{
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    "<!-- <a href=\"https://colab.research.google.com/github/lphansen/RiskUncertaintyValue/blob/main/discrete_elasticity.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a> -->"
   ]
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   "cell_type": "markdown",
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   "source": [
    "# Notebook: Discrete Time\n",
    "\n",
    "Shock elasticities quantify the (local) exposures of macroeconomic cash flows to shocks over alternative investment horizons and the corresponding prices or investors’ compensations. Here we cover shock elasticities for models that are exponential-quadratic. This model structure is particularly tractable with quasi-analytical solutions.    \n",
    "- Section 1 introduces the exponential–quadratic framework. \n",
    "- Section 2 provides an illustration using a long-run risk model.\n",
    "- Section 3 provides more details on the computation.\n",
    "  \n",
    "This notebook provides both written explanations and accompanying code. Please refer to the following papers for further details:\n",
    "\n",
    "[\"Term Structure of Uncertainty in the Macroeconomy” joint research with Jaroslav Borovička – Handbook of Macroeconomics](https://larspeterhansen.org/wp-content/uploads/2016/10/macroterm_main.pdf) \n",
    "\n",
    "[\"Examining Macroeconomic Models Through the Lens of Asset Pricing” joint research with Jaroslav Borovička – Journal of Econometrics](https://larspeterhansen.org/wp-content/uploads/2016/10/Examining-Macroeconomic-Models-through-the-Lens-of-Asset-Pricing.pdf) \n",
    "\n",
    "[\"Shock elasticities and impulse responses\" joint research with Jaroslav Borovička and José A. Scheinkman - Mathematics and Financial Economics](https://link.springer.com/article/10.1007/s11579-014-0122-4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "# 1. Exponential-linear-quadratic Framework\n",
    "\n",
    "We suppose a linear-quadratic specification of the state dynamics:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "X_{t}^0&= \\bar{x} \\notag \\\\\n",
    "X_{t+1}^1&=\\Theta_{10}^x+\\Theta_{11}^x X_{t}^1+\\Sigma_{10}^x W_{t+1} \\tag{1} \\\\\n",
    "X_{t+1}^2&= \\Theta_{20}^x+\\Theta_{21}^x X_{t}^1+\\Theta_{22}^xX_{t}^2+\\Theta_{23}^x\\left(X_{t}^1 \\otimes X_{t}^1\\right) \\\\ \n",
    "&+\\Sigma_{20}^x W_{t+1}+\\Sigma_{21}^x\\left(X_{t}^1 \\otimes W_{t+1}\\right) +\\Sigma_{22}^x\\left(W_{t+1} \\otimes W_{t+1}\\right) \\notag .\n",
    "\\end{align} \n",
    "$$\n",
    "\n",
    "The code will take the coefficients as inputs. \n",
    "\n",
    "Furthermore, we suppose that the logarithms of macroeconomic and stochastic discount factor processes that interest us grow or decay stochastically over time with stationary increments.  Let $Y$ be the logarithm of such a process. The process $Y$ will display linear growth or decay:\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "Y_{t+1} - Y_t &= \\Theta_0^y + \\Theta_{1}^y X_{1,t} + \\Theta_{2}^y X_{2,t} + \\left( X_{1,t} \\right)' \\Theta_{3}^y X_{1,t} \\\\\n",
    "&+ \\Sigma_0^y W_{t+1} + \\left(X_{1,t} \\right)' \\Sigma_1^y W_{t+1} + \\left( W_{t+1} \\right)' \\Sigma_2^y W_{t+1}  \\tag{2}\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "Following the steps of our approximation of $X$, we write \n",
    "\n",
    "$$\n",
    "\\begin{aligned} \n",
    "\\Theta_0^y &=  \\kappa\\left({\\bar x},0,0 \\right) & \\Sigma_0^y &=  \\kappa_2  \\\\\n",
    "\\Theta_1^y &=  \\kappa_1 & \\Sigma_1^y &=  \\kappa_{12} \\\\\n",
    "\\Theta_2^y &=  \\kappa_{1} & \\Sigma_2^y &=  \\frac 1 2 \\kappa_{22} \\\\ \n",
    "\\Theta_3^y &=   \\frac 1 2 \\kappa_{1,1}  &  &\n",
    "\\end{aligned}\n",
    "$$ \n",
    "\n",
    "where $\\kappa_i$ is the derivative of $\\kappa$ with respect to argument $i$ evaluated at $(\\bar x, 0, 0)$ and similarly for the second derivatives.   \n",
    "\n",
    "In what follows, $M$ will be a macro growth process, a stochastic discount factor process, or a product of the two. The user inputs are the quadratic specifications in equation (1) and equation (2).  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6fbe5c6",
   "metadata": {},
   "source": [
    "We consider two types of multiplicative processes,  one that captures macroeconomic growth, denoted by $G$, and another that captures stochastic discounting, denoted by $S$. \n",
    "- The stochastic discount factor process,  $S$, is typically computed from the underlying economic model to reflect equilibrium valuation dynamics. \n",
    "- For instance, the growth process $G$ might be a consumption process or some other endogenously determined cash flow, or it might be an exogenously specified technology shock process that grows through time.  \n",
    "- The interplay between $S$ and $G$ will determine uncertainty compensations over multi-period investment horizons.\n",
    "\n",
    "Consider the pricing of a vector of payoffs $G_tW_1$ in comparison to the scalar payoff $G_t$. \n",
    "<!-- - The **shock-exposure elasticity** is constructed as from the ratio of expected payoffs $E[G_tW_1 |X_0 =x]$ relative to $E [G_t | X_0 = x]$. -->\n",
    "- The **shock-exposure elasticity** is constructed as from the ratio of expected payoffs $E[G_tW_1 |X_0 =x]$ relative to $E [G_t | X_0 = x]$. To calculate shock-exposure elasticity, the multiplicative functional $M$ is set as $G$.\n",
    "\n",
    "    $$\n",
    "    \\varepsilon_{g}( x, t)=   \\frac{(\\alpha_0 + \\alpha_1 x) \\cdot {\\mathbb E}\\left[\\left( \\frac {G_t}{G_0}\\right) W_1 \\mid X_0 = x\\right]}{{\\mathbb E} \\left(\\frac {G_t}{G_0}  \\mid X_0 = x\\right)}\n",
    "    $$\n",
    "\n",
    " - This is done by the function *\\_exposure\\_elasticity*.\n",
    "- The **shock-price elasticity** includes an adjustment for the values of the payoffs $E [S_t G_t W_1 | X_0 = x]$ relative to $E [S_t G_t | X_0 = x]$. To calculate shock-price elasticity, the multiplicative functional $M$ is set as the product $SG$. \n",
    "\n",
    "$$\n",
    "\\varepsilon_{sg}( x, t)=   \\frac{(\\alpha_0 + \\alpha_1 x) \\cdot {\\mathbb E}\\left[\\left( \\frac {S_tG_t}{S_0G_0}\\right) W_1 \\mid X_0 = x\\right]}{{\\mathbb E} \\left(\\frac {S_tG_t}{S_0G_0}  \\mid X_0 = x\\right)}.\n",
    "$$ \n",
    "\n",
    "The shock-price elasticity is: \n",
    "\n",
    "$$\n",
    "\\varepsilon_{g}( x, t)-\\varepsilon_{sg}( x, t)\n",
    "$$\n",
    "\n",
    " - This computation is done by the function *price\\_elasticity*. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5111f4ff",
   "metadata": {},
   "source": [
    "# 2. An Illustration using the Long-Run Risk Model\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca746c7b",
   "metadata": {},
   "source": [
    "We will now cover how to use the code on a basic level. You can see the package requirements [here](../../requirements.txt)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "12545561",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fatal: destination path 'RiskUncertaintyValue' already exists and is not an empty directory.\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "<IPython.core.display.HTML object>"
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   ],
   "source": [
    "import os\n",
    "import sys\n",
    "workdir = os.getcwd()\n",
    "!git clone https://github.com/lphansen/RiskUncertaintyValue \n",
    "workdir = os.getcwd() + '/RiskUncertaintyValue'             \n",
    "sys.path.insert(0, workdir+'/src')\n",
    "from IPython.display import display, HTML\n",
    "display(HTML(\"<style>.container { width:97% !important; }</style>\"))\n",
    "import numpy as np\n",
    "np.set_printoptions(suppress=True)\n",
    "from scipy.stats import norm\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from numba import njit, prange\n",
    "import seaborn as sns\n",
    "\n",
    "from lin_quad import LinQuadVar\n",
    "from lin_quad_util import next_period, log_E_exp, kron_prod, distance\n",
    "from utilities import mat, vec, sym\n",
    "from elasticity import exposure_elasticity, price_elasticity\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "269a21e2",
   "metadata": {},
   "source": [
    "We use the long-run risk model adapted from {cite}`HansenKhorramiTourre:2024` as an example; the model is outlined in {ref}`section:solvingplanner`. In a later lecture, you will learn how to solve such models using expansion methods. For now, suppose that we have solved the model and have the following linear-quadratic approximations for the states $X_t = [X_{1,t},X_{2,t}]$ and consumption growth ${\\widehat C}_{t+1} - {\\widehat C}_t$:\n",
    "\n",
    "First-order approximation:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "X_{1, t+1}^1 & = .9 X_{1,t}^1  +  \\begin{bmatrix} 0 & .06 & 0 \\end{bmatrix} W_{t+1}   \\cr\n",
    "X_{2, t+1}^1 & =  .8X_{2,t}^1  + \\begin{bmatrix} 0 & 0 & .5 \\end{bmatrix} W_{t+1} \\cr\n",
    "\\log C_{t+1}^1 - \\log C_t ^1& = .01 + .03 X_{1,t}^1 +   \\begin{bmatrix} .008 & .01 & 0 \\end{bmatrix} W_{t+1}. \n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "Second-order approximation:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "X_{1, t+1}^2 & = .9 X_{1,t}^2  +   X_{2,t}^1 \\begin{bmatrix} 0 & .06 & 0 \\end{bmatrix} W_{t+1}   \\cr\n",
    "\\log C_{t+1}^2 - \\log C_t^2 & =  .01 X_{1,t}^2 +   X_{2,t}^1 \\begin{bmatrix} .008 & .01 & 0 \\end{bmatrix} W_{t+1}. \n",
    "\\end{aligned}, \n",
    "$$ \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1c24dce",
   "metadata": {},
   "source": [
    "Note that the superscript refers to the approximation order and the subscript refers to the state. We store the approximations in objects of class `LinQuadVar`. For example, we can form the approximations described above as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "49bcd65f",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_X = 2 #Two states\n",
    "n_W = 3 #Three shocks\n",
    "\n",
    "# State approximation where first row is X_1 and second row is X_2\n",
    "X1_tp1 = LinQuadVar({'x': np.array([[0.9, 0.   ],     \n",
    "                                    [0.   , 0.8]]),\n",
    "                     'w': np.array([[0., 0.06, 0.       ], \n",
    "                                    [0., 0.    , 0.5]])},\n",
    "                             shape=(2, n_X, n_W))\n",
    "\n",
    "X2_tp1 = LinQuadVar({'x2': np.array([[0.9, 0.   ],\n",
    "                                     [0.   , 0.]]),\n",
    "                     'xw': np.array([[0., 0., 0., 0., 0.06,  0.      ],\n",
    "                                     [0., 0., 0., 0., 0.    , 0.]])},\n",
    "                             shape=(2, n_X, n_W))\n",
    "\n",
    "### Log consumption growth\n",
    "gc_tp1 = LinQuadVar({'c': np.array([[0.01]]),\n",
    "                     'x': np.array([[0.03, 0.]]),\n",
    "                     'w': np.array([[0.008, 0.01, 0.]]),\n",
    "                     'x2': np.array([[0.01, 0.]]),\n",
    "                     'xw': np.array([[0., 0., 0., 0.004, 0.01, 0.]])\n",
    "                     }, shape=(1, n_X, n_W))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8aa70213",
   "metadata": {},
   "source": [
    "Next, we input these approximations into the `exposure_elasticity` function to compute exposure elasticities."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "320eab86",
   "metadata": {},
   "source": [
    "## 2.1 Exposure Elasticity for Consumption Growth\n",
    "\n",
    "To calculate the exposure elasticity for consumption growth using the *exposure\\_elasticity* defined above, we need six inputs\n",
    "- Consumption growth, *gc\\_tp1*. This is a *LinQuadVar* object. \n",
    "- First order expansion of the state evolution equations, *X1\\_tp1*. This is a *LinQuadVar* object. \n",
    "- Second order expansion of the state evolution equations, *X2\\_tp1*. This is a *LinQuadVar* object. \n",
    "- Time periods, $\\text{T} = 30$ years\n",
    "- Shock index, $0$ stands for the growth shock, which means $\\alpha' =\\begin{bmatrix}1 & 0 & 0 \\end{bmatrix}$, $1$ stands for the volatility shock, $2$ stands for the consumption shock.  The fourth shock alters dividend growth and its shock prices are zero.  \n",
    "- Percentile, $0.5$ stands for the median"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "09afaa54",
   "metadata": {},
   "outputs": [
    {
