{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "\n",
    "# Flutter Analysis of Goland's Wing\n",
    "\n",
    "## Description\n",
    "This is  simple rectangular wing with constant properties originally proposed by Martin Goland in 1945 as a flutter benchmark case. This example generates a beam/UVLM model with the original properties in SHARPy and computes flutter around an arbitrary equilibrium point using the following general process:\n",
    "\n",
    "* Calculate steady aerodynamic forces and deflections for a given angle of attack using a nonlinear solver\n",
    "\n",
    "* Linearise the dynamic aeroelastic equations about this reference condition\n",
    "\n",
    "* Reduce the size of the (linearized) structural subsystem using modal projection\n",
    "\n",
    "* Reduce the size of the (linearized) aerodyanic subsystem using a Krylov projection\n",
    "\n",
    "* Evaluate the stability of the linearised aeroelastic system at different velocities and plot the results.\n",
    "\n",
    "## Wing properties\n",
    "Span: b=20 ft., chord: c=6 ft., weight: 4 psi., radius of gyration about CG: .25c, elastic axis: 0.33c, centre of gravity: 0.43c\n",
    "\n",
    "### References\n",
    "\n",
    "Goland, M. (1945). The Flutter o a Uniorm Cantilever Wing. Journal of Applied Mechanics,12(4):197-208.\n",
    "\n",
    "Maraniello, S., & Palacios, R. (2019). State-Space Realizations and Internal Balancing in Potential-Flow Aerodynamics with Arbitrary Kinematics. AIAA Journal, 57(6):1–14. https://doi.org/10.2514/1.J058153\n",
    "\n",
    "#### Latest update, RPN 14.05.2023\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Required Packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import os\n",
    "import sys\n",
    "import sharpy.cases.templates.flying_wings as wings  # See this package for the Goland wing structural and aerodynamic definition\n",
    "import sharpy.sharpy_main  # used to run SHARPy from Jupyter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem Set-up"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Operatig conditions\n",
    "\n",
    "The UVLM is assembled in normalised time at a velocity of $1 m/s$. The only matrices that need updating then with free stream velocity are the structural matrices, which is significantly cheaper to do than to update the UVLM."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "u_inf = 1.\n",
    "alpha_deg = 2.  # Define angle of attack for static aeroelastic analysis.\n",
    "rho = 1.02      # Air density."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Discretisation\n",
    "\n",
    "Note: To achieve convergence of the flutter results with the ones found in the literature, a fine grid is needed. If you are running this notebook for the first time, set `M = 4` initially to verify that your system can perform!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "M = 16             # Number of chordwise panels\n",
    "N = 32             # Number of spanwise panels\n",
    "M_star_fact = 10   # Length of the wake in chords.\n",
    "num_modes =  8     # Number of vibration modes retained in the structural model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ROM\n",
    "\n",
    "A moment-matching (Krylov subspace) model order reduction technique is employed. This ROM method offers the ability to interpolate the transfer functions at a desired point in the complex plane. See the ROM documentation pages for more info. Note that this ROM method matches the transfer function but does not guarantee stability. Therefore the resulting system may be unstable. These unstable modes may appear far in the right hand plane but will not affect the flutter speed calculations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "c_ref = 1.8288 # Goland wing reference chord. Used for reduced frequency normalisation\n",
    "rom_settings = dict()\n",
    "rom_settings['algorithm'] = 'mimo_rational_arnoldi'  # reduction algorithm\n",
    "rom_settings['r'] = 6  # Krylov subspace order\n",
    "frequency_continuous_k = np.array([0.])  # Interpolation point in the complex plane with reduced frequency units\n",
    "frequency_continuous_w = 2 * u_inf * frequency_continuous_k / c_ref\n",
    "rom_settings['frequency'] = frequency_continuous_w"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Case Admin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The case to run will be: goland_csM16N32Ms10_nmodes8rom_MIMORA_r6_sig0000_0000j\n",
      "Case files will be saved in ./cases/goland_csM16N32Ms10_nmodes8rom_MIMORA_r6_sig0000_0000j\n",
      "Output files will be saved in ./output/goland_csM16N32Ms10_nmodes8rom_MIMORA_r6_sig0000_0000j/\n"
     ]
    }
   ],
   "source": [
    "case_name = 'goland_cs'\n",
    "case_nlin_info = 'M%dN%dMs%d_nmodes%d' % (M, N, M_star_fact, num_modes)\n",
    "case_rom_info = 'rom_MIMORA_r%d_sig%04d_%04dj' % (rom_settings['r'], frequency_continuous_k[-1].real * 100,\n",
    "                                                  frequency_continuous_k[-1].imag * 100)\n",
    "\n",
    "case_name += case_nlin_info + case_rom_info\n",
    "route_test_dir = os.path.abspath('')\n",
    "\n",
    "print('The case to run will be: %s' % case_name)\n",
    "print('Case files will be saved in ./cases/%s' %case_name)\n",
    "print('Output files will be saved in ./output/%s/' %case_name)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulation Set-Up"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Goland Wing\n",
    "\n",
    "`ws` is an instance of a Goland wing with a control surface. Reference the template file `sharpy.cases.templates.flying_wings.GolandControlSurface` for more info on the geometrical, structural and aerodynamic definition of the Goland wing here used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "ws = wings.GolandControlSurface(M=M,\n",
    "                                N=N,\n",
    "                                Mstar_fact=M_star_fact,\n",
    "                                u_inf=u_inf,\n",
    "                                alpha=alpha_deg,\n",
    "                                cs_deflection=[0, 0],\n",
    "                                rho=rho,\n",
    "                                sweep=0,\n",
    "                                physical_time=2,\n",
    "                                n_surfaces=2,\n",
    "                                route=route_test_dir + '/cases',\n",
    "                                case_name=case_name)\n",
    "\n",
    "ws.clean_test_files()\n",
    "ws.update_derived_params()\n",
    "ws.set_default_config_dict()\n",
    "\n",
    "ws.generate_aero_file()\n",
    "ws.generate_fem_file()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulation Settings\n",
    "\n",
    "The settings for each of the solvers are now set. For a detailed description on them please reference their respective documentation pages"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### SHARPy Settings\n",
    "\n",
    "The most important setting is the `flow` list. It tells SHARPy which solvers to run and in which order."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "ws.config['SHARPy'] = {\n",
    "    'flow':\n",
    "        ['BeamLoader', 'AerogridLoader',\n",
    "         'StaticCoupled',\n",
