{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c07226ce",
   "metadata": {},
   "source": [
    "# Case 15 - Heated circular cylinder in cross-flow\n",
    "\n",
    "Validation of the **curved voxel Dirichlet scalar BC** against the\n",
    "Churchill-Bernstein (1977) surface-averaged Nusselt correlation, for forced\n",
    "convection from a fixed-temperature cylinder.\n",
    "\n",
    "The case (`validation/thermal/02_heated_cylinder/02_heated_cylinder.nassu.yaml`) reuses the\n",
    "flow-over-cylinder momentum setup (case 09) and adds a passive scalar\n",
    "`temperature` (D3Q7, RRBGK) with the cylinder wall held at `phi_w = 1.0`\n",
    "(heated) and the freestream at `phi = 0` (clean). Unlike case 09, the body is\n",
    "**voxelized** (band-only surface BC), not IBM, so the only\n",
    "wall treatment under test is the staircased curved Dirichlet band.\n",
    "\n",
    "## Re / Pr -> lattice mapping (Pr = 0.71, air; buoyancy OFF)\n",
    "\n",
    "Fixed lattice freestream `U = 0.05` (Ma = `U*sqrt(3)` = 0.087 < 0.1). With the\n",
    "diameter `D` in lattice units:\n",
    "\n",
    "- `Re = U * D / nu`  ->  `nu = U * D / Re`,  `tau = 3*nu + 1/2`\n",
    "- `Pr = nu / D_s`    ->  `D_s = nu / Pr`,    `tau_phi = D_s/0.25 + 1/2`\n",
    "\n",
    "| Re  | D  | nu      | D_s     | Nu_D (Churchill-Bernstein) |\n",
    "|-----|----|---------|---------|----------------------------|\n",
    "| 40  | 40 | 0.05000 | 0.07042 | 3.38                       |\n",
    "| 40  | 80 | 0.10000 | 0.14085 | 3.38                       |\n",
    "| 100 | 40 | 0.02000 | 0.02817 | 5.18                       |\n",
    "| 100 | 80 | 0.04000 | 0.05634 | 5.18                       |\n",
    "\n",
    "`Re = 40` is steady; `Re = 100` sheds a laminar Karman street.\n",
    "\n",
    "## Mandatory two-resolution convergence\n",
    "\n",
    "The curved Dirichlet wall flux on a staircased voxel surface is **first-order\n",
    "in `D/dx`**. The case runs each Re at **D = 40 and D = 80** lattice units so the\n",
    "convergence trend of `Nu_D` toward the correlation can be reported. We do NOT\n",
    "assert a single number; we show `D = 40` vs `D = 80` and the trend.\n",
    "\n",
    "> Authored to run after the GPU results exist; it is not executed here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2dd812f9",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2026-06-29T17:44:03.956371Z"
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   "source": [
    "import os\n",
    "import pathlib\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "import nassu.viz as common\n",
    "from nassu.cfg.model import ConfigScheme\n",
    "\n",
    "common.use_style()\n",
    "\n",
    "\n",
    "def _find_project_root() -> pathlib.Path:\n",
    "    here = pathlib.Path.cwd().resolve()\n",
    "    for cand in [here, *here.parents]:\n",
    "        if (cand / \"pyproject.toml\").exists() and (cand / \"nassu\").is_dir():\n",
    "            return cand\n",
    "    raise RuntimeError(f\"Could not locate Nassu project root upward from {here}\")\n",
    "\n",
    "\n",
    "PROJECT_ROOT = _find_project_root()\n",
    "# Result save_paths in the config are repo-root relative; resolve them by\n",
    "# running from the project root regardless of the notebook's launch directory.\n",
    "os.chdir(PROJECT_ROOT)\n",
    "CASE_PATH = PROJECT_ROOT / \"validation/thermal/02_heated_cylinder/02_heated_cylinder.nassu.yaml\"\n",
    "COMPARISON = PROJECT_ROOT / \"validation/thermal/02_heated_cylinder/reference\"\n",
    "\n",
    "# Physical constants of the case.\n",
    "U_INF = 0.05  # lattice freestream velocity\n",
    "PR = 0.71  # Prandtl number (air)\n",
    "PHI_W = 1.0  # heated-wall scalar value\n",
    "PHI_INF = 0.0  # freestream (clean) scalar value\n",
    "DELTA_T = PHI_W - PHI_INF  # driving scalar difference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "83edfd0a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-29T17:44:03.958031Z",
     "iopub.status.busy": "2026-06-29T17:44:03.957858Z",
     "iopub.status.idle": "2026-06-29T17:44:03.990231Z",
     "shell.execute_reply": "2026-06-29T17:44:03.989940Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sim_id=0: Re= 40 D= 40 nu=0.05000 D_s=0.07042"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sim_id=1: Re= 40 D= 80 nu=0.10000 D_s=0.14085"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sim_id=2: Re=100 D= 40 nu=0.02000 D_s=0.02817"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sim_id=3: Re=100 D= 80 nu=0.04000 D_s=0.05634"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Churchill-Bernstein Nu_D:"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " "
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{40: np.float64(3.3813), 100: np.float64(5.1838), 200: np.float64(7.2275), 3900: np.float64(32.2902)}"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "# Load the four unrolled variants keyed by (Re, D). Each variant differs only\n",
    "# by sim_id; we recover (Re, D, D_s) from the diameter implied by the STL scale\n",
    "# and the per-variant nu = cs^2 * (tau - 1/2).\n",
    "CS2 = 1.0 / 3.0\n",
    "\n",
    "all_cfgs = ConfigScheme.sim_cfgs_from_file_dct(str(CASE_PATH))\n",
    "\n",
    "variants = {}\n",
    "for (name, sim_id), cfg in all_cfgs.items():\n",
    "    nu = CS2 * (cfg.models.LBM.tau - 0.5)\n",
    "    # STL scale carries the diameter: raw D = 2.5, scaled by `scale`.\n",
    "    scale = float(cfg.domain.bodies[\"cylinder\"].transformation.scale[0])\n",
    "    D = round(2.5 * scale)\n",
    "    Re = round(U_INF * D / nu)\n",
    "    D_s = cfg.models.scalar_transports[\"temperature\"].adv_diff_equation.D\n",
    "    variants[(Re, D)] = {\"cfg\": cfg, \"nu\": nu, \"D\": D, \"Re\": Re, \"D_s\": D_s, \"sim_id\": sim_id}\n",
    "    print(f\"sim_id={sim_id}: Re={Re:3d} D={D:3d} nu={nu:.5f} D_s={D_s:.5f}\")\n",
    "\n",
    "# Churchill-Bernstein reference table.\n",
    "cb = pd.read_csv(COMPARISON / \"churchill_bernstein.csv\")\n",
    "cb = cb.set_index(\"Re\")[\"Nu_D\"]\n",
    "print(\"\\nChurchill-Bernstein Nu_D:\", dict(cb))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff800d5f",
   "metadata": {},
   "source": [
    "## Churchill-Bernstein correlation\n",
    "\n",
    "The surface-averaged Nusselt number for a cylinder in cross-flow\n",
    "(Churchill & Bernstein 1977), valid for `Re*Pr > 0.2`:\n",
    "\n",
    "$$ Nu_D = 0.3 + \\frac{0.62\\,Re^{1/2}\\,Pr^{1/3}}{\\left[1 + (0.4/Pr)^{2/3}\\right]^{1/4}} \\left[1 + \\left(\\frac{Re}{282000}\\right)^{5/8}\\right]^{4/5} $$\n",
    "\n",
    "Correlation scatter is **~10-20%**, so the validation tolerance is ~10-15%.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b004c87a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-29T17:44:03.991029Z",
     "iopub.status.busy": "2026-06-29T17:44:03.990944Z",
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     "shell.execute_reply": "2026-06-29T17:44:03.992378Z"
    }
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   "outputs": [],
   "source": [
    "def churchill_bernstein(Re: float, Pr: float = PR) -> float:\n",
    "    \"\"\"Surface-averaged Nu_D (Churchill & Bernstein 1977).\"\"\"\n",
    "    return 0.3 + (0.62 * Re**0.5 * Pr ** (1.0 / 3.0)) / (\n",
    "        1.0 + (0.4 / Pr) ** (2.0 / 3.0)\n",
    "    ) ** 0.25 * (1.0 + (Re / 282000.0) ** (5.0 / 8.0)) ** (4.0 / 5.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6452175f",
   "metadata": {},
   "source": [
    "## Loading the temperature and velocity fields\n",
    "\n",
    "Each variant exports a spanwise mid-plane (`plane_series.mid_span`) carrying\n",
    "`temperature_phi` and the velocity. We average all snapshots after the spin-up:\n",
    "steady state for `Re = 40`, a time-mean window for the shedding `Re = 100` runs.\n",
    "\n",
    "The plane is the x-z cross-section through the cylinder (the cylinder axis is\n",
    "the spanwise `y`). The loader returns regular `(n_z, n_x)` grids of the scalar\n",
    "and the in-plane velocity components plus the node coordinates, matching the\n",
    "loader used by the ABL plane notebooks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e35b91d7",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-29T17:44:03.993293Z",
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     "shell.execute_reply": "2026-06-29T17:44:03.995748Z"
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   "outputs": [],
   "source": [
    "def load_plane_fields(cfg):\n",
    "    \"\"\"Return (xs, zs, T, ux, uz) time-mean grids for the mid-span plane.\n",
    "\n",
    "    Averages all exported snapshots after the spin-up so a shedding run yields a\n",
    "    time-mean field; a steady run just averages a few late snapshots. The\n",
    "    velocity is loaded alongside the scalar because the surface-averaged Nusselt\n",
    "    is taken from a control-volume heat balance (advective + diffusive flux),\n",
    "    which needs the in-plane velocity.\n",
    "    \"\"\"\n",
    "    plane = cfg.output.exports[\"plane_series\"].series.planes[\"mid_span\"]\n",
    "    pts = pd.read_csv(plane.points_filename)\n",
    "\n",
    "    xs = np.sort(pts[\"x\"].unique())\n",
    "    zs = np.sort(pts[\"z\"].unique())\n",
    "    ix = {v: i for i, v in enumerate(xs)}\n",
    "    iz = {v: i for i, v in enumerate(zs)}\n",
    "    cols = [str(int(i)) for i in pts[\"idx\"]]\n",
    "    col_xi = np.array([ix[x] for x in pts[\"x\"]])\n",
    "    col_zi = np.array([iz[z] for z in pts[\"z\"]])\n",
    "\n",
    "    def _mean_grid(macr):\n",
    "        df = plane.read_full_data(macr)\n",
    "        start = int(df[\"time_step\"].max() * 0.6)  # drop the spin-up\n",
    "        df = df[df[\"time_step\"] >= start]\n",
    "        arr = df[cols].to_numpy(dtype=float).mean(axis=0)  # time-mean per point\n",
    "        grid = np.full((zs.size, xs.size), np.nan)\n",
    "        grid[col_zi, col_xi] = arr\n",
    "        return grid\n",
    "\n",
    "    return xs, zs, _mean_grid(\"temperature_phi\"), _mean_grid(\"ux\"), _mean_grid(\"uz\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c976097",
   "metadata": {},
   "source": [
    "## Surface-averaged and local Nusselt number\n",
    "\n",
    "The local Nusselt number is the nondimensional wall heat flux\n",
    "\n",
    "$$ Nu(\\theta) = \\frac{q_w(\\theta)\\,D}{D_s\\,\\Delta T},\\qquad q_w = -D_s\\,\\left.\\frac{\\partial T}{\\partial n}\\right|_{\\mathrm{wall}} $$\n",
    "\n",
    "and the validation quantity is its surface average `Nu_D`.\n",
    "\n",
    "**Surface-averaged `Nu_D` (control-volume heat balance).** In steady state (or\n",
    "in the time mean) the net scalar flux `phi*u - D_s*grad(phi)` leaving any box\n",
    "enclosing the cylinder equals the total heat released at the wall, so\n",
    "\n",
    "$$ Nu_D = \\frac{Q'}{\\pi\\,D_s\\,\\Delta T},\\qquad Q' = \\oint_{\\partial\\Omega}\\left(\\phi\\,\\mathbf{u} - D_s\\,\\nabla\\phi\\right)\\cdot\\mathbf{n}\\,\\mathrm{d}\\ell $$\n",
    "\n",
    "with `Q'` the net outward flux per unit span. This is a conserved quantity that\n",
    "is **independent of any near-wall gradient sampling**, so it is robust to the\n",
    "staircased voxel band: the box only needs a margin of clear fluid around the\n",
    "cylinder, and the result is box-size independent.\n",
    "\n",
    "**Local `Nu(theta)` (wall-referred radial rays).** For the angular distribution\n",
    "we still cast rays outward from the centre, but two corrections are essential.\n",
    "The heat spreads radially, so the local gradient decays like `1/r` (flux\n",
    "conservation `q*2*pi*r = const`); a slope sampled at radius `r` must be referred\n",
    "back to the nominal wall `R = D/2` by the factor `(r/R)`, otherwise it reads\n",
    "systematically low. And the gradient is fit on **clean fluid nodes** one lattice\n",
    "node beyond the heated band edge, away from the interpolation noise on the\n",
    "staircase:\n",
    "\n",
    "$$ Nu(\\theta) = -\\frac{D}{\\Delta T}\\,\\left.\\frac{\\partial T}{\\partial r}\\right|_{r}\\,\\frac{r}{R} $$\n",
    "\n",
    "The control-volume `Nu_D` is the headline number; the ray-based `Nu(theta)`\n",
    "gives the angular shape (front-stagnation peak, separation minimum) and its\n",
    "angular mean tracks the balance to within a few percent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "acfd87b4",
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    "execution": {
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   "source": [
    "def nu_surface_balance(xs, zs, T, ux, uz, D, D_s, box_half=None):\n",
    "    \"\"\"Surface-averaged Nu_D from a control-volume heat balance.\n",
    "\n",
    "    The net scalar flux ``phi*u - D_s*grad(phi)`` leaving a box around the\n",
    "    cylinder equals the total wall heat release per unit span, so\n",
    "    ``Nu_D = Q' / (pi * D_s * dT_drive)``. This is independent of any near-wall\n",
    "    gradient sampling and is robust to the staircased voxel band; the box only\n",
    "    needs to enclose the cylinder with a margin of clear fluid (default one\n",
    "    diameter each side, where the result is box-size independent).\n",
    "\n",
    "    Args:\n",
    "        xs, zs: 1-D node coordinates of the plane grid (lattice units).\n",
    "        T, ux, uz: (n_z, n_x) time-mean scalar and velocity grids.\n",
    "        D: cylinder diameter (lattice units).\n",
    "        D_s: scalar diffusivity.\n",
    "        box_half: half-width of the control box (lattice units); defaults to D.\n",
    "    \"\"\"\n",
    "    cx = 6.0 * D\n",
    "    cz = (zs.min() + zs.max()) / 2.0\n",
    "    H = box_half if box_half is not None else D\n",
    "    i0 = int(np.searchsorted(xs, cx - H))\n",
    "    i1 = int(np.searchsorted(xs, cx + H))\n",
    "    k0 = int(np.searchsorted(zs, cz - H))\n",
    "    k1 = int(np.searchsorted(zs, cz + H))\n",
    "\n",
    "    def _flux_x(i):  # outward-x advection minus diffusion, summed over z (dz=1)\n",
    "        dphidx = (T[k0 : k1 + 1, i + 1] - T[k0 : k1 + 1, i - 1]) / 2.0\n",
    "        return np.nansum(T[k0 : k1 + 1, i] * ux[k0 : k1 + 1, i] - D_s * dphidx)\n",
    "\n",
    "    def _flux_z(k):  # outward-z advection minus diffusion, summed over x (dx=1)\n",
    "        dphidz = (T[k + 1, i0 : i1 + 1] - T[k - 1, i0 : i1 + 1]) / 2.0\n",
    "        return np.nansum(T[k, i0 : i1 + 1] * uz[k, i0 : i1 + 1] - D_s * dphidz)\n",
    "\n",
    "    q_net = _flux_x(i1) - _flux_x(i0) + _flux_z(k1) - _flux_z(k0)\n",
    "    return q_net / (np.pi * D_s * DELTA_T)\n",
    "\n",
    "\n",
    "def nu_local_theta(xs, zs, T, D, n_theta=180, n_ray=4, n_skip=1):\n",
    "    \"\"\"Local Nu(theta) from wall-referred radial rays.\n",
    "\n",
    "    For each angle a ray is cast outward from the cylinder centre. We locate the\n",
    "    heated band edge (first node below phi_w), step ``n_skip`` lattice nodes past\n",
    "    it onto clean fluid nodes (clear of the interpolation noise on the\n",
    "    staircased band), and fit dT/dr over ``n_ray`` nodes by least squares.\n",
    "    Because the heat spreads radially the local gradient decays like 1/r, so the\n",
    "    slope sampled at radius r is referred back to the nominal wall R = D/2 by the\n",
    "    flux-conservation factor (r/R):\n",
    "\n",
    "        Nu(theta) = -(D / dT_drive) * (dT/dr)|_r * (r_mean / R)\n",
    "\n",
    "    theta is measured from the front stagnation point (0 faces the inlet).\n",
    "\n",
    "    Args:\n",
    "        xs, zs: 1-D node coordinates of the plane grid (lattice units).\n",
    "        T: (n_z, n_x) temperature grid.\n",
    "        D: cylinder diameter (lattice units).\n",
    "        n_theta: number of surface angles.\n",
    "        n_ray: number of fluid nodes used for the slope fit.\n",
    "        n_skip: lattice nodes stepped past the band edge before sampling.\n",
    "    \"\"\"\n",
    "    from scipy.interpolate import RegularGridInterpolator\n",
    "\n",
    "    interp = RegularGridInterpolator((zs, xs), T, bounds_error=False, fill_value=np.nan)\n",
    "    cx = 6.0 * D\n",
    "    cz = (zs.min() + zs.max()) / 2.0\n",
    "    R = D / 2.0\n",
    "\n",
    "    thetas = np.linspace(0.0, 2.0 * np.pi, n_theta, endpoint=False)\n",
    "    nu_local = np.full(n_theta, np.nan)\n",
    "    for i, th in enumerate(thetas):\n",
    "        nx, nz = np.cos(th), np.sin(th)\n",
    "        # Locate the heated band edge: first sample below phi_w scanning outward.\n",
    "        r_scan = R + np.arange(0.0, 0.4 * D, 0.25)\n",
    "        t_scan = interp(np.column_stack([cz + r_scan * nz, cx + r_scan * nx]))\n",
    "        below = np.where(t_scan < 0.99 * PHI_W)[0]\n",
    "        if below.size == 0:\n",
    "            continue\n",
    "        r_wall = r_scan[below[0]]\n",
    "        # Step onto clean fluid nodes and fit the near-wall slope.\n",
    "        radii = r_wall + n_skip + np.arange(n_ray)\n",
    "        vals = interp(np.column_stack([cz + radii * nz, cx + radii * nx]))\n",
    "        if np.any(~np.isfinite(vals)):\n",
    "            continue\n",
    "        A = np.vstack([radii, np.ones_like(radii)]).T\n",
    "        slope = np.linalg.lstsq(A, vals, rcond=None)[0][0]\n",
    "        nu_local[i] = -(D / DELTA_T) * slope * (radii.mean() / R)  # wall-referred\n",
    "\n",
    "    # theta measured from the front stagnation point (upstream, -x).\n",
    "    theta_deg = (np.degrees(thetas) + 180.0) % 360.0\n",
    "    order = np.argsort(theta_deg)\n",
    "    return theta_deg[order], nu_local[order]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "2ad7fae6",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-29T17:44:04.001474Z",
     "iopub.status.busy": "2026-06-29T17:44:04.001409Z",
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     "shell.execute_reply": "2026-06-29T17:44:38.400946Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Re= 40 D= 40: Nu_D(sim)= 3.537  Nu_D(CB)= 3.381  rel= +4.6%"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Re= 40 D= 80: Nu_D(sim)= 3.322  Nu_D(CB)= 3.381  rel= -1.8%"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Re=100 D= 40: Nu_D(sim)= 5.762  Nu_D(CB)= 5.184  rel=+11.1%"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Re=100 D= 80: Nu_D(sim)= 5.309  Nu_D(CB)= 5.184  rel= +2.4%"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "# Compute Nu_D (control-volume balance) and the local Nu(theta) for every\n",
    "# variant (requires GPU results on disk).\n",
    "results = {}\n",
    "for (Re, D), v in sorted(variants.items()):\n",
    "    xs, zs, T, ux, uz = load_plane_fields(v[\"cfg\"])\n",
    "    nu_avg = nu_surface_balance(xs, zs, T, ux, uz, D, v[\"D_s\"])\n",
    "    theta, nu_th = nu_local_theta(xs, zs, T, D)\n",
    "    results[(Re, D)] = {\n",
    "        \"theta\": theta,\n",
    "        \"nu_theta\": nu_th,\n",
    "        \"nu_avg\": nu_avg,\n",
    "        \"nu_cb\": churchill_bernstein(Re),\n",
    "        \"xs\": xs,\n",
    "        \"zs\": zs,\n",
    "        \"T\": T,\n",
    "    }\n",
    "    rel = 100.0 * (nu_avg - results[(Re, D)][\"nu_cb\"]) / results[(Re, D)][\"nu_cb\"]\n",
    "    print(\n",
    "        f\"Re={Re:3d} D={D:3d}: Nu_D(sim)={nu_avg:6.3f}  \"\n",
    "        f\"Nu_D(CB)={results[(Re, D)]['nu_cb']:6.3f}  rel={rel:+5.1f}%\"\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae49eab6",
   "metadata": {},
   "source": [
    "## Nu_D vs Churchill-Bernstein - both resolutions and the convergence trend\n",
    "\n",
    "For each Re we plot the control-volume `Nu_D` at `D = 40` and `D = 80` against\n",
    "the correlation, with the +/-15% tolerance band. The balance-based `Nu_D` lands\n",
    "within the band at both resolutions; the residual `D = 40` vs `D = 80`\n",
    "difference reflects the first-order convergence of the staircased curved\n",
    "Dirichlet wall flux (the finer grid sits closer to the correlation)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "509bae3b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-29T17:44:38.402292Z",
     "iopub.status.busy": "2026-06-29T17:44:38.402198Z",
     "iopub.status.idle": "2026-06-29T17:44:38.649327Z",
     "shell.execute_reply": "2026-06-29T17:44:38.649071Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6L875FkVpPo+4qRXuZu7u7pbn9+bbLbZQ2HvUfMv3mWeesUqu7qRRo0ZWyZWZOSGzdfy2EhkZyfbt2/P1wdq9ezfk9Vm7Obkya9SoEW3btiUtLS3fbWazqVOn3vbYffv2tUpCzAp6zurWrYuPjw/nz59n+/btpR4okZKSwvHjx3Fycio0TvPt9OK+h4tzXkVRJVuwzDQaDX379rVk0Dk5ORw9epQlS5awdu1a1qxZQ8uWLW06QqNhw4Ylfuznn3/ODz/8cNttbn6zme+/mz+Q7+Ty5cuQ9wY1l4kwf3mqqmr1RXr9+nXL/5988kl27tyZb38hISH4+fmVKHaAsWPH8umnn7J161bS09Mtt0jMX0Tjx49Hq/3nb4SSxn+z212f4p6D+ZZzQckOeYlKnTp1iImJsVpe0vOIi4sDoEmTJgUez93dvcDjlcSkSZOYN28ep06dYsOGDTavGderVy+mTp3KH3/8wYgRI2jcuDHt2rWjc+fODB48mDp16pRoW1u8RmytuK/z4pzv7ZjfmyUduGJWv379Apebz6OgDtWlUdB7VFEUy3kUt8RNvXr1ClxeVvGT17p9890DsylTpuSr/3RzmQbyWh4jIiL48ssvWbhwIVFRUfz000+W9ebX+AcffGApp3Lza/vm1/ithUzJ+5ww91MuTHGeM51Ox4cffsjMmTN5+umn8fHxISgoiKCgIPr27UunTp1ue6xbxcbGoqoqRqPR0pp067mZ/y3ue9jWr4Uq24JVEBcXF3r27Mlnn31m+aussJEwhbnTX/Nubm4liu3ixYv8+OOPaLVannvuOdauXcvRo0cJDw8nIiKi0PvpxWH+y0JVVRRFQVEUTCYTJpMp33kVp7N0SWP38/Nj4MCBZGVlsX79egCMRiNr166Fm/7yt2X8hV2f8nj+bXUet2uRsFVrk06ns9xC+OqrryyjgEqisJj+/e9/s2bNGp577jkaNGjA3r17effddxkyZEi+OlxF3basXuOlUdzXOcV8bgpj/sPrypUrpSoeW9oWsFuV5DO0NK9rW8df1vz8/OjVqxc//PADzs7Oln5jZubXuMlksnqN3/oHBIW8xl1dXe8Yw80Jf1EMHjyY7du3884779C3b1+io6P5+uuvue+++5gyZUqBiV5hbm4BK+g9fPM5Fvc9XNzzupMq3YJ1O7169WLZsmX5Or6bR1NkZGRQrVq1fI+79TaXrRw6dAhVVRk9erTl9szNCurMZ+64evr06SIdw9w0Om7cOD799NMix3anVp2SxG42ceJEtmzZwvLly7n33nvZuXMnSUlJdOnSJd/omZLGXxQlOYdatWoBFHobJzs7m6tXr+ZbXtLzMD+usOdTr9dbWrlsYeTIkbRr146TJ0/etiNwad4zLVu2tNxqUlWVsLAw3njjDX799Vc6duxoNYK0KNuWxWvEFl/QxXmdmxXnuSlIUFAQNWvWJDExkYULF/L666+X+jyKoiw+Q52cnAgICCA+Pp7Tp0+XSf9ZW7JFsVIfHx/q1KlDdHQ0Z86coUuXLpD3ORAeHs6nn37KuHHjbBRx6fn6+nLfffdx3333QV7L6RdffMHy5cuZM2cOX375JRTh/WR+D3t6enLgwIF8IxwdibRgFcI8H2DNmjWtlps7hJ44cSLfYzZs2FBmU0mYmyYL+ustPT2dxYsX51vet29ftFotBw8ezDe6rSD9+vVDq9WyY8cOoqKibBR5yWI3GzBgADVq1ODYsWNcunTJUm+qoL/qyyr+kp6DuYP0zp07C7wt98cffxTY8lPS8zD3I9m1a1eBSd3ChQtL1dJUEHNpgW+++abQejy2es9oNBqCgoIYM2YMgFV5kaJuWxavEfNQ98JqLBVFcV7nBSnOc2Pm7OzMY489BnkFR+80c8WWLVvYuHFjkeK5nbL6DDUPtvjuu++qREHU5ORkyx9oN5db6N+/P+R9vpTF7U1bCQgIsLz+bn693un9VLNmTdq2bUtGRgZLly4tp2hLpkomWPv372fKlCl88803HD58mJiYGLKzs0lNTSUsLIx///vf/P7773BTZzkzc2fTjz/+mJCQEDIzM7l69SoLFy60FAotC+aicqtXr2bJkiWkpKSQkpLC3r17mTZtWoFN/A0aNGD8+PGoqsqTTz7JggULiIuLIycnh+joaFauXGlV/6Zhw4ZMmjSJtLQ0pk+fzu+//05UVBRZWVncuHGD8PBwFi5cyJQpU4r1V2ZJYjdzcnKy/BX2yy+/sHPnzny1r8o6/pKeQ+vWrenSpQsGg4Gnn36a/fv3k5OTQ3JyMosWLSq0WGdJz8NcJNBoNPLUU0+xb98+srOzuXHjBgsWLGDu3LnFOuei6N27N7169SI+Pp5NmzYVuE1J3jP//e9/LWVFoqOjycnJITU1lZ07d1oKbpq/qIuzbVm8Rsx9ntauXWsZmVdcxXmdF+d87+TBBx+kb9++KIrC888/z+uvv87+/ftJSUnBYDAQHx/P+vXrefjhh/nXv/5FWlpaic7vZmX1GfrYY4/h5ubGgQMHePTRRzl06BB6vZ60tDROnDjBnDlz8tWxq4iSk5MJCQnhySefxGAw4OzsTJ8+fSzr7777bho2bMixY8eYMWMGW7dutXzux8XFceTIET7//HNLclPWDhw4wMMPP8zSpUuJiIggLS0NvV7PmTNnLKUXbn69mt9P+/fv5/z58wX+UfjCCy+g0Wh47733mDNnDqdOnSIlJYXMzEwuXLjA5s2befHFF+1+vavkLUKTycTx48c5fvz4bbfr27dvvg7uDz74IMuWLSM2NpaHHnoo3/ZxcXGFjswoja5du9KnTx/27t3LrFmzrD6IdDqdpdPrrWbPns3Vq1fZv38/77//Pu+//77V+lun5Zk9ezbXr19nx44dvPfee4XGU5w+DyWN3WzSpEn88ssvluKCo0aNKrTwX1nEX5pz+OCDD5g2bRpnz57NN9S7U6dOZGRkEBkZmW90X0nP4/3332fq1KlcvHgx3/Dum49nSzNnzmTy5MmFVjouyXsmNTWV5cuXs3z58gL32aRJE0t5jOJsSxm8RkaMGMHixYtZt24d69atsyz/5ptvilQLy6yor/Pinu/tmEvW/Pvf/2bFihWsXLmy0FkJRo8efcfbjkVRVp+hTZo04bPPPuOVV15h37597Nu3L982BRVzdXSFlWkgr+Xyrbfesqpj5urqyo8//sgTTzzBsWPHePbZZwt8bGGDYWxNUZRCrwd5LVYvvfSS5fcuXbrg7+9PXFyc1eCZsWPHWhKyAQMG8H//93988MEHLFy4kIULFxa4b3MFenupki1YPXv25K+//uJf//oX3bt3p379+ri6uuLq6krdunUZOnQoX3zxBT///HO+Dn/+/v78+eefjBw5Eh8fH1xcXGjSpAkvvvgi33//vU2GwRfm22+/5bHHHqNu3bo4OTnh5+fHkCFDLIX3CuLh4cH8+fN5//336d69O9WrV8fFxYXGjRszceJES0udmaurK9999x1z585l0KBB1KxZE2dnZ2rUqEHbtm158MEH+fvvvwsdOWTL2M1atmxpNRLydnV+yir+kp5D48aNWbp0KZMmTbLE0qBBA5544gl++eUXy221W79IS3oeDRo0YOnSpUyePNnqeI8//ji//PJLmfRXaN++vaWwZEFK8p559dVX+eijjxg0aBANGjTAxcWFmjVrEhQUxJtvvsnSpUst/XeKsy1l8Brp1asXH330EW3bti1wWHxRFfV1XtzzvRNXV1c++ugjli5dyn333Ufz5s3x8vLC2dmZunXrMn78eP744w+++OILm1Q0L8vP0KFDh7J69Wruu+8+GjZsiIuLC76+vnTq1IlZs2Yxbdq0Usdvby4uLjRo0IAJEyawZMmSAksVNGnShJUrV/Laa6/RqVMnqlWrZrme3bp145VXXil2VfKS6tGjB7/++iv33nsvLVu2xMvLCy8vL5o1a8a0adNYtWqVVQuci4sLP//8M4MGDcLHx6fQjufTpk1jxYoV3HvvvTRq1AhXV1c8PT1p1qwZo0aN4quvvuKBBx4ol3MsjEYtiyI2Qog7Sk1NpWfPnjg7O3Ps2DGbj2ARQghhP/KJLoSdLFy4EEVR6NKliyRXQghRycinuhBlKD4+nmeffZZdu3YRFxeHwWAgOjqazz77jK+//hryKlMLIYSoXKpkJ3chyouqqmzdupWtW7cWuP6ee+6xTM0ihBCi8pA+WEKUsW3btrFs2TIiIyOJj4/H3d2dwMBA7rnnHsaOHVvhKkkLIYS4M0mwhBBCCCFsTPpgCSGEEELYmPTBKkRiYiKbNm2icePGpaptI4QQQgjHptfruXTpEiNGjMg3RV5JSYJViE2bNtm9SJkQQgghys/vv/9us4K0kmAVonHjxpD3ZLdu3dre4diFoihERkbSsmVLdDqdvcMRBZBr5PjkGlUMcp0cX1leo/DwcB544AHLd78tSIJVCPNtwdatW9O5c2d7h2MXiqKg1Wrp2LGjfOA4KLlGjk+uUcUg18nxlcc1smWXIOnkLoQQQghhY5JgCSGEEELYmCRYQgghhBA2JgmWEEIIIYSNSYIlhBBCCGFjMoqwFAwGA4qi2DuMMmM+t6ysLBlV46Cq6jXS6XQ4OzvbOwwhhCiUJFglZDAYOH/+PJV5KkdVVXFyciIqKkomJHZQVfUaaTQamjVrJkmWEMJhSYJVQoqioKoqdevWxdXV1d7hlAlVVdHr9bi7u1epL++KpCpeo+zsbK5cuYKiKJJgCSEcliRYpeTq6oqbm5u9wygTqqpiMplwc3OrMl/eFY1cIyGEcEwVIsEymUxs3LiR3bt3k5iYSMOGDZk4cSLt27e/42NjYmJ46623ClzXpEkT3n333TKIWAghhBBVmcMnWCkpKTz99NMcOXLEavmiRYv47rvvGDx48G0fr9frOXjwYIHrMjIybBqrEEIIIQQVIcF65ZVXOHLkCP7+/jz66KM0b96ca9eu8ddff5GWllbk/dx3332MHj3aapmnp2cZRCyEEEKIqs6h62Dt37+f3bt34+vry5IlS3j44Yfp168fd999N3///TdDhgwp8r4aNmxIjx49rH7atWtXpvFXFQaDgeeff57169fbOxQrISEhPP/88yQkJNxx2+PHj/P8889z+fLlYi8Thbt06RLPP/88J0+etHcoQghRrhy6BWvTpk0APPLII9SpUyffei8vryLvKyQkhGPHjpGdnU2TJk0YP348bdu2tWm8lVFCQgJ79+4lIiKCzMxM/P39adq0KSNGjKBatWqQ10du06ZNtGjRwt7hWrl8+TKbNm1i5syZd9w2Li6OTZs28fTTTxd7WWHee+89q+TOycmJWrVq0b17dwYOHOjwndLPnj3L//73P55++mlat25don0kJyezadMmJk6caPP4hBDCkTl0ghUeHg7A4MGD2bhxI2vXrsVgMNCqVSvuu+++ApOuwuzZs8fy/927d7NgwQJefvllnnjiids+Li0tjZSUFMvvLi4uuLi4WMo0mH8qox9//JGvv/6ajh07MmTIEPz8/IiLi2PBggXMmTOH//3vf/Tr189y/o72XBQnro4dO/Lll19Sr149q8fd+vji7HP37t0oisKrr74KeS194eHhvPjii3Tu3Jmffvqp1MVBb43Llq5fv86mTZuYPHkyrVq1KtE+GjVqxJdffknbtm1tFqP5uVcUpUIU+jXHWBFircrkOjm+srxGZbFPh06wUlJS0Gq1bNq0iblz51qW79y5k99//52ff/6ZTp063XE/TZs2ZeLEibRo0YL09HSCg4NZs2YNn332GZ07d6Zr166FPnbGjBlWZRgmTZrE5MmTIa9FQq/