{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Inverse design of a waveguide crossing using S-Matrix optimization\n",
        "\n",
        "In this notebook, we will use inverse design to create a compact,\n",
        "high-performance waveguide crossing. This device is a fundamental\n",
        "component in photonic integrated circuits, allowing two separate optical\n",
        "signals in different waveguides to cross each other with minimal signal\n",
        "loss and crosstalk.\n",
        "\n",
        "Instead of manually designing the structure, we will use an **adjoint\n",
        "optimization** method. We’ll start by defining the *function* we want\n",
        "the device to perform in terms of its scattering matrix (S-matrix).\n",
        "Then, we will use `tidy3d`’s automatic differentiation capabilities to\n",
        "discover a geometric structure that achieves this function.\n",
        "\n",
        "<img src=\"img/adjoint_27.png\" width=400 alt=\"Schematic of the crossing\">\n",
        "\n",
        "This example highlights the use of the\n",
        "`tidy3d.plugins.smatrix.ComponentModeler`, a powerful tool for\n",
        "optimizing devices based on their multi-port scattering properties. It\n",
        "simplifies the process by automatically running the necessary\n",
        "simulations to compute the full S-matrix, which we can then use directly\n",
        "in our objective function. For more details on the `ComponentModeler`,\n",
        "see [this\n",
        "tutorial](https://docs.flexcompute.com/projects/tidy3d/en/latest/notebooks/SMatrix.html).\n",
        "\n",
        "If you are new to inverse design, we recommend our tutorials on the\n",
        "[Learning\n",
        "Center](https://www.flexcompute.com/tidy3d/learning-center/inverse-design/)\n",
        "and our [primer on automatic differentiation with\n",
        "tidy3d](https://www.flexcompute.com/tidy3d/examples/notebooks/Autograd1Intro/)."
      ],
      "id": "dad2759a-a75c-427f-b458-f0853350e855"
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {},
      "outputs": [],
      "source": [
        "import autograd as ag\n",
        "import autograd.numpy as np\n",
        "import matplotlib.pylab as plt\n",
        "import tidy3d as td\n",
        "\n",
        "np.random.seed(2)"
      ],
      "id": "f766110f"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Setup\n",
        "\n",
        "First, we define the basic parameters for our simulation.\n",
        "\n",
        "Our device will consist of two parallel input waveguides and two\n",
        "parallel output waveguides. Between them lies a rectangular “design\n",
        "region.” We will optimize the pixel-by-pixel permittivity within this\n",
        "region to make light from the top input guide cross over to the bottom\n",
        "output guide, and light from the bottom input guide cross to the top\n",
        "output guide.\n",
        "\n",
        "This example is a 2D simulation for speed and reduced FlexCredit usage,\n",
        "but it can be easily extended to 3D by defining a vertical dimension\n",
        "(`Lz`), adding a substrate, and modifying the structures accordingly."
      ],
      "id": "9cd84763-3c88-4447-87f5-bd1d0b3a07be"
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {},
      "outputs": [],
      "source": [
        "# material information\n",
        "n_si = 3.49\n",
        "n_air = 1\n",
        "\n",
        "# source\n",
        "wvl0 = 1.5\n",
        "freq0 = td.C_0 / wvl0\n",
        "fwidth = freq0 / 10\n",
        "run_time = 200 / fwidth\n",
        "\n",
        "# size of waveguides\n",
        "wg_width = 0.3\n",
        "wg_length = 1.5\n",
        "wg_spacing = 1.5\n",
        "\n",
        "\n",
        "# size of design region\n",
        "lx = 4.5\n",
        "ly = 4.5\n",
        "lz = td.inf\n",
        "\n",
        "# spacing between design region and PML in y\n",
        "buffer = 1.5\n",
        "\n",
        "# size of simulation\n",
        "Lx = lx + wg_length * 2\n",
        "Ly = Lx\n",
        "Lz = 0.0\n",
        "\n",
        "# fabrication constraints (feature size and projection strength)\n",
        "radius = 0.150\n",
        "beta0 = 2\n",
        "\n",
        "# resolution information\n",
        "min_steps_per_wvl = 18\n",
        "dl_design_region = 0.01"
      ],
      "id": "e3e3b2c3"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Static Simulation\n",
        "\n",
        "Before we define the optimizable design region, we will set up the\n",
        "“static” parts of the simulation—the components that do not change\n",
        "during the optimization. These include the input and output waveguides\n",
        "and the ports used to inject and measure light."
      ],
      "id": "56525e3e-7422-4e89-bd6f-eacfbe5645c3"
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {},
      "outputs": [],
      "source": [
        "wg_vert = td.Structure(\n",
        "    geometry=td.Box(\n",
        "        center=(0, 0, 0),\n",
        "        size=(td.inf, wg_width, lz),\n",
        "    ),\n",
        "    medium=td.Medium(permittivity=n_si**2),\n",
        ")\n",
        "\n",
        "wg_horz = td.Structure(\n",
        "    geometry=td.Box(\n",
        "        center=(0, 0, 0),\n",
        "        size=(wg_width, td.inf, lz),\n",
        "    ),\n",
        "    medium=td.Medium(permittivity=n_si**2),\n",
        ")\n",
        "\n",
        "wgs = [wg_vert, wg_horz]\n",
        "\n",
        "fld_mnt_name = \"field\"\n",
        "\n",
        "# field monitor that measures fields on the z=0 plane at the design freqs\n",
        "fld_mnt = td.FieldMonitor(\n",
        "    center=(0, 0, 0),\n",
        "    size=(td.inf, td.inf, 0),\n",
        "    freqs=[freq0],\n",
        "    name=fld_mnt_name,\n",
        ")\n",
        "\n",
        "sim_static = td.Simulation(\n",
        "    size=(Lx, Ly, Lz),\n",
        "    grid_spec=td.GridSpec.auto(\n",
        "        min_steps_per_wvl=min_steps_per_wvl,\n",
        "        wavelength=wvl0,\n",
        "    ),\n",
        "    structures=wgs,\n",
        "    sources=[],\n",
        "    monitors=[fld_mnt],\n",
        "    boundary_spec=td.BoundarySpec.pml(x=True, y=True, z=True if Lz else False),\n",
        "    run_time=run_time,\n",
        "    symmetry=(0, 0, 0),\n",
        ")"
      ],
      "id": "608c59e7"
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
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bb75ZEydO1OzZs7VgwQJt375dpaWlatasmVq0aKGjjz5agwcPNnfcqS4pKUnv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mXlvsfOGgAAAACiS3x8vNLT06372dnZnOME8CBqQpOUlBRlZmZ6/PB2vep58+bpyiuvlNPp1Akn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\nAADs4un4P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          }
        }
      ],
      "source": [
        "ax = sim_static.plot_eps(z=0.01, freq=freq0)\n",
        "ax.set_aspect(\"equal\")"
      ],
      "id": "f30f7cd4"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Define design region\n",
        "\n",
        "Next, we define the design region as a pixelated grid of permittivity\n",
        "values that get generated from our optimization parameters.\n",
        "\n",
        "We first define the overall geometry as a `td.Box` and also the number\n",
        "of pixels in x and y static on our design region resolution."
      ],
      "id": "cc37d72b-3efe-42fb-97aa-ed3d9ef088df"
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {},
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "451 451"
          ]
        }
      ],
      "source": [
        "nx = (int(lx / dl_design_region) // 2) * 2 + 1\n",
        "ny = (int(ly / dl_design_region) // 2) * 2 + 1\n",
        "print(nx, ny)\n",
        "\n",
        "design_region_geo = td.Box(size=(lx, ly, lz), center=(0, 0, 0))"
      ],
      "id": "c8d5d457"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Next we write a function to give us the pixelated array as a function of\n",
        "our parameters through our filtering and projection methods, which are\n",
        "used to make the resulting structures easier to fabricate. For more\n",
        "details, refer to our 4th lecture in the [inverse design 101 lecture\n",
        "series](https://www.flexcompute.com/tidy3d/learning-center/inverse-design/),\n",
        "which focuses on fabrication constraints.\n",
        "\n",
        "We also wrap this function in another one that generates the entire\n",
        "`td.Structure` corresponding to the design region, for convenience\n",
        "later.\n",
        "\n",
        "> Note: we will enforce here that the design region has both 90 degree\n",
        "> rotational symmetry and also x and y mirror symmetry, since we expect\n",
        "> the final device to respect these symmetries to work in all\n",
        "> orientations."
      ],
      "id": "e372160c-7016-44ee-a785-8b89080de890"
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {},
      "outputs": [],
      "source": [
        "from tidy3d.plugins.autograd import make_filter_and_project, rescale\n",
        "\n",
        "filter_project = make_filter_and_project(radius, dl_design_region)\n",
        "\n",
        "\n",
        "def get_density(params: np.ndarray, beta: float) -> np.ndarray:\n",
        "    \"\"\"Get the density of material (0, 1) as a function of the parameters (0,1)\"\"\"\n",
        "    fp0 = filter_project(params, beta=beta)\n",
        "\n",
        "    # make sure density has 90 degree rotation symmetry\n",
        "    fp_90 = np.rot90(fp0)\n",
        "    fp_180 = np.rot90(fp_90)\n",
        "    fp_270 = np.rot90(fp_180)\n",
        "    fp_rot_symm = (fp0 + fp_90 + fp_180 + fp_270) / 4.0\n",
        "\n",
        "    # make sure density has x=0 and y=0 mirror symmetry\n",
        "    fp_xy_symm_lr = np.fliplr(fp_rot_symm)\n",
        "    fp_xy_symm_ud = np.flipud(fp_rot_symm)\n",
        "    fp_xy_symm_lrud = np.flipud(np.fliplr(fp_rot_symm))\n",
        "    return (fp_rot_symm + fp_xy_symm_lr + fp_xy_symm_ud + fp_xy_symm_lrud) / 4.0\n",
        "\n",
        "\n",
        "def make_eps(params: np.ndarray, beta: float) -> np.ndarray:\n",
        "    \"\"\"Construct density values and rescale them to relative permittivity values between air and silicon.\"\"\"\n",
        "    density = get_density(params, beta=beta)\n",
        "    return rescale(density, 1, n_si**2)\n",
        "\n",
        "\n",
        "def make_custom_medium(params: np.ndarray, beta: float) -> td.Structure:\n",
        "    \"\"\"Make td.Structure containing custom medium with the permittivity data as a function of parameters.\"\"\"\n",
        "    eps_data = make_eps(params, beta).reshape((nx, ny, 1))\n",
        "    return td.Structure.from_permittivity_array(eps_data=eps_data, geometry=design_region_geo)"
      ],
      "id": "9a23f804"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Construct Simulation\n",
        "\n",
        "With all of these functions and variables defined, we can write a single\n",
        "function to return our variable `td.Simulation` as a function of our\n",
        "design parameters. This function first constructs the design region, a\n",
        "mesh override structure to control the resolution in this region, and\n",
        "then creates a copy of the original `td.Simulation` with all of the\n",
        "basic parameters."
      ],
      "id": "6c953383-bce4-40a7-a536-802cd3f6376a"
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {},
      "outputs": [],
      "source": [
        "def get_sim(params, beta, include_extra_mnts: bool = True):\n",
        "    design_region = make_custom_medium(params, beta=beta)\n",
        "\n",
        "    design_override = td.MeshOverrideStructure(\n",
        "        geometry=design_region.geometry,\n",
        "        dl=[dl_design_region, dl_design_region, dl_design_region],\n",
        "    )\n",
        "    grid_spec = sim_static.grid_spec.updated_copy(\n",
        "        override_structures=list(sim_static.grid_spec.override_structures) + [design_override]\n",
        "    )\n",
        "\n",
        "    update_dict = dict(\n",
        "        structures=list(sim_static.structures) + [design_region],\n",
        "        grid_spec=grid_spec,\n",
        "    )\n",
        "\n",
        "    # if include_extra_mnts is False, update sim to only include mode monitors, to save data.\n",
        "    if not include_extra_mnts:\n",
        "        update_dict[\"monitors\"] = []\n",
        "\n",
        "    return sim_static.updated_copy(**update_dict)"
      ],
      "id": "ce7bcd74"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Let’s test out our function. We’ll make an initially uniform array of\n",
        "parameters and generate the static simulation to plot and inspect."
      ],
      "id": "164a917d-424d-4285-a3a9-13956bcd1174"
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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vatasWWC61rBhw2Sz2fTdd98FjlnbYpT1/X3XxVFHHRV4fX2EWqQ12o4//nht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gAAAADClyPh11Ho0Vo4YXoO7BIzRZOCggLt3bvX67LqLnQqSa+++qrGjBkjSerUqZM++ugjv69j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\nXe8iI0kdO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          }
        }
      ],
      "source": [
        "params0 = 0.5 * np.ones((nx, ny))\n",
        "\n",
        "\n",
        "sim0 = get_sim(params0, beta=100)\n",
        "sim0.plot_eps(z=0, freq=freq0)\n",
        "plt.show()"
      ],
      "id": "928419c6"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Next we will set up an initial set of parameters to approximate the\n",
        "waveguide crossing represented by two intersecting waveguides. We’ll use\n",
        "this as the starting point for our optimization since it already mostly\n",
        "works.\n",
        "\n",
        "Below we’ll import a helper function to set this up automatically by\n",
        "looking at a base `Simulation` object and a parameterization\n",
        "corresponding to the design region `Structure`."
      ],
      "id": "51846adf-bb6e-4a99-8757-745939349bcf"
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {},
      "outputs": [],
      "source": [
        "from tidy3d.plugins.autograd.invdes import initialize_params_from_simulation\n",
        "\n",
        "params0 = initialize_params_from_simulation(\n",
        "    sim=sim_static,\n",
        "    param_to_structure=make_custom_medium,\n",
        "    params0=params0,\n",
        "    verbose=False,\n",
        "    beta=10,\n",
        ")"
      ],
      "id": "99609966"
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {},
      "outputs": [],
      "source": [
        "sim0 = get_sim(params0, beta=10)"
      ],
      "id": "7c69e8d8"
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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HH3981CBE2hXW/OlPf9LEiRP14Ycfav78+dqwYYNqa2vVqVMndenSRfvvv79G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\nPv2PT//9U3L8Q3KTZaoOv3/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nH3bYYZIkr9cbcV2UBQsWSNr1H3/o0KGWl5EI4bYVDl7j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\nHN127drp5JNP1ooVK7R06dI6P75Dhw7OB09Nl2Irv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          }
        }
      ],
      "source": [
        "ax = sim0.plot_eps(z=0.01, freq=freq0)\n",
        "ax.set_aspect(\"equal\")"
      ],
      "id": "43dd5a97"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The simulation with design region and initial parameters looks very\n",
        "similar to our initial waveguide crossing.\n",
        "\n",
        "### Component Modeler\n",
        "\n",
        "Next we use the `ComponentModeler` to wrap the `Simulation`, together\n",
        "with a set of `Port` objects, in an object that makes it straighforward\n",
        "to generate scattering matrices. The `ComponentModeler` figures out\n",
        "which simulations need to run for a given specification and can perform\n",
        "parallel processing and final assembly for us. For more details, refer\n",
        "to [this\n",
        "tutorial](https://docs.flexcompute.com/projects/tidy3d/en/latest/notebooks/SMatrix.html).\n",
        "\n",
        "> Note: we will use `run_only` argument to only compute one column of\n",
        "> the scattering matrix, helping save computation time. The structure\n",
        "> works the same when turned 90 degrees so we can determine everything\n",
        "> we need using the single port excitation + applying symmetry in the\n",
        "> design region."
      ],
      "id": "caa9c16b-d35d-4e0f-af4a-c9fd3981ded1"
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {},
      "outputs": [],
      "source": [
        "from tidy3d.plugins.smatrix import ModalComponentModeler, Port\n",
        "\n",
        "# set up the ports\n",
        "spc = -Lx / 2 + wvl0 / 5\n",
        "\n",
        "ports = []\n",
        "for side in \"-+\":\n",
        "    for axis, dim in enumerate(\"xy\"):\n",
        "        center_axis = spc if side == \"-\" else -spc\n",
        "\n",
        "        center = td.Box.unpop_axis(center_axis, (0, 0), axis=axis)\n",
        "        size = td.Box.unpop_axis(0, (lx / 2, td.inf), axis=axis)\n",
        "\n",
        "        port = Port(\n",
        "            center=center,\n",
        "            size=size,\n",
        "            direction=\"+\" if side == \"-\" else \"-\",\n",
        "            name=f\"port_{dim}_{side}\",\n",
        "        )\n",
        "        ports.append(port)\n",
        "\n",
        "\n",
        "def get_modeler(params, beta, include_extra_mnts: bool = True):\n",
        "    \"\"\"return the ComponentModeler given the parameters\"\"\"\n",
        "    sim = get_sim(params, beta, include_extra_mnts=include_extra_mnts)\n",
        "    return ModalComponentModeler(\n",
        "        simulation=sim,\n",
        "        ports=ports,\n",
        "        freqs=[freq0],\n",
        "        run_only=[(\"port_x_-\", 0)],\n",
        "    )"
      ],
      "id": "1c4926ae"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Let’s first plot the fundamental simulation generated by the\n",
        "`ComponentModeler` to verify that everything looks sufficient."
      ],
      "id": "eee85804-16b2-44c6-8ec2-ea734019e56f"
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "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\">13:13:47 UTC </span><span style=\"color: #800000; text-decoration-color: #800000\">WARNING: </span><span style=\"color: #008000; text-decoration-color: #008000\">'ModalComponentModeler'</span><span style=\"color: #800000; text-decoration-color: #800000\"> was refactored </span><span style=\"color: #800000; text-decoration-color: #800000; font-weight: bold\">(</span><span style=\"color: #800000; text-decoration-color: #800000\">tidy3d </span><span style=\"color: #008000; text-decoration-color: #008000\">'v2.10.0'</span><span style=\"color: #800000; text-decoration-color: #800000; font-weight: bold\">)</span><span style=\"color: #800000; text-decoration-color: #800000\">.</span>\n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #800000; text-decoration-color: #800000\">Existing functionality is available differently. Please consult the</span>\n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #800000; text-decoration-color: #800000\">migration documentation:                                           </span>\n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #0000ff; text-decoration-color: #0000ff; text-decoration: underline\">https://docs.flexcompute.com/projects/tidy3d/en/latest/api/microwav</span>\n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #0000ff; text-decoration-color: #0000ff; text-decoration: underline\">e/microwave_migration.html</span><span style=\"color: #800000; text-decoration-color: #800000\">                                         </span>\n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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eRo4cmbcyBqLufkikDLRvFmk/7af9Dell2t+79ndHhRNX0E3Kcp10SJZaA7PP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\nAElFTkSuQmCC\n"
          }
        }
      ],
      "source": [
        "modeler = get_modeler(params0, beta=10, include_extra_mnts=False)\n",
        "\n",
        "for name, sim in modeler.sim_dict.items():\n",
        "    ax = sim.plot(z=0)\n",
        "    ax.set_title(name)\n",
        "\n",
        "plt.show()"
      ],
      "id": "d156cafc"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Defining Objective Function\n",
        "\n",
        "With our simulation fully defined as a function of our parameters, we\n",
        "are ready to define our objective function.\n",
        "\n",
        "First, we generate a matrix where the `ij` element represents our\n",
        "“desired” transmission from port `i` to port `j`.\n",
        "\n",
        "> In this case, since we only need to specify one port due to symmetry,\n",
        "> we just describe our desired column of the scattering matrix. But this\n",
        "> can be easily generalized to a full scattering matrix."
      ],
      "id": "c8aee3d3-d9cf-4154-a5d7-c216952e03c2"
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {},
      "outputs": [],
      "source": [
        "# the S-matrix column we want\n",
        "s_matrix_desired = np.array([0.0, 0.0, 1.0, 0.0])\n",
        "norm = np.linalg.norm(s_matrix_desired)"
      ],
      "id": "9e140029"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The next step is writing a python function that combines everything\n",
        "together."
      ],
      "id": "5fe6a94c-5aa7-4ca3-81ed-2cd68fe4e4e7"
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {},
      "outputs": [],
      "source": [
        "import tidy3d.web as web\n",
        "\n",
        "\n",
        "def objective(params, beta: float, include_extra_mnts=False, verbose: bool = True) -> float:\n",
        "    \"\"\"Construct and run the modeler, then compare S-matrix column to desired.\"\"\"\n",
        "    modeler = get_modeler(params, beta=beta, include_extra_mnts=include_extra_mnts)\n",
        "    modeler_data = web.run(modeler, verbose=verbose, task_name=\"crossing\")\n",
        "    smatrix = modeler_data.smatrix()\n",
        "    smatrix = smatrix.sel(port_in=\"port_x_-\")\n",
        "    smatrix_array = np.abs(smatrix.data.squeeze()) ** 2\n",
        "    return np.linalg.norm(smatrix_array - s_matrix_desired) / norm"
      ],
      "id": "5d14b1a7"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Differentiating the objective\n",
        "\n",
        "Finally, we can simply use `autograd` (`ag`) to transform this objective\n",
        "function into a function that returns our objective function value and\n",
        "our gradient, which we will feed to the optimizer."
      ],
      "id": "4c6f21d2-8e5a-41aa-b0a3-12ccf57aad56"
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {},
      "outputs": [],
      "source": [
        "grad_fn = ag.value_and_grad(objective)"
      ],
      "id": "93b3a0f8"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Let’s try out our gradient function to verify that it works properly."
