{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<script async src=\"https://www.googletagmanager.com/gtag/js?id=UA-59152712-8\"></script>\n",
    "<script>\n",
    "  window.dataLayer = window.dataLayer || [];\n",
    "  function gtag(){dataLayer.push(arguments);}\n",
    "  gtag('js', new Date());\n",
    "\n",
    "  gtag('config', 'UA-59152712-8');\n",
    "</script>\n",
    "\n",
    "# Start-to-Finish Example: Setting up Polytropic [TOV](https://en.wikipedia.org/wiki/Tolman%E2%80%93Oppenheimer%E2%80%93Volkoff_equation) Initial Data, in Curvilinear Coordinates\n",
    "\n",
    "## Authors: Zach Etienne, Phil Chang, and Leo Werneck\n",
    "### Formatting improvements courtesy Brandon Clark\n",
    "\n",
    "## This module sets up initial data for a TOV star in *spherical, isotropic coordinates*, using the *Numerical* ADM Spherical to BSSN Curvilinear initial data module (numerical = BSSN $\\lambda^i$'s are computed using finite-difference derivatives instead of exact expressions).\n",
    "\n",
    "**Notebook Status:** <font color='green'><b> Validated </b></font>\n",
    "\n",
    "**Validation Notes:** This module has been validated to exhibit convergence to zero of the Hamiltonian constraint violation at the expected order to the exact solution (see [plots](#convergence) at bottom). Note that convergence at the surface of the star will be lower order due to the sharp drop to zero in $T^{\\mu\\nu}$.</font>\n",
    "\n",
    "### NRPy+ Source Code for this module: \n",
    "\n",
    "* [TOV/TOV_Solver.py](../edit/TOV/TOV_Solver.py); ([**NRPy+ Tutorial module reviewing mathematical formulation and equations solved**](Tutorial-ADM_Initial_Data-TOV.ipynb)); ([**start-to-finish NRPy+ Tutorial module demonstrating that initial data satisfy Hamiltonian constraint**](Tutorial-Start_to_Finish-BSSNCurvilinear-Setting_up_TOV_initial_data.ipynb)): Tolman-Oppenheimer-Volkoff (TOV) initial data; defines all ADM variables and nonzero $T^{\\mu\\nu}$ components in Spherical basis.\n",
    "* [BSSN/ADM_Numerical_Spherical_or_Cartesian_to_BSSNCurvilinear.py](../edit/BSSN/ADM_Numerical_Spherical_or_Cartesian_to_BSSNCurvilinear.py); [\\[**tutorial**\\]](Tutorial-ADM_Initial_Data-Converting_Numerical_ADM_Spherical_or_Cartesian_to_BSSNCurvilinear.ipynb): *Numerical* Spherical ADM$\\to$Curvilinear BSSN converter function\n",
    "* [BSSN/BSSN_constraints.py](../edit/BSSN/BSSN_constraints.py); [\\[**tutorial**\\]](Tutorial-BSSN_constraints.ipynb): Hamiltonian constraint in BSSN curvilinear basis/coordinates\n",
    "\n",
    "## Introduction:\n",
    "Here we use NRPy+ to set up initial data for a [simple polytrope TOV star](https://en.wikipedia.org/wiki/Tolman%E2%80%93Oppenheimer%E2%80%93Volkoff_equation).\n",
    "\n",
    "The entire algorithm is outlined as follows, with links to the relevant NRPy+ tutorial notebooks listed at each step:\n",
    "\n",
    "1. Allocate memory for gridfunctions, including temporary storage for the Method of Lines time integration [(**NRPy+ tutorial on NRPy+ Method of Lines algorithm**)](Tutorial-Method_of_Lines-C_Code_Generation.ipynb).\n",
    "1. Set gridfunction values to initial data \n",
    "    * [**NRPy+ tutorial on TOV initial data**](Tutorial-ADM_Initial_Data-TOV.ipynb)\n",
    "    * [**NRPy+ tutorial on validating TOV initial data**](Tutorial-Start_to_Finish-BSSNCurvilinear-Setting_up_TOV_initial_data.ipynb).\n",
    "1. Evaluate the Hamiltonian constraint violation\n",
    "    * [**NRPy+ tutorial on BSSN constraints**](Tutorial-BSSN_constraints.ipynb)\n",
    "1. Repeat above steps at two numerical resolutions to confirm convergence of Hamiltonian constraint violation to zero."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='toc'></a>\n",
    "\n",
    "# Table of Contents\n",
    "$$\\label{toc}$$\n",
    "\n",
    "This notebook is organized as follows\n",
    "\n",
    "1. [Step 1](#initializenrpy): Set core NRPy+ parameters for numerical grids and reference metric\n",
    "1. [Step 2](#adm_id_tov): Set up ADM initial data for polytropic TOV Star\n",
    "    1. [Step 2.a](#tov_interp): Interpolating the TOV data file as needed\n",
    "    1. [Step 2.b](#source): Compute source terms $S_{ij}$, $S_{i}$, $S$, and $\\rho$\n",
    "    1. [Step 2.c](#jacobian): Jacobian transformation on the ADM/BSSN source terms\n",
    "    1. [Step 2.d](#tensor): Rescale tensorial quantities\n",
    "1. [Step 3](#adm_id_spacetime): Convert ADM spacetime quantity initial data from Spherical to BSSN Curvilinear coordinates\n",
    "1. [Step 4](#validate): Validating that the TOV initial data satisfy the Hamiltonian constraint\n",
    "    1. [Step 4.a](#ham_const_output): Output the Hamiltonian Constraint\n",
    "    1. [Step 4.b](#apply_bcs): Apply singular, curvilinear coordinate boundary conditions\n",
    "    1. [Step 4.c](#enforce3metric): Enforce conformal 3-metric $\\det{\\bar{\\gamma}_{ij}}=\\det{\\hat{\\gamma}_{ij}}$ \n",
    "1. [Step 5](#mainc): `TOV_Playground.c`: The Main C Code\n",
    "1. [Step 6](#plot): Plotting the single-neutron-star initial data\n",
    "1. [Step 7](#convergence): Validation: Convergence of numerical errors (Hamiltonian constraint violation) to zero\n",
    "1. [Step 8](#latex_pdf_output): Output this notebook to $\\LaTeX$-formatted PDF file"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='initalizenrpy'></a>\n",
    "\n",
    "# Step 1: Set core NRPy+ parameters for numerical grids and reference metric \\[Back to [top](#toc)\\]\n",
    "$$\\label{initializenrpy}$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Step P1: Import needed NRPy+ core modules:\n",
    "from outputC import lhrh,outCfunction,outputC  # NRPy+: Core C code output module\n",
    "import NRPy_param_funcs as par   # NRPy+: Parameter interface\n",
    "import sympy as sp               # SymPy: The Python computer algebra package upon which NRPy+ depends\n",
    "import finite_difference as fin  # NRPy+: Finite difference C code generation module\n",
    "import grid as gri               # NRPy+: Functions having to do with numerical grids\n",
    "import indexedexp as ixp         # NRPy+: Symbolic indexed expression (e.g., tensors, vectors, etc.) support\n",
    "import reference_metric as rfm   # NRPy+: Reference metric support\n",
    "import cmdline_helper as cmd     # NRPy+: Multi-platform Python command-line interface\n",
    "import shutil, os, sys           # Standard Python modules for multiplatform OS-level functions\n",
    "\n",
    "# Step P2: Create C code output directory:\n",
    "Ccodesdir = os.path.join(\"TOVID_Ccodes/\")\n",
    "# First remove C code output directory if it exists\n",
    "# Courtesy https://stackoverflow.com/questions/303200/how-do-i-remove-delete-a-folder-that-is-not-empty\n",
    "# !rm -r ScalarWaveCurvilinear_Playground_Ccodes\n",
    "shutil.rmtree(Ccodesdir, ignore_errors=True)\n",
    "# Then create a fresh directory\n",
    "cmd.mkdir(Ccodesdir)\n",
    "\n",
    "# Step P3: Create executable output directory:\n",
    "outdir = os.path.join(Ccodesdir,\"output/\")\n",
    "cmd.mkdir(outdir)\n",
    "\n",
    "# Step 1: Set the spatial dimension parameter\n",
    "#         to three this time, and then read\n",
    "#         the parameter as DIM.\n",
    "par.set_parval_from_str(\"grid::DIM\",3)\n",
    "DIM = par.parval_from_str(\"grid::DIM\")\n",
    "\n",
    "# Step 2: Set some core parameters, including CoordSystem MoL timestepping algorithm,\n",
    "#                                 FD order, floating point precision, and CFL factor:\n",
    "# Choices are: Spherical, SinhSpherical, SinhSphericalv2, Cylindrical, SinhCylindrical,\n",
    "#              SymTP, SinhSymTP\n",
    "CoordSystem     = \"Spherical\"\n",
    "\n",
    "# Step 2.a: Set defaults for Coordinate system parameters.\n",
    "#           These are perhaps the most commonly adjusted parameters,\n",
    "#           so we enable modifications at this high level.\n",
    "\n",
    "# domain_size     = 7.5 # SET BELOW BASED ON TOV STELLAR RADIUS\n",
    "\n",
    "# sinh_width sets the default value for:\n",
    "#   * SinhSpherical's params.SINHW\n",
    "#   * SinhCylindrical's params.SINHW{RHO,Z}\n",
    "#   * SinhSymTP's params.SINHWAA\n",
    "sinh_width      = 0.4 # If Sinh* coordinates chosen\n",
    "\n",
    "# sinhv2_const_dr sets the default value for:\n",
    "#   * SinhSphericalv2's params.const_dr\n",
    "#   * SinhCylindricalv2's params.const_d{rho,z}\n",
    "sinhv2_const_dr = 0.05# If Sinh*v2 coordinates chosen\n",
    "\n",
    "# SymTP_bScale sets the default value for:\n",
    "#   * SinhSymTP's params.bScale\n",
    "SymTP_bScale    = 0.5 # If SymTP chosen\n",
    "\n",
    "# Step 2.b: Set the order of spatial finite difference derivatives;\n",
    "#           and the core data type.\n",
    "FD_order  = 4        # Finite difference order: even numbers only, starting with 2. 12 is generally unstable\n",
    "REAL      = \"double\" # Best to use double here.\n",
    "\n",
    "# Step 3: Set the coordinate system for the numerical grid\n",
    "par.set_parval_from_str(\"reference_metric::CoordSystem\",CoordSystem)\n",
    "rfm.reference_metric() # Create ReU, ReDD needed for rescaling B-L initial data, generating BSSN RHSs, etc.\n",
    "\n",
    "# Step 4: Set the finite differencing order to FD_order (set above).\n",
    "par.set_parval_from_str(\"finite_difference::FD_CENTDERIVS_ORDER\", FD_order)\n",
    "\n",
    "# Step 5: Set the direction=2 (phi) axis to be the symmetry axis; i.e.,\n",
    "#         axis \"2\", corresponding to the i2 direction.\n",
    "#         This sets all spatial derivatives in the phi direction to zero.\n",
    "par.set_parval_from_str(\"indexedexp::symmetry_axes\",\"2\")\n",
    "\n",
    "# Step 6: The MoLtimestepping interface is only used for memory allocation/deallocation\n",
    "import MoLtimestepping.C_Code_Generation as MoL\n",
    "from MoLtimestepping.RK_Butcher_Table_Dictionary import Butcher_dict\n",
    "RK_method = \"Euler\" # DOES NOT MATTER; Again MoL interface is only used for memory alloc/dealloc.\n",
    "RK_order  = Butcher_dict[RK_method][1]\n",
    "cmd.mkdir(os.path.join(Ccodesdir,\"MoLtimestepping/\"))\n",
    "MoL.MoL_C_Code_Generation(RK_method, RHS_string      = \"\", post_RHS_string = \"\",\n",
    "    outdir = os.path.join(Ccodesdir,\"MoLtimestepping/\"))\n",
    "\n",
    "# Step 7: Polytropic EOS setup\n",
    "# For EOS_type, choose either \"SimplePolytrope\" or \"PiecewisePolytrope\"\n",
    "EOS_type = \"SimplePolytrope\"\n",
    "# If \"PiecewisePolytrope\" is chosen as EOS_type, you\n",
    "#   must also choose the name of the EOS, which can\n",
    "#   be any of the following:\n",
    "# 'PAL6', 'SLy', 'APR1', 'APR2', 'APR3', 'APR4',\n",
    "# 'FPS', 'WFF1', 'WFF2', 'WFF3', 'BBB2', 'BPAL12',\n",
    "# 'ENG', 'MPA1', 'MS1', 'MS2', 'MS1b', 'PS', 'GS1',\n",
    "# 'GS2', 'BGN1H1', 'GNH3', 'H1', 'H2', 'H3', 'H4',\n",
    "# 'H5', 'H6', 'H7', 'PCL2', 'ALF1', 'ALF2', 'ALF3',\n",
    "# 'ALF4'\n",
    "EOS_name = 'SLy' # <-- IGNORED IF EOS_type is not PiecewisePolytrope."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='adm_id_tov'></a>\n",
    "\n",
    "# Step 2: Set up ADM initial data for polytropic TOV Star \\[Back to [top](#toc)\\]\n",
    "$$\\label{adm_id_tov}$$\n",
    "\n",
    "As documented [in the TOV Initial Data NRPy+ Tutorial Module](Tutorial-TOV_Initial_Data.ipynb) ([older version here](Tutorial-GRMHD_UnitConversion.ipynb)), we will now set up TOV initial data, storing the densely-sampled result to file (***Courtesy Phil Chang***).\n",
    "\n",
    "The TOV solver uses an ODE integration routine provided by scipy, so we first make sure that scipy is installed:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "!pip install scipy > /dev/null"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we call the [`TOV.TOV_Solver()` function](../edit/TOV/TOV_Solver.py) ([NRPy+ Tutorial module](Tutorial-ADM_Initial_Data-TOV.ipynb)) to set up the initial data, using the default parameters for initial data. This function outputs the solution to a file named \"outputTOVpolytrope.txt\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1256 1256 1256 1256 1256 1256\n",
      "Just generated a TOV star with\n",
      "* M        = 1.405030336771405e-01 ,\n",
      "* R_Schw   = 9.566044579232513e-01 ,\n",
      "* R_iso    = 8.100085557410308e-01 ,\n",
      "* M/R_Schw = 1.468768334847266e-01 \n",
      "\n"
     ]
    }
   ],
   "source": [
    "##########################\n",
    "# Polytropic EOS example #\n",
    "##########################\n",
    "import TOV.Polytropic_EOSs as ppeos\n",
    "\n",
    "if EOS_type == \"SimplePolytrope\":\n",
    "    # Set neos = 1 (single polytrope)\n",
    "    neos = 1\n",
    "\n",
    "    # Set rho_poly_tab (not needed for a single polytrope)\n",
    "    rho_poly_tab = []\n",
    "\n",
    "    # Set Gamma_poly_tab\n",
    "    Gamma_poly_tab = [2.0]\n",
    "\n",
    "    # Set K_poly_tab0\n",
    "    K_poly_tab0 = 1. # ZACH NOTES: CHANGED FROM 100.\n",
    "\n",
    "    # Set the eos quantities\n",
    "    eos = ppeos.set_up_EOS_parameters__complete_set_of_input_variables(neos,rho_poly_tab,Gamma_poly_tab,K_poly_tab0)\n",
    "    rho_baryon_central = 0.129285\n",
    "elif EOS_type == \"PiecewisePolytrope\":\n",
    "    eos = ppeos.set_up_EOS_parameters__Read_et_al_input_variables(EOS_name)\n",
    "    rho_baryon_central=2.0\n",
    "else:\n",
    "    print(\"\"\"Error: unknown EOS_type. Valid types are 'SimplePolytrope' and 'PiecewisePolytrope' \"\"\")\n",
    "    sys.exit(1)\n",
    "\n",
    "import TOV.TOV_Solver as TOV\n",
    "M_TOV, R_Schw_TOV, R_iso_TOV = TOV.TOV_Solver(eos,\n",
    "                                              outfile=\"outputTOVpolytrope.txt\",\n",
    "                                              rho_baryon_central=rho_baryon_central,\n",
    "                                              return_M_RSchw_and_Riso = True,\n",
    "                                              verbose = True)\n",
    "\n",
    "# domain_size sets the default value for:\n",
    "#   * Spherical's params.RMAX\n",
    "#   * SinhSpherical*'s params.AMAX\n",
    "#   * Cartesians*'s -params.{x,y,z}min & .{x,y,z}max\n",
    "#   * Cylindrical's -params.ZMIN & .{Z,RHO}MAX\n",
    "#   * SinhCylindrical's params.AMPL{RHO,Z}\n",
    "#   * *SymTP's params.AMAX\n",
    "domain_size = 2.0 * R_iso_TOV"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='tov_interp'></a>\n",
    "\n",
    "## Step 2.a: Interpolate the TOV data file as needed to set up ADM spacetime quantities in spherical basis (for input into the `Converting_Numerical_ADM_Spherical_or_Cartesian_to_BSSNCurvilinear` module) and $T^{\\mu\\nu}$ in the chosen reference metric basis \\[Back to [top](#toc)\\]\n",
    "$$\\label{tov_interp}$$\n",
    "\n",
    "The TOV data file just written stored $\\left(r,\\rho(r),P(r),M(r),e^{\\nu(r)}\\right)$, where $\\rho(r)$ is the total mass-energy density (cf. $\\rho_{\\text{baryonic}}$).\n",
    "\n",
    "**METRIC DATA IN TERMS OF ADM QUANTITIES**\n",
    "\n",
    "The [TOV line element](https://en.wikipedia.org/wiki/Tolman%E2%80%93Oppenheimer%E2%80%93Volkoff_equation) in *Schwarzschild coordinates* is written (in the $-+++$ form):\n",
    "$$\n",
    "ds^2 = - c^2 e^\\nu dt^2 + \\left(1 - \\frac{2GM}{rc^2}\\right)^{-1} dr^2 + r^2 d\\Omega^2.\n",
    "$$\n",
    "\n",
    "In *isotropic coordinates* with $G=c=1$ (i.e., the coordinate system we'd prefer to use), the ($-+++$ form) line element is written:\n",
    "$$\n",
    "ds^2 = - e^{\\nu} dt^2 + e^{4\\phi} \\left(d\\bar{r}^2 + \\bar{r}^2 d\\Omega^2\\right),\n",
    "$$\n",
    "where $\\phi$ here is the *conformal factor*.\n",
    "\n",
    "The ADM 3+1 line element for this diagonal metric in isotropic spherical coordinates is given by:\n",
    "$$\n",
    "ds^2 = (-\\alpha^2 + \\beta_k \\beta^k) dt^2 + \\gamma_{\\bar{r}\\bar{r}} d\\bar{r}^2 + \\gamma_{\\theta\\theta} d\\theta^2+ \\gamma_{\\phi\\phi} d\\phi^2,\n",
    "$$\n",
    "\n",
    "from which we can immediately read off the ADM quantities:\n",
    "\\begin{align}\n",
    "\\alpha &= e^{\\nu(\\bar{r})/2} \\\\\n",
    "\\beta^k &= 0 \\\\\n",
    "\\gamma_{\\bar{r}\\bar{r}} &= e^{4\\phi}\\\\\n",
    "\\gamma_{\\theta\\theta} &= e^{4\\phi} \\bar{r}^2 \\\\\n",
    "\\gamma_{\\phi\\phi} &= e^{4\\phi} \\bar{r}^2 \\sin^2 \\theta \\\\\n",
    "\\end{align}\n",
    "\n",
    "**STRESS-ENERGY TENSOR $T^{\\mu\\nu}$**\n",
    "\n",
    "We will also need the stress-energy tensor $T^{\\mu\\nu}$. [As discussed here](https://en.wikipedia.org/wiki/Tolman%E2%80%93Oppenheimer%E2%80%93Volkoff_equation), the stress-energy tensor is diagonal:\n",
    "\n",
    "\\begin{align}\n",
    "T^t_t &= -\\rho \\\\\n",
    "T^i_j &= P \\delta^i_j \\\\\n",
