{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Muon in Cu octahedral site.\n",
    "\n",
    "This example shows how to use the Celio approximation as implemented in UNDI.\n",
    "The simulations that follow reproduce the results of Phys. Rev. Lett. 56 2720 (1986).\n",
    "The expected level crossing resonance discussed in the paper is reproduced."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "try:\n",
    "    from undi import MuonNuclearInteraction\n",
    "except (ImportError, ModuleNotFoundError):\n",
    "    import sys\n",
    "    sys.path.append('../undi')\n",
    "    from undi import MuonNuclearInteraction\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define lattice structure\n",
    "\n",
    "The octahedral muon site in Cu is defined below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "angtom=1.0e-10 # m\n",
    "a=3.6212625504 # Cu lattice constant, in Angstrom\n",
    "\n",
    "Cu_Quadrupole_moment =  (-0.211) * (10**-28) # m^2\n",
    "atoms = [\n",
    "    \n",
    "    {'Position': np.array([0.5, 0.5, 0.5]) * a * angtom,\n",
    "     'Label': 'mu'},\n",
    "\n",
    "    {'Position': np.array([0.0    ,    0.5   ,     0.5])*angtom*a,\n",
    "     'Label': '63Cu',\n",
    "     'ElectricQuadrupoleMoment': Cu_Quadrupole_moment # 'OmegaQmu': 3.2e6 # s^-1\n",
    "    },\n",
    "    \n",
    "    {'Position': np.array([0.5    ,    0.0   ,     0.5])*angtom*a,\n",
    "     'Label': '63Cu',\n",
    "     'ElectricQuadrupoleMoment': Cu_Quadrupole_moment, # 'OmegaQmu': 3.2e6 # s^-1\n",
    "    },\n",
    "    \n",
    "    {'Position': np.array([1.0    ,   0.5   ,     0.5])*angtom*a,\n",
    "     'Label': '63Cu',\n",
    "     'ElectricQuadrupoleMoment': Cu_Quadrupole_moment, # 'OmegaQmu': 3.2e6 # s^-1\n",
    "    },\n",
    "    \n",
    "    {'Position': np.array([0.5    ,    1.0   ,     0.5])*angtom*a,\n",
    "     'Label': '63Cu',\n",
    "     'ElectricQuadrupoleMoment': Cu_Quadrupole_moment, # 'OmegaQmu': 3.2e6 # s^-1\n",
    "    },\n",
    "    \n",
    "    {'Position': np.array([0.5    ,    0.5   ,     0.0])*angtom*a,\n",
    "    'Label': '63Cu',\n",
    "    'ElectricQuadrupoleMoment': Cu_Quadrupole_moment, # 'OmegaQmu': 3.2e6 # s^-1\n",
    "    },\n",
    "    \n",
    "    {'Position': np.array([0.5    ,    0.5   ,     1.0])*angtom*a,\n",
    "     'Label': '63Cu',\n",
    "     'ElectricQuadrupoleMoment': Cu_Quadrupole_moment, # 'OmegaQmu': 3.2e6 # s^-1\n",
    "    }\n",
    "]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Set Electric Field Gradient\n",
    "\n",
    "There are two ways of treating quadrupole coupling with UNDI.\n",
    "One can either explicitly set the EFG tensor, or specify 'OmegaQmu'\n",
    "that assumes that the EFG is only generated by the muon, which is\n",
    "the case for nuclei occupying positions with cubic symmetry.\n",
    "We opt for the first option here since the latter is deprecated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "elementary_charge=1.6021766E-19 # Coulomb = ampere ⋅ second\n",
    "\n",
    "def Vzz_for_unit_charge_at_distance(r):\n",
    "    epsilon0 = 8.8541878E-12            # ampere^2 ⋅ kilogram^−1 ⋅ meter^−3 ⋅ second^4\n",
    "    elementary_charge=1.6021766E-19     # Coulomb = ampere ⋅ second\n",
    "    Vzz = (2./(4 * np.pi * epsilon0)) * (elementary_charge / (r**3))\n",
    "    return Vzz\n",
    "\n",
    "def Vzz_from_Celio_PRL():\n",
    "    # The value used for the EFG is taken from PRL 39 836, that reports\n",
    "    #    q = 0.27(15) angstrom^−3\n",
    "    # (4 pi epsilon_0)^−1 (0.27 angstrom^−3) elementary_charge = 3.8879043E20 meter^−2 ⋅ volts\n",
    "    #\n",
    "    # the factor 1.02702 appearing below is only used to obtain exactly the value\n",
    "    # used by Celio in his pioneering work, namely omega_q = 3.2e6 s^-1.\n",
    "    #\n",
    "    Vzz = 1.02702 * 3.8879043E20\n",
    "    return Vzz\n",
    "\n",
    "def gen_radial_EFG(p_mu, p_N, Vzz):\n",
    "    x=p_N-p_mu\n",
    "    n = np.linalg.norm(x)\n",
    "    x /= n; r = 1. # keeping formula below for clarity\n",
    "    return -Vzz * ( (3.*np.outer(x,x)-np.eye(3)*(r**2))/r**5 ) * 0.5\n",
    "    # Final note, the last 0.5 is required since\n",
    "    #  that the formula \n",
    "    #     ( (3.*np.outer(x,x)-np.eye(3)*(r**2))/r**5 )\n",
    "    # \n",
    "    #  would give for p_mu=np.array([0,0,0.]) and p_N=np.array([0,0,1.])\n",
    "    #\n",
    "    #    array([[ 1., -0., -0.],\n",
    "    #           [-0.,  1., -0.],\n",
    "    #           [-0., -0., -2.]])\n",
    "    #\n",
    "    # thus the largest eigenvalue is 2 (absolute value is intended),\n",
    "    # that multiplied by Vzz would give 2Vzz.\n",
    "\n",
    "\n",
    "for idx, atom in enumerate(atoms):\n",
    "    if atom['Label'] == '63Cu':\n",
    "        atoms[idx]['EFGTensor'] = gen_radial_EFG(atoms[0]['Position'], atom['Position'], Vzz_from_Celio_PRL())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Polarization function\n",
    "\n",
    "The muon polarization is obtained with the method introduced by Celio."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:undi.undi:Hilbert space is 8192 dimensional\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing signal 4 times with LF 0.0 T..."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1..."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2..."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3..."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Hilbert space is 8192 dimensional\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "done!\n",
      "Computing signal 4 times with LF 0.001 T..."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1..."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2..."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3..."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Hilbert space is 8192 dimensional\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "done!\n",
      "Computing signal 4 times with LF 0.003 T..."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1..."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
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      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2..."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
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      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
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      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3..."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Hilbert space is 8192 dimensional\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "done!\n",
      "Computing signal 4 times with LF 0.007 T..."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1..."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2..."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "3..."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
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      "INFO:undi.undi:Hilbert space is 8192 dimensional\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "done!\n",
      "Computing signal 4 times with LF 0.008 T..."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "1..."
     ]
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      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3..."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Hilbert space is 8192 dimensional\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "done!\n",
      "Computing signal 4 times with LF 0.01 T..."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1..."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2..."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3..."
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n",
      "INFO:undi.undi:Adding interaction between mu and 63Cu with distance 1.8106312752000003e-10\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "done!\n"
     ]
    }
   ],
   "source": [
    "steps = 200\n",
    "tlist = np.linspace(0, 16e-6, steps)\n",
    "signals = np.zeros([6,steps], dtype=np.float)\n",
    "\n",
    "\n",
    "\n",
    "# import matplotlib as mpl; mpl.style.use(['bmh', 'paper', 'paper_twocol'])\n",