      ],
      "id": "85d215a1-dc0e-4a13-b029-c402cb4dae86"
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"abb1de9dee5a4703aac136a0b8bbf5f0\",\"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\":\"cebd4a004ea54a9b8068b622dfe804cb\",\"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\">13:13:52 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\">13:13:54 UTC </span>Maximum FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.067</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\":\"ed73ebbc2af049b982be10b23380a1e7\",\"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\">13:13:55 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": [
              "<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\">13:13:56 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\">13:14:00 UTC </span>Maximum FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.067</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\":\"1e17c33fb7e449f3b83c8294c62a5a0b\",\"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\">13:14:01 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\":\"c49b974df66e422b88023f06d5daa2aa\",\"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>"
            ]
          }
        }
      ],
      "source": [
        "J, grad = grad_fn(params0, beta=1)"
      ],
      "id": "ab2d6bab"
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {},
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "J = 0.2556\n",
            "gradient shape = (451, 451)\n",
            "gradient norm = 0.0286"
          ]
        }
      ],
      "source": [
        "print(f\"J = {J:.4f}\")\n",
        "print(f\"gradient shape = {grad.shape}\")\n",
        "print(f\"gradient norm = {np.linalg.norm(grad):.4f}\")"
      ],
      "id": "b8404485"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Run Optimization\n",
        "\n",
        "Finally, we are ready to optimize our device. We use Tidy3D’s Adam\n",
        "optimizer to minimize the S-matrix mismatch while keeping the plotting\n",
        "callback explicit.\n",
        "\n",
        "We record a history of objective function values and parameters for\n",
        "visualization later."
      ],
      "id": "e8e60505-e767-4b26-9682-74c4a2b8391f"
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
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          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "step = 1\n",
            "    J = 2.8375e-01\n",
            "    beta = 30.00\n",
            "    grad_norm = 1.9465e-02"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "step = 2\n",
            "    J = 2.1593e-01\n",
            "    beta = 30.00\n",
            "    grad_norm = 7.9061e-03"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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UuefVJYLT8zzU63WBrSK6DIOT1FUqFbGr6lK1iC7B4CR1eZ6LLTwsuZo8UVkM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\nAAAASUVORK5CYII=\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "step = 3\n",
            "    J = 1.9010e-01\n",
            "    beta = 30.00\n",
            "    grad_norm = 6.4550e-03"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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rIReGIR4fH/ldThLF4CQRWmuEYYjxeGz1slprjclkgiAIeLlOYhicJEZr/SFn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\nYII=\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "step = 4\n",
            "    J = 1.7442e-01\n",
            "    beta = 30.00\n",
            "    grad_norm = 6.3818e-03"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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L6uL008fgJG0SiQTS6bTyuslk8qu9c4hUY3CSNqlUCisrK0ovq4UQQdtcIl0Y\nnKRNPB5HuVxWGpyRSASlUgmJREJZTaLHMDhJCyEEotEoXr9+/cW2x9/Ksiz87Gc/C1oEE+nA4CRt\nIpEIdnZ2sLi4qKxmoVDA3t4eDMNQVpPoMQxO0mp9fR37+/tKLteFENjZ2cHW1paCmRHNjsFJ2ggh\nkM1m8f3338M0zdD1DMPA/v4+isWigtkRzY7BSVpZloWDgwMkk8mfVC2ieTA4SSv/KXg2mw1dK5VK\nYXt7G4Zh8MEQacXgJK2EEFhbW0OhUAhdK5vNYmNjg6FJ2jE4SbtcLod8Ph+6TiaTQaFQYHCSdgxO\n0i4ejyObzYYKPCEEMpkM72/Ss2BwknamaSKRSIQ+U4zH40qezhPNi8FJ2gkhlLywzodC9FwYnKSd\nlBKO44ResV1FDaJvweAk7RzHQb/fD11nMBg8SSsOoscwOEm70WiETqcT6mxRSolut4vhcKhwZkSz\nYXCSdt1uF51OJ3Sdfr+PdrutYEZE82FwklZSStzc3CgJzl6vh6urK97nJO0YnKSVlBKXl5fo9Xqh\naw2HQ1xcXGAymTA8SSsGJ2nleR7q9ToGg0HoWrZt4/T0FI7jKJgZ0ewYnKSVbduo1+tKws51XZyd\nnSkJYaJ5MDhJq263i7dv38LzvNC1JpMJarUams2mgpkRzY7BSdpIKdFsNvH+/Xtl9yQ/fvyI29tb\nJbWIZsXgJG2klPj48SMajYaymqqDmGgWDE7SRkqJs7MzpS+t+/dMJ5OJsppEj2Fwkjau6+Lk5ASu\n6/6kaxI9hsFJWvgLe1xeXio9O5RS4urqCuPxmJfrpA2Dk7RxHEf5n0hKKdHpdLjYB2nF4CRtPM97\nkoBzHEfJ601Es2JwkjaqFjD+HBc0Jt0YnKSNaZrIZDJKawohkEqlEI1GldYl+hoGJ2kTi8WwvLyM\nSETdbieEwPLyMmKxmLKaRI9hcJIWQgiYpolSqaS0wZphGNja2kIsFuPlOmnD4CRtDMNApVJBIpFQ\nVjMej2N3d1fpWSzRY7i3kTZCCGxubmJpaUlZzYWFBZRKJQYnacW9jbQRQmBpaQk7OztKgk4IgVKp\nhPX1dQWzI5odg5O0ymQy+P7775U8BTcMA/v7+ygWiwpmRjQ7BidpFYvFsLe3p+Q+p2VZ2NvbQzwe\nVzAzotkxOEkr/wFRPp8PXSudTmNvb0/pU3qiWTA4SSshBNbW1lAoFELXymaz2NjYQCQS4atIpBWD\nk7QrFAooFouhwy6fz/P+Jj0LBidpZ1kWcrlcqBpCCGSzWaXvhBLNisFJ2hmGgXg8HuqMUwgBy7Ke\nZNEQoscwOEk7KWXoZeD8Gly8mJ4Dg5O0cxwHnU4ndOj1ej0uYEzPgsFJ2vX7fbRarVDBKaVEu91G\nt9tVODOi2TA4SbubmxslLYJbrRaurq54uU7aMThJq8lkgvfv3yvpPdTr9YLWwAxP0onBSVp5noda\nrabkEns4HOL4+BiO4yiYGdHsGJyk1Wg0wrt375Q81HEcBycnJ+j3+wpmRjQ7Bidp1el0cHR0pKQr\n5WQywfHxsZL7pUTzYHCSNlJK3N3d4fz8XNk9yQ8fPuD6+lpJLaJZMThJGyklLi4ucH9/r6xmq9XC\n+fk5JpOJsppEj2FwkjaTyQT1eh22bSurOR6PcXp6yuAkrRicpIWUEq7r4vz8HK7rKqvreV5Qk68k\nkS4MTtLGcRxcX18rPTuUUuL6+pp/eklaMThJm/F4jFarpbSm/6eXKi//iR7D4CRtHMfBYDBQfkk9\nHA55xklaMThJG8/zlLy/qasu0UMYnKRNJBJ5koWHDcNQ0qedaFbc20ibaDSKRCKhvLFaPB5HLBZT\nWpPoaxicpE0sFlPSFniaEAL5fB6WZSmtS/Q1DE7SJhaLYXV1VelltRACKysrPOMkrRicpIUQAqZp\nYnt7G9FoVFld0zRRLpcRjUbZW520YXCSNpFIBOVyWWlL33g8jkqlwm6XpBWDk7QRQuDly5dYXV1V\nVnNpaQmlUolnm6QVg5O0EUJgYWEBlUpFyX1OIQRKpRJWVlYUzI5odgxO0iqTyeD169dK7nOapomD\ngwMUi0UFMyOaHYOTtIpGo9jd3UUymQxdy7Is7O7uIh6PK5gZ0ewYnKSVYRioVCpK3udMp9PY29uD\nYRi8x0laMThJKyEE1tbWlFxeZ7NZvHjxgn9uSdpxjyPtcrkcisViqLNEIQQKhQLvb9KzYHCSdpZl\nIZvNhr68zmQyvL9Jz4LBSdpFIpHQfyIphEA0GuVlOj0L7nWk3WQyCb3wsJQSjuNwHU56FgxO0s62\nbbTb7dArwXc6HYxGI0WzIpodg5O0a7VauL+/DxWcUko0m000m02FMyOaDYOTtJJS4vLyEvf396Fr\ndTodXFxcYDKZsDUwacXgJK08z0OtVlPS7bLX66FarfI+J2nH4CStHMfBu3fvMBwOQ9eybRvHx8dK\nahHNg8FJWnW7Xbx58waO44Su5Xkejo6OeJ+TtGNwkjZSStzf36NWq2EymSipV6/XcX19rWB2RLNj\ncJI2Ukqcn5/j6upKWc3b21vU63U+HCKtGJykzWQywcnJCQaDgbKao9EItVqND4hIKwYnaSGlhOu6\nqNVqcF1XWV2/puM4POskbRicpM14PMbV1ZWS+5s+KSWurq5g27aymkSPYXCSNqPRSPkTcCklWq0W\n//SStGJwkjbj8RiDwUD5JfVwOOQZJ2nF4CRtXNcNvSrSlziOo+S9UKJZMTiJiObE4CRtTNNU0hb4\nc9FoFKZpKq9L9BAGJ2kTi8WQSqWUd6RMJBJsoUFaMThJG8uylLQFniaEQD6fZ3CSVgxO0sayLKyt\nrSntEySEwOrqKizLUlaT6DEMTtJCCAHTNFEqlZTejzQMA6VSCdFoVPktAKKHMDhJm0gkgkqlgkQi\noaxmIpHAzs4Ou12SVtzbSBshBDY2NrC0tKSsZqFQwNbWFoOTtOLeRlotLS1hd3dXSdAJIbC9vY21\ntTUFMyOaHYOTtBFCIJPJYH9/X8l9TsMwsLu7i0KhoGB2RLNjcJJWlmXh4OAAyWTyJ1WLaB4MTtIq\nEomgXC4jm82GrpVKpbCzswPDMPhEnbRicJJW/gOixcXF0LXy+TwfDNGz4B5H2uXzeSwsLIQ6SxRC\noFAooFgsKpwZ0WwYnKRdIpFAsVgMfXldKBR4f5OeBYOTtDMMA6lUKlQNIQSSySQMw1A0K6LZMTiJ\niObE4CTtPM/DcDgMVUNKidFopLTxG9GsGJyk3Xg8RqvVCt17iE3a6LkwOEm7fr8fOjillOh0Ouj1\negpnRjQbBidp12q10G63Q9fpdrtoNBrKu2YSPYbBSVpJKdFoNJScKQ6HQ9zd3TE4STsGJ2nlB2fY\nh0MAYNs2bm9vGZykHYOTtJJSot1uK+mv7rouWq0WJpMJw5O0YnCSVlJKDAYDeJ4Xupbneej3+3wl\nibRjcJJWUkq4rqvkDFFKqSSAieYlJK9xiIjmwjNOIqI5MTiJiObE4CQimhODk4hoTgxOIqI5MTiJ\niObE4CQimhODk4hoTgxOIqI5MTiJiObE4CQimhODk4hoTgxOIqI5MTiJiObE4CQimhODk4hoTgxO\nIqI5MTiJiOb0/wBw9PM1squCfAAAAABJRU5ErkJggg==\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "step = 5\n",
            "    J = 1.6128e-01\n",
            "    beta = 30.00\n",
            "    grad_norm = 7.1813e-03"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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1TcdifRC3vZFO39yb2/Z6vQiHw33/Oxnbtk7NrG/fx9rezXrW3/DwMIaHhzE1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\niMFJRDQgBicR0YD+H93gDIH5ZM/zAAAAAElFTkSuQmCC\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "step = 6\n",
            "    J = 1.4569e-01\n",
            "    beta = 30.00\n",
            "    grad_norm = 8.4199e-03"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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0Mn3IavQ3t10qlZDNZpHJZJDJZFAsFgHAnBb7fD7zGovR/RF4+Cr4N0cpxvUa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\nEIOTiKhB/w0h9GGJzvQpOQAAAABJRU5ErkJggg==\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "step = 7\n",
            "    J = 1.3025e-01\n",
            "    beta = 30.00\n",
            "    grad_norm = 9.9025e-03"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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n57G2tqa3O9BGg1arFU6nU1+BWmvWNjIyojdPs9lsVXVDPNkn5fDwECsrK5ie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\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "step = 8\n",
            "    J = 1.1000e-01\n",
            "    beta = 30.00\n",
            "    grad_norm = 1.0920e-02"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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b6CAMThJC1/WarWBk1OaIk0RhcJIwtVypnaNNEonBSUJIkgSn01mTK982mw1Op7MmV+yJ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\nAABJRU5ErkJggg==\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "step = 9\n",
            "    J = 9.0933e-02\n",
            "    beta = 30.00\n",
            "    grad_norm = 1.0897e-02"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "step = 10\n",
            "    J = 7.3210e-02\n",
            "    beta = 30.00\n",
            "    grad_norm = 9.7456e-03"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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JyUmkUinD2kyn05iYmCjo6SOiUjE4SQhN05DJZDA9PW1oyKmqiunp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\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "step = 11\n",
            "    J = 6.0922e-02\n",
            "    beta = 30.00\n",
            "    grad_norm = 8.5674e-03"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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02pAxnz9/jj/+8Y8YGhpicJIwDE4ynaqqUBQFV69excWLF5FIJAwbW1EUXL9+HRcuXEAs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\nsGvXLlRWVsJutyM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UFRWZuJdEC2NwUl7Isoyqqio0NTVlvEYpSRIcDgeWLVuG6upqU55C\nIsoEg5PyQrtQ5HK5sjpVlyQJTqdTn6XyNJ3ygcFJeaGqKmKxGCYnJ5FIJDIq0KGqKhRFweTkJObm\n5vR/RyQag5PyIp1Oo6+vD11dXYjFYhm/Lh6Po6enB0+fPkUymTRxD4kWxuAk4VRVxdzcHK5cuYK+\nvj6kUqmMX5tKpTA0NIRLly6x6jvlDYOT8mJoaAinTp3CzMxM1q+NRCI4ffo0nj59ylN1ygsGJwml\nqiqSySSuXr2K+/fv53S6nUql0N3djYsXLyKZTDI8STgGJwkXCARw4sQJTE9P5zxGMBjEDz/8gImJ\nCQP3jCgzDE4SSlVVPHz4UG/pm6t0Oo2uri7cuXOHrYFJOAYnCRWPx3Hp0iUMDw8veazJyUmcP39e\nvzWJSBQGJwkVDodx8+bNrG5BWkgikcDt27cRCAQM2DOizDE4SRhVVTE1NYXu7m5DWvmqqoonT55g\ndHTUgL0jyhyDk4QaHR3F+Pi4YeNNTU1heHiYa5wkFIOThEmn0xgaGkI0GjVszFgshoGBAQYnCcXg\nJGHS6TQGBgYMfVQymUxicHBwSVfoibLF4CQhtBvfh4eHDVnf1KTTafj9fiiKwlknCcPgJGHi8TjG\nxsYMDThVVTE+Pm7IVXqiTDE4SZhYLIZgMGj4zDAcDvNeThKKwUnCxONxU2aGsViMM04SisFJwiST\nSVMu4qTTadbmJKEYnCSMLMuwWCyGj2u1WrNqv0G0VDzaSBi73Y7CwkJD+wRJkgSXy5VTf3aiXDE4\nSZiCggLU1tYaOjuUJAk1NTVsFUxCMThJGJfLhY6ODjgcDsPGdDgcWLNmDQoKCgwbk2gxDE4Sxm63\nY+vWrWhsbDTkdF2SJNTW1mLHjh08VSehGJwkhCRJkCQJK1euxNtvvw2Xy7XkMe12O3bu3In29nbI\nsswe6yQMg5OEkSQJxcXF+Pzzz7Fy5colBZ0kSWhoaMDhw4dRXl5u4F4SLY7BSUJZLBasX78eH374\nIdxud87jFBQU4P3338emTZtgtVo52yShGJwknMfjwSeffILOzk7YbLasX2+xWLBmzRp8/vnnKCkp\nMX4HiRbB4CSh5q91Hjx4EGVlZVnNFiVJgtfrxYEDB7B69WqubVJeMDhJOEmSUFhYiLfeegvt7e1Z\nXRG32Wxobm7Gnj17UFxcbOJeEi2MwUl5Icsy6urqsGbNGhQWFmZ0U7wkSSgoKEBbWxsaGhpMeXyT\nKBMMTsoLSZLgcDjg8/mymnHa7Xb4fD44nU79tJ9INAYn5U0ikUAwGISiKBm/RlEUBINBxONxqKrK\nqu+UFwxOyotUKoWxsTF0dXVhdnY2o3YaqqoiGo2iu7sbw8PD7DNEecPgJOG0ADx37hzu37+PRCKR\n8WsTiQS6u7vx66+/IhKJmLiXRAtjcJJQ2un18+fPcfToUYyNjWXVvE1VVQQCAZw4cQLd3d1Ip9M8\nXSfhGJwkXDgcxvfff4/r169nNdvUKIqCO3fu4MiRIwgGgybsIdHrMThJqFQqhdu3b+Po0aMIhUI5\njxOJRPDjjz/i2rVrSCaTnHWSUAxOEkY7zf7zn/+Mnp6eJYWdqqro7+/Hn/70J4yOjhq4l0SLY3CS\nEKqqIp1O48GDBzhz5owhXSnj8TjOnz+PmzdvIpVKcdZJwjA4SZhoNIrTp0/D7/cbFnKjo6M4deoU\nZmdnDRmPKBMMThImEAjgzp07OV0QWoiiKLh37x4mJiYMG5NoMQxOEkJVVYyOjmJoaMjQU2pVVTEy\nMgK/35/VbU1ES8HgJCG0C0Nm3LQejUYxOTnJNU4ShsFJQqiqikgkYshFoZcpioJwOMzgJGEYnCRM\nIpEw5fnyVCpl6Lop0WIYnCSMWdWMtFudiERhcJIQkiTBarVmVLA4W7Isw2q1Gj4u0UIYnCSM0+k0\nJeAsFgtcLheLGpMwDE4SQpIkuN3urKq9Z8pms8Hj8TA4SRgGJwkhSRKKi4tRUFBg+NgOhwMlJSUM\nThKGwUnCeL1eeL1ew8f1eDzw+XwMThKGwUnClJSUoLa21tALRJIkobq6Gj6fz7AxiRbD4CRh3G43\nOjs7DV3ntNlsWL9+PTwej2FjEi2GwUlCSJIEm82GLVu2oKKiwrBxfT4ftm3bBrvdzlN1EobBScLI\nsozVq1dj165dhsw6rVYrtm3bhs7OTlPuDyVaCI82EkaSJJSWluLQoUOorq5e8ng+nw+HDh1CVVWV\nAXtHlDkGJwlltVqxa9cu7N27Fw6HI+dx7HY7du/ejT179phybyjR6zA4SbjS0lJ8+umnWLZsWU6n\n2JIkoa6uDp999hnKy8v1f0ckCoOThJIkCRaLBRs2bMBHH32U09XwwsJC7N+/H9u2bYPVamVoknAM\nThJOkiSUlJRg7969WL58OSwWS8avtVgsqK+vx/vvv4+ysjIT95JoYQxOyguLxYK2tjZ0dnaioKAg\n41mj0+lER0cH1qxZA5vNZvJeEr0ag5PyQpIkFBYWor6+PuPKRpIkwel0or6+HkVFRZAkiafplBcM\nTvqXxDYZlE8MTsoLVVURCoXQ39+Pubm5jIJQVVXEYjH09/cjGAyaVlGeaDEMTsqLZDKJBw8e4ObN\nm4hGoxkHYCwWw71793D37l32GaK8YXCScKqqYmpqCqdOnUJfX19WDdxSqRT8fj9OnjyJ0dFRE/eS\naGEMThJKVVUkk0ncuHEDp06dyqnPejQaxZkzZ3Dp0iUoisLTdRKOwUnCBQIBnDhxAkNDQzl1p1RV\nFSMjIzh+/DgmJyf1f0ckCoOThEqlUrh//z4uXLiAeDye8ziJRAJXr17FrVu3oCiKgXtItDgGJwmj\nXRW/fv06RkZGljRLVFUVExMTuHr1KqLRqIF7SbQ4BicJNTs7i97eXkPCLh6P48mTJwiFQgbsGVHm\nGJwklKIoiEQiOa1tvkxVVUQiEd6WRMJJKlfViYiywhknEVGWGJxERFlicBIRZYnBSUSUJQYnEVGW\nGJxERFlicBIRZYnBSUSUJQYnEVGWGJxERFlicBIRZYnBSUSUJQYnEVGWGJxERFlicBIRZYnBSUSU\nJQYnEVGWGJxERFn6f9736auUNE9qAAAAAElFTkSuQmCC\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "step = 12\n",
