{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Exact Value Function for Recursive Utility"
      ],
      "id": "4f236b6c-6e68-4228-9577-49c8f843f03f"
    },
    {
      "cell_type": "raw",
      "metadata": {
        "raw_mimetype": "tex"
      },
      "source": [
        "\\renewcommand{\\perp}{\\mathrel\\bot}\n",
        "\\newcommand{\\ev}{\\operatorname{E}}\n",
        "\\newcommand{\\var}{\\operatorname{V}}\n",
        "\\newcommand{\\cov}{\\operatorname{Cov}}\n",
        "\\newcommand{\\Normal}{\\mathcal{N}}\n",
        "\\newcommand{\\qedf}{\\qed{\\parfillskip=0pt \\par}}\n",
        "\\renewcommand{\\vec}[1]{\\mathbf{#1}}\n",
        "\\newcommand{\\gvec}[1]{\\pmb{#1}}\n",
        "\\newcommand{\\inner}[1]{\\langle{#1}\\rangle}\n",
        "\\newcommand{\\norm}[1]{\\lVert{#1}\\rVert}\n",
        "\\newcommand{\\prob}{\\operatorname{P}}\n",
        "\\newcommand{\\1}[1]{1\\kern-0.25em\\text{l}_{\\{#1\\}}}"
      ],
      "id": "44852ab6-82e5-43c4-b786-5cba3d0dbcba"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Introduction\n",
        "\n",
        "The [Affine Recursive Utility in Continuous\n",
        "Time](https://www.lorenzonaranjo.com/class-materials/asset-pricing/continuous-time-asset-pricing/recursive-utility-affine-model.html)\n",
        "notebook derived the exact nonlinear ODE for the log continuation-value\n",
        "function $$\n",
        "  q(x) = \\ln h(x),\n",
        "$$ in the one-factor Gaussian endowment economy $$\n",
        "  d\\ln c_t = (\\mu_0 + \\mu_1 x_t)\\,dt + \\sigma_c\\,dB_t,\n",
        "  \\qquad\n",
        "  dx_t = \\xi(\\bar{x} - x_t)\\,dt + \\sigma_x\\,dB_t.\n",
        "$$ That notebook then switched to a local affine approximation because\n",
        "it delivers closed-form intuition. This notebook goes the other way: it\n",
        "solves the exact boundary-value problem numerically and uses it to\n",
        "assess the affine approximation.\n",
        "\n",
        "For one benchmark calibration, how much does the exact nonlinear\n",
        "solution differ from the affine approximation? Everything below is\n",
        "organized around that question. First we solve the boundary-value\n",
        "problem, then we recover the implied equilibrium objects, and finally we\n",
        "compare them with the affine benchmark.\n",
        "\n",
        "With the homothetic value function $$\n",
        "  V(W,x) = \\frac{W^{1-\\gamma}}{1-\\gamma} h(x),\n",
        "$$ the exact nonlinear ODE is $$\n",
        "  0\n",
        "  =\n",
        "  \\theta\\!\\left(\\delta^\\psi e^{-(\\psi/\\theta) q(x)}-\\delta\\right)\n",
        "  + (1-\\gamma)(\\mu_0+\\mu_1x)\n",
        "  + \\psi\\xi(\\bar{x}-x)q'(x)\n",
        "$$ <span id=\"eq-exact-bvp\">$$\n",
        "  \\qquad\n",
        "  + \\frac{1}{2}\\psi\\sigma_x^2 q''(x)\n",
        "  + \\psi(1-\\gamma)\\sigma_c\\sigma_x q'(x)\n",
        "  + \\frac{1}{2}\\psi^2\\sigma_x^2 q'(x)^2\n",
        "  + \\frac{1}{2}(1-\\gamma)^2\\sigma_c^2,\n",
        " \\qquad(1)$$</span> where $$\n",
        "  \\theta = \\frac{1-\\gamma}{1-1/\\psi}.\n",
        "$$ The boundary conditions are $$\n",
        "  q'(x_{\\min}) = 0,\n",
        "  \\qquad\n",
        "  q'(x_{\\max}) = 0,\n",
        "$$ which approximate the tail conditions $q'(x)\\to 0$ as\n",
        "$x\\to \\pm \\infty$ on a finite interval.\n",
        "\n",
        "Once $q(x)$ is known, the main equilibrium objects follow immediately:\n",
        "$$\n",
        "  m(x) = \\delta^\\psi e^{-(\\psi/\\theta)q(x)},\n",
        "$$ $$\n",
        "  \\sigma_W(x) = \\sigma_c + \\frac{\\psi}{\\theta} q'(x)\\sigma_x,\n",
        "$$ and $$\n",
        "  \\mu_W(x)\n",
        "  =\n",
        "  \\mu_0+\\mu_1x+\\frac{\\psi}{\\theta}q'(x)\\xi(\\bar{x}-x)\n",
        "  + \\frac{1}{2}\\frac{\\psi}{\\theta}q''(x)\\sigma_x^2\n",
        "  + \\frac{1}{2}\\sigma_W(x)^2.\n",
        "$$\n",
        "\n",
        "## Calibration\n",
        "\n",
        "The numerical solution needs a concrete parameterization. The values\n",
        "below are chosen to make the recursive-utility channel visible while\n",
        "keeping the boundary-value problem well behaved on a compact grid. The\n",
        "goal is not a broad sensitivity analysis, but a single clean benchmark\n",
        "against which to judge the affine approximation."
      ],
      "id": "bad4b429-5821-40f0-9fc4-48fd772c2b1e"
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {},
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "from scipy.integrate import solve_bvp\n",
        "from scipy.optimize import root_scalar"
      ],
      "id": "027dbd75"
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "\n",
              "</div>"
            ]
          }
        }
      ],
      "source": [
        "params = {\n",
        "    \"delta\": 0.02,\n",
        "    \"gamma\": 8.0,\n",
        "    \"psi\": 1.5,\n",
        "    \"mu0\": 0.015,\n",
        "    \"mu1\": 0.02,\n",
        "    \"xi\": 0.35,\n",
        "    \"xbar\": 0.0,\n",
        "    \"sigma_c\": 0.02,\n",
        "    \"sigma_x\": 0.06,\n",
        "}\n",
        "\n",
        "delta = params[\"delta\"]\n",
        "gamma = params[\"gamma\"]\n",
        "psi = params[\"psi\"]\n",
        "theta = (1 - gamma) / (1 - 1 / psi)\n",
        "alpha = psi / theta\n",
        "\n",
        "param_table = pd.Series(\n",
        "    {\n",
        "        \"δ\": delta,\n",
        "        \"γ\": gamma,\n",
        "        \"ψ\": psi,\n",
        "        \"θ\": theta,\n",
        "        \"μ₀\": params[\"mu0\"],\n",
        "        \"μ₁\": params[\"mu1\"],\n",
        "        \"ξ\": params[\"xi\"],\n",
        "        \"x̄\": params[\"xbar\"],\n",
        "        \"σ_c\": params[\"sigma_c\"],\n",
        "        \"σ_x\": params[\"sigma_x\"],\n",
        "    }\n",
        ")\n",
        "\n",
        "param_table.to_frame(\"Value\")"
      ],
      "id": "a1ec994f"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Solving the Boundary-Value Problem\n",
        "\n",
        "Write $y_1(x)=q(x)$ and $y_2(x)=q'(x)$. Then\n",
        "(<a href=\"#eq-exact-bvp\" class=\"quarto-xref\">1</a>) becomes a\n",
        "first-order system: $$\n",
        "  y_1'(x) = y_2(x),\n",
        "$$ $$\n",
        "  y_2'(x)\n",
        "  =\n",
        "  -\\frac{2}{\\psi \\sigma_x^2}\n",
        "  \\Bigg[\n",
        "    \\theta\\!\\left(\\delta^\\psi e^{-\\alpha y_1(x)}-\\delta\\right)\n",
        "    + (1-\\gamma)(\\mu_0+\\mu_1x)\n",
        "    + \\psi\\xi(\\bar{x}-x)y_2(x)\n",
        "$$ $$\n",
        "    \\qquad\n",
        "    + \\psi(1-\\gamma)\\sigma_c\\sigma_x y_2(x)\n",
        "    + \\frac{1}{2}\\psi^2\\sigma_x^2 y_2(x)^2\n",
        "    + \\frac{1}{2}(1-\\gamma)^2\\sigma_c^2\n",
        "  \\Bigg].\n",
        "$$\n",
        "\n",
        "We solve this system on the truncated interval\n",
        "$[x_{\\min}, x_{\\max}] = [-0.12, 0.12]$ using\n",
        "`scipy.integrate.solve_bvp`. As an initial guess, we use the\n",
        "deterministic steady state obtained by setting $x=\\bar{x}$ and imposing\n",
        "$q'(\\bar{x})=q''(\\bar{x})=0$."
      ],
      "id": "ee0c6b30-246e-4f02-8cac-671be2a54213"
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {},
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The algorithm converged to the desired accuracy.\n",
            "Solver status: 0\n",
            "Mesh points used: 401"
          ]
        }
      ],
      "source": [
        "x_min, x_max = -0.12, 0.12\n",
        "x_grid = np.linspace(x_min, x_max, 401)\n",
        "\n",
        "steady_term = (\n",
        "    (1 - gamma) * (params[\"mu0\"] + params[\"mu1\"] * params[\"xbar\"])\n",
        "    + 0.5 * (1 - gamma) ** 2 * params[\"sigma_c\"] ** 2\n",
        ")\n",
        "m_steady = delta - steady_term / theta\n",
        "q_steady = -(1 / alpha) * np.log(m_steady / delta**psi)\n",
        "\n",
        "\n",
        "def recursive_utility_ode(x, y):\n",
        "    q = y[0]\n",
        "    q_prime = y[1]\n",
        "\n",
        "    forcing = (\n",
        "        theta * (delta**psi * np.exp(-alpha * q) - delta)\n",
        "        + (1 - gamma) * (params[\"mu0\"] + params[\"mu1\"] * x)\n",
        "        + psi * params[\"xi\"] * (params[\"xbar\"] - x) * q_prime\n",
        "        + psi * (1 - gamma) * params[\"sigma_c\"] * params[\"sigma_x\"] * q_prime\n",
        "        + 0.5 * psi**2 * params[\"sigma_x\"] ** 2 * q_prime**2\n",
        "        + 0.5 * (1 - gamma) ** 2 * params[\"sigma_c\"] ** 2\n",
        "    )\n",
        "\n",
        "    q_second = -2 * forcing / (psi * params[\"sigma_x\"] ** 2)\n",
        "    return np.vstack((q_prime, q_second))\n",
        "\n",
        "\n",
        "def boundary_conditions(left, right):\n",
        "    return np.array([left[1], right[1]])\n",
        "\n",
        "\n",
        "initial_q = q_steady + 0.15 * (x_grid - params[\"xbar\"])\n",
        "initial_q_prime = np.full_like(x_grid, 0.15)\n",
        "initial_guess = np.vstack((initial_q, initial_q_prime))\n",
        "\n",
        "solution = solve_bvp(\n",
        "    recursive_utility_ode,\n",
        "    boundary_conditions,\n",
        "    x_grid,\n",
        "    initial_guess,\n",
        "    tol=1e-6,\n",
        "    max_nodes=20_000,\n",
        ")\n",
        "\n",
        "print(solution.message)\n",
        "print(f\"Solver status: {solution.status}\")\n",
        "print(f\"Mesh points used: {solution.x.size}\")"
      ],
      "id": "7880e4ac"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "To analyze the solution, evaluate it on a fine grid and recover $q''(x)$\n",
        "from the ODE rather than from numerical differentiation."
      ],
      "id": "288a5b13-e6d5-46b1-898b-90342305cc9a"
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {},
      "outputs": [],
      "source": [
        "x_plot = np.linspace(x_min, x_max, 801)\n",
        "q_exact, q_prime_exact = solution.sol(x_plot)\n",
        "\n",
        "forcing_exact = (\n",
        "    theta * (delta**psi * np.exp(-alpha * q_exact) - delta)\n",
        "    + (1 - gamma) * (params[\"mu0\"] + params[\"mu1\"] * x_plot)\n",
        "    + psi * params[\"xi\"] * (params[\"xbar\"] - x_plot) * q_prime_exact\n",
        "    + psi * (1 - gamma) * params[\"sigma_c\"] * params[\"sigma_x\"] * q_prime_exact\n",
        "    + 0.5 * psi**2 * params[\"sigma_x\"] ** 2 * q_prime_exact**2\n",
        "    + 0.5 * (1 - gamma) ** 2 * params[\"sigma_c\"] ** 2\n",
        ")\n",
        "q_second_exact = -2 * forcing_exact / (psi * params[\"sigma_x\"] ** 2)\n",
        "\n",
        "m_exact = delta**psi * np.exp(-alpha * q_exact)\n",
        "sigma_w_exact = params[\"sigma_c\"] + alpha * q_prime_exact * params[\"sigma_x\"]\n",
        "mu_w_exact = (\n",
        "    params[\"mu0\"]\n",
        "    + params[\"mu1\"] * x_plot\n",
        "    + alpha * q_prime_exact * params[\"xi\"] * (params[\"xbar\"] - x_plot)\n",
        "    + 0.5 * alpha * q_second_exact * params[\"sigma_x\"] ** 2\n",
        "    + 0.5 * sigma_w_exact**2\n",
        ")"
      ],
      "id": "8788178a"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The next table summarizes the range of the exact solution over the state\n",
        "grid."
