{
 "cells": [
  {
   "cell_type": "markdown",
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   "metadata": {},
   "source": [
    "# Choosing a Sparse Root Solver\n",
    "\n",
    "gEconpy provides several solvers for nonlinear systems with sparse Jacobians. All of them are used through\n",
    "one function, `sparse_root`, which accepts a solver instance. This notebook walks through the available\n",
    "solvers, shows how to configure them, and compares their behavior on problems of increasing difficulty.\n",
    "\n",
    "The objective function must return a tuple `(residuals, jacobian)`, where the residual is an ndarray\n",
    "and the Jacobian is a scipy sparse matrix."
   ]
  },
  {
   "cell_type": "code",
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   "id": "3b88074c",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2026-03-15T17:40:20.462619Z"
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   "source": [
    "import time\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy.sparse as sp\n",
    "\n",
    "from gEconpy.plotting import set_matplotlib_style\n",
    "from gEconpy.solvers.sparse_root import (\n",
    "    Chord,\n",
    "    GaussNewtonTrustRegion,\n",
    "    InexactNewtonKrylov,\n",
    "    LevenbergMarquardt,\n",
    "    NewtonArmijo,\n",
    "    NewtonNonmonotone,\n",
    "    SparseDogleg,\n",
    "    sparse_root,\n",
    ")\n",
    "\n",
    "set_matplotlib_style()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "99885d26",
   "metadata": {},
   "source": [
    "## Test Problems\n",
    "\n",
    "We define three test problems. The first is a small system to demonstrate the API. The second and third\n",
    "are large sparse systems where solver choice actually matters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "bb2d77c1",
   "metadata": {
    "execution": {
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   "source": [
    "def quadratic(x):\n",
    "    \"\"\"x^2 - [1, 4] = 0. Solution at [1, 2].\"\"\"\n",
    "    return x**2 - np.array([1.0, 4.0]), sp.diags(2 * x, format=\"csc\")\n",
    "\n",
    "\n",
    "def broyden_tridiagonal(x):\n",
    "    \"\"\"Broyden tridiagonal system. Classic large sparse test problem.\"\"\"\n",
    "    n = len(x)\n",
    "    res = (3.0 - 2.0 * x) * x + 1.0\n",
    "    res[:-1] -= 2.0 * x[1:]\n",
    "    res[1:] -= x[:-1]\n",
    "    jac = sp.diags(\n",
    "        [-np.ones(n - 1), 3.0 - 4.0 * x, -2 * np.ones(n - 1)],\n",
    "        [-1, 0, 1],\n",
    "        format=\"csc\",\n",
    "    )\n",
    "    return res, jac\n",
    "\n",
    "\n",
    "def trigonometric(x):\n",
    "    \"\"\"Trigonometric system (More, Garbow, Hillstrom). Many near-solutions.\"\"\"\n",
    "    n = len(x)\n",
    "    sumcos = np.sum(np.cos(x))\n",
    "    idx = np.arange(1, n + 1, dtype=np.float64)\n",
    "    res = float(n) - sumcos + idx * (1.0 - np.cos(x)) - np.sin(x)\n",
    "\n",
    "    diag_vals = (1.0 + idx) * np.sin(x) - np.cos(x)\n",
    "    off_diag = np.sin(x)\n",
    "    J_dense = np.tile(off_diag, (n, 1))\n",
    "    np.fill_diagonal(J_dense, diag_vals)\n",
    "    jac = sp.csc_matrix(J_dense)\n",
    "    return res, jac"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46971800",
   "metadata": {},
   "source": [
    "## Basic Usage\n",
    "\n",
    "With no solver argument, `sparse_root` defaults to Newton's method with Armijo backtracking. This is\n",
    "a good general-purpose choice."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3f568a32",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-15T17:40:20.469048Z",
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     "shell.execute_reply": "2026-03-15T17:40:20.471884Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success: True\n",
      "Solution: [1. 2.]\n",
      "Iterations: 5\n"
     ]
    }
   ],
   "source": [
    "result = sparse_root(quadratic, np.array([2.0, 3.0]), progressbar=False)\n",
    "print(f\"Success: {result.success}\")\n",
    "print(f\"Solution: {result.x}\")\n",
    "print(f\"Iterations: {result.nit}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "953f9801",
   "metadata": {},
   "source": [
    "To choose a different solver, pass an instance to the `solver` argument."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2594bf13",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2026-03-15T17:40:20.476948Z"
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success: True, iterations: 5\n"
     ]
    }
   ],
   "source": [
    "result = sparse_root(quadratic, np.array([2.0, 3.0]), solver=LevenbergMarquardt(), progressbar=False)\n",
    "print(f\"Success: {result.success}, iterations: {result.nit}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9cdeaa18",
   "metadata": {},
   "source": [
    "## The Solvers\n",
    "\n",
    "The solvers fall into two families.\n",
    "\n",
    "**Line-search solvers** compose a direction strategy with a globalization strategy. They are\n",
    "constructed via factory functions:\n",
    "- `NewtonArmijo()` — exact Newton direction + Armijo backtracking\n",
    "- `Chord()` — reuses the Jacobian for several steps, reducing factorization cost\n",
    "- `InexactNewtonKrylov()` — solves the Newton system approximately via GMRES, good for very large systems\n",
    "- `NewtonNonmonotone()` — allows the merit function to increase temporarily, helping escape narrow valleys\n",
    "\n",
    "**Trust-region solvers** manage their own step acceptance:\n",
    "- `SparseDogleg()` — Powell dogleg within an adaptive trust region\n",
    "- `GaussNewtonTrustRegion()` — Gauss-Newton with Steihaug-CG subproblem solver\n",
    "- `LevenbergMarquardt()` — damped Gauss-Newton with adaptive $\\lambda$\n",
    "\n",
    "Let's compare all seven on the Broyden tridiagonal system at $n = 1000$."
   ]
  },
  {
   "cell_type": "code",
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   "id": "e70c4c1a",
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    "execution": {
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     "shell.execute_reply": "2026-03-15T17:40:20.507512Z"
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    {
     "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>success</th>\n",
       "      <th>iterations</th>\n",
       "      <th>f_evals</th>\n",
       "      <th>max |residual|</th>\n",
       "      <th>time (ms)</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>solver</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>NewtonArmijo</th>\n",
       "      <td>True</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>6.66e-16</td>\n",
       "      <td>7.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Chord</th>\n",
       "      <td>True</td>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "      <td>4.37e-11</td>\n",
       "      <td>2.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>InexactNewtonKrylov</th>\n",
       "      <td>True</td>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "      <td>2.11e-13</td>\n",
       "      <td>4.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NewtonNonmonotone</th>\n",
       "      <td>True</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>6.66e-16</td>\n",
       "      <td>1.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SparseDogleg</th>\n",
       "      <td>True</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>7.77e-16</td>\n",
       "      <td>2.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GaussNewtonTR</th>\n",
       "      <td>True</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>1.11e-15</td>\n",
       "      <td>4.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LevenbergMarquardt</th>\n",
       "      <td>True</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>2.51e-13</td>\n",
       "      <td>2.9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                     success  iterations  f_evals max |residual| time (ms)\n",
       "solver                                                                    \n",
       "NewtonArmijo            True           5        6       6.66e-16       7.9\n",
       "Chord                   True           8        9       4.37e-11       2.3\n",
       "InexactNewtonKrylov     True           8        9       2.11e-13       4.1\n",
       "NewtonNonmonotone       True           5        6       6.66e-16       1.5\n",
       "SparseDogleg            True           7        8       7.77e-16       2.6\n",
       "GaussNewtonTR           True           7        8       1.11e-15       4.1\n",
       "LevenbergMarquardt      True           5        6       2.51e-13       2.9"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solvers = {\n",
    "    \"NewtonArmijo\": NewtonArmijo(),\n",
    "    \"Chord\": Chord(),\n",
    "    \"InexactNewtonKrylov\": InexactNewtonKrylov(),\n",
    "    \"NewtonNonmonotone\": NewtonNonmonotone(),\n",
    "    \"SparseDogleg\": SparseDogleg(),\n",
    "    \"GaussNewtonTR\": GaussNewtonTrustRegion(),\n",
    "    \"LevenbergMarquardt\": LevenbergMarquardt(),\n",
    "}\n",
    "\n",
    "n = 1000\n",
    "x0 = -np.ones(n)\n",
    "\n",
    "rows = []\n",
    "for name, solver in solvers.items():\n",
    "    t0 = time.perf_counter()\n",
    "    result = sparse_root(broyden_tridiagonal, x0.copy(), solver=solver, progressbar=False)\n",
    "    elapsed = time.perf_counter() - t0\n",
    "    rows.append(\n",
    "        {\n",
    "            \"solver\": name,\n",
    "            \"success\": result.success,\n",
    "            \"iterations\": result.nit,\n",
    "            \"f_evals\": result.nfev,\n",
    "            \"max |residual|\": f\"{np.max(np.abs(result.fun)):.2e}\",\n",
    "            \"time (ms)\": f\"{elapsed * 1000:.1f}\",\n",
    "        }\n",
    "    )\n",
    "\n",
    "pd.DataFrame(rows).set_index(\"solver\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9515e2d",
   "metadata": {},
   "source": [
    "## Composing Direction and Globalization Strategies\n",
    "\n",
    "The line-search solvers are built from two interchangeable pieces:\n",
    "\n",
    "- A **direction strategy** computes the search direction at each step\n",
    "- A **globalization strategy** chooses how far to step in that direction\n",
    "\n",
    "The factory functions pick sensible defaults, but you can mix and match. For example, here we pair a\n",
    "Krylov direction (iterative linear solve) with a nonmonotone line search:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "baa1deba",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-15T17:40:20.508875Z",
     "iopub.status.busy": "2026-03-15T17:40:20.508791Z",
     "iopub.status.idle": "2026-03-15T17:40:20.513961Z",
     "shell.execute_reply": "2026-03-15T17:40:20.513795Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success: True, iterations: 8\n"
     ]
    }
   ],
   "source": [
    "from gEconpy.solvers.sparse_root.direction import KrylovDirection\n",
    "from gEconpy.solvers.sparse_root.globalization import NonmonotoneBacktracking\n",
    "from gEconpy.solvers.sparse_root.line_search import LineSearchSolver\n",
    "\n",
    "custom_solver = LineSearchSolver(\n",
    "    direction=KrylovDirection(krylov_method=\"gmres\"),\n",
    "    globalization=NonmonotoneBacktracking(memory=10),\n",
    ")\n",
    "\n",
    "result = sparse_root(broyden_tridiagonal, -np.ones(1000), solver=custom_solver, progressbar=False)\n",
    "print(f\"Success: {result.success}, iterations: {result.nit}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ca9519f",
   "metadata": {},
   "source": [
    "## Scaling: Krylov vs Direct Solvers\n",
    "\n",
    "For large systems, the Jacobian factorization in `NewtonArmijo` can become the bottleneck.\n",
    "`InexactNewtonKrylov` avoids factorization entirely by solving the Newton system iteratively. Let's see\n",
    "how they scale on the Broyden tridiagonal system as $n$ grows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "8f3ec44d",
   "metadata": {
    "execution": {
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     "iopub.status.idle": "2026-03-15T17:40:20.755500Z",
     "shell.execute_reply": "2026-03-15T17:40:20.755256Z"
    }
   },
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 2016x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sizes = [100, 500, 1_000, 5_000, 10_000]\n",
    "newton_times = []\n",
    "krylov_times = []\n",
    "\n",
    "for n in sizes:\n",
    "    x0 = -np.ones(n)\n",
    "\n",
    "    t0 = time.perf_counter()\n",
    "    sparse_root(broyden_tridiagonal, x0.copy(), solver=NewtonArmijo(), progressbar=False)\n",
    "    newton_times.append(time.perf_counter() - t0)\n",
    "\n",
    "    t0 = time.perf_counter()\n",
    "    sparse_root(broyden_tridiagonal, x0.copy(), solver=InexactNewtonKrylov(), progressbar=False)\n",
    "    krylov_times.append(time.perf_counter() - t0)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(sizes, newton_times, \"o-\", label=\"NewtonArmijo (direct)\")\n",
    "ax.plot(sizes, krylov_times, \"s-\", label=\"InexactNewtonKrylov (GMRES)\")\n",
    "ax.set_xlabel(\"System size $n$\")\n",
    "ax.set_ylabel(\"Wall time (s)\")\n",
    "ax.set_title(\"Scaling: direct vs iterative Newton\")\n",
    "ax.legend()\n",
    "ax.set_xscale(\"log\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd4879c5",
   "metadata": {},
   "source": [
    "## Difficult Problems: Trigonometric System\n",
    "\n",
    "The Moré-Garbow-Hillstrom trigonometric system has many near-solutions and is hard for monotone\n",
    "line-search methods. Trust-region and nonmonotone solvers tend to do better here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "4a359d1c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-15T17:40:20.756828Z",
     "iopub.status.busy": "2026-03-15T17:40:20.756731Z",
     "iopub.status.idle": "2026-03-15T17:41:08.513658Z",
     "shell.execute_reply": "2026-03-15T17:41:08.513346Z"
    }
   },
   "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>success</th>\n",
       "      <th>iterations</th>\n",
       "      <th>f_evals</th>\n",
       "      <th>max |residual|</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>solver</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>NewtonArmijo</th>\n",
       "      <td>True</td>\n",
       "      <td>11</td>\n",
       "      <td>38</td>\n",
       "      <td>2.64e-13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Chord</th>\n",
       "      <td>True</td>\n",
       "      <td>28</td>\n",
       "      <td>217</td>\n",
       "      <td>5.00e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>InexactNewtonKrylov</th>\n",
       "      <td>False</td>\n",
       "      <td>500</td>\n",
       "      <td>7658</td>\n",
       "      <td>1.05e-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>NewtonNonmonotone</th>\n",
       "      <td>True</td>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>4.61e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SparseDogleg</th>\n",
       "      <td>True</td>\n",
       "      <td>290</td>\n",
       "      <td>346</td>\n",
       "      <td>4.87e-04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GaussNewtonTR</th>\n",