            "    J = 5.0627e-02\n",
            "    beta = 30.00\n",
            "    grad_norm = 8.9224e-03"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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Pnj2PFPm4ePEi7t69i9nZWd2KfLhcLqxbtw579+59pMjHtWvXcO3aNd0KbagF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\nHDE4iYhyxOAkIsoRg5OIKEf/B1ddhMNeWK5qAAAAAElFTkSuQmCC\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "step = 13\n",
            "    J = 3.8604e-02\n",
            "    beta = 30.00\n",
            "    grad_norm = 5.7748e-03"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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Nl8ulVUAcHh7WNiU2iiRJcDgc8Pl88Pl8AIBwOKzteWj0H9lms8Hj8aC6uhp2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\nAAAAAElFTkSuQmCC\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "step = 14\n",
            "    J = 3.8729e-02\n",
            "    beta = 30.00\n",
            "    grad_norm = 5.6027e-03"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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KsdSJoUlWMEovu91u6Lp+y2SPCMaSJYfDgWQyKbTSqDFh6nQ6zWWEy90S+bsL\nzqX/37iRm41F0cb9VdHD1KWPLt6+UJxovYwlgMa1Lfq7ZVzb2fpuGVZ633+3wfltt3T2j8hKvLZW\nZuXnw23lBOKFTXbhtSUWg5OIKEMMTiKiDDE4iYgyxOAUiJNnZBdeW2IJLZ2RzeVI2V4yweVIZJdv\n+3KkbGSKkOA0nl83Fsou3R1cBIfDAY/HA7fbDVVVze3pRHzQxiJdYy/NeDyOWCzGBfBkCWOjF4/H\nY26wsdwuS1YyHjf1er1wOBxIJBJCH+4wFv8rimI+q25sAm4324NTlmX4fD4Eg0E0NDQgJycH09PT\nGBgYQCgUsn0PSON5eWMz4GQyiYGBAdy4cQMLCwu2P3JpPO7Z0NAAp9OJkZER9Pb2YmJiwvbH0ugf\nm9PpRHFxMTZt2oSamhpomoaBgQFzmzo7A0ySJAQCAdTU1KChoQEejwfj4+O4fv06bt68aeseDMbm\nxxUVFaivr0dxcTGi0Sj6+/sxMjJi+/casDE4jUcNy8rKsGvXLjzxxBNoaWmB3+9HJBJBd3c3jh49\nis8//xzj4+O2PKbl9XrR2NiIp556Co8++ijKysqQTqdx/fp1HD9+HCdPnlz3lld3YjzHW19fj337\n9mHXrl2ora2FLMsYGRnBZ599hiNHjmBgYMC2CpDG7QGj3o7T6TT3hUwmk7xdYJGlm/AaNZkSicSK\nj/+tl8vlQm1tLfbv3489e/agpqYGADAyMoKOjg589NFHuH79ui0hYmzd+Pjjj5vlRFwuFyYmJtDR\n0YFjx47h6tWrWFxctPz9y7KM4uJiPPTQQzhw4ADuuece5OXlIRaLobu7GydPnsRnn32GsbExW/fB\nsPTJIWM3bKfTifz8fDzwwAM4ePAgnnjiCVRVVZlb8Bub6Q4NDeHjjz/G73//e3R1dWFxcdGS85Ak\nCbm5udi1axdeffVVtLa2ori42Ny/L5lMYnR0FEePHsUbb7yBzs5Oy7a0c7lcCAaDePrpp3Hw4EFs\n374deXl5UBTF3IV7cnISH374IX73u9/h4sWLloWn8dn7fD6Ulpaivr4eGzduNLeVm5mZQXd3N/7y\nl79gdHRUaNnef0SKoqCyshL33HMPWlpaUFRUhHQ6bZa/6O/vN3dzt3II6XK5sHXrVvz0pz/FgQMH\nUF5eblYCSKfTmJ+fR2dnJz744AMcPXoUQ0NDlv1dezwebNmyBYcOHcJ3v/vdW/YhVVUVMzMz+Pzz\nz/G73/0OJ0+etHS/V4/Hg6amJvzTP/0TDhw4gA0bNphb2hlbVYbDYZw8eRIffPABzp8/j5mZGXNf\nCis7Z5YG544dO+D1elFfX4/W1lazp+X3+2/ZtXnpRsbGpqfvvvsu/vjHP2JwcHBdw3dFURAMBvGD\nH/wAL774Ipqbm80Pdyld1xGJRMwNV//85z+vaZs3I6wCgQCqq6vxyCOP4ODBg7j//vvNImC30zQN\nkUgEFy9exH/8x3/g1KlTmJ6eXvV7NnqTRq2W/Px8FBcXo7q6Go2NjdiyZQvq6urMCo5GyYBUKoWb\nN2/iiy++wOHDh3H27FlMTk6y95khSZJQWFiIhx56CD/84Q+xY8cOc9NqAGaJCmO3oO7ubly9ehXD\nw8O4efMmZmdnzdpZmfRKJUlCXl4eHnnkEfz85z9HW1sbcnNzv7FJt3EOs7Oz6OzsxIcffoiTJ09i\naGgI8/Pzawpx45fE3r178fLLL2Pbtm13PLbRKbp+/TrefPNNHD58GIODg2seuhvD8urqajz99NM4\ndOgQtm7dikAgcNdMicViGB4extmzZ9HR0YHr168jGo3iwoULazqHO56XlcHZ3t4Or9eL0tJSFBYW\nmj3M5ZZKGLNhkUgEly5dwgcffIDjx49jcHDQ3AB2pS+2sftSbm4uHnroIbz44ovYv38/ioqKlj2+\nMQs4OTmJs2fP4s0338S5c+cwMTFxx+Hs0l2evF4vCgoKUFVVhc2bN+O+++7D9u3bsXHjRuTk5Kzq\nfadSKfT29uL111/HG2+8gZGRkbvu2mTsMm/c02psbMTGjRtRW1uL2tpalJWVIS8vzxyWL1eILJlM\nor+/H2+//TZee+01DA4OcrJqlRwOB4LBIF566SX88Ic/RGNj4x3r8Cz9IhvD97m5OUxMTGBoaAiD\ng4O4fv06ent7ce3aNdy8edOsrHm3EhaVlZV47rnn8Oqrr95y3Lsxru9oNIq+vj588cUX+PLLL3Ht\n2jUMDQ2ZRdOMncpuv96N/VxLSkrw4IMP4tChQ+am4MvVWjKOOzs7i+PHj+P1119HR0eHudXdSpFj\nfM98Ph+qq6vx+OOP49lnn8WOHTuQl5e36kwxduKfmJhANBpFW1vbssfNhKXBaVStW0tFPOPDXlhY\nwNDQEK5cuYLOzk4MDAxgcnLSrI8Sj8dvKfLk8XiQn5+PxsZGtLa24tFHH0V1dfWqqwEab9/ojV27\ndg0XL1685Qa70+mE3++/pVhbWVkZioqKkJeXh0AgYNb6ybRYm6ZpmJ6exunTp/Huu++aGzunUik4\nnU7k5OQgGAyiubkZbW1t2LJlCyoqKpCTk2OuUlh6vNUWDjPqPB07dgz//d//jQsXLiAajfKZ57uQ\nJAlerxf33Xcf/vmf/xnPPvvsir+Yl7p9Q10jTI0a9d3d3Whvb0dXVxdGRkYQiUTMa6CwsBD33HMP\nnn/+eTO4MikVbASJqqpm3fi5uTlMT08jHA5jZGQEoVAIk5OTiEajSKVSt0xsbt++Hc3NzSgtLTV7\n1av9XhnVW9vb23HmzBn09PRgenr6lu+xMTtu1PEqKipCXV0d7rnnHmzduhU1NTXIyclZdWG82z9v\n45eRUQHCCn9zddWX1g4xJjNisRii0Sii0SgWFxfN3qBRJsL4sAOBQMaVJm8/rqZp5nIpY9bbqG9u\n7KS+liqeKx3bKKlx7do1jIyMIB6PIycnB5WVlaivr0dJScmKxe/WctxoNIpLly7hV7/6FT777DNz\ntn/pZbG092p8CbOxXtBqS9fXLn1vt793Y2VGa2srfvazn2HXrl0IBAKW/R0A/1dcbHJy0lxxMjc3\nB5fLhaqqKjQ2NqKyshJut9s8LyuOa/xdGjvXp9NpM9CMJYSKoqz5ujM+z1QqhYWFBUxPT2Nubs5c\nkmdMIvv9fvh8PvOfxnHvVmwx2/7mgnOp1W5IevuHup4PeTXDCDss7RUYoWQUZLMypG8/JvDXybIb\nN27gzJkzOHPmjFlh1Ni9PxAImDXrU6mU2VMZHx/H7OwsYrHYLUO923tX2dh79U69cFmWzTW9eXl5\nKC8vN0cOLpcLyWQSkUjEHN2oqgqv14vKykq0trbiscceQ319vWXhdbulYaaqKlRVNcPd6G3Zef0t\nx8rv1ErfXyuOabe/6eAkMYwv6sLCAm7evImZmRkkk0koimL2AIxFzsaEnlGQzKjgODo6ipmZGcTj\ncXPJk/FnaS/GbkvrLBm7/rvdbvOWTkVFBTZv3oympiZs2rQJpaWl8Pv9Zr2geDx+y8jGKL1SUlKS\n8XCR/nExOAnArUNGo+e4dIh++8SHcUsjGo1icnIS4XAYoVAI4XAYQ0NDGB4exsDAAMLhsBnEdl9q\nxrDP6E1u2LABNTU1qK6uRkVFBYLBIMrLy1FSUgK/3w+Xy/WNe4VLh+vG+d4+pCdicNI3LA2MlX7G\n6K0mk0nEYjFEIhGMjY2hp6cHHR0dOH/+PPr6+mwvjGecr8/nQ11dHR566CG0trZi8+bNqKysRF5e\nHrxer1n3ajW3P1bzOdC3k9BNPujvw2qCYunPOJ1OcyIhJycH+fn5KCwsBABMTExgeHgY0WjUtvNd\nyuVyobq6Gjt37kRraysqKirg8/ngdDozntRjYNLdMDhpXYxw0XXdXHHg9/tRVlaGxsZG1NTUmEtY\nRJyLoijmLHR5eTkCgYCtE2z07cTgJEvc3gP1+XyoqKhAdXX1igu1rWQs3wkGg/D7/RmvrSVaDQYn\nWcoIKIfDgZycHFRUVMDr9Qo7vsfjQXl5OXJzcxmaZBvuAE+2MB5OqKysRH5+/h2fp7aaLMvIzc1F\nMBiEz+cTckz6duKVRZYzengulwvl5eWorKw0nwCxkyzL5vHu9Pw4kVUYnGQbh8OBkpISNDU1CRmu\nu91ubN68GeXl5UKCmr69GJxkC6O35/f70dTUhPz8fNuPmZOTg+bmZuTk5LC3SbZicJKtFEXBxo0b\nUVZWZmuQSZKEoqIic7s1IjsxOMk2xqOKJSUlKC8vt3WyRpIklJaWmsdhb5PsxOAkWxnD9YKCAtt7\nnPn5+bdUGyCyC68wsp2xY5HdvcCl+zcS2YnBSbYzdju3ez8Zo6Y3960huzE4yVa6rpu7JtkZaEbd\nKjtK0hLdjsFJtjLKc4gITqO8CoOT7MbgJFvpuo7FxUXL6tYvJx6PY2FhgeWOyXYMTrLN0kJdIsLM\nOFY26hzRtwuDk2zncrng8/lsX47k9XqFbmFH314MTrKNsQC+oKAAVVVVUBTFtmMpioLKykoUFhZy\nATzZjsFJtjKeHNq9ezdKS0ttCTTjccvdu3ejoqKCC+DJdrzCyHaBQAC7d+/GI488Ar/fb3n7Ho8H\nra2t2LNnj7nBB5GdGJxkK0mS4HA4sGHDBvzrv/4rduzYAafTusIDDocD9957L/7t3/4NjY2NrHtO\nQjA4yXZGvfPt27fjX/7lX1BTU2PJcFqSJFRVVeGnP/0pdu7cCY/Hw9AkIRicJIzf78f+/fvxyiuv\noKioaN3t5efn40c/+hG+973vIRAIWHCGRKvD4CQhjI2F8/Ly8IMf/ABtbW3r2jfT6MEeOnQIxcXF\n5jGIRGBwklCyLKO+vh6HDh1CMBhc05DdqC30wgsvYPPmzbyvScIxOEko437n/fffj61bt8LlcmXc\nhtPpRHNzM3bs2MEF75QVDE4STpIklJSUoLm5GR6PJ+PXu1wuNDU1oaKigqFJWcHgJOGMXmdBQcGa\nliY5HA7k5+ezthBlDYOTsiaVSiGdTmf8OlVVkUwmbTgjotVhcFJWJJNJjI2NIZFIZPzaVCqFcDiM\neDxuw5kRrYzBScIZu7Vfv359TT3HVCqF/v5+zMzM2HB2RCtjcJJwuq4jHA6jv79/Tft0apqGwcFB\njIyMcN9NygoGJwmn6zoGBgYwMTGx5uCbmppCX18fd3unrGBwknDpdBpdXV1YXFxccxuxWAxdXV1r\nmlwiWi8GJwml6zoSiQR6enrWFXqqqqK3txexWIzDdRKOwUnCzc7OYnh4eF2Bp+s6QqEQpqenLTwz\notVhcJJwExMTmJqaWnc7MzMzGBsbY4+ThGNwklC6ruPGjRuYnZ1dd1sLCwvo6+tjcJJwDE4SSlVV\nDA0NIRqNrrutRCKBgYEBsyQwkSgMThIqHo+jt7d3TU8M3S6VSqGvr29ds/NEa8HgJGF0XcfCwgJ6\ne3stWX+paRqfIKKsYHCSUGNjY+jp6bFsaD0wMIChoSFL2iJaLQYnCaNpGq5cuWLJjLphZmYGX3/9\nNVRVtaxNopUwOEkIXdcRi8XQ3t5u6a5GyWQS7e3tWFxc5AQRCcPgJGFu3ryJK1euWPp8uaZp6Onp\nwdjYmGVtEq2EwUlC6LqO/v5+jI6OWt72+Pg4ent7OVwnYRicJEQ6ncbo6CgikYjlbcdiMYyMjHDD\nDxKGwUlCaJqGSCRiS7ipqopIJMIeJwnD4CQhJEmCx+OBoiiWt+10OuH1elnxkoRhcJIQsiyjuroa\nhYWFlgdcXl4eampq1lQxk2gtGJwkhMPhQGNjI+6//35Le52KomDr1q1oaWmBw+GwrF2i5TA4SQhJ\nklBeXo7nnnsOwWDQkl7n7W3KMi9nEoNXGgkhSRJcLhceffRRvPjiiygsLFx3m7m5uXj++eexb98+\nuN1u3uMkYRicJIwkSSgsLMRLL72Exx57DG63e81tuVwu7Ny5E6+88grKysosPEuilTE4SShZlrFp\n0yb84he/wIMPPrim8HS5XLjvvvvwi1/8As3NzXA4HOxtklAMThJKkiQoioIHH3wQL7/8Murq6jKa\nLHI6naiqqsJLL72EtrY2uFwuhiYJx+Ak4SRJQk5ODp5++mk8++yzKC0tXdVSIqfTieLiYjz99NM4\nePAg8vPz7T9ZojtgcFJWyLKM4uJiPPLII9i0aRO8Xu+ys+KyLMPtdqO+vh6PPvooysvLOUSnrGFw\nUtYoioKqqipUVVXB4/FAluU7BqEkSZBlGS6XC8FgEDU1NXC5XFk4Y6K/YnBS1kiSBE3TkEqloKoq\ndF2/456axn83ftbKbemI1oLBSVmTSqUwODiI/v5+LC4uLhuImqYhHo/jxo0b6O/vRyqVEnimRLdi\ncFLWzM3N4ezZsxgYGEAymVx2B3dd15FMJjE0NIQzZ85genr6rj1UIrsxOCkrUqkULl26hI8//hgz\nMzOrGn7ruo65uTmcOnUKn3/+OZLJpIAzJfomBicJp+s6pqam8Kc//Qn9/f0Z7aOpqiqGh4dx5MgR\njI+P23iWRHfH4CThNE3Dl19+iT//+c+IRqMZvz4ej+PEiRPo6Ojg5sWUFQxOEkrXdUQiERw9ehSh\nUGhN9yh1XUc4HMYHH3yAubk53uck4RicJJSu67h+/TpOnz69rnuUqVQKHR0d6O7uZnCScAxOEiqd\nTuPixYsYGRlZd1vj4+M4d+7cijPyRFZjcJJQsVgMX331lSXVLmOxGDo7O22pnEm0HAYnCbWwsIBr\n165ZMqmjaRquX7+OmZkZC86MaPUYnCSMsQ5zZGTEkqG1rusYGxvD9PS0BWdHtHoMThJqamoKs7Oz\nlrU3Pz+Pmzdv8h4nCcXgJGF0Xcf4+DgWFxctazMWi2FsbIzBSUIxOEkYTdMwNDRk6QYd6XQaw8PD\n3DGJhGJwkhC6rkNVVYyOjlr6tI+maRgdHUU6nWavk4RhcJIwqVQKU1NTlgac8dw7t5kjkRicJEw6\nnV7Ts+krWVxcZHCSUAxOEkZVVaTTacvbTafT3OyDhGJwklCrqWa5ljZZtI1EYnCSMIqioLCwcNlq\nlpmSJAkFBQUZ1WYnWi8GJwnjcrlQX19vaYVKRVHQ0NAAt9ttWZtEK2FwkjCKouDBBx9EaWmpZW0W\nFxfjoYceYrlgEorBSUIYtdE3b96MnTt3WhJ0TqcT27dvx9atW+9ak53IDgxOEqqkpASHDh1CVVXV\nutsqLS3FoUOHEAwGLTgzotVjcJIwkiRBURS0tbXhqaeegtfrXXNbHo8He/bsweOPP85hOgnH4CTh\niouL8ZOf/ATbtm1b0/Ikh8OBLVu24OWXX0ZZWRkkSeIwnYRicJJQxr3OlpYWvPjii6ioqMhoeZIs\nyygpKcELL7yA7du3w+FwMDRJOAYnCSdJEgKBAA4cOIA9e/YgEAisKvwkSYLf78euXbvwne98B/n5\n+fafLNEdMDgpK2RZRmVlJZ588kls2LBhVfcpFUVBVVUV9u3bh6qqKs6kU9YwOClrXC4XNm7ciLq6\nOng8nmWH7LIsw+12o7a2Fo2NjfB4PALPlOhWDE7KKqfTCZfLtWLv0bg36nK5bHnenSgTDE7KGlVV\nMT4+jnA4vGJtdE3TkEwmzZ+3Y5clotVicFJW6LqOyclJnD59Gr29vYjH48uWv9B1HYlEAgMDAzh1\n6hQmJiagaRp3faesYHCScLquIx6Po6OjAx999BGmpqZWtZ+mpmmYmZnByZMn8dlnn1la9I0oEwxO\nEkrXdWiahitXruDXv/41enp6Mtq9PZVKYWBgAL/97W/x5ZdfQlVV9jpJOAYnCTc1NYU33ngDHR0d\niMViGb8+kUjgwoUL+MMf/mDWVGd4kkgMThLGGKIfPXoUb7/9Nubn59fcViQSwZEjR/Dee+/ZUseI\naDkMThLC6BUODw/jzTffRCgUWncv8ebNmzh8+DD6+vrY6yShGJwkTDKZxOnTp3H+/HlLqlKm02l8\n+eWXOH78OBKJhAVnSLQ6DE4SZmFhAWfPnl3XEP1ObXZ0dFjaJtFKGJwkzNTUFHp7ey0t5auqKvr6\n+sxJIiIRGJwkhK7rmJ+fx+zsrOUBNz8/j5mZGUvbJFoOg5OEicViiMfjlrebSCSwuLjIHicJw+Ak\nYVRVXfaxyrXSNM3S4T/RShicJEwmO72vpW3uzUmiMDhJCEmS4HK54HA4LG/b4XDA7XZb3i7R3TA4\nSRifz2fLBsQulwt+v9/ydonuhsFJwgQCgXWVBL4bj8eDnJwcDtVJGAYnCePz+ZCbm2t5u4FAAIFA\nwPJ2ie6GwUnCeL1eFBcXW9ozlCQJRUVFHKqTUAxOEsbj8aCurs7SCSJZlrFhwwYWbyOhGJwkhCRJ\ncDqd2LZtm6W9Q5/Ph/vuuw8ul4v3OEkYBicJ43A4sGXLFtTW1loWcsFgEPfee68ty5yI7obBSULV\n1NTgiSeesGRo7Xa78dhjj2Hjxo0WnBnR6jE4SRhJkhAIBHDw4EHU1tauu72ysjI8++yzyM/PX//J\nEWWAwUlCybKMBx98EM8++yx8Pt+a2/F6vdi/fz9aW1vhdDp5f5OEYnCSUJIkIScnB9///vfR0tKy\npnuTsiyjsbERL7zwAvLy8hiaJByDk4STJAktLS348Y9/jLKysoyCT5IkFBYW4sUXX8QDDzxg68Yh\nRHfDq46EkyQJPp8P+/btw8MPP5zRRJHb7cYDDzyA/fv32/IUEtFqMDgpK2RZRk1NDQ4ePIhgMAin\n07niaxwOB8rLy7F//37U19dzKznKGgYnZY3b7UZTUxPq6upWXMAuSRIURUFtbS1aWlr4pBBlFYOT\nskKSJHOiqLCwEIqirCo4CwoKkJuba76eKBsYnJQVuq5D0zREo1FEIhGoqrpszSBd16GqKiKRCBYW\nFqBpGmsMUdYwOClrEokEurq60NfXh0QisWJwJpNJ3LhxA5cvX0YsFhN4pkS3YnBSVmiahpGREXzy\nyScIhUJIp9MrvkZVVYTDYZw4cQKDg4Mr9lKJ7MLgJOF0XUc0GsUnn3yCs2fPrrq0r67riMViuHDh\nAj766CPMz88LOFuib2JwklDGvc0bN27ggw8+wPj4eEYlgzVNw9TUFI4dO4be3l7e66SsYHCScIlE\nAmfPnsWXX36JZDKZ8etTqRQuX76MTz/9lPc6KSsYnCTc9PQ0Ojo6MDMzs+be4tzcHDo6OjA5OQld\n19nrJKEYnCSUpmmYmJjAwMDAqiaE7iadTmNoaAjhcDijoT6RFRicJJSu61hcXEQsFltXL9GYKIpG\nowxOEk7SOcYhIsoIe5xERBlicBIRZYjBSUSUIQYnEVGGGJxERBlicBIRZYjBSUSUIQYnEVGGGJxE\nRBlicBIRZYjBSUSUIQYnEVGGGJxERBlicBIRZYjBSUSUIQYnEVGGGJxERBlicBIRZej/A+gYLhso\nwc6MAAAAAElFTkSuQmCC\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "step = 15\n",
            "    J = 4.7555e-02\n",
            "    beta = 30.00\n",
            "    grad_norm = 1.8023e-02"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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81WpFXV0dnxiijGFwUkaIooiCggI4HI6UptuCIMBut6OwsFDT8nREqWBwUsaIorik8DMY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\nB0ueAAAAAElFTkSuQmCC\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "step = 16\n",
            "    J = 3.4660e-02\n",
            "    beta = 30.00\n",