      ],
      "id": "710ef93c-1c29-470e-b127-bae2ff27141f"
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "\n",
              "</div>"
            ]
          }
        }
      ],
      "source": [
        "summary = pd.DataFrame(\n",
        "    {\n",
        "        \"Minimum\": [\n",
        "            q_exact.min(),\n",
        "            q_prime_exact.min(),\n",
        "            q_second_exact.min(),\n",
        "            m_exact.min(),\n",
        "            sigma_w_exact.min(),\n",
        "            mu_w_exact.min(),\n",
        "        ],\n",
        "        \"Maximum\": [\n",
        "            q_exact.max(),\n",
        "            q_prime_exact.max(),\n",
        "            q_second_exact.max(),\n",
        "            m_exact.max(),\n",
        "            sigma_w_exact.max(),\n",
        "            mu_w_exact.max(),\n",
        "        ],\n",
        "    },\n",
        "    index=[\n",
        "        \"q(x)\",\n",
        "        \"q′(x)\",\n",
        "        \"q″(x)\",\n",
        "        \"m(x)\",\n",
        "        \"σ_W(x)\",\n",
        "        \"μ_W(x)\",\n",
        "    ],\n",
        ")\n",
        "\n",
        "summary.round(6)"
      ],
      "id": "851ff9b5"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Comparing Exact and Affine Solutions\n",
        "\n",
        "The affine approximation from the earlier notebook provides the\n",
        "benchmark. The point here is not to re-derive that approximation, but to\n",
        "measure what it misses relative to the exact nonlinear solution.\n",
        "\n",
        "Under that approximation, $$\n",
        "  q_{\\text{aff}}(x) = a + bx.\n",
        "$$ Its coefficients solve $$\n",
        "  \\psi b(\\xi + \\bar{m}) = (1-\\gamma)\\mu_1\n",
        "$$ and $$\n",
        "  \\delta\\theta\n",
        "  =\n",
        "  \\theta\\bar{m}\n",
        "  + (1-\\gamma)(\\mu_0+\\mu_1\\bar{x})\n",
        "  + \\frac{1}{2}(1-\\gamma)^2\\sigma_w^2\n",
        "  + \\frac{1}{2}b^2\\sigma_x^2\n",
        "  + (1-\\gamma)b\\sigma_w\\sigma_x,\n",
        "$$ where $$\n",
        "  \\sigma_w = \\sigma_c + \\frac{\\psi}{\\theta} b \\sigma_x.\n",
        "$$ This leaves a single nonlinear equation in $\\bar{m}$, which we solve\n",
        "numerically and then use to recover $a$ and $b$."
      ],
      "id": "7af1e055-5c5b-4e98-beea-9c28d43b9579"
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "\n",
              "</div>"
            ]
          }
        }
      ],
      "source": [
        "def affine_residual(m_bar):\n",
        "    b = (1 - gamma) * params[\"mu1\"] / (psi * (params[\"xi\"] + m_bar))\n",
        "    sigma_w = params[\"sigma_c\"] + alpha * b * params[\"sigma_x\"]\n",
        "\n",
        "    return (\n",
        "        theta * m_bar\n",
        "        + (1 - gamma) * (params[\"mu0\"] + params[\"mu1\"] * params[\"xbar\"])\n",
        "        + 0.5 * (1 - gamma) ** 2 * sigma_w**2\n",
        "        + 0.5 * b**2 * params[\"sigma_x\"] ** 2\n",
        "        + (1 - gamma) * b * sigma_w * params[\"sigma_x\"]\n",
        "        - delta * theta\n",
        "    )\n",
        "\n",
        "\n",
        "m_bar = root_scalar(affine_residual, bracket=[1e-4, 0.05]).root\n",
        "b = (1 - gamma) * params[\"mu1\"] / (psi * (params[\"xi\"] + m_bar))\n",
        "a = theta * np.log(delta) - (theta / psi) * np.log(m_bar) - b * params[\"xbar\"]\n",
        "\n",
        "q_affine = a + b * x_plot\n",
        "m_affine = delta**psi * np.exp(-alpha * q_affine)\n",
        "sigma_w_affine = params[\"sigma_c\"] + alpha * b * params[\"sigma_x\"]\n",
        "\n",
        "q_error = q_exact - q_affine\n",
        "m_error = m_exact - m_affine\n",
        "sigma_w_error = sigma_w_exact - sigma_w_affine\n",
        "\n",
        "comparison = pd.Series(\n",
        "    {\n",
        "        \"m̄\": m_bar,\n",
        "        \"a\": a,\n",
        "        \"b\": b,\n",
        "        \"σ_w\": sigma_w_affine,\n",
        "        \"max_x |q(x) - q_aff(x)|\": np.max(np.abs(q_exact - q_affine)),\n",
        "        \"max_x |m(x) - m_aff(x)|\": np.max(np.abs(m_exact - m_affine)),\n",
        "    }\n",
        ")\n",
        "\n",
        "comparison.to_frame(\"Value\")"
      ],
      "id": "3a508917"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The affine approximation is not exact, but the discrepancy is easy to\n",
        "quantify directly rather than judge only from the plots."
      ],
      "id": "e32a54b2-c63c-4c7e-b868-5ce74f47397c"
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "\n",
              "</div>"
            ]
          }
        }
      ],
      "source": [
        "error_summary = pd.DataFrame(\n",
        "    {\n",
        "        \"Max abs. error\": [\n",
        "            np.max(np.abs(q_error)),\n",
        "            np.max(np.abs(m_error)),\n",
        "            np.max(np.abs(sigma_w_error)),\n",
        "        ],\n",
        "        \"RMS error\": [\n",
        "            np.sqrt(np.mean(q_error**2)),\n",
        "            np.sqrt(np.mean(m_error**2)),\n",
        "            np.sqrt(np.mean(sigma_w_error**2)),\n",
        "        ],\n",
        "    },\n",
        "    index=[\n",
        "        \"q(x)\",\n",
        "        \"m(x)\",\n",
        "        \"σ_W(x)\",\n",
        "    ],\n",
        ")\n",
        "\n",
        "error_summary.round(8)"
      ],
      "id": "7d7682d3"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The cleanest way to see what the affine approximation misses is to look\n",
        "directly at the curvature of the exact solution. Because the affine\n",
        "specification imposes $q''(x)=0$, any nonzero curvature is a genuinely\n",
        "nonlinear feature of the Epstein-Zin problem."
      ],
      "id": "da48529f-8b83-48cd-b7b1-789ecdf295de"
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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wtnsAAtwdJa6o9qxiVHhpaSmSkpJw8uRJ/PDDDzh58iR2796NDRs2VGq7bNky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\n"
          }
        }
      ],
      "source": [
        "plt.figure(figsize=(7, 4))\n",
        "plt.plot(x_plot, q_second_exact, lw=2)\n",
        "plt.axhline(0.0, color=\"black\", ls=\"--\", lw=1)\n",
        "plt.title(r\"Curvature of the Exact Value Function $q''(x)$\")\n",
        "plt.xlabel(r\"$x$\")\n",
        "plt.ylabel(r\"$q''(x)$\")\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "id": "1e05b199"