    "\n",
    "LongitudinalFields = (0.0, 0.001, 0.003, 0.007, 0.008, 0.01)\n",
    "for idx, Bmod in enumerate(LongitudinalFields):\n",
    "\n",
    "    # Put field along muon polarization, that is always z\n",
    "    B = Bmod * np.array([0,0.,1.])\n",
    "    NS = MuonNuclearInteraction(atoms, external_field=B, log_level='info')\n",
    "\n",
    "    # rotate the sample such that the muon spin is aligned with\n",
    "    # the 111 direction (and, just for convenience, the muon position is\n",
    "    # set to (0,0,0) )\n",
    "    NS.translate_rotate_sample_vec(np.array([1.,1.,1.]))\n",
    "\n",
    "    print(\"Computing signal 4 times with LF {} T...\".format(Bmod), end='', flush=True)\n",
    "    signal_Cu = NS.celio(tlist,  k=2)\n",
    "    for i in range(3):\n",
    "        print('{}...'.format(i+1), end='', flush=True)\n",
    "        signal_Cu += NS.celio(tlist, k=2)\n",
    "    print('done!')\n",
    "    signal_Cu /= float(i+1+1)\n",
    "    del NS\n",
    "\n",
    "    signals[idx]=signal_Cu"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "...and the results is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1,1)\n",
    "for i, Bmod in enumerate(LongitudinalFields):\n",
    "    color = list(np.random.choice(range(256), size=3)/256)\n",
    "    axes.plot(1e6*tlist, signals[i], label='{} mT'.format(Bmod*1e3), linestyle='-', color=color)\n",
    "axes.set_ylim((-0.1,1.1))\n",
    "axes.set_ylabel(r'$P_z(t)$')\n",
    "axes.set_xlabel(r'$t \\mathrm{(\\mu s)}$')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exact solution\n",
    "\n",
    "This takes a long time and requires quite some memory!\n",
    "Results have been stored for comparison.\n",
    "Set `RUN_EXACT_SOLUTION` to True to recompute it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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HBvq7U2e28MzarQwdOpTevXuj0+lYtGgRw4cPp2fPntTU1PDGG28wdkBf+nk5Uak38NH+E4zq0Ylodwdyymv5cOtuJkyYQLt27cjPz2fp0qXcdNNNtG3blpycHD777DNmjhxKe0cbUspr+HjnXmaPHkyEvYak0lq+3LWX2bNnExwcTFJSEt988w1z5swhICCAhIQEVq9ezb3jRxGkkjlRWM6qfYe5f/xwvJQSxwsq2HDoKPfcORdXFxdOn4lj646d3DNvLo4O9pw8fYZde/fy0MQxGCvKOZlfzC9Jqdx6U3cUBSbOF1ZxMjWdObdPQ1mv4GTcOeLOJzBv5i3oanWcOhfPhbQ05o0ZwYWE86SWVZNdVcaQyeHoj9aRWaknr6aCiTePwFRo4vS585SUlTNl7BhKSko4fT6BqtpaJvfryfHjx8mtq6dGVU+HUV5UbKmg2AQGGzMDRvVAn2LgbMIFkCRuGDKIrKxs4hIvoFKpGNWzK9t37KRKqUR2UxAy3IncZXkY7OxQe9oQO6g91SeqSUhJw83Vhf69e5GYeIHzycl4urvTt2MMG9ZvQG9vi12wLd49NOR8nku9oz0uoc5Ed2lDxYkKElLTCAkOolNMDIkJ5zmfkkpYSAjRwYFs3bIFnZ0Gj3bOuLZSk7Mqh1o7DQHtfYkIb0V5XBnnklLo0C6a0OAgzickkJyeSaeYdng42rN58xYkDye8erhga68g8/sscLMnpEcQAW6+5J0oILegkK6dO+Pi4szpM2coKa+ge5fOmOoNbN22DecQL9wGOqGolMn8MQu7QBdC+wfhbnIj82gWdQYDPbp1Q7ZYOHXmDEaTmZ7du5Gfm8u+/ftxbeOF6wgnzPFGsn7OwTnSjVaDQ3HIsyf1WCo2Nhr69OlNaUkJcXFnUdnY0L9PH86cOc2ZuDic27jhdqMzhp16is+Wog21I2pUW9QJKjLPZ4EkMWzoELIyM0lKSsYsy4wcNpR9e/aQV1CA7KnAd6YHNd9Uoy8xUu9spvtN3bCcMpOZkkWtro7JEydwITGRtLR0aurquGn8jWzcsIEavQG9g5HAOzwoX1KB2aykzsbAgFv6YjhpIDk5lTq9nikTJ5KclERiUjJ6g4EpY0ezds0a6pVKDFojIbPdKXq/CIuNLfUaE4On9EN3to64c/HIwMRx40hLS+XkmTiUSiWTRgxj1apVGGxskJwUhE5zI+fdHAwaLRoXDQNv7EttYi0HjxzFN9yDl957mX6thzTaZ+FfJfDmNJFLi9OhQwc+X/EtOzeuo06dz7HNyfRY0oP9B/YT4hvSKOdQ2NgQMmUK86dMQbZYMOblMejNN2mdBcfOfEL3bt3Zl3iavMI8onsGoa0PRadOZUNNOfWFhQQtXoyypIShM2bgMnkyCju7K46pjU8bPn/uc8beMJYVGSt4fP/jvPLKK+jO6Nj04yYC/AKu+BwGk4Hd6fs4fOowe1bs4fiB4zz86MOo/O0Z0b0nN/S7AX///31RuufVNy7Z/8mnn6a0uIiqkmKK8nJRPPwAns7OtA30o95kokdmMZ27dGbIDSOwSArOyVo6dehAu+hoLBYz5nvvoU14GJ4e7uTk5TJ86EBC2gRSrpZJikvB29eTGlcLKcpKSouriO0ag9pVT3FJMoWp+YwfMZxAN2fKszLIT01lzNDBePv5k1FRQnpJKX37xqIO1lKot6ArqmfokD54etggGcpxVslMHnsDId7O2ClMhHi6Mm3ijcT27I6bvT1yRiZ6e2d69BuEh6MDqgvJ6NRa/D3csdVoCfX3p3e3rng4OaDRaAjw8aZzTAz+AQFo/Xyp1mZRaZFo5xaFybaWCimPIp0Be5UDklrC0dERR0cHJLUN9i422Ds6oraxQV1XRbSPB5UWiaLaOqIKPTD71lNpKaO4tg5HvJC9QZ2WiaG4BIvWFreAQBRp6dSWlmFTVkjvEH82peVTVWWiS5IrhLuyITWf2lod7nIQhMHZlHRqamqwaGwJiGjNmZQ0aurq0BRkMbZ9G749n46lQkHfOA+I9WDFuTTkChV+pnDoAGdT0qiu0yNrbGnToQNxycnU1tVhX5DJtB4d+exkIpoSGwae94ae3iw5dh5FhZYARWsCusLx+PNU1+lROTjSrmt3jp6Np7amGo+KAmb06szbB07iWGjHIJUb9PLmjX0n0FQ5EaBtTUA32Hv0OFV6A7au7nTs3pMDx05QXV5KF1U9d/TrxqLdv9AuI5C+Xk7o+njz9u4jtCt3IzQkCq9uwRz79FOqDQZCvX3o0sOOzz77jHZBfnR11uLfrzsf7D1KN58QOrvYUtDXm6U/H6ZbVA/atGmDW1cfVq5cSUyHjoSHh4Pahm+++YYuwX70cVDi1zuW5QeOM9Q7nHB7NUm9fPh63xEGxQwmICQAR7ML69atI7ZbN8LbRCIrlGzYsIH+of7c4ONEgLo9Pxw9zUS/tnh7SJzq4M2Pv5wkomcbXCNdURk17Ny5E5NFJjK6HXqjid27d2OTncqEVj4ctrPh57OJ3H64I3ahFg7aVbDvXCKta9qijlKjrzVx9OhRUKpoG9OeKl0dWSdPYpeVxNR2rfg5p4QzmTmMO+CP1M6Pn/LKSczNJ7QuHNpCaVklmZmZoFASERlJQUkp+fn52GUkMLNLFNuyiiiq0THqsC/E+rI1u5gynQG/ugAIh9y8Amp1tUiSRFirMLJycqnXG7DNvMDsnp3YlFGIRVIw7Jgn9PLmx4xCFDYavOo8INiDlLR0fE0aPGuuTi/o74kWeCP49NNP+OKLLzHZVGOsUjFy8kjumn0XgT6B/7zzv6Q36Vm0dhEXNl5g+47trFm/hn49+nHs2DEyUnKJTzjLh0veo31UF2ZNn86BY/v47PPPeaxrV25X2+B+++24Tr0ZxV+McP+3LLKFHRk7eP7p58k7mkf4S+GMDh+NdEqiR7sedO3aFZXqn78n1tbWUqYr43TVab7f+D1bF25l6pSpuLm7UaArACO8+MSLeHn+98GCV4Msy+hMOsr15dQaa6mqriI/Nx9bR1sUCgVmoxnZKBPgH4CzgzNutm7Yqmyv2+vrsiyDLGOxWJBlGVm2IFss8A+fQ/9/icJiNmOxmJHNFiwWCxazGdlixmKxNCymIEm/eW+lhv9+U5akhjrIcsP5fz3G/8fTEJsZi9mCQqFAUiguHlOlUiEpFFh+jVUhKZBlCyazGdnyv9dh+fWxRbYgm2Ussrlhf2VDD1W90Yji17IsyxhNpl/fC7nhdcmWi++LxdIQo0IClVKJ2WzGUG9EpVKiUiqxWCwYjMY/e8N+fY0N751KqUCpkDCbGvZXKxUoFApMJiP1RlPDLvxuQQrpfz/UKhVKhQKzxYLRZMZGpUShVGIyWzCbzb9WvPS9V0gN7z8SqJVKFAolFlnGbLagVitRSA3Hs8gy0m/2bfgVSfDr4FJJouF3IUlYfn1tCklC+nXbb3+v0q+/84vxNPwB/Dps5tdzSFzcfvFlStIl+//+uL/u/f/B/eVx/7+eq18AmkZoLF38VYgu9KvHaDTSJ7Ydkq0rE6Z3oKLcHX2NnrZt2nLHbXc02nmOnDvCwvcX0smvE0ovJfOnzcfV+dLrLFWVVcyZdRdaRzXhrcII9GxNXPIvzBsxHLvvVvP5kSNsMRhYdv/9RM+di6KR7uG2yBYO5BxgddJqDuUeIunuJCLbRDJm7BhUdirWr11Pt57dGDdhHI4ujhw/dhxHH0ccwx3Zd2gfH97+IV1md6Gubx1uRW5kfZLFnAfmMH/mfFwcXRolRkEQhJZIJPCrLC0rl63LXqcCZ8L6+/DKYx+TFJfEwZMHiY3+w/v+r+3M3MndE+8m+1w273z1DvOmzPvbVlx2ej5rV/3I1j3rOHXyNJt/2EnXPu156u67WblhAxucXbB3d6dw7Fi63X0XNvb2Vxzj/yurK2PJ90vILMvEaGNErpLZ8v4WOsZ0pHfP3hiNRl555RU6j+xM/U31aM1aWAODJg1i5tiZtHVvK27tEgRB+JVI4E3g67XrObhzC7qsOG5e/Dwvf/kyDj0ceHfgu0S4RFzWvdy/t3n7ZnZX7mZ73XZa17fm1tBbGTtk7GXtK8syi19+jx9+XMP02OdoPyCIDsP9cHCyo+7oMXLfe5eeW7YQ7OvLO/fdR/ep09C4OP/rGP9JVX0VGZUZlOvLKa0opaKggrT4NPr070NMRIy4F1sQBOFviATeBCwWC93btyYhPZ+zP7xJTafePLD7Acr2lVG1o4qfd/5McHDw5R1LtvD9ie+Z0WsGYV3CuOP9O7i3072olf9+MRNDnYlf1qdycEccr6+byyPzn+bhJ+9FaQNvPvEEefn5eLRpg6KqipQTJ3lizu2EjxqFyrXxboMQBEEQ/hsxCr0JKBQKbrn3Kdokf4znsdcJ7R/H6jGrmbp/KsXGYl4+/TLPuD5DkFPQXx7DaDLy7tfvctztOPFl8fS9ry/P3PoMA2IG/Oe4NLYq+k1tg8qnhq+PBFKWZuLLBQep0qZx9EIWjz72CC66Cj7+6kuW792DOjSE6JMnKczKJi4jnedGjCQ8NJRaBwfsfHxwDAxE5eWJ0sHhP8ckCIIgXBnRAr8K3vvqW+5Nm0duzD0ETHoVk8XEN+e/4cMzH1KfXk/KohTGTxpPp46dKC8rZ8XyFYyZMAavVl7s+2kfO9ftZNjTw5g/az6jQkc1+v3Vpbk1XDhSwIdfLmb11s95+OGHcbR1RVdlwCKZ6NEunKrCfLYeOMi6nTvY1K07AcXFvIHMF0lJ/BzTHm+DgfOursjeXvTu0ROHrrHY9+zZKLepCYIgCP8jutCb0LFzKcybOBCT2ULciV/AueG+6CJdEUt2LGHVolVEdIvAy9+L6qJqDm04RPch3fEP8kdtUlOcX8xHb36EvbbxBpb9lZSEDBJOp5Oalsyy1R+Snp7Gww8+ip9jBL369KRNlwCUKgWyTsfG779nw5YtvDl9OpaiIqYsWcLhhASeve8+vItLKElJITgoiBHTp+M4oH+jjXAXBEG4nokE3oTq6+vpGduR7n6wcEZ3nG754pLnTRYTqRWppFakUm4ox0HtgLe9Nx08O2CrapoJAP5MWUkFm9Zup6amlsKqTL5Y9gVdIvvxxP0v0X5gwCXzrwPExcVx8OBBvDw9yUxN5d2PPsJkMnHPrbfiX1CIs62WQbNn49Cly3V737MgCMKVEgm8ieWV17L57XncrtiE4q5D4B1l7ZD+lZTkFGbOnEVkSAe6OE8EtUxwVw0jp/ZCqf7jiHFZljl//jxnz5xBWVNDQnY2r7/1Fl2DglgWHo7L5Mk4jRkjBsYJgiD8SyKBW8Fr3+/Hds1tuAZEcOubW6wdzn8iyzJlebU8+ejzLPv+XZ65/QNmzp9ISIzH3+5XW1vLO2+8iY9Bz6DkFDLj4ri/TsdTAwcx8tZbse/VU3SxC4IgXAYxCt0K9In7eXNnCf5eZmY8eBJFQGdrh/SvSZKEu78Dcx+eSmldFqFe7dj8YRzl2gQm334DbWJC/3Q/e3t7nnru2YvlEx9/TOaCBRhSU8i5+26O2ttx3sODWbfcQquBg7AJ8Bfd7IIgCP+CaIFfRTU1Ndw2awaRUTHc6JNL57s/t3ZIV8xssnB8WypDp8Xi6+PLS4+/ybipQ9HY2vzjvkajEaXFgu74cW578knWHjjAE088gb3FQurx45SUlvL4jeMJigjHJSwMdXAwKk9PkdgFQbiuiS50K9mwfTfJh7eisBi4e9Y0tK26WzukRrH5x23s3bUfe3cbzHoFCoXEsy89edmzzRmNRk6dPIm5qIic1FQ+WbOGuKQk7p4/H4BdGzeiLytjuasbmqAg8jzcCWoXg3u3rmhjYsQ96IIgXDdEAreS+vp67rxjNj9u3s6swVG8sXqftUNqVId+OsWri19g8/YNPHjPY9w6cxYdurb9T8cyGAzk5+aSnZjIh0s/obS0hBUjb6A+M4PBmzYhSxIbHZ1Akljt4U639h3od9MU7Lp1E9fTBUG4ZokEbkWTb7mVjLO/0LF9DB++/hw2/u2sHVKjqqvV8+bLH4KNEbPCQEp8JsOHjeSW2yYhKRqn+/ujjz6ivraWOT16Uhd3hrDHH6dVWBizBgzAv7AQg8nMsPE34jZ8OCp390Y5pyAIQnMgErgVlZeX8+HbizErNQzyrqTvnW9ZO6SroqZSx7pvtzD/kdm0iYjmnmFvEB7rjcqzlu79OzTqtezz588Tf/YsVQUFJGZn88abbzKiXz9uCQwi2NaWgK5dCRg3FrW3d6OdUxAEwRpEAreyd1f8ABd28POpND5681X8I7tYO6SrJjcnj7gjKcjFLhw