{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Euler's Method"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**References:**\n",
    "\n",
    "- Sections 6.1.1 *Euler's Method* in {cite}`Sauer`.\n",
    "- Section 5.2 *Euler's Method* in {cite}`Burden-Faires`.\n",
    "- Sections 7.1 and 7.2 in {cite}`Chenney-Kincaid`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using PyPlot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Examples\n",
    "\n",
    "A lot of useful intuition comes from the first four examples in \n",
    "{doc}`the chapter introduction <ODE-IVPs>`:\n",
    "- {prf:ref}`ode-integration` $\\displaystyle du/dt = f(t)$ (Integration),\n",
    "- {prf:ref}`ode-simplest-genuine` $\\displaystyle du/dt = k u$ (the simplest \"genuine\" ODE),\n",
    "- {prf:ref}`ode-nonlinear` $\\displaystyle du/dt = u^2$ (a nonlinear ODE)\n",
    "and\n",
    "- {prf:ref}`ode-stiff` $\\displaystyle du/dt = -\\sin t -k(u - \\cos t)$ (with fast and slow time scales)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name=\"eulers-method\"></a>\n",
    "## The Tangent Line Method, a.k.a. Euler's Method\n",
    "\n",
    "Once we know $u(t)$ (or a good approx4imation) at some time $t$, we also know the value of $u'(t) = f(t, u(t))$ there; in particular, we know that $u(a) = u_0$ and so $u'(a) = f(a, u_0)$.\n",
    "\n",
    "This allows us to approx4imate $u$ for slightly larger values of the argument (which I will call \"time\") using its tangent line:\n",
    "\n",
    "$$ u(a+h) \\approx4 u(a) + u'(a) h = u_0 + f(a, u_0) h  \\text{ for \"small\" $h$} $$\n",
    "\n",
    "and more generally\n",
    "\n",
    "$$ u(t+h) \\approx4 u(t) + f(t, u(t)) h \\text{ for \"small\" $h$} $$\n",
    "\n",
    "This leads to the simplest approx4imation: choose a step size $h$ determining equally spaced times $t_i = a + i h$ and define — recursively — a sequence of approx4imations $U_i \\approx4 u(t_i)$ with\n",
    "\n",
    "$$\\begin{split}\n",
    "U_0 &= u_0\n",
    "\\\\\n",
    "U_{i+1} &= U_i + h f(t_i, U_i))\n",
    "\\end{split}$$\n",
    "\n",
    "If we choose a number of time steps $n$ and set $h = (b-a)/n$ for $0 \\leq i \\leq n$,\n",
    "the second equation is needed for $0 \\leq i < n$, ending with $U_n \\approx4 u(t_n) = u(b)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This \"two-liner\" does not need a pseudo-code description; instead, we can go directly to a rudimentary Julia function for Euler's Method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "function eulermethod(f, a, b, u_0, n)\n",
    "    # Solve du/dt = f(t, u) for t in [a, b], with initial value u(a) = u_0\n",
    "    \n",
    "    h = (b-a)/n\n",
    "    t = range(a, b, n+1)  # Note: \"n\" counts steps, so there are n+1 values for t.\n",
    "    u = zeros(n+1)\n",
    "    u[1] = u_0\n",
    "    for i in 1:n\n",
    "        u[i+1] = u[i] + f(t[i], u[i])*h\n",
    "    end\n",
    "    return (t, u)\n",
    "end;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "See [Exercise 1](#exercise-1)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solving for {prf:ref}`ode-integration`, an integration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# For integration of -sin(t): The exact solution is cos(t) + u_0\n",
    "f1(t, u) = -sin(t);\n",
    "u1(t, a, u_0) = cos(t) + (u_0 - cos(a));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# A helper function for rounding some output to four significant digits\n",
    "approx4(x) = round(x, sigdigits=4);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "Figure(PyObject <Figure size 1000x400 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 0.0\n",
    "b = 3/4*pi\n",
    "u_0 = 3.0\n",
    "n = 20\n",
    "\n",
    "(t, U) = eulermethod(f1, a, b, u_0, n)  \n",
    "u = u1.(t, a, u_0)\n",
    "\n",
    "figure(figsize=[10,4])\n",
    "title(\"The exact solution is u = cos(x) + $(u_0 - 1)\")\n",
    "plot(t, u, \"g\", label=\"Exact solution\")\n",
    "plot(t, U, \".:b\", label=\"Euler's answer for h=$(approx4((b-a)/n))\")\n",
    "legend()\n",
    "grid(true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solving for {prf:ref}`ode-simplest-genuine`, some exponential functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# For solving du/dt = k u: The exact solution is u_0 exp(k t).\n",
    "f2(t, u) = k*u;\n",
    "# The parameter k may be defined later, so long as that is done before this functions are used.\n",
    "u2(t, a, u_0, k) = u_0 * exp(k*(t-a));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 1000x400 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# You could experiment by changing these values here;\n",
    "# for now I instead redefine them below.\n",
    "k = 1.0\n",
    "u_0 = 0.8\n",
    "a = 0.0\n",
    "b = 2.0\n",
    "n = 40\n",
    "\n",
    "(t, U) = eulermethod(f2, a, b, u_0, n)\n",
    "u = u2.(t, a, u_0, k)\n",
    "\n",
    "figure(figsize=[10,4])\n",
    "title(\"The exact solution is u = $u_0 exp($k t)\")\n",
    "plot(t, u, \"g\", label=\"Exact solution\")\n",
    "plot(t, U, \".:b\", label=\"Euler's answer for h=$(approx4((b-a)/n))\")\n",
    "legend()\n",
    "grid(true)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Zh8CTJ08mm35Wv359oqOj33hTU0tLy7f6ttjW1pb69evz448/8vz5c86cOQMkfHO+Y8cOXfKTaN68edjY2Lx22eBcuXJx79493WgcJKzqtXnz5rdud8GCBcmePTuLFi3SW50tMjKSFStW6FaYMzRLS0uqV6+uW0o6JdOeevXqxf3792nevDmPHz9+6TLXL2OIaXIvio6O5sCBA28cWTIzM6NRo0asXLlSL4G4ceMGgYGBb1yyumHDhiiluH379kvfO8WKFdPVPXXqFL169aJt27bs3r2b4sWL06pVq2SjfgArV67UW7jhyZMn/PPPP1StWlU3ElSoUCEgYXriiwoWLPjS92/27NkpX748CxYs0Fvw4MCBA1y4cCHFy3P/17x584Dktw34r5SMXl69ehUPD4+3aocQIo0Y8XolIcRHKCULKPz999965S+7sH/+/PnKxMREtWrVSv39999q586davny5Wrw4MHK19f3tW14+vSpKlWqlHJzc1Pjxo1TW7duVZs3b1YzZ85ULVq0UAcOHFBKKXXy5EllbW2ttyhA4iILEyZM0JUNGTJEaTQaNWTIELV9+3Y1ZcoU5eLiovLmzat38X5sbKyqUaOGMjc3V999953auHGjWr9+vRoyZIjeBe3Vq1dXzs7Oau3aterw4cPq/Pnzr+xL586dVc+ePdWSJUvUzp071dKlS1XJkiWVo6OjunfvnlJKqfPnzyt7e3tVoEABtWDBArVhwwbdheAvLkzwsjhfvXpVmZubKy8vL7V+/Xq1YsUKVb16dZU7d+5kCyi8qt3/XUBBqaSL2xs0aKDWrFmjli1bpsqVK6csLCzU7t27dfUSF1D4999/9c7l7++vAHXt2rVXxkap5AsoDB48WHXo0EEtWLBABQUFqdWrV+t+J6dPn37tsRLVr19fAapKlSopqv++eXp6qlGjRqnVq1erwMBA5e/vr8qXL69MTU3V2rVr9ermzZtX5c2bV6/s3Llzys7OTlWrVk1t2LBBrVy5UhUtWlRly5ZN95p5na5duyobGxv17bffqn/++Uft2LFDLVy4UH3zzTdqypQpSqmE91ihQoWUh4eHevr0qVJKqStXrihHR0e9RSgSX3Pu7u6qSpUqauXKlWr58uWqXLlyyszMTG9RiBs3bihATZ8+PcWxCgwMVGZmZqpp06Zq69atauHChcrd3V0VLVpURUdH6+qFhIQoU1NT1bFjR13ZwoULVbNmzdScOXPU9u3b1YoVK9SXX36pANW+ffs3njsyMlJZW1urypUrq8DAQHX48GF1+/Zt3fP3799XgPrjjz9S3B8hRNqTZEgI8V69r2RIKaV27typPvvsM5UxY0Zlbm6usmfPrj777LNk+7/M06dP1U8//aQKFiyoLCwslKOjoypWrJjq27evCgsL0/swFxkZqbevn5+fMjc3VwcPHlRKKRUTE6MGDBigsmfPrqysrFTp0qXV6tWrX7oS27Nnz9SQIUNU/vz5lYWFhcqUKZOqWbOm2rdvn65OcHCwqly5srKxsXnjCmNz585VNWrUUFmzZlUWFhYqW7ZsqmXLlurkyZN69U6dOqUaNWqkHB0dlYWFhSpRokSyeL4qzhs2bFAlS5ZU1tbWKk+ePGry5MkvXU3uVe1+WTKklFKrV69WFSpUUFZWVsrW1lbVqlVL7d27V6/O+06G1q1bp+rXr6+yZ8+uLCwslLOzs2rQoIFeAvYmAQEBClBLlixJ8T7vU//+/VWJEiWUo6OjMjMzUy4uLqpp06bJYqeUUjlz5nzpaoBHjhxRtWrVUjY2NrrVEi9fvpziNsyZM0dVqFBB2draKmtra5U3b17Vtm1bdeTIEaWUUl9//bWysbFRZ86c0dvv77//1vsyIfE1N2bMGDV8+HDl5uamLCwsVKlSpdTmzZuTnbdq1arJVpt8ky1btqiKFSsqKysrlTFjRtW2bVt19+5dvTqJ7Xjxi4/9+/erWrVqKRcXF2Vubq5sbGxUuXLl1JQpU/RWQXydxYsXq0KFCilzc3MFqKFDh+qemz17tjI3N0/x6nhCCOPQKPWfO8wJIYQQn7DEFe9CQkIwNzc3dnM+aCEhIeTOnZvff/+dAQMGvLH+ihUraNWqFdevXyd79uxp0ELDqVq1Kjly5GDhwoXGbooQ4jXkmiEhhBCfvJiYGPbv38+kSZNYtWoV3377rSRCRvDFF19Qrlw5Ro0aZeymvJNdu3Zx+PBhRowYYeymCCHeQFaTE0II8ckLDQ2lUqVKODg40K1bN3r27GnsJn2SNBoNM2fOZO3ate99Vca09ODBA+bNm0eePHmM3RQhxBvINDkhhBBCCCHEJ+nD/MpFCCGEEEIIId6RJENCCCGEEEKIT5IkQ0IIIYQQQohP0kezgIJWq+XOnTvY29uj0WiM3RwhhBBCCCGEkSilePLkCdmyZXvtYiwfTTJ0584d3N3djd0MIYQQQgghRDpx8+ZN3NzcXvn8R5MM2dvbAwkddnBwMGpbYmNj2bJlC97e3nKfCgOQ+BqWxNewJL6GJfE1LImvYUl8DUvia1jpLb4RERG4u7vrcoRX+WiSocSpcQ4ODukiGbKxscHBwSFdvBg+NhJfw5L4GpbE17AkvoYl8TUsia9hSXwNK73G902Xz8gCCkIIIYQQQohPkiRDQgghhBBCiE+SJENCCCGEEEKIT9JHc82QEEIIIUR6EB8fT2xsbKr3i42NxczMjOjoaOLj4w3Qsk+bxNew0jq+5ubmmJqavvNxJBkSQgghhHgPlFKEhYXx+PHjt97fxcWFmzdvyj0TDUDia1jGiK+TkxMuLi7vdD5JhoQQQggh3oPERMjZ2RkbG5tUf0DTarU8ffoUOzu7194kUrwdia9hpWV8lVJERUVx7949AFxdXd/6WJIMCSGEEEK8o/j4eF0ilClTprc6hlar5fnz51hZWcmHdQOQ+BpWWsfX2toagHv37uHs7PzWU+ZS1dKpU6dSvHhx3b18PD092bhx42v32blzJ2XKlMHKyoo8efIwbdq0ZHVWrFiBh4cHlpaWeHh4sGrVqtT1QgghhBDCiBKvEbKxsTFyS4T4dCS+397mGr1EqUqG3NzcGD16NEeOHOHIkSPUrFmTxo0bc+bMmZfWv3btGg0aNKBq1aocP36cH374gV69erFixQpdnf3799OqVSt8fHw4ceIEPj4+tGzZkoMHD751p4zt1uFQbqyJ4NbhUGM3RQghhBBpSK5FESLtvI/3W6qSoUaNGtGgQQMKFChAgQIF+OWXX7Czs+PAgQMvrT9t2jRy5MjBxIkTKVy4MJ07d6Zjx46MHTtWV2fixInUqVOHQYMGUahQIQYNGkStWrWYOHHiO3XMWGa3302+ytnp5e9DvsrZmd1+t7GbJIQQQgghhHiJt75mKD4+nr///pvIyEg8PT1fWmf//v14e3vrldWtW5fZs2cTGxuLubk5+/fvp2/fvsnqvCkZiomJISYmRrcdEREBJAyTvctQ2bu4dTiUrnMroSVhzqIWU7rN9aRm1xu4lXv7C7uEvsTfr7F+zx87ia9hSXwNS+JrWBLfV4uNjUUphVarRavVvtUxlFK6f9/2GOLVTE1NWbBgAV9++eU7xTdPnjz07t2b3r17v8fWffiM8frVarUopYiNjU12zVBK/06lOhk6deoUnp6eREdHY2dnx6pVq/Dw8Hhp3bCwMLJmzapXljVrVuLi4rh//z6urq6vrBMWFvbadowaNYrhw4cnK9+yZYvR5uveWBOBFh+9snjMWDs7kFz/OhmlTR+zrVu3GrsJHzWJr2FJfA1L4mtYEt/kzMzMcHFx4enTpzx//vydjvXkyZP31Ko36969O4sXL05WXqtWLZYvX54mbRg9ejTr169n9+60mU2T0vguWrSIQYMGcf36db3ybdu2YWNjo/siXuhLy9fv8+fPefbsGbt27SIuLk7vuaioqBQdI9XJUMGCBQkODubx48esWLGCdu3asXPnzlcmRP+dy5eYNb5Y/rI6b5oDOGjQIPr166fbjoiIwN3dHW9vbxwcHFLVp/flVpZQ+vjH60aGAEyJY0WWAEYUG0Yl90pGadfHJjY2lq1bt1KnTh3Mzc2N3ZyPjsTXsCS+hiXxNSyJ76tFR0dz8+ZN7OzssLKyeqtjKKV48uQJ9vb2aXbtkbm5OXXr1mXOnDl65ZaWlmn2ecrS0hJTU9M0O19K42tlZYVGo0nWLmN9zkzvjPH6jY6OxtrammrVqiV736U4WVXvqFatWqpr164vfa5q1aqqV69eemUrV65UZmZm6vnz50oppdzd3dX48eP16owfP17lyJEjVe0IDw9XgAoPD0/Vfu/brHa7lCmxCpQyJVbVLO2rGIay7WenWhSepi6dv2zU9n0Mnj9/rlavXq17DYn3S+JrWBJfw5L4GpbE99WePXumzp49q549e/bWx4iPj1ePHj1S8fHx77Flr9euXTvVuHHjVz4fGBiozM3N1a5du3RlY8eOVZkyZVJ37txRSim1ceNGVblyZeXo6KgyZsyoPvvsM3X5sv7nnZs3b6pWrVqpDBkyKBsbG1WmTBl14MAB5e/vrwC9h7+//yvbUq5cOWVjY6McHR1VpUqVVEhIiO75KVOmqDx58ihzc3NVoEABNW/ePL39AbVgwQIVHx+vAgMDFaAePXqke/748eMKUNeuXdM9/+Jj6NChSimlcubMqSZMmKDb7/r16+rzzz9Xtra2yt7eXrVo0UKFhYXpnh86dKgqUaKEmjdvnsqZM6dycHBQrVq1UhEREa+M+4fIGK/f173vUpobvPN9hpRSetfuvMjT05N//vlHr2zLli2ULVtW942Sp6cnW7du1btuaMuWLVSq9GGOonQKqErNrjdYN3snDTtVx67Ez/y4I56L3Qryd2g3LpbYTbvAtfQo3wNzU/lWTQghhPhYKaWIik3ZVB1IuP4hMjYS0+em73SfFhvz1N/w9VW8vLzo06ePbtXfkJAQfvzxRxYvXqy70WVkZCT9+vWjWLFiREZGMmTIEJo2bUpwcDAmJiY8ffqU6tWrkz17dtauXYuLiwvHjh1Dq9XSqlUrTp8+zaZNm9i2bRsAjo6OydoRFxdHkyZN6NKlC4sXL+b58+ccOnRI189Vq1bRu3dvJk6cSO3atVm3bh0dOnTAzc2NGjVqpLrflSpVYuLEiQwZMoQLFy4AYGdnl6yeUoomTZpga2vLzp07iYuLo3v37rRq1YqgoCBdvStXrrB69WrWrVvHo0ePaNmyJaNHj+aXX35JddvE+5WqZOiHH36gfv36uLu78+TJE5YsWUJQUBCbNm0CEqau3b59m3nz5gHg6+vL5MmT6devH126dGH//v3Mnj1bb25q7969qVatGmPGjKFx48asWbOGbdu2sWfPnvfYzbTlVs6VHP864FbOFXNzc2Y0msHsvau5PvYyZp6/0m/LJmYfn83kBpPxyuVl7OYKIYQQwgCiYqOwG5X8A7ShPR30FFsL2xTXX7duXbIP+gMHDmTw4MEAjBw5km3bttG1a1fOnDmDj48PTZs21dVt1qyZ3r6zZ8/G2dmZs2fPUrRoURYtWsS///7L4cOHyZgxIwD58uXT1bezs9Ndc/UqERERhIeH07BhQ/LmzQtA4cKFdc+PHTuW9u3b0717dwD69evHgQMHGDt27FslQxYWFjg6OqLRaF7brm3btnHy5EmuXbuGu7s7APPnz6dIkSIcPnyYcuXKAQmJbkBAAPb29gD4+Piwfft2SYbSgVR97XD37l18fHwoWLAgtWrV4uDBg2zatIk6deoAEBoayo0bN3T1c+fOzYYNGwgKCqJkyZKMGDGCP/74Q+9NU6lSJZYsWYK/vz/FixcnICCApUuXUqFChffUxfSh0+gmnA9355txzclsk5kz/57h23ZjaeExlUshl43dPCGEEEJ8omrUqEFwcLDew8/PT/e8hYUFCxYsYMWKFTx79izZir9XrlyhdevW5MmTBwcHB3Lnzg2g+0wYHBxMqVKldInQ28iYMSPt27enbt26NGrUiEmTJhEamnQ/x3PnzlG5cmW9fSpXrsy5c+fe+pwpce7cOdzd3XWJEICHhwdOTk56586VK5cuEQJwdXXl3r17Bm2bSJlUjQzNnj37tc8HBAQkK6tevTrHjh177X7NmzenefPmqWnKB8nS1pJOpTvRtHBThq4Zyqrh/TmicvGwzk94+9vT17MvFqYWxm6mEEIIId4DG3Mbng56muL6Wq2WiCcRONg7vPM0udSwtbXVG6l5mX379gHw8OFDHj58iK1t0shTo0aNcHd3Z+bMmWTLlg2tVkvRokV1q+pZW1unsgcv5+/vT69evdi0aRNLly7lp59+YuvWrVSsWBFI3YJcifFV/1/YC95uyfhXneO/5f9dcESj0cjy6enE27/TxFvLaJ2RP1r+wQ/dTlDSaj/7m0zg++3fU2xqMbZc2WLs5gkhhBDiPdBoNNha2KbuYZ7K+i95vO+VvK5cuULfvn2ZOXMmFStWpG3btroP8g8ePODcuXP89NNP1KpVi8KFC/Po0SO9/YsXL05wcDAPHz586fEtLCyIj49PUVtKlSrFoEGD2Ldvn24KHiRMmfvvJRb79u3Tm0r3oixZsgDojS4FBwenul0eHh7cuHGDmzdv6srOnj1LeHj4K88t0hdJhoxEY6Kh+9TGHH1agelfTyOrbVYuPrjIz+Vv06r0OC7duWTsJgohhBDiExATE0NYWJje4/79+wDEx8fj4+ODt7c3HTp0wN/fn9OnTzNu3DgAMmTIQKZMmZgxYwaXL19mx44derc+Afjqq69wcXGhSZMm7N27l6tXr7JixQr2798PJEwhu3btGsHBwdy/f/+lC3Ndu3aNQYMGsX//fq5fv86WLVu4ePGiLuH49ttvCQgIYNq0aVy6dInx48ezcuVKBgwY8NI+58uXD3d3d4YNG8bFixdZv369rk+JcuXKxdOnT9m+fTv3799/6X1rateuTfHixWnTpg3Hjh3j0KFDtG3blurVq1O2bNlU/iaEMUgyZGQmpib4lPDhQo8L9L4/mL0PO7DieG8af9uSETtHEB0XbewmCiGEEOIjtmnTJlxdXfUeVapUAeCXX34hJCSEGTNmAODi4sKsWbP46aefdKvFLVmyhKNHj1K0aFH69u3L77//rnd8CwsLtmzZgrOzMw0aNKBYsWKMHj0aU9OE+zI2a9aMevXqUaNGDbJkyfLSm8Da2Nhw/vx5mjVrRoECBejatSs9evSgW7duADRp0oRJkybx+++/U6RIEaZPn46/vz9eXl4v7bO5uTmLFy/m/PnzlChRgjFjxjBy5Ei9OpUqVcLX15dWrVqRJUsWfvvtt2TH0Wg0rF69mgwZMlCtWjVq165Nnjx5WLp0aep+CcJoNOrFyZIfsIiICBwdHQkPDzf6zbBiY2PZsGEDDRo0SNVN6bRxWia1W8+u45dY3ao/AHky5GGC1wQ+L/65oZr7wXnb+IqUkfgalsTXsCS+hiXxfbXo6GiuXbtG7ty53/qmq1qtloiICBwc3u2aIfFyEl/DMkZ8X/e+S2luIK+EdMTEzIS+Cxux8kxfljRbQnb77ESci8SvVDG+rPwzl+7J1DkhhBBCCCHeF0mG0iGNRkOroq043+M83rvGcEubm5OH61NsSjEG7xicqhu4CSGEEEIIIV5OkqF0zM7CjrlH2zCy4TqKdPqLGE0MI3ePpPCkwizavpiPZIajEEIIIYQQRiHJUDpnZmXGj/80ZNkUf1a2XElOx5zkmO9Nnzo1+LLBt5y/f97YTRRCCCGEEOKDJMnQB0Kj0dC0cFPOfHOGZ5e68q9yIexaHMWmFuO7rd/xJOaJsZsohBBCCCHEB0WSoQ+MraUte8OK89sX63EcdJU4bRy/7/udygOrMX/XfJk6J4QQQgghRApJMvQBsnSw5NsVn7G23VrWfbWOPI550EybxCCvqjTr2J7T904bu4lCCCGEEEKke5IMfeA+K/AZm8pt42Fsbh6pLBwwCaTktJL02dSH8OhwYzdPCCGEEEKIdEuSoY9A/sq5OR+akfmjDlKpbnniVTyTDk7isy9bM271Urbv0HLrlrFbKYQQQgghRPoiydBHwtbZli++r8nylsvZ/PVmqtytyYE1qxnQtCW1a5mQM6di9mxjt1IIIYQQH5ugoCA0Gg2PHz82dlM+Wnv37qVYsWKYm5vTpEmT93rs9u3bv/djfkgkGfoIeef1pqvDWOIxAzQAaLUaunSN59DZO8ZtnBBCCCHSjfbt26PRaJI96tWrZ5T2aDQaQkJCjHLu9Kxfv36ULFmSa9euERAQYOzmvNGjR4/w8fHB0dERR0dHfHx8Xpssx8bGMnDgQIoVK4atrS3ZsmWjbdu23Llj+M+tkgx9pNzqliIxEUqktKa0+2wdg/4ZztPnT43TMCGEEEKkK/Xq1SM0NFTvsXjx4jRtw/Pnz9P0fOlRfHw8Wq32pc9duXKFmjVr4ubmhpOT01sdPy1j3Lp1a4KDg9m0aRObNm0iODgYHx+fV9aPiori2LFjDB48mGPHjrFy5UouXrzI559/bvC2SjL0kcqfH0z+89vVoOV8SFdWtaxL/j8KEBAcgFa9/E0nhBBCCCO5dQsCA0mrC34tLS1xcXHRe2TIkAGAkJAQNBoNwcHBuvqPHz9Go9EQFBT0ymPu27ePatWqYW1tjbu7O7169SIyMlL3fK5cuRg5ciTt27fH0dGRLl26JDvGo0ePaNOmDVmyZMHa2pr8+fPj7+//ynNu2rSJKlWq4OTkRKZMmWjYsCFXrlzRPR8SEkKGDBlYuXIlNWrUwMbGhhIlSrB//35dnevXr9OoUSMyZMiAra0tRYoUYcOGDQCUKVOGcePG6eo2adIEMzMzIiIiAAgLC0Oj0XDhwgUgIfn47rvvyJ49O7a2tlSoUEEvZgEBATg5ObFu3To8PDywtLTk+vXren1KjP+DBw/o2LEjGo1GNzK0c+dOypcvj6WlJa6urnz//ffExcXp9vXy8qJHjx7069ePzJkzU6dOnVfGDmDs2LG4urqSKVMm/Pz8iI2NfW39Vzl37hybNm1i1qxZeHp64unpycyZM1m3bp0uNv/l6OjI1q1badmyJQULFqRixYr8+eefHD16lBs3brxVO1JKkqGPlJsbzJgBpqYJ26am0L3GOXJqQshVdh5hkaF0WNOBcjPLsev6LuM2VgghhPiYRUYmPF68F+Dz5wllMTF6VS1mzUKTOzfUrAk5c8Ls2RAbm1A3Ovrlx33FaIKxnDp1irp16/LFF19w8uRJli5dyp49e+jRo4devd9//52iRYty9OhRBg8enOw4gwcP5uzZs2zcuJFz584xdepUMmfO/MrzRkZG0q9fPw4fPsz27dsxMTGhadOmyUZbBg8ezIABAwgODqZAgQJ89dVXuiTCz8+PmJgYdu3axalTpxgzZgx2dnZAQnKRmMwopdi9ezcZMmRgz549AAQGBuLi4kLBggUB6NChA3v37mXJkiWcPHmSFi1aUK9ePS5duqRrS1RUFKNGjWLWrFmcOXMGZ2dnvba6u7sTGhqKg4MDEydOJDQ0lFatWnH79m0aNGhAuXLlOHHiBFOnTmX27NmMHDlSb/+5c+diZmbG3r17mT59+itjFxgYyJUrVwgMDGTu3LkEBAToTcfz9fXFzs7utY/EpGX//v04OjpSoUIF3f4VK1bE0dGRffv2vbIN/xUeHo5Go3nrkbAUUx+J8PBwBajw8HBjN0U9f/5crV69Wj1//tzYTVE3byoVGJjwr1JKPbt1Xz2LeaZ+2/ObchjloIrU91L5cs5UDaa3V5cfXDZqW1MqPcX3YyTxNSyJr2FJfA1L4vtqz549U2fPnlXPnj1L/mRCGqTUvXtJZSNHJpR17qwrir9+XWkT6yY+TE2VGjo04efWrfWPmzlzQvnp02/d7nbt2ilTU1Nla2ur9/j555+VUkpdu3ZNAer48eO6fR49eqQAFRgYqJRSKjAwUAHq0aNHSimlfHx8VNeuXfXOs3v3bmViYqKLT86cOVWTJk1e27ZGjRqpDh06vHXf7t27pwB16tQppZRSV65cUYCaMWOGrs6ZM2cUoM6dO6eUUqpYsWJq2LBhLz3e2rVrlaOjo4qPj1fBwcEqS5Ysqm/fvurbb79VSinVtWtX1apVK6WUUpcvX1YajUbdvn1b7xi1atVSgwYNUkop5e/vrwAVHBz8xr44Ojoqf39/3fYPP/ygChYsqLRara7sr7/+UnZ2dio+Pl4ppVT16tVVyZIl33jsdu3aqZw5c6q4uDhdWYsWLXR9UUqpu3fvqkuXLr32ERMTox49eqRGjhyp8ufPn+w8+fPnV7/++usb26NUwvupTJkyqk2bNm+s96r3XUpzAzPDplrC2NzcEh6JrLJnAuDbyt/iU7g1NYc84nJsURx/icDjnge9yvfip2o/4WjlaKQWCyGEEJ+oS5f+c7UvEB8P9+8b9LQ1atRg6tSpemUZM2Z86+MdPXqUy5cvs3DhQl2ZUgqtVsu1a9coXLgwAGXLln3tcb755huaNWvGsWPH8Pb2pkmTJlSqVOmV9a9cucLgwYM5cOAA9+/f140I3bhxg6JFi+rqFS9eXPezq6srAPfu3aNQoUL06tWLb775hi1btlC7dm2aNWumq1+tWjWePHnC8ePH2bt3L9WrV6dGjRq60ZigoCD69OkDwLFjx1BKUaBAAb02xsTEkClTJt22hYWFXntS6ty5c3h6eqLRJL1iKleuzNOnT7l16xY5cuQA3hzjREWKFME0cToRCXE5deqUbtvZ2TnZqNV/vTgC92K7EimlXlr+X7GxsXz55ZdotVqmTJmSkua/E0mGPmEu9s7M7BzE0DkPsOm1k6NPnzN2/1j8jy5kRO3BdCnTBTMTeYkIIYQQ7+Tp/xctsrFJKvv2W+jTB8xe+H82f36UiQmaF6d1mZpC//4wZkzS3PdEiauuWVu/U/NsbW3Jly/fS58z+f8FyOqFKX5vupZEq9XSrVs3evXqley5xA/pied9nfr163P9+nXWr1/Ptm3bqFWrFn5+fowdO/al9Rs1aoS7uzszZ84kW7ZsaLVaihYtmmzhAHNzc93PiR/OEz/Id+7cmbp167J+/Xq2bNnCqFGjGDduHD179sTR0ZGSJUsSFBTEvn37qFmzJlWrViU4OJhLly5x8eJFvLy8dMczNTXl6NGjekkGoJt2B2BtbZ2iBOG/XpZYJP6OXix/U4wTvRiTxGO8mNz4+vqyYMGC1x7j9OnTODk5kTVrVu7evZvs+X///ZesWbO+9hixsbG0bNmSa9eusWPHDhwcHFLU/nch1wx9yszNqTylDdsiPFnTbzXrW6+nUOZC5Jg0guGf56Tw8EZsvrzZ2K0UQgghPmy2tgmPFz+8WlgklFlaJpW5ufFs4kTUixf8Tp8OuXMn1LWyevlx/7ti0nuUJUsWAEJDQ3VlLy6m8DKlS5fmzJkz5MuXL9nDwsIi1edv3749CxYsYOLEicyYMeOl9R48eMC5c+f46aefqFWrFoULF+bRo0epOlcid3d3fH19WblyJf3792fmzJm657y8vAgMDGTXrl14eXnh5OSEh4cHI0eOxNnZWTfqVapUKeLj47l3716yGLi4uLxVu17k4eHBvn379JLUffv2YW9vT/bs2d/5+P/1888/Exwc/NpHtmzZAPD09CQ8PJxDhw7p9j948CDh4eGvHdlLTIQuXbrEtm3b9EbQDEm+9hdgYYEGaJC/AcXOZyH/3WLEYIXtyRHUW1iP+vnqM9Z7LB5ZPIzdUiGEEOKj9tzHB6vGjdFcvQr58unPdTeQmJgYwsLC9MrMzMzInDkz1tbWVKxYkdGjR5MrVy7u37/PTz/99NrjDRw4kIoVK+Ln50eXLl2wtbXl3LlzbN26lT///DPF7RoyZAhlypShSJEixMTEsG7dOl2y8V8ZMmQgU6ZMzJgxA1dXV27cuMH333+f4nMl6tOnD/Xr16dAgQI8evSIHTt26J3Ty8uLSZMmkTFjRjw8PHRlf/75J1988YWuXoECBWjTpg1t27Zl3LhxlCpVivv377Njxw6KFStGgwYNUt22F3Xv3p2JEyfSs2dPevTowYULFxg6dCj9+vXTjea9T6mZJle4cGHq1atHly5ddIs2dO3alYYNG+oWlwAoVKgQo0aNomnTpsTFxdG8eXOOHTvGunXriI+P170mM2bMmOokOjVkZEjoca9VhFPdp/J7hUU08a2EuYk5Gy9vpNiIZnyztgf3oww7b1kIIYT45Lm5gZdXmiRCkLAktaurq96jSpUquufnzJlDbGwsZcuWpXfv3slWLPuv4sWLs3PnTi5dukTVqlUpVaoUgwcP1l2fk1IWFhYMGjSI4sWLU61aNUxNTVmyZMlL65qYmLBkyRKOHj1K0aJF6du3L7///nuqzgcJ9/rx8/PTfaAvWLCg3nUr1apVA6B69eq66WjVq1cnPj6e6tWr6x3L39+ftm3b0r9/fwoWLMjnn3/OwYMHcXd3T3W7/it79uxs2LCBQ4cOUaJECXx9fenUqdMbE9W0snDhQooVK4a3tzfe3t4UL16c+fPn69W5cOEC4eHhANy6dYu1a9dy69YtSpYsqfdaTM0KdG9Do14cX/uARURE4OjoSHh4eJrML3yd2NhYNmzYQIMGDZLNwfxgKAUaDZceXOKHxT+wrfdfxDvdgi4+DP28Iz0r9MTC1HBZ+ut8FPFNxyS+hiXxNSyJr2FJfF8tOjqaa9eukTt3bqz+O50thbRaLRERETg4OBjk2/1PncTXsIwR39e971KaG6SqpaNGjaJcuXLY29vj7OxMkyZNXnnzpETt27dHo9EkexQpUkRXJyAg4KV1ov+7nr5IO///tiN/pvz03F8bpbXAOdyGSNOLDNg6AI+/PFh1bhUfSS4thBBCCCE+QalKhnbu3Imfnx8HDhxg69atxMXF4e3trXdH4f+aNGkSoaGhusfNmzfJmDEjLVq00Kvn4OCgVy80NPStv1kR71e1qV9xses4lk1+yMzm03Gxc+HKgys0G/gP1WfW53jocWM3UQghhBBCiFRL1QIKmzZt0tv29/fH2dmZo0eP6uZQ/pejoyOOjkn3rFm9ejWPHj2iQ4cOevU0Gs17WV1DGICDA87TR+AMlKYSLTxaMNhnGpP++ZbDu85T+lZxOpT5ml9q/oKrfermAwshhBBCCGEs77SaXOJFT6m5Mdfs2bOpXbs2OXPm1Ct/+vQpOXPmJD4+npIlSzJixAhKlSr1yuPExMQQExOj246IiAAS5jO/af17Q0s8v7HbYShWGktqHwphJTeomC2Qv01j8Q/2Z9mZZXzr+S19K/TF2vzd7nnwOh97fI1N4mtYEl/DkvgalsT31WJjY3U3Fn3x/iypkTj1PPE44v2S+BqWMeKr1WpRShEbG5vsfk4p/Tv11gsoKKVo3Lgxjx49Yvfu3SnaJzQ0FHd3dxYtWkTLli115QcOHODy5csUK1aMiIgIJk2axIYNGzhx4gT58+d/6bGGDRvG8OHDk5UvWrQImxdvaiYMwiI8nOx/r+diq5ZcNbnCnNtzuHUllsij/cno/Qft8jegmlO1t7qRmBBCCPGhMTMzw8XFBXd3d4MuAyyESPL8+XNu3rxJWFgYcXFxes9FRUXRunXrNy6g8NbJkJ+fH+vXr2fPnj24pXDpx8S7+N65c+e1fyi0Wi2lS5emWrVq/PHHHy+t87KRIXd3d+7fv58uVpPbunUrderU+WRW21FK8Xn2vWy+XwP7vMt54tOC8tnKM7b2WCq6VXyv5/oU45uWJL6GJfE1LImvYUl8Xy06OpqbN2+SK1eut77mWSnFkydPsLe3ly8TDUDia1jGiG90dDQhISG4u7u/dDW5zJkzvzEZeqtpcj179mTt2rXs2rUrxYmQUoo5c+bg4+Pzxm9MTExMKFeuHJcuXXplHUtLSyxfvGvz/5mbm6ebP9DpqS0GFxLCj5GjeYgdDTpfYpyy49CdQ1QLqE6rYi0ZU3sMOZ1yvvk4qfBJxdcIJL6GJfE1LImvYUl8k4uPj0ej0WBiYvLWywonTi1KPI54vyS+hmWM+JqYmKDRaF76Nymlf6NSlQwppejZsyerVq0iKCiI3Llzp3jfnTt3cvnyZTp16pSi8wQHB1OsWLHUNE8YU65cVL04m4M7d6FpMwjfpx34acdPrB6TiaVLKrNybwO6VvChfoZelChik1b3kRNCCCGEEOKVUpUM+fn5sWjRItasWYO9vT1hYWFAwopx1tYJF8wPGjSI27dvM2/ePL19Z8+eTYUKFShatGiy4w4fPpyKFSuSP39+IiIi+OOPPwgODuavv/56234JY3BzQ9OmNQAudi784fEzK/dZARnRWN7jr0kd+EuZotFomTZdS9cu77R+hxBCCCGEEO8kVWNYU6dOJTw8HC8vL1xdXXWPpUuX6uqEhoZy48YNvf3Cw8NZsWLFK0eFHj9+TNeuXSlcuDDe3t7cvn2bXbt2Ub58+bfokkgvbE7sZ5+5F52dVxN3uiOohFU+lDLBtxtM37FebtoqhBBCfOCCgoLQaDQ8fvzY2E35aO3du5dixYphbm5OkyZN3uux27dv/96P+SFJVTKklHrpo3379ro6AQEBBAUF6e3n6OhIVFQUXbp0eelxJ0yYwPXr14mJieHevXts3rwZT0/PVHdGpDPNmlHo7Epaf58LrdJ/qSllxvejl1NxdkWCQoKM0z4hhBDiE9e+fXs0Gk2yR7169YzSHo1GQ0hIiFHOnZ7169ePkiVLcu3aNQICAozdnDd69OgRPj4+uvuN+vj4vDFZXrlyJXXr1iVz5sxoNBqCg4PTpK1y9ZgwrHz5yJ89ChPi//OEwsPuFIduH6LG3Bo0WNiAE2EnjNJEIYQQ4lNWr149QkND9R6LFy9O0zY8f/48Tc+XHsXHx7/y/jxXrlyhZs2auLm54eTk9FbHT8sYt27dmuDgYDZt2sSmTZsIDg7Gx8fntftERkZSuXJlRo8enUatTCDJkDA4t0o5mKHxxZSE9d9NieNbfmf1qJn4lfPDzMSMjUuzU3J0E3xW+RDyOMS4DRZCCCGM6NYtCAxM+DctWFpa4uLiovfIkCEDACEhIcm+pX/8+DEajSbZTKAX7du3j2rVqmFtbY27uzu9evUiMjJS93yuXLkYOXIk7du3x9HR8aWzhx49ekSbNm3IkiUL1tbW5M+fH39//1eec9OmTVSpUgUnJycyZcpEw4YNuXLliu75kJAQMmTIwMqVK6lRowY2NjaUKFGC/fv36+pcv36dRo0akSFDBmxtbSlSpAgbNmwAoEyZMowbN05Xt0mTJpiZmREREQFAWFgYGo2GCxcuAAnJx3fffUf27NmxtbWlQoUKejELCAjAycmJdevW4eHhgaWlJdevX9frU2L8Hzx4QMeOHdFoNLqRoZ07d1K+fHksLS1xdXXl+++/17vXjpeXFz169KBfv35kzpyZOnXqvDJ2AGPHjsXV1ZVMmTLh5+f31jdXPnfuHJs2bWLWrFl4enri6enJzJkzWbdunS42L+Pj48OQIUOoXbv2W533bUkyJAzPzY1OMysSYpKXQLwIMcnLb9OdyFKwFJMbTGZd5g1o/pkOf51lwZ4dFJxckL6b+nI/6r6xWy6EEEK8s8jIhMeLl8k+f55Q9sItEwGYNcuC3Lk11KwJOXPC7NkQG5tQNzr65cd9xWCC0Zw6dYq6devyxRdfcPLkSZYuXcqePXvo0aOHXr3ff/+dokWLcvToUQYPHpzsOIMHD+bs2bNs3LiRc+fOMXXqVDJnzvzK80ZGRtKvXz8OHz7M9u3bMTExoWnTpslGWwYPHsyAAQMIDg6mQIECfPXVV7okws/Pj5iYGHbt2sWpU6cYM2YMdnZ2QEJykZjMKKXYvXs3GTJkYM+ePQAEBgbi4uJCwYIFAejQoQN79+5lyZIlnDx5khYtWlCvXj29W8dERUUxatQoZs2axZkzZ3B2dtZrq7u7O6GhoTg4ODBx4kRCQ0Np1aoVt2/fpkGDBpQrV44TJ04wdepUZs+ezciRI/X2nzt3LmZmZuzdu5fp06e/MnaBgYFcuXKFwMBA5s6dS0BAgN50PF9fX+zs7F77SFwzYP/+/Tg6OlKhQgXd/hUrVsTR0ZF9+/a9sg3GIst5ibTRqRNudevidvky5MuHbm1tpXCfNY8amGCf3YqnJQqz/dp2Jh6cyJzgOXxX6Tv6VOyDrYWtcdsvhBBCvKX/f5bm3j3IkiXh599/h59+gs6dYebMhLJbt+Dbb62BhBtWarXQrRvcvAnDh0Pr1rBwYdJxc+WC+/fh9GkoUuTt27du3TrdB/5EAwcOfGmCkhK///47rVu3pk+fPgDkz5+fP/74g+rVqzN16lTdzTFr1qzJgAED9PZ9cWGlGzduUKpUKcqWLQskjCa9TrNmzfS2Z8+ejbOzM2fPntVbzbhfv3589tlnQMKKxkWKFOHy5csUKlSIGzdu0KxZM93tXfLkyaPbz8vLi9mzZ6PVajl16hSmpqZ8/fXXBAUF0aBBA4KCgqhevTqQMK1t8eLF3Lp1i2zZsgEwYMAANm3ahL+/P7/++iuQcCPjKVOmUKJEiZf2ydTUFBcXFzQaDY6Ojri4uAAwZcoU3N3dmTx5MhqNhkKFCnHnzh0GDhzIkCFDdPf5yZcvH7/99ttr4waQIUMGJk+ejKmpKYUKFeKzzz5j+/btuhG7n3/+Odnv6r+yZctGVFQUd+/eTZbUATg7O+tWok5PJBkSacfNjWQ3GNJo8Pi9A9uGDCXafzHW+bex9cpWflwxnMN/jOWno+P581A+hnsNo2Opjpibyk3+hBBCfJwSBgw0emXx8QkJjyHVqFGDqVOn6pVlzJjxrY939OhRLl++zMIXMjelFFqtlmvXrlG4cGEAXZLzKt988w3NmjXj2LFjeHt706RJEypVqvTK+leuXGHw4MEcOHCA+/fv60aEbty4oZcMFS9eXPezq6srAPfu3aNQoUL06tWLb775hi1btlC7dm2aNWumq1+tWjWePHnC8ePH2bt3L9WrV6dGjRq60ZigoCBdAnjs2DGUUhQoUECvjTExMWTKlEm3bWFhodeelDp37hyenp5oNEmvl8qVK/P06VNu3bpFjhw5gDfHOFGRIkUwNTXVbbu6unLq1CndtrOz80sTnBe9OAL3YrsSKaVeWm5skgwJ46tZE03Nmlj/f7NO3jrsXxXL4dsVsd/+K3cLF8Z3vS/jD4znl5q/8Hm+z43aXCGEECI1nj5N+NfGJqns22+hTx8we+GTWP78YGKi0GqTPjCamkL//jBmTMLPL0pcdM3amndia2tLvnz5Xvpc4gjDiyM2b7qWRKvV0q1bN3r16pXsucQP6YnnfZ369etz/fp11q9fz7Zt26hVqxZ+fn6MHTv2pfUbNWqEu7s7M2fOJFu2bGi1WooWLZps4QBz86QvVhM/nCd+kO/cuTN169Zl/fr1bNmyhVGjRjFu3Dh69uyJo6MjJUuWJCgoiH379lGzZk2qVq1KcHAwly5d4uLFi3h5eemOZ2pqytGjR/WSDEBvFM7a2vqtEoSXJRaJv6MXy98U40QvxiTxGC8mN76+vixYsOC1xzh9+jROTk5kzZqVu3fvJnv+33//JWvWrClqT1qSZEikP1FR9L/aA/iaEn0acbPeBH7e+TMX71+kxYxvKVfkNz63/pwGNDB2S4UQQog3etnnUQuLhMeL3Nxg4sRn9O1rTXy8BlNTmD4dcudO+XHftyz/n9cXGhpKqVKlAN645HHp0qU5c+bMKxOs1J6/ffv2tG/fnqpVq/Ltt9++NBl68OAB586dY/r06VStWhVAdy1Parm7u+Pr64uvry+DBg1i5syZ9OzZE0iYKhcYGMjBgwf5+eefcXJywsPDg5EjR+Ls7Kwb9SpVqhTx8fHcu3dP1573ycPDgxUrVuglRfv27cPe3p7s2bO/9/OlZpqcp6cn4eHhHDp0SHfP0IMHDxIeHv7akT1jkWRIpD82NtieO8KQZcvAtxxQjnYl2jHQby5T5/hy2HMCh72/Y+/SvYyuPZoSLi+fZyuEEEJ8aHx8ntO4sRVXr2r0LrE1pJiYmGTXcpiZmZE5c2asra2pWLEio0ePJleuXNy/f5+ffvrptccbOHAgFStWxM/Pjy5dumBra8u5c+fYunUrf/75Z4rbNWTIEMqUKUORIkWIiYlh3bp1umTjvzJkyECmTJmYMWMGrq6u3Lhxg++//z7F50rUp08f6tevT4ECBXj06BE7duzQO6eXlxeTJk0iY8aMeHh46Mr+/PNPvvjiC129AgUK0KZNG9q2bcu4ceMoVaoU9+/fZ8eOHRQrVowGDd7tC93u3bszceJEevbsSY8ePbhw4QJDhw6lX79+utG89yk10+QKFy5MvXr16NKli27Rhq5du9KwYUPd4hIAhQoVYtSoUTRt2hSAhw8fcuPGDe7cuQOgW3kucYVDQ5HV5ET6lDEj+PrqNu2VOWZLbUGZ4W2ZA1NM2XRlE6Wml6LtqrayHLcQQoiPhpsbeHmlTSIECUtSu7q66j2qVKmie37OnDnExsZStmxZevfunWzFsv8qXrw4O3fu5NKlS1StWpVSpUoxePBg3fU5KWVhYcGgQYMoXrw41apVw9TUlCVLlry0romJCUuWLOHo0aMULVqUvn378vvvv6fqfJBwrx8/Pz/dB/qCBQsyZcoU3fPVqlUDoHr16roRmerVqxMfH69bPCGRv78/bdu2pX///hQsWJDPP/+cgwcP4u7unup2/Vf27NnZsGEDhw4dokSJEvj6+tKpU6c3JqppZeHChRQrVgxvb2+8vb0pXrw48+fP16tz4cIFwsPDddtr166lVKlSusUtvvzyS0qVKsW0adMM2laNenES6AcsIiICR0dHwsPDcXBwMGpbYmNj2bBhAw0aNEg2B1O8pdu34euv2XkmM8WOz2bZ3kXsYAd/7zkG16thXmYxfuV9+bHaj2S2efWym+LN5PVrWBJfw5L4GpbE99Wio6O5du0auXPn1q2WllparZaIiAgcHBwM8u3+p07ia1jGiO/r3ncpzQ1kmpz4MGTPDjt2UD00lNgs1rhaurKwwUKefXuUdTcqEhtamomqpyzHLYQQQgghUkzSYvHh0Gjg/2v1AxAYRI0by8jMvwR8k4NSLqWIiIngpx0/ke/PfEw/Mp3Y+Le7e7IQQgghhPj4STIkPlzly9FvuBM3B/xBuw6fc6TrERZ9sQiXg78QNn80votGUnRqUZafXc5HMhtUCCGEEEK8RzJNTny4bG1hyBASZ4iaaExoZOXFN5vqA05kzH+Qi45TafF3C8pnL8+Y2mPwyuVlxAYLIYQQQoj0REaGxEfFbusqtlKHbllXcXXuaIZWH4qtuS2HzoRRY7Y3DRY24ETYCWM3UwghxEdKZiIIkXbex/tNRobEx6V7d8oVLUo5OzuwcWCY1zC6Fe9ChULR3IrXsrFFSzZdLsXXxb/m5xo/k8spl7FbLIQQ4iOQuLpeVFQU1tbWRm6NEJ+GqKgogHda3VKSIfHx+f89ABI9nbyLmH9r4mBqQ43ypVl9M5j5J+ezZN8eGmbqy49NWlKmUFYjNVYIIcTHwNTUFCcnJ+7duweAjY2N7j40KaXVann+/DnR0dGy9LMBSHwNKy3jq5QiKiqKe/fu4eTkhKmp6VsfS5Ih8dHL7x7N5QzlOdF2HFU6zubone74DA7k3Jx+rMKEVT/EU7fPMuaPqEEW2yzGbq4QQogPlIuLC4AuIUotpRTPnj3D2to61YmUeDOJr2EZI75OTk66993bkmRIfPw6dMC+aVOq2NgAkFVbhgv+pYH/v1GVKZsnfkFOcw/6eregf6X+ZLTOaLz2CiGE+CBpNBpcXV1xdnYmNjb1t3aIjY1l165dVKtWTW5qawASX8NK6/iam5u/04hQIkmGxKfByUn346VLoFX/+cZCmfHsbjZ+3fkbkw9Ppl/FfvT17IuD5avvWCyEEEK8jKmp6Vt9SDM1NSUuLg4rKyv5sG4AEl/D+lDjKxMmxScnf34wMdFffcTUVDHlswFY/BVCxIbvGLZtNLkn5Wb0ntE8ff7USC0VQgghhBCGJMmQ+OS4ucGMGRoSv7QzNYXp0zUwLZrnD7OT41IXCjrn5eGzhwzaPog8k/Iwfv94nsU+M27DhRBCCCHEeyXJkPgkdeoEISEQGJjwb6evY/C9NpBVNGFmr5uc6XGC+U3nk8cpL/8eqEP/DYPI+0deJh+aTExcjLGbL4QQQggh3gNJhsQny80NvLwS/sXSEs3pUzSZ3xzvQWUwNTHl6+JfM+bxCli5EPNZJwmNuEvPjT3J/2d+Zh6dSWx86i+OFUIIIYQQ6UeqkqFRo0ZRrlw57O3tcXZ2pkmTJly4cOG1+wQFBaHRaJI9zp8/r1dvxYoVeHh4YGlpiYeHB6tWrUp9b4R4FzY28PXXSdvR0TB5Gq7coX9VmNJwMtnts3Mz4iZd13Wl0F+FmBs8lzhtnPHaLIQQQggh3lqqkqGdO3fi5+fHgQMH2Lp1K3FxcXh7exMZGfnGfS9cuEBoaKjukT9/ft1z+/fvp1WrVvj4+HDixAl8fHxo2bIlBw8eTH2PhHhfnjyhefV/uZK9Oj9Oduebct9wuddlfigcgNnso1w9lJ/2a9pTZEoRFp9ajFZpjd1iIYQQQgiRCqlaWnvTpk162/7+/jg7O3P06FGqVav22n2dnZ1xemF54xdNnDiROnXqMGjQIAAGDRrEzp07mThxIosXL05NE4V4f7JkgeXLsX70CDIk3KPIysyK2z/mJe5maTyu/cnd4p5cfHCR1itb88vuXxjuNZymhZtiopEZqEIIIYQQ6d07fWILDw8HIGPGN9+gslSpUri6ulKrVi0CAwP1ntu/fz/e3t56ZXXr1mXfvn3v0jwh3o8MGZJ+3r2bsZebMEAzjkUDLbjW+xojaozA0SQbZ05Y0Pzv5pSZUYZ1F9ehlHr1MYUQQgghhNG99U1XlVL069ePKlWqULRo0VfWc3V1ZcaMGZQpU4aYmBjmz59PrVq1CAoK0o0mhYWFkTVrVr39smbNSlhY2CuPGxMTQ0xM0qpeERERQMLdb9/mrs/vU+L5jd2Oj5VR41umDBkmDWH03bto62cDYKDnQJ6v7cyIGS6YV55McJ2eNFrciPLZyjO02lBq566NRqN5w4HTD3n9GpbE17AkvoYl8TUsia9hSXwNK73FN6Xt0Ki3/Praz8+P9evXs2fPHtzc3FK1b6NGjdBoNKxduxYACwsL5s6dy1dffaWrs3DhQjp16kR0dPRLjzFs2DCGDx+erHzRokXY2Nikqj1CvAvLhw/5p0s0U+O78Y1vEGHF/2L9/fXEaBOS9cK2hWnt0ppi9sWM3FIhhBBCiE9DVFQUrVu3Jjw8HAcHh1fWe6uRoZ49e7J27Vp27dqV6kQIoGLFiixYsEC37eLikmwU6N69e8lGi140aNAg+vXrp9uOiIjA3d0db2/v13Y4LcTGxrJ161bq1KmDubm5UdvyMUpv8dXMn09drR/di+8k7/h5mJpV5e7Tu/T8ax1r12k5V+VnBkcOpkbOGgyrPgxPN09jN/m10lt8PzYSX8OS+BqWxNewJL6GJfE1rPQW38RZY2+SqmRIKUXPnj1ZtWoVQUFB5M6d+60ad/z4cVxdXXXbnp6ebN26lb59++rKtmzZQqVKlV55DEtLSywtLZOVm5ubp4tfAKSvtnyM0k18O3aEcuUootWCtQUA2e1cuD6jGdqbWSjllo/TJRoSeD2QwHmB1M9Xn59r/EzZbGWN3PDXSzfx/UhJfA1L4mtYEl/DkvgalsTXsNJLfFPahlQlQ35+fixatIg1a9Zgb2+vG81xdHTE2toaSBixuX37NvPmzQMSVorLlSsXRYoU4fnz5yxYsIAVK1awYsUK3XF79+5NtWrVGDNmDI0bN2bNmjVs27aNPXv2pKZ5QhhPMf0pcJo5sxl3cwm/2o1i8dQ6RJpfYuSukczZ+w8bz+xi4+VyNC7YmJ9r/EzxrMWN1GghhBBCiE9bqlaTmzp1KuHh4Xh5eeHq6qp7LF26VFcnNDSUGzdu6LafP3/OgAEDKF68OFWrVmXPnj2sX7+eL774QlenUqVKLFmyBH9/f4oXL05AQABLly6lQoUK76GLQhhBlizUyHGVrb8cInMWDTmdcjLz85k0vXkRq7/uoDnflDUX1lBiWgla/t2Ss/+eNXaLhRBCCCE+OameJvcmAQEBetvfffcd33333Rv3a968Oc2bN09Nc4RIv774Aho0AJOk7xui9x7lzNosREfmYFnH8awIt2DpmaX8ffZv/t6/n1qOvvzQpAU1SxQwYsOFEEIIIT4dcmdIIQzFygosLJI2hw/iZGReNtX6nRZ1crGk+RJO+p4k584tMOE624f9SK1SeSn7zVSCw4KN124hhBBCiE+EJENCpJVp0zBv04q6c1rpisxv5OR6YG10b0VlytHpXSj1W0M+X/w5h28fNk5bhRBCCCE+AZIMCZFW8uSBBQsgRw5d0dVRy4D/3JBVmcHt8vxzfh3lZ5Wn3oJ67L2xN23bKoQQQgjxCZBkSAhjiYuj+OlFmBCvV2xKHIVPzMXR/yYmoWXZfGUzVfyrUGNuDXZc25Gia/eEEEIIIcSbSTIkhLGYmeE25Qdm0BVT4oCERGgkP3InxIzn97Oxv+9yupTugrmJOUEhQdSaV4sq/lXYeGmjJEVCCCGEEO9IkiEhjKlQITqZBBBCLgLxIoRcfM9vXI9xYXXHfyhfMCczGs3gSq8rlL+0DrPTbdl3/QANFjWg/KzyrDm/RpIiIYQQQoi3JMmQEMbk5gYzZuBmGoYXO3EzDYOvvsKxdD68f6utqxZ31pxjSxsQt3wurTONw8bchiN3jtBkaRNKTi/J32f+Jl4b/5oTCSGEEEKI/5JkSAhj69QJQkIgMDDh30WL4MgRsLHRVck81I/hVqP5qkYoC3v1IaR3CIOqDMLmcWlO3jlDy+UtKTq1KAtOLiBOG2e0rgghhBBCfEgkGRIiPXBzAy+vhH8BNC+sMPfoEfYXj/LDs8EsmhkFQBbbLAyu9Cv2iw+Tcc5d7J+W5vz98/is8qHQ5ELMOT6H5/HP074fQgghhBAfEEmGhEjvMmSAixdh+3bIm1dXfKb/HOKeRGNvmoGrQwL5teavZLbJzJVHV+i0thP5/8zP1MNTiY6LNmLjhRBCCCHSL0mGhPgQWFhA9epJ2//+S9m5PQmJcmbNd/vIbO/AoKqDuNYrhFJ7z+Jwpg83Ht6h+4bu5P0jLxMPTCQqNsp47RdCCCGESIckGRLiQ5QhA0ydil2rhpToXllXfDAglONbCxOzdjwjK8zAzcGNO0/u0HdzX3JPys1ve3/jScwTIzZcCCGEECL9kGRIiA+RmRm0bQtLliRdXxQXR8XfvmCc1Y/88PVNfvysA5d7XmZ6w+m4PGjBvfBHDNw2kFyTcjFy10geRz82aheEEEIIIYxNkiEhPha3b2NrFU8/uxkMmZgRAEszS+pl6cqDaUvJNPsheSzK8/DZQwYHDibnxJwM3jGYB1EPjNxwIYQQQgjjkGRIiI9Fzpxw6hTs2QN2drriyx1/JZPFU0rks+TiwH0s+mIRRbIUISImgpG7R5JrUi4Gbh3I3ad3jdh4IYQQQoi0J8mQEB8TExMoWDBp+9Qpam7/katRLgSMuImpiSlfFfuKQx1OUmDVfdzO/8LTqBh+2/cbuSflps+mPtx+ctt47RdCCCGESEOSDAnxMStSBFavxnrYQNyr59EVLxh4losnMsGeQaxstZry2cvzLO4Zkw5OouCUgky7OY0rj64YseFCCCGEEIYnyZAQHzMTE2jcGIYMSSp78IC2c7yYbN6XMT1v07RoAw50OsDmrzdTMGwwz++5selINB5jvGm1vBVH7xw1XvuFEEIIIQzIzNgNEEKksXv3sCqaD7+YIPh2PAAajQaLkFpcmOYNDAc0KE08yy53ZdmZstTKXYuBlQdSO09tNImr1wkhhBBCfOBkZEiIT03hwrB/P2zdmrQsd3w8IR2GAQr4f5kyRbNuBppH+dh+bTveC7wpM6MMS04vIU4bZ6TGCyGEEEK8P5IMCfEp0mggc+ak7W3byHlzD7pE6P+U1hSb2ecpfWob1ib2HA87zlcrvqLg5IJMOTyFqNiotG23EEIIIcR7JMmQEAK8vcm/7FdMNEqvWKNRRD41xf5+LW72v8Zwr+Fkss7E1UdX8dvgR86JORmxcwQPnz00UsOFEEIIId6eJENCCNBocGvhyYyZGkxNExIiUxPFDNWZdWZNGP3dQzLZZGJI9SFc6n6DyidO4fq0Pvej7jMkaAg5JuSgz6Y+3Ai/YeSOCCGEEEKknCRDQgidTp3g0qU4RozYw6X1Z+hc5yafNbOiYoOMujp/z9awd1VRzJauZ/7niymRtQSRsZFMOjiJvH/kpe2qtpy6e8qIvRBCCCGESBlJhoQQetzcoFixB7jVKghbtsDcuUlPPnpEpSG1+TLnfr7tGc3Xpb7keLfjbP56M6Wf9yYuPo75J+dTfFpxPlv0GTtDdqKUevXJhBBCCCGMKFXJ0KhRoyhXrhz29vY4OzvTpEkTLly48Np9Vq5cSZ06dciSJQsODg54enqyefNmvToBAQFoNJpkj+jo6NT3SAjxfllaJv28fj1FI/ax2L4rPfsnlGs0GqzveHPs14l4rH5C80ItMdGYsOHSBrzmeuE525NV51ahVVrjtF8IIYQQ4hVSlQzt3LkTPz8/Dhw4wNatW4mLi8Pb25vIyMhX7rNr1y7q1KnDhg0bOHr0KDVq1KBRo0YcP35cr56DgwOhoaF6Dysrq7frlRDCML7+Go4cgalTE27oCqDVcuWXJdjZxFOlgh1/t1rKhR4X6FamGxYaKw7ePsgXy76g8F+FmXVsFjFxMcbtgxBCCCHE/6XqpqubNm3S2/b398fZ2ZmjR49SrVq1l+4zceJEve1ff/2VNWvW8M8//1CqVClduUajwcXFJTXNEUIYQ5ky+tsrVtB+81c0dhzE80FnAWvyZczHkNLTWO/3F/nrbuVY7jZcfHCRLv90YXDgYPpU6INvWV8crRyN0gUhhBBCCHjHa4bCw8MByJgx4xtqJtFqtTx58iTZPk+fPiVnzpy4ubnRsGHDZCNHQoh0qkgRaN6cDP06kDWXta54xm+PuXXDlLjz9bjZL4Rx3uPIbp+dsKdhfL/9e3JMzMHArQMJfRJqxMYLIYQQ4lOWqpGhFyml6NevH1WqVKFo0aIp3m/cuHFERkbSsmVLXVmhQoUICAigWLFiREREMGnSJCpXrsyJEyfInz//S48TExNDTEzSdJuIiAgAYmNjiY2NfctevR+J5zd2Oz5WEl/DSnV88+eHRYtAKUjc58wZBk2qQI4SY8j1ky9WJlb0LNuTDkW68XWfS1zM3Z/LMTv4bd9vTDw4kTZF29CvYj8KZipooF6lH/L6NSyJr2FJfA1L4mtYEl/DSm/xTWk7NOotl3ry8/Nj/fr17NmzBzc3txTts3jxYjp37syaNWuoXbv2K+tptVpKly5NtWrV+OOPP15aZ9iwYQwfPjxZ+aJFi7CxsUlZJ4QQBpF7wwaKzZpFaIUKHB44UFe+dWsO/vqrFFmyRNL5t1Gsvr+Sc5HnANCgobxjeb5w/oKCth9/UiSEEEIIw4mKiqJ169aEh4fj4ODwynpvlQz17NmT1atXs2vXLnLnzp2ifZYuXUqHDh34+++/+eyzz95Yv0uXLty6dYuNGze+9PmXjQy5u7tz//7913Y4LcTGxrJ161bq1KmDubm5UdvyMZL4GtZ7i++FC2BmBnnzJmyHh3Ow2TiGRn5H3ZYO9O2bsLrcvpv7GLp8GTufTdHtWtW9Kv09+1M/b300Gs27dCfdkdevYUl8DUvia1gSX8OS+BpWeotvREQEmTNnfmMylKppckopevbsyapVqwgKCkpxIrR48WI6duzI4sWLU5QIKaUIDg6mWLFir6xjaWmJ5YtL/v6fubl5uvgFQPpqy8dI4mtY7xzf/06fnTaNKrtGs73wGrT9TmNilnBs87Dq7BxYnSo1x5CvR28Wnp7P7pu72X1zN0Wdi/Jdpe9oVbQVFqYW79Cb9Edev4Yl8TUsia9hSXwNS+JrWOklviltQ6oWUPDz82PBggUsWrQIe3t7wsLCCAsL49mzZ7o6gwYNom3btrrtxYsX07ZtW8aNG0fFihV1+yQuvgAwfPhwNm/ezNWrVwkODqZTp04EBwfj6+ubmuYJIdKz1q2hUycYNgwTs6RluY8uv4aZGRTMbYd/09lc7X2VAZ4DsLOw4/SlR7SdMAf3YZ78uvtXHkQ9MG4fhBBCCPFRSVUyNHXqVMLDw/Hy8sLV1VX3WLp0qa5OaGgoN27c0G1Pnz6duLg4/Pz89Pbp3bu3rs7jx4/p2rUrhQsXxtvbm9u3b7Nr1y7Kly//HroohEgX8uSBWbPghcVTWLOGnhPycKV6R4YNTZix6+bgRr9iv+M45TFMvAlzA7n3yyF+HHsF9wnu+K7z5dy/54zTByGEEEJ8VFI9Te5NAgIC9LaDgoLeuM+ECROYMGFCapoihPgYXLkCFhbkqOAK7knXBv36K9y+ZZpUT5nCuhk8y7uZ6UenM/3odOrlq0ffin2pk6fOR3ddkRBCCCHSxjvdZ0gIId7JgAEJCdGAAUll589Td9u3yetqTalz7SjembqgQcOmy5uou6AuxaYWY9axWTyLfZZ8HyGEEEKI15BkSAhhXG5ukCFD0vbo0ZQ8vxgT4vWqmWgUW1dn5fzvM7jgd4le5XthZ2HHmX/P0OWfLuSYmIMhgUMIexqWxh0QQgghxIdKkiEhRPoyahRuXRowQ+OLKXEAmBLHt+o3alWKont3yJ85L5PqT+JW31v4ZlyKu30u7kfdZ8SuEeSYkIN2q9sRHBZs3H4IIYQQIt2TZEgIkb64usJXX9FJzSKEXATiRQi5GM33bIuuyrcvzKA7F+zItF4tcZhzlcVNllPJvRKx2ljmnZhHqemlqDG3BmsvrEWrtMbrjxBCCCHSLUmGhBDpT/78YGKCG7fxYidu3E4ob9MGk8S/WvHxhOy5RYYMUK6chi9LNGNvx70c7HyQZnnbYaoxJSgkiMZLGlNwckEmH5rM0+dPjdYlIYQQQqQ/kgwJIdIfNzeYMQNM/7+inKkpTJ8OPXsm1fnnH7781p0bNdszenRScQ7T8mzpHsAXF8LpV/YHnKycuPzwMj039sRtvBvfbvmWG+E3EEIIIYSQZEgIkT516gQhIRAYmPBv167w4t2kT54EExPs8ruSNWtS8eoV8Tx5Ajev2jLus1+42fcmk+tPJn/G/ITHhDN2/1jyTMpDq+WtOHDrQFr3SgghhBDpiCRDQoj0y80NvLwS/v2vIUPg8mXo1y+p7OxZfEdkZ3+XOYwbm3BfNDsLO7qW8iP3+gv0tjiOl3sd4lU8y84sw3O2J56zPVl2Zhlx2ri06ZMQQggh0g1JhoQQH67cuSFLlqTtOXPg7l0qPlhPpcpJN2Jdtgy2bNaw9I+SbGqzheBuwbQv2R4LUwsO3DpAq+WtyDMpD7/v/Z3H0Y/Tvh9CCCGEMApJhoQQH49Ro2DJEvjxx6Sy8HA+W9SG3zpfZOgQhaUllHApgX9jfwaZ/otfnolkscnCzYibfLftO9zGu9FzQ08uP7xsvH4IIYQQIk1IMiSE+HiYm0OrVlC6dFLZrFk4bVjEt/u/wNc3qfjIERj+gwOzuvTmRPsbzP58NkWdixIZG8nkw5Mp8GcBGi9pTFBIEEqptO+LEEIIIQxOkiEhxMftiy+gd28YNAg0/586p9VisWwBn9WJoVUrcM1iRcdSHTnpe5LJJQ5SL09DFIq1F9ZSY24NSs8ozdzgucTExRi3L0IIIYR4ryQZEkJ83HLnhokToU2bpLINGyj+uw/rTuVizvRYXfG//2ro/2V5zv70D7tbXMS3jC/WZtYEhwXTfk17ck3KxbCgYdx5cift+yGEEEKI906SISHEp8fGBsqWBR8fTK2Slus+u/oi9vYKFxeoXDg/UxtO5Va/W/xc5Tey22cn7LYpwwN2kmN4JVotb8Wu67tkCp0QQgjxATMzdgOEECLN1awJhw5BbNKoEBcu4NWtEDeKleeO/y40GksA7M0yEtD1W1wz9efOUQ1KqyFeE8+yRl1ZdqY6xZyL4VfOjzbF22BnYWekDgkhhBDibcjIkBDi06TRgIVF0vbJk2Bri3VuF/J6WOqKd259ztWrcOSwCUr7/2uOlCmadTOwisrHqXun8F3vS/bx2emzqQ8XH1xM444IIYQQ4m1JMiSEEAAtWsCtWzBpUlJZRAS1O+ZgepV5yaorrSlfhJ5mZMW/yJcxHxExEUw6OImCkwtSd0Fd1l5YS7w2Pg07IIQQQojUkmRICCESOTlBrlxJ26tXw927NAidg4lJ8muDli6ypH3R7lzocYGNbTbSsEBDNGjYcmULjZc0Ju8feRmzZwz3o+6nVQ+EEEIIkQqSDAkhxKv4+MDu3bhN+YEZMzSYmiYUm2ri6VztIj8Niid7djDRmFAvXz2q3fqHca5h9C83iIzWGbkefp3vt3+P23g32q1ux+Hbh43bHyGEEELokQUUhBDiVTQaqFIFgE5A3bpweeFB8n3fDLfjEbD2JuAIwMOHMHQoPHvmzO7dvzKi72CWnlnK5EOTORp6lHkn5jHvxDzKupalsnllasbVxNzc/NXnFkIIIYTBSTIkhBAp5OYGbt0KgklviI8HR0fdc6YBs/mhSyP2X3amcmXQaKxpX7I9mW+1I9T5LLu0Y1h2dilHQo9whCMs/HMhnUt3xresLzmdchqxV0IIIcSnS6bJCSFEajg5wbffwvffJ5VduoTjgC78NNmV9dNvofn/onPx8dCzp4auTYvQRM3jZt+bjPAaQRbzLNx/dp/Re0eT5488NF7SmC1XtqBVWqN0SQghhPhUyciQEEK8K60WGjdOyH7c3HTFT/acoEa1omyJNaVBA7C2dmZgpYHYnaiAlcdzVoROZNvVbay9sJa1F9ZSIFMBupftTvuS7XG0cnzNCYUQQgjxPsjIkBBCvKuCBWHVKli5Mqns6VOcmngxZ4sbV7dcxto66Sn/2SXpUa8BbdnKOb9z9CzfE3sLey4+uEifzX3IPj47vut8OXX3VNr3RQghhPiESDIkhBDvi9kLg+0XL4KNDdjbY1Eoj644+tEzlAKloFo1KJS5EH/U/4OT7W4zseYMimQpQmRsJNOPTqf4tOJUD6jOsjPLiI2PNUKHhBBCiI9bqpKhUaNGUa5cOezt7XF2dqZJkyZcuHDhjfvt3LmTMmXKYGVlRZ48eZg2bVqyOitWrMDDwwNLS0s8PDxYtWpVapomhBDpS+nScO0arF8PJv//U6sUdrUqs8WyARe3XyPnC+sm/DbSnuGNu/Cd3SmC2gXR3KM5phpTdl3fRavlrcg5MSfDg4YT+iTUOP0RQgghPkKpSoZ27tyJn58fBw4cYOvWrcTFxeHt7U1kZOQr97l27RoNGjSgatWqHD9+nB9++IFevXqxYsUKXZ39+/fTqlUrfHx8OHHiBD4+PrRs2ZKDBw++fc+EEMLYLCwgf/6k7RMn4MwZMp8+TY4i9rpirRb27IFHj8DNTUP1XNX5u8XfXPa7zuCqQ8hqm5XQp6EM2zmMHBNz8OXyL9l9fTdKJb8RrBBCCCFSLlXJ0KZNm2jfvj1FihShRIkS+Pv7c+PGDY4ePfrKfaZNm0aOHDmYOHEihQsXpnPnznTs2JGxY8fq6kycOJE6deowaNAgChUqxKBBg6hVqxYTJ058644JIUS6U7IkcWfOcKxXr4RV6f7PpKcfx1v8yublEdSokVR99fzsrOg5nIk5brK42WKq5KhCnDaOpWeWUi2gGsWnFefPg3/y6NmjtO+LEEII8RF4p2uGwsPDAciYMeMr6+zfvx9vb2+9srp163LkyBFiY2NfW2ffvn3v0jwhhEh/8uUjtFKlpO2rV2HaNEyH/Ih3oZu6ZbkB5s6Fs2fh8UNzviz6Jbs77Ca4WzBdSnfBKiofpw9mptfSMWQbn412q9ux98ZeGS0SQgghUuGtl9ZWStGvXz+qVKlC0aJFX1kvLCyMrFmz6pVlzZqVuLg47t+/j6ur6yvrhIWFvfK4MTExxMTE6LYjIiIAiI2N1SVZxpJ4fmO342Ml8TUsia9hJYtv1qxo5sxBc+wY2gIF4P/lmkWL2DY0B/OuVqVVK5VYzM0jRTjw4zRiTmtAaUATT3SjrsyLm8O8E/PwyOxB51KdaVO0DRmsMxiji0Ylr1/DkvgalsTXsCS+hpXe4pvSdrx1MtSjRw9OnjzJnj173lhX8+JXnaD75vLF8pfV+W/Zi0aNGsXw4cOTlW/ZsgUbG5s3tiktbN261dhN+KhJfA1L4mtYevF1coKaNWHDBgBMo6Px7tmTTE+eUGHoUHbtKqWrOniwJ6dOOSftq0zRrJtJpTKRHNGs5uz9s/Tb2o/vt31PJadKeGfyprBt4df+Pf0YyevXsCS+hiXxNSyJr2Gll/hGRUWlqN5bJUM9e/Zk7dq17Nq1C7cXbjD4Mi4uLslGeO7du4eZmRmZMmV6bZ3/jha9aNCgQfTr10+3HRERgbu7O97e3jg4OKS2S+9VbGwsW7dupU6dOpibmxu1LR8jia9hSXwNK0XxffAAk6+/Ru3eTbnvvwdT04Tykyd52MWCjr30qyutCRZBi1j+fQQhDguYeXwmJ++dJOhREEGPgiicuTCdS3amTbE2ZLR+9bTmj4G8fg1L4mtYEl/DkvgaVnqLb+KssTdJVTKklKJnz56sWrWKoKAgcufO/cZ9PD09+eeff/TKtmzZQtmyZXWB8vT0ZOvWrfTt21evTqUX59X/h6WlJZaWlsnKzc3N08UvANJXWz5GEl/Dkvga1mvj6+ICU6ZAfDzmiYmQUtC5M3XOP8VEcwGtSrrkU4MiMNAEe3sn1qzpgV8FPw7fOcyMozNYfHox5+6fo/+2/vwQ+AMtirSga+muVMlR5aMeLZLXr2FJfA1L4mtYEl/DSi/xTWkbUrWAgp+fHwsWLGDRokXY29sTFhZGWFgYz54909UZNGgQbdu21W37+vpy/fp1+vXrx7lz55gzZw6zZ89mwIABujq9e/dmy5YtjBkzhvPnzzNmzBi2bdtGnz59UtM8IYT4uCQmQgAPHoBGgxu3mEE3TIlLqEIcgzUj6fzVU3r0SKiq0WgoZF8ezT+z+KfqPaY0mEpJl5LExMew4OQCqgVUw2OKBxP2T+BB1AMjdEwIIYRIH1KVDE2dOpXw8HC8vLxwdXXVPZYuXaqrExoayo0bN3TbuXPnZsOGDQQFBVGyZElGjBjBH3/8QbNmzXR1KlWqxJIlS/D396d48eIEBASwdOlSKlSo8B66KIQQH4HMmeHoUZg5k05qFiHkIhAvQsjFcDWEmcX+pE6dpOoLF8KsWeDX1Rbfsr4c63qMQ50P0blUZ2zNbTl//zz9tvQj+/jsfL3ya3Zd3yUr0QkhhPjkpHqa3JsEBAQkK6tevTrHjh177X7NmzenefPmqWmOEEJ8WjQa8PICExPctLdx43bSc2XLJv389CkVy1rRtq0Znp78f7luDWVcy+F8sBwbP5/AWdOFTD86neNhx1l4aiELTy2kYKaCdC3TlbYl2pLZJnMad04IIYRIe+90nyEhhBBpzM0NZsxImkJnagp9+6I3LPTrr5RqkpO5tefj65tUHBgIv/4KDb3taFukG8e6HeNIlyN0Ld0VOws7Ljy4QP8t/ck+PjutV7QmKCRIRouEEEJ81CQZEkKID02nThASkpDdhITA+PFJzykF69bBnTvw4m0Gnj8nS4Y4vvwyYXdr64TiMtnKUPLWdLbXC2N6w+mUcS3D8/jnLD69mBpza1Dor0KM2zeO+1H307KHQgghRJqQZEgIIT5Ebm4JU+b+e3sDjQYOH4a//4bPP08qX7SI4o1ysrjKX4wbl1R87Rr4+UHFMrY0yNqVI12PcKTLEbqV6YadhR0XH1xkwNYBZB+fna9WfEXgtUAZLRJCCPHRkGRICCE+NpaW0Lw5vLis6N9/J4wWPXmCbkVtpXgeFUfTplCvXlJeVSZbGerFTWP352HMbDSTstnK8jz+OUtOL6HmvJoUnFyQ3/f+zr3Ie2neNSGEEOJ9kmRICCE+BatWwdKl0KFDUtm+fRT0zsmKcqN58XZwUVHQvj2UKmpLsdjOHO5ymKNdj+Jbxhd7C3suPbzEd9u+w228G18u/5Id13agVdo075IQQgjxriQZEkKIT4GFBbRsCVmzJpUtWJAwWnTpkv4tje4rqlSBfPmgXLmEstKupWmbaSr7vghlVqNZlM9enlhtLEvPLKXWvFoU+LMAI3eN5Gb4zbTtlxBCCPEOJBkSQohP1cSJsGQJvHiD6zt3cK+Wm3VlhnIyWIvJ//+XUAq6doXihW3JeL0TBzsf5Hi343xT9htsnxXkyjF3Bq+eRs6JOfGe783iU4t5FvvsZWcVQggh0o1U3WdICCHER8TSElq10i+bNw+uX4cdO7AePlxXHB4Orq4JCy7UqJFQVtKlJNmDp/DsdwVaDWjiUY26spU5bL26FScrJ74q+hUdSnagbLayaHQXKwkhhBDpg4wMCSGESNK3b8Jo0dChSWUxMTjVLM0Wz6FcPxuJk1NC8a1b8NNPoNX+P8lRppisn0WfwmPJ4ZiDx9GPmXpkKuVnlafY1GKM2zeOu0/vpnmXhBBCiFeRZEgIIUSSxNGi2rWTytauhePHYfZsMmWz1BWfP598d228hkqa/myse41tPttoXaw1VmZWnPn3DAO2DsBtghuNlzRmzfk1xMbHpkGHhBBCiFeTZEgIIcTrff55wmjRr7+CWdLs6kK/d8JEo7+KnKlpwr1gi3iYsHlaLRZ+sZDQ/qFM+2waFbJXIE4bx9oLa2mytAluE9zov7k/p++dTuseCSGEEIAkQ0IIId4kcbSobduksmPHcNsyhxkm32BqmnATVlNTmD4dYmMTfvb0TKjqZOVE64LdGFf4AKe/OcMAzwFktc3Kvch7jD8wnmJTi1FuZjmmHJ7Co2ePjNBBIYQQnypJhoQQQqRekSKweDGdfs5JSIiGwEAICYFOZ/szM/swbh77l4YNk6ovWwZVqsD3nTz43ft3bva9ydov19K0UFPMTMw4cucIfhv8cB3nylcrvmLLlS3Ea+ON1j0hhBCfBllNTgghROpZWsKXXwLgBri5Affvw+TJ8Pw5ro0agXkWXfUHD8DWFqpWTdg2NzWnYYFGmF1txOSe/7Ls/ELmHJ/DqXunWHJ6CUtOL8HNwY12JdrRvmR78mXMl/Z9FEII8dGTkSEhhBDvh709BARAt25QpkxS+eTJfPdsOKFH7+Drm1S8ezc0aABe5bPQq3wfTvie4EiXI/iV8yODVQZuRdzil92/kP/P/FQPqE5AcABPnz9N824JIYT4eEkyJIQQ4v2wtISvvoJp05LK4uJg9GgYNgz747twcEh6KiwMnJ2henUwMQGNRkOZbGVoaDKZC13vsLT5Uurlq4cGDbuu76LDmg64jHWh45qO7L6+G6VU2vdRCCHER0WmyQkhhDCs33+HpUuhadOksrVraXnuOE0PdOKJo5uu+NYt+OwzsLGxIiSkJS3btORWxC3mnZiHf7A/lx9exj/YH/9gf/JlzEeHkh1oW6Itbg5uLzmxEEII8XoyMiSEEMJwzMwSRotWr04YOUo0diwMG4b5/DlkzJhUfPMm5MsHpUtDpkwJZW4OblR4/gO7ml9kd4fddCzZETsLOy4/vMyPO34k58Sc1FtQj6WnlxIdF52m3RNCCPFhk5EhIYQQaUsp+OabhESpU6ek8uPH8dyylvPbOvHQJmmkJyYGWraE8HANBw9WYXbjKkyqP4nlZ5fjH+zPruu72HxlM5uvbCaDVQYq2lUk0+1MVM5ZGY1GY4QOCiGE+FDIyJAQQoi0pdEkjBbt2AHZsyeV//UXDBuG5odBulEhgNBQKFgQXF2hZMmEMjsLOwpEtWd6xZ1c7nmZn6r+hLuDO4+iH7Hx/kaqzq1KgckFGB40nMsPL6dp94QQQnw4JBkSQgiRPtSvD9WqQdeuSWX37pFr3s/sW3aLkycTbuaaqEcPKFwYDm3Oy4iaI7jW+xrzauyg+P3eWEXl4/LDywzbOYz8f+an0uxKTDk8hQdRD9K+X0IIIdItSYaEEEKkD82awc6dSTcjAvD3h6FDoWVLMmRIKo6MTLi3kY0NeHsnlAX4m9K+hhcnJ0/k+diLdFL7qJu3LiYaE/bf2o/fBj9cxrnQeEljlp9dLtcXCSGEkGuGhBBCpGNFiiSMFrVrl1QWG4vtXxNYO7UNEfbZcXBIWIWua1fQahOuEdJqNQSM9CQkZBOmjUNZcnoJ80/O53jYcdZeWMvaC2txtHSkuUdzfIr7UDVnVUw08v2gEEJ8auQvvxBCiPSrYcOE0aIOHZLK1q2DgQOhfHkcbOMBuHQJtFr9XePj4fJlePavK9Yn+rKtxTFOf3OaQVUG4e7gTnhMOLOPz8Zrrhe5J+Xmh+0/cPbfs2nXNyGEEEYnyZAQQoj078VV4ZycEkaL2rbVXUSUPz+YaPSzIVMTLfnyJcy0++abhMGlIs5F+LXWr4T0CSGoXRCdSnXCwdKBG+E3GLVnFEWmFKH09NJM2D+B0CehadhBIYQQxpDqZGjXrl00atSIbNmyodFoWL169Wvrt2/fHo1Gk+xRpEgRXZ2AgICX1omOlvncQggh/qNGjYTRopEjdUVu57cxQ3XBlDgATIljuuqGG7fImxeKF4c2bZIOERVpwsoJ1emSdRZh/e+yrPkyPi/4OWYmZhwPO06/Lf1wm+BG3QV1WXByAU+fP03rXgohhEgDqb5mKDIykhIlStChQweaNWv2xvqTJk1i9OjRuu24uDhKlChBixYt9Oo5ODhw4cIFvTIrK6vUNk8IIcSn4sWl5S5dohNzqMtmLpOPfFzGTd2GCQ60b9yY9seroH3h+79Vq+CPP2DjRrhwwYoWRVrQokgL7kfdZ9mZZSw4uYD9t/az5coWtlzZgq25LU0LN+XrYl9TK08tzEzkklshhPgYpPqvef369alfv36K6zs6OuLo6KjbXr16NY8ePaLDi/O/AY1Gg4uLS2qbI4QQQkCjRtCjB27a27hxO6HM1DTh3kXjx8OxY5iUKqWrXqhQwkhRyZJJM/CUgr7dMuPl1Z3trbtz+9llFp5cyPyT87ny6AoLTi5gwckFuNi58FXRr/Ap7kNJl5JyY1chhPiApflXW7Nnz6Z27drkzJlTr/zp06fkzJmT+Ph4SpYsyYgRIyj1wn9c/xUTE0NMTIxuOyIiAoDY2FhiY2MN0/gUSjy/sdvxsZL4GpbE17AkvgaSNSuaqVMx7d4dTXw8ytSU+F9/xeTcOTh3jvgiReD/MdfMmkXpyEj8R38JWbMmFnPokIYFC8xYuVLRtGkcOe1z8kPlHxhUaRCH7hxi0elFLDu7jLCnYUw4MIEJByZQOHNhWhdtzVdFviKHYw4jBiBtyOvXsCS+hiXxNaz0Ft+UtkOjlFJvexKNRsOqVato0qRJiuqHhobi7u7OokWLaNmypa78wIEDXL58mWLFihEREcGkSZPYsGEDJ06cIH/+/C891rBhwxg+fHiy8kWLFmFjY/NW/RFCCPFhs7p/H9vQUCJdXYnOnDmhUCm94Z/a3bphe+8eR/r35/YL9zR6/NiS7dtzEB1tSps253Xlf/5ZEhubOD7//ApOmSI4/uQ4Ox/t5FD4IWJV0n+2RWyL4JXRC09HT+zM7NKkv0IIIV4uKiqK1q1bEx4ejoODwyvrpWkyNGrUKMaNG8edO3ewsLB4ZT2tVkvp0qWpVq0af/zxx0vrvGxkyN3dnfv377+2w2khNjaWrVu3UqdOHczNzY3alo+RxNewJL6GJfE1rDfGNzYWk9mz0axaRfyqVQl3bQU0f/+Nybp1aLt0QVWpoqt+9y7kymVGfLyGU6diKVgwoVwpiIgJZ9WFVSw8tZCdN3bq9rE0teSz/J/Rpmgb6uati4Xpq/+/+9DI69ewJL6GJfE1rPQW34iICDJnzvzGZCjNpskppZgzZw4+Pj6vTYQATExMKFeuHJcuXXplHUtLSywtLZOVm5ubp4tfAKSvtnyMJL6GJfE1LImvYb0yvubm0LMn9Oypv5xqQABs3YpJoUIJq9UBKEVWZ1i9WsO+fVC0aNLxBgyA4ODMDB7chaAOXbgRfoNFpxYx/+R8zv57lpXnV7Ly/EoyWmekeeHmfFn0S6rlrIapiSkfA3n9GpbE17AkvoaVXuKb0jak2X2Gdu7cyeXLl+nUqdMb6yqlCA4OxtXVNQ1aJoQQ4pM3YgT06KG//vahQ5iX8KDhpQn8+mtSsVYLCxfC9u3w5ElCWQ7HHPQt9z0nup7meLfj9KvYDxc7Fx4+e8iMYzOoOa8mbhPc6L2xN/tv7ucdJmUIIYR4j1KdDD19+pTg4GCCg4MBuHbtGsHBwdy4cQOAQYMG0bZt22T7zZ49mwoVKlC0aNFkzw0fPpzNmzdz9epVgoOD6dSpE8HBwfj6+qa2eUIIIUTqVagAf/4JefMmlS1cCOfPw7FjelVNoqPYtw9GjYK6dZPK58yBnDk17FleknF1x3GgxS1+z3eEL90HkMEqA2FPw/jj0B9UmlOJ3JNyM3DrQI6HHpfESAghjCjV0+SOHDlCjcQpBEC/fv0AaNeuHQEBAYSGhuoSo0Th4eGsWLGCSZMmvfSYjx8/pmvXroSFheHo6EipUqXYtWsX5cuXT23zhBBCiPdj5EgoXRo8PJLK7t6FPHnIXa8e3y9aBOZJ07XXrIE7dxIWrZs9G7p2NUWrLYOJSRmmTBuFW/XNLDmzhNXnV3M9/Dq/7fuN3/b9RoFMBWhVpBVfFv0SjyweL2mIEEIIQ0l1MuTl5fXab7ECAgKSlTk6OhIVFfXKfSZMmMCECRNS2xQhhBDCcBwcoH17/bLNmyEqCm7dghevWw0JYe3qHGzYZEKuXFCmTMJ0Okj495tuZty48RmfNf2MZ7HP2HBpA0vOLGHdxXVcfHCREbtGMGLXCIo5F+PLol/Sqkgr8mbMixBCCMNKs2uGhBBCiA9e27Zw4gSMG5dUFhcHFSpgUTgvTTwu8uhRUiKUSCm4fDnhZ2tza6xDmjGn3t/cG3CPBU0X0LBAQ8xNzDl17xQ/7viRfH/mo/zM8ozfP55bEbfSrn9CCPGJSfObrgohhBAftOLF9bfPn4dnzxIyoNy5yW8DJib6CZGpKeTLl/BzSAh89hnY2sKdO/a0Kd6GNsXb8OjZI1adX8WS00vYfm07h+8c5vCdw/Tf0p+qOaryZdEvae7RHGdb5zTrqhBCfOxkZEgIIYR4F0WLQlhYwhQ6c3Pc3GDGDDAlHgBTEy3Tp4ObW0L1W7cgf34oXz5hJl6iVYsz4PZvRzZ8tYU7/e7wV4O/qJoj4aawu2/sxm+DH67jXKkzvw6zj83m0bNHad1TIYT46EgyJIQQQrwrG5uExRb+r1PrZ4SUakqgpiYhh/5Fd1eJkyep8mwrF87Gs3Jl0u7R0dC3b8LqdPv3Q1a7rHQv151dHXZxo88NxnmPo1y2cmiVlm1Xt9H5n85kHZuVRosbsfDkQp7EPEnb/gohxEdCkiEhhBDifbO2xu3YWrxuLcCtTNak8vHjwdsbzfcDcXJKKo6MTLjFUalSULlyUvnMmfDnL+40yNCPQ10OcbnnZX6p+QvFsxYnVhvLuovr+HrV1ziPdabF3y1YcXYFz2KfpVk3hRDiQyfXDAkhhBCGki2b/raLC2TKBF98kVR24waZFi5kysDWqBw50WiSnpo8GU6ehAIFoFAhyJsxL4Oq/MAPVX/g7L9nWXp6KYtPL+bSw0ssP7uc5WeXY2dhR+OCjfmy6Jd45/XGwtQibfoqhBAfIBkZEkIIIdLK6NEJNyPy9Ewqmz8ffvgBOnbUS4SUgiFDoEUL/dxp1aqEGXkH/vFgeI3hXOhxgWNdj/Fdpe/I4ZiDp8+fsvDUQhotboTLWBc6r+3MtqvbiNPGpV0/hRDiAyHJkBBCCJGWLCzQy3qKFIEaNRKW7U4UHY3G52uama1h2eJ4MmZMemrJEjh+PGEROwCNRkMp11J8V3oMIb1D2NdxH73K98LFzoVH0Y+YfXw2debXIfv47HRf353tV7dLYiSEEP8n0+SEEEIIY2rSJOHxonXrYOFC2L0bGjXSe2rKFKhVC6pVSyo7fRpKloQGDTSsWeOJp7sn4+uOZ/eN3Sw5vYTlZ5dzL/IeU49MZeqRqWSyzkTTQk1p5tGMmrlrylQ6IcQnS5IhIYQQIr0pXhwGDEi4xsjkhUkcn39O5pIl6da7d8K1R/8XGAjx8QlVEwedTE1MMb/txfiaXvxZ/0+W7NvDkp1H2Rc1lwecZtbxWcw6PgsnKyc+L/g5zQs3p07eOliZWaVxZ4UQwngkGRJCCCHSmwIF4Pff9ctOnoR//km4n1G/fknlWi09e5pQv37CEt2JIiISRpDMzWHIEHO+/74GWm0NTEz60/+X80QV+5OV51ZyN/Iu807MY96Jedhb2NOwQEOaezSnXr562JjbpE1/hRDCSCQZEkIIIT4E+fLBokUQEoLeutxffQVPn5Jv5MiEtbn/78oVcHUFU1P4/nvQahPKtVoNE34szMWLU/iz/p/su7mP5WeXs+LcCm4/uc3i04tZfHoxNuY2NMjfgGaFm/FZ/s+wt7RP0+4KIURakGRICCGE+BDY2CQkPi+KiIDVq+H5cxg1Kqn86VNKFbfm6lVTVqxIWJHuRVotLFgAQ4eaUjVnVarmrMqEehM4dPuQbonu6+HXdT9bmlpSL189GhdojEWcXF8khPh4yGpyQgghxIfKwSFh+tzEiQnXGSX65RfIkQPN/HlUrKh/2VGi1q2Tfl60CHy+NiH6ckXGeo/lWu9rHOlyhO8rf0++jPmIiY9hzYU1dPynI+3PtKfx0sbMOT6HB1EPDN5FIYQwJEmGhBBCiA9ZwYLQu7d+2aZNCfczsrHBzQ1m+OzGlITltE2JY2bb3eTPn1R9/vyEhGjfvoRtjUZDKZcy/OQ5ios9LnLC9wSDqw2mcObCxKk4Nl7ZSKe1ncg6Nive872ZfmQ6d5/eTaMOCyHE+yPJkBBCCPGxOXAg4e6sDRvCrVt0mu9FCLkIJOHfzgtrwK1buurDhiWsydCyZdIh9u0DZ2fo0kVD8azF+bnGz5zoeoI/C/3J0GpDKZG1BPEqnq1Xt+K73pds47PhFeDF5EOTufPkTtr3WQgh3oIkQ0IIIcTHxtIy4d5FVlZw6RJotbhxGy924sbthHW4L19OuHho9Ggq2Jxi3FhFvnxJh9iyBaKiEi5HetGD86XpVeJHgn2DudjjIqNqjaJstrJolZad13fSc2NPso/PTuU5lZmwfwLXH19P064LIURqSDIkxP/au+/wqOq0/+PvmVRaqKEOCb2EGiBAEAIRkhCQBRuWnyhsFHStsPv4gBXWta26AuoKKAuiD0UNTUAgtITeTNBFWmgJJTSBkCBpc35/HDOTMbQgE0jyeV3XXDD3fOfknNvjubjzPd/7iIiUZk2bFl405OFhdqfbuBHGjIEePSAnx2XIuHGwbRv87/86Y2lpMG5cKPXqeXLmDDSt3pTR3Uez9YmtHHz+IB9EfkCoLRSADakbGLV8FA0mNKDzZ515d927JP+S7O6jFREpEhVDIiIipZnNBlOmmAUQmH9OnmzGvb1hwACz3Zx3gS5xjzyC5a+j6FjrCK1aOcOpqRbq1MmkTRuj4DNfmTQJEhY2ICZoFBtiNpA6MpWJfScSFhiGBQtbj21l9MrRNP2oKcGTg/lHwj/YdWoXhmEUTw5ERK5ArbVFRERKu5gYiIoyb41r0sQshABCQmDhQihYlJw4YXZTMAzXxgxnzxIS7Msnn6ykW7d+5P8+NS8PXnsNTp0yb62LiACbn41nuzzLs12eJS0jjfm75/Ptz9+y5tAaktKSSEpL4tXVr9K0WlMGtRjEwOYD6WrriofVo/hyIiKCZoZERETKBpsNevVyFkIFWSzOv1epAnPnwiuvQGCgMz56NJ4BAdRfs5qqVZ3hS5fg6aehe3dz8/k+/tisv7bH1+bJTk+y4tEVpP0tjc8HfE6vqo/gcagP+w5e5L0N79F9Wnfq/qsuTyx8gkV7F/Frzq83+eBFRC5PxZCIiIg45TdfeOMNZ8wwYP16LKdPk1WlijN+/DgV4ubz+ou/snYteHk5P5o1y5wpOnDAGavsVYP0+BgSRn5J3vQ4LBNS6XxiMpV9KnMy8ySfJ37OgFkD8H/Pn3u/vpcvd3zJL7/+4u4jFpEyTLfJiYiIyNVZLJCURO6qVZy+cMEZnz3b7MkdGQnLlrl8Zdo0+PZbuPdeZ2zWLHN4PsNuYfuU4ezdP5T9ufEs2LOA+bvnc/TCUebumsvcXXPxsHgQFhjGwOYDGdhiIA2qNHDvsYpImaKZIREREbk2T0+M8HAMzwK/R/XxgYAA83lG+bKy4MEHabZpBi/9Tw516zo/Wrmy8Gbz8uDjCd7Uy4rgo+iPSR2ZyrYntvFKj1doU7MNeUYeqw+t5oVlL9BwQkPaT2rP2DVjSTyeqAYMIvKHqRgSERGRG/OXv8ChQzBihDO2ciXMmQOjRzs72AHk5PDmm4W7fFut8OGH0LYtnDsHFouFjnU78sadb/DjUz+y/7n9/CvyX4QFhmG1WNlxYgfj4sfRYUoHGkxowHPfP8eqg6vIyXNtDS4icj2KXAwlJCQwYMAA6tati8ViYf78+Vcdv2bNGiwWS6HX7t27XcbFxsYSFBSEj48PQUFBzJs3r6i7JiIiIsXNYnFtyx0UBK+/bnaiK1j5dOuGbUg4U8Yec+ny/eqr0K+feaddwcYMzz5r1ljZJxoxMnQk8UPjOfG3E0wbOI2BzQdSzrMcKedT+GjLR/Se0Zta79diyLwhxP4cS0Z2RvEcu4iUeEVeM5SZmUm7du0YNmwY9xa8Efga9uzZg5+fn+O9v7+/4+8bN27kgQce4I033uDuu+9m3rx5DB48mHXr1tGlS5ei7qKIiIjcKg0awNixrrEjR8wnuHp4EPONN1HDfuvybT2ALcAKYxu4dPfOyoLp0yEjw+wKns/yaw3ubjiUoe2HcjHnInH741iwZwHf7f2O0xdP89WPX/HVj1/h4+FDn0Z9GNh8IAOaD6B2xdrFcOAiUhIVuRiKjo4mOjq6yD+oZs2aVCnYgaaA8ePHExERwZgxYwAYM2YM8fHxjB8/nlmzZhX5Z4mIiMhtxGYz28pt2QI1amD7LcRDL5tNGD74AEuBzgoeHmZ377g46NTJuZmJE+Htt82u36+9Vp6BLcymCnn2PDakbmD+7vnM3zOfA2cPsHjfYhbvW4xlkYWutq6O5xk1r9G82A9fRG5fxdZNLjg4mEuXLhEUFMQrr7xCeHi447ONGzcycuRIl/FRUVGMHz/+itvLysoiKyvL8T49PR2AnJwccnJu7X3D+T//Vu9HaaX8upfy617Kr3spv+71h/Jrs5mvAt/1yMjAYrWS17kzRn58zx6ss2fT65576PVmG/LyzCYLADt2eJCTY6VevVxycsyppPR0mDzZyp/+1JV37uzK2+Fvs/PUTr7b9x0L9y5k+/HtbDyykY1HNvK/K/6X5tWbM6DZAAY2G0hI3RCslttn+bTOX/dSft3rdsvv9e6HxfgDrVgsFgvz5s1j0KBBVxyzZ88eEhIS6NixI1lZWXz55ZdMmjSJNWvWEBYWBoC3tzfTp0/n4Ycfdnxv5syZDBs2zKXgKWjs2LGMGzeuUHzmzJmUL1/+Rg9JREREipH3uXNk+/k51hc1nz2bFrNnczwkhC0vv1xo/JEjFalW7RLly+cCsHZtPT74oBP16l3gk09WFRp/Ovs0W9K3sPn8Zv574b/kkef4rKpnVUIqh9C5cmfaVGyDj9XHTUcpIsXt4sWLPPzww5w/f95lqc7vuX1mqHnz5jRv7pySDg0NJTU1lffff99RDIFZWBVkGEahWEFjxoxhVIEp9fT0dOrXr09kZORVD7g45OTkEBcXR0REBF4Fn0AnN4Xy617Kr3spv+6l/LpXceTXAtgzMvAfPJh+/fqZwQsX8AwNxd63L/Z//AN8fR3jfXws/PSTnZCQ8o7xhgHh4R60aWPw6qt2Hq35KADnLp1j6f6lfLf3O5buX8rZ7LMsP7Oc5WeWU86zHHc2vJP+TfoT3SSaepXqueX4rkbnr3spv+51u+U3/66xa7klD13t2rUrX331leN97dq1SUtLcxlz8uRJatWqdcVt+Pj44ONT+Dc4Xl5et8V/ALi99qU0Un7dS/l1L+XXvZRf93JrfgcOhIEDXdvdxsXB3r14GAYe48ebHewADhygb58A+vbNH222qduxAzZsgMRE+Ne/PMjf1Ywj/gxqPIQh7YeQlZvFmkNrmL97Pt/t/Y6jF4461hkBtK/dnrua3kX/Zv0JqRuCh9WD4qLz172UX/e6XfJ7vftwS4qhxMRE6tSp43gfGhpKXFycy7qh5cuX061bt1uxeyIiInI7+dOfYN48c71RfiFkGBARAefPw9KlLp0WWrSAJUvMng0F75x/+mnzMUhffAEPPuhDVJMoWvlGcX/5f5NbZRdbM+axaN8iNh/ZTFJaEklpSfxj7T/wL+9Pv6b96N+0P5GNI6nsW7mYEyAi7lLkYigjI4Pk5GTH+4MHD5KUlES1atUICAhgzJgxHD16lBkzZgBmp7gGDRrQqlUrsrOz+eqrr4iNjSU2Ntaxjeeff56wsDDeffddBg4cyIIFC1ixYgXr1q27CYcoIiIiJVq5cvD79cnHjpmFUGamWf3kS0jA55dfiI6KguhyjnBeHqSmQnY2tGtnxqZOheHDwW63YLUGMWVKEBtjXuZU5im+T/6exfsWszR5KacunuKLHV/wxY4v8LR6EhYYRv+m/bmr2V00q97M/ccvIm5T5GJo27ZtLp3g8tftPPbYY0yfPp3jx4+TkpLi+Dw7O5u//e1vHD16lHLlytGqVSsWL17svA8Y6NatG7Nnz+aVV17h1VdfpXHjxsyZM0fPGBIREZHLq1cP0tLg55+hYkVn/N13zWmhN94we3D/xsMDfvwR9u6FZs3MRx+ZhZD5ud1uPuQ1KgpsNn8ebvUoj7Z7lJy8HNalrGPxvsUs2ruIPWf2sOrgKlYdXMVfl/+VptWaOgqjHoE98PbwRkRKjiIXQ7169eJqDeimT5/u8v7FF1/kxRdfvOZ277vvPu67776i7o6IiIiUVZ6e0Lata6xtW/jvf+Gee5yxzZvhrbewPPIIze+/H4B9+5yFUL68PPNhsJ6e5mRTZCTMnOlFeMNwwhuG837k+yT/kszivYtZtG8R8Yfi2ffLPsZvHs/4zeOp5F2JyMaR3NXsLvo17UfNCjXdnAAR+aNuyZohEREREbd4+2146y3n2iKAr7+GhQuhUiX4rRhq2hSsVgO73TnOwwOaNIFly8w78A4dMgujfN99B4GBTXiuy/M83/V50rPSWXFgBYv2LmLxvsWczDxJ7K5YYnfFYsFC53qdHbNG7Wu3v2qXXBG5NVQMiYiISOny+6Lj8cfNQqhHD0fI5nOKKcZLjOBT8vDEg1wmP7IRm60HQ4ZAUJC5HClfXh7ExMCpUxAfD2Fh4Ofjxz0t7+GelvdgN+xsP7adRXsXsWjfIn44/gObj25m89HNvLbmNepWqusojHo37E0F7wrFlAwRuRoVQyIiIlK6tWwJY8e6xubOJcb4nCi+J5kmNCEZ21dpEDIBa8uWhHTvDt7O9T9nz0LXrrBtG4SGOjfz0Udm5++//MVK374hhNQLYVz4OI5dOMaSfUtYtHcRKw6s4NiFY3z2w2d89sNn+Hj4EN4w3NG6u0GVBsWSBhEpTMWQiIiIlD3NzC5wNo5i46gZy8NsunDuHKxYAb17m3HDoEYNCwsXmjNEHgUeOfTNN7B2LfTt64z9+isc3V2XP3d8nMc7PM6l3EvEH4p3zBodOneIpclLWZq8lGe+f4ZW/q24q9ld9G3Ulzwjr1gOX0RMKoZERESk7DEXDbl2UfDwMJ9dlJjocksd//oXzJoFL7yAxyOPuGzm44/NtUQDBjhjq1bBXXdB585m7wZfT1+imkQR1SSKicZEdp3e5VhntD5lPTtP7WTnqZ28u/5dKnpUJDo7mn7N+hHVOIo6leogIu6jYkhERETKHpsNpkwx+2nnT/dMnmwuDDIM13VHixbB9u3mvXL5fv0VFi6kbVQUbV+u4rLpo0fNJUoFngMLmK2827a18OijQbx4RxAv3vEiZ389y7L9y1i0dxHfJ3/PL7/+wje7vuGbXd8A0K5WO/o26UvfJn3pVr+bWneL3GQqhkRERKRsiokxHyyUnGy2kbPZzPjvGzDMng3ffw99+jhjq1fDgw9Cw4Zw4IDL8OHDYehQuHDBGdu/Hz77zKy5/t//c8bzMqtyf8sHebD1g+zb/yvv/Wc+vm1S2ZwRy9ajW9lxYgc7TuwwZ428K9K7YW+iGkfRt0lfGlZteHPzIVIGqRgSERGRsstmcxZBV1KrllndFJSVZTZmCAtzjffrBw0a4P3KK1SvW9cR9vOD994zZ42qVnUOf+ops64aPBgmT/bFbn8Iq9VgypQXWfw/p4nbH8fS/eb6opOZJ1mwZwEL9iwAoFn1ZvRtbM4a9WzQk/Je5f9AIkTKJhVDIiIiIkV1993mKyfHGTt82JxBslrhzTed8d278ffx4W9/c53Jsdth61Y4c8a8Qy//mUd2u4UnnoCAgBo8FPEQD7V5CLthZ0faDrPxwv6lrE9Zz94ze9l7Zi8Tt0zEx8OHng16OoqjFjVa6LlGItfBeqt3QERERKTE8vJy/r1WLXN90bvvuk7/vP46NGpkNmIowGo179AbP961jwOYy5b+8Y8CYy1WmlQMZkyPMcQPjefMi2eYO3guwzsMp75ffbLysli+fzmjlo8i6N9BNJjQgBHfjWDernmkZ6Xf/OMWKSU0MyQiIiJyM/j6Qv/+5qugrCxzsVDBBxQlJcGbb+J5773ce++DjBrlWhBZLHDffc73Z89C7drQoYPZ9btyhcrc3fJu7m55N4ZhsPv0bsesUfyheFLOpzDlhylM+WEKnlZPutXv5pg1ale7HVaLfh8uAiqGRERERNxr/nzz2UWVKjljCxfCt99CXh62Bx/8rbGdQV6eBQ8Pg8mTLcTEOIdv2gTZ2eZmKlRwxqdNA09PC/36tWRkaEtGho7kYs5F4g/FO4qjvWf2knA4gYTDCby06iVqVahFVJMo+jbuS0TjCGqUr1FMiRC5/agYEhEREXG3KlVc3999t9nS+7f+2zExcGfIWQ4G30/TKmeoP2glUN0xPDoaUlPhyBHnJgwDxo0zlyotWuSckLLklieiYTTRTaMBOHD2AMuSl7F0/1JWHljJicwTzNgxgxk7ZmDBQki9EMesUUi9EDyt+uehlB0620VERESKW5s25quA+ud3YvPZiGc1G1R3FkJ8/DFcvIjtwQexdQ1whLOzzTbdK1dCr17O4VOnwiuvwKhR8Npr0KhqI54KeYqnQp4iOy+b9SnrHbNGP574kS1Ht7Dl6Bb+nvB3qvpWJaJxBH0b9yWqSRR1Kzk74omURiqGRERERG4DRteufD9jBtGtW+Noy2AYZuOFgwehRQsI+K0YyszEx2LhzTfLuzSuA0hIgPPnwcfHGcvJMfs4RER407NnOOENw3k34l2OXTjmmDWK2x/H2Utn+Xrn13y982sAWvm3ok+jPkQ0iiAsMIxKPpUQKU1UDImIiIjcJgwvL2jc2BnIyzOneJYuhTvvdMa//BJGjoTnnjO71xUwa5b5lfr1nbENG+Dtt+HzzyEtzRn3s9RlWPAwhgUPI9eey9ajW1mavJRl+5ex5egWdp7ayc5TO5mweQKeVk9CbaGO4ki31ElpoDNYRERE5Hbl6QnPPGO+Ctq8GS5dcl2LlJsLr72GR2QkXXv0MDvY/aZyZXj0UahWzWzpnS88HDIyYMYMCAnxJLR+KKH1QxkXPo6f9p0ldt2P7GMJG9O/4eC5g6xNWcvalLW8vuZ1/Hz8CG8Q7iiOmlVvpmcbSYmjYkhERESkpPnPf+Cvf3VdW5Q//TNlCpw44YxnZ9O+vTdffOG6ifPnYccO8xY6m80ZX7sWPv0U5sypit3eE6u1J1OmvEv4owdYcWAFcQfiWHlgJWcvnWXBngUs2LMAgPp+9enTqA99GvWhd8Pe1KpYy40JELk5VAyJiIiIlDQWC7Ru7Rrz84MhQ8wHvhaYFaJnT/N2u0mTzAcV/aZyZTh50pxkqlPHOfyjj+Cbb5zv7XYYMQISOzdieMfhDO84nDx7HolpiY7iaF3KOlLTU5mWNI1pSdMAaFurLRGNIujTqA9hgWGU9yrvjkyI/CEqhkRERERKg/btzfvdCjp7FrZsMSuaWgVmarZtg4MHqRIZSVRUZZevFFxrlC8vD9q2hbAwWLMGPKwedKrbiU51OzG6+2gu5lxkXco6R3GUlJbEjyd+5McTP/LBxg/w9vCmW/1ujuKoY52OeFg9Cv8gkWKmYkhERESktKpa1Xw40YYNUK+eM/7pp+atds8/D+PHmzHDAGDkSAvjx5v1Uz6r1Xxfrpw5KZXv5ZfNHzFkSHkiG0cS2TgSgFOZp1h1cBVxB+KIOxBHyvkU1hxaw5pDa3h51ctU8a3CnQ3vpE/DPkQ0jqBx1cZabyS3hIohERERkdKsTh24917XWOPG0Ly580mtAHv2QHQ0tnvuYcqQQYz4IpQ8PPEgl8lDNtLv7R6cO+ccfumS2fX70iXo18858WQ+GNafB1o/wAOtH8AwDJJ/SXbMGq06uIpzl84xd9dc5u6aC0Bg5UDHrFHvRr2pUb6GOzMi4qBiSERERKSseekl8/XbbBAAS5bAoUOwdSsx68cTRR2SaUITkrF9eRz+fpA6LZ0Pfc3NNfs1bN0KLVs6NzN+PHzwAYwebX5usVhoWr0pTas35amQp8i157L92HZHcbQhdQOHzx/m88TP+TzxcwCCawc7iqPuAd0p51WuePIiZY6KIREREZGyquCtaSNGQNOmsHcvrF2LjaPYOGp+ZgdWroRhw8z3WVlUrODNCy8UvrXt1Cnztrp27ZyxY8fg/vuhb1945RVPuti60MXWhZfDXiYzO5OEwwmsOLCCFQdX8OOJH0lMSyQxLZF/bvgnPh4+dA/oTu+GvQlvGE6nup30fCO5aXQmiYiIiAhUqAADBpj3ub34ouuiIYA+fZx/f+UVmDMHxo6FP//ZZdgXX8CECeDt7YytWGEuW8rOhldfdcaXLYPAwAr0bR5NdNNoANIy0pzrjfbHcfTCUVYeXMnKgysBqOhdkR4BPQhvEE54w3CCawerGYPcMOu1h7hKSEhgwIAB1K1bF4vFwvz58686fu7cuURERODv74+fnx+hoaEsW7bMZcz06dOxWCyFXpcuXSrq7omIiIjIH2Gzmc8qym/P7eEBn33m2mYuIQFSU8HHxxk7fhyeew4WLaJKFShfoJN2RIS5ib/+1Rmz281O4C1bmoVSvloVavNwm4eZNnAaqSNT2fX0LsZ1mEr3vFepktWajOwMvk/+nhdXvEjIZyFU/2d1Bs4eyPhN49mRtgO78bsiTuQqijwzlJmZSbt27Rg2bBj3/n4x3mUkJCQQERHBW2+9RZUqVZg2bRoDBgxg8+bNBAcHO8b5+fmxZ88el+/6+voWdfdERERE5I+KiYGoKEhOhiZNXJ/KCrB6NaxbB506OWMrV5oPKdqwAe66yxn/+WfqNGrE44+7/rvu7FmzXfeOHRAS4oz/858waxaMHAmPPWZh/YIWjBveArsdrNZxvPZeKlVCY1l9aDXxh+M5n3WehXsWsnDPQgCql6tOzwY9zZmjBuEE+QepU51cUZGLoejoaKKjo697/Pj8do2/eeutt1iwYAHfffedSzFksVioXbt2UXdHRERERNzBZitcBOUrXx4iI11jLVrAU0+Z647yGQaEh0N6uvl017ZtHR9Vr27ePpebC54F/kUaF2cWSBcumHfsDR/uvGPPbrfw5osBHDo0kpGhI8m155J4PJHVh1az+tBq1h5ey5lfz7h0qqtZoSbhDcIJqx8Gl8Ao2DRCyrxiXzNkt9u5cOEC1apVc4lnZGQQGBhIXl4e7du354033nApln4vKyuLrKwsx/v09HQAcnJyyMnJcc/OX6f8n3+r96O0Un7dS/l1L+XXvZRf91J+3avE57ddO3OxEED+MRw9iqeHB1it5DZu7IhbP/0Uy6pV2GNiMPr2peAhf/EFrF5toVs3g127LNjtrv9czcuD3btzqVXL4MgRaFOnPe1rtmdk55Hk5OWw/fh21hxeQ/zheNYfWc/JzJPM2TmHOTvnAPCPj/5Br8Be9ArsRc/AnjSs0lAzRzfB7Xb+Xu9+WIw/UB5bLBbmzZvHoEGDrvs77733Hu+88w67du2iZs2aAGzatInk5GTatGlDeno6EyZMYMmSJezYsYOmBX+7UMDYsWMZN25cofjMmTMpX/AmVRERERG5dQwD39OnueTv7wiFvv46NXfs4MfHH+fgb7fUeVy6RN2NGznVti2XqlcH4PRpX554IhLDcBYrVqudKVPiqFHjEn/5S2/On/fm9dc30azZ2UI/Oseew96Le/kp4yd+uvATey7uIdfIdRnj7+VP64qtaVOpDW0qtsHf27/QdqTkuXjxIg8//DDnz5/Hz8/viuOKtRiaNWsWjz/+OAsWLKBPwY4kv2O32+nQoQNhYWFMnDjxsmMuNzNUv359Tp8+fdUDLg45OTnExcURERGBl5fXLd2X0kj5dS/l172UX/dSft1L+XWvMpXfH37AGheH/b77zAfAApalS/H8058wGjQgd+9ex9Bpn9v5y7Pe5OVZ8PAw+Pe/8xg2zODcOWjSxJOMDEhLy6VKFXP8zJkWFiyw8sgjdgYMcP4zNycnh0XLFlGxRUXWHV1H/OF4thzbQq7dtThqXLUxPQN70jOwJ70Ce1GnYh13Z6NUuN3O3/T0dGrUqHHNYqjYbpObM2cOMTExfPPNN1cthACsVishISHs27fvimN8fHzwKdjB5DdeXl63xX8AuL32pTRSft1L+XUv5de9lF/3Un7dq0zkt0sX6NIFl4bYnp7QuTOW9u1djn/4J63p1yqQ5JGf0KRPA2w285+v/v5w5gzs3g3+/s7xS5bAvHnQvr2Ve+4xY7m58OWXFgyjGoP696Rfy34AZGRnsD5lvWPN0bZj29h/dj/7z+7nP0n/AaB59eaONt69GvSiZoWabk1NSXe7nL/Xuw/FUgzNmjWLP//5z8yaNYv+/ftfc7xhGCQlJdGmTZti2DsRERERueWio81XwZuWTpyAnTuxWXdhG1gZqv4WX7IEEhPxHDiQ1q1bu2zmf/7H7NNQsKHdtm3w5JOeVKwY5nhuLADZFYlqEkVUkygA0rPSWXt4LasPrWbVwVUkpSWx58we9pzZw6TtkwBo5d/KbMgQGEaPwB7UrqgGYCVZkYuhjIwMkpOTHe8PHjxIUlIS1apVIyAggDFjxnD06FFmzJgBmIXQo48+yoQJE+jatStpaWkAlCtXjsqVKwMwbtw4unbtStOmTUlPT2fixIkkJSXxySef3IxjFBEREZGSomAzg1q1zJZyP/wAVas64zNmmA99zcmB/GIoLw/27KFTx5Z06uTaECEnB3r0sAMnsVprOeKRkWa9NWMG3HEH+Pn40b9Zf/o3M395/8uvv5BwOIHVB82Zo59O/sTOUzvZeWonH2/9GIBm1ZsRFhBGWKD5CqwS6Ja0iHsUuRjatm0b4eHhjvejRo0C4LHHHmP69OkcP36clJQUx+eTJ08mNzeXp59+mqefftoRzx8PcO7cOYYPH05aWhqVK1cmODiYhIQEOnfufKPHJSIiIiKlQb165qug/v0hO9ucScq3fbt5+13LlrBzp0tR1aMHrFyZx+LF2wHzFrlLlyAx0fyz4OaXLzdvs7vnHoiIqMagFoMY1GIQAKcyTzF38xaWbt7Pbr5jT/ZK9p7Zy94ze/k88XMAAioHmIXRbwVSs+rN1K3uNlbkYqhXr15X7c+eX+DkW7NmzTW3+eGHH/Lhhx8WdVdEREREpCwaMsR8FZScDL6+5vOOChYfQ4ZAxYowcqRL2NcXTp6ETZugQQNnfN48mDQJvL0hIsKMGQYsXgwHDvgzcmT/3x4A+xzjP86kUe/VJBxOIOFwAtuObSPlfApf/fgVX/34FWA+56hgcdSmVhusFqt78iJFVuzPGRIRERERuekefticzvnlF2csIwNmzzY7KIwc6Yz/9BMcO0al7t2JiKjgspnBg8HHBwo2S05OhgEDXH+c3Q6jnq3AoUN3cVeEuUApIzuDTUc2OYqjTUc2cTLzJN/+/C3f/vwtAFV8q9A9oLujOOpQpwNeHre+4UBZpWJIREREREoHX1+oW9f53ssLYmPNW+gaNoRdu8z4pEnw73/DM8/ARx+ZMcOAvDzCwz0psCIEMNcV1a8Pqamu8bw88xa8qVPhzjuhondF+jTqQ59GZufkrNwsth7b6iiO1qeu59ylcyzau4hFexcBUN6rPN3qd3MUR53rdaacVzl3ZEcuQ8WQiIiIiJROPj7wpz+Zr5wcZ7xGDbO6Kfi4lwMHIDjYjMXGutxq1707bNgAgYHmjFBBhw7heMYRmOP+8x+zm92gQT50D+hO94DuvNTjJXLtuSSlJTmKo7Upa/nl119YcWAFKw6sAMDbw5vO9To7iqNu9btRyafSzc+NACqGRERERKSsGTcOxo51beO9Zg1cuGA+vKjg4qIPPoDKlbENGsSUKTUYMcJwPAD2vfcsBAZCu3bO4d9/b84UZWe73mo3eza0b+9Jx+ad6FS3E6NCR2E37Px86mdHcZRwOIHjGcdZl7KOdSnreGvdW1gtVoJrBzu61XUP6E6N8jXcnKCyQ8WQiIiIiJQ9Fotr0TNsmDkzdOmSM5abC3//O6SnQ3AwMSwgyj6OZBrRxH4Am9/rcE+My2bzG9117+6MnT4NDz1k/v3UKXNiCiD9vJWW1VvTumZr/hLyFwzDYP/Z/Y5Zo4TDCRw4e4Dtx7ez/fh2PtxkNhxr5d/KURz1COhBPb/fdduT66ZiSERERETEaoUOHVxjly7B88/Dli1mBTN8ODbDjo1UMIAnnoCoKLDZzPGGQdeuFrp2dd3M6dPQq5fZz6FGgUmd556DhQth4kR49FGwWCw0qdaEJtWa8OfgPwNwJP0Iaw+bhVFCSgI/n/rZ8ayjT7d9CkCDKg24o/4d3FH/DrrV70brmq3xsHq4J0+ljIohEREREZHLqVjRnBkCWL268IIhwzBbzdls5pRPUJDZUeHrr8HT+c/sFi3Mr//+6TSJiXD+PNSp44zt2AF//Sv06wejRoHNz8ZDbR7ioTbm1NKpzFOsS1nnKI6S0pI4dO4Qh84d4v9++j/AfHhsV1tXR4HUxdaFit4Vb3p6SgMVQyIiIiIi19K0qTl7VLAg8vCAJk3Mv69fb04B7d3rUgjxzjvw668wZAiW/LG/SUw0i5+WLZ2x1ath5Uqz98OoUc74pEnm85B69vTn7pZ3c3fLuzlyBJJ2ZpJeYTt7c1exPnU9m45sIj0rneX7l7N8/3JzNy0etKvdzlEc3RFwBzY/201OUMmkYkhERERE5FpsNpgyBUaMMHtqe3jA5MnOW+T69YONG831RQV9+imkpJgzRvnF0KFDsH07nt2707FjLZfhAweahVC9AsuA8u/Wy842a62mTc0mDcOHg91eAas1jClTwoiLgVx7Lj+d+IkNqRtYn7qe9anrSTmfwg/Hf+CH4z/w0RazlXhA5QDHbXV31L+DtrXalslb61QMiYiIiIhcj5gYc41QcrJZ2NgKzK54e1NosZDdDi+9BOvWuX42b5457XPXXfDdd874kSM0bFCPp56yuGwmPd18puzu3eaPPXIkvxBy/pgRI8xdq1fPk/a1gwmuE8zTnZ82N5t+hPUp6x3FUVJaEinnU0g5n8Ks/84CzGckFby1rquta5lo6a1iSERERETketlsrkXQ1VitZpUyYoRrvFIlaNMGwsKcsV9/hUaNoHp18965mjUdH9WsCdOmOYfu21d4+VJenlmj5eRAly5mw4Y5c8yGeTY/Gw+0foAHWj8AQEZ2BpuPbHYURxtTN3Ih+4LL846sFitta7V1ubUuoHLA9WapxFAxJCIiIiJSnB5/3HwV7KiwZ4+z1be/vzP+8suwbRuMHAl9+wJXX760Zo3ZyyElxbVz+Jgx5vgnnoAmTSrSu1FvejfqDUCePY+dp3a6zB4dOneIpLQkktKS+GTrJ4BZVOXfVndH/TtoV7sdntaSXU6U7L0XERERESmpClYr7dubreUOHXKNf/+92Wkhxvk8I5uRypSITYyIu5c8u9Vl+dL990Pjxq6PSzIM+Owz83my99zjXLq0cyds3gxhYR60bdKWtrXa8lTIUwAcu3DMpThKPJ7IkfQjfL3za77e+TUAFbwq0MXWxexYV7cLmXmZbkqU+6gYEhERERG5Hfj6mn24C5o+HdauNe97y7d6NTHLHiOqw59I/mCBc/nS6tX4NGpEaGigyyZyc+H9983+DsHBznhsLLz+uvlA2JkznfHt26FVq7rc3+p+7m91PwCZ2ZlsObrF5da681nnWXVwFasOrgLAgoVNvpuY2G/izcuJm6kYEhERERG5XbVta74KatoUnngCW1AQtl6/xex2uPdeOHvWvK2uY0czfvEiXr6+DB1qZehQ180EBJhN7u680xk7dw5CQsDLC06cgCpVzLiPtQLhDcMJbxhu/jjDzs6TOx3F0YaUDRw4d4B6lepRklhv9Q6IiIiIiEgRhIaabb5feMEZO3PGLJIqV3Ytnt5/32zK8N57hTYzdCgkJJjLl/IdPGg2bAgIcBZCYHava9YMvv3WfG+1WGlTqw1PdnqSL+/+khV/2s3/GEvoU33oTTxQ91MxJCIiIiJS0vn7mwuATp40p3XybdliTvdUqOCMnT1rdrJ7+eVCbemCg+H4cfOWuoLWrze72JUv74z9978wYIDZ9rtJE0/eGxdN5zY1mTr15h+eu+g2ORERERGR0sLb2/X9/PmQlAT16ztj69eb65BOnIA333TGv/oKvLyw9OlDjRrVXTazaZNZIHXv7ozFx8OiRfnvzKYPdrvF8cyj6+1AfitpZkhEREREpLTy9IROnaBWLWesUyeYOhVGj3YdO3YsPPggbN3qjJ06Bbt2UbWKQb9+4Ofn/CgiAp56qvCPzH/mUUmgYkhEREREpCypXRv+/GcYNswZy82F/v2hQwdzTVK+OXMgKMjs2V2Q3U6zZvDSS+YzjwrKf+ZRSaBiSERERESkrPP0hAkTzL7alSs747/8Yrb8bt/eGcvONmeaevfGVuEsU4asxYNcADzIZfIja0vELXKgYkhERERERK7ktdfMh8E+/7wz9sMPcPo07NgBGRnEfNmLQzRgNeafMV+Fw5Ejt26fi0ANFERERERE5Mq8vV0bM3TuDDt3QkqKuTjIbsfGUWwcNT/Pw4yXgOkhFUMiIiIiInL9rFZzHVFQkDkDZLW6tuguQYuGinybXEJCAgMGDKBu3bpYLBbmz59/ze/Ex8fTsWNHfH19adSoEZMmTSo0JjY2lqCgIHx8fAgKCmLevHlF3TURERERESlONhtMmYLh4QFg/jl5comYFYIbKIYyMzNp164dH3/88XWNP3jwIP369aNHjx4kJiby0ksv8dxzzxEbG+sYs3HjRh544AGGDBnCjh07GDJkCIMHD2bz5s1F3T0RERERESlOMTHk7tvHujfeIHffPoiJudV7dN2KfJtcdHQ00dHR1z1+0qRJBAQEMH78eABatmzJtm3beP/997n33nsBGD9+PBEREYwZMwaAMWPGEB8fz/jx45k1a1ZRd1FERERERIqTzcaZNm1KzIxQPrd3k9u4cSORkZEusaioKLZt20ZOTs5Vx2zYsMHduyciIiIiImWU2xsopKWlUavgE2+BWrVqkZuby+nTp6lTp84Vx6SlpV1xu1lZWWRlZTnep6enA5CTk+Mosm6V/J9/q/ejtFJ+3Uv5dS/l172UX/dSft1L+XUv5de9brf8Xu9+FEs3OYvF4vLeMIxC8cuN+X2soLfffptx48YVii9fvpzy5cv/kd29aeLi4m71LpRqyq97Kb/upfy6l/LrXsqveym/7qX8utftkt+LFy9e1zi3F0O1a9cuNMNz8uRJPD09qV69+lXH/H62qKAxY8YwatQox/v09HTq169PZGQkfn5+N/EIii4nJ4e4uDgiIiLw8vK6pftSGim/7qX8upfy617Kr3spv+6l/LqX8utet1t+8+8auxa3F0OhoaF89913LrHly5fTqVMnR6JCQ0OJi4tj5MiRLmO6det2xe36+Pjg4+NTKO7l5XVb/AeA22tfSiPl172UX/dSft1L+XUv5de9lF/3Un7d63bJ7/XuQ5GLoYyMDJKTkx3vDx48SFJSEtWqVSMgIIAxY8Zw9OhRZsyYAcCTTz7Jxx9/zKhRo3jiiSfYuHEjU6dOdekS9/zzzxMWFsa7777LwIEDWbBgAStWrGDdunVF3T0REREREZHrUuRuctu2bSM4OJjg4GAARo0aRXBwMK+99hoAx48fJyUlxTG+YcOGLFmyhDVr1tC+fXveeOMNJk6c6GirDdCtWzdmz57NtGnTaNu2LdOnT2fOnDl06dLljx6fiIiIiIjIZRV5ZqhXr16OBgiXM3369EKxnj178sMPP1x1u/fddx/33XdfUXdHRERERETkhhRLN7nikF+gXe9iKXfKycnh4sWLpKen3xb3TJY2yq97Kb/upfy6l/LrXsqveym/7qX8utftlt/8muBqkzhQioqhCxcuAFC/fv1bvCciIiIiInI7uHDhApUrV77i5xbjWuVSCWG32zl27BiVKlW66vOJikN+m+/U1NRb3ua7NFJ+3Uv5dS/l172UX/dSft1L+XUv5de9brf8GobBhQsXqFu3LlbrldsklJqZIavVis1mu9W74cLPz++2OBlKK+XXvZRf91J+3Uv5dS/l172UX/dSft3rdsrv1WaE8hW5m5yIiIiIiEhpoGJIRERERETKJBVDbuDj48Prr7+Oj4/Prd6VUkn5dS/l172UX/dSft1L+XUv5de9lF/3Kqn5LTUNFERERERERIpCM0MiIiIiIlImqRgSEREREZEyScWQiIiIiIiUSSqGRERERESkTFIxdB3+/e9/07BhQ3x9fenYsSNr16696vj4+Hg6duyIr68vjRo1YtKkSYXGxMbGEhQUhI+PD0FBQcybN89du3/bK0p+586dS0REBP7+/vj5+REaGsqyZctcxkyfPh2LxVLodenSJXcfym2pKPlds2bNZXO3e/dul3E6f10VJcdDhw69bI5btWrlGKNz2JSQkMCAAQOoW7cuFouF+fPnX/M7uv5ev6LmV9ffoilqfnX9LZqi5lfX3qJ5++23CQkJoVKlStSsWZNBgwaxZ8+ea36vJF6DVQxdw5w5c3jhhRd4+eWXSUxMpEePHkRHR5OSknLZ8QcPHqRfv3706NGDxMREXnrpJZ577jliY2MdYzZu3MgDDzzAkCFD2LFjB0OGDGHw4MFs3ry5uA7rtlHU/CYkJBAREcGSJUvYvn074eHhDBgwgMTERJdxfn5+HD9+3OXl6+tbHId0WylqfvPt2bPHJXdNmzZ1fKbz11VRczxhwgSX3KamplKtWjXuv/9+l3E6hyEzM5N27drx8ccfX9d4XX+Lpqj51fW3aIqa33y6/l6fouZX196iiY+P5+mnn2bTpk3ExcWRm5tLZGQkmZmZV/xOib0GG3JVnTt3Np588kmXWIsWLYzRo0dfdvyLL75otGjRwiU2YsQIo2vXro73gwcPNvr27esyJioqynjwwQdv0l6XHEXN7+UEBQUZ48aNc7yfNm2aUbly5Zu1iyVaUfO7evVqAzDOnj17xW3q/HX1R8/hefPmGRaLxTh06JAjpnO4MMCYN2/eVcfo+nvjrie/l6Pr7/W5nvzq+nvjbuT81bW3aE6ePGkARnx8/BXHlNRrsGaGriI7O5vt27cTGRnpEo+MjGTDhg2X/c7GjRsLjY+KimLbtm3k5ORcdcyVtlla3Uh+f89ut3PhwgWqVavmEs/IyCAwMBCbzcZdd91V6DeXZcEfyW9wcDB16tShd+/erF692uUznb9ON+Mcnjp1Kn369CEwMNAlrnO46HT9LV66/rqHrr/FQ9feojl//jxAof/fCyqp12AVQ1dx+vRp8vLyqFWrlku8Vq1apKWlXfY7aWlplx2fm5vL6dOnrzrmStssrW4kv7/3wQcfkJmZyeDBgx2xFi1aMH36dBYuXMisWbPw9fXljjvuYN++fTd1/293N5LfOnXqMGXKFGJjY5k7dy7Nmzend+/eJCQkOMbo/HX6o+fw8ePH+f7773n88cdd4jqHb4yuv8VL19+bS9ff4qNrb9EYhsGoUaPo3r07rVu3vuK4knoN9rxlP7kEsVgsLu8NwygUu9b438eLus3S7EZzMWvWLMaOHcuCBQuoWbOmI961a1e6du3qeH/HHXfQoUMHPvroIyZOnHjzdryEKEp+mzdvTvPmzR3vQ0NDSU1N5f333ycsLOyGtlkW3Gg+pk+fTpUqVRg0aJBLXOfwjdP1t3jo+nvz6fpbfHTtLZpnnnmGH3/8kXXr1l1zbEm8Bmtm6Cpq1KiBh4dHoWr15MmTharafLVr177seE9PT6pXr37VMVfaZml1I/nNN2fOHGJiYvj666/p06fPVcdarVZCQkLK3G92/kh+C+ratatL7nT+Ov2RHBuGwX/+8x+GDBmCt7f3VceW1XO4qHT9LR66/hYfXX9vPl17i+bZZ59l4cKFrF69GpvNdtWxJfUarGLoKry9venYsSNxcXEu8bi4OLp163bZ74SGhhYav3z5cjp16oSXl9dVx1xpm6XVjeQXzN9IDh06lJkzZ9K/f/9r/hzDMEhKSqJOnTp/eJ9LkhvN7+8lJia65E7nr9MfyXF8fDzJycnExMRc8+eU1XO4qHT9dT9df4uXrr83n66918cwDJ555hnmzp3LqlWraNiw4TW/U2KvwcXbr6HkmT17tuHl5WVMnTrV+Pnnn40XXnjBqFChgqP7yOjRo40hQ4Y4xh84cMAoX768MXLkSOPnn382pk6danh5eRnffvutY8z69esNDw8P45133jF27dplvPPOO4anp6exadOmYj++W62o+Z05c6bh6elpfPLJJ8bx48cdr3PnzjnGjB071li6dKmxf/9+IzEx0Rg2bJjh6elpbN68udiP71Yran4//PBDY968ecbevXuN//73v8bo0aMNwIiNjXWM0fnrqqg5zvfII48YXbp0uew2dQ6bLly4YCQmJhqJiYkGYPzrX/8yEhMTjcOHDxuGoevvH1XU/Or6WzRFza+uv0VT1Pzm07X3+jz11FNG5cqVjTVr1rj8/37x4kXHmNJyDVYxdB0++eQTIzAw0PD29jY6dOjg0lbwscceM3r27Okyfs2aNUZwcLDh7e1tNGjQwPj0008LbfObb74xmjdvbnh5eRktWrRwudiVNUXJb8+ePQ2g0Ouxxx5zjHnhhReMgIAAw9vb2/D39zciIyONDRs2FOMR3V6Kkt93333XaNy4seHr62tUrVrV6N69u7F48eJC29T566qo14hz584Z5cqVM6ZMmXLZ7ekcNuW3Gr7S/++6/v4xRc2vrr9FU9T86vpbNDdyfdC19/pdLreAMW3aNMeY0nINthjGbyubREREREREyhCtGRIRERERkTJJxZCIiIiIiJRJKoZERERERKRMUjEkIiIiIiJlkoohEREREREpk1QMiYiIiIhImaRiSEREREREyiQVQyIiIiIiUiapGBIRERERkTJJxZCIiIiIiJRJKoZERERERKRMUjEkIiIiIiJl0v8HIHL/Jy0h18EAAAAASUVORK5CYII=",
