notebooks/09a-rank-deficient-least-squares-reaction-rate.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ChEn-3170: Computational Methods in Chemical Engineering Fall 2018 UMass Lowell; Prof. V. F. de Almeida **22Oct2018**\n",
    "\n",
    "# 09a. Rank-Deficient Least-Squares Reaction Rates\n",
    "$  \n",
    "  \\newcommand{\\Amtrx}{\\boldsymbol{\\mathsf{A}}}\n",
    "  \\newcommand{\\Bmtrx}{\\boldsymbol{\\mathsf{B}}}\n",
    "  \\newcommand{\\Mmtrx}{\\boldsymbol{\\mathsf{M}}}\n",
    "  \\newcommand{\\Imtrx}{\\boldsymbol{\\mathsf{I}}}\n",
    "  \\newcommand{\\Pmtrx}{\\boldsymbol{\\mathsf{P}}}\n",
    "  \\newcommand{\\Lmtrx}{\\boldsymbol{\\mathsf{L}}}\n",
    "  \\newcommand{\\Umtrx}{\\boldsymbol{\\mathsf{U}}}\n",
    "  \\newcommand{\\Smtrx}{\\boldsymbol{\\mathsf{S}}}\n",
    "  \\newcommand{\\xvec}{\\boldsymbol{\\mathsf{x}}}\n",
    "  \\newcommand{\\avec}{\\boldsymbol{\\mathsf{a}}}\n",
    "  \\newcommand{\\bvec}{\\boldsymbol{\\mathsf{b}}}\n",
    "  \\newcommand{\\cvec}{\\boldsymbol{\\mathsf{c}}}\n",
    "  \\newcommand{\\rvec}{\\boldsymbol{\\mathsf{r}}}\n",
    "  \\newcommand{\\mvec}{\\boldsymbol{\\mathsf{m}}}\n",
    "  \\newcommand{\\gvec}{\\boldsymbol{\\mathsf{g}}}\n",
    "  \\newcommand{\\zerovec}{\\boldsymbol{\\mathsf{0}}}\n",
    "  \\newcommand{\\norm}[1]{\\bigl\\lVert{#1}\\bigr\\rVert}\n",
    "  \\newcommand{\\transpose}[1]{{#1}^\\top}\n",
    "  \\DeclareMathOperator{\\rank}{rank}\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Table of Contents\n",
    "* [Rank-Deficient Reaction mechanism](#rxnmech)\n",
    "* [Full-Rank Reaction Sub-Mechanisms](#submech)\n",
    "* [Full-Rank Least-Squares Reaction Rates](#lsr)\n",
    "* [Residuals of All Sub-Mechanisms](#residuals)\n",
    "* [Rank-Deficient Least-Squares Reaction Rate Solution](#rankdef)\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Rank-deficient reaction mechanism<a id=\"rxnmech\"></a>\n",
    "Refer to course Notebook 09."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['NO3', 'NO', 'N2O4', 'N2O5', 'O2', 'NO2']\n",
      "r0 :  2 N2O5         <=> 2 N2O4 + 1 O2\n",
      "r1 :  1 N2O5         <=> 1 NO2  + 1 NO3\n",
      "r2 :  1 NO2 + 1 NO3  <=> 1 N2O5\n",
      "r3 :  1 NO3          <=> 1 O2 + 1 NO\n",
      "r4 :  1 NO  + 1 N2O5 <=> 3 NO2\n",
      "r5 :  2 NO2          <=> 1 N2O4\n",
      "n_reactions = 6\n"
     ]
    }
   ],
   "source": [
    "'''Read a reaction mechanism and create data structures'''\n",
    "\n",
    "from chen_3170.toolkit import reaction_mechanism # replace with your code\n",
    "\n",
    "# build the stoichiometric matrix\n",
    "(species, reactions, stoic_mtrx, dummy, dummy) = reaction_mechanism('data/nox-rxn.txt')\n",
    "\n",
    "print(species)\n",
    "from chen_3170.help import print_reactions\n",
    "print_reactions(reactions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "matrix shape = (6, 6)\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1440x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "stoic_mtrx=\n",
      " [[ 0.  0.  2. -2.  1.  0.]\n",
      " [ 1.  0.  0. -1.  0.  1.]\n",
      " [-1.  0.  0.  1.  0. -1.]\n",
      " [-1.  1.  0.  0.  1.  0.]\n",
      " [ 0. -1.  0. -1.  0.  3.]\n",
      " [ 0.  0.  1.  0.  0. -2.]]\n"
     ]
    }
   ],
   "source": [
    "'''Check the stoichiometric matrix'''\n",
    "\n",
    "from chen_3170.help import plot_matrix\n",
    "\n",
    "plot_matrix(stoic_mtrx, title='Stoichiometric Matrix')\n",
    "import numpy as np\n",
    "np.set_printoptions(precision=3,threshold=100,edgeitems=5)\n",
    "print('stoic_mtrx=\\n',stoic_mtrx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Full-rank, reaction sub-mechanisms<a id=\"submech\"></a>\n",
    "Refer to course Notebook 07."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# reactions =  6\n",
      "# species   =  6\n",
      "rank of S =  4\n",
      "# of all possible sub_mechanisms = 15\n",
      "# of full-rank sub_mechanisms = 9\n"
     ]
    }
   ],
   "source": [
    "'''Build the full-rank sub-mechanism reactions list'''\n",
    "\n",
    "from chen_3170.toolkit import sub_mechanisms # replace with your code\n",
    "\n",
    "sub_mechanisms = sub_mechanisms( species, reactions, stoic_mtrx )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(0, 3, 4, 5), ['2 N2O5         <=> 2 N2O4 + 1 O2', '1 NO3          <=> 1 O2 + 1 NO', '1 NO  + 1 N2O5 <=> 3 NO2', '2 NO2          <=> 1 N2O4'], array([[ 0.,  0.,  2., -2.,  1.,  0.],\n",
      "       [-1.,  1.,  0.,  0.,  1.,  0.],\n",
      "       [ 0., -1.,  0., -1.,  0.,  3.],\n",
      "       [ 0.,  0.,  1.,  0.,  0., -2.]]), 10.0]\n"
     ]
    }
   ],
   "source": [
    "'''Top reaction sub-mechanism'''\n",
    "\n",
    "sub_mechanism_1 = sub_mechanisms[0]\n",
    "print(sub_mechanism_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "S_1=\n",
      " [[ 0.  0.  2. -2.  1.  0.]\n",
      " [-1.  1.  0.  0.  1.  0.]\n",
      " [ 0. -1.  0. -1.  0.  3.]\n",
      " [ 0.  0.  1.  0.  0. -2.]]\n"
     ]
    }
   ],
   "source": [
    "'''Top reaction sub-mechanism stoichiometric matrix'''\n",
    "\n",
    "stoic_mtrx_1 = sub_mechanism_1[2]\n",
    "\n",
    "#( dummy, dummy, stoic_mtrx_1 ) = reaction_mechanism( reactions = reactions_1 ) # taking advantage of this function\n",
    "\n",
    "#plot_matrix(stoic_mtrx_1, title='Sub-Mech 1')\n",
    "print('S_1=\\n',stoic_mtrx_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(0, 1, 3, 4), ['2 N2O5         <=> 2 N2O4 + 1 O2', '1 N2O5         <=> 1 NO2  + 1 NO3', '1 NO3          <=> 1 O2 + 1 NO', '1 NO  + 1 N2O5 <=> 3 NO2'], array([[ 0.,  0.,  2., -2.,  1.,  0.],\n",
      "       [ 1.,  0.,  0., -1.,  0.,  1.],\n",
      "       [-1.,  1.,  0.,  0.,  1.,  0.],\n",
      "       [ 0., -1.,  0., -1.,  0.,  3.]]), 8.928571428571429]\n"
     ]
    }
   ],
   "source": [
    "'''Another top reaction sub-mechanism'''\n",
    "\n",
    "sub_mechanism_2 = sub_mechanisms[1]\n",
    "print(sub_mechanism_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "S_2=\n",
      " [[ 0.  0.  2. -2.  1.  0.]\n",
      " [ 1.  0.  0. -1.  0.  1.]\n",
      " [-1.  1.  0.  0.  1.  0.]\n",
      " [ 0. -1.  0. -1.  0.  3.]]\n"
     ]
    }
   ],
   "source": [
    "'''Another top reaction sub-mechanism stoichiometric matrix'''\n",
    "\n",
    "stoic_mtrx_2 = sub_mechanism_2[2]\n",
    "\n",
    "#( dummy, dummy, stoic_mtrx_2 ) = reaction_mechanism( reactions = reactions_2 ) # taking advantage of this function\n",
    "\n",
    "#plot_matrix(stoic_mtrx_1, title='Sub-Mech 2')\n",
    "print('S_2=\\n',stoic_mtrx_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Full-rank least-squares reaction rates<a id=\"lsr\"></a>\n",
    "Refer to course Notebook 07."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "'''Assume a species production rate as random'''\n",
    "\n",
    "import numpy as np\n",
    "g_vec = np.random.random(len(species))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, let's compute $\\rvec_1$ for \n",
    "$\n",
    "\\Smtrx_1\\,\\Smtrx_1^\\top\\,\\rvec_1  = \\Smtrx_1\\,\\gvec .\n",
    "$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "species production rates g_vec = [0.51  0.365 0.306 0.67  0.468 0.915]\n",
      "reaction rates r_vec_1= [ 0.183 -0.038 -0.253 -0.682]\n",
      "residual norm g - ST_1 r_1 = 1.20229e+00\n"
     ]
    }
   ],
   "source": [
    "'''Compute the LS reaction rates for random species production rates'''\n",
    "\n",
    "# build A x = b LS problem\n",
    "a_mtrx = stoic_mtrx_1 @ stoic_mtrx_1.transpose() # A = S ST, A is the normal matrix\n",
    "b_vec  = stoic_mtrx_1 @ g_vec                    # b = S g\n",
    "\n",
    "from chen_3170.toolkit import lu_factorization # replace with your code\n",
    "\n",
    "# matrix LU factorization of A, the normal matrix\n",
    "(P,L,U,s_rank) = lu_factorization( a_mtrx, 'partial' ) # matrix is full rank; partial pivoting works\n",
    "assert s_rank == np.linalg.matrix_rank(stoic_mtrx_1)\n",
    "\n",
    "from chen_3170.help import forward_solve\n",
    "from chen_3170.toolkit import backward_solve # replace with your code\n",
    "\n",
    "# solve the LS problem: A x = b\n",
    "y_vec = forward_solve( L, P @ b_vec)   # L y = P b\n",
    "x_vec = backward_solve( U, y_vec)      # U x = y\n",
    "assert np.linalg.norm(x_vec - np.linalg.solve(a_mtrx,b_vec)) < 1e-12\n",
    "\n",
    "print('species production rates g_vec =',g_vec)\n",
    "\n",
    "r_vec_1 = x_vec # r_1 = x\n",
    "print('reaction rates r_vec_1=',r_vec_1)\n",
    "residual_vec_1 = g_vec - stoic_mtrx_1.transpose() @ r_vec_1\n",
    "print('residual norm g - ST_1 r_1 = %8.5e'%np.linalg.norm(residual_vec_1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r0 :  2 N2O5         <=> 2 N2O4 + 1 O2\n",
      "r1 :  1 NO3          <=> 1 O2 + 1 NO\n",
      "r2 :  1 NO  + 1 N2O5 <=> 3 NO2\n",
      "r3 :  2 NO2          <=> 1 N2O4\n",
      "n_reactions = 4\n",
      "(0, 3, 4, 5)\n",
      "\n",
      "r0 :  2 N2O5         <=> 2 N2O4 + 1 O2\n",
      "r1 :  1 N2O5         <=> 1 NO2  + 1 NO3\n",
      "r2 :  1 NO2 + 1 NO3  <=> 1 N2O5\n",
      "r3 :  1 NO3          <=> 1 O2 + 1 NO\n",
      "r4 :  1 NO  + 1 N2O5 <=> 3 NO2\n",
      "r5 :  2 NO2          <=> 1 N2O4\n",
      "n_reactions = 6\n"
     ]
    }
   ],
   "source": [
    "'''Which reaction rates are these?'''\n",
    "\n",
    "from chen_3170.help import print_reactions\n",
    "\n",
    "print_reactions(sub_mechanism_1[1])\n",
    "print(sub_mechanism_1[0])\n",
    "print('')\n",
    "print_reactions(reactions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, let's compute $\\rvec_2$ for \n",
    "$\n",
    "\\Smtrx_2\\,\\Smtrx_2^\\top\\,\\rvec_2  = \\Smtrx_2\\,\\gvec .\n",
    "$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "species production rates g_vec = [0.51  0.365 0.306 0.67  0.468 0.915]\n",
      "reaction rates r_vec_2= [-0.158  0.341  0.303  0.088]\n",
      "residual norm g - ST_2 r_2 = 1.20229e+00\n"
     ]
    }
   ],
   "source": [
    "'''Compute the LS reaction rates for random species production rates'''\n",
    "\n",
    "# build A x = b LS problem\n",
    "a_mtrx = stoic_mtrx_2 @ stoic_mtrx_2.transpose() # A = S ST, A is the normal matrix\n",
    "b_vec  = stoic_mtrx_2 @ g_vec                    # b = S g\n",