            "    grad_norm = 1.0959e-02"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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YsQKpqakQBAGhUAjd3d04evQo/vSnP+HGjRsIBoO61sHhcKCmpgbf//73sXHj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\nlCAGJxFRghicREQJYnASESXo/wEMTcB4pjLRXgAAAABJRU5ErkJggg==\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "step = 17\n",
            "    J = 5.2472e-02\n",
            "    beta = 30.00\n",
            "    grad_norm = 4.3957e-02"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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aQiAQuK0rgmbHYrEgJycHhYWFcLlciMViGB0dhd/vv6k/3mhutxubN2/GCy+8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\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "step = 18\n",
            "    J = 3.0562e-02\n",
            "    beta = 30.00\n",
            "    grad_norm = 1.1185e-02"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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7W8crI5ocBicZShAEmM1mNDU1TWtQx263o6mpCVarlf2bZDgGJxlOkiTMmTNnyo/rgiCg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\n/T9i8pQAKM0xXgAAAABJRU5ErkJggg==\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "step = 19\n",
            "    J = 4.3431e-02\n",
            "    beta = 30.00\n",
            "    grad_norm = 4.2612e-02"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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EQUB6ejq+973v4Sc/+Qlqamq0Hq8sywgEArhy5QreeustvPPOO+jr69P1by1J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\nE4OTiChODE4iojgxOImI4sTgJCKK0/8DfE+CMmAr2e0AAAAASUVORK5CYII=\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "step = 20\n",
            "    J = 1.8338e-02\n",
            "    beta = 30.00\n",
            "    grad_norm = 3.7752e-03"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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VFRUVqK2txZIlS5CSkoLx8XFcunQJn3/+OTo6Omi39HkSRRHFxcVYu3Ytamtr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\nDAYAAAAASUVORK5CYII=\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "step = 21\n",
            "    J = 4.1059e-02\n",
            "    beta = 30.00\n",
            "    grad_norm = 6.0642e-02"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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OYDCgvr4excXFM55m5+fnY/ny5by/SWnB4CTdSZKEqqoq1NfXw2QyJf39RqMRS5cu1Ww9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\nf6T4TL0+0OHYAAAAAElFTkSuQmCC\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "step = 22\n",
            "    J = 1.7024e-02\n",
            "    beta = 30.00\n",
            "    grad_norm = 4.0538e-03"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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gMIj29na0tLSgs7MTHo8nI1OxzGYzGhsb8b3vfQ+rV69OPQOUZRmRSARtbW14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\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "step = 23\n",
            "    J = 3.0526e-02\n",
            "    beta = 30.00\n",
            "    grad_norm = 2.6434e-02"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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hSQXB4CTTSZKEkpIS3H///aiqqsor/CRJQmlpKdavX8/n06lgGJxUEDabDZ/73Ocwf/78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\n57uup639jrbbeTweRzQaze2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hdHZ26lomWAiBrq4uBINBDtXJNAxOMk00GsXw8LCuASeE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\nUZ7+P+kw+0VBeqqbAAAAAElFTkSuQmCC\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "step = 24\n",
            "    J = 2.7335e-02\n",
            "    beta = 30.00\n",
            "    grad_norm = 2.3402e-02"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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A7XYnj7FwOIwrV67g3XffxRtvvIGWlpbkdUstSJIEr9eLBx98EBs3bsT8+fOR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\niFLE4CQiShGDk4goRf8P869parx7QUEAAAAASUVORK5CYII=\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "step = 25\n",
            "    J = 1.7779e-02\n",
            "    beta = 30.00\n",
            "    grad_norm = 5.4527e-03"
          ]
        }
      ],
      "source": [
        "from tidy3d.plugins.autograd import adam, optimize\n",
        "\n",
        "# hyperparameters\n",
        "num_steps = 25\n",
        "learning_rate = 0.04\n",
        "\n",
        "# we will just have the same projection strength for beginning and end in this case\n",
        "beta = 30\n",
        "\n",
        "# initialize adam optimizer with starting parameters\n",
        "params = params0.copy()\n",
        "optimizer = adam(learning_rate=learning_rate)\n",
        "\n",
        "# store history\n",
        "params_history = []\n",
        "beta_history = []\n",
        "\n",
        "\n",
        "# defines what should happen between the iterations: logging the progress and plotting our design\n",
        "def record_step(current_params, grad, state, step_index, objective_val):\n",
        "    # make a plot of density to check on progress\n",
        "    density = get_density(current_params, beta=beta)\n",
        "    plt.subplots(figsize=(2, 2))\n",
        "    plt.imshow(np.flipud(1 - density.T), cmap=\"gray\", vmin=0, vmax=1)\n",
        "    plt.axis(\"off\")\n",
        "    plt.show()\n",
        "\n",
        "    print(f\"step = {step_index + 1}\")\n",
        "    print(f\"\\tJ = {float(objective_val):.4e}\")\n",
        "    print(f\"\\tbeta = {beta:.2f}\")\n",
        "    print(f\"\\tgrad_norm = {np.linalg.norm(grad):.4e}\")\n",
        "\n",
        "    params_history.append(np.array(current_params).copy())\n",
        "    beta_history.append(beta)\n",
        "\n",
        "\n",
        "# run optimization\n",
        "params, opt_state, history = optimize(\n",
        "    lambda current_params: objective(current_params, beta=beta, verbose=False),\n",
        "    params0=params,\n",
        "    optimizer=optimizer,\n",
        "    num_steps=num_steps,\n",
        "    bounds=(0.0, 1.0),  # keep params between 0 and 1\n",
        "    callback=record_step,\n",
        "    direction=\"min\",\n",
        ")\n",
        "params_history.append(np.array(params).copy())\n",
        "beta_history.append(beta)\n",
        "Js = history[\"objective_fn_val\"]"
      ],
      "id": "ea0354ab"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Visualize Results\n",
        "\n",
        "Let’s visualize the results of our optimization.\n",
        "\n",
        "### Objective function vs Iteration\n",
        "\n",
        "First we inspect the objective function value as a function of\n",
        "optimization iteration number."
      ],
      "id": "ebbac8a5-7b4a-41cb-9840-ea4129767968"
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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qeu2115ScnHxd9z5+/Ljmz5+vZ599VnXq1FHx4sUVFBSkwMBAFS1aVA888IC+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\ngg==\n"
          }
        }
      ],
      "source": [
        "plt.plot(Js)\n",
        "plt.xlabel(\"iteration number\")\n",
        "plt.ylabel(\"objective function\")\n",
        "plt.show()"
      ],
      "id": "22b3e1db"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Final Device Performance\n",
        "\n",
        "Now, let’s take a closer look at the final, optimized design. We take\n",
        "the best parameters found during the optimization and run the\n",
        "`ComponentModeler` one last time."
      ],
      "id": "2c5ba634-502e-43e2-9f77-07593779c76f"
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {},
      "outputs": [],
      "source": [
        "# we'll sample the modes at a finer frequency resolution for this final evaluation, for smoother plots\n",
        "freqs = np.linspace(freq0 - fwidth, freq0 + fwidth, 201)\n",
        "\n",
        "modeler_start = get_modeler(params_history[0], beta=beta, include_extra_mnts=True).updated_copy(\n",
        "    freqs=freqs\n",
        ")\n",
        "modeler_final = get_modeler(params_history[-1], beta=beta, include_extra_mnts=True).updated_copy(\n",
        "    freqs=freqs\n",
        ")"
      ],
      "id": "a3b5b7d1"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Let’s take a look at our final design."
      ],
      "id": "c9e2381b-3f3d-4e4f-9cd9-3508158fccd9"
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'final design')"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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Tf/rfnbb2pOCE8pzueeGFF/T1r39dknTOOedo9erVCRH0RAKr56BHsPoFw+B2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          }
        }
      ],
      "source": [
        "ax = modeler_final.simulation.plot_eps(z=0, monitor_alpha=0, freq=freq0)\n",
        "ax.set_title(\"final design\")"
      ],
      "id": "f53642fd"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The field plots below show the device operating at the central design\n",
        "frequency. We can clearly see the crossover behavior: light entering the\n",
        "top-left port is efficiently routed to the bottom-right port, and light\n",
        "from the bottom-left is routed to the top-right."
      ],
      "id": "3dc4a97f-ce9f-4e36-83df-89afa8ac80b6"
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"a4c956c6cf574dff8e75839e903df098\",\"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\">13:21:23 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\">13:21:24 UTC </span>Maximum FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.132</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\":\"ffce326d3de749cda758612f2b127bdc\",\"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\">13:22:12 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": {
            "image/png": 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+9ztJ0lNPPaUjjjgiLzF6i4ogDE782sNw1ctq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elNXLhwgfPnz5NlGf/3//5ffvzHf5z/9J/+EwDLy8u85z3vmVnOt3zLt/C+972PP/iDP+Bbv/Vb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\n2vIlT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Wf7Mc2YMSOoGGeeeaaRZFq0aBEwiVZSUmIPhRo5cmRIYjRF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\nv/8FFWPq1Kl2jPnz51fZ7vF4zBFHHGEkmXbt2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          }
        }
      ],
      "source": [
        "simulations = modeler_final.sim_dict\n",
        "bd = web.run_async(simulations)\n",
        "for task_name, sim_data in bd.items():\n",
        "    sim_data.plot_field(field_monitor_name=\"field\", field_name=\"E\", val=\"abs^2\")"
      ],
      "id": "ec3914a7"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Next, let’s look at the S-parameters over a range of frequencies to see\n",
        "how our final device behaves."
      ],
      "id": "350b5a57-03be-49bd-8a8b-aedafcaafa7a"
    },
    {
      "cell_type": "code",
      "execution_count": 24,
      "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\">13:22:16 UTC </span>Created task <span style=\"color: #008000; text-decoration-color: #008000\">'start'</span> with resource_id                              \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #008000; text-decoration-color: #008000\">'sid-e4db8e16-c5b6-4ba2-84ea-a675e5215695'</span> and task_type           \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #008000; text-decoration-color: #008000\">'MODAL_CM'</span>.                                                        \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
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              "</script>"
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        {
          "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>"
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        },
        {
          "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\">13:22:28 UTC </span>Estimated FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.048</span>. Use <span style=\"color: #008000; text-decoration-color: #008000\">'web.real_cost(task_id)'</span> to  \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>get the 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\">13:22:30 UTC </span>Subtasks status - start                                            \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>Group ID: <span style=\"color: #008000; text-decoration-color: #008000\">'pa-82bc988f-9ca0-45c9-8265-1e0236cb87b0'</span>                \n",