XYzKZSn2ujubXX39l7ty5vPLKK0ydOtVq3f33389PP/3ElStXyMzMJDs7G/ISiMzMTDtFnF9OTg7kDXS4U1ze3t70798fwLKt+fFZWVm3XVYYk8mEp6enZb8AQ4YMwcvLi7lz57Jt2zb69u1bqnM00+v1NtnPzczXtSjnWhgXF5d8z6st4jIYDJw5c8Ym+ysvYWFh9g5BFIFcJ8dXFtcoMjLS5vt06ATLyckJrVbL/Pnzeeqpp+jUqROZmZmsXr2aHTt28Pbbb9+x30+jRo1Ys2YNTk7/nOrYsWNp27Yt77//PqtWrbptgrVgwQI6duxo+d3cgpWVlUVUVBTu7u6Vrg7W9evX+fHHH+nTpw9Tp04tsIjlSy+9RHp6Oh4eHpZWGGdnZ4xGI3/88Qfnz5+nTp06TJ06ldq1a1sel5CQwHvvvcf9999Pr169rPb5zjvv0LhxYx588EHIS9hmzpzJqFGj6NWrF3/99Rdnz55l4sSJ9OnTB4ADBw6wa9cuEhISqFu3LmPGjKFly5aQd60A3N3duXTpEsuWLSMtLY0uXbpw9913W70mjh8/zvz583nttdeoX7++1ePd3Nzw8PAodFlhtFotWq0233bm+PR6fb518fHxrFq1ivPnz6PVauncuTPjx4+3HNf83A8YMIAhQ4bw119/cerUKcaOHUudOnX47rvveO6553B2duavv/4iMTGRNm3acP/99+d7nZ45c4Z169Zx7do1fH196d69u2VU7oEDB/jxxx8hL9les2YN5P2BMXDgQMs+QkND2bJlC1evXqV69eoMGTLEcm3I64P1+eef88QTT1j6PIaHhxcrzoKeV2dnZ5o3b14h3nuKohAWFkb79u2r1HRGFY1cJ8elmhRM+nhyMq4QccWpTK5RWTSUOHSCVaNGDSIjI3nuued46KGHLMtHjRrFlClTCA0NJTY2lnr16hW6j8KqrI8fP57333+fmJiY28bg7e1N9erV8y3X6XRoNBrLj5mqqpa//B2Bq6trsfv6bN++naysLMaPHw9505IUtA9vb2/LevLKXrz44ov07t2bLl26sGDBAlasWMGGDRss2+r1ejZv3kz//v3z7XP37t2kpKRYlquqyubNm6lVqxaLFi1iwIABBAYGcu3aNVRV5dVXX2Xjxo3cc8899OrVi8TERN544w1efvll+vXrZ9nP3r172bNnD4MHD+bq1avMmTOHkydPMmfOHMux4+Pj2bx5M88884zlcTf/e7tld3Lzduaabk5OTnTp0sVq3a5du3jxxRdp164do0aNwmAw8PPPP/Pnn3+yYMECS5/DzZs3U61aNZYvX07v3r1p1aoV165dw9nZmc2bN9O5c2eCg4Mtt3W//vpr9u3bx88//2w51vr165k5cyb33nsvvXv3JjU1lRUrVrBr1y7effddGjRoQK9evTh8+DDdunWz9MFq2rSpJeZPP/2UX375hbvvvps+ffoQHR3Ns88+y5QpUyy151JSUti8eTOTJk2yPC4xMbHIcRb2fGo0GnQ6XYX6Iqxo8VZVcp0ch6rkoGRexpR5BdVkRGsC8C6Ta1QW19yhE6xWrVoREhJCo0aNrJZrNBoaNGhAaGhoiWtZxcXFQV5LhC1lZ2dz77332nSfpfH3338X+xzPnj0LQPPmzYv1uJUrV7Jy5UpL37jevXszYsQI/vzzTx5//PFi7etmK1asYOXKlTRo0ADynuPffvuNtWvX8s033zB06FDLto899phVnznyRqN+9913li94nU7Ht99+y7PPPlusfnwlERsby/PPPw95txcjIyNxcXHh559/tpwPQFJSEi+//DK9e/fm66+/tsQ6duxYRowYwddff80bb7xh2X7NmjUsWbKEZs2akZmZiU6ns9R727RpEwsXLrRMI+Pn58fbb7/NiRMnCAoKgrw6cn369OGdd96x7HPGjBmWTvn16tWjW7duAHTp0sXqNid5Sd7PP//MnDlzuOeeeyzL27dvz7PPPsvgwYPp2bPnbZ+bosQphKh6TIYMTBkxKFnXQK24XXAcukzD8OHDAfjtt9+sal6dOHGCnTt34urqavUlVZBFixZx+vRpq2VRUVGWv7Bvd3uwqsrKyoISJJ+9e/e2SlgaNWpEvXr1St1XpkePHlbX2dXVlWXLlhEYGGiVXJGXPPn5+Vktu7n1xBynoig2ueeenJzM888/b/Vz+PBhy/pq1aoxevRoRo8ezdixY7n33nvJyMjg559/tnpNb9y4kfT0dB599FGrWP38/BgyZIhlRK1Zhw4drBLgm1tqx48fbzVHX+/eveGmQSPm7c+ePcv58+et9uvv71+k8166dCk+Pj6W/ohmQ4cOxdfXN1+8BSlKnEKIqsOUnYwh6QSGxEMo+rgKnVzh6C1YnTt3ZtiwYWzZsoX+/fvTtGlTsrKyOH/+PKqq8sQTT+Du7g55SdOsWbPo1q2bpcWAvNtd7777Lr6+vtSvX5+0tDRiYmJQFIWGDRty33332TRmV1dX/v77b5vuszRKMhG1j48P5CUPN/efupOCkl0/P78i1aG6nYYNG+ZbdunSJYYNG1aiuMwJWGnjIi8ZvTWZGDJkiCVx9/b2ZuTIkVbrhw4dypgxY/jiiy+YPXs2ABcvXgRg3rx5LFy40GqUYmRkJHFxcaiqakm+CnpOinO+L7/8Ms8//zyjR4+mefPmdOvWjYEDBzJgwIAi3fo0x/vyyy/DTSP7VFXFaDRy9erVO+6jLK+LEKJiUFUVU1YCpowYTIaiFw+vCBw6wQL45JNPePfdd1m9erWlWKGHhwcPPvigVSKVmZnJwYMH8fX1tXr8jBkzyMjI4NixY9y4cQPyWjlGjBjB22+/XaxaWkWh0WgqRMfb2zGPzDx27Fixhuff3BphptForIbnmztrm0fj3Sw1NbXA/RZUcd/FxaXII+dujevmPl6l5ePjw1dffWW17E63t5o3b05AQADBwcGWZeYO90OGDMnX8X3UqFH59nG7WQiKcr7t2rVj8+bNHDt2jEOHDrFv3z4WL17MoEGDrG6nFsbJyQkfHx9GjBiRb93o0aOpWbPmbR9f1DiFEJVTbsf1qygZl1GVLHuHUyYcPsHy8PDgo48+4o033iAqKgonJyeaN2+er2WmYcOGLFiwIN/toQEDBjBgwABSUlKIiopCq9XSpEkTmSbnNvr370/9+vX5888/mTBhQoGj5TIzM4mOji52fSR/f390Op2lD5xZVFRUsaY+6tixIydPniQ7O7tErXS24ubmlq+FqigyMzMtra/knQ95AzsGDBhg0xgL4+TkRLdu3ejWrRvPPPMMn376KT///DMxMTE0bNjQ0umzoISnY8eObNq0if79+99xNKUQQpjd2nG9MnPoPlg38/HxoUOHDrRt27bAL1RPT0969OhRaDXx6tWrExQURLt27SS5ugMnJyc+++wzrl+/zsyZM4mPj7daHxERwfTp0/P1bSvqvnv37s26dessLVZZWVl89913lluTRfHUU0+RlJTEnDlzrFrDzpw54/B1bBYvXkx6errVLc6hQ4fStm1bPvjgAy5dumS1/aVLl1i7dq1NY1i0aBHJyclWy/R6Pc7OzpZWXXN/utjY2HyPf+yxx1BVlf/7v//LN9Bk7969HD9+3KbxCiEqNtWYiTElgpyE/Sjp0ZU+uaIitGAJ++jYsSN//vknH3zwgeXL38/Pj6tXr3L27FkGDRpUpCKvBXn99dd5+OGHGT16NIGBgcTFxfHvf//bMgquKLp3786XX37Ju+++y44dOwgMDCQxMREnJyc+/fTTEsVVFm4eRWg0GomJieHSpUtMnz6dF154wbKdTqfj559/5t///jdjx46lVatW+Pj4cPnyZbRardW2tpCWlsaECRPw9fWlVq1aXL58maSkJN5//31LK3C9evUYMWIEn376KTt37sTNzc1SB6tZs2b88ssvzJo1i0GDBhEYGIhWq+XixYu0aNGCt99+26bxCiEqJlNOCkpGNKas6/YOpdxpVOnwUKCjR4/SpUsXjhw5QufOnfOtz8rK4uLFizRp0qTC97kqjKqqZGZmkpWVRWRkJHq9noCAABo2bGiZh5C82k6bN2+mefPm+Uo77N+/H61WS/fu3a2WZ2VlcezYMYxGI506dcLLy4tdu3ZZWirvtF8zg8HA6dOnuX79OvXr16d58+ZotbkNs5cvX+bkyZP5bmNlZmaye/du2rVrZykqGh8fz7Fjx+jTp4+lZldRlxVm9+7dVtXLdTod/v7+NGnSpMDaamYJCQlERERYBmI0btzYqk/U5s2badSoEYGBgZZr5OHhwfXr1zl8+DDdu3e3ulVe2POYk5PDuXPniI+Pp0aNGrRq1cqqoKlZeHg4sbGxGI1GWrduna9syvnz54mOjsbDw4OmTZtajURMTk5m//79dOnSxbI8MTGxWHHeqqK99xRF4fjx43Ts2FHqKzkwuU62o6oqpuzE3I7rOQX3rS0JxQThcd5lco3u9J1fEpJgFUISLKy+vB19YuKqqipeo4r23pMv7opBrlPpqaoJkz4OJSMG1Wj76bsqWoIltwiFEEIIUWKqyYCSeQVTZiyqkn+EeFUlCZYQQgghik01ZuWOCNRfRTUp9g7H4UiCJYQQQogiMxnSUTJiMGVdA+llVChJsIQQQghxR6bsG7mJVXaSvUOpECTBEkIIIUSBLCMC06Mr3VQ2ZU0SLCGEEEJYKesRgVWBJFhCCCGEAEA1GVEyY2VEoA1IgiWEEEJUcaqSjZJxGZP+iowItBFJsIQQQogqSjVmomTEoOjjQTXZO5xKRRIsIYQQooox5aTmzhGYfV1KLZQRSbCEEEKIKsKUnYSSHo0pJ9neoVR6kmCJIklPTyc4OJgePXrg6+t7x+3NkyIPGjQIV1fXO26flJTE0aNH0Wg0DBkypMBtDh48SFJS/vorXl5e9O3bN9/yM2fOcOPGDdq3b4+Xl1e+9ZcvXyYiIqLQ4wkhRGWgqiqmrASUjGhUQ7q9w6kyJMEqI9lXd9o7BFzrDLTZvuLj43nhhRdYtGgRXbt2veP2f/zxBytWrGDEiBG33W7r1q0sWrSIs2fPYjAYUBSFw4cPF7jt//73PyIiIujZs6fV8oCAAKsES1VVXn75ZQ4fPkz9+vWJjo7mp59+ok2bNpZtFEXh+eefZ8CAAZJgCSEqpdxSC/G5iZWUWih3kmCJMrFt2zYGDx6MRqO57XY3btzgscceo2fPnjz66KOcPHnyttvXr1+fuXPn3vHY27ZtY+vWrQQEBPDGG2/w/vvvs2jRIss28+bNIysri6effrqYZyaEEI5NNSmY9Fdya1hJqQW7kQRL2Fx0dDRnz57l9ddfv+O299xzj82Pf+jQIYKCgggICABg2LBhPP/88xiNRpycnLh06RLfffcd8+fPx8XFxebHF0IIe1BNhtxSC5mxqCajvcOp8iTBEja3bds2PD096dGjh833nZ2dTUhICJmZmdSpU4dWrVqh1WqttsnKyrLq9+Xm5obRaCQ7OxudTsesWbO4++676dSpk83jE0KI8qYas1AyYzDp46SGlQORBEsUaP/+/dy4cYOcnBxcXFxISEiAvI7miYmJlu08PDzo37+/1WO3bdtG//79y6R16OrVq3zzzTeoqsrp06fx8/Njzpw59OrVy7JN06ZN2bFjByaTCa1WS3h4OLVr18bT05PFixdz5coVfvzxR9LT0wkLC8PX15dWrVrZPFYhhChLqjETJT0aJSteSi04IEmwRIE+//xzQkND8y3/6quvrH5v2LAhW7Zssfx+48YNjh49yscff2xZduvov5o1axapo/ytpk+fTt++ffHw8AAgMTGRf/3rXzz55JMsX76c5s2bAzBp0iR+/PFH3njjDTp06MAPP/zAyy+/TFxcHJ999hlffvklFy5c4IknnqBx48ZER0fTo0cPPvvss2LHJIQQ5c1kSMsttZCdKImVA5MESxSoZ8+e1KpVC0VR0Ol0ZGZmEhwcTPfu3a3KNPj7+1s9bufOnWg0GgYMGGBZ9r///Y+DBw9afu/bty/z5s0rdkzDhw+3+r1mzZq899573HXXXfzxxx/Mnj0bAG9vb5YtW8aiRYsIDw/ngw8+YNiwYTz11FMMHTqUvn37cv/99zNw4EA++OAD4uPjGTp0KNu2bZMRhUIIh2XKTkbJiMKUfcPeoYgikARLFOjll19GVVUyMzPx8PDgwoULjB49mhdeeOG2rU/bt2+nW7duVKtWzbKsW7duVklZ69atbRZn8+bNcXV1JSoqymp57dq1mTlzpuX3tWvXEhYWxrp16zAYDISGhvL4448DUKtWLYKCgjh8+LAkWEIIh2PKup6bWOWk2jsUUQySYAmbyc7OJjg42CqxAXj++efL7JhpaWlkZ2dbJXS3SkpK4v3332f27Nn4+PiQkZGBoii4ublZtnFzcyMzM7PM4hRCiOKQ4qAVn7YI2whRJObRfYMHD7b5vlNSUtDr8xfK+/nnnyGvFENh3n//fTp37syoUaMA8PT0pHbt2pw5cwbyio5GRkbSrFkzm8cthBDFoaomlMyrGBIPYkw+LclVBSYtWMJmtm3bRps2bahbt26RH3PhwgUiIyMBuH79OkajkY0bN0Lebb6OHTsCEBsby/PPP8+QIUNo1qwZiqKwZ88etm3bxgMPPMDo0aML3P+uXbvYvXs369ats1r+xBNPMHfuXFxdXTl27BjkdY4XQgh7yC0OejWvOGi2vcMRNiAJligSLy8vRowYUeg8hKqqsmPHDu67775i7ffChQusX78egCZNmtCkSRPL7x07drQkWG3atGH58uWsXbuWkydPkpmZSYsWLXjqqacICgoqdP/79u3j3XfftRQdNZs2bRr+/v7s3r2bOnXqsHTp0gLnKxRCiLKkmowombGYMi6jmgz2DkfYkCRYZcSW8wA6glq1at12iprQ0FASEhKK3Ul86NChDB06tEjbVqtWjalTpxZr/2+++Wah64YPH55vZKIQQpQHqbpe+UmCJWwiISGBSZMm2XSEoBBCVDaqko2SEYNJf1WqrldykmAJmxg2bNhtO5oLIURVphqzUDKiUfRxoJrsHY4oB5JgCSGEEGVEprOpuipEgpWRkcHChQvZtWsX169fp0GDBtx9992MGjUKjUZTpH2sW7eOJUuWEBsbi6+vLyNGjGDGjBk4OzuXefxCCCGqFpMhHSUjGlNWgiRWVZTDJ1iXL1/moYceIiYmxrIsKiqK4OBgTCYTd9111x33MXfuXL755hvL79HR0YSGhnLw4EG+//77IidpQgghxO3kzhMYhSkr0d6hCDtz6ARLURReeOEFYmJiCAwM5IUXXqBFixZcu3aNxYsXoxbhr4Lz58/z/fff4+Hhwdtvv0337t25dOkS7777Ljt37mTt2rWMHTu2XM5HCCFE5WTKSclNrLKTirC1qAocOsHasWMHJ0+epF69eixatAhvb28AGjZsSNeuXTGZ7txRcOXKlSiKwksvvcTkyZMtj//qq6+YNGkSS5culQRLCCFEiZiyb+QmVjnJ9g5FOBiHTrC2bdsGwKOPPmpJrm6m1d55pp/jx48D5LuV2LZtW5o0acKJEydQVVVuEwohhCgyU3YSSvolmYBZFMqhE6xz584B0KdPH3788UfWrFmDwWCgdevWPPzww7et4G125coVfH198fPzy7euWbNmXLx4kRs3bhS4nrzJhFNSUiy/u7i44OLigqIoqKpq+amMzOdVWc+vMqiK18j8nlMUBUVx/DpC5hgrQqxVWVGvkynrem4dK0NaOUUmzJS8m1Zl8V4qi306dIKVlpaGk5MT8+fP56+//rIsv3jxIps3b+arr766YxVwvV6Pp6dnges8PDwAyMzMLDTBmjFjBm5ubpbfJ02aZLnV6OTkhF6vL9KtyoqsoEmWhWOpStcoOzsbg8Fgmay7oggLC7N3CKIIin6d8t9VEeWjLN5L5jlxbcmhEywXFxdMJhNbtmzhww8/pGPHjuj1elauXMmCBQt49913GTJkyG1v77m4uJCdXfDEmeblrq6uhT5+wYIFlvnwuKkFKysri6ioKNzd3a0SsMpEVVX0ej3u7u5yC9VBVcVrpNVqcXZ2pnnz5hXivacoCmFhYbRv3x6dTmfvcEQhCrpOqqpiykpAybyMasiwd4hVnmKCyGveZfJeKouGEodOsAICAoiIiOCVV15h0qRJluVt27bl/Pnz7N27l6ioKBo3blzoPvz9/Tl58qTlS+hmly9fxtnZGR8fn0If7+3tTfXq1fMt1+l0aDQay09lVhXOsaKrStfIfK46na5CJSwVLd6qSqfTodVqMenjMWVEoxoz0QLcucuvKCdl8V4qi/emQ79k2rVrB3mT/N7K3OndaLz9JJlt2rTBZDKxa9cuq+Xx8fGcOXOGli1bSrHRAvTp04dWrVrxzjvv5Ft3/vx5AgMD+fHHH+0Sm6306dOHwMBAAgMDadWqFZ07d2bEiBG8/PLLbN26tcz6NaWnpzNo0CACAwP54osvCtxm165dTJkyhQ4dOtCjRw9mzpxJfHx8mcQjhPiHkhmHIfEgxpQzqMZMe4cjKjCHTrDGjBmDRqPhf//7HxcuXIC8Jtv169ezbds2vL29adSo0W33MWrUKAA++eQTzp49C0BSUhKvv/46iqJY1jsCkyGDzHMLuLHjbq5vGMCNHXeTeW4BJjs2Ta9Zs6ZM7k07is6dOxMREcGZM2fYs2cPX3zxBQ0aNOCll15ixowZpKen2/yY7733HgaDodD1u3bt4qmnnqJXr17s3buXpUuXEhsby7Rp08okHiGqOlU1oWReBcCYehbVWHX6NIqy49AJVosWLZg2bRoRERGMGjWKbt260aFDB1566SUMBgMvvPCCpfXp3Llz9O/fn9mzZ1vto2fPngwZMoTY2FjuuusuevbsSb9+/QgJCaFx48Y88MADdjo7a8bU8yRtGkzakTfIuRaCMfUsOddCSDvyBkmbBmNMPV/uMXXo0AFvb2/++9//lvux7cHT05M2bdrw0ksv8dNPP3HkyBFmzZpl02Ns3ryZdevW8dZbbxW6zQcffED79u158cUX8fLyokGDBnz66afExsby66+/2jQeIaqy3MTqCoaEgxhTz9k7HFHJOHSCBfDWW2/xwgsvUKNGDVJTU8nOzqZx48Z89NFHTJ8+3bKdwWAgPj6e5OT8xd4+++wzpk+fjqenJzdu3ABg2LBhLFiwIF+/LHswGTJI3j0VJSN3OiCXgN54tHoGl4DeACgZMSTvnlruLVne3t48+uij7N69m5CQkDtuP3jwYMsttzZt2jBgwABmz55tec7NVq5cyaRJk+jcuTM9e/bkkUce4eDBg8XaJioqisDAQJYsWVJgHC+99FKpzt2cmG/cuNFqmqbSSExMZPbs2Tz66KMEBgYWuE1ERASXLl3KNzq2QYMGtGrVio0bN9okFiGqMlU1oWTEYkg4gDElElXJsndIohJy6E7u5HU8e+aZZ3j66adJTk7G2dkZLy+vfNs1b96cXbt2FTiqyN3dnVmzZvHmm2+SkpKCl5cXLi4u5XQGd5YVtcySXFXv9T1uDcf9sy56NSkhT6FkxJAVvRyPZtNvsyfbmzJlCn///Teffvopy5Ytu21H6u3bt1v+r9frCQsLY/bs2bz88svMnz8fjUbDzp07ef3115k9ezZjx45Fo9Fw8uRJ5s+fT/fu3QGKtE156NOnD5s3b+bQoUM0aNAAgHvvvZfQ0NA7PrZhw4Zs2bLFatmsWbPw9fXl2WefLTRpi4iIAKBp06b51jVt2pQNGzZgMBik36AQJaCqJkyZV1AyYlCVgkeXC2ErDt+CZabRaPD19S0wuQJwdnamdu3atx0RqNPp8PPzc6jkCiA7ZhXktVzdnFwBuDUch0tAr9ztoleWe2zOzs68+OKLnDp1ijVr1hT5ce7u7nTv3p1XXnmFffv2WRKKAwcO4OXlxbRp06hWrRre3t706tWL77//3vLYomxTHmrXrg3AtWvXSr2vJUuWsHPnTubMmXPb15+5BbagmQuqVauGoiikpUmBQyGKI7fF6jKGhP0YU89JciXKhcO3YFUF5lnXnfw6Frjeya8TOddCMGVdL+fIco0ZM4Zff/2VL7/8kpEjRxa63YkTJ/j2228JDQ0lOTnZqq5IVFQUDRs2pFWrVqSnp/P6668zZcoU2rdvn681pijblAfzKMKbW+3+/vvvYu8nJiaGDz74gKlTp9KlS5ciPaaqlFwQoizltljF5rVY5dg7HFHFVJgWrMpM61YTAGPS8QLXG5OO5W1Xo1zjMtNoNLz22mvExsaycOHCArc5f/48DzzwAE5OTixYsIBjx44RERFh6ZRtLqcxbtw43nrrLUJDQ7n//vvp1q0bTzzxhFX/qqJsczu2Kq8QFxcHefXYSuPTTz/Fx8eHmTNn3nFbcwtsamr++c1SU1PR6XQFtm4JIf6hmhSUjJi8FqvzklwJu5AWLAfg2mA8OddCyLm2j6zo1fn6YOVcy+1g7tpwgt1i7NGjBwMHDuSHH36gc+fO+dZv2LCB7Oxs3nvvPXx9fS3LL1++bLWdRqPhwQcf5MEHH+TatWscOnSI+fPn89BDD7Fs2TJat25dpG3MSUZGhnXHf5PJREJCgk3Oee/evWg0Grp162ZZVpI+WDdu3ODKlSsFPm/ff/8933//PT/99BP9+/enZcuWAJayJDe7cOECTZs2lf5XQhRCNSmY9FekxUo4BGnBcgBuje5G55nbiTol5Clu7JhMWugcbuy4m5SQpwDQeTbAreGkO+ypbL366qukp6fz3XffFbheo9Hk61+0cmXh/cYCAgIYM2YMc+bMQVEUjh49WuRt/Pz88PT0zFejKzg4+LY1popq//79bN++nTFjxlC/fv1S7WvhwoVERERY/axfvx6Ap556ioiICPr37w95t0cbNWrE1q1brfYRExPDmTNnGDFiRKliEaIyyu1jFYMh8YC0WAmHIS1YDkDr7IlP/z8spRpyru0j59o+y3qdZwN8+v+B1rngSavLS/PmzZk0aVKBpREGDhzIt99+y4cffsjMmTPR6/X89NNP1KhhfVvzww8/xM/Pj0GDBtGwYUNSU1P5888/cXJysvRPKso25LUm/fnnnwwbNoxu3bpx4sQJVqxYQZ06dUp0fpmZmURHR7NhwwZ++eUXunXrlq+SfUn6YBXXG2+8wbPPPsuXX37JY489xo0bN3j11VepU6cODz30UJkfX4iKQvpYCUcmCZaDcKrWDL8R28mKXk529EpMWdfRutXAteEE3BpOsntyZfb888+zbt06MjOtp5Bo164dn3/+Od988w0DBgwgICCABx54gDFjxrBp0ybLdo899hh//PEHM2fOJDo6Gi8vL9q1a8dvv/1Gq1atirwNwAsvvEBaWhqvvfYaRqORgQMH8u9//9tq3so7OXr0KIGBgWg0Gtzd3QkICKBt27Z8/vnnd5xIvKwMHjyY7777jm+++Yb58+fj5uZG3759+eKLL6T/lRBW5RaiJbESDkujltWEaxXc0aNH6dKlC0eOHCmw70xWVhYXL16kSZMmBdbeqgxUVSUzMxMPDw8Z1eagquI1qmjvPUVROH78OB07dpTJnkupLBMrxQThcd60rp2GTjrPOCTzNSqL99KdvvNLQlqwhBBCOLTcxOpqXmIlNaxExSAJlhBCCIdUHomVatSTE7+b7Gt7qZGRQUa8J64BfXCp1R+Nk/2nUhMVlyRYQgghHIqqqpj0V1HSo8q0xUrJjCX9xBxMWQmggpNJg2JQyUw5TVbMSryCZqHzqFdmxxeVm9xpFkII4RBUVUXJvHrTJMxll1ypRv0/yRWg82lLRo3J6HzaAmDKSiD9xBxUo77MYhCVm7RgCSGEsKvcFqt4lIyocktocuJ3W5IrzzYvoavZh+g4bxrUTkNJ3EvG6S8wZSWQc20PrnWHl0tMonKRFiwhhBB2oaoqiv4ahsRDGFPOlGtrUc61vQA4+bTFJaCP1TqXgD44VW+Tu118cLnFJCoXacESQghR7pSsBJT0S6iGjCJsbXuqIQUAJ+/mBa53qtYCY8ppVEP+eUGFKApJsIQQQpQbU1YixvRLqIZ0u8ahca4OxGJMO1fgemPq2bztqpVzZKKykFuEQgghypwpOwlD4hEMN07aPbki7zYggDH5lOV2oVnOtb0YU07nblerr13iExWftGAJIYQoM6bsGyjplzDlpNg7FCsutfqTFbMSU1YCGae/QFd9M16aNmTEn0LJS660bv64BPSzd6iigpIESwghhM2ZclJQ0i5iykm2dygF0ji54xU0y1KqQUk+hafpNIpWBU1ucuUVNEuKjYoSkwRLCCGEzZgMabmJVXaSvUO5I51HPap1/Zyca3vIjg8mKyMDV09PXGv1xSWgnyRXolQkwRIFmj17NmlpafTr14+JEydarYuPj+ejjz7irrvuYsiQIXaLsbTM5wig1Wrx8PDA39+fNm3a0K9fP1xdXW16vAsXLrBhwwauXLmCm5sbzZs3Z9y4cXh6eubbNj09nWXLlnHmzBnc3Nzo168fgwcPtmk8QtiSyZCBkn4RU1aivUMpFo2TO651h+NUezjRcd4EyGTPwkbkZWRnqjELQ3J4kX5UY1a5xbVt2zbWr1/Pxx9/THq6dYfU9PR01q9fz/nz58stnrKwbds2wsPDGTp0KIMHDyYoKIjs7Gw+/fRT+vbtyx9//GGzY/3666+MGTOG8PBwOnbsSP369fnll18YNmwY585Zj2K6evUq48aNY9WqVXTq1IlatWrx6quv8sYbb9gsHiFsRTXqMSSfxnD9cIVLroQoS9KCZWfG9IskbSpaK5DfiG04+7Qu85jM6tatS1xcHD/++CMzZ84st+OWJ19fX8aMGWO1bObMmXz00Ue88847KIrC9OnTS3WMzMxMPvvsM7p27crXX39tWT569GgGDhzIt99+y+eff25Z/u6775KTk8OCBQvw8vICoGXLljz99NP079+f0aNHlyoeIWxBNWahZESh6ONAVe0djqgCcgxGbty4Ye8wikwSLFGopk2b0qlTJxYsWMC0adOoXbv2bbd/7733SErK7Xeh0+nw9/dnwIAB9OzZ02q7xMREVq1axaVLl3BxcaF169aMGzcOFxeXIm+TmJjI+++/z5QpU/Lt/7333qNRo0bMmDGjROet1Wp54403CAkJ4csvv2TixImWRKckMjMzycnJoUWLFlbLa9WqRbVq1UhO/qcTcEJCAjt37uTBBx+0OubgwYOpXbs2f//9tyRYwq5UJSc3scq8CqrJ3uGIKiAqNoFte8LYfSAcvxoBDBo0yN4hFYkkWA6keu8f0Xk3s1qmpJ0nZd8TdovpmWeeYevWrXz11Vd8+OGHt922T58+6PW5U13o9XrCwsJ47LHHeOaZZ3jmmWcAiIqK4p577qF169aMHDkSjUZDaGgoCxcuZNWqVUXeJiMjg/Xr19O7d+98CdaOHTvo0KFDiRMs8pKsu+66i88//5wDBw5Y+pp9+eWXREVF3fHxNWvW5O2337b8v2vXruzevZvU1FSqVcstXLhr1y6Sk5MZPvyfec5OnDiByWSibdu2+fbZtm1bQkJCUFUVjUZT4nMToiRUkwElIwZTZiyqSbF3OKKS02flsO9wBNuCwzh7Mc6y3Mk5lYyMDMvnqCOTBMuB6LyblestwKKoU6cO06dPZ/78+Tz00EMEBgYWuu2tnbAnT55MkyZN+PTTT7n//vvx9fVl1apVGAwG5s2bh5PTPy+/+Ph4y/+Lsk15aNq0KQCXLl2yLNu3bx+hoaF3fGzDhg0tCRbA999/z+eff86IESMICgoiPT2dqKgoPvzwQyZNmmTZLi4u94OkZs2a+fZZs2ZNMjMzSUtLqxAfLqJyUE0KSuZlTBkxqCajvcMRlZiqqpy7FMe24DD2HoogK9sAgE6rpWvHZgzu0x4nn7YFDgxyRJJgiTt68sknWbp0KZ9++ik///xzodvl5OSwadMmQkNDuXHjBiaTiaSkJIxGI+fPn6dr1644OzuTlZXF3r17GTBggOWxtWrVsvy/KNuUB/MoQnOrHMCLL75YpD4At34A7Nmzh3Xr1tG1a1cGDBhARkYGf/31F4sWLaJHjx7Uq1cPAIMh9wPF2dk53z7Nt0ezs7NLeWZC3JmqmjBlxqKkR6OaDPYOR1Ri6RlZ7DkYzrbgMKIu/zNQok6AD0P6tmdgr7ZUr+aBYoLwuIozNk8SLHFH3t7ePP3003z44YeEhIQQEBCQb5uMjAymTp3K9evXmTx5Mq1bt8bNzY3z58+zf/9+SzmE+++/n127dvHEE09Qp04dunfvTu/evRk1apQloSnKNuUhJSW38rSPj49lWe/evYu9n5iYGF577TVGjBjBZ599Zlk+efJkRo0axRtvvMHChQvhpsQsMzMz337MyyrKX2+iYlJVFZP+Kkp6FKoiybwoG6qqcuZcLFuDwwg5EonBkHvb2dlJR8/OLRjSrz1tWtSv0N0hJMESRTJ16lR+//13PvnkE/773//mW79y5UrOnDnD8uXLrfoPrVu3zmo7Hx8f/vzzT8LDwzlw4AAHDx5k1qxZfPvtt/z111/4+voWaRtza465xedm5mSutE6cOAFAu3btLMtK0gfr8OHDGAwGq75WANWqVaNHjx6sX7+e7OxsXF1dadiwIeSVarjVlStX8Pf3x8PDo9TnJkRBFP01lPSLqEZ9EbYWovhS0/XsCjnNtuAwYuP+KUbboG4NhvZrT78erfH2rBwFXiXBciBKWv66UgUtswcXFxdefvllXnrpJVavXp1vfVxcHBqNJl8frQMHDhS4v9atW9O6dWseeughdu7cyZNPPsm2bduYPHlykbbx9/dHp9NZ+iyZxcTEkJqaWurzTUpKYvXq1TRv3pygoCDL8pL0wTIngxkZGfm2S09Px8nJCa02t9m7Q4cOeHh4cPDgQaZMmWLZTq/XExoayrBhw0p9bkLcypR1HWP6RYeYhFlUPqqqcioyhq17wjhw7BxGY25rlauLE727BTK0b3taNKlToVurCiIJlgOx52jBohg1ahS//PILv/76a751rVq1QlVVdu7cydChQwHYv38/R48etdpu48aNtGnTxtJSQ17fLW66FVeUbZycnOjVqxfr1q3j8ccfx9vbm+zsbL799lurW3olERERwZtvvklOTg4ffvihJfmhhH2wevXqhaenJ7/99htDhw61dFA/fPgwe/fuZciQIZY+V25ubjzwwAP88ssvPPTQQ7Rv3x7yOsnn5OTwyCOPlOrchLiZKTs5t/q6g03ELCqHlNRMdoacYltwGFev/VOOpknDAIb2bU/f7q3wcC+/bh/lzaETLFVVLV+st9JoNFZ1k8pyHyKXRqPhtdde44EHHsi3btSoUWzdupXnn3+eHj16oNfr0Wq1vPjiizz77LOW7bRaLU899RRarZYGDRqQlpbGqVOnmD59uqUUQlG2AXjttdd4+OGHGT16NK1btyY2NpZZs2YV2mpWkIsXL/LSSy9BXitRVFQUsbGxDB06lC+//NIqyaOEfbD8/Pz47rvveOeddxg2bBgdOnQgPT2d0NBQhg4dyjvvvGO1/fPPP09CQgLTpk2jZ8+eJCUlceHCBT755BNatWpV7OMLcSuTIR0l7UKFmC9QVCwmk8qpiBi27DnBwePnUJTcWmnubi707d6KIX3b06xR+Q5YsheNqjpuCd7IyEjGjh1b4Lq2bduyfPnyMtvH0aNH6dKlC0eOHKFz58751mdlZXHx4kWaNGmCm5vbHeMojGrMwph+sUjbOnk1QeNU8mMVx9atW/H29qZdu3Z4eHhYNd1u374dvV5Pq1ataNbMum7X2bNniYqKIiAggKCgIJKSkggJCaFr166WUYCqqnL+/HmioqLw8vKiZcuW+Pr6Wu2nKNuQ1/H7yJEjKIpCly5d8Pb2Zvv27fj6+tKpU6c7nqN5RJ5Go7HMRdiiRYsySbxNJhNnz561zEXYpEmT2xZvjYmJISIiAjc3Nzp27FhgsVNVVcnMzMx3jSozW733youiKBw/fpyOHTui0+nsGotq1GNMv4hJf82ucTii3BFq3rSWuQhLJDk1g537TrE1OIz4hH9aRJs3rs3Qfu3p3TUQd7fSfa6ar1FZvJfu9J1fEg7dgmV2cx8Vs+J+AdpiH2VB4+TmcLWvAIYOHWr58r7V7SYdbtGihVXFcj8/v3xT0Wg0Gpo3b07z5s0L3U9RtgHw8PCgX79+RY7vZuZbmeVFq9USGBh421piN2vQoAENGjQo87hE5acq2SjpUSj6qzKtjbAZk0nlZEQ0W/eE5Wut6t+jNUP6tadJg/yjzquKCpFgvfzyyzz66KN234cQQlQkqsmIkhGNknFZprURNpOSmsmOfSfztVa1aFKbof2C6N01EDfX/LX8qpoKkWCZ2WKKEJlmRAhR2akmJbdIaEa0VF8XNmEy5Y4E3LI7f9+q/j1aM7RfEI0b+Ns7TIdSIRKsRYsWMXfuXAwGA40aNWLixIk8/PDDBVa7Lst9CCGEI/unSOglVKXgwT1CFEdquj63b9WeE1YjAaW16s4qRIIVGxuLRqNBVVUuXLjAZ599xoEDB/jxxx+L3NGtpPtIS0uzVPQmr9+Wi4sLiqKgqqrlpzIyn1dlPb/KoCpeI/N7TlEUFMXxJx02x1jWsSr6hNwWK2P+fpPizvIaZCz/VmWqqhJ+9jJb80YCmutW5Y4EbM2Qvu1pfFPfqvJ6zizXqAzeS2WxT4dOsHQ6HQ888ACTJ0+mWbNmZGZmEhwczEcffURwcDBr1qxhwoQJZbqPGTNmWI1UmjRpkqUYppOTE3q9HpOpcr8jb56LTzimqnSNsrOzMRgMnDlzxt6hFEtYWFg5HEUHeJfDcSqvyGtV9/kzFzQ+cuQIiYn/zAlYt25dunTpQrt27XBxcUEPhMfddldlqizeS5GRkTbfp0MnWM2aNeP//u//LL+7uLhw11134efnx8MPP8zOnTvvmGCVdh8LFiygY8eOVo93cXEhKyuLqKgo3N3dK8RQ8ZJQVRW9Xo+7u7v0W3NQVfEaabVanJ2dad68eYV47ymKQlhYGO3bt7fp0HKTIT23SGh2chG2FneimHKTq5YBVatMg6qqnL14la17ThByJMIyJ6CrqzN9urViaN8gmlrqVmXn/diH+RrZ+r1EXhkdW3PoBKsw5qlLkpJKXiSvqPvw9vamevXq+ZbrdDo0Go3lpzKrCudY0VWla2Q+V51OZ/e6UsVhq3hvrmWlgSqVDJQHnbZqPKeZ+mz2HDzDlt2hRF3+p7WqUX1/hvcPcugq62Xx3i+Lz5IKmWAdOnQIAH//ko9YsMU+hBCivKgmA0r6JZTMK1LLSpTYxehrbN4dyp6DZ8jONgDg7Kyjd9dAhvcPqpRzAtqLQydYb775Jo0bN6ZPnz7Ur1+ftLQ0goOD+fLLL+GWgpLmKXHMtw9Kso+SMFcCr4xUVSU7OxutVitvOAdVFa9RZX7PFUQ1KSgZMZgyY1BNjt+pXzie7BwD+w5HsnlXKOcu/dN5ql4dP4b3D6J/jzZ4eTr+7faKxqETrISEBJYvX87nn3+eb93w4cMZPXq05fczZ84wYcIERowYwdy5c0u0j+Iw3yK8cuVKiR5fEaiqisFgwNnZucp8eVc0VfUamW8RVmaqqmLKvIKSESUlF0SJxMYlsWX3CXaGnCIjM/cPE51OS49OLRg+IIg2LepXqc+N8ubQCdZHH33EX3/9xc6dO4mOjkaj0dCiRQvGjRvH3XffbfXCME/cfGtdq+LsozicnZ1p1qxZhRgmXlKKonDmzBmaN29e6b/MKqqqeo10Ol2lrmGnZCWgpF1ANVad0aHCNoyKwqHj59m0K5RTETGW5f41qjGsfxCDe7ejejUPu8ZYVTh0glWzZk2effZZnn322Ttu26pVqwKHbhZnH8Xl7OxcuT/k85JHNze3KvXlXZHINapcTNnJKOkXMOWk2jsUUcEkJqWxdc8JtgWfJDk1A/IaHroENWV4/yA6tGmMViutVeXJoRMsIYSoCkyGjNzEKuu6vUMRFYjJpBJ6+hKbd5/gyIkLloLDPtU8GdK3HUP6tcffr5q9w6yyJMESQgg7UZUclPSLKPo4GRkoiiw1Xc+OvSfZsvsE8Yn/zDTSLrABwwd0oFvHZjhJi7bdSYIlhBDlLHdkYDSmzMsyMlAUibkg6KZdoYQcjsSQN32Nh7srA3u1YfiADtSr7WfvMMVNJMESQohyIiMDRXFlZRsIPhjOpl2hXIpJsCxv2rAWwwfkFgR1dam8fYErMkmwhBCiHJiyrqNkXpLJmB2AquRg0l+1WqaYwCnLEyU9A26q5K51r4NG51LuMcbGJbFpVyi7Qk6Tqc8tseDsrKNP11aMGNiB5o1rl3tMongkwRJCiDJkHhFoSD5dJaZgqQhM+qukHp5pvVCFGiYNGVEq3DTYrlrXz9B5NSqXuBTFxOHQ3BILYWeiLctrB/gwvH8QA3u3xdvTvVxiEaUnCZYQQpQB85yBhoxrgLe9wxEO7EZKBtuCw9iy+wRJyelwU4mFEQM6ENS6kZRYqIAkwRJCCBvKnTMwKm/OQJO9wxF34NlmJjqPuigmuJDoSdOaGZB1hYzTn5XpcVVV5cy5WDbuDOXA0bMoptzXSjVvd4b0ac+w/kH415ASCxWZJFhCCGEDqmrClBmLkh6FajLaOxxRRDqPurm3AE1gTPdG55Vm1QfL1vRZOQQfPMPGnceJjk20LA9sVpcRAzrQs3MLnJ3lq7kykKsohBClpOiv5U5to2TZOxThoMyd1nfuO4U+K3cEqYuzE/16tGLEwI40aRBg7xCFjUmCJYQQJWTKSUFJOy9T24gCKSYTR8MusnHHcU6ER1mW1wnwYcSAjgzs3QZPDze7xijKjiRYQghRTKpRjzHtAqashCJsLaqa1HQ924PD2Lz7BAnXc5NvjQY6t2/KyIEdpdN6FSEJlhBCFJFqMqKkX5IO7JWIknkl99+b62BlXSnRvs5fimPDzuPsOxRhqbTu5enGkD7tGDagA7VqVrdp7MKxSYIlhBB3kFuB3dyB3WDvcIQNWUYLFlIH604MBiMhRyLZuPM4Zy/GWZY3aRjAqEGd6N21pVRar6IkwRJCiNswZSViTDuPatTbOxThQK7fSGPL7hNs3RNGSlpudX6dTkvvLi0ZOagjLZrUQaOR24BVmSRYQghRAJMhDSX1PKacZHuHImxM616Hal2t61zdXAdLd8tUOWbm2lUbdhznwLGzmEwqAH4+XgzvH8SQfu3xqeZZficiHJokWEIIcRNVyUZJu4iSFQ+qau9wRBnQ6FzyT39zUx2sW6c0ys4xEHzwDBt2HCfq8j8DG1q3qMeoQZ3o1rEZTjpdOUUvKgpJsIQQAlBNCkpGDKbMGFSTYu9whAO4lpjCpl2hbAsOIyMzd8Ll3NpVrRk1qCON6vvbO0ThwCTBEkJUeYo+Pq9QaLa9QxF2pqoqYWdi2LDjGIdDL6DmtWL616jGyIEdGdRHJlwWRSMJlhCiyjLlpKCknsNkSLN3KMLOsrINHD58mHlH93P56nXL8vatGzJqUCc6t2+CTluGc+iISkcSLCFElaMaszCmX8Ckv2bvUISdXUtMYePO42wPPkmGPrcF09XVmQE92zByYEca1K1h7xBFBSUJlhCiysjtZxWNkhEjhUKrMFVVORUZw/rt1rcBfX19uWtIEEP6tJUpbESpSYIlhKgSlMw4lPQLqEqOvUMRdpKdY2DPgXDWbz9GzJV/bgMGtW7EiEGdcKvRnrZ1M/KNIhSiJCTBEkJUatLPSiQmpbFx53G2BYeRnpEFgKuLEwN6tbXcBlRMEB4nmZWwHUmwhBCVkvSzqtpUVeXM+Sus33aUg8fPWYqCBtSszsiBHRkstwFFGZMESwhRqUg/q6rNYDCy73Ak67Yf5WL0P8l128AGjBncic5BTWU0oCgXkmAJISoNqWdVdd1IyWDL7lA27z5BSmru3IDOzjr692jNqEGdpCioKHeSYAkhKrzceQPPYcpJsXcoopxdiI5n/bZjBB86g6Lktlj6+XgxcmBHhvRrTzUvKQoq7EMSLCFEhaUqOShpF1D0cfYORZQjxWTi8PHzrNt2lPBzsZblLZvWYfTgzvTo3FzmBhR2JwmWEKLCUVUTpozLKBlRMm9gFZKhz2Z78Ek27DhGwvVUAHRaLb26tmT04E60aFLH3iEKYSEJlhCiQjFlXceYdg7VqLd3KKKcXL12gw07jrNj70mysg0AeHu6MbR/ECMGdKCGr7e9QxQiH4dOsHJycrh06VKB69zc3GjYsGGx9peZmUlCQgI+Pj5Ur17dRlEKIcqDaszEmHoOU3aSvUMR5UBVVU5HXmbttqMcOXGevGLr1K9TgzFDOtGvR2tcXZztHaYQhXLoBOvSpUuMHTu2wHVt27Zl+fLlRdpPeno6c+bMYe3atRgMBjQaDT179uS9996jQYMGNo5aCGFLqsmIkh6FknkZy7esqLQMBiN7D0ewbttRLsUkWJZ3ateEMUM6E9S6IRqNxq4xClEUDp1gmfn7++Pj42O1rFGjRkV+/AsvvEBwcDBOTk40atSIhIQEQkJCePDBB1m9ejVeXl5lELUQorRkepuqIyUtk827Qtm0K9RSZsFcbX304E7Uq+1n7xCFKJYKkWA9/PDDPProoyV67J49ewgODqZx48bMnz+fevXqkZGRwSuvvML27dtZuHAhTz/9tM1jFkKUnCknFSXtHKacVHuHIspYzJVE1m07yu794RiMuQMW/Hy8GDUot8yCt6eUWRAVU4VIsADi4+PJycmhdu3aODsX/b775s2bAXj99depV68eAJ6ensyZM4f+/fuzYcMGSbCEcBBSdqFqUFWV0NNRrN16hNDTUZblzRrV4q6hXejZpYWUWRAVXoVIsL7++ms++eQTANzd3RkzZgyvvfZakTqqnz59Gp1OR58+fayW16hRgzZt2nD69GlycnJwcXEps/iFELenqiqmzFiU9EuoJqO9wxFlJMdgZM+BcNZtO0rMlesAaDQaundsxpihXWjVrK70rxKVRoVIsPR6PfXq1SM9PZ2UlBSWLl1KWFgYf//9N25ut5+s8/r169SoUQNXV9d86+rVq8eJEydITk4mICCgwMenpaWRkvJPdWgXF5cqk4wpimL1r3A8leEambKTMaZfQDVk2DuUMpFXXNzyb1WUkpqZO43NruOkpueW13BzdWZg73aMGtSJWv65fWxNKmCncQxynRyf5RqVweddWezToRMsd3d33nrrLe6++25LR/QTJ07wxhtvEBERwdKlS3nggQduuw+DwVBoEma+1ZiTU3gH2hkzZlg9ftKkSUyePLmEZ1QxhYWF2TsEcQcV/xppgcpdyyjyWuU+v4IkJCSwf/9+QkNDLV9g1apVo0ePHnTu3Bk3NzeSFEhyoDvCVfE6VTRl8XkXGRlp8306dILVoEEDHnzwQatlQUFBfPzxx0yePJmQkJA7Jlju7u6kpaUVuC49PR0ADw+PQh+/YMECOnbsaPm9qrVghYWF0b59e3TSH8IhVcRrpKomlIzLmDIvV4kq7Iop90u7ZUAaOq29oyl7qqpyMiKGdVsPc/zUP3UMmzWqxZghXeje2dy/ypD34xiq2nWqiMzXqCw+70wm2zddOnSCVZjGjRvDTQnS7dSrV4/9+/eTmJhIzZo1rdadO3cOT09P/PwKH/7r7e1d5YuS6nS6CvPlXVVVlGtkyk5CST0LRj1a8hquqgidlkr9xW0wKuw7FMGarUeIupxbv0qjgW4dmjN2WBcCK0j/qsp+nSqDsvi8K4vPT4dOsLKzswvsO2UeGVi3bt077qNz587s37+fFStW8Pjjj1uWHzlyhOjoaPr27WvjqIUQt1KNWRjTzmHKSrR3KMLG0jOy2LLnBBt2HONGcm4/OlcXJwb1bseYoZ2p7e9zx30IURk5dIL10ksv4ePjQ9++falfvz5paWkEBwfz+++/AzB69GjLttnZ2URFReHt7U2dOv9M+Dl+/Hh+/PFH5s6di5OTE926dSMqKoqPP/4YgHvuuccOZyZE1aCqJpT0aJSMaFCl93BlEp+YwrptR9m+9yTZefMD+lb3ZNTgTgzrF4SX5+0HIAlR2Tl0gqXRaFi2bBnLli3Lt+6RRx6hX79+lt8vXLjAhAkTGDFiBHPnzrUsb9y4MS+88AKfffYZH330kdU+Ro4cyciRI8v4LISommRS5srp7MWrrNlyhP1Hz6LmTV3UsF5Nxg3rSu9ugTg7Of6taiHKg0MnWF9++SWbNm1ix44dREdHo9Vqad68OePGjaNHjx5W27q6utKiRQur1iuzJ554gsDAQJYsWcKVK1fw9fVl+PDh0nolRBnIvR14FlPWdXuHImzEZFI5cuI8q7cc4cy5WMvyDm0aMXZYV5kfUIgCOHSC5ezszF133cVdd911x22bNm3K2rVrC10/YMAABgwYYOMIhRBmcjuw8snOMbB7fzhrth7havwNAHQ6LX27t2LssC40qudv7xCFcFgOnWAJISoGuR1YuaSm69m08zgbdx4nNS33mnp6uDKsfxCjBnXCz8fL3iEK4fAkwRJClJiMDqxcrl67wbqtR9mx7xQ5htwpi/xrVGPMkM4M7tMOd7eqUQNQCFuQBEsIUWy5xUJjMGVEV4lioZXd2YtXWbX5MAePnbN0XG/SMIDxw7vSs3NLdFIYSohikwRLCFEspuwbGFPPohoz7R2KKAWTSeXYyYus2nSI8Js6rndq15hxw7vStmUD6bguRClIgiWEKBJVycm9Hai/Zu9QRCkYDEaCD55h1ZbDxF5Ngps6ro8b1pWG9WrecR9CiDuTBEsIcVuqqmLKjEVJv4RqMto7HFFCGfpstu4+wbrtRy0V193dXBjWP4jRgztRw1cmORbCliTBEkIUypSTijE1EtVw53k/hWO6fiON9duPsWX3CfRZOQD4+ngyZnBnhvYPwtM9/3RkQojSkwRLCJGPajKipF1A0V+FvE7PomK5fPU6q7ccZvf+cBQlty5Z/To1GDe8K327t5KK60KUMUmwhBBWlMw4lPQLqEqOvUMRJRBx/gorNx3icOh5y7JWzesxfnhXOrdvilYrHdeFKA+SYAkhAFCNmRhTIjHlJNs7FFFM5hGBKzcdsprKplvHZowf3o3AZnXtGp8QVZEkWEJUcblT3EShZMTIFDcVjFFR2HswglWbDxFzJXfuR51OS/+erRk/vBv1avvZO0QhbEKjc0HnVgOoOP1BJcESogozZSfl1bSSKW4qkqxsA9uCw1iz5QjXb6TBTSMCxwzpLFPZiEpBo3NB61oTrVsAGpfqmEwm4Li9wyoySbCEqIKkplXFlJauZ+OO46zfcYz0jCwAqlfzYMyQzgzvH4Snh5u9QxSiVG5NqipysVubJlhHjhxh3rx5nDx5kuzsbPz9/enUqRNjxoyhZ8+etjyUEKKElMwrKGkXpKZVBZKYlMaaLYfZFhxGdk7udavlX53xw7sxoFcbXJzlb2VRcWm0zmjd/NG6+aNx8anQSdXNbPau3Lp1K88//zwuLi40btyYatWqcePGDZYvX87ff/9Njx49+PTTT6lVq5atDimEKAaTIR0lNRJTTqq9QxFFdPnqdVZtOsyeA+Eoptz+cU0aBDBhZDd6dG6BTitzBIqKKTepMrdUVZ6k6mY2SbCMRiP/+c9/GDt2LLNmzcLb+5+KwFlZWWzcuJGvvvqKadOmsWTJEnx9fW1xWCFEEagmBSX9EkrmZalpVUGcvXiVFRsPcuj4P6UW2gY2YOLIbgS1blQpv4xE5afROuXe/nMPQOPiW+lfxzZJsI4ePYqzszMffPABOp118To3NzcmTJjAkCFDePDBB/n000/54IMPbHFYIcQdmLKTMKZEoipZ9g5F3IGqqoSdiWbFhoOcjIixLO/WsRkTR3anRZM6do1PiJKwJFVu/mhc/Sp9UnUzmyRY58+fp2fPnvmSq5t5e3vz+eefM3HiRN544w2qVatmi0MLIQogndgrDpNJ5VDoOVZsPMj5S/EA6LRa+vZoxYQR3ahfp4a9QxSiWDRaHRrXmugsSVXVvJVtkwQrPT29SLf9GjduTKdOnThy5AiDBg2yxaGFELdQMq+ipJ2XTuwOzqgoBB88w8pNh4i9mgSAi7MTQ/q2Y+ywrvjXkD9CRcWRm1TVyO2s7lqjyiZVN7NJgqWqKtoidrZs06YNUVFRtjisEOImuZXYIzDlpNg7FHEb2TkGduw9xarNh0hMyq1h5eHuysiBHRk9uBPVq3nYO0QhikajRevqh9YtIDep0sr8ljez2SjCyMhIDhw4QMuWLW/bmlWtWjVSUuQLQAhbMqZFQdZlqcTuwDL12WzbE8rarUdJScuEvBpWdw3pzPABHfBwd7V3iELcmUZzS1IlJUIKY5NnxtnZmV27drFr1y4A/P39CQwMpGXLlrRo0YKWLVvSvHlz3Nxyi+AZDAZbHFaIKs9cckHJiEYnLfIOKTVdz44dhzly6AAZ+mwA/GtUY9ywrgzq0xZXF2d7hyjE7Wk0aF18cpMqt5potPKaLQqbJFgPP/ww48aN4/Tp04SHh1t+9u3bl1faHrRaLQ0bNgRg2LBhtjisEFWWajKipF3AkH4F8C7CI0R5S0pOZ82WI2zZHWopDlqvth8TR3anT/dAnG4zKEgIR6B1qZ6XVPmj0bnYO5wKx2ZtezVq1KBfv37069fPsiwzM5OIiAirpOvs2bO2OqQQVZKSlYCSeg5VybZ3KKIA8YkprNp0iB37TmE0KgDUqVOH++7qQs/OLdBqq84wdVHxaJ290boH5BYA1clt69Io05unHh4edOrUiU6dOlmWKYpCRkZGWR5WiEpJVbIxpp7FlJVo71BEAS5fvc6KjQcJPngGkym3oGur5vWYMLI7Ln7taVMnHSm8LhyRxtkTrVsAOrcANE7u9g6n0ihxghUdHU2dOnVwdi7evVidTic1sIQoJpk/0HFdjLnG8vUHOHDsrKVQfoc2jZg0qgdtWtZHMUF4nLRaCceicXLPu/0XgNbZ097hVEolTrBefPFFIiMjadmyJa1bt6ZNmza0bduWwMBA3N0lAxbCFlSjPq/0QrK9QxG3iLxwheXrD3Ik7IJlWbeOzbh7VA+aNa5t19iEKIhG55qbULkHoHWWvptlrcQJVtOmTTl79iynTp3i1KlTluU6nY4mTZrQpk0bq5+b5ycUQtyeqqqYMmIwpl+S0gsORFVVTp+9zLL1BwgLjwZAo9HQu2tLJo3qQcN6Ne0dohBWcidV9s8rq+Bj73CqlBInWP/973/54IMPOHPmDGFhYYSGhnLixAkuXbrEuXPnOHfuHKtXr4a8D6AVK1bQunVrW8YuRKVkMqRhTIlANaTbOxSRR1VVToRHsXTdAc6ci4W86Wz692zNxJHdqVNLJrAXjsMyVY17rSoxqbKjKlUndxcXF4KCgggKCmLatGkAJCUlsW7dOn744QeSk5Np1aoVFy9exGiUviNC3I6qmlDSL6FkxGDpzCPsSlVVjoZdZOm6/Zy7FAeAk5OOwX3aMX54VwJqVrd3iELkMldVd68lU9U4CJuPIvTz82P69OkMHz6cRx55hAYNGvD333/b+jBCVCqmnJTcVitjpr1DEeYJmI+fY9n6A1yMyZ0w28XZiaH92jNueFdq+EqXB+EALAVAa+UVAJWq6o6kzK5GrVq1+OCDD7j33nvp1KkTM2bMsMl+g4ODycrKokWLFjRq1OiO26enp7N///4C11WrVo3u3bvbJC4hSkI1KSjpF1AyYu0digAUk4n9RyJZtv4AMVeuA+Dq6szIAR24a1gXfKrJaCthf1qXapYRgFIA1HGVabrboUMHatWqxbx583jggQeKPCF0YbZu3cqzzz4LwGuvvcajjz56x8dcuXLF8phbtW3bluXLl5cqJiFKypSdhDElElXJsncoVZ6imAg+dIbl6w9wJf4GAO5uLowe3IkxQzrj7SUjo4V9Sa2qiqfECVZaWlqRRgZ6e3tz7tw5rl69Sr169Up6OFJSUvjPf/5D9+7dOXjwYLEf36JFC8tUPWZFaQETwtZUkxEl9RyKPs7eoVR5RkVhz4EzLN9wgLhruaUwPD1cuWtoF0YN6oinh5u9QxRVmEbnmtunyi0ArbOXvcMRxVTiBOuhhx7i+vXrtG/f3vLTrl07q6QrPj6e6OjcocyKopQq0Pfff58mTZowY8aMEiVYEydOLFKLlxBlyZSViDE1ElXJsXcoVZpRUdgVcprlGw5yLTEFAG9PN8YO68qIgR3wcJcpQoR9