    "\n",
    "from chen_3170.toolkit import lu_factorization # replace with your code\n",
    "\n",
    "# matrix LU factorization of A\n",
    "(P,L,U,s_rank) = lu_factorization( a_mtrx, 'partial' ) # matrix is full rank; partial pivoting works\n",
    "assert s_rank == np.linalg.matrix_rank(stoic_mtrx_2)\n",
    "\n",
    "from chen_3170.help import forward_solve\n",
    "from chen_3170.toolkit import backward_solve # replace with your code\n",
    "\n",
    "# solve the LS problem: A x = b\n",
    "y_vec = forward_solve( L, P @ b_vec )\n",
    "x_vec = backward_solve( U, y_vec )\n",
    "assert np.linalg.norm(x_vec - np.linalg.solve(a_mtrx,b_vec)) < 1e-12\n",
    "\n",
    "print('species production rates g_vec =',g_vec)\n",
    "\n",
    "r_vec_2 = x_vec # r_2 = x\n",
    "print('reaction rates r_vec_2=',r_vec_2)\n",
    "residual_vec_2 = g_vec - stoic_mtrx_2.transpose() @ r_vec_2\n",
    "print('residual norm g - ST_2 r_2 = %8.5e'%np.linalg.norm(residual_vec_2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r0 :  2 N2O5         <=> 2 N2O4 + 1 O2\n",
      "r1 :  1 N2O5         <=> 1 NO2  + 1 NO3\n",
      "r2 :  1 NO3          <=> 1 O2 + 1 NO\n",
      "r3 :  1 NO  + 1 N2O5 <=> 3 NO2\n",
      "n_reactions = 4\n",
      "(0, 1, 3, 4)\n",
      "\n",
      "r0 :  2 N2O5         <=> 2 N2O4 + 1 O2\n",
      "r1 :  1 N2O5         <=> 1 NO2  + 1 NO3\n",
      "r2 :  1 NO2 + 1 NO3  <=> 1 N2O5\n",
      "r3 :  1 NO3          <=> 1 O2 + 1 NO\n",
      "r4 :  1 NO  + 1 N2O5 <=> 3 NO2\n",
      "r5 :  2 NO2          <=> 1 N2O4\n",
      "n_reactions = 6\n"
     ]
    }
   ],
   "source": [
    "'''Which reaction rates are these?'''\n",
    "\n",
    "from chen_3170.help import print_reactions\n",
    "\n",
    "print_reactions(sub_mechanism_2[1])\n",
    "print(sub_mechanism_2[0])\n",
    "print('')\n",
    "print_reactions(reactions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the sub-mechanisms rates $\\rvec_1$ and $\\rvec_2$ are different, but the corresponding residuals $\\gvec - \\Smtrx_1^\\top\\,\\rvec_1$, and $\\gvec - \\Smtrx_2^\\top\\,\\rvec_2$, are equal!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r_vec_1 - r_vec_2             = [ 0.341 -0.379 -0.557 -0.77 ]\n",
      "g - ST_1 r_1 - (g - ST_2 r_2) = [-2.220e-16 -1.665e-16  0.000e+00  1.110e-16  0.000e+00  0.000e+00]\n"
     ]
    }
   ],
   "source": [
    "print('r_vec_1 - r_vec_2             =',r_vec_1 - r_vec_2)\n",
    "np.set_printoptions(precision=3)\n",
    "print('g - ST_1 r_1 - (g - ST_2 r_2) =',(g_vec-stoic_mtrx_1.transpose()@r_vec_1)-(g_vec-stoic_mtrx_2.transpose()@r_vec_2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Residuals of all sub-mechanisms<a id=\"residuals\"></a>\n",
    "Let us verify the previous residual result for all sub-mechanims. Here we will compute $\\Smtrx_k$ for $k=1,\\ldots,$# of full-rank sub-mechanisms and the corresponding LS reaction rates $\\rvec_k$ and residuals\n",
    "\n",
    "\n",
    "\\begin{equation*}\n",
    "\\gvec - \\Smtrx_k^\\top\\,\\rvec_k .\n",
    "\\end{equation*}\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rxns ids = (0, 3, 4, 5)\n",
      "       r = [ 0.18 -0.04 -0.25 -0.68]\n",
      "   ||r|| = 7.515e-01\n",
      "g - ST r     = [0.47 0.15 0.62 0.78 0.32 0.31]\n",
      "||g - ST r|| = 1.202e+00\n",
      "\n",
      "rxns ids = (0, 1, 3, 4)\n",
      "       r = [-0.16  0.34  0.3   0.09]\n",
      "   ||r|| = 4.910e-01\n",
      "g - ST r     = [0.47 0.15 0.62 0.78 0.32 0.31]\n",
      "||g - ST r|| = 1.202e+00\n",
      "\n",
      "rxns ids = (0, 1, 3, 5)\n",
      "       r = [-0.07  0.25  0.22 -0.18]\n",
      "   ||r|| = 3.827e-01\n",
      "g - ST r     = [0.47 0.15 0.62 0.78 0.32 0.31]\n",
      "||g - ST r|| = 1.202e+00\n",
      "\n",
      "rxns ids = (0, 1, 4, 5)\n",
      "       r = [ 0.15  0.04 -0.22 -0.61]\n",
      "   ||r|| = 6.611e-01\n",
      "g - ST r     = [0.47 0.15 0.62 0.78 0.32 0.31]\n",
      "||g - ST r|| = 1.202e+00\n",
      "\n",
      "rxns ids = (0, 2, 3, 4)\n",
      "       r = [-0.16 -0.34  0.3   0.09]\n",
      "   ||r|| = 4.910e-01\n",
      "g - ST r     = [0.47 0.15 0.62 0.78 0.32 0.31]\n",
      "||g - ST r|| = 1.202e+00\n",
      "\n",
      "rxns ids = (0, 2, 3, 5)\n",
      "       r = [-0.07 -0.25  0.22 -0.18]\n",
      "   ||r|| = 3.827e-01\n",
      "g - ST r     = [0.47 0.15 0.62 0.78 0.32 0.31]\n",
      "||g - ST r|| = 1.202e+00\n",
      "\n",
      "rxns ids = (0, 2, 4, 5)\n",
      "       r = [ 0.15 -0.04 -0.22 -0.61]\n",
      "   ||r|| = 6.611e-01\n",
      "g - ST r     = [0.47 0.15 0.62 0.78 0.32 0.31]\n",
      "||g - ST r|| = 1.202e+00\n",
      "\n",
      "rxns ids = (1, 3, 4, 5)\n",
      "       r = [ 0.18  0.15 -0.07 -0.32]\n",
      "   ||r|| = 3.994e-01\n",
      "g - ST r     = [0.47 0.15 0.62 0.78 0.32 0.31]\n",
      "||g - ST r|| = 1.202e+00\n",
      "\n",
      "rxns ids = (2, 3, 4, 5)\n",
      "       r = [-0.18  0.15 -0.07 -0.32]\n",
      "   ||r|| = 3.994e-01\n",
      "g - ST r     = [0.47 0.15 0.62 0.78 0.32 0.31]\n",
      "||g - ST r|| = 1.202e+00\n",
      "\n"
     ]
    }
   ],
   "source": [
    "'''Compute the LS residual for all full-rank reaction sub-mechanisms'''\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "sub_mech_rxn_rates_mtrx = np.zeros( (s_rank,len(sub_mechanisms)) )       # column-wise storage of all r_k's\n",
    "sub_mech_residuals_mtrx = np.zeros( (len(species),len(sub_mechanisms)) ) # column-wise storage of all g - ST_k r_k\n",
    "\n",
    "np.set_printoptions(precision=2)\n",
    "\n",
    "for sub_mech in sub_mechanisms:\n",
    "    \n",
    "    stoic_mtrx_k = sub_mech[2] # view of stoichiometric matrix for sub-mechanism\n",
    "  \n",
    "    # assemble LS problem matrix and right side\n",
    "    a_mtrx = stoic_mtrx_k @ stoic_mtrx_k.transpose()  # A = S ST, A is the normal matrix\n",
    "    b_vec  = stoic_mtrx_k @ g_vec                     # b = S g\n",
    "\n",
    "    # matrix LU factorization of A\n",
    "    (P,L,U,s_rank) = lu_factorization( a_mtrx, 'partial' ) # matrix is full rank; partial pivoting works\n",
    "    assert s_rank == np.linalg.matrix_rank(stoic_mtrx_k)\n",
    "\n",
    "    # solve the LS problem: A x = b\n",
    "    y_vec = forward_solve( L, P @ b_vec)  # L y = P b\n",
    "    x_vec = backward_solve( U, y_vec)     # U x = y\n",
    "    assert np.linalg.norm(x_vec - np.linalg.solve(a_mtrx,b_vec)) < 1e-12\n",
    "    \n",
    "    r_vec = x_vec  # r = x\n",
    "    sub_mech_rxn_rates_mtrx[:,sub_mechanisms.index(sub_mech)] = r_vec\n",
    "    \n",
    "    print('rxns ids =',sub_mech[0])\n",
    "    print('       r =', r_vec)\n",
    "    \n",
    "    rate_norm = np.linalg.norm(r_vec)\n",
    "    print('   ||r|| = %8.3e'%rate_norm)\n",
    "    \n",
    "    residual = g_vec - stoic_mtrx_k.transpose() @ r_vec\n",
    "    sub_mech_residuals_mtrx[:,sub_mechanisms.index(sub_mech)] = residual\n",
    "    print('g - ST r     =',residual)\n",
    "    print('||g - ST r|| = %8.3e'%np.linalg.norm(residual))\n",
    "    print('')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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sTEg0JVoGHOFpmosWczsW5SBCjYoeZikvSdWA7c1sqygxNRHoRWiq8gShZtKb7l7iJ3u5+5tmNpfQD9X1hJtk449kXkrFudZETYeaAQvSJC3TNreNZHOfZ0PB8ftq8gR3X2dmbwI7JU0qOG/3SXPetoheWxNqGBW1/vX88cTTRNMJtTX2KWIZmSroZP6+pPH/Bm6Jpl+epXVtECUMzol+3OhMSFT8KRp2A/5pZn9z9+ezsLoF7v5NivHTCc3R9gEwswb8kSxOdIu7b9Js0d2/jZp39TCzfoQmb3Uo/Nzan3AeWZrjpOCHjdYJ4w4kJIymFbLcZJucU+6+xsyWkOKcKuF17z1P3Rz9WzI7PktyvUt1rShIxs1OMa0gKZfY31nWr7MiUnEo8SQi5c3ZhP4FEq1j0xuJge5+XdTXURPCF/wLCf08HJviS92ThL4KviD0Z/ID4cYWwhOI0tXGSZUkKUh4pKvB8efo9bkSJJ3gj18Ta6WYNoDQD8ZhHp6KVlxbkOLXymxy95mEpi7Ahj6L/k34Qj2A0K9Epk5394eiX42bE5oNnEj4xT255k1Bwq6ojm/rJsTWj9BPzjLCl+ivCdvH+aPvl8Rjo6Bz6JS/ymfBVtFrytpuCeNTdVJdkmM1nf+6ewcAM2tI2Oa3EW442rn7j4mFS7Adi9KAkORJTn4lqwv86u4zzOzPhL5cTiLqx8fMPiHUTnu0kGUU5h5CEuEoQs2cd9z9oyLmKc61pmB//5BmWenGF8jmPs+Got7P4hTjCs7bfxax7LpFTIfQ5PeHFEnpguTBMlKfO8USnRPdCcf7pKTJDxGe/HimmQ3wze9bLSV3X0yoVXt/QkwjCTX07jOzHVNth2Iqaj8W7O8GpD5X7yF9f1l3EzrvP5mQpFtI6EsxnYLj5IBoSCfxONkKWFLMfZDuh5F1JJ1Tm3Hdy3gdqZTwepfqyXjrMphWfTPXKyKVhBJPIpIL+YRfHVN1Ir1ZX+rdPeWTdQopn0/oW6iXme1AuBn4FzCuoEyU+DiW8KvnMYlfxqOExpVkV1dCh6H/NrPq7p78i3hRCm7qG6aYti/hV9/X09QEOczCk5qWuvtGNZuimhhbUnStgaxy97fNrA+hplKRT/VLs4z1wGdm1oNQG+efZjbJ3RNvVAq+PHdJGp9StD0GEX713dfdf0iafmiK2QpuGBoT+g3JtoL3kK6z+O2TyuVc1ETzzqip5K2EpN9JBdNLuB2L8huw1t23LUacbxI6oq4J7Ee4qe0F/D8z+6E4zVITPEBoEnM3YZ9cXVjhElxrCvbjdmkWmW58aSm4vqf6PpnqWl/U+0l1XBfM08bd5xYjtlSWA9uYWdXk5o5RbdEGhCTB5jqTkFCoCaxJcy1uxB81X3PO3Zea2bmEJOkOhNp2BbUT80l/T1DYZ3ZR+/HXaN3z2fjhA5l4jpDAGkT48WhomiaqBQqOk5HunmlNsl8Jx0ONbCcAc3Tdy1iOrndldr0iUvapjycRyYWfCdeXVM3T9ivlWBJdQujDaJCZJf7qWdBU49k0zbNqZDmOrwm1nj4HJlh4ClpxFNwsbPI4ZsIN7YQUw+PR9MXR/w+mmLdgee8XM55sKGj+uFlNOaMbk4ujf0dGNd4KvB29ZvqFfztCIu6NFDcN9Ujd5KFgHUdnsPyCm6ji1Dx5L3o9PM30gvG5fppVKmMIndGeaBs/Wrwk27GobfM20MjMWqWZnpa7r3H3N919AOFJTkZ4MmWxRUm3pwg3xsuBon7RL9a1xt1/JiTOm5rZjimWV6xEfAkUtR8Kmvumii3Vtb7guDwseYKZVWPT2qxQ/PO2MO8REiypttvhhGMhG+dOQT9Rj5D6evxUNP28TWfNneiHmIK+rRKvtT8Tmqam2s+FfWbvnOa4PDx6fS/FtIxE58d9hHMrn9BvVWHeIdQkKs5x8jbhu0q6Phw3R0mue1mXzetdeViviJRdSjyJSC78L3rd6Eu1mXUiNMmJhbsvIHzpb0T4IlTgq+j18MTyZrYdoT+mXMSykHDzNQe4w8wuLmKWRNOj1wOTJ7j77e5+bvJAqPoO8Gk0rm/yvAnLe6UYsWTEzA40s3+Y2RYpptUA+kf/pup7pViiX1yfJ/yin9jB9NOEfd3HzFLeaJjZwWZW0ITxe2A10M7M6iTFezup+8gZR7hZH2RmmyQGzSwxGVtQs6I4nbm/RqhJdbiZHZe07FOAg4F5hEdal6oo6Tco+jexA/+SbMeitk1B58H3mNn2yRPNrG5i8svM/hzd7CUrqLFRkmapBa4k1KTs7AkdVqfxVfR6eOLIIq41DxASP8MtoeqMmTUldb852bQ0ek23H9Jd6/ci1HJI9jrh+D3SzLokTbuITft3gnDN/g0YYmabJEHMrKqZHZ4mvmQFyYsRidei6LgsOGYnZLislKKmRrsBH7n7qWmuxycRnuL2Fwud0meNmQ02s2Zppp1M6PB8KZBYe+x/hKTnGUnlz6XwZmvVgBuSjsvmhH2fxx8dUJfUKMK5dZS7f1VYQQ8duE8EDjSzK1Ml0cysRdK2KTjnbklzHUnXt2MmSnLdy4ocX+/K3HpFpHxQUzsRyYUJhNpFA81sH8KN8G6Ejk6fBv4WY2zDCH1cXGJmY919GeEm/W3gJDNrArxJaCrwV8LTsYrqR6VE3P2H6IbpRWCUmdV09xsymPUDQv8wHdI0ZyypToR+G5L7JMnELWaW7kvl1YRfrf8NjDWzNwjHxGpC07CjCV9MPyX00ZQN1xCOt0FmNtHd86I+XI4nJKWet9CR8fuEPjeaAu0IzfQaAavdfb2ZjSH0OfWRmU0iNJ05ktA3yKsk1dxw94/MrDeh9s/7ZvYsYV81jJa/jPBYbtz9VzObBRxhZg8RmjjmA8+4+8ep3pS755vZGYTOz580s2cI2203wq/JvxE6rI/r6UGPEfb3kWb2F3f/bwm3Y6Hbxt1fMLMBhKc3fm5m/wEWEPpv2Sla3ivAMdEiL4+WNZ3wxKgVwB6EY28ZRXQIXhgPT5f7OsPiJbnWjCDs29OA1mb2EqH500mEbXccfzR5y7a3COfpJWbWiD+a+