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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idFzmWIgcDM6u9q+riIg0WlrHsoYULKXRykyEHx+EAyvKljI6mZsvdBwJXcZD\n94n2r5+IiDQ6CpY1pGApjV5hbtlSRnuWmC2bJ2t/IUxZWB81ExGRRkZjLEWaO1dP6DzOPCwWOLyh\nLGQm7TSXKzpZehx8fmXZUkZt+lc8U11ERKQSarGshFospUlLPQjufuAZWHburw9g8fSy157B0GmM\nuZd5+2Hg5m3/eoqISIOgFksRqVxFu/cUZoObHxRkmK9zk2Hz5+bh5Abth5qtmV0uNbeoFBEROYVa\nLCuhFktplqxLGS2BmJ/M7vFTXfcNRF1k/7qJiEi90eSdGlKwlGbPMCBpV+k+5ovh8Hpw8YIZB8DF\nvazcqpfNmejRY81dgrSUkYhIk6NgWUMKliKnyDoGSTugw/Cyc4YBr/eC9FjztasPdBxhTv6Jush2\nDKeIiDRaGmMpIrXLp6V5nCznuO1amYVZsHOBeTg4QcQgc/JP9DgI6mDP2oqISD1Qi2Ul1GIpUk0W\nCxzZVNZlnrSjfJmgKJi63v51ExGRWqEWSxGxD0dHaNPPPEY8CWmx5lqZMYvg0B9gKTbX0jxZYQ4s\nnmEuZ6SljEREmgy1WFZCLZYitSA/A/Ytg5bdISS67Pzun+CryebXTm7Q7oKyvcx9w+qnriIiUilN\n3qkhBUuROvTLE7D6zYqvteptjsmMHguhPcDBwa5VExGR8hQsa0jBUqQOGQYcjykbl5nwN1DBr6IJ\n70LvyXavnoiI2NIYSxFpuBwcoEVn8xjyEGQnwZ6fzZB5YAUU5ZrlTl7aCMyF2/PTIWqUljISEWmA\nFCxFpP55t4C+N5hHUR4cXAmJW8En1Lbc6jcg9k9wcCxdymisljISEWlA7N4VvnXrVmJjY4mKiqJz\n587lru/fv5+dO3cSFhZGv379qnxeTEwMMTExhIWF0b9//0rLzZ8/H19fX0aOHFmteqorXKSByUuH\nF9uDUVL+WlBUWcgMPxccnexePRGRpqzBjbHcvn07N998M0VFRYSHh/PHH38wfPhw5s6di7OzM9nZ\n2dxwww3s3r2bTp06sXHjRsLCwvj555/x9/cv9zzDMLj55pv58ccfGThwIFu2bKF79+4sWLAANzc3\nm7Lvv/8+U6dOpW/fvqxdu7Za9VWwFGmArEsZLYZDq8yljE4V2B6mbtSkHxGRWlTdXORorwrl5OTw\nwQcfsHnzZn744Qe2b9/O0qVL+eqrrwAoKCjg3nvvZdeuXSxcuJC9e/eSmprKW2+9VeHz5s6dy3ff\nfceWLVv48ccf2b17N/v27StX/uDBg7z44ovccccddf4ZRaSOBUTCgDthygJzz/Ir50CPq8Hdr6xM\nWF/bUGkYsPFTyDhs9+qKiDQ3dhtjOWDAAJvXrVu3Jjg4mOTkZACCgoJsuqnd3d1p3bo1OTk5FT5v\n/fr19OvXj9atWwPg5eXFyJEj+eabb5g2bRpQ1qr53HPPsXPnzrr4WCJSX9z9oPtE8ygpgri1Zktm\n+wttyyVuge+nml+36nXSUkY91aopIlLL6m3yzqJFizhy5AgXX3yxzflly5aRmJjImjVrSElJ4b77\n7qvw/latWnHw4EFKSkpwcjLHU+3du5f9+/dby7z22msEBgZy9dVX89RTT522PkVFRRQXl3Wr5eXl\nneUnExG7c3KBdkPM41Qxi8u+TtxiHr89B76tzZ1/oseZ9zm7lb9XRETOiN26wk+2bt06rrvuOj74\n4AOioqJsrv3+++989913LF26lE6dOuFQSYvCjTfeSF5eHhMnTuSjjz7itttuY+fOnZSUmAP7Y2Ji\nePnll3nnnXeqVadZs2bh6elpPYKCgmr2IUWkYTjnNrjsbeh8Cbh4lp3PPAzrP4L/XWFOCtr2Tf3V\nUUSkibD7rPCVK1cyYcIEXn/9dW644YZKyxmGwYQJE3B2dubbb7+tsExSUhLvvfceBw8epHfv3qSk\npLBo0SLWr1/PpZdeiqenJxMmTADgm2++YcuWLTzzzDNccskleHvb7k1cUYtlUFCQJu+INCUnljKK\nWWSuiZl9tOza7cuh9UkrURzfY3aVB0eVf46ISDPTIBdI//nnn7nmmmuYPXs2V155pc21pKQkWrRo\nYX3t4OBAu3bt2LZtG2AGzblz53L++efTpk0bAJycnJg5cyYAhYWFdO3a1TpJp2/fvuzevZsFCxYA\nsHv3btLS0liwYAHDhg0rFyxdXFxwcXGpk88tIg2Eiwd0Gm0eF1sgcXPpzj/roFUf27Ir/wPbvoag\njmVLGbU5F5y0/K+ISGXs1mL522+/MXr0aCZNmsTYsWOt56Ojo+nTpw/ffPMNb7/9NpdccgmBgYGs\nX7+e2bNn8/XXX3PZZZdRXFyMi4sL8+bNs4bSc889lyuvvBI3Nzc++eQTvL29WbZsGa6uruXe/6mn\nnmLJkiVabkhEqlZSBP/pAPkZtuc9As1QGj3W3BXIzad+6iciYmcNrsUyOzubyy+/nIKCAmsrIsC4\ncePo06cPV155Je3bt2fu3Lns3LmTiIgItm7dSnR0NACOjo5cc801hIeHW+/9/vvvefPNNzl69ChT\np07l+uuvr7TVsXv37tbxlyIiVRr/utmauedncxtJgLxU2PKleTi5mjPQr/1KC7KLiJSy+xjLxkIt\nliICQEkxxJcuZRSzCFIPlF2LGAS3LLEtfzwGgjtpKSMRaVIaXIuliEij5OQMbc83j1HPQvLe0sk/\ni6Gz7XJpZB2Dt88FnzCILl3KqO0QcHGvn7qLiNiZWiwroRZLEamSYdi2TG78tGwx9hNcvKDjcDNk\nRo0Cr2D71lFEpBY0uL3CGxsFSxE5Y4c3wqbPzNbMrMTy1x0cIXwADJkGURfZv34iImdJXeEiIvbW\nuq95XPxK2VJGMYvgqLlsGoYF4tZAcb7tfQVZ4OyhpYxEpNFTi2Ul1GIpIrUmPR72LDFDZvzfMG03\nuJ20lu6yp2D9nJOWMhoB7r71Vl0RkVOpK7yGFCxFpE4U5ZefzPP2ADi+u+y1Y+ne59HjzP3M/cMR\nEalP6goXEWmITg2VJUXmeEtLMaTsM89ZimD/cvNY9DC07GG2ZF7wMDi72b/OIiLVpBbLSqjFUkTs\nLnlv6bjMxebamYal7Jp/BNy/1XYWuqVEi7OLiF2oxVJEpLEJjjKPwf+AnBTY+4s5LnPfr9BprG2o\nLC6A13pAm3PM1syo0eAdUn91FxFBLZaVUouliDQYRflQlAuegWXn9i2Dz684qZADhJ9rhszocdr9\nR0RqlVosRUSaChf38mMzLRZo1QsSt5SeMCD+L/NY9hQEtjdbOXtdY5YTEbEDBUsRkcao0yjzyEgo\nXcpoMRxcCSWF5vXUA7D2bXNspoKliNiJusIroa5wEWl0CrLMmeQxS8ywmZcK92+BgLZlZTZ8DDsW\nmN3l0WPM4CkiUgWtY1lDCpYi0qhZSszdf1r3sz3/2UTY/2vZ65bdS8dljoVWfcDR0a7VFJHGQWMs\nRUSaM0en8qHSYgGjxNyz/MRSRse2m8fK/4B3qNmKGT0OOgwHJxf711tEGjW1WFZCLZYi0mTlptou\nZVSYbXvdxRNmHCw/YUhEmi21WIqISMU8A6HXJPMoLoBDq8oWZs88bLZWnhwqDQPm3WROAooeByHR\nWspIRCqkFstKqMVSRJodw4CjW82vT55JnrQb3hlQ9jqgXenkn7EQMVBd5iLNgFosRUTkzDg4VLw0\nUdIOcHItW8oo7aC5lNHat8HdD6JGmSGz40jztYg0W2qxrIRaLEVETlKQXbqU0WLY+zPkppQvc95U\nGPWs/esmInVOLZYiIlJ73Lyh66XmYSmBhL/NyT8xiyF5j1km+mLbew79AftXmN3mYVrKSKQ5UItl\nJdRiKSJSTcn7zFnmA+40lzk6YeF9sOkz82vvltCpdCmj9kPBRb9XRRoTLZBeQwqWIiI1YBjwZj9I\n3V/+mrOHOfM8eowZNr1b2L9+InJGFCxrSMFSRKSGigvM7nDrUkYJ5cs4OMLDe8Er2P71E5FqU7Cs\nIQVLEZFaZBhwdJu5h3nMIjiyyTwf1gfu+M227F/vQ4suEDFISxmJNBAKljWkYCkiUocyj5gh080X\nelxZdj43Ff7T0dx60t0POl5UtpSRh3+9VVekuVOwrCEFSxGRerDtG/j21vLnHZ0hcnDpwuxjIKCt\n3asm0pwpWNaQgqWISD2wlEDC+pOWMoqpuJzWzBSxK61jKSIijY+jE0QMMI+LnoaU/WWTf+LWmF3k\nAK16296XehCSdkH7C8HV0961FpFSCpYiItJwBXWA8+4zj9xU2LfMbM3sOMK23Na58Ntz4OwO7YeZ\n4zI7jQGflvVTb5FmSl3hlVBXuIhII/L+BZC4pfz51v3MkBk9Dlp0NfdDF5EzpjGWNaRgKSLSiBzd\nVtplftJSRqfyj4CbF4NfG/vWTaQJ0BhLERFpPkJ7mMfQGZCZWLpe5mI48BuUFJhligvAJ8z2vri/\nIKQTeATYvcoiTZGCpYiINC2+raD/zeZRmAP7V5gh0zsEHB3LypUUwxdXQ0EWRJ5XupTRWAhsV391\nF2nk1BVeCXWFi4g0cYf+gI8vLn8+pEvpuMyx0Lq/bRgVaaY0xrKGFCxFRJq4rGOw/VtzXGbs6rKl\njE7mFQKD7oPzH7B79UQaEo2xFBEROR2fljDoHvPIS4O9y2DPYti7FAoyzTI5x8vfl58JRbngE2rf\n+oo0AgqWIiIiHgHQ8yrzKC6EuNVls8yjx9mW3bkAvp9qLmXUqbTLvGU3LWUkgrrCK6WucBER4cQ/\nkSeHxi8nQ8xPtuX8IsrGZUYOBmdX+9VRxA7UFS4iIlJTFbVCdr0UDAscWAHF+ea5jDhY9755uPma\nOwONelZrZkqzoxbLSqjFUkRETqsw11wnM2aRuW7myeMxnVxhxkFw8y47l58J7r52r6ZIbVCLpYiI\nSF1y9YTO48zDYoHDG8zJPzGLwbe1bagE+GgUYJRtMdm6Hzg61UvVReqKXVssFy9ezJw5c4iNjSUq\nKooHH3yQfv36Wa9v3bqVV199lZ07dxIWFsZdd93F6NGjK33erl27+Pe//01MTAxhYWFMnz6dwYMH\nV/v9TkctliIictaK8sDlpH87Ug/AG31sy3gGQ6cxZtDsMAxcvexbR5EzUN1cZLdVXz///HPefvtt\nrr76at544w1atGjBkCFD2LlzJwCHDx/mnnvuYeTIkbz11ltceOGFjB8/nqVLl1b4vNjYWAYMGEBo\naChvvPEGF1xwAaNGjWLz5s3Vej8REZE643LKP7wlxdD9CnDzKzuXmwybP4e518EL7eB/V8P2+fat\np0gts1uLZUFBAW5ubjbnOnXqxB133MHDDz9McXExTk5OOJw0UHrUqFF0796dV155pdzz/v3vf/PF\nF1+wfft267mJEyfi6enJ559/XuX7VUUtliIiUutKiszF2GMWmzPL0+Nsr597B4z7T9lri8WcQKSl\njKSeNbgWy1NDXlZWFocPHyYyMhIAZ2dnm1CZmJjIjh07Ku26zszMJCgoyOZccHAwa9eurdb7naqo\nqIi8vDybQ0REpFY5uUD7oTD2ebh/K9y9BoY/aW4dCWa3+MkOrIDXesCi6bB/ubnGpkgDVi+zwi0W\nC5MmTSI+Pp5Vq1bh7Fw2h+i6665j/fr1xMXF8fDDD/PMM89U+IxFixZx+eWX8+eff9K/f39iY2M5\n99xzKSwsJC0trdrvd8JTTz3F008/Xe68WixFRMQuso6ZC7WfvAbmTw/D3x+WvXb1gaiR5uSfjiPB\nM9D+9ZRmqcHuFV5SUsLNN9/M9u3bWbp0ablWxwMHDpCens7mzZt55JFHeP7557n11lsrfNaTTz7J\nSy+9RGhoKIWFhVx44YWsWrWKuLiyroWq3u+EoqIiiouLra/z8vIICgpSsBQRkfqz/FnY8AnkJJW/\n5uAEEYPMVs5e14JXxf++idSGBhksCwsLmTx5MgkJCSxZsgR/f//Tln/iiSdYvnw5q1evrrRMQUEB\nCQkJtGnThttuu42CggK+/vrrs3q/k2mMpYiINAgWCxzZaK6XGbMEknaUL/OPzRDYzu5Vk+ajwY2x\nzMvLY8KECSQnJ7Ns2bJyIW/RokWsXLnS+jopKYklS5bQrVs3wGx57N69u80s8ddeew0XFxc6dOjA\n4sWLmTdvHtOnT6/W+4mIiDQKjo7Qpj+MmAn3rIb7t8CYF6DdUHB0hhZdy4fK+XfCgntg1w9QkF0/\n9ZZmyW4LpL///vssXryYDh06MHDgQOv5G264gUceeYRu3bpx7733MnHiRPz8/EhMTGT8+PG89NJL\nABiGwY4dO8jIyLDee/z4cVq2bAmAu7s7c+fO5ZxzzqnW+4mIiDRKAW1h4F3mkZcOGQm21wuyYMd8\nKCmEzf8DJzdzwlD0WOg0Fnxb1UetpZmwW1d4SkoKiYmJ5c4HBwcTGhpqfZ2ZmUlKSgphYWHlZnZv\n376diIgIfH3LtsTKysoiOTmZtm3b2swqr+77VUZd4SIi0igd3Q5fTYb02Iqvh/UxJ/90vhhadrNv\n3aTRapBjLBsTBUsREWm0DAOO7y4dl7kYEtYDp/xz3/kSmPS/eqmeND7aK1xERKS5cnCAFl3MY8g0\ncymjvT+bIXP/CijOK79m5vE9sGKW2