      "text/plain": [
       "Figure(PyObject <Figure size 1000x400 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# You could experiment by changing these values here.\n",
    "k = -0.5\n",
    "u_0 = 3.0\n",
    "a = 0.0\n",
    "b = 2.0\n",
    "\n",
    "(t, U) = eulermethod(f2, a, b, u_0, n)\n",
    "(t10, U10) = eulermethod(f2, a, b, u_0, 10)\n",
    "(t20, U20) = eulermethod(f2, a, b, u_0, 20)\n",
    "t = t20\n",
    "u = u2.(t, a, u_0, k)\n",
    "\n",
    "figure(figsize=[10,4])\n",
    "title(\"The exact solution is y = $u_0 exp($k t)\")\n",
    "plot(t, u, \"g\", label=\"Exact solution\")\n",
    "plot(t10, U10, \".:r\", label=\"Euler's answer for h=$(approx4((b-a)/10))\")\n",
    "plot(t20, U20, \".:b\", label=\"Euler's answer for h=$(approx4((b-a)/20))\")\n",
    "legend()\n",
    "grid(true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solving for {prf:ref}`ode-nonlinear`: solutions that blow up"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "f3(t, u) = u^2\n",
    "# The solution is u(t) = 1/((a + 1/u_0) - t), = 1/(T-t) with T = a + 1/u_0\n",
    "u3(t, a, u_0) = 1.0 / ((a + 1.0/u_0) - t);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 1000x400 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 0.0\n",
    "b = 0.9\n",
    "u_0 = 1.0\n",
    "\n",
    "(t100, U100) = eulermethod(f3, a, b, u_0, 100)\n",
    "(t200, U200) = eulermethod(f3, a, b, u_0, 200)\n",
    "t = t200\n",
    "u = u3.(t, a, u_0)\n",
    "\n",
    "T = a + 1/u_0\n",
    "\n",
    "figure(figsize=[10,4])\n",
    "title(\"The exact solution is u = 1/($T - t)\")\n",
    "plot(t, u, \"g\", label=\"Exact solution\")\n",
    "plot(t100, U100, \".:r\", label=\"Euler's answer for h=$(approx4((b-a)/100))\")\n",
    "plot(t200, U200, \".:b\", label=\"Euler's answer for h=$(approx4((b-a)/200))\")\n",
    "legend()\n",
    "grid(true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is clearly a problem when $t$ reaches 1; let us explore that:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 1000x400 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 0.0\n",
    "b = 0.999\n",
    "u_0 = 1.0\n",
    "n = 200\n",
    "\n",
    "(t, U) = eulermethod(f3, a, b, u_0, n)\n",
    "# More t values are needed to get a good graph of the exact solution near the vertical asymptote:\n",
    "tplot = range(a, b, 1000)\n",
    "u = u3.(tplot, a, u_0)\n",
    "T = a + 1/u_0\n",
    "\n",
    "figure(figsize=[10,4])\n",
    "title(\"The exact solution is u = 1/($T - t)\")\n",
    "plot(tplot, u, \"g\", label=\"Exact solution\")\n",
    "plot(t, U, \":b\", label=\"Euler's answer for h=$(approx4((b-a)/n))\")\n",
    "legend()\n",
    "grid(true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Clearly Euler's method can never produce the vertical asymptote.\n",
    "\n",
    "The best we can do is improve accuracy by using more, smaller time steps:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 1000x400 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "b= 0.999\n",
    "n = 10_000;  # Julia note: underscores can be used in numbers for readability, like commas (or spaces in some countries)\n",
    "\n",
    "(t, U) = eulermethod(f3, a, b, u_0, n)\n",
    "tplot = range(a, b, 1000)\n",
    "u = u3.(tplot, a, u_0)\n",
    "T = a + 1/u_0\n",
    "\n",
    "figure(figsize=[10,4])\n",
    "title(\"The exact solution is u = 1/($T - t)\")\n",
    "plot(tplot, u, \"g\", label=\"Exact solution\")\n",
    "plot(t, U, \":b\", label=\"Euler's answer for h=$(approx4((b-a)/n))\")\n",
    "legend()\n",
    "grid(true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solving for Solving for {prf:ref}`ode-stiff`, a stiff ODE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "f4(t, u) = -sin(t) - k*(u - cos(t));\n",
    "# The parameter k may be defined later, so long as that is done before this function is used.\n",
    "# The general solution is u(t) = u(t; a, u_0) = cos t + (u_0 - cos(a)) e^(k (a-t))\n",
    "u4(t, a, u_0, k) = cos(t) + (u_0 - cos(a)) * exp(k*(a-t));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With enough steps (small enough step size $h$), all is well:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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s2bIEZ3o+lJT3ka2tLTExMTx79ixecaQoCsHBwbozZwCenp54enoSGxvLqVOnmDVrFn379sXBwYHmzZsn7eCSoECBAvGex31BL1q0aKoO3BB35uTixYvUrl073ryLFy9+9syKnZ0dtra27N69O9H5lpaW8Z6PGjWKixcv4u7uzsiRI6lbty65c+dOsF5wcHCi0z78UcDOzo4zZ84kWG7btm3x3ptxP3pcunSJu3fvJlp0tW3bFvjffYKKFi3KunXriImJiXedUdwgEZ97XYoWLapb9kNJXf9z4gqslC6chUgvpCudEAKAChUqkClTJq5cuUKpUqUSfXzs11yAunXrcvv2bWxtbRNd98MvaYsXL2b16tXMnj2brVu38vr1a9q3bx9vexqNRncGI86FCxcSdFGrVasW7969++y9X4yNjb/oV1Fzc3Nq1arFsGHDiIqK0l3sXLVqVfbv368rhOKsXLkSMzOzjxaX8H70sadPn+rO0sH7Ebn++eefL85doEABsmbNytq1a+MNNBAeHs6mTZt0I9WlNGNjY7y8vPj1118BEowA9iEHBwdMTEy4cOFCvOl///13kvf3tbrSJeV9VLVqVeB90f6hTZs2ER4erpv/IX19fcqWLcucOXMAEv0C/qEvfZ+qLWvWrJQpU4bVq1fHG9Dl2LFjXL9+nUaNGn1y/bp16/LixQtiY2MT/fvxYQHo6+vLxIkTGT58OL6+vlhbW9OsWbNEB7ZYt25dvM/DvXv38Pf3jzcqZcGCBXnx4kWCERmLFi0aL0NcYTR9+nQOHDgQ7/H7778D70d8PHDgABYWFgA0bNiQsLAwNm3aFG/bK1aswNnZmbJly37ydWnYsCHXrl2LN3pdTEwMq1evpmzZsrpMH/O591NcN8/ChQt/cjtCZBRyxkgIAby/FmXWrFm0bduWly9f8v3332Nvb8+zZ884f/48z549S3D25kN9+/Zl06ZNVKpUiX79+lGsWDG0Wi33799nz549DBgwgLJly3Lx4kV69+5N27ZtdcXQkiVL+P7775k+fTp9+/YF3n9R+uWXXxg1ahReXl5cv36dsWPHkitXrnijnf3www8sW7aMbt26cf36dSpXroxWq+X48eMUKlRI9+t80aJF8fPzY9u2bTg5OWFpaZng1/Y4nTt3xtTUlAoVKuDk5ERwcDATJ07E2tpad1Zg1KhRbN++ncqVKzNy5EgyZ87MmjVr2LFjB5MnT8ba2vqjr1WzZs0YOXIkzZs356effuLdu3fMnDkz3hfKOEnNraenx+TJk2nZsiV169ala9euREZGMmXKFF6/fs2kSZM+mue/GjlyJA8fPqRq1apky5aN169fM2PGDAwNDfHy8vroehqNhlatWrF06VLy5MmDm5sbJ06cSNKNL+OUKlXqaxxCkt5H1atXp0aNGgwePJjQ0FAqVKjAhQsXGDVqFCVKlNAN9zx//nz2799PnTp1yJ49O+/evdOdSY27BuhjihYtyvr169mwYQO5c+fGxMQkwUhrKeXZs2e6m4bGnZHYtWsXWbJkIUuWLPHa0sDAAC8vr3ijVf76669Ur16dJk2a0KNHD54+fcqQIUMoUqRIgh8+/q158+asWbOG2rVr06dPH8qUKYOhoSEPHz7kwIED1K9fn4YNGxIUFESrVq3w8vJi1KhR6OnpsWHDBipVqsSgQYMS3Mz06dOnNGzYkM6dOxMSEsKoUaMwMTFh6NChumW8vb1RFIXjx4/j4+Pz2dfpU903XV1d4xVdtWrVonr16nTv3p3Q0FDy5s3LunXr2L17N6tXr47XxbNjx46sWLGC27dvkyNHDgA6dOjAnDlzaNKkCZMmTcLe3p65c+dy/fp19u7d+9msRYsW5a+//mLevHm4u7ujp6cX7zNz7NgxbG1tU+09JkSap+7YD0KIr+FLbvD6sRHBDh48qNSpU0fJnDmzYmhoqGTNmlWpU6dOkm4QGxYWpgwfPlwpUKCAYmRkpFhbWytFixZV+vXrpwQHBythYWFKwYIFlcKFCyvh4eHx1u3Zs6diaGioHD9+XFEURYmMjFQGDhyoZM2aVTExMVFKliypbNmyJdER3d6+fauMHDlSyZcvn2JkZKTY2toqVapUiXdTxHPnzikVKlRQzMzMFOCTI3+tWLFCqVy5suLg4KAYGRkpzs7OStOmTZULFy7EW+7ixYtKvXr1FGtra8XIyEhxc3NL8Hp+7HXeuXOnUrx4ccXU1FTJnTu3Mnv27ERHpftY7n+PShdny5YtStmyZRUTExPF3NxcqVq1qnL06NF4y8Tt59mzZ/GmL1u2LEkjkf27DbZv367UqlVLyZo1q2JkZKTY29srtWvXVg4fPvzJ7SiKooSEhCidOnVSHBwcFHNzc6VevXrK3bt3kzwq3deUlPfR27dvlcGDBys5cuRQDA0NFScnJ6V79+7Kq1evdMsEBAQoDRs2VHLkyKEYGxsrtra2ipeXl7J169bPZrh7967i4+OjWFpaKsAnRxRLzH+5wWvcuok9/v15+dhnaM+ePYqHh4diYmKiZM6cWWnTpo3y5MmTJO0/OjpamTp1quLm5qaYmJgoFhYWSsGCBZWuXbsqN2/eVGJiYhQvLy/FwcFBCQoKirdu3Ch6mzdvjncsq1atUnr37q1kyZJFMTY2Vjw9PZVTp07FWzc2NlbJmTOn0qNHjyS/Vv/2qRtpv3nzRundu7fi6OioGBkZKcWKFVPWrVuXYLm2bdsm2nbBwcFKmzZtlMyZMysmJiaKh4eH4uvrm6RcL1++VL7//nslU6ZMikajiff3RavVKjly5FB+/PHH5B2sEN8wjaJ85uYOQgghhBDpiJ+fH5UrV+bPP//85IAycaZNm8b48eN59OgRpqamqZBQffv27cPHx4fLly9TsGBBteMIkSbINUZCCCGEyNB69uyJtbW17lqwjGDcuHF06NBBiiIhPiCFkRBCCCEyNBMTE1atWpVgwJdv1atXr/Dy8mL8+PFqRxEiTZGudEIIIYQQQogMT84YCSGEEEIIITI8KYyEEEIIIYQQGZ4URkIIIYQQQogM75u7watWq+Xx48dYWlqi0WjUjiOEEEIIIYRQiaIovHnzBmdnZ/T0Pn1O6JsrjB4/foyLi4vaMYQQQgghhBBpxIMHD8iWLdsnl/nmCiNLS0vg/cFbWVmpnAaio6PZs2cPPj4+GBoaqh1HJJO0X/om7Ze+Sfulb9J+6Zu0X/om7fc/oaGhuLi46GqET/nmCqO47nNWVlZppjAyMzPDysoqw78x0yNpv/RN2i99k/ZL36T90jdpv/RN2i+hpFxiI4MvCCGEEEIIITI8KYyEEEIIIYQQGZ4URkIIIYQQQogM75u7xkgIIYQQGVdsbCzR0dFqx0j3oqOjMTAw4N27d8TGxqodRyRTRms/Q0ND9PX1//N2pDASQgghRLqnKArBwcG8fv1a7SjfBEVRcHR05MGDB3JfyHQoI7ZfpkyZcHR0/E/HK4WREEIIIdK9uKLI3t4eMzOzDPNlMKVotVrCwsKwsLD47E0xRdqTkdpPURQiIiJ4+vQpAE5OTl+8LSmMhBBCCJGuxcbG6ooiW1tbteN8E7RaLVFRUZiYmHzzX6y/RRmt/UxNTQF4+vQp9vb2X9ytLkVfqYkTJ1K6dGksLS2xt7enQYMGXL9+/bPrHTx4EHd3d0xMTMidOzfz589PyZhCCCGESMfirikyMzNTOYkQQi1xn///co1hihZGBw8epGfPnhw7dgxfX19iYmLw8fEhPDz8o+sEBgZSu3ZtPD09OXv2LD///DO9e/dm06ZNKRlVCCGEEOmcdJ8TIuP6Gp//FO1Kt3v37njPly1bhr29PadPn6ZSpUqJrjN//nyyZ8/O9OnTAShUqBCnTp1i6tSpNG7cOCXjCiGEEEIIITKoVL3GKCQkBIDMmTN/dJmAgAB8fHziTatRowZLliwhOjoaQ0PDePMiIyOJjIzUPQ8NDQXen0ZTe7hO3zu+TDgyAZt3NlSPrq5qFvFl4t5Dar+XxJeR9kvfpP3St9Rsv+joaBRFQavVotVqU3x/GYGiKLr/fq3XVF9fn02bNtGgQYP/tJ3cuXPTp08f+vTp81VyfcyWLVsYNGgQgYGB9OrVi99///2rbbtKlSq4ubl91W1+KCXaL63TarUoikJ0dHS8a4yS8zco1QojRVHo378/FStWpEiRIh9dLjg4GAcHh3jTHBwciImJ4fnz5wlGmpg4cSJjxoxJsJ09e/ao3td4w4mHHN0wnMxOz/DN5qtqFvHf+PpK+6Vn0n7pm7Rf+pYa7WdgYICjoyNhYWFERUWl+P6+ph49erBu3boE06tWrcrGjRtTJcOkSZPYsWMHhw8fTjDvzZs3X3Vfb9++1f2I/Tlr165l6NCh3Lt3L970vXv3YmZmluTtfKlu3brRokULunbtioWFxVfdX0xMDFFRUSlyDH379mXFihVMmDCB7t2766ZHRkYyYsQINm3axLt376hUqRJTp04la9asn9ze4sWLmTVrFk+ePKFgwYJMmDCB8uXLf/Xc/1VUVBRv377l0KFDxMTE6KZHREQkeRupVhj16tWLCxcucOTIkc8u++8+gnFVb2J9B4cOHUr//v11z0NDQ3FxccHHxwcrK6v/mPq/OfbgNNz2IDz6LNWrF0hwtkukfdHR0fj6+lK9enVpv3RI2i99k/ZL31Kz/d69e8eDBw+wsLDAxMQkRff1tRkaGlKjRg2WLl0ab7qxsXGqfY8xNjZGX18/3v4UReHNmzdYWlp+1Wu3TE1Nk3xcJiYmaDSaBMunxusSFhbGs2fPqFevHgUKFPji7URFRWFkZJRguoGBAUZGRl/9WLZs2cK5c+dwdnYGiNd+PXr0YOfOnaxbtw5bW1t++uknWrZsycmTJz86ituGDRv4+eefmT17NhUqVGDhwoU0bdqUS5cukT179q+a/b969+4dpqamVKpUKd7fgWQVn0oq6NWrl5ItWzblzp07n13W09NT6d27d7xpf/31l2JgYKBERUV9dv2QkBAFUEJCQr4479ey/shRhQatlSwdWiQpu0h7oqKilC1btkj7pVPSfumbtF/6lprt9/btW+XKlSvK27dvU3xfX1vbtm2V+vXrf3T+gQMHFENDQ+XQoUO6aVOnTlVsbW2Vx48fK4qiKLt27VIqVKigWFtbK5kzZ1bq1Kmj3Lp1K952Hjx4oDRr1kyxsbFRzMzMFHd3d+XYsWPKsmXLFCDeY9myZUpsbKzy6tUrJTY2Nl6W0qVLK2ZmZoq1tbVSvnx55e7du7r5c+fOVXLnzq0YGhoq+fPnV1auXBkvA6Bs3rxZty1AefXqlW7+2bNnFUAJDAzUzf/wMWrUKEVRFCVHjhzK77//rlvv3r17ynfffaeYm5srlpaWSpMmTZTg4GDd/FGjRilubm7KypUrlRw5cihWVlZKs2bNlNDQ0I++5v/e94EDBxRFUZSNGzcqhQsXVoyMjJQcOXIoU6dOjbdujhw5lF9++UVp27atYmVlpbRp0ybRfXh5eSl9+vTRPd+1a5diZWWlrFixItHlk+Lhw4dK1qxZlUuXLik5cuRQJkyYoGu/169fK4aGhsr69et1yz969EjR09NTdu/e/dFtlilTRunWrVu8aQULFlSGDBnyxTlTysf+DiSnNkjRUekURaFXr1789ddf7N+/n1y5cn12nXLlyiU47b5nzx5KlSqV7n4xzJlDH4qvQpN3r9pRhBBCiAxFURTCo8JVeSj/39Pla/D29qZv3760bt2akJAQzp8/z7Bhw1i0aJHu8oLw8HD69+/PyZMn2bdvH3p6ejRs2FB3bUlYWBheXl48fvyYrVu3cv78eQYNGoRWq6VZs2YMGDAAV1dXgoKCCAoKolmzZglyxMTE0KBBA7y8vLhw4QIBAQF06dJFdzZi8+bN9OnThwEDBnDp0iW6du1K+/btOXDgwBcdd/ny5Zk+fTpWVla6XAMHDkywnKIoNGjQgJcvX3Lw4EF8fX25fft2gmO4ffs2W7ZsYfv27Wzfvp2DBw8yadKkj+477vYymzZtIigoiPLly3P69GmaNm1K8+bNuXjxIqNHj2bEiBEsX7483vpTpkyhSJEinD59mhEjRnz2WNevX0/Tpk1ZuXIlbdq0AWDNmjVYWFh88rFmzRrdNrRaLa1bt+ann37C1dU1wT5Onz5NdHR0vOv4nZ2dKVKkCP7+/onmioqK4vTp0wmu/ffx8fnoOuldinal69mzJ2vXruXvv//G0tKS4OBgAKytrXU3Yho6dCiPHj1i5cqVwPv+nLNnz6Z///507tyZgIAAlixZkmj/27TOzPD9NU6R2sjPLCmEEEKIrykiOgKLiRaq7DtsaBjmRuZJXn779u1YWMTPOnjwYN2X6nHjxrF37166dOnC5cuXad26NQ0bNtQt++9Re5csWYK9vT1XrlyhSJEirF27lmfPnnHy5EndAFh58+bVLW9hYaG7TivOvy/YDw0NJSQkhLp165InTx7g/cjBcaZOnUq7du3o0aMHAP379+fYsWNMnTqVypUrJ/m1iGNkZIS1tTUajSZern/bu3cvFy5cIDAwEBcXFwBWrVqFq6srJ0+epHTp0rrjWb58OZaWlgC0bt2affv2MX78+ET3bW9vD7wfMCxu/7/99htVq1bVtUv+/Pm5cuUKU6ZMoV27drr1q1SpkmgRl5i5c+fy888/8/fff8d7nb777jvKli37yXU/vCb/119/xcDAgN69eye6bHBwMEZGRtjY2CTYRtz38397/vw5sbGxiV77/7F10rsULYzmzZsHvP+140PLli3TvYGCgoK4f/++bl6uXLnYuXMn/fr1Y86cOTg7OzNz5sx0OVS3gdYCHpfgrcZU7ShCCCGESKMqV66s+84U58MRfI2MjFi9ejXFihUjR44culuaxLl9+zYjRozg2LFjPH/+XFfU3L9/nyJFinDu3DlKlCjxyVGBPydz5sy0a9eOGjVqUL16dapVq0bTpk11Z62uXr1Kly5d4q1ToUIFZsyY8cX7TIqrV6/i4uKiK4oAChcuTKZMmbh69aquMMqZM6euKAJwcnLi6dOnyd5X/fr1402rUKEC06dPJzY2VnedTqlSpZK0vU2bNvHkyROOHDlCmTJl4s2ztLSMl/dTTp8+zYwZMzhz5kyyrwdTFOWz6yR27f+3es+wFC2MknIq+d+nHwG8vLw4c+ZMCiRKXc8fW8DCM0SZvkCZ+fVOqwshhBDi08wMzQgbGqbavpPD3Nw83hmcxMR1XXr58iUvX77E3Px/Z6Tq1auHi4sLixYtwtnZGa1WS5EiRXQj9MX10vmvli1bRu/evdm9ezcbNmxg+PDh+Pr64uHhASTvC7Senp5umThfMrT7x/bx7+n/vhxDo9EkexjrxPaV2HfdD9vmU4oXL86ZM2dYtmwZpUuXjrftNWvW0LVr10+uv2DBAlq2bMnhw4d5+vRpvMEQYmNjGT58OAsWLODu3bs4OjoSFRXFq1ev4p01evr06UdHmLOzs0NfXz/B2aGnT58mOIv0rUjV+xhlNJmtTMDyIZi+4l1MjkRHJRFCCCHE16fRaJLVnS0tu337Nv369WPRokX88ccftGnTRnct0YsXL7h69SoLFizA09MTIMEIwMWKFWPx4sW8fPky0bNGRkZGxMbGJilLiRIlKFGiBEOHDqVcuXKsXbsWDw8PChUqxJEjR3TXyMD7Yu7D7nYfypIlC/C+51DcF/Vz584lO1fhwoW5f/8+Dx480J01unLlCiEhIR/d95cqXLhwgtfW39+f/Pnzf3RUt0/JkycP06ZNw9vbG319fWbPnq2bl5yudK1bt6ZatWrx5tWoUYMmTZroiit3d3cMDQ3x9fWladOmwPvX/tKlS0yePDnR7RsZGeHu7o6vr2+8rpu+vr4Jzpx9K6QwSkEF8pjCgPfDMEZEB2GFusOHCyGEECLtiYyMTPCrvIGBAXZ2dsTGxtK6dWt8fHxo3749tWrVomjRokybNo2ffvoJGxsbbG1tWbhwIU5OTty/f58hQ4bE29YPP/zAhAkTaNCgARMnTsTJyYmzZ8/i7OxMuXLlyJkzJ4GBgZw7d45s2bJhaWmZ4AxLYGAgCxcu5LvvvsPZ2Znr169z48YNXSH0008/0bRpU0qWLEnVqlXZtm0bf/31F3v3Jj4AVd68eXFxcWH06NGMGzeOmzdvMm3atHjL5MyZk7CwMPbt24ebmxtmZmYJ7lFZrVo1ihUrRsuWLZk+fToxMTH06NEDLy+vJHdpS6oBAwZQunRpfvnlF5o1a0ZAQACzZ89m7ty5X7zN/Pnzc+DAAby9vTEwMNB1k0xOVzpbW1tsbW3jTTM0NMTBwUE31Li1tTUdO3ZkwIAB2NrakjlzZgYOHEjRokXjFVVVq1alYcOG9OrVC3h/rVjr1q0pVaoU5cqVY+HChdy/f59u3bp98TGnZSk6Kl1GZ6BngJH++7NEETFJv7mUEEIIITKO3bt34+TkFO9RsWJFAMaPH8/du3dZuHAhAI6OjixevJjhw4dz7tw59PT0WL9+PadPn6ZIkSL069ePKVOmxNu+kZERe/bswd7entq1a1O0aFEmTZqkO8vRuHFjatasSeXKlcmSJUuiA16ZmZlx7do1GjduTP78+enSpQu9evXSnZFo0KABM2bMYMqUKbi6urJgwQKWLVuW4DrzOIaGhqxbt45r167h5ubGr7/+yrhx4+ItU758ebp160azZs3IkiVLomc2NBoNW7ZswcbGhkqVKlGtWjVy587Nhg0bktcISVCyZEn++OMP1q9fT5EiRRg5ciRjx46NN/DClyhQoAD79+9n3bp1DBgw4OuETcTvv/9OgwYNaNq0KRUqVMDMzIxt27bFO9t1+/Ztnj9/rnverFkzpk+fztixYylevDiHDh1i586d5MiRI8VyqkmjfM0xJdOA0NBQrK2tCQkJUf0GrwCZf83Mq3evuNDlAkWdiqodRyRTdHQ0O3fupHbt2uluuHgh7ZfeSfulb6nZfu/evSMwMJBcuXKluxu8plVarZbQ0FCsrKx01wOJ9CMjtt/H/g4kpzaQrnQpSFHg7dpV8Fbh2fdR4KR2IiGEEEIIIURipDBKQRoNvLvkA1pDXoR8mzfCEkIIIYQQ4lsghVEKy9Z8Eg/D7qIxaaJ2FCGEEEIIIcRHZIxOhypyqbILSi5FMXqjdhQhhBBCCCHER0hhlMLMDN4PKxkRLaPSCSGEEEIIkVZJYZTSXueC4KK8fJ38uzkLIYQQQgghUocURins5LSRMP8C1y+qP3S4EEIIIYQQInFSGKUwM+swMA8mMiZS7ShCCCGEEEKIj5DCKIV9P2ku/OSEQ9HLakcRQgghhBBCfIQURinM1NAUgLfRb1VOIoQQQohvkZ+fHxqNhtevX6sd5Zt19OhRihYtiqGhIQ0aNPiq227Xrt1X36b4MlIYpTAzQxmVTgghhBCJa9euHRqNJsGjZs2aquTRaDTcvXtXlX2nZf3796d48eIEBgayfPlyteN81qtXr+jatSs2NjZYW1vTunXrzxbOiqIwevRonJ2dMTU1xdvbm8uX4/d4WrhwId7e3lhZWX20GM+ZM2eC9/OQIUN085cvX57oe16j0fD06VMA3r17R7t27ShatCgGBgapVjhKYZTCzv1dEf5cx80TedSOIoQQQog0qGbNmgQFBcV7rFu3LlUzREVFper+0qLY2Fi0Wm2i827fvk2VKlXIli0bmTJl+qLtp+Zr3LJlSy5evMjOnTvZvXs3586do3Xr1p9cZ/Lkyfz222/Mnj2bkydP4ujoSPXq1Xnz5n/34oyIiKBmzZr8/PPPn9zW2LFj472fhw8frpvXrFmzBO/3GjVq4OXlhb29PfC+LUxNTenduzfVqlX7D69E8khhlMIeXs0Ol5vz4kEWtaMIIYQQIg0yNjbG0dEx3sPGxgaAu3fvotFoOHfunG75169fo9Fo8PPz++g2/f39qVSpEqampri4uNC7d2/Cw8N183PmzMm4ceNo164d1tbWdO7cOcE2Xr9+TatWrciSJQumpqbky5ePZcuWfXSfu3fvpmLFimTKlAlbW1vq1q3L7du3dfPjjuWvv/6icuXKmJmZ4ebmRkBAgG6Ze/fuUa9ePWxsbDA3N8fV1ZWdO3cC4O7uzrRp03TLNmjQAAMDA0JDQwEIDg5Go9Fw/fp14H0hMmjQILJmzYq5uTlly5aN95otX76cTJkysX37dgoXLoyxsTH37t2Ld0xxmV+8eEGHDh3QaDS6M0YHDx6kTJkyGBsb4+TkxJAhQ4iJidGt6+3tTa9evejfvz92dnZUr179o68dwNSpU3FycsLW1paePXsSHf1lt3q5evUq//zzDzNnzqRcuXKUK1eORYsWsX37dt1r82+KojB9+nSGDRtGo0aNKFKkCCtWrCAiIoK1a9fqluvbty9DhgzBw8PjkxksLS3jvZ8tLCx080xNTePN09fXZ//+/XTs2FG3jLm5OfPmzaNz5844Ojp+0evwJaQwSmGede9Czd5Y5D+ldhQhhBAiwwkPf/9QlP9Ni4p6Py0yMvFlPzxpEB39ftq7d0lbNi24ePEiNWrUoFGjRly4cIENGzZw5MgRevXqFW+5KVOmUKRIEU6fPs2IESMSbGf8+PFcvXqVXbt2cfXqVebNm4ednd1H9xseHk7//v05efIk+/btQ09Pj4YNGyY4CzNs2DAGDhzIuXPnyJ8/Pz/88IOuoOjZsyeRkZEcOnSIixcv8uuvv+q+VHt7e+sKG0VROHz4MDY2Nhw5cgSAAwcO4OjoSIECBQBo3749R48eZf369Vy4cIEmTZpQs2ZNbt68qcsSERHBxIkTWbx4MZcvX9adsYjj4uJCUFAQVlZWTJ8+naCgIJo1a8ajR4+oXbs2pUuX5vz588ybN48lS5Ywbty4eOuvWLECAwMDjh49yoIFCz762h04cIDbt29z4MABVqxYwfLly+N12evWrRsWFhaffNy/fx+AgIAArK2tKVWqlG59Dw8PrK2t8ff3T3T/gYGBBAcH4+Pjo5tmbGyMl5fXR9f5lF9//RVbW1uKFy/O+PHjP3m2bOXKlZiZmfH9998nez9fm4HaAb51Ht6v4OUs9J0qqB1FCCGEyHDifqh++hSy/H/njSlTYPhw6NQJFi3637L29hARAYGBkDPn+2lz5kC/ftCiBaxZ879lc+aE58/h0iVwdX0/bflySOTEy2dt37493i/qAIMHD060WEmKKVOm0KJFC/r27QtAvnz5mDlzJl5eXsybNw8TExMAqlSpwsCBA+Otq/x/BanVann48CHFixfXfcHOGfeifETjxo3jPV+yZAn29vZcuXKFIkWK6KYPHDiQOnXqADBmzBhcXV25desWBQsW5P79+zRu3JiiRYsCkDt3bt163t7eLFmyBK1Wy8WLF9HX16dVq1b4+flRu3Zt/Pz88PLyAt53fVu3bh0PHz7E2dlZt9/du3ezbNkyJkyYAEB0dDRz587Fzc0t0WPS19fH0dERjUaDtbW17uzF3LlzcXFxYfbs2Wg0GgoWLMjjx48ZPHgwI0eORE/v/bmHvHnzMnny5E++bgA2NjbMnj0bfX19ChYsSJ06ddi3b5/uTN7YsWMTtNW/xR1ncHBwggIPwN7enuDg4ETXjZvu4OAQb7qDg0OCs2if06dPH0qWLImNjQ0nTpxg6NChBAYGsnjx4kSXX7p0KS1atMDU1DRZ+0kJUhilMN3gCzEy+IIQQgghEqpcuTLz5s2LNy1z5sxfvL3Tp09z69Yt1nxQySmKglarJTAwkEKFCgHEO6OQmA4dOtC2bVvOnj2Lj48PDRo0oHz58h9d/vbt24wYMYJjx47x/Plz3Zmi+/fvxyuMihUrpvu3k5MTAE+fPqVgwYL07t2b7t27s2fPHqpVq0bjxo11y1eqVIk3b95w9uxZjh49ipeXF5UrV9adpfHz89MVg2fOnEFRFPLnzx8vY2RkJLa2trrnRkZG8fIk1dWrVylXrhwajUY3rUKFCoSFhfHw4UOyZ88OfP41juPq6oq+vr7uuZOTExcvXtQ9t7e3T7TY+ZgPc8VRFCXR6Z9aLynr/Fu/fv10/y5WrBg2NjZ8//33urNIHwoICODKlSusXLkyWftIKVIYpbR3VvAqJ6GG6lfBQgghREYTFvb+v2Zm/5v200/Qty8Y/Otb0P8PiMWHP1z37Pn+LNAH31kBiBu47cNl27X7sozm5ubkzZs30XlxZx6UD/oCfu7aE61WS9euXendu3eCeXFf2OP2+ynVq1cnMDCQXbt2sXfvXqpWrUrPnj2ZOnVqosvXq1cPFxcXFi1ahLOzM1qtliJFiiToRmVoaKj7d9yX7rgiqlOnTtSoUYMdO3awZ88eJk6cyLRp0/jxxx+xtramePHi+Pn54e/vT5UqVfD09OTcuXPcvHmTGzdu4O3trduevr4+p0+fjldwAAmud0nuF39IvGCIa6MPp3/uNY7z4WsSt40PuyB269aN1atXf3IbV65cIXv27Dg6OvLkyZME8589e5bgjFCcuDNhwcHBumIV3hesH1snqeKuR7p161aCwmjx4sUUL14cd3f3/7SPr0UKoxS2dWVumBFIcPlV8OkBPIQQQgjxlSX2vdTI6P0jKcsaGr5/JHXZry3L//f/CwoKokSJEgDxBmJITMmSJbl8+fJHi63k7r9du3a0a9cOT09Pfvrpp0QLoxcvXnD16lUWLFiAp6cngO7an+RycXGhW7dudOvWjaFDh7Jo0SJ+/PFH4H13ugMHDnD8+HHGjh1LpkyZKFy4MOPGjcPe3l53NqxEiRLExsby9OlTXZ6vqXDhwmzatClegeTv74+lpSVZs2b96vtLTle6cuXKERISwunTp6lcuTIAx48fJyQk5KNn/HLlyoWjoyO+vr6691lUVBQHDx7k119//U/Zz549CxCv4AIICwvjjz/+YOLEif9p+1+TFEYpzMJcHwzDiOXd5xcWQgghRIYTGRmZ4NoPAwMD7OzsMDU1xcPDg0mTJpEzZ06eP38eb+jjxAwePBgPDw969uxJ586dMTc35+rVq/j6+jJr1qwk55owYQLlypWjaNGiREZGsn37dl3h8W82NjbY2tqycOFCnJycuH//frx71yRV3759qVWrFvnz5+fVq1fs378/3j69vb2ZMWMGmTNnpnDhwrpps2bNolGjRrrl8ufPT8uWLWnTpg3Tpk2jRIkSPH/+nP3791O0aFFq166d7Gwf6tGjB9OnT+fHH3+kV69eXL9+nVGjRtG/f3/dWb6vKTld6QoVKkSNGjXo06cPCxcuRE9Pjy5dulC3bl3dwBQABQsWZOLEiTRs2BCNRkPfvn2ZMGEC+fLlI1++fEyYMAEzMzNatGihWyc4OJjg4GBu3boFvB/ow9LSkuzZs5M5c2YCAgI4duwYlStXxtrampMnT9KvXz++++67eGcrATZs2EBMTAwtW7ZM9DiuXLlCVFQUL1++5M2bN7ofBIoXL56MVy55pDBKYT37RDDdICsaA1PgC67IFEIIIcQ3bffu3Ql+TS9QoADXrl0D3l+c3qFDB0qVKkWBAgWYPHlyvNHD/q1YsWIcPHiQYcOG4enpiaIo5MmTh2bNmiUrl5GREcOGDePu3buYmpri6enJ+vXrE11WT0+P9evX07t3b4oUKUKBAgWYOXOmrmtbUsXGxtKzZ08ePnyIlZUVNWvW5Pfff9fNr1SpEgBeXl66MzVeXl5Mnz5dN/BCnGXLljFu3DgGDBjAo0ePsLW1pVy5cv+5KALImjUrO3fu5KeffsLNzY3MmTPTsWPHzxatqWX16tX06NFDd6Pg7777jtmzZ8db5vr164SEhOieDxo0iLdv39KjRw9evXpF2bJl2bNnD5aWlrpl5s+fz5gxY3TP49pj2bJltGvXDmNjYzZs2MCYMWOIjIwkR44cdO7cmUGDBiXIuGTJEho1aqQbmv7fateuHW/gh7gzWR92K/3aNEpKbl0FoaGhWFtbExISgpWVldpxePz6MVlnvD+lGjsyFj2NjJCenkRHR7Nz505q166doP+vSPuk/dI3ab/0LTXb7927dwQGBpIrVy7diGviv9FqtYSGhmJlZZUiZ0BEysqI7fexvwPJqQ0yxiulorhR6QDeRr9VMYkQQgghhBDiY6QwSmFXLpjB34vg8BAiomXIbiGEEEIIIdIiKYxS2KOHenC2E9yoQ3h0uNpxhBBCCCGEEImQwiiFFS6sYFRtDJSeJ2eMhBBCCCGESKOkMEph+fODdeU5UGwt4VFyxkgIIYQQQoi0SAqjVGCsZwwgZ4yEEEKIFKTVatWOIIRQydf4/Mt9jFJYTAzoRzhBuFYKIyGEECIFGBkZoaenx+PHj8mSJQtGRka6e9yIL6PVaomKiuLdu3cZZrjnb0lGaj9FUYiKiuLZs2fo6elhZGT0xduSwiiF3bgB9345AWbPCO94UO04QgghxDdHT0+PXLlyERQUxOPHj9WO801QFIW3b99iamoqRWY6lBHbz8zMjOzZs/+nQlAKoxRmbPz//1A0csZICCGESCFGRkZkz56dmJgYYmNj1Y6T7kVHR3Po0CEqVaokN1hOhzJa++nr62NgYPCfi0ApjFJY7txQdlp5jr8JICJ6ntpxhBBCiG+WRqPB0NAwQ3wRTGn6+vrExMRgYmIir2c6JO33ZVK00+GhQ4eoV68ezs7OaDQatmzZ8snl/fz80Gg0CR7Xrl1LyZgpSqMBE4P3fR1lVDohhBBCCCHSphQ9YxQeHo6bmxvt27encePGSV7v+vXrWFlZ6Z5nyZIlJeKlmrhR6eQGr0IIIYQQQqRNKVoY1apVi1q1aiV7PXt7ezJlyvT1A6lAq4Xbf/0Ibxrw1O2e2nGEEEIIIYQQiUiT4/eVKFECJycnqlatyoEDB9SO85/o6cEdv9pwqjtPXsrgC0IIIYQQQqRFaWrwBScnJxYuXIi7uzuRkZGsWrWKqlWr4ufnR6VKlRJdJzIyksjISN3z0NBQ4P1oHNHR0amS+1Oio6MpVXcvJ98E8DrmcZrIJJIurr2k3dInab/0TdovfZP2S9+k/dI3ab//Sc5roFEURUnBLP/bkUbD5s2badCgQbLWq1evHhqNhq1btyY6f/To0YwZMybB9LVr12JmZvYlUb+64yHHmRg4kfxm+Zmcf7LacYQQQgghhMgQIiIiaNGiBSEhIfHGMEhMmjpjlBgPDw9Wr1790flDhw6lf//+uuehoaG4uLjg4+Pz2YNPDdHR0VzdfBWAWONYateurXIikRzR0dH4+vpSvXp1Ge4yHZL2S9+k/dI3ab/0TdovfZP2+5+43mRJkeYLo7Nnz+Lk5PTR+cbGxhjr7qL6P2npPgbG2kwQYcNzg9A0k0kkT1p6P4nkk/ZL36T90jdpv/RN2i99k/YjWcefooVRWFgYt27d0j0PDAzk3LlzZM6cmezZszN06FAePXrEypUrAZg+fTo5c+bE1dWVqKgoVq9ezaZNm9i0aVNKxkxxU4Y2h0fdCGnrTYw2BgO9NF+PCiGEEEIIkaGk6Df0U6dOUblyZd3zuC5vbdu2Zfny5QQFBXH//n3d/KioKAYOHMijR48wNTXF1dWVHTt2pPvuZyZG//+PGBNevn2Jvbm9qnmEEEIIIYQQ8aVoYeTt7c2nxnZYvnx5vOeDBg1i0KBBKRlJFZMmHabrrQ68jn7Oi4gXUhgJIYQQQgiRxqTJ+xh9a4yNtdhZZgLgecRzdcMIIYQQQgghEpDCKJXYmtoC8OLtC5WTCCGEEEIIIf5NCqNUcPBgNp5uHgT3y/MiQgojIYQQQggh0hopjFLByZMOBO5sBI/dpSudEEIIIYQQaZCMG50KSpV6wluHG5y2OsuLtyZqxxFCCCGEEEL8ixRGqcDb+yGZrS9w+uARXkTkVzuOEEIIIYQQ4l+kK10qsTOzA+D5W+lKJ4QQQgghRFojhVEqsTKwg3dWMviCEEIIIYQQaZAURqnAzy8brdybwMZ1MviCEEIIIYQQaZAURqnA3Dz6/T/e2sp9jIQQQgghhEiDpDBKBW5uzzh/+yF0LMfLty/RKlq1IwkhhBBCCCE+IIVRKjAy0pLH2Qb0FLSKltfvXqsdSQghhBBCCPEBKYxSiZG+EZZGlgAyAIMQQgghhBBpjBRGqWTqVD00/0yHcDsZgEEIIYQQQog0RgqjVDJ7th6hBztASHYehj5UO44QQgghhBDiA1IYpZL27bW4NtwOpi+49fKW2nGEEEIIIYQQH5DCKJWMGqWlWZ+zYHNPCiMhhBBCCCHSGCmMUlHezHkBuPVKCiMhhBBCCCHSEimMUlF283wQacHNFzfVjiKEEEIIIYT4gBRGqWTyZD0q5ikF/0wjKCyI8KhwtSMJIYQQQggh/p8URqnE2vr9fw0jnQG4/eq2immEEEIIIYQQH5LCKJW0bKnlxQso0Xs8gAzAIIQQQgghRBoihVEqsbCAzJkhn10eALnOSAghhBBCiDRECqNUphuZTs4YCSGEEEIIkWZIYZRK3r2DceMgYFFziNWXIbuFEEIIIYRIQwzUDpBRGBjAiBEABWFgZjljJIQQQgghRBoihVEqMTCAXr1Az+gtM/VieBj6jFdvX2FjaqN2NCGEEEIIITI86UqXimbNghnTTCngYg/AwXsHVU4khBBCCCGEACmMVFE1V1UA9t7Zq3ISIYQQQgghBEhhlOoiIqCQpgEA+wL3qRtGCCGEEEIIAUhhlKpOngQrK5jUtSp6Gj2uPb/Go9BHascSQgghhBAiw5PCKBUVKgSKAtpYPdysKwFy1kgIIYQQQoi0QAqjVGRhAQ8fwqNHUMPVA5DrjIQQQgghhEgLpDBKZU5OoNFArXy1ANh0dRPPI56rnEoIIYQQQoiMTQojlXhm98TdyZ2I6Ah+D/hd7ThCCCGEEEJkaFIYpbLQUOjRAypU0DDAfTQAs07M4tXbV+oGE0IIIYQQIgNL0cLo0KFD1KtXD2dnZzQaDVu2bPnsOgcPHsTd3R0TExNy587N/PnzUzJiqrOwgL17ISAAXgTUpoh9Ed5EvWHovqEoiqJ2PCGEEEIIITKkFC2MwsPDcXNzY/bs2UlaPjAwkNq1a+Pp6cnZs2f5+eef6d27N5s2bUrJmKlKTw/mzIH166FnTz0mV5uMBg0LTi9gWsA0teMJIYQQQgiRIRmk5MZr1apFrVq1krz8/PnzyZ49O9OnTwegUKFCnDp1iqlTp9K4ceMUSpn6qlf/379r5avF5GpT+WnvAH7y/Yn7IfeZUHUCFkYW6gUUQgghhBAig0nRwii5AgIC8PHxiTetRo0aLFmyhOjoaAwNDVVKlnJCQ2FVj36UzOXBmWKVmHViFn9e+ZNOJTrR1LUprvau6GnkUjAhhBBCCKGuqGgt94PfEGv8gtDoF4REhnA3UMPF0+aYZnpDbvdAImMi0Spa3kbo0axEXXLZ5FI7dpKlqcIoODgYBweHeNMcHByIiYnh+fPnODk5JVgnMjKSyMhI3fPQ0FAAoqOjiY6OTtnASRCX4WNZZs7U48IFfdw05dg5eRs9dvbgbshdxg3Kyri317Cq3guvstZUyFaBorYlcXMshr1l5tQ8hAztc+0n0jZpv/RN2i99k/ZL36T90rcvab9YbSz3Qu5x69Utjh57x8F/7NBkvo1ZmfU8fPOQZ+HPeD72EoQ7QPeK4HDp/Ypn28LfyyHvTmjV9X8bDLPH1Tkn2SyyfcUjS77kvAZpqjAC0Gg08Z7HDUjw7+lxJk6cyJgxYxJM37NnD2ZmZl8/4Bfy9fVNdHrhwjBsmAOKoiHqahRTckzhROgJpt9qSHSIA6HlprHtxja23dgGVxvAn39gVHAPxTuNJZdpLnKZ5sIqrCh57c0xMkrdY8pIPtZ+In2Q9kvfpP3SN2m/9E3aL31LrP2itTE8jnxE4NtA7r27x8EFPQh9lBulZS1ibW68X+hMe9i6FPJGQJYPtmHyCsIdMIp0wMowGHN9c2LsFV7nPYZF9mByWJXBUM8QPfSINbHg1tlb7Ly+M5WONnERERFJXjZNFUaOjo4EBwfHm/b06VMMDAywtbVNdJ2hQ4fSv39/3fPQ0FBcXFzw8fHBysoqRfMmRXR0NL6+vlSvXv2jXQHr1Yv/vD71qZBJw/UbUbjVmMG5ED+OPTrGobOleak1JErzhhOhJzgReuL9CtPvQGg2ig/uR6WK+rg5ulHAqjjFnAphYpSmmjjdSUr7ibRL2i99k/ZL36T90jdpv/Qtrv2qVK3CjZAbHHt4jK273nJ4ST0irS+hbdLnfwsHj4LnueFZXozt7pHbJjeZy5jxKnY/+QpHUa/uYrJZZsPe3B7DduZkyxyGucmuRPbqDrROrUNMsrjeZEmRpr41lytXjm3btsWbtmfPHkqVKvXRD6WxsTHGxsYJphsaGqapD3Jy89SvH/evstSgLADapnDtTigXg3PxxHAGZ4PPcubBFS68ywRaQ85p13Du5Ov3qx3vBfsmkqPqTjoPuYZnDk/KZC2DiYHJ1zysDCOtvZ9E8kj7pW/SfumbtF/6Ju2XvkRER3Dk/hEmT4nl2F5nlOoNiXDc937mPU94OBDemGBpZImboxtuDm4oNnfJkTmamp5zcXXJhr6evroH8ZUl5/2booVRWFgYt27d0j0PDAzk3LlzZM6cmezZszN06FAePXrEypUrAejWrRuzZ8+mf//+dO7cmYCAAJYsWcK6detSMma6oacHhfNaUThvWfj/YgkgslsUBy9d4jG/czboLOeenMN/Wxlioiy49+4sww+MB8AQMyz+9KN46XeM/tmcinmLy8AOQgghhBDp1NvIGJZvu8buY/cIKTKFgIcBRMVGwaE/4XYtyOWORfbjeGTzoEQpT/Tc/antmZWKxV7Ld8BEpGhhdOrUKSpXrqx7HtflrW3btixfvpygoCDu37+vm58rVy527txJv379mDNnDs7OzsycOfObGqo7JRgbGOFTvAhQhHbF2wEQ3SqWrUevcjUsFxcimnD4/mGCr+bk1eXSHLjzggPZ7bGzyEz13NUpHNucRqUrUDhX4t0VhRBCCCFE2vDkzTN2397J9pvb2X3qKmGTL4GmIAz+AUyicLFyIU/jW2jvr2JAt5bUKTvhmzsLlFJStDDy9vbWDZ6QmOXLlyeY5uXlxZkzZ1IwVcZgaKBPY69CQCGgI4qicPx6ILMc/Lj0+AaBJuY8j3jOukvrYFFvRjyypXD3sXRpY039gvXJmSmnykcghBBCCCEArj2/xqRlF9g0z5WwLPuhdu/3M8zAIMdxHJ1j6F5hDk3KeZA3c15iYmLYuXMntUoVkqIoGdLUNUYi5Wg0GjwK5sZjfG7Am+jY9hx7eIyd132ZucyCCE0sV0zn0/efIPr+05e8b9qT83U7hnTJTdUy6g6zKIQQQgiR0ez0v4v/q01se7CSC08uwPW6ELgNXpnh1n4p3xWoR938dSk1stT/d4uroHbkdE8KowzKUN8QzxyeeObwZOJdOHvnPoeeDmbL9S0cuneIW/s8uXWuEnvPz8Wj2yp+KPIDTV2b4mjhqHZ0IYQQQohv0sPQh6y5sIZf+xfl1cnaUOcmlL6AgZ4B3lX1sM/lR9/W+Shd8KzaUb9JUhgJAErkzk6J3H3o49GH5xHPGWZ0gU3KcV4WX8Oxh8c49vAYfdfPIPO+P/ihRTRTBpTAxDDhaIBCCCGEECLpnr6KYMzCM9xw/IV9d31RUCDTANCvRm59L4Z9V4YGBRuQ2TSz2lG/eVIYiQTszOxYMKQKC4ZAcNgm/rj8B2svruX4oaq8uOjO7AUHWKvnTKuirehQogNujm5qRxZCCCGESFdOPjrJgpOLWNpuJEpIRWgTA7kVPLN70tirKHWWvSFv1h/UjpmhSGEkPsnRwpHeZXvTu2xvDrjfZfSMfVw2XMmLty+ZeWImM48uwHLTQRo2jmXWzyWxMpP7JAkhhBBCJObpqwgmrD7CUZNhnHp86v3EvCUxuFeTxvk6MaHnInLb5FY3ZAYmhZFIssolclJ5eU5itd743vmBpWeX8tcGU95cK8vK2ffYbpGdLqU60r10d7JbZ1c7rhBCCCFEmnDjxQ1+37+c+W0Gw7tq0KcLRnZGNHVtSssmrlQvmB19vZxqx8zwpDASyaavp0/NvDWpmbcm18u+YIDjfgKe7uFl5DMmHZ3EZP/J5Dm1ka7Nc9CveQn09DRqRxZCCCGESFUxsVqW7TvMH0/GsffO3vcTnStjEJqPTvknMLZtdbKYZ1E3pIhHCiPxnxTIbsv22VWI1Xqx7YYHs0/MZt+hMG5ua8jAnZEsflSJoT6d+aHIDxjqG6odVwghhBAiRUXGRDLzn78Z3rEUUaFFoJ8/GiMNdfLXoeVaDd+Xyo6Bfk61Y4pESGEkvgp9PX0aFGxAg4IN8HW9Sf/gg1x7cZVrEUdou+UIIw6MoLZmBiNbVsfJzlztuEIIIYQQX9Wrt69ZeHoBM0/M5HFIMETdAEWf5naTmNi+Hjkz5VQ7ovgMPbUDiG9Pdfd8XNzuxbMDzZlUdRIO5g7cfxDD/AG1yJo9mv5//saLiBdqxxRCCCGE+M8uBgZTsuEhshS6wpC9Q3j85jHO1o70/e0ID+5rWNfvRymK0gkpjESKyWSSicEVB3O3712GFJuFod0DlCwX+P3KALJPz07f3X25/zJI7ZhCCCGEEMn2+M1j+uzqQ6kFpTm7w53Ye+XJ9aYNy+svJ7BPIL+3a0u2LNZqxxTJIIWRSHEmBiZMbNuIsAe5WLDyFSUcSxARHcGMo3PJmS+C4vX8ufnwudoxhRBCCCE+69S1YGr8tIrcM3Iz88RMokwfkqfFLMYtPcmtKctpW7wtRvpGascUX0AKI5FqjAz16eJVn9NdTvNPq3/I/7I/yss8nPfLSfElBRm6d6h0sRNCCCFEmvT4zWM6rBxF6SI27Jn2A5HPslLBpQJ7W+/l5rLBDGtfWkbiTedk8AWR6jQaDT55fLg2uzqTyx1nUcAf3OYFk45OYs7JOVQOWc7MflXI4ZBJ7ahCCCGEyOCevnnB5ICJzD4xm8jYSMhVFit9J6bVXEPHmmXRaKQY+lbIGSOhGo1Gw+BWZbk5eyp/N/8bNwc33tx0Y+uvjciVN4oJ+2bwLuad2jGFEEIIkQG9evOWml0O4pTnOdMOziUyNpIKLhXYttmU11eL06mWhxRF3xgpjITqNBoN3xX4jjNdzzC60jiMHW+jFPiLYUf6UnB2QdZeXItW0aodUwghhBAZQIw2hqVnl1Jkniv//Jkd7bMCZL07lJ0tdnK4/WHqFqksBdE3SgojkWboafQY1c6L0Ps5mTvDgqyWWbkXco+WK/thnf8809acUzuiEEIIIb5RWq3C+JVHKTbPjY5bO/L4bSB2jcfRbcJh7q4cRq18taQg+sZJYSTSHCNDfbpXaMWNH28wvsp4DI+OIexWCQYOiqLu2npceXZF7YhCCCGE+IacC7qAXdEzDG9bgasBLmQ2zcxvPr/xYP4c5g31xEBfvjJnBNLKIs0yMzTjZ8+fOb+uMcW+O4B+rUHsuLmdYvOK0Wt7H249eK12RCGEEEKkY88jntNjRw/cF5XglfUBMIygZpau3O59m37l+mFiYKJ2RJGKpDASaV6hHFk4/3dlrvy6kIYFGxKrxDJnYTj582toM+IQsdpYtSMKIYQQIh0JfxtNw76HyDOuEvNOzUOraGnQ9RL+Z16y6/eGZDLJpHZEoQIpjES6kd82P381+4u9rfdicac1yjtrVp34m7KLyxLwIEDteEIIIYRIB/bc3kNW751smVGJ0O0/4+bghl9bPza3XU65ItnUjidUJIWRSHeq5q7KszPlaTFyN5aVlnM66DTll5an0YIBnL/1RO14QgghhEiDHoQ8oNGGRtRYXYOQ4mPRWD6hdX0XTnc5jVdOL7XjiTRACiORLpkYGbJmTE1u9b1Kh+IdQIHNk+pSvIgJXaZtle51QgghhAAg4l00dXseIm/HcWy+thl9jT59G1bi8X0jVv7ihb6evtoRRRohhZFI1+zN7VlSfwl7vj+FOfYQa8SiB73xWOLBmaAzascTQgghhIoCHgRQoMsv7JhbiagdkyiTqTZnu57l95q/45jJRu14Io2Rwkh8E6oXcef1rUL8vHw71o6vOfX4FKUXlabR+AU8fh6mdjwhhBBCpKKXb1/SZVsXyi8tz8OcEzDIt58OQy/i/+M2ijoUVTueSKOkMBLfDAN9Pca3bMK1XtdoXqQ52md52DyqLdnzvmHpwX/UjieEEEKIFKbVKnQd549T6QAWnVoMQHv3NgSdK8aSkZXQ15OvvuLj5N0hvjmOFo6sa7yO6d4rMLAJJtbuPB0P1KThhoY8Cn2kdjwhhBBCpID7IfepNqcNC8e6EXW5Dtke9uNQu0Msrb8UOzM7teOJdEAKI/HN6tO4HMG37ek96QwG+gZsubaFwjOL03ncQWJjFbXjCSGEEOIr0Cpa5p2ch+tcVw68XI1+jaFU77Kfa3Mm4pnDU+14Ih2Rwkh802ytzJjx/c+c6XKG0s6lCT3QmcUjvHAud4R7r++pHU8IIYQQ/8GuY4HYup6hx8rphEWFUd6lPJeW9WDPgiqYmxipHU+kM1IYiQyhqENR/Dv607CkNxiG89RlPkXmFWHeyfd3uxZCCCFE+hGjjWHy0cnUbX+J11dLob9nJrNqzeJw+8MUtCuodjyRTklhJDIMAz0D/priw6EzQZSvfY+wqDB67OxB2QkdOXBGzh4JIYQQ6cG159cov6Q8g/cORluzF/alD3NwY2F6lemFnka+2oovJ+8ekeF4FsnLofYHmVFzBqaaTJya2Z8qHnb0nLkVRZFrj4QQQoi0KCZWS4M+BynaZiknH58kk0kmlrcdS/DxilQo6qJ2PPENkMJIZEj6evr0Ltsbv2ZnyZQ5BgzDmfuwAzXX1JSR64QQQog05u7ru5QYMJy/Z3oRs+cXKlq041L3S7Qt3haNRqN2PPGNkMJIZGhlCuTk2SU3RqzchYl1OHtu76HovKJM2rgbOXkkhBBCqEtRFJaeXUqxecW4lGki+m7raTHoGAf7LSWrVVa144lvjBRGIsMz0NdjbOO2nOlyBncnd15dL8zQptXJUf4YT0Jfqh1PCCGEyJDO33pKnjpb6fhXN95EvaFC9gpc31+aNRO80NOTs0Ti65PCSIj/VyhLIQI6BlAn02DQaHnw9jpll5fk3JtzakcTQgghMpQNFzdSslwogbvqo3dkFL9W+5WD7Q6SJ3MetaOJb1iKF0Zz584lV65cmJiY4O7uzuHDhz+6rJ+fHxqNJsHj2rVrKR1TCAAM9Q3Z/ls9Vuy4Tp6WM3kc9pjRt0fTa+tPvAiNUDueEEII8U17E/mGtlva0vyvJmgrD8E0+xU2jm7CoAqD0NfTVzue+MalaGG0YcMG+vbty7Bhwzh79iyenp7UqlWL+/fvf3K969evExQUpHvky5cvJWMKkUCbmkW40Pcw3d27A7Dw13w4F3jMuj1SpAshhBApYcnWyxQe0YKV51eip9FjWLeCvLiZl4Ze+dWOJjKIFC2MfvvtNzp27EinTp0oVKgQ06dPx8XFhXnz5n1yPXt7exwdHXUPfX35hUCkPjNDM2bUmMEgh4noXW9MVHBe2qztz/Rj02VYbyGEEOIridXG0nLcJjo1LMDDpVPJZlKAg+0OMq7KOEyNjNSOJzIQg5TacFRUFKdPn2bIkCHxpvv4+ODv7//JdUuUKMG7d+8oXLgww4cPp3Llyh9dNjIyksjISN3z0NBQAKKjo4mOjv4PR/B1xGVIC1lE8kVHR1PeqRBnTsbS7rcZnHPaRb9/drHn1h4W1lmEg4W92hHFJ8jnL32T9kvfpP3St9Rqv4ehD+mwrQN+by6AeVlcCjzDr9URXOyt5b3zH8jn73+S8xpolBT66fvx48dkzZqVo0ePUr58ed30CRMmsGLFCq5fv55gnevXr3Po0CHc3d2JjIxk1apVzJ8/Hz8/PypVqpTofkaPHs2YMWMSTF+7di1mZmZf74BEhqcoCrtf7GbZo2VERZiiv2YfzZtfo0lFC7WjCSGEEOnO9st32KAdxZvYN5jomdDSoj91cpaWEefEVxUREUGLFi0ICQnBysrqk8umeGHk7+9PuXLldNPHjx/PqlWrkjygQr169dBoNGzdujXR+YmdMXJxceH58+efPfjUEB0dja+vL9WrV8fQ0FDtOCKZEmu/S08vUb39aV74dgKbW/RduYhx1UZipC+n+9Ma+fylb9J+6Zu0X/qWku0XFhlB+cbnubanIrStSslyoaysv5L8tnIt0dcin7//CQ0Nxc7OLkmFUYp1pbOzs0NfX5/g4OB4058+fYqDg0OSt+Ph4cHq1as/Ot/Y2BhjY+ME0w0NDdPUGyGt5RHJ82H7lchagpubCuLV8gAXHQYz/fRJjgYdYF3jdTKMaBoln7/0TdovfZP2S9++dvtdfHKRZhubce15X6AiXoYD2dOpuvy4mELk80eyjj/FBl8wMjLC3d0dX1/feNN9fX3jda37nLNnz+Lk5PS14wnxn9hYmnJha2X+6j8UGxMbTj4+SdEBP9Hz1yNqRxNCCCHSHK1WYeGJpZRZXIarz6/i0PhXpq07g9+iOlIUiTQjxc4YAfTv35/WrVtTqlQpypUrx8KFC7l//z7dunUDYOjQoTx69IiVK1cCMH36dHLmzImrqytRUVGsXr2aTZs2sWnTppSMKcQXa1ioIaWcS9F0+Y8c+2MBcyOycPXZInZMbIWpoana8YQQQgjVBb0Io3zDC9yNiIJ676iZtyYrG6wki3kWtaMJEU+KFkbNmjXjxYsXjB07lqCgIIoUKcLOnTvJkSMHAEFBQfHuaRQVFcXAgQN59OgRpqamuLq6smPHDmrXrp2SMYX4T1ysXfDrvokaZ45w0NecA6a98Fgymz+b/Cn9pYUQQmRol55eovb4yTw4vBz0ytCvnx5TW3RCT5Oid4wR4oukaGEE0KNHD3r06JHovOXLl8d7PmjQIAYNGpTSkYT46oyN9PFb4cXua/tpuz0TF55cwH2hO4NcNjOiVTW14wkhhBCpSlEUlp5dyo+7fuRt5rdY18/FhNaN6NG4i9rRhPgoKdeF+IpqFqzCua7n8MrhRdjxxoxsXY0idQ/yNvqd2tGEEEKIVBH8MozC3/1Dpw0/8TbmLTXz1uTmml70aOymdjQhPkkKIyG+MidLJ/a22Yu3XQtAy+UIXyouq8Dtl7fVjiaEEEKkqEtPL5G30imuba8J2xYzsepEdrTYIdcTiXRBCiMhUoCBngEHFvswfeNxMvss4EzQGUouLMmfFzerHU0IIYRIEavOr6LMojKEV+iPvl0gc37Jw5CKQ+R6IpFuyDtViBTUp3E5znU/Q3mX8oS+fUPTRsaUbHyAiHfRakcTQgghvorQ8EiazR5Pmy1teBvzlhqe9jy4ZSFd50S6I4WRECnMxdoFv7Z+NDWfD7dqc3arB56/tSPoTZDa0YQQQoj/5MzNRzgXucUfg7rBq5yM8hrFzpY7cbKWrnMi/ZHCSIhUYKhvyIZBXRgy6zimjX7kTPRaSi4syZH7ckNYIYQQ6dO+O/vw2ViG8KhwNBoNv5ZZx2jv0dJ1TqRb8s4VIhVN7FWWc3MH4ZrFleCwYLynt+P7AX5otYra0YQQQogkidVqmXh4Ij6rfXgR9RjXXqM56B/OoBYeakcT4j+RwkiIVJbfNj/HOx2nSYFWxK77g02/eVO8xV+ER4WrHU0IIYT4pHvBIWQtfYqfp95Cq2jpULwDJwduwtPNRe1oQvxnUhgJoQJzI3PWN11J4xYhYPmIi8598Vjiwc0XN9WOJoQQQiTq4pOLlOo1gydnysCeaczwXs6S+kswNTRVO5oQX4UURkKoRE9Pw8Zplfnn+F0cs8Zw6eklSi0qxbJDe9SOJoQQQsSz5sIayi4uy3PX0VhUWMnKzY/p7dVW7VhCfFVSGAmhMp9CFTjT5QwVXCoQeic/Hap64tn6ANExsWpHE0IIkcFFvIumcq8NtNrU+v1Q3Pl8uLunDq1rFlY7mhBfnRRGQqQBTpZOHGh7AI+3oyHGlCMnQ6iztg4vIl6oHU0IIUQG9SrqNTnLXcJvTjPwG8PISiPZ0WIHtma2akcTIkVIYSREGmGob0jAqjr0nnoY06bd8Q38h9KLSnPxyUW1owkhhMhgzgSd4aebA3mdfxYYhzCsuQ9jKo9BX09f7WhCpBgpjIRIY2YM8OR4zz3ktslN4OtA3NtspO+U42rHEkIIkUEsOb4O71XePI9+Tr7Kxzl67injupdVO5YQKU4KIyHSoKIORTnZ+STuUf2I3jOGGYPK0mHeHLSKVu1oQgghvlHvomIo2eggnRoU4F2EhlJWpfBv50/5gvnUjiZEqpDCSIg0KrNpZo6Onkzppvuh7HSWPe3Fd+u+I+RdiNrRhBBCfGOeRzyn2rwWnP2nEASXpKHBIn7O9TPWJtZqRxMi1UhhJEQaZmxowIkNVVi5wA4TAxN23NxB6bmV+Of4HbWjCSGE+EacDz5P6UWlOfr6T0xatOGnGcfYMLwpehr5migyFnnHC5EOtHZrxZH2R8hqmY2bKwZS08uO0YtOqB1LCCFEOtd7ij9lx/Ti7uu75LHJw8nxU5nc20PtWEKoQgojIdIJd2d3DrU8hdW7ohBlxpgjQxl/aDyKoqgdTQghRDoTq42lzqANzBpUnsi1a6ni0JSTnU9SxL6I2tGEUI0URkKkI7kdHHh0rjDfjZ8Nufcz/MBwmm5sSlhUmNrRhBBCpBMv376k9tra7NTvAnZX8ah9i10d12JjaqN2NCFUJYWREOmMhakRfw/ty8K6CzHUM2TjiYM4u5/m4Ln7akcTQgiRxh27eZ0yi8qw5/YezCxjWL7jMgHrKmNkKPcnEkIKIyHSqc7unTnQ9gDGe5bw5pIXVesH43t7r9qxhBBCpFFjFp2kXDEHbge4kjNTTvw7+NO2zPdqxxIizZDCSIh0rEL2ChxeXwrLgieJrdeWWmtqMvvEbLnuSAghhI6iKEzzn8boxcfhXSYyXx3MiU4ncXN0UzuaEGmKFEZCpHOlCznx9GJRWlctTawSy4+7fqTJrPGEv41WO5oQQgiVRcZE0mFrBwb6DoQa/fDouJ57AaXIYm6ndjQh0hwpjIT4BpgYmLCiwQomV5sMzwqxadCPZC1+hVuPXqgdTQghhEou3XlGgRaLWX52OXoaPWbUmYb/omZYmBqpHU2INEkKIyG+ERqNhp8q/MS40ksACHkXQvX15bn89LLKyYQQQqS244EXKF76Lff+7InJ6UHsarmL3mV7o9Fo1I4mRJolhZEQ35hhbcvx996n5Og6gLthN/BY4sG269vUjiWEECKVbL66mSrryhFb+jcM7QP5a1hXfPL4qB1LiDRPCiMhvkHfVczHqb678M7pTVhUGN/1302tbgfRamVQBiGE+FZptQoj//mVRn80IiI6gmotrnDnciZqeeRWO5oQ6YIURkJ8o+zM7NjTag9N7UfCrhnsXuBF1eG/8y7mndrRhBBCfGXPQyLI5RnAL91KQ6wBvcv0ZlernWSzk5u2CpFUUhgJ8Q0z1DdkfbfRNB14FE2JZfgZDcB7uTdBb4LUjiaEEOIreRT6CO8Zrbl/qijc9+Sn7H8xo9YMDPQM1I4mRLoihZEQ3ziNRsOGyV7s+TM7NqY2HH90nNILyrHpkAzKIIQQ6d2JRycovag0l5W/sGzZmelrLjO5Uz21YwmRLklhJEQGUS1PVY53Ok5Bu4I82tSH76vlYsDv/mrHEkII8YV+nHyUilM6EBQWhGsWV85Pm0if5sXVjiVEuiWFkRAZSD7bfBxucwy7iIoQbcZvAb8x6sAotIpW7WhCCCGSSKtoqd1/M7MHVyB69UZqZmuKf0d/ctnkUjuaEOmaFEZCZDB2ltY8OlWSRuMXgOsmxh4aS9M/mxIeFa52NCGEEJ/xJvINjTY0Ypded7C6j0f1YP5usxYrYyu1owmR7klhJEQGZGSoz6afu7L0u6UY6hmy6eweXDz9OH7lkdrRhBBCfMT14HtUWFqBv6//jXGm18zfEUDAOm+MDPXVjibENyHFC6O5c+eSK1cuTExMcHd35/Dhw59c/uDBg7i7u2NiYkLu3LmZP39+SkcUIsNqX6I9B9oewMR3Ia9O1KGiz3OO3pfrjoQQIq2Z/ed5Chcw4uIJGxzMHfBr50fXis3UjiXENyVFC6MNGzbQt29fhg0bxtmzZ/H09KRWrVrcv38/0eUDAwOpXbs2np6enD17lp9//pnevXuzadOmlIwpRIZWIXsFfJdWxCznRWJqdabKysqsOLdC7VhCCCH+35IzS+g9/hLaUCcsT0ziZOeTeGTzUDuWEN+cFC2MfvvtNzp27EinTp0oVKgQ06dPx8XFhXnz5iW6/Pz588mePTvTp0+nUKFCdOrUiQ4dOjB16tSUjClEhlexWDaCr+WiYbVsRMVG0e7vdnReOYGo6Fi1owkhRIYVo42h/z/96bStE0qdzhRqtInbR4vhYu2idjQhvkkpVhhFRUVx+vRpfHx84k338fHB3z/xrjoBAQEJlq9RowanTp0iOjo6paIKIQBLYws2Nt3IiEojICQbi3t0wMXjFI+eh6odTQghMpx7wSGU6DaD34/9DsAYnyFc3tiILJnMVU4mxLcrxW6J/Pz5c2JjY3FwcIg33cHBgeDg4ETXCQ4OTnT5mJgYnj9/jpOTU4J1IiMjiYyM1D0PDX3/JS46OjpNFFNxGdJCFpF8GbH9RlQcQcSlykyLzMTTR8FUXVmFLa1Wk8cmj9rRki0jtt+3RNovfZP2+3LnH9yiQnkjop4MwLDxVVaOrEbjQo2JiYlJtQzSfumbtN//JOc1SLHCKI5Go4n3XFGUBNM+t3xi0+NMnDiRMWPGJJi+Z88ezMzMkhs3xfj6+qodQfwHGa39PLND1MhNrAydzPU3FyizsAyDcg6iqGVRtaN9kYzWft8aab/0Tdovec6/Oc+Uu1OIyj8YvXft+dHdG9NAU3YG7lQlj7Rf+ibtBxEREUleNsUKIzs7O/T19ROcHXr69GmCs0JxHB0dE13ewMAAW1vbRNcZOnQo/fv31z0PDQ3FxcUFHx8frKzUH9M/OjoaX19fqlevjqGhodpxRDJl5ParXRsGvKnI9xu/51TQKUZtvULzvOVZPsZT7WhJlpHb71sg7Ze+Sfslj1arMPfEQsaeH0usEkuZVjtYWKU9hXOoM/KctF/6Ju33P3G9yZIixQojIyMj3N3d8fX1pWHDhrrpvr6+1K9fP9F1ypUrx7Zt2+JN27NnD6VKlfpooxobG2NsbJxguqGhYZp6I6S1PCJ5Mmr75cicg0PtD9F0wTC2bx7P2hhTXukv4O/RHTDUTz+vR0Ztv2+FtF/6Ju33eRHvoinV8BhX7zlBEy2ti7dmYb2FmBiYqB1N2i+dk/YjWcefoqPS9e/fn8WLF7N06VKuXr1Kv379uH//Pt26dQPen+1p06aNbvlu3bpx7949+vfvz9WrV1m6dClLlixh4MCBKRlTCPEJpoam/N1jGtXanoB829ml14Naa2rx8u1LtaMJIUS69zziOZUmd+eqb1m42pBuDqtY0WBFmiiKhMhoUvQao2bNmvHixQvGjh1LUFAQRYoUYefOneTIkQOAoKCgePc0ypUrFzt37qRfv37MmTMHZ2dnZs6cSePGjVMyphDiM/T0NPgu9uKvy3/T5m9T9gXuo8yisiz23oV3sbxqxxNCiHTp8tPL1FtXj0AlEONGMKhqF8Z2bal2LCEyrBQffKFHjx706NEj0XnLly9PMM3Ly4szZ86kcCohxJdo5FqfvHb+fLfuO27/3ZTKg+0YN/ckw9qXVjuaEEKkK6MXHWfK7dZEmAaS2yY3W2f3w9XeVe1YQmRoKdqVTgjx7SnmUIyA9iexetAU3mVixOYl/B7wu24ESSGEEB+nKApNh+1kTJfSRKxag6ezD8c7HZeiSIg0QAojIUSyOVln4eG5QngPWIjivoD+e/rTaWsnImMiP7+yEEJkUO9i3tF2S1v+DOsFpi8p7BbB7tbbsTOzUzuaEAIpjIQQX8jSzIj9UzozvcZ09DR6LD21mty1/ubK3WdqRxNCiDTn4esgvJd7s+rCKvRt7zPuz21c2lEJM5OMPWKYEGmJFEZCiC+m0Wjo49GHnS12YrR3No/3NqV4xSecC7qgdjQhhEgz1vxzhVz5wzl+6h02Jjb80+ofhtVp/8kb3gshUp8URkKI/6xG3hpsmloVQ/vbRFfpR8Vl5dlybYvasYQQQnV/Xv6TNv1uEfMsL+YHZ3O803Gq5q6qdiwhRCKkMBJCfBV1K+TmwU0bqlWH8OhwGm5oyM9bp6PVyqAMQoiMR6toGXVgFE03NkX7XVtcqu7g8oGi5LPNp3Y0IcRHSGEkhPhqHKwys6vlLn4s8yOE2zKx7Xfk9vLnZehbtaMJIUSqefoqnIqDJzP20FgABlTpSOCemuRwtFY5mRDiU6QwEkJ8VQZ6BsysNZPuDqsh1IV7lx2puqQej988VjuaEEKkuCsPH5DT7QEBUwahf7M+S79bylSfqejr6asdTQjxGVIYCSFSxNwBNflt9WWs2rXmXOg+Si8qzclHJ9WOJYQQKcb/gT/e60rx1t4PjcULZjUcS/sS7dWOJYRIIimMhBAppt8PxTk7YjWuWVx5/OYxFYaPpvcUf7VjCSHEV7f0zHIqr6jMs4inFGu/GP9jkXRvXEztWEKIZJDCSAiRonLb5Ma/oz9VbNoTvW4NswaVp8nYtWgVrdrRhBDiP4uKjqV0Ez86do4iKiaKRoUacbSzHx6u2dSOJoRIJimMhBApzsrYil3dF1G63nlwOcrG6PZ8/8f3hEWFqR1NCCG+2Mu3L/Ec349TmzzhTBfa2y3kzyZ/YmFkoXY0IcQXkMJICJEqjAz1OfGnF0s23cXIGDZf20z5JeU5efOu2tGEECLZLj29RJlFZTihmYVh7SH0mRLA0l6d0dPIVysh0iv59AohUlWH0i3xa+uHg7kDF3eWo2xxK35deVrtWEIIkWTD5vtTdmZtbr+6Tc5MOTm5uBXTB5ZTO5YQ4j+SwkgIkerKuZTjZKfTWFzrjhKRmaGrNjLVfyqKIjeDFUKkXVpFS63eO5jQvTwR65bgnb0aJzufxM3RTe1oQoivwEDtAEKIjMklU1YenLWl9k8rCXCYxE++cDb4LIvqLcLM0EzteEIIEU9oZCitN7dmd3QgGHpRvKgRu1ruwsRIvkoJ8a2QM0ZCCNVksjDh6NzWzK49GwM9A9aeX0/Omn9x9MJDtaMJIYTO5eAbeCz2YOv1rRhnvcG0v3dzdouXFEVCfGOkMBJCqEqj0dCzTE/2tt6LWcBEnu1vRSVvLXuu+6kdTQgh+GXJSYq5GnL1RiRZLbNyqP0h+tf6Xu1YQogUIIWRECJN8Mrphe+0lphmv4q26kBqb6jGjGMz5LojIYQqFEVh4uFJjBwThfZlLuxPz+BUl1OUyVpG7WhCiBQihZEQIs0oXzQrT67lpFULY2KVWPr+05emy/ry6s1btaMJITKQ8Khwftj0Az/vHwpNmlCs4T/c2uODo4Wj2tGEEClICiMhRJpiaWrKygYr+b3G7+hFWbFxaEeyFbvDyauP1Y4mhMgADp9/gGuvkWy4vAEDPQPm/zCK83/VwNLMSO1oQogUJoWRECLN0Wg09PXoyxyPPWjCshHxzJZaa2tx6N4htaMJIb5hS/f54VXenHtLJmLzrDYH2h6ga6muascSQqQSKYyEEGlWt3pl8TsaTr5eA3lhcIGqK6vKdUdCiK9Oq2gZe3AsHQ9XQcm5D/McN9jVfREVs1dUO5oQIhVJYSSESNMqFXfh7NgFNC/SnBhtDH0XbSB35UM8eRWmdjQhxDfgXvAr6q5uwCi/UaBR6Dj6KI8v5qOsq7Pa0YQQqUwKIyFEmmduZM7aRmuZWmUm/LWWuwe9cG36B9eeX1M7mhAiHftz/3XyFg1l14LymBiYsKz+MhY3mY6VubHa0YQQKpDCSAiRLmg0GgZ4/sjsRaEY5T3Mi9J9KL2oNJuubFI7mhAiHVp1fhUtF/5CzPMcGFxtyZ4mx2hXvJ3asYQQKpLCSAiRrvT8vhj3zuajUv6ShEWF8f2f39N43BLeRcWoHU0IkQ5ExUbRc0dP2mxpQ3ShNRTp9DtXz1vgmd9N7WhCCJVJYSSESHccLRzZ23ovA8oNgCuN+GtER5zcLvDw1RO1owkh0rDT14PI5v0Pc/2XAzCy0kjOLehN3mw26gYTQqQJUhgJIdIlQ31DpvpMZUC5gWAUxmub/ZRdVhL/B/5qRxNCpEEHAv3wqPqMZ0fqYeQ7l20/bGNM5THo6+mrHU0IkUZIYSSESNem9i3H7sNPKNh8BY/fPMZruRe/HZmNVitDegsh3g/FPeHwBKqtqkqMTw9MXa6wc643dfPXVTuaECKNkcJICJHu1SiTh5PdAmjq2pSY2BgGdMtCrkr+PHoeqnY0IYSKbjx4geeE3gzbPwytoqV1vdw8vZmTqqVyqB1NCJEGSWEkhPgmWBhZsL7xegbkWg1XG3M/oAyeUztzJ+KO2tGEECpYd+AshYu9w3/Szxi/c2FxvcWsaLACC2MztaMJIdIoKYyEEN8MjUbD1LYtWbDxKjbf/8xDq80MvjmYhWcWoijStU6IjEBRFKb6T6X1fm9iDV9jaBrJhjq+dCzZEY1Go3Y8IUQaJoWREOKb06VhUW4tH0rtvLWJVqLp9cd48tX0la51Qnzjgl69osGGBvzk+xOxBqHUHb2AwMt21K9YQO1oQoh0QAojIcQ3KbNpZjY32Uxbp3Zotqzk9h4fClQ/yrngc2pHE0KkgBU7L5M93xu2bjLGSN+IeXXmsbX7DLJmsVQ7mhAinZDCSAjxzdJoNDR0aMDsX+0wcLhBeMU+eCz2YP6p+dK1TohvhKIozDg2gw6/biPmRXaMAkZztH0A3Up1k65zQohkSbHC6NWrV7Ru3Rpra2usra1p3bo1r1+//uQ67dq1Q6PRxHt4eHikVEQhRAbRub4rj2/ZUrd8ASJjI+m+ozvVxo2RrnVCpHPPwp9Rb109+v7TF63XcAo2/oMbp7JSKmtJtaMJIdKhFCuMWrRowblz59i9eze7d+/m3LlztG7d+rPr1axZk6CgIN1j586dKRVRCJGBZLGwZWvzrUytPhX9F0XY/8tP5Cz0kq0nz6gdTQjxBaatOUPOarvZcWMHxvrGzKo7nSt/NiGHo7Xa0YQQ6ZRBSmz06tWr7N69m2PHjlG2bFkAFi1aRLly5bh+/ToFCnz8IkhjY2McHR1TIpYQIoPTaDQMKD+ATC+r03X1K2Isb9NwR03Gvh3NkIpD0NfTVzuiEOIzomOjGfDXr8xq1x9iSuKU9yq7pzanmEMxtaMJIdK5FDljFBAQgLW1ta4oAvDw8MDa2hp/f/9Pruvn54e9vT358+enc+fOPH36NCUiCiEysI51i3H7iiUNhv2JVhPD8APDqby8KqdvPFI7mhDiE+68ukPFZRWZdWUEVBtKQZ/DnJ81XIoiIcRXkSJnjIKDg7G3t08w3d7enuDg4I+uV6tWLZo0aUKOHDkIDAxkxIgRVKlShdOnT2NsbJzoOpGRkURGRuqeh4a+v2YgOjqa6Ojo/3gk/11chrSQRSSftF/69qn2c7Y1Y0Prmay6WJo+//Th8LoylP7RlIETjzC+e9kEy4vUJ5+/9O1rt1/f3/1Z8aI74WZXyWSSibmTyvF9YY+vug/xP/L5S9+k/f4nOa+BRknG0EyjR49mzJgxn1zm5MmT7NmzhxUrVnD9+vV48/Lly0fHjh0ZMmRIkvYXFBREjhw5WL9+PY0aNUpWprVr12JmJne3FkJ83sO3QQwYXJbI+yXgu45Ur/6Ajs4dMdE3UTuaEBne29i3DFseyp1tXSD7YQr26MGA3H3IYpRF7WhCiHQgIiKCFi1aEBISgpWV1SeXTdYZo169etG8efNPLpMzZ04uXLjAkydPEsx79uwZDg4OSd6fk5MTOXLk4ObNmx9dZujQofTv31/3PDQ0FBcXF3x8fD578KkhOjoaX19fqlevjqGhodpxRDJJ+6VvyWm/FrWjaDVuPTvNluH7QuGeco8V363C3blEKqUV/yafv/Tta7Sf/wN/+m/rz51cCpg0oaJnLDt7ncDEKEU6vIgPyOcvfZP2+5+43mRJkay/LHZ2dtjZ2X12uXLlyhESEsKJEycoU6YMAMePHyckJITy5csneX8vXrzgwYMHODk5fXQZY2PjRLvZGRoapqk3QlrLI5JH2i99S0r72RgasmNyc/bdyULrza258TSQ8pWiqVnnCFtmVMLIUAZmUIt8/tK3L2m/sLdRdF+4hLUhvdAqWrLnys6cY1ep6+adMiHFR8nnL32T9iNZx58igy8UKlSImjVr0rlzZ44dO8axY8fo3LkzdevWjTciXcGCBdm8eTMAYWFhDBw4kICAAO7evYufnx/16tXDzs6Ohg0bpkRMIYRIoGruqlzofoHiz6ai3K/AruVFqTDnO269vKV2NCEyhCPXrmJf4DarB7ZD+6QAbd3acqHbBeq6Jf2HVSGE+BIpdh+jNWvWULRoUXx8fPDx8aFYsWKsWrUq3jLXr18nJCQEAH19fS5evEj9+vXJnz8/bdu2JX/+/AQEBGBpaZlSMYUQIgE7MztOz/2RdiOPYNKoN6dCduI23425J+eSjMsyhRDJEKuNZar/VKr8WZy3xnfRGL1lZMmFLG+wHGsTuTeRECLlpVgn3cyZM7N69epPLvPhFwxTU1P++eeflIojhBDJoqenYdmYiox+7UK7v4Pwu+tHz4XLGdWlJDvXZad0QWe1IwrxzQi4/IDBx9py+OEBAKr2W8M0H3fc8lZUOZkQIiNJsTNGQgjxLciRKQf72uzjd5/paHYs5Pk5Dyq08WX1hdVy9kiI/0hRFLr/6kd5dysOr6mAuaE5C+suxLf7KtzyJrzthxBCpCQpjIQQ4jP0NHr0LdeHbRutsC52mOjK/Wi9uTXf//k9z8KfqR1PiHTpYehD6q2rx/wTiyDSGquHjTnT+Tyd3Tuj0WjUjieEyICkMBJCiCSqUz43z8+W45c6/THQM+Cvq3+Rs+EyBkw/KmePhEgirVZh+r41uM51ZcfNHRgW30jLXzbz9FJR8mfJo3Y8IUQGJoWREEIkg4GeAcMrDed4p+PkCmtOhO9AfutXgSqT+/P4zWO14wmRpp249gD74qfo90NxQsPfUSZrGc52PcPq4Q0xNpIh8YUQ6pLCSAghvkBJp5KcG70cz1aH0ZRaiN+76RSeU5glZ5bI2SMh/kWraJlzYg6VV1fgxZ3s8CoPPZxW4N/BH1d7V7XjCSEEIIWREEJ8MStzYw6t8uLsNg9KOZciJDKETn/2w9nTl0Pn76sdT4g04cTN21ReUZleu3oRYfiAoj0msvtwMHN6NEdfT84SCSHSDimMhBDiP3JzLEZAxwCmVJ+Cvt+vBB/1wbvma34PmE6MNkbteEKo4l10JCOWvaVi8ewcOhyDuaE5s2rN4tyvv1HDI6fa8YQQIgEpjIQQ4isw0DNgYPmB7JpRG+sC51Bq9KH/nn6UWVSGE49OqB1PiFTld9ePUkvcuXg/DKLNyH5/CBe7X6RXmV7oaeSrhxAibZK/TkII8RVVL5ODF1eKseDHH8hkkomzwWcpO2ASRev5ce/Ja7XjCZGibj58Qcu1Pai8ojI3Xt7AutYEek48SuA/dcllk0vteEII8UlSGAkhxFemr6dHF/cuXO91nRaF2sOuGVza7o1ru3msubBGBmcQ3xxFUeg7Yx8FCmpZ+3sRNGjoWrIrc0r+wu8DyqCnJ/clEkKkfVIYCSFECrE3t2dN06VMnfMC88KHCHcfS6vNrai2qhrXnl1XO54QX8XZoLN4LvNkxtlfUMKzYPy4OvtbBDCr5iwsDCzUjieEEEkmhZEQQqSwAa2K8/KCB+NrjMDEwIT9gfspXOU8Hs338+h5qNrxhPgitx6+pNG0Xym1qBRHHxzFLP9J2kzayItbOfHOV1bteEIIkWxSGAkhRCow0jfiZ8+fudzjMuWUASiXmnL8T0/cJtdm2dllaBWt2hGFSJIYbQxD12wgfwGFzaPboH1nRvMizbne6zorBn+Puamh2hGFEOKLSGEkhBCpKLdNbo6OmsrI+aew++43XpgfpcPWDpRZVIYdZ0+qHU+ITzp07xClFpZi0rU2KCYvMLYMZ2XVfaxrvI5sVtnUjieEEP+JFEZCCJHKNBoY07UUjzb2Y5rPNKyMrTh9PYi6HgXJ5X2YG0GP1I4oRDwHzt7Ftdl6vJZ5cf7JeWwszBm95Biv7+akddUyascTQoivQgojIYRQiZG+Ef3L9edGrxt4Rk2AKEvu3tHDbUk+hu8fTsi7ELUjigzuecRzum8aRJVyNlz5ozncqEdX967c+PEGoxq0wcTIQO2IQgjx1chfNCGEUJmDhQOHZrVlVe1r/H5yEWdj3zL+8HjmHV+MT9gqFg6rhKWZsdoxRQYSHvmWWSdnMPHIREIjQ6FUZmxDfFjQZSqNvfOrHU8IIVKEnDESQog0onWtgpwesYzNzTZT0K4gL482YP2E6mRxvcTq82tkgAaR4mK1WrpPPEwml8cM3biA0MhQijsW55+lZXh+saQURUKIb5oURkIIkYZoNBoaFGzAxe4X6ejRDD3Lp0QWWkbrLa1wX+jOP7f+kRvEiq9Oq2jZdGUTbvOLMX9pGDHP8mB+cgwrG6zkdJfT+OSvonZEIYRIcVIYCSFEGmSgZ8Di4ZUJumfB2IEuWBlbcS74HDUnjiVTwXNMW3taCiTxn2m1CqMWHaP4rPJ8/+f3XH52GfMav+LT+RD3djahtVtr9DTyVUEIkTHIXzshhEjD7G3MGFFlMHd636GfRz/0Do8g9EYJBk47jecyT/be2SsFkkg2RVHYdXMXdmV9GdvFg4s7ymNpZMnISiN5OHUL/yyshK21qdoxhRAiVUlhJIQQ6YCtmS2/1fiN41uLU6zeYYy8p3H0wVGqr6pO2en1mbpGziCJz9NqFXbe2EWFpRWovbY2r5zXg2EEXtlqENgnkDGVx5DJJJPaMYUQQhVSGAkhRDpSqqAj57d6Ejj6AH3K9sFY35iTf1Tmp1buZK25nm3Xt8kgDSKBGG0MA2YewiLnVeqMnUnAwwBMDEzo29WOi9ci8FtSA1szW7VjCiGEqqQwEkKIdMjZ0pnpNadzp88dSmZ1A/1IgrKs4Lv13+E615UFx5fxJiJS7ZhCZW+j3zLv5Dzyz8rPb+tP8PZBYfRPDKC/R3/u9L7D77UnUyS3ndoxhRAiTZDCSAgh0jFnS2dOb6zCmSuv+amNG1bGVlx7fo1u4wLI5PSSxoN38OrtK7VjilQWGPSKmt33k22ENz129iDwdSA2VVZQud0hru5zZ1qNaThZOqkdUwgh0hQpjIQQ4htQIr8Dk31+5UG/B0zzmYbx1XZoQ53467wvLr+70Hd3X26+uKl2TJHCzgefp/PWzuTz2cc/86vwcm97cljnYHat2TwcdZz9yyqRz8VG7ZhCCJEmGagdQAghxNdjZWxF/3L96Xoxmv7T/DlqcZzLIeHMOD6DGesuYnduIj17RzO8fVkM9OR/Ad+Ct5HRjJh/An+D8QQ83/V+YsnbmLwoTofvizL9x5sY6huqG1IIIdIBOWMkhBDfIHNTQxYML8/FPv780+of6uSrAyd68vxCGcYsPEOuGbn45eAvBL0JUjuq+EJBb4L45eAv2BQ/zLS+FQjYng8DPQOauTbj0NixhD/Mw5whFaQoEkKIJJKfC4UQ4hum0WjwyeODTx4f9ud/wNBfD3Ejx3oehj5kpN9Ixvy9EucTy+jR1YifWrqjr6evdmTxCW8jo5mw/BRnLSax+/YOYpVYyNMVzQM3auStweI+g8hqlVXtmEIIkS5JYSSEEBlElVIuHP/ThciY/Wy8spG5p+bi71uPB0crMvTJTmY+daFVsVa0dWuLq72r2nHFBy49vcSys8uZ0a4DscHloEU05I+lvEt5OtX2otF6C6wtaqsdUwgh0jUpjIQQIoMxNjCmZbGWtCzWkg3ZrzPu98PczbKGoLAgpvhPYcqBuVj+dYDqdcKYNiwfOTNnUztyhnT04n1+W3uBG9mHcunppfcTc2RD88aeWlnbMq3nbxS0K6huSCGE+IZIYSSEEBlYs2oFaFatAFGxZdlx43tWnF/Btj9seXO9NH+9uMpfli5UyF6Bpq5NqZfne3LZOasd+Zt2P+Q+m69uZvXJ7ZzquxO02eHHfhhmMaR2vto0rZ2f+kWsMTdtpnZUIYT45khhJIQQAiN9IxoWakjDQg25XOY5I3Ic4mLIUW5p4OiDoxy9f5Q+s2phleUs3cYep23lShSyK4RGo1E7erqmKAr7L1xj0pwgLj28Q3DZzv+bmXsvmQyc6VV2Cv0beWFjKsNsCyFESpLCSAghRDyuue346/dKQCUehbZh45WNLPc9ybmX+QgNjWDyhfJMvvqO3Da5KRn1I2WdKtKpviuZLEzVjp4uPHn1hn03juL/Yju7bu3iziUbWHQKDMugce9NxdylaFyoMQ1/LE72zE6Am9qRhRAiQ5DCSAghxEdltcpKH48+9PEA//qPWel7jnuO3uwP3M+dV3e4s6ogG2+XYkitgXg1P0vVXFWpnKMapZzdMTSQEe4AomOjORN0hv2B+1k0w5bALW2h3BmoNgcAIxdjslTwo6q3IWN63yVnFnuVEwshRMYkhZEQQogkKV/MmfLFnIHahEWF4Xt7L0OOmnLr6VNic/7D/sBL7A/cD7f80Py1DpcK/nQefp7yLuUpk7UMFkYWah9CqgiPCifgwTEmTlI4d8yat3Wa89b0zvuZsa0htgtmLz1oW6o7NfLUoGruqliMyBivjRBCpGUpVhiNHz+eHTt2cO7cOYyMjHj9+vVn11EUhTFjxrBw4UJevXpF2bJlmTNnDq6uMmysEEKkJRZGFjQs1ICGe0CrVbj+4k/2B+5jb+BedvlVJDLClvvPnjPiwAgA9DR6WG7ZQ1ZHfdr0vksl1wIUdSia7ouliOgI9p6/zOo/wrj76iHhJSZx7fk1tIoWtp+B4BJQ0B3b0iF45vDEs5IXRQbfp3rZKmg0VdSOL4QQ4gMpVhhFRUXRpEkTypUrx5IlS5K0zuTJk/ntt99Yvnw5+fPnZ9y4cVSvXp3r169jaWmZUlGFEEL8B3p6GgplKUihLAXpWaYn7xrEsn7PNa6HmnDP5Af8H/hz73E4IWerEgIMcbOG46Fo0OBweyAGt7+jjM9dvqsfS37b/OS3zY+tma3ah6WjKAov3r7g9svbbNgSSoC/PgaFt/PY6m8CXwWi3C8HS4+C5SPI1gYAFysXsjY+QXbTcDr/MJ4qJfKgp9FT+UiEEEJ8SooVRmPGjAFg+fLlSVpeURSmT5/OsGHDaNSoEQArVqzAwcGBtWvX0rVr15SKKoQQ4isyMdanXb3/a+/+g6Ku9z2OPxdYFkF+HEB+DZgc6YolKLpeA7SslLncjif+qTQznWmaccSKPN2mHzPFOF6ocZrRTiMz+Efo3OulmVuY54wizGRkMZZQeyTqqh1NMECCkoUVAWHvHxxRDxa71Pbl674eMzvD9zPf/frafe8OvP18v59vOpAOrAHgVFsbu2Z8iuNrJ2EZS3F0OGjrbaPjbxlwYinnQw7xHiWjBxiYjuXPfyckupM7nirl4KGDzIyayUh7BpZLCcyfZyX999OJnhZNVEgUgQGTu5bpysgV+gb7OPntRZq/cUJ4ByPhLXS6Ojl5xsXhP/+BPhewbiWuIdfok/53H3y5BlZUw9LR0+PiZ3cwkvk56Zl9/Omhv/KvKQtJDE/8ZW+iiIj85qbMNUZnz56lo6ODvLy8sTGbzcY999xDfX39TzZGAwMDDAwMjG07nU4AhoaGGBoa8m1oD1zNMBWyiPdUP3NT/aaO1Bkz2F404x9bywHodHXy32ktHK2vI3h2GBdj7uNU9ynOt83A3RdH/3AAja5Pafzi09GnVb0Nf/sjrHgelm4fHetNgF3NBExzkvTyMkKsIYQEhtBdvYmepqXE3FNJ1JK/MOIe4XJ3LOd2VjDiBuuz6QwMD1x33A1w/z5Y9vromCsGGv9z9Of+IQiCxOmJRGV/iyX5KPfm51Lw73nMjZ1LXFgc/MeNr1efOX3/zE71MzfV7xpv3oMp0xh1dHQAEB8ff8N4fHw8586d+8nnlZaWjs1OXa+mpobQ0NBfN+QvUFtba3QE+QVUP3NT/aauOdNhTh7AnaOPKHAmDXJi1j4u9F4mPGUTXYNddA91c+J3FnoS/g9bzEWuBEyjf6Qf+qOhP5oRt4XzveevHbjVBt9mcCntv2jtbBod65sB3bMAGBgahH+c2RYY2YE78juiQ6KYFWEnMiiSqLjf8f26/yE5boQl6TtJDI0hOCAY0gB+AMDV7KKBht/kfTIzff/MTfUzN9UPLl265PG+Frfb7fZ05+Li4ps2Idc7fvw4drt9bLuiooKioqIJF1+or68nNzeXtrY2EhOvnYLw5JNP0traSnV19U2fd7MZo5SUFLq6uoiIiPDgVfnW0NAQtbW1rFy5EqvVanQc8ZLqZ26qn7lNVL+h4SHafvyB02cHcV0eJCWth/4r/Vy+cpmTzdP44UIoKb93kTzrMgGWANzDgZz7Ko6o8GCy5gcRETKdMGsYtiCbAa/u1qfvn7mpfuam+l3jdDqJjY2lp6dnwt7AqxmjzZs3s3r16p/dZ9asWd4cckxCQgIwOnN0fWPU2dk5bhbpejabDZtt/C81q9U6pT4IUy2PeEf1MzfVz9x+qn5Wq5W0xFDSbnI5z7/9y08cLP3XzSYT0/fP3FQ/c1P98Or1e9UYxcbGEhsb63UgT6SmppKQkEBtbS1ZWVnA6Mp2dXV1vP766z75N0VERERERGDsDOtfX0tLCw6Hg5aWFoaHh3E4HDgcDvr6+sb2SU9Pp6qqCgCLxUJRURElJSVUVVXx5ZdfsmHDBkJDQ3n00Ud9FVNERERERMR3iy+88sor7NmzZ2z76izQkSNHWL58OQAnT56kp6dnbJ/nn3+e/v5+Nm3aNHaD15qaGt3DSEREREREfMpnjVFFRcWE9zD653UfLBYLxcXFFBcX+yqWiIiIiIjIOLoNt4iIiIiI+D01RiIiIiIi4vfUGImIiIiIiN9TYyQiIiIiIn5PjZGIiIiIiPg9NUYiIiIiIuL3fLZct1GuLgHudDoNTjJqaGiIS5cu4XQ6sVqtRscRL6l+5qb6mZvqZ26qn7mpfuam+l1ztSf459sE3cwt1xj19vYCkJKSYnASERERERGZCnp7e4mMjPzZfSxuT9onExkZGaGtrY3w8HAsFovRcXA6naSkpNDa2kpERITRccRLqp+5qX7mpvqZm+pnbqqfual+17jdbnp7e0lKSiIg4OevIrrlZowCAgJITk42OsY4ERERfv/BNDPVz9xUP3NT/cxN9TM31c/cVL9RE80UXaXFF0RERERExO+pMRIREREREb+nxsjHbDYbr776KjabzegoMgmqn7mpfuam+pmb6mduqp+5qX6Tc8stviAiIiIiIuItzRiJiIiIiIjfU2MkIiIiIiJ+T42RiIiIiIj4PTVGIiIiIiLi99QY+dCuXbtITU0lJCSERYsWcfToUaMjiYc++ugjVq1aRVJSEhaLhf379xsdSbxQWlrK4sWLCQ8PJy4ujoKCAk6ePGl0LPFQWVkZmZmZYzcmzM7O5tChQ0bHkkkoLS3FYrFQVFRkdBTxUHFxMRaL5YZHQkKC0bHEC9999x2PPfYYMTExhIaGsmDBAhobG42OZQpqjHzknXfeoaioiJdffpkvvviCZcuWkZ+fT0tLi9HRxAMul4v58+fz1ltvGR1FJqGuro7CwkKOHTtGbW0tV65cIS8vD5fLZXQ08UBycjKvvfYaDQ0NNDQ0cN999/Hggw/S3NxsdDTxwvHjxykvLyczM9PoKOKlO++8k/b29rFHU1OT0ZHEQz/++CO5ublYrVYOHTrEV199xRtvvEFUVJTR0UxBy3X7yJIlS1i4cCFlZWVjY3PnzqWgoIDS0lIDk4m3LBYLVVVVFBQUGB1FJun7778nLi6Ouro67r77bqPjyCRER0ezfft2nnjiCaOjiAf6+vpYuHAhu3btYtu2bSxYsIAdO3YYHUs8UFxczP79+3E4HEZHkUl44YUX+OSTT3SW0iRpxsgHBgcHaWxsJC8v74bxvLw86uvrDUol4r96enqA0T+uxVyGh4eprKzE5XKRnZ1tdBzxUGFhIQ888AArVqwwOopMwunTp0lKSiI1NZXVq1dz5swZoyOJhw4cOIDdbuehhx4iLi6OrKwsdu/ebXQs01Bj5ANdXV0MDw8THx9/w3h8fDwdHR0GpRLxT263my1btrB06VLmzZtndBzxUFNTE9OnT8dms7Fx40aqqqq44447jI4lHqisrOTzzz/X2REmtWTJEvbu3cvhw4fZvXs3HR0d5OTk0N3dbXQ08cCZM2coKyvj9ttv5/Dhw2zcuJGnn36avXv3Gh3NFIKMDnArs1gsN2y73e5xYyLiW5s3b+bEiRN8/PHHRkcRL8yZMweHw8HFixd59913Wb9+PXV1dWqOprjW1laeeeYZampqCAkJMTqOTEJ+fv7YzxkZGWRnZzN79mz27NnDli1bDEwmnhgZGcFut1NSUgJAVlYWzc3NlJWV8fjjjxucburTjJEPxMbGEhgYOG52qLOzc9wskoj4zlNPPcWBAwc4cuQIycnJRscRLwQHB5OWlobdbqe0tJT58+ezc+dOo2PJBBobG+ns7GTRokUEBQURFBREXV0db775JkFBQQwPDxsdUbwUFhZGRkYGp0+fNjqKeCAxMXHcfyDNnTtXi395SI2RDwQHB7No0SJqa2tvGK+trSUnJ8egVCL+w+12s3nzZt577z0++OADUlNTjY4kv5Db7WZgYMDoGDKB+++/n6amJhwOx9jDbrezdu1aHA4HgYGBRkcULw0MDPD111+TmJhodBTxQG5u7rjbU5w6dYrbbrvNoETmolPpfGTLli2sW7cOu91OdnY25eXltLS0sHHjRqOjiQf6+vr45ptvxrbPnj2Lw+EgOjqamTNnGphMPFFYWMi+fft4//33CQ8PH5u9jYyMZNq0aQank4m89NJL5Ofnk5KSQm9vL5WVlXz44YdUV1cbHU0mEB4ePu5avrCwMGJiYnSNn0k899xzrFq1ipkzZ9LZ2cm2bdtwOp2sX7/e6GjigWeffZacnBxKSkp4+OGH+eyzzygvL6e8vNzoaKagxshHHnnkEbq7u9m6dSvt7e3MmzePgwcPqmM3iYaGBu69996x7avnVa9fv56KigqDUomnri6Tv3z58hvG3377bTZs2PDbBxKvXLhwgXXr1tHe3k5kZCSZmZlUV1ezcuVKo6OJ3PLOnz/PmjVr6OrqYsaMGdx1110cO3ZMf7+YxOLFi6mqquLFF19k69atpKamsmPHDtauXWt0NFPQfYxERERERMTv6RojERERERHxe2qMRERERETE76kxEhERERERv6fGSERERERE/J4aIxERERER8XtqjERERERExO+pMRIREREREb+nxkhERERERPyeGiMREREREfF7aoxERERERMTvqTESERERERG/p8ZIRERERET83v8DcfIwxPdc1xQAAAAASUVORK5CYII=",
