{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "99cbfc22",
   "metadata": {},
   "source": [
    "```{try_on_binder}\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "bfdedc63",
   "metadata": {
    "load": "myst_code_init.py",
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The pymor.discretizers.builtin.gui.jupyter extension is already loaded. To reload it, use:\n",
      "  %reload_ext pymor.discretizers.builtin.gui.jupyter\n"
     ]
    }
   ],
   "source": [
    "from IPython import get_ipython\n",
    "ip = get_ipython()\n",
    "if ip is not None:\n",
    "    ip.run_line_magic('load_ext', 'pymor.discretizers.builtin.gui.jupyter')\n",
    "    ip.run_line_magic('matplotlib', 'inline')\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\", category=UserWarning, module='torch')\n",
    "import pymor.tools.random\n",
    "pymor.tools.random._default_random_state = None\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f427ed12",
   "metadata": {},
   "source": [
    "# Tutorial: Linear time-invariant systems\n",
    "\n",
    "In this tutorial,\n",
    "we discuss finite-dimensional, continuous-time, linear time-invariant (LTI)\n",
    "systems of the form\n",
    "\n",
    "```{math}\n",
    "\\begin{align}\n",
    "    E \\dot{x}(t) & = A x(t) + B u(t), \\\\\n",
    "    y(t) & = C x(t) + D u(t).\n",
    "\\end{align}\n",
    "```\n",
    "\n",
    "where\n",
    "{math}`u` is the input,\n",
    "{math}`x` the state, and\n",
    "{math}`y` the output of the system,\n",
    "and {math}`A, B, C, D, E` are matrices of appropriate dimensions\n",
    "(more details can be found in {cite}`A05`).\n",
    "In pyMOR, these models are captured by {{ LTIModels }},\n",
    "which contain the matrices {math}`A, B, C, D, E` as {{ Operators }}.\n",
    "We start by building an {{ LTIModel }} and then demonstrate some of its properties,\n",
    "using a discretized heat equation as the example.\n",
    "\n",
    "We focus on a non-parametric example,\n",
    "but parametric LTI systems can be handled similarly\n",
    "by constructing {math}`A, B, C, D, E` as parametric {{ Operators }} and\n",
    "passing {{ parameter_values }} via the `mu` argument to the methods of the\n",
    "{{ LTIModel }}.\n",
    "\n",
    "::: {note}\n",
    "\n",
    "Discrete-time LTI systems can be constructed by passing positive values for the\n",
    "`sampling_time` to any constructor of an {{LTIModel}}.\n",
    "\n",
    ":::\n",
    "\n",
    "## Building a model\n",
    "\n",
    "We consider the following one-dimensional heat equation over {math}`(0, 1)` with\n",
    "two inputs {math}`u_1, u_2` and three outputs {math}`y_1, y_2, y_2`:\n",
    "\n",
    "```{math}\n",
    "\\begin{align}\n",
    "    \\partial_t T(\\xi, t) & = \\partial_{\\xi \\xi} T(\\xi, t) + u_1(t),\n",
    "    & 0 < \\xi < 1,\\ t > 0, \\\\\n",
    "    -\\partial_\\xi T(0, t) & = -T(0, t) + u_2(t),\n",
    "    & t > 0, \\\\\n",
    "    \\partial_\\xi T(1, t) & = -T(1, t),\n",
    "    & t > 0, \\\\\n",
    "    y_k(t) & = 3 \\int_{\\frac{k - 1}{3}}^{\\frac{k}{3}} T(\\xi, t) \\, \\mathrm{d}\\xi,\n",
    "    & t > 0,\\ k = 1, 2, 3.\n",
    "\\end{align}\n",
    "```\n",
    "\n",
    "There are many ways of building an {{ LTIModel }}.\n",
    "Here, we show how to build one from custom matrices,\n",
    "instead of using a discretizer as in {doc}`tutorial_builtin_discretizer`\n",
    "(and the {meth}`~pymor.models.basic.InstationaryModel.to_lti` method of\n",
    "{{ InstationaryModel }} to obtain an {{ LTIModel }}).\n",
    "In particular, we will use the\n",
    "{meth}`~pymor.models.iosys.LTIModel.from_matrices` method of {{ LTIModel }},\n",
    "which instantiates an {{ LTIModel }} from NumPy or SciPy matrices.\n",
    "\n",
    "First, we do the necessary imports and some matplotlib style choices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "4ff56861",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import scipy.sparse as sps\n",
    "from pymor.models.iosys import LTIModel\n",
    "\n",
    "plt.rcParams['axes.grid'] = True"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bb134db6",
   "metadata": {},
   "source": [
    "Next, we can assemble the matrices based on a centered finite difference\n",
    "approximation using standard methods of NumPy and SciPy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "78b22cce",
   "metadata": {
    "load": "heat_equation.py"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.sparse as sps\n",
    "\n",
    "k = 50\n",
    "n = 2 * k + 1\n",
    "\n",
    "E = sps.eye(n, format='lil')\n",
    "E[0, 0] = E[-1, -1] = 0.5\n",
    "E = E.tocsc()\n",
    "\n",
    "d0 = n * [-2 * (n - 1)**2]\n",
    "d1 = (n - 1) * [(n - 1)**2]\n",
    "A = sps.diags([d1, d0, d1], [-1, 0, 1], format='lil')\n",
    "A[0, 0] = A[-1, -1] = -n * (n - 1)\n",
    "A = A.tocsc()\n",
    "\n",
    "B = np.zeros((n, 2))\n",
    "B[:, 0] = 1\n",
    "B[0, 0] = B[-1, 0] = 0.5\n",
    "B[0, 1] = n - 1\n",
    "\n",
    "C = np.zeros((3, n))\n",
    "C[0, :n//3] = C[1, n//3:2*n//3] = C[2, 2*n//3:] = 1\n",
    "C /= C.sum(axis=1)[:, np.newaxis]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa3f3988",
   "metadata": {},
   "source": [
    "Then, we can create an {{ LTIModel }} from NumPy and SciPy matrices `A`, `B`, `C`,\n",
    "`E`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "980ae209",
   "metadata": {},
   "outputs": [],
   "source": [
    "fom = LTIModel.from_matrices(A, B, C, E=E)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ab2325b",
   "metadata": {},
   "source": [
    "We can take a look at the internal representation of the {{ LTIModel }} `fom`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d0b31433",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LTIModel(\n",