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Vnv3777+YPHmySvCZssTERGzZsgXz58/Xe936eP/+Pbp27ao2+EzZrVu30LdvXwQGBqb5c9avXy8JPlPUokULyXRoaCi6d++OzZs3qw0+UxYXF4fNmzejX79++PLli8r7TZo0Ea/Dw8NFMJomyoFjUVFROpeRZ1sEgMaNGxssSDA8PBz9+vWDm5ubzvNAREQExo8fj3Pnzhnks4mIiIiIiNKDAWhERERERPTTmDFjhiS44/nz59iyZYtKudevX2Pp0qVi2szMDMuWLUP27Nm1rt/Lywvbtm0DAFhYWOD333+Hu7s7Hj9+jGvXrmHevHmSz4+JicGIESO03hyfM2cOjh07JpnXrl07bNu2Dbdv38bjx49x7tw5lcwwwcHBGDp0KD58+KB2vUuXLsWrV6/EdL169bBx40bcuHEDPj4+Yiim3377TbLdjx8/xtatW7V+D8aWkpKCefPmaXy/ZcuWkulDhw5h4cKFkpvdzZo1w6ZNm+Dh4YHHjx/j8uXLmDdvnmSIqydPnmD48OEGDTqaOXMm3N3dxbSFhQX69euH/fv34969e3j48CFOnjyJsWPHSrKoHD16FIsWLcrQZ8fFxWHMmDGSG7S1atXCmjVrcPXqVTx+/BiPHz/GlStXsGrVKtSuXVuy/KNHj+Dm5qZ23du2bcOdO3fEdKVKlbBq1SpcuXIFjx8/xv3793Hy5ElMmDABuXPnFuX8/PywYsUKybq6dOkCX19f+Pr6onPnzpL35PN9fX0lw2+mhaurqxj2TK5FixZif/Dx8cGFCxcwYcIEyb5/8+ZNLF++PE2fldZtMTU1RceOHUWZuLg4vQKKEhIScPr0aTHdsmXLdGUqXLhwoajTggULJO/t2LFDUmfFjJJJSUkYO3asJHNM1qxZ8csvv2Dv3r3w9PTEw4cPcerUKZV9+927dxg8eLBeAZlRUVGStlmZ8rGvD/n27NixQzJ/wYIFku3V5ujRo0hOToa5uTl69OiBvXv34s6dO3j48CGOHDmC3r17S4YSfPz4sco+qCg4OBiDBw+WBHoUKVIEs2bNwoULF/D48WPcvn0b27ZtkwQaxsbGYuzYsWkK0tLl2LFjWLZsmWSes7MzVq9eLc4XV69exezZs5E3b15R5tmzZ5gxY4badRrrvKYoIiICf/75J1JSUmBlZYWhQ4fiyJEj8Pb2hqenJ3bt2qWSXfDy5csag7IN2cZ9C2PHjkVSUhIsLS0xcOBAHD16FA8ePMDdu3excuVKFCxYUJSNiYnBuHHjMGXKFMhkMtjb2+N///uf2NYLFy5g+PDhkoxQDx8+1CvwxVDXSaNHjxbHprOzs5hvb2+vsZ3SV2a1Zy9fvhRtv62tLcaNG4dTp07h0aNH8PDwwKZNm1CjRg3JMrt379YZDKWvmJgYDBs2TBIgaWdnh5kzZ+Ly5cvi2mj27NkoUKAAgNSMW/oMW6ro48eP+OeffzS+r9huR0dHY9iwYXj+/LmYZ2lpiaFDh8LNzQ337t3D/fv34ebmhiFDhkgCjr29vdVesykGoAGp53JtdX3//r3KfMVjX9nTp08l32GzZs0AGGYfffHihfi9HRwcMG/ePJw/fx6PHz/GzZs3sWTJEsl1q0wmw9y5c40eLE9ERERERKQJA9CIiIiIiOinYW1tjQULFkgCAdatW4c3b96I6cTEREycOBFxcXFi3pgxY1C5cmWd64+IiAAA5MmTBwcOHMC4ceNQqlQpmJubI3/+/OjevTtOnDghuaEYHh6uMbDoypUr2Ldvn5jOli0bNmzYgOXLl6Nu3bqwtbWFubk5ihUrhv79+8Pd3R3169eX1OePP/5QyZoQGxsrufnfsmVLbNmyBY0bN4adnR3MzMxgY2ODcuXKYfz48di6davkJt+uXbv0yshjLMHBwSJ4rnfv3jhz5gy8vb1x/PhxDB48GK1atRJl3717h//9739iOmvWrFi2bBlcXV3RqFEj5M6dG+bm5ihUqJD4fdq1ayfK+/j4YOXKlQap9/Hjx3H06FExnT9/fhw4cADTp09HtWrVYG1tDUtLS5QpUwbDhw/HyZMn4eDgIMrv3LlTMsxTWu3YsUNliMbt27ejZcuWKFCgAMzNzWFubo6CBQuidevW2L59O4YMGSJZx8mTJ9WuWzGYpmrVqti7dy9at26NggULwtzcHNmzZ0eZMmUwbNgw7N+/XxKgcezYMZ3ZXwzl7du3cHV1FdNmZmZYunQp1q5dK/YHMzMzFClSRNQ1V65covzOnTv1ynKVEcpDZ2rK9qXo0qVLku8ws4ff3L9/Py5fviymbW1tsWfPHsyZMwdOTk6wsbGBpaUlSpcujeHDh8Pd3R0VKlQQ5f39/TUGKyl68eIFQkNDkTVrVowcORKXLl3CgwcPcOjQIfTu3RuNGzc2xubpxc7ODrt378b//vc/ODk5IVeuXLC0tESFChUwa9YszJw5U1JesS1QNmnSJEmgaOvWrXHixAn07t0bRYoUgbm5OWxtbVG3bl2sWLECq1evhpmZGYDUc9jYsWMl57D0kmdgVPTnn39i586daNWqlThfFChQAL169YKbmxsKFy4syp47d04le5WxzmvK4uLiEB8fD3t7exw5cgQTJ05EhQoVkC1bNtjY2KBmzZpYv349fv31V8lyhw8fVru+H6WN0yQ6Ohq2trbYuXMnpk6divLly8PKygo5c+ZEmzZtsGXLFrEPAamBYomJiXB0dMTRo0fRo0cPsa1FihTB2LFjMWfOHMlnKAbBamLo6yRjyKz2LDIyEjKZDBUrVsSJEyfw+++/o3Tp0rCwsEDu3LnRqFEj7NixA61btxbLyLP1GYKrq6skW1vVqlVx6tQp9OnTB4UKFRLXRr169cKpU6dQs2bNdH3O/fv3kZCQACsrK0ydOhXXrl3DvXv3sHv3bvTu3RvVqlUTZdeuXYvHjx+L6SJFiuDYsWOYOHEiKlasCGtra2TPnh0VK1bEn3/+iSNHjsDe3l6Uf/TokUqgeMWKFSXD4GoLQFMeflNOWwDalStXxGsLCwvUq1dPY9n06tmzJ9zc3NC9e3cULVoU5ubmyJs3Lzp06IBDhw5JgtCCg4Nx/fp1g9eBiIiIiIhIHwxAIyIiIiKi70r//v1RtmzZdP8bMWKE1vXXrl0bAwcOFNPx8fGSwIDVq1fj6dOnYrpOnToqQTjaZMmSBevWrUO5cuXUvm9tbY1169bBzs5OzDt9+jT8/Pwk5WQymUrWlHnz5qlkclBet6urK8qUKSPmPXnyBBcvXpSUe//+vWQYzW7dukmC8pRVq1ZNkr0pLCxMZ0agzDBixAjMmjULJUqUQLZs2VC2bFlMmjRJciPun3/+kQRi/PXXX2jfvr3GdZqbm2PJkiVwdHQU8/bs2aNXNhNtUlJSsG7dOjGdNWtWbNiwQeN+AqQGqG3evFmSXUVxHWmlGDyWK1cuTJ8+XevvDqRm8FAMPlT3u0dGRkqCsjp27Ahzc3ON6yxatCgGDRokppOTk+Hp6anXNmTUP//8Ixl2948//oCLi4vG8mXKlMHkyZPFdFJSEg4dOmTUOhYtWlQSfOHh4aFzmELFgFJ7e3uV7HXGFBsbi/Xr14vpLFmyYO3atahatarGZezs7LBlyxZJO3ju3Dk8e/ZMr8+cM2cOxowZA3t7e1hZWaFy5cqYNWtWurK+GcrixYtRpUoVje/37t0bpUuXFtPPnz9HbGysSjkvLy9JEISjoyOWLl2KbNmyaVx3q1at8Ndff4npgIAAgwSp7N69WxI41atXL63nw/z58+Pvv/+WzNu/f794bczzmiarVq2SnBOUjR07VhIspi7Q5Edq47SZMmWKxn20VKlSkkA/IPV8uHLlSsk5SFG3bt0kGer0zcxlqOskY8js9szCwgKurq6SZRVlyZIF06dPR9asWcW827dv67MpWkVERGDXrl1iOk+ePNiwYQNy5syptry1tTU2bNigMrx5Wri6umLgwIHInz8/rK2tUaNGDcyaNUtchwQFBWHPnj2ivJWVFTZv3qz1+C1ZsiQ2b94saR/37NkjOWeamJhI2pgHDx5oHEpese2tVKmSeH3v3j3JtYMixeE369atq7WtTo8aNWpgzpw5kgBRRTly5MDYsWMl87y9vQ1aByIiIiIiIn0xAI2IiIiIiH4648ePl9zM9vT0xNGjR+Ht7Y3NmzeL+bly5cKiRYtgaqp/16lLly6S4CV1cuXKheHDh4vplJQUlcxST58+lQxB5OzsrDVwSs7CwgLTpk2TzFO8oQdAJXOMPsFkv/76K9asWYMjR47Ay8tLa+BUZsiVKxd+++03rWW+fv2K48ePi+lSpUqhV69eOtedJUsWjBo1SkzHxsZmOJjj+vXrkkwjXbt2lWRM0SR//vySOj98+DBdw28lJCSgbt26aN68OcqWLYuuXbvqHFIWSB36qlSpUmJaXRaf9OxPnTp1wooVK3Dw4EF4eHiIIauMSXmYSjs7O5XsR+p06NABtra2YpnMyGSkGPCZnJyMU6dOaSwbGhoqyXbSuXNnnYGFhnT9+nXJzf4OHTqoDBunTu7cuVVumiu3VeqULl0aXbt2TXM9jal27dqoW7euznINGzYUr1NSUhAQEKBSRjEoBEgNGtIUeKCoZ8+ekmEU9fkudVFsP83NzVV+L3Vq1aqF8uXLA0jNHKUY6GHM85o6NWvW1Jm91NLSUpLZKSYmBpGRkZIyP0obp02hQoUkw/uqoxxk1aJFCzH0ojomJiaSLJ2hoaF61cVQ10nGkNntWZs2bbR+x0Dqeads2bJiWtuw7fo6c+aMJAD2t99+kwRiqmNtbY1x48al6/MaNWqEOnXqaC3j7u4ueWBg0KBBWoPP5EqWLCk5l8fHx6tkMlQMQEtMTFQbECqTyeDh4SGmFfe/mJgYSWY2ubCwMMmQx8rD+hrCuHHjdJ7TGzRoICmjmO2WiIiIiIgoMzEAjYiIiIiIfjryLFeKN/UXL16MKVOmICUlRcybP3++JLuHPnr06KFXORcXF0lgm/KQQMrTaQm4qFOnDooWLSqm7927h4SEBDEtH75Hbs2aNdi5cyfi4+M1rrNYsWJo2bIlKlSogBw5cuhdF2OpVauWJDOXOsrb3bZtW72DCWvXrg0rKysxrW34JX0oZyzRlnVLmfINzfTUxdzcHFOmTMG6detw/PhxTJo0Se9lFQPVkpOTVYIxbGxsJMNbHThwAKtWrUJUVJTGddrZ2aFt27aoUqWKzpvehvLo0SNJMEybNm0kWWU0yZo1Kw4dOoT79+/jxo0beg2tllFt2rSR7H/ahuF0d3dHYmIigNSAkE6dOhm7ehLKbVW3bt30XtbFxUWynfpk9mnYsGGmBtjpQ5/gMwCSoeIAqAQ6AdLvoHDhwpLh6bTJkiWLJMDt5cuXegcEqRMYGCgJmm3QoIFkOFptNmzYAE9PT9y+fRtr164V8415XlPH2dlZr3UrZ3VSzo70o7Rx2tSsWVPncZMnTx7JdPXq1XWuVzFjlqasUsoMdZ1kDJndnum7jyq2HeoyJ6aVYtYuExMTdOjQQa/lWrduna5Mk4ptkyYZ+e6V9ynl775OnTqSa0Z1+9KzZ88QFhYGIDUAsmnTppLMdOquva5fvy76DcqZ1gzB0tJSZ7AmkBocqHgsfushf4mIiIiI6OfFADQiIiIiIvqu7NixA76+vun+5+rqqtfnlC9fXpLlKiQkBG/fvhXTvXr1QvPmzdNUdysrK8mQPdrY2NhIMjsoD9X06NEjybQ+N4IVOTk5iddxcXF4+fKlmM6ePbvkZmNCQgLmzZuH2rVrY/jw4di9e7fku/ge6ROUcf/+fcm0PCuPPrJmzSrJ/JXR4YwyUhfFDDOGqIsusbGx8PHxwd69ezFu3DiVrB+KQZpyilnaZDIZXF1dUadOHQwaNAhbt27F8+fPVQLXMpvyMaZtuERlhQsX1itjnKFkz54dLVu2FNM+Pj4aj0nF4TednZ1RpEgRo9dPkWJbZWZmlqbv1cLCAhUrVhTTfn5+Ooe71TcgKzMpBkZpoxicAkAlgOrNmzciAAJIWzsBQJIlSSaTqZxH0iIjx0uBAgXUDttozPOaOoptuDbKQ+YlJyerlPkR2jhtihUrprOMckCuYkY9TfTJzqfIkNdJxpDZ7Vl69lFNQ0GmheJ2FitWTGT51MXc3FyyjfrSp91WrFOhQoX02v/kChYsKAkkVW5rLC0tJRnYFIfaVDfP2dkZpqamkuCvu3fvqixz9epV8bpKlSoah1JNr8KFCyNLlix6lVW8RtEVnEtERERERGQsuh/1JSIiIiIi+o8aOnQorly5ggcPHkjmly5dGlOmTEnz+kqVKpWm4TqLFCmCN2/eAACio6MREREhMhgoZq4xMzNLc1CJ8rBFISEhkukpU6bg0aNHePHihZgXExODS5cu4dKlSwBSb+jVq1cPDRs2RIMGDVSCJ74lfTLTffr0STI9YsSIdH9eWFgYkpKS9MqYpU9d0hp4oUhxeLCMCAoKwsOHD/Hq1St8+PAB/v7+8Pf3R2BgoNZACnXvDRkyBHfu3JFkHUlISMDNmzdFppE8efKgTp06aNiwIRo1aqR3NiVDUR7uMLMDtdKqc+fOOHr0qJg+ceIExowZIynz5s0byY32Ll26ZFb1BMW2qlChQpLsivooXry4ZDi0kJAQrftGWrNSZgbFzDNpoXwsKQ+td/78eUlQWVplpK0wxvFi7POaMn0zNSmft9UF2f4IbZw26cnCZoxzviGvk4whs9szfTPKKn5nGQ10jIuLw+fPn8V0Wo/DEiVKpDkTq652OykpSZK1S5+hN5UVL15ctFvR0dGIj4+HhYWFeL9p06a4fPkygNQMkUFBQZJ6KQag1a5dG0Bq5sBz584BSH2QICEhQewTycnJuHHjhljGGMPsqgvkJSIiIiIi+p4xAxoREREREf20smTJgsmTJ6vM7969u87hHdVJ601R5RuPisN5KWbNSM9wR8o3rSIiIlQ+e8+ePejZs6fG7AqBgYE4dOgQxowZg9q1a2PcuHF49epVmutiDPp814Yegkj5O0wLQ9YlI/UAUjN29OnTB40aNcLo0aOxatUquLm54e7duwgICFC5ua1P0J25uTk2bdqE33//XXLDV1FISAhOnjyJSZMmoV69ehg2bJhK8KcxKQ+Xl57jKjPVqlVLMuyaumE4FbOfZc+eHa1atcqUuilSbKvSMzyvrrZKmTGDT9JL3ww1umT02FamK/uSNsY4Xox9XlOWnvO4Jj9CG6dNWgOpABhlqFtDXicZQ2a3Z5r2JWNSvh5J67GYnqAoXb97RESE5NrDEN+9cvvXuHFjyT6tGHCWkJCAe/fuiWl5AJr8fyA1O6xiwLe3t7fkM4wRgJbehx6IiIiIiIi+FQagERERERHRT23Tpk0q81xdXVUy0egjrTeKlIf5UlxeXQaWtFBeXl2ARI4cOTB37lxcvnwZkydPRo0aNTRuQ3x8PNzd3dGhQwfs2LEjQ3UzBH2G/TLEMFWK4uLi0r1sYmLiN69HQkICpkyZgmHDhsHLy0ttFhUTExMULVoUbdq0wbRp03Du3DnJsHfaWFhYYNy4cbh69Spmz56N+vXrawx6SEpKwtWrV/HLL79g8eLF6dqetDJGMIUxmZiYoHPnzmLaz88PDx8+FNMymUwSlNa2bVuVoQQzQ0az8ejTVilK65B/PxJDt1nx8fHpXtYYx0tmnNeM6Xtv47T5Xto/Q14nGUNmt2ffg7Qel+n5jnQFQGa0bVC3DuXvPl++fKhQoYKYlmcuBIB79+6Jays7OzsxNKqDgwPy5s0ryilmfrt27Zp4XbRoUZQuXTrD20BERERERPSj42M0RERERET00zp06JAYblJRREQE/vrrL2zZsiVN60trZg7l8ooZHxSHbEpPxg/lDBfahtLKnz8/Bg0ahEGDBiEyMhKenp64c+cO7ty5g+fPn0tuNiYnJ2P+/PkoWrQoGjdunOZ6qWPI4CxFytkwbt68KbmRmJly5syJL1++AABKliyJ06dPZ3od/v77bxw5ckQyr2rVqqhduzbKlSuHkiVLonjx4ipZg5QDAHSxtbVFr1690KtXL8TGxuL+/ftif3r8+LHK+rZs2QJ7e3v06dMnfRumJ+X9ITo62qifZwidOnXCunXrxDF44sQJVK1aFUDqDfOPHz+Kst9i+E0g9XuVD/UYGRmZ5uXT0lb91ynvoxMmTMCwYcO+i7oY4njJzPOaMX3rNs5Y58zMYMjrJGP4Gdoz5SFBM/qbGIJyhjRjffdNmzbFkydPAAAeHh6QyWQwMTGBh4eHKKOY9Uw+ffLkSQCpAWgjR44EkJpNVs4Y2c+IiIiIiIh+RMyARkREREREPyV/f3/8/fffYjpHjhyoWbOmmL5x4wZ2796dpnUGBASkqfzbt2/Fazs7O8nNMsVAqcTERHz48CFN637z5o1kulChQnotlyNHDjRt2hRTp07F0aNHcf36dUyfPh0FChSQlFu7dq3KssoZVvTN5hMWFqZXubTKkyePZNrPz88on6OP3Llzi9cBAQFpDurKqOfPn2Pv3r1iOnv27Ni6dSsOHDiA8ePHo23btihXrpzaIesycrM5W7ZsqFevHsaPH4/9+/fDw8MDCxYsQMmSJSXl1q9fb/TvRHl/8Pf313vZsLAwhISEGLpKOhUpUkTSLp0/f168PnfunHhdvHhxvTPVGZqdnZ14HRAQgISEhDQtr9xWFSxY0CD1+hEp76NpbfcNKSPHS1RUFIKCglQyJX2r85oxZaSNUz5n6tsGZmRo1W/NkNdJxvAztGfm5uaSa5L379+naXljtEvm5uaSIDTF311fr1+/Fq9z5cqldl9p0qSJeP3lyxf4+voCgM4ANDlvb2/Ex8cjKCgIz549E/ObNm2a5voSERERERH9FzEAjYiIiIiIfjopKSmYMmWKJKPL5MmTsWjRIskNqyVLluDdu3d6rzcgIEDvIJWQkBDJDX1HR0fJ+1WqVJFM37t3T+96yGQyPHjwQEybmZmhaNGikjKJiYl4/fq1pJw6dnZ26NevHw4fPizJmvH06VOVLCzKwx3FxMTorGtSUlKab0jrq3LlypJpxRuM+njz5g1CQ0MNUhfF3zMuLk7n964oOTkZL168yFAg2LFjxyTTEyZMQL169fT6bOWbzeqG30pOToafn59keCp1cubMiS5duuDw4cMoXry4mB8cHGy0/UCuUqVKkmkfHx+9l92wYQPq1q2LatWqoW3btgbbL/ShmNns06dPePz4MQDg8uXLYn7Xrl0zrT7KFPftxMREyTChusTGxkpu4hcsWBDW1tYGrd+PpEyZMpIg0Nu3b6dp+S9fvsDf398gQ3lm5Hhxc3NDw4YNUaVKFbRq1QrPnz8HYPzzmjEZo41LzzkT+LbB1BllyOskY/hZ2jN5Jk0A+Pjxo97ntOTkZJFBzNAUv/vAwMA0XRN8+PBBZK4DoHE4zIoVKyJ//vxi+ubNm4iOjsbTp0/FPOUAtDp16ojX8fHxePDggST7Wa5cuVC9enW960pERERERPRfxgA0IiIiIiL66Wzbtg2enp5iuk6dOujevTvs7e0xbtw4MT82NhaTJ09OU2Ym+TA9uhw9elQyrTycZa1atSTThw4d0rsOHh4ekqH5qlWrJglqGDFihAikGT58OFJSUnSuM2/evHB2dhbTycnJKpnLsmfPLplWvBmoyYMHD9KcYURfzs7OkgwzR44c0TswIygoCB06dECdOnVQtWpV9O3bN0N1Uf49Dx48qPey58+fh4uLC6pXrw5nZ2csXbo0zZ+vnE1EuT6a3LhxQyUoQnl/mTdvHqpWrYoWLVpg4MCBKsNgqWNlZSXJRAJADFGqSDlDUEZUrlwZ5ubmYvrMmTN67fsAcP36dQCpbcLXr18l2WP0ld5tadWqlSQw9sKFC3j16pUIQsmSJQs6duyYrnUbQkbaqpMnTyIuLk7jujKTIfe19DI3N5dksvPz80tTENq0adPQrFkzVK5cGY0aNUpT8IyyQoUKwd7eXkxfu3ZN7yBY+fGSkJAAf39/EShmzPOaMRmrjUvPOfPjx48/dAAaYLjrJGP4r7RnujRo0EC8lslkcHd312u5GzduGC1rreI1JpC27165rLbvXnE/unnzJu7duyeuDQsXLozChQtLyivPu337tiQArVGjRirBpERERERERD8rBqAREREREdFP5cWLF1i5cqWYtrKywv/+9z8x3bdvX0mWDW9vb2zcuFHv9f/zzz+IiIjQWubLly/YtGmTmLa2tkbr1q0lZapWrYry5cuLaU9PT71u2iYkJGDBggWSeZ06dZJMFy5cWNxsCwsLw9mzZ3WuF5AOwWZhYQFbW1vJ+8pDTV28eFHnOletWqXXZ6dHwYIF0ahRIzH94cMHbNmyRa9llyxZIjK8xcXFoUKFChmqS8uWLSVBSydOnICXl5fO5eLi4rBixQoxHRERgWrVqmWoLoB+w55GRUVh7ty5KvOVM98VKVJEzEtJScGBAwf0qoPykH7qhipTvqmrb8CYOpaWlmjfvr2YDggIwL59+3Qud+XKFcnQXsrHqr7Suy1WVlaSz7x48SIuXbokpuvVqyfJ6JLZmjdvLhlaUd99OywsTOX4V26rMpMh97WM6Nmzp2R6wYIFkqAWTW7duoUrV64ASK17QkJChtstxex7sbGxWL9+vc5lnj9/jps3b4rphg0bigBKY57XjMlYbZzyEKIXLlzQuU5jnjMzi6Guk+SyZs0qXmf0uP2vtGe6dOzYURLYvGnTJkRGRmpdJjExEcuXLzdanbp06SIJEt+2bZteWYjfvXuHHTt2iGkTExOtQdmKw2V6eXnhxo0bYlox25kixfnXr1+XZNRt1qyZzjoach8lIiIiIiL6njEAjYiIiIiIfhqJiYmYNGmSJOPW+PHjUaRIETFtamqK+fPnw8zMTMxzdXXVe8ih4OBgjBw5UmOmmNDQUPz2228IDw8X84YOHaqSCQUAhg8fLpmePn26ZNg9ZdHR0Rg5ciRevHgh5pUoUQIdOnSQlFMerm/evHmSABt1Dhw4IBmiqEGDBpLvCFC9cbd161a8efNG7fqSkpIwd+5cSSY6Y/j9999havp/Xd+VK1diz549WpfZtGkTTpw4IaYtLS0xePDgDNXD0tISgwYNEtPJyckYNWqU1iHoEhISMGHCBMkN2PLly+t1s1NZqVKlJNMbN27UmtnPz88PAwYMUAmgAKASDOPi4gILCwsxvXbtWp037K9duyYJUCxfvjwKFCigUk7xBjkAyXGTHoMHD5bcCF60aJEkk4myt2/fYvr06WLazMwM/fr1S9dnZ2RbFAOBXr58KQmcU3zvWzA3N5ccH/J9W1v2rZCQEAwZMkSS8cnZ2Vnjzf/MoNwGZ3RfS6+WLVuiTJkyYvr58+cYNWqU1uxjvr6+mDBhgmTeb7/9ptJGp1Xv3r0lQwhu3bpVa/bGL1++YPz48ZK2RbHdA4x3XjMmY7VxNWvWlLRHR48e1XpO2LRpk8pwyj8iQ14nAdK2NSIiQu0w0fr6r7RnulhbW2PgwIFiOigoCCNHjpQMTa8oISEBf/75pxhO1xjy5s2LHj16iOmYmBgMGTJEaxDau3fvMGTIEEmm1k6dOqFYsWIal6lTpw6yZcsGIHVITcU2TXn4TcVl5Hx8fMT3ZG5ujvr162vfMBh2HyUiIiIiIvqeMQCNiIiIiIh+GmvWrMGzZ8/EtJOTE/r06aNSrlSpUpKb5PLAtfj4eL0+x9PTEy4uLjhw4ACCgoKQkJCAjx8/YufOnXBxcYGPj48oW6VKFY3BTa1atZLcjIuNjcXw4cMxYcIEeHh4IDw8HAkJCfDz88OuXbvQtm1bXLt2TZS3tLTE4sWLJRklAKBs2bKSTFBfvnxBt27dsHz5cjx+/BhRUVFITk5GeHg47ty5g8mTJ2PmzJmivJmZGUaPHq1S37Jly6JSpUpiOiwsDH379sX27dvx4cMHxMfH48OHDzh06BC6dOmC3bt3A1DNAmNIjo6OGDlypJhOSUnBnDlzMGDAAJw9exZfvnwRw8SdP38evXr1wrJlyyTrmDRpkkEyTA0ePFhyEzMsLAz9+/fHX3/9hTt37iAiIgJxcXF4/fo1du/ejdatW0sy4lhYWGDevHnpGirQxcVFstz169cxcOBAXLt2DREREUhMTMSnT5/g4eGBadOmoWPHjpL9VJFylpTcuXNLbmTHxsZiwIABmDt3Lry8vPD161ckJycjMjIS3t7emDdvHkaMGCGygJiYmEiGvlVkZ2cnmV6yZAkiIiKQkJCgM4OOOqVLl5Z8VlxcHH7//XdMnToVXl5eiIyMREJCAl6/fo1169aha9eukqCCkSNHar2xrU1GtqVGjRpiGEMAYijCXLlypSsg0dAGDhwouQkfFhaG3r17Y/bs2bh//z4iIyMRFxeHV69eYePGjWjbtq1k/8qdOzf+/vvvb1F1Qfn32bVrF168eIGkpCSEhoZmWj1MTU2xcuVKScDC9evX0bp1a2zZsgWvX79GfHw8wsLC8PDhQ8yePRvdunWT1FHTuS2tcufOjXnz5onplJQUTJ8+HSNHjsSNGzcQHh