    "\\text{All other components of }T^\\mu_\\nu &= 0.\n",
    "\\end{align}\n",
    "\n",
    "Since $\\beta^i=0$ the inverse metric expression simplifies to (Eq. 4.49 in [Gourgoulhon](https://arxiv.org/pdf/gr-qc/0703035.pdf)):\n",
    "$$\n",
    "g^{\\mu\\nu} = \\begin{pmatrix} \n",
    "-\\frac{1}{\\alpha^2} & \\frac{\\beta^i}{\\alpha^2} \\\\\n",
    "\\frac{\\beta^i}{\\alpha^2} & \\gamma^{ij} - \\frac{\\beta^i\\beta^j}{\\alpha^2}\n",
    "\\end{pmatrix} =\n",
    "\\begin{pmatrix} \n",
    "-\\frac{1}{\\alpha^2} & 0 \\\\\n",
    "0 & \\gamma^{ij}\n",
    "\\end{pmatrix},\n",
    "$$\n",
    "\n",
    "and since the 3-metric is diagonal we get\n",
    "\n",
    "\\begin{align}\n",
    "\\gamma^{\\bar{r}\\bar{r}} &= e^{-4\\phi}\\\\\n",
    "\\gamma^{\\theta\\theta} &= e^{-4\\phi}\\frac{1}{\\bar{r}^2} \\\\\n",
    "\\gamma^{\\phi\\phi} &= e^{-4\\phi}\\frac{1}{\\bar{r}^2 \\sin^2 \\theta}.\n",
    "\\end{align}\n",
    "\n",
    "Thus raising $T^\\mu_\\nu$ yields a diagonal $T^{\\mu\\nu}$\n",
    "\n",
    "\\begin{align}\n",
    "T^{tt} &= -g^{tt} \\rho = \\frac{1}{\\alpha^2} \\rho = e^{-\\nu(\\bar{r})} \\rho \\\\\n",
    "T^{\\bar{r}\\bar{r}} &= g^{\\bar{r}\\bar{r}} P = \\frac{1}{e^{4 \\phi}} P \\\\\n",
    "T^{\\theta\\theta} &= g^{\\theta\\theta} P = \\frac{1}{e^{4 \\phi}\\bar{r}^2} P\\\\\n",
    "T^{\\phi\\phi} &= g^{\\phi\\phi} P = \\frac{1}{e^{4\\phi}\\bar{r}^2 \\sin^2 \\theta} P \n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "thismodule = \"TOVID\"\n",
    "rbar,theta,rho,P,expnu,exp4phi = par.Cparameters(\"REAL\",thismodule,\n",
    "                                                 [\"rbar\",\"theta\",\"rho\",\"P\",\"expnu\",\"exp4phi\"],1e300)\n",
    "IDalpha = sp.sqrt(expnu)\n",
    "gammaSphDD = ixp.zerorank2(DIM=3)\n",
    "gammaSphDD[0][0] = exp4phi\n",
    "gammaSphDD[1][1] = exp4phi*rbar**2\n",
    "gammaSphDD[2][2] = exp4phi*rbar**2*sp.sin(theta)**2\n",
    "\n",
    "T4SphUU = ixp.zerorank2(DIM=4)\n",
    "T4SphUU[0][0] = rho/expnu\n",
    "T4SphUU[1][1] = P/exp4phi\n",
    "T4SphUU[2][2] = P/(exp4phi*rbar**2)\n",
    "T4SphUU[3][3] = P/(exp4phi*rbar**2*sp.sin(theta)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Output C function ID_TOV_ADM_quantities() to file TOVID_Ccodes/ID_TOV_ADM_quantities.h\n"
     ]
    }
   ],
   "source": [
    "expr_list = [IDalpha]\n",
    "name_list = [\"*alpha\"]\n",
    "for i in range(3):\n",
    "    for j in range(i,3):\n",
    "        expr_list.append(gammaSphDD[i][j])\n",
    "        name_list.append(\"*gammaDD\"+str(i)+str(j))\n",
    "\n",
    "desc = \"\"\"This function takes as input either (x,y,z) or (r,th,ph) and outputs\n",
    "all ADM quantities in the Cartesian or Spherical basis, respectively.\"\"\"\n",
    "name = \"ID_TOV_ADM_quantities\"\n",
    "outCparams = \"preindent=1,outCverbose=False,includebraces=False\"\n",
    "\n",
    "outCfunction(\n",
    "    outfile=os.path.join(Ccodesdir, name + \".h\"), desc=desc, name=name,\n",
    "    params=\"\"\"  const REAL xyz_or_rthph[3],\n",
    "\n",
    "                const ID_inputs other_inputs,\n",
    "\n",
    "                REAL *gammaDD00,REAL *gammaDD01,REAL *gammaDD02,REAL *gammaDD11,REAL *gammaDD12,REAL *gammaDD22,\n",
    "                REAL *KDD00,REAL *KDD01,REAL *KDD02,REAL *KDD11,REAL *KDD12,REAL *KDD22,\n",
    "                REAL *alpha,\n",
    "                REAL *betaU0,REAL *betaU1,REAL *betaU2,\n",
    "                REAL *BU0,REAL *BU1,REAL *BU2\"\"\",\n",
    "    body=\"\"\"\n",
    "      // Set trivial metric quantities:\n",
    "      *KDD00 = *KDD01 = *KDD02 = 0.0;\n",
    "      /**/     *KDD11 = *KDD12 = 0.0;\n",
    "      /**/              *KDD22 = 0.0;\n",
    "      *betaU0 = *betaU1 = *betaU2 = 0.0;\n",
    "      *BU0 = *BU1 = *BU2 = 0.0;\n",
    "\n",
    "      // Next set gamma_{ij} in spherical basis\n",
    "      const REAL rbar  = xyz_or_rthph[0];\n",
    "      const REAL theta = xyz_or_rthph[1];\n",
    "      const REAL phi   = xyz_or_rthph[2];\n",
    "\n",
    "      REAL rho,rho_baryon,P,M,expnu,exp4phi;\n",
    "      TOV_interpolate_1D(rbar,other_inputs.Rbar,other_inputs.Rbar_idx,other_inputs.interp_stencil_size,\n",
    "                         other_inputs.numlines_in_file,\n",
    "                         other_inputs.r_Schw_arr,other_inputs.rho_arr,other_inputs.rho_baryon_arr,other_inputs.P_arr,other_inputs.M_arr,\n",
    "                         other_inputs.expnu_arr,other_inputs.exp4phi_arr,other_inputs.rbar_arr,\n",
    "                         &rho,&rho_baryon,&P,&M,&expnu,&exp4phi);\\n\"\"\"+\n",
    "    outputC(expr_list,name_list, \"returnstring\",outCparams),\n",
    "    opts=\"DisableCparameters\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As all input quantities are functions of $r$, we will simply read the solution from file and interpolate it to the values of $r$ needed by the initial data.\n",
    "\n",
    "1. First we define functions `ID_TOV_ADM_quantities()` and `ID_TOV_TUPMUNU()` that call the [1D TOV interpolator function](../edit/TOV/tov_interp.h) to evaluate the ADM spacetime quantities and $T^{\\mu\\nu}$, respectively, at any given point $(r,\\theta,\\phi)$ in the Spherical basis. All quantities are defined as above.\n",
    "1. Next we will construct the BSSN/ADM source terms $\\{S_{ij},S_{i},S,\\rho\\}$ in the Spherical basis\n",
    "1. Then we will perform the Jacobian transformation on $\\{S_{ij},S_{i},S,\\rho\\}$ to the desired `(xx0,xx1,xx2)` basis\n",
    "1. Next we call the *Numerical* Spherical ADM$\\to$Curvilinear BSSN converter function to conver the above ADM quantities to the rescaled BSSN quantities in the desired curvilinear coordinate system: [BSSN/ADM_Numerical_Spherical_or_Cartesian_to_BSSNCurvilinear.py](../edit/BSSN/ADM_Numerical_Spherical_or_Cartesian_to_BSSNCurvilinear.py); [\\[**tutorial**\\]](Tutorial-ADM_Initial_Data-Converting_Numerical_ADM_Spherical_or_Cartesian_to_BSSNCurvilinear.ipynb).\n",
    "\n",
    "$$\n",
    "{\\rm Jac\\_dUSph\\_dDrfmUD[mu][nu]} = \\frac{\\partial x^\\mu_{\\rm Sph}}{\\partial x^\\nu_{\\rm rfm}},\n",
    "$$\n",
    "\n",
    "via exact differentiation (courtesy SymPy), and the inverse Jacobian\n",
    "$$\n",
    "{\\rm Jac\\_dUrfm\\_dDSphUD[mu][nu]} = \\frac{\\partial x^\\mu_{\\rm rfm}}{\\partial x^\\nu_{\\rm Sph}},\n",
    "$$\n",
    "\n",
    "using NRPy+'s `generic_matrix_inverter3x3()` function. In terms of these, the transformation of BSSN tensors from Spherical to `\"reference_metric::CoordSystem\"` coordinates may be written:\n",
    "\n",
    "$$\n",
    "T^{\\mu\\nu}_{\\rm rfm} = \n",
    "\\frac{\\partial x^\\mu_{\\rm rfm}}{\\partial x^\\delta_{\\rm Sph}}\n",
    "\\frac{\\partial x^\\nu_{\\rm rfm}}{\\partial x^\\sigma_{\\rm Sph}} T^{\\delta\\sigma}_{\\rm Sph}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Output C function ID_TOV_TUPMUNU_xx0xx1xx2() to file TOVID_Ccodes/ID_TOV_TUPMUNU_xx0xx1xx2.h\n"
     ]
    }
   ],
   "source": [
    "r_th_ph_or_Cart_xyz_oID_xx = []\n",
    "CoordType_in = \"Spherical\"\n",
    "if CoordType_in == \"Spherical\":\n",
    "    r_th_ph_or_Cart_xyz_oID_xx = rfm.xxSph\n",
    "elif CoordType_in == \"Cartesian\":\n",
    "    r_th_ph_or_Cart_xyz_oID_xx = rfm.xxCart\n",
    "else:\n",
    "    print(\"Error: Can only convert ADM Cartesian or Spherical initial data to BSSN Curvilinear coords.\")\n",
    "    exit(1)\n",
    "\n",
    "# Next apply Jacobian transformations to convert into the (xx0,xx1,xx2) basis\n",
    "\n",
    "# rho and S are scalar, so no Jacobian transformations are necessary.\n",
    "\n",
    "Jac4_dUSphorCart_dDrfmUD = ixp.zerorank2(DIM=4)\n",
    "Jac4_dUSphorCart_dDrfmUD[0][0] = sp.sympify(1)\n",
    "for i in range(DIM):\n",
    "    for j in range(DIM):\n",
    "        Jac4_dUSphorCart_dDrfmUD[i+1][j+1] = sp.diff(r_th_ph_or_Cart_xyz_oID_xx[i],rfm.xx[j])\n",
    "\n",
    "Jac4_dUrfm_dDSphorCartUD, dummyDET = ixp.generic_matrix_inverter4x4(Jac4_dUSphorCart_dDrfmUD)\n",
    "\n",
    "# Perform Jacobian operations on T^{mu nu} and gamma_{ij}\n",
    "T4UU = ixp.register_gridfunctions_for_single_rank2(\"AUXEVOL\",\"T4UU\",\"sym01\",DIM=4)\n",
    "\n",
    "IDT4UU = ixp.zerorank2(DIM=4)\n",
    "for mu in range(4):\n",
    "    for nu in range(4):\n",
    "        for delta in range(4):\n",
    "            for sigma in range(4):\n",
    "                IDT4UU[mu][nu] += \\\n",
    "                     Jac4_dUrfm_dDSphorCartUD[mu][delta]*Jac4_dUrfm_dDSphorCartUD[nu][sigma]*T4SphUU[delta][sigma]\n",
    "\n",
    "lhrh_list = []\n",
    "for mu in range(4):\n",
    "    for nu in range(mu,4):\n",
    "        lhrh_list.append(lhrh(lhs=gri.gfaccess(\"auxevol_gfs\",\"T4UU\"+str(mu)+str(nu)),rhs=IDT4UU[mu][nu]))\n",
    "\n",
    "desc = \"\"\"This function takes as input either (x,y,z) or (r,th,ph) and outputs\n",
    "all ADM quantities in the Cartesian or Spherical basis, respectively.\"\"\"\n",
    "name = \"ID_TOV_TUPMUNU_xx0xx1xx2\"\n",
    "outCparams = \"preindent=1,outCverbose=False,includebraces=False\"\n",
    "outCfunction(\n",
    "    outfile=os.path.join(Ccodesdir, name + \".h\"), desc=desc, name=name,\n",
    "    params=\"\"\"const paramstruct *restrict params,REAL *restrict xx[3],\n",
    "              const ID_inputs other_inputs,REAL *restrict auxevol_gfs\"\"\",\n",
    "    body=outputC([rfm.xxSph[0],rfm.xxSph[1],rfm.xxSph[2]],\n",
    "                 [\"const REAL rbar\",\"const REAL theta\",\"const REAL ph\"],\"returnstring\",\n",
    "                 \"CSE_enable=False,includebraces=False\")+\"\"\"\n",
    "      REAL rho,rho_baryon,P,M,expnu,exp4phi;\n",
    "      TOV_interpolate_1D(rbar,other_inputs.Rbar,other_inputs.Rbar_idx,other_inputs.interp_stencil_size,\n",
    "                         other_inputs.numlines_in_file,\n",
    "                         other_inputs.r_Schw_arr,other_inputs.rho_arr,other_inputs.rho_baryon_arr,other_inputs.P_arr,other_inputs.M_arr,\n",
    "                         other_inputs.expnu_arr,other_inputs.exp4phi_arr,other_inputs.rbar_arr,\n",
    "                         &rho,&rho_baryon,&P,&M,&expnu,&exp4phi);\\n\"\"\"+\n",
    "    fin.FD_outputC(\"returnstring\",lhrh_list,params=\"outCverbose=False,includebraces=False\").replace(\"IDX4\",\"IDX4S\"),\n",
    "    loopopts=\"AllPoints,Read_xxs\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='adm_id_spacetime'></a>\n",
    "\n",
    "# Step 3: Convert ADM initial data to BSSN-in-curvilinear coordinates \\[Back to [top](#toc)\\]\n",
    "$$\\label{adm_id_spacetime}$$\n",
    "\n",
    "This is an automated process, taken care of by [`BSSN.ADM_Numerical_Spherical_or_Cartesian_to_BSSNCurvilinear`](../edit/BSSN.ADM_Numerical_Spherical_or_Cartesian_to_BSSNCurvilinear.py), and documented [in this tutorial notebook](Tutorial-ADM_Initial_Data-Converting_Numerical_ADM_Spherical_or_Cartesian_to_BSSNCurvilinear.ipynb)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Output C function ID_BSSN_lambdas() to file TOVID_Ccodes/ID_BSSN_lambdas.h\n",
      "Output C function ID_ADM_xx0xx1xx2_to_BSSN_xx0xx1xx2__ALL_BUT_LAMBDAs() to file TOVID_Ccodes/ID_ADM_xx0xx1xx2_to_BSSN_xx0xx1xx2__ALL_BUT_LAMBDAs.h\n",
      "Output C function ID_BSSN__ALL_BUT_LAMBDAs() to file TOVID_Ccodes/ID_BSSN__ALL_BUT_LAMBDAs.h\n"
     ]
    }
   ],
   "source": [
    "import BSSN.ADM_Numerical_Spherical_or_Cartesian_to_BSSNCurvilinear as AtoBnum\n",
    "AtoBnum.Convert_Spherical_or_Cartesian_ADM_to_BSSN_curvilinear(\"Spherical\",\"ID_TOV_ADM_quantities\",\n",
    "                                                               Ccodesdir=Ccodesdir,loopopts=\"\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='validate'></a>\n",
    "\n",
    "# Step 4: Validating that the TOV initial data satisfy the Hamiltonian constraint \\[Back to [top](#toc)\\]\n",
    "$$\\label{validate}$$\n",
    "\n",
    "We will validate that the TOV initial data satisfy the Hamiltonian constraint, modulo numerical finite differencing error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='ham_const_output'></a>\n",
    "\n",
    "## Step 4.a: Output the Hamiltonian constraint \\[Back to [top](#toc)\\]\n",
    "$$\\label{ham_const_output}$$\n",
    "\n",
    "First output the Hamiltonian constraint [as documented in the corresponding NRPy+ tutorial notebook](Tutorial-BSSN_constraints.ipynb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Output C function Hamiltonian_constraint() to file TOVID_Ccodes/Hamiltonian_constraint.h\n"
     ]
    }
   ],
   "source": [
    "# Enable rfm_precompute infrastructure, which results in\n",
    "#   BSSN RHSs that are free of transcendental functions,\n",
    "#   even in curvilinear coordinates, so long as\n",
    "#   ConformalFactor is set to \"W\" (default).\n",
    "cmd.mkdir(os.path.join(Ccodesdir,\"rfm_files/\"))\n",
    "par.set_parval_from_str(\"reference_metric::enable_rfm_precompute\",\"True\")\n",
    "par.set_parval_from_str(\"reference_metric::rfm_precompute_Ccode_outdir\",os.path.join(Ccodesdir,\"rfm_files/\"))\n",
    "\n",
    "import BSSN.Enforce_Detgammabar_Constraint as EGC\n",
    "enforce_detg_constraint_symb_expressions = EGC.Enforce_Detgammabar_Constraint_symb_expressions()\n",
    "\n",
    "\n",
    "# Now register the Hamiltonian as a gridfunction.\n",
    "H = gri.register_gridfunctions(\"AUX\",\"H\")\n",
    "# Then define the Hamiltonian constraint and output the optimized C code.\n",
    "import BSSN.BSSN_constraints as bssncon\n",
    "import BSSN.BSSN_stress_energy_source_terms as Bsest\n",
    "bssncon.BSSN_constraints(add_T4UUmunu_source_terms=False)\n",
    "Bsest.BSSN_source_terms_for_BSSN_constraints(T4UU)\n",
    "bssncon.H += Bsest.sourceterm_H\n",
    "\n",
    "# Now that we are finished with all the rfm hatted\n",
    "#           quantities in generic precomputed functional\n",
    "#           form, let's restore them to their closed-\n",
    "#           form expressions.\n",
    "par.set_parval_from_str(\"reference_metric::enable_rfm_precompute\",\"False\") # Reset to False to disable rfm_precompute.\n",
    "rfm.ref_metric__hatted_quantities()\n",
    "\n",
    "desc=\"Evaluate the Hamiltonian constraint\"\n",
    "name=\"Hamiltonian_constraint\"\n",
    "outCfunction(\n",
    "    outfile  = os.path.join(Ccodesdir,name+\".h\"), desc=desc, name=name,\n",
    "    params   = \"\"\"rfm_struct *restrict rfmstruct,const paramstruct *restrict params,\n",
    "                  REAL *restrict in_gfs, REAL *restrict auxevol_gfs, REAL *restrict aux_gfs\"\"\",\n",
    "    body     = fin.FD_outputC(\"returnstring\",lhrh(lhs=gri.gfaccess(\"aux_gfs\", \"H\"), rhs=bssncon.H),\n",
    "                              params=\"outCverbose=False\").replace(\"IDX4\",\"IDX4S\"),\n",
    "    loopopts = \"InteriorPoints,Enable_rfm_precompute\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='bc_functs'></a>\n",
    "\n",
    "## Step 4.b: Set up boundary condition functions for chosen singular, curvilinear coordinate system \\[Back to [top](#toc)\\]\n",
    "$$\\label{bc_functs}$$\n",
    "\n",
    "Next apply singular, curvilinear coordinate boundary conditions [as documented in the corresponding NRPy+ tutorial notebook](Tutorial-Start_to_Finish-Curvilinear_BCs.ipynb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wrote to file \"TOVID_Ccodes/boundary_conditions/parity_conditions_symbolic_dot_products.h\"\n",
      "Evolved parity: ( aDD00:4, aDD01:5, aDD02:6, aDD11:7, aDD12:8, aDD22:9,\n",
      "    alpha:0, betU0:1, betU1:2, betU2:3, cf:0, hDD00:4, hDD01:5, hDD02:6,\n",
      "    hDD11:7, hDD12:8, hDD22:9, lambdaU0:1, lambdaU1:2, lambdaU2:3, trK:0,\n",
      "    vetU0:1, vetU1:2, vetU2:3 )\n",
      "Auxiliary parity: ( H:0 )\n",
      "AuxEvol parity: ( T4UU00:0, T4UU01:1, T4UU02:2, T4UU03:3, T4UU11:4,\n",
      "    T4UU12:5, T4UU13:6, T4UU22:7, T4UU23:8, T4UU33:9 )\n",
      "Wrote to file \"TOVID_Ccodes/boundary_conditions/EigenCoord_Cart_to_xx.h\"\n"
     ]
    }
   ],
   "source": [
    "import CurviBoundaryConditions.CurviBoundaryConditions as cbcs\n",
    "cbcs.Set_up_CurviBoundaryConditions(os.path.join(Ccodesdir,\"boundary_conditions/\"),Cparamspath=os.path.join(\"../\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='enforce3metric'></a>\n",
    "\n",
    "## Step 4.c: Enforce conformal 3-metric $\\det{\\bar{\\gamma}_{ij}}=\\det{\\hat{\\gamma}_{ij}}$ constraint \\[Back to [top](#toc)\\]\n",
    "$$\\label{enforce3metric}$$\n",
    "\n",
    "Then enforce conformal 3-metric $\\det{\\bar{\\gamma}_{ij}}=\\det{\\hat{\\gamma}_{ij}}$ constraint (Eq. 53 of [Ruchlin, Etienne, and Baumgarte (2018)](https://arxiv.org/abs/1712.07658)), as [documented in the corresponding NRPy+ tutorial notebook](Tutorial-BSSN-Enforcing_Determinant_gammabar_equals_gammahat_Constraint.ipynb)\n",
    "\n",