    "         'AerogridPlot',\n",
    "         'BeamPlot',\n",
    "         'Modal',\n",
    "         'LinearAssembler',\n",
    "         'AsymptoticStability',\n",
    "         ],\n",
    "    'case': ws.case_name, 'route': ws.route,\n",
    "    'write_screen': 'off', 'write_log': 'on',    # Change to 'on' as neded.\n",
    "    'log_folder': route_test_dir + '/output/',\n",
    "    'log_file': ws.case_name + '.log'}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Beam Loader Settings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "ws.config['BeamLoader'] = {\n",
    "    'unsteady': 'off',\n",
    "    'orientation': ws.quat}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Aerogrid Loader Settings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "ws.config['AerogridLoader'] = {\n",
    "    'unsteady': 'off',\n",
    "    'aligned_grid': 'on',\n",
    "    'mstar': ws.Mstar_fact * ws.M,\n",
    "    'freestream_dir': ws.u_inf_direction,\n",
    "    'wake_shape_generator': 'StraightWake',\n",
    "    'wake_shape_generator_input': {'u_inf': ws.u_inf,\n",
    "                                    'u_inf_direction': ws.u_inf_direction,\n",
    "                                    'dt': ws.dt}}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Static Coupled Solver"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "ws.config['StaticCoupled'] = {\n",
    "    'print_info': 'on',\n",
    "    'max_iter': 200,\n",
    "    'n_load_steps': 1,\n",
    "    'tolerance': 1e-10,\n",
    "    'relaxation_factor': 0.,\n",
    "    'aero_solver': 'StaticUvlm',\n",
    "    'aero_solver_settings': {\n",
    "        'rho': ws.rho,\n",
    "        'print_info': 'off',\n",
    "        'horseshoe': 'off',\n",
    "        'num_cores': 4,\n",
    "        'n_rollup': 0,\n",
    "        'rollup_dt': ws.dt,\n",
    "        'rollup_aic_refresh': 1,\n",
    "        'rollup_tolerance': 1e-4,\n",
    "        'velocity_field_generator': 'SteadyVelocityField',\n",
    "        'velocity_field_input': {\n",
    "            'u_inf': ws.u_inf,\n",
    "            'u_inf_direction': ws.u_inf_direction}},\n",
    "    'structural_solver': 'NonLinearStatic',\n",
    "    'structural_solver_settings': {'print_info': 'off',\n",
    "                                   'max_iterations': 150,\n",
    "                                   'num_load_steps': 4,\n",
    "                                   'delta_curved': 1e-1,\n",
    "                                   'min_delta': 1e-10,\n",
    "                                   'gravity_on': 'on',\n",
    "                                   'gravity': 9.81}}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### AerogridPlot Settings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "ws.config['AerogridPlot'] = {'include_rbm': 'off',\n",
    "                             'include_applied_forces': 'on',\n",
    "                             'minus_m_star': 0}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### BeamPlot Settings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "ws.config['BeamPlot'] = {'include_rbm': 'off',\n",
    "                         'include_applied_forces': 'on'}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Modal Solver Settings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "ws.config['Modal'] = {'NumLambda': 20,\n",
    "                      'rigid_body_modes': 'off',\n",
    "                      'print_matrices': 'on', # 'keep_linear_matrices': 'on',            'write_dat': 'off',\n",
    "                      'rigid_modes_cg': 'off',\n",
    "                      'continuous_eigenvalues': 'off',\n",
    "                      'dt': 0,\n",
    "                      'plot_eigenvalues': False,\n",
    "                      'max_rotation_deg': 15.,\n",
    "                      'max_displacement': 0.15,\n",
    "                      'write_modes_vtk': True,\n",
    "                      'use_undamped_modes': True}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Linear System Assembly Settings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "ws.config['LinearAssembler'] = {'linear_system': 'LinearAeroelastic',\n",
    "                                'linear_system_settings': {\n",
    "                                    'beam_settings': {'modal_projection': 'on',\n",
    "                                                      'inout_coords': 'modes',\n",
    "                                                      'discrete_time': 'on',\n",
    "                                                      'newmark_damp': 0.5e-4,\n",
    "                                                      'discr_method': 'newmark',\n",
    "                                                      'dt': ws.dt,\n",
    "                                                      'proj_modes': 'undamped',\n",
    "                                                      'use_euler': 'off',\n",
    "                                                      'num_modes': num_modes,\n",
    "                                                      'print_info': 'on',\n",
    "                                                      'gravity': 'on',\n",
    "                                                      'remove_sym_modes': 'on',\n",
    "                                                      'remove_dofs': []},\n",
    "                                    'aero_settings': {'dt': ws.dt,\n",
    "                                                      'ScalingDict': {'length': 0.5 * ws.c_ref,\n",
    "                                                                      'speed': u_inf,\n",
    "                                                                      'density': rho},\n",
    "                                                      'integr_order': 2,\n",
    "                                                      'density': ws.rho,\n",
    "                                                      'remove_predictor': 'on',\n",
    "                                                      'use_sparse': 'on',\n",
    "                                                      'remove_inputs': ['u_gust'],\n",
    "                                                      'rom_method': ['Krylov'],\n",
    "                                                      'rom_method_settings': {'Krylov': rom_settings}},\n",
    "                                    }}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Asymptotic Stability Analysis Settings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "ws.config['AsymptoticStability'] = {'print_info': True,\n",
    "                                    'velocity_analysis': [100, 180, 81],\n",
    "                                   'modes_to_plot': []}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Write solver settings config file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "ws.config.write()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Run SHARPy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "fatal: not a git repository (or any of the parent directories): .git\n",
      "/home/rpalacio/anaconda3/envs/sharpy/lib/python3.10/site-packages/scipy/sparse/_index.py:146: SparseEfficiencyWarning: Changing the sparsity structure of a csc_matrix is expensive. lil_matrix is more efficient.\n",
