SolvingMicroDSOPs.ipynb

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    "# Solution Methods for Microeconomic Dynamic Stochastic Optimization Problems (MicroDSOP)\n",
    "\n",
    "- Author: Tao Wang and Chris Carroll (as of Feb 2022)\n",
    "\n",
    "This notebook reproduces all the figures (except for those associated with the \"method of moderation\") in Chris's Carroll's [SolvingMicroDSOP lecture notes](https://llorracc.github.io/SolvingMicroDSOPs/).   \n",
    "\n",
    "The purpose here is to mirror the results from the original lecture notes as closely as possible. Therefore, the notebook contains a stand-alone chunk of code specific to the content of each section in the paper. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Some Python-related specifics: import necessary classes\n",
    "\n",
    "The implementation takes advantage of Python's ability to bundle parameters with functionality via its object-oriented framework. We will import classes for CRRA utility, a class that discretes approximation to continuous distributions, and the \"gothic\" class that encapsulates functions $\\mathfrak{v}$, $\\mathfrak{v}'$, $\\mathfrak{c}$, which all involve expectations.  \n",
    "\n",
    "- The `utility` function class allows us to create an instance of a utility function, setting the risk aversion parameter once, and has a convenient \"prime\" method which executes the first derivative. \n",
    "\n",
    "- `DiscreteApproximation` fully implements an instance of the discrete approximation to a continuous distribution, taking advantage of SciPy's \"frozen distribution\" framework. It has a convenient way of calculating the expected value of any defined function of the random variable. \n",
    "\n",
    "- The `Gothic` class is bundled with methods that execute $\\mathfrak{v}$, $\\mathfrak{v}'$, $\\mathfrak{c}$, and interpolations of each. They all involve calculating expectations of utility/marginal utility/value/marginal value, which will loop over discretized values of the income shock. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from copy import copy\n",
    "\n",
    "# First import all necessary libraries.\n",
    "import numpy as np  # Import Python's numeric library as an easier-to-use abbreviation, \"np\"\n",
    "import pylab as plt  # Import Python's plotting library as the abbreviation \"plt\"\n",
    "import scipy.stats as stats  # Import Scientific Python's statistics library\n",
    "from numpy import log, exp  # for cleaner-looking code below\n",
    "from scipy.interpolate import InterpolatedUnivariateSpline\n",
    "from scipy.optimize import brentq as scipy_find_root # Import the brentq root-finder\n",
    "from scipy.optimize import minimize as scipy_minimize\n",
    "\n",
    "from Code.Python.resources import (\n",
    "    Utility,\n",
    "    DiscreteApproximation,\n",
    "    DiscreteApproximationTwoIndependentDistribs,\n",
    ")\n",
    "\n",
    "## notice that the resources directory is stored in the subfolder Code/Python.\n",
    "## It can be imported only if there is an __init__.py file in that folder\n",
    "\n",
    "import warnings\n",
    "\n",
    "warnings.filterwarnings(\"ignore\", category=UserWarning)\n",
    "## the user warning is surpressed for a cleaner presentation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "### for comparison purposes\n",
    "## import some modules from HARK libararies\n",
    "from HARK.ConsumptionSaving.ConsIndShockModel import init_lifecycle\n",
    "from HARK.ConsumptionSaving.ConsPortfolioModel import (\n",
    "    PortfolioConsumerType,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 0. Define Parameters, Grids, Utility Function \n",
    "Set up general parameters, as well as the first two major class instances: the utility function and the discrete approximation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "code_folding": [],
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "# Set up general parameters:\n",
    "\n",
    "rho = 2.0  ### relative risk aversion coefficient\n",
    "beta = 0.96  ### discount factor\n",
    "PermGroFac = np.array([1.0])  # permanent income growth factor\n",
    "# A one-element \"time series\" array\n",
    "# (the array structure needed for gothic class below)\n",
    "R = 1.02  ## Risk free interest factor\n",
    "\n",
    "# Define utility:\n",
    "u = Utility(rho)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Discretization of the Income Shock Distribution \n",
    "\n",
    "We assume that the transitory shock to income is lognormally distributed,\n",
    "\n",
    "\\begin{align}\n",
    "\\theta & \\sim \\mathcal{N}(-\\theta^{2}/2,\\theta^{2})\n",
    "\\end{align}\n",
    "\n",
    "and we approximate it by an equiprobable discretization.\n",
    "\n",
    "- See detailed discussion [here](https://llorracc.github.io/SolvingMicroDSOPs/#Discretizing-the-Distribution)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "code_folding": [],
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "theta_expected =  1.0000000000000087\n"
     ]
    }
   ],
   "source": [
    "# Create a discrete approximation instance:\n",
    "\n",
    "theta_sigma = 0.5\n",
    "theta_mu = -0.5 * (theta_sigma**2)\n",
    "theta_z = stats.lognorm(\n",
    "    theta_sigma, 0, np.exp(theta_mu)\n",
    ")  # Create \"frozen\" distribution instance\n",
    "theta_grid_N = 7  ### how many grid points to use approximate this continuous distribution\n",
    "\n",
    "theta = DiscreteApproximation(\n",
    "    N=theta_grid_N, cdf=theta_z.cdf, pdf=theta_z.pdf, invcdf=theta_z.ppf\n",
    ")\n",
    "\n",
    "# Retrieve the values and the probabilities and show that their dot product is approximately 1.0\n",
    "theta_vals=theta.X\n",
    "theta_prob=theta.pmf\n",
    "theta_expected=np.dot(theta_vals,theta_prob)\n",
    "print('theta_expected = ',theta_expected)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "code_folding": [],
    "lines_to_next_cell": 2
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   "outputs": [
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i8uXLuHz5Mrp06YKIiAgsXbrUrGCpPmgZNW/eXOqTpenXTtPpdCguLjaZbunzUalUZgc4KxQKNG/e3Oy9Hn30UWg0GlRUVOA///mPzT5X17RpU7NpGo3GbLpGowFwtYA1mjx5Ml555RUMGTIEGzduxM8//4w9e/aga9euKCsrq3EbqjP2y9LZbS1atDDrd0BAgFnO09Oz1u9vbIO196/exhuZf02WrfHfa9c5lUplsd+A+edhPDDY+HnY+/naOsvQ2jpyvXWnuLgYMTEx+Pnnn/Hmm29i27Zt2LNnD9LT003a6kjGP9a2xry7774bGzZsQGVlJUaNGoXQ0FB07twZq1atqvH7aLVa+Pr61jhvbYwAbnw9s+XSpUsQQti1nl9v3XJHPGusAdu8eTMMBoPJwaGWxMTEICYmBgaDAXv37sWHH36ISZMmITg4GA8//DCaNWuGH374AVVVVdcthq492M/f31/638fTTz9t8TWtW7e2OU/j2SFTp07F0KFDLWY6dOhg9fW///47fvjhBwBXDyK3JDMzUyrMgP8rvqq7cOECAPOBwjj92mkajcbkf2GA+ecTEBCAyspKXLx40eQPphACFy5ckP73CgAGgwGPPvoo/P394enpibFjx+LHH3+U/gDVlc8++wyjRo3C22+/bTI9Pz8fTZo0qdU8jZ9hbm6u2dlk58+fNzkjqK4EBAQgNzfXbLrxwNAbbUNNl63xs/jnn3/QsmVLKVdZWVnrP5L2fr51cY2n77//HufPn8e2bdukrUAAzA4Ud6Svv/4aAK475t1///24//77UVFRgZ9++gkzZ87EiBEjEBERgR49elz3fez9vKyNEcD/LSvjVuWKigqp+ACu/588W/z9/eHh4VGn67k74BahBur06dNISUmBn58fnnrqqRq9RqlUolu3btLZXPv37wcAxMfHo7y8vFYX6dJqtejTpw8OHDiALl26IDo62uxhHAis/c+jQ4cOaN++PQ4dOmTx9dHR0WjcuLHVNhivF/TJJ58gOzvb5JGRkQG1Wo1PP/3U5DVXrlyRBlWjzz//HB4eHrj77rtNpqenp5tsQbly5Qo2btyImJgYKJVKm5+P8WyTzz77zGT6F198gZKSEul5AJg+fTpycnKwcuVKrFmzBocOHbJrq1BtKRQKk4EZuFpkX7tLwZ7/ORp3w1zb7z179uDYsWMm/b5R1rYc9evXT/pjXd3y5cuh1Wpv+DTkmi5b4/pU/UwnAFi/fj0qKytr9d71+flaYywWrl13qp/F6kiHDh3C22+/jYiICLPdjNZ4enoiNjYW77zzDgDgwIED0nTAcVtBvvvuO5P/XBkMBqxZswZt27aVClXjmV+HDx82ee3GjRsttrsmbfPx8UG3bt2Qnp5ukq+qqsJnn32G0NBQ3HTTTbXpklvhFqEG4MiRI9IxM3l5ecjJyUFaWhqUSiW+/PJLm9eVWbhwIb7//nsMHDgQrVq1Qnl5uVQU3HPPPQCARx55BGlpaRg/fjyOHz+OPn36oKqqCj///DMiIyPx8MMP22zf3LlzcddddyEmJgYTJkxAREQErly5gj///BMbN26UjqVo27YtvL29sXLlSkRGRqJRo0Zo0aIFWrRogUWLFiE+Ph4DBgzA6NGj0bJlS/z77784duwY9u/fj3Xr1ll878rKSixfvhyRkZEYN26cxczgwYPx9ddfm/zPPSAgABMmTMDp06dx0003ISMjA5988gkmTJhgtlVJqVSif//+mDx5MqqqqvDOO++gqKgIM2bMsPm5AED//v0xYMAAvPTSSygqKkKvXr1w+PBhTJ8+HbfddhtGjhwJAMjKysLMmTPxyiuvSH/EZs6ciZSUFPTu3RsPPPDAdd+rtgYNGoSlS5eiY8eO6NKlC/bt24d3333XbEuDreV3rQ4dOuDJJ5/Ehx9+CA8PD8THx+PkyZN45ZVXEBYWhueff95h7b/llluwbds2bNy4ESEhIWjcuDE6dOiA6dOnY9OmTejTpw9effVVNG3aFCtXrsTmzZsxa9Ys+Pn5XXfeFy5cwPr1682mR0RE1HjZ3nzzzXjkkUcwe/ZsKJVK9O3bF0ePHsXs2bPh5+dXo13S16rPz9eanj17wt/fH+PHj8f06dOhVquxcuVKswse1sa+ffvg5+cHvV6P8+fP47vvvsOKFSsQFBSEjRs32txK+uqrr+Ls2bPo168fQkNDcfnyZcydO9fk+CV71uWaCAwMRN++ffHKK6/Ax8cH8+fPx2+//WZyCn1CQgKaNm2KsWPH4vXXX4dKpcLSpUtx5swZs/ndcsstWL16NdasWYM2bdrAy8sLt9xyi8X3njlzJvr3748+ffogJSUFGo0G8+fPx5EjR7Bq1SqnvdOAU5HzSG2yzXiUv/Gh0WhEUFCQiI2NFW+//bbIy8sze821Zybs2rVLPPDAAyI8PFx4enqKgIAAERsbK77++muT15WVlYlXX31VtG/fXmg0GhEQECD69u1rcoo4rjm9vLoTJ06IMWPGiJYtWwq1Wi2aNWsmevbsKd58802T3KpVq0THjh2FWq0WAMT06dOl5w4dOiSGDx8ugoKChFqtFs2bNxd9+/YVCxcutPoZbdiwQQAQqampVjPGs3tmz54thLh6Fs3NN98stm3bJqKjo4Wnp6cICQkRL7/8sslZa8YzNN555x0xY8YMERoaKjQajbjtttuk02mNbJ3tUlZWJl566SURHh4u1Gq1CAkJERMmTJAuX3D+/HkRFBQk+vbta3L2TlVVlRg8eLBo0qSJdEaJtbPGbr75ZrP3tXbW07XL8dKlS2Ls2LEiKChIaLVacdddd4mcnBwRGxtrduaKteVn6YwYg8Eg3nnnHXHTTTcJtVotAgMDxWOPPSadpny99ls6Q8eSgwcPil69egmtVisAmLT5l19+EYMHDxZ+fn5Co9GIrl271vhyDOHh4Sbfv+oP45le11u2RuXl5WLy5MkiKChIeHl5ie7du4tdu3YJPz8/kzPzrJ0pmp2dLQCI7OxsadqNfr7G9fvdd9+1+F7VT/221radO3eKHj16CK1WK5o1aybGjRsn9u/fb3Zmk71njRkfxu9mXFycmDt3rigqKjJ7zbXryaZNm0R8fLxo2bKlNGYmJCSInJwck9dZW5eTkpKEj4+PxfZZO2vs6aefFvPnzxdt27YVarVadOzYUaxcudLs9bt37xY9e/YUPj4+omXLlmL69Oli8eLFZt/pkydPiri4ONG4cWPpEgdCWD5rTAghcnJyRN++fYWPj4/w9vYW3bt3Fxs3bjTJ2LNuuRuFEDU4DJ/IhfTu3Rv5+fk4cuSIzdzJkyfRunVrvPvuu0hJSamn1pG72LlzJ3r16oWVK1dixIgRcjeHyG1x1xgRUR3LysrCrl27EBUVBW9vbxw6dAj/+9//0L59e6snCBBR/WAhRERUx3x9fbF161akpqbiypUrCAwMRHx8PGbOnGlyjSoiqn/cNUZERERuS9bT53fs2IHBgwejRYsWUCgU2LBhw3Vfs337dkRFRcHLywtt2rTBwoUL676hRERE5JJkLYRKSkrQtWtXzJs3r0b5EydOICEhATExMThw4ABefvllPPfccxbvME5ERER0PU6za0yhUODLL7/EkCFDrGZeeuklfP311yb3sBk/fjwOHTp0w/cNIiIiIvfToA6W3rVrF+Li4kymDRgwAEuWLIFer4darTZ7TUVFBSoqKqTfq6qq8O+//yIgIIAXmiIiImoghBC4cuVKje+NWVMNqhC6cOGC2Y0Lg4ODUVlZifz8fIs3nps5c2aNrgBMREREzu/MmTNmV76/EQ2qEALMb4Zn3LNnbevO1KlTMXnyZOn3wsJCtGrVCgcPHoS/v79ZXqlUmpzOWlJSYrUtHh4e8Pb2rlW2tLQU1vZKKhQKaLXaWmXLyspQVVVllqusrMT27dsRHx8vbTmzljXy8fGRfi4vLze7g3tts1qtVlpeFRUVNu+3ZE/W29tb+l+CTqeDXq+X+h0bGwuVSmUza42Xl5d0TzF7snq9HjqdzmrW09NTapM92crKSpOtnNcy3n4gOzsbMTExNpexRqOR1geDwWByT7VrqdVqad72ZKuqqmzeN8merEqlku4TJYRAaWmpyfPVl7eXl5fNbHX2fO+dcYwoKiqSbn5afT23lLXne+9MY4TBYEBJSQnKyspQUlKC8vJyFBcXY9++fYiMjERFRQWuXLkiZcrLy1FWVgadToeysjJUVFRAr9ejvLwcOp0OpaWlKC8vR0VFBXQ6nbT3wPio7X3gGioPDw8olUrpX+PP1/6uUChMnrv2d7VaLU03zvfah/E1KpVKygkhoFAozHLG91er1dDpdPjqq69s3nuyNhpUIdS8eXOzu/zm5eVBpVKZ3THcyNPT0+ymgAAQGhpq9TXV1STjTFlr9Ho9mjZtioCAAIu7EF2Vsd9hYWFu12+tVovg4GC367cjlrczfJftyfr6+jrdei6EQHFxMYqKilBYWIhz586hqKgIRUVFuHLlisnP1R/FxcVSQVNcXCz9a+s/CvVBrVbD09MTGo0GGo1G+tti/Nn4vLGwN/4nw/hvTR4qlcrsZ5VKJT2MBQEA7N27F3fddZf0nsbCwli0VH9N9WnVf7+2GHF2BQUF+Oqrrxze3gZVCPXo0cPsTr1bt25FdHS003z5iYhchRACJSUlKCgowL///iv9a3xcunQJ//77Ly5fvozLly/j0qVL0s+FhYU2tybVloeHB3x8fODj4wOtVguDwYDg4GDpd29vb5OHVquFl5eX9LvxZy8vL7OHp6en9G/1nzUajVMVC8YtWz179uTfPgeQtRAqLi7Gn3/+Kf1+4sQJHDx4EE2bNkWrVq0wdepUnDt3DsuXLwdw9QyxefPmYfLkyXjiiSewa9cuLFmyBKtWrZKrC0REDUpxcTH++ecf5OXlIS8vz+TnixcvIj8/HxcvXpR+vtEtMUqlEn5+fvDz84Ovr6/Jo3HjxmaPRo0aoVGjRmjcuDF8fHzQqFEjqfDx8fGBp6enVJTo9XpkZGQgISGBBQHVmqyF0N69e9GnTx/pd+OxPElJSVi6dClyc3Nx+vRp6fnWrVsjIyMDzz//PD766CO0aNECH3zwAYYNG1bvbSciciZlZWU4fvw48vLycP78eZw7dw7nz59Hbm4ucnNzceHCBVy4cAHFxcV2z1uj0SAgIAABAQFo2rSp9PD390fTpk3RpEkT+Pv7o0mTJtLDWPxUP96HyBnJWgj17t3b6sGAALB06VKzabGxsdi/f38dtoqIyLkYDAacO3cOp06dkh6nT5/GmTNncObMGZw9exaXL1+u8fyMx48FBQUhKCgIwcHBaNasmfQIDAyU/g0ICICPjw+LGXJZDeoYISIiV1VUVIQ//vgDf//9N/766y/8/fff0uPMmTM1OoupcePGaNmyJVq2bIkWLVqgRYsWCAkJkR7NmzdHSEgIGjVqVA89ImoYWAgREdUTvV6Pv/76C8eOHcNvv/2G48eP488//8Qff/yBvLw8m69Vq9UICwtDeHg4wsPD0apVK4SFhSEsLAzNmzfHr7/+isTERB4rQ2QnFkJERA6m1+vx+++/48iRIzh69CiOHDmCX3/9FX/99ZfNLTtBQUFo164d2rZtizZt2kiPiIgIhISESNeosvR+J0+erKPeELk2FkJERDcgPz8fhw4dwsGDB6V/f/vtN6sX3vTx8UHHjh3RsWNHdOjQAe3bt5cevr6+9dx6ImIhRERUQwUFBdi3bx/27t0rPc6cOWMx27hxY9x8883o3LkzOnfujE6dOiEyMhItW7bkgcdEToSFEBGRBXq9HocOHcKuXbvw008/YdeuXThx4oTFbNu2bXHrrbfi1ltvRdeuXdGlSxe0atWKBQ9RA8BCiIgIwJUrV7Bz507s2LEDOTk52LNnj8X7qd10002Ijo5GdHQ0oqKicOutt3KXFlEDxkKIiFyCwWDA9u3bsWPHDvj4+KBPnz5WDy4Grl5heceOHfjuu++wfft2HDhwwOyWEP7+/ujevTt69OiBHj16IDo6Gk2aNKnjnhBRfWIhREQNXnp6OiZOnIizZ88CAObMmYPQ0FDMnTsXQ4cOBXD1zvQ//fQTsrKy8N133+Hnn382O4MrIiICd999N+6++27cdddduOmmm7h7i8jFsRAiogYtPT0diYmJZlepP3fuHIYNG4ann34aeXl5yMrKMrv6ckREBPr164c+ffrg7rvvRlhYWD22nIicAQshImqwDAYDJk6caPFWPcZpH330kTStadOmuOeee3DPPfegX79+aNOmTb21lYicEwshImqwcnJypN1htowcORITJkzAnXfeafO4ISJyPyyEiKjBEULgp59+wjvvvFOjfHx8PHr06FHHrSKihoiFEBE1GEePHsXy5cuxevVqnD59usavCwkJqcNWEVFDxkKIiJzaxYsXsWrVKixbtgz79++Xpjdq1AiDBw/G1q1bUVBQYPG1CoUCoaGhiImJqa/mElEDw0KIiJxOVVUVtm7dikWLFmHTpk3Sae4qlQoDBw7EY489hoEDB8Lb21s6awyAyUHTxtPeU1NTeVwQEVnFQoiInMY///yDTz/9FB9//LHJ3dSjoqIwatQoPPLII2jWrJnJa4YOHYr169ebXEcIAEJDQ5GamipdR4iIyBIWQkQkKyEEdu3ahblz5yI9PV3a+tOkSROMGjUKTzzxBDp37mxzHkOHDsX999+P7OxsfPPNN4iPj7/ulaWJiAAWQkQkE71ejy+++ALvv/8+du/eLU3v3r07nnrqKQwfPhxarbbG81MqlYiNjUVJSQliY2NZBBFRjbAQIqJ6VVRUhIULF+LDDz+UdmV5enri0UcfxXPPPYeuXbvK3EIicicshIioXhQUFOCDDz7ABx98IN3qIigoCMnJyZgwYQKCgoLkbSARuSUWQkRUpy5cuIDZs2djwYIFKCkpAQB07NgRL774Ih555BF4eXnJ3EIicmcshIioTuTn5+Odd97BvHnzUF5eDgC49dZbMW3aNDzwwAM8hoeInAILISJyqKKiIrz//vuYPXs2rly5AgDo0aMH/vvf/yI+Pl66vg8RkTNgIUREDlFRUYGPPvoIb7/9tnSl59tuuw1vvfUW7r33XhZAROSUWAgR0Q0RQmDDhg1ISUnB33//DQDo0KED3njjDQwbNgweHh4yt5CIyDoWQkRUa4cOHcLzzz+P7OxsAFdvbvrGG28gKSkJKhWHFyJyfhypiMhuBQUFmDp1KhYvXgwhBDw9PZGSkoIpU6agUaNGcjePiKjGWAgRUY0JIbBixQq88MILyM/PBwA89NBDeOeddxAeHi5z64iI7MdCiIhq5Pjx45gwYYK0G6xz585YsGAB7rrrLplbRkRUezyKkYhs0ul0mDFjBrp06YLs7Gx4e3vjf//7H/bv388iiIgaPG4RIiKrDh06hKSkJBw6dAgAEB8fj48++gitW7eWuWVERI7BLUJEZKayshJvvfUW7rjjDhw6dAiBgYFYvXo1Nm/ezCKIiFwKtwgRkYljx44hKSkJe/bsAQAMGTIECxcuRHBwsMwtIyJyPG4RIiIAV88IW7RoEW6//Xbs2bMHfn5+WLFiBdLT01kEEZHL4hYhIsLly5fx5JNPYt26dQCAuLg4LFmyBKGhoTK3jIiobnGLEJGb2717N2677TasW7cOKpUK7777Lr755hsWQUTkFrhFiMhNCSEwZ84cTJkyBZWVlYiIiMDq1avRrVs3uZtGRFRvWAgRuaHi4mI8/vjjWL9+PQAgMTERn3zyCZo0aSJvw4iI6hkLISI38/fff2PIkCH45ZdfoFarkZqaigkTJkChUMjdNCKiesdCiMiNZGVl4aGHHsKlS5cQHByM9evX8+rQROTWeLA0kRsQQmD27Nm49957cenSJdx5553Yu3cviyAicnsshIhcXGVlJZ566imkpKSgqqoKo0ePxvbt23lWGBERuGuMyKUVFxfj0UcfxTfffAOFQoH3338fzz33HI8HIiL6/9y2ECopKYGXl5fZdKVSaTK9pKTE6jw8PDzg7e1dq2xpaSmEEBazCoUCWq22VtmysjJUVVWZ5fR6PcrLy02mWcsa+fj4SD+Xl5fDYDA4JKvVaqU/xBUVFaisrHRI1tvbGx4eVzdy6nQ66PV6qd8lJSVQq9U2s9Z4eXlBqVTandXr9dDpdFaznp6eUKlUdmcrKytRUVFhNavRaAAA//77L/r27YuDBw/Cy8sLS5cuxaBBg1BaWmqSNX4uBoPBbB2pTq1WS/O2J1tVVYWysjKHZFUqFTw9PQFc3d1XvS8ATJa3t7e3zWx19nzvnXWMsLSeW8ra87139jFCr9ebfEa1GSMcka3vMcLSuGbvGGF8nT1ZZxgj6oRwM4WFhQKA1UdCQoJJXqvVWs3GxsaaZAMDA61mo6OjTbLh4eFWs506dTLJdurUyWo2PDzcJBsdHW016+vrK3Q6nZSNjY21mtVqtSbzTUhIsPm5VZeYmGgzW1xcLGWTkpJsZvPy8qRscnKyzeyJEyekbEpKis3skSNHpOz06dNtZnfv3i1lZ82aZTObnZ0tZefNm2czu2nTJimblpZmM7t27Vopu3btWpvZtLQ0cfDgQdGsWTObOQBi3rx50nyzs7NtZmfNmiVld+/ebTM7ffp0KXvkyBGb2ZSUFCl74sQJm9nk5GQpm5eXZzOblJQkZYuLi21mExMTTdZhW1lnHCMiIyOtZu0ZIwIDA02yDWGMWLZsmTSucYy4qiZjhNGmTZtsZp1pjMjPzxcARGFhoXAkHiNE5GL++OMP9O7dGxcvXkRISIjczSEicmoKIaxse3VRRUVF8PPzw6lTpxAQEGD2vLNu9q5p1tausczMTAwdOlTazOnsm73tzVrbNZaZmYkBAwa4xa6x7OxsDB8+HGVlZejYsSOysrLg7+9vdb7OttnbEbvGjMvbnXaNFRYWYsuWLWbruaWsq+0a27ZtGwYOHAi1Wu1Wu8auHdfcYddYQUEBAgMDUVhYCF9fX6t5e7ntMUI+Pj4mX0xbOXvmWVPVByZHZqsPpNXp9XqzY6KsZS2xdDyVI7Kenp7SHytHZjUaDTQajdRvHx8fsz8Q12btmW9NqNVqq+95I1mVSiUNeNVt3LgRDz74ICoqKtC/f3+MGzcOwcHBNZ6vUqms8TpsT9bDw6NOsgqFwixrbXlbytriDFl7x4jrredG9nzvnX2M0Ov1Jgf+12aMkDNb2zHieuOatTHCEnuyzjBG1AXuGiNyAWvWrMHQoUNRUVGBIUOGID09vcZ/EIiI3BkLIaIGLi0tDSNGjEBlZSVGjBiBtWvXsggiIqohFkJEDdiSJUswZswYVFVV4YknnsDy5ctrvKmdiIhYCBE1WJ999hmeeOIJAMDEiROxaNEi6SBMIiKqGRZCRA3Q+vXrkZSUBCEEkpOT8f777/Nq0UREtcBCiKiB2bhxIx555BFUVVVhzJgx+PDDD1kEERHVEgshogYkMzMTiYmJ0oHRH3/8sXStEyIish9HUKIG4scff8SQIUOg0+kwbNgwLFu2jMcEERHdIBZCRA3AsWPHMHjwYJSXl2PgwIH4/PPPa3wRNCIiso6FEJGTO3/+PO69915cunQJ3bt3x9q1a+v2TsxERG6EhRCREysqKkJCQgJOnz6Nm266CRs3brTr1gtERGQbCyEiJ6XT6TB06FAcOnQIwcHB2LJlCwIDA+VuFhGRS2EhROSEjKfGf/fdd2jUqBEyMjLQunVruZtFRORyWAgROaE33ngDK1euhEqlwhdffIHbb79d7iYREbkk2Quh+fPno3Xr1vDy8kJUVBRycnJs5leuXImuXbtCq9UiJCQEjz/+OAoKCuqptUR174svvsBrr70GAFi0aBHi4uLkbRARkQuTtRBas2YNJk2ahGnTpuHAgQOIiYlBfHw8Tp8+bTH/ww8/YNSoURg7diyOHj2KdevWYc+ePRg3blw9t5yobhw6dAijRo0CAEyaNAljxoyRuUVERK5N1kJozpw5GDt2LMaNG4fIyEikpqYiLCwMCxYssJj/6aefEBERgeeeew6tW7fGXXfdhaeeegp79+6t55YTOV5eXh7uu+8+lJaWon///nj33XflbhIRkcuT7YpsOp0O+/btw5QpU0ymx8XFYefOnRZf07NnT0ybNg0ZGRmIj49HXl4e1q9fj4EDB1p9n4qKClRUVEi/FxUVAQD0ej30er0DetIwGPvqTn0GnLvfBoMBP/zwA3JzcxEYGIg333wTp0+fRrt27fDZZ59BCFHrdjtzv+sS+81+uwN377ejKYQQok7mfB3nz59Hy5Yt8eOPP6Jnz57S9LfffhvLli3D8ePHLb5u/fr1ePzxx1FeXo7Kykrcd999WL9+PdRqtcX8a6+9hhkzZphN//zzz3k9FpLNrl27sHjxYrPj2zQaDWbPno2wsDCZWkZE5JxKS0sxYsQIFBYWwtfX12Hzlf0a/dfeNVsIYfVO2r/++iuee+45vPrqqxgwYAByc3Pxn//8B+PHj8eSJUssvmbq1KmYPHmy9HtRURHCwsLQp08fBAQEOK4jTk6v1yMrKwv9+/e3WjS6Imfs95dffolZs2bB0v9BdDodgoKCkJCQcEPv4Yz9rg/sN/vtDty133V1YpRshVBgYCCUSiUuXLhgMj0vLw/BwcEWXzNz5kz06tUL//nPfwAAXbp0gY+PD2JiYvDmm28iJCTE7DWenp7w9PQ0m65Wq91qBTJiv+VlMBjwwgsvWCyCgKv/MUhJScGwYcMcckNVZ+l3fWO/3Qv77R7qqq+yHSyt0WgQFRWFrKwsk+lZWVkmu8qqKy0thYeHaZONfyxk2sNHZJecnBycPXvW6vNCCJw5c+a6l5EgIiLHkPWsscmTJ2Px4sX49NNPcezYMTz//PM4ffo0xo8fD+Dqbi3jqcQAMHjwYKSnp2PBggX4+++/8eOPP+K5557DnXfeiRYtWsjVDaIay83NdWiOiIhujKzHCD300EMoKCjA66+/jtzcXHTu3BkZGRkIDw8HcPWPQfVrCo0ePRpXrlzBvHnz8MILL6BJkybo27cv3nnnHbm6QGQXS7tvbyRHREQ3RvaDpZOTk5GcnGzxuaVLl5pNe/bZZ/Hss8/WcauI6kZMTAyCgoKQl5dn8XmFQoHQ0FDExMTUc8uIiNyT7LfYIHInxutYWWI8WzI1NdUhB0oTEdH1sRAiqkfJycnSmZHXHtcWGhqK9evXY+jQoTK1jojI/ci+a4zIXXz++edYvXo1lEolvv76a+kmw7m5uQgJCUFMTAy3BBER1TMWQkT14PTp09KxcK+++iruvPNOAEDv3r1lbBUREXHXGFEdq6qqwujRo1FYWIhu3brh5ZdflrtJRET0/7EQIqpj77//PrKzs6HVarFixQqoVNwQS0TkLFgIEdWhw4cPS1uA3n//fbRv317mFhERUXUshIjqSHl5OR577DHodDoMGjQITzzxhNxNIiKia7AQIqojb7zxBn755Rc0a9YMixcvlq4TREREzoOFEFEdOHjwIGbNmgUAWLBgAYKDg2VuERERWcJCiMjBKisrMXbsWFRWVmLYsGEYNmyY3E0iIiIrWAgROdicOXOwf/9+NGnSBPPmzZO7OUREZAMLISIH+v333zF9+nQAV88Sa968ucwtIiIiW1gIETlIVVUVnnjiCZSXl6N///5ISkqSu0lERHQdLISIHOTjjz/Gjh07oNVqsWjRIp4lRkTUALAQInKAs2fP4sUXXwQAvP3222jdurXMLSIioppgIUTkAJMnT8aVK1fQrVs3PPPMM3I3h4iIaoiFENEN+vbbb7Fu3Tp4eHhg0aJFUCqVcjeJiIhqiIUQ0Q3Q6XTSFqCnn34aXbt2lblFRERkDxZCRDfg/fffx/HjxxEUFITXX39d7uYQEZGdWAgR1dKZM2fwxhtvAABmzZqFJk2ayNsgIiKyGwsholp64YUXUFJSgl69emHkyJFyN4eIiGqBhRBRLVQ/QPqjjz6Chwe/SkREDZFK7gbIpaSkBF5eXmbTlUqlyfSSkhKr8/Dw8IC3t3etsqWlpRBCWMwqFApotdpaZcvKylBVVWWW0+v1KC8vN5lmLWvk4+Mj/VxeXg6DweCQrFarlS42WFFRgcrKSodkvb29pYJEp9NBr9dL/S4pKYFarbaZtcbLy0s6E0yn06GkpATJyckAgCeffBLt2rWTln31rF6vh06nszpfT09PqFQqu7OVlZWoqKiwmtVoNNLPlZWVNuer0Wikz8VgMJitI9Wp1Wpp3vZkq6qqUFZW5pCsSqWCp6cnAEAIgdLSUpPnqy9vb29vm9nq7PneO+sYYWk9t5S153vv7GOEXq83+YxqM0Y4InvtGFHTbG3HCEvjmr1jhPF19mSdYYyoE8LNFBYWCgBWHwkJCSZ5rVZrNRsbG2uSDQwMtJqNjo42yYaHh1vNdurUySTbqVMnq9nw8HCTbHR0tNWsr6+v0Ol0UjY2NtZqVqvVmsw3ISHB5udWXWJios1scXGxlE1KSrKZzcvLk7LJyck2sydOnJCyKSkpNrNHjhyRstOnT7eZ3b17t5SdNWuWzWx2draUnTdvns3spk2bpGxaWprN7Nq1a6Xs2rVrbWbT0tKETqcTGzZsEBs2bLCZnTdvnjTf7Oxsm9lZs2ZJ2d27d9vMTp8+XcoeOXLEZjYlJUXKnjhxwmY2OTlZyubl5dnMJiUlSdni4mKb2cTERJN12FbWGceIyMhIq1l7xojAwECTbEMYI5YtWyaNaxwjrqrJGGG0adMmm1lnGiPy8/MFAFFYWCgcidvziexg63/0RETU8CiEsLLt1UUVFRXBz88Pp06dQkBAgNnzzrrZu6ZZW7vGMjMzMXToUGkzp7Nv9rY3a23XWGZmJgYMGOCQXWPPPvss5s2bh86dO+PHH380u3iiM+0ay8jIQFxcnM1l7GybvR2xa8y4vN1p11hhYSG2bNlitp5byrrarrFt27Zh4MCBUKvVbrVr7NpxzR12jRUUFCAwMBCFhYXw9fW1mreX2x4j5OPjY/LFtJWzZ541VX1gcmS2+kBanV6vNzsmylrWEkvHUzki6+npKf2xcmRWo9FAo9FI/fbx8TH7A3Ft9nr++OMPLFy4EAAwZ86c634R1Wq11fe8kaxKpZIGPGuMA7FKparxfJVKZY3XYXuyHh4edZJVKBRmWWvL21LWFmfI2jtGXG89N7Lne+/sY4Rerze5uXFtxgg5s7UdI643rtVkjKhN1hnGiLrAXWNENTRlyhRUVlYiPj4e/fv3l7s5RETkACyEiGogJycH6enp8PDwwLvvvit3c4iIyEFYCBFdR1VVFV544QUAwLhx43DzzTfL3CIiInIUFkJE17F69Wrs2bMHjRo14v3EiIhcDAshIhvKy8sxdepUAFePEQoODpa5RURE5EgshIhs+Oijj3D69GmEhobi+eefl7s5RETkYCyEiKy4cuUK/ve//wEAXn/9dbtOZyYiooaBhRCRFampqcjPz0eHDh14d3kiIhfFQojIgn///RfvvfceAGDGjBk1vuAYERE1LCyEiCx49913UVRUhK5du+LBBx+UuzlERFRHWAgRXePChQv44IMPAABvvPGGdL8hIiJyPRzhia4xc+ZMlJaWolu3bhg0aJDczSEiojrEQoiomtOnT0s3Vn3rrbdMbuhIRESuh4UQUTVvvPEGdDod+vTpg379+sndHCIiqmMshIj+vz///BNpaWkArm4NIiIi18dCiOj/e/vtt2EwGJCQkIAePXrI3RwiIqoHLISIAJw8eRIrVqwAALz66qsyt4aIiOoLrxJHbstgMCAnJwe5ublYvXo1Kisr0b9/f3Tr1k3uphERUT1hIURuKT09HRMnTsTZs2dNpsfExMjUIiIikgN3jZHbSU9PR2JiolkRBADTp09Henq6DK0iIiI5sBAit2IwGDBx4kQIIaxmJk2aBIPBUI+tIiIiubAQIreSk5NjcUuQkRACZ86cQU5OTj22ioiI5MJCiNxKbm6uQ3NERNSwsRAitxISEuLQHBERNWwshMitxMTEIDQ01OrzCoUCYWFhPHuMiMhNsBAit6JUKjF37lyLzxlvsJqamgqlUlmfzSIiIpmwECK3M2jQIDRt2tRsemhoKNavX4+hQ4fK0CoiIpIDL6hIbmf16tX4999/ERISgqVLl6KgoAAhISGIiYnhliAiIjfDQojcihAC7733HgDgueeeQ1xcnMwtIiIiOXHXGLmVrKws/PLLL/Dx8cFTTz0ld3OIiEhmLITIrbz77rsAgHHjxsHf31/m1hARkdxYCJHbOHjwIL799lsolUpMmjRJ7uYQEZETYCFEbmP27NkAgAcffBARERHyNoaIiJwCCyFyC2fOnMHq1asBACkpKTK3hoiInAULIXIL8+bNQ2VlJfr06YOoqCi5m0NERE5C9kJo/vz5aN26Nby8vBAVFXXdu35XVFRg2rRpCA8Ph6enJ9q2bYtPP/20nlpLDVFJSQkWL14MgFuDiIjIlKzXEVqzZg0mTZqE+fPno1evXli0aBHi4+Px66+/olWrVhZfM3z4cPzzzz9YsmQJ2rVrh7y8PFRWVtZzy6kh+fbbb3HlyhV06tQJ8fHxcjeHiIiciKyF0Jw5czB27FiMGzcOwNV7PGVmZmLBggWYOXOmWX7Lli3Yvn07/v77b+kWCTzolWwxGAzIyMgAAEyaNEm6nxgREREgYyGk0+mwb98+TJkyxWR6XFwcdu7cafE1X3/9NaKjozFr1iysWLECPj4+uO+++/DGG2/A29vb4msqKipQUVEh/V5UVAQA0Ov10Ov1DuqN8zP21Z36DACbNm3CP//8A39/fwwfPtxt+u+uy5v9Zr/dgbv329FkK4Ty8/NhMBgQHBxsMj04OBgXLlyw+Jq///4bP/zwA7y8vPDll18iPz8fycnJ+Pfff60eJzRz5kzMmDHDbHp2dja0Wu2Nd6SBycrKkrsJ9erNN98EAMTGxmLbtm3yNkYG7ra8jdhv98J+u4fS0tI6ma/s9xq7dleFEMLq7ouqqiooFAqsXLkSfn5+AK7uXktMTMRHH31kcavQ1KlTMXnyZOn3oqIihIWFoU+fPggICHBgT5ybXq9HVlYW+vfvD7VaLXdz6sWvv/6KQ4cOwcPDA2+//TbatWsnd5PqjTsub4D9Zr/dg7v2u6CgoE7mK1shFBgYCKVSabb1Jy8vz2wrkVFISAhatmwpFUEAEBkZCSEEzp49i/bt25u9xtPTE56enmbT1Wq1W61ARu7U70WLFgEA7rjjDrRr185t+l2dOy3v6thv98J+u4e66qtsp89rNBpERUWZbdrLyspCz549Lb6mV69eOH/+PIqLi6Vpv//+Ozw8PBAaGlqn7aWGpbCwEMuXLwcADBo0SObWEBGRs5L1OkKTJ0/G4sWL8emnn+LYsWN4/vnncfr0aYwfPx7A1d1ao0aNkvIjRoxAQEAAHn/8cfz666/YsWMH/vOf/2DMmDFWD5Ym95SWloaSkhLcfPPN6Ny5s9zNISIiJyXrMUIPPfQQCgoK8PrrryM3NxedO3dGRkYGwsPDAQC5ubk4ffq0lG/UqBGysrLw7LPPIjo6GgEBARg+fLh0QCwRcPVYsnnz5gEAnn76aZ4yT0REVsl+sHRycjKSk5MtPrd06VKzaR07dnS7I+XJPt988w3++usvNGnSBI888gi2b98ud5OIiMhJyX6LDSJH++CDDwAA48aNg4+Pj8ytISIiZ8ZCiFzKb7/9hq1bt0KhUFjd0khERGQk+64xuZSUlMDLy8tsulKpNJleUlJidR4eHh4mB2nbky0tLYUQwmJWoVCYXOzRnmxZWRmqqqrMcnq9HuXl5SbTrGWNqm9NKS8vh8FgcEhWq9VKx+1UVFTYvFecPVlvb28sXLgQADBw4EAEBQWhpKQE5eXlKCkpMTn10tvbGx4eV/8foNPpbF6x1MvLC0ql0u6sXq+HTqezmvX09IRKpbI7W1lZaXK19GtpNBrp58rKSpvz1Wg00udiMBjM1pHq1Gq1NG97slVVVSgrK3NIVqVSSZfDEEKYXWDNuJ6XlJTA29vbZrY6e773zjpGWFrPLWXt+d47+xih1+tNPqOajBE1/d478xhRfT03Lm97xwjj6+zJOsMYUSeEmyksLBQArD4SEhJM8lqt1mo2NjbWJBsYGGg1Gx0dbZINDw+3mu3UqZNJtlOnTlaz4eHhJtno6GirWV9fX6HT6aRsbGys1axWqzWZb0JCgs3PrbrExESb2eLiYimblJRkM5uXlydlk5OTbWaPHTsmmjRpIgCIYcOG2cweOXJEmu/06dNtZnfv3i1lZ82aZTObnZ0tZefNm2czu2nTJimblpZmM7t27Vopu3btWpvZtLQ0odPpxIYNG8SGDRtsZufNmyfNNzs722Z21qxZUnb37t02s9OnT5eyR44csZlNSUmRsidOnLCZTU5OlrJ5eXk2s0lJSVK2uLjYZjYxMdFkHbaVdcYxIjIy0mrWnjEiMDDQJNsQxohly5ZJ49r1xogTJ05I801JSbGZdfUxwmjTpk02s840RuTn5wsAorCwUDgSd42Ry9i0aRMuX76MiIgI3oyXiIhqRCGElW2vLqqoqAh+fn44deqUxVtsOOtm75pmbe0ay8zMxNChQ6XNnM6+2dve7D333IOffvoJb731FlJSUqQb62ZmZmLAgAFut2ssIyMDcXFxNpexs232dsSuMePydqddY4WFhdiyZYvZem4p62q7xrZt24aBAwdCrVa71a6xa8c1d9g1VlBQgMDAQBQWFsLX19dq3l5ue4yQj49Pjc4osuesI3uy9tzw1Z6stQtL6vV6s2Oi7LkIpaXjqRyRtXYLFHuzhw8fxk8//QSVSoUxY8ZAo9FAo9FI/fbx8bF6eXZjtibsydpz+Xt7siqVShrwrDEOxCqVqsbzVSqVNV6H7cl6eHjUSVahUJhlrS1vS1lbnCFr7xhxvfXcyJ7vvbOPEXq93uQ6YfaMJ3X1va+PMeJ641pNxojaZJ1hjKgL3DVGLsF4X7EhQ4agefPmMreGiIgaChZC1OCVlJTgs88+AwA89dRTMreGiIgaEhZC1OCtXr0aRUVFaNu2Lfr27St3c4iIqAFhIUQNnvHaQU899ZR0cCMREVFN8K8GNWj79+/H3r17odFoMHr0aLmbQ0REDQwLIWrQjAdJDx06FM2aNZO5NURE1NCwEKIGq6ioCCtXrgQAjB8/XubWEBFRQ8RCiBqsVatWoaSkBB07dsTdd98td3OIiKgBYiFEDdann34KABg7dqzJRdWIiIhqioUQNUhHjhzB7t27oVKpMHLkSLmbQ0REDRQLIWqQ0tLSAACDBg1CcHCwzK0hIqKGyq5CaNSoUbhy5Yr0+6FDh2zeXI6oLuh0OqxYsQIAMGbMGJlbQ0REDZldhdDKlStN7hAbExODM2fOOLxRRLZs3rwZFy9eRPPmzREfHy93c4iIqAGzqxASQtj8nag+GA+SHjVqVI3vmkxERGQJjxGiBuX8+fPIyMgAwN1iRER04+z+7/Svv/6KCxcuALi6Rei3335DcXGxSaZLly6OaR3RNVasWIGqqir06tULHTp0kLs5RETUwNldCPXr189kl9igQYMAAAqFAkIIKBQKGAwGx7WQ6P8TQki7xbg1iIiIHMGuQujEiRN11Q6i69q5cyd+//13+Pj44MEHH5S7OURE5ALsKoTCw8Prqh1EVhkMBuTk5GDGjBkAgAcffBCNGzeWuVVEROQKanXKzR9//IGvvvoKJ0+ehEKhQOvWrTFkyBC0adPG0e0jN5eeno6JEyfi7Nmz0rTNmzcjPT0dQ4cOlbFlRETkCuwuhGbOnIlXX30VVVVVCAoKghACFy9exJQpU/D2228jJSWlLtpJbig9PR2JiYlml2m4ePEiEhMTsX79ehZDRER0Q+w6fT47Oxv//e9/MW3aNOTn5yM3NxcXLlyQCqEpU6Zgx44dddVWciMGgwETJ060ea2qSZMm8cB8IiK6IXYVQgsXLsS4cePw2muvwd/fX5retGlTvP766xgzZgwWLFjg8EaS+8nJyTHZHXYtIQTOnDmDnJycemwVERG5GrsKod27d9u80/fIkSPx008/3XCjiHJzcx2aIyIissSuQuiff/5BRESE1edbt24tXWyR6EaEhIQ4NEdERGSJXYVQeXk5NBqN1efVajV0Ot0NN4ooJiYGoaGhVp9XKBQICwtDTExMPbaKiIhcjd1njS1evBiNGjWy+NyVK1duuEFEAKBUKjF37lwMGzbM7DmFQgEASE1NhVKprO+mERGRC7GrEGrVqhU++eST62aIHGHQoEHw9fVFUVGRyfTQ0FCkpqby1HkiIrphdhVCJ0+erKNmEJnbsmULioqK0Lx5c3z22WfIy8tDSEgIYmJiuCWIiIgcwq5jhL7//nt06tTJ7H/oAFBYWIibb76ZpzOTwyxfvhwAMGLECPTr1w+PPPIIevfuzSKIiIgcxq5CKDU1FU888QR8fX3NnvPz88NTTz2FOXPmOKxx5L4uXbqEjRs3AgBGjRolc2uIiMhV2VUIHTp0CPfee6/V5+Pi4rBv374bbhTR2rVrodPpcMstt6Br165yN4eIiFyU3dcRUqvVVp9XqVS4ePHiDTeKaMWKFQC4NYiIiOqWXYVQy5Yt8csvv1h9/vDhw7zAHd2wv/76Cz/++CM8PDwwYsQIuZtDREQuzK5CKCEhAa+++irKy8vNnisrK8P06dMxaNAghzWO3NPKlSsBAPfccw9atGghc2uIiMiV2XX6/H//+1+kp6fjpptuwjPPPIMOHTpAoVDg2LFj+Oijj2AwGDBt2rS6aiu5ASEEPv/8cwDAY489JnNriIjI1dlVCAUHB2Pnzp2YMGECpk6dCiEEgKtX+h0wYADmz5+P4ODgOmkouYcDBw7g+PHj8PLywpAhQ+RuDhERuTi7b7ERHh6OjIwMXLp0CX/++SeEEGjfvj38/f3ron3kZoxbgwYPHozGjRvL3BoiInJ1dhdCRv7+/rjjjjsc2RZyc1VVVVi9ejUA8CBpIiKqF3YdLE1Ul3JycnDu3Dn4+fkhPj5e7uYQEZEbYCFETsO4WywxMRGenp4yt4aIiNwBCyFyCjqdDuvWrQPA3WJERFR/WAiRU8jMzMSlS5cQEhKC2NhYuZtDRERugoUQOQXjbrGHH36Yd5cnIqJ6w0KIZFdcXIyvvvoKAHeLERFR/WIhRLL76quvUFZWhnbt2iEqKkru5hARkRthIUSyM+4WGzFiBBQKhcytISIid1LrCyo2dCUlJfDy8jKbrlQqTaaXlJRYnYeHhwe8vb1rlS0tLZVuUXIthUIBrVZbq2xZWRmqqqrMcnq93uxmudayRj4+PtLP5eXlMBgMDslqtVqp4Dl37hwyMzMBAPfff7/ZZ1g9W1FRgcrKSqvz9fb2hofH1dpep9NBr9dL/S4pKYFarbaZtcbLy0s6bsmerF6vh06ns5r19PSESqWyO1tZWYmKigqrWY1GI/1cWVlpc74ajUb6XAwGg8UbKhup1Wpp3vZkq6qqUFZW5pCsSqWSLq0ghEBpaanJ89WXt7e3t81sdfZ87511jLC0nlvK2vO9d4Yxwtb3Xq/Xm3xGtRkjHJGt7zHC0rhm7xhhfJ09WWcYI+qEcDOFhYUCgNVHQkKCSV6r1VrNxsbGmmQDAwOtZqOjo02y4eHhVrOdOnUyyXbq1MlqNjw83CQbHR1tNevr6yt0Op2UjY2NtZrVarUm801ISLD5uVWXmJhoM1tcXCxlu3fvbjObl5cnZZOTk21mT5w4IWVTUlJsZo8cOSJlp0+fbjO7e/duKTtr1iyb2ezsbCk7b948m9lNmzZJ2bS0NJvZtWvXStm1a9fazKalpQmdTic2bNggNmzYYDM7b948ab7Z2dk2s7NmzZKyu3fvtpmdPn26lD1y5IjNbEpKipQ9ceKEzWxycrKUzcvLs5lNSkqSssXFxTaziYmJJuuwrawzjhGRkZFWs/aMEYGBgSZZZxgjkpKSbGaXLVsmjWscI66qyRhhtGnTJptZZxoj8vPzBQBRWFgoHIm7xkhWJ06ckLsJRETkxhRCWNn26qKKiorg5+eHU6dOISAgwOx5Z93sXdOsrV1jmZmZGDp0qLSZU+7N3ufPn0fLli0BAL/++itatWplNQvUftdYZmYmBgwY4Ha7xjIyMhAXF2dzGTvbZm9H7BozLm932jVWWFiILVu2mK3nlrKutmts27ZtGDhwINRqtVvtGrt2XHOHXWMFBQUIDAxEYWEhfH19rebt5bbHCPn4+Jh8MW3l7JlnTVUfmByZrT6QVqfX682OibKWtcTS8VQ3ml2/fj0AoHv37oiMjLxu3tPTs8a33tBoNNBoNFK/fXx8zP5AXJu1Z741oVarrb7njWRVKpU04FljHIhVKlWN56tUKmu8DtuT9fDwqJOsQqEwy1pb3paytjhD1t4x4nrruZE933u5xwjA9vder9ebnGBRmzFCzmxtx4jrjWs1GSNqk3WGMaIucNcYyWbNmjUArl5EkYiISA4shEgWZ86cwc6dO6FQKPDggw/K3RwiInJTLIRIFmvXrgUAxMTEoEWLFjK3hoiI3BULIZKFcbfYQw89JHNLiIjIncleCM2fPx+tW7eGl5cXoqKikJOTU6PX/fjjj1CpVLj11lvrtoHkcH///Tf27NkDDw8PDBs2TO7mEBGRG5O1EFqzZg0mTZqEadOm4cCBA4iJiUF8fDxOnz5t83WFhYUYNWoU+vXrV08tJUcy7hbr06cPgoODZW4NERG5M1kLoTlz5mDs2LEYN24cIiMjkZqairCwMCxYsMDm65566imMGDECPXr0qKeWkiNxtxgRETkL2a4jpNPpsG/fPkyZMsVkelxcHHbu3Gn1dWlpafjrr7/w2Wef4c0337zu+1RUVJhcLKqoqAgApIvtuQtjX+Xu8/Hjx3Hw4EGoVCoMHjy4ztvjLP2ub+w3++0O2G/37LejyVYI5efnw2AwmO0aCQ4OxoULFyy+5o8//sCUKVOQk5NT4wtAzZw5EzNmzDCbnp2dbdcFy1xFVlaWrO9v3BrUpUsX/Pzzz/X2vnL3Wy7st3thv92Lu/Xb1tXhb4TsV5auflVQ4Oql8K+dBly9XPeIESMwY8YM3HTTTTWe/9SpUzF58mTp96KiIoSFhaFPnz4Wb7HhqvR6PbKystC/f/8aX8m0LkydOhUAkJycjISEhDp/P2fpd31jv9lvd8B+u1e/CwoK6mS+shVCgYGBUCqVZlt/8vLyLB5Ae+XKFezduxcHDhzAM888A+Dq/UmEEFCpVNi6dSv69u1r9jprl1y359LmrkTOfh85cgTHjh2DRqPBsGHD6rUdXN7uhf12L+y3e6irvsp2sLRGo0FUVJTZpr2srCz07NnTLO/r64tffvkFBw8elB7jx49Hhw4dcPDgQXTr1q2+mk61ZDxbbMCAAWjSpIm8jSEiIoLMu8YmT56MkSNHIjo6Gj169MDHH3+M06dPY/z48QCu7kY5d+4cli9fDg8PD3Tu3Nnk9UFBQfDy8jKbTs5HCIF169YBAIYPHy5za4iIiK6StRB66KGHUFBQgNdffx25ubno3LkzMjIyEB4eDgDIzc297jWFqGE4evQofvvtN2g0GgwePFju5hAREQFwgoOlk5OTkZycbPG5pUuX2nzta6+9htdee83xjSKHM24NGjBgAPz8/GRuDRER0VWy32KD3IOxEOKd5omIyJmwEKI6d/ToUelssfvuu0/u5hAREUlYCFGdM24NiouL424xIiJyKiyEqM4ZT5vnbjEiInI2sh8sTa7LYDBg+fLlOHbsGFQqFQYOHCh3k4iIiExwixDVifT0dERERGDMmDEAgMrKStx6661IT0+XuWVERET/h4UQOVx6ejoSExNx9uxZk+nnzp1DYmIiiyEiInIaLITIoQwGAyZOnAghhNlzxmmTJk2CwWCo76YRERGZYSFEDpWTk2O2Jag6IQTOnDmDnJycemwVERGRZSyEyKFyc3MdmiMiIqpLLITIoUJCQhyaIyIiqksshMihYmJiEBoaavV5hUKBsLAwxMTE1GOriIiILGMhRA6lVCoxd+5ci88pFAoAQGpqKpRKZX02i4iIyCIWQuRwnTt3tjg9NDQU69evx9ChQ+u5RURERJbxytLkcF988QUAoH///nj55ZeRm5uLkJAQxMTEcEsQERE5FRZC5HDr168HAAwfPhy9e/eWtzFEREQ2cNcYOdTff/+N/fv3Q6lUYsiQIXI3h4iIyCYWQuRQxt1ivXv3RmBgoMytISIiso2FEDmUcbdYYmKizC0hIiK6PhZC5DCnTp3C7t27oVAo8MADD8jdHCIioutiIUQOY7yr/N13343g4GCZW0NERHR9LITIYbhbjIiIGhoWQuQQ586dw86dOwGAF0wkIqIGg4UQOYRxt1ivXr3QokULmVtDRERUMyyEyCG4W4yIiBoiFkJ0wy5cuICcnBwA3C1GREQNCwshumFffvklhBDo1q0bWrVqJXdziIiIaoyFEN0w426xYcOGydwSIiIi+7AQohty8eJFbNu2DQCPDyIiooaHhRDdkA0bNqCqqgpRUVFo3bq13M0hIiKyCwshuiE8W4yIiBoyFkJUawUFBfjuu+8A8PggIiJqmFgIUa19/fXXMBgM6Nq1K9q3by93c4iIiOymkrsBcikpKYGXl5fZdKVSaTK9pKTE6jw8PDzg7e1dq2xpaSmEEBazCoUCWq22VtmysjJUVVWZ5fR6PcrLy02mWcsa+fj4SD+Xl5fDYDCYPL969WoAwH333Wcy3VK2Oq1WC4VCAQCoqKhAZWWlQ7Le3t7w8Lha2+t0Ouj1eqnfJSUlUKvVNrPWeHl5QalU2p3V6/XQ6XRWs56enlCpVHZnKysrUVFRYTWr0WiknysrK23OV6PRSJ+LwWAwW0eqU6vV0rztyVZVVaGsrMwhWZVKBU9PTwCAEAKlpaUmz1df3t7e3jaz1dnzvXfWMcLSem4pa8/3/kbHiNpma/q91+v1Jp9RbcYIR2Tre4ywNK7ZO0YYX2dP1hnGiDoh3ExhYaEAYPWRkJBgktdqtVazsbGxJtnAwECr2ejoaJNseHi41WynTp1Msp06dbKaDQ8PN8lGR0dbzfr6+gqdTidlY2NjrWa1Wq3JfBMSEmx+btUlJibazBYXF0vZpKQkm9m8vDwpm5ycbDN74sQJKZuSkmIze+TIESk7ffp0m9ndu3dL2VmzZtnMZmdnS9l58+bZzG7atEnKpqWl2cyuXbtWyq5du9ZmNi0tTeh0OrFhwwaxYcMGm9l58+ZJ883OzraZnTVrlpTdvXu3zez06dOl7JEjR2xmU1JSpOyJEydsZpOTk6VsXl6ezWxSUpKULS4utplNTEw0WYdtZZ1xjIiMjLSatWeMCAwMNMk2hDFi2bJl0rjGMeKqmowRRps2bbKZdaYxIj8/XwAQhYWFwpG4a4yIiIjclkIIK9teXVRRURH8/Pxw6tQpBAQEmD3vrJu9a5q1tWssMzMTQ4cOlTZz3shm7wcffBDffPMNpk6dimnTptXJZm97s9Z2jWVmZmLAgAFut2ssIyMDcXFxNpexs232dsSuMePydqddY4WFhdiyZYvZem4p62q7xrZt24aBAwdCrVa71a6xa8c1d9g1VlBQgMDAQBQWFsLX19dq3l5ue4yQj4+PyRfTVs6eedZU9YHJkdnqA2l1er3e7Jgoa1lLqr+2qKhIOltsxIgRZv22dOyVNZ6entIfK0dmNRoNNBqN1G8fHx+zPxDXZu2Zb02o1Wqr73kjWZVKJQ141hgHYpVKVeP5KpXKGq/D9mQ9PDzqJKtQKMyy1pa3pawtzpC1d4y43npuZM/3vrZjhCOztr73er1eKpiul71WXX3v62OMuN64VpMxojZZZxgj6gJ3jZHdNm3aBJ1Ohw4dOuDmm2+WuzlERES1xkKI7Fb9IorV/zdGRETU0LAQIrsUFxfjm2++AcCrSRMRUcPHQojskpGRgfLycrRt2xZdu3aVuzlEREQ3hIUQ2WXdunUAuFuMiIhcAwshqrGSkhJs3rwZwNXT54mIiBo6FkJUY5s3b0ZZWRnatGmD22+/Xe7mEBER3TAWQlRjxt1iDz74IHeLERGRS2AhRDXC3WJEROSKWAhRjXC3GBERuSIWQlQj3C1GRESuiIUQXVf13WLDhw+XuTVERESOw0KIrqv6brHbbrtN7uYQERE5DAshuq61a9cC4G4xIiJyPSyEyKaSkhJkZGQA4G4xIiJyPSyEyCbuFiMiIlfGQohsMu4WGz58OHeLERGRy2EhRFZV3y3GiygSEZErYiFEVnG3GBERuTqV3A0g52MwGJCTk4P33nsPAJCYmMjdYkRE5JK4RYhMpKenIyIiAn369MGePXsAAEuXLkV6errMLSMiInI8FkIkSU9PR2JiIs6ePWsyPS8vD4mJiSyGiIjI5bAQIgBXd4dNnDgRQgirmUmTJsFgMNRjq4iIiOoWCyECAOTk5JhtCapOCIEzZ84gJyenHltFRERUt1gIEQAgNzfXoTkiIqKGQPZCaP78+WjdujW8vLwQFRVlc4tDeno6+vfvj2bNmsHX1xc9evRAZmZmPbbWdYWEhDg0R0RE1BDIWgitWbMGkyZNwrRp03DgwAHExMQgPj4ep0+ftpjfsWMH+vfvj4yMDOzbtw99+vTB4MGDceDAgXpuueuJiYlBaGio1ecVCgXCwsIQExNTj60iIiKqW7IWQnPmzMHYsWMxbtw4REZGIjU1FWFhYViwYIHFfGpqKl588UXccccdaN++Pd5++220b98eGzdurOeWux6lUom5c+dafM54DaHU1FQolcr6bBYREVGdku2CijqdDvv27cOUKVNMpsfFxWHnzp01mkdVVRWuXLmCpk2bWs1UVFSgoqJC+r2oqAgAoNfrodfra9HyhsnYV1t9Hjx4MNq1a4c///zTZHrLli0xe/ZsDB48uMF9ZjXptytiv9lvd8B+u2e/HU22Qig/Px8GgwHBwcEm04ODg3HhwoUazWP27NkoKSnB8OHDrWZmzpyJGTNmmE3Pzs6GVqu1r9EuICsry+pz//zzD/788094eHggJSUFlZWV8Pf3R6dOnaBUKqX7jjVEtvrtythv98J+uxd363dpaWmdzFf2W2xce+sGIUSNbuewatUqvPbaa/jqq68QFBRkNTd16lRMnjxZ+r2oqAhhYWHo06cPAgICat/wBkav1yMrKwv9+/eHWq22mJk1axYAoHfv3njzzTfrs3l1pib9dkXsN/vtDthv9+p3QUFBncxXtkIoMDAQSqXSbOtPXl6e2Vaia61ZswZjx47FunXrcM8999jMenp6wtPT02y6Wq12qxXIyFa/165dCwB45JFHXO6z4fJ2L+y3e2G/3UNd9VW2g6U1Gg2ioqLMNu1lZWWhZ8+eVl+3atUqjB49Gp9//jkGDhxY1810G7/++isOHz4MtVqNoUOHyt0cIiKieiHrrrHJkydj5MiRiI6ORo8ePfDxxx/j9OnTGD9+PICru7XOnTuH5cuXA7haBI0aNQpz585F9+7dpa1J3t7e8PPzk60frmDVqlUAgAEDBtg8+JyIiMiVyFoIPfTQQygoKMDrr7+O3NxcdO7cGRkZGQgPDwdw9SrG1a8ptGjRIlRWVuLpp5/G008/LU1PSkrC0qVL67v5LqOqqgqfffYZAGDEiBEyt4aIiKj+yH6wdHJyMpKTky0+d21xs23btrpvkBv68ccfcfLkSTRu3Bj333+/3M0hIiKqN7LfYoPkZ9z1mJiY6JaXFCAiIvfFQsjNlZeXY926dQCAkSNHytwaIiKi+sVCyM1t3LgRhYWFCAsLQ2xsrNzNISIiqlcshNyccbfYY489Bg8Prg5ERORe+JfPjeXl5WHLli0AuFuMiIjcEwshN7Z69WpUVlYiOjoakZGRcjeHiIio3rEQcmMrVqwAwK1BRETkvlgIualjx45h7969UKlUePjhh+VuDhERkSxYCLkp49age++9F0FBQTK3hoiISB4shNxQ9VtqjBo1SubWEBERyYeFkBvavn07zpw5Az8/PwwePFju5hAREcmGhZAbSktLAwA8+OCD8PLykrk1RERE8pH9pqtyKSkpsVgEKJVKk+klJSVW5+Hh4QFvb+9aZUtLSyGEsJhVKBQm9/yyJ1tWVoaqqiqznF6vR3l5OS5duiTdUuOxxx6z2WYfHx/p5/LychgMBodktVotFAoFAKCiogKVlZUOyXp7e0sXhdTpdNDr9VK/S0pKoFarbWat8fLyglKptDur1+uh0+msZj09PaFSqezOVlZWoqKiwmpWo9FIP1dWVtqcr0ajkT4Xg8GA8vJyq1m1Wi3N255sVVUVysrKHJJVqVTw9PQEAAghUFpaavJ89eXt7e1tM1udPd97Zx0jLK3nlrLWxgij6t9le7JyjBF6vd7kM6rNGOGIbH2PEZbGNXvHCOPr7Mk6wxhRJ4SbKSwsFACsPhISEkzyWq3WajY2NtYkGxgYaDUbHR1tkg0PD7ea7dSpk0m2U6dOVrPh4eEm2ejoaKtZX19f8f777wsA4pZbbhGxsbFWs1qt1mS+CQkJNj+36hITE21mi4uLpWxSUpLNbF5enpRNTk62mT1x4oSUTUlJsZk9cuSIlJ0+fbrN7O7du6XsrFmzbGazs7Ol7Lx582xmN23aJGXT0tJsZteuXStl165dazOblpYmdDqd2LBhg9iwYYPN7Lx586T5Zmdn28zOmjVLyu7evdtmdvr06VL2yJEjNrMpKSlS9sSJEzazycnJUjYvL89mNikpScoWFxfbzCYmJpqsw7ayzjhGREZGWs3aM0YEBgaaZBvCGLFs2TKh0+mEEBwjjGoyRhht2rTJZtaZxoj8/HwBQBQWFgpH4q4xN7NkyRIAwJNPPilzS4iIiOSnEMLKtlcXVVRUBD8/P5w6dQoBAQFmzzvrZu+aZm3tGps3bx5eeeUVeHl54fz58/Dy8nLqzd72Zq3tGsvMzMSAAQPcbtdYRkYG4uLibC5jZ9vs7YhdY8bl7U67xgoLC7Flyxaz9dxS1tV2jW3btg0DBw6EWq12q11j145r7rBrrKCgAIGBgSgsLISvr6/VvL3c9hghHx8fky+mrZw986yp6gOTI7PVB9LqjAMGAAwfPhz+/v41nicAuw6qtifr6ekp/bFyZFaj0UCj0UCv18PLyws+Pj5mfyCuzdoz35pQq9VW3/NGsiqVShrwrDEOxCqVqsbzVSqVNV6H7cl6eHjUSVahUJhlrS1vS1lbnCFr7xhxvfXcyNoYcaNZOcYIvV4vFUzXy16rrr739TFGXG9cq8kYUZusM4wRdYG7xtxEUVERfvjhBwDAE088IXNriIiInAMLITexevVqVFRUoGPHjujVq5fczSEiInIKLITcxOLFiwEAY8eONdmUTERE5M5YCLmBffv24eDBg1CpVHj00Uflbg4REZHTYCHkBj755BMAQI8ePRAYGChza4iIiJwHCyEXV1xcjJUrVwIA4uLiZG4NERGRc2Eh5OJWr16N4uJitGvXDp07d5a7OURERE6FhZALE0Jg7ty5AIBx48bxIGkiIqJrsBByYd9++y2OHDkCHx8fjBkzRu7mEBEROR0WQi5szpw5AK6eMt+kSRN5G0NEROSEWAi5qKNHj2LLli1QKBSYOHGi3M0hIiJySiyEXFRqaioA4IEHHkCbNm3kbQwREZGTYiHkgv755x+sWLECADB58mSZW0NEROS8WAi5oAULFqCiogJ33nknevbsKXdziIiInBYLIRdTVlaG+fPnA7i6NYinzBMREVnHQsjFrFy5EhcvXkSrVq0wbNgwuZtDRETk1FgIuRAhhHTK/HPPPQeVSiVzi4iIiJwbCyEXkpmZiWPHjqFRo0YYN26c3M0hIiJyeiyEXIQQAjNmzABw9XYafn5+MreIiIjI+bEQchGbNm3CTz/9BG9vb7z44otyN4eIiKhBYCHkAqqqqvDf//4XwNVjg0JCQmRuERERUcPAQsgFrF27FocPH4avry+3BhEREdmBpxU1UAaDATk5OTh79iymTp0KAEhJSUHTpk1lbhkREVHDwUKoAUpPT8fEiRNx9uxZaZqHhwfvKUZERGQnFkINTHp6OhITEyGEMJleVVWFkSNHwtvbG0OHDpWpdURERA0LjxFqQAwGAyZOnGhWBFU3adIkGAyGemwVERFRw8VCqAExHhNkjRACZ86cQU5OTj22ioiIqOFiIdSA5ObmOjRHRETk7lgINSA1vT4QryNERERUMyyEGpCYmBi0bNnS6vMKhQJhYWGIiYmpx1YRERE1XCyEGhClUokBAwZYfE6hUAAAUlNToVQq67NZREREDRYLoQbk5MmTWLNmDQCgSZMmJs+FhoZi/fr1PHWeiIjIDryOUAMhhMBTTz2FkpIS3H333fj222/x448/Ijc3FyEhIYiJieGWICIiIjuxEGogVqxYga1bt8LT0xOffPIJ1Go1evfuLXeziIiIGjTuGmsA/vnnH0yaNAkA8Nprr+Gmm26St0FEREQugoWQk9PpdHjkkUdw6dIl3HrrrXjhhRfkbhIREZHLYCHkxIQQGD9+PLKzs9GoUSMsX74carVa7mYRERG5DBZCTmzmzJlIS0uDh4cH1qxZg1tuuUXuJhEREbkUFkJOas2aNZg2bRoA4MMPP0RCQoLMLSIiInI9LISc0K5du5CUlATg6t3kk5OTZW4RERGRa2Ih5GT++OMP3H///aioqMB9992H9957T+4mERERuSwWQk5k69at6NatGy5evIjbb78dn3/+OS+SSEREVIdYCDkBIQRmzZqF+Ph4XLp0Cd26dcPmzZvh4+Mjd9OIiIhcGgshmZWUlODhhx/GSy+9hKqqKowbNw7bt29H8+bN5W4aERGRy+MtNmR04MABjB49GocPH4ZKpcKHH36Ip556SrqTPBEREdUt2bcIzZ8/H61bt4aXlxeioqKQk5NjM799+3ZERUXBy8sLbdq0wcKFC+uppY6zc+dODBw4ELfffjsOHz6M4OBgZGdnY/z48SyCiIiI6pGshdCaNWswadIkTJs2DQcOHEBMTAzi4+Nx+vRpi/kTJ04gISEBMTExOHDgAF5++WU899xz+OKLL+q55fYTQuC7775D37590atXL2RkZMDDwwMjRozAvn37cNddd8ndRCIiIrcj666xOXPmYOzYsRg3bhwAIDU1FZmZmViwYAFmzpxpll+4cCFatWqF1NRUAEBkZCT27t2L9957D8OGDavPpl+XwWDAoUOHsGPHDuzYsQM5OTnIz88HAKjVaiQlJeGll15Cu3btZG4pERGR+5KtENLpdNi3bx+mTJliMj0uLg47d+60+Jpdu3YhLi7OZNqAAQOwZMkS6PV6u+7DtXHjRvj6+trMCCGkf40/V1VVQa/XQ6fTQafTQa/Xo7S0FHl5ebhw4QL++ecfXLhwAadOnUJxcbHJ/LRaLcaMGYP//Oc/aNWqVY3bSkRERHVDtkIoPz8fBoMBwcHBJtODg4Nx4cIFi6+5cOGCxXxlZSXy8/MREhJi9pqKigpUVFRIvxcWFgIAHn/88RvtwnU1btwY3bp1Q48ePdCrVy906dIFGo0GAFBQUFDn71+dsWArKChwqxu3st/stztgv9lvd/Dvv/8C+L+NFI4i+1lj1x4cLISwecCwpbyl6UYzZ87EjBkzbrCVtXPlyhV8++23+Pbbb2V5fyIiIldTUFAAPz8/h81PtkIoMDAQSqXSbOtPXl6e2VYfo+bNm1vMq1QqBAQEWHzN1KlTMXnyZOn3y5cvIzw8HKdPn3boB+nsioqKEBYWhjNnzlx3l6ArYb/Zb3fAfrPf7qCwsBCtWrVC06ZNHTpf2QohjUaDqKgoZGVl4YEHHpCmZ2Vl4f7777f4mh49emDjxo0m07Zu3Yro6Girmwc9PT3h6elpNt3Pz8+tViAjX19f9tuNsN/uhf12L+7abw8Px57wLuvp85MnT8bixYvx6aef4tixY3j++edx+vRpjB8/HsDVrTmjRo2S8uPHj8epU6cwefJkHDt2DJ9++imWLFmClJQUubpAREREDZisxwg99NBDKCgowOuvv47c3Fx07twZGRkZCA8PBwDk5uaaXFOodevWyMjIwPPPP4+PPvoILVq0wAcffOB0p84TERFRwyD7wdLJyclITk62+NzSpUvNpsXGxmL//v21fj9PT09Mnz7d4u4yV8Z+s9/ugP1mv90B++3YfiuEo89DIyIiImogZL/XGBEREZFcWAgRERGR22IhRERERG6LhRARERG5LZcshObPn4/WrVvDy8sLUVFRyMnJsZnfvn07oqKi4OXlhTZt2mDhwoX11FLHsqff27Ztg0KhMHv89ttv9djiG7djxw4MHjwYLVq0gEKhwIYNG677GldY3vb22xWW98yZM3HHHXegcePGCAoKwpAhQ3D8+PHrvq6hL+/a9NsVlveCBQvQpUsX6aKBPXr0wDfffGPzNQ19WQP299sVlrUlM2fOhEKhwKRJk2zmHLHMXa4QWrNmDSZNmoRp06bhwIEDiImJQXx8vMn1iKo7ceIEEhISEBMTgwMHDuDll1/Gc889hy+++KKeW35j7O230fHjx5Gbmys92rdvX08tdoySkhJ07doV8+bNq1HeVZa3vf02asjLe/v27Xj66afx008/ISsrC5WVlYiLi0NJSYnV17jC8q5Nv40a8vIODQ3F//73P+zduxd79+5F3759cf/99+Po0aMW866wrAH7+23UkJf1tfbs2YOPP/4YXbp0sZlz2DIXLubOO+8U48ePN5nWsWNHMWXKFIv5F198UXTs2NFk2lNPPSW6d+9eZ22sC/b2Ozs7WwAQly5dqofW1Q8A4ssvv7SZcZXlXV1N+u2KyzsvL08AENu3b7eaccXlXZN+u+LyFkIIf39/sXjxYovPueKyNrLVb1db1leuXBHt27cXWVlZIjY2VkycONFq1lHL3KW2COl0Ouzbtw9xcXEm0+Pi4rBz506Lr9m1a5dZfsCAAdi7dy/0en2dtdWRatNvo9tuuw0hISHo168fsrOz67KZTsEVlveNcKXlXVhYCAA2b8Doisu7Jv02cpXlbTAYsHr1apSUlKBHjx4WM664rGvSbyNXWdZPP/00Bg4ciHvuuee6WUctc5cqhPLz82EwGMzuXh8cHGx213qjCxcuWMxXVlYiPz+/ztrqSLXpd0hICD7++GN88cUXSE9PR4cOHdCvXz/s2LGjPposG1dY3rXhastbCIHJkyfjrrvuQufOna3mXG1517TfrrK8f/nlFzRq1Aienp4YP348vvzyS3Tq1Mli1pWWtT39dpVlDQCrV6/G/v37MXPmzBrlHbXMZb/FRl1QKBQmvwshzKZdL29purOzp98dOnRAhw4dpN979OiBM2fO4L333sPdd99dp+2Um6ssb3u42vJ+5plncPjwYfzwww/XzbrS8q5pv11leXfo0AEHDx7E5cuX8cUXXyApKQnbt2+3WhS4yrK2p9+usqzPnDmDiRMnYuvWrfDy8qrx6xyxzF1qi1BgYCCUSqXZVpC8vDyzqtGoefPmFvMqlQoBAQF11lZHqk2/LenevTv++OMPRzfPqbjC8naUhrq8n332WXz99dfIzs5GaGiozawrLW97+m1JQ1zeGo0G7dq1Q3R0NGbOnImuXbti7ty5FrOutKzt6bclDXFZ79u3D3l5eYiKioJKpYJKpcL27dvxwQcfQKVSwWAwmL3GUcvcpQohjUaDqKgoZGVlmUzPyspCz549Lb6mR48eZvmtW7ciOjoaarW6ztrqSLXptyUHDhxASEiIo5vnVFxheTtKQ1veQgg888wzSE9Px/fff4/WrVtf9zWusLxr029LGtrytkQIgYqKCovPucKytsZWvy1piMu6X79++OWXX3Dw4EHpER0djUcffRQHDx6EUqk0e43Dlrldh1Y3AKtXrxZqtVosWbJE/Prrr2LSpEnCx8dHnDx5UgghxJQpU8TIkSOl/N9//y20Wq14/vnnxa+//iqWLFki1Gq1WL9+vVxdqBV7+/3++++LL7/8Uvz+++/iyJEjYsqUKQKA+OKLL+TqQq1cuXJFHDhwQBw4cEAAEHPmzBEHDhwQp06dEkK47vK2t9+usLwnTJgg/Pz8xLZt20Rubq70KC0tlTKuuLxr029XWN5Tp04VO3bsECdOnBCHDx8WL7/8svDw8BBbt24VQrjmshbC/n67wrK25tqzxupqmbtcISSEEB999JEIDw8XGo1G3H777SanmSYlJYnY2FiT/LZt28Rtt90mNBqNiIiIEAsWLKjnFjuGPf1+5513RNu2bYWXl5fw9/cXd911l9i8ebMMrb4xxlNHr30kJSUJIVx3edvbb1dY3pb6C0CkpaVJGVdc3rXptyss7zFjxkjjWbNmzUS/fv2kYkAI11zWQtjfb1dY1tZcWwjV1TJXCPH/jywiIiIicjMudYwQERERkT1YCBEREZHbYiFEREREbouFEBEREbktFkJERETktlgIERERkdtiIURERERui4UQETmtbdu2QaFQ4PLly3I3hYhcFAshInIavXv3xqRJkxw+X4VCgQ0bNjh8vkTU8LEQIiIiIrfFQoiInMLo0aOxfft2zJ07FwqFAgqFAidPngQA7Nu3D9HR0dBqtejZsyeOHz9u8tqNGzciKioKXl5eaNOmDWbMmIHKykoAQEREBADggQcegEKhkH7/66+/cP/99yM4OBiNGjXCHXfcgW+//ba+uktEToKFEBE5hblz56JHjx544oknkJubi9zcXISFhQEApk2bhtmzZ2Pv3r1QqVQYM2aM9LrMzEw89thjeO655/Drr79i0aJFWLp0Kd566y0AwJ49ewAAaWlpyM3NlX4vLi5GQkICvv32Wxw4cAADBgzA4MGDcfr06XruORHJiTddJSKn0bt3b9x6661ITU0FcPVg6T59+uDbb79Fv379AAAZGRkYOHAgysrK4OXlhbvvvhvx8fGYOnWqNJ/PPvsML774Is6fPw/g6jFCX375JYYMGWLz/W+++WZMmDABzzzzTJ30j4icj0ruBhARXU+XLl2kn0NCQgAAeXl5aNWqFfbt24c9e/ZIW4AAwGAwoLy8HKWlpdBqtRbnWVJSghkzZmDTpk04f/48KisrUVZWxi1CRG6GhRAROT21Wi39rFAoAABVVVXSvzNmzMDQoUPNXufl5WV1nv/5z3+QmZmJ9957D+3atYO3tzcSExOh0+kc3HoicmYshIjIaWg0GhgMBrtec/vtt+P48eNo166d1YxarTabb05ODkaPHo0HHngAwNVjhowHZxOR+2AhREROIyIiAj///DNOnjyJRo0aSVt9bHn11VcxaNAghIWF4cEHH4SHhwcOHz6MX375BW+++aY03++++w69evWCp6cn/P390a5dO6Snp2Pw4MFQKBR45ZVXavR+RORaeNYYETmNlJQUKJVKdOrUCc2aNavR8ToDBgzApk2bkJWVhTvuuAPdu3fHnDlzEB4eLmVmz56NrKwshIWF4bbbbgMAvP/++/D390fPnj0xePBgDBgwALfffnud9Y2InBPPGiMiIiK3xS1CRERE5LZYCBEREZHbYiFEREREbouFEBEREbktFkJERETktlgIERERkdtiIURERERui4UQERERuS0WQkREROS2WAgRERGR22IhRERERG6LhRARERG5rf8HoBaGKYzFoqsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The distance between two adjacent horizontal dash lines represent the equiprobable bin.\n"
     ]
    }
   ],
   "source": [
    "#############################\n",
    "## Figure 1\n",
    "############################\n",
    "\n",
    "x_min = theta_mu\n",
    "x0 = 0.0\n",
    "x1 = 4.0\n",
    "\n",
    "theta.plot(x0, x1)\n",
    "\n",
    "print(\n",
    "    \"The distance between two adjacent horizontal dash lines represent the equiprobable bin.\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "## Other parameters\n",
    "\n",
    "# Self-imposed lower bounds(for period T)\n",
    "# the minimum asset (the maximum debt) is the discounted value of lowest possible transitory income shock\n",
    "## the so called \"natural borrowing constraint\"\n",
    "\n",
    "self_a_min = -min(theta.X) * PermGroFac[0] / R  # self-imposed minimum a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A Gothic Class\n",
    "\n",
    "\n",
    "The main code used to implement the solution can be found in the \"Gothic\" class definition, which contains methods implementing the $\\mathfrak{v}$, $\\grave{\\mathfrak{v}}$  (linear interpolation of $\\mathfrak{v}$), $\\mathfrak{v}'$, $\\grave{\\mathfrak{v}}'$, and $\\mathfrak{c}$, $\\grave{\\mathfrak{c}}'$ functions. These are essentially expected value, expected marginal value, and expected marginal utility, respectively, as functions of next-period value and consumption policy functions. \n",
    "\n",
    "Since these functions all involve computing expectations, we bundle them together as a Gothic class and use an instance of the class below to solve a consumption function; this mirrors the content from [Discretizing-the-Distribution](llorracc.github.io/SolvingMicroDSOPs#Discretizing-the-Distribution) to [Improving-the-a-Grid](llorracc.github.io/SolvingMicroDSOPs#Improving-the-a-Grid) in the [lecture notes](https://llorracc.github.io/SolvingMicroDSOPs/).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Import and create instance of the \"Gothic\" class\n",
    "\n",
    "Create a particular instance of the `gothic` class, using $u$, $\\beta$, $\\rho$, $\\Gamma$, and the $\\theta$-approximation.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "from Code.Python.gothic_class import Gothic\n",
    "\n",
    "gothic = Gothic(u, beta, rho, PermGroFac, R, theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Solving the Model by Value Function Maximization\n",
    "\n",
    "- See detailed discussion [beginning here](https://llorracc.github.io/SolvingMicroDSOPs#Solving-the-Next-To-Last-Period)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we numerically maximize the value function over a very fine set of gridpoints of market resources (m) to get the benchmark solution to the consumption policy function and value function. We use this to represent the \"accurate\" solution in this notebook. \n",
    "\n",
    "This approach will be improved in different ways in the sections below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "# Boundaries for the plot\n",
    "m_min, m_max, m_size = 0, 4.0, 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "code_folding": [],
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "### solve the model with very fine mVec_fine\n",
    "\n",
    "cVec = []  # Start with an empty list. Lists can hold any Python object.\n",
    "vVec = []  # Empty list for values\n",
    "\n",
    "## fine grid of m\n",
    "mVec_fine = np.linspace(m_min, m_max, 100)\n",
    "\n",
    "for m in mVec_fine:\n",
    "    c_max = m + PermGroFac[0] * theta.X[0] / R  ## spend everything for the given X\n",
    "\n",
    "    ## Define the a one-line (negative) value function of the T-1 period\n",
    "    neg_value = lambda c: -(\n",
    "        u(c) + gothic.V(m - c)\n",
    "    )\n",
    "    \n",
    "    ## negative value to be minimized\n",
    "    ## using the scipy.optimize.minimize tool we imported as scipy_minimize\n",
    "    ## notice here V takes market resources at T-1 as input since this is the T-1 period\n",
    "    ## the consumption policy in the terminal period T is trivial\n",
    "    ## for this mTm1, find the c that maximizes the value from T-1 and T\n",
    "    residual = scipy_minimize(\n",
    "        neg_value,\n",
    "        np.array([0.3 * m+0.1]),  ## an initial guess of the c\n",
    "        method=\"trust-constr\",    ## choose the 'trust-constr' optimization algorithm\n",
    "        bounds=(\n",
    "            (1e-12, 0.999 * c_max),\n",
    "        ),  ## consumption has to be between ~0.0 and c_max\n",
    "        options={\"gtol\": 1e-12, \"disp\": False},\n",
    "    )\n",
    "    c = residual[\"x\"][0]  # maximizer of the value\n",
    "    v = -residual[\"fun\"]  ## value\n",
    "    cVec.append(c)\n",
    "    vVec.append(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "code_folding": [],
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Look at the solution\n",
    "\n",
    "caption=plt.title(r\"$c_{T −1}(m_{T-1})$ (solid)\")\n",
    "plt.plot(mVec_fine, cVec, \"k-\")  ## c(m)\n",
    "plt.xlabel(r\"$m_{T-1}$\")\n",
    "plt.ylabel(r\"$c_{T-1}$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, solve the model with only a small number of grid points of m."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "solving at the points [0. 1. 2. 3. 4.]\n"
     ]
    }
   ],
   "source": [
    "# very sparse m_grid\n",
    "\n",
    "mVec = np.linspace(m_min, m_max, m_size)\n",
    "print('solving at the points',mVec)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "code_folding": [],
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solution obtained for m= [0. 1. 2. 3. 4.]  is c= [0.28253707281109547, 0.8795623121994506, 1.421774864612849, 1.9483828229724722, 2.4682182851054986]\n"
     ]
    }
   ],
   "source": [
    "cVec0 = []  # Start with empty list. Lists can hold any Python object.\n",
    "vVec0 = []\n",
    "\n",
    "for m in mVec:\n",
    "    c_max = m + PermGroFac[0] * theta.X[0] / R\n",
    "\n",
    "    nvalue = lambda c: -(\n",
    "        u(c) + gothic.V(m - c)\n",
    "    )  # Define the a one-line value function of the T-1 period\n",
    "\n",
    "    res = scipy_minimize(\n",
    "        nvalue,\n",
    "        np.array([0.2 * m+0.1]),\n",
    "        method=\"trust-constr\",\n",
    "        bounds=((1e-12, 0.999 * c_max),),\n",
    "        options={\"gtol\": 1e-12, \"disp\": False},\n",
    "    )\n",
    "    c = res[\"x\"][0]  # maximizer of the value\n",
    "    v = -res[\"fun\"]  ## value\n",
    "    cVec0.append(c)\n",
    "    vVec0.append(v)\n",
    "\n",
    "print('Solution obtained for m=',mVec,' is c=', cVec0)  # Look at the consumption from the list."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. An Interpolated Consumption Function\n",
    "\n",
    "Although we have now solved optimal $c$ above for a finite set of predetermined gridpoints of $m$, how do we know the consumption value at different values of $m$ not among these grid points? We need interpolation.\n",
    "\n",
    "- See detailed discussion [here](https://llorracc.github.io/SolvingMicroDSOPs/#an-interpolated-consumption-function)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The interpolated consumption function is not very different from the true consumption function. (See Figure 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "code_folding": [],
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## interpolated cFunc based on the solution from a small number of m gridpoints\n",
    "\n",
    "cFunc0 = InterpolatedUnivariateSpline(mVec, cVec0, k=1)\n",
    "mVec_int = np.linspace(0.0, 4.0, 50)\n",
    "cVec_int = cFunc0(mVec_int)\n",
    "\n",
    "######################################\n",
    "### Figure 2\n",
    "######################################\n",
    "plt.plot(mVec_fine, cVec, \"k-\")  ## c(m)\n",
    "plt.plot(mVec_int, cVec_int, \"--\")  ## 'c(m)\n",
    "plt.xlim(self_a_min, 4.0)\n",
    "plt.xlabel(r\"$m_{T-1}$\")\n",
    "plt.ylabel(r\"$c_{T-1}$\")\n",
    "plt.title(r\"$c_{T −1}(m_{T-1})$ (solid) versus $\\grave c_{T-1}(m_{T-1})$(dashed)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It turns out that the interpolated value function only poorly approximates its true counterpart. (See [Figure PlotvTm1Simple](https://llorracc.github.io/SolvingMicroDSOPs#PlotvTm1Simple)). The reason for this is that the value function is highly concave."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "code_folding": [],
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## interpolated v func\n",
    "vFunc0 = InterpolatedUnivariateSpline(mVec, vVec0, k=1)\n",
    "\n",
    "vVec_int = vFunc0(mVec_int)\n",
    "\n",
    "#########################################\n",
    "### Figure 3\n",
    "########################################\n",
    "\n",
    "plt.plot(mVec_fine, vVec, \"k-\")  ## v(m)\n",
    "plt.plot(mVec_int, vVec_int, \"--\")  ## 'v(m)\n",
    "plt.xlim(self_a_min, 4.0)\n",
    "plt.xlabel(r\"$m_{T-1}$\")\n",
    "plt.ylabel(r\"$V_{T-1}$\")\n",
    "plt.title(r\"$v_{T −1}(m_{T −1})$ (solid) versus interpolated $\\grave v_{T-1}(m_{T-1})$ (dashed)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Interpolating Expectations\n",
    "\n",
    "- See detailed discussion at [Interpolating-Expectations](https://llorracc.github.io/SolvingMicroDSOPs/#Interpolating-Expectations)\n",
    "\n",
    "The program above turns out to be __inefficient__. For every value of $m_{T −1}$ the program must calculate the utility consequences of various possible choices of $c_{T−1}$ as it searches for the best choice. But for any given value of $m_{T-1}-c_{T-1}=a_{T−1}$, there is a good chance that the program may end up calculating the corresponding v many times while maximizing utility from different $m_{T −1}$’s. \n",
    "\n",
    "An improvement can be made: we can construct a direct numerical approximation to the value function based on a vector of predefined $a=m-c$ grid and use the interpolated function to calculate $\\mathfrak{v}_{T-1}$ for a given $a$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "code_folding": [],
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Our new solution for m= [0. 1. 2. 3. 4.]  is cVec1= [0.40099953272583333, 1.188019140068963, 1.1880191637006452, 1.9999999784042706, 2.372419489606577]\n"
     ]
    }
   ],
   "source": [
    "# A grid:\n",
    "a_min, a_max, a_size = 0.0, 4.0, 5\n",
    "aVec = np.linspace(a_min, a_max, a_size)\n",
    "\n",
    "## gothic v values for a vector of a\n",
    "## get the values from a finely constructed a\n",
    "gothicvVec = np.array([gothic.V(a) for a in aVec])\n",
    "## then create an interpolation of that to use in solving the models\n",
    "gothicvFunc0 = InterpolatedUnivariateSpline(\n",
    "    aVec, gothicvVec, k=1\n",
    ")  ## this is the interpolated gothic v func\n",
    "\n",
    "## solve the model again\n",
    "\n",
    "cVec1 = []  # Start with empty list. Lists can hold any Python object.\n",
    "vVec1 = []\n",
    "\n",
    "for m in mVec:\n",
    "    c_max = m + PermGroFac[0] * theta.X[0] / R\n",
    "\n",
    "    ## Below, instead of using gothic.V func, we use the interpolated gothicvFun\n",
    "    nvalue = lambda c: -(u(c) + gothicvFunc0(m - c))\n",
    "    ##################################################################################################\n",
    "    #### Notice here, instead of drawing Gothic.V function, we use the interpolation of it gothicvFunc0\n",
    "    ###################################################################################################\n",
    "\n",
    "    residual = scipy_minimize(\n",
    "        nvalue,\n",
    "        np.array([0.3 * m+0.1]),\n",
    "        method=\"trust-constr\",\n",
    "        bounds=((1e-12, 0.999 * c_max),),\n",
    "        options={\"gtol\": 1e-12, \"disp\": False},\n",
    "    )\n",
    "    c = residual[\"x\"][0]  # maximizer of the value\n",
