QMC-NDA_is_Better.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\newcommand{\\calf}{{\\cal F}}\n",
    "\\newcommand{\\dnu}{d \\nu}\n",
    "\\newcommand{\\dmu}{d \\mu}\n",
    "\\newcommand{\\dmup}{d \\mu'}\n",
    "\\newcommand{\\vf}{{\\bf f}}\n",
    "\\newcommand{\\vq}{{\\bf q}}\n",
    "\\newcommand{\\mg}{{\\bf G}}\n",
    "\\newcommand{\\mK}{{\\bf K}}\n",
    "$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[36m\u001b[1m[ \u001b[22m\u001b[39m\u001b[36m\u001b[1mInfo: \u001b[22m\u001b[39mPrecompiling NDA_QMC [top-level]\n"
     ]
    }
   ],
   "source": [
    "include(\"nda_note.jl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problems with NDA and QMC\n",
    "\n",
    "Here are the things I've been doing to figure out what the problems are.\n",
    "\n",
    "The first thing is to see if the low-order problem is correct. I know that the QMC code is returning good cell-average fluxes because I'm getting good results with the Krylov solves. So I will check the coefficients and boundary conditions of the low-order problem\n",
    "\n",
    "$$\n",
    "\\frac{d}{dx}\\left[ -\\frac{1}{3\\Sigma_t} \\frac{d\\phi}{dx} + \\hat{D} \\phi\\right] + (\\Sigma_t - \\Sigma_s)\\phi = q,\n",
    "$$\n",
    "with boundary conditions $\\phi(0)=\\phi^{HO}(0)$ and $\\phi(\\tau)=\\phi^{HO}(\\tau)$. For our example $q=0$.\n",
    "\n",
    "The coefficient is\n",
    "$$\n",
    "{\\hat D} = \\frac{ J^{HO} + \\frac{1}{3} \\frac{d \\phi^{HO}}{dx} } {\\phi^{HO}},\n",
    "$$\n",
    "\n",
    "In my formulation $\\hat D$ is a cell-average qantity and the low-order flux $\\phi$ is a cell edge quantity.\n",
    "As you saw from my email of July 13, the QMC code returns strange cell-edge valueds for the flux. The QMC code then differentiaes the edge values numerically to get $d \\phi/dx$. NDA with that $d \\phi/dx$ diverges.\n",
    "\n",
    "I fixed(?) that by taking using the cell averages to get cell edges and then differentiate that numerically. The Julia code for that is\n",
    "```Julia\n",
    "function avg2edge!(phi_edge, dphi, phi_avg, dx,AVE)\n",
    "Nx=length(phi_avg)\n",
    "m=length(phi_edge)\n",
    "Nx==length(dphi) || error(\"dphi lives on cell centers\")\n",
    "m == Nx+1 || error(\"edges and averages fail to match\")\n",
    "phi_edge[1]=1.5*phi_avg[1] - .5*phi_avg[2]\n",
    "for ie=2:Nx\n",
    "phi_edge[ie] = .5*(phi_avg[ie-1]+phi_avg[ie])\n",
    "end\n",
    "phi_edge[Nx+1]=1.5*phi_avg[Nx] - .5*phi_avg[Nx-1]\n",
    "cphi=copy(phi_edge)\n",
    "aphi=AVE*cphi\n",
    "for id=1:Nx\n",
    "#dphi[id]=(phi_edge[id+1]-phi_edge[id])/dx\n",
    "dphi[id]=(aphi[id+1]-aphi[id])/dx\n",
    "end\n",
    "#return (phi_edge=phi_edge, dphi=dphi)\n",
    "phi_edge .= aphi\n",
    "return (phi_edge=aphi, dphi=dphi)\n",
    "end\n",
    "```\n",
    "The NDA iteration no longer diverges, but the solution is terrible and is discontinuous at the right boundary. Here's a plot. I'm using my very questionable implementation ```qmc_nda.jl``` for this. All the codes I use for QMC work in this note book are in the __src/Tim_QMC__ directory. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are a few sanity checks to see what the fluxes and the derivative $d \\phi/dx$ look like. I'll repeat\n",
    "the computation from the email first and them compare my fix to what I get from a standard SN transport sweep. Here's the script and plot from the email."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.legend.Legend object at 0x18a111fd0>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Nx=100;\n",
    "na2=11;\n",
    "s=1.0;\n",
    "phit=ones(Nx,);\n",
    "data1=qmc_init(1000,Nx,na2,s);\n",
    "data2=qmc_init(10000,Nx,na2,s);\n",
    "phiout1=qmc_sweep(phit, data1);\n",
    "phiout2=qmc_sweep(phit, data2);\n",
    "plot(phiout1.phi_edge,\"k-\");\n",
    "plot(phiout2.phi_edge,\"k--\");\n",
    "legend([\"N=1000\", \"N=10000\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now look at the average values. They do get smoother as N increases."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.legend.Legend object at 0x219a6cfa0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(phiout1.phi_avg,\"k-\");\n",
    "plot(phiout2.phi_avg,\"k--\");\n",
    "legend([\"N=1000\", \"N=10000\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now here's trouble. The average flux looks pretty decent, but has jumps all over. This \n",
    "spells trouble for $d \\phi/dx$. Even the small fluctuations elsehwere lead to big problems with dphi. So $d \\phi/dx$ is nuts and I may have to do the smoothing unless you can get me a $d \\phi/dx$ directly from QMC (ie with no difference approximation).\n",
    "\n",
    "Start by setting up the plain vanill sn_data to have the same number of cells (Nx) as qmc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "nx=Nx+1;\n",
    "na2=20;\n",
    "s=1.0;\n",
    "sn_data=sn_init(nx, na2, s);\n",
    "dx=sn_data.dx;\n",