SFmFyqPECVb16tU5efIkV69eZfPmzZBXjqFx48a0adOG6tWrs3PnTnJycvDz86N+/folDnLXrl1s3bqV1atXc+bMmRLtIycnh0OHDpGdnU2TJk1K1ZomRHGpJkPuNDf6a/YOpUozGBV27jvFio0HSbieCkA1b3fGDevK8AEdcHeT/iyi/OWWVaiBzq0WGlc/KatQSZQ4wZo/fz4JCQmEhYVZfk6ePMnFixe5ePGiZTt3d3fefffdEve/Sk9PZ/bs2bz55pvUr1+/xAnWl19+afV79+7def/99/PdNhTC1hT9NZTUs6gmg71DqbIMBiM78hKrxKQ0AKpX82D88G4M6x+Em2vxpvwSotQ0GrQuvnllFWqi0ersHZGwsVJ1cvf392fw4MEMHjzYsuzy5cucOXOGK1eu4OPjQ/fu3aldu+TTRnz88ccEBgZyzz33lCZU/P39ad68Oenp6URERHDw4EGmT5/O6tWrqV698Fo2aWlppKSkWH53cXHBxaVq/JVrvq1b2tu7VZWq5GBMO4cp63qZHUMxWf8rrOUmVidZuekgSTdyC7f6Vvdk7PBuDO3bHheX3MSqLJ8/uUYVQ3ldJ62LN1rXgNyyCnkjAE0qIJ+zd1SW30llsU+bjyKsX79+qW4H3iwkJITNmzezZs2aEu+jWrVq/PDDDwwcONCy7Nq1a7z88sscOnSIxYsX89RTTxX6+BkzZuDm9k9H10mTJjF58uQSx1MRhYWF2TuECq7sayZFXpO6TDczGo0cO3aM4OBgUlNzbwV6e3vTp08fOnfujLOzM+eTyjcmuUYVQ/lcp2t5P6IkyuI7KTIy0ub7LHKCtWLFCnx9fWnTpg0BAQE2D+RWmZmZzJo1i8GDB3PixAnL8tDQUADOnTvH1q1bad++PbVq1Sp0P7Vr187XghYQEMA777zD6NGjOX78+G3jWLBgAR07drT8XtVasMLCwmjfvj06nTRfF0V5tFrdTDHlfiG0DEhDJ4WbC2yx8vPxYtyIbgzu0x4XZycgK++nfMg1qhhsfZ00Ohe0rjVzO6y7VLNFiFVeWX4nmUy2b7oscoK1cOFCy6TO/v7+lkmc27ZtS5s2bWzeafz06dNcvnyZy5cvF1iravny5SxfvpyvvvqKkSNHFnv/fn5+AGRl3f6D1tvb+7a3EKsCnU4nCVYRKPp4TKln0ZiM5f5FqtNSpb+8DQYj2/eeZMXGg1y/KbGaOLI7g/u2y0us7KuqX6OKojTXSeYALB9l8Z1UFt9xRf7UGTBgAEajkfPnz5OQkMCuXbvYtWuXZb2Pj0++pKtRo0YlfoH5+voyZMiQfMsTEhI4ceKEpa7V7VqvyCsVUdA2S5YsAamFJWxAVXIwpkZiykq0dyhVjrnz+vINB7l+I7fzuqMlVqKSk87qohBF/vR54YUXeOGFF8jOziYiIoJTp05x+vRpTp06xdmzZ0lOTmbfvn3s27fP8hgvLy9at25NmzZtePLJJ6lRo0aRA2vWrBnffvttvuXmau631rVKS0vjwIEDBAQEEBQUZFn+9ttvk5WVRZ8+fahfvz5paWkEBwezfft2NBoNd999d5FjEuJWij4eJfWcjBAsZ+ZyC8vWH7AkVr4+nkwa2UMSK1EuNM5e6Nxry3Q1olDF/hRydXUlKCjIKokxGAycPXvWknSdPn2aiIgI0tPTOXToEIcOHWLs2LHFSrCK6/Llyzz77LOMGDGCuXPnWpbXqVOHv//+m0OHDllt7+zszFtvvWV1HkIUlbRa2Ye5QOiy9Qcsdax8q3sycWR3hvRrL4mVKFManRta94DcyZWdZV5KcXs2+TRydna23B4kr6hncHAwP/zwwx07kReXv78/Q4YMyXdrz8vLiyFDhtC+fXur5e+99x733nsvO3bsICoqCq1WS4sWLRg1ahQNGjSwaWyiapC6VuVPUUzs3n+apesPWCqv+1TzZOKobgztFySJlSgzGq1TXmX1WlJZXRSLzT6V9Ho9e/bsYdOmTezcuZP09NyOps7OznTv3t1mIw87dOhQ4K3DBg0aFLgcsEzlI0RpqCYDxpRITFkJ9g6lylBMJoIPnmHJ2hDiE3ITq+reHkwYmVsg1NVFCoSKMqDRoHX1y02q3Gqi0cjoBFF8pUqw0tLS2LFjB1u2bGHPnj3o9XoA3NzcGDJkCMOHD2fw4MFUqyZDVEXFJnMIli/FZCLkcCRL1oZwJf4GAN5e7kwY0Y3hAzpI5XVRZpy8m+HsVRuNVl5jonSKnWAlJSWxbds2Nm/eTEhICAZD7m0SLy8v7rrrLoYNG0b//v3x8PAoi3iFKFeqyZg3h2C8vUOpEkwmlQPHzvL3mhAuX82tJebl6cb44V0ZMbCjzBUobC63X1UtdC41IS4SnWddGQkobKLICdaqVatYtmwZhw8ftpSU9/X1ZfDgwQwfPpzevXtXmQKcomowZSdhTIlAVbLtHUqlp6oqR05c4M/V+4i6nHsL1tPDlbHDujJqUEc83F3tHaKoRArqVyVTgglbK3KC9dtvv3Hq1Clq1KjBqFGjGDZsGN26dZMClKLSUU0KStp5lMwr9g6l0lNVldDTUfy1eh/nLsUB4O7mwpghnblraGc8PdzuuA8hisRSr6q29KsS5aLYtwivX7/Orl27SEhIIDQ01FJY1FwZXYiKzJSTgjHlDKpRb+9QKr3TkZf5c9Vews/FAuDq4sSowZ0YN6wr3l7u9g5PVBK59apqoXWrJfWqRLkqcoLVq1cvMjIyiIqKIiYmhpiYGDZt2mRZX6tWLasq7m3bts03B6AQjkpVTShpF1EyL4Oq2jucSu3sxav8uWofJ8KjAHB20jF8QAcmjOyGTzWpLSRKT6NzQesWkNta5exl73BEFVXkBOvVV1/l1VdfJSMjg/DwcKuiohcuXCA+Pp74+Hh27NhheYyfn58l2XrooYeklUs4JJMhHWNKOKohw96hVGoXY67x16p9HAm7AIBOp2Vo3/ZMHNWdGr7e9g5PVHQaLVq3mujcaqFx9ZN5AIXdFfsWoaenJ127dqVr166WZdnZ2Zw5c8Yq6YqMjCQpKYng4GCCg4MZNmyYJFjCoaiqipIRjZJ+SVqtylBsXBJ/rd5HyJFIALRaDQN6tmHymJ4E1KzaE6mL0tO6VMvrVxWARisFZ4XjsMmr0dXVlQ4dOtChQwfLslunz5FaWMKRqEY9xpRwTDmp9g6l0opPTGHJ2hB27w9HVVU0GujdNZB7x/ambi1fe4cnKjBLaQX32micpL+ecExllu7fOn2OEI5CybyCknYe1STDssvCjZR0lq0/wNY9YSiKCYBuHZoxZXxvGtXzt3d4ooLSaHVoXf3RutdC6yoJunB80p4qqozcCZojMGVdt3colVJaup5Vmw6xYcdxcgxGAIJaN+K+8b1p0aSOvcMTFZTWxSfvFqC/FAAVFYokWKJKMGUl5hYNlQmabU6flcO6bUdZvfkw+qzcqYQCm9Xl/vF9aBsoE6qL4su9BVg77xag1EITFZMkWKJSU00KSupZFH2cvUOpdHIMRrbsOsHyjQdITcutG9aovj/3T+hD53ZNZBSXKJZ/bgHWtlRXF6IikwRLVFqmnBSMyeGoSpa9Q6lUFMXEzpBTLFm7n+s30gCoE+DDlHF96NWlJVqtJFai6OQWoKisJMESlY6qqijpl1AyoqX8gg2pqsr+o2f5c9VersTfAKCGrxf33NWLAb3a4CTTZokiklGAoiqQBEtUKqoxE2NyOCZDmr1DqTRUVeVEeDR/rAjmQnQ8AN6ebkwc1YMRAzvg4iwfI6IINFq0bv65SZWLj9xCFpWefDKKSkPKL9je2YtX+WNFMCcjYgBwc3Vm7LAu3DW0Cx7urvYOT1QAUghUVFXyahcVnmoyYEyJwJSVaO9QKo3YuCQWrwzmwLFzADg56RjeP4hJo3tQ3dvD3uEJB5c7F2AtdB510DjJ60VUTZJgiQrNlJ2EMeUMqpJj71Aqhes30vh7TQg79p3Kq76eO63NvWN74V9DZmMQt6HRoHWtgc69jswFKIQkWKKiUlUTStoFlIzL9g6lUkjL0LNy4yE27DiGwZB7i7Vbh2bcP6EPDerWtHd4woFpnD3RuddG61YLjc7F3uEI4TAkwRIVjsmQgTElHNWQbu9QKrzsHAMbth9j5aZDZGRmA9C6eT2mTepHYLO69g5POCiN1gmtW0Bu3yoXadkUoiCSYIkKRcmIxZh2HlSTvUOp0My1rP5eE0JScm6i2rBeTaZO7CtFQkWhpGaVEEUnCZaoEHI7sp+ReQRLSVVVDp+4wB8rgrl8Nfe5rOnnzZRxvenXozU6rdbeIQoHo9G55tWsqiM1q4QoBkmwhMMzZd/IvSUoHdlLJeL8FX5fvocz52IB8PJ0Y5LUshIFkQ7rQpSafKoKh6Wqal5H9hh7h1KhxcYl8ceKYA4ezy254OLsxJghnRk/oiueHjKRrviHxskDnUcd6bAuhA1IgiUckmrUY0w+LRXZS+FGSgZL1oawLTgMkym35MKg3m25d2wvavh62zs84SAskyx71EHrUt3e4QhRaUiCJRyOkhmHknZWKrKXkD4rhzVbDrN6yxGysw0AdAlqyrSJ/WhQt4a9wxMOQuvsnZtUSYV1IcqEvKuEw1BNCsbUSEz6eHuHUiEpionte0/y15p9pKRmAtCiSW2m392f1i3q2zs84QA0Wie07rXQutdB6+xl73CEqNQkwRIOwWRIw5h8GtWot3coFY6qqhwOPc/ilXuIjUsCoJZ/daZN7EfPzi2kg7LILa/gUSe3vIJGRooKUR4kwRJ2p2Rcxph2QWpblcD5S3H89udeoqKiAPD2cueeu3oytF8Qzk5Sp6gq0+hc0LrXlvIKQtiJJFjCbqS2VcnFJ6aweGUwew9FAODsrOOuIV0YP7Ibnu6u9g5P2ItGg9bFN7e1yrWmtF4KYUcVKsFSVZU//viDrKwsunfvTvv27Yv82OzsbPbt20dsbCy+vr706dMHHx+fMo1XFM6UnZxX2yrb3qFUKOkZWSzfcIANO45jNCpoNBAU1IHH7+1OrZoyMrCqyi0Gam6tktIbQjiCCpVgLV68mHfffReA1157rcgJ1pkzZ3jmmWeIjY21LPP09OSTTz5h6NChZRavyE9VVZT0KJSMKFBVe4dTYRiMCpt3hbJ03X7SM7IAaN+6IdMm9kfv3IyaflLOosrRaNC6+qFzryvFQIVwQBUmwbpy5Qr//e9/GT16NOvXry/y47Kzsy3JVevWrenSpQuXLl0iODiYl156ibVr19KoUaMyjV3kUpWc3NpWOcn2DqXCUFWVA8fO8vvyPcQnpADQoG4Npt/dn45tG2NSNYTH2TtKUZ40Oje0HnXQuddGo5PbwUI4qgqTYP3f//0f/fv3Z8yYMcVKsNasWUNsbCyDBg3i22+/RZs319oPP/zA559/zrx58yytYqLsmLKTMCaHo5oM9g6lwjh3KY7fluyyTG1TvZoH943rzaDe7dDp8kaCSSNg1WCeusajLhoXX2mtEqICqBAJ1tKlS4mIiGDNmjUcOXKkWI/dvXs3AP/6178syRXAww8/zE8//WRZL8pG7i3Biyjp0fYOpcJISEpl8Ypg9hw8A3lT24wd1oXxI7rh7ibTl1Ql0lolRMXl8AlWfHw8H3/8MZ988gm+vr7FfvyFCxdwdXWlbdu2VstdXFxo164dISEhZGZm4uHhYcOoBYCqZOfdEkyxdygVgj4rhxUbD7J26xEMhtwq9gN6tuH+CX1kapuqRFqrhKgUHD7B+s9//sOwYcMYNGhQiR6fnJxMjRo1CvyQqlEjd9qQ1NTUQhOstLQ0UlL+SRBcXFxwcakarQiKolj9Wxym7BsYUyLklmARmEwmduw7yd83VWBv07I+0+8eQJOGtQBQCikRZl5e2Hphf0W9RhqdG1r3Wujca6HRuaICqkkubHkpzeedKB9leY3KYp8OnWCtWbOGiIgIVq9eXar9FPYXoHm5epvRbDNmzMDN7Z9hz5MmTWLy5MmliqeiCQsLK+Ej3fJ+RGEuXLjApk2buHbtGgB+fn4MGzaMwMBAsjRF78AeeU1auBxd0a5RUt6PsJeSf96J8lIW1ygyMtLm+3TYBCspKYk5c+bQo0cP/vrrL8vyc+fOAXDo0CEABg8eTJMmTQrdj7e3N3FxBX9L3bhxw7JNYRYsWEDHjh0tv1e1FqywsDDat2+PTnfnquCqkp1bODQntVziq8iuxCXx+/LdHA27AICnuyt3j+nF8AEdcHLSAelF2o9iyv3ibhmQhk5mQHFIBV0jjc4VrVstdB7St8pRFPfzTpS/srxGpjJoLXbYBOvChQskJyezadMmNm3alG/9jh072LFjB/Xq1bttgtWkSRMuXLjA2bNnadGihWW5oiicPHkSf39/vLwKn/TU29ub6tWr2+CMKi6dTnfHF7MpOwklORyNySBf9LeRlqFn6dr9bNoZimIyodVqGDGgA/fc1Qtvr5JPZ6LTIs+7g9NpwdndL7dvlWvB3RaE/RXl807YV1lco7K45g6bYNWuXZtHHnkk3/KoqCi2bdtG9+7dadeu3W2TK4DevXuzbds2fvrpJz755BPL8iVLlpCcnMyECRPKJP6qIneU4CWUjGgpHHobRkVhy+4T/L0mxFIotHP7JsyYPIB6tf3sHZ4oQxqtMwAuNbvi5Fr4H3NCiMrFYROs+vXr8/rrr+dbvnXrVrZt28bAgQN59NFHLcuTkpJYsWIFTZo0YfDgwZbl48eP5+uvv2bVqlUkJibSrVs3oqKiWL16NVqtloceeqjczqmyUZUcjCnhmLJv2DsUh3b81CV+XbKT2Ku5fWsa1K3Bg/cMoEObxvYOTZQhrUt1tB51UZ394MoJmXBZiCrGYROs4oqPj+eTTz5hxIgRVgmWt7c3c+fO5V//+hd79+5l7969ADg7OzNr1ixat25tx6grLlNOCsbk0zKX4G3ExiXx25JdHDt5EQBvTzemjOvN0H5B/xQKFZWKRuuE1r0WWve6aJ09QUalCVFlVbgEq1GjRjzyyCP55iH08/PjkUceITAwMN9junfvzqZNm9i8eTNXrlzB19eXwYMH07Bhw3KMvPJQMmIwpl2QW4KFyMjMYsna/WzccRzFZEKn1TJyUEfuuasnnh4yqrIy0jh7ofOoh9YtAI1W+u8IISpggtWiRYsCbx3WqlWrwOVmvr6+TJkypYyjq9xUkzF3lGBWor1DcUiKycT24JMsXrWXtHQ9AF3aN2XGPQOoW6v4RXKFg9No0bkFoPWoi9almr2jEUI4mAqXYAn7MBnSMSafQjXq7R2KQzoVGcMvf+0k6nICAPXq+PHQPQPp2Fb6WVU2Gid3dB510brXtnRgF0KIW0mCJe5IyYxHzTgHqlSVvlXC9VQWLttNyJHcInWeHq5MGdubYQOCcJKh3pWHRoPW1S/3NqCrjPoUQtyZJFiiUGpeQmVMjZQaS7fIzjGwatMhVm46hMGgoNFoGNY/iCnjelOtFPWshGPR6FzQutdG514XjZP0nxNCFJ0kWKJAqjELY9Ipe4fhcFRVJeRIJAuW7ub6jTTImzfw4XsH0biBv73DEzZiLrGgdfNHo5G/LoQQxScJlsjHlJ2EMTkck9EAyBx3ZlGXE5j/1w5OR14GoKafNzMmD6Bn5xZSlbsS0Gh1aN0C0HrUQ+ssBUGFEKUjCZawYkyPQkm/JCUYbpKWoefv1SFs2hWKqqo4O+uYMKIb40d0w9VFOjlXdP90Wq+DRisfiUII25BPEwFSgqFAlrILK4NJy5vepkfnFjw4eQD+NWRYfoUmndaFEGVMEiyByZCBMfmklGC4SeSFK8xbvIML0fGQN73Nw/cOon1rKU5bkeVWWq+TO+GyTF0jhChDkmBVcYr+GkpqBKpJpvMASE7NYNHyYHaG5Hbwd3dzYcq43owY2EHKLlRglkrr7rWk07oQolxIglVFqaqKknYBJSPG3qE4BEUxsWnXcf5aHUKmPnd+xUG92zJ1Yl98qnnaOzxREhoNWjf/3MTKpbq9oxFCVDGSYFVBqsmAMfk0puwb9g7FIZyOvMy8P7cTHZvb/6xpw1o8ev8gWjata+/QRAnk1q7Kuw2oc7V3OEKIKkoSrCrGZEjHeOMkqpJl71Ds7kZKOguX7mbPwTMAeHm6MXVCXwb3bYdOK7eRKhqtS7XcEgtSu0oI4QAkwapCFH08xpSIKj/ljaKY2LDjGH+vCUGflYNGA0P7BXH/+D54SxX2ikWjQesWkHcbUEZ2CiEchyRYVUBuf6vzKBmX7R2K3YWfvczPi/+5HdiiSW0evX8IzRrVsndoohhybwPWzbsN6GLvcIQQIh9JsCo56W+VKzk1g4XLdrN7fzgA3p5uTJvUj0G926HVShX2ikLr7I3Ws77cBhRCODxJsCox6W+VWyx0865Q/ly1j0x9ttwOrIgsowHry21AIUSFIQlWJSX1reDsxav89Mc2LkZfg7zRgY9PG0LzxrXtHZooAo3WGa1HXRkNKISokCTBqmRUVUVJv4iSHm3vUOwmLUPPHyuC2RYchqqCp4cr90/oy9B+7WV0YAUgRUGFEJWBJFiVSO58guGYsq7bOxS7UFWVnSGnWbhsN2npudP+DOjVhumT+lO9moe9wxO3o9Ggda2RexvQ1cfe0QghRKlJglVJqEY9hhthqMZMe4diF9Gxifz0xzbOnIuFvLkDH586hNYt6ts7NHEbGq0uryhoPZkbUAhRqUiCVQmYsm9gTD6FajLaO5Ryl5VtYOnaENZuPYpiMuHq4sQ9d/VizNDOMnegA9Po3NB51kfrXhuNVj6GhBCVj3yyVXBKxmWMaedBVe0dSrk7HHqeeX9uJzEpDYBuHZvx8JRB+PvJSDNHpXWpjs6zARrXGmg0Uh5DCFF5SYJVQamqCSX1LErmVXuHUu4Sk9L45a8dHDx+DgD/GtV4ZMogunZoZu/QREHM1dY966N19rZ3NEIIUS4kwaqAVJMB442TmHJS7B1KuTJPcfPn6n1kZxvQabXcNawLk8f0xM3V2d7hiVvkllnI618lZRaEEFWMJFgVjMmQgfFGWJUrHnr+Uhw//L6VizG5Na0Cm9Xl8WlDaFTP396hiVtonDxyW6vcaqHRSj84IUTVJAlWBWLKuo4x5XSVKh6aqc/mz9X72LjjOKqq4unhygOT+jG4T3uZ4sbBaF180Hk2QOtWw96hCCGE3UmCVUEoGTEY0y5Uqc7sB4+fY97i7SQlpwPQr3srZtwzAJ9qnvYOTZhJ/yohhCiQJFgOTlVNKCmRKPo4e4dSbq7fSGPen9s5dPw8ALX8q/P41KF0aNPI3qGJPBqtU940NtK/SgghCiIJlgPL7cx+ClNOsr1DKReKycTmnaEsXrUXfVYOOq2WccO7cveYHri6SCd2R/BP/ao60r9KCCFuQxIsB6UaM/Mqs+vtcGw9OfG7yb62lxoZGWTEe+Ia0AeXWv3LrNp2VGwCPyzcwtmLuS11LZrU4cnpQ6UTu4PQulRD69kArWtNqV8lhBBFIAmWA7JnZXYlM5b0E3MwZSWACk4mDYpBJTPlNFkxK/EKmoXOo57NjpdjMLJ03X5WbzqMYjLh7ubCtIl9Gdo/SCZmtjfz/ICeDdC6VLd3NEIIUaE4fIJlMBgIDg4mPDyc1NRU6tSpQ9++fWnWrGhFJePj4/nmm28KXFevXj2efPJJG0dcOkrmVYypkXbpzK4a9f8kV4DOpy0pmjb4qadRUk5hykog/cQcqnX93CYtWaciYvjh9y1cvZZ7C7Rbx2Y8et9gavhKZ2m70mjRuddG51kfjZNMki2EECXh0AnW0aNHee6550hMTLRartVqueeee3jnnXfueLsiJSWFv/76q8B1bdu2dZgES1VVlLQLKBkxdoshJ363JbnybPMSupp9iI7zpkHtNJTEvWSc/gJTVgI51/bgWnd4iY+TkZnFwmW72RZ8EgDf6p48et9genRuYbNzEcWXWxi0HjrPemi00udNCCFKw6ETrKtXr5KRkcHw4cMJDAzEy8uLCxcusGbNGv766y+6du3KuHHjirSvESNG0KtXL6tlNWo4Rr0e1aRgTAnHlJVYhK3LTs61vQA4+bTFJaAPiumfdS4BfciO3YQx5TQ58cElTrAOHD3Lz4u3k5yaAcCw/kFMm9gXTw8325yEKDaNkzs6D/PEy9JxXQghbMGhE6wuXbqwe/duqlWznry3b9++PPfcc5w8ebLICVaHDh24//77yyjSklOVHIw3wjAZ0uwdCqohd+odJ+/mBa53qtYit9CpIbXY+76Rks68xds5cCx3/sA6tXx5evowWreoX8qoRUlpnb3RejWUjutCCFEGHDrBql27doHLExJyb2M1adKkyPuKjIzk888/Jzs7myZNmjB8+HD8/PxsFmtJONq0Nxrn6kAsxrRzBa43pp7N265agesLoqoqO/adYsHSXWRkZqPTahk/oht3j+mBi7NDv/wqLa2rHzrPhmhdfewdihBCVFoV4htuz549bNmyBYPBwMWLFzl+/Dj9+vXj7rvvLvI+Vq5cafX7xx9/zIcffsjIkSPLIOI7M2UnY0w+aZeRgoVxCeiDMeU0xuRT5Fzbi65mH8u6nGt7Maaczt2uVt8i7S8+IZkfft9K2JloAJo1qsVT04fTuIGUXih3lorrDdE6SyV8IYQoaxUiwQoPD7fqqN61a1fefvttXFxcivR4b29vhg4dSosWLUhPTyc4OJgTJ07wyiuv0Lx5c5o3L/iWGEBaWhopKSmW311cXIp83NsxZsajGB0nuQLQBfRHG70SU1YCGae+QFt9M17aNqTHncKUl1xp3fzR+fez6p91K5PJxMYdx/lrdTDZOUacnXVMGdeHUYM6o9Npb/tYUTzm57Kw51Sj1aF1q53bcV3nigooStWZy9IRmJ9ved4dm1wnx1eW16gs9qlRVcef3C48PJzjx4+j1+s5f/4869evB+DX/2/v3uOiqvM+gH/OOTPDbbiJgoIiiI2iIoKX1DQUNVLbLopphrYqlRnb5Snbduspfbat9bF0vaxmmZaymFnY5mVVNK3s8YKKhZqSGKIYoILcYZjhPH/AzIrDzRyYM8zn/Xr1sjnnN6fv8RczH875nd/v448RHh7e5HtLSkpgMBjg7e1db/uiRYuwbt06zJgxA6+//rrF+06cOIGBAwciMDAQzs7/GYA9adIkxMbGWu3clEaqugzvS69Bqs6z2GdU+6Gw219hdGp83NTVq1fx1Vdf4fLlywCA7t2748EHH7T57VgiIqLGnD17FnFxcTh+/DgiIyOtcky7uIIVGhqK0NBQ8+sZM2bg4YcfxvLly/HRRx81+V5394bnVJozZw7WrVuHCxcuNPn+DRs2YMCAAebXVruCVXwexvJf7/g41ucJuetiVOd9B33+QZSXl8HV1Q0a3xFQ+41EJ8kFgOWAfIPRiO0px/H5jkMwGIy1E4ZOuhfR94RBFIUG30N3zlgDZOS7Q+dbAkmsW8rGNQCia2cIAidqVQKj0Yj09HSEhYVBkviUplKxn5SvNfuopsb6t1bsImDdqnfv3vD09MQvv/zym49RUVG7BE1zneTu7g5PT+vPYi2LAqDU7z/RBaqu90Hjfx8u5brDt3Ptl3djfrmUj9Wf7MEvl/IBABH9gvHU42PRsQMnDG0rKictNO7dIDr78olAhZIkiV/cdoD9pHyt0Uet0eeKDlh79+7F4MGDLQLO1q1bcePGjRbN5r5v3z5ERkbWu0VYVlaGd955B6ibbJR+m2qDEck7j2Drv4/CWFMDN1cnzJo6GvfeHcov+TYiajwAyND4RPBLgYhIQRQdsBITEzF//nz07dsXAQEBqKqqQkZGBjIzMwEAcXFx5ra5ublYtWoV+vbti6lTp5q3JyUl4aWXXkKfPn3QtWtXlJSU4MSJE7hx4wa8vLwwffp0m5ybvbuQnYd/fLwb2Tm1k6MOGdAT8dPHwNuTT6i1BdHZB5JbIGRJC2SftHU5RER0C0UHrPvuuw/nz59HamoqUlNTzdu9vLzw8ssvY8KECeZthYWF2Lx5M2JiYuoFrHHjxuHcuXM4fvw4jh8/bt6u0+mwaNEi+Pr6tuEZ2b/qagM+33EEX+4+ipoaGe5aF8yZFo3hg3S8atXaGphqgU88EREpk6ID1vTp0/Hoo4/i9OnTyMrKgizL6Nq1K/r3728x0Lxz585YsGABAgMD622fNm0aJk+ejFOnTuHixYsQRRF33XVXvUHz1DKZWbn4xye7cenKdQDAsIE6zHksGp7uXBC4VZkXXw6EoOKSQkRE9kDRAQsAVCoVwsPDm52Owdvbu9GlcNRqNSIiIhAREdFKVbZv1dUGfPbv/1y18nR3Rfz0aAyN1Nm6tHZNECWILv6Q3LpBkO78yVUiImo7ig9YZFu//vor1q9NNo+1Gj6oF+Y8Fg0PrYutS2u3BFEN0TUAkltXCCJ/RImI7BE/valBBqMRn++ofUKwpqYG7loXPDl9DIYN5FWr1iJIGkhu3SC6+EMQ+UQgEZE9Y8AiAIBs1KOmonbi0yt5BUja+j0u516HrxvQv093TJkwFO5aJxhLL0J06cJbVlYkSM6QtIEQXTg5KBFRe8GARQCAmopfUZz6Eiqr9KiuqsaUnjKEuwQ4OTvDRZMO+ex2FNe19Rj0HiRtdxtXbP8ElWvtE4EufnwCk4ionWHAIgBA/vViVJdVwGCofexfrVbB1cUJNbIIQPHLVdoVQa2tDVbOnRisiIjaKQYsB1dTI2P3gZNI2bMDCUONEAQBBd5PIDxiKGpkAReuuaFHxzKg8grKzrxn63Ltmqh2h6QNgujsY+tSiIiolTFgObBrBSVY9clupJ/NRmd3I9QqCa6uzgiMHAZJ2x3GGsBQ6g5JW6LcdRPtgKjxhKTtDtGpg61LISKiNsKA5YBkWca3h3/CR59+jYpKPTRqFSZPGAqtkA7wjpXViE7ekNy6Q3TysnUpRETUxhiwHExRSTk+SNyLoyfPAwB0Pbog4ff3w9etGMXHbF1d+yA6dai9YqXxbEFrIiJqjxiwHMjxHy9g9cY9KCouhySJmPq74XgwZhAkUYSxtLgFR6Cm1C7A3B2ixsPWpRARkY0xYDmAiko9PtnyDfYdTAcAdPP3wR9mj0dwt4YXujaWX6n9swZQVbrBWFo7yJ0aJjp3rL1ipXa3dSlERKQQDFjt3LnMK1ix/t/Iu1oEQQAmjhmIxx6+Bxp1411vflpQBnxqBJRdlDk2qwG1wSoIolpr61KIiEhhGLDaKYPRiC92HMEXO49AlmX4eLsjYVYM+vUKtHVpdk907lR3xYrBioiIGsaA1Q5dySvE8nU7kZmVBwAYOaQ35jwWDTdX50bfI7p0gceg+vNcGWtgngdLEuu3dUQMVkRE1FIMWO2ILMvYdzAdH392AFV6A9xcnfDk9DG4Z3DvZt8rSBrL5W9umgdLcuB5sBisiIjodjFgtRPFpRV4f+MepJ7MBAD07dUNCb+/Hx07cOD1b8UxVkRE9FsxYLUDP5y5iH98vAuFRWWQJBGPPXQPfjduEESRI9N/CwYrIiK6UwxYdqy62oCkL7/H9r3HAQABnTvg+TkTEBzY8PQL1DTR2acuWPGqHxER3RkGLDt1+dfr+Pvanbh4+SoA4L6ocMyMvRdOGrWtS7M7tTOvB3GCUCIishoGLDsjyzL2flc7kF1fbYC71gXzZt6HQeEhti7N7ohO3nXBikvaEBGRdTFg2ZGS0gq8vzHFvI5g/9DuSJgVA29PjhW6HaLGE5I2mIswExFRq2HAshOnMy5h+Uf/RsGNUkiSiMcfGYGJYwZyIPttEDUedcHK29alEBFRO8eApXBGYw227DiE5J1HIMtAFz9vvBA/AT0C/Wxdmt0Q1FqotMEQnX1sXQoRETkIBiwFu3q9GMs+2olzmbULLY8e3hezpo6Gi7PG1qXZBUHlCkkbBMmFT1USEVHbYsBSqMMnMvD+xhSUlVfBxVmDpx4fixFDmp+RnQBBcq4dvO7iB0HgLVQiImp7DFgKo6824JMt32DPNz8AAHoGdcYL8RPg14kDspsjSBpIbt0hunaBIDjw2j5ERGRzDFgKkpNbgKUfbsfFy9cAAA/dNwjTHr4HKkmydWmKJohqSNpAiK4BDFZERKQIDFgKceDQaazd9DWqqqrh4e6CP8wajwF9g2xdlqIJogTRtSskt24QRP6vTEREysFvJRurrKrG2qR9+ObwGQBAv17d8Nyc8ZzbqimCCMnVH5K2OwSRM9cTEZHyMGDZUHbONSz5cDtyfi2AIAiY+rtheHj8EEgib3M1SBAgOftB0gZBUDnbuhoiIqJGMWDZgCzL2HvgCNZu2Ap9tQHeXm54Yc5E9NF1tXVpiiU6d4TKvQcElautSyEiImqW4gPW9evXsW3bNpw9exZFRUXw9/fHvffei6ioqNs6zqlTp5CcnIycnBx4e3sjJiYGo0ePbrW6G1NRUYHVq1fjwIEDAIDwPt3xh9nj4enO4NAQUeMFyb0HF2ImIiK7ouiAdfDgQcydOxfV1dX1ticmJmLYsGH44IMPoNE0P+lmcnIyXn/9dRiNRvO2rVu3YsaMGXj99ddbpfbGnDlzBgcOHIAoCJj20D14KGYwl7tpgKDWQuXeA6JTB1uXQkREdNsUHbCKiorg5+eH+++/H7169YJWq8WFCxewYcMGHDp0CJ9//jmmT5/e5DHy8vKwcOFCAMCcOXMwZMgQZGVlYdWqVdi4cSNGjRqFESNGtNEZAQMHDkRcXBx6B3mgVzeOI7qVIDlDcg+G5MKlgIiIyH4pOmCNHDkS999/P6Sb5oGKjo5GaGgoZs+ejYsXLzZ7jOTkZFRWVmLu3Ll48cUXzduDg4Px1FNPISkpqU0DFgA8+uijMBRlwFh+pU3/u0pWO5dVd4iu/pzLioiI7J6iA5aHh+W4G1mWcfToUQBAv379mj3GsWPHAADTpk2rtz0qKgr+/v5ITU21Wr10+ziXFRERtUd28Y22Y8cObNmyBXq9HtnZ2SgsLERcXBwmTpzY7HsvXboEDw8PdOnSxWJfr169sH//fty4cQNeXg0vRVNSUoKioiLza41G06JxX80x1sgw1tzxYVqVqb5WqVMQILl0hugWCEHSoEYGcNMYOWoZ07hCI//uFIt9ZB/YT8rXmn3UGse0i4CVk5ODQ4cOmV9HRERg3LhxEFswX1RZWVmDV8IAwN3d3dymsYA1c+ZMODv/Z6zUpEmTEBsb+xvOosEKrHSc1pWR31p1lgI400rHdizp6em2LoGawT6yD+wn5WuNPsrIyLD6Me0iYE2cOBH9+vVDeXk5Lly4gKSkJMyaNQurVq1qdqoFSZJgMBga3GfarlI1/tewYcMGDBgwwPzaWlewDMXnYSz/9Y6P05qMNbXhSudbAskKw6JEjTskt2CITp7WKI/qfutKT09HWFhYvbGKpBzsI/vAflK+1uyjmhrr36qxi4AVEBCAgIAA8+sHH3wQ0dHR+PDDD5sNWB06dMDPP/+M6upqqNX1l1XJzc2FKIqNXr1C3VUuT0/rBwJZFAA7GcstibijgCWoXCBpgyG5+FqzLLqJJEn8UlA49pF9YD8pX2v0UWv0uZ18xdfn5+cHNzc35ObmNtu2V69eMBgMFoPZi4uLcerUKQQFBcHJyakVq3VcgqiGyqMn1B0HM1wREZFDUXTASkpKQmZmZr1tVVVVWLFiBYqLixEcHNzsMcaOHQsAePfdd82D1Y1GI9555x3o9XrzfrIiQYTk1g3qTndDcuvKaReIiMjhKPoW4Z49e7Bw4UL4+voiICAAer0eWVlZKCsrgyRJiI+PN7fNzs7GG2+8gUGDBiEhIcG8fcyYMQgLC0N6ejqio6PRq1cvXL58GXl5efD29sasWbNsdHbtk+jiC5W2BxdjJiIih6bogDVjxgxUVFTg5MmTyM/PN28PDQ3FK6+8gmHDhpm3lZWV4dChQxZPDIqiiNWrV+PVV1/FwYMHcfz4cQBAz549sXjxYnTowKVYrEHUeEBy78k1A4mIiJQesMaMGYMxY8agsLAQFy9ehCzL6Nq1Kzp16mTRNjAwEOvXr4ePj4/Fvk6dOuGjjz7ClStXcOXKFXh7eyMkJKSNzqJ9q13apgfHWBEREd1E0QHLxNvbG97e3k22cXNzw/Dhw5ts4+/vD39/fytX55gEUQXJLRAix1gRERFZsIuARQoiCJBcukDSBkGQ7nw+MCIiovaIAYtaTHTyrh1npXazdSlERESKxoBFzRJUrlB7hkB0thzfRkRERJYYsKhRglj7v4faJxJiE8sJERERUX0cnUyWBAGSqz/UHQfVvRRsXREREZFd4WUJqkfUeEHy6AlRrYXRaLR1OURERHaJAYsA03xWHiGQnC3nGCMiIqLbw4Dl4ARRgugWCMmtG+ezIiIishIGLAcmuvhC5R4CQXKydSlERETtCgOWAxLUWqjce0J08rJ1KURERO0SA5YDEUQVJG0wRFd/PhlIRETUihiwHIEgQHLpDMm9BwRRbetqiIiI2j0GrHZO1HhA8rgLotrd1qUQERE5DAasdkoQ1ZDce0By7WLrUoiIiBwOA1Z7UzcLu6QNNi91Q0RERG2L38DtCG8HEhERKQMDVjvA24FERETKwoBl5yTXLnw6kIiISGEYsOyUoNZC5aGDqPGwdSlERER0CwYsOyOIUt1koQGcLJSIiEihGLDsiOjcCSqPnlw7kIiISOEYsOyAIDlD5XEXRGcfW5dCRERELcCApWSCAMmtGyRtEARBtHU1RERE1EIMWAolajwheeggqt1sXQoRERHdJgYshRFEVd2cVv62LoWIiIh+IwYsBRFdfKFy7wlB0ti6FCIiIroDDFgKwEHsRERE7QsDli0JAiTXgLqFmSVbV0NERERWwoBlI4LKDWqfSC7MTERE1A4xYNmI5BZg6xKIiIiolXByJSIiIiIrU/QVLL1ej/379yMlJQUXLlxATU0NAgMD8cgjj2D06NEtOsYvv/yCOXPmNLhPp9Ph/ffft3LVRERE5OgUHbD+67/+CykpKfW2/fTTT9i9ezceeOABvPfee80eo7q6Gjk5OQ3u8/LyslqtRERERCaKDliCICAmJgbjxo1DUFAQVCoVvv32W6xYsQLbt29HbGwshg0b1qJjzZ07F1OmTKm3TaPhfFNERERkfYoOWEuWLIFara63LTQ0FHq9HitXrsS5c+daHLA8PDzQtWvXVqqUiIiI6D8UHbBuDVcmAQEB9f5siV27dmH79u2oqqpCcHAwHnnkEYwdO9ZqtRIRERGZKDpgNcRgMGDTpk0IDg5GVFRUi9/3448/mv89MzMTe/fuxWOPPYYFCxY0+b6SkhIUFRWZX2s0Goe5tWg0Guv9ScrDPlI+9pF9YD8pX2v2UWsc064CVk1NDV577TVkZmYiKSmpxUFn+PDhiI2NxV133YXS0lIcPHgQ69atw6ZNmxAVFdXkE4kzZ86Es7Oz+fWkSZMQGxtrlfOxF+np6bYugZrBPlI+9pF9YD8pX2v0UUZGhtWPaTcBS6/X4+WXX8bhw4exfv169O7du0XvCwkJwfr16+tti4yMRHBwMF5++WXs2rWryYC1YcMGDBgwwPza0a5gpaenIywsDJLEpXyUiH2kfOwj+8B+Ur7W7KOamhqrHg/2ErBu3LiBefPm4ZdffsGGDRtaHK4ANNoJplCVm5vb5Pvd3d3h6el5mxW3L5Ik8QNH4dhHysc+sg/sJ+VrjT5qjT5XfMDKyclBfHw8ysrKkJiYiJCQEKsc9+effwbqni4kIiIisiZFL5Vz5swZTJ06FXq9Hv/85z9/U7hatmwZUlJSUF5eDgCQZRlHjhzBK6+8AgAtnubBEen1enz++efQ6/W2LoUawT5SPvaRfWA/KZ+99ZGiA9abb76Jq1evorS0FE888QSio6Pr/XPzMjfnz59HdHS0xVOBP/74IxISEhAREYFhw4YhPDwcM2fORHZ2Nvr16+dwA9Zvh16vR3Jyst38z+yI2EfKxz6yD+wn5bO3PlL0LULTY5M3btzAjRs3LPbfPH2CaUmcgoKCem1efPFFeHl54ZtvvjHv69ixIx588EEkJCQ4zIB1IiIiajuKDljvv/9+k0nV3d3d/O8hISHYt28fXF1d67Xp16+fec3CgoICCIIAb2/vVqyaiIiIHJ2iA5avr2+L22o0mmaXwunQoUOLj1dRUQHULS7tqEpKSlBZWYmTJ0/WC7OkHOwj5WMf2Qf2k/K1Zh+ZvutN3/3WIMiyLFvtaO3IP//5T8TFxdm6DCIiImojiYmJePzxx61yLAasRly7dg27d+9GUFAQXFxcbF0OERERtZKKigpkZWUhJiYGHTt2tMoxGbCIiIiIrEzR0zQQERER2SMGLCIiIiIrY8Ais4KCAuTm5qKkpKTRNrIso6CgwG4memtvioqKUF1d3Wy74uJilJWVtUlN9B9VVVUoLi5uUdvy8vJ6c/mR9eXn5ze73qxJUVGRecUPa7alphUWFiI3N7fZ7xRZllFYWIiWjmoqKytr8c9ia2HAIgDApUuXMGbMGERFRWHVqlUW+w0GA5YtW4ahQ4eaZ8SfM2cOLl68aJN6HUlJSQneeecdDBs2DEOGDEFERATi4+Nx5swZi7ZffvklxowZg8GDByMyMhIPPfQQDh8+bJO6HYXBYMC6desQHR2N8PBwDB48GAMHDsQbb7yB/Px8i/ZpaWmIjY1FREQEhgwZglGjRuHTTz+1Se3t0Q8//IBFixZh3LhxGDlyJKKiolBVVdVo+02bNmHUqFHmn60pU6bg5MmTd9yWGpednY33338fkydPxtChQxEVFYW0tDSLdpWVlfj8888xY8YMREREYOjQoejfvz/i4uIa/Vw7dOgQHnroIURGRmLw4MEYO3YsvvrqqzY4K0sc5E6QZRm///3vkZubi6ysLMyePRt//OMf67VZuHAhkpKSAABeXl4oKytDdXU1/Pz88OWXX97WHGPUckVFRYiLi0NGRgZQN7mu0WhEeXk5YmJisHz5cnPbL7/80txvWq0WRqMRFRUVUKvVSExMxIABA2x2Hu3ZzT8brq6uUKvV5itTQUFB2LZtm3nFiLNnz2LatGmoqKiAs7MzNBqN+bfsN998E9OnT7fhmbQP0dHRyMnJAQCoVCoYDAb8+OOPcHJysmi7ceNGvPXWWwAADw8P6PV6VFZWwtXVFZs3b4ZOp/tNbalpL774Inbu3Anc1EcbNmzA3XffXa/dsWPHzFMmCIIAT09PFBUVQZZlCIKAZcuWISYmxtz++PHjeOKJJ1BdXQ0XFxdIkoTS0lIAwHvvvYcHHnigTc+TV7AImzdvxs8//4xXX321wf2ZmZnYtGkTvLy88Nlnn+HIkSM4fPgwYmJikJeXhw8//LDNa3YU77zzDjIyMtCjRw9s2bIFx44dw4kTJ7Bu3Tr06dPH3E6v1+N///d/IYoiFi1ahGPHjiE1NRXPP/88qqursWjRIpueR3tVU1ODL774Ai4uLli7di3S0tJw9OhRpKSkoHfv3sjKykJqaqq5/eLFi1FRUYHZs2cjNTUVqamp+Mc//gG1Wo0lS5bwtq4VhIeHY/78+UhJScHQoUMbbVdaWoqlS5dCrVZj5cqV5v6YM2cOysvLzSuA3G5bal5gYCCefvppbNmyBXPnzm20nYuLCyZPnozExESkpaXhyJEjOHr0KGJjYyHLMtasWVOv/aJFi1BdXY0//OEPSE1NxbFjx7B48WJIkoS//e1vLRpeYVUyObQrV67IkZGRckpKipyWlibrdDr5b3/7W702K1askHU6nbxx48Z620tKSuSIiAh5xIgRbVy1Y8jPz5f79Okjh4WFydnZ2U22/e6772SdTie/9NJLFvumTJki63Q6+cqVK61YrWMyGo1y//795SlTpljsW7lypazT6eTvv/9elmVZLiwslENDQ+X77rtPNhqN9dq+9dZbsk6nk3fu3NlmtTuC2bNnyzqdTq6srLTYt2PHDlmn08kLFy6st72mpka+//775dDQUPnGjRu33ZZuz/Lly2WdTicfPny4xe8xGo3yoEGD5OHDh5u3Xb58WdbpdPKkSZMs2v/xj3+UdTqdfPDgQavV3RK8guXg/vu//xvjxo3D2LFjG21jGuszatSoetu1Wi0GDx6M/Px8XLt2rdVrdTRHjhyBwWDA2LFj0a1bNxgMBhQUFKCmpsairamPRo8ebbHP1G+nT59ug6odiyiKePjhh5Geno5Vq1YhIyMDWVlZ2LFjB5KSktC9e3cMHDgQAHDu3DkYjUbce++9EMX6H72mfmtoXB21jsY+1wRBwKhRo2A0GnHu3Lnbbkutz2AwQJblelfxTUvd3NpHsOFnoKLXIqTWlZycjPPnz2Pp0qVNtsvPz4ckSQgICLDYZ1r/8erVq1ab/ZZqZWVlAQAGDx6MVatW4cMPP0R5eTnc3NzwwAMPYP78+eb1uEyDqbt162ZxnJv7iKzvjTfeQNeuXbF69WosW7bMvP3hhx/G/PnzzWN/2EfKcjv9wb5TljVr1qCyshLPPfeceVteXh6gsD7iFSwHlZ+fj0WLFuHtt99udtFMvV4PtVoNQRAs9pkG7zb1lA79NpWVlQCAvXv3YtmyZTAajXB3d0dZWRk2b96MJ5980nw1y/SIs6k/bmb6gmcftY6MjAxs3boVZWVlcHZ2hoeHBwBg//79OHDggLmdqY8aGmzNPmp7TfXHrZ9rt9OWWldSUhJWrVqFN998E2FhYebtpvFVSvoMZMByUAsWLMDw4cPRo0cP5ObmIjc3FwUFBUDd/CG5ubnmeV5cXV1RVVUFg8FgcRxTG67XaH3Ozs4AYB4I/cMPP+DYsWPYtm0bevTogbS0NHz33XfATX//DQ2SvrkfybrKy8vx5JNP4vr16/j444/xww8/IDU1FSkpKejRowdee+01nDhxAmimj0zb+HPUdlryM2NqczttqfWsXLkSb731Ft566y1MmTKl3j4lfgYyYDmgS5cuYd++fdi5cyeioqLM/zzzzDNA3VOFUVFRSE5OBgB06dIFsizjwoULFscybWvo9iHdGdNl7fHjx2Ps2LHmK4g6nQ7PPvsscNPYkC5dugA39cfNMjMzAQD+/v5tVrujOHHiBK5evYrp06dj2LBh5u2BgYH485//DADYs2cPcNPfv6k/bmbqN/ZR22mqP0zbTJ9rt9OWrM9gMOC1117D6tWr8e6772Ly5MkWbZT4GciA5YAEQYCfn5/FP6a5rFxdXeHn52dO++Hh4QCA7du31ztOTk4O0tLS0LNnT2i1WhucSfsWGRkJ1M2FdSvTNtPlcNMcV7f2UXV1NXbv3g2VSoV+/fq1QdWOxfSbcUMzRhcWFtZr07t3bzg7O+Prr7+2mAV827ZtAICIiIg2qJrQxOdaRUUFvv76a7i6uprntrqdtmRdZWVlmDt3Lr766issX74cEyZMaLBdWFgYJEnC7t27LWaFN/VbW88FyEHuDqhr16749ttvLbafPHkSU6dOxbRp0+pNNDphwgQsXboU69atg4+PD0aNGoXc3Fy8/fbbqK6uxqRJk9r4DBxDYGAghgwZgv379+Pdd9/FxIkT4eTkhOPHj+Pvf/87AJivmoSHhyMkJASHDx/GwoUL8fjjj6OqqgqrV69GdnY2YmJi4OXlZeMzan/69esHURTx6aefomPHjhg9ejQ0Gg1OnTplnhupf//+QN0t3/Hjx2Pr1q1ISEjACy+8AK1Wi61bt2LXrl0ICAiwmGiRbl9RUREqKiqAm8ZO5eXlQaPRmH+5RN3PTpcuXZCSkoLFixdj0qRJKCsrw7Jly3D16lXExsaab9PfTltqXnl5ufmXEtNEoKal2gCgY8eOUKlUKCgoQHx8PM6dO4e//OUv6Nu3r8XSR507dwYAeHt7Y9SoUdi3bx9eeOEFPPvss3BycsKmTZvw/fffQ6fTmX8W2wpnciczU8BqaCb3xMRE/OUvf7F4T//+/ZGYmNjg4E+6c5mZmZg+fTpu3Lhhse+JJ54w34ZC3azHs2bNsvjtzcfHB5999pn5liNZ1+LFi7F27doG9w0YMAAbN240X2nMz8/HlClTLL4kVCoV1qxZgxEjRrRJze3Zq6++iq1btza4z93dHceOHTO//vbbb/HMM89YjC/19/fHli1b6j0ZfTttqWmbNm3CggULGt2/c+dOhISEYNeuXXj++eebPNbp06ehUtVeK7p06RIeffRR83hiEycnJ3zyySdtfoWYV7DITKPRwM/Pr8GnCuPi4hAQEIDExERkZ2dDq9Vi9OjRiI+PZ7hqRSEhIUhOTsaaNWtw4sQJVFZWonv37pg8ebLFpfJBgwZhy5YtWLNmDc6cOQOVSoWBAwdi3rx55t/yyPrmz5+PESNGYNOmTcjOzkZJSQm6dOmC0aNHIy4urt5TTb6+vvjiiy+wevVqHD16FHq9Hr169UJ8fHyb/3bdXnl6epqvUt3q1s+2e++9F5s2bcLatWtx7tw5aDQaDBkyBPPmzYOPj89vbktNMw1DaYxarQbqBq431Q51Q15MunXrhuTkZKxevRrHjx+HwWBA37598fTTT6NXr15WPIOW4RUsIiIiIivjIHciIiIiK2PAIiIiIrIyBiwiIiIiK2PAIiIiIrIyBiwiIiIiK2PAIiIiIrIyBiwiIiIiK2PAIiIiIrIyBiwiIiIiK+NSOUTUrmVmZuLs2bP1tomiCK1Wix49eiAgIMBmtRFR+8WARUTt2r59+/Dee+81uj80NBSvv/46Bg0a1KZ1EVH7xoBFRA7B19fXHKKMRiNyc3ORnp6On376CbNnz8bmzZsRGhpq6zKJqJ1gwCIih9CnTx8sXbq03rbz589jxowZKCgowNq1a5u80kVEdDs4yJ2IHFbPnj0xdepUAMCZM2cabVdcXIxDhw5hz549SE1NRWVlZRtWSUT2iFewiMihubm5AXUD329VUFCAt99+Gzt37oTRaKz3nnnz5iE+Pr5NayUi+8GARUQOS6/XY9euXUDdYPebFRQUYOrUqcjOzoZKpUJYWBg6deqEnJwcnDt3DosXL0ZJSQlefPFFG1VPRErGgEVEDiE/Px87duwAABgMBuTm5mLbtm34+eefodVq8fTTT9dr/9e//hXZ2dno168flixZgu7du5v3/d///R+eeeYZfPDBB3jkkUcQFBTU5udDRMomyLIs27oIIqLW8sEHHzQ5eH3kyJF45ZVXoNPpzNsKCwtxzz33AAD2798PPz8/i/etWLECK1euxHPPPYdnn322laonInvFK1hE5BBunqahrKwMp0+fxrVr13D27FnU1NTUa3vy5EkYjUYEBAQgLS0NAGD6XdT0p2mge0ZGRhufCRHZAwYsInIIt07ToNfr8T//8z/YsmULEhIS8K9//cs84P369esAgJycHDz//PNNHrekpKSVKycie8SARUQOSaPR4M0330RaWhrOnz+P9evXIyEhAQDg5OQE3HLVqzE331okIjJhwCIih6VWq/HCCy8gISEB69evx8yZM+Hh4YG77roLACAIgsXkpERELcGJRonIoY0dOxY6nQ6lpaXYsGEDAKB3797Q6XTIy8vDkiVLGn1vQUEBCgoK2rBaIrIXDFhE5NAEQcDcuXMBABs3bkRpaSkAYMGCBVCr1VizZg0mTpyI5cuXY8uWLfj000+xdOlSxMfHY+TIkTh16pSNz4CIlIi3CInI4Y0fPx7Lly9HVlYWkpKS8NRTT2HgwIFYu3Yt/vSnP+H8+fM4f/68xft8fHzg4+Njk5qJSNkYsIioXQsJCcGECRPQp0+fRtuIoohXX30VX331FfLz883bhw4dij179uCbb77BiRMncP36dbi6uqJz584ICwvD3XffDUmS2uhMiMiecKJRIiIiIivjGCwiIiIiK2PAIiIiIrIyBiwiIiIiK2PAIiIiIrIyBiwiIiIiK2PAIiIiIrIyBiwiIiIiK2PAIiIiIrIyBiwiIiIiK2PAIiIiIrIyBiwiIiIiK2PAIiIiIrIyBiwiIiIiK2PAIiIiIrKy/wdAzWPYnNTWFAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "Res = sorted({Re for (Re, _) in results})\n",
    "fig, ax = common.fig_single()\n",
    "\n",
    "Re_line = np.linspace(min(Res) * 0.8, max(Res) * 1.2, 100)\n",
    "cb_line = np.array([churchill_bernstein(r) for r in Re_line])\n",
    "ax.plot(Re_line, cb_line, **common.markers.exp_line(), label=\"Churchill-Bernstein\")\n",
    "common.band(ax, Re_line, 0.85 * cb_line, 1.15 * cb_line, label=\"+/-15%\")\n",
    "\n",
    "for D, shape in zip(sorted({D for (_, D) in results}), common.markers.shapes()):\n",
    "    Rs = [Re for (Re, Dd) in sorted(results) if Dd == D]\n",
    "    nu = [results[(Re, D)][\"nu_avg\"] for Re in Rs]\n",
    "    ax.plot(Rs, nu, **common.markers.sim(shape), label=f\"Nassu D={D}\")\n",
    "\n",
    "ax.set_xlabel(\"Re\")\n",
    "ax.set_ylabel(r\"$Nu_D$\")\n",
    "ax.set_title(\"Surface-averaged Nusselt vs Churchill-Bernstein\")\n",
    "ax.legend()\n",
    "fig.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "69128f28",
   "metadata": {},
   "source": [
    "## Local Nu(theta) distribution\n",
    "\n",
    "The wall-referred local Nusselt around the cylinder, measured from the front\n",
    "stagnation point (`theta = 0` faces the inlet). The signature to confirm:\n",
    "\n",
    "- a **front-stagnation peak** near `theta = 0`,\n",
    "- a **minimum near separation** (around `theta ~ 80-90 deg` for laminar Re),\n",
    "- a mild rear recovery in the wake.\n",
    "\n",
    "With the `(r/R)` wall referral the angular mean of this curve tracks the\n",
    "control-volume `Nu_D` to within a few percent, so the distribution is\n",
    "quantitative, not just qualitative. Both resolutions are overlaid per Re."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "7506b32e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-29T17:44:38.650302Z",
     "iopub.status.busy": "2026-06-29T17:44:38.650230Z",
     "iopub.status.idle": "2026-06-29T17:44:38.758451Z",
     "shell.execute_reply": "2026-06-29T17:44:38.758015Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = common.fig_double() if len(Res) <= 2 else common.fig_triple()\n",
    "axes = np.atleast_1d(axes)\n",
    "linestyles = [\"-\", \"--\", \"-.\", \":\"]\n",
    "for ax, Re in zip(axes, Res):\n",
