtb3sbPve5z2G//fbDvffeO8a9JIQQQsho87vf\n/Q7GGOy88864/vrroce7kwYZErGpQFTsucekLxXcbXmEUh5mo6CT7ZF1jUlcZdLYJHFimCCAKAOT\nOscgdagpIVKR5yaTxsVEMDaGSWkYCERUEq+UdzP9Q72Rxu9CFJJIIQWEWhBqewalwKBcihGWDIIO\ngZ6uoWa2AWtNswfOngmZNxcYZ38UbkhbG2TeXKg13cCaHgCA6qlCr4kQ9BiE3fZ8S5FBGNsxCLVA\nGyTSigYOMkAWcWXHXJLrYTdaVxmBJDFLuVeMbaPoIhPDOsZEqprUaWAkhkHVi1Uquse4zjH1HGMa\nxS+524zENdsJIZa///3vOOWUU7DJJpsAAN7xjnfg4YcfxuGHH47//d//xVFHHYXrrrtubDtZgCIZ\nQqY4m266KQAgimgVRwghhBBCyFQntcFuZXtk8qC1xvz582u2n3HGGViwYAE+/vGP433vex++/OUv\nj0HvCCGEENIq0omZBx54IAUykxgjEQSSRCkVrrMgE7woZUUHWfQSrHBGZUIGK5jRMJCknlQwI8oK\nbESMPT7RYmgEibKlVihjyxUMFCIIlAiMEhipjVuqlUPkKIUkSsiJW1KpQMQgCAzCNoOgA9DTQ6jO\ndmB2p+3vnNmQOXMHPaZjicyZC6zuskIZAGpNH/SqPgRrKvY8e42NmUrGwI9baj6HxqAQt5ReBwiM\nCKJUPAODCDFiZQUpRYFMrKIsXglAFrEUI8rEMcVYJVcYI2LqCmKKMUzeuEhtNNNkpL+fh5Fui0wu\n6r0LmD17Nm699VZ8+MMfxg033ICTTz55jHpXH347IWSKc8wxxwAAbr/99jHuCSGEEEIIIYSQiczW\nW2+NZ599tm7ZMcccg2uuuQavvPIKPvOZz7S4Z4QQQghpJZyYOTUwUs0/pvYTS+R9jHE+yXHWocOu\nx5IfY6RqXUPECiBSB5E42c8gRqzsdgMDo6xbiCj7SR1JRKxLSepYYmCFAP2J9VO9h0YilAEQKJMJ\nQ0pBjFI5RthuoDs01IwyML0NmNkJzOyEzJnTpPbxi8yZk50DprdBzShDd2iE7QalcoxSEGdjECjj\njQ/Qv5urJEIMkznKILk+dj1KrmH2X7JcFMhIUkOMaiaQiVFN7qMov0+kasVcYpx7Nb8Pa+/ROvey\nc58TQuqz/fbb48knn6zZ3tbWhuuuuw4f/OAHcdlll+GWW24Zg97Vh04yhExx9txzT3z605/GJZdc\ngg984AN473vfO9ZdIhOI4pfe8SYAHrn+jfczdRmZvtZGOo3roK1xTjEGyF0rXq/Gev2i02cM90WT\nr3tWKn9oC7T/da9S7fXWeyqrsuXlwVKv7IVVndnyPYv9h/sPLbrV79CRB9Ttt+1Pfp7DyR7t7c37\n3ixeCQDE6V+x7y+s6suWl4t/zu54AP54xZH/MBw56zXxSrH/IlBMrZVrvfXalzTFDfz5Gzr5fThy\nCUETKcxnZPo63s94vPdvImBn9XEkydCYOXMmdt11V9xxxx3Yd999a8qPOOIIxHGcTdYghBBCyOTk\nkEMOwVprrYXf/va3Y90VMooYE0Ep+56ixkkGyJxilDgRSul+YqBFQyljtxWcYIwCtACxqkKJQaBK\niFFFgBIAWCcRZd1qJBFU6OR/07btdpWJMtLIpaTDiauJeO893SchDUApgYLkTjKBPScdCILQQJcA\n1a6hOkpA5zRI5wx7cGcnJiSdndk5qM5pUB1roNo1dMnY8w3yMQgiOyYKAqWsHxBQ5+10Ms5Z7JJI\n7uiTCZcku47psi03mSDGFcjEyJ1k7LY8Vqmec4yIKcQu+e4wUtju93+qOMmoLK6sFW21imXLluHG\nG2/EI488gtdeew2zZ8/GZptthoMOOgg77bRTv8e/9NJL+MUvfoG//e1v6Orqwrrrrov9998fBxxw\nAMJwYDKL8VLHaPLBD34Qe++9N84991wEQeCVhWGIa665Bh/60Ifw61//eox6WMvYjxohZEypVCo4\n55xzMG/ePBx66KE49thjcfTRR2PbbbfF9OnTmx5bLpdpl0kIIYQQQgghJOO//uu/8PLLLzcsP+qo\nowAAixcvblWXCCGEENJiZsyYgR/84Af4yEc+gnPOOQdf+MIXxrpLZBQwEkMns1CK4gIFbSOSlBWx\nKJWsSxrBFCCGjVDKxDJJ7JI93kCgrShGAbEgE8oAQICSFU4oAyUxFHSynIhYlIIRK+BII32MSpU4\nVpTRbJpFGiEEIIkUEgRaEOgkbimIEZQEuh1QbQEwrQxMnwakIpmJTHoO06cB08pQbQF0e4SgJPa8\nkzEIdDIuiVDKHbNGmEQFlf0r4shgJHeRUblIxiCGUfleqasQAE8gkznMOJFKrjjGFbukx6f7eP82\nmMRoJrlIZrJRrVZxzjnn4JxzzvEmXqZ88YtfxLvf/W7cddddDes455xzcNZZZ6Fa9SdOfve738VO\nO+2En//859hmm22a9mO81DHaLFiwAJ/97GfxyiuvYOONN64pL5VKuPbaa/GFL3whc5sbayiSIWSK\ns//+++N3v/tdtn7JJZfgkksuGdCxd911F9797nePUs8IIYQQQgghrSaZB9jCFulaM9nYfffdsfvu\nuzfdJxXKEEIIIWRyEkURDjvsMCxatAgnn3wy/vCHP+Ckk07C2972NsyaNctznC1SKpVqZqGT8YmI\ngTG5k67rJuMJYwqCGcCKYFTi+pK6xiQFaQWJOKaaCWVEdFYuiGFEQyld4yZjCWAgKN5JZpAGvWmc\nUKAEGrkgJAgEumSgSgqqPQQ62oCOdsj0iS+SSc9BdbQDHW1Q7SFUqWLdZAJHFJOMhxu3NBAaXYNU\nOJNey3Q5dZExEltBTOIWY8vrC2Rc4UsqkEnFMb6jsy+Mae7+3NgBfHLQyncBo9tOpVLBkUceiRtv\nvBEAsMcee+BDH/oQNtlkE8RxjKeeegq//vWv8cILLzSs4+yzz8aXvvQlAMCuu+6K448/HnPmzMED\nDzyASy65BI8++ij23XdfPPjgg1hvvfXGdR2t4tRTT21aXi6Xcf7557eoN/1DkQwhhBBCCCGEEEII\nIYQQQggZEb7yla/g7LPPztZvueUW3HLLLQM69utf/3r2B0EyvhGJoFTorLsiggZOMq6cQiFzlxEV\nQEEjSP9smUYvKesmogUwymRiGqN0HqlUcJMBkLjIJO4joiEqifjp52/zqROKTnZNBSBawXOS0Vqg\nA0CVFdAWAm0lSEc70NExtMEcTyTnIB3tUG0loC2EKivoQKCdMbBOMvn4KOTL/ZHGLQnExi85UUtG\n5SKZootMGqfkxiZlkUyOQCaWKCuviV8Sg2ZOMmjgJCMS1d1Oxh9f+MIXcOONN0IphQsvvBCnnXZa\nzT5nnXUWXnzxxbrHP/300zjrrLMAAAcffDB+9atfoVSyUW9HHnkkDj/8cLz73e/G4sWL8e///u+4\n5pprxm0dpDEUyRAyxTnjjDOGPItvq622GuHeEDLCFGelyCCnCkwQ3NOcpKc4ikidJYtqiXLeb7XZ\n9TOFBzRt8v4Z5T+kGZPPk4ljvyyOfVvGatSXLXdHK72y17AiW35y5QKv7IW7/bk4mxzRuPMdI/SC\noL29PVvu7u72yqQweG7/nlzpl70W5+dVPGd3PAB/vIpj6c6WcpcBQArTYow38wT+vmP8gys1d78L\nHR4GQ5PJkJOHKXGSUxvB4GdXDrc9QgghhBBCCCGEjB1GWvcWcDTfOTz66KP4zne+AwD4zGc+U1cg\nk1IvFggAvvGNbyCOY5RKJfzgBz/IhCkpe++9N04++WR897vfxS9+8Qt8/etfxxZbbDEu6yCNoUiG\nkCnO+9///rHuwpB59dVXcf755+Omm27Cyy+/jCAIsPnmm+OII47A6aefjhkzRsbacCTaaVVfCSGE\nEEIIIYQQQgghZCw57LDDsMEGGwzp2P5iG0ebnp4eXHTRRVi0aBGeeeYZ9PX1YcMNN8TBBx+MM844\no+EfVceinVb1tRFBKFAqblAaN52AJkgmEaURTQLAAPlUpfxYN8YpjerK05k0IPn2rD4IVBLHJMlx\nWnQ28cPWqaGgbB1KQyPInG60Cm2JhNAqRIAQoZSgkz+rhhIilBAllBCqLrSpHpTUYpT1AwCA9lCh\nPVToCBSmB4LOErBW2WBuW4QFM3oBAGuv14POHddC+J7dEK6zLsqlEsJSiCCwbQSBhtZ6QH876Orq\ngjEGcWyySV5RNUKlWkW05J+I7noIqx97E6+/2oHXuuwktOV9Id6saKyuAmtihZ5Y0BvZDwBUjKAq\nBn0SIxJBFREi1YsomaxnECFSVcSIYCSCUREEApO6uCQxSZDUCcZeZBGTzSAzykDEhvyIGIgy9tp7\nk82seiOP6qqdcOa7GDll7i2Y7qP8zd4E1CbTOJQWRI1udzJu+N73vgdjDNrb2/HlL3950MdHUZTF\nNB1wwAFYf/316+533HHH4bvf/S5EBL/85S/xn//5n+OuDtIcimQIIROS3/3ud/jABz6AFStWeNsf\ne+wxPPbYY/jRj36E22+/HZtvvvmYt9OqvhJCCCGEEDJcpKU55GQy8cc//hGnnHJKS9rae++9cfHF\nF7ekLUIIIYQMnt122w277bbbWHdj0Lz88svYb7/98PTTT3vbn3vuOVx00UW46qqr8Itf/AIHHHDA\nmLfTqr42wxcm1EbUDMgsQhquNN3cvymv4x5dd1+ps10ABM4x+Q5WVOPX6UZHZSIdL04qF+QoAEoF\n0EojCKwbRPmxDrTfOQOzLl2FLYItcPDGHTj0F2/v78QGzP9+9GHc8mIPno2fxcreV9