6OxMREfPjwAdu3b0fHjh0lwczdu3dHzZo1Jes01nnNmIzVxuXMmVNy/MbHx2Po0KFYu3Yt3r59i/j4eAQGBsLd3R29e/cW5yZjnjMzi6GukwDpsRsTE4OVK1ciJiYG8fHxeg8bq+i/0J7pY/jw4ZLg9Dt37qB9+/bYt28fAgICkJCQgM+fP+PYsWPo1KkTTp8+rbIOQw9d/Oeff6JcuXJi+sOHD+jUqROWLl2KJ0+eIDo6GjExMXj69CmWLVuGjh074sOHD6J88eLFMXXqVK2fYWFhIbkWUwxe0zR0p6bAtNq1a2sMjFRk6H2UiIiIiIjoe5VVdxEiIiIiIqLM079/f4OsZ9SoUZIgqQcPHmDz5s1i2sLCAvPnz5dkx1I0bNgwnD17Fr6+vgCAV69eYfny5TpvbNWqVQt37txBQEAAZsyYobVs2bJlsWHDBq1ZambMmIGYmBgxTJlMJsPJkyd1DluWI0cOrFmzBlWqVFH7/syZM/HixQuRVSYmJgYbN27UOdxolixZsGzZMskNQuX1DhgwALGxsQBSM4P8/fffGm/GNmzYEG3atNH5vWbEyJEjERkZiX///VfMu337Nm7fvq1z2WHDhhkkkANIDSxZtWoVRo8ejTt37gBIzQR3+PBhHD58WOuyFhYWWL58uSTALy3KlSuHgQMHYtu2bWLe3bt3cffuXa3LmZubo3bt2pIAkA8fPqBEiRKScvIMMfLvNCkpCbt37xZBhtpMnTpVMlSqIuXhRt3c3ODm5gYgNXvQrl27dK5f2eDBgxEcHCz2h5SUFMl6NenevTt+//33NH+eXEa2RT6k2Jo1ayTz27dvn6mBOJqYmppixYoVGDNmjBiaLCkpCXv37sXevXu1Lps/f35s2rRJkonyW8iTJw+KFCkighkCAwPh4uIi3r9w4UKm1bF06dJwdXXF2LFjRRao4OBgLF68GIsXL9a6bPny5bFmzZoMZz+Ta9OmDYKCgrBo0SIRUHXhwgWdw0U2bNhQErisyFjnNWMyVhv3559/wtPTUwQQRkdHY82aNSrHulzFihXxxx9/YNiwYenckm/P0NdJ1apVk7QzGzZswIYNGwCkZsNatGhRmur3X2jP9GFubo5Nmzahb9++CAwMBJA6NPWsWbM0LlO+fHlER0fDz89PrMOQLC0tsXHjRvz+++/igZHY2Fj8888/+Oeff7QuW7p0aWzatAk5c+bU+TlNmzaVDGUtX145EFkuT548cHBwkGRilK9HH4beR4mIiIiIiL5XzIBGRERERET/eTExMZg8ebJkWLBRo0ahZMmSGpcxMzPD/PnzkSVLFjFv+/btInBIkw0bNkiyi6mTNWtW9O7dG/v27UOePHm0ljU3N8eyZcswc+ZMnWXlmjVrhqNHj2od/ilnzpzYuXOnzroqKleuHLZv345WrVppLFO1alVs3rxZkq1JHVNTUwwaNAjr1q2TfMfGYGJigqlTp2L58uWwt7fXaxk7OzssX75cZVi7jMqZMye2bt2KUaNG6ZU1A0gNONizZw+aN2+eoc+ePHkyhg4dqjHoUpmjoyMOHjyIMWPGSOarC9yT38ju16+f3r9n4cKFsW7dOgwYMEBjmZo1a0qCgBQp3wjWl3x/WLRoEfLly6ezvJWVFaZPn57u7HNyGd2Wzp07q3z+tx5+U5GNjQ02b96M0aNH67VvZ8mSBV26dMHRo0c1BrRmthkzZmgMdJEHI2eWOnXq4ODBg2jcuLFe5U1NTdG7d2/s2rULefPmNWhdBg4ciA0bNqB48eI6y5qZmWH48OFYv369xuAUY53XjMlYbVyRIkWwY8cOVKhQQef6OnXqhO3bt+t97vheGfo6ycXFRSXTnlx6j9v/Qnumj8KFC2P37t16DSPZrFkzbN++XZKd0RgB0AUKFMDevXvRr18/vdZvYWGBQYMG4eDBg3pf4zVu3FjlfKopy5mm901MTPQOQDPGPkpERERERPQ9YgY0IiIiIiL6z1u4cCHev38vpitWrKh1OCe5ypUrY8CAAdi6dSuA1CwtU6dOxfHjx2Ftba12GSsrKyxbtgzdu3fHoUOHcP/+fQQHB8Pc3BzFixdHvXr10K1bN50BWsr69OmDzp07w93dHTdu3MDTp08RGhqK2NhYWFtbo2TJknB2dkb79u1RpkwZvdaZK1cuLFu2DMOHD8fJkyfx8OFDvH79GpGRkUhMTESuXLlgZ2cHJycnNGnSBHXr1tUreKlGjRo4deoUTp06hfPnz+PZs2f48uULrKysUKBAAdSrVw+dO3fWu56G0q5dO7Rs2RLnz5/HjRs38PDhQ3z58gVRUVGwtLRE3rx5UalSJTRq1AgtW7aEpaWlUeqRNWtWjB49Gv369cOpU6dw69YtvHjxAqGhoYiLi4O1tTXs7e1RuXJltG7dGrVr1zbIMFcmJiaYOHEiOnfujIMHD8LT0xMfPnxAdHQ0zM3NkSNHDhQvXhwVKlRAs2bNxM1SmUwGe3t7Mezj0aNH8ccff8DCwkKyfgsLC0yfPh0DBw7EqVOn4OXlhdevXyMsLAwJCQnImTMn8uTJg8qVK6Np06Zo2LChXjeXlyxZgurVq+PYsWN49+4dIiMjYWVlhYIFCyIiIkKvbCfqdOrUCa1bt4a7uzuuXbuGp0+fIiQkBPHx8ciVKxfKlCmD+vXro2vXrsiVK1e6PsOQ22Jvb4+aNWuKrHUODg6oWLGiQeplKFmzZsWoUaPQp08f0VbJ9+3ExETY2NigdOnSqFOnDlxcXFC4cOFvXWWJRo0aYc+ePdi2bRvu37+PkJAQZMmSBXnz5hVZHTNT0aJFsXHjRjx58gTnzp0TWaPkWdFy5syJ0qVLo2bNmujYsaPewRfp0ahRI9SrVw/nz5/H1atX4e3tjZCQEMTGxiJHjhwoWbIk6tSpg+7du+s9ZLExzmvGZKw2rkyZMjh8+DDOnz+Ps2fP4tGjRwgODoaZmRkKFCiAGjVqoHPnzqhatWombKXxGfo6KUuWLNi6dSv+/fdfnDlzBv7+/oiOjoa1tXWGzuM/enumL3t7e2zZsgW3bt3C6dOnce/ePQQHByM+Ph558+aFk5MTunTpgrp16wJIHbpaLnfu3EapU7Zs2TB9+nQMGTIEJ0+exK1bt/D27VuEhYUhKSkJtra2cHBwQIMGDeDi4qJ3IKucnZ0dKlWqhMePH4t5ugLQ6tSpgx07dojpihUr6t3WGWsfJSIiIiIi+t6YyGQy2beuBBERERER0Y9qypQpOHLkiJhmJgMiMgaZTIZmzZqJQMC//vpLa2YlIqLvAa+T/ltq1qyJr1+/AuDwkURERERERCTFDGhERERERERERN85T09PEXxmbm6ODh06fOMaERHRj+jly5d4//49ChcujMKFC2vM6qvMz89PBJ8BqZk4iYiIiIiIiOQYgEZERERERERE9J07cOCAeN2mTRvY2tp+w9oQEdGPytfXFxMmTBDTGzduROPGjXUuJx+SXk4+VDcRERERERERAJh+6woQEREREREREZFmvr6+OHPmjJjm0JtERJRelStXlkxv2LABcXFxWpc5fPgw9u/fL6YdHBxQpUoVo9SPiIiIiIiIfkzMgEZERERERERE9J0ICQnB169fYW9vj9jYWNy8eRN///03EhMTAQBNmzZFxYoVv3EtiYjoR1WsWDHUrl0bt2/fBgA8ePAAnTp1Qp8+fVCnTh3kz58f2bJlQ3h4OJ4+fYpjx47h1KlTkMlkAICsWbNi1qxZ33ITiIiIiIiI6DvEADQiIiIiIiIiou+Ev78/evToofY9GxsbzJ49O3MrRERE/znz5s1D79698fnzZwDA27dvMW/ePJ3LZc2aFfPmzUONGjWMXUUiIiIiIiL6wXAITiIiIiIiIiKi70TRokXVzre2tsbatWuRP3/+TK4RERH91xQpUgQHDhxA48aN9V7GwcEBO3fuROfOnY1XMSIiIiIiIvphMQMaEREREREREdF3wtbWFs2aNYO3tzciIyORL18+1KtXD0OGDNEYnEZERJRWBQsWxMaNG/Hs2TO4u7vD29sbb9++xdevX5GcnIzs2bOjcOHCqFSpElq0aIH69evDxMTkW1ebiIiIiIiIvlMmMplM9q0rQURERERERERERERERERERERERD8eDsFJRERERERERERERERERERERERE6cIANCIiIiIiIiIiIiIiIiIiIiIiIkoXBqARERERERERERERERERERERERFRujAAjYiIiIiIiIiIiIiIiIiIiIiIiNKFAWhERERERERERERERERERERERESULgxAIyIiIiIiIiIiIiIiIiIiIiIionRhABoRERERERERERERERERERERERGlCwPQiIiIiIiIiIiIiIiIiIiIiIiIKF0YgEZERERERERERERERERERERERETpwgA0IiIiIiIiIiIiIiIiIiIiIiIiShcGoBEREREREREREREREREREREREVG6MACNiIiIiIiIiIiIiIiIiIiIiIiI0oUBaERERERERERERERERERERERERJQuDEAjIiIiIiIiIiIiIiIiIiIiIiKidGEAGhEREREREREREREREREREREREaULA9CIiIiIiIiIiIiIiIiIiIiIiIgoXRiARkREREREREREREREREREREREROnCADQiIiIiIiIiIiIiIiIiIiIiIiJKFwagERERERERERERERERERERERERUbowAI2IiIiIiIiIiIiIiIiIiIiIiIjShQFoRERERERERERERERERERERERElC4MQCMiIiIiIiIiIiIiIiIiIiIiIqJ0YQAaERERERERERERERERERERERERpQsD0IiIiIiIiIiIiIiIiIiIiIiIiChdGIBGRERERERERERERERERERERERE6cIANCIiIiIiIiIiIiIiIiIiIiIiIkoXBqARERERERERERERERERERERERFRujAAjYiIiIiIiIiIiIiIiIiIiIiIiNKFAWhERERERERERERERERERERERESULgxAIyIiIiIiIiIiIiIiIiIiIiIionRhABoRERERERERERERERERERERERGlCwPQiIiIiIiIiIiIiIiIiIiIiIiIKF0YgEZERERERERERERERERERERERETpwgA0IiIiIiIiIiIiIiIiIiIiIiIiShcGoBEREREREREREREREREREREREVG6MACNiIiIiIiIiIiIiIiIiIiIiIiI0oUBaERERERERERERERERERERERERJQuDEAjIiIiIiIiIiIiIiIiIiIiIiKidGEAGv30tmzZgrJly6Js2bKoX7++3suNHz9eLFe2bFnMnj1br+WioqJQoUIFsdzt27fFe4rr0+bLly8ICgpS+96UKVPEOtzc3PTeHvo5PHnyxGDrioqKwvv37w22PkPStp1NmzYVx4i/v38m1oq+JT8/P0RFRal9r1+/fmKfuHPnTibXLP3c3NxEvadMmfKtq2Nwa9asEdu3Zs2ab10dIiIA7DvQz4V9B/Yd6Oem6djw9/cXx0XTpk0zuVY/jv96+6HvdQgRUUaxD0Y/E/bB/vvXUJntW127p6Sk4NmzZ2rfu3PnjqhTv379VN7X1U7qu498z8dAevyXr7/Zx/xvYQAa/fRq1aolXgcHB+t1QSOTyeDh4SGZd+vWLb0+z9vbG8nJyQAACwsLODk56V1XmUyGAwcOoE2bNnj37p3eyxHFxMRg4cKF6N69u0HWd/78ebRt2xb37t0zyPoMxdDbST++xMREbNy4Ee3bt0d4ePi3rg4REf3g2HegnwH7DkQ/t48fP2Lo0KFYuHDht64KERER+2D0U2AfjP5LfH198csvv2D79u3frA7f6zFA9DPI+q0rQPStVahQATY2Nvj69SuA1A5G4cKFtS7z7NkzhIaGSua9f/8e/v7+OpdVPNlVr14d5ubmetd1ypQpOHr0qN7lieTatWuHgIAAg6xr9erVWLdunUHWZWiG3E76b/j111/h6en5ratBRET/Eew70M+AfQein9eLFy/Qs2dPxMTEwNnZ+VtXh4iIiH0w+imwD0b/FTdv3sSwYcOQlJSEkiVLfpM6fM/HANHPgBnQ6KdnamqKGjVqiGlvb2+dy9y8eVO8LlOmjNr5mih2YOrUqaNnLVPxwozSy5D7zve8H37PdaNvg/sEEREZEvsO9DNg34Ho5xUWFoaYmJhvXQ0iIiKBfTD6GbAPRv8VQUFBSEpK+qZ14H5G9G0xAI0I0jTODx480Flenq7ZxMQEQ4cOFfN1dWCSkpLw+PFjMV27dm3J+76+vuIfERERERF9f9h3ICKin1nhwoXF+efSpUvfujpERPQTYB+MiOi/o1atWqIt3blzZ5qXv3TpklheV1ZLIsp8DEAjgrQj4evri7i4OI1l4+PjxVMwZcqUQfPmzWFmZgYAuH37NlJSUjQu+/TpU/EkqY2NDSpVqmSI6hMRERERUSZh34GIiIiIiCjzsA9GRERE9GNgABoRgLJlyyJXrlwAgMTERPj4+Ggs6+Xlhfj4eACAs7MzsmfPjsqVKwMAIiIitC6rmL65Vq1aMDXlIUhERERE9CNh34GIiIiIiCjzsA9GRERE9GPI+q0rQPQ9MDExgbOzM86dOwcA8Pb2Ro0aNdSWVUzTXKdOHfH//fv3xftVqlRRu6y8jOKyisqWLSteK6ZxVpwv179/f/F6wYIF6NKli9rPBICHDx9i3759uHv3LoKDg2FlZQV7e3u0atUK3bp1Q+7cuTUuq49+/frh7t27sLKywoMHD/D69WssWbIEd+/eRdasWVG4cGE0b94cI0aMUFu3o0eP4s6dO/j8+TMSEhKQN29eVKlSBW3atEHLli1hYmKisw5Xr17FyZMn4e3tjc+fPwMAbG1tUaZMGdSrVw9du3ZFjhw51C67Zs0arF27FgCwe/du1KhRA3fv3sXOnTvx6NEjhISEIEeOHKhQoQJcXFzg4uKCLFmy6PXdGGr7AODDhw84ePAgbt68iXfv3iE+Ph42NjYoV64cWrRogc6dO8PS0lKUv3PnjmQ/kVPcny5evKh3itqmTZvi48ePknlTp07F1KlTAQCjRo3C6NGjVZZLSEjAyZMncfHiRfj4+CA0NBQWFhbInz8/nJ2d0bFjR1SrVk2vOqhjiO08ffo0jh07Bh8fH4SHhyN37twoWbIkOnToABcXF/GUnDaJiYk4fvw4Lly4gGfPniEkJATZsmVDgQIFULduXXTv3h2lSpVK30Zq8OTJE+zZswd3797Fp0+fYGlpiRIlSqBt27bo1asXLCws0Lp1a7x9+xYAVNLDu7m5id9v1apVaNq0KdatW4cjR44gIiICdnZ2qF69OkaNGoUiRYpIlg0MDMS+ffvg4eGB9+/fIzo6Grly5ULx4sXRsGFDdO/eHba2tip1njp1Ktzc3AAAI0eOxJgxY9RuW2xsLGrWrInExEQAwKJFi9CpUye1ZX19fdGhQwcAQJUqVbBixQo0a9ZMpZzivB07dkjS9yu7ceMGDh8+jAcPHiAkJAQ2NjYoWrQo2rVrh86dOyN79uwal00LLy8vHD9+HF5eXggMDERSUpL4HuVtl52dnd7r+/TpE3bu3Ilr166J47VAgQKoV68efvnlF733wUePHuHw4cPw8vLCp0+fkJiYiNy5c6NChQpo1qwZOnTooNdxAQBfvnzBwYMHcfXqVbx58wbR0dGwtrZGmTJl0LhxY/To0QM2NjZ6b6OihIQEDB8+HDdu3AAAWFlZYfPmzahevXq61kdEpA/2Hdh3YN9BN/YdtPsWfYeoqCgcPnxYDFcSGRkJKysrlChRAvXr18cvv/yCfPnyaV1HSkoKLly4gDNnzsDb2xshISEwNTVFvnz54OTkhHbt2qF+/foal/f39xfX5H369MHMmTMRHR2NgwcP4syZM/Dz80NkZCTy5MkDJycndOnSRev65DJyTa3YJ+rcuTMWLlyo9bPkbRigvk8h35eaNWsGV1dXxMbG4vDhwzh58iTevXuHuLg45M+fH/Xq1cOAAQNQrFgxsWxQUBD27NmDCxcuICAgACYmJqJ/17dvX1hYWGj9Trt164b58+cjODgY27dvx8WLFxEYGAgTExMUK1YMjRo1Qt++fdV+F4ptm9zdu3fF9tjb24vhNhU/U3G+Ohk9phWP2UmTJmHw4MEICQnB/v37ceHCBXz8+BGxsbHIly8fatWqhR49eqBq1aoa15cWX79+xZEjR3DlyhX4+vri69evyJYtG/LmzQsnJyc0b94cTZo0SdM6DdF+REdHw83NTdQrPDwc2bNnR8GCBVGnTh107doVpUuX1rtOV69exYkTJ+Dt7Y2goCBxTDs6OqJ79+6oWbNmmrZR0c2bN/Hbb7+Jfn2rVq2wYsUKvc+LRERy7IOxD8Y+mG7sg2ln7D7YoUOHMG3aNACAg4MDTpw4oXOZo0ePYvLkyQAAR0dH7Nu3T6VMRvtgaREeHo7jx4/j9u3bePHiBcLDwxEXF4ccOXIgX758qFmzJjp27CiCehVNmTIFR44ckcw7cuSImOfs7CyG21TcJxTn60txX1fcd/Q5BgYNGoR69eohNjYWAPDvv/+qbe8VJScno0GDBggJCQEAXLhwQeV+mT4+f/6Mw4cP48aNG3j16hWioqJgbW0tvts2bdqk6do7KSkJR44cwalTp/DixQtERkYib968KFu2LDp37qx3+xUWFoYDBw7gxo0beP36Nb5+/YocOXKgcOHCqFevHnr06IFChQrpVafk5GScPXsWp0+fxuPHj/HlyxeYmZmhYMGCqFGjBnr16oXy5cvrvY3K3Nzc8Ndff0EmkwEABgwYgL/++ivd6yPjYAAa0f9Xq1YtSQdGk1u3bgEAsmbNKlI/161bF+vWrRPvDx8+XO2yih0YxbTRxpKcnIz//e9/2L17t2iMgdQ01GFhYfDx8cGOHTuwatUqg92s9/f3R58+fRAWFibmRUREoGDBgpJyMTExmDFjBk6ePKmyjo8fP+Ljx484ffo0KleujJUrV2q8+IyIiMAff/wBDw8PlfcCAwMRGBiIa9euwdXVFXPnzkXr1q11bsPatWuxdu1ayXcWGhqKGzdu4MaNG9izZw82bNigteNnqO0DUn/HFStWYNu2bUhKSpK8FxISgps3b+LmzZvYtm0bVq9ejXLlyuncxszi5eWFSZMmqVz0JSQkIDIyEq9evcKePXvQpk0bzJs3D9bW1plav7CwMEyZMgWenp6S+UFBQQgKCoKHhwf279+P1atXI3/+/BrX8+jRI/z555949+6dZH5CQgIiIiLg6+uLHTt2YMCAAfjzzz8z/PRccnIyFi9ejO3bt0v204SEBDx8+FD80cLV1TVN6/3zzz9x5swZMf3hwwcEBgaKTpD8s9evX48NGzaIPyLLBQcHIzg4GJ6enti4cSMmT56MHj16SMo0bNhQBKB5eHhoDEDz8vKSrP/u3bsaA9CuX78uXjdu3FivbdUkLi4OY8aMwdmzZyXzv3z5gi9fvuD+/fvYuXMnXF1dM9QhTUhIwNSpU9W2EZ8/f8bnz59x9+5drF+/HhMnTkS/fv10rtPNzQ3/+9//xFABcq9fv8br16+xd+9eTJs2Db169dK4jvDwcMycOVNl+4H/a1MvXryIDRs2YPHixXB0dNRap3///RcrVqxQGRohPDwcnp6e8PT0xLZt27B06VKdHT1lKSkpmDhxogg+y5YtGzZu3MjgMyLKFOw7sO8gx76D4bDvYJy+AwCcPHkSc+fORUREhGT+169fRf9h+/btmDt3Ltq1a6d2HS9evMDEiRNVHmoBgHfv3uHdu3dwc3ND7dq1sXTpUr0eonj8+DHGjh0Lf39/yfzAwECcOnUKp06dQps2bbBkyRK1N5WMcU1tSK9evcLo0aPx5s0byXz593X06FGsW7cOderUwbVr1/Dnn38iPDxcUtbHxwc+Pj5wd3fH9u3bde73jx49wogRIxAcHCyZ/+zZMzx79gw7d+7EihUr0KhRI4NsozbGOKavX7+OSZMmITQ0VDL/w4cP+PDhAw4fPowBAwaIm0zp5eHhgXHjxknOT0DqjcuvX7/izZs3OHToEKpUqYK1a9dqPeYBw7Uf586dw8yZM1XqFR4ejvDwcDx79gzbt29Hr169MGXKFK03Yz98+IA///wTDx48UHnPz88Pfn5+OHbsGDp06ID58+fD3Nxc6zYqe/DgAUaNGiX69c2aNcOyZcsYfEZE6cY+GPtgcuyDGQ77YIbrg7Vu3Rpz585FfHw8Xrx4gVevXul8KMDd3V28dnFxUXnfGH0wTbZv345Vq1YhOjpa5b3Q0FCEhobi+fPn2LlzJ3r06IFZs2Yha9YfL8wke/bsaNasmTj2T506pfO+hIeHhwg+q169erqCz06ePIkZM2ao3LuRX8e/ePECu3fvRqNGjbB8+XKdx9qHDx8wYsQIvHjxQjI/ICAAAQEBuHz5Mho3boxly5ZpXdfevXuxePFilXrJf/NHjx5hy5Yt+P333zFixAitAW1PnjzBpEmT8OrVK8n8xMREcY/q4MGDGDhwICZNmqR3cK/c+fPnMX36dNH29+nTh8Fn36kfr2UgMhLFp1Y1dWDkJ1gAqFy5smi0q1atCisrK8TExODBgweIjo5WyY7z7t07fPnyBQCQP3/+NAUu9OzZEwBw6dIl8UfEJk2aiKeTS5QooXa51atXi6dJ8ubNi6pVq8LGxgYvX74UqaaDg4MxevRonDp1Sm22orSaOnWqyh/CAEj+iB0dHY3+/ftL0l2XLFkSFSpUQNasWfHu3Ts8evQIKSkpePz4MXr27Ik9e/ZIngwGAJlMhjFjxuD27dsAAFNTU1SuXBnFihWDqakpAgICcP/+fSQlJSEiIgLjx49H3rx5NT4dBQAHDx7E0aNHAaReiNSpUwfZs2fH06dP8fLlSwCpT8X06dMHu3fvVtuJMdT2yU2YMAGnT58W0zly5ECNGjWQM2dO+Pn5wdvbGykpKXj//j0GDBiAQ4cOoUiRIsiXL5/Yd/bv3y+Wl8+Tb6O+XFxcEBYWhjt37ogLdWdnZ7H/VapUSVL+6tWrGDFihOh0mZiYoEqVKihRogTi4+Nx//59BAUFAUh9guX169fYs2ePxiedNMnIdo4YMUIcIyVKlECFChVgYmKCBw8eiE6Xt7c3Jk+ejH///VftOjw8PDB8+HDxxISZmRkcHR1RuHBhxMTE4OHDhwgMDERycjK2bt2Kjx8/YtWqVWm+uFI0a9YsHDx4UEzb2trC2dkZFhYWePr0KV69eoW3b9/i119/VQkS0+To0aO4fPmyyvw6deqI/Vwmk2Hy5MmSp3eyZ88OZ2dn2Nraihs8CQkJiIqKwowZMxAYGIg//vhDlK9fvz6yZs2KpKQkPH78WG17CUAc13JeXl4a664YgNakSRNkz55d/P4nTpwQF8/t27cXn6Upu8P06dPFPmFvb49KlSohW7ZsePz4MV6/fg0gtT0fM2YMjhw5kuY/wsvNmjVL8geOsmXLokyZMjA3N8enT59w//59xMXFIS4uDvPmzYOtrS3at2+vcX03btwQTxNZWlqiRo0ayJcvHz59+gRPT08kJiYiMTERc+bMQenSpdU+SfP161f07dtXtHVA6vnK0dER2bJlw5s3b/Do0SPIZDL4+flhwIABWLNmjcabV4sXL8aWLVvEtLxednZ2on1OTEzEly9f8Ntvv2Hnzp1pylYwY8YMEShnYWEBV1dXODs76708EVFGsO/AvgPAvoM27Dv8q3Yd36LvsHv3bsydO1dMyz/T3t4enz9/xoMHDxATE4OoqChMnDgR5ubmaNGihWQdT548Qd++fSV/lC5btizKli2L5ORk+Pj44P379wBSr+O7d++O3bt3w97eXmO9Pnz4gKFDhyIsLEzyPcj3G/lnnT59Gvb29vjzzz9V1mHoa2pDCgkJweDBg/Hp0yeYmpqiRo0aKFy4MD5//gwPDw8kJycjOjoakyZNwqJFizBy5EgkJCTAzs4ONWrUgJmZGe7duyf2LR8fHyxfvhwzZ87U+JmfPn3C77//jpCQEJiYmKBatWooUaIEgoKCcPfuXSQmJiI6OhojR47EihUrJL9zpUqV0LNnT3z+/Fn0C+3s7NC0aVMASHObb4xj+uHDh1i9ejXi4uIkfZ7Pnz/jzp07SExMhEwmw7///otixYqhd+/eaaqz3OvXr/H777+Lh2hy5MgBJycn5M2bF1FRUXjx4oXIMv7o0SMMHjwYR48e1XoDzhDtx4EDBzBjxgwxnTVrVjg6OqJIkSKIjIyEp6cnwsPDkZycjF27duH169f4559/1AahffjwAb169ZIEKpYoUQIVK1ZEUlISfHx8RGDo8ePHERMTIwI39PH8+XP89ttv4jhu3LgxVq5cqXcWbSIiddgHYx8MYB9MG/bB/lW7jszqg1lbW6Np06ZiX3B3d9f48D2QGngkD5g1MzND27ZtJe8bow+myYYNG7BixQoxnSdPHlStWhW5c+dGQkIC3r59Cx8fHxH4c+DAAdjb2+P3338Xy9SqVQvm5uZ4+/atyBhdvHhx0XZragcNSd