Y728JCGpwjH9+lRImwmoTP0bsAzJDS5hA3H7zmE4/dZCx0Qf0mo/XEEocbmUUnzLDGzEwl9Y/0vev9zCbVbdiTUktqSzPp4epDQ1PlvwJzo/DFCcqMZ8EgW+qE5P3q9J12B6Jy4n9Cn3Xlktzl3wWfve4QOo38inGf7EZJI64DzPTzhsMBoQn8846MfiL4j7JMDgClAcpKwwPuE2mOzzewFQlPFk6L19SsqWVQUd19COI4ydQGhVuFwQh9abxA67t6e8EPEfoQfv76Olj/VzEYQHsTxSXQ8fEc4J9sTEqUlesphSa57WZSz610ZXa+IlAfurkGDBg1FDoQv+V6M8m0JT/ZaDvxOuAk8lPAlzoHTksp/B8xPGpeybBHrvS6aZ0AhZUZHZW5IGLcNcCfhC+lqwq/ywwidbRcrNkJS34GXksY/FI1vkjS+PuFm1IFrM3yfl0TlO2ZYvkVUfnqa6VtH7/uJYh4X3xUcG4UMexCe3PV3Qke3HxJuhtYRvoy+SfjCWqcY6y3YlmmPDeDZqMwFSeO3I3TuO4fwC+zvhGaPjxNqSFVN2peXERJlqwi/Yj9AuOFNuT+j+Q4hJFl/BNYS+vn4D9A9qdyuwORoO+QnvidCgirlsUx4MtPDUTx50euDQMtCzon2hRwX92S43QtieqmQMt2jMm9vznYsbNsklPkz8ES0fdcSbjLfI3Tou29Cuc7RsTeP0K/L74RmgaOBphm+94Lz+qsMy49IE3OxrjUJ5+eY6H2uiWK/mNA8z4Gb0pwfqY7NlMdVIev+K+H69Dt/nNNNEqY3JSQcfyacT+8QEk+FHb/tCMmn3wnJ0hcJSY7CjtVdCDUK50fb7ddoO/wb6FqMa0dVQo2c2VG8KwkJmguAKoVcazbZlmn206oovgZFlN0pOq6/B6qn2wcU83MwOieGE554+G10XqyIttV4YI9C5ns92h6/EvpY2iPVPkk4F14i/KjwMOHcWx1t11My3R9Jx59nWPZfhRxbNQk1AWdE72M14Vx7iVCrbpP9QkhQTyNca9ZE2+1JwlNwCz1vCjt/KOZ1jyKux9E+XVfU8UExrnep9m8mx16q7VGc9WrQoKHyDeYe14+iIiJSUmZWn1DTYLq7b3YNMjPrS2i+dLC7l3ozLREpPjO7gJCMOdfdN6uJmIiIiEiuKPEkIlJOWXgS3K2Emh0l7hDczGoTqsVPd/dTshWfiGSHme3g7ouSxjUj1BbcllCbYHHKmUVERERipj6eRETKr3GEvk22Z/OeRLczoelPUU8NEpF4PBv13/wu8AvhnD2G0DzvMiWdREREpCxTjScRERGRMizqsP5UwhPJ6hH6TnkXuN3di9P5soiIiEipU+JJRERERERERERyokrcAYiIiIiIiIiISMWkxJOIiIiIiIiIiOSEEk8iIiIiIiIiIpITSjyJiIiIiIiIiEhOKPEkIiIiIiIiIiI5ocSTiIiIiIiIiIjkhBJPIiIiIiIiIiKSE0o8iYiIiIiIiIhITijxJCIiIiIiIiIiOaHEk4iIiIiIiIiI5IQSTyIiIiIiIiIikhNKPImIiIiIiIiISE4o8SQiIiIiIiIiIjmhxJOIiIiIiIiIiOSEEk8iIiIiIiIiIpITSjyJiIiIiIiIiEhOKPEkIiIiIiIiIiI5ocSTiIiIiIiIiIjkhBJPIiIiIiIiIiKSE0o8iYiIiIiIiIhITijxJCIiIiIiIiIiOaHEk4iIiIiIiIiI5IQSTyIiIiIiIiIikhPV4g4gl7bZZhvfaaed4g4jK9auXUuNGjXiDkNioH1feWnfV17a95WT9nvlpX1feWnfV17a95VXRdn3s2fP/sndG2VStkInnnbaaSdmzZoVdxhZ8dVXX1FRkmhSPNr3lZf2feWlfV85ab9XXtr3lZf2feWlfV95VZR9b2ZfZ1pWTe1ERERERERERCQnlHgSEREREREREZGcUOJJRERERERERERyQoknERERERERERHJCSWeREREREREREQkJ5R4EhERERERERGRnFDiSUREREREREREckKJp3JgxYoVXHTRRaxcuTLuUEREREREREREMqbEUzkwY8YMJk2axIwZM+IORUREREREREQkY0o8lQMvvfTSRq8iIiIiIiIiIuVBqSeezKyzmX1qZvPN7IoU00eZ2fvR8JmZ/ZIwbX3CtEmlG3l8pkyZAsDkyZNjjkREREREREREJHOlmngys6rAWOBoYHegh5ntnljG3fu6+97uvjdwO/BUwuRVBdPcvWupBV6KunXrhpltNHz22WcAfPbZZ5tM69atW8wRi4iIiIiIiIikVto1nvYH5rv7l+6+FpgIFJY56QH8v1KJrIwYPnw4TZs2pVatWhvGrV27dqNXgFq1atGsWTOGDx9e6jGKiIiIiIiIiGSitBNPjYFvE/7/Lhq3CTNrBuwMvJwwupaZzTKzt83suNyFGZ82bdowd+5cunbtSu3atVOWqV27Nt26dWPOnDm0adOmlCMUEREREREREclMaSeeLMU4T1P2FOAJd1+fMK6pu+8H/B241cyab7ICs/Oj5NSsJUuWbH7EMahTpw6PPvooQ4YMYYsttthoWq1atRgyZAgTJ06kTp06MUUoIiIiIiIiIlK00k48fQfsmPB/E2BRmrKnkNTMzt0XRa9fAtOBfZJncvfx7r6fu+/XqFGjbMQcmy+++IL169djZtSsWRMIze2+/PLLmCMTERERERERESlaaSeeZgItzWxnM6tBSC5t8nQ6M2sFbA3MSBi3tZnVjP7eBjgEmFsqUcfg+++/55577gGgadOm3HbbbdSrV4/8/HzGjx/P4sWLY45QRERERERERKRwpZp4cvd1QC9gGjAPeMzd55jZEDNLfEpdD2Ciuyc2w2sNzDKzD4BXgBHuXmETT0OHDiUvL4/u3bszZ84cOnXqxGeffcYWW2zBunXrGDx4cNwhioiIiIiIiIgUqlppr9DdpwJTk8Zdk/T/oBTzvQW0zWlwZcjKlSuZMGECZ599NgBLlixhu+2248EHH+SEE05g9uzZMUcoIiIiIiIiIlKPK1+XAAAgAElEQVS4Uk88SWbuv//+lOOPP/54jjrqKN566y2+//57tt9++9INTEREREREREQkQ6Xdx5NsJjPj9ttvZ82aNVx//fVxhyMiIiIiIiIikpZqPJVDLVu2ZMqUKRx00EFxhyIiIiIiIiIikpYST+VUhw4dAFi9ejVVq1alevXqMUckIiIiIiIiIrIxNbUrx5YtW0bbtm0ZNWpU3KGIiIiIiIiIiGxCiadyrEGDBhxzzDH86U9/ijsUEREREREREZFNqKldOafaTiIiIiIiIiJSVqnGUwWwatUq+vfvz7Rp0+IORURERERERERkAyWeKoAqVarwzDPP0KtXL1avXh13OCIiIiIiIiIigBJPFULNmjUZM2YM8+fPZ+TIkXGHIyIiIiIiIiICKPFUYXTs2JGTTjqJ4cOHs2DBgrjDERERERERERFR4qkiueWWW6hWrRp9+vSJOxQRERERERERESWeKpLGjRszaNAgJk+ezKRJk+IOR0REREREREQqOSWeKpg+ffrQpk0b+vTpw8qVK+MOR0REREREREQqMSWeKpjq1aszbtw4vv76a4YPHx53OCIiIiIiIiJSiSnxVAH9+c9/5vTTT+frr7/G3eMOR0REREREREQqqWpxByC5MWHCBKpXrx53GCIiIiIiIiJSianGUwVVkHSaN28er7zySszRiIiIiIiIiEhlpBpPFZi7c9ZZZ7FixQo+/PBDzCzukERERERERESkElHiqQIzM+6//34aNmyopJOIiIiIiIiIlDolniq43XbbDYD8/Hx+/vlnGjZsGHNEIiIiIiIiIlJZKPFUSRx77LH8/vvvTJ8+XbWfRERERERERKRUqHPxSuK4447jtdde46GHHoo7FBERERERERGpJJR4qiTOOeccDjjgAC699FJ++eWXuMMRERERERERkUpAiadKokqVKowbN46ffvqJgQMHxh2OiIiIiIiIiFQCSjxVIvvuuy8XXHAB48aN49133407HBERERERERGp4JR4qmSuu+46ttlmG3r27El+fn7c4YiIiIiIiIhIBabEUyVTv359Ro4cyTvvvMO9994bdzgiIiIiIiIiUoEp8VQJnX766Rx66KFcccUVLFu2LO5wRERERERERKSCqhZ3AFL6zIxx48bxxhtvsNVWW8UdjoiIiIiIiIhUUEo8VVJ77LEHe+yxBwDujpnFHJGIiIiIiIiIVDRqalfJTZw4kaOOOor169fHHYqIiIiIiIiIVDClnngys85m9qmZzTezK1JMH2Vm70fDZ2b2S8K0M8zs82g4o3Qjr5iqVKnCmjVr1NeTiIiIiIiIiGRdqTa1M7OqwFigI/AdMNPMJrn73IIy7t43oXxvYJ/o7wbAtcB+gAOzo3l/LsW3UOGceOKJnHjiiWpqJyIiIiIiIiJZV9o1nvYH5rv7l+6+FpgIdCukfA/g/0V/HwW86O7LomTTi0DnnEZbCZgZZsaiRYu488474w5HRERERERERCqQ0k48NQa+Tfj/u2jcJsysGbAz8HJx5jWz881slpnNWrJkSVaCrgzuvPNOLrjgAl5//fW4QxERERERERGRCqK0E0+p2nN5mrKnAE+4e0Gv1xnN6+7j3X0/d9+vUaNGJQyz8rniiito1qwZPXv2JC8vL+5wRERERERERKQCKO3E03fAjgn/NwEWpSl7Cn80syvuvFJMtWvXZvTo0Xz88cfcfvvtcYcjIiIiIiIiIhVAaSeeZgItzWxnM6tBSC5NSi5kZq2ArYEZCaOnAZ3MbGsz2xroFI2TLOnatStdunTh2muvZeHChXGHIyIiIiIiIiLlXKkmntx9HdCLkDCaBzzm7nPMbIiZdU0o2gOY6O6eMO8yYCgheTUTGBKNkywxM2677TbWrVtHv3794g5HRERERERERMq50q7xhLtPdfdd3b25uw+Lxl3j7pMSygxy9ytSzHuvu7eIhvtKM+7KYpddduHKK6/kscce46WXXoo7HBEREREREREpx0o98SRl3+WXX07z5s258MILWbNmTdzhiIiIiIiIiEg5pcSTbKJWrVqMGTOGL7/8kjfeeCPucERERERERESknKoWdwBSNnXu3JkvvviCpk2bxh2KiIiIiIiIiJRTqvEkaRUknT744IOYIxERERERERGR8kiJJynUs88+y9577820adPiDkVEREREREREyhklnqRQRx99NLfeeiuHHXZY3KGIiIiIiIiISDmjPp6kUDVq1OCiiy4CID8/nypVlKsUERERERERkcwoiyAZmTlzJrvvvjvz58+POxQRERERERERKSeUeJKMNGnShEWLFtG7d2/cPe5wRERERERERKQcUOJJMrL99tszZMgQnn/+eZ5++um4wxERERERERGRckCJJ8lYr1692HPPPbn44otZsWJF3OGIiIiIiIiISBmnxJNkrFq1aowbN45vv/2WoUOHxh2OiIiIiIiIiJRxSjxJsRxyyCGcddZZ3HzzzcybNy/ucERERERERESkDFPiSYrthhtuYMstt+TCCy9UR+MiIiIiIiIikpYST1JsjRo1Yvjw4bzyyitMnDgx7nBEREREREREpIyqFncAUj6dd955vPLKKzRq1CjuUERERERERESkjFLiSUqkatWqPProo3GHISIiIiIiIiJlmJrayWZZuXIlAwcO5IMPPog7FBEREREREREpY1TjSTbL6tWrueuuu6hTpw577bVX3OGIiIiIiIiISBmixJNslgYNGjB37ly22WabuEMRERERERERkTJGTe1ksxUknT788EOWLVsWczQiIuXbihUruOiii1i5cmXcoYiISA7pei8ilYUST5IVP/zwA+3atePqq6+OOxQRkXJtxowZTJo0iRkzZsQdioiI5JCu9yJSWWSceDKz1mY20MzGm9kDScO/cxmklH3bbbcdF1xwAXfddRczZ86MOxwRkXLrpZde2uhVREQqJl3vRaSyyCjxZGb/AD4CrgG6AIemGKSSGzx4MNtttx09e/Zk/fr1cYcjIlIuTZkyBYDJkyfHHImIiOSSrvciUllkWuNpIPAs0MjdG7v7zknDLjmMUcqJrbbaiptvvplZs2Zx9913xx2OiEiZ161bN8xso+Gzzz4D4LPPPttkWrdu3WKOWERESkLXexGpzDJNPP0fMM7df8llMFL+9ejRg8MPP5yrrrqKJUuWxB2OiEiZNnz4cJo2bUqtWrU2jFu7du1GrwC1atWiWbNmDB8+vNRjFBGRzafrvYhUZpkmnt4EWucyEKkYzIyxY8eyfPly+vfvH3c4IiJlWps2bZg7dy5du3aldu3aKcvUrl2bbt26MWfOHNq0aVPKEYqISDboei8ilVmmiadewPlm1sPMGppZleQhl0FK+bL77rvTt29f7rvvPt588824wxERKdPq1KnDo48+yimnnLLJtOrVqzNkyBAmTpxInTp1YohORESypeB6P2TIELbYYouNptWqVUvXexGpsDJNGH0HvAc8BPwI5CUNa9PPKpXRNddcQ5MmTbjyyivjDkVEpFwo6FzWzDY0xcjLy+OFF16IMywREcmyV199lfXr1290vV+zZg1ffvllzJGJiORGpomnu4EewDPACGBI0jA0J9FJuVW3bl0ef/xxHnvssbhDEREp877//nt+/vlnqlevTtOmTRk9ejQ77rgjZsaLL77I4sWL4w5RRESy4JNPPuG5554jLy9vw/W+fv36uDt33XWXrvciUiFlmnjqBlzm7n9z96vdfXDykMsgpXw68MAD+b//+z/y8/NZsWJF3OGIiJRJq1atYsiQIeTl5XH88cczZ84cOnXqxLx58+jevTvuztChQ3H3uEMVEZHNVNCsumPHjhuu9wsWLKBevXqsX7+ea6+9NuYIRUSyL9PE0wpgbjZWaGadzexTM5tvZlekKXOSmc01szlm9kjC+PVm9n40TMpGPJJb+fn5dOrUifPPPz/uUEREyqQrr7ySJ554gvHjx2/Ut0edOnV48sknmTBhAj/++CPt27fno48+ijlaEREpqS+++IIPP/yQQw45hGnTpm243tevX59nn30WgHfeeSfOEEVEcqJahuXuA/4OvLg5KzOzqsBYoCOh36iZZjbJ3ecmlGkJXAkc4u4/m9m2CYtY5e57b04MUrqqVKnCX//6V+rXrx93KCIiZdL+++9PvXr1OO+881JOP/vssznyyCPp0qULv/zySylHJyIi2XL55ZdTu3btlF1RHH744fz973/nySefZP78+bRo0SKGCEVEciPTxNPXQA8zexF4Hvg5uYC735vBcvYH5rv7lwBmNpHQjC+xNtV5wFh3/zla7o8ZxihlVL9+/eIOQUSkzPr73/9eZJmddtqJDz/8kKpVqwKhE9qaNWvmOjQREcmSV199laeeeoqhQ4eyww47pCwzcuRInnvuOfr06cOUKVMws1KOUkQkNzJtancH0Az4CzASuCdpuDvD5TQGvk34/7toXKJdgV3N7E0ze9vMOidMq2Vms6Lxx2W4TikD3J0xY8YwduzYuEMRESkTpk+fzs0338zatZk9GLYg6XTbbbfRrl07li1blsvwREQkS/Lz8+nXrx877rgjl1xySdpyO+ywA4MHD+Y///kPzzzzTClGKCKSW5kmnnYuYtglw+WkStsn95ZaDWgJHE54kt49ZlbQTqupu+9HaPZ3q5k132QFZudHyalZS5YsyTAsybWCJzNdfvnlfPvtt0XPICJSga1fv54+ffowZswY8vPzizVvmzZt+PTTT+nSpYse3CAiUg488MADvPvuu4wYMYItttii0LK9e/embdu2DBw4UA+VEJEKo8jEk5lVB/YGqrj71+mGDNf3HbBjwv9NgEUpyjzr7nnuvgD4lJCIwt0XRa9fAtOBfZJX4O7j3X0/d9+vUaNGGYYlpWH06NG4O3379o07FBGRWE2YMIGPPvqIG2+8kVq1ahVr3r/85S9MnDiR//3vfxx//PGsWbMmR1GKiMjmWrduHYMGDeKAAw6gR48eRZavVq0aDz/8MNOmTVNTOxGpMIpMPLl7HvAYsFMW1jcTaGlmO5tZDeAUIPnpdM8ARwCY2TaEpndfmtnWZlYzYfwhZOlJe1I6dtppJwYMGMCTTz7JtGnT4g5HRCQWv/32GwMHDqR9+/accMIJJVpG9+7dueeee3jhhRc4/fTTWb9+fZajFBGRbKhWrRrTpk3j7rvvzjiR1LZtWxo3boy789tvv+U4QhGR3Mu0c/EvgW2LLFUEd19nZr2AaUBV4F53n2NmQ4BZ7j4pmtbJzOYC64HL3H2pmR0M3GVm+YSE2YjEp+FJ+XDJJZfw73//m169evHRRx8V+5d+EZHybvjw4fz444+b3XHsWWedxbJly7j00kupX78+d911l34dFxEpQ/Ly8qhevTqtWrUq0fzdu3dn1apVPP/887q+i0i5lmni6UbgajN72d03q+Mkd58KTE0ad03C3w70i4bEMm8BbTdn3RK/mjVrMnbsWDp27MjIkSMZOHBg3CGJiJSaBQsWMGrUKP7xj3+w3377bfbyLrnkEpYtW8bw4cNp2LAh119/fRaiFBGRbDjrrLPIz8/n4YcfLlHiqGvXrqxbty4HkYmIlK5ME09HAg2ABWb2NvA9G3cK7u5+RraDk4qpQ4cOnHTSSQwfPpzTTjuNnXfeOe6QRERKRf/+/alWrRrDhw/P2jKvu+46li5dyogRI9h2223Vj56ISBng7rRp0wZ3L3FtpbPPPjvLUYmIxCPTxFN7IA9YAjSPhkR65IIUyy233MLUqVPp06cPzz33XNzhiIjk3BtvvMHjjz/OoEGDaNy4cdaWa2aMHTsWM6N9+/ZZW66IiJScmXHllVdmZVnjx4/np59+4qqrrsrK8kRESluRnYsDuPvORQy75DpQqVgaN27MoEGDWLZsGcuXL487HBGRnJs4cSKNGzfm0ksvzfqyq1atyh133EG7du0A+OKLL7K+DhERycyUKVN4/PHHCT2IbL4ZM2Zw7bXXMm/evKwsT0SktGWUeBLJhYsvvpjXX3+dLbfcMu5QRERy7vbbb+ftt9+mTp06OV3PvffeS+vWrZk9e3ZO1yMiIptatWoVPXv2ZNiwYeTn52dlmTfccAN169alV69eWUtmiYiUpowTT2ZW28x6mdnjZvZfM3vMzHqaWe1cBigVV9WqValSpQo//PADTz75ZNzhiIjkxMqVK1m0aBFmRpMmTXK+vu7duzNgwAD22muvnK9LREQ2NmrUKL755htGjRpF1apVs7LMbbfdlmHDhvHyyy/z2GOPZWWZIiKlKaPEk5n9H/AucBuwH1AbaAeMAWab2XY5i1AqvGuuuYYzzzyTX375Je5QRESy7qabbmLXXXfl+++/L5X1bb311lxzzTVUq1aNRYsWMXfu3FJZr4hIZbd48WKuv/56jjvuOI444oisLvuf//wn++67L/369VM3FSJS7mRa4+lGYGvg0KhPp4PcfWdCp+P1gRtyFaBUfEOHDmXWrFnUr18/7lBERLLu1FNP5brrrmP77bcv1fW6OyeffDIdOnRgwYIFpbpuEZHKaMCAAaxZs4aRI0dmfdlVq1Zl3LhxLFq0iMGDB2d9+SIiuZRp4ulo4Ep3fzNxpLu/BQwAumQ7MKk8tt12W1q1agXAkiVLYo5GRCS7mjdvzsUXX1zq6zUz7rjjDlavXk3Hjh1ZvHhxqccgIlJZvP/++9x777307t2bFi1a5GQdBxxwAOeeey633norH3/8cU7WISKSC5kmnuoCi9JM+y6aLrJZrrrqKvbee29VHxaRCmHWrFkcc8wxLFy4MLYY9thjD6ZOncrixYs56qij1KRZRCQH3J1+/frRoEEDBg4cmNN1XX/99Wy11VZceOGF6mhcRMqNTBNPnwKnp5l2GvBJdsKRyuzYY49V9WERqRDcnYsvvpiZM2fG/uTOAw88kKeffpp58+bRpUsXVqxYEWs8IiIVzaRJk3jllVcYPHhwzruO2Gabbbj++utZvXo1y5Yty+m6RESyJdPE001ADzN7yczONrOjzewsM5sG/B3IfkNmqXQOOuggVR8WkQrhiSee4M0332To0KHUq1cv7nDo2LEjjzzyCG+//TYnnHACa9eujTskEZEKY/z48bRu3Zp//vOfpbK+c889lxkzZtCwYcNSWZ+IyObKKPHk7g8B/wL2AO4BpgATgD2Bf7n7IzmLUCoVVR8WkfJu9erVXH755bRt25Zzzjkn7nA2OOGEE7jrrrt4/vnnOeOMM1i/fn3cIYmIVAhPP/00kydPplq1aqWyvipVqlClShWWLFnCo48+WirrFBHZHJnWeMLdxwM7AG2AQ6PXxu5+d45ik0pom222YcSIEbz22ms89NBDcYcjIlJso0eP5quvvuKWW26hatWqcYezkXPPPZcbb7yRiRMn8vDDD8cdjohIufbrr7+yYsUKatSowS677FLq6x8+fDhnnnmmHs4jImVexoknAHfPd/d57v5m9Jqfq8Ck8jrnnHM44IADuPTSS9URroiUKz/88APDhg3jmGOOoUOHDnGHk9Jll13GpEmTOO200+IORUSkXBswYAC77747K1eujGX9AwcOZPbs2TRq1CiW9YuIZCptfVAz+3NxFuTur21+OCKh+vC4ceNo164dAwcO5Pbbb487JBGRjFxzzTWsWrWKm266Ke5QCnXssccC8NVXX/Hyyy9z9tlnxxyRiEj506NHD3bZZRdq164dy/obNGhAgwYNAFiyZIkSUCJSZhXWEHk6kK6THYtePeG1dBo1S6Ww7777csEFFzBu3DjOPvts9tlnn7hDEhEp1EcffcQ999xDr169aNWqVdzhZOSmm27ikUceoVu3buqkVkSkmA4++GAOPvjguMNgyJAhjB07lk8//TTnT9UTESmJwpradQQ6pRk6Al2BFwhJKPVQKll33XXXMWjQoHJzAycilduHH37IDjvswLXXXht3KBm7+eabefvtt5V0EhEphhdeeIELLriA3377Le5QgFCL9aeffmLgwIFxhyIiklLaxJO7/zfVQKgJ1QK4g5CAegRoXSrRSqVSv359Bg4cSO3atfWEOxEp80499VS++OKLDc0eyoOaNWuy66674u5cf/31/Pe//407JBGRMm3dunX07duXF198kZo1a8YdDgD77LMPPXv2ZNy4cbz33ntxhyMisolidS5uZqcBnxKSTrOBvd39NHf/MhfBiQC89dZbHHTQQSxdujTuUERENpGXl8fUqVNxd2rUqBF3OCWyatUqHnnkEY477jhmzpwZdzgiImXW3Xffzdy5c7nxxhvLTOIJYOjQoTRs2JCePXuSn6/nP4lI2ZJR4snMupvZR8ADwFfAge5+nLt/nMvgRADq1avHihUrWLRoUdyhiIhs4qGHHqJLly688cYbcYdSYrVr1+aFF16gUaNGHH300cydOzfukEREypxffvmFa665hsMOO4zu3bvHHc5G6tevz8iRI3n77be5//774w5HRGQjhSaezKyTmf0PeBL4Hejg7h3c/X+lEp0IsMcee/Dhhx/Stm3buEMREdnE6aefzlNPPUX79u3jDmWzbL/99rz44otUr16dTp068fXXX8cdkohImTJs2DCWLl3KLbfcgpkVPUMp+8c//kH79u3p378/y5YtizscEZEN0iaezGw68B+gBtDN3Q9y95dLKzCRRGbG77//zs0338z69erLXkTKhry8PKpVq0b37t3L5E1IcTVv3pwXXniBFStW0LFjR3744Ye4QxIRKRO++OILRo8ezRlnnMG+++4bdzgpmRljx47l559/ZsCAAXGHIyKyQWE1nv5MeGLdNsBYM/umkEE/i0rOTZs2jUsvvZQ77rgj7lBERPj000/Zeeedee211+IOJavatm3LlClTWLhwIZ07d+bXX3+NOyQRkdhdfvnl1KhRg2HDhsUdSqH23HNPevXqxZ133sns2bPjDkdEBIBqhUx7ANCjxKTMOP744+nQoQMDBgzgxBNPZLvttos7JBGpxC677DJ+++03WrVqFXcoWXfwwQfz1FNPceyxx3Lsscfy/PPPU7t27bjDEhGJxauvvspTTz3FkCFD2GGHHeIOp0iDBw+mfv36FfLzSUTKp7SJJ3c/sxTjECmSmTFmzBjatm3LZZddxgMPPBB3SCJSSb300ks899xzjBgxosImwY866igefPBB+vbty7fffqsbGBGptN566y2aNWvGJZdcEncoGdlqq60YNGhQ3GGIiGyQ0VPtRMqKVq1acemll/Lggw9WuOYtIlI+rF+/nn79+rHTTjtx0UUXxR1OTp188sl89tlnG5JO7qoILSKVz5VXXsnHH39c7mp+vvPOOxxyyCH89NNPcYciIpWcEk9S7lx99dU0bdqUnj17kpeXF3c4IlLJTJgwgY8++ogbb7yRWrVqxR1OztWtWxd3p3///vTu3VvJJxGpNH7//XdmzZoFhGtheVO3bl2WLVvGd999F3coIlLJKfEk5U6dOnUYPXo0c+bM4bbbbos7HBGpRH777TcGDhxI+/btOeGEE+IOp1Tl5+ezfv16JZ5EpNIYPXo0+++/P/Pnz487lBJp06YNc+bMYe+99447FBGp5ArrXFykzOrWrRt//etfGTRoEKeccgqNGzeOOyQRqQSGDx/Ojz/+yOTJkzGzuMMpNWbGjTfeuOHvlStXlrsmJyIixdW7d2922WUXWrRoEXcoJValShVWrFjBhAkTuPDCC6latWrcIYlIJaQaT1IumRm33XYb69at48knn4w7HBGpBBYsWMCoUaM4/fTTadeuXdzhlDozw8z46quvaN26tR7wICIVWn5+PvXq1aNHjx5xh7LZnn/+eS666CLGjx8fdygiUkkp8STlVvPmzfnkk0/o06dP3KGISCWwfPlyDjjgAIYPHx53KLHafvvtadmyJWeffTbPPvts3OGIiGTdO++8w5577sknn3wSdyhZcfzxx3PkkUdy1VVXsWTJkrjDEZFKKOPEk5nVMbM+ZvaEmb1iZi2j8aeY2W7FWE5nM/vUzOab2RVpypxkZnPNbI6ZPZIw/gwz+zwazsh0nVJxNWvWDIB58+axZs2amKMRkYpszz335LXXXqNJkyZxhxKrmjVr8swzz/CnP/2Jk08+menTp8cdkohI1rg7ffv2ZenSpRXmem9mjBkzht9//53+/fvHHY6IVEIZJZ7MbEfgQ2Ak0BL4M7BlNPkI4NIMl1MVGAscDewO9DCz3ZPKtASuBA5x9zbAxdH4BsC1wAHA/sC1ZrZ1JuuViu3zzz9nzz33ZPTo0XGHIiIVUH5+PiNHjmTp0qVxh1Jm1K1bl6lTp9K8eXO6du3K7Nmz4w5JRCQrHn30UWbMmMGwYcPK5ZPs0mndujX9+vXjvvvu46233oo7HBGpZDKt8XQzsIaQdPoTkNij6quERFQm9gfmu/uX7r4WmAh0SypzHjDW3X8GcPcfo/FHAS+6+7Jo2otA5wzXKxVYy5YtGT16NGeddVbcoYhIBTRr1iyuuOIKpk6dGncoZUrDhg154YUXaNiwIZ07d64wTVJEpPJatWoV/fv3Z++99+aMMype44qBAwfSpEkTevbsybp16+IOR0QqkUwTTx2Ba939GyD5OcoLgUwfKdYY+Dbh/+9SzLsrsKuZvWlmb5tZ52LMK5VUz549adSoEfn5+XGHIiIVzP7778/cuXM59dRT4w6lzGncuDEvvvgiVatWpWPHjnzzzTdxhyQiUmKjRo3im2++YdSoURXy6W9169Zl1KhRfPDBB9xxxx1xhyMilUimiacawPI007YC8jJcTqpnTycnsqoRalYdDvQA7jGz+hnOi5mdb2azzGyWOs+rXBYuXMiBBx7IlClT4g5FRCqI77//HoBWrVpRpYqex5FKixYtmDZtGsuXL6djx478+uuvcYckIlJsixcv5vrrr+e4447j8MMPjzucnJjqdtoAACAASURBVPnb3/5Gx44dGTBgAD/88EPc4YhIJZHpt+gPgb+lmXY0kGnnDt8BOyb83wRYlKLMs+6e5+4LgE8JiahM5sXdx7v7fu6+X6NGjTIMSyqCRo0a8fvvv9O7d29WrVoVdzgiUs4tXLiQli1bctttt8UdSpm31157MXnyZE488UTq1asXdzgiIsU2YMAA1qxZw8iRI+MOJacKOhpfvXo1jz32WNzhiEglkWniaSRwjpndzR/9Oe1uZoOBc6LpmZgJtDSznc2sBnAKMCmpzDOEDssxs20ITe++BKYBncxs66hT8U7ROBEAatSowdixY1mwYAEjRoyIOxwRKeeuuuoq8vLyOOaYY+IOpVxo37491113HWbGggUL9AOAiJQb77//Pvfeey+9e/emRYsWcYeTc7vuuitz586ld+/ecYciIpVERoknd38K6AmcCLwUjX6A8MS5Xu7+fIbLWQf0IiSM5gGPufscMxtiZl2jYtOApWY2F3gFuMzdl7r7MmAoIXk1ExgSjRPZ4IgjjqBHjx7ccMMNzJ8/P+5wRKScmjVrFg888AB9+/Zll112iTuccmX58uUcfPDBXHDBBXGHIiKSkZ9++om9996bgQMHxh1KqWnevDkA8+fPJy8v015TRERKJuMOK9z9TkJn3kcBpxGa2DVx9/HFWaG7T3X3Xd29ubsPi8Zd4+6Tor/d3fu5++7u3tbdJybMe6+7t4iG+4qzXqk8br75ZmrUqEHv3r1x36QbMBGRQrk7ffv2Zdttt+Wqq66KO5xyZ8stt2TEiBFcccUVcYci/5+9O4+zuWz8P/66Zif7miVb9j0NLZZKKJGlzfINU6IYhrFGMnbGNiahbElUEiVREYpIlpQlSdGdkETKMpaZuX5/GH7ubnQwM9c5Z97Px+M8nPP5nGNe9y3HnGuuz3WJiEfq1avH5s2byZEjh+uUdLVz507Kly/P5MmTXaeIiJ/zaODJGNPWGJPbWnvSWvuptfZNa+0n1trjxphcxpi2aR0q4qkCBQowdOhQPv74Y9577z3XOSLiYxYsWMAXX3zB0KFDtV7RdWrXrh1ly5bFWsuSJUv0QwAR8Upnz55lypQpnDlzBmMut4+RfytbtiyjRo2iZcuWrlNExM95OuPpNeDWK5wrnnJexGtERkZSpUoVunfvzsmTJ13niIiPOH36NH369KFSpUq0b9/edY7PW7hwIY0bN2bo0KGuU0RE/seHH35I586d+fzzz12nOGGMoUePHuTPn18/IBCRNOXpwNPVfgRwE5CYCi0iqSYoKIjJkyezb98+feAREY/Fx8ezd+9exo8fT2BgoOscn9e8eXPatWtHTEwMEydOdJ0jIvJfHnnkEb766ivq16/vOsWpffv2UatWLT777DPXKSLip4KudMIYUxWodsmhh40xFf/xtEyc35ludxq0idyQu+++mx49elCqVCnXKSLiAw4dOsTw4cNp3Lgx9erVc53jFwICApg+fTrHjh0jKiqKXLly8X//93+us0REOHbsGDly5KBGjRquU5zLkycPBw4cIDIykm+++Ybg4GDXSSLiZ6448AQ0BWJS7lvghSs87wig6xHEK40bN851goj4iLCwMDp27EiHDh1cp/iVoKAg3n77bR566CHatWtH9uzZady4sessEcnAdu7cSXh4OHPmzKF58+auc5zLlCkTL730Ek2aNCE+Pp5evXq5ThIRP3O1S+0mcH79phKcv9TukZTHl94KAvku7Egn4o2Sk5OZOnUqCxcudJ0iIl4se/bsjB07ljJlyrhO8TthYWEsWrSI2267jccff5zVq1e7ThKRDKxXr14EBwdTq1Yt1yle4+GHH+bhhx9m0KBB/Prrr65zRMTPXHHgyVr7l7X2P9banzk/yLQ05fGlt9+sVqITL2etZdq0acyfP991ioh4IWstXbt21doWaSxr1qx89NFHFCtWjIcffpgtW7a4ThKRDGjZsmUsXbqUAQMGkDdvXtc5XiU+Pp6kpCTNeBKRVOfR4uIpg0xn0zpGJC0EBgby8ccf8+abb7pOEREvdPjwYT788EO2bt3qOsXv5cmTh+XLl5MjRw7at2+vXZREJF0lJibSo0cPbr31Vrp27eo6x+sUL16cfv36MW/ePFasWOE6R0T8yNXWePovxpiOQCegDBD6z/PWWm3/I14rd+7cAOzfv59Tp05pwXERuShfvnzs3LlTu9ilk8KFC7N8+XJCQkIw5mqb5oqIpK7p06ezY8cOFixYQGjo/3ycEaBPnz7Mnj2byMhItm7dSkhIiOskEfEDHs14Msa0BSYCG4Ew4DVgDvA38BMwJK0CRVJLUlIStWvXJiIiguTkZNc5IuIFNm7cSEJCAmFhYdrFJx2VLl2aYsWKkZyczMiRI/njjz9cJ4mInzt27Bgvvvgi99xzjxYUv4qwsDAmTpzIrl27GD9+vOscEfETHg08Ad2BkZyf8QQw2VrbjvMLjydwfmc7Ea8WGBjIgAEDWLduHa+//rrrHBFx7OjRozzwwAN07NjRdUqG9f333zNkyBBdCi0iaW748OEcOXKE8ePHa7blv2jYsCERERHkyZPHdYqI+AlPL7UrBawGklNuIQDW2j+NMcOB4cDLaVIokooiIiKYPn06ffr0oWnTpuTKlct1kog4MmTIEP766y/69OnjOiXDKl++PFu3bqVkyZKuU0TEj/3000/Ex8fTrl07qlWr5jrHJ7z22muuE0TEj3g64ykBCEjZwe43zs90uuAEUDC1w0TSQkBAAJMnT+bo0aO88MILrnNExJFdu3YxadIknnnmGSpVquQ6J0MrVaoUxhi2bdvGs88+S2JiouskEfEzISEhPPHEEwwfPtx1ik9JTk5m5syZWmhcRG6YpwNP24ALP45cA/Q3xtxljKkODAK+T4M2kTRRtWpVunTpwquvvsrGjRtd54iIA7179yZTpkwMGaIlCr3FunXrmDp1Kh06dNA6fCKSqm655RbmzJlDwYL6Wfm1OHfuHLGxscyePdt1ioj4OE8HnqYCOVPuvwhkAb4A1gOlgZ6pnyaSdoYMGUL+/Pnp3LkzSUlJrnNEJB2tWLGCxYsX88ILL5A/f37XOZLi2WefZfDgwcyaNYtevXpxfpK1iMj1S05Opnv37uzcudN1ik8KDQ1l1apVzJo1y3WKiPg4jwaerLXzrLUjU+7/CFQAHgCaAyWttZ+lWaFIGsiePTtjx45l06ZNTJs2zXWOiKSTpKQkevToQbFixejWrZvrHPmHF198kaioKOLi4hgxYoTrHBHxcd9//z2zZs1iy5YtrlN8VsGCBTHG8Ntvv7F//37XOSLiozxdXPy/WGtPAp9eeGyMCbXWnkm1KpF00Lp1a6ZPn05MTAwRERGEhYW5ThKRNDZz5ky2bt3KO++8o7/zXsgYQ1xcHH/++ScDBgwgV65cdOrU6d9fKCJyGeXLl+enn37SZjI36MyZM9x+++1Ur16d999/33WOiPggTy+1uyxjTJgxJhrYk0o9IunGGMPUqVNZuXKlPoCKZAAnT55kwIAB1KpVi8cee8x1jlxBQEAAM2bM4OGHHyYyMpK33nrLdZKI+KCtW7eSnJxM7ty5Mca4zvFpoaGhREVFsWjRIpYsWeI6R0R80FUHnowxRYwxfYwxLxtjuhtjsqccDzHG9AR+BsYBe9M+VST1lSpVigoVKgBw4sQJxzUikpYyZ87MzJkzmThxoj6EeLng4GDmzZtH7dq1adu2LUuXLnWdJCI+ZN++fdx5550MHDjQdYrfiI6OpmzZskRFRZGQkOA6R0R8zBUHnowxNYGtwCigMzAeWG+MKQVsBsYAvwKNrbW10qFVJM1ER0dTq1YtbeMt4qestRhjaNSoEVWrVnWdIx7IlCkTH3zwAZUrV9b6LCJyTfr164e1lg4dOrhO8RshISG8/PLL7Nmzh9GjR7vOEREfc7U1nmKAI8BDwNdAcWAKsA7IDDxlrX09zQtF0sE999xDzpw5tYW3iJ+KiIigVKlSDBgwwHWKXIPs2bOzdu3ai5dDJycnExBwQ6sEiIif27BhA3PnzqV///4ULVrUdY5fuf/++2nRogUjR46kTZs2lChRwnWSiPiIq333Vh0YZK1dZ609ba3dyfmZT7mB5zXoJP6kWbNmDBw4kJCQENcpIpLKEhMTSU5OJikpyXWKXIcLg06bNm2iUqVK7N6923GRiHgray3du3fn5ptv5vnnn3ed45fGjRtHcHAwUVFRWGtd54iIj7jawFN24J/f3V14vCFtckTcWrx4Mb1793adISKpKCgoiDfeeENrffi4LFmykCVLFs14EpErmjdvHl9++SXDhg0ja9asrnP8UqFChRg0aBBLlixh8eLFrnNExEf823dv//zx8IXrkM6mQYuIcxs3bmTs2LGsWrXKdYqIpIJPP/2Ub7/9FkALivu4smXLsn79em699VastRw/ftx1koh4kYSEBPr27UvVqlWJiIhwnePXoqKiqFChAj169NBsYhHxyNXWeAIYbIz545LHF75rH2qMOXrJcWutbZe6aSLpr1+/fsyZM4fIyEi++eYbXXon4sNOnjxJREQEhQsX5ssvv9TAkx+48GcYGRnJ5s2b+fTTTzWrQUQAiIuL45dffmHWrFkEBga6zvFrwcHBzJo1i5CQEP1/LSIeudqMp1+AckDtS261gP8AFf5xvHbaZoqkj0yZMjFx4kR27tzJhAkTXOeIyA0YO3Ys+/fvZ+zYsRp08jMPPvggmzdvpnnz5pw5c8Z1jog4dujQIUaOHEmzZs247777XOdkCOHh4VSuXBmAs2d1MYyIXN0VB56stcWstcU9vGlLA/EbjRo1omnTpgwePJh9+/a5zhGR67B//35Gjx7N448/Tq1atVznSCpr0qQJM2fOZMWKFbRu3ZrExETXSSLiUO7cuRkzZgyjR492nZLhdO7cmaZNm2qhcRG5Kq3QKXIZ8fHxWGuJjo52nSIi16F///4kJiYSGxvrOkXSSNu2bZkwYQILFy7k2Wef1YcekQwsKCiI5557jlKlSrlOyXAqVqxIeHi41noSkavSwJPIZRQtWpQBAwawYMECPvnkE9c5InINNm3axOzZs4mOjqZ48eKucyQNdevWjYEDBzJz5kz69OmjwSeRDMZaS8uWLXnjjTdcp2RYnTt3ZujQoQQF/dvSwSKSkWngSeQKevbsSenSpenSpQunT592nSMiHrgwUzFfvnz079/fdY6kg0GDBtGlSxfGjh2rGW4iGczff//NgQMH+Ouvv1ynZHhLliwhPj7edYaIeCkNPIlcQWhoKJMmTcJay3/+8x/XOSLigQULFvDFF18wdOhQsmXL5jpH0oExhvj4eFq3bk2/fv2YPXu26yQRSSfZs2fn888/p1OnTq5TMrx33nmH3r17s2vXLtcpIuKF0n3gyRjzoDFmlzHmR2PM85c5H2GMOWyM+Sbl9swl55IuOf5B+pZLRlSvXj127txJmTJlXKeIyL+w1jJ8+HAqVapE+/btXedIOgoICGDWrFlERUVRt25d1zkikg6WLVvGgQMHMMYQGBjoOifDGz16NJkzZ6Zr16667FlE/ke6DjwZYwKBSUBDoDzQyhhT/jJPnWetrZpym37J8YRLjjdJj2aR4OBgTp06xeuvv65/SEW8mDGGjz/+mLlz5+pDSAYUHBxMfHw8hQsXJikpiW3btrlOEpE0cuTIEVq0aEFkZKTrFEmRP39+hg0bxvLly3n33Xdd54iIl0nvGU81gB+ttXustWeBt4Gm6dwgcs1mzZpFREQEX3/9tesUEbmMhIQErLXkz5+fSpUquc4Rx2JiYrjzzjv55ZdfXKeISBoYNGgQx48fZ9iwYa5T5BLPPfccVatWJTo6mhMnTrjOEREv4tHAkzEmxBgTY4z53hhzKuWSt0tviR5+vULAvkse/5py7J8eNcZsNca8a4y55ZLjYcaYTcaY9caYZh5+TZEb1qFDB9atW8ftt9/uOkVELiM6Opp7771X2zkLAFFRUUyYMIEiRYq4ThGRVLZz506mTJlCx44dqVChguscuURQUBCTJ09m//79DBkyxHWOiHgRT/e9HANEAh8BC4Ez1/n1zGWO/fPapcXAW9baM8aY54DXgQsLNhSx1h4wxpQAVhpjtllrf/qvL2BMR6AjoG84JdUEBwdz1113AXD48GHy5s3ruEhELnXnnXdSqFAhXWInAOTLl48OHToAsGXLFrJly8att97quEpEUkOvXr3IkiULgwcPdp0il3HXXXfx9NNPExcXR0REBOXLX25VFRHJaDwdeHoMiLHWDr/Br/crcOkMpsLAgUufYK09csnDaUDsJecOpPy6xxjzGXAb8NM/Xj8VmAoQHh6uBXkkVb355ps888wzbNmyRQuOi3iRiIgI1wnihRITE3nsscew1vLFF19QsGBB10kicgOWLVvG0qVLGTNmjH4I6MVGjRrFwoUL6dKlCytWrMCYy809EJGMxNM1nrIAX6bC19sIlDLGFDfGhAAtgf/anc4YU+CSh02AnSnHcxpjQlPu5wFqAt+lQpOIx+6//35