              "</pre>"
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              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
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              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>Batch status = preprocess                                          \n",
              "</pre>"
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          "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\">13:23:02 UTC </span>Batch status = preprocess                                          \n",
              "</pre>"
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        {
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          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">13:23:04 UTC </span>Batch status = running                                             \n",
              "</pre>"
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        {
          "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\">13:23:35 UTC </span>Batch status = postprocess                                         \n",
              "</pre>"
            ]
          }
        },
        {
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          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">13:23:39 UTC </span>Batch status = success                                             \n",
              "</pre>"
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        },
        {
          "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\">13:24:01 UTC </span>Batch status = postprocess_success                                 \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\">13:24:03 UTC </span>Modeler has finished running successfully.                         \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>Billed flex credit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.083</span>.                                    \n",
              "</pre>"
            ]
          }
        },
        {
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          "metadata": {},
          "data": {
            "text/html": [
              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>"
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        {
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          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"b59d04dbe7f7495db43a8b1e6b9bb89a\",\"version_major\":2,\"version_minor\":0,\"quarto_mimetype\":\"application/vnd.jupyter.widget-view+json\"}\n",
              "</script>"
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        {
          "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>"
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        },
        {
          "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\">13:24:05 UTC </span>Loading results from cm_data.hdf5                                  \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\">13:24:06 UTC </span>Created task <span style=\"color: #008000; text-decoration-color: #008000\">'final'</span> with resource_id                              \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #008000; text-decoration-color: #008000\">'sid-704aa5ee-988c-48f5-9158-8f99ddb8e2a2'</span> and task_type           \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #008000; text-decoration-color: #008000\">'MODAL_CM'</span>.                                                        \n",
              "</pre>"
            ]
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
              "{\"model_id\":\"ba8c7cac17804d3481e9ebe7286e66ae\",\"version_major\":2,\"version_minor\":0,\"quarto_mimetype\":\"application/vnd.jupyter.widget-view+json\"}\n",
              "</script>"
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        },
        {
          "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>"
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        {
          "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\">13:24:16 UTC </span>Estimated FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.048</span>. Use <span style=\"color: #008000; text-decoration-color: #008000\">'web.real_cost(task_id)'</span> to  \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>get the 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\">13:24:17 UTC </span>Subtasks status - final                                            \n",
              "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>Group ID: <span style=\"color: #008000; text-decoration-color: #008000\">'pa-078618c7-2d4b-4607-a936-f6b473d6c078'</span>                \n",
              "</pre>"
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          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
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              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>Batch status = preprocess                                          \n",
              "</pre>"
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        },
        {
          "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\">13:24:50 UTC </span>Batch status = running                                             \n",
              "</pre>"
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          }
        },
        {
          "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\">13:25:23 UTC </span>Batch status = postprocess                                         \n",
              "</pre>"
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          }
        },
        {
          "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\">13:25:27 UTC </span>Batch status = success                                             \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\">13:25:49 UTC </span>Batch status = postprocess_success                                 \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\">13:25:51 UTC </span>Modeler has finished running successfully.                         \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>Billed flex credit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.089</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\"></pre>"
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          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<script type=\"application/vnd.jupyter.widget-view+json\">\n",
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              "</script>"
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        {
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          "data": {
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              "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>"
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          }
        },
        {
          "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\">13:25:53 UTC </span>Loading results from cm_data.hdf5                                  \n",
              "</pre>"
            ]
          }
        }
      ],
      "source": [
        "smatrix_start = web.run(modeler_start, task_name=\"start\").smatrix()\n",
        "smatrix_final = web.run(modeler_final, task_name=\"final\").smatrix()"
      ],
      "id": "979d4386"
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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s2bOVOqZkWmeg+je0AQEBUKvVsFgssNvt+Pvvv6HRaKp1TiIiIiIiIqo+h8OBTz75RNy/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\nuRlfrPoJ+cXOddezi/Lw+Pw38dV9b0K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HTqdBnSUQy5QJgoCiIuebur6+vmWWfSh1XriZ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vhpiAmNVDAy32CyyhK2ej1wxvU9nkzY5uUX4Z99hyV7fXp1QXxcVAP3IDptbJ9hmPPl/5zrLUd3\nw2KzQq/VKRcUERERuZ1/fTJERERERESKq6qqQnp6eoO35+bmori4tq1namqqc//Mr//5559GH2PP\nnj0AgM6dO7cmVI+qq7Jds2YNjh07hgMHDjhn+Lq7upaI/MONIycjLjTauTbZLHj71yUKRuQ75C2R\nDTrpxT01HmqJbLPbse6PbTg1oh0AEBQUgMHn9fXI45PvS43pgITw0yMeTDYLth1r/HUSERER+R4m\nbImIiIiIyO1WrFjR4G1ffvml8+tRo0Y5vx4xYgQ0mtomQMuXL2/w/seOHcOWLVsAAKNHj25VnDpd\nbXWK3W5v1Xma4+qrr0ZUVBREUcQHH3zgrK7VaDTOGbdERGcyaPV4cNItkr1PNnyD3NIChSLyHfKW\nyEaXhK0D4plZ1DYgiiLWrtuCktJyyf6oEYOg1bLpHTWPIAgY0f1cyd7GQ9saOJqIiIh8FRO2RERE\nRETkdi+99BIyMjJc9jMzM/H8888DAAYOHIhzzz39AWRUVBSuueYaAMDSpUuxfv16l/vb7XbMmDED\noihCEATcc889rYozOrq2cq2qqgolJSWtOldTdDodbr31VgDARx99hE8++QQAcNlllyE2NrZNH5uI\nfNe04ZdLquvMNgve+vUTBSPyDfIK2wCDEWq19GMwextX2W7ZthfHTmRJ9rp37YgOSXFt+rjkf0b2\nOE+y3nCQCVsiIiJ/w4QtERERERG5VWJiIvr164fhw4fjk08+wcmTJ5GZmYlly5Zh+PDhyM/Ph1qt\nxjvvuM4LfvXVVxEREQGHw4FLLrkEL730Eo4cOYK8vDysXr0a48ePx6+//goAeOSRR9CvX79WxTp4\n8GDn148//jiOHDmCkpISlJaWoqysrFXnrs9dd90FQRCQk5ODoqIiAGyHTESN02t1eGjSrZK9pRu+\nQ05JvjIB+YhqiyxhqzNCrVZL9mracI7toSMnsHP3QcleRHgIhg8d0GaPSf5rZA9phe3OE/tRYapS\nKBoiIiJqC0zYEhERERGR2y1evBgBAQG45ZZbkJycjA4dOuDGG29ERkYGdDodPvnkEwwdOtTlfklJ\nSVizZg06dOiAqqoqPPHEE+jWrRvi4uIwbtw4rFu3DgBw33334eWXX251nP369cPFF18MAFi4cCG6\ndeuGiIgIhIeHIyUlpdXnl+vatSvGjBnjXCcmJuKiiy5y++MQkX+5fthlSIw4XZVpsVsxbyWrbBtT\nbZW2RA7QG6DRSBO2bVVhW1BYgvUbpBWQRoMekyaMgE6nbZPHJP8WFxaNrnEdnesaRw3+OrJDuYCI\niIjI7ZiwJSIiIiIit+vQoQM2b96MZ599Fueccw5iY2PRvXt33HHHHdi9ezduuOGGBu/bv39/HDx4\nEG+++SbGjRuHlJQUxMTEoHfv3rjjjjvw119/4e2333aplKpjNBoRGhqK0NDQZsX69ddf49VXX8UF\nF1yAxMREhIeHt+j+LXXbbbc5v7711lsb/D7aWnBwMEJDQ6HX65s+mIgUpdNo8X+yKttlf36Hwoq2\nbeXuy0xW+QzbehK2bVBhK4oiNm7aCYfj9HxctVqFiyYMR3BwoNsfj9oPeZUt2yITERH5F43SARAR\nERERkX8KDw/Hc889h+eee67F9w0ICMCDDz6IBx98sMX3nTt3LubOndvs4/V6PR599FE8+uijLX6s\ns3HkyBEAgCAIkuStp61du1axxyailpsy9BLMW/kxThblAACsdhu++OtnzJgwTeHIvFN9LZHtaule\nW7RETjuWibz8Isne6JHnITYm0u2PRe3LyB7n4cN1K5xrJmyJiIj8CytsiYiIiIiIPEQURSxevBgA\ncOGFFyI1NVXZgIjIZ+g0Wtw66mrJ3tKN30IUxQbu0b7V1xJZ3cYtke32Gmzeukeyl5Icj65dkt36\nONQ+Det2DlTC6Y9yD2anIb+sqJF7EBERkS9hwpaIiIiIiMhDvv/+e5w4cQIAMGPGDGWDISKfM2Xo\nJdCqTzdLO5Z/EpsOc45lfVwqbPVGaNRt2xJ5z97DqKysdq5VgoChg/u79TGo/QoNCEa/5B6SvY2H\nWGVLRETkL9gSmYiIiIiIqAF2ux2VlZUtuo/D4UB1dTWCgoIAABUVFbBardixYwceeOABAEDPnj1x\n5ZVXuvVxAUCj0Tgfl4j8T1RwOC4eOBrfbfvdubd043cY3n2QckF5KZcK2/pm2Lqxwraq2oSduw9K\n9nr37oKw0GC3PQbRBT3Pw670/c71hoPbcNX5ExWMiIiIiNyFCVsiIiIiIqIGrFu3DuPHj2/x/QYP\nHoyVK1cCAAYOHIi0tDTnbVqtFvPnz4dK1XDDo7N93OHDh2Pjxo0tvh8R+Y6bRkyWJGx/2rkWRZWl\niAwKUy4oLySvsDXqDFDLKmzdOcN2566DsNnszrVer8O5A3u57fxEADCyx7mYt/Jj53rDwa0QRRGC\nICgYFREREbkDE7ZEREREROQWRqMRoaGhCA0NVToUt9FqtWf1/ZxZ5RoSEuL8/9KvXz889dRTGDJk\nSJs8bnAwK7mI/N2wbuegU3QSjhdkAgCsdhu+3Pwz7hl3g8KReReTywxbo2uFrRsTtukZ2ZL1eef0\nhl6vc9v5iQDg3NS+0Gt0sNitAIDM4lxkFGYjJTpR4ciIiIiotZiwJSIiIiIit5g7dy7mzp2rdBhu\nNWrUKJSWlrboPg6HA+Xl5c71jh0tny95No9LRO2DSqXCtBFX4Plv3nHuLdnwLe4eez2r7M7g2hK5\nnhm2bmqJXFlVjYozZ9eqVOjRvZNbzk10JqPOgHM798Wfh7Y797Ye28OELRERkR9ouAcXERERERER\nERF5nSlDL4FWffoa/LS8DOzOONjIPdoXURTrqbA1QK1pm5bIObmFknVMdLhLNS+Ru5zbqY9kve3Y\nXoUiISIiIndiwpaIiIiIiIiIyIdEh0RgXJ/hkr2fd65TJhgvZLJZIIqic63X6KBWqaFRSxvNuavC\nVp6wjY+Ldst5iepzbud+kvW2Y/8oFAkRERG5E1siExERERERERH5mEvPuRC/7F7vXP+0cy2euOIe\ntkUGUG0xSdZGnQEA2myGbW5ugWQdFxfllvMS1WeQrMJ2f+ZRVJmrEWgIUCgiamuV5iqcKMhCTmkB\nckrykVNagNxTf7JL81FQVgSHKEIlCBBUKujUGnSL74QBKT0xoGMvnNOpN2JD+e8SEZG3Y8KWiIiI\niIiIiMjHjOs7HFq1BrYaO4DatsiHco6jR0KqwpEpr752yIBrwrbGDRW2ZrMVxSXlkr24mMhWn5eo\nIRFBoegcm4y0vAwAgEN0YGf6AYzoPkjhyMhd7DV27Di+D+sObMEfB7Zgx/F9cIiOFp0jp7QA6w9s\nca77JXfHpeeMwSUDL0Tn2GR3h0xERG7AhC0RERERERERkY8JDQjGiB7nYu2+zc69n3euY8IWQLVF\nlrDVGQEAarX7K2xz86TtkCMjQqHX61p9XqLGDOrUx5mwBYDtx/5hwtYPmKxmLN3wHd5etQR5ZYVN\n36EF9mQcwp6MQ/jPt++hV2IXXHLOhbh04Bh0T+jk1schIqKzxxm2RERERNTunDnXjojcjz9jRJ5x\nyYDRkvXPu9YpEoe3qbZKWyI3VGHrjoStfH4t2yGTJ5yb2ley5hxb32a2WbBo7RcY8sw1eObL/7o9\nWSu3P+soXv1hIUb9+3qMfG4qXv1hIXJK8tv0MYmIqGmssCUiIiKidkOlqr1e0W63QxRFzvkjagMO\nhwM2mw2AazUbEbnXxP4X4LFPX3ZeJLH35GGkF2QhJTpR4ciUJZ9hW1dhq5FX2LqhJXJunnR+bXxs\ndKvPSdSUc1Olc2y3H9vL17Y+avXeTZj92as4WZTT6HGdopPQITIecWHRiA+LPvXfGMSFRyMuNAo6\njQ4O0QFRFFFaXY7d6Qew88R+7Di+D7vSDzR4Md2R3BN4/acP8OYvi3HJORfijguvw7mpffl3iYhI\nAUzYEhEREVG7YTQaYTKZ4HA4UF1djcDAQKVDIvI75eXlzg8FAwICFI6GyL9Fh0RgcJcB2Hxkp3Pv\np53rMGPCNAWjUl61bIatUVdbYauWz7BtZYWtzW5HQUGJZC+eFbbkAd0TUhFkCECluRoAUFxVhmP5\nJzmb1IfklhbgmS/+hx92rK73dqPOgIv6X4BRPc/HqJ7nIz48ptnnjg6JQNe4jrhm8CQAQH5ZEX7e\ntQ4/7liLTYd31DsP1+6owXfbfsd3237HOZ164/nrHsE5nXqf3TdHRERnhS2RiYiIiKjdCAkJcX6d\nnZ2Nqqoqtm4lchOr1YrCwkLk5JyuEAkLC1MuIKJ24tKBoyVrtkWup8K2riWymyts8/OL4TjjdURI\ncCACA42tOidRc6hVapzTUZpMY1tk3yCKIpZs+BYjn5tab7LWqNXjnnE3YMvzX+O92/+NqcMubVGy\ntj4xoZG4ddTVWPHw29jzyk94/cYncGGvIdCo6u+EsuP4Plzyyh2Y9