9joEOHDqIfef78ecyaNUvrdapin7Njx45prtft27cxceJE8f3lyZMH1apVg62tLcLCwvD8+XOxP1+9ehV//PGH5L6KOr179xbHRvny5VG6dGkkJSXBy8tLnIeuXLmCv//+G3///bfadaxYsQIbNmwQ0xYWFqhRowby58+PsLAw3L17F9HR0UhISMDq1avh5+eHRYsWqV3Xo0ePMGDAAMn+Wr58eZQpU0YcZ8HBwUhJScHWrVuRnJycpuCxW7duYfz48UhOTgYA9OjRQ9I3ou+MjIiEOnXqyBwcHGQODg6yDx8+qLx/4sQJ8f7KlSsl7w0dOlS8d/nyZZVlDx06JN6fNGmS2s+Xv+/g4KD2/b59+4r3b9++rbbM5MmTJeupUKGCbMuWLbL4+HhJuStXrsgqV66scXvSQrFeDg4Osnr16snOnz8vi4qKkvn5+clcXV1l0dHRovykSZNE2UaNGslu3bqlss5Xr17JunXrJsp16tRJlpCQIClz9epV8X7NmjVlT548UVnP+/fvZe3btxfl+vfvr1Jm9erVkvo7ODjIxo4dK/v69auknLu7u6xq1aqizLRp09R+H4baPplMJtu7d6+kXgsWLJDFxMRIyjx69EjWuHFjUWbQoEEq69G1b6WF4j52+PBhtWX8/Pxk1apVk2yfr6+vpExKSops7969skqVKolyI0aMyFDd9NnOJk2aSMrVqlVLduXKFUmZ5ORk2Zo1ayTl1P2OwcHBknZj9OjRsqCgIJXtPHr0qOT72Lx5c7q38cyZM5J6LVy4UOX4Pnv2rMzR0VFlv1Z2+PBhlTJLly6VBQUFycLDw2Vnz56VXb9+XZTftGmTpOy8efMkx7ZMJpOFhITIRo8eLSl3/vx5SZk+ffqI95S/e7kuXbqo1O3Tp08q5aKjo2UVK1aUOTg4yBo0aKDyvuLvra5dl8lU27CqVavKjhw5IktOTpaUO3DggKxs2bKi3MGDB9WuT5dXr16JdVSqVEl27do1lTKfP3+W9e/fX5Rr3ry5Shl1v9+kSZNkISEhknJv376VNW/eXJTp3bu32noNGTJElKlSpYrswIEDspSUFEmZZ8+eSdrUGjVqqP1eFdtnBwcH2fjx42VhYWGSMm/evJF16NBBlGnTpo3k8xTb5tWrV0uWXbhwoeQ7vHr1qtptIiIyJvYd0od9Byn2Hdh3UN5OQ/Ydnj9/Lq6VHRwcZL/++qssICBAUiYoKEg2YMAAUcbZ2VkWFRUl3v/69ausXr164v0mTZrIPD09VT7r7Nmzsho1aohyXbt2VdlPP3z4oHL8DBw4UObv7y8pFx4eLhs8eLAoU7lyZVlkZKSkjDGuqSdPnqzzO9XVtipvX8eOHWXv3r2TlLl3757kdylXrpzMwcFBtmbNGsl3lpSUJJs9e7aknxIbG6vzO23SpInM29tbUs7Pz0/WtWtXyb4cERGhUv/bt2+LMn379lX7HSh+ZpMmTVTeN+QxrVgfxb6Fcp8nMDBQ1rlzZ1GmQYMGKn0ZfY0dO1as57fffpMcD3InTpyQVahQQZQ7cuSIShlDth/379+XlS9fXpQZMGCAynETHx8vW7t2raTPOn/+fLXb2LNnT8kxr3wtkpSUJNuyZYukXidPnpSU0dSGvnv3TtJmDBo0SOW6gogovdgHSx/2waTYB2MfTHk7DdUHu3jxolhHq1attJbdt2+f5JpTkbH6YJqu3RV/49WrV8sSExNVyr169Urm4uIiytWtW1fl/olMpl//SlefQ9c+rOuej67lk5KSZHXr1tV6TpCLi4uTOTk5yRwcUvud6vpQunTv3l181vTp01V+o6SkJNnWrVsl+7O631u5HWzWrJnswYMHkjLx8fGy6dOnS8r5+fmprMvd3V1SZty4cSp9rKioKEl/1MHBQfbvv/+q/Y4Uf5OmTZvK7t+/r1JmwYIFknUpltG2nz548EByfE6ZMiXdfT3KHBnP40/0H6KYOUXdUzQ3b94Ur+vWrSt5TzFFp2I5uXv37qkta2wzZ87EoEGDVLL0NGrUCEOHDhXTytmG0svExAQbN25E8+bNkT17dhQpUgTDhw+HlZUVgNSoffkTKjlz5sTOnTvVfh+lSpXC9u3b4eDgAAB4+vQpTp06JSmjWOeBAweiQoUKKuspWrQoVq9eLaa9vLwQFRWldRvkwwIoP8nRpk0bLFu2TEwfPnxYJb2pIbcvJSUFa9euFdODBg3ClClTkC1bNkm5ypUrY+3atSItsHyc7m9p3bp1ItK9ePHi2Llzp9hWORMTE/zyyy+SJysuXLiAO3fuZFo9zczMsGPHDpUMTqamphg1apSkTVB3jGzYsEGk3m3RogVWrVqlklnLxMQEHTt2xPr168VTM+vXr9e5H2qycuVK8bpfv36YPHmyyvHdsmVLuLq6pvkpnX79+mHChAnIly8fcubMiZYtW6J+/foAgMjISGzatEmUHTp0KKZNmyaObbncuXNj5cqVaNmypZi3aNEi8WQCkDoMp5y69OuRkZF49uwZgNSnQeTUZUG7ffu2yPKW0eE35dauXYtOnTqppNru3r27ZBjQ9Labist16NABDRo0UCljZ2eHNWvWiOPdz89P53Hdvn17LFq0SOXJvuLFi2PevHli2tvbW2VIzLt37+LatWsAUvfZ1atXo3v37ir7ULly5bBr1y6RZvrr16+SdkpuzZo14nWrVq2wdOlS5MqVS1KmRIkSWL9+vXga9fXr12I4TW3Wr1+PrVu3Akg9hletWiXZp4iIMgv7DhnHvgP7DgD7DooM3XdYv369uFZ2dHTExo0bVYZXypcvH9asWSOelA8PD5dkPP7333/FE9S2trbYs2eP2qwULVu2xJYtW8ST448fP5asR52KFSti48aNKk/p58yZE8uXL0fOnDkBpA5DpfxbG+ua2pBsbW2xY8cOlWwZTk5Okn5FSkoKevXqhVGjRkmevM+SJQumTp0qru9jY2NFP0mTHDlyYPv27SqZhYsUKYJt27aJ4aPCwsKwcePGjGyeRsY8pps0aYKlS5eq9HkKFCiAVatWieEdg4KC1A5VpA/FfWv27NlqM3K0b98egwcPFtNXrlzRus6Mth/Lly8XfeoaNWpg06ZNKseNubk5Ro4cKRl+dNeuXfDz85OUu3r1qhh208zMDFu3blXpS2fJkgWDBg3CgAEDxLwdO3Zo3UYg9Xv/9ddfRZtRq1YtrFu3Lt2Zw4mIlLEPlnHsg7EPBrAPpsiQfbAGDRqITIVv377Veu2uuD916NBB8p4x+2DKDh8+jISEBACp7c7o0aPVZvYtVaoUlixZIqa/fPkisgL/aLJkySLJOKd8bCu6cuWK2BeaNGkCGxubNH2WPPsXkDpCzIwZM1SyrWXJkgW//vqrJFu3utGKFOXMmRN79+5FtWrVJPPNzc0xa9YsFC1aVMxTPjaSkpIkx3W7du2wbNkylT5W9uzZMWvWLEmfYPXq1YiMjJSUO3z4sMjgZmNjg127dsHR0VFSxsLCAlOmTEHz5s3FvJ07d2rdRgDw9fXFsGHDJKMczZ8/P0NZ4sn4GIBGpEBXB0YeKGFlZaXSqH+PHZjixYujR48eGt9v3bq1eK38B6n0qlGjBipWrKjx/V27donXAwYM0DpWtpWVFUaNGiWm9+3bJ3lfnjIXSP2DtCYlSpTAX3/9hYULF2L79u1a//Blbm6OOXPmaBzjvVmzZiLQISUlRZJaGTDs9t2/f19cZObMmRNjx47VuK6KFSuK/crGxibdf2g1hOjoaElK2mnTpmkdY7x58+Zo1aqVmN69e7dR66eoU6dOKh0rRdqOkdjYWBw+fBhAaiflr7/+0nrRU7t2bfFH3cjISLi7u6e5vs+ePcObN28ApP7OEyZM0Pp5yh0XXRQvJJWdOnUKX79+BQAULFhQMqymMlNTU8yZMwcWFhYAUr87eXATAEmHUV0A2t27d8Uf1/v27SuZr0xx+E1DBKDVrVtXBN2pY4h2U9+2y8bGBjNmzMC8efOwfft25M+fX+t61Q1LJFerVi3R+U1KShIdAjnF9qdNmzYah9UEUtujadOmiemTJ08iIiJCTH/69AmPHj0CkNp5mjZtmsZjo1ChQqKzZ2VlJRn+U53du3eLIMysWbNi+fLlYlggIqLMxr5DxrHvwL4D+w7qGaLvkJCQgKtXr4rpqVOnahxWJEeOHOL4t7CwEH0OQDpMzh9//IECBQpo/MwqVaqgX79+YlpxH1dnyJAhGo8xGxsbSTsrHw5QzljX1IY0YMAAjTcolIeOHzJkiNpy5ubmknZSPgySJqNGjdLYluTIkUPSh0zPfqWLsY/pESNGaDx2ihQpgrJly4pp5X1GX/ruW927d8eff/6JNWvWYPTo0VrXmZH2482bN5K+8Ny5c7WemwYMGCCGF0pOTsbevXsl7587d0687tq1q9bz8KBBg2BqagoTExMEBwerPMikKCwsDL/++qvoa1avXh0bNmyApaWlxmWIiNKKfbCMYx+MfTD2wdQzRB9MeShNTev4/PkzPD09Afzf0J2KjNkHU5Y1a1ZUq1YNuXPnltyLUads2bKS/k14eHiaPut7ojiU5sWLFzW2UYrBaYoPEelL+fpZHuynzqBBgzB16lS4urril19+0breX3/9FXZ2dmrfy5o1qyTQSz5Uq5yHh4eYZ2lpiZkzZ2o9NiZOnCj60VFRUTh27JjkfcX+xdChQ1UeelMkf4gnS5YsOs9rfn5+GDx4sLj31Lp1ayxevFhj+0/fD/5CRArkY1EDqh2Y169fIzAwEABQs2ZNlT/cli1bVmTqef36tRh7GQBCQ0PFeNMlS5bMtD941q1bV+tJQ/HiWjF4ICOqV6+u9X3FYBNtQR5yDRo0ENvg4+MjOVmXLl1avN66dSv27t2r8SJhwIAB6Ny5M2rUqKG1A9O0aVONJ205FxcX8VrxD/qAYbdPMcK9efPmIphHkwULFuDmzZvw9PRUGS8+M3l5eYmn7PPly6f2SXRl3bp1E6/v3LkjxkI3tnr16ml9X/50OAARfCXn7e0tou5LlCiBQoUK6fw8xe9CXTCVLsr7hPLTVMo6d+6s97rz5cuntcOtuG+7uLhovHkllzt3bjRr1kxMKz5lUbZsWXER6uvri9DQUMmy8rKmpqbo1auX2E51GdDkGbMsLCwM8schXfuEIdrNMmXKiNcnT57EunXrND5R1bVrV3Tv3h21a9fW+oeA0qVLa+2IAtK6K+/Pik+udenSRet6gNQgQnlbmZiYKPltLl26JF7XrFlT5zlv3Lhx4in8QYMGaSx3/Phx/O9//wOQ2kFZsmSJJNMeEVFmY98h49h3YN+BfQfNMtp38PDwEJ9ZpEgRlYxYyvr27YsLFy7A29sbf/31FwDg1atX4qaamZmZXg+4KP4+z54909pe1K5dW+u6FL8n+bbIGeOa2tCUM68oyps3r3hdoEAByf6jTDGTsOKNXGVmZmY6r+WbN28uMpwEBAQY/OanMY/p7Nmzo3LlylrXpW2f0Zfi+WL06NEiY4GyIkWKYMiQIWjZsiVKlSqldZ0ZaT8UzxXVqlXT+VmA9DtVznigmK1N8RylToECBXDq1Cl4e3vj0qVLGoPJoqKiMGTIEJHNpVq1ati0aZNKxnQiooxiHyzj2AdjH4x9MM0y2gcDpNnMNAWgnT59GikpKQBSs5gpXmMZuw+mbNSoUdi/fz88PDz0GmVEMfOgfD/6EVWqVElcV0dHR6vNaBwVFSXm29ra6nWsKMudO7fILBYXF4fhw4fj1atXastWrFgRAwcORLNmzbTeqwPSdh9LW/+iWbNmKiPXKDM3N5fsh4r9i6ioKMm9IV39CycnJ7i7u8Pb2xuHDh3SWE45s3Lz5s2xbNkykfGavm+qORSJfmKlSpWCnZ0dgoOD8fz5c8TFxYkT/61bt0Q5dX9ENDExQe3atUU0tJeXl7iI/Fbpm7X9AROA5KLGUBcK2v4QFhISIjqBQGr6fnVDGSgzNzdHfHw8EhMT8fbtW5QvXx5A6ols1apViIiIQEJCAmbPno1Fixahdu3aaNCgAerXr68y1IUuujpgACR/8FTM1mPo7VNMw6ztqSS5zHySWxvFtMJVq1bVKxWqYjrW8PBwBAYG6tUhyKi0HCPKTyb4+PiI15GRkZg5c6bOz1PcP3RlelLnyZMn4rWuP7wDqU+/mJiY6NUhVPyDgDrPnz8Xr5WfINTE0dFRdLKU0003bNgQ+/fvh0wmw+3btyWdbvkFbPny5WFra4uKFSvCy8sLr169QmhoqLhgf/funXhKonbt2joD8vSha59Q/ENCettNedv0/v17yGQyrF69GuvXr0eNGjVE26X45L4h6g1obvODgoLw5csXMa3P72tqaopq1arh/PnzAFJ/X3nAoWLGDH3aLuXUzurcunULGzZsEPuyubk5qlSponM5IiJjYt8h49h3YN+BfQfNMtp3SOs1mbW1tUpwluLvU6ZMGb320VKlSiFXrlwIDw9HSkoKXrx4gZo1a6qUy5Ejh87rQMXPk2dIljPGNbWhabtpoPiHc13Ho+IQONr6dmXKlNE5JIy5uTnKli0rhmB89eqVQb8nYx7TRYoU0bk+bfuMvvr06YMpU6YASH1gqkePHihUqBAaNGiAhg0bpiuQMSPtR3r74nK+vr5ISUmBqakpwsPDRd/PxMREnEO0KVmypM4yw4cPl7RzFSpUyNRgTyL6ebAPlnHsg7EPxj6YZhntgwGp12vFixfHu3fv4O/vj0ePHqn8HVvb8JvG7IOlVVJSEj58+ICXL1/i8ePHuHPnDgICAsT7mRWIaCwdOnQQQ1GeOnVKkukPAM6fPy+CZtu1a6czKYMmffr0wZo1awCkBja2a9cOJUqUQMOGDdGgQQPUrFkzzVmDM3L+yGj/QnEfff/+vVh/7ty5tWY/k9P1QE1sbCwGDx4syWjt6OiodmhY+j7xlyJSUqtWLZw8eRKJiYnw8fER42orpmXW9BRrnTp11HZg7t+/LymTWdI6FrUh5MyZU+N7igEOACRpfvWlmNLVxsYGq1evxqhRo8SY07Gxsbh8+bJ4+qR48eJo2rQp2rVrJ4Yg0EZXVDkAyRM2CQkJiIyMRI4cOQy+fYpZoZTHpf+ehYWFide6MjLJ5ciRA1ZWVuKJlLCwsEzpwGTkGAkJCRGvg4ODJWmR9ZGe9MSKn6nPPpE9e3bkyJFD5QkHdbQdu0D6flfFTrXi8sD/BaABkASghYaGis6d/KnGGjVqiKcovLy8RNYrQw+/CWROu5klSxasW7cOgwYNEk9bJiYmwsPDAx4eHli8eDEKFCiApk2bok2bNqhZs6bOPwQoPnmkD8XOoeJvI99n9KH4+yruz2ndT/WheB4FUtv62bNnY/PmzQZZPxFRerHvkDHsO/wf9h3Yd9Amo30HXVkiNFH8fdJywyxfvnyizsr9ADl9bqQoDq2hfHPDGNfUhqbvPqMrW4a+9GmTAOn+oNwWZZQxj+mM7jP66ty5M548eYKdO3eKeQEBAdi/fz/2798PMzMzVK9eHS1btkSbNm30eqAmI+1HRvviycnJ+Pr1K3LlyiVpF7Jnz67Xd6oP5Qwh+/btQ4cOHSQ3qoiIDIV9sIxhH+z/sA/GPpg2GRle0sXFRQQcnT59WhKA5u/vLzLs5s+fX5LZETBuH0wbeaKAa9eu4cWLF/Dz80NAQACSkpK0LvMjc3FxwcqVKyGTyXD16lVER0dLro8V2wjFITvT6vfff4evr69kqMq3b9/i7du32L59OywtLVGnTh20aNECrVq10utBjrQcG8q/kyHv9Rni7w7KQkNDVUZNWrt2LVq1aqV3n5e+LQ7BSaREXRrnpKQk8ccUOzs7jWOOK3Zs5ON3A//XgTE1NYWzs7Ohq6zRt0hFqS1KW9NwGGkRHR0tmZY/tdS3b1+1aULfvXuHrVu3omvXrhg4cCA+fPigdf36/PFNOcuSfLsMvX2KF7hpjX7/lhS3IS0ZqRSHZtA2rIghZeQYyejvnZ7hQBQv7PS9SaHvb6BrH0vP76pYTnms+7p164p06oopfxVTeMvbS8V2WfEP28YIQMusdrNMmTJwd3fH77//rrYj+enTJ+zZswf9+vVD165dJdnv1MnI0x+Kv21ahkhR/H0Vj1ljtl09e/YUNw6vX7+erj8UEREZEvsOGcO+Q8aw75CKfQf1FPeJ9GYKNvR1oiJDtDmGvqY2tMx+QlvfYCLFNsIQbZEiYx7TmXmemj59OrZu3Yr69eurfG5iYiJu376NuXPnolGjRli5cqXObGsZqXt6vlPl41XeHzdEu6BJiRIlxHVRSkoKZs6c+UMPy0RE3y/2wTKGfbCMYR8sFftg2ilmNTt9+rQkAEhxWM527dpJHqAAjNsH0+TJkyfo1KkTBg4ciK1bt+LGjRvw8/OTBJ/lzZsXXbp00Tlc44/E3t5eBDHHxcXh0qVL4r3Q0FBx36pkyZIZGo0la9asWLNmDVasWAEnJyeVB6Pi4uJw+fJl/PXXX2jUqBF27Nih1zrTy5D3+ozZv3BychLnc3lCAvoxMAMakRLFDsyjR48AAA8fPhQNcu3atTUua29vj6JFi8LPzw8vX75EREQELC0txR85K1SooDPL0H+Z4skne/bsKhlt0it//vyYMWMGpk6dinv37uH69eu4ffs2njx5IsZRB1KDXPr164fDhw8jT548atclT6eqjXInSv60q6G3T3F9+tTre5Hejkh6Oz7fimKnsl+/fpg+fbrRP1Mx6Ezf71Y58Cu9rKysRCY1fT9b8TdV7oRbWVmhZs2auHnzJvz8/ODv74/ChQuL4TezZMkiLv6dnJxgZmaGxMREkQktISFB/GGpbNmymfLElaHlyJED48aNw9ixY/H48WNcu3YNHh4eePjwoeQP9U+ePMHAgQOxb98+nemJ00PxDzdp6VhrOma1BR5mxKRJkzB48GAAEE+s/f3336hfv/5/quNLRD8W9h2Mh32HtGHf4fv2LfoOhrgmU/x9DHGdaAyZfU2d3mEdM4O+x77i76NP9q60+C8d0/Xq1UO9evUQFhaG69ev4+bNm7h9+zY+ffokyiQkJGD9+vUIDQ3F3LlzjVKP9HynyuceeRukuC5D9tWKFy+O7du3IyEhAe3bt0dcXBxevHiBf/75ByNGjDDY5xARAeyDGRP7YGnDPtj37Vv0weSKFi0KR0dHPHjwAIGBgbh//74YPlbxgWrl4TeBzO+D+fj4oF+/fpLPKl68OCpWrIiSJUuiVKlSqFChghgut3HjxhnKDve96dChgwhIPnXqFFxcXACkBg7K+34ZyX6mqG3btmjbti2CgoJw7do13Lx5E3fu3JFk+4qKisL8+fMRFxeHYcOGGeRzlWW0f6F4bBmrf+Ho6Ih//vkHL168QO/evSGTyXDjxg0cO3bMYL8HGQ8zoBEpKVasmEg5+fTpUwDSjDua0jfLyVM0y2QyPH36FI8fPxZ/9NS17H+dYoBAdHS0SgrNjMqaNStq1aqFiRMn4tChQ7h9+zaWL1+O+vXrizKBgYH4999/Na5DMV2oJop/bMyRI4cICjL09imuTz6kiDZJSUkq49x/C7a2tuJ1YGCgXsuEhYVJLnTy5s1r8HoZmuLv4+fnlymfqfi9BAUF6SwfGxsr0ptnVHp+V8Vy6tLvNmzYULyWP00ib2/LlSsnhoK0tLQUT5j4+vri69evuHv3rthnmjRpkpZN+e6YmJigSpUqGDVqFHbv3o27d+/C1dUVbdq0EWW+fv2KdevWGeXzFX/b6OhovYZsBaS/r+K+qXhsBAcH61yPTCbT2Tnp3r27CD6bMGGC+MNRSEgIFi1apFd9iYiMgX0H42HfIW3Yd/i+fYu+Q1qvyQDVGxyKv4/ivqyNTCaTlM2s3ye919SKT5/rE1xm6IxhhqTvcJqKv4+hhkmR+y8e07a2tujQoQMWLVqEq1evwt3dHRMmTJA8BHXgwAG8fv3aaJ8vp+93GhAQIF6bm5uLYArFdiEqKkqvm5r63JTasWMH8ufPjyJFiuC3334T89evX4+3b9/qVWciIn2xD2Y87IOlDftg37dv0QdTpBhcdubMGQDA69ev4evrCyA1m3P58uVVlsvsPti0adPENaGDgwOOHj2Ks2fPYvny5Rg1ahTatGkjgs8A6H3v4EfRunVrMVLPzZs3xXdx9uxZAKn9RXlQmqHkz58f3bt3x8qVK3Hr1i24ublh+PDhkt/e1dXVaIF+hrzXZ4i/OyjLlSsXNm/eDGtrazg5OaFr167ivYULF6ZriFnKXAxAI1JD/hTNhw8f8PXrV9y7d0+8p6sTovi+r68vHjx4IKblnZufVcGCBSUnozt37uhcJjk5GQcPHsStW7fg5+cn+YOwTCbDx48fcevWLbXL5syZE+3atcOWLVskEdGK6bWV6TMkx+PHj8XrSpUqideG3r6yZcuK18+ePdO5ritXrqBq1apo0qQJFixYoLO8sVSoUEG8fvjwoV7jwMvHvAcAa2tr5MuXzyh1MyTFzsH9+/f1Glri5cuXOHnyJLy9vfXqLCtT3N/02VefPn0qeYosIxS3V57eXhfFciVLllR5v1GjRuL17du3ERoaijdv3gCQPs0I/N9wnCkpKfD09MSNGzfEe4YafjMzBQUFwcPDQ+3TcVZWVmjWrBlWrlwpeVpc8Y9phpQ/f37JU4X6/L4pKSniKVNA+vumte3y9fVFtWrV0KBBA4wbN05jHeVy5syJSZMmiWk3NzeROY+I6Ftg38E42HdQxb7D/5WTY99Bs7TuE1+/foWTkxPq1q2Lvn37IiUlRfL7vHr1Sq/gK8VyJiYmKFGiRJrrri9DXFMrDuuj66EIeTvyvfL19dXZ/4uLi8OrV6/EdMWKFQ1ah//CMR0fH4/nz5/j+fPnat8vVaoUhg0bhgMHDogHY2QymcjWbWjp6YsrfqfFixcXgZYFChQQ5x6ZTKZxGxVNnDgR1apVQ/v27cWDY8oU+2tDhgwRx31CQgJmzpypV52JiNKCfTDjYB9MFftg/1dO7nu4XtPHt+iDKWrbti3MzMwAQAztKA9EA9RnPwOQqX2wZ8+eietBExMTrFmzRm1QnFx4eLgkE5Y++873zsbGRiQ4SEhIwK1btxAVFSUyJNasWRP29vYZ+ozo6Gj4+PiofTDDxMQEFStWxNixY7F7926xz8TGxsLHxydDn6tJRu/1Ke5fDg4Ooq8REhKiV+KM3r17w8nJCZ06dZL0TeWyZ88Oa2trMT1x4kTRdoeGhjIhwQ+AAWhEaigGPvj4+IiGtWTJkuLpGk1q164txux++fKluEFvbm4OJyenDNVLeVzoH42JiYnku923b5/OZc6fP4/p06fj119/Rdu2bcVFVFJSEmrVqoWmTZvi119/FU8NaNKyZUvxWtsF27lz53Q+9Xz8+HHxukWLFuK1IbcPSL2wkbt48aLOC+Rr164hJSUFAQEBkqEa5XUzFF3rcnR0FBdJwcHBuHbtms51Hj58WLx2dnZOd30z8xipXr262M7IyEicOnVK5zJLly7FhAkT0LNnT8yZMyfNn9mgQQPx+tKlSzpTe+tTJ33JA8AA4MSJEzr3x9DQUFy5ckVMKweUAakXqvKnZ+7cuSP544Li5ykvf/fuXVy/fh1A6tMaVatW1ViP77HddHFxQcOGDTFw4EDcvHlTa1nFtks5fbwhKbY3bm5uOstfuXJFdMIVh0tVXtfdu3d1Pk147do1yGQyfP78WZw/dencubPkM2fNmvVDpbonov8W9h2Mg30HVew7pGLfQT9OTk4iuOrdu3c6A02uX78OmUyGkJAQJCUlwdTUFKVKlRJPzycmJkr2Z00Ufx8HBwfJ09WGZKhrasXh6HVlGHj48OF3nQEtPDxc53dx5swZcd1cqVIlFCxYUPK+vtfjmnzLY9oQTp8+jWrVqqFjx47466+/tJa1s7ODo6OjmDbWvqF4rnj48KFemdYUv1PF5U1MTCTXF4o3QdVJSEjAnTt3EBsbi5cvX+q8rgFSr2FmzZolpu/evYuDBw/qXI6IKC3YBzMO9sFUsQ+Win2wtMuVK5e4n+Pv74+XL1/i/PnzAFK/h/bt26tdLjP7YIoBUba2tihevLjW8vL6y6k7FjPanzCEtO5nisGAly5dwq1bt8TxnNHhHrdu3SqyeC1fvlxr2VKlSqFUqVJiOjP6F5cuXdKZaS0hIQEnTpwQ04pDXdvY2MDBwUFM6+pfBAUFwdfXF9HR0Xj16pUkq7Qmtra2mDhxopg+cuSIxgdj6Pvw7VsBou+QYuN79OhRMYSdPimYc+XKJaKHX7x4IZ62cHR0lIyLnB7yiyUAekXrf4969eolXt++fVtroENUVBSWLVsmpps1ayaGDciaNavk6ZXt27dr/VzFJ1C0XUR9+vQJmzdv1vi+u7u7yLRjYWEh6RgBhts+IDWrkzyVaUhICDZu3KhxXR8/fpRciCpfvGbNmlW8zmiaZ137oY2NDdq2bSum//77b60XSpcuXcK5c+fEdPfu3dNdN0Nupy65cuWSDOeydOlSram2r169KgnIUkwbq6+aNWuKTFMRERFYs2aNxrLPnz/HgQMH0vwZmnTo0EHcnPn06RNWrVqlsaxMJsPs2bPFjQ07OztJtjNF8mE4g4ODsX//fgCqAU1A6g00eSrkM2fOiCcjGjVqpLVTo7hPfC/tZrVq1cTrnTt3as1SoG/blVG//PKLeH3mzBlcvXpVY9nIyEjJU3rNmjUTT/4DqU9pydvnxMRELFmyROu6duzYIaY1dbzVmT17tmiP3r17B1dXV72XJSIyJPYdjId9h//DvkMq9h30lzt3bjRv3lxML1q0SON1Z2JiIjZt2iSm5fuEiYkJevToIeavWrVKa5DWkydPsGvXLjGdkd9HF0NdUytO+/j4aByeJzk5GUuXLk1XXTPTkiVLND6YER4ejhUrVohpdUPJZLT/9C2PaUNQ3K+ePHmiNQNLUlISXr58KaaN1V8rXbq0pH88c+ZMrb/Nrl27RHYYExMTdOvWTfJ+z549xev9+/eLLOTqbN++XVzXVKxYUe9sGnXq1JGcW5YsWZLhLCJERIrYBzMe9sH+D/tgqdgHSz/F4KU9e/aI/bxmzZoaA28ysw8mv98CpCYU0DaEYkBAgEp/SN3+9T3cj0lrW9yoUSORYevq1au4fPkyAMDS0hKtW7fOUF0U+xfXrl3Teu0dFRUFf39/MW2s/kX9+vVRuHBhAKkZsufOnas1m92KFSvEvmFhYaHSj1TsX2zcuFFrQoL169eLvnvTpk1hZWWlV527desmCRKfOXOmzgzm9O0wAI1IjcKFC4uUmqdPnxbz9enAAP+XqvnZs2diXGR9l9UmR44c4vXTp08zvL5voU6dOiLgBACmT5+OzZs3q1wEvH79GkOGDBF//DU3N8fo0aMlZXr37i1eHz58GMuXL1c7dvTZs2fxzz//iGldF44rVqzApk2bVKL33dzcMHnyZDH966+/Ssa6NvT2mZmZ4Y8//hDTa9euhaurq8q6Xr16haFDhyI2NhYA0KpVK0nEOZDaqZDL6L6juB9qSnk9cuRIEaz07t079OvXDy9evJCUkclkOHjwIMaOHSvmtWzZEk2bNk133Qy5nfoYNWqU2M7g4GD06dNHpOaVk8lkOH78uGRowRo1amgMyNJFcR/8559/sGrVKpV94vbt2xg8eLBBL/Bz5MiB4cOHSz7777//VjnmQkNDMX78eJw9e1bMmzNnjqQzo0jxeJE/rV+uXDnJfgakXthWqVIFgDQzga7hNzN7n9BHr169xFM4t27dwrRp09RelHt6ekrSCRui06uJYtslk8kwZswYHDp0SKXj8eLFC/Tt21e0XTY2Npg6darK+saNGye20c3NDXPnzlXZVwIDAzFs2DDRealSpUqajosyZcpgwIABYnrLli06n6YkIjIG9h2Mh30H/bePfYe0+xn6DqNGjRLZFW7duoWxY8eqXHeGh4dj7NixIkOavb09unTpIt4fMGCAGF4vPDwcffr0kQxzJXfx4kUMGjRI7HNVqlSR3OAzNENdU5cqVQpFihQBkDrM/B9//KEybEhAQAB+++03rcFI3wtfX18MHTpUZRtev36N/v37i75UsWLF1P4+isfF+/fv0/XU/bc6pg2hYMGCYggeABg7dqzarCCxsbGYPn26aJfz5csnyVhuaBMmTBA387y8vDBs2DAEBARIyiQmJmLjxo2YP3++mDdw4ECUK1dOUq5Ro0YioC0uLg6//vqryvCh8t9n5cqVYp7yeUeXKVOmiHNARESEpF5ERBnFPpjxsA+m//axD5Z2P0MfTFHTpk3F7yF/+B5Q/yCIoszqg1WrVk3ycP+kSZNU+lRJSUlwd3dH165dVTJlqQsAUtz/Xrx4gaSkJL3rYyj6HAOKzMzMRLDily9fRLavZs2aSYaCTA8nJycR9BwXF4fhw4erHfYyLCwMY8eOFf2vSpUqqVzHG0qWLFkwYcIEMX3q1ClMnDhR5bePiYnBvHnzsHXrVjHvzz//RJ48eSTlunTpIoLlQkJCMGDAAJX2JDExEevWrcPevXsBpAYqKt5v1MXExASzZ88WfSI/Pz+sW7dO7+Upc2XVXYTo51SrVi24ubmJKPysWbOqHUJOnTp16qhctMo7NRmhGO28evVqPH36FNmyZUPz5s3RrFmzDK8/syxatAi9evXCu3fvkJycjCVLlmDLli2oUaMGrKys4Ofnh4cPH4oOhImJCWbOnInSpUtL1iPf7osXLwJIjazev38/ypcvj4IFCyIhIQE+Pj549+6dWKZNmzaSPyYqs7a2Fk+27Nq1CzVq1ECWLFng7e0teRK6bt26GDVqlFG3D0h9WsHLywtHjx6FTCbDqlWrRL2sra3h5+eHe/fuiYjxokWLSoY6kCtevLh42nT48OFo1KgREhMTMXbsWPHHdn0p7ocHDhxAcHAwbG1t4ejoKJ6uKFasGBYsWIAJEyYgMTERT58+RYcOHVC1alWUKFEC8fHxuH//viSQqEyZMvjf//6XproYczv1obydfn5+6NWrF8qXLw8HBwfExcXh2bNnkn0nf/78GXpyvnHjxvjll19EinBXV1fs378fNWvWRLZs2eDr6ys6b3ny5BHfh+KTJ+k1ZMgQPH78WASXbd++HYcOHYKzszNsbW3x+fNneHp6Sp64HzZsmNb2qVatWsiWLZvogMvnaSqr+IdxMzMznX/kL168uEilP2PGDFy+fBmmpqbo3bu35OmTzFShQgX069dPZP5yc3PDmTNnUKlSJRQqVAgpKSl48eKFZJik6tWrS558MgbFtisuLg7Tpk3DmjVr4OjoiGzZsuHt27fw9vYWQWkWFhZYsGCB2qe16tevjxEjRohOwO7du3H8+HHUrFkTtra2+PTpE+7evSvOk7a2tli0aFGaU3SPHDkS7u7uCAgIQGJiImbOnIm9e/d+F6m+iejnwr6D8bDvwL4D+w7p7zs4ODhgxowZmDFjBmQyGc6ePYurV6+iZs2ayJcvH0JDQ3Hnzh1xI9DS0hKLFy+WPIWcK1curFy5EoMHD0ZMTAz8/f3Ru3dvlCtXDmXLlkVycrLKsVOgQAEsW7bMIH0QTQx5TT1ixAjxUMXTp0/RokULODs7I2/evPj48SPu3buH5ORk2NjYoHXr1gbNNG1IFhYWSElJwZ07d9C8eXPUqlULdnZ28Pf3F9sApN6QWbVqlcrQT0BqAKKZmRkSExMRGhqKX375BVWrVkVycjIWLlyoVz2+1TFtKFOnToWnpye+fv2KL1++YOjQoShZsiRKliyJXLly4cuXL7h3757ItpMlSxbMnj1b40NXhuDk5ITJkyeLIK5bt26hRYsWcHJyQuHChREdHQ1PT0/JTSNnZ2eMHz9eZV0mJiZYunQpevbsiaCgIHz69Al9+vRBhQoVUKZMGaSkpMDb2xsfPnwQy/Tr10/r+VAdOzs7jB07Vvyup06dQseOHQ1yM5eICGAfzJjYB2MfjH0ww2Q+Njc3R+vWrXHw4EGxP8nnaZNZfbC8efOia9euYrj0W7duoXnz5nB0dES+fPkQEhKCp0+fSjKj2djY4OvXrwCg9gEgxYy5L168QK9eveDg4AAbGxtJgKgx6XMMKOvYsaMIjjLU8Jtyc+bMQZ8+fZCYmIh3796hZ8+eKFeuHIoVKwZra2sEBQXBy8tLBPRly5ZNbTthSG3btsWjR4+wbds2AMDJkydx/vx58beCsLAweHp6Sh5Iat++Pfr166eyrmzZsmHFihXo378/IiMj8eLFC3Ts2FG0J7GxsfDy8pLsRxMmTBCBefoqW7Ys+vfvLwLitm7dinbt2hktUI/SjwFoRBrIOzBylStX1jvSuUaNGjA3NxedH2tra0m64fTq0aMHdu7ciaioKCQmJoqneywsLH6oDkzu3Lmxf/9+TJkyRaQyDQ0NlaTxlbOxscGsWbM0Dsu2fPlyTJ48WYwrHR4ernbsZ3na2unTp2utW79+/RAQEIBjx44hKChI7bjw3bp1w4wZMyRpXI21fQCwcOFCFChQAJs3b0ZSUhJCQkIk2aXkHB0dsXLlSpXocyD1aZ/79+9DJpMhNDQUR44cAZAawZ/WC/s2bdrA1dUVAQEBkMlkuHTpEoDUJ0gUL95atWqFnDlzYsqUKQgMDIRMJoO3t7fa6P6OHTti9uzZeqdb1cSQ26mvVq1aiSxQ8ifmnj17JkkbLletWjUsW7YMBQsWzNBnzpo1C1mzZsXu3bshk8kQEhKiMrZ6uXLlMGPGDPTp0wcADPLHcBMTE6xcuRIrVqzAtm3bkJiYiOjoaLGfK7KyssLcuXN1Ps1jYWGBWrVqSdJbOzs7qy3r7OwseaqhevXqOtvlfv364fTp06Ku8qdXypQp880C0IDUmxoymQy7du2CTCZDTEwM7t69q7ZsixYt8Pfffxv1hgaQ2nYdOHAAkydPFr/pp0+fJE+SyhUtWhSrVq1ChQoVNK5vzJgxsLW1xbJlyxAbG4vIyEjRXigqWbIkVq1aJYaXTQsrKytMmzYNI0eOBAB4e3tjz5496Nu3b5rXRUSUEew7GA/7DvpvH8C+Q1r8LH2H7t27w9raGrNnz0Z4eDji4uJw/fp1lXL58uXD8uXLJUP9yTk5OWHv3r2YMGECXr16BQB4/vy5JLhLrn79+liyZIlkiHZjMdQ1dZcuXeDv7y+GA4mPj1f5jgoVKoQVK1ao3Se/F3nz5sWUKVMwefJkxMTEqP2dS5UqheXLl2v8I72lpSV69eolAvtevnwphplU97S7Jt/imDaUIkWKYOvWrfjjjz/w8eNHAMCbN2/UDpeTO3duzJo1K1POq/3790fevHkxZ84chIeHIykpCXfv3lXZ501NTTFw4EBJ1jRlBQsWxIEDBzB27Fg8ePAAQGrwpXImElNTU/z222+S7C5p0bt3b7i5uYnME3PmzMHJkye/m9+aiH5s7IMZD/tg+m8fwD5YWvwsfTBFHTp0EAFeQGqCAcVMcJpkVh9s+vTpCAwMxI0bNwAA0dHR4rWi7NmzY8qUKQgPDxdD0z58+FAlIKlo0aKSwNNHjx7h0aNHsLKywqRJk0QWa2PS9xhQ5OjoiKJFi4pgxLx586JevXoGqU/VqlXh6uqKyZMni6A9Tb9l4cKFsWDBAjEakDFNmTIFBQsWxMqVKxETE4P4+Hi1v72ZmRnGjx+PQYMGaVxXhQoVsGfPHowdOxavX79GSkoKHjx4IPoacubm5pgyZYq4b5lWo0aNgru7Oz59+oSkpCTMmDED+/fvZ0KC7wwD0Ig0qF27tmQ6LU/AWFpawtHREXfu3AGQGjSRJUuWDNepUKFC2L9/P1avXo179+4hIiICtra24umJH0muXLmwYcMG3Lt3DydOnICnpyc+f/6MmJgY5MiRA2XKlEGDBg3QrVs3rRdNlpaWWLVqFTw9PXH8+HF4e3sjICAAcXFxyJEjB/Lnz4+6devCxcVFa6CEXJYsWbB48WK0atUKe/fuxZMnTxAZGYl8+fKhVq1a6N27NypXrpxp2wekdr7GjRuHzp07Y//+/fDw8EBAQABiYmKQK1cuVKpUCR07dkSrVq00nmRbtGiB9evXiyHq4uPjYWdnh+joaJ3bosza2hr79u3DypUrcfPmTYSGhiJnzpxq9/HatWvj3LlzOHr0KC5duoRnz54hNDQUpqamsLe3h7OzM7p06WKwiylDbmda1KlTB+fOncOxY8ck2wmkXqhWrlwZ7du3R7NmzQxyIWRqaooZM2bAxcUFBw4cEPuXmZkZSpUqhQ4dOqBHjx54//69WCajqYIVP3vChAno0aMHDh06hBs3bsDf3x9RUVGwtrZG6dKl0ahRI3Tv3h22trZ6rbNRo0YiAC1Llixqb3oBqZ0AxT8O6fMEdpUqVbBjxw6sX78ejx49QnR0NOzs7MQ6vhVTU1NMnz4dXbp0gZubG+7fvw9/f39ER0cje/bssLOzg7OzM9q2bYuaNWtmWr1y5syJDRs2wMvLC8ePHxf7VlxcHGxtbVGpUiW0bt0abdu21Ssgrl+/fmjVqhX27duH69evw8/PD9HR0ciRIwfKly+PNm3aoGPHjhkKrmvevDmaNGki/mC0fPlyNG/eHAUKFEj3OomI0op9B+Ni34F9B/YdMqZNmzaoV68e9u/fj6tXr+LNmzf4+vUrsmfPjtKlS6NFixbo3r27GJ5GnXLlyuH48eM4ffo0zp8/j8ePHyMkJAQpKSkoWLAgnJyc0KFDB4MMX6UvQ15TjxkzBi1atMDevXtx+/ZtfPr0CdmyZUPRokXRunVr9OjRAzly5PiuA9CA1GGRypcvj61bt+LatWsICgqClZUVKlasCBcXF3To0EFnVoSpU6fC3t4ehw8fhr+/P0xMTJA/f358/vxZ7wA0IPOPaUOqXLkyTp06hZMnT+LixYt4/vw5wsLCkJycjDx58qBkyZJo0qQJOnbsiJw5c2Zavdq2bYuGDRvi0KFDuHr1Kl6+fInw8HCYmZmhWLFiqFOnDrp164ZSpUrpXFeBAgWwb98+XLhwAe7u7vD29kZISAhMTExQsGBB1K5dG3369FGb7UVfpqammD17Nnr27ImUlBR8/PgRq1atEhkHiYgygn0w42IfjH0w9sEMo2bNmrC3txcPNnTo0EHvZTOjD2ZpaYnNmzfj1KlTOH78OJ48eSKuL3PlyoXSpUvD2dlZHAvPnz8XAWiXLl1CZGSkZMhLAFi5ciXWr18Pd3d3BAYGwsLCAgUKFEBISAjy5s2b7rrqKy3HgCIXFxeRAKFdu3YGzejdsGFDnDlzBkeOHMH169fh6+uLiIgImJiYIG/evHBwcECzZs3g4uICS0tLg32uLgMGDEC7du1w4MAB3LhxA+/evUNERAQsLS1RsmRJ1K9fHz169NArKNPBwQEnTpzAiRMncO7cOTx9+hQhISHImjUrihQpgvr166Nv375qR9TRV/bs2TFt2jQxJPKjR4+wa9cu9O/fP93rJMMzkcnHUfrOvX37FuvWrcO9e/cQEhKCAgUKoE2bNvjtt9/SHHEdFBQEV1dX3Lp1C58+fULevHnRtGlTjBw5UuVComzZsnqts3Pnznqnoiei78uaNWuwdu1aAKnR0/ITF9GPzsvLSzxJUKlSJRw+fPgb14iIiDRhf4fox8C+AxF9T/z9/UVGFXt7e7UZh4mIjOFb9V/kHj9+DFdXV/j4+ODr168oUqQIOnXqhAEDBkiyHt25c0fvm5ILFixAly5d0lR3IjI+9sGIKDPMnz9fZII+cuSIXkGxRKTqh8iA9ujRIwwYMAAxMTGoUqUKKleujPv372PDhg24fPky9uzZo3dmlw8fPqBXr14IDg6Gg4MDmjRpgqdPn2LXrl24cOEC9u/fL8mYoW3osISEBJFGtWLFihnbSCIiIh1ev36NEydOoGjRoqhQoYLOsc0fPnwoXjs4OBi7ekRElE7s7xARERER0Y/iW/ZfAODy5csYNWoUUlJSUKNGDdjY2MDT0xNLlizBrVu3sHHjRhGEljdvXq19noCAANy7dw9mZmYoU6ZM+r8UIiIi+mElJyeLYZPLli3L4DOiDPjuA9CSkpIwfvx4xMTEYP78+ejWrRsAIC4uDuPGjcOlS5ewfPlyzJw5U6/1TZkyBcHBwRg5ciTGjBkDILVRmTt3Lvbt24dZs2Zh48aNovzSpUs1ruuvv/4CALRv315ljGMiIiJDS0xMxPr16wEA+fLlw5UrVzSmDY6MjBRPawDI1KFwiIhIf+zvEBERERHRj+Jb918iIiIwceJEAMA///yD+vXrAwDCw8MxbNgw3Lx5Ezt27MDgwYMBAKVKldLY54mNjUWPHj0AADNnzvx/7N13eFRl/v7xe2bSEwJJgIQQigKhiQiCiAQRFBTElWaHlUW/iIjYEAWxwSLsT5e1IixWsCNYsCFCUJqUEKQTEqq0hJJG2mRmfn9kMxATyGRSJid5v66LK+SU5zyTD4HczOc8x6XH9gEAgJrn119/VUpKiiTpjjvu8PBsAGOr2AcZV4Lvv/9ehw8fVvfu3Z1hRip4JvFLL72kgIAAffHFF0pLSyt1rE2bNmnTpk1q3ry5xo0b59xusVg0ZcoURUZGauXKlUpMTCx1rK+//lqLFi1SVFSUpk6d6t6LAwCgDKKjo9WgQQNJUnJysqZMmVLiv39JSUkaNWqUjh8/LkmKjIxUv379qnSuAADXkHcAAAAAGIWn88vHH3+szMxMDRo0yNl8Jkn16tXTjBkzJEnvv/++bDZbqdefOnWqEhISdOONNzob0QAAQO2SkpKif/3rX5Kk4OBg3XrrrR6eEWBs1b4BbcWKFZKkvn37FtsXEhKibt26yWq1atWqVS6Pdf3118tsLvrSvb291adPH0nS8uXLLzpOamqqM8xMmzZNgYGBpb8QAADKyWw26/HHH3d+vnjxYvXq1UsjR47UU089pfHjx2vo0KG6+eabtXXrVkmSr6+vXn75Zfn6+npq2gCAiyDvAAAAADAKT+eXwnNKutGyRYsWio6OVkpKivP/xS5kw4YNWrx4serWravnn3++1LkCAICaY/z48Zo0aZLGjx+v/v3768CBA5KkRx55xOXHiAMoWbVvQEtISJBU8LzdkrRs2VKStHv3bpfHio6OLtdYs2bNUmpqqm688UYeaQYAqFJDhgzRc889J39/f0kFjwtYt26dvv76ay1dulTbt2+Xw+GQJDVp0kQffPCBunTp4skpAwAugrwDAAAAwCg8nV/27t1b5nP+Kj8/X9OmTZNU8AZ0WFhYqXMFAAA1x+nTp7V48WItXbpUGRkZkqQbb7xR99xzj4dnBhifl6cnUJrk5GRJUnh4eIn7GzZsWOS4yh7r8OHD+vLLL2UymTR+/PhSrwkAQEW75557dMMNN2jx4sVas2aNkpKSnD8kN2jQQG3bttUNN9yggQMHysfHx8OzBQBcDHkHAAAAgFF4Mr+kpaUpJyen3NdfsmSJEhIS1KhRIx69CQBALdSzZ0/t379fGRkZioqK0tChQzVy5EiZTCZPTw0wvGrfgJaVlSVJ8vPzK3F/4fbC41wZq3DVGHfGeu+992Sz2dSvXz/n3TQAjO3hhx/Www8/7OlpAGUSHh6uBx98UA8++KCnpwIAKAfyDmAsZAcA1UlUVJT27Nnj6WkAqEU8mV8KP/r4+BR7ZKer13c4HHrvvfckSffddx83bgIGQAYDUNEeeOABPfDAA56eBlAjVftHcFosFkkqteO08HFjlTlWWlqaFi9eLEkaPXp0qddzhSvzBgAAAFAz1fS8c7HrAQAAADAWT+aXwqYzV1YnudD1V69erYSEBIWEhFTo6mdkHgAAAMAAK6AFBgYqNTVV2dnZJe4vXHL5QnfJ/HUsSW6PtWzZMuXk5KhVq1bq0KFDqddzhd3uUHp66XcDVQaLxazgYH+lp2fLZrN7ZA4oG2pmTNTNeKiZMVE346FmxuNqzYKD/WWxVPt7XaqFmp53JDIPyoaaGQ81MybqZjzUzHiomTGReS7Ok/ml8Pjc3FzZ7fYSV0Er7fpLliyRJA0YMEC+vr6lztFVnso8/D1jTNTNeKiZ8VAzY6JuxkPNjKey8061b0Br2LChUlNTlZKSoiZNmhTbn5yc7DzOlbF27NihlJSUEveXNtbSpUslSQMHDnRp7q7Kz/fsN6PNZvf4HFA21MyYqJvxUDNjom7GQ82Mh5pVnNqQdyQyD8qOmhkPNTMm6mY81Mx4qJkxUbeSeTK/BAUFKSgoSJmZmUpJSVF4eHiZrm+1WhUbGyup5mUe/rwaE3UzHmpmPNTMmKib8VAz46msmlX7W3Rat24tSUpMTCxxf+H2wuMqa6zc3FytW7dOknTTTTeVei0AAAAAKA15BwAAAIBReDq/REdHu339uLg4paenKzw8XJ06dSp1fgAAAADKpto3oPXq1UvSubvxz3fmzBmtX79e3t7e6tGjh8tjLVu2THZ70W4+q9Wq5cuXS5J69+5d7NydO3fKarWqQYMGat68eVlfBgAAAAAUQ94BAAAAYBSezi8Xu35SUpISEhIUGhqqjh07Ftv/xx9/SJK6dOkik8lU6vwAAAAAlE21b0Dr27evIiMjtXr1an388cfO7Tk5OXrmmWeUlZWlYcOGqX79+s59VqtVSUlJSkpKktVqdW7v3LmzOnTooKSkJM2aNUsOh0OSZLPZNH36dB07dkzXXnut2rZtW2we27ZtkyRdccUVlfRKAQAAANQ25B0AAAAARuHp/DJkyBAFBQVp0aJFzgY1SUpNTdXkyZMlSaNGjZK3t3exuZN5AAAAgMrl5ekJlMbPz08zZ87U6NGjNXXqVC1atEhRUVGKj49XcnKy2rVrpwkTJhQ558SJExowYIAkafny5YqKinLumzFjhoYPH6558+Zp+fLlatWqlXbt2qVDhw6pcePG+uc//1niPA4fPixJatKkSSW9UgAAAAC1DXkHAAAAgFF4Or80bNhQL7zwgiZOnKiHHnpInTp1UlhYmDZu3KjU1FT17NlTI0eOLHHuhZmnadOmFfgVAQAAAFCo2q+AJkndunXTwoULdeONN+ro0aNauXKl6tSpo7Fjx2rBggUKCgpyeaxWrVpp8eLFGjJkiDIyMhQbGytJGjFihL744guFh4eXeN7p06clSY0aNSr/CwIAAACA/yHvAAAAADAKT+eXW265RQsWLFDPnj2VmJioNWvWKDw8XJMmTdLs2bNLXP1MOpd5IiIi3HjVAAAAAEpjchSuawyPsNnsOn36rEeu7eVlVkhIoM6cOav8fLtH5oCyoWbGRN2Mh5oZE3UzHmpmPK7WLDQ0UBaLIe51QRUg86AsqJnxUDNjom7GQ82Mh5oZE5kH7vBU5uHvGWOibsZDzYyHmhkTdTMeamY8lZ13SEgAAAAAAAAAAAAAAAAAALd4eXoCAAAA1Y3D4ZDNZpPDwR0blcluNyknx6K8vFzZbCzKWx2ZTGZZLBaZTCZPTwUAAAAViMxT+cg7xmA2W2SxWDw9DQAAAFQwm80mu93m6WnUaGSe6q+q3+OhAQ0AAOB/7Ha7MjPTlJOTJbs939PTqRVOnjTLbudNr+rMbPaSn1+AgoLqigWUAQAAjI3MU7XIO8bg4+OnoKB68vHx9fRUAAAAUE55ebnKzExVXl6Op6dSK5B5qr+qfI+HBjQAAAAVvBFz5kyy8vOt8vMLlK+v//+eb87KT5XJYjFxZ0y15ZDNZldubrayszNlteaqQYMIT08KAAAAbiLzVD3yTnXnUH6+VWfPZujMmWSFhUXIy4smNAAAAKPKz7fqzJlkWSxeqls3TF5e3iLvVC4yT3VW9e/x0IAGAAAgKTMzTfn5VoWGNpS3N//hXFW8vMzKz+fumOrK21vy8/NXQECgTp9OVkZGqsLC6nh6WgAAAHADmafqkXeqP29vX/n6BujUqWPKzEyVn1+4p6cEAAAAN2VkpMpsNis0NFxmM0/zqApknuqtqt/j4bsOAADUeg6HQzk5WfLzC+SNGKAE3t6+8vMLVFbWWTkc3M0EAABgNGQe4MLMZrP8/AKVm5tD3gEAADAoh8OhvLwc+fsH0nwG/EVVvcfDdx4AAKj1bDab7PZ8+fr6e3oqQLXl6+svmy1fVqvV01MBAABAGZF5gIvz8fGVw2GXzZbv6akAAADADTZbvhwOOzfcABdQFe/x0IAGAABqPYejYHlgi4UfjYALKfz+sNtZThsAAMBoyDzAxRWukkHeAQAAMKbCVZ1Y/QwoWVW8x8N3HwAAgJPJ0xMAqjG+PwAAAIyPn+mAkvG9AQAAUDPwcx1Qssr/3qABDQAAAAAAAAAAAAAAAADgFhrQAAAAAAAAAAAAAAAAAABuoQENAAAAqMYcDoenpwAAAAAAlYK8AwAAAKAmq02ZhwY0AAAAuOXQoYOaOvVZDR06UH369NCddw7W3LlvKTs7u1zjpqWl6tZbb9TEiY9WzEQN6vjx43ruuUnasmVzke3jxo1WTEwXxcb+4tw2ffoLionpok8+WVDV0wQAAABqJPJO5SLvAAAAAJ5F5qlctTHz0IAGAACAMtu1a4fuu2+Efv75R4WGhumaa3ooOztbCxa8rzFjRuns2Uy3xs3OztYzz0zUqVOnKnjGxjN58hNasWJZrbo7BgAAAKgOyDuVj7wDAAAAeA6Zp/LVxszj5ekJAAAAwFjy8/P1/POTlZ2dpaefflYDB94qScrNzdHzz0/W6tW/ae7ct/T440+VadyjR4/o+ecnadeunZUxbcOx20sOJVOmTFVubo4aNGhQxTMCAAAAaj7yTtUg7wAAAACeQeapGrUx87ACGgAAAMpk+fKfdfToEV155VXOYCJJvr5+mjTpOfn7+2vJkq+Vnp7u0ni5uTlasOAD/eMfd2vXrp2KjGxcWVOvESIiItSsWXM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      "text/plain": [
       "<Figure size 2500x800 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Calculate exposure elasticity for consumption growth\n",