    "    v = -residual[\"fun\"]  ## value\n",
    "    cVec1.append(c)\n",
    "    vVec1.append(v)\n",
    "\n",
    "print('Our new solution for m=',mVec,' is cVec1=',cVec1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The interpolated functions are of course identical at the gridpoints chosen for $a_{T− 1}$ and even in the interpolated areas they appear reasonably close except in the region below $m_{T −1} = 1.0$. (See [this Figure](https://llorracc.github.io/#PlotOTm1RawVSInt))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "code_folding": [],
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#################\n",
    "### Figure 4\n",
    "#################\n",
    "### get real gothic v\n",
    "aVec_fine = np.linspace(a_min, a_max, 100)\n",
    "gothicvVec_fine = np.array([gothic.V(a) for a in aVec_fine])\n",
    "\n",
    "# plt.plot(mVec,vVec1,'-.')\n",
    "plt.rc('font', size=12)\n",
    "\n",
    "plt.plot(aVec_fine, gothicvVec_fine, \"k-\")\n",
    "plt.plot(aVec, gothicvVec, \"--\")\n",
    "plt.xlabel(r\"$a_{T-1}$\")  ### this is different from lecture note\n",
    "plt.ylabel(r\"$\\mathfrak{v}_{T-1}$\")\n",
    "plt.title(\n",
    "    r\"End of period value $\\mathfrak{V}_{T^{+}-1}}}(a_{T-1})$ (solid) vs $\\grave \\mathfrak{V}_{T-1}(a_{T-1})$ (dashed)\"\n",
    ")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nevertheless, the resulting consumption rule obtained when $\\grave{\\mathfrak{v}}_{T-1}(a_{T-1})$ is used instead of $\\mathfrak{v}_{T −1}(a_{T−1})$  is surprisingly bad. (See Figure 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '$c_{T-1}(m_{T-1})$ (solid) versus $\\\\grave c_{T-1}(m_{T-1})$ (dashed)')"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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7OtotxIfb/uWXXwojIyPx5MmTD64rQ3bbK4Otra0oU6aM+OKLL8TkyZPFpEmTROPGjQUA0aBBg0xX72Tcp8fBwUGMGjVKTJ06VdSpU0cAEC1atCj0fXrGjh2b7/tjFGR7ZFAqlaJixYrC2NhYde+W7Pj7+wtjY2Mhk8lE586dxaRJk8TYsWNF165dhZ2dnahevfoH2/1f+dnmvr6+AoBwcnISo0ePFsOHDxeVKlUSLVq0EE5OTlm2SX7WnZP8HhuE0J3vSE6f9aI6PujScVEI9R8fhMjf9/Lq1avCxMREmJqair59+4qpU6eKTz/9VEgkEtGnT58sw1v5+bwWZHhLiPx/fwtyHBKicMeivGDoUYMzZ86Izz77TJQsWVLIZDLh6Ogo2rdvLwICArLMW716dfH1119/cJ1v3rwRN2/ezPUnMTEx13V86MudmpoqypQpIzw8PFTTQkJCBADx1VdfZZn/0aNHAoDo0aNHltcSExOFkZGRaNasWY7vl5e2q6PdQuTe9piYGGFmZpblvjAfkt32yrBhwwbRrVs3UbFiRWFubi5Kliwp3N3dxXfffSfi4uKyzL9r1y7RvHlzYWVlJUxNTUWtWrXEggULsr1/SX5Dj1KpFGvWrBE1atQQJiYmomzZsmLUqFEiJiYm28uzC7o9/mvOnDmqPzpBQUE5znft2jUxYMAAUb58eWFiYiJKliwpateuLb766itx/PjxD7b7v/KzzZVKpfjuu+9EpUqVhLGxsXBxcRFTp04ViYmJ2W6T/O7PnOTn2CCE7nxHcvqsF9XxQZeOi0VxfBAi/9/Lc+fOidatW4sSJUoIKysr0bx5c7F///5sb8GQn89rQUOPEPn7/ua3vUKo51j0IQw9GhQfHy+kUqn43//+p5H3y8v/aBYtWiQAiNDQ0CKtRZfavnr1agFAnDlzJt/r1dT20qTCbA9SH136jghhmMcGIXh80CZNHIsYejTozJkzuV65ow7x8fEiLCxMhIWFCXNzczF37lwRFhaW5RbhGZKTk0X58uVF586di6wmIXSn7UlJSaJs2bKZHo+QH5raXppS2O1B6qMr35EMhnZsEILHB23S1LGIoUeDfvjhB2FrayuUSmWRvUdG1+f7P7ld9nv69Gnh6+srEhISiqwuXWn7P//8I+bMmVOo2/9rYntpijq2B6mHrnxH/suQjg1C8PigTZo6FkmE+PfaSiIiIqJijJesExERkUFg6CEiIiKDwNBDREREBoEPHP2XUqnEixcvYG1tDYlEou1yiIiIKA+EEIiPj4eTkxOk0tz7chh6/vXixQu4uLhouwwiIiIqgKdPn6JcuXK5zsPQ8y9ra2sA7zaajY2NlqshIiKivIiLi4OLi4vq73huGHr+lTGkZWNjw9BDRESkZ/JyagpPZCYiIiKDwNBDREREBoGhh4iIiAwCQw8REREZBJ0IPSdOnMDgwYNRo0YNWFpawtnZGV27dsXly5c/uOz27dshkUiy/Xn16pUGqiciIiJ9oBNXb23YsAFRUVEYP348atWqhTdv3mD58uXw9PTE4cOH0aZNmw+uY9u2bahRo0amafb29kVVMhEREekZnQg969atg4ODQ6ZpHTt2RJUqVbBo0aI8hZ46deqgUaNGRVUiERER6TmdGN56P/AAgJWVFWrVqoWnT59qoSIiIiIqbnQi9GQnNjYWoaGhqF27dp7m79y5M4yMjGBnZ4cePXrg+vXruc6fmpqKuLi4TD9ERERUfOls6Bk9ejQSExMxc+bMXOdzdHTEzJkzsXnzZpw8eRLz589HcHAwPD09cfXq1RyXW7x4MWxtbVU/fO4WERFR8SYRQghtF/G+2bNnY8GCBVizZg3GjBmT7+UfPXqEunXrok2bNjhw4EC286SmpiI1NVX1e8azO2JjY/kYCiIiIj0RFxcHW1vbPP391okTmf9r7ty5WLBgARYuXFigwAMAFSpUQIsWLXDhwoUc5zE1NYWpqWlByyQiIiI9o1PDW3PnzoWvry98fX0xY8aMQq1LCAGpVKeaR0REZLCUSiXi4+O1WoPOpIL58+fD19cXs2bNwpw5cwq1rocPH+LcuXPw9PRUU3VERERUUE+fPkXbtm3h7e0NbZ5VoxPDW8uXL8e3336Ljh07olOnTlmGpTLCy5AhQ+Dn54f79+/D1dUVANCuXTt89NFHqFevHmxsbBAeHo6lS5dCIpFg/vz5Gm8LERER/b89e/ZgxIgRiImJgaWlJW7fvp3lZsKaohOh5+DBgwCAQ4cO4dChQ1lez0iFCoUCCoUiU0qsW7cu9uzZg2XLliE5ORkODg5o06YNZs+ejWrVqmmmAURERJRJbGwsxo4dC39/fwCAh4cHAgICULVqVa3VpJNXb2lDfs7+JiIiopz99ddf8PHxwePHjyGVSjFz5kzMnj0bxsbGan8vvb56i4iIiPRTeno65s6di8WLF0OpVKJixYrw9/dH8+bNtV0aAIYeIiIiUoM7d+7Ax8cHwcHBAID+/ftjzZo1OjV6ojNXbxEREZH+EUJg06ZNqF+/PoKDg1GyZEns2bMHfn5+OhV4APb0EBERUQG9efMGw4YNUz39oE2bNvDz80O5cuW0XFn22NNDRERE+Xbo0CHUq1cPBw4cgImJCb7//nscPXpUZwMPwJ4eIiIiyofk5GRMnz4da9asAQDUqlULgYGBcHNz03JlH8aeHiIiIsqTq1evonHjxqrAM3bsWISEhOhF4AEYeoiIiOgDlEolli9fDg8PD9y4cQNlypTBn3/+idWrV8Pc3Fzb5eUZh7eIiIgoR8+ePcOAAQNw4sQJAMDnn3+OzZs3o3Tp0lquLP/Y00NERETZCgoKQr169XDixAlYWFjgp59+wi+//KKXgQdgTw8RERG9Jz4+HuPGjcP27dsBAI0aNcLOnTv1/pmW7OkhIiIilfPnz8Pd3R3bt29XPTfr/PnzBQ48aXKlmissOIYeIiIiglwuh6+vL1q2bIkHDx7A1dUVp06dwoIFCwr0oNCEVDnWnriLZktO4OnbpCKoOP84vEVERGTg7t27Bx8fH1y8eBEA4OPjg7Vr18LW1jbf60pMlWPH34+x8cx9RCelAwB2Bz/B1E9qqLXmgmDoISIiMlBCCGzbtg3jxo1DYmIibG1tsWHDBnh5eeV7XclpCgRceIwfT99HVGIaAKBSKUuMb1cVnes5qbv0AmHoISIiMkBRUVEYPnw4fv75ZwBAq1atsGPHDpQvXz7f61IoBT5bfRYPIxMBAK72Fhjftio+d3OCzEh3zqRh6CEiIjIwx44dw4ABA/DixQvIZDIsWLAAU6ZMgZGRUZ7XkSZXwkT2LtAYSSXoVLcsfrnyHOPaVkWP+s46FXYySIQQQttF6IK4uDjY2toiNjYWNjY22i6HiIhI7VJSUjBjxgysXLkSAFC9enXs3LkTDRs2zPM60uRK7L38FOtO3MOy3m5oVrkUgHfDW0ZSiSoIaUp+/n6zp4eIiMgAXL9+Hd7e3rh27RoAYMSIEVi+fDksLCzytHy6Qol9oc+w+vg9PI9JBgDsOP9YFXrMTfLeS6QtDD1ERETFmFKpxJo1azB9+nSkpqaidOnS2LJlC7p06ZKn5eUKJQ5ceYHVJ+7icdS7S89LW5ti1MeV4eWR//N/tImhh4iIqJh6+fIlBg0ahMOHDwMAPv30U2zduhWOjo55XsdX/pdx4lYEAKCUlQlGtKoM7yauetGz8z6GHiIiomLowIEDGDp0KCIjI2FmZoZly5Zh1KhRkEgkuS6nVAoohVCdiNzFrSzCnkRjRKvK6NfUFRYm+hsd9LdyIiIiyiIxMRETJ07Epk2bAABubm4IDAxErVq1cl1OqRQ48s8rrDx6Fz5NXdHP0xUA8LmbM9rXcoSVqf5HBv1vAREREQEAQkJC4O3tjTt37kAikWDy5MlYsGABTE1Nc1xGCIFjNyOw8ugd/PMyDgDg//cj+DQpD4lEAiOppFgEHoChh4iISO8pFAosXboU3377LeRyOZydnbFjxw60adMmx2WEEDh1+w1WHL2D8OexAAArUxkGN6+AIS0qfXAYTB8x9BAREemxx48fo3///jhz5gwAoFevXvjxxx9hZ2eX63ILf7+JzX89BABYmBhhYLMKGNayEkpamhR5zdrC0ENERKSnAgMDMWrUKMTGxsLKygpr165F//79s+2lEUIgXSFUNw/s4uaEnRefoH9TV3z1USXYW+U8BFZcMPQQERHpmZiYGIwePRqBgYEAgKZNm8Lf3x+VK1fOdv6LD6Kw4ugd1CxrA9/PawMA3FxK4MKMtrA1N9ZY3drG0ENERKRHzp49Cx8fHzx58gRGRkaYPXs2Zs6cCZks65/0y4/fYsXROzh3LwoA8M+LOEz9pDos/z0x2ZACD8DQQ0REpBfS09Ph6+uLJUuWQKlUolKlSti5cyc8PT2zzBv2JBorj93FmTtvAADGRhL0aeyCUR9XUQUeQ2S4LSciItITd+7cgbe3N0JCQgAAgwYNwqpVq2BtbZ1l3sCLTzBjfzgAQCaVoFejchjdugrKlczbM7aKM4YeIiIiHSWEwObNmzFhwgQkJSWhZMmS2LhxI3r27JlpvjS5UnWCcvtaZbDoj5v4tI4jxrapivL2DDsZGHqIiIh0UGRkJIYNG4ZffvkFANCmTRv4+fmhXLlyqnluv4rHD8fuIClNAb/BHgDePQz03NdtDO58nbxg6CEiItIxR44cwYABA/Dq1SsYGxtj0aJFmDRpEqTSd7059yLi8cOxu/g9/CWEACQS4P6bBFQubQXA8E5QziuGHiIiIh2RkpKCr7/+GqtWrQIA1KxZE4GBgXB3dwcAPHiTgNXH7+LA1RcQ4t0yneqWxfh2VVWBh3LG0ENERKQDwsPD4e3tjfDwdychjxkzBkuXLoW5uTkA4Pz9SPhsvgjlv2Hnk9plMKFdNdQsa6OtkvUOQw8REZEWKZVKrFmzBtOnT0dqaiocHBywbds2fPbZZ0iTK1XzNXK1g1MJc9RwtMaEdtVQx9lWi1XrJ4YeIiIiLXn58iUGDRqEw4cPAwA6deqErVu3Qm5ijRn7w3Hp4Vv8Ob4ljI2kMJFJ8fu4ljxfpxAYeoiIiLTgwIEDGDp0KCIjI2FmZoYVK1agm9dArD19H7svXUaa4l0vz5k7b9C2ZhkAPEG5sBh6iIiINCgxMRGTJk3Cxo0bAQDu7u5Yu2UHjj2XotWyU6ohLc9KdpjYrhqaVLLXZrnFCkMPERGRhoSEhMDb2xt37tyBRCLBlClTMHzSDHRa9zdS0t+FncYVSmJi+2poVrmUlqstfhh6iIiIiphCocDSpUvx7bffQi6Xw9mlPHZs34Y2bdoAABqUL4nkdAUmt6+O5lXsIZFItFxx8cTQQ0REVIQeP36M/v3748yZM5CaWaHp4BlIK9cQbh7NVfP82K8hrE1lDDtFTKrtAoiIiIqr3bt3w83NDWcvhKB06wGoMjEQL0rWQ2RiOvaFPlfNZ2NmzMCjAezpISIiUrO4uDiMGTMGAXuCYN2wC1yb9oIwNkeqEqr77HxSu4y2yzQ4DD1ERERqdO7cOfj4+ODxsxdwHr4JRlb2EACqOlhhYvtq6FjbEVIpe3W0gaGHiIhIDeRyOXznLcDihfOhVCpRsWJFtK3jhPuJMkxoVw2d6paFEcOOVjH0EBERFdI/t+/iy5lr8NaxMWSlK+LLT5pjzZo1kJpawEwmhcyIp9DqAoYeIiKiAkpJl2PS2iD8dj8d0iqfQAbg88nL4De1m7ZLo2ww9BAREeVTmlyJ7WduY9kf4UiTWUNqBRilxmLSJ7UwrF09bZdHOWDoISIiygchBD5ddhj3Y5SAzBKK+Eh87JCKn+YOgoUpn42lyxh6iIiIPkCuUEIqkUAuT8fs2bMRfPwmbDx7wez+KQT6jkCzJo21XSLlAUMPERFRDhRKgYNXX2DV8bv4srYVNs4ajtDQUMBIhl4NnLA6aDUsLS21XSblEUMPERHRe5RKgd/DX+KHY3dw/00iAGBuYAhehobC3t4eW7ZsQdeuXbVcJeUXQw8REdG/lEqBwzdeYeWxO7jzOgEAYKRIQeRfexAf+hs6dOiA7du3o2zZslqulAqCoYeIiOhf03++hr2XnwEAzI2AuOD9eHI6EMZQYMV332HcuHGQSnnPHX3F0ENERAZLCAG5UsD435sHdnFzwh/hL1Eu8Q6O/jADIjURtWvXRmBgIOrV46Xo+o5xlYiIDI4QAqfvvEG39eex7uQ91fQSKS8hOTgbR1aMh0hNxLhx4xAcHMzAU0ywp4eIiAyGEALn70dhxdE7uPw4GgDwMiYZI1tVwo/r12H69OlITU1FmTJlsG3bNnz66adarpjUiaGHiIgMwoUH78LOpYdvAQCmMil8PF3Ro4YVunbpjMOHDwMAOnXqhK1bt8LBwUGb5VIRYOghIqJib8Op+/ju0C0AgIlMir4e5THq48q4cOoIPm46BJGRkTAzM8OKFSswYsQISCR8GnpxxNBDRETFUppcCRPZu1NXP6vriNXH76Jnw3IY1boybI0FJk+eiB9//BEA4O7ujsDAQNSsWVObJVMRY+ghIqJi5dqzGKw8egdWZsZY41UfAOBqb4kLM9rC1twYoaGhaN23L27fvg0AmDx5MhYuXAhTU1Ntlk0awNBDRETFwo0XsVh59C6O3XwNADA2kiAiriYcbMwAANamRvj+++8xc+ZMpKenw8nJCX5+fmjXrp02yyYN0olL1k+cOIHBgwejRo0asLS0hLOzM7p27YrLly/nafmIiAgMHDgQpUqVgoWFBZo2bYrjx48XcdVERKQLbr2Kwwj/y+i0+i8cu/kaUgnQo4Ezjk5spQo8z549Q/v27TFt2jSkp6eje/fuuHbtGgOPgdGJnp4NGzYgKioK48ePR61atfDmzRssX74cnp6eOHz4MNq0aZPjsqmpqWjbti1iYmKwatUqODg4YN26dejYsSOOHTuGVq1aabAlRESkSYeuv8KIgHf/QZZIgM/dnDCubVVULm2lmufnn3/GsGHDEB0dDQsLC6xatQpDhgzhycoGSCKEENouIiIiIsulgQkJCahSpQrq1KmDY8eO5bjs+vXrMXr0aJw/fx5NmzYFAMjlcri5ucHKygoXL17MUw1xcXGwtbVFbGwsbGxsCt4YIiIqUv89QTkxVY5W359Ek0r2mNC2KqqWsVbNl5CQgPHjx2Pr1q0AgEaNGmHnzp2oVq2aVuqmopGfv986MbyV3b0QrKysUKtWLTx9+jTXZffv34/q1aurAg8AyGQy+Pj44NKlS3j+/Lna6yUiIs17FJmISf+7gl4/nkfG/9ctTWU4PvljrOvbIFPguXTpEurXr4+tW7dCIpHgm2++wblz5xh4DJxODG9lJzY2FqGhobkObQHA9evX0bJlyyzTM24ZfuPGDTg7O2d5PTU1Fampqarf4+LiClkxEREVBSEEVh69g3Wn7kOhfBd2Lj+ORqMKdgAAW3Nj1bwKhQJLlizBnDlzoFAo4OLiAn9/f57qQAB0pKcnO6NHj0ZiYiJmzpyZ63xRUVGws7PLMj1jWlRUVLbLLV68GLa2tqofFxeXwhdNRERqt+H0faw+cQ8KpcDH1UvjwOjmqsDzX48fP0br1q0xa9YsKBQK9OrVC1evXmXgIRWdDD2zZ8/Gzp07sXLlSjRs2PCD8+d2MlpOr33zzTeIjY1V/XxoGI2IiDTvfyFPsfTQu/vpzO5cC9sHecDNpUSW+Xbv3g03NzecPXsWVlZW2L59O/bs2YOSJUtquGLSZTo3vDV37lwsWLAACxcuxJgxYz44v729fba9OW/fvnu2Sna9QABgamrKG1EREemwk7ci8M2+cADAiFaVMaRFxSzzxMXFYcyYMfD39wcANGnSBDt37kTlypU1WivpB50KPXPnzoWvry98fX0xY8aMPC1Tt25dhIeHZ5meMa1OnTpqrZGIiDTDxc4CjjZm8Kxkj+kdq2d5/e+//4a3tzcePnwIqVSKmTNnYvbs2TA2Ns5mbUQ6NLw1f/58+Pr6YtasWZgzZ06el+vevTtu3bqV6dJ0uVyOgIAANGnSBE5OTkVRLhERFbEqDlb4ZXRzLPmibqZTFeRyOebNm4eWLVvi4cOHcHV1xenTpzFv3jwGHsqVTtynZ/ny5ZgyZQo6duyYbeDx9PQEAAwZMgR+fn64f/8+XF1dAby7Cqthw4aIi4vDkiVL4ODggPXr1+PgwYP5ujkh79NDRKR9L2OT8fBNIppVKZXt6w8fPoSPjw/Onz8PAOjbty/Wr18PW1tbTZZJOiQ/f791Ynjr4MGDAIBDhw7h0KFDWV7PyGUKhQIKhQL/zWmmpqY4fvw4pk2bhrFjxyIpKQnu7u74888/ecY+EZEeiU1Kx4Ctl/AwMhHrvRuifa0ymV4PCAjAqFGjEB8fDxsbG6xbtw4+Pj5aqpb0kU709OgC9vQQEWlPSroC/bZcRPCjaJSxMcXPI5uhXEkLAO/u2zZq1CgEBgYCAJo1a4aAgABUrJj1xGYyPHp3R2YiIjJccoUS43aFIfhRNKzNZPAb7KEKPH/99Rfc3NwQGBgIIyMjzJ07F6dPn2bgoQLRieEtIiIyTEIIzD5wHUf+eQ0TmRSb+zdCDUcbpKenY968eVi0aBGUSiUqVqyInTt3ZnrkEFF+MfQQEZHWrDx2F7suPYVUAqz+0h1NKtnj/v378Pb2Vl2V279/f6xZs4anHlChcXiLiIi0QgiBZ9FJAIB5Xevgk9qO8PPzg7u7Oy5evAhbW1vs2rULfn5+DDykFuzpISIirZBIJFjeyw3d6zujTikZvLy8sGfPHgBAy5Yt4e/vr7o9CZE6sKeHiIg06l5Egupp6RKJBOLlTbi5uWHPnj0wMjLCggULcPLkSQYeUjuGHiIi0pibL+PQfd05jN4ZioSkFMyaNQutW7fG06dPUblyZZw7dw4zZ86EkZGRtkulYojDW0REpBFP3yZhwNZLiE+V43lULNq0bYvgC+/urDxo0CCsWrUK1tbWWq6SijOGHiIiKnJvE9MwYOslRMSnwsFUjtML+iI+6jVKlCiBn376Cb1799Z2iWQAGHqIiKhIJaXJMWh7MB5EJsIkPQGh60ZDkRCFVq1awd/fHy4uLtoukQwEz+khIqIik65QYtTOUFx9GgORmoCH26dAkhKLRYsW4fjx4ww8pFHs6SEioiJz/Wk0zt5+BWW6HK//NwcV7Myw889z8PDw0HZpZIAYeoiIqEjcvXsXw7298fxFAiSmlvDp2ByrVq2ClZWVtksjA8XQQ0REaiWEwMat2zF5/FgkJiaiRIkS2PTDJvTs2VPbpZGBY+ghIiK1iY6ORs9Ji3Hbog7SLB3QqlF5nqxMOoMnMhMRkVqcPn0a9Tr0wb1SzSCztsdnI2bzZGXSKQw9RERUKOnp6ZgxYwY6fDkUkhbDIDEyRrNyptg3ZyDvrEw6hcNbRERUYHfv3oW3tzfC7j6Do89SSE0t4FmhBLYN9YRUKtF2eUSZsKeHiIjyTQiBrVu3on79+rj8z104frkARpYlUdvJBpsGesBUxh4e0j3s6SEionyJjo7G8OHDsXfvXgBA7UGLkWBbBi525tg2qDGszYy1XCFR9tjTQ0REeXb69Gm4ublh7969kMlkWLx4Mc6vnYiu7k7YMbgJHKzNtF0iUY7Y00NERB+Unp4OX19fLF68GEIIVK5SBbsCA9G4cWMAwKov62u5QqIPY+ghIqJc3bt3D97e3rh06RIAYNDgwXDqNBaXEqzQSAhIJDxhmfQDQw8REWVLCIEdO3ZgzJgxSEhIQIkSJbBx40a8KV0fSw/dBgC0rFoK9cqV0G6hRHnEc3qIiCiLmJgYeHl5YeDAgUhISMBHH32Ea9euQVT0VAWe2Z1rMfCQXmHoISKiTM6ePQs3Nzfs2bMHMpkMCxcuxIkTJ3AnwQTf7AsHAAxvVQlDWlTUcqVE+cPhLSIiAgDI5XLMmzcPCxcuhFKpROXKlREYGAgPDw9cfhyN0YGhUCgFejRwxtcda2i7XKJ8Y+ghIiI8ePAA3t7euHDhAgBg4MCBWL16NaytrRGdmIYhfsFISVfi4+ql8d0X9XjyMuklDm8RERkwIQT8/f3h7u6OCxcuwNbWFnv27MG2bdtgbW0NAChpaYKpn1RHQ9eSWO/dAMZG/NNB+ok9PUREBio2NhYjR47Erl27AAAtWrRAQEAAXF1ds8zr3cQVXzYuDyM+T4v0GOM6EZEBOn/+PNzd3bFr1y4YGRlh/vz5OHXqlCrwpKQr4PvrDbxNTFMtw8BD+o6hh4jIgMjlcsydOxctW7bEo0ePULFiRZw9exazZs2CkdG7h4QqlALjd4dh+/lHGLw9GEIILVdNpB4c3iIiMhCPHj2Cj48Pzp07BwDo168f1q5dCxsbG9U8QgjM+uU6Dt94DROZFF9/WoMnLVOxwZ4eIiIDsHv3bri5ueHcuXOwsbHBzp07sWPHjkyBBwB+OHYXuy49gUQCrOrjDs9K9lqqmEj92NNDRFSMxcfHY8yYMdixYwcAoFmzZggICEDFillvLBhw4TFWHb8LAJjftQ4+rVtWo7USFTX29BARFVMXL16Eu7s7duzYAalUijlz5uD06dPZBp4jN17h2wPXAQDj2laFj2fWK7iI9B17eoiIihmFQoElS5Zgzpw5UCgUcHV1RUBAAFq0aJHjMtXKWKNcSQs0r1IKE9tV1WC1RJrD0ENEVIw8ffoUPj4+OHPmDACgT58++PHHH1GiRIlcl6tQyhK/jG4OGzMZT1ymYovDW0RExURQUBDq1auHM2fOwMrKCn5+fti1a1eOgedZdBLO3Hmj+t3O0gQy3m2ZijF+uomI9FxiYiKGDh2KXr16ISYmBo0bN0ZYWBj69++fY6/N28Q09N96CYO3B+PQ9VcarphIOxh6iIj0WGhoKBo0aIAtW7ZAIpHg66+/xrlz51ClSpUcl0lKk2Pw9mA8eJMIB2tTuLnYarBiIu3hOT1ERHpIqVRixYoVmDFjBtLT0+Hs7Ax/f3+0bt061+XSFUqM3hmKK09jUMLCGDuGeKCsrbmGqibSLoYeIiI98/LlSwwYMABHjx4FAPTo0QMbN26EvX3uNxIUQuDrn8Nx8vYbmBlLsWVAY1RxsNZEyUQ6gcNbRER65ODBg6hXrx6OHj0Kc3NzbNy4EUFBQR8MPADw3aHb+Dn0GYykEqzr2wANXUtqoGIi3cGeHiIiPZCcnIwpU6Zg/fr1AAB3d3cEBgaiZs2aeVpeqRSI/veJ6Yt71EXbmmWKrFYiXcXQQ0Sk48LDw+Hl5YUbN24AACZPnoyFCxfC1NQ0z+uQSiVY8kVd9GjgjCZ8nhYZKA5vERHpKCEE1qxZg8aNG+PGjRsoU6YMDh8+jGXLluU58Nx6FQe5QgkAkEgkDDxk0Bh6iIh0UEREBDp37oxx48YhNTUVnTp1wrVr19ChQ4c8ryP8WSy+WH8eIwIuIzlNUYTVEukHhh4iIh1z5MgR1KtXD3/88QdMTU2xZs0aHDx4EA4ODnlex+OoRAzafgmJaQokpysg5dGeiOf0EBHpitTUVMyYMQMrVqwAANSuXRu7du1C3bp187WeN/Gp6LflEiIT0lDbyQY/+jSEqcyoKEom0isMPUREOuD27dvw8vJCWFgYAGDUqFFYtmwZzM3zd+PA+JR0DNx2CU/eJsHFzhzbBjWGtZlxUZRMpHfY4UlEpEVCCGzevBkNGjRAWFgY7O3tceDAAaxbty7fgSdVrsCIgMu48SIO9pYm8B/cBA7WZkVUOZH+YU8PEZGWREdH46uvvkJQUBAAoG3bttixYwecnJwKtL67rxMQ9iQGFiZG2DaoMSqUslRnuUR6j6GHiEgLTp8+DR8fHzx79gwymQwLFy7ElClTIC3EGcd1nG0ROMwTCSly1CtXQn3FEhUTDD1ERBqUnp6OefPmYeHChRBCoEqVKti1axcaNWpU4HXGpaTD5t/zdtxdSqipUqLih+f0EBFpyMOHD/HRRx9hwYIFEEJg0KBBCAsLK1TgCbr8DG2WncK1ZzHqK5SomGLoISLSgMDAQLi5ueHChQuwtbXF7t27sXXrVlhZWRV4nSdvRWD6z9cQmZCGIzdeq7FaouKJw1tEREUoPj4eo0ePhr+/PwCgefPmCAgIQIUKFQq13tAn0Ri1MxQKpUCP+s6Y1L6aGqolKt7Y00NEVESCg4NRv359+Pv7QyqVwtfXF6dOnSp04LkXkYDB24ORnK5Aq2ql8V3PepBKJeopmqgYY08PEZGaKZVKLF26FLNnz4ZcLkf58uWxc+dOtGjRotDrfhWbggFbLyEmKR1u5Wyx3rsBjI34/1eivGDoISJSo+fPn6N///44ceIEAKBXr1746aefULJkSbWsf/mR23gek4yKpSyxdWBjWJryME6UV/y2EBGpyYEDBzBkyBBERUXB0tISa9aswcCBAyGRqG/oaW7X2gCAcW2rwt7KVG3rJTIEDD1ERIWUnJyMKVOmYP369QCABg0aYNeuXahWTT0nFwshVMHJwkSG73u5qWW9RIaGA8FERIVw/fp1eHh4qALP5MmT8ffff6s18Mz85TpWHr0DIYRa1klkqHQi9MTHx2PatGno0KEDSpcuDYlEAl9f3zwtu337dkgkkmx/Xr16VbSFE5HBEkJg3bp1aNSoEa5fv44yZcrg8OHDWLZsGUxMTNT2PquO30XgxSdYfeIurj+PU9t6iQyRTgxvRUVFYePGjXBzc0O3bt2wefPmfK9j27ZtqFGjRqZp9vb26iqRiEglMjISQ4YMwa+//goA+Oyzz7Bt2zY4ODio9X12XnyMH47dBQDM61oHdcvZqnX9RIZGJ0KPq6sroqOjIZFIEBkZWaDQU6dOnULdyp2IKC9OnDiBfv364cWLFzAxMcHSpUsxbtw4tZ6sDACHb7zC7F+uAwDGtamCfp6ual0/kSHSieGtjOEoIiJdlZ6ejm+++Qbt2rXDixcvUKNGDVy8eBHjx49X+/Hr0sO3GLsrDEoBeHm4YCLvtkykFjoRetShc+fOMDIygp2dHXr06IHr16/nOn9qairi4uIy/RARZef+/fto0aIFlixZAiEEhg0bhpCQELi7u6v9vaIT0zDULxhpciXa1SyD+V3r8D+FRGqi96HH0dERM2fOxObNm3Hy5EnMnz8fwcHB8PT0xNWrV3NcbvHixbC1tVX9uLi4aLBqItIXAQEBqF+/Pi5duoQSJUpg79692LhxIywtLYvk/UpammB251rwrGSHtX3rQ8a7LROpjUTo2DWQkZGRKF26NObMmZPnK7je9+jRI9StWxdt2rTBgQMHsp0nNTUVqampqt/j4uLg4uKC2NhY2NjYFOh9iaj4eP9BoS1atEBAQABcXTVzbo1SKfg8LaI8iIuLg62tbZ7+fhfL/0JUqFABLVq0wIULF3Kcx9TUFDY2Npl+iIiA7B8UevLkySILPElpcnyzLxxv4v//P2IMPETqp/bQo1QqsWPHDnWvNt+EEJBKi2WmI6IiolQq8d1336FZs2a4f/8+ypcvj9OnT2POnDmQyYrmYtd0hRJjAsOw69ITDPUL5g0IiYqQ2lNBeno6Bg0apO7V5svDhw9x7tw5eHp6arUOItIfL1++xCeffIKvv/4acrkcPXv2xJUrV9TyZPScCCHw9c/hOHErAmbGUnzbpRZPWiYqQgX6r8u8efNyfC09Pb1Ahfz5559ITExEfHw8AOCff/5BUFAQgHc3/rKwsMCQIUPg5+eH+/fvq7qZ27Vrh48++gj16tWDjY0NwsPDsXTpUkgkEsyfP79AtRCRYfntt98waNAgREZGwsLCAqtWrcKQIUOKPIAsPXwbP4c+g5FUgrVeDdDQ1a5I34/I0BUo9CxYsADdu3fP9jwYhUJRoEJGjhyJx48fq37fu3cv9u7dC+Bdz02FChWgUCigUCgydf/WrVsXe/bswbJly5CcnAwHBwe0adMGs2fPVtuzb4ioeEpJScH06dOxevVqAIC7uzt27dqV5e7uRWHbuYfYcOo+AGBR9zpoV6tMkb8nkaEr0NVbDRs2xLx589CpU6csr6WkpMDCwgJKpVItBWpKfs7+JiL9d/PmTXh5ealubTFhwgQsWbIEpqamRf7ef4a/xKjAUAgBTP2kOka3rlLk70lUXOXn73eBenqGDRuWY4+OsbEx5syZU5DVEhEVOSEENm/ejPHjxyM5ORmlS5fG9u3b8dlnn2mshjrOtqhgb4mPqpbCqI8ra+x9iQydzt2nR1vY00NU/EVHR+Orr75SnS/Yrl077NixA2XLltV4LbFJ6bAyk8GIl6YTFYrB36eHiOh9586dg7u7O4KCgiCTybB06VIcPnxYY4HncVQijt98rfrd1sKYgYdIwxh6iKhYUygUmDdvHj766CM8efIElStXxvnz5zF16lSN3cvrTXwq+m+9hGE7QvBn+EuNvCcRZVU0d9siItIBT58+hY+PD86cOQMA6NevH9atWwdra2uN1ZCQKseg7ZfwOCoJ5Uqao6FrSY29NxFlprb/5vDkZSLSJfv374ebmxvOnDkDKysr+Pv7Y8eOHRoNPGlyJUb4X8b153GwtzSB/5AmcLAx09j7E1Fmags933//vbpWRURUYMnJyRg1ahR69OiB6OhoNGrUCGFhYfDx8dFoHUqlwJS9V/HXvUhYmBhh26DGqFiqaJ7MTkR5o7bQw4vAiEjbrl+/jsaNG2PDhg0AgGnTpuHcuXOoUkWz98ERQmDhHzfx69UXkEkl+NGnIeqVK6HRGogoK7Wd08PnxRCRtggh8NNPP2HixIlISUlBmTJlsGPHDnTo0EFL9bwb2gKAZb3c8FG10lqpg4gy44nMRKTX3r59i6FDh2L//v0AgI4dO8LPzw8ODg5aq0kqlWBe19ro3sAZDcrzxGUiXcFL1olIb505cwZubm7Yv38/jI2NsWLFCvz+++9aCzzXn8ciXfGuh0cikTDwEOkYntNDRHpHLpfD19cXrVu3xrNnz1C1alVcuHABEydO1Ni9d94X9iQavX78G0P8QpCUJtdKDUSUO7UNbzVv3lxdqyIiytGTJ0/g4+ODs2fPAgAGDhyINWvWwMrKSms13X+TgMHbg5Gc/u6ZhMZG7EQn0kVq+2YeO3ZMXasiIsrWvn374O7ujrNnz8La2ho7d+7Etm3btBp4XseloP+WS4hOSodbOVts8G7A0EOko3giMxHpvOTkZEyaNAk//vgjAKBx48bYtWsXKlfW7hPKY5PTMWDrJTyPSUbFUpbYOrAxLE15WCXSVQX670i7du3UXQcRUbZu3LiBxo0bqwLP9OnT8ddff2k98KSkKzBsRwhuvYpHaWtT7BjsAXsrU63WRES5K9B/SS5duqTuOoiIMhFCYOPGjZgwYYJO3HvnffciEvDPizhYm8rgN8gDLnYW2i6JiD6A/bBEpHOio6MxbNgw/PzzzwCATz75BH5+fihTpoyWK/t/dZxtsfsrTySkylHLyUbb5RBRHhQo9KSkpGDKlCmoV68e6tWrh9q1a8PY2FjdtRGRATp37hz69u2LJ0+ewNjYGIsXL9bqpejvi0lKQwkLEwDvgg8R6Y8ChR6JRIL4+Hhs2LAB169fR1paGqpVq6YKQfXq1cOnn36q7lqJqBhTKBRYvHgxfH19oVAoULlyZezevRuNGjXSdmkqgRef4PvDt7BlYGPeeJBIDxUo9JiamuKnn35S/X7//n1cvXoV165dw8WLF7F582bcvXtXbUUSUfH2/Plz+Pj44NSpUwAAb29vrF+/HjY2ujNsdPjGK8z6JRxKAZy584ahh0gPFSj0vH/35cqVK6Ny5cro0aOHWooiIsPx22+/YeDAgYiKioKlpSXWrVuH/v3769RDjC89fItxu8KgFMCXjV0wvm1VbZdERAVQoEHyVatWqbsOIjIwqampGD9+PLp06YKoqCjUr18foaGhGDBggE4Fntuv4jHULxipciXa1SyDBd3q6FR9RJR3+erp+frrrxEdHZ1paIuIKL9u376NL7/8EleuXAEATJgwAUuWLIGpqW7d5+Z5TDIGbL2EuBQ5GrqWxBqv+pDxbstEeitf396goCDUqFEj29f8/f1x8+ZNtRRFRMWTEAJ+fn5o2LAhrly5glKlSuG3337DypUrdS7wAMCqY3fwKi4FVR2ssGVAI5ibGGm7JCIqhHz19Dx//hxubm7ZvvbPP/9g9+7d+P3339VSGBEVL/Hx8Rg5ciR27twJAGjdujUCAgLg5OSk5cpyNq9rHRgbSTG6dRXVZepEpL/y1dNjY2ODyMjIbF9r2rQpLl++rJaiiKh4CQkJQf369bFz504YGRlhwYIFOHr0qE4GHqXy/y/UMDM2wsLudeFUwlyLFRGRuuQr9DRv3hx79+7N9jVra2vExsaqpSgiKh6USiVWrFiBZs2a4f79+yhfvjzOnDmDmTNnwshI94aKhBD4et81LD10K8tVqkSk//IVeiZOnIh9+/Zh5cqVWV47f/48nJ2d1VYYEem3iIgIdO7cGZMnT0Z6ejp69OiBK1euoFmzZtouLUfLjtzG/0Ke4cfT93HjRZy2yyEiNcvXOT0tW7bE999/j8mTJ2PPnj3w8vKCk5MTrl27hhUrVmD48OFFVScR6ZETJ07Ax8cHL1++hKmpKX744QcMHz5cpy/13n7uIdadvA8AWNS9Lh8xQVQMSUQB+nAPHTqEGTNmqC43Bd49EHD37t2wtdXPA0VcXBxsbW0RGxurU3eBJdIncrkcvr6+WLRoEYQQqFmzJvbs2YO6detqu7Rc/XbtBcbuCoMQwOT21TCWNx8k0hv5+ftdoNCT4dWrV3j+/DmcnZ3h6OhY0NXoBIYeosJ58uQJ+vbti3PnzgEAhg4dih9++AGWlpZarix35+5FYuC2S0hXCPRv6oq5n9fW6R4pIsosP3+/C/QYigyOjo56H3aIqPD279+PwYMHIyYmBjY2Nti4cSP69Omj7bI+KDoxDSP8LyNdIfBZXUfM6cLAQ1Sc8daiRFRgKSkpGD16NHr06IGYmBh4eHggLCxMLwIPAJS0NMH8bnXQsmoprOjtDiMpAw9RcVaonh4iMly3bt1Cnz59cO3aNQDAtGnTsGDBAhgbG2u5svzpVt8ZXd2d2MNDZADY00NE+SKEwLZt29CwYUNcu3YNDg4OOHToEL777ju9CDwJqXJM+t8VRMSlqKYx8BAZBoYeIsqz+Ph4+Pj4YPDgwUhKSkK7du1w9epVfPLJJ9ouLU/S5EqMDLiMfaHPMWxHCG9ASGRgGHqIKE8uX76MBg0aIDAwEEZGRli8eDEOHz6sNxczKJUCU4Ou4uzdSFiYGGFe1zrs4SEyMDynhyiP5Apljq9JJJJMJ8HmNi8AyIz+//8buj6vEALr1q7BtGnTkJ6ejvKurggI2ImmTZtCKQDle8v+d70Kpci1N8VIKlEFj6Ked8mft3DgygvIpBJs8GkIN5cSOS5PRMUTQw9RHlWb9SeUOfyd/ahaaewY7KH63X3eUSSkyrOdt3GFktg74v8fxeC5+AQiE1Kznbe2kw1+H9dS9Xub5afx5G1StvNWKm2JE5M/Vv3eec1fuPUqPtt5y9qa4e9v2qp+7/nj37jyNCbbeY3kKXiwfCIAoHv37pC1n4R+v8UAv/2ZZV4TmRR3Fnyq+n24fwiO3YzIdr0AcH/RZzD6NyuO3x2G3669zHHecN8OsDZ7d87QN/uu4X8hz3Kc99LMtnCwNgMAzP/tH2w//0j12ve96qFVtdI5LktExReHt4goV2np6TA1NcW6devw888/QybTz/8rmcik+LZzLXSvX07bpRCRlhTqjszFCe/ITO97EpUEWwtj2Jq/612ITUrPcV4jIwmsTP8/DORr3uR0IIdvoVQKVe8GAMSlpEPkMBIlkQI2/5k3PiUdypxGrSRQtev9eRVKBZYvX47vvvsOQqlElapV8L8AP7i5uQF4d/WTQpHzYcPW4v/Xm5gqhzyXeW3MZaphqPzMm5QmR7o853mtzWSQ/jvcmJymQJpcCROZFOYmuvdkdyIqHI3dkZmouHoZmwyvTRdgY26MHYM9UNraNNMf8w/J17zmeZ/3v6HmQ6wLMO+LFy/g7e2NU6dOAQAGDhyItWvXZnqUxH8D24dYFtG8FiYywCRv85qbGDHsEBEAhh6iLN4mpqHflkt4HpMMU5kUhnKBz59//on+/fsjMjISlpaW2LBhA/r166ftsoiI1Ibn9BD9R3xKOgZuu4R7EQkoa2sG/6FNUMrKVNtlFam0tDRMmTIFn332GSIjI+Hu7o7Q0FAGHiIqdtjTQ/SvlHQFhu0IwbVnsbCzNIH/kCZwLmGu7bKK1IMHD+Dl5YVLly4BAMaOHYvvv/8epqbFO+gRkWFi6CECkK5QYkxgKC48eAsrUxl2DPZAFQcrbZdVpPbu3YuhQ4ciLi4OJUuWxNatW9GtWzdtl0VEVGQ4vEUEICI+FTdexMFUJsXmAY1Qx9lW2yUVmeTkZIwcORK9e/dGXFwcmjVrhitXrjDwEFGxx54eIgDOJcwRNLIZHrxJgGcle22XU2Ru3bqF3r17Izw8HBKJBF9//TXmzp2rFw8KJSIqLIYeMmhPopJQ3t4CwLvgU5zP4fHz88OoUaOQlJQEBwcH+Pv7o0OHDtoui4hIYzi8RQZry18P0W7FaRy6/krbpRSphIQE9O/fHwMHDkRSUhLatm2Lq1evMvAQkcFh6CGDtDfkKeb/9g/SFErci8j++VTFwdWrV9GwYUP4+/tDKpViwYIFevVkdCIideLwFhmcQ9dfYfrP1wAAQ1tUxOjWVbRckfoJIfDjjz9i4sSJSE1NhbOzM3bt2oWWLVt+eGEiomKKoYcMyrl7kRi3KwxKAfRuVA4zO9VUPc+puIiJicGwYcMQFBQEAOjcuTO2bduGUqVKabkyIiLt4vAWGYywJ9EYtiMEaQolOtZ2xKLudYtd4AkODkaDBg0QFBQEY2NjrFixAr/++isDDxER2NNDBuSXsOdISlOgZdVSWOXlDplR8cn8Qgj88MMPmD59OtLT01GxYkXs3r0bHh4e2i6NiEhnMPSQwZjTpTZc7Czg5VEeprLi89TtqKgoDBo0CAcPHgQA9OzZE5s3b4atbfG9wSIRUUEUn//qEmUjOjENCqUAAEilEgxtWQmWpsUn6587dw7u7u44ePAgTE1NsX79evzvf/9j4CEiygZDDxVbMUlp+HLjBYzfHYY0uVLb5aiVUqnEkiVL0KpVKzx79gxVq1bFhQsXMHLkyGJ3nhIRkboUn//yEv1HYqocg7YH4/breEQnpSEyIRVOxeRuyxEREejXrx+OHDkCAOjbty9+/PFHWFtba7kyIiLdxp4eKnZS5QqMCLiMsCcxKGFhjIChTYpN4Dl16hTc3d1x5MgRmJubY9OmTQgICGDgISLKA4YeKlbkCiXG77qCs3cjYWFihG0DG6NaGf0PBAqFAvPmzUPbtm3x8uVL1KxZE5cuXcLQoUM5nEVElEcc3qJiQwiBGfvDcejGK5gYSbGpfyPUL19S22UV2qtXr+Dt7Y0TJ04AAAYNGoQ1a9bA0tJSy5UREekXhh4qNu68TsCBKy8glQCrveqjeRX9vyHf8ePH4e3tjdevX8PS0hIbNmxAv379tF0WEZFe0onhrfj4eEybNg0dOnRA6dKlIZFI4Ovrm+flIyIiMHDgQJQqVQoWFhZo2rQpjh8/XnQFk06q7mgNv8EeWNbLDR3r6PcDNeVyOb799lu0b98er1+/Rt26dRESEsLAQ0RUCDoReqKiorBx40akpqaiW7du+Vo2NTUVbdu2xfHjx7Fq1SocOHAAZcqUQceOHXH69OmiKZh0SlKaXPVvz0r26NGgnBarKbwXL16gXbt2mD9/PoQQGDZsGC5evIgaNWpouzQiIr2mE8Nbrq6uiI6OhkQiQWRkJDZv3pznZbds2YLr16/j/PnzaNq0KQCgdevWcHNzw7Rp03Dx4sWiKpt0wC9hz7Hkz1vwG+yB6o76f8LykSNH4OPjgzdv3sDKygobN26El5eXtssiIioWdKKnRyKRFPgKlP3796N69eqqwAMAMpkMPj4+uHTpEp4/f66uMknHHL/5GpP3XsWruBT8ckW/97NcLsfMmTPRsWNHvHnzBm5ubrh8+TIDDxGRGulET09hXL9+HS1btswyvV69egCAGzduwNnZOcvrqampSE1NVf0eFxdXdEWS2l14EIVRO0OhUAp0r++MqR2qa7ukAnv+/Dm8vLxw9uxZAMDIkSOxYsUKmJmZabkyIqLiRSd6egojKioKdnZ2WaZnTIuKisp2ucWLF8PW1lb14+LiUqR1kvqEP4vFUL8QpMqVaFfTAUt71oNUqp/3qjl06BDc3d1x9uxZWFtbY8+ePVi/fj0DDxFREdD70AMg16GxnF775ptvEBsbq/p5+vRpUZVHanQvIgEDtl1CQqocnpXssLZvAxgb6d/HOGM469NPP0VkZCTq16+P0NBQ9O7dW9ulEREVW3o/vGVvb59tb87bt28BINteIAAwNTWFqalpkdZG6rf00C28TUxDvXK22NS/EcyMjbRdUr69P5w1atQoLF++nL07RERFTP/+i/yeunXrIjw8PMv0jGl16tTRdElUhJb3dkOfRi7YPsgD1mbG2i4n37Ibzlq3bh0DDxGRBuh96OnevTtu3bqV6dJ0uVyOgIAANGnSBE5OTlqsjtRBrlCq/m1tZozvetaDnaWJFivKv/eHs9zd3TmcRUSkYToTev78808EBQXh4MGDAIB//vkHQUFBCAoKQlJSEgBgyJAhkMlkePz4sWq5wYMHo3bt2ujVqxcCAwNx7Ngx9O7dG7dv38Z3332nlbaQ+iSnKeC16QJ+PH1f26UU2IsXL9C2bVssWrQIwLurs/7++29UqVJFy5URERkWnTmnZ+TIkZnCzN69e7F3714AwMOHD1GhQgUoFAooFAoIIVTzmZqa4vjx45g2bRrGjh2LpKQkuLu7488//0SrVq003g5SnzS5EiN3Xkbwo2jcehWPHvWd4WCjX8NA/73ZoLW1NTZt2oQ+ffpouywiIoMkEf9NEAYsLi4Otra2iI2NhY2NjbbLMXgKpcD43WH47dpLmBlLETCkCRpVyP6kdF2kUCjg6+uLhQsXQggBd3d3/O9//0PVqlW1XRoRUbGSn7/fOtPTQ5RBCIHZB67jt2svYWwkwU/9GulV4Hn58iX69u2LU6dOAQCGDx+OH374gScrExFpGUMP6Zylh28j8OITSCTAyj7uaFWttLZLyrPjx4/D29sbr1+/5rOziIh0jM6cyEwEAJcfR2PDqXcnLS/qXhed6+nH1XcKhQLz5s1D+/bt8fr1a9StWxchISEMPEREOoQ9PaRTGrqWxNzPayM5XQEvj/LaLidPIiIi4O3tjWPHjgF4d5Xh6tWrYWFhoeXKiIjovxh6SCcIIVSPDBnQrIJ2i8mHM2fO4Msvv8TLly9hYWGBDRs2oH///toui4iIssHhLdK6U7cj0GfjBcQkpWm7lDxTKpX47rvv0KZNG7x8+RI1a9ZEcHAwAw8RkQ5j6CGtCnn0FiMCLuPSw7fYeOaBtsvJk6ioKHTp0gVff/01FAoFfHx8EBwcjFq1amm7NCIiygWHt0hr/nkRh0Hbg5GSrsTH1UtjQrtq2i7pgy5cuIDevXvj6dOnMDMzw5o1azBkyBDV0BwREeku9vSQVjyMTET/rZcQnyJHI9eS2ODdECYy3f04CiHwww8/oGXLlnj69CmqVq2KCxcuYOjQoQw8RER6gj09pHEvY5Phs/kiIhNSUausDbYMbAxzEyNtl5Wj2NhYDB48GPv27QMA9OrVC5s3b+adu4mI9AxDD2ncxD1X8DwmGRVLWcJvsAdszY21XVKOwsLC0LNnTzx48ADGxsZYsWIFRo8ezd4dIiI9pLvjCVRsLepeF41cS8J/iAdKW5tqu5xsCSGwceNGNG3aFA8ePICrqyvOnTuHMWPGMPAQEekp9vSQxlUqbYW9I5rqbHhITEzEiBEjEBAQAADo3Lkz/Pz8YGenP8//IiKirNjTQ0UuXaHEuF1hOH3njWqargaemzdvwsPDAwEBATAyMsKSJUtw4MABBh4iomKAoYeKlFIpMD3oGn69+gJjdobq9A0IAwMD0bhxY/zzzz8oW7YsTpw4genTp0Mq5deEiKg44NGciowQAvN++wf7wp7DSCrByj7uKGFhou2yskhNTcWoUaPg7e2NxMREtGnTBmFhYfjoo4+0XRoREakRQw8VmZXH7mL7+UcAgOW93NCuVhntFpSNR48eoUWLFtiwYQMAYNasWThy5AjKlNG9WomIqHB4IjMViS1/PcTq43cBAPO61ka3+s5ariir3377Df3790d0dDTs7OwQEBCATz/9VNtlERFREWFPD6ndX3cjMf+3fwAAk9tXQ/+mFbRb0HvkcjlmzJiBLl26IDo6Gh4eHggLC2PgISIq5tjTQ2rnWckOXzQoh5IWxhjTpoq2y8nk1atX8PLywqlTpwAAY8eOxbJly2BionvnGhERkXox9JDayYyk+L5nPQC6dWn62bNn0adPH7x8+RJWVlbYvHkz+vTpo+2yiIhIQzi8RWpx5WkM5hy4DoVSAACkUgmkUt0IPEIILFu2DK1bt8bLly9Ru3ZtBAcHM/AQERkY9vRQod1+FY+B2y4hJikdDjZmGN1ad4a03n9YqLe3N3766SdYWlpquTIiItI0hh4qlKdvk9Bvy0XEJKXD3aUEBjaroO2SVK5du4YvvvgC9+7dg4mJCVatWoXhw4fr1JAbERFpDkMPFVhEXAq8N19ERHwqqpexxvZBjWFpqhsfKT8/P4wcORLJyckoX748goKC0LhxY22XRUREWsRzeqhAYpLS0G/LJTx5m4TydhbwH+KhE3dbTklJwfDhwzFw4EAkJyejY8eOCA0NZeAhIiKGHso/IQS+2nEZt1/Hw8HaFAFDmsDBxkzbZanurrxx40ZIJBLMmzcPv//+O+zt7bVdGhER6QDdGIsgvSKRSDDy48p4si8JfoM9UN7eQtsl4c8//4S3tzeio6Nhb2+PwMBAdOjQQdtlERGRDmFPDxVI6xoOODX1Y1R3tNZqHQqFAnPmzEGnTp1Ud1cODQ1l4CEioiwYeihPhBBYdvg2HkUmqqaZGRtpsSIgKioKn332GebNmwchBEaNGoUzZ86gfPnyWq2LiIh0E0MPfZAQAov+uIm1J++hz8a/kZQm13ZJCAkJQYMGDXDkyBGYm5vD398f69atg6mpqbZLIyIiHcXQQx+0/tR9bDr7EAAwuUN1WJho71QwIQQ2bdqE5s2b48mTJ6hSpQouXrwIHx8frdVERET6gaGHcuV/4TG+P3wbADCrU030buSitVqSk5MxZMgQfPXVV0hLS0PXrl0REhKCunXraq0mIiLSHww9lKMDV57j2wPXAQDj2lTB0JaVtFbLw4cP0bx5c2zbtg1SqRSLFy/Gvn37YGtrq7WaiIhIv/CSdcrWX3cjMel/VyEE0L+pKya2r6a1Wv57OXqpUqWwe/dutG3bVmv1EBGRfmJPD2WrtpMN6jjbopu7E3y71NbK86qUSiXmzp2ruhy9SZMmCA0NZeAhIqICYU8PZaukpQkChzaBiUwKqVTzgSc6Oho+Pj74448/AAAjR47EypUreXUWEREVGHt6SOX+mwTsCX6i+t3SVAZjI81/RK5cuYKGDRvijz/+gJmZGbZv347169cz8BARUaGwp4cAAM9jktFv80W8iE2BRCLR2lVaAQEBGDZsGFJSUlCxYkXs27cP7u7uWqmFiIiKF/b0ECITUlWBp3JpS7St4aDxGtLS0jB27Fj069cPKSkp6NixI0JCQhh4iIhIbRh6DFxcSjoGbL2EB5GJcC5hDv8hTWBvpdlhpJcvX6JNmzZYu3YtAGD27Nn47bffYGdnp9E6iIioeOPwlgFLTlNg6PYQ3HgRh1JWJvAf4gGnEuYareGvv/5Cr1698OrVK9ja2sLf3x9dunTRaA1ERGQY2NNjoBRKgVE7L+PSo7ewNpPBb7AHKpW20tj7CyGwdu1atG7dGq9evUKdOnUQHBzMwENEREWGocdASSVAowp2MDOWYuvAxqjtpLk7GyclJWHAgAEYO3Ys5HI5+vTpg7///htVq1bVWA1ERGR4OLxloCQSCUa3roIeDZxR1lZzQ1qPHj1Cjx49EBYWBiMjIyxduhQTJ07Uys0PiYjIsLCnx8D8L+QpElLlqt81GXiOHTuGRo0aISwsDKVKlcLRo0cxadIkBh4iItIIhh4DsvHMfUwLugbvTReQJldq7H2FEPj+++/xySefICoqCo0aNUJoaChat26tsRqIiIgYegzEnuAnWPTHLQBAxzplYSLTzK5PTEyEl5cXpk2bBqVSiUGDBuHs2bNwcdHOzQ+JiMhw8ZweA/BH+Et8sy8cADCiVWWM/LiyRt73/v376N69O8LDwyGTybB69WqMGDGCw1lERKQVDD3F3Jk7bzB+dxiUAvDyKI/pHatr5H0PHz4MLy8vREdHo0yZMggKCkKLFi008t5ERETZ4fBWMXb5cTSG+19GukKgU72yWNCtTpH3sgghsGTJEnz66aeIjo6Gp6cnLl++zMBDRERax56eYszCxAiWpjJ4VLTDyt7uMJIWbeBJSEjA4MGDsXfvXgDA0KFDsXbtWj4dnYiIdAJDTzFWs6wN9o9qhlJWpkV+4vKDBw/QrVs3hIeHw9jYGGvWrMHw4cOL9D2JiIjyg6GnmHkVm4Jn0UloVOHdwzpd7CyK/D2PHj2KPn36IDo6Go6OjggKCkLz5s2L/H2JiIjyg+f0FCPRiWnot+UivDdfxF93I4v8/YQQWLZsGTp27Ijo6Gh4eHggJCSEgYeIiHQSQ08xkZAqx8Btl3A3IgElLUzgal+0PTxJSUnw8fHB1KlToVQqMXjwYJw+fRrOzs5F+r5EREQFxeGtYiAlXYFhfiG4+iwWJS2METDUo0iHtZ48eYJu3bohLCwMMpkMK1euxOjRo3n/HSIi0mkMPXpOrlBi7K4w/P0gClamMvgN9kAVB+sie7+zZ8/iiy++wJs3b1CqVCkEBQWhVatWRfZ+RERE6sLhLT2mVApM+/kajv7zGiYyKTb1b4R65UoU2fv9+OOPaNOmDd68eQN3d3eEhIQw8BARkd5g6NFjcqVASroCRlIJ1vdtgKaV7YvkfdLS0jBixAiMHDkScrkcffr0wblz5+Dq6lok70dERFQUOLylx0xkUqzxaoArT6PR0NWuSN4jIiICPXv2xNmzZyGRSLBo0SJMnz6d5+8QEZHeYejRQxceRMGjgh2kUgmMpJIiCzxhYWHo1q0bnjx5AhsbGwQGBqJTp05F8l5ERERFjcNbeubny8/w5cYLmBp0DQqlKLL32bt3L5o3b44nT56gWrVquHjxIgMPERHpNYYePXLkxitM+/kaAMDW3BhF8SgtpVKJb7/9Fr1790ZycjI++eQTXLx4ETVq1FD/mxEREWmQToSehIQETJgwAU5OTjAzM4O7uzt27979weW2b98OiUSS7c+rV680ULnmnL8XiTGBYVAoBXo2LIdZnWqq/byahIQE9OzZE/PnzwcATJ48Gb///jtKlCih1vchIiLSBp04p6dHjx4IDg7GkiVLUK1aNQQGBsLLywtKpRJ9+/b94PLbtm3L0hNhb180VzJpw5WnMRi2IwRpCiU+qV0GS3rUhVTN3TyPHj3C559/jvDwcJiYmGDjxo0YMGCAWt+DiIhIm7Qeev744w8cPXpUFXQAoHXr1nj8+DGmTp2KPn36wMjIKNd11KlTB40aNdJEuRp393U8Bm67hMQ0BZpXsceqL+tDZqTeDrozZ87giy++QGRkJMqUKYP9+/ejadOman0PIiIibdP68Nb+/fthZWWFXr16ZZo+aNAgvHjxAhcvXtRSZbrhYWQiElPlcHcpgY39GsHMOPcAmF9btmxBu3btEBkZiQYNGiA4OJiBh4iIiiWth57r16+jZs2akMkydzrVq1dP9fqHdO7cGUZGRrCzs0OPHj3ytExqairi4uIy/eiiDrUdsWNwE2wf1BiWpurrmJPL5Zg4cSKGDh2K9PR09OrVC2fPnoWLi4va3oOIiEiXaD30REVFwc4u631mMqZFRUXluKyjoyNmzpyJzZs34+TJk5g/fz6Cg4Ph6emJq1ev5vq+ixcvhq2trepHl/7Yxyal40VMsur3ppXtUcLCRG3rj4mJQefOnfHDDz8AAObOnYs9e/bAwqJon8xORESkTRIhRNHd7CUPqlWrhsqVK+PPP//MNP3ly5dwcnLC4sWL8fXXX+d5fY8ePULdunXRpk0bHDhwIMf5UlNTkZqaqvo9Li4OLi4uiI2NhY2NTf4boiZJaXL4bL6I13Gp8B/igUqlrdS6/nv37qFLly64desWzM3NsWPHDvTs2VOt70FERKQpcXFxsLW1zdPfb62fyGxvb59tb87bt28BINteoNxUqFABLVq0wIULF3Kdz9TUFKampvlad1FLlSsw3P8yQp/EwNbcGGkKpVrXf+rUKXzxxRd4+/YtypUrhwMHDqBBgwZqfQ8iIiJdpfXhrbp16+LmzZuQy+WZpoeHhwN4d2VWfgkhIJVqvWn5olAKTNxzBWfvRsLc2AjbBjVGDUf19Tht2rQJ7du3x9u3b+Hh4YFLly4x8BARkUHRejLo3r07EhIS8PPPP2ea7ufnBycnJzRp0iRf63v48CHOnTsHT09PdZZZpIQQmLEvHH+Ev4KJkRQb+zdEg/Il1bJuhUKBiRMn4quvvoJcLseXX36JU6dOoWzZsmpZPxERkb7Q+vDWp59+ivbt22PkyJGIi4tDlSpVsGvXLhw6dAgBAQGqe/QMGTIEfn5+uH//PlxdXQEA7dq1w0cffYR69erBxsYG4eHhWLp0KSQSiequwrpOCIHFf97CnpCnkEqA1V7uaFm1tFrWHRcXh759++L3338HAMyfPx8zZ87kE9KJiMggaT30AMC+ffswc+ZMfPvtt3j79i1q1KiBXbt24csvv1TNo1AooFAo8N/zruvWrYs9e/Zg2bJlSE5OhoODA9q0aYPZs2ejWrVq2mhKviWlKXDmzhsAwJIe9dCxjnp6YB49eoQuXbrg+vXrMDMzw44dO7LcC4mIiMiQaP3qLV2Rn7O/1S0mKQ2n77xBV3dntazv77//Rrdu3RAREQFHR0f8+uuvaNy4sVrWTUREpEvy8/db6+f0GKrn/7kPTwkLE7UFnt27d6N169aIiIiAu7s7Ll26xMBDREQEhh6tOHHrNT7+/iS2n3uotnUKITBv3jx4eXkhNTUVn3/+Oe+wTERE9B8MPRp26eFbjAwIRbpC4MrTGKhjdDE1NRX9+/fHnDlzAACTJ0/Gvn37YGWl3hsbEhER6TOdOJHZUFx/Hosh24ORKleibQ0HfN/LrdBXUkVGRqJ79+7466+/YGRkhPXr1+Orr75SU8VERETFB0OPhtx/k4ABWy8hPlUOj4p2WOfdAMZGhetou337Njp16oT79+/D1tYWe/fuRfv27dVUMRERUfHC0KMBz2OS0W/zRUQlpqGOsw22DGgEM2OjQq3z9OnT6N69O6Kjo1GhQgX8/vvvqFWrlpoqJiIiKn54To8GHLr+Ci9iU1CptCX8BnnA2sy4UOvz9/dH+/btER0dDU9PT1y8eJGBh4iI6APY06MBQ1pUhImRBG1rloG9VcEfciqEgK+vL+bNmwcA6NWrF/z8/GBubq6uUomIiIothh4N6de0QqGWT01NxdChQxEQEAAAmD59OhYtWqR3D1YlIiLSFoYePRAdHY0ePXrg1KlTMDIywoYNGzBs2DBtl0VERKRXGHp03KNHj/DZZ5/h5s2bsLa2RlBQEDp06KDtsoiIiPQOQ48OCw4ORufOnREREQFnZ2f8/vvvcHNz03ZZREREeoknhOiogwcP4uOPP0ZERATc3Nxw8eJFBh4iIqJCYOjRQRs2bEC3bt2QlJSETz75BGfOnIGzs3oeSEpERGSoGHp0iFKpxDfffINRo0ZBqVRiyJAhOHjwIGxsbLRdGhERkd7jOT06IjU1FYMHD0ZgYCAAYO7cuZg9e3ahn81FRERE7zD06IDY2Fh0794dJ0+ehEwmw6ZNmzBw4EBtl0VERFSsMPRo2fPnz/Hpp58iPDwcVlZW+Pnnn3lJOhERURFg6NGiGzdu4NNPP8XTp0/h6OiIP/74A/Xr19d2WURERMUST2TWkjNnzqBFixZ4+vQpqlevjr///puBh4iIqAgx9GhBxhBWTEwMmjVrhnPnzqFChQraLouIiKhYY+jRsPXr16NXr15ITU1Ft27dcOzYMdjb22u7LCIiomKPoUdDhBCYNWsWRo8eDSEERowYgaCgIJibm2u7NCIiIoPAE5k1QC6XY/jw4di6dSsAYN68eZg1axbvwUNERKRBDD1FLCkpCX369MFvv/0GqVSKn376CUOHDtV2WURERAaHoaeIPXz4EKdPn4aZmRn27NmDzz//XNslERERGSSGniJWu3ZtHDhwACYmJmjevLm2yyEiIjJYDD0a0Lp1a22XQEREZPB49RYREREZBIYeIiIiMggMPURERGQQGHqIiIjIIDD0EBERkUFg6CEiIiKDwNBDREREBoGhh4iIiAwCQw8REREZBIYeIiIiMggMPURERGQQGHqIiIjIIDD0EBERkUHgU9b/JYQAAMTFxWm5EiIiIsqrjL/bGX/Hc8PQ86/4+HgAgIuLi5YrISIiovyKj4+Hra1trvNIRF6ikQFQKpV48eIFrK2tIZFI1LruuLg4uLi44OnTp7CxsVHrunVBcW8fUPzbyPbpv+LexuLePqD4t7Go2ieEQHx8PJycnCCV5n7WDnt6/iWVSlGuXLkifQ8bG5ti+UHOUNzbBxT/NrJ9+q+4t7G4tw8o/m0sivZ9qIcnA09kJiIiIoPA0ENEREQGgaFHA0xNTTFnzhyYmppqu5QiUdzbBxT/NrJ9+q+4t7G4tw8o/m3UhfbxRGYiIiIyCOzpISIiIoPA0ENEREQGgaGHiIiIDAJDDxERERkEhp5CSEhIwIQJE+Dk5AQzMzO4u7tj9+7deVo2IiICAwcORKlSpWBhYYGmTZvi+PHjRVxx/hS0fdu3b4dEIsn259WrVxqoPG/i4+Mxbdo0dOjQAaVLl4ZEIoGvr2+el9eHfViYNur6fjxx4gQGDx6MGjVqwNLSEs7OzujatSsuX76cp+X1Yf8Vpo26vv8A4MqVK+jUqRPKly8Pc3Nz2NnZoWnTpggICMjT8vqwDwvTRn3Yh9nZvHkzJBIJrKys8jS/Jvcj78hcCD169EBwcDCWLFmCatWqITAwEF5eXlAqlejbt2+Oy6WmpqJt27aIiYnBqlWr4ODggHXr1qFjx444duwYWrVqpcFW5Kyg7cuwbds21KhRI9M0e3v7oio336KiorBx40a4ubmhW7du2Lx5c56X1Zd9WJg2ZtDV/bhhwwZERUVh/PjxqFWrFt68eYPly5fD09MThw8fRps2bXJcVl/2X2HamEFX9x8AxMTEwMXFBV5eXnB2dkZiYiJ27tyJfv364dGjR5g1a1aOy+rLPixMGzPo8j583/PnzzFlyhQ4OTkhNjb2g/NrfD8KKpDff/9dABCBgYGZprdv3144OTkJuVye47Lr1q0TAMT58+dV09LT00WtWrWEh4dHkdWcH4Vp37Zt2wQAERwcXNRlFopSqRRKpVIIIcSbN28EADFnzpw8LasP+1CIwrVR1/fj69evs0yLj48XZcqUEW3bts11WX3Zf4Vpo67vv9w0adJEuLi45DqPvuzDnOSljfq4Dzt37iy6dOkiBgwYICwtLT84v6b3I4e3Cmj//v2wsrJCr169Mk0fNGgQXrx4gYsXL+a6bPXq1dG0aVPVNJlMBh8fH1y6dAnPnz8vsrrzqjDt0xcZ3cQFoQ/7EChcG3Wdg4NDlmlWVlaoVasWnj59muuy+rL/CtNGfVaqVCnIZLkPROjLPsxJXtqobwICAnD69GmsX78+z8toej8y9BTQ9evXUbNmzSwf2nr16qlez23ZjPmyW/bGjRtqrLRgCtO+DJ07d4aRkRHs7OzQo0ePPC2jL/RhH6qLPu3H2NhYhIaGonbt2rnOp8/7L69tzKAP+0+pVEIul+PNmzdYv349Dh8+jOnTp+e6jL7tw4K0MYM+7MOIiAhMmDABS5YsydfDuzW9H4tXzNSgqKgoVKpUKct0Ozs71eu5LZsxX36X1ZTCtM/R0REzZ86Ep6cnbGxsEB4ejiVLlsDT0xPnzp2Dm5tbkdWtKfqwDwtLH/fj6NGjkZiYiJkzZ+Y6nz7vv7y2UZ/236hRo/DTTz8BAExMTLB69WoMHz4812X0bR8WpI36tg+rV6+OkSNH5ms5Te9Hhp5CyG3Y4ENDCoVZVlMKWmPHjh3RsWNH1e8fffQROnXqhLp16+Lbb7/FgQMH1FqntujDPiwMfduPs2fPxs6dO7FmzRo0bNjwg/Pr4/7LTxv1af/NmDEDQ4cORUREBA4ePIgxY8YgMTERU6ZMyXU5fdqHBWmjvuzDn3/+GQcPHkRYWFiBtrsm9yNDTwHZ29tnm0Dfvn0LANkmV3UsqynqrrFChQpo0aIFLly4oJb6tE0f9mFR0NX9OHfuXCxYsAALFy7EmDFjPji/Pu6//LYxO7q6/8qXL4/y5csDAD777DMAwDfffIMBAwagdOnS2S6jb/uwIG3Mjq7tw4SEBIwePRpjx46Fk5MTYmJiAABpaWkA3l29ZmxsDEtLy2yX1/R+5Dk9BVS3bl3cvHkTcrk80/Tw8HAAQJ06dXJdNmO+/C6rKYVpX06EEJBKi8dHTh/2YVHRtf04d+5c+Pr6wtfXFzNmzMjTMvq2/wrSxpzo2v7LjoeHB+RyOR48eJDjPPq2D9+XlzbmRJf2YWRkJF6/fo3ly5ejZMmSqp9du3YhMTERJUuWhLe3d47La3w/qv16MAPxxx9/CABi9+7dmaZ37Njxg5d0r1+/XgAQFy5cUE1LT08XtWvXFk2aNCmymvOjMO3LzoMHD4SVlZXo1q2bOstUm/xezq0P+/B9+W1jdnRtP86bN08AELNmzcrXcvq0/wraxuzo2v7LSb9+/YRUKhURERE5zqNP+zA7eWljdnRtHyYnJ4uTJ09m+fnkk0+EmZmZOHnypAgPD89xeU3vR4aeQmjfvr0oWbKk2Lhxozhx4oQYNmyYACACAgJU8wwePFgYGRmJR48eqaalpKSI2rVrCxcXF7Fz505x9OhR0b17dyGTycSpU6e00ZRsFbR9bdu2FXPnzhX79+8Xx48fFz/88INwcnIS1tbWuX74teGPP/4Qe/fuFVu3bhUARK9evcTevXvF3r17RWJiohBCv/ehEAVvo67vx2XLlgkAomPHjuLvv//O8pNBn/dfYdqo6/tPCCGGDRsmJk+eLPbs2SNOnTolgoKCRJ8+fQQAMXXqVNV8+rwPC9NGfdiHOcnuPj26sB8ZegohPj5ejBs3Tjg6OgoTExNRr149sWvXrkzzDBgwQAAQDx8+zDT91atXon///sLOzk6YmZkJT09PcfToUQ1W/2EFbd+ECRNErVq1hLW1tZDJZMLJyUn4+PiI27dva7gFH+bq6ioAZPuT0SZ93odCFLyNur4fW7VqlWO7/tuJrc/7rzBt1PX9J4QQW7duFS1bthSlSpUSMplMlChRQrRq1Ur4+/tnmk+f92Fh2qgP+zAn2YUeXdiPEiGEUOdwGREREZEu0o0zoYiIiIiKGEMPERERGQSGHiIiIjIIDD1ERERkEBh6iIiIyCAw9BAREZFBYOghIiIig8DQQ0RERAaBoYeIiIgMAkMPEemkDh06oEWLFjhy5AhatGgBCwsLVKhQAXv27AEA7NmzB40aNYKFhQVq1aqFkydParliItJ1fAwFEemk0qVLw9zcHI6Ojpg0aRJKlCiB6dOn49atWxg1ahSuXLmCsWPHwsjICOPHj0d6ejqeP3+u7bKJSIexp4eIdM7jx48RGRkJR0dH/PXXX/jyyy/RsWNHTJs2DWlpabh9+zZOnDiBHj16oGvXrhg5ciRevHiB6OhobNmyBVZWVrCysoKJiQmMjY1Vv7dp06bANW3YsAENGjSAsbExfH191ddYItIYhh4i0jmXL18GAMyfPx8mJiaq6XFxcQCAJUuWQCKRqKYnJCTA2NgY1tbWGDJkCBISEpCQkICBAwdi7Nixqt9PnDhR4JrKli2LuXPnolu3bgVeBxFpF0MPEemc0NBQmJqaZumZuXz5MpycnFCvXr1M08PCwlCnTh3IZLJM069du5Zl3oLq1q0bunTpAltbW7Wsj4g0j6GHiHTO5cuX4ebmBmNj40zTQ0JC0KhRo2znb9iwYaZpQghcv35dbaGHiPQfQw8R6ZzQ0NAs4SYlJQU3btzIMv3ly5d49epVltBz//59pKamonbt2kVeLxHpB4YeItIpz549Q0RERJZwc/XqVcjl8izTM87/yW7+atWqwdTUNNv3adu2LczMzLL9mT17thpbRES6QvbhWYiINCenEJPbdGNjY9StWzfT9A+dz3P8+HF1lEtEeoQ9PUSkU7p27QohRJYQM2rUKAghULp06UzT58yZg7S0tCw9Ouo8iRkA5HI5UlJSoFAoMv2biPQHQw8RFUvqDj0LFiyAubk5tm/fjoULF8Lc3Bz+/v5qWz8RFT3ekZmIiIgMAnt6iIiIyCAw9BAREZFBYOghIiIig8DQQ0RERAaBoYeIiIgMAkMPERERGQSGHiIiIjIIDD1ERERkEBh6iIiIyCAw9BAREZFBYOghIiIig/B/H7l5OLiiCpoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "####################\n",
    "### Figure 5\n",
    "####################\n",
    "\n",
    "plt.plot(mVec_fine, cVec, \"k-\")\n",
    "plt.plot(mVec, cVec1, \"--\")\n",
    "plt.xlabel(r\"$m_{T-1}$\")\n",
    "plt.ylabel(r\"$c_{T-1}$\")\n",
    "plt.title(r\"$c_{T-1}(m_{T-1})$ (solid) versus $\\grave c_{T-1}(m_{T-1})$ (dashed)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. Value Function versus the First Order Condition\n",
    "\n",
    "- See more detailed discussion [here](https://llorracc.github.io/SolvingMicroDSOPs/#Value-Function-versus-First-Order-Condition)\n",
    "\n",
    "Our difficulty is caused by the fact that consumption choice is governed by the marginal value function, not by the level of the value function (which is what we tried to approximate). \n",
    "\n",
    "This leads us to an improved approach to solving consumption policy by working with marginal utility/values that come the first-order conditions (FOC). For every exogenously set m grid, we can find the solution to the FOC. \n",
    "\n",
    "\\begin{equation}\n",
    "u^{\\prime}(c_{T-1}(m_{T-1})) = \\mathfrak{v}^{\\prime}(m_{T-1}-c_{T-1}(m_{T-1}))\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "##########################\n",
    "### Figure PlotuPrimeVSOPrime (omitted here)\n",
    "##########################\n",
    "\n",
    "# u′(c) versus v′_{T −1}(3 − c), v′_{T −1}(4 − c), v`′_{T −1}(3 − c), v`′_{T −1}(4 − c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we solve for consumption using the FOCs instead of value function maximization. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.2825370803194411, 0.8795623189192019, 1.4217748839030457, 1.9483828428740233, 2.4682183015706145]\n"
     ]
    }
   ],
   "source": [
    "cVec2 = []  # Start with empty list.\n",
    "for m in mVec:\n",
    "    mintotwealth = m + PermGroFac[0] * theta.X[0] / R\n",
    "    foc_condition = lambda c: u.prime(c) - gothic.VP_Tminus1(\n",
    "        m - c\n",
    "    )  # Define the a one-line function for the FOC\n",
    "    c = scipy_find_root(foc_condition, 1e-12, 0.999 * mintotwealth)  # Zero-find on the FOC\n",
    "    cVec2.append(c)\n",
    "\n",
    "print(cVec2)  # Look at the consumption from the list."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The linear interpolating approximation looks roughly as good (or bad) for the marginal value function as it was for the level of the value function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "code_folding": [],
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "data": {
      "image/png": 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sOVfTnz0hhDh79qwYM2aMaNSokbC1tRXu7u6idevWYuLEiWLXrl213t+afvfWjmGIzObDDz8UAMSpU6dqva6srCyhVCrF+vXrTVBZ1aoKQ5999pkAIPbt21ftdZvye5GL2nwf1qS+nhM8H6TDc69mGIbIbPLy8kSjRo3E448/Xut17du3TwAod3RZU8nKyhKnT58Wp0+fFvb29uKdd94Rp0+fLjNkfm5urvDz8xNPPvlkjbZjyu9FDmr7fViT+nhO8HyQDs+9muMN1GQ2Go0Gq1atwgMPPICcnJxarevUqVNwdXUt88ipKZ04cQLt2rVDu3btkJeXh3nz5qFdu3Z4++23S33uxo0bmDhxIhYvXlyj7Zjye5GD2n4f1qQ+nhM8H6TDc6/mFEIIIXURFcnKysJ7772HM2fO4PTp00hOTsa8efMwf/58o9onJiZi9uzZ+PXXX5Gbm4vw8HC8//776N27d90WTkRERBZD1j1DKSkp+Prrr1FQUIAhQ4ZUq21BQQF69+6NXbt2YcmSJdi8eTN8fX3Rr18/k41ZQkRERJZP1iNQBwUFIS0tDQqFAsnJydUaa+Tbb7/F+fPncejQIXTt2hVA8ZgL4eHhmD17No4ePVpXZRMREZEFkXXPUMmEejWxadMmtGzZ0hCEgOL5Yp599lkcO3as3AkfiYiIyPrIumeoNs6fP4/u3buXWV4yauuFCxcqnNeloKCg1OR9er0eqamp8PT0rHE4IyIiIvMSQiArKwv+/v5QKivu/6m3YSglJQUeHh5llpcsq2xyzAULFuCdd96ps9qIiIjIfOLi4tCwYcMK36+3YQhApb04lb03Z84czJgxw/D/GRkZaNSoEeLi4oyabVguTpw4gd69e8PPzw+XLl2SupxSTt9KRbCnE9wdbaUuhYiI6qnMzEwEBgbC2dm50s/V2zDk6elZbu9PyYR35fUalbCzs4OdnV2Z5S4uLhYVhlq1agUAuHv3LjQaDWxt5RM8eoRZzvdIRESWrapbXGR9A3VttGnTBufOnSuzvGRZWFiYuUsyO19fX2g0GgghcPv2banLISIikqV6G4aGDh2KS5culXqEXqvVYvXq1ejcuTP8/f0lrM48FAoFGjVqBAC4efOmxNWUlpiZjwVbozH7xz+lLoWIiKyc7MPQtm3b8OOPP+KXX34BAFy8eBE//vgjfvzxR+Tm5gIAxo8fD7VaXeov/HHjxqF169YYPnw41qxZg507d+Lpp59GTEwMFi1aJMm+SCEoKAhA8TDtcrNsXyx+PHkbeYU6qUshIiIrJvt7hiZPnlwq5GzYsAEbNmwAAFy/fh3BwcHQ6XTQ6XS4f2YROzs77Nq1C7Nnz8bUqVORm5uLiIgIbNu2DT169DD7fkilcePGAIq/KznxdraDl5MtkrMLEXMvCxGBblKXREREVkr2YciYHo2VK1di5cqVZZb7+voiKirK9EVZkJJJG2NjYyWupDSFQoFQPxfsv5KMiwmZDENERCQZ2V8mo9qRaxgCgFb+xU+UXbyTIXElRERkzRiG6rmmTZsCAK5duyZxJWW18isOQ9F3siSuhIiIrBnDUD1X0jOUmJiI7Oxsiasp7e8wlAm9XlTxaSIiorrBMFTPubm5GQaYlNulssZejrBTK2GrViIxq6DqBkRERHVA9jdQU+01adIEqampiI2NNUxUKwdqlRIHXnsEXk62nACXiIgkw54hK1By35DceoaA4kfsGYSIiEhKDENWoOS+ITneRE1ERCQ1hiErIOeeobsZ+Zj4/QkMW3pQ6lKIiMhK8Z4hKyDnniEnjRq/X7wHAEjOLoCXk53EFRERkbVhz5AVKOkZunHjBnQ6ec0D5mSnRrCnA4DiR+yJiIjMjWHICgQEBMDGxgZFRUW4ffu21OWUYRiJOoFhiIiIzI9hyAqoVCrDhK1yvG+oZPDFi+wZIiIiCTAMWQk53zdU0jPEy2RERCQFhiErIecnylr5uQIAriXlIL9IXvc0ERFR/ccwZCXk3DPk62IHf1cNwvxdkJJTKHU5RERkZfhovZWQc8+QQqHAwdcf4UjUREQkCfYMWQk59wwBYBAiIiLJMAxZiZKnydLS0pCWliZxNRXT6vRSl0BERFaGYchKODk5wdfXF4A8e4fuZeaj3//tQ4f3d0KvF1KXQ0REVoRhyIq0aNECAHDlyhWJKynLw9EWsck5yMgrwq3UXKnLISIiK8IwZEVKwtDly5clrqQsG5USLX2dAXDwRSIiMi+GISvSvHlzAPIMQ8B9I1FzWg4iIjIjhiErIueeIeC+OcrYM0RERGbEMGRF7r9nSAj53aTMaTmIiEgKDENWpGnTplAoFMjIyEBSUpLU5ZQR0qD4nqE7GflI5UjURERkJgxDVkSj0aBRo0YA5HmpzFljgx4tvDE4wh95nKOMiIjMhNNxWJkWLVrg5s2buHLlCh566CGpyykjalwnqUsgIiIrw54hKyP3m6iJiIjMjWHIylhCGNLpBeI48CIREZkJw5CVkftYQynZBQib9xt6Ld6LfN43REREZsAwZGVKeoauXr0KvV5+k6J6ONrCzkYJrV7gamK21OUQEZEVYBiyMkFBQbCxsUF+fj5u374tdTllKBQKjkRNRERmxTBkZdRqNZo2bQpAvpfKDGGIgy8SEZEZMAxZoZL7huQ4ez1w37Qc7BkiIiIzYBiyQnJ/ouz+aTnkOG0IERHVLwxDVkjuYaiptxNsVUpkFWhxOy1P6nKIiKie4wjUVqjkMllMTIzElZTPRqXEs12C4GSngq2aeZ2IiOoWw5AVCgkJAQBcv34d+fn50Gg0EldU1ttPtJK6BCIishL8Z7cVatCgAVxdXaHX62V7EzUREZG5MAxZIYVCgVatinteoqOjJa6mfEII3M3Ix/4rSVKXQkRE9RzDkJUKDQ0FAFy8eFHiSsqXVaBFlwW7MPrbY0jPLZS6HCIiqscYhqxUSRiSa8+Qi8YGgR72ADj4IhER1S2GISsl9zAEgNNyEBGRWTAMWamSMHT58mXodPKcHb6VnysA9gwREVHdYhiyUkFBQdBoNCgoKMD169elLqdcnJaDiIjMgWHISqlUKrRs2RKAfC+VlYShq4nZKNDKs/eKiIgsH8OQFSt5vF6uT5T5u2rgam8DrV7gamK21OUQEVE9xRGorZjcb6JWKBSY2bcFHO3U8He1l7ocIiKqpxiGrJjcwxAAjO4aLHUJRERUz/EymRW7PwwJISSuhoiISBoMQ1asefPmUKlUyMrKQkJCgtTllEur0+NIbAqiDt1gYCMiojrBMGTFbG1t0bRpUwDyvVSmF8Bz3x7DvC0XcDstT+pyiIioHmIYsnJyf6LMVq1EMx8nABx8kYiI6gbDkJWT+4StAAdfJCKiusUwZOXCwsIAAOfPn5e4kooZ5ihjzxAREdUBhiEr16ZNGwDFYUiuNyizZ4iIiOoSw5CVa9myJdRqNTIyMnD79m2pyylX6F89Q/HpecjILZK4GiIiqm8Yhqycra2tYY6yc+fOSVxN+VztbdDQvXgE6ui77B0iIiLTYhgiw6UyuYYhAHhvSBg2Tu6KiEA3qUshIqJ6hmGISt03JFe9WvqgQ5AHNDYqqUshIqJ6hmGIDE+UyblniIiIqK7IOgxlZ2dj+vTp8Pf3h0ajQUREBNatW2dU2z179qBPnz7w8fGBk5MT2rZti88++ww6na6Oq7Y8JT1D0dHRKCqS5w3KWp0e/z1+C/M2n0ehVi91OUREVI/IOgwNGzYMUVFRmDdvHrZt24aOHTsiMjISa9asqbTdzp078eijj0Kr1WL58uX4+eef0bNnT7z88suYMWOGmaq3HEFBQXByckJhYSGuXLkidTnlUikV+OB/0Yg6fBNXE7OlLoeIiOoRtdQFVGTr1q3YsWMH1qxZg8jISABAr169cPPmTcyaNQvPPPMMVKry7x9ZuXIlbGxs8Ouvv8LR0REA8OijjyImJgYrV67EkiVLzLYflkCpVCIsLAxHjhzB+fPnDVN0yIlCoUArfxcciU3FxTuZhrGHiIiIaku2PUObNm2Ck5MThg8fXmr52LFjkZCQgKNHj1bY1sbGBra2trC3ty+13M3NDRqNpk7qtXSWcN9QyXhDHHyRiIhMSbZh6Pz58wgNDYVaXbrzqm3btob3K/Liiy+isLAQ06ZNQ0JCAtLT07Fq1Sps2rQJs2fPrnLbBQUFyMzMLPWq7yzh8fq/p+XIkLgSIiKqT2QbhlJSUuDh4VFmecmylJSUCtt27twZu3fvxqZNmxAQEAB3d3eMHTsWH3zwAV599dUqt71gwQK4uroaXoGBgTXfEQthCY/X3z8th1ynDiEiIssj2zAEFN8nUpP3Tp48iaFDh6JDhw745ZdfsHv3bsyZMwdvvvkm3nvvvSq3O2fOHGRkZBhecXFxNarfkpSEodjYWOTk5EhcTfma+zjDRqVAZr4W8el5UpdDRET1hGxvoPb09Cy39yc1NRUAyu01KjFlyhT4+vpi06ZNhpuse/XqBaVSifnz52PUqFFo0qRJhe3t7OxgZ2dXyz2wLF5eXmjQoAHu3r2LCxcuoFOnTlKXVIatWolmPs6IvpOJy/ey0NDdQeqSiIioHpBtz1CbNm0QHR0NrVZbannJPS0lN/yW58yZM+jQoUOZp806duwIvV6P6Oho0xdcD5Tcj/Xnn39KXEnFloyIwIk3H8UjIb5Sl0JERPWEbMPQ0KFDkZ2djY0bN5ZaHhUVBX9/f3Tu3LnCtv7+/jhx4kSZARYPHz4MAGjYsKHpC64HIiIiAACnT5+WtpBKtPB1hpeTdfXaERFR3ZLtZbL+/fujT58+mDx5MjIzM9GsWTOsXbsW27dvx+rVqw29PuPHj0dUVBSuXbuGoKAgAMArr7yCadOm4YknnsCkSZPg4OCAXbt24eOPP8ajjz6K8PBwKXdNttq1aweguGeNiIjIWsg2DAHATz/9hLlz5+Ltt99GamoqQkJCsHbtWowYMcLwGZ1OB51OV+rpoqlTpyIgIACffvopJkyYgLy8PAQHB2PevHl45ZVXpNgVi1DSM/Tnn39Cp9NVOKillPR6gY9+j8HFhEx8FtkOrvY2UpdEREQWTiH4jHKVMjMz4erqioyMDLi41N+Rj3U6HVxcXJCbm4vo6GiEhIRIXVK5ui3cjfj0PPx3Yhd0buIpdTlERCRTxv79Ldt7hsj8VCqV4SZqOV8qM4w3dKf+D4ZJRER1j2GISim5b0jON1FzWg4iIjIlhiEqpeS+IVn3DPmxZ4iIiEyHYYhKub9nSK63k7X+6zLZlXvZKNTqJa6GiIgsHcMQlRIWFgaVSoWkpCQkJCRIXU65Grrbw9lOjUKdHteSsqUuh4iILBzDEJVib29veIpMrpfKFAoFQv1d4Gynxt3MfKnLISIiC8cwRGVYwk3Uy0c/gLPz+6JXSx+pSyEiIgvHMERlWMJN1K4ONlAoFFKXQURE9QDDEJVhCT1DREREpsIwRGWU9AzFxsYiLS1N2mIqIITAtLWn0fOjPYhPz5O6HCIismAMQ1SGh4cHmjRpAgA4efKkxNWUT6FQ4PK9LNxIyUU0B18kIqJaYBiicnXs2BEAcOLECYkrqRin5SAiIlNgGKJyPfDAAwCA48ePS1xJxVpxWg4iIjIBhiEql0X0DHFaDiIiMgGGISpX+/btoVAocOvWLSQmJkpdTrlKJmy9lZqLzPwiiashIiJLxTBE5XJ2djaMRC3X3iF3R1v4u2oAAJfuZElcDRERWSqGIaqQJdw3FNHIDWEBLpywlYiIakwtdQEkXx07dsSqVatk2zMEAF+MbM+RqImIqFbYM0QVKukZOnHiBIQQEldTPgYhIiKqLYYhqlBERARUKhXu3r2L+Ph4qcupVKFWD71enoGNiIjkjWGIKmRvb4+wsDAA8r2JGgCeWXYYredtx5XEbKlLISIiC8QwRJUqGW9IzjdRCwEU6QQu3smQuhQiIrJADENUqZL7ho4dOyZxJRUzTMvBkaiJiKgGGIaoUl26dAEAHD16FDqdTuJqyseRqImIqDYYhqhSYWFhcHR0RFZWFqKjo6Uup1yh981RJten3oiISL4YhqhSKpUKnTp1AgAcPnxY4mrK19zXCSqlAmm5RbibmS91OUREZGEYhqhKXbt2BSDfMKSxUaGZtxMA3jdERETVxxGoqUolYejIkSMSV1KxR0J90MzXCa72NlKXQkREFkYheJNFlTIzM+Hq6oqMjAy4uLhIXY7ZJSUlwcfHBwCQmpoKd3d3iSsiIiKqmrF/f/MyGVXJ29sbzZo1A1D8VBkREVF9wjBERpH7fUMAoNcL3EzJQX6RPIcAICIieWIYIqNYQhjq+3/70OOjvTgfz5GoiYjIeAxDZJT7B1/U6/USV1O+IA8HABx8kYiIqodhiIzSpk0bODo6IjMzU7aDL3JaDiIiqgmGITKKWq02TNp66NAhiaspH6flICKimmAYIqN169YNAHDgwAGJKylfybQcl+5mQauT56U8IiKSH4YhMlr37t0BAPv27ZO4kvI18nCAo60KhVo9YpNzpC6HiIgsBMMQGe3BBx+EUqnEjRs3cPv2banLKUOpVJSatJWIiMgYDENkNGdnZ7Rr1w4AsH//fomrKd+QdgGY0qspWvg6S10KERFZCIYhqpaHH34YgHwvlT3bJQizHgsxPFlGRERUFYYhqpaS+4bk2jNERERUXQxDVC0PPfQQAODChQtISUmRuJryJWUV4I/LScjIK5K6FCIisgAMQ1Qt3t7eCA0NBSDfR+xHfXMEY1Ycw6mbaVKXQkREFoBhiKpN7pfKOPgiERFVB8MQVZvcb6LmtBxERFQdDENUbSU9Q6dOnUJ2drbE1ZTVys8VAHuGiIjIOAxDVG2NGjVCUFAQdDodjhw5InU5ZYT6FY8xdCMlB9kFWomrISIiuWMYohop6R36448/JK6kLE8nO/i62EEIIOYue4eIiKhyDENUIz179gQA7NmzR9pCKtCK03IQEZGR1FIXQJbpkUceAQAcPXoU2dnZcHJykrii0kZ3DcKANn7o0sRT6lKIiEjm2DNENdK4cWM0btwYWq1Wlk+VPRLii+EPBCLQw0HqUoiISOYYhqjGevfuDQDYtWuXxJUQERHVHMMQ1Zjcw9DpW2n4/vAN3MnIk7oUIiKSMd4zRDXWq1cvAMCff/6J5ORkeHl5SVxRae/9ehGnbqXD1d4GgyMCpC6HiIhkij1DVGO+vr4ICwsDIM+nygwjUXPwRSIiqgTDENWKnC+VGUai5uP1RERUCYYhqhVZh6H75igTQkhcDRERyRXDENXKww8/DKVSiatXr+LWrVtSl1NKS19nKBVASk4hkrIKpC6HiIhkimGIasXV1RUdO3YEIL/eIXtbFRp7OQIALvC+ISIiqgDDENWavC+V8b4hIiKqHMMQ1VqfPn0AADt27IBer5e4mtImdm+C9ZO64rmuQVKXQkREMiXrMJSdnY3p06fD398fGo0GERERWLdundHtN2/ejB49esDFxQWOjo5o3bo1vv766zqs2Do9+OCDcHJyQmJiIk6fPi11OaW0aeiKTo094KyxkboUIiKSKVmHoWHDhiEqKgrz5s3Dtm3b0LFjR0RGRmLNmjVVtl24cCGGDRuGsLAwrF+/Hlu2bMG//vUvFBYWmqFy62Jra2u4VLZ9+3aJqyEiIqoehZDpM8dbt27FwIEDsWbNGkRGRhqW9+3bFxcuXMCtW7egUqnKbXvy5El06tQJCxYswOzZs2tdS2ZmJlxdXZGRkQEXF5dar68+WrZsGV588UV069YNBw4ckLqcUradu4PjN9LwTMdAtGzgLHU5RERkJsb+/S3bnqFNmzbByckJw4cPL7V87NixSEhIwNGjRyts+/nnn8POzg5Tp06t6zLpL/369QMAHD58GGlpaRJXU9q643FYcfA6jt9IlboUIiKSIdmGofPnzyM0NBRqdenp09q2bWt4vyL79u1DaGgoNm7ciJYtW0KlUqFhw4Z4/fXXjbpMVlBQgMzMzFIvqlxQUBBCQ0Oh1+tl91QZp+UgIqLKyDYMpaSkwMPDo8zykmUpKSkVto2Pj8eVK1cwbdo0TJs2DTt37sTzzz+PxYsXY+zYsVVue8GCBXB1dTW8AgMDa74jVqSkd2jbtm0SV1JaK7+/R6ImIiL6J9mGIQBQKBQ1ek+v1yMrKwtLly7FlClT0KtXL7z//vuYOnUq1qxZg6tXr1a63Tlz5iAjI8PwiouLq/E+WJP+/fsDKL6JWk63opX0DF26mwmdXj51ERGRPMg2DHl6epbb+5OaWnzfR3m9Rve3BYDHHnus1PKSv6xPnTpV6bbt7Ozg4uJS6kVV6969OxwcHJCQkFDpZUxzC/Z0hL2NCvlFelxPzpG6HCIikhnZhqE2bdogOjoaWq221PJz584BAMLCwipsW3Jf0T+V9FYolbLdbYum0WjQq1cvAPK6VKZSKgxPkfG+ISIi+ifZpoKhQ4ciOzsbGzduLLU8KioK/v7+6Ny5c4Vtn3zySQBl/0LeunUrlEqlYS4tMj3Z3jf016Wya4nZEldCRERyI9txhoDiMYVOnDiBRYsWoVmzZli7di2WL1+O1atXY9SoUQCA8ePHIyoqCteuXUNQUPGUC0VFRejSpQuuXbuGd999F61atcLOnTuxePFiTJ48Gf/5z3+qVQfHGTJebGwsmjZtCrVajaSkJLi5uUldEgAgIT0PapUCPs4aqUshIiIzsfhxhgDgp59+wujRo/H222+jX79+OHr0KNauXWsIQgCg0+mg0+lK3bBrY2ODHTt2YMSIEfjwww8xYMAAbNq0CQsXLsSSJUuk2BWr0aRJE7Ru3RparVZWvUP+bvYMQkREVC5Z9wzJBXuGqueNN97AggULMGLECKxdu1bqcoiIyErVi54hskyDBg0CUHzfkJzmgos6dAPjVx7H0diKx6giIiLrwzBEJtepUyf4+voiIyMD+/btk7ocg+M3UrHrUiJO3UqXuhQiIpIRhiEyOaVSiSeeeAIAsGXLFomr+Run5SAiovIwDFGdKLlUtmXLFtmMRv33tBwZEldCRERywjBEdaJ3796wt7fHzZs3cfbsWanLAfB3z9D15BzkFeokroaIiOSCYYjqhIODA/r06QNAPpfKfJw18HKyg14AMfeypC6HiIhkgmGI6szgwYMByCcMAUCo31/TcnAGeyIi+gvDENWZgQMHQqFQ4MSJE7h165bU5QAovlTmYKtCVn6R1KUQEZFMMAxRnfH19UX37t0BFI8mLgfTe7fA+fmPYVKPplKXQkREMsEwRHXqqaeeAgBs2LBB4kqK2duqoFQqpC6DiIhkhGGI6tSTTz4JADh06BDi4+MlroaIiKgshiGqU/7+/ujWrRsAYOPGjRJXU+yT32PwyMd7se3cHalLISIiGTBbGNLr9fj+++/NtTmSkeHDhwMAfvzxR4krKZaUXYjYpByc5+CLREQEM4ahoqIijB071lybIxkpuVR24MAB3LkjfW+MYVoOPl5PREQA1KZc2bvvvlvhe0VFfJTZWjVs2BBdu3bF4cOHsXHjRrz00kuS1mOYloNzlBEREUzcM/T+++/jwoULiIuLK/PizbPWreSpMjlcKgtp4AyFAriXWYDk7AKpyyEiIokphAln0ezQoQPeffddDBw4sMx7+fn5cHBwgF6vN9XmzCYzMxOurq7IyMiAi4uL1OVYpFu3biEoKAgKhQIJCQlo0KCBpPU8sngvYpNzsGp8J3Rv7i1pLUREVDeM/fvbpD1DL7zwAnS68ifAtLGxwbx580y5ObIgjRo1QpcuXSCEwH//+1+py0Eo7xsiIqK/mDQMvfjiixg0aFC576lUKoYhKzdy5EgAwA8//CBxJUB4Q1eE+rnA0c6kt80REZEFMullsvqKl8lMIzExEf7+/tDpdLh8+TKaN28udUlERFSPSXKZjKgyPj4+6NOnDwB59A4REREBDENkZqNGjQJQHIbk0Cmp1emRX1T+fW5ERGQd6jwM8T4hut+QIUPg4OCAq1ev4vjx45LW8vbm82g17zf8fJrDPhARWbM6D0MfffRRXW+CLIiTkxMGDx4MQPpLZfY2KhRq9Rx8kYjIytV5GJLDpRCSl5JLZevWrYNWq5WsDk7LQUREgBnCkEKhqOtNkIXp27cvvLy8kJiYiJ07d0pWR8m0HNF3MqHXM7QTEVkr3kBNZmdjY4MRI0YAAFauXClZHY29HGGnViKnUIdbqbmS1UFERNJiGCJJjBs3DgCwadMmpKamSlKDWqVESANnAJy0lYjImvGeIZJEu3btEBERgcLCQqxZs0ayOkL9eN8QEZG1q/Mw1K1bt7reBFmosWPHAgC+++47yWro2tQT/cMaoOVfPURERGR9OB2HETgdR91ISUmBv78/CgsLcfr0aUREREhdEhER1SOcjoNkz9PT0zDmkJS9Q0REZN0YhkhSJTdSr169GgUFBZLUIIRAXGoukrOl2T4REUnLpGHo0UcfNeXqyAr06dMHAQEBSE1NxebNmyWpYcb6P9H933vw06nbkmyfiIikZdIwdOzYMVOujqyASqXC888/DwD4+uuvJamhqbcjACD6TpYk2yciImnxMhlJbsKECVAoFNi1axcuX75s9u1zWg4iIutm0jCUn5+PmTNn4vvvv8eZM2dQVFRkytVTPRUcHIwBAwYAAJYtW2b27bfycwUAXE3KRn6RzuzbJyIiaVU7DFX2JL5CoUBWVha+/PJLdO/eHU5OTmjTpg1GjRqFRYsWYdu2bbUqluqvyZMnAyh+qiwvL8+s2/Z1sYOHoy10eoEr97LNum0iIpJetcNQkyZN8Oijj2Lz5s3Q6/Wl3rOzs8OyZctw+PBhZGVl4eLFi3jnnXfQvHlzHD16FNOmTTNZ4VS/9OvXD0FBQUhLS8P69evNum2FQmGYtPXinQyzbpuIiKRX7TC0ceNGdOvWDYsWLUKzZs3w4YcfIikpCUDZXqOmTZti2LBhmD9/Pn766SdcuXLFNFVTvaNSqTBp0iQAwJdffmn27fO+ISIi61WrEagzMzOxe/dunDx5Eu+99x5WrFhhGDemPuEI1OZx7949BAYGoqioCKdOnUK7du3Mtu1DV5Ox70oyujf3QrdmXmbbLhER1R2zjEDt4uKCIUOGoHnz5hg8eDBWr16Nxx57TJJ/2ZPl8/X1xbBhwwAAS5cuNeu2H2zmhdf7hzAIERFZoVrPTbZ48WK89tprZS6Rvfrqq/joo49qVZxcsGfIfPbv34+HH34YGo0GcXFx8PJiOCEiopox29xkixcvRseOHXH8+HFotVro9XpkZ2cjOzsbK1asqO3qyco89NBD6NChA/Lz883+mH1aTiEOXk1GbBKfKCMisia1DkORkZGYP38+OnToAKWyeHUODg44efIk5s2bV+sCybooFApMnz4dAPDFF1+gsLDQbNteuO0SRn1zFJtOx5ttm0REJD11bVfQs2dPLFy4sNRUHJmZmTh58iTmz59f29WTFXr66acxe/Zs3LlzB+vXr8ezzz5rlu2WPFEWfYdPlBERWZNahaFTp05hxIgRKCgowL59+0q9p1AoMHDgwFoVR9bJ1tYWL730EubOnYtPP/0Uo0aNgkKhqPPt8vF6IiLrVOPLZBMnTsQjjzyCpk2bYu3atdizZ4/htWPHDjz99NNo2bKlKWslKzJp0iRoNBqcOnUK+/fvN8s2Qxo4AwASMvKRlmO+y3NERCStGj9NptfrceHCBYSGhkKtrvXVNlnj02TSmDRpEr7++msMGTIEmzZtMss2e3y0BzdTcrFmQmc8yMfsiYgsWp0/TaZUKtGmTZt6H4RIOiU3Um/evBnXrl0zyzb/npaDl8qIiKyFSWetJzKl0NBQ9O/fH0IILF682CzbNIQh3jdERGQ1aj3oojXgZTLp7Nu3Dz169ICtrS1u3LgBPz+/Ot3epbuZOHMrHe0auaPlX/cQERGRZTLboItEdal79+7o1q0bCgsL8cknn9T59kIauGBEp0YMQkREVoRhiGRNoVDgjTfeAAB89dVXSE1NlbgiIiKqbxiGSPb69++P8PBwZGdn4/PPP6/z7V2+l4XVR27ixA0GLyIia8AwRLKnUCgwZ84cAMCSJUuQnV23c4etPx6HN38+j1/P3qnT7RARkTwwDJFFeOqpp9CsWTOkpqZi+fLldbotjkRNRGRdGIbIIqhUKrz++usAgI8++gh5eXl1tq375yjjw5ZERPUfwxBZjNGjR6NRo0a4c+cOvvrqqzrbTlNvJ9iqlMgq0OJ2Wt2FLiIikgeGIbIYtra2eOuttwAACxcuRE5OTp1sx0alRIsGTgCAC7xURkRU7zEMkUUZM2YMmjRpgsTERHzxxRd1th1Oy0FEZD1kHYays7Mxffp0+Pv7Q6PRICIiAuvWrav2et58800oFAqEhYXVQZVkTjY2Npg3bx4A4N///jeysrLqZDucloOIyHrIOgwNGzYMUVFRmDdvHrZt24aOHTsiMjISa9asMXodZ86cweLFi+Hr61uHlZI5jRw5Ei1btkRKSgqWLFlSJ9vo27oB1r7QBR8PD6+T9RMRkXzIdm6yrVu3YuDAgVizZg0iIyMNy/v27YsLFy7g1q1bUKlUla5Dq9WiY8eOePjhh/Hnn38iOTkZ58+fr3YtnJtMftauXYuRI0fCzc0N169fh5ubm9QlERGRzFj83GSbNm2Ck5MThg8fXmr52LFjkZCQgKNHj1a5joULFyI1NRUffPBBXZVJEnnmmWfQunVrpKen46OPPpK6HCIismCyDUPnz59HaGgo1Gp1qeVt27Y1vF+Zixcv4v3338eXX34JJyenam27oKAAmZmZpV4kL0qlEu+//z4A4NNPP0V8fLzJt3E0NgUfbo3G9vMciZqIqD6TbRhKSUmBh4dHmeUly1JSUipsq9frMW7cOAwbNgwDBgyo9rYXLFgAV1dXwyswMLDa66C6N3jwYHTr1g15eXmGR+5N6UhsKr7eF4vfL94z+bqJiEg+ZBuGgOI5qWry3ieffIIrV67g//7v/2q03Tlz5iAjI8PwiouLq9F6qG4pFAosXrwYALBy5UqcO3fOpOv/eyTqunlijYiI5EG2YcjT07Pc3p/U1OKZxMvrNQKAW7du4e2338a8efNga2uL9PR0pKenQ6vVQq/XIz09vcqpHOzs7ODi4lLqRfLUpUsXDB8+HEIIzJ4926TrLglDVxOzUKjVm3TdREQkH7INQ23atEF0dDS0Wm2p5SX/+q9ozKDY2Fjk5eXh5Zdfhru7u+F18OBBREdHw93d3TADOtUPH374IWxsbLB9+3bs3LnTZOv1d9XA1d4GRTqBK4nsHSIiqq9kG4aGDh2K7OxsbNy4sdTyqKgo+Pv7o3PnzuW2i4iIwJ49e8q8wsPDERwcjD179uCll14yxy6QmTRr1gyTJ08GAMyaNQt6vWl6cRQKBQdfJCKyAuqqPyKN/v37o0+fPpg8eTIyMzPRrFkzrF27Ftu3b8fq1asNYwyNHz8eUVFRuHbtGoKCguDm5oaePXuWWZ+bmxu0Wm2575Hle+utt7By5UqcOXMGK1aswIQJE0yy3lb+Ljgcm8JpOYiI6jHZ9gwBwE8//YTRo0fj7bffRr9+/XD06FGsXbsWo0aNMnxGp9NBp9NBpmNHkpl4eXkZpumYM2cO0tPTTbLekp6hmym5JlkfERHJj2xHoJYTjkBtGYqKihAeHo7o6GhMmzbNJFN1ZOYXIadAiwYumkqfYCQiIvmx+BGoiarLxsYGn332GQDgiy++qNHUK//korGBn6s9gxARUT3GMET1yqOPPophw4ZBp9Nh2rRpvHxKRERVYhiieufjjz+GRqPBnj178OOPP9Z6fb9fuIsXvj+BlQevm6A6IiKSG4YhqneCg4Px2muvAQBeeeWVWs8tdzstDzsu3sPBaxVPAUNERJaLYYjqpddeew3NmjVDfHw85s6dW6t1lYxEzbGGiIjqJ4Yhqpfs7e3x1VdfASi+mfro0aM1XlfoX4/Xx6fnISOvyCT1ERGRfDAMUb3Vu3dvjB49GkIIvPDCCygqqlmQcbW3QUN3ewBANAdfJCKqdxiGqF77+OOP4enpiXPnzuGTTz6p8Xo4LQcRUf3FMET1mre3Nz7++GMAwPz583H16tUarcdw3xB7hoiI6h2GIar3nnvuOTzyyCPIz8/HuHHjajSRays/F2hslNDrOW4REVF9w+k4jMDpOCzf9evX0bZtW2RnZ+OTTz7BK6+8Uq32RTo9lAoFVEqORE1EZCk4HQfRfRo3bozFixcDAN544w3ExMRUq72NSskgRERUTzEMkdWYOHEi+vbti/z8fIwZMwZarbZG62FnKhFR/cIwRFZDoVDgm2++gYuLC44ePWroKTLWptO30ffTP7Bg26U6qpCIiKTAMERWJTAwEEuWLAEAzJs3D2fPnjW6rVYncPleNs7eTq+j6oiISAoMQ2R1xowZgyeeeAKFhYWIjIxEbm6uUe3un5aDl8qIiOoPhiGyOiWXy3x9fXHx4kXMmDHDqHbNfZxho1IgM1+L+PS8Oq6SiIjMhWGIrJKPjw9WrVoFAFi2bBk2btxYZRtbtRLNfJwBANF3suq0PiIiMh+GIbJaffr0wezZswEAEyZMwK1bt6psw2k5iIjqH4YhsmrvvfceOnbsiPT0dIwaNarKx+3/npYjwxzlERGRGTAMkVWztbXF2rVr4ezsjAMHDmDevHmVfj7M3wUtfJ3QyMPBTBUSEVFd43QcRuB0HPXf2rVrMXLkSADA5s2bMWjQIIkrIiKi2uJ0HETVEBkZialTpwIonti1prPbExGR5WEYIvrL4sWL8eCDDyIjIwNPPvlkpeMP6fQCmflFZqyOiIjqCsMQ0V9sbW2xfv16+Pj44OzZs5g0aVK5gyv+cPQmWs/bjvd+uShBlUREZGoMQ0T3CQgIwH//+1+oVCqsXr0an3/+eZnPeDraIb9Ij4t3+Hg9EVF9wDBE9A89e/bEokWLAACvvPIKfv/991Lvt/7r8for97JRqNWbvT4iIjIthiGicsyYMQNjxoyBTqfD008/jUuX/p6pvqG7PZzt1CjU6XEtKVvCKomIyBQYhojKoVAosGzZMnTr1g0ZGRl44oknkJqaangv9K+RqKN5qYyIyOIxDBFVwM7ODps2bUJwcDCuXr2Kp556CkVFxU+Q3T+DPRERWTaGIaJKeHt745dffoGTkxP27NmDF198EUKIv+coY88QEZHFYxgiqkJYWBjWrVsHpVKJFStWYN68eQgPdEOfVr7o1dJH6vKIiKiWOB2HETgdBwHA8uXLMXHiRADAl19+iRdffFHiioiIqDKcjoPIxF544QXDRK5TpkzBzz//LG1BRERkEgxDRNUwb948vPDCC9Dr9YiMjMSWnftxPTlH6rKIiKgW1FIXQGRJFAoFli5dirt372JvAjBtZya6XjqKtS89InVpRERUQ+wZIqomtVqNdevWoYWPEwDg0M1MvLrqADJyOXErEZElYhgiqgEHBwdsX/0FbJJioFDZYOOFDDy0aCeW74tFfpFO6vKIiKgaGIaIasjLwx2HFz0H++PfoTDpJrIK9PhgazR6f/wHzsdnSF0eEREZiWGIqBa8vLywd80XcD74HyRv/T8gNx3Z+YVo5OkgdWlERGQkhiGiWvL19cXuXTvhmxOLW1+OQ/b/FiE98Q4AQAiB9369yJ4iIiIZYxgiMoGAgADs3r0bwYEBiD2xFw8//DCuXbuG3y7cxbcHruPx/xzA9HWnEZeaK3WpRET0DwxDRCYSFBSEP/74A82bN8fNmzfRo0cP2OenYEiEPwDg5zMJ6P3xH3jv14tIyymUuFoiIirB6TiMwOk4qDru3LmDRx99FBcvXoSvry927twJuAdiwbZoHLyaAgBw1qgxuWdTTHioCWzV/DcJEVFd4HQcRBLx8/PD3r17ER4ejnv37qFnz57IjY/B6vGdETWuE0L9XJCVr8WWMwlQKRVSl0tEZPXYM2QE9gxRTaSmpqJfv344fvw4HBwcsHHjRvTr1w96vcDPZ+Lh52qPrk09AQD5RTocjk1BzxbeUCgYkIiITIE9Q0QS8/DwwK5du9CnTx/k5ubiiSeewKpVq6BUKjCsfUNDEAKAFQevY+x3xzHi6yM4E5cuXdFERFaIYYioDjk7O+PXX3/FyJEjodVq8dxzz2Hx4sVlPqfVCdiqlTh6PRVDvjiIKWtO4WYKJ4AlIjIHXiYzAi+TUW3p9XrMmjULn3zyCQBg2rRp+OSTT6BSqQyfiU/Pw8e/x2DT6XgIAaiVCjzbJQhTH2kGTyc7qUonIrJYvExGJCNKpRIff/wxPvroIwDAZ599hkGDBiEzM9PwmQA3e3zydAT+N7U7erTwhlYvsPLQDbz360WpyiYisgoMQ0RmNHPmTGzYsAH29vbYunUrunXrhhs3bpT6TCt/F0SN64Q1EzqjXSM3TOvd3PBeZn4RtDq9masmIqrfeJnMCLxMRqZ24sQJDBo0CHfu3IG3tzd+/vlnPPjgg1W2m7nhT5y+lYbX+oWgTytfPnlGRFQJXiYjkrEHHngAx44dQ7t27ZCUlIRevXohKiqq0jZZ+UXYG5OIa0k5mLjqJIZ/dRgnb6aZqWIiovqLYYhIIg0bNsT+/fsxZMgQFBYW4vnnn8eUKVNQWFj+VB3OGhvsntkT/+rZFBobJU7cTMOTXx7CpFUncC0p28zVExHVH7xMZgReJqO6pNfr8d577+Gdd96BEAJdunTBjz/+iICAgArb3M3Ix6c7LmPDyTjoBaBSKrB0VHs81rqBGSsnIpI3XiYjshBKpRLz5s3Dr7/+Cjc3Nxw5cgTt27fH3r17K2zTwFWDRU+1xfbpD6N3iA9cNOpSgzgSEZHxGIaIZGLAgAE4ceIEwsPDkZiYiEcffRQLFy6EXl/x02MtfJ3x7fMd8fsrPeCisQEACCEwadUJrDp8A0V88oyIqEoMQ0Qy0rRpUxw6dAijR4+GTqfDnDlz8Nhjj+HOnTuVtvN2/ntQxj0xifjtwj28tfkC+n66D1vP3QGvhhMRVYxhiEhmHBwcEBUVhW+//RYODg7YuXMnwsPDsW3bNqPad2/ujXcHt4anoy2uJ+fgXz+cwrAvD+HY9dQ6rpyIyDLxBmoj8AZqkkp0dDRGjBiBs2fPAgBmzJiBDz/8EHZ2VU/PkV2gxdf7YvHN/ljkFuoAAI+G+mDx8HC4OdjWad1ERHLAG6iJ6oHQ0FAcPXoUU6dOBQB88skn6Nq1K86fP19lWyc7NWb0aYG9s3piVOdGUCkVuJ2WB+e/7i0iIqJisg5D2dnZmD59Ovz9/aHRaBAREYF169ZV2e6nn35CZGQkmjVrBnt7ewQHB2PUqFG4cuWKGaomMi2NRoPPPvsMW7ZsgaenJ06fPo0OHTpg0aJF0Ol0Vbb3cdbgg6Ft8PsrD2PRk22hUhaPWp1fpMMXe64iM7+orneBiEjWZH2ZrG/fvjh+/DgWLlyIFi1aYM2aNfjmm2/www8/YOTIkRW269y5Mxo0aIAhQ4agSZMmiIuLw4cffoi4uDgcOXIErVu3rlYdvExGcnHnzh1MmjQJv/zyCwCgS5cuWLlyJVq2bFntdX259xoWbb8ED0dbTH2kGUZ1DoKtWtb/PiIiqhZj//6WbRjaunUrBg4ciDVr1iAyMtKwvG/fvrhw4QJu3boFlUpVbtvExET4+PiUWpaQkIDg4GA899xz+Oabb6pVC8MQyYkQAt9//z2mTZuGzMxMaDQaLFiwAFOnTq3wnCjPnkuJeO9/FxGblAMACPSwx6zHQvB4Gz8olZzzjIgsn8XfM7Rp0yY4OTlh+PDhpZaPHTsWCQkJOHr0aIVt/xmEAMDf3x8NGzZEXFycyWslMieFQoExY8bg/Pnz6NOnD/Lz8/HKK6+gW7duhhutjdErxAe/T38YHw5tA29nO8Sl5mHa2tMY/MVBHLqaXId7QEQkL7INQ+fPn0doaCjUanWp5W3btjW8Xx2xsbG4efOmUZfICgoKkJmZWepFJDeBgYH47bff8NVXX8HZ2RlHjx5Fhw4d8PrrryM3N9eodahVSozs3Ah/zOqJV/u0gKOtCufiMxB1+EbdFk9EJCOyDUMpKSnw8PAos7xkWUpKitHr0mq1GD9+PJycnPDKK69U+fkFCxbA1dXV8AoMDDS+cCIzUigUmDRpEqKjozFs2DBotVosWrQIbdq0wY4dO4xej4OtGlN7N8cfs3thTNcgzO4XYngvMSsfCel5dVE+EZEsyDYMAcW/6Gvy3v2EEBg/fjz279+P77//3qhgM2fOHGRkZBhevLRGchcQEICNGzfi559/RsOGDREbG4u+ffsiMjISt2/fNno9Xk52eGdwGJp6OxmWfbQ9Bj0X78WCbdHIyOWTZ0RU/8g2DHl6epbb+5OaWjyKbnm9Rv8khMCECROwevVqrFy5EoMHDzZq23Z2dnBxcSn1IrIEgwcPxsWLFzFt2jQoFAqsW7cOLVu2xIcffoj8/Pxqr0+r0yM+PQ+FWj2W/RGLhz/ag+X7YpFfVPUj/URElkK2YahNmzaIjo6GVqsttfzcuXMAgLCwsErblwSh7777Dt988w2effbZOquVSE6cnZ2xZMkSnDhxAt26dUNubi7mzp2L1q1bY/PmzdWap0ytUuKHCZ2x4vkH0MLXCRl5RfhgazR6f/wHfjp1G3q9LB9GJSKqFtmGoaFDhyI7OxsbN24stTwqKgr+/v7o3LlzhW2FEHjhhRfw3XffYdmyZRg7dmxdl0skO+3bt8f+/fvxww8/wN/fH7GxsRgyZAgee+wxXLhwwej1KBQKPBLii20vP4x/P9kWDVw0iE/Pw4z1f2LFwet1uAdEROYh2zDUv39/9OnTB5MnT8by5cuxZ88eTJw4Edu3b8e///1vw3gq48ePh1qtxs2bNw1tp02bhm+//RZjx45FmzZtcOTIEcPr9OnTUu0SkdkpFAqMHDkSMTExmDNnDmxtbbFjxw60bdsW48ePr9b9RCqlAk93DMSemT0xu19LNPJwwPAH/r4Hr1Crr4tdICKqc7IddBEono5j7ty5WL9+PVJTUxESEoI5c+ZgxIgRhs88//zziIqKwvXr1xEcHAwACA4OLhWO7hcUFIQbN25Uqw4Oukj1xdWrV/Haa6/hp59+AlA81cfLL7+M119/HW5ubtVal04vDFN7CCHwzLIj8HfT4NW+LRHo4WDq0omIqs3iR6CWE4Yhqm8OHz6M2bNn48CBAwCKH0iYO3cupkyZAjs7u2qv7+ztdAz6/CAAwFalxOiuQXipVzO4O9qatG4iouqw+BGoiajudO3aFfv27cOWLVvQqlUrpKam4tVXX0Xz5s3x1VdfobCwsFrra9vQDb9OfQjdmnmiUKfHtweu4+GP9mDp3qt88oyIZI89Q0ZgzxDVZ1qtFt9//z3efvttxMfHAwAaNWqEN954A2PHjoWtrfG9O0II7LuSjIXbLiH6TvHI7Q1cNFg3sQuCvRzrpH4iooqwZ4iIjKJWqzFu3DhcvXoVn332Gfz8/HDr1i28+OKLaN68Ob7++muje4oUCgV6tPDG/6Y+hE+eDkeAmz1c7W14DxERyRp7hozAniGyJnl5eVi+fDkWLlyIO3fuACjuKZo5cybGjRsHR0fje3jyi3S4m5Fv6BXKL9Jh1o9nMf6hxogIdKuL8omIDHgDtQkxDJE1Ki8UeXp64qWXXsJLL70ELy+vaq9z2R/XsGDbJQDAwLZ+mP1YSwR58vIZEdUNhiETYhgia5aXl4eoqCgsXrwY165dAwDY29tjwoQJmDFjhmFIC2PEp+fh499jsOl0PIQA1EoFRnVuhKm9m8PLqfpPsRERVYZhyIQYhogAnU6HjRs3YtGiRTh16hQAQKVS4emnn8a0adPQuXNnoydQvpiQiUXbL+GPy0kAACc7NV7s0QRTejUzeh1ERFXhDdREZFIlwefEiRPYuXMn+vTpA51Oh7Vr16Jr167o1KkTVq1ahYKCgirX1crfBVHjOmHNhM5oE+CK7AItzt7OYBAiIkmwZ8gI7BkiKt/p06fx2WefYe3atYYQ5OPjg4kTJ+LFF19EQEBAlevQ6wV+PXcHrf1d0NTbCQBwNyMfZ2+no08rXwYkIqoxXiYzIYYhosolJSVh+fLl+PLLLw3znanVagwbNgyTJk1Cz549oVQa3xH92o9n8d8TcegY7I7X+4eiQ5B7XZVORPUYL5MRkdl4e3vjjTfewPXr17FhwwZ0794dWq0W69evR+/evdGiRQssXLgQd+/erXJdQgj4uthBY6PE8RtpePLLQ3hx1UlcS8o2w54QkTViz5AR2DNEVH1nzpzBsmXL8MMPPyArKwtA8X1HTzzxBF544QU89thjUKlUFba/m5GPT3dcxoaTcdALQKVUYETHQLz8aHP4OGvMtRtEZMF4mcyEGIaIai4nJwfr16/H8uXLcfjwYcPywMBAjB49GqNHj0ZISEiF7S/fy8K/t1/CzuhEAMC/ejbF7H4Vf56IqATDkAkxDBGZxoULF/DNN9/g+++/R2pqqmH5Aw88gNGjR2PEiBHw8fEpt+3R2BR8sfca/jOiHVwdbAAA9zLz4eFoCxsVr/gTUVkMQybEMERkWvn5+diyZQtWrVqF7du3Q6vVAii+jNavXz88++yzGDx4MOzt7StchxACTy87jOTsQsx6rCX6hzXgk2dEVArDkAkxDBHVnaSkJKxbtw6rVq3C8ePHDcudnJwwaNAgDB8+HP369YNGU/o+ofj0PAz6zwGk5BRPItuukRvm9A9Fp8YeZq2fiOSLYciEGIaIzOPSpUtYvXo1Vq9ejZs3bxqWOzs744knnsDTTz+Nxx57zBCMsgu0+HpfLJbvi0VekQ4A8GioD17rF4Lmvs6S7AMRyQfDkAkxDBGZl16vx9GjR7FhwwZs2LDBMHYRUByMSnqM+vTpAwcHByRm5uP/dl3Bf4/HQacXUCqAdRO7speIyMoxDJkQwxCRdCoLRvb29ujTpw8GDRqExx9/HNlKR3y0PQaxydnYOq071H/dWC2E4P1ERFaIYciEGIaI5OH+YPTTTz+VupSmUCjQpUsXDBo0CH0GPIH2bVpBoVAgv0iH4V8dxrD2ARjVOQi2aj55RmQtGIZMiGGISH6EEDh37hw2b96MLVu24MSJE6Xeb9asGR5//HHYt+mLNZf1AIBGHg6Y+VhLPN7GD0ole4qI6juGIRNiGCKSv/j4ePzyyy/YsmULdu3ahcLC4qfMoFDCvcMAuD88GjobRwBAmwAXzOkfigebeUlYMRHVNYYhE2IYIrIsWVlZ+P3337F9+3Zs374dt2/fhsLGDi4dh8Kl0zAo7RwAACGuenw/8SH4eHIiWKL6iGHIhBiGiCyXEAIXL17Eb7/9hu3bt2P/sTOw7zgMzhH9kRd7Aik/f4gOHTqgxyO9kRf8MB7pEIK2QV4I8nTkyNZEFo5hyIQYhojqj5ycHPzxxx/Y+Ps+7P/jD1w5cwQAYOPdGP7j/mP4nBJ6+Dup0DbYB6F+rujR0httG7pJVDUR1QTDkAkxDBHVX7dv38aePXvwyx/HcTTDGYX2nrDxDDRcSivRXh2Hf/Vshi5duiCtUIlPdlxGc18ntPR1RgtfZwS42fOmbCKZYRgyIYYhIusghMD169exa9dubNt3FEejbyJb5QIbr0bIPvs7Cm5fgEqlQmifSGSFjyjV1sFWheY+Tmju64zIToHoEMQBH4mkxjBkQgxDRNZJCIFLly5h7969OHjwIA4cOICbN29C7dEQDi26wtY7CDZeQbD1DARUakO7/4yIwBMRAQCAA1eS8enOy2jh64TmPs5o2cAZzX2d4O1kx4EgieoYw5AJMQwRUYnbt28bgtGBAwdw9uxZ6AWgdvf/Kxw1gv7qQbQPaYxOnTohJ/BB/C/epsx63B1s0NzXGW8MCEVEoBsAQK8XvNRGZEIMQybEMEREFcnMzMSRI0dw4MABHDx4EMeOHUN2drbhfZWLN+wCQuEe3AoejVsDLv7IEnYo+cX769SHEBbgCgD47uB1LN17rVQvUgvf4ktvLpqygYqIKscwZEIMQ0RkLJ1Oh5iYGBw7dgxHjx7FsWPHcPbsWWi1WsNnFGpbqD0aomHrjmjnBXSIaIv27dtjW7I7Np9PLne9fq4arBrfCc18nAEAqTmFsFMr4WinLvfzRMQwZFIMQ0RUG3l5eTh9+jSOHTtmeF27dq3M5xQ2Gvi1bIeg8K5wDQyB3tkXqTo7JOUUB6lz8/vC+a8eovlbLmDloRto6G6PFn890dbC1wktfJ3RzMcJGhuVWfeRSI4YhkyIYYiITC0lJQVnzpzBqVOncPr0aZw+fRoxMTEo71eym7cfQjo+jAeaeCMsLAxt2rTBtzFK7IpJKXfdSgVw+q2+cHUoDk4XEzKhVAJNvJw4US1ZFYYhE2IYIiJzyMnJwdmzZ0sFpPPnz/89z9o/NGoWisbtusGzSRhUHg2Ro3JBfLaAWqXAiTf7GD73/HfHsDcmCWqlAsFejmjp62wYI6m5rzOaejvyyTaqlxiGTIhhiIikUlhYiOjoaJw5cwbnz5/H+fPnce7cOcTHx5f7eZVKhWat2qJtSDOEhoYiJCQEW1J8cC6pCNkFujKfd9aocXZeX0MY2nruDlRKBVr6OiPQwwEqPt1GFszYv7955x0RkYzZ2toiPDwc4eHhpZanpaUZwlFJQDp37hzS09MRc+40Ys6dLrOuRiHhCGzdCa5BoVC6ByBb5QxvV/tSn/notxhcT84BANiplWju64QWPsU9SK39XfBwC++621kiibBnyAjsGSIiSyCEQEJCgiEgXbp0yfBKTi7/KTUAcHV1RUhICFqGhCChYW/k2LgiuUCFQn3pz4UFuODXqd0N///x7zFwtbcx3MDt68KBJEleeJnMhBiGiMjSJScnIyYmplRAunTpEmJjY6HX68s2UCihdmsAzyZh8GraFva+jeHvYoOnQx3QrFkzBDVugu5LjqNI9/dfIS4aNVr8dR9SlyYeGPzXKNxEUmEYMiGGISKqrwoKCnD16lVDOLp69arhdffu3QrbKWw08OkxEi6BIVC5ByDfxgUCf/cK9W/tiy9HPwCgeGTt51ceR7CnQ6lhANwcbOt8/8i6MQyZEMMQEVmjrKwsxMbGGsLRlStXDH8ucwO3Sg0bj4bFc7V5NUJh0nW4ZcYiODgYfs3CcMJvUJn1+zjboYWvMwaF++PpjoFm2iuyJgxDJsQwRERUWm5ubqmgdOPGDcPr+vXryM3NNXxWYecIh+adYeNVPHebrVcQ1K4+hvcbZl7AQy6pCAwMhLNPQ3wWbYvmPs4IC/Qw9CQ193WCgy2f+aHqYRgyIYYhIiLjCSGQnJxcKiDdH5Ru3LiBfB3+CkaNUHgvFoX3ikfk1gRHwPeZ98tbKRwVBejukYOBoe4IDAxEA/8AuLm5Q8OQRBVgGDIhhiEiItMRQiApKckQjuLi4v5+JdxDfK4S2SpnqD0DYetd3JukcnQHACRvXYKcczsAAHYNW8M3cgEUuamwE4VwUAs42ynh7mALH1dHPNTEDV1CGsLPzw9qOwdk5mvh5mDDqUqsCMcZIiIiWVIoFPDx8YGPjw86depU7mcKCwuRkJBgCElXbl3CpTuZyGzuiXu2HRAXF4dcz4ZQKJWAkxcKABQASANwKx9APrB2xYfIOb8bAOAW2g2ug+YAAJT6ItgptHBUA64aNTyd7DCkrQ8GdGgKV1dXpOUW4eztdLg72MLD0RZuDjZwslNz2IB6jGGIiIhkx9bWFsHBwQgODq7wM/n5+Th39SZOX4lH3L1UJKRkIDEjB6nZBcgs0MHOSYW7Li7IzMxEoVBA6HVQKFXQK22QBxvk6YDkHOBajh5bX56NnAu7YWtrC5+IR6Dq9VKpbSkh4KAWcLFTYmS4O57s2BheXl5IzNHif2cT4OZgC3cHW7g72Pz15+L/cgRvy8DLZEbgZTIiIsuVk5ODO3fuID4hATdu38X1hCTcTkrDnZRMJGXmIT23ECnn9yP1ZjQAQBPcDu49x0Jp7wylvQuUNnal1pf86yfIuVDc4+QT8QjsH5tR4bafa61B5AP+8PT0RJrOFsv23ygVmkp6ntwdbBHgbg8XjU3dfRFWiPcMmRDDEBFR/ZeXl4fExETD6969e0hMTERCYjISkjOQmJ6DlOx8pFy/iKRbV6DX62HboDmcHxgElb0zlBoXKO2d//qzEwAg+dePkXNhDwDAvmlH+Dw1r8Lt9/HMwIBm9vDy8kI6nPD58XR4OdvDw8muVI+Tu4MtwgPd0NjLEUDxOE4KBXgZrxwMQybEMERERPfT6/VISUkpE5xK/nwvMQl307KQlnQPqYl3kJqaCrW7Pxyad4XSweWvwFTc86RycIFS44zUXcuRG/0HgKqDU1hhNDo4Z8Hd3R1Zdt5YecsVTrZKuGnUcHe0g5eLPbxdNHBzsEXvEB88EOwBAMgr1CE+Pc9qLuMxDJkQwxAREdWGVqtFWloaUlJSkJycjOTk5Er/nJJdgFyNN5QaJygdXIpDk8a5+M8aF2Qe34T82BMAAPumneDz1NsVbtvm3Gb4ZlyEu7s7lD7N8Kf3o3+9I2CvFHCyVcBFo4aHoy2GtPXBoPZBcHJyQmaeFgevJRsu47k72Frc03gMQybEMEREROam0+mQlpZWKiylpKQgLS0NqampSEtLK/5zegZScoqQnluErEI9cnUKwNYRKgdXKO2dkXvpAAri/7ofKigc3kPmGC7j/VPqzmXIOvkLlEol3Jt3gNOQsr1TKqGFnUKHDg4peNBbC1dXV8DeFcdT7eDl4gBfd0f4e7jC38sVnk52kj6Nx0friYiILJhKpYKXlxe8vLyq1U4IgaysrPtC0whDcCpedgYpaelIzshFSk4B0vOKkJWvQ65OgcK4cwCKLwNmZWZAffsCVPYuf13Sc4ZCqYJOoUYu1Ni85ResPvkLAMAuIBQNnv0Ifw9wcLtUTbaXd8An8QRcXFxg5+GPeJ/OcFQDTrYKuGrUeMhXh9EjR8DR0dEE31z1sWfICOwZIiIiayCEQG5uLjIyMkq9MjMzkZ6egaT0LCRl5iIlKx9FmUnIT7uHzMxMpBTZINO3HQoVttCpNVDYOf31NJ4zlDYapO74ClmnfgUA2AW0QoNn/11qu7c+fhL3EuLg7e1t0v1hzxARERFVi0KhgKOjIxwdHeHv71/j9eTn5xuCVFJaBjIfeRl52WORkZGBhLQcXMiIQ0aeFtlFAnlagTb9+kja2cAwRERERCal0Wig0Wjg6+uLFka1mFbHFVVOKenWiYiIiCTGMERERERWjWGIiIiIrBrDEBEREVk1hiEiIiKyagxDREREZNUYhoiIiMiqyToMZWdnY/r06fD394dGo0FERATWrVtnVNvExEQ8//zz8PLygoODA7p27Ypdu3bVccVERERkaWQ96OKwYcNw/PhxLFy4EC1atMCaNWsQGRkJvV6PkSNHVtiuoKAAvXv3Rnp6OpYsWQIfHx988cUX6NevH3bu3IkePXqYcS+IiIhIzmQ7N9nWrVsxcOBAQwAq0bdvX1y4cAG3bt2CSqUqt+3SpUsxZcoUHDp0CF27dgUAaLVahIeHw8nJCUePHq1WLZybjIiIyPIY+/e3bC+Tbdq0CU5OThg+fHip5WPHjkVCQkKlgWbTpk1o2bKlIQgBgFqtxrPPPotjx44hPj6+zuomIiIiyyLby2Tnz59HaGgo1OrSJbZt29bw/oMPPlhh2+7du5dZXtL2woULCAgIqHDbBQUFKCgoMPx/RkYGgOKESURERJah5O/tqi6CyTYMpaSkoEmTJmWWe3h4GN6vrG3J56rbFgAWLFiAd955p8zywMDAStsRERGR/GRlZcHV1bXC92UbhgBAoVDU6L3atp0zZw5mzJhh+H+9Xo/U1FR4enpW2bY6MjMzERgYiLi4uHp5L1J93z+g/u9jfd8/oP7vI/fP8tX3fazL/RNCICsrC/7+/pV+TrZhyNPTs9wenNTUVAAot+fHFG0BwM7ODnZ2dqWWubm5VVVyjbm4uNTLH/AS9X3/gPq/j/V9/4D6v4/cP8tX3/exrvavsh6hErK9gbpNmzaIjo6GVqsttfzcuXMAgLCwsErblnyuum2JiIjIusg2DA0dOhTZ2dnYuHFjqeVRUVHw9/dH586dK2176dKlUk+cabVarF69Gp07d66yu4yIiIish2wvk/Xv3x99+vTB5MmTkZmZiWbNmmHt2rXYvn07Vq9ebRhjaPz48YiKisK1a9cQFBQEABg3bhy++OILDB8+HAsXLoSPjw+WLl2KmJgY7Ny5U8rdKsXOzg7z5s0rc0muvqjv+wfU/32s7/sH1P995P5Zvvq+j3LYP9kOuggUT8cxd+5crF+/HqmpqQgJCcGcOXMwYsQIw2eef/55REVF4fr16wgODjYsv3fvHmbPno1ff/0Vubm5iIiIwHvvvYdHH31Ugj0hIiIiuZJ1GCIiIiKqa7K9Z4iIiIjIHBiGiIiIyKoxDBEREZFVYxiqA9nZ2Zg+fTr8/f2h0WgQERGBdevWGdU2MTERzz//PLy8vODg4ICuXbti165ddVxx9dR0/1auXAmFQlHu6+7du2ao3DhZWVmYPXs2+vbtC29vbygUCsyfP9/o9pZwDGuzj5ZwHHfv3o1x48YhJCQEjo6OCAgIwODBg3Hy5Emj2sv9GNZm/yzh+J05cwYDBw5Eo0aNYG9vDw8PD3Tt2hWrV682qr3cjx9Qu320hGNYnm+++QYKhQJOTk5Gfd6cx1G2j9ZbsmHDhuH48eNYuHAhWrRogTVr1iAyMhJ6vR4jR46ssF1BQQF69+6N9PR0LFmyBD4+Pvjiiy/Qr18/7Ny5Ez169DDjXlSspvtX4rvvvkNISEipZZ6ennVVbrWlpKTg66+/Rnh4OIYMGYJvvvnG6LaWcgxrs48l5Hwcv/zyS6SkpODll19Gq1atkJSUhI8//hhdunTBb7/9hkceeaTCtpZwDGuzfyXkfPzS09MRGBiIyMhIBAQEICcnBz/88ANGjx6NGzdu4M0336ywrSUcP6B2+1hCzsfwn+Lj4zFz5kz4+/sbJj+vjNmPoyCT+t///icAiDVr1pRa3qdPH+Hv7y+0Wm2Fbb/44gsBQBw6dMiwrKioSLRq1Up06tSpzmqujtrs33fffScAiOPHj9d1mbWi1+uFXq8XQgiRlJQkAIh58+YZ1dYSjqEQtdtHSziO9+7dK7MsKytL+Pr6it69e1fa1hKOYW32zxKOX0U6d+4sAgMDK/2MJRy/yhizj5Z4DB9//HHxxBNPiDFjxghHR8cqP2/u48jLZCa2adMmODk5Yfjw4aWWjx07FgkJCaVGxS6vbcuWLdG1a1fDMrVajWeffRbHjh1DfHx8ndVtrNrsn6Uo6W6uCUs4hkDt9tES+Pj4lFnm5OSEVq1aIS4urtK2lnAMa7N/lszLywtqdeUXNCzh+FXGmH20NKtXr8Yff/yBpUuXGt3G3MeRYcjEzp8/j9DQ0DI/zG3btjW8X1nbks+V1/bChQsmrLRmarN/JR5//HGoVCp4eHhg2LBhRrWxFJZwDE3F0o5jRkYGTp06hdatW1f6OUs9hsbuXwlLOH56vR5arRZJSUlYunQpfvvtN7z22muVtrG041eTfSxhCccwMTER06dPx8KFC9GwYUOj25n7ONav+CkDKSkpaNKkSZnlHh4ehvcra1vyueq2NZfa7F+DBg0wd+5cdOnSBS4uLjh37hwWLlyILl264ODBgwgPD6+zus3FEo5hbVnqcZwyZQpycnIwd+7cSj9nqcfQ2P2zpOP3r3/9C8uWLQMA2Nra4rPPPsOkSZMqbWNpx68m+2hpx7Bly5aYPHlytdqZ+zgyDNWByi4/VHVpojZtzaWmNfbr1w/9+vUz/P/DDz+MgQMHok2bNnj77bexefNmk9YpFUs4hrVhicfxrbfewg8//ID//Oc/6NChQ5Wft7RjWJ39s6Tj98Ybb2DChAlITEzEL7/8gpdeegk5OTmYOXNmpe0s6fjVZB8t5Rhu3LgRv/zyC06fPl2j792cx5FhyMQ8PT3LTaypqakAUG7SNUVbczF1jcHBwXjooYdw5MgRk9QnNUs4hnVBzsfxnXfewfvvv48PPvgAL730UpWft7RjWN39K49cj1+jRo3QqFEjAMCAAQMAAHPmzMGYMWPg7e1dbhtLO3412cfyyO0YZmdnY8qUKZg6dSr8/f2Rnp4OACgsLARQ/DSdjY0NHB0dy21v7uPIe4ZMrE2bNoiOjoZWqy21/Ny5cwCAsLCwStuWfK66bc2lNvtXESEElMr68aNoCcewrsjxOL7zzjuYP38+5s+fjzfeeMOoNpZ0DGuyfxWR4/H7p06dOkGr1SI2NrbCz1jS8SuPMftYETkdw+TkZNy7dw8ff/wx3N3dDa+1a9ciJycH7u7uGDVqVIXtzX4cTf58mpXbunWrACDWrVtXanm/fv2qfPR86dKlAoA4cuSIYVlRUZFo3bq16Ny5c53VXB212b/yxMbGCicnJzFkyBBTlmky1X3s3BKO4T9Vdx/LI8fj+O677woA4s0336xWO0s5hjXdv/LI8fiVZ/To0UKpVIrExMQKP2Mpx68ixuxjeeR2DPPy8sSePXvKvB577DGh0WjEnj17xLlz5ypsb+7jyDBUB/r06SPc3d3F119/LXbv3i1eeOEFAUCsXr3a8Jlx48YJlUolbty4YViWn58vWrduLQIDA8UPP/wgduzYIYYOHSrUarXYu3evFLtSrpruX+/evcU777wjNm3aJHbt2iX+7//+T/j7+wtnZ+dKTwopbN26VWzYsEGsWLFCABDDhw8XGzZsEBs2bBA5OTlCCMs+hkLUfB8t4TguXrxYABD9+vUThw8fLvMqYanHsDb7ZwnH74UXXhCvvvqq+O9//yv27t0rfvzxR/HMM88IAGLWrFmGz1nq8ROidvtoCcewIuWNMySH48gwVAeysrLEtGnTRIMGDYStra1o27atWLt2banPjBkzRgAQ169fL7X87t274rnnnhMeHh5Co9GILl26iB07dpix+qrVdP+mT58uWrVqJZydnYVarRb+/v7i2WefFTExMWbeg6oFBQUJAOW+SvbJko+hEDXfR0s4jj169Khw3+7vELfUY1ib/bOE47dixQrRvXt34eXlJdRqtXBzcxM9evQQq1atKvU5Sz1+QtRuHy3hGFakvDAkh+OoEEIIU152IyIiIrIk8rjTioiIiEgiDENERERk1RiGiIiIyKoxDBEREZFVYxgiIiIiq8YwRERERFaNYYiIiIisGsMQERERWTWGISIiIrJqDENEZNGOHTuGZ555BsHBwbC3t4ePjw+GDh2Ka9euSV0aEVkITsdBRBbt66+/RnJyMlq3bg13d3fExcXhww8/hFqtxp9//il1eURkARiGiKje0Ov10Ov1iIqKwoQJE5CWloaNGzfi5ZdfBgAUFhZCCAE7OzsAQKdOnbB79+4abevLL7/E8uXLce7cOcydOxfz58831W4QkZkxDBGRxRJCYOPGjVi6dCkuXbqEu3fvouRXmlKpRG5uriH4AMDEiRPh5OSETz75pNbb/vnnn6FSqfD999+jdevWDENEFoz3DBGRxZo4cSIiIyPRqlUrLF26FPv378fx48cRHh6OZs2alQpCAHD27Fm0bdvWJNseMmQInnjiCbi6uppkfUQkHbXUBRAR1URMTAy++eYb/Pvf/8asWbMMy5OTk3HhwgU8/fTTpT4vhMD58+dNFoaIqP5gzxARWaSbN28CAFq1alVq+csvvwytVosHHnig1PJr166hoKAArVu3NluNRGQZ2DNERBYpPDwcDg4OeOutt6BQKJCXl4fly5fj6tWrAFAmDP35559o0aJFmUtnJXr37o2DBw+W+96sWbPw3nvvmXYHiEg2GIaIyCL5+vpi/fr1mDlzJoYNG4amTZti0qRJyMrKwttvv4127dqV+nxV9wvt2rWrrksmIpliGCIiizVw4EAMHDiwzPK5c+eWWXb27Fl06tTJZNvWarXQarXQ6XTQarXIz8+HjY0NVCqVybZBRObBe4aIyCqY8kkyAHj//fdhb2+PlStX4oMPPoC9vT1WrVplsvUTkflwnCEiIiKyauwZIiIiIqvGMERERERWjWGIiIiIrBrDEBEREVk1hiEiIiKyagxDREREZNUYhoiIiMiqMQwRERGRVWMYIiIiIqvGMERERERWjWGIiIiIrNr/A+Gg95MLlqn4AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "########################\n",
    "## Figure PlotOPRawVSFOC\n",
    "########################\n",
    "\n",
    "\n",
    "# get the VP for fine grids of a\n",
    "\n",
    "aVec_fine = np.linspace(0.0001, 4, 1000)\n",
    "vpVec_fine = [gothic.VP_Tminus1(a) for a in aVec_fine]\n",
    "\n",
    "# Examine the interpolated GothicVP function:\n",
    "vpVec = [gothic.VP_Tminus1(a) for a in aVec]\n",
    "\n",
    "## this is the interpolated gothic v func\n",
    "gothicvpFunc = InterpolatedUnivariateSpline(aVec, vpVec, k=1)\n",
    "\n",
    "plt.plot(aVec_fine, vpVec_fine, \"k-\")  ## gothic v'(a)\n",
    "plt.plot(aVec, gothicvpFunc(aVec), \"--\")  ## 'gothic v'(a)\n",
    "plt.ylim(0.0, 1.0)\n",
    "plt.xlabel(r\"$a_{T-1}$\")\n",
    "plt.ylabel(r\"$\\mathfrak{v}^{\\prime}_{T-1}$\")\n",
    "plt.title(\n",
    "    r\"$\\mathfrak{v}^{\\prime}(a_{T-1})$ (solid) and $\\grave \\mathfrak{v}^{\\prime}(a_{T-1})$ (dashed)\"\n",
    ")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The new consumption function (long dashes) is a considerably better approximation of the true consumption function (solid) than was the consumption function obtained by approximating the level of the value function (short dashes). (See Figure 8)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "code_folding": [],
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x16457e700>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#########################\n",
    "## Figure 8\n",
    "########################\n",
    "\n",
    "plt.plot(mVec_fine, cVec, \"k-\", label=r\"$c_{T-1}(m_{T-1})$\")  ## real c func\n",
    "plt.plot(\n",
    "    mVec, cVec1, \"-.\", label=r\"$\\grave c_{T-1}(m_{T-1})$ via $\\mathfrak{v}$\"\n",
    ")  ## interpolated c func based on interpolated level of value\n",
    "plt.plot(\n",
    "    mVec,\n",
    "    cVec2,\n",
    "    \"r--\",\n",
    "    label=r\"$\\grave \\grave c_{T-1}(m_{T-1})$ via $\\mathfrak{v}^{\\prime}$\",\n",
    ")  ## interpolated c func based on interpolated marginal value\n",
    "plt.xlabel(r\"$m_{T-1}$\")\n",
    "plt.ylabel(r\"$c_{T-1}$\")\n",
    "plt.title(\n",
    "    r\"$c_{T-1}(m_{T-1})$ (solid) versus two methods of constructing $\\grave c_{T-1}(m_{T-1})$\"\n",
    ")\n",
    "plt.legend(loc=4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6. Transformation\n",
    "\n",
    "- See more detailed discussion [here](https://llorracc.github.io/SolvingMicroDSOPs/#Transformation)\n",
    "\n",
    "\n",
    "However, even the new-and-improved consumption function diverges from the true solution, especially at lower values of m. That is because the linear interpolation does an increasingly poor job of capturing the nonlinearity of $v′_{T −1}(a_{T −1})$ at lower and lower levels of a."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "cVec3 = []\n",
    "cVec4 = []\n",
    "\n",
    "for a in aVec:\n",
    "    c = gothic.C_Tminus1(a)\n",
    "    cVec3.append(c)\n",
    "\n",
    "for a in aVec_fine:\n",
    "    c = gothic.VP_Tminus1(a) ** (-1 / rho)\n",
    "    cVec4.append(c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7. The Self-Imposed ‘Natural’ Borrowing Constraint and the $a_{T−1}$ Lower Bound\n",
    "\n",
    "- See more detailed discussion [here](https://llorracc.github.io/SolvingMicroDSOPs/#The-Self-Imposed-Natural-Borrowing-Constraint-and-the-a-Lower-Bound)\n",
    "\n",
    "As the marginal utility from zero consumption goes to infinity, the agents will try to have at least a little of consumption in the \"worst\" case. This cutting-edge case happens when the $a_{T-1}$ is exactly equal to the present value of the worst possible transitory shock. As a result, there is a self-imposed borrowing constraint, i.e. a lower bound for the value of $a_{T-1}$. \n",
    "\n",
    "In general, preset grids of a may not necessarily include this point. We hence insert this self-imposed bound to the beginning of the list of grid to make sure the consumption policy close to this bound is correctly interpolated. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "code_folding": [],
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "## Augment the mVec and cVec with one point with bottom\n",
    "\n",
    "aVecBot = np.insert(aVec, 0, self_a_min)\n",
    "cVec3Bot = np.insert(cVec3, 0, 0.0)\n",
    "\n",
    "aVecBot_fine = np.insert(aVec_fine, 0, self_a_min)\n",
    "cVec4Bot = np.insert(cVec4, 0, 0.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This ﬁgure well illustrates the value of the transformation (Section 6): The true function is close to linear, and so the linear approximation is almost indistinguishable from the true function except at the very lowest values of $a_{T−1}$. (See Figure 9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "code_folding": [],
    "lines_to_next_cell": 2,
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x164820dc0>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "##############\n",
    "## Figure 9\n",
    "##############\n",
    "\n",
    "\n",
    "plt.plot(\n",
    "    aVecBot_fine,\n",
    "    cVec4Bot,\n",
    "    \"k-\",\n",
    "    label=r\"$(\\mathfrak{v}^{\\prime}_{T-1}(a_{T-1}))^{-1/\\rho}$\",\n",
    ")\n",
    "plt.plot(aVecBot, cVec3Bot, \"--\", label=r\"$\\grave c_{T-1}$\")\n",
    "plt.xlabel(r\"$a_{T-1}$\")\n",
    "plt.ylabel(r\"$\\mathfrak{c}_{T-1}$\")\n",
    "plt.ylim(0.0, 5.0)\n",
    "plt.vlines(0.0, 0.0, 5.0, \"k\", \"-.\")\n",
    "plt.title(\n",
    "    r\"$\\mathfrak{c}_{T-1}(a_{T-1})$ (solid) versus $\\grave \\mathfrak{c}_{T-1}(a_{T-1})$\"\n",
    ")\n",
    "plt.legend(loc=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "## compute gothic_v' as c^(-rho)\n",
    "\n",
    "vpVec_fromc = lambda a: InterpolatedUnivariateSpline(aVecBot, cVec3Bot, k=1)(a) ** (\n",
    "    -rho\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And when we calculate $\\grave{\\grave{\\mathfrak{v}}}^{\\prime}_{T-1}(a_{T−1})$ as $[\\grave{\\mathfrak{c}}_{T-1}(a_{T-1})]^{-\\rho}$  (dashed line) we obtain a much closer approximation of $\\mathfrak{v}^{\\prime}_{T-1}(a_{T-1})$. (See Figure 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#############################\n",
    "## Figure 10\n",
    "############################\n",
    "\n",
    "plt.plot(aVec_fine, vpVec_fine, \"k-\")\n",
    "plt.plot(aVec_fine, vpVec_fromc(aVec_fine), \"--\")\n",
    "plt.xlabel(r\"$a_{T-1}$\")\n",
    "plt.ylabel(\n",
    "    r\"$\\mathfrak{v}^{\\prime}_{T-1},\\quad \\grave \\grave \\mathfrak{v}^{\\prime}_{T-1}$\"\n",
    ")\n",
    "plt.title(\n",
    "    r\"$\\mathfrak{v}^{\\prime}_{T-1}(a_{T-1})$ (solid) versus $\\grave \\grave \\mathfrak{v}^{\\prime}(a_{T-1})$\"\n",
    "    + \"\\n constructed using $\\grave \\mathfrak{c}_{T-1}$ (dashed)\"\n",
    ")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8. Endogenous Gridpoints: Use Algebra to Find $c_{T-1}(m_{T-1})$\n",
    "\n",
    "- See more detailed discussion [here](https://llorracc.github.io/SolvingMicroDSOPs/#The-Method-of-Endogenous-Gridpoints)\n",
    "\n",
    "We now take advantage of the fact that \n",
    "\n",
    "$$m_{T−1,i} = c_{T−1,i} + a_{T−1,i}\\;\\;\\forall a_{i} \\in \\mathbb{A}_{grid},$$\n",
    "\n",
    "to find optimal consumption as a function of $m$, once we have the optimizing choice and $a$ in hand. \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "code_folding": [
     0
    ],
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "# Create the first point in the consumption function:\n",
    "mVec_egm = [self_a_min]  ## consumption is zero therefore a = m here\n",
    "cVec_egm = [0.0]\n",
    "\n",
    "for a in aVec:\n",
    "    c = gothic.C_Tminus1(a)\n",
    "    m = c + a\n",
    "    cVec_egm.append(c)\n",
    "    mVec_egm.append(m)\n",
    "\n",
    "# Set up the interpolation:\n",
    "cFunc_egm = InterpolatedUnivariateSpline(mVec_egm, cVec_egm, k=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compared to the approximate consumption functions illustrated in Figure 8 $\\grave c_{T-1}$ is quite close to the actual consumption function. (See Figure 11)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "code_folding": [],
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '$c_{T-1}(m_{T-1})$ (solid) versus $\\\\grave c_{T-1}(m_{T-1})$ using EGM')"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "####################\n",
    "## Figure 11 ####\n",
    "####################\n",
    "\n",
    "\n",
    "# Plot the first consumption function (c_{T-1}). We will plot the rest in the loop below.\n",
    "# plt.plot(mVec_egm, mVec_egm, color='0.7')    # Gray 45 deg line\n",
    "# plot_m_max = 5.0                               # Max plotting point.\n",
    "# plot_c_max = cFunc_egm(plot_m_max)\n",
    "temp_c_values = cFunc_egm(mVec_egm)\n",
    "\n",
    "plt.plot(mVec_fine, cVec, \"k-\")\n",
    "plt.plot(mVec_egm, temp_c_values, \"--\")\n",
    "plt.xlim(self_a_min, 4.0)\n",
    "plt.ylim(0.0, 3.0)\n",
    "plt.xlabel(r\"$m_{T-1}$\")\n",
    "plt.ylabel(r\"${c}_{T-1}(m_{T-1})$\")\n",
    "plt.title(r\"$c_{T-1}(m_{T-1})$ (solid) versus $\\grave c_{T-1}(m_{T-1})$ using EGM\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 9. Improve the $\\mathbb{A}_{grid}$\n",
    "\n",
    "- See more detailed discussion [here](https://llorracc.github.io/SolvingMicroDSOPs/#Improving-the-a-Grid)\n",
    "\n",
    "We will improve our $\\mathbb{A}_{grid}.$ \n",
    "\n",
    "We use a multi-exponential growth rate (that is $e^{e^{e^{...}}}$ for some number of exponentiations n) from each point to the next point is constant (instead of, as previously, imposing constancy of the absolute gap between points)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "code_folding": [
     2
    ]
   },
   "outputs": [],
   "source": [
    "### This function creates multiple-exp a_grid\n",
    "\n",
    "\n",
    "def setup_grids_expMult(minval, maxval, size, timestonest=20):\n",
    "    i = 1\n",
    "    gMaxNested = maxval\n",
    "    while i <= timestonest:\n",
    "        gMaxNested = np.log(gMaxNested + 1)\n",
    "        i += 1\n",
    "\n",
    "    index = gMaxNested / float(size)\n",
    "\n",
    "    point = gMaxNested\n",
    "    points = np.empty(size)\n",
    "    for j in range(1, size + 1):\n",
    "        points[size - j] = np.exp(point) - 1\n",