    "Applying curvilinear boundary conditions should affect the initial data at the outer boundary, and will in general cause the $\\det{\\bar{\\gamma}_{ij}}=\\det{\\hat{\\gamma}_{ij}}$ constraint to be violated there. Thus after we apply these boundary conditions, we must always call the routine for enforcing the $\\det{\\bar{\\gamma}_{ij}}=\\det{\\hat{\\gamma}_{ij}}$ constraint:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Output C function enforce_detgammabar_constraint() to file TOVID_Ccodes/enforce_detgammabar_constraint.h\n"
     ]
    }
   ],
   "source": [
    "# Set up the C function for the det(gammahat) = det(gammabar)\n",
    "EGC.output_Enforce_Detgammabar_Constraint_Ccode(Ccodesdir,\n",
    "                                                exprs=enforce_detg_constraint_symb_expressions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='cparams_rfm_and_domainsize'></a>\n",
    "\n",
    "## Step 4.d: Output C codes needed for declaring and setting Cparameters; also set `free_parameters.h` \\[Back to [top](#toc)\\]\n",
    "$$\\label{cparams_rfm_and_domainsize}$$\n",
    "\n",
    "Based on declared NRPy+ Cparameters, first we generate `declare_Cparameters_struct.h`, `set_Cparameters_default.h`, and `set_Cparameters[-SIMD].h`.\n",
    "\n",
    "Then we output `free_parameters.h`, which sets initial data parameters, as well as grid domain & reference metric parameters, applying `domain_size` and `sinh_width`/`SymTP_bScale` (if applicable) as set above"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Step 3.d.i: Generate declare_Cparameters_struct.h, set_Cparameters_default.h, and set_Cparameters[-SIMD].h\n",
    "par.generate_Cparameters_Ccodes(os.path.join(Ccodesdir))\n",
    "\n",
    "# Step 3.d.ii: Set free_parameters.h\n",
    "# Output to $Ccodesdir/free_parameters.h reference metric parameters based on generic\n",
    "#    domain_size,sinh_width,sinhv2_const_dr,SymTP_bScale,\n",
    "#    parameters set above.\n",
    "rfm.out_default_free_parameters_for_rfm(os.path.join(Ccodesdir,\"free_parameters.h\"),\n",
    "                                        domain_size,sinh_width,sinhv2_const_dr,SymTP_bScale)\n",
    "\n",
    "# Step 3.d.iii: Generate set_Nxx_dxx_invdx_params__and__xx.h:\n",
    "rfm.set_Nxx_dxx_invdx_params__and__xx_h(Ccodesdir)\n",
    "\n",
    "# Step 3.d.iv: Generate xxCart.h, which contains xxCart() for\n",
    "#               (the mapping from xx->Cartesian) for the chosen\n",
    "#               CoordSystem:\n",
    "rfm.xxCart_h(\"xxCart\",\"./set_Cparameters.h\",os.path.join(Ccodesdir,\"xxCart.h\"))\n",
    "\n",
    "# Step 3.d.v: Generate declare_Cparameters_struct.h, set_Cparameters_default.h, and set_Cparameters[-SIMD].h\n",
    "par.generate_Cparameters_Ccodes(os.path.join(Ccodesdir))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='mainc'></a>\n",
    "\n",
    "# Step 5: `TOV_Playground.c`: The Main C Code \\[Back to [top](#toc)\\]\n",
    "$$\\label{mainc}$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Part P0: Define REAL, set the number of ghost cells NGHOSTS (from NRPy+'s FD_CENTDERIVS_ORDER)\n",
    "\n",
    "with open(os.path.join(Ccodesdir,\"TOV_Playground_REAL__NGHOSTS.h\"), \"w\") as file:\n",
    "    file.write(\"\"\"\n",
    "// Part P0.a: Set the number of ghost cells, from NRPy+'s FD_CENTDERIVS_ORDER\n",
    "#define NGHOSTS \"\"\"+str(int(FD_order/2)+1)+\"\"\"\n",
    "// Part P0.b: Set the numerical precision (REAL) to double, ensuring all floating point\n",
    "//            numbers are stored to at least ~16 significant digits\n",
    "#define REAL \"\"\"+REAL+\"\"\"\n",
    "// Part P0.c: Set TOV stellar parameters\n",
    "#define TOV_Mass  \"\"\"+str(M_TOV)+\"\"\"\n",
    "#define TOV_Riso  \"\"\"+str(R_iso_TOV)+\"\\n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Writing TOVID_Ccodes//TOV_Playground.c\n"
     ]
    }
   ],
   "source": [
    "%%writefile $Ccodesdir/TOV_Playground.c\n",
    "\n",
    "// Step P0: Define REAL and NGHOSTS. This header is generated by NRPy+.\n",
    "#include \"TOV_Playground_REAL__NGHOSTS.h\"\n",
    "\n",
    "#include \"rfm_files/rfm_struct__declare.h\"\n",
    "\n",
    "#include \"declare_Cparameters_struct.h\"\n",
    "\n",
    "// Step P1: Import needed header files\n",
    "#include \"stdio.h\"\n",
    "#include \"stdlib.h\"\n",
    "#include \"math.h\"\n",
    "#ifndef M_PI\n",
    "#define M_PI 3.141592653589793238462643383279502884L\n",
    "#endif\n",
    "#ifndef M_SQRT1_2\n",
    "#define M_SQRT1_2 0.707106781186547524400844362104849039L\n",
    "#endif\n",
    "\n",
    "// Step P2: Declare the IDX4S(gf,i,j,k) macro, which enables us to store 4-dimensions of\n",
    "//           data in a 1D array. In this case, consecutive values of \"i\"\n",
    "//           (all other indices held to a fixed value) are consecutive in memory, where\n",
    "//           consecutive values of \"j\" (fixing all other indices) are separated by\n",
    "//           Nxx_plus_2NGHOSTS0 elements in memory. Similarly, consecutive values of\n",
    "//           \"k\" are separated by Nxx_plus_2NGHOSTS0*Nxx_plus_2NGHOSTS1 in memory, etc.\n",
    "#define IDX4S(g,i,j,k) \\\n",
    "( (i) + Nxx_plus_2NGHOSTS0 * ( (j) + Nxx_plus_2NGHOSTS1 * ( (k) + Nxx_plus_2NGHOSTS2 * (g) ) ) )\n",
    "#define IDX4ptS(g,idx) ( (idx) + (Nxx_plus_2NGHOSTS0*Nxx_plus_2NGHOSTS1*Nxx_plus_2NGHOSTS2) * (g) )\n",
    "#define IDX3S(i,j,k) ( (i) + Nxx_plus_2NGHOSTS0 * ( (j) + Nxx_plus_2NGHOSTS1 * ( (k) ) ) )\n",
    "#define LOOP_REGION(i0min,i0max, i1min,i1max, i2min,i2max) \\\n",
    "  for(int i2=i2min;i2<i2max;i2++) for(int i1=i1min;i1<i1max;i1++) for(int i0=i0min;i0<i0max;i0++)\n",
    "#define LOOP_ALL_GFS_GPS(ii) _Pragma(\"omp parallel for\") \\\n",
    "  for(int (ii)=0;(ii)<Nxx_plus_2NGHOSTS_tot*NUM_EVOL_GFS;(ii)++)\n",
    "\n",
    "// Step P3: Set UUGF and VVGF macros, as well as xxCart()\n",
    "#include \"boundary_conditions/gridfunction_defines.h\"\n",
    "\n",
    "// Step P4: Set xxCart(const paramstruct *restrict params,\n",
    "//                     REAL *restrict xx[3],\n",
    "//                     const int i0,const int i1,const int i2,\n",
    "//                     REAL xCart[3]),\n",
    "//           which maps xx->Cartesian via\n",
    "//    {xx[0][i0],xx[1][i1],xx[2][i2]}->{xCart[0],xCart[1],xCart[2]}\n",
    "#include \"xxCart.h\"\n",
    "\n",
    "// Step P5: Defines set_Nxx_dxx_invdx_params__and__xx(const int EigenCoord, const int Nxx[3],\n",
    "//                                       paramstruct *restrict params, REAL *restrict xx[3]),\n",
    "//          which sets params Nxx,Nxx_plus_2NGHOSTS,dxx,invdx, and xx[] for\n",
    "//          the chosen Eigen-CoordSystem if EigenCoord==1, or\n",
    "//          CoordSystem if EigenCoord==0.\n",
    "#include \"set_Nxx_dxx_invdx_params__and__xx.h\"\n",
    "\n",
    "// Step P6: Include basic functions needed to impose curvilinear\n",
    "//          parity and boundary conditions.\n",
    "#include \"boundary_conditions/CurviBC_include_Cfunctions.h\"\n",
    "\n",
    "// Step P8: Include function for enforcing detgammabar constraint.\n",
    "#include \"enforce_detgammabar_constraint.h\"\n",
    "\n",
    "// Step P4: Declare initial data input struct:\n",
    "//          stores data from initial data solver,\n",
    "//          so they can be put on the numerical grid.\n",
    "typedef struct __ID_inputs {\n",
    "    REAL Rbar;\n",
    "    int Rbar_idx;\n",
    "    int interp_stencil_size;\n",
    "    int numlines_in_file;\n",
    "    REAL *r_Schw_arr,*rho_arr,*rho_baryon_arr,*P_arr,*M_arr,*expnu_arr,*exp4phi_arr,*rbar_arr;\n",
    "} ID_inputs;\n",
    "\n",
    "// Part P11: Declare all functions for setting up TOV initial data.\n",
    "/* Routines to interpolate the TOV solution and convert to ADM & T^{munu}: */\n",
    "#include \"../TOV/tov_interp.h\"\n",
    "#include \"ID_TOV_ADM_quantities.h\"\n",
    "#include \"ID_TOV_TUPMUNU_xx0xx1xx2.h\"\n",
    "\n",
    "/* Next perform the basis conversion and compute all needed BSSN quantities */\n",
    "#include \"ID_ADM_xx0xx1xx2_to_BSSN_xx0xx1xx2__ALL_BUT_LAMBDAs.h\"\n",
    "#include \"ID_BSSN__ALL_BUT_LAMBDAs.h\"\n",
    "#include \"ID_BSSN_lambdas.h\"\n",
    "\n",
    "// Step P10: Declare function necessary for setting up the initial data.\n",
    "// Step P10.a: Define BSSN_ID() for BrillLindquist initial data\n",
    "\n",
    "// Step P10.b: Set the generic driver function for setting up BSSN initial data\n",
    "void initial_data(const paramstruct *restrict params,const bc_struct *restrict bcstruct,\n",
    "                  const rfm_struct *restrict rfmstruct,\n",
    "                  REAL *restrict xx[3], REAL *restrict auxevol_gfs, REAL *restrict in_gfs) {\n",
    "#include \"set_Cparameters.h\"\n",
    "        // Step 1: Set up TOV initial data\n",
    "    // Step 1.a: Read TOV initial data from data file\n",
    "    // Open the data file:\n",
    "    char filename[100];\n",
    "    sprintf(filename,\"./outputTOVpolytrope.txt\");\n",
    "    FILE *in1Dpolytrope = fopen(filename, \"r\");\n",
    "    if (in1Dpolytrope == NULL) {\n",
    "        fprintf(stderr,\"ERROR: could not open file %s\\n\",filename);\n",
    "        exit(1);\n",
    "    }\n",
    "    // Count the number of lines in the data file:\n",
    "    int numlines_in_file = count_num_lines_in_file(in1Dpolytrope);\n",
    "    // Allocate space for all data arrays:\n",
    "    REAL *r_Schw_arr     = (REAL *)malloc(sizeof(REAL)*numlines_in_file);\n",
    "    REAL *rho_arr        = (REAL *)malloc(sizeof(REAL)*numlines_in_file);\n",
    "    REAL *rho_baryon_arr = (REAL *)malloc(sizeof(REAL)*numlines_in_file);\n",
    "    REAL *P_arr          = (REAL *)malloc(sizeof(REAL)*numlines_in_file);\n",
    "    REAL *M_arr          = (REAL *)malloc(sizeof(REAL)*numlines_in_file);\n",
    "    REAL *expnu_arr      = (REAL *)malloc(sizeof(REAL)*numlines_in_file);\n",
    "    REAL *exp4phi_arr    = (REAL *)malloc(sizeof(REAL)*numlines_in_file);\n",
    "    REAL *rbar_arr       = (REAL *)malloc(sizeof(REAL)*numlines_in_file);\n",
    "\n",
    "    // Read from the data file, filling in arrays\n",
    "    // read_datafile__set_arrays() may be found in TOV/tov_interp.h\n",
    "    if(read_datafile__set_arrays(in1Dpolytrope, r_Schw_arr,rho_arr,rho_baryon_arr,P_arr,M_arr,expnu_arr,exp4phi_arr,rbar_arr) == 1) {\n",
    "        fprintf(stderr,\"ERROR WHEN READING FILE %s!\\n\",filename);\n",
    "        exit(1);\n",
    "    }\n",
    "    fclose(in1Dpolytrope);\n",
    "    REAL Rbar = -100;\n",
    "    int Rbar_idx = -100;\n",
    "    for(int i=1;i<numlines_in_file;i++) {\n",
    "        if(rho_arr[i-1]>0 && rho_arr[i]==0) { Rbar = rbar_arr[i-1]; Rbar_idx = i-1; }\n",
    "    }\n",
    "    if(Rbar<0) {\n",
    "        fprintf(stderr,\"Error: could not find rbar=Rbar from data file.\\n\");\n",
    "        exit(1);\n",
    "    }\n",
    "\n",
    "    ID_inputs TOV_in;\n",
    "    TOV_in.Rbar = Rbar;\n",
    "    TOV_in.Rbar_idx = Rbar_idx;\n",
    "\n",
    "    const int interp_stencil_size = 12;\n",
    "    TOV_in.interp_stencil_size = interp_stencil_size;\n",
    "    TOV_in.numlines_in_file = numlines_in_file;\n",
    "\n",
    "    TOV_in.r_Schw_arr     = r_Schw_arr;\n",
    "    TOV_in.rho_arr        = rho_arr;\n",
    "    TOV_in.rho_baryon_arr = rho_baryon_arr;\n",
    "    TOV_in.P_arr          = P_arr;\n",
    "    TOV_in.M_arr          = M_arr;\n",
    "    TOV_in.expnu_arr      = expnu_arr;\n",
    "    TOV_in.exp4phi_arr    = exp4phi_arr;\n",
    "    TOV_in.rbar_arr       = rbar_arr;\n",
    "    /* END TOV INPUT ROUTINE */\n",
    "\n",
    "\n",
    "    // Step 1.b: Interpolate data from data file to set BSSN gridfunctions\n",
    "    ID_BSSN__ALL_BUT_LAMBDAs(params,xx,TOV_in, in_gfs);\n",
    "    apply_bcs_curvilinear(params, bcstruct, NUM_EVOL_GFS, evol_gf_parity, in_gfs);\n",
    "    enforce_detgammabar_constraint(rfmstruct, params,                   in_gfs);\n",
    "    ID_BSSN_lambdas(params, xx, in_gfs);\n",
    "    apply_bcs_curvilinear(params, bcstruct, NUM_EVOL_GFS, evol_gf_parity, in_gfs);\n",
    "    enforce_detgammabar_constraint(rfmstruct, params,                   in_gfs);\n",
    "\n",
    "    ID_TOV_TUPMUNU_xx0xx1xx2(params,xx,TOV_in,auxevol_gfs);\n",
    "\n",
    "    free(rbar_arr);\n",
    "    free(rho_arr);\n",
    "    free(rho_baryon_arr);\n",
    "    free(P_arr);\n",
    "    free(M_arr);\n",
    "    free(expnu_arr);\n",
    "}\n",
    "\n",
    "// Step P11: Declare function for evaluating Hamiltonian constraint (diagnostic)\n",
    "#include \"Hamiltonian_constraint.h\"\n",
    "\n",
    "// main() function:\n",
    "// Step 0: Read command-line input, set up grid structure, allocate memory for gridfunctions, set up coordinates\n",
    "// Step 1: Set up initial data to an exact solution\n",
    "// Step 2: Start the timer, for keeping track of how fast the simulation is progressing.\n",
    "// Step 3: Integrate the initial data forward in time using the chosen RK-like Method of\n",
    "//         Lines timestepping algorithm, and output periodic simulation diagnostics\n",
    "// Step 3.a: Output 2D data file periodically, for visualization\n",
    "// Step 3.b: Step forward one timestep (t -> t+dt) in time using\n",
    "//           chosen RK-like MoL timestepping algorithm\n",
    "// Step 3.c: If t=t_final, output conformal factor & Hamiltonian\n",
    "//           constraint violation to 2D data file\n",
    "// Step 3.d: Progress indicator printing to stderr\n",
    "// Step 4: Free all allocated memory\n",
    "int main(int argc, const char *argv[]) {\n",
    "    paramstruct params;\n",
    "#include \"set_Cparameters_default.h\"\n",
    "\n",
    "    // Step 0a: Read command-line input, error out if nonconformant\n",
    "    if((argc != 4) || atoi(argv[1]) < NGHOSTS || atoi(argv[2]) < NGHOSTS || atoi(argv[3]) < 2 /* FIXME; allow for axisymmetric sims */) {\n",
    "        fprintf(stderr,\"Error: Expected three command-line arguments: ./BrillLindquist_Playground Nx0 Nx1 Nx2,\\n\");\n",
    "        fprintf(stderr,\"where Nx[0,1,2] is the number of grid points in the 0, 1, and 2 directions.\\n\");\n",
    "        fprintf(stderr,\"Nx[] MUST BE larger than NGHOSTS (= %d)\\n\",NGHOSTS);\n",
    "        exit(1);\n",
    "    }\n",
    "    // Step 0b: Set up numerical grid structure, first in space...\n",
    "    const int Nxx[3] = { atoi(argv[1]), atoi(argv[2]), atoi(argv[3]) };\n",
    "    if(Nxx[0]%2 != 0 || Nxx[1]%2 != 0 || Nxx[2]%2 != 0) {\n",
    "        fprintf(stderr,\"Error: Cannot guarantee a proper cell-centered grid if number of grid cells not set to even number.\\n\");\n",
    "        fprintf(stderr,\"       For example, in case of angular directions, proper symmetry zones will not exist.\\n\");\n",
    "        exit(1);\n",
    "    }\n",
    "\n",
    "    // Step 0c: Set free parameters, overwriting Cparameters defaults\n",
    "    //          by hand or with command-line input, as desired.\n",
    "#include \"free_parameters.h\"\n",
    "\n",
    "   // Step 0d: Uniform coordinate grids are stored to *xx[3]\n",
    "    REAL *xx[3];\n",
    "    // Step 0d.i: Set bcstruct\n",
    "    bc_struct bcstruct;\n",
    "    {\n",
    "        int EigenCoord = 1;\n",
    "        // Step 0d.ii: Call set_Nxx_dxx_invdx_params__and__xx(), which sets\n",
    "        //             params Nxx,Nxx_plus_2NGHOSTS,dxx,invdx, and xx[] for the\n",
    "        //             chosen Eigen-CoordSystem.\n",
    "        set_Nxx_dxx_invdx_params__and__xx(EigenCoord, Nxx, &params, xx);\n",
    "        // Step 0d.iii: Set Nxx_plus_2NGHOSTS_tot\n",
    "#include \"set_Cparameters-nopointer.h\"\n",
    "        const int Nxx_plus_2NGHOSTS_tot = Nxx_plus_2NGHOSTS0*Nxx_plus_2NGHOSTS1*Nxx_plus_2NGHOSTS2;\n",
    "        // Step 0e: Find ghostzone mappings; set up bcstruct\n",
    "#include \"boundary_conditions/driver_bcstruct.h\"\n",
    "        // Step 0e.i: Free allocated space for xx[][] array\n",
    "        for(int i=0;i<3;i++) free(xx[i]);\n",
    "    }\n",
    "\n",
    "    // Step 0f: Call set_Nxx_dxx_invdx_params__and__xx(), which sets\n",
    "    //          params Nxx,Nxx_plus_2NGHOSTS,dxx,invdx, and xx[] for the\n",
    "    //          chosen (non-Eigen) CoordSystem.\n",
    "    int EigenCoord = 0;\n",
    "    set_Nxx_dxx_invdx_params__and__xx(EigenCoord, Nxx, &params, xx);\n",
    "\n",
    "    // Step 0g: Set all C parameters \"blah\" for params.blah, including\n",
    "    //          Nxx_plus_2NGHOSTS0 = params.Nxx_plus_2NGHOSTS0, etc.\n",
    "#include \"set_Cparameters-nopointer.h\"\n",
    "    const int Nxx_plus_2NGHOSTS_tot = Nxx_plus_2NGHOSTS0*Nxx_plus_2NGHOSTS1*Nxx_plus_2NGHOSTS2;\n",
    "\n",
    "    // Step 0j: Error out if the number of auxiliary gridfunctions outnumber evolved gridfunctions.\n",