enLKK0qb9VjExFR87HCloiI\niIjaDYPBgKCgIFRWVsJutyMjIwMqlQoajcajbb9EUXS2jC0qKmLLMT/T3p5fURRRU1ODGlniIyIi\nAlqtVqGoiNqPSQNG4+kv/utcbzv2D3JLCxAX1n5b85pcKmxPtUR28wxbzq8lJQ1K7Ys/Dm51rrcf\n24spQy9RMCJqSm5pAR5e8gLW7tvscptKUOHWUVfh/yZNR0xoZJvFEBUcjmkjrsC0EVegpKoM3279\nDR+u+xJHctMlx4miiE/++AY/71yHf1/7f7jyvAl+/5qWiEhpTNgSERERUbshCAISExORlZWFyspK\nALXzNq1Wq0fjEEURJlNt9Y/RaOSHH36Gzy8QFxeH8PBwpcMgahcSI2IxIKUXdqXvd+79umcDbrng\nKgWjUpa8JXJdha18rrb8QpOWysmVza+Na79JcvI8+RxbVth6t2+3/YbZn76K0mrXitV+yT3w2o2z\n0S+5h0djCg8MxfTR1+DWUVfjjwNbsHDtF/j9nz8lxxRWlGDGh8/il11/4JVpsxAeGOrRGImI2hMm\nbImIiIioXVGpVEhKSoLZbEZ5eblzpq0nORwOFBUVAQBCQ0OhUnFSiT9pj8+vSqWCVqtFUFAQAgMD\nodHwrSaRJ00acIEkYbty1x/tO2Erb4ncBhW2oigiv6BYssf5teRJgzpJE7YHs4+h0lyFIEOgQhFR\nfWocNXjmi//iw3UrXG4L0Bvx5BX3YProa6BuoD2xJwiCgFG9BmNUr8FYv/9vPPH5aziWf1JyzA87\nVmNr2h7Mu/UZXNDzfIUiJSLyb3wXTURERETtjiAIMBqNMBqVmTNntVqxb98+AMDgwYOh0+kUiYPa\nBp9fIvK0i/qPwovfzXeuNx7ahgpTFYKN7TNxI6+wNepqK2zlF9CI4tlfsFVVbYLNZneudTotQkOC\nzvp8RC0VFhiCrnEpzla2DtGBnSf2Y2SP8xSOjOqYbRbc/9G/8OOONS63De7SH/NumYOU6EQFImvY\nqF6DseaZpXhn1VLM++VjWOynOxHllhXgujcfxN1jp+KJyffCoNUrGCkRkf/x/0u9iYiIiIiIiIj8\nWLf4jkiN6eBc22rsWL1vk4IRKcssb4nsTNhKW9Q7HOJZP0ZZWaVkHRoa1C5b4JOyzk3tJ1lvTWNb\nZG9RbqrE9fP+zyVZq9No8cxV9+PrR971umRtHYNWj5mX3I7fnvoY/ZK7u9z+/urPcdGLt2F/5hEF\noiMi8l9M2BIRERERERER+TBBEDCx/wWSvZW7/lAoGuWZbRbJuq4KTCVLqDrEs0/YlpZVSNZhIcFn\nfS6isyWfY7v9+F6FIqEzFVaU4MrX78VfR3ZK9uPDovHz4x/gvgk3KtoCubm6xXfCj7MW4cGLbnG5\nIOVgdhoueuk2zP/9U4+PlyEi8ldM2BIRERERERER+bhJsoTt6r2bYLXbFIpGWRabVbLWa2tb0wuy\nlsitSTKUyRK2oaFM2JLnndOpt2S9J+MgxFZciECtZ7FZMf29Wdgnqz7tGpeCH2YtRJ8O3RSK7Ozo\nNFo8OflefP3Iu0iMiJPcZrXb8NyKeZj2ziMoqSpTKEIiIv/BhC0RERERERERkY8blNoHUcHhznWF\nuQqbDu9QMCLlnDlzEQAMuvorbEU3tkQOC+X8WvK8rnEdJXNEC8qLkVdWqGBE7Zsoinh02UvYekza\nmvrc1L747tEFSJIlPH3J0K4DsfaZpbhm8EUut63dtxkXvXgbDmanKRAZEZH/YMKWiIiIiIiIiMjH\nqVVqTOg3QrL3y671CkWjLLO8wlZTW2HrMsNWPPsK29JyVtiS8jRqDXoldZHs7ck4qFA09PaqJfhy\n88+SvRHdz8UX//cWIoJCFYrKfUKMQXh7+nOYf/tchAZI/81LL8zC5DdmYHsO//4REZ0tJmyJiIiI\niIiIiPzARf1HSdar9mxol7MFXWfYnmqJLMhbIp9dhW2Nw4GK8irJXmgIK2xJGf2Se0jWu9OZMFPC\nyl1/4D/fvifZ6xybjEV3/QcBOoNCUbWNyeeNx5qnl+Lc1L6S/WqrCQt2fYMfj2xka24iorPAhC0R\nERERERERkR8Y2eNcBOiNznVOaQF2t8NqO4ssYas/1TJWXmF7tgmFiooqOM64b4DRAJ1Oe1bnImot\necKWFbaedzjnOGZ89Kzk35TQgGB8MuM1hAWGKBhZ20mMiMVXD7+DG0dc4XLbD0c34JUfFzJpS0TU\nQkzYEhERERERERH5AaPOgAt7DZHsrWyHbZEtspbIdTM+BXlL5LOsPpbPrw3l/FpSUP8UecL2kEKR\ntE9mmwX3LHoG1RaTc0+tUmPRXf9B59hkBSNre3qtDq/d+ARenTYbWrVGcts7vy3Fv756i0lbIqIW\nYMKWiIiIiIiIiMhPXNT/Asl65Z4NCkWiHJcZtqdaIqtkLZHFs2yJXMb5teRFusV3cs5pBoC8skLk\nlRUqGFH7Mvfrt7E/66hk7/nrHsbIHucpFJHn3TRyMlY8/DaCDYGS/fm/f4pnvvgvk7ZERM3EhC0R\nERERERERkZ8Y13cY1Cq1c30o+xiO5WUoGJHnNTTDVt4S2SGKZ5VIKJVV2IYxYUsK0qo16JXURbLH\nObae8evuP/DB2i8le5PPHY9bR12tUETKGdxlAD69/78I0Ejn9S5a+wWeWv46k7ZERM3AhC0RERER\nERERkZ8IDwzF0K4DJXsrd7evKtsGWyILAgRpzhZnk0MoK5NV2IawJTIpi3NsPS+nJB//98nzkr3k\nqAS8Mu1xCPJ/aNqJ/sk98PD51yNQa5Tsf7huBeZ+/TaTtkRETWDCloiIiIiIiIjIj1zUf6Rk/eue\nPxSKRBnyhK3+VMIWAAR5W2Sx5XNsXRK2rLAlhbnOsWXCti05HA7cv/hfKKkqd+5pVGrMv/3fCDG2\n7ws4kkPjMHPwDYgMCpPsv/vbMrz+0wfKBEVE5COYsCUiIiIiIiIi8iMTZXNst6TtQUF5sULReJ7F\nLm2JXDfDFqinLXIL59ja7HZUVpkke6EhgQ0cTeQZfTt0l6z3pB9SKJL24aP1X+HPQ9sle49fcTfO\n6dRHoYi8S2JwDD5/4E1EBIZK9l/7cRHe/nWJQlEREXk/JmyJiIiIiIiIiPxIh8h49O3QzbkWRRG/\n/bNRwYg8y2yVzbDVnJGwFVzn2LZEeXmVZB0cHAi1Wt3A0USe0T0hFTqN1rnOLStAflmRghH5r/TC\nbLzw7buSvQt6nIf7xt+oUETeqXt8J3z+0JsuFcfPf/MOFq39QqGoiIi8GxO2RERERERERER+5qIB\noyTrlbvbR1tkURRhtstbIp9O2AoqWUtkR8taIsvbIYeFtu/2p+QddBoteiZ2keztyWCVrbuJooiZ\nS/6DasvpKvsgQwD+e/PTUKn4Mbtcv+Qe+OyB/yFQHyDZf3r5G1i28TuFoiIi8l78TUJERERERERE\n5GcukrVFXr9/C6rM1QpF4zm2GjvEM6pmNSo1NGqNc+1SYdvClsil8vm1IZxfS96hfzLn2La1JRu+\nxcZD2yR7z139IBIjYhWKyPsNSu2DJfe9BsMZs8QB4NFlL+Grv1cqFBURkXdiwpaIiIiIiIiIyM/0\nSuyCDpHxzrXFbsWmIzsVjMgzzDb5/FppkkCQz7BtYUvksrJKyTqUFbbkJfoly+bYMmHrVieLcvCv\nr96S7F3Q4zxMG3GFQhH5jmHdzsHie1+RtO0WRREPfjwXP+5Yo2BkRETehQlbIiIiIiIiIiI/IwgC\nxvYZJtn76/AOhaLxHIssYWvQSRO28raljpa2RC6Xt0RmhS15h34prLBtS08vfwNVltNdCgL0Rrx2\n4xMQZFX7VL/RvQZj0V3/gUZ1euZ3jaMG9yx6Bmv3bVYwMiIi78GELRERERERERGRHxradaBk/Ve7\nqLCVzq81aHSStbwlstjilsjyClsmbMk79EjoDO0Z7b+zS/JRUF6sYET+Y/ORXfh1zwbJ3pyr7kdy\nVIJCEfmmCf1G4p3b/gWVcDolYXfU4I4FT+IfzlwmImLCloiIiIiIiIjIH8kTtnsyDqHSXKVQNJ5h\nkSVs9Vppwta1JXLzK2wtFivM5tMVvCqVCkGBAWcRJZH76TRa9EzsLNnbe/KwQtH4D1EU8fw370j2\nBnXqg5tHXqlQRL7tinPH4X+3PC3Zq7JUY9rbj+BkUY5CUREReQcmbImIiIiIiIiI/FBMaCS6xKY4\n1zWOGmxN+0fBiNqe6wxbeYWt9KOwllTYlpXLqmtDAqFSsR0qeY/eSd0k6wNZaQpF4j9+2bUe245J\n/92cc/X9Lu3VqfmuG3Ix5l77sGQvv7wIN7z1MEqqyhSKiohIefzNQkRERERERETkp4Z2a19tkeUV\ntgatfIatvMK2+QnbqiqTZB0UFNjC6IjaVq/ELpL1/qyjCkXiH+w1dvzn2/ckexP7jcTgLgOUCciP\n3Dl2Cu4ed71k70juCUx/73GXC2+IiNoLJmyJiIiIiIiIiPzUEFli4a/DO5QJxENcK2ylCVtBNsPW\n4Wh+S+SqamnCNjDQ2MLoiNqWvCXywWxW2LbGZ5t+xNG8dOdaJajw5OQZCkbkX5696gFcPmisZG/z\n0V149ss3FYqIiEhZTNgSEREREREREfmpod3Okax3pR9AtdWsUDRtz2KXV9jKWiLL2piKraiwDQxg\nwpa8Sw9ZwvZwznHYauwKRePbqiwmvPbjIsne1GGXoHtCJ4Ui8j8qlQrzbp3jcmHRx398jW+2rlIm\nKCIiBTFhS0RERERERETkpxLCY5ASlehc22rs2HFsr4IRtS2zVVZhq5EnbOUVtq1oicwKW/IyUcHh\niAmJdK6tdhuO5Z1UMCLf9ckfXyOvrNC5Nmj1ePTSOxWMyD8ZtHp8dO/Lkt9TADBz6Ys4kntCmaCI\niBTChC0RERERERERkR+Tz7Hd5MdzbF0qbHXylsjSj8Ja0hK5sqpasmZLZPJG8rbIB7I5x7al7DV2\nLFr7pWTvzjFTkBAeo1BE/i08MBQL73pBcoFNtcWEOxc85dcdIYiI5JiwJSIiIiIiIiLyY0O7ShO2\n/jzH1myTJmybqrBtUUtklxm2AS2Mjqjt9UzsIlkfyGTCtqV+2fUHsopznWuDVo97xt+gYET+r19y\nD8y97mHJ3sHsNDzx2asKRURE5HlM2BIRERERERER+bEhsoTtjuP7YLZZGjjat1lk35dBK62wPduW\nyKIocoYt+QTXCts0hSLxXQvXfC5ZXzP4IkQGhSkTTDty08jJuOq8CZK95X/9hM82/ahQREREnsWE\nLRERERERERGRH0uOjEdieKxzbbFbsevEAQUjajvyRLQ8YStviSyKzWuJbLXaYLfXONcatRp6vfYs\noyRqO71kFbb7WWHbIjtP7MeWtD2SvTvGTFEomvZFEAS8Om02usalSPaf+OxV7M88olBURESew4Qt\nEREREREREZEfEwQBQ7oOkOztPLFPmWDamEXeElnbeEvk5lbYyqtrAwKNEAShgaOJlNM1viPUKrVz\nnVmci3JTpYIR+ZZFa5ZL1qN7DUaPhFSFoml/Ag0BWHjXizCecbGN2WbBHQueRIWpSsHIiIjaHhO2\nRERERERERER+bkBKL8l6T8YhhSJpWy4zbOUJW1mS1dHMGbYu82vZDpm8lEGrR2pMB8newSy2RW6O\nnJJ8fLftd8nenayu9bgeCal4edrjkr1j+Sfx6LIXWzR3nIjI1zBhS0RERERERETk5/qldJes92Qc\nVCiStiVviSxP2AoqWUtkR/NaIlfKKmyDApmwJe/FObZnZ/H6r2B3nG593iU2BRf2GqJgRO3XdUMu\nxrThl0v2vtv2Oz5a/5VCERERtT0mbImIiIiIiIiI/FyfpG6SFr5peRl+2V7SIkvYGmUzbF0qbM+y\nJXIgE7bkxTjHtuVMVjOWbPhWsnfHmOugUvHjc6U8P+URl7/Lz375P+w8sV+hiIiI2hZ/4xARERER\nERER+blAQwC6xKZI9v456X9tkV1n2EoTtoJ8hq3YvArbqqpqyZoJW/Jm8grbg6ywbdJPO9eiuKrM\nuQ4NCMa1Qy5WMCIy6gxYdNd/EGQIcO7Zauy4a+FTKK0qVzAyIqK2wYQtEREREREREVE70D+lh2Tt\nj22RLfamZthKPwprdoUtZ9iSD+kpq0o8kJXG2Z9N+PTPHyTr64ddhkA9f86VlhqbjDduekqyd7Io\nBw99PJd/p4nI7zBhS0RERERERETUDvRLliVs0/0vYWuySlsiG+QtkWUVtuJZt0QOaOBIIuV1iIyX\nVCWWmyqRVZKnYETe7URBJjYd3iHZu2H4ZQpFQ3KXDxqL2y+8VrL3654NeO+3TxWKiIiobTBhS0RE\nRERERETUDrgkbDP8sCWyrMLWIKuwPfuWyJxhS75DEAT0SJC2RT6QxbbIDflMVl17bmpfdIvvpFA0\nVJ85Vz2AASm9JHsvfPsuthzdrVBERETux4QtEREREREREVE70LdDNwjC6YRlWn4GKs1VCkbkfhab\ntMJWr2l9S2S7vQZmy+lEsCAICDAaWhElUdvr5dIW+ahCkXg3e40dy//6WbLH6lrvo9fqsODO5xEW\nEOLcq3HU4O5FT6O4sqyRexIR+Q4mbImIiIiIiIiI2oFAQwC6xCY716Io4p+ThxWMyP0sNvkM2yZa\nIjdjBqJ8fm2A0eByHiJv0yORFbbNsXb/38gtK3CuA/RGXD5orIIRUUOSoxIw79Y5kr2c0gI8tuxF\nzrMlIr/AhC0RERERERERUTvh73NszbIKW4NOnrCVV9g23RKZ7ZDJF/WUJWwPZjNhW5/P/vxesr5i\n0DgEGQIVioaaMqHfCMwYP02y99POdfhs0w8N3IOIyHcwYUtERERERERE1E64zrH1t4StrMJW1hL5\nzJbQQDMrbJmwJR/UNa6jZH0iP7NZFyi0JwXlxVi1Z6Nkj+2Qvd/sK+5B/5Sekr2nlr+BtLwMhSIi\nInIPJmyJiIiIiIiIiNqJfin+nbCVt0Q2aGUzbGWtjJszw7ayqlqyZsKWfEFkUJhk3qfJZkF2ab6C\nEXmfFX//ArujxrnuGpeCc1P7KhgRNYdOo8W7t/0LRt3pWeImqxkzPnwWVrtNwciIiFqHCVsiIiIi\nIiIionaib4dukvXRvAxUmqsUisb9XBO20pbIgnAWLZFlM2wDA5iwJe8nCAJSYztI9tJy0xWKxvuI\noojP//pJsnf9sMtdqvDJO3WOTcYLUx6R7O1OP4BXf1ioUERERK3HhC0RERERERERUTsRZAhE59hk\n51oURew9eUTBiNxLPsNWr5XPsG15S+RqtkQmH9U5NkWyTss/qVAk3udgdhoOZR9zrjUqNa4dcpGC\nEVFLXT/sMlwycLRk751VS7HzxH5F4iEiai0mbImIiIiIiIiI2hH5HNt/Mg4pFIn7WVwStrKWyMLZ\ntESWJmyDAgPOMjoiz+ocI6uwzWOFbZ1vt/4mWV/Q83xEh0QqFA2dDUEQ8Oq0JxAfFu3cc4gOzFzy\nH9hq7ApGRkR0dpiwJSIiIiIiIiJqR/old5esd/vJHFtRFGG2Nz7DVlDJWiKLbIlM/kteYXssjxW2\nQO2/Fd9u+12yN/m88QpFQ60RERSK1296UrK3P+so3l21VKGIiIjOHhO2RERERERERETtiLzCdo+f\nJGytdpukxbFWrYFapZYc49ISuYkKW4dDRHW1WbLHlsjkKzrLZtgeZYUtAGDnif1IL8xyrvUaHSb1\nH6VgRNQaY3oPxTWDpe2s3/jpQxzlzGYi8jFM2BIRERERERERtSN9ZRW2R3PTUWUxNXC077DIqmvl\n7ZCB+loiN15hazKZJUlgvV4HjUbdyD2IvEenmA4Qzvg7n1mcC5PV3Mg92ofvtknbIY/rOwzBxkCF\noiF3+Ne1/4eIoDDn2mK34tGlLzb5bzwRkTdRJGFrsViQmZmJo0ePoqysTIkQiIiIiIiIiJqttLQU\nR48eRWZmJiwWS9N3IPJiIcYgpJ4x29IhOrDv5GEFI3IP1/m1epdjXFsiN15h6zq/ltW15DuMOgMS\nw2Oda1EUcaIgq5F7+D+Hw4Hvtq2W7F1xLtsh+7rIoDC8MOURyd7mo7uwZOO3ygRERHQW2jxhK4oi\n/vzzT8ydOxdjx45FaGgoDAYDOnTogK5duyIsLAw6nQ69e/fGjBkzsHz5cpSUlLR1WERERERERET1\nKikpwfLly3HvvfeiV69e0Ol0CA8PR9euXdGhQwcYDAaEhYVh3LhxmDt3Lv78809JBR6RL/DHtshm\nm2x+rabpCtumWiJXy+bXBnB+LfmYzrHJknVaO2+L/HfabuSWFTjXAXojxvUdrmBE5C6Tzx2PsX2G\nSfbmfv02ckryFYqIiKhl2ixhW1RUhNdeew1du3bFiBEjMGfOHKxZswbl5eUux9psNuzfvx/vvfce\npk6disTEREyfPh1btmxpq/CIiIiIiIiIJLZu3YrbbrsNiYmJmDp1KubPn48DBw7AZrO5HFtWVobV\nq1djzpw5GDFiBLp27YrXXnsNRUVFCkRO1HLyhO3ujEMKReI+ZlmFrUFXX4WtrCWy2Hi7zCpZwjaQ\nCVvyMfKE7bH8kwpF4h2+3Spth3xRv5EI0BkUiobcSRAEvHzDLATqA5x7leZqzP7sVV5YR0Q+QePu\nE1ZWVuLll1/G66+/DpPp9Itag8GAgQMHok+fPoiIiEBkZCT0ej2KiopQXFyMjIwM/P3338jLy4PJ\nZMLixYuxePFiXHjhhXjjjTcwYMAAd4fqdhaLBTt37sTff/+NLVu2YMuWLcjJyQEA3HrrrXj77beb\nfa68vDy88847+Omnn5CZmQm9Xo+uXbti6tSpmD59OjQatz91RERERERE7dKuXbswc+ZMrFmzRrIf\nFxeHwYMHo0OHDoiMjERERATMZjOKi4tRVFSEvXv3YufOnbBYLEhLS8Njjz2GOXPm4JFHHsHs2bMR\nFBSk0HfUfHl5ediyZYvzfezOnTud7+XXrl2L8847r9nnWr9+PRYsWICtW7eiuLgYUVFRGDp0KO69\n916cf/75bfUt0Fnql+J/FbYWWYWtvt4KW1lL5CYqbG02u/Sceu1ZRkekjFRZwvZobvutsLXX2PHD\nDunv+snnsR2yP0mKiMOTk+/FU8tfd+79umcDftixBpcPGqtgZERETXNr1u/TTz/FzJkzkZubCwBI\nSkrCtGnTcOWVV2LgwIHQ6VxfKMsdP34cq1evxtKlS/HHH39g7dq1GDRoEG699Vb897//RUhIiDtD\ndqvx48djw4YN9d5mNpubfZ7169fjmmuuQWFhoWT/5MmTWLNmDRYuXIiff/4ZUVFRrYqXiIiIiIio\nPSsvL8fDDz+MxYsXw+FwQBAEjBo1CjfeeCPGjh2Ljh07NnkOq9WKHTt24JtvvsGnn36KzMxMvPDC\nC/jggw/w+uuv44Ybbmj7b+QsHT58GN27d2/w9pqammaf6+GHH8b//vc/yV5RUREOHTqETz75BM89\n9xyeeeaZsw2V2kC/ZOlzfyTnBKosJgTqfbeC1CVhq60nYatqWUtkq1VaYa/TMWFLvqVLbIpk3Z4r\nbDcc3IbiylLnOjQgGKN6DlYuIGoT00ddjW+2rsK2Y/849578/DWM7HEuwgNDFYyMiKhxbm2J/MYb\nbyA3Nxfjx4/H77//jvT0dLz00ksYPHhws5K1ANCpUyfccccdWLduHU6cOIEnn3wSAQEB+PDDD3H4\n8GF3hut2Op0OgwcPxgMPPIAlS5Zgz549LT7H0aNHccUVV6CwsBDx8fH4/PPPkZOTg6NHj+LZZ5+F\nWq3G1q1bccUVV7TozTMRERERERFJHT58GB9++CECAwPx5JNP4sSJE1i7di1uv/32ZiVrgdr3gUOG\nDMHLL7+M9PR0/P777xg/fjxyc3PxxhtvtO030EoOhwOxsbG49NJL8e9//xsrV67E3LlzW3yeF198\n0Zmsveyyy7BlyxYUFBRg48aNGD16NBwOB+bMmYOFCxe6+Tug1ggxBqFTdJJz7RAd2J95RMGIWs+l\nJbK29S2R5RW2Wi07npFvSY3pIFm35xm2P+1cK1lfPGB0vRd2kG9TqVR4/cYnodOcvsCmsKIE//rq\nLQWjIiJqmltfZY4ePRpvvvkmhg93z6D25ORkvPDCC3jkkUfwyiuvwGj07qs8f/vtNwjC6Rf+Lamq\nrfPYY4+hrKwMRqMRa9eulVzt/NxzzyE6Ohr3338/Nm3ahI8//hi33XabW2InIiIiIiJqb4xGI2bN\nmoVZs2YhMjKy1edTqVQYO3Ysxo4di40bN+Lbb79tfZBtqHv37s4OWXWOHGlZwi4rK8uZ5L3ooovw\n3XffOd8XR0VFYdWqVRgxYgS2bNmC2bNn49prr0VYWJhb4qfW65fSA8cLMp3r3RkHcV7nfgpG1DrN\nSdi2tCWyVTbDWqdlhS35lqSIOOg1OljstRXoJVXlKK4sQ0RQ+6o0FEURq/dukuxdNmiMQtFQW+ue\n0AkPTboVr/5w+mKxzzf9iKvOm4ALenJMAxF5J7dW2L722mtuS9aeKTIyEi+//DJ69+7t9nO705nJ\n2rORkZHhfEN/11131duaasaMGejcuTMA4M0332zV4xEREREREbVnvXv3xssvv+yWZK3ciBEj8Npr\nr7n9vO7U2vewAPD+++87Z96+8sorLufUarV46aWXAADFxcVYsmRJqx+T3KdfsmyObbpvz7E9q5bI\nYhMzbK2ssCXfplKp0IlVtjiYfQw5pQXOtVGrx7Bu5ygYEbW1BybejO4JqZK9mUtfRJW5WqGIiIga\n59aELbXOmVdfT506td5jBEHAddddBwDYs2cPjh075onQiIiIiIiIiFzUvY/t3bs3+vbtW+8xo0eP\nRkxMDADgm2++8VRo1Az95QnbjEMKReIedRWEdepP2MorbBtviexSYcsZtuSDOscmS9ZpeRkKRaKc\nNfv+kqyHdR9UbxU++Q+dRos3bnxScjHZyaIczP3mHQWjIiJqGBO2XmTLli0AamcgDRo0qMHjhg0b\n5vx669atbR4XERERERERkZzJZMK+ffsAAEOHDm3wOEEQnLdv27bNI7FR8/RNlnb2OpxzHNXWlo93\n8hYmazNm2AotrLDlDFvyA0zYuiZsx/Ru+PcW+Y9BqX1w54VTJHuL13+FjQf5eoSIvA8Ttl7k4MHa\n1kMdOnSAtpGZKKmpp1s5HDhwoM3jIiIiIiIiIpI7dOiQszqxbnRPQ+rex1ZUVCAzM7PRY8lzQgOC\n0TE6ybl2iA7sz2zZHGNvYpHNsG1OS+SmZtjaOMOW/IBrwrZ9tUSuNFdhy9Hdkr2xfZiwbS9mT74H\nnc74XQcADy95ga2RicjrKHpZoMPhwNq1a7F582aUlZUhOjoaI0eOxJAhQ5QMSzH5+fkAgNjY2EaP\ni4uLc35dUFDQyJGuSkpKGryttLTU+bXVaoVOd/qNjfwNCvm+M59TPr/+ic+xf+Pz69/4/Po/Psf+\njc9vy1mt1qYP8hJFRUX44YcfcPjwYQiCgM6dO+Piiy+WvE9rL+rewwItfx+blJTUyNFSzX0fy5+9\ns9MnqStOFJxOou84thf9kro3cg/lNPUcV5tNkrVWpXH596WmpsZl3di/QRar/HFEn/o3y5fwZ7jt\nJEfES9ZH8zIU+Xus1HO8du9m2GpOV8t3ik5CQmgMf5bdzFt/hjVQ4dUbZuPaeQ84uyqcLMrBcyvm\n4YXrHlE4Ot/hrc8vuQ+f45Zz9++RNkvYZmVlYf78+di1axd0Oh369OmD++67zzm3Ji0tDVdddRX2\n7Nnjct/Ro0fj888/b/INn7+prKwEABiNxkaPO/P2uvs0V0RERLOO+/333xEUFCRZk//i8+v/+Bz7\nNz6//o3Pr//jc+zf+Pw2T0vf17SVX3/9FcuXL0d2djbi4+MxYcIETJkyxTnzcsGCBXj44YdRXS2t\nyDAYDPjXv/6FWbNmKRG2Ys583rzhfez69eud72P5s9d8OlmB0a+b1yK2KkCZYFqgvud4T9peyTor\nIxO//PKLZM9mk86sLS0rcznmTCaT9IO49evXuVTpkvvxZ9i9qqzSixmO5WXgp59/gkpQrvmiJ5/j\nZXtXStYdA2Ib/bmn1vPGn+ExKedi9YnT4wWXbPwWUVYjekR2VC4oH+WNzy+5F5/j5nH3+9g2Sdhu