      "  self._set_arrayXarray(i, j, x)\n",
      "/home/rpalacio/anaconda3/envs/sharpy/lib/python3.10/site-packages/sharpy/linear/src/lingebm.py:313: UserWarning: Euler parametrisation not implemented - Either rigid body modes are not being used or this method has already been called.\n",
      "  warnings.warn('Euler parametrisation not implemented - Either rigid body modes are not being used or this '\n",
      "/home/rpalacio/anaconda3/envs/sharpy/lib/python3.10/site-packages/sharpy/rom/krylov.py:242: UserWarning: Reduced Order Model Unstable\n",
      "  warn.warn('Reduced Order Model Unstable')\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<sharpy.presharpy.presharpy.PreSharpy at 0x7f90aedb16c0>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sharpy.sharpy_main.main(['', ws.route + ws.case_name + '.sharpy'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Nonlinear equilibrium\n",
    "\n",
    "The nonlinear equilibrium condition can be visualised and analysed by opening, with Paraview, the files in the `/output/<case_name>/aero` and `/output/<case_name>/beam` folders to see the deflection and aerodynamic forces acting on the wing."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Stability \n",
    "\n",
    "The stability of the Goland wing is now analysed under changing free stream velocity. The flutter modes involves the two lowest frequency modes near the imaginary axis (1st bending and 1st torsion if aerodynamics is removed). The two modes are seen quite separated at 100 m/s. As speed is increased, the damping of the torsion mode decreases until it crosses the imaginary axis onto the right hand plane and flutter begins."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "file_name = './output/%s/stability/velocity_analysis_min1000_max1800_nvel0081.dat' % case_name\n",
    "\n",
    "velocity_analysis = np.loadtxt(file_name)\n",
    "u_inf = velocity_analysis[:, 0]\n",
    "eigs_r = velocity_analysis[:, 1]\n",
    "eigs_i = velocity_analysis[:, 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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85y9evBgmkwnjx49HRUUFhg4diuXLl0NV1ZZ8HCIiIgoDrSoYklLWezwqKgpr1qxpMB2bzYbs7GxkZ2c3VdaIiIjOuFA7UHPSxdq1qmCIiIiI6sZgqHm0qg7URERERC2NNUNEREThItQRYawYqhWDISIiojDBZrLmwWCIiIgoTDAYah4MhoiImpjT6UJZhR2VDhccmoTdoaHCKaHpOlw6oEkJXRpfIQQkBFRFQFEEIF0AgJ3HimC1WGBWAatJhUkVsJpUWBQBsypgMSlQhICisOsnUagYDBERNQFd1/Hsshz8+Y01qKh0uPcKQDEBZitgjQLMNsASBVhtUC0WY20tqxlmixkmiwkWi4o2NhVz+gEz/r4LwmSG1aLC5tnMxhZtURFtURBtVhBjURFtVhBlUWFT3ZtJQZSqwqIqMKkKLCYBs6rAYlKMQMqswuIOqGxmBarC2oJwwZqh5sFgiIgoRLqu4/ppryBny95qRySgOwGHDkgd0HVjn9Sh6dJ4KaXfZnFX9DjsLkhNQHfXInk26fPas2nuTbfAfb7q3W8FIKFAl7qxT1egSQ0uVYFTk3BqElZ3UMTPydaPwVDzYDBERBSidz/9upZAyIfUAJcTUFRjU02AywlNVSEUAcWlQFGMzeXSAACaBujQoSgCiqLDpAq4XAJOxWhSs2sCJk3ApEioLh0mRcDk0qEKAVXoUDVhvNYEFCHdH6LS2DRACAlFCLh0CaFJSOiIYkBEEYrBEBFRiBYuXdvwSVIDNFfVproAXYeu+Wy6DqkZ0Yim6ZBCgXTXHmm6UdPj0iQ0VUJz1+o4VQmzLuHybjpcioBLSmi6hEvRYdIFdCGhC0BXJHQpoOsSmiKh6IAqJDQhoOkSJpXRUKvGofXNgsEQEVGIfjryS8MnSQlAAnA3mUnPPvdhSL8liTyHPZuu69B1o7O1rHaOX7NZ1V38Nr+sVEvfc41LB0xcwrFVYzNZ82AwREQUIlVVoOlaSGmIBv5kF4pS5wcZP9/obPXxxx8HfM3w4cMRFRUV0DUMhoiIQjTy1xfhk/U76z9JKO5NNUaYud97+gop7mDHCHgkFAFIBVAUI9hRBaAIAVVRvMPwVUVAEca6SsZxQBXCeA9jv2erN2vVvlLrFWk1Q9dff31A5wsh8MMPP6Br164BXccJKoiIQvTw7zIbPsnTcdpkNoIh1QRhMjpQezZVVaGYjF/LiqJAVRUoioDJpEBVBUyqJwAyvpoEYFaMYfMm1Zh/yKQYHadN3nMUdyds9yYEVAGoStXcRlX7mrmgKGSeYCiULdzk5+e7m4kb3qKjo4O6B7/1iYhCdGmPdCybP6nu5irVDJgsxnxD3s0Ck8lkzDVkMTbVrMJsNn4tmy0KzGYFZrMKi1mBRVVgNRnzDFnN7rmFzAqiLApsJgGrKmBRFZiFgEVRYFYVmBVjXiFVETApMAIlRUBVjYBJcdc4eWqeON8QtTaTJk0KqMnr9ttvR1xcXMD3YTMZEVETuCXzV7i6/wV4IvsTrPrXf1FSboeEYtQEWaIBazRgiYKw2KC6gx/PhItmiwlmiwlWq4pYmwLAidhoMxSzBTaLaswD5Jl00WIEQZ4JF6PMCqLMKqyqAptqfPW8NrsnXTS7J100KcZrk6rApAhYVOGdlNFq4rD6sBBho8mWLVsW0Pkvv/xyUPdhMERE1EQ6JMThlTm34ZU5twWdhtPpxGeffYZP/zAAZrO5SfKl6zpcmgZNNyZwBIxlPEyKEQwxCAofkdZnqKUwGCIiOsspigIL1zA7K0RyMFRRUQEppbdf0KFDh7Bq1Sr07NkTI0aMCClt/nQQERFRq3fdddfh7bffBgCcPn0a/fv3x1//+ldcd911QTePeTAYIiIiChMCIY4mC7DT0MaNGzF69GikpaVBCIHVq1fXOOe7777DmDFjEB8fjzZt2uCKK67A4cOHvcftdjumTZuGpKQkxMTEYMyYMTh69GjAz/7tt9/iyiuvBAC8//77SE5OxqFDh/D222/jhRdeCDg9XwyGiIiIwkRLD60vKytDnz59sGTJklqP//jjjxg0aBAuvPBCrF+/Hv/973/x+OOPw2azec+ZPn06Vq1ahZUrV2Lz5s0oLS3FqFGjoGmBTVRaXl6ONm3aAADWrl2LsWPHQlEUXHHFFTh06FBAaVXHPkNERERUq8zMTGRm1j2P1qOPPorf/OY3WLhwoXef74SHRUVFWLp0KVasWIFhw4YBAN555x2kp6fjiy++wMiRIxudl27dumH16tW44YYbsGbNGsyYMQMAUFBQENRwel+sGSIiIgoXogk2AMXFxX6b3W4POCu6ruPTTz/F+eefj5EjR6JDhw7o37+/X1Nabm4unE6nXwfntLQ09OrVC1u2bAnofk888QSysrJw7rnn4vLLL8eAAQMAGLVEl156acD598VgiIiIKEw0VTNZeno64uPjvduCBQsCzktBQQFKS0vxpz/9Cddccw3Wrl2LG264AWPHjsWGDRsAGLNHWywWtGvXzu/a5ORk5OfnN+o+jzzyCL7++mvcdNNNOHz4MLZt24Y1a9Z4jw8dOhSLFy8OOP++2ExGREQUYY4cOeLXtGS1WgNOQ9d1AMYoL0+T1SWXXIItW7bglVdewVVXXVXntVLKRvdfysvLw6hRo6CqKkaPHo3rrrsOPXv29Ob58ssvDzjv1bFmiIiIKEw0Vc1QXFyc3xZMMJSUlASTyYSePXv67e/Ro4d3NFlKSgocDgcKCwv9zikoKEBycnKj7rNs2TL8/PPP+Pvf/462bdti1qxZSEpKwtixY7F8+XKcOHEi4LxXx2CIiIgoTAgR+tZULBYLfvWrX2Hfvn1++7///nt07twZANC3b1+YzWbk5OR4j+fl5WH37t0YOHBgo+8lhMCVV16JhQsX4n//+x++/vprXHHFFXj99ddxzjnnYPDgwfjLX/6CY8eOBfUsbCYjIiKiWpWWlmL//v3e9wcOHMCOHTuQkJCATp064cEHH8TNN9+MwYMHIyMjA59//jk++eQTrF+/HgAQHx+PKVOmYNasWUhMTERCQgKysrLQu3dv7+iyYPTo0QM9evTA7NmzUVBQgE8++QQff/wxACArKyvg9BgMERERhQmjdieU5TgCO3/btm3IyMjwvp85cyYAYzX55cuX44YbbsArr7yCBQsW4P7778cFF1yADz74AIMGDfJes3jxYphMJowfPx4VFRUYOnQoli9fDlVVg34OXx06dMCUKVMwZcqUoNNgMERERBQuQm3qCvDaIUOGQEpZ7zl33XUX7rrrrjqP22w2ZGdnIzs7O7Cb16KyshI7d+5EQUGBtwO3x5gxY4JOl8EQERFRmIjkhVo///xzTJw4sdYO00KIgGe09sUO1ERERNTqTZ06FePGjUNeXh50XffbQgmEANYMERERhY1QR4SFccUQCgoKMHPmzEYPyQ8Ea4aIiIjChKKIkLdwddNNN3lHqTU11gwRERFRq7dkyRKMGzcOmzZtQu/evWE2m/2O33///UGnzWCIiIgoTERyM9m7776LNWvWICoqCuvXr/frDC6EYDBEREQUCSJ5NNljjz2Gp556Cg899BAUpWl7+bDPEBEREbV6DocDN998c5MHQgCDISIiorDRmtYma2mTJk3Ce++91yxps5mMiIgoTERyM5mmaVi4cCHWrFmDiy++uEYH6kWLFgWdNoMhIiIiavV27dqFSy+9FACwe/duv2OhBnkMhoiIiMJEJNcMrVu3rtnSZp8hIiKiMBFpfYZ27txZY0HW+uzZswculyvg+zAYIiIiChMCwls7FNQW6LL1Z9ill16KkydPNvr8AQMG4PDhwwHfh81kRERE1CpJKfH4448jOjq6Uec7HI6g7sNgiIiIKExE2gzUgwcPxr59+xp9/oABAxAVFRXwfRgMERERhYlI60DdXAuzVsc+Q0RERBTRWDNEREQUJiKtmaylMBgiIiIKE5HWTNZSWlUz2YIFC/CrX/0Kbdq0QYcOHXD99dfX6DglpcTcuXORlpaGqKgoDBkyBHv27PE7x263Y9q0aUhKSkJMTAzGjBmDo0ePtuSjEBERUZgIqGbo448/DvgGw4cPb3TP7g0bNuAPf/gDfvWrX8HlcuHRRx/FiBEjsHfvXsTExAAAFi5ciEWLFmH58uU4//zzMW/ePAwfPhz79u1DmzZtAADTp0/HJ598gpUrVyIxMRGzZs3CqFGjkJubC1VVA34GIiKi1oDNZM0joGDo+uuvDyhxIQR++OEHdO3atVHnf/75537vly1bhg4dOiA3NxeDBw+GlBLPPfccHn30UYwdOxYA8NZbbyE5ORnvvvsu7rnnHhQVFWHp0qVYsWIFhg0bBgB45513kJ6eji+++AIjR44M6BmIiIhaCzaTNY+A+wzl5+ejQ4cOjTrXU1MTrKKiIgBAQkICAODAgQPIz8/HiBEjvOdYrVZcddVV2LJlC+655x7k5ubC6XT6nZOWloZevXphy5YttQZDdrsddrvd+764uBgA4HQ64XQ6Q3qGs5GnTFg2tWP51I/lUz+WT8NaWxm1lnxEok8//RSffvopoqOjce6552Lq1KlBpRNQMDRp0qSAJjO6/fbbERcXF3CmAKNv0MyZMzFo0CD06tULgBGIAUBycrLfucnJyTh06JD3HIvFgnbt2tU4x3N9dQsWLMCTTz5ZY/+6desaPetlJMrJyTnTWWjVWD71Y/nUj+XTsNZSRuXl5S13s1DXFzvLKoaWLFmCTz75BCaTCUOHDm2ZYGjZsmUBJf7yyy8HdL6vqVOnYufOndi8eXONY9Wr+aSUDVb91XfOww8/jJkzZ3rfFxcXIz09HRkZGUhMTAwi92c3p9OJnJwcDB8+HGaz+Uxnp9Vh+dSP5VM/lk/DWlsZeVoTWgKbyfzdd999mDp1Kmw2G8aPHx90OkEPra+oqICU0ltzcujQIaxatQo9e/b0a6IKxrRp0/Dxxx9j48aN6Nixo3d/SkoKAKP2JzU11bu/oKDAW1uUkpICh8OBwsJCv9qhgoICDBw4sNb7Wa1WWK3WGvvNZnOr+EFrrVg+9WP51I/lUz+WT8NaSxm1ZB7YgdqfoigoLy9HWloaysrKgk8n2Auvu+46vP322wCA06dPo3///vjrX/