    "    //              This is a limitation of the RK method. You are always welcome to declare & allocate\n",
    "    //              additional gridfunctions by hand.\n",
    "    if(NUM_AUX_GFS > NUM_EVOL_GFS) {\n",
    "        fprintf(stderr,\"Error: NUM_AUX_GFS > NUM_EVOL_GFS. Either reduce the number of auxiliary gridfunctions,\\n\");\n",
    "        fprintf(stderr,\"       or allocate (malloc) by hand storage for *diagnostic_output_gfs. \\n\");\n",
    "        exit(1);\n",
    "    }\n",
    "\n",
    "    // Step 0k: Allocate memory for gridfunctions\n",
    "#include \"MoLtimestepping/RK_Allocate_Memory.h\"\n",
    "    REAL *restrict auxevol_gfs = (REAL *)malloc(sizeof(REAL) * NUM_AUXEVOL_GFS * Nxx_plus_2NGHOSTS_tot);\n",
    "\n",
    "    // Step 0l: Set up precomputed reference metric arrays\n",
    "    // Step 0l.i: Allocate space for precomputed reference metric arrays.\n",
    "#include \"rfm_files/rfm_struct__malloc.h\"\n",
    "\n",
    "    // Step 0l.ii: Define precomputed reference metric arrays.\n",
    "    {\n",
    "    #include \"set_Cparameters-nopointer.h\"\n",
    "    #include \"rfm_files/rfm_struct__define.h\"\n",
    "    }\n",
    "\n",
    "    // Step 1: Set up initial data to an exact solution\n",
    "    initial_data(&params,&bcstruct, &rfmstruct, xx, auxevol_gfs, y_n_gfs);\n",
    "\n",
    "    // Step 1b: Apply boundary conditions, as initial data\n",
    "    //          are sometimes ill-defined in ghost zones.\n",
    "    //          E.g., spherical initial data might not be\n",
    "    //          properly defined at points where r=-1.\n",
    "    apply_bcs_curvilinear(&params, &bcstruct, NUM_EVOL_GFS,evol_gf_parity, y_n_gfs);\n",
    "    enforce_detgammabar_constraint(&rfmstruct, &params, y_n_gfs);\n",
    "\n",
    "    // Evaluate Hamiltonian constraint violation\n",
    "    Hamiltonian_constraint(&rfmstruct, &params, y_n_gfs,auxevol_gfs, diagnostic_output_gfs);\n",
    "    char filename[100];\n",
    "    sprintf(filename,\"out%d.txt\",Nxx[0]);\n",
    "    FILE *out2D = fopen(filename, \"w\");\n",
    "    LOOP_REGION(NGHOSTS,Nxx_plus_2NGHOSTS0-NGHOSTS,\n",
    "                NGHOSTS,Nxx_plus_2NGHOSTS1-NGHOSTS,\n",
    "                NGHOSTS,Nxx_plus_2NGHOSTS2-NGHOSTS) {\n",
    "        REAL xx0 = xx[0][i0];\n",
    "        REAL xx1 = xx[1][i1];\n",
    "        REAL xx2 = xx[2][i2];\n",
    "        REAL xCart[3];\n",
    "        xxCart(&params,xx,i0,i1,i2,xCart);\n",
    "        int idx = IDX3S(i0,i1,i2);\n",
    "        fprintf(out2D,\"%e %e %e %e\\n\",xCart[1]/TOV_Mass,xCart[2]/TOV_Mass, y_n_gfs[IDX4ptS(CFGF,idx)],\n",
    "                log10(fabs(diagnostic_output_gfs[IDX4ptS(HGF,idx)])));\n",
    "    }\n",
    "    fclose(out2D);\n",
    "\n",
    "    // Step 4: Free all allocated memory\n",
    "#include \"rfm_files/rfm_struct__freemem.h\"\n",
    "#include \"boundary_conditions/bcstruct_freemem.h\"\n",
    "#include \"MoLtimestepping/RK_Free_Memory.h\"\n",
    "    free(auxevol_gfs);\n",
    "    for(int i=0;i<3;i++) free(xx[i]);\n",
    "\n",
    "    return 0;\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Compiling executable...\n",
      "(EXEC): Executing `gcc -Ofast -fopenmp -march=native -funroll-loops TOVID_Ccodes/TOV_Playground.c -o TOV_Playground -lm`...\n",
      "(BENCH): Finished executing in 1.6148104667663574 seconds.\n",
      "Finished compilation.\n",
      "(EXEC): Executing `taskset -c 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15 ./TOV_Playground 96 96 2`...\n",
      "(BENCH): Finished executing in 0.21198439598083496 seconds.\n"
     ]
    }
   ],
   "source": [
    "import cmdline_helper as cmd\n",
    "cmd.C_compile(os.path.join(Ccodesdir,\"TOV_Playground.c\"), \"TOV_Playground\")\n",
    "cmd.delete_existing_files(\"out96.txt\")\n",
    "cmd.Execute(\"TOV_Playground\", \"96 96 2\", \"out96.txt\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='plot'></a>\n",
    "\n",
    "# Step 6: Plotting the single-neutron-star initial data \\[Back to [top](#toc)\\]\n",
    "$$\\label{plot}$$\n",
    "\n",
    "Here we plot the conformal factor of these initial data on a 2D grid, such that darker colors imply stronger gravitational fields. Hence, we see the single neutron star centered at the origin: $x/M=y/M=z/M=0$, where $M$ is an arbitrary mass scale (conventionally the [ADM mass](https://en.wikipedia.org/w/index.php?title=ADM_formalism&oldid=846335453) is chosen), and our formulation of Einstein's equations adopt $G=c=1$ [geometrized units](https://en.wikipedia.org/w/index.php?title=Geometrized_unit_system&oldid=861682626)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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SWBZtZkyzzSjXwLJmezUDbAFlk1WqrAKl77DOafvlN3V7XGBr2rm3DAFMI1ZY4Mznr74AzXRelgXm62rPWWgAmQccaHmsEQENY033e8BX68vrnUAzrXdYYJcMmu3zboNmWKcZNOf7eRyOMe8T9kqg2TdQbRdFuajbVPKzImcSMK30wHKsbvgaWHomRolZF/oSw9JKgGwxS18Bm2WUxfoWKMb1M1W8AtgAuHUbs71io3P1f5k5+gUGuyZbAbZWZddk1CGfV2vfYDppn9eABwmMEwJrHEnsr9XW9K+uXT3AgGYh4ueAC0C53mXWKk32GMapGTQtcyyP1wdNCM++ZZrhHGURNPcl5wzzlIhHF8HSV+FSa2A57z/tV4JlC0Ass2wxx8X1LINoGGuDjTbAssUkW229ykxtn+/TtoNukS37uhpUNopf2TddgwscFur7yKS223bAjHmOuMKWmdhhre4Htd5CE3m/4n5FZtlaT8PGWd9rC5pJPa/Pvsc0l0B2CTT3IUETvLLCFs8sYCZZY5ZW1pjlzIbZAMtafe05dKbtLq/vMcowpr4jp+vEqRhluY9V/2UOsAssYiu77IHimvMotfEdhrnKPNVNwNmRAALT8oDnPfFxnzmBhELVH0Tn59ZgjQ4f/8ysWr7AOKU8tlXTp+V639TrHDSzGHa6xDRrGdEmaO5T/B5U+9MkZxIwkzF5H8zSgmXLAx629cGyZpY9z/eSx/so6nftsa7V7gSSPVDrgt0OzPK4XnPf2f/C2n7x2yELtr3KJBOBzInHI6XzSClUYV8tT236arpXl51AM4hK+7ZU+6SmN5hm6FeaoFkfwBGf5Q5oJlTNjp/0njSYJrIfmFOWCcxZlDMJmFaOwyzr7VZ6avgWdXvNVtlav8Yoa093i03WgD7rY4vZYAEs/ewP5dI4g1zn3iaW2mSaOuT1JQC56AE35yKu8LSXx07e9+p6Vowze9Ej+NVAntX3rg2zrbYvOYSsFDZLjsc09ynnDPOUiI2zvFTMcskL3gsVsgyyFUMJ8J6KadWM0ton31PZHq263QLIGrx77HGNLY7qLlkcZn2cCzLO7IdJvA6gwyxWM4ThDJFRTs9GsH+W1zCBomWe6T5dFUOP3qNlWFLNOEcduMqEBqXRDJZxLrLUOdMsjgWz0KM0ntFuWFHPtzDNo9iWW6LAxSvMhnn540WOKFu8b0dhltO23UKGWstWegHnaZ1Xlz8pwDx95m0lf5LaPffMz8ExMcj6c1GH5nq7vWaXl1I8smmMrfXNa1DdS3vd7bUFpn6qe2Kve7b5mrZJWg67vG3DH1o91hFZvBet53vE2vrXZV+ebSVEpmz5bBERebiIvEpEXi0is7nMReSDReTXReQPJcwvf53Z9iUi8ifx8yVm/ceKyB/FPn9AZNmIeyYZ5lKM2FpQeotZbglG7z/MJbNcs1W2XqAeo2yFA9XsyzeYX99J5IqXzS731OuWw+hSy8Uc/O2bgeswmQtCtkzF4mppME+ItlNza5JNMPyeYiqHFA9qA7wNewzB6iG4PbQl2zbtfck2zxbTtJLOp8M0p3ZmMK0wpQWmWcs+4jDR6X07rojIQJhO5qGEyl0vFZEbVPWVptn3AM9W1Z8Qkc8A/jXwOBG5M2F6nY8Lo+Jlcd+/IkxB85WEaaBfQKgM1a3ufiYBM0nvn2ktKN3+f/biK+3vXW2Y5RgnZlkwzMoG2fN4t4LKa1ZSH29u/4x9NeypizbLzKQuH7ssRBxoGzTTeTgZy3MydsMimL1ha0y2xCSutnUSbJljAjgbRC+ld9wZm6YT37Vt2uNusWGuhR4lNb1ls1yzadYZQccVZRuj3SgPBF6tqq8FEJHnEqq7W8C8H2GWAQgT7qXC2A8jzIB6S9z3V4GHi8iNhFqjL47rn02YfvvKBMwkW9Ide8xyCnS2KlqbWW7xgnezdwyotlIXW4yyxe62MMyWB72lxi3ZJa1aulUu6rBz7KYTv5orbsd0iMPJPBfbSgmM4fwcOrsGFyhf6MAwS7tky1vuRFcZZ5F6qQcV04xtGErvesE08xnM0xg7Qe552xGYZi8j6HjSjlvuyDUicpNZvl5VrzfL11LOqvlGwpTLVv4n8A+B7wc+H7i9iLx/Z99r4+eNjfVdObOAaQtpbE13bDHL0FcDTJo2zDZYhr7bHu86PrLl/bZguebprte1AHo+hranPh2rzWJ3V8V9B5gXRR3jrnOQddIjnWg8l8a4G17tUctg9DbDLPtqedgzSDVSLy3TDG3KviA8I3X65DQmB/gu07Rjz22OyDRbGUHHkeD02fw83KyqH3fMQ/5T4AdF5PHAbxFmX91rbuaZBUxYB8tWUHoKRj8Ks2zaME2bcHw3A8maWdZZORYs1/LNEyO0IUC+OPb8Ab3ohwbYtxmkBe01tuhp5NcfgWFeHC2QaTd0Jh9DJDO9IntngYF6FS640SwPODQU0ogA5TQU2xhiqFJgmOX7Ngu7ScwygqZNvUzhShPTnDSImnE6yyJnNkxYYppu5i0nj6dVuGPJe75Ppqn1mI4nb6Kchvi6uG46nuqbCQwTEXlf4AtU9VYReRPwoGrfG+P+11Xriz5rOZOAqWwDS8zvloPnKMxy5rCpgG/JsZOOvwSWLa9uLUkNr1ljT71up0a22x767R7xi/74YUbz86UAtvY+Uc1WbZLJUeEC4yw10s1Cz1hcbjHMWVxhsmVKI/UyMs7ENOdpkYBG1pqAlLLdxCyPxjStep6ZJOsFO/YVDLRH+/dLgXuLyL0IoPYo4DG2QZzO+RYNUwo/mTADLMALge8SkfeLy58JPFlVbxGRt4vIJxCcPl8M/IelQZxJwLSylVmGNsdjlq0g9BazbHvU3aqtsp1aWbI9q3LPPN6zTCTLFqW53kpSqVs1M32j/5MKNfJV3drAGBtquASAb227yMBgVHcnyt/pwYyV5ramj/RnYtM30zFmhSmMA+g95nVKxT4KBlqM3RegOWOadbt4vkdhmlY9P2oa5VFknwxTVQ9F5IkE8BuAZ6rqK0Tk6cBNqnoDgUX+6zjP/G8RphkmAuO/IoAuwNOTAwj4WuBZwG0Jzp7F+c/PLGD2iv+eJLNshQyFvufMslccYw0sewzTMsIxA1vfQWTjNGvxKhx2GGaPNQZWemnCi+r7c6HzKic22kqxPGCsnDDhe1CPlzo1supffFbVU98pXXPOMH0BmhNolbZNO5YE2Nlm2mCa09govOuXgmnui19qw+5/rP5UX0AI/bHrnmp+/yzws519n8nEOO36m4D7bx3DqQBMEbkT8KOEgSvwZar6oqV99sEsIQHNnFmGbSWzXPOC233ScafxLjt20vF3ceIsscZWSFAa25Lt0ZtrVZ/H5aqLeREKppTEoRng5yxzyCp4sS2GJhUyW+fmaYw0+oIpO0fbKZcFaNbrgSGFQVVMsxhLWm/CowoHlWGapRni6ExzX3JqQtL2JKcCMAlhAL+sqv+PiFwFvM9S43Svt6Q79phlL93RMsuZut1QyXvMchdbpQXLEnAnJrmFUdZ2ydoeOWo7oH2JPe5i0zwxiWM7qPLGA2iE3xcq1pidL+KLuMJk97QB1RcqNpoYp01vTIzzoj8oA+Mzw/TYlMtc7NiCpu0/Hi+XkWt40XP/FjSxjqc502yp50tMs1ewYx8cU5FZ2u9Zl8sOmCJyR+DTgMcDqOp7gPcs7qS6qIbXsmsdyzlotcFkiVm2yq3VYFkfe8nzvYVR1myyBrolO+TcFCB5+1aWcFQ2sRRTaeUQh4vHmHnBY0jR3MPuGIyn2yMzu+fsD2GJcUY1vTiOBU2iZ9qo6TMbZlxvy8hZptmanyhVW0pTZ4R92pXcW+p5OIvqmtEv2MEecsA1jfsKkssOmIRJ7N8G/LiIfBTwMuAbVPVdtpGIPAF4AsC114Z//6Wg9J5scfC0mKVdTmIdPIntWYfBmq1yF0Y5Z4/z/hNI9uyQh1plFKnjsMssd8/wOdRh532cKAcbA9eLfVwJKodjm4UOaPtflGD/dGict2cCiEF9YdJMz9cImWnmFMz8Bwc25TIXOW7YMIsQJJnWFfsUbdMJ9JnmmiOoltEeuKGe78tLvsewolMhpwEwD4CPAZ6kqr8nIt8PfBvwL2yjGPV/PcADHnDhWPezl+64xCyLqkOFajy3WbZslZZZthgl0AXLtQDz1GeyTTbb5W1zx1BLfEd9X5KjZAeFse3KQuYpi9ALXA/cqRXbmVVUdSRUTQBj+0/9FpWMClW87dkeZCyZZt4+scUiyDzuk7OIkhNIyyB3yzRtOuWaI2iL7NNTrtpOmDjLchoA843AG1X19+LyzxIA81iyVqLtOMwy7ddilqn8Wi8I3X63UhjTuqMyyuS0qZlky5njVTj0HYa5gS0eeoce06g/EsJ6kkiDPdbikCZrTAHrBThqAMs6NGkQDfZZw8AuuBGnGrzoDcZZF5LIvLhKxcwplqkm54w1NoLdK6ZZ1PCsmKVlmmmeo3BufaZp+0/nfynkstu/9yyXHTBV9S0i8gYR+XBVfRXwYMqE+k2yxXbZY5ZWjsssw7Z1x07P+532b8VUTseewLLFKJtMsuHwWsro2cIWtQHCxxWn22yhbVZaPgWZLWbnUMk8J0YapGacNkSoDnpPtTO99VYzpVyG34lhViy0sm3WTHMazzamWeyzwDS32DL3KcHpc9khZq9yWs7mScBzoof8tcCXru3QCiEaDbPaB7NsTRS2lVn2amX6BRaZUhhrsJrWlYHlljlaRnloGScy68/GYc5DnELbJeZ4aP4YTkJS8PZBr2iwaDsFUl1ePpAy0ycxzwQWXocCJSzjdFmljvuID8HtBpAvYhw/NcOUKTbUWdXdjNOC5qiOq+QwM83wHPpLwjSR5XnPjyPnTp8TElX9A0KtuiNLCyyLbbPlSsVuMMvW73KfPrOcOXQ6zLLbdzU+q34X4NdSvxuqt90nqdvNXHK/XEDDqzB21Ph9ST4f13FaxO2qCpX6nmyNhwwheN1IZoS5rS2OkdglGey8aEjTVBfKxpl7koKOapupLeoxWtAqGOY82H3a5/hMcy243TLNtXnPjyutrLGzLKcCMHcVJbDL4zLLad++zdIW11jyhq+lNyawTNXDYZ5VczEC2YgrWGLYlqp7l2rwqDJjlLVdso6lrG2XSbVeci6pLm8/CUnHcaJIAzidKIejy+xRsvNEOHCeQ2MbrVXqsJIcphSWx5mH+mIKQWrEk6esoQsGmL0OOfvogowF02vW3qxDj4xNs2aaCVSXmObWNEryf1J73vN9xWFe7uLT+5YzCZiwDJbYbQvMspXu2HPwFMsNb/gWZpm83xMI1yxyys7pxVC21O8aDFuxlgXD9G7GbC+OywHGXvse+JOS0XimW69dvu/JUWTH5imdR9I2P9jLfOiHAJpmn2T79BVgh30dqGeUcnQ5wwitQMxPMZpxuQWaLaZpbZPh9NpMc5c0yh7T3G+mzzlgnhq5FMwSMPvMC2j04ivtvjWztEytZ6ucpy5KVyVPbNHaOev+k13Sbiv67oChmrY9u+a+VPSh4R0fVTJYOdGmscCZ7WYt4+gy83QSvN+2nR+DSp7tns6XbD2r5HPV0kUwQlzBPq3aH8rQuRloZinCk5hnBlVB772Qo30zzX2p58qcFJx1OZOAqREMt87uuMQsbbpjj1nW6Y5rYNkLRrfMMgFU7f0+1KHp5U6pizX7TAHmdRB6sjXW7LMFbkvsUTfYLA/H409jsSXbZ3C+qZorgHdowcimfQIYxOOgYZ3xcKdg90PvSlYagXJEwJdjvEiYyqEu8oEGB5ETxdlC1gvxmptAkykDqOkISv3tyDQty7ag2f5r2k2UfhnBsypnEjBPUpZCh7aCZS8YvWaWreIYCSwtMNbrauboTf81+ywYrK+PN+UM16BoWeXo2y9PYpz7MOyPKhCzdVqgGMTlbUWRCRVwQY2VahvelY4hATHXKTPPGEqU2LoTBUnl4zQCpFG1Iwhlppn7dzlIfZFp5vbbQLOZRsk8rOg0iWrfqXlW5RwwG7KLg6cOEeoFo1uATG16xTESo2ylLiZGWQeWtxhlHVh+6MsIPK/CYcd2Ofp1Zjl6t4+U46k/QKStmofjhe/Bec+STcMAACAASURBVAZXeZLjWA+GcXaOVrxoYRBVNQCsE1imsKQDF7OKTKiTE59LziWmmSQXNTZMs2CnjSB3D8X3kiMI2kzzdMr+43Qvt5x5wGw5evK2lj2xcwPXSrQtecOtDXTaL6n5bYfMmmMn/27ZMhvbLPtMolUba4+ctpfXIbNG30omLNuEGg37fiGmYPIe0wzg6Jttgp12kjo43VGBaGSctfjIHFsOtOwEig6huriHdQhBmGky71sxwxxOFJ06Pe+5dQRtLdhhC3P0lteC2o8jyjnDPBUSboQs2i4ToPXmDZ8Fqxeq9fGYZV1hqMcsa1tlKo6RmGUd/hPaDHm9BSuPzDzdNaMcvStYo1fwLTV9AQRVYRxP8iUQxog/w+DpTS8zepedOUmS6uzMPoPzhUpeA+AIMExMEyYW2kzBdBFUvElhLJw+nlyL003JFY4pHz0V7QiOGzky05wV7EhB7IuzUbYC6fOlz8v7gs19On1E5OGEUpAD8KOq+t3V9nsAPwHcKbb5NlV9gYg8Fvhm0/QBwMeo6h/EqXY/CHh33PaZqvrW3hjOJGDCfpjlluK/uzDL3r9pj1k2y6012aOb9VWnJbZiJGsPt68YZVpnXw5VaarZavrZP6tsi/eTzbLNNqVw9HiVYJ80ZyQq4EvbZ8E4pXR8QJmeaR2BiZlN9zAV2LDXI66Lf+T2eEN12awd8ihMM4zFURchbqVL7so09yHKXEM6qojIAPwQ8FBC/YmXisgNqmrTqJ8CPE9VnyEi9yNUZ7+nqj4HeE7s5yOBn4/JMkkeGyuvr8qZBMwQrnDyzLKX7rjFdlmnOaZgdMsse+XWLLOsbZWJWR5WYDv6xE6lUMWT2u19G3RrGce2XVJVUH/pwBLAjwEoxbUD11vs0zJPJ4qP2OGcx0noL7DQ4C23sZxJkt2xtncWjLNimkmGYt0wt2lGplnPYJnSKUuGOXcE1WmUwIkwzf0ErrfTi48oDwReraqvBRCR5wKfS1l3QoE7xN93BN7c6OfRwHOPOogzCZhWtjLL3uyOs/4Mswx99OMs19Ica294zSxbsZbl95xt2qycGrzSui1qt294vhO7bIGi+ksbtG7H5LrVIRTvpWnHnLWP3nKX791kJ/UqRXNP8Gy3CoGkfG3LHq0JYFSJxyiZZm3TtM9KnU5ZTEFxlDTKimn25j1fYpr7kXbh7o5cIyKW5V0fSzomuRZ4g1l+I/DxVR9PA35FRJ4E3A54SOM4X0gAWis/LiIj8HzgO1T7rswzDZhbmWVqC8dnljXDrKUAyBVmWac/HhqA7NkqU5vEKIvjxrZjxQRHlYJhagRR+1h4L0w52qVarwlcO4+Rmn2PLJFJtmQUIYQ7ltGBIoofw77O7BuYp0cNBVXnwU+ukQCy7TClwa4zBMzaNg8YOfRu1ibsuI1pDnjq+FNr01wKOVoq2LE4G+UGprkvx08wCW22Yd6sqseqJ0Fgj89S1X8nIp8I/KSI3D9Ou4uIfDzwN6r6v8w+j1XVN4nI7QmA+Tjg2b0DnGnATHIUZrmU7hj62BZnWbPKCbBLZmlDhvLvmZe8BMuerXKyR5bMM6nfs5jKChy1YpiqoB2vuHqZALMj+wFM6JIROzADjAnYg91ychCpgogUO3rvkCIoXRAZcaRrXA7FxXXegO7cthkZnG2TUx99Zprgp9TMyDSdKCOOaeagyWOefofBtEFziWmW9s/OvOcLTHOfskeb6JuAu5vl6+I6K18OPBxAVV8kIlcD1wDJifMo4GfsDqr6pvj9DhH5aYLqf+UB5lHVwxazXAtKX+orgVkqpFGr4TZzx3rBfQP0WsyyZatMoDsWrHFiljM1smKcvgLBGkAhgSCgbSdQaJTasBfAVB+dLx17pfro5BEKNhq4oiv2G3EV69QIopP4nB3kSrU+stGa/dW2Tcs0bZuDIkZT40sWmGbODPJTGmUq2BFOxnWD0ZcKdljmORib5VFAcF+mF9UyCuSY8lLg3iJyLwJQPgp4TNXm9YR6us8SkfsCVxOmv0FEHPCPgE9NjUXkALiTqt4sIheARwK/tjSIMwuYdfrjkftZAcu1G95Ld6zB0jLLww5gWrDMIUkVW0yOnbFS1ROzVOae7hajLF6KCHyFKj6usEYFxj15B4BML4UQEFIdejofmQGqiIZzNuucanHOzlEsi4RrKYZpJhmjvVMpqxmN0TaanD2pIlJdRu6QkMOegLJgmhY0qzRKANeZ32itYEdaPm4l9f16yefO0CP3pXooIk8EXkh4Qp6pqq8QkacDN6nqDcA3AT8iIt8YD/94Y4/8NOANyWkU5TbACyNYDgSw/JGlcZxJwLSWrDLMZwK6Qm02XvKjSqvq0FK64xZmWTh3Yl+JWbbapeMk9btmlPm7wyhzaBClXVJVoFa7fQcM98kqW5L6Tip6CwCcFHZDRVDVoJLHIXkDgSKpAs90/xPjVMjZTqmM3ODIanrNHlOQu0Ny7vlhtEkmZ1ASG+TuVdpMc0saZVUabhepqxjNVf22mr6PXHKq9/C4oqovIIQK2XVPNb9fCXxyZ98bgU+o1r0L+NhdxnAmARNs+mI/hCi1W7Jd7nQsA5Y5qH2jg2cpGN2CpWWWEyst2U8Cy9TGN9Trgi1GD/fMHqmgvSB0X4LStE9n/V4ljtExY5phDA0s9wH8ZPCTek90FLmoZdsjSDiAmOpCzqVAeJ+32aB3BXKRj4ppIhMc5z+5WeiRK0CzlUbZLdhxBNCsbZm5OAdmeS3U6BgSnD4n8Kd6GeXMAia0Q4pazBLmRTV2KdW2C7PsOngKxtgOP2oxyzp8yDp2JvW7Y49MbDT+zuwttfXzdZk1evPbisZg8K3vbt1u6/sjxOybxg42CNEy0AiUhbc9MmEPyBhDkKIKX8dxqoKKxljOySGUD2tGY5lm6Qiyw9S4PjDNKci97Qia2vaZ5i4l4ZxxILlUAd5WMTJ9WQfQ/jjhfjN9ToOcacCEuRq+xixTIO1RwPKiDpvTHXvMsldQIzl4amZZF8dIpdQSs1SVWapi8njrWMVqNhgmY7XcYZCiAm3zWlckstSEaQkrtBM+NNs/jW2gyOgJcTRMDHQGfPactABeEUWGoHB68dXOHtXgLDoch3bJuVTcwzDNVpB77C4AUcU0a0fQLI2yVbDjCKAZAPEwXoeDmJLJItMc9qg+7DPT57TImQXMzc6YilmGdX2wTO1azLI8fsUyEzPYkVlCspe1mWVdHMNHxpiY5SyV0TBKrZigztgkE0jmA1AWo1DbVpomxaJdtc5qd6leRavYRY95qgDeeLjt0LwGe2Y6di6IYdpoSUKVcA4qOvP+F0VFot2xVZykZpp1kLsF2vAMlEzTOoLW0ihzwQ4Dmmk2ytm8552ScC2mOXScS2nM+5LzSdBOSGKu6E3Am1T1kUttleQlX78Zx2GWNu1xV2aZ1veYpfWA95jlUkpjSmEMDh0TXsTELGee7hBYWF7IyrkjledbjC2zC5ZeNpu9eu+pOooYy9wepgD0ip0Gp40d7BxUa+8/0QEkUjqGAEY8zk3tReZMMxf3sExTJRT58BSB8Pl+V0zzAKb6mivB7RlIkcZslNW85xuY5oX25TfXIAD6PoIfVOHiCU+Yd6nl1AAm8A3AHzPlgm6SVqxkHbReFK/IKvucebaC04/KLOu2dR/TeOb20MQsW+XZpvTF+GInRpkbGWZZ2xrtcupXDeNrMc6KJc5EA1geM5ol+BsaIUNQqfRaoqGk2E0I4JnO0e5UUMmwbJnmdJzE1hP7lMw0bZtkA01MMzHDxDSRCeiKU8y2zmWm2SoNB6YUXIdp5qD3mAoZUiLT7JYxpZOQW16nQZ5E8LpuCMs7a3IqAFNErgM+G/hO4J+stU+z0dWOHjvlRC9XvCcprrNZWGOHQhqWWbYAs2aWaTkFoodlyfnfszjMilmGohjm2lhmWcdJGiePVA6fbC+s8Eq82cZ8W97/uIApkX2KzIqST1Kr3JJtmOoUKZaZvMM1XsYg98Q0k3gniGrMCHIzp5CIRkapeIXBaVDtmadTtlIu07OQ4jSdyuY0Sq9SzEZpmaZjew64zTUvprSAwpa5n7Ci/cZ1ngY5FYAJfB/wLcDtew1E5AnAEwDuereoXlsvOSV4tqSV/milxSxLG+huhTSWDN62gEZtt7Rl1+Z2tpJZzoplWGZZg0XcLl4KZ49oCX5WpBOPKfT3OYpkXEmA12rj05veGAwSGei0Sp1O4GAlssfENKf1of2caabNggwBvFIbT2gvlOmUiWnW0rJzrhXsSG1nBTqyI2gs+l8r0DEd12XQTFn2+/SSK/N37KzLZQdMEXkk8FZVfZmIPKjXLlYuuR7gwx9wdfc1TSr3e/IMjdtDiE5CWkHplllONs6SWWYwnRXNKJllZpS5kWGWtX0y2SO9zGyJMxbpIw5VoJvDFNPvfb8QiaFBID+VPVJivKV9q1XCfpWyHsdHyVhl+k5MsxANTNPh47FLpilSMk0X2ahWjLKVRpmC2/ctPjuFDqJNsx9qhHhGHbgqntM+veJzOVfJT0I+Gfi/ReQRhNzPO4jIT6nqF+3aUc0Kd423PAmx6nnyhic1Ozl4WswyhQzVDDKHDKX1deELbXymwWQHTYETjbbiO7ZLBbfXlMhaJBFGPNquuO7Kw+cMH9s22UTRuQde7beU+zhADYsUn1mmSConR5NpjvHeuahxuEHLEnHSqVJ3TOmVgluKzyzZ6o7xYjvI+Zw+exZVfTLwZIDIMP/pKliqDREqCwP35CjB6amgRj2Jma9iLGFSzaeYy6HLLLMt1DBLNcuJWaqCr2MsE4hGO6Va9ToBXFTJM6OMTDAxrpldsnbsaAMwdfKEr5KklimglhrgGpLyuIM9sqeKx2PNkNU4fXx0JkVfS8bJ1KUNSbRDF8oiJQn3RAqmCalSUmCayRFky7950SL33G4LM1dG55JPdskU3O7i/sIFog3Tjewa1L7EbEdzYQbx4d3awx9i8JKfT7N72UWpAtPN757sApY27RFK2+VSQY3UNtk4E1j20h0tONbB6OF7bgPKanhilh5yVk4R8yghuFuD+l3gTZX22LJHyihzEN1IRLrs1HbnWHDuTP0AsRhHxaKLwTK3e4qQ4gcEUBF0ADQ4h4IKbRxdEVDVdiRalG6zZeQSaAZcc7HCuy+YZi+N0hbs8CIVUIZOZ/Oeq2dM85OrzgEyXbAOaC6FE1lbZlLb96FAnAeun7DEBPkbt7ZvOXrq8m1JHd8itlybddq0mOUEivOCGnWJtnp7jqX0pRqe1fIIlqWqLXM1PMVVWkZZXFCZwMv01VTJ0zrDRDep6Gl71d8WU10RUL70XkkJrqHvRPc02jArkplV8tjMaVS5g7PHBs9n8PRx8LG4hyaSF22kAVdD7Kf3EmM2yaFHY1TXncyD26Es2JHqaSam2ZqNEkqmmSoa5bCknNa4/k8WinCUtswEqg5fgOY+7ZrnKvkpklk6ZAcst4QXeaRgmEshRCFwfQpGT+AI/RJtvaB0yyy9dxOztOFEWjl4NKrhhllO6rcBicgspWaUCdAMYCW7pIzl+rzPAmDKuA0g632sqIPFSmDVmJKdU4cAUnZOnkJVz/tHZVtLICVVLUqgqblZwTTFBbXea7IZ+/gHFzzpzmlmmtna0UijTEwzOYIS00yhRolp1vOep1CjgSnUKIxt24UfK8ZZg2a+XuJXg9u3inLuJT81sjXGsg4hannt1mZ9rKU3b7hdt8QsbVC6ZZYpIH0Ts0ztlFwMo2aYYgHVboiMEiZWaR0/rXcw1qyoQGg6zj4C16eDVb+12p4O78wYRpnYZsS+QouPQZfilBpINQJizjlPXhzLNDXFeU62UY1hR/neFUyzDG6HkmlOQeyRSabgd8M0t0wVMarLhTp6dkqvkucR2uKl32dJtnMv+SkQZQc1ewfb5S6yxCyXCmlYZjkmx45x8PgaLFvMUsl2SDHfzVAhbQCa7zPKmkkWyzXLs7bRYwJmnl5C5kwzb1uwe0psqLH4sKcCxsyiCrdO3qhRTQ+pl5NtcwvThAk0LdNsplE2Cna0ZqO8sEOlk6ROX/QH+GgH9Wj8jiCpwbm0hT16HPsIXE/vwZUkZxIwW2LV8bB8dNtlXt/Yvx2kXjFLyyDM+iWZbbfMsmaBvmSWrdJtmX1CETtJWtY5ODbBtcU498ksqz4L73mlWqswA/5Zu2jvFKXIgJLkCY9Ms6rIQUqhlKhm4yXktms8QApybzFNJWf26GyQLKZRWqZp2V8KZnfVY2HnAUpB6qlAxy62zEFs/GZ/WozjyrlKfoqkNwPkFttlSoFseccPvSscPcleaW2XJyprzFIjeywYJs1QIdFkYzTb/ASWLU94YQ6s7ZOJlQLSn430yCKQA/G1mqoiasZlY8o2aYyoZJAEyDMV5H2k3CHuk5nmEEEz7lMEuRumeVLiNdgvExN14rN98yIDg/qiJBzig+0d4QJ0YyuTLfM9GtM5a1um9vfdVfZtwxSRhwPfT4ib+FFV/e5q+z2AnwDuFNt8m6q+QETuSahT8arY9MWq+tVxn48FngXcllDN/Ruu2Gl2j1NF3UpyzsAUQhR+pyydOh3yeMdLtssk3fRH4wEvbYwls8y2Sgt0GJtjvS3vE/trbcuDobHvOlCsYcnSJcxA7KrCIrUtNtkwDQPN10Oq65oYZFqstolP9s/Yzkf1vDA5VEzT/j9VhNXrflIMfQ5zSh70wCRHgtd8Kgm3jWH25KRmjtwXYMZqZj8EPJQwJ/lLReSGOC1FkqcAz1PVZ4jI/QgAeM+47TWq+vcbXT8D+Erg92L7hwO/1BvHmQXMJZD0uDy3+KyQRoqx3Og5v+iHDJb2d0pn7M3ymApqTLZKKYr/tkq0zdIdj8AsJQw8M8sch+kNSGLU8g6jtIBqRbzi1t7LjXGYa4jiU4iPGVuOuTQOn6mB+dZk17RtDSsMGJMJVt6pZppVvwXTVLoFO+rScGm6C/VuVqijtmW6tKyCF42B6iEI/MLqxbd1LweQMX5HNiph+1VymCsZldfcMe4prGjPcZgPBF6dJjETkecCnwtYwFSmamd3BN681KGIfBBwB1V9cVx+NvB5XGmAqRudNLVnvP62tsvWvjnAnPL35PVu2y6th9zOF156xScm2U13TKCVwNKGDiVQbBTHmGyUEwNNANh16FAxT99mkq0YzVkbzyqoVlFNjU7isRpjUCdhe2KSCaQqG2Zoa85RmOIw7fEThsaMoByp0GKaDe95GGu/NJzXAIaFLVPLQh2119yrZAwf42+H5uewVQ3e2jJzObfZd3tfK6Pux+mTx7RNrhGRm8zy9bF+RJJrgTeY5TcCH1/18TTgV0TkScDtgIeYbfcSkZcDbweeoqq/Hft8Y9XntUuDPJOAmWRftssp3tJm6yz1scwsE9i2JiyrmWWed0eD7S5n8LSYpQFNqVhmEsssJwYatrmReTxmskf6EgzdqE3VXOw3076FaFSre++lxLRHq9JG5miXxZv1hfobHR2mTb5dBRKGcfrBjLHFNM0mSbp8Ypo0mGY6NXMcL+2CHYlpDpmBBqZp5z1vFupQ7QKbjxH12bnoIHizord8qy0zntM+5jJviSqzCf8W5GZV/bhjHvLRwLNU9d+JyCcCPyki9wf+HLiHqv5ltFn+vIh8xFEOcKYBM8kuEy2NVSiRTXts2S570mOWtRqewFJhVlAjM8uohpM+nopJdphl/m0G1mCWGQg7jDIAZwlwksZg29YplmlbDa4bpLJOxsD1yrQQT1mH0uYpkL3SACJhX5U45hoEE+v0RQch/tISIAn3InnBrUe9CG6PaZSZaQIpjTIV7ICyUMcYc84HN817Dn2m2ROvky1zTICrylR02GQAoVxYsWum8m/B+75/T/keVfI3AXc3y9fFdVa+nGCDRFVfJCJXA9eo6luBv4vrXyYirwHuE/e/bqXPQs4sYK4V3OjFXq7221DBbWHgZLvcKqqlap5nddQSPPMEZeHtoUh3nIHgBJbWKZGD0C2Qpu+GV3ymqlsMa7R1YwMtmfd7ZGmgccBAKcu5wRzoJK5Lk6M1us5MM7ePwJjaRxzMoJnqaWZwNaDpww4xyCinUQbQlWk8gPeBWYZiIsvqcJKkvRw4z6EfonrgslqOsE29zjYK6wn3RSX3uv2wp5pKe7ZhvhS4t4jciwBqjwIeU7V5PfBg4Fkicl9C9bO3ichdgFtUdRSRDwHuDbxWVW8RkbeLyCcQnD5fDPyHpUGcWcBcLBSMy2BZO3u22FSsc6cFlruEFaW0R6uK18yym+5YM8vk4NE2SGUgzSmRFMyyDhFKHu+stpt3z7XCiVqgqPFdPmaIkUSm1bo9s7BJpeRC0b6nLja2Q9HpK5eBS8cxYJhtojA5gyLA5X43plEmppnmCErnsAsOJbV7BppC/n2w8ijnCA/CXD7pO12vXs74PjN91uKPt/ejhyLyROCFhJChZ6rqK0Tk6cBNqnoD8E3Aj4jINxLuyONVVUXk04Cni8hFwmX4alW9JXb9tUxhRb/EgsMHzjBg1rJL3nhoX6rj1pFj+6zFFgS2TqDR2D+to2dnWWCW3VicWkVPdkbDHrPq3QLBxvpZOJFvqN06ge5G4tQXCZkptS0TgvqtNoK7sqEmwEr2zJp9FgHuiV0S1iemmauz16Ih5KjLNFdOXA2rrB1AI0Eld3Fbch4BJt2xrVL7HA/sJxJg1PItIUZjwTiPewPbss/iG6r6AkLoj133VPP7lYT6uvV+zwee3+nzJuD+W8dw5gEzVxDKMZnLLNAW17AzQGav94qaXzh3EC6OKUypbbvcSSXJqrPk78T86tkckxQqumGWljXaUCExavXkIKJIq7TMszhOY9/9Bq8HYFRX/jcEgJmOk23ACScgs1OHVv8rUoJ/1O4LJxHktMjisUnXRSLoSdghzR+UQXZjyUeFuQOIqUp7cvqkc3WiOG2zQJi84hcx6ZQRNC/GQbVsmOE599QFhi/sD9uAqAnsTyU/FXImAXPXkIdku1wKIwIK22VeVzBK40U39plWCJEmzyrk9dP4yTbM5I2dgWHnQcsaZWaBfWaZGaBhgnXaY2agM0ZpWKeW/afjL3nCN8VhNveLb7BVndP5WJJp1fSoTqd4y+LKeZ3UdKM+ZzYal7ODR3XOXmeDr5ilxkFUs1GmcUzznUebqQpeNTPNlJueLoknqPQZSLPNsizUMYUb9SVXVmd9ojQ7h/l+wormk/iddTmjgBlAMM013ssZb80EuSSrtsuFhyhVTK9DiELZNpmC02E+b/hogHNNsld7B2YZmWArzdEdpv5KoAhttRGrqcjhCrP0Cfj6om7pTddQ8PcAVCQz21x8Q6Wo5KMSWaifmKY9x4CI8RobZtllmvHcdIvdUSU4mgTq2ShTOWDVZMt0uDjTpFPJTBNgGNoq9KEO1MHsuJDWeOiHUMm9s28qWeh1iLbL5Rkmx2TSksNjW1iS7MuGeVrkTAIm0FS5k4rda7c8x3hpu+yp9D0Vw1sWEWUq/RW3QZtZmo+0+k92TSpmWTG/LrNU7bNI075kjyUzLfbpgaHdv+NRnzqSqThG45RFNfyROC32ydfKU6jkmq5PYpq5H7JHexPTzNe2SqMsKG3qO8Rp2kiFHtOcIiKmUKZk3yw1mpJZNgPUDdNMyyFYPfTTmss871fNMJna1nOY70OUc5X81MvWmSBt7GVikmtibZc5YN1vqVpIAMoes7QOnjqdsSrRVjDL+mOZpZKZYGnDnIZkmWXBKC14esUdlupnDwxtPOaabVN9VP2q+MtZn4bdetK1CeioQo6/TLbLxDTzcQYmkEWxBTXSd8E0zR+XJrDOyDnZMjXGYwZbZtnfbN7z2s3fEGsKsrZMl2I+FyQ8j0MOYB9lqmg0a5tDjA7ilBh9b/mxJf0BXUFy5gGzVWrNfvek8JB3nsh6vbVdFjM8GttlTzLT7DDLxJqCVzaB1gKzNDGUJUM14BptjJaB1jbMSZVXs2/JKGns0zrZRfZZt83HqOyBSZzMXrYQQ6l5HBmIEii5iWlmSQxS07YImlHdTjhq7bmQsLFimhEBi+kuvDlgh2kuSfKa51JtWnrNZ+0pzRF2fdgnTmWxcFivcf7zinEuzWF+VDmfouIUScs73m43Zfdc9MNqZlA9T88WBpoKA49qp5pItss6r6UjmelVLFITe5TKLkkZlD5ObTOztH2OlXpt2KiL7NQdaoFf4nXuHT8szyaArUbA3+2FkwR0ImXokFeiubK6RmL2DSmSYYqKOH7mXvKU8j31F9VzoQC7mEBjjhX2n6VRJqapjfE1xKuEbEgAwnzmwSPvwWT99PY91CHP52Pn/1nyrKXIjzTDpEObNS+9Cu/hIKZGwlJQ+66i506f/YuI3B14NnBXwiN6vap+/y59JABcAsKUCmlnguy1s+FDdcGNlhQzP8bq6RYsvcq2N0tlYpbeMMsEoJZZQmalhVoemWWdxZOYYzNwPbPTyEhrm6XFwASOFlQP/ZrGuXDOEWhF4cAaH4nTz1gQTScdd42VgpQyVrL4b8vxkkwxmkKwjfoSNLPz2zDNHH/p2kzTxln2zzEE5SfQdFHd9t4hzkdHU1ttz8+dTM+sr4PzG/s40VwCbksa1sh+Jz9Lcq6S718OgW9S1d8XkdsDLxORX63q3M1kpD+trvWOr4YSpThODROajQsqelLDR++y7XIt1nKaEhdIs0FG1TvZ04pUxxVJIJgKadRsMzBCuzwxTuuUKdXxiVnOvOVeM6NMQJoYZwbWI0XoV+cFiCa7ZrguLurLmXkepJZR4hw8iWmSbIlS2iRTqFK2VWaM05APbjEvXpeURrkWXCFKdE4ZwI3/dBqn4g2ZRAJD+zql5yqxzfw8ueRnb8tFdcHj7clzmXcD3c1FSdP5trzlIeV4fyh37iXfs6jqnxOqiaCq7xCRPyaUWOoCpjKfJqKWbjsMRQAAIABJREFUXebrqecY77bDhAxhnEBrBCMCpgXOme2yUaat3VmlhhdOn8kOWTh/Glk6aZ0bDau0jDO1GzWr3IUqrooc7pmRjAQAi1QwAbIeCCrCzI8h0ycxYQ8ROCVXPErjbTLNtN44bjTsvjpvem6c7AGpz+TtSYpF+u2mudJnp+4lAqwpCuwdrgOyU3GYaS7zJSaZp9HNVYr6mUBhXvXjA12uk3AFyWUHTCuxlPxHExLh621PAJ4A8P53u2q2bx1sviRbHD6pnS3jVosWx0zOIKOO6woGamKXZv5wb50+TMxzIwNdkmyKM+p7AtYpvrPBMEeNqrPO+2vpXLNk74ak/OzZvsGeWfQ7ggzM+0zqsoRz0GG6Vtmpc8z3NYcdpTCmBLY+/HEnANRoS1XXv0npcoUqRgFk03O79MTmfHIGDhj74UaV42epMEdy/IyEzKC1Ih5HlfOwohMSEXlfQr7nP1bVt9fbYzHR6wHu9ZHvm+9uygm/qAebqhLZVMhDHRaZamuO8aV+i7nFo+1SfWcflRhGJMY5Iwa4iKp3abs81nNt2GZillkVj8BYe7oTw8QrMk6IJQp0GKZ4byab6cggqGvBRMPZk1L4HGUaopMwhiEwuMQwQ9A4cR/ZxhRb56FM1Y/G6FwKnqU01NIBhKlc1LhR6oOTMtsXXUT3hfGFZ86Bx4Bm+7qHZzmA6kWGmCrZ7jdUMRpIM0te4DDYMTfYO3eRcxvmCYiIXCCA5XNU9ef22bedc3zJcQNz73hYN29fbqcMTm89IFYdTx/M95IYsLQOiSmovLRJ1m2yrbLVvsEss8c7Hz+wS0kpgzbkKJWNL8ar0Vyw/OIpDtFxzjIlTQ8xLeN1Snu0h0voOOoy04znm/wfWd3WSSuftfemTVxfxGr2T2z6jr/Vx1CkumlxmQVPOZd5zfrqoPYt3vIEuE7GOHXFfiY42yJKIBBXklx2wJSgm/wY8Meq+r277Ju83lu842upkR6ZzTXe9YrDbI7xrijoGBlSFai+BphFSJC1S/pyfV2irU53tEHpBbNMy14nW2bt8Y7MsmaUIYwox8qEdd7DuI2hZLY6uJJpupB6qRlINbhrvMLgymsmgXYG5udzikuTaarMgts9RPOlnZaCiclm0M5DQapixk1JBzf7qgrSmbcjpdXaucyHg8Nu94exbfKWd2MzVRjFZbK/xB7HWGsz+MH2xzKvMIJ5+QGTUI7pccAficgfxHX/LJZyaou5C4uMsRF43mzXZJHTS6yGbc5TL+dm/GzsNsxzYh5Rxdbp5c7bI+Op2yZJLNEuZwbUY5YVG83MMrOqMqyoxSJDOz8xz/TtK5bZYpxrojqxUYkmDIksVxJrj8quatF9XkcMx0pMUw3TrFijDW4vCnYkW6UanEzM1N5yo4Ln6B4lmwQ03ltNO6YOJYJm6t+kSKYubAGOtJyKcNgiHbN5f9K+jce7Z+9siU2V3AvSpffgCpLLDpiq+jt0LS2dfUjhD31mmebt2eIhX5trPKVCppkgl4JxU5ENbz3iHUnl22ZFgf1ku+zvy2RzrIPZK2Zpg9KDPZJss5wxy9pW6RXGCGCHfmKW4eKlk94dKKcLFg8k4GIQTZoF07ngOSYwTlHBooIODjmkzTTjH4K6FFKjm5mmiLTDifIfkOCH1B/TH1v0uGvHsx1MM8SpLUKJtaGj+OQ/5visHTjfrSJ30Q8hVEh1cU7xUR0XCUkYt+mwyBCPuTHdd4tcYRTzzBoY1iY6W5Ndq6bbmSB7klmlXS4aVL/VrDPf0trWYpp1u2r/VlB6Zp5jm1km9Xs6RgpUn77xGlTvtKwx9OgYH9sXo0/G4dmxC3tsHIOY86vPLZ+fL69b3s78WtZMvnXf7P7Ne9bc10xLklb1zD7medOV566W4z7/+664vuWzRUTk4SLyKhF5tYh8W2P7PUTkN0Tk5SLyhyLyiLj+oSLyMhH5o/j9GWafG2OffxA/H7A0hsvOMPct40rcpS22kcq59STFWfbEzteTpp/oNw5gGsqxrdgw1RQOroPTU4m2Df/czaD0yhuemKVEkMrglfoYA6NM3wEsSxaTgOs4IlqZNpK+6iTYNAeJljrDfiV4yWumWXjPFbDB7aqs5v7pZLYIB4rfphRcCKZvnLMSwqAkquXO6u1122n6knA+k+rdkjx5Wmf4XiXPXZ6KcfSKcEB4V06SMSlB49qHiMgA/BDwUMJ0uC8VkRuqBJenAM9T1WeIyP0I1dnvCdwMfI6qvjnOIvlCyul0Hxsrr6/KFQWYfkW1Dm2mepcwt3O22q5m8mRytPJvGdW5rMbNOgtf1jY584gbe2W9b23fLJiXr9hZCkaPLHKyZZa54xksE7OMbLK6CJudPV0ZXNVvyJRJaZMyEkqlmfc/eMMFRo+KyzbN7HRJ18lrTqNM6afp8lubpTl0vv5pFodsA4V5vnl9K6OdU1RQr92K7NPzMs1l3hOvkucK6raJfyl2krRuWFEqUsOyGn8s6T3nR5MHAq9W1dcCiMhzgc+lTHBR4A7x9x2BNwOo6stNm1cAtxWR26jq3+06iCsCMLfMCLkeUjQVCk7xlz3wC8xzhX36WMbNp8/S4CyTXLddJu/29JsJFA0bPZb9KKnAllkmW2UdMlQzzFabWpyj8Hq0ANdLk2mGzJmjv4g5vZQQriQ5xjI5bqZUSwuusz5MTqVC38AV21qi2QozAvJ0vCL9ykGH6kJ2j4/TWDhtOnzA2EIXLleaWXLfMZhwbMXDyrXAG8zyG4GPr9o8DfgVEXkScDvgIY1+vgD4/Qosf1xERkJo43eo9kd9Zm2YtSyBZgLLVCuz34cUsZhLkuYa70r6d03MZKG/5LEtGORCvznV0Zf7lWFGx3xSE1gmZul9sG9Wtstgb/RBTTcfPVz+1O1JIUnWLpqOlwDbjunI52Wuj86vHeYart8H81k8ZkTj9Bws9KuwyQxkn9We+GKOq3a7tbqxxxbd+IFrROQm83nCEY72aOBZqnod8AjgJ0Ukn5yIfATwb4CvMvs8VlU/EvjU+Hnc0gHONMNMILhlfvIl2VpAOGisy2q3QgxS77RRmM0xvsYorU1tA1ZkNd4bW6XxjNfpjqKT7bKwWVpArEHSStye/5i9wsLkXQCa8saJtkjvyUHoYeVkY7CMdXBBPc8KqI/7x7JuKRa+uPyRCaYK7jG3u8cep0FCrnoWSW0XW9J9Rckpmz1vOfEZWUqjTA6RDSFBqYDwMPRjN1MK5DLTDG32Vd4Ntjt0gJtV9eMWtr8JuLtZvi6us/LlwMMBVPVFInI1cA3wVhG5DvivwBer6mvSDqr6pvj9DhH5aYLq/+zeIM40YMKyt88z5Yz3JFUn2uKFTE6gccGQran+5dJzXqvfK4C5iXnmAUwMqa5AJIemkEYGSJ9jGFPIUK2GZ1ZpmJ5VuTWv38H5o2O2NaoER01xVVMwe1ovxinkJgeQ4CKYafyXiEZHa+s9mK6dpDCing5byaS+L4AlTOCabJIxvrMJUBrCmZasCuEZc3Hen2VJtspRpTtXecox90jTpHpiavn+VPKXAvcWkXsRgPJRwGOqNq8HHgw8S0TuC1wNvE1E7gT8IvBtqvq7qbGIHAB3UtWbY7bhI4FfWxrEGQXM8FQsMcetFYq2yFpYR2YDKx7B7PDpdmSZZ9dZGttOjqDCfrnygIa5cgyzVKag9IYaXjBLC5YRGDWv91ObXcQBePCGLcLEOJNhMRwsArUrHUFxHEJkmo5csGOp6k7ChjTveU6BXPoDSyaWxDa14y2HeI+it7y1WRPTDM+QNG5eUqe3VkJPqZBr8Zi9FMkRF3LQ91CtiHR+exBVPRSRJxI83APwTFV9hYg8HbhJVW8Avgn4ERH5xnB0Hq+qGvf7MOCpIvLU2OVnAu8CXhjBciCA5Y8sjeNMAqbCYqqjR9ZTIVVWA9Zt23FNFc+Fghc6SlXTO21mKY9L7DOq6S6HCE1Msie5tmWV7jgLSu8xSx/U88woffXSjePugKkCw5AZpwK4YWKWa0wzplEGtVlmaZQi/Wkikp0yzXseHOzSV9PTH5RMy3mai7rvBBaq/XnLNTxbzrPoSR9VIFYsWhIf5yi/sOBhDOnEIU2yGwivaxPy7iJ70++J2X8vqNY91fx+JSFzsN7vO4Dv6HT7sbuM4UwC5qWUpSIckMjXApim+MukEjaexC4wavk72yETu+zskyura1qmDWRVCmTBIpeYpbVRNvpdcDKW553ZpGnvJPTto4u6xzRz+JBScDyTUpnFK2LmCJK4XwtIi2vrNVQ7WjoJc43rdtlGqhAoadqh0Y1K97olhrlLmuOpkTM23DU5B8wFOVS3WFF9Clhf+BctbFsd8SEVsms+0sQ8pzTHRbvnoXHwaLRd1vGV5YlMLHIcY/pkBEfDMmfMsmKU2gw5qlioyQUM+OFKVdQwzsA2G0xTFZyiw7QuxAc1AHDUjMFF2TiVwOqaNsZ4vYVYzi3Mkd4SiffO02eS4uMMlN3LnwLYQ8m3nmoeAtc5uVkeT0LOAfNcNosFtp4azvL2Xr89ppqD1ZMkQMvj0Nw2fFuw6gyixyxXWOu0Kh6zLgzck8jsmkzTIlximnFdnt8nYVPalpp4LbJ8cnGN6vBSdhuPRXa2zwPV4350bmP1HKjuU1E9xaKwx8D1UyFXFGD6WMZtMc88pUQuPLJpzvFFZuk3pEKm+cc7surcycyyAraltgvtbCpkabNkm+1xjVkahlmEGOUhagZMMWxQU+GNGB6E88Hem2ybw7qdmVGL0nCZTYo05z2fJoRbsTuntjGioWcaD5EGBJtmzzhYzIneUb/jVBWuY6fJ06KIcjC0mWZ6xi90ysnB5BS9ACeX6cO2/8ezJFcUYG6RtbmAIKpIKxwg2S77DVh+EXOKJMug2mGT9bFsGuSqpKc42gG7IFuDYlpXg2ulhmfP+UKfQYM25+39pK6nfSWqw6qlvbMGQK9hBsdYGo7EZNeygeL1z4xyQbrFNXJfhj0v5IOvPRdbZqH0yFIIZ5Ytz/qJy5685KdF3usA8zgyesfh6BYfxBSHufjM+wV7ZZRcZKO3PXnFfUiNXMrsScyyC2KGIWbPeM6wMbbL2W4ls9wlcB3vYvjPGOcmd+g4TkyzaKuk2bgxxYZzwY4UUd4CyHTuB66c9zz3Ea8hEosNqylePJd0T5YD2AkOpaUyb3GmSem0GVVgjKXdhktXJX3fctZ8VGtyDpg7ymrsZvaK97zmkxreDS8ybbYEtbPCLHO85eK4TaUiG05U2y6t5LqYZptpqx2AFmufTCCWGKZlmnlsDVvm6HPBjrXIsFxgpKc1aDp/mdp32qU4zGbRDsw9W4rht9rFgpz5CcQ2nONZk/cawAwTny3nkaeiG1eE6MRAl5yqslL8VzUCoGr2eKtV6e3yBrBM2yxo5plfq/5EjS0TH4O7e6AXKrdrtyJvYofatGmeRUlFOJZmiDz0A16E20g/bfLkZNmGfxblvQYwfZyjfL34xpVzg6ciEguq+JZaljnzJwFj6eAJ6wJYZqBcyyWPBSbEGaZp+7MViUTXy8SMkXkedBomBm295mdcNqXznnDNy1V5b2SYIvIOylO3ARaqqndo7niJJFUq2mel6MsimlTshTZ+Y5tFh1OcR2cJ02zQerG6sbzFZrkkhml2GSSE4yQPTa+dBxEfJ1brZPisDTfbIVnM0knzAJ11OdFCwmcoZHSLbGWYvw58IPBzwHNV9fUnN6SjyYmWqLpUkmyXnYcs2TbdQvhQUZWo6/0mFNtYqlnpPTr6RWSpwVItcK7Gk6R93Ew972KQejRWM6c5p3mMxUxziTfATjQ6gYYwL3wrBEhUYzA6K/UwF5w/Z0ROtJCwcmX8oxjZdLtV9fOAhwFvIyS3/6aIfK2I3Hkfg1ibq+NKkbVSbjvJKVN1lmyWR913a4pltdORx7F3UbIj6b1Viir/C5+zIpv/H1X1r1X1x4HPAv4T8HTg8ccdgJmr47OA+wGPjvNxXFmSvKtXgoqSCv4et0hxS1JaZp1SeQYlO9zOECDsXXTj54zIZqePiHwSoaLxpwK/A3y+qv72HsawZa6OK0LO0j/pmhyJ/b0XSi/86FzOpmx1+rwOuBV4LvAE4DCu/xgAVf39Y4xhy1wdxJL1TwC4891uc4zDncu5nMulkiuJJMB2hvk6wh/lw+LHigKfUe+wb1HV64HrAT74/rc/k7dhKWPurEmeRvZcFuUK83nsJsp7bWrkY1T1zSc0hi1zdZx9EXKx2ROsdXBpZBi6YUfHFifzGSXPqKgjeAnO/qkcXa6w/9StTp8fFZEXi8h3i8iD4lwY+5I8V4eIXEWYq+OGPfZ/akSd7u/lOWUvoWycI2eXfRdjMrudxX1OQ7iPxHv+Xiz79JKvRdOIyD1E5DdE5OUi8oci8giz7clxv1eJyMO29lnLJuBT1UfEGdgeBHw+8D0i8nrgl4FfPk5cZm+ujl37ceLPfuC6THF9LRaqcbsHnAqtWuDqCEUmRNA0V08tDhgExYViGy1xDhliTKO2KbGIhPH6MNugOMkZPKsRy5IyfWRadgupj7GNDK4bgwmEwhkLqY8qgh64fC17bfwQr2UvE9PF/U/ZH9euMojHxc+JyJ7+L0w0zUMJfo6XisgNcVqKJE8Bnqeqz4iRNi8A7hl/Pwr4COBuwK+JyH3iPmt9FrKZKarq34rIvYGnqepfxdnbPgv4QRH5QFV94Na+Gn3P5urYRZx4UIcXj1+Zy+dUSyq6s/SQpTlkll5Ut5LJIoI6h3SAMLVBJKYs2tUlTNegeSTZApYQxmJTJpttCFk+C23iPGEL4zHq9FqbMw6YAPucwWcm++t6SzSNAinr8I5AMiN+LiHh5u+APxWRV8f+2NBnIbuq1ncFXiIiLweeCTxDVX84qtKnWhKoOvHdrKBUwOCsmxiThNOUfqVzkThZWJUX3mpn53eor984RmB1ITccDNPsdFkxS2BijqmARl6/ApIQzmMJTEVQJ1cMyEF4Xtfm+HGstzkp2TEo/RoRucksXx8dvUm2RNM8DfgVEXkScDvgIWbfF1f7Xht/r0boWNlJh1XVpwD3AX6MELT+JyLynQRHzamWCzJysFCB2olyICMHV0RkOYEBDbLKlNbYmIgEUBMJQCahXqXIxPbyspO5qt3qs6GGN/sTF48p+bgLA4354x2JKvSVUqkI4EA8BzIuAuKBGy/vHEBetn3gZlX9OPO5fq3rhjwaeJaqXgc8AvhJEdmrnW7nzjRELL8lfg6BOwPPF5F/u8+BnVZZ/bdes2TLZBtbnGgy2c/W2jgioPSHpLIwdWwel2TbZ2ZrCUwNEBaSJyYz2yrQbH3ixolB9vrKY3MTy0xjimPUDewzXOslsE3nv2y3TNXKFm2bpk33nmzwdgjhWWtNiHaWZI9Ony3RNF8OPA9AVV8EXA1cs7DvzhE6OwGmiHyDiLwM+LfA7wIfqapfQ5jb9wt26essyuA8B4NnWHrQnYYq2os2xvWitzqsFHZIDHIgOigWbHYuODrotUlA5FyYidG5AEguMDxx7X1FBEkMcBiQYSiZ5tInMcthyCwy7z+7XhLGMAzF2PJYl1hyPPfe9dEIun6I13xY+fNx9OfsAWP/XEABARnCtBo9cXHOnjM3rW4t+0uN3BJN83rgwQAicl8CYL4ttnuUiNwm+l7uDbxkY5+F7GrDvDPwD1X1z+xKVfUi8sgd+7osEuZ3Xm4joqtzpoT3U+m+XYkd9vpJc89I/N3pJ7HMRQ6VWY0sTlUBxNkY49hFAnh7affvJEwuhnH2OEON07GcK2yg2RFk29g+Y5tyvZu1abZtAZ+TOJEak701AfeSxGu7xOST6Fo7MX+SSyC3ciwRXTXXOrYxz6U/9ksieyys0YumEZGnAzep6g3ANxGKA31jODqPjxrxK0TkeQRnziHwdarB47lrhM5OgKmq376w7Y936eskxInnQvx9sUMDHMoFN+JHYew8uQfO41Vw2p6/R0QZYptujQjRcAsWXNpZbfOdFhLZjICOsjxzZGI2CyitEezyrIoaZllENMxw2Zu3PIkbgid8GKbZHX2coGwYivzyfD4yzfXTLMtWs8rETrNHfKMSNIT2ehDYpj9w8ZosM8stTiAVWWX8Gu/VounDaZjnZwFFnNNFVdzFZ2+JeaZn3C1Qt0E8F2Q8uXCiJHvE7FY0jao+1fx+JfDJnX2/E/jOLX0uyXtNxfXLIpZN9GxeadOajbHqVxusMzEgFQOuTmLh3bSvECb6ItZ6NG2zl9k85QnkvM+ecDR6xVt/Fg16VADilmD02s5pbZf1serpejGglSu2V/3m9m2AmzHJtfsY13Wxodp/wZF/xcmV4kNNcg6YC3IQphMMTLLHNAeP9y5P2T1vRPDQprmtW+JCAVenndkkE9N0gkdzIeGe6AGBMRIihhyBGDqlrbJnQArbVCTMbDma0u0S1XaJGeSJaRqmI+pLAFNtOnGajLJYDuskOZ+ynTQ6epLtMq5b8vTrIPghqOc+2ieT7bevXk82ZB2WHWbqwA+6Eomgi6q4iAZm6fwqs7xiojjOqJwD5ook1ceJdkAz2Z20PU95tm1N7KfFDJvve8Vysg3Ra2ZHs90iw8TpVBVciN7p6mU0bFITIKZAdcve0roe00wy1t1vpEy12txiljZo3QbVt1hno//MGiV5uXuquv3Ist0S02ePqeY2K17xBdulfQbPnJzBIS/JmQRMIcRV9lIhHcoFGfFI35YpygU8F2HFHT09qH7FO+48jCL9h2Qggp003x11sU16cXSuIU8HDCzIIxm0HQHYpGOLDN7yqEqLC/ZHXGC/VDbNdNi4rcU0GVw5TUXFODeJtVXabJ8es0wgmtYdVN9Dsk1KSP9cix5wU5RB9oAvMc8UEraWOikESr8S6eBk2VsuogyRXa6JE88FWbZvDuJDMPsCkl2QnnV/R9mj0+e0yJkEzIQgAx7feSKHlTTJYOx2m/4BAxgtb5c0s+FCmpCKrgRfB4RUB6lCe79teimjLdJJnBJ36Uwik4zOqJDSqAiSGaYOEvLYXezcGzW7ZpoQvedx5kf87pG9FiwLT3mHWaYQpwiOSPSQRzY4xZLKcuwlTHGXTgowXI5pnfabIhx65xbu+fKp6/T8NGRLNs+8/TK4DgvbpyD3fbm399PNaZEzCpiThKIbfY/4gAdx3SlJB4n/thv+Ul3+p3f0alZktuClP71MZia6Os9PeokdRPa4MkhJL3OcxCuN0xPu9hh/J1COqZGiYbyCC8C+gWmaQwbbpg03WssrN4HrOcvHzim+lVkOE3gmz3cKaFdnGSc58ylnQG2QlCnll5hnuggu2CszS+0y1cgql5ig28YqIcZsynJ8sJPwLvSY5cA60B5JzgHz9IiT8GJ6XJeMpTaHC9TnwI0c+vWiHQKLbCC1wWlkFo03RqITQBNQ6uJEWakYh5am0EXJDHVyhWP88UGS9hz7xkkATTwyGqY5xOtWM00MOEbGOanT2itwNF2GBIJJLKPMjSpmOcxBEueazHIGli6GBkUGv5RpNR0fUkrl9CfXb6sxISH8YS0jhThdxt/4nG1Rjd0GsBtYD4Lf0mYXETj3kp9WyRWLmtt0AleRrqoeHhYfbIFEm2WPmTrPuFRgIqlrKVDcdwCU5MyZFhYfMpnU7wSDaoEPMhj3bJmbJMYeWvU8M01LnVNutgU/XTE9wDxMKDFKIwWzrNTwo59XvH6ZiVfflZq+3I/5LB4zmmsSkC5ZZWCRWYooB3G7W7FXOvEZBHvtToxZwrkN87TKElhObeKd69xAFx9Er8FO53FdVhpU8wCuPdCcVPN0SOnbN4sXLqjHPUkvd3D2BM9qUr1VJarvGlf2z3dVkl0QjyRDKQRUbjkprI2iFaC+Jq06l3Xe+EE/fGgXsbbL5OgpHDluCjtarIc5GEa5dLoOSKmQbtnJMzjP4JbtlolRHrhlMIRtNtCTBs0rSa4IwEziJLDDpULCThQX9Vuv4eHr+QSdKKraDSkConou8T1eCC+CAIwpM6aVVhkXU5jRlF5IVg8zA/0/7Z17sDXZWdZ/b/c5kwCKCRliQpIKkzISlcjFGFAECQQcKSRoUdQXSgGxTIEElTIiGI2pAUrwlsISgRHCRSKDDgSmYGJIDPFKcCY4uXFzEiPJGMSI4VJIZs7u1z/Wele/a/VavXuf0/s754z9VJ3v2929evXqvXs/+1nvbZWXkHEGbn0EB0Yg1pDl4+IBU/hQdPr0HezCtNoLcKFL03Q7R60knLXRqTo8GGZ/dNve6ZNNw/05MipR7dx0XMb3IDl1RJZPxb3yTP04Z49vOzlfSQ6fuUmITbuT5WEP8e0p1Wb2yX5B26MXDjZshHm10aOzhYT76Mk9G3pOux2PDP2s6qQbONs1VGT89TZP6DDITAC7JqJSs1vOOAW0l+m4bFuW2YYCyQSNGKbRYoZYODObZHT6nIFKB2dDpnBNYZaOIE+YCvtz2PeN1dbyMVSUpdks0zmCCyuKZBkDzUPBjagWT3DpjQsUqlebXn3G/2e94wL0jizn4i9TwHoMWmeeNPemRMqYErmkrNtRCwdHbFPyK4J+ZkmKMEWfd+J0B1Rn70QZjBxhXm1K9DjH7cxs76fIMv6lwHUttinaFupRZHosnY8pzKhW4xQ+TTN7gZ2mY6XSHO9JXH8uuN07fSwU6iLwijIi1bcsQofScSPUqB6TGrTsnPT+Fo4e93/52ivKcWz560n4UdkHrXOdoky3XWcU+zG2vPLDQouWxWy2MBd2dDA2wrx8BF00xDjMOumdxvibYe8UfeBUhEG0qSTDL3Z8iIYOZhw+XacxOrQLNkXV5lKjYYEsGdWnfZMkOJxk16gihKmf0Wap0bwXsjklpkQGMhskKMCBkHopO9L1BoaoAgqlaRjMzDA6mRI77qI9zrZVacZbteC95UaMhSOpDEoVYnjVAAAgAElEQVRP2KcsY7k227bQIEuRHJyKTPs72uRvZBltl6ODyG/PMIQQazEr0g10e8q7WcD6SdcOBwKSqlwSf3kqu71xmB3DIu/8XuxzYF5DXEvC9J9msC/Wm5UPWSdajcf0+0cj+ZC+ORK95Tb99gqz1qfEKZti6s6N2YLTsYBxsnAhO8e39crS+NW2zdZpdk3tQAenMC3EKL4WDQRhAQBh4bKp0jRovBcLbrcblOj80WGUw+JDj5ZCikrpMYY0CzrPVKRXoDJVlmZ3dE6bmrL0XvLSXultyZPHJcWhOvHk2ifbpeRtw21opjKzbiFTkbZt+0yJWmC6HbNnvKVADw16zwawBjaFuR5E5O8Dfwp4GHgn8OdV9QNLz+8luKAHpJnxE355o9pUaXu+CcG/QyRGaBOsACf9DlXhEUBU2iFGAtIPgVhgfIDSPLd9f5nNzJ9rX+qBmObovOM6es1LpYkkP0/4fxf/76ZKM6FIo7RjiuQ2TUD7Hk66EGBv65ZX35OifmV57CS3ZZbpjuP7U1GWPjjdkWhIgdyvLEdP+fiX2TSXEInZLq2QtHnGG+dauUAR5bRvF+AwpLAictKcDEM0hRWd7sl46OOMbdXpODzqbJgXtTxdFK8DPlZV/yDwi8DXrX0BewB6WRKC4X65pf3LnR8nC2avCixh/MJ4O9fcl8+1yVPxxi+uutcTu1yxv9q+xxHFmFqoMv6l8CJxxzu3r+vyv753weNd/c8CzPu+cn7s2zJ14jXzcRTecK8svWe7y++9+l5Ko335fnfMf27lMfdZtMgyF9GanqXWc+r3jc/pPMGFqf34Hbjp0IV/1wSXqjBV9Sfc5puALzi0j14GdnScckZHx0CYc85l/pyy4xF6TtgBfbMC+4nsOKMPv+gDQNcOpUwhJCE0Z0dHpxqS0Wo2TIl2R+JUeABMCdrghVTOzSvS8/5q+/V/SqWZbAFnxbTaK1n3+6q2VVGR2nX74xKh/usisfhv1p+kQhrehpmUpRG52Sy9srzA1DKLzew1U/