    "quantile = [0.1, 0.5, 0.9]\n",
    "T = 30\n",
    "\n",
    "expo_elas_shock_0_015 = [exposure_elasticity(gc_tp1, X1_tp1, X2_tp1, T, shock=0, percentile=p) for p in quantile] # The first shock is the growth shock\n",
    "expo_elas_shock_1_015 = [exposure_elasticity(gc_tp1, X1_tp1, X2_tp1, T, shock=1, percentile=p) for p in quantile] # The second shock is the volatility shock\n",
    "expo_elas_shock_2_015 = [exposure_elasticity(gc_tp1, X1_tp1, X2_tp1, T, shock=2, percentile=p) for p in quantile] # The third shock is the consumption shock\n",
    "\n",
    "## Plot the exposure elasticity for consumption growth\n",
    "index = ['T','0.1 quantile','0.5 quantile','0.9 quantile']\n",
    "fig, axes = plt.subplots(1,3, figsize = (25,8))\n",
    "expo_elas_shock_0 = pd.DataFrame([np.arange(T),expo_elas_shock_0_015[0].flatten(),expo_elas_shock_0_015[1].flatten(),expo_elas_shock_0_015[2].flatten()], index = index).T\n",
    "expo_elas_shock_1 = pd.DataFrame([np.arange(T),expo_elas_shock_1_015[0].flatten(),expo_elas_shock_1_015[1].flatten(),expo_elas_shock_1_015[2].flatten()], index = index).T\n",
    "expo_elas_shock_2 = pd.DataFrame([np.arange(T),expo_elas_shock_2_015[0].flatten(),expo_elas_shock_2_015[1].flatten(),expo_elas_shock_2_015[2].flatten()], index = index).T\n",
    "\n",
    "n_qt = len(quantile)\n",
    "plot_elas = [expo_elas_shock_1,expo_elas_shock_0, expo_elas_shock_2] # For illustration purpose, the consumption shock is plotted in the second column, the volatility shock is plotted in the third column\n",
    "shock_name = ['growth shock', 'consumption shock', 'volatility shock']\n",
    "qt = ['0.1 quantile','0.5 quantile','0.9 quantile']\n",
    "colors = ['green','red','blue']\n",
    "\n",
    "for i in range(len(plot_elas)):\n",
    "    for j in range(n_qt):\n",
    "        sns.lineplot(data = plot_elas[i],  x = 'T', y = qt[j], ax=axes[i], color = colors[j], label = qt[j])\n",
    "        axes[i].set_xlabel('')\n",
    "        axes[i].set_ylabel('Exposure elasticity')\n",
    "        axes[i].set_title('With respect to the ' + shock_name[i], fontsize=25)\n",
    "axes[2].set_ylim([0,0.007])\n",
    "axes[1].set_ylim([0,0.07])\n",
    "axes[0].set_ylim([0,0.07])\n",
    "fig.suptitle('Exposure elasticity for the consumption growth', fontsize=30)\n",
    "fig.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6038a5c",
   "metadata": {},
   "source": [
    "## 2.2 Calculate Price Elasticity for Consumption Growth\n",
    "\n",
    "Similarly, to calculate the price elasticity for consumption growth using the *price\\_elasticity* defined above, we need to input an approximation for the log stochastic discount factor. In the simple case that you will encounter in your problem set, you will be able to deduce this from the consumption growth equation. For now we will presume that we already have the approximation ready:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "27bc1ed8",
   "metadata": {},
   "outputs": [],
   "source": [
    "log_SDF = LinQuadVar({'c' : np.array([[-0.02005034]]),\n",
    "                      'x' : np.array([[-0.0299976,  -0.02903654]]),\n",
    "                      'xw': np.array([[ 0.        ,  0.00001026,  0.        , -0.03199734, -0.12719014,  0.        ]]),\n",
    "                      'xx': np.array([[ 0.0000006 ,  0.        ,  0.0000006 , -0.00725869]]),\n",
    "                      'w' : np.array([[-0.06399468, -0.24439539,  0.06087257]])}\n",
    "                      ,shape=(1,n_X,n_W))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "651aa5f9",
   "metadata": {},
   "source": [
    "Next, we compute price elasticities for the three shocks using the function `price_elasticity`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "4ab6059f",
   "metadata": {},
   "outputs": [],
   "source": [
    "quantile = [0.1, 0.5, 0.9]\n",
    "price_elas_shock_0 = [price_elasticity(gc_tp1, log_SDF, X1_tp1, X2_tp1, T, shock=0, percentile=p) for p in quantile]\n",
    "price_elas_shock_1 = [price_elasticity(gc_tp1, log_SDF, X1_tp1, X2_tp1, T, shock=1, percentile=p) for p in quantile]\n",
    "price_elas_shock_2 = [price_elasticity(gc_tp1, log_SDF, X1_tp1, X2_tp1, T, shock=2, percentile=p) for p in quantile]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8564dc1f",
   "metadata": {},
   "source": [
    "We can then plot our results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "038746c0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2500x800 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Plot the price elasticity for consumption growth for only ρ = 2/3 (rho 006)\n",
    "fig, axes = plt.subplots(1, 3, figsize=(25, 8))  # 1 row, 3 columns for each shock\n",
    "\n",
    "# Create DataFrames for each shock type with quantiles at ρ = 2/3\n",
    "price_elas_shock_0_df = pd.DataFrame({\n",
    "    'T': np.arange(T),\n",
    "    '0.1 quantile': price_elas_shock_0[0].flatten(),\n",
    "    '0.5 quantile': price_elas_shock_0[1].flatten(),\n",
    "    '0.9 quantile': price_elas_shock_0[2].flatten()\n",
    "})\n",
    "\n",
    "price_elas_shock_1_df = pd.DataFrame({\n",
    "    'T': np.arange(T),\n",
    "    '0.1 quantile': price_elas_shock_1[0].flatten(),\n",
    "    '0.5 quantile': price_elas_shock_1[1].flatten(),\n",
    "    '0.9 quantile': price_elas_shock_1[2].flatten()\n",
    "})\n",
    "\n",
    "price_elas_shock_2_df = pd.DataFrame({\n",
    "    'T': np.arange(T),\n",
    "    '0.1 quantile': -price_elas_shock_2[0].flatten(),\n",
    "    '0.5 quantile': -price_elas_shock_2[1].flatten(),\n",
    "    '0.9 quantile': -price_elas_shock_2[2].flatten()\n",
    "})\n",
    "\n",
    "# List of data and names for each shock\n",
    "plot_elas = [price_elas_shock_1_df, price_elas_shock_0_df,price_elas_shock_2_df]\n",
    "shock_name = ['growth shock', 'consumption shock', 'volatility shock']\n",
    "quantiles = ['0.1 quantile', '0.5 quantile', '0.9 quantile']\n",
    "colors = ['green', 'red', 'blue']\n",
    "\n",
    "# Loop over each shock to plot on its respective axis\n",
    "for k, ax in enumerate(axes):\n",
    "    for qtl, color in zip(quantiles, colors):\n",
    "        sns.lineplot(data=plot_elas[k], x='T', y=qtl, ax=ax, color=color, label=qtl)\n",
    "    ax.set_xlabel('T')\n",
    "    ax.set_ylabel('Price elasticity')\n",
    "    ax.set_title(f'With respect to the {shock_name[k]}', fontsize=25)\n",
    "\n",
    "axes[0].set_ylim([0,0.5])\n",
    "axes[1].set_ylim([0,0.5])\n",
    "axes[2].set_ylim([0,0.5])\n",
    "axes[0].set_xlim([0,30])\n",
    "axes[1].set_xlim([0,30])\n",
    "axes[2].set_xlim([0,30])\n",
    "\n",
    "fig.suptitle('Price elasticity for the consumption growth', fontsize=30)\n",
    "fig.tight_layout()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "938eefcd",
   "metadata": {},
   "source": [
    "## 2.3 Additional Features\n",
    "In general, you will not have to input the approximations of the state and consumption growth variables manually. Instead, these will be the outputs of our solution code. We have included some sample solutions of the long-run risk model with different parameters of $\\rho$ below. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "4b5ef9c8",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pickle\n",
    "pd.options.display.float_format = '{:.3g}'.format\n",
    "sns.set(font_scale = 1.5)\n",
    "\n",
    "\"\"\"\n",
    "load the long-run risk model solutions when ρ = 2/3, 1, 1.5, 10\n",
    "\"\"\"\n",
    "\n",
    "with open(workdir + '/data/res_006.pkl', 'rb') as f:\n",
    "    res_006 = pickle.load(f)\n",
    "with open(workdir + '/data/res_010.pkl', 'rb') as f:\n",
    "    res_010 = pickle.load(f)\n",
    "with open(workdir + '/data/res_015.pkl', 'rb') as f:\n",
    "    res_015 = pickle.load(f)\n",
    "with open(workdir + '/data/res_100.pkl', 'rb') as f:\n",
    "    res_100 = pickle.load(f)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c78dbf2",
   "metadata": {},
   "source": [
    "Then we can access the approximations without inputting them manually, for example:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "857854bf",
   "metadata": {},
   "source": [
    "Below is a brief UI to select parameters shown in the long-run risk model. The stochastic volatility process has been normalized with its mean equal to 1. By changing the inputs of parameters, we can see how shock elasticities vary with respect to these parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "6d4e2287",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "5a850e6483eb434f889f155e913a4429",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(Dropdown(description='γ', index=1, options=(('5', 5), ('10', 10), ('15', 15), ('20', 20)…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from ipywidgets import interact\n",
    "from BY_example_sol import solve_BY_elas\n",
    "\n",
    "interact(solve_BY_elas, γ=[('5',5), ('10',10),('15',15),('20',20)],\\\n",
    "                        β=[('0.995',0.995),('0.998',0.998), ('0.999',0.999)],\\\n",
    "                        ρ=[('2/3', 2./3),('1', 1.0001),('1.5', 1.5),('10', 10)],\\\n",
    "                        α=[('0.969',0.969),('0.979',0.979),('0.989',0.989)],\\\n",
    "                        ϕ_e=[('0.0002',0.0002),('0.0003432',0.0003432),('0.0004',0.0004)],\\\n",
    "                        ν_1=[('0.977',0.977),('0.987',0.987),('0.997',0.997)],\\\n",
    "                        σ_w=[('0.03',0.03),('0.0378',0.0378),('0.04',0.04)],\\\n",
    "                        μ=[('0.0005', 0.0005),('0.0015', 0.0015),('0.003',0.003)],\\\n",
    "                        ϕ_c=[('0.002',0.002),('0.0078',0.0078),('0.01',0.01)]);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c47c53a",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07daabf6",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "# 3. Shock Elasticity Appendix\n",
    "## 3.1 Analytical framework\n",
    "Shock elasticities are used to quantify the date $t$ impact on values of exposure to the shock $\n",
    "(\\alpha_0 + \\alpha_1 X_0) \\cdot W_1$ at date one. It has the form shown in equation 3: \n",
    "\n",
    "$$\n",
    "\\varepsilon( x, t)=   \\frac{(\\alpha_0 + \\alpha_1 x) \\cdot {\\mathbb E}\\left[\\left( \\frac {M_t}{M_0}\\right) W_1 \\mid X_0 = x\\right]}{{\\mathbb E} \\left(\\frac {M_t}{M_0}  \\mid X_0 = x\\right)}\\tag{3}\n",
    "$$\n",
    "\n",
    "Using the linear-quadratic dynamics of section 1, the computer software recursively computes the logarithm of the denominator of formula (3):  \n",
    "\n",
    "$$\n",
    "\\log {\\mathbb E}\\left(\\frac {M_t}{M_1}  \\mid X_1 =x\\right) = \\Phi_{0, t}^*+\\Phi_{1, t}^* x_1 +\\Phi_{2, t}^*x_2 +\n",
    "{\\frac 1 2} (x_1)' \\Phi_{3, t}^*x_1 \\tag{4}\n",
    "$$\n",
    "\n",
    "Form \n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "&{\\mathbb M} \\left[ \\Phi_{0} +\\Phi_1 x_1+\\Phi_2 x_2 + {\\frac 1 2} (x_1)'\\Phi_3 x_1\\right] \\\\ &\\equiv\n",
    "\\log {\\mathbb E} \\left[\\left( \\frac {M_2}{M_1}\\right)\\exp\\left[\\Phi_{0} +\\Phi_1 x_1+\\Phi_2 x_2 + {\\frac 1 2} (x_1)'\\Phi_3 x_1\\right] \\mid X_0 = x \\right]  \n",
    "\\end{align*}\n",
    "$$ \n",
    "\n",
    "Conveniently, we can express the outcomes as: \n",
    "\n",
    "$$\n",
    "{\\mathbb M} \\left[ \\Phi_{0} +\\Phi_1 x_1+\\Phi_2 x_2 + {\\frac 1 2} (x_1)'\\Phi_3 x_1\\right] =\n",
    "{\\widetilde \\Phi}_{0} + {\\widetilde \\Phi}_1 x_1+ {\\widetilde \\Phi}_2 x_2 + {\\frac 1 2} (x_1)'{\\widetilde \\Phi}_3 x_1\n",
    "$$ \n",
    "\n",
    "for some specification of ${\\widetilde \\Phi}_i$, $i=0,1,2,3$. In words, the ${\\mathbb M}$ operator maps linear-quadratic functions into linear-quadratic functions.  The code uses this mapping repeatedly.   \n",
    "\n",
    "By a direct application of the Law of Iterated Expectations we have that \n",
    "\n",
    "$$\n",
    "\\log {\\mathbb E}\\left(\\frac {M_t}{M_1}  \\mid X_1 =x\\right) = {\\mathbb M}^{t-1}[1]\n",
    "$$ \n",
    "\n",
    "where ${\\mathbb M}^{t-1}[1]$ means to apply the operator ${\\mathbb M}$ $t-1$ times in succession to a function that is identically one.  Observe that ${\\mathbb M}^{t-1}[1]$ is a function of $x$.  \n",
    "\n",
    "The function *_Φ_star* defined below calculates the linear-quadratic dynamic coefficients in $\\mathbb{M}$ mappings and iterations.\n",
    "\n",
    "To complete the calculation of the elasticity, \n",
    "note that \n",
    "\n",
    "$$\n",