    "        point = point - index\n",
    "        for i in range(2, timestonest + 1):\n",
    "            points[size - j] = np.exp(points[size - j]) - 1\n",
    "    a_grid = points\n",
    "    return a_grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "code_folding": []
   },
   "outputs": [],
   "source": [
    "def set_up_improved_EEE_a_grid(minval, maxval, size):\n",
    "    gMinMin = 0.01 * minval\n",
    "    gMaxMax = 10 * maxval\n",
    "    gridMin = log(1 + log(1 + log(1 + gMaxMax)))\n",
    "    gridMax = (\n",
    "        log(1 + log(1 + log(1 + gMaxMax))) - log(1 + log(1 + log(1 + gMinMin)))\n",
    "    ) / size\n",
    "    index = (\n",
    "        log(1 + log(1 + log(1 + gMinMin)))\n",
    "        + (log(1 + log(1 + log(1 + gMaxMax))) - log(1 + log(1 + log(1 + gMinMin))))\n",
    "        / size\n",
    "    )\n",
    "    i = 1\n",
    "    point = 0\n",
    "    points = []\n",
    "    while point < gridMin:\n",
    "        point = point + index\n",
    "        points.append(point)\n",
    "        i += 1\n",
    "\n",
    "    new_a_grid = exp(exp(exp(points) - 1) - 1) - 1\n",
    "    return new_a_grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.00544505 0.01151539 0.01832306 0.02600821 0.03474848 0.04477235\n",
      " 0.05637847 0.06996458 0.08607189 0.10545534 0.12919912 0.15891542\n",
      " 0.19710444 0.24785046 0.31827969 0.42194498 0.58784314 0.88957933\n",
      " 1.57247134 4.        ]\n"
     ]
    }
   ],
   "source": [
    "### create the new grid with multiple exponential approach\n",
    "\n",
    "a_size_splus = 20  ## just need a little more than 5 to cover the whole range of a well\n",
    "\n",
    "aVec_eee = setup_grids_expMult(a_min, a_max, a_size_splus)\n",
    "print(aVec_eee)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Find the consumption function using the improved grid and exogenous gridpoints, and plot against the earlier versions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "code_folding": [],
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a grid: [0.00544505 0.01151539 0.01832306 0.02600821 0.03474848 0.04477235\n",
      " 0.05637847 0.06996458 0.08607189 0.10545534 0.12919912 0.15891542\n",
      " 0.19710444 0.24785046 0.31827969 0.42194498 0.58784314 0.88957933\n",
      " 1.57247134 4.        ]\n"
     ]
    }
   ],
   "source": [
    "cVecBot = [0.0]\n",
    "mVecBot = [self_a_min]  # Use the self-imposed a-min value.\n",
    "\n",
    "for a in aVec_eee:\n",
    "    c = gothic.C_Tminus1(a)\n",
    "    m = c + a\n",
    "    cVecBot.append(c)\n",
    "    mVecBot.append(m)\n",
    "\n",
    "print(\"a grid:\", aVec_eee)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the endogenous gridpoints of $m$ naturally \"bunch\" near the area with the most curvature. \n",
    "\n",
    "It allows a better characterization of the consumption and marginal values of at small values of $a$ (See Figure 12 and 13).\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "code_folding": [],
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '$c_{T-1}(m_{T-1})$ (solid) versus $\\\\grave c_{T-1}(m_{T-1})$\\n using EGM and EEE grid of $a$ (star)')"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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zmvLly5sePXqY9evXP3a/H5aUYx4dHW0++OADU7p0aePs7GyKFy9uBg0aZG7dumX1mCT195mQpHw2GGM/75GEXutp9flgT5+LqfF+yIoUiiTJbty4YRwcHMzXX3+dLs+XmL+I3n//fQOY3bt3p2kt9rTv06ZNM4D55Zdfkrzd9Dpe6Sklx0NSjz29R4zJmp8Nxuj9kFwaUyRJtmfPHqKjo1N0qvDj3Lx5k71797J3716io6M5ffo0e/fuTfAWCm+99Raenp6MHDkyzWoC+9n3O3fuMH78eFq1ahXn0gGJlV7HK72k9HhI6rGX90iMrPbZAHo/pIitU5lkPFOmTDHu7u4mOjo6zZ4j5uq9/3486rTmzZs3m8DAQHPz5s00q8te9v3QoUNm1KhRKbq9Qnocr/SSGsdDUoe9vEcelpU+G4zR+yElLMb8c86liIiISBam7jMRERERFIpEREREAIUiEREREUChSERERARQKBIREREBFIpEREREAIUiEREREUChSERERARQKJIM6uTJk1gsFjp37mzrUiQNlSxZkpIlS9q6jAwjue+L9DjOQUFBlC9fnhw5cmCxWJgyZUqaPp81HTt2pFChQty6dSvdnzupdu3ahcVi4bPPPrN1KVmKQpFIKrJYLI997N271+q6hw8fpl+/fvj5+ZE3b16cnZ3Jly8fzzzzDMOGDePQoUMJPp+joyOnTp1KsK5y5crFLrtu3brU2l27k9Tjn5zfV0p+x1nV119/TZ8+fXB1daVfv36MGjUKf3//dK1h586dLFq0iGHDhpEzZ84kr5/ef4hVrlyZFi1a8O6773Lz5s10eU4BJ1sXIJIcxYoV4/Dhw7i7u9u6FKtGjRqV4LzChQvH+dkYw8iRIxk3bhzGGKpVq0b79u1xd3cnLCyMPXv2MHHiRCZMmMDSpUt55ZVX4qzv5OREZGQk8+bNIzAwMN7zbd26lcOHD8culxUk5fgnZ/nkrpPW7PV98f333wPwww8/ULRoUZvUMGzYMPLkycMbb7xhk+dPjqFDh1KtWjWmTZvGsGHDbF1O1mDbW6+JZC78c4PGpBg5cqQBTKlSpcyOHTusLnP69GnTu3dv8+mnn8Z7vmLFiplKlSoZT09PExUVFW/dzp07G2dnZ/P8888bwPz8889Jqs+WSpQoYUqUKJHo5ZN6/JPz+0rOOvYuqcc5qerXr2/TYxYcHGwsFovp3bt3srdx4sSJx96UOi2UK1fOeHp6msjIyHR93qxK3WeSZjZt2oTFYrHaegEJj2NYsWIF9evXp3Dhwri6ulK4cGFq1apFUFBQ7DLWmrIfnnby5EnatGlD/vz5yZYtG5UrV479a/XfjDFMnTqVcuXKkS1bNooVK0afPn0ICwtL87EWx48f5/3338fV1ZU1a9ZQtWpVq8sVL16coKAgunTpYnV+9+7dOX36ND///HOc6eHh4SxbtoyXXnqJggULJrm++fPn06pVK0qXLk327NnJnTs3NWvWZOHChfGWTcnxnzFjBuXLl489/gEBAYSFhSW53owmqa+9h4/xkSNHePnllylQoAAODg5s2rTpkV08qX2cly5dSu3atXF3dyd79uz4+Pjw/vvvc/fu3dhlAgMDsVgsbNy4EYjb9ZgYixcvpn379pQtW5ZcuXKRN29eqlatyrx585JU6+eff44xhtatW1ud/7jPnMDAQEqVKgXAggUL4uzH/PnzY7eT3PeLtd9ljNatW3P69OlM3e1tT9R9JnZl1qxZ9O7dm8KFC/PSSy+RP39+Ll++zL59+5g/fz4BAQGP3capU6eoVq0apUuX5rXXXuPatWssXbqU5s2b8/PPP/Pss8/GWT4gIIBZs2ZRtGhRevTogYuLC99//z07duzg/v37ODs7p9XuMn/+fCIjI2nTpg1eXl6PXd7Jyfpbtl27dgwcOJC5c+fy3//+N3b64sWLuXXrFt27d2fJkiVJrq9Xr16UK1eOOnXqUKRIEa5evcqqVavo1KkTR44c4f3334+3TlKPf//+/Zk2bRpFihShR48eODs7891337Fjxw7u3buHi4tLkuvOKJL72jt27Bj+/v54eXnRoUMHbt68Sa5cuR75XKl5nIcMGcLEiRMpUKAA7du3J2fOnKxevZrhw4ezdu1a1q1bh4uLC/Xq1QMevM5PnTr1yC7Hf7tx4wadOnWiSpUq1K5dm4IFC3L58mW+++47unbtyqVLl3jnnXcSta2ff/4ZJycnq390JOYzp169eoSGhjJ16lQqVqxI8+bNY9f38/OL/X9y3i+P+10+88wzAPz0009x3tuSRmzaTiWZ2saNGw1gRo0aZXW+tSb7p59+2ri4uJhLly7FW/7KlSux/7fWlB0zDTCBgYFx1l27dq0BTOPGjeNM/+WXXwxgypYta65fvx47PSIiwtSuXdsAyeq+GTVqlNXH+PHj4ywf063w2WefJfo5/v18xYoVM8YY07FjR+Pi4hLnOFWuXDm2W61Tp05J7j47duxYvGl379419erVM05OTubMmTOx05Nz/Ldu3WoA85///MeEhITETr9z547x9/dP8+Of1OWTu441yXntPXyMhw4dGm+bCXXxpOZx3rJlS+zyD79P79+/b1544QUDmLFjx8ZZp27duknuPrtx44a5cOFCvOnnzp0zOXLkMGXLlk3Udm7evGkcHBxMhQoVrM5PyWfOvyX3/WLtdxkjNDTUAKZKlSoJLiOpR6FI0kxyQlGlSpVMjhw5zLVr1x657UeFopIlS1rtf/f09DT58uWLM61bt24GMAsWLIi3/MMf/okV8yGX0MPd3T3O8k899ZQBzJo1a+Jt6/Dhw/G+cP8dnh4ORTFfsh999JExxpg9e/bEOf7JCUUJWb58ebzjlpzj3717dwOYzz//PN7yMa+ftDz+SV0+uetYk5zXXswxLlSokLl792689RL64k7N4xxT95w5c+LNO3LkiHFwcDClSpWKMz05oehRnnzySVOoUKFELRscHGwA89xzz1mdn5LPnMR61Pslod/lw7Jly5bo/ZWU0ZgisSvt27fn9u3blC9fngEDBvC///2PK1euJGkbfn5+ODo6xptevHhxrl+/Hmfanj17AKhVq1a85f39/RPsrnoc8+APjniP0NDQeMsBVsdYHDlyhNGjR8d5fP755wk+Z+3atfHy8oq9rsmcOXNwcHCga9euydoHgNOnTxMQEIC3t3fs9WUsFgsvv/wyAOfOnYu3TlKO/+7duwGoW7eu1f1J6+Of3OWTu87DUvLaq1ixIq6urol6Hkjd4xxTd/369ePN8/Ly4oknnuDEiROJPg4JuX79OmPGjMHf35+8efPi6OgY+/r766+/8PT0TNR2QkJCAMibN6/V+anxmRMjOe+XxPwuPTw8uHr1arJqkqTRmCKxKwMGDCB//vzMnDmTqVOnMnnyZCwWC/Xr1+fDDz+kUqVKj91GQqcjOzk5ER0dHWdazCDTQoUKxVve0dGRfPnyJWMvEq9w4cIcOXLE6odl8+bNY0PTyZMnYwd6Pkq3bt0YPHgwGzZsYPHixTz33HOJ/vL4t7///ptq1apx/fp1ateuTaNGjXB3d8fR0ZGTJ0+yYMECIiIi4q2XkY6/LaVk35N6yn9qHueYbSVUQ5EiRTh9+jRhYWHkyZMnSXXG2LdvH40aNeLSpUtUq1aNNm3a4OHhgbOzMydOnGDhwoVUrFgxUdvKnj07QJwB4A9Ljc8cSP77JTG/yzt37sTuh6QttRRJmnFwePDySujaOAmd9dKxY0e2bdtGSEgIq1atolu3bmzatIlGjRol+y+4hOTOnRuAS5cuxZsXFRUV+1dmWqlZsyYAGzZsSJXtderUCWdnZzp16kRoaCjdunVL9rY+/vhjQkJC+Oyzz9i0aRPTpk1jzJgxBAYGptqAz5gAZavjb0spee0l9uytGKl5nGO2dfHiRavzL1y4EGe55HjttdcIDQ1lw4YNbN++nVmzZjFu3DgCAwNjQ37lypUTta2Ysy4ftY+p8ZmT3PfL436X0dHRhIaGJuvsUUk6hSJJMzHN1WfOnIk379ixY49tXs+TJw8vvPACc+bMoXPnzoSEhPDrr7+mao1PP/00AFu2bIk3b9u2bWl+scPOnTvj6OjI8uXLCQ4OTvH2ChYsSNOmTTl79iz58+enWbNmyd7WsWPHAGjVqlW8eZs3b072dh8W81e4te39+uuvmfpik+n52kvN4xxT98Onjcc4duwYZ8+epVSpUsluJTpz5gz79u2jXr168brorl+/Hns6fmJDUZEiRShQoECi3l+P+syJ6RKOioqyum5avV+Cg4MxxsQ5y03SjkKRpBlvb29y587Nd999x+XLl2On37lzhzfffNPqOmvXrrX6AR2zfrZs2VK1xo4dOwIwbty4OC1X9+7dS5cryJYpU4Zhw4YRERHB888/zx9//GF1uaSMz/joo49YsWIFq1atStHp7DHXyIm5xkyMH3/8kblz5yZ7uw+LuZ7OuHHjuHbtWuz0u3fvMnTo0FR5DnuVnq+91DzOMWPUxo4dG6cVJSoqioEDBxIdHZ2iFsqY9/jff//N/fv3Y6dfvXqVV155hXPnzuHk5ESFChUStT2LxUKdOnW4evVqbHB5WGI/c/LmzYvFYrH6Rx6k3ftl27ZtgPUxXJL6NKZI0oyzszMDBgwgMDCQp59+mhYtWhAZGcnPP/9M0aJFrV7uv02bNmTLlo1atWpRsmRJjDH8+uuv/PHHH1SqVImGDRumao1169alR48efPrpp5QvX55WrVrh7OzMypUrcXd3p2jRorHdgEmR0AUr4cFYoYf/6hs9ejTR0dG8//77VKtWjWrVqlG1alXy5MnDtWvXOHbsGBs2bMBisVgdlPtvpUqVStT4o8fp3bs38+bN49VXX6VVq1YUK1aMAwcOsHbtWl599VWWLl2a4ueoWbMmffv2Zfr06fj4+PDyyy/HXj8nb968FClSJFnbTcrxT87yyV3nYWn12rMmNY/zM888w+DBg5k4cWLstnLmzMmaNWs4cOAAtWrVYtCgQcmutUCBAjRo0IANGzZQvXp1GjZsyIULF1i9ejUNGjTAYrHg4+OTpIHmrVq14ptvvuHHH3+kTJkyceYl9jPHzc2N6tWr88svv9ChQweefPJJHB0deemll6hQoUKavV9++uknHB0dU9TqK0mQLue4SZYVHR1tPvjgA1O6dGnj7OxsihcvbgYNGmRu3bpl9ZT8WbNmmebNm5tSpUqZ7Nmzm7x58xo/Pz/zwQcfmPDw8NjlHnVKfkKnzCZ0WnBUVJT5+OOPjZeXl3FxcTFFihQxvXv3NqGhocbNzc34+fklen95zOnagJk3b57VdQ8ePGj69u1rfH19Te7cuY2Tk5Px8PAw/v7+ZsiQIebgwYNWny/mlPzHSc4p+Vu3bjX169c3efLkMW5ubqZmzZpmxYoVVi+3kNzjHx0dbaZPn268vb3jHf/k3uYjscc/Ob+vlPyO/y2pr73HHeNHzU/N42yMMV999ZWpWbOmcXNzM66urqZcuXJm7Nix5s6dO/GWTeop+ZcvXzavvfaayZ8/v3FzczM1atQwCxYsMLt27TKA6dq1a5JqjYiIMIUKFTLVqlWLNy+xnznGGPPXX3+Zpk2bGg8PD2OxWOL9rlPz/WLMg2sUZcuWzTRr1ixJ+yvJZzHmn9NbRCSOv/76i7Jly9KmTRu++uorW5cjWYhee6lv/PjxDBs2jN27d8eOi7J306dP58033+SXX36hdu3ati4nS9CYIsnyLl68GO9U8du3b9O/f3/A+sBJkdSg1176eeutt/D09GTkyJG2LiVR7ty5w/jx42nVqpUCUTqyq1C0d+9emjRpgqenJ9mzZ8fDw4MaNWqwaNGiRK1/+fJlOnfuTP78+cmRIwc1atRg/fr1aVy1ZHRTpkyhVKlSdOrUiXfeeYfOnTvj5eXF6tWradKkib6YJM3otZd+smXLxhdffEGVKlW4deuWrct5rJMnT9KjRw8mTZpk61KyFLvqPtu0aRNLliyhVq1aFCtWjFu3bvHll1+yZMkSxowZw7vvvpvguhEREVSpUoXQ0FAmTJhAwYIFCQoKYtWqVaxbt87qlVxFANavX8/kyZPZu3cvV69exdHRES8vL9q1a0e/fv3S9IawkrXptSdiX+wqFCXE39+f8+fPc/r06QSXmTlzJgEBAfz222/UqFEDeHDRwIoVK+Lm5sb27dvTq1wRERHJgOyq+ywh+fPnf+y9eVasWIGXl1dsIIIHtxXo0KEDO3bssHobBREREZEYdnmdoujoaKKjo7l+/TrLli3jxx9/ZMaMGY9c58CBA1YHo8Vc4OvgwYMUK1bM6roRERFx7kkTHR3NtWvXyJcvX5Ivpy8iIiK2YYzhxo0byb7Ol12Got69ezN79mwAXFxcmDZtGj179nzkOiEhIXh4eMSbHjPtUfe9GT9+PKNHj05BxSIiImIvzpw5wxNPPJHk9ewyFA0bNozu3btz+fJlVq5cSZ8+fbh16xYDBw585HqPatV51LyhQ4cyYMCA2J/DwsLw9PTkzJkzsTdtFBEREfsWHh5O8eLFyZUrV7LWt8tQ5OnpGXsn5BdeeAF4EFw6depEgQIFrK6TL18+q61BMff5sdaKFMPV1dXqJeNz586tUCQiIpLBJHfoS4YYaF2tWjUiIyP5+++/E1zG19eX/fv3x5seM83HxyfN6hMREZGML0OEoo0bN+Lg4EDp0qUTXKZFixYcOXIkzqn3kZGRLFq0iOrVq1u9+aiIiIhIDLvqPuvRowe5c+emWrVqFCpUiKtXr7Js2TKWLl3KoEGDYrvOunXrxoIFCzh+/DglSpQAoGvXrgQFBfHKK6/EXrxx5syZBAcHs27dOlvuloiIiGQAdhWKatSowbx581iwYAGhoaG4ublRsWJFvvjiCzp06BC7XFRUFFFRUTx83UlXV1fWr1/P4MGD6du3L7dv38bPz481a9boatYiIiLyWBniitbpLTw8HHd3d8LCwjTQWkREJINI6fd3hhhTJCIiIpLWFIpEREREUCgSERERARSKRERERACFIhERERFAoUhEREQEUCgSERERARSKRERERACFIhERERFAoUhEREQEUCgSERERARSKRERERACFIhERERFAoUhEREQEUCgSERERARSKRERERACFIhERERFAoUhEREQEUCgSERERARSKRERERACFIhERERFAoUhEREQEUCgSERERARSKRERERACFIhERERFAoUhEREQEUCgSERERARSKRERERACFIhERERFAoUhEREQEUCgSERERARSKRERERACFIhERERFAoUhEREQEUCgSERERARSKRERERACFIhERERFAoUhEREQEUCgSERERARSKRERERACFIhERERFAoUhEREQEUCgSERERARSKRERERACFIhERERFAoUhEREQEUCgSERERAewsFG3YsIGuXbvi7e1Nzpw5KVasGM2aNWPXrl2PXXf+/PlYLBarj4sXL6ZD9SIiIpKROdm6gIfNmjWLkJAQ+vXrR7ly5bhy5QofffQR/v7+/PjjjzRo0OCx25g3bx7e3t5xpuXLly+tShYREZFMwq5CUVBQEAULFowzrXHjxpQpU4b3338/UaHIx8eHKlWqpFWJIiIikknZVffZvwMRgJubG+XKlePMmTM2qEhERESyCrsKRdaEhYWxe/duypcvn6jlmzZtiqOjIx4eHrRs2ZIDBw48dp2IiAjCw8PjPERERCRrsftQFBAQwK1btxg+fPgjlytcuDDDhw9n7ty5bNy4kTFjxvDHH3/g7+/Pn3/++ch1x48fj7u7e+yjePHiqbkLIiIikgFYjDHG1kUkZMSIEYwdO5bp06fTp0+fJK9/8uRJfH19adCgAd99912Cy0VERBARERH7c3h4OMWLFycsLIzcuXMnq3YRERFJX+Hh4bi7uyf7+9uuBlo/bPTo0YwdO5Zx48YlKxABlCxZklq1arFt27ZHLufq6oqrq2uynkNERETsw7Vr11K0vl12n40ePZrAwEACAwMZNmxYirZljMHBwS53U0RERFJBdHQ0c+fOpXLlyinajt21FI0ZM4bAwEDeffddRo0alaJtnThxgq1bt9KwYcNUqk5ERETsyc6dOwkICGDHjh0p3pZdhaKPPvqIkSNH0rhxY5o0aRKv28vf3x+Abt26sWDBAo4fP06JEiUAaNiwIXXq1KFChQrkzp2b/fv3M3HiRCwWC2PGjEn3fREREZG0ExISwrBhw5gzZw7GGHLlysXQoUNT1MNkV6Fo5cqVAKxdu5a1a9fGmx8zJjwqKoqoqCgeHiPu6+vL0qVLmTRpEnfu3KFgwYI0aNCAESNGULZs2fTZAREREUlTUVFRzJ07l2HDhsWOIerQoQMTJ04kZ86cKQpFdn32ma2kdPS6iIiIpL7t27cTEBAQe09UX19fgoKCqF27NpDy72+NQBYRERG7duXKFbp3746/vz+7du0id+7cTJ06ld27d8cGotRgV91nIiIiIjGioqKYPXs27777LtevXwegY8eOTJw4kUKFCqX68ykUiYiIiN35/fff6dOnD7t37wbAz8+PGTNmULNmzTR7TnWfiYiIiN24fPkyXbt25ZlnnmH37t24u7szffp0/vjjjzQNRKCWIhEREbEDkZGRfPLJJ4wYMYLQ0FAAunTpwoQJEyhYsGC61KBQJCIiIja1detWAgICYm/g/vTTTxMUFESNGjXStQ51n4mIiIhNXLp0ic6dO1OrVi3+/PNP8uTJQ1BQEH/88Ue6ByJQS5GIiIiks8jISGbNmsWIESMICwsDHtytYvz48RQoUMBmdSkUiYiISLrZsmULAQEB7Nu3D4DKlSsTFBRE9erVbVyZus9EREQkHVy8eJGOHTtSu3Zt9u3bh4eHB5988gnbt2+3i0AECkUiIiKShiIjI5kyZQpeXl588cUXWCwWXn/9dYKDg+nZsyeOjo62LjGWus9EREQkTfzyyy/06dOH/fv3A1ClShWCgoKoVq2ajSuzTi1FIiIikqouXLjAa6+9Rt26ddm/fz8eHh7Mnj2bbdu22W0gAoUiERERSSUPd5UtWrQIi8VCz549OXr0KD169LCrrjJr1H0mIiIiKfbLL78QEBDAgQMHAKhWrRpBQUFUqVLFxpUlnlqKREREJNkuXLhAhw4dqFu3LgcOHCBfvnzMmTOH33//PUMFIlAoEhERkWS4f/8+kydPxsvLiy+//BKLxcIbb7zB0aNH6d69Ow4OGS9iqPtMREREkmTz5s306dMntqusevXqzJgxI8O1DP1bxotxIiIiYhPnz5+nffv21KtXjwMHDpA/f37mzp3Lb7/9luEDESgUiYiIyGPcv3+fjz76CC8vLxYvXozFYqFXr14EBwfTrVu3DNlVZo26z0RERCRBGzdupE+fPhw6dAh40FUWFBRE5cqVbVxZ6ssc0U5ERERS1blz52jbti0NGjTg0KFD5M+fn88++4zffvstUwYiUCgSERGRh9y/f59Jkybh7e3NkiVLsFgs9O7dm+DgYLp27ZppusqsUfeZiIiIAPG7yvz9/QkKCqJSpUo2rix9ZN64JyIiIolirats7ty5bN26NcsEIlAoEhERybJiziqz1lWWmc4qSyx1n4mIiGRBWb2rzJqsFQFFRESyuPPnz9OuXbs4XWWff/55lusqs0ahSEREJAt4+AKMX331FQ4ODgQEBHD06FG6dOmS5brKrFH3mYiISCb3766yGjVqMGPGjCzfMvRvioUiIiKZVEJdZVu2bFEgskKhSEREJJP5d1fZw/cqU1dZwtR9JiIikols2rSJPn36cPDgQSBz36sstSkqioiIZALnz5+nffv21K9fn4MHD2aJe5WlNoUiERGRDOz+/ftMnjwZb29vFi9eHKerLLPfqyy1qftMREQkg9q8eTMBAQHqKkslio8iIiIZzIULF+jQoQP16tXj4MGD5MuXj7lz56qrLIUUikRERDKImK4yLy8vvvzySywWC2+88QZHjx7NkvcqS23qPhMREckAfvnlFwICAjhw4AAAVatWZebMmVSpUsXGlWUeipQiIiJ27OLFi7z22mvUrVuXAwcO4OHhwezZs9m2bZsCUSpTKBIREbFDkZGRTJ06FS8vLxYtWoTFYqFnz54cPXqUHj16qKssDaj7TERExM78+uuv9OnTh3379gEPusqCgoKoWrWqjSvL3BQzRURE7MSlS5fo1KkTderUYd++fXh4ePDpp5+ybds2BaJ0oFAkIiJiY5GRkUyfPp2yZcuycOFCLBYLPXr04OjRo7z++uvqKksn6j4TERGxod9++43evXvz559/AlClShWCgoKoVq2ajSvLehQ9RUREbODy5ct06dKFmjVr8ueff5I3b14++eQTtm3bpkBkI3YVijZs2EDXrl3x9vYmZ86cFCtWjGbNmrFr165ErX/58mU6d+5M/vz5yZEjBzVq1GD9+vVpXLWIiEjiRUVFERQUhJeXF/Pnzwega9euBAcH07NnTxwdHW1bYBZmV6Fo1qxZnDx5kn79+rF69WqmTp3K5cuX8ff3Z8OGDY9cNyIigmeffZb169czdepUvvvuOwoVKkTjxo3ZvHlzOu2BiIhIwmIGTPfp04fQ0FCefvppfv/9dz777DMKFChg6/KyPIsxxti6iBiXL1+mYMGCcabdvHmTMmXK4OPjw7p16xJcd+bMmQQEBPDbb79Ro0YN4MHAtYoVK+Lm5sb27dsTXUd4eDju7u6EhYWRO3fu5O2MiIjIP65cucLQoUP57LPPAMiTJw/jxo1Ty1AqS+n3t121FP07EAG4ublRrlw5zpw588h1V6xYgZeXV2wgAnBycqJDhw7s2LGDc+fOpXq9IiIijxIVFcUnn3yCl5dXbCDq0qULwcHB9O7dW4HIzthVKLImLCyM3bt3U758+Ucud+DAASpUqBBvesy0gwcPpkl9IiIi1uzYsYPq1avTq1cvrl+/TsWKFdm6dSuff/651UYAsT27PyU/ICCAW7duMXz48EcuFxISgoeHR7zpMdNCQkISXDciIoKIiIjYn8PDw5NZrYiIZHUhISEMHTqUuXPnYowhd+7cjB07ll69euHkZPdfu1maXbcUjRgxgi+//JLJkydTuXLlxy5vsViSNW/8+PG4u7vHPooXL56sekVEJOuKjo5mzpw5lC1bljlz5mCMoWPHjhw9epS+ffsqEGUAdhuKRo8ezdixYxk3bhx9+vR57PL58uWz2hp07do1AKutSDGGDh1KWFhY7ONx45dEREQetmvXLmrUqEGPHj24du0aPj4+/PLLLyxYsIBChQrZujxJJLuMraNHjyYwMJDAwECGDRuWqHV8fX3Zv39/vOkx03x8fBJc19XVFVdX1+QVKyIiWda1a9d49913+eSTTzDGkCtXLkaPHk2fPn1wdna2dXmSRHbXUjRmzBgCAwN59913GTVqVKLXa9GiBUeOHIlz6n1kZCSLFi2ievXqFC1aNC3KFRGRLCg6Opp58+bh5eXFrFmzMMbQrl07jhw5wltvvaVAlEHZ1XWKPvroIwYOHEjjxo2tBiJ/f38AunXrxoIFCzh+/DglSpQAHgyWrly5MuHh4UyYMIGCBQsyc+ZMVq5cybp166hbt26i69B1ikREJCF79+6ld+/e/P777wA89dRTBAUFUb9+fRtXJin9/rar7rOVK1cCsHbtWtauXRtvfkx+i4qKIioqiofznKurK+vXr2fw4MH07duX27dv4+fnx5o1a5IUiERERKwJDQ1l5MiRBAUFER0dTc6cOQkMDKRfv35qGcok7KqlyF6opUhERGIYY1i0aBGDBg3i0qVLALRu3ZpJkybxxBNP2Lg6eVimaikSERGxJ/v37ycgIIBff/0VAC8vL2bMmEHDhg1tXJmkBbsbaC0iImJr4eHhvP322zz99NP8+uuv5MiRgwkTJrBv3z4FokxMLUUiIiL/MMawdOlSBgwYwIULFwBo2bIlkydPxtPT08bVSVpTKBIREQEOHz5Mnz592LBhAwBlypRh+vTpNG7c2MaVSXpR95mIiGRpN2/eZMiQIVSoUIENGzaQLVs2xowZw/79+xWIshi1FImISJZkjOHbb7+lf//+nD17FoCXXnqJKVOmUKpUKRtXJ7agUCQiIlnOX3/9Rd++ffnxxx8BKFWqFNOmTaNp06Y2rkxsSd1nIiKSZdy+fZt3330XHx8ffvzxR1xcXBg5ciQHDx5UIBK1FImISOZnjGHlypW8+eabnDp1CoDGjRszffp0ypQpY+PqxF4oFImISKb2999/8+abb7Jq1SoAihcvzpQpU2jRogUWi8XG1Yk9UfeZiIhkSnfv3uW9996jfPnyrFq1CicnJ4YMGcLhw4dp2bKlApHEo5YiERHJdNauXUvfvn05duwYAA0aNGDGjBk89dRTNq5M7FmKW4qio6O5fft2atQiIiKSIqdPn6ZVq1Y8//zzHDt2jCJFivDVV1+xbt06BSJ5rCSHort37zJ//nxeeeUVihYtiouLC7ly5SJHjhxUqVKFwYMH8+eff6ZFrSIiIlbdu3ePDz74gKeeeopvv/0WR0dH3nrrLY4cOUKbNm3UVSaJYjHGmMQseOfOHSZOnMjUqVMJCwvD29ubSpUqUbBgQbJly8a1a9f4+++/2bFjB+Hh4TzzzDNMnDiRGjVqpPU+pLrw8HDc3d0JCwsjd+7cti5HREQeYcOGDQQEBHDkyBEAatWqxcyZM/H19bVxZZLeUvr9negxRU8++SQ5c+bk3XffpX379hQqVMjqcsYYNm7cyLx586hfvz4zZsyge/fuSS5MRETkUc6fP8/bb7/NkiVLAChYsCAffvghr732mlqGJFkS3VL0+eef06lTJxwdHRO98b///pvTp09Tr1695NZnE2opEhGxL/vOhjJ+9RGGvuBNucJuTJ8+nVGjRnHjxg0cHBzo1asXY8eOJU+ePLYuVWwopd/fiQ5FWYlCkYiIfQn8/iDzfztJo5IubJv5Nvv37wegWrVqzJo1i0qVKtm4QrEH6dZ9JiIikp7OXr/N9Vv3sVjguz0Pbti65uBlLl++Tf6ylRjSL4ABb3TGwUGX3JPUkWahKDo6mkWLFtGxY8e0egoREcnEan2wMfb/xhgsFgsOOdwp0nkqADNOw0AFIklFafZqun//Pl26dEmrzYuISCb3ZtXcEB0FEDtwOuZfJwcLU1r72ao0yaRS1FL03nvvJTjv/v37Kdm0iIhkUdeuXWP48OHMnj0b54KlY1uGHva/gJr4FHO3QXWSmaUoFI0dO5YWLVpYHcwUFRWVkk2LiEgWEx0dzYIFCxg8eDBXr14F4IUmTdgDWCxgzP//K5IWUhSKfH196dixI02aNIk3L+bK1yIiIo+zb98+evXqxW+//QZAuXLlmDlzJmX9qvHS9K0UyZON1lWLs/SPM1wIvUs+NxcbVyyZUYpC0euvv55gi5CzszOjRo1KyeZFRCSTCw8PZ9SoUUyfPp2oqChy5sxJYGAg/fr1w9nZGYAt79THxdEBi8VCu2qe3IuKxtUp8dfME0ksXafICl2nSEQkbRljWLJkCW+//TYXLlwA4OWXX2by5Mk88cQTNq5OMipdp0hERDKUI0eOEBAQwIYNGwAoU6YMM2bM4L///a+NK5OsThd4EBGRdHH79m2GDRtGhQoV2LBhA9myZeO9995j//79CkRiF9RSJCIiacoYw/fff0+/fv04deoUAE2aNGHatGmULl3axtWJ/L9UbynS4GoREYlx4sQJXnrpJZo3b86pU6fw9PTkf//7HytXrlQgEruT6qHoww8/TO1NiohIBhMREcHYsWMpV64cP/zwA87OzrzzzjscOnSIZs2axV6ZWsSepHr3mU5mExHJ2n7++WcCAgL466+/AGjQoAFBQUF4e3vbuDKRR0v1liKlfxGRrOncuXO0bt2aRo0a8ddff1G4cGEWL17MunXrFIgkQ9DZZyIikiL379/n448/xtvbm6+//hoHBwf69evHkSNHaNu2rf5YlgxDZ5+JiEiybdmyhd69e7N//34A/P39mTVrFn5+frYtTCQZUr2lSGOKREQyvytXrtClSxdq167N/v378fDwYO7cuWzdulWBSDKsVA9FNWvWTO1NioiInYiOjmb27Nl4eXnF3vS7e/fuBAcH061bNxwcNCpDMq5U7z5bt25dam9SRETswO7du+nVqxc7duwAwM/Pj5kzZ1KjRg0bVyaSOhTpRUTkkUJDQ+nbty9Vq1Zlx44d5MqViylTpvDHH38oEEmmkqJQ1LBhw9SqQ0RE7Iwxhi+//BJvb29mzJhBdHQ0bdu2JTg4mH79+uHkpHN1JHNJ0Ss6pglVREQyl8OHD9O7d282bdoEgJeXFzNnzqRBgwa2LUwkDan7TEREYt26dYuhQ4dSoUIFNm3aRPbs2Xn//ff5888/FYgk00tRS9Hdu3cZOHAgFSpUoEKFCpQvXx5nZ+fUqk1ERNLRd999x5tvvsnp06cBaNq0KdOmTaNUqVI2rkwkfaQoFFksFm7cuMGsWbM4cOAA9+7do2zZsrEhqUKFCjz//POpVauIiKSBkydP8uabb7Jy5UoAPD09mTZtGs2aNbNxZSLpy2JScLXF3LlzEx4eHvvz8ePH+fPPP9m3bx/79u1j//79sTcEzEjCw8Nxd3cnLCyM3Llz27ocEZE0ERERwUcffcTYsWO5c+cOzs7ODBw4kOHDh5MzZ05blyeSZCn9/k5RKMqVKxc3btxI7up2S6FIRDK7DRs20Lt3b4KDgwGoV68eM2fO5KmnnrJxZSLJl9Lv7xQNtJ46dWpKVhcRkXR28eJF2rdvz7PPPktwcDCFChVi0aJFbNiwQYFIsrwUhaKuXbumVh2xbty4weDBg2nUqBEFChTAYrEQGBiYqHXnz5+PxWKx+rh48WKq1yoiklFERUUxY8YMvLy8WLx4MRaLhYCAAI4cOUL79u11J3sRUjjQOiwsjFy5cqXqvW5CQkL49NNPqVixIs2bN2fu3LlJ3sa8efPw9vaOMy1fvnypVaKISIbyxx9/8MYbb7B7924AqlSpwqxZs6hSpYqNKxOxL8kKRZs2beK1117j/PnzODs74+PjQ+XKlalcuTJVqlTB19c32afmlyhRguvXr2OxWLh69WqyQpGPj4/e7CKS5V2/fp3hw4fzySefYIzB3d2d8ePH06NHDxwdHW1dnojdSVYoCggIwMnJifHjx3Pz5k327NnDypUrmTNnDgCurq7cuXMnWQWpCVdEJGWMMSxatIiBAwdy+fJlAF577TU+/PBDChUqZOPqROxXskLRyZMnWbJkCS+++GKc6RcvXmTnzp2xTbS20rRpU65cuYK7uzv16tXjvffew8fHJ8HlIyIiiIiIiP354csMiIhkJIcOHaJ3795s3rwZgKeeeopZs2ZRt25dG1cmYv+SFYrKlStHVFRUvOmFCxemadOmNG3aNMWFJUfhwoUZPnw4/v7+5M6dm/379zNhwgT8/f3ZunUrFStWtLre+PHjGT16dDpXKyKSem7dusWYMWP46KOPiIyMJHv27IwcOZIBAwbg4uJi6/JEMoRkXado6dKlfPrpp6xfvz4taop19epVChQowKhRoxJ9Btq/nTx5El9fXxo0aMB3331ndRlrLUXFixfXdYpEJEP4/vvvefPNNzl16hQAL774ItOmTaNkyZK2LUwkndnkOkWtW7emYsWKNG3alIMHDyZnE+mmZMmS1KpVi23btiW4jKurK7lz547zEBGxd6dOnaJZs2Y0a9aMU6dO4enpyXfffcf333+vQCSSDMnqPvv666+ZOXMm9+7dY82aNRQtWpQqVarEedjTKfDGmFS9bICIiC3du3ePyZMn895773H79m2cnJx4++23GTFihG7PIZICyQpFQ4YMwdvbm8GDBxMeHs6uXbvYuXMnq1atIjIyEovFYnXMkS2cOHGCrVu30rBhQ1uXIiKSZPvOhjJ+9RGGvuBNhSfy8Msvv9CrVy8OHToEQJ06dZg5cybly5e3caUiGV+yQtHly5eZPXs2jRo1ijM9IiKCvXv3pvjsszVr1nDr1q3Y+6odOnSI5cuXA/DCCy+QI0cOunXrxoIFCzh+/DglSpQAoGHDhtSpU4cKFSrEDrSeOHEiFouFMWPGpKgmERFb+Hb3OX7/O4Qvtx7j4zUzWLBgAQAFChRg0qRJvPbaa7qUiUgqSVYoqlSpEqGhofGmu7q6Ur16dapXr56ionr16hU7YBBg2bJlLFu2DHjQ8lOyZEmioqKIiori4XHivr6+LF26lEmTJnHnzh0KFixIgwYNGDFiBGXLlk1RTSIi6eXs9dtcv3UfiwVW/nkegK+2HuXS2i24FC5Dm+ZNmTxuBB4eHjauVCRzSdbZZz///DMjRoxgy5YtODml6E4hdimlo9dFRFKi5Dur/v8HY8BiwRgTp0Xo5IQmNqhMxL7Z5Oyz9957j4sXL1K7dm3WrVtnN+OHREQyg/HNvLCY6Ac//BOEYgKRk4OFKa39bFSZSOaWrGae7Nmzc/v2bbZv385///tfXF1dqVixYpyzzzToT0QkaYwxfPPNNwzs14+rUdkp0nlqvGX+F1ATn2LuNqhOJPNLVij66aefADh9+jS7du1i9+7d7Nq1i2XLlhEUFGRXZ5+JiGQEx48fp0+fPqxduxaA0pXrEsWDhqJ/etBI+mAHEUmKFA0I8vT0xNPTkxYtWsROO3fuHLt27UpxYSIiWUFERAQffvgh48aN4+7du7i4uDBkyBC6BLzFq3N2USRPNlpXLc7SP85wIfQu+dx0yw6RtJKsgdaZnQZai0h62LBhA7179yY4OBiAZ599lpkzZ8aeLRsRGYWLowOWfwZa34uKxtXJ0ZYli9i1dBto7ePjw4oVKxK94QsXLvDmm28yYcKEJBclIpKZXbp0iddee41nn32W4OBgChcuzOLFi/n555/jXD7E1ckxdoC1xWJRIBJJY4kORa+++iodO3bE09OToUOH8uOPP3LlypXY6wTduXOHAwcOMHfuXF588UVKlCjBrl27eOmll9KseBGRjCQ6OppPPvkEb29vFi1ahMViISAggMOHD9O2bVtdhFHExpLUfXbhwgWmTJnC559/TkhICBaLBYvFgrOzM/fu3QMenD1Ru3Zt+vXrR8uWLdOs8LSk7jMRSW179uyhV69ebN++HXhwEdzZs2dTpUoVG1cmknmk9Ps7WWOK7t+/z/bt2/n99985f/48d+7cIX/+/Hh7e1OvXj2eeOKJJBdiTxSKRCS13Lhxg5EjRzJt2jSio6PJlSsX48aNo3fv3jg6qjtMJDXZJBRldgpFIpJSMdcc6tevH+fPP7hVR+vWrfn4448pWrSojasTyZxS+v2d+e7RISJiY3///Td9+vRhzZo1APznP/9h5syZ8W6iLSL2JVm3+UiM6OhoFi5cmFabFxGxO/fu3eP999+nfPnyrFmzBhcXF0aMGMH+/fsViEQygDTrPouIiCBHjhwZ8srW6j4TkaTavHkzvXr14vDhwwA0aNCAmTNn4uXlZePKRLIOm3afvffeewnOu3//fko2LSKSIVy5coVBgwaxYMECAAoWLMjHH39Mu3btdIq9SAaTolA0duxYWrRoYTWNZcQWIhGRxIqOjmbevHkMHjyYa9euYbFY6NmzJ++//z558+a1dXkikgwpCkW+vr507NiRJk2axJt39+5d5s+fn5LNi4jYpQMHDvDGG2+wdetWACpWrMgnn3yCv7+/jSsTkZRI0UDr119/PcEWIWdnZ0aNGpWSzYuI2JVbt24xZMgQnn76abZu3UrOnDmZNGkSO3fuVCASyQR0nSIrNNBaRP7thx9+oE+fPpw6dQqA5s2bM23aNIoXL27jykQkRrrdEFZEJCs6e/YsrVq14sUXX+TUqVN4enry3XffsWLFCgUikUxGoUhE5B/7zobS9tNt7DsbSmRkJFOmTOGpp57i22+/xdHRkUGDBnHw4EHd6Fokk9IVrUVE/vHt7nP8/ncIs9bsZvusgezZsweAGjVq8Mknn1ChQgUbVygiaSnVW4o0uFpEMpKz12+z/2wYB86F8f3ecwD8sO8CB8+H41HGj4kz5rJlyxYFIpEsINUHWufIkYPbt2+n5ibTnQZai2QdJd9ZFft/YwwWiyX23xgnJ8S/7IiI2B+7G2itk9lEJCMZVr8omGiA2CAU86+Tg4Uprf1sVZqIpLNUD0W6rL2IZAT37t1j/Pjx9Gv+DBcWvGV1mf8F1KT508XSuTIRsRUNtBaRLGfLli307NmTQ4cOAVCzYVXOAhYLGPP//4pI1qJT8kUky7h27Rrdu3endu3aHDp0iAIFCrBw4UK+/uIzCri54lvMnXEtfPAt5k4BN1fyubnYumQRSUep3lKkMUUiYm+MMSxatIi3336bK1euANC9e3c++OADPDw8ANjyTn1cHB2wWCy0q+bJvahoXJ0cbVm2iKSzVA9FNWvWTO1Niogk29GjR+nVqxcbNmwAoFy5csyePZtatWrFWe7hAGSxWBSIRLKgVO8+W7duXWpvUkQkySIiIhg9ejS+vr5s2LCBbNmyMW7cOPbs2RMvEImIgAZai0gmtGnTJt544w2Cg4MB+O9//8vMmTMpXbq0jSsTEXuWopaihg0bplYdIiIpdvXqVbp06UL9+vUJDg6mcOHCLFmyhDVr1igQichjpSgU7dixI7XqEBFJNmMMCxYswNvbm/nz52OxWOjVqxeHDx+mdevWun6aiCSKus9EJEMLDg7mjTfeYNOmTQD4+voye/ZsatSoYdvCRCTDSVFL0d27dxk4cCALFy5k79693L9/P7XqEhGxat/ZUNp+uo2df19h9OjRVKhQgU2bNpE9e3YmTJjArl27FIhEJFlS1FJksVi4ceMGs2bN4sCBA9y7d4+yZctSoUKF2Mfzzz+fWrWKiPDt7nP8/ncIrYes4O/lEwFo3LgxM2fOpFSpUjauTkQyMotJwdUWc+fOTXh4eOzPx48f588//2Tfvn3s27eP/fv389dff6VKoekppXfZFZHUdfb6ba7fuk9YWChd5u/kvmM2om6FErVhGgMHDeKVl16guEcOW5cpIjaW0u/vFIWiXLlycePGjeSubrcUikTsS8l3VsX+3xjzYOB0zE3K/nFyQhNblCYidiSl398pGlM0derUlKwuIvJYf/31FwWPr8ZERQL8/5lk//zr5GBhSms/G1UnIplJssYUvfPOO1y/fp3Zs2endj0iIgDcu3ePiRMnMnbsWCIiInArvpF87T6Mt9z/AmriU8zdBhWKSGaTrJai5cuX4+3tbXXeF198weHDh1NUlIhkbVu2bMHPz48RI0YQERFBo0aNWLZ8GfD/PWa69JCIpLZkhaJz585RsWJFq/MOHTrEwIEDU1SUiGRN169fp0ePHtSuXZvDhw9ToEABvvzyS9auXUtFr9IUcHPFt5g741r44FvMnQJuruRzc7F12SKSSSSr+yx37txcvXrV6rwaNWowb968FBUlIlmLMYalS5fSv39/Ll26BEC3bt2YOHEiHh4eABRxz86Wd+rj4uiAxWKhXTVP7kVF6272IpJqktVSVLNmTZYtW2Z1Xq5cuQgLC0tRUSKSdZw8eZImTZrQtm1bLl26hLe3N5s3b2bu3LmxgSiGq5Nj7EBri8WiQCQiqSpZoeitt97i22+/ZfLkyfHm/fbbbxQrVizFhYlI5hRzReo9p0KYNGkS5cqVY82aNbi4uDB69Gj27t1LnTp1bF2miGRByeo+q127Nh9++CFvv/02S5cupW3bthQtWpR9+/bx8ccf07Nnz9SuU0QyiZgrUrd5ZyVHl7wPQN26dZk9ezZeXl42rk5EsrJkX6dowIABrF69mnv37vHWW2/RunVrxo0bR506dRg1alSyC7px4waDBw+mUaNGFChQAIvFQmBgYKLXv3z5Mp07dyZ//vzkyJGDGjVqsH79+mTXIyIpd/b6bfafDWP70fMs3hoMwO385chXxo+xMxfyxberFYhExOZSdEXrGBcvXuTcuXMUK1aMwoULp2hbJ0+exM/Pj4oVK1K2bFnmzp3LqFGjEhWMIiIiqFKlCqGhoUyYMIGCBQsSFBTEqlWrWLduHXXr1k1UDbqitUjq0hWpRSQ9pPT7O0U3hI1RuHDhFIehGCVKlOD69etYLBauXr3K3LlzE73uZ599xoEDB/jtt99i75Jdv359KlasyODBg9m+fXuq1CgiiXfhwgVKX/6F4/meweLoZPWK1JNesX6JDxGR9JSi23ykBYvF8v8fmkm0YsUKvLy8YgMRgJOTEx06dGDHjh2cO3cutcoUkceIjo5m9uzZPPXUU2ycN5HLXw6yutz/AmrS/GmdnCEitmd3oSglDhw4QIUKFeJNj5l28ODB9C5JJEs6fPgwdevW5Y033iAsLIwqVaqwaNEiQFekFhH7lalCUUhISLzrmgCx00JCQqyuFxERQXh4eJyHiCROzCn2+86GEhERQWBgIBUrVmTLli3kzJmTKVOmsG3bNp6p7KsrUouIXUuVMUX25FFdbwnNGz9+PKNHj06rkkQytZhT7Gf88Ae/Tn2TI0eOANCkSRNmzpyJp6cnoCtSi4j9y1QtRfny5bPaGnTt2jUAq61IAEOHDiUsLCz2cebMmTStUySjiznF/sC5ML7f+2Cs3pqDl/n7+n0Kl6vGJwu/ZuXKlbGBKIauSC0i9ixTtRT5+vqyf//+eNNjpvn4+Fhdz9XVFVdX1zStTSQzqfXBxtj/x5xi75DDnSKdpwIw/iD01KAhEclgMlVLUYsWLThy5EicU+8jIyNZtGgR1atXp2jRojasTiTzGPmcJ5hogDgtP/DgFPsprf1sVZqISLLZZShas2YNy5cvZ+XKlQAcOnSI5cuXs3z5cm7fvg08uIO2k5MTp06dil2va9eulC9fnldeeYXFixezbt06Xn31VYKDg/nggw9ssi8imUl0dDRBQUH0b1GTCwvesrqMTrEXkYzKLrvPevXqFSfsLFu2jGXLlgFw4sQJSpYsSVRUFFFRUTx8QW5XV1fWr1/P4MGD6du3L7dv38bPz481a9Yk+mrWIvL/9p0NZfzqIwx9wRvHsHO8/vrr/P777wBU9m/IVR6cWh9zceqUXx9fRMR2UuU2H5mNbvMh8kDg9weZ/9tJvB0usmFSL+7fv0+uXLkYP348zdt1pnnQ7xTJk43WVYuz9I8zXAi9y/d9a1LEPbutSxeRLMgubvMhIpnH2eu3uX7rPhYLfLvzQYvtwRvZsHh48mydOkwIfJcq5UoD6BR7EclU1FJkhVqKJCuzdvPW2Ju4/kM3bxURe5TS72+7HGgtIunn4StSA7xWJgoTHQXozDIRyVrUfSaSxcVckXrRlr848c1Eli9fjkuh/8Rec+hh/wuoiU8xdxtUKSKS9hSKRLKgh8cNrfzzPABLfvuLS7/uIVvRsrz8Wld+RWeWiUjWolAkkoXEnGL/+98P3Q7nn9RjyZ47tnXoV6CAm2u8M8t081YRycwUikSykJiustpl8rHl2FUMlgfNQMQdNzTplYo871tYZ5aJSJaiUCSSyVnrKtty8BSXf5xFgZcGxVve2rgh3bxVRLIChSKRTMpqVxkGsBDtkjNeINK4IRHJ6nRKvkgmFdtV9mR+HGIvMRS3qwygeN7sjGvhg28xdwq4uWrckIhkWWopEslErHWVbQ8+x6UfplntKlvR+xn8iufRuCERERSKRDKVWh9sjDctwuKSYFeZ8z8DqR9M07ghEcna1H0mkonUfjJ/vGnqKhMRSRy1FIlkYPvOhhL43UE61CjBkwXd2H3iMgn9raOuMhGRR1MoEsnAvt19jt1nQtl9JhQAYyw81DAUh7rKREQeTaFIJIM5e/02O05cY97Wk5y+dhv4/7vZW/6ViBwsUCxPdu7ej1ZXmYjIYygUiWQQj7pFR0K+71OL8kVzq6tMRCQRNNBaJINY+Nspfv87BL8n3HlwEUbi3aIjxsM/qqtMRCRx1FIkYsce7irbfy4MgL1nwxJsIHqyoBuda5bUDVxFRJJBoUjETu07G8pLM7Y+NOXBLTogfstQjI9frYjvE3l0dpmISDIoFInYoXWHLjLkm/3/mprw2KEnC7oRevs++XO5PlhSXWYiIkmmUCRiR9YdusjU9cdiu8rg/88se5SPX61I2cK5FIRERFJAoUjETpy9fpvuC3fFm55QIAqo/x9+/esqF0Lvkj+XqwKRiEgKKRSJ2FjMTVxfnLElUcv/p0BOwm7fp4N/CQY28tLYIRGRVKJQJGJjcW7i+pjrDgFMae0Xp6tMgUhEJHXoOkUiNvZBi6ewmOgHPzwiED1Z0I0Cbq7qKhMRSSNqKRKxoc2bNzO8WzfO34QinacmuFzeHM4s6FqVfG4KRCIiaUUtRSI2cPPmTfr27Uu9evU4fvw4BQsWtLrckwXdyJ/Thf8F1KRonhwKRCIiaUgtRSLpbNOmTXTt2pUTJ04A0L17dwaNHEf7BfsokicbrSoVY/mus1wMi1DrkIhIOrIYY4yti7A34eHhuLu7ExYWRu7cuW1djmQSN2/e5J133iEoKAiA4sWLM3fuXBo1agRARGQULo4OWCwWjDE6q0xEJIlS+v2tliKRdPDv1qEePXrw4YcfxnnTPhyAdEVqEZH0pzFFImno5s2b9OnTh/r163PixAk8PT35+eefmT17tlohRUTsjFqKRNLI5s2b6dKlS2zrUM+ePfnwww/JlSuXjSsTERFr1FIkkspu3bpFv379qFevXpzWoU8++USBSETEjqmlSCQVbdmyhS5dunDs2DEAXn/9dSZNmqSuMhGRDEAtRSKp4M6dO7z99tvUqVOHY8eO8cQTT/Djjz/y6aefKhCJiGQQaikSSaHt27fTqVMngoODAejatSsff/wx7u7uNq5MRESSQi1FIskUERHB0KFDeeaZZwgODqZo0aKsWrWKzz77TIFIRCQDUkuRSDLs2bOHjh07cuDAAQA6dOjAtGnTyJs3r40rExGR5FJLkUgS3L9/n/fee49q1apx4MABChYsyLfffssXX3yhQCQiksGppUgkkQ4dOkSnTp3YuXMnAK1atWLWrFkUKFDAxpWJiEhqUEuRyGNERUXx0UcfUalSJXbu3EnevHlZvHgxy5YtUyASEclE1FIk8ggnTpygU6dO/PrrrwA8//zzzJ07l6JFi9q4MhERSW1qKRKxwhjDnDlzqFChAr/++itubm58+umnrFq1SoFIRCSTUkuRyL9cuHCB7t27s3r1agBq167N/PnzKV26tI0rExGRtKSWIpGHLF++HF9fX1avXo2LiwuTJk1i48aNCkQiIlmAWopEgNDQUPr06cOXX34JwNNPP83ChQvx8fGxcWUiIpJe7K6l6ObNm/Tv35+iRYuSLVs2/Pz8WLJkyWPXmz9/PhaLxerj4sWL6VC5ZFTr16/H19eXL7/8EgcHB4YPH862bdsUiEREshi7aylq2bIlf/zxBxMmTKBs2bIsXryYtm3bEh0dTbt27R67/rx58/D29o4zLV++fGlVrmRgd+/eZdiwYUyePBmAMmXK8MUXX+Dv72/jykRExBbsKhStXr2an3/+OTYIAdSvX59Tp04xaNAgWrdujaOj4yO34ePjQ5UqVdKjXMnA9uzZQ4cOHTh06BAAb7zxBpMmTSJnzpw2rkxERGzFrrrPVqxYgZubG6+88kqc6V26dOH8+fNs377dRpVJZhEVFcWECROoXr06hw4dolChQvzwww/MmjVLgUhEJIuzq1B04MABnnrqKZyc4jZgVahQIXb+4zRt2hRHR0c8PDxo2bJlotaJiIggPDw8zkMyn5MnT1K/fn2GDh3K/fv3ad68Ofv376dJkya2Lk1EROyAXYWikJAQPDw84k2PmRYSEpLguoULF2b48OHMnTuXjRs3MmbMGP744w/8/f35888/H/m848ePx93dPfZRvHjxlO2I2BVjDAsXLoxzIcbPP/+cb7/9VrfpEBGRWBZjjLF1ETHKli3Lf/7zH9asWRNn+oULFyhatCjjx4/nnXfeSfT2Tp48ia+vLw0aNOC7775LcLmIiAgiIiJifw4PD6d48eKEhYWRO3fupO+I2I1r167Rq1cvvv76awBq1qzJwoULdd0hEZFMKDw8HHd392R/f9vVQOt8+fJZbQ26du0agNVWpEcpWbIktWrVYtu2bY9cztXVFVdX1yRtW+zfhg0b6NixI+fOncPJyYnAwECGDBkSr3tWREQE7Kz7zNfXl8OHDxMZGRln+v79+wGSdd0YYwwODna1m5LGIiIiGDRoEA0bNuTcuXM8+eST/PbbbwwfPlyBSEREEmRXaaFFixbcvHmTb775Js70BQsWULRoUapXr56k7Z04cYKtW7fqujNZyJEjR/D392fSpEkYY+jRowd79uyhatWqti5NRETsnF392fz888/z3HPP0atXL8LDwylTpgxfffUVa9euZdGiRbHXKOrWrRsLFizg+PHjlChRAoCGDRtSp04dKlSoQO7cudm/fz8TJ07EYrEwZswYW+6WpANjDJ9++ilvvfUWd+7cIV++fHz22Wc0a9bM1qWJiEgGYVehCODbb79l+PDhjBw5kmvXruHt7c1XX31FmzZtYpeJiooiKiqKh8eI+/r6snTpUiZNmsSdO3coWLAgDRo0YMSIEZQtW9YWuyLp5OrVq3Tv3j12MP1zzz3HggULKFKkiI0rExGRjMSuzj6zFykdvS7pZ/369bz22mtcuHABFxcXxo8fT//+/TWOTEQkC8pUZ5+JJNa9e/cYOXIkEydOxBgT26Lo5+dn69JERCSDUiiSDOevv/6iXbt27Ny5E4AePXowefJkcuTIYePKREQkI1Mfg2QoX3zxBZUqVWLnzp3kzZuXb775htmzZysQiYhIiqmlSDKEGzdu0Lt3bxYtWgRA3bp1WbRoEU888YSNKxMRkcxCLUVi93bu3MnTTz8de1mGMWPGsH79egUiERFJVWopErsVHR3NlClTeOedd7h//z6enp4sXryYmjVr2ro0ERHJhBSKxC5duXKFzp07s3r1agBatWrFnDlzyJs3r40rExGRzErdZ2J3Nm3ahJ+fH6tXryZbtmx88sknLFu2TIFIRETSlEKR2I2oqChGjx7Ns88+y/nz5/H29mbHjh307NkTi8Vi6/JERCSTU/eZ2IULFy7Qrl07Nm3aBECXLl2YPn06OXPmtG1hIiKSZSgUic399NNPdOjQgStXrpAzZ04++eQTOnToYOuyREQki1H3mdhMZGQk7777Lo0bN+bKlStUqFCBXbt2KRCJiIhNqKVIbOL8+fO0a9eOzZs3A/DGG2/w8ccfkz17dhtXJiIiWZVCkaS7n3/+mfbt23PlyhVy5crFnDlzaN26ta3LEhGRLE7dZ5JuoqKiCAwM5L///S9XrlyhYsWK7Nq1S4FIRETsglqKJF1cvnyZ9u3bs27dOuDBne2nTJmi7jIREbEbCkWS5rZs2ULr1q05f/48OXLkYPbs2RpMLSIidkfdZ5JmjDFMmjSJevXqxV6M8Y8//lAgEhERu6RQJGnm2LFjvPvuu0RFRdGuXTv++OMPypUrZ+uyRERErFL3maSZJ598kqCgIO7fv69bdYiIiN1TKJI01a1bN1uXICIikijqPhMRERFBoUhEREQEUCgSERERARSKRERERACFIhERERFAoUhEREQEUCgSERERARSKRERERACFIhERERFAoUhEREQEUCgSERERARSKRERERACFIhERERFAoUhEREQEUCgSERERARSKRERERACFIhERERFAoUhEREQEUCgSERERARSKRERERACFIhERERFAoUhEREQEUCgSERERARSKRERERACFIhERERFAoUhEREQEsMNQdPPmTfr370/RokXJli0bfn5+LFmyJFHrXr58mc6dO5M/f35y5MhBjRo1WL9+fRpXLCIiIpmB3YWili1bsmDBAkaNGsWaNWuoWrUqbdu2ZfHixY9cLyIigmeffZb169czdepUvvvuOwoVKkTjxo3ZvHlzOlWfvvadDaXtp9vYdzbU1qWIiIhkeBZjjLF1ETFWr15NkyZNWLx4MW3bto2d3qhRIw4ePMjp06dxdHS0uu7MmTMJCAjgt99+o0aNGgBERkZSsWJF3Nzc2L59e6LrCA8Px93dnbCwMHLnzp2ynUpDgd8fZP5vJ+n8TEkCXypv63JERERsKqXf33bVUrRixQrc3Nx45ZVX4kzv0qUL58+ff2SwWbFiBV5eXrGBCMDJyYkOHTqwY8cOzp07l2Z1p6ez12+z/2wYB86FsfLP8wCs/PM8B86Fsf9sGGev37ZxhSIiIhmTk60LeNiBAwd46qmncHKKW1aFChVi5z/zzDMJrlu7du1402PWPXjwIMWKFbO6bkREBBEREbE/h4eHJ6v+9FDrg42x/7f88++1W/doOn1L7PSTE5qkc1UiIiIZn121FIWEhODh4RFvesy0kJCQNFl3/PjxuLu7xz6KFy+e1NLTzZTWfjg5PIhDMf2eMf86OViY0trPFmWJiIhkeHYVigAsFkuy5qVk3aFDhxIWFhb7OHPmzOMLtZHmTxfjfwE1rc77X0BNmj9tvTVMREREHs2uus/y5ctntUXn2rVrAFZbglJjXVdXV1xdXZNars1ZLGDM//8rIiIiyWdXLUW+vr4cPnyYyMjIONP3798PgI+PzyPXjVkuqetmNPncXCjg5opvMXfGtfDBt5g7BdxcyefmYuvSREREMiy7OiV/zZo1vPDCCyxZsoTWrVvHTn/++efZt2/fI0/JnzVrFr1792bbtm1Ur14deHBKvp+fH25ubmzbti3RdWSEU/IjIqNwcXTAYrFgjOFeVDSuTtaPjYiISFaQ0u9vu+o+e/7553nuuefo1asX4eHhlClThq+++oq1a9eyaNGi2EDUrVs3FixYwPHjxylRogQAXbt2JSgoiFdeeYUJEyZQsGBBZs6cSXBwMOvWrbPlbqWJhwOQxWJRIBIREUkhuwpFAN9++y3Dhw9n5MiRXLt2DW9vb7766ivatGkTu0xUVBRRUVE83Mjl6urK+vXrGTx4MH379uX27dv4+fmxZs0a6tata4tdERERkQzErrrP7EVG6D4TERGRuDLVFa1FREREbEWhSERERASFIhERERHADgda24OYYVb2fA80ERERiSvmezu5w6UViqy4ceMGgF3fA01ERESsCwkJwd3dPcnr6ewzK6Kjozl//jy5cuV67P3W5NHCw8MpXrw4Z86c0Zl8dka/G/um34/90u/GfoWFheHp6cn169fJkydPktdXS5EVDg4OPPHEE7YuI1PJnTu3PjzslH439k2/H/ul3439cnBI3pBpDbQWERERQaFIREREBFAokjTm6urKqFGjcHV1tXUp8i/63dg3/X7sl3439iulvxsNtBYRERFBLUUiIiIigEKRiIiICKBQJCIiIgIoFEkauXnzJv3796do0aJky5YNPz8/lixZYuuyhAdXbB88eDCNGjWiQIECWCwWAgMDbV2WABs2bKBr1654e3uTM2dOihUrRrNmzdi1a5etS8vy9u7dS5MmTfD09CR79ux4eHhQo0YNFi1aZOvSxIq5c+disVhwc3NL0noKRZImWrZsyYIFCxg1ahRr1qyhatWqtG3blsWLF9u6tCwvJCSETz/9lIiICJo3b27rcuQhs2bN4uTJk/Tr14/Vq1czdepULl++jL+/Pxs2bLB1eVlaaGgoxYsX5/3332f16tUsXLiQkiVL8tprrzF27FhblycPOXfuHAMHDqRo0aJJXldnn0mqW716NU2aNGHx4sW0bds2dnqjRo04ePAgp0+fxtHR0YYVZm0xb3mLxcLVq1cpUKAAo0aNUmuRHbh8+TIFCxaMM+3mzZuUKVMGHx8f1q1bZ6PKJCH+/v6cP3+e06dP27oU+ceLL76IxWLBw8OD5cuXc/PmzUSvq5YiSXUrVqzAzc2NV155Jc70Ll26cP78ebZv326jygQehCHd088+/TsQAbi5uVGuXDnOnDljg4rkcfLnz4+Tk+6YZS8WLVrE5s2bmTlzZrLWVyiSVHfgwAGeeuqpeB8UFSpUiJ0vIokTFhbG7t27KV++vK1LER7cMDwyMpIrV64wc+ZMfvzxR4YMGWLrsoQHLa39+/dnwoQJyb5/qeKtpLqQkBBKly4db7qHh0fsfBFJnICAAG7dusXw4cNtXYoAvXv3Zvbs2QC4uLgwbdo0evbsaeOqBB78bry8vOjVq1eyt6FQJGniUd0z6roRSZwRI0bw5ZdfMn36dCpXrmzrcgQYNmwY3bt35/Lly6xcuZI+ffpw69YtBg4caOvSsrRvvvmGlStXsmfPnhR9xygUSarLly+f1daga9euAf/fYiQiCRs9ejRjx45l3Lhx9OnTx9blyD88PT3x9PQE4IUXXgBg6NChdOrUiQIFCtiytCzr5s2bBAQE0LdvX4oWLUpoaCgA9+7dAx6cOejs7EzOnDkfuy2NKZJU5+vry+HDh4mMjIwzff/+/QD4+PjYoiyRDGP06NEEBgYSGBjIsGHDbF2OPEK1atWIjIzk77//tnUpWdbVq1e5dOkSH330EXnz5o19fPXVV9y6dYu8efPSvn37RG1LLUWS6lq0aMGcOXP45ptvaN26dez0BQsWULRoUapXr27D6kTs25gxYwgMDOTdd99l1KhRti5HHmPjxo04ODhYHUcp6aNw4cJs3Lgx3vQJEyawefNm1qxZQ/78+RO1LYUiSXXPP/88zz33HL169SI8PJwyZcrw1VdfsXbtWhYtWqRrFNmBNWvWcOvWLW7cuAHAoUOHWL58OfCgSyBHjhy2LC/L+uijjxg5ciSNGzemSZMmbNu2Lc58f39/G1UmPXr0IHfu3FSrVo1ChQpx9epVli1bxtKlSxk0aJC6zmwoW7Zs1KtXL970+fPn4+joaHVeQnTxRkkTN2/eZPjw4Xz99ddcu3YNb29vhg4dSps2bWxdmgAlS5bk1KlTVuedOHGCkiVLpm9BAkC9evXYvHlzgvP1cW078+bNY968eRw+fJjQ0FDc3NyoWLEi3bt3p0OHDrYuT6zo3Llzki/eqFAkIiIiggZai4iIiAAKRSIiIiKAQpGIiIgIoFAkIiIiAigUiYiIiAAKRSIiIiKAQpGIiIgIoFAkIiIiAigUiYiIiAAKRSIiIiKAQpGIZACNGjWiVq1a/PTTT9SqVYscOXJQsmRJli5dCsDSpUupUqUKOXLkoFy5clbvmC0i8ji695mI2L0CBQqQPXt2ChcuzIABA8iTJw9DhgzhyJEj9O7dm71799K3b18cHR3p168f9+/f59y5c7YuW0QyGLUUiYhdO3XqFFevXqVw4cJs2bKFNm3a0LhxYwYPHsy9e/cIDg5mw4YNtGzZkmbNmtGrVy/Onz/P9evX+eyzz3Bzc8PNzQ0XFxecnZ1jf27QoEGya5o1axaVKlXC2dmZwMDA1NtZEbEphSIRsWu7du0CYMyYMbi4uMRODw8PB2DChAlYLJbY6Tdv3sTZ2ZlcuXLRrVs3bt68yc2bN+ncuTN9+/aN/XnDhg3JrqlIkSKMHj2a5s2bJ3sbImJ/FIpExK7t3r0bV1fXeC07u3btomjRolSoUCHO9D179uDj44OTk1Oc6fv27Yu3bHI1b96cF198EXd391TZnojYB4UiEbFru3btomLFijg7O8eZvnPnTqpUqWJ1+cqVK8eZZozhwIEDqRaKRCRzUigSEbu2e/fueOHn7t27HDx4MN70CxcucPHixXih6Pjx40RERFC+fPk0r1dEMi6FIhGxW2fPnuXy5cvxws+ff/5JZGRkvOkx44+sLV+2bFlcXV2tPs+zzz5LtmzZrD5GjBiRinskIvbM6fGLiIjYRkIh51HTnZ2d8fX1jTP9ceOJ1q9fnxrlikgGp5YiEbFbzZo1wxgTL+T07t0bYwwFChSIM33UqFHcu3cvXotQag6yBoiMjOTu3btERUXF+b+IZGwKRSKS6aV2KBo7dizZs2dn/vz5jBs3juzZs/PFF1+k2vZFxDZ0RWsRERER1FIkIiIiAigUiYiIiAAKRSIiIiKAQpGIiIgIoFAkIiIiAigUiYiIiAAKRSIiIiKAQpGIiIgIoFAkIiIiAigUiYiIiAAKRSIiIiIA/B/ceEtZsImppgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "###################\n",
    "## Figure 12\n",
    "###################\n",
    "\n",
    "plt.plot(mVec_fine, cVec, \"k-\")\n",
    "plt.plot(mVecBot, cVecBot, \"*\")\n",
    "plt.xlim(2 * self_a_min, 4.0)\n",
    "plt.ylim(-0.1, 3.0)\n",
    "plt.xlabel(r\"$m_{T-1}$\")\n",
    "plt.ylabel(r\"${c}_{T-1}(m_{T-1})$\")\n",
    "plt.title(\n",
    "    r\"$c_{T-1}(m_{T-1})$ (solid) versus $\\grave c_{T-1}(m_{T-1})$\"\n",
    "    + \"\\n using EGM and EEE grid of $a$ (star)\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '$\\\\mathfrak{v}^{\\\\prime}_{T-1}(a_{T-1})$ (solid) versus $\\\\grave \\\\grave \\\\mathfrak{v}^{\\\\prime}(a_{T-1})$\\n using EGM with EEE grid of a (star)')"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "##################################\n",
    "## Figure 13\n",
    "#################################\n",
    "\n",
    "vpVec_eee = [gothic.VP_Tminus1(a) for a in aVec_eee]\n",
    "\n",
    "plt.plot(aVec_fine, vpVec_fine, \"k-\")\n",
    "plt.plot(aVec_eee, vpVec_eee, \"*\")\n",
    "plt.xlabel(r\"$a_{T-1}$\")\n",
    "plt.ylabel(r\"$\\mathfrak{v}^{\\prime}_{T-1}$\")\n",
    "plt.title(\n",
    "    r\"$\\mathfrak{v}^{\\prime}_{T-1}(a_{T-1})$ (solid) versus $\\grave \\grave \\mathfrak{v}^{\\prime}(a_{T-1})$\"\n",
    "    + \"\\n using EGM with EEE grid of a (star)\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 10. Artifical Borrowing Constraint \n",
    "\n",
    "- See more detailed discussion [here](https://llorracc.github.io/SolvingMicroDSOPs/#Imposing-Artificial-Borrowing-Constraints)\n",
    "\n",
    "Some applications assume an externally imposed borrowing constraint. For instance, when the external borrowing constraint is exactly zero, it is binding before the self-imposed borrowing constraint takes effect.  \n",
    "\n",
    "This can be easily taken care of by replacing the first point in the m grid with 0 instead of a self-imposed borrowing constraint. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "code_folding": [
     0,
     11
    ],
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "## set the bool for constrained to be TRUE\n",
    "\n",
    "constrained = True\n",
    "\n",
    "# Create initial consumption function:\n",
    "cVec_const = [0.0]\n",
    "mVec_const = [self_a_min]\n",
    "\n",
    "## now the a_min depends on if artifical borrowing constraint is tighter than the natural one\n",
    "if constrained and self_a_min < 0:\n",
    "    mVec_const = [0.0]\n",
    "for a in aVec_fine:\n",
    "    c = gothic.C_Tminus1(a)\n",
    "    m = c + a\n",
    "    if constrained:\n",
    "        c = np.minimum(c, m)\n",
    "    cVec_const.append(c)\n",
    "    mVec_const.append(m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "code_folding": [
     0
    ],
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "## set the bool for constrained to be FALSE\n",
    "\n",
    "constrained = False\n",
    "\n",
    "# Create initial consumption function:\n",
    "cVec_uconst = [0.0]\n",
    "mVec_uconst = [self_a_min]\n",
    "\n",
    "## now the a_min depends on if artifical borrowing constraint is tighter than the natural one\n",
    "if constrained and self_a_min < 0:\n",
    "    mVec_const = [0.0]\n",
    "for a in aVec_fine:\n",
    "    c = gothic.C_Tminus1(a)\n",
    "    m = c + a\n",
    "    if constrained:\n",
    "        c = np.minimum(c, m)\n",
    "    cVec_uconst.append(c)\n",
    "    mVec_uconst.append(m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not surprisingly, the main difference between the two c functions lies in the area of negative wealth. (See Figure 18)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "code_folding": [
     0
    ],
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Constrained (solid) and Unconstrained Consumption (dashed)')"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#####################\n",
    "### Figure 18\n",
    "#####################\n",
    "\n",
    "plt.plot(mVec_const, cVec_const, \"k-\")\n",
    "plt.plot(mVec_uconst, cVec_uconst, \"--\")\n",
    "plt.xlabel(r\"$m_{T-1}$\")\n",
    "plt.ylabel(r\"$c_{T-1}(m_{T-1})\")\n",
    "plt.ylim(0.0, 5.0)\n",
    "plt.vlines(0.0, 0.0, 5.0, \"k\", \"-.\")\n",
    "plt.title(\"Constrained (solid) and Unconstrained Consumption (dashed)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 11. Solving for $c_t(m_t)$ in Multiple Periods\n",
    "\n",
    "- See more detailed discussion [here](https://llorracc.github.io/SolvingMicroDSOPs/#x1-210006)\n",
    "\n",
    "We now employ the recursive nature of the problem to solve all periods. Recall that in general,\n",
    "\n",
    "$$\\mathfrak{v}'(a_{t}) = \\mathbb{E}_{t}[\\beta \\mathrm{R} \\PermGroFac^{-\\rho} _{t+1} \\mathrm{u}' (c _{t+1} (\\mathcal{R} _{t+1}a _{t}+\\theta _{t+1}))]$$\n",
    "\n",
    "That is, once we have $c _{t+1} (\\mathcal{R} _{t+1}a _{t}+\\theta _{t+1})$ in hand, we can solve backwards for the next period, and so on back to the first period. \n",
    "\n",
    "As with $c_{T-1}$, we will employ the first-order condition\n",
    "\n",
    "$$u'(c_{t}) = \\mathfrak{v}'(m_{t}-c_{t}) = \\mathfrak{v}'(a_{t})$$\n",
    "\n",
    "to obtain our consumption function from $\\mathfrak{v}^{'}_{t}(a_t)$. \n",
    "\n",
    "To get smoothness, we will make a very large \"EEE\" grid. \n",
    "\n",
    "We will also use Python's \"time\" module to time the whole procedure as it executes.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "from time import time\n",
    "\n",
    "T = 60  # How many periods/consumption functions?\n",
    "aVec_eee = setup_grids_expMult(\n",
    "    a_min, a_max, 40\n",
    ")  # Create a bigger grid, for smoother curve.\n",
    "\n",
    "self_a_min_life = T * [self_a_min]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "code_folding": [
     11,
     33
    ],
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "## to make the solution simpler for life cycle, i.e. no need to update self_a_min every period\n",
    "constrained = True\n",
    "\n",
    "##########################################################\n",
    "# Create initial consumption function for the second to the last period\n",
    "#########################################################\n",
    "\n",
    "cVec = [0.0]\n",
    "mVec = [self_a_min]\n",
    "if constrained and self_a_min < 0:\n",
    "    mVec = [0.0]\n",
    "\n",
    "for a in aVec_eee:\n",
    "    c = gothic.C_Tminus1(a)\n",
    "    m = c + a\n",
    "    if constrained:\n",
    "        c = np.minimum(c, m)\n",
    "    cVec.append(c)\n",
    "    mVec.append(m)\n",
    "\n",
    "# Set up the interpolation:\n",
    "cFunc = InterpolatedUnivariateSpline(mVec, cVec, k=1)\n",
    "\n",
    "## save it in a dictionary\n",
    "cFunc_life = {T - 1: cFunc}\n",
    "\n",
    "########################################\n",
    "## backward iteration over life cycle\n",
    "########################################\n",
    "\n",
    "# Loop for all consumption functions in our range:\n",
    "for t in range(T - 2, -1, -1):\n",
    "    cVec = [0.0]\n",
    "    mVec = [self_a_min]\n",
    "    if constrained and self_a_min < 0:\n",
    "        mVec = [0.0]\n",
    "    for a in aVec_eee:\n",
    "        c = gothic.C_t(\n",
    "            a, cFunc\n",
    "        )  ## notice here the c func from previous period is the input !!!\n",
    "        m = c + a\n",
    "        if constrained:\n",
    "            c = np.minimum(c, m)\n",
    "        cVec.append(c)\n",
    "        mVec.append(m)\n",
    "\n",
    "    # Update the consumption function\n",
    "    cFunc = InterpolatedUnivariateSpline(mVec, cVec, k=1)\n",
    "\n",
    "    # Save updated function:\n",
    "    cFunc_life[t] = cFunc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "code_folding": [],
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Convergence of $\\\\grave c_{T-n}(m)$ Functions as $n$ Increases')"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "##############################\n",
    "#### Figure 19\n",
    "##############################\n",
    "\n",
    "\n",
    "for t in range(T - 1, T - 10, -1):\n",
    "    cFunc = cFunc_life[t]\n",
    "    cVec_fine = cFunc(mVec_fine)\n",
    "    plt.plot(mVec_fine, cVec_fine, \"k-\")\n",
    "\n",
    "plt.xlabel(r\"$m$\")\n",
    "plt.ylabel(r\"$\\grave c_{T-n}(m)$\")\n",
    "plt.title(r\"Convergence of $\\grave c_{T-n}(m)$ Functions as $n$ Increases\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The consumption functions converge as the horizon extends."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 12. Multiple Control Variables (MC)\n",
    "\n",
    "- See more detailed discussion [here](https://llorracc.github.io/SolvingMicroDSOPs/#Multiple-Control-Variables)\n",
    "\n",
    "Besides consumption, the new control variable that the consumer can now choose is the portion of the portfolio $\\varsigma_t$ to invest in risky assets with a return factor $\\mathbf{R}_{t+1}$.  The overall return on the consumer’s portfolio between $t$ and $t + 1$, $\\pmb{\\mathfrak{R}}_t$, is equal to the following.\n",
    "\n",
    "\n",
    "\\begin{equation}\n",
    "\\pmb{\\mathfrak{R}}_t = R + (\\mathbf{R}_{t+1}-R) \\varsigma_t\n",
    "\\end{equation}\n",
    "\n",
    "Now, $\\mathfrak{v}_t$ is a function of both $a_{t}$ and the risky asset share $\\varsigma_t$.\n",
    "We also need to define $\\mathfrak{v}^{a}$ and $\\mathfrak{v}^{\\varsigma}$, the expected marginal value from saving and risky share, respectively.\n",
    "\n",
    "We can solve the problem sequentially in two separate stages. \n",
    "\n",
    " - At the first stage, solve the optimizing share $\\varsigma^*$ for a vector of predetermined $a$ relying on the FOC condition associated with $\\mathfrak{v}^{\\varsigma}$. \n",
    " - At the second stage, use optimal $\\varsigma^*$ to construct $\\pmb{\\mathfrak{R}}$ and solve the consumption exactly in a similar way as before with only one single choice variable.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we need to redefine and add additional Gothic functions for the portfolio choice problem. In the meantime, some elements of the class remain the same. One easy and consistent way of achiving this end is to ''inherit'' the existing Gothic class and superimpose some of the functions with modified ones. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "code_folding": [
     6,
     32,
     64,
     96,
     99,
     115,
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    ]
   },
   "outputs": [],
   "source": [
    "## MC stands for multiple controls\n",
    "\n",
    "## Now the GothicMC takes Distribution as a new input, which\n",
    "## is a class of two discretized log normal distributions, for income and risky asset return\n",
    "\n",
    "\n",
    "class GothicMC(Gothic):  ## inheriting from Gothic class\n",
    "    ## inheritance from Gothic and adds additional functions/methods for portfolio choice\n",
    "    def __init__(\n",
    "        self,\n",
    "        u,\n",
    "        beta,\n",
    "        rho,\n",
    "        PermGroFac,\n",
    "        R,\n",
    "        Distribution,\n",
    "        share_grid_size,\n",
    "        Income=None,\n",
    "        Return=None,\n",
    "        variable_variance=False,\n",
    "    ):\n",
    "        super().__init__(u, beta, rho, PermGroFac, R, Income, variable_variance=False)\n",
    "        ## super(). here initialize the GothicMC class as Gothic does\n",
    "        self.Return = Return\n",
    "        self.Distribution = (\n",
    "            Distribution  ## a class instance of two log normal distributions\n",
    "        )\n",
    "        ## x1 is income and x2 is asset return\n",
    "        ### additional discretized risky asset returns\n",
    "        self.share_grid_size = share_grid_size\n",
    "        self.varsigma_grids = np.linspace(0.0, 1.0, self.share_grid_size)\n",
    "\n",
    "    def varsigma_Tminus1(self, a):\n",
    "        \"\"\"\n",
    "        Optimization of Share on continuous interval [0,1]\n",
    "\n",
    "        \"\"\"\n",
    "\n",
    "        ## make an array storing FOCs for different shares at this value of a\n",
    "        share_girds = self.varsigma_grids\n",
    "        FOC_s = np.empty_like(share_girds)\n",
    "        for j in range(len(share_girds)):\n",
    "            FOC_s[j] = self.Vsigma_Tminus1(a, share_girds[j])\n",
    "\n",
    "        ## find the optimal share\n",
    "        if a < 0:\n",
    "            varsigma_opt = 0.0\n",
    "        else:\n",
    "            if FOC_s[-1] > 0.0:  ## mv of the share=1 is still positive\n",
    "                varsigma_opt = 1.0\n",
    "            elif FOC_s[0] < 0.0:  # mv of the share=0 is still negative\n",
    "                varsigma_opt = 0.0\n",
    "            else:\n",
    "                crossing = np.logical_and(FOC_s[1:] <= 0.0, FOC_s[:-1] >= 0.0)\n",
    "                idx = np.argwhere(crossing)[0]\n",
    "                bot_s = share_girds[idx]\n",
    "                top_s = share_girds[idx + 1]\n",
    "                bot_f = FOC_s[idx]\n",
    "                top_f = FOC_s[idx + 1]\n",
    "                alpha = 1.0 - top_f / (top_f - bot_f)\n",
    "                varsigma_opt = (1.0 - alpha) * bot_s + alpha * top_s\n",
    "        return np.squeeze(varsigma_opt)\n",
    "\n",
    "    def varsigma_t(self, a, c_prime):\n",
    "\n",
    "        ## make an array storing FOCs for different share at this value of a\n",
    "        share_girds = self.varsigma_grids\n",
    "        FOC_s = np.empty_like(share_girds)\n",
    "        for j in range(len(share_girds)):\n",
    "            FOC_s[j] = self.Vsigma_t(a, share_girds[j], c_prime)\n",
    "\n",
    "        ## find the optimal share\n",
    "        if a < 0:\n",
    "            varsigma_opt = 0.0\n",
    "        else:\n",
    "            if FOC_s[-1] > 0.0:  ## mv of the share=1 is still positive\n",
    "                varsigma_opt = 1.0\n",
    "            elif FOC_s[0] < 0.0:  # mv of the share=0 is still negative\n",
    "                varsigma_opt = 0.0\n",
    "            else:\n",
    "                crossing = np.logical_and(FOC_s[1:] <= 0.0, FOC_s[:-1] >= 0.0)\n",
    "                idx = np.argwhere(crossing)[0]\n",
    "                bot_s = share_girds[idx]\n",
    "                top_s = share_girds[idx + 1]\n",
    "                bot_f = FOC_s[idx]\n",
    "                top_f = FOC_s[idx + 1]\n",
    "                alpha = 1.0 - top_f / (top_f - bot_f)\n",
    "                varsigma_opt = (1.0 - alpha) * bot_s + alpha * top_s\n",
    "        return np.squeeze(varsigma_opt)\n",
    "\n",
    "    def C_Tminus1(self, a):\n",
    "        return self.Va_Tminus1(a) ** (-1.0 / self.rho)\n",
    "\n",
    "    def C_t(self, a, c_prime):\n",
    "        return self.Va_t(a, c_prime) ** (-1.0 / self.rho)\n",
    "\n",
    "    def Va_Tminus1(self, a):\n",
    "\n",
    "        \"\"\"\n",
    "        gothic v's first derivative with respect to the a given optimal share varsigma_opt at a\n",
    "        \"\"\"\n",
    "        varsigma_opt = self.varsigma_Tminus1(a)\n",
    "        ## the g function below computes the gothic v' for a particular realization of risky return and income shock\n",
    "        Va_func = lambda tinc_shk, rreturn: (\n",
    "            self.R + (rreturn - self.R) * varsigma_opt\n",
    "        ) * self.u.prime(\n",
    "            (self.R + (rreturn - self.R) * varsigma_opt) * a / self.PermGroFac[-1] + tinc_shk\n",
    "        )\n",
    "        ## the Distribution.E() calculates the expectation of g values over the joint distribution of return and income shock\n",
    "        GVTm1Pa = self.beta * self.PermGroFac_to_minusRho[-1] * self.Distribution.E(Va_func)\n",
    "        return GVTm1Pa\n",
    "\n",
    "    def Va_t(self, a, c_prime):\n",
    "        varsigma_opt = self.varsigma_t(a, c_prime)\n",
    "        Va_func = lambda tinc_shk, rreturn: (\n",
    "            self.R + (rreturn - self.R) * varsigma_opt\n",
    "        ) * self.u.prime(\n",
    "            c_prime(\n",
    "                (self.R + (rreturn - self.R) * varsigma_opt) * a / self.PermGroFac[-1]\n",
    "                + tinc_shk\n",
    "            )\n",
    "        )\n",
    "        GVtPa = self.beta * self.PermGroFac_to_minusRho[-1] * self.Distribution.E(Va_func)\n",
    "        return GVtPa\n",
    "\n",
    "    def Vsigma_Tminus1(self, a, varsigma):\n",
    "        \"\"\"\n",
    "        gothic v's first derivative with respect to the portfolio share varsigma in the last period\n",
    "        \"\"\"\n",
    "        if a != 0.0:\n",
    "            Vshare_func = lambda tinc_shk, rreturn: (rreturn - self.R) * self.u.prime(\n",
    "                (self.R + (rreturn - self.R) * varsigma) * a / self.PermGroFac[-1] + tinc_shk\n",
    "            )\n",
    "            # Because next period the consumer spends everything,\n",
    "            # we substitute\n",
    "            GVTm1Psigma = (\n",
    "                self.beta * a / self.PermGroFac[-1] * self.Distribution.E(Vshare_func)\n",
    "            )\n",
    "        else:\n",
    "            GVTm1Psigma = np.inf\n",
    "        return GVTm1Psigma\n",
    "\n",
    "    def Vsigma_t(self, a, varsigma, c_prime):\n",
    "        \"\"\"\n",
    "        gothic v's first derivative with respect to the portfolio share varsigma in all earlier periods\n",
    "        \"\"\"\n",
    "        if a != 0.0:\n",
    "            Vshare_func = lambda tinc_shk, rreturn: (rreturn - self.R) * self.u.prime(\n",
    "                c_prime(\n",
    "                    (self.R + (rreturn - self.R) * varsigma) * a / self.PermGroFac[-1]\n",
    "                    + tinc_shk\n",
    "                )\n",
    "            )\n",
    "            GVtPsigma = (\n",
    "                self.beta * a / self.PermGroFac[-1] * self.Distribution.E(Vshare_func)\n",
    "            )\n",
    "        else:\n",
    "            GVtPsigma = np.inf\n",
    "        return GVtPsigma"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We create a discretized distribution of the risky asset return $\\mathbf{R}_{t+1}$ with an expected excess return of 2 percent and a standard deviation of 15%. See more details regarding the log-normal distribution [here](https://www.econ2.jhu.edu/people/ccarroll/public/LectureNotes/MathFacts/MathFactsList.pdf)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