xj/KWLxew12DBbjpxUwg36qCS7fTGXkfAs5vJkRin28bgpytmwIjQVEDYVujqhXjMyXILLVpgeXwa8pnVQRF4kIveLyP2/8auPTI7nv74LfnUtA2LmE+3cA3hSyb6Qyi++xdN1Xe4Nrd8U4Qvmv3T2WkjZIfb6wp5onJKaU5r+z+yEsaZk+ktKTKZ/fYeezvz18a96rpgBb/wr0x2z8cWxe5ulv7+Lvl9eubrPY0KWnZFluy+BGNM/2jGXBJZ7spxrb1P0JSmO9h1ZOx3SQ2DNRdAQkdtF5BdE5EER+drK8VeIyAPx7xdF5ANx//Pc/gdE5LdF5PPjse8Rkf/mjn383BiOrjBF5PXAkyqHXqqqPxrbvJSw1sarWv3EZTfvBHjGsz9M963Nk0gzekSWVC7qrUTQTNm4vguVeczW2XchbnF2We9OsRxGS2Mkpi861/Oyb3j8soq6H2/rB4mFL0jOnaBWJZ0ggxGwU5p2y60pkjKGJUFMuZRRIV4wBjMhqkdTkRak7rcnCtPI2ytLGd/KkfBGL7mR3lhQOCfa9OO0hHAFUhk3e2zMhmk/mpFI52MsXRgRpGeraZ+MXvF+4dTcyrpZwPp8W0VWkoZrcbGI9MC3Ap9FWD/8PhG5Jy5LAYCqfrVr/1XAJ8T9Pwl8fNz/EcCDgJ/d/nVVvXvJOI5OmKr6/LnjIvKlwOcCn6na8hJM0TOwazh7epQBpbfpy56woh4JbeO0O+a2VMYaFWlUm4NKeD2TUx5CSIAYYiRKyASyUmzqvpytxcgczCM+9MWMdmCcVpvnJ3Jw9PVnweUZQQp5cHtGgJKeEo3HrBaxEZqcDRf+YqQgdHdZq5Q+jjmP98yC0p3yK2MoxwIc1i8ZcSZF6hw+SVUuGbc5d8w7bgSZ/meWOcxu2XcjAVqQ+hzJWu3L0y4853NEaGRpzp9W0LqF662G9cTrc4EHVfVdACJyF/ACwsJmNbwQ+DuV/V8AvEZVf+s8g7jUKbmI3A58DfB5570BGGv4zX3Q9sBYm33TmpMidGNuKhSm4LF9tFGlabnZqJYwimhUf0GxmBBNZcNKz61TQ/mfTNRSuT/fZ1NscQQjY3sZ//Dph/Z30oV4yDIlcclfLGpsS+GOzh6J1/Jt87HZmPP9+9+LkkQn76mUfeg43Q8PSZiCG0ku+FytULBNxy27x0hxXz1M/wzuTZGMx8zrPWd2MqxKkh7LnT63mskt/r2o6OkpwHvc9nvjvglE5OnAbcAbKodvAD9Q7PtGEXlrnNI/Zu52LjsO858AjwFeF6vbvElVv3zpyb0oFnTYM/AwJ9VftF6GoBi1C0G+qnxQ27duU3T/YA4qDDMxhqGgT1Cb0gXHzzAEtguOlYXT7TSN1qlTxKc3UihNa5pUY5CBaU0fpzR9d1aoY+jNCVSsTlmM2/ojU6thADJwcIpkqRoTunENntTW1uKxbUt3dKqxPMdCiOjGNuP0nfH/gjS9sydN24mfT1bGbf89erLsYsB6Ir9u8CK6em5pR18yBbcA9SQUGu07UW6Rs/Ca+ZqaB+MA+yTwflV9zkpXvgHcbUvpGkTkycCzCcvqGr4O+GXgFoLJ728Ad7Q6vmwv+e+5aB+lLTOkPHbp/xY6UXoNxYWDN3v61Nam5lZseJBQhd1smbZEROsxTuv+mD3REV/6vwPUCmWY7VNCLV5rLoFI7dZSIY74lxSQEqf4mgW4+x8UYVSwST6ps6Uq+LWBDCpk8ZDuSLqZ2SWBIQWmm6Op/qaRE2Y3qmAbh6naMkSo7GM8Nk2TzN4/T4TSVpaa7JTTPvy5+2IqfShREPBjKmRNGc7bNA9z+JSke5R1zNfr8iHgaW77qXFfDTeAr6zs/0Lg1aqavMaq+r748oMi8t3AS+YGcdkKc3Wk4Fs9CWwyU4RjEAkKtWNRAWHv5KEjBbUPMYB9FqJIrymUB1XU5t1AjDlHkHjMvqVTpaldXIHSEUpSkK6/MDiJfTAhkzK4XRXoJa1KKTFP3H+tZlerjAVDRINdcw4WDjSn0MrK6D7NMbNVOmWZFKWhVJamHmvK0gett5SlrT2ejmsiR9snfZj1dOnYgilxYbtcEjc83uJYbMNIs9lWhhhSFFTl0abiEStGKt0HPFNEbiMQ5Q3giybXE3kW8Hjgpyp9vJAi1ltEnqyq75Mwxf184O1zg7i2hNm54htdzN6uLUfhlWa5zo89jDvNf23DL23dsz6XXrlTSWmUQLJlioBqXDPHthtKU6VSD9NUpW9u+2TcZw6hxLVJ7Uiwixbcqx1ZGqUd0six6fwsf9vdX01Fxt+gugJ11zZlWz0W1Wc/vk7jNcXnidT9GJTT5DFgPbeHTpRltr9QlrZvMk5N91xVllE1js9BnhLp0x0Nrdce5h3329a+PMdPxUtFmV2LdruLYC3RqqpnIvJiwnS6B16pqu8QkTuA+1X1ntj0BnBX6UAWkY8mKNR/W3T9KhH5SMKn9wAwaxK8loQpRC+fnDFox65RgMO85cjAKbDTYJdshf6edjt2KpwNfQpEH7RLanLYtcsSjFWyO0R2DEMXCVTiPhhkQDXWdK8pzfTtnIEXpRJrawop2H2iNJ0HPilNg07TKMfLBNNA4oSoODUYjJMKbU255pbdgEIFZifm0+zQdlSa3vnjzynTHQ2TtEcZ24zK0ylLc7gtK2SFT4EslaU5AM3RY8HqvbNdhoLBbYI6kZ2LwwwhQaeR0E663fw6PmgWStSjsyXdgkIN7fY8hcswOnRWgareC9xb7HtZsf3yxrnvpuIkUtXPOGQM15QwD/sUAnGGX9vWsruQ2yfHYhwDXZRfVtm9k1C9BwkJMF5dmi3TlGLwv9h4Jf1bVZrZTTpbokO6c4lq8RClaUWE/WiMgMwWapeOfWRD8LdhHWtdaS4mHH9O8tLn103TZjfw6rZTi9mxQkGWbZvKsoWSpBrKMh12nnCJ22VKrQ8hKr3go2d8VJZWzWifBzylRS74znhluVYc5pqEeRVwLQnTI/wi+rklICFJsub0sQfoEfp4TscpcQ1zmJE+pF9585aHSuO5LROIFdeD0jzb9cuLZUWnjCnHtJCa2TJVJqoukItbQycemyjNpNjcFDfaLpPS1LEL2clk+tj5c+M/+5TmYlSUpcHWDU/XLhRgrholn5Jndkm7DqOyTApTJ9cd244rQWqvKcwr/AgddIuc9LukLEWUU7NZFrZLK+k2Gz4USfTUZQD5Yhttz/ho6wye9JW94+5+j+FHukxce8I0+BCjufqXY/sQOmSkCeaBzG2ZZbFgrzKBpDTNa95JULMlwSxGJEkVDaXXzGutxJCdSp8SvsBSeNSz4HTi/+6tEQ2kmalRO1YQV1r3vEAg3Vy5ngsizaVsJwuSVVRkIrdSnYojzFJZpjCiClmmvouVIOMP1Kgq5+97mj47Kktz9HiveB5rOe+8KYvFHJoTfkyyNFy0Ev9Vw7UlzFBxfcYDHlnjFNgh6f9O2wU0DN6WGVREWIb3pBs4Gzrm0idLhFi76IFmQFWCnlVh8FPkwU2fYzqjxvXCLdQnEEFY3iK19YTXOa+OI8lsdu+JYSD1a0rTH8oU5tDmxGAHvZjVq1SNk2PdTFunLJtta8rSSFDGtomMo4pMNlELXk/KUlOCgV/czPLDEaXvxyD1feFFJbpCaZq90r/e24dN4yf/z2fzrFaEY2Ub5lXAtSXMkMLVzS5gNk7TzSDX7Q3/6cQtkiaRRKqkuQx+3R81r34XlZ0tSmY2QyDVNY+MmJSjU5qpoO+Q85/GOM7QnkSmE6WZBsdIqMVxu3XfNgS1V27youoSI7rpZ+kDzBMqNs2U5li0rWXyNJWlJ8t+Gm+ZKcuSLEXTWuPSaWa3XLJeT4kaWZ6kMm37s30MNbLcV8Vofv3Vw7BNya8gQl55Nwlir7Y1G6b2UZqN0/JeY454jPKeW/cnZQCJhu+OmGMpGvzjMhZhMcXw2pSmxrgd6XKlaXZBbC3zGEc0UZrxmJHmdJrtyNWgFRKMU3QFRCIZxj9bkiI1jV1aG/9FUCmI1H4MZuAD0MM21e0sBMiOGblWp9cNcp1MzZXa9N2noTaVpdkupa4sUyUiI07G5XOtWHBtOj5XCzPdjgxOOY7hRH463jFvw/QwpXrU1MhHEa41YfYmn6ItZjCZRtuO6e1CE9KM4UPJltnsI6SrDYwhRwwkZ1Cnktb+KR1AFrsX+KSLNsAhj+206bkNdRC0j1PxmtKsDdKUZuy2WbAj/h7YshVWG9PWPS9hbeb4UAbo9qSCTgLMJ51UlKXdml83vKEo/XYiy0a6Y2pbpj1aiJFNv2Xcl03DuzFXfAwfIinL0tHTR/UoTkX2RejQXtJs2C49We5b6OxUdimUCIK63Cquz+NaEqbED3Yu9REs3MeC3Pvi/y4Rbs2maWEbflruX4cHekiOnVJpdqLJhWQOIAt6L9cyD8rNFJOOU2hTmp0G0uwKpTmEYynQPT6c1pV2udIU9xsgOk7VxZ2XbKJdVIHlAx/X/5nzZ9l9z8EcNPvaZGv7wKg2a/ZKrzSdzXaiLP1x65NwLCnaUlmm/YzKUlzNU6csU6A6U0fPWDe1rizL9XrK8CFTpjV0jvDK9Ecf3L4PvQytn+HDsRHm1UCPNu2RHQO3yFlQmRIVoMQgdNkxaDe7dvnYj2Zrl3tn0Ek3jMpyRmmeZUoz1KyoKk0J6/4MvuK6KU176IyvB0FRxm9rIEbZxaaeiFx6kN2uDIQAUtevh3ZOGQzk6W2dhGSAOfT7lUVNOU7a9DJRj3Zvacpehhd5x87E+dNQli50qKksi+D0YynLMkjd2yttdch96BuOnjKUqIbgG1iPLFcWrJeOa0uYED5cc+q0nD9LYCFGu6gQew020TGEyCRX9LRLPT1y8biL80XyKa4FpCelaXFC8WVSmhJIM1glNJtv19Io07GolJJ33Q65c9JU3va7JkTnzJyd8gJvD34lyOxjrSnKso1Xntn+UVnaW+qPjSFHDWXpjlVXfXTbpizXwBhqNNouIa+UfkgoUQtHmY6zTcmvFGzVyNwTHtKYH47752yZp4QHcrRlWlFg6FR5hJ4uFhYeJMZkDuwNcL8wJMRgJhYtC3WYTdOC273SNBSMpe7JlY5Qtq0ktYriTAHwvtlJaCO7htf8AvBB6CWGuJTGpK0/v1iDJ8FsmFj/OjknU5Y2La8py5vABJYCWYYTASlQ/by2yzADG4sOG1l2tMvAnRsrRFBcJVxrwvTwDqBBuzGQ/YBzxzTHuD963z3Cg6rFvrotc6eS2TJLiGiaqouMtsyggOL64FIpCWc2TbFcck+a1rmzcwoWmw+Et2VS7s1+eMgHm9pBRqQWktSa1h+MeG311yuOlbbHzCMu4z4fHpTamrI0Yiz7TwrUkWVLWUay9LbL1FXNUVZ4v1u2S4+WrdJ7s1N/B6hDH6juyfJY2BTmFYDEWLFW0Q2PYLMhKs8BW1ky1K4MD+ojQygFN5dnXuJEYnC8fSkrtky6QIAMkU6LtcwZulDyTYjFhgkh9yrR7tpQmun5HkkzpVFmyKfi7g1MdkjpoZZymXpwTqLse6VRqcX9F/1iePujjdGPoe4tpwhKH1Wllmo07dOKKq0oS/OGN5SlhRB1nf8bUgiRX2O8LN12IkPVdgmkSv+HICnM7qxquwT2rkvuEUrMrMB0/gf1UYJrSZiwv5CGb7eLqYwtu6OVfbO2+zDakuL6P7HfidKMT0ty8BB51GyUOnrNg2dVYkEOdUbEitI073kkyUSanebMEr/oSWnablNfqbnztNcUHnHgha1wcvwCmM30aY0pKsDk0Cn3+7ZRWSa7Z2obydKUZVKY4+tSWdp5mUfcecX7qGBzBVnxkBdecQBvr1wCX1W9Bev7kJTJtbA5fa4QepM39mwVtkzEgtL355dbKaxky0SCDZOdi8+0TKGOU4YQZjSQlOagwgljfCYDgUAbSnPQqdIcl7YYoKU0a2mURqzuixYWLQuvMqVZPsQKQyxubNk2E8VZ/60Jp3c5lyzxjpZOmTknUenxzkhddKpOcY4fQ7F+eD6WirIs0h0PUZbeK14qS/OQ+3hLH0JknnAjzlPXzlRismEeTKxhOu7LuHmPuXnX18RGmFcIXZr3jsrQ2zIz0lyA0paZYt9SgY6wwmSabyuZ0uxEU655h6Q0ypbS7FPmT640Q+qkTJVm5MMsTtNijYgKE2seValf7iJCC/mV+lUbXejPP+yZvbOCjFsXvN0TQtvTdkKGpaLs8jEkJ45tu2l7slX682UkyyzO0r+nkD6HcW3xXFmW8ZalsrSwIZ8rDrmytNe9a1fzip/HdrmPLNdMiwxT8kfXnPxaEqZQqsuRIGvL7gKpGnstvzx9w91rK8mWFj+LpHkSAo6S0gwPXvSkRycPwAk7zgjxmi2lqRKD3G3ZiyEoUyNRK9jh5de0YIeRn46kEslWEBiiAtMx9VE8ETOePtnhVZ+5y5eox9YU2sMcKnP9eAeOI7ja9H1yPZfemM43YjWytT4TSU6VZWZPFCukMRKmKchUgaiyVK5XlpYldoiy9DGUJVmWBYJbsZdz8GRpr/d8NItxUdt21ldYZfZbCPlp36mq31QcfwXwvLj5ocATVfVx8dgOeFs89kuq+nlx/23AXcATgDcDf05VH26N4UoQpoj8NeAfAB+pqu/ff0JQdrtodzTSnDNrjyFIC0kz7Qv1MncSnS1OaeZEGVf/i4HrZ0OXkaYPalfnPZfozk3kOHSxUAfJg57FaOpIZMGC6bguOmEsKD1XZhpCiVJVIdepQpZ7Xv22jLnu3a40EB4BEswEtbFMnEDiptW+jdktJ/bN2Lbov0x3FNtnxxNh5tNwnyPuVWMZnO7J0hfWADLiBDKyPOmGC5HlPhXqydKuvRpjrvSciEgPfCvwWYQldu8TkXtUNa1Lrqpf7dp/FfAJrov/q6ofX+n6m4FXqOpdIvLtwF8Avq01jiMGEy6DiDwN+Gzgly7aV6ou7T74HsuWsF9P/2udP2jHgK9xKFFReBuXL8KQrR7Y5WomTQHTWtbhCxzCX/wf7T8jkEg46S+Ry/inHejJaD/0bYZeGU4CEfljq/zFvofkufbH4phqY/X35MiSbub9SOSp+TQ8KkuJn1P1s4DsczNl2bvtSejQkZ6xJVk9fjoO0+/KMVC+vXN/C/Bc4EFVfVdUgHcBL5hp/0Km64/n4wtVtz8DuDvu+l7CQmhNXAWF+Qrga4AfXaMzs8HcYo6eqrIct5esMHmh8ciAWTV9yFFWqANioeKQVbQbJFOa5R2mgh0+jdJQWY0yHYokkZbGiJBoa8quFbuQIb+GQkh9hKhkVyYBYZK6mI2pjKGM51Cqzl7RRJiFwiyC0dOhRrpjNoSGslyS9ngslCtBdjJda7xluzwqVA8pIHyriNzvtu9U1Tvd9lOA97jt9wKfVOtIRJ4O3Aa8we1+bOz/DPgmVf0RwjT8A6p65vqcrPvjcamEKSIvAB5S1bdILV4wb/si4EUAv/ujwrB7NKVE1hxAJaz8WyvUyB5qCzHy/4fjmmyZtpa5OX16xursvlZhLZRJpF6ow2yapnAGlVgSzpGbAEwLdhgmQe4ecbdGhWSspNFphFJhKhdyVHSV5ifLVUITPsWx5TFPZdc84nnZlLyyXbb3IUPpkL1lMirNcpmOmrJsFdSoobRdwhikngpkkFchMnhV6KfjZf8ec4WGa46e1Wday7t7v6o+Z6Wr3gDuVlVvpXu6qj4kIs8A3iAibwN+7dCOj06YIvJ64EmVQy8F/iZhOr4X8dfmToBn/cHHaO/yyEf7I3gHUAgnWqYaaytMnsou/N/tEkGmtYBMLdInW6Y5dgbtOGHgLDJKTsrO4VAoTYGYHSTshKQ0jY2SaIz3mRXsIOt2qjQJ74d9NxLxDIF4k51vR85YnlkL6J6g90OQebFbbSbhRZrK04U+dCRx66fwlntlmdYNj5grpGEwZbmvoIb15zHaMUdP+amFDEXb5UmR9liGEPn/LczoEJLzKZCloyeMMUzp16pWtKLT5yHCMrmGp8Z9NdwAvtLvUNWH4v/vEpE3EuybPwQ8TkROosqc6xO4CYSpqs+v7ReRZxNks6nLpwI/IyLPVdVfXtq/FcjwxTeC8jTVOZZzI+4b6LK0R1u73PqiojTH65ksaytNCzsym1WpMk09eqVZS6M0xWKYLQ0XMbsapegomUTjj4qYOyde02wWaUeW7TOBxID6FQLXJymLdswrxWJ6XQ0PyhRlfbu2uuNcibbUJL6eS3eEKVmmNk5N7lOWU7U4VZbl/zCmT9bWGk9hRBVCXN1soLC3ovdy3Ac8M3q1HyKQ4heVjUTkWcDjgZ9y+x4P/JaqflBEbgU+Bfh7qqoi8pPAFxBsol/CHtPgpU3JVfVtwBNtW0TeDTxniZc86LpALWWud4n0YMQ1zFu2TFOrveyClCmUZocyiCxWmo8Q3twxqF0TqZzpuIiaScKujzGclTRKQ0deGm4YAnHu3BcjiMh83fP0npf55kmyOsItpuDaa5qq69AottHXbK3hnPI7OKki5Ade60Igy+vOjjlFCVFxFgTZ5bGUXll2xXrgfg0eX6LNo5bu2FKWtqTESbdbrCxbwek1ZXmaFdCYd/QsVaFhvZ/1worWmuGr6pmIvBh4LWFe8UpVfYeI3AHcr6r3xKY3gLs0X7Hv9wHfIRJVTbBhmnf9bwB3icg3AP8F+K65cVwFp8+5YGFFLZid0qc7joWDtUmaNaU5FvWYKk0rCbdEaZqSLfvwBTuqaZTZfedB7mCqcIRQKE3bLxX7oFdtGi6opSowFavatC/WYIu1pe7NOdNQkk10hZJ0+6cKklxUT7ZHZTmxT/o/TBEW95SpxNxmWVeVA0uV5XiOe10JIbJ+7f8WWfp2sNwzvqbSXHFKjqreC9xb7HtZsf3yynn/CXh2o893ETzwi3BlCFNVP/o8501smekDGrc784TDYqVZi8/0SpMhlJGDsSScKU0YOCEozWn6pE6nr857Xga3m9L0sCLE0iuDrWKZ3kdBNdrdIiMMMd4mlYKzthaT6R9qTbcwUZ4W5ymDLFIOIbe9aLqUcEvHTXasYqu0vgtFGTzfoZ1X9T743FAqSyv+m/oqlKWpRv/ao1SWZXB6WNhsarMEUttavOWoMEev+D5laW1LR09ebHh9z/m2zO4VQuYldwSX0iTjnLCmNOdCjeZI0/Yl21VyNY82zTCkwH4W1F4qTY8lBTsMttxFHxdZqxWztdTKlP88WMp5PiUX88Bn59sDLg37kxFv5dCaMGXYUpZ9/YsoJcnGPsyhk3Y7NZntg0iATI5PlKXMl2grleW4L6+k7m2W/rlqBaeHfsb+5uItIVeWfmreF33Cyl7yaMp5NOHaEuaYGukU1h6laccPrc6ergUZgQ6E4hi9ULVpmtKEbswKSkpTxipHhC/5XBplgltYDYYQxxn7U0jHvAVnCKfF2MTYLqpL6aKCVQpFSZ0UlVHdXXAt8iaM2GYIM7dLekdO3GWZOvF8iQHn6RQxT3ju2AmhQrkXPF22UJZZbjhTYvXKEsiWnWgpy7lMnkNRFgbepyzXTuIIH9+jizGvJWFK9nCOXvJaqNGgXZZ3vs9J1EKVNGeU5gk7PGnWlCZufwcpjbIs2OFtWjp0MVZT4xK+0Q4ap+mW76xFFHryvBMcND7n3ky62SnRnjmFZv+triCEqeNm0kYzj3rIgCIj164bMuVt0+3xnFFR2vQ7689Ir3AMeWXpc8PL415Z7puGL1GW50UZNpTUZoMs03uw1ge7/iz/UnEtCRPGqcOF1vJhWDYth+YKlX06XijNgjS9I8i852cFebcKdviwpHLdc4NN01UlOXwMqkrnLjUMkpMwwYM+CbZOhYun77GtGZSmXYd4g2owdRhVZTWPIdkgKabX0+mz2SjH7edDr/0AAB5jSURBVFxhAimN0abfaX+xbrihpiyN/Mo2NQfPPmU5h65CdK3p+EXQM11R4CLYFOYVgcUuHoqs/BsssmW2SDn1ha0oOZZ5CzJwqjQt5MiUpv+yWcGOVhpluvdU2Sh39gSbqaZ0y3SsUJwikitt1UL3joSkQ158OB1Pbx7oGsU4RJGGXdKPSSoedoGY9z3us+m2oeumXuwu2ipt+p3OlTwYPbWnvn542aYMHaqRpS/r5utazhHnQbninH/piZq3/1zYbJhXE2Xwut+2yegOV9moQoQ+bXKJA8hCjMoq7RYQ39k8t+IIMqVZEtv4oA6UawT5NgPTh3pH7hDynnXthuhNT3vitD1sBad/9Kyr5F75WHRC5x7+bubYUhRqLj8GVsQ38+eIjo6tquLM25YB6N6xU9oqfZpj2UeaalfahPOnyrKW7liqQU9wh1QhKtMfa4ualemPpaPnOLnuB+WSXwtca8LMpg5zDiDclLogzV52IftHO5BYBGOB19yC2gempNexW5xGmWHIS8NlSrNoA2SEa69Hh9Bo22ToEKeCQn/Fl7UP5w6DTMKYICjN1hIf+5ThRVF6uNN14zS7RrSlouxEk6I0pLV3umFCpmUwuvVRKktfos2wNN2xeq8Vr/hSZentlIfaLlO7tSXhNiW/WqiFFrWUpjk6vNIsC3XUCnTUSHOI/ZSFOgyD9uOXYkHBjjBeTUWIR2dQTlI+yD2jPCteLEaU5oEXiAWKc+UYT8sKe1ihj7pn2rijRqjHgPdw11djZGKX9KmJ3vNd2irN422vJ+FDTIPRS2Vp+zyWpjuW0+UyqPw8ytLOL5fL7QpyTG2PGVIEeD/powXXkjCDVnOe1Mz41laaPQOddoE4K0rThyDuVLhFzmKJuKnSPCU4nMpCHYaDCnZElEHuYWfu0W7ZNjtRuiHEffYxnW/nQpc0vt4NknpTFXbDtEpjTRSoCjgVejPg1WObML1nt2KPtHJtnigLEuwLhVnaKse2QxZG5IPRfX9LC2mkMVa84kuVJVCEJE0La8AyZTmaCtZMjdwU5pWAPXCmJpcqTY9SafrUxX02zQGrcMREYZaq1R7EVhqloQw98qtRjvddt20iFvhO0Z8ZKjXW2HQEHb8kQ6EyazE9Rjhh6YzzhWYdglQpaOaba2FBhtH2mO/rC1Kd2jLnbZU1lCFD4/5cWY5t62qwfH2osvQFgUtlmfo+QFkGol2R5B5dfHk9CVOID41ThMDRlGbNppkpTKc0ByR5zzvZZQU7YJpG2fv1oqPirCpN16Zm2xTN29qxzO5YqC8r7pG5g6ygcUV5pm4iU7fsnReBD/9pOYFMSdbanJbe8QWKspdCYTpbZRmHWUtzPC1smPsKadg14fw2S+s3jX8lZRnGs+KaPsOja05+LQnTYw2lGfoZVlOa4NSDjmsNtZRmGoMpTh1fTz2w0cNeuQd1/XWi84qTenGPMfg7j/PMmpjaLEvBrYDJwmMVWE3K1tgyBUldURr8EiJpX8VWOTlGXYF6m6W198eatssDlGWZ9tiqnn6pyhKIwSCPKlx7wjwG0kqQF1CaCealny3YEVBb9/yUXbRFBvukLajW6ejcGbRL9sysOnrpYadQpUB3cpb25w4g4aQfop2zrjfGH4B19IgRQktZ9l1uixzHGu2UxbjsdenpzhwiMnq7jSRtv7dhWngQ1GIti/6LoPSykMZ4v+dTlsdaf2ptCLoFrj/a4e2QnXs9VxKuWqjDsCCNcsSAX/c8FeuIwe6dwNkQFtSxvmwddOvf9gcCdI4xCG5unx3k2kIuBowcxjClGuJ97LpmyNFSdKKc9PNypHTo+HN7mapBO2evooxEdVJta9PfctpusZbF9N55w/3n7R07WR8LydLap+tcF/fzRpiXD0GTl3ynMhKQxBTFyjQdxmLD1TXNATT3SFs/Q7KDHljdyLCvYEe6sXLd84C0fK/ZN90zmHLPZUenwZQQHEo5eQ4qdEgonkvF/lkW+bChizqHz3G9431XJwGvKmsjqHq6HVnVqqPbsYmqLDzeFnRej7Ucyc2fs6+QRrrfFZTlxF5ZxF+G/eX2mP4Yrjfedx+3V8sl3wjz6qBFmoCbTo+2RKKdMm170rS2kTRrSnNKkuW2I02Dv35FaWaqaIj9JaXpDkWiDCmY47Gzoc8cE4MOUXWO78WZ9hlBhuNTpVlmHmXXV8nClDzKquRrYk49GsoURghkdTIJOi+cMxVF6Ykxy9CZ2DJHcqsV6LD+5gppHBKU7u9rHG+xHo93/CQSLbe16uix+129vNs1EcJLcW0J0/zfNdLMleUypVkGtZdK8+A0SopKSYzHMo+5wyCSBbln9+scQvk0exem6YaK06QrpuZW3MOgzjZaG5fdM0MX7/0mxWHal7qhPEtl6Kfr9el1xYGDP2eXe9SdrbLmfPMk5+GD0Gtkua+QRjg3v15JZLXg9EOUZbp+hSzXDBpb00suIrcD3wL0wHeq6jcVx18BPC9ufijwRFV9nIh8PPBtwIcTsoi/UVV/MJ7zPcAfZ1xB8ktV9YHWGK4lYYawItzU9LhKcxeJ75A0ynJRtrJyu61GmQW7s2NnZFlNm1QeGfriy9uBU0WDdtUnPlOY9BlBIopR7m7oJsU+DHZOy3u+NsppdokydTHtTw6bvOxaPUTIq7dp1XRz2Eyn5HlQ+thHfRpeEt6h6Y7Wd7jv4yjLLl2nFol7HuhqU3IR6YFvBT6LsH74fSJyj1ubB1X9atf+qwgrQwL8FvDFqvpfReSjgDeLyGtV9QPx+F9X1buXjONaEmYNF1GaMFWWfUGacM40SkNjNcoynXK8n3F/KOYRpvN+Sj7E6kj5050X9TB7poeVkSudPgCWRgl1m2UnI5kfS2nauEryMtTSH/154dxp2TWA3EY5TBSl7Qc/JR9JqDbWWqhQq1J66OfwdMdxjHVlmbU/p7JcHcqaNsznAg/GNXgQkbuAFwA/22j/QuDvAKjqL6Yhqf4PEfkV4COBDzTObeLaEmYHmYr003PbR9EmbOdKMzzcXVSNbaVpaCnNZhol7roWGM/CdMp0rzseoaeL546hRCEX3U/JjdAsjrRDo7PIkagKJ/HLfzZ02f2Nds+259uIYzdMi49cFC3V6GFhQJNzK3ZL32/p5T4tiMam5KUzCMYgcb9dBqNDTpbl6o7+2udZ5bFUlmmdHkfAfttet4LTbTv0PYa8rTp/WD4jv1VE7nfbd6rqnW77KcB73PZ7gU+qdSQiTwduA95QOfZc4BbgnW73N4rIy4B/A3ytqn6wNchLJ8wonb+SYFv4cVX9mvP043J63L79SrOVLrma0jSY/dI5kUqFOarQacB6r34d9WhNj4RNt0sEGTzwpbW9Sz8YXnGOgewV5bSACCfpmSugtfpiiVrKYukFB68aC5VXesxlaJJlOe2286qhQk5Z+nHmCnMdZVnDUmWZ3Uu1p3VwQBzm+1X1OStd9gZwt6pmv1Qi8mTgnwNfoprCU74O+GUCid5JWHb3jlbHl0qYIvI8gqz+uLjI+hP3nbMU6QE8stL0/VeVJuNxv+65V5pjm3pYkgW5e0fQgLCLDpgTIYUTmeLMvuCxv0e0yyrHm/KsKsmhKPpRQRk3OadKW/DB4cvPmXqmra8lStJQKkrroyTIJbZKv7+1bnjZ31y6Y3ZfR1CWNw3rTckfAp7mtp8a99VwgyDCEkTkw4EfB16qqm8ah6fviy8/KCLfDbxkbhCXrTC/grCo+gcBVPVXlpyUMjo4X9TCnNLsJKx3vlRp7k2jNBTrnnulObbJYznHVS41pVMaxsIctm9UnEPjS2G22xEVr7sdaSjPOSxRpbXrtApczJ9TU0rTdMW5kKSWorRrtLZrjp2x3VRZTsi2oSx9IY3xntrKci7N8bx2SXtiVzG0qMJuNS/5fcAzReQ2AlHeAL6obCQizwIeD/yU23cL8Grg+0rnjog8WVXfJyICfD7w9rlBXDZh/l7gU0XkG4HfBl6iqvfVGorIi4AXATzlKR09YQ5f2jIpyLBEenAbShOcsmoozXFQONU47su856ltbtsMdlABCdPpNN5YtANCmJEvUpw7Z6aK0wppnPS7pDgzDAWpyRji9IgPTYKxwAbtwsElylCopVgyBbd2fortYQUwauE/ZXEMryiBSUHfWjD6nKIsHTs+fKgWerSkkIZvW/OGh+vsV5YtzNku++oZ58RKClNVz0TkxcBrCUN8paq+Q0TuAO5X1Xti0xvAXZqvAviFwKcBTxCRL437LHzoVSLykYRv5gPAl8+N4+iEKSKvB55UOfTSeP2PAD4Z+MPAvxSRZxQ3C0A0AN8J8HEfd4v2cd0EI017xJbYMg1eafrCHGNK5FRp5v0O+IId4ZwijTLdABlpphhN2J8h5Gyb47EhV7DkZNFJiM+sFvcozhnLyrn95vyJqZhLsJT4zosyDCi7doMkasUxyhChUrEuCRXy/ZcVgMb9U1tlGEM73bFlm8yWm6h43O11TVkusV16suzDGh/VcRyMFTN9VPVe4N5i38uK7ZdXzvt+4PsbfX7GIWM4OmGq6vNbx0TkK4AfjgT5n0VkAG4F/tdcn/ZRlqQZyMs+fE2NLQwnn3rnSrMMOYKG0pyQGplHfJJG6QftSDN39pxUSbOTgUeGEzrZ8Yg6L3nw9FCmVZ7i4zElessdYTIGzueV3smLefgY0v4sC2O6DPgwn2y/I8mSGPtMjU7th0sVpWEspHGWX8eRpdkWy36nqnGa7tiqZ1lLd6ylSraUZR7HOQ1O76VClqw1JQe2NX1WxY8AzwN+UkR+L8FT9f4lJ6ZMnwppAinUCOIXzX1uu0x1uWNueu6VZjW4HXdOJM2q0jSU6ZQRSd3V0iqBwTzq/hFeqDjLfT4sqZx4mRNqGhhPdCpJlt9+M1EWvsiOdVMnCUzjMA3lUhF+X9quKEmfr+1RTsdrtkqvKMfr1abo03CiWlC6jWPfNLyMtxz7rE/DjSzX+1nU/Ef9UYDLJsxXAq8UkbcDDxPc/Yt+kvrIPjXS9NPzfUpz7G/qCGoX7BjRWo1yEuRc5KBnIUKtYHdGm+OpXS/aOB/RvmibK85eGLOGKOyfafnfHEMRGJ8jlJzL2q8cgzleaWqHrE3FSw93eU6pGmv7075syjxdL7wWHgTTIPRxf90LXp5bKstySn5ouqPfP/ZRT3tskWVZx+DcUNZ0+lwJXCphqurDwJ+9SB9rKM29jqDUVy3kp5i2N4ivtGGm4O+5YHdgSAphDFFJDh3N1aMPdg/vzQ6EOJ13CkN10tb6aNks+0q4S+koWgst1ViiZo9MfVQUZi1kp7b/VHaZM8ejrjADWd5STsmLYPSyn5qyrE7Jk5KcT3fMzrlUZemwVSu6fAjQiUSlpk3SPJrSjNi37nnWLoYJmUOoDFfKSNOhDNXZaU8nYRE2+1KUSm+yrZKlgXaiyd458YA7u+c+m2VbjZ4f3vbYQhkzmR+re9FLxwvgSGWYbLcU5ZT46gU4ao6dMi98bt3wEjdDWYZ9Qiey3txhI8yrgyWk2UyfvIjSNBSVidI5On5JBrqRPOUsBsZ39IwrO04KeDhMvPMxDKmXXUitRNK1LdUyOHXG8yzlMu8nEql0hWNo544d9rCXXvklmFOJLdQyb6Du0Enn1MKBGh7v1rZdu3bNOVtl6djxYyiVZWmrtH7Ooyz3hQ7VpuHdWt5xINgwN8K8EuiRQJR7SNPDq85e9EJKE8hDkShUo8E5hOwcT2bVSu4RtXAfU5hj/7nVq1bUo2oiiO9IGRCf4UCD/SBS0vte1NTZknNaY64VwwAm5Ajz09+xv7p9dDynTpbluS0veBjbfrL0Y1yiLMe+p2hNw40sV7VhbougXT0YaQbkjqAEpzT99Lw6+8vaUg1uz9pGQspWo8Sda4pT49ttSjO1CcrSptoDXZy+V8YnxVQ5nmOwdYU8/NR9V9g9m5BxKr80cP0xhQ1vbcwpSENpj/TKcjIl36Moy5RG3/9cqFDZV0plLPt3BFqmOaZ+Z5Rl3tdVUpYOm8K8OrAPezcJxThcaZZ2s/nScHkbrzSnY9SU5mjFOdI5hkJZmuJMhTz8uLQ8t1CY8XpDpmKL8KjUV7ugSBijqd/Lib8sMUeWtRAgqCtLaE23awqzNb2fDxUqx1ILGWpdt6Ug9xXSOK+yHI+vTZq6ecmvAuZM0r2ThwcpTQ+ttaWeiZMC1cmUpiEQUZcpTa8iU7/+2W8oTrtOHiJERVFKsnVO0FCYNa95up79MF1S4HrplKmh5QH3xTAMNSeM7a8VybB+lirKlq2yGZjurlufli8rpHEeZdnCKm4fBd3iMK8Gumg1nG+z33ve6mFfaTiYKsulSjP0PzqRpnZJqooztC1UpzuWioCkH4Jcac4VuZhz1vTxusdbuWceLZXo0Tpes0nWiBLqCtZ7sfcpyqrH+0Bl2SLLrM3MD8dSb/gcujUDjLZMn6uBQIKBNHvEkYb9CteV5pKCHXtLw3lEkpwozey4bbgCwox211ukUG+F4uwFHk5tgz3M2ofUNrNRlgr4JIufrBb7iHiMI9f69Hw3IaVjKc5W+E+rXXUqXNj+PGopjKHddFpv5HdLtQjwNEzIXpe2yur+irKsmwmOpyxLR09Hl9qvgs2GebVgStO85vU26ytNv6+qNA1FqTZDqTjnvNqDS7PsKzqvZxgD4NM5koLcs2sCVpNz0k8MU2rhOGHqU7Sm1yVqBLOvj7kUxn3nl2qwpmpbirKW3uj7WmLDPJay9GS5KlQ3L/lVgBA/XBnYqWakeR6lOSnY4S5UW/fckD3YpdL0g81y0T1Gm2euMJlRqfnY8nPGzaQ8ZTfxcoeVz+vEGO5gan6oobSdZtfYoz7nptj76mMmRbWnj1ZQe22Vxzn75NhfXVHato2tld445wVPP2YTc0F93fCsTbrOxZQl8Zz203EObArzaqEXmZDmoUqzNuUeMBXYWI2S8Zw5G2ZvtspWumR6UIO622mX