Fb6UIl6slc\nk00WReRcS29Q0hgi14nbFAxmVeE+UE55jKI3iS2rfd4s1tmMQRncykg829pr6p/n5KOV7wJGqx1j\nDK699loAVlgye/bsQdfx+OOPZ3/L22effRrut9NOO2H27NlYsWIF7rnnHk+cMl7qaBVnnnkmbr31\n1pa0de655+J973vfiNRFkQwhZNB87Wtfw5o1a3DuueeOSfvPP/88Fi5ciJUrV2K99dbDJZdcgn33\n3ReVSgW/+MUvcMYZZ+Af//gHDjzwQPzlL3/BtGnTxqydVvWVEEIIIYQQQsaSVatW4dFHH21JW+us\ns05L2iGEEELI1KFSqeDggw/G008/jba2NnzrW9/CMcccg46ODtx111045ZRT8OKLL+KII47AQw89\nhG222WbM2mlVX/tDJEY9cczoUkeMk2k4GitniqIXi64TgZ3HaadlSulEIOHuG0AQZ/vlghm7TVnr\nk+TYGAINpQygA6gkQj2SXsRSQsV0YVXQg1d6ZkDfdCewcP+G5zEQ9E13AgBe6enEKvSgYroQSx8i\n6YUxUeb0YkycnGMqhkn+rYmHN44IKL3uKco7VilVEB+5QqOioMYer1Qz0VMqNHL7A3hipKaMRK5P\nrViIjE+efPJJvPnmmwDsxArATub41a9+hRdeeAHlchlbbrklDj30ULztbW+rW8ff/va3bHnbbbdt\n2JZSCltuuSUefPBB75jxVEereOGFF1r2LqBoRjAcKJIhhAwKEcGiRYvwxBNP4LTTThuybeZw+OIX\nv4iVK1eira0Nv/3tb7HddtsBAKZNm4YTTzwR66yzDhYuXIhnnnkG3/nOd/DFL35xzNppVV/HC0X9\nL782EjJ0ah+8/J8w8Wav+Psakz9wxsb3AY1jfz2KK9lyJe72ytaEq7Ll5b1zvLLl3e3e+sZOF6ZP\nH33BX1FU2NW1xlt3+7e8t+qVrUF+XsVzdscD8MerOJbuONfavBbXG5cRQoYO/U5GHpHRzQev1x6Z\nHGy77ba44IILWtLWJpts0pJ2CCGEENI6Fi1ahBtuuAGXXXYZpk+f3vL2L7nkEjz++OMAgCuvvBJH\nH310VnbQQQfhzjvvxI477oiuri78x3/8B37961+PWTut6mv/DOTL/Ah94R+Ii0ddZ5hGq7k4JMlj\nalytpMIZV5hht2XxT1n/tNeUQiq0sUIaEYFJhSVGIzJVVKQbq9VKvNI1Fy/eBmyysGFXBsSLt9l/\nX+kyWK1WoiLdiEwVYmIYRM75iI1BEl8kk+Ov13+flb4rS8evge2PcoucsVZSOKRwHZQ0qNbpmxqo\nYKY/+nvDMLkfXo207h2L+85h5cqVngiryGDcYJ566qlseb311sMHP/hBXH/99TX7ffWrX8Xhhx+O\nH/3oR5g5c6ZXtnjxYq+OZqQRSK+88sq4rKNVfPzjH8fb3z5yLljN2GWXXUasLopkCJninHjiifjT\nn/404P2XLl2Kl19+GQCwZMmSlotkXn/9dSxatAgA8K//+q+Z6MTlsMMOwx577IEHHngAF198Mb7w\nhS80/T/Z0WqnVX0lhBBCCCGE1PLqq6/iwQcfxAMPPIAHH3wQDz/8MFatskLJyy67DCeccELT47u6\nutDZ2Tmgtr773e/iU5/6VNN9HnroIXz3u9/F7373O7z22mtYa621sPPOO+O4447Dhz/84QG1M17q\nqMfGG2+M008/fcjHE0IIIWRq83//93+45pprcNhhhw3rO8lQ+d73vgcAeMtb3uKJTlI222wznHDC\nCbjwwgtx00034cUXX8TGG288Ju20qq/9Y9Dvn9VHRFfQxCHGnUTWz/G15fl21Uhg422Pa8Q0Vjei\nnOXUUUU72+xhRgQaAZA4sRiJYUwFselDD1biteoaPLhsFjZpeB4D48FlswAAr1VXogcrEZs+GFOB\nkRiQOBO7GIlhY6dSwUmtWCY93boCGW+bK4SpneiXa2Q8tUxhO1C8Su5W1ehekwHchwOh9iYoNjT8\nNkgNm2++edPywUw2dF1G/t//+3944YUXsPXWW+OTn/wkNt10UyxZsgRXX3017r//flx//fVYsmQJ\n7r77bpRKpey41atXZ8v9CTbT8mq1ikqlgnK5PK7qaBUHHnggDjzwwJa2ORJQJEPIFOfpp58elEgm\nZfPNN8cOO+wwCj1qzk033ZTN3D/yyCMb7nfkkUfigQcewKuvvoqHHnoIu+++e8vbaVVfCSGEEEII\nIbVstNFGNQ5qY8V5552HM8880+vP0qVLcfvtt+P222/Hz3/+cyxatMh7OTde6yCEEEII6Y9LLrkE\nV1xxxYD37+7uxpNPPgkA+Oc//zla3WrI3/72Nzz77LMA+n+Pe+GFFwIAbrzxRnz6059ueTut6msr\nKMb6DPbokaR+X/ytNkJJsrK8oNbJJI8fSteVjRuCARB4LRiJUZEevKnexFNvzkL8vRsAAMFnDh/0\necTfuwFPvWldJ95Ub6IiPTASF8RERWfkojimniDGdZVxopdqBC++CGYkyduqJ4gZWJsNhTZkUtDb\n25stv/DCC3j3u9+N3/zmN+jo6Mi2n3zyyTjuuONw1VVX4Y9//CMuvfRSnHbaaVl5tZo7kodhcxmF\n+9zsilPGSx2kORTJEDLFOeCAA/q1qq5UKnj++efx4IMPwhiDQw45BD/+8Y/R3t7e9LjR4KGHHsqW\n99hjj4b77bnnntnyww8/PGjhyUi006q+EjLVmXAxDW6Hh+Uc5cYtFZtoHANkJG64XrRVdY+cHvoP\n/LscWxz4sb4Qfvu7HJv39/qvFmawOENQPOfm41ObyZwvN+/PkJlAN3ixqzRGI2RiIgCMtO4HeDR/\ny62//vp461vfit133x2777471qxZg4ULFw6prksuuQQnnXTSkI5dtGgRPv/5zwMA3vnOd+Jb3/oW\ndtppJyxevBjf+ta38IMf/AA33HADPvWpT+EHP/jBuK6DEEIIIWQgLF68eEgTMzs6OvC+971vFHrU\nHPc9brPIiF133RVhGCKKIjz88MNj0k6r+jow+v82P/Lf95vFLg3VCaTZcfUFIV6p925JZ3sDCiIm\ncZWJM6GMf3y+XlG9eKNSxROPzgMAvLVJrxrxxKPz8EalmtVXr53sfESQxiXVF8gYb7V/zx5pUtYo\njqlJTJNXXmxnaBFLzYRZ/T8FT5x3dEPBiGqZiMh95/Dcc88NKlKpGdOmTcuWlVK47LLLPIFMuv17\n3/sebrjhBqxcuRKXXXaZJ5Jx6+jr62vaXk9PT93jxksdpDkUyRAyxTnzzDMHvO/f//53LFy4ELfc\ncgvuuusuHH744JXMw+Xpp58GAKy99tpNrc833XTTbNnNIWxlO63qKyGEEEIIIaSWF1980Vu/++67\nW96H3t5enHHGGQCA7bbbDrfffns22WDzzTfHpZdeCmMMLrvsMlx22WU48cQTazK2x0sdhBBCCCED\nZZdddsHHP/7xpvvEcYx//vOfuO+++9Dd3Y3NN98ct956K7bYYosW9TInfY8L2KiiRpTLZay//vp4\n8cUXh/XOeTjttKqvhBDSCmbNmjViIplZs2ZlyzvssEPD/z+ZPn069t13X1x33XX461//iq6uLsyY\nMaOmDje+qR4rV64EAHR2dkLrXLg1XuogzeFIEUIGzFZbbYWf//znEBF89rOfHVQW4EixbNkyAMD8\n+fOb7ueWL1++fEzaaUVfV6xY0fCT/h8jIYQQQgghA0Va/JnsXH/99Vi8eDEA4Gtf+1pdN86vf/3r\nKJVKEBFcfPHF47aOgbBy5Urce++9eOKJJ4Z0fMrzzz+Pb3zjG1i0aNGw6iGEEELI2HD44Yfjqquu\navq5+uqrcccdd+CVV17BwoUL8dxzz+HSSy8dk/6m73GB/t/lLliwAMDw3jkPp51W9HV8vHM2DT6t\nJo0jqt++fa4puK+g6MqSH6eggeSjlIJWAQJdQgltKEs7tFJYVS1hVXVo8aerqiVopaCVQlnaUUIb\nAl2CVkHiYqOhko/f52J/Hffkhv4r7ri0+umu0f0xFvfI5GAyvAvYcssts+UNN9yw6b4bbbQRAOuo\n9Prrr2fbXWFNceJNkZdeeqmm3fFURyt5+umnce+993r/HzUUfv3rX+Mb3/hGFsE4mlAkQwgZFDvu\nuCM233xzvPTSS55qvVV0dXUBQI1FWhGtNdra2rxjWt1OK/o6Z86chp9mMwkIIYQQQggho8+NN94I\nAGhvb8ehhx5ad58FCxbgXe96FwD7Qqg4GWG81DEQ7r//frzzne/Ev//7v9ct/8Mf/oAddtih3+iq\np59+Gl/4whdw5ZVXDroPhBBCCJlYzJ49Gz/72c+wYMECfPvb38YLL7zQ8j6472T7e5eblg/nnfNw\n2mlFX8fmnfMoCB1E/E+9bY22D7KftTKSYgSTFakopWw+tVJQKkSgyyjpDnToWZgjszG/PcSschWz\nytUhnfKschXz20PMbw8xR2ajQ89CSXcg0GUoFSbt5h8gAOoKZuqd1wCv0WDGd8DjPhgompmqbL31\n1tmEkP4iinp78zgydxLJjjvumC0/8sgjDY/v6urK/kb6lre8xSsbL3W0krPOOgvvfOc7cccdd9Qt\n//znP48ddtgBt956a9N6fvazn+ELX/gCHn300dHopgdFMoSQQZMq1MfSqWQgL2xHwulmJNppVV8J\nIYQQQggZLiIKpoWfyf4t+KGHHgJgIwfK5XLD/fbcc08AdmZw8Q9D46WOkWD16tV44oknxuSPX4QQ\nQggZv3R0dOCAAw6AiDT8A1urGIl3va1qp1V9nZAM99wz0Yb0Y3vhijCat5m6yGiE0AgRqBJC3YF2\nNQtzzdrYsKMDu86JsOMpndjxlM4hdXvHUzqx65wIu86JsGFHB+aatdGuZiHUHQhUCRohMiebfv9E\nXBTINNtthIQuU/meHWNa+R7AiBqVcyiXy9hvv/0AAI8//jiMaXzf/uUvfwEAzJw503Pl2mCDDTKx\nyW9+85uGx992222I4xgAcPDBB3tl46WO8cTLL7+MJ554YlwlYFAkQwgZNC+//DIAYP31129522ku\noKvyrIcxBpVKxTum1e20oq9vvPFGw88//vGPQdVFCCGEEEIIqc/FF1+MTTbZBG1tbVhrrbWwww47\n4OSTT8af//znhsf09vZmtsibb7550/rdGblPPfXUuKuDEEIIIWS0GcuJme472f7e5fb09NQc08p2\nWtHXsXnnPMw/V462uGKY1efuLRpaB9A6QBi0oRzMwEyZhwWladhhFvCufV6D2XknmJ13GlI7Zued\n8K59XsO79nkNO8wCFpSmYabMQzmYgTBog9YBlNLJJ3WTGQajrWkZ9nXln8GnGscddxwAYOnSpQ3j\nex955BHcd999AICDDjoIQRB45R//+McBAH/7299w88031xxvjMF5550HAJg3bx4OOuigmn3GSx2k\nMfztQAgZFA8++CAWL16MPfbYo99Mv9Fg7bXXBgC89tprTfdzy+fNmzcm7bSir7Nnz274mTVr1qDq\nIoQQQgghRNA83X2kPynd3d1YsWJFw89Y89e//hUvvvgiKpUKVq1ahSeeeAKXXnopdtllF3zmM5/J\nZm65vPHGG9nMNXdmWj3ccjfDe7zUQQghhBAy2ozlxMz0PS4w8He5w3nnPJx2WtHXgb9zVk0+Q0EX\nPoNguGKPgdBQsDFQIYeGUgG0LkHrEgLVjnbMxBx0YpNOjXdstAT6hPrRqINBn3Ao9AmH4h0bLcEm\nnRpz0Il2zESg2qF1CUoFUKoYs9SMBufXCteXQV/XYdxDeaNNPpOXVr4HGM0QrIULF2KfffYBAJx0\n0kn43//9X6/8z3/+Mw4//HCICNra2vClL32ppo5TTz0VG2+8MQDg+OOPzwQ1gBUnnnrqqbj//vsB\n2Jih6dOnj9s6SGPCse4AIWRiICL43e9+hxNOOAHrrLMOrrjiijHpxzbbbIM777wTy5Ytw6pVqzBz\n5sy6+z3//PPZ8rbbbjsm7bSqr4RMdYrPSuPelXPEHtrzeopVKqWdZb9Qq6Dhunuc3wKwJvIfXx65\nyh/oXfYZ6wdFv/1Hrsr7uyZSDfcsnnPz8SnU442z3xupeXAe4o05gW7wVryPIoRMXs466yycddZZ\nDcvHwipeKYU99tgDxxxzDN7+9rdjo402wuzZs/Hqq6/i1ltvxdlnn41XXnkFF110EaIowsUXX+wd\n39XVlS27Gef16OjoqHvceKmDEEIIIWQ0efPNN3HnnXdixowZOPDAA1ve/jbbbJMtP/fccw3d9/r6\n+vDqq68CGPo75+G206q+Dh/l/G99pN93Je47m9H8s/pokws2FFQSeQSUdQemSyfmtpewTWcFs4/d\nYkRbnX3sFtjm60vxwpslLO3qxBrdgT50QXlXJe3bRB/fgaEmudCFWBYtWoR3vOMdePbZZ3HQQQdh\nyy23xKabboolS5bg8ccfh4igXC7jqquuwvbbb19zfHt7O2688Ubss88+WLp0Kfbaay/svPPOmD17\nNh577DEsX74cAPDRj34Up556at0+jJc6SGPoJEPIFOeYY47BFlts0fSz+eabY9q0aXjPe96D5557\nDnEc47DDDmu4/wMPPDBq/d1tt92y5VQhWY8//vGP2fKuu+46Ju20qq+EEEIIIYSMFDZGXrX0M16Z\nPn067r//fpx22mnYbbfdsGDBApTLZWyyySY46aST8Je//CV7ofb9738fDz30UMO6hm1jPo7qIIQQ\nQggZSZ555hl88IMfxJtvvokf/ehHY+KOPdD3uA899BCiKAIwuu+cm7XTqr4OjKJrR52PUg1n1agm\n//XfVj80abc1aACqMMFKQ6sw+wQoY7pMw7x2je3WXQbZeusR7YFsvTW2W3cZ5rVrTJdpCFD22i/2\nzUqaxvDPxgO+Zs3vhcHdV267A7ifJzGT6T3AggUL8Kc//QmnnnoqZs6ciWeeeQa33347HnvsMSil\nsN9+++Hee+/FUUcd1bCOnXbaCX/5y1/w/ve/H2EY4i9/+QvuuusuLF++HBtssAEuuugi/PjHP276\njD1e6iD1oZMMIVOcxYsX47nnnhvUMUuXLsXSpUsblqdZp6PBIYccgiAIEMcxfvGLX2D//fevu1+a\nNbjBBhvgbW9725i006q+EkIIIYQQMtH56le/itNOO22suzEo5s6dix/+8IfYe++9AQBXX32190eL\nGTNmZMv9PSO55e5x46UOQgghhJDBcMEFF9S47NVj2bJlePPNNwEAnZ2dOPPMM3HmmWfW3feMM87A\nKaecMqL9TNlmm22w9dZb4+mnn8YvfvELfPnLX667X/oeFwAOO+ywMWmnVX0lhJCJzMyZM/G9730P\n559/Pp588km8/vrrmD59OrbddlvMnj17QHVsuummuPHGG/HGG2/g73//O7q6urDeeuth2223HbAo\nZbzUQWqhSIaQKc6HPvQh7LzzziNa5wYbbDCi9bnMmzcPH/nIR/CTn/wEP/nJT/CZz3wGO+64o7fP\nddddl83iPO200+r+n0Qcx5llexjW/iociXZGqq+EEEIIIYS0CsHYGG1PmzZtwC+qxhN77bUXFixY\ngNdeew1/+tOfvLI5c+ZAaw1jTNNJBgC88nnz5o27OgghhBBCBsPy5csHPTFz9erVWL16dcPyN954\nY7jdasppp52GT33qU/jb3/6Gq666Cscee6xX/ve//x2XX345AOADH/gANtxww5o6jDEwxn6brvfO\neaTaGYk6RgaF5oFK6T5mYA4hTsSq7/pRL5hpgDHXbrujFuHa/NyU0lDQUEolbjI22ruk2jFNlzC3\nbLDWHs1jUYfKWnu0Y+7TBtN0CSVph1ZB5iCjlEr6pSHS7ClQYcgx4v0xoL+H9DO+zfYZ8N9bJrdL\nzEAw6P+neSTbahVtbW3D/hvonDlz8Pa3v31S1EFyKJIhZIrzqU99aqy7MGjOPvts/O///i+WL1+O\n/fffHxdddBH2228/9PX1YdGiRfjP//xPAMB2222HT3/603Xr2HvvvbNYKGnw5Xgk2hmJOiYSo/WY\nQchUpCiaKz7TueXFfbXOH+wCHXhlQeCvh0E5Wy4H07yy6ZiZLc9tL3llc6etati/7u5ur2zaNL/e\nkaDYRnF85k7rzZfbZ3plS9bk66sL5xwG/gs5d7yKYxk742xM8XoV1pusjdo7GkKmAMUfH8qNyVgw\nf/58vPbaa1ixYoW3vb29HRtvvDGef/75fv9I9I9//CNb3mabbcZdHYQQQgghg2GvvfbCZz7zmRGt\nc4899hjR+or827/9G6688ko88sgjOPHEE7Fs2TIcc8wx6OjowJ133olPf/rT6OnpwcyZM3HuuefW\nreOMM87AhRdeCAC477776v4xcyTaGYk6RoJU9NE/dp/mQgwAqkG5SJ1nPbsll88UBTsN6iq+QBro\nSxmVt9nPTv1XlYpURCNUCrNKBuqtWw6sH4NEvXVLzLpmMUKloEQP8HplR6PpG/90LAf6XmuYgpWG\ncUlN625+voMbj7GYTkIIGS0okiGETDg22mgj/PrXv8bChQvx2muv4cMf/nDNPltvvTVuueUWtLcP\nXYE9Eu20qq+EEEIIIYSMBALAtFC8Nxl0gqn7Sj0nnN122w3PP/88HnnkEVQqFZTL5Zp9APtHFMC6\nt2yyySbjso7B8MILL+C8886r2f700083LS/uRwghhJCJyUEHHYSDDjporLsxKEqlEm666SYccMAB\nePzxx/H5z38en//85719Zs+ejeuuuw5bbjl0QcNItNOqvvaHUmFTkUFRFFO7b1F0oOpPaFW6zr4A\nxEBBeTKZXDTjtiVo6jQj0lhkIQBUs6cWXah7cI4kbYHGzguWw2y016COGyhmo42x84LHcPers4Dq\nQI9Kz8EUtjUSHiX/00wD01QgU+tIVBTEZGt177fabfnktWK7wxHNTG6RjJHWTTzihMHJy80334xX\nXnmlZnv6jN+ovLhfK6BIhhAyIdlrr73w17/+FRdeeCFuuukmvPTSSwiCAFtssQU+9KEP4VOf+hQ6\nOjoaHh+GYY2bwmi0M1J1EEIIIYQQQsYf9913H1577TUAwC677FJTfthhh2HRokXo7e3Fr3/9a3zo\nQx+q2Wfp0qX43e9+BwB4//vfX+NGNl7qGAxPP/10zR9qBlNOCCGEEDIWrLfeenjooYdw6aWX4he/\n+AWeeeYZ9PX1YcMNN8TBBx+M008/Heutt17D44MgyN45N/suNdx2RqqO4bLD9jsiDF3n4Tp+L060\nj93DESEo7W13y2xEkXWqSeOKkGyz+wfQUMk2jUCFALTdlparEDZQKICWABoaOvmzqIaClgABAihR\nsEsaQdIHrRQCKARKQyuFUAGBUgi0rT9UCqEGAq1QVkAYAG0aKCWn0K6BNi3oCA1mhDE6wwhrtfdh\n1sxuzNjIKgTCHRbA7L37MK5ATmdnZ8OyjW84FT8HoP/wIKK/voaul+w5rFw1DW/2tmF1FKIrCtAT\nafQZhd5EC1I1QJ8BohioCBAbQWSAKFE4xEYQiyASwIggFoMYApOWwySfGKIEMWIYFcNAYBABAAxM\nsi2GQGAkgsDug2SPWCIIDCAGBgJJ9gUAiK1NJPlAPHGWJK0BSaJAUiaO4CUVZtV3OsrVHFFUxZ8e\nuav/i0HIFOanP/0pfvrTnw65vJVQJEMImbDMnz8fZ599