       "      <td>True</td>\n",
       "      <td>34</td>\n",
       "      <td>70</td>\n",
       "      <td>8.48e-04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LevenbergMarquardt</th>\n",
       "      <td>True</td>\n",
       "      <td>28</td>\n",
       "      <td>50</td>\n",
       "      <td>7.00e-04</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                     success  iterations  f_evals max |residual|\n",
       "solver                                                          \n",
       "NewtonArmijo            True          11       38       2.64e-13\n",
       "Chord                   True          28      217       5.00e-11\n",
       "InexactNewtonKrylov    False         500     7658       1.05e-03\n",
       "NewtonNonmonotone       True           9       10       4.61e-11\n",
       "SparseDogleg            True         290      346       4.87e-04\n",
       "GaussNewtonTR           True          34       70       8.48e-04\n",
       "LevenbergMarquardt      True          28       50       7.00e-04"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 50\n",
    "x0 = np.ones(n) / n\n",
    "\n",
    "rows = []\n",
    "for name, solver in solvers.items():\n",
    "    result = sparse_root(trigonometric, x0.copy(), solver=solver, progressbar=False, maxiter=500)\n",
    "    rows.append(\n",
    "        {\n",
    "            \"solver\": name,\n",
    "            \"success\": result.success,\n",
    "            \"iterations\": result.nit,\n",
    "            \"f_evals\": result.nfev,\n",
    "            \"max |residual|\": f\"{np.max(np.abs(result.fun)):.2e}\",\n",
    "        }\n",
    "    )\n",
    "\n",
    "pd.DataFrame(rows).set_index(\"solver\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "37e08771",
   "metadata": {},
   "source": [
    "## Tuning Solver Parameters\n",
    "\n",
    "All solvers expose their parameters as constructor arguments. Here are a few examples.\n",
    "\n",
    "**Armijo parameters**: `c1` controls how much decrease the line search demands. Smaller values are more\n",
    "permissive (accept steps more readily); larger values are stricter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f5d9e51f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-15T17:41:08.515626Z",
     "iopub.status.busy": "2026-03-15T17:41:08.515510Z",
     "iopub.status.idle": "2026-03-15T17:41:08.534558Z",
     "shell.execute_reply": "2026-03-15T17:41:08.534295Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loose  c1=1e-6: 7 iterations, 8 f-evals\n",
      "Strict c1=0.5:  15 iterations, 31 f-evals\n"
     ]
    }
   ],
   "source": [
    "from gEconpy.solvers.sparse_root.globalization import ArmijoBacktracking\n",
    "\n",
    "loose = NewtonArmijo(globalization=ArmijoBacktracking(c1=1e-6))\n",
    "strict = NewtonArmijo(globalization=ArmijoBacktracking(c1=0.5))\n",
    "\n",
    "x0_far = np.full(1000, 100.0)\n",
    "\n",
    "r_loose = sparse_root(broyden_tridiagonal, x0_far.copy(), solver=loose, progressbar=False)\n",
    "r_strict = sparse_root(broyden_tridiagonal, x0_far.copy(), solver=strict, progressbar=False)\n",
    "\n",
    "print(f\"Loose  c1=1e-6: {r_loose.nit} iterations, {r_loose.nfev} f-evals\")\n",
    "print(f\"Strict c1=0.5:  {r_strict.nit} iterations, {r_strict.nfev} f-evals\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa37e04a",
   "metadata": {},
   "source": [
    "**Chord recompute frequency**: the `Chord` solver reuses the Jacobian factorization for several steps,\n",
    "trading accuracy for speed. The `recompute_every` parameter controls this tradeoff."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "cd918005",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-15T17:41:08.535940Z",
     "iopub.status.busy": "2026-03-15T17:41:08.535855Z",
     "iopub.status.idle": "2026-03-15T17:41:08.557769Z",
     "shell.execute_reply": "2026-03-15T17:41:08.557520Z"
    }
   },
   "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>iterations</th>\n",
       "      <th>success</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>recompute_every</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>8</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>12</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>21</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 iterations  success\n",
       "recompute_every                     \n",
       "1                         5     True\n",
       "3                         7     True\n",
       "5                         8     True\n",
       "10                       12     True\n",
       "20                       21     True"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from gEconpy.solvers.sparse_root.direction import ChordDirection\n",
    "\n",
    "rows = []\n",
    "for freq in [1, 3, 5, 10, 20]:\n",
    "    solver = Chord(direction=ChordDirection(recompute_every=freq))\n",
    "    result = sparse_root(broyden_tridiagonal, -np.ones(1000), solver=solver, progressbar=False)\n",
    "    rows.append({\"recompute_every\": freq, \"iterations\": result.nit, \"success\": result.success})\n",
    "\n",
    "pd.DataFrame(rows).set_index(\"recompute_every\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ffa48c0a",
   "metadata": {},
   "source": [
    "**Levenberg-Marquardt damping**: the initial damping parameter $\\lambda_0$ controls how cautious the\n",
    "first steps are. Too large and the solver crawls; too small and it may overshoot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "6bea9b4e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-15T17:41:08.559088Z",
     "iopub.status.busy": "2026-03-15T17:41:08.558993Z",
     "iopub.status.idle": "2026-03-15T17:41:08.580524Z",
     "shell.execute_reply": "2026-03-15T17:41:08.580291Z"
    }
   },
   "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>iterations</th>\n",
       "      <th>f_evals</th>\n",
       "      <th>success</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>lam0</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.000001</th>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.001000</th>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.000000</th>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100.000000</th>\n",
       "      <td>12</td>\n",
       "      <td>13</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            iterations  f_evals  success\n",
       "lam0                                    \n",
       "0.000001             5        6     True\n",
       "0.001000             5        6     True\n",
       "1.000000             8        9     True\n",
       "100.000000          12       13     True"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rows = []\n",
    "for lam0 in [1e-6, 1e-3, 1.0, 100.0]:\n",
    "    solver = LevenbergMarquardt(lam0=lam0)\n",
    "    result = sparse_root(broyden_tridiagonal, -np.ones(1000), solver=solver, progressbar=False)\n",
    "    rows.append({\"lam0\": lam0, \"iterations\": result.nit, \"f_evals\": result.nfev, \"success\": result.success})\n",
    "\n",
    "pd.DataFrame(rows).set_index(\"lam0\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61b9446aa2933fd3",
   "metadata": {},
   "source": [
    "## Cheap Merit Evaluation with `merit_fun`\n",
    "\n",
    "During backtracking, the line-search solvers evaluate the objective function at every trial step to\n",
    "check the Armijo condition. By default this calls the full `fun`, which computes both residuals **and**\n",
    "the Jacobian — even though the Jacobian is only needed at the finally accepted point.\n",
    "\n",
    "When the Jacobian is expensive (as in large stacked DSGE systems), this is wasteful. You can pass a\n",
    "`merit_fun` to the globalization strategy that returns **only the residuals**. The solver will use it\n",
    "for all trial evaluations during backtracking, then call the full `fun` once at the accepted point to\n",
    "obtain the Jacobian."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "43cfe964572fb8e4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success: True, iterations: 5, f_evals: 11\n"
     ]
    }
   ],
   "source": [
    "def broyden_residuals_only(x):\n",
    "    \"\"\"Residuals without the Jacobian — much cheaper to evaluate.\"\"\"\n",
    "    len(x)\n",
    "    res = (3.0 - 2.0 * x) * x + 1.0\n",
    "    res[:-1] -= 2.0 * x[1:]\n",
    "    res[1:] -= x[:-1]\n",
    "    return res\n",
    "\n",
    "\n",
    "solver_with_merit = NewtonArmijo(globalization=ArmijoBacktracking(merit_fun=broyden_residuals_only))\n",
    "\n",
    "result = sparse_root(broyden_tridiagonal, -np.ones(1000), solver=solver_with_merit, progressbar=False)\n",
    "print(f\"Success: {result.success}, iterations: {result.nit}, f_evals: {result.nfev}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ff14624d6ba657c",
   "metadata": {},
   "source": [
    "The solver converges to the same solution but avoids computing the Jacobian at every rejected trial\n",
    "point. The benefit grows with system size and Jacobian cost — in perfect foresight simulation (below),\n",
    "the Jacobian involves assembling a block-tridiagonal sparse matrix across hundreds of time periods,\n",
    "so skipping it during backtracking is a significant win."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13789bfaa5e00b82",
   "metadata": {},
   "source": [
    "## Application: Perfect Foresight Simulation\n",
    "\n",
    "In practice, these solvers are used under the hood by `ge.solve_perfect_foresight`. A perfect foresight\n",
    "simulation stacks the model equations across all time periods into one large sparse nonlinear system.\n",
    "The size of that system grows linearly with the simulation length, so solver choice matters.\n",
    "\n",
    "`solve_perfect_foresight` automatically compiles a residual-only version of the stacked system and\n",
    "attaches it as the `merit_fun` on the solver's globalization strategy. You don't need to do anything\n",
    "— the optimization described in the previous section is applied for you whenever the default\n",
    "`NewtonArmijo` solver is used, or whenever you pass a line-search solver with an `ArmijoBacktracking`\n",
    "or `NonmonotoneBacktracking` globalization strategy.\n",
    "\n",
    "Let's start with the RBC model using defaults, then switch to the larger New Keynesian model with a\n",
    "custom solver."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e1412d26",
   "metadata": {},
   "source": [
    "### RBC model with defaults"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "29888272",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-15T17:41:08.581900Z",
     "iopub.status.busy": "2026-03-15T17:41:08.581817Z",
     "iopub.status.idle": "2026-03-15T17:41:16.215040Z",
     "shell.execute_reply": "2026-03-15T17:41:16.214785Z"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "607785891a54476fb394ebd08ac79b60",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success: True, iterations: 3\n"
     ]
    }
   ],
   "source": [
    "import gEconpy as ge\n",
    "\n",
    "rbc = ge.model_from_gcn(ge.data.get_example_gcn(\"RBC\"), verbose=False)\n",
    "\n",
    "T = 500\n",
    "shock = np.zeros(T)\n",
    "shock[0] = 0.05\n",
    "\n",
    "trajectory, result = ge.solve_perfect_foresight(rbc, simulation_length=T, shocks={\"epsilon_A\": shock})\n",
    "print(f\"Success: {result.success}, iterations: {result.nit}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e992964",
   "metadata": {},
   "source": [
    "The system solved here has $T \\times n_{\\text{vars}}$ unknowns. Let's look at how big that is, and\n",
    "how sparse the Jacobian is at the solution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "b93e3a66",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-15T17:41:16.218938Z",
     "iopub.status.busy": "2026-03-15T17:41:16.218870Z",
     "iopub.status.idle": "2026-03-15T17:41:16.221041Z",
     "shell.execute_reply": "2026-03-15T17:41:16.220837Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variables per period:     9\n",
      "Simulation length:        500\n",
      "Total unknowns:           4,500\n",
      "Jacobian shape            (4500, 4500)\n",
      "Jacobian nonzeros:        15,492\n",
      "Density:                  0.076504%\n"
     ]
    }
   ],
   "source": [
    "n_vars = len(rbc.variables)\n",
    "print(f\"{'Variables per period:':25} {n_vars}\")\n",
    "print(f\"{'Simulation length:':25} {T}\")\n",
    "print(f\"{'Total unknowns:':25} {T * n_vars:,}\")\n",
    "print(f\"{'Jacobian shape':25} {result.jac.shape}\")\n",
    "print(f\"{'Jacobian nonzeros:':25} {result.jac.nnz:,}\")\n",
    "print(f\"{'Density:':25} {result.jac.nnz / np.prod(result.jac.shape):.6%}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "a5eda4ed",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-15T17:41:16.222180Z",
     "iopub.status.busy": "2026-03-15T17:41:16.222096Z",
     "iopub.status.idle": "2026-03-15T17:41:16.332241Z",
     "shell.execute_reply": "2026-03-15T17:41:16.332017Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1728x576 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 2, figsize=(12, 4))\n",
    "\n",
    "axes[0].spy(result.jac, markersize=0.05)\n",
    "axes[0].set_title(f\"Jacobian sparsity pattern ({result.jac.shape[0]:,} × {result.jac.shape[1]:,})\")\n",
    "\n",
    "steady_state = pd.Series({k.removesuffix(\"_ss\"): v for k, v in rbc.steady_state().items()})\n",
    "(trajectory - steady_state).plot(ax=axes[1], legend=True)\n",
    "axes[1].set_xlabel(\"Period\")\n",
    "axes[1].set_title(\"RBC impulse response (perfect foresight)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef7d0f06",
   "metadata": {},
   "source": [
    "The Jacobian has a banded structure — each period's equations only depend on variables at $t-1$, $t$,\n",
    "and $t+1$. This is why sparse solvers are essential: a dense factorization of a matrix this size would\n",
    "be extremely expensive."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70e221fb",
   "metadata": {},
   "source": [
    "### New Keynesian model with a custom solver\n",
    "\n",
    "The New Keynesian model has more variables per period (sticky prices, sticky wages, monetary policy),\n",
    "so the stacked system is considerably larger. Here we use `LevenbergMarquardt`, a trust-region solver\n",
    "that adapts its damping parameter $\\lambda$ each step."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "bbf446d5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-15T17:41:16.333657Z",
     "iopub.status.busy": "2026-03-15T17:41:16.333553Z",
     "iopub.status.idle": "2026-03-15T17:41:24.865281Z",
     "shell.execute_reply": "2026-03-15T17:41:24.865057Z"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "cb1c0e05504c43b998c23fffc51e40ff",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success: True, iterations: 13\n"
     ]
    }
   ],
   "source": [
    "nk = ge.model_from_gcn(ge.data.get_example_gcn(\"New_Keynesian\"), verbose=False)\n",
    "\n",
    "T_nk = 300\n",
    "shock_nk = np.zeros(T_nk)\n",
    "shock_nk[0] = 0.01\n",
    "\n",
