{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Annular Collision Probabilities Pin Cell Problem\n",
    "\n",
    "In this example, we will look at simulating a single UO2 pin-cell using the annular collision probabilities solver in Scarabée. To start, we will load the libraries we will be using, and initialize the nuclear data library object (`NDLibrary`) which contains the nuclear data for the simulation. We will be using the ENDF/B-VIII.0 library in the SHEM-281 group structure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[info] Loading Nuclear Data Library from /home/hunter/Documents/nuclear_data/scarabee/endf8_scarabee125.h5\n",
      "[info] Nuclear Data Library based on ENDF/B-VIII.0 using SCARABEE-125 group structure\n"
     ]
    }
   ],
   "source": [
    "import scarabee as scrb\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "ndl = scrb.NDLibrary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will start by defining the materials for the simulation. Firstly, we will need fuel, which will be 3 w/o enriched UO2. Scarabée has several helper functions to facilitate this process:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "UO2_comp = scrb.MaterialComposition(name=\"UO2\")\n",
    "UO2_comp.add_leu(enrichment=3., fraction=1.)\n",
    "UO2_comp.add_element(name=\"O\", fraction=2.)\n",
    "UO2 = scrb.Material(UO2_comp, 800., 10.96, scrb.DensityUnits.g_cm3, ndl)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `MaterialComposition.add_leu` method allows you to add low enriched Uranium up to 5 w/o to the material composition. The last line of this cell makes the final material object, where we have taken the fuel to be at a temperature of 800 K and a density of 10.96 g/cm$^3$. Next, we need natural He gas for the gap between the fuel pellet and the cladding:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "He_comp = scrb.MaterialComposition(name=\"He\")\n",
    "He_comp.add_element(\"He\", 1.)\n",
    "He = scrb.Material(He_comp, 600., 1.66322E-4, scrb.DensityUnits.g_cm3, ndl)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the PNNL Materials Compendium, we can also create a material for Zircaloy-4 for the fuel rod cladding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "Zirc_comp = scrb.MaterialComposition(fractions=scrb.Fraction.Weight, name=\"Zircaoloy-4\")\n",
    "Zirc_comp.add_element(\"O\", 0.001196)\n",
    "Zirc_comp.add_element(\"Cr\", 0.000997)\n",
    "Zirc_comp.add_element(\"Fe\", 0.001993)\n",
    "Zirc_comp.add_element(\"Zr\", 0.981859)\n",
    "Zirc_comp.add_element(\"Sn\", 0.013955)\n",
    "Zirc = scrb.Material(Zirc_comp, 590., 6.56, scrb.DensityUnits.g_cm3, ndl)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lastly, we need the moderator. We will use light water at 575 K under a pressure of 15.5 MPa and with 650 PPM boron. This is fairly representative of the moderator conditions one might find in a PWR. Scarabée has a helper function to generate such a water material for us at the correct density and nuclide fractions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "H2O = scrb.borated_water(temperature=575., pressure=15.5, boron_ppm=650., ndl=ndl)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will assume that the fuel pellet has a radius of 0.3975 cm, the gap a radius of 0.4125 cm, and the cladding a radius of 0.4750 cm. The pin pitch is 1.26 cm. Since we can only simulate a cylindrical system of rings with white boundary conditions when using the annular collision probabilities solver, we need to determine the equivalent radius for our pin cell. If the pin pitch is denoted as $p$, then the equivalent radius $R_{cell}$ can be found with\n",
    "\n",
    "$$\n",
    "    p^2 = \\pi R_{cell}^2\n",
    "$$\n",
    "\n",
    "$$\n",
    "    R_{cell} = \\frac{p}{\\sqrt{\\pi}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "R_fuel = 0.3975\n",
    "R_gap = 0.4125\n",
    "R_clad = 0.4750\n",
    "R_cell = 1.26 / np.sqrt(np.pi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before proceeding, we must first do the self-shielding calculations for the fuel and cladding. This requires the appropriate Dancoff corrections that account for shadowing in the fuel lattice. While Dancoff factors are best calculated for the true square geometry using the method of characteristics, we can get reasonable corrections using the annular collision probabilities solver for our use case here. To compute the Dancoff corrections we will use the neutron current method which requires four calculations in total (two for the fuel and two for the cladding). For each material, a simulation with an \"isolated\" fuel pin is performed, and then the \"true\" geometry. Additionally, for the non-resonant materials, the cross sections will only be the potential scattering cross section of the material. Here is the calculation for determining the fuel Dancoff correction:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[info] Solving cylindrical cell.\n",
      "[info] Calculating collision probabilities.\n",
      "[info] Solving system of equations for cylindrical cell.\n",
      "[info] Solving for keff.\n",
      "[info] keff tolerance: 1.00000E-05\n",
      "[info] Flux tolerance: 1.00000E-05\n",
      "[info] \n",
      "[info] Simulation Time: 6.26815E-04 s\n",
      "[info] Solving cylindrical cell.\n",
      "[info] Calculating collision probabilities.\n",
      "[info] Solving system of equations for cylindrical cell.\n",
      "[info] Solving for keff.\n",
      "[info] keff tolerance: 1.00000E-05\n",
      "[info] Flux tolerance: 1.00000E-05\n",
      "[info] \n",
      "[info] Simulation Time: 5.18839E-04 s\n",
      "\n",
      "Fuel Dancoff Correction: 0.3197234709823614\n"
     ]
    }
   ],
   "source": [
    "# Define 1-group cross sections\n",
    "Et = np.array([1.E5])\n",
    "Ea = Et\n",
    "Es = np.array([[0.]])\n",
    "FuelXS = scrb.CrossSection(Et, Ea, Es)\n",
    "\n",
    "Et = np.array([He.potential_xs])\n",
    "Ea = Et\n",
    "HeXS = scrb.CrossSection(Et, Ea, Es)\n",
    "\n",
    "Et = np.array([Zirc.potential_xs])\n",
    "Ea = Et\n",
    "ZircXS = scrb.CrossSection(Et, Ea, Es)\n",
    "\n",
    "Et = np.array([H2O.potential_xs])\n",
    "Ea = Et\n",
    "H2OXS = scrb.CrossSection(Et, Ea, Es)\n",
    "\n",
    "# Define the cell geometry for an isolated pin\n",
    "isolated_cell = scrb.CylindricalCell([R_fuel, R_gap, R_clad, 50.*R_cell],\n",
    "                                     [FuelXS, HeXS, ZircXS, H2OXS])\n",
    "isolated_cell.solve()\n",
    "\n",
    "# Create the flux solver for the isolated pin\n",
    "isolated_flux = scrb.CylindricalFluxSolver(isolated_cell)\n",
    "isolated_flux.albedo = 0.\n",
    "isolated_flux.sim_mode = scrb.SimulationMode.FixedSource\n",
    "# Set the sources of the non-resonant materials to the potential xs\n",
    "isolated_flux.set_extern_src(1, 0, HeXS.Et(0))\n",
    "isolated_flux.set_extern_src(2, 0, ZircXS.Et(0))\n",
    "isolated_flux.set_extern_src(3, 0, H2OXS.Et(0))\n",
    "isolated_flux.solve()\n",
    "\n",
    "# Define true cell geometry\n",
    "true_cell = scrb.CylindricalCell([R_fuel, R_gap, R_clad, R_cell],\n",
    "                                 [FuelXS, HeXS, ZircXS, H2OXS])\n",
    "true_cell.solve()\n",
    "\n",
    "# Solve flux for true pin\n",
    "true_flux = scrb.CylindricalFluxSolver(true_cell)\n",
    "true_flux.sim_mode = scrb.SimulationMode.FixedSource\n",
    "true_flux.set_extern_src(1, 0, HeXS.Et(0))\n",
    "true_flux.set_extern_src(2, 0, ZircXS.Et(0))\n",
    "true_flux.set_extern_src(3, 0, H2OXS.Et(0))\n",
    "true_flux.solve()\n",
    "\n",
    "# Compute the Dancoff correction for the fuel\n",
    "C_fuel = (isolated_flux.flux(0, 0) - true_flux.flux(0, 0)) / isolated_flux.flux(0, 0)\n",
    "print(\"\\nFuel Dancoff Correction: {:}\".format(C_fuel))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We follow a similar procedure to get the Dancoff correction for the cladding:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[info] Solving cylindrical cell.\n",
      "[info] Calculating collision probabilities.\n",
      "[info] Solving system of equations for cylindrical cell.\n",
      "[info] Solving for keff.\n",
      "[info] keff tolerance: 1.00000E-05\n",
      "[info] Flux tolerance: 1.00000E-05\n",
      "[info] \n",
      "[info] Simulation Time: 4.17986E-04 s\n",
      "[info] Solving cylindrical cell.\n",
      "[info] Calculating collision probabilities.\n",
      "[info] Solving system of equations for cylindrical cell.\n",
      "[info] Solving for keff.\n",
      "[info] keff tolerance: 1.00000E-05\n",
      "[info] Flux tolerance: 1.00000E-05\n",
      "[info] \n",
      "[info] Simulation Time: 6.17809E-04 s\n",
      "\n",
      "Clad Dancoff Correction: 0.29426243311815026\n"
     ]
    }
   ],
   "source": [
    "# Define 1-group cross sections\n",
    "Et = np.array([UO2.potential_xs])\n",
    "Ea = Et\n",
    "Es = np.array([[0.]])\n",
    "FuelXS = scrb.CrossSection(Et, Ea, Es)\n",
    "\n",
    "Et = np.array([1.E5])\n",
    "Ea = Et\n",
    "ZircXS = scrb.CrossSection(Et, Ea, Es)\n",
    "\n",
    "# Define the cell geometry for an isolated pin\n",
    "isolated_cell = scrb.CylindricalCell([R_fuel, R_gap, R_clad, 50.*R_cell],\n",
    "                                     [FuelXS, HeXS, ZircXS, H2OXS])\n",
    "isolated_cell.solve()\n",
    "\n",
    "# Create the flux solver for the isolated pin\n",
    "isolated_flux = scrb.CylindricalFluxSolver(isolated_cell)\n",
    "isolated_flux.albedo = 0.\n",
    "isolated_flux.sim_mode = scrb.SimulationMode.FixedSource\n",
    "# Set the sources of the non-resonant materials to the potential xs\n",