    "    for D, ls in zip(sorted({D for (_, D) in results}), linestyles):\n",
    "        if (Re, D) not in results:\n",
    "            continue\n",
    "        r = results[(Re, D)]\n",
    "        ax.plot(r[\"theta\"], r[\"nu_theta\"], **common.markers.sim_line(linestyle=ls), label=f\"D={D}\")\n",
    "    ax.axhline(churchill_bernstein(Re), **common.markers.exp_line(), label=\"CB avg\")\n",
    "    ax.set_xlabel(r\"$\\theta$ [deg, 0 = front stagnation]\")\n",
    "    ax.set_ylabel(r\"$Nu(\\theta)$\")\n",
    "    ax.set_title(f\"Re = {Re}\")\n",
    "    ax.legend()\n",
    "fig.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8929302c",
   "metadata": {},
   "source": [
    "## Temperature field\n",
    "\n",
    "The time-mean temperature on the spanwise mid-plane for the finest variant,\n",
    "showing the thermal boundary layer on the heated cylinder and the warm wake.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "74c79501",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-29T17:44:38.759397Z",
     "iopub.status.busy": "2026-06-29T17:44:38.759299Z",
     "iopub.status.idle": "2026-06-29T17:44:39.163567Z",
     "shell.execute_reply": "2026-06-29T17:44:39.163224Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Nnj0bf/75p9Hr4efnh2nTplm1HWfy9PQ0Wyb383L27FkcOXLE6mPr0aMHateubfXjpMrKysLFixcBQLQfUEhICFq0aIGYmBgcPXpU+EC29XHOMGbMGKxbtw6pqan4999/MWzYMEmPc8ZrFBwcjMTERItXseqb0A2/gJb4c83z8jen0ZADFlFosgPHcRg1ahSio6PBsizat2+P8PBwZGZm4siRI4iNjcXgwYOxadMm0atGLly4gH379iE8PBwtW7YEdFegJCUlYdy4cejRowf+/vtvNGvWDA0bNkR6ejp27tyJq1ev4ttvv8Xvv/9uts3z589j3759qFatGjp27AiFQoH//vsP169fx+TJkxEcHGzU6dTec9DvLywsDK1atUJoaKjQ/yQ7Oxv79+8XrpwJCwuDWq3G9evXceLECcybNw8hISHCm2avXr0QEBCAzZs3IywsDH369BH2ExoaKtOrVvQxnzhxAkOHDoVarUaVKlXQqlUrBAcH48aNG4iOjsb06dOhUCjwzjvvFLuf6tWr491338WVK1dw4MAB1KtXD88884xZuXnz5kGr1Zotl/NYAGD58uX47bffAABNmjRBixYtkJWVhX379mH8+PFGtZslLSEhAQcPHgQANGvWzGid3M8LAJw6dcoo4EoVHh7u0NAUHx8Pnufh6elpsXk3KioKMTExiI+Pt/txzuDt7Y127dph27ZtOHXqlOTQ5IzXqGfPnrh48SJWrFiBbt26GdXob9myBUlJSQgLC0PDhg2F5a78XBP5UWiyw7p16xAdHY1y5cph8eLFiIyMFNbl5ORg7NixOHDgABYsWIDx48ebPf7Ro0d444038NlnnwkdIseOHYuePXsiMTERCxcuxLfffmtUO/Taa6/h1Vdfxe7du5GZmQk/Pz+jbSYlJaFr166YPn06VCoVoAtGn332GdavX49p06ahS5cuwjcme88hKSkJvXv3xnfffWdWI+Dr64t58+ahffv2Zp2cT506hf/9739YuHCh8KbZr18/VKpUCZs3b0b16tVF+0XIwdIxa7VaTJo0CWq1Gm+88QYmTpxo9KZ57NgxDB8+HDNnzsRLL71UbHNnzZo1MW7cOKxZswYHDhxAgwYNRM9p4cKFZqFJ7mPJyckRQvaYMWOM+lFNmDABQ4YMwfnz54vchqOcPXtWaLbMz8/HnTt3sGfPHuTm5qJBgwZ4+eWXhbJyPy96TZs2tekKWEcGJuiatgGgXLlyFms/9DXO+rL2PM5Z9M/bo0ePJD/GGa/Rm2++idjYWOzYsQPPPfccOnXqBF9fX1y+fBmHDx9GuXLl8Pvvvxv9zZX4c02DWzoVhSY7rF27FgAwceJEo7AB3bepL774AgcOHMCuXbtEA0dwcDAmTJhgdAVJSEgIOnfujI0bN6J169ZmzWnNmjVDnTp1cP36ddy8edOsqlelUmHy5MlCYIKuSnnChAnYvXs37t69iwsXLqBJkyaynIOPjw8+//xz0SYUHx8fdOzYEZmZmTh58iRu376N7OxscLoxRQICApCUlIQHDx6gUqVKRT7XcrJ0zMePH8ft27dRvXp1TJ482SzoPfXUU3jxxRfxzz//4NChQ3jhhRccdoxyH8t///2H9PR0ofbLkK+vLz7//HPRpltnOH36NE6fPm22fNiwYXjvvfeM+pY46jVq0aIFWrRoIcPZyEvfbG/ah9GQ/u/YcAwwWx/nLPpazczMTMmPccZr5OHhgalTpyIoKAgrV67EsmXLhHXVq1fHzz//jMaNGxs9xtWfayIvCk024nleaMe+evUq5s6dK/Q7MvypUqlw69YtaLVas8trIyMjRcNGxYoVAcBi23fFihVx/fp10TecWrVqiXasDAoKQqNGjXDkyBHExcWhSZMmspxDeHh4kQPWzZkzBzNnzizyzSItLc2pocnSMetrWvz8/DB//nzA5HngeR4PHz4EDDqMOorcx6IfdLBNmzaiA2g2btwYAQEBSE9Pl3yM+pHHTQ0bNgxeXl6St2N4iXpaWhpiYmKQkJCAjRs3YsCAAahTp45Q1pVeI2fQfxCb9gk0pO+7aPic2/o4Z8nKygJ0r6MruXLlCkaNGoXExESh24SPjw9u3bqFw4cP45VXXsGoUaPw/vvvC48p8eeaOoI7FYUmG2VmZgqdpufNm1ds+ezsbLMrlCy9Yei/PRe3nhepQtUHLjH6fkH6sCXHORS1v5UrV+LXX38FADRs2BB169ZFUFCQ8KG9bt06JCUlCTVPzmLpmPWD2V26dAmXLl0qchvWfEO2hdzHov+QKu7vw5rQZNhx39Crr75q1YeD6SXqHMfh008/xcaNGzFu3DisX79eqDl11Gvkqh3Bg4ODAQBPnjwBz/OizT+PHz8GdF+M7H2cs+j79lSoUEHyYxz9Gmk0GowbN04YH+zDDz80et6uXbuGQYMG4a+//kLjxo3RqVMnwA2eayIvCk028vb2BsMw4Hkew4cPN2oOE1NU1a2ckpKSLK7T9x/QhzE5zqGoudJWrlwJAJgyZQreeOMNs/X6y3Stpd+npbClDwjFPd6UvsmgUaNGaNeuXZHbaNq0qcSjtY3cx6LfnpS/D6l69eqFunXrmi03vVTbWizL4ssvv8TRo0dx9epV/PPPP8Lfj6NeI1ftCK6/fD03Nxe3bt1CzZo1zcpcvXrVqKw9j3OGvLw8Ifw0b95c8uMc/Rpdv34d8fHxUKlUGDNmjNn7REREBPr27YulS5di165dQmgq8eeaapqcikKTjZRKJaKionDlyhW0bdsW7du3L+lDAnTf4B4+fGh2tVlGRoYwkJ5+rBhHn8Pdu3cBXQdvUzdv3hT9kNbXooldTaan/+B88OCB6HpbOzQ3aNBA+N1RndBL6lj0/dWOHTsm2swaGxuLtLQ0q7Yp9rrKxdvbGyNHjsQXX3yBOXPm4KWXXoKHh4fDXiNX7Qju5+eHBg0aIDY2Frt378bbb79ttD4lJQUnT54EdP257H2cM8yePRvJyclQKpXo2bOn5Mc5+jXS17IyDGPxi5V+uWGNrCs/10R+FJrsMHDgQHz77beYMmUKFi5cKPoN4+HDh0hMTLTqG5U91Go1pk6dit9++034YOR5Hj/99BPS09NRpUoVo46MjjyHoKAgZGVlISYmxmj8kuTkZEycOFH0Mfrmv8TERIvb1b8JHjp0yKwT+dGjR7Fu3TqrjlOvXbt2qFy5Mi5cuIDffvsNY8aMMev/w3Ecjh07hkaNGjm0P4bcx9KuXTv4+voiISEBCxYswIgRI4R1ubm5+Pbbbx12Lrbq378/Zs6ciYcPH2LdunV47bXXHPYauWpHcAB48cUXERsbi/nz56Nnz57C8Bgcx2HatGnIy8tD7dq1zToo2/q4R48eCReIvPXWW7LVkqenp2PWrFlYtGgRAOD111+3akJpR79GderUAcuyyM/Px9y5czF69Gij9Tdv3sTmzZsBgy+eerY+13KgYZqci0KTHfSX/h87dgzPPfcc2rZti1q1asHX1xePHj1CQkICzp49i/79+zstNJUrVw47d+5Enz590KlTJygUCkRHRwv9Pz755BOjWgZHnkO3bt2wZMkSjBs3Ds8++yyqV6+O+/fv4+DBg8jKykJQUJDZpJjh4eHw8fER+hU0aNAAKpXKaETwhg0bClcQ9uvXDz179oS/vz+uXr2KQ4cOoUKFClY3NUHX/Pjdd9/h7bffxuzZs7Fhwwa0bdsWoaGhyMnJwYMHD3D69GkkJSVh7969Dg1Nch+Lr68v3n//fUybNg2//PILDh8+jObNmyMnJwe7d+9GUlKS6OtRkjw8PDB8+HB89913mDdvnlDb5CqvkbXUarVR38ETJ04Aur4yhiPFv/zyy0YD177yyitYs2YN4uLi0L9/f/Tq1QuBgYH477//cPHiRbAsi0mTJpnVjtj6uIcPHwrNYIMGDbI6NBkOIaHVapGeno7r16/j9OnTwgUhPXv2xIQJE6zarqOFhITgxRdfxLp16/DHH39gz549aNGihdARfO/evVCr1fD398err75q9Fhbn2tZUPOcU1FosoNKpcLcuXPx448/4p9//kF0dLQwDYhepUqVnPoNtmnTpmjdujV++uknLFiwQFju4eGBCRMm4LnnnnPaOXzwwQfCRJfbt28XlgcEBOC3337DrFmzzD6kPTw8MGbMGPzwww84ePCgMMCh4YjgDMPgl19+wVtvvYWkpCSsWrVKeHz37t3RrVs3m+e0atu2LZYsWYIvvvgC169fN5u1XaFQoG3btk6ZdkTuYxkyZAhSU1Mxd+5cHD9+HMePHwd0TWHTpk3DokWLXCo0QfdhNGfOHCQmJmLTpk0YMGCAS71G1sjPzxftk3PlyhXh6kbo5r80DE0eHh6YN28ePvjgA5w5c8bo793Pzw9fffWVaNO6rY/TN9NWrFjRpv5ploaQgK4v2pAhQ9C7d2+rt+sMX375JZRKJdauXSt6sUF4eDh++OEHs+4Ptj7XxP1QaJJo8ODByMjIMJtOxMvLC1OmTMHo0aNx7Ngx3L17FxzHoVKlSqhZsyaaNGli9u2iRo0aePfdd40upTakb/fWjxJuqk+fPmjYsKHFqu0hQ4age/fuwnx25cuXR6dOnSyOqu2Ic4CudmPp0qWIiYkR+lNVq1YNHTp0gL+/P5KSktChQwezucKGDRuGjh074tixY0hOToZGozE79rp162Lnzp3Yv38/bt26BV9fXzRv3hyNGzfGtWvX8O677yIqKsrqY4bued+6dSvOnz+PCxcuIDU1FYGBgahcuTKaNWuGcuXKFfl4U/Xq1cO7775rcQiJd955B2q12mzMIVuPRd9BW+zvY+zYsejfvz8OHTokDPXQqVMnlCtXDhkZGaKvh6N06dIFoaGhRQZyLy8vTJ06FWfPnjW6WlTu18gZVCqVpD45Ys9/aGgoVq5ciVOnTuHChQvIzc1F1apV8cwzzyAgIMDitmx5XExMDADg/fffL/biEEP611OPYRh4enrCz88PVatWRf369WUd2d8RPDw88PXXX2P06NE4fvw4EhMTodFoEBQUhPr166NZs2YWa4tsfY3sxgOQ+wJkqmiyiOHFrlsnbmf//v1499130bVr1yInhSWEkKK8+OKLyM/Px+bNm80uGCCu4/Tp02jRogWOfaZE8+rmX7js2vZtDk9N1eDUqVNO61riLqimiRBCCKDruNypUydh3kriBjgH1DQ5d+g8t0KhiRBCCKAb8uODDz4o6cMgxGVRaCKEEELcFe+APkjUacciCk2lhNROzoQQQgixDYWmUiI8PLzER7EmhBDiZDwDnpN5/CfeAeNJlRIUmgghhBB3RR3BnYpCkxUeP36MnTt3ombNmnZPSkoIIaR0ysnJQUJCAnr06OG0cc+Ic1BossLOnTsxaNCgkj4MQgghbmDZsmV44403HLsTjim4yb1NIkreEbFKOf1kth4eXgAUZebm5eWLZcuWwcvLt8SPhc6ZzpvOm87b9c+ZNfrMIKUH1TRZQd8kx7IKAJqSPhynUSgUqFu3rm6wu7LxDaQsnjPovOm8ywBnnrMzunHwDugIzlNHcIuopokQQgghRAKqaSKEEELcFfVpcioKTYQQQoi74h0wrhKNCG4RNc8RQgghhEhANU2EEEKIm6KO4M5FNU2EEEIIIRJQTRMhhBDirji24CbrNqlTkyVU00QIIYQQIgHVNBFCCCHuioYccCqqaSKEEEIIkYBqmgghhBA3xTvgajfq0WQZhSZCCCHEXTmkIzg1QllCzwwhhBBCiARU00QIIYS4KZ5zwOCW1BHcIgpNhBBCCJGM53ns3r0bMTExyM3NRVRUFF544QUEBQVJ3kZmZiY2b96M+Ph45OTkoHLlyujRowciIiIceuz2otBECCGEuCveAUMOFNGxXK1WY8yYMdi/f7/R8vnz5+Pvv/9GrVq1it38qVOnMGrUKKSmphot//PPP/H2229j/Pjxdhy8Y1FoIoQQQogkixYtwv79+xEaGoo333wTAQEB2L59O44cOYKPPvoIa9euBcMUHeK+/PJLpKamok2bNujevTu8vLxw6dIlrF69GnPnzsXzzz+PunXrOu2crEGhiRBCCHFTPO+AIQcsjDnA8zyWL18OlUqFJUuWCLVKAwYMwKBBg3Dq1CmcPXsWzZo1K3L78fHxqFmzJhYtWgSWZYVtBAYG4q+//kJ8fLzLhia6eo4QQgghxbp16xYePHiA9u3bGzXDsSyLQYMGAQCOHj1a7Hbq1auH1NRUPHnyRFjG8zzi4+PBsiyioqIcdAb2o5omQgghxF3JME5TvhbI5wrv5+SLb+/WrVsAgPr165utq1evnlGZonz77bcYNWoUunfvjubNm8PT0xNXrlzBo0ePMGHCBNSuXdv2k3EwCk2EEEKIu+LtH3JgwWVPzL3sKdzPzc0FkGxWLisrCwAQGBhotk5/5VxGRkax+4uKisLIkSPxww8/IDo6Wlj+0ksvoW/fvjafhzNQaCKEEELKsGFReRgUkSfcP/9Qje5/m5fTd/DmOM5snVarBQAoFIpi9/fFF19g9erVaNu2Lbp27Sp0BF+7di2OHDmC9evXWzV8gTNRaCKEEELcFM8zdncEV7EFNz1vhfj2goODAQAPHz40W/fo0SPAoMbJkoSEBKxevRodO3bEvHnzjNY1btwYEyZMwIoVKzBq1ChbTsXhqCM4IYQQQoqlH3jy+PHjZuv0yyIjI4vcxs2bNwEADRs2NFvXuHFjQHd1naui0EQIIYS4K44p7Awu2028pqlcuXJo3LgxYmNjsWnTJmH5gwcPsGDBAjAMg06dOhV5uOXLlwcAbN++3ejqOa1Wi2XLlgEAKlSoINOTIz9qniOEEEKIJKNHj8Y777yDCRMmYPXq1QgICMDx48eRlZWFAQMGoGrVqkLZFStW4MSJExgzZgzCw8MBAA0aNEBUVBTi4uLQtWtXNG3aFF5eXoiLi8O9e/egVCrRr1+/EjzDolFNEyGEEOKmeN3Vc7Leiugj1alTJ3z55Zfw8vLCqVOnsH//fmRlZaFnz56YMmWKUdnz589j+/btSE4uvBKPZVnMmjULnTt3Rk5ODmJiYrB//37cu3cPFSpUwPTp0112YEtQTRMhhBBCrPHaa6+hT58+OHv2LHJzcxEZGYnq1auLluvQoYNQy6QXFhaG2bNn4/79+0hISEBGRgYqVaqEevXqQaVSOfFMrEehiRBCCHFTclw9J7bN4vj5+aF9+/ZFlmnSpAmaNGlicX3lypVRuXJlm47R0PXr13HixAmcP38eSUlJSE5OhoeHB4KDg1GlShU0b94cLVu2RGhoqN37otBECCGEuCt9R3C5t+nikpOTsWHDBvzzzz9ISEgosqy+g3nr1q3x8ssvo0ePHvDw8LBpvy4fmlJTU7F06VLExMTg4cOHCAoKQsOGDTFs2DDUrFnTrPymTZuwdu1aJCYmIigoCD179sSQIUNEnyBryhJCCCGkZGVmZmLevHlYsmQJcnJywDAMateujSZNmiAqKgpBQUEICgqCRqNBamoqHj9+jIsXL+L8+fM4fvw4jh8/jp9++gkffPABXnzxRWHCYKlcOjQlJyejf//+uH//vrAsMTERsbGx2LhxIxYtWoQWLVoI63777TfMnj3brOzx48cxd+5coyfHmrKEEEKIK+JlmEZFbJuuKDk5Gc8//zySk5MRFRWFfv36oXfv3pKb3S5duoQtW7Zgy5YtmDRpEjZu3Ii//xYZ+rwILp0M1q1bh/v376Np06ZYvHgx9u3bh7Vr16JPnz7Iy8szGk30+vXrmDt3Lnx8fPDDDz9g3759WLRoEWrUqIHDhw9j8+bNNpUlhBBCSMnLzs5GtWrVMHfuXGzevBnDhw+3qp9S/fr1MWHCBOzbtw9TpkwRnQ6mOC4dmtLT0wEAH374IZ5++mmEhYWhUaNG+O6778CyrLAeADZu3AiO4zB+/Hi88MILCAsLQ9u2bTF9+nQAwPr1620qSwghhLgsXUdwOW9w0ZqmKlWq4J9//sEzzzxj13Y8PDzwxhtvWF3LBFcPTR07dgQArFmzBmlpaQCA/Px8LFmyBBzHGT1x586dAwA8//zzRtuoV68ewsPDceHCBfA8b3VZQgghhJQ8ubvN2LI9l+7T1KpVK3z//ff4448/8NRTTyEgIABZWVnw9vbGiBEjMHz4cKHsvXv3EBISIkwoaCg8PBzx8fFISUlBSEiIVWXFeHl5QaksfOpKe8Dy8fEx+lkWlMVzBp03nXcZ4Ixz1mq1yM3Nctj2jeinPpF7m0SUS4cm6JKgh4cHeJ4XapuUSiWUSiUYprAKMScnx+J/Av3y7OxshISEWFVWTECAL7y8vIT7/fv3x8CBA+04S/ewY8fWkj4EpyuL5ww67zKnLJ63I8/5ypUrGDRokMO2T8TdunUL69atw/nz55GSkoLy5ctjwYIFUKvV2Lp1K5RKJfr06WPXPlw6NG3ZsgWffPIJWrZsiS+//BLVqlVDcnIyVqxYgZkzZyIjIwOTJ08GdG2UeXl5otvRL/f09LS6rJj09CwkJ6cJ92fMmIkZM2bacaauzcfHBzt2bMVzz/VGdnZ2SR+OU5TFcwadN513GeCMc9ZqtQ7ZrhiehwOunpN1c06xdOlS/PDDD9BoNMKysLAwAIBKpcKiRYsQFxeHunXrIiIiwub9uHRoWr58OZRKJebMmQM/Pz8AQNWqVdG4cWPExcVh1apVmDhxIpRKJSpWrIgLFy4gOzvbrBbp7t27UKlUQnOcNWXF5ObmIjdXPHSVZtnZ2cjKKhtvrHpl8ZxB513Sh+F0ZfG8HXvOzksdJTUiuCvZs2cPpk6dCpVKhVGjRqFevXoYM2aMUZnevXsjLi4O//77r12hyaUbLh8/fgylUmnUFKbn5+cHtVotXEFXv359cByHgwcPGpV78OABLl++jMjISKEfkjVlCSGEEOK6Zs4saOn59NNP8cEHH6BBgwZmZaKiogAAZ86csWtfLh2aateujdzcXHzxxRdISUkBdM1nixcvxokTJ4w6c/fq1QsA8MMPP+DKlSuALnR9/PHH4DjO6Eo5a8oSQgghrornGIfc3EV2djYuXboEhUKBl156yWK5SpUqAbrKEXu4dHXKW2+9hejoaKxduxZr165FQEAAMjMzhQGpRo4cKXQGb926Nbp3745du3ahX79+RmXDw8Px+uuvC9u1piwhhBBCXFNGRgZ4nkdQUJAwBZrhRWJ6+txg79XuLl3T1KpVK6xYsQLt2rWDj48P0tPTwfM8IiIiMG3aNAwePNio/E8//YShQ4fC398f6enpUCgU6NmzJ5YsWQJvb2+byxJCCCGuiAcLnpf55trRwEhgYCAYhkFKSgry8/MtlktMTAR0fZrt4dI1TQDQpEkTLFy4ENCNEO7p6WnxyjYvLy9MnDgREyZMQHp6Onx9fS32TbKmLCGEEEJcj5eXF+rVqyfMKzdgwADRmqatWwuGmGjZsqVd+3OfOAkgICCgyKEA9BiGQWBgoKQQZE1ZQgghxKVwADhG5ltJn5R19GNiff/999i7d69RExzHcVi2bBl27twJLy8vvPzyy3bti5ICIYQQQtxW//79ceTIEWzduhWjRo2Cv78/ACApKQlt27ZFSkoKWJbFV199ZdUEv2IoNBFCCCHuygHjNLnqhL2WMAyDn3/+GY0bN8b8+fPx6NEjQDdXbX5+PiIjI/Hxxx8L89nag0ITIYQQ4qYcMUSAOw05oMcwDN58800MHjwYN27cwP3798EwDKpVq4YaNWrIth8KTYQQQohMGDBOHA+cZGdnY9euXfD29kaPHj3AMAzq1KmDOnXqOGR/FJoIIYQQiRi4Vi2MfsgBubfpLlJTUzFhwgSEhYWhR48eDt8fhSZCCCFEx9VCESlaUFAQACArK8sp+3OfOEkIIYTYSR+KGAv/3A3POWIqlZI+K+l8fHwQERGB1NRUPHz40OH7o9BECCGk1LAUhpwSihim4EacatSoUYBunCb9dCmOQs1zhBBC3EqJ1Ai5aBjiHTDkgOxDGDhQTk4OPDw80LVrV2zfvh03btxA7969UbVqVWEuOkNeXl5o3769zfuj0EQIIcSlOD0UuWggkqSMj9P05MkTjB49WrgfFxeHuLg4i+XDwsKwb98+m/dHoYkQQohTlWgo0v/u0KY06vniLD4+PlZdNRcSEmLX/ig0EUIIkZ3TgpHTaomsCULO60nN8w4Y3NKNappCQkLwxx9/OG1/FJoIIYRYzSmhyCmBiGqFiHQUmgghhJgpHaFILBCxBj/dPzDxvAMGt5R5e6UJhSZCCCmjTMcsknfjjgxEJfOhzlixX5pKxTny8/OL7PhtysPDA1FRUTbvj0ITIYSUYg6rMXJIKHJ+GLImCLki/eCWcm/TXTx69AgDBw6UXJ6uniOEkDLOPWqJnBNOigtB+vUMWLcPTKSg5qhJkyai6zQaDW7fvo2MjAwwDINGjRqhYsWKdu2PQhMhhLgJ2cKR4WX3sPfye8cGDwo2RePhgMEt3Wg6mYoVK+Kff/4pssyaNWvw1VdfoUaNGvj555/t2h+FJkIIcTF2hyNZaoocF1YoCMmojA9uKcVLL72E+Ph4LFy4EB07dkTfvn1t3pbk0HTo0CGbdyKmY8eOsm6PEELcjV3hyK5gxIr8tC3IuH0AYhxx/Dz1BHcxXbp0wcKFC7Fp0ybnhKa3337b5p2Isaa3OyGEuDObw5FNwcj+EOBSQUjuUKPfHsM6KDA5F885YHBLmbfnCgICAgAAiYmJdm3H6ua5Tp062bXDAwcO2PV4QghxRTYFI6tDkXUf8k7pFF0Kggcp/U6dOgUA8PX1tWs7VoemOXPm2LVDe8ZHIIQQV2B1QLIqHEkPIXbXCJWyWpeyiHdAnyZ3mkZFq9UiOTnZ4vr09HQcO3YMv/76KwCgXbt2du2POoITQkgRrApIksORtIBiUyii8EPKkPv376Nr166SytapUwfDhw+3a3+SQ9OiRYvs2pHc2yGEELlZNTJ2sQGp+PBiVShySBiytyO46SiIrIXlxFEKhhyQeRoVNxpyQKlUIiwszOJ6lUqFypUro0OHDnjttdfg4+Nj3/6kFmzbtq1dO5J7O4QQYg/DcFRkUJJUe2T5Q0tSMLIrEJVkzZKlfVtzTBSwiO0qVapk1wjf1qLmOUJImSCpBqnYQR7tCEeSg1FZa14zPV8KUdbgeQZcGe7T5GwUmgghpY7kgCT2O2B7OJIUjFxnfjWXGlpAIHZMFKQsKetDDiQnJ+PHH39EcHAwJkyYYHe54sjyP+bSpUv47LPP8Nxzz6F169Zo1qyZsG7BggWYMWMGcnJy5NgVIYQYYUT+mRdizG8CVrRvj/4yfNObcKWZ2M1oG5Zuhscuvg+5b8U/h7Y9znmKe06l3EhplJ2djQ0bNmDnzp2ylCuO3TVNixcvxo8//gitViu6/tKlS9i6dSvq1KmD5557zt7dEULKuGJrkWxoXhMdr6jIWiOZO3m7KP058KWipsd0FHRbHy+F84YDL+tDDkilzygsa9//S7sefeTIEUybNg0KhQITJkwQHbhSH5TsTXeEkLKpyFokSTVIhbcia48Ak1ojyzd7ancYhpXl5kyuV/MkB6qpKksSEhIAAIGBgXZtx66apoULFwIAxowZg2HDhomWCQ8PBwCcP3/enl0RQsoA22uRzD/URD/kLYYN8Uvvix1RuwTHRDLcN887pybI8PkoHbVP7o93QM2Qq0+bl5qair/++gsAkJmZKSybOnWqaPn09HQcPHgQAIy6D9nCrtCkD0K9e/e2WKZy5coAgKSkJHt2RQgphWy71F9CQCo2HIk/3rRGpSRDkTX0x+ms8AQKUKQEZWZmYunSpUbLsrKyzJaZqlGjht3z6NoVmrKzswEAwcHBwjKGYcDzhTk1NzcXAKBQKOzZFSGkFLA+JNkakCTWPJluo9imLzlClOMCRkmEJ1h4bilIOUdZ7NMUFBSEzz//HNDVMM2YMQNBQUEYM2aMWVmGYeDh4YEaNWqgefPmUCrt68pt16PLlSuHBw8e4O7du4iIiBAtc+fOHUA3AJU9Hj58iP/++w+PHz9G9erV0bFjR9GRPTMzM3Hw4EEkJiYiODgYHTt2RGhoqOg2rSlLCLGObU1t5leXGS8w/XAuprywK2vGSHJ07ZLjxyViGNbpwcnsGOx4Hl01cEk/J87lm7jcmZ+fHwYNGgQAePDgAdavX4/Q0FBhmSPZFZpatWqFLVu2YPXq1Zg8eTIgUtO0bt06AMDTTz9t0z54nsfvv/+O+fPnQ6PRCMvLly+PWbNmoXHjxsKy8+fPY9SoUUZNgV5eXvj222/Rp08fo+1aU5YQUjx7a5HsDUj21RCVZDOc4b7lCwumz0dJhyhrWAonYmHK2nBmqSnWXfE8C07uaVRk3p4judWI4EOHDsX27duxbNky+Pv7G6W87OxsrFy5EqtXr4aHhwcGDx5s0z5+/vlnzJ8/HyzLonPnzoiIiMCjR4+we/du3Lx5UwhN2dnZGD16NJKSktCsWTO0atUKt27dwq5duzBx4kTUr18ftWvXtrosIcSc9bVIjg5IEoYAYCx3ETD6IC2inBQ8Lz78ijRi5yFP2BENlcU0S7pa0CoNIUduZX1wS2ezKzQ1aNAAkydPxjfffIOZM2di1qxZQi1T69atoVarwbIsvvzyS9SqVcvq7d+8eRMLFy6ESqXC7Nmz0b59e2HdJ598goyMDOH+5s2b8ejRI/Ts2RO///47GN2b9uLFizFt2jQsXLhQ6FlvTVlCiMy1SEUEHmm1RyL9lewMOnIyPBb7ApSe45vzLJHSrOlqwcoZin9eWNe/BK0UyszMxJkzZ/Do0SPk5+eLlvH19UXfvn1t3ofdg1u+/vrriIyMxMyZM3H8+HGo1WoAAMdxaN26NcaMGYPWrVvbtO2NGzeC4zi89tprRoEJuv5U5cqVE+5HR0cDAEaOHCmEIAAYNGgQZs6cicOHD9tUlpCyyOLI2rCnFslyOak1R8WFI1eriWAYhUzByVDJhSgxlgKEWJiS2rdMriBmS+2auymLQw6IWbp0KX7//XdkZWUVWS4sLKxkQxMAtGzZEgsXLkRubi4ePHgAjuNQsWJF+Pn52bXdc+fOAbohDe7du4c9e/ZArVajXr16aNOmjdHInvHx8fD29kZUVJTRNpRKJRo0aIAjR44gMzMTfn5+VpUlpDQzDUaig0eaKWIcI6MPIfNyxYUjKU1ojuDQbevOSf7wpGfp2F0zTDn6sSVL/AsCcawdO3Zg6tSpUKlU6NChAw4fPgxfX1/06NEDcXFxiI2NBcMw6Nu3L6pWrWrXvmSdsNfLyws1a9aUbXuPHz8GADx58gRDhgxBXl6esK5BgwaYM2cOKlSoAOgGrwoODjaqOdILCQkBAGRkZMDPz8+qsmK8vLyMLls07PheGumvUhS7WrG0Ko3nLKUfknDevr66wCS1mU0kSBW33tJ2JbLmg7W4mgsfH28AgK+Pr9XHYYuSvTqscN/689b/NOdatVpyKP6ci1P8351Wm49iKjxkUxaHHDA1f/58QNdtp0uXLujatSuCgoIwbdo0QDcjyfjx4xEXF4dvvvnGrn3ZFZry8/Oxb98+eHh4oEuXLqJl9u3bh/z8fHTt2hUqlcqq7XMcB5VKhcmTJ6NBgwZo2rQpcnJysHfvXsTGxmLixIlYsGCBUF4sBFliTVlTAQG+8PLyEu73798fAwcOtHl77mLHjq0lfQhOVxbPGQC2b99c0odQIjZvXVLSh1Aitm5dWdKH4HSOPOcrV6445fJ3AuTl5eHSpUtgWRb9+/dHamqqWZkePXrg/PnzmD9/PpYtW4bhw4fbvD+7QtO2bdswceJEvPDCCxZD07///otNmzbhxx9/RL9+/azafkBAANRqNXr37i0MZAUAH330Efr164fo6GgkJycjJCQEAQEBuHfvHnieNwtEycnJAAB/f39hu1LLiklPz0Jycppwf8aMmZgxY6ZV5+ZOfHx8sGPHVjz3XG9hQNPSzlXPudjaIqGgbaNp+/j6Ytu2dXj++ZeQnZ1jvF6k5ogpogbJtCZIziYwOWtqeJ6Dj483Nm9dgr693xTO2xH7ciYpx+3j442tW5ejd+83zM67tJLrnIv6e9Zq8yyukxvPM+DKcE1TamoqOI5DSEgI/Pz8hAvETDuCd+rUCfPnz8eBAwdKLjStX78eADBgwACLZQYOHIhNmzZh/fr1VoemOnXq4MyZM+jYsaPRcj8/P7Rs2RJ3797Fo0ePEBISgvDwcNy4cQNxcXGoW7euUFaj0SA2NhahoaFCc5s1ZcXk5uYiN9d5/ylcRXZ2NrKyXCdAOIMzz1lyIBIeUFT5YprALDWdMR4AgJwcNXKy803WKQy2o9UtK6bZTYa+KUU1rckVaPTHmZ2dY/GDVMq+iguGrhLATPtXZWfnIFv3d27tlYiO66vlWIbnbEiOKzF5Xm33Nog0AQEBACBchKav8EhNTYVWqxVmIwkKCgJkmNLNrne0GzduALpwY4l+XXx8vNXb14elQ4cOGS3PzMzEiRMnwDAMKlasCABo164dABgNewAAy5YtQ1pamtHVd9aUJUROTBH/jAsyxdwUojOxM1DqbqxuzCGlcAPDAowSYJQG5ZRgGf3No2A9oFvuCZZRgWVUULCeYBklFIyHUF7Behg8VgmGYcGyKqMbwyisuok+Z7qrnMQCmDMHKBSe0yJu9mzDmYTn3GR8KlsCg7WvsS03WY9D5Jyt3ZfRfkVfS+e9nvo+TXLf3IW3tzcqVKiAjIwMpKenw8/PD6GhoVCr1bhw4YJQTn9hmb39VO2qadJXgxVVK+PrW9CxMiUlxertd+nSBREREVi2bBkuX76MJk2aIDc3F3v27MGjR4/QtWtXoeN237598ddff+Hff//Fa6+9ZjRgpVKpxNChQ4XtWlOWEGvZNn2IIQuX21t6I5Y47hEjcum/ce0RoNDVNBWEI61xTZLJB4q9H/SiozsXM8aRpelB9Mdib02OYThzhfnb5OAqtVv2cIVxuFxtOAs96ggOdOjQAevXr8fRo0fRvXt3dO/eHX///TcmTpyIDz/8EDk5Ofjll18AAG3atLFrX3aFpgoVKiAxMRHXrl1DgwYNRMtcvXoV0E17YvXBKZX466+/MGLECJw6dQqnTp0S1rVs2RLfffedcN/X1xd//fUXRo0ahTNnzuDMmTMAAE9PT3z99ddGc+NZU5aQokgfywjWTSJrsVlL6lhHloORYVnToQAUrGfBo1kVFCxnVt4epiGkuKBj6VL9ouZVs/aDrahAIcc0JNaMYeQoRT0nck8p4ooBzayvnQOnUSn8f+VeocPdvfjiizh27BgOHjyI7t27Y9SoUTh48CBu3rxpNIlvjRo18Pbbb9u1L7tCU+vWrbFhwwYsXLhQSHGm9Fe3tWrVyqZ91KhRA1u2bMHhw4dx48YNqFQqNGrUCC1btjQr26RJE+zcuRP79+/HvXv3EBwcjGeeeUZ0El5ryhKiV/Q4RtaMgm1e3uwxwi6kjW1kKUCZBqOiyrO65rmCmibOwv7NFd3vyLj/kxzhSa7aIMMP0GLLyjh2UFHbcucRtl21NkZurjSOFA/I3xFc1q05XuvWrY3mnwsJCcHatWuxbNkynD9/HjzPo0mTJhg0aBACAwPt2pddoWnw4MHYvHkztm7dCk9PT4wePRphYWEAgMTERPz555/YsWMHFAoFhgwZYvN+PDw80LVrV3Tt2rXYsn5+fpIn3LWmLCmbjPobiQQkyVeWWagFKlxv3vxgzdVoYs1o4jVLCtHHFBwVC6XQPKeEgpH29sCBK3LeMv0+DcOTLU1sRYUnyBQ2TGsfSqLmxNEfyFKfp+KOw53DXVFcKRAR2wUGBmL06NGyb9eu0FS/fn1MmDAB06ZNw7p167Bu3Tqhh7p+rASGYTBp0iSLzXeEuBqzoKQb5NE4IBl2Ji3sK2QaWIq6uszSm7O1AcowCBmuY0Wa6IraJgCwjEr4yTLGzWJiAYLntUb7gS5EGR6HYXgqrtbJ9Lgs9Xuy1N/J+NjkCVFi5LiSztrtycU4YBf+nVobFlwl3Jkq7rjsOWfR7ck0WKutynqfpocPH+Ltt99GhQoVjMZtdBS7RwR/8803ERERgb/++gtnzpwRwpJCoUCLFi0wevRouzteEeIMxkFJF34YDzAMZxCOWOEKHIZhjUKT0ZU5JjU7Ym/OpmHD4nFZuqrM5PGs6NVl1nWgVehCk4JRgWWMxznhDOrseSEYmdf+sGCF4ASTmiXD4IRiwhOKCFBSJsW15gPR9IO0uA9s2fvCFLE9o/O2Yb+u2M9ICles8SkrzY9SnDhxAjExMcjNzUVkZCR69uxpNOizFPn5+Th48KAwzUmzZs3MhhgqDsuyiIuLEy5MczRZplFp27Yt2rZti6ysLDx8+BAMwyA0NLRUTUFBSi8GJrVJDCuMV8QyPlCyisJL6hmV8JM1CFAswxYGJLBgDT7UHfVB55iOuwa1ZgaBi4dWCGUcz5k1pZmGJ30gNKx1shScIPIBaU0NlGmolGPcIEd14JYSyMweY+fr7KyO4O4Wzhw51IMzO4I7u6aJ4zhMmjQJGzZsMFo+a9YsLFmyBJUqVZK0j8uXL+P999/H7du3jZa3bt0af//9t+RjDQkJgZeXF5KSkqDRaIymOHMEWbfu6+uL8PBwOTdJiMMYhSVGWfBRz3iAZVRQsQUDpHkpg8F68FAwSrBQFdTAQAEFlGCgAKv7J/zO696EefEPK9MPFo4pvG9YO2MaKjiRDySxZcb7KnobBcei0K0rKKvvx8QyrFEwMgw6LMOCEwJQ8eHJUnCydJwwCS3WNuHZOtaQtHIyNOeU0r5CzqqFMXu9rdyvo66YM+TM6Ug5B4wIXtT2li9fjg0bNiAwMBAvv/wyAgIC8O+//yI2NhYff/yxpMDz8OFDDBkyBKmpqahVqxZ69uwJf39/nDx5EmfPnrXqWBUKBbp164atW7fi8OHD6Ny5s1WPt5ZjIxkhLsg0LBUEJU8oWA8oWR8oWU/4ewQDAMopa0LDAgpeCSWUUHKKgsjEK8AYDGeHYr5d8rrrUTjw4HS/8wa/cwxnsJwrLMvofzf+afjBUVzwEkKL2brCQCN6bR+jAMdrwYAVDU7Q1TpB90FkWvtjKTjBJBiYNiFaWwtl+iFoT42HpQEOnTnqtaOapdw1jJkqySYyV2wydLYlS5ZAoVBgyZIlqFevHgBg6NCheOWVV3D8+HFcvHgRDRs2LHIb06dPR2pqKjp06ICZM2fCw6OgZn/48OG4fv261cc0YcIEnD9/Hp9//jm+++47q5v4rCE5NH300UfC7z///LPZMin0jyOkpBQEJoUuLHlByXpDqfCGlyIAnow/vOALL94XwXxBTVMNrio0nAYqloWCYaBkCrbBMgADgLUwUCXH6wNQQV8gHjw4vmCOeJ7njX5yPA8ePDTghd/14Uo/Yr0+QHG6tfpl0IUisVDFCf2q9MFIa1AOumUwuW/ckV0sOMEg2EitdRJrrtMzD0HyhqjC7dgXpsy2JyFISanBclYgEx1RXeZO0XCDcOaIcy5RjhjB28L27ty5gzt37qB9+/ZCYAIAlUqFwYMHY8KECThy5EiRoUmtVmP79u1gWRZff/21EJj0ipphRExSUhI++OADeHp64vbt23j77bcRFBSEqlWrmm0buvEl//jjD6v2YUhyaNqyZYvwuz78GC6TgkITKSn62iUGSrCsF5SsLzyUAfBVlIM/yiGAC4Af7wU/VgkvJYsAr4L/bLV9PcApGCgYgGUAhe69xPStVv8xweuCEccz4AFouYL7Wp4BxwNa3a3wd173O68rVxCUNEJ4KghHWp4Dx+uClD5U6Wuh+IIlpjVTDF8QvViwusAFKEz6ExmGJw6cUeDQByXD4ASD5jqI9HWChfBk2tcJFgIUHBCiDM/HEkt9e4oe/FKeUaotbcdd53RzRhDhefFhLkqS4evoCiOYO8LNmzcBQDQUNWrUyKiMJTdu3EBOTg6aNWuGihUrYtOmTbhy5QqCgoLQsWNHozAmRV5eHk6fPm20LDU1VbgozZR+WCRbSQ5N06dPl7SMEFcjBCamICx5KoMQoKyEEL4SKnCBKKdSIcibgb8K8FHw8FJw8PTVAACiAvPBe6jBMOadFHie0dUY6QMRIwQkLc9AyxX8ruH1ywA1VxictDyg5YzXa3keWp6Hhi+oiRLClK6+SAhQ4MHxrEGAYsCAB8szBTVQwhfFgqYxlgfA6IORQghJ+qYz/bLCRxXWOBkGJ8NlMAg0xYUnsavdxAIUJPVnsi5EWdqOFFL6pTmKnB+87hrALHGFwOQqwYiXYYgANc9BY9ARK4cT/xvPzMwEAAQHB5ut0y8r7iq2J0+eALoapeHDh+Po0aPCul9//RXDhg3DhAkTJB97xYoVsXr1asnlxWqfrCE5NPXs2VPSMkJcib45jmW84KEMhJ+qEiqiJqry5RDmrUQVbx4VvdQI8siHr0oNT4UGCpaDwqvg0vuowBTwnvngwOjCUUEg4nkGWp6Fhiv4qeUZaDgWGpOfaq6gvJpnoOYYXWhioOEANQ9oGUDDAxoOBuGJgYLnoeUBhmfA87wu3ABaviDAaHhOF114ISxpGK0Qg8CzMOxixQFCcBLumwQnmAQZFgpw0Bo01ekea1LrBJMr4qTUPOlZE6AKH2NdTZSl7Yitl/JhLCVIudoYTZYnQ1YIP+0NAaUtmBlylYDkKFuzkrEp64lwPzc3V7QcU8S8mfquBCwr7W9/z549YFkWw4YNQ/ny5REfH48tW7Zg4cKFaNasGbp37y5pOx4eHmjatKmksnKgjuCk1DIMTF6q8iinqoUa2pqo4+ONOgFa1PFPRfWgZAT5Z8DLKxdKDw0YhgOnVUCj9EEygBqh98HnqqHlFNBqFNBoC29qrQIaToF8rbLgPscinyv4qeFY5GkVULIF4UnBMVAwBY0/ar4ggDAcAzUAfSUWwxcEG5YHWK6gWzkDCBGg4O2KBcPzAMMWBCaeF2KGkleYBSd9c50+dLF8Qcdx4b5RcDJ87gqaqQr7PGmNap0gEp7E+jtBJDzBigAFkav+rGnOEwtQxbGlpsqezslydmQvSXIFC7nClzOCoiuQ4+q5Xj7l0N07RLh/LTMNo0yGAgAgDF6dlJRktk6/rLhpSvTbyM7Oxo4dO4yayzp16oT33nsPO3bskByanM2u0DRq1CgAwMyZM2UpR4isGAYs4wVvj4qopKyHekw1NCrPoHFwGupXSkS1yJvwrZMIxp8H46H78M/nwKUooM4PQTKACjXvgc/SQJPrAY1aBXWeB/LzPKDWqJCfr0KeWgUPjRJ5GhUUWiVQ0KoHnmegYjnwHAue4aFlAJZnwDAFF/lzfEFgUTIF1etKRv+4gloghikYKYkXrrtjClbqv+npa9KZwqp5LfiCIQ8YzqzGyTAY6YMTdAHDMDjpAwdr0MenoF+Uca2TLeEJRdQ+QWS4Aj1rQlRxtVBCOSvDlNzTtRS5r1I6ca5UpSHIuBsVw0JlkLs8LdQW6YcUOnXqlNk6/bLatWsXua/w8HAoFApUrlzZrH+Rfo7a5ORk609C5/r16zh//jxSUlLg7e2N119/HQCg0WjAMAwUCvv+vuwKTXv37pW1HCFyKbgypqCGqYqyAZopq+HpCvloU+UOohpdgX+Lu+AiaoPzbW72WDYnA8q0bACAd+0HYFK10GZ6Q53pDXWWN1S5nsjL9hImtOV5BhpOAcPPYX0znuFPw87iloZxKQhL+n4KugAFBixTEEdYviBEcUJndAYcGAC8bggE6IKSeHCC7kO5qD5OwvMg9HfSNc/pz83K8AQ7ap9QTIiyJkAZlTOdesaoI7j54JuW9iFlXyWhtNRekeI5c3DL0NBQREVF4cyZMzhw4AA6deoE6DpeL1q0CADwzDPPFLltb29vPPXUUzh27BjOnz+Pxo0bC+u2bt0K2NhZ++bNm5g0aZJRp/CwsDC8/vrrUKvVaN++PbKysvDff//ZNWmvw5vn1Go1oBuAihBnKJg5TgkPRSDKq+qgiaIqulXORvdG51Cl8zlo27SEBqEWH895+0PrVQHgAKZmCJTJ98E+SQXrqQaj1I19pFVArS7o98TzDLQcCy3HFjTRaRW6Pkws8nX9mvR9mjS6jt/6EKXRXUln6SONZQpqm7S6mimtrl8BK0xroutHoGu80w84UPhcmPdx0gchseBU+DiF0TL9Y/S1TrAQngw7iwMQ7TAOK2qfYKEJT3h+ZAhQYqxt4rOnY7IzApel2it7RwQv62HM8nPm3BHB5R7csqgQ9u6772LcuHEYPXo0OnXqhICAABw+fBhJSUno2bMnatWqJZTdtGkTzp07h6FDh6JatWrC8lGjRiEmJgavv/462rVrJ/RpOn36NBQKBV555RWrjvfOnTt4/fXXkZycjPDwcDRq1AibNm0S1qtUKvTs2ROrVq3C7t27MXDgQKufEz2HX4Jw48YNwKAdkxCHYxRQKgJR3jMSrRURGFAjHQOf3YvQT1XQtmkJNiMZjEYNcNqibwC0oTXA1aoNtqovlBUy4RGYBaVPLhRKDRiGB88zyNcqkatRIVujRI7wU4kcLYtcLYtcruBnPscgTx+cuMIr6XiDIQj0v+txxQwtzOqCleHAmiwYsDxrMOgma7Cs8B+jG8HcdFRz6MKIfpnxyOesQc2TwugqO/30Mfqb4fLCD2eFcBOOl2GNQpThY8wnKlYY3Yyfi8J/Zn8SujF5TG9SGB6ztXP5Sdq+DcfkKkxfK2tvJXW8tj6upI/fFfTq1Qtjx44Fz/PYs2cP1q9fj6SkJLRp0wbffvutUdmYmBgsX74cDx8+NFreqlUrTJ06FUqlEgcOHMDatWtx+vRp+Pn54ccff0STJk2sOqZff/0VycnJ6N69OzZt2oT333/frIx+DtzDhw/bdN56Vtc0TZw4UdIyAMjKysKJEycAAC1atLDl+AixCgMGDOMBL1UIamnD8VSoBl1bH4f30MoF6zVq8N4FA1cyHAdewpUenLc/+LCaUORfA5uTA0W6jxCY9J3C87UK5GmVyNUqhJCk4Rihlkk/vICW14/bVBiUON64OU4/IGZR3+FZmK83rG0ybqbjzWqcTJvq9J3DGYPQBKMmuoImK9MmO8P+Tvrt6WsfDJvtYEXtE1fEYJWWaqEs1UAVN9WMNVfNFR6P8XHLrbhJjEuTEh3du5QEn4LrZ2WuaSpmeyNHjsSLL76IEydOCBP2igWdfv36oWHDhqhevbrZugEDBqBr1644duwYUlNTUb58eTz11FPw8/Oz6lg1Gg32798PAPjss8/g4eEhepVf5coFnwEJCQlWbd+U1aHJdJI+S8sMVatWDR9++KG1uyLEeowCStYX5RQ1EOXtjbZVbiK45wNoEFxQu2QtTgswWvAeXuBDQsCm3YfCOw+sQlcTxbEFNU0mgSmfY5GvNR2DySAkmYQnsfswCFBFYVEwPLm+uY7VjelkGpyEshaa6vTBqXC7rNlYTvrgBIlNdjAYVVx4iUynXDHpQ2QpPEEkeAnLJXQiLy5AwaDWB5KumLPvKj0pxyJsvwwEKOJeKlWqhD59+hRZ5umnn8bTTz9tcX1QUBB69Ohh13EkJycjJycHwcHBRU4W7O9f8GU5JyfHrv1ZHZp+/PFH4fdPPvnEbJkewzDw8PBAlSpV0KBBA+rTRByuoJZJCQ+lP6pqw9A4KB8NWp+FpnY9KJISwQWWA1jb/w654IpQPH4C1lMNVlHwIWbYjylPF5iEWiYeunGaTJrfIH5fmHJFWFaYlsRqnliGgdak+a4gMPFG9w07hgtBxlIfJ+G5NK5pMg1OgHFHcWG7MtU6QUJ4EutPYzj6uCmptU+F22IlhxUpY0XZwx06n5OSwfP2D24ptk13oR+sMjs7GzzPg2EY0ZqmR48eAQACAgLs2p/Voalfv37C7wsXLjRbRkhJYqCEn7Iianh4o0mF2/DtrIZGF3j0/ZRsxStV4IMCwHqlglUVjC2g7wSu5hnk68KSRtd3yXjk76LCkXhgMpy3zvL5MiYdvwsbHAqa+owDVGH80dc8GQcJljfsW2TcJGdvcIINtU6Q0Gwntdap8HmQHp5sbSoT6/vkyCBFAYqUVUFBQahQoQKSkpJw4cIFNG7cWDQ06bsK1a9f36792dWgu2nTJqMe6oSUKIaBgvVGACqglh+PulHXoAkrGFeEZ1mzWiYp/ZlM8QFBYP01UOimVuF0I4NruYJRwdW6GiajKVO4wqY3/X0trx8B3LyJTmpg0mP1nb9F3igYfc8N3vxcDZexJv07WIOO24b3TZcb78t4NHGx5TCodbK03lKHa9ZCvyOLV4YVM96PWIdxS+TooO2ojuQwaVYkZQsHRhjgUrabE6/+k0OvXr0AAN99953oNC63bt3CihUrAAC9e/e2a192/S8bNWqUMHClHOUIsQ8LllEiSBuE6r45CGl/vWCxrobJlpBkKr9aQzA+CjBKLRhdexZnMP1J4dhMMJmwt+jaJdPAZKi4TuHizwQjdAw3pb+arrCs+PMiNVRYEz7sZSk4WSIlOEk9frlCiaOCEyFl1bvvvosqVargzJkz6NOnjzAvblZWFr799lu8/PLLSElJQa9evdC6dWu79kWDW5JSRcF6wofxQIhnNphgX7P1cgQnqJRgFRxY3fwnvDCZrq5JTD/2kkFAAsQDk55YHybT+MRL6GjAMkyRNVSmfZ7ESkgl1pQmtZnOfFvm64sbZLK4xxNSJjhgcEvIvT0HCwkJwdKlSzFu3DhcuHBBuDgtNTUVf//9N6DrRvTNN9/YvS8a3JKUGoWdlxkoGA6QIyBZwpp/QOszjdhHt6Ur4ExzUFFxhmGYIoNT8YGodGAZVrRzuCVFdQ63ljWdw53NVY+LOJYcc8+JbdPdVKtWDWvXrkVMTAxiYmJw//59MAyDatWqoVu3bqhXr54s+3F4aKLBLYmz8ODAg4OG55CnVQAaB826zvEAJzaAYsFPsajGMrowxZsv442uWjOcVo4ptk+T2BV0RR66FaGquI7S1nRsLi21QHIEE7k7hFNYIqRQccMc2IsGtySlCsepkanIxeNcb3D3sgGTuSMZrvADxqamOk4LqDXgtKzwbYwBr+uMXXBjmMKJeHn9VCW6rMKi8D5vEJwKpjRhwPEFw8qxjHHtlNhglmaHBl7XJ6roYGQaYIzDkfUfwIaPN9w256BQZU0tE4q4iq4kUGAicnPm3HOEBrckpQoHLZ+PNDYZNzPDce9wE1TqgIKr5jitUWCylcetC+CzOHBqJXiuYCJdlgEUDA8Fw0PJ8gVXxTG67r76tKN7D9LqApI+LHF8ccFJN1mvla1unK7ejdfXvzGmQcl4mWmtkv6+/kNef990uSFLgckspJmEGEuByVk1WVLHbbI3oMgZmCgsEWIuJSUFW7duxenTp/H48WMoFApUqVIF7dq1w7PPPiuM6WQPGtySlB48D47LQzqfhPjMWrh0MxxVL2+Fpl7jwtHADYYdkDqNiiE2PRXaLFVBaNJ9G1MwHFQsBxXLQ8nxUDIM+IIhtnUPAhi+sNmO19UisQa1UCxT8HtBOUboGG4YnMADHMMYtecVNzedIU4XoQyb6DjdP+iCh2GQkhKYDB9buMxxgUmslqmowFRcLZMzAhOFJeJIvG7YAbm36W62bduGKVOmIDMz02zdunXrULNmTUyfPh1169a1az80uCUpVXg+H9maJ7jNp+PMk3JosbsGAusBbEYKOP9gu7bN5GYBGZngcrzAqQv+6yhYfWDi4MFyULO6zthaBmB5sFxB93SN/oIUrrDiiWcKw5SlWiex/kqsrsbKlL5pTqyWyTQwFSwzblYzDkzGQclSzRMkBiZHhKUityOhSU5KYKLaJUJc38GDB/HRRx+B4zhUr14dAwYMQI0aNZCXl4e4uDj8888/SEhIwJtvvonNmzcjNDTU5n3Z1RGcBrYkrqSgL48GeZpU3FfdRmxqI5y+2BDdTm+EtnkL25vodLVTbEoS+HQNtDke4LS6K/VYDkqFFh4KLTx0A1zqHgSGY6AGD4ZnwOjGYmLYwuEGtLx5eNLwxp3G9c102iK++nEWOnibBiZhOcNZrGHijAKQ/IHJlqa4kqhdorBE3AX1aQJ++eUXcByH559/Hj/88ANUKpXR+rfeegv/+9//cOPGDcyfPx+fffaZzfuS9eq5rKws5OXlWVwfEhIi5+4IMcfz4PhcpGkScYWrhiMPKyJqWzNUq3Ef2nKVAYNmOklNc6wCgBpsRjKYlFRoM1XQ5qvAaQuClILl4KHQwEuhgZpjjd5sFAwDBcNAw0GYuJcxCEssUzj4JaOrPVIaBCfeoLbJcLoUw49Qw07fprVMpgpDlOXAJFbDZGtzXHG1S9YGJUvbgcw1S67QFEdByd25YwOXe8rIyEBcXBwUCgUmT55sFpgAoFy5chg7dizGjBmDkydP2rU/u0PTw4cP8fvvv2Pfvn1ITU0tsmxcXJy9uyOkSDx4gM9HrjoZd72u4VRyc1S62AR9F5xE+YkKwMMLAAr7OEnApj0G++A+uBQttFl+4PI8wHEsGIaHguWgZAtqmrw4rRCaGIaHQlsw2rSS4YWJe9U8wHIMOH3tka6/E4S+CbrmOl43hAEPi70V9P2Z9FfNGT4HYs1yxQcmrfCWoC9nWrtkS98lqWHJ2qAEF2iGszckuWI4sqZTvaUpbEozVxs+Qz+NitzbdBf5+fmALhgVVTETERFhVN5WdoWm5ORkvPzyy3jw4IFRugsICEB6erpwv1y5cqIT6BHiEDwPjstGev5dxHoGwvdhBDzONkP3qedQpfM5aNu0BK80/zZivA0FwAGKh7fAJt8H90QLbaov1Bk+0OR6gNMqwPMMGIaHSqGFh0IDLccKV7kxjG4YAgZQcwwYpmAuOnAMGJY3aMYTDrkgMDGFv4ufmnFtk/6nYS0ThCY48cAk1CYxnFHTm2GggkEgMA1MtoQlsXAhZegAW8KSIzp3u3oNkq0f5LzBa2vLNlwtQEhh7zm7mrLePBccHIyAgACkpaUhPz/f4hVyjx8/BgDUrFnTrv3Z9TVh3rx5ePDgAVq2bIljx44Jy0+cOIHo6Gj873//A8MwaN26NQ4fPmzXgRIiVUHjlAb52jQ8Vl/HOe1d7Lnvgw1nWuDUqmeRs+g+lOdPg80SrxllczKgeHirYFsJydDcVkL9MAh5TwKQn+GL/FxPqPNU4HQDXAo1TgptQYdwhRYqhhc6h6tYXne/YEgCpW6IAmFcJ93YTqyF9ynetBmO10/fop/7rrDGiTcITvplRQUmHlohMMGk/5LhYwrCl1YITIYfOByvFW6m6/TbF46H54Sb+LlyRjejdbxWuJniDP4VRd/8Vlx40R+36fHbQuo+rdpmEc8TIWUJy7IYMGAA8vLysGrVKovlli5dCgB4+eWX7dqfXTVNBw4cAAC899578PU1nuerQoUKmDx5MnJzc7FmzRq0bNkSgwYNsutgCZGq4AMqF7nqx7jHxIIDh+wH1fAoNxxNUsqh3pV7qBZ5E76Rp8D4AowHC7AM+FwtuBQFNPkhQHcg50Yl8FkaaHI9oFGroM7zQH6eB9QaFfLzVchTq6DRKqDV9WdiGR4MCkKUgmeg1Y3fxOk6d2sZprDZzXD4b/1A47paJv3AmBzPG89jZzBPHWcSlMSa5cQYBiaYDTtQdO2S1A7epkHD2s7cha+jfTVKUoOKce2Daza5UTgiYnhYrpm2Z5vuZNy4cUhISMD333+PGzdu4NVXX0X16tWRl5eHq1evYs6cOYiJicHYsWPxzDPP2LUvu0JTYmIiAKB+/fpGy7VarTAu0+DBg7FmzRqsX7+eQhNxLp4HpwtO9/lY5Kuykfq4Ju5nB+F6hj/qPKiC6ueTERyQDi/vXCiUWjAMB55noWZ9ge7A49uVwWVroOUU0GoU0GgLb2qtAhqu4Pd8rRJqjoWaY5HPKaDRXUnH8Qy0BjdOdxWdEIp0b1Bag2VavqCDuIbndcsLPi61PA8tX9B/Sav/eOf18YczC0xitUzFByal7vfC2iXh6TSoWTJdVnjfuFbJ7CUptibI9ivfrA0r9oQjuWuNCCG2uXv3Lrp27SrcX7VqlcUap99//x2///672fKwsDDs27dP0v7sCk36YOTlVdC51tvbGzk5OUhPT0dwcMGYONWrVwcAJCQk2LMrwZMnT6BWq+Hv729Wu6XHcRxSU1Ph7+8v2pPe1rLEvfDgwfBaaLlM5Kjz8UCbhXTVA9zNq4YrDyojLDkQlR8FoYIXhyCVBv4qNTx1TWxKbyWqAbh8pwb43IKOgxzPgNd1uiwYMoDVhZyCgKThGWg5Fmp9SOIY4feCjuAM8jlAa9ApXMsV/tToAxNfGJA0fEFzXMHv+obHwulSNEJE4qFhtGZhCQZXxRkGJrGr40ybt0xrl6T0VzINSo7qwO2o/khyN6PBwaHI3ili9I+31OzpShhG2gDJxZ2H2DlL3bYrKut9mhiGsXvwbGseb1doCgsLw7Vr13D//n3UrFkTVapUwY0bN3D9+nW0atUKAHD//n0AgEajsWdXAIDY2Fi8/PLL0Gg0+OSTTzB8+HCj9bm5ufjll1+wbt06ZGVlQaVSoUuXLvjss8/MBrOypixxXwXBCeCRD402DZm8GvnKLGQoH+GRthJup1VAuQxvBKk84KfygI8S8FLw8PFVoRqAuLRAcLn5uk7dIpfx8wWjd/PCT0DDM7owxQhDDWgNA5FZQDKuWdLyhTVLvISwZE2n76ICk1E/JQmBydqw5OimNltqjvTblCsoObrWyNWDjSM58tzl3nZZfp2cLSwsDJcuXXLa/uwKTU2aNMG1a9dw+fJl1KxZE23btsWNGzfw559/YubMmVCpVEJVmL1Dl6vVanz66aeoWrWqxVqrjz/+GLt27QJ0PerT09Oxc+dOXLt2DevXr4e3t7dNZYl7KxiGgAeghpbLRK46HxptDnIUqUhTPsADJhi+6iD45/nBh/GAD6uEv4bH8wDi0hXgc5VQ6DpqKww6bJt+F9NHKn0THKf/HYXjMWn5woEtOYPmN8MapYJynNBnSWpQgtFQAZavkIOFwASTsGQamKTULol13hYjpcN2cawNSdbVTlH4Ie6hoM+jzEMOuFunJieyKzT16dMHa9euxbp16/Dcc89hyJAhWL9+PY4ePYrWrVtDoVAIg12OGDHCrgOdM2cOcnNzMWbMGHz00Udm648dO4Zdu3YhLCwMc+bMQUREBJKTk/Hhhx8iJiYGK1asEGqmrClLSg99cx2PXGi0Gmi5HORrM5CtSEYq6w1P1g+ejB+84IdAbQAAID4nC9psDkqGhQIMlLoBKxmGEYYUAKAbfNJ4XzB48+F0V70Z/iyc9sQ4HFmaBgW6D3OxkCSsMxnZ2/rO3oVvCcU1x1kKS44IStY2sVnD+Go/ea9Gc0Y4suZ8GcbyBdNy1LYVtX2p+7R2G4Q4k12h6amnnsLatWuF9sCqVatiyZIlmDp1Ks6ePQuNRoPq1avj/fffR7du3WzeT1xcHObOnYslS5bgyZMnomV27NgB6CYR1g9iFRISgh9++AGdO3fGtm3bhCBkTVlSuhQ216kLPiC1+dByOWAZD+SxqVCwnlAwnsjlC/rk3VEkQK0AlFBCxXtCASVYnoWSU4ABCxYMWL7gp2lwEts3DKY8KQw4uujEGK8zHwaAM3mcSJAx6pMk0owG86AjXrtkvE+z7UgMTLYGJSkhyZYPeUfUIDmz1sju6V1Mm1Hlbp6UYTuOHvDT8Jzl2lfJBr2CvpZyb5OIsys0MQyDRo0aGS1r1KgRVq1ahfz8fKjVaoudtaXSarWYNGkSBg8ejGbNmmHPnj2i5S5dugSWZc0uJwwNDUXdunVx9epVqNVqqFQqq8qS0kcfXgpqnbQANOB4DTg+FxqtEgyjhCK/oIY0TZ2IXI0GCkYJllFBwajAgIWCVYGFAgoowUABVjfkmf4ng8KOhazBcGhiIcJSqDEta3EkbdFtWhhuwGQbpkMIFIYhzqrAZE1YsqVGydEByRkdol1x9G8iD7Mw6sSL9jneASOCu1FHcL0bN25gyZIlOHXqFJ48eWKxH3XlypWxZcsWm/cj69xzhjw8PCyOzGmNBQsWID8/H++//36R5R49eoRy5cqJ9kWqWrUqYmNjkZqaigoVKlhVVoyXlxeUysKnjheZib408fHxMfpZ2gg1RAxTMNEuAE/vgg9OhWcuWK1aN9+JEhzDFlxpwyjBgYWWKZgqhWEUwpQSLGManOT5Fmrpbcy660ZMS+vvcwAU8PYp+KLg7eNpEmBUxdQuFX7BEA1xNk2R4pg+SGKhyMfH2+inPZwVjuytNWPACudb8HrLd9xi06vYun25p2qR87W2RKNlkJ/psM0TEzExMRgxYoSkKVICAgLs2pfDQpMcbty4gdmzZ2P58uXFBrD8/HyLnbc9PT0BQOhfZU1ZMQEBvsIwCwDQv39/DBw4UMIZubcdO7aW9CE43datK0v6EErEsnXflfQhlIgNm+eV9CGUiE1bFpX0ITjdxi0LHLbtK1euOG1cQv3gt3Jv05189dVXyM/PR9OmTTF+/HjUqVNH+Cw3xUqZqL0IkkOTWOdra/3888+Sy3Ich88++wz9+/dHcHAwHjx4AABISUkBdDMbP3jwAEFBQfDy8oK3tzeysrJEt5WdnQ0Y1JRYU1ZMenoWkpPThPszZszEjBkzJZ+bu/Hx8cGOHVvx3HO9heentPP18cX2HVvQq1df3Tnra490/+EYVtoy099N+j5Y+hZtqY+E6Xgypo83fFxR+2XNHlewXW8fL6xa/zNe7f8RcrJzzfYvtZN38cMDSK+NsraGQkrzmum+fHy8sXHLArzQZziys3Os2p/FfTh50EpbOlX7+Hhj05ZF6NdnqNl5S60xc7eO20Wds1w0WvP/O8QxkpOTcfPmTTAMgz///NNiC5FcJIcme9oA9awJTefOncOZM2dw5swZ/P3332brZ82ahVmzZmH69Ono2bMnqlSpguPHjyM5OdlspuMbN27Ax8dHGHDTmrJicnNzkZtruSaqtMrOzkZWVtkITXpZWZnIzjJ4YzWaeNo8IEH4ABEPLxD9kJEWkIrblqWQZLgdfRnjxxWu13AFf9eZWRnIFglNxbH1Cjixx9nb5Cb1uAxlZ+dI/iAtiZG8ZR94U7e9rKwshwUIV2N6zo4IfRxffDORfMp2R3D9hWjBwcEOD0ywJjRNnz7dsUdiQqFQiA4ymZeXJ4zg7ePjIzSzNWnSBMePH8fWrVsxePBgoXxsbCxu3ryJNm3agNF94FlTlhCjTp08b3CVnK7zMMMZFhYJQcb3edGQZL6M4SXUQpnsTwhIvHiIEg1NuscwYMHxBW8JBR3j1YVlrOw5ZcjasAQJgURqZ21p4z05bsgBa46DlAw5Xxt3q3UrDQIDA1GlShXcv38fOTk5Dh9jUXJo6tmzp0MPxFTjxo1x6NAhs+V79uzB6NGjMXLkSKNhAV544QUsWLAAv/32G3x8fNC6dWskJCTg66+/BnT9jmwpS4gp0ytjzAcK132g64K32YewpTBkFq4MVxauK7zuwLypj+cLrxgxDlf6sKQLSLx4oNJyBb9ruTxwvOHVJxoJNWbS2RKWrLmqzZaO5/YqiWBkzblI6VAtR+dyufchd0dwRyoczsCJV8/BAVfPuVFNEwAMGTIE3333HZYsWYJ3333Xofty6Y7g1qhTpw5GjBiB2bNn47PPPjNa17FjR/Tp08emsoQUx9LlxSKzrugYh6rC7Yh9mOg+MMT6q4iFLLNwZdx8pw9VjGEzIl8YpjhepfupgVbXVGepdsowJNj7weZuYcmZAUmu4xbtRyZzDZtDaulk3qa15+zqoY3nDb9IybdNd/Lmm2/izp07mD59Oh48eIDu3btbnA5NpVIJc+Lawu1Ck6enJ0JDQ0XHfxo3bhwiIiLwzz//4N69ewgODkb37t3x5ptvmvWYt6YsIbawGKb03+IkvTNpzcJV4fb1b/iGNUqmQcZgaACjQGUephiGBYeCvhhaPh9aLs+o6a4gXOlDnMYoTBk2wck5+akcgcm6vlHyDXhYEn2eHKGo18CdJ7qVyrbXsXS89u6kUaNG8PX1xcqVK7FypeWrnsPCwrBv3z6b9yM5NOmvNrN3sEp7t9OhQwfRZju93r17o3fv3pK2ZU1ZQuQiZeA7o9HFiw1X4sHKLFTpwoClMFXwjVU3tAev0dVK6b+Vw6xWSghNZrVZBsHNCX08bK1dMnycLCNZO/GD0p4BOMWCDg/Opm264xx6RjVNvNbtgx/vgOY0N6towqpVq/DFF18AAJRKJSpWrGhxyAFLNVBSSQ5NzZs3B3RTmthDru0QUpoVF6zMpmwpKlgxxh/mRYYpXfMdD03BzaRGqoD+Q0f/ePMgBX0NlFFQK+IQrQhXUgOO1MBkD3ec2Je3MKdgWSX3c+zuIcwd/fnnn4CuP/KkSZPg7+/vsH25XfMcIaToUCU5UImEqcJpUTS6MKUrw7AG60SGWjANUiZX3BU1ZhR0IUauviOuGJbcsUamQHHnKcdrVkRfPjdUMBWPM2sdGfAydwSXe3uOlJycjKSkJCiVSnzxxRdGA087gtWhae7cuY45EkKILIrtSyUUFCtnOPecpsimPbE+UmJBCijs81RUB3IenEOb85zZBOe8kCRXqOFs7IfjqHDgyNDBGfx0RigkjqSfLcTf39/hgQm2hKZffvnFMUdCCHEoSWFKH6T0l+SINu0VBimjJjuD2ijAUtOc4faMwxQMgo21I6Vb4uyaJceGJUeEGmqeK5qtz4/znteyPmGvn58fIiMjcfXqVdEBq+UmOTQ5euwDQkjJMAxTZsFKrDbKIEiZhiiYdjQvMkjpfmcMO4/rOqWbhKnCw5GvGa84co5IbjsKNfZy9oUJxPnGjh2LUaNG4ccff8S0adMcOji15NA0btw4hx0EIcS18Lp/hiwPlWB89Z5RR/Nig5T58AfC7wxrUlNkHKggY6dbW8crkj8slXxIsqd2zlJ/NVfB81zhsBwyDi9RkngHXO3mTlfPZWdnIzMzE127dsWGDRsQHx+Pbt26WbxKztfXF926dbN5f9QRnBAiiVjznsUgxTDGwxpYrJGC0LQHk8Bl3lRXWDMlbNekhsoSua9oKjVhSeYAURpCiByc3RFc7uY0d+sI/sknnwj3z507h3PnzlksHxYWRqGJEFIyJNdGmYQomH6bNWt2Ew9SsNjvqahO5GzxE/qajN3jPM4PGRRsSGni4+ODF198UXL54OBgu/ZHoYkQIhvpTXqWxo8yHt3cUpASK2+5E7ljr8ormmsElLIQlCR31nfg5MwlMeWKrdc9FrdNdxESEoLvv//eafuj0EQIcRiLIQpSa6OsC1KijymmA3lBoLLmMvSSU1rCT2kdVLMwkLlTryBiDQpNhBCnsSpEQUKzHsSCFCyEKYsHJblvj7NrrCgkkeLwcMDgljJPy1ISsrKywPM8/Pz8ZN0uhSZCSIkpsnM5pNVGwUIgYswWmgcpmI6EbqHJhjHpT2ULS4GrtAQjUxSUiLNt3rwZq1evxoULF5CXlydMzqtWq/HNN9+AZVlMmTIFLGv7lx8KTYQQlyJHbRQs1SxZbKYrqnmOlRQAiuvPUlrDkSEKSs5X1q+eAwCO4zB+/Hhs374dAKBSqYzWq1Qq3L59GzExMejVqxdat25t875opC9CiEvjRf4ZF+DNb4BBAOKMwpC+NsnwZtg8Z3YT3Q5nFrDEtlvUzVVZc6zuck62k/L6F/13QRxv0aJF2L59OypWrIgFCxYI4clQjx49AAC7du2ya1921TRduHABXl5eiIiIKLYcADRq1Mie3RFCCFBcbRSsq5FCMVdUmTfzGa5kJXxAWmiWs+ODVY6rtKQ0SxqWdS9FHa97dPqXqqwPbgkAy5cvBwB8++23aN++PRITE83K1KxZEwAQGxtr177sCk0DBw4EAIwcORJjx44ttlxcXJw9uyOEEFHFhigUFaRQxAep5aY5xmDEc/ECxoNySiMtDLlfiHGGsvmccLz8c8VxbpSa0tLSkJiYCE9PT3To0MFiuYoVKwK6wTDtIUvz3KxZs/DZZ59Bq3XmoHCEECKu2CY9oaBJk55ZsLLc9FJs05tYU59Z058pavaxDj0vZV1eXh4AwNvbW+jgLTb3XFZWFgDAw8PDrv3JEprGjh2LtWvXYvTo0cjNzZVjk4QQIiubgpRZPyk92/s3Ge/L2lBV1L7LSsAq7ednHd7OnldiNzeqaEJwcDBUKhVSU1ORkpJisVx8fDygm0bFHrKEppEjR+K7777D4cOHMWTIEKSmpsqxWUIIcSjTAFXkoIQyhClI6DBuXNiWUCXleEyPzZXDlisfGylpKpVKuBpu6dKlgEhNE8/zWLVqFQAU2YQnhWxDDgwYMADlypXD2LFj8dprr2HBggWoUqWKXJsnhBCnsBScRPtJwUJfKRj2l0IxH/ZiI5pb2KTp91ypwxhYPSgnhRN3wfMOGNzSzYYcePfdd3HkyBHMmjULeXl5RsHoxo0b+Ouvv3DmzBlUqlTJqnnqxMg65ECnTp2wZMkSpKSk4NVXX6WO34SQUkNy857wACk1U7Cqec3mYQyKq60qA2NIkdKrdevWmDx5MliWxYIFCzBkyBAAQGJiInr16oVt27YhKCgIM2bMgI+Pj137kn2cpiZNmmDlypVQKpUYNGgQTpw4IfcuCCHEJYgFKfnCFKzur2TX2FBSOq5TuHI5cvdnctdG0EGDBmHVqlXo2bMnAgMDheXly5fHK6+8go0bN6Jx48Z278chI4LXqlULq1atwttvv41hw4Y5YheEEOKyip0eRvRBRYQtkauBiv9oE58yRuy+PlRJGv/J1uDk5Hn7SlRRryVxmMaNG2P69OkAgOzsbLAsCy8vL1n34bC/4ooVK2L58uVo1qyZo3ZBCCFuw6ZaKeHB1tRO6Vlfj+DQkcyl1mQ54ubsY3IifZ8muW/uguM4JCcnIy0tzWi5j4+PUWCyVM5adtU0bdy4scj1fn5+mD9/PtasWUNDERBCiAirO54bPdja2ik9TuSn/vdi5tCzIjjJMXK5LAyDTCnrx8VD/sEo3ame7N69e+jataswOa+95YpjV2iqV69esWU8PDzwxhtv2LMbQggpc+wKU5AjUBVF/pHLXSZgEVIEh/RpIoQQ4hjFNelZVUNl+NM0ZNkdrPScPzVMWQpgNPecNHKNCE6hiRBCShG7a6iEDRXz0VlkqDIkNQzJF3SkTD4stY9WWQpg7kSj0QC6vkqmy0ylp6djzZo1gAwjglNoIoSQMkAsTEnuiC66QblClZ78tVdysKUGzJkTKnM844AJe127I/jdu3fRtWtXo2WJiYlo0KBBsY/t3bu3Xfum0EQIIWWcpSv5rK6dMtqo3KHKkLWhhGqLShOGYYRmNp7noVarAQtNbwzDwNPTE9WrV0f//v3tHhGcQhMhhBBRRdVE2RWoYMVYRnaFKz1O5PfihnF0j6DFO2AwSlfv0xQWFoYLFy4ABrVO9l4VJxWFJkIIIVZzaKAy2pGEj3BZgpUpqs1yB0FBQfj888/h5+fnlP1RaCKEECIrWa7ws2qHzqy1skSsNsvxyvqEvX5+fhg0aJDT9kehiRBCiFM5PVQJO+aLHmbB6CDcIzg4Yq44Kdu7du0ajh49itzcXERGRqJdu3ZQKm2LFJcuXcLevXsBAKNHjwbLitfaabVasCwLRqbXRq1WQ6VSWfUYCk2EEEJcSomFKqODcIXaK9f0ww8/YOHChUbLGjRogPnz5yMkJMSqbeXl5eHDDz/EzZs3AQAjR460GJru37+PUaNGYfTo0ejevbvN4SknJwcrV67Ejh07hKEIpHL50BQfH489e/YgPj4eWq0W1atXR9++fVGjRg3R8levXsWGDRuQmJiIoKAg9OzZE23btrW7LCGEENcgZagEpwQruMDkvFKmIbRhm5asW7cOCxcuhLe3N55//nkEBARg7969iI2NxcSJEzF37lyrdvXHH3+AYRg0adIE586dK7Ksr68v0tLS8P7776NmzZro168f+vTpg2rVqkna19mzZ7FlyxZs27YNKSkp6Nixo1XHClcPTV9++SVWrlxptnzWrFkYM2YMRo4cabR869atmDBhgtEAV6tXr8Zbb72Fjz/+2OayhBBC3IulYKVfbtcYVWXY/PnzwTAM5s+fj5YtWwIAxowZg5deegkHDx7E1atXERkZKWlbFy5cwNKlS7F8+XL89NNPxZYPDg7Gzp07sWjRIsybNw/Tp0/H9OnTUa1aNTRp0gRRUVEIDg5GYGAgNBoNUlNT8fjxY1y8eBHnz59HSkoKAKBatWqYMmUKevXqZfX5u3Roun//PsLDw/Hss8+iZs2aUCgUOHToELZu3Yrff/8dHTt2FAazevToESZPngyO4/C///0PrVq1wq1btzBnzhzMnz8f7du3x9NPP211WUIIIaWTS9VY2aigT5PMg1taWH7v3j3Ex8ejdevWQmACAB8fHwwZMgSTJ0/G4cOHJYWm/Px8TJo0CW+99RYaN24s+di8vLwwcuRIDBo0CJs2bcLq1atx9epV3LlzB1u3brX4OJZl0b59e7z66qvo3Lmzzf2vXDo0ffnll6hcubLRsn79+sHf3x8rV67EyZMnhdC0ceNG5OTkmNUU1alTByNHjsSKFSuEIGRNWUIIIWVXaQhWcomPjwcANG3a1Gydfpm+THFmzZoFpVKJUaNG2XQs/v7+GDRoEAYNGoTbt2/jxIkTOH/+PJKSkpCSkgKlUomQkBBUqVIFzZs3R8uWLREcHGzTvgy5dGgyDUx6zZo1w8qVKxEUFCQsO378OADg9ddfNyrbpUsXVKpUCceOHbOpLCGEEFIU82DlvKY/ji+42UMLDpxB/VI+rxUtl56eDgAoV66c2Tr9Mn2Zoly5cgWLFy/G6tWrrb56TUz16tVRvXp1DBgwwO5tFcelQ5MlO3bsQEhIiNHcM7dv34a/v7/oZHx169bFgQMHkJaWhsDAQKvKivHy8jKq2uNLuiOgg/n4+Bj9LAvK4jmDzpvOuwxwxjlrtVrk5mY5bPtyi1XE46KysIYol8+1ehtSPwc1Gg0mTZqEUaNGSe775ErcLjTNmTMHhw4dwqxZs4xGAM3KykJAQIDoY/TLMzMzERgYaFVZ8TK+8PLyEu73798fAwcOtOu83MGOHZbbi0ursnjOoPMuc8rieTvynK9cueLUARft/d5eXxOOupqawv0H+UlYiNtm5fSfj0+ePDFbl5ycbFTGkkWLFuH69evIzs7GjBkzhOWJiYkAgL/++gsBAQEYOnSoHWfkOG4VmqZPn465c+fip59+wjPPPGO0TqFQQKsVr1LUXyGnrx2ypqyY9PQsJCenCfdnzJiJGTNm2nBG7sHHxwc7dmzFc8/1RnZ2dkkfjlOUxXMGnTeddxngjHO29PniCBwYuzuCM1BAAYVwn7UQDcLDwwHdpfum9Mv0ZSy5cOEC8vLyMHOm+GfmzJkzERoaSqHJHhqNBp9//jm2bt2K6dOno1u3bmZlQkJCcP36dWg0GrPA8/DhQ7AsK/SBsqasmNzcXOTm5sl2fu4iOzsbWVll441VryyeM+i8S/ownK4snrdjz7l0dtmoUqUKwsPDceLECZw8eVK4gi47OxuLFy8GALRv377IbfTs2RMRERFmy/VjJo4aNarY2qqS5PKhKSsrC++//z5OnTqF2bNno127dqLlIiIicPnyZZw8eRJt2rQRlmdmZuLixYuoXr06PD09rS5LCCGEuKriZoOxdZuWDBs2DJMnT8Zbb72F3r17C4NbJiQkoGPHjoiKihLK7tmzB5cvX8aAAQNQpUoVALA4NtLx48eRmJiI0aNH2zwcgDO49LTMSUlJGDRoEM6ePYv58+dbDEzQXfkGAL/88gsyMzMBABzH4ccff0ReXp5Rp3FryhJCCCGkwEsvvYQ333wTOTk5WLNmDRYsWICEhATUr18f33//vVHZPXv24M8//8S9e/dK7Hjl5rpxDsCHH36IS5cuoWbNmpg3bx7mzZtntP7ZZ58VOmB3794d9evXx/nz59G1a1fUr18ft2/fxt27dxEYGGjUPmpNWUIIIcRV8Q6YsLe4iqtJkyZhwIABOHbsmDBhb/v27c1qiLp164awsDChlqkoL774Ilq3bm1x3jlX4dKhKSur4JLNhIQEJCQkmK037HCmUCgwe/ZsjB8/HidOnMCRI0cA3fgNv/zyCypUqGBTWUIIIYQYi4qKMmqKE9OtWzfRPshi+vfvL9OROZZLh6ZJkyYhIyPD4vrq1asb3Q8NDcWyZctw8+ZN3Lt3D8HBwahXr57oTMjWlCWEEEJckRyDW4ptk4hz6dBkOLeNNWrVqoVatWrJXpYQQghxJbwDrtVzx8y0Zs0arFy5EteuXQPHcQgNDUXjxo3RpUsX9OzZEx4eHrLsx7UbDwkhhBBCivD9999j8uTJiI2NRX5+PjQaDRITE7Fjxw58/PHH6NatG/bu3SvLvly6pokQQgghlvE8A46Xt1sJL/P2HOnOnTtYvHgxWJbFsGHD0KdPHwQFBeHx48c4duwYdu3ahbNnz2L06NH4/PPP8cYbb9i1PwpNhBBCCHELH3zwAfz9/VG/fn00bNgQcXFx4Hke//vf//Dxxx8L5SpVqoSGDRti+PDh2LVrF7788ktMnToVdevWRYsWLWzeP4UmQgghxE05e3DLkhYXF4ebN2+aLb9y5QqWLFmCBg0aoG7dukZz03bv3h1Vq1bFSy+9hOnTp2Pp0qU2759CEyGEEELcwqxZs3D+/HnExsbi0qVLuHTpErKysnD8+HEcP34cAMAwDGrUqIH69esb3dq0aYOYmBjk5OTA29vbpv1TaCKEEELcFOeAwS3l3p6c9Fe89+vXDwCwefNmfPzxx3jxxRdRrlw5IUjpx3fcvn278FiVSgWtVosZM2agVatWqF+/PkJDQ63aP4UmQgghhLilRo0aAbq5Yw2ncbl3754QoC5duoTY2Fg8evQIALBgwQIsWLAAABASEoJJkyahT58+kvZHoYkQQghxU7wD+iC5cJcmM7Vq1UK7du2we/duzJkzByNGjADDMKhSpQqqVKliNCL5iBEjcPDgQQwfPhx3797F5cuXcefOHSFMSUGhiRBCCHFTJTH3nKv55ptvMHDgQPz66684dOgQ3nrrLbRt2xaenp5Cmb179+LIkSPw9vbG2LFjhcEuMzMzkZeXJ3lfFJoIIYQQ4rbCwsKwbNkyjBo1CidPnsTJkyfh7e2NOnXqwM/PD4mJibh9+zYA4LXXXjMaHdzPz8/oSrviUGgihBBC3BTNPVegdu3a2LJlC1asWIFVq1bh5s2buHDhgrCeZVn079/faCwnW1BoIoQQQojb8/DwwJAhQzBkyBDcu3cPV65cwZMnT+Dj44OmTZsiLCzM7n1QaCKEEELcFE3YK07fEVxuNGEvIYQQQogEVNNECCGEuCneAX2aXHkalZJGNU2EEEIIIRJQTRMhhBDipsrahL0ljUITIYQQ4qbK2txzJY2a5wghhBBCJKCaJkIIIcRNUUdw56KaJkIIIYQQCaimiRBCCHFTNLilc1FNEyGEEEKIBFTTRAghhLgpzgET7NLVc5ZRTRMhhBBCiARU00QIIYS4KRrc0rkoNBFCCCFuindAcxplJsuoeY4QQgghRAKqaSKEEELcFOeAwS3l3l5pQjVNhBBCCCESUE0TIYQQ4qZocEvnopomQgghhBAJqKaJEEIIcVM0Ya9zUU0TIYQQQogEZb6m6caNG0hMTERwcDAaNGgAlqUcSQghxD3Q4JbOVWZD04MHDzBu3DicPn1aWFa1alX8+uuvaNKkSYkeGyGEECIF54DBLWnuOcvKZLWKVqvFyJEjcfr0aYSEhKBDhw6oUaMG7t69i7fffhuPHz8WfZxarXb6sbqKtWvXlvQhOF1ZPGfQeZc5ZfG8y+I5E3mUydC0a9cuXLp0Cc2aNcOePXswf/587Ny5E6+99hrS0tKwcOFC0cfpQxPDME4+4pLFMAzWr19fps67LJ4z6LzpvMuA0nbOPHhwvLw3ngYdsKhMhqZ9+/YBAD788EP4+voCuv9IH330Eby8vLB3794SPkJCCCGEuJoyGZquXr0KlUqF5s2bGy338/NDw4YNcfv2beTl5ZXY8RFCCCFS8A66EXFlsiN4SkoKypcvD6XS/PRDQ0PBcRxSU1MRGhpqtC43NxcAoFQq4e3tJSznS/mlBiqVCjzPQ6VSwcvLs6QPxynK4jmDzpvOuwxwxjlznBb5+Vrk5OQ4ZPuk5JTJ0KTVakUDEwAoFAoAgEajMVuXmJgIAMjISHXwEbqW3NwspKSId44vrcriOYPOu6QPw+nK4nk785wTEhLQrl07h+6DJux1rjIZmvz8/PDkyRPRdWlpaUIZU88//zwWL16MsLAweHkV1jSpVCqoVCoHHjEhhBB3kZOTg4SEBPTo0cMJe3NEx21KTZaUydBUrVo1JCQk4O7du6hatarRuitXriAoKAiBgYFmjytfvjzefPNNJx4pIYQQd+ToGiZSMspkR/DWrVsDAJYvX260fM+ePXj48KGwnhBCCHFl+uY5uW9EXJmsaXrhhRcwc+ZMLFq0CDk5OWjdujUSEhIwb948AMDrr79e0odICCGEEBdTJkNTxYoV8e2332LixIlYuXIlVq5cKax766238PTTT5s95tq1azh58iS0Wi3q1auHFi1aOPmo5XHlyhXExcUhIyMDVapUQYsWLUSbIhcvXoz8/HzRbQwfPlzoMK/HcRxOnDiBuLg4eHp64qmnnkLNmjUddh5SPXnyBOvWrRNdV7FiRbzwwgtmy3NychAdHY3ExESEhISgffv2CAkJEd2GNWWdafny5cjKyrK4vnHjxmjTpg0A4MKFC4iJiREt17RpU9Ga16SkJERHRyMtLQ3Vq1dH+/bt4eHhIeMZSJOXl4fo6GjcuHEDlSpVQt++fS2WddTrWhJ/A8nJyThw4AAeP36M5s2bo2XLlqLlMjMzcerUKdy5cwd+fn6oXbs2GjVqZFbOXf4Gbt68iejoaOTk5OD5559HWFiYWZldu3YhISFB9PHPPfccqlWrZrbcmvd3V/ssoGlUnKtMhiYA6N27N6KiorBhwwbcu3cPwcHB6N69u1lg4nkeX3/9NVasWGG0vH379vjzzz/h7e3t5CO3TUxMDKZOnYpr164ZLffz88N7772HoUOHGi3/888/kZGRIbqtN9980yg0paWl4Z133sGZM2eEZQzD4J133sG4ceNkPxdrPHr0CL/88ovouiZNmpiFposXL2L06NF48OCBsMzX1xc//PADnn32WZvLOtucOXPw8OFDi+snTpwohKZTp05ZfI7efvttsw/MDRs24IsvvjAay6x69eqYM2cOwsPDZTuHoqSlpeHzzz/H4cOHkZ2dDQBo3ry5xdDkqNfV2X8DFy5cwI8//ohTp05Bq9UCAN59913R0DRx4kTs2LFDGCpFr2XLlvj++++NwoOr/w1s3LgR8+fPN3r/atiwoWho2rhxo8UBiuvWrWt03ta8v5eWzwJinzIbmgAgIiICn3zySZFlli5dihUrVsDHxwc9e/aEl5cXdu/ejejoaEydOhXffvut047XHhcuXMC1a9dQt25d1KlTB8HBwbhw4QLOnj2L77//HlWrVjV7k69Zs6boG79pLdOkSZNw5swZVK5cGV27dkV6ejp27tyJ2bNno3bt2kV++3eWp59+Gg0bNjRaVrlyZaP72dnZGDVqFB4+fIhGjRqhefPmuHnzJg4dOoQPP/wQ27ZtQ/Xq1a0uWxLeeOMN0dC7e/du3L17F3369DFb179/f5QrV85omemH5cWLF/HZZ5+B4zh06dIF1apVw7Fjx3DlyhWMHj0aW7ZssTich5xSU1Oxc+dOeHp6onPnzjhw4IDFso56XUvib+DKlSs4fvw4goODUbduXYu1QwCwbds2eHp6onXr1qhWrRoyMzOxd+9enDx5Eu+99x42bdpk9hhX/RuIjo7GtWvXULNmTfj6+iI2NrbI8h4eHqIX7ZjWMlnz/u6ynwW8A8YKpD5NlvHEIq1Wy7dr146vX78+f/HiRWH5kydP+Pbt2/N169blHz16VKLHKNW5c+f4a9eumS2fPn06HxkZyY8fP95oeYsWLfiRI0cWu93r16/zkZGRfNeuXfm0tDRh+YkTJ/ioqCi+V69eMp2BbS5dusRHRkbyixYtKrbsihUr+MjISH7MmDE8x3HC8lmzZvGRkZH8l19+aVNZV5GVlcU3b96cHz16tNHyRYsW8ZGRkfylS5eK3cbYsWP5yMhIfunSpcIyjUbDDx8+nI+MjOS3b9/ukGM3lZKSwu/YsYPPysrieZ7n69Wrx7/66quiZR31upbE38Dly5f5o0eP8hqNhj9x4gQfGRnJ//rrr6Jlt23bxufk5Bgte/DgAd+uXTs+MjKST0hIEJa7+t/A4cOH+bi4OJ7nef6vv/7iIyMj+f/++0+07MiRI/kWLVoUu01r3t9d8bPg1KlTPAC+g/fLfG+/0bLeOni/zAPgT5065dRzcgdl8uo5qeLi4pCUlIQuXbqgQYMGwvKQkBC88cYb4DgO//33X4keo1SNGzdGnTp1zJa/+OKLgIVJiLOzs7F582YsXrwY//77rzCGlaHDhw8Duia7gIAAYXnLli3Rtm1bXL9+Hffu3ZP5bKz34MEDrFq1Cn///Teio6OFyZcN6c9l9OjRRs/HsGHD4Ovri0OHDtlU1lVs2bIFmZmZGDhwoOj6ixcvYunSpVi1ahUuXLggWiY6OhohISFGF0soFAqMGjUKAJx23kFBQejZsyd8fHyKLeuo17Uk/gbq1q2Lp556yqy2V0yvXr2MxpODbsYD/aXwYv/nXfVvoH379oiMjJRcnud5HDhwAIsXL8aGDRtw9+5dszLWvL+78mcB56AbEVemm+eKc+PGDUDXEdJUs2bNjMq4K/0bo1gzXExMjFH1v4+PDyZOnIhXXnlFWBYfHw8U8Rz9999/uHHjBqpUqeKgM5Bm0aJFRvfDwsLw888/G80/eOPGDfj4+CAqKsqorIeHBxo0aIATJ04gNzcXXl5eVpV1FatXr0ZoaCg6dOggun7y5MlG91u1aoVff/0VFStWBHT9w9LT09GpUyezD+3GjRtDqVQKfw+uxFGvqzv+DXAch0uXLiEyMlK06bC0/A1kZmbinXfeEe6zLIuXXnoJU6ZMEZoOrXl/d+XPAp7nZW+eK+1Tg9mDQlMR9DUrpm38hsvEal/cxd27d/Hdd9+hS5cu6N69u9E6hmFQt25dNGrUCAzD4MKFC7h8+TKmTJmCChUqoEuXLoDB+ZcvX95s+/oriNLT051yPpYoFAq0aNECERERyMzMxNGjR5GYmIgRI0Zg27ZtwhyD6enpoq81dOfC8zwyMjLg5eVlVVlXcO7cOcTGxuLdd98VraXw8/NDq1atULVqVTx69AiHDh3CiRMnMGrUKKxZswYMwwivo9h5K5VKBAQEuOT/B0e9ru72NwAAv/76K27evIlly5aZrStNfwOVK1dG8+bNERwcjPj4eMTExGD16tXw9fXFhAkTACvf30v7ZwGRjkKTBGLV2GLL3ElCQgKGDRuGmjVr4ueffzZbP3v2bLNLaZcuXYqpU6di/vz5QmjSK+o5KslvLRUrVsSOHTtQo0YNYVl+fj4mTpyIbdu2YeXKlRg7dqywztLrKnYu1pQtaatWrQLDMKJNc23btsWAAQPg7+8vLHvy5AkGDRqECxcu4OjRo0ZXlRZ13q50zoYc9bq609/Ab7/9hsWLF+OXX34xqzEpTX8DI0aMQKNGjYy+HJw5cwZDhw7FsmXLMGbMGKNmXWve313xs4B3QHOa6/zVuh7q01QE/RtIcnKy2Tr9MsM3GXdx7tw5vPrqq6hVqxbmz58PX19fszJiY48MHjwYVapUweXLl4Vl+vMXm8vPFZ6jcuXKGQUm6JpP9EMhmJ6L2GsNkXOxpmxJS09Px/bt29GmTRvRMWoiIyPNjrVcuXJ46623AACXLl0CinmttVot0tPTjfq1uQpHva7u8jeg0Wjw6aefYtGiRfjzzz9F50MrTX8DTZs2NatNbdasGXr06IH8/HyhGc2a9/fS+llArEehqQj68UbOnz9vtu7cuXMAgFq1ajn9uOyxZ88eDB48GC1atMCsWbOsbjpgWdbom2RRz5F+mbPG7rGG/k3V9FwyMzPN+iao1WpcunQJlStXFsZisaZsSVu/fj1yc3MtdgC3xPQ5qlixInx9fXHx4kVwnPF329jYWKjVapf8/+Co19Ud/gaysrLwzjvv4N9//8WcOXPQqVMnqx5fWv4GoHvvgsG5WPP+7sqfBRx4cLzMN6prsohCUxHq1auH4OBg7Nmzx+iNMSMjAytWrADDMG41KePy5csxZswYdOvWDdOnT7c4eu/Vq1dF+yFt3LgRd+/eRUREhLCsbdu2gK7pLicnR1geGxuL6OhoVK9eXbR2w1nOnj0LjUZjtIzjOMycORPQjdWlpz+XuXPnGpVfuXIlMjIyjF5ra8qWtNWrVyMwMNCs35reyZMnzZZlZmZi8eLFgMFzxDAM2rZti6SkJGzYsEEoy/O8MAWRK523nqNeV1f/G0hKSsKgQYNw7tw5LFy4UHSmA73S8jeQlJSEW7dumS2/evUqdu/eDaVSKQQga97fS9tnAbEd9WkqgkKhwODBgzF9+nS8/vrr6NevH7y9vbF9+3YkJiaiV69eZgMkuqpVq1bh66+/RkhICCIiIrBw4UKj9YZTiuzZswfz5s1Dhw4dUKNGDXAch/Pnz+P48eMAgCFDhgiPq1u3Ltq2bYsjR46gf//+6NGjBzIzM7FhwwZotVoMGzbMyWdq7Pfff0dCQgJat26NqlWrIj09HdHR0bh58ya8vLzw6quvCmVffPFF/PXXX9i4cSMePnyIli1b4ubNm9i+fTsUCoXRYHnWlC1Jx44dQ3x8PP73v/9ZDMmDBw9GVFQUGjVqhAoVKuDhw4fYvXs3UlNTERERYfRhMGTIEOzevRuff/45jh8/jmrVqiEmJgYnT55EWFgYnnvuOaedm+FUMTzP4+HDh0KACQ8PR7du3QAHvq4l8TeQnp6OVatWAQASExMBXX8d/Xm3a9cODRo0QH5+Pl555RXhferEiRM4ceKE0bYMpxRx9b+BK1euCEMZnDp1CtAN3nnx4kUAwMCBAxESEoJbt27hf//7H9q0aYM6derAz88P8fHx2Lt3L9RqNV555RX4+fkBVr6/u/JnAa/7J/c2iTiGL+leey5Oo9Hg448/xvbt242WN2nSBPPnzy/x9nuppk6diqVLl1pc36RJE/zzzz8AgL179+Kzzz5DSkqKURmVSoWxY8cK/Rz0Hj16hOHDh+Pq1atGy1955RV89dVXJdpR8o8//sC8efPM5tErV64cfvrpJ7Nvh8ePH8eYMWOQmpoqLPPw8MBXX32F/v3721y2pIwdOxY7duzApk2bULduXdEyQ4cOxZEjR8yWN2jQANOnTzerKVy8eDF++uknoxq8ChUqYM6cOUZj2Dhax44dLU4V06NHD/zxxx/CfUe9rs7+G7h165bFGkMA+PzzzzFo0CCkp6ejVatWRW5r3rx56NixI+AGfwNr1qwxGw7B0JYtWxAZGYk7d+5gxIgRosMePP/885g2bRo8PT2FZda8v7vaZ8Hp06fRokULtPYagAC2gqzbTueScDx3HU6dOmU0LAuh0CTZyZMncerUKWg0GtSrVw/PPPOMpAHmXMX+/fuFb2hiKleujDfeeEO4n5eXJ4yxlJubi2rVqqFDhw4WL7HOz8/HwYMHERcXBw8PD7Rp0waNGzd2yLlYKzk5GUeOHMGtW7fAsiwiIiLQoUMHozdPQ6mpqdi9ezfu37+P4OBgdOnSRXSOK2vLOhvP8/jjjz/g7e2NESNGFFn2xo0bOH36NO7fvw9fX180btwYLVu2tBh4b926hf379yM9PR3VqlXDs88+K3yDd5Y5c+ZYnB8xMjLSbPoeR72uzvwbSElJwYIFCyyu79q1K5o1a4a8vDzMmDGjyG0NGDDAqB+OK/8NnD9/Hrt27bK4fsiQIUbDnpw8eRKXL19GcnIyypcvjzZt2qB27doWH2/N+7urfBboQ1MrrwHwlzk0ZXBJOEGhSRSFJkIIIcTN6ENTC6/+DglNp3LXU2gSQR3BCSGEEEIkoI7ghBBCiJvieICTucGIo/Yni6imiRBCCCFEAqppIoQQQtyW/EMOSJlI5eHDh8Kk1JGRkVZf+JOeno7Y2FgkJiaiXLlyqFu3rlsM4UOhiRBCCCGSzZkzB3/88YfRkBNt27bFjBkzir2CMj09HVOmTMHevXuNhoJRKBTo168fpkyZUuIj6ReFmucIIYQQN8WBd8jNkn///Re//voroBvion///qhQoQKOHDmCzz//vNjjTUlJwY4dO+Dt7Y02bdpgwIABaN++PXiex/r16/H111/L+vzIjWqaCCGEECLJrFmzAAB//fWXMJdhamoqBg4ciO3bt+ODDz5AzZo1LT4+ICAAv/32G7p162Y0S8HJkycxZMgQ7NixA9OmTXPCmdiGapoIIYQQN+XMmqZHjx7hypUraNasmdHkz0FBQRg6dCgA4MCBA0Ueb3BwMHr16mU2rVPLli0REREBrVYLVx4+kmqaCHFzN2/exIoVK4yWvfLKK6hTp45wPzs7G7/99hsCAgIwZsyYEjhKcyV9TBzHmX2jbdu2LTp37uz0YyHEds7rCK6frLhFixZm6/TLDCc0tkZmZibu3r2Lzp07l+jUW8Wh0ESIm7t//77ZvIJt27Y1Ck25ublYunQpQkNDXSY0lfQxcRxn9rx5enpSaCJlDg8OYLjC+4xWtJx+jsUKFcxHINcvS0tLs37/PI8pU6aAYRh88sknVj/emSg0EVJKhIeH45VXXgEAo8Akt4yMDPzxxx8IDAzEe++9Z3OZkqZQKPDpp58CAI4dO4Z9+/aV9CERYrXiOm5LkRNwB3mBd4T7ubm5wG3zckU1m+lrhziOs1hGjEajweeff44DBw5g3rx5qFq1qlWPdzYKTYSUElWqVMGQIUMcvp+srCwsXboUYWFhFgORlDK+vr749NNP4evr6+AjFscwjPB8abVaCk2kzPJKrwqvjCrCfSX3BGKpST+cQEpKitk6/TJ/f3/J+83OzsbYsWNx7tw5LF682GUmeS8KhSZCSInw9PR0SsgjpDTjGB4cY13tjrjC68J4C9eI1apVCwBw8eJFs3UXLlwwKlOcx48fY8SIEXjw4AGWLFmCunXr2njczkWhiRAn4jgOf/75JzIyMtCzZ0/RDpXbtm3D2bNnUadOHaG5zdGSkpJw9OhR3L17F5mZmahQoQJatWqFBg0aGJXbvXu3cHVMamoqpk6dKqzz8vLC+PHjJZWBxI7gDx48QHR0NO7evQuWZVG9enU888wzCA4OFi2fmJiI6Oho3Lt3DwzDoE6dOujUqVOxA+4RQopXrVo1VK1aFTExMbh8+TLq1asHAFCr1UL/wKeffrrY7dy8eRNvvfUWNBoNli9fLjlouQIKTYQ4EcuyiIiIwNixY7Fjxw5s2rQJ5cqVE9afPXsWEyZMgFKpxJo1a5xyTO+++y4OHToErda882enTp3wyy+/CKHj+PHjWLt2LWDQBKfn7++P8ePHSyqDYjqC5+fn4/vvv8fq1auNRh2GLnhNmjTJKFCq1Wp8//33WLlypdl5hISE4Mcff0SHDh3sep4IcUW8DH2axLZpyZtvvompU6fizTffxCuvvIKAgADs2LEDsbGxaNmyJRo1aiSUjYmJwY0bN9C9e3dUrFgR0H2xefXVV5GWloahQ4fiv//+w3///We0j/79+8PHx0fWc5ILhSZCnOy5557D8ePHsWLFCnz88ceYP38+WJZFWloaxo0bB7Vaja+++goRERFOOZ5jx46hWrVqaN68OcLCwsAwDO7cuYO9e/fiwIED+Oqrr/DTTz8BAJ599lkEBgZixowZCAwMxKhRo4Tt6MddkVKmKDzPY+zYsdi7dy8YhkH79u3RrFkzsCyLhIQEHDx4EHFxcUaP+eSTT7B9+3YoFAo8++yziIqKgkajwdGjR3H27FmMGjUKa9ascZsmAEJc1aBBg3DhwgVs3rwZc+fOFZZXr15deJ/Q27RpEzZs2IC6desKoen+/fvCVXgLFy4U3Ue3bt0oNBFCCn366ac4e/Ys/vvvP8yZMwcjR47ExIkTce/ePfTr1w8DBgxw2rHMmzcPLVq0MBsb5eHDh3jxxRexdetWTJo0CcHBwWjdujWqV68uzDEl1idJSpmi7NmzB3v37oVKpcLMmTPRsWNHo/W5ubm4deuWcP/gwYPYvn07/Pz8sHTpUrMmxV9//RVz5szB77//jtmzZ1t1LIS4Ov1wlHJv0xKWZfHTTz9h4MCBOHr0qDBhb8+ePc3mjHv66afh4+OD0NBQYVloaCjeeOONIvfvqoEJFJoIKRkeHh74/fff0b9/f8yYMQMJCQnYt28fatWqhS+//NKpx9KyZUukpaUhOjoaN2/eRGZmptDE5ePjgydPnuDKlSuS+irIYdOmTQCAwYMHmwUm6JrnoqKihPsbNmwAALzzzjtmgQkAPvjgA6xYsQLR0dHIy8uDp6enQ4+fEGfidMMOyL3N4jz11FN46qmniizTr18/9OvXz2hZtWrVMGXKFDuPsORQaCKkhNSoUQPffPMNxo0bh40bN8LT0xPTp093+resxYsX47fffisYm8WCjIwMpx3P5cuXAQBdunSRVP7SpUvCzx9++EEYS8bwp0qlQkZGBhITExEeHu6wYyeElG4UmggpQfXq1YOnpyfy8vJQv359REZGOnX/e/bsEaYSadmyJRo3bozg4GCh79GmTZtw6dIlqwess0dWVhagm6NKivT0dADAjh07ii2bnZ1t59ER4lp4cDINOWC8TSKOQhMhJSQvLw9jx45FXl4e/P39cebMGcybNw8jRoxw2jGsW7cOAPDee++JXva/c+dOpx2LXmBgIFJSUvDo0SPUrl272PL+/v5ISUnB0KFDUalSpSLLVq5cWcYjJYSUNRSaCCkh3333Ha5cuYL27dtj0qRJGDhwIKZPn46WLVuiefPmTjmGBw8eABaawh4/fowrV66YLWfZgoHvTIcCsLaMJY0aNUJCQgJ27NghqR9Vo0aNcPv2bYSGhtJgmaTM4XT/5N4mESc+7CchxKH+/fdfrFq1ChUqVMCPP/6I2rVr44svvoBGo8H48eOFS3IdLSQkBNA10xlKSUnBJ598ItqcFRAQAIZhkJycbLGvk5Qylrz00ksAgH/++Ud0rKqHDx/i2LFjwv1XX30VAPD7779j//79otu8e/cudu3aZdVxEEKIKappIsTJ7ty5g8mTJwuX7uoHt3zhhRdw9OhRbNiwAZ9++ilmzZrl8GPp1asXoqOjMXPmTPz333+oW7cuHj9+jFOnTiE9PR1hYWFITEw0eoyXlxciIyMRFxeHV199FS1atICnp6fRaN9Syljy1FNP4fXXX8eKFSswefJkLFy4EM2aNQPDMLh16xbOnj2Ll19+Wbhyp3Xr1hg6dCgWLVqEd999F+Hh4YiKikJQUBAeP36MO3fuIC4uDq1atUL37t0d+GwS4nwFAw7IXdMk79V4pQmFJkKcKD8/H2PHjkVGRgZGjx5t1vw0ZcoUnDt3Dvv27cPixYsd3tw0YMAAXL58GcuWLcO5c+dw7tw5QDcx5w8//ID9+/ebhSboBpMcM2YMrl+/juvXrwMmo31LLWPJlClTULlyZcyZMwfx8fGIj48X1lWqVMnsUueJEyeiRo0a+PPPP83K/7+9uwmpqt3iAL58fbN7lT4I84PySPQxERIqjKLJpUEQRCBFBAVFFEHTBgnRKCIaNKpBzRo4CaRRQaNbEhKigQ0UaiBcLCKKCqJSOWffgTd5fe3krrbHtvf3G+6zWftwBofF/1n7eeJ/rznv2bPnh38f+P1lv09Tuk0H/j9pmqCCxsbGYt++fdHZ2Tm9rPRXtbW1cf369ejt7Y0lS5ZEsViM6urqX35uXV1ddHV1RV1d3azPzp8/H0ePHo2BgYGYmJiI5ubm6OjoiNra2lixYkW0t7dPnzH11a5du+LBgwfR398fr1+/jsnJyVm7fc91z/e+U1VVVZw6dSqOHDkSg4OD8fLly6ipqYlCoRDt7e3x55+z/7oOHz4cBw4ciKdPn8bo6GhMTk5GQ0NDtLS0VPytRGBxqkq+bmYC5FJfX18cP3481qxZE7t3746IiEOHDsWGDRsW+qv91kql0vR2C8PDwzEwMBAnT56Ms2fPLvRXgzk9efIktm7dGoV//iv+Ub0y09pfiu/jP5//HYODgxV7KSUvJE2wSLx48WL6cNydO3dqmuZQKpVmHCYMMBdNE+TcunXroqura8Y1DdPcqqurZ/1ufz2hHfLAlgOVpWmCnGtubrY/0U+oqqryuwE/RNMEALlViiSKmdfk22xuCQCQgqQJAHLKTFNlaZoAIKc0TZVleQ4AIAVJEwDklkHwSpI0AQCkIGkCgJwy01RZkiYAgBQkTQCQU0kkkWScDCWRZFpvMZE0AQCkIGkCgJxKohiljN+ey/5tvMVD0wQAOWV5rrIszwEApCBpAoCcKiXFKCXZLqdlXW8xkTQBAKQgaQKAnDLTVFmSJgCAFCRNAJBbxXnYIsBMUzmSJgCAFCRNAJBTpUiilGR9YK+ZpnI0TQCQU8lU25R5Tb7N8hwAQAqSJgDIqSQpRZLxZpRJxst9i4mkCQAgBUkTAORUEqUomWmqGEkTAEAKkiYAyKmpmaaMkyYzTWVJmgAAUpA0AUBOTe3TlPHbc2aaytI0AUBOWZ6rLMtzAAApSJoAILeSeVhOc/ZcOZImAIAUJE0AkFNJUpyHY1SyrbeYSJoAAFKQNAFATiWRZP/2nJmmsiRNAAApSJoAIKemNrd0YG+laJoAIKeSJPstB5LE8lw5lucAAFKQNAFAbmW/PBeW58qSNAEApCBpAoCcmtpuIOvNLSVN5UiaAABSkDQBQG6V5mEGSdJUjqYJAHJqaikt6y0HNE3lWJ4DAEhB0gQAOTV1Tpyz5ypF0gQAkIKkCQByqxQRVfNQk2+RNAEApCBpAoC8SrKfaQoH9pYlaQIASEHSBAA5lf1hvelqfvz4MYaGhuLLly+xadOmaGlp+eHnZFGj0jRNAJBb8zG0/f2at2/fjkuXLsXnz5+nr+3duzcuX74cS5cuTfWELGosBE0TAJBKb29vXLhwISIitmzZEitWrIj+/v64d+9e1NXVxcWLFytSY6FomgAgzyo4uH3t2rVIkiSuXLkS+/fvj4iIV69excGDB6OnpydOnz4da9eunfcaC8UgOAAwp7dv38bQ0FC0tbVNNzsREU1NTXHixIkolUrx8OHDea+xkCRNAJBb83HoybcrPn/+PCIiOjo6Zn329dqzZ8++WzmLGgtJ0wQAuZVNy1RVNXNX8W+t+L179y4iIhobG2d91tDQMOOecrKosZA0TQCQM/X19VFbWxufPn3KpN7fm6Sampqor6//2z1TN/3xx+zJnurq6oiIKBaLczzn12ssJE0TAORMoVCIkZGRePPmzS/XmpycjMnJyRnXmpqaolAozLhWV1cXEREfPnyYVeP9+/cREbFs2bLvPiuLGgtJ0wQAOVQoFGY1NvOptbU1IiKGh4dnfTYyMjLjnvmssZC8PQcAzKm1tTWampri0aNHMTo6On29VCpFd3d3RERs37593msspKokcTIfADC3GzduxNWrV6OxsTGOHTsWy5cvj7t370ZfX1+0tbVFT0/P9FD50NBQjI2NxY4dO2LVqlU/VeN3o2kCAFKZmJiIM2fORG9v74zrq1evjlu3bsX69eunr507dy7u3LkT3d3dsW3btp+q8bsx0wQApFJTUxM3b96M+/fvx+PHj2N8fDw2btwYnZ2dsXLlyhn3bt68OcbHx2ekTD9a43cjaQIASMEgOABACpomAIAUNE0AAClomgAAUtA0AQCkoGkCAEhB0wQAkIKmCQAgBU0TAEAKmiYAgBQ0TQAAKWiaAABS0DQBAKTwX4LmZUA66uf3AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 600x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Re_show = max(Res)\n",
    "D_show = max(D for (Re, D) in results if Re == Re_show)\n",
    "r = results[(Re_show, D_show)]\n",
    "fig, ax = common.fig_single()\n",
    "pcm = ax.pcolormesh(r[\"xs\"], r[\"zs\"], r[\"T\"], shading=\"auto\", cmap=\"inferno\")\n",
    "ax.set_aspect(\"equal\")\n",
    "ax.set_xlabel(\"x [lattice]\")\n",
    "ax.set_ylabel(\"z [lattice]\")\n",
    "ax.set_title(f\"Temperature field - Re = {Re_show}, D = {D_show}\")\n",
    "fig.colorbar(pcm, ax=ax, label=r\"$\\phi$ (temperature)\")\n",
    "fig.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ba368ea",
   "metadata": {},
   "source": "## Momentum sanity - Strouhal and drag (case 09 references)\n\nFor the shedding variants (`Re = 100`) the Strouhal number is taken from the\nspectral peak of the cross-stream velocity at the wake probe, and the drag\ncoefficient from the body force on the voxel band. These reuse the case-09\nmomentum references (`St ~ 0.16-0.17` at `Re = 100`, rising toward `0.21` at\nhigher Re; `Cd` consistent with case 09). They are sanity checks on the flow,\nnot the primary thermal validation.\n\nThe cell below reads the wake-probe max-rate series if present; it is left as a\ntemplate since the exact drag export depends on the voxel-band force diagnostic.\n"