Ns4+++xBH3vvvfe2pJ2RrIMQQgghhBAy\nflixYgVOPPHEbP1jH/tYzT4f+MAHsP7662Px4sX4yle+gkMOOaTGQfJLX/oSqtUqlFI49dRTx20d\nhBBCCCFTgba2NnzmM58ZUlzU+eefj/PPP3/U2xnJOkaGVMyiMqGL0gE0QmgVINBlaFVGoEoIlHU0\nDFFCCe0ooR1lKaMkJbSpEkqJqKZNa5S1Rlugkg9Q1kB7Mu+1LQDatUF7IOgIDNp1jI4gRkdoxRcd\npQjlcoS29giljhjhNEBPA/SMpMczSlAzysD0DqBzOjBjOqSzEzIj2aHsx46PBq32JTF77w69N7Jw\n9ZlN9x4GFWtZo7q6oFavBrrWAKvXAGt6IF0VSFcFpivpUzcQdQeo9pTR1xuiUgnRUw3RE9k/X/fE\nAXpNgJ5YozdW6DUafTHQGydNGaAvBvpiQV8sqBiDPmNQTQQvfVJFVVVRURVU0YsqehGhilgqAIBY\nqjBSQWwqMBLDIIKY2BPWWPEMrU8ImWxQJEPIFOGee+7BnnvuiTAc+R/7Z555Bh0dHdhggw1GvG5C\nhsUU8e2bIqc5Sqg6S2PTPuA7jxYnHOmC3afS+Q5a+7/b3fUg8MuCwH/IL4Vt2fK0cJZXtiDIYyO2\nneV3aJN3x4W+q7rLANDb25stDydazq2nv9ntbv+2fd3fd1lvfl6rMMsr6wlXeuvueBXHUsf5utb+\neBRnn2iTXz9Tx044P65Q1IKH8KKFLX+lDB33+g3DgGF8U7xJJ+2JTl0ECjJG/6843njXu96Ft7zl\nLTjooIOw6aabYp111sGMGTPw6quv4rbbbsPZZ5+Nl156CQBwyimnYPfda2eBdnR04Nvf/jY+/OEP\n44knnsD++++P8847DzvuuCMWL16M8847D5dddhkA4JOf/GRdN5rxUsdA2GuvvfDQQw8N6dh6rLXW\nWiNWFyGEEEIIGVlyN45USKCzR0QRgSgDIEjcPGIIAqTSEIFAlMCIQeYPIgZh8ixiYN1JjCjEAsQG\nMAqIk0fSyACRUtbJxChESiMSQdVYFU1oBEEsiCODoCowFQNVMpA+K6JRpcT2JawCpV4gDPMP0BKR\nzKQlfX/X0wP09tn1virQFwF9EaQvglTtfWAqgKlqxJFGHAeoGvuJxL5Hi0QjMvYeiEQhMvYeSCOC\nY2fdiL0jJXG1Aex9ZpL/REniGuO4y8ARxMA4rjKuu4xk5ZOZVr4L4DuHycd///d/43Of+9yI1bf5\n5puPWF2NoEiGkCnCf/3Xf+GVV17BWWedhaOPPnpAUUP98Y9//ANf//rXcfXVV+OOO+6gSIYQQggh\nhBAybjjhhBNwxRVX1C375Cc/iU9+8pPZ+nvf+17ccccd3j4vvvgifv/73+Piiy9u2IZSCp/97Gfx\nzW9+s+E+Rx55JF566SWceeaZuOeee7DHHnvU7LNw4UJ873vfG/d19MfMmTOx6667Dvl4QgghhEws\nHnnkEWy++eajImx944038NJLL2HnnXce8brJyCEwXkxSKiRIt6XxN6Iki8YBAFFpGE8EowLEiBFK\ngDgRJBgRGKWS+B4rkAiRi2RMIoywAhlBJApVoxAmKp1qrBEojSDQ0FUDpRVUKFBhInjoi4CShgqq\nNisp7IUqhUDJ/tlUSiHQ0THq4zfp6OmB6u0BAKi+RCDTWwV6q1Yc0xdBKgLTZ3eP+xSiqkIUaVQj\njWpsRTFVY69jJApRcp3Tax4LkE5Vy6KekjsrXU7jmGKVRjxFSaRTbIUvjogmjWlKqSeGmewCGUKG\ny2abbYbNNttsrLsxKHT/uxBCJgNbbbUVnnvuOfzrv/4rNttsM/y///f/8NRTTw26np6eHvz85z/H\nQQcdhK222gpXXXUVOjs7MX/+/FHoNSGEEEIIIaSViOQvnFvxGc/uVffeey8uu+wyHHHEEXjLW96C\nuXPnIgxDzJ49G7vtthvOOOMM/PWvf8X555/f7ySEz33uc7jvvvvw0Y9+FBtuuCHK5TLWXntt7Lff\nfrjmmmvwq1/9CqVS89mq46UOQgghhJCU66+/HptuuinOPvtsrF69ekTqfPPNN3HWWWdh0003xc03\n3zwidRJCCGlOK98DmPH8IoBMGegkQ8gU4Yc//CEOPfRQfP7zn8fTTz+N//7v/8Z///d/Y9ttt8We\ne+6JPfbYAzvssAPmzp2LOXPmoL29HStWrMDy5cvxyiuv4KGHHsL999+P++67D11dNjAyDEOceuqp\n+OpXv4q5c+eO8RmSsWC8f5cZuf6N9zN1GZm+jkXky+SlGKnU2E5SOZFKqiZeyV93o3+Kf5gLQyci\nKPT/0FUu+XFHHeU8gXiu8gWPm8zMo5jeuf4bfn+OPKDQ98ZxSy59fX0NywZDf3FLcPr3zj/e6hW9\n3D0nW35jpX/O3WX/PCtRd7YcxX7fQxNlyyIRfPyv2THyctV08knjKCbbjrfWrCJSgzMrSBpHnQ21\nzqSmoVbUAkamr+P9jMd7/0hrufzyy3H55ZcP+fgNNtgAJ5xwAk444YQR6c9uu+2Gq6++elLUQQgh\nhBAC2DiEN998E1/60pfwrW99C0cccQQ+9rGP4Z3vfGf/z+0Oxhjcfffd+PGPf4xf/vKX6OrqQhiG\nE25W+tQjj6lR0BAxUCp5RyUGolTi0qEAMTBKoDKnGYGRCIIwCVsSxDAIYY+PRaybjFGIFRDARiyl\nb1silbjLODE8kdKoJg+FoRFUjUYYBdBKoLVA9+VOMggMdBgBWkOFOneTSd+xhSVIGAIUkA+cahWq\npxeqJ41b6gV6K0BvBdJbhfRGML0Gps9xkqkqRJUAURSgajQio1EVJ27JKESiEIvKXGViY+8FwN6B\nsQDGJC4yYj1hYrhxS0nokkRJ0JIN+LI7GHuPpi5HqcNMFqMujosM3WQImUxQJEPIFOLQQw/FgQce\niKuuugrf+9738Oijj+LJJ5/Ek08+iSuvvHLA9cyYMQNHH300zjjjDGy99daj2GNCCCGEEEJIa2ld\nDjkhhBBCCJnYfOITn8Cuu+6KM844A3fccUcmUl5//fWx1157YY899sAuu+yC+fPnY86cOejs7MSq\nVavwxhtv4LXXXsOf/vQnPPDAA/jjH/+IJUuWZPUeeOCBOP/887HtttuO4dmRgWHghlZIMrtHKbss\nygAIEqlCDEGQHScQiBIYSWULgjgRJwQAYtGJ8CGP2kmnIIWCRBgDBE7kUiqeqCoNbQKEsRXIBJFA\nVwHVm4h0AgMpxVBBBGQimeRfAAg0VKAhnTMBzeejfjEC1d0NdK+xEUtAErVUsXFLfRGkL4b0GZhe\nIK7aeyaOAkRxgGocoGpSoYwVPgHIopai5Hqn90DqRJLGL9n7BDBiEDvxSSaVxChJ7k2T3YtAHqMk\nMNm9K7WzRzEVBDLSwncBfOdAxgMUyRAyxQjDMJsNed999+F//ud/cOedd+KZZ55pelxnZyf23ntv\nvP/978dHP/pRdHZ2tqjHhBBCCCGEEEIIIYQQQsYjb3nLW/Db3/4Wt956Ky688ELcdtttWLx4Ma69\n9lpce+21A64nCAIcfPDBOP300/Ge97xnFHtMRopcTGB9OZQrlkncZeyyWKcOJblTBwxExTCIYRDB\nqAAxYgSJg4iBzoQPgQhiAxilMnFEZKymxXWTqRogSJyZAwMExqAaawRKIwgUVEVBB/aP86pPoEID\nCaJEENMHBBpInGSU1pAgsOszZozySE4CutcA3d3WRSZzkqkAPX2Q3gjSF0F6DUwfYKoKUSURwUQK\nUaRRjTUio1A1GlXRqJpUJJO7yBjkQpn0PoiNZA4yRqzkxcAgVlYEY1RyfyG2Ii2xbjGpiEacZQCO\na4w466m7DB2dCZlMUCRDyBRmzz33xJ577gkAWLJkCR5++GEsWbIEr7/+Onp7ezFv3jysvfba2GKL\nLfDWt761Js6DEEIIIYQQMrkwaG0+ON8zTh7++Mc/4pRTTmlJW3vvvTcuvvjilrRFCCGEkIFxwAEH\n4IADDsA//vEPXHHFFbj99tvx5z//GXEcNzymVCph1113xQEHHIDjjjsOG2ywQQt7TEYCEfGitdKY\nGqUCL3IJybpRidMMDFQSsySZj4xkMThGBEYJYqhEAGHdRHSiYQgCK5jQsG4y2igEyrqOAEAEhcho\nREpQNQF0VaA1EPUl7WuB0gIoA62qgIaNWkrPRSkbfR4EVizT0dGC0Zyg9PRAdXdDdfcA3T3Amlwk\nIz1VSE8VptvA9NiYpahPIY7s35qq1RBVE9hrZaxQJo1YAoCq4yITGSBGsuw5yVhfGINUKCOOk4wb\nuORELUnuDNM4agnOPpP/wdVI6yKrW/nOgYw+Z555Jm699daWtHXuuefife9734jURZEMIQQAsM46\n6+CQQw4Z626QCcC4/v4yBb6sAlPmNFvCyH3xV3UXATTN4C6Waa2dMu2VBdoXKrrCxVIhH7lcKmfL\nbeVpXtm0trW89ZmldbLl9cJZXtmOs/Obbd0jZhc7X1hVdZeLqOGM+hAPLfZ9x0vy81qyZpZX9qZa\nx1uvtvVky7Gp+hWL+6Iv8suKNqxNfnDdIlN4Siw+hCvtvngqVtRwZVC4w8xfN0OneH2a/FhMbMb5\nibq9G189I2TysWrVKjz66KMtaWudddbpfydCCCGEjAmbbbYZzj77bJx99tlYvXo1HnjgASxevBiv\nv/46Vq1ahVmzZmHttdfGhhtuiN133x3Tpk3rv1IyAUjdZOz7KiueyUutUAZOzE1gj5EYokIbk4MY\nGqmTTGBjmEQlAhmBTtxkABux47rJ6GS9mjz5BUojMAINgVYCraxQRiUiHR0AShuowMCEgFYK0BVk\nr+O0skIZZf8VrYG2tlEfxQlHXx9UVxdU1xpgTTfQ3Qv09gEApLsC6Y5g0pilPiCuaETVANVqIpKJ\nA1RjjUqsPReZyHGScV1k4sRFJk7en0UiibNMGtsliJP/ADhRS5mMJrsHgVpBTBa5lL3Xm/wxS4QM\nlxdeeKFl7wJWrFgxYnVRJEMIIYQQQgghhBAAVvfEWV1kKGy77ba44IILWtLWJpts0pJ2CCGEEDI8\nOjs7se+++451N8ioEQMoFdxkCtE1oiHKwMpVTCaiQeLeIUqyyCVRQe4AIsZKZkSy2CUjCnHqIGKA\n2HGT0coKaQJJxRVAxWhoBWgjUJFAIchFMjqxzVAGgTYwiODMXbOTvJQCtM4mLMnMmRTKuPT1Qa1a\nBbVmjXWQ6e4FuvsgXRUAViRjeiNIj0HcA0R9GlFFo1oNUElEMpVIo2I0qhKgYnQmikmdYiJRnouM\ncYQyALKYpdxNJhHFKCtuyaOWJItaAnIRTOZfJFITtZSST2Br7Io1GaCTDBkqH//4x/H2t7+9JW3t\nsssuI1YXRTKEEEIIIYQQQgghZFhsvPHGOP3008e6G4QQQgghpKXEAIKarSLGRi4VtonK/zqe+n4I\nQi9yydZqEIpdjwXQAsSQ7I/rrnuMFcIAVaUQJOUVI1BWFgOFwAppjEBHVgmjtQZUIu7RggAGoiJb\nGXwnXyAXD8jMmXZhKotl+qxTTCaQ6eq2nzW9QHcF0mudmKUnF8jEfQpRRaFa1ahG1jUGAKomQCUO\nUI0VqkahYuy1raZipyRaKXWRiRLXmDgTU9ntIgIRQexEKwFAHr4Uw7jCmDqRSkD9qCXL5BbIEDIc\nDjzwQBx44IFj3Y1BQ5EMIYSQpkxNUe9EO+uR6a+fmDEadU50mkQqNTtqELFE2olUqolXCv1IpdBZ\nL5f9XORyKbcq7mjr9Mqmt8311tfButnyFrP8B/zdN3o1X3nH+72yZudVpFnZYHCjmmpiiJq0Ie/w\nley73/LrbPkfXet5ZSuWreut97atypYj0+fX68YtqeY3uxufpSI/tik27oN287glb70m5satpTAe\nNd2bmD+cI5fsUxzX4v08EvWO93Cf4j0w3vs7fKbeGQ+dmt8hk6QtQgghhBBCCCGE1CJQLXs+53sA\nMh6gSIYQQgghhBBCCCGEEEIIIYQQMiRs5JLJJicoBHYbDEQp69ChgizuxihBAMBAoCWGqDCJWLIT\niTQ0YhhoKARiHWSMUYiS+rWy0TtRAASJm0hsFKpZ+xqBMqiKhjKCQGnoOEiNYqC9+UsGgCRRTNVs\nizJWNmAzaQ2UkWz2jkyfAUyfhinHmm6oNV0AANW1BuhaA6yxUUvSZV1kZE3qJCPWRaZHodqnUa0E\nqFZDVOMQ1dhODqwajapRqIqNWkrXY2MvVJxc2wh51FJk7DJgXWVSZxnrFWPvocw1RglE4sxZxkCy\nexBI3I1gY5jSiWk2dik5fnLNACWEOFAkQwghhBBCCCGEEADWrpr54IQQQgghhJCBUy9yqfahwsYt\npZE3MXKZjMAghkEESSKabMySQSCJWEaCRAxhiQwQKD9yKUhimQD7b9VYT2KlNLSBFbwkIhmVOALb\nciAVygSJKEKjmjwYCZRB8qBkoOKkB3EMiWNgpu/gPKlZtRpqTZcVxwDAmjRiqQ/S3QfprkJ6Iphu\ne41TgUxU0YgSgUwlDtAXB6jE1nG5YjSqolExNm4pSiKVoixWKxHFpNuNJLFbSSyXALGY5N6wcV6i\nDEwipzKIkwgvk0QvxfbfhrFK9R6Gp0bUkpHWOe7ynQMZD1AkQwghhBBCCCGEEEIIIYQQQggZMANx\n2bAuHRqiDATa2W4dPQQGomIIQghM5vgRI0aAIJHQSCKaAXTiMGJ07iqig1Q0A+gkTlkJoIwVwGij\nrRgGQGpFowuiHnsqVihjMVASQScCGWUEiGP7AaCMgapGkCiCdM4ASn5M+qSiWoVa3QXV1QX09Fj3\nGMAKZHqqiUAmgumNID0GcY8tTh1kokqASiKQqUQBKpFGxdjxrxht3WNEWaGMKESicpGMsRKVKHGR\nSbRKiDPXF0lEVsk9YqUyiRsMsq0iiVsM8uPsv9ZBJt2/GXSVIWRyQZEMIYSQGibU170p8OV0tE6x\ntt5WjOXot6EKknf3PNVg9PCq6WqhzbxUad2wrLiutf9VLAjyB/Qw8MvCUtlfD9uz5bZyh1fW1jY9\nW57ePtsrmx9s6K1vMm1GtrzLnIpXNnvh+tmyNDkPoDC2TQZrUNeggDj3T7H9mlurSTPuee2ypM8r\ne713hrfe3Z2PV9Te45UZ5N68SjV/mNY671BUvLfifEMc+4XGRN66+0BevCZijLtjoRF/1cv+bfJj\nWRxGKexcvAyjg9vmaDXon5eI8zM9Qk3WXJLJGr/s/dId3yfZijtrImLn2LW2PUIIIYQQQsjkQ8RA\nqaIYxT5tKBgYZeOYlBe5ZN+DCALEKk6cZDS0CLRSmdNLKpxQSlmXGA0EJn+201CINVBNHGQUFDRU\n1h8dF94DZP1LloyBjg0QRdBJzo+KYqvUAIBqDPRVoKIIqPbZ+KUZ/julSUFXl3WPWZOIY7p7gZ7k\n/WF3H6SnCumpwnQbmF4D0wtEvfbdaFRRWcRSJpCJNaoSoJqInapGoWLsv7HYmKWqsdcWyJ1kii4y\nqbdLnCwbGMQqTuQxESRxCkqjlkwqwJLGLjKN3WWmBgYtdJJpUTuENIMiGUIIIYQQQgghhBBCCCGE\nEELIoBCRZCJTDJHAmUSk83IYiFI2binLO2oUuWRFLFYgEyRRS3arEZWJI7RRMDqJ4UniliKTz9UI\nBIAo6yYDDQ0DpTQQp/0LkdnKeCeUlAsQxAaSWJioWKCqsRXKAFCVCIhi67LS1wfVW4H09EBSoUxH\nR23dE4UeO0lMdXVBdfcA3d1Ad48Vx6zpg/RakYx0VyF9MaTbIO4RmD4grmhEFXvtq1VdI5DpMyEq\nsUJFkn2MQtVoREahIk7cUnIZUregNBY4dZFJ45aMGMRiMv+YWMWJIMZep2LUEpDEfknqNJM4zHgz\nm9z19BhO7yBkskGRDCGEEEIIIYQQQgghhBBCCCFkRBAYqEKkUd3yOpFLQOIMYj1kkuXcTQYAlEge\nqaQVjAGiwK4DjqOMBmCUFfLEAILEATo2AEIYia2XjSgYo2CMFUUYEyOMgdAIxAiCKIbqEOhUvVE1\nVijTVwF6q0BPH1RvL1RPrz2/6dMg06ZNLLFMTw9UdzfUmu5sHWt6gJ4+oLcP6K5C+iJIj3VWNr3G\nxiv1AaZPIepTiKoBqlV73avVAFUToC+2EUtVCTKBTCVxUq6IskKZRAxTSVxkUvlSYuKDyAgisZ8Y\nedxS6iKT3i8mE8SkcUp51JJdb+5hMpDYJULI5IAiGUIIIYQQQgghhCQoL3KMEEIIIYQQQoZGKlQw\ngGiIMhBop9TKGYqRS7bQQFQifxBB7LjJADauJRZAi41gikQBSewSAOjEkQRGQQUCZZQ1t0mtaALr\nKiM6sIoMAUyQ1y+iYGIrmgkjgVQNdNUAlcRRpGKg2yKovgiqI7Iikp4+oCNxYVmzBqqjHTJtGqS9\nA5g+DQgai4bGjDgG1nRD9VqBDHp67XkAuTim1wpjpDeC6YuB3kSg0uu4x1QVokqAKA5QSUUyRqMa\nWweZirERS6lApiJ53FIEoGKsi0xccJKJBMn1zx1k7MfuEEsii1H2fgEMRAlEErGTE7WUC2ckE8OI\niCOMmdpuMSLKj2cfzbYYek3GARTJEDLFefHFF7HxxhuPdTdIi5msX/eGd14TaVTGd1/Hm/ukUo2/\ndA/q67hTT/E4pfMHfO0s12s/CEJn2X84DoNSvlwq+WVhm7deLuUzUcplP/N4evucbHlOaUOvbKPS\n2t76DrPzPuy8/T+9Mnn7wmy52TjaHZoVqQHt1x/K+aOtFH8OivU6xcW+y9t3zZZ3vucGr2xxzwbe\neleUj1ev6vHKjGfL6/enOFwV57bQ2i/U1bww0lWvLI5VYT1vs2j16s11Mf7Ml+KPpXKPbXJNao5r\nNtBjQPH3TX+3aWupHb3xjdvfgfd1op1lI/q7kyfqeRFCCCGEEEIIIYQQQnwokiFkivPxj38cy5cv\nx/HHH4+PfexjmDt37lh3iRBCCCGEEDJGGKClBtPjTFtLCCGEEEJGgGXLlmHZsmVoa2vDpptuOqhj\n1l57bb6jnmCISP+Tq2qOMVAwgEojbkzi75E6gASZC0iMGAE0YgA6mS2joKATl5HIKDtpxgDpvKTI\nVg2lrVsJtC3PjGxiQLTOgnkECkYUjE7bVwhjhbIomNggiBTCyECqtn1dEaAsQF8M3RtBtYdQbVWg\nPXFhaQuBtjJURxdUWxvQ0Q7paId0dABtyUS4wgS5llCtAn22j6qnx8ZD9fTabT19Nj6qL5mg1ZvE\nKzkOMqZi3WMAIK4oRBWNONKIIo1KNUBkAlQjO8hVE6BqNCrJp2pU4iZj/wWAarIcJ+4xURavZNtI\nXWWsewwyR5nUEEggWcxS7hoTO5PrTO4UI8ZGLw2S4iS1yYpB6yYITY0RJeMd3f8uhJDJzl//+ld8\n9rOfxXrrrYcPf/jD+O1vfwtjmL1ICCGEEEIIIYQQQgghZHB85zvfwbbbbovNNtsMZ5111qCOueSS\nS0a5d6SVZKIEsWIFkfwDAII4Ey9IIm4QCIyKYRDZNSWIYWy0TvaxsTuxsUfFRjyhRSquqGYflQky\nUqFGn1GoGI0+o9Eba/TGAfqST28Uoi8K0dtXQl9fCZW+AJWeEJU1GpU1GtXVCtFqQbzSIF5ZRbyi\nD/EbPTDLumCWdUGWdwHLVgGvrwBeWwb8cynUq0ugF78K/fIr0C+/ArX4VajXXwdWrbYiFTPC0gEj\ntt5Vq6Fefx0qbXvxq9CLX4V6dQnwz6W2f6+vAJatgizvys4hfqPHntfKKuKVBtFqQXW1ysag0hOi\n0hegr69kxykK7bilYxgH6I3t+NpxzgUyVXGvh71G7nWLU0GMc33dqKU4/aTxShAYRDAqvYdi+xGT\n3Htxdj9Kei/Clnn3KSFkykAnGUKmOJ/73Oegtcbdd9+NSqWCRYsWYdGiRdh4443xiU98Ap/4xCew\n0UYbjXU3yTCZVMrcKaLcHo3TrK1zZBpp3texv14DVsAXZrzURCq5cUvFfZvELQVBqbCexxuVwkKk\nkjODpFTy45XCsN1bL5enZ8vTyrO8stlteWTQRljfK9tqlt/mrvNXZMvth2zjlUmzqKrBzBAaqWkI\nbj393Fpu/4ozPtyy4jnv+tIr3vob1dnZcu9yfyzjNjcaKfbKVEGKrpyIpSDwC917xo1eAoCq8uOX\nlFNxHPtlLsXhKY6BNFhOds7ba9hCg2NHnebhPl6K1LDuu7wikcLP+wjdzyPX13HM+M7DGhRNf2Ym\nGSIj/262v/YIIYQQQsjk5Wtf+xqeeeYZXHnllWhvb+//ADJlEMfaxcBAQaDEupgopWAQIFYxlCgo\nqMxNBgCUGGgJoCCAse9dtAii5Blep1UbZC4zgMqsAyRWEJ2IK0RDtErEN/b4khhEWiHWVowRRBql\n0CAMbXlQFQQVg6Ak0L0Gupx8SslzbymCKuvkE0KVA6CkgVIItNl3c6oUAqUQqlyy20P7kfS9URDY\nj1JAGt/uvjZKdR1xZB+s4hiIY6g4tWGJ7KcaAZWq/bcaAX3J+6RqBFQNpBJDKhGkYiAVAyRuOaYq\nMBXYT6QRVxXiSGfR4FEUohppxKJRja0QJjYaVZM6yShEolFJRDFRIlCKkjK7jyNoEiBO1k3yoGjL\nxLrHCBJhTB7DHqf/qThzkTESwSTlBqkYS3JHGVIXI61zkmnlOwdCGkGRDCFTnEMOOQSHHHIInn32\nWVx++eW46qqr8Nprr+HFF1/EV77yFXzta1/Dfvvth+OPPx6HHXYYyuXyWHeZEEIIIYQQQgghhBBC\nyDhnvfXWw6uvvoprrrkGL7zwAm644QbMnz9/rLtFRpF0ko5SuQDGxjEl5ZloQdvIJWUDcXQWuZQ4\nfiDMwnMyNxkxUImIRSkNJSb51zqORFBIpzVEWlmBTAA7rykAYJCJYEQLxCgbtaTsUbHSiFPxhQCh\naMTGIDIGoTaoGoNSEiUUBgZBYBD0GYQlY4UyIaBDe366LNChgSoBKqwCJQVd1kCooUrJBLpAQYWJ\neCYIgDCw29LJVIFOBDLJ/vWyQTKhTJwIZQyQpgTEAkRWOIOqgUQxEAukmkiNIgOTiGIkEkgVMJEV\nxQBWGGMiwMQaUdUKYOJYI4pTEYzdFiXCmEh0InbRSfUKUeIWk/8LVJJ4JcCKYKoxECEXyMRGsrgl\n6yBjL2EkNkgpdZAB4LjIpO4wktxD6X1mMsGMdZCpFcv4E8vMlIlXImSqQ5EMIQQAsMUWW+Ab3/gG\nvv71r+Omm27CZZddhttvvx3GGNx222247bbbMG/ePHzsYx/DCSecgO22226su0wIIYQQQggZBfhK\nkBBCCCGEjAQnn3wypk+fjs997nO47777sMcee+Dmm2/G9ttvP9ZdIy1AYKCQOyq7Ypl8o4Eoq2IR\nMTCJg66WGKJCQIznJqMTrwsjykpoRCXyGiuwyEQ06UNNKpCJAdHIhCYVo2C01ZPEVk+DWAFxcnys\nFUIRhAqIRCM0BoE2qGpbcRgbhIFBqAyCSBAEMbQSBKEt14FBEAqUFuhQoAKBCg1UCOjEjQYBrCgm\nABBoqEBZUUyYCoEUoFXuytpMJJNYgoqIHYhkm9jMIkiMJL8IMEm5RMknBkykIEYhjhRMIoKJIwUj\nCnEcII6tK0wUWzEMYEUwsSOOiUQjShxjkFwPVyRjy2w3qqnZjbECmShO90+0PYlQJY9YkjxmCwZx\nIqZKXWSQxi5JbKUyTnxSGunl3XZ1hDBT3WlG0Lp3AXznQMYDFMkQQjxKpRIOP/xwHH744XjppZdw\n5ZVX4sorr8TLL7+MZcuW4YILLsAFF1yAt7/97Tj++ONx1FFHYcaMGWPdbUIIIYQQQgghhBBCCCHj\njM9+9rPYYostcPTRR+OFF17A3nvvjUWLFmH//fcf666RFmIFM7nKw7p6KIhKhDRiYJTJJDXW7yNG\nDAVAZ24yaQyP9ZyxEUtWPiOAOOIYAyswAXKBjKOByNaVgmgbv2S0wKg85idUCqEjlgmMRqhtJaFS\n0HGAUBvoSBAGATQEOi0P7LJWAh0ItE4EM1qsKAaADgRQBjoAoIzdrpwI7+RfpVBfIJNinBhb4+hB\nxApgIICJAYiCiRUkiUsyxgpjjLHbjSgYoxFl5RoGClGsYUQhMhpG4IhkdCJoycUxNiopFckk2wDE\nSVkarZQ6xbgRS2m0UiQ2XgmAE7OU+sMkfjHJdUpdZGJEsD4zfsxSOhgCY++5olhmigtjCJnKUCRD\nCGnIRhtthK985Sv48pe/jFtvvRXf//73ccsttwAA7r//ftx///04/fTT8dGPfhSnn346ttlmmzHu\nMZm0jIrF4UTSKw+9r/7Qjcw59385xnZs1SDSU5U7faUwlaVYS2Z1CkBr/8k0CIKGZWFY8tZLYf71\nKyyVC/vm66VSh1dWLk331qe1zcqWZ5bW88o2xMbZ8haz/LzvXWb3+fvuWc2WZbtt0QhVM9VnELi3\nxHDCbYd4axX77s4WKZ7zhns+763v8n/5eHXH/lhGK/NxlrbYKyveB90qX68Uytz+FY/T2u97NYqc\n4/wBMSZ/sI/juGFZsgEDoT+LWffnTcbkZ7/YptOfQtHQb2G/IpG8osHV2biv449R6qt7UYbzO4WM\nKgb5S81WMJG+kRFCCCGEkKFx6KGH4t5778UhhxyCV155BQcffDAuuuginHzyyWPdNTLqFJ6pE1GC\nJ5hJhA8684Sx7h+C0IohCm4yAKChoEUhykQOGjBOW6kIJn2vkqQ/pRoJAWCU/WhRiLUVa8SpyYtS\nMEoysUygFEItCBKXFK00Qg0ExlhxTCwIlUAn72q0EgTargfKAEqS9KRcSKOUQMGKYrSWbFuq9Ekf\nm4vvf+qOchojleZHOdusGCZxCkmEMGl5bOz+sVghTGxU9jxoEvcXYxQM7D6RE1kVw4pgYsnFMZG4\nUUq5e4xxXWJMbnZTTyATGUFscrFSJAaR2Bik1EUmc5JxXWScqKX0PksDlryxqiuM4ZOpkcG9Vx9u\nW4SMNRTJEEL65dlnn8Xdd9+Nhx56qKZszZo1+MEPfoDLLrsMJ510Er797W+jra1tDHpJCCGEEEII\nIYQQQgghZDyy00474cEHH8Shhx6KP/3pTzjllFPw9NNP49vf/nbNhBEysRjwxCoxyGxUYMUxIgYK\nfuQSABiloSSCUspzkzHKlsdiEgeZwMbwQCFWKnOSMQaItNQIZRITFBhjU42MAsJEUGOUgkmTjRQQ\nwQpjIiUIlEJgxO6LRAQjgiCRFVhBDKwgBnaqiRXHAKESQNkzUJBMEKMdEYwCrBtOUnc+uINQEzji\nlnyMVSaOsWVWNJOWGSggiUWCALHoTC5ihTPWBUZgRTGx5CKayKTbEoGMUVai4ohkjOTuMbEjlEnn\nbhUFMiYR1KRTv9KYJdu+QQzrOOQ6xqQuMkaihlFL1rnIGUupJ5Spj1Kq30lkhJCJB795EELq0tvb\ni5/85Cd417veha233hrf+ta3sHTpUiilsP/+++P666/H73//exx77LGYPn06jDH4/ve/j9NOO22s\nu04IIYQQQggZBtLCDyGEEEIImTqsu+66+P3vf4/DDz8cAHDhhRfisMMOQ1dX1xj3jBBCpjatfA/A\ndwFkPEAnGUKIx6OPPorLL78cP/nJT7By5cps+4IFC/CJT3wC//Zv/4ZNN9002/7Od74TF1xwAT73\nuc/hiiuuwJVXXolzzz0Xs2fPHoPek0nDIJTZg/tCNX6/fo2UGL22npGpuHn/xnZc+7OBbDabxS0r\n7ldc106kkhuvVFwPgkK8Uqm4Xm6ybx6xVC778UodpZne+szyutnyek68EgBsOmNatrzDWv7MiG03\nWeb3fc8ds+XiHIpRsdgcBz+GzSKCgj39+KVtn3ssW15Z9WOt+uJ8nKMu/xqgXDzRfF3pxvdazX1X\njGbSlYb7xnG1SVkhfsntWeEHfDCXyD22eL+MffxSMWbLKRnWrZ1XJFK8lkOssTBU4y+JqPG4DnnP\n8X/ShBBCCCGEkFFg2rRpuO6663DmmWfim9/8Jm6++Wa84x3vwE477TTWXSOjhIiBUv67NIHxIpfs\nRpM5xQQwDSOXAOTxS6IApaHEQIlG5FQXGuW5yRgAYfJCxCjrKmPEPsfGKnWWSeOUEjcZAwRQCJRA\nKwWdPMsGSiGAZPtpEWjYGCYgdY0JoJQgUPaRt+gUU9c9pvBoPBingxpvlNRVJ41fSlqrcZpJ3F1E\nknLkjjRpHK+R1OElj1NKt8diHWRiZz8gd44xqZMM4EUv2Tp8F5lIkuVknGMxSd3WRSZWsXWPUZnX\nTE3UkoFp6BRTL2pJBuEqQwiZPFAkQwjB6tWr8fOf/xyXXXaZF6mklMJ73vMenHTSSVi4cGHNH3pT\nZs2ahR/84Ae49dZbsXjxYjz77LPYbbfdWtV9QgghhBBCyAghzkvNlrTXuqYIIYQQQsg4QSmFc889\nF1tvvTVOOukkPProo3j00UfHultkFBERKJVPtknnSYgYiDIANAwEOhExiBgYpaElhnEil0wijtCi\nESOGTuKClNKAMQiTyUYGQARfKBMoQJKGAwVAEqGMAQIARucRSIFCInpRCFUumtFIRTQ2gkkBiRBG\n2SilpNyKYuwxCvbcU8GLciKUUrmKrvNkNJSpJPWer1LRS1rmTvgxsM+AApUJhtI5LQZ2uyugSaOV\n0nKTrKdiGJPsg6QsTsQx6XIWt5SJYOAJZEzyiZI8phiCWEwSqxQnkVtWKGPLbdSSSJxFLQkMTHK2\nVjxj/AgmZ9IOY5RyjAztnhtqW4SMNRTJEDLF+epXv4pvfetbWLNmTbZt3rx5OPbYY/Fv//Zv2HLL\nLQdUTxAE2HzzzbF48WKvLkIIIYQQQgghhBBCCCGkyHHHHYfNNtsMhx9+OFasWDHW3SEtxnOYEQNR\nMZAKMJRBgFTkIBAlMBLBJFKTGDGUUogT8YMRq0pRjughhBXKaKvBgYjKHFskUcMYY4UsRlkRR+p3\nkwpmlFiXmSAR14SpikBZdxkr3cnFMpnoJRHJWEGMcgQy+fkrR9IyGMeYweK5CbvuyuKXZ04yku7r\nusskjjuiMrVN6gYTp040yMUwgCOOSQU0iYNMbCR3m4EgStZN4iITi/UQAuw2K5CxjjGxXYJJPINy\nF5lk/8RFxrrKwHOUoWMMIcSFIhlCpjh33XVXJmrZZ599cNJJJ+GDH/wgyuVyP0fWsscee6CjowNz\n5swZ6W4SQgghhBBCCCGEEEIImQB88IMfxBZbbIFddtml333f/e534/7778eZZ56JSqUy4EmbZHzQ\nLOa8iBuxlC5L4v6hVD2ZSBK5JApGKSioTByhlUIscSKMUYhhANGIMsmHzv43hEJkBOI4wUi6rhSC\nRCSTimUAK/SwTjJWJJOKXiKV167daCY7GJ4jjHWTUU5vCmM34JEbOeo7zeRlrrGKSVx6UscYIHeL\nSZdTYUz2cfZ1xTGpe0wsRScZScQzkpQLIjF5eeIKE6vYOskoA4Moi01KXWTSqKW65ywmE9Gkx9WL\nXWrGYO5zQsjEgCIZQqY4c+fOxemnn44TTzwR22yzzbDq+uY3vzlCvSJTDtoa1mGoYzL0sWx+GcbX\nNVLuY2ThIaXmkcUpL5YpnT+i6kI9OvCzkgNnPSiUhWEeR1cK/Wi6sFRuuG8Ydnhl5fL0bLmjNNMr\n6yyv462vg42z5U06Or2yLZ1Dt5mz0iub9pbp3rrZbNNsWY3S47mMs/vHpXjO7ngAwLS3PJctb7N8\npVe2KspFoVXjXwPTs7G3jjb3JUnhnnXv0UJZFPU03Ld4z1Yjt55qw+MAIHbWTRx7ZcZ7I+K/NChe\nSdWsTNyysbgHGrfpWgvXY+DvPpqNyGCO5cuWmv8T4guoMcOg0atFQgghhBBCBsZb3/pWvPWtbx3w\n/ltttRWuv/76UewRGQ3qCQeGI5pJI5eQLiWRS8pzk7FPKxFiG4OUxC7llaZxS4l9DKybTGANXVKj\nGojjLCNaQQkysQySI7W27zZSEYx1hrHlgcqX81ildC3fNtFIhS8pUtgmkscpSSqScfYxxhfRpA4z\nqXtMDBut5IpkrOOMJIIZK5CJszglP2YpSmUzqSNQHqjkRS0VRTHF5WYoperGME12oYxBC+OWWtQO\nIc2gSIaQKc5111036f/PnRBCCCGEEEIIIYQQQggho0XQ/y5AHn+j8v0zJ5k0cgkARCWRS7VuMhYD\ng0Qgo1A7h0V0IrRRCJSGKCu1SafLaYPMWcbEkrnIpBOSlAJ0nAtktE5EMsnxadRQUTzjCmPq/dWl\n0Z9iRnMO6WDadDeZOmIYdx8pCGNSJ5ksxkmk4DAjmXNMLpJJtxsroEkEMrlIJoZRJotZAlIhTJz0\nIXeR8aKWmsUsDSp2KQAQ97sXIWTiQZEMIVMcCmQIIYQQQgghGdJakz8aChJCCCGEEDL1EBEolQpk\ngprIJQOp6yYTqyipINkxFcg0EMrY7amrjMqcalJnmVgJAmWlN4EoqMShxLrKWIeZVDAD5CIYnbad\nbhNfFDNSf3YZzPPSaLSZLhrJN5jCtlQYY+OaxHOaiSGJ+4zdIXWOcYU09QQyqTtQKpCJVQyDCDEi\nxCpynGJqXWT8czGFf/kA2oj0GraqLULGmnoxeIQQQgghhBBCCCGEEEIIIYQQQgghhEwq6CRDCCGk\nNYyQPHhwtYxvSbI/JEPv61CHtvlx423s/KkQzVywimXuek2ZzvXCQeDbwmrta4nDMHSWS15ZyVkP\nS2WvLAgK+5Y6suVyabpX1l6amS13ti3wyuZjQ299g3Jntrxxp39em3f2ZMvz1u/2ytS6G8BngNNM\n+rslxpsx2RBvYVW819adnS3PW/8Vr2zznmnZ8pq4wyurmE5v3VSc69dW22rD9mvu9Z6GZU3vdVUt\nNtq4jTi3ka2ZhFX4xeH/Givs7dRb+/tmrH/HFNv3x8Dt72BmYg31uGJ/RNxrOZh6WkHzsRvanvUO\nbnKPjL9BmVQIFExLf6nzehJCCCGEEDKVEUhiBJM6viRPCWK8yCUjgFb2/ZwogREDwEArBSMKSinE\nUojGSdxkRGJoaATJ84ck3jQqdaFRNn4pfTqJRUHDut0oWLcYlTjLpCjV2IlAD/Axx7Tw9chw++RG\nKQG5c4zJXGSSfVKXl4KDjMDGKwls7JJty+RRTI6LjCQDbWAgyiD9T5R1FDISJX3wo5aQtC9w4pbG\n/B3UxMBA1byXHM22CBlrKJIhhBBCCCGEEEIIIYQQQgghhAyBoP9d6iAwUInMJItbSoUOKgYQ2jCd\nJHJJI84mlRhl/6BvECECECaRR4GyfXHFMkYUgqTu9PhA6SSlKRfLGEf0opVdT/+UrxzRTIpy9s22\npTs00WU0i/wZSdFMI1FMs8mHLm4/036JV14rihGxghcgFdX44hgrnDHZMTHydVcgk8ctxYhgo5Zs\nnFIMkTgRx8CLWrL9i7N7yPbJFcvky4MjSHpKCJlMUCRDCCGEEEIIIYQQAPkMQEIIIYQQQgjpn0YC\nmUYeKz51hTJA4gUi0I6bjIGGSgUZEMQqQiAhAOMJZQBAK50vQwFi3WNS4YhIDJWIZ1KxjIJkvVYi\nUCrpWSKeieEbm6bLSlzRycAfpooOJ/09h9Ur70/vUixXcAZpELhCmGJ/jB1cTxRjtyfCmYI4JnWO\nSY9NPGIQI4ZJXWOUFaVEiVOMwCBWUeISY++NtJXURcYkZbZvviBm4AIZnfS8SACgsUvzZCAx/WlZ\nW4SMNRTJEEIIGT1a/m1nfH+7GqnhGGpsyfiLO+mP/ClODzFeqbhejFDSTsRSMW7JjVey63lsUqkQ\nt+RGLDWLV7LreURPhxOvBADTy/Oz5blY3ytbrzTLX5+W93e99sgrm9eRR/KEMwtj19b469+w7Edd\nu9kxsMwcKevUmr4741UcS3ec1+v1Y7bWVP1xjmRWthxXCw/qbXnfa2714ssMZ4dqtadh2WB+LqLI\nv39ciq8FjBn4rBt3xlHxZ7h2ZtRY/z5q3L5IcewGVs/gjmtSY+MUq3HCsEKVhtjkkHOtCCGEEEII\nIYSMGP67tIE6lBSx4hhbVypmsL4tvpuMUmm8TvLMrQLrOiIRAoQw0EAirkAaoyTIpC8CG8sEWCcZ\nBcnEMkopaFEwqfDFFc0IoGBFM7nwxj3xAb7TaBJj5I/H8N6R1LsOeX+LLxkGWKlzmNvfRqIYIHWa\nkWQfSVxnfCeZ1EHGCmNygYwrgokRZTFLuYtM4hxTdJFBrSCmKJgZCOkY+tdiaI5JhJDxCUUyhBBC\nCCGEEEIIAWBfWg7VhHqo7RFCCCGEEEKmBq4Ixt8ugOMkAzGACjw3GS2AScsRQQsQKyBQIWKxE4BM\nUm+oEoGDSlxpxCBAYF1lYMsUFHTiLqPF9ix1haknmoFIzTyNVEQzEOo9ZxX1MI0mgTXTzdRoYpKd\nixPB6mmY9CAeyGrFPMm/dUQx7vbUOSZ1enGdYNJ4JUmcZESZzD3GlkdJ/FIEERu7lEYs2bpzFxnb\naC6ecfvg9bulT7wTB4OWTHsCwPcAZHxAkQwhhBBCCCGEEEIIIYQQQgghZEgMxEVGkggju2KsT4sy\nnmAmFTcopROBQ+4mYwAESMURSfSSxDBKQasARgxyCY0VysRixSJp/FLqKpMKZFJ3GQ3rJqMysYXd\n0xXN2O32n1RsEw9ijEw9wUZB/dJIJNNM1tFI6FIrkqnnMDN4WUTxPFxRjOcyk5QVxTGSXU1k7jEC\n8QQyabkogUGcOMik4hqn3HGRaRS1lO4nIo6IZmAyDaXUsJ19CCHjE4pkCCGEEEIIIYQQAiCZ/dfC\nd4B83UgIIYQQQshkIhe8FN1iGiEwNtJIBd42JfDcZKC0I6JJ43UCGImsBYbKBRIBQkQAtBIrBEni\nl1IhhRIbppSKZVIXmVRYkm1LnWQKQomBnVkD95jieqHuemKawZALX9x4b+U4zDQ6bmDUOMqk/0rq\nHJOLZnI3mVwckzrH2O15vJIVvuTxSkjWjERIvWaQRG/ljfsuMvWilgbqHGMjvgzsSEw9txkjrXOS\naeU7B0IaQZEMIYSQodMiFXXzVibyN6rR77t/icb7WPlfw3WTGSjuzIfiLIjiutb5I14Q+l99giCo\nuwwAYVj21kthKS8rlQr7OmVhh1dWLk0rrM/IlqeX5nllc9S62fLaai2vbF6737+57fn1nF2OvLK2\ntnxdBYVx7K14q7J6Vb7S2YmRoNGsl4mANx4AlDNexbF0x7l4DeYWrld3nK/3xv61NeLMOyr5D+Gm\n8FDe7GG1+aStYuHAfr7iYqWRf57GDOylQfGFT/Hn24zr31XFGVLu759WtNmqVxQjReO+j8pZ9fdd\nZPQuEiGEEEIIIYQQQgghZAJCkQwhhBBCCCGEEEIAJJbYY90JQgghhBBCyIRhIFFLA0GQx+EopfNt\nhcglwEYMGaWhC24yOnGjiSVKnGxCABpQsY17Sp1ikjgnJQoxAJ24yqTYNZU9HBWjiwYSU1QTS9TP\net04pkE8nRX7CDj9bHAeI31eeSSSu55HJ2VuMqnbjDKZi4xBZI9OIpYAeC4yBgKRNJ7JOG3Efh/E\nDGrc+mOqRC618l3A5B9NMhGgSIYQQgghhBBCCCGEEEIIIYQQMmCUUiMmkCkiYgCFmsil1NzVAAhg\nYFArlAESsYxY4QWg7X5p9BKQC2aUFci4MUwAIF5slC+eSdtvRn8CGbuPI/RQwxPIpNQTyihx+18b\nqjQUoQyAGjFMvj0XxaRl2TZIJozJ982FL6lAxkiU758IZNz9UjFVMWrJi2IaQUbzXieEjA0UyRBC\nCBkcY66aHuv2B85IDVVtPRNnDJpTjElqsmeTSKVm8UqAH7FUG6kUOst+hFKpsB448UvFfcOw3Tmu\nGLc0w1ufVpqTLXfq+V7ZLOQxPLPLfhsz/VXMCPKHvlD7D4DaebCWauF+Wd3j7/v6smzZjFDc0kTG\nHQ8A3ngVx9Id5+I1cK8PAMws5fde8dr29eXXvaqrXllc8uONXJrPYmker+T+2BR/9pTy+9AUJ35p\noNFLQG3f3T64cUbJloH3Z1zROKYJGHoKUPGyj+93NMVrNwaddQdsfA/WuEHQ2nzwMf9qSQghhBBC\nCBkhagUYI0HqJmMQQKciCKUhYqAUaoUysAINpRQ0ArsfNFKxDID6ghlYhxnAyjFc8UgqNHECs/vv\nt2oulPFEMvVcZNTgBR9K6ohgVGORTI2zTOKsMxjc86wrlkmEMXabZMKYdB9XHCMQiOTOMK5AJhPA\nSC6yKbrIjBzpOI2O6GY8YqR1b21a+c6BkEZQJEMIIYQQQgghhBBCCCGEEEIIaSkiAqRiEAGQiFSQ\niWGsm4wojTR2ye5qpRZaUCOUsTvEiQNN7LjKALnoobFgxiUTkRTUA67YxDQRUngxQAXRS9Ftpn49\ngxFp2FipRv2060VRTMExp4FKYiDnWxMnVSOMSY92xUH1BTKSxi05Ahk3ZiktTyO6UheZNGopFdRI\nKsLh7AxCSAGKZAghhBBCCCGEEEIIIYQQQgghQ6ToUKKzpYaIyUUxAyQVlqTRS/WFMgAQABJD4LvK\n5I4w1l1GQyeyjVww459V/f6bBn4rReGL3Wa8tWbl0kCAAtSPZFI1brxOGbQjCUodclxyUU29GCb3\n3Budr0tj0Y/vGgPk5+KKY4BivFJSq/gxS/XGeEA0jWJSAAQKunANNKaSmwwhUwmKZAghhBBCCCGE\nEALAxh9xkh0hhBBCCCFk4IxczJI4cUqN3WSQRS/VE8pYImgoqEQsAxUgRpRFD2kENqonaSMX9fjn\nYgZ8fvWFFM0EMK7opZEIpd8oITdOu4GgRyPI6i+KapQjnikKZfLeDu3887il+sKYFNc9xhXH2LJa\ngYwXsdTERWbkmBpCGZHWBZ7znQMZD1AkQwghZNx9K6mTwDoGvRgNhnoeAz+u9lKO37FThee2mgxc\nZwelGpdp7T+oBUHQcD0M/a8+YViquwwAYalcqMfdt90rK4Ud2XK5NMMraw9neusz9Lxseaas5ZXN\ndPowveSfc7t/Wgid09aF6xzF+bHxmsIMmBXd/vpry7Jl1dbmlcn662Gyoxa/6m9wxgMAjDNexbF0\nx7l4DcLC+wP3+hWv7cwov+59kX9PRLri9yeMsuXhWMW6P1LD+i3RpA/GDOIFgltNMbN73P0ac1/k\nFH83Dey4ZO9Btze448Yjbk558cVcK5ofxM3U/GISQgghhBBCCIHGSAlkUiGFalafmEQoA1gvmFqh\nTCpmUEp7EUwiURInFCRHR1m8UCqYAVBXYNG0T07fa7Y3EMHUxBKJL5DpVxjTD8V3rAYRVHLe9pT9\ncp1EVBnEDZ1phjIG9c4/PTfXOcb+mwpkjHcNGgpk+hHCSEGgM3xG7l4nhIwPKJIhhBBCCCGEEEII\nACSvJVvbHiGEEEIIIYQQQsYOg9ZNy5r8vjxkIkCRDCGEEEIIIYQQQgghhBBCCCFkWPTnOJIiMANw\nJ3EcQ1Rt3VLHTSbFj1+y0Uupo4ytTkEAqCSGKd1WVAm4LjP1GEhMUn9OMW79ZgSnEWjnZJTjrDpY\np5m8vqDu9rye2rGoNw7etkLEUhqvlJf7LjK19ftRS/0xEGcZBT2CDjSEkPEKRTKEEEIIIYQQQggB\nYFOpDO1dCCGEEEIIIS1CRGqi1kUMlNLeOlSe0CxKJ0IXXyiT4sYvpdFLuVjGOlqqOqIZF1dA07jv\nAxDJ9CuCcUQh/cQIDQajXFFRbbsDFdFkNagBiFDqjEe9sfDHIY9YyuKVsgN8gUwqnMrilArjVW/8\nhhNXPpUw0kInGV4SMg6gSIYQQqYC4/yLYG3vxnd/mzFSQz2Yevx9x/vYDe2rdvFBWWtddxkAdODP\nagic9TAseWVhGNZdtseVCuvlfN+gzSsrhR3Zcls43Svr0LO89ekyM19Wfj3tTl9L2r+WYWEM3Asf\nFfKCq9W8nuoaf3yC5RVvXbW96a75ZX29eXPz5vntd87EhGH1Km9VLVuWr7z2hlcmr73prRtnvIpj\n6Y5z8RoUf4hDp7h4bd3rPj3274k+8ce5qvNrYkL/RY37ImIgLwkalzX+PVJ8seCuN3vpYEyxP4P5\nXeWO7Xj7HVccD+cFUz+/7twh6G/fVtTTeooz5wq/f1rZlXo0u0fH+fcqQgghhBBCCBkLap1hBv9k\nl4of0rpSUUQqmMnKpb5QJqvHcZbxxTIptaIZ227+jiYV0PTf51phSK0YprEQxhRcS4brYpJdB3HP\nNr826VgWxyJfq71urqBooBTHxXWMyfZxxDH2GOP1u5lAxq3DF+IMdfwU0jshv//oKEPIZIUiGUII\nIYQQQgghhACwrwRbKQOi5IgQQgghhIw3brvtNixatAjPPPMM+vr6sOGGG+Lggw/GUUcdhY6Ojv4r\naMLq1atx77334ve//z2ef/55/POf/0RXVxfmzJmDnXfeGUcccQR23333cdHXwTDQmKUaxACOAMat\nx3WTScUUrrsMxNQIZVJcZxlfLJP0t1CGrN3BCUFy6jmYuGKPQoRQzc6124YSvaShautXGrGzTUlh\nwmFBQFPbE19EM3gaT+TyxDFA5hyT7VsQyBTrkDrbvPqyDUMTu0yl6KVWvgvgewAyHqBIhhBCCCGE\nEEIIIYQQQgghhExp1qxZg6OPPhq//vWvve0PPvggfvnLX+Kb3/wmrr/+emy77bZDqv/mm2/GwoUL\nEcf1I3ruuOMOnHfeeVi4cCGuvPJKzJ49e8z6OhiGLJBxKEYuuYIZgWQRQJkQQiXtJkIZS5w5wRhI\n5ixTFMvYjcYTh6ROM4Prc3NHmPQ83Db9/YsOq/1HNzUiHZ9iDQoB4DgP14hoHAFNOp4udowcgc0I\nj5ErjrHlkmx3xDFOuTjRTHkdjV1kRiJqaSoJZQiZSlAkQwghZEwYyJf7ic9wznH0x2eozwjDifNw\njy3m2xYjldz1mjInYikoxCQVY5Pc9SAolDmRSm6cUr11N1KpVPJn4pTDadlye+DH43Sowrppz48L\n/AfL0JnSEhYeOos/M252a9X449NTzc+rbY0/00Ov8OOWSmpN3mal8Ci9pidbVG/4MUTo9GOlpLMz\nX5nuj4+05eeMsj+uTW+o4k1ayfvuRkEV+woAavXqfGX1Gn/flV358hvdXlG03K+3uiJf7l3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          }
        }
      ],
      "source": [
        "f, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2, 2, figsize=(12, 8), tight_layout=False)\n",
        "\n",
        "ax1.plot(objective_values_history)\n",
        "ax1.set_xlabel(\"iterations\")\n",
        "ax1.set_ylabel(\"objective function\")\n",
        "\n",
        "density = get_density(params_final, beta=beta)\n",
        "ax2.imshow(np.flipud(1 - density.squeeze().T), cmap=\"grey\")\n",
        "ax2.set_title(\"antenna density pattern\")\n",
        "\n",
        "sim_data_final.plot_field(\"field_xy\", field_name=\"E\", val=\"abs^2\", ax=ax3)\n",
        "sim_data_final.plot_field(\"field_xz\", field_name=\"E\", val=\"abs^2\", ax=ax4)\n",
        "ax3.set_title(\"intensity antenna (xy) plane\")\n",
        "ax4.set_title(\"intensity side (xz) plane\")\n",
        "\n",
        "plt.show()"
      ],
      "id": "4dd1e3a4"
    }
  ],
  "nbformat": 4,
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