    "isolated_flux.set_extern_src(0, 0, FuelXS.Et(0))\n",
    "isolated_flux.set_extern_src(1, 0, HeXS.Et(0))\n",
    "isolated_flux.set_extern_src(3, 0, H2OXS.Et(0))\n",
    "isolated_flux.solve()\n",
    "\n",
    "# Define true cell geometry\n",
    "true_cell = scrb.CylindricalCell([R_fuel, R_gap, R_clad, R_cell],\n",
    "                                 [FuelXS, HeXS, ZircXS, H2OXS])\n",
    "true_cell.solve()\n",
    "\n",
    "# Solve flux for true pin\n",
    "true_flux = scrb.CylindricalFluxSolver(true_cell)\n",
    "true_flux.sim_mode = scrb.SimulationMode.FixedSource\n",
    "true_flux.set_extern_src(0, 0, FuelXS.Et(0))\n",
    "true_flux.set_extern_src(1, 0, HeXS.Et(0))\n",
    "true_flux.set_extern_src(3, 0, H2OXS.Et(0))\n",
    "true_flux.solve()\n",
    "\n",
    "# Compute the Dancoff correction for the clad\n",
    "C_clad = (isolated_flux.flux(2, 0) - true_flux.flux(2, 0)) / isolated_flux.flux(2, 0)\n",
    "print(\"\\nClad Dancoff Correction: {:}\".format(C_clad))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the Dancoff corrections obtained, we can generate the `CrossSection` objects for each material. For the fuel region, we will use Carlvik's two-term rational approximation, and for the cladding we will use Roman's two term rational approximation. The He gas and the water moderator do not contain resonant isotopes, so they do not need to be self-shielded. We will simply use infinite dilution for all nuclides in the material.\n",
    "\n",
    "For the fuel and cladding, we need the escape cross section for each region which is defined as\n",
    "$$\n",
    "    \\Sigma_e = \\frac{1}{\\bar{l}}\n",
    "$$\n",
    "where $\\bar{l}$ is the mean chord length of the region. For the fuel, $\\bar{l}_f = 2R_{fuel}$ and for the cladding $\\bar{l}_c = 2(R_{clad} - R_{gap})$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "Ee_fuel = 1. / (2.*R_fuel) # Fuel escape cross section\n",
    "FuelXS = UO2.carlvik_xs(C_fuel, Ee_fuel, ndl)\n",
    "\n",
    "Ee_clad = 1. / (2.*(R_clad - R_gap)) # Clad escape cross section\n",
    "CladXS = Zirc.roman_xs(C_clad, Ee_clad, ndl)\n",
    "\n",
    "HeXS = He.dilution_xs(He.size*[1.E10], ndl)\n",
    "\n",
    "H2OXS = H2O.dilution_xs(H2O.size*[1.E10], ndl)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have the self-shielded cross sections, so we can construct the fuel pin geometry and run the simulation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[info] Solving cylindrical cell.\n",
      "[info] Calculating collision probabilities.\n",
      "[info] Solving system of equations for cylindrical cell.\n",
      "[info] Solving for keff.\n",
      "[info] keff tolerance: 1.00000E-08\n",
      "[info] Flux tolerance: 1.00000E-08\n",
      "[info] -------------------------------------\n",
      "[info] Iteration    1          keff: 1.23655\n",
      "[info]      keff difference:     1.02224E+01\n",
      "[info]      max flux difference: 9.99924E-01\n",
      "[info] -------------------------------------\n",
      "[info] Iteration    2          keff: 1.23655\n",
      "[info]      keff difference:     4.97279E-09\n",
      "[info]      max flux difference: 8.14941E-09\n",
      "[info] \n",
      "[info] Simulation Time: 1.69431E-02 s\n"
     ]
    }
   ],
   "source": [
    "pin_cell = scrb.CylindricalCell([R_fuel, R_gap, R_clad, R_cell], [FuelXS, HeXS, CladXS, H2OXS])\n",
    "pin_cell.solve()\n",
    "\n",
    "pin = scrb.CylindricalFluxSolver(pin_cell)\n",
    "pin.keff_tolerance = 1.E-8\n",
    "pin.flux_tolerance = 1.E-8\n",
    "pin.solve()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That was fast ! This is the power of the annular collision probabilities solver, as it does an excellent job for single pin-cell problem domains with very fine energy group structures. Let's use the results to make a plot of the flux spectrum in the fuel, moderator, and the average flux spectrum in the entire pin."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The moderator is at the ring with index = 3\n",
    "moderator_flux = pin.homogenize_flux_spectrum([3])\n",
    "\n",
    "# The fuel is at the center with index = 0\n",
    "fuel_flux = pin.homogenize_flux_spectrum([0])\n",
    "\n",
    "# Without a list of region indices, this method will average over the entire pin cell\n",
    "avg_flux = pin.homogenize_flux_spectrum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These 1D arrays contain the resulting energy-integrated flux in each group of the data library. The indices follow the standard convention, where g=0 corresponds to the fastest energy group and as g increases the energy decreases (lethargy increases). If we plot these spectra right now (using the group bounds from the nuclear data library), they will look rather odd:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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iYiK6du2qVW2//PILOnXqhCVLlqiW1d42riWRSOoF8B49eiA1NRWpqamqq3aJiYkoKChAYGDLbgURtXdBzj6I6MEpGY1FW7YyYZNhw8Fgp2sSK8GGjLeUmZmZ6rbqwwMIrK2t8eqrr2LBggWqkcirVq1CSUkJpk2bBgB45ZVXsHbtWixYsADTp0/HuXPn6vW/e+ONN/Doo49i5syZmD59OqytrZGYmIjDhw/jk08+abQ2f39/pKSkYOfOnQgJCcG+ffuwZ88etW18fX1Vo6U7duwIW1tbhIeHo1evXhg/fjzWr1+PyspKvPbaaxgyZEiDt3uJiExVW7QyqW0yPDHkAdycCpFVVIZPfy5GvnygQQW72iuKhnA1UV9a8cAEmRI7O7tGn1tbuXIlnnvuOUycOBF9+/bFzZs3cfDgQTg6OgI1t1K/+eYb7N27F0FBQdi4cSPee+89tX307t0bx44dw/Xr1zF48GD06dMHS5cuhaenZ5N1jRo1CnPnzsXMmTMRHByMX375pd5cv8899xyGDx+OoUOHwtXVFf/5z38gEonw3XffwdHREU888QTCw8PRuXNn7Nq1q9XnioiI1DnaeUOmUGL1vR8x/3osVmeuQ1WXz1CQe1Ho0oCHriiO+PgEwtceQ1pBqdBl6QWv2LVTzc0osXfvXtX3lpaW+Oijj/DRRx81uv2IESMwYsQItWUP9xIMCQnBoUOHGt3H7dsN97hatWoVVq1apbas9jYwamYL2b17d733+fj44Lvvvmv0eMuXL8fy5csbXU9EZMia6w14/e6ZNqvFw7MfvovYhvyiVADA2aRTWH3vR8jld9ushqbUnbasTGJt0lOWMdg1oj00KCYiIuN06fovmHbypWZ7A1oqlPBw9m2Tmjw8+8HDsx8AIDW/BLj3Y5scVxNq05Zhi0lPWcZg14j20qCYiIiMT0bubTwQi/CSVTgCOoY0up0pz9ZRd8qw5p6ZqzttWUM97R6efqwuY3sej8GOiBrW1EwDepwQnIg0F9AxBBED/y50GW3u4SnDmp0urM60ZQ/3tGto+rG6jG0qMgY7IqqvIBUZGx9VTcr9MEexFB6v/MpwR6QnhvT8nCGqN2VYzXRhgA/y5eXIKmrgd1fNtGUP97RrcPqxuoxsKjIGOyKqJyP3Gka7OTQ604BMocB3udfgwWBHpHOG+Pycoak7ZRgALO7ggoRrF/DqmfMoU96Hj/Qq4PnnaFhN9/VwI2djnIqMwY6I6smvKEapWIw5PlPQwX2Q2rrszBNYn7IF+RXF8BCsQmqtjPRzqhGMzcnKM4yWFe0Fn59rXt3myzKJGXBnG765chTmPmdgLq5Abs0foF3snbTa18ONnI1xKjIGu0ZwVCy1Z3kl1Q8R7zxWiBsP1CcQ97csBPz+3IaMT0b6OYw6GNXsFaG6LBVKWFt31Gtd7YWmt1nb6/Nz2ii39Ub3Dh0gS96CArdfYKlQYn1mDhyrqqofGXHW/CpbQ42cjXEqMga7RnBULLVn8rLqZ00mDvRF357qV+zOX8nG6sw/tyHjk5SZhAdiEQLTg5FX1lmj95SL3OD3bONXj0gzvM2qe3VHvDqKpfB4fgdg5dJuB3kx2BFRo9zspOjppf6HTVqKFMgUrCTSgdpQ/kzfYejbc6xG7zG2lg9C0eRqHG+z6lidEa/tNczVxWBH9UyePBkFBQVqs08IydfXF3PmzFHNNiESibBnzx6MGTNG6NKIjFpDwZ0a11xoyylIxYeZX2h0NW5I0F8Z3HSpZsQrMdi1S5MnT8a2bdsAABYWFvDx8cGkSZPw5ptvwtzcHB9++CGUSqVOjnX06FGsXr0av/32G0pLS+Hr64vIyEjExMTAy8tLJ8dozKlTpzBo0CAMHz4c+/bt0+uxiMi0aXwLFcAbHSbAtYmQwatxpE8Mdu3U8OHDsWXLFpSVleHHH39EdHQ0LCwssHjxYp09U/jZZ5/htddeQ1RUFL755hv4+voiJSUF27dvx9q1a7Fu3TqdHKcxmzZtwuuvv45NmzYhPT0dnp6eejuWUqlEVVUVzM35nxSRKeJIVTIWDTepIsTFxSEwMBAhIab5sLBUKoW7uzs6deqEV199FeHh4fj++++Bmit6dW9zhoWFYdasWVi4cCGcnJzg7u6O5cuXN7n/u3fvYtasWZg1axY2b96MsLAw+Pr64oknnsDnn3+OpUuXqrY9ceIEBg8eDJlMBm9vb8yaNQtyubxVn6+4uBi7du3Cq6++imeeeQZbt25Vrfv73/+OcePGqW1fUVEBFxcXbN++HQCgUCgQGxsLPz8/yGQyBAUFYffu3artf/rpJ4hEIuzfvx/9+vWDVCrFiRMnkJSUhNGjR8PNzQ02NjYICQnBkSNH1I6VkZGBZ555BjKZDH5+fvjqq6/g6+uL9evXq7YpKCjA9OnT4erqCjs7OwwbNgwXL7LlBJHQakeqNvbFUGc8sorKcCWtsOFmxkaMwa4R0dHRSExMxJkz7aO7t0wmQ3l54+0rtm3bBmtra/z2229YtWoV3nnnHRw+fLjR7b/++muUl5dj4cKFDa53cHAAACQlJWH48OF47rnncOnSJezatQsnTpzAzJkzW/V5/u///g/du3dHt27dMGHCBGzevFl1e3n8+PH473//i+LiYtX2Bw8eRElJCZ599lkAQGxsLLZv346NGzfi6tWrmDt3LiZMmIBjx46pHWfRokVYuXIlfv/9d/Tu3RvFxcV4+umnER8fjwsXLmD48OEYOXIkUlJSVO+ZNGkS0tPT8dNPP+Gbb77Bv/71L2RnZ6vt969//Suys7Oxf/9+nDt3Dn379sWTTz6JvLy8Vp0XImpCQSqQntDgl+S+Zj3/yPDVNi3+4tRtjPj4BL44dVttubEzjU9BLaZUKhEfH4+DBw/i9ddfb3S73r17Y9myZQAAf39/fPLJJ4iPj8df/vKXBre/ceMG7Ozs4OHRdAvb2NhYjB8/XjUwwt/fHx999BGGDBmCDRs2wNLSskWfa9OmTZgwYQJQc9u5sLAQx44dQ1hYGCIiImBtbY09e/Zg4sSJAICvvvoKo0aNgq2tLcrKyvDee+/hyJEjGDhwIACgc+fOOHHiBD777DMMGTJEdZx33nlH7Rw4OTkhKChI9frdd9/Fnj178P3332PmzJn4448/cOTIEZw5cwb9+/cHAHz++efw9/dXvefEiRM4ffo0srOzIZVKAQBr1qzB3r17sXv3brz00kstOidE7V5T8x+X3EPa15NQqGz4D1y5hQXQwQUKqZ1+ayS9c7KSAAD+NsQeHdxdkZ1pj/Upfy43dgx2OlZaWYrkwuQ2P66fvR9k5pq3Ivjhhx9gY2ODiooKKBQK/P3vf2/y9mrv3r3VXnt4eKiuMr3yyiv48ssvVeuKi4uhVCohEjXf/PTixYu4dOkSduzYoVqmVCqhUCiQnJyMHj16aPyZal27dg2nT5/Gnj17AADm5uYYN24cNm3ahLCwMJibm+OFF17Ajh07MHHiRMjlcnz33XfYuXMnAODmzZsoKSmpF1rLy8vRp08ftWW14azuZ1++fDn27duHjIwMVFZWorS0VHXF7tq1azA3N0ffvn1V7+natSscHR3VzklxcTGcnZ3V9l1aWoqkpCStz4e+SO7XXN0A2GKA2ozaz91DLuemI724oMF1ZmWF8PhtBURVDxpcn29mhjnurk0PjlBYwN39kZYVTq2WVlCKfHk5HK1bF8AcLWwgUyiwPmULkLIFqJmlwtHCRkeVCovBTseSC5Mx7odxGmypW7tG7EKgc6DG2w8dOhQbNmyARCKBp6dnsw/9W1hYqL0WiURQKBRAzVWr+fPnq60PCAhAYWEhMjIymrxqV1xcjJdffhmzZs2qt87Hx0fjz1PXpk2bUFlZqTZYQqlUQiqV4pNPPoG9vT3Gjx+PIUOGIDs7G4cPH4ZMJsPw4cNVNQHAvn376o3crb2CVsva2lrt9fz583H48GGsWbMGXbt2hUwmw/PPP9/kbe6HFRcXw8PDAz/99FO9dbW3sIVUe8VCfnE9Es+uBoDqpqCv/MpwR3rT0M9dXflmZpjbwaXR+Y0BAO6Oja9DdXB7rcc/0dHWpcHVHe1d0cfTT8vKSRfSCkoR/uFelCnvQyqyxbJBLZ/5pm5D41razlJhyBjsdMzP3g+7RuwS5LjasLa2RteuXXVy7A4dOqBDhw5qy55//nksWrQIq1atwgcffFDvPQUFBXBwcEDfvn2RmJios1oqKytVo26feuoptXVjxozBf/7zH7zyyit47LHH4O3tjV27dmH//v3461//qgqvgYGBkEqlSElJUbvtqomTJ09i8uTJqmf1iouLcfv2n32vunXrhsrKSly4cAH9+vUDaq4Q5ufnq7bp27cvMjMzYW5uDl9fw+s8L7P3BxTmWNzhz//5yRQKfJd7DR4MdqQn7u6PABct1H7uHiZSmGNexxnwsGr4DyCF1A6Vsg4NrgODm0G7kZsCc59VMBdXAgpzpMnHt3xndRsa1zKhuw4MdjomM5dpdeXMVHl7e+ODDz7AzJkzUVRUhEmTJsHX1xd3797F9u3bYWNjg7Vr1+KNN97Ao48+ipkzZ2L69OmwtrZGYmIiDh8+jE8++UTr4/7www/Iz8/HtGnT6rVtee6557Bp0ya88sorQM3o2I0bN+L69es4evSoajtbW1vMnz8fc+fOhUKhwKBBg1BYWIiTJ0/Czs4OUVFRjR7f398f3377LUaOHAmRSIS33npLdWUTALp3747