       "    NumpyMatrixOperator(<101x101 sparse, 301 nnz>, source_id='STATE', range_id='STATE'),\n",
       "    NumpyMatrixOperator(<101x2 dense>, range_id='STATE'),\n",
       "    NumpyMatrixOperator(<3x101 dense>, source_id='STATE'),\n",
       "    D=ZeroOperator(NumpyVectorSpace(3), NumpyVectorSpace(2)),\n",
       "    E=NumpyMatrixOperator(<101x101 sparse, 101 nnz>, source_id='STATE', range_id='STATE'),\n",
       "    presets={})"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fom"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7aaf6639",
   "metadata": {},
   "source": [
    "From this, we see that the matrices were wrapped in {{ NumpyMatrixOperators }},\n",
    "while the default value was chosen for the {math}`D` matrix\n",
    "({class}`~pymor.operators.constructions.ZeroOperator`).\n",
    "The operators in an {{ LTIModel }} can be accessed via its attributes, e.g.,\n",
    "`fom.A` is the {{ Operator }} representing the {math}`A` matrix.\n",
    "\n",
    "We can also see some basic information from `fom`'s string representation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "05f8ae94",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LTIModel\n",
      "    class: LTIModel\n",
      "    number of equations: 101\n",
      "    number of inputs:    2\n",
      "    number of outputs:   3\n",
      "    continuous-time\n",
      "    linear time-invariant\n",
      "    solution_space:  NumpyVectorSpace(101, id='STATE')\n"
     ]
    }
   ],
   "source": [
    "print(fom)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2e815cf",
   "metadata": {},
   "source": [
    "which gives the dimensions of the underlying system more directly,\n",
    "together with some of its properties.\n",
    "\n",
    "## Time-domain simulation\n",
    "\n",
    "The `solve` and `output` methods can be used to respectively compute the\n",
    "solution and output trajectories.\n",
    "For this, it is necessary to set the final time and the time-stepper.\n",
    "This could have been done in the `from_matrices` call.\n",
    "Instead of creating a new model using `from_matrices`,\n",
    "we can redefine `fom` using its `with_` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "723dad4d",
   "metadata": {},
   "outputs": [],
   "source": [
    "from pymor.algorithms.timestepping import ImplicitEulerTimeStepper\n",
    "fom = fom.with_(T=4, time_stepper=ImplicitEulerTimeStepper(200))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4fe5af56",
   "metadata": {},
   "source": [
    "With this done, we can compute the output for some given input and plot it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "627c01c9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "29e705aeb9454d19921a683c47a47a4a",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Accordion(children=(HTML(value='', layout=Layout(height='16em', overflow_y='auto', width='100%')),), selected_…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Y = fom.output(input='[sin(4 * t[0]), sin(6 * t[0])]')\n",
    "fig, ax = plt.subplots()\n",
    "for i, y in enumerate(Y.T):\n",
    "    ax.plot(np.linspace(0, fom.T, fom.time_stepper.nt + 1), y, label=f'$y_{i+1}(t)$')\n",
    "_ = ax.set(xlabel='$t$', ylabel='$y(t)$', title='Output')\n",
    "_ = ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2039b18",
   "metadata": {},
   "source": [
    "Additionally, there are the `impulse_resp` and `step_resp` methods for computing\n",
    "the impulse and step responses, respectively.\n",
    "\n",
    "Impulse response for continuous-time LTI systems is given by\n",
    "\n",
    "```{math}\n",
    "h(t) = C e^{t E^{-1} A} E^{-1} B + D \\delta(t),\n",
    "```\n",
    "\n",
    "where {math}`\\delta` is the Dirac function.\n",
    "\n",
    "For computations, we ignore the {math}`D` term and compute the first part by\n",
    "integrating the ODE system\n",
    "\n",
    "```{math}\n",
    "E \\dot{x}_i(t) = A x_i(t),\\ x_i(0) = E^{-1} B e_i\n",
    "```\n",
    "\n",
    "for canonical basis vectors {math}`e_i` to get the {math}`i`-th column of\n",
    "{math}`h_i(t) = C x_i(t)`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "cf47ff5e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_impulse = fom.impulse_resp()\n",
    "fig, ax = plt.subplots(fom.dim_output, fom.dim_input, sharex=True, constrained_layout=True)\n",
    "for i in range(fom.dim_output):\n",
    "    for j in range(fom.dim_input):\n",
    "        ax[i, j].plot(np.linspace(0, fom.T, y_impulse.shape[0]), y_impulse[:, i, j])\n",
    "for i in range(fom.dim_output):\n",
    "    ax[i, 0].set_title(f'Output {i + 1}', loc='left', rotation='vertical', x=-0.2, y=0.2)\n",
    "for j in range(fom.dim_input):\n",
    "    ax[0, j].set_title(f'Input {j + 1}')\n",
    "    ax[-1, j].set_xlabel('Time')\n",
    "_ = fig.suptitle('Impulse response')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ffdae45c",
   "metadata": {},
   "source": [
    "Step response for continuous-time LTI systems is the output corresponding to the\n",