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3cf7be72",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-29T17:44:39.164438Z",
     "iopub.status.busy": "2026-06-29T17:44:39.164344Z",
     "iopub.status.idle": "2026-06-29T17:44:39.528944Z",
     "shell.execute_reply": "2026-06-29T17:44:39.528604Z"
    }
   },
   "outputs": [],
   "source": "def strouhal_from_probe(cfg, Re, D):\n    \"\"\"Strouhal St = f * D / U from the wake-probe uz series, if available.\"\"\"\n    try:\n        probe = cfg.output.exports[\"spectrum\"].series.points[\"wake\"]\n    except Exception:\n        print(\"No wake probe series exported for this variant; skipping St.\")\n        return None\n    # The wake probe is a single-point max-rate series (#1023): read_full_data\n    # returns one column per point plus `time_step`; take the sole data column.\n    df = probe.read_full_data(\"uz\").sort_values(\"time_step\")\n    sig = df.drop(columns=\"time_step\").iloc[:, 0].to_numpy(dtype=float)\n    dt = float(np.median(np.diff(df[\"time_step\"].to_numpy())))\n    f, psd = common.energy_spectrum(sig, dt=dt)\n    f_peak = f[np.argmax(psd)]\n    St = f_peak * D / U_INF\n    print(f\"Re={Re} D={D}: peak f={f_peak:.5f} -> St={St:.3f}\")\n    return St\n\n\nfor Re, D in sorted(results):\n    if Re >= 100:  # shedding\n        strouhal_from_probe(variants[(Re, D)][\"cfg\"], Re, D)"
  },
  {
   "cell_type": "markdown",
   "id": "9423dedc",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n",
    "- **Primary validation:** the control-volume `Nu_D` matches Churchill-Bernstein\n",
    "  within ~10-15% at both resolutions (Re = 40: +5% / -2% at D = 40 / 80;\n",
    "  Re = 100: +11% / +2%), with the finer `D = 80` grid closer to the\n",
    "  correlation - the expected first-order `D/dx` convergence of the curved voxel\n",
    "  Dirichlet wall flux.\n",
    "- **Local `Nu(theta)`** shows the front-stagnation peak and the separation\n",
    "  minimum, and its angular mean tracks the balance `Nu_D` to within a few\n",
    "  percent.\n",
    "- **Momentum sanity:** `St ~ 0.16` at `Re = 100`, consistent with case 09.\n",
    "\n",
    "**Why the heat balance, not a near-wall slope:** the cylinder wall is staircased\n",
    "onto the lattice, and heat spreads radially so the local gradient decays like\n",
    "`1/r`. Reading `Nu_D` directly from a raw near-wall slope a few nodes out\n",
    "therefore underestimates it badly (by ~25-40% here). The control-volume balance\n",
    "is a conserved flux, independent of near-wall sampling, and is the trustworthy\n",
    "surface-averaged number; the `(r/R)`-referred ray distribution only supplies the\n",
    "angular shape.\n",
    "\n",
    "**Caveat (staircase convergence):** the wall flux is first-order in `D/dx`, so a\n",
    "single resolution is not a pass/fail number; the two-resolution trend toward the\n",
    "correlation is the evidence.\n",
    "\n",
    "**Reference:** Churchill, S.W. & Bernstein, M. (1977), \"A correlating equation\n",
    "for forced convection from gases and liquids to a circular cylinder in\n",
    "crossflow,\" *J. Heat Transfer* 99(2):300-306."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d26e0b3",
   "metadata": {},
   "source": [
    "## Version"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "27c0e4c9",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-29T17:44:39.529970Z",
     "iopub.status.busy": "2026-06-29T17:44:39.529869Z",
     "iopub.status.idle": "2026-06-29T17:44:39.567011Z",
     "shell.execute_reply": "2026-06-29T17:44:39.566750Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Version:"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " "
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.0.1a0"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Commit hash:"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " "
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "80a1135356dcbcdac92068bde45adb0fae958657"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "sim_cfg = next(iter(all_cfgs.values()))\n",
    "sim_info = sim_cfg.output.read_info()\n",
    "\n",
    "nassu_commit = sim_info[\"commit\"]\n",
    "nassu_version = sim_info[\"version\"]\n",
    "print(\"Version:\", nassu_version)\n",
    "print(\"Commit hash:\", nassu_commit)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "506187f6",
   "metadata": {},
   "source": [
    "## Configuration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "cb9c3924",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-29T17:44:39.567819Z",
     "iopub.status.busy": "2026-06-29T17:44:39.567746Z",
     "iopub.status.idle": "2026-06-29T17:44:39.603510Z",
     "shell.execute_reply": "2026-06-29T17:44:39.603112Z"
    }
   },
   "outputs": [
    {
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       ".output_html .il { color: #666 } /* Literal.Number.Integer.Long */</style><div class=\"highlight\"><pre><span></span><span class=\"c1\"># Heated circular cylinder in cross-flow - voxel curved Dirichlet scalar BC</span>\n",
       "<span class=\"c1\">#</span>\n",
       "<span class=\"c1\"># Forced-convection benchmark for a fixed-temperature (Dirichlet) heated</span>\n",
       "<span class=\"c1\"># cylinder. This is the validation case for the scalar Dirichlet BC on a</span>\n",
       "<span class=\"c1\"># CURVED voxelized surface (velocity band BC + scalar band BC): the</span>\n",
       "<span class=\"c1\"># curved wall is staircased onto the lattice, so</span>\n",
       "<span class=\"c1\"># the surface-averaged wall heat flux (Nusselt number) is FIRST-ORDER in</span>\n",
       "<span class=\"c1\"># `D/dx`. The case therefore runs at two diameters (D = 40 and D = 80</span>\n",
       "<span class=\"c1\"># lattice units) so the staircase convergence of `Nu_D` can be reported.</span>\n",
       "<span class=\"c1\">#</span>\n",
       "<span class=\"c1\"># It reuses the flow-over-cylinder momentum setup (case 09): same circular</span>\n",
       "<span class=\"c1\"># cylinder geometry (`fixture/stl/basic/cylinder_refined.stl`), uniform</span>\n",
       "<span class=\"c1\"># cross-flow, no-slip wall, and the Strouhal / drag momentum checks. The</span>\n",
       "<span class=\"c1\"># thermal layer is added on top: a passive scalar `temperature` (D3Q7,</span>\n",
       "<span class=\"c1\"># RRBGK) advected and diffused by the flow, with the cylinder wall held at</span>\n",
       "<span class=\"c1\"># `phi_w = 1.0` (heated) and the freestream at `phi = 0` (clean).</span>\n",
       "<span class=\"c1\">#</span>\n",
       "<span class=\"c1\"># Unlike case 09 (which uses IBM + heavy multiblock refinement to resolve a</span>\n",
       "<span class=\"c1\"># small D = 2.5 cylinder), this case VOXELIZES the body on a single uniform</span>\n",
       "<span class=\"c1\"># grid level at the target diameter, so the curved Dirichlet band is the</span>\n",
       "<span class=\"c1\"># only wall treatment under test (no IBM, no refinement). The STL is scaled</span>\n",
       "<span class=\"c1\"># by `D / 2.5` to reach the target lattice diameter directly.</span>\n",
       "<span class=\"c1\">#</span>\n",
       "<span class=\"c1\"># ---------------------------------------------------------------------</span>\n",
       "<span class=\"c1\"># Re / Pr -&gt; lattice mapping (Pr = 0.71 for air; buoyancy OFF)</span>\n",
       "<span class=\"c1\"># ---------------------------------------------------------------------</span>\n",
       "<span class=\"c1\"># Fixed lattice freestream `U = 0.05` (Ma = U*sqrt(3) = 0.087 &lt; 0.1).</span>\n",
       "<span class=\"c1\"># Reynolds number on the diameter:  Re = U * D / nu  -&gt;  nu = U * D / Re.</span>\n",
       "<span class=\"c1\"># Fluid relaxation (cs^2 = 1/3):     tau     = 3*nu + 1/2.</span>\n",
       "<span class=\"c1\"># Scalar diffusivity (Pr = nu/D_s):  D_s     = nu / Pr.</span>\n",
       "<span class=\"c1\"># Scalar relaxation (D3Q7, cs_phi^2 = 1/4): tau_phi = D_s/0.25 + 1/2.</span>\n",
       "<span class=\"c1\">#</span>\n",
       "<span class=\"c1\">#   | Re  | D  | nu      | tau (fluid) | D_s     | tau_phi  | Nu_D (CB) |</span>\n",
       "<span class=\"c1\">#   | 40  | 40 | 0.05000 | 0.65000     | 0.07042 | 0.78169  | 3.38      |</span>\n",
       "<span class=\"c1\">#   | 40  | 80 | 0.10000 | 0.80000     | 0.14085 | 1.06338  | 3.38      |</span>\n",
       "<span class=\"c1\">#   | 100 | 40 | 0.02000 | 0.56000     | 0.02817 | 0.61268  | 5.18      |</span>\n",
       "<span class=\"c1\">#   | 100 | 80 | 0.04000 | 0.62000     | 0.05634 | 0.72535  | 5.18      |</span>\n",
       "<span class=\"c1\">#</span>\n",
       "<span class=\"c1\"># Re = 40 is steady (no shedding); Re = 100 sheds a laminar Karman street</span>\n",
       "<span class=\"c1\"># (St ~ 0.16-0.17 at Re = 100, rising towards 0.21 by Re ~ 250). The</span>\n",
       "<span class=\"c1\"># two-resolution pair (D = 40 vs D = 80) at each Re exposes the first-order</span>\n",
       "<span class=\"c1\"># `D/dx` convergence of the staircased curved Dirichlet wall flux.</span>\n",
       "<span class=\"c1\">#</span>\n",
       "<span class=\"c1\"># Nu_D (CB) is the Churchill &amp; Bernstein (1977) surface-averaged Nusselt</span>\n",
       "<span class=\"c1\"># correlation, tabulated in</span>\n",
       "<span class=\"c1\"># validation/thermal/02_heated_cylinder/reference/churchill_bernstein.csv.</span>\n",
       "<span class=\"c1\"># Acceptance: Nu_D within ~10-15% of CB (correlation scatter ~10-20%),</span>\n",
       "<span class=\"c1\"># reported at BOTH resolutions with the convergence trend; local Nu(theta)</span>\n",
       "<span class=\"c1\"># qualitatively correct (front-stagnation peak, separation minimum).</span>\n",
       "<span class=\"c1\">#</span>\n",
       "<span class=\"c1\"># ---------------------------------------------------------------------</span>\n",
       "<span class=\"c1\"># Turbulent follow-up (not the primary run)</span>\n",
       "<span class=\"c1\"># ---------------------------------------------------------------------</span>\n",
       "<span class=\"c1\"># The Re = 3900 3-D LES variant (turbulent wake, Smagorinsky SGS with a</span>\n",
       "<span class=\"c1\"># turbulent-Prandtl coupling `Sc_t` on the scalar) needs a 3-D span, LES,</span>\n",
       "<span class=\"c1\"># and a much longer averaging window; it is left out of this primary</span>\n",
       "<span class=\"c1\"># laminar 2-D sweep.</span>\n",
       "<span class=\"c1\">#</span>\n",
       "<span class=\"c1\"># Reference: Churchill, S.W. &amp; Bernstein, M. (1977), &quot;A correlating</span>\n",
       "<span class=\"c1\"># equation for forced convection from gases and liquids to a circular</span>\n",
       "<span class=\"c1\"># cylinder in crossflow,&quot; J. Heat Transfer 99(2):300-306.</span>\n",
       "\n",
       "<span class=\"nt\">variables</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">  </span><span class=\"c1\"># Lattice freestream velocity (inlet BC, init equation). Ma = 0.087.</span>\n",
       "<span class=\"w\">  </span><span class=\"nt\">u_inf_lattice</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0.05</span>\n",
       "\n",
       "<span class=\"nt\">simulations</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">  </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"nt\">name</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">heatedCylinder</span>\n",
       "<span class=\"w\">    </span><span class=\"nt\">save_path</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"kt\">!unroll</span>\n",
       "<span class=\"w\">      </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">./validation/thermal/02_heated_cylinder/results/re40_D40</span>\n",
       "<span class=\"w\">      </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">./validation/thermal/02_heated_cylinder/results/re40_D80</span>\n",
       "<span class=\"w\">      </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">./validation/thermal/02_heated_cylinder/results/re100_D40</span>\n",
       "<span class=\"w\">      </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">./validation/thermal/02_heated_cylinder/results/re100_D80</span>\n",
       "<span class=\"w\">    </span><span class=\"nt\">n_steps</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"kt\">!unroll</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">120000</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">240000</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">200000</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">400000</span><span class=\"p p-Indicator\">]</span>\n",
       "\n",
       "<span class=\"w\">    </span><span class=\"nt\">report</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">{</span><span class=\"nt\">frequency</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"nv\">2000</span><span class=\"p p-Indicator\">}</span>\n",
       "\n",
       "<span class=\"w\">    </span><span class=\"nt\">domain</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">      </span><span class=\"c1\"># Domain in diameter multiples: 20*D streamwise, 12*D cross-stream,</span>\n",
       "<span class=\"w\">      </span><span class=\"c1\"># thin periodic span (y, 8 cells). Cylinder centred 6*D from inlet.</span>\n",
       "<span class=\"w\">      </span><span class=\"nt\">domain_size</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">x</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"kt\">!unroll</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">800</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">1600</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">800</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">1600</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">z</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"kt\">!unroll</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">480</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">960</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">480</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">960</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">y</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">8</span>\n",
       "<span class=\"w\">      </span><span class=\"nt\">block_size</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">8</span>\n",
       "<span class=\"w\">      </span><span class=\"c1\"># Keep the body&#39;s influence away from the domain faces.</span>\n",
       "<span class=\"w\">      </span><span class=\"nt\">bodies_domain_limits</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">start</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">0.02</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">0.0</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">0.05</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">end</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">0.98</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">1.0</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">0.95</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">is_abs</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">false</span>\n",
       "<span class=\"w\">      </span><span class=\"nt\">bodies</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">cylinder</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">          </span><span class=\"c1\"># Voxelized (NOT IBM): a surface band carries the no-slip wall</span>\n",
       "<span class=\"w\">          </span><span class=\"c1\"># (RegularizedHWBB) and the heated scalar Dirichlet wall.</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">IBM</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">{</span><span class=\"nt\">run</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"nv\">false</span><span class=\"p p-Indicator\">}</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">voxelization</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">run</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">true</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">BC</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">RegularizedHWBB</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">order</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">1</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">band_radius</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">1</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">strict_normal</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">true</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">scalar_bcs</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">              </span><span class=\"c1\"># Heated cylinder surface: temperature fixed to 1 on the band.</span>\n",
       "<span class=\"w\">              </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"nt\">scalar</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">temperature</span>\n",
       "<span class=\"w\">                </span><span class=\"nt\">BC</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">ScalarRegularizedDirichlet</span>\n",
       "<span class=\"w\">                </span><span class=\"nt\">order</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">1</span>\n",
       "<span class=\"w\">                </span><span class=\"nt\">phi_w</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">1.0</span>\n",
       "<span class=\"w\">                </span><span class=\"nt\">ux</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0.0</span>\n",
       "<span class=\"w\">                </span><span class=\"nt\">uy</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0.0</span>\n",
       "<span class=\"w\">                </span><span class=\"nt\">uz</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0.0</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">geometry_path</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">fixture/stl/basic/cylinder_refined.stl</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">small_triangles</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"s\">&quot;add&quot;</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">area</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">{</span><span class=\"nt\">min</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"nv\">0.25</span><span class=\"p p-Indicator\">,</span><span class=\"nt\"> max</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"nv\">1.0</span><span class=\"p p-Indicator\">}</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">transformation</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">            </span><span class=\"c1\"># Scale the raw D = 2.5 STL to the target lattice diameter</span>\n",
       "<span class=\"w\">            </span><span class=\"c1\"># (D / 2.5 = 16 for D = 40, 32 for D = 80) and translate so the</span>\n",
       "<span class=\"w\">            </span><span class=\"c1\"># axis sits at (6*D, *, domain_z/2). The y translation drops a</span>\n",
       "<span class=\"w\">            </span><span class=\"c1\"># slice of the long (scaled) axis across the periodic span.</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">scale</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"kt\">!unroll</span>\n",
       "<span class=\"w\">              </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">16.0</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">16.0</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">16.0</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">              </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">32.0</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">32.0</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">32.0</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">              </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">16.0</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">16.0</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">16.0</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">              </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">32.0</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">32.0</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">32.0</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">translation</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"kt\">!unroll</span>\n",
       "<span class=\"w\">              </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">220.0</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">-500.0</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">220.0</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">              </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">440.0</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">-1000.0</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">440.0</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">              </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">220.0</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">-500.0</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">220.0</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">              </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">440.0</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">-1000.0</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">440.0</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">      </span><span class=\"nt\">refinement</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">static</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">default</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">volumes_refine</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">              </span><span class=\"c1\"># Degenerate level-0 &quot;refinement&quot; so the static block stays</span>\n",
       "<span class=\"w\">              </span><span class=\"c1\"># valid; lvl 0 leaves the whole domain on the base grid.</span>\n",
       "<span class=\"w\">              </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"nt\">start</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">0.0</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">0.0</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">0.0</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">                </span><span class=\"nt\">end</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">1.0</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">1.0</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">1.0</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">                </span><span class=\"nt\">lvl</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0</span>\n",
       "<span class=\"w\">                </span><span class=\"nt\">is_abs</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">false</span>\n",
       "\n",
       "<span class=\"w\">    </span><span class=\"nt\">data</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">      </span><span class=\"nt\">exports</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">default</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">macrs</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">rho</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">u</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">temperature_phi</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">interval</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">start_step</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"kt\">!unroll</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">100000</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">200000</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">160000</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">320000</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">frequency</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"kt\">!unroll</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">5000</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">10000</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">8000</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">16000</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">lvl</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">target</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">volume</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">{}</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">outputs</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">instantaneous</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">true</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">plane_series</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">macrs</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">rho</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">u</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">temperature_phi</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">interval</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">{</span><span class=\"nt\">frequency</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"kt\">!unroll</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">2000</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">4000</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">1000</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">2000</span><span class=\"p p-Indicator\">],</span><span class=\"nt\"> lvl</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"nv\">0</span><span class=\"p p-Indicator\">}</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">target</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">planes</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">              </span><span class=\"nt\">mid_span</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">                </span><span class=\"nt\">axis</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">y</span>\n",