ZoZdZGWMpKzohbLSqjFUkREmqSiPDjwO4Sfaxse/3gVlj1l\nfm1dymiMGTSDOtRLVaXhUFd4DSlYiohIs/Ld3bDli4qvBXcyWzijx0Gbc8DRyb51k3qnYFlDCpYi\nItLspMXCniXm2MxDf4CluHyZmxZB28H2r5vUKwXLGlKwFBGRZi0/A/YtM8dl7v3FfO0RAA/vA6eT\npmj89b7ZgtlpLPi1rr/6Sp1SsKwhBUsREZFSJUUQtwayjkLPq8vOWyzwcnTZlpOtepnd5Z3GmF+f\ntAygNG4KljWkYCkiIlKFYzvh3fMot5QRgG9rM2BGj4N2Q8DZrXwZaTQULGtIwVJERKQaso+ftJTR\ncijKLV8mYhDcssT+dZNao3UsRUREpO55h0Cf682jKA8OripbmD37qFmm/TDbe/LSYOOnZmtmcJT9\n6yx1Ri2WlVCLpYiISA1YLJC42QyY3a+AFp3Lrm2dB/NvM78O6njSUkbn2k4MkgZDXeE1pGApIiJS\nR765BbZ/W/68RyB0Gm0GzQ7Dwc3H/nWTCilY1pCCpYiISB3Jz4T9v5qtmXt+hvz08mWcXOG6edD+\nQnvXTiqgMZYiIiLSMLn7QrfLzaOkGOLXmiEzZhGkHjDLWErMJYtOdugPcPXWUkYNmFosK6EWSxER\nETszDEjeawbMrKMw9nnb6+8PNcdt+oSVjsscC22HgIt7vVS3OVFXeA0pWIqIiDQgGYfh1a7lz7t4\nQcfh5uSfqFHgFWz/ujUDCpY1pGApIiLSgBQXwIHfYc9is9s8K7F8GQdH6HwJXPOZ/evXxGmMpYiI\niDQdzm7QaZR5XPxK2VJGMYvg6DazjGEBD3/b+0qKIf4vCB+gpYzsQN9hERERaVwcHCCsj3kMewzS\n42HPEjNodrnUtmzCOvh4HHgEQFTpUkYdR2gpozqirvBKqCtcRESkCfjlCVj9pu05J1doe745LrPT\nGPAPr5+6NSIaY1lDCpYiIiJNwOENsH2+2ZqZur/iMqE9YOx/IHKQfevWiGiMpYiIiEjrfuYxelbZ\nUkYxi81xl4bFLHN0G3gG2t6XmWh2n2spozOiFstKqMVSRESkCctJhr2/mEEz7RDcucp20fWvroP9\nK6DDsNIu89HNeikjdYXXkIKliIhIM2EYtqGyKA9ebA9FuScVcjBnlkePNYNmcFSz2v1HwbKGFCxF\nRESaqfwMWPNO6VJGWysuE9geuk6Akf9n16rVFwXLGlKwFBERETISStfLXAyHVkFJYdm1jiPh+m9t\nyxdkg5u3fetoB5q8IyIiIlJTfm3g3NvNoyAL9i83Q+aeJWa3+MlSD8Jb50C7Ic12KSO1WFZCLZYi\nIiJSqZJisBTbzhpf+y4sedS2XMsepeMyx0Kr3uDoaNdq1ha1WIqIiIjUFSfn8ltE+oRCxHkQv7Zs\nKaNj28xj5Yvg08psxTz3dmjZzf51tgO1WFZCLZYiIiJyVnJSypYy2vcrFOXYXr9+vrmt5AkWS4Nv\nydTknRpSsBQREZEaK8qHQ3/AntIJQPmZMGM/OLuVlVn8CBzeWLaUUUh0g1vKSMGyhhQsRUREpFYZ\nBqTHQUCk7bnXekBGfNm5gHZl4zIjBoGTi/3regoFyxpSsBQREZE6l58B39wCB1faLmV0grsfRI0y\nQ2a3ifXWkqlgWUMKliIiImI3BVnmFpInljLKS7W9HtIF7l1bP3VDs8JFREREGg83H+h6qXlYSiB+\nnTn5J2YxpOwtv2ZmQTZ8cgmccxv0ub5+6lwBBUsRERGRhsTRCSIHmceoZyB5H7ic0kq4fzkc2QS5\nqRU/o54oWIqIiIg0ZMEdy5/LPgau3uYs8gZEYywroTGWIiIi0qAVF4Kzq13eqrq5qGGvxikiIiIi\nFbNTqDwTCpYiIiIiUisULEVERESkVihYioiIiEitsHuwPHDgACtWrCA+Pr7C64mJiaxYsYKYmJhq\nPS8hIYHly5eze/fuCq8nJyezbNkytmzZctZ1FhEREZGq2W25oZiYGO644w4OHz5MeHg469evZ+LE\nicyZMwdHR0dyc3O58847WblyJR07dmTr1q307NmThQsX4u3tXeEz77vvPj7//HN69+7Nzp07GTp0\nKF988QUuLuaemp9//jl333033bt35+DBg3Tv3p3vv/8eT09Pe31sERERkWbDbi2Wx48fZ9asWezb\nt48VK1awZcsWvv32W+bOnQtATk4OV1xxBbGxsfz6668cPHiQAwcO8NZbb1X4vG+//ZaPP/6YTZs2\n8dtvv7Fnzx7Wr1/Pe++9Z32/O++8k3fffZc1a9awZ88e4uLieOmll+z1kUVERESaFbsFy/PPP5/z\nzz/f+rp9+/aEhoaSmJgIQEhICBMmTLBe9/b2pl27dqSlpVX4vLVr13LOOefQrl07APz9/RkzZow1\nqC5atAhPT08mT54MgK+vLzfddBPffPNNXXw8ERERkWav3nbeWb58ObGxsYwda7v35Z9//klSUhJr\n1qwhLi6O//73vxXeHxISQnx8PBaLBUdHMx8fPHiQvXv3ArB//37atWtnvQbQoUMH9u/fX+HzioqK\nKC4utr7Oy8ur0ecTERERaW7qZVb4li1buPrqq3nrrbfo0qWLzbXvvvuOd999ly+++IJBgwbh5eVV\n4TOmTJlCWloa1113HXPnzuWBBx5gw4YNFBUVAWZQdHd3t7nH3d2dwsLCCp83a9YsPD09rUdQUFAt\nfFIRERGR5sPuwXLdunWMGDGCZ599ljvvvLPc9ZdeeolffvmFQ4cOkZyczNSpUyt8TmhoKJs3byY8\nPJxvvvmGkJAQ7r77biIjIwGzRfPYsWM29yQlJdGyZcsKn/f444+Tm5trPVJSUmr4SUVERESaF7t2\nha9cuZLLLruM1157jRtvvNHmWlpaGgEBAWUVc3ama9eubNy4EQDDMPjpp5/o378/oaGhAPj5+fHi\niy8CUFxcTI8ePbjuuusAGDJkCNOmTePAgQO0b98egCVLljB48OAK6+bi4mKdTS4iIiIiZ85uwfLP\nP/9kzJgxXHPNNQQFBfHjjz8C5iSerl27smTJEj777DMuu+wyAgMDWb9+PW+//TaffPIJACUlJYwf\nP5558+Zx5ZVXAjBq1CimTJmCm5sbc+bMwcfHh2nTpgFwzjnnMH78eCZOnMhDDz3E5s2bWbx4MWvW\nrLHXRxYRERFpVuwWLJOSkhg+fDjHjx+3LgkEcNlll9G1a1euvfZawsPD+fLLL0lOTiYiIoLVq1fT\nt29fABwdHbn44otp1aqV9d65c+fyyiuvcPToUa655hpuv/12m3GVX3/9NW+++SYLFy4kJCSE1atX\n06tXL3t9ZBEREZFmxcEwDKO+K9EQ5eXl4enpSW5uLh4eHvVdHREREZF6U91cpL3CRURERKRWKFiK\niIiISK1QsBQRERGRWlFvO++Iae2BFAwDnBwdcHIERwcHnB0dcXQsPefggKOjA86ODrg5O+Hu4oi7\nixNuzo44ODjUd/VFRERErBQs69ltn6wnu6C46oIVOBEy3Z2d8HA1w6aXmzM+7s74uLvg7eaMr3vZ\nax93Z7zdzK/9PV0I9HLF39MFN2enWv5UIiIi0hwpWNazYovlrO/NL7KQX2QBimpUB283ZwK8XAj0\ndCXAy7Xsz9IjxNuNFr5utPBxJ9jbFWcnjaAQERGR8hQs69nMS7pRVGKhxGJgMQxKLAYlhkFJifmn\npfR1scWgoMhCQXEJeYUlZqgsLiG/qPTrIvPr7IISsvKLKCiufmDNLigmu6CY+NS8Kss6OECQlyvB\n3m608HWnhY9b2eHrTis/d8L8PQjxdsPRUV31IiIizYnWsaxEY1/HsrDYQnZBMVn5RWTlF5ceRdY/\n0/OKSMspJDXX/DMlp7D0dSGFZxBKK+Pi5EBLXzNktvb3sAbOMH/zz1Z+Hvi6O2ucqIiISCNQ3Vyk\nFssmytXZkUBnsyv7TBiGQW5hCak5haTlFpKSXcjxrAKSsvJJyiogKfOkr7MKKg2hRSUGCWl5JKRV\n3grq7eZMmL87EYGehAd6EnHSER7oibuLxn6KiIg0JmqxrERjb7G0B8MwyMwr5nh2PkmZBRzLyudI\nej6JGXkcSc/nSHoeR9LzyMw/u8lJLXzcbIJmRKAnEUHmny183NTaKSIiYifVzUUKlpVQsKw92QXF\nJKbncTg9j8SME4HT/DMhPZcj6fmUWM7sP0NPVyfaBnnRLsSL9sFetCs92gd74+fpUkefREREpHlS\nsKwhBUv7KS6xkJiRT1xqrs0RX/pneu6ZzXoP9HK1Bk0zbJoBtG2Ql7rXRUREzoKCZQ0pWDYcGXlF\nxJ8UNA+l5HIoOYeDyTkczcw/o2e19vcgqqU3US28iWrhQ4cW3nRs4Y2fh1o5RUREKqNgWUMKlo1D\nTkExh1LMkHnwuPnngeQcDhzPPqOxnS193Yhq4UPH0qAZ1cKbqJY+Zzz5SUREpClSsKwhBcvGzTAM\n0nKLOJiczYETgfN4DgeSszmYnENRSfX+sw/ycrUJm51a+hAd6kOQt1sdfwIREZGGQ8GyhhQsm66i\nEguxKbnsS8pi77Fs9h3PZu+xbPYfz672wvIhPm50DvUhujRodg71Jaqlt8ZwiohIk6RgWUMKls1P\nicUgIS2XfUnZ7E0yw+a+pCz2JWWTU1hS5f2ODtA22Ks0cPoSHepDl1Y+hAd4ahciERFp1BQsa0jB\nUk4wDIPEjHz2HMtiz7Esdh/NYneiGTgLS6pu4fR0dSKqpQ+dS1s3u7TypWsrXy2LJCIijYaCZQ0p\nWEpVikssHErJsQbN3UeziDmWWa0918Gcod4tzJeuYWbQ7NbajzA/dy38LiIiDY6CZQ0pWMrZyi4o\nNls2E7OIOZpZGjizqrUep5+HixkyTwTOMF86hHjj4uRoh5qLiIhUTMGyhhQspTYZhsGxzAJ2H81k\nV2IWO45ksDMxk4PJOVT1N9DV2ZHolj42rZtdWvni5eZsn8qLiEizp2BZQwqWYg+5hcXsSsxiZ2Im\nO49ksvNIBruPZlU5O93BAdoGedE1zJcerf3o0dqP7mF+GrcpIiJ1QsGyhhQspb4Ul1g4kJxjBs3E\nTHYcyWDHkcxqdaVHBHrSo42fwqaIiNQqBcsaUrCUhuTEzPRTw2ZCWtUThSKDPOneWmFTRETOnoJl\nDSlYSmOQkVvE9iMZbE3IYPvhDLYdziAuNbfK+04Omz1b+9GttZ/2SxcRkUopWNaQgqU0VifC5rbD\nGWxLOPOw2bO1Hz3b+NOjjR/emiAkIiIoWNaYgqU0JTZhszRwVhU2HRwgqoU3Pdv40yvcn95t/IkO\n9cHVWUsfiYg0NwqWNaRgKU3d2YRNV2dHurbypXe4P73CzZbNdkFe2rJSRKSJU7CsIQVLaY4ycovY\ndjiDLQnpbIlPZ0tCOscyC057j4+7M73a+NOzjZ/ZshnuT0tfdzvVWERE7EHBsoYULEVMRzPybYLm\n1oQMsvKLT3tPS183ep3oQg83x2v6umtykIhIY6VgWUMKliIVs1gMDqbksCXeDJmb49PZeSSTwpLT\nL+rePsSL3ieFzS6tfDVeU0SkkVCwrCEFS5HqKyy2EHM0i80nWjbj09l3PPu021W6OjvSo7UffcL9\n6RMRQJ8If1r5uePgoPGaIiINjYJlDSlYitRMdkEx2xIySrvP09kSn8Hh9NMv6N7S140+4QH0jvCn\nT2kXuqerljwSEalvCpY1pGApUvuSsvLZEp/Bprg0NsWZYzZzC0sqLe/k6EDnUB/6RPjTJ9xs1WwX\n7KVWTRERO1OwrCEFS5G6V2Ix2JuUxaa4dGvY3JuUfdp7/Dxc6B3ub4bNiAB6t/HXFpUiInVMwbKG\nFCxF6kdGXhFbE9LZFJfO5ngzcKblFp32ng4hXmbILA2c0S19cHbSxCARkdqiYFlDCpYiDYNhGMSm\n5LIpPq20ZTOdXYmZFFsq/9Xl4eJEzzZ+1klBfSMCCPFxs2OtRUSaFgXLGlKwFGm48gpL2H4kg81x\n6dbAmZiRf9p7IoM86RsRQN/IAPpG+NM51Bcn7RgkIlItCpY1pGAp0rgkZuSVBk2z+3xrQgYFxZWv\nrenl6kTvCH/6RQTQJzKAvuEBGqspIlIJBcsaUrAUadyKSizsTsxiY1waG+PS2BCbRkLa6Zc7imrh\nTd+IAPpFBtA30p/2wd7aB11EBAXLGlOwFGl6jmXmszG2LGhuP3z6HYP8PFzoWzpGs19kAL3C/fFy\n07qaItL8KFjWkIKlSNNXUFzC9sOZbIw1g+aGuDSOZxVUWt7RATqH+tIvsrRVMyKA8EAPraspIk1e\ngwyWq1atYs6cOcTGxhIVFcU//vEPunbtar2+d+9e3njjDXbu3ElYWBh33nkn559/fqXP279/P6+8\n8gq7d+/Gz8+PK664guuuu67a109HwVKk+TEMg4S0PLP7vDRo7krMouQ0M9CDvd3oF1nWqtm9tR/u\nLk52rLWISN2rbi6yW5/OV199xfvvv8+NN95IeHg4c+fOZcCAAWzcuJGoqCiOHDnC5MmTue2225g4\ncSKrV69m+PDh/PLLL1x44YXlnpeRkcH555/PiBEjePzxxzl06BD33HMPWVlZ3HXXXVVeFxE5lYOD\nA+GBnoQHenJZ79YA5BYWsyU+wyZspp+0rmZydgE/7zjGzzuOAeDi5EC3MD+bVs1QP/d6+TwiIvZm\ntxbLnJwcvLy8bM517NiRe+65h4ceeoiioiIcHR1xcir7P/2RI0fSs2dPXnnllXLP+/333xk2bBh5\neXm4uZnr002dOpVDhw7xww8/VHm9KmqxFJGKGIbBgeQcm7Gae5OyOd1v0tb+HvSNDKBfhD/92wbS\nOVQLuItI49LgWixPDZW5ubkcO3aMsLAwAFxcbJf5SE1NZc+ePZV2XUdHR+Pu7s66desYMmQIhYWF\nbNq0iZEjR1br+qmKioooLi62vs7LO/3sURFpnhwcHOgQ4k2HEG+u6h8OmLsFbY5PZ0NsmnVryuyC\nst8nh9PzOJyexw9bjgDg6epEn9Kljvq1DaRPhD++7lrqSEQav3qZvGMYBjfddBPbtm1j7dq1uLq6\nWq/ddtttbNq0ib179zJ16lRmzZpV6XN+/fVXJk+eTGhoKImJiYwbN46PPvrI2upZ1fWTPfXUUzz9\n9NPlzqvFUkTOVInFYM+xLGuL5sbYNA6l5FZa3sEBolv60L9tAP0jA+kXGUCbAE0KEpGGo0FO3gEz\nVN59992sXLmS5cuXExoaanN9x44dpKSksHnzZp5++mneeOONClstY2NjGTx4MJMmTeLiiy/myJEj\nPPHEE9x77708/PDDVV4/VUUtlkFBQQqWIlIrkrMLzJnnsWmsP5Ra5VJHLX3dSsdpBtI/MoCuYb64\nqPtcROpJgwyWJSUl3HzzzWzdupWlS5cSEhJy2vKPPfYYv/32G6tXry537bnnnuN///sf27dvt56b\nM2cOjz76KMeOHavyelU0xlJE6lJ+UQnbD2ewPjaN9YfS2BCbStpJk4JO5eHiRK9wP2uLZt8I7RQk\nIvbT4MZYFhYWMnnyZBISElixYgUBAQE215cuXUpQUBB9+/YFzFnfv/32G506dQLMUDp48GCee+45\nhg0bRuvWrYmPj+fQoUO0bdsWi8XCqlWraNOmDUCV10VE6pO7ixP92wbSv20gDC2bFLThUGmrZmwq\n+4/nWMvnFZWw9kAqaw+kWs91aultbdHs3zaAiEBPdZ+LSL2yW7B8//33+fbbb+nevTtjx461np80\naRIPPPAA7dq14/bbb2f//v0EBASwf/9+hg4dyssvvwyYv3T/+usvUlJSALjuuuv49ddf6dq1K1FR\nURw/fhxPT0++/PLLal0XEWlITp4UdPU55qSg1JxCNsamsT7WbNHckpBB4Un7n+85ls2eY9l8uS4O\nKFtTs39kIP3aBtA9zA9XZ3Wfi4j92K0rPDExkdjY2HLnW7VqRWRkpPX10aNHOX78OG3atCnXqrl2\n7Vo6depEYGCg9VxaWhpxcXH4+voSGRmJo6PtL9GqrldGXeEi0tAUFJew40gmGw6ZLZobYtNIzi6s\ntLybsyO92vjTr22AOQM9MoAAL9dKy4uIVKZBjrFsTBQsRaShMwyD2JRca4vmhtg09hzLPu09HUK8\nrC2a/SMDaBfspe5zEamSgmUNKViKSGOUkVvExjizRXP9oTS2JKSTX1T57PNAL1f6RgSULnWkLSlF\npGIKljWkYCkiTUFRiYWdRzKtrZrrD6WRlFVQaXlXJ0d6tPGjf2QAfSPNsBnk7WbHGotIQ6RgWUMK\nliLSFBmGQUJanrVFc0NsGjHHsk67JWW7YC/6lYbM/m0DaB/sjaOjus9FmhMFyxpSsBSR5iIzv4hN\ncelsOJTK+tg0Nsenk1tYUml5f08X+pZOBuofGUCvcH91n4s0cQqWNaRgKSLNVXGJhV2JWWbXeelu\nQYkZ+ZWWd3FyoFuYn7VFs29kAC183O1YYxGpawqWNaRgKSJS5nB6HusPpZZuSZnG7qOZWE7zr0dE\noKd1nGa/yAA6tfTBSd3nIo2WgmUNKViKiFQuu6CYzXHp1vU0N8Wlk11QXGl5Hzdnekf4l+5/HkDv\ncH983LUlpUhjoWBZQwqWIiLVV2Ix2H0007pT0PpDaRxOz6u0vKMDRIf60i+yNGxGBBIe6KE1NUUa\nKAXLGlKwFBGpmaMZ+WyMO7H3eRo7DmdQfJr+8xAfN+sOQX0jA+je2hc3Z00KEmkIFCxrSMFSRKR2\n5ReVsDUhgw0n7RSUlltUaXlXZ0d6tvazBs1+kQEEa01NkXqhYFlDCpYiInXLMAwOJuewITbN3C3o\nUBp7k06/JWXbIE9ryOwXGUBUC00KErEHBcsaUrAUEbG/jNwiNsanmWM1D5lrauYVVb6mpo+bM30i\nA6xd6L0j/PF2c7ZjjUWaBwXLGlKwFBGpf8UlFnYfzSrtPjePqiYFdQ71tbZo9osMoE2AJgWJ1JSC\nZQ0pWIqINEyJGXlsjE23jtXccSTztJOCWvi4WUNm38gAuof54ersaMcaizR+CpY1pGApItI45BWW\nsDUhnQ1xaWw4lMaGuDTSq5gU1KuNnzlWM8IMm5oUJHJ6CpY1pGApItI4GYbBgdJJQSeC5r4qJgW1\nC/aiT4Q/fSIC6BPuT+dQH5yd1KopcoKCZQ0pWIqINB3puYVsiksvXVMzlS3xGaedFOTh4kTPNn5m\n0Izwp0+Ev/Y/l2ZNwbKGFCxFRJquohILuxOzzPU049LZcCiVIxn5p72nTYCHtUWzT4Q/3TRWU5oR\nBcsaUrAUEWlejmbkszk+jY1x6WyKS2NrQgYFxZZKy7s6O9I9zNfaqtk3IoBWfu6agS5NkoJlDSlY\niog0bydaNTfGpbEpLo1N8enEpuSe9p6Wvm70CQ+wjtfs0doPD1dtSymNn4JlDSlYiojIqVKyC9gU\nl86m+DQ2xaWzJT6dnMLKx2o6OzrQpZWvdZxm34gAIgI91aopjY6CZQ0pWIqISFVKLAZ7k7LYGJtu\nbdWsagZ6oJerdZxmr3B/erb2x8/TxU41Fjk7CpY1pGApIiJnIyOviM3xpUGzdLxmZn7xae9pF+xF\nrzZ+9Ao3w2bXVr64u6gLXRoOBcsaUrAUEZHaYLGY62qeaNHcFJdOzNFMTrNZEM6ODnRu5UOvNv7m\nEe5PxxbeODmqC13qh4JlDSlYiohIXckuKGb74Qy2xKezJSGdLfEZp90DHcDT1YkerUtbNdv40yvc\nj9b+2gdd7EPBsoYULEVExJ6OZxWwNSG9NGxmsCUh/bRbUwIEebnaBM1ebfwJ8HK1U42lOVGwrCEF\nSxERqU+GYRCXmsvm+HS2Jpitm9uPZJBfVPnamgARgZ70aONHj9Z+dA/zo3trX/w9FTalZhQsa0jB\nUkREGpriEgt7jmWXdp+nszk+nT3Hsk47XhMgPNDDDJqlYbNHaz+1bMoZUbCsIQVLERFpDHILi9lx\nJLOsCz0+nbjU0y/kDtDa3wybPdr40S3Mlx6t/QjydrNDjaUxUrCsIQVLERFprDJyi9h+JIPthzPY\ndtj881AVuwYBhPm5m62arf2sLZwhPgqbomBZYwqWIiLSlGTkFbHzSKZN2DyQnFPlfS193ejSytd6\ndG3lS7tgLy191MwoWNaQgqWIiDR1Wflm2DwRNLcfyWT/8WyqSgbuLo5Et/Sha1hZ4Owc6oOPu3YQ\naqoULGtIwVJERJqjnIJidiZmsi3BDJs7EzPZl5RNcVUzhDBnpHdp5UPXVn50aeVDl1a+tAnQWptN\ngYJlDSlYioiImAqKS9iXlM2uxCx2JWay80gmu45mVrnOJoCPuzPRLX2IaulDdEtvOrX0oVOoD8Ga\nKNSoKFjWkIKliIhI5QzD4GhmvhkyEzPZlZjFzsRMDqXkVNmVDhDo5UqnE0HTenhrzc0GSsGyhhQs\nRUREzlxOQTExx7KsgXP30Sz2HMsiK7+4Wve38HEjOtSHqBY+RLX0pkOIN+1DvAjyclWXej1SsKwh\nBUsREZHacaJ1c8+xbPYczSLmWBZ7j2Wx51g2eUUl1XqGr7szHVp40z7YDJodQrzoEOJNRJAnbs5O\ndfwJRMGyhhQsRURE6pbFYnA4PY+Yo1nsScpiz1EzbO47nk1h8em3rjzB0QHCAz3Nls1gL9qFeBEZ\n6EVkkCet/NxxdnKs40/RPChY1pCCpYiISP0oLrEQm5rL/qRsDiTncOB4NvuPm3+mVWPC0AnOjg60\nDvAgItCTiEBPIoM8iQj0Ml8HeeLt5lyHn6JpUbCsIQVLERGRhic1p5ADx7M5cDyH/cnZ7E/K4UBy\nNnEpudVaEulkQV6uhAd6EubvTis/D8L8PQjzcyfM34NW/u4Ee7nhqIXgAQXLGlOwFBERaTyKSizE\npeYSm5JDbEoucam5xKXkEpuaS3xqLgXV7Fo/mauTI6F+7oT5uxPmZ4bNEG83QnzcCfFxsx5erk5N\nfmJRgw2WSUlJxMbG0q5dO4KDg8tdz8jIYM+ePYSFhdG6desqn5eSksKBAwfw8/MjKiqqwh/soUOH\nSE1NpUePHri4VG9XAAVLERGRpsFiMUjKKrAGz/hUM3DGpuRyOD2P41kFNXq+h4sTwT6upaHTjSBv\nNwI8XfD3cMXP0wV/Dxf8PV3x83DB39MFPw8X3F0a14SjBhcsDxw4wNSpU9mwYQPh4eHs3LmTm266\nibfeegsHBwfy8vJ46KGHmD9/Pm3btmX37t1ceOGFfPXVV5V+gCeffJJXX32Vrl27cvjwYYKCgvjp\np58IDw8H4OjRo1x77bVs3bqVDh06kJOTw1dffUWPHj2qrK+CpYiISPNQUFzCsYwCjmTkcSQ9j8SM\nfA6n55GYnseR9HyOZORVe7mk6nJzdsTbzRlPNyc8XUr/dHXC09XZ+qe7iyMuTo44OTrg4uiAs5Mj\nzk4OuDia55wcHXAonbw0LLpFrdbvVA0uWP7222/k5+czZswYAHbt2kW/fv349NNPufLKK0lKSuKX\nX35h8uTJODo6kpaWRq9evZg6dSrTp08v97ydO3fSrVs3Vq9ezaBBgygqKmLEiBFERUXx0UcfATBo\n0CDatm3Lxx9/jJubG3Fxcezfv59hw4ZVWV8FSxERETkhK7+Ioxn5HM8u4HiWeSRnF5pfn3QuNaeA\nMxzqWWOjurbkgyn96/Q9qpuL7DYd6sILL7R53aVLF1q3bk1sbCwALVq04Prrr7deDwgIoFOnThw7\ndqzC56WlpeHg4ECfPn0AcHFxoWfPnhw5cgSAVatW8ffff/P9998TExODi4sLUVFRRERE1MGnExER\nkabMx90FH3cXolr6nLZcicUgLbeQjLwi0nOLyMgrJD3X/Do9r4iM3ELSS6/lFZaQU1hs/TO3sITc\nwhJKzjCZNqThnfU2z/7PP//k4MGDjBo1yub8xo0bSUlJYc2aNezZs4d33323wvsHDRrE2LFjuemm\nm7jxxhuJjY1l4cKFzJs3D4D169fTsmVLrr32WpKSksjMzMTV1ZX58+fTvXv3cs8rKiqiuLismTsv\nL68WP62IiIg0B06ODgR7u531XuiGYVBYYiGvsIT8IgtFJRaKLQbFJRaKSgyKLeafJRbDGkADvRrO\nNpj1Eix3797NxIkTefHFF8uNd5w9ezabN29mz549XH755RVO8AFwdHRk/PjxPPvssxw8eJCjR49y\nzjnnWFskc3JyOHLkCP/85z+57777sFgs3HDDDdxxxx2sXr263PNmzZrF008/XfsfVkRERKSaHBwc\ncHN2arS7Cdl9VvjWrVsZNWoU06dPZ9q0aZWWy8/P5+KLLyYsLIzPPvus3PVvv/2WW2+9la1btxIR\nEYFhGNx5553s2rWLVatW8f7773PXXXeRnp6On58fAD/++COXX345+fn5ODnZ/sAqarEMCgrSGEsR\nERFp9qo7xtKu+xytW7eO4cOH83//93/lQmV2drbNa3d3d/r3709cXBxgNg3/9ttvHD9+HIC9e/fS\nunVrawulg4MDAwcOZO/evQAMHjwYgMOHD1ufefjwYQIDA8uFSjDHaHp4eNgcIiIiIlJ9dusK//vv\nvxk5ciRXXXUVXbp04bfffgOgTZs2dOzYkfnz5/Pjjz9y2WWXERgYyPr163nzzTetYyxLSkoYNmwY\n8+bN48orr2TcuHE89dRT3H///YwZM4ajR4/y1FNPccUVVwDQvXt3rrrqKqZMmcJjjz1GRkYGM2fO\n5KGHHrLXRxYRERFpVuzWFT537twKJ+JceeWV3HfffQD8/PPPfPHFFyQnJxMREcHkyZMZMmQIYAbL\nESNG8PTTTzN06FAANm3axIcffsjBgwfx9fVl+PDh3HLLLdZF0AsKCnjjjTdYsWIFfn5+TJgwgWuu\nuaZa9dVyQyIiIiKmBreOZWOjYCkiIiJiapBjLEVERESk6VKwFBEREZFaoWApIiIiIrVCwVJERERE\naoWCpYiIiIjUinrbK7yhOzFZXnuGi4iISHN3Ig9VtZiQgmUl8vPzAQgKCqrnmoiIiIg0DPn5+Xh6\nelZ6XetYVsJisZCeno67uzsODg71XZ0G48Qe6ikpKVrfs5HRz65x0s+tcdLPrXHSz61yhmGQn5+P\nv78/jo6Vj6RUi2UlHB0dCQwMrO9qNFjaT73x0s+ucdLPrXHSz61x0s+tYqdrqTxBk3dEREREpFYo\nWIqIiIhIrVCwlDPi7OzM//3f/+HsrFEUjY1+do2Tfm6Nk35ujZN+bjWnyTsiIiIiUivUYikiIiIi\ntULBUkRERERqhYKliIiIiNQKBUup1GuvvUa/fv3o3r0706dPP+32lo8++iht27albdu2dOvWrcbP\nk7O3cOFCLrjgAjp37swNN9zAkSNHzrr8p59+av25njgeffTRuv4ITVpxcTFPPfUUvXr1onfv3jzz\nzDOUlJScdfkzfZ6cvY8//piBAwfSpUsX7rnnHtLT08+6/AsvvFDu79Zrr71Wp/Vvrn777TdGjhxJ\ndHQ0V155Jfv27au07C+//GLzM1m7dm2NntcsGSIVePXVV43g4GDjhx9+MP7880+jV69exnXXXVdp\n+eTkZOPgwYPGO++8Y3h5edX4eXJ2fvvtN8PNzc147733jPXr1xsTJ040unfvbhQVFZ1V+TfffNMY\nMGCAcfDgQeuRnJxsz4/U5EybNs1o166dsWLFCmPZsmVGZGSk8cgjj5x1+TN9npydL7/80vDy8jK+\n+uor46+//jKGDh1qjBw58qzLP/LII8aECRNs/m6lpaXZ4ZM0L9u3bzfc3d2NF154wdi4caNx6623\nGm3atDGysrIqLJ+Tk2McPHjQ2L17twEYK1asqNHzmiMFS6lQmzZtjNdee836euXKlYajo6ORmJh4\n2vvmzZtXYbA82+fJmZkwYYJx/fXXW1+np6cbbm5uxk8//XRW5d98801j6NChdVrn5iQ3N9fw9PQ0\nvvnmG+u5L774wvD29jby8/PPuPyZPk/OXv/+/Y1HH33U+nrPnj0GYGzZsuWsyj/yyCP6n2s7uOuu\nu2wCfVFRkREcHGx89NFHp70vLy+vwmB5ts9rTtQVLuUcPXqUhIQEzj//fOu5wYMHA7Bx48Z6f55U\n7u+//7b5Pvv5+dG9e3fWr19/1uW3bt1Kt27dGDhwII8++miV3X9SuR07dpCbm2vzPR8yZAjZ2dnE\nxMSccfkzfZ6cneLiYjZv3mzzfY6KiqJly5YV/t2qbvlly5bRpUsXzj//fJ599lkND6oDp/6Oc3Z2\nZsCAAZX+TrT385oirQDajEydOpUffvih0usPP/ww9913H2lpaQA2e6U7Ojri7+9PamrqGb9vbT+v\nufnwww+ZNWtWpddHjRrFBx98AJjf61P3uA8KCqr0+1xV+RtvvJFLLrkEi8XC/v37efzxx1m1ahUr\nV67EycmpJh+rWaro70JQUBBAhT+jqsoXFRWd0fPk7GRlZVFcXFztv1vVKf/II49w1113UVJSws6d\nO5k+fTqbNm3i22+/rbsP0gyd6e9Eez+vKVKwbEZmzpzJtGnTKr0eEBAAlG0yn52dbXM9OzsbLy+v\nM37f2n5ec3PNNddw0UUXVXr9xPf3xNenfp+zsrIq/T5XVd7HxwcfHx8A2rdvT+fOnYmIiGDr1q30\n6dPnrD5Pc3by34UTf9+ysrIAKvwZVVW+sLDwjJ4nZ8fDwwMo/zussr9b1SkfEBBg/Zl16NCB4OBg\nzjvvPI4fP05ISEitf4bmqrLfcSe+9/X9vKZIXeHNSEhISLlZiCcffn5+AISHh+Pr68u2bdus98bE\nxFBYWEjXrl3P+H1r+3nNja+v72l/bi1atLCW7datm833uaioiJiYmEq/z2daPiAgAAcHB3Jycmrp\n0zUvnTt3xtHR0eZ7vm3bNpycnOjUqdMZlz/T58nZcXd3p0OHDjbf55SUFBITEyv8u3Km5aGs1Vl/\nt2rXqb/jALZv337W//bU9vOapPoe5CkN091332307t3bSE1NNQoLC41JkyYZ5557rvX6Aw88YNxy\nyy3l7qts8k5Vz5Pa8dFHHxlBQUHGrl27DIvFYjz//PNGQECAkZ6ebr3ev3//apd/8sknjYMHDxqG\nYU4kufPOO41WrVoZ2dnZdv9sTcX48eONkSNHGrm5uUZOTo4xbNgwY+LEidbr11xzjfHYY49Vu3xV\n16V2PP3000a7du2Mw4cPG8XFxcbUqVON9u3bW1dQmDVrljF+/Phql58+fbpx9OhRwzAMIy0tzbj8\n8suNrl272v+DNXE//fST4eHhYfz111+GYRjGnDlzDHd3dyMuLs4wDMP4/vvvjcjIyHL3VTZ5p6rn\niWaFSyWysrKMyy67zHB1dTU8PT2Nfv36Gfv377dev+6664yLL77Y+vqTTz4xIiMjjZCQEMPBwcGI\njIw0IiMjjZycnGo9T2qHxWIxHnroIcPNzc3w9fU1IiIibH4xvvrqq0bLli2rXX7hwoVGdHS0ERQU\nZLi5uRmDBg0y1q9fb8dP1PQcPXrUGDp0qOHu7m64u7sbw4YNM5KSkqzXhw4datx5553VLl/Vdakd\nBQUFxpQpUwxXV1fD29vb6Ny5s7F582br9WnTphn9+vWrdvk5c+YY4eHhRkhIiOHq6mqMGjXK2LNn\nj10/U3Mxa9Ysw9PT0/Dz8zNatGhhzJ8/33rtyy+/NE5uY4uPjzciIyONiIgIAzBatmxpREZGGt9/\n/321nieG4WAYhlHPjabSgGVkZFBYWFhuzE9ycjIWi8XaDZuVlUVKSkq5+yMjI3FwcKjyeVK78vLy\nSE9PJzQ01Ob7n5mZSUZGBuHh4dUqf0JqaipeXl64ubnVed2bixOD/U+dCHD06FFcXFysk3CqKl/d\n61I7srOzycnJoWXLljbn09LSyM/Pp1WrVtUqf0JycjL+/v44O2vKQ10qKCggNTWVFi1a2Ew8zMnJ\n4fjx47Rt2xYwZ/QnJCSUuz8kJMRmPG1lzxNQsBQRERGRWqHJOyIiIiJSKxQsRURERKRWKFiKiIiI\nSK1QsBQRERGRWqFgKSIiIiK1QsFSRERERGqFgqWIiIiI1AoFSxERERGpFQqWIiIiIlIrFCxFRBqg\nGTNmMGHCBOvrdevW0aFDB1avXl1/lRIRqYK2dBQRaYCOHj1KVFQUCxYsoGXLlowYMYJ3332XiRMn\n1nfVREQqpWApItJAPfvss8ydO5e0tDSef/55rr/++vqukojIaakrXESkgRozZgzbt29nwoQJCpUi\n0iioxVJEpAHav38/Q4cO5cILL2TFihXs2bMHLy+v+q6WiMhpqcVSRKSBSUhIYOTIkfzzn//ks88+\nIywsjBdffLG+qyUiUiW1WIqINCBJSUlccMEFTJkyhcceewyAFStWcMkll7Bnzx5at25dzzUUEamc\ngqWISAOSn59PTk4OQUFBNudTUlLw9vbGzc2tnmomIlI1BUsRERERqRUaYykiIiIitULBUkRERERq\nhYKliIiIiNQKBUsRERERqRUKliIiIiJSKxQsRURERKRWKFiKiIiISK1QsBQRERGRWqFgKSIiIiK1\nQsFSRERERGqFgqWIiIiI1AoFSxERERGpFQqWIiIiIlIrFCxFREREpFYoWIqIiIhIrVCwFBEREZFa\noWApInKWDMPgzTffZP/+/Wd034YNG/j000/rqFZnJyUlhZdeeonU1FSOHj3KSy+9xN69e8uV+/jj\nj3nppZcoLi62OZ+ens5LL73E33//ba8qi0gDpGApInKWPv74Y1544QVat259Rve1atWKu+66iz//\n/LOOanbm5s+fz/PPP4+fnx+pqalMnz6dtWvX2pTZs2cPt9xyC9OnTyctLc3m2uzZs5kxYwa+vr72\nrLaINDAKliIiZ6GoqIgnnniChx9+GHd39zO6NywsjJtuuolHHnmkjmp35hYsWMD48eNxcnLC398f\ngMzMTJsyb7zxBl5eXgBkZGRYz1ssFt555x1Gjx5NdHS03eosIg2PgqWINFvvvfceq1atIj09nblz\n5/L222+zceNG6/X9+/cze/ZsPvnkk3ItdN988w3Hjx/nuuuuszn/66+/8vLLL1NQUGBzftGiRbzy\nyitkZ2cDcOONN/Lnn3+yadOmOvp0tjZu3MiHH37InDlzOHTokM217Oxsfv31VyZMmACAn58fYBss\nMzMz+eSTT7j33nvLXfvxxx85ePAg999/f91+CBFp8BQsRaRZys7O5p577uHVV1/lggsuYOnSpcyd\nO5d+/foxb948HnroIaZMmcL69et54okn6Nu3rzUUAnz55ZcMHDiQkJAQm+cGBAQwffp03n//feu5\nhQsXcumll+Li4oK3tzcAAwYMoEWLFnz55Zd1+jkTEhK44IILGDduHMuXL+fXX39lyJAhfPLJJ9Yy\nixcvxsnJiVGjRgHg5eWFs7OzTXj873//i6OjozU8ntxi+eabb9KpUydGjx5dp59FRBo+5/qugIhI\nfdi8eTOGYZCUlMQff/yBr68vJSUltGvXjilTpvDYY49Zx0CuWbOG8847j5UrVzJu3DgMw2DVqlXc\neuut5Z7bt29frrrqKv79739z2223sXHjRiZNmsQ///lPpk6dalN2wIABrFixotI6fvHFFxw5cqTK\nz3LttddWOM4zIyODiy66iIiICHbt2kVAQAAAqampxMXFWcstWLCAUaNG4eHhYT3n5+dnDZaGYfD2\n229z6623EhoaiqOjo/Xarl27WLZsGW+99RYODg5V1lVEmjYFSxFpljZv3gzAhx9+aJ1w4uTkREhI\nCAEBATzxxBPWsi1btgTMcZUAx48fJz09nYiIiAqf/eyzz9K1a1emTp3K/PnzueGGG3jmmWfKlYuI\niGDlypWV1jElJYWjR49W+VlO1OtU//rXv0hKSmLNmjXWcZMAgYGBBAYGWu9dtGgRr732ms29JwfL\nn376iQMHDjB16lQcHBzw9va2tli+9dZb+Pn5ceONN1ZZTxFp+hQsRaRZ2rRpE126dKFLly7WcxaL\nhZiYGKZPn27T+rZ7924Aa9n09HSASmdAR0VFMWXKFP773/8yYcIE3n333QrL+fn5kZGRgcViwdGx\n/MikU1s4z0RxcTFz5szh5ptvtgmVp/rtt9/IysrikksuqbBuYE7aufTSS2nXrh1gfu7MzEwyMzP5\n9NNPuf32261d/CLSvClYikiztGnTJs455xybc3v37iUnJ6fc+U2bNuHl5UXHjh2BskCZlZVV4bP3\n79/PTz/9BEB4eDhOTk4VlsvKysLb27vCUAk16wo/cOAAaWlpDBgw4LT3LliwgCFDhhAUFGRz3t/f\nn8zMTHbt2sXSpUv57bffrNd8fX3JyMhgzpw55Obmct9991VZRxFpHhQsRaTZKSoqYseOHUyZMsXm\n/Inu8d69e5c737NnT2sADAkJwcvLi4SEhHLPPnr0KKNGjaJr167ccsstvPzyyzz44IPW1r6TJSQk\n0L59+0rrWZOu8BPnqhr3+P333/Pwww+XO+/n50dsbCxvvPEGvXv3ZujQodZrvr6+pKen88knnzB+\n/PjTfgYRaV4ULEWk2dmxYweFhYX06dPH5vzmzZsJCQkhLCys3PmLLrrI+trJyYnBgwfz119/2ZTL\nzMxk7Nix+Pr6smDBAhwcHPjggw+YOXMmn332Wbl6rFu3jiuuuKLSetakK7xjx454eXnx888/c9VV\nV1nPp6SkUFJSQosWLfj7779JSEiwLjN0Mj8/P44cOcJnn33GW2+9ZXPN19eX+fPnc+DAAd57772z\nrqOIND1abkhEmp0Ta0ee2jK5ZcuWcueys7PZv39/ufNXX301a9eutY63LCgo4NJLLyUjI4PFixfj\n6+uLj48Pjz76KF988QVbt261uX/btm0cPnzYJvTVJjc3N15//XU++eQTLr30Uv71r39xyy23cPHF\nF+Pq6gqY3eC9e/cmMjKy3P3+/v4cO3YMLy8vrr32Wptrvr6+HDhwgO7duzN8+PA6qb+INE5qsRSR\nZic0NJSnnnrKuhD4CUOHDqVTp04257KysnjooYcYMWKEzfnJkyczY8YMvvrqK+666y5WrVpF//79\nmT17NqGhodZy9957L8ePH2ffvn307NnTev7TTz+lV69enH/++XXwCU233norQ4YM4ZdffiE5OZlx\n48bx/vvv4+LiApjB8uqrr67w3jFjxuDs7MzAgQNxc3OzuXbllVcSGRnJmDFj6qzuItI4ORiGYdR3\nJUREGqPXX3+dN998k927d+PsXP3/T09JSaF9+/Z89dVXjB07tg5rWLm8vDxmzpzJXXfdRYcOHeql\nDiLS9ChYioicpeLiYv7v//6PKVOmnNEe2X/++Sd//vknM2bMqMPaiYjYn4KliIiIiNQKTd4RERER\nkVqhYCkiIiIitULBUkRERERqhYKliIiIiNQKrWNZCYvFQnp6Ou7u7lVuiSYiIiLSlBmGQX5+Pv7+\n/tbtbSuiYFmJ9PR0goKC6rsaIiIiIg1GSkoKgYGBlV5XsKyEu7s7YH4DPTw86rk2IiIiIvUnLy+P\noKAgaz6qjIJlJU50f3t4eChYioiIiECVwwM1eUdEREREaoWCpYiIiIjUCgVLEREREakVCpYiIiIi\nUisULEVERESkVihYioiIiEitULAUERERkVqhYCkiIiIitULBUkRERERqhYJlQ1BcABZLfddCRERE\npEYULBuCDZ/AK13gh/thz89QlFffNRIRERE5Y9orvCGIWQTZR2HDx+bh4gkdhkP0WIgaDd4h9V1