CQkLo0qWLFhoX8QLLli3jpZde4ty5c65TxAsFBQXx9ttvc/jwYR544AGOHj3qOklErlNiYiI9evTg1ltvpWvXrq5z5Cry5s3LiBEj2Lt3LwcPHnSdIyJewNOBp8VAnRv9YtbaRKAL8AnnB5TesdbuMMYMMcZc2KUuyhizwxjzLRAFRKQcLwdsSjm+ChhlrdXAk6SrCzt2fPrpp8yfP991jkiGdu7cOaKiopg0aZLrFPFi1atXZ9GiRfzwww80atRIC96K+Kjp06ezY8cORo8eTWhoqOsc+RcdO3Zkx44dmmkqIoDnA08TgVbGmIHGmHBjTIl/3jz9gtbapdba0tbaWy9cumetHWit/SDlfj9rbQVrbRVr7X3W2u9Tjq+z1lZKOV7JWjvjWv/HiqSGTp06cdtttxEdHc3x48dd54hkWK+88gq7du1i7NixBAcHu84RL1a3bl3mzZvHhg0beOSRRzhz5nqXqhQRF86ePcuQIUO45557aN68uesc8UBgYCCZM2cmISGBTz75xHWOiDjm6cDTl0ApYBDwFbD7MjeRDCEwMJDJkydz4MABLWwp4sjRo0cZNGgQ999/P40bN3adIz6gWbNmTJ8+neXLl/Pkk09qB0QRHxISEsKnn37K5MmTtV6QjxkyZAiNGzdm3759//5kEfFbni4u/jT/u/ucSIZ155138swzzzBhwgQiIiKoWLGi6ySRDGXIkCEcO3aM8ePH60OIeOypp57izz//pGfPnjz33HNMnTpV//2IeLlz584RHBys3dF8VK9evahfvz633HLLvz9ZRPyWRwNP1tpZadwh4nNGjhzJwoULiYyM5LPPPtOHF5F0smvXLiZNmkT79u2pXLmy6xzxMT169ODo0aMMHz6c1q1bc99997lOEpGraNWqFdmzZ2fGDK2y4Yty585N3bp1ATh16hSZM2d2XCQiLnh6qR0A5rwKxpjaxpjyRp+0JQPLkycPo0aNYvXq1cydO9d1jkiG0bt3bzJlysTQoUNdp4iPGjp0KKtXr9agk4iXS05OplKlSpQrV851itygKVOmUKZMGY4dO+Y6RUQc8PRSO4wxzwDDgLyXHP7dGDNAC31LRtW+fXsOHjxI/fr1XaeIZAgrVqxg8eLFjBo1ivz587vOER9ljKF27doArF27lt27dxMREeE2SkT+R0BAADExMa4zJBXUqFGD/fv3ExMTQ3x8vOscEUlnHs14Msb8HzAV2Mb59Z4eSvl1GzDVGNMqzQpFvFhAQAADBw7UB2CRdPLWW29RrFgxunXr5jpF/ERcXByxsbHa6U7Ey7z//vu8//77WKtlZv3B7bffTqdOnXj55Zf59ttvXeeISDrz9FK7PsBca219a+3r1tpPUn5tALwJ9E27RBHvt3fvXurUqcPXX3/tOkXEr02bNo01a9YQFhbmOkX8xOzZs/n8888JDQ11nSIiKU6cOEHnzp0ZOXKkBp78yLBhw8iVKxedO3cmOTnZdY6IpCNPB57KAHOucG5OynmRDCtnzpz8+eef/Pbbb65TRPzS8ePHOXToEMYYChcu7DpH/EjmzJnJly8f586do0OHDqxfv951kkiGN3r0aA4ePEhcXBwBAde0JK14sZw5czJ69GjWrVvH7NmzXeeISDry9J38OHCl7/QLp5wXybBy5MjB1q1beeihh1yniPilkSNHUrp0af744w/XKeKnjh07xqpVq3jooYfYvn276xyRDGvfvn2MHTuWFi1acPfdd7vOkVTWrl077r77bvr06cOff/7pOkdE0omnA08fASOMMbUvPWiMuYvzC45/lNphIr7GGENiYiKTJ0/myJEjrnNE/EpERATDhg0jT548rlPET+XNm5fly5eTKVMmGjRowJ49e1wniWRI/fr1Izk5mdjYWNcpkgYCAgKYNGkSR44cYcCAAa5zRCSdXMsaT38BnxljfjHGfGWM+Q/wBfB3ynmRDG/37t1ERUXRr18/1ykifqV06dJ07drVdYb4ueLFi7Ns2TLOnDlD/fr1OXjwoOskkQxlw4YNzJ07lx49elC0aFHXOZJGqlatSmRkJFOmTGHz5s2uc0QkHXg08GSt/Q2oCnQDvuT8YNN6oCtwm7X2UJoViviQcuXK0a1bN6ZPn651QkRSwdq1a2nevLnWT5N0U6FCBZYuXcqhQ4d44IEHdCmISDqx1hIdHU3+/Pn1A7wMYOjQoXTs2JECBQq4ThGRdODxan3W2lPW2pettS1SdrdrYa2dbK09lZaBIr5m0KBBFChQgM6dO5OUlOQ6R8RnJScnEx0dzYYNG8iaNavrHMlA7rjjDt5//3127dpF48aNOXnypOskEb/3zjvvsG7dOoYPH673/Awge/bsvPLKKxQsWNB1ioikA20TIZLKsmbNyvjx49myZQtTpkxxnSPis9588002btzIyJEjuemmm1znSAZTr1493nrrLdavX89jjz3G2bNnXSeJ+LWpU6dStWpVIiIiXKdIOtq1axfNmzfX+qgifu6KA0/GmD3GmCop9/emPL7S7af0Sxbxfk888QT16tVjwIABHDqkK1FFrtXJkyd5/vnnCQ8P58knn3SdIxnUI488wtSpUzl48CB///236xwRv7Z06VIWLlxIYGCg6xRJR2fOnGHdunV89913rlNEJA0FXeXc55xfy+nCfZv2OSL+wRjDyy+/TKVKlejduzezZ892nSTiU8aOHcv+/ft5++23CQjQ5Fxxp3379rRp04aQkBASExMJDAzEGOM6S8RvHDt2jJCQEDJnzkzx4sVd50g6q1y5Mv/5z38ICwtznSIiaeiK381ba5+y1u5NuR+R8viKt/RLFvENZcqUoVevXrzxxhusXr3adY6Iz9i/fz+jR4/m8ccfp1atWq5zRAgJCeHs2bM8+uijvPDCC65zRPxK7969qVy5MmfOnHGdIo6EhYWRlJTE22+/rfVRRfyURz9GNsYMNMZcduU3Y0wBY8zA1M0S8Q8vvPACRYoU4fXXX3edIuIz+vfvT2JiIrGxsa5TRC4KDg6mYMGCFCpUyHWKiF9p06YN3bt3JzQ01HWKOLR06VJatWrF9OnTXaeISBq42qV2l4oBPgYOXOZcwZTzQ1IrSsRf3HTTTaxZs4bChQu7ThHxCZs2bWL27Nn07dtXl1yIVzHGMHny5IuX2R09epRcuXI5rhLxfXXq1KFOnTquM8Sxxo0bc++999KvXz8effRR8uTJ4zpJRFKRpwtnXG0xg5yA5saKXEGRIkUICAjgt99+47fffnOdI+LVtm3bRtGiRenfv7/rFJH/cWHQacOGDRQvXpyFCxc6LhLxXR9++CFRUVGcOHHCdYp4gQvrox4/fpznn3/edY6IpLKr7Wp3rzFmiDHmwkymZy88vuQ2BngJ2JEutSI+KiEhgapVq9KzZ0/XKSJe7amnnuKHH34gW7ZsrlNErqhChQpUqFCBVq1asWLFCtc5Ij7n7Nmz9OjRg+XLl+sSO7moQoUKdO/enRkzZrB+/XrXOSKSiq52qd09wICU+xa43ALiZ4HvgKhU7hLxK5kyZSIuLo7bb7/ddYqIVzp9+jSff/45DRo0ICQkxHWOyFXddNNNfPjhh9xzzz00bdqUlStXUqNGDddZIj5j8uTJ7N69myVLlhAcHOw6R7zIwIEDefPNN+ncuTMbN24kMDDQdZKIpIKr7Wo32FobYK0N4PyldnddeHzJLcxaW81a+2X6JYv4platWlG6dGkAkpOTHdeIeJfXXnuNBx98kM2bN7tOEfFIrly5WLZsGfnz56dhw4Z89913rpNEfMKRI0cYPHgwDzzwAA0bNnSdI14ma9asxMXFsWXLFl555RXXOSKSSjxa4yllkOmrtI4R8XdnzpyhWbNmjBo1ynWKiFdp3749CxcuJDw83HWKiMcKFCjA8uXLCQkJoUGDBvz888+uk0S83qBBgzh+/Djjxo27uG6ayKUef/xx7r//fl544QV+//131zkikgo8GngyxjxljBl0hXODjDHtUrVKxE+FhoYSGBjIsGHD9AFFJMW5c+cICQmhefPmrlNErlmJEiVYtmwZJ0+epH79+hw6dMh1kojX2rlzJ1OmTKFjx45UqFDBdY54qQsLjZ86dUqznkT8hKe72nUDjlzh3O9A99TJEfF/EyZMwBhD9+76ayOybds2SpQooUVExadVqlSJpUuXcuDAARo2bMi5c+dcJ4l4pV69epElSxYGDx7sOkW8XNmyZVm7di0DBgz49yeLiNfzdOCpJFfeuW4ncGvq5Ij4v1tuuYWBAweyaNEilixZ4jpHxBlrLT179uTkyZMX1z8T8VV33XUXCxcupFu3blosWeQyli1bxtKlSxkwYAB58+Z1nSM+oHr16gQEBHD48GESExNd54jIdBafnwAAIABJREFUDfB04CkRyHOFc/qXQ+QaRUdHU65cObp27UpCQoLrHBEnli5dyvLly4mJiSFXrlyuc0Ru2AMPPEC7dudXH/j6668180nkEuvWraNkyZJ07drVdYr4kJ9//pnSpUszadIk1ykicgM8HXjaADx3hXPPARtTJ0ckYwgJCWHSpEns3btXC41LhnTu3Dl69uxJ6dKl6dy5s+sckVT1yy+/cPfddxMTE+M6RcRrDBo0iC1bthAaGuo6RXxI0aJFiYyMpEGDBq5TROQGBHn4vOHAp8aYr4DpwH6gEPAMUA2onzZ5Iv7rvvvuo3Xr1sTGxtKmTRtKlizpOkkk3UyZMoVdu3bxwQcf6LIk8TtFihRh6tSpNGrUyHWKiHN//fUXe/fupWrVqmTJksV1jvgYYwzDhg1znSEiN8ijGU/W2s+Bx4B8wKvAhym/5gUetdZ+llaBIv5s7NixhIaG0rVrV6y1rnNE0sXRo0cZNGgQ999/P40bN3adI5Im2rZtS+7cuTlz5gzz5s1znSPizJgxYwgPD2ffvn2uU8SH/fHHHzzxxBN8/vnnrlNE5Dp4eqkd1tpF1triQDmgFlDWWlvCWvvBtXxBY8yDxphdxpgfjTHPX+Z8hDHmsDHmm5TbM5eca2eM2Z1ya3ctX1fEGxUoUIBRo0YRHh5OUlKS6xyRdDFkyBD++usvxo8fjzHGdY5ImnrllVdo2bIlEyZMcJ0i4kSvXr2YM2cOt9xyi+sU8WGZM2dmw4YNREZGav08ER/k6aV2F1lrd13vFzPGBAKTOH9p3q/ARmPMB9ba7/7x1HnW2i7/eG0uIAYIByywOeW1f15vj4g36NSpk+sEkXSza9cuJk2aRPv27alcubLrHJE016VLF9asWUN0dDS5cuWibdu2rpNE0k1ycjI5cuSgZcuWrlPEx2XOnJn4+HiaNWvGxIkT6dGjh+skEbkGHs94AjDGVDHGPGGMafvPm4e/RQ3gR2vtHmvtWeBtoKmHr30AWG6tPZoy2LQcePBa+kW82dKlS4mLi3OdIZKmTp48yZ133snQoUNdp4iki8DAQObOnUu9evV4+umnWbRokeskkXTx+eefc9ttt/Hjjz+6ThE/0aRJExo1akRMTAwHDhxwnSMi18CjgSdjTA5jzFrga+AtYFbK7bVLbp4oBFx6gfevKcf+6VFjzFZjzLvGmAvzcj19rYhPmj9/PrNmzdL0YfFr1apVY82aNeTPn991iki6CQ0N5b333iM8PJwWLVqwatUq10kiaSo5OZkePXrw559/UqiQvl2X1GGMIT4+nnPnztGrVy/XOSJyDTyd8TQCyA3UAQzQHKgLzAX2cH4mkycut5jHP1dUXgwUs9ZWBj4FXr+G12KM6WiM2WSM2XT48GEPs0Tci4+PZ+PGjdrhS/xSUlISsbGx/Pmnro6WjClLliwsWbKEW2+9lSZNmrBp0ybXSSJpZvbs2Xz99deMGjWKTJkyuc4RP3Lrrbfy/PPP89Zbb7Fy5UrXOSLiIU8Hnh7g/ODT+pTHv1prP7PWtuX84FA3D3+fX4FLVxYsDPzXPElr7RFr7ZmUh9OA2z19bcrrp1prw6214Xnz5vUwS8S9bNmyERISwvHjx9m8eTNw/rKkbt26cerUKcd1Ijdm7dq19OvXjxUrVrhOEXEmd+7cLFu2jDx58vDggw+yc+fOi+f0fi/+4sSJE/Tv35877riDVq1auc4RP9S3b19KlChBly5dOHv2rOscEfGApwNPBYA91tok4DSQ9ZJzC4FGHv4+G4FSxpjixpgQoCXwX7viGWMKXPKwCXDhu7JPgAbGmJzGmJxAg5RjIn7lySefpHHjxvz11198+eWXfPDBB3z55Zeus0RuSJ06dfjuu+949NFHXaeIOFWoUCGWL19OUFAQ/fr1u3hc7/fiL0aPHs3BgweJi4vTzqWSJjJlysRLL73Ezp07iY+Pd50jIh7wdODpNyBHyv3/AHddcq6kp1/MWpsIdOH8gNFO4B1r7Q5jzBBjTJOUp0UZY3YYY74FooCIlNceBYZyfvBqIzAk5ZiIXxkwYACHDh0iJiaGTz/9FODiryK+6ODBgwCULVtWH0JEgJIlS7Jq1Spmz5598Zje78Uf7Nu3j7Fjx9KyZUvuuuuuf3+ByHVq1KgRjz32GAkJCa5TRMQDng48fcH/H2x6A4gxxrxqjJkEjOEaZh5Za5daa0tba2+11g5POTbQWvtByv1+1toK1toq1tr7rLXfX/Lamdbakik3Txc0F/Ep1atXp2PHjkycOJEFCxYA8OGHHzquErk+e/fupUSJErz66quuU0S8Srly5ciWLRsnT54kOjqaDz44PwFc7/fiy/r164e1llGjRrlOkQzgnXfeYeDAga4zRMQDQR4+bzBQMOX+GM4vNN4CyMz5S+W6pn6aSMbStGnTix88Lvjpp58A+OGHH/5npkiTJk20Lbd4vb59+2KMoVEjT6/IFvF/l3u/Dwo6/y2Z3u/FV23YsIG5c+fSv39/ihYt6jpHMoAL75XLli0jLCyMOnXqOC4SkSvxaMaTtfYna+2alPvnrLU9rbWFrbW5rLWtrbVH0jZTxP+NGDGCIkWKEBYWdvGYtec3brx04cSwsDCKFi3KiBEj0r1R5Fp88cUXzJ8/nz59+lC4cGHXOSJe43Lv94mJiYDe78V3HTlyhGrVqvH888+7TpEM5Ny5c0RGRhIbG+s6RUSuwtNL7S4yxmQxxhQ1xmjPd5FUVKFCBb777juaNGlC5syZL/uczJkz07RpU3bs2EGFChXSuVDEc8nJyURHR1OwYEF69+7tOkfEq+j9XvxRw4YN2bRpE1mzZv33J4ukkuDgYJYsWcLChQtdp4jIVXg88GSMaWyM+Rr4C9gDVEo5Pt0Y0zqN+kQylJtuuol58+YxZMgQMmXK9F/njDEMHDiQt99+m5tuuslRoYhn5s6dy6ZNmxg5cqT+exW5jKu93wPUrFmTN954Q39/xOudPn2aV199lbNnz2oDCXGidOnShIaGcvLkSQ4fPuw6R0Quw6OBJ2NMM2AR8AfQF7j0X5W9QLvUTxPJuH766SeSkpIwxhAWFoYxhoCAAH755Rfg/GwSEW916tQp+vXrR3h4OE8++aTrHBGvdqX3++XLl3PXXXexc+dO14kiV7VgwQKee+451q9f7zpFMrDExETCw8N59tlnXaeIyGV4OuMpBnjNWtsAmPCPc9uBiqlaJZKBHTx4kOnTpwNQpEgR4uPjueWWWwgMDGTatGnMmTOHO+64g/379zsuFbm8sWPHsn//fsaPH09AwDVf0S2SYVzp/T4oKIjAwED27NnDbbfdRlxcnH7gIF6rdevWfPXVV1rYWZwKCgqibdu2vPfee3z00Ueuc0TkHzz9RFAOmJdy3/7j3J+c3+VORFLB0KFDOXfuHM2bN2fHjh00aNCA7777jmbNmnHu3DneeustsmbNSp48eVynivyP/fv3Exsby2OPPUbt2rVd54h4tau93yclJdGkSRMaNGhAjx49uP/++/n5559dJ4v8l2PHjmGMoUaNGq5TROjRowelS5ema9eunD592nWOiFzC04Gnv4ErfcotBuhiWpFUcurUKWbMmPFfazldWAtkxowZ5M2blxUrVhAaGsrff/9NmzZt+M9//uO4WuS8zJkz06FDB+0uI+KBf3u/B1i0aBEzZsxg06ZNNG7cWDOfxGt8++23FCpUiKVLl7pOEQEgNDSUl19+mZ9++okxY8a4zhGRS5gL27Vf9UnGzOX8YuJ1gOPAOeB24DtgDfCNtbZjGnZel/DwcLtp0ybXGani559/plixYq4zxIGr/dmvWbOGRo0aARAfH09ERIQW9vQj+nufcenPPmO62p/73r17+f3337njjjs4e/Ysx44dI1++fOkbKGnG1/7OW2upV68e33zzDT/++CM5c+Z0neSzfO3P3hc88cQTLF68mO+++47ixYu7zrki/dlnXP7yZ2+M2WytDffkuZ7OeHoBuBnYBUzn/OV2zwPfAIWBQdeeKSI3qnbt2mzdupVq1arx9NNP06xZMw4dOuQ6SzIgay2dOnVi7dq1rlNE/FLx4sW54447gPOX6FWsWJHff//dcZVkVIsXL2blypUMHjxYg07idcaPH09gYCDdunVznSIiKTwaeLLW/gxUAz4E6gNJnJ/9tB64w1p7IK0CReTqihUrxsqVKxk/fjyffPIJFStW5L333nOdJRnMgQMHWLJkCdu3b3edIuL3WrVqRXR09MUZT4mJiY6LJCM5e/YsvXr1omzZstpBTLxS4cKFiYmJYfHixSxevNh1jojg+YwnrLW/WmvbW2sLW2tDrLUFrLVPWWv3pWWgiPy7gIAAoqOj+frrrylSpAiPPPII7dq149ixY67TJIMoVKgQ33//Pe3bt3edIuL3ypcvT79+/QD45ptvKFOmDJ9++qnjKskoJk+ezO7duxk3bhzBwcGuc0Quq1u3bpQrV45u3bpx9uxZ1zkiGd4N73NtjAk1xmgeo4gXKF++POvXr2fgwIHMnTuXypUr8+eff7rOEj+3YcMGzpw5Q+bMmQkKCnKdI5KhWGsJDg6mfv36REVFcerUKddJ4seOHDnC4MGDadCgAQ0bNnSdI3JFISEhTJs2jSlTphASEuI6RyTD82jgyRiTx/xjxWJjTCZjTE/gZ2B8GrSJyHUIDg5m8ODBfPnll3To0OHi2gvaCUnSwu+//069evXo0qWL6xSRDOm2227j66+/plu3bkycOJHbbruNDRs2uM4SPzV48GD+/vtvxo0bp81MxOvVrFmTBx54ADg/SC8i7lxx4CllJlO8MeYEcAg4YozplHLuSWAPMAb4BXgwPWJFxHPVq1fnxRdfBGDz5s1UrlyZnTt3Oq4SfzNw4EASEhLo1auX6xSRDCtz5sxMmDCBFStWkJCQwN13383AgQN1eYmkqu+//57JkyfTsWNHKlas6DpHxGPDhw/nkUce0eCTiENXm/E0EOgKrOP8ANNyIN4YMxGYDfwFNLXW3mGtXZ7mpSJy3U6fPk22bNm4+eabXaeIH9m2bRvTpk2jc+fOlClTxnWOSIZXt25dtm3bxpNPPsnQoUO566672LFjh+ss8RNhYWG0aNGCIUOGuE4RuSaZM2cmR44cGowXcehqA08tgMnW2gbW2uettS2A54BIzg9CVbbWapsAER9Qs2ZN1q5dS86cOTl37hxPPfWUPozIDbHW0rNnT7Jnz05MTIzrHBFJkT17dmbNmsV7773Hvn37uP/++0lISHCdJX6gWLFizJ07l7x587pOEbkm3bt357XXXiM0NNR1ikiGdbWBp1uAf+7JvjDl1/HWWg0Zi/iQC2sx/PDDDyxZsoTbb7+dcePGkZSU5LhMfNHSpUtZvnw5MTEx5MqVy3WOiPxDs2bN2L59O2+++SaZMmXCWsuBAwdcZ4kPSkxMJCoqih9++MF1ish1ufA98JYtW5gxY4bjGpGM6WoDT8HA8X8cu/D4cNrkiEhaq1ChAtu3b+fBBx+kV69e1K1bl71797rOEh9y7tw5evbsSenSpencubPrHBG5gnz58lG3bl0AXn31VcqUKaO1/uSabd++nVmzZrF9+3bXKSI3ZMKECXTu3FmDqCIO/NuudoWMMSUu3IASlzueck5EfES+fPl47733mDVrFt988w2VK1dmxowZWnRRPPLKK6+wa9cuxo4dS3BwsOscEfFAw4YNiYqKomzZssD5WSwinqhatSp79+6lefPmrlNEbkhsbCxhYWF07dpV3/OKpLN/G3h6F9h9ye37lOPv/+P47rQKFJG0YYyhXbt2bNu2jRo1avDMM8/QpEkTfvvtN9dp4sX++usvYmJiqFevHo0bN3adIyIeKlq0KMOHD8cYwy