\n3rwZEydORHl5uXPv66+/xrx587B582ZERkZi4sSJSEtLq/f+69atw7hx47Bt2zbo9e1v+Lt8nkpj\ntzc1a4WIiIiIiIia9tBDD2HevHmSvcWLF+PLL7/EV199hc8//xz33HNPve/BzGYzHn/8cWg0Gjzy\nSPus1OD7WN/VIUR6sfzJ8vwGjvR+thppNYhWVc/HXvK/qo38dRRFEfK/rk38VSfySoE6I4K0RlTa\nahO3dkcNik3liAoIUzYwDxBFEXsLpJ9B94luvI0/+afJ3Ubhn/yjyK8+3bnjk39+xrMj7oBe49pC\nn4jI09yesDWbzZg6daozWSsIAnQ6HSwWC0pLS/HAAw9g6NChSEtLQ1RUFO69916cd9550Ov1OHHi\nBD7++GNs2rQJe/fuxdtvv42ZM2e6Nb7evXsjPb11cxqKioraJJEcGBiIkpISmEymRo878/Yzq2Cb\no7i4uMHbSktLnXOFxo0bh6CgIOeVFOPGjWt0ri75HpvNxufXz/E59m98fv0bn1//x+fYv/H5bbnG\nWt56wjfffCNJ1ur1elitVoiiiG+++QYrVqzAo48+ClEUMXLkSNx0001ISUmB2WzGli1bMH/+fBQV\nFeGpp57CzTffjKioKLfFtm7dOlx66aWtOsfUqVOxaNEiN0V0WmBgoPNrb3gfO2rUKGzfvh0Af/Za\n4vyKUry59XPnOreqCOMmjIdWregUrXo19e/rDstxIG2Tc92nV29MGjdJckxJaTm++X6tcx0UFIhJ\nk8Y2+HhLPvvZuVar1bj44otb/X1Q/fj7s20tOPgDth8/XYXeoWcqRvca7NEYlHiOD+ecQPHK00VF\neq0OD0y9EwZd+ysSamu+8DOc0KsTrnnzfufFY0WmMuyrycJTl81QODLv5wvPL7UOn+OWc/f7WLe/\n+v7222+Rnp4OlUqFF154ATNmzEBgYCD+/vtv3HjjjVi7di327t2LqKgo7NixAx06dJDc/84778TN\nN9+MpUuXYvHixW5P2FZVVaGqqqpV52irq4GjoqKQmZnZ5FzaM+cERUZGtugxwsPDm3WcTqeT/EBq\ntVrJTFvyL3x+/R+fY//G59e/8fn1f3yO/Ruf3+ZR+v/Rm2++CQDo1KkTlixZgiFDhqCqqgrvvfce\nnnzySTz66KPIzs7Grbfeig8//FBSLXr55ZfjjjvuwLnnnouioiIsX74c9913n9tis9vtrX4Pazab\n3RSN1JmJaW94H8v3sGcnPjIG8WHRyCmtfQ6tNTakF2WhV1JXhSNrXH3Psc1hl6wDDUaXY+QX4DvE\nhv8Nstmk8251Og3/XnkIf4bdr3NssiRhm12Wr+j/Y089xxsOb5Wsh3U7ByFBwW3+uO2dt/4MD+8x\nCLePvhaL1n7h3Fu49gtcPeQi9EvuoWBkvsVbn19yHz7HzePu/0duH1SwZs0aAMDVV1+N2bNnIyQk\nBGq1GsOGDcPChQtht9uRk5OD+++/3yVZC9RW5L788ssQBAH79u1DRUWFW+Pbv38/KioqWvXHYDC4\nNaY63bt3BwBkZGSgpqamweNOnDjh/LpHD/4iISIiIiIiOltWqxWbNtVW5C1atAjDhw+HWq1GSEgI\nHn/8cVx11VXIyMiAIAj4z3/+U2/r344dOzqTtJs3b3ZrfBdeeGGr38N+8MEHbo2pTvfu3Z3/P44d\nO9bosXXvYwMCApCcnNwm8dDZ692hm2T9z8nDCkXSOhabdN6sQetaQaeS/QyLDofLMXWsNlmLZVaa\nkA9LjkqQrE8W5SgUiWet2feXZD2291CFIiFvMfuKu5EYfnocgEN0YOaS/8BeY2/kXkREbc/tCdu6\nubRXXXWVy21jx45FaGgoAGDo0IZ/OSYkJCAlJQWiKCInx70vHgICAhAUFNSqP21l0KBBAGqvft69\ne3eDx535AUDdfYiIiIiIiKjl0tPTYbPZEBoaijFjxrjcXvfetmPHjoiPj2/wPMOGDQMAZGVluTU+\ntVrd6vewbTHSB6htbdy1a20V5t9//93osXXvYwcOHNjkvFvyvL6yhO2+k0cUiqR1zDaLZK2vJ2Er\nqKQfhTka6aJms0k/vNdpva9NNFFzdYiU/g5rDwnbKnM1/j4q/Yx1DBO27V6QIRAv3TBLsvfPycNY\nsHq5QhEREdVye8K2srISAJCUlFTv7YmJiQCabmkUEREBAG6vsPVmkydPdn795ZdfNnjcihUrAADd\nunVjhS0REREREVErNPUetm6f72Hrd8UVVwAAdu3ahaNHj9Z7zObNm5GZmSk5nrxLH5cK20MKRdI6\nZlmFrV7r2qbOtcK24YSt1coKW/If7TFhu/noLljtp3+OU6IS0SnGteMjtT/j+w7HFeeOk+y9+sMC\npBe498I7IqKWcHvCtq6Vb0Ntg41GIwA0eUVt3e1tNS/WG3Xt2hXjxtX+onjvvfecb2jP9Nlnn2Hv\n3tp5E+6ci0RERERERNQe8T1s69x1113QaDQQRRFPP/20y+1n7gcFBeHmm2/2dIjUDH2SZBW2mUd8\n8u+yxd6Mlsgq6c+yQ2y4JbJLha2OFbbku9pjwnaLrLp2VM/z2eWBnJ6/7mGEBYQ41yabBbM/f9Un\nf/8RkX9we8KWWue1116DwWBAWVkZxo4di/Xr16OmpgZVVVV4//33cdtttwEA+vTpg3vuuUfhaImI\niIiIiKg969KlCx5++GEAwPLly3HnnXc6Lz5OS0vDlClTsHr1agDAM888g9jY2AbPRcpJjkpAsCHQ\nuS43VSLDB5M5FllLZEM9FbaCIGuJ3FiFLWfYkh+JD4uGWqV2rgsrSlBtNSsYUdv7O22PZD24S3+F\nIiFvFB0SiTlXPyDZW7tvM1bt2aBQRETU3jFh60Yff/yxZE5QVFRUg7fFxcXVe47+/fvj008/RUBA\nAA4fPozRo0dDr9cjKCgI99xzD8xmM7p06YIff/wROp3rGw8iIiIiIiKi5hozZozkverMmTMbvO3x\nxx+v9xwvvvgipk6dCgBYtGgROnToAK1Wiy5dujjH/dx7772YNWtWvfcn5QmCgN6ytsh7fbAtstkq\nn2FbT0tkWYVtY5VUnGFL/kSj1iAhPEayl+mDF2Y0l9Vuw64T+yV75zNhSzLXD7sUQ7oOlOw98+X/\nYPLzixmIyDu12SvNLVu2oLS01GW/bp5PQ7fLj/MlNpsNVVVV9d5mt9tht9vrvU3uyiuvxK5du/DK\nK6/g559/Rm5uLnQ6Hbp06YIpU6Zg5syZCAwMbPpERERERERE1CwVFRX4/fffXfYPHz7c6O3y43xN\ndXV1g+9jTSaTZG2xWOo9Tq1W47PPPsPkyZOxYMECbNmyBZWVlQgJCcGwYcNw33334dJLL3V77ORe\nfTt0w+YjO53rvSeP4JKBFyoYUcvJWyLr622JLK+wbbglsnyGrU7HClvybR0i4yWtkE8W5aBbfCcF\nI2o7/2QcgvmMqvv4sGgkRdRfQEPtlyAI+M+URzDuhVucLfIzCrPx3m+f4pFLblM4OiJqb9osYdvU\nfFV/nL966623Oq8qbkpT8xK6du2KhQsXAqhN9qrVas5YICIiIiIiaiOHDx/G+PHjz/p2X7V27Vrn\nHN+mNNXlacqUKZgyZQqA2gua2T7Wt/TxhwpbW9MzbAV5hW0jLZHlFbZaVtiSj2tPc2z/ls2vPb9L\nf362SvXqldQV00dfjQ/Wfunce2vlx7h2yCSXnxkiorbEV5pupNFoEBQU1CbnJSIiIiIiInI3o9HY\nJudlstb3yBO2+zKPKBTJ2TM3Y4atSpawcYgiRFGsN5Ejn2Gr499r8nHy5FNGYbZCkbS9LWmyhG1n\ntkOmhj126Z34ZutvKK4sBQCYbBb866u3sOiu/ygbGBG1K27PBD7zzDMoKChw2/k6duzotnMRERER\nERERnaljx47O7kbuEB0d7bZzEXlSt/hO0Gm0sNprk5TZJfkoqixFZFCYsoG1gEVWYavXuCZsBUGA\nIABnjq4VRaC+wjuXClsdL6gn3+ZaYZurUCRtSxRFbEnbI9k7v3M/haIhXxAWGIKnJt+LmUtfdO79\nuGMNNhzcipE9zlMwMiJqT9z+SvOKK65w9ymJiIiIiIiI2kRUVBTuuOMOpcMgUpxWrUGPhFTsyTjd\nCnlvxiGM6jVYwahaxiVhW09LZAAQBBVE8fTs2tqv1S7HucywZYUt+bj20hI5LS/DWSkJAEGGAPRM\n7KxcQOQTrh92GT7Z8C12px9w7j3x2WtY/fQS6Ovp2EBE5G4qpQMgIiIiIiIiIiLl9U6StkX+5+Rh\nhSI5OxZ5S2Rd/QlblWyOraOBObacYUv+xiVhW+yfCVt5O+RzU/tCo+bPLzVOpVLhxakzJXtH89Lx\n1q+fKBQREbU3TNgSERERERERERF6J3WRrI/mpSsUScuJogiTLGGr19RfEVvfHNv6uMyw1bHClnxb\nfFg01KrT1eRFFSWospgUjKht/H1UmrA9j+2QqZnO6dQHN46QdhCdt/JjHM31nd+HROS7mLAlIiIi\nIiIiIiJ0jk2RrI/lZSgUScvVzd6to1VrJImpMwkq6cdhosNR73E2Kytsyb9o1BokhMdI9jL9cI7t\nVtn82sGd+ysUCfmip6+8D1HB4c611W7DrE9fhtjAxT1ERO7i1leac+bMwbFjx9x5SsydOxedOnVy\n6zmJiIiIiIiIjh8/jmeeecat50xNTcW///1vt56TyFM6xyZL1kd9KGFrsUvn1xoamF8L1FNh20BL\nZJcKW86wJT/QITJeMrv2ZFEOuif4z2evBeVFOJZ/0rlWq9QY2Km3ghGRrwkLDMHc6x7GvR/Mce5t\nOrwDy//6CVOHXapgZETk79yasP3555+xfft2d54S//d//8eELREREREREbldUVERli1b5tZzDho0\niAlb8lmJEbHQa3TO5GdxZSlKqsoQHhiqcGRNk8+v1Wt1DR4ryGfYig1U2HKGLfkhlzm2RdkKRdI2\ntsiqa/t26I5AvVGhaMhXTT53PJb/9RPW7f/buffvr97C+H4jEBkUplxgROTX3PpKs2/fvtBoGj6l\nKIrYvn07ampqoFKp0LFjR4SHh8NsNuPEiROoqqoCAHTu3BlRUVEAgKCgIHeGSERERERERASg9v3m\n4MGDGz2msLAQaWlpAIDAwEB07NgRBoMBxcXFOHHiBERRhFqtxqBBgyAIAnr27OmJ0InahFqlRseY\nJBzKPt097Xj+SYR38v6ErckqT9g2UmEra4lcX4WtKIr1JGxZYUu+zzVhm9PAkb5JnrA9n/Nr6SwI\ngoCXr5+FUf++AeZTFwQVV5XhuRXz8Natc5q4NxHR2XFrwvajjz5q8Lbs7GzccMMNCA8Px7/+9S9M\nmzYNoaGnX/A7HA5s3LgRzz77LPbs2YOXX34ZV199tTvDIyIiIiIiInLq0aMHNm/e3ODtK1aswF13\n3YUxY8bgueeew/DhwyWJntLSUixbtgzPPvssAgIC8OmnnyI+Pr7B8xH5gs4xHSQJ26N5GTinUx8F\nI2oe15bIDVfYylsii/UkbOXJWo1GDZWsMpfIF7kmbP1rhu2Wo7sl6/O7MGFLZyclOhEzL7kdL3z7\nrnPvy80/Y8qQizGix7kKRkZE/krV9CGtZzKZcPHFF+Off/7B5s2bMWPGDEmyFqi9uvGCCy7A6tWr\nMW7cOEydOhWrV6/2RHhEREREREREEqtWrcLUqVMxceJE/Pbbbxg5cqRLVV5YWBjuu+8+/PXXX9i9\nezcuueQSmM1mhSImco/OsSmS9TEfmWNrsTV/hm1zWiJbZQlbzq8lf+HPFbZmmwV7Tx6W7J3fub9C\n0ZA/uGf8DeiR0FmyN+vTl51Vt0RE7uSRhO2SJUuwe/duPPbYY+jcuXOjx6pUKrz11lsAgNmzZ3si\nPCIiIiIiIiKJ2bNnQxAEzJs3zyVRK9e1a1c8+uij2Llzp9tn4hJ5WmpssmSdlndSoUhaRp6wbWyG\nrUqQ/kzXW2FrtUnWWh3n15J/cEnYFvtPwvZAVhpsNacvtkiMiENMaKSCEZGv06o1eO1GaY7iWP5J\nvPnLxwpFRET+zCMJ219//RUAMGzYsGYdHxMTgy5dumDbtm0oKipqy9CIiIiIiIiIJAoKCrBz5050\n7doV0dHRzbrP8OHDAQArV65sy9CI2lznmA6SdVpeukKRtIxJVu2k1zSSsHWpsHVN2LLClvxVfFg0\n1Cq1c11UUYIqi0nBiNxnT8ZByXpASg+FIiF/cm5qX9x8wZWSvbd//QSHso8rFBER+SuPJGxzc2tn\nIdhstiaOPK3u2Jwc/7nKi4iIiIiIiLwf38NSe9Y5TtoS+Xj+STgcri2DvY1FlrA16BpuiSyvmq/v\n+5P//Gu1rLAl/6BRa5AQHiPZy/STOba70w9I1v2SmbAl93hq8gzEhJyu1rbV2DHr05d84vcjEfkO\njyRso6KiANTOAGqOo0eP4tixYwCAyEi2rSAiIiIiIiLPqXsPm5aW5nxv2pS6zlJ8D0u+LiIwFGEB\nIc61yWZBTmmBghE1j8sMW00jM2wFaYWtWE+FrY0VtuTHkqMSJGt/mWO7J+OQZN0/padCkZC/CQ0I\nxtzrHpbs/X10Nz7b9INCERGRP/JIwnbs2LEAgHnz5mHjxo2NHltZWYnp06dDFEX07NkT8fHxjR5P\nRERERERE5E7x8fHo2bMnRFHE9OnTUV1d3ejx69evx1tvvQXg9PtfIl8lCAJSY32vLbJZ3hK5sRm2\n8pbI9cywtXKGLfkxlzm2RdkKReI+ZpsFB7PSJHussCV3unzQWIztIx35+O+v30ZBOUc6EpF7eCRh\nO336dCQlJcFsNmPMmDF44IEHsHnzZpjNZgC1VzKeOHEC8+fPR79+/ZxJ3Tlz5ngiPCIiIiIiIiKJ\nuvejf/zxB/r164f3338fJ06ccFbimc1mbN68Gffffz/GjRsHi8WCpKQkTJ8+Xcmwidyic6y0LXJa\nXoZCkTSfWVZh21jCVhCa0xJZWmGrZYUt+RHXhK3vV9juzzwKu6PGue4QGY+IoFAFIyJ/IwgCXpz6\nKIw6g3OvrLoCz62Yp2BURORPPHJ5YHBwML777juMHz8excXFePvtt/H2228DAAwGA6xWq8uL49mz\nZ2Pq1KmeCI+IiIiIiIhIYurUqdi9ezdeeuklpKWl4Z577gFQO/tSp9M5L0CuExERge+//x7BwcFK\nhEvkVp1j5BW23p+wdZlhq21shm3TLZGtshm2Os6wJT/imrD1/Rm2ezIOStasrqW2kByVgMcuvRP/\n/vot595XW37FdUMuxqhegxWMjIj8gUcqbAHgnHPOwZ49ezBlyhRoNKdf5JrNZkmytmfPnvjmm2/w\n4osveio0IiIiIiIiIhcvvvgivvnmG/TseXoGnsPhkCRrNRoNpkyZgj179mDgwIFKhEnkdqmxyZJ1\nWr4PJGztshm2rWyJ7DLDVscKW/If/lhhuztdmrDtn8KELbWNO8dOQe+krpK9WZ++ApPV3MA9iIia\nx6OXByYmJuLzzz9Hfn4+1q9fj0OHDqGsrAwGgwEJCQkYMmQI3+ASERERERGR15g8eTImT56MnTt3\nYvPmzcjOzobZbEZoaCi6d++OUaNGISYmRukwidyqiyxheyzvpEKRNJ/ZKp9h23CFrbwlsii6tkR2\nmWHLClvyI0kRcZL1yWLfT9jKK2z7s8KW2ohWrcGr02bjklfucHZoSC/Mwn9//ghPTr5X4eiIyJcp\n8mozJiYG1157rRIPTURERERERNRiAwcO5AXG1G50lLVEPlmUA4vN2uhcWKXJK2wbi/WsKmw5w5b8\nSFxYNARBcCabiipKvP5nvDEmqxkHs49J9voyYUtt6JxOvTF91NX4cN0K5967q5biyvMmoGdiZwUj\nIyJf5rGWyERERERERERE5P0CdAYkhsc61w7RgRMFWQpG1DSzTd4SuZEZtoI8YVtPha2NFbbkv7Rq\nDaKDIyR7eWWFCkXTegeyjqLGUeNcJ0clICIoVMGIqD144op7ERca7VzbHTWY/dkr9c5FJyJqDiZs\niYiIiIiIiIhIIjVWWmV7zMvn2Fps8pbIDVcKCirpx2GOej5c5wxb8ndxYdGSdW5pgUKRtJ58fm0/\nVteSBwQbA/HC1Ecke38f3Y2vt/yqUERE5OvcmrDNzs525+kkKisrUV5e3mbnJyIiIiIiovalvLwc\nlZWVbXb+rCzvrkgkakzn2BTJ+mheukKRNI9ZlrA1aBppiSyrsBXraYnMGbbk7+JlCdscX07YyufX\npjBhS55x8YDRGNtnmGTvX1+9hQpTlUIREZEvc2vCdvLkyZgyZQoOHDjgtnNWV1fj1VdfRadOnXD4\n8GG3nZeIiIiIiIjat8OHD6NTp0547bXXUF1d7bbz7t+/H9dddx2uvPJKt52TyNM6xyRL1sfzTyoU\nSfNY5C2RdQ23RBbkM2xF15bInGFL/k5eYZtTmq9QJK23R1Zh258VtuQhgiDg+esehk5z+ndEfnkR\nXvtpkYJREZGvcmvC1mg04osvvkCfPn1w5ZVX4ptvvoHVam36jvX4559/MGvWLHTq1AmzZs1CcXEx\njEajO8MlIiIiIiKidsxoNKK4uBiPPfYYUlNT8fjjj2Pfvn1ndS6LxYKvvvoKV1xxBfr27Ysvv/yS\n72HJp6VEJ0jWJ4tyFIqkeeQzbPWaxmbYyloi11dhK59hq2OFLfmXhPAYydpXK2xNVjMO5RyX7PVN\n7q5QNNQedYrpgBnjp0n2Fq35AgezjykUERH5KrcmbH/66Sc89dRT0Ov1+Pbbb3HVVVchPj4eN910\nE9555x1s374dJpPJ5X41NTVIT0/Hl19+iUcffRQDBgxAv3798OqrryI/Px9jxozBjh070Lt3b3eG\nS0RERERERO1Y7969sX37dowZMwZ5eXl45ZVX0KdPHwwcOBCPPfYYVqxYgYyMDDgcrtV3JpMJ27Zt\nwzvvvIMbb7wR8fHxuOaaa/D9999Dr9fj6aefxs8//6zAd0XkHkkRcZJ1ZlGuQpE0j8UuS9g2UhGr\nUrW8JTIrbMnf+MsM2/2ZR1HjqHGuU6ISER4YqmBE1B49OOlWJJ7xe7PGUYOnlr8OsZ4Z6UREDXHr\n5YFBQUF4/vnncffdd2Pu3LlYtmwZiouLsXTpUixdutR5nNFoREREBPR6PYqLi1FWVlbvP17Dhw/H\n7Nmzcemll7ozTCIiIiIiIiIAwIABA7B69Wp8//33eOmll/DXX39h165d2LVrl/MYQRAQGhqKiIgI\nWCwWFBUVwWw2u5wrKCgI06ZNw9NPP42kpCQPfhdE7pcUGS9ZZ5XkweFwQKVy67X/bmORz7DVnn1L\nZIdDhN1eI9njDFvyN/IZtr6asN2VLh3N14/tkEkBAToD/nXNg7hjwZPOvT8Pbcd323/H5HPHKxgZ\nEfmSNnmV3aFDByxYsADZ2dl48803MWjQIMkLepPJhKysLBw7dgylpaWSZG1SUhLuu+8+/PPPP9i4\ncSOTtURERERERNTmLr/8cmzatAm7du3C3Xffjbi401USoiiitLQUx44dQ1ZWliRZq1arMXjwYLzz\nzjvIzs7G/PnzmawlvxBiDEJoQLBzbbXbkF9epGBEjZPPsNVrdQ0eK086y1si2+zS+bVarQaCIE3y\nEvm6eFlL5OwS35xh+8/JQ5J1/xQmbEkZlwy8EKN6ni/Zm/PF/1BWXaFQRETka9r08sDQ0FA8+OCD\nePDBB1FWVoaNGzdi+/btyMvLQ0FBAaxWK6KiohAdHY2uXbti1KhR6Ny5c1uGRERERERERNSg/v37\nY/78+Zg/fz4OHz6MP/74A0ePHkVBQQEKCwthMBgQHR2NuLg4DBo0CCNGjEBwcHDTJybyQR0i4yUf\nNGcW57q0UfUWLjNsG6mwVcmSr/Kubzb5/FpW15IfklfY5pUVQhRFn7s44WCWdE5o76SuCkVC7Z0g\nCHh+yiMYM/dG2GpqL/zJLy/CC9++i1dueFzh6IjIF3jsFWdoaCguueQSXHLJJZ56SCIiIiIiIqKz\n1q1bN3Tr1k3pMIgUkxQRh70nDzvXmUW5ODe1r4IRNcxlhq2mJRW20pbIVqu0wpbza8kfBRkCEWQI\nQKW5GkBtFX1RZSmigsMVjqz5HA4HDuVIE7Y9E1kMRMrpGtcR90+8Cf/9+SPn3id/fINrB0/CeZ37\nKRgZEfkCXiJIRERERETkw0SHAygrglicD5QUQiwthlheCrGsDKishFhZDbHaBFRbIZpsEC01gEWE\naANEmxq6Sd2hvfNRpb8NIvJCSRFxkvXJohyFImmavCWyoZGWyPIKwiYrbHX8+Iz8U3xYDI7knnCu\nc0ryfSphe7IoBybr6TEFYQEhiA2NUjAiIuChSbfiu22/41j+Sefeo8tewm9PfgydhhcAEVHD+IqT\niIiIiIhIQWJNDVBefNYJV9RoAKiafJxa2lN/znj8cs7VIqL6dYiMl6xPFntzwtYiWesarbCVJmzl\nM2xZYUvtRXxYtDRhW1qAvsndlQuohQ5mp0nWPRJSfa6lM/kfg1aPV254HNf8737n3qHsY3jvt2V4\naNKtygVGRF6PCVsiIiIiIqJWEGtqaitcS/KBkiKIhfnoun87dBYLHCd2w1ptglhlBkyWUwlXh1sT\nrq1WZXLv+YjIbyRFSitsM4tyFYqkaRa7tCpW32iFbeMtkTnDltoL+Uzq3NIChSI5Owezpe2Quyek\nKhQJkdSIHudiytBLsPyvn5x7b/z0IS47ZwxSY5MVjIyIvBlfcRIRERERUbsm2u21Fa51CdfSYohl\npRDL6ypcq1qccE059d8a5KHGuSsAaDiBoBSxmglbIqqfS4Wtn7REllfYylsiW22ssKX2ISE8RrLO\n8fGEbQ8mbMmLPHv1g/jtnz9RXFkKoHbW+iNL/oOvH3nXZZY6ERHAhC0REREREfk40VQFlBZCLCuG\nWF4ClJe1OuFaP+9MuAIAVHYIGjugdUDQCRD0KsCggRCghRBghBBoBIKCIIQEQwgJBUIjIIRFQoiI\nBmQf1hIR1UmKkCZsM4tzIYqiV7YclbdE1mv1DR6rEhpvicwZttReyCtsc0rzFYrk7Li0RE7srFAk\nRK4igkLx72sfwv0f/cu5t/noLixY8znuGXeDgpERkbfiK04iIiIiIvI4lyRrRTnEilMJ1qoqoLp2\nbqtosgJmK0SLHbDYIVpFwAaINgFijQqoUQOiupmP6r8JV8FgVPo7ICI/FB4YggC9EdWW2kp8k9WM\n4qoyRAaFKRuYjL3GDrvjdD8DlaCCRtXw7wZB1XhLZM6wpfYi3odbIttq7Diamy7Z6x7PClvyLlef\nfxG+3rIKa/b95dx78dv5uLDXUHRP6KRgZETkjZiwJSIiIiKiBol2O1BdAVSUQqwoBaoqIFZVAFWV\nEKurgepKiNVmwGyCaLYAZgtEi+1UctUdSdY6Gnj12xdnwlWEoAOssKFGKyAgMhSqQCOEwAAgOBBC\ncEhtwjUsvDbhGh4DRMRA0BuU/g6IiFwIgoAOkfE4dEbb0ZNFOV6XsK1vfm1jVcDylsgOsYkKW86w\nJT8VF+a7LZGP5Z2Ereb0xRWxoVGICApVMCIiV4Ig4I2bnsTof09DaXU5gNrWyA8s/hd+enwRtGr+\nfiGi0/gvAhERERGRDxMtZqCqHDBVQqwsB0zVtdWr1dWAuRqiyVSbTDWZALMZotlcW7FqtgIWW21S\n1eaAaHUANhGiHUANTidWHa15y+DlSdYzqWwQNDWnK1wNpypcjToIAYYWJVytVivW/fILAGDSpEnQ\n6by0qpeIqBmSIuIkCdvMohwMSOmpYESuWjK/FnBtiSzKK2w5w5baiYRwWUvkEt9piezSDpnza8lL\nxYVF48XrH8W9H8xx7u3JOIg3f1mMRy+9Q8HIiJQjiiLyygpxoiALGUXZyCis/VNhqkKwMRAhxiCE\nBAQj1BiEnomdcX6X/jA0Mu7CX/jIpydERERERL5BtFpqK1KrKiBWVwKmqtoEqqm6NplqNkGsrETv\no0ehrrHDcWxn7QfDFitEqw2w2gFbDURbTe1/7SJgF2uTqHYANQJEhwDUqACHGs2bvdoYf3hL4ADU\ndggaR22FqxbShGvgqYRrUBCEkLqEawSEsIjahGt4NCtciYgakBQRJ1lnFucqFEnDXObXahr/QM+l\nJbKswrampkayVmta2hWCyDdEBoVDq9Y4K1XLTZWospgQqPf+UQsHz7iQBOD8WvJuk88dj592rsOP\nO9Y49/7380cY33cE+qf0UDAyorZnr7Fjb+YR7DqxHwey0nAo+xgOZKehrLqi2ecwavUY0m0gLuw1\nBKN6Dka3+I6NdlPxVf7w6QwRERERUb3qTZ6aqyXJU2fVqcUKWC0QLdbar2111ac1EG21VaiwO6QJ\n1BrUJlBrBMDRsgRq/Kn/1qAANS63CvCp6tSzUk+SVScAOjUEgxYwaCEY9RCMRiAwAEJAABAcDCEo\nBAgJhRAcBiEsEgiJAIyBLh++ExGRe3SIjJesTxblKBRJwyx2aYVtUxWxrhW2YqNreQtlIn+hUqkQ\nExqFrDMuxMgtLUDn2GQFo2qeQy4VtkzYkvcSBAEv3zALfx/dhYLyYgCA3VGDBxb/C6ueXNwuKgep\n/RBFEXtPHsaGg9uw6cgO/H1kFyrMVa06p8lmwdp9m7F232YAQGJ4LJ675iFcNmiMO0L2Gv78CRAR\nEREReRHJLNQzK0/NpnqSpxbAavVY8rRp6lN/2imhpja5qhYBjQhBIwIaAYJOBWjVEHQaQK+BoNcC\nBj0Egx4wGCEEGGurWoNDgeAQCCHhEELCgbAoJlmJiHxEUqSswrbI+ypszbKWyHpN4y2RBZcZto5G\n1yqBv6/IfyWERUsStjk+krB1qbBlS2TycpFBYXj9xidw87uPOfcO5xzHS9+9j+eueVDByIjco8ZR\ng5W7/8BbK5dgV/r+Nn2srJI8hAeGtOljKMErErYWiwWLFi3Chg0boNFoMHHiRNx4441+WdJMRERE\n5O1Eux2oLIVYXgJUltXORa2qhFhVAVRVQ6yuAkwmiCZzbYLVYgPMtlPtfGuks1Dt7pqFeqZ2njx1\n4QBUNYDKUZtQVYsQ1Kh9pa8WIGgFQKM6I6mqAwy6U0lVQ20Fa0BgbQVrYBAQGAQhMBgIDq9NtAaG\nQuDsPiIXhw8fxvz585Geno4OHTrgjjvuQJ8+fZQOi8jtkn2gwtZqb+kMW1lLZFlFrXwtT/AS+ZO4\nsBjJ2hfm2JqsZhwvyJTsdYvvpFA0RM03od9ITB12KT7f9KNz7/3Vn2Fi/5EY2nWggpERnT2LzYqv\ntqzEO6uWIi0vo9n3C9QHoHNsMpKjEpAcGY+U6ESEB4ai0lyNclMFyk1VyC7Jw4YDW5FVkie5r1Fn\nwHmd+7n7W1GcRxK2drsdffr0QVVVFfbu3YvQ0FDJbRdddBHWrVvn3Fu2bBm+//57LF++HCpedU9E\nRETULKLNBpQXQSwpBMqKIZaXQqwoAyorIFZUAdVVEKtMEE0WwGyFaLZDtNQAVhGiDYBdgGhXA46z\nTc4xkVrLAahqk6iCWgRUZyRQNQIEjQBRI8Bks8ChFhAUHgaVXgvodRB0OkCvA/R6CHo9YAw4lVQN\nAIxGCAHBtXsBwRACgwBjMKA3sFKVqA189dVXuO+++3Dttdfirbfektz2999/Y+zYsaiqOt3a6733\n3sNXX32FSy+91NOhErWppAhpwtY7Z9jKKmybaC0pb3Hs0hJZNtNW3kKZyJ/Eh0VL1rmlBQpF0nxH\nck9Ifk5TohJ9Yu4uEQDMvfZhbDi4zVnZLooiHvp4LtY8vQRBhkCFoyNqmQ0Ht+LRpS8hvTCr0eMi\nAkMxpOsA9EvugZ6JndEjsQs6RMQ1K/8niiKO5J7Auv1/Y+3+zdh8eCeGdx8EfRMX6PkijyRsf//9\ndxw6dAgXX3yxJFkLAB999JEzWRseHo6AgABkZWVhxYoV+PjjjzF9+nRPhEhERETkFURTNcTck4jK\nOw6DqQLiD0WwV1VCLC+HWFGbcEW1BaLJDtFcA9EiAjbVWSRaBQDaU3/8WV3y1AFB5ThdfXoqgSpo\nVIBGBWhVELTqU+19tYBOA+h0tV/r9bUJVIOhNnlqMAIGI2AMgGAMrG3tGxgEGE/9aUYC1Wq1YsMv\nvwAAJk2aBJ3O/95oEPm6JUuWIC8vDxMmTHC5bcaMGc5kbWpqKrKzs2E2mzF9+nSkpaUhJMT/2nNR\n+xUVHA69RuecE1tuqkRZdQVCA4IVjuw014RtExW2st/T8hbIrjNseWEU+a/4cGnCNqfU+yts2Q6Z\nfFmwMRBv3vw0rvnf/c69jMJs/Ourt/DqtNkKRkbUfOWmSvz7q7ewdON3DR5zYe8hGNtnGIZ3Owfd\n41PP+vWUIAjoFt8J3eI74a6xU2G2WVBcWXa2oXs1jyRsf/31VwDAxIkTXW5buHAhAGDEiBFYtWoV\njEYjHnroIcybNw/vvfceE7ZERETkk0S7HSjOhZifDbEwD2JRIcSSYohlZUBZJcRKM0ST7VTSFYBN\ngGjXONsGDzh1HjtyYXc5uwqAjyb4hBpAXeNMnkKNU9WntZWnLslTrRbQN5A81Z9q51uXPDUEAAGB\ntdWnAc1PnhIR1WfVqlUQBMElYbtjxw7s2LEDALBgwQLceeedyM3NxeDBg5GRkYEVK1bgtttuUyJk\nojahUqmQFBknaXGXWZzrVQnbVs+wlbdEliVw2RKZ/Fm8rCWyL1TYHsxKk6yZsCVfM6LHubj9wmvx\nwdovnXtLNnyLi/pfgLF9hikYGVHTfvvnT8xa9hJy6vl9oVGpceX5E3HfhBvb7N9mg1aPhPCYpg/0\nQR5J2GZm1s4USE6WDqwvKirCtm3bAACzZs2C0VjbuuKZZ57Bu+++i+3bt6O6uhoBAQGeCJOIiIio\nQWJlOcScdIgF2RALC4CSYoilpRDLKyFWmCBWWSBW2yFaANGqAmxa1CZWGyLAq5OuKjsEdQ2gdkDQ\noPZVo1aAoFMBOjUEvRbQa0/NQ9VDMBpOtewNAAIDa1v3BgVBCAoBgkIhBIcBQWGchUpEPqGoqAgm\nkwmxsbHQ66WtVVeuXAkASExMxB133AEAiIuLw4wZMzB79mxs2LCBCVvyO0kRsoRtUQ56J3VVMCIp\ni90iWTc9w1bWEllsfIYtWyKTP4uTtUTOLvGBhK28wjaxs0KREJ29p668D+v2/y35/frYspfwx7Of\nsTUyeaXiyjI888Ub+GrLry63CYKAm0ZOxgMTb0aHyPh67k3N4ZGEbW5ubT/2mBhp1nvTpk0QRREa\njQZjxoxx7kdFRSExMRHp6ek4efIkunfv7okwiYiIqJ0Ry0sgZp+AmJcFMb+uCrYUYlklxAoLxCo7\nRDMgWjTNaDfsJe2FVTYImhpAI0LQAYJOAPSnEqxGHQSjHkKgEQgMgBAUDAQHQwgOhRAaAYSGQwiN\nBEIiIGg88jKRiMgrNfQeFgD+/PNPAMCECRMgnJHE6d+/PwDgxIkTbR8gkYfJP3g76WVzbFs+w1bW\nEtkha4ksS+AKTNiSH4sP970K20NsiUx+IEBnwFu3zsGlr9zl7OyQXZKPF7+bjxemzFQ4OiKpH7av\nwROfv4rCihKX27rEpuC/Nz+F8zr3UyAy/+LRT+LKyqR9pf/44w8AwIABAxAYKL1qpG7mj8UivUqS\niIiIqDGi1QIx+zjErBMQc7JrE7ElZRDLqmrbEFfV1CZhrVpn++H6KZWAdQBqO0SNHaKmBpoALQSj\nBkKADkKAAQgKgBASDCEkBEJYOBAeCSE8GkJkDBASyUQrEZEbyd/D1tTUOBO2w4cPl9zG97Dkz5Ii\n4iTrk0U5CkVSP3lLZJ2m8ddw8gSsa4WtNIHLGbbkz+JCoyTr/PIi2Gvs0Ki9831FuakSWSV5zrVG\npUbn2BQFIyI6e+d06oN7xl2Pd39b5tz7cN0KXHneBJyb2lfByIhq5ZcV4YnPX8VPO9e53KZWqTFj\n/DTMvPR2GJq4WI6axyO/eTt06AAA2L59OyZNmuTc//HHHwEAF1xwgct98vJqf/HGxsZ6IEIiIiLy\ndqLNBjHnBMTsdIg5mRDz8yEWFkMsrYRYboZY5YBoVkG06VDbbrg+Hm5BrLJB0Nkh6AHBoIIQqAWC\nDBBCgmqTrmFhtUnXsFNJ16hYIDQStpoa/PLLLwCASZMmQafz4tbJRER+KCkpCQCQlZWFvLw85/vS\nDRs2OJO48vexfA9L/iwpUpqwzSzytgpb6YUS+qZaIjc1w9bBCltqP/RaHSKCwlBcWQqgdoZzfnmx\n184HlFfXpsYmN3mRBpE3e/SyO/HTznVIL8wCUHsR0SNL/oPfn/qEf7dJUev2/437PnoORfVU1fZK\n7IL/3vw0+qf0UCAy/+WRhO3IkSPx2Wef4d1338W1116L7t2744MPPsDBgwcBQJLEBWqvWi4sLIRG\no0F0dHR9pyQiIiI/ITocQN5JOE6mQczOhFiQB7GoBGJJRW0ittJem4i16tDwTFhPXMnngKCzQtCL\ngEGAEKCBEKiHEBwIITQYQng4hPBICNGxQHQ8hJhECMaznDtTU+Pe0ImIqEVCQ0PRr18/7NmzB7Nn\nz8aCBQtgs9nw3HPPAQA6d+6Mrl2l8zvr2ignJCR4OlyiNpcUIW2JnOltLZHt0gpbg6bx14aCIGuJ\nLDbeElme4CXyN/Fh0c6ELQDkluZ7bcL2WP5JybprXEdlAiFykwCdAa9OexzXvfmgc+9wznG89esn\nmHnJ7QpGRu1VjcOBV39ciLd/W+rymkir1uDhi2/D/RNv4gUFbcAjCdvrr78ezz77LHJyctCjRw+E\nh4ejpKQ2K9+rVy/J/FoA2LFjBxwOB84//3y2nSEiIvJhot1em4zNOAox6yTEvFyIhcVwFFdCrLBC\nrAJEiw4Q1Q2cQYc2rYoVaiBobRAMIoQAFYQgPYSQAAjhIRAiIiBEx0CITYQQ3wGIjGe7YSKiduSh\nhx7C7bffjsWLF2P58uUAAJPJBAC4//77XY7ftm0bAOD888/3XJBEHiKvsM3ysoSt1W6TrFtfYcuW\nyNS+xIfHYF/mEec6x4vn2J4oyJKsO0YnKhQJkftc0PN8TBl6CZb/9ZNz781fFuOyc8agW3wnBSOj\n9qbEXIFFu77D0ZKTLrcNSOmF/978FHomdlYgsvbBI586hoWFYcWKFbjqqqtQVFTkTNampKTg008/\ndXnhW9cCcOLEiZ4Ij4iIiM6CaLdDzEmHePIoxKxMiLk5EItK4CipglhuhVjdWDJWDcDYdsFpLFAZ\nHBACVRCC9RDCAiGEhUCIrK2AFWITIMQnA5FxEPgBHBER1WP69OnYtWsX3nrrLWeiFgCmTZuGBx54\nwOX4lStXAgAmTJjgsRiJPCUuNApqlRo1jtouIIUVJTBZzTDqDApHVks+w7bJhK18hq2j8QpbtkQm\nfxcfJu1w6M0J2/SCTMm6U3SSQpEQudezVz+I1Xs3ofBU+1mr3Yb/++R5fP/o+147U5r8y+70A3jh\nzw9RYa2W7KsEFWZeejseuugW/l1sYx77v3vBBRfg6NGj+Omnn5CTk4PU1FRMmDABQUFBLsdGR0fj\nvvvuw5QpUzwVHhEREZ1BtNkgZh+HeDKtNhmbnwexoBiO0iqIFTaIVQJEq9bzyVi1FYKhBqpA4VQi\nNghCZBiEmBgIsfEQElMgJKRCMAa0zeMTEVG7IQgC5s2bhzvvvBPr1q2DSqXCoEGDMGTIEJdjS0pK\ncOWVVyIyMhLx8fH1nI3It2nUGsSFRUsqa7OK89AlLkXBqE5r6Qxb+QV7Tc2wZUtk8ncxIZGSdUFZ\nkUKRNO1EobzClglb8g8RQaF4fsojuGfRM869Hcf34Z1VS/HQpFuVC4zaha1pe3DDO4+4JGtjQiLx\n3u3/xvDugxSKrH3xaDo8LCwM06ZNa/K4e++91wPREBERtU+izQYx5wREZ5viPDgKSyCWnErGVgu1\nlbH1zovVoE1ePqhsEAx2CAECVCE6CKGBECJCIURHQ4hLgJCQDCGpM4TAYPc/NhERUSP69u2Lvn37\nNnpMeHg43n77bQ9FRKSMDhFxsoRtrhclbFs2w9alJbKsolY+01YlsCML+bfokAjJuqCiWKFImiZv\niZzClsjkR64YNA7fbv0NK3f/4dx77cdFGNd3OHondVUwMvJnfx3ZiWlvP4Jqi0myP6rn+Xh7+rOI\nll3UQ22H9ctERER+RLTbT1fGZp6UVsaWK5SMVdcmY1WBAoRQA4TwYAgxURDi46FKTIGQ0hVCRKz7\nH5eIiIiI3CZR9not04vm2FrsbdwSmRW25OfkCdu6lqzeptxUieLKUudaq9YgITxGuYCI3EwQBLw6\n7XFsSdvj/Ltuq7Hj/o+ew8rZHzX5+42opTYc3Iqb33kUJlm3knvH3YBnrrrfZZwptS2vSNhaLBYs\nWrQIGzZsgEajwcSJE3HjjTdyRggREdEZnDNjM45APJmOAbt3w1BlRs3vP8FUaa9tU+zxZOypFsVB\nqtpkbEQwhOgoqOITICR1hNChM4QIvoEmIiL/c/jwYcyfPx/p6eno0KED7rjjDvTp00fpsIjaTFJE\nnGTtTQlb+QxbnUbb6PEuLZHlFbbylsj8fIr8XHSwrMK23DsrbE/I5tcmRyVArapvTA+R74oOicQr\nN8zCHQuedO4dyErDaz8uwlNXzlAwMvI36/b/jVvfmwWzLFl7edeReOLye5isVYBHErZ2ux19+vRB\nVVUV9u7di9DQUMltF110EdatW+fcW7ZsGb7//nssX76cfymIiKhdEO12IC8DjvQjtTNjc3MgFpXA\nUVzZ4MzYKAgAjKitB2j8Q6mzorZCZayBEKSCEGqsTcbGREMVFw+hQycIyV0ghLItChER+aevvvoK\n9913H6699lq89dZbktv+/vtvjB07FlVVVc699957D1999RUuvfRST4dK5BFJkdL5zJnFeQpF4ko+\nw9agbaIlskuFrdjoWp7gJfI3UcHhkrX3Jmxl7ZCj2A6Z/NOl54zB1edPxFdbfnXuvbNqKSb0G4Hz\nOvdTMDLyFztP7Mf0+Y+7JGuv7DYaF3UeqlBU5JGE7e+//45Dhw7h4osvliRrAeCjjz5yJmvDw8MR\nEBCArKwsrFixAh9//DGmT5/uiRCJiIjajDMZm5EGMTMDYl4uxMJiOEqqIJZbIVajtjJWrO/K4Lar\njK03GRufcCoZ2xVCSHjT5yEiIvJTS5YsQV5eHiZMmOBy24wZM5zJ2tTUVGRnZ8NsNmP69OlIS0tD\nSEiIp8MlanMuLZGLchSKxJV8hm2TLZFdKmwdja5ZYUv+Tj6fsLCiBKIoel33w3RZwrZTTJJCkRC1\nvRemzMSmwzuQU1oAoPZ3070fzMHvT32CsEC+1qSzd6IgEze+MxMmq1myP+fK+5FoDlYoKgI8lLD9\n9dfaK0EmTpzoctvChQsBACNGjMCqVatgNBrx0EMPYd68eXjvvfeYsCUiIq8mWi21bYqzjkPMzqpN\nxhYUw1FS2YxkrBqA0f1Bqa0QjKfaFIcYIESGnE7GJnWEkNKNyVgiIqImrFq1CoIguCRsd+zYgR07\ndgAAFixYgDvvvBO5ubkYPHgwMjIysGLFCtx2221KhEzUpry5JXKLZ9jKZtLKWyC7Vth6V9KKyN2C\nDAEwaPXOSiuzzYJKczWCjYEKRyYlb4ncMYoJW/JfYYEheOOmp3D9W//n3MsszsX/ffI8PrrnZa+7\noIJ8Q2FFCW5462EUyWaVz732Ydwy8kr88ssvCkVGgIcStpmZtb9Mk5OTJftFRUXYtm0bAGDWrFkw\nGms/tH7mmWfw7rvvYvv27aiurkZAQIAnwiQiInISbTaIuRm1idicTIj5+RCLSiCWVECsMEOsckA0\nqSDatKh/ZmwbJmMNNRCCBFSp7bAE6BDVoxs0iR1OJWO7sk0xERFRKxUVFcFkMiE2NhZ6vbS16sqV\nKwEAiYmJuOOOOwAAcXFxmDFjBmbPno0NGzYwYUt+KVGWsM0pyUeNo8Yr5ke6VNhqGk/Yyj/kFuUz\nbEXOsKX2RRAERAWHSy7EKCgv8rqE7XFZwjYlmi2Ryb9d2HsI7rjwOixa+4Vzb+XuP7Bg9ee4e9z1\nCkZGvqjaasYt7z6GY/knJfv3T7wJd46dAqvV2sA9yVM8krDNza39ZR8TEyPZ37RpE0RRhEajwZgx\nY5z7UVFRSExMRHp6Ok6ePInu3bt7IkwiImoHatsTn4Qj6zjE7EyIBXmnE7HlZoiVdohmFUSrDvUn\nYgGg8ZlYZ01tg2CwQxUk1D8z9oxkrNVqxZ+nrnqbNGkS1LrGP5QiIiKi5mvoPSwA/PnnnwCACRMm\nSJI+/fv3BwCcOHGi7QMkUkCg3oiIwFAUV5UBAOyOGuSVFSEh3PXnxNPkFbZNzrCVt0R2OBpdy48n\n8kfRIRHShG1FMVJjkxu5h+fJWyJ3ZMKW2oFnrrofW4/9g93pB5x7c79+G+d17otzOvVRMDLyJTWO\nGsz4YA62H98r2b/6/Il48op7FYqK5DySsK1TVlYmWf/xxx8AgAEDBiAwUHrFVt3MH4tFOvSYiIhI\nTnQ4gOI8iDkZEPOyTyVhiyCWlkEsrYJYaYFY7YBoEppIxOpO/WkDdcnYQAFCqAFCRAiEmCgIcfFQ\n1SVjw6La5rGJiIjorMjfw9bU1DgTtsOHD5fcxvew1B4kRcY5E7ZA7Rxbr0jYtnCGrbzFsbwFsrzi\nlm0nqT2IDomQrAtl7TKVZrFZkV2a71wLgoDkqAQFIyLyDL1WhwV3voDxL9yMclMlgNqLpu5a+DR+\ne+pjhAeGKhwheTtRFPHU8jewcvcfkv0R3c/Ff29+mhemeRGPJGw7dOgAANi+fTsmTZrk3P/xxx8B\nABdccIHLffLy8gAAsbGxHoiQiIi8jehwAEW5ZyRhcyEWFUMsKYdYXpeErTlVDattYEZsnTaqiK2j\nqW1TrAo4lYwND65NxsYnQJXUEUJyFwgRyn+QRURERM2TlFQ7Ey8rKwt5eXnO96UbNmxwJnHl72P5\nHpbag6SIOOzJOORcZ5XkKRjNaS1N2MpbHDtEEaIoOhOz8pm28pm3RP4oKjhcsi4oL1YokvplFGVL\nLqaID4tuspqeyF+kRCXgfzc/jdven+3cyyzOxSOf/Acf3vMSLyyiRr29agkWr/9KstczsTM+vOcl\n6DRahaKi+ngkYTty5Eh89tlnePfdd3Httdeie/fu+OCDD3Dw4EEAkCRxgdqrlgsLC6HRaBAdHe2J\nEImIyAPEynKIeRkQ83Nqq2CLi4DSUohlFRDLTacrYc1C7WxYJZOwwOl5sQECVCE6CKFBECJCIcTE\nQIhLgJCQAiEpFYKXzfUhIiKi1gkNDUW/fv2wZ88ezJ49GwsWLIDNZsNzzz0HAOjcuTO6du0quU9d\nG+WEBFb7kP+Sz7HNLMpt4EjPMtukle26ZsywFQTgzEJaUcSpPZEVttQuRQdLK2y9LWF7wqUdcpJC\nkRAp4+KBo3HnmClYuGa5c++X3euxbON3uHHkZMXiIu/21d8r8cI370r2EsJjsOz+/yLEGKRQVNQQ\njyRsr7/+ejz77LPIyclBjx49EB4ejpKS2rYavXr1ksyvBYAdO3bA4XDg/PPPZzk2EZGXEh0OoLwY\nYu5JiAU5EAvzIRYXQywtBcoqIVaaIFbZIJpOVcHaNICjqV87Hro69sxEbLAOQmgghMgwCNHREGLj\nISQkQ0jqDCEw2DPxEBERkdd56KGHcPvtt2Px4sVYvrz2gzGTyQQAuP/++12O37ZtGwDg/PPP91yQ\nRB6WJEvYnizOUSgSKdcZtk2POREEFUTx9Kza2q/V9SZrmbCl9kDeErmgwrsStukFmZI159dSe/TM\nVfdja9o/2JW+//Tel//DkK4D0SUuRcHIyBttOLgV//fJ85K9EGMQlt3/X68YaUGuPJKwDQsLw4oV\nK3DVVVehqKjImaxNSUnBp59+6pKU/eWXXwAAEydO9ER4RESEM1oQ52XWth8uLKhNwJaVQSyvhFhh\nBqptEE0iREtzKmBV8FgCFgBUdgg6GwQDIASqIQQZIIQGQAgPgxAZCSEqFkLiqURsUIjn4iIiIiKf\nNH36dOzatQtvvfWWM1ELANOmTcMDDzzgcvzKlSsBABMmTPBYjESelhghbfmdVeylLZGbqLAFatsc\nO07na+FwiFCr2Q6Z2q8o+QxbL6uwPe6SsGWFLbU/Oo0W7972HMb95xZUW2pfn5qsZsz48Fn8OGsh\n29uS04Gso7ht/mzYauzOPZ1Gi4/ueRk9EzsrGBk1xiMJW6B2vs/Ro0fx008/IScnB6mpqZgwYQKC\nglzLridVi7QAAQAASURBVKOjo3HfffdhypQpngqPiMjviDV2BFYUI6CqBOKa72AvLT6VgD1zBqwd\nolkELKraBCwa62qgPvXHg+qSsEZACFBDCDZACAmEEB4KITIKQkwshLhECAkdIYRGe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HZ2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\nd+8eNBoNfH198dJLL+Xq+OLixIkTZmfBzKpKlSp49dVX9bZl/R3x8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GCAACAcHR0N3pus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\nrkJggg==\n"
          }
        }
      ],
      "source": [
        "_, axes = plt.subplots(1, 2, tight_layout=True, figsize=(10, 4))\n",
        "\n",
        "wvs = td.C_0 / freqs\n",
        "\n",
        "for ax, smatrix, label in zip(axes, [smatrix_start, smatrix_final], [\"before\", \"after\"]):\n",
        "    for port in ports:\n",
        "        amps = smatrix.sel(port_in=ports[0].name, port_out=port.name).data.squeeze()\n",
        "        ts = np.abs(amps) ** 2\n",
        "        loss = 10 * np.log10(ts)\n",
        "        ax.plot(wvs, loss, label=f\"{port.name}\")\n",
        "        ax.set_title(label)\n",
        "        ax.set_ylim([-25, 1])\n",
        "        ax.set_ylabel(\"loss (dB)\")\n",
        "        ax.set_xlabel(\"wavelength (um)\")\n",
        "        ax.grid(\"on\")\n",
        "        ax.legend()\n",
        "plt.show()"
      ],
      "id": "32f9b07a"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "As we can see, through transmission is very low loss whereas the\n",
        "transmission to the side ports is suppressed."
      ],
      "id": "5c54d1a6-0afc-4818-9505-7a0a0a0ef8b4"
    },
    {
      "cell_type": "code",
      "execution_count": 26,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/plain": [
              "array([4.15922956e-03, 7.02270607e-04, 9.78097464e-01, 7.02442584e-04])"
            ]
          }
        }
      ],
      "source": [
        "abs(smatrix_final.interp(f=freq0).data.squeeze()) ** 2"
      ],
      "id": "4eedee61"
    }
  ],
  "nbformat": 4,
  "nbformat_minor": 5,
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    }
  }
}