D\nERERqYGHH36Y7OzscudfffVVPDw86vS977rrLmbOnElYWFidvg+Ag2EYRp2/SyOUl5eHp6cnubm5\ndfsDNwz4+XHYuRAyEyoo4ABtzjFD5rm3g5tP3dVFRERE6kRwcDCXXnop5557rs35W265BVdX1zp9\nbwcHB7Zt20b37t3P+hnVzUVqsaxvDg4w5t8wehYc3QYxi80WzMTNpQUMSFgHSTth0L229xqGeb+I\niIg0eMOHD+f6668vd37t2rXMnTuX5557Dnd3dwBmz55Nfn4+9913HwCPPPIIGRkZuLi4EBUVxY03\n3oifn5/Nc5YvX87KlStxdHTkhhtuoF27dsycOROAZ555hoCAAIYNG8Y111xTZ59RYywbCgcHaNUT\nLnwE7vwdHtwJF78CHS8CJ1eza9zZray8YcAHF8L8O2DHd5CfWW9VFxERkbN3zjnnsGnTJqZOnQrA\n0qVLmTZtGiNHjrSW6datG7179yYqKooVK1bQt29f8vLK5mRMnTqVyZMnU1JSgsViYeLEiRw7dowu\nXboAEB0dTe/evWndunWdfhZ1hVfCbl3h1VGQBXnp4B9edu7YTnh3UNlrRxdoNwSix0GnMbZlRURE\nmrjbPvmb2JRcu75nZJAns288p1plg4OD6dWrF1FRUdZzQUFBzJo1C4DExER69+7NtGnTeOmll3jt\ntdeYPHlypc+74IILuPnmm7n55ptZv349gwcPZvv27dbnZ2Rk4OTkhLe3t7rC5RRuPuXHVuYkQWAH\nSN1vvrYUwf7l5rHoYQjtYYbMrhOgZVe7V1lERMSeYlNy2ZtUfnJMQxIZGUnv3r2tr318yv5tb9Wq\nFR999BHjx4/npptuKhcq4+LimDdvHvHx8eTn55OSksKePXsAWLduHV27drUJrad2k9uLgmVj1f5C\n+MdGSN5rjsmMWQzxf4FRuh7m0W3mUVwAFz1dr1UVERGpa5FBng3+PSsbY3nCvHnzaNGiBevWrSM3\nNxdPT/P5+/fvp3///lx++eX06NEDDw8PduzYQVZWFgCurq4UFBSc/QepRQqWjV1wFATfD4Pvh5xk\n2PuLGTT3LYeiHLPV8mR7l8LGTyD6YogaBV5B9VNvERGRWlTdLumG6qOPPmLp0qVs3ryZG264gXvu\nuYePP/4YgD///JM2bdrw3//+FzC7pV977TXrvUOHDuXee+9l+fLlDB8+HIDdu3cTEhJCUFAQXl5e\n5ObaZ5iAxlhWokGNsTwbRflw6A/oMAwcncrOL7wXNn1ufu3gCOEDzaWMosdBcMf6qauIiEgTV9EY\nS4CZM2eSnJzM+eefzw8//MDQoUM5duwYvXv35t///jc333wzsbGx9O7dmz59+hAeHs7q1atxcXFh\n+PDhvPXWWwC8/fbbPPLIIwwbNgxnZ2fi4+NZtmwZ/v7+XHbZZRw6dIiBAwcyfPjws5oVXt1cpGBZ\niUYfLCvz2eXmOMyKBEWVhczwc20DqYiIiJy1Tz75xGYW9wnXXHMNf//9NxaLhTFjxljPb968mW3b\ntnHDDTcAkJyczLJlyyguLmbIkCHEx8cDcP7551vvSUhI4K+//sLNzY0RI0ZY80thYSG//PILR44c\noWvXrjb3VJeCZQ012WAJkB4HMUvMLvNDf5gTf041LQZ8Qu1fNxEREWlw6mxWeElJCfHx8QQEBFRr\nxtHpysfExHAi1wYEBNCyZUub67t37y73vOjoaBxOWRQ8OzubzMzMSrcqqup6s+MfAQPuMI/8DNj3\nqzn5Z+/P5uvW/cqHyqUzwT/SbNH01fdRREREyjujFssVK1Zw/fXXU1hYSGZmJjfddBPvvPMOTk4V\nd5lWVb579+4UFxeTkJDATTfdZB0nYK2cgwPt2rWz2epo69at1teZmZnceeedfPfdd7Ro0YLQ0FC+\n/PJLOnToUK3rp9OkWywrU1IEcWvNFswOw8vO56bCfzqUzThv1dvsLo8eay5rpN1/REREmrRab7HM\nysriqquu4uGHH+bRRx8lLi6OgQMH0qNHD+t2Q2dafvv27QBccskllb7v999/X+mCnldffTUODg4k\nJiYSEBDAli1b2LVrlzU4VnVdTuFUusj6qRL+Nnf6OSFxs3n89m/wCy8dlzkWIs8H57rd71REREQa\nrmq3WH799dfcfvvtJCUl4eZmbi34xBNPsHTpUv76668alb/kkkto27ZthS2Wf/zxBxEREbRu3RpH\nx7IdKP/++28GDhxIXFwczs7OuLq6EhAQUO3rVWmWLZank50Ee342u8z3L4fi8gOQ6TUZLn/X/nUT\nERGROlXdXFTtvcJ37dpFx44drSERoGvXruzatatWylckOjqa2267jXPPPRdfX1/+9a9/Wa+tWbOG\nsLAwpk+fTs+ePYmMjOS8887j0KFD1bp+qqKiIvLy8mwOOYl3C+h7A1z7BTxyEK6dC31vBO+TxsV2\nHGF7z/EYWP0WpB6wb11FRESkXlQ7WObl5eHt7W1zzsfHp9IFN8+0fEV2797Nrl27SExMZMmSJfzn\nP/+xLhaamZlJQkICnTp14tixYyQlJREQEMDtt99ereunmjVrFp6entYjKEgLh1fKxQOix8Clb8BD\nu+G25TBkGnQcaVtu+3z45XF4ow+8PQCWPQXx68BSUi/VFhERkbpV7WAZEBBASkqKzbmUlBQCAwNr\npXxVzj//fK666ioWL14MYH3OP/7xDwDc3d258847WbVqFRaLpcrrp3r88cfJzc21HqfWXSrh6Aht\n+sGImeDhb3tt789lXx/fDX+8Ch9dBC9Hmwu17/4JCnPsWl0RERGpO9UOlueeey67d+8mKSnJem7l\nypWce+651te7d++27ltZnfKnU1xcXO5cUlKSdcP2AQMGAJCWlma9npaWhpeXF46OjlVeP5WLiwse\nHh42h9TQDQvgio+g+5XgdtJSUznHzd1/vpoML7aHlP31VkURERGpPdWeFT506FD69evHlClTmDlz\nJps3b+aLL76wtiAWFxfTpUsX5s2bx5VXXllleYDY2Fjy8vLIyckhPT2d3bt34+vrS1hYGJ9//jlr\n167lyiuvxMfHh/nz5/PLL7+wcuVKAPr168fIkSO54447eOaZZ8jIyOCpp56ydnVXdV3swMMfelxp\nHsWFELfanPwTs8hcpB3AIwAC2tnet+tHCGwPLbpoKSMREWk2SkpKeOmll1i5ciUXXngh06dP55df\nfuG9994jMzOTZcuW1XcVq3RG61geP36cJ554grVr1xISEsIDDzxgXSqopKSEbt268cYbbzBq1Kgq\nywNceeWV1iWHThg9ejSvv/46hmHw6aef8sUXX5CWlkanTp24//77Oeecsk3mMzMzefrpp1mxYgV+\nfn5MmDCB++67z7pOZlXXT0ezwuuQYUDSTjNgOrnC4PvLrpUUmWtm5meULsheul5m5HnmckgiIiJN\n1DvvvMNHH33EM888Q9u2bQkNDSUiIoI33niDiIgIhg4dytixY/n000/tvumLtnSsIQXLenJwJXwy\nvvx5Nz+IusgMmR1Hlh/PKSIi0gi8+OKLLF26lC+++IKQkBCba5dffjkXXHABDz74IAALFy5k5syZ\nbNmyBQCLxcLy5csZPHiw3bNJrS83JGIXrfvBNf+D3teDZ3DZ+YIM2P4NfHur2aL58+P1V0cREZGz\nkJuby3PPPUdKSgpz5swpd/348ePWuSQVvXZ0dGTkyJENusFLLZaVUItlA2ApgYT1Zpd5zGJIjim7\ndtEzMPgfZa9zUyHtILTqY85UFxERaWD++9//Mm/ePB599FFuu+029uzZg0PpXIKrr76an3/+mdat\nW1u7uQ8fPkxiYiL9+/e3ec6JrnCLxcKoUaN47rnn+Prrr9m7dy89evTgkUcesS75aLFYmD17Nr//\n/jsAl112GVdfffUZ173Wt3QUsTtHJ4gYYB4XPW3OHo9ZbB7R42zL7voBfvgHeIeaa2xGj4N2F5hr\nboqIiDQAH3zwAf/6178YOnQovr6+LF++nBEjzM1Fpk6dyvbt2xk7dixjx44F4Mcff+TXX3/l0Ucf\nBczNXMaNG2ddE9xisfDrr79y3XXXMW3aNAYNGsTTTz/NsWPH+OCDDwCYOHEix44d4/7776e4uJh/\n/vOfJCQk8NBDD9XJZ1SwlMYjqAOcd595nCqmdLWB7KOw4WPzcPGEDsPNcZlRo8E7pPx9IiLSdKz7\nEP6eXXW5ETOh88Vlr3f/BL/+q/LyJ5xzG5x7dqvLbNmyhezsbOsE5wcffJD333/fGiyHDBmCr68v\nXbp0YeRIc8ORffv2sX79euvr/Pz8Cp/9/PPPM3HiRMDsLj8xRnPlypUsX76chIQEfH19AYiIiGDi\nxIkKliKnNfBu8GtjBszMBPNcUS7s/tE8cIDwATDhHTOgiohI05OTbG7IUZX8zPKvq3NfTvLZ1Qt4\n//33ycrKsobEoqIi1qxZQ1JSEi1atDjr5wJ06dLF+nVwcLB1De8Tk35OhM4T75uSkkJKSkqd7DKo\nYClNQ/uh5jHuP3B0a9l6mYlbSgsYcGQT+ITa3pcWC76twUl/FUREGj2vYAjpXHU5d9/yr6tzn1dw\n1WUqkJOTw9dff81nn32Gi0vZ0nmffPIJc+bM4ZFHHjmr557gUMmaz35+fgQFBVm70k926rbbtUX/\nmkrT4uAArXqZx4WPQkYC7FliBk0XD3D1si3/v6sg+xh0Gm2Oy+w4Atx8Kn62iIg0bOfefnZd1Z0v\ntu0ar2VfffUV3bp1s46dPMHR0ZE77riDGTNmVBoOa2LEiBHcf//9FBYWMm6cOTchOzub//3vf9aW\n09qmYClNm18bc0zMObeZC7OfLGV/2UzzrXPNw8kV2g4xx2VGjzXvFxERqYH333+fK664otz5IUOG\nkJSUxLJly7joootq/X1bt27NF198wR133IGPjw/e3t7Ex8fzxBNP1Pp7naDlhiqh5YaagfR4WPc+\n7F4EqZXsVx7aE/pOOevB2iIi0rxZLBZWrFhB7969KxzT+PfffxMYGEiHDh34+++/T7vc0KkLpBuG\nwa+//sp5552Hp6cnABkZGWzevJmhQ4da36OoqIh9+/aRk5NDt27dzirXaOedGlKwbGaS95atlxm3\nFjjpr8WAu2DsC2WvS4rBKAFnN7tXU0REpD5oHUuRMxEcBcH3m/uW5yTDnp/NoLl/udklfrKDv8HX\nN5YuZTQOokaBV+3PrBMREWls1GJZCbVYCgBF+eDobDtr/KdptuukOThC+MDScZnjILij/espIiJS\nh9RiKVIbXNzLnwuKgpY94Ng287VhgbjV5rH0SfN69FizC92vtX3rKyIiUo/UYlkJtVhKldLjIGaJ\n2WV+6A+wFNlev38rBESWvTYMczkkERGRRkaTd2pIwVLOSH4G7PvVnPyz92fwC4e7/7Qt8+W1YCk2\nWzM7jQXfVvVTVxERkTOkYFlDCpZy1kqKICsR/CPKzuVnwovtbVs1w/qYYzKjx0LL7mrNFBGRBkvB\nsoYULKVWJe+FBXdDwnpsljI6wS/cDJhdLoV2Q+xePRERkdNRsKwhBUupE1nHzK7ymMWwfwUU59le\n73wJTPpf/dRNRESkEpoVLtIQ+bQ0d/LpOwUKc+Hg76ULsy+BnCSza/xkSbth0cNlXeaB7eqn3iIi\nItWgFstKqMVS7MpigSMbIagDeASUnV/1Cvz6dNnrkC5l62W27geOjvavq4iINDtqsRRpTBwdoU3/\n8uezj4GDk7mFJMDxXebxxyvg1QI6jTZDZvsLwdXTrlUWERE5lVosK6EWS2kw8tJg7zKzy3zfMijI\nLF/m5iUQOcj+dRMRkWZBLZYiTYVHAPS8yjyKCyH2T3PyT8xiyIgDj0AIP9f2nlWvmDsCdb4YQjpr\nKSMREbELtVhWQi2W0uAZBhzbAemxZoA8wVICL3WC3GTzdUDbssk/EYPAyaVeqisiIo2XlhuqIQVL\nabSO74H3zoeSgvLX3P0gapQZMjuONF+LiIhUQcGyhhQspVErzDHXyYxZBHuWQG5K+TJtzoHbltm/\nbiIi0uhojKVIc+bqBV0uMQ9LCST8Xbpe5mJI3mOWiRpte09uKqx9x2zNbNVHSxmJiMgZU4tlJdRi\nKU1W8j7Ysxg6jYXgjmXnt8yF7+4wv/YOhegx5tjMdheAi/4OiIg0Z+oKryEFS2l2vr0Nts0rf97F\nEzoMN0Nmp9HgFWz/uomISL1SsKwhBUtpdooL4NCqsqWMMg9XUMgBrv/GnPgjIiLNhoJlDSlYSrNm\nGHB0a2nIXASJW8zzjs4wfT94+JeV3fcrOLtD+ABw0rBtEZGmSJN3ROTsOThAq17mceGjkJFgzi7P\nSLANlQDLnjJDqEeAOSEoeix0HAFuPvVRcxERqUdqsayEWixFqiEjAV7tVv68kyu0HWKGzOix4NfG\n/nUTEZFao67wGlKwFKmGkmKI/6t0KaNFkHqg4nJRo+C6CiYGiYhIo6CucBGpe07O0HaweYx6FpL3\nlq2XGf8XUPr/rb5htveVFMPB38xWTWc3e9daRETqiIKliNQOBwcI6WQe5z8A2cdh7y9m0OxyqW3Z\n+LXw+RXg6m2Ox