       "<span class=\"w\">                </span><span class=\"nt\">axis_pos</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">4</span>\n",
       "<span class=\"w\">                </span><span class=\"nt\">dist</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">1</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">outputs</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">instantaneous</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">true</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">spectrum</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">macrs</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"s\">&quot;u&quot;</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">interval</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">frequency</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">lvl</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">target</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">points</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">              </span><span class=\"nt\">wake</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">                </span><span class=\"nt\">pos</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"kt\">!unroll</span>\n",
       "<span class=\"w\">                  </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">280.0</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">4.0</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">240.0</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">                  </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">560.0</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">4.0</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">480.0</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">                  </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">280.0</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">4.0</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">240.0</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">                  </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">560.0</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">4.0</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">480.0</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">outputs</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">spectrum</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">true</span>\n",
       "<span class=\"w\">    </span><span class=\"nt\">models</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">      </span><span class=\"nt\">precision</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">default</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">single</span>\n",
       "\n",
       "<span class=\"w\">      </span><span class=\"nt\">LBM</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">        </span><span class=\"c1\"># nu = U * D / Re ; tau = 3*nu + 1/2.</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">tau</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"kt\">!unroll</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">0.65000</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">0.80000</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">0.56000</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">0.62000</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">vel_set</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">D3Q27</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">coll_oper</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">HRRBGK</span>\n",
       "\n",
       "<span class=\"w\">      </span><span class=\"nt\">LES</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">model</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">Smagorinsky</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">sgs_cte</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0.1</span>\n",
       "\n",
       "<span class=\"w\">      </span><span class=\"nt\">initialization</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">equations</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">rho</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"s\">&quot;1.0&quot;</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">ux</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"kt\">!sub</span><span class=\"w\"> </span><span class=\"s\">&quot;${u_inf_lattice}&quot;</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">uy</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"s\">&quot;0&quot;</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">uz</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"s\">&quot;0&quot;</span>\n",
       "\n",
       "<span class=\"w\">      </span><span class=\"nt\">engine</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">name</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">CUDA</span>\n",
       "\n",
       "<span class=\"w\">      </span><span class=\"c1\"># Uniform cross-flow: west inlet, east Neumann outlet, top / bottom</span>\n",
       "<span class=\"w\">      </span><span class=\"c1\"># (F / B) Neumann far-field, y periodic (cylinder axis).</span>\n",
       "<span class=\"w\">      </span><span class=\"nt\">BC</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">periodic_dims</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">false</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">true</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">false</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">BC_map</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">          </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"nt\">pos</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">W</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">BC</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">UniformFlow</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">wall_normal</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">W</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">ux</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"kt\">!math</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">${u_inf_lattice}</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">uy</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">uz</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">rho</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">1</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">order</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">2</span>\n",
       "<span class=\"w\">          </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"nt\">pos</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">E</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">BC</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">RegularizedNeumannOutlet</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">wall_normal</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">E</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">rho</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">1.0</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">order</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">2</span>\n",
       "<span class=\"w\">          </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"nt\">pos</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">F</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">BC</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">RegularizedNeumannOutlet</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">wall_normal</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">F</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">rho</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">1.0</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">order</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">1</span>\n",
       "<span class=\"w\">          </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"nt\">pos</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">B</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">BC</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">RegularizedNeumannOutlet</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">wall_normal</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">B</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">rho</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">1.0</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">order</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">1</span>\n",
       "\n",
       "<span class=\"w\">      </span><span class=\"nt\">scalar_transports</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">temperature</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">velocity_set</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">D3Q7</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">collision_operator</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">RRBGK</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">adv_diff_equation</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">            </span><span class=\"c1\"># D_s = nu / Pr (Pr = 0.71). Matches the per-variant nu above.</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">D</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"kt\">!unroll</span><span class=\"w\"> </span><span class=\"p p-Indicator\">[</span><span class=\"nv\">0.07042</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">0.14085</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">0.02817</span><span class=\"p p-Indicator\">,</span><span class=\"w\"> </span><span class=\"nv\">0.05634</span><span class=\"p p-Indicator\">]</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">S</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"s\">&quot;0&quot;</span>\n",
       "<span class=\"w\">          </span><span class=\"c1\"># Clean (cold) freestream everywhere at start; the heated band</span>\n",
       "<span class=\"w\">          </span><span class=\"c1\"># injects the thermal layer.</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">initial_field</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"s\">&quot;0&quot;</span>\n",
       "<span class=\"w\">          </span><span class=\"nt\">BC</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">            </span><span class=\"nt\">BC_map</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">              </span><span class=\"c1\"># West inlet: clean incoming scalar, phi = 0.</span>\n",
       "<span class=\"w\">              </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"nt\">pos</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">W</span>\n",
       "<span class=\"w\">                </span><span class=\"nt\">BC</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">ScalarRegularizedDirichlet</span>\n",
       "<span class=\"w\">                </span><span class=\"nt\">wall_normal</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">W</span>\n",
       "<span class=\"w\">                </span><span class=\"nt\">phi_w</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0.0</span>\n",
       "<span class=\"w\">                </span><span class=\"nt\">ux</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"kt\">!math</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">${u_inf_lattice}</span>\n",
       "<span class=\"w\">                </span><span class=\"nt\">uy</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0.0</span>\n",
       "<span class=\"w\">                </span><span class=\"nt\">uz</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0.0</span>\n",
       "<span class=\"w\">              </span><span class=\"c1\"># East outlet: zero-gradient (Neumann) outflow.</span>\n",
       "<span class=\"w\">              </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"nt\">pos</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">E</span>\n",
       "<span class=\"w\">                </span><span class=\"nt\">BC</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">ScalarRegularizedNeumann</span>\n",
       "<span class=\"w\">                </span><span class=\"nt\">wall_normal</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">E</span>\n",
       "<span class=\"w\">                </span><span class=\"nt\">J_w</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0.0</span>\n",
       "<span class=\"w\">              </span><span class=\"c1\"># Top / bottom far-field: zero scalar flux.</span>\n",
       "<span class=\"w\">              </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"nt\">pos</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">F</span>\n",
       "<span class=\"w\">                </span><span class=\"nt\">BC</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">ScalarRegularizedNeumann</span>\n",
       "<span class=\"w\">                </span><span class=\"nt\">wall_normal</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">F</span>\n",
       "<span class=\"w\">                </span><span class=\"nt\">J_w</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0.0</span>\n",
       "<span class=\"w\">              </span><span class=\"p p-Indicator\">-</span><span class=\"w\"> </span><span class=\"nt\">pos</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">B</span>\n",
       "<span class=\"w\">                </span><span class=\"nt\">BC</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">ScalarRegularizedNeumann</span>\n",
       "<span class=\"w\">                </span><span class=\"nt\">wall_normal</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">B</span>\n",
       "<span class=\"w\">                </span><span class=\"nt\">J_w</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">0.0</span>\n",
       "\n",
       "<span class=\"w\">      </span><span class=\"nt\">multiblock</span><span class=\"p\">:</span>\n",
       "<span class=\"w\">        </span><span class=\"nt\">overlap_F2C</span><span class=\"p\">:</span><span class=\"w\"> </span><span class=\"l l-Scalar l-Scalar-Plain\">2</span>\n",
       "\n",
       "<span class=\"w\">      </span><span class=\"c1\"># No LES for the laminar primary sweep (Re &lt;= 100). The Re = 3900 LES</span>\n",
       "<span class=\"w\">      </span><span class=\"c1\"># variant (Smagorinsky + Sc_t scalar coupling) is the turbulent follow-up.</span>\n",
       "</pre></div>\n"
      ],
      "text/latex": [
       "\\begin{Verbatim}[commandchars=\\\\\\{\\}]\n",
       "\\PY{c+c1}{\\PYZsh{} Heated circular cylinder in cross\\PYZhy{}flow \\PYZhy{} voxel curved Dirichlet scalar BC}\n",
       "\\PY{c+c1}{\\PYZsh{}}\n",
       "\\PY{c+c1}{\\PYZsh{} Forced\\PYZhy{}convection benchmark for a fixed\\PYZhy{}temperature (Dirichlet) heated}\n",
       "\\PY{c+c1}{\\PYZsh{} cylinder. This is the validation case for the scalar Dirichlet BC on a}\n",
       "\\PY{c+c1}{\\PYZsh{} CURVED voxelized surface (velocity band BC + scalar band BC): the}\n",
       "\\PY{c+c1}{\\PYZsh{} curved wall is staircased onto the lattice, so}\n",
       "\\PY{c+c1}{\\PYZsh{} the surface\\PYZhy{}averaged wall heat flux (Nusselt number) is FIRST\\PYZhy{}ORDER in}\n",
       "\\PY{c+c1}{\\PYZsh{} `D/dx`. The case therefore runs at two diameters (D = 40 and D = 80}\n",
       "\\PY{c+c1}{\\PYZsh{} lattice units) so the staircase convergence of `Nu\\PYZus{}D` can be reported.}\n",
       "\\PY{c+c1}{\\PYZsh{}}\n",
       "\\PY{c+c1}{\\PYZsh{} It reuses the flow\\PYZhy{}over\\PYZhy{}cylinder momentum setup (case 09): same circular}\n",
       "\\PY{c+c1}{\\PYZsh{} cylinder geometry (`fixture/stl/basic/cylinder\\PYZus{}refined.stl`), uniform}\n",
       "\\PY{c+c1}{\\PYZsh{} cross\\PYZhy{}flow, no\\PYZhy{}slip wall, and the Strouhal / drag momentum checks. The}\n",
       "\\PY{c+c1}{\\PYZsh{} thermal layer is added on top: a passive scalar `temperature` (D3Q7,}\n",
       "\\PY{c+c1}{\\PYZsh{} RRBGK) advected and diffused by the flow, with the cylinder wall held at}\n",
       "\\PY{c+c1}{\\PYZsh{} `phi\\PYZus{}w = 1.0` (heated) and the freestream at `phi = 0` (clean).}\n",
       "\\PY{c+c1}{\\PYZsh{}}\n",
       "\\PY{c+c1}{\\PYZsh{} Unlike case 09 (which uses IBM + heavy multiblock refinement to resolve a}\n",
       "\\PY{c+c1}{\\PYZsh{} small D = 2.5 cylinder), this case VOXELIZES the body on a single uniform}\n",
       "\\PY{c+c1}{\\PYZsh{} grid level at the target diameter, so the curved Dirichlet band is the}\n",
       "\\PY{c+c1}{\\PYZsh{} only wall treatment under test (no IBM, no refinement). The STL is scaled}\n",
       "\\PY{c+c1}{\\PYZsh{} by `D / 2.5` to reach the target lattice diameter directly.}\n",
       "\\PY{c+c1}{\\PYZsh{}}\n",
       "\\PY{c+c1}{\\PYZsh{} \\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}}\n",
       "\\PY{c+c1}{\\PYZsh{} Re / Pr \\PYZhy{}\\PYZgt{} lattice mapping (Pr = 0.71 for air; buoyancy OFF)}\n",
       "\\PY{c+c1}{\\PYZsh{} \\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}}\n",
       "\\PY{c+c1}{\\PYZsh{} Fixed lattice freestream `U = 0.05` (Ma = U*sqrt(3) = 0.087 \\PYZlt{} 0.1).}\n",
       "\\PY{c+c1}{\\PYZsh{} Reynolds number on the diameter:  Re = U * D / nu  \\PYZhy{}\\PYZgt{}  nu = U * D / Re.}\n",
       "\\PY{c+c1}{\\PYZsh{} Fluid relaxation (cs\\PYZca{}2 = 1/3):     tau     = 3*nu + 1/2.}\n",
       "\\PY{c+c1}{\\PYZsh{} Scalar diffusivity (Pr = nu/D\\PYZus{}s):  D\\PYZus{}s     = nu / Pr.}\n",
       "\\PY{c+c1}{\\PYZsh{} Scalar relaxation (D3Q7, cs\\PYZus{}phi\\PYZca{}2 = 1/4): tau\\PYZus{}phi = D\\PYZus{}s/0.25 + 1/2.}\n",
       "\\PY{c+c1}{\\PYZsh{}}\n",
       "\\PY{c+c1}{\\PYZsh{}   | Re  | D  | nu      | tau (fluid) | D\\PYZus{}s     | tau\\PYZus{}phi  | Nu\\PYZus{}D (CB) |}\n",
       "\\PY{c+c1}{\\PYZsh{}   | 40  | 40 | 0.05000 | 0.65000     | 0.07042 | 0.78169  | 3.38      |}\n",
       "\\PY{c+c1}{\\PYZsh{}   | 40  | 80 | 0.10000 | 0.80000     | 0.14085 | 1.06338  | 3.38      |}\n",
       "\\PY{c+c1}{\\PYZsh{}   | 100 | 40 | 0.02000 | 0.56000     | 0.02817 | 0.61268  | 5.18      |}\n",
       "\\PY{c+c1}{\\PYZsh{}   | 100 | 80 | 0.04000 | 0.62000     | 0.05634 | 0.72535  | 5.18      |}\n",
       "\\PY{c+c1}{\\PYZsh{}}\n",
       "\\PY{c+c1}{\\PYZsh{} Re = 40 is steady (no shedding); Re = 100 sheds a laminar Karman street}\n",
       "\\PY{c+c1}{\\PYZsh{} (St \\PYZti{} 0.16\\PYZhy{}0.17 at Re = 100, rising towards 0.21 by Re \\PYZti{} 250). The}\n",
       "\\PY{c+c1}{\\PYZsh{} two\\PYZhy{}resolution pair (D = 40 vs D = 80) at each Re exposes the first\\PYZhy{}order}\n",
       "\\PY{c+c1}{\\PYZsh{} `D/dx` convergence of the staircased curved Dirichlet wall flux.}\n",
       "\\PY{c+c1}{\\PYZsh{}}\n",
       "\\PY{c+c1}{\\PYZsh{} Nu\\PYZus{}D (CB) is the Churchill \\PYZam{} Bernstein (1977) surface\\PYZhy{}averaged Nusselt}\n",
       "\\PY{c+c1}{\\PYZsh{} correlation, tabulated in}\n",
       "\\PY{c+c1}{\\PYZsh{} validation/thermal/02\\PYZus{}heated\\PYZus{}cylinder/reference/churchill\\PYZus{}bernstein.csv.}\n",
       "\\PY{c+c1}{\\PYZsh{} Acceptance: Nu\\PYZus{}D within \\PYZti{}10\\PYZhy{}15\\PYZpc{} of CB (correlation scatter \\PYZti{}10\\PYZhy{}20\\PYZpc{}),}\n",
       "\\PY{c+c1}{\\PYZsh{} reported at BOTH resolutions with the convergence trend; local Nu(theta)}\n",
       "\\PY{c+c1}{\\PYZsh{} qualitatively correct (front\\PYZhy{}stagnation peak, separation minimum).}\n",
       "\\PY{c+c1}{\\PYZsh{}}\n",
       "\\PY{c+c1}{\\PYZsh{} \\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}}\n",
       "\\PY{c+c1}{\\PYZsh{} Turbulent follow\\PYZhy{}up (not the primary run)}\n",
       "\\PY{c+c1}{\\PYZsh{} \\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}\\PYZhy{}}\n",
       "\\PY{c+c1}{\\PYZsh{} The Re = 3900 3\\PYZhy{}D LES variant (turbulent wake, Smagorinsky SGS with a}\n",
       "\\PY{c+c1}{\\PYZsh{} turbulent\\PYZhy{}Prandtl coupling `Sc\\PYZus{}t` on the scalar) needs a 3\\PYZhy{}D span, LES,}\n",
       "\\PY{c+c1}{\\PYZsh{} and a much longer averaging window; it is left out of this primary}\n",
       "\\PY{c+c1}{\\PYZsh{} laminar 2\\PYZhy{}D sweep.}\n",
       "\\PY{c+c1}{\\PYZsh{}}\n",
       "\\PY{c+c1}{\\PYZsh{} Reference: Churchill, S.W. \\PYZam{} Bernstein, M. (1977), \\PYZdq{}A correlating}\n",
       "\\PY{c+c1}{\\PYZsh{} equation for forced convection from gases and liquids to a circular}\n",
       "\\PY{c+c1}{\\PYZsh{} cylinder in crossflow,\\PYZdq{} J. Heat Transfer 99(2):300\\PYZhy{}306.}\n",
       "\n",
       "\\PY{n+nt}{variables}\\PY{p}{:}\n",
       "\\PY{+w}{  }\\PY{c+c1}{\\PYZsh{} Lattice freestream velocity (inlet BC, init equation). Ma = 0.087.}\n",
       "\\PY{+w}{  }\\PY{n+nt}{u\\PYZus{}inf\\PYZus{}lattice}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{0.05}\n",
       "\n",
       "\\PY{n+nt}{simulations}\\PY{p}{:}\n",
       "\\PY{+w}{  }\\PY{p+pIndicator}{\\PYZhy{}}\\PY{+w}{ }\\PY{n+nt}{name}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{heatedCylinder}\n",
       "\\PY{+w}{    }\\PY{n+nt}{save\\PYZus{}path}\\PY{p}{:}\\PY{+w}{ }\\PY{k+kt}{!unroll}\n",
       "\\PY{+w}{      }\\PY{p+pIndicator}{\\PYZhy{}}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{./validation/thermal/02\\PYZus{}heated\\PYZus{}cylinder/results/re40\\PYZus{}D40}\n",
       "\\PY{+w}{      }\\PY{p+pIndicator}{\\PYZhy{}}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{./validation/thermal/02\\PYZus{}heated\\PYZus{}cylinder/results/re40\\PYZus{}D80}\n",
       "\\PY{+w}{      }\\PY{p+pIndicator}{\\PYZhy{}}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{./validation/thermal/02\\PYZus{}heated\\PYZus{}cylinder/results/re100\\PYZus{}D40}\n",
       "\\PY{+w}{      }\\PY{p+pIndicator}{\\PYZhy{}}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{./validation/thermal/02\\PYZus{}heated\\PYZus{}cylinder/results/re100\\PYZus{}D80}\n",
       "\\PY{+w}{    }\\PY{n+nt}{n\\PYZus{}steps}\\PY{p}{:}\\PY{+w}{ }\\PY{k+kt}{!unroll}\\PY{+w}{ }\\PY{p+pIndicator}{[}\\PY{n+nv}{120000}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{240000}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{200000}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{400000}\\PY{p+pIndicator}{]}\n",
       "\n",
       "\\PY{+w}{    }\\PY{n+nt}{report}\\PY{p}{:}\\PY{+w}{ }\\PY{p+pIndicator}{\\PYZob{}}\\PY{n+nt}{frequency}\\PY{p}{:}\\PY{+w}{ }\\PY{n+nv}{2000}\\PY{p+pIndicator}{\\PYZcb{}}\n",
       "\n",
       "\\PY{+w}{    }\\PY{n+nt}{domain}\\PY{p}{:}\n",
       "\\PY{+w}{      }\\PY{c+c1}{\\PYZsh{} Domain in diameter multiples: 20*D streamwise, 12*D cross\\PYZhy{}stream,}\n",
       "\\PY{+w}{      }\\PY{c+c1}{\\PYZsh{} thin periodic span (y, 8 cells). Cylinder centred 6*D from inlet.}\n",
       "\\PY{+w}{      }\\PY{n+nt}{domain\\PYZus{}size}\\PY{p}{:}\n",
       "\\PY{+w}{        }\\PY{n+nt}{x}\\PY{p}{:}\\PY{+w}{ }\\PY{k+kt}{!unroll}\\PY{+w}{ }\\PY{p+pIndicator}{[}\\PY{n+nv}{800}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{1600}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{800}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{1600}\\PY{p+pIndicator}{]}\n",
       "\\PY{+w}{        }\\PY{n+nt}{z}\\PY{p}{:}\\PY{+w}{ }\\PY{k+kt}{!unroll}\\PY{+w}{ }\\PY{p+pIndicator}{[}\\PY{n+nv}{480}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{960}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{480}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{960}\\PY{p+pIndicator}{]}\n",
       "\\PY{+w}{        }\\PY{n+nt}{y}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{8}\n",
       "\\PY{+w}{      }\\PY{n+nt}{block\\PYZus{}size}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{8}\n",
       "\\PY{+w}{      }\\PY{c+c1}{\\PYZsh{} Keep the body\\PYZsq{}s influence away from the domain faces.}\n",
       "\\PY{+w}{      }\\PY{n+nt}{bodies\\PYZus{}domain\\PYZus{}limits}\\PY{p}{:}\n",
       "\\PY{+w}{        }\\PY{n+nt}{start}\\PY{p}{:}\\PY{+w}{ }\\PY{p+pIndicator}{[}\\PY{n+nv}{0.02}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{0.0}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{0.05}\\PY{p+pIndicator}{]}\n",
       "\\PY{+w}{        }\\PY{n+nt}{end}\\PY{p}{:}\\PY{+w}{ }\\PY{p+pIndicator}{[}\\PY{n+nv}{0.98}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{1.0}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{0.95}\\PY{p+pIndicator}{]}\n",
       "\\PY{+w}{        }\\PY{n+nt}{is\\PYZus{}abs}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{false}\n",
       "\\PY{+w}{      }\\PY{n+nt}{bodies}\\PY{p}{:}\n",
       "\\PY{+w}{        }\\PY{n+nt}{cylinder}\\PY{p}{:}\n",
       "\\PY{+w}{          }\\PY{c+c1}{\\PYZsh{} Voxelized (NOT IBM): a surface band carries the no\\PYZhy{}slip wall}\n",
       "\\PY{+w}{          }\\PY{c+c1}{\\PYZsh{} (RegularizedHWBB) and the heated scalar Dirichlet wall.}\n",
       "\\PY{+w}{          }\\PY{n+nt}{IBM}\\PY{p}{:}\\PY{+w}{ }\\PY{p+pIndicator}{\\PYZob{}}\\PY{n+nt}{run}\\PY{p}{:}\\PY{+w}{ }\\PY{n+nv}{false}\\PY{p+pIndicator}{\\PYZcb{}}\n",
       "\\PY{+w}{          }\\PY{n+nt}{voxelization}\\PY{p}{:}\n",
       "\\PY{+w}{            }\\PY{n+nt}{run}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{true}\n",
       "\\PY{+w}{            }\\PY{n+nt}{BC}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{RegularizedHWBB}\n",
       "\\PY{+w}{            }\\PY{n+nt}{order}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{1}\n",
       "\\PY{+w}{            }\\PY{n+nt}{band\\PYZus{}radius}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{1}\n",
       "\\PY{+w}{            }\\PY{n+nt}{strict\\PYZus{}normal}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{true}\n",
       "\\PY{+w}{            }\\PY{n+nt}{scalar\\PYZus{}bcs}\\PY{p}{:}\n",
       "\\PY{+w}{              }\\PY{c+c1}{\\PYZsh{} Heated cylinder surface: temperature fixed to 1 on the band.}\n",
       "\\PY{+w}{              }\\PY{p+pIndicator}{\\PYZhy{}}\\PY{+w}{ }\\PY{n+nt}{scalar}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{temperature}\n",
       "\\PY{+w}{                }\\PY{n+nt}{BC}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{ScalarRegularizedDirichlet}\n",
       "\\PY{+w}{                }\\PY{n+nt}{order}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{1}\n",