+//ELZsmVZsGCB6yzxclu3bsVaS+7cuS9eriTiq26++WaGDh3KsmXLWLhw4b+/QERSzdUGnp4Cnr7M7UrHRcQHFSlShOXLlxMfH8+nn35KxYoVdemdXFG2bNl47bXXiIuL04cQER919uxZcubMyWOPPUabNm04duyY6yTxQnv27KF69eoMHz7cdYpIquncuTNVqlShe/funDx50nWOSIYRdKUT1trX0zNERNwJCAggKiqKBg0a8Nprr1GsWDEAkpOTCQj4t4mRklFYazHG0LRpU9cpInIDSpYsybp16xgxYgRDhw5l1apVvPbaa9SvX991mniRPn36EBwczNNP6+fL4j+CgoKYNGkStWrVYujQoYwaNcp1kkiGoE+UInJR2bJliY2NxRjD3r17qVixIuvXr3edJV6idevWjB071nWGiKSC4OBgYmJiWL9+PdmyZaNBgwZ06dJFMwAEgNWrV7NgwQL69u1LwYIFXeeIpKqaNWsSERHBuHHjtOGCSDrRwJOIXNbJkyfJli0bBQoUcJ0iXuDs2bMkJyeTlJTkOkVEUlF4eDibN28mOjqaSZMmcdttt+kHDhlccnIyPXr0oHDhwvTs2dN1jkiaiI2N5aabbtJC4yLpRANPInJZFStW5Msvv6Ro0aJYa4mMjNSHkQwsJCSEefPm0adPH9cpIpLKMmXKxPjx41m5ciVnzpyhbt26HD582HWWOPLGG2+wefNmRo0aRebMmV3niKSJfPnyMXz4cDZv3qy1TUXSgQaeROSKLiweffDgQZYsWULNmjUZMGAAZ8+edVwm6enjjz9mx44dAFpQXMSP3XfffWzbto358+eTN29eAPbv3++4StLTyZMn6d+/PzVq1KBVq1auc0TS1HPPPccPP/xAiRIlXKeI+D0NPInIvypYsCBbt24lIiKC4cOHc8cdd7Bt2zbXWZIO/v77b9q1a0dkZKTrFBFJB9myZaNRo0YALF68mBIlSrBmzRrHVZJeRo8ezYEDB4iLi9PmIuL3AgMDyZs3L8nJyWzYsMF1johf078oIuKRbNmyMWPGDBYtWsSBAwcIDw9nzJgxWvPHz40cOZLff/+dMWPGuE4RkXR255130q1bN+644w4Avd/7uV9//ZUxY8bQsmVL7r77btc5Iulm1KhR1KxZk927d7tOEfFbGngSkWvSpEkTtm/fTuPGjenTpw/33nsvP/30k+ssSQM///wzcXFxPPnkk1SvXt11joiks7x58zJ69GhCQkI4duwYlSpVYtq0aVqI10/lz5+f2NhYbS8vGU7Hjh2ZOXMmJUuWdJ0i4rc08CQi1yxv3ry8++67vPHGG2zbto0qVaqwadMm11mSyvr27UtAQAAjR450nSIijp0+fZqCBQvSsWNHGjduzMGDB10nSSoLDg6ma9euFC1a1HWKSLrKkycPbdq0wRijmZ0iaUQDTyJyXYwxPPnkk2zbto2nn36aKlWqAOe3YRbft3btWt555x169+5N4cKFXeeIiGM333wzy5YtY+LEiaxatYqKFSvyzjvvuM6SVGCt5dFHH2XevHmuU0Scmj9/PhUqVODvv/92nSLid9J94MkY86AxZpcx5kdjzPNXed5jxhhrjAlPeVzMGJNgjPkm5fZK+lWLyJXccsstvPTSSwQHB3P06FGqVq3KRx995DpLbkBycjLR0dEULFiQPn36uM4RES8REBBAly5d2LJlCyVLlqRFixa0bt2ao0ePuk6TG3D06FEOHjzIiRMnXKeIOFWsWDF++OEHYmJiXKeI+J10HXgyxgQCk4CGQHmglTGm/GWelxWIAr76x6mfrLVVU27PpXmwiFyT48ePkz17dvLnz+86RW7Am2++ycaNGxkxYgQ33XST6xwR8TJlypRh7dq1DB06lPnz51OpUiU++eQT11lynXLnzs3atWt56qmnXKeIOFW9enU6duzIxIkT2bp1q+scEb+S3jOeagA/Wmv3WGvPAm8DTS/zvKHAaOB0esaJyI0pWrQoq1evplq1agAMGDCAjz/+2HGVXAtrLcOHD+f222+nTZs2rnNExEsFBQUxYMAAvvrqK3LkyMGDDz7Izp07XWfJNfroo484dOgQxhgCArQCh8iIESPIkSMHkZGR2khBJBWl978whYB9lzz+NeXYRcaY24BbrLUfXub1xY0xW4wxnxtjal/uCxhjOhpjNhljNh0+fDjVwkXEM8YYAE6cOMH7779Pw4YN6dSpEydPnnRcJp4wxrBixQpef/11fQgRkX9VrVo1Nm/ezIIFCyhXrhwA+/fvd1wlnvjtt9944okn6N69u+sUEa+RK1cuYmNj+eKLL3jjjTdc54j4jfT+VGEuc+ziULIxJgCIA3pe5nkHgSLW2tuAHsCbxphs//ObWTvVWhturQ3PmzdvKmWLyLXKkiULmzZtomfPnrz66qtUqVKFdevWuc6Sq0hISMBaS8GCBalQoYLrHBHxEWFhYTzyyCMAbNy4kRIlSvDuu+86rpJ/8+KLL3LmzBmGDBniOkXEqzz11FPceeed9O7dm2PHjrnOEfEL6T3w9CtwyyWPCwMHLnmcFagIfGaM+Rm4E/jAGBNurT1jrT0CYK3dDPwElE6XahG5LmFhYYwdO5bPPvuMpKQkateuTb9+/Thz5ozrNLmMTp060aBBA+1MKCLXrWzZsnTr1o369esDaGtyL/Xtt98yY8YMunTpQqlSpVzniHiVgIAAJk2axB9//MGLL77oOkfEL6T3wNNGoJQxprgxJgRoCXxw4aS19i9rbR5rbTFrbTFgPdDEWrvJGJM3ZXFyjDElgFLAnnTuF5HrUKdOHbZu3crTTz/NqFGjqFGjhhZt9EI1a9akXr16usRORK5b1qxZGT16NNmzZ+fMmTPcddddjBo1SgNQXsRaS48ePciVK5c+VItcQbVq1ejUqROTJ09my5YtrnNEfF66frqw1iYCXYBPgJ3AO9baHcaYIcaYJv/y8jrAVmPMt8C7wHPWWu3fK+IjsmbNyrRp01i8eDGHDh0iPDycjz76yHWWXKJDhw707dvXdYaI+InTp09TpEgR+vXrR506dfjxxx9dJwmwePFiVq5cyaBBg8iZM6frHBGvNXToUJo2bUpYWJjrFBGfl+4/1rbWLrXWlrbW3mqtHZ5ybKC19oPLPPdea+2mlPsLrLUVrLVVrLXVrLWL07tdRG5c48aN2b59Ox07dqRmzZoAurTLsQ8//JApU6ZoRoKIpKrs2bMzf/585syZw44dO6hSpQqvvPKKdopy6OzZs/Tq1YuyZcvy7LPPus4R8Wo5c+Zk4cKFFzdOEJHrp+spRCTd5cmTh5dffpls2bJx+vRp7r77bubMmeM6K0M6ffo0UVFRTJ48WR8GRSTVGWP4v//7P7Zv307NmjXp1KkTDRs21M53jkyePJndu3czbtw4goODXeeI+ISDBw/y7LPPcvSoLrYRuV4aeBIRp06cOEH27NnJnTu365QM6aWXXmLv3r2MHz+eoKAg1zki4qcKFy7MJ598wqRJk1i9ejWVKlXi7bffdp2VoSQkJDBs2DAaNGhAw4YNXeeI+Izff/+dOXPmaHdmkRugTxki4lSePHn4+OOPMcYAMG7cOAoWLEjLli0vHpO08fvvvzNs2DAaNWp0cQcqEZG0Yoyhc+fO1K9fn7Zt29KqVSvy5ctH3bp1XadlCJkyZWLlypWEhYXp31eRa1ClShV+/fVXrYkmcgM040lEnLvwDXBSUhLvv/8+rVu3pmXLlhw5csRxmX8bOHAgCQkJjB071nWKiGQgpUqVYs2aNcybN4/77rsPgAMHDjiu8m/nzp0DoHLlypQuXdpxjYjvuTDotGrVKq1NKnIdNPAkIl4jMDCQVatWMXz4cN577z0qVqzI0qVLXWf5pW3btjFt2jQ6depE2bJlXeeISAYTFBTEE088gTGGPXv2ULp0aV5++WXXWX7rkUceoXPnzq4zRHzaypUrqVu3LjNnznSdIuJzNPAkIl4lKCiI/v37s2HDBvLkyUOjRo149tlnOXHihOs0v2GtpWfPnmTPnp2YmBjXOSKSwRUqVIju3bvTtGlTAO2wmcqSkpKoUqWKfsggcoPuu+8+6tSpw/PPP69Z+SLXSANPIuKVqlatyqZNm+jTpw/Tpk2jSpUqfPHFF66z/MLSpUtZvnw5MTExWtRdRJwLDQ1l2LBh3HLLLSQnJ9OoUSP69OnDmTNnXKf5hcDAQIYNG0ZUVJTrFBGfZoxh0qRJHDt2jP79+7vOEfEpGngSEa8VGhpKbGwsq1evBqBOnTq8/vrrjqt831tvvUXp0qV12YWIeJ1z585RtGhRxowZQ3h4ON98843rJJ82f/58lixZgrXWdYqIX6hYsSLdunVj2rRpbNiwwXWOiM/QwJOIeL1atWrx7bff0q1bt4u7r2lhx+s3e/ZsVq5cSXBwsOsUEZH/EhoayquvvsqSJUv4448/qFGjBiNGjCAxMdF1ms/566+/iIyMJDY21nWKiF8ZNGgQBQoUoHPnzro0WMRDGngSEZ+QJUsW4uLiKFiwIMnJyTz00EPExcW5zvIpx44d4/DhwwQEBFCoUCHXOSIiV/TQQw+xfft2mjdvzgsvvEDt2rXZvXu36yyfMnz4cP744w/i4uIu7h4rIjcua9asjBs3js2bNzN16lTXOSI+QQNPIuJzEhISyJ49O1mzZnWd4lOGDBlC2bJlOXbsmOsUEZF/lTt3bubNm8dbb73Frl27qFq1KpMnT9ZlYx7Ys2cP8fHxtG3blttvv911jojfadGiBffddx/9+/fn8OHDrnNEvJ4GnkTE59x0003MmzeP9u3bA/D6668zadIkfRj5Fx06dGDIkCHkyJHDdYqIiMdatmzJtm3bqF27NpGRkcydO9d1ktfr06cPQUFBjBgxwnWKiF8yxvDyyy9z4sQJRo8e7TpHxOsFuQ4QEbleFy4dWLJkCfPnz2fRokXMnDmTwoULOy7zTuXKlaNcuXKuM0RErlmhQoX46KOPmD9/Po888ggABw4coECBArqM7B9Wr17NggULGDx4MAULFnSdI+LIS58TAAAgAElEQVS3ypcvz5IlS6hdu7brFBGvpxlPIuLz5s2bxyuvvMLatWupWLEic+fO1eynS6xcuZLHH39cU8FFxKcZY3jiiScICgriyJEjVKtWjRdeeMF1lldJTk6mR48eFC5cmF69ernOEfF7DRo0IFOmTCQkJGgTBJGr0MCTiPg8YwzPPvss3377LRUqVODJJ5/kiSee4I8//nCd5lxSUhLR0dFs2rRJa2KJiN/IkSMH0dHRtGzZEkA7S6V444032Lx5M6NGjSJz5syuc0QyhN9++43y5cszZcoU1ykiXksDTyLiN0qWLMnq1asZNWoUixYtomLFinz44Yeus5x67bXX2Lp1K7GxsYSFhbnOERFJFYGBgfTt25fKlSsD8Mwzz9ChQweOHz/uuMwday2vvvoqNWrUoFWrVq5zRDKM/Pnz89BDD118PxKR/6WBJxHxKxc+jGzatIn8+fPz8MMPM2rUKNdZTvz9998MGDCAmjVr8vjjj7vOERFJE8nJydx8883MnDmTypUrs3r1atdJThhjWLFiBe+88w4BAfoWXyS9GGOYNGkS99xzj+sUEa+lf5VExC9VrlyZDRs20K9fPxo3bgyc/3CSkYwcOZJDhw4RFxenxXdFxG8FBAQwcuRIVq9eTWBgIPfeey+9evXi9OnTrtPSzdGjRzl9+jSZMmWiaNGirnNEMqQTJ07Qs2dP1qxZ4zpFxOto4ElE/FZoaCgjRoygYsWKAERERNCvXz/HVenj559/Ji4ujjZt2lC9evX/1959h0lRZm0c/p0hD5hAxQRiWnUJJgzoroqKuqsyYFgzCgqY1oCAooIBZc0EURcE17QuBgwoa0JFPgRMGAgqouLqmsCALkFg5nx/VDU2bQ9xumu63+e+rrmGqa6uPszTVT19+q23ki5HRCTn9ttvP9555x26d+/OLbfcQuvWrZk6dWrSZeXFBRdcwG677cbSpUuTLkUkWGbGo48+yrnnnquJxkUyqPEkIkEoLy+nQYMG1KtXL+lS8uKSSy6hpKSEAQMGJF2KiEjeNGjQgDvvvJNnnnmG77//nr333ptrr7226N8Edu7cmfPPP59atWolXYpIsOrXr8+gQYOYNm0aQ4cOTbockWpFjScRCUKNGjW444476Nu3LwDPPvts0b4ZefXVV3n44Yfp3bs3W221VdLliIjk3eGHH8706dM57rjj6Nu3LzfffHPSJeXUQQcdxNlnn510GSLB69ChA4cffjj9+vXjq6++SrockWpDjScRCUpqrqNnn32Wvn37st9++/Hhhx8mXFXVmj59Ottuuy29evVKuhQRkcQ0bNiQBx98kMcee4zzzjsPiC57Xkzz/Y0ePZoePXqwaNGipEsREaK/M2+77TZ++eUXevbsmXQ5ItWGGk8iEqRBgwYxatQoZs+ezW677cZtt91WNG9Gunfvzvvvv0/9+vWTLkVEJHEdO3akQYMGLF68mLZt29KlS5ekS6oSixcvpmfPnrz00kvUrl076XJEJLb99ttzySWX8OCDDzJ+/PikyxGpFtR4EpFgHX/88UybNo0DDzyQ888/n0MPPZTPP/886bLW2sKFCxk3bhyA3oSIiGSoU6cOF110EaeccgoQzf3n7glXtfYGDRrEnDlzuPXWW6lRo0bS5YhImksvvZRmzZpx7rnnatJ/EdR4EpHAbbHFFowdO5bhw4czZcoUWrRowf3331+Qb0aGDRtGu3btmDZtWtKliIhUO2ZGt27dOOSQQwC48sorOeaYY5g7d27Cla25r7/+muuuu46ysjIOOuigpMsRkQylpaUMGTKEmTNnMnjw4KTLEUmcGk8iEjwzo2vXrrz77ru0atWKTp06cf755ydd1ho755xzeOKJJ2jZsmXSpYiIVHsNGzZk7NixtGjRgieffDLpctZI3759+eWXX7jpppuSLkVEKnHUUUdx5JFH8tFHHyVdikji1HgSEYltt912jB8/nhtvvJGjjz4aoGBGPi1dupQ6depQVlaWdCkiIgWhR48evPnmm2y++eZ06NCBLl268NNPPyVd1iq9++67jBw5kvPOO48ddtgh6XJEZCVGjx7NsGHDki5DJHFqPImIpKlRowa9evWibdu2APTp04cuXbpQXl6ecGWVe+utt9h+++156623ki5FRKSgtGzZktdff53LLruMe++9l1atWlXryYDdnR49etCwYUP69u2bdDkisgqpOTenTZvGa6+9lnA1IslR40lEZCXq1KlDnTp1qu3Ere7OhRdeyKJFi/TJt4jIWqhduzbXXXcdEydOpHbt2rRt25YePXqwaNGipEv7jaeeeoqXXnqJq666io022ijpckRkNVRUVHDcccfRs2fPpEsRSYwaTyIiK3H11Vdzxx13ADB16tRq92Zk9OjRTJw4kf79+7P++usnXY6ISMFq06YNb7/9Nueeey4DBw6kd+/eSZf0G5MmTWLnnXeme/fuSZciIquppKSEUaNG8cQTTyxftmDBAi644AIWLlyYYGWShFCzV+NJRGQVzAyAcePGMXDgQHbffXfefPPNhKuCxYsX07t3b1q0aMEZZ5yRdDkiIgWvfv36DB06lOeff57LL78cgLlz51aby6Fff/31vP7669SqVSvpUkRkDey66640atSI8vJy5s+fz+TJkxkzZgyTJ09OujTJs1Czz3vjycwON7MPzWy2mV26kvWONTM3s9Zpy/rE9/vQzA7LT8UiIpHevXvz3HPP8fPPP7PPPvtw9dVXJ/pmZMiQIXz66afceuut1KxZM7E6RESKTbt27dhss82oqKjgmGOO4U9/+lOiF5v47rvvmD59OgANGjRIrA4RWXsVFRUceOCBnHnmmYwbNw5g+XcJR6jZ57XxZGY1gNuBPwG/B040s99nWW894HzgtbRlvwdOAJoDhwN3xNsTEcmbQw89lGnTpnHCCSdw1VVXse+++/L+++/nvY5vv/2Wa6+9liOOOIJ27drl/fFFREJQUlLC+eefT9euXTEz3J2Kioq813H99dezxx578M033+T9sUWkapSUlHD44Yfz6KOP8tBDDwHw9NNPJ1yV5NvYsWOB8LLP94invYDZ7v6Juy8BRgHZrv3dH7gRWJy2rAwY5e6/uPunwOx4eyIiebXRRhvxwAMP8Mgjj/Dpp5+y++67M3jw4Ly+GenXrx+LFi3i5ptvzttjioiE6Nhjj+X4448HYNiwYRxyyCF89tlnea3h0ksv5f7776dx48Z5fVwRWXdlZWWYGWbGFVdcAcCcOXMAmDVr1vLbUl9lZdneHkshSs8+9TVr1iwgvOzzfW7GlsDnaT9/AeydvoKZ7QY0cfenzaxnxn2nZNx3y8wHMLNuQDeApk2bVlHZIiK/deyxx/KHP/yBrl27cuGFFzJhwgRGjx6d88edNm0ad911F+eeey477bRTzh9PREQipaWlvPHGG7Rs2ZIhQ4Zw2mmnLZ8HMFcqKipo1KgRf/nLX3L6OCKSGwMGDOCdd97h22+/ZfHixSvctmTJkuX/LikpoUmTJgwYMIBbbrmFiRMn8vjjjwPQp08fJk2atNLHadiw4Qrrz507lxEjRgDQrVs3Pvzww5Xef4cddlhh/YYNG3L99dcDcMwxxzBv3ryV3r9NmzYrrL/PPvvQq1cvAA444ICV3hfgyCOPXGH90047jS5duvDdd99x9NFHr/L+mev36NGDsrIyZs2aRdeuXVd5/8z1BwwYwH777cekSZPo06fPKu+fuf6wYcMYMGAAkydPZt68ectP105lnp593bp1ady4MQMGDFjl4xSqfI94yvbKvPyEeTMrAQYCF6/pfZcvcB/u7q3dvfUmm2yy1oWKiKyOzTbbjDFjxjBy5Mjln4i7e07nAlm4cCH77rsvV155Zc4eQ0REfqtTp06899577LbbbnTu3JmOHTvy7bff5uzxnn/+efbcc8+8j7ASkarTvHlzZs6cSfv27SktLc26TklJCY0aNWL69Ok0b958+QiY9NtX9ZVt/RQzW61tpK+/ro9fVfdf3doz11/Xx1+X311qe82bN+eOO+5g4403XmGddKWlpZSVlTFjxgyaN2+edZ1iYPmcKNHM2gBXufth8c99ANz9b/HPGwAfA/+L77IZ8D3QHmiXse5z8bYqnQ6+devWXh2uPFUV5syZQ7NmzZIuQxKg7AvP0KFDGTduHP/85z+pX7/+Wm9H2YdL2YdJuReOiooKBg4cyGWXXcYGG2zA8OHD6dChw1pvL1v2y5YtY9ddd2XRokXMnDmTOnXqrGPVUh1pvw/LLbfcQt++fVm0aNHyZfXq1aN///5cfHG2sRdSLIoxezN7y91br3rN/I94egPYwcy2MbPaRJOFj0nd6O7z3X1jd2/m7s2ITq1r7+5vxuudYGZ1zGwbYAfg9TzXLyKyWkpKSir9VGttLV26lBtuuIGffvqpSrcrIiJrpqSkhIsvvpipU6ey1VZb0bFjR04//XTmz59fZY8xYsQIZsyYwY033qimk0iR+PjjjykvL8fMqFu3LmZGeXk5n3zySdKlSY6Fnn1eG0/uvgw4D3gOeB942N1nmNk1ZtZ+FfedATwMzASeBc519/Jc1ywisqbOO+88Ro8ejZkxZ84czjrrrCp5M/Lyyy9z6aWXMmHChCqoUkRE1lXz5s2ZMmUKffv25YEHHqBz585Vst358+fTr18/9t9//9Wa20REqr+vvvpq+RxKTZs2ZfDgwTRp0gSAu+66i6+//jrJ8iSHlH3+Rzzh7v9299+5+3bufl28rJ+7j8my7oHxaKfUz9fF99vR3Z/JZ90iImsidZ74hAkTGDFiBC1btuTFF19cp20eeuihzJw5kyOOOKIqShQRkSpQu3ZtrrnmGl599VX+9re/AfDjjz+ycOHCtd7mddddx7x587j11ltzPnm5iORH//79Wbp0KR07dmTGjBnL/67r0KEDS5cupX///kmXKDmi7BNoPImIhKRTp05MmjSJevXqccghh3DBBRes1ZuR1CchO++8s96EiIhUQ3vvvTc77rgjAGeddRb77LMPS5cuXePtfPLJJwwePJhOnTqxxx57VHWZIpKQhQsXMnLkSEaNGrV8DtD69evz0EMPMXLkSBYsWJBwhZIryh5qJl2AiEix22uvvXj77bfp06cPQ4YM4bnnnuO+++5jr732Wq37z5o1i1atWjF8+HA6deqU42pFRGRdde3alVmzZlGrVi0AysvLqVGjxmrdt3fv3tSsWbOoL6stEqJ77rmn0tu6dOlCly5d8leM5JWy14gnEZG8KC0tZfDgwYwbN44FCxaw77770q9fv0o/DV+wYMHy0VG9evWidu3aHHbYYXmuWkRE1sbBBx/M2WefDcBTTz3F3nvvzcyZM7Oum368nzBhAqNHj+aSSy5hiy22yGfJIiIiOaPGk4hIHh188MFMmzaNk08+mf79+3PAAQdQXv7b6yRMnjyZMWPGcPvttzNmzBguu+wyGjdunEDFIiKyLkpKSvjss8/YfffdGThwIBUVFSvcnjreT548mR9++IE99tiDnj17JlStiIhI1VPjSUQkzzbccEPuvfdeRo8ezSmnnLL89At3X77OuHHjALjpppto1qwZF154YSK1iojIujniiCOYPn06hx12GD169OCggw5izpw5y29PHe/HjRtHWVkZb7zxBqWlpQlVKyIiUvXUeBIRScjRRx/NOeecA8Djjz9O27ZtmTt3LgBjx44FYO7cudxwww3UrVs3sTpFRGTdNG7cmCeeeIK7776bqVOn0qpVK+6++27cffnx/r777mPZsmW6gISIiBQdNZ5ERBJWVlbG0UcfzSuvvMKmm26KmTFr1iwAzIzjjz8eM1v+VVZWlnDFIiKypsyMJ554gp9//pmff/6ZM844g5KSkuXH+y+//JJatWrpeC8iIkVHjScRkYQNGDCApk2brjCqacmSJcCKp9/VrVuXrbfeWlc6EhEpUCs73qfT8V5ERIqJGk8iIglr3rw5M2fOpH379pXO61FaWkpZWRkzZsygefPmea5QRESqgo73IiISIjWeRESqgfr16/PQQw9xzTXXUK9evRVuq1evHtdccw2jRo2ifv36CVUoIiJVQcd7EREJjRpPIiLVyMcff0x5eTlmRt26dTEzysvL+eSTT5IuTUREqpCO9yIiEgo1nkREqomvvvqKESNGANC0aVMGDx5MkyZNALjrrrv4+uuvkyxPRESqiI73IiISEjWeRESqif79+7N06VI6duzIjBkzOPTQQ5k5cyYdOnRg6dKl9O/fP+kSRUSkCuh4LyIiIVHjSUSkmli4cCEjR45cYW6P1FwgI0eOZMGCBQlXKCIiVUHHexERCUnNpAsQEZHIPffcU+ltXbp0oUuXLvkrRkREckbHexERCYlGPImIiIiIiIiISE6o8SQiIiIiIiIiIjmhxpOIiIiIiIiIiOSEGk8iIiIiIiIiIpITajyJiIiIiIiIiEhOqPEkIiIiIiIiIiI5ocaTiIiIiIiIiIjkhBpPIiIiIiIiIiKSE+buSdeQM2Y2F/gs6TqqyMbAvKSLkEQo+3Ap+3Ap+zAp93Ap+3Ap+3Ap+3AVS/Zbu/smq7NiUTeeiomZvenurZOuQ/JP2YdL2YdL2YdJuYdL2YdL2YdL2YcrxOx1qp2IiIiIiIiIiOSEGk8iIiIiIiIiIpITajwVjuFJFyCJUfbhUvbhUvZhUu7hUvbhUvbhUvbhCi57zfEkIiIiIiIiIiI5oRFPIiIiIiIiIiKSE2o8iYiIiIiIiIhITqjxVKTMrEb83ZKuRfJL2YdL2YdL2YdJuYdL2YdL2YtIIVLjqcikXozcvTz+7vFyvTgVOWUfLmUfLmUfJuUeLmUfLmUvZlYSf1fmgSmG7DW5eBExs+ZAN+D3wATgO+Atd38tvr2E6HVKoRcZZR8uZR8uZR8m5R4uZR8uZR82M9vA3ecnXYfkXzFlrxFPxWVDYC4wFjgQOBIYY2Yvmtku7l7h7l7InVKplLIPl7IPl7IPk3IPl7IPl7IPlJntCAw1s+lmNtDMbjazdknXJblXbNlrxFMRM7OdgZ2Bc4G2wE3Apfo0pPgp+3Ap+3Ap+zAp93Ap+3Ap+3CY2a7AjkBt4I/ABkB74APgKnd/Ml6vxN0rEitUqlyxZa/GU5GJP+koSZ3/HS/bCDgeOAcYD1zh7j+ZmekFqnjE2ddy9yVpy5R9ALTfh0vZh0nH+3Bpnw+XshcAM9sYaAr0AE4C7gM6K+/iV+jZ61S7Ame/XtniCDNr4ZHyeFkJgLv/QPTEHAy0AY6JlxfEk1SyS8t+OzPbMs5+iZmVpIZaK/vipP0+XMo+TDreh0v7fLiUvaRYJJX5PHef6u6nAEcAewFPm9nWqXUTLFWqWDFlr8ZTgUv71GMM0DLjtoq0fy9095HAHUB/Mzswb0VKTqRl/ywwyMz+Ymalmef5K/vio/0+XMo+TDreh0v7fLiUfbjSmo7Hmdk+cdOxIl62HNFrwl+J3tOfCGo6Frpizl6n2hWw1PmcZnYn0Nrd9zSzmkBjoi7oXOAbd5+Ucb9rga/c/fb8Vy1Vycx2A6YArwM1gdeAJ939ZTNrDzxNNCx7Wby+si9w2u/DpezDpuN9eLTPh0vZC4CZVQBnuvvdq1jvKGAEcLG7P5CX4iSnijF7NZ4KVOrcbTNrBswGWrn7TDO7CugA7AD8GN/2L3f/e9p9NgJ2cffxyVQvVcXM6gIjgTeAWkQd73nAx0B3oEX8vEj9AaPsC5j2+3Ape9HxPiza58Ol7MOW0XTcw933MrNaRLl3BP4H/MfdH8+435lAPWBodR/5ItkVe/ZqPBU4M7sbOAFoBGwFvABcCzwAbA9cBrQD2rr79NQLU1L1StUzs1OBk9z9T2a2B9AF6AR8C1wHjHX3b5R98dB+Hy5lHzYd78OjfT5cyj48GU3Hj4g+UPjQzG4EDgO2BL4AyoFxQD9gSXyfBkBzd38tmeplXYSQveZ4KmDxp58fEQ27f4NoCP4j7j7C3Re7+3TgVKInaHOo/ud+yppz9/uBZWZ2sLu/BUwADJhDdJWT282ssbIvDtrvw6XsRcf7sGifD5eyD1Nahr2BGsA8M9uG6MqFf3P3jYEyovl9zgT2Sd3H3f9X3RsPUrkQslfjqYC5+2LgBuBS4N/AVKInIwDxueB1gGlEn5RIkYkzBniT6NKaAEOAS4BDgIeAz939mwTKkxzQfh8uZR82He/Do30+XMo+XPGpVa8AzxN9qPA+UdNxFIC7f+bulwPfATsnVadUvWLPXqfaFbD0IbVmth6wC/BR+h+dZtYSGA/8wd3f1zDc4mRmmxFdTrcmsDnQxt1/jG+r6e7LUucNJ1mnrDvt9+FS9gI63odE+3y4lL2YWVPgKKIPFka6+9Px8lqAA48Db7n7VYkVKTlRrNmr8VQEKnuhMbOdgMHAt+5+qv4QLW5m1gfoCXRx9yfNll9eWzt5EdJ+Hy5lLzreh0X7fLiUfXgymo51gO2Icp6Xtk4L4P+Imo4zlH9xKPbs1XgqUmbWCLiJ6Lzvtu6+sJCemLLmLLqSye+BKe5ennQ9kn/a78Ol7MOi471onw+Xsg+bmbUCBgL/dfdOyj4chZ69Gk9FzMxKgS3d/SMzq6E/TkWKn/b7cCl7kbBonw+Xsg9T/KHDFUQfPByjpmM4iiF7NZ6KVKE9EUVk3Wm/D5eyFwmL9vlwKfuwxVc83MTdP1fTMSyFnr0aTyIiIiIiIiLVmJqO4SqG7NV4EhERERERERGRnChJugBZfWamvAKXunKRhEfZh0fH/LBpnw+Xsg+PjvciUux0kKvGMv/wcPeKyl6YUuumfVe2RaiSS+oq+wAo++KnY76k0z4fLmVf/HS8lxTlGa7Qsg/qP1uAUi8wvc3sYjNbL3VuZ+YT1d3dzFoDE81s00I/BzR0qXzNbBczu9TMLjOzdpnrmJkp++Ki7IOmY36AtM+HS9kHTcf7QGU2EuOmY41sIx3T1t04/q737gUs9OwL/j9QzOInY1PgeuAvwH1mdkz8B0iFmdXLuMumQBOgR75rlaqTlu+uwP3AyfHXtWbWMLWeu1ekfSqq7IuAsg+bjvnh0T4fLmUfNh3vg5ZqMlxvZreY2UbuXh43GGukrxgv2x141cx2UNOx4AWdvRpP1d9PwHTgi/jny4HhZtYcGGdmrdO6pC8QvSAdYmbr5b9UqQppf2DeBbwC7AEcAtQA2pjZ5WZ2q5kdknY3ZV8ElL2gY35QtM+HS9kLOt4HKW4sbg70Ao4EXjKzs+Pbys2soZmtn3G3JcDVyr6whZ69rmpXAMysC7AZMAI4G2gD7AA0A/Z096kZ62/r7p/ku05Zd2nD6TsCg4DdgB/jA9V04Jd41W+JnhPnuPvktPsr+wKl7CVFx/wwaJ8Pl7KXFB3vw2Vm44CvgO+BPwOfAVcCtwB9gPGwfOTL3kSNyVPdfX4iBUuVCTV7jXiq5uLzOd8AOgGN3f1q4GZgK+AToiHZF5lZrdQQPb0gFa60T0BbAPcCi+I/RI8Htga6u/sewAVAY+AwAGVf+JS9gI75IdE+Hy5lL6DjvXAH0ai3vkB/4BvgcWAvYLHHANz9NaIGdEE3HmS5ILNX46mai8/tnwY8AXSLFx8HvE30ZF0AnAiUunt5MlVKDjwKjHH3RfHPrYDr3P1NAHefBTwM1DezEmVfVJR9wHTMD5L2+XAp+4DpeB+uuOn4OrA/sJ+730fUdFwf+JDolMtbzaxOWtPxi0o3KAUj5Ox1ql2BiCcXuxYYALwItHX3SWa2GdDE3d+I/ygp+InHJJIaip/t5/hANBF4zN1vylxXCpuyFx3zw6J9PlzKXnS8D5eZnQO0cfdTzWwYsAtwCXAUcDBwsLt/n2SNkhshZq/GUwGIJxYsAcYChxJd/eR0WGG4thSptLkg0v8YPQu42t0bp6+TaKFS5ZR9mHTMD5f2+XAp+zDpeB82M9uW6AIDdwIPEDUbXjWzDYhOv5xlZjU04q34hJh9zaQLkFWLX3jKzawb8Ffg73oxCkfaOb4eD8/sApwLXAxgZjXdfVmCJUqOKPsw6ZgfLu3z4VL2YdLxPmzu/omZfU50Su29wKR4+Xxgfvzvomk8yK9CzF4jngpE2idh9fzXuQAkMGZWEzgB2Mjdb0u6HskfZR8WHfNF+3y4lH1YdLwPm5nVI7qQwCPu/nHS9Uj+hJa9Gk8iBSh1rr/O+Q+PshcJi/b5cCl7keKmfTtcIWavxpNIAdH8DuFS9iJh0T4fLmUvIiLFRo0nERERERERERHJiZKkCxARERERERERkeKkxlPC4suopv/8m0wy15FwKPtwKftwKfvily1j5R4GZR8uZS8iIVPjKSFpLzQ1zayhme1iZqXZJhlLnedvZn/Oa5GSF9majSnKvrgp+3Ap+zCkv6k0s3pmtr6Z1c42f49yLy7KPlzKXlZzYEFJZbdJ4VL2lQvqP1udpL34XANMBu4HbjGzDdPXM7Ma8fcOwNNmdl5eC5WcMbM9AFLNxsoOPsq++Cj7cCn7sKS9qewGTADGAtebWZNs6yv34qHsw6Xsw5X2ml7XzJqY2eFmtn4lAwtSy840s9L8VSm5oOxXTY2nBKR1OXsCHYAbgPuAY4AmZtbIzFoAuHt5fLcJwOXAQWa2cf6rlqqQln13YLSZ9Tez5hAdhCyWcbdXUfYFT9mHS9mHKS33i4AewIvA68CRwJmV3E25FwFlHy5lH7a0hsLNwEvAEOBRM2uavl7a8+RQ4O9An3zWKVVP2a+armqXEDOrB/wH6Obuj8fLHgDqAnsANYD3gDPc/Zv49q2A7u7eN5mqpSqYWR3gfeB7YAkwH3gGeCgta4MVPjXbEjhL2Rc2ZR8uZR+m+LX+M6LX7tRr/WlEo533dPdvs9xHuRcBZR8uZR8mMyuJP0zqDZwOXAHUAq4DOgFfAZu7+6R4fXN3N7OTgdOAc9x9dsEOc+0AABMkSURBVDLVy7pQ9qtHjaeEmNnFwFHAke7+v7j7+TNwNzARKAeuB4a6+6DkKpWqZmbHAxcCfwU2BroA2wCzgceAx919mZmdCGzj7gMSK1aqlLIPl7IPk5mdBZxANKL5R3cvt+iU+hlAL3d/MF7vj8BO7n5XctVKVVL24VL24Yqbjp8CZ6c1HUcCOwBbAZsCs4Cj3X1OfPsGwAnuPiyRoqVKKPtV06l2CYibTDOA4cDSePHNwEfAJe7+ENEbkQ+A36Xuk+VUDClMrwMPA3Pc/VmiTvddRG9GLwYGmdlRRM8Jg1/n+pKCp+zDpewDE7/WLwI+BpbGbz7N3X8EHgEOitcz4B5gvfhn5V7glH24lH3wziRqLrwMy58PJwJT4tv+CJQSfQgFgLvPD6XxUOSU/SpoxFNCzKw2UN/df4h/3h6o6e4fmFmN+IXqZqCRu3dOtFipcmZWy92XmllNd18WL2tCdGA6EGgFfOvuO8a3WbaroUjhUfbhUvbhiedr2dXdx2UsP5bog6Y9zawXcKG7b5lIkZITyj5cyj5cFl1AZDvgaXdfaGZXAIcB7dx9cbzOSKLTsDoDFbDCRaekQCn7VVPjqRpInReasWwL4F3gJHd/Ids6UhziT73Mf73K1fHAv4CD3f3l9DepUlyUfbiUfdjMbEeiCYWPBcYAJ7v7U8q9+Cn7cCn74he/ttdz94Xxz02JBhZ8kjYP0ABgO3c/PtFipUop+1VT46kaij8BvxFo6O6H6VPvMNivl+F8Bqjr7gco+zAo+3Ap+3CZ2Tii025edveDlXs4lH24lH04smVr0STy7wEnuvvzGlhQnJR9dprjqZoxs/WBU4H1+fWyq8opAPHBpwbwX5R9UJR9uJR90CYQzfN4evyzcg+Hsg+Xsg9ElsbDDsAg4PW48WChNR5Coeyz04inasjMNgXWd/fZIXZDJaLsw6Xsw6XswxGPbm7t7o+n5nZMuibJD2UfLmUfJjOrD3QC/kA0z9cXyj8Myv5XajyJVCN60xkuZR8uZS863SZcyj5cyj4sZrYhUOruX+p1PyzKPqLGk4iIiIiIiIiI5ITOKxYRERERERERkZxQ4ylP0q5cJIFR9uFS9uFS9mFS7uFS9uFS9iIiq6YDZR6s7FzO1ItVPKE4Zmb5rE1yS9mHS9mHS9mHSbmHS9mHS9mLhEn785rTHE85kHoRMrO9gf2BPYE5wKPAbHf/PmP9JsBDwKnu/nG+65Wqo+zDpezDpezDpNzDpezDpewFYFVXJUvdbmbbAP8J8QpmxSz9wgCZzWdlXzmNeKpi8ROxwsy2JHqhOR5YBrQHJgBDzGxv+1UJsAGwPXCnmW2cWPGyTpR9uJR9uJR9mJR7uJR9uJR92CztlMpUM8HMamRbN248NAFeBPbLT4WSK/br6MXfmVlX4EYz6wyQOeJR2VdOjacqlnZZ1IHAa8Ce7n6Su+8EnEj0BHwCaO+RCnefHi+fC9RKom5Zd8o+XMo+XMo+TMo9XMo+XMo+XGlNx83M7AUzOxSWNxlK0ptS8folwBKixuRQM2uaQNlSBdKy3xx4AOgJtAZ6mlnP1Drp66Pss1LjKQfMrD6wETDd3d3MasRP2sfdfRvgEeBfZtY+dR93/wi41t2/SqhsqQLKPlzKPlzKPkzKPVzKPlzKPng3AwcDw81slJltHzcYK8ysZmqleNk3QEui0XB6z134hgOfAvsAxwKPAReY2VZpTWniprOyz0K/iBxw9wVET8w/xz+nhmPWiVfpAUwBDo+Xl8TrvZ/3YqVKKftwKftwKfswKfdwKftwKfswxU3GnYDmwEXAjcAWwEtmNsDM6rr7MoB4VNTv4vv9Alzv7nMSKl3WUZz9rkSNpH7u/oO7fwdcSTSScf/UumZW08zqxvdT9hnUeKpiaUPt7gC2NbNnzWzXuPv5i0UTkC0DxgC/N7P1vJKrYUhhUfbhUvbhUvZhUu7hUvbhUvbB2xj4HJjk7ncQNRn/QTTH19TUnD/ADcC9qTu5+xf5LlSq3O+AmUAFLJ9AvAJ4Czgsbb07gfGpH5T9itR4qiJmtrmZHZQaaufu7wDdiM7nHmZmV5nZ5vFQzE2AQ4DP3f3n9PNCpfAo+3Ap+3Ap+zAp93Ap+3ApewFw94lEub8Z//wm0al3PYCJQD8zmwqcTDQqqtLJx6XgvAf826PTZiFuQAHjgP0tmufrd8ApKPtKmf96SqKsAzM7GbgOONKjiQRTyw8ETgB2B5oBHwH1gVJgL3f/0TIuwyiFRdmHS9mHS9mHSbmHS9mHS9mHy6IJpXd295cylpunvYk2s82AdsA9wF3ufpayL2yZ2ZtZqbsvTM/ezNYDZhHN+9UPqOPuHZV9dmo8VSEzG050Kmj3jOWlwF7AdkQTkk0Eprj7h/FQvfL8VytVSdmHS9mHS9mHSbmHS9mHS9mHKbPpmJlpRhPiZKJT7Bq5+3w1HwpbWvbt3f09M6sZn0qbur0kHuX4JFAHOBDYwt2/V/bZqfFUhcysFdF53R8A57v7rIRLkjxR9uFS9uFS9mFS7uFS9uFS9uHK1nTMMuKpFBgNvOru12Y2KaQwrWb2NwI9gd7ufrOyr5zmeKpC7v4ecDxgwC1mdpJFl10FwMxqxd9rVrIJKVDKPlzKPlzKPkzKPVzKPlzKPmhDgcMsmkw+dbU6j+f1sfjnhcA57n5tfB+NdCsOlWVvafO33QPc5u43xz8r+0poxFMOmNmfgbOBTYjO+3zZ3f+RbFWSD8o+XMo+XMo+TMo9XMo+XMo+TGa2N3ANsAT4F/Ckuy+Ib9NpVUVsdbI3sw3jOd10eu1KqPGUIxZd1aILsAfQAtgceBzYBhgCPJ960kpxUfbhUvbhUvZhUu7hUvbhUvZhUtMxXMq+aqjxlGNm1hioC+wCbA3MB7529+cTLUxyTtmHS9mHS9mHSbmHS9mHS9mHR03HcK0i+8HAC8p+5dR4EhEREREREVkNajqGS9mvPTWe8iRzBnwJh7IPl7IPl7IPk3IPl7IPl7IXEVk1NZ5ERERERERE1oCajuFS9mtOjScREREREREREcmJkqQLEBERERERERGR4qTGk4iIiIiIiIiI5IQaTyIiIiIiIiIikhNqPImIiATKzE43M0/7WmJmH5vZADOrWw3qu8rMDsqy/B4zm5NAPY3NbIiZzTKzRWY2z8zeMrPBZlZnLbZ3j5l9sQ71XBXntsjMNshye3q+26/t46zk8ZvF2z6zqre9Go893szG5/txRUREZM2p8SQiIiLHAW2AI4DngD7ATYlWFLkS+E3jCegPdMxnIWa2PvAacCQwEPgz0B34N3AUUC+f9WRYChybZXkn4Oc815Iv58RfIiIiUs3VTLoAERERSdw77j47/vcLZrYDcIaZXeDuFUkWlo27f5zAwx4LbA3s6u7vpi0fbWb9Eqgn3WPAqcDI1AIzawIcANwHnJ5MWbnj7jOTrkFERERWj0Y8iYiISKapRCN4Nk5faGbbmNk/zWyumf1iZu+YWceMdbY3s/vN7NP4FLBPzOxOM9so80HM7AAze8HM5pvZAjN718zOiG/zeLXL004Xuyq+7Ten2pnZ5mZ2X3z62y9m9p6ZnZKxTurUs33i/8dPZvZlfPrcqk4tbBh//zrzBo+lPc7yWtOWpU5LOz3L72FfM3vDzBab2Rwz++sqasl0H7C/mW2dtuxU4D/AhGx3MLOjzWyKmS00sx/N7BEza5plva5mNjXO8gcze8XM9s1YrYaZXWNmX8XbesrMtsrYzglm9lL83Pmfmb1tZqdleTw3s2vN7Pz4OfRz/JjNM9Zb4VQ7M2tgZreZ2X/i/L8xs3FmtlOWbV9sZp/Fz7mxZrZp/PVw/Fz83MwuqfzXLSIiImtCjScRERHJ1AyYD3yXWhCPoHkN2AW4CGhP1KAabWbt0+67BfAFcCFwGHANcDDRKWmkba8MeBGoTXTKWhlwN9GoIohO/QO4J/53G2BEtmLNrD7wCvAn4DKgAzANuN/MumW5y/3Ax8DRwJ3AuUSnF67M6/H3UWZ2WPyYVWF94CHgXqK6xwNDsjWoVuL/gDnAyWnLTgUeADxzZTM7CxgNzCQaydUdaAG8Ymbrpa13MzCcKOe/AKcQNbIyG1R9gO2BLsAFRFn9M2OdbYFH4xo7AE8BI+JaMp1CdNrnBUDn+PGeNLOVjdQfGNd4NdAOOAt4B9gwY71TiU7fPAf4K/BHosbd48B7wDFEz9XrzezPK3k8ERERWU061U5ERERqxG/q1yOaO+kY4EJ3L09b5yrAgAPcPdWQei5uSF0DjAFw9wmkjbIxs0nAbOD/zGw3d3/bzAwYTNQYaJt2Ot+41P3cfUq0Gv919ymrqL8zsEO8rfHxsmfMrDFwrZmNzPi/POjuV6Ye08z2Bk4kmlMqK3efYGZXAlcAzwLlZvYO8DQwyN1/XEWNlVkP6Obuo+KfnzWzLYGrzeze9JFUK+FETaZTgQFmthewE1FDZb/0Fc2sAXAD8A9375K2/DVgFnAGMMiiycgvAga6e4+0TYzN8vifuftJadvaBLjJzLZw9y8B3H1A2u0lRA22zYGzgb9nbG8pcKS7L43XB3gE2AuYVMnvoA3wT3cfmbbs8Szr/QKUufuyeNst4v9nX3e/Nl42nmg/OI6MhqmIiIisOY14EhERkQ+I3ux/TzRP0DB3H5qxzuFEb8Lnm1nN1BfRZOS7WDT5NmZW28wuM7MPzGxRvN3/i7exY9r3rYERVTSH1P5EDarxGcsfADYBfp+xPLN5Mo3fjuL5DXe/Jl7vTKJRU42ImlXT4ybX2ignGn2UblT8OFsCpP++VzLq5z5gJzPbk2hS8Snu/lGW9doQjbL6Z8Y2vyB6Huwfr3cI0d+Jw1fj/5Dt9wlpv1Mz28HM/mVm/yV6Tiwl+j3uyG+9kGo6Vba9LN4ATo+fe63NrEYl672QajrFPoi/P5daEN8+G2iykscTERGR1aTGk4iIiHQE9iS6Uts44Bwz65SxzqZEDY2lGV+pq981ir//jWh01ANEp0vtRXRKG0DdjHW/qKL6GwJfZVn+ddrt6b7P+PkXoM7qPJC7f+3uI929s7tvA5xH1CDqtQb1pvsho8kC8E38fUsza0bG7zxellnXbGAy0YilE4gaUdlsGn8fl7ldoCW/ZrMmGWX7fUKcdzzK6gWi0zQvJTq9bU+iUyuz/d5Xur1K/BUYRnS63xvAt2Y20MxKM9b7IePnJStZvqp5v0RERGQ16FQ7ERERmZ66qp2ZvUQ0181NZjba3RfE63xHNHLphkq28WX8/QTgvtRpS/E2G2SsOy/+vmVVFE/UqMg2cmaz+Pt3WW6rEu5+u5n1Z8VRVb8QzV2VrhHZbWRmtTKaT6nRU/8FviVq0qT7kuzuA24HlhHNG5VN6ndxOjAjy+0/x9/TM/qwkm2trjZEI9z+6O4TUwtXMWfTGnH3/xHNNdXHoknWjwWuJ2ogaaJwERGRBKnxJCIiIsu5+y9m1gt4kmgC5tSIpmeJGggz3H3RSjZRSjR6Jl3njJ9nEU2GfaaZDV/JPEZLiK6utyqvAMeZ2X7u/mra8pOIGjfvr8Y2VsrMNgPmZZymhZltDmzAiiOuPiOarDvdEZVsugbRnFqj0padQHRFuv/Gv5s3V7PMh4gmdH/P3TNHDaVMImoube/u965kW+OACqAbcPFqPn5lUqOOlj8vLLrKYdk6bjcrd/8MuMXMTua3OYiIiEieqfEkIiIiK3D3MWb2BtDTzIbGjaZ+RFd2m2BmQ4kaRxsRvbHfNm2i6meB08xsGtE8OUcD+2Zs383sQuAx4CUz+zswF9gZ2DRt4u+ZwBFm9izRqVBfpiarznAP0RXQHjOzy4lODzuZ6Opm3TMmFl9bpwDnm9k/gCnAQuB3RE2ZJUQjjVJGAVfEtUwhOrXsxEq2+zNwo5ltDHwUr3cIcPpqTiy+nLv/QHTa5MrW+SluLN4eTwL+DNEVDLcEDgDGu/uD7v6xmQ0EesRXuhtDNB/VXsAH7l7ZiKpsJgE/xY95JVCfaJL2eURNu3VmZpPjGqcB/4v/L7sQXS1QREREEqTGk4iIiGRzBdGEy2cRXdnsP2bWmmj+pgFEk3Z/B0xnxTf3fyW6+t118c//JmqmvJ6+cXd/0szaAX2JJjQH+BgYlLbaecAQ4CmiuYCujh9/Be6+wMwOAG4kOr1qPaLTw0519wfW/L+e1Vii5kz7uK71iRonrwInufvUtHX/BmwYr3cp0e/gVOC1LNv9iWiE02CiOZa+AS5YxWikdeLuw8zsc6J5qU4CahGd1jeB6EqDqfV6mtlsopFvpwELiE7DfH4NH2+umXUEbgEeJTpVcDDR3FuVXklwDU0A/kL0+64JfAJc5O5Dqmj7IiIispZsDT9MExERERERERERWS26qp2IiIiIiIiIiOSEGk8iIiIiIiIiIpITajyJiIiIiIiIiEhOqPEkIiIiIiIiIiI5ocaTiIiIiIiIiIjkhBpPIiIiIiIiIiKSE2o8iYiIiIiIiIhITqjxJCIiIiIiIiIiOaHGk4iIiIiIiIiI5MT/A65gu+izxx71AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1440x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''Plot the LS reaction rates for all full-rank sub-mechanisms'''\n",
    "\n",
    "from matplotlib import pyplot as plt # import the pyplot function of the matplotlib package\n",
    "fig, ax = plt.subplots(figsize=(20,6))\n",
    "\n",
    "ax.plot(range(sub_mech_rxn_rates_mtrx.shape[1]), np.linalg.norm(sub_mech_rxn_rates_mtrx,axis=0), \n",
    "        '-.',color='black', marker='*',markersize=12)\n",
    "\n",
    "plt.xticks(range(sub_mech_rxn_rates_mtrx.shape[1]),[sm[0] for sm in sub_mechanisms],rotation=60,fontsize=14)\n",
    "ax.set_ylabel('Reaction Rate Norm',fontsize=16)\n",
    "ax.set_xlabel('Reaction Sub-Mechanism',fontsize=16)\n",
    "ax.xaxis.grid(True,linestyle='-',which='major',color='lightgrey',alpha=0.9)\n",
    "fig.suptitle('Full-Rank (%i) LS Reaction Rates Magnitude of All Sub-Mechanisms'%(s_rank),fontsize=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sub-mechanism id.              = 2\n",
      "minimum norm sub-mech rxn rate = 3.8266e-01\n",
      "sub-mechanism rxn id           = (0, 1, 3, 5)\n",
      "r0 :  2 N2O5         <=> 2 N2O4 + 1 O2\n",
      "r1 :  1 N2O5         <=> 1 NO2  + 1 NO3\n",
      "r2 :  1 NO3          <=> 1 O2 + 1 NO\n",
      "r3 :  2 NO2          <=> 1 N2O4\n",
      "n_reactions = 4\n",
      "sub-mechanism rxn score        = 8.93\n"
     ]
    }
   ],
   "source": [
    "'''Print the LS reaction rate with minimum norm (unique)'''\n",
    "\n",
    "rate_min = np.linalg.norm(sub_mech_rxn_rates_mtrx,axis=0).min()\n",
    "idx_min = np.argmin( np.linalg.norm(sub_mech_rxn_rates_mtrx,axis=0) )\n",
    "print('sub-mechanism id.              = %i'%idx_min)\n",
    "print('minimum norm sub-mech rxn rate = %8.4e'%rate_min)\n",
    "print('sub-mechanism rxn id           =', sub_mechanisms[idx_min][0])\n",
    "print_reactions(sub_mechanisms[idx_min][1])\n",
    "print('sub-mechanism rxn score        = %4.2f'%sub_mechanisms[idx_min][3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''Plot the LS residual norms of all full-rank sub-mechanisms'''\n",
    "\n",
    "from matplotlib import pyplot as plt # import the pyplot function of the matplotlib package\n",
    "fig, ax = plt.subplots(figsize=(20,6))\n",
    "\n",
    "ax.plot(range(sub_mech_residuals_mtrx.shape[1]), np.linalg.norm(sub_mech_residuals_mtrx,axis=0),\n",
    "        '-.',color='red',marker='*',markersize=12)\n",
    "\n",
    "plt.xticks(range(sub_mech_residuals_mtrx.shape[1]),[smr[0] for smr in sub_mechanisms],rotation=60,fontsize=14)\n",
    "ax.set_ylabel('Residual Norm',fontsize=16)\n",
    "ax.set_xlabel('Reaction Sub-Mechanisms',fontsize=16)\n",
    "ax.xaxis.grid(True,linestyle='-',which='major',color='lightgrey',alpha=0.9)\n",
    "fig.suptitle('Full-Rank LS Residuals of All Sub-Mechanisms w/ Rank = '+str(s_rank),fontsize=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Rank-deficient least-squares reaction rate solution<a id=\"rankdef\"></a>\n",
    "Despite all the foregoing development, we have not solved the original problem yet, namely\n",
    "\n",
    "\\begin{equation*}\n",
    "\\Smtrx^\\top\\,\\rvec = \\gvec .\n",
    "\\end{equation*}\n",
    "\n",
    "However this problem is related to the series of sub-mechanisms we just analyzed. To see this, assemble the matrix of sub-mechanism reaction rates mapped into the original reaction dimension $m$ by completing the additional entries with zeros. We denote this vector mapping $\\rvec_k\\longrightarrow\\hat{\\rvec}_k$ and the vectors \n",
    "$\\hat{\\rvec}_k$ as **basic** vectors. \n",
    "\n",
    "Then we show that all **basic** vectors produce the same residual vectors, that is:\n",
    "\n",
    "\\begin{equation*}\n",
    "\\gvec - \\Smtrx^\\top\\,\\hat{\\rvec}_k\n",
    "\\end{equation*}\n",
    "\n",
    "is invariant for any $\\hat{\\rvec}_k$ and equal to the residuals $\\gvec - \\Smtrx_k^\\top\\,\\rvec_k$. All residuals being equal, we choose the rank-deficient least-squares **basic** solution as the $\\hat{\\rvec}_k$ of minimum norm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "'''Map r_k --> \\hat{r} rates'''\n",
    "\n",
    "mech_rxn_rates_mtrx = np.zeros((len(reactions),len(sub_mechanisms)))\n",
    "\n",
    "for sm in sub_mechanisms:\n",
    "    sm_idx = sub_mechanisms.index(sm)\n",
    "    rxn_idxs = sm[0]\n",
    "    mech_rxn_rates_mtrx[rxn_idxs,sm_idx] = sub_mech_rxn_rates_mtrx[:,sm_idx] # map "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "matrix shape = (6, 9)\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1440x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.18 -0.16 -0.07  0.15 -0.16 -0.07  0.15  0.    0.  ]\n",
      " [ 0.    0.34  0.25  0.04  0.    0.    0.    0.18  0.  ]\n",
      " [ 0.    0.    0.    0.   -0.34 -0.25 -0.04  0.   -0.18]\n",
      " [-0.04  0.3   0.22  0.    0.3   0.22  0.    0.15  0.15]\n",
      " [-0.25  0.09  0.   -0.22  0.09  0.   -0.22 -0.07 -0.07]\n",
      " [-0.68  0.   -0.18 -0.61  0.   -0.18 -0.61 -0.32 -0.32]]\n"
     ]
    }
   ],
   "source": [
    "'''Show the mapping in the form of a matrix'''\n",
    "\n",
    "from chen_3170.help import plot_matrix\n",
    "\n",
    "plot_matrix(mech_rxn_rates_mtrx)\n",
    "np.set_printoptions(precision=2,threshold=100,edgeitems=5)\n",
    "print(mech_rxn_rates_mtrx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute $\\gvec - \\Smtrx^\\top\\,\\hat{\\rvec}_k$ for all $k$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "residual k = 0 [0.472 0.149 0.622 0.783 0.323 0.311]\n",
      "residual k = 1 [0.472 0.149 0.622 0.783 0.323 0.311]\n",
      "residual k = 2 [0.472 0.149 0.622 0.783 0.323 0.311]\n",
      "residual k = 3 [0.472 0.149 0.622 0.783 0.323 0.311]\n",
      "residual k = 4 [0.472 0.149 0.622 0.783 0.323 0.311]\n",
      "residual k = 5 [0.472 0.149 0.622 0.783 0.323 0.311]\n",
      "residual k = 6 [0.472 0.149 0.622 0.783 0.323 0.311]\n",
      "residual k = 7 [0.472 0.149 0.622 0.783 0.323 0.311]\n",
      "residual k = 8 [0.472 0.149 0.622 0.783 0.323 0.311]\n"
     ]
    }
   ],
   "source": [
    "'''Subtract above from g column by column'''\n",
    "\n",
    "np.set_printoptions(precision=3)\n",
    "\n",
    "for j in range(mech_rxn_rates_mtrx.shape[1]):\n",
    "    tmp = g_vec - (stoic_mtrx.transpose() @ mech_rxn_rates_mtrx)[:,j]\n",
    "    print('residual k = %i'%j,tmp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''Plot of the input species production rate'''\n",
    "\n",
    "from matplotlib import pyplot as plt # import the pyplot function of the matplotlib package\n",
    "fig, ax = plt.subplots(figsize=(20,6))\n",
    "\n",
    "ax.bar(range(len(species)), g_vec, color='blue')\n",
    "plt.xticks(range(len(species)),species,rotation=60,fontsize=14)\n",
    "ax.set_ylabel('Species Production Rate',fontsize=16)\n",
    "ax.set_xlabel('Species',fontsize=16)\n",
    "ax.xaxis.grid(True,linestyle='-',which='major',color='lightgrey',alpha=0.9)\n",
    "fig.suptitle('Input Species Production Rates ('+str(len(species))+')',fontsize=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Select as **basic** solution of the rank-deficient LS problem: \n",
    "\n",
    "\\begin{equation*}\n",
    "\\min\\limits_k \\norm{\\hat{\\rvec}_k} \\quad\\ \\forall \\quad\\ k=1,\\ldots,\\text{# of full-rank sub-mechanisms} .\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''Basic least-squares reaction rates'''\n",
    "\n",
    "from matplotlib import pyplot as plt # import the pyplot function of the matplotlib package\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(20,6))\n",
    "ax.bar(range(len(reactions)), mech_rxn_rates_mtrx[:,idx_min], color='orange')\n",
    "plt.xticks(range(len(reactions)),reactions,rotation=60,fontsize=14)\n",
    "ax.set_ylabel('Reaction rate',fontsize=16)\n",
    "ax.set_xlabel('Reaction',fontsize=16)\n",
    "ax.xaxis.grid(True,linestyle='-',which='major',color='lightgrey',alpha=0.9)\n",
    "fig.suptitle('Basic LS Reaction Rates (%s)'%str(s_rank),fontsize=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.6.5"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autoclose": false,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}