4weZ7ZqegbWS9VFRKR2nFVXeFFRES4uLjUun5OTw4m3d3V1xdXV1eZ6dnZ2uXu8\nvb0rfI+SkhKcnJwqrUNubi4ODg7V7tZWV7hIHfr5cVjzlu05B0eIGGSGzOixENShfuomIiLlVDcX\nndGebVu2bKF///54eHgQEBDAM888U6PyrVu3JjQ0FH9/fx566KFy9/v4+NCiRQtCQ0OtR0FBgfV6\nYWEh06dPJzg4GG9vbyZMmEBSUlK55/z111/4+voybNiwM/m4IlJXek2CC6ZDy+5l5wwLxP4JvzwO\nb/aFt86FQ3/UXx1FROSMVTtY5ufnM378eIYMGUJWVhZLlizh1Vdf5dNPPz3r8unp6WRnZzNmzJhK\n33fdunVkZ2dbDze3svFYN998MytXrmTVqlXk5uZyxx13sHz58nL1uPXWW0/7HiJiZ6E9YPgTcPef\ncP9WGPsitL/QXCfzhOQY8G5pe196PBSU78kQEZGGodpd4QsXLmTy5MkkJSXh5eUFwLRp0/j7779Z\nuXJljcpfcskltG3blrfesu0ac3BwYNu2bXTu3BlnZ9vhoDt27KBHjx7ExMTQoUMHHBwccHBwKFeP\nBx98EDc3N9zd3VmyZAlr166tzsdVV7hIfcjPgH3LzMk/qQfh9l9tr395rbkge/uhpVtMjgHfVvVT\nVxGRZqTWu8K3bt1Kp06drCERoE+fPmzbtq1WylfEy8uLYcOG4enpSVRUFP/973+t137//XfatGnD\nhx9+iI+PD76+vlx99dUcP37cWmblypX8/PPPPPXUU1W+V1FREXl5eTaHiNiZux90vwKumA23LbO9\nVpgL+1dASYE5KejHB+CVzvDBMPj9P3B0u7ljkIiI1JtqB8vs7Gx8fX1tzvn5+ZGVlVUr5St7xvHj\nx8nOzuaZZ57h7rvv5rvvvgMgNTWV+Ph4srKySElJYd++fRw+fJg777zTeu+tt97K7NmzcXd3r/K9\nZs2ahaenp/UICgqqdj1FpA6c2gNhKYah06HNOcBJ145shBXPwnuD4bWe8MuTdq2miIiUqXaw9PPz\nIz093eZcWloafn5+tVL+dFxdXZk0aRJXX30133zzDYA1tD799NO4u7vTsmVLpk2bxpIlS7BYLPzz\nn/9k+PDh9OzZk+zsbAoLC7FYLGRnZ1NR7//jjz9Obm6u9UhJSTnjeopIHXL3hSHTzJbMaTFw6Ztm\nd7jzSV0yGXGQtKv8vfkZ9quniEgzVu1g2adPH3bv3k1GRtkv6LVr19KnTx/r6+zsbEpKSqp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aOaucJEDccWyzqwxZKIiJqF2WzZ5ef0b8CIRwGV16Xn/ngJ2PmW5euArtVd5lMsa2tKZbVfj6gJ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\nQmCC\n"
          }
        }
      ],
      "source": [
        "fig, axes = plt.subplots(3, 1, figsize=(7, 12))\n",
        "\n",
        "axes[0].plot(x_plot, q_exact, lw=2, label=\"Exact\")\n",
        "axes[0].plot(x_plot, q_affine, \"--\", lw=2, label=\"Affine\")\n",
        "axes[0].set_title(r\"$q(x) = \\ln h(x)$\")\n",
        "axes[0].set_xlabel(r\"$x$\")\n",
        "axes[0].legend(frameon=False)\n",
        "\n",
        "axes[1].plot(x_plot, m_exact, lw=2, label=\"Exact\")\n",
        "axes[1].plot(x_plot, m_affine, \"--\", lw=2, label=\"Affine\")\n",
        "axes[1].set_title(r\"$m(x) = c/W$\")\n",
        "axes[1].set_xlabel(r\"$x$\")\n",
        "axes[1].legend(frameon=False)\n",
        "\n",
        "axes[2].plot(x_plot, sigma_w_exact, lw=2, label=\"Exact\")\n",
        "axes[2].axhline(sigma_w_affine, ls=\"--\", lw=2, label=\"Affine\")\n",
        "axes[2].set_title(r\"Wealth volatility $\\sigma_W(x)$\")\n",
        "axes[2].set_xlabel(r\"$x$\")\n",
        "axes[2].legend(frameon=False)\n",
        "\n",
        "fig.tight_layout()\n",
        "plt.show()"
      ],
      "id": "1716ae50"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The next figure makes the same comparison in error form by plotting\n",
        "exact minus affine."
      ],
      "id": "d12589d5-8c71-4e4e-afd1-63a65d6ec869"
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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//wr3ZzKZYDAYrB5EREREVLU6u8bSZDJh7NixVZb55ptv4O/vj7S0NAQEBFit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\nRERERHrx/8aXrge58D9fAAAAAElFTkSuQmCC\n"
          }
        }
      ],
      "source": [
        "fig, axes = plt.subplots(3, 1, figsize=(7, 10))\n",
        "\n",
        "axes[0].plot(x_plot, q_error, lw=2)\n",
        "axes[0].axhline(0.0, color=\"black\", ls=\"--\", lw=1)\n",
        "axes[0].set_title(r\"Error in $q(x)$: exact minus affine\")\n",
        "axes[0].set_xlabel(r\"$x$\")\n",
        "\n",
        "axes[1].plot(x_plot, m_error, lw=2)\n",
        "axes[1].axhline(0.0, color=\"black\", ls=\"--\", lw=1)\n",
        "axes[1].set_title(r\"Error in $m(x)$: exact minus affine\")\n",
        "axes[1].set_xlabel(r\"$x$\")\n",
        "\n",
        "axes[2].plot(x_plot, sigma_w_error, lw=2)\n",
        "axes[2].axhline(0.0, color=\"black\", ls=\"--\", lw=1)\n",
        "axes[2].set_title(r\"Error in $\\sigma_W(x)$: exact minus affine\")\n",
        "axes[2].set_xlabel(r\"$x$\")\n",
        "\n",
        "fig.tight_layout()\n",
        "plt.show()"
      ],
      "id": "4d930a0e"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The exact solution also delivers the endogenous expected return on\n",
        "aggregate wealth."
      ],
      "id": "250c5e38-dcd8-440b-860f-3405d74a51d8"
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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XAZ81eaem9Z8mkUggkUiwf/9+aGlp4cMPP0SnTp3w448/YtmyZXB2dla6DT5m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\nYElEREREKsFgSUREREQq8X+mZBDb6b+z7wAAAABJRU5ErkJggg==\n"
          }
        }
      ],
      "source": [
        "plt.figure(figsize=(7, 4))\n",
        "plt.plot(x_plot, mu_w_exact, lw=2)\n",
        "plt.title(r\"Expected Return on Wealth $\\mu_W(x)$\")\n",
        "plt.xlabel(r\"$x$\")\n",
        "plt.ylabel(r\"$\\mu_W$\")\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "id": "5777f0ea"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Interpretation\n",
        "\n",
        "Three features are worth emphasizing.\n",
        "\n",
        "1.  In this benchmark calibration, the exact and affine solutions are\n",
        "    close for $q(x)$, $m(x)$, and $\\sigma_W(x)$, so the affine\n",
        "    approximation captures most of the quantitative variation.\n",
        "2.  The remaining difference is curvature: the exact solution has\n",
        "    $q''(x)\\neq 0$, while the affine approximation rules that out by\n",
        "    construction.\n",
        "3.  That curvature matters most for objects such as $\\mu_W(x)$ that\n",
        "    depend directly on $q''(x)$, so the exact solution is most useful as\n",
        "    a benchmark for what the affine approximation leaves out.\n",
        "\n",
        "This notebook therefore complements the analytical affine solution in a\n",
        "focused way: the affine approximation remains the tractable workhorse,\n",
        "and the exact numerical value function tells us how much nonlinear\n",
        "curvature that workhorse is ignoring in a representative calibration."
      ],
      "id": "bf0b28a8-f5b7-400a-bf9e-c17d2f2949a3"
    }
  ],
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  "nbformat_minor": 5,
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      "name": "python3",
      "display_name": "Python 3 (ipykernel)",
      "language": "python",
      "path": "/home/lnaranjo/.pyenv/versions/3.14.7/share/jupyter/kernels/python3"
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    "language_info": {
      "name": "python",
      "codemirror_mode": {
        "name": "ipython",
        "version": "3"
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.14.7"
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}