    "\\frac{{\\mathbb E}\\left[\\left(\\frac { M_t}{M_0}\\right)  W_1 \\mid X_0=x\\right]}{{\\mathbb E}\\left[\\left(\\frac {M_t}{M_0}\\right)  \\mid X_0=x\\right]}=\n",
    "\\frac{{\\mathbb E}\\left[ \\left(\\frac {M_1}{M_0}\\right)  {\\mathbb E}\\left(\\frac{M_t}{M_1} \\mid X_1\\right) W_1 \\mid X_0=x\\right]}{{\\mathbb E}\\left[\\left(\\frac {M_1}{M_0}\\right)  E\\left(\\frac{M_t}{M_1} \\mid X_1\\right) \\mid X_0=x\\right]} .\n",
    "$$ \n",
    "\n",
    "This leads us to construct the nonegative random variable: \n",
    "\n",
    "$$\n",
    "L_{t}\\equiv\\frac{\\left(\\frac {M_1}{M_0}\\right) \\exp\\left[ {\\mathbb M}^{t-1}[1](X_1) \\right]}{{\\mathbb E}\\left[\\left(\\frac {M_1}{M_0}\\right) \\exp\\left[ {\\mathbb M}^{t-1}[1](X_1) \\right]\n",
    " \\mid X_0=x\\right]} \n",
    "$$ \n",
    "\n",
    "Notice that $L_{t}$ depends only date one information and has expectation one conditioned on date zero information. Multiplying this positive random\n",
    "variable by $W_1$ and taking expectations is equivalent to changing the conditional probability distribution and evaluating the conditional expectation of $W_1$ under this change of measure. Since $W_1$ is normally distributed, the exponential quadratic construction of $L_{t}$ implies that $W_1$ remains normally distributed but with a different mean and covariance matrix.  The computer codes use this observation to evaluate formula (5) by taking an altered conditional expectation of $W_1$.\n",
    " <!-- The derivation details to compute the conditional moments under the change of probability measure implied by $L_t$  can be found in [2], Appendix B, and [3], Appendix A. -->\n",
    "\n",
    "For the purposes of the code, denote the conditional mean induced by $L_{t}$ as $\\mu_{t}^0 + \\mu_{t}^1 x_1$ and the conditional covariance matrix ${\\widetilde \\Sigma}_t$.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b7b56ed6",
   "metadata": {},
   "outputs": [],
   "source": [
    "def _Φ_star(log_M_growth, X1_tp1, X2_tp1, T):\n",
    "    r\"\"\"\n",
    "    Computes :math:`\\Phi^*_{0,t-1}`, :math:`\\Phi^*_{1,t-1}`, :math:`\\Phi^*_{2,t-1}`, :math:`\\Phi^*_{3,t-1}` in equation (4).\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    log_M_growth : LinQuadVar\n",
    "        Log growth of multiplicative functional M.\n",
    "        e.g. log consumption growth, :math:`\\log \\frac{C_{t+1}}{C_t}`\n",
    "    X1_tp1 : LinQuadVar\n",
    "        Stores the coefficients of laws of motion for X1.\n",
    "    X2_tp2 : LinQuadVar or None\n",
    "        Stores the coefficients of laws of motion for X2.\n",
    "    T : int\n",
    "        Time horizon.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    Φ_star_1tm1_all : (T, 1, n_X) ndarray\n",
    "    Φ_star_2tm1_all : (T, 1, n_X) ndarray\n",
    "    Φ_star_3tm1_all : (T, 1, n_X**2) ndarray\n",
    "\n",
    "    \"\"\"\n",
    "    _, n_X, _ = X1_tp1.shape\n",
    "    \n",
    "    Φ_star_1tm1_all = np.zeros((T, 1, n_X))\n",
    "    Φ_star_2tm1_all = np.zeros((T, 1, n_X))\n",
    "    Φ_star_3tm1_all = np.zeros((T, 1, n_X**2))\n",
    "    log_M_growth_distort = log_E_exp(log_M_growth)\n",
    "    X1X1 = kron_prod(X1_tp1, X1_tp1)\n",
    "\n",
    "    for i in range(1, T):\n",
    "        Φ_star_1tm1_all[i] = log_M_growth_distort['x']\n",
    "        Φ_star_2tm1_all[i] = log_M_growth_distort['x2']\n",
    "        Φ_star_3tm1_all[i] = log_M_growth_distort['xx']\n",
    "        temp = next_period(log_M_growth_distort, X1_tp1, X2_tp1, X1X1)\n",
    "        log_M_growth_distort = log_E_exp(log_M_growth + temp)\n",
    "\n",
    "    return Φ_star_1tm1_all, Φ_star_2tm1_all, Φ_star_3tm1_all"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8eb1562c",
   "metadata": {},
   "source": [
    "The function `_elasticity_coeff` defined below calculates the conditional mean induced by $L_{t}$ as $\\mu_{0,t} + \\mu_{1,t} x_1$ and the covariance matrix as ${\\widetilde \\Sigma}_{t}.$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d4d82edc",
   "metadata": {},
   "outputs": [],
   "source": [
    "def _elasticity_coeff(log_M_growth, X1_tp1, X2_tp1, T):\n",
    "    r\"\"\"\n",
    "    Computes :math:`\\mu_{t,0}`, :math:`\\mu_{t,1}`, :math:`\\tilde{\\Sigma}_t`. Corresponding formulas can be found in [3], Jaroslav and Hansen (2014), Appendix B.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    log_M_growth : LinQuadVar\n",
    "        Log difference of multiplicative functional.\n",
    "        e.g. log consumption growth, :math:`\\log \\frac{C_{t+1}}{C_t}`\n",
    "    X1_tp1 : LinQuadVar\n",
    "        Stores the coefficients of laws of motion for X1.\n",
    "    X2_tp2 : LinQuadVar or None\n",
    "        Stores the coefficients of laws of motion for X2.        \n",
    "    T : int\n",
    "        Time horizon.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    Σ_tilde_t_all : (T, n_W, n_W) ndarray\n",
    "    μ_t0_all : (T, n_W, 1) ndarray\n",
    "    μ_t1_all : (T, n_W, n_X) ndarray\n",
    "\n",
    "    \"\"\"\n",
    "    _, n_X, n_W = log_M_growth.shape\n",
    "    \n",
    "    Φ_star_1tm1_all, Φ_star_2tm1_all, Φ_star_3tm1_all = _Φ_star(log_M_growth, X1_tp1, X2_tp1, T)\n",
    "    Ψ_0 = log_M_growth['w']\n",
    "    Ψ_1 = log_M_growth['xw']\n",
    "    Ψ_2 = log_M_growth['ww']\n",
    "    Λ_10 = X1_tp1['w']\n",
    "    if log_M_growth.second_order:\n",
    "        Λ_20 = X2_tp1['w']\n",
    "        Λ_21 = X2_tp1['xw']\n",
    "        Λ_22 = X2_tp1['ww']\n",
    "    else:\n",
    "        Λ_20 = np.zeros((n_X,n_W))\n",
    "        Λ_21 = np.zeros((n_X,n_X*n_W))\n",
    "        Λ_22 = np.zeros((n_X,n_W**2))\n",
    "    Θ_10 = X1_tp1['c']\n",
    "    Θ_11 = X1_tp1['x']\n",
    "    \n",
    "    Σ_tilde_t_all, μ_t0_all, μ_t1_all \\\n",
    "        = _elasticity_coeff_inner_loop(Φ_star_1tm1_all, Φ_star_2tm1_all, Φ_star_3tm1_all, Ψ_0, Ψ_1, Ψ_2, Λ_10, Λ_20, Λ_21, Λ_22, Θ_10, Θ_11, n_X, n_W, T)   \n",
    "    \n",
    "    return Σ_tilde_t_all, μ_t0_all, μ_t1_all\n",
    "\n",
    "@njit\n",
    "def _elasticity_coeff_inner_loop(Φ_star_1tm1_all, Φ_star_2tm1_all, Φ_star_3tm1_all, Ψ_0, Ψ_1, Ψ_2, Λ_10, Λ_20, Λ_21, Λ_22, Θ_10, Θ_11, n_X, n_W, T):\n",
    "    \n",
    "    Σ_tilde_t_all = np.zeros((T, n_W, n_W))\n",
    "    μ_t0_all = np.zeros((T, n_W, 1))\n",
    "    μ_t1_all = np.zeros((T, n_W, n_X))    \n",
    "\n",
    "    kron_Λ_10_Λ_10 = np.kron(Λ_10,Λ_10)\n",
    "    kron_Θ_10_Λ_10_sum = np.kron(Θ_10,Λ_10) + np.kron(Λ_10,Θ_10)\n",
    "\n",
    "    temp = np.kron(Λ_10, Θ_11[:, 0:1].copy())\n",
    "    for j in range(1, n_X):\n",
    "        temp = np.hstack((temp, np.kron(Λ_10, Θ_11[:, j:j+1].copy())))\n",
    "\n",
    "    kron_Θ_11_Λ_10_term = np.kron(Θ_11, Λ_10) + temp\n",
    "\n",
    "    for t in prange(T):\n",
    "        Φ_star_1tm1 = Φ_star_1tm1_all[t]\n",
    "        Φ_star_2tm1 = Φ_star_2tm1_all[t]\n",
    "        Φ_star_3tm1 = Φ_star_3tm1_all[t]\n",
    "\n",
    "        Σ_tilde_t_inv = np.eye(n_W)- 2 * sym(mat(Ψ_2 + Φ_star_2tm1@Λ_22 + Φ_star_3tm1@kron_Λ_10_Λ_10, (n_W, n_W)))\n",
    "        μ_t0 = (Ψ_0 + Φ_star_1tm1@Λ_10 + Φ_star_2tm1@Λ_20  + Φ_star_3tm1 @ kron_Θ_10_Λ_10_sum).T\n",
    "        μ_t1 = mat(Ψ_1 + Φ_star_2tm1 @ Λ_21 + Φ_star_3tm1 @ kron_Θ_11_Λ_10_term,(n_W, n_X))\n",
    "        Σ_tilde_t_all[t] = np.linalg.inv(Σ_tilde_t_inv)\n",
    "        μ_t0_all[t] = μ_t0\n",
    "        μ_t1_all[t] = μ_t1\n",
    "    \n",
    "    return Σ_tilde_t_all, μ_t0_all, μ_t1_all"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05e31659",
   "metadata": {},
   "source": [
    "## 3.2 Exposure and Price Elasticities\n",
    " \n",
    "Then we use the functions above to compute our shock elasticities. Since the shock elasticity function depends on $x_1$, the code computes percentiles of the shock elasticity based on the stationary distribution of $x_1$. This is done by the internal function *\\_compute\\_percentile* in *exposure\\_elasticity* and *price\\_elasticity*. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c8bf1f9e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def exposure_elasticity(log_M_growth, X1_tp1, X2_tp1, T=400, shock=0, percentile=0.5):\n",
    "    r\"\"\"\n",
    "    Computes exposure elasticity for M.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    log_M_growth : LinQuadVar\n",
    "        Log growth of multiplicative functional M.\n",
    "        e.g. log consumption growth, :math:`\\log \\frac{C_{t+1}}{C_t}`\n",
    "    X1_tp1 : LinQuadVar\n",
    "        Stores the coefficients of laws of motion for X1.\n",
    "    X2_tp1 : LinQuadVar\n",
    "        Stores the coefficients of laws of motion for X2.        \n",
    "    T : int\n",
    "        Time horizon.\n",
    "    shock : int\n",
    "        Position of the initial shock, starting from 0.\n",
    "    percentile : float\n",
    "        Specifies the percentile of the elasticities.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    elasticities : (T, n_Y) ndarray\n",
    "        Exposure elasticities.\n",
    "\n",
    "    Reference\n",
    "    ---------\n",
    "    Borovicka, Hansen (2014). See http://larspeterhansen.org/.\n",
    "\n",
    "    \"\"\"\n",
    "    n_Y, n_X, n_W = log_M_growth.shape\n",
    "    if n_Y != 1:\n",
    "        raise ValueError(\"The dimension of input should be 1.\")\n",
    "\n",
    "    α = np.zeros(n_W)\n",
    "    α[shock] = 1    \n",
    "    p = norm.ppf(percentile)\n",
    "\n",
    "    Σ_tilde_t, μ_t0, μ_t1 = _elasticity_coeff(log_M_growth, X1_tp1, X2_tp1, T)\n",
    "\n",
    "    kron_product = np.kron(X1_tp1['x'], X1_tp1['x'])\n",
    "    x_mean = np.linalg.solve(np.eye(n_X)-X1_tp1['x'],X1_tp1['c'])\n",
    "    x_cov = mat(np.linalg.solve(np.eye(n_X**2)-kron_product,\n",
    "                                vec(X1_tp1['w']@X1_tp1['w'].T)), (n_X, n_X))\n",
    "\n",
    "    elasticities = _exposure_elasticity_loop(T, n_Y, α, Σ_tilde_t, μ_t0,\n",
    "                                             μ_t1, percentile, x_mean, x_cov, p)\n",
    "\n",
    "    return elasticities\n",
    "\n",
    "@njit(parallel=True)\n",
    "def _exposure_elasticity_loop(T, n_Y, α, Σ_tilde_t, μ_t0, μ_t1, percentile, x_mean, x_cov, p):\n",
    "    elasticities = np.zeros((T, n_Y))\n",
    "    if percentile == 0.5:\n",
    "        for t in prange(T):\n",
    "            elasticity = (α@Σ_tilde_t[t]@μ_t0[t])[0] +(α@Σ_tilde_t[t]@μ_t1[t]@x_mean)[0]\n",
    "            elasticities[t] = elasticity\n",
    "    else:\n",
    "        for t in prange(T):\n",
    "            elasticity = (α@Σ_tilde_t[t]@μ_t0[t])[0] +(α@Σ_tilde_t[t]@μ_t1[t]@x_mean)[0]\n",
    "            A = α@Σ_tilde_t[t]@μ_t1[t]\n",
    "            elasticity = _compute_percentile(A, elasticity, x_cov, p)\n",
    "            elasticities[t] = elasticity\n",
    "    return elasticities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9a98e511",
   "metadata": {},
   "outputs": [],
   "source": [
    "def price_elasticity(log_G_growth, log_S_growth, X1_tp1, X2_tp1, T=400, shock=0, percentile=0.5):\n",
    "    r\"\"\"\n",
    "    Computes price elasticity.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    log_G_growth : LinQuadVar\n",
    "        Log growth of multiplicative functional G.\n",
    "        e.g. log consumption growth, :math:`\\log \\frac{C_{t+1}}{C_t}`\n",
    "    log_S_growth : LinQuadVar\n",
    "        Log growth of multiplicative functional S.\n",
    "        e.g. log stochastic discount factor, :math:`\\log \\frac{S_{t+1}}{S_t}`\n",
    "    X1_tp1 : LinQuadVar\n",
    "        Stores the coefficients of laws of motion for X1.\n",
    "    X2_tp2 : LinQuadVar or None\n",
    "        Stores the coefficients of laws of motion for X2.        \n",
    "    T : int\n",
    "        Time horizon.\n",
    "    shock : int\n",
    "        Position of the initial shock, starting from 0.\n",
    "    percentile : float\n",
    "        Specifies the percentile of the elasticities.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    elasticities : (T, dim) ndarray\n",
    "        Price elasticities.\n",
    "\n",
    "    Reference\n",
    "    ---------\n",
    "    Borovicka, Hansen (2014). See http://larspeterhansen.org/.\n",
    "\n",
    "    \"\"\"\n",
    "    if log_G_growth.shape != log_S_growth.shape:\n",
    "        raise ValueError(\"The dimensions of G and S do not match.\")\n",
    "    else:\n",
    "        n_Y, n_X, n_W = log_G_growth.shape\n",
    "        if n_Y != 1:\n",