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     0
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   },
   "outputs": [],
   "source": [
    "## set parameters for risky asset returns, i,e, make sure there is positive excessive return\n",
    "## otherwise, the problem will be trivial\n",
    "## discretized log-normal asset returns\n",
    "\n",
    "theta_sigma_port = 0.15\n",
    "theta_mu_port = -0.5 * theta_sigma_port**2\n",
    "# Create \"frozen\" distribution instance\n",
    "theta_z_port = stats.lognorm(s=theta_sigma_port, scale=exp(theta_mu_port))\n",
    "\n",
    "RiskyR_grid_N = 7\n",
    "RiskyR_sigma = 0.15  ## standard deviation of risky asset return\n",
    "phi = 0.02  ## excess return from risky asset\n",
    "RiskyR_mu = R + phi\n",
    "# Create \"frozen\" distribution instance\n",
    "mu = np.log(RiskyR_mu**2 / np.sqrt(RiskyR_sigma**2 + RiskyR_mu**2))\n",
    "\n",
    "sigma = np.sqrt(np.log(RiskyR_sigma**2 / RiskyR_mu**2 + 1))\n",
    "\n",
    "RiskyR_z = stats.lognorm(s=sigma, scale=np.exp(mu))\n",
    "\n",
    "Distribution = DiscreteApproximationTwoIndependentDistribs(\n",
    "    theta_grid_N,\n",
    "    theta_z_port.cdf,\n",
    "    theta_z_port.pdf,\n",
    "    theta_z_port.ppf,\n",
    "    RiskyR_grid_N,\n",
    "    RiskyR_z.cdf,\n",
    "    RiskyR_z.pdf,\n",
    "    RiskyR_z.ppf,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "code_folding": [
     0,
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    "lines_to_next_cell": 2,
    "scrolled": true
   },
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'GothicMC' object has no attribute 'PermGroFac'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "Input \u001b[0;32mIn [43]\u001b[0m, in \u001b[0;36m<cell line: 34>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     33\u001b[0m \u001b[38;5;66;03m# print('period'+str(T))\u001b[39;00m\n\u001b[1;32m     34\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m a \u001b[38;5;129;01min\u001b[39;00m aVec_eee_big:\n\u001b[0;32m---> 35\u001b[0m     varsigma \u001b[38;5;241m=\u001b[39m \u001b[43mgothicMC\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mvarsigma_Tminus1\u001b[49m\u001b[43m(\u001b[49m\u001b[43ma\u001b[49m\u001b[43m)\u001b[49m  \u001b[38;5;66;03m## optimal share for a\u001b[39;00m\n\u001b[1;32m     36\u001b[0m     \u001b[38;5;66;03m# print(varsigma)\u001b[39;00m\n\u001b[1;32m     37\u001b[0m     c \u001b[38;5;241m=\u001b[39m gothicMC\u001b[38;5;241m.\u001b[39mC_Tminus1(a)  \u001b[38;5;66;03m## optimal c given varsigma being optimal\u001b[39;00m\n",
      "Input \u001b[0;32mIn [41]\u001b[0m, in \u001b[0;36mGothicMC.varsigma_Tminus1\u001b[0;34m(self, a)\u001b[0m\n\u001b[1;32m     41\u001b[0m FOC_s \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mempty_like(share_girds)\n\u001b[1;32m     42\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m j \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(\u001b[38;5;28mlen\u001b[39m(share_girds)):\n\u001b[0;32m---> 43\u001b[0m     FOC_s[j] \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mVsigma_Tminus1\u001b[49m\u001b[43m(\u001b[49m\u001b[43ma\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mshare_girds\u001b[49m\u001b[43m[\u001b[49m\u001b[43mj\u001b[49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     45\u001b[0m \u001b[38;5;66;03m## find the optimal share\u001b[39;00m\n\u001b[1;32m     46\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m a \u001b[38;5;241m<\u001b[39m \u001b[38;5;241m0\u001b[39m:\n",
      "Input \u001b[0;32mIn [41]\u001b[0m, in \u001b[0;36mGothicMC.Vsigma_Tminus1\u001b[0;34m(self, a, varsigma)\u001b[0m\n\u001b[1;32m    131\u001b[0m     Vshare_func \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mlambda\u001b[39;00m tinc_shk, rreturn: (rreturn \u001b[38;5;241m-\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mR) \u001b[38;5;241m*\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mu\u001b[38;5;241m.\u001b[39mprime(\n\u001b[1;32m    132\u001b[0m         (\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mR \u001b[38;5;241m+\u001b[39m (rreturn \u001b[38;5;241m-\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mR) \u001b[38;5;241m*\u001b[39m varsigma) \u001b[38;5;241m*\u001b[39m a \u001b[38;5;241m/\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mPermGroFac[\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m] \u001b[38;5;241m+\u001b[39m tinc_shk\n\u001b[1;32m    133\u001b[0m     )\n\u001b[1;32m    134\u001b[0m     \u001b[38;5;66;03m# Because next period the consumer spends everything,\u001b[39;00m\n\u001b[1;32m    135\u001b[0m     \u001b[38;5;66;03m# we substitute\u001b[39;00m\n\u001b[1;32m    136\u001b[0m     GVTm1Psigma \u001b[38;5;241m=\u001b[39m (\n\u001b[0;32m--> 137\u001b[0m         \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mbeta \u001b[38;5;241m*\u001b[39m a \u001b[38;5;241m/\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mPermGroFac\u001b[49m[\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m] \u001b[38;5;241m*\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mDistribution\u001b[38;5;241m.\u001b[39mE(Vshare_func)\n\u001b[1;32m    138\u001b[0m     )\n\u001b[1;32m    139\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m    140\u001b[0m     GVTm1Psigma \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39minf\n",
      "\u001b[0;31mAttributeError\u001b[0m: 'GothicMC' object has no attribute 'PermGroFac'"
     ]
    }
   ],
   "source": [
    "## Solve the portfolio choice problem in the second-to-the-last period\n",
    "\n",
    "t_start = time()\n",
    "\n",
    "#######################################################\n",
    "## new parameterization for the portfolio problems\n",
    "#######################################################\n",
    "\n",
    "## higher risk aversion coefficient\n",
    "rho_port = 6.0\n",
    "u_port = Utility(CRRA=rho_port)\n",
    "\n",
    "### create a GothicMC instance\n",
    "## notice we use a bigger coefficient of risk aversion\n",
    "gothicMC = GothicMC(\n",
    "    u_port, beta, rho_port, PermGroFac, R, Distribution=Distribution, share_grid_size=20\n",
    ")\n",
    "\n",
    "### set the a grid\n",
    "\n",
    "a_max = 100.0\n",
    "a_grid_size = 800\n",
    "aVec_eee_big = setup_grids_expMult(a_min, a_max, a_grid_size)\n",
    "\n",
    "#################################\n",
    "### the last period\n",
    "###############################\n",
    "\n",
    "cVec_port = [0.0]\n",
    "mVec_port = [0.0]\n",
    "varsigmaVec_port = [0.0]\n",
    "\n",
    "# print('period'+str(T))\n",
    "for a in aVec_eee_big:\n",
    "    varsigma = gothicMC.varsigma_Tminus1(a)  ## optimal share for a\n",
    "    # print(varsigma)\n",
    "    c = gothicMC.C_Tminus1(a)  ## optimal c given varsigma being optimal\n",
    "    m = c + a\n",
    "    c = np.minimum(c, m)\n",
    "    cVec_port.append(c)\n",
    "    mVec_port.append(m)\n",
    "    varsigmaVec_port.append(varsigma)\n",
    "\n",
    "# Set up the interpolation:\n",
    "cFunc = InterpolatedUnivariateSpline(mVec_port, cVec_port, k=1)\n",
    "varsigmaFunc = InterpolatedUnivariateSpline(mVec_port[1:], varsigmaVec_port[1:], k=1)\n",
    "\n",
    "## save the grid in a dictionary\n",
    "mGridPort_life = {T - 1: mVec_port}\n",
    "cGridPort_life = {T - 1: cVec_port}\n",
    "varsigmaGrid_life = {T - 1: varsigmaVec_port}\n",
    "\n",
    "## save the interpolated function in a dictionary\n",
    "cFuncPort_life = {T - 1: cFunc}\n",
    "varsigma_life = {T - 1: varsigmaFunc}\n",
    "\n",
    "#################################\n",
    "### backward to earlier periods\n",
    "###############################\n",
    "\n",
    "for t in range(T - 2, 0, -1):\n",
    "    # print('period'+str(t))\n",
    "    cVec_port = [0.0]\n",
    "    mVec_port = [0.0]\n",
    "    varsigmaVec_port = [0.0]\n",
    "    for a in aVec_eee_big:\n",
    "        # print(a)\n",
    "        varsigma = gothicMC.varsigma_t(a, cFunc)  ## optimal share for a\n",
    "        # print(varsigma)\n",
    "        c = gothicMC.C_t(a, cFunc)  ## optimal c given varsigma being optimal\n",
    "        m = c + a\n",
    "        c = np.minimum(c, m)\n",
    "        cVec_port.append(c)\n",
    "        mVec_port.append(m)\n",
    "        varsigmaVec_port.append(varsigma)\n",
    "\n",
    "    # Update the consumption function and share function\n",
    "    cFunc = InterpolatedUnivariateSpline(mVec_port, cVec_port, k=1)\n",
    "    varsigmaFunc = InterpolatedUnivariateSpline(\n",
    "        mVec_port[1:], varsigmaVec_port[1:], k=1\n",
    "    )\n",
    "\n",
    "    ## save the policy grid in a dictionary\n",
    "    mGridPort_life[t] = mVec_port\n",
    "    cGridPort_life[t] = cVec_port\n",
    "    varsigmaGrid_life[t] = varsigmaVec_port\n",
    "\n",
    "    # save interpolated function:\n",
    "    cFuncPort_life[t] = cFunc\n",
    "    varsigma_life[t] = varsigmaFunc\n",
    "\n",
    "t_finish = time()\n",
    "\n",
    "print(\"Time taken, in seconds: \" + str(t_finish - t_start))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Figure 20 plots the ﬁrst-period consumption function generated by the program; qualitatively it does not look much diﬀerent from the consumption functions generated by the program without portfolio choice. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
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   "source": [
    "############################\n",
    "## Figure 20\n",
    "############################\n",
    "cFunc = cFuncPort_life[1]\n",
    "plt.plot(mVec, cFunc(mVec), \"k-\")\n",
    "plt.xlabel(r\"$m$\")\n",
    "plt.ylabel(r\"$c_{1}(m)$\")\n",
    "plt.title(r\"$c_{1}(m)$ with Portfolio Choice\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Figure 21 plots $\\varsigma_1(a_{1})$, the optimal portfolio share as a function of the end-of-period asset $a$ in the first period.\n",
    "\n",
    "- First, even with a coeﬃcient of relative risk aversion of 6, an equity premium of only 4 percent, and an annual standard deviation in equity returns of 15 percent, the optimal choice is for the agent to invest a proportion 1 (100 percent) of the portfolio in stocks (instead of the safe bank account with riskless return R  ) is at values of at  less than about 2. \n",
    "\n",
    "- Second, the proportion of the portfolio kept in stocks is declining in the level of wealth - i.e., the poor should hold all of their meager assets in stocks, while the rich should be cautious, holding more of their wealth in safe bank deposits and less in stocks. This seemingly bizarre (and highly counterfactual) prediction reﬂects the nature of the risks the consumer faces. Those consumers who are poor in measured ﬁnancial wealth are likely to derive a high proportion of future consumption from their labor income. Since by assumption labor income risk is uncorrelated with rate-of-return risk, the covariance between their future consumption and future stock returns is relatively low. By contrast, persons with relatively large wealth will be paying for a large proportion of future consumption out of that wealth, and hence if they invest too much of it in stocks their consumption will have a high covariance with stock returns. Consequently, they reduce that correlation by holding some of their wealth in the riskless form."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "#####################################\n",
    "## Figure 21\n",
    "####################################\n",
    "varsigmaGrid = varsigmaGrid_life[1][1:]\n",
    "## drop the first point (share for zero asset corner solution)\n",
    "plt.plot(aVec_eee_big, varsigmaGrid, \"k-\")\n",
    "plt.xlabel(r\"$a$\")\n",
    "plt.ylabel(r\"$\\varsigma_{1}(a)$\")\n",
    "plt.title(r\"Portfolio Share in Risky Assets in the First Period $\\varsigma(a)$\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cross-validation of the results \n",
    "\n",
    "In order to validate the method, we compare the MicroDSOP solution with that from HARK toolkit's PortfolioConsumer class. We configure the HARK class with exactly the same parameters used above. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "code_folding": [],
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "# Solve the agent over a standard life-cycle\n",
    "\n",
    "init_life_cycle_new = copy(init_lifecycle)\n",
    "T_cyle = T - 1  ## minus 1 because T_cycle is nb periods in a life cycle - 1 in HARK\n",
    "init_life_cycle_new[\"T_cycle\"] = T_cyle\n",
    "init_life_cycle_new[\"CRRA\"] = rho_port\n",
    "init_life_cycle_new[\"Rfree\"] = R\n",
    "init_life_cycle_new[\"LivPrb\"] = [1.0] * T_cyle\n",
    "init_life_cycle_new[\"PermGroFac\"] = [1.0] * T_cyle\n",
    "init_life_cycle_new[\"PermShkStd\"] = [0.0] * T_cyle\n",
    "init_life_cycle_new[\"PermShkCount\"] = 1\n",
    "init_life_cycle_new[\"TranShkStd\"] = [theta_sigma_port] * T_cyle\n",
    "init_life_cycle_new[\"UnempPrb\"] = 0.0\n",
    "init_life_cycle_new[\"RiskyAvg\"] = [R + phi] * T_cyle  ## phi is risk premium\n",
    "init_life_cycle_new[\"RiskyStd\"] = [RiskyR_sigma] * T_cyle\n",
    "init_life_cycle_new[\"RiskyCount\"] = RiskyR_grid_N\n",
    "init_life_cycle_new[\"RiskyAvgTrue\"] = R + phi\n",
    "init_life_cycle_new[\"RiskyStdTrue\"] = RiskyR_sigma\n",
    "init_life_cycle_new[\"DiscFac\"] = beta\n",
    "init_life_cycle_new[\"PermGroFacAgg\"] = 1.0\n",
    "# init_life_cycle_new['aXtraMin'] = a_min+0.00001\n",
    "init_life_cycle_new[\"aXtraMax\"] = a_max\n",
    "init_life_cycle_new[\"aXtraCount\"] = 800\n",
    "\n",
    "LifeCycleType = PortfolioConsumerType(**init_life_cycle_new)\n",
    "\n",
    "LifeCycleType.cycles = 1  ## life cycle problem instead of infinite horizon\n",
    "LifeCycleType.vFuncBool = False  ## no need to calculate the value for the purpose here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "code_folding": [
     0
    ],
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "## solving the model\n",
    "t0 = time()\n",
    "LifeCycleType.solve()\n",
    "LifeCycleType.cFunc = [\n",
    "    LifeCycleType.solution[t].cFuncAdj for t in range(LifeCycleType.T_cycle)\n",
    "]\n",
    "LifeCycleType.ShareFunc = [\n",
    "    LifeCycleType.solution[t].ShareFuncAdj for t in range(LifeCycleType.T_cycle)\n",
    "]\n",
    "t1 = time()\n",
    "print(\n",
    "    \"Solving a \"\n",
    "    + str(LifeCycleType.T_cycle)\n",
    "    + \" period portfolio choice problem takes \"\n",
    "    + str(t1 - t0)\n",
    "    + \" seconds.\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "code_folding": [
     0
    ],
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "## compare the consumption function for the T-1 period\n",
    "which_period = 1\n",
    "mGrid = mGridPort_life[which_period]\n",
    "c_hark = LifeCycleType.cFunc[which_period - 1](mGrid)\n",
    "c_dsop = cFuncPort_life[which_period](mGrid)\n",
    "\n",
    "plt.plot(mGrid, c_hark, \"r--\", label=\"HARK\")\n",
    "plt.plot(mGrid, c_dsop, \"k-\", label=\"MicroDSOP\")\n",
    "plt.legend(loc=0)\n",
    "plt.title(\"consumption function solved by MicroDSOP and HARK at $t=1$\")\n",
    "plt.xlabel(\"m\")\n",
    "plt.ylabel(r\"$c_{1}(m)$\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "code_folding": [
     0
    ],
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "## Compare the solutions for portfolio at the first period in life cycle\n",
    "which_period = 1\n",
    "\n",
    "\n",
    "share_hark = LifeCycleType.ShareFunc[which_period - 1](mGrid)\n",
    "share_dsop = varsigma_life[which_period](mGrid)\n",
    "\n",
    "mGrid = mGrid\n",
    "plt.plot(\n",
    "    mGrid,\n",
    "    share_hark,\n",
    "    \"r--\",\n",
    "    label=\"HARK solution\",\n",
    ")\n",
    "plt.plot(mGrid, share_dsop, \"k-\", label=\"MicroDSOP solution\")\n",
    "plt.legend(loc=3)\n",
    "plt.title(\"share function solved by MicroDSOP and HARK (at $t=1$)\")\n",
    "plt.xlabel(r\"$m$\")\n",
    "plt.ylabel(r\"$\\varsigma_{1}(m)$\")\n",
    "plt.legend(loc=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As shown in the two figures above, the two methods produce visually identical values of optimal consumption and shares at $t=1$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Additional sanity checks\n",
    "\n",
    "We undertake a few additional sanity checks. \n",
    "\n",
    "First, let's check if the solutions are identical in the __second to the last__ period ($T-1$). In dynamic programming problems, it is always wise to start from the terminal solution. There are many good reasons for doing so. For instance,\n",
    "\n",
    "1. solutions to earlier periods of life all depend on the terminal solution. \n",
    "2. the terminal consumption function is trivial (consuming everything) and does not involve interpolation, we can focus on results unrelated to the use of interpolation tools. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "code_folding": [
     0
    ],
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "## Compare the solutions for portfolio at the first period in life cycle\n",
    "\n",
    "which_period = T - 1\n",
    "mGrid = mGrid\n",
    "share_hark = LifeCycleType.ShareFunc[which_period - 1](mGrid)\n",
    "share_dsop = varsigma_life[which_period](mGrid)\n",
    "share_diff = share_hark - share_dsop\n",
    "\n",
    "## plot\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(9, 4))\n",
    "ax1.plot(\n",
    "    mGrid,\n",
    "    share_hark,\n",
    "    \"r--\",\n",
    "    label=\"HARK solution\",\n",
    ")\n",
    "ax1.plot(mGrid, share_dsop, \"k-\", label=\"MicroDSOP solution\")\n",
    "ax1.set_title(\"share function solved \\n by MicroDSOP and HARK (at $T-1$)\")\n",
    "ax1.set_xlabel(r\"$m$\")\n",
    "ax1.set_ylabel(r\"$\\varsigma_{T-1}(m)$\")\n",
    "ax1.legend(loc=0)\n",
    "ax2.plot(mGrid, share_diff, \"b--\", label=\"Difference\")\n",
    "ax2.set_xlabel(r\"$m$\")\n",
    "ax2.legend(loc=0)\n",
    "ax2.set_title(\"Differences in solutions\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Second, let's use the exactly identical $a$_grid to solve the problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "## this is the a grid used in HARK solution\n",
    "a_grid = LifeCycleType.solution[0].aGrid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "code_folding": [
     0,
     20,
     47
    ],
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "## Solve the portfolio choice problem in the second-to-the-last (T-1) period\n",
    "\n",
    "t_start = time()\n",
    "\n",
    "#######################################################\n",
    "## new parameterization for the portfolio problems\n",
    "#######################################################\n",
    "\n",
    "## new a grid\n",
    "aVec_eee_big = a_grid[1:]\n",
    "\n",
    "#################################\n",
    "### the last period\n",
    "###############################\n",
    "\n",
    "cVec_port = [0.0]\n",
    "mVec_port = [0.0]\n",
    "varsigmaVec_port = [0.0]\n",
    "\n",
    "# print('period'+str(T))\n",
    "for a in aVec_eee_big:\n",
    "    varsigma = gothicMC.varsigma_Tminus1(a)  ## optimal share for a\n",
    "    # print(varsigma)\n",
    "    c = gothicMC.C_Tminus1(a)  ## optimal c given varsigma being optimal\n",
    "    m = c + a\n",
    "    c = np.minimum(c, m)\n",
    "    cVec_port.append(c)\n",
    "    mVec_port.append(m)\n",
    "    varsigmaVec_port.append(varsigma)\n",
    "\n",
    "# Set up the interpolation:\n",
    "cFunc = InterpolatedUnivariateSpline(mVec_port, cVec_port, k=1)\n",
    "varsigmaFunc = InterpolatedUnivariateSpline(mVec_port[1:], varsigmaVec_port[1:], k=1)\n",
    "\n",
    "## save the grid in a dictionary\n",
    "mGridPort_life = {T - 1: mVec_port}\n",
    "cGridPort_life = {T - 1: cVec_port}\n",
    "varsigmaGrid_life = {T - 1: varsigmaVec_port}\n",
    "\n",
    "## save the interpolated function in a dictionary\n",
    "cFuncPort_life = {T - 1: cFunc}\n",
    "varsigma_life = {T - 1: varsigmaFunc}\n",
    "\n",
    "#################################\n",
    "### backward to earlier periods\n",
    "###############################\n",
    "\n",
    "for t in range(T - 2, 0, -1):\n",
    "    # print('period'+str(t))\n",
    "    cVec_port = [0.0]\n",
    "    mVec_port = [0.0]\n",
    "    varsigmaVec_port = [0.0]\n",
    "    for a in aVec_eee_big:\n",
    "        # print(a)\n",
    "        varsigma = gothicMC.varsigma_t(a, cFunc)  ## optimal share for a\n",
    "        # print(varsigma)\n",
    "        c = gothicMC.C_t(a, cFunc)  ## optimal c given varsigma being optimal\n",
    "        m = c + a\n",
    "        c = np.minimum(c, m)\n",
    "        cVec_port.append(c)\n",
    "        mVec_port.append(m)\n",
    "        varsigmaVec_port.append(varsigma)\n",
    "\n",
    "    # Update the consumption function and share function\n",
    "    cFunc = InterpolatedUnivariateSpline(mVec_port, cVec_port, k=1)\n",
    "    varsigmaFunc = InterpolatedUnivariateSpline(\n",
    "        mVec_port[1:], varsigmaVec_port[1:], k=1\n",
    "    )\n",
    "\n",
    "    ## save the policy grid in a dictionary\n",
    "    mGridPort_life[t] = mVec_port\n",
    "    cGridPort_life[t] = cVec_port\n",
    "    varsigmaGrid_life[t] = varsigmaVec_port\n",
    "\n",
    "    # save interpolated function:\n",
    "    cFuncPort_life[t] = cFunc\n",
    "    varsigma_life[t] = varsigmaFunc\n",
    "\n",
    "t_finish = time()\n",
    "\n",
    "print(\"Time taken, in seconds: \" + str(t_finish - t_start))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "code_folding": [
     0
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    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "## Compare the solutions\n",
    "\n",
    "which_period = T - 1\n",
    "mGrid = mGrid\n",
    "share_hark_same_a = LifeCycleType.ShareFunc[which_period - 1](mGrid)\n",
    "share_dsop_same_a = varsigma_life[which_period](mGrid)\n",
    "share_diff_same_a = share_hark_same_a - share_dsop_same_a\n",
    "\n",
    "\n",
    "## plot\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(9, 4))\n",
    "ax1.plot(\n",
    "    mGrid,\n",
    "    share_hark_same_a,\n",
    "    \"r--\",\n",
    "    label=\"HARK solution\",\n",
    ")\n",
    "ax1.plot(mGrid, share_dsop_same_a, \"k-\", label=\"MicroDSOP solution\")\n",
    "ax1.legend(loc=0)\n",
    "ax1.set_title(\"share function solved by MicroDSOP and HARK\")\n",
    "ax1.set_xlabel(r\"$m$\")\n",
    "ax1.set_ylabel(r\"$\\varsigma_{T-1}(m)$\")\n",
    "\n",
    "ax2.plot(mGrid, share_diff_same_a, \"b--\", label=\"Difference\")\n",
    "ax2.set_xlabel(r\"$m$\")\n",
    "ax2.legend(loc=0)\n",
    "ax2.set_title(\"Differences in solutions\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see the two solutions give almost identical optimal share values."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Third, let's directly compare the marginal values of a particular share is equal in the two procedures. We again focus on the second to the last period. \n",
    "\n",
    "- The marginal value of share $\\varsigma$ is computed in SolvingMicroDSOPs with the function ''gothicMC.Vsigma_Tminus1($a$,$\\varsigma$)''. \n",
    "- In the HARK.PortfolioConsumerType class, the marginal values at different grid of $a$ and share are saved as an attribute named _EndOfPrddvds_fxd[a_idx, share_idx]_."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "## prepare the same a and share grid\n",
    "\n",
    "a_grid_size = len(a_grid)\n",
    "share_grid = LifeCycleType.ShareGrid\n",
    "share_grid_size = len(share_grid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "## get the marginal values of share from HARK\n",
    "\n",
    "HARK_mv = LifeCycleType.solution[which_period - 1].EndOfPrddvds_fxd[0:, :]\n",
    "## which_period -2 is second the last period here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "## get the marginal values of for different $a$ and share from SolvingMicroDSOP\n",
    "\n",
    "DSOP_mv = np.empty((a_grid_size, share_grid_size))\n",
    "\n",
    "for i, a in enumerate(a_grid):\n",
    "    for j, share in enumerate(share_grid):\n",
    "        DSOP_mv[i, j] = gothicMC.Vsigma_Tminus1(a, share)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "code_folding": [
     0
    ],
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "## for a randomly choose a, plot the marginal value of share\n",
    "a_grid_random = a_grid_size // 2\n",
    "\n",
    "\n",
    "## plot\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(9, 4))\n",
    "\n",
    "ax1.set_title(r\"$\\mathfrak{v}^{\\varsigma}(a,\\varsigma)$ at a random $a$\")\n",
    "ax1.plot(share_grid, DSOP_mv[a_grid_random, :], label=\"SolvingMicroDSOP\")\n",
    "ax1.plot(share_grid, HARK_mv[a_grid_random, :], label=\"HARK\")\n",
    "ax1.hlines(0.0, xmin=0.0, xmax=1.0, linestyle=\"--\", color=\"k\", label=\"FOC\")\n",
    "ax1.set_xlabel(r\"$\\varsigma$\")\n",
    "ax1.set_ylabel(r\"$\\mathfrak{v}^{\\varsigma}$\")\n",
    "ax1.legend(loc=0)\n",
    "\n",
    "ax2.plot(\n",
    "    share_grid,\n",
    "    DSOP_mv[a_grid_random, :] - HARK_mv[a_grid_random, :],\n",
    "    label=\"Difference\",\n",
    ")\n",
    "ax2.set_title(\"Differences between \\n solutions\")\n",
    "ax2.set_xlabel(r\"$\\varsigma$\")\n",
    "ax2.legend(loc=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The figure above plots the marginal values $\\mathfrak{v}^{\\varsigma}$ at different value of share $\\varsigma$, at a random value of $a$, according to HARK and SolvingMicroDSPOs, respeceptively. The numerical differences are at an order of $10^{-9}$, which are almost infinitesimal."
   ]
  }
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