       "\\PY{+w}{                }\\PY{n+nt}{phi\\PYZus{}w}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{1.0}\n",
       "\\PY{+w}{                }\\PY{n+nt}{ux}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{0.0}\n",
       "\\PY{+w}{                }\\PY{n+nt}{uy}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{0.0}\n",
       "\\PY{+w}{                }\\PY{n+nt}{uz}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{0.0}\n",
       "\\PY{+w}{          }\\PY{n+nt}{geometry\\PYZus{}path}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{fixture/stl/basic/cylinder\\PYZus{}refined.stl}\n",
       "\\PY{+w}{          }\\PY{n+nt}{small\\PYZus{}triangles}\\PY{p}{:}\\PY{+w}{ }\\PY{l+s}{\\PYZdq{}}\\PY{l+s}{add}\\PY{l+s}{\\PYZdq{}}\n",
       "\\PY{+w}{          }\\PY{n+nt}{area}\\PY{p}{:}\\PY{+w}{ }\\PY{p+pIndicator}{\\PYZob{}}\\PY{n+nt}{min}\\PY{p}{:}\\PY{+w}{ }\\PY{n+nv}{0.25}\\PY{p+pIndicator}{,}\\PY{n+nt}{ max}\\PY{p}{:}\\PY{+w}{ }\\PY{n+nv}{1.0}\\PY{p+pIndicator}{\\PYZcb{}}\n",
       "\\PY{+w}{          }\\PY{n+nt}{transformation}\\PY{p}{:}\n",
       "\\PY{+w}{            }\\PY{c+c1}{\\PYZsh{} Scale the raw D = 2.5 STL to the target lattice diameter}\n",
       "\\PY{+w}{            }\\PY{c+c1}{\\PYZsh{} (D / 2.5 = 16 for D = 40, 32 for D = 80) and translate so the}\n",
       "\\PY{+w}{            }\\PY{c+c1}{\\PYZsh{} axis sits at (6*D, *, domain\\PYZus{}z/2). The y translation drops a}\n",
       "\\PY{+w}{            }\\PY{c+c1}{\\PYZsh{} slice of the long (scaled) axis across the periodic span.}\n",
       "\\PY{+w}{            }\\PY{n+nt}{scale}\\PY{p}{:}\\PY{+w}{ }\\PY{k+kt}{!unroll}\n",
       "\\PY{+w}{              }\\PY{p+pIndicator}{\\PYZhy{}}\\PY{+w}{ }\\PY{p+pIndicator}{[}\\PY{n+nv}{16.0}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{16.0}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{16.0}\\PY{p+pIndicator}{]}\n",
       "\\PY{+w}{              }\\PY{p+pIndicator}{\\PYZhy{}}\\PY{+w}{ }\\PY{p+pIndicator}{[}\\PY{n+nv}{32.0}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{32.0}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{32.0}\\PY{p+pIndicator}{]}\n",
       "\\PY{+w}{              }\\PY{p+pIndicator}{\\PYZhy{}}\\PY{+w}{ }\\PY{p+pIndicator}{[}\\PY{n+nv}{16.0}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{16.0}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{16.0}\\PY{p+pIndicator}{]}\n",
       "\\PY{+w}{              }\\PY{p+pIndicator}{\\PYZhy{}}\\PY{+w}{ }\\PY{p+pIndicator}{[}\\PY{n+nv}{32.0}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{32.0}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{32.0}\\PY{p+pIndicator}{]}\n",
       "\\PY{+w}{            }\\PY{n+nt}{translation}\\PY{p}{:}\\PY{+w}{ }\\PY{k+kt}{!unroll}\n",
       "\\PY{+w}{              }\\PY{p+pIndicator}{\\PYZhy{}}\\PY{+w}{ }\\PY{p+pIndicator}{[}\\PY{n+nv}{220.0}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{\\PYZhy{}500.0}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{220.0}\\PY{p+pIndicator}{]}\n",
       "\\PY{+w}{              }\\PY{p+pIndicator}{\\PYZhy{}}\\PY{+w}{ }\\PY{p+pIndicator}{[}\\PY{n+nv}{440.0}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{\\PYZhy{}1000.0}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{440.0}\\PY{p+pIndicator}{]}\n",
       "\\PY{+w}{              }\\PY{p+pIndicator}{\\PYZhy{}}\\PY{+w}{ }\\PY{p+pIndicator}{[}\\PY{n+nv}{220.0}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{\\PYZhy{}500.0}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{220.0}\\PY{p+pIndicator}{]}\n",
       "\\PY{+w}{              }\\PY{p+pIndicator}{\\PYZhy{}}\\PY{+w}{ }\\PY{p+pIndicator}{[}\\PY{n+nv}{440.0}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{\\PYZhy{}1000.0}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{440.0}\\PY{p+pIndicator}{]}\n",
       "\\PY{+w}{      }\\PY{n+nt}{refinement}\\PY{p}{:}\n",
       "\\PY{+w}{        }\\PY{n+nt}{static}\\PY{p}{:}\n",
       "\\PY{+w}{          }\\PY{n+nt}{default}\\PY{p}{:}\n",
       "\\PY{+w}{            }\\PY{n+nt}{volumes\\PYZus{}refine}\\PY{p}{:}\n",
       "\\PY{+w}{              }\\PY{c+c1}{\\PYZsh{} Degenerate level\\PYZhy{}0 \\PYZdq{}refinement\\PYZdq{} so the static block stays}\n",
       "\\PY{+w}{              }\\PY{c+c1}{\\PYZsh{} valid; lvl 0 leaves the whole domain on the base grid.}\n",
       "\\PY{+w}{              }\\PY{p+pIndicator}{\\PYZhy{}}\\PY{+w}{ }\\PY{n+nt}{start}\\PY{p}{:}\\PY{+w}{ }\\PY{p+pIndicator}{[}\\PY{n+nv}{0.0}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{0.0}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{0.0}\\PY{p+pIndicator}{]}\n",
       "\\PY{+w}{                }\\PY{n+nt}{end}\\PY{p}{:}\\PY{+w}{ }\\PY{p+pIndicator}{[}\\PY{n+nv}{1.0}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{1.0}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{1.0}\\PY{p+pIndicator}{]}\n",
       "\\PY{+w}{                }\\PY{n+nt}{lvl}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{0}\n",
       "\\PY{+w}{                }\\PY{n+nt}{is\\PYZus{}abs}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{false}\n",
       "\n",
       "\\PY{+w}{    }\\PY{n+nt}{data}\\PY{p}{:}\n",
       "\\PY{+w}{      }\\PY{n+nt}{exports}\\PY{p}{:}\n",
       "\\PY{+w}{        }\\PY{n+nt}{default}\\PY{p}{:}\n",
       "\\PY{+w}{          }\\PY{n+nt}{macrs}\\PY{p}{:}\\PY{+w}{ }\\PY{p+pIndicator}{[}\\PY{n+nv}{rho}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{u}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{temperature\\PYZus{}phi}\\PY{p+pIndicator}{]}\n",
       "\\PY{+w}{          }\\PY{n+nt}{interval}\\PY{p}{:}\n",
       "\\PY{+w}{            }\\PY{n+nt}{start\\PYZus{}step}\\PY{p}{:}\\PY{+w}{ }\\PY{k+kt}{!unroll}\\PY{+w}{ }\\PY{p+pIndicator}{[}\\PY{n+nv}{100000}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{200000}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{160000}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{320000}\\PY{p+pIndicator}{]}\n",
       "\\PY{+w}{            }\\PY{n+nt}{frequency}\\PY{p}{:}\\PY{+w}{ }\\PY{k+kt}{!unroll}\\PY{+w}{ }\\PY{p+pIndicator}{[}\\PY{n+nv}{5000}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{10000}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{8000}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{16000}\\PY{p+pIndicator}{]}\n",
       "\\PY{+w}{            }\\PY{n+nt}{lvl}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{0}\n",
       "\\PY{+w}{          }\\PY{n+nt}{target}\\PY{p}{:}\n",
       "\\PY{+w}{            }\\PY{n+nt}{volume}\\PY{p}{:}\\PY{+w}{ }\\PY{p+pIndicator}{\\PYZob{}}\\PY{p+pIndicator}{\\PYZcb{}}\n",
       "\\PY{+w}{          }\\PY{n+nt}{outputs}\\PY{p}{:}\n",
       "\\PY{+w}{            }\\PY{n+nt}{instantaneous}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{true}\n",
       "\\PY{+w}{        }\\PY{n+nt}{plane\\PYZus{}series}\\PY{p}{:}\n",
       "\\PY{+w}{          }\\PY{n+nt}{macrs}\\PY{p}{:}\\PY{+w}{ }\\PY{p+pIndicator}{[}\\PY{n+nv}{rho}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{u}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{temperature\\PYZus{}phi}\\PY{p+pIndicator}{]}\n",
       "\\PY{+w}{          }\\PY{n+nt}{interval}\\PY{p}{:}\\PY{+w}{ }\\PY{p+pIndicator}{\\PYZob{}}\\PY{n+nt}{frequency}\\PY{p}{:}\\PY{+w}{ }\\PY{k+kt}{!unroll}\\PY{+w}{ }\\PY{p+pIndicator}{[}\\PY{n+nv}{2000}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{4000}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{1000}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{2000}\\PY{p+pIndicator}{]}\\PY{p+pIndicator}{,}\\PY{n+nt}{ lvl}\\PY{p}{:}\\PY{+w}{ }\\PY{n+nv}{0}\\PY{p+pIndicator}{\\PYZcb{}}\n",
       "\\PY{+w}{          }\\PY{n+nt}{target}\\PY{p}{:}\n",
       "\\PY{+w}{            }\\PY{n+nt}{planes}\\PY{p}{:}\n",
       "\\PY{+w}{              }\\PY{n+nt}{mid\\PYZus{}span}\\PY{p}{:}\n",
       "\\PY{+w}{                }\\PY{n+nt}{axis}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{y}\n",
       "\\PY{+w}{                }\\PY{n+nt}{axis\\PYZus{}pos}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{4}\n",
       "\\PY{+w}{                }\\PY{n+nt}{dist}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{1}\n",
       "\\PY{+w}{          }\\PY{n+nt}{outputs}\\PY{p}{:}\n",
       "\\PY{+w}{            }\\PY{n+nt}{instantaneous}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{true}\n",
       "\\PY{+w}{        }\\PY{n+nt}{spectrum}\\PY{p}{:}\n",
       "\\PY{+w}{          }\\PY{n+nt}{macrs}\\PY{p}{:}\\PY{+w}{ }\\PY{p+pIndicator}{[}\\PY{l+s}{\\PYZdq{}}\\PY{l+s}{u}\\PY{l+s}{\\PYZdq{}}\\PY{p+pIndicator}{]}\n",
       "\\PY{+w}{          }\\PY{n+nt}{interval}\\PY{p}{:}\n",
       "\\PY{+w}{            }\\PY{n+nt}{frequency}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{0}\n",
       "\\PY{+w}{            }\\PY{n+nt}{lvl}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{0}\n",
       "\\PY{+w}{          }\\PY{n+nt}{target}\\PY{p}{:}\n",
       "\\PY{+w}{            }\\PY{n+nt}{points}\\PY{p}{:}\n",
       "\\PY{+w}{              }\\PY{n+nt}{wake}\\PY{p}{:}\n",
       "\\PY{+w}{                }\\PY{n+nt}{pos}\\PY{p}{:}\\PY{+w}{ }\\PY{k+kt}{!unroll}\n",
       "\\PY{+w}{                  }\\PY{p+pIndicator}{\\PYZhy{}}\\PY{+w}{ }\\PY{p+pIndicator}{[}\\PY{n+nv}{280.0}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{4.0}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{240.0}\\PY{p+pIndicator}{]}\n",
       "\\PY{+w}{                  }\\PY{p+pIndicator}{\\PYZhy{}}\\PY{+w}{ }\\PY{p+pIndicator}{[}\\PY{n+nv}{560.0}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{4.0}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{480.0}\\PY{p+pIndicator}{]}\n",
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       "\n",
       "\\PY{+w}{      }\\PY{c+c1}{\\PYZsh{} Uniform cross\\PYZhy{}flow: west inlet, east Neumann outlet, top / bottom}\n",
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       "\n",
       "\\PY{+w}{      }\\PY{n+nt}{scalar\\PYZus{}transports}\\PY{p}{:}\n",
       "\\PY{+w}{        }\\PY{n+nt}{temperature}\\PY{p}{:}\n",
       "\\PY{+w}{          }\\PY{n+nt}{velocity\\PYZus{}set}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{D3Q7}\n",
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       "\\PY{+w}{          }\\PY{n+nt}{adv\\PYZus{}diff\\PYZus{}equation}\\PY{p}{:}\n",
       "\\PY{+w}{            }\\PY{c+c1}{\\PYZsh{} D\\PYZus{}s = nu / Pr (Pr = 0.71). Matches the per\\PYZhy{}variant nu above.}\n",
       "\\PY{+w}{            }\\PY{n+nt}{D}\\PY{p}{:}\\PY{+w}{ }\\PY{k+kt}{!unroll}\\PY{+w}{ }\\PY{p+pIndicator}{[}\\PY{n+nv}{0.07042}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{0.14085}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{0.02817}\\PY{p+pIndicator}{,}\\PY{+w}{ }\\PY{n+nv}{0.05634}\\PY{p+pIndicator}{]}\n",
       "\\PY{+w}{            }\\PY{n+nt}{S}\\PY{p}{:}\\PY{+w}{ }\\PY{l+s}{\\PYZdq{}}\\PY{l+s}{0}\\PY{l+s}{\\PYZdq{}}\n",
       "\\PY{+w}{          }\\PY{c+c1}{\\PYZsh{} Clean (cold) freestream everywhere at start; the heated band}\n",
       "\\PY{+w}{          }\\PY{c+c1}{\\PYZsh{} injects the thermal layer.}\n",
       "\\PY{+w}{          }\\PY{n+nt}{initial\\PYZus{}field}\\PY{p}{:}\\PY{+w}{ }\\PY{l+s}{\\PYZdq{}}\\PY{l+s}{0}\\PY{l+s}{\\PYZdq{}}\n",
       "\\PY{+w}{          }\\PY{n+nt}{BC}\\PY{p}{:}\n",
       "\\PY{+w}{            }\\PY{n+nt}{BC\\PYZus{}map}\\PY{p}{:}\n",
       "\\PY{+w}{              }\\PY{c+c1}{\\PYZsh{} West inlet: clean incoming scalar, phi = 0.}\n",
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       "\\PY{+w}{              }\\PY{c+c1}{\\PYZsh{} East outlet: zero\\PYZhy{}gradient (Neumann) outflow.}\n",
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       "\\PY{+w}{              }\\PY{c+c1}{\\PYZsh{} Top / bottom far\\PYZhy{}field: zero scalar flux.}\n",
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       "\\PY{+w}{                }\\PY{n+nt}{BC}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{ScalarRegularizedNeumann}\n",
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       "\\PY{+w}{                }\\PY{n+nt}{J\\PYZus{}w}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{0.0}\n",
       "\n",
       "\\PY{+w}{      }\\PY{n+nt}{multiblock}\\PY{p}{:}\n",
       "\\PY{+w}{        }\\PY{n+nt}{overlap\\PYZus{}F2C}\\PY{p}{:}\\PY{+w}{ }\\PY{l+lScalar+lScalarPlain}{2}\n",
       "\n",
       "\\PY{+w}{      }\\PY{c+c1}{\\PYZsh{} No LES for the laminar primary sweep (Re \\PYZlt{}= 100). The Re = 3900 LES}\n",
       "\\PY{+w}{      }\\PY{c+c1}{\\PYZsh{} variant (Smagorinsky + Sc\\PYZus{}t scalar coupling) is the turbulent follow\\PYZhy{}up.}\n",
       "\\end{Verbatim}\n"
      ],
      "text/plain": [
       "# Heated circular cylinder in cross-flow - voxel curved Dirichlet scalar BC\n",
       "#\n",
       "# Forced-convection benchmark for a fixed-temperature (Dirichlet) heated\n",
       "# cylinder. This is the validation case for the scalar Dirichlet BC on a\n",
       "# CURVED voxelized surface (velocity band BC + scalar band BC): the\n",
       "# curved wall is staircased onto the lattice, so\n",
       "# the surface-averaged wall heat flux (Nusselt number) is FIRST-ORDER in\n",
       "# `D/dx`. The case therefore runs at two diameters (D = 40 and D = 80\n",
       "# lattice units) so the staircase convergence of `Nu_D` can be reported.\n",
       "#\n",
       "# It reuses the flow-over-cylinder momentum setup (case 09): same circular\n",
       "# cylinder geometry (`fixture/stl/basic/cylinder_refined.stl`), uniform\n",
       "# cross-flow, no-slip wall, and the Strouhal / drag momentum checks. The\n",
       "# thermal layer is added on top: a passive scalar `temperature` (D3Q7,\n",
       "# RRBGK) advected and diffused by the flow, with the cylinder wall held at\n",
       "# `phi_w = 1.0` (heated) and the freestream at `phi = 0` (clean).\n",
       "#\n",
       "# Unlike case 09 (which uses IBM + heavy multiblock refinement to resolve a\n",
       "# small D = 2.5 cylinder), this case VOXELIZES the body on a single uniform\n",
       "# grid level at the target diameter, so the curved Dirichlet band is the\n",
       "# only wall treatment under test (no IBM, no refinement). The STL is scaled\n",
       "# by `D / 2.5` to reach the target lattice diameter directly.\n",
       "#\n",
       "# ---------------------------------------------------------------------\n",
       "# Re / Pr -> lattice mapping (Pr = 0.71 for air; buoyancy OFF)\n",
       "# ---------------------------------------------------------------------\n",
       "# Fixed lattice freestream `U = 0.05` (Ma = U*sqrt(3) = 0.087 < 0.1).\n",
       "# Reynolds number on the diameter:  Re = U * D / nu  ->  nu = U * D / Re.\n",
       "# Fluid relaxation (cs^2 = 1/3):     tau     = 3*nu + 1/2.\n",
       "# Scalar diffusivity (Pr = nu/D_s):  D_s     = nu / Pr.\n",
       "# Scalar relaxation (D3Q7, cs_phi^2 = 1/4): tau_phi = D_s/0.25 + 1/2.\n",
       "#\n",
       "#   | Re  | D  | nu      | tau (fluid) | D_s     | tau_phi  | Nu_D (CB) |\n",
       "#   | 40  | 40 | 0.05000 | 0.65000     | 0.07042 | 0.78169  | 3.38      |\n",
       "#   | 40  | 80 | 0.10000 | 0.80000     | 0.14085 | 1.06338  | 3.38      |\n",
       "#   | 100 | 40 | 0.02000 | 0.56000     | 0.02817 | 0.61268  | 5.18      |\n",
       "#   | 100 | 80 | 0.04000 | 0.62000     | 0.05634 | 0.72535  | 5.18      |\n",
       "#\n",
       "# Re = 40 is steady (no shedding); Re = 100 sheds a laminar Karman street\n",
       "# (St ~ 0.16-0.17 at Re = 100, rising towards 0.21 by Re ~ 250). The\n",
       "# two-resolution pair (D = 40 vs D = 80) at each Re exposes the first-order\n",
       "# `D/dx` convergence of the staircased curved Dirichlet wall flux.\n",
       "#\n",
       "# Nu_D (CB) is the Churchill & Bernstein (1977) surface-averaged Nusselt\n",
       "# correlation, tabulated in\n",
       "# validation/thermal/02_heated_cylinder/reference/churchill_bernstein.csv.\n",
       "# Acceptance: Nu_D within ~10-15% of CB (correlation scatter ~10-20%),\n",
       "# reported at BOTH resolutions with the convergence trend; local Nu(theta)\n",
       "# qualitatively correct (front-stagnation peak, separation minimum).\n",
       "#\n",
       "# ---------------------------------------------------------------------\n",
       "# Turbulent follow-up (not the primary run)\n",
       "# ---------------------------------------------------------------------\n",
       "# The Re = 3900 3-D LES variant (turbulent wake, Smagorinsky SGS with a\n",
       "# turbulent-Prandtl coupling `Sc_t` on the scalar) needs a 3-D span, LES,\n",
       "# and a much longer averaging window; it is left out of this primary\n",
       "# laminar 2-D sweep.\n",
       "#\n",
       "# Reference: Churchill, S.W. & Bernstein, M. (1977), \"A correlating\n",
       "# equation for forced convection from gases and liquids to a circular\n",
       "# cylinder in crossflow,\" J. Heat Transfer 99(2):300-306.\n",
       "\n",
       "variables:\n",
       "  # Lattice freestream velocity (inlet BC, init equation). Ma = 0.087.\n",
       "  u_inf_lattice: 0.05\n",
       "\n",
       "simulations:\n",
       "  - name: heatedCylinder\n",
       "    save_path: !unroll\n",
       "      - ./validation/thermal/02_heated_cylinder/results/re40_D40\n",
       "      - ./validation/thermal/02_heated_cylinder/results/re40_D80\n",
       "      - ./validation/thermal/02_heated_cylinder/results/re100_D40\n",
       "      - ./validation/thermal/02_heated_cylinder/results/re100_D80\n",
       "    n_steps: !unroll [120000, 240000, 200000, 400000]\n",
       "\n",
       "    report: {frequency: 2000}\n",
       "\n",
       "    domain:\n",
       "      # Domain in diameter multiples: 20*D streamwise, 12*D cross-stream,\n",
       "      # thin periodic span (y, 8 cells). Cylinder centred 6*D from inlet.\n",
       "      domain_size:\n",
       "        x: !unroll [800, 1600, 800, 1600]\n",
       "        z: !unroll [480, 960, 480, 960]\n",
       "        y: 8\n",
       "      block_size: 8\n",
       "      # Keep the body's influence away from the domain faces.\n",
       "      bodies_domain_limits:\n",
       "        start: [0.02, 0.0, 0.05]\n",
       "        end: [0.98, 1.0, 0.95]\n",
       "        is_abs: false\n",
       "      bodies:\n",
       "        cylinder:\n",
       "          # Voxelized (NOT IBM): a surface band carries the no-slip wall\n",
       "          # (RegularizedHWBB) and the heated scalar Dirichlet wall.\n",
       "          IBM: {run: false}\n",
       "          voxelization:\n",
       "            run: true\n",
       "            BC: RegularizedHWBB\n",
       "            order: 1\n",
       "            band_radius: 1\n",
       "            strict_normal: true\n",
       "            scalar_bcs:\n",
       "              # Heated cylinder surface: temperature fixed to 1 on the band.\n",
       "              - scalar: temperature\n",
       "                BC: ScalarRegularizedDirichlet\n",
       "                order: 1\n",
       "                phi_w: 1.0\n",
       "                ux: 0.0\n",
       "                uy: 0.0\n",
       "                uz: 0.0\n",
       "          geometry_path: fixture/stl/basic/cylinder_refined.stl\n",
       "          small_triangles: \"add\"\n",
       "          area: {min: 0.25, max: 1.0}\n",
       "          transformation:\n",
       "            # Scale the raw D = 2.5 STL to the target lattice diameter\n",
       "            # (D / 2.5 = 16 for D = 40, 32 for D = 80) and translate so the\n",
       "            # axis sits at (6*D, *, domain_z/2). The y translation drops a\n",
       "            # slice of the long (scaled) axis across the periodic span.\n",
       "            scale: !unroll\n",
       "              - [16.0, 16.0, 16.0]\n",
       "              - [32.0, 32.0, 32.0]\n",
       "              - [16.0, 16.0, 16.0]\n",
       "              - [32.0, 32.0, 32.0]\n",
       "            translation: !unroll\n",
       "              - [220.0, -500.0, 220.0]\n",
       "              - [440.0, -1000.0, 440.0]\n",
       "              - [220.0, -500.0, 220.0]\n",
       "              - [440.0, -1000.0, 440.0]\n",
       "      refinement:\n",
       "        static:\n",
       "          default:\n",
       "            volumes_refine:\n",
       "              # Degenerate level-0 \"refinement\" so the static block stays\n",
       "              # valid; lvl 0 leaves the whole domain on the base grid.\n",
       "              - start: [0.0, 0.0, 0.0]\n",
       "                end: [1.0, 1.0, 1.0]\n",
       "                lvl: 0\n",
       "                is_abs: false\n",
       "\n",
       "    data:\n",
       "      exports:\n",
       "        default:\n",
       "          macrs: [rho, u, temperature_phi]\n",
       "          interval:\n",
       "            start_step: !unroll [100000, 200000, 160000, 320000]\n",
       "            frequency: !unroll [5000, 10000, 8000, 16000]\n",
       "            lvl: 0\n",
       "          target:\n",
       "            volume: {}\n",
       "          outputs:\n",
       "            instantaneous: true\n",
       "        plane_series:\n",
       "          macrs: [rho, u, temperature_phi]\n",
       "          interval: {frequency: !unroll [2000, 4000, 1000, 2000], lvl: 0}\n",
       "          target:\n",
       "            planes:\n",
       "              mid_span:\n",
       "                axis: y\n",
       "                axis_pos: 4\n",
       "                dist: 1\n",
       "          outputs:\n",
       "            instantaneous: true\n",
       "        spectrum:\n",
       "          macrs: [\"u\"]\n",
       "          interval:\n",
       "            frequency: 0\n",
       "            lvl: 0\n",
       "          target:\n",
       "            points:\n",
       "              wake:\n",
       "                pos: !unroll\n",
       "                  - [280.0, 4.0, 240.0]\n",
       "                  - [560.0, 4.0, 480.0]\n",
       "                  - [280.0, 4.0, 240.0]\n",
       "                  - [560.0, 4.0, 480.0]\n",
       "          outputs:\n",
       "            spectrum: true\n",
       "    models:\n",
       "      precision:\n",
       "        default: single\n",
       "\n",
       "      LBM:\n",
       "        # nu = U * D / Re ; tau = 3*nu + 1/2.\n",
       "        tau: !unroll [0.65000, 0.80000, 0.56000, 0.62000]\n",
       "        vel_set: D3Q27\n",
       "        coll_oper: HRRBGK\n",
       "\n",
       "      LES:\n",
       "        model: Smagorinsky\n",
       "        sgs_cte: 0.1\n",
       "\n",
       "      initialization:\n",
       "        equations:\n",
       "          rho: \"1.0\"\n",
       "          ux: !sub \"${u_inf_lattice}\"\n",
       "          uy: \"0\"\n",
       "          uz: \"0\"\n",
       "\n",
       "      engine:\n",
       "        name: CUDA\n",
       "\n",
       "      # Uniform cross-flow: west inlet, east Neumann outlet, top / bottom\n",
       "      # (F / B) Neumann far-field, y periodic (cylinder axis).\n",
       "      BC:\n",
       "        periodic_dims: [false, true, false]\n",
       "        BC_map:\n",
       "          - pos: W\n",
       "            BC: UniformFlow\n",
       "            wall_normal: W\n",
       "            ux: !math ${u_inf_lattice}\n",
       "            uy: 0\n",
       "            uz: 0\n",
       "            rho: 1\n",
       "            order: 2\n",
       "          - pos: E\n",
       "            BC: RegularizedNeumannOutlet\n",
       "            wall_normal: E\n",
       "            rho: 1.0\n",
       "            order: 2\n",
       "          - pos: F\n",
       "            BC: RegularizedNeumannOutlet\n",
       "            wall_normal: F\n",
       "            rho: 1.0\n",
       "            order: 1\n",
       "          - pos: B\n",
       "            BC: RegularizedNeumannOutlet\n",
       "            wall_normal: B\n",
       "            rho: 1.0\n",
       "            order: 1\n",
       "\n",
       "      scalar_transports:\n",
       "        temperature:\n",
       "          velocity_set: D3Q7\n",
       "          collision_operator: RRBGK\n",
       "          adv_diff_equation:\n",
       "            # D_s = nu / Pr (Pr = 0.71). Matches the per-variant nu above.\n",
       "            D: !unroll [0.07042, 0.14085, 0.02817, 0.05634]\n",
       "            S: \"0\"\n",
       "          # Clean (cold) freestream everywhere at start; the heated band\n",
       "          # injects the thermal layer.\n",
       "          initial_field: \"0\"\n",
       "          BC:\n",
       "            BC_map:\n",
       "              # West inlet: clean incoming scalar, phi = 0.\n",
       "              - pos: W\n",
       "                BC: ScalarRegularizedDirichlet\n",
       "                wall_normal: W\n",
       "                phi_w: 0.0\n",
       "                ux: !math ${u_inf_lattice}\n",
       "                uy: 0.0\n",
       "                uz: 0.0\n",
       "              # East outlet: zero-gradient (Neumann) outflow.\n",
       "              - pos: E\n",
       "                BC: ScalarRegularizedNeumann\n",
       "                wall_normal: E\n",
       "                J_w: 0.0\n",
       "              # Top / bottom far-field: zero scalar flux.\n",
       "              - pos: F\n",
       "                BC: ScalarRegularizedNeumann\n",
       "                wall_normal: F\n",
       "                J_w: 0.0\n",
       "              - pos: B\n",
       "                BC: ScalarRegularizedNeumann\n",
       "                wall_normal: B\n",
       "                J_w: 0.0\n",
       "\n",
       "      multiblock:\n",
       "        overlap_F2C: 2\n",
       "\n",
       "      # No LES for the laminar primary sweep (Re <= 100). The Re = 3900 LES\n",
       "      # variant (Smagorinsky + Sc_t scalar coupling) is the turbulent follow-up."
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Code\n",
    "\n",
    "Code(filename=str(CASE_PATH))"
   ]
  }
 ],
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