+K6667LugaISklpk6dig8//BD//ve/0aVLF7/jXbp0QUpKil/VqMPhwIYNG7yBTt++fWE2m/3OycvLw+7du+sMhoiIiCj8vPjii1i2bBmeeOIJ/N///V/Q6QRdM/Ttt99i8eLFAID3338fycnJ2L59Oz744AM88cQT+P3vfx9wmn/4wx/w7rvv4qOPPkKbNm28fXzi4+MRFRUFIQSmT5+O+fPno3v37ujevTvmz5+P6OhoTJgwwXvulClTMGvWLCQmJiIhIQFZWVno3bu3d3QZERFROGIzmb+pU6ciKysL0dHRGDduXNDpBB0MlZeXe0eLrV27FmPHjoWiKLjiiiu8nZkD5alRGjJkiN/+ZcuWYfLkyQCA2bNno6KiAvfddx8KCwvRv39/rF271m/k2uLFi2EymTB+/HhUVFRg6NChWL58OecYIiKisMZmMn+/+c1v8Jvf/CbkdIIOhrp164bVq1fjhhtuwJo1azBjxgwARt+cUEaQNUQIgblz52Lu3Ll1nmOz2ZCdnY3s7Oyg8kFERESty6lTp7xT7TS1oIOhJ554AhMmTMCMGTMwdOhQDBgwAIBRS3TppZc2WQaJiIjIEMnNZElJSejYsSP69Onjt3Xv3j3k5wo6GLrpppswaNAg5OXloU+fPt79Q4cOxQ033BBSpoiIiKimSA6G9u7dix07dmD79u345ptv8Oqrr+LUqVOIiorCRRddhK1btwaddsDB0COPPILrr78el19+OVJSUrzD3T0uv/zyoDNDREREVJsLL7wQF154IW655RYARteazz//HNOmTcPQoUNDSjvgofV5eXkYNWoUUlNT8bvf/Q6ffvqp31IWRERE1Dw8HahD2c4WQghkZmbinXfewfHjx0NKK+BgaNmyZfj555/x97//HW3btsWsWbOQlJSEsWPHYvny5Thx4kRIGSIiIqLaeZrJQtnCla7rte6/4oorsH79+pDSDmrSRSEErrzySixcuBD/+9//8PXXX+OKK67A66+/jrS0NAwePBh/+ctfcOzYsZAyR0RERGfOxo0bMXr0aKSlpUEIgdWrV/sdnzx5co1g64orrvA7x263Y9q0aUhKSkJMTAzGjBmDo0ePBpyX2NhYXH755fjd736HF198EV9++SVOnDiBzz77DKWlpaE8ZvAzUPvq0aMHZs+ejS+//BLHjh3D5MmTsWnTJvztb39riuSJiIgILd9MVlZWhj59+mDJkiV1nnPNNdcgLy/Pu3322Wd+x6dPn45Vq1Zh5cqV2Lx5M0pLSzFq1ChomhZQXj788EPceOONKC0txYsvvoghQ4YgOTkZY8aMwaxZswJ7sGoC6kDtu5hpQz766KOAM0NERER1a6rRZNUXl61rjc7MzExkZmbWm6bVaq0xmMqjqKgIS5cuxYoVK7yrQLzzzjtIT0/HF198gZEjRzY679dccw2uueYa7/vKykr8+OOPSExMrPP+jRVQMLR9+3a/97m5udA0DRdccAEA4Pvvv4eqqujbt29ImSIiIqKaBEKcgdr9NT093W//nDlz6p3MuD7r169Hhw4d0LZtW1x11VV45pln0KFDBwBGnOB0Ov0WcE9LS0OvXr2wZcuWgIKh6mw2Gy666KKgr/cVUDC0bt067+tFixahTZs2eOutt7yrwxcWFuLOO+/ElVde2SSZIyIioqZ35MgRv9UiaqsVaozMzEyMGzcOnTt3xoEDB/D444/j6quvRm5uLqxWK/Lz82GxWLxxgkdycrJ3/dHWIOhJF//6179i7dq1fg/Yrl07zJs3DyNGjAi5/Y6IiIj8KUJACaFqyHNtXFxc0Etn+br55pu9r3v16oV+/fqhc+fO+PTTTzF27Ng6r5NStqqRbUF3oC4uLsbPP/9cY39BQQFKSkpCyhQRERHV1NrnGUpNTUXnzp3xww8/AABSUlLgcDhQWFjod15BQQGSk5ObNzMBCDoYuuGGG3DnnXfi/fffx9GjR3H06FG8//77mDJlSr3RIBEREZ2dTp48iSNHjiA1NRUA0LdvX5jNZuTk5HjPycvLw+7duzFw4MAzlc0agm4me+WVV5CVlYXbb78dTqfTSMxkwpQpU/Dss882WQaJiIjI0NJrk5WWlmL//v3e9wcOHMCOHTuQkJCAhIQEzJ07FzfeeCNSU1Nx8OBBPPLII0hKSvKuURofH48pU6Zg1qxZSExMREJCArKystC7d2/v6LLWIOhgKDo6Gi+99BKeffZZ/Pjjj5BSolu3boiJiWnK/BEREZGbIowtlOsDsW3bNmRkZHjfe6bYmTRpEl5++WXs2rULb7/9Nk6fPo3U1FRkZGTgvffeQ5s2bbzXLF68GCaTCePHj0dFRQWGDh2K5cuXQ1XV4B+kGkVRMGTIEDz77LNBjWgPOhjyiImJwcUXXxxqMkRERNTKDBkyBFLKOo+vWbOmwTRsNhuys7ORnZ3dlFnz8+abb+LQoUO4//778eWXXwZ8fcjB0N69e3H48GE4HA6//WPGjAk1aSIiIvIlAm/qqn792Wjy5MkAjPmSghF0MPTTTz/hhhtuwK5duyCE8EaOnn+kQKfZJiIiovqFOiKsFY1mD9jkyZNx1113YfDgwU2edtCjyR544AF06dIFP//8M6Kjo7Fnzx5s3LgR/fr1C3n1WCIiIiJfJSUlGDFiBLp374758+c36WLwQQdD//nPf/DUU0+hffv2UBQFiqJg0KBBWLBgAe6///4myyAREREZRBP8F64++OADHDt2DFOnTsU//vEPnHvuucjMzMT777/vHdUerKCDIU3TEBsbCwBISkrC8ePHAQCdO3fGvn37QsoUERER1eQZTRbKFs4SExPxwAMPYPv27fj666/RrVs33HHHHUhLS8OMGTO8kz0GKuhgqFevXti5cycAoH///li4cCG+/PJLPPXUU+jatWuwyRIREVEdPPMMhbKdDfLy8rB27VqsXbsWqqriN7/5Dfbs2YOePXti8eLFAacXdAfqxx57DGVlZQCAefPmYdSoUbjyyiuRmJiI9957L9hkiYiIiGpwOp34+OOPsWzZMqxduxYXX3wxZsyYgdtuu807r9HKlSvx+9//HjNmzAgo7aCDoZEjR3pfd+3aFXv37sWpU6fQrl27sybyJCIiak0ieTRZamoqdF3Hrbfeiq+//hqXXHJJjXNGjhyJtm3bBpx2UM1kTqcTGRkZ+P777/32JyQkMBAiIiJqJp5V60PZwtUDDzyAo0eP4sUXX/QLhKSUOHz4MACgXbt2OHDgQMBpBxUMmc1m7N69m4EPERERtYi5c+eitLS0xv5Tp06hS5cuIaUddAfqiRMnYunSpSHdnIiIiBrP00wWyhau6loWpLS0FDabLaS0g+4z5HA48MYbbyAnJwf9+vWrsUDrokWLQsoYERER+WvpVetbA8/isEIIPPHEE4iOjvYe0zQNW7durbX/UCCCDoZ2796Nyy67DABq9B0Kx8ImIiKi1mf79u0AjJqhXbt2wWKxeI9ZLBb06dMHWVlZId0j6GBo3bp1Id2YiIiIAhOJo8k88cadd96J559/HnFxcU1+j4D6DO3cuRO6rjf6/D179sDlcgWcKSIiIqopkkeTLVu2rFkCISDAmqFLL70U+fn5aN++faPOHzBgAHbs2MEZqYmIiChgM2fOxNNPP42YmBhv36G6hNJXOaBgSEqJxx9/3K/zUn0cDkdQmSIiIqKahHsL5fpwsn37du8irJ6+Q7UJta9yQMHQ4MGDA1qEdcCAAYiKigo4U0RERFRTpI0m8+2f3Jx9lQMKhtavX99M2SAiIqKGhLryfLivWt9cgp50kYiIiKilLFiwAG+++WaN/W+++Sb+/Oc/h5Q2gyEiIqIw4WkmC2ULV6+++iouvPDCGvsvuugivPLKKyGlHfQ8Q0RERNTywjieCUl+fj5SU1Nr7G/fvj3y8vJCSps1Q0RERNTqpaen48svv6yx/8svv0RaWlpIabNmiIiIKExE2mgyX3fffTemT58Op9OJq6++GgDwr3/9C7Nnz8asWbNCSpvBEBERUZiI5NFks2fPxqlTp3DffffB4XBASomoqCj88Y9/xMMPPxxS2k0SDLlcLuzbtw+7d+/2bqtWrWqKpImIiIgghMCf//xnPP744/juu+8QFRWF7t27w2q1hpx2wMHQTz/9hF27dvkFPt9//z1cLhcsFgt69OiB3r17h5wxIiIi8hfJzWQAcPr0aSxduhTfffcdhBDo2bMn7rrrLsTHx4eUbkDB0O23346//e1vEEIgOjoaZWVluPbaa/HEE0+gd+/e6N69O1RVDSlDREREVLtIW47D17Zt2zBy5EhERUXh8ssvh5QSixYtwjPPPIO1a9fisssuCzrtgEaTvf/++8jOzkZpaSmOHz+OqVOnYu3atfjmm2/QuXNnBkJERETULGbMmIExY8bg4MGD+PDDD7Fq1SocOHAAo0aNwvTp00NKO6Bg6MEHH8TEiRNhs9kQGxuL559/Hl9++SXWrVuHnj174vPPPw8pM0RERFQ3RYiQt3C1bds2/PGPf4TJVNWoZTKZMHv2bGzbti2ktAMKhp5++mnExsb67evbty++/vprTJ8+HTfffDMmTJiAX375JaRMERERUU1ChL6Fq7i4OBw+fLjG/iNHjqBNmzYhpd0kky4KIfDAAw9g7969sNvttU6XTURERKGJ5OU4br75ZkyZMgXvvfcejhw5gqNHj2LlypW4++67ceutt4aUdpPOM3TOOefggw8+wKefftqUyRIREVGE+8tf/gIhBCZOnAiXywUAMJvN+P3vf48//elPIaXdLJMuXnvttc2RLBERUUQLtakrjCuGYLFY8Pzzz2PBggX48ccfIaVEt27dEB0dHXLanIGaiIgoTITaCTqcO1B7REdHN/l8hq1qodaNGzdi9OjRSEtLgxACq1ev9js+efLkGm2fV1xxhd85drsd06ZNQ1JSEmJiYjBmzBgcPXq0BZ+CiIjo7NDQ57Kve+65B0IIPPfcc377Q/lcnjlzZqO3ULSqmqGysjL06dMHd955J2688cZaz7nmmmuwbNky73uLxeJ3fPr06fjkk0+wcuVKJCYmYtasWRg1ahRyc3M5DxIREYW1lm4ma8znMgCsXr0aW7durXX1+FA+l7dv396ofIbaMbxVBUOZmZnIzMys9xyr1YqUlJRajxUVFWHp0qVYsWIFhg0bBgB45513kJ6eji+++AIjR45s8jwTERG1lJZejqMxn8vHjh3D1KlTsWbNmhp9hkP9XF63bl1A+Q1WswRDiqJgyJAhePbZZ9G3b98mTXv9+vXo0KED2rZti6uuugrPPPMMOnToAADIzc2F0+nEiBEjvOenpaWhV69e2LJlS52FbrfbYbfbve+Li4sBAE6nE06ns0nzfzbwlAnLpnYsn/qxfOrH8mlYayuj1pKPQHg+5zysVmtQC57quo477rgDDz74IC666KIax4P9XG5pzRIMvfnmmzh06BDuv/9+fPnll02WbmZmJsaNG4fOnTvjwIEDePzxx3H11VcjNzcXVqsV+fn5sFgsaNeund91ycnJyM/PrzPdBQsW4Mknn6yxf926dU3SS/1slZOTc6az0KqxfOrH8qkfy6dhraWMysvLW+xeCkLr7Ou5Nj093W//nDlzMHfu3IDT+/Of/wyTyYT777+/1uPBfi7XZdOmTXj11Vfx448/4v3338c555yDFStWoEuXLhg0aFDA6XkEHQwdPnwY6enpNarcpJS4+uqr0alTJ8yZMyfojNXm5ptv9r7u1asX+vXrh86dO+PTTz/F2LFj67xOSllv1eDDDz/s1/mquLgY6enpyMjIQGJiYtNk/izidDqRk5OD4cOHw2w2n+nstDosn/qxfOrH8mlYayuj6rUszampmsmOHDmCuLg47/5gaoVyc3Px/PPP49tvvw04Tw19Ltfmgw8+wB133IHbbrsN27dv97bolJSUYP78+fjss88CSs9X0MFQly5dkJeX522i8jh16hS6dOkCTdOCzlRjpaamonPnzvjhhx8AACkpKXA4HCgsLPSLQgsKCjBw4MA606mretBsNreKH7TWiuVTP5ZP/Vg+9WP5NKy1lFFryEOg4uLi/IKhYGzatAkFBQXo1KmTd5+maZg1axaee+45HDx4MOjP5drMmzcPr7zyCiZOnIiVK1d69w8cOBBPPfVUSM8SdG1bXVFdaWkpbDZbSJlqrJMnT+LIkSNITU0FYKyTZjab/apO8/LysHv37oALnYiIqLURAlBC2JpymqE77rgDO3fuxI4dO7xbWloaHnzwQaxZswZA034u79u3D4MHD66xPy4uDqdPnw7pWQKuGfI0Jwkh8Pjjj/v1qdE0DVu3bsUll1wSVGZKS0uxf/9+7/sDBw5gx44dSEhIQEJCAubOnYsbb7wRqampOHjwIB555BEkJSXhhhtuAADEx8djypQpmDVrFhITE5GQkICsrCz07t3b24udiIgoXHmCmlCuD0R9n8udOnWq0ZXEbDYjJSUFF1xwAYCm/VxOTU3F/v37ce655/rt37x5M7p27RrYg1UTcDDkGfMvpcSuXbv85vmxWCzo06cPsrKygsrMtm3bkJGR4X3vCbwmTZqEl19+Gbt27cLbb7+N06dPIzU1FRkZGXjvvff8VqtdvHgxTCYTxo8fj4qKCgwdOhTLly/nHENERBT2WnpofX2fy8uXL29UGk31uXzPPffggQcewJtvvgkhBI4fP47//Oc/yMrKwhNPPBFQWtUFHAx5xvzfeeedeOGFF/wCkVANGTIEUso6j3uq3epjs9mQnZ2N7OzsJssXERFRJGroc7m6gwcP1tjXVJ/Ls2fPRlFRETIyMlBZWYnBgwfDarUiKysLU6dODSntoDpQO51OHDx4EHl5eU0aDBEREVHdWrqZrDXYsWOHt/vNM888g0cffRR79+6Fruvo2bMnYmNjQ75HUMGQ2WzG7t27Q57+moiIiBovEletv+yyy3DppZfi7rvvxoQJExAfH49+/fo16T2CHk02ceJELF26tCnzQkREROTnyy+/xGWXXYaHHnoIqampuP3225t8mY6g5xlyOBx44403kJOTg379+iEmJsbv+KJFi0LOHBEREVVRhIASQvVOKNeeKQMGDMCAAQPwwgsv4O9//zuWLVuGYcOG4dxzz8Vdd92FSZMmoWPHjiHdI+hgaPfu3bjssssAAN9//73fMTafERERNb2mWo4jHEVFRWHSpEmYNGkSfvzxRyxbtgyvvvoq5s6di+HDh5+ZGahbaiVZIiIiIl/nnXceHnroIaSnp+ORRx5p1Gjz+oS8UOvevXtx+PBhOBwO7z4hBEaPHh1q0kREROQjEjtQV7dhwwa8+eab+OCDD6CqKsaPH48pU6aElGbQwdBPP/2EG264Abt27YIQwjsPgaeJrCXWJiMiIookCkLsM4TwjIaOHDmC5cuXY/ny5Thw4AAGDhyI7OxsjB8/vkaf5WAE3Xz4wAMPoEuXLvj5558RHR2NPXv2YOPGjejXrx/Wr18fcsaIiIiIhg8fji5duuCll17CTTfdhO+++w6bN2/GnXfe2SSBEBBCzdB//vMf/Pvf/0b79u2hKAoURcGgQYOwYMEC3H///d5lO4iIiKhpRGIzWVRUFD744AOMGjWq2ZbWCjoY0jTNO+tjUlISjh8/jgsuuACdO3fGvn37miyDREREZIjEGag//vjjZr9H0MFQr169sHPnTnTt2hX9+/fHwoULYbFY8Nprr4W8eiwRERHVJERocwWFY81QSwg6GHrsscdQVlYGAJg3bx5GjRqFK6+8EomJiXjvvfeaLINEREREzSnoYGjkyJHe1127dsXevXtx6tQptGvXjpMuEhERNYNI7DPUEkKeZ8hXQkJCUyZHREREPiKxz1BLCDgYKi8vx4MPPojVq1fD6XRi2LBheOGFF5CUlNQc+SMiIiICAFRWVmLnzp0oKCiArut+x8aMGRN0ugEHQ3PmzMHy5ctx2223ISoqCu+++y5+//vf4x//+EfQmSAiIqKGCfd/oVwfrj7//HNMnDgRJ06cqHFMCBHSZM8BB0Mffvghli5diltuuQUAcNttt+HXv/41NE1rtvH/REREFNnNZFOnTsW4cePwxBNPIDk5uUnTDngG6iNHjuDKK6/0vr/88sthMplw/PjxJs0YERERkUdBQQFmzpzZ5IEQEEQwpGkaLBaL3z6TyQSXy9VkmSIiIqKaPDVDoWzh6qabbmq25b4CbiaTUmLy5MmwWq3efZWVlbj33nv91gj58MMPmyaHREREBMDoGxPK9DXhPPXNkiVLMG7cOGzatAm9e/eG2Wz2O37//fcHnXbAwdCkSZNq7Lv99tuDzgARERFRQ959912sWbMGUVFRWL9+vV9gJ4Ro2WBo2bJlQd+MiIiIghfJHagfe+wxPPXUU3jooYegKAH38qlXk066SERERM0nkmegdjgcuPnmm5s8EAKC6EBNREREZ4YiRMhbuJo0aVKzrX3KmiEiIiJq9TRNw8KFC7FmzRpcfPHFNTpQL1q0KOi0GQwRERGFiUjuM7Rr1y5ceumlAIDdu3f7HQt1lByDISIionARYp+hMF6NA+vWrWu2tIMOhmbOnFnrfiEEbDYbunXrhuuuu44r2RMREVGrFnQwtH37dnz77bfQNA0XXHABpJT44YcfoKoqLrzwQrz00kuYNWsWNm/ejJ49ezZlnomIiCKSAgElhOqdUK5tLfbu3YvDhw/D4XD47W/RVes9PLU+y5YtQ1xcHACguLgYU6ZMwaBBg/Db3/4WEyZMwIwZM7BmzZqgM0hERESGSB5a/9NPP+GGG27Arl27IISAlBJAVX+hUFatD3po/bPPPounn37aGwgBQFxcHObOnYuFCxciOjoaTzzxBHJzc4POHBEREREAPPDAA+jSpQt+/vlnREdHY8+ePdi4cSP69esX8pplQQdDRUVFKCgoqLH/l19+QXFxMQCgbdu2NaqxiIiIKDiRvFDrf/7zHzz11FNo3749FEWBoigYNGgQFixYENJSHEAIwdB1112Hu+66C6tWrcLRo0dx7NgxrFq1ClOmTMH1118PAPj6669x/vnnh5RBIiIiMkTypIuapiE2NhYAkJSUhOPHjwMAOnfujH379oWUdtB9hl599VXMmDEDt9xyC1wul5GYyYRJkyZ5Jz668MIL8cYbb4SUQSIiIqJevXph586d6Nq1K/r374+FCxfCYrHgtddeQ9euXUNKO+iaodjYWLz++us4efKkd2TZyZMn8dprr3kjt0suuQSXXHJJSBkkIiIig6cDdShbIDZu3IjRo0cjLS0NQgisXr3a7/jcuXNx4YUXIiYmBu3atcOwYcOwdetWv3PsdjumTZuGpKQkxMTEYMyYMTh69GjAz/7YY49B13UAwNNPP41Dhw7hyiuvxGeffYYXXngh4PR8hTzp4uHDh3H8+HE4HA4cOnTIuz+UIW5ERERUk4LQmroCHVpfVlaGPn364M4778SNN95Y4/j555+PJUuWoGvXrqioqMDixYsxYsQI7N+/H+3btwcATJ8+HZ988glWrlyJxMREzJo1C6NGjUJubi5UVW10XkaOHOl9fd5552Hv3r04deoU2rVrd+ZmoG7OIW5ERERUU0sPrc/MzERmZmadxydMmOD3ftGiRVi6dCl27tyJoUOHoqioCEuXLsWKFSswbNgwAMA777yD9PR0fPHFF34BTmNs2rQJr776Kn788Ue8//77OOecc7BixQp06dIFgwYNCuzhfATdTFZ9iNvu3bubbIgbERERNZ/i4mK/zW63h5ymw+HAa6+9hvj4ePTp0wcAkJubC6fTiREjRnjPS0tLQ69evbBly5aA0v/ggw8wcuRIREVFYfv27d48l5SUYP78+SHlPehgqPoQN1VVm2yIGxEREdWkNMEGAOnp6YiPj/duCxYsCDpP//znPxEbGwubzYbFixcjJycHSUlJAID8/HxYLBa0a9fO75rk5GTk5+cHdJ958+bhlVdeweuvv+63Yv3AgQPx7bffBp1/IIRmstqGuF1wwQVNMsSNiIiIahJChNQ/xnPtkSNH/CZNtlqtQaeZkZGBHTt24MSJE3j99dcxfvx4bN26FR06dKjzGillwM+xb98+DB48uMb+uLg4nD59OtBs+wm6ZsgzxA2Ad4jbl19+iaeeeirkIW5ERETUfOLi4vy2UIKhmJgYdOvWDVdccQWWLl0Kk8mEpUuXAgBSUlLgcDhQWFjod01BQQGSk5MDuk9qair2799fY//mzZvP3NB63yFu8+bNa9IhbkRERFSTaIKtuUkpvf15+vbtC7PZjJycHO/xvLw87N69GwMHDgwo3XvuuQcPPPAAtm7dCiEEjh8/jv/3//4fsrKycN9994WU56CbyXx7gHft2rVJh7gRERFRTaHOIh3otaWlpX61MQcOHMCOHTuQkJCAxMREPPPMMxgzZgxSU1Nx8uRJvPTSSzh69CjGjRsHAIiPj8eUKVMwa9YsJCYmIiEhAVlZWejdu7d3dFljzZ49G0VFRcjIyEBlZSUGDx4Mq9WKrKwsTJ06NaC0qgt5niFfCQkJTZkcERERnUHbtm1DRkaG9/3MmTMBAJMmTcIrr7yC//3vf3jrrbdw4sQJJCYm4le/+hU2bdqEiy66yHvN4sWLYTKZMH78eFRUVGDo0KFYvnx5QHMMeTzzzDN49NFHsXfvXui6jp49e3r7L4cipGCosrISO3fuREFBgbfJzIOTLhIRETW9lmx7GTJkiHcewdp8+OGHDaZhs9mQnZ2N7OzsoPPhGZ7/6quv4vzzz0e/fv2CTqs2QQdDn3/+OSZOnIgTJ07UOCaE4KSLRERETaylJ11sLcxmM3bv3t1s3XCC7kA9depUjBs3Dnl5edB13W9jIERERERNaeLEid5Rak0t6JqhgoICzJw5M+ChcURERBScpppnKBw5HA688cYbyMnJQb9+/RATE+N3fNGiRUGnHXQwdNNNN2H9+vU477zzgr45ERERNZ7vLNLBXh+udu/ejcsuuwwA8P333/sdO2MLtS5ZsgTjxo3Dpk2b0Lt3b7+psQEEtSTHxo0b8eyzzyI3Nxd5eXlYtWoVrr/+eu9xKSWefPJJvPbaaygsLET//v3x4osv+vVat9vtyMrKwt/+9jdvr/WXXnoJHTt2DPZRiYiIWoVIrhl666230LFjRyiKf0gnpcSRI0dCSjvoYOjdd9/FmjVrEBUVhfXr1/sVsBAiqGCorKwMffr0wZ133okbb7yxxvGFCxdi0aJFWL58Oc4//3zMmzcPw4cPx759+9CmTRsAwPTp0/HJJ59g5cqVSExMxKxZszBq1Cjk5uYGNYyPiIiIzrwuXbogLy+vxjIfp06dQpcuXULqrxx0MPTYY4/hqaeewkMPPVQjSgtWZmYmMjMzaz0mpcRzzz2HRx99FGPHjgVgRInJycl49913cc8996CoqAhLly7FihUrvJM5vfPOO0hPT8cXX3zhN1EkERFRuAl1FunwrRdCnUP8S0tLYbPZQko76GDI4XDg5ptvbrJAqCEHDhxAfn4+RowY4d1ntVpx1VVXYcuWLbjnnnuQm5vrnYvAIy0tDb169cKWLVvqDIbsdrt36nAAKC4uBmDMa+B0OpvpicKXp0xYNrVj+dSP5VM/lk/DWlsZtWQ+IrGZzDPRoxACTzzxBKKjo73HNE3D1q1bcckll4R0j6CDoUmTJuG9997DI488ElIGGis/Px8AaoxeS05OxqFDh7znWCwWtGvXrsY5nutrs2DBAjz55JM19q9bt86v0Mmf71ozVBPLp34sn/qxfBrWWsqovLz8TGfhrLZ9+3YARs3Qrl27YLFYvMcsFgv69OmDrKyskO4RdDCkaRoWLlyINWvW4OKLL67RgTqUIW71qR7VSikbjHQbOufhhx/2Rp6AUTOUnp6OjIwMJCYmhpbhs5DT6UROTg6GDx9e49+dWD4NYfnUj+XTsNZWRp7WhJYQiaPJ1q1bBwC488478fzzzyMuLq7J7xF0MLRr1y5ceumlAIzhbs0tJSUFgFH7k5qa6t1fUFDgrS1KSUmBw+FAYWGhX+1QQUFBvavjWq1WWK3WGvvNZnOr+EFrrVg+9WP51I/lUz+WT8NaSxm1ZB4isZnMY9myZc2WdtDBkCdSayldunRBSkoKcnJyvEGYw+HAhg0b8Oc//xkA0LdvX5jNZuTk5GD8+PEAgLy8POzevRsLFy5s0fwSERFR6LZu3YpTp075DbB6++23MWfOHJSVleH6669HdnZ2rZUajRVwMOQZyVUfIQQ++OCDgDNTWlqK/fv3e98fOHAAO3bsQEJCAjp16oTp06dj/vz56N69O7p374758+cjOjoaEyZMAADEx8djypQpmDVrFhITE5GQkICsrCz07t3bO7qMiIgoXEXiaLK5c+diyJAh3mBo165dmDJlCiZPnowePXrg2WefRVpaGubOnRv0PQIOhuLj44O+WUO2bduGjIwM73tPP55JkyZh+fLlmD17NioqKnDfffd5J11cu3atd44hAFi8eDFMJhPGjx/vnXRx+fLlnGOIiIjCXiQu1Lpjxw48/fTT3vcrV65E//798frrrwMA0tPTMWfOnJYNhpqzzW7IkCF1ziMAGDVOc+fOrfeBbTYbsrOzkZ2d3Qw5JCIiOnMUCCgh1O+Ecu2ZUlhY6DeSfMOGDbjmmmu873/1q1+FPAN1OHYsJyIiogiRnJyMAwcOADD6Cn/77bcYMGCA93hJSUnIndgZDBEREYUJTzNZKFu4ueaaa/DQQw9h06ZNePjhhxEdHY0rr7zSe3znzp0hLxof9GgyIiIialnC/V8o14ebefPmYezYsbjqqqsQGxuLt956y2/ixTfffNNv5YlgMBgiIiKiVqt9+/bYtGkTioqKEBsbW2NA1D/+8Q/ExsaGdA8GQ0REFDTPmJdwbH4JR5E4msyjrtHsCQkJIafNYIiIiALmdOmodEno7mBIFQIWE2BWlbD+wG3tRIijycKxmawlMBgiIqKAFJU7UO6oCoQUIWBSAaemwGICoi0MiCi8MBgiIqJGO1VaiaIKHS7daCITAFQVMLkDIQAwqYDVxMHKzSGSm8maE4MhIiJqFLvdjoJiF5ya7q0VEsIIhFRFeifNVRUBi8oP3ubAYKh5MHQnIqJG+emEHWV2DeV2DeUOY6t06KhwaLC7NNidOlyaDr2elQSIQrFp0ybcfvvtGDBgAI4dOwYAWLFiBTZv3hxSugyGiIioQXa7HSWVGsocLpQ6XSh1GFuJw4lyhwt2pw67S4NT06HpDIaai2iC/8LVBx98gJEjRyIqKgrbt2+H3W4HYMxAPX/+/JDSZjBEREQN+i6vAqUODSUOF0ocLhQ7nMZmd6LE4UKZ3eWuGTI6ErE5pnkoIvQtXM2bNw+vvPIKXn/9db/lNwYOHIhvv/02pLTZZ4iIiBpUVOlCqcOJCk2DU0q4dAkJowO1RdPg1E0wKUAbaYJNbSg1ClYkzkDtsW/fPgwePLjG/ri4OJw+fTqktBkMERFRg8qcLpS5XKhwabBrEi5NQnNHQyYB2C06TAJIFjbE2EJbNJOoNqmpqdi/fz/OPfdcv/2bN29G165dQ0qbwRARETWowqWh3KWh3KHDrkk4NWmMKoNRO1Ri1+DSdAyOaXOms3pWi+TRZPfccw8eeOABvPnmmxBC4Pjx4/jPf/6DrKwsPPHEEyGlzWCIiIgaVKnrsLskKl0SFU4NDk3CqRvNZXD3ly6udMHJrqjNSiC0pq4wjoUwe/ZsFBUVISMjA5WVlRg8eDCsViuysrIwderUkNJmMERERA1yaDrsLh2VLs0IijQdTpeESwKaZ94hKfHY2gN4dtT5iLGyqYya3jPPPINHH30Ue/fuha7r6NmzZ8iLtAIMhoiIqBF0CTh1CYdLwu7+6nAZo8d0KaFJCV2XKHdquPcfe3DPgHQMOi/xTGf7rBPqiLBwHk3mER0djX79+jVpmqzPJCKiBtnMClw64JKAS5NwaEYg5NJ1OFw67A5j0sUKuwullS785d8/4Y4V23H8dMWZzvpZJZLnGQI46SIREZ1Bo3skAwB0dz8hKQFNNwIip6Z7N5cmjdmoXToKiu2Y9M5/cdPSbfjqwKkz/AQU7jjpIhERnVFxURZEmwUkjCYzTZPQ3a916QmOjJoilybhdBk1Rk6XhoKiSjz44V5ctWgTpv9jF376pexMP07Y8owmC2ULxMaNGzF69GikpaVBCIHVq1d7jzmdTvzxj39E7969ERMTg7S0NEycOBHHjx/3S8Nut2PatGlISkpCTEwMxowZg6NHjwb87M056SKDISIiapTf9e8E1edTw1M7pOsSmi6h6To0He7XEpqmw+XSvV/tDh3/2X8SN7/2Na5YsB53v5WLf+0tgKbpZ+6hwoxogi0QZWVl6NOnD5YsWVLjWHl5Ob799ls8/vjj+Pbbb/Hhhx/i+++/x5gxY/zOmz59OlatWoWVK1di8+bNKC0txahRo6BpWkB54aSLRER0xkVbzbj+og74f9/mw+6zX7pH10sJSHdHas9mvIf7ve7d75TA1z8WYuv+QgAS8VEm9D4nHmMuTcXQnsmwmPi3emuQmZmJzMzMWo/Fx8cjJyfHb192djYuv/xyHD58GJ06dUJRURGWLl2KFStWYNiwYQCAd955B+np6fjiiy8wcuTIRueFky4SEVGr0L9zAk6Vu/Dhrp8hfP6wl9JYnkN39yeS7pXrdd19zC9IqgqapJTQNIlfHHb863QBcnb9DCklLKpAp8Ro9O3SDlf37IBfd09ClJUfWQoElBBmTlTcdUPFxcV++61WK6xWa0h5A4CioiIIIdC2bVsAQG5uLpxOJ0aMGOE9Jy0tDb169cKWLVsCCoY46SIREbUamT06oK3NhNe+OmoM1fb5bJbu//sHRNIdEPnXHnkCIU/tkfFeh5QS5U6J744WYe+R03h7/U+QUkJVBDrEWdGtfRRuPQ/YsDcfPTomIi0hCiKcp1YOQDBNXdWvB4D09HS//XPmzMHcuXNDSBmorKzEQw89hAkTJiAuLg4AkJ+fD4vFgnbt2vmdm5ycjPz8/IDS56SLRETUqgzokoAeyTHI+mQfXGVOaEJAQNb5QV09IPLdVz0Qkp5zvceN/ZpL4sgvThScLMGt51kxOftLVDgkFAFYTQrObR+D1IQo/Kpbe1x4Tjwu6tQO5yRGw2Y5iz7qmigaOnLkiDdgARByrZDT6cQtt9wCXdfx0ksvNXi+lDKoAJaTLhIRUavSNtqKN26+GB/89zj+37bjcOmAUASELiCErOfKqsDIu8f9RupVX30DIe97TYfurn/SNXfnbSnhcLiw86Ad/z0g8dk3h93X6IAuYVKAhFgzEmIt6J4ah87JsejTtQO6pbVFl5Q4JMVHQ1Ujq49SXFycXzAUCqfTifHjx+PAgQP497//7ZduSkoKHA4HCgsL/WqHCgoKMHDgwIDuMWLECLz66qs4//zzm3zSRQZDREQUkhv7pOH63il4ceNBrPnfL2hokJB/EGR89dQSGfuqBVIS/vt93tdWgyR13QiqpA7oxgKyBScrUHBCx/9+ynfv1wGpAboGSAmTkIiPtiA+2oJzU9uiQ9so9OmeivSUtji/Uwece047xERZoShnNmgKdeLEpp500RMI/fDDD1i3bh0SE/1nHe/bty/MZjNycnIwfvx4AEBeXh52796NhQsXNvo+ZrMZu3fvbrbmUAZDREQUMlVRcP+Qrph2VRf8Y/txvPXVUZRUOiGlDkURkFJAd9f6CCFqBjy+qgU/vrVGngDIs7/WTXe3xemaNyDyBkC+QZBn0zS4pI6TFRU4+YuGnw4eB6SOlbpuXCeNof9WiwlTbvw1Zk0ejrQObZunIBsS4qr1gcZCpaWl2L9/v/f9gQMHsGPHDiQkJCAtLQ033XQTvv32W/zzn/+EpmnefkAJCQmwWCyIj4/HlClTMGvWLCQmJiIhIQFZWVno3bu3d3RZY02cOBFLly7Fn/70p8AeohEYDNXDqdVXzUtERNUJITD+snMw/rJzUFBSicX/+glf7j8Ju5TuoEi6J/8TAIzXUsL7NWDVAyfdU9Xkrp4yOiRVfZU+AZI3OPIESr7BkwR0l9+t7A4XXl65Ee+v/RYb3pqFc89JCq6Qwsi2bduQkZHhfT9z5kwAwKRJkzB37lx8/PHHAIBLLrnE77p169ZhyJAhAIDFixfDZDJh/PjxqKiowNChQ7F8+XKoqhpQXhwOB9544w3k5OSgX79+iImJ8Tu+aNGiAJ+uCoOhepwud0EtccKsCphUAZtJgUmNjBELRESh6tDGhgXX9wQAHD5Vjjc2HcTm/SdxqsQBKQFVFe4mNQkhFAihQ0IatRfB/i3qjag8PbU9G7w1PNA9XzXP8Laq87ztdv6BUFXyEicLS/H7J9/F/712f5CZDF5TjSZrrCFDhtRbi1dvDZ+bzWZDdnY2srOzA7y7v927d+Oyyy4DAHz//fd+x0JtPmMwVA8JCV0CdpeEQ5OocBojJVQBWM0KzCqgCuHzVw4REdWmU0I0nrrOCIycmo5/fVeA9785hr3HinGyxO6uHRIQigB04/evpzlNKAJSlw03r9Wl+iVS9w+aPPtqHKudpkus/+Z77D9UgG6dOwSen1C0dDTUCvz000/o0qUL1q1b12z3YDBUn1p+HiQAHUaAZHfBGEoqBMyKhEkFFCGgKgyOiIjqYlYVXNMrBdf0SgEAaJqO7YdO47Odedj4vxM4frIcpZVOQAcURfEu2yAUASGFf58Zdy1S9cDJT301Tb4xkbeDduMCrt37j7d8MBSBunfvjry8PHToYJT1zTffjBdeeAHJyclNdg8GQ/XYfuw0EspVxEeZER9lRozVBJtZhdEf3/1XCgBICacu4NQBIYw2cFVIqAJQFQZHRET1UVUF/bomoF/XBO++CrsL/z10Gpv2/YIv9xXgyIky5BVWuI8awZGiGE1rED7NNcITHanu83yqUoQwgh6hGH2H/PaJqsCokc10Nou54ZOaWGsbTdYSqtcGfvbZZ1iwYEGT3oPBUD0kgApNh6PUjhNlDihCwKwIRJlVtLGqaBdjRRubyS/Q8XQE1KSxqRKABijCCJ5UxWhmY2xERFS3KKsJV5yfhCvOT8KDo3t495dVurD1h3yU/JSLkZd1xK7DRfi5sBwl5Q4AgK7rgKIYH6BSAIoK6NIdAEkA7n3SOM87D4B3SffGtUPFRFlwZb9uTf/gDQhm5fnq11NNDIbq4e1HB0AFoEsJlw6UOTSUOTQUlDrcTWRAnM2CWJvJCJSiTFAV4U7DCIJ0aTSpSV1AA2BR+U1JRBSoGJsJV16YjM9+Al67dwDMZqN2xunSUVhWiT2HT2PnwVPY/tNJHMwrwoG8IhSXVqCy0mdpWV0Cisn916sEFBh/vUIYAZLufl1H9ZAAMO22qxETFfpaXtQwIUSN1pWmbm1hMNQIRlOyJ6iRNRbJc+rA6QoHiiqdUN2L6FlNCmJsKuKjTIiymGBRFSiK8NbEOjQGRERETcVsUtAhPhodekcjo3dajeNSSpwoqsD3x07jv/t/xqH809j1Yz5+OVWCo/mFKC+rgKPSUdV85pmnyCcg8gz/n3zDQDx2729a6Mn8RWD/aUgpMXnyZO+SIZWVlbj33ntrDK3/8MMPg74Hg6EA+f6doEujycuzXwDQIAEJVLp0OMp0FJUbwzNVAURZVcRYTIixmRAXZYIMy9ZbIqLwI4RA+7bRaN82Gr++qGaw5HGyqByH805h/+FfsOfHPBw+fhKHj59Em2grLuiSjNtH90ev7ue0YM6ricBoaNKkSX7vb7/99ia/B4OhJuJpigaqAiNP05inmazCoaPC4cBJd/OaSQVirSribCZEWVVEW1Rv8xoREbW8xPhoJMZH49ILO2IcLj3T2akhEjtQL1u2rNnvwWCoHp4mLIGq9snGfBtJVEVGvi3PnqY2zz6XBhRVaCiu1CAAb/NatFVBXJQJbayqu2kt/L55iYiIwgWDoUbwXZbPt79QKDGKNzDyTEPv3md36bC7dJwud0EIAUUA0RYF0VYVNrOKWCtrj4iIIhVHkzUPBkP1EDBGkXlqZhQh/IMhn3N94xMlwGpIT0DkGbXmS5dAuUN3z35tBEgmBbCahTF6zaTAbFIYIBERRYAI7DLUIhgM1SPabNTCSFkzEFKEb5BU9zC/YL/xPAGS3z73AZcuoDkkKpxO4/4ALCYBm1mFzawg1t28RkRERA1jMFSPK7slIiEhAafLXThZ5sDpCidKKl1w6VXnKMK/6UyFqDNIqut1Q2oNjHwmW9UBODXAqWkotWs4WeaCIgCrSYHNrMCsCtjMrD0iIgp7rBpqFgyGGiCEQLsYM9rFGBN7SSnh1CQqnBoKShwoqnCiwqFD1/07WlcPknzjEL9ldQJs//UZtOa/v1ofJGOBWR0OTXrvaVIELCZjkVmru2mt+pxJRK2RS9OhCAFNlygssyMuyoySCidKKlxIbGPF8cJySAm0i7Xi2KkyxFhNMKsKTpTY0b6NDcWVTjhcOpLjbThRaofFpKBttAWnyhxIirXCpUs4XDpS2lpRUqkhxqIiymqCw6Uj1qpyEAO1GpE4mqwlMBgKkBACFpOAxaQgPqoqQCqtNGalLql0oajcCafvDO/wH41W1y9W347aNRYiDIDvrNeqz7WaBCqcRpAkhG4ESKqAWVVgUY3nYu0RBcOzdlBZhQM/nyxBtM2Mn44XoqLSCYem4fgvJaiwu1BU7oDd7kC/FOCev3yG02VOFFc4YXfqKLO7UOHQUOHQIQGU2TU4dcBkUlHu0AEIqKoCHe6VzeFZm8r4IfPMUltj85yrKlU/h0rt5/mmZYzkNPrkAYCqAlazCpOqIMqswmpRYFEVxEebYbOoiLWakBhrhdmk4Jx2NpgUgXPaRSHWqqJdtAWJMRZEmVVYTEqN8iOiM4vBUBMQQqBNlAltokxIia+anr3coeFUqRNldhfK7TpcuqzWVFb78P0a6dfxujGqD+cH/If7uzQJTddhdwHCYfzNYFYAi0mBSTEWmmX/I/JVXuHAyv/7Bis++goHjp2E3elCUZnDvdalAimEsQ6UZ2kD4f7wV4wp16OsKpZNuwSr1+9Ghct9rhDu4/7nAoDDafKuGaUB3tdCUaDruhEQwVix3PMXhZQSiuJ+oxvBj67p3oBI6tLvrw/ffZ60dABC6HC6jLQ0HXBpxiCGUsXl/bnwTH+huBdkVlXhE0xV7fe8N6kCFpOKGKuKaLOKxFgL2thMSIu3IinGipRYYxhFucOFOJOpzt8LFJk4mqx5MBhqRtEWFdEJxi82Y9i8hMOlobjShZIKDXaXbjRroXp/Ip+apHr6HQVL1tLWZvxhb7SxOXVAd3ma14zlR1TVaGYzqzVXEKbIcaKwFCN/+zz2/phXy1EBqcD9TSvdC2RqRtAhFPdrtarDm5SArruPe851/6b3nOt5rZoASG8HOqkba0oJIaoCIiG8wb+RvPTuM761jYBINbnHbLp/DqSUVed6AiLPfBcC0HUJIao1Q+vS+7NZtc+oPdI0CVV1P5oC6LqAokjve5cG6FKDw6WjWHXhlzIHFEVgx1H3Uj6qjgmJwNQPvoMUintwhAmxVhPaRqlIbmNBx3gbOraNQsd4G+JsDJgiCbsMNQ8GQy1ECAGb2ejIHBdlBtoZ+ysdRqfncvfiry6t6poaHbD90vOP8IP9ZVhbH6TqE0QaNUiApks4NEBzB0oOl4RQJBRFgJVHkeHux9/GvoM/13FUVgUuUhqrgnuDIPc3rPSZQMK7ErJWVTvkDXzgM3KgKggy1o0yqnSkLiHU6lF9tSDIZ793hnif457+E75BlPeSWo5L6f9aCM8fBzXP8xwzAja4AyQJVRVGMKW6F3CWPmUBI4gCAE3XoQsBaAKadKHSpeNUucDBwkp8q5bCohq1TGbFaOK2mRTEWkxoG2VC+xgz0uJtSG1jQ7toM1SFTXNE9WEwdIbZLCpslqrZhYwO2jqKKoy+E5VOHZrurqXxqy2qSqN6X6PG9E+qje+oNb9mNZ9f8J5jAKDpxoKzQjdqj8wqGBSdxfYfKsCaL/c2cJZP4KLrgKpU7TeqYXxqhnT4tGtVBT6+afm9Fv7n+gQQtQUz/rnyWQmwjsCotltVpV9Lmg0EQYDwu84vCHN/1XXjZ0bXhVFp5vPUUkpId1q6LozaKQBSCrh0//KSLkCXOpy6E2VODQVlDnx/otzoC+jpF6gIRJlMiDWb0DbahIRoC5JijYWkFQZL4YNVQ82CwVA9fi6xo11CzVXqm5PRQVtF+zZVAZLDpcPh0lHh7mTq1Kp+X/t1zq7RpOaTrt89Gs5HbU1pNc7x+bCSMAIjq9q49Cn8bNnxYyPPrCOaaC3fF7XUqIq6flhamC79f6aklEbtkTt4kj61U8Yxo9ZJE4CiG83aAjqEe+rXqn6COiAVSGhw6hKlDhd+LnHAekKBWTE6gpsUAbPJWBIoyqygTZQZ0VYBk6IwWGpFOJqseYTVd/jcuXNrjABJSUnxHpdSYu7cuUhLS0NUVBSGDBmCPXv2BH2/Zd8cxVNr9+O5jQfw4a58fH34NA4VVsCp6Q1f3IQsJgWxNhPat7Hg3KRodE+ORtekKLRvY0GbKBPMqqhRI6RUe19nc5vva1H764Z4fjkD8JuDic4uTd9VrKEApLbv1KpqUeFTDVlbv7oG+9o11MzsW/tay71qv2c96QWpeu2S735NVgVNUhp/nuiyjg2AJiVcug6nlNAk4NQlHLoOh6bDqRv9GssdOooqNeQXO3DklANHCx04XmjHiRIHiitccLr7OtKZ4WkZCGWjmsKuZuiiiy7CF1984X2vqlU1KAsXLsSiRYuwfPlynH/++Zg3bx6GDx+Offv2oU2bNgHfS5OAXdPxS5kTJ8ud2JlXAkUAJgWItZiQ0sbqbpe3IjXOhmhL9cU0mo9JFWgbXfXPp+kSmi5R6TRqkJya+y9K+P9iVnx+GOprRgv250WTgDnIa6l1+/Wl5zXyTG9E4LNLqTrm2a8oxjcMRNVx4fMz5L2+2jU1jvsEIw0FSD4LH9f2ve/5I6uu62u7fe2BUs331dMVQnh/Bj0pKDWaChv/4eXpemQERO5aI1QFQ5qUUKQwmt5g9ElSYMw3pkvjd4giBDQJKO73Rl7dzZmagIQx+tRiMtZM5AcrnS3CLhgymUx+tUEeUko899xzePTRRzF27FgAwFtvvYXk5GS8++67uOeee4K6ny7dbfoSUKSEDgFNB0ocGkpPluNgYYUx2koxZnxOjDYjuY0VKW2sSGljQ9uolgkNVMWYI8hiUhAXZezzBEdOzeiH5FtrU6O2yOeXdX0zZzdGbTNmU/jr1rkDRv66J7746n/Q6qwd9Y226wiAvKe6P/i9f9BUO8/7Wq1Kz52mcA+RFwCEO03fQMY7/xCqAiShCG9zj29Q5DnXd04i3+Oq6kkfPvv8a6h9H03xC7jg99V3OL7/V28J+JakX/qeZ/Qtvjrqzmolfb56m9xg/J5QVaNXlS4lFAjvaDldN87T3CPqFGHk2aVLVDh1RJkZELU0gdBacvnPVbuwC4Z++OEHpKWlwWq1on///pg/fz66du2KAwcOID8/HyNGjPCea7VacdVVV2HLli31BkN2ux12u937vri4GACgSg2K1KBI97ePbvwi8B0OL6TRfit1wOnSkV/swoniCuwVwjtPT6zVhMQYMzrEGPOIJMWYm7QavT4WxdhgNu6nSwm7J0DSjdojwD8QgjD+ogSM59T9/roFXC4XAEBzubztz75/HasRXoXudK8Z5/l6Nnn5iVtxw/0v4wf3iLIa/9TCPSeQd34hUTVE3h3g2KzGrx2bWQUUE6xWM3QImM0mxERZoSoqoqLMsFrMiLJZYDGpiLJaYLOaYDIpiLWZoaoCVrMJUWYViqrAYlZgUhV3/xZjlJWqKNClhMVkTNQIKSEU44Pd049bA+ByN/s4pES5XYOqCpRUuIzaVgkUVxr/juV2F+zuPywcmoRdM7o7uzQjcIAwpqCo3iShKEYNiyKkbzFAUdybqBqRqQjAqho/fWYhoUOHCuGdLV6F7l0nUYEGiyKM4xBQJWByvzZBgQqjJkjRfYM2T02cUeMjoUBKAQkFulSgSwFNKkYHCikgVAVSF0ZTvFQA3ejsLVUFUhMQulHWLa21/Yy1aD4YDTWLsAqG+vfvj7fffhvnn38+fv75Z8ybNw8DBw7Enj17kJ+fDwBITk72uyY5ORmHDh2qN90FCxbgySefrLH/Mv0gorVo4zdmiMoAHHBvZ4tN679o+KQIlpOTc6az0CwevvUiABeFnM7Lv+0RwNlO99ZIGqp+bl2NvEYAsLlft4K23hvb1TaXUy0kAn9Wn9NdACoDu6zVaC0/Y+Xl5Wc6CxSisAqGMjMzva979+6NAQMG4LzzzsNbb72FK664AkDNJp2GhtwCwMMPP4yZM2d63xcXFyM9PR3fKufCpMbD5KnKFvAuV2FSqtr6ze5qdOOvPGOfSVQ7z/da919pnuYoBcZ1qhBoY1XRNsqMhGgLkttYYFJbfoFVY3i/UUWuAdB9mr0EjBqhzeu/wJVDhsFs9q/lsnA0GZxOJ3JycjB8+HCYza3gU7WVYflUcWo6iitdOFHqQF6JHb+UOZBfWIbzyr/HRu1clDvhrb1V1arfIyZ3TZLJ+9poqje7h9F7zjHB6F9ozEfk3i+MEWJmxdhnUgTMQvE2tZtUBar7PqqqQBXCnYZ7Vnr3PUyKMceR1XxmaoZa0/eQpzWhJXA0WfMIq2CoupiYGPTu3Rs//PADrr/+egBAfn4+UlNTvecUFBTUqC2qzmq1wmq11tivCRUmRfU2EylKVZOR7glkBKCLqj4FnnZ4qVSdpyjGPk9TknQHQzqMXzjGqkuAJgSKnUCpy4XjJS7sLTD6I0WbVSNIijYhKdYKm3uh1eZsarP4vPaMVNGkUUXucP8wmc1mmC3GmQoAMwMhP2azuVX8om6tWD6A2QxE26xIaRuDXu59TqcTn332Pf40uqe3fHQpcarciaOnK3G0qAL5JXYUVjhR6dShS2kELsIIgFT3RIyqJ1iqJRDyfFW8AZDqDaqqmhmFe/6wqiDJm7474LKYjOH4Z678Wsf3UEvmwdP8Gsr1VFNYB0N2ux3fffcdrrzySnTp0gUpKSnIycnBpZdeCgBwOBzYsGED/vznPweVvm/TrG+HY98Oxr5zEDX2e0yXVXMXVV87zHNMByDc6yNVOI2lO06WOXHgZKVRG6UAMVYT4m0mxEebEW1REWVRm6UWydPfQAEAFe4ZTNx/hXr6P/AHjKjZKEIgKcaCpBgLLjknrtZzKpwafimxI6+kEifKHMaM9rr0/h7zDYJMQnhrj8yK4u6vZARCqqevk/CspwZv0CTcAZbnZ/5M9Bciag5hFQxlZWVh9OjR6NSpEwoKCjBv3jwUFxdj0qRJEEJg+vTpmD9/Prp3747u3btj/vz5iI6OxoQJE4K6nyqqmsJUn9Eeng/+uoIl398PgQyL9b72TOEPY+ECTRq/0CDcM+UKY/2wEruGEruGvCIHhDB+idnMCmKsKmJtJsRajQCpuVbJVhWfCYaJ6IyKMqvolBCNTgnRtR6vdLpwqsyJU6VOVLiX/hF+QZCxqKzRXOZpNoO3qd4T/Hia9C0mLsNzJrD/dPMIq2Do6NGjuPXWW3HixAm0b98eV1xxBb766it07twZADB79mxUVFTgvvvuQ2FhIfr374+1a9cGNccQAJybGI1iKLC7jMnMPH8xeQIkk+/wW98Rwz5f/UZpuTV2RuvaFiPQpZGP6uuHeY7ZXRJ2lwuny11++bSajVFtMVYVUVbVPSSWPxZEkcJmNiGtrQlpbaNqHJNSotKpobTShUqnNOYkEsZUBKq7P5LJ3YfIpAhYTWdmFBmB0VAzCatgaOXKlfUeF0Jg7ty5mDt3bpPc7+Y+qUhMTAQAHC+uxJHTlTheVImCUjvKHBo0WTNA8tQmAdUCJN/aIp+vvrNEB8obBMGYG6S2AEkCcOkSmgOocDpxoszp7bBtUgWirSqiLAqiLSpirSoDJKIIJIRAlMVYp6w2us/6iPwVQWejsAqGzqS0OBvS4mx++4oqjQ6NP5fYcaLMgdOVTu+cI0q1oMjz2ixqTsgG1FGbhJrHG+INgupaHkoY88nCPWKsuMKFkkoBRTi9v+hsJgU2s4Ioi4JYq+ruK8DfgESRSmF7WKvB0WTNg8FQCOJtZsSnmHFRSlUznN2lI6+4AifLnThRZsepCifsLh0CRgfk2jphq377a3bI9qtBqiWAqkv1WiJjn3vUG6qCJiHcM2y791Y6ddhdEsWVGgqE093UBljNKqwmAYvQvekTEVELCnE0GWOh2jEYamJWk4JzE2JwbkLVPl1KnChzoKjCiZPlDpwsc6LcqRlT3sO347WoNUBSGxixFur3dm1Na35VS8JYgFV36KhwALpmzOx2tNCBKKuERRWwmFVYVJyReZGIiCIFuww1DwZDLUARAh1iregQa0V39z4pJUrsLpTa3SM8yp0otWtwarrf4o2+AZJfbZLv8H7UHiwF2h+pvqY13/5IHroEnLqx8nW50+Wed0lzd7YELCYVJtU9pNenqZCIiKg14cDoM0QIgTibGWnxUeiVFofB3RLxm4s6YGSP9hjcLRG9U2NxTrwNMVaTd82iWjtpQ9QeINURdzRFPOLbOla9qcxY/RpwaECZXUNxhY7CchdOlGkoLHehpFJDhXttNDazEREFSDTBFoCNGzdi9OjRSEtLgxACq1ev9jv+4YcfYuTIkUhKSoIQAjt27KiRht1ux7Rp05CUlISYmBiMGTMGR48eDSwjzYzBUCtjM6toG23GuUkxuLRTPAZ3T8DQC5NwZbd26NOxDTol2BAfZYZZCG8gVD1A8q1Bakx/o9qO16a20KX6Sti1HpPGMZcOODWJSqdEmV1HcaVEcaWOMruOCqcOh0v3W0STiIj8iSb4LxBlZWXo06cPlixZUufxX//61/jTn/5UZxrTp0/HqlWrsHLlSmzevBmlpaUYNWoUNK0JFv5sImwmCwOqUjXstUMbY9kQKY0V5yscGk6XO40aF4duNLPVEQh5gh0FjQ+QfAXS3Oa5vHrTmiYBk/Dvl6QB0HVjrUnhHo0nhDHDtSoaDtKIiKh5ZGZm+q0LWt0dd9wBADh48GCtx4uKirB06VKsWLECw4YNAwC88847SE9PxxdffIGRI0c2eZ6DwWAoTHlmnI61mRBr8/9ndGo6Tpc5UebQUeHQUOnUvZ2jawZItdcmVd2ngXw0Mr+1BUh+0wC4E/Md9eZyB0hc/JWIyCBC/APRc231xWXrWqMzVLm5uXA6nRgxYoR3X1paGnr16oUtW7YwGKLmY1YVtI+zor3PPl1KlFZqqHBoqHAatUiaMULeLygKtDbJl7cGqBHNbXWd4lmCBIB36RFPbRIRUaRrqtFk6enpfvvnzJnTZBMW+8rPz4fFYkG7du389icnJyM/P7/J7xcsBkMRQhECcVEmxEVV/ZMbU/DrcLgkKpxGDZLTZSwOC9QdCDVYm+T7Ooj5kapz6WBzGRFREzpy5Aji4qoW/W2OWqH6VO9CcaYxGIpgxhT8KqIsQLzPt4JLk3BqOuwu3RssuXym4/e9HvCvTVJ8gpbW821ORHSWaKKqobi4OL9gqLmkpKTA4XCgsLDQr3aooKAAAwcObPb7NxZHk1ENJtUIktpGm5ESb0WnRBvOTbIhvZ0VKXFmxEcb3zaqqD8QCqQ2iYiIGtbSo8lC1bdvX5jNZuTk5Hj35eXlYffu3a0qGGLNEDWKIgQUk4AZgEmYAQCpbS0wmUzQdIlKlw6nBmiaUYtUVyCk1FKbVL1vUnUCbCIjIjoTSktLsX//fu/7AwcOYMeOHUhISECnTp1w6tQpHD58GMePHwcA7Nu3D4BRI5SSkoL4+HhMmTIFs2bNQmJiIhISEpCVlYXevXt7R5e1BgyGKCRCCJhUgVjVP4yRUsKhSWi6hKbD3cxWfyBUV22SifWXREQAQv/jMNBLt23bhoyMDO/7mTNnAgAmTZqE5cuX4+OPP8add97pPX7LLbcA8O+QvXjxYphMJowfPx4VFRUYOnQoli9fDlVV0VowGKJmIYSAtdoQMM/cSJpufHXpPuej9kDIrAAqgyEiIgBNN5qssYYMGVLvagGTJ0/G5MmT603DZrMhOzsb2dnZAd695TAYohbjmRup+kKuniBJSkDCmH9IERxBRkRUXVPNM0T+GAzRGecJkoiIiM4EBkNERERho6UbyiIDgyEiIqIwwWay5sGuqURERBTRWDNEREQUJthI1jwYDBEREYUJNpM1DzaTERERUURjzRAREVGYCHV9sZZemyxcMBgiIiIKF+w01CzYTEZEREQRjTVDREREYYIVQ82DwRAREVGY4Giy5sFgiIiIKEywA3XzYJ8hIiIiimisGSIiIgoX7DTULBgMERERhQnGQs2DzWREREQU0VgzREREFCY4mqx5MBgiIiIKG6GNJmNDWe3YTEZEREQRjTVDREREYYLNZM2DNUNEREQU0RgMERERUURjMxkREVGYYDNZ82AwREREFCa4NlnzYDBEREQUJlgz1DzYZ4iIiIgiGmuGiIiIwgTXJmseDIaIiIjCBaOhZsFmMiIiIoporBkiIiIKExxN1jwYDBEREYUJjiZrHmwmIyIioojGmqF6FJTY4TLb4dIlTIpRuajpgEkVEJBwuV9DSugSMCkCupSQUuDQsV/w1Y4fcbygCGazigqHhiibBRV2J2JjolBUZkdifDROFFcioW0MTpdWom2bGBSWVCIhPgqFpU7ExVhR4dBgtZjg1CTMJhUSgCaBKKuKMruOuGgTSipcaBtrRVGpA+3ibCgstSOpjQ2F5Q60jbWipMKJNlFmlNl1xNpU2F06zKoCoQjoEjCrCpy6jmiLinKnhjibCSWVGtpFm3G60oWEGAtOVziREGNBsd2JeLNAGwArtx2DXQpYVAVSSuzffwxff7MHR4+dhCYBqZpgtlihqyZY3F9NFjN0YYLZYoIQCixmFRAKzCYVQhUwm1QoqgJVUaCqCoSiwGQyqoVNJgFFEbCYVACAxaxAwv3vIYz9UhjPowjArBp/QpkVQCgKFCGMf0chYFYEIACTokAIwGJSAClhVhQoivFvCWmkoQgBRQFURUBVjLQVIaEK9zEY+VIVAalLqNABANsOFsJssUAVAlJKmFQFQgoIIaG68wEpjed0f8+pivFKAFAU4f4rTsBkZAeKEBCKUdVtPIJxjqoAEMb3pRBG2r5/6SiedAW8x1Rv+kQULth/unkwGKrHd3mlaFNhcX/oeD5EjA9AAO4PxarXQggUFpVi/gvv4+sdP1RLTQCK8cEPRXF/Vateq+5jqsm9v/q5JuOTzP1VqIqRH8X4KtwfroqiQFEU9+0Uv+PVz/V8Vb1pGR+aijct4f1ANs4BFEWBzQTMPB9Y9p/DcEFBeeFp/PDvjXCUl9d8ZtUMmMyAyer+aqnap5oBkwmqyQRVVb35VUzur6pStV9VYDKpUFUjv578qKqAyaS493me0civ2WTs8wQtJlXA5Am0PNcqijeQURQBi2oETIowAiKT+3pVMYIskyKgeo55r4MRRAn3dVKHFUBeqQMmVffeX1VE1Tmi6nxPYOQbACne18L7fWYEOfB+P9Z23BOoVZ3r2QeffdI4XzeCMrPCqnOisMFoqFmctc1kL730Erp06QKbzYa+ffti06ZNAach3V916fMaErqU3v2+rysq7XjgiTewbef+2lPTXYDUAV3z+SoBXTc2zz7PJj37PddWfZWaDikldN34KnXp/969z/d99XM9XzVvWoCuS2ia53wJKT1Z9Lw29gPG6/KiYnz3fzm1BELuZ9acgOYCNAfgcm+aE3A5jWfRNOiaBk3ToGu6kUfNnTdP/nUJXdPhcmnQNCO/Rp6N4qna53lGI79Ol7FPk8a/maYDLk2HpuvQpFHL59J145ndm0OTcOkSmgRcEnC5rzfOdZ/nOea9DnDqOnR3DaHm/b6R0ADv/T3fL8Y5vvuMspRAVXl7X1ddZ/w7Vn0/+h6X8D0XPuf6H/dcr7tfa7qEUw/4R4OIIsTGjRsxevRopKWlQQiB1atX+x2XUmLu3LlIS0tDVFQUhgwZgj179vidY7fbMW3aNCQlJSEmJgZjxozB0aNHW/ApGnZWBkPvvfcepk+fjkcffRTbt2/HlVdeiczMTBw+fDjgtKRPsON9DVnr/jUbduDQ0V+8wUIdCXpeGJvU3V+lT+Cj1fwKVH2Vul9aUvrfT0rpTrJm4KPrujsJ/2urvqLaV/8gyBNYAUZ283bvha5pqJs7/5rL/XzuIA9VgZ90B0HVN29Q582MEeR4gjb/czx5hHe/kUf3Pp/zNF1WvUdVYOB579J9Ag0YQZPuDmhcuvT+m+swmiw912nVyxJV5+m+ZendL/2CGN/yrv7aNz3f137nooFzazleFRzV809IRK2GaIL/AlFWVoY+ffpgyZIltR5fuHAhFi1ahCVLluCbb75BSkoKhg8fjpKSEu8506dPx6pVq7By5Ups3rwZpaWlGDVqFLR6Pzta1lnZTLZo0SJMmTIFd999NwDgueeew5o1a/Dyyy9jwYIFNc632+2w2+3e90VFRQCAshLja63NYtWay4QQWPvvrxClulD/54oLUMzGS8UECN3dJKa5m8Q8X3UYsaoGQADSZVRvSpPxHmZAN/rCQAKKVAHNaMYS0vPV3TwGo3+Q0b9EQJFGsxh0d9OJasTEJndfHFWFux+Ku2lMGF+huNMzAeXl5RCVCioO/wSb2lDVgg4IaSQqNeO99ARGTkBaIKQKRaoQugIFAipUKEIxvkoFiu5+Bl2BSapQdMCkCyiaYvSzUQSEyThHcfchEqowmhhNCqAAUlGgC0BRBXQhoCkKfNqQAFVACgGpGv1yjHOM5jBdAJq7WUxXBFzu5jGTuwnN0wznhICADlFeDntRIRTVZDSPAe7mOeNXkafJTHX3N/I0Z3mayzzNYYq7acvTbOltrvU0lXmbO92v4fm3M0peeNP3PW48n1LtuFlt4J+xiTidTpSXl+PkyZMwm80tc9MwwvJpWGsrI88Hf/U/TJvnXsUhNWuXlBQDAIqLi/32W61WWK3WGudnZmYiMzOz1rSklHjuuefw6KOPYuzYsQCAt956C8nJyXj33Xdxzz33oKioCEuXLsWKFSswbNgwAMA777yD9PR0fPHFFxg5cmTwD9OU5FnGbrdLVVXlhx9+6Lf//vvvl4MHD671mjlz5rirabhx48aNG7fgtiNHjjTbZ1tFRYVMSUlpknzGxsbW2DdnzpwG8wBArlq1yvv+xx9/lADkt99+63femDFj5MSJE6WUUv7rX/+SAOSpU6f8zrn44ovlE088EXK5NJWzrmboxIkT0DQNycnJfvuTk5ORn59f6zUPP/wwZs6c6X1/+vRpdO7cGYcPH0Z8fHyz5jccFRcXIz09HUeOHEFcXNyZzk6rw/KpH8unfiyfhrW2MpJSoqSkBGlpac12D5vNhgMHDsDhcISclpTGIAtftdUKNcTzmVrb5+2hQ4e851gsFrRr167GOXV9Jp8JZ10w5FH9H7q2f3yPuqoH4+PjW8UPWmsVFxfH8qkHy6d+LJ/6sXwa1prKqCX+cLbZbLDZbM1+n0AF8nkbyDkt6azrQJ2UlARVVWtEnAUFBTWiVyIiIgpOSkoKANT7eZuSkgKHw4HCwsI6z2kNzrpgyGKxoG/fvsjJyfHbn5OTg4EDB56hXBEREZ1dunTpgpSUFL/PW4fDgQ0bNng/b/v27Quz2ex3Tl5eHnbv3t2qPpPPymaymTNn4o477kC/fv0wYMAAvPbaazh8+DDuvffeRl1vtVoxZ86coNpQIwHLp34sn/qxfOrH8mkYy6jllJaWYv/+qrnzDhw4gB07diAhIQGdOnXC9OnTMX/+fHTv3h3du3fH/PnzER0djQkTJgAwmg+nTJmCWbNmITExEQkJCcjKykLv3r29o8taAyFlC4wFPANeeuklLFy4EHl5eejVqxcWL16MwYMHn+lsERERhY3169cjIyOjxv5JkyZh+fLlkFLiySefxKuvvorCwkL0798fL774Inr16uU9t7KyEg8++CDeffddVFRUYOjQoXjppZeQnp7eko9Sr7M2GCIiIiJqjLOuzxARERFRIBgMERERUURjMEREREQRjcEQERERRTQGQ9Wce+65xkKWPttDDz3kd87hw4cxevRoxMTEICkpCffff3+TTJEeTux2Oy655BIIIbBjxw6/Y5FcPmPGjEGnTp1gs9mQmpqKO+64A8ePH/c7J1LL5+DBg5gyZQq6dOmCqKgonHfeeZgzZ06NZ4/U8gGAZ555BgMHDkR0dDTatm1b6zmRXD6AMVK4S5cusNls6Nu3LzZt2nSms0RngbNynqFQPfXUU/jtb3/rfR8bG+t9rWkarr32WrRv3x6bN2/GyZMnMWnSJEgpkZ2dfSaye0bMnj0baWlp+O9//+u3P9LLJyMjA4888ghSU1Nx7NgxZGVl4aabbsKWLVsARHb5/O9//4Ou63j11VfRrVs37N69G7/97W9RVlaGv/zlLwAiu3wAY8K6cePGYcCAAVi6dGmN45FePu+99x6mT5+Ol156Cb/+9a/x6quvIjMzE3v37kWnTp3OdPYonJ2BxWFbtc6dO8vFixfXefyzzz6TiqLIY8eOeff97W9/k1arVRYVFbVADs+8zz77TF544YVyz549EoDcvn2737FILx9fH330kRRCSIfDIaVk+VS3cOFC2aVLF+97lo9h2bJlMj4+vsb+SC+fyy+/XN57771++y688EL50EMPnaEc0dmCzWS1+POf/4zExERccskleOaZZ/yqoP/zn/+gV69efqsTjxw5Ena7Hbm5uWciuy3q559/xm9/+1usWLEC0dHRNY5Hevn4OnXqFP7f//t/GDhwIMxmMwCWT3VFRUVISEjwvmf51C+Sy8fhcCA3NxcjRozw2z9ixAhvzStRsBgMVfPAAw9g5cqVWLduHaZOnYrnnnsO9913n/d4fn5+jcXl2rVrB4vFUmOxurONlBKTJ0/Gvffei379+tV6TiSXj8cf//hHxMTEIDExEYcPH8ZHH33kPcbyqfLjjz8iOzvbb5kclk/9Irl8Tpw4AU3Tajx/cnLyWf/s1PwiIhiaO3dujU7R1bdt27YBAGbMmIGrrroKF198Me6++2688sorWLp0KU6ePOlNTwhR4x5Sylr3h4PGlk92djaKi4vx8MMP15tepJaPx4MPPojt27dj7dq1UFUVEydOhPSZ6D3SywcAjh8/jmuuuQbjxo3D3Xff7XeM5VO/s618AlX9OSPp2an5REQH6qlTp+KWW26p95xzzz231v1XXHEFAGD//v1ITExESkoKtm7d6ndOYWEhnE5njb9YwkVjy2fevHn46quvaiyO2K9fP9x222146623Irp8PJKSkpCUlITzzz8fPXr0QHp6Or766isMGDCA5QMjEMrIyPAuouyL5VO/s7F8GispKQmqqtaoBSooKDjrn51awJnrrhQePvnkEwlAHjp0SEpZ1YHx+PHj3nNWrlwZER0YDx06JHft2uXd1qxZIwHI999/Xx45ckRKGdnlU5vDhw9LAHLdunVSSpbP0aNHZffu3eUtt9wiXS5XjeORXj4eDXWgjtTyufzyy+Xvf/97v309evRgB2oKGYMhH1u2bJGLFi2S27dvlz/99JN87733ZFpamhwzZoz3HJfLJXv16iWHDh0qv/32W/nFF1/Ijh07yqlTp57BnJ8ZBw4cqDGaLJLLZ+vWrTI7O1tu375dHjx4UP773/+WgwYNkuedd56srKyUUkZ2+Rw7dkx269ZNXn311fLo0aMyLy/Pu3lEcvlIafzBsX37dvnkk0/K2NhYuX37drl9+3ZZUlIipWT5rFy5UprNZrl06VK5d+9eOX36dBkTEyMPHjx4prNGYY7BkI/c3FzZv39/GR8fL202m7zgggvknDlzZFlZmd95hw4dktdee62MioqSCQkJcurUqd4Pu0hSWzAkZeSWz86dO2VGRoZMSEiQVqtVnnvuufLee++VR48e9TsvUstn2bJlEkCtm69ILR8ppZw0aVKt5eOpWZQysstHSilffPFF2blzZ2mxWORll10mN2zYcKazRGcBIaVPz04iIiKiCBMRo8mIiIiI6sJgiIiIiCIagyEiIiKKaAyGiIiIKKIxGCIiIqKIxmCIiIiIIhqDISIiIopoDIaIiIgoojEYIiIioojGYIiolRoyZAimT59+prMRsMceewxWqxUTJkxo1PlDhgyBEAJCCOzYsaNZ8hRKWU6ePNmbv9WrVzdpvoiodWAwRBQg3w9Hk8mETp064fe//z0KCwvPWD7MZjO6du2KrKwslJWVhZx2KMHD7NmzsWjRIvztb3/D/v37G3XNb3/7W+Tl5aFXr15B3TMYkydPxkMPPdTgec8//zzy8vJaIEdEdKYwGCIKwjXXXIO8vDwcPHgQb7zxBj755BPcd999ZywfP/30E+bNm4eXXnoJWVlZQafncDhCzlNcXBzuuusuKIqCXbt2Neqa6OhopKSkwGQyNVu+fOm6jk8//RTXXXddg+fGx8cjJSWlSe9PRK0LgyGiIFitVqSkpKBjx44YMWIEbr75Zqxdu9Z7XEqJhQsXomvXroiKikKfPn3w/vvv+6Xx+eefY9CgQWjbti0SExMxatQo/Pjjj0HlIz09HRMmTMBtt93m15TT0D2GDBmCqVOnYubMmUhKSsLw4cMxefJkbNiwAc8//7y35ungwYMB5cvlciE6Ohq7d+8O6Lr68tWY5wGAsrIyTJw4EbGxsUhNTcVf//rXGul/+eWXUBQF/fv3BwC8//776N27N6KiopCYmIhhw4Y1SQ0bEYUHBkNEIfrpp5/w+eefw2w2e/c99thjWLZsGV5++WXs2bMHM2bMwO23344NGzZ4zykrK8PMmTPxzTff4F//+hcURcENN9wAXdeDzktUVBScTmdA93jrrbdgMpnw5Zdf4tVXX8Xzzz+PAQMGeJuu8vLykJ6eHlA+HnvsMZSWlgYdDNWWr8Y+z4MPPoh169Zh1apVWLt2LdavX4/c3Fy/tD/++GOMHj0aiqIgLy8Pt956K+666y589913WL9+PcaOHQspZdB5J6IwI4koIJMmTZKqqsqYmBhps9kkAAlALlq0SEopZWlpqbTZbHLLli1+102ZMkXeeuutdaZbUFAgAchdu3ZJKaW86qqr5AMPPFBvPq677jrv+61bt8rExEQ5fvz4gO5xySWX1DivoXvXZ9u2bdJischrr71W9uzZs8Hza7tXXfmqrvrzlJSUSIvFIleuXOk95+TJkzIqKsrvHueff778+OOPpZRS5ubmSgDy4MGD9d4LgFy1alWDeSKi8MOaIaIgZGRkYMeOHdi6dSumTZuGkSNHYtq0aQCAvXv3orKyEsOHD0dsbKx3e/vtt/2adH788UdMmDABXbt2RVxcHLp06QIAOHz4cKPz8c9//hOxsbGw2WwYMGAABg8ejOzs7IDu0a9fv5DKwpeu67jnnnswdepUTJw4Ed9//33Q/X1qy1dDz/Pjjz/C4XBgwIAB3msSEhJwwQUXeN9/9913OHr0KIYNGwYA6NOnD4YOHYrevXtj3LhxeP3111u8MzwRnVm191YkonrFxMSgW7duAIAXXngBGRkZePLJJ/H00097m2w+/fRTnHPOOX7XWa1W7+vRo0cjPT0dr7/+OtLS0qDrOnr16hVQ8JCRkYGXX34ZZrMZaWlpfk11jb1HTExMwM9fl+zsbPzyyy946qmncPjwYbhcLuzbtw+9e/cOOK3a8tXQ88hGNG19/PHHGD58OKKiogAAqqoiJycHW7Zswdq1a5GdnY1HH30UW7du9QZbRHR2Y80QUROYM2cO/vKXv+D48ePo2bMnrFYrDh8+jG7duvltnr43J0+exHfffYfHHnsMQ4cORY8ePYKqjfAEZZ07d64RCIVyD4vFAk3TAsrLsWPH8Pjjj+Oll15CTEwMunfvDqvVGlK/IV+NeZ5u3brBbDbjq6++8u4rLCzE999/733/0UcfYcyYMX7XCSHw61//Gk8++SS2b98Oi8WCVatWNUm+iaj1Y80QURMYMmQILrroIsyfPx9LlixBVlYWZsyYAV3XMWjQIBQXF2PLli2IjY3FpEmT0K5dOyQmJuK1115DamoqDh8+3Kg5bwIRyj3OPfdcbN26FQcPHkRsbCwSEhKgKPX/7XT//fcjMzMT1157LQDAZDKhR48eTRYMNeZ5YmNjMWXKFDz44INITExEcnIyHn30UW/eCwoK8M033/iNuNu6dSv+9a9/YcSIEejQoQO2bt2KX375BT169GiSfBNR68eaIaImMnPmTLz++us4cuQInn76aTzxxBNYsGABevTogZEjR+KTTz7xNrsoioKVK1ciNzcXvXr1wowZM/Dss882aX5CuUdWVhZUVUXPnj3Rvn17b5+c5cuXQwhR4/x//vOf+Pe//43nn3/eb3/v3r2bLBhq7PM8++yzGDx4MMaMGYNhw4Zh0KBB6Nu3LwDgk08+Qf/+/dGhQwfv+XFxcdi4cSN+85vf4Pzzz8djjz2Gv/71r8jMzGySfBNR6ydkYxrZiYgAzJ07F+vXr8f69eubLM0hQ4bgkksuwXPPPddkadZlzJgxGDRoEGbPnh3wtUIIrFq1Ctdff33TZ4yIzijWDBFRo61ZswYLFy5s8nRfeuklxMbGNnrG6mANGjQIt956a0DX3HvvvYiNjW2mHBFRa8CaISI6o44dO4aKigoAQKdOnWCxWM5wjvwVFBSguLgYAJCamtqko++IqHVgMEREREQRjc1kREREFNEYDBEREVFEYzBEREREEY3BEBEREUU0BkNEREQU0RgMERERUURjMEREREQRjcEQERERRTQGQ0RERBTR/j9N034c0UoO3QAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "plt.scatter(eigs_r, eigs_i, c=u_inf, cmap='Blues')\n",
    "cbar = plt.colorbar()\n",
    "cbar.set_label('Free Stream Velocity, $u_\\infty$ [m/s]')\n",
    "\n",
    "plt.grid()\n",
    "plt.xlim(-50, 5)\n",
    "plt.ylim(0, 300)\n",
    "plt.xlabel('Real Part, $\\lambda$ [rad/s]')\n",
    "plt.ylabel('Imag Part, $\\lambda$ [rad/s]');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "natural_frequency = np.sqrt(eigs_r ** 2 + eigs_i ** 2)\n",
    "damping_ratio = eigs_r / natural_frequency\n",
    "cond = (eigs_r>-25) * (eigs_r<10) * (natural_frequency<100) # filter unwanted eigenvalues for this plot (mostly aero modes)\n",
    "\n",
    "plt.scatter(u_inf[cond], damping_ratio[cond], color='k', marker='s', s=9)\n",
    "\n",
    "plt.grid()\n",
    "plt.ylim(-0.25, 0.25)\n",
    "plt.xlabel('Free Stream Velocity, $u_\\infty$ [m/s]')\n",
    "plt.ylabel('Damping Ratio, $\\zeta$ [-]');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "cond = (eigs_r>-25) * (eigs_r<10) # filter unwanted eigenvalues for this plot (mostly aero modes)\n",
    "plt.scatter(u_inf[cond], natural_frequency[cond], color='k', marker='s', s=9)\n",
    "\n",
    "plt.grid()\n",
    "plt.ylim(40, 100)\n",
    "plt.xlabel('Free Stream Velocity, $u_\\infty$ [m/s]')\n",
    "plt.ylabel('Natural Frequency, $\\omega_n$ [rad/s]');"
   ]
  }
 ],
 "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": "3.10.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}