7fIrnV8zilrF3Mn/2I0TEeuHu79CoybysrIwvv/wSpcFATX09KRkZrFixgkWdOjEhLBxz927YtG+Pf58+KDSaRjuvIAhCUxAJ3MoKyyoY07cLx86n8fjsMby27Edrh9Qk0pLTefbpF+nZZhRSiTvnCw+wJ34N99/xBFNmjsXZs3HnTjeZTPz88898/N57PNanD15Hj/JeQgLvXbjA2s5d6BwZSUFQEPbBQbTq2g1NWCuUzo2/hKogCEJjEfeBW5m3mwse7QexqKsX94afhfpasLn6c51bW6uIUFaubphKtq66nhef3UvZoWIyys7ywbu5uGoCGDtlCAFtGue6tUqlYtiwYQwbNuzitjGbN1P++ed069qN+pMneemHdWxPSeG1e+7BuaaGpNRU6kwmbh80CK/gYJzDI7AJDUXt54v0H9ZwFwRBaAqiBd6EzuVW8uwHy1ineR5ueAO63WHtkKzCbDZz9PAJ9u3bx/sfvYOzvSsL5ixi6ISe+Ia5XPXz79yxgx2bNtGhdWvKKitZ9t135Oblcc899wCwYc0aDFVVrHF1QxMSQpanB6FduuAZG4u2bVsU9tf+Fy9BEJoP0YXeTAx/dSOhex7hQrGJ3SeS4Tpu4RmNRl595VVSklMJbx2GQm9HTamRh56cj3dI03VrWywWcnJyqKuroyQ7my+++ILKsjI+6D8AQ3oa/davR2Njw3p7B1Ao2OblSUxMe7oMGoh9ly6oAwPFZDOCIFw1ogu9mXDL/InTeUb0RjO1cT9i3/FGa4dkNWq1mueefw6z2czJE6f44P0PWL7yK0qKyrh53Gy6j22Fk/vVX51NoVAQFBQEQJs2beg9ZMglzz/RuTMWnY6Ajh2pPX2GJ554nJjaWibZ2+G6dSs//3KUQVFtuWHgINxiY9G2i0Zh888z0wmCIFwJ0QJvYklpWdzy8jJ2ha3E2T8SZm2ydkjNhsFg4M033qJX+GgS95dyNGMLjr5KXn3zWeydrLfM6m9ZLBYOHDhASXExck0NyampPP3qqwwePJhevXqhLitj1bp13BYezsTItkhBgVgCAvCIbodNaAhKFxfRWhcE4V8RXejNyP2rThGS+BmTdN/hcNt6XCN7WzukZqe6TE/P3t2prK7gmSlf0X1UGFF9fFFrml+nUXV1NdnZ2ZTm5HDswAEWL13KXX37Mt1Qz+H0dKbHn+O5jh25qU5Pkq0ty0xGJrVvT9uAQOxcnHHw9MIlOAi1jw8qb29U7u5ISqW1X5YgCM2ESODNyLoDZ1n45P2cOryfByb3Y/E3P1k7pGbJbDZz4tBZCk7KpMTlsHjzPKZPms0zLz6Jk1vzHkgmyzKSJJEQH88bCxcya+BAopVKvt67j4dWLOe2227Dz8+PxMREVq1axQPTp9PG3oHirEzi0tO528+PUG8fpMBA7EJD0YSGYhMSgk1wkJg2VhCuM+IaeDPSN9KPaUcPM7hPV7Rufsg1xUgOntYOq9lRKpV069sR+sKuTbU47nGirK6Ad959B3s8aRvdmmHj+6JSN7/W6v93k7eNjubzFSsubr/31lu5c+nHVFRUUFVVxalTp9AolbTv1g1DvZEzBfmsu3CBeUOHIZWX88bOHXwaH8/GyLYEGAwcU6nIdLBnTHQ03kFB/0vsISGo/fyQVOJ/aUG4XogWuJU8tfhjnGvTqJPsmdHJjlZjH7V2SC3CuZNJ7N2zj7WbvmH37t088cCLRId1pEvPjkR08Eepavmj+mtqatBqtahUKr7//nu++vJLvnntNcjJYcbChWw5fJgnn3wStSxzZPdu0jIyeHzgQOz0BrKqq5BVam7u2BG1uxsqN3eU7m4onZxROjmicHRq+OnkJAbaCUILIbrQm5kdh05zeOcGqkvyqc45z9K1u0HR/FqSzdWZM3F8+dkKfH18qTNVs2HDj1gMsPjRr4jo4kNgpBtKdctP5r9XVFREXFwcrq6uFBcX892333Lu3DkmT5iAzmTi+++/Jz8/n4PR0cilZcytraXAWM+Pjk4AfKRSolcqmeDnh9ZsoVy24OvpSXBoKGo/P9S+fg0/A/xR+/iIFr0gNAMigTczJpOJ7j17ozFVc/xcMkm7lhPSf6q1w2pxZFkmLzefRx96jLLSCia2f4z6OhMb4t5ncP/h3HHfDNx8m/f18sZiNpvJzMwkJyeHfv36IVssPP344+RkZbHksQVYqqvoc/fdVNXVceuttwLw+eefo1QquWP6dOxqati0axe+ksST9UZQKjnt5oqfrx8RYWENSd3fH5uAANT+/qi8vMRgO0FoAuIaeDOjUqlw9PDGUqvhgQdGknL6oEjg/4EkSfgH+PHNdysBMBstnD2axmPDdqJUg0N5awIiXWg30J9WMV6Ntrxpc6RUKmnVqhWtWrUCQFIoeGXRokvqnI6Px2AwoNPpqK6uJjAwkJqaGsLDw6koL6f4p59QurvjO38+9bm5zH/2WSLLyviqoABTURGTa2uI9vdnbKsw7AwGjuXm0MbVlfbe3tjb2qGytcXO1RWlqytKVxdUbm4oXV1ReXqi8vZB6XB9fJkShKYgWuBWdPB0Irs2rMbbRkeVQeLB+XNQe4ZbO6xrQkVFBdXlOgoT6lmxYgUrt7/LvdOe5abpE2nTzQ/FNZzIG9OKFStwdXVl9OjRmPR6evTsSauQEDp17ozeZOKll16iT58+DB48GIvFwksvvcSETp14qVaHSZa5Ta9nrJsrk+r01AM7Hexp7+1DKx8fbL29UXt7ofb2QeXjjdrbG5WPj7hXXhB+R7TAm6FeHdqw+UcNSaVVbNuylfrCCzy95Adrh3VNcHFxwcXFhcBQSKlsza4z3phcilizZTm6rxSMvGEEvW+IQam89q6TN6YZM2ZcfKzSajl+6tTFsl6vZ8yYMciyjJ2dHeXl5WRnZ9O/f38ip02jMC2N7P790fXoid8NN5AQf45Hn3iC0aNHExsUSG15Ocuee46JvXrR3ccXY2UF+xMTGW1rR6yrK2YPDyrdXAkMCsLG2/vX1rwbSjfXhsdubmJ5WOG6JlrgVjZq8gy2rv2GsGB/RsZ48N66w6ASH0qNTZZlUlNS2bV9Dy+++iwSEo/MeZluPWLpMTT6mhzw1txUV1ezbds2XF1dsbOzIy0tjaVLl9K3Vy98vLxITE5mydKlvDRjBrM9vfgpMYFbt2zhhS6xTK6p4YjGhoUlJUzt1o1we3sqysqJy8tlSGgofi6uKNQqZK0twf5+2Hp4onR3Q+XujtLVDZW7SPhCyyVa4M3UzJnTya/U8eS0AUzKeBrOb4D2U6wd1jVHkiTCI8IJjwgnom0ou7btplqZw/Yj6cy+dzJTxt7KI4/fj4t3465PLvyPo6MjkydPvlju1asX06dPv6TOK6+91jA+xNGRHklJPNimDeNnz6Z1UBAJa9civ/IKxlatyHN15URcHN+dOYOqVy+8vb05e/Ysa9eu5fOevehZVsaPSiWfVpTzjocnYQYDv9jYcFCpYHREa9wdHTApVShttYQEBGLr4Y7KxRWlszNKFxeULs4Nj52ckNTqpn6rBOGyNFkLXJKkEcC7gBL4TJblhb973hlYCQTR8MXiDVmWv/in47b0FjjAsLf34qpVsdp4L+drnIh6co+1Q7ou1NbWsvbbH3nyuccY0nUCXX3G4RggU2mTzu13zcDOUbTWmjOTyUReXh5qtRqj0cj58+fZu3cvd999N34uLnzx6ae8+fHHrHnpJfwkicdXrOSTTRtZsGABtra2HDhwgF27dvHEE09gq1Jx4sgRjp46xdrAIFx0OtapVBw0m1nk4IDW0ZFjWi05SgX9IyOxtbfHYqPB3sUFNy8v1K4uKJ2cUDg5Nfx0dEJhbyeu5QuNwqq3kUmSpASSgKFADnAMmCrL8vnf1HkScJZleYEkSZ7ABcBHluX6vzv2tZDA39h6jqVfrGSAfIIv1v3MhUObCOs+0tphXTdkWaaqTEfy0WIWv/sy323/nEenvUOvLn3xj3KmdRc/nD2bx2Iqwn9nNpvJz8/H1taWuro6Tp48ydGjRxk+bBh1VVXs3LGDfQcPsnHRYjR1ddz30Yes27+fC088AZVV3LZzB3sTEnj88ccB2LRpEwkJCTz66KOo6+v5efduCgoKWKW1RWmx8LmNmgK1muc9PFA6OvGT2YROo6V76wg09vZUmS04uDjj6+eH1sUVjYtzw4Q7jg4oHByQtFrxBUAArN+F3g1IkWU57ddgVgHjgPO/qSMDjlLDX6wDUAaYmig+q4pQlZPy/eu0nzSJu0e0xTF1E4gE3mQkScLZ3Z7YkfZ83H0xHT9ozYD2o8iIK+XBp+8kMz+JBXMWEhPTjnY9Q3HzsxcfrC2QUqkkICDgYjkgIICxY8deLA8bPfqS+l+NHsVXvyl/cMcc0tPTiYiIQK/X4+3tTVpyMn06daauuooLycmYAb8HHkCuruH4B++Tlp+P7YCBmKureG/XLkr0eua1jQS9nuXLl2MwGLjjjjsA+Prrr9HIMt8pGz6W77WY0dja8q67BwoHB54tKcbOyYnhnTtjo1ZzJCkJDxcXukVFY2OrJb2oGC9PD7q274DC3p7cykqcPDxw9/dDYWcHkiT+bq8xTZXA/YHs35RzgO6/q/MB8COQBzgCN8mybPmzg0mSNBeYC1xcx7klGze0LwPmPoeiXV/eC1wH8T+A/lXQOls7tOuOq5srTzz7GAA9bwznrK47x45JlCqS2BOfxJOLdxPkGcGds+8nplfodTNJjADh4eGEh//vNs/IyMhLnh99yy2XlPfcftsl5W/j4ykvLyckJASDwYCPlxe6igq6d+iAobqGvC5dUMoyPjfeiKWmBvWnn6JWq7Hr1g1LbQ2/nDqJo4sLwd26YZIkPt6xAz8/P6p8fAB4++23aePjw5c0JOkeOdl08PdnqdQwQLNvUSFRUVEMHzgIBTJLli2jQ1QUg7p3RylJfLJ6NYOjoniye3fQaJn+3WqGderEnP79MSmULFi9ig5RUUS3bo2sULDv6FGiWrehVUgwFlnm7IULdGrXjg7R0RiMRrbv309MdDThYWHo6us5dvo03j4+uLi6IksSBoMBR0dHNBoNSqUSpVKJWq1GpVLx/z3D4gvH32uqBP5nv4Xf990PB04Dg4AwYKckSftlWa76w46y/AnwCTR0oTduqNYxbvI03v0pmcJBU/nu2234ffA8Ex9529phXfdeXfgyAKWlpZw6cYaVK1aCysiec2s5cMKJzLRs5sy5gy4D2lwT87ALV090dPQl5bC77rqkPPCmSwevbp0z55Jy8vvvX3wsyzK3z5mDUa/HUaPBUFVFmLs7LlotQe3aYdHpuGflSoJd3fCKisKi09F/9WrCfH2ItFgwm834Ozrhp1TiVluLWZapq67GkJ9PxZq1GOrqOJKRjm9tLQW791ApSXyRmMDQqioqVCp0Oh2L3nuPESNG0KNHD6qrq3nzzTeZ3SWWR2tqyLaYmZyczN0dO3JPnZ7zKhWT4s8xfvx4OnToQFFRER999BGTJk2iXbt2FBQU8Nlnn7Ggd29utcgctZi5Ky6OZ7p1Y4JGy36TicdPnWTC6NEE+fuTlZvLxm3bmDB6NH7e3mRkZ7Plp594qU8fBtjZs7O8jEWnT7Oobz+6ODuzuaSYj0+dYuKwYbg5OZGWlcXB06eZMHAgzvb2pGRncyw+nuc7diRUUrCluJjvc3NY2DYKL0libVkpP+bmMWnAAGzUKs6np3MmNZUpAwaiUiqIT08nPiODt8LCsa+rw/fFF7Dt2LFx/4D+RFMl8Bwg8DflABpa2r81G1goN3z1SpEkKR2IBI42TYjWNSrGl0/eeIkHyz3Yur2EyMTNTHz4LRDfQJsFd3d3hgwbRHJKMsXFxcSdPseWLVv4dPXbFJUUMnb7nUT29CG6nz/OHmIku3B1SZJ0yeUAgOm/+4LwyqBBl5TX3nvPJeUpC1+7pHzbO+9cUq4yGrHo9ch6PWa9npKyMhRmM2pZxlBdzYSoKJzt7HG01aKr0xP7/PNE+Pri6+GJo66WD44eo1NwEN6enqiqqnn52FHaB4fg4+REKRKKUaPoGRSEn0pFob09Zd270yUqGns3V/xKSulRU0OrgAA0zi64lZYQ4uJCK1km0GAAkwkPrZZAoxF/XR0GgwEnhQI7Qz1miwVLVTUWvR6Ki6kvK6W6opLCoiKU1dWolEqqyspISk/H2L07ZrWawpISjickUBcSilmlJL20hCPx8ejDwkGtJquqihMXEhk7cABKpZLc8nKOJSRw45AhWFQq0kpK2H/2LIqu3VArFUhNdLtiUw1iU9EwiG0wkEvDILZpsizH/6bOEqBQluXnJUnyBk4CHWRZLvm7Y18Lg9j+X1BYG2w1Njx3xzgSyxXcP7EP7h2GWTss4S9YLBY2btyIp30I5UkSazd9zZbjy3nu7g8YfmM/gmPcxUQxgiBcMasOYpNl2SRJ0j3AdhpuI1smy3K8JEl3/vr8x8BLwJeSJJ2loct9wT8l72vNnCcWIufG0XbgWFI3/MDxfdsYLhJ4s6VQKBg3blxDYQhkWQ7zS4YHqlpXtn58lvNl+/AIsOe+R+7E3c/RusEKgnDNETOxNSOn0gtZ/9VSPMPaUXhkLct/3MOZQz/jEtjG2qEJ/4LFbCEzvowBo2ORsTBn1jwclT6YZSM3ThpJWHSQGJwjCMJl+6sWuOjfa0Y6hnix51gcb76wgA5d+2CWJfas+cTaYQn/kkKpILS9B/Hnz7Hkg6X4+wRRYcrh6YUPMGXGBN58filrPt3Fif0JmIxma4crCEILJaZSbUYkScLF04fi9PPE9BnOU3dnUlijRzYZkVRiOseWxsHBgVFjG+7nr6+vJzwsjKz0PAzKcg4lbGHKvHe5ecQd3DL6boKi3QiJ8cDRTWvlqAVBaClEAm9m7n/wYfav9+RQXBJd27dh/ZFUzmz5jI5j7/rnnYVmy8bGhhmzGub9tlgsHDt6nKz0XPrE9qU0t4atOzex5uD73DvlZQYNGUCrjp54BTuKrnZBEP6SSODNTL92wWxcb4fu/DluemAew2YEcXCrN7tFAr9mKBQKuvfoxpofVgMN9/SaP01hxzkngnyDObUji48+eZ+M4nM8OPdpuvdvj2+4q1jDXBCES4gE3syolAqSk1PZtuoz7pg2kXmTBxNSfwEKzoFPO2uHJ1wFkiQxe+5MZs+dCYC+1sjemZ+RlHWOuNw9xK84QnJ8JsEBrbh97mwCI93EpDGCIIgE3hwNGT6CrPQUTqUV8to7n8BbbeHYpzDmXWuHJjQBrb2a1Wu/pqamhsTzFzh94ixLPn8Pe3t71C5GbE2e6PU6xowfRXS3UNQapbVDFgTBCsRtZM1QXb2ZTi/t4OauQTw/NpqcL27j3e/28urqw6idvKwdnmAF1dXVHD58hLysQlLSL/D6ooV069iHmT2eIzDKDZ1tLqMmDcLWQSyBKgjXGmuvRib8C7Y2SvqEe7B5+y4eGhDIdznevLEtje5LX2LSo+//8wGEa46joyPDhg0FQK/X07pNBLYKF7xVfuzfdZinP5/F5G/mcNOQO3ENVqNy1tNrcBdUatE6F4RrlUjgzZR7wVGOf/QA74bCo48+R2fzSfqr9oLFDArxoXw902q1zJw582I5vK8DFU4L6BI+ALla5uuvV7Js42Lm3noPHSN74OnpQWT7MKI6t0IhpnYVhGuGSODN1H23T2fbgROYfduj1WoZMGkerJkNyTuhzQhrhyc0I37+fix+a+HFcugxJZJbFRGtwykypLJu1Zf8dMdPPPXAy4T4tcbd043Y3jH4h3mI29QEoQUT18CbsZuWHqZCZ2T7g/2wGA2M69ceLzcnPt98zNqhCS2EwWBg88atbNywiaioaHT1VWzYsIGUlBTenLueoEgvlC46OvZqg7uvk0jogtAMiWvgLVC/EHs++ngpP0aZGTt8IBVmLZVlYCpIROUTae3whBZAo9EwYdKNTJh0I9AwGM7DzYuzp+MJifYmJ7GcF765FYVC4vlbluMf6UqNIpe+Q7vh5u1k3eAFQfhbIoE3Y7H+9iRsWMKHcjFjhw/ky2XLWLl2E/E7ltNh5qvWDk9ogRwdHZl/7/8mBZJlmXzHuVSX1eEZ7EjqqUIe+uRGWke04ZYb78DXO4Dq+jJG3TiMgGAfK0YuCMLviQTejHVvF8a0ux8lwNsDgFbRnfHY9AObT+YQM7kSha2zlSO8jlnMUJ4BRQlQkQV15aCvaPhp0mNRaKlXaNDYOiBpHcHJH5wDwfnXnxoHa78CoGESmSefXnCxrNcbKHB8grpaAwZlJWcy0lm0aBGDNw5hSO9ROGidiEs8xbSp0+g7uDtKtRgUJwjWIhJ4M9emcy8s2afJLigi0McLJCVPvbuCYG9nbnlC3FLWZOoqIOMApO3Bkn2MHXH5KOR6hnmXU2dWMOJHF2LaRhAd3Y7SOmdeXPweffr2ZUj/XmiMhXz69UfM6e7CI5G56E0yi5NCGdk5iNiOMeDZ5n//bF2t+jK1Wg3PvvgU0NA6z8vLx8ctANmsAEnmbNpRPl2+FH05JGzUU29XyvrDS7nnjocYMLQvrj72YspXQWgiIoE3cz07RfPqynfJq6hj6dsLuXX+o2zYvpvK6hqwWEAhWkBXTXkmxH0HSVvJTEkgvdaWAb566r06Me7zDEYM6MWwp9aicQkm8ZNo/KM9cGvdHX9bW8ZPyGHo0KEEBgaSm5ODrN6GMXwETOxFyqnjPPvK69Qr7Ig1LeNMiYIbvq3ntuHtGdTWEzt7ByrMWnr0HYhzRI+G1rsVBpdJkoS/vx8PLrj34jaLxcLsmbejMNhiqtKyfssRDh8/QNegURQc1nCueDfbjn/L/NsfoXPHTgSH+RHc2heVWnzUCEJjE6PQmzmT2YKvfwAhYeEcO7gPgP3ff8TP54u5c0QM3t0nWDnCa4y+Es6tw3hqNb/Ep6J3aU2KTRTPv7cCJ0dHLpw/h6TWsGrVKrp27UpYWNi/PkV9fT1nz57Fx8cHf19fDv/0I/MfeZrB/fvg6O5Dalo6y5cvZ+bMmXQOdcdQmsnRsyk8M70fHbr1RfaOQfKIAGXzSIp1dXqqSwyU5epY8c0XfLPhM6bdMhUbjQ2HDh1iz549PPvoa/h5+VNn1OHgquWmWyai0dhYO3RBaBH+ahS6SOAtwMNvLcexOp2HH34ERwd76mqqePihBzAWpfLp+r3WDu/aUJENRz7CfGIlp4zBzPuhnJSMHB5++GGCg4MpLS2lbdu2jBgx4qreamUymUhJSWHH1k208nHGUF3Otn1H+XL1Bnbd05r+zjksjnPh1Z/K2fdYF2LaRXGqyoMsvR1Dx92EnWewVVrrv1dXpyflfAYb1v/IwcP7GdB/EHpzNRs3/Uh8fDyLb1uPu7cLuxNXUVZTwOKX3sPd3wGFxoy9g724nU0QfkPcRtaCxXZqT9K+dH7+5QzjBvfC1sGJ/Iwkdh48xatnf8YzZpC1Q2y5aopg3xuYjn7BOwnuWCKnUaewY/goA1Ocnbn33nuxs7NrsnBUKhWRkZFERv7vNsGJc+HDZfUokaE8lYCVXxKTvY1QLwdI2s7bmyVW7kvlycxqPNQGkhPPkZlTwPN3T8bDN4g6pROOfq0JCGu6Ww9tbbXEdIkkpksk8BgAJqOJYQNHcvzoKbqEh1OaV8PZCyfJLcpky5KzALz/033UGWp4aP7jODu5kJh0lgBfTyaNG4KXuxaFxQRmA5jqwVyPbNJjNuiRLAaUWJCNenS11dhIFtSSGYuxjqqqauxslNhobRtmMVSoQaECpbrhn8oWVBpQ//pTZQtqLah+80+t/V898eVCaCZEC7wFqKitZ+iQQchIHD+8H4DM5HjklZMIadcdJn9p3QBbIrMRflkKexaCUcd2m5GMePIbpk6dygsvvEB4eHiLaQUmnjrCoZ+3Eu7jSHFpGV/9uJdj51K48667AVi/fj2pqamUPeWNytmHOzfrSS8zsv3VW8DJl4+3xlFlkBk7ehRqW0cSUrNR2Wjo2q0barWanJwclEolbdq0ASAzMxOlJBHg5w3mejLT0zCb6vFyc8ZsNHDydBxqpURYkB9mYz3bfj6Ap7OGcT3bgL6SB95dS4SvE/MH+IO+ipGLj9OuVTQdW7VnW9xpKur0dOvWA1lVzwdL3sPNzY2pU6eCLLFy+XJcnbwZ0bonN4VksDMzlzf2FNAhJoQBfbpRZ6jnuYXvcMPQgfTt1YManY5XFr/L/BFRfNA9h8xqBa3eruTJ0a14qXMx8ZW29Pm8mmnDu9MrOoiKyireW7OPqQPaEhvmSXllNV/siueBHjaM9S8nrVrJwhOOzOmsopufiuw6LWsvyAxo60mghyP1FomCWmgd4o+9iyey1gXJzrVhcKLWpeGnrUvDYxt78WVAuCyiBd6CudjbgJ0LxppKZFlGkiSCI6Kh9yQ4/AGm4hRUnuHWDrPlyD8D6+/m04NFJJnDWPz+5wz3COebkNFMnjwZlapl/W8R2akHkZ16XCxPvK9hsFllcS5lWRcItteTnZmJqq0HVOVRrbtAdY0edr8MwEdfO1Kqk6lTNNza9tVXX2Eymbj99tsBWLZsGRqlTNIcM1hMDFxiwcFOS9wtVQD0WqLGyc2Tm2++GYAPPvgALy8vpkyZAsC7735AmwA3xuUVA7B8k0yXcG/mexwBjRNJ+eXgkIN/dDDdeoby+cq1OCUaGNCjO8/eex8Hj17AplqNj6c7vp7+ONt74e02gt2VEo9vGEWnqB6MDH8aZbmZ99fO5Yah4+jXfSDOjo6kZhxj5i2z6TdmJJaJ47EvKWJ8+j10nDIRxoxAk5xMhxOP4BLWmTqvQCooRmF3jmK7NiRqQ8krLyQu/yTpnqNgcCQXjibz6VtL6dx1Mt1ae3PwSC4Pfv0DM2fOpJWpFampqaxYsYLbZt9KRLATqUn7+HL1Br67LZTxfkWsy7DnyZ/q+epGDd09dOwo9GDpKQt3DIvGz92R7LI6TqaXMqFvO9zcXCmtNZNXYaBv1xhsndzQWdTUS7Y4e/o13J6ocQS1vRjM+ncsFpDNIMsgKRp6Ya7iFyfZIiNDk9yNIVrgLcQne1N5dWsiBxYMJMC1oUu3Ji+Zbr360K9LFB+v3W3lCFsAixn2vwl7Xwc7d/qvdSIlK5/09HRsbK7DAVVGPVTnU5x5garyYuyVFur11ZxPSkVvMNIqwBuj2cKRs6nYKGTu6B8ECiUf7kxFbWPD3OHtQKHmnY2nUdvY0q1DJEqVirNJmTg52NO2dSuUKjW5haV4eHrSrl0MaJzQWVSo7ZxRX8F7bjFbqKkwsOnHzShlLaFe0RTnl/P427OJbNOWdh2i0Rt0LFy4kKFDh9K7d2/0ej1vv/U2N429ldk3PohJqefNz59m0tipjBh2AxZlPfFJcXTq0gEvL89LemD+/4uz2WymuroarVaLVqulrKyMU6dO4erqikqlIi8vj6NHjxITE4OtrS0pFxLYuWsXz9w3m9gwT77btItnPviWr5+6mdhALa+vPcELX2xn7ty5uLq6cuLECTZu3MiDDz6Is7MzR48eZcuWLZx6JIyO9sU8esSFN7ZnkfGYD8G2OhYcdePTA8Usvm8SjloV+06nsO90Mi/fOQ6NWsWhuFSOJ2ax7qH+aDRqVhzK5WBiEUvmD0FSa/j+YBrnMou55Ya+KBQSJxPTKSypZMzAWBQKBXFJWZRX1TJ9RDckScG+06mUVusYP6AzSAp2n7hAZY2OHjGtkS0mTp5PwWAw0DU6FNli4dDpC1jMRqb1CQeLkRU/x2M2m5nVJxDMRt7fkYKMRL+YIGSLmQ0HE7HVKBnQPgiLxczqvQl42yt4orsZLEbu3FxPoKuap7rVg2zh5h8lfDycGdKpFRZZ4qONxwjzc2No51aAzPvrj9IjSMMrnfIBGLDOicFhWp7pUIQsKRmw1pHYNv70iwlGluGddYfpGRVI7+hAzGYLn2w+x6j2PkyIdKDMaM+b++vpE+ZJa09HdmdVUlHjSphnK6qNOnad30a7qE7420Zz89QO+Hdrd6X/h14kWuAt3OAob17dmsjm46nMGxoDgINfBH4+PrhbikFXBnZuVo6yGasthXVzWPHTWdp3HUOH2W/x7TQ9bm5u12fyhobrum6heLqF4vmbzUHDL63W5Xe7zR96afmB3peWO/+ufsTvyo0xokChVODkbsu02ZN+szWUUXecAcBkMlOUU0rPjv0x1JnBoiC/IJ8esf3wdAwm7XQxmfnJ/LxvF27qIPTxvuRUJbDw23uYOHEiMe06UF5Sweo13zJp7FTate1AbW0Nh47tY+rEWcR27kqlLovT544zcFB//IP8sFjMREdHM2LEbxYbGjGCe+5/8GJxyn39mXLfSxfLjw2UeeCteurrG/5VV1fzzDPP4OzsjNlsplfPHowcMoiQ8cNBCwPDdlPpuQ/3CeNAWU9Q/UHalZ3C7BREqSxTQSG1ZiUX6tww6SQOZRk4kZCLMe0AGrmKTfsU/HgilyXtTwHwxWYP9p4vQOHb8JmyYcNeUlJSKLMNBmDdus1kZWUxw/AlAE+vdSIxv5bxpeaG+Fe7kFWm5+67Gy7XfP3199TU1DBv3jwAli/firlezzRjDQCvLLdFVqiY5aQEpQ1vr69BobGn3KMhNy3dtQEnJyf0gf0A+PbQdgK93XhiXA9QqNh6fhPhgd48NW0IKJQcTl9DkNmVAEUkCgkuFB1EdrIlQhOJJEtkVRwjJLQtee3vokavQGu/i1qHcI55RPBTYgr+vjq02kgSixz4+ew6Wrcfi31AMPuLK1i7cTW9evaiOCCUVzJLWLp0KZOH3Y7OOIkN8fEs/m4R00bejae9K/l1hezcvw1nN2dc/MBe6X/Ff+OXQ7TAW5CY/qPJOLWfivIylMpflxQtjIclvWDQ09DvUesG2FxlH8Py3SzWFwUw9Z099O3bl127dlk7KsHKLBaZuup6airrMOosZGflsmnbD/j5BKHV2pKRmcoPW1YxsN8QvHw8SU1P4qsVX3L35GeJcutPXN5uPtn4MvdNfpnWbj05XbCDzzYs4s477iLAP5j09DR27d7B9Cmz8fH0Jzc/m5NnjjFv2kOEBIaRmnOeE+cOM3ncLXh6epBfnENuQRZt20ZhZ6+l3liPxWLB28cDG60GtUqFUqVAkiSkf9E9a7FYGvaRJAwGA3q9HmcnJzAbKSrIoaK8Agd7W8xmM2UlZdTW6fD19sRiMZOXX0BNTQ0jB/YC2cLhY6cpKa9gzOA+IFvYd+QkFdW1tI4IB0kiMzcfi0UiIiIcSakiP78QhdqGXr37gEJF/PnzWCwWoqKisZhk0tPSsZjB0cERXa2e6soaTPUWzCYLmZkZmE0yTg4u1NcbOXJ8P+7O3nRrOwizycIn614j2DeCfu3GYTZaeP3be2kVEkFMu/aYLPV8/PkHdOrYia7dYjEajbz22msM7TOGMW3vQ1dfw2NfjGP0wClM7nk/ermCea+NYuyo8QzoM5j6egNLl33EuFET6NGtN0aTkfWbvmfKxGkMHjgYo6xn9/6ddO/eHW9vb0wmEwaDAZ1Oh7OzM66ujTshk2iBXwM6de+NpFRSWFqBn5d7w0bvaMwhg1j+5XJmdrsLpbZ5TNHZbBz7jIqNz/OjzVjS7bx59tl+zJ8/39pRCc2AQiFh76zB3lkDQECkGz2HxVxS56U3n7z42GKRefft9zHoTFiMErEZnrTu7kOntr1wsHHB5nwXCvUTCPOLRqu1RaPMR61UY7aYqNSVkpwRz54DO+kZMo58G/jpwvf8sOcLHCoicNX4s+PCMn7c8zULFizA1taWgwcPsnPnTp544gk0Gg379+9n3759vHbbarQ4s/PClxw6t53nb16JSmHDrgsriEs9zK03z0WSJI6fPkJ6Rgo3jb8VCYnjZ46Qm5fFXaNeRalQseXEl2QVJTN/7GsoFLWsP/IpBaVZjBo2AUnK4ciJA1RXVzJi0Bg+TN7N4eMH0Ol0zBq+gPUra1m58y10hhpmD32KuEyZT7c+T72ljhFDR3MqLpf1m75HpVJxw/DR/PTTEVav+QZ7rSMzu77MPvbw5ta5uDq7c1uv1wB4Ye1UfHy9mThxIgBvvfUWoaGhjB8/HoCPl79N24gYfCwdUaokNv/0A11ietAjbBRKlYL0rFTc3Nyxt3VArbLBy82bQO9QokI7o9FqmDIxg8EDhzJ5Ug9sbFUEDP2Gzp0706ZNG2RZ5tbn9Gg0mou/7wXPPnTJ38L023/b2+PQMLDSykQCb0HunHcH0xTtiSsy4uf1v+1Lclpz7xfrqQ94kHkvfmq9AJsTixl2PM3+LauZ8LWOG0bX8sADY+nUqZO1IxNaKIVCwtndAX797uzTKobug/6X8LuNDuWOxyb/bq+3/3Ac2SJjMloYkxfJ3YkziWrTHklW0uqMgq692xPbuTsSEi4ab4J8wunYujdYZAztJWwkO7oNb4ONUkuGIoTcyhBi+gUhoeBwkRqLbMLWUY0sy9TV11BaWYxCY0JGpqSygMy8NJy9bVHISgrLc0jPSUFrp8JikckuSCcjNxm9uQoZmeT0eIpLiunVuycyMmfOH6Oquppp/UwolBLZBRnU6WvQ2qtQKCQMRj1GSz32tg4oJAX2to6oVWo8nH1RKJQE+obg6OBM7KgQlEoFPUr64OLkSr+bW6NUKYgzTMbVzYX+PYZha6vB2cENf38/evXuha29hlGjRuHl5UVQUBAAU54pw8bG5uJYhfEPF1zyPt/18KxLymOnDLuk/NsELEnSJcm7pRBd6C2I0Wyh8wtb6azM4avn5l3cXl9fz9yZN9E70ps7nnq74X7W61m9DnntHRy9kMMmUx/W/bCehQsXMmbMGGtHJgiC8K/9VRe6uPegBVErFbif/Zblz9/JhQtJF7fb2Nhw18zJ5Em+ZP90nbfAa4qo+3wUM5fFs8ncj6jodhw/flwkb0EQrjkigbcw46dMY/LkyZxJyb5ke6chk0g8d5q7Xv4UjHVWis7KytLh86F8fSiXlbvO4OjoyM0334yt7XXeIyEIwjVJXANvYWaOHUzehdMkp2dest3GxgalbOJkWil5u5bgN/KhvzjCNarwPPLy8UgWA3NeW0vEnBr69+9v7agEQRCuGtECb2Fc7TWUWzQc2bWJ+vr6S55775OvuGvuHE6cPHl9tcJzjpP1wVjaf2pge6vnIKCLSN6CIFzzRAJvgYy1VWza8APffP/DJdvd3NzoEhnEL7WBnFn7hpWia2Jpe+CrsdTI9hSW15JdabZ2RIIgCE1CdKG3QHfePgttXTFVFvUfnus/ZipzHgzjBzsV58Y/hKSxt0KETSRlF5mfz8E/IJSo+9aS/Yxri7wVRBAE4b8QLfAWqFvbEGx8IijKyfzDc/b29jw0dzoP9XeDIx9aIbomkrKL0x/Po8NHZcw7EQ6OPiJ5C4JwXREJvAWSJAmzwobdm9aQmJT8h+cfeeENbh8Wg3Tw3Yb1rq81KbvI/eYBtjrcRLuY9twy/VZrRyQIgtDkRAJvoUL8vTly5Agr1/z4p89bBj3LnbvU3HXrlCaO7CpL2cXWN+9mad1I7Fw82bhxI4MGDbJ2VIIgCE1OXANvoe64aQxfx3+Jfcc/TM4DgMKrDecq7VGU5WApiEfhE93EEV4FKbu48OUDTF6RR+uIXezZuxcnJydrRyUIgmAVogXeQjnbaWjTOpy9ScV/WWf71m3svcmIYtuChsXsW7KUXeR88yDrbMYzc+YMVqxcKZK3IAjXNZHAW7C2mgrOLbmHFavX/unz9l6BSEOeITHuOLu+eKWJo2tEKbvY9dY8nk9rj72zOwsXvk509DXQoyAIgnAFRAJvwYZ0ikBXkseRM4l/WcfS6VaGfGvhtqffx1RT1oTRNZKUXfDtNO7fUc+PW3Yy7ZbpouUtCIKAuAbeovWKCaPNw6swB/714vEKlZo3n1/AofNZHF+9iB63L2zCCK/Qr8kbz9Zs3/oxJbUmPDw8rB2VIAhCsyBa4C2YJEkMiPTiYEoJ+nrjX9abMvchuoW6sCdbQfW5nU0Y4RVI2cXB9+Yy/ic/6m9eQ0BEOzp27GjtqARBEJqNJkvgkiSNkCTpgiRJKZIkPf4XdQZIknRakqR4SZL2NlVsLVmkrY7cD2fwyFPP/WUdSZIYNmUOazdtZ8Ls+VBf24QR/gdJO+DbaXyf7sBPJ9NIzi21dkSCIAjNTpMkcEmSlMCHwEggCpgqSVLU7+q4AB8BY2VZjgYmN0VsLd2N/Tvh7etLZc3fL17i6RdIeJAveo0XOWueaqLo/oOETRi/mQ5ekby9ajfnz58XA9YEQRD+RFO1wLsBKbIsp8myXA+sAsb9rs40YJ0sy1kAsixfg1OINT5nOw0jZtxDiI8HFovlb+t++e1abrxhCFuTDJjPrmuiCP+F+B/Y/M59tPpUyZG2zyHZuxMQEGDtqARBEJqlpkrg/kD2b8o5v277rdaAqyRJeyRJOiFJ0sy/OpgkSXMlSTouSdLx4uK/vg/6ehEcGoZsrOPgsdN/W0+j0TBizHhOFsKN857CXJLaNAFejrjvuLDmZbYqhmJBgdJWjDQXBEH4O02VwKU/2fb7mUVUQBdgFDAceEaSpNZ/djBZlj+RZTlWluVYT0/Pxo20BerRLozFixfzymuv/WPd6JgOYKxjX3wu5z6+zfrXw2UZDr3Pd0tfZzVj6NipM4mJiXTt2tW6cQmCIDRzTZXAc4DA35QDgLw/qbNNluVaWZZLgH1AhyaKr0Xr1iaI7gNH4OPrd1n1P/xkGSc3fEwHcxxsmG+9WdrMJuTNj/Diu19w00cnqdPVMXPWbBwdHa0TjyAIQgvSVAn8GBAhSVKoJEk2wM3A71fh2AD0lSRJJUmSHdAdSGii+Fo0hUKi15hbCPVxo6qq+jLqKwgbMA150LPc+/HPLL7PCuMFDTVYVt3CxuOZ1EfcwIwZM3juhRewsbFp+lgEQRBaoCZJ4LIsm4B7gO00JOXvZFmOlyTpTkmS7vy1TgKwDYgDjgKfybJ8riniuxa0axtBSUkJX6/deNn7GGLvZEc6bD5wGvlQE64dXpFF5ccjmfRpIkdNkQwePJivvvoKrVbbdDEIgiC0cJLcwhe5iI2NlY8fP27tMKyuoEJHeKA3YW2iOHP8l8ver6SoEOddD6FO2gQ3vAHd7riKUQJJ22HdXJZfsGX28mTeeOMNHnzwwat7TkEQhBZMkqQTsiz/YelJMRPbNcLHxY4eUx8gcvTcf7Wfh5c36smfk+ExhK4zXyRuxdNXJ8D6WiwbH2Lfe/PAJYiZb27h+PHjInkLgiD8RyKBX0MG3TiNU0Y/dPWmf7ejWktOzL0k5VWydPs5dOsfAlN94wWW8hMs6c0D761n0Mc5HI5+Gdxa0alTp8Y7hyAIwnVGJPBrSN8ID+Tkvbz05gf/et8+/Qdw7Ogv+LXpyDendcS/cQOUpV1ZQKWp1Cy/hZRPbgVJwUPPLeKBBx6gS/eeV3ZcQRAEQVwDv5bojWZahUWgUkBWxn9LvomJibz5xmKWLfuCJ2/pz73TbsBryD2gtr38gxQlwOEPSDx5kCGf5OHh4cHJEydQ2PyLYwiCIAjAX18DF8uJXkO0aiV97nyZSqXLfz5GZGQkjy14nOqqCpTBbVhyVIfih5voGBHAmFkPgEcESH8yL09VPlzYAvE/kHb+JCfsB3NeMZ5+AxIYPmKkSN6CIAiNTCTwa8zQPj14ZUsC+ZV1+Dr/t6QZERHBqu/WotPpOLpjDfNWLuft7/eTVf09Dq7e4B4Ojr5gMVJQWMJX+9MJ8PVEdgpkb5o9n63I5/bbNcycOZCnnnoKlUr8mQmCIDQ20YV+jUksqGLC7HuJ8rRhzfJPG+WYpaWl/LJ7CzcE12NK3Uuvl/Yzr6c7t7c3c6TInp6vHGTC+BsZNngAWntnjp84wZw5c+jQQUykJwiCcKVEF/p1oo23I4bss5xKrkGWZaQ/6+7+l9zd3blh0gwAkux7UlS7jwzfkXDfS3QxGtk95CDdu3fH1rahxX/rrFlXfE5BEATh74kEfo2RJInxdz2BY8l5ioqK8fb2atTjR0VFkZGRcbGsVqsZMGBAo55DEARB+GfiNrJrUNeO7QA4dCreypEIgiAIV8u/TuCSJNlLkqS8GsEIjWNg+1C27d7PKy88a+1QBEEQhKvkHxO4JEkKSZKmSZK0WZKkIiARyJckKV6SpMWSJEVc/TCFf8PLUUu9pKVeV43J9C9nZRMEQRBahMtpge8GwoAnAB9ZlgNlWfYC+gJHgIWSJE2/ijEK/8GEOx5k4oTxJKdmWDsUQRAE4Sq4nAQ+RJbll4BKWZYt/79RluUyWZbXyrI8EVh91SIU/pPeHdtikSUOnIyzdiiCIAjCVfCPCVyWZeOvD3/4/XOSJPX4XR2hmegR4c0PW3fxwgKx2pcgCMK16B9vI5MkaQrQGXCUJKktkCTLsvnXpz8B2l/F+IT/SKtW4hUeg43WFpPJJGZDEwRBuMZczqf6QcAWcAXeAtpIklQB5AF1Vy804UrdfOfDvLw5gcIaI/4uIoELgiBcSy7nGnieLMtfAeNkWR4py3IrYAjwHDAIQGqM6b6ERtc3whNZtrBuj5hqVhAE4VpzWaPQJUm6F8j+/w2yLJcBZ4HukiR9Bdx6leITrkBrbwdsdi3iyZmjsFgs/7yDIAiC0GJcTr/qCOA24FtJkkKBChq61BXADuBtWZZPX60Ahf9OkiS6DB5LalAb9IZ67Gy11g5JEARBaCT/mMBlWdYDHwEfSZKkBjyAOlmWK65ybEIjuHnqNB5YfZqUUj3tA0QCFwRBuFb8q6lUZVk2yrKcD7wnSZIWQJIkl6sRmNA4eod7oKorY+kXK6wdiiAIgtCI/utiJgrgY0mSbIGHGjEeoZF5OmqwPb6cT158iJqaGmuHIwiCIDSS/3pvUTrwObAEKG28cISrYciE6XRvG0x6Vg4xUZHWDkcQBEFoBP+1Bf6pLMsZwPM0DHITmrFxNwzFLyCIo2cvWDsUQRAEoZFczmpkt0qSVCJJUpkkScslSXKUZTkLQJblDFmWo69+mMKV6BHuzYXCGtatEtfBBUEQrhWX0wJ/BhgKRAKZwKtXNSKh0WnVSrKzs9m6YR2ZmZnWDkcQBEFoBJdzDbxKluVTvz5+RpKkX65mQMLVMe6W2+gTFUhmQTHBwcHWDkcQBEG4QpfTAveVJGmuJEl9JUnyBNRXOyih8Y3p3w2lnTMnxXVwQRCEa8LlJPDnaFhx7GXgAtBOkqQtkiS9JknS1KsandBo2vo6cTarhBVL38NsNv/zDoIgCEKzdjkzsX3y27IkSQE0JPQY4Abg26sTmtCYJEnCYrZwISGes2fP0bFjB2uHJAiCIFyBf30fuCzLOUAOsKXxwxGuphnz7ibFpz8qzxBrhyIIgiBcof96H7jQAg1uF0y9pGF/com1QxEEQRCukEjg1xEvJy2BxUd4+dahVFZWWjscQRAE4QqIBH6dCfN2BmTOnk+0diiCIAjCFfivc6ELLdSsW2eyx9IWk1uotUMRBEEQroBogV9nuoe6Y6NSsCchD4vFYu1wBEEQhP9IJPDrjK2NkrDyYyy8uSe//CIm1RMEQWipRAK/DvXu2Z2oqLYkJKdZOxRBEAThPxLXwK9DEwb1pCT5Jkqraq0diiAIgvAfiRb4daitryNlSnfy05OoqKiwdjiCIAjCf9BkCVySpBGSJF2QJClFkqTH/6ZeV0mSzJIkTWqq2K43kiSBsY6333qT5SvEGuGCIAgtUZN0oUuSpAQ+pGFd8RzgmCRJP8qyfP5P6r0ObG+KuK5n48eOJveXTRhkcRVFEAShJWqqT+9uQIosy2kAkiStAsYB539X715gLdC1MU5aVVVFUVERRqOxMQ53TWltL/PCCy+ilGQSEhL+1b729vYEBASgUIgrMIIgCNbSVAncH8j+TTkH6P7bCpIk+QPjgUH8QwKXJGkuMBcgKCjoT+tUVVVRWFiIv78/tra2Dd3GwiUyCkqR66rw8vLC3t7+svaxWCzk5uZSUlKCl5fXVY5QEARB+CtN1YT6s+wp/678DrBAluV/XKxaluVPZFmOlWU51tPT80/rFBUV4e/vj52dnUjef8FGraa0tJTi4uLL3kehUODt7S3mUhcEQbCypmqB5wCBvykHAHm/qxMLrPo12XoAN0iSZJJlef1/OaHRaMTW1va/7HrdcHW0o8LNGwdXt3+1n1qtxmQyXaWoBEEQhMvRVAn8GBAhSVIokAvcDEz7bQVZli9Ozi1J0pfApv+avH9znCvZ/ZqnVStB64zO9O/eJ/G+CoIgWF+TdKHLsmwC7qFhdHkC8J0sy/GSJN0pSdKdTRGD8EeSJOGgUVBdVkR5ebm1wxEEQRD+hSa7h0iW5S3Alt9t+/gv6s5qipgEcNSqKa4qoxgjrq6u1g5HEARBuEziPqBmwGw28+ijj+Lp6YmjoyMTJ06kpKSk0Y4fHR2Ng4MDDg4OaDQalErlxXKgtztl9RJOXgGNdj5BEATh6hMJvBlYuHAhGzZs4JdffiEnJweAGTNmNNrx4+PjqampoaamhmeeeYa+ffteLNfU1BAaFkGNQQxKEwRBaElEAm8GPvnkExYsWECrVq1wdnZm0aJFbNu2jYyMjD+t//zzzzN48GAWLFiAp6cn7u7uvPXWW2RmZjJo0CAcHR3p0qXLZU/Q4qhVUVeaR/avXx4EQRCE5u+6mkfzhY3xnM+rapJzRfk58dyY6H+sV1lZSVZWFl26dLm4LSwsDCcnJ+Li4ggJCfnT/fbt28fUqVMpKChgx44djB49mi1btvDhhx8SHh7O7Nmzuf/++9mxY8c/xuCoVVFgrKdWLE4mCILQYogWuJVVVTV8oXB2dr5ku4uLy8Xn/kzr1q2ZM2cOSqWSkSNH4u7uzvDhw2nbti1qtZpp06Zx7Nixy4rBVq3E0cMHJ0dHzOZ/nEdHEARBaAauqxb45bSIm5qjoyPAH2Y2q6iowMnJ6S/38/X1vaRsZ2d3yTY7Ozuqq6svKwZJkrDRaMFgxGAwYGdnd7nhC4IgCFYiWuBW5uLiQlBQECdPnry4LS0tjaqqKtq3b99kcTjaaSgvryArO/ufKwuCIAhWJxJ4MzB37lxef/110tPTqaqqYsGCBQwfPvwvr39fDY4aNShVSIAs/36aekEQBKG5ua660Jurxx9/nPLycrp27YrBYGDo0KGsXLmySWNQKCQc3TxRmeowGo3Y2Ng06fkFQRCEf0dq6a2t2NhY+fjx43/YnpCQQNu2ba0QUctVUq3HUFWG1tYWd7e/n5VNvL+CIAhNQ5KkE7Isx/5+u+hCFy5ysrWhrLycnBxxHVwQBKG5E13owkU2KgU2do5gMSPLslh1TLhseqOZrDIdhVV6SmvqKakxUFpbT53BhMliwWQBo1lGowJHjQpnew2OWjVedkpCvRwI8XDCRiXaE4Lwb4gELlzC2d2L4mo9ZouMSikSuPBHFbp6jqaXcSyjjKTCGtKLqymvrMQBA3J+AqaSTGI6dcFJMnBo2zqyszIJumc5aqWC8jXPUJKXid3MpQBotjxLVXEeM+bdR73Slsy0FJwcHblx/I10CPPH39sTjUZj5VcsCM2TSODCJZxsVRRVWSgqLcfPy93a4QjNgMUicyKrnK1nCziUWsKFwmpkuaHHxu3YJyQd28d9992LJElsv7CLM8eOMX1IZzw9/NDU9SU/P5wVTw0B4DX5FzIzM3nnpRFU1Rl5TfqFrOwcnD39qKup5MTPm1FIMq3ctcTtg2+//RYbe2ee/ngNsSGupJ05QlRUFH5+flZ+VwTB+sQgNuESsiwTfyEZfU0VHTp0QK1W/2k98f5e+4qq9aw+ms23R7PIq9Rjo1IQqTvLmR8+5oOV6xnaLZqVX33BmjVrePbZZ/Hz88NsNuPk5ISHh8d/ugRjMBhISs8ho0JPQno+a79aQi221HScCsiUfzwdv1aRPPLet3QNcmHZ2y/Ss0cPBgwYgKenJwqF6IYXrj1/NYhNtMCFS0iShIOLO0qNnfgwvE5ll+lYsjeV749n4aTLR3N+M3dMmMz9s6ZwZL+aOessOBrL0KqVzJkzhzlz5jTauTUaDTGRYcQAY3pE89jUIVgsMmklNRxJLWWN/lHy9Gpe2nQeO1MVie++y6mTJ0lMTEQGtmzezNixYxk5ciS+vr54eXmhUomPOeHaJP6yhT9wdXaiyqSkzmjBQam0djhCE6nUGXnv52SWH87AiTqmuRVhMGfyxk8b6RUThoNmGkOGDPnLVfKuFoVCItzLkXAvR6b3fAqA/Mo6jmWUs6fdbhIz8thXb0RbncuFlDROnD6D2WymoqKCZcuW8dprr3H33XdTXV1NaWkpwcHBYoCmcE0QCVz4AweNCoXFRF5uDmEhQShFEr+mybLMupO5vLT5PHV1dYQmraEg+Qy206Yx8sYbefDBB/H29rZ2mJfwdbZlbAdbxnZouBZeqTNyMqucfjeM52hqCRvyilHXpeIc2Ibvks3k/nAWS+LPvP7Ug6xbt44bb7yRhIQE8vLy6NWrF7a2tlZ+RYLw74kELvyBUiGhwUhleSnlzo54eHhYOyThKsmrqOPJH86yJ7GQod51tNJk8HNVAQ4ODtxxxx24u7eMgYzOdmoGRnoxMNILaLitLS6nkmM33cixjDI2nM5Dn68ipPcYPk5UkbAlgfg1b/P1F59y//33Ex4ejk6nQ6fTMWnSJIKCgnB0dBQtdaFZEwlc+FNubq7YYAJJXAe/FsmyzDdHs3htSyKqyhxUWxZR37MHPgMGsHz58j+sdtfSaNVKuoW60S3UDQCj2UJcTlcOpgzjYEoJyw6mY9TEEjFaoj6gC5WygW2bvufI4UPIsoxCoSAuLo7Kykp27NiBQqEgIyMDJycn3NzcrPzqBKGBSODNwKpVq/jwww85c+YMOp0Ok8nUqMePjo4mMzMTAKPRiMlkuqTL8Pz58wQFBV2yj7OtDVVKG+rrDWJSl2tMpc7II2vOsPN8Ib3D3XliZgyj179ETEwMs2bNuiZ/12qlgi7BbnQJduO+wRHo6k0cyyjnUEpfDqSUsDWvCku3B/GLvIk4ez9aO1ko050gKyubrLI6At3suOmmm8jJySE3NxeA++67D4vFwqRJk3BxcUGpVOLr64uzs/Nf3r0hCI1JJPBmwNXVlbvvvpu6ujrmzp3b6MePj4+/+Pjll19m165d7Nmz52/3USkVyJKSivJStBqNaHVcI85kVzD/m5NUpZ3BI24tnzyzHXt7e9LS0q6ruw7sbFT0b+1J/9aeAFTrjcTlVHI6u4JTWeXsza2ioMM86AAD3tiDjUqBR9shREXqWLw9kWA3e3bu+hmzqR5Pz4ZjfPrpp9ja2jJ9+nTs7Ow4cOAAbdu2ZeHChQBs3LiRkJAQYmJiAKipqcHW1laMMRH+M5HAm4Hhw4cD/GNS/X/PP/88+/fvJzY2lmXLlmGxWHjqqaeYOHEis2fP5tixY7Ru3ZqVK1de0b3aDvZ2VBToqa6pEQm8hZNlmS8PZfDqlgS8HLWM8tPzwTdnOHv2LD169LiukvefcdSq6R3uQe/w/433qNIbSS2qIbmohuTCapKL3EktruHjvWmYLTKMfR3ZbOSbehVhzkrCB1bi7mCDY2gHbKnn9JmP0BvqLx5v+vTp9OjRg+3bt2MymYiIiKBt27YMHToUW1tb1q1bR1RUFF27dkWlUrFlyxaGDRvG7bffjslk4sknn2To0KEMHToUnU7Hhg0b8PPzw93dHZVKhVqtRq1Wo1KpLpbt7OzQaDQXlwi+FntXrmfXVwLf+jgUnG2ac/nEwMiFV+3w+/btY+rUqRQUFLBjxw5Gjx7Nli1b+PDDDwkPD2f27Nncf//97Nix4z+fw8VeQ623P2qFLLrRWzCDycyT686x7ng6PWwLWXLfbFzsBvHIPXNbzCA1a3DSqukU5EqnoEtX5jOZLeRV6Mkq0138l12mI9N2PEmlOk6cNwFqpJs/IFGWiXp2G16OGjre/ChO3t48vjYOe7VEUJsO+EREYuMdhtFoIP58IvYuHrSqM2MxGfjuu++osahw6zwcU10tixcvJj2/FJvgjpQXZDNt2jSGDh1K79690el0LFq0iBtuuIFu3bpRU1PDZ599xrz59zHvgcdITUpg3oybmHvvg0yYeivnTp/kxccfoGev3oSEhlJVXc2Bffvo3rMXQcGh1BkMXEhMYPDoiUS170h1WQnnT/1Crz598fXxwWTQUVddhZ2dLRqNBo1Gg42NjfiMaGLXVwK/hrRu3friBBojR47E3d2d4cOHX2xxT5s2jVtuueWKzmGjUoJSDRa9WCO8hSqrrefOFSc4l1GA/9EP+OHIQV64ZSAurVuL5P0fqZQKgtztCHK3+9PnK3XG/yX2ch1FVQaKqvUUOQ2mpMZAZmIRNQYTuh73UggcSgKwx3HOFyQACTkNPSZBj6znHDIPrj6DLFvwu30JR2wdObbsKJjq8R33CGlegRTq/ZCMtfj1mUiWZweqDK2wmCrRBLRlTZqCVW/sQVmVT7kBlh7KZ0nBPrTlaeRm5uLUxkKlm5bKwmIOHjyIjXcYVSpXSnJSWfPFEg6W2qELrcUh5wjxX79M65ufwhDcE/ec/ST+8D7Tpk0jICCAnJwc9u/fz+BhI3H28KKwuJjE+Hg8B81C7RGMVJiEMf04fn0m4O7phY2uGKWhCjc3N5wc7HF2tMfV0R53ZwdcHLQ4adVo1eLSwj+5vhL4VWwRN7XfjxK2s7O7ZJudnR3V1dVXfB5brZbi7Fzq6uoICwu74uMJTSelqJrbvjyOubqYW1wyqOzWhZFDB9G6dWtrh3ZNc7ZTE2PnTEyA89/WM1tk6oxmzJaGHi6LzCWPLbKM2SJjssiYzBaMZhmj2YLJ0vDYZO6L0Wy5WMcye1jDz1/LTB+LQgJJAomOSHNHIklSwzY6I90zCYUEICFJcP8DDyIBCgXU6/WMmjQNL28/NHb25Of7cbiVEzE9BmDr4klKfD2aogTcovuhcHFFXwnlNXpMzn7ITp4UJ6VxaPcOJvSfhlqpICfxOPtXfUgP71jq8kwojq7k1OYVPPjggzg7O3P27FmOHDnC9OnTsdHakZyeQUpKKorBD2Dv7IpTURwUJeE7aCYu9lrkwmQsNaX4BQSi1digtVFjb6vBTqvBwVaDo50WRzstAT5eaNUNl4euxd6B6yuBC/+as72GEqUaFOLbcEtyNL2M2786iu3ZH5ByzuB4yzTm3v7oxQFXgvUpFRIOmmb8Edwx+H+P23ozfVCn/5V7hfDSHeN/U3k0vPXcb8qzMH/1MQqFAkmSKJ/UhvRHb6Ndu3bY2Nhw7JgrG7q0YuzEm6irN2FQaElKyySwXXeMZgvV8Rc4fewwD967iFqLmmM79nJs5w8MaDuB6voq6rctJf7wTzz77LNUAtu3b+fkyZM88cQTAOzdu5eU1FQUUz9CpZDwjluBrjAdn+mLcdSo0B/4Al1pHn0GDEahUJKanEi9Xk9sj16olUrSUy6gUCqZ//AT2Noo+frzpVjMJh595GEkSeK9996jrq6ONm3aIEkSOTk5KBQKgoODCQ8Pb7Ivyc34r+f6YTabMRqN1Nc3DHjR6/VAw7zQ1v7WqFUpULn5oVCJBN5SHEguYc7yo/SzzSWxOIGS6ipmzJiBq6vrP+8sCI3kt6PrXV1dL/n769q1K127dr1Y7h8bw6vPLLhYfuDWicDXF8tFQ5aQk/MUnTt3BuD4CBfi4s4ycuyNVNbqcfEJJrLjKToPGU9tnYH0Eh16hZbpI9pQozex8RyUVdXQxUVLtd5EYkICxVnJhPUYjsVsZt/+A1SWFuEWGoUCmU0//khVZRVr6QVA/fefUG+oY0lZW7QqJVUr30chm5l+2zwUkszyT5egUquZOes29qZXM9vJh0gfp6v11l4kEngzsGLFCmbPnn2x/P/3aKenpxMSEmKlqBpIkoSzVk1JjYE6vR5brdaq8Qh/76eEQu76+gS9lan4G8u48fHHGTJkiBi/ILRoXl5eeHl5XSzHxsYSG9uwOJevB0TOmwXMuvj8zUO6XrL/YyO+vfSA8/ZffCjLMiUPzKK0qhYbe2eq9SYGDx1BZa0eZy8/6oxmsjp/TJ3RiJNnQEPZazF6g5kq31DqjGYip3lgMFv4xTESvc7MFEPjzuXxV8RyosI/qjWYSE2+gGw206FDe0C8v83R5rh87l91CvdTX5D8y08sWbKEKVOmWL0XRxCEKyOWExX+MzsbJWo7J5SSuJ2sudp6Np97vz1J5yBXJnS4ie80RiZNmiR+V4JwDRMJXPhHkiTh5OZBeW09FhmUIic0K4dSSrh/1SmipRyW3z4cOxsV026aZO2wBEG4yq7v6ZeEy+Zsq0Y2m8grKLR2KMJvnMutZO6KE3ilb2fzwrv4cd0aa4ckCEITES1w4bLY2yhR1JVTWF2Bl7sYzdwcZJTUMuuLozjbqvni9ad4183MxIkTrR2WIAhNRLTAhcsiSRKOru54eHhgNBqtHc51r6haz4xlv6A8v5UPJ7UhItCLDz74QKyCJQjXEZHAhcvm5uSAUq2hVqe3dijXNYPJzF0rT6JOP8TRb9/mo0UvWDskQRCsQHShC5fNXqOiwAK1ZSWYzWZrh3NdkmWZZ9fHU5SdzhAfMz2ffJJnnnnG2mEJgmAFIoELl02SJJRKJRU1NVgsFmuHc1366lAGG3btY5A6Cb/QGGbNmiW6zQXhOiUSuPCveLi5ojDXU5Cfb+1QrjuHUkp4ffNZ6ne9x6qyEl56Plkkb0G4jolr4M3AU089RWhoKE5OTnh5eTFp0iSysrIa7fjR0dE4ODjg4OCARqNBqVReLDs4OPyrczloVJiVGixmU6OsdiZcnuwyHfO/PsFwuwwmTbiRZcuWieVABeE6JxJ4MzBjxgxOnz5NVVUVGRkZBAUFcfPNNzfa8ePj46mpqaGmpoZnnnmGvn37XizX1NQQFBR02ceSJAkbjRadTscTTz3daDEKf81gMnP31yfxzPoZF1MZU6dO5cYbb7R2WIIgWJlI4M1AZGQkzs4NawfLsoxCoeDChQt/Wf/5559n8ODBLFiwAE9PT9zd3XnrrbfIzMxk0KBBODo60qVLFxISEq5KvC72WmQZcgpLrsrxhUu9ujmBjF+2s3PZIqqqqujUqdM/7yQIwjWvya6BS5I0AngXUAKfybK88HfP3wL8/3pyNcBdsiyfacwYXj/6OolliY15yL8U6RbJgm4L/rnir7755hvuuusuqqqqUKlUvPXWW39bf9++fUydOpWCggJ27NjB6NGj2bJlCx9++CHh4eHMnj2b+++/nx07dlzpS/kDe40KhYMrHjc82OjHFi61OS6frw5nMmvyZEYHmsSIc0EQLmqSFrgkSUrgQ2AkEAVMlSQp6nfV0oH+siy3B14CPmmK2JqLadOmUVlZSX5+Ps8//zwxMTF/W79169bMmTMHpVLJyJEjcXd3Z/jw4bRt2xa1Ws20adM4duzYVYlVkiTsbFTsTSoiMTXzqpxDaJhp7cnlPxHjYuTJUe147bXXsLOzs3ZYgiA0E03VAu8GpMiynAYgSdIqYBxw/v8ryLJ86Df1jwABjR3Ev2kRW4uPjw933HEHrVq1IisrCzc3tz+t5+vre0nZzs7ukm12dnZXdZCZrVoJez6gyzt7KSkpubiGudA49EYz878+QfkPL1FUVw0P3QCINb0FQfifpkrg/kD2b8o5QPe/qX87sPWvnpQkaS4wF/hXA7BaCpPJRG1tLXl5eX+ZwK3NRqXAv0NfvN1d0Ov1IoE3spc3nyc+v5p7FzyHbX0ZNjYieQuCcKmmGsT2ZwtQyn9aUZIG0pDA/7K5LMvyJ7Isx8qyHOvp6dlIIVqHxWLhgw8+oKioCICcnBzmz59PSEgIkZGRVo7u702ePJmcqFuokTXWDuWasvFMHmv2nmJev1Y8Onca99xzj7VDEgShGWqqBJ4DBP6mHADk/b6SJEntgc+AcbIslzZRbFa3ZcsW2rVrh729Pd27d8fOzo5du3ahUjXveXbGdvADi4kXF79HTk6OtcO5JqQV1/Ds0jVkLJlH/QmxNKggCH9NkuU/bQg37kkkSQUkAYOBXOAYME2W5fjf1AkCfgZm/u56+N+KjY2Vjx8//oftCQkJtG3b9kpDF/7C/7+/o574mC0L7+LRRx9l0aJF1g6rRdMbzUz4YC9hRfs5unsrK1esICIiwtphCYJgZZIknZBlOfb325ukiSfLskmSpHuA7TTcRrZMluV4SZLu/PX5j4FnAXfgI0mSAEx/FrDQvEwdNxJ19u34BFx7YxGa2gs/nsOt9CwethKrvv2W0NBQa4ckCEIz1mR9tLIsbwG2/G7bx795PAeY01TxCI1jVIwvq0N7UV2eTUlJCR4eHtYOqUXacDqXH7/6AN3ZXdz8/vsieQuC8I/ETGzCFXG1t8E3pDXHjh/nxRdfsnY4LVJ2mY5FPxyltaocJycnhg0bZu2QBEFoAUQCF67Y2K6tOHshnR07d4hlRv8lk9nCg98eo4eURM+ePThw4IC4ZUwQhMsiErhwxYa09ab1pIeYevPNZGRkWDucFuXdn5I5v+IFCpLPMnnSRBwdHa0dkiAILYRI4MIV06qV9O4WS72s5JfjJ60dTotxNL2MpdtOUZaZiFKpENe9BUH4V0QCFxrFzT1C2Hcug7vn3UFxcbG1w2n2KnVGHlh1Cj9fb46fjuOzzz6zdkiCILQwIoELjSLSxwn74Gg8fQPIzBQLnPwdWZZ59NvDVO78kNfHtiHA20Nc9xYE4V8TCVxoNLNvmkj92NeQPVpZO5Rm7fsTORzYuJrzu9eTc+6wtcMRBKGFEglcaDRjOvrhoFGzbPsp8vL+MFOuQMNUqc//GE+HG2Zw4OBBJk6caO2QBEFooUQCbwaio6NxcHC4+M/W1hZJkjh5snEGhP32+BqNBqVSecn5srKyGuU8djYqhoWo+XT+CB5b8HijHPNaUm+yMP+DDThVpPDWTR3o3auntUMSBKEFEwm8GYiPj6empubiv4ceeoioqCg6d+7c6Md/5pln6Nu37yXna8wlWf+vvTsPj6q82zj+/SWEkCFhDwhEdoIREJEoVIkLiAEMi7ggoCCrQKXYKoKv1VJbcSvU1oKALUVES1EjLsSK8Kqo1RZQEDBsLsGIoGwhAZMQ8rx/ZPSFAAphMmcmuT/XxUXOmbPcT5b5zXO2Z8RVnUjqfh3nXDEgYNusKKa/vonMfzzAJ0/dQ2xEkddxRCTMqYCHmKKiIubNm8ett9560mWmTp1K9+7dmTx5MvHx8dStW5cZM2aQlZVFt27diIuLo1OnTmRmZgYxeYl2jWvSNG087x6oQzAGygkX723bzaoP3mFAWk/+8Oijut9bRM5YaI9XGWA7p02jIHNTUPYVnXQOZ/3P/5z2ekuWLCEnJ4ehQ4f+6HIrV65k0KBB7Ny5k2XLlpGWlkZGRgYzZ86kVatWDB8+nIkTJ7Js2bKyNqHMBl3UhPvnL6VXnz+QvngRPp8v6BlCyd6Dhdz315dIidnJeZdexoD+/byOJCIVgHrgIWbOnDkMHDiQWrVq/ehyiYmJjBo1isjISHr16kXdunVJTU0lKSmJqKgoBg8ezKpVq4ITupS+HRrhy81mxeuvsXjxYk8yhArnHL+c97/8d9aveO+9f5PWu5fXkUSkgqhUPfCy9IiD6dNPP2XFihW8//5P31rUsGHDY6Z9Pt8x83w+H7m5uQHPeCriqkXR97pBJJ8VRc6BXIqLi4mIqJyfFRd+kEXEro0kJ3firkl36n5vEQmYyvmuGqLmzJlDhw4d6Ny5s9dRztjwri3YGt2K/fv2snbtWq/jeGLrrlz+mbGCZlF5PDhtGj169PA6kohUICrgIaKwsJD58+czduxYr6MERLN61WnV+hxeeX05/fr3r3SjlOUfPsLYRxawau49VKlarUJ8KBOR0KICHiLS09P57rvvGDJkiNdRAmZESnMKGpxHyxYtPLki3ksP/2sTu3bvIbpaNINvvAEz8zqSiFQwFu63+iQnJ7vVq1cfNz8zM5OkpCQPElUOp/L9dc7R9/GVtNv/PolnN2D48OFBSuetNzd/w/C/r+KWi5txX1pSpT3/LyKBYWZrnHPJpefrnUXKjZkx7opE1hbU55133iEjI8PrSOXu29wC7pjyaxpseJa7UhNVvEWk3OjdRcpVatuzKIhtyOLnnuP+++/3Ok65Ki523PncOvZt+5Cczz4iSn9dIlKOKtVtZBJ8kRHG2CvbsWfLFO4a1dfrOOVq/r+/4O0t3/Lb2Yvpk1SLqKgoryOJSAWmPoKUu/4dGxPb5mc8tfZAhX286obs/fzxvl9xWYPDDL24OXXq1PE6kohUcCrgUu6qVolgQrdWbFy7mhYtW/Pee+95HSmgDhYUMeXRJ8hc+Qo1t7+jK85FJChUwCUoru2UQKNGDTl46CBbt27zOk7AOOf4zbMr6VT7MPf+7iEem/6o15FEpJJQAZegiIqM4PZ+F+MbNpd6F1ScJ5LNefU/fPnmM1SJqc7kX96mq85FJGj0biNB0+/8xrQ5qyYPL93IK68u9TrOGdv0dQ6P338HLy56mn69U6lWrZrXkUSkElEBl6CJjDDuuTqJ3a/9mb59+rBixQqvI5XZocIiHpm/hP5XXc7D0x/jvPbtvI4kIpWMCngI2LlzJwMHDiQ+Pp7atWvTrVs31q1bF7Dtt23bltjYWGJjY4mOjiYyMvKH6djYWLZv3x6wff2USxPj6TTwF/S59gbWb9zI4cOHg7bvQHHOMe7Bv9L40Kc0bXMet982zutIIlIJqYCHgPHjx7N37142b97Mrl27SE5OJi0tLWC3XG3cuJG8vDzy8vK49957SUlJ+WE6Ly+PJk2aBGQ/p+o313Vhb5t+5Ozbx9Kl4Xco/cF/vsWiaRN5ffkKhg8aoKvORcQTKuAhYNu2bVx//fXUqVOHqlWrMnLkSLKzs9mzZ88Jl586dSrdu3dn8uTJxMfHU7duXWbMmEFWVhbdunUjLi6OTp06hewAIq0bxNHzZx34d3Y+Q4YM4emnn/Y60ilb/skunlx3iB433cbCp/6uh7WIiGcq1ZPY3lm8hd1f5gVlX/XOjiXlhsRTWnbSpEksXLiQAQMGEBsby9y5c+natSv16tU76TorV65k0KBB7Ny5k2XLlpGWlkZGRgYzZ86kVatWDB8+nIkTJ7Js2bJANSmgbu+RyNI1F9O05Wts3PgJBQUFREdHex3rRy3/zzru/PubtGubzOLfPkJM1UivI4lIJaYeeAi45JJLOHLkCPHx8cTGxpKens6TTz75o+skJiYyatQoIiMj6dWrF3Xr1iU1NZWkpCSioqIYPHgwq1atClILTl9sdBV+c+2FxKbdTUxMTMh+0PjevoOFjLx5MJ//Yyp/vLaNireIeK5S9cBPtUccTMXFxVx55ZX07NmT9PR0qlWrxoIFC0hJSWHDhg00aNDghOs1bNjwmGmfz3fMPJ/PR25ubrlmP1OpbRvw0rmt+PiT3fxr2jSys7MZNy70Lgg7VFjEqAWr8aXezm1JRqtG8V5HEhFRD9xre/fu5fPPP2fChAnUqFGDqlWrMmrUKIqLi/nggw+8jleuzIzf929HVlQzPsv6MiRvKzuYX8C14+/ho6w9TB+TxqTxo7yOJCICqIB7rl69eiQmJjJr1iwOHjxIUVER8+bNIzc3l/bt23sdr9zVjY3moYHJ1Bo0nQ7Dfut1nGMcLjrCtcN/zr/+9gjX1fyC3u0b/vRKIiJBUqkOoYeqJUuWMGnSJJo2bcrhw4dp1aoVzz33HC1atPA6WlBceW4Dbkhpy9/e+4J6BV9T/dAOhg4d6mmm4mLHfXNfoHNiYxpNmMTDU27zNI+ISGkW7sM7Jicnu9WrVx83PzMzk6SkJA8SVQ6B/v4WFB3hhjkfsGbGCPJz9vDVV195dlV6cbHjunF30bpWBLWaJjFl3DDd6y0injGzNc655NLz1QOXkBBdJZKZgzvSf+sd1IiN4VCR4UX9Lig8zB0P/oVX5j1G8sWX8s4DD6h4i0hI0jlwCRkJtX08cft1ZFOPMQtW8YuJt/Ppp58Gbf9fZO9g6owniOcAY6fcz9tvvEaVKvqMKyKhSQVcQsqFzerwxxvOZ/3HHzP7iVlMmDCBnTt3lvt+X359Oe3PPYcv1q8ivn0Kj//ubqpWrVru+xURKSt1LyTkXH1eQ/YO683DxQV0bHyIefPm0aNHDy688MJy2d9H2/fx0PsHqX92Cy7udT3jB3Qrl/2IiARS0HrgZtbTzDab2TYzm3KC183M/ux//WMzuyBY2ST03NylKZNv6U/6oSS+zTd69erFyJEjAzbAC0BOTg5pN9zMjbPeJiImjpeWvc2Em/oGbPsiIuUpKAXczCKBmUAv4FxgkJmdW2qxXkBr/78xwBPByCah6+afNeN311/I0sIkGrZuT3FxMYsXL6agoOCMt707r4DBdz/G0ucW0ipnLa9O6Eq7xjUDkFpEJDiCdQj9ImCbc+4zADNbBPQDPjlqmX7AAlfSxfrAzGqZWUPn3NdByigh6LpOCZxdO4ZbY2LYV7yDTZs2M378eG699VYuuuii09rW4cOHmTXrCd776BM2Nx/Ad3Uu4rdPvsCvR1xDRISuNBeR8BKsAt4Y+PKo6Wyg8yks0xhQAa/kOreoS8bES7nzuXVkbIHM56ez45vdvPbKSxQVFTFr1iz69OlD8+bNj1s3Ly+P9PR0YmNj2Zi5iecX/5MdO3fRbeoQfj/gfFo3iPOgRSIiZy5YBfxE3ZvSJzNPZZmSBc3GUHKYnSZNmpxZMgkLjWrFsHBkZ575b0MePzKdHTnfMnTef0mO2cPEiRPZu3cvU6dOZcuWLdx7773cdNNNOOd4/PG/sHz5G0z41V3s8TUhof+d/KbPpVzTqYnu7xaRsBasAp4NnH3UdAKwowzLAOCcmwvMhZInsQUupoSyiAjj5i5N6X/+MOa9+wWLVm3nnb35tBs+jTVV2zBx0UfsW7ecF154gbi4OBqe3Yy4pK60je9EdrNUbrqkFX07NKJKpO6eFJHwF6x3slVAazNrbmZVgRuBl0st8zIw1H81ehcgp7Kc/160aBEpKSnUqFHjpA8OWbBgAS1btsTn89G5c2fWrFkTsP2PHTuW2NhYYmNj8fl8mNkP07GxsTzzzDMB21cgxFWLYuKVrXl3cjcWjOnKTTdcQ/V6DVn75X4+julAx3tfYm+bfuxtmUq/G4fy6p9/TfqEyxlwQYKKt4hUGEHpgTvniszsNuB1IBKY55zbaGZj/a/PBjKA3sA24BAwPBjZQkHt2rUZP3483333HWPGjDnu9XfffZdx48bx4osvctlll/GnP/2J3r17s3XrVmrUqHHG+589ezazZ8/+YV8pKSnk5eWd8XbLW2SEkdI6npTWGp9bRCqfoHVHnHMZzrlE51xL59wD/nmz/cUbV+Ln/tfbO+eOH6GkgkpNTWXQoEEnHX3sySefZMCAAVx11VVER0czadIkoqOjefHFF0+4/FtvvUWVKlV49tlnadmyJdWrV2fo0KEcOHCA0aNHU7t2bZo2bUp6enp5NktERMpRpXoS25vz5/JN1mdB2Vf9pi244pbje9NlsW7dOm655ZYfps2Mjh07sm7dupOuc+TIEd566y3Wr1/P7t27SU5OpkuXLjz66KPMmTOHuXPnMmLECHr27InP5wtIThERCR6dEAwDubm51Kx57ENGatWqxYEDB350vQceeACfz0eTJk24/PLLad68OVdffTUREREMHTqUnJwctm7dWp7RRUSknFSqHnigesTBFhcXR05OzjHz9u/fT8uWLU+6TmRkJPHx/39u2OfzHXO+/Pted25uboDTiohIMKgHHgY6dOjAhx9++MO0c461a9fSoUMHD1OJiIiXVMBDwJEjR8jPz6ewsBCA/Px88vPzfxi4Y/To0aSnp7NixQoKCwuZPn06+fn5XHPNNV7GFhERD6mAh4Cnn36amJgYUlNTOXLkCDExMcTExJCVlQVA165dmTVrFqNHj6ZmzZosXryYjIyMgNxCJiIi4ckCOTyjF5KTk93q1cffcZaZmUlSUpIHiSoHfX9FRILDzNY455JLz1cPXEREJAypgIuIiIQhFXAREZEwpAIuIiIShip0AS8uLvY6QoUU7hc+iohUBBW2gFevXp2vvvqKwsJCFZwAcs6xZ88eqlWr5nUUEZFKrcI+SjUhIYHdu3eTlZVFUVGR13EqlGrVqpGQkOB1DBGRSq3CFvCIiAjq169P/fr1vY4iIiIScBX2ELqIiEhFpgIuIiIShlTARUREwpAKuIiISBhSARcREQlDYT8amZl9C2QFcJP1gN0B3J5X1I7QUlHaARWnLWpHaKko7YDAt6Wpcy6+9MywL+CBZmarTzRsW7hRO0JLRWkHVJy2qB2hpaK0A4LXFh1CFxERCUMq4CIiImFIBfx4c70OECBqR2ipKO2AitMWtSO0VJR2QJDaonPgIiIiYUg9cBERkTCkAi4iIhKGVMD9zKynmW02s21mNsXrPGVlZmeb2ZtmlmlmG81soteZzoSZRZrZR2b2qtdZysrMapnZ82a2yf9z+ZnXmcrCzH7p/53aYGb/MLOwGRTezOaZ2TdmtuGoeXXM7A0z2+r/v7aXGU/FSdrxqP9362Mze9HMankY8ZScqB1HvXanmTkzq+dFttNxsnaY2QR/PdloZo+U1/5VwCkpEsBMoBdwLjDIzM71NlWZFQF3OOeSgC7Az8O4LQATgUyvQ5yhPwH/cs6dA3QgDNtjZo2BXwDJzrl2QCRwo7epTst8oGepeVOAFc651sAK/3Som8/x7XgDaOecOw/YAtwd7FBlMJ/j24GZnQ30ALYHO1AZzadUO8zsCqAfcJ5zri3wh/LauQp4iYuAbc65z5xzhcAiSn4AYcc597Vz7kP/17mUFIvG3qYqGzNLAK4G/up1lrIysxrApcDfAJxzhc65/Z6GKrsqQIyZVQF8wA6P85wy59xKYG+p2f2Ap/xfPwX0D2amsjhRO5xzy5xzRf7JD4CEoAc7TSf5eQD8EbgLCIurq0/SjnHAQ865Av8y35TX/lXASzQGvjxqOpswLXpHM7NmQEfgPx5HKavHKPljLvY4x5loAXwL/N1/KuCvZlbd61Cnyzn3FSU9ie3A10COc26Zt6nOWAPn3NdQ8sEXqO9xnkAYAbzmdYiyMLO+wFfOuXVeZzlDiUCKmf3HzN42swvLa0cq4CXsBPPC4hPgyZhZLPACcLtz7oDXeU6XmaUB3zjn1nid5QxVAS4AnnDOdQQOEh6Hao/hPz/cD2gONAKqm9lN3qaSo5nZPZScQnvG6yyny8x8wD3AfV5nCYAqQG1KTmFOAhab2YlqzBlTAS+RDZx91HQCYXR4sDQzi6KkeD/jnEv3Ok8ZXQL0NbMvKDml0c3MFnobqUyygWzn3PdHQZ6npKCHmyuBz51z3zrnDgPpwMUeZzpTu8ysIYD//3I71FnezGwYkAYMceH5cI+WlHw4XOf/m08APjSzszxNVTbZQLor8V9KjiCWywV5KuAlVgGtzay5mVWl5OKclz3OVCb+T3p/AzKdczO8zlNWzrm7nXMJzrlmlPw8/tc5F3Y9PufcTuBLM2vjn9Ud+MTDSGW1HehiZj7/71h3wvBivFJeBob5vx4GvORhljIzs57AZKCvc+6Q13nKwjm33jlX3znXzP83nw1c4P/7CTdLgG4AZpYIVKWcRllTAQf8F4DcBrxOyZvSYufcRm9TldklwM2U9FjX+v/19jpUJTcBeMbMPgbOB6Z5G+f0+Y8gPA98CKyn5L0jbB59aWb/AN4H2phZtpmNBB4CepjZVkqufH7Iy4yn4iTt+AsQB7zh/3uf7WnIU3CSdoSdk7RjHtDCf2vZImBYeR0V0aNURUREwpB64CIiImFIBVxERCQMqYCLiIiEIRVwERGRMKQCLiIiEoZUwEVERMKQCriIiEgYUgEXEcwswcwGlpoX4x+MIbIM26tqZiv9I5eJSDlQARcRKHk0aulntI+g5JnOR053Y/5heVcAA39qWREpGxVwkUrOzLoCM4Dr/I/ibO5/aQj+54ObWTP/oyG/X+dOM5tqZtXNbKmZrTOzDaV68Uv82xCRcqDDWyKVnHPuXTNbBdzpnNsAJYfAgRbOuS9+YvWewA7n3NX+9Woe9doGoNzGQhap7NQDFxGANsDmo6brAftPYb31wJVm9rCZpTjncr5/wX/ovdDM4gKaVEQAFXCRSs/M6gI5/nG+v/cdUK30okd9HQXgnNsCdKKkkD9oZveVWicayA9sYhEBFXARgebAjqNnOOf2AZFmdnQRb2pm8WYWAVzqf70RcMg5txD4A0ddCOf/YPBtqQ8GIhIgOgcuIpuAev6L1MY45/7tn78M6Aos90/vARYAZ/nnDQWygZ+bWTFwGBh31HavADLKP75I5aTxwEXkhMysI/Ar59zNZtYMeNU51+401k8H7nbObf7JhUXktOkQuoickHPuI+DNsj7IBVii4i1SftQDFxERCUPqgYuIiIQhFXAREZEwpAIuIiIShlTARUREwpAKuIiISBhSARcREQlDKuAiIiJh6P8A6sXVs6NHmkIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "RUN_EXACT_SOLUTION = False\n",
    "steps = 50\n",
    "exact_tlist = np.linspace(0, 16e-6, steps)\n",
    "#exact_signals = np.zeros([6,steps], dtype=np.float)\n",
    "# Time Interval between 0 and 16 us, 50 steps, LongitudinalFields = (0.0, 0.001, 0.003, 0.007, 0.008, 0.01)\n",
    "exact_signals = np.array([[ 1.        ,  0.98282653,  0.93964818,  0.8727281 ,  0.78028361,\n",
    "         0.67469059,  0.56109296,  0.44254458,  0.33016254,  0.22835089,\n",
    "         0.14071887,  0.07266857,  0.02508912, -0.00138344, -0.00777295,\n",
    "         0.00332417,  0.02902002,  0.06492124,  0.10737172,  0.15200355,\n",
    "         0.19525238,  0.23504429,  0.26796097,  0.29364225,  0.31249597,\n",
    "         0.32294924,  0.32736432,  0.32758011,  0.32305998,  0.3168234 ,\n",
    "         0.31049457,  0.30331904,  0.29736902,  0.29326092,  0.28955219,\n",
    "         0.28722038,  0.28623668,  0.28491011,  0.28388694,  0.28322455,\n",
    "         0.28156636,  0.27978173,  0.27826943,  0.27607753,  0.27416934,\n",
    "         0.27298859,  0.27164413,  0.27081398,  0.27069118,  0.27024463],\n",
    "       [ 1.        ,  0.98293689,  0.94103195,  0.87974072,  0.80302765,\n",
    "         0.72482631,  0.65413908,  0.59895465,  0.56280528,  0.54742553,\n",
    "         0.55334184,  0.57318891,  0.60218095,  0.63512508,  0.66574397,\n",
    "         0.69081457,  0.70740053,  0.71651987,  0.71913932,  0.71600087,\n",
    "         0.71090861,  0.70542094,  0.70019074,  0.69693086,  0.6955793 ,\n",
    "         0.69528207,  0.69608999,  0.69741402,  0.69823249,  0.69877767,\n",
    "         0.69893606,  0.69820817,  0.69717636,  0.69597567,  0.69432885,\n",
    "         0.69276073,  0.69138666,  0.68998791,  0.68896328,  0.68837029,\n",
    "         0.68798691,  0.68802579,  0.68841152,  0.68882866,  0.68930834,\n",
    "         0.68973257,  0.68982279,  0.68966208,  0.68929406,  0.68864183],\n",
    "       [ 1.        ,  0.98379849,  0.95110385,  0.92430074,  0.92333194,\n",
    "         0.94322695,  0.96888701,  0.98229823,  0.97805614,  0.96199376,\n",
    "         0.94602602,  0.94102634,  0.94716167,  0.95813592,  0.96467449,\n",
    "         0.96437462,  0.95925356,  0.95489471,  0.95351849,  0.95495805,\n",
    "         0.95698291,  0.95811534,  0.95793408,  0.95721899,  0.95668732,\n",
    "         0.9566025 ,  0.95680559,  0.95701551,  0.95707425,  0.95701427,\n",
    "         0.9569539 ,  0.95694134,  0.9569614 ,  0.95701089,  0.95704409,\n",
    "         0.95702411,  0.95701233,  0.9570149 ,  0.95701059,  0.9570523 ,\n",
    "         0.95710172,  0.95710734,  0.95712119,  0.95711323,  0.95706506,\n",
    "         0.95704849,  0.95704016,  0.95703239,  0.95707086,  0.95711522],\n",
    "       [ 1.        ,  0.9875797 ,  0.98140832,  0.98621011,  0.97075648,\n",
    "         0.95669399,  0.95541905,  0.94319278,  0.92842263,  0.92389329,\n",
    "         0.91594141,  0.90336002,  0.89654501,  0.89062457,  0.88065119,\n",
    "         0.87288486,  0.86795318,  0.86108697,  0.85435035,  0.85031619,\n",
    "         0.84608276,  0.84103892,  0.83743184,  0.83435711,  0.83042769,\n",
    "         0.82696249,  0.82416836,  0.82088203,  0.81775033,  0.81520849,\n",
    "         0.81250997,  0.80989694,  0.80777116,  0.80572486,  0.80367457,\n",
    "         0.80205509,  0.80067282,  0.79915915,  0.7980214 ,  0.79720875,\n",
    "         0.79614609,  0.79538015,  0.79497777,  0.7942634 ,  0.79376039,\n",
    "         0.79363704,  0.79320925,  0.79291028,  0.79302161,  0.79286575],\n",
    "       [ 1.        ,  0.98879191,  0.98699508,  0.98589855,  0.96748469,\n",
    "         0.96150537,  0.94988836,  0.93042286,  0.92044974,  0.90441159,\n",
    "         0.88659453,  0.8748919 ,  0.85867707,  0.84326163,  0.8318069 ,\n",
    "         0.81687864,  0.80418869,  0.79334047,  0.78042514,  0.77008204,\n",
    "         0.7599696 ,  0.74953374,  0.74097611,  0.73229548,  0.72431931,\n",
    "         0.71752935,  0.71086347,  0.70512305,  0.70026205,  0.69563065,\n",
    "         0.69186035,  0.68876905,  0.68581902,  0.68370366,  0.6819059 ,\n",
    "         0.68029858,  0.67945545,  0.67848443,  0.67807933,  0.67807028,\n",
    "         0.67782256,  0.67848698,  0.67905924,  0.67970109,  0.68120834,\n",
    "         0.68242028,  0.68400175,  0.6861668 ,  0.68811348,  0.69043407],\n",
    "       [ 1.        ,  0.99130363,  0.99367316,  0.98441018,  0.98244009,\n",