w8HC89NJL2LBhAywsLDBv3jzIZDLVrevw8HAMHDgQY8aMwapVqxAQEID09HTs27cPzz77bL3bv23N39kHlSkLUaa8DwDwkV5Fruf/kFSYh6afqCRquT6eftge8Q3uFuY0ug2DmekqLbwBiCvxUn4h/uVoj4qy9Nbt0IQbGjPYkd689tprCAgIwJo1a/Dss8+qGhSPGDECMTExQM2ze8eOHcOSJUswePBgKJVKdOnSpV47Ek1t2rQJ4eHhDfbie+6557Bq1SpcunQJvXv3xvjx47FixQp06tQJjz/+uNq27777LlxdXREbG4tbt26pri6++eabTR5/3bp1mDp1Kh577DG4uLjgjTfeQFFRkdo227dvx7Rp0/DEE0/A3d0dsbGxuHr1qmqgiEgkwo8//oglS5ZgypQpyMnJgbu7O5544gm4ubm16LxopM6D5U2NAPRykOHI7DHIl1ffCjl/5Vuszvwf544lvevj6cfg1o5kFZUhraAUXg4yiMtqfo86PQYor8K8qkTo8gwWg107VLenmybrG3rWS9PpxsLDwxEeHt7kNiEhITh06FCj6+veykTN83KN+e9//9voutDQULX39ujRo9F9iUQizJ49G7Nnz25wfVhYWIPv9fX1xf/+9z+1ZdHR0WqvPTw88OOPP6pe3717F9nZ2Wq3o21tbfHRRx/ho48+avTz6FRBKhAXClRU/7J0k1gAXh6NjgD0cpCp5g3l3LFEpEu1bUc2n09A7K+WODL7z76qZRIHwLTazukcg10j4uLiEBcXh6qqKqFLIRPzv//9D8XFxejVqxcyMjKwcOFCVfNmwZTkIkNRhvzh7wAOnXAq4xaQsqXJ55HIsGWkn0N+UcNXXrPy2OyaDFcXeyfIFArkev4P5orjuJHbF8W8I6AxBrtGREdHIzo6GkVFRTqbYosINbNcvPnmm7h16xZsbW3x2GOPYceOHfVGHreljNJ7GN3RA6XXPlctUyosYCvhz74xykg/h1EHo5ps3WGpUMLaumOb1kWkidpRq+fMFFjcwQV3067iPyeSAW9AYmYmdHkGj8GOqI1FREQgIiJC6DLU5FcUo1QsxhyfKejgPgipeSVYvT8NLk+5C10atUBSZhIeiEUITA9GXlnnBrcpF7nB71nTnDKRjFzNqFXr018BGV+i7H4eLHAPAGAlNQP4eF2TGOyICHkl1QMhdh4rxI0H1aMOZRbOrW4ESsKoHcjyTN9h6NtzbIPbOFpLVM9JEhkcB2+U23oDGUBJaTLSvI7CUgHYSBtvd0PVGOyISBUEJg70Rd+egwD+j98kuNlJ0dOLt9PJuJVV5uKBWIS3O06GtZUHB2s1g8FOB5oapUnUFnT1M8ggQESGytqKnTI10cTcK9Qcs5qHOLWZLopIH0pKqh86EXIABhERCY9X7FrB3NwcVlZWyMnJgYWFBcRNzVFIpAdKpRIlJSXIzs6Gg4OD6o8NIahNzm5C0/MQkbBKytnqRBsMdq0gEong4eGB5ORk3LlzR+hyqB1zcHCAu7swI1gbmpzdUSyFxyu/MtwRUYvVNir+I6MYcK9+zRlumsdg10oSiQT+/v68HUuCsbCwEPRKnczeH1CYq03OLlMo8F3uNXgw2BFRDW2bDDtZVY/K7+kvw+X71a8Z7JrHYNcIbWaeEIvFqnk+idobF0t3FCfNx4JIL3g7WSE78wTWp2xBfkUx+KgzEQFAWkEp/n0qEfD880pccxwtbCBTKPCf+2chUyjgaGGDVDaxaxaDXSM48wSRZhytJbAUOWPVf+UA5PC3LAT8/uyNR0R0IzcFGe4HIFMo0MXeSaP31M5Aka8oq368w7kbLmVn671WY8dgR9SeFaQCJbnVAx9ayMtBhiPzhiBfXh3kzl/JxupM8JYJEamUFt6AQlyFtTlF8HDuptmbamag8CjJ5YAsLTDYEbVXBanI2Pgo8hVlkFtYAB1cVAMhtOXlIFM1M05LkbKBKBGpEZcVAQDK+r+pXUBz8Gag0xKDHVE7lZF7DaPdHFBa26ZHYV49EIKISE+qpHy0Sd8Y7IjaqfyKYpSKxYjt+QqUViGYteMGXJ4SpmUKERHphkbBrm/fvlrtVCQS4fvvv4eXl1dL6yKiNmJR7ohSsReUlTlCl6JzGennkF9U//lBRztveHj2E6QmIiJ90ijYJSQkYN68ebCxsWl2W6VSiZUrV6KsrEwX9RGRntSOWl1z8BpuPLCHzMIMjtYSocvSmYz0cxh1MAoPxKJ66ywVSnwfsY3hjohMjsa3YhcsWIAOHTpotO3atWtbUxMRtYHaUasTB/qib89BcLSWqAZAmIKkzCQ8EIsQmB6MvLLOquVO0ltI9ExAUmYSgx1RG0grKEVWES/2tBWNgl1ycjJcXV013mliYiI8PT1bUxcRtRE3Oyl6epneA821wfWZvsPQt+dY1fLzV75FYmYC27EQtYH8knKEf7gXbpIErZoTU8tpdIY7deqk1U69vTk0mYgMw8PBle1YiNpOmvwezH12IFdcqVVzYmo5sbZvOHDgAE6cOKF6HRcXh+DgYPz9739Hfn6+rusjIiIiI1VRlg6IKxGbfQ/fZRVo3pyYWkzrYLdgwQIUFVU3Grx8+TLmzZuHp59+GsnJyYiJidFHjURERGSEzKuq53a1DpoDj1d+Ndpmw1lFZbiSVtjoV1pBqdAlqmh9szs5ORmBgYEAgG+++QYjRozAe++9h/Pnz+Ppp5/WR41ERERkxMptjXMGidpnAr84dRtLj55odDuZhRmOzBtiEAPQtA52EokEJSXVCfzIkSOYNGkSAMDJyUl1JY+IDFxBaqvmhyUi0kRJuXEPUnKyqm4BNTHkAdycChvcJquoDJ/+XIx8+UDjDHaDBg1CTEwMHn/8cZw+fRq7du0CAFy/fh0dO3bUR42CiIuLQ1xcHKqqqoQuhUi3ClKBuFC4iSoAL48Wzw9LRNSY2itdN+/dAZyNdzSso503ZAolVt/7Ebj3Y6PbWXZRoiA3CPB6ok3ra4jWZ/qTTz7Ba6+9ht27d2PDhg2q2SX279+P4cOH66NGQURHRyM6OhpFRUWwtze9VhDUjpXkIkNRhrN9ZwD3fkSlTLP+lPrw8MwQnBGCyDR0ce8Cy4tKXHDOhKVCiS7uXYQuqUU8PPvhu4htDc5gU+ts0imsvvcj5PK7bVpbY7QOdj4+Pvjhhx/qLf/ggw90VRMR6VFG6T2M7uiB0ns/QqmwgK1EmD9cGpoZoj3NCMFQS6bMw7Mfvq8JRMb+s+3h2a/J+lPzS5q8mtfWtA52ZmZmyMjIqDcLRW5uLjp06MBbl0SGqiAVKMlFfs5VlIrFmOMzBf+Md4PLU+6ClPPwzBC1M0Icv7IbvWoCj7H/D6Ex7T3UUvvQXCAi/dA62CmVygaXl5WVQSIxnXkmiUxCTZhDyT1g10SgogSQWABeHoDCB8pK4R70fXhmiCs3TuFW8gX8M+MHIKP6roCphp3GQi2nOSPSTFmlQugSDJbGwe6jjz4CAIhEInz++eewsbFRrauqqsLx48fRvXt3/VRJRNqrGSSBiupR7BmWNsh/Zj0S5EXAzc+x4uc8yCx84Gitnz/IsvIuIiO9W7NBpXZmCEfrIdhw7DU4KLOAOnO6tsUVvEvXf0FG7m3Vaw9nX/QOeEznx6n1cKjlNGdEmqkdhHE+8x6g+Uyn7YrGwa72GTqlUomNGzfCzMxMtU4ikcDX1xcbN27UT5VEpL2aQRL5w99BvpUj5l76CKUX1wEAlAoLLI0MwV+6ddf58Hxr646wrBlF9snBffhOwytuXg4yfDV7CvLl5QDQZlfwLl3/BdNOvlTvtugm/Euv4Q51Qi2nOSPSTBd7J8gUClx3vSF0KQZL42CXnJwMABg6dCi+/fZbODo66rMuImol1SCJa58DAGTmMmwM34i8IgvM2nED/Z/qrJeeSw7OQTBLehkvBd3Cv0qOIL8oVeMg5uUgU9XU2BU8Xd+uzMi9jQdiEV6yCkdAxxBcv3sG/yo5gozc2+gN/Qa7Fqm9vQ4AVs5G2fSVqKU8nLthbW4RXnN1ELoUg6X1M3ZHjx7VTyVEpFP5FcUoFYsR2/MVdPYdCkepIzxsPHAFhVBW5ujtuI7WEhSK/PH91XuAH5BXUt6i/Tx8BU/Xtysl91OB9ARVo+aAjiGIGPh34BSA60d0cgydK0hF2oYBKFRWnxN7kQRer/7GcEfth4M3zB5bCtyofjzMWPvj6ZNGZyQmJgbvvvsurK2tm50Pdt26dbqqjYh0oLO1FwKdA5FWUIoraYW4mV2s1+N5OchwZN4QxP+WgdWZaFUQq3sFT1e3K2sbMssvrkfi2dWQW1gAHVyMolHz5dTLmObuiFJx9TTfMoUCm1Ivo5eDt1r7lKy8iwJXSqQ/fm5+kF2rHjzRxd5J6HIMjkbB7sKFC6ioqFB93xiRSNToOiISRmp+CXKu5+CVL86htKK6HZHMwkxvgyZQE8jc7AzzuTF390eAixZY3MHlz4UKi+rlBi69uAClYjEmOo8HAHyRuwPpxQVwaaR9irW16cwGRFTLw7kbvssqUH1P6jQKdnVvv/JWLJGBq3kGqyjzJgBgzcFruPHAHjILM2ybGgpnawkcrSUGMaehEPp4+mF7xDe4W/jn7eiO9q7o4+knaF3aCHL2AQB8UfOo3cPtUwCgXOQGv2dDhCyTSD8cvOHxyq+q70kdb04TmZI6LU7savrV/W1wLwzoPqhdh7mH9fH0M6og15yH26eg5llH/vsmk8VA1yitg51cLsfKlSsRHx+P7OxsKBTqTQJv3bqly/qISBt1WpycKq0CUragg6cPenoJN9+x5H5qdeA0sl/EWXkXkfiHFdCGM2DUDuho6WjX2vYpRNR+aR3spk+fjmPHjmHixInw8PDgc3VEBuThFidCzgVbd5BCxvmPqm+dGEG4q9uHr3b+R33PgPHwgA5HsdRozhcRGRatg93+/fuxb98+PP744/qpiIharG6LE6VVCGbtuCHYXLAye39AYY7FHVwgUyjwXe41eBhBUPHzCYHVHv33z6ur7rlCzWhXTc9XbbsWIiK0JNg5OjrCyYnDi4kMWWdrLyhsu+m1X11zXCzdUZw0H68+moovcncgv6IYHoJVo7nG+udV3Etu1W3Spvg7+6AyZSHKlPfhI72KXM//Iakwr8nzVXuVz+3s6prCPYyiZQsR6ZfWwe7dd9/F0qVLsW3bNlhZWemnKiJqldT8EpSW6rdfXXMcrSWwFDnj8Nnr9RsVF6Qa9JWmuv3zUrNcgcw/b5O2pClw3R5zjnb13+flIMOR2WOQLy/H+SvfYnXm/5rt/1cp6wAAODXwzeoFKVtUy4io/dI62K1duxZJSUlwc3ODr68vLCws1NafP39el/URkRZqw1PdFif67FfXlEYbFRekImPjo5CbKYyiMfDDfe/qNgXWRMZDPeYsFUrM83yh3na1YVLTRsy2EnsoFRZYn7IFEPh5SiIyHFoHuzFjxuinEiJqtdrwNHGgL/r2FL7FSUONijNyr2G0m0P17AkK8+rnywxY3b53vyf9T9UUuJeG76/bYw4AEj0TkF2U1eq6XCzdIU+ah4/GV58/IZ+nJCLDoXWwW7ZsmX4q0aNnn30WP/30E5588kns3r1b6HKI9M6Q214kFeahVCyGc/owZJU/Cv+aZruGrLbvnaTgpqopsKbq9pgDgMTMBJRXVemkLmWlA/zsutV8L9zzlERkODQOdkVFRQ0ut7a2hpmZmS5r0rnZs2dj6tSp2LZtm9ClELV7tUFnat9gPDlgTLtpoutmJ63+RsfTrOl77l8iMi4aBzsHB4cGe9aZmZnBz88P8+fPx4wZM3Rdn06EhYXhp59+EroMIqrDzU7abkKdPjhaSyCzMMOcXQlAG8z/S0TGQeNg19gcsQUFBTh37hwWLFgAc3NzTJkyRasCjh8/jtWrV+PcuXPIyMjAnj176j3HFxcXh9WrVyMzMxNBQUH4+OOPERoaqtVxiKj9uHT9F1y/e0boMvSqdnBKbVsWoZ+nJCLDoHGwGzJkSKPrRo8eDV9fX3z88cdaBzu5XI6goCBMnToVY8eOrbd+165diImJwcaNGzFgwACsX78eERERuHbtGjp0qB7aHxwcjMrK+q0BDh06BE9PT63qISLjdun6L5h28iU8EItgqVDCw9lX6JL0pm5bFiIitGTwRGOGDBmCOXPmaP2+yMhIREZGNrp+3bp1mDFjhiowbty4Efv27cPmzZuxaNEiAEBCQkIrKldXVlaGsrIy1evGni0kIsOUkXsbD8QivGQVjiFBf0XvgMeELomIqM2IdbWjwsJC2NvrdhReeXk5zp07h/DwcNUysViM8PBwnDp1SqfHqhUbGwt7e3vVl7e34U+BRISC6snjDbnpb1sL6BhiUqGuPdxeJqLW08kVu4qKCqxevRoDBgzQxe5U7t27h6qqKri5uaktd3Nzwx9//KHxfsLDw3Hx4kXI5XJ07NgRX3/9NQYOHNjgtosXL0ZMTIzqdVFREcMdGbaCVCAuFKgogZvEglNLmaD2dHuZiFpH42DX0PNvqLlSd/XqVYhEIvz888+6rE1njhw5ovG2UqkUUqlUr/UQ6VRJLjIUZcgf/g5OlVZxaikTxNvLRKQpjYNdY7dZvb298dxzz2H8+PE6vxXr4uICMzMzZGWpd2nPysqCuzs7rFM7V5BaHerSz2B0Rw+UXvscaMdTS9XOx5qVd1HoUvTG1G4vE5HuaRzstmzZot9KGiCRSNCvXz/Ex8erWqAoFArEx8dj5syZej12XFwc4uLiUKWjDvFEOlXn9mu+xAKlXh6I7bsASvPuBj21VEb6Ob0Er4bmY7W27qjz4xARGTqdjYptqeLiYty8eVP1Ojk5GQkJCXBycoKPjw9iYmIQFRWF/v37IzQ0FOvXr4dcLte6rYq2oqOjER0djaKiIp1fiSRqtTq3X29ZmANXNqKzZ38oHngZ7NRS+UU3MfrgeyiteU5Ml8Gr7nyseWWdUS5yg9+zITrbPxGRsRA82J09exZDhw5Vva4duBAVFYWtW7di3LhxyMnJwdKlS5GZmYng4GAcOHCg3oAKovYko/Se2u1XmbkMjlJH5D4QurLGFZfdQ2nNc2I7LnaGw1NBOtt33flY+/Ycy2a9RNRuCR7swsLCoFQqm9xm5syZer/1SmTQap6nq5WfcxWlYjFie76Czr5DUVYmQ26hlUHPG1pSVv1Yw/dX7VAo8tfL9FdudlL09OIVdiJqvwQPdoaKz9iRwajzPJ1KTVuTzs6BsDfzQ/iGYyitqP5ZNdQ5Q8tr/luaONAXTw4YwitqRER6wGDXCD5jRwajJLc61I39N+ASUL2s6Dbw21uArRvy5eUorajC+nHB6NrBxmBvQ5pXVgdTNzupQdZnsApS2XiaiDSms2B39uxZlJSU4IknntDVLomoRoaZGfIlEkBafSXulqT6P92k7GJUPai+/dq1g41B3oasbZZsk3MUcHIQupy2UXvrvKK0daGsIBUZGx+F3EwBdHBh42kiapbOgt3EiRNx/fp13rok0jHVQInf3lJbrlRYYNaOG1BW5hjs7VcAkNn7Q6www4cmFOryi24i8Y+9cLTzhodnP/WVBalI2zAAhcpyPBCJITc3U4UycZl2c09n5F7DaDcHlIrFgMIcMnt/3X4QIjI5Ogt28fHxqKio0NXuiKhGfkWx2kAJ1Fypm7XjBj54Lsygb78CgIulO5zTIpDj/aPQpejMisyvgcyvIVMo8V3ENrVwdzn1Mqa5O1aHsVo1oaws+5xWx0kqzEOpWAzn9GHIKn8U/s4+uvwYRGSCdBbsPD09dbUrg8DBEySYh0bAouAOAKCztRcCnQMBAIoHhVBW5hjs7de6HK0lkMFK6DJ0boI0AF+WXUd+UapasEsvLkCpWIyeFXa4YlEEv7xOuFE0Hv7OPriiZbCrbeMytW8wnhwwxmDDOxEZjhYFu6qqKuzZswe///47AKBHjx4YM2YMzM1NZywGB0+QIJoYAQtL4/w59HKQYeogPyy/I3QlunXxjgXgDuSVlDe43kVZfWu8j4M7NkypDmVXWngsDjghIk1pncSuXr2KUaNGITMzE926dQMAvP/++3B1dcV///tf9OzZUx91ErUPTYyATSq1hiKtEAAMul9dQ6zsnFTft3YAQFbeRWSkd6v/bFsb6+5hg8vKP6+qNcZWZs5QRkRtRutgN336dDzyyCM4e/YsHB0dAQD5+fmYPHkyXnrpJfzyyy/6qJOo3Xh4BOy5iuoG3rN3JUDx4M/pwgx5wMTDZPb+gML8z+9bwNq6IywVSqy+9yM+PrgP3z/0bFtbs5KYA2WCHZ6IqEFaB7uEhAS1UAcAjo6OWLFiBUJCODcjUWs0NQJ2aWQI+nfsrFpmyAMmHubv7IPKlIWq71vCzycEVnteQ2fJKSR6JiApM0nwq3ZERIZG62AXEBCArKwsPPLII2rLs7Oz0bVrV13WRtTuNDUCtv9TnQ1+oERjvBxkODJ7jOr7lu7jq9lTEP+bDImZCc3eAiUiao80CnZFRX/2XoqNjcWsWbOwfPlyPProowCAX3/9Fe+88w7ef/99/VXaxjgqloTU0AhYY6eLq4teDjK42UmBTJ2UpHucJYKIBKZRsHNwcIBIJFK9ViqVeOGFF1TLlMrqZ4BGjhxpMkGIo2KJSCsPzRJRKZIKXRERtUMaBbujR4/qvxIiIiP28CwRZmYOANKELouI2hmNgt2QIUMAAJWVlXjvvfcwdepUdOzYUd+1EZmuh5sQq5abWLO3duThWSI6+MUDSqGrIqL2RqvBE+bm5li9ejUmTZqkv4qITF1DTYhr1TQjvlNibrQ969qrh2eJ+M+BY2yHQkRtTutRscOGDcOxY8fg6+urn4qITF1DTYhr5GVeBy6/i+jv06F4cEK13Jh61rWVnALDHKTAWSKISEhaB7vIyEgsWrQIly9fRr9+/WBtba22ftSoUbqsj8h0uQQAnsFqi/ILq6enmv+XADzh20e13Jh61umbh7MvLBVKfJj5BXpfH4zeAY8JXRIRkcHQOti99tprAIB169bVWycSiUxmVCzbnZA+ZZiZIb/otmp2iVpp8upn7LydrIy2Z52+9Q54DLOTJuL97C+RkXsbvcFgR0RUS+tgp1Ao9FOJgWG7E9KXxmaXqKVUWMBWwp+5prg6eAPZQldBRGR4tA52jSkoKMCXX36JmTNn6mqXRCapodklatXOMuHylLtg9RERkfFqdbCLj4/Hpk2bsGfPHlhZWTHYEWmo7uwStUxllgkiIhKGuCVvSk1NxTvvvAM/Pz889dRTEIlE2LNnDzIzDXWeHyIiIiLTp3Gwq6iowNdff42IiAh069YNCQkJWL16NcRiMZYsWYLhw4fDwsJCv9USERERUaM0vhXr5eWF7t27Y8KECdi5cyccHR0BAC+++KI+6yMiIiIiDWl8xa6yshIikQgikQhmZmb6rYqIiIiItKbxFbv09HR888032LRpE2bPno3IyEhMmDABIpFIvxUKhH3sSN9S80tU04bV4vRhxse8JKd6mjgiIgOgcbCztLTE+PHjMX78eCQlJWHLli2YNWsWKisrsWLFCkyePBnDhg0zmat57GNH+pJXUj27xJqD13DjQf2fLU4fZmTOxSLjzCqYhywUuhIiopa1O+nSpQv++c9/4p133sHBgwexadMmjBgxAra2trh3757uqyQyIbWTxU8c6Iu+PQfVW8/pw4zLHDdXyBQKLChNE7oUIqLW9bETi8WIjIxEZGQkcnJy8MUXX+iuMiJjUpAKlORqtKnkfvVtOzc7KacNM2JSc2dYlirxQCxCqViMQsUDoUsiItLdzBOurq6IiYnR1e6IjEdBKhAXClSUaLS5m8QC8PKAQmqn99JIf6xkfjBLeBnR/bIQV/Sd0OUQEQGaBjsnJydcv34dLi4uGu3Ux8cHP//8Mzp16tTa+ogMX0ludagb+2/AJaDZzVPvJALXY1Ep69Am5ZF+WFuao1Dkj28u3gP8gJIyDrQiIuFpFOwKCgqwf/9+jQcR5ObmcjQptT8uAYBncLOblReWt0k5pF+OVhIcmTcE8b9lYHUmUM7feURkADS+FRsVFaXfSoiItCQvyRD0+F4OMrjZSQHOpkhEBkKjYKdQKPRfCZERyzAzQ37RbUDafJuSNPmdNqnJlFlbd4SlQonYlC0YmB4mdDlERAZDZ4MniNqrjNJ7GN3RA6W/vaXxe5QKC9hKOCK2pfx8QtBp3zBc8zyKpMwkocshIjIYDHZErZRfUYxSsRixPV9BZ9+hzW6flF2MWTtuwOUp9zapzxR5Ocjw4sD+WH7nqKovIBERMdg1ilOKkbY6W3sh0Dmw2e0UDwqhrMxpk5pMmY2Uv76IiB4mFroAQxUdHY3ExEScOXNG6FKIiIiINMJgR0RERGQitA52W7dubXB5ZWUlFi9erIuaiIiIiKgFtA52s2bNwl//+lfk5+erll27dg0DBgzAf/7zH13XR0REREQa0jrYXbhwAXfv3kWvXr1w+PBhxMXFoW/fvujevTsuXryonyqJiIiIqFlaDyvr0qULTp48iTlz5mD48OEwMzPDtm3b8OKLL+qnQiIiIiLSSIv6Bezbtw87d+7EwIEDcf36dWzatAlDhgyBp6en7iskMhKp+SVQpBU2u93N7OI2qYeMn1lZ8z9PRER1aR3sXn75ZWzbtg0rVqxATEwMsrKyMHXqVPTq1QsbNmzACy+8oJ9KiQxUXkk5AGDNwWu48UCz2SRkFmZwtG5++jFqv8xLciC5sAZwdYBCaid0OURkJLQOdidPnsRvv/2GoKAgAIC7uzt+/PFHxMXFYerUqQx21O7UznwwcaAv+vYcpNF7HK0l8HKQ6bky0rW6AUvfYSuvNA2rne0gVphBZu+v12MRkenQOtidO3cOUqm03vLo6GiEh4frqi4io+NmJ0VPL87/aspk9v6AwvzP7/Uoo1SOUrEYXunD4e/so9djEZHp0DrYNRTqanXr1q219RARGSx/Zx9UpixUfa9P5TXTGc4YGMiru0SkMa2DnZ+fH0QiUaPrb9261dqaiIgMkpeDDEdmj1F93xY4Jy4RaUPr3xhz5sxRe11RUYELFy7gwIEDWLBggS5rIyIyOLx6RkSGTOtgN3v27AaXx8XF4ezZs7qoiYjIpN0vzxS6BCIyUVrPPNGYyMhIfPPNN7raneDi4uIQGBiIkJAQoUshIhORX3QTAPCtMknoUojIROks2O3evRtOTk662p3goqOjkZiYiDNnzghdChGZiOyiLKFLICITp/Wt2D59+qgNnlAqlcjMzEROTg4+/fRTXddHRNQk85IcVFq5Cl2GRmpHuhIR6YvWwW7MmDFqr8ViMVxdXREWFobu3bvrsjYiokaZl+QAADIvroIkYLzQ5RARGQStg92yZcv0UwkRkRZSClIAACudnYDc/UKXQ0RkEDQKdkVFRRrv0M6OcxoSkf7lVsjrLasdnGAK/O5+D7g6C10GERkZjYKdg4NDk02JUfOsnUgkQhWfISGiNuBo2x8oO4nnzF9CQvJ1JHn/BJhz6i0iat80CnZHjx7VfyVERFoYEPxX3P/YA8+/PghDQ8oRtXk4eoYPErosnVnOq3VE1AIaBbshQ4bovxIiIi309LLH7ZXPqF7X/Z6IqL3SuI/dpEmTcP/+fdXrixcvoqKiQl91EREREZGWNA52O3bsQGlpqer14MGDkZqaqq+6iIiIiEhLGgc7pVLZ5GsiIiIiEpbOphQjIiIiImFp1aA4MTERmZmZQM0Vuz/++APFxcVq2/Tu3Vu3FRIRERGRRrQKdk8++aTaLdgRI0YAAEQiEfvYtVZBKlCSK3QV1AKS+3zWlIiIDIPGwS45OVm/lbRnBalAXChQUSJ0JdQCbhILwMsDCilnXSEiImFpHOw6deqk30ras5Lc6lA39t+AS4DQ1ZCWUu8kAtdjUSnrIHQpRETUzml1K5b0zCUA8AwWugrSUnlhudAlEBERARwVS0RERGQ6GOyIiIiITITJB7vU1FSEhYUhMDAQvXv3xtdffy10SURERER6YfLP2Jmbm2P9+vUIDg5GZmYm+vXrh6effhrW1tZCl6Ymw8wM+UW3AalE6FJIS2nyO0KXQEREBGga7Pr06QORSKTRDs+fP9/amnTKw8MDHh4eAAB3d3e4uLggLy/PoIJdRuk9jO7ogdLf3hK6FGohpcICthJ7ocsgIqJ2TqNgN2bMGNX3Dx48wKefforAwEAMHDgQAPDrr7/i6tWreO2117Qu4Pjx41i9ejXOnTuHjIwM7NmzR+14ABAXF4fVq1cjMzMTQUFB+PjjjxEaGqr1sc6dO4eqqip4e3tr/V59yq8oRqlYjNier6Cz71ChyyEtJWUXY9aOG3B5yl3oUoiIqJ3TKNgtW7ZM9f306dMxa9YsvPvuu/W2SU3VvgO/XC5HUFAQpk6dirFjx9Zbv2vXLsTExGDjxo0YMGAA1q9fj4iICFy7dg0dOlT3DQsODkZlZWW99x46dAienp4AgLy8PEyaNAn//ve/ta6xrXS29kKgc6DQZZCWFA8KoazMEboMIiIi7Z+x+/rrr3H27Nl6yydMmID+/ftj8+bNWu0vMjISkZGRja5ft24dZsyYgSlTpgAANm7ciH379mHz5s1YtGgRACAhIaHJY5SVlWHMmDFYtGgRHnvssWa3LSsrU70uKirS6vMQERERCUXrUbEymQwnT56st/zkyZOwtLTUVV0AgPLycpw7dw7h4eGqZWKxGOHh4Th16pRG+1AqlZg8eTKGDRuGiRMnNrt9bGws7O3tVV+GdtuWiIiIqDFaX7GbM2cOXn31VZw/f171nNtvv/2GzZs34623dPvw/71791BVVQU3Nze15W5ubvjjjz802sfJkyexa9cu9O7dG3v37gUAfPHFF+jVq1eD2y9evBgxMTGq10VFRQx3RNQs80r1uZ5LLD2Aspp/EhG1Ea2D3aJFi9C5c2d8+OGH+PLLLwEAPXr0wJYtW/DCCy/oo8ZWGTRoEBQKhcbbS6VSSKVSvdZERKZDIbUDAHhnHgFcnVXL5TJPoLDmn0REbaRFfexeeOGFNglxLi4uMDMzQ1ZWltryrKwsuLtzBCIRCa9S1kHoEoiIVFo080RBQQE+//xzvPnmm8jLywNq+telpaXptDiJRIJ+/fohPj5etUyhUCA+Pl7VakVf4uLiEBgYiJCQEL0eh4hMk7tlF7V/EhG1Ba2v2F26dAnh4eGwt7fH7du3MX36dDg5OeHbb79FSkoKtm/frtX+iouLcfPmTdXr5ORkJCQkwMnJCT4+PoiJiUFUVBT69++P0NBQrF+/HnK5XDVKVl+io6MRHR2NoqIi2Nuz8SwRacdD1hX3f18Jjx5dW7Uf8xK20iEizWkd7GJiYjB58mSsWrUKtra2quVPP/00/v73v2tdwNmzZzF06J9NeWsHLkRFRWHr1q0YN24ccnJysHTpUmRmZiI4OBgHDhyoN6CCiMgUmZWz5RIRaU7rYHfmzBl89tln9ZZ7eXkhMzNT6wLCwsKgVCqb3GbmzJmYOXOm1vsmIiIiak+0fsZOKpU22LT3+vXrcHV11VVdguMzdkSkjXwzM7XXPb3s1f5JRNQWtA52o0aNwjvvvIOKigoAgEgkQkpKCt544w0899xz+qhRENHR0UhMTMSZM2eELoWIDJitxB4ihTk+dHJQW97Tyx63Vz7TZLCrbZVCRKQrWge7tWvXori4GB06dEBpaSmGDBmCrl27wtbWFitWrNBPlUREBsrF0h0uaU9p/0aFOWT2/vUWc7AEEbWG1s/Y2dvb4/Dhwzh58iQuXryI4uJi9O3bV23aL2qZ1PwSKNIKhS6DtHQzu1joEkhgZpXaTafYNbczEvJegMtT9ftxcrAEEbWG1sFu+/btGDduHB5//HE8/vjjquXl5eXYuXMnJk2apOsaTV5eSTkAYM3Ba7jxgM/jGCOZhRkcrSVCl0FGQlYhg6XIucGfmZyq+4LURESmQetgN2XKFAwfPhwdOqh3W79//z6mTJliMsEuLi4OcXFxqKqq0vux5GWVAICJA33Rt+cgvR+PdM/RWgIvB5nQZZCBq50/1quTP1YPH9Lgz0yh4oEgtRGRadA62CmVSohEonrL7969a1KNfIVoUOxmJ+UIOiITZus4GCjcDU+PofxDgIj0QuNg16dPH4hEIohEIjz55JMwN//zrVVVVUhOTsbw4cP1VScRkdH7S9d++HD/SvwlvF+j25SU6f8uARGZLo2D3ZgxYwAACQkJiIiIgI2NjWqdRCKBr6+vSbU7ISLStdoWKE0pb4PHP4jIdGkc7JYtWwYA8PX1xbhx42Bpqd0oMCIiIiLSL62fsYuKitJPJURERETUKlo3KK6qqsKaNWsQGhoKd3d3ODk5qX2ZCk4pRkRERMZG62D39ttvY926dRg3bhwKCwsRExODsWPHQiwWY/ny5fqpUgCcUoyIDAH72hGRNrQOdjt27MC///1vzJs3D+bm5njxxRfx+eefY+nSpfj111/1UyURUTvFvnZEpA2tg11mZiZ69eoFALCxsUFhYfUUWCNGjMC+fft0XyERERERaUTrYNexY0dkZGQAALp06YJDhw4BAM6cOQOpVKr7ComIiIhII1oHu2effRbx8fEAgNdffx1vvfUW/P39MWnSJEydOlUfNRIRERGRBrRud7Jy5UrV9+PGjUOnTp3wyy+/wN/fHyNHjtR1fYJpy7liich4OVpLIDHX+m9kIiK90Oq3UUVFBaZOnYrk5GTVskcffRQxMTEmFerAUbFEpCEvBxmmDvITugwiIkDbYGdhYYFvvvlGf9UQERkhG6nWNz+IiPRC6/sHY8aMwd69e/VTDRERERG1mNZ/Zvr7++Odd97ByZMn0a9fP1hbW6utnzVrli7rIyIiIiINaR3sNm3aBAcHB5w7dw7nzp1TWycSiRjsiIiIiASidbCrO3CCiIh0q8TSAygTugoiMlYco09EZEDkMk+hSyAiI6b1FbuYmJgGl4tEIlhaWqJr164YPXo0nJycdFEfEVG74m7ZRegSiMiIaR3sLly4gPPnz6OqqgrdunUDAFy/fh1mZmbo3r07Pv30U8ybNw8nTpxAYGCgPmpuE2xQTERC8JB1Ra/MR3DZ/arQpRCREdL6Vuzo0aMRHh6O9PR01QCKu3fv4i9/+QtefPFFpKWl4YknnsDcuXP1U3EbYYNiItKUeUmO6nuF1E7QWoiofdM62K1evRrvvvsu7Oz+/OVlb2+P5cuXY9WqVbCyssLSpUvrjZglIjJVZuVFqu8rZR0ErYWI2jetg11hYSGys7PrLc/JyUFRUfUvNwcHB5SXl+umQiKidqSnl73QJRCREWvRrdipU6diz549uHv3Lu7evYs9e/Zg2rRpGDNmDADg9OnTCAgI0Ee9REQmraeXPYb14FU/ImoZrQdPfPbZZ5g7dy7+9re/obKysnon5uaIiorCBx98AADo3r07Pv/8c91XS0RERESN0jrY2djY4N///jc++OAD3Lp1CwDQuXNn2NjYqLYJDg7WbZVERERE1KwWNyjOzMxERkYG/P39YWNjA6VSqdvKiIiIiEgrWge73NxcPPnkkwgICMDTTz+NjIwMAMC0adMwb948fdRIRERERBrQOtjNnTsXFhYWSElJgZWVlWr5uHHjcODAAV3XR0REREQa0voZu0OHDuHgwYPo2LGj2nJ/f3/cuXNHl7UJijNPEBERkbHR+oqdXC5Xu1JXKy8vD1KpVFd1CY4zTxAREZGx0TrYDR48GNu3b1e9FolEUCgUWLVqFYYOHarr+oiIiIhIQ1rfil21ahWefPJJnD17FuXl5Vi4cCGuXr2KvLw8nDx5Uj9VEhEREVGztL5i17NnT1y/fh2DBg3C6NGjIZfLMXbsWFy4cAFdunTRT5VERERE1Cytr9ilpKTA29sbS5YsaXCdj4+PrmojIjIKOVX3Vd/bSjjXKxEJR+srdn5+fsjJyam3PDc3F35+frqqi4jIaBQqHgAAAnL84WLpLnQ5RNSOaR3slEolRCJRveXFxcWwtLTUVV1EREZHWiURugQiauc0vhUbExMD1IyCfeutt9RanlRVVeG3337jHLFEREREAtI42F24cAGouWJ3+fJlSCR//mUqkUgQFBSE+fPn66dKIiIiImqWxsHu6NGjAIApU6bgww8/hJ2dnT7rIiIiIiItaT0qdsuWLfqphIjISFXYeAL5QJrSWehSiKid0zrYyeVyrFy5EvHx8cjOzoZCoVBbf+vWLV3WR0Rk8CpsqufOToeL0KUQUTundbCbPn06jh07hokTJ8LDw6PBEbJERERE1Pa0Dnb79+/Hvn378Pjjj+unIiIiIiJqEa372Dk6OsLJyUk/1RARERFRi2kd7N59910sXboUJSUl+qnIQMTFxSEwMBAhISFCl0JERESkEa1vxa5duxZJSUlwc3ODr68vLCws1NafP39el/UJJjo6GtHR0SgqKoK9Ped+JCIiIsOndbAbM2aMfiohIiKgTvsU1fdERBrSOtgtW7ZMP5UQERFQp33Kw98TETVH62fsiIiIiMgwaXzFztHRUaOedXl5ea2tiYiIiIhaQONgt379ev1WQkREREStonGwi4qK0m8lRERERNQqrXrG7rXXXsO9e/d0Vw0RERERtVirgt2XX36JoqIi3VVDRERERC3WqmCnVCp1VwkRkZHysw0AAFQ98BK6FCJq57TuY0dEROr87Lrh/u8rhS6DiEj7YCeXy2FtbQ0AuH//vj5qIiIiIqIW0PpWrJubG6ZOnYoTJ07opyIiIiIiahGtg92XX36JvLw8DBs2DAEBAVi5ciXS09P1Ux0RERERaUzrYDdmzBjs3bsXaWlpeOWVV/DVV1+hU6dOGDFiBL799ltUVlbqp1IionaidjAGEZG2Wjwq1tXVFTExMbh06RLWrVuHI0eO4Pnnn4enpyeWLl2KkpIS3VZKRNRO+Nl1gzz59ervGfKISAstHhWblZWFbdu2YevWrbhz5w6ef/55TJs2DXfv3sX777+PX3/9FYcOHdJttURE7YTigRfu/74SfuHdhC6FiIyI1sHu22+/xZYtW3Dw4EEEBgbitddew4QJE+Dg4KDa5rHHHkOPHj10XSsRERERNUHrYDdlyhT87W9/w8mTJxESEtLgNp6enliyZIku6mu1goIChIeHo7KyEpWVlZg9ezZmzJghdFlEREREOqd1sMvIyICVlVWT28hkMixbtqw1demMra0tjh8/DisrK8jlcvTs2RNjx46Fs7Oz0KURERER6ZTWwa6ysrLB+WFFIhGkUikkEomuatMJMzMzVRAtKyuDUqnkVGhERERkkrQeFevg4ABHR8d6Xw4ODpDJZOjUqROWLVsGhUKh0f6OHz+OkSNHwtPTEyKRCHv37q23TVxcHHx9fWFpaYkBAwbg9OnTWtVcUFCAoKAgdOzYEQsWLICLi4tW7yciIiIyBlpfsdu6dSuWLFmCyZMnIzQ0FABw+vRpbNu2Df/4xz+Qk5ODNWvWQCqV4s0332x2f3K5HEFBQZg6dSrGjh1bb/2uXbsQExODjRs3YsCAAVi/fj0iIiJw7do1dOjQAQAQHBzcYP+8Q4cOwdPTEw4ODrh48SKysrIwduxYPP/883Bzc9P2oxMREREZNK2D3bZt27B27Vq88MILqmUjR45Er1698NlnnyE+Ph4+Pj5YsWKFRsEuMjISkZGRja5ft24dZsyYgSlTpgAANm7ciH379mHz5s1YtGgRACAhIUGj2t3c3BAUFISff/4Zzz//fIPblJWVoaysTPW6odvORERERIZI61uxv/zyC/r06VNveZ8+fXDq1CkAwKBBg5CSktLq4srLy3Hu3DmEh4erlonFYoSHh6uO1ZysrCzcv38fAFBYWIjjx4+jW7fG+0LFxsbC3t5e9eXt7d3qz0FERETUFrQOdt7e3ti0aVO95Zs2bVKFoNzcXDg6Ora6uHv37qGqqqrebVM3NzdkZmZqtI87d+5g8ODBCAoKwuDBg/H666+jV69ejW6/ePFiFBYWqr5SU1Nb/TmIiIiI2oLWt2LXrFmDv/71r9i/f7+qj93Zs2fxxx9/YPfu3QCAM2fOYNy4cbqvtgVCQ0M1vlULAFKpFFKpVK81EREREemD1sFu1KhRuHbtGj777DNcu3YNqHlObu/evfD19QUAvPrqqzopzsXFBWZmZsjKylJbnpWVBXd3d50cg4iIiMhUaBXsKioqMHz4cGzcuBGxsbH6q6qGRCJBv379EB8fjzFjxgAAFAoF4uPjMXPmTL0eOy4uDnFxcaiqqtLrcYiIiIh0RatgZ2FhgUuXLum0gOLiYty8eVP1Ojk5GQkJCXBycoKPjw9iYmIQFRWF/v37IzQ0FOvXr4dcLleNktWX6OhoREdHo6ioCPb29no9FhEREZEuaH0rdsKECdi0aRNWrlypkwLOnj2LoUOHql7HxMQAAKKiorB161aMGzcOOTk5WLp0KTIzMxEcHIwDBw6wDx0RERHRQ1o0pdjmzZtx5MgR9OvXD9bW1mrr161bp9X+wsLCmp3ia+bMmXq/9UpERERk7LQOdleuXEHfvn0BANevX1dbJxKJdFcZEREREWlF62B39OhR/VRiYDh4goiIiIyN1g2Ka928eRMHDx5EaWkpADR7O9XYREdHIzExEWfOnBG6FCIiIiKNaB3scnNz8eSTTyIgIABPP/00MjIyAADTpk3DvHnz9FEjEREREWlA62A3d+5cWFhYICUlBVZWVqrl48aNw4EDB3RdHxERERFpSOtn7A4dOoSDBw+iY8eOasv9/f1x584dXdZGRERERFrQ+oqdXC5Xu1JXKy8vz6TmWI2Li0NgYKBqPlwiIiIiQ6d1sBs8eDC2b9+uei0SiaBQKLBq1Sq1RsPGjoMniIiIyNhofSt21apVePLJJ3H27FmUl5dj4cKFuHr1KvLy8nDy5En9VElEREREzdL6il3Pnj1x/fp1DBo0CKNHj4ZcLsfYsWNx4cIFdOnSRT9VEhEREVGztL5iBwD29vZYsmSJ7qshIiIiohZrUbArKCjA6dOnkZ2dDYVCobZu0qRJuqpNUJx5goiIiIyN1sHuv//9L8aPH4/i4mLY2dmpzQ8rEolMJthFR0cjOjoaRUVFsLe3F7ocIiIiomZp/YzdvHnzMHXqVBQXF6OgoAD5+fmqr7y8PP1USURERETN0jrYpaWlYdasWQ32siMiIiIi4Wgd7CIiInD27Fn9VENERERELab1M3bPPPMMFixYgMTERPTq1QsWFhZq60eNGqXL+oiIiIhIQ1oHuxkzZgAA3nnnnXrrRCIRR5ESERERCUTrW7EKhaLRL1MKdZwrloiIiIyN1sGuveBcsURERGRsNA52Tz/9NAoLC1WvV65ciYKCAtXr3NxcBAYG6r5CIiIiItKIxsHu4MGDKCsrU71+77331PrWVVZW4tq1a7qvkIiIiIg0onGwUyqVTb4mIiIiImHxGTsiIiIiE6FxsBOJRGrzwtYuIyIiIiLDoHEfO6VSicmTJ0MqlQIAHjx4gFdeeQXW1tYAoPb8HRERERG1PY2DXVRUlNrrCRMm1Ntm0qRJuqnKAMTFxSEuLs6kevMRERGRadM42G3ZskW/lRiY6OhoREdHo6ioCPb29kKXQ0RERNQsDp4gImqltIJS1feO1hJBayGi9o3BjoiolfLl5QCABRHd4OUgE7ocImrHGOyIiHTEmVfriEhgDHZEREREJoLBjoiIiMhEMNgRERERmQgGOyIiIiITwWBHREREZCIY7IiIiIhMBINdI+Li4hAYGIiQkBChSyEiIiLSCINdI6Kjo5GYmIgzZ84IXQoRERGRRhjsiIiIiEwEgx0RERGRiWCwIyIiIjIRDHZEREREJoLBjoiIiMhEMNgRERmYtILSBr8nImoOgx0RkYHJl5c3+D0RUXMY7IiIiIhMBIMdERERkYlgsCMiIiIyEQx2RERERCaCwY6IiIjIRDDYEREZmJ5e9kKXQERGisGuEXFxcQgMDERISIjQpRBRO9PTyx4rx/YSugwiMkIMdo2Ijo5GYmIizpw5I3QpRNQO1V6149U7ItKGudAFEBFRfT297HF75TNCl0FERoZX7IiIiIhMBIMdERERkYlgsCMiIiIyEQx2RERERCaCwY6IiIjIRDDYEREREZkIBjsiIiIiE8FgR0RERGQiGOyIiIiITASDHREREZGJYLAjIiIiMhEMdkREREQmgsGOiIiIyEQw2BERERGZCAY7IiIiIhPBYEdERERkIhjsiIiIiExEuwl2JSUl6NSpE+bPny90KURERER60W6C3YoVK/Doo48KXQYRERGR3rSLYHfjxg388ccfiIyMFLoUIiIiIr0RPNgdP34cI0eOhKenJ0QiEfbu3Vtvm7i4OPj6+sLS0hIDBgzA6dOntTrG/PnzERsbq8OqiYiIiAyP4MFOLpcjKCgIcXFxDa7ftWsXYmJisGzZMpw/fx5BQUGIiIhAdna2apvg4GD07Nmz3ld6ejq+++47BAQEICAgoA0/FREREVHbMxe6gMjIyCZvka5btw4zZszAlClTAAAbN27Evn37sHnzZixatAgAkJCQ0Oj7f/31V+zcuRNff/01iouLUVFRATs7OyxdurTB7cvKylBWVqZ6XVRU1IpPR0RERNR2BL9i15Ty8nKcO3cO4eHhqmVisRjh4eE4deqURvuIjY1Famoqbt++jTVr1mDGjBmNhrra7e3t7VVf3t7eOvksRERERPpm0MHu3r17qKqqgpubm9pyNzc3ZGZm6uWYixcvRmFhoeorNTVVL8chIiIi0jXBb8W2pcmTJze7jVQqhVQqbZN6iIiIiHTJoK/Yubi4wMzMDFlZWWrLs7Ky4O7uLlhdRERERIbIoIOdRCJBv379EB8fr1qmUCgQHx+PgQMH6vXYcXFxCAwMREhIiF6PQ0RERKQrgt+KLS4uxs2bN1Wvk5OTkZCQACcnJ/j4+CAmJgZRUVHo378/QkNDsX79esjlctUoWX2Jjo5GdHQ0ioqKYG9vr9djEREREemC4MHu7NmzGDp0qOp1TEwMACAqKgpbt27FuHHjkJOTg6VLlyIzMxPBwcE4cOBAvQEVRERERO2d4MEuLCwMSqWyyW1mzpyJmTNntllNRERERMbIoJ+xExKfsSMiIiJjw2DXiOjoaCQmJuLMmTNCl0JERESkEQY7IqJW6ullr/ZPIiKhCP6MHRGRsevpZY/bK58RugwiIl6xIyIiIjIVDHaN4OAJIiIiMjYMdo3g4AkiIiIyNgx2RERERCaCwY6IiIjIRDDYEREREZkIBjsiIiIiE8Fg1wiOiiUiIiJjw2DXCI6KJSIiImPDYEdERERkIhjsiIiIiEwEgx0RERGRiWCwIyIiIjIRDHZEREREJoLBrhFsd0JERETGxlzoAgxVdHQ0oqOjUVhYCAcHBxQVFentWHJ5CapKqyCXl+j1OERERKRbbfH/8Nr9KpXKZrcVKTXZqh27e/cuvL29hS6DiIiI2rnU1FR07NixyW0Y7JqhUCiQnp4OW1tbiEQiocsRTFFREby9vZGamgo7OzuhyzFqPJe6w3OpOzyXusNzqTs8l9WUSiXu378PT09PiMVNP0XHW7HNEIvFzabj9sTOzq5d/8elSzyXusNzqTs8l7rDc6k7PJeAvb29Rttx8AQRERGRiWCwIyIiIjIRDHakEalUimXLlkEqlQpditHjudQdnkvd4bnUHZ5L3eG51B4HTxARERGZCF6xIyIiIjIRDHZEREREJoLBjoiIiMhEMNgRERERmQgGO9KLkpISdOrUCfPnzxe6FKOVmpqKsLAwBAYGonfv3vj666+FLsmo/PDDD+jWrRv8/f3x+eefC12O0eLPoe7x96NuJCcnY+jQoQgMDESvXr0gl8uFLskgcFQs6cWSJUtw8+ZNeHt7Y82aNUKXY5QyMjKQlZWF4OBgZGZmol+/frh+/Tqsra2FLs3gVVZWIjAwEEePHoW9vT369euHX375Bc7OzkKXZnT4c6h7/P2oG0OGDME///lPDB48GHl5ebCzs4O5OSfU4hU70rkbN27gjz/+QGRkpNClGDUPDw8EBwcDANzd3eHi4oK8vDyhyzIKp0+fxiOPPAIvLy/Y2NggMjIShw4dEroso8SfQ93i70fduHr1KiwsLDB48GAAgJOTE0NdDQa7dub48eMYOXIkPD09IRKJsHfv3nrbxMXFwdfXF5aWlhgwYABOnz6t1THmz5+P2NhYHVZtmNriXNY6d+4cqqqq4O3trYPKDV9rz216ejq8vLxUr728vJCWltZm9RsSXf6ctrefw4fp4ly2l9+PzWntubxx4wZsbGwwcuRI9O3bF++9914bfwLDxWDXzsjlcgQFBSEuLq7B9bt27UJMTAyWLVuG8+fPIygoCBEREcjOzlZtExwcjJ49e9b7Sk9Px3fffYeAgAAEBAS04acShr7PZa28vDxMmjQJ//rXv9rkcxkCXZxbqqarc9kefw4f1tpz2Z5+PzanteeysrISP//8Mz799FOcOnUKhw8fxuHDh9v4UxgoJbVbAJR79uxRWxYaGqqMjo5Wva6qqlJ6enoqY2NjNdrnokWLlB07dlR26tRJ6ezsrLSzs1O+/fbbOq/d0OjjXCqVSuWDBw+UgwcPVm7fvl2n9RqTlpzbkydPKseMGaNaP3v2bOWOHTvasGrD1NKfU/4c1teSc9lefz82pyXn8pdfflE+9dRTqvWrVq1Srlq1qg2rNly8Ykcq5eXlOHfuHMLDw1XLxGIxwsPDcerUKY32ERsbi9TUVNy+fRtr1qzBjBkzsHTpUj1WbZh0cS6VSiUmT56MYcOGYeLEiXqs1rhocm5DQ0Nx5coVpKWlobi4GPv370dERISAVRsmTc4lfw41o8m55O9HzWhyLkNCQpCdnY38/HwoFAocP34cPXr0ELBqw8FgRyr37t1DVVUV3Nzc1Ja7ubkhMzNTsLqMkS7O5cmTJ7Fr1y7s3bsXwcHBCA4OxuXLl/VUsfHQ5Nyam5tj7dq1GDp0KIKDgzFv3jyOiG2AJueSP4ea4e9P3dH0v/H33nsPTzzxBHr37g1/f3+MGDFCoIoNC4eQkN5MnjxZ6BKM2qBBg6BQKIQuw2iNGjUKo0aNEroMo8efQ/3g78fWi4yM5OjiBvCKHam4uLjAzMwMWVlZasuzsrLg7u4uWF3GiOdSf3hudYfnUnd4LnWH57J1GOxIRSKRoF+/foiPj1ctUygUiI+Px8CBAwWtzdjwXOoPz63u8FzqDs+l7vBctg5vxbYzxcXFuHnzpup1cnIyEhIS4OTkBB8fH8TExCAqKgr9+/dHaGgo1q9fD7lcjilTpghatyHiudQfnlvd4bnUHZ5L3eG51COhh+VS2zp69KgSQL2vqKgo1TYff/yx0sfHRymRSJShoaHKX3/9VdCaDRXPpf7w3OoOz6Xu8FzqDs+l/nCuWCIiIiITwWfsiIiIiEwEgx0RERGRiWCwIyIiIjIRDHZEREREJoLBjoiIiMhEMNgRERERmQgGOyIiIiITwWBHREREZCIY7IiIiIhMBIMdEZEBCgsLg0gkgkgkQkJCgk73ffv2bdW+g4ODdbpvIhIWgx0RGb3Jkyergkrdr+HDhwtdWqvMmDEDGRkZ6Nmzp0bbjxw5stHP/PPPP0MkEuHSpUvw9vZGRkYG5s2bp+OKiUho5kIXQESkC8OHD8eWLVvUlkmlUr0es7y8HBKJRG/7t7Kygru7u8bbT5s2Dc899xzu3r2Ljh07qq3bsmUL+vfvj969ewMA3N3dYWNjo/OaiUhYvGJHRCZBKpXC3d1d7cvR0VG1XiQS4fPPP8ezzz4LKysr+Pv74/vvv1fbx5UrVxAZGQkbGxu4ublh4sSJuHfvnmp9WFgYZs6ciTlz5sDFxQUREREAgO+//x7+/v6wtLTE0KFDsW3bNohEIhQUFEAul8POzg67d+9WO9bevXthbW2N+/fva/U5m6pxxIgRcHV1xdatW9XeU1xcjK+//hrTpk3T6lhEZHwY7Iio3Xj77bfxwgsv4NKlS3j66acxfvx45OXlAQAKCgowbNgw9OnTB2fPnsWBAweQlZWFF154QW0f27Ztg0QiwcmTJ7Fx40YkJyfj+eefx5gxY3Dx4kW8/PLLWLJkiWp7a2tr/O1vf6t3NXHLli14/vnnYWtrq3H9zdVobm6OSZMmYevWrVAqlar3ff3116iqqsKLL77Y4nNHREZCSURk5KKiopRmZmZKa2trta8VK1aotgGg/Mc//qF6XVxcrASg3L9/v1KpVCrfffdd5VNPPaW239TUVCUA5bVr15RKpVI5ZMgQZZ8+fdS2eeONN5Q9e/ZUW7ZkyRIlAGV+fr5SqVQqf/vtN6WZmZkyPT1dqVQqlVlZWUpzc3PlTz/91OhnGjJkiHL27NlqyzSp8ffff1cCUB49elS1zeDBg5UTJkyod4xly5Ypg4KCGq2BiIwPn7EjIpMwdOhQbNiwQW2Zk5OT2uva58tQcyXNzs4O2dnZAICLFy/i6NGjDT53lpSUhICAAABAv3791NZdu3YNISEhastCQ0PrvX7kkUewbds2LFq0CF9++SU6deqEJ554QqvPqEmN3bt3x2OPPYbNmzcjLCwMN2/exM8//4x33nlHq2MRkXFisCMik2BtbY2uXbs2uY2FhYXaa5FIBIVCAdQ8hzZy5Ei8//779d7n4eGhdpyWmD59OuLi4rBo0SJs2bIFU6ZMgUgk0mofmtY4bdo0vP7664iLi8OWLVvQpUsXDBkypEV1E5Fx4TN2REQA+vbti6tXr8LX1xddu3ZV+2oqzHXr1g1nz55VW3bmzJl6202YMAF37tzBRx99hMTERERFRemtxhdeeAFisRhfffUVtm/fjqlTp2odIonIODHYEZFJKCsrQ2ZmptpX3RGtzYmOjkZeXh5efPFFnDlzBklJSTh48CCmTJmCqqqqRt/38ssv448//sAbb7yB69ev4//+7/9Uo1LrhilHR0eMHTsWCxYswFNPPVWvHYkua7SxscG4ceOwePFiZGRkYPLkyVofi4iME4MdEZmEAwcOwMPDQ+1r0KBBGr/f09MTJ0+eRFVVFZ566in06tULc+bMgYODA8Tixn9V+vn5Yffu3fj222/Ru3dvbNiwQTUq9uE+etOmTUN5eTmmTp3aos+oTY3Tpk1Dfn4+IiIi4Onp2aLjEZHxESnrjoknIqJWW7FiBTZu3IjU1FS15V988QXmzp2L9PT0Zhsbh4WFITg4GOvXr9dbncuXL8fevXt1PmUZEQmHV+yIiFrp008/xZkzZ3Dr1i188cUXWL16tdozdCUlJUhKSsLKlSvx8ssvazxbxaeffgobGxtcvnxZp/WmpKTAxsYG7733nk73S0TC4xU7IqJWmjt3Lnbt2oW8vDz4+Phg4sSJWLx4MczNqxsPLF++HCtWrMATTzyB7777TqOpvNLS0lBaWgoA8PHx0enUZZWVlbh9+zZQc7vY29tbZ/smImEx2BERERGZCN6KJSIiIjIRDHZEREREJoLBjoiIiMhEMNgRERERmQgGOyIiIiITwWBHREREZCIY7IiIiIhMBIMdERERkYlgsCMiIiIyEf8P6WYIncfIKN4AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.stairs(fuel_flux, edges=ndl.group_bounds, label=\"Fuel\")\n",
    "plt.stairs(moderator_flux, edges=ndl.group_bounds, label=\"Moderator\")\n",
    "plt.stairs(avg_flux, edges=ndl.group_bounds, label=\"Pin-Cell Average\")\n",
    "plt.xscale(\"log\")\n",
    "plt.yscale(\"log\")\n",
    "plt.xlabel(\"Energy [eV]\")\n",
    "plt.ylabel(\"Energy-Integrated Flux [Arb. Units]\")\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since these values of the flux spectrum are integrated over the energy range of each group, they each have a unique normalization which depends on the energy width of the group. To fix this, we will divide each group by the energy width of the bin:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "norm_fuel_flux = fuel_flux.copy()\n",
    "norm_moderator_flux = moderator_flux.copy()\n",
    "norm_avg_flux = avg_flux.copy()\n",
    "\n",
    "for g in range(ndl.ngroups):\n",
    "    # Group bounds also go from high to low energy !\n",
    "    delta_E = ndl.group_bounds[g] - ndl.group_bounds[g+1]\n",
    "    norm_fuel_flux[g] /= delta_E\n",
    "    norm_moderator_flux[g] /= delta_E\n",
    "    norm_avg_flux[g] /= delta_E\n",
    "\n",
    "plt.stairs(norm_fuel_flux, edges=ndl.group_bounds, label=\"Fuel\")\n",
    "plt.stairs(norm_moderator_flux, edges=ndl.group_bounds, label=\"Moderator\")\n",
    "plt.stairs(norm_avg_flux, edges=ndl.group_bounds, label=\"Pin-Cell Average\")\n",
    "plt.xscale(\"log\")\n",
    "plt.yscale(\"log\")\n",
    "plt.xlabel(\"Energy [eV]\")\n",
    "plt.ylabel(\"Flux [Arb. Units]\")\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This looks much more reasonable ! However, you might also be more accustomed to looking at the *lethargy normalized* flux spectrum, which we can also plot here:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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+WL9+PQBAr9cjMTER4eHhUKlU6NSpEzZu3Gg4/q+//oIgCPjll1/QtWtXKJVK7Ny5EykpKRg2bBiaN28ONzc3dO/eHb///rvRtTIyMjBkyBCoVCqEh4fjiy++qNbcnJeXhyeffBJ+fn7w8PBAv379cPTo0QbdEyIiooZisLMTKpUKpaWlte7/5JNPoFarsXfvXrz11ltYsGABtm3bVuvx33zzDUpLS/HCCy/UuL/yiWBKSgoGDRqEBx98EMeOHcOGDRuwc+dOTJ48uUGf5+uvv8Ztt92Gtm3b4vHHH8fHH38MURQBAKNGjcKPP/4IjUZjOH7r1q0oKirCAw88AABITEzE+vXrsXLlSpw8eRLTp0/H448/jqSkJKPrvPjii3jzzTfxzz//oGPHjtBoNLj33nvxxx9/4PDhwxg0aBCGDh2KCxcuGN4zZswYXLp0CX/99Re+/fZbfPTRR8jOzjY678MPP4zs7Gz88ssvOHjwILp06YK7774bV69ebdB9ISKihknP0+JEer7hKz1PK3VJjcpZ6gKobqIo4o8//sDWrVvx/PPP13pcx44dMW/ePABAREQEli1bhj/++AP33HNPjcefPXsWHh4eCAwMrPP6iYmJGDVqFKZNm2Y499KlSxEXF4cVK1bAxcWlXp9rzZo1ePzxx4Hrzc75+flISkpCnz59MHDgQKjVanz//fcYPXo0AOCLL77A/fffD3d3d5SUlGDhwoX4/fffERsbCwBo1aoVdu7ciQ8//BBxcXGG6yxYsMDoHjRr1gydOnUyvH7ttdfw/fffY/PmzZg8eTL+97//4ffff8f+/fvRrVs3AMDq1asRERFheM/OnTuxb98+ZGdnQ6lUAgDefvtt/PDDD9i4cSOefvrpet0TIiJqmPQ8LfovToJWV27YppI74fcZcQj2UklaW2NpcsFOW6ZFan5qo14z3DMcKmfzfqC2bNkCNzc36HQ66PV6PPbYY3U2r3bs2NHodWBgoOEp08SJE/HZZ58Z9mk0GoiiCEEQblnH0aNHcezYMXz++eeGbaIoQq/XIzU1Fe3atTPrcwHA6dOnsW/fPnz//fcAAGdnZ4wcORJr1qxBnz594OzsjEceeQSff/45Ro8ejcLCQmzatAlfffUVACA5ORlFRUXVQmtpaSk6d+5stK0ynFX97K+++ip++uknZGRkoKysDFqt1vDE7vTp03B2dkaXLl0M72nTpg28vb2N7olGo4GPj4/RubVaLVJSUsy+H0REZBm5haXQ6sqxZGQM2vi7ITlbg2kbjiC3sJTBzlGl5qdi5JaRJhxpORvu24Aonyiz3tO3b1+sWLECCoUCQUFBcHau+69KLpcbvRYEAXq9Hrj+1GrmzJlG+yMjI5Gfn4+MjIw6n9ppNBo888wzmDJlSrV9oaGhZn2mSmvWrEFZWRmCgoIM20RRhFKpxLJly+Dp6YlRo0YhLi4O2dnZ2LZtG1QqFQYNGmSoCQB++uknBAcHG5278glaJbVabfR65syZ2LZtG95++220adMGKpUKDz30UJ3N3DfTaDQIDAzEX3/9VW2fJQa1EBFRw7Txd0N0sKfUZUiiyQW7cM9wbLhvQ6Nf01xqtRpt2rSxyPX9/f3h7+9vtO2hhx7Ciy++iLfeegvvvvtutffk5eXBy8sLXbp0walTpyxWS1lZGdavX4/FixdjwIABRvuGDx+OL7/8EhMnTsSdd96JkJAQbNiwAb/88gsefvhhQ3iNioqCUqnEhQsXjJpdTbFr1y6MGzfO0FdPo9Hg/Pnzhv1t27ZFWVkZDh8+jK5duwLXnxDm5uYajunSpQsyMzPh7OyMli1bNuh+EBFR3Sr7yDWVJ24N1eSCncpZZfbTM0cUEhKCd999F5MnT0ZBQQHGjBmDli1b4uLFi1i/fj3c3NywePFizJ49G3fccQcmT56MJ598Emq1GqdOncK2bduwbNkys6+7ZcsW5ObmYsKECfD0NP7X1IMPPog1a9Zg4sSJwPXRsStXrsSZM2ewfft2w3Hu7u6YOXMmpk+fDr1ej549eyI/Px+7du2Ch4cHxo4dW+v1IyIi8N1332Ho0KEQBAFz5swxPNkEgNtuuw39+/fH008/jRUrVkAul2PGjBlQqVSGpuv+/fsjNjYWw4cPx1tvvYXIyEhcunQJP/30Ex544IFqzb9ERFQ/lX3mADSpfnINwVGxTdhzzz2H3377Denp6XjggQdw22234cknn4SHh4eh6bZjx45ISkrCmTNn0KtXL3Tu3Blz5841akY1x5o1a9C/f/9qoQ7Xg92BAwdw7Ngx4Pro2FOnTiE4OBh33XWX0bGvvfYa5syZg8TERLRr1w6DBg3CTz/9hPDwup+OvvPOO/D29sadd96JoUOHYuDAgUb96QBg/fr1aN68OXr37o0HHngATz31FNzd3Q0DRQRBwM8//4zevXvjiSeeQGRkJP7zn//g33//RfPmzet1X4iIqLrKPnNaXTlyC03vMtOUNbkndvbgVqtK3Ly/pr5epi7p1b9/f/Tv37/OY7p3747ffvut1v1VmzJxvb9cbX788cda9/Xo0cPove3atav1XIIgYOrUqZg6dWqN+/v06VPje1u2bIk///zTaNukSZOMXgcGBuLnn382vL548SKys7ONmqPd3d2xdOlSLF26tNbPQ0RE1NgY7Ihu8ueff0Kj0aBDhw7IyMjACy+8YJi8mYiIyJYx2BHdRKfT4aWXXsK5c+fg7u6OO++8E59//nm1kcdERES2hsGO6CYDBw7EwIEDpS6DiIhukp6nNfS181YrOJiiBgx2REREZPPS87R4eOVuw6oSTW1FCVMx2BEREZHNq7qqBIBaV5QQnPOQWnAaMhc3pBZoIDjnSVSxNBw+2NU1QpOoMfBnkIjIctr4u9W6L6c4E+rWi/HSPp1hm7q1HDnF3QA0jZUoHHYeu8qO7kVFRVKXQk1c5XJlTk5OUpdCROTQrpXmQ5DpMKn9XGy4bwMmtZ8LQabDtdJ8qUtrNA77xM7JyQleXl7Izs4GALi6upq06D2RJen1ely+fBmurq63XO+XiIgsI1gdhiifKKRka6QupdE59P9pAgICAMAQ7oikIJPJEBoayn9YEBGR1Tl0sBMEAYGBgfD394dOpzPhHUSWp1AoIJM5bK8HIiKrqhz8cIVLipnEoYNdJScnJ/ZvIiIisjOVgyEA4O0/ZkAl94G3WnHLdWMVecnAJUXFn01Mkwh2REREZH8qB0MAgOBciJWPDUCwl6rWYOesreh6FbJ9ClCqQ4hCDgQHGrY3BWwfIiIiIrvgo1bUuV9WUgAAyOo2C3g6qeLPKtubAgY7IiIiciil7iFAUEzFn00Mm2KJiIjILuQUZ+LUlfQmuaKEqRjsiIiIyObJnPMw8+/HUaIvBprgihKmYlMsERER2TzBuRAl+mIk9kpskitKmMqkJ3abN282+8T33HMPVCqVCUcSERERVVd1NKsnNCgB0MqzFcSSpreihKlMCnbDhw8366SCIODs2bNo1apVfesiIiKiJq7qaFY1ilEiaTX2weQ+dpmZmfD39zfpWHd394bURERERA4iPU9bbd65rAJGNGsxKdiNHTvWrGbVxx9/HB4eHg2pi4iIiOxcep4W/RcnQasrN9oe4XIeCAfUSo7htDST7ujatWvNOumKFSvqWw8RERE5iNzCUmh15VgyMgZt/N0M29Mv5GPmGaCZa90TDldV7lQxGhaXz0CRV2SNch1Cg6NyQUEB/vzzT7Rt2xbt2rWzTFVERETkMNr4uyE6+Ma0JLJrrmafI99/H1z0Iry/GQ84yZrcUmGmMnu6k0ceeQTLli0DAGi1WnTr1g2PPPIIOnbsiG+//dYaNRIRERFhSfZlBA5baVgq7PLlyziRno/0PK3UpdkMs4Pdjh070KtXLwDA999/D1EUkZeXh6VLl+L111+3Ro1ERERE8C4vB3wjIfcNBwB8uvs87nt/J/ovTmK4u87sYJefn49mzZoBAH799Vc8+OCDcHV1xZAhQ3D27Flr1EhERERkUNk3b+bAtlgyMgZaXXm1kbdNldnBLiQkBLt370ZhYSF+/fVXDBgwAACQm5sLFxcXa9RIRERETUBWQYlZT95CvF2NBmVQPYLdtGnTMGrUKLRo0QJBQUHo06cPcL2JtkOHDvUu5M0334QgCJg2bVq9z0FERET2p3Lak093n2ezagOZHeyee+457NmzBx9//DF27twJmaziFK1atcIbb7xRryL279+PDz/8EB07dqzX+4mIiMh+VTatjo5tWWezqujkArj6NHJ19sXsYLdgwQK0a9cODzzwANzcbjz+7NevH37//XezC9BoNBg1ahRWrVoFb29vs99PREREjqG5h7LO/Rm3vwx4hTRaPfbI7GA3f/58aDTVF98tKirC/PnzzS5g0qRJGDJkCPr373/LY0tKSlBQUGD0RURERE1DudLThKOaNrMnKBZFEYIgVNt+9OhRw2hZU3311Vc4dOgQ9u/fb9LxiYmJ9QqPREREJA3BOQ+pBachc7nRyneuMF3SmhyZycHO29sbgiBAEARERkYahbvy8nJoNBpMnDjR5AunpaVh6tSp2LZtm8mjaRMSEhAfH294XVBQgJAQPpIlIiKyRTnFmVC3XoyX9umq7VPp9fCWc0SrpZkc7JYsWQJRFDF+/HjMnz8fnp43HocqFAq0bNkSsbGxJl/44MGDyM7ORpcuXQzbysvLsWPHDixbtgwlJSVwcnIyeo9SqYRSWXf7OxEREdmGa6X5EGQ6TGo/F73D29/YcfkMvL8Zj0CVr5TlOSSTg93YsWMBAOHh4bjzzjshl8sbdOG7774bx48fN9r2xBNP4LbbbsPs2bOrhToiIiKyT8HqMET5RN3YUFIKlJdLWZLDMinYFRQUwMPDAwDQuXNnaLVaaLU1zzFTedytuLu7Izo62mibWq2Gj49Pte1ERERENztXmA5RPA3BOU/qUmyGScHO29sbGRkZ8Pf3h5eXV42DJyoHVZQzgRMREZEVecvdoNLrkXBiJYCVULeW48DFKMgKSqQuTXImBbs///zTMOJ1+/btVivmr7/+stq5iYiIyDEEqnyx6WIGch/+GAd1It46NBcLftmP1kgHwm+sZNEUmfTJ4+LiavyeiIiI6FYUecnAJcWNDTlnajzuYnEmBGfRpHMGlpcj0KMloFQAh4D3RsZAkeeGmWdurGTRFNUr0ubl5WHfvn3Izs6GXq832jdmzBhL1UZERER2zFmbDQAI2T4FKL1pyhO5q2F5sMqm1SUX1kLdWo6c4m4AzJuMuLW/GyC4Wq54O2V2sPvxxx8xatQoaDQaeHh4GPW3EwSBwY6IiIgAALKSihWisrrNQlT0QOOdrj6G5cEqm1Z/7vkKllxYi2ul+VKU6xDMDnYzZszA+PHjsXDhQri6MhkTERFR3UrdQ4CgmDqPCSwvRwuXAPNOnHMGUDTdZteamB3s0tPTMWXKFIY6IiIikoarT0VT7ndPAQo5EBwIXMuSuiqbIDP3DQMHDsSBAwesUw0RERHRrXiFAJP2AU8nAf3mVGwrZvMt6vPEbsiQIZg1axZOnTqFDh06VFuB4v7777dkfURERNQEpedpkVXXvHReIRVfBecbsyybZ3awe+qppwAACxYsqLaPExQTERFRfSmupQEAsq+VoP8XSWjhdB4Il7oq+2J2U6xer6/1i6GOiIiIzHa9z1zzA4sAAKV5GdDqyjE6tqXUldkds4MdERERkUVd7zOX1W0WAEChq5gmpbmH0uRTnCtMx7nCdKuVaC9MboqNj4+vcbunpyciIyMxYsQIKJWm/wUQERERGXiFVEyLkmHe24zXjQVUej285W7WqdEOmBzsDh8+XOP2vLw8JCcnY86cOfjzzz8RGhpqyfqIiIiIalV13VgA8P5mPAJVvlKXJRmTg9327dtr3VdQUIBRo0bhxRdfxBdffGGp2oiIiIhuybBuLAA08f7+Fulj5+HhgTlz5mDXrl2WOB0RERER1YPFBk/4+vri6tWrljodEREREZnJ7HnsarNnzx60bt3aUqcjIiIiMl3OGakrsAkmB7tjx47VuD0/Px8HDx7EwoULMW/ePEvWRkRERFS3quvGAhXfu/pIXZVkTA52MTExEAQBoihW2+fr64v4+Hg899xzlq6PiIiImiDBOQ8Xi7NufWDlurFFVypeu/pUbGuiTA52qampNW738PCAt7e3JWsiIiKiJiyvPA/q1h9gyQWdaW+oXDeWTA92YWFh1q2EiIiICEChvhCCTIdpoU+g5f63MK25n9Ql2Q0uKUZEREQ2qYVLAALLyhp8nqyCEpxIz0d6ntYiddkyBjsiIiJySGplRcPkp7vP4773d6L/4iSHD3cMdkREROSQmrkqAAAzB7bFkpEx0OrKkVtYKnVZVmWxeeyIiIiILElxLc0i5wnxdoXe3c0i57J1fGJHRERENkWhywcAND+wSOpS7I7Fgt3YsWPRr18/S52OiIiImijn8iIAQFa3Wci4fY7U5dgVizXFBgcHQybjA0AiIiKyjFJ3zk1nLosFu4ULF1rqVERERERAlZGtN39PNWvQIzZRFGtcYoyIiIjIEipHtt78PdWsXsFuzZo1iI6OhouLC1xcXBAdHY3Vq1dbvjoiIiIiMpnZzzTnzp2Ld955B88//zxiY2MBALt378b06dNx4cIFLFiwwBp1EhEREdXLucJ0iOJpCM55UpdidWYHuxUrVmDVqlV49NFHDdvuv/9+dOzYEc8//zyDHREREdkEb7kbVHo9Ek6sBLAS6tZy5BR3A+ApdWlWY3ZTrE6nQ7du3apt79q1K8ossJ4bERERkSUEqnyx6WIGNtz+Gia1nwtBpsO10nypy7Iqs4Pd6NGjsWLFimrbP/roI4waNcpSdRERERE1WGB5OaI8WiJYHSZ1KY3CpKbY+Ph4w/eCIGD16tX47bffcMcddwAA9u7diwsXLmDMmDHWq5SIiIiI6mRSsDt8+LDR665duwIAUlJSAAC+vr7w9fXFyZMnrVEjERERUf3lnIGisGl0FzMp2G3fvt36lRARERFZkqsPIHcFvnsKIQo5EBwIZ2221FVZlVl97HQ6HZydnXHixAnrVURERERkCV4hwKR9wNNJyOo2CwAgKymQuiqrMivYyeVyhIaGory83HoVEREREV1XOWWJSq+Ht9zN/BN4hQBBMU1m3VmzR8W+/PLLeOmll3D16lXrVERERER0XeWUJZsuZiBQ5St1OTbP7AmKly1bhuTkZAQFBSEsLAxqtdpo/6FDhyxZHxERETVxgWwpNJnZwW748OHWqYSIiIiIGsTsYDdv3rxa97HvHREREZF0zO5jV5MzZ85g9uzZaNGihSVOR0RERET1UO9gV1RUhLVr16JXr16IiopCUlKS0QoVRERERA1WORed3LXie6qT2U2xe/bswerVq/HNN98gNDQU//zzD7Zv345evXpZp0IiIiKyO+l5WmQVlDT8RJVz0VV+T3Uy+Ynd4sWL0b59ezz00EPw9vbGjh07cPz4cQiCAB8fJmgiIiKqkJ6nRf/FSfh093kAgFpp9nMkY14hDHUmMjnYzZ49G8OHD8e///6LRYsWoVOnTtatjIiIiOxSbmEptLpyjI5tCQBo5qqQuqQmw+Rg99prr+Gbb75BeHg4Zs+ezWXFiIiIqE7NPZRSl9DkmBzsEhIScObMGXz66afIzMzE7bffjk6dOkEUReTm5lq3SiIiIiK6JbNHxcbFxeGTTz5BZmYmnnvuOXTt2hVxcXG488478c4771inSiIiIiK6pXpPd+Lu7o5nnnkGe/fuxeHDh9GjRw+8+eablq2OiIiIbFJ6nhYn0vONvtLztFKX1eQ1cJhKhQ4dOmDJkiVYtGiRJU5HRERENqxy1KtWZ7zilEruhN9nxElWF5n4xG7p0qUoLi6+5XFyuRwAsHLlSly7dq3h1REREZHNqRz1umRkDLY83xNbnu+JJSNjoNWVI7ewFAAgOOfhYnGm1KU2OSYFu+nTp5sV1F544QVcvny5IXURERGRjWvj74boYE9EB3uijb+bYXtOcSbUrRdjyYW1UOn18Ja71XkeshyTmmJFUcTdd98NZ2fTWm61WraxExERNVXXSvMhyHSYFvoE7t35OgJVvlKX1GSYlNTmzZtn1kmHDRuGZs2a1bcmIiIicgAtXAIQWF5uwpHGikrLrFJPU2CVYEdERERkrsqlx/6XoQECLLAUWRNU7+lOiIiIiOqiuJZm1vGVS4/1a+dv9JpMxyhMREREZhOc85BacBoyl4qBEakFGgjOeQAAZ202AKD5gUWA3BVw9THr3N4qOcBFreqFwY6IiIjMUjnq9aV9OqPt6tZy5BR3g6ykAACQ1W0Wono8BniFSFRp08NgR0RERGapHPU6qf1c9A5vDwDYkXoSy08uwLXSfFQ2oJa6hzDUNTKz+9ht377dOpUQERGRXQlWhyHKJwpRPlEIVodJXQ7VJ9gNGjQIrVu3xuuvv460NPM6RRIRERGR9Zgd7NLT0zF58mRs3LgRrVq1wsCBA/H111+jtLTUOhUSERGRTVLkJQOXjgCXjlR8T5IzO9j5+vpi+vTpOHLkCPbu3YvIyEg899xzCAoKwpQpU3D06FGTz7VixQp07NgRHh4e8PDwQGxsLH755RdzSyIiIqJGVDnqNWT7FOCjOOCjuIrvq+xriEu6ggafo6lq0Dx2Xbp0QUJCAiZPngyNRoOPP/4YXbt2Ra9evXDy5Mlbvr9FixZ48803cfDgQRw4cAD9+vXDsGHDTHovERERSaPqqFc8nQQ8nVTxfZV99eEtd4NKr8dHl/dwjdl6qlew0+l02LhxI+69916EhYVh69atWLZsGbKyspCcnIywsDA8/PDDtzzP0KFDce+99yIiIgKRkZF444034Obmhj179tSnLCIiImpEpe4hQFAMEBRT8X0DBap8seliBja0Ho1NFzO4xmw9mD3dyfPPP48vv/wSoihi9OjReOuttxAdHW3Yr1ar8fbbbyMoKMis85aXl+Obb75BYWEhYmNjzS2LiIiIHEBgeTkCVc2BeqwxS/UIdqdOncL777+PESNGQKlU1niMr6+vydOiHD9+HLGxsSguLoabmxu+//57REVF1XhsSUkJSkpKDK8LCtgGT0RERFTJ7GD3xx9/3Pqkzs6Ii4sz6Xxt27bFkSNHkJ+fj40bN2Ls2LFISkqqMdwlJiZi/vz55pZMRERE9iSf06nVl9nBbvPmzTVuFwQBLi4uaNOmDcLDw00+n0KhQJs2bQAAXbt2xf79+/Hee+/hww8/rHZsQkIC4uPjDa8LCgoQEsIZrYmIiByCq0/F2rI76rfGLNUj2A0fPhyCIEAURaPtldsEQUDPnj3xww8/wNvb2+yC9Hq9UXNrVUqlstbmXyIiIrJzXiHApH1A0ZWKUMflyMxm9qjYbdu2oXv37ti2bRvy8/ORn5+Pbdu24fbbb8eWLVuwY8cOXLlyBTNnzrzluRISErBjxw6cP38ex48fR0JCAv766y+MGjWqvp+HiIiI7JnX9ZG2DHX1YvYTu6lTp+Kjjz7CnXfeadh29913w8XFBU8//TROnjyJJUuWYPz48bc8V3Z2NsaMGYOMjAx4enqiY8eO2Lp1K+655x7zPwkRERFRE2d2sEtJSYGHh0e17R4eHjh37hwAICIiAjk5Obc815o1a8y9PBERERHVwuym2K5du2LWrFm4fPmyYdvly5fxwgsvoHv37gCAs2fPclADERERUSMz+4nd6tWrMXz4cLRo0cIQ3tLS0tCqVSts2rQJAKDRaPDKK69YvloiIiIiqpXZwe62227DqVOn8Ntvv+HMmTPA9bno7rnnHshkFQ8Ahw8fbvlKiYiIiKhOZgU7nU4HlUqFI0eOYNCgQRg0aJD1KiMiIiIis5jVx04ulyM0NBTlXL+NiIiIyOaYPXji5ZdfxksvvYSrV69apyIiIiKyW5qSMqlLaNLM7mO3bNkyJCcnIygoCGFhYVCr1Ub7Dx06ZMn6iIiIyA6olRWR4uOdqRgdGyZ1OU1WvZYUIyIiIqqqmasCAFBapkdhMZ/aScXsYDdv3jzrVEJEREREDWJ2HzsiIiIisk1mP7ErLy/Hu+++i6+//hoXLlxAaWmp0X4OqiAiIiKShtlP7ObPn4933nkHI0eORH5+PuLj4zFixAjIZDK8+uqr1qmSiIiI7EK5c7HUJTRpZge7zz//HKtWrcKMGTPg7OyMRx99FKtXr8bcuXOxZ88e61RJRERENs1b7gaVXo+c4N+QV54ndTlNltnBLjMzEx06dAAAuLm5IT8/HwBw33334aeffrJ8hURERGTzAlW+eDc7B6KsDIX6QqnLabLMDnYtWrRARkYGAKB169b47bffAAD79++HUqm0fIVERERkF7y5MpXkzA52DzzwAP744w8AwPPPP485c+YgIiICY8aMwfjx461RIxERERGZwOxRsW+++abh+5EjRyI0NBS7d+9GREQEhg4daun6iIiIyB64+kB0cgEAKHT5UlfTZJkd7G4WGxuL2NhYy1RDRERE9skrBBm3vwz8+wGcy4ukrqbJqlewO3v2LLZv347s7Gzo9XqjfXPnzrVUbURERGRHypWeUpfQ5Jkd7FatWoVnn30Wvr6+CAgIgCAIhn2CIDDYEREREUnE7GD3+uuv44033sDs2bOtUxERERER1YvZo2Jzc3Px8MMPW6caIiIiIqo3s4Pdww8/bJi7joiIiIhsh0lNsUuXLjV836ZNG8yZMwd79uxBhw4dIJfLjY6dMmWK5askIiKiRpOep0VuYWmt+7MKShq1HjKdScHu3XffNXrt5uaGpKQkJCUlGW0XBIHBjoiIyI6l52nRf3EStLraV5GIcDkPhANqZYNnTSMLM+lvJDU11fqVEBERkeRyC0uh1ZVjycgYtPF3q/GY9Av5mHkGaOaqaPT6qG5m97FbsGABioqqTzyo1WqxYMECS9VFREREEmrj74boYM8av0K8XaUuj2phdrCbP38+NBpNte1FRUWYP3++peoiIiIiIjOZHexEUTSalLjS0aNH0axZM0vVRURERERmMrnXo7e3NwRBgCAIiIyMNAp35eXl0Gg0mDhxorXqJCIiokYiOOchteA0ZC4197E7V5je6DWRaUwOdkuWLIEoihg/fjzmz58PT88b68EpFAq0bNkSsbGx1qqTiIiIGkFOcSbUrRfjpX26Oo9T6fXwltcc/Eg6Jge7sWPHAgDCw8Nx1113wdmZQ5yJiIgczbXSfAgyHSa1n4ve4e1rPujyGXh/Mx6BKt/GLo9uwex0FhcXh5SUFKxduxYpKSl477334O/vj19++QWhoaFo376WHwIiIiKyG+E6HaJKapmkuLQUKK99njuSjtnBLikpCYMHD8Zdd92FHTt24I033oC/vz+OHj2KNWvWYOPGjdaplIiIiKzOWZsNAAjZPgUoraM5Vu4KuPo0XmFkErOD3YsvvojXX38d8fHxcHd3N2zv168fli1bZun6iIiIqBHJSgoAAFndZiEqemDtB7r6AF4hjVcYmcTsYHf8+HF88cUX1bb7+/sjJyfHUnURERGRhErdQ4CgGKnLIDOZPY+dl5cXMjIyqm0/fPgwgoODLVUXERERkcVlFZTgRHo+TqTnIz1PK3U5Fmf2E7v//Oc/mD17Nr755hsIggC9Xo9du3Zh5syZGDNmjHWqJCIiImoAtbIi8ny6+zzmbt8JAFDJnfD7jDgEe6kkrs5yzH5it3DhQtx2220ICQmBRqNBVFQUevfujTvvvBMvv/yydaokIiIiaoBmrgoAwMyBbbHl+Z5YMjIGWl05cgtrGflrp8x+YqdQKLBq1SrMnTsXx48fh0ajQefOnREREWGdComIiIgsJMTbFVHBniYcaZ/qPctwSEgIQkJujIY5duwYunXrhtJSx0q+RERERPbC7KbY2oiiiHJOVkhEREQkGYsFOyIiIiIAKCotk7qEJosLvhIREZFFVI48/V+GBgi48dqWnCtMB66cQmqBBoJzntTlWJzJd7ygoKDO/deuXbNEPURERGSnKkee9mvnj+O5Jw2vbYG33A0qvR4JJ1YCJ1YCANSt5cgp7gbAcQZTmBzsvLy8IAhCrftFUaxzPxERETUNWmfbm/g3UOWLTRczkPvwx4BfJHaknsTykwtwrTRf6tIsyuRgt337dutWQkRERHat8qnYR5f3QKXXw1vuJnVJRgLLyxHo0RLwiUJKtkbqcqzC5GAXFxdn3UqIiIjIrhmeivV9Ed7b30SgylfqkqrLOQMAUOQlS12JVdher0YiIiKyW4Hl5QgsLQVsbQo0Vx9A7gp89xQAIEQhB4ID4azNlroyi2KwIyIiIsuoDE87FlX86eojdUU3eIUAk/YBRVcAAFkntgIZn0FWUvfgUHvDYEdERESWUTU8ufpUvLYlXiGGmkr/PQVkSF2Q5THYERERkeVUCU/U+MxeeWL8+PE1zllXWFiI8ePHW6ouIiIiIjKT2cHuk08+gVZbfX4arVaL9evXW6ouIiIiIjKTWStPiKIIURRx7do1uLi4GPaVl5fj559/hr+/v7XqJCIiIqJbMHvlCUEQEBkZWW2/IAiYP3++pesjIiIiIhOZtfKEKIro168fvv32WzRr1sywT6FQICwsDEFBQdaqk4iIiIhuweyVJ1JTUxEaGsp1YYmIiIhsjEnB7tixY4iOjoZMJkN+fj6OHz9e67EdO3a0ZH1EREREZCKTgl1MTAwyMzPh7++PmJgYCIIAURSrHScIAsptbQkRIiIioibCpGCXmpoKPz8/w/dEREREZHtMCnZhYWE1fk9EREREtqNeS4qdPXsW27dvR3Z2NvR6vdG+uXPnWqo2IiIiIjKD2cFu1apVePbZZ+Hr64uAgACj0bGCIDDYEREREUnE7GD3+uuv44033sDs2bOtUxERERER1YvZa8Xm5ubi4YcftsjFExMT0b17d7i7u8Pf3x/Dhw/H6dOnLXJuIiIioqbG7GD38MMP47fffrPIxZOSkjBp0iTs2bMH27Ztg06nw4ABA1BYWGiR8xMRERE1JWY3xbZp0wZz5szBnj170KFDB8jlcqP9U6ZMMflcv/76q9HrdevWwd/fHwcPHkTv3r3NLY2IiIioSTM72H300Udwc3NDUlISkpKSjPYJgmBWsLtZfn4+ABitQ0tERESWkZ6nRW5haZ3HZBWUNFo9ZHlmBztrTVCs1+sxbdo03HXXXYiOjq7xmJKSEpSU3PiBKygosEotREREjiY9T4v+i5Og1dW9QlSEy3kgHFAr6zUjGknMZv7WJk2ahBMnTmDnzp21HpOYmIj58+c3al1ERESOILewFFpdOZaMjEEbf7daj0u/kI+ZZ4BmropGrY8sw+RgN2LEiBq3e3p6IjIyEk8++aRh2TFzTZ48GVu2bMGOHTvQokWLWo9LSEhAfHy84XVBQQFCQkLqdU0iIqKmRnDOg5NLOmQutQc7nSK3UWsiyzI52Hl6eta4PS8vD6tWrcKiRYuwY8eOWptRayKKIp5//nl8//33+OuvvxAeHl7n8UqlEkql0uTzExERUYWc4ky4tX4bL+0ru+WxKr0e3vLawx/ZLpOD3dq1a2vdp9fr8dRTTyEhIQE//vijyRefNGkSvvjiC2zatAnu7u7IzMwErodIlUpl8nmIiIiobtr8s4CsDInZOWil09V5rLdMiUCfto1WG1mORfrYyWQyTJkyBYMHDzbrfStWrAAA9OnTx2j72rVrMW7cOEuURtR05aUBRVdq3ufqA3ixGwNRUyIrqRhwqO40DVHRA+s+mL8j7JbFBk+o1WoUFRWZ9R5RFC11eSKqKi8NWN4D0NXy36TcFZi0j7+4iZqgUvcQIChG6jLISiwW7LZt24bIyEhLnY6IGqLoSkWoG7EK8L3pv8ucM8B3T1Ucw2BHRORQTA52mzdvrnF7fn4+Dh48iNWrV2P16tWWrI2IGso3kv8yJyJqQkwOdsOHD69xu7u7O9q2bYvVq1fjP//5jyVrIyIiIiIzmBzs9Hq9dSshIovKcHJCbsF5QHnTJKMF5+Ht5IRAqQojIiKrsZmVJ4jIcjK0ORjWIhDavXNq3K9qEYhN2hyGOyIiB8NgR+SAcnUaaGUyJEZPRKuWfY32nTu/HQknViJXp2GwIyJyMAx2RA6slToYUT5Rxhsvn6n4M+9f4NKRiu85ZxURkUNgsCNqalyuLw/452tA6dyK7zmvHRGRQ5CZc3BZWRnWr1+PrKws61VERPWTl1bxBO7SkYqncbVxb17x54jVwNNJFXPd6YpqX6WCiIjshllP7JydnTFx4kT8888/1quIiMx380oTCjkQHHjj6VxN/CKBm5tpiYjIrpndFNujRw8cOXIEYWFh1qmIiMx380oTBeeBvXNuPJ2rwbn8cxXfcPoTIiKHYXawe+655xAfH4+0tDR07doVarXaaH/Hjh0tWR8RmaNypYnrc9elZGugL843OiSn2AlKJxck/DfBsI3TnxAROQazg13l6hJTpkwxbBMEAaIoQhAElJeXW7ZCIjJb9rUSAMDUDUegL75cbb9KFY8VY2+Dv7uS058QETkQs4NdamqqdSohogaputLE/3KSAQAz74lE75adjY5LztZg2oYj8JW3QpSP543pT4iIyO6ZHezYt47I9tS00oSolyMqIBDRwXUMoCAiIodi1nQnlT799FPcddddCAoKwr//VkyrsGTJEmzatMnS9RGRCaquNLHhvg1Y2GMNClNmwNclQOrSiIioEZkd7FasWIH4+Hjce++9yMvLM/Sp8/LywpIlS6xRIxGZqHKliXCPthDLvOo8NjlbgxPp+UjLLWq0+oiIyLrMDnbvv/8+Vq1ahZdffhlOTk6G7d26dcPx48ctXR8RWZi3WgGV3AnTNhzBfe/vxNtbTwMArhaVSl0aERE1UL0GT3Tu3LnadqVSicLCQkvVRURWEuylwu8z4pBbWBHkDp3IxqJMoLCkTOrSiIgaXVZBCU6k59e4z1utQLCXqtFragizg114eHiNExT/+uuvaNeunSVrIyIrCfZSGX5ZpV9QAplSV0RE1LjUyooI9Onu85i7fWeNx6jkTvh9RpxdhTuzg118fDwmTZqE4uJiiKKIffv24csvv0RiYiJWr15tnSqJiIioTul5WsOT+JpkFZQ0aj22rplrxUTuMwe2RXBoz2r7K6eGyi0sdexg9+STT0KlUuGVV15BUVERHnvsMQQFBeG9994zTF5MREREjSc9T4v+i5Og1dW+SECEy3kg/MaTKqoQ4u2KKAeaFqpef7ujRo3CqFGjUFRUBI1GA39/f8tXRkRmS8stgj49H8nZGqlLIaJGlFtYCk/xLBL6uqG5h7LGY7KuFmNRzo0nVeSY6h3bs7Ozcfp0xWg6QRDg5+dnybqIyAyVI1rf3noaZ4sr/uWpkjvBW81f4ERNQd6Voyhv/SEWZQp19plV6UV4e4Q0Zmk271xhOnDlVLXtqQUaCM55ktTUEGYHu2vXruG5557Dl19+Cb1eDwBwcnLCyJEjsXz5cnh6Os7jTCKbl5cGFF2BLqdiqb/RsS3RJbqir4g9juYiovopLLyIYpmAWb73olvr2FqP8/YIQWBQ10atzVZ5y92g0uuRcGIlcGJljceoW8uRU9wNgP1km3r1sTt8+DB++uknxMZW/PDs3r0bU6dOxTPPPIOvvvrKGnUS0c3y0oDlPQBdEZor5EBwIPz8/Oq9hJjiWhpw6UjFC1cfwIv/qieyN82bdULUbcOlLsMuBKp8seliBnLvmQd4VV8udXfGOSy5sBbXSmueCsVWmR3stmzZgq1bt6JnzxsjSAYOHIhVq1Zh0KBBlq6PiGpTdAXQFQEjViGtsAw4k4gylfn9XfVKDwBA8wOLgL8XVmyUuwKT9jHcEZHjcvVBoEyJwF/n1rxfIceS4EA4a7Mbu7IGMTvY+fj41Njc6unpCW9vb0vVRUSm8o1Eqbz+q0ZUhsG0vksRFRYF5JwBvnuqIjgy2BGRo/IKqfgHbNGVGndnndgKZHwGWUlBo5fWEGYHu1deeQXx8fH49NNPERBQscB4ZmYmZs2ahTlz5lijRiJqBKlyOU4pFYBCAW8nJwRKXRARkbV5hdT6D9jSf08BGY1eUYOZHexWrFiB5ORkhIaGIjQ0FABw4cIFKJVKXL58GR9++KHh2EOHDlm2WiIykuHkhNyC80gv1NX7HO4KT4h6OZafXIDlJyu2qVoEYpM2h+GOiMjOmB3shg9np0wiW5ChzcGwFoHQ7q14Ui7q5XBXmD9wwtclAIUpM7B0VARa+7vh3PntSDixErk6DYMdEZGdMTvYzZs3zzqVEJFZcnUaaGUyJEZPhOjaHVM+PwvfAQH1OpdY5oVwj7aI8vEELp+xeK1ERNQ4uK4IkZ1rpQ6G3r0txLLLUpdCREQSY7AjIuD6gtcAkJ5bJHUpRERUTwx2RE2ct1oBldwJ0zZUTE4c4XIaCL+xTBkREdkPBjuiJi7YS4XfZ8Qht7AiyB06kY1FmUBhSZnUpRERkZlk5r6huLi41n0ZGXY44QsRIdhLhehgT0QHe6K5h1LqcoiIqJ7MDnZdunTBkSNHqm3/9ttv0bFjR0vVRUQmSsstMvSPIyKips3sYNenTx/ccccd+L//+z8AQGFhIcaNG4fRo0fjpZdeskaNRFSDyj5wb289jWkbjkAld4K3WiF1WUREJCGz+9h98MEHGDJkCJ588kls2bIFGRkZcHNzw759+xAdHW2dKonohrw0oOgKdDmpAIDRsS3RJbonvNUKBHuppK6OiKzg8KVUXMyvfUqjf65caNR6yHbVa/DE4MGDMWLECKxYsQLOzs748ccfGeqIGkNeGrC8B6ArQnOFHAgOhJ+fH6KDzV9xgojsw+FLqRiz9UFAVvfSgSq9HkFuXo1WF9kms4NdSkoKHnvsMWRmZmLr1q1ISkrC/fffj6lTp+KNN96AXC63TqVEBBRdAXRFwIhVSCssA84kokzlb5VLKa6lAZeOAK4+tS6STUTWl5l5EpDpkJidg1a62sOdp6BAcEiHRq2NbI/ZwS4mJgZDhgzB1q1b4eXlhXvuuQf33nsvxowZg23btuHw4cPWqZSIbvCNRKncOvPM6ZUeAIDmBxYBfy8E5K7ApH0Md0QSkZUUAADUnaYhKnpg7QfyH2FU3z52o0ePNtp255134vDhw5g2bZolayMiCVQ+AUzruxRRamfgu6cqnhTyfxhEkip1DwGCYqQug2yc2cHu5lBXyd3dHWvWrLFETURUhwwnJ+QWnEd6Yd39bRoqVS7HKYUc3k5OCLTqlYiIyFLMDnbr16+vdZ8gCLUGPyJquAxtDoa1CIR27xwAgKiXw11h2YET7gpPiHo5lp9cgOUAVC0CsUmbw3BHRGQHzA52U6dONXqt0+lQVFQEhUIBV1dXBjsiK8rVaaCVyZAYPRGia3dM+fwsfAcEWPQavi4BKEyZgaWjIiAU7UfCiZXI1WkY7IiI7IDZwS43N7fatrNnz+LZZ5/FrFmzLFUXEdWhlToYeve2EMtqn9eqIcQyL4R7tIVMuGSV8xMRkXWYvfJETSIiIvDmm29We5pHRPYrOVuDtNwiqcsgIiIz1GuC4hpP5OyMS5f4r3sie+etVkAld8K0DUcQ4XIaCL+xfBkRWdaxM38j48r5Oo85c3F/o9VD9s/sYLd582aj16IoIiMjA8uWLcNdd91lydqISALBXir8PiMOuYWlOHQiG4sygcKSMqnLInI4x878jQm7nkaxTLjlsS56EYE+LRulLrJvZge74cOHG70WBAF+fn7o168fFi9ebMnaiEgiwV4qBHupkH5BCWRKXQ2RY8q4ch7FMgFPu/ZHZIvudR4b6NMSHSPvbLTayH6ZHez0er11KiEik6XlFkGr1UhdBhFZQGSL7hgY+5jUZZCDsFgfOyKyorw0oOgKCjKTAQBvbz2Ns8WeUMmd4K1WWP3yimtpFTVw9QkiIptmUrCLj483+YTvvPNOQ+ohopvlpQHLewC6Ingo5EBwIP7TqwNuv60nvNUKBHuprHZpo3Vj9y/hmrFERDbOpGB3+PBhk04mCLfuAEpEZiq6AuiKgBGrkFZYBpxJhH9QKKKDLbviRE0q14090GkCvA+tQiDXjCUismkmBbvt27dbvxIiqptvJErljTvtSOXyYotyfsYyLi1GZJZbTWXCaUzIGkzuY3fu3DmEh4fzqRxRE1K5vNgrd2dhyYW1XFqMyESmTmXCaUzI0kwOdhEREcjIyIC/f0XTzMiRI7F06VI0b97cmvUREYAMJyfkFpxHeqGu0a8tlnmhhQv/QUdkDlOnMuE0JmRpJgc7URSNXv/8889ITEy0Rk1EVEWGNgfDWgRCu3cOAEDUy+GusH7/uqqyCkoa9XpEjoJTmVBj43QnRDYuV6eBViZDYvREiK7dMeXzs/AdENAo165cXuzT3ee5tBgRkR0wOdgJglCtfx372xE1nlbqYOjd20Isu9xo16xcXuyPvRlYlAkUF1xptGsT2Squ70q2zKym2HHjxkGpVAIAiouLMXHiRKjVaqPjvvvuO8tXSUSSCfZSwc/PD8gEAve+AcTcxylPqMni+q5k60wOdmPHjjV6/fjjj1ujHiKyQZXz2eVBVzGvHoMdNVFc35VsncnBbu3atdathIhslrvCE4LeGdP9fTmXHTk0U+ee46AIslWSDp7YsWMHFi1ahIMHDyIjIwPff/89hg8fLmVJRDYrLbcIWq1Gkmv7ugTAN30ALof8jNxraQx2ZJ+ur7lcm5MXT2LCyUTOPUd2TdJgV1hYiE6dOmH8+PEYMWKElKUQ2azKkahvbz2Ns8WeUMmd4K1WNHodhWU+Fd/8Ngdo2Z/NsWRf8tKQvuJ25Iu1j+xOlctR7O+L8Z7DENU8qtbj2MRKtkzSYDd48GAMHjxYyhKIbF5hSRkAYHRsS3SJ7glvtQLBXqpGrcFbrUCBczM4A8gV2c+ObFQdT+T+SfkbYwO8oZXJ6j6HXo4+PSagc1C4dWoksjLOY0dkq67/T0pxLQ0A0NxDiejgxp2YuFKwlwoLh92BeQeWs58dSSLj0kHkFqTVfkBxLsStcyCUF9e4+5xcDq2/Lx5r/hSiw+6o9TQtPP0Y6siu2VWwKykpQUnJjRnwCwoKJK2HyGry0oDlPQBdEZor5EBwIPRKD0lLimgWcqOfHdeMJUur42lbRu5Z3L9v/q2nGAnwrnu/Xo5BHYcyuJFDs6tgl5iYiPnz50tdBpH1FV0BdEXAiFVIKywDziQaphyRklOZS8U3ef9W/I+YzbFkCXlpyFh5B3L1NS9dd+5637ewS7EoKan9nxTFzu545t5YeKrkNe7n0zhqCuwq2CUkJCA+Pt7wuqCgACEh/B8LOTDfSJTKbWMZL2+1AsXO7gCAc/99E95/vYXAiXsY7qjBMq6cxrDmXnX3f9M746F+z6Jbi1a1HiJF/1MiW2NXwU6pVBpWviBydBlOTsgtOI/0Qp3UpQDX+9nFDxuEuQc+R4K/L1R6PTZdOY1ABrsm75b9327h+IW90Mpk8LnUDxdK2td4jFJwxz0P3MbgRnQLkgY7jUaD5ORkw+vU1FQcOXIEzZo1Q2hoqJSlEUkqQ5uDYS0Cod07BwAg6uVwV0gzcKKqiGYh0KTMxCt3Z2HJhbXsa0fIuHQQ928da9ISW3Vx0YuYGDsY0RGxNe7n0zgi00ga7A4cOIC+ffsaXlc2s44dOxbr1q2TsDIiaeXqNNDKZEiMngjRtTumfH4WvgMCpC4LACCWeUFeahvNwyS9lMwUFMsERF2KwdWS2ptJb6VUaI5eD8QxvBE1kKTBrk+fPhBFUcoSiGxaK3Uw9O5tIZZdlroU4PpTE5XcCZ/uPg+EAwWZyYDHEcDVh33t7FRDm1HPZRwEAAzp0g9dous/0TyfyBFZhl31sSMiaQV7qfD7jDj8elCDJRe/Q87+xTj195vwlik5kMIOWbIZtVVga8nmWSSiGxjsiMgswV4qtG7ZAbjgjAR/XwDgQAo7Zclm1PAHulu0NiKqHwY7IjKbr0sANCkzMWtwMJSlhziQwkaY26zKZlQix8NgR0Rm81Yr4CL44K0fCxHhkg+EA1eLOKDC4upYjeFmGblnMWzffGjNbFZlMyqRY2GwI7JhablF0Go1UpdRTWVfu9zCUhw6kY1FmRVPf5r9TwEA8PYIQWBQV6nLtG+3WI3hZpVroc4IfBiB7m1Mek9WQQk++K8GXgM6NbBYIrIVDHZENqjy6dfbW0/jbLEnVHIneKsVUpdlJNhLhWAvFfKutIbLJRGLcn4Gcn4GAKj0IjYN/IThrgFMWo3hZno55u9oDbHM9KdvKnmgzf1sEVH9MdgR2aDCkjIAwOjYlugS3dOm+zB5+XSCU8ozmNXLDc09lMi6ehSLcn5GbkEag10dKvvDecvdEKjyvbHj+tQxKflXq63GoHSW4eV729W4Fmra1SIs+iUd7z7YB2383Uyuw5Z/tojIfAx2RDasuYfS5vs+easVyBciMHd7OQAgwsXFeI47gPPc3aTqNCMqvR7vZufAu7zi/lVOHVMZ7sd3iUGX6BG4UliKiZ8exCtf59V6XpXcB93DmzGoETVhDHZEtuR6Z3nFtfpPGNvYqva3A4C9/9MazXGHKmGF4a4i1O04sRHFMgERWVFI9juDiQH+hv2VU8dUqhruq97nmvDpGxEx2BHZirw0YHkPQFeE5go5EBwIvdJD6qpMUtnfDgByio3nuENlWEn+FYFB1+c6c7QneDWNXq3hM2ZcOohhW8dCKxPgohcxqONovLv3GkrEawCAUOVJXAn6Eyn5V2u8TNX7TERUEwY7IltRdAXQFQEjViGtsAw4k4gylb8Jb7QtET6hKLvwgiGs+ChSoA3+GQe3z