    "AVE=data2.AV;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now try to average the qmc cell average fluxes and get dphi and phi_edge from that."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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j0eg9P2HCBMybNw+9evXClStXsHz5cqxevRqnT58GAMjlcrzyyit499134ezsDAB46623sHLlSuzatQsKhQIODg4YO3YsnnzySbRt23Imrmo0GpSUlMDLy6vOfZRKJZRKpe7nxqxBNapHAFbsvYI9F/JQoVLD2VHarHqJqOkYZIiMrKKiAi+99BJycnLg6+uLxx57DH/7298M7rt+/Xps3rwZbdq0QVhYGJ599lm4u7sjMzMTr7/+ut6tOXx8fNCzZ0+Eh4fj2WefRZ8+fXTPderUCcuXL8fChQvx888/w8XFBU899RRcXV313s/JyQmzZs3CrFmzTPLZLcVnn32GsrIyPPXUU3XuExsbi/fff79Jr9+jjQfatnLGjcIKHLicj+HdDF+FSURmILQwCoVCACAoFAqxSyEbFRsbKwDQPezt7YWMjIxa+12+fFlwdHTU29fLy0t44oknBAcHB92xixYtEjIzMwWNRiPCp2kaY/4eAhC2bNnS4P1/+uknwcXFRYiPj693v8rKSkGhUOgeGRkZjar5jf8kC+3/8Zvwf/GpDa6NiOrW1POGWRbEI7IVBQUF+PjjjwEAc+fOxf3334/q6mosX7681r5z5syBSqVCZGQk3nzzTXTp0gW3bt3Cpk2bUFVVhYEDB+Lo0aN45513dFfvUP02btyIyZMn4z//+Q+GDRtW774ymQweHh56j8YI9XcHAKTmlDS5XiJqPgYZIiP68MMPoVAo0KtXLyxevFg3dPHNN9/ozcH4888/sW3bNtjb22PNmjVYvHgxzp8/j/Xr12Pu3Lk4dOgQEhISjH7FTUv2888/4/nnn8dPP/2Ehx9+2OTv15VBhsgiMMgQGcmFCxfw1VdfAQCWLFkCOzs7jB49GqGhoSguLsbq1asB1Ewyff311wEAr732GsLCwgAAUqkUEyZMwCeffIKoqChxPoSFKC0tRXJyMpKTkwEAV69eRXJysu6Kq7vXn/r5558xadIkfPbZZ4iMjEROTg5ycnKgUChMVqM2yFwrKENlldpk70NE9WOQITKC0tJSjBs3DiqVCiNHjtTdwd3Ozg5vvPEGgJoJqHl5efj000+RmpoKX1/fBl8abGuOHz+O++67T9eRmjNnDu677z7d/193rz/1zTffoLq6Gq+++ioCAgJ0D21gNIXWbjK0cnGARgAu3Sw12fsQUf141RLRPVy7dg3r16/HuXPnkJaWBqBmfkXPnj0RHR0Nd3d33crVgYGBWLdund7xzz77LD788ENcu3YNQ4cOxaVLlwAAS5cuhaenp5k/jXUYMmRInQv0Aaj1//HevXtNW5ABEokEXf3dcTjtFlJvliC8rdzsNRARgwxRnYqLi/Gvf/0Ly5cvh0qlqvV8QkICvvzyS93P9vb2+OWXX2rdENXJyQlxcXEYOHAgzpw5AwB46KGHMGHCBNN+ADK5UH+PmiCT0/A1aIjIuBhkiAy4efMmhg0bhrNnzwKo6RCMGjUKnTt3hlQqRUlJCY4ePYpjx46huroazs7OmDVrVp03Q+3atSt27NiBIUOGoLq6GitWrOBVSC2Adp7MBU74JRINgwzRXW7cuIGhQ4fi4sWL8Pf3x+rVqzFq1KhaweOZZ55p1Ov27t0b165dQ1lZGdq0aWPMkkkkXfx45RKR2BhkiO5QWFiI4cOH4+LFi2jXrh127dqFTp06Ge31PT09OS+mBdF2ZHJLlCgsU6GVq6PIFRHZHl61RHSbSqXCE088gQsXLqBt27ZISEgwaoihlsdNZo+2rWruY5V6k10ZIjEwyJBNSU9Px5w5czBv3jy9NUZUKhUmTZqEPXv2wM3NDb///jvat28vYqVkLbreHl66yCBDJAoOLZFN0Gg0mDdvHr744gtUVVUBAH766Sf861//Qnh4ON5++23s3LlTd+VRz549Ra6YrEVHXzfsupCLtLwysUshskkMMmQTfvjhByxduhQA8OCDDyIjIwOXL1/G5MmTdfu4urriv//9L0aOHClWmWSFQnxq7jB+NZ9BhkgMHFqiFq+oqAjz5s0DUHMvpN27d+P06dN47733EBkZCW9vb4SFhWHfvn0MMdRoDDJE4mJHhlq8d999F3l5eQgNDcXcuXMBAM7Ozli4cCEWLlwobnFk9Tq0rgkyNwrLoaxWQ2YvFbkiItvCjgy1aElJSbobOX755ZdwdOTlsWRcrd1kcJPZQyMA6QXlYpdDZHMYZMiilZWVITExsd777tRFpVLhhRdegEajwdNPP42hQ4eaoEKydRKJRDe8lMbhJSKz49ASWSxBEDBy5EgcOHAATzzxBNatWwc3NzcANXeb3rRpE27cuIHKyko888wzCA0N1Tv+448/xpkzZ+Dj44Ply5eL8RHIRoT4uOJMpoLzZIhEwCBDFus///kPDhw4AADYtGkTLl68iP/7v/9D+/bt8dhjj+HcuXO6fZctW4YffvgBjz32GICaS6s/+OADAMAXX3yB1q1bm71+sh26Cb+8BJvI7BhkyCJVVlbiH//4B4Caexrt3LkTZ86cwbBhwyCVSqFWqxEQEIDRo0fjwoULOHjwIB5//HEMHToUnp6e2LRpEwBg/PjxGD9+vJgfhWyAdsIvOzJE5sc5MmSRPv/8c1y/fh1t2rTBv//9b5w8eRIzZsyAi4sL1Go1oqKikJSUhFWrVmHPnj147bXXAAC7du3ShZgFCxZg/fr1vMs0mVwHn5ohz7T8UpErIbI9EqEpsygtWHFxMeRyORQKBTw8PMQuh5qoY8eOSEtLw9q1a/H888/rthcUFODo0aN46KGHIJPJ9I45e/YsDh06hNTUVIwcORLDhw83c9WkZY2/h82puaSyCuELdwAATr0XA7mzgylKJGrRmvo7yKElsjhZWVlIS0uDnZ0dxo0bp/ect7c3Ro0aZfC4Hj16oEePHuYokUiPu5MDWrvLkFeixLX8MvQK8hS7JCKbwaElsjj79+8HAPTq1ctq/jVPxBV+icTBIEMWR3ul0sCBA0WuhKjhOmjXksnjPBkic2KQIYuj7cgwyJA10XVkuLovkVkxyJBFKSoqwunTpwEAAwYMELkaoob7a2iJHRkic2KQIYuivR1Bp06d4O/vL3Y5RA2mDTLX8subdEsNImoaBhmyKBxWImvVztsFEglQqqxGXqlS7HKIbAaDDFkUBhmyVjJ7Kdq2cgbAWxUQmRODDJlNWVkZPvroI2zdutXg8xUVFTh69CgAzo8h6xRye4XfawUMMkTmwgXxyCwSEhLwwgsvIC0tDS4uLigoKICTk5PePkeOHIFKpUJAQAA6deokUqVETRfi7YIEAGlcS4bIbNiRIZO7fv06hg8fjrS0NABAeXk5EhISau23b98+AMDgwYN5fySySrwLNpH5MciQySUmJkKlUqFbt2546qmnAAB//PFHrf3uDDJE1iikNYeWiMyNQYZM7tKlSwCAfv364W9/+xuA2kFGqVQiMTERAIMMWa8Q79uXYBeUQ63hJdhE5sAgQyanDTKdO3fGsGHDIJVKkZqaiqtXr+r2OXbsGCorK+Hr64vQ0FCxSiVqljatnOEglUBVrUFWUYXY5RDZBAYZMrk7g4ynpyeio6MBAHFxcbp9tMNKgwYN4vwYslpSOwna67oyHF4iMgcGGTK5O4MMAIwaNQqA/vCSdvIvh5XI2gV78y7YRObEIEMmVVhYiIKCAgDQXVKtDTI7d+5EdnY2MjIyONGXWowOrbV3wWaQITIHriNDJqXtxgQEBMDNreaKjl69eqF///44cuQI5s+fD0EQoFQqMWjQIPTo0UPMcomarcPtS7C5lgyReTDIkEndPawEABKJBJ9//jkiIyPx3Xff6ebEfPbZZ5wfQ1aPd8EmMi8OLZFJGQoyANC/f39MmjQJACAIAp555hn06dPH7PURGVuH22vJ3CisQGWVWuRqiFo+BhkyqbqCDADExsZCLpfD1dUVH374oblLIzIJHzdHuMvsIQjA9YJyscshavEYZMik6gsygYGBSE5OxunTp9G+fXtzl0ZkEhKJRDfhl8NLRKbHIEPNFh8fj4iICOzatUtvuyAI9QYZAAgODkaHDh1MXiOROWmHl67wyiUik2OQoWZJSUnBk08+iRMnTmDx4sV6zxUUFKCoqAgA0LFjRxGqIxLHXxN+GWSITI1BhpqsqKgIjz76KIqLiwEAe/fuhUKh0D2v7ca0bdsWLi4uotRIJIa/1pLh0BKRqTHIUIMdPXoUM2fORHx8PJKTkxEZGYlLly4hKCgIISEhqKqq0rvtwJkzZwCA904im8OODJH5MMhQg73yyiv44osvEBMTg/vuuw+pqalo06YNfv31V91drbdt26bbPykpCQAQEREhSr1EYtEGmcLyKhSWqUSuhqhlY5ChBsnKysKJEycgkUjg7u4OAHj44YeRnJyMXr164ZFHHgEAbN++HVVVVQAYZKjpEhISMHbsWAQGBkIikWDr1q33PGbfvn2IiIiAk5MTOnTogJUrV5q+0Dq4ONojUO4EgCv8Epkagww1iPYGj3379kVWVhaOHTuGbdu2wcfHBwAQGRmJ1q1bo6ioCPv374dKpdINLTHIUGOVlZWhV69e+PLLLxu0/9WrVzF69GgMHDgQJ0+exNtvv42ZM2di06ZNJq60biGcJ0NkFrxFATXI9u3bAQCjR4+Gm5tbrVV4pVIpxowZg7Vr12Lr1q3w9PSESqVCq1atEBISIkbJZMVGjRqlu7loQ6xcuRLt2rXDsmXLAABhYWE4fvw4Pv30UzzxxBMmqrJ+HXzccPByATsyRCbGjgzdk0qlQnx8PICaIFMX7V8YGzZsQGJiIoCabgzvn0SmlpiYiJiYGL1tI0aMwPHjx3VDnXdTKpUoLi7WexgTr1wiMg8GGbqnAwcOoKSkBL6+vvUOE8XExMDX1xd5eXn49NNPAXBYicwjJycHfn5+etv8/PxQXV2N/Px8g8dob5GhfQQFBRm1po5cFI/ILEwaZAoLCzFx4kTdiWLixIm6BdIMqaqqwj/+8Q+Eh4fD1dUVgYGBmDRpErKyskxZJt2Ddlhp1KhRsLOr+z8ZBwcHPPvsswCAa9euAWCQIfO5u/MnCILB7Vrz58+HQqHQPTIyMoxaj7Yjc72gDNVqjVFfm4j+YtIgM2HCBCQnJyMuLg5xcXFITk7GxIkT69y/vLwcJ06cwDvvvIMTJ05g8+bNuHjxou6KGBLH7t27AQAjR468577PPfec3s8MMmQO/v7+yMnJ0duWm5sLe3t7eHt7GzxGJpPBw8ND72FMgXJnODnYoUotIKOwwqivTUR/Mdlk35SUFMTFxeHw4cPo378/AODbb79FVFQUUlNT0bVr11rHyOVy3VwMrS+++AL9+vVDeno62rVrV+sYpVIJpVKp+9nY49y2Tq1WIyUlBQBqTfA1pGfPnrjvvvtw8uRJTvQls4mKisKvv/6qt23Hjh3o06cPHBwcRKnJzk6CDj5uOJ9djCu5pbq1ZYjIuEzWkUlMTIRcLteFGKDmEl25XI5Dhw41+HUUCgUkEgk8PT0NPm/qcW5bl5aWhsrKSjg5OTU4lLz44osAgOjoaE70pSYpLS1FcnIykpOTAdRcXp2cnIz09HQANcNCkyZN0u0/bdo0XL9+HXPmzEFKSgrWrFmD1atXY+7cuWKUr6Ob8Mu7YBOZjMk6Mjk5OfD19a213dfXt1YLuC6VlZV46623MGHChDrbvvPnz8ecOXN0PxcXFzPMGNG5c+cA1FzOKpVKG3TMK6+8AmdnZwwdOtSUpVELdvz4cTz44IO6n7W/48899xzWrVuH7OxsXagBgJCQEGzfvh2zZ8/GV199hcDAQCxfvly0S6+1dBN+cznhl8hUGh1kFi5ciPfff7/efY4dOwbA8CQ7QRAa9K/0qqoqPP3009BoNFixYkWd+8lkMshksnu+HjWNNsh07969wcdIpVJMnjzZVCWRDRgyZIhusq4h69atq7Vt8ODBOHHihAmraryOvtorl9iRITKVRgeZGTNm4Omnn653n+DgYJw+fRo3b96s9VxeXl6tyyTvVlVVhaeeegpXr17F7t27jT4JjxquKUGGiGp08NEOLbEjQ2QqjQ4yPj4+umXp6xMVFQWFQoGjR4+iX79+AIAjR45AoVAgOjq6zuO0IebSpUvYs2dPnVcckHkwyBA1nXaOzK0yFW6VqeDl6ihyRUQtj8km+4aFhWHkyJGYOnUqDh8+jMOHD2Pq1KkYM2aM3hVLoaGh2LJlCwCguroaTz75JI4fP47169dDrVYjJycHOTk5UKl4B9k7paam4pNPPkFlZaXJ3qO6uhoXLlwAwCBD1BR6N4/k8BKRSZh0HZn169cjPDwcMTExiImJQc+ePfHDDz/o7ZOamgqFQgEAuHHjBrZt24YbN26gd+/eCAgI0D0ac6WTLXj77bfx5ptv4ueffzbZe1y5cgUqlQouLi4IDg422fsQtWTaeTJpXOGXyCRMetNILy8v/Pjjj/Xuc+eEvuDg4Hon+NFfsrOzAUB3eaop3HnFUn0r+hJR3Tq2dsP+S/m4zI4MkUnwbycrpb3Vw9mzZ032HufPnwfAYSWi5uh4e57MlVwGGSJTYJCxUtogo+2amAIn+hI1n3ZoiR0ZItNgkLFShYWFAICbN28iLy/PKK958eJF3eReQRBw8uRJAAwyRM3R6XaQybhVjsoqtcjVELU8DDJWqLKyUu9qpeZ2ZZRKJd566y2EhYXhvvvuw9WrV3Hs2DGkpqZCJpMhKiqquSUT2azWbjJ4ONlDIwBXuZ4MkdGZdLIvmYb2Ki+ts2fPYsiQIU16LY1Gg5iYGCQkJACoCUmLFy/W3Yhz/Pjx8PLyala9RLZMIpGgk68bTqQX4XJuKcICuMAnkTGxI2OFtPNjtJoz4Tc9PR0JCQmwt7fHe++9BwBYs2YNNmzYAKDmZnxE1Dydfd0BAJc44ZfI6BhkrNDdQaY5Q0uZmZkAgHbt2mHhwoUYNGgQqqqqUFlZiZ49eyIyMrI5pRIR/ponwyuXiIyPQcYKaSf6OjnVrBh69uzZJq+/c+PGDQBAmzZtAADvvPOO7rlp06Y16AafRFQ/bZC5zCBDZHQMMlZI25G57777IJVKUVRUhKysrCa9lrYjow0yQ4cOxYQJE9C/f388++yzRqmXyNZpg8zV/DJUqzUiV0PUsjDIWCFtkPH390fnzp0BNH2ejLYj07ZtWwA1ExPXr1+Pw4cPw93dvfnFEhHaeDrDycEOKrUGGYUVYpdD1KIwyFghbZDx9PREt27dAEC3/ktj3d2RISLjs7OToGNrDi8RmQKDjBW6M8hoL40uKSlp0msxyBCZh3Z46VJu035XicgwriNjhe4MMtXV1QCAioqmtavvHloiItPoxI4MkUmwI2OFtFcteXp6wsXFBQBQXl7e6NfRaDS6ScLsyBCZVmc/BhkiU2CQsUJ3dmS0QaYpHZn8/HxUVVVBIpEgICDAmCUS0V06+91eFO9mKTSapi2XQES1MchYIW2QadWqFZydnQE0rSOjHVby8/ODg4OD0eojotrae7nAQSpBRZUamUW8conIWBhkrJCxOjKc6EtkPvZSO3Tw4YRfImNjkLFCdwYZY3RkONGXyDy082Qu3eQ8GSJjYZCxMoIgGJzsy44MkeXT3jzyIoMMkdEwyFiZiooKVFVVAWh+R4ZBhsi8uuiuXOLQEpGxMMhYGe2wklQqhZubW7M6MhxaIjIv3dBSLq9cIjIWBhkrc+f8GIlEwo4MkRVp7+0KB6kE5So1shS8conIGBhkrMydQQYAOzJEVsRBaocQH1cAnPBLZCwMMlbm7iDT1I5MSUmJ7v5M7MgQmY9uYTzOkyEyCgYZK3PnFUtA0zsy2m6Mh4cH3NzcjFcgEdWr8+2bR/LKJSLjYJCxMnV1ZCorK6HRaGrtn56ejoiICHz77bd62zMyMgAA7dq1M12xRFSL9hLsS7znEpFRMMhYmTtvTwD81ZEBasLM3Xbu3IkTJ05g8eLFetvT09MBAEFBQSaqlIgM0V2CfbMEgsArl4iai0HGytTVkQEMz5PRDkVduXIF169f121nR4ZIHO29XWFvJ0GZSo0sRe1/fBBR4zDIWJm7g4xUKoWjoyMAw/NktEEGAHbv3q37s7YjwyBDZF6O9n9duXTxJif8EjUXg4yVuXuyL1D/lUv3CjIcWiIyvy63r1y6zAm/RM3GIGNl7u7IAPVfuXTr1i3dn3ft2qUbk+fQEpF4OumuXGJHhqi5GGSsjKGOjDbI3Ksjk52djQsXLkAQBF2QYUeGyPy6+PHKJSJjYZCxMgUFBQAAb29v3Tbt0FJ9c2Ts7e0B1Awv5efno7KyEhKJhIvhEYmgs+7mkaW8comomRhkrIx2qOjOINOQjsywYcMA1AwvaefH+Pn5QSaTmbReIqot+PaVS6XKamTzyiWiZmGQsSIqlUp3W4HGdmSeeOIJAMC+fft0l2FzfgyROBzt7RDMK5eIjIJBxopouzESiQRyuVy3va6OjCAIeh0ZNzc33Lp1C9u3bwfA+TFEYupyx/ASETUdg4wV0QaZVq1aQSqV6rbX1ZEpLS2FWq0GALRu3RoDBgwAAPzyyy8A2JEhElOn27cqYEeGqHkYZKyIoYm+QN0dGW03xsHBAS4uLhgyZAgAoLi4GACDDJGYtB0Z3jySqHkYZKyINsh4eXnpba+rI6MNMq1atYJEIsHgwYP1nufQEpF4uvr91ZHRaHjlElFTMchYkaZ2ZLQ3mIyIiICrq6vueXZkiMQT7OMKR6kdylVq3CisPVGfiBqGQcaKGLr0Gqj7FgV3BxkHBwfdPBmAHRmybCtWrEBISAicnJwQERGB/fv317v/+vXr0atXL7i4uCAgIAAvvPCCLvxbIgepHTreXuE3lfNkiJqMQcaK1DW0VNctCu4OMgB082QcHR3h6+trqlKJmmXjxo2YNWsWFixYgJMnT2LgwIEYNWqUbg2kux04cACTJk3C5MmTce7cOfzyyy84duwYpkyZYubKGyfUv2Z4KTWnWORKiKwXg4wVqWtoqaEdGQAYOXIkJBIJwsPDYWfHr58s09KlSzF58mRMmTIFYWFhWLZsGYKCgvD1118b3P/w4cMIDg7GzJkzERISggEDBuDll1/G8ePHzVx543S9HWQu5LAjQ9RU/JvMitQ1tNSYjkzv3r2RkJCguwSbyNKoVCokJSUhJiZGb3tMTAwOHTpk8Jjo6GjcuHED27dvhyAIuHnzJv773//i4YcfrvN9lEoliouL9R7mpp3wm8ogQ9RkDDJW5F5XLTWkIwMAAwYMQEhIiKnKJGqW/Px8qNVq+Pn56W338/NDTk6OwWOio6Oxfv16jB8/Ho6OjvD394enpye++OKLOt8nNjYWcrlc9xBjzpi2I3M1vwzKarXZ35+oJWCQsSL3umqpIR0ZImshkUj0fhYEodY2rfPnz2PmzJl49913kZSUhLi4OFy9ehXTpk2r8/Xnz58PhUKhe2jvCG9OAXInuDvZo1ojIC2vzOzvT9QS2ItdADVcc69aIrIGPj4+kEqltbovubm5tbo0WrGxsXjggQcwb948AEDPnj3h6uqKgQMH4oMPPkBAQECtY2Qymeg3TZVIJAj1d8exa4VIzSlBWICHqPUQWSN2ZKyEIAhGuWqJyNI5OjoiIiIC8fHxetvj4+MRHR1t8Jjy8vJak9e1t/EQBMtebI4Tfomah0HGSpSXl0OpVAJgR4Zavjlz5mDVqlVYs2YNUlJSMHv2bKSnp+uGiubPn49Jkybp9h87diw2b96Mr7/+GmlpaTh48CBmzpyJfv36ITAwUKyP0SB/TfjlJdhETcGhJSuhHVZycHCAm5ub3nPsyFBLM378eBQUFGDRokXIzs5Gjx49sH37drRv3x4AkJ2drbemzPPPP4+SkhJ8+eWXeOONN+Dp6YmHHnoIixcvFusjNJh2OCklmx0ZoqZgkLESd070vXvCo6FbFAiCwCBDVm369OmYPn26wefWrVtXa9trr72G1157zcRVGV9YgAckEiCnuBJ5JUq0dhd33g6RteHQkpWoa34MYPimkWVlZaiurq7zGCKyDK4ye3RsXdNlPZupELkaIuvDIGMl6rr0GvirI6NUKqFW16xFoe3GODg46J4nIsvUI7BmeOkMgwxRozHIWIm6Lr0G/urIAEBlZSUA/fkxda29QUSWoUcbOQB2ZIiagkHGSjRkaAn4a54M58cQWQ8GGaKmY5CxEvUNLdnZ2ekW9tLOk2GQIbIe3W8PLWUpKlFQqhS5GiLrYtIgU1hYiIkTJ+ruZTJx4kQUFRU1+PiXX34ZEokEy5YtM1mN1qK+oSWg9pVLDDJE1sPdyQEdfFwBAGezuJ4MUWOYNMhMmDABycnJiIuLQ1xcHJKTkzFx4sQGHbt161YcOXLE4hezMpf6hpaA2lcuaQOjp6enyWsjoubrzuEloiYxWZBJSUlBXFwcVq1ahaioKERFReHbb7/Fb7/9htTU1HqPzczMxIwZM7B+/Xo4ODiYqkSrUt/QElC7I8MgQ2RdwtvcvnLpBoMMUWOYLMgkJiZCLpejf//+um2RkZGQy+U4dOhQncdpNBpMnDgR8+bNQ/fu3e/5PkqlEsXFxXqPligvLw9A3UHm7o6MQlFzMmSQIbIO2gm/vASbqHFMFmRycnLg6+tba7uvr2+tu9reafHixbC3t8fMmTMb9D6xsbG6OThyuRxBQUFNrtlSVVdX4/r16wCAkJAQg/uwI0Nk3Xq0kUMiATKLKpBXwgm/RA3V6CCzcOFCSCSSeh/Hjx8HAIPrlwiCUOe6JklJSfj888+xbt26Bq99Mn/+fCgUCt0jIyOjsR/J4mVkZKCqqgoymQxt27Y1uE9dc2TkcrlZaiSi5vFwctCt8Hv6RpG4xRBZkUbfa2nGjBl4+umn690nODgYp0+fxs2bN2s9l5eXBz8/P4PH7d+/H7m5uWjXrp1um1qtxhtvvIFly5bh2rVrtY6RyWS6S49bqsuXLwMAOnToADs7w9nz7o4Mh5aIrE+vtp64nFuKUxlFGBpm+DxJRPoaHWR8fHzg4+Nzz/2ioqKgUChw9OhR9OvXDwBw5MgRKBQKREdHGzxm4sSJGDZsmN62ESNGYOLEiXjhhRcaW2qLoQ0ynTp1qnMfXrVEZP16B8mx6cQNJHPCL1GDmezu12FhYRg5ciSmTp2Kb775BgDw0ksvYcyYMejatatuv9DQUMTGxuLxxx+Ht7d3rcmsDg4O8Pf31zvG1jQkyNTVkeHQEpH16BXkCQA4lVFU7zA8Ef3FpOvIrF+/HuHh4YiJiUFMTAx69uyJH374QW+f1NRU3V+6ZBg7MkS2IdTfA45SOygqqnC9oFzscoisgsk6MkDN4m0//vhjvfsIglDv84bmxdiahgQZd3d3AEBxcTEEQWBHhsgKOdrboVugB5IzinDqRhGCb6/2S0R1472WLJxGo8GVK1cA1B9ktPOW8vLyUFpaCo1GA4AdGSJr01s3vMRONVFDMMhYuMzMTCiVStjb2+tdzXW31q1bA6gJMtphJUdHRzg5OZmjTCIykl5BNV3UU7wEm6hBGGQsnHZYKSQkBPb2dY8EahcfzMvL0xtW4mRBIuvSq60ngJp7LlWpNeIWQ2QFGGQsXEPmxwB/dWRyc3M50ZfIigV7u8LDyR7Kag1Sc0rELofI4jHIWLjGBpk7h5YYZIisj52d5K/LsDm8RHRPDDIWrrFBpry8HFlZWQB4xRKRtdIOL53KKBK1DiJrwCBj4RoaZNzd3XW3arh06RIAdmSIrFUvXrlE1GAMMhZMEASkpaUBADp27FjvvhKJRNeV0YYfBhki69SrbU039WJuCUqV1SJXQ2TZGGQsWHFxMUpLSwGgzrte30kbZLQdGQ4tEVknXw8nBMqdIAg1Vy8RUd1sNsgoFAqcOnUKFy9eFLuUOt24cQMA0KpVK7i63nuFT3ZkiFoO7fDSaU74JaqXzQaZ+Ph49O7dG1OnThW7lDppg0xQUFCD9teuJaNUKgGwI0NkzThPhqhhbDbIaBeXq6623PHnjIwMAA0bVgL+6shosSNDZL20Vy4l88olonoxyFhwkNF2ZBhkiGxPz7Zy2EmAzKIK5CgqxS6HyGIxyFhBkGno0NLdQYZDS0TWy1Vmj7AADwDA8eu3RK6GyHIxyFhwkGns0JJ2jowWOzJE1q1P+1YAgOPXCkWuhMhyMchYcJDh0BKRbesT7AUASLrOIENUFwYZKwgyHFoisk19gms6Muezi1HGhfGIDGKQESHICIKAL7/8EsePH69zn+LiYhQXFwMA2rRp06DXvTPISCQSuLu7N69QIhJVgNwZbTydodYIvHqJqA4MMiIEmX379uG1117DyJEjUVhouGWs7cZ4enrCzc2tQa/r4eEBBwcH3Z/t7Gz26yVqMSI4T4aoXjb7N52YQUZ7C4GCggJ8+OGHBvdp7LASUNOF0U745fwYopZBO7zEK5eIDGOQESHIpKen6/78xRdf4MqVK7X2aewVS1ra4SUGGaKWoU/7mgm/J64XokqtEbkaIsvDICNCkNGGFDs7O6hUKixYsKDWPo29YklLG2Q40ZeoZejq7w5PFweUqdScJ0NkAIOMiEHm1VdfBQD89ttvEARBb5/mBhl2ZIhaBqmdBAM71/xeJ1zME7kaIsvDICNikHnkkUfg4OCAsrIy3ba792nMHBkAnCND1AIN6uwDgEGGyBAGGTMHGUEQdCElJCQEXbp0AQCcP39eb7+mdmTuv/9+AECPHj2aWyoRWYjBXWo6MqczFbhVphK5GiLLwiBj5iCTn5+PysqaG8C1bdsW3bp1AwCcO3dOb7+mTvZ99tlnceXKFcydO9cI1RKRJfD1cEKovzsEAdh/iV0ZojvZfJDRaDTQaMx3JYA2oPj5+UEmk6F79+4A9Dsy+fn5usXw2rdv36jXl0gk6NChAyQSiZEqJiJLoO3KJFzMF7kSIsti80EGANRqtdne9+65L9qOzJ1B5uLFi7p9XFxczFYbEVkuXZC5lFfr4gAiW8YgA6Cqqsps71tfkNGenFJTUwEAXbt2NVtdRJZmxYoVCAkJgZOTEyIiIrB///5691cqlViwYAHat28PmUyGjh07Ys2aNWaq1vQiglvB1VGKvBIlzmQqxC6HyGIwyMC882TuDjKdO3eGVCpFcXExsrKyAPwVZLQTgYlszcaNGzFr1iwsWLAAJ0+exMCBAzFq1Ci9xSTv9tRTT2HXrl1YvXo1UlNT8fPPPyM0NNSMVZuWzF6KwV1rujLx52+KXA2R5WCQgXmDjPZErA0yjo6O6Ny5M4C/hpe0Q0vsyJCtWrp0KSZPnowpU6YgLCwMy5YtQ1BQEL7++muD+8fFxWHfvn3Yvn07hg0bhuDgYPTr1w/R0dFmrty0hnfzAwDsOMcgQ6Rls0FGKpXq/ixGR6Zdu3a6bXdfucShJbJlKpUKSUlJiImJ0dseExODQ4cOGTxm27Zt6NOnD5YsWYI2bdqgS5cumDt3LioqKup8H6VSqbvL/J13m7dkD3b1hdROgtSbJbheUCZ2OUQWwWaDjEQi0YUZMYeWAP15Mmq1GpcvXwbAoSWyTfn5+VCr1fDz89Pb7ufnh5ycHIPHpKWl4cCBAzh79iy2bNmCZcuW4b///a9u9WxDYmNjIZfLdY/GLj4pBk8XR/QPqbn3EoeXiGrYbJABzL+WjFqtRmZmJoC6g8y1a9egUqkgk8n0ujZEtubuJQQEQahzWQGNRgOJRIL169ejX79+GD16NJYuXYp169bV2ZWZP38+FAqF7nH36tqWSje8xCBDBIBBBoD5gkxOTg7UajWkUikCAgJ027VryZw+fRqnT58G8NckYCJb4+PjA6lUWqv7kpubW6tLoxUQEIA2bdro3Sw1LCwMgiDoVsm+m0wmg4eHh97DGmiDzPFrt7jKLxEYZACYL8hoJ/q2adNGL6R0794dQUFBKCkpwUcffQSAw0pkuxwdHREREYH4+Hi97fHx8XVO3n3ggQeQlZWF0tJS3baLFy/Czs6u0atjW7q2rVwQFuABjQDsuZArdjlEomOQgfmCjHZY6e4Tq1QqxcsvvwwAOH78OABO9CXbNmfOHKxatQpr1qxBSkoKZs+ejfT0dEybNg1AzbDQpEmTdPtPmDAB3t7eeOGFF3D+/HkkJCRg3rx5ePHFF+Hs7CzWxzCZ4WE1N4fdmcLhJSIGGZgvyBQWFgIAvL29az03ZcoUODg46H5mkCFbNn78eCxbtgyLFi1C7969kZCQgO3bt+tu2ZGdna23poybmxvi4+NRVFSEPn364JlnnsHYsWOxfPlysT6CSQ0NqxleSriYB2W1+VYmJ7JE9vfepeUyd5DRXt5paCzez88PTz75JH7++WcAHFoimj59OqZPn27wuXXr1tXaFhoaWms4qqUKbyOHr7sMuSVKHE67pbt9AZEtYkcG5gsyCkXNsuJ3Tki8050nbXZkiKgudnYSXVdmJ69eIhvHIAPL6MgANRMWFy1ahE8++QReXl5mqYmIrNOw2/NkdqXc5E0kyaZxaAmW05GRSCR45513zFILEVm3Bzr5wMnBDlmKSqRkl6BboHVcPk5kbOzIwPxBxlrWqyAiy+XkIEV0Rx8AQMKlPJGrIRIPgwzMP7RUV0eGiKgxtJN896UyyJDtsukgo73c2VKGloiIGmNI15ogc/z6LZQqzXfPOCJLYtNBxtIm+xIRNUZ7b1cEe7ugSi0g8UqB2OUQiYJBBuzIEJH10g0vXeTtCsg2MciAHRkisl6Dbw8v7U3N42XYZJMYZGCeIFNVVYWKigoA7MgQkfFEdvCGo9QONworkJZfJnY5RGbHIAPzBBltNwYA3N3dTf5+RGQbXBzt0TekFQBg/0VevUS2h0EG5gky2vkxLi4uejeHJCJqrkGda4aX9l/KF7kSIvNjkIF5gwyHlYjI2AbeDjKJaQVQVWtErobIvBhkYN6hJU70JSJjC/V3h4+bDOUqNZKuF4pdDpFZMciAHRkism52dhIM7Fxzu4L9vF0B2RgGGbAjQ0TW768gw3kyZFsYZMCODBFZvwGdaoLM2SwFCkqVIldDZD4MMmBHhoisn6+HE8ICPCAIvBs22RaTBpnCwkJMnDgRcrkccrkcEydORFFR0T2PS0lJwSOPPAK5XA53d3dERkYiPT3d6PWxI0NELcmDt1f53X2BQYZsh0mDzIQJE5CcnIy4uDjExcUhOTkZEydOrPeYK1euYMCAAQgNDcXevXtx6tQpvPPOO3BycjJ6fWJ0ZBhkiMhUhob5AgD2peaiWs3LsMk22JvqhVNSUhAXF4fDhw+jf//+AIBvv/0WUVFRSE1NRdeuXQ0et2DBAowePRpLlizRbevQoYNJahSjI8OhJSIyld5BrdDKxQGF5VVIul6I/h28xS6JyORM1pFJTEyEXC7XhRgAiIyMhFwux6FDhwweo9Fo8Pvvv6NLly4YMWIEfH190b9/f2zdurXO91EqlSguLtZ7NBSHloioJZHaSfBg15quzO4LvBs22QaTBZmcnBz4+vrW2u7r64ucnByDx+Tm5qK0tBQff/wxRo4ciR07duDxxx/HuHHjsG/fPoPHxMbG6ubgyOVyBAUFNbhGTvYlopbmwdCa8+4uBhmyEY0OMgsXLoREIqn3cfz4cQCARCKpdbwgCAa3AzUdGQB49NFHMXv2bPTu3RtvvfUWxowZg5UrVxo8Zv78+VAoFLpHRkZGgz8LOzJE1NIM6tIaUjsJLueW4noB74ZNLV+j58jMmDEDTz/9dL37BAcH4/Tp07h582at5/Ly8uDn52fwOB8fH9jb26Nbt25628PCwnDgwAGDx8hkMshksgZWr48dGSJqaeTODugX7IXEtAL8eS4HLw3qKHZJRCbV6CDj4+MDHx+fe+4XFRUFhUKBo0ePol+/fgCAI0eOQKFQIDo62uAxjo6O6Nu3L1JTU/W2X7x4Ee3bt29sqffEjgwRtUSjw/2RmFaA388wyFDLZ7I5MmFhYRg5ciSmTp2Kw4cP4/Dhw5g6dSrGjBmjd8VSaGgotmzZovt53rx52LhxI7799ltcvnwZX375JX799VdMnz7d6DWaK8gIgsCODBGZzYge/pBIgFMZRci4VS52OUQmZdJ1ZNavX4/w8HDExMQgJiYGPXv2xA8//KC3T2pqqq5bAQCPP/44Vq5ciSVLliA8PByrVq3Cpk2bMGDAAKPXZ64gU15eDrVaDYAdGSIyPV93J/QP8QIA/HE2W+RqiEzLZOvIAICXlxd+/PHHevcRBKHWthdffBEvvviiqcrSMVeQ0QY1Ozs7uLq6mvS9iIgA4OHwABxOu8XhJWrxeK8lmD7I3DmsVNcVW0RExjSihz/sOLxENoBBBubryHBYiYjMpWZ4qWZl322nskSuhsh0GGRg3o4MEZG5PH5fGwDA5hM3DA7jE7UEDDJgR4aIWqZR4f5wcrDDlbwynLqhuPcBRFaIQQbsyBBRy+Tu5IAR3f0BAJuSbohcDZFpMMjA9EEmPz8fAODtzTvREpF5PXF/WwDAr6ezoKxWi1wNkfExyMD0QSY7u2Ydh4CAAJO+DxHR3R7o5AM/DxmKyqsQf772bWOIrB2DDMwXZPz9/U36PkREd5PaSTC+TxAA4NuENE76pRaHQQamDzI5OTkA2JEhInFMig6GzN4Op24okHilQOxyiIyKQQbsyBBRy+bjJsP4vjVdma/3XRG5GiLjYpABOzJE1PJNHdgBUjsJ9l/Kx+kbRWKXQ2Q0DDIwbZApLy/XXX7NIENEYgnycsEjvQIBAG9vOYMqtUbkioiMg0EGpg0y2mElZ2dnuLu7m+x9iIjuZf6oUMidHXA2sxhf7bksdjlERsEgA9MGmTuHlXjDSCISk6+HExY92h0A8OXuyzibydV+yfoxyMA8HRlO9CUiS/BIr0CMDvdHtUbAu/87y8uxyeoxyMB8HRkiIrFJJBK8N7Y7XBylOJFehK3JmWKXRNQsDDIwT0eGQYaocVasWIGQkBA4OTkhIiIC+/fvb9BxBw8ehL29PXr37m3aAq2Yn4cTXn2wEwDg4z8uoExp2is3iUyJQQbm6chwaImo4TZu3IhZs2ZhwYIFOHnyJAYOHIhRo0YhPT293uMUCgUmTZqEoUOHmqlS6zV5QAjaebngZrES6w5dE7scoiZjkAE7MkSWZunSpZg8eTKmTJmCsLAwLFu2DEFBQfj666/rPe7ll1/GhAkTEBUVZaZKrZeTgxSvPVTTldmUdINzZchqMciAk32JLIlKpUJSUhJiYmL0tsfExODQoUN1Hrd27VpcuXIF7733XoPeR6lUori4WO9ha0aFB0Bmb4e0/DKczbS9z08tA4MMONmXyJLk5+dDrVbDz89Pb7ufn5/u9+luly5dwltvvYX169frfq/vJTY2FnK5XPcICgpqdu3Wxk1mj2Hdav5//h8n/ZKVYpCB6YKMWq1Gbm4uAAYZosa6e90lQRAMrsWkVqsxYcIEvP/+++jSpUuDX3/+/PlQKBS6R0ZGRrNrtkaP3l7t99fTWVBrOLxE1qdh/3RpobRBRhAEaDQa2NkZN9fl5eXpXrd169ZGfW2ilsrHxwdSqbRW9yU3N7dWlwYASkpKcPz4cZw8eRIzZswAAGg0GgiCAHt7e+zYsQMPPfRQreNkMhlkMplpPoQVGdy1NTyc7HGzWIkjaQWI7uQjdklEjcKOzG2m6Mpo58f4+vpCKpUa/fWJWiJHR0dEREQgPj5eb3t8fDyio6Nr7e/h4YEzZ84gOTlZ95g2bRq6du2K5ORk9O/f31ylWyWZvRSjw2s6xr+ezhK5GqLGY0fmturqajg6Ohr19TnRl6hp5syZg4kTJ6JPnz6IiorCv//9b6Snp2PatGkAaoaFMjMz8f3338POzg49evTQO97X1xdOTk61tpNhI3v4Y8OxDOxKya1zCI/IUjHI3GbMjszu3bsxZcoU3cmA82OIGmf8+PEoKCjAokWLkJ2djR49emD79u1o3749gJp/JNxrTRlquMgO3nBxlCK3RImzmcUIbysXuySiBuPQ0m3GDDI//vgjrl69irS0NABAcHCw0V6byFZMnz4d165dg1KpRFJSEgYNGqR7bt26ddi7d2+dxy5cuBDJycmmL7KFcHKQYmDnmrkxO1NuilwNUePYdJC5c3KvMYOMNsC8+OKL+Oc//4m33nrLaK9NRGQKQ0NrJlLvvpArciVEjWPTQ0sSiQT29vaorq42apC5cuUKAGDq1KmIjIw02usSEZnKg6G+kEiAM5kK3CyuhJ+Hk9glETWITXdkAOOvJVNZWYnMzJqFpTp06GCU1yQiMrXW7jL0ausJANiVwq4MWQ8GGSMHmWvXrkEQBLi5uXHtGCKyKsPCfAEAf5zNFrkSooZjkDFykNEOK3Xs2JGXMBKRVRl7e5XfA5fzka2oELkaooZhkDFykNFO9OWwEhFZm/berugX4gVBADaf4L2XyDowyJiwI0NEZG2ejGgLANiUdAOCwHsvkeVjkGFHhohI5+HwALg4SpGWX4YT6YVil0N0Twwy7MgQEem4yuwxqkfNauQbjtrmHcHJujDIGDHIaDQaXUeGQYaIrNWE/u0AAFuTM5FZxEm/ZNkYZIwYZHJyclBZWQmpVIp27do1+/WIiMQQ0b4Vojt6o0otYOXeK2KXQ1QvBhkjBhntsFK7du3g4ODQ7NcjIhLLzKGdAQAbj2UgR1EpcjVEdWOQMWKQ4bASEbUUkR280S/ECyq1Biv3sStDlotBxgQdGV6xREQtwWsPdQJQ05UpLFOJXA2RYQwyRgwy6enpAIDg4OBmvxYRkdgGdPJBtwAPVFSp8cPh62KXQ2QQg4wRg0xRUREAwNvbu9mvRUQkNolEgpcH13SYvzt0DZVVapErIqqNQcYEQcbT07PZr0VEZAlGhwegjaczCspUvG0BWSQGGQYZIqI6OUjt8OKAEADAqgNpvG0BWRwGGQYZIqJ6je8bBDeZPdLyynDgcr7Y5RDpYZBhkCEiqpebzF53M8nvDnHSL1kWBhkjBRmNRoPi4mIADDJE1PI8G9keALDrwk1k3CoXuRqivzDIGCnIFBcX68aO5XJ5s+siIrIknXzdMLCzDwQBvBSbLAqDjJGCjHZYydnZGTKZrLllERFZnOeiggEAPx9Jh6K8StxiiG5jkDFykGE3hohaqodCfdHVzx0lymqsPnhV7HKIADDIGD3IcH4MEbVUdnYSvD6s5maSaw9cZVeGLAKDDIMMEVGDjezuj1B/dmXIcjDIGCnIKBQKAAwyRNSy2dlJ8PrQmq7Mqv1pyCqqELkisnUMMreDTFVV81qk7MgQka0Y0d0ffYNboVylxsJt58Quh2wcgwyHloiIGsXOToIPHw+HvZ0EO87fxI5zOWKXRDbMpEGmsLAQEydOhFwuh1wux8SJE3V/4deltLQUM2bMQNu2beHs7IywsDB8/fXXJquRQYaIqPG6+Llj6qCaO2O/t+0cSpXNXx2dqClMGmQmTJiA5ORkxMXFIS4uDsnJyZg4cWK9x8yePRtxcXH48ccfkZKSgtmzZ+O1117D//73P5PUyCBDRNQ0Mx/qjCAvZ2QrKvHZjlSxyyEbZbIgk5KSgri4OKxatQpRUVGIiorCt99+i99++w2pqXX/B5+YmIjnnnsOQ4YMQXBwMF566SX06tULx48fN0mdDDJERE3j7CjFh4+FAwDWHbqGUxlF4hZENslkQSYxMRFyuRz9+/fXbYuMjIRcLsehQ4fqPG7AgAHYtm0bMjMzIQgC9uzZg4sXL2LEiBEG91cqlSguLtZ7NAaDDBFR0w3q0hqP9Q6EIABvbT6DarVG7JLIxpgsyOTk5MDX17fWdl9fX+Tk1D0xbPny5ejWrRvatm0LR0dHjBw5EitWrMCAAQMM7h8bG6ubgyOXyxEUFNSoOrmyLxFR8/xzTDfInR2Qkl2MH3kfJjKzRgeZhQsXQiKR1PvQDgNJJJJaxwuCYHC71vLly3H48GFs27YNSUlJ+OyzzzB9+nTs3LnT4P7z58+HQqHQPTIyMhr1ediRISJqHh83Gd4c2RUA8NmOi8grUYpcEdkS+8YeMGPGDDz99NP17hMcHIzTp0/j5s2btZ7Ly8uDn5+fweMqKirw9ttvY8uWLXj44YcBAD179kRycjI+/fRTDBs2rNYxMpmsWTdpZJAhImq+p/u2w4ajGTiTqUDsHylY+lRvsUsiG9HoIOPj4wMfH5977hcVFQWFQoGjR4+iX79+AIAjR45AoVAgOjra4DFVVVWoqqqCnZ1+o0gqlUKjMc24qzGCjEaj4cq+RGTTpHYS/OuxHnh8xUFsPpGJJyPaIrrjvf+uIGouk82RCQsLw8iRIzF16lQcPnwYhw8fxtSpUzFmzBh07dpVt19oaCi2bNkCAPDw8MDgwYMxb9487N27F1evXsW6devw/fff4/HHHzdJncYIMqWlpRAEAQCDDBHZrt5BnnimfzsAwNubz6CySi1yRWQLTLqOzPr16xEeHo6YmBjExMSgZ8+e+OGHH/T2SU1N1XUzAGDDhg3o27cvnnnmGXTr1g0ff/wxPvzwQ0ybNs0kNRojyGiHlWQyGZycnIxRFhGRVXpzZCj8PGS4VlCOz3ddErscsgGNHlpqDC8vL/z444/17qPtZGj5+/tj7dq1pixLjzGDDLsxRGTrPJwc8K9He+ClH5Lw74Q0PBTqi77BXmKXRS0Y77XEIENEZFQx3f3xWO9AqDUCZvx0AgWlvIqJTIdBhkGGiMjoPnw8HB1bu+JmsRKzNiZDrRHufRBREzDIMMgQERmdq8weXz8bAScHO+y/lI8Pfj8vdknUQjHIGDHIcFVfIqK/dPFzx2d/6w0AWHvwGr5PvCZqPdQyMciwI0NEZDIP9wzAvBE1S24s3HYOe1NzRa6IWhoGGQYZIou0YsUKhISEwMnJCREREdi/f3+d+27evBnDhw9H69at4eHhgaioKPz5559mrJbqM31IRzwZ0RYaAXjtp5O4dLNE7JKoBWGQYZAhsjgbN27ErFmzsGDBApw8eRIDBw7EqFGjkJ6ebnD/hIQEDB8+HNu3b0dSUhIefPBBjB07FidPnjRz5WSIRCLBR4+Ho1+wF0qU1Zj83XFeyURGwyBzO8hUVVU1+TUKCwsBMMgQGcvSpUsxefJkTJkyBWFhYVi2bBmCgoLw9ddfG9x/2bJlePPNN9G3b1907twZH330ETp37oxff/3VzJVTXRzt7bByYgTaebkg/VY5XvohiSv/klHYfJDR3nBSqWz6vw6uXbsGAAgKCjJGSUQ2TaVSISkpCTExMXrbY2JicOjQoQa9hkajQUlJCby86l6ITalUori4WO9BpuXl6og1z/eBh5M9kq4X4o1fTkHDy7KpmWw+yLi6ugIAysrKmnS8IAi4cuUKAKBjx45Gq4vIVuXn50OtVsPPz09vu5+fH3Jychr0Gp999hnKysrw1FNP1blPbGws5HK57sF/iJhHJ193fDOxDxykEvx+Ohuxf6SIXRJZOQaZZgaZ/Px8lJSUQCKRICQkxJilEdk0iUSi97MgCLW2GfLzzz9j4cKF2LhxI3x9fevcb/78+VAoFLpHRkZGs2umhonq6I0lT/YEAHy7/yq+TUgTuSKyZia915I1uDPINPREeafLly8DANq2bcsbRhIZgY+PD6RSaa3uS25ubq0uzd02btyIyZMn45dffsGwYcPq3Vcmk+mGlsn8Hr+vLXKLlYj94wI+3J6CNq2cMTo8QOyyyAqxI3M7yKjVaqhUqkYfrx1W6tSpk1HrIrJVjo6OiIiIQHx8vN72+Ph4REdH13nczz//jOeffx4//fQTHn74YVOXSUbw0qAOeD46GAAw95dTuJDDeUrUeAwyt4MMAJSXlzf6eG1HhvNjiIxnzpw5WLVqFdasWYOUlBTMnj0b6enpmDZtGoCaYaFJkybp9v/5558xadIkfPbZZ4iMjEROTg5ycnKgUCjE+gjUABKJBP98OAwPdPJGuUqNl75PQlF54/9BSbbN5oOMg4MDHBwcADRtngw7MkTGN378eCxbtgyLFi1C7969kZCQgO3bt6N9+/YAgOzsbL01Zb755htUV1fj1VdfRUBAgO7x+uuvi/URqIHspXb48u/3o20rZ6TfKseb/z0NQeCVTNRwNj9HBqjpyhQVFTUpyLAjQ2Qa06dPx/Tp0w0+t27dOr2f9+7da/qCyGRauTpi5bMRGLfiEHacv4nvE6/judtDTkT3YvMdGQBwcXEBwI4MEZFYerSRY/7oUADAh7+n4PSNInELIqvBIIOmX4JdXFyMvLw8AOzIEBE11/PRwRgW5geVWoPJ3x3HjcLGz1sk28Mgg6YHGW03pnXr1nB3dzd6XUREtkQikeD/xvdCqL878kqUeGHtMSjKm377GLINDDJofpDhsBIRkXG4OzlgzfN94echw6XcUjy58hAybrEzQ3VjkEHTgwwn+hIRGV+gpzO+e7GfLsw8vuIgTqYXil0WWSgGGTQ+yKhUKiQmJuLgwYMA2JEhIjK2UH8PbH31AYQFeCC/VIXx/z6M/yVnil0WWSAGGfwVZBq6IN64ceMQHR2N3377DQCDDBGRKQTInfHLtCgMC/OFqlqD1zckY8Xey2KXRRaGQQaN68golUrd0un3338//v73v+ORRx4xaX1ERLbKTWaPbyb2wcuDOgAAlsSlYtnOi1w0j3S4IB4aF2SSk5OhUqng4+OD48ePN/omk0RE1DhSOwnmjw6D3MXhdpC5BEEAZg/vInZpZAHYkUHjFsQ7fPgwAKB///4MMUREZjR9SCf88+EwAMDnuy7hm31XRK6ILAGDDBrXkTly5AgAIDIy0qQ1ERFRbVMGdsC8EV0BALF/XMD3idfELYhExyCDxgUZbUeGQYaISByvPtgJ04fULHvx7v/OYc2BqyJXRGJikEHDg0xubi6uXr0KiUSCvn37mqM0IiIyYN6Irpg2uCbMLPrtPL7YdYkTgG0UgwwaHmS0w0phYWGQy+Umr4uIiAyTSCT4x8iumDm0MwDgs/iLmPHTSZSrqkWujMyNQQYNDzJ3TvQlIiJxSSQSzBneBR89Hg4HqQS/n8nG6M/349DlfLFLIzNikEHDF8TjRF8iIsszoX87/Dw1En4eMlwrKMeEVUcwa8NJZBVViF0amQGDDBrWkREEAUlJSQCAfv36maUuIiJqmD7BXoifMxgTI9tDIgG2JmfhwU/34rMdqRxuauEYZNCwdWSysrJQVFQEqVSKsLAwc5VGREQN5OHkgH891gP/e/UB9AvxgrJagy92X8awz/Zh+5lsTgZuoRhk0LCOzLlz5wDU3FdJJpOZpS4iImq8nm09sfGlSKx89n608XRGlqIS09efwHNrj+FafsNuDkzWg0EGfwWZiooKaDQag/ucP38eANC9e3ez1UVERE0jkUgwskcAds4ZjJlDO8NRaoeEi3mI+b8EfPzHBZQqOdzUUjDI4K8gA9Q94VfbkenWrZtZaiIiouZzdpRizvAu+HP2IAzq0hoqtQYr913BkE/24j/HMqDRcLjJ2jHIAHB2dtb9ua7hJW2QYUeGiMj6hPi44rsX+mL1c30Q7O2C/FIl3tx0Go9+dRAn0wvFLo+agUEGgJ2dXb0TfgVBYJAhIrJyEokEQ8P8sGP2YCwYHQZ3mT3OZCow7utDmL/5DIrKVWKXSE3AIHNbfRN+s7KyUFxcDKlUii5deNt4IiJr5mhvh6mDOmD33CEYd38bCALw89F0DP1sHzYl3eDVTVaGQea2+hbF4xVLREQtT2t3GZY+1RsbX4pEJ183FJSp8MYvp/DkykScuaEQuzxqIAaZ2+rryHBYiYio5erfwRvbZw7EmyO7wtlBiqTrhRj75QG8+tMJXMkrFbs8ugcGmdvqmyPDIENE1LI52tth+pBO2DN3CB6/rw0A4PfT2Ri2dB+m/ZCEpOu3OORkoRhkbquvI8M1ZIiIbIO/3An/N743/nh9IIaF+UEQgLhzOXji60Q89tVBbDl5A6pqw+uNkTgYZG6rK8hoNBquIUNEZGPCAjyw6rk+2DF7EMb3CYKjvR1O3VBg9sZTGLRkD/6dcAUllVVil0lgkNGpK8icPXsWxcXFcHV1RWhoqBilERGRSLr4uWPxkz2R+NZDmBvTBa3dZcgprsRH2y8g+uPd+PiPC8hW8C7bYmKQua2uILNv3z4AwAMPPAAHBwez10VEROLzdpNhxkOdceAfD2LJEz3RsbUrSiqrsXLfFQxYvAevrj+B/ZfyoOZKwWZnL3YBlqKuIJOQkAAAGDx4sNlrIiIiyyKzl+KpvkF4MqItdqbcxKoDV3H06i38fiYbv5/JRqDcCWN7BWJMz0D0aOMBiUQidsktHoPMbYaCjCAIDDJERFSLnZ0EMd39EdPdHynZxVh/5Dq2JWchS1GJbxLS8E1CGtp4OiOmux9iuvmjb3Ar2Es5CGIKDDK3GQoyFy5cQG5uLpycnNCnTx+xSiMiIgsWFuCBDx4Lxz8f7obdF3Lx++ls7LpwE5lFFVh78BrWHrwGTxcHPNTVF8O7+WFQl9ZwlfGvX2Ph/5O3GVrZV9uNiYqK4oq+RERULycHKUaHB2B0eAAqVGokXMrDn+dysOdCLgrLq7D5ZCY2n8yEzN4OAzv7YER3fwwL80MrV0exS7dqDDK3GVoQTzvRl8NKRETUGM6OUozo7o8R3f1RrdYg6Xoh4s/fxI7zN5F+qxw7U3KxMyUXUjsJItq1wgOdfNA3uBW6BXrA04XBpjEYZG67e2jpzvkxgwYNEq0uIiKybvZSO/Tv4I3+Hbyx4OEwXMgpQdzZHPx5LgcXckpw9NotHL12S7d/oNwJ3QLluK+dJwZ3aY3ugZw0XB8GmdvuDjJXrlxBZmYmHB0dERkZKWZpRETUQkgkEoQFeCAswAOzh3dBxq1yHLicj4OX83EmU4HrBeXIUlQiS1GJnSk38cmfqfDzkGFUjwDEdPPD/e1bwclBKvbHsCgMMrfdHWT27t0LAIiMjISzs7NYZRERUQsW5OWCv/drh7/3awcAKKmsQkp2Cc5kKpB4JR+HrhTgZrES6w5dw7pD1yCzt8N97TzRPVCO7oEe6NFGjg4+rjZ9RRSDzG13B5k9e/YAAIYMGSJWSUREZGPcnRzQL8QL/UK8MHlACJTVahy8nI/fT+cg4VIe8kqUOJx2C4fT/hqKcnKwQ3gbOXoHeaJHGzm6B8oR7O1iM+GGQeY2d3d3AEBubi6USqWuI8MgQ0REYpHZS/FQqB8eCvWDIAi4nFuKk+lFOJelwPnsYpzLKka5So1j1wpx7Fqh7jhHezt08HFFJ183dGzthg6tXdGxtRvaebvAw6llrVJv0iDz4Ycf4vfff0dycjIcHR1RVFR0z2MEQcD777+Pf//73ygsLET//v3x1VdfmfzO0926dUNAQACys7MRGxuLrKwszo8hIiKLIZFI0NnPHZ393AEEAQA0GgFp+TXh5tSNIpzLKkZKdjEqqzS4kFOCCzkltV5H7uyAQE9ntPF0QpCXC9p5uSDYxxUdfdwQ6OlkdZ0ckwYZlUqFv/3tb4iKisLq1asbdMySJUuwdOlSrFu3Dl26dMEHH3yA4cOHIzU1Vdc1MQUHBwe88sorePfdd/HBBx8AqFk/hvNjiIjIUtnZSdDJ1x2dfN3xtz5/hZvMogpcvFmCK3mluJxbirS8MlzNL0NBmQqKiiooKqqQkl1c6/Xs7SRo28oZgZ7O8Jc7IUDuhAC5M9q2ckY7Lxe0beUCR3vLCjomDTLvv/8+AGDdunUN2l8QBCxbtgwLFizAuHHjAADfffcd/Pz88NNPP+Hll182VakAgJdeegkffPABVCoVAA4rERGR9bGzkyDIywVBXi4YGuan91yZsho3CiuQpahAZmEFMgrLcT2/HFfza4KOSq3BtYJyXCsoN/zaEiBAXhNq2rRyRhtPZwR61oQd7f+ae9Vii5ojc/XqVeTk5CAmJka3TSaTYfDgwTh06JDBIKNUKqFUKnU/FxfXTpgN5efnh6effhrff/89AAYZIjGtWLECn3zyCbKzs9G9e3csW7YMAwcOrHP/ffv2Yc6cOTh37hwCAwPx5ptvYtq0aWasmMjyucrs0dXfHV39a49wqDUCbhZXIv1WObIVFchWVCJHUYmsogrcKKzA9YJyVFSpkVlUgcyiijrfw11mDz+5E1q7yeDl5gh3mT1cZfb4e78gdPI1/siKRQWZnJwcADWB4k5+fn64fv26wWNiY2N1nR9jmDlzJr7//nu4ublxfgyRSDZu3IhZs2ZhxYoVeOCBB/DNN99g1KhROH/+PNq1a1dr/6tXr2L06NGYOnUqfvzxRxw8eBDTp09H69at8cQTT4jwCYisj9ROgkDPmmElQwRBQF6pEtcLynGjsBw3btV0drKKKmuCT1ElSpTVNY/cmiGtOz3Y1dcygszChQvvGRyOHTvWrJss3r2CoSAIda5qOH/+fMyZM0f3c3FxMYKCgpr83hEREdi2bRs8PT3h5OTU5NchoqZbunQpJk+ejClTpgAAli1bhj///BNff/01YmNja+2/cuVKtGvXDsuWLQMAhIWF4fjx4/j0008ZZIiMRCKRwNfdCb7uTugb7GVwn1JlNXIUlbhZXIn8UiVulalQdjvctPd2MUldjQ4yM2bMwNNPP13vPsHBwU0qxt/fH0BNZyYgIEC3PTc3t1aXRksmkxn9ho5jx4416usRUcOpVCokJSXhrbfe0tseExODQ4cOGTwmMTFRb0gaAEaMGIHVq1ejqqoKDg61Lzc15rA0EdVwk9mjk68bOvm6me09Gx1kfHx84OPjY4paEBISAn9/f8THx+O+++4DUHNS27dvHxYvXmyS9yQiy5Kfnw+1Wm1wiFk7/Hy3nJwcg/tXV1cjPz9f7x9GWsYeliYicZj0Gqr09HQkJycjPT0darUaycnJSE5ORmnpX+NmoaGh2LJlC4CattWsWbPw0UcfYcuWLTh79iyef/55uLi4YMKECaYslYgsTGOGmOva39B2rfnz50OhUOgeGRkZzayYiMRg0sm+7777Lr777jvdz9ouy549e3RXBKWmpkKhUOj2efPNN1FRUYHp06frFsTbsWOHSdeQISLL4ePjA6lUWqv7Ut8Qs7+/v8H97e3t4e3tbfAYUwxLE5H5mbQjs27dOgiCUOtx52XNgiDg+eef1/0skUiwcOFCZGdno7KyEvv27UOPHj1MWSYRWRBHR0dEREQgPj5eb3t8fDyio6MNHhMVFVVr/x07dqBPnz4G58cQUcthWcvzEREBmDNnDlatWoU1a9YgJSUFs2fPRnp6um5dmPnz52PSpEm6/adNm4br169jzpw5SElJwZo1a7B69WrMnTtXrI9ARGZiUevIEBEBwPjx41FQUIBFixYhOzsbPXr0wPbt29G+fXsAQHZ2NtLT03X7h4SEYPv27Zg9eza++uorBAYGYvny5bz0msgGSATtjLgWori4GHK5HAqFAh4eHmKXQ2STrPH30BprJmpJmvo7yKElIiIisloMMkRERGS1GGSIiIjIajHIEBERkdVikCEiIiKrxSBDREREVqvFrSOjvZqcd7IlEo/298+aVnfguYNIXE09b7S4IFNSUgIACAoKErkSIiopKYFcLhe7jAbhuYPIMjT2vNHiFsTTaDTIysqCu7t7vXfKBWrSX1BQEDIyMqx+AayW9FkAfh5Ld6/PIwgCSkpKEBgYCDs76xjBbui5w9a+S2vCz2KZGvpZmnreaHEdGTs7O7Rt27ZRx3h4eFj9fyhaLemzAPw8lq6+z2MtnRitxp47bOm7tDb8LJapIZ+lKecN6/inEhEREZEBDDJERERktWw6yMhkMrz33nuQyWRil9JsLemzAPw8lq6lfZ7GaGmfvSV9Hn4Wy2Tqz9LiJvsSERGR7bDpjgwRERFZNwYZIiIisloMMkRERGS1GGSIiIjIajHIEBERkdWy2SCzYsUKhISEwMnJCREREdi/f7/YJTVIbGws+vbtC3d3d/j6+uKxxx5Damqq3j7PP/88JBKJ3iMyMlKkiuu2cOHCWnX6+/vrnhcEAQsXLkRgYCCcnZ0xZMgQnDt3TsSK6xccHFzr80gkErz66qsALP97SUhIwNixYxEYGAiJRIKtW7fqPd+Q70OpVOK1116Dj48PXF1d8cgjj+DGjRtm/BSmZ43nDp43LPO8Yc3nDEs6X9hkkNm4cSNmzZqFBQsW4OTJkxg4cCBGjRqF9PR0sUu7p3379uHVV1/F4cOHER8fj+rqasTExKCsrExvv5EjRyI7O1v32L59u0gV16979+56dZ45c0b33JIlS7B06VJ8+eWXOHbsGPz9/TF8+HDdzf0szbFjx/Q+S3x8PADgb3/7m24fS/5eysrK0KtXL3z55ZcGn2/I9zFr1ixs2bIFGzZswIEDB1BaWooxY8ZArVab62OYlLWeO3jesMzzhjWfMyzqfCHYoH79+gnTpk3T2xYaGiq89dZbIlXUdLm5uQIAYd++fbptzz33nPDoo4+KV1QDvffee0KvXr0MPqfRaAR/f3/h448/1m2rrKwU5HK5sHLlSjNV2Dyvv/660LFjR0Gj0QiCYD3fiyAIAgBhy5Ytup8b8n0UFRUJDg4OwoYNG3T7ZGZmCnZ2dkJcXJzZajellnLu4HnDMlnrOUPs84XNdWRUKhWSkpIQExOjtz0mJgaHDh0SqaqmUygUAAAvLy+97Xv37oWvry+6dOmCqVOnIjc3V4zy7unSpUsIDAxESEgInn76aaSlpQEArl69ipycHL3vSSaTYfDgwVbxPalUKvz444948cUX9e6kbC3fy90a8n0kJSWhqqpKb5/AwED06NHDKr6ze2lJ5w6eNyxPSzpnmPt8YXNBJj8/H2q1Gn5+fnrb/fz8kJOTI1JVTSMIAubMmYMBAwagR48euu2jRo3C+vXrsXv3bnz22Wc4duwYHnroISiVShGrra1///74/vvv8eeff+Lbb79FTk4OoqOjUVBQoPsurPV72rp1K4qKivD888/rtlnL92JIQ76PnJwcODo6olWrVnXuY81ayrmD5w3L1JLOGeY+X9g3o1ardmfiBWp+ue/eZulmzJiB06dP48CBA3rbx48fr/tzjx490KdPH7Rv3x6///47xo0bZ+4y6zRq1Cjdn8PDwxEVFYWOHTviu+++001os9bvafXq1Rg1ahQCAwN126zle6lPU74Pa/nOGspa/5vU4nnDMrXEc4a5zhc215Hx8fGBVCqtlfhyc3NrpUdL9tprr2Hbtm3Ys2cP2rZtW+++AQEBaN++PS5dumSm6prG1dUV4eHhuHTpku4qBGv8nq5fv46dO3diypQp9e5nLd8LgAZ9H/7+/lCpVCgsLKxzH2vWEs4dPG9YppZ2zjD3+cLmgoyjoyMiIiJ0s8O14uPjER0dLVJVDScIAmbMmIHNmzdj9+7dCAkJuecxBQUFyMjIQEBAgBkqbDqlUomUlBQEBAQgJCQE/v7+et+TSqXCvn37LP57Wrt2LXx9ffHwww/Xu5+1fC8AGvR9REREwMHBQW+f7OxsnD171uK/s4aw5nMHzxuWfd5oaecMs58vGj8/2fpt2LBBcHBwEFavXi2cP39emDVrluDq6ipcu3ZN7NLu6ZVXXhHkcrmwd+9eITs7W/coLy8XBEEQSkpKhDfeeEM4dOiQcPXqVWHPnj1CVFSU0KZNG6G4uFjk6vW98cYbwt69e4W0tDTh8OHDwpgxYwR3d3fd9/Dxxx8Lcrlc2Lx5s3DmzBnh73//uxAQEGBxn+NOarVaaNeunfCPf/xDb7s1fC8lJSXCyZMnhZMnTwoAhKVLlwonT54Url+/LghCw76PadOmCW3bthV27twpnDhxQnjooYeEXr16CdXV1WJ9LKOy1nMHzxuWe96w1nOGJZ0vbDLICIIgfPXVV0L79u0FR0dH4f7779e7DNGSATD4WLt2rSAIglBeXi7ExMQIrVu3FhwcHIR27doJzz33nJCeni5u4QaMHz9eCAgIEBwcHITAwEBh3Lhxwrlz53TPazQa4b333hP8/f0FmUwmDBo0SDhz5oyIFd/bn3/+KQAQUlNT9bZbw/eyZ88eg/9tPffcc4IgNOz7qKioEGbMmCF4eXkJzs7OwpgxYyzqMxqDNZ47eN6w3POGtZ4zLOl8IREEQWhcD4eIiIjIMtjcHBkiIiJqORhkiIiIyGoxyBAREZHVYpAhIiIiq8UgQ0RERFaLQYaIiIisFoMMERERWS0GGSIiIrJaDDJERERktRhkiIiIyGoxyBAREZHV+n8zFWegaECAegAAAABJRU5ErkJggg==",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 2 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject Text(0.5, 1.0, 'phi_edge')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "phi_avg=phiout1.phi_avg;\n",
    "phi_edge=zeros(Nx+1,);\n",
    "dphi=zeros(Nx,);\n",
    "avg2edge!(phi_edge, dphi, phi_avg, dx, AVE)\n",
    "subplot(1,2,1)\n",
    "plot(dphi,\"k-\")\n",
    "title(\"dphi\")\n",
    "subplot(1,2,2)\n",
    "plot(phi_edge)\n",
    "title(\"phi_edge\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the new averaging, the edge fluxes look good, but the derivative is still very irregular."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6×2 Matrix{Float64}:\n",
       " 1.34766e-02  1.22819e+00\n",
       " 1.28357e-02  1.16107e+00\n",
       " 1.17485e-02  1.15960e+00\n",
       " 1.10119e-02  1.05521e+00\n",
       " 1.03482e-02  1.02942e+00\n",
       " 9.38162e-03  9.97419e-01"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x1=phiout1.phi_avg[95:100];\n",
    "x2=phiout1.phi_avg[1:6];\n",
    "[x1 x2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If I take dphi/dx directly from the QMC code I get in real trouble."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "QMC Exit Distributions\n",
      " mu         I(0,-mu)        I(tau,mu) \n",
      " 0.05     5.88610e-01     5.91510e-06 \n",
      " 0.10     5.32786e-01     6.73579e-06 \n",
      " 0.20     4.47388e-01     9.34555e-06 \n",
      " 0.30     3.85095e-01     1.55884e-05 \n",
      " 0.40     3.37848e-01     4.12782e-05 \n",
      " 0.50     3.00853e-01     1.58181e-04 \n",
      " 0.60     2.71128e-01     5.37995e-04 \n",
      " 0.70     2.46732e-01     1.42872e-03 \n",
      " 0.80     2.26355e-01     3.08198e-03 \n",
      " 0.90     2.09082e-01     5.69219e-03 \n",
      " 1.00     1.94256e-01     9.37139e-03 \n",
      "9.07862e-01  1.02383e-03\n",
      "9.21251e-01  2.07430e-03\n",
      "9.20063e-01  3.43624e-03\n",
      "9.19146e-01  5.55134e-03\n",
      "9.19077e-01  9.87187e-03\n",
      "9.19102e-01  2.17853e-02\n",
      "9.19208e-01  5.99507e-02\n",
      "9.19568e-01  1.83894e-01\n",
      "9.20748e-01  5.91327e-01\n",
      "9.24582e-01  1.92327e+00\n",
      "9.36820e-01  6.19085e+00\n",
      "9.75636e-01  1.97509e+01\n",
      "1.09862e+00  6.27392e+01\n",
      "1.48813e+00  1.98915e+02\n",
      "2.72156e+00  6.30149e+02\n",
      "6.62698e+00  1.99560e+03\n",
      "1.89923e+01  6.31890e+03\n",
      "5.81428e+01  2.00071e+04\n",
      "1.82098e+02  6.33459e+04\n",
      "5.74555e+02  2.00562e+05\n",
      "1.81712e+03  6.35002e+05\n",
      "5.75122e+03  2.01049e+06\n",
      "1.82070e+04  6.36545e+06\n",
      "5.76436e+04  2.01537e+07\n",
      "1.82504e+05  6.38090e+07\n",
      "5.77827e+05  2.02027e+08\n",
      "1.82946e+06  6.39639e+08\n",
      "5.79229e+06  2.02517e+09\n",
      "1.83391e+07  6.41192e+09\n",
      "5.80635e+07  2.03009e+10\n",
      "1.83836e+08  6.42749e+10\n",
      "5.82045e+08  2.03502e+11\n",
      "1.84282e+09  6.44309e+11\n",
      "5.83458e+09  2.03996e+12\n",
      "1.84729e+10  6.45874e+12\n",
      "5.84874e+10  2.04491e+13\n",
      "1.85178e+11  6.47442e+13\n",
      "5.86294e+11  2.04987e+14\n",
      "1.85627e+12  6.49013e+14\n",
      "5.87718e+12  2.05485e+15\n",
      "1.86078e+13  6.50589e+15\n",
      "5.89145e+13  2.05984e+16\n",
      "1.86530e+14  6.52169e+16\n",
      "5.90575e+14  2.06484e+17\n",
      "1.86983e+15  6.53752e+17\n",
      "5.92009e+15  2.06985e+18\n",
      "1.87437e+16  6.55339e+18\n",
      "5.93446e+16  2.07488e+19\n",
      "1.87892e+17  6.56930e+19\n",
      "5.94887e+17  2.07992e+20\n",
      "1.88348e+18  6.58525e+20\n",
      "5.96331e+18  2.08497e+21\n",
      "1.88805e+19  6.60124e+21\n",
      "5.97779e+19  2.09003e+22\n",
      "1.89264e+20  6.61726e+22\n",
      "5.99230e+20  2.09510e+23\n",
      "1.89723e+21  6.63333e+23\n",
      "6.00685e+21  2.10019e+24\n",
      "1.90184e+22  6.64943e+24\n",
      "6.02143e+22  2.10529e+25\n",
      "1.90645e+23  6.66558e+25\n",
      "6.03605e+23  2.11040e+26\n",
      "1.91108e+24  6.68176e+26\n",
      "6.05070e+24  2.11552e+27\n",
      "1.91572e+25  6.69798e+27\n",
      "6.06539e+25  2.12066e+28\n",
      "1.92037e+26  6.71424e+28\n",
      "6.08012e+26  2.12581e+29\n",
      "1.92503e+27  6.73054e+29\n",
      "6.09488e+27  2.13097e+30\n",
      "1.92971e+28  6.74688e+30\n",
      "6.10968e+28  2.13614e+31\n",
      "1.93439e+29  6.76326e+31\n",
      "6.12451e+29  2.14133e+32\n",
      "1.93909e+30  6.77968e+32\n",
      "6.13938e+30  2.14652e+33\n",
      "1.94380e+31  6.79614e+33\n",
      "6.15428e+31  2.15174e+34\n",
      "1.94852e+32  6.81264e+34\n",
      "6.16922e+32  2.15696e+35\n",
      "1.95325e+33  6.82918e+35\n",
      "6.18420e+33  2.16220e+36\n",
      "1.95799e+34  6.84576e+36\n",
      "6.19922e+34  2.16745e+37\n",
      "1.96274e+35  6.86238e+37\n",
      "6.21427e+35  2.17271e+38\n",
      "1.96751e+36  6.87904e+38\n",
      "6.22935e+36  2.17798e+39\n",
      "1.97228e+37  6.89574e+39\n",
      "6.24448e+37  2.18327e+40\n",
      "1.97707e+38  6.91248e+40\n",
      "6.25964e+38  2.18857e+41\n",
      "1.98187e+39  6.92926e+41\n",
      "6.27483e+39  2.19388e+42\n",
      "1.98668e+40  6.94609e+42\n",
      "6.29007e+40  2.19921e+43\n",
      "1.99151e+41  6.96295e+43\n",
      "6.30534e+41  2.20455e+44\n",
      "1.99634e+42  6.97985e+44\n",
      "6.32065e+42  2.20990e+45\n",
      "QMC-NDA Exit Distributions\n",
      " mu         I(0,-mu)        I(tau,mu) \n",
      " 0.05     6.34608e+41     1.59790e+45 \n",
      " 0.10     3.52726e+41     2.85044e+45 \n",
      " 0.20     1.86808e+41     6.52626e+45 \n",
      " 0.30     1.33368e+41     8.06825e+45 \n",
      " 0.40     3.17199e+41     8.34240e+45 \n",
      " 0.50     1.85138e+42     8.11707e+45 \n",
      " 0.60     6.94384e+42     7.71596e+45 \n",
      " 0.70     1.77408e+43     7.26947e+45 \n",
      " 0.80     3.53198e+43     6.82999e+45 \n",
      " 0.90     5.95517e+43     6.41761e+45 \n",
      " 1.00     8.94695e+43     6.03865e+45 \n"
     ]
    }
   ],
   "source": [
    "#plain vanilla SN with simple source iteration\n",
    "snout=sn_solve();\n",
    "#QMC with simple source iteration, works fine\n",
    "qout=qmc_nda(2000, 100, 1.e-7;tabulate=true, nda=false)\n",
    "#QMC with NDA\n",
    "pout=qmc_nda(1000,200, 1.e-7; tabulate=true);\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's a plot of the converged fluxes. QMC and SN agree without NDA and QMC-NDA is wrong."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.legend.Legend object at 0x219ca5eb0>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(pout.phiout,\"k-\")\n",
    "plot(snout,\"k--\")\n",
    "plot(qout.phiout,\"k.\")\n",
    "legend([\"QMC-NDA\",\"SN\",\"QMC\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.8.5",
   "language": "julia",
   "name": "julia-1.8"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}