    "         0.97815888,  0.97460671,  0.9757831 ,  0.97160007,  0.9734014 ,\n",
    "         0.96809696,  0.96718836,  0.9624622 ,  0.95981762,  0.95816497,\n",
    "         0.95578323,  0.95672477,  0.95537404,  0.95691268,  0.95596032,\n",
    "         0.95648078,  0.95585914,  0.95559188,  0.95527909,  0.95483432,\n",
    "         0.95475075,  0.9544889 ,  0.95444332,  0.9543944 ,  0.95427475,\n",
    "         0.95433552,  0.954215  ,  0.95419628,  0.95416875,  0.95403384,\n",
    "         0.95404225,  0.9539122 ,  0.9538729 ,  0.95384906,  0.95378848,\n",
    "         0.95385451,  0.95386919,  0.95395887,  0.95410335,  0.95416793,\n",
    "         0.95437978,  0.95446006,  0.9546102 ,  0.95474143,  0.9547932 ]]);\n",
    "\n",
    "# Same as above, with Cu-Cu dipolar interaction.\n",
    "exact_signals_CuCu = np.array([[ 1.        ,  0.98282657,  0.93964865,  0.87272935,  0.78028696,\n",
    "         0.67470233,  0.56111582,  0.4425802 ,  0.33022139,  0.22843251,\n",
    "         0.14081954,  0.07279242,  0.02522711, -0.00124269, -0.00763999,\n",
    "         0.00343709,  0.02910163,  0.06495036,  0.10734618,  0.15192438,\n",
    "         0.19510024,  0.23483281,  0.26770654,  0.29333427,  0.31215187,\n",
    "         0.3225898 ,  0.32698183,  0.32717626,  0.32264645,  0.31638578,\n",
    "         0.31001279,  0.30279618,  0.29678455,  0.29258872,  0.2888023 ,\n",
    "         0.28637759,  0.28528979,  0.28388913,  0.28278938,  0.28205604,\n",
    "         0.28037023,  0.27855874,  0.27702096,  0.27483837,  0.27292428,\n",
    "         0.27171386,  0.2703522 ,  0.26946707,  0.26924531,  0.2687014 ],\n",
    "       [ 1.        ,  0.98293692,  0.9410324 ,  0.87974179,  0.80302961,\n",
    "         0.72483148,  0.65414674,  0.59895899,  0.56279733,  0.54740125,\n",
    "         0.55329201,  0.57309325,  0.6020493 ,  0.63496702,  0.6655529 ,\n",
    "         0.6906192 ,  0.70722795,  0.7163812 ,  0.71905147,  0.71597761,\n",
    "         0.71095595,  0.70552991,  0.70035639,  0.69714841,  0.6958386 ,\n",
    "         0.6955805 ,  0.69642111,  0.69777791,  0.69863126,  0.69920142,\n",
    "         0.69938316,  0.69867854,  0.69765745,  0.69646563,  0.6948309 ,\n",
    "         0.69326548,  0.6918944 ,  0.69050016,  0.68946443,  0.68884871,\n",
    "         0.6884322 ,  0.68841465,  0.68872886,  0.68907607,  0.6894854 ,\n",
    "         0.68985548,  0.68993525,  0.68980003,  0.68950061,  0.68897442],\n",
    "       [ 1.        ,  0.98379852,  0.95110414,  0.92430114,  0.92333093,\n",
    "         0.94322128,  0.96888409,  0.9823126 ,  0.9780936 ,  0.96203609,\n",
    "         0.94603782,  0.94099934,  0.94711532,  0.95810993,  0.96467949,\n",
    "         0.96440791,  0.95929011,  0.95491137,  0.95350301,  0.95492653,\n",
    "         0.95696769,  0.95813361,  0.95797172,  0.95724139,  0.9566808 ,\n",
    "         0.95657913,  0.95678783,  0.95701476,  0.95708748,  0.95702932,\n",
    "         0.95696214,  0.95694125,  0.95695521,  0.95700292,  0.95703994,\n",
    "         0.95702566,  0.95701792,  0.95702249,  0.95701571,  0.95705066,\n",
    "         0.95709516,  0.95709902,  0.95711357,  0.95711164,  0.95707014,\n",
    "         0.95705628,  0.95704938,  0.95703901,  0.95707135,  0.957112  ],\n",
    "       [ 1.        ,  0.98757971,  0.98140828,  0.98621163,  0.97076027,\n",
    "         0.95669799,  0.9554352 ,  0.9432287 ,  0.92846951,  0.92397853,\n",
    "         0.91606813,  0.90350092,  0.89673768,  0.89084694,  0.88085785,\n",
    "         0.87312326,  0.86819153,  0.86128541,  0.85455822,  0.85051496,\n",
    "         0.84625154,  0.8412079 ,  0.83758677,  0.83448791,  0.83054608,\n",
    "         0.82704993,  0.82422119,  0.82091216,  0.81774283,  0.81516587,\n",
    "         0.81244542,  0.80980092,  0.80764802,  0.80558272,  0.80350751,\n",
    "         0.80186382,  0.80046138,  0.79892606,  0.79775734,  0.79691872,\n",
    "         0.795833  ,  0.79502252,  0.79458771,  0.7938468 ,  0.79329063,\n",
    "         0.79313491,  0.79268038,  0.79233323,  0.79242035,  0.79224303],\n",
    "       [ 1.        ,  0.98879192,  0.98699502,  0.98589969,  0.96748394,\n",
    "         0.96150352,  0.94989131,  0.93041573,  0.92045214,  0.90441505,\n",
    "         0.8865946 ,  0.87492256,  0.85870154,  0.84331849,  0.8318963 ,\n",
    "         0.816977  ,  0.80433922,  0.7935124 ,  0.7806272 ,  0.77031396,\n",
    "         0.76022032,  0.74980401,  0.74125   ,  0.73257968,  0.7245986 ,\n",
    "         0.71780138,  0.71112593,  0.70537017,  0.70048968,  0.69583262,\n",
    "         0.69204068,  0.6889101 ,  0.68592623,  0.68377344,  0.68192056,\n",
    "         0.68027628,  0.67937711,  0.67835476,  0.67790987,  0.67784416,\n",
    "         0.67756101,  0.67818224,  0.67871672,  0.67932472,  0.68078836,\n",
    "         0.68197171,  0.68350124,  0.68561896,  0.68751972,  0.68976525],\n",
    "       [ 1.        ,  0.99130362,  0.99367312,  0.98440939,  0.98243597,\n",
    "         0.97815107,  0.97458831,  0.97576204,  0.97156735,  0.97337462,\n",
    "         0.96806425,  0.96718087,  0.96245435,  0.95984159,  0.9581947 ,\n",
    "         0.95584719,  0.95680812,  0.95550172,  0.9570791 ,  0.95618851,\n",
    "         0.95675983,  0.95620491,  0.95598891,  0.9557301 ,  0.95532813,\n",
    "         0.95528609,  0.95505568,  0.95504378,  0.9550178 ,  0.95492921,\n",
    "         0.95500776,  0.95491351,  0.95491316,  0.95490464,  0.95478939,\n",
    "         0.95481182,  0.95469816,  0.95467092,  0.95465577,  0.954604  ,\n",
    "         0.95467099,  0.95468799,  0.95477421,  0.95491163,  0.95497452,\n",
    "         0.95517234,  0.95525171,  0.95539008,  0.95551605,  0.95556276]])\n",
    "\n",
    "if RUN_EXACT_SOLUTION:\n",
    "    LongitudinalFields = (0.0, 0.001, 0.003, 0.007, 0.008, 0.01)\n",
    "    for idx, Bmod in enumerate(LongitudinalFields):\n",
    "\n",
    "        # Put field along muon polarization, that is always z\n",
    "        B = Bmod * np.array([0,0.,1.])\n",
    "        NS = MuonNuclearInteraction(atoms, external_field=B, log_level='critical')\n",
    "\n",
    "        # rotate the sample such that the muon spin is aligned with\n",
    "        # the 111 direction (and, just for convenience, the muon position is\n",
    "        # set to (0,0,0) )\n",
    "        NS.translate_rotate_sample_vec(np.array([1.,1.,1.]))\n",
    "\n",
    "        print(\"Computing exact signal for B={}\".format(Bmod))\n",
    "        exact_signals[idx]=NS.polarization(tlist, cutoff=2.0e-10)\n",
    "        del NS\n",
    "\n",
    "\n",
    "    exact_signals_CuCu = np.zeros_like(exact_signals)\n",
    "    for idx, Bmod in enumerate(LongitudinalFields):\n",
    "\n",
    "        # Put field along muon polarization, that is always z\n",
    "        B = Bmod * np.array([0,0.,1.])\n",
    "        NS = MuonNuclearInteraction(atoms, external_field=B, log_level='critical')\n",
    "\n",
    "        # rotate the sample such that the muon spin is aligned with\n",
    "        # the 111 direction (and, just for convenience, the muon position is\n",
    "        # set to (0,0,0) )\n",
    "        NS.translate_rotate_sample_vec(np.array([1.,1.,1.]))\n",
    "\n",
    "        print(\"Computing exact signal (Cu-Cu interaction) for B={}\".format(Bmod))\n",
    "        exact_signals_CuCu[idx]=NS.polarization(tlist, cutoff=20.0e-10)\n",
    "        del NS\n",
    "\n",
    "#import matplotlib as mpl; mpl.style.use(['bmh', 'paper', 'paper_twocol'])\n",
    "fig, axes = plt.subplots(1,1, figsize=(7,5))\n",
    "\n",
    "for i, Bmod in enumerate(LongitudinalFields):\n",
    "    p = axes.plot(1e6*tlist, signals[i], label='{} mT'.format(int(Bmod*1e3)), linestyle='-')\n",
    "    axes.plot(1e6*exact_tlist, exact_signals[i], linestyle='-.',  color='gray')\n",
    "    axes.plot(1e6*exact_tlist, exact_signals_CuCu[i], linestyle=':', color='k')\n",
    "\n",
    "axes.set_ylim((-0.1,1.1))\n",
    "axes.set_ylabel(r'$P_z(t)$')\n",
    "axes.set_xlabel(r'$t \\, \\mathrm{(\\mu s)}$')\n",
    "plt.legend(fontsize=13)\n",
    "plt.tight_layout()\n",
    "plt.savefig('Cu.png')\n",
    "plt.show()"
   ]
  }
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