    "trajectory_nk, result_nk = ge.solve_perfect_foresight(\n",
    "    nk, simulation_length=T_nk, shocks={\"epsilon_R\": shock_nk}, solver=LevenbergMarquardt()\n",
    ")\n",
    "print(f\"Success: {result_nk.success}, iterations: {result_nk.nit}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "3d619fc3",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-15T17:41:24.872577Z",
     "iopub.status.busy": "2026-03-15T17:41:24.872513Z",
     "iopub.status.idle": "2026-03-15T17:41:24.874483Z",
     "shell.execute_reply": "2026-03-15T17:41:24.874294Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variables per period:     23\n",
      "Simulation length:        300\n",
      "Total unknowns:           6,900\n",
      "Jacobian shape            (6900, 6900)\n",
      "Jacobian nonzeros:        31,764\n",
      "Density:                  0.066717%\n"
     ]
    }
   ],
   "source": [
    "n_vars_nk = len(nk.variables)\n",
    "print(f\"{'Variables per period:':25} {n_vars_nk}\")\n",
    "print(f\"{'Simulation length:':25} {T_nk}\")\n",
    "print(f\"{'Total unknowns:':25} {T_nk * n_vars_nk:,}\")\n",
    "print(f\"{'Jacobian shape':25} {result_nk.jac.shape}\")\n",
    "print(f\"{'Jacobian nonzeros:':25} {result_nk.jac.nnz:,}\")\n",
    "print(f\"{'Density:':25} {result_nk.jac.nnz / np.prod(result_nk.jac.shape):.6%}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "3d580b2a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-15T17:41:24.875774Z",
     "iopub.status.busy": "2026-03-15T17:41:24.875647Z",
     "iopub.status.idle": "2026-03-15T17:41:24.985937Z",
     "shell.execute_reply": "2026-03-15T17:41:24.985726Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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CdknTQs8++6wafuutt5xu+kb6epDmiuTOb+loWxIsznZK7ogffvhBPb/77ruq9kPt2rWLvW/UUCnJ6C9FLv47WjNHEgZG81H2auNIrQghtWessXfR3ei/QWrfGM0O2fPnn3+q9cm2SVNQvXv3Nt9Rf7F9UJ6MpuGkBo5lfyaWLrnkEqea0CpLM1uS6JBm0VauXImDBw+qvla+/PJLVbPjjz/+UNNI7RYjGSSkaTJjXTt27LC6XKnBtGfPHjXctm3bYtsotYjszSukH5mS85aFNJsmCUY5LqXpM0k0Nm3aFJs2bcLVV1/tUp8ujI/9+BjJlcruV4qIiIiIiIiIiCoWkyt0UdKUUmxsrLo4btmEkqOkY/dffvlFNcW0d+9eVbPC3f0TGIkMW80g2WpKSpI/cqe/1KqQJJAjpImrSy+9VA3LxXpbVqxYoZ47depksxkvW4z3ZD32mtQqWX5JEBidpJfkTHNa7iI1QYxElCQ1rJFaAUYiQpIetmrmSHJOxMTEuG37JDkiNZ3ErbfeWqqJNKMj+GXLllmdX2q+GEk5afrOktEfj615pf+f33//3eq8zpDaKhMnTlQJnY8++kj1USPNysnxJ03TrV+/Htddd12Zm61ifOzH59ChQ+rZ6CeIiIiIiIiIiIj0wOQKXZQkH5577jk1/P7779utcWGL9Icyb948VRNG7uSX5oqc7RzdHqO/lG3btpV6T+7anz59utX5pEbNsGHD1PDUqVNt1q4oafjw4epZagkYtUwsSXNoUptEjBgxwuZFWel43FqfLnKRXNx8881OlX/fvn3qor217bGXCCov0jyWkYjauHGjzen+9a9/qWdJdFg7LmR/GH3FSE0Md5Gm7qT2iPRXcv/995d630i4fPXVV1bj/Prrr6vnzp07l2rSbNSoUeaEkSQXS/r4449VYiYkJMR8DDrrs88+wyOPPKKG3377bdx9993m96T5s+XLl6v+diRZJ+soazN2jI/1+EgfRJs3b1bDUluMiIiIiIiIiIg0YiIymUx33HGHdIhhuuWWW6zuj4KCAlPbtm3VNMZD5rG1nL59+1pdzi+//GIKDAxU03Tt2tWUlpbm8P5fuXKled0HDx4s9t6oUaPU+EaNGplWrVplKiwsVOM3bNig1hMVFWVz3n379pnCw8PVex07djStWLFClVecOXNGbfM111xTbJ6UlBRTvXr11Dzt27c3/fXXX2p8fn6+ae7cuabIyEj13pVXXmlzH0VERJjCwsJMX375pSkvL0+9t2XLFlOXLl3U+7Vr11brsbYPYmJiio2X7QwNDVXv3XzzzaZjx46p8ZmZmaZPP/3UVK1aNVPNmjVtxsbWvjHIeGMaZz344INqvvvuu8/mNOfOnVOxM7Zv165danxubq7pq6++UvtJ3hs+fLjdbfv8889Lvf/hhx+a5syZYzpx4oR5XHx8vOnRRx81+fj4qIeswxrZf7KvZdmdOnUy7dixQ41PT083Pfnkk+b1/vrrr1bnHzFihHpf9v3ChQvNx8js2bNNISEh6r1nnnnGVBayPF9fX7WMV155xeZ0W7duNcd+5MiRZVoX42PdP//8o/arHJ/GZ5iIiIiIiIiIiPTA5Ao5lFwRkjRwNbkifvrpJ5O/v7+armfPnurCrbPJlUOHDhV778CBA6bo6Gjz+8HBweYL8nIRWy5+20sgSEKlRo0a5mmCgoJU8sOyvCXFxcWZkyjykASNrNd4LUkXywv6JffRxIkTTd27dzevr3r16uZ5JVGyevVqm/ugZHJFvP3228W2V7bf2M+SNHrnnXcqJbki5ZD5GjdubE56WbN582ZTrVq1zOuReMh+MV5fccUVptTUVKeTK8b+No4FSTRZHicfffSR3e2X7TKSE/KQOBlJDUnMvPTSSzbnleRh586di8XVskzXXXddmS/KS0JNjrGpU6dedNqNGzeqfWsrCeQIxqe0559/XsXx9ttvL/N+JSIiIiIiIiIiz8RmwchhN954o83+Q5whzRPNmTNHdda+du1aXH/99Q71B5Gbm2selqaULDVr1gwbNmzA6NGjVWf20oG6NPUk/U/89ddfGDx4sN1lS/8Y0jH5U089pZqxkqbQpMkf6cNEmndasGBBqXm6du2qmpSSjtJlOukXROaTfjpee+011R+HbIst0kSaNNU1ZcoU1Y+IlK9WrVoYOXIk/vnnH/Tp0wfOkOahfvrpJ/Ts2VP1uyLbL/1ATJs2TXVwLn2IVAYph+yfw4cPq+2wpUOHDti+fTv+/e9/q75apHkz6W9G+uyRfkVWrVplbv7MktFcl/Q5Is1zlXTHHXfg9ttvV812SXyknxXZnocfflg1Izd27Fi7229sl+xfOc6kaa2aNWvi2muvVf2pSH8n9ppFkzJLX0WyHNlGiXv37t3x4YcfquNKtqks5Pj+448/zE322SP75cCBAxf9HNjD+JT27bffqmfL5tiIiIiIiIiIiEgPPpJhqeyNIHLEl19+qS6SS1ImMzPToY7eqWqQvkmefPJJjBs3TiVK3EkSF08//TRuuukmzJ07163LJtd5a3wkMde+fXuVtJN+dYiIiIiIiIiISC+suUIe4/fff1fPbdq0YWLFwzzwwAOoW7cuvvjiC5w+fdqty5bO2qVGyLPPPuvW5ZJ7eGt8JGEoHKk5RERERERERERE3ofJFarypBmm2bNnq4cYMWJEZW8SOSksLEw1f5aRkYE333zTbftPmn+TZreGDh2qmq2iqsVb43Pw4EF8/fXXuOyyy3DLLbdU9uYQEREREREREVElKFtj/0QV5PLLL8emTZvURVpxySWXqD45yPNI3yZSa6VatWpuW6Y0EZeWlua25ZF7eWt8jh49ikmTJql+d6RWDhERERERERER6Yd9rlCV1qRJE5w4cUJ1+H7DDTeozsOlI28iIiIiIiIiIiIiosrC5AoREREREREREREREZET2OcKERERERERERERERGRE5hcISIiIiIiIiIiIiIicgKTK0RERERERERERERERE5gcoWIiIiIiIiIiIiIiMgJTK4QERERERERERERERE5gckVIiIiIiIiIiIiIiIiJzC5QkRERERERERERERE5AQmV5yUmJiIMWPGoH79+ggKCkKTJk3w2GOP4cyZM6iK5s6di4cffhi9e/dG9erV4ePjg9GjR9udZ926dbjmmmsQFRWF0NBQtG/fHm+99RYKCgpszjN79mx07doV1apVQ0REBPr164dffvnF5vRZWVmYOnUqWrVqheDgYNSuXRsjRozArl274C6nT5/GJ598gmHDhqF58+YICQlR29arVy98+umnKCws9Oryi6eeegoDBw5Eo0aNVPmlTJdddhmmTZum9o+3l7+kL7/8Un0G5CHHhjeXX76bjLKWfNStW9ery27p999/x0033YR69eqp72x5Hjx4MBYtWqRF+YmIiIiIiIiIqJyYyGH79+831a5d2yS7bejQoaannnrK1L9/f/W6VatWplOnTlW5vdmhQwe1fdWqVTO1bt1aDd922202p583b57Jz8/PFBYWZhozZozpiSeeUGWT+YYPH251nscff1y937BhQ9Njjz1mevDBB01RUVFq3Lvvvltq+uzsbFPPnj3V+126dDFNmDDBNGrUKJO/v78pNDTUtH79ereU/YMPPlDrqFevnunWW281TZw40XTXXXeZIiIi1PibbrrJVFhY6LXlFwEBAaZu3bqpcsvx+tBDD6l1yrrr169vOnz4sFeX35KUVWIvnwVZ98cff1xqGm8qf0xMjCrv1KlTSz1ee+01ry674fnnn1frio6ONt15552mp59+2jR27Fi17ieffNLry09ERESe7/PPP1fnDn379jXp4ODBg6q8vFRBRFT873v5Xly5cmWV3y3yeyXbKr9fRDpgcsUJgwcPVl8Q77zzTrHx48ePV+Pvu+8+U1WzYsUK0969e1USQb6E7SVX0tLSTLVq1TIFBgaa/vrrL/P4rKws0xVXXKHm/eabb4rNs3btWjU+NjbWlJKSUuykWC4yBgUFqWFLL774ovmCZUFBQbGLmzK+bdu2xcaX1fLly00LFiwotaykpCRTo0aN1Lrmzp3rteU3tt2aZ555Rq3rgQce8OryG+T4HzhwoKlZs2bqorm15Iq3lV9OvuThCG8ru/j+++/VMq+88kpTenp6qfdzc3O9uvxERER0cXfccYf5Qn7nzp1L3XhlSf6GkulkHlvLsZcAOXHihKl9+/ZqusjISNOGDRscChGTK0QVw7gR7cyZM9zllUz+jpJYvPnmm5W9KVUGkytEVReTKw46cOCAOhFu0qRJqYtfcuFO7naWO4/PnTtnqqoullz59NNP1fu333671USFvNenT59i4//1r3+p8Z999lmpeZ599ln13pQpU8zj5A+Wxo0bq/Hx8fGl5undu7d6T5JC5Wn69OlqPVKTQ8fyb9682XzhWYfyv/XWWyYfHx/T6tWr1UmateSKt5XfmeSKt5VdvqObNm2qvpNPnjypXfmJiIjI+eSKPH788cdySa4cO3bM1KZNGzWN3NAh5+KO+umnn1RtWjn30AFrrlBlMb4HSt4gRZV37crRv2d1wOQKUdXFPlcctGLFCvUsbfX7+hbfbeHh4ejZsycyMzOxfv16eHoZhwwZUuq9Pn36qD4IpE+CnJwch+a5+uqri00jDhw4gMOHD6Nly5Zo2rSpQ/OUh4CAAPXs7++vZfl//vln9Sx9Snh7+aUvi4kTJ+LRRx9V5bDFG8sv2zpnzhy8+OKLePvtt7Fy5Uqr/Yd4W9llWw8ePKj6T4mMjMTChQvxyiuvqH3w559/en35iYiIqGymTJlis1/Gsjpy5Ig6n5BzUun7bdWqVejQoYPD80v/kbt378Z///tft24XEREREbmOyRUH7dmzRz3LhTFrWrRooZ737t0LbyyjJCHkgmB+fj7i4+PVuIyMDBw9elR15Cx/KDiyT6rCfpQyGH+cWF4Y9ebyv/7663juuecwfvx49O7dG88++6xKrEjSwZvLL9v7r3/9C40bN1YJBnu8sfzHjx9X5Z80aRIee+wxDBgwQK1j9erVXl32v/76Sz3XqVMHnTp1wnXXXaeOddkHPXr0QN++fZGcnOy15SciIiLnyLmB3EyxY8cOfP31127bfXKzhyRW9u/fj0aNGqlzsLZt2zI8RERERF6CyRUHpaWlqeeIiAir7xvjU1NToUsZy7JPqsJ+lIus27dvV3e1X3XVVVqUX5Ir06ZNw1tvvYU//vhDJZWWLl2KWrVqeXX5//Of/2DTpk344osvEBISYndabyv/XXfdheXLl6sEiyQDtm3bhvvuuw+HDh1StSS2bNnitWU/efKkep41axaysrLw22+/4ezZs+pzL5/5NWvW4Oabb/ba8hMREZFz6tati4ceekgNyw1JclOFq+SGCUmsyLmX3Kgh5x/GzRTOkPNYHx8f9OvXr9R7TZo0Ue9JbZikpCTcf//9Kokj571t2rTBm2++Wawmzg8//KButKpRowaqV6+Oa6+9Vp0fWXPnnXeqZcv+yM7OxtSpU9G6dWu17Nq1a2PUqFE2bwqReWReWYYtlst3xvz589XfcXITjbRGEBUVhVatWqnt+e677+zW3B86dKiKdWBgoCrD9ddfj19//RVlIfGQ7Zf4yPnbU089pfaPJOlk/1rKzc3Fe++9p/a9bG9QUBBiYmIwZswYVaPJHWWV40y2Rx5i7dq16gYj+XtPtqljx45qGy5WM+unn35SfyvKfLKdDRs2xG233YZ//vnH6vQl1yvH08iRI9V+Dg4OVvvk+eefV/vAGjlHl/c7d+6sWgSR2NSvXx9dunTBk08+afP4PHfunLp57vLLL1fn0bIu+Xw98sgjqraYM4xj0SCfV6NMto5j+Rtz9OjR6vMm+yk6Olr9nfHjjz+iLOQzLOuSz7SQ4/LKK69UMZfjadCgQcVq4MvfFnIDndy4JZ9J2Q45BuVvH1sk9p9++qlKJstyZZ9JWe+9916VAHZku4zjSsor65VaeHJcFbWqBrd8/mRd/fv3V8MJCQnFYmF85gwpKSmYPXs2brrpJnWsyTEUFhamktj//ve/cezYMYeOW2mBZvjw4erGOT8/P3VTnlxLkPflWLTn888/V9NJDJyp+Sh/j99+++2qvHIMybY3a9ZMff7kuo20jGOLlFvKJ/GTeRs0aICxY8eq3wF7pCWLG2+80RwHeZbakY60nhAXF2feXjl25BiQGxmffvpp842EjpDWIORYkH0mN8Hu27fP4XmJqqzKbpfMU4wdO9ZqPw2Gp59+Wr3/0ksvmTy1z5UWLVqo9/ft22f1faNj5z///FO9Pnr0qHrdoEEDq9NLh9HyvnTsbPjqq6/sbsOvv/6q3r/qqqtM5eHtt99Wy2/durXp9OnT2pX/+PHjqt3mli1bmurVq2f6+++/vbb8cXFxJj8/P9OTTz5ZbLytPle8rfy2PP7442odN9xwg9eWXWIuy/L19S3VpnlmZqapYcOG6v1169Z5ZfmJiIjIMUZfKbfccov626B69erq9UcffeRSnys7duww1a1bV42T8+4jR46UOST2OrQ32uCXPuCM9UkZ5BzY6D/C6GPyqaeeUq/lvfDwcPP7NWrUMO3du9dmmSZOnGjq3r27Gg4MDDTvI3lI/3bSp2FJxvm2tX1VcvkyraN9rjzzzDPF+siRcgQHB5tf16lTx+p5mRE742FZBnmU/HvBERIPmffVV181NWvWzHzuJ9sUERFRrL+dDh06mNcl56eW+1+231pfP86W1XK/zZ071+Tv72+OrzFs/A2Ql5dntc9C6X/QmE6OE5nXcrvff//9UvNZrlfOZ0NCQtSw7AOZx3hv6NChpeZNTU01tW3bttg6IiMji80nx21JO3fuNB/78pDySR+4xmtZxh9//OFwLB955BG1P435o6Oj1WvjIe9b+vDDD4tto+wny8/c6NGjTfn5+aay9jEyc+ZM1V+orMPyWJX4//7776pPyUsvvVSNk3LL59KY5tprr7W6/IyMDNPgwYPN0wUEBKgYWS573rx5drdLvouknLJtlvPK49FHH7W63rJ8/rp06aJiaBwTlrGQx7ffflvqb1vLZVvGQvq42rJli93j9rvvvjN/RqRcsm+kPPK9bcR569atNmPXq1cvNc2kSZNMjlq4cKFaj7EN8t1Rcr/s2rWr2DzGMf/ll1+ah+U7WOY15pE+olNSUqyuU7bPmE5iKMetPBvj5LveGuk7dMKECaX2s+VxV/K73vh+lGPG0tmzZ00DBgxQ78nf4AkJCQ7vM6KqjDVXHGTcVWzcfVxSenp6sel0KOPFprd2p3Zl7seZM2eqfjfkLgbJ2MvdGjqVX8hdT3JngtRaOX36tLrzwBvLbzQHJnfyyJ1QjvCm8tsjdzQKuXvSW8su/awIufOnZJvmcoeVUWNtw4YNXll+IiIicp78bSBN6Ao5f7Tsa80Zcjey1GqQ2sOXXHKJagpM7v4vT7LdcgezrFvONeS8wjgHlr+B5A7/N954Q90NbbwvtZqlFoTUupA74G354IMPsHXrVnV3uNQWkPnlrn25Y1nurB4xYgTOnDmD8iZ3mr/88stqWO6UliZepRxyp/6JEycwd+5cVROnpAkTJuCrr75Sd1tLk29SU0LKIM8ffvihqsHz2muv4ZtvvinTdsnd7Xl5eVi8eLHaH7JNGzduVO/JeLlDW+IitZjk/Fu2V6aR4+Pxxx9XtYLk7xbpn8/VshruvvtuVetBmrSV2EiMX331VdV37Lx589RwSTJOms6Wu8nl2JH55JGYmKhqfMsd+VK7y/JviJJuueUWVRtBmsOTdco2v/TSS2qZUgtn0aJFxaaX/hB37typasn88ssv6jMnd+TLPpFaUbIPYmNji80jsZPaPFKj4YYbblA1amS/yLEp65V9KdstNRkcrREu2yHxsGxiWF4bD3nfIP0wPvDAA2p/SE0HqSVj7OPp06erskqfl1LuspBYy+dZ4i5/r0t5pVxXXHGF2i9SW0H+npNj6/fff1fHsTw++eQT1Zyx9DVZcj8LmU+uAUgtB6ndL/PINkuNA/m+kmXfeuutNmujyXZJKwhSdqkdIfNKuR9++GH1/jvvvKOaVXTH50/2v9SgElIbxDIW8pDjzCA1NqRlEjkOjGXLcSSfQfmbT7ZbymWvZo18XuRzahy38jmWmivyvW383Si1U6yRGj/SMojEXVqOcJTsN4mh1AKSGMj+l22Xh3zGpBaK1A6xNa/8vSvHorRQIce+fL6khpN8d1g79r799lt1fAr5HEtLDxI/2T9GDOXzJseutVZQjO8Mib+sQ7ZTPncyLMeTI7Uy5bMt30tSS0aaqJfjV2quEHmFys7ueAq5y11217333mv1feMugN9++83kqTVXjDsKvv7661Lvyd0tkhWXjH52drZ5vNy5LfPIHTklyV3h8p5k8g1yZ7hxB5c1L774onp/8uTJJnd688031XLlDo8TJ05oV35rOnbsqNaVnJzsdeU/c+ZMsTsr7D2Mu2y8qfz2pKWlme+OMXhb2eXuP1mW3PVkzRNPPFGspqG3lZ+IiIicr7linCdFRUWpcW+99ZbTNVfkbmLjjms51zbOs13hSM0VWaec/5Zk3CEsj2nTppV6f82aNebzwpycHKtlksecOXNKzStlq1mzpnr/+eefL/eaK3J3udECgaOkRo7ceS53aB84cMDqNMZyL7nkEpMzjDuz5e7zbdu22b2GcPnllxc7j7T0wAMPqGnGjRvnUlkt95uUxdr6jLjIXefnzp0zj5dh4655a3evSy0M4+783r1721zvoEGD1F3uJV133XXq/bvuuqvY+KuvvlqNf/nllx0up3H3vdSEsbYucc0116hpXnvtNZMzjHJImWwxPlM9e/a0WjvFaNGkWrVq6vvE2Ws18rjzzjtLvS93+Bu1DOSYs1bjfsyYMVb386FDh8w1MGbNmmW1VktsbKx6/1//+pfN7brnnnusbnu7du2sfse48vmzrDFTVvIZMGpGrVq1yuZxK7GUmlvWSKsfRg0YqYVjK97Wvp9tketRxrqlZRFHGd/3Unvn1KlTpd5//fXX1ftNmzYtNl4+J82bN1fvjRw50uqyR40aZd7flvtC1iN/C8t7UlZHlay5kpSUZK5tJTUhbdWuIfJUrLniIKPNR8n2l2xHUTLk0vak3BHdvXt3eCrp7FosWbKk1HuSPZcMvnQGLXc7ODKP3L1jOY2QO08kOy13RMidAY7M46pXXnlF3f0h7cxKjRVp31On8ttitD8qbYp6W/llG+UOFGuPyy67TE3Tq1cv9VruAvK28ttjtNUrtToM3lZ2uTNQ7tyS9lutte9stN1stB3sbeUnIiKispG7qOVOayG1PeSuYGfI3fRGLQ6pMSJt0lcEuZO9ZD8fQu4SFtK2vty5XlLPnj3V3dFyp7etPhekbxC587skKZvcyS6kJkVFxEbIHdP2+iKwJDUx5G93qeFgee5rSfofkHM8uev+Yv0VWCN9GV566aVW35PaPmLcuHHFziMtGft22bJlLpXVktSIsbY+OQYk3lKjxHJ9co1DxslxYhz/luTvxWeffVYNy93mlrU8LEkNAsu+Swyy/0XJ/lOMcjqz3419Kn/fW1uXkD5phGUZ3UHuvJfrCUJqlhh/R1uSfk9kH0ttAms1SBwhyy5J/o4wagdITaLmzZuXmmbgwIFW97PUApHPgfSvcc8995SaT/rkMeIu0xYUFDi8XUJqfVhbb0V8/uyR5UpfNUKu19n7vEitLmukJpa0/iE1PKR2lSUpm5RRSP9JjpK+VYz1laXM0kdOzZo1bX7O5G9Ny9+uzZs3m7/fJ0+ebHWZ0qeW8RtmtO5g9NMl30FSU8b4DnCW1G6Ray9yfMgxKv2hGi1NEHmNys7ueBKjdso777xTbPz48ePV+Pvuu89UlV2s5orcWSHti0rbiX/99Zd5fFZWlrnPgW+++abYPGvXrlXj5U4Hy+yz3Akgd33JXVAl7/ww7tAePnx4say4tPEp4+XuAlt3DjjrP//5j1pm586dS/Wx4u3llzY65Q6BkmTZRhu+PXr08Nry22KrzxVvKv/27dutHu9y15Jx18r06dO9suwl7y4t2fbt0qVLze0EG3d4emP5iYiIyPmaK8Zd3Eb/C/Lb7UzNFel7Q84pZLh+/fo2+3Nzd80Va7VvxSeffGK35qww+qIr2UeFUSbph8MWo8846ePAsuZLedRckfMto1ZR+/btVb8X8fHxJnuMWgZSi6Bkvw2WD+Oufumz0dk7s231uSq1n40+CWS7ba3bOF6krxJXymq53+xNa5zbPvvss+ZxUnPaqGFji5wXG/1SSH8R1tabnp5udd7Fixer9+XvEEuzZ89W4+XcXPopWbRokc1liMOHD5vXJTUJbO1To/ZYmzZtTO6suSKtlBjbK31H2CI1IZzty8e4ViN9n9iqkWPUHrL8XrK2fSX3s+xbGX/zzTfbXL9Ry14e0mdUye2S49GWDz74QE1z5ZVXuu3z50zNFbnuITW/pAaN9E1k2Y+I8bCsGVbyuLV2zcSS0d/I9ddfX2y8HK9GTTD53XBG//791by1a9dWNf82bdp00X56jO/7BQsW2PyMGmVKTEws9Tsgnxl7jJYZpM+fkt/TN954o1PlM74fZd8Zy5XaZrZq8BF5OiZXnLB//3715Wd8MUiVWeNLUU5YrVXNq2z/+9//1BeiPKSjZOOk3xgnHYCVnF5OjqVjtLvvvludELRq1cp8QdDaD/2///1v9b6cmD/22GOmBx980FxF/N133y01vXyhykV9o9ke6aROqiHKyZpUOVy/fr1byv7FF1+YT/Zlu+TEveSjZAdb3lR+aQpNliknNWPHjlXHq1QRNjpclE4vLU+cvK38ziZXvKn8Uka5uD9kyBDV1ICc1Nx0003mTjClqnzJph+8peyW1a2NRJI0XyDfdVIOKaOs7/vvv/fq8hMREVHZkivi7bffVuPlIq10uu1Mh/abN282X9xt3LixurmlvJMrciHS2XkvtgyjTPaagpEbeqw1b1NeHdrLRX3LTtaNv2kkAVSy2R8hF9dLXmS197C1H+1dPJQLlxdr+sfRhytltdxvJc/zLcl5rUxz//33m8fJTaJGZ/f2GElH+Tvb2nptsXehXJpdtyyjXGiXJvUk+VOy+V25+O7M/nS2SamLJVfkZit5X+Jij3yf2GreyxZHkgm2Ogm/2DKM60Dy94otlhfmLY8vR7bL1veMK58/R5MrEhPLjuGNZsiMxI38bWctFpbH7cWSGtK8mUwnf7NZfs8ZnyVbXQfYI82kldw/koSSv9Olw3pJzjr7fW/rGJYEsIyTz5U93bp1U9M999xz5nFyPeFix469Y9V4yPVSa2Ui8hZMrjhJ7paQL2Y5sZEvcTlhfuSRRy5aK6KyGCe2zpxwyF1L0v6p/CjJxVhpG/GNN96w+6MjJ1hysVAuEMqPQp8+fUw///yzzekzMzNNU6ZMURc/5Y4euWNHfpxKXuwvz7Lb+kPDW8ovbf/Kxd4OHTqoC75y4VjuqpDtlH1j65j1lvKXJbniLeWXE2JpT1WSA1JDQ04EZR1yN5HcIWbrbihvKLslOcalZmGTJk3U97XccfV///d/pj///FOL8hMREVHZkityQ0SjRo2K3eHvaHJFSE1YOQeTcXJjk+VdxN6UXJG/NyoyuSIk2fXRRx+ZRowYoWoHWf5tJzeUWTJulJFkmbtd7EK33A1vbNeWLVvKtA5nyupockVuuLKVXJHz4IpOrhhJOjk/7tevn6rBYyxPLoxLrXODnMMb7znTn4m7kyuWtYw8KbkiN93ZIt957k6uuPL5c2S9J0+eVH9/Gd/hGzduLNUvilErq+R3kSPHrbV9b/TjI39nGjXTynqDnCQb5AY/Sc6UTLR06tSpVO0oV5MrF6vJZS254khizt7+ku8bo8ab3FhI5K2YXCEiIiIiIiLt2EquCLmoLe9JMzPSebszyRWxbt0684U/uWv3Yk3PVNXkir0EiVz4ttYsmDRzY2u/GqSWRFmSKyXJDSqSaDDm+eWXX8zvyU0v5dV898UudMtFXtkv1pqXLSt7ZbXcb/Y6ZDdqUVtrFkyaqHWlWTBbnGniSY4juVHJ6CS9Xr165gvm0tyZsS5bN0u54mL7z2h2Sx5yYb88mgUrj+SK0SyY1Iooa7NgZUmuuPL5c2S9RrNy9ppWNj4vriZXpDaJ5WfEqN1o7zPjLPmNkOSN0drEE0884ZbkitEsmCQry9os2LBhw5wqi+Wx+sMPP5i/CyWJSuSN2KE9ERERERERkYW77roLsbGxOHv2LF5++WWn980VV1yhOkCWzqL37t2rOpc/deqUx+3j1atXX/Q96dBdOkM31KhRQz0nJiZanU+uAf79999u2b62bdvio48+Qvfu3Uttr8RA/Pzzz8jLy0NFCggIQJcuXcydhJd3WS3ZGi/H8j///KOGO3XqZB5vDO/btw9Hjx61Ou+aNWuQn59fal53k+PouuuuUx1pGx1+y3aJpk2bqs7F3blPLfn4+KjnomvUpV122WXmaYyO7UtKS0szH9vluZ+cYWxHXFyc6pzcmhUrVqjnsLAwtGrVyi3rdeXzZ3T4bisWlt8v7du3t9ohvcxrlMtVw4cPV99rO3fuVPvx888/d7oj+4upW7cunnjiCTz22GMX/e4tS/ylk3vLzuotyW+U8dm3PG6N75pVq1YhKyurzPvuv//9r4rRf/7zH7z44otlWg5RVcbkChEREREREZEFf39/PPfcc2r4/fffx7Fjx5zeP3379sW8efMQFBSEHTt2YNCgQThz5oxH7edDhw7hm2++KTU+JSVFXegXN998c7H32rVrp57/+usvdXG8pK+++gpHjhxxajtyc3Ptvh8SEqKec3JyzOPuuOMOdUFPYvfSSy/Znb884nLnnXeq5x9//NHmxXhr6y9LWS3NmDHD6jLeeustZGdno3r16hg8eLB5vAzLOLkA/tprr5War6CgAM8//7wa7t27t7oI7A72ymmUsWQ5jX0qn8ldu3bZnF8urEuiwxmyD0RqaqrV96OiotC/f381/Morr6CwsLDUNDJe9nG1atVwzTXXoCq48cYb1efg9OnT5s+sJUm4GHGXaf38/NyyXlc+f0Ys7MUwIiJCPW/fvt1qEubjjz/GgQMH4A7BwcEYPXq0Gn788cexefNmlUD917/+5fSy5HNmL2l0sc+3szp27IjmzZurYVuJDeO3rkmTJujatat5vHy3y/ZIfCQxUla33norPvvsM5WcnDRpkvqOIvImTK4QERERERERWbkgJLUF5I7di10ct0USKnJxXe7IlwtyQ4YMQXp6usfsa7mAOXbsWMyZM8dcc2Hr1q246qqrkJycjNq1a+PBBx8sNk/Pnj1Rv359dfF81KhROHjwoPki7ocffqiWFxkZ6dR2fPDBB2qdX3/9dbGEjVwIlwuGcme1kGkMbdq0Md8FPnXqVIwbNw7x8fHm98+dO4dly5apC6QlE0TucPfdd6s7v+UivNTGePvtt1VSynDy5EmVuOrXr596z5WyWjp8+DCGDRumEmPGfn/jjTcwbdo09fqpp55SNaoMUlvhmWeeUcPvvPMOpk+frvaNkLvZJYZ//PGHulD+wgsvuG3/SG2uRx55RNWKsbwrXhKRRhKlXr165mSdmDhxIpo1a6buwpfk5ezZs83bKiRpJxfVO3fujP/9739Obc8ll1yinuUue0koWSNJJtkPUgNo5MiR5toTsg0SG6OWm2ynkSCobDExMbj33nvN2yUJFuPCvdRYuPbaa7F//351TEyePNlt63Xl89eiRQuVvJDkinx/2jp+5GK9JFfkODKSYvL9KskiWV/NmjXdVh753hJr165Vz/KZlu8/Z8nxLbX9JNkp+99ItEjSRcoqn1V7n29nyT4yPrfz58/Hww8/rBJtQp5l3xkJdJnOshaQ7D+JnZBj+6GHHlLfL0K+12RYtteRxIsk2+T7X7ZHaui8++67bikfUZVQ2e2SEREREREREVWlPlcMc+fOLdbRsKN9rpT0008/mfuskD4Zzp075xF9rkycONHUvXt3NRwUFGSqXr26eV+EhoaaVq9ebbO8vr6+5mllPqP8Y8aMcbpD+zfffLNYHKT/gBo1ahQbJx1Dl5Sfn6868racTvrRkXl9fHzM46QzdWdcrP8Lw4kTJ8x9cMhD1hkZGWnuj8d4WHYiXZayWu43OWaNfS3zGcPyGDp0qOpI29p+uv32283TSR8Jsp3GPpJYWvbFYG29zvaf0aFDB/O8snxZn9HfhHF8ST8n1voHsewAXOaNiopSHc1b7qMvvvjC5IzPPvvMPK9sR+PGjdU2P/7448WmmzVrlvnYNuJp9CkhD+mfSfanM8qzzxWRkZFhGjRokHkbAwICih1T8tmeN29embbL3veMK58/y+MxIiJCbYM8pA8Pw/jx44st2zIW0hn7pEmT3NLniqFLly7m+aRvoLLYtGlTsW2WfS/Hr+X3pawnLS3NLX2uGIx9Yfl5s1ynfNdbU1hYqDq0t9xmiUdgYKDN30V7x+p7771n/ux8+OGHTuw5oqqLNVeIiIiIiIiIrJBmctzRd4LUJJDaH9Lkjtz5fP3115e5DfuKJE2aSa2dKVOmqDvgpTZKrVq11F37cvd+nz59bJZ36dKlqhml8PBwVRNAmqf55JNP8Omnn5apFpHUSLjlllvUHfFyV7vc+S41G/7v//5P3ZEtd0WXJPtbmpCSmhfSrI9RBtn3jRs3VtsptR+k+bbyIHe2S98J0hSaNBMlr2W75Tpo69atVe2WRYsWmWuOuFJWw0033aRiJjUSpPzSxF2HDh3UneLSV4m8trafZD/MnTtXNRMm/UsY65SaK9JXQ8kaSq6SY0Fq08gxIrEwPg+yX+QOeamRMHDgwFLzSRNHmzZtUnGVeaW5LqmtIOWS/jfkznzZ58422ST9LMl+l2aRZFlSCyYhIaFUX0n33XefavJO4iT7R/aT1PCSWmrSV4zxOa9KpFbK4sWL1T6Xpt3ktdRoks/DPffcg23btmHo0KFuX68rn79Zs2bh6aefVn3ASE0biYU8LGsqSa0JqYkj/eHId5XUrpPvGakVsnDhQqvHuqu/B0LifvXVV5dpGfKZls/Z/fffr7ZbPmty/EpNp169eqnPqfxGuLvmk9RKWb58uYpzdHS02o9SM0W+U3777TebTbdJTZM333xT1TCT76QGDRqo+MkxL7+N8t0lTX05SmoUSdzkO1D2gdF/DZEn85EMS2VvBBERERERERFVDdIsk1z0lCZhjPb4qeqSJsCkw3fBSzxE5UMSaJKIkKb1jCbgiIhYc4WIiIiIiIiIiIjICumXRmp+SE0Oqe1DRGRgcoWIiIiIiIiIiIioBGlCS5qbk1ph0pG9NE1HRGRgcoWIiIiIiIiIiIjoPOm7pUmTJqqPkiVLliA4OJjNgRFRKUyuEBEREREREREREZ2XmpqKhIQE+Pn5oUePHli6dCnatm3L/UNExbBD+zLq3Lmzev7777+hI5af8Rc8/vX7/POzr/dnn4iIiIiIiIiINKm5kpiYiDFjxqB+/foICgpSVfoee+wxnDlzprI3jYiIiIiIiIiIiIiIPJA/vNiBAwdU1b2TJ09i6NChaN26NTZs2IC3335btZe4du1a1KxZs7I3k4iIiIiIiIiIiIiIPIhX11x58MEHVWLlnXfewbx581THUytWrMD48eOxZ88eTJo0qbI3kYiIiIiIiIiIiIiIPIzXJlfi4+NVZ1PSDNi4ceOKvTdt2jSEhYXhyy+/REZGRqVtIxEREREREREREREReR6vTa5IDRUxePBg+PoWL2Z4eDh69uyJzMxMrF+/vpK2kIiIiIiIiIiIiIiIPJHX9rkizX6Jli1bWn2/RYsWqmbL3r17MXDgQJvL6dy5s9Xxu3btQps2bdy0tURERERERERERERE5Cm8NrmSlpamniMiIqy+b4xPTU0t0/IlsXJ60H/QZOICi7F+iA7zx82Nc9C6hkmNadWqFVq3bo0lS5YgJyfHvO5+/fph8+bNSEhIMM8ttWxku+Pi4szjOnTooJo2mz9/vnlcnTp10L17d1Xr5sSJE+bxQ4cOxaFDh7BlyxbzuG7duqn1SSLJEBMTg44dO2LVqlXm/RQUFIQhQ4Zg9+7d5sSU6Nu3r3pevXq1eZyU6e+//1ZlMrbLG8rkTJwWLlyoymSUwRvK5EycZs6cqcpkvOcNZXImTlOmTFGvZTneUiZH4/TVV1+pMhnr84YyOROn6dOnqzLJtnlLmazFiYhIF1lZWQgJCanszaAKwFjrg7HWC+OtD8ZaL4y3PrI8/Hzcx2QyFWUBvMy9996Ljz/+WD3uueeeUu8/88wzeOmll9Rj4sSJZVpHk4kLrY6/oWN9vDXysjItk4iIiIiIiIiIiIiIqjav7XPFqJli3M1bUnp6erHp3Gne5mNoO2UJvJ3cLa0zlp/x1xWPfb2PfSIqX4mJiRgzZgzq16+vaqNJrbfHHnsMZ86cKbfl5OXl4e2338Zdd92lasQFBgbCx8cHn3zyCbyd7r9pOmGs9cFY64Xx1gdjrRfGWx+rPPx83GubBZPmToT0qWLNvn377PbJ4oiagQU4netn9b3M3AK0nLwYjw5sgXH9m8Mb2Upc6YLlZ/x1xWNf72OfiMrPgQMH0KNHD5w8eVI1EShN923YsEElPqQJv7Vr16JmzZpuX05GRoZKvBhNFtatWxdHjhzRItS6/6bphLHWB2OtF8ZbH4y1XhhvfaR5+Pm419Zc6d+/v3qW9ukLCwuLvXf27Fn1R6W05ybt3ZfViFjA384ezM0vxJq9yWVePhERERHp48EHH1QJkXfeeQfz5s3Dyy+/jBUrVmD8+PGqH6VJkyaVy3JCQ0OxaNEiHDt2DMePH1c1XoiIiIiIiEjT5EpsbKzqVFg6BZbOty1NnTpV3aF3++23IywsrMzr6FAnEOMHtUL1INsVgOIOpnhtE2HSxITOWH7GX1c89vU+9omofMTHx6ubgqT5rnHjxhV7b9q0aeqc9csvv1TnsO5ejjQDdvXVV6NevXrQje6/aTphrPXBWOuF8dYHY60XxlsfQR5+Pu61HdpbaxKhTZs2iIuLw8qVK1VzYOvWrXOoaQVH9H11JRJSMu1msR6/qpXXNhFGRERERGUn/ZuMHTsW9957Lz788MNS71911VUqafLbb79h4MCB5bqc5557TiViPv74Y9xzzz0MKxERERERkU41V4zaKxs3bsSdd96pkiozZsxQCZdHHnkEf/75p8uJld27d5uHV0/oj9BA6/2vCGmYbFdSOryJZfl1xPIz/rrisa/3sU9E5UOa67LXH2CLFi3s9ifo7uWUVefOnW0+qiLdf9N0wljrg7HWC+OtD8ZaL4y3PnZ7+Pm413Zob2jUqBE+//zzclm2/PEqHYQaZo3ujDs+2wBbVYF+2ZqEbYkrVSLGG5Qsv25YfsZf1+Ofx77exz4RlW9HjhEREVbfN8anpqZWyHLK6w8nI/kj+vbtq55Xr15tHteqVSv1HbtkyRLk5OSYt7lfv37YvHkzEhISzNNKE8BSXrmJytChQwfVJNr8+fPN4+rUqaP6WVy/fj1OnDhhHi8122V7LLepW7duan1Su8cQExODjh07YtWqVeb9K80XDBkypEqWSZpF3rJlC8tkJU5GrBgn7z/2ZDneViZvjJM7yiSCg4O9qkzeGCd3lKnkb7Y3lMkb48Tvcv3i5I4yyXqqQplk2c7y6mbBypscHHJAWxr9aRx2Hk1DSmae1zcRZq38OmH5GX9dj38e+3of+0RUPqQZL2mGy1ZTXM888wxeeukl9Zg4cWK5LkenZsF0/03TCWOtD8ZaL4y3PhhrvTDe+pjv4efjXt0sWGWYc3c3/DNlMGpVC7TbRNi8TUexZm9yhW4bEREREVVNRo0S4w6sktLT0+3WSHH3coiIiIiIiMg+JldcYFQvsmbGiI7w9bE9776T5zB53jZ4a/l1wPIz/rrisa/3sU9E5UOqqNvrC2Xfvn12+1Jx93J0oftvmk4Ya30w1nphvPXBWOuF8dZHXw8/H2dypZz0aVkLPZpHIzzIdif3h1Oy0OzphZi5cn95bQYREREReYD+/Yv65JM2hQsLpZ7zBWfPnsXatWsREhKi2iiuiOUQERERERGRfUyuuMCyQxxbTYRtmzYEjSJDbE5TaALmrE/wyATLxcrv7Vh+xl9XPPb1PvaJqHzExsaqjiClI8eZM2cWe2/q1KnIyMjA7bffjrCwMDUuLy9Pddp44MABl5ajO91/03TCWOuDsdYL460PxlovjLc+Vnv4+bh/ZW+ADqYPa4c7PtsAk433k9Ky8U1cgsd3cE9EREREZff++++jR48eeOSRR7B8+XK0adMGcXFxWLlypWrGa/r06eZpjx49qt6PiYlRiZSyLsfw8ssvq2SN2Lx5s3r+/PPP8ccff6jhXr16eX3n9kRERERERM5gcqWCmgjr2SIafx9KQVZe8eYZDImp2Yh9eiEOvHRtRWwSEREREVUxUutk48aNmDJlCpYsWYJFixahXr16KkkitU6ioqLKbTkyXcm7xtatW6ceBiZXiIiIiIiILmByxQVGh6GOkCbCRK9XliPxTLbVaQpMwBUv/YbY2uHm6b2l/N6I5Wf8dcVjX+9jn4jKV6NGjVSNkYtp0qQJTCaTy8sxrFq1CjrS/TdNJ4y1PhhrvTDe+mCs9cJ466OVh5+P+5js/VVGbid9q8z4dQ+s118pUj8iCOuevpJ7n4iIiIioHBXm5sI3MJD7mIiIiIiInMYO7V0gzSc4S/pV6dEiGuFBfjanOZaWgxbPLII3lt+bsPyMv6547Ot97BMReYPD94zFvr79sLtDRxSkpVX25lAF0P38RSeMtV4Yb30w1nphvPWxxMPP0ZhccUFOTk6Z5pMmv7ZNG4KGkcE2p8krNKH9c7+qmi7eVn5vwfIz/rrisa/3sU9E5A3ykpKQf+KEVONHbmJiZW8OVQDdz190wljrhfHWB2OtF8ZbHzkefo7G5EolGtU1Br4+tt9Pz87Hmr3JFblJREREREReL6BhA/NwXuLRSt0WIiIiIiLyTEyuuCAiIsKlnS9NhN3YqaHdJsLiDqZU2SbCXC2/p2P5GX9d8djX+9gnIvIGgQ0bmYfzWHNFC7qfv+iEsdYL460PxlovjLc+Ijz8HI0d2lcRvV5ZjsQz2Tbfr1UtEDNGdESflrUqdLuIiIiIiLzN6c+/wMlXXlHDNUaNRL2pUyt7k4iIiIiIyMOw5ooLNm/eXGFNhCWfy8VP/yR6bfk9EcvP+OuKx77exz4RkTdgs2D60f38RSeMtV4Yb30w1nphvPWx2cPP0ZhccUFCQoLbAiFNhD0+uBWiwwJtTjNv8zG0nbIE3lh+T8TyM/664rGv97FPROQNAhuxWTDd6H7+ohPGWi+Mtz4Ya70w3vpI8PBzNCZXqhBJsGx8dhAaRYbYnCYztwAtJy/GzJX7K3TbiIiIiIi8RUDDhubhvKNHYSosrNTtISIiIiIiz8PkShU0fVg7+NuJTG5+IdbsTa7ITSIiIiIi8hp+1arB73znmabcXOQn89yaiIiIiIicww7tXZCVlYWQENu1TFwhNVM+XHUA6Tn5NqcJDfTDzv8MgTeW3xOw/Iy/rsc/j329j30iIm9xcPjNyN6+XQ3HfDUHoZ07V/YmUTnS/fxFJ4y1XhhvfTDWemG89eHpsWbNFRekpaWhPJsI2zrtKsREhdptIqzZxIWV1kRYeZbfE7D8jL+ueOzrfewTEXll02CJiZW6LVT+dD9/0QljrRfGWx+MtV4Yb32kefg5GpMrLoiLi0N5Wz2hv6qhYou0Dr0rKR3eWv6qjOVn/HXFY1/vY5+IyFsENmxgHs49wuSKt9P9/EUnjLVeGG99MNZ6Ybz1Eefh52hMrniAWaM7w8fO+79sTULfV1dW4BYREREREXm2gIaNzMOsuUJERERERM5icsUD9GlZCz1bRCMqNMDmNAkpmZXaRBgRERERkSdhs2BEREREROQKJldc0KFDB1SUOXd3wz9TBqNWtUC7TYTN23QUa/Yme135qyKWn/HXFY99vY99IiKvbBaMfa54Pd3PX3TCWOuF8dYHY60XxlsfHTz8HM3HZDKZKnsjyHGSOLnz8w0otBO1xlEhWDNhAHcrEREREZENptxc7O7QEZA/h3x80GrLZvgG2r6RiYiIiIiIyBJrrrhg/vz5qIwmwno0j0Z4kO1O7g+nZKHZ0+XfRFhllL8qYfkZf13x2Nf72Cci8hY+gYHIq1696IXJhPxjxyp7k6gc6X7+ohPGWi+Mtz4Ya70w3vqY7+HnaEyueCBpImzbtCFoFBlicxqp2TJnfQL7YCEiIiIisiEvKso8nHskkfuJiIiIiIgcxuSKB5s+rB187LyflJaNb+ISKnCLiIiIiIg8M7mSd5TJFSIiIiIichyTKy6oU6cOKpM0EdazRTRCAmyHMTE1G7FPL/TK8lc2lp/x1xWPfb2PfSIibxLUuJF5OI+d2ns13c9fdMJY64Xx1gdjrRfGWx91PPwcjR3ae4leryxH4plsm+/XiwhCbO1w1aQYEREREREBaQsW4NiEp9SuCB80CA3ffYe7hYiIiIiIHMKaKy5Yv349qopRXWPsBjMpLQfxJ896bfkrA8vP+OuKx77exz4RkTfZe+6ceTgnPr5St4XKl+7nLzphrPXCeOuDsdYL462P9R5+jsbkigtOnDiBqmJc/+bo0SIa4UF+Nqc5lpaDFs8s8sryVwaWn/HXFY99vY99IiJvkuTvbx7OTUiAKS+vUreHyo/u5y86Yaz1wnjrg7HWC+OtjxMefo7G5IoXkSa/tk0bgoaRwTanySs0of1zv2Lmyv0Vum1ERERERFWNKSgI/vXrFb3Iz0fu4cOVvUlEREREROQhmFzxQqqJMB/b76dn52PN3uSK3CQiIiIioiopqFmseThn/4FK3RYiIiIiIvIc7NDeSz3xwxb8uj0JZ3MKbE4T4OuDfS9eU6HbRURERERUlZx46WWkzJ6thqMfeRi1HnywsjeJiIiIiIg8AGuuuODQoUOoql6/uYNDTYRd/sKyMtdiqcrlrwgsP+OvKx77eh/7RETe9psW2PxCzZXcA+zU3lvpfv6iE8ZaL4y3PhhrvTDe+jjk4edoTK64YMuWLfD0JsKSz+Xip38Svbb85YnlZ/x1xWNf72OfiMjbftOCYpubX+ccYLNg3kr38xedMNZ6Ybz1wVjrhfHWxxYPP0djcsXLjevfHI8PboXosECb08zbfAxtpyyp0O0iIiIiIqoKgmKbmYdz4+NhKrDdrC4REREREZGByRVNEiwbnx2ERpEhNqfJzC1Ay8mLMXPl/grdNiIiIiKiyuQXEQG/WtFq2JSbi7zEstXqJiIiIiIivTC54oJu3brBk0wf1g7+diKem1/oVP8rnlZ+d2P5GX9d8djX+9gnIvLG3zQ2Deb9dD9/0QljrRfGWx+MtV4Yb3108/BzNCZXXBAREQFP0qdlLYwf1ArVg/xtThN3MMXhJsI8rfzuxvIz/rrisa/3sU9E5I2/aUGxFzq1Z78r3kn38xedMNZ6Ybz1wVjrhfHWR4SHn6MxueKCpUuXwhObCNs67SrERIXabSKs2cSFF20izBPL704sP+OvKx77eh/7RETe+JsW1PxCciV3Pzu190a6n7/ohLHWC+OtD8ZaL4y3PpZ6+DkakyuaWj2hP0ID/Wy+XwhgV1J6hW4TEREREVFlCGTNFSIiIiIichKTKxqbNbozfOy8/8vWJPR9dWUFbhERERERUcUr1ixYfDxMhXKrERERERERkW1MrrggJiYGnkz6YOnZIhpRoQE2p0lIybTZRJinl99VLD/jryse+3of+0RE3vib5hcVBb8aNdSwKTMTeceOVfKWkbvpfv6iE8ZaL4y3PhhrvTDe+ojx8HM0H5PJZKrsjaDKd/kLy5B8Ltfm+y1qV8Oz17VVCRkiIiIiIm+TcNddyPxzvRpu8NabqD5kSGVvEhERERERVWGsueKCVatWwVvMGNERvnbaCNt38hwmz9vmteUvC5af8dcVj329j30iIm/9TQtp1948nLW1+HkveT7dz190wljrhfHWB2OtF8ZbH6s8/ByNyRUXpKWlwVtIjZQezaMRHmS7k/vDKVlo9vSFJsK8qfxlwfIz/rrisa/3sU9E5K2/aSHt25mHs7cxueJtdD9/0QljrRfGWx+MtV4Yb32kefg5mn9lbwBVHXPu7qaee7+yAkfOZFmdptAEzFmfoIYbVujWERERERGVn+B2F5IrWTt2wFRQAB8/2zceERERERGR3txSc2Xu3Ll4+OGH0bt3b1SvXh0+Pj4YPXq03XnWrVuHa665BlFRUQgNDUX79u3x1ltvoaCgwOY8s2fPRteuXVGtWjVERESgX79++OWXX2xOn5WVhalTp6JVq1YIDg5G7dq1MWLECOzatQvuEBQUBG80fVg72GkhDElp2fgmLsFry+8olp/x1xWPfb2PfSIib/1NC6hTB/61a5s7tc+Nj6/ELSN30/38RSeMtV4Yb30w1nphvPUR5OHnaG7p0L5jx47YsmWLSno0bNgQu3fvxm233YY5c+ZYnX7+/Pm46aabVMLjlltuUQmWn3/+GXv27MHw4cPxww8/lJrniSeewIwZM9TyZZrc3Fx8++23SElJwbvvvouHHnqo2PQ5OTkYOHAg1q5diy5dumDAgAE4cuSIWnZgYCBWrFiBbt2KampQaaM/jcPfh1KQlVdoc/f4+QAHXrqWu4+IiIiIvMKRhx7Cud+Wq+F606ejxk03VvYmERERERGRN9dcefPNN7F3716kp6fjgw8+sDutTDN27Fj4+fmpDms+/fRTvPbaa9i8eTOuuOIKVQtGkiYla7lIYiU2NhZbt25V65s5cyb+/vtvlZiRxMuhQ4eKzfPGG2+oxIokYuLi4vDKK6/g66+/VsvPzMzEmDFjUFhoO3HgCEkieXMTYbuevxoNI4NtTlNgAq546TeViNGRN8ffESy/vvFn7PWNPRGRt/+mhVxq0TTYtq2VsEVUXnQ/f9EJY60XxlsfjLVeGG997PbwczS3JFf69++PFi1aqObALkaSG8nJyRg5cqSqUWKQWiwvvPCCGi6ZoJk1a5Z6njRpEiIjI83jmzRpgnHjxqlaKp9//rl5vFTGMeZ59dVX4et7oZhDhw5VzZft3LkTq1evdqncUtPG243qGmPnIClAUloO4k+ehY50iL89LL++8Wfs9Y09EZG3/6YV79R+eyVsEZUX3c9fdMJY64Xx1gdjrRfGWx97PPwczS3JFWdIc1xiyJAhpd7r06eP6n9FaqpIwsSRea6++upi04gDBw7g8OHDaNmyJZo2berQPLZ07tzZ5kMH4/o3R48W0QgPst2Z57G0HLR4ZlGFbhcRERERkbsFX3qpeTh7zx4UWvxNQkREREREZMkflZSNksRHSf7+/ioZsmPHDsTHx6NNmzbIyMjA0aNHVX8u9erVKzWP1JgR0iyZI+uwNU9ZSf8xhr59+6pnyxoxrVq1QuvWrbFkyRJzwigiIgL9+vVTTaElJCSYpx08eDDS0tJUM2aGDh06qBo6luupU6cOunfvjvXr1+PEiRPFauVI82jS/41B+pWR9S1dutQ8LiYmRvWTI82yyfqMzoMkeSVVsSwzhlKm925qpcr03N8+OJMrYy0TLQXq/7xCP7R/7lf8X4sQXF7tTJUvkzviJIwyeEuZnImTZfm9pUzOxkmW421lciROlrH3ljI5Eyej/N5UppJxIiLSlV/16ghs0gS50uRwfj5ydu9GSIcOlb1ZRERERETkrR3aW5KLPNJMmK0O7SXhsW/fPvVo3rx5qfd79uypaq7IQ/pgOXbsGBo0aKAeiYmJpabPy8tTHdTLw7g4JH2ryPptbcOyZcvUxS95/Prrr2Uua2pqKmrUqAFdzFy5HzOW7kGhnSOmW9MofHffFdCBbvEvieXXN/6Mvb6xJyLS4Tft6IQJSF/wsxquM2kSov41upK2jtxJ9/MXnTDWemG89cFY64Xx1keqh5+jVXizYBdj5Hoc6b/FkjPTl3UdupMmwm7s1NBuE2FxB1PYRBgREREReayQdu3Nw5l//12p20JERERERFVXhSdXpMkRYTRhUlJ6enqx6S42vTHemK4s6ygry+ZVdPH6zR2wbdoQNIwMNjcJVlJeoQmXv7AMa/Ymw5vpGH9LLL++8Wfs9Y09EZEOv2mhXbuahzP+/BOmAuvnvORZdD9/0QljrRfGWx+MtV4Yb32s9vBztApPrkgb77b6O8nPz8fBgwdV3yvNmjVT48LCwlSTYOfOnUNSUlKpeaR5sZL9q9hbh615yDmjusbAXr2f5HO5+Omf0s24ERERERFVZUEtW8C/Vi01XJiWhuwdOyp7k4iIiIiIqAqq8OTKgAED1LPRKbClNWvWIDMzEz169FCd8joyz+LFi4tNI2JjY9G4cWOVXJFkjSPzkPNNhF3bCIgOC7Q5zbzNx9B2SumYERERERFVVdJ0cFjPnubX5/74o1K3h4iIiIiIqqYKT64MHz4c0dHR+Pbbb7Fx40bz+OzsbEyePFkNP/DAA8Xmuf/++9Xz9OnTcebMGfP4Q4cOYebMmSoRc9dddxX7g8iYZ8KECSgsLDS/N3/+fPz+++9o27Yt+vbt61JZjBoyunpoYEtsfHYQGkWG2JwmM7cALScvxsyV++FtdI8/y69v/Bl7fWNPRKTLb1pYr17m4Yy16ypwi6i86H7+ohPGWi+Mtz4Ya70w3vpo5eHnaD4mo3d3F8ybN089xPHjx/Hrr7+qZr169+6txkky5fXXXy82vSRZgoODMXLkSERFRWHBggXYs2ePGv/999+X6mz+8ccfxxtvvIGGDRuqaXJzc/Hdd9/h9OnTePfdd/HQQw8Vmz4nJ0fVTFm3bh26dOmCgQMH4vDhw/jhhx8QGBiIFStWoFu3bq4WnaTG0d5kjPliA/Iv5LBK6dY0Ct/ddwX3FxERERFVefkpKdjXsxcgfyr5+aHl+j/hFx5e2ZtFRERERETeVnNl8+bNmD17tnpIYkXEx8ebx82dO7fY9DfccIPqrKZPnz748ccfVXIkICBAJU+kRkvJxIqYMWMGvvjiC9StWxcfffQR/vvf/+KSSy7Bzz//XCqxIqQ2y2+//YYpU6YgNTUVb775JpYtW6bW/ddff7klsWKtmTKdGOXv07IWxg9qhepB/janjTuY4nVNhDH+3hVPZ+kcf53LLnQvPxGRDt/p/lFRCG7btuhFQQEy4+IqdsPI7fj7rQ/GWi+Mtz4Ya70w3vpY4uHXWGxfDXfCc889px7O6NmzJxYtWuTUPHfccYd6OCokJATTpk1Tj/IgtWN0Zll+6YNFHn1fXYmElEybTYQ1m7gQj1/VSk3r6Rh/Hv+64rGv97FPRKTLb5r0u2J0Zi/9roRfeWUFbhm5m+7nLzphrPXCeOuDsdYL462PHA8/R6vwPlfIu62e0B+hgX4235eWw3YlpVfoNhEREREROcuyU/uMP9bCDa0pExERERGRF2FyxQURERHQma3yzxrdGaUbdrvgl61JqoaLp2P8efzrise+3sc+EZEuv2mhl3WEb2ioGs5LTETO7t0VuGXkbrqfv+iEsdYL460PxlovjLc+Ijz8HM0tHdoTlTT60zjsPJqGlMw8u5k9b2kijIiIiIi8z9EnJyD955/VcNQdt6PO009X9iYREREREVEVwZorLti8eTN0Zq/8c+7uhn+mDEataoF2mwibt+ko1uxNhidi/Hn864rHvt7HPhGRTr9pEUOHmofTflkIU57tG4eoatP9/EUnjLVeGG99MNZ6Ybz1sdnDz9GYXHFBQkICdOZI+WeM6AhfO22E7Tt5DpPnbYMnYvx5/OuKx77exz4RkU6/aWFXdId/7dpquOD0aZxbu7aCtozcTffzF50w1nphvPXBWOuF8dZHgoefozG5QuWqT8ta6NE8GuFBtju5P5yShWZPL8TMlfsZDSIiIiKqMnz8/BDxf9ebX6fNn1+p20NERERERFUHkytU7qSJsG3ThqBRZIjNaQpNwJz1CUywEBEREVGVUv3//s88fG75ChSkpVXq9hARERERUdXADu1dkJWVhZAQ2wkDb+ds+aVvlTs+2wCTnWka1gjGHxMHwhMw/jz+df3889jX+9gnItLxN+3gjTche+dONVzn2cmIuu22Ctg6cifdz190wljrhfHWB2OtF8ZbH1kefo7GmisuSNP8rjVnyy9NhPVsEY2QANuHXWJqNmKfXghPwPjz+NcVj329j30iIh1/0yKGDTMPn/70U5hyc8txq6g86H7+ohPGWi+Mtz4Ya70w3vpI8/BzNCZXXBAXFwedlaX80kTYruevRsPIYJvTFJiAK176DaM/rdr7l/Gv2vEpbzrHX+eyC93LT0Sk43d6jZtuhF9UlBrOP5aE1J9+KuctI3fj77c+GGu9MN76YKz1wnjrI87Dr7EwuUKVYlTXGLsHX1JaDuJPnq3ALSIiIiIiss43NBQ1777b/PrUrA9RyNorRERERERaY3KFKsW4/s3Ro0U0woP8bE5zLC0HLZ5ZVKHbRURERERkTeSokfCrWVMN5x8/jtS5c7mjiIiIiIg0xuSKCzp06ACduVp+aSJs27QhdpsIyys0of1zv2Lmyv2oahh/Hv+64rGv97FPRKTrb5qqvXLPPebXpz74APlnzpTTlpG76X7+ohPGWi+Mtz4Ya70w3vro4OHnaD4mk8lU2RtBepPEyYyle1Bo50js1jQK3913RUVuFhERERFRMYVZWTgw+CrkJyer1+GDBqHBO2/Dx8eHe4qIiIiISDOsueKC+fPnQ2fuKr80EXZjp4Z2mwiLO5hS5ZoIY/x5/OuKx77exz4Rkc6/ab4hIaj7n2nm12eXLUPa/+aVw5aRu+l+/qITxlovjLc+GGu9MN76mO/h52hMrlCV8PrNHRxqIuzyF5Zhzd6iOwWJiIiIiCpaeP/+qDHyFvPrEy+8gJx9+xgIIiIiIiLNMLlCVcqorjHwtdOqQvK5XPz0T2JFbhIRERERUTF1JkxAYJMmargwMxMJd96F7L17uZeIiIiIiDTC5IoL6tSpA52VR/mlibDHB7dCdFigzWnmbT6GtlOWoLIx/jz+dcVjX+9jn4jIm5T1N006t68/43X1LApOn8bhO+5E9q5dbt5Cchfdz190wljrhfHWB2OtF8ZbH3U8/ByNHdpTldX7lRU4cibL5vuB/r54dGALlZAhIiIi8gaJiYmYMmUKlixZgtOnT6NevXq44YYbMHXqVERGRpbrctatW4cXXngB69evR3Z2Npo3b44xY8bg4Ycfhp+f7b7xdJb5zyYcGTsWhRkZ6rVPQACiH34YNcfcBR9//8rePCIiIiIiKkdMrrhA/vDs3r07dFXe5Ze+VcZ8sQH5hban6dY0Ct/ddwUqA+PP41/Xzz+Pfb2PfSIqPwcOHECPHj1w8uRJDB06FK1bt8aGDRuwcuVKtGrVCmvXrkXNmjXLZTnSkeRNN92E4OBg3HLLLYiKisLPP/+MPXv2YPjw4fjhhx/gjdzxm5a1eTMO3zMWhefOmccFtWmDmmPGoPpVg+ETaLtGdlkVFBagwFSA/MJ8mGCCv68//Hz81MPHxwemvDwUnDuntkmGix75MOXlAvn5F8aZTA6tz8fPTz3g5w8ff7+ixJExLOP9Zdj/wjQBJYaN9yqR7ucvOmGs9cJ464Ox1gvjrY/1Hn6OxtupXHDixAnorLzL36dlLYwf1AofrjqA9Jx8q9PEHUxRTYTt/M8QVDTGn8e/rnjs633sE1H5efDBB1VC5J133lG1RQz//ve/8eabb2LSpEmYNWuW25eTnp6OsWPHqtopq1atQpcuXdT4559/HgMGDMDcuXPx7bffYuTIkfA27vhNC+nYEU2+/QbHJj6N7O3b1bicXbtw7MknceKVV1Ctbx+Ede2K4HbtENCgAXyDgqwuRxIdR88dxYEz+xF/fBdOnTqM7NRTyE5LQV5aKgrOnoVvRjaCswsQmm1CaA4Qlg31HJpjshgGgvNQ9fj4FCVlAgJUDR+VcLF4QJIwAYHFxwf4n0/cFJ9HTWuMV9MFFJ/WmD+waFjGZ27ZgvTUtAvJnoAAi2VbbId6L7DYOPN2y7AvW9au6nQ/V9UN460PxlovjLc+Tnj47zaTK1SlSZNf8uj76kokpGRanSYztwDNJi7E41e1YhNhRERE5JHi4+OxdOlSNGnSBOPGjSv23rRp0/DRRx/hyy+/xIwZMxAWFubW5UjyJDk5Gbfffrs5sSKkFos0EzZw4EB88MEHXplccZeg5s1VguX0Z5/j1HvvwZSbq8YXnDqFtB9/Ug+DX82a8A0Lg29ICAoLC5CRmYqc7AwU5uTAL78QNXOA2o5VKPEsJpOqLQOpMVMJq68H4Og337q8HJOvL0z+vjCpGjvGsx9M/lJTxw/w9QF85dkX8PNVSSX1LK9lXjVepvEt/Tg/nY/Mr4aN6Ype+5in8zMv15j2wjxF2yDTSi0mtTycX46PdBgk42W46H21TGM6i9dqGlmOGifrkwRZ0bzmaUo++xRfltp+ecaF4QvTnH99ftnGeDXf+YfabpldsXzPGGUesJgXKEw6jJTdW4u9r4aM18Y2W4wrWtf5YYvp1JNsq7FS83Zd2I4LCbfz5Tu/ScLX/NpyHotlWW6TZTmsbYex78zFvzBcir33nJnmwta6Z3kOrtOpZRUWwlRY6NKy7O5LIiIiO5hcIY+wekJ/VUNFEinWyKnUrqT0Ct8uIiIiIndYsWKFeh48eDB8S9wZHx4ejp49e6qkiVSbl2SHO5djzDNkSOmawH369EFoaKjqjyUnJwdBNmpdEFSthuh7x6LGjcOQ+sMPOPPNt8g/ebLUrik4fVo9DNJomLsbDiv0ATKDih55fkCBH5AvD9/zz34+KPAFTI5cTzQBvucffoUm+BUCfgWAn4yT4RKPUuMKAH8Z7yUJI5/CQvjkyl8f1mvWV0Uld72XhMKm1nIX7FvvV/ZmUAVpCWD3089Umf1tJ81TnIP5HEc+rw59lzvInctyt6YAtj4zsbI3gyoI462HgnefBxAAT8bkigukDWudVXT5Z43ujDs+22Dz5OKXrUnYlrhSJWIqAuPP419XPPb1PvaJqHxI3yaiZUu5TFRaixYtVFJk7969dpMrZVmOvXn8/f3RtGlT7NixQ9WKadOmjd1ydO7c2eZ7f//9N3T4TfOPjkb0Aw+g5tixyNq6FZkbNiDzr43IPXQIuUlJ6uL8xRQE+KEwLBioFgaf8Grwrx6BoIhIBEZEwj+8unrtWz0cfuHh8A2/8CzTIiwU+cEBKEBRnyy5BbnIK8hDbmGuGjaeS45Try3eN8blFOQUTV9o/f1iyzSmKTG/9AvjU2hSSRaVmClE8eHzCZji75msv1fyudh7jq/DPH2x18WHS712+KopEenK4YYD3Znl9PaMKRF5rTyTyeOvMTG54oJDhw6pJhd0VdHllz5YeraIxs6jaUjJtN6QtDQdVlFNhDH+PP51/fzz2Nf72Cei8pGWlqaeIyIirL5vjE9NTXX7cty17ovZvXu3OZEj+vbtq55Xr15tHteqVSu0bt0aS5YsUTVljPX369cPmzdvRkJCgnlaqZ0j2x4XF2ce16FDB/UdPX/+fPO4OnXqqE4ypbaOZZvO8oecJHwSExPN47p166bWJwkoQ0xMDDp27Kj6ozH2ldTgkZo+DpWpXz80HDMaj817DBvPHUf1TD8E5xb1iyI1TKICayM2qDUaBjXF8MGjkFlYiA2bNjlXpvPbJWWS3+ktW7YUK1N0RHSpMl3e8XJVpqy0LDUuJCgEw4YMKyrTPifilGc/ToMGDUJKagr+3PCnSrIUmgrR5pI2qN+wPhb/uli9ln+RNSPRrn07bNqyCcmnk9U4+dejZw8cTTqKfQf2qdeyjNgWsQgKCVLTGsusUTMSDRo1UPFIz8pU4339fdW2njh5Qj1M5//J/pRlHTx0UPV1I/9k/ZFRkTgQfwD5BflqXGBgIOo3qI+TySeRfjYdJlOhSo41qFMXednZSDlxEj4FReMiQ6shJDgIJ44fL6rdYjIh0M8f1cPDcTYtDfk5ufAtNMHHBERGRCAvKxtZmZkq6STThgWHwN/HFxnpZ9VrGR/o74/ggCBkZ2TAVFCo5pcLt6FBIcjPzUVBbp55/hDpJ6bQhLzs3KL5pQk6X1/4+/khLydXNcsm65bmj2S78vPzgYJC83h/adas0ISC/AI1v/CTJsDgYx6nGsc6vwyZ1phXLuz6yQxq+Px65HF+epiHS75X9FrKdGH8+WVaMDfudX4bFJPl+OLTFXvv/GYVm8bO9CXfs9yWYsMXeb/Udtlbrp0yWS7Lx40X2h1dVsntcIWjy3Jo2xxcFntIIiKq2rZv34bEc4E2z2Hdfl5+kb81ZNnOYnLFBRJwnS+wVUb559zdTT1f/sIyJJ8rasu6JLmhbN6mo2jXIEIlZMoL48/jX9fPP499vY99IqoccgHYHe3Cl2U5zsxzsdop8sdMSdbuVrPWRJn8sVPyD56QkBCr81sbJ8mIkiSx4uj88keXtfJcrExbkrdg2IJhOJ51XPW1cSYc8Pfxx/Wx1+OOS+5AbI3YYvNKKmto48ZlLpP8Rln7nXJnmZyNkzQtd/MNN5ea9vZht5ca17xf6RukutTtAlxWajSub3l96ZHWKm1dApWcKlWGoj8tirNd+arKyy8oxNnsfKRn5yE9Kx9n5fn8cNGzvL7w/rmcPNXsckZOvno+d/65QBInpZgQghzUQAZq+JxDdWSimk8mqiEL4T5ZCEdW6ddWxgX5WL9JTleF8EEh/FDo43vh2ccPJjVc9Nokz/Arelav/WEyprOYpujhi0LfovdlOuknRx7yWg1DhqVvF99i70naysdyOvV9L+PP9/MjzxbzXZjO8lFyGRfWqfqtUdtn9Lvjd747nqL+g1QS7Hy/M0X9/Fj2u1O0LUXd1hjrMfIrPqpm5SXt2pn73jmfujv/dH4Z5n5yioZlHUXNX1n2oXNhuvO99BT1DXR+fvVTaNEnUPG+fM7vG3NyyHI685RFw7LMYh+xovKcf9NibFFGyvKX18ciXWSe5/xv9IXtvbAVlssultCz2LZi4yy3q9Rvvp3X9rr/sejPyOYMpeYv+X7R6xUrV2BA/4HF3lbHswPzOrKx5dX1jjlUjmYFK7GfIPtL9XH4nLHUnGXY3GW/LcegKwdeZIusHV+ucWRxF49lFW1frwr2L3VreBQWLVpcZc5hy4LJFfJIM0Z0xJ2fb1A3TFmz7+Q5TJ63DWsmDKjoTSMiIiJymlE7xLgDq6T09HS7tUtcWY671k2lrTi8AhPWTFBNYxkGNBqACV0noEG1BtxlZPPi1NmcfKRm5CElMxdnMnKRkpGLM5nGc17RuMxcpGbmmpMntvqnLMkf+aiJdET5nFWJkgY4p55V4sT3LGr4FiVQisZdeM+TEiMFvkEo9Ct6mOThX/QM/2A1jPPD6hEQBF81LgC+foHw8Q+Ar788B8FHxvkHAr4B6v2ih7z2L3pWj/PDNqcJOP+eJDv8isb7SlLBT/WNxdoVrtl+ej5ie3h2kzLkmMDwaNRswJvcdBEUGoHIWjxXoqqPyRXySFIjpUfzaGw5fAZnc6z/EXE4JQvNnl6IxweXfxNhRERERK6QKupC+kKxZt++fXb7UnFlOTLPxo0b1Twl+0yRpoMOHjyo+l5p1qyZU2XS3fd7vsf0uOmqySoRERSByd0m46omV5XbHadUtRMmGbkFOJmejeSzOTh5NqfEc9H405I8ychFvq27yGwIQi4a+qSiFtJQ0ycd0T5piD4/XEuGLV5H+pxDZZHaFQiqBp+AMCAgBAgMBWRYPYcCgWElns+PNw+fn9Y/BAg4nxyRxIjF8/xfFmPoDTcUNVVGREREVI58TLbqbNFFHT9+HHXr1tV2T1WV8vd+ZQWOnClqK9qaehHBGN09xu0JlqpS/srC8usbf8Ze39gTUfk5cOAAmjdvrqrCy7DczWw4e/Ys6tWrh8LCQiQnJyMsLMyty/nss89w99134/bbb8fs2bOLLW/FihWq4/s+ffoUa6/YW5TXb9qSg0vw5Jonza8bhTfCB1d+gJjqMW5fF1X++UthoUklRY6lZiEpLQtHU7PNwyfTc5B8Lkc9Z+U5VrOkpGrIRF2fFNTzSVHPdXFh2HiukISJ1MIIiQJCIoHgCCC4OhAkj/Dzj+rnx4UXH2dMI+9JEqSck4u6n6vqhvHWB2OtF8ZbH8c9/HebNVdcoHvTCFWl/NOHtcMdn22w2eJhUlo2volLcHtypaqUv7Kw/PrGn7HXN/ZEVH5iY2NVB+3SYePMmTPx8MMPm9+bOnUqMjIycN9995kTInl5eSp5EhAQoOYt63LE8OHD8dRTT+Hbb79V03fp0kWNz87OxuTJk9XwAw884JXhL4/ftM0nN2PSH5PMry+teSneG/geaobUdPu6qGJiLfcjSg2ThNOZSDidgSMpmUiU5IkkUdKKnnOlc/iyLR1ROItGPifRyCcZjX1OoqHPScT4nUZ93xTUwWmEmmzfSFYm0q9DaE0grNb5ZEmNooSJPELPJ0+KPc6Pk5omHlDrSvdzVd0w3vpgrPXCeOsjwsN/t1lzxQVWO0XUSFUq/+hP4/D3oRRk5dn+o8bPBzjw0rVeWf7KwPLrG3/GXt/YE1H5kmRJjx49cPLkSfU906ZNG8TFxWHlypWqGa9169ahZs2iC/SHDh1C06ZNERMTo4bLuhzDvHnzVJIlODgYI0eORFRUFBYsWIA9e/ao8d9//71XNmXl7t+0xLOJuHXhrTiTc0a9blK9CeZcM0c1CUZVO9bSifvRM1k4eDoDh09nqETKodOZOJySgcMpmci283fGxUhX5fV9TqOV/3G0C05GrP8plUypW3gCUXlJCCzILPOyL6zEH6hWpyhhUq02ECaP6AvD1WoVvSfDkkCRPj+8lO7nqrphvPXBWOuF8dbHfA//3WbNFfIKc+7upp57vbIciWeyrU5TYAKueOk3xNYON09PREREVFVIrRPp+2TKlClYsmQJFi1apJrxeuSRR1StE0l4lNdybrjhBtXs1/Tp0/Hjjz+qWivSvNgbb7yh5vPGxIq7Sd8qUmPFSKxEBkXi/SvfZ2KlisnNL1S1T/afPId9J8+Zn+OTzyEnv+wJlIiQADQPz8dlYafQOuA4miIJdfMSEZl1CMFnE+BbkFM0ofQJ72y/8NKUVvX6QPUG55/PD4fXuzAsiROLZgCJiIiIqPwxuUJeZVTXGMz4dQ9s/VmUlJYDXhogIiKiqqpRo0b4/PPPLzqd9Klir+tER5djqWfPnioRQ2Xzze5v8M/Jf9Swn48f3h7wtuprhSqHfD4Sz2Rhx7F07ExKx6o9vnhnxipVI8XZzuKN5ElMzVA0jgpFs0g/tPVPQpOCQ6iTdQDhaXvgn7wLSD8JpJdhYwOrATVigMgmQGTM+eEYIKJhUeJEmuRigpOIiIioymFyxQXSDIPOqmL5pV+VP+NPY8vhMzibY73DyGNpOWjxzCLse/Earyt/RWL59Y0/Y69v7ImIvI27ftOOnD2Ct/952/z67nZ347Lal7ll2XRx+QWFqvaJJFJ2HEvDzvMJlbPZ+RZTSa2ODLvLqRUehGbRYSqJElMzDI0jQ9A8KAWNc+MRlroTOLEdOLkT2LcfMDlZyyU0GohuAdRsDkQ1O59EkWRKk6Jmupg8cRvdz1V1w3jrg7HWC+OtjxgP/91mnyvktew1ESaqB/vjvr6xbu/onoiIiIj0qiExdtlYxCXFqdfNazTHd9d9h0C/wMreNK+VlJaFzYdTsflIKjYdScW2xDRk5Vm/scqaBjVC0Lx2NfVoIY861dC8Vjgi8k8BxzYBx/45/7wJyDzt+Ib5BQE1Y4sSKEYipWYLILp5Ue0TIiIiIvIqrLniglWrVqFfv37QVVUvv2oibOke2Kr1n56djzV7k8ucXKnq5S9vLL++8Wfs9Y09EZG3ccdv2h9H/zAnVnx9fPF8z+eZWHFzrRSphRIXn4K/E85g05EzOJF+vv8SB5ryuqR+dbStVx1IO4r/63s5YmtVQ1iQP5CZUpREOboJWHc+oXI2ycGt8imqfVKnLVDnUqC2PF9SVAvFizuK9xS6n6vqhvHWB2OtF8ZbH6s8/HebyRUXpKWlQWdVvfySNDl4KgO/bk+y2URY3MGUMjcRVtXLX95Yfn3jz9jrG3siIm/j6m+a1Fp5d9O75tc3t7wZl0Zf6oYt01deQSG2HU1TyZS4g6ex8dAZnMuxbN7LunoRwWjXIAJt61fHJfWLnutHBMNHmtsymfDbD3+g/alk4J/1wOH1wKk9jm1QcARQt31REkUSKJJQqdUaCAxzvbBULnQ/V9UN460PxlovjLc+0jz8d5vJFfJqr9/cQT3sNRGWV2jC5S8sw4wRHdGnZa0K30YiIiIi8kwrDq/ArpRdajjILwj3tb+vsjfJ40iC6kDyOazak4w1+05h46EUZObab+IrNNAP7RtGoGOjSHRsVAOXNa6BOtWDL0xQWAic2Abs+gM4/CdwOA5XZpwEdl5kYwJCgXodgPqdgAadgPqXFdVQYX8oRERERGQFkysuCAoKgs48qfwXayIs+Vwufvon0ankiieVvzyw/PrGn7HXN/ZERN7Gld+0gsICvLf5PfPrUa1HoVYob9RxxNnsPKw7cLooobI3GUdTs+xOX7d6MLo1i0LXplHo1DgSLeuEw8/X58IEJhNwchdwcE3R49AfQHaq/Y3w9QfqtgMadC5KokhCpVYrNuvlBXQ/V9UN460PxlovjLc+gjz8d5sd2pM2Zq7cj8//OIhTGbl274Lb+Z8hFbpdREREROR5lhxcgifXPKmGQ/1DsfimxYgKjqrszaqyjqRk4tcdx7Fs5wnVd0q+rbueznc4L8mU7k1rqufGUaFFzXtZSksE9i8H4lcBh34HMpLtb0BQBNCoK9C4G9Coe1FSJTDUTaUjIiIiIh0xueKC3bt3o3Xr1tCVp5a/9ysrcOSM7bvjAv198ejAFhft6N5Ty+8uLL++8Wfs9Y09EZG3ceU37V+L/oXNyZvV8Nh2Y/FIp0fcvHWeLz75HBZvP44l24+rflRsCQ/yR8/m0ejbqhZ6NY9GoygrSY/8HCBhHbD/t6KkSnJRc2w2hdUGmvYGYnoCjbtjd4oPWrdp64ZSUVWn+7mqbhhvfTDWemG89bHbw3+32SyYC/bs2ePRwde1/NOHtcOYLzYgv9D6+7n5hap5goslVzy1/O7C8usbf8Ze39gTEXmbsv6m7UnZY06s+Pv649Y2t5bD1nmmvSfOYuHWJJVQ2XPirM3pLqlfHX1b1kK/VrVVnykBfr6lJ0qJL0qk7FtWVDslL9P2ikMigSa9gKZ9gaZ9gOiWxfpK2bN+PpMrmtD9XFU3jLc+GGu9MN762OPhv9tMrpB2pF+V8YNa4cNVB5Cek291mriDKWg7ZQmbCCMiIiKiUn7Y+4N5+MrGVyI6JFrrvZR8NgcLthxTfRjuOJZudZoAPx9VO+XqS+uif+vaqB1u0QG9oSAfOLwO2L0I2PdrUXLFFr/AolopzQcWJVTqXAr4WknQEBERERGVEyZXSEtSK0UefV9diYQU63fAZeYWoNnEhXj8qlYXrcVCRERERHrIyMvAzwd+Nr8e0WoEdCS1vZfuPI4f/07Emn2nUGClD5Ugf191Y5MkVAa2qYOIkIDSC8o5BxxYXpRQ2bvEfkf0Uc2A5oOA5lcCTXoCgWFuLhURERERkePY54oLUlNTUaNGDejKW8ovNVQkkWLLde3r4b1bO3lt+cuK5dc3/oy9vrEnIvI2ZflN+37P93h+/fNquFlEM8wbOq90Z+te7PDpTHy94TDm/n0Ep87lWu2/8Mo2tXFNu3ro36o2woKs3M939gSwdzGweyEQvxooyLG+soDQoia+JJkSOwCoGVvm7db9/EUnjLVeGG99MNZ6Ybz1kerh52isuULamzW6M+74bANK32tX5JetSdiWuBKrJ/TXfl8RERER6U6SK5a1VnRIrEitlN92ncCc9Qn4fd8pq9N0bRKFYZ0aqKSK1RoqyXuB3b8AexYBiRsBW2ff4fWB1tcAra4p6kPFP8jNpSEiIiIicg82SuuC1atXQ2feUn5pqqBni2hEhVr5I/A8aTpMmgibuXK/15W/rFh+fePP2OsbeyIi3X/TDqQewJ4ze9RwsF8wro+9Ht4sMzcfs9cdwoAZq3Dfl3+XSqzUiwjGowNb4PcJ/fH9/VdgVNfGFxIrhYVFSZRlU4F3uwAzLweWTwMS/yqdWKl9CdDnSeDeVcC/dwLXzijqS8WNiRXdz190wljrhfHWB2OtF8ZbH6s9/ByNNVeIAMy5u5vaD5e/sAzJVpo3EIUA5m06inYNIlRChoiIiIj0svTQUvNw74a9UT2wOrzRyfRsfLHuEL6KO4y0rLxi70lFnX4ta+G2bjHo16oW/P0s7tcryAMO/Q7sOl9D5WyS9RX4+BZ1Ri+1U1pdDUQ1LecSERERERFVwZorp0+fxieffIJhw4ahefPmCAkJQUREBHr16oVPP/0UhXLHkhXr1q3DNddcg6ioKISGhqJ9+/Z46623UFBgu++L2bNno2vXrqhWrZpaR79+/fDLL7/YnD4rKwtTp05Fq1atEBwcjNq1a2PEiBHYtWuXq8UmLzVjREf42mnZYd/Jc5g8b1tFbhIRERERVRFLEy4kVwY3GQxvTKo8t2AHer26Eu+vOlAssVI92B/3941VtVQ+v6srrmxbpyixkpsB7FwA/HQv8Fos8OUwYOOnpRMr0n9Km+uBG2YBTx4A7vwFuOJBJlaIiIiISN+aKz/88AMeeOAB1KtXD/3790fjxo1x4sQJ/PTTT7jnnnuwePFiNY1lW8Tz58/HTTfdpBIet9xyi0qw/Pzzzxg/fjzWrl2rpi/piSeewIwZM9CwYUOMHTsWubm5+Pbbb3H99dfj3XffxUMPPVRs+pycHAwaNEgtr0uXLnj00Udx5MgRteyFCxdixYoV6NatqLZCWUnSRmfeWH6pkdKjeTS2HD6DsznWE32HU7LQ7OmFuP2y2hgKfXlj/J2hc/l1LrvQvfxERLp+p8enxWN/alETsUF+QejToA+8xcmz2Zi1Kh5fxSUgJ7/4zXGNo0Jxd6+mGN654YXO6TNTgD3SIf0vwIEVQH629QWHRBXVTmlzHdCsHxAQgsrC3299MNZ6Ybz1wVjrhfHWRysPv8biYzKZbPXj7RBJUmRkZODaa6+Fr++FijDHjx9XtUwkoTF37lyVTBHp6emqhktaWpo58SGys7MxYMAA/Pnnn/jmm28wcuTIYrVcevbsidjYWPz111+IjIxU4w8dOoTOnTur9e/evRtNmjQxz/PSSy/hmWeewfDhw/Hdd9+Zt00SOzfccAPatm2Lbdu2FdtmIku9X1mBI2eybO4UaWN6dPcYjOvfnDuOiIiIyMvN2jILMzfPVMNXNr4Sb/Z/E54uPTsPM1fsx+w/DyE7r3hSpX3DCDzYLxaD2taFn/SRcnwLsO83YP9vQOIGwGS9hQJENAJaXwe0vhZofAXgx5aoiYiIiMg7uZxZkISI1B4pmaSoW7cu7r//fjW8atUq83hJtCQnJ6vkiZFYEVKL5YUXXlDDH3zwQbFlzZo1Sz1PmjTJnFgRkkwZN26cqqXy+eefm8dLvsiY59VXXy22bUOHDkXv3r2xc+dOlzvMWbJkCXTm7eWfPqwd7LQQhqS0bHwTlwBdeXv8L0bn8utcdqF7+YmIdP1O96YmwQoKTaqWSv/XVuHDNfHFEivSv+Bnd3bB/LvaYIhpLfzm3Q/MaAl81A9Y+QJwZH3pxEqtNuc7pF8NPLYNuPploGnvKpVY4e+3PhhrvTDe+mCs9cJ462OJh19jKddqGwEBAerZ39+/WE0XMWTIkFLT9+nTR/W/IjVVJGHiyDxXX311sWnEgQMHcPjwYbRs2RJNmzZ1aJ6ysNxGHXl7+aWJsJ4tohESYOtjUoDE1GzEPr0QOvL2+F+MzuXXuexC9/ITEen4nX4w7SD2ndlnbhKsb8O+5bNBuZlAfi7K07r9p3DtO79j0v+243TGhXX1rpePBf1PYUHznzFg9Qj4vN4c+PFuYOu3QEZyiaX4AA0vB66cBjz8DzBuPTBgMlC/Y1GP91UQf7/1wVjrhfHWB2OtF8ZbHzkefo2l3G4lys/Px3//+99SSZE9e/aoZ0l8lNoYf3+VDNmxYwfi4+PRpk0b1eTX0aNHVSf20q9LSS1atFDPe/fudWgdtuaxRZods2XKlCkXnZ8825y7i/rl6fXKciSesd6WdIEJuOKl3xBbO9w8PRERERF5j+WHl5uHezXohVDpnN1VBXlA/Cpg21zg6N/A2eNA7tmi93wDgOAIIKIhUKMRENHYYrgRUKMxEBLpVCIj+WwOpi7YjsXbjqGRTzIG+R5BK58j6BiUhCtCDiPszGHgTzsLCK0JxA4EWgwCYgcAYdGu7wMiIiIiIg9WbsmViRMnYvv27bjmmmtw1VVXmcdLXysiIiLC6nzG+NTU1DJNX9Z5yiIoKEj14WLo27foDjbL5sakU57WrVurKk5GJk7W369fP2zevBkJCRealRo8eLDa9ri4OPO4Dh06qObPLNdTp04ddO/eHevXr8eJEyeKNXkm/dBs2bLFPK5bt25qfUuXXmjGICYmBh07dlTNtRn7SsoiSTDpu8ZITl2sTD4+Pubt8pYy2YpTx2oZOHoG0to0AL9itVdEUlqOakLMk8rkapyE8Z63lMnZOMlyvK1MjsTJMvbeUiZn4mSU35vKVDJORES6sPX3Qkl/HruQdejfqL/rK97yLbB0spUaIecV5gGZp4oeSZutTxMQdj7Z0rAo4SLPgWGAX8CF5E1eJkznTuJoYgKOH03A44Vn8HpQCkJ9LO4QlBa+Mqws38cXaNAFaH4l0OJKoN5lgAf3V+lorMnzMdZ6Ybz1wVjrhfHWR4SHn6O53KG9Ne+88w4effRRddFGOq2Piooyvye1Sfbt26ce0rF9ST169FCd2stDLjodO3YMDRo0UI/ExMRS0+fl5SEwMFBdUMrOLqpZ8PXXX+O2225Tjzlz5pSaRy5OScJHHp7erhtVnNGfxmHL4TM4m1OUULEmwNcH+168hmEhIiIi8hKZeZno+W1P5Bfmq9crbl6BWqG1yrawnHPAoieALd9Yf19qrMjtPOfXVaH8goCGXYDG3Ys6opdmv0JqVPx2EBERERHpWnNl5syZKrHStm1bLF++vFhixTIbZdxlW1J6enqx6S42vbVaKs6uo6xUjYaOHaEr3crvSBNheYUmtH/uV9zXNxbj+pdOHnoT3eJfks7l17nsQvfyExHp9p2+8cRGc2KlZWTLsidWstOAz64GTu64MK5aXaD9zUCboUDN2KKmvkRBLpBxCkhLBNKOAKmHi57ldao8HwFyz6HMwmoBtdsAtS8peq5zCVC3HeAfBG/F3299MNZ6Ybz1wVjrhfHWx2YPv8bi1uTKW2+9hfHjx+PSSy9ViZXatWuXmkaaIdm4caPq76RkfybST8vBgwdV3yvNmjVT48LCwlStFel3JSkpqVS/K1IDpmT/KrIOe32qWJunLKQZGE8Ovqt0Lf+orjGYsXQPCk0FJZoIK5KenY81e5O9Prmia/wNOpdf57IL3ctPRKTbd/rao2vNwz3q9yjbiqSxgPkPFU+sdLgVuOY1IKha6eklyRHRoOiBbtaXl3XGIvlyBDh7DMjPQX5uNjYmnMGuk9nIQQBOm6oj2VQDHdq0xC39uyA0qgEQWvwGOB3w91sfjLVeGG99MNZ6Ybz1keDh11jcllx55ZVXVD8rsjOWLVuG6GjrHRwOGDAAX331lWqOa9SoUcXeW7NmDTIzM9GnTx/VzJflPF9++aWa56677io2z+LFi83TGGJjY9G4cWOVXJFkTdOmTS86D5GjJGly8FQGftmUgGxpo9qKuIMpaPHMIjYRRkREROTh1h1b53pyJW4WsGvBhdfXvgFcfnfZN0o6spcEiTzqtTePTjidgfu+/Bu7j581j2sUFYJXb+qAK2Jrln19RERERERUilt6JHz++edVYkVqokiNFVuJFTF8+HD1/rfffqtqsBikv5TJkyer4QceeKDYPPfff796nj59Os6cOWMeLx3+SjNkkoixTLpIR+vGPBMmTEBh4YUr4NKZ8O+//66aLTM6+CVy1us3d8Ar3UxoGBlscxppIuzyF5apWixERERE5HmOnTuGQ+mH1HCQXxA61enk/EISNxZ1Xm+4fKxriRUb/jxwGkNnri2WWBnasT4WP9qHiRUiIiIioqrYof3s2bNx5513ws/PDw8//LDVfkyaNGmipjHMmzdPJVmCg4MxcuRI1S/LggULsGfPHjX++++/VwkSS48//jjeeOMNNGzYUE2Tm5uL7777DqdPn8a7776Lhx56qNj0OTk5qmbKunXr0KVLFwwcOBCHDx/GDz/8gMDAQKxYsQLdulmpYu+ErKwshISEQFcsfxY+W3/0fBNhtvfTDR3r462Rl8HbMP76fv4Ze31jT0Sk22/a3L1zMe3PaWq4Z/2emDVolnMrkD+1PrsKOBJX9Lp+J2DMErf3bfL9X0fwzP+2If/8SWmgvy+eu/4SjOraqNTfVbrS/fxFJ4y1XhhvfTDWemG89ZHl4edoLjcLJs1uiYKCAtXnijVSQ8QyuXLDDTdg9erVqibKjz/+qGqtNG/eXCVPHnnkEat/AMyYMQPt27fHe++9h48++gi+vr7o1KkTnnzySVx33XWlppfaLL/99htefvllfP3113jzzTdRvXp1te5p06apmiuuSktL8+jgu4rlTzP3q/L5HwdxKiPX6n6at/kYlu48gZ3/GQJvwvjr+/ln7PWNPRGRbr9pLjcJdvjPC4kV3wDg5s/dnlj5YNUBvLJkt/l1dLUgfHR7Z3RqHOnW9Xg63c9fdMJY64Xx1gdjrRfGWx9pHn6O5nKzYM899xyk8ou9x6pVq0rN17NnTyxatEg18yUZqm3btmH8+PGqBowtd9xxB/766y9kZGTg7NmzKkFjLbFikMBIIkU6sJeaLMnJyarmijsSKyIu7vwfSppi+YviLwmWjc8OQqNI218EmbkFaDl5MWau3A9vwfjr+/ln7PWNPRGRTr9phaZCxCXFuZZc+f2NC8MdRgKRTeAu8nfWS4t3FUustK1XHQse6snEihW6n7/ohLHWC+OtD8ZaL4y3PuI8/BzNLX2uEBEwfVg7+Nv5ROXmF7L/FSIiIiIPcTDtINJz09VwVHAUYmvEOreApK3A/mXnX/gAPR9za2LlxUW78OHqePO4bk2j8N193VG/hufe+UdERERE5EmYXCFykz4ta2H8oFaoHmS7tb24gyloO2UJ9zkRERFRFbf55GbzcIdaHZzvu2StRZPJbYcC0UXNybrD28v34ePfi5pnFle2qYPZY7oiPDjAbesgIiIiIiL7mFxxQYcOHaAzlr90/KWJsK3TrkJMVKjdJsKaTVzo8U2EMf76fv4Ze31jT0Sk02/a5uQLyZWOtTs6t+D0JGDH/y687jUe7vLJ7/F467d95teD29bBB6M7ITjAdvPKxPMXneh+rqobxlsfjLVeGG99eHqsfUxSp5yI3E5qqEgixZbr2tfDe7d24p4nIiIiqoKu/9/1OJR+SA3/9+r/4rLalzk+81+fAgv/XTQc0xO4a5FbtmnZzhO498uNMP6Ck5rTH9/eGUH+TKwQEREREVU01lxxwfz586Ezlt9+/GeN7iyta9v0y9Yk9H11JTwV46/v55+x1zf2RES6/KadyT5jTqz4+/qjbc22zi14j0Uypc3/wR12JaXj0W83mRMrlzeJxIejmVhxlO7nLzphrPXCeOuDsdYL462P+R5+jsbkClE5kTsJe7aIRlSo7bavE1IyvaKJMCIiIiJvsiV5i3lYEitBfkGOz5ydDsSvvvC69TUub09KRi7umb3RXCu6UVQIPvxXF4QEssYKEREREVFlYXKFqBzNubsb/pkyGLWqBdqcphDAvE1HsWZvMmNBREREVMU6s+9Yy8n+Vvb/BhTmFQ3XbQfUaOzStkgrzhPmbsHR1Cz1ulqQPz6943JEhdk+vyQiIiIiovLH5IoL6tSpA52x/I7Hf8aIjvC100bYvpPnMHneNngSxl/fzz9jr2/siYh0+U1zqTP73QsvDLe+Dq76cn0Cftt10vz67ZEd0bJOuMvL1Y3u5y86Yaz1wnjrg7HWC+Otjzoefo7GDu2JKsjoT+Ow5fAZnM2x3cm9JGAeH9wK4/o3Z1yIiIiIKkFeYR6u+PoK5BTkqNfLb16O2qG1HZs5Pxd4rTmQk1b0+r7fgXrty7wte46fxfXv/YHcfKnrDIzp2RRTrney/xciIiIiIioXrLnigvXr10NnLP96p5sI2zZtCBpFhticptAEzFmf4BF9sDD++n7+GXt9Y09EpMNv2p6UPebESoNqDRxPrIiEPy4kViIaFzULVkb5BYX49/ebzYmVNvWq46mrW5V5ebrT/fxFJ4y1XhhvfTDWemG89bHew8/RmFxxwYkTJ6Azlr9s8Z8+rB3stBCGpLRsfBOXgKqO8df388/Y6xt7IiIdftOK9bfibJNge5cW78jex95Z38WbA9txLF0NB/n74p2RHRHkzw7sy0r38xedMNZ6Ybz1wVjrhfHWxwkPP0djcoWogvVpWQs9W0QjJMD2xy8xNRuxT1u0101EREREFaJYfyvOdmafuOHCcOzAMm/DifRszFi61/z64QHN0YL9rBARERERVSlMrhBVAmkibNfzV6NhZLDNaQpMwBUv/ab6aiEiIiKi8mcymbDp5Kay1VzJzwGOb7vwukHnMm/HCwt34VxOvhpuVisMY/s0K/OyiIiIiIiofLBDe6JKJH2rzPh1D4pa0raufkQQ1j19ZQVuFREREZGeks4lYfCPg9VwqH8o1o5aC39ff8dmTvwb+GRA0XBkU+DRCzVgnBEXfxq3fHSh7emv7+mGHs2jy7QsIiIiIiIqP6y54oJDhw5BZyy/6/Ef1785erSIRniQ7fazj6XloMUzi1DVMP76fv4Ze31jT0Tk7b9plk2CtavVzvHEiji60eVaK1JzxrI5sKEd6zOx4ia6n7/ohLHWC+OtD8ZaL4y3Pg55+Dkakysu2LJlC3TG8m9xWxNh26YNsdtEWF6hCe2f+1XVdKkqGH99P/+Mvb6xJyLy9t+0Yp3ZO9vfytG/Lww37FKm7fl93ylsOJSihgP8fPDE4FZlWg6Vpvv5i04Ya70w3vpgrPXCeOtji4efozG5QlRFjOoaA18f2++nZ+djzd7kitwkIiIiIn07s3emvxWRaFlzpUvZaq0su1BrZUSXRmgUFer0coiIiIiIqGIwuUJURUgTYTd2ami3ibC4gylVsokwIiIiIk+XmZeJPSl71LAPfNC+VnsnZk4BUg4UDfsGAHXbOb3+5btOYsuRVDUc6O+LhwY0d3oZRERERERUcZhccUG3bt2gM5bf/fF//eYODjURdvkLyyq9Fgvjr+/nn7HXN/ZERN78m7b91HYUmArUcGyNWFQPrO74go79c2G47qVAgO1zOVvetWj+9bZujVEvIsTpZZBtup+/6ISx1gvjrQ/GWi+Mtz66efg5GpMrLoiIiIDOWP6ISmsiLPlcLn76JxGVifHX9/PP2OsbeyIib/5Nc61JsL9dahJs0+EzxWqtPNAv1ullkH26n7/ohLHWC+OtD8ZaL4y3PiI8/ByNyRUXLF26FDpj+ZeWaxNhjw9uheiwQJvTzNt8DG2nLEFlYfz1/fwz9vrGnojIm3/TXOvM3rK/lc5Ob8cX6w6Zh69vXx+1w52v+UL26X7+ohPGWi+Mtz4Ya70w3vpY6uHnaEyuEFVRkmDZ+OwgNIq03SREZm4BWk5ejJkWzUgQERERkXMKTYXYkrylbDVXTCbgqEXNlYbO1Vw5eTYbi7YlmV/f2aOJU/MTEREREVHlYHKFqIqbPqwd/O18UnPzCyu9/xUiIiIiT3Yo7RDSc9PVcGRQJBqHN3Z85rNJQObpouGg6kCUc016fR13GHkFJjXcOSYS7Rp6dtMIRERERES6YHLFBTExMdAZy18x8e/TshbGD2qF6kH+NqeJO5hS4U2EMf76fv4Ze31jT0Tkrb9plv2tdKjdAT4+djq/K+nU3gvDtVoBvo7/iSU3yXwVd9j8mrVWyo/u5y86Yaz1wnjrg7HWC+OtjxgPP0fzMZmkHjsReYK+r65EQkqmzfflT/nHr2qlmhQjIiIiIsdMWTsF/9v/PzX8WKfHcHe7ux3fdRs+BhY9UTTc4VZg2AcOz7pk+3HcP6eoSbE61YPwx1MDEODH+9+IiIiIiDwBz9xdsGrVKuiM5a/4+K+e0B+hgX423y8EsCupqEmL8sb46/v5Z+z1jT0Rkbf+pm06uals/a2I0xZ930U7d4PLgi1HzcM3d27ExEo50v38RSeMtV4Yb30w1nphvPWxysPP0ZhccUFaWhp0xvJXTvxnje4Mew1V/LI1SdVwKW+Mv76ff8Ze39gTEXnjb9qZ7DM4lH5Ivfb39cclNS9xbiGn9l0YrtnC4dnOZufht10nza9vuKy+c+slp+h+/qITxlovjLc+GGu9MN76SPPwczQmV4g8jPTB0rNFNKJCA2xOI02HNZu4EDNXWtxJSURERESlbE3eah5uG9UWwf7Bzu2l0xbJlWjHkyu/7jih+lxR661XHc1rhzM6REREREQehMkVFwQFBUFnLH/lxX/O3d3wz5TBqFUt0OY08qf6vE1HsWZvcrlsA+Ov7+efsdc39kRE3vibVrIze6fkZQGpR4qGfXyBqGYOzzp/84UmwYZ2ZK2V8qb7+YtOGGu9MN76YKz1wnjrI8jDz9HYoT2RB5PEyZ2fb0ChyfY0jaNCsGbCgIrcLCIiIiKPcdeSu7DxxEY1PKPvDAxuMtjxmU/sAD7oUTQc2QR4dItDs508m43uLy43n8OtmzgA9WuEOL/xRERERERUaVhzxQW7d++Gzlj+3VWiibAezaMRHmS7k/vDKVlo9rT7mwhj/Cs//pWFsdc39kRE3mb7zu3Yfmp72TuzL2N/Kwu3JpkTK12bRjGxUgF0P3/RCWOtF8ZbH4y1Xhhvfez28HM0JldcsGfPHuiM5a8a8ZcmwrZNG4JGkbbvdpQ/3uesT3BrgoXxrxrxrwyMvb6xJyLyNqt3rUZ2QbYarh9WH7VDa1dIfyuLtx03D7NJsIqh+/mLThhrvTDe+mCs9cJ462OPh5+jMblC5CWmD2sHHzvvJ6Vl45u4hArcIiIiIqKqbU/enrLXWhGn9judXEnLysPfh8+YX191SV3n10tERERERJWOyRUiLyFNhPVsEY2QANsf68TUbMQ+vbBCt4uIiIioKjKZTNiWt838emDjgc4v5LTzzYL9se8UCs63CdahYQSiq3l2J55ERERERLpih/YuSE1NRY0aNaArlr/qxr/XK8uReKaoiQtr6kUEIbZ2uGpSrKwY/6ob//LG2OsbeyIib7InZQ+G/zxcDYf4h2D1LavVs8NMJuDlGCAnrej143uA8IvXQnnihy2Y+3eiGn5kYAv8e1DLMpaAnKH7+YtOGGu9MN76YKz1wnjrI9XDz9FYc4XIC43qGmP3w52UloP4k2crcIuIiIiIqpZfD/1qHu7XsJ9ziRWRkXwhsRIYDlSrc9FZCgtNWL032fy6f6tazq2TiIiIiIiqDCZXXLB69WrojOWvuvEf1785erSIRniQn81pjqXloMUzi8q8Dsa/6sa/vDH2+saeiMibmgRbcmiJ+fVVTa9yfiGnLDuzbw742Ov9rsjOpHQkn81Rw5GhAWjf0HPv0vM0up+/6ISx1gvjrQ/GWi+Mtz5We/g5GpMrRF5KmvzaNm0IGkYG25wmr9CE9s/9ipkrLTpjJSIiIvJyO1N24sjZI2q4WkA19GrQy/mFnNrrdH8rq/acNA/3bVkLfr4XT8gQEREREVHVxOQKkQ5NhNn5uz09Ox9rLJqnICIiItKpSbD+jfojyK8MncqnxF8YrtncoVlW7blwztWvVW3n10lERERERFUGkysuaNWqFXTG8ntG/KWJsBs7NbTbRFjcwRSnmwhj/D0j/uWBsdc39kRE3tIk2NJDS82vhzQdUrYFpRV1Sq/UaHzxyTPz8M/hM2pYWhDr05L9rVQk3c9fdMJY64Xx1gdjrRfGWx+tPPwczcckf10QkRZ6vbIciWeybb5fq1ogZozoyD/2iYiIyGul5aThidVPYMPxDQgLCMPqEasR4Bfg/II+HQwciSsavuNnoGkfu5Mv23kCY/+7UQ13aFQD88f1LNP2ExERERFR1cCaKy5YsuRCJ5g6YvmXeF0TYcnncvHTPxZ3YdrB+Hte/N2Fsdc39kRE3iAiKAIfD/4YK25egVvDbi1bYkWkHb0wXL3BRSffmJBiHu7WNKps66Qy0/38RSeMtV4Yb30w1nphvPWxxMPP0ZhccUFOTg50xvJ7XvylibDHB7dCdFigzWnmbT6GtlMu/sXG+Hte/N2Fsdc39kRE3qRmSE00MjUq28yFBcDZJOeSK4eKmgQTXWIiy7ZeKjPdz190wljrhfHWB2OtF8ZbHzkefo7G5AqRZiTBsvHZQWgUGWJzmszcArScvBgzV+6v0G0jIiLS2bp163DNNdcgKioKoaGhaN++Pd566y0UFBSU67ISExMxffp03HzzzWjevDl8fX3h4+OD/ft5HmDT2eOA6fy+DKsFBATbjUd2XgG2JqaaX3dmcoWIiIiIyOMxueKCiIgI6Izl9+z4Tx/WDv52vgFy8wuxZm+yzfcZf8+OvysYe31jT0TlZ/78+ejTpw/WrFmDYcOGYdy4ccjNzcX48eMxcuTIcl3Wxo0bMXnyZPz444+qs3edvufLXNZ055oE25qYhryCoq4um9UKQ81qQWVbL5WZTse17hhrvTDe+mCs9cJ46yPCw8/R2KE9kcakZsqHqw4gPSff5jShgX7Y+Z8hFbpdREREOklPT1c1RtLS0rB27Vp06dJFjc/OzsaAAQPw559/4ptvvnEoyVKWZUnNlYMHD6JDhw6oXr06+vXrh9WrV2Pfvn1qWWTF9h+BuWOKhltfB4z8yu5uen/Vfry6ZI8avqVLI7wyvD13KxERERGRh2PNFRds3rwZOmP5N3tFE2Fbp12FmKhQu02ENZu4sFQTYYy/58e/rBh7fWNPROVj7ty5SE5OVgkPIxkigoOD8cILL6jhDz74oNyW1bBhQ/Tu3VslVnRT5t80Zzuzt+xvpQn7W6kMup+/6ISx1gvjrQ/GWi+Mtz42e/g5GpMrLkhISIDOWH7vif/qCf1VDRVbCgHsSkovNo7x9574O4ux1zf2RFQ+VqxYoZ6HDCldU1Sa95I+U6QPFUc6e3TnsnRQ5t80y2bBIuwnVwoLTdh4KMX8+vImUWVbJ7lE9/MXnTDWemG89cFY64Xx1keCh5+jMblCRMqs0Z3hY2df/LI1CX1fXcm9RURE5GZ79hQ1F9WyZctS7/n7+6Np06bIz89HfHx8hS6rLDp37mzz4VXSEh2uubLv5DmkZxc1wRpdLQgxNW3XGCYiIiIiIs/h746FPPXUU6ojzL179+LUqVMICQlBTEwMbrjhBjz00EOoWbNmqXnkjjlpmmD9+vWqDWhpz3nMmDF4+OGH4edn/Q762bNnY+bMmdi5c6ea5rLLLsMTTzyB6667zur0WVlZePnll/Htt9+qLJjRhvS0adPQpk0bdxSdyGv0aVkLPVtEY+fRNKRk5lmdJiElUzUR9vhVrdCwwreQiIjIO0n/KPY6czTGp6amVuiy3G337t3m5I/o27evepb+XQytWrVC69atsWTJEnPtGtlmOYeXJgMs72wbPHiwKm9cXJx5nPQb06RJE8yfP988rk6dOujevbv6u+PEiRPm8UOHDlXPltN269ZNrW/p0qXmcfJ3TceOHbFq1Srz/u13ZCeMPfz71oNIiZ9vs0z7Udc8XD8wCwsWLCjXMh06dAhbtmxxukxBQUGqxlNVjJM7ymQZa28pkzfGyV1lkm32tjJ5Y5zcUSbhbWXyxji5o0zCcl3eUCZvjBO/y/WLkzd9l8uyK6VD+8DAQHTq1Alt27ZF7dq1kZGRoXaSJFzq16+vhhs1amSeXnbqTTfdpNp+vuWWWxAVFYWff/5Z7YDhw4fjhx9+KLUOSaLMmDFDtQkt0+Tm5qqkSUpKCt59912VxLEkO2jgwIHmjjylA88jR46oZcv2SpMJEiRXSPJGEkm6Yvm9N/6Xv7AMyedybb7fonY1PDU4Fldeqm+KRefjX+eyC93LT0TWyR8OzlRpv+222zBnzhxzLRPpPN5WB/I9evRQHdHLQ/4Ysccdy9KpQ/syf6e/1gLIOFk0/Nh2oMaFv3VK+vd3m/HTpqJmxCZf2wb39G5W5u2lsuPvtz4Ya70w3vpgrPXCeOsjy8Ovsbil5kp6erpKlJQ0adIkvPjii3jppZfw/vvvm6cdO3asqnkiWSajo83nn39eJUCkE05JmkgnnJa1XCSxEhsbi7/++guRkUWdQD755JOqiQGj9or8UWt44403VGJFEjHfffcdfH2LWkCTZI7UqJFaMtu2bTOPLwvJkHly8F3F8ntv/GeM6Ig7P9+AQpPt5i2m/LxT6+SKzse/zmUXupefiKyT81Rr58O2yA1IJWuTGHdflSTnz5bT2ePOZemgTN/p+TkXEis+vkB4PbuT7zh2od+6jo1qlGk7yXX8/dYHY60XxlsfjLVeGG99pHn4NRa39Lli6w/JESNGqGe5680gyZPk5GSVPDESK8YypJkw8cEHHxRbzqxZs8zJGiOxIiSZMm7cOFVL5fPPPzePl8o4xjyvvvpqsQSKVJ3q3bu3alrMslpQWVhWddIRyx/n1U2E9WgejfAg253cH0vLRrOnF2Lmyv3Qkc7Hv85lF7qXn4isW758uaqK7uhDzlEtq6cLaWK3JOkf5eDBg6q/lGbNLl7jwZ3L0kGZvtPTj10YrlYX8LN9v1p2XgH2J59Twz4+QJt61cu0neQ6/n7rg7HWC+OtD8ZaL4y3PuI8/BpLuXZoL019ifbt25vHSXNcwmgv0VKfPn0QGhqqaqoY7Z5dbJ6rr7662DTiwIEDOHz4sGoWQTrtdGQeIipuzt3dsG3aEDSKtJ09lpotc9YnaJtgISIicgepvS2k7d+S1qxZg8zMTNWcl7QnXJHLIgc6s4+w35n93hNnUXC+KnDTmmEIC3JLwwFERERERORtyZXXX38dzz33HMaPH69qhzz77LMqsTJx4kTzNEbHMpL4KEnuopNkiNxVFx8fr8ZJ/y1Hjx5FtWrVUK9e6Sr3LVq0KHV3nr112JrHFml2zNaDSAfTh7WDj533k9Ky8U2c423MExERUXHSjG10dLRqGlf6LDRkZ2dj8uTJaviBBx4oVX1easAkJSW5vCxyUnpR/ylKdfvJlZ0WTYK1qc9aK0RERERE3sTf3cmVEydOmF9LTZMvvvgCtWrVMo8z2n+21c6zMT41NbVM05d1nrKoU6cO5s+fb37dt29f9WzZ3Jg0zdC6dWt196BRG0fWLx2Fbt68uVjHp4MHD1bbblkdqkOHDqr5M8v1yHqlA9L169cX29/S5NmhQ4ewZcsW87hu3bqp9S1dutQ8LiYmBh07dlR93hj7Su5elHjJH+lGcupiZZJkmLFd3lImZ+IkjDJ4S5msxenMrnVoGeGD+HQgz1SymbAC9X9ialETYW92z/eIMrkrTrIcbyuTI3Eyyu5NZXImTkb5valMJeNERBWrevXq+Pjjj1ViRD6D0nxuVFQUFixYoD7LMl76DbT0v//9D3fddRfuuOMOdb7tyrLEnXfeaR42vuufeuophIeHq+F77rkHvXr1greR72fXaq40dLi/lbZsEszzYk0eibHWC+OtD8ZaL4y3Pjp4+Dmaj0k6KHEzuUgkTXtJjZWzZ8/il19+QadOncy1SaQPFnk0b9681LzSTMGff/6pHnLR6dixY2jQoIF6JCZa/CFzXl5eHgIDA9UFJbkjT3z99de47bbb1GPOnDml5pGLU1dddZV6WGsygYis6/XKciSeKfqcWVMvIgixtcNVk2JERETknLVr12L69OnqPFjOa+VcecyYMXjkkUfg51f8BgdJqFhLrpRlWcJHOgSxQ/o3tEzAaO2X8cDGz4qGh7wMdLddE+imD9bh74QzaviLuy5Hv1a1K2oriYiIiIjIE/tckbtxhw0bppIYp0+fxu23316q1ohxl21J6enpxaa72PTWaqk4u46ysrwDWUcsv37xH9U1xuJLo6jWiqWktBzEnzwLHeh8/OtcdqF7+Ymo/PTs2ROLFi3CmTNnkJWVhW3btqnmdq0lQyTRIfdIWUusOLssIcuy9/DWxEqZvtPTHGsWTPpa2ZVkUXOFzYJVKv5+64Ox1gvjrQ/GWi+Mtz7me/g1lnLt0F6aLGnbti127NiBU6dOmZshsdXfifS1cvDgQdXcVLNmzdS4sLAwVWvl3LlzpdqUFlIDpmT/KvbWYWseIrq4cf2bo0eLaIQHWb8wI46l5aDFM4u4O4mIiMj7+1yx06F9wukMZOYW3YxSKzwItcODK2LriIiIiIjIG5IrQpr1EsZdcgMGDFDP1prjWrNmDTIzM1XTYNLMl8HePIsXLy42jYiNjUXjxo1VckWSNY7MQ0SOkSa/tk0bgshA29PkFZrQ/rlfMXPlfu5WIiIi8i6Wfa5Ut93nCvtbISIiIiLybi4nV6TDy+PHj5caX1hYiEmTJuHkyZMqWRIZGanGSyea0dHR+Pbbb7Fx40bz9NIW9OTJk9XwAw8Ub7f4/vvvV8/SbrQ0bWCQDn9nzpypEjHS5rRlm9HGPBMmTFDbYlnV6Pfff1c1aowOfl1p/kxnLL/e8R/cvBp87TTPnp6djzV7k+GtdD7+dS670L38RERaf6fnZQHZqUXDvv5AWC2bk+5kk2BVCn+/9cFY64Xx1gdjrRfGWx91PPwai8sd2r/11lt48skn0adPH1VjpGbNmqpD+9WrVyM+Ph5169bF8uXLVTLDMG/ePJVkCQ4OxsiRIxEVFYUFCxZgz549avz3339fqlPNxx9/HG+88QYaNmyopsnNzcV3332n+nR599138dBDDxWbPicnR9VMWbduHbp06YKBAwfi8OHD+OGHHxAYGIgVK1agWzd2uk3kiid+2IJftyfhbE7p/lcMAb4+2PfiNdzRRERE5PlSDwNvtSsaDq8HPL7b5qR3fLYBq8/faPLerZfhuvb1K2oriYiIiIjIE2quXHnllbj33ntVkuOnn37Ca6+9hh9//FElTKZOnar6W7FMrIgbbrhBJV8kISPTSnIkICBAJU+kRkvJxIqYMWOG6rBTkjUfffQR/vvf/+KSSy7Bzz//XCqxIqQ2y2+//YYpU6YgNTUVb775JpYtW6bW/ddff7klsbJ+/XrojOVn/F+/uYNqIqxhZLDdJsIuf2GZ19Vi0fn417nsQvfyExFp/Z1+zuJ8Jiza7qRsFqxq4e+3PhhrvTDe+mCs9cJ462O9h19j8Xd1AZdeeqlqmstZPXv2xKJFznV6fccdd6iHo0JCQjBt2jT1KA9SQ0dnLD/jbxjVNQYzlu5BoY16cMnncvHTP4no09J20xmeRufjX+eyC93LT0Sk9Xd6hmVypbbNyZLP5uDUuRw1HBrohyY1w8q8jeQe/P3WB2OtF8ZbH4y1XhhvfZzw8Gss5d6hPRF5v3H9m+Pxwa0QHWa7l/t5m4+h7ZQlFbpdRERERG6VcfLCcDXbyZX9J8+Zh1vUCYevvY7qiIiIiIjIIzG5QkRuS7BsfHYQGkWG2JwmM7cALScvxsyV+7nXiYiIyPOcO+lQs2AHki8kV2KjWWuFiIiIiMgbudyhPRGRJelbZcwXG5BfaHu/dGsahe/uu4I7joiIiDzL4olA3AdFw4OeB3o+YnWy//y8E5+tPaiGnxjcEg8NaFGRW0lERERERBWANVdccOjQIeiM5Wf8rZF+VcYPaoXqQba7dIo7mOLxTYTpfPzrXHahe/mJiLT+TnewWbD4UxdqrjSrVa1M20buxd9vfTDWemG89cFY64Xx1schD7/GwuSKC7Zs2QKdsfyMv70mwrZOuwoxUaF2mwhrNnGhxzYRpvPxr3PZhe7lJyLS+ju9WIf2tpsFi0/OMA/HMrlSJfD3Wx+MtV4Yb30w1nphvPWxxcOvsTC5QkTlZvWE/ggN9LP5vrQctispnREgIiIiz3DOMrliveZKTn4BEs9kqmEfHyCmpu2bTYiIiIiIyHMxuUJE5WrW6M7wsfP+L1uT0PfVlYwCERERVX0ONAuWcDoThed7tWwYGYLgANs3mhARERERkedicsUF3bp1g85YfsbfEdIHS88W0YgKDbA5TUJKpsc1Eabz8a9z2YXu5Sci0vY7vSAfyEy58Dq0ptXJDpy06G8lmv2tVBX8/dYHY60XxlsfjLVeGG99dPPwayxMrrggIiICOmP5GX9Hzbm7G/6ZMhi1qgXabSJs3qajWLPXormNKkzn41/nsgvdy09EpO13euZpAOerpIREAX7WbxyJP3Whv5VmtcJc3kZyD/5+64Ox1gvjrQ/GWi+Mtz4iPPwaC5MrLli6dCl0xvIz/s6aMaIjfO20Ebbv5DlMnrcNnkDn41/nsgvdy09EpO13umVn9jaaBBMHki/UXGFn9lUHf7/1wVjrhfHWB2OtF8ZbH0s9/BoLkytEVGGkibAezaMRHmS77fHDKVlo9rRnNRFGREREmvW3ElbL5mTxyay5QkRERESkAyZXiKhCSRNh26YNQaPIEJvTSCewc9YnMMFCREREVce55IsmV0wmE+JZc4WIiIiISAtMrrggJiYGOmP5GX9XTB/WDnZaCENSWja+iUtAVaXz8a9z2YXu5Sci0vY7PePiyZXTGblIz84vmiTQD7XDg1zeRnIP/n7rg7HWC+OtD8ZaL4y3PmI8/BqLj0luryIiqgSjP43D34dSkJUn3dlb5+cDHHjp2grdLiIiIqJSlk0B1r5dNDxgMtDnyVKTxMWfxi0frVfD7RtGYMFDvbgjiYiIiIi8FGuuuGDVqlXQGcvP+LujibBdz1+NhpHBNqcpMAFXvPSbSsRUJTof/zqXXehefiIibb/TM05dGA6z3qF9/CmL/laiw1zaNnIv/n7rg7HWC+OtD8ZaL4y3PlZ5+DUWJldckJaWBp2x/Iy/u4zqGmP3yygpLQfxJ8+iKtH5+Ne57EL38hMRafudfu7iHdpb9rfSrFY1l7aN3Iu/3/pgrPXCeOuDsdYL462PNA+/xsLkChFVunH9m6NHi2iEB/nZnOZYWg5aPLOoQreLiIiIyCzDIrlSzXrNlSMpWebhmJqh3HlERERERF6MyRUXBAXp3UEly8/4u5M0EbZt2hC7TYTlFZrQ/rlfMXPlflQ2nY9/ncsudC8/EZG23+nFmgWzXnMlMTXTPNwoismVqoS/3/pgrPXCeOuDsdYL462PIA+/xsIO7YmoSpHEyYyle1Bosj1Nt6ZR+O6+Kypys4iIiEhnJhPwQm2gILfo9TNJQGDp5EnH/yxFamaeGt4waSBqh9u+aYSIiIiIiDwba664YPfu3dAZy8/4l1cTYTd2ami3ibC4gymV3kSYzse/zmUXupefiEjL7/TstAuJlcBqVhMrZ7PzzImVIH9f1Krm2XfheRv+fuuDsdYL460PxlovjLc+dnv4NRYmV1ywZ88e6IzlZ/zLy+s3d3CoibDLX1iGNXuTURl0Pv51LrvQvfxERFp+p2ckX7RJsKOpF/pbaVAjBD4+Pi5vH/1/e/cBHlWZNXD8JKSQUAIhFBWkE0QFFBQpUpfquoqi4gcr1lUXG+oqKKIo6KqAWFhdFdGVVXZtoIKIUtdCrCBKFelEiiGhpJFkvud9MclMkhkSJmXuPf/f8wxzmbkzc9+ce3Mnc+Y9p/xw/taDWOtCvPUg1roQbz02OPwzFpIrAELWlec2lfAAn0vsO5wt7363szI3CQAAaHR47/H7rXg1sz+lbkxlbBUAAACAKkRyBUDIMiXC7hqQKAk1ovyuM3fVbmk3YWGlbhcAAFDGe+ZKzQYlrrLzQGEz+8Z1aWYPAAAAuB0N7YOQmpoqderUEa0YP/GvzP3//MeXyI4Dhd8ILSoqIlxu79faJmQqg+b9X/PYDe3jBwCVv9O/eklkwd3HljtdI3Lh9GKrTPpwrbz82Ra7/LeBiZX2ngSlw/lbD2KtC/HWg1jrQrz1SHX4ZyzMXAHgCJOHnikRAX5jZefkVVn/FQAA4HJH9hcu10gocZWdXl8CaUxZMAAAAMD1SK4EYfny5aIZ4yf+lalnm/oypn+i1I6O8LtO0paUSisRpnn/1zx2Q/v4AUDl7/SMA4XLMfHHbWhPWbDQw/lbD2KtC/HWg1jrQrz1WO7wz1hIrgBwDFNe44eJA6VpvP865unZudJi7HyZsfTnSt02AADgYhkphcux8cftudKEmSsAAACA65FcAeA4y+/pI7FR1fzenyci65IPVuo2AQAAF0v3Sq7E1C129+GsHDmQfrSgD1xCzejK3DoAAAAAVYDkShASExNFM8ZP/KvSCyM7SViA+z/8IVl6PbG0wl5f8/6veeyG9vEDgMrf6ccpC7bLu99KnRgJDw/0LgVVgfO3HsRaF+KtB7HWhXjrkejwz1jCPB6Pp6o3AgBOxMiZSbJ2V5qk/P5NUX8Z5LsGJtqSYgAAACfk6Q4iB7YeW771O5F6LX3uXrxuj1z32jd2+fzWCfL6dV34QQMAAAAux8yVICxcWDmNs0MV4yf+VW32dV3kuwkDpH7NqIAlwuZ+v0tWbNxXrq+tef/XPHZD+/gBQOXv9PQDAcuC7fSeuUK/lZDE+VsPYq0L8daDWOtCvPVY6PDPWEiuBCErK0s0Y/zEP1RMvbyjBKq+sWnvYRk/d025vqbm/V/z2A3t4wcAdb/Tc3NEstJ+/0+YSPW4gM3sG9eNLc9NRDnh/K0HsdaFeOtBrHUh3npkOfwzFpIrAByvZ5v60q1VgtSK9t/kfntKhrQYN19mLP25UrcNAAA4XGZq4XJMHZHw4u83mLkCAAAA6ENyJQhxccW/taYJ4yf+ocSUCFszcZA0CVCKI88jMnvltnJJsGje/zWP3dA+fgBQ9zs9PSVgSTCD5Ero4/ytB7HWhXjrQax1Id56xDn8MxYa2gNwFdNbZdQrX4knwDqN61SXz8b2q8StAgAAjrU9SeSVAceWT+kscsPiYquc9fAiOZB+1C4n3ddPGtauXtlbCQAAAKCSMXMlCKtWrRLNGD/xD9USYd1bJ0hMpP9fbztTM6XluPlBvY7m/V/z2A3t4wcAdb/TM7xmrsTGF7v7SFZOQWIlqlq41K8ZXa7biPLB+VsPYq0L8daDWOtCvPVY5fDPWEiuBGHbtm2iGeMn/qHKlAhb98hgaVzX/7dGcz0iXR/7VEbOTDqh19C8/2seu6F9/ACg7nf6ccqC7TmYWbDcMC5awsPDym37UH44f+tBrHUh3noQa12Itx7bHP4ZC8kVAK515blNA/6SS07Lkl/2HqrELQIAAI6TcaBwOab4zJVfvZMrtSgHBgAAAGhBcgWAa43u00q6tU6QWtHV/K6zOy1LWt+3oFK3CwAAOMhxyoLtPZhVsNwwjuQKAAAAoAUN7YOQkZEhMTExohXjJ/5O2v97PL5Ydh4o/GZpUbWrR8iNvVrahExpaN7/NY/d0D5+AFD3O/2DO0S+nXVsecgUkXNv8Ln7n8s3y2MfrbfL13ZvLhMubFdh24sTx/lbD2KtC/HWg1jrQrz1yHD4ZyzMXAlCWlqaaMb4ib/jSoQFKIF+MDNHVmzcV+rn07z/ax67oX38AKDud7pPWbCSeq54zVypTTP7UMX5Ww9irQvx1oNY60K89Uhz+GcsJFeCkJR0Yo2w3YLxE38nMTNSLjm7ccASYUlbUkpdIkzz/q957Ib28QOAut/pxykL5tPQvjZlwUIV5289iLUuxFsPYq0L8dYjyeGfsZBcAaDGlMs6yJqJg6RxXf8ffBzN88g5kz4p0ywWAADgYunHm7lCcgUAAADQiOQKAHWOVyJs3+Fsefe7nZW5SQAAIFT5lAUrYebKIe/kCmXBAAAAAC1IrgShQ4cOohnjJ/5OZUqE3TUgURJqRPldZ+6q3dJuwkK/92ve/zWP3dA+fgBQ9zs9QFkwj8fj03OlAWXBQhbnbz2ItS7EWw9irQvx1sPpsQ7zmL8IAECp8x9fIjsOZPi9PyoiXG7v19omZAAAgDJHM0UmNzy2HB4h8sB+kbDC6a8HjmTLWY98YpdrRkfIjxMHVtWWAgAAAKhkzFwJwrx580Qzxk/83WDy0DMlIsBvwuycvBL7r2je/zWP3dA+fgBQ9Tu9aEkwr8RK0ZJgDSgJFtI4f+tBrHUh3noQa12Itx7zHP4ZC8kVAKr1bFNfxvRPlNrREX7XSdqSErBEGAAAcKkAJcEM75JgjSgJBgAAAKhCcgWAeqbk1w8TB0rT+Fi/P4v07FxpMXa+zFj6s/qfFwAAaqR7JVdi6ha7e89B72b21StrqwAAAAC4Nbny+uuvS1hYmL28/PLLJa7zxRdfyJAhQyQ+Pl5iY2Olffv2Mn36dMnNzfX7vK+99pqce+65UrNmTYmLi5PevXvLhx9+6Hf9jIwMefDBByUxMVGqV68uDRo0kMsvv1zWrVtXLuNs2PD3+stKMX7i7zbL7+kjsVHV/N6fJyLrkg+K9v1f89gN7eMHAFW/04uWBStir1dyhbJgoY3ztx7EWhfirQex1oV469HQ4Z+xlHtD+x07dsiZZ55pkySHDx+Wl156Sa6//vpitdQuvfRSm/C44oorbILlgw8+kA0bNsiwYcPkrbfeKva8d999t0ydOlUaN25s18nOzpY5c+ZISkqKPPvss3LLLbf4rJ+VlSX9+vWTzz//XDp37ix9+/a122aeOyoqSpYsWSJdunQpz6EDcAHTX2XUK19JoF+MZoaLScQAAACX+/ZVkQ9uP7Z81kiRi2b43D1+7hqZvXK7XZ7wx3ZybY/mVbGVAAAAAJw+c8Xkaa655hqpV6+e3HTTTSWuc/DgQbnhhhukWrVqsmzZMpk5c6Y8+eSTsmrVKunatau8/fbbNmlSdJaLSay0bNlSfvjhB3nqqadkxowZ8u2339rEjEm8bN261ecx06ZNs4kVk4hJSkqSxx9/XN544w37/Onp6XLttddKXp75HvqJW7lypWjG+Im/W3uwdG+dIPGxkX7X2ZaSLs0Vlwjj2Nd97AOAqnPaccuCefVciaMsWCjT/v5FE2KtC/HWg1jrQrz1WOnw92jlmlx55pln7IyQWbNmSY0aNUpcxyQ39u3bJ8OHD7czSvKZWSyTJk2yy88//7zPY1544QV7ff/990vduoV/1DRr1kxGjx5tZ6mY1/RO8uQ/5oknnpDw8MJhXnTRRXL++efL2rVrZfny5UGNd8+ePaIZ4yf+bjX7ui7y3YQBUr9mlN91PJIrc7/fZWe6aMOxr/vYBwBV57QylAVrWDu6XLcN5Uv7+xdNiLUuxFsPYq0L8dZjj8Pfo5VbcsX0MRk7dqzcfvvt0rNnT7/rmeSLMWjQoGL3mceZ/itmpopJmJTmMYMHD/ZZx9i8ebNs375d2rRpI82bNy/VYwCgqKmXd5TwMP8/l017D9tyIAAAwKUyvGauxMYHnLnSoBYzVwAAAABNyiW5kpOTI3/+85/l1FNPlUcffTTguqavimESH0VFRETYZIh5vl9++cXeduTIEdm1a5dtYn/SSScVe0zr1q3t9caNG0v1Gv4e40+nTp38XgC4mykR1q1VgtSK9t/kfntKhrQYp7dEGAAArpZ+wG9ZsNw8j+w77JVcYeYKAAAAoEpEeTzJww8/LN9//7189tlnEhMTE3DdtLQ0ex0XF1fi/fm3p6amntD6J/qYE5GYmCjz5s0r+H+vXr3stXe5MbNO27ZtZeHChQWzcczr9+7d2/aZ2bZtW8G6AwYMsNtuesTk69Chgy1/5v06DRs2lPPOO8/WpPOeOmVKnpneM6tXry64rUuXLvb1Fi1aVHBb06ZNpWPHjrbnTf7PKjo62s4MWr9+fUFy6nhjMo/J3y63jKkscTLyx+CWMZUlTt7jd8uYSorTZQm/ymUJIg9/Gya/ZecnWXK9rqtJnkfk5WUbZN3atdK/sSfkxxRsnLxj75YxlSVO+eN305iKxgkAtDC/c0+0LNhvh7NsgsWoGxsp0RH+v4wBB8QarkGsdSHeehBrXYi3Hhc5/D1amMc0KAnCV199Jd26dZM777zT9jfJ99BDD8nEiRPlpZdekuuvv77gdjObZNOmTfbSqlWrYs9nnuvLL7+0F/Oh0+7du+WUU06xl507dxZb/+jRoxIVFWU/UMrMPFbz2DSuHzFihL3Mnj272GPMh1MDBw60l/wPyk6E+fDLfFimFeMn/pr2f9NbZdQrX0mgX5iN61SXz8b2E7fj2Nd97AOAqnPajC4i+459sUBu/kKk4ekFd63ZmSYXPveZXW7bqJYsvMN/aWRUPe3vXzQh1roQbz2ItS7EW4+tDn+PFl4e5cBMwuSRRx4p1WPyZ43kf8u2qIMHD/qsd7z1S5qlUtbXOFHe3yrWiPETf20lwrq3TpCYyPAis1cK7UzNlJbj5ovbcezrPvYBQNU5LT3Fb1mwPT7N7Om3Euq0v3/RhFjrQrz1INa6EG89Vjv8PVpQyZXDhw/bviWmmX316tUlLCys4GJmrRg33HCD/f8dd9xRUIbEX78Tk6zZsmWL7b3SokULe1uNGjXsrBXzWsnJycUeY2bAFO2vEug1/D0GAI5n9nVdZN0jg6VxXf8foOR6RLo+9qmMnFlYEgoAADiQmeDvUxbMN7nyq09yJboytwwAAACA03uumFJc1113XYn3fffdd7YPS48ePWyyo2vXrvb2vn37yr///W9bjuvKK6/0ecyKFSskPT1devbsaZ87n3nM66+/bh9zzTXX+Dzmo48+KlgnX8uWLeXUU0+1yRWTrGnevPlxHwMApXXluU1lysdr/ZYIS07LkjB+nAAAONvRdJG8o8eWq0WLRPr2ltzLzBUAAABAtaB7rvjjr+eKKcllkh/m+vPPP5fOnTvb202/FJPsML1W3nzzTRk+fHjBY7744gvp3r27fdzXX38tdevWLajJ1qlTJzly5Iht3utdn+2xxx6T++67T4YNGyb/+c9/JDz82CQd00z