0UrnQ6w5yd41wNchjYHubqK0crFV1OApP+Di6g3OtRTUCD44fWAq68h5OUWpEErE/C0a398frQV7hzQC0PuUBiewh068R0WZf5paIYlIjIXgx2RDclwckKuQoHU0oYt8SSlYC8Vfp863BBWDlw8h8Wnfqv2BO/dE5+hVWB3BPq0temAZxjkIDgD3z+Dc0IZpvv7Go9WDWpe7X0uehFLvh0F7/JyQ5CtHO28+aQH8oUIQ9Np5VO49AtKILPxPhsROR4GOyIbkaHNwbAWgdDunQMAEPVyuCtse+BEbaqGFW/1bfi/X288wfN1ugSxxUZMTPkCqrOf4d0r19Bq8GIEBt9RY9NlbkGaZPPiVVtLNbAZAEDQO8MvbQBauO3FYe+KJtg+sigM6DYDAPC/yxlYn/Kqoe9cZb+5qqOd7749rtZmVXvqY0lEtoXBjshG5Oo00MpkSIyeCNG1O6Z8fha+AwKkLqvBbn6Cd6WwFHO/9Ie707+4ErwVE/08odr3qiHgwcUbuToNcq9dxLQTK1F8vT9aQugTULtWX7RMrXRGM9cb87BZMgRWrqXa+UoADvtUPErzudQPWaV3YN6j/fHnrgQcRkWwC5N7Y2i7HgCAcI98fPBb9SXXKjX3UNYY6ir7VDY/sOj6zbOffpZEZBsY7IhsTCt1MPTubSGWXZa6FIu5udP/F1OfQHK2BhO/jIG77DRKWvyAiX6ewIEFRu9zARB1KQbnAg5j3sV1Jl3LRS9iSfREeLu3AIDq88RVdYtBHMUFFaGtjW8YDosVwW58lxjcfftwBHupsP+QM1DDwhD1XXKtsk9lWt+lFRvstJ8lEUmHwY6IGl1l0Pt96vDrAa8t3GWnUdxiEwDAN30AnMpcUCo0x3OPPgyn4n9QWHix2nk0JWX4eGcqSssqBi6ona8iPXg7Jp760HDMzfPEVeUpKBD87N6aw11eGpQHFgJ+XlCoPICiis1Vn7YVuQTWGOxqWnKt2a/PoazzVJPuT6q8+gTERESmYLAjIsncHPDGrY8AADxz9+2Ii/SrMi+bX63nuCNGe1Mzbzt4iVkAgHLnYuQE/2Y0T1xVKr0ea9KOo0MNwS7jymnM8PGATO8EuTLIEOyqKlQFAfl1f7bKAREjgwMxO3tnnffDXeEJUS/H8pMVTy7tuZ8lEUmDwY6IJFcZgtaNGYCxH+9DXKSfyStu1NTMW3US35zi8bhWWj19/ZPyJz698jlS0vehg09QxcYqTbOVfR790gbCy9+rxmsHuLQ263OeLzgNeLjX2m/O1yUAhSkzsHRURcB1lH6WRNR4GOyIbExabhG0Wo0JRzqeuEg/nH9zSIPOUX0S35oDoreuGN9c/gwLM76B39EVRtOSwCvE0CdOBVeoXWr+VRmoaoNmGb1xNXBHRbOsierqNyeWeSHco+317x2nnyURNQ4GOyIbURkk3t56GmeLPaGSO8Fbrbjl+6h+vHw6QfbvGJS12mA8LUn6HgR6hdxYq7VnOFw9mgHXu/jd/LTtEnzhUtksewvn2HeOiKyMwY7IRlSd46xLdE+u+2ll3moFCso7ovhMMATnQgSoUnEtYAtyf5peMafedW5KZ5RWecJW9WlbdLAnyouDARObZferXIDrfemIiKyBwY5IateXqaqclLbqou9kPVVHriZnaxC/6SeoAeSKOqDoCpxKahkVUUV0sCcW3jsIL34XjMB2bWo85uYnfJGXI+DrUne/ueTsptkUT0QNx2BHJKW8NGB5D0BXhOYKOSekbWSV/fG81QooBXcIemdM9/fFpuwTCNz7BhDgDb3SwzBaFfV42nZzfzplee3N695qBVRyJ0zbcAQA2BxPRGZjsCOSUtEVQFcEjFiFtMIyTkgrkWAvFVY+2h/zvz6CyyE/I1dzCUJ5MXA9mFWOVgVg1VGqVZ8i4nrQY3M8EZmDwY5IYhlOTshVKJBaKkhdSpPmo1bAqczF8DrXyclov1hW85QnllZ9VC8RkekY7IgklKHNwbAWgdDunQNwQlpJeasVUDjLAAApVy/gNX9fCHrnW/59VPaHrK1fZGUzriDTWaFqIiJjMqkLIGrKKifBTYyeiIU91qAwZcYtO9aTdQR7qTCmbycAQOmZ76CVyeCbPuCWfx/RwZ44/+aQWoNdZTNumyutrFI3EVFVfGJHZANaqYOhd2/LCWkl5trMeC66qk2zDSGWeUGlu9G8ygERRGQtDHZERDe5uX9d5WhVWCCUtQ/2YB86IrIaBjsiG9CUlxGzJe4KTwh6Z7zXzHigROVo1crvG0LpzB4wRGQ9DHZEEuIyYrbF1yUAvukDcDnk52r7+JSNiOwBgx1RY7u+0gQA6HJSAS4jZlMs1a+uUtVmXCIia2OwI2pMVVaaAGBYbcLPz4/LiNkghbOswU9QK5tx12zeiOOixUojIqoRO3sQNaYqK03g6SSk9V0K1LDsFNmG8T3DLfIENdhLBXiEAACKXAItUBkRUc34xI6okVWuNAGlAqlyudTlUB3clJb7FVmoCgLyr/9JRGQlDHZEjejmlSbA1SaIiMiCGOyIGlHVlSZateyLlGwNpnx+1qoLy5Ppqi4rRkRkjxjsiCTQSh2MKJ8o6IvzudqEDalcVuz15I0AAL3SQ+qSiEhiWQUlOJGeX+t+W5vNgMGOSAJpuUXQp+cjOZuTEtuaqsuKcVALUdOlvt7H9uNDR/Dqbl2txykFd/w+dbjNhDsGO6JGdPOExAA4KTERkQ1q7dkMKr0eV4L+hBp/1n6g3hlnr3RBsFfbxiyvVgx2RI2osKQMqDIhMWzwMT4REQGBPm2xKSsPufqSWo85J5cjwd8X2vyzABjsiJqGKitNKK6lAQCaeyg5ITERkS3zCkHgxD0IvP77uyZZJ7YCGZ9BVlLQqKXVhcGOyJpqWWmCnfKJiOyAV0jFVy1K/z0FZDRqRbfEYEdkTUVXkKEvQe6gBYBXGHZnnAMurGWnfCIisgoGOyIrMkxIfHq1YRsnJCYiImthsCOyIk5ITEREjYnBjqgRcEJiCnBpbfQnEZE1MNgRNQJOSEyBqja49s+bCGzXRupSiMiBMdgRWREnJLY/7gpPiHq54XsiInvCYEdkRZyQ2P74ugSgMGVGxffsC0lEdobBjqgRcEJi+yKWeUldAhFRvTDYEVlSlVUmUGWlCSIiosbAYEdkKXlpyFh5h9G6goVyOeDvy5UmiIioUTDYEVlIxpXTGNbcC1qZzHiH3hkqzwipyiIioiaEwY7IQm6ejBgAJyQmIqJGxWBHZGHyUm/oi4MBAOXFGk5ITEREjYbBjshCapqzDpy3joiIGhGDHZGF1DRnHThvHRERNSIGOyIL45x1REQkFQY7InPcNE9dVZyzjoiIpMZgR2SqGuapq4pz1hERkdQY7IhMVOs8dVVxzjoiIpIQgx2RiSrnqZsW+gT8A3pW2592tQiLfknnnHVERCQZBjsiE1VOZ/JVUj7OFtc8N51K7sOpTYiISDIMdkQmqm06k6o4tQkREUmJwY6arjpGuNakctQrpzMhIiJbZRPBbvny5Vi0aBEyMzPRqVMnvP/+++jRo4fUZZEjy0tD+orbkS+WmvwWjnolIiJbJ3mw27BhA+Lj47Fy5UrcfvvtWLJkCQYOHIjTp0/D399f6vLIQR1PO44JAd51j3CtiV6OgID21iqLiIioQSQPdu+88w6eeuopPPHEEwCAlStX4qeffsLHH3+MF198UeryyEFd0uRBK5NhtM8otGvdz+T3tfD0Q+egcKvWRkREVF+SBrvS0lIcPHgQCQkJhm0ymQz9+/fH7t27qx1fUlKCkpIbk8Pm5+cDAAoKCqxe69nzR/Fv9mmrX4caR3L6IZRry9HGxRdxwbeZ9d7G+Hkj6WiuFUBfUmT4vqBAsMh5W3oI0JcUoaWHwJ8hIgdRWFiEcm05CguLrPrfdeW5RVG89cGihNLT00UA4t9//220fdasWWKPHj2qHT9v3jwRAL/4xS9+8Ytf/OJXk/tKS0u7ZbaSvCnWHAkJCYiPjze81uv1uHr1Knx8fCAIlvlXtb0rKChASEgI0tLS4OHBTv6WxHtrPby31sH7aj28t9bDe1udKIq4du0agoKCbnmspMHO19cXTk5OyMrKMtqelZWFgIDqs/crlUoolUqjbV5eXlav0x55eHjwPwgr4b21Ht5b6+B9tR7eW+vhvTXm6WnaNFtmDgm0LIVCga5du+KPP/4wbNPr9fjjjz8QGxsrZWlEREREdkfyptj4+HiMHTsW3bp1Q48ePbBkyRIUFhYaRskSERERkWkkD3YjR47E5cuXMXfuXGRmZiImJga//vormjdvLnVpdkmpVGLevHnVmqyp4XhvrYf31jp4X62H99Z6eG8bRhBNGjtLRERERLZO0j52RERERGQ5DHZEREREDoLBjoiIiMhBMNgREREROQgGO0JRURHCwsIwc+ZMqUtxGGlpaejTpw+ioqLQsWNHfPPNN1KXZLe2bNmCtm3bIiIiAqtXr5a6HIfBn1Hr4u9V60hNTUXfvn0RFRWFDh06oLCwUOqSbA5HxRJefvllJCcnIyQkBG+//bbU5TiEjIwMZGVlISYmBpmZmejatSvOnDkDtVotdWl2paysDFFRUdi+fTs8PT3RtWtX/P333/Dx8ZG6NLvHn1Hr4u9V64iLi8Prr7+OXr164erVq/Dw8ICzs+Qzt9kUPrFr4s6ePYv//e9/GDx4sNSlOJTAwEDExMQAAAICAuDr64urV69KXZbd2bdvH9q3b4/g4GC4ublh8ODB+O2336QuyyHwZ9R6+HvVOk6ePAm5XI5evXoBAJo1a8ZQVwMGOxu2Y8cODB06FEFBQRAEAT/88EO1Y5YvX46WLVvCxcUFt99+O/bt22fWNWbOnInExEQLVm0fGuPeVjp48CDKy8sREhJigcrtS0Pv86VLlxAcHGx4HRwcjPT09Ear35ZZ8me4Kf+M3swS97Wp/l69lYbe27Nnz8LNzQ1Dhw5Fly5dsHDhwkb+BPaBwc6GFRYWolOnTli+fHmN+zds2ID4+HjMmzcPhw4dQqdOnTBw4EBkZ2cbjomJiUF0dHS1r0uXLmHTpk2IjIxEZGRkI34q22Dte1vp6tWrGDNmDD766KNG+Vy2xhL3mWpmqXvb1H9Gb9bQ+9qUf6/eSkPvbVlZGf773//igw8+wO7du7Ft2zZs27atkT+FHRDJLgAQv//+e6NtPXr0ECdNmmR4XV5eLgYFBYmJiYkmnfPFF18UW7RoIYaFhYk+Pj6ih4eHOH/+fIvXbuuscW9FURSLi4vFXr16ievXr7dovfaqPvd5165d4vDhww37p06dKn7++eeNWLV9qO/PMH9G61af+8rfq6apz739+++/xQEDBhj2v/XWW+Jbb73ViFXbBz6xs1OlpaU4ePAg+vfvb9gmk8nQv39/7N6926RzJCYmIi0tDefPn8fbb7+Np556CnPnzrVi1fbBEvdWFEWMGzcO/fr1w+jRo61Yrf0y5T736NEDJ06cQHp6OjQaDX755RcMHDhQwqrtgyn3lj+j5jPlvvL3av2Ycm+7d++O7Oxs5ObmQq/XY8eOHWjXrp2EVdsmBjs7lZOTg/LycjRv3txoe/PmzZGZmSlZXY7AEvd2165d2LBhA3744QfExMQgJiYGx48ft1LF9smU++zs7IzFixejb9++iImJwYwZMzgi1gSm3Fv+jJqPv3etx9TfBwsXLkTv3r3RsWNHRERE4L777pOoYtvF4SQEABg3bpzUJTiUnj17Qq/XS12GQ7j//vtx//33S12Gw+HPqPXx96rlDR48mKONb4FP7OyUr68vnJyckJWVZbQ9KysLAQEBktXlCHhvGwfvs/Xw3loH76v18N5aDoOdnVIoFOjatSv++OMPwza9Xo8//vgDsbGxktZm73hvGwfvs/Xw3loH76v18N5aDptibZhGo0FycrLhdWpqKo4cOYJmzZohNDQU8fHxGDt2LLp164YePXpgyZIlKCwsxBNPPCFp3faA97Zx8D5bD++tdfC+Wg/vbSORelgu1W779u0igGpfY8eONRzz/vvvi6GhoaJCoRB79Ogh7tmzR9Ka7QXvbePgfbYe3lvr4H21Ht7bxsG1YomIiIgcBPvYERERETkIBjsiIiIiB8FgR0REROQgGOyIiIiIHASDHREREZGDYLAjIiIichAMdkREREQOgsGOiIiIyEEw2BERERE5CAY7IqJG0KdPHwiCAEEQcOTIEYue+/z584Zzx8TEWPTcRGRfGOyIyOaMGzfOEFSqfg0aNEjq0hrkqaeeQkZGBqKjo006fujQobV+5v/+978QBAHHjh1DSEgIMjIyMGPGDAtXTET2xlnqAoiIajJo0CCsXbvWaJtSqbTqNUtLS6FQKKx2fldXVwQEBJh8/IQJE/Dggw/i4sWLaNGihdG+tWvXolu3bujYsSMAICAgAG5ubhavmYjsC5/YEZFNUiqVCAgIMPry9vY27BcEAatXr8YDDzwAV1dXREREYPPmzUbnOHHiBAYPHgw3Nzc0b94co0ePRk5OjmF/nz59MHnyZEybNg2+vr4YOHAgAGDz5s2IiIiAi4sL+vbti08++QSCICAvLw+FhYXw8PDAxo0bja71ww8/QK1W49q1a2Z9zrpqvO++++Dn54d169YZvUej0eCbb77BhAkTzLoWETk+Bjsislvz58/HI488gmPHjuHee+/FqFGjcPXqVQBAXl4e+vXrh86dO+PAgQP49ddfkZWVhUceecToHJ988gkUCgV27dqFlStXIjU1FQ899BCGDx+Oo0eP4plnnsHLL79sOF6tVuM///lPtaeJa9euxUMPPQR3d3eT679Vjc7OzhgzZgzWrVsHURQN7/vmm29QXl6ORx99tN73jogclEhEZGPGjh0rOjk5iWq12ujrjTfeMBwDQHzllVcMrzUajQhA/OWXX0RRFMXXXntNHDBggNF509LSRADi6dOnRVEUxbi4OLFz585Gx8yePVuMjo422vbyyy+LAMTc3FxRFEVx7969opOTk3jp0iVRFEUxKytLdHZ2Fv/6669aP1NcXJw4depUo22m1PjPP/+IAMTt27cbjunVq5f4+OOPV7vGvHnzxE6dOtVaAxE5PvaxIyKb1LdvX6xYscJoW7NmzYxeV/Yvw/UnaR4eHsjOzgYAHD16FNu3b6+x31lKSgoiIyMBAF27djXad/r0aXTv3t1oW48ePaq9bt++PT755BO8+OKL+OyzzxAWFobevXub9RlNqfG2227DnXfeiY8//hh9+vRBcnIy/vvf/2LBggVmXYuImgYGOyKySWq1Gm3atKnzGLlcbvRaEATo9Xrgej+0oUOH4v/+7/+qvS8wMNDoOvXx5JNPYvny5XjxxRexdu1aPPHEExAEwaxzmFrjhAkT8Pzzz2P58uVYu3YtWrdujbi4uHrVTUSOjX3siMghdenSBSdPnkTLli3Rpk0bo6+6wlzbtm1x4MABo2379++vdtzjjz+Of//9F0uXLsWpU6cwduxYq9X4yCOPQCaT4YsvvsD69esxfvx4s0MkETUNDHZEZJNKSkqQmZlp9FV1ROutTJo0CVevXsWjjz6K/fv3IyUlBVu3bsUTTzyB8vLyWt/3zDPP4H//+x9mz56NM2fO4OuvvzaMSq0apry9vTFixAjMmjULAwYMqDYdiSVrdHNzw8iRI5GQkICMjAyMGzfO7GsRUdPAYEdENunXX39FYGCg0VfPnj1Nfn9QUBB27dqF8vJyDBgwAB06dMC0adPg5eUFmaz2X33h4eHYuHEjvvvuO3Ts2BErVqwwjIq9eR69CRMmoLS0FOPHj6/XZzSnxgkTJiA3NxcDBw5EUFBQva5HRI5PEKuOoSciomreeOMNrFy5EmlpaUbbP/30U0yfPh2XLl265cTGffr0QUxMDJYsWWK1Ol999VX88MMPFl+yjIjsB5/YERHd5IMPPsD+/ftx7tw5fPrpp1i0aJFRH7qioiKkpKTgzTffxDPPPGPyahUffPAB3NzccPz4cYvWe+HCBbi5uWHhwoUWPS8R2R8+sSMiusn06dOxYcMGXL16FaGhoRg9ejQSEhLg7FwxkcCrr76KN954A71798amTZtMWsorPT0dWq0WABAaGmrRpcvKyspw/vx54HpzcUhIiMXOTUT2hcGOiIiIyEGwKZaIiIjIQTDYERERETkIBjsiIiIiB8FgR0REROQgGOyIiIiIHASDHREREZGDYLAjIiIichAMdkREREQOgsGOiIiIyEH8P4HLyfCBWSuKAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "leth_norm_fuel_flux = fuel_flux.copy()\n",
    "leth_norm_moderator_flux = moderator_flux.copy()\n",
    "leth_norm_avg_flux = avg_flux.copy()\n",
    "\n",
    "for g in range(ndl.ngroups):\n",
    "    # Group bounds also go from high to low energy !\n",
    "    u = np.log(ndl.group_bounds[g] / ndl.group_bounds[g+1])\n",
    "    leth_norm_fuel_flux[g] /= u\n",
    "    leth_norm_moderator_flux[g] /= u\n",
    "    leth_norm_avg_flux[g] /= u\n",
    "\n",
    "plt.stairs(leth_norm_fuel_flux, edges=ndl.group_bounds, label=\"Fuel\")\n",
    "plt.stairs(leth_norm_moderator_flux, edges=ndl.group_bounds, label=\"Moderator\")\n",
    "plt.stairs(leth_norm_avg_flux, edges=ndl.group_bounds, label=\"Pin-Cell Average\")\n",
    "plt.xscale(\"log\")\n",
    "plt.xlabel(\"Energy [eV]\")\n",
    "plt.ylabel(\"Flux per Unit Lethargy [Arb. Units]\")\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is also likely to be a familiar results to most seasoned nuclear engineers. There is of course far more that can be done. We could use the `CylindricalFluxSolver` to homogenize the cross sections across the entire pin-cell for use in subsequent simulations. These flux spectra could also be used to condense the original cross sections for another calculation, like is done in the lattice physics calculation chain."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}