2TdDu+m5zeIe/r2JX86Hy4/ZZRrVkJTmXtKrq7h9RAvz6nCNc2v2yDJ1MfW3J4Yy9Ffmm7en3/scO+X+fLsyJW+EDKU2e6bhLdTIcl0ourssy/dxcG0Js4s6c2CokmbT891QmqVWSeRaI82I2jS9rDhUkulkf3blxvS9QcT5qpeaBZrny2mUAffKKdEW2vpKaWFvPQBepTbb7FGRNZT2v3qb6ZTb7x/HmCvKubb7pt8TRdlwKtXuoaYsl8RXljg0zrJFlt2a+lLZnD5XCXtJM8IygmyavldpGhzJtkjTq9OmDdM7hPz+luJsTMHLaXr5RT0VokNnmnpZkkCqloRWA9NTfCbdXqVZQ0t9XgQ1lZYfz8OAJscXxk6GY+3pt+1rhQrZWP11rM+2DTN37OTXmq4bnt+X9VNXlq0MnqOSpWHFsCIRuR34FsKtfqeqflNx/BXA8+LmhwJPVNXHxWNfAvyteOwbVPV74/4/BHwP8CGE4sR/Za5i2rUkTEHopWOnwyxpljikYEcJrzRTfzMOIdvvp+mpQhFdffqeiLJOpp24qbR5tCe2qUbqJYXqtP41fAHbSjMQQvP4TUJLOZbHZ1MP90y7Qz9jLGV+bmU6PTP99mOa7q+ryTmybGGOLK2QRv28Nln20q0Sh6mArqQwRaQHvhX4LMISu/eJyD2qmtYlV9Wvdu2/CviE+PojCGuUPycO683x3P8DfBvwF4GfJhDm7cBrWuO4loRpKEkTyNIYh/TLHj58n3seG9WVpsGpRz89z1CEHqUQn8whM1LVUChOfz1bsbInBKzvXJrlOD22pXzt3rqpg6VIvTRFskMpqwvN9uPOPSXW4LwE7POazy3t0KpFWQ3haQScZ+cVJNnK/64d89Pvlq3ykJChsc38NLymLD1Rhv9HslwNqmsqzOcCD6rquwBE5C7CirM/22j/QgJJAvwJ4HWq+qvx3NcBt4vIG4EPt1UkReT7CAuhPToJcx9KpVlzCM2pyvO086gV9ZgLbp+cX4QF1ceVO3uqqZcGpZrmmIqQzNgVa2maNxP7AtdDm1o4TnvaXfbbIt1DxxGu255+H4p5x818u9Y0/GZhRafPU4D3uO33Ap9UaygiTwduA94wc+5T4t97K/ubuJaE+ea3fvA3+yc/+AuXPQ6HW1m4tMZNwlUbD1y9MW3jmcfHXLSD3+D/vPb1evetC5s/VkTud9t3xoUPz4MbwN2quroh/VoSJvALqvqcyx6EQUTu38Yzj6s2pm088yjI61xQ1dvXGEvEQ8DT3PZT474abgBfWZz76cW5b4z7n7qwT2Be7W/YsGHDVcF9wDNF5DYRuYVAiveUjUTkWcDjgZ9yu18LfLaIPF5EHg98NvBaVX0f8Osi8skiIsAXAz86N4jrqjA3bNjw/xFU9UxEXkwgvx54paq+Q0TuAO5XVSPPG8BdPjRIVX9VRL6eQLoAd5gDCPhLjGFFr2HG4QPXlzDPa9s4Frbx7MdVG9M2nnlctfGgqvcSQn/8vpcV2y9vnPtKwiq15f77gY9dOgZZuKrthg0bNvx/j82GuWHDhg0LsRHmhg0bNizEtSBMEflBEXkg/r1bRB5otHu3iLwttrtwWMTMeF4uIg+5MX1Oo93tIvILIvKgiHztEcfz90Xk50XkrSLyahF5XKPdUd+fffcrIo+Jn+WDIvLTIvLRa4+huN7TROQnReRnReQdIvJXKm0+XUR+zX2WL6v1teKYZj8DCfjH8T16q4h84hHH8jHuvh8QkV8Xkb9atLmp78+Vh6peqz/gHwIvaxx7N3DrTRjDy4GX7GnTA+8EngHcArwF+P1HGs9nAyfx9TcD33yz358l90vwSH57fH0D+MEjf05PBj4xvv6dwC9WxvTpwI8d+5lZ+hkAn0Pw1ArwycBP36Rx9cAvA0+/zPfnqv9dC4VpiLFSXwj8wGWPZQFS7quqPgxY7uvqUNWfUFUr9vgm8mDcm4Ul9/sC4Hvj67uBz4yf6VGgqu9T1Z+Jr38D+Dn2pL5dAbwA+D4NeBPwOBF58k247mcC71TV/34TrnVtca0IE/hU4H+q6n9tHFfgJ0TkzSLyoiOP5cVxyvTKGAxbopW/emx8Ge1YsmO+P0vuN7WJBP9rwBNWHkcVcfr/CYSqNCX+iIi8RUReIyJ/4MhD2fcZXNZzc4O2ELmZ78+VxpWJwxSR1wNPqhx6qapa9P0LmVeXf0xVHxKRJwKvE5GfV9V/t/Z4CCWhvp7w8H89wUzwZee5zhrjsfdHRF4KnAGvanSz2vtznSAivwP4IeCvquqvF4d/hjAN/c1oi/4R4JlHHM6V+wxi5sznAV9XOXyz358rjStDmKr6/LnjInIC/BngD8308VD8/1dE5NWEaeK5HsZ943Hj+mfAj1UOHZL7euHxiMiXAp8LfKZG41Olj9XenwqW3K+1eW/8PH8X8L9Xun4VInJKIMtXqeoPl8c9garqvSLyT0XkVlU9SiGMBZ/Bqs/NQvxJ4GdU9X+WB272+3PVcZ2m5M8Hfl5V31s7KCIfJiK/014THCFvP8ZACpvSn25cZ1Hu60rjuR34GuDzVPW3Gm2O/f4sud97gC+Jr78AeEOL3NdAtI9+F/BzqvqPGm2eZHZUEXku4TtxFBJf+BncA3xx9JZ/MvBrGnKej4nmzO1mvj/XApftdVr6R8j3/PJi30cB98bXzyB4Zt8CvIMwVT3WWP458DbgrYQH/MnleOL25xA8s+888ngeJNi9Hoh/316O52a8P7X7Be4gEDnAY4F/Fcf7n4FnHPmZ+WMEs8lb3XvzOcCX27MEvDi+H28hOMz+6BHHU/0MivEIobL4O+Mz9pwjv0cfRiDA3+X2Xcr7cx3+ttTIDRs2bFiI6zQl37Bhw4ZLxUaYGzZs2LAQG2Fu2LBhw0JshLlhw4YNC7ER5oYNGzYsxEaYG46KmE73VBF5o4j8ks8dF5EfEZHfvMzxbdhwCDbC3HA0iMiHAE/QMdngA8CnxGOPI1QT2rDh2mAjzA0Xhoj84ViI5LExm+UdIvKxhNJgb3RN7yJkAEFIc52kKm7YcJWxEeaGC0NV7yNkPH0D8PeA71fVtxNylP+1a/pvgE8TkZ5YD/Nmj3XDhovgyhTf2HDtcQchn/y3gb8c930K8BLXZgf8BwJZfoiqvvuI5TA3bFgdG2FuWAtPAH4HcAo8VkR+N/AeDcWEPe4CXk2oWr9hw7XCRpgb1sJ3AH8buI2wTMbPkU/HDf8e+Ltcj6r5GzZk2Ahzw4UhIl8MPKKq/yLaJ/8ToYzbs8u2Gqq9/IObPMQNG1bBVq1ow+oQkccA/1FVn3PZY9mwYU1shLlhw4YNC7GFFW3YsGHDQmyEuWHDhg0LsRHmhg0bNizERpgbNmzYsBAbYW7YsGHDQmyEuWHDhg0L8f8ATpSCQHIPjkYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.interpolate import griddata\n",
    "from pylab import savefig\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.cm as cm\n",
    "from IPython.display import Image\n",
    "\n",
    "x96,y96,valuesCF96,valuesHam96 = np.loadtxt('out96.txt').T #Transposed for easier unpacking\n",
    "\n",
    "bounds = 7.5\n",
    "pl_xmin = -bounds\n",
    "pl_xmax = +bounds\n",
    "pl_ymin = -bounds\n",
    "pl_ymax = +bounds\n",
    "\n",
    "grid_x, grid_y = np.mgrid[pl_xmin:pl_xmax:100j, pl_ymin:pl_ymax:100j]\n",
    "points96 = np.zeros((len(x96), 2))\n",
    "for i in range(len(x96)):\n",
    "    points96[i][0] = x96[i]\n",
    "    points96[i][1] = y96[i]\n",
    "\n",
    "grid96 = griddata(points96, valuesCF96, (grid_x, grid_y), method='nearest')\n",
    "grid96cub = griddata(points96, valuesCF96, (grid_x, grid_y), method='cubic')\n",
    "\n",
    "plt.clf()\n",
    "plt.title(\"Neutron Star: log10( max(1e-6,Energy Density) )\")\n",
    "plt.xlabel(\"x/M\")\n",
    "plt.ylabel(\"y/M\")\n",
    "\n",
    "# fig, ax = plt.subplots()\n",
    "# ax.plot(grid96cub.T, extent=(pl_xmin,pl_xmax, pl_ymin,pl_ymax))\n",
    "# plt.close(fig)\n",
    "fig96cf = plt.imshow(grid96.T, extent=(pl_xmin,pl_xmax, pl_ymin,pl_ymax))\n",
    "cb = plt.colorbar(fig96cf)\n",
    "savefig(\"BHB.png\")\n",
    "from IPython.display import Image\n",
    "Image(\"BHB.png\")\n",
    "# #           interpolation='nearest', cmap=cm.gist_rainbow)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='convergence'></a>\n",
    "\n",
    "# Step 7: Validation: Convergence of numerical errors (Hamiltonian constraint violation) to zero \\[Back to [top](#toc)\\]\n",
    "$$\\label{convergence}$$\n",
    "\n",
    "The equations behind these initial data solve Einstein's equations exactly, at a single instant in time. One reflection of this solution is that the Hamiltonian constraint violation should be exactly zero in the initial data. \n",
    "\n",
    "However, when evaluated on numerical grids, the Hamiltonian constraint violation will *not* generally evaluate to zero due to the associated numerical derivatives not being exact. However, these numerical derivatives (finite difference derivatives in this case) should *converge* to the exact derivatives as the density of numerical sampling points approaches infinity.\n",
    "\n",
    "In this case, all of our finite difference derivatives agree with the exact solution, with an error term that drops with the uniform gridspacing to the fourth power: $\\left(\\Delta x^i\\right)^4$. \n",
    "\n",
    "Here, as in the [Start-to-Finish Scalar Wave (Cartesian grids) NRPy+ tutorial](Tutorial-Start_to_Finish-ScalarWave.ipynb) and the [Start-to-Finish Scalar Wave (curvilinear grids) NRPy+ tutorial](Tutorial-Start_to_Finish-ScalarWaveCurvilinear.ipynb) we confirm this convergence.\n",
    "\n",
    "First, let's take a look at what the numerical error looks like on the x-y plane at a given numerical resolution, plotting $\\log_{10}|H|$, where $H$ is the Hamiltonian constraint violation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "grid96 = griddata(points96, valuesHam96, (grid_x, grid_y), method='nearest')\n",
    "grid96cub = griddata(points96, valuesHam96, (grid_x, grid_y), method='cubic')\n",
    "\n",
    "# fig, ax = plt.subplots()\n",
    "\n",
    "plt.clf()\n",
    "plt.title(\"96^3 Numerical Err.: log_{10}|Ham|\")\n",
    "plt.xlabel(\"x/M\")\n",
    "plt.ylabel(\"y/M\")\n",
    "\n",
    "fig96cub = plt.imshow(grid96cub.T, extent=(pl_xmin,pl_xmax, pl_ymin,pl_ymax))\n",
    "cb = plt.colorbar(fig96cub)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we set up the same initial data but on a lower-resolution, $48\\times 8\\times 2$ grid (axisymmetric in the $\\phi$ direction). Since the constraint violation (numerical error associated with the fourth-order-accurate, finite-difference derivatives) should converge to zero with the uniform gridspacing to the fourth power: $\\left(\\Delta x^i\\right)^4$, we expect the constraint violation will increase (relative to the $96\\times 16\\times 2$ grid) by a factor of $\\left(96/48\\right)^4$. Here we demonstrate that indeed this order of convergence is observed as expected, *except* at the star's surface where the stress-energy tensor $T^{\\mu\\nu}$ sharply drops to zero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(EXEC): Executing `taskset -c 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15 ./TOV_Playground 48 48 2`...\n",
      "(BENCH): Finished executing in 0.21283507347106934 seconds.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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mBxF5CrgX2GI/7hWRJ30dWE0SHx9PXFwcvXv3Zvjw4dSqVYv169f7OyyllG3Pnj0kJSUxcOBALrzwQgYMGADAhg0b/ByZ73hTchgE9DfGzDDGzAAGAFf4NqyaIysri02bNhEXFweAw+GgW7dumhyUqkRcv0fX79T1Nz4+3m8x+Zq3XXa7j8YW5YtAaqpt27aRkZFB9+7d86bFxcURHx9Pbm653nyulCqj9evX43A4OOusswBo2LAhDRo0qPHJ4QlgvYi8KyLvAWuBKb4Nq+Zw7VzuyeHss8/m1KlTbN++3V9hKaXcrFu3jtjYWMLCwvKmde/eveYmB/sO6VygN/AF8DnQxxgzqwJiqxHi4+MJCQmhffv2edNcRVatWlKqcli/fn3e79Kle/fubN68mczMTD9F5Vve3CH9oDHmT2PMV/bjYAXFViPEx8dz1llnERBw+qrizp07ExgYqMlBqUrg8OHDHDhwoNDkkJmZydatW/0UmW95U620SETGi0gzEanjevg8shrAGEN8fHy+KiWAoKAgunTposlBqUrA9Ts8++yz8013/W6ra9WSN8nhBmAs8CNWe8NaYI0vg6op9u/fz7FjxzySA1hVS+vXr0cHwlPKv1zJoeDvtF27doSGhlbbkzhv2hz+aYxpVeDRuoLiq9YKa4x2iYuL48iRIyQkJFR0WEopN+vWraNVq1bUrl0733Sn00nXrl1rZsnBbnP4RwXFUuPEx8cjInTt2tVjnjZKK1U5FNYY7eK67Lw6lvC1zcGP4uPjadeuHeHh4ezfv5+MjIy8ed26dUNENDko5UfJycls377do70hOTmZ7OxsunfvTlJSEnv37vVThL6jbQ5+5GqMnjhxIs2aNSMsLIy2bdsyfPhwcnJyaN++vSYHpfzI1T2Ge8mhd+/eREVF0aVLF1q1agVUz0Zpb3plbVURgdQ0J06cYOfOnYwcOZKsrCxuuOEGOnTowG+//cbMmTPp2bMncXFx/PLLLyWvTCnlE+vWrQOgadOmpKSkUKtWLUaMGMHAgQOZMmUKzz33HCJCfHw8Q4cO9XO05avE5CAiYVjjOTQ3xowSkXZAB2PMPJ9HV41t3LgRsM5IBg4ciDEG13hKv/zyC71792bq1KnMnDmTY8eOERMT489wlaqR1q9fT4MGDZgyZQpr165l69ated3r169fn7vvvpuYmJhqWXLwplrpHSATONd+nQA87rOIaojVq1cDkJKSAoD7QHvnnnsuDocjbzyHTZs2VXyASik2bdpEy5YtmT17NsOHD893s+pdd93FqFGjaNWqVbXsndWb5NDGGPMMkAVgjEnFGg3Op0Tk7yJiRKSur7flDwsWLADI11eLu++//55bb70VgGPHjlVYXEqp044ePcqePXuoW7cu48ePzzdPRJg2bRoXXnghhw8f9lOEvuNNcsgUkVDAAIhIGyCj+LecGRFpBlwGVL9LAGy7du3C4XAwaNCgQud37do17/K4pKSkigxNKWU7cuQIBw8e5KGHHiIysvCRkZ1OJykpKezfv7+Co/Mtb5LDv4FvgGYi8hGwGHjQp1HB8/Y2qt/Fw1jdZhw4cICQkJAil4mJieGBBx4A4Ndff62o0JRStpycHFJTU4mKimLMmDHFLgfw7bffVlRoFaLE5GCM+Q64GhgBfAL0NMYs9VVAIjIUSDDGFFuJJyKjRGSNiKw5cuSIr8LxiYSEBNLS0oo8E3EZNWoUAJs3b66IsJRSbpKTkwF4+OGHCQ4OLnK5Dh06AFS7KwtLvFoJwBhzDPi6xAW9JCKLgIaFzHoImIRVpVRSTNOB6QA9e/asUiWM9PR0GjRoQP369YtdrlGjRjgcDnbv3l0xgSml8iQmJgJQt27xzZ516lj3BK9du9bnMVUkr5JDeTPG9CtsuoicBbQCNthX7zQF1onIOdWpq/C2bdvSokWLvJ2qOPXq1aN1a+3KSqmK9uGHHwIQGhpa7HJRUdbgmFu2bCErK4vAwECfx1YRvB0mtEIYY341xtQ3xrQ0xrQE9gNnV6fEAHD8+HGSk5NLrFYC6+Ybp9NZAVEppdz99NNPADRo0KDY5Vy/48zMTLZt2+bzuCqKV8lBRM4Xkb/az+uJiN41XUY5OTk0b96c/fv3e5UcIiIi2LlzZ7UdUESpymrLli0AREdHF7uc63c8Y8YMunTp4vO4KkqJyUFE/g1MACbakwKBD30ZlItdgjhaEduqKFu2bCElJYWsrCyvkkPt2rXZunUrM2fOrIDolFJgtTccOHAA8D45ZGdn+zyuiuRNyeEqYAiQAmCMOQBE+DKo6mzVqlUAZGRkeJUc6tatS0BAACtXrvR1aEop25o1p/sWLTiOQ0Gu3/EPP/yQ17VGdeDVTXDGuhvLdRNcLd+GVL2tXLkyb2dzNWQVJzo6GmMMq1atqpZ9xitVWTVt2hSHw0F4eHixy4WHhyMi7N+/n+nTp+ddAlvVeZMcZovINKC2iNwJLALe9G1Y1deqVavo1q0bgNfVSjk5ORw/fpydO3f6OjylFNC/f3+GDBlCdHR0vn7PCiMiREZG5p3IuZc6qjJvboKbCnwGfA50AP5ljHnZ14FVVxMmTOD6668HvE8OLq4qKaWU7xhjyMzMJCkpqcQqJZfIyMi8ftKqSxWwN112PwDMsu+UVmfopptuYtmyZYB3ycHVGDZv3jwGDhzo09iUUrBv3z7at29PbGxsiY3RLpGRkaSnp9O+fftqcxLnzU1wEcC3InIcmAV8aow55NuwqqeNGzeSm5ubVydZmpJDTEwMDkelui1FqWpp1apVZGRkkJOTU+Ld0S6RkZEkJydzySWXcPz4cR9HWDG8qVb6jzGmM9ZQoY2AH+zuL1Qpvfrqq1x22WV5ycHbBmmA5cuXc9ddd5GVleXTGJWq6VatWkVQUBCZmZlelxyioqJITk7mjTfeYPbs2T6OsGKU5lT0MHAQOAYU3ymQKlRCQgJNmjQpU8lh9+7dTJs2LW8EOaWUb6xcuZK4uDhOnDhRqjaH6nKVkos3bQ53A9cD9YBPgTuNMVt8HVh1dODAgVInB9eZi+vvxo0b6dGjh++CVCXKycnh0KFD/Pzzz6xZs4adO3eyb98+Dh06REZGBg0aNCAjI4M///yTjIzTQ58EBAQQFhZGbGwsLVu2JCUlhejoaDp06EBcXBw9evTwqjSpfGvjxo3ceOONbNiwoVRtDsnJyWzYsIG//vWvvPrqq/Tp08fHkfqWN20OzYD7jDHVb5DUCpaQkEDPnj05ceIEIkKtWiXfMuI6WDidTpxOJzt27PB1mMp2/PhxVq9ezZIlS1i5ciU7d+4kMTGRjIyMQqv3nE4nkZGRtGzZkuDgYIwxnDhxAoDc3FyysrJwOp3k5OSwePHiQgeHCQ4OJi4ujtatWxMaGkrv3r0599xziY2NLfGSSnXmcnJy+Pvf/063bt144403SlVyOHHiBMHBwaxfv55du3ZV3+QgIpHGmGTgWft1vi5EjTHVo9WlgmRlZXH48GGaNGlCYmIiERERXjUwh4SEEBISQnJyMi1atNDk4GOnTp1i2bJlvPnmm8yZM4fc3Ny8eU6nk+joaMaMGUOrVq3Iysqibt26dO/enXbt2pW6N86jR48SHx/Phg0b+O2339i+fTtZWVmEhoby888/s3fvXt5++23A6mNr4MCBPPTQQ3Tt2rVcP7M6zel0MnnyZA4etPr6LE1ySElJyeukLyEhwWcxVpTiSg4fA1cCa7HujnY/bTGA9iNdCiLCokWLaN68OU8++WSpqg+io6NJSkqiXbt2nDp1yodR1jzGGL7//nveeustfvjhh7z+dOrWrctVV12Fw+Ggb9++XH755bRo0aJcz97r1q1Lv3796NfPswf7nJwclixZwjfffMMPP/zAxo0bmT17Np999hkXXXQRffr0ITo6mlGjRnlVPam8c/ToUbKysvLGcihNgzRYv/Pw8PDqnRyMMVfaf7UH1nIQEBBA3759Abzurtuldu3aJCUlMX/+fL2ctRzk5OTw+eefM3PmTL7++msyMzMB66yxbdu2/O1vf2P06NHFjv7la06nk/79+9O/f3/ASmJffvklCxYsYM2aNTz55JMYY/jHP/5B48aNGThwIJMmTdKxP87QtGnTmDx5MkuWLAFKV3IA67fdpEmTvJOMqsybXlkXezNNFW/79u189tlnpKSkcOLEiVIlh+joaBITEzUxnKG0tDSmTJlChw4duOGGG/j+++8JDw/nqquuYsGCBWRlZfHHH38wbtw4vyaGwogIw4YNY9q0aaxdu5b9+/czefJkOnbsyMGDB3n77bdp06YNEydO1Mudz8COHTto1KgR6enpgPclB9fv+cSJE/Tr14927dr5LMaKUuTRRkRC7HaGuiISLSJ17EdLoElFBVhdLFiwgOuuu46UlJQylxx+/fVXBg8ezKZNm3wYafWze/du7rzzTqKjo5k8eTL79+/n448/5ujRoxw7dowvvviCAQMGVKkG38aNG/PYY4/x22+/cerUKV555RWaN2/OU089RY8ePRg3bhxffPEFOTk5/g61StmxYwdt2rTJq1YqS8nhlVdeYcqUKT6LsaIUdyo6Gqu9oaP91/X4EnjF96FVLwcOHCAwMJC6deuSnJxc6jaHxMREjDHMmzePzZs3+zDS6iMxMZEBAwbQqlUr3nrrLTIyMhg8eDAHDhzgpptuqjYj7IWGhjJ27Fj27NnD3LlzSUxM5OWXX+aaa66hTp06jB8/npSUFH+HWSW4kkNSUhJQ+jaH6nSvQ5HJwRjzot3eMN4Y09oY08p+dDPGaHIopYSEBBo1aoTD4ShzycFVn6xXLBUtJyeH5557juuuu45GjRqxcOFC6taty4QJE9i9ezdfffWVV2N3V1VDhw7Nq8Ls3bs3J0+e5LnnniMqKoqRI0dy7Ngxf4dYaaWlpZGQkJCv5ODtSZx7yeGjjz6ifv36HD1atccp86b7jJdFpIuIXC8i/+d6VERw1YnrBjgoe4N0WFgYDRo00ORQiOTkZMaPH09ERATjx49n3rx53HHHHaxbt47Dhw/z1FNP0aJFC3+HWSGCg4O55pprWL58OYmJiYwfP55atWoxY8YMmjZtys0331xteg4tb++++y5Dhw4lKSmJ0NBQr9ue3JNDcHAwR44cqfKN0t4OE/qy/bgEeAZrZDhVCgkJCTRu3JicnBxOnTpV6gbp3NxcTp06RZs2bTQ5FDB16lRiYmJ47rnnyMrK4pZbbuHAgQO88sorxMXFVam2hPIWFRXFs88+y4kTJ4iPj+e2225j1qxZ9O7dm27duuXdpKes6rnbbruNrl27kpiY6HWVEuRvkG7cuDFQ9e918Obyl2uBvsBBY8xfgW6A3uNfSv/73/948sknOXnyJOBd1xkurkaxxMREevXqVa2rRUpr+vTp/OMf/yA3N5c77riD48eP88EHH5Tqh11TuO76/fzzz2nSpAkbN26kWbNmeV3I13S///47q1evxhhTqrEcAGrVqoWI5F3KClT/kgOQZozJBbJFJBKrA75mvg2r+mnbti3t2rUrVY+sLq4DXVJSEi+88AJffPGFT2KsShYvXszjjz/O6NGjueSSS/j999958803iYjQ4c1LMnToUPbu3cvYsWM5efIk559/Pq+//rq/w/K7l19+Oe+GxKSkpFKdYDgcjrz+lRo1agTUjJLDGhGpjTU06FpgHbDcp1FVM4cPH+b5559nz549pep0z8W95FDTpaamMnr0aPr168fDDz/MsGHD+Oabb2jTpo2/Q6tSHA4Hr7zyCp988glOp5MXXniBn376qUZf+uq6UklESExMLFXJAU53vhcUFMSIESPo0KGDjyKtGN40SN9tjEkyxrwB9Adus6uXfEZE/iYiW0Vks4g848ttVYQtW7bwwAMPsGPHjrw63tK2OYB1NvPHH3/QvXt3vv32W5/EWpmtXLmS1q1bM336dADuvPNOZs+eTVBQkJ8jq7puvPFGFi5cSFpaGhdeeCENGzZk3LhxNTJJbN++nbZt2wKlLznA6c73AN555x1uuOGGco+xIhV3E9zZBR9AHSDAfu4TInIJMBToZg8yNNVX26ooruJl48aNz6jk4KoHdXXUVpO89NJL9OnTh1p2QVEAACAASURBVEOHDtGtWzfWr1/P9OnTS93ZnfLUt29ftm7dyuTJk/PukejYsSOHDtWcAR9zcnLYvXt3Xgn0TEoOLlX9TvXiSg7PFfPw5QF7DPCUMSYDwBhz2IfbqhCuhqnSjuXg4l6tVLduXSIiIti+fXv5B1oJpaSkMH78eO677z5CQkKYMWMG69evp3v37v4OrVoJCwvjscceY8+ePfTo0YPt27fTvHlzPv74Y3+HViH27dtHVlYWbdq0ITc3t1QD/bi4J4d7772X5s2b+yLUClNcx3uXVGQgbtoDF4jIFCAd6ya81QUXEpFRwCig0v8TEhISCA8PJyIiokwN0lFRUYgISUlJiEiNuZx1xYoVXHHFFRw/fpzRo0fz1FNPlfoHq0qnSZMmrFmzhqeffppJkyZx8803s2PHDiZNmlRt7igvTIMGDVi8eDEdOnTg5MmT5ObmlrpaKSoqij179gDWCd2hQ4fIysqqsqVbb+5zCBORySIy3X7dTkSuPJONisgiEdlUyGMoVsKqA/QG/gHMlkIuVDfGTDfG9DTG9KxXr96ZhONzBW+Ag9KVHFxXQrgapKt7cjDG8Pzzz3Puuedy/Phxpk6dWqqBV9SZmzBhAlu2bGHw4MH861//YsCAAXljHFRHoaGhXHrppTRp0iSv64wzKTk0adIEY0yVrprzZiS4d7CuUjrXfp2ANVzovLJu1Bjj2YG9TUTGAF8YYwywSkRygbrAkbJuz9/eeeedvB2uNKPAuXON6QBwySWXEBYWVu5xVhZjxoxh2rRpiAhvvvkmd9xxh79DqpE6dOjAl19+ydtvv81dd91FbGwsv/76K02bNvV3aOXuhx9+4MSJEwwZMqTU/Sq5uDdIu98IV1W/L28uZW1jjHkGyAIwxqSSf+Cf8jYX605sRKQ9EARU6U5KatWqla/k4O0ocO5q166dV3IYO3Ys77//frnHWRls2rSJadOm4XA4mDNnjiYGPxMRhg8fTpcuXUhKSmLMmDH+DsknXn75ZR588EGAUvfI6uIaDS4nJ6da3AjnzREqU0RCsUZ/Q0TaABnFv+WMzABai8gmYCbWpbPGh9vzKdeALD/++CNQ+n6VXNxLDu7rrm7+9a9/AfDWW28xdOhQP0ejwGqs/vnnn4mJiWHevHl8//33/g6p3O3YsSOvY8szKTkAnDx5kpYtW3LffffRsmXLco2zInmTHP4NfAM0E5GPgMXAg74KyBiTaYy5xRjTxRhztjFmia+2VRGOHTvG1KlTWb9+PUCpu+t2cS85HDp0iLp16/Laa6+Va6z+tnfvXubNm8eoUaP46199eiuNKqXw8HDmzJkDwLBhwzh8uMpfRJgnOzs73z0OZS05uHfbHR0dzfPPP09cXFz5BluBvLkJ7jvgamAE8AnQE9jp27CqD/fLWIFSjwLn4uqZFaB+/fpERETwzTfflF+gfjZnzhyuv/56jDE89NBD/g5HFeKCCy7g8ssvJzk5uVr1x7Rs2TJOnTrFxRdfDHBGDdJAXrtDWlpale62u9gGaRHpgzXq24/GmK9FpCvwEnAB2r+SV1w3wLm3OZSlUzjXgD9g1QMPGTKE6dOnk5qa6pPGaWMMR44cISEhARHB6XSSnZ3NkSNHiI6OpmvXruU2lOapU6cYOXIkSUlJ3HbbbZX+0uSabOrUqSxcuJD4+HiuuuqqcluvMYa9e/eyc+dOUlNTSU1Nxel00q1bN6Kjo4mIiPDZJaFLliwhKCiIyy67DLBKDiJS6pM49267wbpwJCIigu+++658A64gRSYHEXkWuBKIByaIyELgDuBJ4PaKCa/qc5UcXFcvJCcnl2lcgdq1a5OamkpmZiZBQUEMGTKEl156iUWLFjFkSOl7UM/NzeWnn37is88+Izk5mczMTHbs2MGmTZvIzMz0qvsEp9NJWFgY5513HpdeeildunShQ4cOpR7k/vXXX8/7QWqpoXLr0qULV111FS+++CItWrRg+PDhhISEeP1+Ywyvv/46CxcuZPfu3YSHh5OQkMD+/ftL3OdEhMDAQEJDQ4mKiqJ+/fpcccUVXHjhhfzlL38p9RWALo888gi33XYb4eHhgFVyiIqKKvVFIwWTQ5MmTap0TwbFlRyuAOKMMekiEg3sA7oYY3ZXSGTVxNGjRxGRvJ4ay9rm4CptnDhxgnr16nHBBRcQGRnJV199VWhyyM3NZe3atRw+fJigoCByc3PZtGkTs2bNYufOnRw/fjyvQTswMJAWLVpQp04datWqRePGjalTpw5169YlOjqauLg4WrZsybFjx9i4cSNJSUns2bOHhIQEjh07xtq1a/NVcXXp0oVJkyZxww03lPgDS01N5ZlnnsHhcHDTTTfl1fuqymvy5MnMmTOHkSNHkpaWxtixY0t8z/bt25kyZQqzZs0iLS0tb/pZZ53FBRdcQG5ubl6Ppq5BdnJycoiNjSU1NZUVK1bk7XvJyckcOHCAvXv3smbNGsC6Fyg4OJjGjRvTqVMnevbsSbt27bjyyiuJiIjIO6kqjIjkO6EpS79K4DlUaJMmTVi8eHGp11NpGGMKfQDrCrxeX9Sy/n706NHDVGZpaWl5z2vVqmUeeOCBUq/jgw8+MIDZtm1b3rS3337bLF26NN9y8fHx5tZbbzVRUVEG6wozj0doaKhp27atuemmm8xHH31kkpKSyv7hbEePHjVvvfWWadWqVd527rnnnhLf9/zzzxvAOJ1Os2PHjjOOQ1WMa6+91jgcDtO4cWOTnp5e7LJ//vmnCQ8PN4AJCgoyw4cPNxs2bDDZ2dlnFENGRoZJTEw0X3/9tbn88stNnTp1jMPh8NjfGzVqZGJiYszZZ59tPvjgA5OTk5O3jtdee82MHDnSZGVl5U278sorTVxcXKnj2b9/vwHMtGnTjDHGPPnkkwYwycnJZ/Q5fQlYY4o4rhZXcmgtIl+5vW7l/toYo6PBeclV7M7JySElJaXMl7IC+S5nveWWW9i2bRuffPIJmzdv5tdff2XBggV5HX61adOGv/zlL8TGxnLRRRfRtm1b6tSpU25tBe5iYmIYOXIkI0eO5IcffuCyyy7jtddeY+LEiXlVaoVp2rQpIsKYMWNKXR2l/GfKlCl88cUXHDhwgPfee49Ro0YVuezkyZPJyMjghRde4I477ihz9U9BQUFBBAUFMWjQIAYNGgRYJ7u//fYbixcv5tSpU4gI69ev58svv2TdunXceuutTJgwgcGDB9O5c2feeOMNAgMDCQg4fSgsa8mhYLVSp06dANi4cSPnnXfemX7cildU1gAuKu5R1Pv88aisJYesrCxz1VVXmYULFxpjjElMTDSA+e9//1vqdf38888GMLfccou5/vrrTadOnUxAQEDe2ZHT6TSxsbFm8ODB5vHHHzf79+8v749TKv/85z8NYK6//vpil7v22mtNeHi4OXToUAVFpsrL6NGjDWCaNm1qMjMzC11mzZo1BihTabk8ZWRkmK+//tp07tzZAHklGdejfv365tJLLzX33nuvadSokbn66qtLvY2cnBwjIubhhx82xhhz+PBh8+yzz5q9e/eW98cpNxRTcvD7gb08HpU1OWzYsMEA5qOPPjLGGLNnzx4DmLfeeqvU69qzZ48REQOYVq1amSFDhpiHHnrIdOrUybRt29Z8+umnJRbvK1Jqaqq57777DGBWr17tMT89Pd3cfPPNBjCPPPKIHyJUZ+rAgQMmODjYREZGFlolmJubazp16mQA89lnn/khQk9paWmma9eu5rrrrjNTp041gBk/fry5/fbbTa9evUxYWJgBzP3331+m9UdGRpp77723nKP2nTIlB+B/wGAgsJB5rYFHgduLen9FPiprcpgxY4YBzNatW40xxvz6668GMJ9++mmZ1rdv3z6P+sv//ve/eWc/Tz/99BnHXJ5OnDhh6tWrZ3r16mVyc3PzzXv99dcNYKKioip1nawq3qRJkwxg4uPjPebNmjUrr87/TNsXytPBgwdNdna2GTJkiGnRokW+fTMnJ8fs2rWrzCdazZo1M3/961/zbWvx4sVnHLOvFJcciruU5E6s+xm2ishqEZkvIktEZCcwDVhrjJlRxtqsGmHt2rWEh4fTrl07gDKNAueuadOmHmMku65UOuussxg3btwZRFv+IiMjiYmJYfXq1cydOzdvemZmJk8++SQiwp133qnjPldhrn1u/vz5bNu2LW+6MYZ77rkHsAZqqkzdfTdo0ACn00m7du244447cO/02eFw0LJlyzK3y7l3vgfwyiuv0L9/f1JTU8847opWZHIwxhw0xjxojGkDXAc8BjyAdTlrf2PMlxUVZFW1du1a4uLi8i7nLEt33SVp06YN77zzDl9++WWprjevKHfffTcAb7/9dt60Dz74gL1792KM4ayzzvJXaKocNGjQgJiYGJ5//nmGDx/uqllg/fr1HDlyhObNm3PNNdf4OcrCTZ06lcmTJ5frOguOBtejRw9yc3PZsGFDuW6nIngznkMDrPEVMoA/jdUrqyqBMYaIiAguuOCCvGm+SA4AI0aMoFWrVuW6zvIyatQoQkNDmT9/PnPmzCE7O5snnngibzjGjh07+jlCdaY6duxI7dq1WbduXd7dwD/99BMAEydOzHdmXt0VlhwA1q1b56+Qyqy4O6S7A28AUVhjOAA0FZEk4G5jTNX7tBVIRPj222/zTfNVcqjMgoODGTx4MHPmzOHaa69lxowZXHrppWRlZbFjxw5NDtVAbGws27Zto2nTpjz66KNcdtlleXc7X3vttX6OrmJFRkbmjQYHVlVwvXr1WLt2rR+jKpviSg7vAvcaY2KNMf3sR0fgPqwBgFQpueoiy3KHdFUWFxdHVlYWt956KwMGDODNN98ErC5FalKirK46duzI0aNHGTNmDMuWLeP+++9ny5Yt1KtXj7p16/o7vAoVFRWVr81BROjRo0e1Sw61jDErC040xqwAyuculmpswoQJXHrppYBVxbRt2zaWLVtWplHgqrrOnTsDMHr0aBo0aADA1q1btdRQTbj+j+eccw7XXHMNF110EVu2bMn7v9ckkZGRHD9+nAULFpCeng7AU089xaxZs/wcWekVlxwWiMjXInKDiJxrP24Qka+xxndQxfjpp584fPgw9913H+3bt6djx47MnTuX/v37l7pDr6rOdafoli1bgNN3scbGxvozLFVOXP/HPXv28NlnnzF06FA2b96c93+vSS644AIcDgeDBg0iJiaGIUOGsGLFiio5rG+RbQ7GmHEiMhAYitVtN1htD68aY+ZXRHBVza5du1iwYAHz589n+fLlgDXC1MUXX8z999/PFVdcUaYeWau6li1bEhoayubNmwE4ePAgycnJWnKoJlq0aEFwcDBbt24FrJ6Ik5OTa2TJYdiwYRw7doylS5fy9ddfM2/ePP73v/8B1u/guuuuY+DAgZx33nlFdgRYWRQ7noMxZgGwoIJiqXIOHDjA5s2bWb58Oe+99x47d1pjILnGbnjggQd47LHHquRZQ3lyOp107Ngxr+TgOohocqgenE4n7du3z+ue2nUSUBNLDgChoaEMHDiQgQMH8vLLL/Pbb7/Rq1evvP6lnn32WaKiohg4cCDDhg2jRYsWnHPOOZWuRqHY5FAUEZlujCm6p60awBjDoEGDPK5fvummmxgwYAC33XYbt99+e41PDC6dOnXKG0fbdRDRaqXqIzY2Nq/R1XUSUFOTgzsRoVOnTpx//vkcPnyYr776ioSEBGbMmMHMmTOZOXMmAL1792batGl07drVzxGfVmSqEpE6RTxigEEVGGOlcejQISZOnMiIESNo3bo1GzZsIDg4mLFjx7Jt2zYefvhhzj//fBo3bswNN9xAhw4d/B1ypdG5c2f27dtHcnIyW7duJSIiotjeWlXV0rFjR3bt2kV6ejpbtmyhbt261K9f399hVRo9evQgPj6eCy+8kO7du/Pll1/yySef5JWeV6xYQffu3Rk5ciQbN27Mu5nQr4rqVwPIwRorepfbw/U6s6j3+ePhq76VUlNTzdy5c83VV19tYmJi8vowCgoKMsOGDTOvvfaa+fPPP32y7epm7ty5BjArVqww/fv3N7169fJ3SKocffLJJwYwGzduNOeee6658MIL/R1SpbJ8+XLTqlUr89prr+XrZyonJ8csWLDAjBo1ytSpUyfvGBMZGWm6d+9uHnvsMbN7926fxUUZO977A2hexLx9Rb3PH4/yTg7ffvutGTBggAkKCsrXJXa3bt3ME088oR3FlcHvv/9uADNjxgzTtGlTc+utt/o7JFWO1q9fbwAza9YsU7t2bXPXXXf5O6Qqad++feadd94xbdq0ydeleGRkpBkxYoQ5efJkuW6vuORQXJvDC0A0sLeQec+UuahSArc7s0OAbKy7sVf5ansue/fu5fnnn+edd97hxIkTNGzYkLFjx5KTk8OAAQPo16+fzwY4rwlat25NcHAwK1euZP/+/doYXc20b98eEeH7778nKSmpRl6pVB6aNm3KiBEjGDFiBHv37mXGjBnMmTOHzZs38+677zJ//nwmTpxIz5496dOnj287NCwqa/jrAXwLDLSfDwKWlvSespYcDh8+bO688858xTmn02kGDRpU7hlaGdOtWzfToEEDA5gvvvjC3+GoctayZcu8/29l7qa6KkpPTzdz5841l156ad6xKiAgwHTr1u2MvmvK2GU3ACJydSGPviLiq9YmA7j6VIgCDvhoO+zdu5c333yTkydP0q1bNx577DGOHz/O119/TXh4uK82W2N17tyZQ4cOAXoZa3XUsWPHvP+vlhzKV3BwMEOHDmXx4sUsWrSIYcOGERUVxYYNG3jrrbd8sk1vLmUdCfQBvrdfXwysxRpT+lFjzAflHNN9wEIRmYp1NdW5hS0kIqOAUQDNmzcv04a6d+/O1q1b84rEyrdclzYGBATQtm1bP0ejyltsbCzffPMNderU0SuVfKhv37707dsXsDrzdO8Ftjx5kxwCgFhjzCHI68L7feAvwI9AqZODiCwCGhYy6yGgL3C/MeZzEbkeeBvoV3BBY8x0YDpAz549y3Tdl9Pp1MtNK5ArObRp00bbb6ohV2mwU6dOerJVQSIjI33WeaU3yaGZKzHYDtvTjotIVlk2aozxONi7iMj7wL32y08B35SZVIVzVTVolVL15Pq/apVS9eBNclgqIvOwDtQA19rTagFJPojpAHARsBS4FOuSWlUNtG7dmjp16tCzZ09/h6J8oEuXLoSEhNCrVy9/h6LKgTfJYSxwNXC+/fo94HO7pfsSH8R0J/CiiAQA6djtCqrqCwgIYMuWLdSuXdvfoSgfqFOnDjt27Mjrll1VbSUmB2OMEZGfgUysK4lW2YnBJ4wxPwM9fLV+5V964KjetEuU6sObS1mvB1ZhVSddD6wUkZo19p9SStUw3lQrPQT0MsYcBhCResAi4DNfBqaUUsp/vOlA3OFKDLZjXr5PKaVUFeVNyeEbEVkIfGK/vgHQkeCUUqoa86ZB+h8icg1wnj1pujFmjm/DUkop5U9ejQRnjPkc+NzHsSillKokikwOInIS69JVj1lYV7j65p5tpZRSfldkcjDGRFRkIEoppSoPvepIKaWUB00OSimlPHjVIK1qtuPHjpGw+w8yTQBoV8xKVX7GECTZNGnZjjoxMWVahSYHVazjx46xb8cW2iyfQFjSNhwm298hKaVKkCsBpNbuwB+ZT3Asqg7tOnUt9Tq0WkkVK2H3H7RZPoHwxM2aGJSqIhwmm/DEzbRbNYnjRw6yadWPpV+HD+JS1UimCSAsaZu/w1BKlUFY0jYCakWz6Iv3OHpwf6neq8lBFU9ESwxKVVEOkw3iQBzCiWOHS36D+3t9FJNSSqnKIheys0s3qrMmB6WUUh40Oahqa8TcNOQ/yTz4XXq+6fuTc5H/JLN0d/lWl/20J5uL302h9lPJ1Hk6mf+bk8ax1FyP5X7ck82l76UQ/kQy4U8k0+vNU+xK9FxOKX/S5KCqtZAAeGllJnuSvD/4ZuaUfhTcTYdz6P9BKuc0cbLqzlosuDmMP47nMmxWGu6j6n6zPZuBH6VyccsAfhlZi/i7wvnXhcGEBZZ6k0r5lCYHVa2d28xJt4YOJi1JL3T+7iSrFPHRxiwGfZRKrSeSeXhJRqm3M3NTFi1rO3imfwjtY5z8pWkArw0K4ee9OSzdnQNArjHc/XUa484J4l8XBdO1gZO2dRwM7hBIg3D9KarKRW+CU9WaAFP7h3DRu6nc3zuHno2dhS43YVE6T/cL4dVBIXnTwp9ILnH9pyZZnROnZ1ulFHehdmngxz05XNIqgHV/5rIrydA00sGF76Sw9WguraMdTDgviKtiteigKhdNDqrU7vsmnfiDORW+3e4NnbwwIKTkBQu4oEUAQzsGMP7bdJaOqFXoMqN7BHFz1/wH6Pi7wr3exsC2ATy3PJNpazK5PS6Q5AzDxMVWCeTASatKa8dx6+/k761EdE4TJ/N+z+aa2WksvEXo30Z/jqry8MveKCLXAY8AscA5xpg1bvMmAiOBHGCcMWahP2JU1cvT/YLp/FoKX23L4uxGnqWHc5p4Tmtbx/uqnr6tA3h5YAgTF6czdn46AQ64r3cQDWoJDrs7qly76eGOuCBG9QgCrIS3Yn8OL6/K1OSgKhV/7Y2bgKuBae4TRaQTcCPQGWgMLBKR9saYij9NVUUqy9m7v7WPcTK6RyATFmWw4OYwj/m1gjzfU5pqJYB7zglibK9ADp4yRAYLBnj2l0za2EmmUYSVJTrXz590Otdz8M0OvdFQVS5+SQ7GmN8AxLOHz6HATGNMBrBLRLYD5wDLKzZCVR39+6JgPth4iulrM71avjTVSi4ikpcE3lpnbWdYR6u6qmdjJ6EBsPVo/iunth3LpWVtbZBWlUtlK8c2AVa4vd5vT/MgIqOAUQDNmzf3fWSqyqtXy8E/zwvmsR+9uxqpNNVKAM8uy+CyNgEEB8DC7dn8c3EGk84PyltPeJDwt3OCeHV1Jl0bOO02hyz+93s2393qWZpRyp98lhxEZBHQsJBZDxljvjzT9RtjpgPTAXr27Fn6C9NVjXR/nyBeX5PJvuTy32W+25nNEz9nkJoFHWIcvDQghDt75K+veqJvMMEB8OB36SSmG2LrOphzQyiXtqps52mqpvPZHmmM6VeGtyUAzdxeN7WnKVVq7w4L9ZgWEiDsvT//8Ojm35Eey5XFt7cWfiWUO6dDePSSEB69pOq126iapbJVdH4F3CgiwSLSCmgHrPJzTEopVeP4JTmIyFUish/oA3wtIgsBjDGbgdnAFuAbYKxeqaSUUhXPX1crzQHmFDFvCjClYiNSSinlrrJVKymllKoENDkopZTyoMlBKaWUB00OSimlPGhyUEop5UGTg1JKKQ+aHJRSSnnQ5KCU8nDxuync8VVaqd/3yNJ02r500gcRWcYtSOee+aWPy5+W78um+fMnScsquj+vtQdyiHoqmVpPJPPz3srRfbsmB1VtjZibhvwnmQe/yz9+9P5ka9zopbt99yPMNYa+76cg/0nmw435uwjfmZjLtbNTqf/sSWo9kUzctFPM3JTls1jKQ7/3Uxgx178H5W1Hc5ixPpPJFwYXOn/JrmycjyYXmpxeW51Jp1dPETYlmUbPneS2uWkcOpXrsdz3u7Kp9+xJcnIN2bmGZ5Zl0OGVU4Q8nky7l0/x6irP7t5zcg1P/WwtF/x4MvWfPcmYeae/qz7NAuhS38lzywvvKn7z4Rwu/zCVqzoGcstZgVzxcSprDxTfMURxn7W8aFeQqloLCYCXVmYytlcQLUoxZkJmjiHI6THeiNce/SGDWoGFv3/wJ6nUCxMW3BxGdKjw0cYshn+eRvMo4dxm+pMsyksrMxnULoCG4Z7/x4OncrltbhqXtXHyx7H8B/1PN2dx7zfpvH5FCP1aB7A/OZe75qXzf3PTWHhL/s4S52zNZkj7AJwO4aHF6Uxfl8X0K0Po1tDJ8n05jJqXRpCTfL3tjvgyneX7snmmfwjdGzo5mWHYnZQ/hjvODmTs/HQmnBdEoNt+tf14Lv0+SOX/ugXy3GXBiAgxYcLlH6byw4gwOtf3HKGwuM9anrTkoKq1c5s56dbQwaQl6UUuszvJKkl8tDGLQR+lUuuJZB5e4t2YD4VZsiubGeuzeGeoZ8+rSemGLUdy+XufIHo0dtI62sHDFwUTHSqsTihdN2ItXzjJw0vSGTMvjdpPWWesr6zKJCPb8Lf5aUQ/nUyT/1rT3BVWmimuZDBibhqLd+Xw3oYs5D/JXpW6Pv41i9YvniTk8WT6f5CSd7DcmZiL4z/J/LIv//t/3GOdCe9JKvxgl2sMn2zKyhs4qeC8W75IY2yvIP5SyHCvy/bl0LWBgzvODqJlbQfnNw9gdI8gVhX4vo0xzN2axVWxVoJ+b0MWf+8TxFWxgbSOdnBz10DuiAtiyk+n943vd2Xzya9ZfHljGFfby3Vr6GRogTgHtQvgeJph8a7T29x3Ipd+76dwT68g/nt5SN7gZ0/0DeGhC4K47MPUvHHHvf2s5UlPU1SZXPxuise06zsHcnevIFKzDIM+SvWYP6J7ICO6B3E0NZdrZ3seiMb0DOKGLoHsO5HLrXM85y8dUXKX2AUJMLV/CBe9m8r9vXPo2bjoH9SERek83S+EVwedPqiXdqjQQ6dy+b85aXx4dSgxYZ7nXrVDhC71HXz0axYXtgggIhhmb84mNcvQt3Xpf44vr8rkXxcFs2ZUODM3ZfG3BenM/yObfq2drL4znE83ZzFuQTqXtnLSqV7ZDiYvDghhZ2IujSKEF+0hYuuEFl2q+vOU4bXVmcy+Lgxj4J4FaVw9K5W1o2rROtpB/zZO3lyXla+U9Oa6LC5r4yyydPfroVwS0wsf6/uxHzIRgQnnBfGfHzyT+vnNnUxfm8nS3dlc1MLJoRTDZ79lcUW7/AfwNQdySUo39Lf/D+nZAGkyYgAAD5BJREFUVsnTXWgg7Dlh2JOUS4vaDj7/LYvW0Q4W7cxm6MxUMnKgT1MnUy8LoXnU6c8SEiB0a+Dg+13ZDGhrrbRZlIPd9+XvPt7l/j7B3N/Hs/qspM9anjQ5qGrvghYBDO0YwPhv04tNMKN7BHFz1/wHjNIMFZprDDd/kcbtcYFc3LLon9aiW8O4/rM0aj99kgAHhAXC59eH0qWQKoSSXNwygAfsg8ikC4J4ZlkGTgd50yacH8Qzv2SwZFdOmZNDVIgQ5ITQACm0Sqeg1CxrLA3XCHgfXBVKh1dSWLIrh76trbP2W+ek8eKAECKDhaR0w+dbsvjoas/xN1x22SWKJhH5k9L3u7J5Y20m60fXKmzYYQCu7RTIiXTrhCUrF7Jz4Yp2Abw9JH/Jbs7WLAa2CyA4wFrPwHYBvLQyk76tAuhS38GqhBxmrLfahg6ctJLDjsRc9p7I5f2NWbw5OJTgAHhoSQaXvpfCprvDCQk4HVPTSAc7iygZecObz1qeNDmoMinuIBsWKMXOrxvmKHZ+s6ji55fF0/2C6fxaCl9ty+LsRoUfJAs7Ky3NUKFP/JRJRo41VnVRjDGMnZ+OU2DpbWFEhQhf/JbFjZ+l8f1tDnoUU7IpTLcGp+NziFCvltC1fv5p9Ws5OJziu7rpguqFSb7vrX2Mk7phwuYjVnIY0iGAqGCrrWVMryA+3JhFVIgwuEPRh6M0u70+2G2Ro6m53DInjXeGhhabtH7ak82kJRk82z+EC1o4SUjO5R/fZXD7V2l8dPXp4VnnbM3O9797cUAId81Lo/u0FARoHCGMjAvkqWWZOOxjc66BjBx4f1hoXvvArGsdNHruFPP/yObq2NMnGyEBkFzGk31vP2t50uSgaoT2MU5G9whkwqIMFtxc+HjNtYI8p5WmWmnRzmx+2ZdD8OP5ryC5bW46j/+YydZ7wvl+dw6f/5bNn38Pz/uRd2/oZNm+HJ5fkcmHxZw9FyawQKO5AIEF8otgHcTcX5sCV1VmVVzuIMBhHWTfXJfJmF5BvLUuk792DyTAUfTZcL1a1rzENENMmPV80+FcDpw0XPnx6SrMXAMGCHg0mfevCmX4WYE8tCSDqzsGMPYc6x/ctYGT8CDhwndT+c/FubSt4+C3IznsSszlinanD4l1QoXZ14WRmWM4nGJoHCG88f/t3Xl4VfWdx/H3JzcLuUEWCShNEIILlkUsDdRqTdW44IzbdLH6jFr1mfKUR6362PaxdsbWFrXVTqe2M4o+dakFddSCdnGr05YROzoQRUBR6lYQXCLW1iRkIffbP86JWe5NcpOQe04u39c/5J6cGz735uZ8z/n9fuf3WxtUqenjg9/d5NEFiHY+OrHzgD2prIDypNL6T97baUzea3AH9mxf6+7kxcHtMb716RJ+vr6BW+oyDynMZCDNSrefWkpjj7Hsc25q5OpjSvhs2MnZ2Bp8v+dAqITAyM1S6JPKxPYPOv+vll1BJ3lVH6O5ihOiPct49U3GK++l2D+8eti8o513m6xbs9a/zCvmmtWtLF3byvq3U6z4QobK3MXH9i1AwPP1KWqmBj93/kcSbFjc/QrzxjWt/HrzLh765yRTxgT7NbYZPetOInypFlbJFZt2UTu9kL1K0gtUcUJUjgm2372xjZqpCSaWBT/gyP0S/Oy5NjbvSHFwefD6djSleLfJmNbj/dzwToqTDxrcATzb17o7eXFwe4yJZQVcfkQJ3/3f7K/tB9KsVDU+876VY8SBE4IDx+FTEkxMinMfbOa7R5cwpiRoVnr81Xbu/fzArhoG69jphSyta6VmaoK9SsTVT7TQ2s+Rv2qc+P3r7bzyXoqxo2BsidKuWjoki+C8B3fywxOCNv2LHm7m0H0LqK3qLA5TxxWw8IBCLn6kmdrpiQ/PxHszIVnAgooEq15vp2ZqcNgqK1ZaP82ksqB/pOv202YUce3qFhZUJKiZGgxlveTRZg7Zp+DDArbyxTYWV3cvUGu2tfP6+ynmTU7wTmOKf/+/Vta91c7q8zoP0mfOKeLqJ1o4/8FmfnziKIoTwcCGA/Yu4MQuVyF/2tHOmx9Yt20Dke1r3Z18KKvbo1z6yWLKk8PfmdebCckCHjs7aNY6YVkThy5t4K4Nbdx6yig+N7PzrPLcB3Yy7UfDc4PTD44vYfakBCcsa+LE5U3U7FfI/H76Oi47vITypJi7tIGJ1zfw5Nbeh91OHi0WfbyIz93bxKduayRZBCtOT6Z1oi6aV0RrOyya1/dVQ4fF1UX8fP3Abxa84shi/rWmhGtWtzLzxga+cP9ODi4v4FdnJimQ2PLXFOveSnFKjz6PlnbjqlUtzL6pgYXLg5FIfzy/jLn7dr5XySLx+DlllCfFUXc0cuydTYwuFo+fnezWGb1sfRvH7d9/EYwTWc/GxxGourra1q5dG3WMvFRXV8fHf3VM1DH2ODW3N/LR8gJuPjk3VxNRuHFNK1etamHrpaOzuuGwrd04ZGkj19aWZLzfYbBueKqFFS/uYtVuHgTRoaHVOODHDTxwRimHVea+sabu5N+x+r6bWHjml5gx9xPdviepzsyqMz1v5JQx5/YQf9lpvLQjxTW1vY96GskaWo0X323nuidbuGB+cdZ3ohclxM9OK6Ux+y6jrEzeq6DPEWZD9dpfUiw5piSSwjAUIyutc3uA8aXi7a9mvjkqH1z4UDN3bWjjuP0L+drh2TUpdVhQkcg45HgoTp+1e0f59DRnnwRz9hneu5mHgxcH51xO3XFaKXeclr/NZfkikmYlSZ+X9LyklKTqLtuPk1QnaUP4rzd2O+dcBKK6ctgIfAa4ucf2d4GTzWy7pNnAo0BFrsO5LsxIqZACi8cc88657KVUCDa4OxwjuXIws01m9lKG7c+a2fbw4fNAqaT87JUbIYq1i6ZxM6KO4ZwbhKZxM0g1B3f5D3Q+pjiPVvos8IyZZbxjSdIiSWslra2vr89xtD1HxbQDefkT19IwflZwFuKci72UCmkYP4vN85fw1pZXMYzSsoENchi2v3ZJjwP7ZvjWN83swX6eOwv4PnB8b/uY2S3ALRDc5zCEqK4Pe0+YQPPOKja1fQeVjkWK8/mEcw4AS5Fq/htvvvYyf36hjkkVU5lUMW1AP2LYioOZHTuY50mqBFYC55jZK7s3lRuMj1Tux+hkkl/e+RN2vL0tJ9MFO+eGLpVKUVF1ECeddQElowY2QixW7QSSxgG/AS43syejzuM6jdm7nLMuuYq21hbaWnfzXUjOuWFRVFxCUfHA7iXpEElxkPRPwE+AicBvJK0zsxOAC4EDgCslXRnufryZvRNFTpcu+LD5GAHn8l0kxcHMVhI0HfXcvgRYkvtEzjnnuvLeReecc2m8ODjnnEuTF1N2S6oH/txjcznBHddx5hmHLu75IP4Z454P4p8x7vkgc8apZjYx0855URwykbS2t3nK48IzDl3c80H8M8Y9H8Q/Y9zzwcAzerOSc865NF4cnHPOpcnn4nBL1AGy4BmHLu75IP4Z454P4p8x7vlggBnzts/BOefc4OXzlYNzzrlB8uLgnHMuTV4XB0mHSnpK0rpw7YcFUWfKRNJFkl4Ml069Luo8mUi6TJJJKo86S0+Srg/fv/WSVoYTOEZO0kJJL0l6WdLlUefpSdIUSb+X9EL42bs46kyZSEpIelbSr6POkomkcZLuDz+DmyR9MupMPUm6NPwdb5R0t6RR/T0nr4sDcB1wlZkdClwZPo4VSUcDpwJzzWwW8IOII6WRNIVgbY0tUWfpxW+B2WZ2CLAZ+EbEeZCUAP4LOBGYCZwpaWa0qdLsAi4zs5nAYcAFMcwIcDGwKeoQfbgBeMTMDgbmErOskiqArwDVZjYbSABn9Pe8fC8OBowJvx4LbO9j36gsBr7XseJdTGeg/Q/g6wTvZ+yY2WNmHy5y/RRQGWWe0ALgZTN71cxagXsITgJiw8zeNLNnwq8/IDioxWrN9nB9l38Efhp1lkwkjQVqgFsBzKzVzN6PNlVGhQTLLhcCSbI4FuZ7cbgEuF7SVoIz8sjPKDM4CDhS0tOSVkmaH3WgriSdCmwzs+eizpKl84GHow5BcJDd2uXxG8TswNuVpGnAx4Cno02S5kcEJyapqIP0ogqoB24Pm75+Kqks6lBdmdk2guPfFuBN4K9m9lh/z4vVYj+D0ddypEAtcKmZ/ULS6QTVfVAr1A1FPxkLgb0JLuvnA/dKmm45HGPcT74r6GO51lzJZtlZSd8kaCpZnstsI52k0cAvgEvM7G9R5+kg6STgHTOrk3RU1Hl6UQjMAy4ys6cl3QBcDvxbtLE6SRpPcNVaBbwP3CfpLDNb1tfzRnxx6Gs5Ukl3ErRXAtxHRJem/WRcDKwIi8H/S0oRTJBVH3U+SXMIPlDPhUuDVgLPSFpgZm/lKh/0v+yspHOBk4DaXBbWPmwDpnR5XBluixVJRQSFYbmZrYg6Tw9HAKdI+gdgFDBG0jIzOyviXF29AbxhZh1XXPcTFIc4ORZ4zczqASStAA4H+iwO+d6stB34dPj1McCfIszSmweAowEkHQQUE5PZHc1sg5lNMrNpZjaN4A9hXq4LQ38kLSRoejjFzJqizhNaAxwoqUpSMUEH4C8jztSNgop/K7DJzH4YdZ6ezOwbZlYZfvbOAH4Xs8JA+LewVdKMcFMt8EKEkTLZAhwmKRn+zmvJotN8xF859ONLwA1hJ0wzsCjiPJncBtwmaSPQCnwxJme+I8l/AiXAb8MrnKfM7MtRBjKzXZIuBB4lGB1ym5k9H2WmDI4AzgY2SFoXbrvCzB6KMNNIdBGwPDwJeBU4L+I83YTNXfcDzxA0uz5LFlNp+PQZzjnn0uR7s5JzzrlB8OLgnHMujRcH55xzabw4OOecS+PFwTnnXBovDs4NE0kPS6qU9AdJW8Ix5h3fe0BSQ5T5nOuLFwfnhoGkUmCCmb0Rbnqf4L4CwinFJ0eVzblseHFwbggkzQ/XkRglqSycM382cBTwhy673kPnNMmfAeI2VYVz3XhxcG4IzGwNwbQYSwjWC1lmZhsJ1nF4pMuu/wPUhOs8nAH8d66zOjcQ+T59hnO58B2CuZSaCRZVgaAJ6atd9mkHVhMUhlIze71LF4RzsePFwbmhmwCMBoqAUZL2AbaGi/x0dQ+wEvh2buM5N3BeHJwbupsJ5u+vAr5PMOPlIxn2ewK4Frg7d9GcGxwvDs4NgaRzgDYzuyvsT/gj8EVgTs99w9l2Y7dGuHOZ+Kyszu1GkkqAJ82sOuoszg2FFwfnnHNpfCirc865NF4cnHPOpfHi4JxzLo0XB+ecc2m8ODjnnEvjxcE551yavwM+KZED0iIe6QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Now rerun TOV_Playground with twice lower resolution.\n",
    "cmd.delete_existing_files(\"out48.txt\")\n",
    "cmd.Execute(\"TOV_Playground\", \"48 48 2\", \"out48.txt\")\n",
    "\n",
    "x48,y48,valuesCF48,valuesHam48 = np.loadtxt('out48.txt').T #Transposed for easier unpacking\n",
    "points48 = np.zeros((len(x48), 2))\n",
    "for i in range(len(x48)):\n",
    "    points48[i][0] = x48[i]\n",
    "    points48[i][1] = y48[i]\n",
    "\n",
    "grid48 = griddata(points48, valuesHam48, (grid_x, grid_y), method='cubic')\n",
    "\n",
    "griddiff_48_minus_96 = np.zeros((100,100))\n",
    "griddiff_48_minus_96_1darray = np.zeros(100*100)\n",
    "gridx_1darray_yeq0 = np.zeros(100)\n",
    "grid48_1darray_yeq0 = np.zeros(100)\n",
    "grid96_1darray_yeq0 = np.zeros(100)\n",
    "count = 0\n",
    "outarray = []\n",
    "for i in range(100):\n",
    "    for j in range(100):\n",
    "        griddiff_48_minus_96[i][j] = grid48[i][j] - grid96[i][j]\n",
    "        griddiff_48_minus_96_1darray[count] = griddiff_48_minus_96[i][j]\n",
    "        if j==49:\n",
    "            gridx_1darray_yeq0[i] = grid_x[i][j]\n",
    "            grid48_1darray_yeq0[i] = grid48[i][j] + np.log10((48./96.)**4)\n",
    "            grid96_1darray_yeq0[i] = grid96[i][j]\n",
    "        count = count + 1\n",
    "\n",
    "plt.clf()\n",
    "fig, ax = plt.subplots()\n",
    "plt.title(\"Plot Demonstrating 4th-order Convergence\")\n",
    "plt.xlabel(\"x/M\")\n",
    "plt.ylabel(\"log10(Relative error)\")\n",
    "\n",
    "ax.plot(gridx_1darray_yeq0, grid96_1darray_yeq0, 'k-', label='Nr=96')\n",
    "ax.plot(gridx_1darray_yeq0, grid48_1darray_yeq0, 'k--', label='Nr=48, mult by (48/96)^4')\n",
    "ax.set_ylim([-12.5,1.5])\n",
    "\n",
    "legend = ax.legend(loc='lower right', shadow=True, fontsize='x-large')\n",
    "legend.get_frame().set_facecolor('C1')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='latex_pdf_output'></a>\n",
    "\n",
    "# Step 8: Output this notebook to $\\LaTeX$-formatted PDF file \\[Back to [top](#toc)\\]\n",
    "$$\\label{latex_pdf_output}$$\n",
    "\n",
    "The following code cell converts this Jupyter notebook into a proper, clickable $\\LaTeX$-formatted PDF file. After the cell is successfully run, the generated PDF may be found in the root NRPy+ tutorial directory, with filename\n",
    "[Tutorial-Start_to_Finish-BSSNCurvilinear-Setting_up_TOV_initial_data.pdf](Tutorial-Start_to_Finish-BSSNCurvilinear-Setting_up_TOV_initial_data.pdf) (Note that clicking on this link may not work; you may need to open the PDF file through another means.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Created Tutorial-Start_to_Finish-BSSNCurvilinear-\n",
      "    Setting_up_TOV_initial_data.tex, and compiled LaTeX file to PDF file\n",
      "    Tutorial-Start_to_Finish-BSSNCurvilinear-\n",
      "    Setting_up_TOV_initial_data.pdf\n"
     ]
    }
   ],
   "source": [
    "import cmdline_helper as cmd    # NRPy+: Multi-platform Python command-line interface\n",
    "cmd.output_Jupyter_notebook_to_LaTeXed_PDF(\"Tutorial-Start_to_Finish-BSSNCurvilinear-Setting_up_TOV_initial_data\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}