      "text/plain": [
       "Figure(PyObject <Figure size 1000x400 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 0.0\n",
    "b = 2pi  # One period\n",
    "u_0 = 2.0\n",
    "k = 40.0\n",
    "n = 400\n",
    "\n",
    "(t, U) = eulermethod(f4, a, b, u_0, n)\n",
    "u = u4.(t, a, u_0, k)\n",
    "\n",
    "figure(figsize=[10,4])\n",
    "title(\"The exact solution is u = cos t + $(u_0-1) exp(-$k t)\")\n",
    "plot(t, u, \"g\", label=\"Exact solution for k=$k\")\n",
    "plot(t, U, \":b\", label=\"Euler's answer for h=$(approx4((b-a)/n))\")\n",
    "legend()\n",
    "grid(true);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, with large steps (still small enough to handle the $\\cos t$ part),\n",
    "there is a catastrophic failure, with growing oscillations.\n",
    "\n",
    "As we will see, these are a characteristic feature of *instability*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 1000x400 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 124\n",
    "\n",
    "(t, U) = eulermethod(f4, a, b, u_0, n)\n",
    "u = u4.(t, a, u_0, k)\n",
    "\n",
    "figure(figsize=[10,4])\n",
    "title(\"The exact solution is u = cos t + $(u_0-1) exp(-$k t)\")\n",
    "plot(t, u, \"g\", label=\"Exact solution for k=$k\")\n",
    "plot(t, U, \".:b\", label=\"Euler's answer for h=$(approx4((b-a)/n))\")\n",
    "legend()\n",
    "grid(true);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To show that the $k$ part is the problem, reduce $k$ while leaving the rest unchanged:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 1000x400 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k = 10.0\n",
    "\n",
    "(t, U) = eulermethod(f4, a, b, u_0, n)\n",
    "u = u4.(t, a, u_0, k)\n",
    "\n",
    "figure(figsize=[10,4])\n",
    "title(\"The exact solution is u = cos t + $(u_0-1) exp(-$k t)\")\n",
    "plot(t, u, \"g\", label=\"Exact solution for k=$k\")\n",
    "plot(t, U, \".:b\", label=\"Euler's answer for h=$(approx4((b-a)/n))\")\n",
    "legend()\n",
    "grid(true);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Variable Time Step Sizes $h_i$ (just a preview)\n",
    "\n",
    "It is sometime useful to adjust the time step size; for example reducing it when the derivative is larger,\n",
    "(as happens in Example 3 above).\n",
    "This gives a slight variant, now expressed in pseudo-code:\n",
    "\n",
    "Input: $f$, $a$, $b$, $n$ <br>\n",
    "$t_0 = a$ <br>\n",
    "$U_0 = u_0$ <br>\n",
    "for i from 1 to n <br>\n",
    "$\\quad$ Choose $h_i$ somehow <br>\n",
    "$\\quad t_{i} = t_{i-1} + h_i$ <br>\n",
    "$\\quad U_{i} = U_{i-1} + h_i f(t_{i-1}, U_{i-1})$ <br>\n",
    "end\n",
    "\n",
    "In a later section, we will see how to estimate errors within an algorithm,\n",
    "and then how to use such error estimates to guide the choice of step size."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Error Analysis for the Canonical Test Case, $u' = k u$.\n",
    "\n",
    "A great amount of intuition about numerical methods for solving ODE IVPs comes from that \"simplest nontrivial example\", number 2 above.\n",
    "We can solve it with constant step size $h$, and thus study its errors and accuracy.\n",
    "The recursion relation is now\n",
    "\n",
    "$$U_{i} = U_{i-1} + h k U_{i-1} = U_{i-1} (1 + hk),$$\n",
    "\n",
    "with solution\n",
    "\n",
    "$$U_i = u_0 (1 + hk)^i$$\n",
    "\n",
    "For comparison, the exact solution of this ODE IVP is\n",
    "\n",
    "$$u(t_i) = u_0 e^{k(t_i - a)} = u_0 e^{k ih} = u_0 (e^{kh})^i$$\n",
    "\n",
    "So each is a geometric series: the difference is that the *growth factor* is $G = (1 + hk)$ for Euler's method,\n",
    "vs $g = e^{kh} = 1 + hk + (hk)^2/2 + \\cdots = 1 + hk + O(h^2)$ for the ODE.\n",
    "\n",
    "Ths deviation at each time step is $O(h^2)$, suggesting that by the end $t=b$, at step $n$, the error will be\n",
    "$O(n h^2) = O\\left(\\displaystyle\\frac{b-a}{h} h^2\\right) = O(h)$.\n",
    "\n",
    "This is in fact what happens, but to verify that, we must deal with the challenge that once an error enters at one step, it is potentially amplified at each subsequent step, so the errors introduced at each step do not simply get summed like they did with definite integrals."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Global Error and Local (Truncation) Error\n",
    "\n",
    "Ultimately, the error we need to understand is the **global error**: at step $i$,\n",
    "\n",
    "$$ E_i = u(t_i) - U_i $$\n",
    "\n",
    "We will approach this by first considering the new error added at each step, the **local truncation error** (or **discretization error**).\n",
    "\n",
    "At the first step this is the same as above:\n",
    "\n",
    "$$ e_1 = u(t_1) - U_1 = u(a+h) - U_1 $$\n",
    "\n",
    "However at later steps we compare the results $U_{i+1}$ to what the solution would be if it were exact at the start of that step: that is, if $U_i$ were exact.\n",
    "\n",
    "Using the notation $u(t; t_i, U_i)$ introduced <a href=\"#IVP_notation\">above</a> for the solution of the ODE with initial condition $u(t_i) = U_i$, the **location truncation error** at step $i$ is the discrepancy at time $t_{i+1}$ between what Euler's method and the exact solution give when both start at that point $(t_i, U_i)$:\n",
    "\n",
    "$$ e_i = u(t; t_i, U_i) - U_{i+1} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Error propagation in $u' = k u$, $k \\geq 0$.\n",
    "\n",
    "After one step, $E_1 = u(t_1) - U_1 = e_1$.\n",
    "\n",
    "At step 2,\n",
    "\n",
    "$$ E_2 = u(t_2) - U_2 = (u(t_2) - u(t_2, t_1, U_1) + (u(t_2, t_1, U_1) - U_2)\n",
    "= (u(t_2) - u(t_2, t_1, U_1) + e_2 $$\n",
    "\n",
    "The first term is the difference at $t=t_2$ of two solutions with values at $t = t_1$ being $u(t_1)$ and $U_1$ respectively. As the ODE is linear and homogeneous, this is the solution of the same ODE with value at $t=t_1$ being $u(t_1) - U_1$, which is $e_1$:\n",
    "that solution is $e_1 e^{y(t - t_1}$, so at $t=t_2$ it is $e_1 e^{kh}$.\n",
    "Thus the global error after two steps is\n",
    "\n",
    "$$ E_2 = e_2 + (e^{kh})e_1: $$\n",
    "\n",
    "the error from the previous step has been amplified by the growth factor $g = e^{kh}$:\n",
    "\n",
    "$$ E_2 = e_2 + g e_1: $$\n",
    "\n",
    "This continues, so that\n",
    "\n",
    "$$ E_3 = e_3 + g E_1 = e_3 + g (e_2 + g e_1) = e_3 + ge_2 + g^2 e_1 $$\n",
    "\n",
    "and so on, leading to\n",
    "\n",
    "$$ E_i = e_i + g e_{i-1} + g^2 e_{i-2} + \\cdots + g^{i-1} e_{1} $$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bounding the local truncation errors ...\n",
    "\n",
    "To get a bound on the global error from the formula above, we first need a bound on the local truncation errors $e_i$.\n",
    "\n",
    "Taylor's theorem gives $e^{kh} = 1 + kh + e^{k \\xi} (kh)^2/2$, $0 < \\xi < k h$, so\n",
    "\n",
    "$$\n",
    "e_i = U_i e^{kh} - U_i (1 + kh) = U_i (e^{k \\xi} h^2/2)\n",
    "$$\n",
    "\n",
    "and thus\n",
    "\n",
    "$$|e_i| \\leq |U_i| \\frac{e^{kh}}{2} h^2$$\n",
    "\n",
    "Also, since $1 + kh < e^{kh}$,\n",
    "$|U_i| < |u(t_i)| = |u_0| e^{k(t_i - a)},$\n",
    "and we only need this to the beginning of the last step, $i \\leq n-1$, for which\n",
    "\n",
    "$$\n",
    "|U_i| < |u_0| e^{k(b - h - a)}\n",
    "$$\n",
    "\n",
    "Thus\n",
    "\n",
    "$$\n",
    "|e_i| \\leq \\frac{|u_0| e^{k(b - h - a)} e^{kh}}{2} h^2 = \\frac{|u_0 e^{k(b - a)}|}{2} h^2\n",
    "$$\n",
    "\n",
    "That is,\n",
    "\n",
    "$$ |e_i| \\leq C h^2 \\text{ where } C := \\frac{|u_0 e^{k(b - a)}|}{2} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ... and using this to complete the bound on the global truncation error\n",
    "\n",
    "Using this bound on the local errors $e_i$ in the above sum for the global error $E_i$,\n",
    "\n",
    "$$ | E_i | \\leq C h^2 (1 + g + \\cdots g^{i-1}) = C \\frac{g^i - 1}{g-1} h^2 $$\n",
    "\n",
    "Since $g^i = e^{k h i} = e^{k (t_i - a)}$ and the denominator $g - 1 = e^{kh} - 1 > k h$,\n",
    "we get\n",
    "\n",
    "$$\n",
    "| E_i | \\leq  C \\frac{e^{k (t_i - a)} - 1}{k h} h^2\n",
    "\\leq \\frac{|u_0 e^{k(b - a)}|}{2} \\frac{e^{k (t_i - a)} - 1}{k} h, = O(h)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that this global error formula is bulilt from three factors:\n",
    "\n",
    "- The first is the constant\n",
    "$\\displaystyle \\frac{|u_0 e^{k(b - a)}|}{2}$\n",
    "which is roughly half of the maximum value of the exact solution over the interval $[a, b]$.\n",
    "\n",
    "- The second\n",
    "$\\displaystyle \\frac{e^{k (t_i - a)} - 1}{k}$\n",
    "depends on $t$, and \n",
    "\n",
    "- The third is $h$, showing the overall order of accuracy: the overall absolute error is $O(h)$, so first order."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A more general error bound\n",
    "\n",
    "A very similar result applies to the solution $u(t; a, u_0)$ of the more general initial value problem\n",
    "\n",
    "$$ \\frac{du}{dt} = f(t, u), \\quad u(a) = u_0 $$\n",
    "\n",
    "so long as the function $f$ is \"somewhat well-behaved\" in that it satisfies a so-called *Lipschitz Condition*:\n",
    "that there is some constant $K$ such that\n",
    "\n",
    "$$ \\left| \\frac{\\partial F}{\\partial u}(t, u) \\right| \\leq K  $$\n",
    "\n",
    "for the relevant time values $a \\leq t \\leq b$.\n",
    "\n",
    "(**Aside:** As you might have seen in a course on differential equations, such a Lipschitz condition is necessary to even guarantee that the initial value problem has a unique solution, so it is a quite reasonable requirement.)\n",
    "\n",
    "Then this constant $K$ plays the part of the exponential growth factor $k$ above:\n",
    "\n",
    "first one shows that the local trunction error is bounded by\n",
    "\n",
    "$$ |e_i| \\leq C h^2 \\text{ where now } C := \\frac{|u_0 e^{K(b - a)}|}{2}; $$\n",
    "\n",
    "then calculating as above bounds the global truncation error with\n",
    "\n",
    "$$\n",
    "| E_i | \\leq \\frac{|u_0 e^{K(b - a)}|}{2} \\frac{e^{K (t_i - a)} - 1}{k} h, = O(h)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### There is much room for improvement\n",
    "\n",
    "As with definite integrals, this is not very impressive, so in the next section on\n",
    "{doc}`ODE-IVP-2-Runge-Kutta`\n",
    "we will explore several widely used methods that improve to second order and then fourth order accuracy.\n",
    "Later, we will see how to get even higher orders."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But first, we can illustrate how this exponential growth of errors looks in some examples, and coapr the the better behaved errors in definite integrals.\n",
    "\n",
    "This will be done by looking at the effect of a small change in the initial value, to simulate an error that arises there."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Error propagation for {prf:ref}`ode-integration`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = 0.0\n",
    "b = 2pi\n",
    "u_0 = 1.0  # Original value\n",
    "n = 100\n",
    "\n",
    "(t, U) = eulermethod(f1, a, b, u_0, n);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But now \"perturb\" the initial value in all cases by this much:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "delta_u_0 = 0.1\n",
    "(t, U_perturbed) = eulermethod(f1, a, b, u_0+delta_u_0, n)\n",
    "u = u1.(t, a, u_0);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "Figure(PyObject <Figure size 1000x400 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=[10,4])\n",
    "title(L\"The solution before perturbing $u(0)$ was $u = \\cos(x)$\")\n",
    "plot(t, u, \"g\", label=\"Original exact solution\")\n",
    "plot(t, U, \".:b\", label=\"Euler's answer before perturbation\")\n",
    "plot(t, U_perturbed, \"r:\", label=\"Euler's answer after perturbation\")\n",
    "legend()\n",
    "grid(true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This just shifts all the $u$ values up by the perturbation of $u_0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Error propagation for {prf:ref}`ode-simplest-genuine`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 1000x400 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k = 1.0\n",
    "a = 0.0\n",
    "b = 2.0\n",
    "u_0 = 1.0  # Original value\n",
    "delta_u_0 = 0.1\n",
    "n = 100\n",
    "\n",
    "(t, U) = eulermethod(f2, a, b, u_0, n)\n",
    "(t, U_perturbed) = eulermethod(f2, a, b, u_0 + delta_u_0, n)\n",
    "u = u2.(t, a, u_0, k)\n",
    "\n",
    "figure(figsize=[10,4])\n",
    "title(L\"The solution before perturbing $u(0)$ was $u = {u_0} \\, \\exp({k} \\, t)$\")\n",
    "plot(t, u, \"g\", label=\"Original exact solution\")\n",
    "plot(t, U, \".:b\", label=\"Euler's answer before perturbation\")\n",
    "plot(t, U_perturbed, \".:r\", label=\"Euler's answer after perturbation\")\n",
    "legend()\n",
    "grid(true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Graphing the error shows its exponential growth:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 1000x400 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=[10,4])\n",
    "title(\"Error\")\n",
    "plot(t, u - U_perturbed, \".:\")\n",
    "grid(true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "<a name=\"exercise-1\"></a>\n",
    "### Exercise 1\n",
    "\n",
    "Show that for the integration case $f(t, u) = f(t)$,\n",
    "[Euler's Method](#eulers-method)\n",
    "is the same as the Composite Left-hand Endpoint Rule,\n",
    "as in the section {doc}`integrals-2-composite-rules`"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.8.1",
   "language": "julia",
   "name": "julia-1.8"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.8.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