    "            raise ValueError(\"The dimension of inputs should be (1, n_X, n_W)\")\n",
    "    α = np.zeros(n_W)\n",
    "    α[shock] = 1          \n",
    "\n",
    "    p = norm.ppf(percentile)\n",
    "\n",
    "    Σ_tilde_expo_t, μ_expo_t0, μ_expo_t1 \\\n",
    "        = _elasticity_coeff(log_G_growth, X1_tp1, X2_tp1, T)\n",
    "    Σ_tilde_value_t, μ_value_t0, μ_value_t1\\\n",
    "        = _elasticity_coeff(log_G_growth+log_S_growth, X1_tp1, X2_tp1, T)\n",
    "\n",
    "    kron_product = np.kron(X1_tp1['x'], X1_tp1['x'])\n",
    "    x_mean = np.linalg.solve(np.eye(n_X)-X1_tp1['x'],X1_tp1['c'])\n",
    "    x_cov = mat(np.linalg.solve(np.eye(n_X**2)-kron_product,\n",
    "                                vec(X1_tp1['w']@X1_tp1['w'].T)), (n_X, n_X))\n",
    "    \n",
    "    elasticities = _price_elasticity_loop(T, n_Y, α, Σ_tilde_expo_t, Σ_tilde_value_t, \n",
    "                           μ_expo_t0, μ_value_t0, μ_expo_t1, μ_value_t1,\n",
    "                           percentile, x_mean, x_cov, p)\n",
    "\n",
    "    return elasticities\n",
    "\n",
    "@njit(parallel=True)\n",
    "def _price_elasticity_loop(T, n_Y, α, Σ_tilde_expo_t, Σ_tilde_value_t, \n",
    "                           μ_expo_t0, μ_value_t0, μ_expo_t1, μ_value_t1,\n",
    "                           percentile, x_mean, x_cov, p):\n",
    "    elasticities = np.zeros((T, n_Y))\n",
    "    if percentile == 0.5:\n",
    "        for t in prange(T):\n",
    "            elasticity = (α @ (Σ_tilde_expo_t[t] @ μ_expo_t0[t] \\\n",
    "                               - Σ_tilde_value_t[t] @ μ_value_t0[t]))[0]\\\n",
    "                          +(α@(Σ_tilde_expo_t[t]@μ_expo_t1[t]@x_mean\\\n",
    "                              - Σ_tilde_value_t[t] @ μ_value_t1[t]@x_mean))[0]\n",
    "            elasticities[t] = elasticity        \n",
    "    else:\n",
    "        for t in prange(T):\n",
    "            elasticity = (α @ (Σ_tilde_expo_t[t] @ μ_expo_t0[t]\\\n",
    "                               - Σ_tilde_value_t[t] @ μ_value_t0[t]))[0]\\\n",
    "                            +(α@(Σ_tilde_expo_t[t]@μ_expo_t1[t]@x_mean\\\n",
    "                              - Σ_tilde_value_t[t] @ μ_value_t1[t]@x_mean))[0]\n",
    "            A = α @ (Σ_tilde_expo_t[t]@μ_expo_t1[t]\\\n",
    "                     - Σ_tilde_value_t[t]@μ_value_t1[t])\n",
    "            elasticity = _compute_percentile(A, elasticity, x_cov, p)\n",
    "            elasticities[t] = elasticity\n",
    "    return elasticities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d689b7ed",
   "metadata": {},
   "outputs": [],
   "source": [
    "@njit\n",
    "def _compute_percentile(A, Ax_mean, x_cov, p):\n",
    "    r\"\"\"\n",
    "    Compute percentile of the scalar Ax, where A is vector coefficient and x follows multivariate normal distribution.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    A : (N, ) ndarray\n",
    "        Coefficient of Ax.\n",
    "    Ax_mean : float\n",
    "        Mean of Ax.\n",
    "    x_cov : (N, N) ndarray\n",
    "        Covariance matrix of x.\n",
    "    p : float\n",
    "        Percentile of a standard normal distribution.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    res : float\n",
    "        Percentile of Ax.\n",
    "\n",
    "    \"\"\"\n",
    "    Ax_var = A@x_cov@A.T\n",
    "    Ax_std = np.sqrt(Ax_var)\n",
    "    res = Ax_mean + Ax_std * p\n",
    "    return res"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3da1b0e7",
   "metadata": {},
   "source": [
    "## 3.3 Limiting Behavior\n",
    "\n",
    "The operator ${\\mathbb M}$ typically has a solution to the following equation: \n",
    "\n",
    "$$\n",
    "{\\mathbb M} \\left[\\Phi_1^e x_1+\\Phi_2^e x_2 + {\\frac 1 2} (x_1)'\\Phi_3^e x_1\\right] \n",
    "= \n",
    "\\eta^e + \n",
    " \\left[ \\Phi_1^e x_1+\\Phi_2^e x_2 + {\\frac 1 2} (x_1)'\\Phi_3^e x_1\\right] \\tag{6} \n",
    "$$\n",
    "\n",
    "\n",
    "The solution of interest when, it exists, can be deduced by iterating on the ${\\mathbb M}$ operator allowing for a constant shift $\\eta^e$.  This solution gives a characterization of the limiting elasticity.  Construct \n",
    "\n",
    "$$\n",
    "L_{1,\\infty} = \\left(\\frac {M_1}{M_0} \\right)\\left(\\frac{\\exp\\left[\\Phi_1^e X_{1,1} +\\Phi_2^e X_{2,1} + {\\frac 1 2} (X_{1,1})'\\Phi_3^e X_{1,1} \\right]}{ \n",
    "\\exp(\\eta) \\exp\\left[ \\Phi_1^e X_{1,0} +\\Phi_2^e X_{2,0} + {\\frac 1 2} (X_{1,0})'\\Phi_3^e X_{1,0}\\right]} \\right) . \n",
    "$$ \n",
    "\n",
    "The elasticities are given by conditional linear combinations of conditional expectations of $W_1$ under this limiting change of measure.\n",
    "\n",
    "To express the equation of interest differently, consider the operator, ${\\mathbb P}$ that maps $\\Phi_{0} +\\Phi_1 x_1+\\Phi_2 x_2 + {\\frac 1 2} (x_1)'\\Phi_3 x_1$ into $\\exp\\left({\\mathbb M} \\left[ \\Phi_{0} +\\Phi_1^e x_1+\\Phi_2 x_2 + {\\frac 1 2} (x_1)'\\Phi_3 x_1\\right] \\right)$.   Rewrite equation (6) as: \n",
    "\n",
    "$$\n",
    "{\\mathbb P} \\left[ \\Phi_1^e x_1+\\Phi_2^e x_2 + {\\frac 1 2} (x_1)'\\Phi_3^e x_1\\right] \n",
    "= \n",
    "\\exp(\\eta) \n",
    " \\left[ \\Phi_1^e x_1+\\Phi_2^e x_2 + {\\frac 1 2} (x_1)'\\Phi_3^e x_1\\right]\n",
    "$$ \n",
    "\n",
    "which is an eigenvalue equation where $\\exp\\left[ \\Phi_1^e x_1+\\Phi_2^e x_2 + {\\frac 1 2} (x_1)'\\Phi_3^e x_1\\right]$ is a postive eigenfunction and $\\exp(\\eta)$ is a positive eigenvalue. [^1] \n",
    "\n",
    "\n",
    "The codes below solve the eigenvalue problem using the  *M_mapping*.\n",
    "\n",
    "[^1]: This eigenvalue problem is the so called Perron-Frobenius problem. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "abe4f3f5",
   "metadata": {},
   "outputs": [],
   "source": [
    "def M_mapping(log_M_growth, f, X1_tp1, X2_tp1, second_order = True):\n",
    "    r'''\n",
    "    Computes coefficients of a LinQuadVar after one iteration of M mapping\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    log_M_growth : LinQuadVar\n",
    "        Log difference of multiplicative functional.\n",
    "        e.g. log consumption growth, :math:`\\log \\frac{C_{t+1}}{C_t}`\n",
    "    f : LinQuadVar\n",
    "        The function M Mapping operate on. \n",
    "        e.g. A function that is identically one, log_f = LinQuadVar({'c': np.zeros((1,1))}, log_M_growth.shape)\n",
    "    X1_tp1 : LinQuadVar \n",
    "        Stores the coefficients of laws of motion for X1.\n",
    "    X2_tp2 : LinQuadVar or None\n",
    "        Stores the coefficients of laws of motion for X2.  \n",
    "    second_order: boolean\n",
    "        Whether the second order expansion of the state evoluton equation has been input\n",
    "        \n",
    "    Returns\n",
    "    -------\n",
    "    LinQuadVar, stores the coefficients of the new LinQuadVar after one iteration of M Mapping\n",
    "    '''\n",
    "    if second_order:\n",
    "        return log_E_exp(log_M_growth + next_period(f, X1_tp1, X2_tp1))\n",
    "    else:\n",
    "        if X2_tp1 != None:\n",
    "            print('The second order expansion for law of motion is not used in the first order expansion.')\n",
    "        return log_E_exp(log_M_growth + next_period(f, X1_tp1))\n",
    "    \n",
    "def Q_mapping(log_M_growth, f, X1_tp1, X2_tp1, tol = 1e-10, max_iter = 10000, second_order = True):\n",
    "    r'''\n",
    "    Computes limiting coefficients of a LinQuadVar by recursively applying the M mapping operator till convergence, returns the eigenvalue and eigenvector.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    log_M_growth : LinQuadVar\n",
    "        Log difference of multiplicative functional.\n",
    "        e.g. log consumption growth, :math:`\\log \\frac{C_{t+1}}{C_t}`\n",
    "    f : LinQuadVar\n",
    "        The function M Mapping operate on. \n",
    "        e.g. A function that is identically one, log_f = LinQuadVar({'c': np.zeros((1,1))}, log_M_growth.shape)\n",
    "    X1_tp1 : LinQuadVar \n",
    "        Stores the coefficients of laws of motion for X1.\n",
    "    X2_tp2 : LinQuadVar or None\n",
    "        Stores the coefficients of laws of motion for X2.  \n",
    "    tol: float\n",
    "        tolerance for convergence\n",
    "    max_iter: int\n",
    "        maximum iteration\n",
    "    second_order: boolean\n",
    "        Whether the second order expansion of the state evoluton equation has been input\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    Qf_components_log : List of LinQuadVar\n",
    "        stores the coefficients of the LinQuadVar in each iteration of M Mapping\n",
    "    f: LinQuadVar\n",
    "        The function M Mapping operate on. \n",
    "        e.g. A function that is identically one, log_f = LinQuadVar({'c': np.zeros((1,1))}, log_M_growth.shape)\n",
    "    η: float\n",
    "        The eigenvalue\n",
    "    η_series: list of float\n",
    "        The convergence path of the eigenvalue \n",
    "    '''\n",
    "    η_series = []\n",
    "    Qf_components_log = []\n",
    "    for i in range(max_iter):\n",
    "        Qf_components_log.append(f)\n",
    "        if second_order:\n",
    "            f_next = M_mapping(log_M_growth, f, X1_tp1, X2_tp1, second_order = second_order)\n",
    "        else:\n",
    "            if X2_tp1 != None:\n",
    "                print('The second order expansion for law of motion is not used in the first order expansion.')\n",
    "            f_next = M_mapping(log_M_growth, f, X1_tp1, second_order = second_order)\n",
    "        η = (f_next['c'] - f['c']).item()\n",
    "        η_series.append(η)\n",
    "        \n",
    "        if distance(f, f_next, ['x', 'xx', 'x2']) < tol:\n",
    "            break\n",
    "        f = f_next\n",
    "    \n",
    "    if i >= max_iter-1:\n",
    "        print(\"Warning: Q iteration may not have converged.\")\n",
    "    Qf_components_log.append(f_next)\n",
    "        \n",
    "    return Qf_components_log, f, η, η_series"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "410d59c1",
   "metadata": {},
   "source": [
    "For example, to compute the limiting behaviour of the example above, we can use:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7c0c0914",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Growth Shock</th>\n",
       "      <th>Consumption Shock</th>\n",
       "      <th>Volatility Shock</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.1 quantile</th>\n",
       "      <td>0.004241</td>\n",
       "      <td>0.001273</td>\n",
       "      <td>0.019480</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.5 quantile</th>\n",
       "      <td>0.008000</td>\n",
       "      <td>0.001613</td>\n",
       "      <td>0.036833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.9 quantile</th>\n",
       "      <td>0.011759</td>\n",
       "      <td>0.001953</td>\n",
       "      <td>0.054186</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              Growth Shock  Consumption Shock  Volatility Shock\n",
       "0.1 quantile      0.004241           0.001273          0.019480\n",
       "0.5 quantile      0.008000           0.001613          0.036833\n",
       "0.9 quantile      0.011759           0.001953          0.054186"
      ]
     },
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     "output_type": "display_data"
    }
   ],
   "source": [
    "## Calculate exposure elasticity for consumption growth at the limit\n",
    "log_f = LinQuadVar({'c': np.zeros((1,1))},gc_tp1.shape)\n",
    "Qf_components_log_C, _, η_C, η_C_series = Q_mapping(gc_tp1, log_f, X1_tp1, X2_tp1, tol = 1e-7)\n",
    "expo_elas_shock_0_015_limit = [exposure_elasticity(gc_tp1, X1_tp1, X2_tp1, len(η_C_series), shock=0, percentile=p)[-1].item() for p in quantile]\n",
    "expo_elas_shock_1_015_limit = [exposure_elasticity(gc_tp1, X1_tp1, X2_tp1, len(η_C_series), shock=1, percentile=p)[-1].item() for p in quantile]\n",
    "expo_elas_shock_2_015_limit = [exposure_elasticity(gc_tp1, X1_tp1, X2_tp1, len(η_C_series), shock=2, percentile=p)[-1].item() for p in quantile]\n",
    "expo_limit = pd.DataFrame([expo_elas_shock_0_015_limit, expo_elas_shock_2_015_limit,expo_elas_shock_1_015_limit],\\\n",
    "            columns = ['0.1 quantile','0.5 quantile','0.9 quantile'],\\\n",
    "            index = ['Growth Shock','Consumption Shock','Volatility Shock']).T\n",
    "expo_limit"
   ]
  }
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