44osvlnbt2smaNWsKbj8Rv/76qzRq1Ei0YvzEX/P+f8U/VsjaPelyKKt4ebB8keFhsunRIeI2HPu6j30AUHNOS9sl8lS7Y8s1G4rc7Tsrfty7a+TNr7bb5YcvOl2u6urcWtEaaH//ogmx1oV460GsdSHeevzq8PdoQc1cORG1a9e2CReT9Ojdu7dNosTHx8v7778vGzZssLdfccUVxZrc33nnnTJt2jRp3769XSc7O9smTVJSUuTZZ58t1vjGrP/hhx/K22+/LV26dJF+/frJ9u3b5a233pLY2Fh55ZVXgkqslEfPFqdj/MRfs1evOUdiYmKkx+OLZeeBwrIg3o7meaT9Qx/Ljb1ayug+rcQtOPZ1H/sA4CYBz2mZqYXL1esUuzvlSFbBcr0alAULddrfv2hCrHUh3noQa12Itx5xDn+PFlx24QSZmSPLly+35b/eeecdmxyJjIy0yZM5c+bYHi1FTZ06VV599VWbyXrxxRflX//6l5x++unywQcfyC233FJsfVNW7NNPP5UJEyZIamqqPPXUU/LJJ5/Y1zazX0zCJViLFi0SzRg/8dcsf/83JcLCA9QAO5iZIys27hM34djXfewDgJpzWoZXciWmeHLlt8PZBcv1akaV+7ahfGl//6IJsdaFeOtBrHUh3noscvh7tAqbuWLKgpmLP6bM14IFC8r0nKNGjbKX0jLfKjelycwFACqCmZGyZf8R+fjHZL8lwpK2pEjr+xa4skQYAACudZyZK78dKUyuJJBcAQAAANSpkpkrAOAmUy7rIGsmDpLGdav7XceUCDtn0ieum8UCAIBrHWfmyv7DlAUDAAAANCO5EoSmTZuKZoyf+GtW0v5/vBJh+w5ny7vf7RSn49jXfewDgJsEPKcFmLmSlZMrhzJz7HK18DCJi4mssG1E+dD+/kUTYq0L8daDWOtCvPVo6vD3aGEej8dT1RsBAG4xY+nPMuuzLbLfq1RIUbFR1WTtw4MqdbsAAEAZLZkssuKJY8u97hXpc1/BXclpGdL1sSV2uX6taPn6/j/w4wUAAACUYeZKEJYtWyaaMX7ir5m//d/0YPnmgf7SpG6M38emZ+dKm/Ef2USME3Hs6z72AcBNAp7TAsxc8WlmX4Nm9k6g/f2LJsRaF+KtB7HWhXjrsczh79FIrgQhLS1NNGP8xF+z4+3/k4eeKREBfsNm5+Q5tv8Kx77uYx9Axfniiy9kyJAhEh8fL7GxsdK+fXuZPn265ObmVuhzff7553LPPffIOeecI/Xr15fo6Ghp3ry5XH/99fLzz878IkC5nNMC9Fzx7reSUDO6QrYN5Uv7+xdNiLUuxFsPYq0L8dYjzeHv0UiuAEAF6Nmmvozpnyi1oyP8rpO0JUXaTVjIzx8AIPPmzZOePXvKihUrZOjQoTJ69GjJzs6WMWPGyPDhwyv0uS699FKZOnWqVK9eXUaMGCG33nqrnHzyyTJz5kzp2LGjfPnllzojVNqZKzWZuQIAAABoRHIlCOZbfZoxfuKvWWn2f1Mi7IeJA6VpfGzAEmEtxs53VIkwjn3dxz6A8nfw4EG54YYbpFq1anZavElqPPnkk7Jq1Srp2rWrvP322zJnzpwKey6TdNmxY4f873//s7NbpkyZYmezTJ48WY4cOSJ/+ctfXBv2gOc0n5krdX3u+u1I4cyVejU4LziB9vcvmhBrXYi3HsRaF+KtR7TD36PR0B4AKoGZoWISKf78sf1J8tz/nU0sAEChV155Ra677jq56qqr5LXXXvO5b8mSJdKvXz87E2X58uWV+lymhFitWrUkIyND9u/fL/Xq1RNVnjtHZP/GY8t/XSnS4LSCux5bsE7+ueIXu/y3gYn2CxUAAAAAdGHmShDWr18vmjF+4q9ZWff/F0Z2krAA93/4Q7L0emKpOAHHvu5jH0D5M0kPY9CgQcXuM4kQ0zPF9FDJysqq1OcKCwuTiIhj5S3NTJjS6NSpk9+L485pGf7Lgu33KguWQFkwR9D+/kUTYq0L8daDWOtCvPVY7/D3aP6bAeC4NmzYIG3btlX7k2L8xJ/9v22ZerB0b50ga3elSUr60RLX2ZaSbkuE3RXi34Dl2Nd97AOomN+rRps2bYrdZ5Ibprn8Tz/9JL/88oucdtpplfZcb731lhw6dEjOO+88qVPHN7lwon845W+f0atXL3vtPYsmMTHR/o5duHBhQQIoLi5OevfubUubbdu2rWDdAQMG2AaYSUlJBbd16NBBmjVrZvvO5GvYsKEdw8qVK2XPnj0Ft1900UV2e7y3qUuXLvb1Fn38sfwxPUUKUkoxdWyZtfyGmxu2Fv4Z9fOPq2Te7u9DZkxbt26V1atXFx/TokUFtzVt2tT20/EekynJYJJyoRin8hpT/rjcNCY3xqk8xmSex21jcmOcymNMhukZ5qYxuTFO5TGmoudsN4zJjXHid7m+OJXHmMzrhMKYzHOXFWXBgmB2DrNDa8X4iT/7/4kd/+dM+kT2eX3jtajWDWrKA39sZxMyoYhjX/exD6D8mUTIpk2b7KVVq+LJ9e7du9vZJuZi+qZUxnNt2bLF/kFz4MAB+wdJt27dxI38ntOy00UePenYcrVokQf2+tz9p+c+kx92HvuD7r2/dpOzTvXtyYLQo/39iybEWhfirQex1oV46zHP4e/RKAsGAJVs6uUdJTxAjbBNew/L+LlrKnOTAABBMt/KMmW0SnsZOXJkqZ/b4/HYa/O4YJXmufbu3SuDBw+Wffv2ydNPP+3axEpAmd7N7IvP2vnNpyyYs5twAgAAADgxlAULQv70Iq0YP/HXLJj938xI6dYqQVZvPyCHskpucr89JUNajJsvdw0IvRJhHPu6j30AJWvZsqUtS1JaJ598csGymYpu5E9tL+rgwYM+6wUS7HOZxErfvn3tlHqTWPnrX/8qbub3nBag34pJUO0/XNizph49VxxB+/sXTYi1LsRbD2KtC/HWo5fD36ORXAGAKjD7ui72+vzHl8iOAxklrpPnEZm98lgNy1BLsAAAfC1evPiEfySm9u8333wjGzduLNb4PScnx5boMv1SWrRoUaHPlZycLP369bP1imfMmOH6xMqJzlw5kp0rWTl5x+6KrCaxUfxJBQAAAGhEWbAgeDfE0YjxE3/Nymv/nzz0TAlU5CU5LVPeTCpsEhYKOPZ1H/sAyp+ZKWKYxopFrVixQtLT021pLtOssaKea+fOnfZbYyax8sILL6hJrPg9pwWYufIbs1YcSfv7F02ItS7EWw9irQvx1mO5w9+jkVwBgCpkSoR1b50gMZH+fx3vTM2UluPmV+p2AQAqz7BhwyQhIUHmzJljZ53ky8zMlPHjx9vlm2++2ecxpuyXSYSY2SbBPtf27dttYmXz5s0yc+ZM+ctf/lIh43TLzJX9Xv1W6tWIqsytAgAAABBCmMMOACFSIqzH44tl54HMEtfJ9Yh0fexTadmgVsH6AAB3qF27trz00ks2MdK7d28ZPny4xMfHy/vvv297n5jbr7jiCp/HvPfee3LNNdfIqFGj5NVXXw3quUxiZevWrbaM2LZt2+Shhx4qto1XX321NGvWTNQo9cwVmtkDAAAAWpFcCYKpaa0Z4yf+mlXE/n/luU1l6scb5FgV9+KS07IClhCrLBz7uo99ABXj4osvtlPiJ0+eLO+8846dadKqVSuZNm2a3HbbbRIWFlZhz2USK8a3335rLyUxiRo3Jlf8ntMCzFz57QgzV5xI+/sXTYi1LsRbD2KtC/HWI9Hh79HCPB6Pp6o3AgBwzMiZSbJ6+wE5lJXr90cSGR4mmx4dwo8MAICKsuBvIl+9eGx54GMiXQt70Dy3ZJNMWbTRLt/Uq6WMHdyWOAAAAAAK0XMlCCU1CtWE8RN/zSpq/zclv9ZMHCSN61b3u87RPI+0f+hjmbH0Z6kKHPu6j30AcBO/57SM0vVcSahJzxWn0P7+RRNirQvx1oNY60K89Vjo8PdoJFeCkJVVWG9ZI8ZP/DWr6P3flAgLD1AB5mBmjqzYuE+qAse+7mMfANzE7zktM0DPFe+yYCRXHEP7+xdNiLUuxFsPYq0L8dYjy+Hv0UiuAEAIGt2nlVxydmOpFV3N7zpJW1Kk9X0LKnW7AABQIcDMlZQjXg3ta9DQHgAAANCK5EoQ4uLiRDPGT/w1q4z9f8plHUpVIuycSZ9U6iwWjn3dxz4AuMJ7N4vMHCD9Nk4QSd1RtpkrXmXBmLniHNrfv2hCrHUh3noQa12Itx5xDn+PRkN7AAhxprfK1EUbJM/jf52LO54s04efVZmbBQCAc/2jq8jetceWb/pMpNGZvvc/2VrkyN5jy3euE6l9csFdnSd9KvsPH5u9knRfP2lY2/+XIAAAAAC4FzNXgrBq1SrRjPETf80qc/83JcLuGpAoCTX8N82du2q3tJtQOU3AOPZ1H/sA4ApRNQuXs4/43ufx+J25kpfn8SkLVjeWhvZOof39iybEWhfirQex1oV467HK4e/RSK4EYdu2baIZ4yf+mlX2/m8SLN880F+a1I3xu056dq60Gf+RnelSkTj2dR/7AOAKUTUKl7MO+953NEMk9/fSX9WiRCILz72HsnIKZpLWio6QqAj+nHIK7e9fNCHWuhBvPYi1LsRbj20Of4/GXwMA4CCTh54pgT7Hyc7Jq9T+KwAAOFK098yVIsmVorNWwsIK/puWfrRgOS42smK3EQAAAEBII7kCAA7Ss019GdM/UWpHR/hdJ2lLSqWVCAMAwPllwYokVzK8kisxvs3sUzMKm9nXIbkCAAAAqEZD+yBkZGRITIz/Ej1ux/iJP/t/1R7/vZ5YKttS0gNmz+8amGhLipUnjn3dxz4AuML8u0W+funY8uAnRLrcWHjfti9EZg0+ttz4XJHrPym4y8wOveqVr+xyj1YJMvv6LpW73Thh2t+/aEKsdSHeehBrXYi3HhkOf4/GzJUgpKWliWaMn/hrFgr7//J7+khsVDW/9+eJyLrkg64ce1XSPn4AcF/PlUNlmLlCWTCn4vytB7HWhXjrQax1Id56pDn8MxaSK0FISkoSzRg/8dcsVPb/F0Z2ksJK8MV9+EOyneHixrFXFe3jBwD39Vw5Erjnipe0dK+yYDH0XHESzt96EGtdiLcexFoX4q1HksM/YyG5AgAO78HSvXWCxAeo+25Kh7UYO19mLP25UrcNAABn9lw5ULgcU9fnrlTvhvYkVwAAAADVSK4AgMPNvq6LfDdhgNSvGRWwRNjc73fZWvEAAKgXFWDmSnpK4XJsPb9lwWhoDwAAAOhGciUIHTp0EM0YP/HXLBT3/6mXd5TwADXCNu09LOPnrnHl2CuT9vEDgOt7rqT/VrgcG+935kqdGP9fakDo4fytB7HWhXjrQax1Id56dHD4ZywkV4LQrFkz0YzxE3/NQnH/NyXCurVKkFrR/pvcb0/JkBbjgisRFopjr0zaxw8ArhBdy//MlYwUv2XB0jIKe67EBSjJidDD+VsPYq0L8daDWOtCvPVo5vDPWEiuBGHevHmiGeMn/pqF6v5vSoStmThImtSN8btOnkdk9sptJ5xgCdWxVxbt4wcA181cKdpzxacsmO/MlTTvsmD0XHEUzt96EGtdiLcexFoX4q3HPId/xkJyBQBcaPLQMyVAhTBJTsuUN5O2VeIWAQDggp4r3mXBYikLBgAAAGhGcgUAXMiUCOveOkFiIv3/mt+Zmiktx82v1O0CACDke674lAUr0nOFhvYAAAAAfkdyJQgNGzYUzRg/8dfMCfu/KRG27pHB0rhudb/r5HpEuj72qYycmeSqsVck7eMHAPf1XPEqC+bx+C0L5vF4JM1r5kocZcEchfO3HsRaF+KtB7HWhXjr0dDhn7GEecxfCQAA1zK9VaZ+vEHyAqxzcly0fDHuD5W4VQAAVCFTCuzRk48tR1QXGb+n5Nvv/1Uk7FihzfTsHGk34WO7XD0yXNY/Mrhqth0AAABASGDmShBWrlwpmjF+4q+Zk/b/0X1aSbfWCVIruprfdXanZUnr+xa4buwVQfv4AcAVImNFwn7/UygnUyQ359hy+m++JcF+T6wU67cSQ78Vp+H8rQex1oV460GsdSHeeqx0+GcsJFeCsGfP799wU4rxE3/NnLb/mxJhayYOClgi7GieR9o/9LGd6eKmsZc37eMHAFcwSROfpva/lwbzUxKseDP7yIrfRpQrzt96EGtdiLcexFoX4q3HHod/xhJR1RsAAKg8V57bVKYu2iB5fgpCHszMkRUb99nZLgAAuL6pfdbBwuRKTB3fZvZFkysZ2QXL9FsBAABAXl6epKSkyKFDhyQrK8v26EPZNGjQQNatWyflKSwsTKKjo6VWrVoSHx8v4eEVN7+EmSsAoIhJmlxyduOAJcKStqSUukQYAACO5TNz5UjxmSumLJgXmtkDAADAO7GyY8cO2bdvn2RmZpJYOUEmAVLeTJLLxMTExsTIxKqi0NAeAJTq8fhi2Xkg0+/99WtGydTLO0rPNvUrdbsAAKgU/+wlkrzq2PL1S0QadxJJelHko78du63ztSJ/fKpg9Te/2i7j3l1jly/v3FieGNaBQAEAACi1f/9+++F9RESENGrUSGrUqFGhMyRQeiaZcuTIEfn1118lJydH6tevLwkJCVIRiHgQtm7dKpoxfuKvmRv2f1MiLLywT28x+w5ny7vf7XTl2IOhffwA4BrRtYr3XPEpC1YvQM8VGto7DedvPYi1LsRbD2KtixPibUqBGSaxYmZfkFg5MaacWnkzsTAxMbHxjlVFILkShNWrV4tmjJ/4a+aG/d+UCLtrQKIk1PD/AdHcVbul3YSFrht7MLSPHwBc1XMlUEP7ImXB6LnibJy/9SDWuhBvPYi1Lk6Id35SwMxYwYnLyMiQipIfm4pI4OQjuQIAipkEyzcP9JcmdWP8rpOenSttxn8kM5b+XKnbBgBA5fdc+c1vQ3vvnit1YiMJDgAAgGL5zeuZsRK6TGN771hVBJIrAACZPPRMiQhwRsjOyZMVG/fxkwIAuHPmStah4mXBis5c8U6uxFAWDAAAAHBCcqUilUtypVmzZnZjS7rk1zYr6osvvpAhQ4ZIfHy8xMbGSvv27WX69OmSm5vr93Vee+01Offcc6VmzZoSFxcnvXv3lg8//DDgtKIHH3xQEhMTpXr16tKgQQO5/PLLZd26deUxbOnSpYtoxviJv2Zu2/9N0/ox/ROldnSE33WStqTYEmFuG3tZaR8/ALiz50r+zJUAPVcysguWmbniPJy/9SDWuhBvPYi1LsRbjxoOL6vm/1O0MjLJjjvuuKPY7SYRUtS8efPk0ksvtQmPK664wiZYPvjgAxkzZox8/vnn8tZbbxV7zN133y1Tp06Vxo0byw033CDZ2dkyZ84cufDCC+XZZ5+VW265xWd9U0utf//+9vk6d+4st99+u+zYscM+9/z582XJkiVBH6hmzJoxfuKvmRv3f1MizFx6PbFUtqWk+y0R1m36t3LXwES7rkZujD0AqHS8niuxdX1WT8vIKViOi6EsmNNw/taDWOtCvPUg1roQbz2qVasmTlZuZcHq1KkjDz30ULGLSYp4O3jwoE2OmB/csmXLZObMmfLkk0/KqlWrpGvXrvL222/bpEnRWS4msdKyZUv54Ycf5KmnnpIZM2bIt99+axMz5jW2bt3q85hp06bZxMqwYcMkKSlJHn/8cXnjjTfs86enp8u1114reXl5QY150aJFohnjJ/6auXn/X35PH4mN8n9yy5NcWZd8ULRyc+wBQLT3XAlQFiwtnZkrTsb5Ww9irQvx1oNY60K89Th40NmfL1V6zxWT3Ni3b58MHz7czijJZ2axTJo0yS4///zzPo954YUX7PX9998vdevW9SlHNnr0aDtLZdasWQW3myY1+Y954oknfBoLXXTRRXL++efL2rVrZfny5RU4UgBwrhdGdpJAlSk//CHZznABAMA1PVdysgtnsIRVE6nuO1MxNcO7oT09VwAAAIBLLrnEtgYxkyH8+frrryUyMlKaN2/u+GRKhSVXTIJj9uzZ8uijj8rTTz8tS5cuLbF/iinHZQwaNKjYfT179rT9V8xMFfN8pXnM4MGDfdYxNm/eLNu3b5c2bdrYoJXmMf506tTJ7wUA3Mr0YOneOkHiY/2XPTGlw1qMnS8zlv5cqdsGAECF9FzxnrUSG286YBb8Nysn15bGNCLCw6RGgBmeAAAAgBYvvfSSnHTSSTJu3DhZs2ZNsftNBamRI0faClKvv/661K5dW9yk3Hqu/Prrr/LnP//Z5zaT2DAzSnr16lVw24YNG+y1SXwU25iICPuYn376SX755Rc57bTT5MiRI7Jr1y7bu8UEqqjWrVvb640bN5bqNfw95kTr/5n+Mfnyx+k9IyYxMVHatm0rCxcuLEgYmcf17t3blkLbtm1bwboDBgyQtLQ0W8YsX4cOHewMHe/XadiwoZx33nmycuVK2bNnj8+sHFMebfXq1QW3mb4y5vW8p9M1bdpUOnbsaMuymdczoqOjbfJq/fr1BT+/443JlHbL3y63jKkscTLyx+CWMZUlTt7jd8uYyhon8zxuG5N3nK5vmSFpCRky/uswOZRT9EOkYx8w5Uk1effb7XJ4+1ppW8cT8mMqjzjlx95NYyoaJwBQ2XMl/Tf/JcF8Zq1E2m/nwVnMeRM6EGtdiLcexFoX4u0c9erVs5//m8kMI0aMsLNUzGcT+e666y77Gfx9990nPXr0KPb4qChnzwgP85gaWkGaOHGiLbV1+umnS61atWxi5LnnnpMXX3zRlvv68ssv7QdL+QmPTZs22UurVsWbIXfv3t3OXDEX04Nl9+7dcsopp9jLzp07i61/9OhRGwRzyf9wyPRWMcE0FzObpqhPPvnEfvhlLh9//HGwwwcAV1uxcZ9cPesryQtwtjg1PkZW3NO3MjcLAIDg/LJc5F9/OrbctIdI77Eir/3x2P9P7SZy7UcFq27ac0j6P7XCLreoX0OW3EUiGgAAQLN169bZazM5ACK33XabPPvsszJmzBjbC91YsGCBXHDBBbYClMkPmNJgbotTuZQFe/DBB6Vv3772W7imrNcZZ5xhe57ceeedkpGRYRvbl1Z+rqes3wYry/on+hpFmW8La8b4ib9mmvZ/UyKsW6sEqRXtvwTK9pQMaTFOR4kwTbEHAD0N7Q8XLwvmr99KTOX/UYjgcf7Wg1jrQrz1INa6EG/neeKJJ6Rdu3Yyffp0Wbx4sezfv1+uvfZamyv497//7TexcujQIXGyCm1of9NNN9nrFSuOfcsrv+SIkV/CpKj8pjb56x1v/fzb89c7kdc4Uf6eXwvGT/w107b/z76ui6yZOEia1I0pKAlWlJnZMnvlNtcnWLTFHgBcK7pmgLJgdX1WTU2nmb3Tcf7Wg1jrQrz1INa6EG/nqV69ekESZdSoUXLVVVfZEuhTpkyxZcn9Kalnu8qeKyVp0KCBvTZ9U/KZH+Y333xja60VbQqfk5MjW7Zssb1XWrRoYW+rUaOGLQlm+q4kJycX67tiyosV7a+SHzB/PVVKegwA4PgmDz1TrnrlS7/3J6dlyptJ22R0n+JlHwEACN2eK0dE0r1nrtTzWTU1PbtgmZkrAAAAOJ5mY+c75oe09e8XlMvzdOzYUR555BG599577Wf5piTYzTffLG5WoTNXTC01Iz9RYpjyYUZ+U2BvZoZLenq6dOvWzafxTaDHfPTRRz7rGC1btpRTTz3VJldMsqY0jzkR3tuoEeMn/ppp3f9NibDT6lSTmEj/p4+dqZnScpxz3kSUldbYA4Cry4JlmbJgB/yWBfNuaB8XS1kwJ+L8rQex1oV460GsdSHeznX33XdLo0aN7PKTTz553PWDbdvh+OTKTz/9JCkpXt/y+t22bdvklltuscsjR44suH3YsGGSkJAgc+bMsTNY8mVmZsr48ePtctGMVn55scmTJ8uBA4V/9GzdulVmzJhhD7hrrrnGJyj5j7nnnnskLy+v4L558+bJ//73P1sDrlevXkGNfdCgQaIZ4yf+mmne/z8ae4Gse2SwNK5b3e86uR6Rro99KiNnJonbaI49ALi654pPWbB4/2XBYqIqZfNQvjh/60GsdSHeehBrXYi3c4WHhxckx2JiTGn5wIJt2+H4smBvvfWW/P3vf5c+ffpI8+bNpVatWrJ582aZP3++TZgMGTLEZqzy1a5dW1566SWbZOndu7cMHz5c4uPj5f3335cNGzbY26+44gqf1zAzWe68806ZNm2atG/f3q6TnZ0t//nPf2xi59lnn5VmzZr5PMas/+GHH8rbb78tXbp0kX79+sn27dvt9ppGOq+88ooNdjDWr18vbdu2Fa0YP/Fn/2+r+ti/8tymMvXjDVKYvvaVnJYlzv7+Qcm0/+4DANeoFiF51aIlPDdLRDwiaTsDNLT3KgvGzBVH4vytB7HWhXjrQax1cUO8y6vUlttlZGSUKgnj2pkrJqkydOhQW37rjTfesAmQ5cuXS48ePeS1116zCY6oKN9vd1188cV2nZ49e8o777xjkyOm2Y15rJnRUtJ0oKlTp8qrr75qpxW9+OKL8q9//UtOP/10+eCDDwpmyHgzGbJPP/1UJkyYIKmpqfLUU0/JJ598Yl/766+/tgmXYJlkkGaMn/hrpnn/zx+76avSrXWC1Iqu5nfd3WlZ0vq+BeImmmMPAG5zNMzr75TU7QF6rng3tKcsmBNx/taDWOtCvPUg1roQbz2ysswXnRTPXDGltU6kvFb37t1lwYKyfeA2atQoeyktk/WaOHGivQAAyt/s644lqns8vlh2HsgscZ2jeR5p/9DHcmOvljS6BwCElJzw6hIth4795+Auv2XBfHquxJBcAQAAAFDBDe0BADqYEmHhAWqAHczMkRUb91XmJgEAUKrkSoG8nGPX4ZEidZr4Ta7UiaXnCgAAAACSK0E5kRk7bsL4ib9mmvf/ksZuSoRdcnbjgCXCkrakuKJEmObYA4Db1KjboPiNp5wtEhkToKE9M1eciPO3HsRaF+KtB7HWhXjrUbNmTXEyZq4AAMrFlMs6yJqJg6RxXa9vAZdQIuycSZ8wiwUAEBI8kTWK33jqecVuSk2noT0AAABQGlu3bhWPxyPNmjVz/Q+M5EoQli9fLpoxfuKvmeb9/3hjP16JsH2Hs+Xd73aKU2mOPQC4zb6DGcVvPLWbz39z8zy2vKURFiZSqzozV5yI87cexFoX4q0HsdaFeOtx+PBhcTKSKwCAcmVKhN01IFESavivST931W5pN2EhP3kAQJX4dtsBWbp+r+w9Gl38zlO7+Pz3oFe/lVrREVIt0DcIAAAAAKhBcgUAUCEJlm8e6C9N6vrWrPeWnp0rbcZ/JDOW/kwEAACVauw7P8g1r34tq9Jife9o0E4kpq7PTak0swcAAABQApIrQUhMTBTNGD/x10zz/l+WsU8eeqZEBDjTZOfkOa7/iubYA4BbREceOzmlS5E+Yad2LbYu/VbcgfO3HsRaF+KtB7HWhXjrER1dwkxyByG5EoS2bduKZoyf+Gumef8vy9h7tqkvY/onSu3oCL/rJG1JcVSJMM2xBwC3iI6oZq8Pe0qRXPGauRIXQ78Vp+L8rQex1oV460GsdSHeesTE+K944gQkV4KwcKFzPgysCIyf+Gumef8v69hNibAfJg6UpvFFSq8UKRHWYux8R5QI0xx7AHCL6N+nVR6RIn/MNS2eXElLL0yu1In1308MoY3ztx7EWhfirQex1oV465GWliZORnIlCFlZWaIZ4yf+mmne/0907Mvv6SOxUce+KVySPBFZl3xQQp3m2AOA25Ir6eJVhiCuiUhc48BlwZi54licv/Ug1roQbz2ItS7EWw+PxyNORnIFAFBpXhjZScIC3P/hD8nS64mlRAQAUCllwbbmNSq8sWWfEtf1bWhPWTAAAAAAx5BcCUJcXJxoxviJv2aa9/9gxm56sHRvnSDxAT6c2paSHtIlwjTHHgDc1tD+a0+i/NT2NpGzrxLp+0CJ66Z6lQWj54pzcf7Wg1jrQrz1INa6EG89qlXzX+HECcI8Tp97AwBwpHMmfSL7DheWWimqdYOa8sAf29mEDAAA5emet1fLf7/ZaZf/fsmZMvzcU/2uO+Y/q+S973fZ5SmXdZBhnYqXDgMAAIAu69ats9ennXZaVW8KqjBOzFwJwqpVq0Qzxk/8NdO8/5fX2Kde3lHCA9QI27T3sIyfu0ZCjebYA4DbyoIZWTmm65d/9FxxB87fehBrXYi3HsRaF+KtR3p6ujgZyZUgbNu2TTRj/MRfM837f3mN3cxI6dYqQWpF+58Cuj0lQ1qMC60SYZpjDwBua2hvZOXkBlw3jZ4rrsD5Ww9irQvx1oNY60K89cjO9l/RxAlIrgAAqszs67rImomDpEndGL/r5HlEZq/cFlIJFgCAO3quGFlHjzNzheQKAAAAgBKQXAEAVLnJQ8+UABXCJDktU95MYsYIAKDyy4KleTW0rx0TSQgAAAAAWCRXgjBgwADRjPETf8007/8VMXZTIqx76wSJ8fomcVE7UzOl5bj5UtU0xx4AtJUF83g8PjNX4kiuOBbnbz2ItS7EWw9irQvxdqb169fLrbfeKmeccYbExcVJVFSUnHzyyXLBBRfIzJkzJTMzs9hjateuLU5GciUIaWlpohnjJ/6aad7/K2rspkTYukcGS+O61f2uk+sR6frYpzJyZpJUFc2xBwA3JleyA8xcOZyVI7mmPqWIxEZV85nxAmfh/K0HsdaFeOtBrHUh3s7z8MMPy+mnny7PPfec1KpVS0aNGiV33323DB482CZdrr/+eunRo0exx+XmBu5/GOpIrgQhKanqPtwLBYyf+Gumef+v6LFfeW7TgCen5LQs+WXvIakqmmMPAG4RHVm6smCpXiXB6jBrxdE4f+tBrHUh3noQa12It7M8+uij8uCDD8opp5wiK1eulC+//FKeeeYZe7uZsbJ582b54IMPbNKlqCNHjoiTkVwBAISU0X1aSbfWCVIr2v+3g3enZUnr+xZU6nYBANxaFsx/ciXNuyRYbFSFbxcAAADgJFu3bpWHHnpIIiMjZcGCBdKlS5cS1/vjH/8oCxcuFLchuQIACDmmRNiaiYMClgg7mueR9g99LDOW/lyp2wYAcFtDe/+lCJi5AgAAAPg3a9YsOXr0qFx66aW210rA9+DR0a77UZJcCUKHDh1EM8ZP/DXTvP9X5thtibAw//cfzMyRFRv3SWXSHHsAcOXMlaMByoJlZBcs14mNrPDtQsXh/K0HsdaFeOtBrHUh3s7x2Wef2et+/fqd0ONjYmLEySKqegOcrFmzZqIZ4yf+mmne/ytz7KZE2Jb9R+TjH5PlUFbJ3yxO2pJiS4RtenRIpWyT5tgDgFtER5auLJjPzBWSK47G+VsPYq0L8daDWOviing/FCeO8VDaCT80OTnZXjdu3PiEHu/02SzMXAnCvHnzRDPGT/w107z/V/bYp1zWoVQlws6Z9EmlzGLRHHsA0FYWzKfnSgw9V5yM87cexFoX4q0HsdaFeDuHx+Ox12FhAcqOBJCamipORnIFAOAIxysRtu9wtrz73c7K3CQAgMsb2qemUxYMAAAA8Ofkk0+21zt36vw8hrJgAABHMCXCjFmfbZH9Rwo/7PI2d9VuWbR2j6x9eFAlbx0AwEmiSttzxbssWAw9VwAAAFDxpbacpEePHrJkyRJZvHixXHfddaINM1eC0LBhQ9GM8RN/zTTv/1U5dpNg+eaB/tKkrv+GZ+nZudJm/EcyY+nPFbINmmMPAO6cueK/LFiqV1kweq44G+dvPYi1LsRbD2KtC/F2jmuuuUYiIyPlnXfekbVr1wZcNysrq9htERHOnvtBciUI5513nmjG+Im/Zpr3/1AY++ShZ4rX52LFZOfkVVj/lVAYPwB3+uKLL2TIkCESHx8vsbGx0r59e5k+fbrk5uZW6HOtWLFC/vznP8sZZ5wh9erVk+rVq0vz5s3lT3/6k/0GmhtFR3r3XPE/cyXNa+ZKbWauOBrnbz2ItS7EWw9irQvxdo5mzZrJQw89JNnZ2XLBBRfIN998U+J6CxculMGDBxe7vWbNmuJkJFeCsHLlStGM8RN/zTTv/6Ew9p5t6suY/olSO9r/NxyStqRIuwkLXTl+AO5s2tmzZ0+b6Bg6dKiMHj3a/oEyZswYGT58eIU+l5nGby5t2rSRESNG2PW6desmS5culT/84Q/ywAMPiNaeK94N7evQ0N7ROH/rQax1Id56EGtdiLez3HfffTJx4kTZvn27nHPOOdK9e3e5/fbb5f7775frr7/e/p1hEiuHDh0q9tjDhw+Lkzl73k0V27Nnj2jG+Im/Zpr3/1AZuykRZi69nlgq21LS/ZYIazF2vtw1MLGgZ4tbxg/APQ4ePCg33HCDVKtWTZYtWyadO3e2tz/yyCPSt29fefvtt2XOnDmlSrKcyHONHTvWftusqF27dsnZZ58tjz76qPz1r3+Vk046SVyZXDkaqCwYDe3dgvO3HsRaF+KtB7HWhXg7z4QJE+Syyy6Tf/zjH/ZLWrNmzZLMzEw7M75jx45y7733ysiRI4s9LicnR5yMmSsAAEdbfk8fiY0qLO9SlPk+8rrkg5W6TQBQFibhsW/fPpvwyE+GGKY816RJk+zy888/X2HPZe4rySmnnGJnsOTl5ckvv/ziqqBGR5SuLJhPQ/tYGtoDAAAA/px22mny7LPPyo8//mi/9GVmzycnJ8tHH31km91HR0e77odHcgUA4HgvjOwkYQHu//CHZDvDBQBCkSnJZQwaNKjYfaa8l+mZYnqolNQAsiKfa+/evZKUlGT/CEpMTBQ3iawWJmG/nzhy8jySk1s8wZJ5NLcg8RJVLVxivPq0AAAAAECYx+Px8GMAADjdyJlJsnZXmqR4fcu4pG8UlGeJMAAoD6YusWn8aC6dOnUqdr9pNP/TTz/J2rVr7bfBKuq5zGM+/PBDOzV/586d8v7779tvnJlvn918882lGktJr5nv22+/lVDS9oGPJPPoseTJ2ocHSmyUb8XkX9My5bzHFtvl+rWi5ev7/1Al2wkAAIDQs27dOnt9vPfncHec6LkShK1bt0qzZs1EK8ZP/Nn/dR7/oXrsz76ui70+Z9Insu9wYY18b+YjtLnf75IzT4mTnm3qu2r8AJwrLS3NXsfFxZV4f/7tqampFfpcJrliGlHmq1Wrlq2V/Oc//1nKw/r162XDhg0F/+/Vq5e9Xr58ecFtZoZM27ZtZeHChQWza8w29+7dW1atWiXbtm0rWHfAgAF2vGZ2Tb4OHTrY39Hz5s0ruK1hw4Zy3nnn2cao3vW7oyNiCpIrc9+fLzUiRbp06WJfb9GiRbL7SOGfS3ViIm0Pm/yfr5nNY2YHhdqYLrroInueWr16dcFt3mPK17RpU1v7mjERJ/Y9jien/44w6xr83nP/+anoc7phTG6Mk6YxmffT5v2yuTbrxsTE2Mfmz2MwPRDN/enp6bY8Vr7atWtLbm6uHDli32xa5rHmObzfo0dEREjNmjVtw3fvviR16tSxP7eMjIyC22rUqGFfz3wxKl9UVJSdtW6ayJvXM8LCwuzYzWO9Z7Kb1ynaXN4tY8rNzbXrm/3lePue2QfKipkrQTBBMQepVoyf+LP/6zz+Q/3YX7Fxn1w96yvJCzAv89T4GFlxT19Xjh9A1TB/4Hn/IXg8I0aMkNmzZ9vlNm3ayKZNm+ylVaviM+tM35Mvv/zSXswfjYGUx3OZxpNbtmyRF154QZ555hm58cYb7bLbnDv5U9l76NgfVSvH9ZNGcb69Z1b+8psMf3GlXT6nWV1566ZuVbKdKB+cv/Ug1roQbz2ItS5OiDczV8qHSb6Y5EpFYeYKAABlYGakdGuVIKu3H5BDWce+yVDU9pQMaTFuvtw1gBJhAMpHy5Yt/TaGL8nJJ59cbDZJ/rfkisr/tpa/2SjeyuO5zDjMtPmnn37afqPrn//8p/zhD3+QYcOGiZtERxa2n8zKyQ3YzD4uJqrStgsAAACAM1AWDADgOvklws5/fInsOFA4rdSbmdkye+Wxb5nTgwVAsBYvPtab40SY6emmJNfGjRuL9Swx0+XNLBIzhb5FixaV+lzG4MGDbXLFlEhwXXIlorBBffbvjeu9pWUUljqoExtZadsFAAAAwBkKv66FMjM1+jRj/MRfM837v5PGPnnomRIW4P7ktEx5M6n0ZXycNn4AztC377Eyhab2b1ErVqywNY1NOS9Ts7gyn8vYtWuXvTYJGbeJjvCeuZIXcOaK6bkCZ+P8rQex1oV460GsdSHeetSoUUOcjORKEEpTmsHNGD/x10zz/u+ksZsSYd1bJ0iMV+mXonamZkrLcfNdOX4AzmBmhCQkJMicOXPsrBPv3ifjx4+3yzfffLPPY0zZL9NcMzk5OejnMg1G8/KKJxc2b94skydPtssXXHCBuDu5UkJZsAyv5AozVxyP87cexFoX4q0HsdaFeOtRrVrhbHInIrkShEWLFolmjJ/4a6Z5/3fa2E2JsHWPDJbGdf33Qsj1iHR97FMZOTPJdeMHEPpq164tL730kuTm5krv3r3l+uuvl3vuuUc6duxoG8+bhMkVV1zh85j33nvP9kUZN25c0M9lmoWaMmHm9rvvvlvuuOMOufDCC6Vt27aye/duufXWW6V///7iNt5lwbKOBp65EsfMFcfj/K0HsdaFeOtBrHUh3noc/L0npFO5b34/AAAluPLcpjL14w1S/OOzY5LTsgKWEAOAinTxxRfbGSRmpsg777xjZ5q0atVKpk2bJrfddpuEhYVV2HNNnDjR/gG7cuVK+eCDD2xipmHDhvZ5THJm4MCB4ka+De0D91yJi6WhPQAAAABfJFcAACqYpvVf/vKbrN5+QA5lFS//YuxOy5LW9y2QTY8OqfTtA4Du3bvLggULSvWDuPrqq+2lPJ7r9ttvtxdtjlsWjJ4rAAAAAAKgLFgQmjZtKpoxfuKvmeb938ljNyXC1kwcFLBE2NE8j7R/6GOZsfRn140fAOCnLFiJM1foueImnL/1INa6EG89iLUuxFuPqChnzxAnuRIEU7taM8ZP/DXTvP+7YeymRFh4gAo7BzNzZMXGfa4dPwCgyMyV4/RcqRPj7D/6wPlbE96r6UK89SDWuhBvPWJjY8XJSK4EYdmyZaIZ4yf+mmne/90wdlMi7JKzG0ut6MJvLReVtCXFlghz4/gBAEV7ruQGnLkSFxvJj8zhOH/rQax1Id56EGtdiLd7vfrqq7YHpLk2Dh06JE5GciUIaWlpohnjJ/6aad7/3TL2KZd1KFWJsHMmfeIzi8Ut4wcA7QKVBTuamyeHs3LsspnpWCuaVpVOx/lbD2KtC/HWg1jrQrz1yM0tuSeuU5BcAQCodrwSYfsOZ8u73+2szE0CAFR6Q/s8/7NWYiIlPNCJAgAAAECpDB06VNatW2ev3YCvYAUhOjpaNGP8xF8zzfu/28ZuSoQZsz7bIvuPZJe4ztxVu2XR2j2y9uFBrhs/AGjlM3PlaK7/fiux9FtxA87fehBrXYi3HsRaF+LtXnFxcfaSz5QIc7Jynbnyv//9Ty699FI56aST7EFgrgcMGCALFhSvWf/FF1/IkCFDJD4+3jauad++vUyfPj3gVKDXXntNzj33XKlZs6YNQu/eveXDDz/0u35GRoY8+OCDkpiYKNWrV5cGDRrI5ZdfbrNj5WHQoEGiGeMn/ppp3v/dOHaTYPnmgf7SpG6M33XSs3OlzfiPZHP0sWQMAMDZogLOXMn2mbkC53Pj+xeUjFjrQrz1INa6EG/n2Lp1q02QXH311bJ+/Xq5+OKL7ef9NWrUkB49esiiRYsC9lzxTrSoTq5MmjRJevbsKStWrLAHwF133SUXXnihHDhwoFgTonnz5hWsa6YAjR49WrKzs2XMmDEyfPjwEp//7rvvtkFKTk6WG264QUaOHClr1qyxr/Hcc88VWz8rK0v69+8vDz/8sNSuXVtuv/12+cMf/iDvvfeedO7cWZKSkoIes9lhNGP8xF8zzfu/m8c+eeiZ4vVZWzHZOXmycNXWytwkAEAVlAXznblCcsUN3Pz+Bb6ItS7EWw9irQvxdp4tW7ZI165d5bfffpMbb7xRLrvsMvn2229l8ODB8p///Cfg5AjRnlx566235IEHHrDJi19++UVmzZoljz76qLz44ovy9ddfy+TJkwvWPXjwoE2OVKtWzSZdZs6cKU8++aSsWrXKBuDtt9+WOXPmFJvlMnXqVGnZsqX88MMP8tRTT8mMGTNsgEwmzCReTJbM27Rp0+Tzzz+XYcOG2UTK448/Lm+88YZ9/vT0dLn22mslL8/3j6iy2rBhg2jG+Im/Zpr3fzePvWeb+jKmf6LUDtC4eM2edGk3YWGlbhcAoPxFR3onVwKUBWPmiiu4+f0LfBFrXYi3HsRaF+LtPCtWrJDrr7/eVrZ67LHH7MwUsxweHi433XSTzQmUxEyQUN1zxSQo7r33XlvayyQvatWqVWydyMjCb3uZ5Ma+ffvkqquusjNI8pmyXWb2S79+/eT555/3mcHywgsv2Ov7779f6tatW3B7s2bN7KyXRx55xCZ0Jk6caG/3eDwFj3niiSdsEPNddNFFcv7559vgLl++XPr06RPsjwAA4LISYebS64mlsi0l3W+JsBZj58tdAxMLerYAAJzcc6XIzJUiDe0BAACAsjjztTMd8wNbM2pN0M8RFxcnEyZM8LnNfPY/YsQI2+rDVJMaNWqUuE3QM1fMrBIz7cf0TzGJj/nz59tZIk8//bR8+eWXxdZfsmSJ39p5plSYSdKY5/TOWgV6jJla5L2OsXnzZtm+fbu0adNGmjdvXqrH+NOpUye/FwCAey2/p4/ERhV+8FaU+RhuXXLJ37wAADi7LFhaulfPFRraAwAAAAGdffbZJU66MD3Tje+//96VP8GgZ66Ysl9Gw4YN7Q/R9EEpmjAxs1Xq16/vM63LJD6KbUxEhE2G/PTTT7a82GmnnSZHjhyRXbt22Sb2J510UrHHtG7d2l5v3Lix4LZAr+HvMSeiadOmtn9Mvl69etlrMyMmX2JiorRt21YWLlxYkDAymTyzY5lSaNu2bStYd8CAAZKWlubTD6ZDhw52ho7365if9XnnnScrV66UPXv2+MzKMeXRVq9eXXBbly5d7Ot5Nw8y292xY0dbls28nhEdHW2TV6amoffUu0BjioqKKtgut4ypLHEy8sfgljGVJU7e43fLmMoaJ/M8bhtTaeLkHXu3jMlfnEa1DJPn15n/FU2ymPIx1eTDH5Llm80fybj22Y4ZU2niBAD6kiu5fmeuUBbMHfLPhXA/Yq0L8daDWOtCvJ2nYcOGJd7eqFEje53/uUVR5jN/JwvzmBpaQRg3bpz8/e9/tz1UTGLElOMyHwKZD89MU/uPP/7YHhD5Te1NwmPTpk320qpV8VIq3bt3tzNXzMX0YNm9e7eccsop9rJz585i6x89etR+yG8u+R8OmfJkZsqRucyePbvYYz755BP74Ze5mO07UampqVKnTh3RivETf/Z/nce/tmN/5MwkWbsrTVK86u8XZT6eo0QYADjL8o37ZNQrX9nl81snyOvXdSm477Y3v5f3V++2y9Mu7yCXnN24yrYT5UPb+xfNiLUuxFsPYq2LE+K9bp39JqadHKDZ1q1bbU7AtN4oqUqU6b1yzTXXyO233y7Tp08v+L9p8XH11VdLTk6OnXDh1DgFXRYsN/fYt7xMjsbMUDE9U0zG6fTTT7e11Bo3bmy/KVtSibCS5Od6wsLCyrQdZVn/RF+jKO9vAGvE+Im/Zpr3f21jn31dF/luwgCpXzPq91t8v91smGIyc7/fJSs27qv07QMAlH9ZMJ+ZK7H0XHEDbe9fNCPWuhBvPYi1LsTbeb777js5dOhQsdvzJ1ycddZZJT7u8OHD4mRBJ1fyG8y3aNHClj3xFhMTIwMHDrTLX331VUHJkUBTgQ4ePOiz3vHWz789f70TeQ0AAI5n6uUdJTxATn7T3sMyfm7wTeAAACHWcyUmP7kOAAAAoCRpaWny8MMP+9z2zTffyL///W/7GfzQoUNd+YMLOrliarYb/qZq5SdfMjIyfNYvqd+JmQa0ZcsWOxXIJGuMGjVq2JJgJouVnJxc7DGmvFjR/iqBXsPfYwAACKRnm/rSrVWCRAc4c25PyZAW4+bLjKU/88MEgBAXHVHYTyvrqO+sxDRmrgAAAACl1rNnT3n55ZfttWkjYkp+nX/++ZKXlyf//Oc/pXbt2q78aQadXDE/MJMMMQmL7OzCb3jl+/HHH+21aeRr9O3b116bBrpFrVixQtLT06Vbt262KW++QI/56KOPfNYxWrZsKaeeeqpNrphkTWkecyLykzhaMX7ir5nm/V/z2E2JsHlXtZEmdWP8rpPnEZm9chsJFgAIcdGRhX8KZQcqCxZDWTA30Pz+RRtirQvx1oNY60K8nad58+a2h7qZaGF6sv/3v/+Vs88+WxYsWCBXXHGF38d55wBUJlcSEhLsD6ikqT+mcbxpGG+m/gwaNMjeNmzYMPuYOXPm2KlB+TIzM2X8+PF2+eabb/Z5nptuusleT548WQ4cOODTMGfGjBk2CKYRTj7TSyX/Mffcc4/NkOWbN2+e/O9//5N27dpJr169ghp727ZtRTPGT/w107z/ax57/vgnDz1TAnXtSk7LlDeTtlXiVgEAyqssWF6ex2fmShzJFVfQ/v5FE2KtC/HWg1jrQryd6bTTTrOfvZvP780Eis8//7ygZUg+M6PF9EM31/ltRVQnV4xp06ZJq1atbPLDzGS5++675bLLLpPBgwdLtWrV5KWXXiooG2amAJn/5+bmSu/eveX666+3CZCOHTvapvcm+VI0m2Vmstx5552yefNmad++vYwZM0ZGjx4tnTt3lpSUFJkyZUrBzJh8Zn3zuLffflu6dOkiY8eOlf/7v/+zzx8bGyuvvPKKhIcHN/ySZtJowviJv2aa93/NY88fvykR1r11gsR4feu5qJ2pmdJy3PxK3TYAwAmWBcspLAt2KDNHPJ5jy7WiIySiWrn8yYQqpv39iybEWhfirQex1oV465Hmp2e6U5TLXwoNGjSQpKQkm/TYsWOHPPPMM7JkyRK54IIL7CwRk2jxdvHFF8vy5cttIuadd96RZ599ViIjI22SxsxoMTNPipo6daq8+uqr0qhRI3nxxRflX//6l5x++unywQcfyC233FJsfTOb5dNPP5UJEyZIamqqPPXUU3YmjXntr7/+2iZcgpWVlSWaMX7ir5nm/V/z2L3Hb0qErXtksDSuW93vurkeka6PfSojZyZV4hYCAMpaFizraOHMldQMr2b2sZQEcwvt7180Ida6EG89iLUuxFsPT/63mhwqoryeKD4+3iZHzKU0unfvbmuulcWoUaPspbTMtKKJEyfaCwAAFeHKc5vK1I83iG+1/kLJaVkBS4gBAEKrLFhqule/FZIrAAAAAPxgjnsQTC8ZzRg/8ddM8/6veewljX90n1bSrXWC1IouLC9T1O60LGl9X9m+UAAAqFhRXuW+snPzbK+Vos3s6bfiHtrfv2hCrHUh3noQa12It3M0a9bMzj4xFadOhGkp4mRhHqfPvQEAIET0eHyx7DyQ6ff+2tUj5MZeLW1CBgBQ9RLHf1Qwa2X9I4OkemQ1mbdql9w+Z5W97YIzT5IZI86u4q0EAABAqFm3bl1BE3fojRMzV4KwatWxP7q0YvzEXzPN+7/msR9v/KZEWHiAGmAHM3NkxcZ9FbNhAIAyiwjzFOu7cuAIPVfcSPv7F02ItS7EWw9irQvx1iM9PV2cjORKELZt2yaaMX7ir5nm/V/z2I83fjMj5ZKzGwcsEZa0JYUSYQAQIqp5dczKysm113sPFTY+b1Arukq2C+VP+/sXTYi1LsRbD2KtC/HWIzu78ItNTkRyBQCAcjTlsg6yZuIgaVy3ut91juZ55JxJnzCLBQCqmFdP+4LyYL7JFf+/ywEAAADoRnIFAIAKcLwSYfsOZ8u73+3kZw8AVSjSJ7nCzBUAAAAApUdD+yBkZGRITEyMaMX4iT/7v87jn2O/9Mf+jKU/y6zPtsh+r/r9RcVGVZO1Dw8qxwgBAEpr8PTlsu7Xw3b5w1t7yBmnxMmg6Stk/a+H7G3v39Jd2jeuww/UBbS/f9GEWOtCvPUg1ro4Id40tC8feXl5Eh5ecfM/aGgfwtLS0kQzxk/8NdO8/2see1nHb3qwfPNAf2lS1/+bwvTsXGkz/iObiAEAVK5w8RQrC7aPsmCupP39iybEWhfirQex1oV465Gbe2z2uFNRFiwISUlJohnjJ/6aad7/NY/9RMc/eeiZPnX9i8rOyaP/CgBUgaz0w4XLOblyNDdPfvt9tmFYmEhCzSji4hLa379oQqx1Id56EGtdiLceR44cEScjuQIAQAXr2aa+jOmfKLWjI/yuk7QlRdpNWEgsAKASRYR5fBLd+w8XNrOvVyNKIqrx5xIAAACAkvHXAgAAlcCUCPth4kBpGh8bsERYi7HzKREGAFXS0D5P9h4sTK7Ur1WdOAAAAADwi+RKEDp06CCaMX7ir5nm/V/z2Mtj/Mvv6WOb2PtjKv6vSz4Y1GsAAEonIb6OT3Jlz8HMgv83rB3Nj9FFtL9/0YRY60K89SDWuhBvPWJifHvUHj16VP71r3/JxRdfLE2aNLH3x8bGSvPmzWXo0KHy8ssvh1QpsTCPx1M4Fx4AAFS4FRv3yahXvvJqo1ycmeFiEjEAgIpz139Xyzvf7bTLTw5rbxMs4+f+aP9/eefG8sQwPpAHAABAcevWrbPXp512Gj+ecrJ+/Xq59NJLZe3atVKnTh3p27evTapERETIrl27ZMWKFbJ9+3ZJSEiQffv2hUScmLkShHnz5olmjJ/4a6Z5/9c89vIav+nB0r11gsTHRvpdZ1tKOiXCAKCCJe/a7lsW7FBhWbAGlAVzFe3vXzQh1roQbz2ItS7EW4/U1FR7nZycLP369bOJlVtvvVV27Ngh77zzjkyZMkX+/ve/y+uvvy7btm2TRYsWySmnnCKhguQKAABVYPZ1XeS7CQOkfs2ogCXC5n6/y850AQCUv8gw8Umu7DtUWBasAWXBAAAAgIC2bt0qYWFhcvXVV8vGjRvliiuukAYNGkh4eLgsW7as1D+9++67T3bv3i3/93//J88884zUrFmzxPX69+8v33zzTchEheQKAABVaOrlHSXc68O9ojbtPSzj566pzE0CADUifBra5/o0tG9Qi54rAAAAQGls3rxZunTpYpMtI0aMkHTUWWEAABvKSURBVL/85S9Su3btUj02PT1d3nzzTbv84IMPHnd9UyYsVITOljhQw4YNRTPGT/w107z/ax57RYzflAjr1ipBVm8/IIeycktcZ3tKhrQYN1/uGpAoo/u0KtfXBwDN6tSqISIZdjnrqG9ZsPqUBXMV7e9fNCHWuhBvPYi1LsTbeT777DMZN26cPProo2V6nEmUmJkoWVlZ0rhxY2nTpo04CQ3tAQAIEec/vkR2HDj2IV9JToqrLiPPa0qCBQDKyT+W/SxPLNxgl2/q1VLe+36n7Pl99sr/7ukjTeJj+VkDAACgzI3S17V1TqP709YfG8uJ2Lp1q206bxJipidKdHTZZ3//97//teXEzMyXlStXFrv/1Vdfta/j7eKLL5aOHTse97lpaB/CSgq2Joyf+Gumef/XPPaKHv/koWdKgAphkpyWKW8mbauw1wcAbX7duaNgOSM7R/Yfzi74f33KgrmK9vcvmhBrXYi3HsRaF+LtPB06dDihxMrhw4fF4/HYZdO7pSQmuTJx4kSfy6pVqyQU0HMlCHv27BHNGD/x10zz/q957BU9flMirHvrBImJ9H963pmaKS3Hza+wbQAATTKOHPJJYOfmHfvDLi4mUqpHVqvCLUN50/7+RRNirQvx1oNY60K8nadRo0Yn9LicnBw56aST7PKuXbtKXGfZsmU2AWMu999/v4QSeq4AABBCZl/XxV73eHyx7DyQWeI6uR6Rro99Ki0b1CpYHwBQdt65bO+yjDSzBwAAQFWV2nKiMD+zTkqjc+fOdtbLjh07ZNOmTdK6dWtxCmauAAAQgq48t2nAk3RyWpb8srfwG9cAgLKL8vpFu2X/4YLlBrXLXtIAAAAAQNnFxsbKlVdeaZcffvhhcRIa2gMAEKJGzkyS1dsPyKGsXL/rRIaHyaZHh1TqdgGAW+xKzZAejy+R38s8Fxh61iny1BXHb5AJAAAAnSq6UbpTbP29of2oUaNsb5QTtXv3bjnnnHPs9R133CGTJk2SGjVqFFvv1ltvleeee05mzZolV1999XGfl4b2Ib7zaMb4ib9mmvd/zWOv7PGbkl9rJg6SxnWr+13naJ5H2j/0scxY+nOlbRcAuMXR1D3SN7FBsduZueI+2t+/aEKsdSHeehBrXYi3HllZWfb65JNPlsWLF9tk1fTp06VJkyYybNgwueeee2Ts2LFyzTXXSJs2bWxipUGDBtK2bVsJBZQFC8Lq1atFM8ZP/DXTvP9rHntVjd+WCAtQvvRgZo6s2LivMjcJAFzzO/3PXZsWu71BLf9JbTiT9vcvmhBrXYi3HsRaF+KtR0ZGYd9DkzBZtWqVnQHTo0cP+fLLL+WZZ56Rp59+WpYsWWITLy+//LJs3rxZzjvvPAkFNLQHACDEje7TSrbsPyIf/5jst0RY0pYUaX3fAkqEAUAZ9WxdX06Nj5XtKekFt9HQHgAAADi+Zs2aiadojd0gREVF2RJj5uIEzFwBAMABplzWoVQlws6Z9AmzWACgDMLDw2Tkeaf63EZyBQAAAMDxkFwJQpcuXUQzxk/8NdO8/2seeyiM/3glwvYdzpZ3v9tZmZsEAI7/nX5ZpyYSHVH4p9FJcTFVuFVw4/kblYdY60K89SDWuhBvPWqU0LTeSSgLFoS4uDjRjPETf8007/+axx4K4zclwoxZn22R/UeyS1xn7qrdsmjtHln78KBK3joAcObv9Lo1ouTO/m3k8YXrpX+7htIknuSK21T1+RuVh1jrQrz1INa6EG/ne/XVV2Xr1q3HXa99+/ZyySWXiFOFecqzKJoy8+bNk4suuki0YvzEn/1f5/HPsR86x/75jy+RHQcKm78VFRURLrf3a12QkAEABD6nZeXkSlS1cAkLCzBFEI6k/f2LJsRaF+KtB7HWxQnxXrdunb02TdZRXO/evWX58uVyPFdeeaW88cYb4tQ4URYMAACHmjz0TPGqYlNMdk4e/VcAoAyiI6qRWAEAAACCtGzZMtvo/niXf/zjH47+WZNcAQDAoXq2qS9j+idK7Wj/VT6TtqRIuwkLK3W7AAAAAAAA3I7kShCaNm0qmjF+4q+Z5v1f89hDcfym5NcPEwdK0/hYv+ukZ+dKi7HzZcbSnyt12wAg1IXa73RUHGKtB7HWhXjrQax1Id56REVFiZPRcwUAAJcwM1RMIsWfP7Y/SZ77v7MrdZsAAAAAAHAbeq6EPlN2bP369XaZnishWjtOM8ZP/DXTvP9rHnuoj/+FkZ0kUAvmD39Ill5PLK3ELQKA0BbKv9NRvoi1HsRaF+KtB7HWxQnxDgs79td3Xl5eVW+Kox06dKhCkyvesaoIlAULQlpammjG+Im/Zpr3f81jD/Xxmx4s3VsnSHxspN91tqWkUyIMABzwOx3li1jrQax1Id56EGtdnBDv6Ohoe33kyJGq3hRHy831X30jWPmxyY9VRSC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      "text/plain": [
       "<Figure size 1728x576 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 2, figsize=(12, 4))\n",
    "\n",
    "axes[0].spy(result_nk.jac, markersize=0.02)\n",
    "axes[0].set_title(f\"NK Jacobian ({result_nk.jac.shape[0]:,} × {result_nk.jac.shape[1]:,})\")\n",
    "\n",
    "steady_state_nk = pd.Series({k.removesuffix(\"_ss\"): v for k, v in nk.steady_state().items()})\n",
    "\n",
    "(trajectory_nk - steady_state_nk)[[\"Y\", \"C\", \"pi\", \"r_G\"]].plot(ax=axes[1])\n",
    "axes[1].set_xlabel(\"Period\")\n",
    "axes[1].set_title(\"NK impulse response to monetary shock\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e7b34a3d138c66a",
   "metadata": {},
   "source": [
    "# Authors\n",
    "\n",
    "- Authored by Jesse Grabowski in March 2026, with assistance from Claude Opus 4.6 "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "84ed76e9fde2bf33",
   "metadata": {},
   "source": [
    "# Watermark"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "7bda9acd6b273b1a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Last updated: Sun, 15 Mar 2026\n",
      "\n",
      "Python implementation: CPython\n",
      "Python version       : 3.12.13\n",
      "IPython version      : 9.11.0\n",
      "\n",
      "gEconpy: 2.0.4.dev37+g9a1a488f7.d20260315\n",
      "\n",
      "gEconpy   : 2.0.4.dev37+g9a1a488f7.d20260315\n",
      "matplotlib: 3.10.8\n",
      "numpy     : 2.4.2\n",
      "pandas    : 3.0.1\n",
      "scipy     : 1.17.1\n",
      "\n",
      "Watermark: 2.6.0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -n -u -v -iv -w -p gEconpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fa24f1ad",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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          "text/html": "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">                                                                                                    \n <span style=\"font-weight: bold\"> Finding Roots                                  </span> <span style=\"font-weight: bold\"> Elapsed </span> <span style=\"font-weight: bold\"> Iteration </span> <span style=\"font-weight: bold\"> Residual   </span> <span style=\"font-weight: bold\"> ||jac||      </span> \n ────────────────────────────────────────────────────────────────────────────────────────────────── \n  <span style=\"color: #729c1f; text-decoration-color: #729c1f\">━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━</span>   <span style=\"color: #808000; text-decoration-color: #808000\">0:00:00</span>   <span style=\"color: #008000; text-decoration-color: #008000\">5/5      </span>   0.00000000   818.85377418  \n                                                                                                    \n</pre>\n",
          "text/plain": "                                                                                                    \n \u001b[1m \u001b[0m\u001b[1mFinding Roots                                 \u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mElapsed\u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mIteration\u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1mResidual  \u001b[0m\u001b[1m \u001b[0m \u001b[1m \u001b[0m\u001b[1m||jac||     \u001b[0m\u001b[1m \u001b[0m \n ────────────────────────────────────────────────────────────────────────────────────────────────── \n  \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m   \u001b[33m0:00:00\u001b[0m   \u001b[32m5/5      \u001b[0m   0.00000000   818.85377418  \n                                                                                                    \n"
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          "text/html": "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">                                                                                                    \n <span style=\"font-weight: bold\"> Finding Roots                                 </span> <span style=\"font-weight: bold\"> Elapsed </span> <span style=\"font-weight: bold\"> Iteration </span> <span style=\"font-weight: bold\"> Residual   </span> <span style=\"font-weight: bold\"> ||jac||       </span> \n ────────────────────────────────────────────────────────────────────────────────────────────────── \n  <span style=\"color: #729c1f; text-decoration-color: #729c1f\">━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━</span>   <span style=\"color: #808000; text-decoration-color: #808000\">0:00:00</span>   <span style=\"color: #008000; text-decoration-color: #008000\">15/15    </span>   0.00000000   1427.49642023  \n                                                                                                    \n</pre>\n",
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