    "zero initial condition and inputs {math}`u_i(t) = e_i`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "720745cf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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6deuaPEYhhKiP1ti/ZWdnc9999xEVFcWcOXOa/f1F85GEUrQZHh4eNSa4BAQEUFBQUKNu9+7da5T16NGD1NTUpgpPCCHqrTX2b6WlpfzhD3+guLiYtWvX1hhbKdoWueQt2gyNRtOox1OpVCiKUqP80kHwQgjRHFpb/2Y0GpkwYQIHDx5kw4YN9OvXr1GOK1ouOUMpXNLJkydrlJ04caLa7OuAgAAKCwtr1EtLS6u2rVKpGjs8IYSoN2f3b1arlalTp5KcnMxnn33G6NGj63wM0fpIQilc0po1azh//rx9e/fu3ezatYtbb73VXhYdHc2xY8fIycmxl/3yyy/89NNP1Y7l5eUFUGvnLIQQzc3Z/dtjjz3G6tWr+ec//2mfGS7aPrnkLVxSt27duP7665k1axYGg4GkpCTat29fbdD4jBkzWLhwIfHx8TzwwANkZ2ezePFi+vbti16vt9fz9PSkT58+rF69mh49ehAYGEi/fv2ueInnk08+IS0tjbKyMgB+/PFHXn75ZQCmTJlCly5dmqjlQoi2zpn9W1JSEv/85z8ZMWIEXl5erFy5strrd955J97e3k3TcOFUklAKlzR16lTUajVJSUlkZ2czbNgw3nvvPTp06GCv07t3b1asWMHcuXNJSEigT58+fPLJJ3z22Wc1bkP24Ycf8thjj/HUU09hNBqZN2/eFRPKpUuX8sMPP9i3t2zZwpYtWwC4/vrrJaEUQtSbM/u3AwcOAJCSkkJKSkqN18+ePSsJZRulUmoblStEG5WamkpUVBRvvvkmTz/9tLPDEUKIRiP9m3AmGUMphBBCCCEaRBJKIYQQQgjRIJJQCiGEEEKIBpExlEIIIYQQokHkDKUQQgghhGgQSSiFEEIIIUSDuPw6lFarlQsXLuDr6yu30BNC1ImiKBQXF9OxY0fU6pb3/Vz6NyFEQ9Slj3P5hPLChQtEREQ4OwwhRCuWkZFBp06dnB1GDdK/CSEagyN9nMsnlL6+voDtw/Lz87tqfZPJxMaNG4mLi8Pd3b2pw2sxpN3SbldQ13br9XoiIiLs/UhLU9f+DeR3L+12DdLuxu/jXD6hrLoM5Ofn53BC6eXlhZ+fn8v9EUq7pd1tXX3b3VIvJ9e1fwP53Uu7XYO0u/H7uJY36EcIIYQQQrQqLn+GUghXZbEqGM1WjBYrRrMVk8WKxapgtipUGIxcKIVfL+hRqTWYrUrla7/VsVgUe7lFUbBYrZgtym+v2x+tWBWwKgqKAlarcsn2b8+tCpXbSrX6jtSpvq1gtVY+x1ZfUfjtOdiPA1S+VhWblYJ8Nbfd1nSf+6JFi3jzzTfJzMxk4MCBvPvuuwwbNuyy9QsLC/m///s/vvrqK/Lz8+nSpQtJSUnc1pRBCtEKWK0Kpsp+x2yxPTdZbNsmixVT5aPZqmC22Po6S2XfZDSZOZSvwu1IFiq1Bou1ql9RsFhtx7b1a7Y+xdbPVS+v6sssimIvt1Ye33pJv6LY+6JL+yUAW19lr1dZrlzad/Fbf1W5y299Y1W/VflC1TGsv+/zftfHqUrVNEXvIQmlEC2A2WKlxGCmxGCmwmSh3Gil3GShzFi5fUlZudFcbbvCZMFgtmA0WzGYf0sOqxJF27ZS+ZoFk0Wxd6xX5gYHdzZL+1sSTRNevl69ejUJCQksXryY2NhYkpKSiI+P5/jx44SEhNSobzQaGTt2LCEhIfznP/8hPDyctLQ0/P39myxGIepKUWz9S5nRQqnBTKnRTKnB1n9VPVaYrBjMlss+GqoezdbKPu23R5PZiqkyKTRX9l9VX1obRgPHf2mUz6A1Cfdqmj5OEkohGoHFqlBUbqKgzEhBqZGCMhMFpUb0FSaKK8wUV5gpMfz2vNhgprjCREnldrnJ4uwmoNWocdOo0KhVaFQqzGYj3h4euGnUaNQq3NSVr6lVlfXU9rLqj5XlmsptlQq1WoVaBWqVCpXqt+dqFZXblWVqFaqqely9zpWOqVKBiqpt2/PK/2yvU1le+ZpKBRaLhYMHDjTZZ7xw4UIefPBBpk+fDsDixYv59ttvWbZsGc8++2yN+suWLSM/P58dO3bYxztFRkY2WXzCNVkUyCs1UmYyUFRuQl9hpqjcZHte+WPfruzTSg22ZLHUaKbMaGmE5K5xuFX2T+4aNe4aW19ke67CrXK7qp8o1hcRGOCPm0aNWvVb/1b1etVzjdrWh2lUtbz+u3KNmsr+rrLvoaovqt4vVZWp1bbkrrb+SqX6XV9VWV9VuUNVH/nb8S+tX/m6+rdjAVgtFo4fPtA0n32THFWINsBgtnCxsJzUYth4JIv8MjNZegPZxRXklxrJLzVSWGYiv8xIUbmJxriJqdZNjZdWg6d75Y/2t0ePyjKvqueX1NO5q9Fq1GjdbJ2o1s32o9OocXf77TXtpc8vqe+uUVUbdG0ymVi3bh233Tba5Qasa87tb5JjG41G9u7dS2Jior1MrVYzZswYUlJSat3n66+/ZsSIETz66KOsXbuW4OBg7rvvPp555hk0Gk2N+gaDAYPBYN/W6/WArV0mk8mhOKvqOVq/rWhr7TaYrWTpK8gpNpBXarT9lNj6rart3BJbWWG5G+zc2ijv6+GuxlvrhpdWg7dWg5fOrbKfUqNzs/VVOjc1Hu4adG625zp3NR5ul25rKuvY+il7cqhR2RJD9W8JovslCaSbWuXwBDmTycSmTZsYO3awy/Vx6nNKnfsDR0hCKVySoijklxo5V1Be+VNmf7xQWEF2cQUFZVX/I7nBYccui/h6uBHgpSXAW0uAlzvtPN3x9XDDR2d7rPqp2vbRueHn4Y5P5XOtm8yTa6tyc3OxWCyEhoZWKw8NDeXYsWO17nPmzBm+//57Jk+ezLp16zh16hSPPPIIJpOJefPm1ai/YMEC5s+fX6N848aNeHl51SneTZs21al+W9Ea2m1VQG+EPAMUGlUUGqCg8rHQqKLQCMWmul/W9NQoeLqBpwa83C59Dp5uiu1RA55uoNMo6NSg01T+qEGrAdsJN+PV30wBTJU/5b9rX2VReY2dGl9r+H03BUfbXVZW5vAxJaEUbZaiKOSUGDidXcqZ3BJOZ5dyNreEjMrEscJkveox3DUqfDRWOof4E+rnQYifjhBfD4J8dAR6u+PvpSXQW0uAlxZ/L3fcNZIQisZjtVoJCQnhgw8+QKPREBMTw/nz53nzzTdrTSgTExNJSEiwb1etIRcXF1enZYNsZ27GutyZm5bUbqtV4UJRBWfzSknPLyc9r4z0/DLS8svIKCh3qP/SuqkJ8dUR5KOlvbeWIB9bf9Xeu2pbh59OzeE9O/jjLWPw0GmboWUtQ0v7fTeXura76iqHIyShFG1CTrGBIxf1HL2o50RWMadzSjmTXUKxwXzZfVQqCPX1oFOAZ+WPF50CPOng70mon45QXw+83eG7777jtttiXarTEY0vKCgIjUZDVlZWtfKsrCzCwsJq3adDhw64u7tXu7zdu3dvMjMzMRqNaLXVEwCdTodOp6txHHd39zr//dZnn7agudutKAqZ+gpOZJVwMquY45nFnMgu4VRWMaXGy4+t1qhVdPT3oGM7Tzr6exLWzoOO7Tzo0K7yub8nAV7uV70EbDKZSP0FPHRa+X27EEfbXZfPRhJK0aooiu1b+/70Ag6f19uTyJxiQ6311SqICPSia5A30cE+dA32oXNgVeLogc6t5ji0S7WV8VTC+bRaLTExMSQnJzN+/HjAdgYyOTmZ2bNn17rPddddx2effYbVarXfR/fEiRN06NChRjIpWj5FUThXUM7Bc0UcPF/IoXNFHD5fhL6i9i++7hoVXdp7E9neiy7tvelS9RjoRXiAp1wRES2KJJSiRSs3Wjh0voj96QXsSy9gf3oh2bUkjyoVRAV507uDH71CfekWYkseu7T3wsP9ykmjEM0lISGBadOmMWTIEIYNG0ZSUhKlpaX2Wd9Tp04lPDycBQsWADBr1izee+89nnjiCR577DFOnjzJq6++yuOPP+7MZggHVZgs7E8vZPfZfPamF3DoXOElY7N/o1GriGzvRc8wX7qH+NIzzJceoT50ae8tSaNoNSShFC2K0WzlQEYhP53KZcfpXA5kFGKyVJ8+7aZW0aejH/3D29Gnox99OvjRM8wXL638OYuWbeLEieTk5DB37lwyMzMZNGgQ69evt0/USU9Pt5+JBIiIiGDDhg089dRTDBgwgPDwcJ544gmeeeYZZzVBXEGJwczPqfnsPmv7OXiuZv/lrlHRK8yP/p3aMSC8Hf3C29E91OeqV0uEaOnkX2DhVIqicDK7hC3HsvnpdB4/n82vsSZjiK+OwZ0DuKazP4O7BNCvYzs8tdL5itZp9uzZl73EvXXr1hplI0aMYOdO11tgvjWwWhWOXNTz48kcfjiew960Asy/W48x1E/HsKj2DI0MYFCEPz3DfCV5FG2SJJSi2ZksVn4+m8/mo9lsPppFen71ZQnae2sZEd2e67oFcW10ezoHejm8tpgQQjQlg9nCT6dyWX84k++P5ZBbUn0ITudAL2KjAhkWFUhsVHsiAj2l/xIuQRJK0SzMFis7Tufxv18usOHXzGqD0LVuakZ0bc+oHsFcG92enqG+9rsHCCGEs5UZzWw5lsP6XzPZciybkktWj/DSarg2uj2jewQzqkcwXdp7OzFSIZxHEkrRZBRFYU9aAV8fuMC6QxfJK/1tsdv23lpu6hXCzb1DGdk9CG+d/CkKIVoOi1Vh55k8vtp3nu8OX6TskiV8Qv103NI3jLi+YQyJDJBL2EIgCaVoArklBr7ce47VP2dwJrfUXh7oreW2/mGMG9CRIZGBaOQspBCihUnNK+WrA5ms2X+ei0UV9vKIQE9u69eBW/qFMbCTv1xFEeJ3miShXLRoEW+//TZnzpxpisOLFkhRFH46lcfnu9PZeCTTPrPRW6vhln4dGDewA9d1C5IlMIQQLY7FqpB8LJv3j6g5lvKTvdzPw40/DOzIXYPDGdw5QMZCCnEFTZJQFhYWkpaW1hSHFi2MwWxh7YELfLjtDCeySuzlAyP8mTQ0gnEDO8rlbCFEi1RYZmTVzxms3JnGuYJyQI1KBTf0COZPQyK4qVeIrGMrhIMc/pc+PT3d4YMWFhbWJxbRihSWGfl0VzrLd6Ta71Ljo3NjwuBw7h3amT4dHbtvsBBCNLfs4gqWbjvLyp1p9tsb+nu6M9jfwP/dO4ro0HZOjlCI1sfhhDIyMtLh0/2KosilgTaqoMzIRymn+XhHqn2QepifBzOuj+TeYZ3x83C9e6IKIVqHcwVl/OuHM6zek4HRbAWgV5gvM66P4tY+wXy/aQOdA72cHKUQrZPDCaVOp6NPnz7cd999V62bnJzMhg0bGhSYaFn05SbWpav528JtlBpsiWSvMF8eGt2V2/t3ROsmYyOFEC1Tlr6CpM0n+WJPhn3h8cGd/Zl9Uzdu7BmCSqXCZKp5S0QhhOMcTigHDx5MSUkJ/+///b+r1q2oqJCEso0wmq18sjONfySfoKhcDVjo3cGPhLE9GNM7RM5ECyFaLH2FiX/9cJql289SYbKdkbyuW3sevbEbI7q2l/5LiEbkcEI5bNgw3nvvPUpLS/H2vvLCrYqioCjKFeuIlk1RFDYdyWLBd8c4W7n0T5inwv/dMYjbB4TLkhlCiBbLYlX4fHc6b288TkGZ7cxjTJcAnr21F0MjA50cnRBtk8MJ5axZsxg0aJBDlwUef/xxpkyZ0qDAhPOczS3l+TWH2X4qF4AgHx1P3RyNV9ZBbukbKsmkEKLF2pdewNy1hzl8Xg9AdLA3c27pRVyfUDkjKUQTcjih7NGjBz169HCorp+fH35+Msu3tTGYLSzeeoZFW09hNFvRuql5cGQUs27ohk6tsG7dQWeHKIQQtSoqM/HKuiP8e885AHx1biTE9WDK8C64yfq3QjQ5WSBQALAnNZ85Xx7kTI7t8vbI7kG8PL6f/b60MmBdCNFSbTqSxf/99xDZlUuY3R3TiWdu6UWwr87JkQnhOiShdHEGs4WkzSf51w+nsSq2y9tzx/Vh3IAOcnlICNGiFZQaeeF/v7L2wAUAugZ788ZdAxgi4ySFaHaSULqwoxf1PLX6AMcyiwG4a3An5o7rQztPWUtSCNGy7Tidy5OrDpBdbECtggdHdeWpMT3kzjZCOIkklC5IURRW7krnpf8dwWixEuit5dU7+3NLvzBnhyaEEFdktlhJ2nySRVtPoSi2STdv3zOIQRH+zg5NCJfW4kYqL1q0iMjISDw8PIiNjWX37t0O7bdq1SpUKhXjx49v2gBbuVKDmSdWHeD5NYcxWqzc3CuEDU+OkmRSCNHiXSgsZ+IHO3lviy2ZvHdoBP977HpJJoVoAeqVUKanp1NeXn7Z18vLy+t07+8qq1evJiEhgXnz5rFv3z4GDhxIfHw82dnZV9wvNTWVp59+mpEjR9b5PV3Jiaxi/vjedr7+5QIatYrnbu/Nh9OGyMB1IUSLt+tMHuPe3c7etAJ8dW68O+kaXrtrAF5audAmREtQr4QyKiqK//73v5d9/euvvyYqKqrOx124cCEPPvgg06dPp0+fPixevBgvLy+WLVt22X0sFguTJ09m/vz5dO3atc7v6So2H8li/KKfOJ1TSpifB6v/MpyZI7vKxBshRIumKAqf7Exj8oe7yCs10qeDH+ueGMm4gR2dHZoQ4hL1+mp3tbvgmEwm1Oq65apGo5G9e/eSmJhoL1Or1YwZM4aUlJTL7vfiiy8SEhLCAw88wLZt2676PgaDAYPBYN/W6/X2mB1ZGqeqTmtZRkdRFD7akcZrG06gKDCiayB/v2cA7b21dWpDa2t3Y5F2S7sdqS+ahtFsZd7Xh/l8dwYA4wZ25I27BuCplYk3QrQ0DieUer2ewsJC+3ZeXl6tl7ULCwtZtWoVHTp0qFMgubm5WCwWQkNDq5WHhoZy7NixWvfZvn07S5cu5cCBAw6/z4IFC5g/f36N8o0bN+Ll5eXwcTZt2uRwXWexWOGLs2pSsm3J/bUhVu4OzmbXD5vrfczW0O6mIO12LY62u6ysrIkjcV0lBjOzVu5l28lcVCp45pZePDRKrqoI0VI5nFD+/e9/58UXXwRApVLx5JNP8uSTT9ZaV1EUXn755UYJ8HKKi4uZMmUKS5YsISgoyOH9EhMTSUhIsG/r9XoiIiKIi4tz6O4+JpOJTZs2MXbsWNzdW+7yOmVGM7M//4WU7DzUKnj2lp7cP6JzvTvj1tLuxibtlnZfSdUVDtG4cooNzFj+M4fOF+HprmHR5Gu4qVfo1XcUQjiNwwllXFwcPj4+KIrCnDlzmDRpEoMHD65WR6VS4e3tTUxMDEOGDKlTIEFBQWg0GrKysqqVZ2VlERZWcwby6dOnSU1NZdy4cfYyq9Vqa5SbG8ePHyc6OrrGfjqdDp2u5iQUd3f3Ov3DWdf6zamozMT0j/exL70QT3cN7913DTf3bpzOuCW3uylJu12Lo+2uz2ezaNEi3nzzTTIzMxk4cCDvvvsuw4YNu+p+q1atYtKkSdxxxx2sWbOmzu/bWqTllTJ12W7S8soI9Nay7P6hMotbiFbA4YRyxIgRjBgxAoDS0lImTJhA//79Gy0QrVZLTEwMycnJ9qV/rFYrycnJzJ49u0b9Xr16cejQoWplzz33HMXFxbzzzjtEREQ0WmytSXZxBVOX7uZYZjHtPN35aPpQBncOcHZYQgh+W8li8eLFxMbGkpSURHx8PMePHyckJOSy+7nKShYns4qZtGQXuSUGIgI9WTEjlqggb2eHJYRwQL0m5cybN6+x4wAgISGBadOmMWTIEIYNG0ZSUhKlpaVMnz4dgKlTpxIeHs6CBQvw8PCgX79+1fb39/cHqFHuKs4VlDH5w12k5ZUR7KvjkweG0Svs6pfxhRDN49KVLAAWL17Mt99+y7Jly3j22Wdr3efSlSy2bdtWbSx7W3JpMtm7gx8fzxhKiK+Hs8MSQjioXgll1VjKK1GpVDz//PN1Ou7EiRPJyclh7ty5ZGZmMmjQINavX2+fqJOenl7n2eOuIrOogvuW7CI9v4yIQE8+fWA4nds7PslICNG0mmMli4auYlFV99LH5nAyu4Qpy/aQV2qkd5gvH98/mAAPTbPGICsbSLtdQVOuZFGvhPKFF1647GsqlQpFUeqVUALMnj271kvcAFu3br3ivsuXL6/z+7UF2cUV3LdkJ+n5ZXQO9GL1Q8Pp0M7T2WEJIS7RHCtZNNYqFtB8M/wzy+DdIxpKTCo6eStM6VRAytb6r0TRULKygWuRdl9ZXVayqFdCWTX55fdlaWlpLFq0iB9//JHvvvuuPocWdZRXYmDykl2cyS0l3N+Tzx6MlWRSiDagPitZNHQVC2jeGf4XCsu554PdlJgM9Ongy8f3D8HfyzmTwGRlA2m3K2jKlSwa7Z5VarWaqKgo3nrrLSZPnsxjjz3GZ5991liHF7XQV5iYsnQ3J7NLCPXT8dmDsXQKkMvcQrREzbGSRWOtYlHffeqioNTIjBX7yCo20CPUh09nDifAW9tk7+coWdnAtUi7r17PUU0yIHHUqFGsW7euKQ4tKhnNVmat3MuRi3qCfLR8OnM4XdrLbEghWqpLV7KoUrWSRdUKGpeqWsniwIED9p8//vGP3HjjjRw4cKBVr2RRYbIwc8UeTueU0qGdBx/PGNYikkkhRP012hnKS+3Zs0cmzzQhRVF49quD/HQqDy+thuXTh9EtxMfZYQkhrkJWsgCzxcrsz/azN60APw83Pp4xTIbpCNEG1CuhXLFiRa3lhYWF/Pjjj3z11VfMnDmzQYGJy/v7phN8te88GrWKRZMH0y+8nbNDEkI4QFaygFfWHWXz0Sx0bmqW3j+UHqG+zg5JCNEI6pVQ3n///Zd9LSgoiGeffZa5c+fWNyZxBf/+OYN/fH8KgFfG9+PGnpdfDFkI0fK48koW/96TwUc/pQKQNHEQQyMDnRuQEKLR1CuhPHv2bI0ylUpFQEAAvr7ybbOp7E0r4P/W2O4O9NhN3bh3WGcnRySEEI7Zm1bAc/89DMBTY3pwa/8OTo5ICNGY6pVQdunSpbHjEFeRra9g1sq9mCwKt/UPI2FsD2eHJIQQDskpNjBr5V6MFiu39gvjsZu6OTskIUQja9CknMOHD7Nu3TpSU1MBiIyM5NZbb23Ue3wL24zuRz7dR3axge4hPrxx90BUKpWzwxJCiKuyWBWeWn3A3n+99aeBqNXSfwnR1tQroTQYDDz00EN88sknKIpiH0RutVpJTExk8uTJfPjhh2i1sgxEY3j52yPsSSvAV+fGv6bE4KNrksn5QgjR6P655RTbT+Xi6a7hn5MH4y39lxBtUr2mEz7zzDOsWLGCWbNmcfToUSoqKjAYDBw9epSHH36YlStXMmfOnMaO1SV9te8cK1LSAEi6dxBdg2V5ICFE67D7bD5/33wCgJfG96O7zOgWos2q11fFlStXMmXKFN57771q5T179mTRokXo9XpWrlxJUlJSY8ToslJzS3l+jW0Q++M3d+fm3qFX2UMIIVqGEoOZhH8fwKrAhMHh3B3TydkhCSGaUL3OUJpMJoYPH37Z16+99lrMZnO9gxJgslh5YtV+So0WhkUF8sTN3Z0dkhBCOOyVb49wrqCccH9P5v+xr7PDEUI0sXollPHx8WzYsOGyr69fv564uLh6ByVsi5f/cq4IPw83kiYOQiOD2IUQrcSWY9l8vjsDgLf+NBBfD9e7V7IQrqZel7xfeukl7rnnHiZMmMCjjz5Kt262JSBOnjzJokWLSEtLY/Xq1eTn51fbLzBQFrF1xI7Tubz/w2kAXrtrAB395bZkQojWobjCxLNfHQRgxnVRjIhu7+SIhBDNoV4JZe/evQE4dOgQa9eurfaaoigA9OnTp8Z+FoulPm/nUgrLjCSs/gVFgYlDIrhNFv8VQrQiCzedIEtvoEt7L+bc0tPZ4Qghmkm9Esq5c+fKOohN5OVvj5KpryAqyJu542om5UII0VIdPl/ExztSAXjpjn54uGucG5AQotnUK6F84YUXGjkMAfDjiRz+s/ccKhW89acBsl6bEKLVsFgV/u+/h7AqMG5gR0b1CHZ2SEKIZlSvSTkzZsxg165dl3199+7dzJgxo95BuaJSg5nEr2z36Z42IpKYLjLeVAjRenyxJ4NfzhXhq3Pj+dt7OzscIUQzq1dCuXz5ck6fPn3Z18+ePcvHH39c76Bc0ZsbjnO+0LbExl/jZdyREKL1KDOaWbjJtoD5E2O6E+Ln4eSIhBDNrV4J5dVcuHABT0+ZmeyovWn5fJySCsCCCf3lUrcQolVZuu0s2cUGOgd6MXVEpLPDEUI4gcOZy9q1a6vN6P7ggw/YvHlzjXqFhYVs3ryZoUOHNk6EbZzRbOWZLw+hKHB3TCcZdySEaFVySwwsrlzm7K/xPdG6Ncl5CiFEC+dwQnnkyBG++OILAFQqFbt27WLv3r3V6qhUKry9vRk1ahQLFy5s3EjbqI93pHIqu4QgHy3PybgjIUQr84/kk5QaLQzs1I7bZZkzIVyWwwllYmIiiYmJAKjVapYuXcp9993XZIG5guziCt5JPgnAnFt64e+ldXJEQgjhuMyiCj7fnQ7As7f2Ri139BLCZdVrsJ7Vam3sOFzSG+uPU2IwM7BTO+4e3MnZ4QghRJ18uO0MJovCsKhAuSOOEC5OBrs4yf70Av6z9xwAL/yxr3yzF0K0KgWlRj6rPDv5yA3RTo5GCOFs9TpDqVarHbpTjtxqsXZWq8ILX/8K2CbiXNM5wMkRCSFE3SzfkUqZ0ULfjn6MlsmEQri8Rrv1osViITU1lTVr1tCzZ0/+8Ic/1CugRYsW8eabb5KZmcnAgQN59913GTZsWK11lyxZwooVKzh8+DAAMTExvPrqq5et31L8Z985fjlXhI/OTe51K4RodUoMZpZX3mLxkRu6ya14hRCNf+vFixcvMnz4cHr06FHn465evZqEhAQWL15MbGwsSUlJxMfHc/z4cUJCQmrU37p1K5MmTeLaa6/Fw8OD119/nbi4OH799VfCw8Pr/P7Nodxo4e2NxwF4/OZuhPjKAsBCiNblq33nKCo30TXIm1v6hTk7HCFEC9DoYyg7dOjAww8/zEsvvVTnfRcuXMiDDz7I9OnT6dOnD4sXL8bLy4tly5bVWv/TTz/lkUceYdCgQfTq1YsPP/wQq9VKcnJyQ5vRZD5OSSVLbyDc35Np10Y6OxwhhKgTRVH4bJdt7OTUEV3QyPhvIQT1PEN5Nd7e3pw9e7ZO+xiNRvbu3WtfmghsYzXHjBlDSkqKQ8coKyvDZDIRGHj5+2AbDAYMBoN9W6/XA2AymTCZTFd9j6o6jtT9PX25ife3ngLgiZuiUStWTKbWMWO+Ie1uzaTd0m5H6tdFax/WcyCjkGOZxejc1Nx5jaxOIYSwafSE8vDhw/zjH/+o8yXv3NxcLBYLoaGh1cpDQ0M5duyYQ8d45pln6NixI2PGjLlsnQULFjB//vwa5Rs3bsTLy8vheDdt2uRw3SrfpKspKlcT5qngfuEA6y4eqPMxnK0+7W4LpN2uxdF2l5WV1em4bWFYT9W6k7cP6EA7L3enxCCEaHnqlVBGRUXVOgi7sLCQoqIivLy8WLNmTUNjq5PXXnuNVatWsXXrVjw8Lj8uMTExkYSEBPu2Xq8nIiKCuLg4/Pz8rvo+JpOJTZs2MXbsWNzdHe9Ms4sNPPv3bYCVeXdew5jeNf/xaMnq2+7WTtot7b6Sqiscjrp0WA/A4sWL+fbbb1m2bBnPPvtsjfqffvppte0PP/yQL7/8kuTkZKZOnVqn924M+goT//vlIgD3Devc7O8vhGi56pVQjh49ukZCqVKpCAgIIDo6mnvvvfeKl51rExQUhEajISsrq1p5VlYWYWFXHvT91ltv8dprr7F582YGDBhwxbo6nQ6dTlej3N3dvU7/cNa1/uIfj1NusnJNZ39u6d+x1c6KrGu72wppt2txtN11+WyaY1hPQ4f0VNW99PFSX+1Jp9xkoVuwNwM6+rSpIREyzEPa7QqaclhPvRLK5cuX12e3K9JqtcTExJCcnMz48eMB7BNsZs+efdn93njjDV555RU2bNjAkCFDGj2uxpCeV2a/TPTMLb1abTIphKi/5hjW01hDeqD2y/4fHtQAKvp76/nuu+/qdLzWQoZ5uBZp95XVZVhPg8ZQlpaWotfr8fX1xcfHpyGHAiAhIYFp06YxZMgQhg0bRlJSEqWlpfbLQ1OnTiU8PJwFCxYA8PrrrzN37lw+++wzIiMjyczMBMDHx6dR4mks7205idmqMKpHMMO7yu3JhBB158iwnoYO6YHLX/ZPzSvlXMpPaNQqnrn3Ztp7axvWoBZGhnlIu11BUw7rqXNCmZqayhtvvMG3337LuXPn7OXh4eGMGzeOp59+mqioqLoeFoCJEyeSk5PD3LlzyczMZNCgQaxfv97+jT49PR21+reVjt5//32MRiN33313tePMmzfvimtlNqfzheV8te88AE+O6e7kaIQQztIcw3oaa0hPbfus/zUHgOu6BRHm712nY7UmMszDtUi7r17PUXVKKNeuXcuUKVMoKSkhMjKScePG4evrS3FxMQcPHuT9999nxYoVrFy5kjvuuKMuh7abPXv2ZS9xb926tdp2ampqvd6jOX3ww2nMVoURXdszWG6xKITLau3Der45aJuM84cBHZwWgxCi5XI4oTxy5AgTJ06ka9eu/Otf/2LkyJE16mzbto2HH36Ye++9l71799KnT59GDba1ySk2sOrnDABm39TNydEIIZyttQ7rOZtbyvGsYtw1KuL7yJ1xhBA1OZxQvvrqqwQFBbF9+/bLzjAcOXIk27ZtY8CAASxYsIBPPvmk0QJtjZZuP4vBbGVQhD/XRsvYSSFcXWsd1pN81HaZPjaqvaw9KYSolcMJ5ZYtW5g5c+ZVlwMKDAxkxowZLF26tMHBtWZFZSZW7kwDYPaN3WRmtxACaJ3DejZXJpQ39Wpd6+cKIZqPw/fyzsvLIzIy0qG6UVFR5OXl1TemNmH5jlRKDGZ6hflKJyyEaLWKykz8nFoAwJjeoVepLYRwVQ4nlEFBQQ7fn/vs2bMEBQXVO6jWrtRg5qMdts/qkRu7oVbL2UkhROu07VQOFqtCtxAfOrev21qWQgjX4XBCecMNN7B06VLy8/OvWC8/P5+lS5dyww03NDS2VuvLfecoLDPRpb0Xt/eXGZFCiNZrx2nb1aaR3V33JIEQ4uocTij/9re/kZeXx6hRo9ixY0etdXbs2MHo0aPJy8urdnsxV2K1Knz0UyoAM66LQiNnJ4UQrdiOU7kAXBctCaUQ4vIcnpTTp08fPvvsM6ZOncrIkSOJjIxk4MCB1dahPHv2LB4eHqxcuZK+ffs2Zdwt1vfHsjmbW4qfhxt3x3RydjhCCFFv5wvLSc0rQ6NWEdv1yhMyhRCurU4Lm0+YMIFBgwbxxhtv8M0337BmzRr7ax06dGDmzJn89a9/pVs3111zcdlPtrGTk4Z1xlvXoDtbCiGEU1Wdnewf3g5fD1kuSAhxeXXOeLp27crixYsB2z0ei4uL8fX1dfg+sW3ZkQt6dpzOQ6NWMe3aSGeHI4QQDbL7rG3M/AhZR1cIcRUNOoXm5+cnieQlllfO7L61Xxgd/T2dHI0QQjTM/oxCAGLktrFCiKtweFKOuLKiMhNrD1wAYPp1kc4NRgghGqio3MSp7BIAruns79xghBAtniSUjeSLvRkYzFZ6d/BjsHybF0K0cgfPFQHQpb0X7X10To5GCNHSSULZCKxWhU93pQPw5+Gd5TaLQohWr+pyt3xBFkI4QhLKRrDjdB5nc0vx0bkxflC4s8MRQogGO5BhO0M5WC53CyEcIAllI1i5Mw2ACYPDZakgIUSbcDSzGIB+4e2cHIkQojWQhLKBsvQVbDqaBcCfh3dxcjRCCNFweiPklhhRqaBnmK+zwxFCtAKSUDbQl/vOYbEqxHQJoEeodLxCiNbvQpltHHhUe2+8tHLVRQhxdZJQNoCiKHyx5xwAE4dEODkaIYRoHBfKbI+9OsiXZCGEYyShbIA9aQWczS3FS6vh9gEdnB2OEEI0igultjOUvcLkxhVCCMdIQtkA//45A4A/DOggk3GEEG1G1SXv3h0koRRCOEYSynoqMZj59tBFAO6Ry91CiDbCZLGSWW573ksm5AghHCQJZT19dziLMqOFrkHexHSRhX+FEG3DhcIKLIoKnZuacH9PZ4cjhGglJKGspzWV9+2+e0gnuTOOEKLNSM0rBaBLoBdqtfRtQgjHSEJZDwUG2J1aACB3xhFCtCmpebYp3l3aezk5EiFEayIJZT3sy7V9ax8WFUhHuSQkhGhD0ioTykhJKIUQddDiEspFixYRGRmJh4cHsbGx7N69+4r1v/jiC3r16oWHhwf9+/dn3bp1TR7j3lzbxyZnJ4UQddXS+7hUSSiFEPXQohLK1atXk5CQwLx589i3bx8DBw4kPj6e7OzsWuvv2LGDSZMm8cADD7B//37Gjx/P+PHjOXz4cJPFeDKrhPNlKtw1Km7rH9Zk7yOEaHtaQx8nl7yFEPXRohLKhQsX8uCDDzJ9+nT69OnD4sWL8fLyYtmyZbXWf+edd7jlllv461//Su/evXnppZcYPHgw7733XpPF+L+DtqWCRnUPwt9L22TvI4Roe1p6H2c0WzlfaFszSM5QCiHqosWsxm00Gtm7dy+JiYn2MrVazZgxY0hJSal1n5SUFBISEqqVxcfHs2bNmsu+j8FgwGAw2Lf1ej0AJpMJk8l0xRgVReHryoTytr7BV63fllS11ZXaDNJuabdj9R3RHH1cQ/o3gLM5pVgV0KoVAjzULvX7l795abcraMo+rsUklLm5uVgsFkJDQ6uVh4aGcuzYsVr3yczMrLV+ZmbmZd9nwYIFzJ8/v0b5xo0b8fK68jfy1GI4X+iGTq1gzTjIugsHr1i/Ldq0aZOzQ3AKabdrcbTdZWVlDh+zOfq4hvRvAIcLVICGYA/YvHnzVeu3RfI371qk3VdWlz6uxSSUzSUxMbHaN369Xk9ERARxcXH4+V35NmNWq8I1Mbms376H228Zi7u7e1OH22KYTCY2bdrE2LHSblcg7Xas3VVnAFuKhvRvAMNLjQw8m8eBAwfkd+8ipN3S7iupSx/XYhLKoKAgNBoNWVlZ1cqzsrIIC6t98ktYWFid6gPodDp0Ol2Ncnd3d4c+3BHdgik4oThcv62RdrsWaffV6zmqOfq4hvZvof7uxPfTYknfL797FyPtdi1N0ce1mEk5Wq2WmJgYkpOT7WVWq5Xk5GRGjBhR6z4jRoyoVh9sp3EvV18IIZxF+jghRFvWYs5QAiQkJDBt2jSGDBnCsGHDSEpKorS0lOnTpwMwdepUwsPDWbBgAQBPPPEEo0eP5u233+b2229n1apV7Nmzhw8++MCZzRBCiFpJHyeEaKtaVEI5ceJEcnJymDt3LpmZmQwaNIj169fbB6Wnp6ejVv92UvXaa6/ls88+47nnnuNvf/sb3bt3Z82aNfTr18/h91QUBXB8nIDJZKKsrAy9Xu9Sp8ml3dJuV1DXdlf1G1X9yNU0dx9X1/4N5Hcv7XYN0u7G7+NUiqM9YRt17tw5IiIinB2GEKIVy8jIoFOnTs4Oowbp34QQjcGRPs7lE0qr1cqFCxfw9fVFpVJdtX7VrMmMjAyHZk22FdJuabcrqGu7FUWhuLiYjh07Vjuz2FLUtX8D+d1Lu12DtLvx+7gWdcnbGdRqdb3OLPj5+bnUH2EVabdrkXZfXbt27Zo4mvqrb/8G8rt3NdJu19IUfVzL+0othBBCCCFaFUkohRBCCCFEg0hCWUc6nY558+bVunhwWybtlna7Aldt96Vc9TOQdku7XUFTttvlJ+UIIYQQQoiGkTOUQgghhBCiQSShFEIIIYQQDSIJpRBCCCGEaBBJKIUQQgghRINIQimEEEIIIRrE5e+UU59bkwkhBLTNWy8KIUQVufViHVy4cIGIiAhnhyGEaMUyMjLqfYvDpiT9mxCiMTjSx7l8Qunr6wvg8I3STSYTGzduJC4uDnd396YOr8WQdku7XUFd263X64mIiLD3Iy1NXfs3kN+9tNs1SLsbv49z+YSy6jKQozdKN5lMeHl54efn53J/hNJuaXdbV992t9TLyXXt30B+99Ju1yDtbvw+ruUN+hFCCCGEEK2Ky5+hFKItUhQFk0XBYLZgMFsxWxRMFmvlz2/PzVYFk9mKqfLRbLVitCgYjCb2Zqko3J2BFRVmi4LRYsViVbBYFayK7dGiKFitChYrNcrM1srXlN/tc0nd38qUS8pAqWyDotjqKrWVXbKt8Fu9qkd+Xwa2upXP7cf9/TEsGm67zUm/OCFEnSiKra8xmq0YzNbKR4t929b/2fo6s1XBXNkHGk0m9uSoMOy/gKJSYbLY+h9TZT9nvuS57TXbfmbrpf2grc+wXvpcUbBaL3muYO/flN8/v6SO1Vrb85rHrWpzVX92ad8Glf3n7/u7S/tPIETbNH1ci0soFy1axJtvvklmZiYDBw7k3XffZdiwYZetX1hYyP/93//x1VdfkZ+fT5cuXUhKSuI2+RdBtGBmi5VSo4Uyo5lSg4VSg5lSo5kyg4XSyrIyo5kSg5kyo+11g9lKhclS7dFwyXaFydaRVj1alYZGqYEzRxujua2KumVevRaiVTJZrBRXmNGXmyg1mik3Wig1Wig32vq2MqOlssz2mr3MZOsHyyv7uN8nipdu17+v08Cpw43Z3FbB1ESZX4tKKFevXk1CQgKLFy8mNjaWpKQk4uPjOX78OCEhITXqG41Gxo4dS0hICP/5z38IDw8nLS0Nf3//5g9euBxFUSgzWsgtMZBbYqSwzEhRuanGj77c1pleWlZusjRrrO4aFW5qNe4aFe4aNe4aNW4aFdrKR9u2Gm1lPTc15Ofl0DEsDJ27xva6WoWbRo1GDRqVCrVahUalQqP+7flvZVR//Xf1NGrsZdVeV6lQq2yvqSofqdoGe5nt+W91bI8Aqmp1ql6zHUaFWm17vLS+WmU7lloFZrOZH7ZubdbfjRAtnaIo6CvM5JcayS81kF9qsj8WlZvQV5jsSWNxhQl9hdn2WG5u9r7OTa1C56ZG66ZG56ZB61bZx6nVaNQqW1+oUaNWQVFBHqHBwWjdNJWv2erY62tUuKtVaCr7Tk1lH+imrtlfqdW1P9dc0k9p1LbnNfZV2fom+/PfbWvUcGlfdWnfBlTrB1X2erZ9VL/rP81mM9t/2No0n32THLWeFi5cyIMPPsj06dMBWLx4Md9++y3Lli3j2WefrVF/2bJl5Ofns2PHDvvg0sjIyCu+h8FgwGAw2Lf1ej1gG6hqMpmuGmNVHUfqtiWu1G6LVSG72EBmUQUZ+aVsv6ji1w3HKSg3k1diJLfUQH6JkdxSIxUma4Pey02twlunwVvrhpdWg1flc2+tBi+tW+W2Bi+tBp2bBg939SWPanTuGnRuajwqO0+du/q3Om5qe8da10kjJpOJTZs2MXZsXxcbsK6ivYfjf+eu8P+DaLsqTBYuFJRxWg/fHsokt9RElr6CLL2B3BJDZQJppKDMiMnSsEse3loN3jpbP+dZ2cd5VvZtXlo323P3yu2qeu62Oh6VieHvE0Wd/ce2rXWzJYSOMJlMrFu3jttui3GxPs6Ev65pjt1iEkqj0cjevXtJTEy0l6nVasaMGUNKSkqt+3z99deMGDGCRx99lLVr1xIcHMx9993HM888g0ajqXWfBQsWMH/+/BrlGzduxMvLy+F4N23a5HDdtqQttNtshTwD5FSoyKuAQoOKAiMUGlUUGEBvBCuXdkoaSE277PHc1Qq+7uDtBp5uCl5u4KUBTzfwqtz2rCzzclPwdANPDeg04KYGuEpSYgUqahYrlcUVQFFdPwQHtYXfd3042u6ysrImjkSI+iuuMJGRX05GQRkZ+WWcKygnI7+M84XlZOkrKCir6nvc4NeDVz2et1ZDoI+WQG8dgV7uBHrraOfpjp+nG34e7vh6uOHnWfno4U67yuc+OjfcNDIHuK1rMQllbm4uFouF0NDQauWhoaEcO3as1n3OnDnD999/z+TJk1m3bh2nTp3ikUcewWQyMW/evFr3SUxMJCEhwb5dtcZSXFycw8sG2c7cjHW5bzWtqd1Wq0JGYTkns0o4m1dKen456XllpOWXcaGowj5p43I0ahWhvjrC/HRYywro0zWCYF8Pgnx0BPloae+tpX3lo7euxfxv1Gha2++7sdS13VVXOIRwFpPFSlpeKaeySzmdU8Lp7BJO55SQnl92ScJ4eTo3NT4aC1FhAXTw9yLMT0eon62vC/TWVvvxcK/9RI0Q0IISyvqwWq2EhITwwQcfoNFoiImJ4fz587z55puXTSh1Oh06Xc3zve7u7nX6h7Ou9duKltZuRVHI0hs4nlXMicxi22Plz5UuR3trNXRp703nQC86+nvS0d+DDu086eDvQcd2ngT76tCoVZdcFnGtS79VWtrvu7k42m5X/GyEcyiKwrmCcn69UMSRC3qOZRZzKqeE9LwyzFeYlRLorSUiwJNOgV5EBHhV9nkehLXzIMzPAy83+O6777jttmHy9ywapMUklEFBQWg0GrKysqqVZ2VlERYWVus+HTp0wN3dvdrl7d69e5OZmYnRaESr1TZpzKL55ZYYOHiukF8yijh0voiD5wrJLTHWWlfrpqZbsA/dQnyIbO9Fl/beRAZ50TnQmyAfbYtdjFoI4dqqkse9aQUcPFfEkYu2JFJfYa61vrdWQ3SID92CfYgO8SE62Jsu7b2JCPTC5ypXUGQcsGgsLSah1Gq1xMTEkJyczPjx4wHbGcjk5GRmz55d6z7XXXcdn332GVar1X7T8hMnTtChQwdJJtsARVE4lV3CrrP57Dqbz760As4Xlteop1ZBVJA3PcN86RHqS89QX3qG+dI50EvG7QghWjyD2cLh83r2pRWwN62AvekF5BQbatRz16joEepL345+9O7gR/cQX6JDvAnz85AvyMLpWkxCCZCQkMC0adMYMmQIw4YNIykpidLSUvus76lTpxIeHs6CBQsAmDVrFu+99x5PPPEEjz32GCdPnuTVV1/l8ccfd2YzRD0pisKJrBJ2nM5l99l8dp/NJ6+05tnHrsHeDOzkz4BO7RjQyZ++Hf1kbI8QotWwWhV+vaBn+6lcfjqVy8+p+RjM1YfouGtU9OnYjmsi/OnT0Y++HW0JpNZNviSLlqlFJZQTJ04kJyeHuXPnkpmZyaBBg1i/fr19ok56err9TCRAREQEGzZs4KmnnmLAgAGEh4fzxBNP8MwzzzirCaKOiitM/HQql63Hc/jhRA4Xi6pPZ9a5qRncOYDYroEMjQykf6d2+HnIOB8hROuSpa/g+2PZbD+Zy0+ncyn83YSZ9t5aBncJIKbyp394O/miLFqVFpVQAsyePfuyl7i31rLg8IgRI9i5c2cTRyUaU5a+gg2/ZrL+cCa7z+ZXG1Cuc1MzLCqQ4V3bExtlSyB1btKpCiFaF0VROJldwqYjWWz8NZNfzlVf3MtH58bwru25vlt7ru8eRHSwj1y2Fq1ai0soRdt0obCcdYcusv5wJnvTC6ot29M1yJvRPYO5oWcIsVGB8q1cCNFqncouYe2B8/zvlwuk5v22TqlKBYMi/LmhRwjXdw9iYKd2MsZbtCmSUIomU2Y0s/5wJv/Ze46UM3nVksjBnf25tV8H4vqG0qW9t/OCFEKIBsrSV/D1gQus/eU8h8//tjap1k3NddHtiesbxs29Qwjx9XBilEI0rTollAaDgU8//ZSjR48SFBTE3XffTXR0dI16mzdv5tVXX+X7779vtEBF66AoCnvSClj9cwbfHbpIqfG3+7gOiwrk9v4diO8bRlg76ViFEK2Xxarw44kcPt2VxvfHsqkaueOmVjGqRzB3DOrIzb1Dr7psjxBthcN/6UVFRVx77bUcPXrUXvb888/z9NNP8/LLL1ebLJOVlcUPP/zQuJGKFq3CZGHtgfMs35HG0Yu/fUPv0t6LuwZ34s5rwokIdPzWlkII0RJlF1fw758z+Hx3RrVlzGK6BDB+UEduH9CRQG9Ztk64HocTypdeeonTp0/z8ccfc+edd3Lx4kVef/11XnvtNX755Re++OKLOt0LW7QN5wvLWZGSyuqfM+yzFj3c1fxxYEf+NCSCIV0CZKC5EKLVO5lVzL9+PMPaA+cxWWynI9t5unN3TCcmDetMtxAfJ0cohHM5nFB+8803zJo1iylTpgDQvXt3PvzwQ2666SZmzpzJTTfdxLp16wgMDGyyYEXLkZZXyj+3nObLfefss7Q7BXgyZXgXJg6NwN9LvqELIVq/Pan5LP7hNJuPZtvLrunsz59ju3D7gA4yiVCISg4nlBkZGfTv379G+X333UdERAR33HEH119/PevXr2/UAEXLciq7hA+2p7H2wHn7mKHhXQOZcV0UN/cORaOWs5FCiNZvx+lc/r7pBD+nFgC2WdpxfUJ5aHQ0gzsHODk6IVoeh9csCAsLIz09vdbXRo4cyZYtWygoKOC6667j8OHDjRagaBkyCsr4+ISa297bwX/325LJG3oG8+WsEaz6ywji+oZJMimEAxYtWkRkZCQeHh7Exsaye/duh/ZbtWoVKpXKfmta0TQOZBQy+cOd3LdkFz+nFqDVqJk4JILNCaP515QhkkwKcRkOn6EcOnQoa9as4YUXXqj19YEDB7J9+3bi4uJ44403Gis+4WQFpUbe/f4Un+xMxWSxff+I6xPKYzd1p3+ndk6OTojWZfXq1SQkJLB48WJiY2NJSkoiPj6e48ePExISctn9UlNTefrppxk5cmQzRuta0vLK+PCYmkMptgTfXaNi0rDOPHpjN0L9ZFUKIa7G4YTynnvu4aGHHuLHH39k1KhRtdaJjo5mx44dxMfHc+jQoUYLUjQ/s8XKxylpJG0+QXGFGYCe7ay8ft+1DOrS3snRCdE6LVy4kAcffJDp06cDsHjxYr799luWLVvGs88+W+s+FouFyZMnM3/+fLZt20ZhYeFlj28wGDAYDPZtvd624oLJZMJkMl1ut2qq6jlav7UrMZh5/4czfLQjDZNFjVoFd17Tkdk3RNMpwBNo25+Fq/2+q0i769YfOMLhhHLChAlMmDDhqvVCQ0M5cOCAwwGIlufn1HyeX3OYY5nFAPTu4Mdf47pRfGI3fTv6OTk6IVono9HI3r17SUxMtJep1WrGjBlDSkrKZfd78cUXCQkJ4YEHHmDbtm1XfI8FCxYwf/78GuUbN26s8yocmzZtqlP91kZRYE+uiq/T1OhNtuE6vdpZuTPSSpgunYMp6Rx0cozNqa3/vi9H2n1lZWVlV69USVZcFXYFpUZeWXeU/+w9B4C/lztz4nsxcWgEVouZdSecHKAQrVhubi4Wi4XQ0NBq5aGhoRw7dqzWfbZv387SpUsd/pKemJhIQkKCfVuv1xMREUFcXBx+fo59GTSZTGzatImxY8fi7u7u0D6tTUZBGXO/Psr2U3kAdAn04pm4aIyp+4mLa7vtro0r/L5rI+12rN1VVzkcIQmlAGDjr5n87b+HyS2xXS6bNCyCv8b3si/Qa7VcaW8hRGMrLi5mypQpLFmyhKCgIIf20el06HS6GuXu7u51/kezPvu0dBarwrLtZ1m46QTlJgtaNzVP3NydB0d2RaVYWJe2v0222xHSbtfiaLvr8tlIQuniCsuMzP/fEf67/zwA3UJ8eOPuATKTUYhGFhQUhEajISsrq1p5VlYWYWFhNeqfPn2a1NRUxo0bZy+zWq0AuLm5cfz48VpvfStql5FfxlOrD7AnzbYM0PCugbx6Z3+6BtsWJDeZ5FuzEA0hCaUL23kmjydW7SdLb0Ctgr+MiubJMd1loV4hmoBWqyUmJobk5GT70j9Wq5Xk5GRmz55do36vXr1qTG587rnnKC4u5p133iEiIqI5wm71FEXhv/vPM3ftr5QYzPjo3Hju9t5MHBohd/ESohFJQumCLFaF974/xTvJJ7Aq0DXIm7fuGShnJYVoYgkJCUybNo0hQ4YwbNgwkpKSKC0ttc/6njp1KuHh4SxYsAAPDw/69etXbX9/f3+AGuWidsUVJv7238P875cLAAzpEsDfJw4iIlBuEyxEY6tXQpmenk5wcDCenp61vl5eXk5OTg6dO3duUHCi8WXrK3hi1QFSztgGo981uBMv3tEXb518txCiqU2cOJGcnBzmzp1LZmYmgwYNYv369faJOunp6ajVDt9vQlzByaxiHlq5lzM5pWjUKp68uTuzbojGTSOfrxBNoV5ZRFRUFJ988gn33Xdfra9//fXX3HfffVgsMialJTmQUchfVuwhu9iAl1bDy+P7MWFwJ2eHJYRLmT17dq2XuAG2bt16xX2XL1/e+AG1Qd8cvMCc/xykzGihQzsPFk0eLFdghGhi9UooFUW54usmk0m+ZbcwX+07x7NfHcJottI9xIfFU2KIrhyMLoQQbYHFqvDad0dZsu0sANdGt+cfk64hyKfmzHchRONyOKHU6/XV7tCQl5dX6729CwsLWbVqFR06dGiUAEXDWKwKr68/xgc/ngFgbJ9Q/j5xED5yiVsI0YaUGc08ueoAG4/YZtE/PDqap+N6yCVuIZqJw1nF3//+d1588UUAVCoVTz75JE8++WStdRVF4eWXX26UAEX9VZgsPLFqPxt+tXWwj93UjafG9ECtlpmNQoi2I7u4gpkf7+HguSK0GjVv/mkAdwwKd3ZYQrgUhxPKuLg4fHx8UBSFOXPmMGnSJAYPHlytjkqlwtvbm5iYGIYMGdLowQrHFZWbePDjPexOzUerUfP2PQMZN7Cjs8MSQohGdSq7mGnLfuZ8YTkBXu58MHUIQyMDnR2WEC7H4YRyxIgRjBgxAoDS0lImTJhA//79mywwUX9Z+gqmLdvNscxifHVuLJk2hOFd2zs7LCGEaFSHzxcxddlu8kuNRAV5s+z+oUQFeTs7LCFcUr0Gl8ybN6/JkslFixYRGRmJh4cHsbGx7N6926H9Vq1ahUqlsi8Y7Koy8su46/0dHMssJthXx+qHRkgyKYRoc/amFTBpyU7yS40M6NSOL2ddK8mkEE5Ur5kZVWMpr0SlUvH888/X6birV68mISGBxYsXExsbS1JSEvHx8Rw/fpyQkJDL7peamsrTTz/NyJEj6/R+bU1Gfhn3frCT84XlRAV5s2LGMFnAVwjR5qSczuOBj3+mzGhhaGQAS+8fip+H692PWYiWpF4J5QsvvHDZ11QqFYqi1CuhXLhwIQ8++KD9rhGLFy/m22+/ZdmyZTz77LO17mOxWJg8eTLz589n27Zt1Waiu5JLk8muQd6s+stwQvw8nB2WEEI0qh2ncpm+/GcMZivXdwvig6kxeGll1QohnK1e/xdardZay9LS0li0aBE//vgj3333XZ2OaTQa2bt3L4mJifYytVrNmDFjSElJuex+L774IiEhITzwwANs27btqu9jMBgwGAz2bb1eD9jWzjSZTFfdv6qOI3WbS0ZBGX9euocLRRVEtffikxlDCPDUNGqMLbHdzUHaLe12pL5oHnvTCpi5Yg8Gs5Wbe4WwaPJgPNw1zg5LCEEj3stbrVYTFRXFW2+9xeTJk3nsscf47LPPHN4/NzcXi8VivwVZldDQUI4dO1brPtu3b2fp0qUcOHDA4fdZsGAB8+fPr1G+ceNGvLwcvzy8adMmh+s2pSIjJB3WkG9QEeKhMD1Sz55tyU32fi2l3c1N2u1aHG13WVlZE0ciqvx6oYj7P9pNmdHCyO5B/PPPg9G5STIpREvRJNcJRo0axTPPPNMUh7YrLi5mypQpLFmyhKCgIIf3S0xMJCEhwb6t1+uJiIggLi4OPz+/q+5vMpnYtGkTY8eOxd3duWN2iitM3Ld0D/mGYjoHevL5zGGE+DbNHSFaUrubk7Rb2n0lVVc4RNM6lV3C1KW7Ka4wMzQygH9NiZFkUogWpkkSyj179tT51otBQUFoNBqysrKqlWdlZREWFlaj/unTp0lNTWXcuHH2sqpL8W5ubhw/fpzo6Oga++l0OnS6mkmXu7t7nf7hrGv9xlZhsvDI579wLLOYIB8dKx8YTngzTMBxdrudRdrtWhxttyt+Ns0ts6iCKUt3kVdqpF+4H0vvHypjJoVoger1f+WKFStqLS8sLOTHH3/kq6++YubMmXU6plarJSYmhuTkZPvSP1arleTkZGbPnl2jfq9evTh06FC1sueee47i4mLeeecdIiIi6vT+rYnFqpDw7wPsPJOPj86N5dOH0rm9zOYWQrQtpQYzD3z8MxeLKogO9mbFjFiZzS1EC1WvhPL++++/7GtBQUE8++yzzJ07t87HTUhIYNq0aQwZMoRhw4aRlJREaWmpfdb31KlTCQ8PZ8GCBXh4eNCvX79q+/v7+wPUKG9rXl13lHWHMtFq1HwwJYZ+4e2cHZIQQjQqi1XhiVX7+fWCnvbeWpZPH0agt9bZYQkhLqNeCeXZs2drlKlUKgICAvD19a13MBMnTiQnJ4e5c+eSmZnJoEGDWL9+vX2iTnp6ep0vpbc1X+zJYOl22+f/9j0Dubab4+NHhRCitXj52yNsPpqNzk3NkmlDZE1dIVq4eiWUXbp0aew47GbPnl3rJW6ArVu3XnHf5cuXN35ALcjetAL+77+HAXji5u5yb24hRJv0SUoqH/2UCsDCewYxuHOAcwMSQlxVg0Y2Hz58mHXr1pGamgpAZGQkt956q9zjuwlkFlXw8Mq9GC1W4vuG8sTN3Z0dkhBCNLq9afnM/98RAP4a35PbB3RwckRCCEfUK6E0GAw89NBDfPLJJyiKYr8MbbVaSUxMZPLkyXz44YdotTLepTFUmCz85ZM95BQb6BXmy8J7BqFWq5wdlhBCNKrcEgOPfLoPs1XhDwM68MgNNVfqEEK0TPUakPjMM8+wYsUKZs2axdGjR6moqMBgMHD06FEefvhhVq5cyZw5cxo7Vpf10jdHOHiuiAAvd5ZMHYK3TpbMEEK0LWaLlcc+20+W3kC3EB9ev2sAKpV8cRaitahXZrJy5UqmTJnCe++9V628Z8+eLFq0CL1ez8qVK0lKSmqMGF3atwcv8umudFQqeOfea2RguhCiTVq46QQpZ/Lw0mpY/OfB8sVZiFamXmcoTSYTw4cPv+zr1157LWazud5BCZuM/DKe/fIgALNGRzOqR7CTIxJCiMaXfDSLf249DcDrdw2gW0j9VwsRQjhHvRLK+Ph4NmzYcNnX169fT1xcXL2DEmA0W5n9+X6KDWZiugSQMLaHs0MSQohGl1NsYM5/bF+c7782UlavEKKVqtc1hZdeeol77rmHCRMm8Oijj9KtWzcATp48yaJFi0hLS2P16tXk5+dX2y8wMLDhEbuINzcc45eMQtp5uvOPSdfgpnHt9TeFEG2Poig8++VB8kqN9ArzJfG2Xs4OSQhRT/VKKHv37g3AoUOHWLt2bbXXFEUBoE+fPjX2s1gs9Xk7l5NyOo8l22yLl79x9wDC/T2dHJEQQjS+z3dnkHwsG61GTdK9g9C5aZwdkhCinuqVUM6dO1dm3zWRUoOZOV/+AsCkYZ2J7xvm5IiEEKLxnc0t5aVvfltvsleYn5MjEkI0RL0SyhdeeKGRwxBVXl9/jIz8csL9PfmbXP4RQrRBZouVp1YfoNxkYUTX9jxwfZSzQxJCNFC9BubNmDGDXbt2Xfb13bt3M2PGjHoH5ap2nM5lRUoaYJvp6Ovh7uSIhBCi8S376SwHMgrx9XDj7XsGyo0ahGgD6pVQLl++nNOnT1/29bNnz/Lxxx/XOyhXVGow22c63hfbmeu7Bzk5IiGEaHwZ+WX8fdNJAJ67vTcdZYy4EG1Ck0wdvnDhAp6e0knUxRvrj3GuoOpSd29nhyOEEI1OURSeW3OYcpOF4V0DuWdIhLNDEkI0EofHUK5du7bajO4PPviAzZs316hXWFjI5s2bGTp0aONE6AIOnStixc7fLnX7yB0ihBBt0Ne/XOCHEzlo3dS8emd/mdwpRBvicOZy5MgRvvjiCwBUKhW7du1i79691eqoVCq8vb0ZNWoUCxcubNxI2yirVeG5tYdRFLhjUEe51C2EaJMKy4y8+D/brO7HbuxG12AfJ0ckhGhMDl/yTkxMpLi4mOLiYhRFYenSpfbtqh+9Xs/Fixf55ptv6NFD7uziiFU/Z/BLRiE+Ojf+Ty51C9HmLVq0iMjISDw8PIiNjWX37t2XrbtkyRJGjhxJQEAAAQEBjBkz5or1W7JX1x0lr9RI9xAfHhod7exwhBCNrF5jKK1WK/fdd19jx+Jy8kuNvLHhGABPje1BiJ+HkyMSQjSl1atXk5CQwLx589i3bx8DBw4kPj6e7OzsWutv3bqVSZMmsWXLFlJSUoiIiCAuLo7z5883c+QNcyCjkH/vOQfAggn90brJnb+EaGvk/2onemP9MQrLTPQK82XaiC7ODkcI0cQWLlzIgw8+yPTp0+nTpw+LFy/Gy8uLZcuW1Vr/008/5ZFHHmHQoEH06tWLDz/8EKvVSnJycjNHXn+KovDi/34F4K7BnRgSKbfgFaItqtfsD7Va7dBgarnV4uXtTy9g1c8ZALw0vp/cq1uINs5oNLJ3714SExPtZWq1mjFjxpCSkuLQMcrKyjCZTAQG1p6UGQwGDAaDfVuv1wNgMpkwmUwOvUdVPUfrX83/Dl5kX3ohnu5qnrq5a6Mdt7E1drtbC2m3tNuR+o5otFsvWiwWUlNTWbNmDT179uQPf/hDfQ7tEhRF4eVvjwIwYXA4Q+UbuxBtXm5uLhaLhdDQ0GrloaGhHDt2zKFjPPPMM3Ts2JExY8bU+vqCBQuYP39+jfKNGzfi5eVVp3g3bdpUp/q1MVrglQMaQMWNYSb2bv++wcdsao3R7tZI2u1aHG13WVmZw8ds9FsvXrx4keHDh8uknCvYeCSLvWkFeLireeYWub2iEOLqXnvtNVatWsXWrVvx8Kh9vHViYiIJCQn2bb1ebx936efn2L2yTSYTmzZtYuzYsbi7N+xuXe9tOU2h8TQd23nw+vTr8HDXNOh4Takx292aSLul3VdSdZXDEY2+4GGHDh14+OGHeemll5g0aVJjH77VM1msvP6d7WzEzOu7EioTcYRwCUFBQWg0GrKysqqVZ2VlERYWdsV933rrLV577TU2b97MgAEDLltPp9Oh0+lqlLu7u9f5H8367HOpzKIKPtiWCkDibb3x9WodfV1D291aSbtdi6Ptrstn0yQD97y9vTl79mxTHLrVW/1zBmdySwn01vLQ6K7ODkcI0Uy0Wi0xMTHVJtRUTbAZMWLEZfd74403eOmll1i/fj1DhgxpjlAbxVsbj1NushDTJYA/DOjg7HCEEE2s0RPKw4cP849//KPel7zb8hptpQYzSZtt97B94ubu+Hq43rciIVxZQkICS5Ys4eOPP+bo0aPMmjWL0tJSpk+fDsDUqVOrTdp5/fXXef7551m2bBmRkZFkZmaSmZlJSUmJs5rgkFPZJXy1z7ZM0HO395Y74gjhAup1yTsqKqrWDqKwsJCioiK8vLxYs2ZNnY9btUbb4sWLiY2NJSkpifj4eI4fP05ISEiN+lVrtF177bV4eHjw+uuvExcXx6+//kp4eHh9mtaklmw7Q26JgS7tvZg0rLOzwxFCNLOJEyeSk5PD3LlzyczMZNCgQaxfv94+USc9PR21+rfv+e+//z5Go5G777672nHmzZt3xbHszpa0+QRWBcb0DuWazgHODkcI0QzqlVCOHj26RkKpUqkICAggOjqae++997LLWlzJpWu0ASxevJhvv/2WZcuW8eyzz9ao/+mnn1bb/vDDD/nyyy9JTk5m6tSpdX7/ppRbYuCDH88AMCe+lyzsK4SLmj17NrNnz671ta1bt1bbTk1NbfqAGtnRi3q+OXgRgISxMjlTCFdRr4Ry+fLljRxG86zRBg1fp62+a1ct3nqKMqOFAeF+jO3VvtWtfSVrdkm7XUFTrtHmKt7eeAKAPwzoQJ+Ojs0sF0K0fg2a5V1aWoper8fX1xcfH58GBdIca7RB463TVpe1q0pMsGKfbS224b4FfPfddw7v29LIml2uRdp9ZXVZo80VHMgoZPPRLNQqeHKMnJ0UwpXUOaFMTU3ljTfe4Ntvv+XcuXP28vDwcMaNG8fTTz9NVFRUowbpCEfWaIOGr9NWn7Wr3tp4EqP1LP06+vH0fbGtcoC6rNkl7XYFTblGmyt4e+NxACYM7kS3kIadZBBCtC51SijXrl3LlClTKCkpITIyknHjxuHr60txcTEHDx7k/fffZ8WKFaxcuZI77rijToE0xxpt0HjrtDlav6DUyMpd6QA8MaYHWq3W4fdoiWTNLtci7b56PWHzc2o+207m4qZW8cTN3Z0djhCimTk8M+TIkSNMnDiRTp068cMPP3DmzBnWrFnDJ598wpo1azhz5gw//PADnTt35t577+XIkSN1CqStrtG2dPtZSo0W+nTwY0zvmjPVhRCiLVi05RQAfxoSQURg3W7zKIRo/RxOKF999VWCgoLYvn07I0eOrLXOyJEj2bZtG+3bt2fBggV1DqatrdFWVGZi+Y5UAB6/uXurvNQthBBXc+SCnq3Hc1Cr4GG5YYMQLsnhS95btmxh5syZV10OKDAwkBkzZrB06dI6B9PW1mhb+tNZSgxmeoX5Etcn9Oo7CCFEK/SvH08DcFv/DnRp7+3kaIQQzuBwQpmXl0dkZKRDdaOiosjLy6tXQG1ljbZSg5nlP9luP/n4zd1Rq+XspBCi7UnPK+N/v1wA4OHR0U6ORgjhLA5f8g4KCnL4/txnz54lKCio3kG1BV/syUBfYSYqyJtb+l55UpEQQrRWS7adwarAqB7B9Atv5+xwhBBO4nBCecMNN7B06VLy8/OvWC8/P5+lS5dyww03NDS2VstiVVj2UyoAM66PkrOTQog2KbfEwL/3ZAAydlIIV+dwQvm3v/2NvLw8Ro0axY4dO2qts2PHDkaPHk1eXl61yTOuZtORTNLzy/D3cufuwZ2cHY4QQjSJ5T+lYjBbGRjhz4iu7Z0djhDCiRweQ9mnTx8+++wzpk6dysiRI4mMjGTgwIHV1qE8e/YsHh4erFy5kr59+zZl3C3ah9tsQwP+HNsFT63GydEIIUTjKzWYWZGSCsCs0dGyioUQLq5OC5tPmDCBQYMG8cYbb/DNN9+wZs0a+2sdOnRg5syZ/PWvf6Vbt26NHWersT+9gD1pBWg1aqaO6OLscIQQokl8te+cfZy4rGIhhKjzrRe7du3K4sWLAdttx4qLi/H19XXotoWu4MPttrOTfxzUkRC/y98CUgghWitFUexr7E4b0UXGiQsh6p5QXsrPz08SyUtk5Jfx3aGLADxwffPfz1wIIZrD9lO5nM4pxVur4a4YGScuhKjDpBxxdStSUrEqMLJ7EL07SKIthGibPq48O/mnIRH4esj9zIUQklA2mgqThX/vOQfA9OsinRuMEEI0kfS8MpKPZQPIOHEhhJ0klI1k3aGLFJWbCPf3ZHSPEGeHI4QQTWJFSiqKAqN7BNM12MfZ4QghWghJKBvJp7vSAbgvtjMaGaAuhGiDSg1mVlcuZH7/tZHODUYI0aJIQtkIjl7UszetADe1ij8NkQHqQoi26b/7z1NcYSayvRejewQ7OxwhRAsiCWUj+Kzy7GR83zBCfGWpICFE26Moin0h86kjImWpICFENZJQNlCpwcx/958HbJe7hRCiLdp5Jp8TWSV4aTXcLVdihBC/IwllA/3vlwuUGGx3i5B72Qoh2qpPdqYCMP6acPxkqSAhxO9IQtlA9sk4wzrLJSAhRJt0saicDb9mAbJUkBCidpJQNsDBc4UcOl+EVqOWu0UIIdqsz3elY7EqDIsKpFeY3LRBCFGTJJQN8O/K5TNu6RdGoLfWydEIIUTjM5qtfLbb1tfJ2UkhxOVIQllPBpOF//1iu2+3LBUkhGir1v+aSW6JgRBfHfF9w5wdjhCihZKEsp6+P55DUbmJDu08uDY6yNnhCCFEk/ikcqmgScM6466RfzKEELWT3qGevtp/AYA7rwmXO+MIIdqkIxf0/Jxqu2mDLIsmhLgSSSjrQW+EbafyAGQyjhCizVq6/Sxgu2lDqJ/ctEEIcXmSUNbDnlwVFqvCNZ39iQ72cXY4QgjR6M4VlLPmgO2mDTNHRjk5GiFES9fiEspFixYRGRmJh4cHsbGx7N69+4r1v/jiC3r16oWHhwf9+/dn3bp1TRqfoijszrZ9bHfL2UkhRB219D6uyuIfz2CxKozsHsQ1nQOa5T2FEK1Xi0ooV69eTUJCAvPmzWPfvn0MHDiQ+Ph4srOza62/Y8cOJk2axAMPPMD+/fsZP34848eP5/Dhw00W45GLxVwsV6F1U/OHAR2b7H2EEG1Pa+jjAFKL4d97bWcnH7upe5O+lxCibWhRCeXChQt58MEHmT59On369GHx4sV4eXmxbNmyWuu/88473HLLLfz1r3+ld+/evPTSSwwePJj33nuvyWL8snIyztheIbTzlNuPCSEc1xr6uItFFXx2WoOiwITB4QyLCmyy9xJCtB1uzg6gitFoZO/evSQmJtrL1Go1Y8aMISUlpdZ9UlJSSEhIqFYWHx/PmjVrLvs+BoMBg8Fg39br9QCYTCZMJtOVYzRb7WtPjusfctX6bUlVW12pzSDtlnY7Vt8RzdHHNaR/A9iTVsDszw+QV66ivbeWZ+K6u8zfgPzNS7tdQVP2cS0moczNzcVisRAaGlqtPDQ0lGPHjtW6T2ZmZq31MzMzL/s+CxYsYP78+TXKN27ciJeX1xVjTCuGkgoNfu5QdnYf61KvWL1N2rRpk7NDcAppt2txtN1lZWUOH7M5+riG9G8Ap/VQUKYh3Ase6FHGzh82X3Wftkb+5l2LtPvK6tLHtZiEsrkkJiZW+8av1+uJiIggLi4OP7+r36P2nuIyVq/byi1xY3F3d51L3iaTiU2bNjF2rLTbFUi7HWt31RnAlqKh/RtA/2NZFJ7cy+23yO/eFUi7pd1XUpc+rsUklEFBQWg0GrKysqqVZ2VlERZW++2+wsLC6lQfQKfTodPpapS7u7s79OG29/Ui0tfx+m2NtNu1SLuvXs9RzdHHNbR/A7ihVyjrzsjv3tVIu11LU/RxLWZSjlarJSYmhuTkZHuZ1WolOTmZESNG1LrPiBEjqtUH22ncy9UXQghnkT5OCNGWtZgzlAAJCQlMmzaNIUOGMGzYMJKSkigtLWX69OkATJ06lfDwcBYsWADAE088wejRo3n77be5/fbbWbVqFXv27OGDDz5w+D0VRQEcP61rMpkoKytDr9e71Lcaabe02xXUtd1V/UZVP3I1zd3H1bV/A/ndS7tdg7S7Cfo4pYV59913lc6dOytarVYZNmyYsnPnTvtro0ePVqZNm1at/r///W+lR48eilarVfr27at8++23dXq/jIwMBZAf+ZEf+an3T0ZGRovs46R/kx/5kZ/G+HGkj1MpioNfrdsoq9XKhQsX8PX1RaVSXbV+1SD3jIwMhwe5twXSbmm3K6hruxVFobi4mI4dO6JWt5gRRHZ17d9AfvfSbtcg7W78Pq5FXfJ2BrVaTadOdb+Fop+fn0v9EVaRdrsWaffVtWvXromjqb/69m8gv3tXI+12LU3Rx7W8r9RCCCGEEKJVkYRSCCGEEEI0iCSUdaTT6Zg3b16ta721ZdJuabcrcNV2X8pVPwNpt7TbFTRlu11+Uo4QQgghhGgYOUMphBBCCCEaRBJKIYQQQgjRIJJQCiGEEEKIBpGEUgghhBBCNIgklEIIIYQQokEkoRRCCCGEEA0iCaUQQgghhGgQSSiFEEIIIUSDSEIphBDNaNGiRURGRuLh4UFsbCy7d+92aL9Vq1ahUqkYP3580wYohBD14ObsAJzNarVy4cIFfH19UalUzg5HCNGKKIpCcXExHTt2RK2++vfz1atXk5CQwOLFi4mNjSUpKYn4+HiOHz9OSEjIZfdLTU3l6aefZuTIkXWKT/o3IURD1KWPc/lbL547d46IiAhnhyGEaMUyMjLo1KnTVevFxsYydOhQ3nvvPcCW8EVERPDYY4/x7LPP1rqPxWJh1KhRzJgxg23btlFYWMiaNWscikv6NyFEY3Ckj3P5M5S+vr6A7cPy8/O7an2TycTGjRuJi4vD3d29qcNrMaTd0m5XUNd26/V6IiIi7P3IlRiNRvbu3UtiYqK9TK1WM2bMGFJSUi6734svvkhISAgPPPAA27Ztu+J7GAwGDAaDfbvqfMHZs2cdihFsn8GWLVu48cYbXe53L+2Wdrd1dW13cXExUVFRDvUfLp9QVl0G8vPzczih9PLyws/Pz+X+CKXd0u62rr7tduRycm5uLhaLhdDQ0GrloaGhHDt2rNZ9tm/fztKlSzlw4IBDcSxYsID58+fXKE9JScHLy8uhYwB4eXmxa9cuh+u3FdJu1yLtvrqysjLAsT7O5RNKIYRoiYqLi5kyZQpLliwhKCjIoX0SExNJSEiwb1edQY2Li3PoCzPYkupNmzYxduxYl/syIe2Wdrd1dW23Xq93+NiSUAoh7BRFwWxVqDBZMFhAX25CZVQwW61YrApmi2J7tFY9WqtvW6qXV/1YFbAqClZFQbE/p3L70tdtMVitl77uQH3ld/WtCgq/bSuKbVtRQKGyrHKbqm0FLFYr58+pua0JPtugoCA0Gg1ZWVnVyrOysggLC6tR//Tp06SmpjJu3Dh7mdVqBcDNzY3jx48THR1dbR+dTodOp6txLHd39zr/o1mffdoCabdrubTdiqJgstj6L3Nlf2a2WDFZFSwWBZPVitmiYLJY7f2cyXJpP1f5YwVLZV9lsf7W91kv3bYqWKr6LWvVa7a+yGI/ju11W/kl9Ss7sN/6x0v6NeV3fV9lu6r6UYvVSmm2mtsc/H3X5W9CEkohWhBFUTCYrZQbLZSbKn+M1R8rTBbKjNW3DWYrRrPV/miy2B6Nv3+seu2S7arnJosVa7Upem6we4uzPgqn0TTRbGitVktMTAzJycn2pX+sVivJycnMnj27Rv1evXpx6NChamXPPfccxcXFvPPOOzLZRrRJFqtCmdFMmdHWz5UazJSbKh+NFkor+z1DZb/3W99XvR80mCwYLVYMppqv2fo9CxUVGv62NxmT1ZY4Vu//2q5wr6bp4yShFKIRGcwWCkpNFJQZKSg1oq8wUVxhprjCTInBTHGFiRKDGX2FmZKK37aLK7dLjGZa4roLahW4qdVo1Crc1Co0mspHtap6+SU/l26rVZU/alCrVKhUKtQqKsv53bYK1SWv1aivvnJ91SXbKrC/rgKoLLNt/1auqtzParFw8sTxJvscExISmDZtGkOGDGHYsGEkJSVRWlrK9OnTAZg6dSrh4eEsWLAADw8P+vXrV21/f39/gBrlQrQEZouVgjITReUm9BUm9OUm9BXmykcT+nJzjfJSQ1XyaHs0mK3NGLEKLJYr11CBe1Ufp1HhrlHjVtm/uWnUuFX2hWrVJX2d2tYXaX7X72nUtr5MY+/LKutd0kfa6ly6b/U6tfV1VX2ZuvK5urJTu7T/U1/Sx1042zR9nCSUQlyB1aqgN8KRi3ryyy1k6yvI1hvIKzXaksYyEwWlRvJLjRSWGSk1XrlzqgutRo2nVoOnuwZPrQYPdw2e7mq8tG6251rbtqe7Bp27Bq1GjdZNjXvlo9ZNjU6jxt1NhVajsZe5a1To3NT2MneNyvaaRm1PEK1WM5s3buT2227BQ6tFrXaNNQxNJhPrSmufINMYJk6cSE5ODnPnziUzM5NBgwaxfv16+0Sd9PR0h9azFKK5lBjMZBZVkK2vIKfEQH5lf5dbYiS/1LadV2okr8RIUbmp0d5XrQJvrRueWg3eOjc83TV46zR4at3wctegc1ejc1Ojc7P1Y7qqPs9Nc8lztb1v/K2+re9TKRZ+2r6Nm2+8AQ+dO+6V/Z+7ujJJ1Pz2Zbktaco+ThJK4bIURSG/1Mi5gnLOFZRzvrCMcwXlXCgsJ7vYQLbeQE6JAYvVDfbudPi4GrWKAC93/L20tPN0x9fDDR+dG74etue+Ojd8PGzbPjo3/Dx+2/bWaWwJo5saN43zEguTCbQacNeoXSaZbC6zZ8+u9RI3wNatW6+47/Llyxs/IOGyKkwWUnNK+bVAReHuDHJKTGTqK8jSV3CxqIKsogqKDeY6HVOlAj8Pd/w83WyPlz73rL7tW9n3eWnd8NbaviRXJZE6N3WTLsZvMpk47QVd2nu55NjRpiAJpWjTrFaF84XlnMkt5XR2CWdzS8koKON8ZRJZbrr6GUUVCu19dIT4ehDipyPEV0eQj45Aby3+XloCvd0J8NLafry1+OrcJAkTQrQIZUYzp7NLOZVTTHpeOen5ZWTkl5GeX0amvqKylgaOHb3sMXx1boS28yDIR0t7bx3tfbQEemtp762lfWVfWPW8nad7mzurJxwjCaVoEyxWhdS8Uo5e1HMiq4TTOSWczi4hNa+UCtPlx+SoVBDiq6NTgBedAjzpFOBJh3aehPnZkscATw0/b/uecbffIN9ihRAtVnGFiRNZxZzMKuFUdgkns22P5wvLr7ift1aDv5uZnhEhdKzs/0L9POjQzoNQPw/C2nngo5NUQVyd/JWIVsdotnLkop7D54s4clHP0Yt6jl0svuzZRq1GTZf2XkQH+9A12JvOgV72BLKDvwc6N81l38tkMqGRL9tCiBakoNTI4QtFHD6v5/CFIn49X0RqXtll6wf5aIkO9iGyvTed23sREehF58ofH3f47rvvuO22a+RLs2gQSShFi3exqJx9aYXsTy9gX3oBhy/oMdYyE9DDXU3PMD96hfrSLcSWPEYH+9ApwNOp4xGFEKK+LFaFE1nF7EkrYG9qPnvTC8jIr/2sY4d2HnQL8aF7iK0P7B7qQ7dgHwK8tZc9vsnUeBNphGuThFK0OBeLyvnpVB47TuWSciaPi0UVNeoEeLnTv5M/fTv60buDH306+BEV5C1jd4QQrZrFqnDofBHbT+awO7WA/WkFtU6MiWzvRd/wdvTr2I5+4X707diOwCskjkI0NUkohdPpK0xsP5nLT6dy2XE6j7O5pdVe16hV9Arz5ZrO/gzuHMA1nQOIbO/VpDMAhRCiuZwrKGP7yVy2ncxl+6ncGsvveGk1XNPZn5gugQzpEsDACH/aecrladGySEIpnCI9r4zNR7NIPpbFrjP5mC+5RYFaBf07+XNddHuujQ5icBd/vLTypyqEaBusVoX9GYVs/DWTTUezOJNT/Uu0r4cb10a3Z0TX9gyJDKRXmK8M2xEtnvwrLZrNmZwS/vfLRdYdusjxrOJqr0UHezOqRzDXRgcR2zUQPw/59i2EaDvMFispZ/JYfziTTUeyyC422F/TqFVcE+HPyO7BXN89iIGd2kkCKVodSShFk7pQWM43By/w9S8XOHxeby/XqFUMjQxgTO9QxvQOJTLI24lRCiFE41MUhV8v6Plq33m+/uUCuSW/JZG+Ojdu6h1CXJ8wRvYIki/RotWThFI0OqPZyuajWXy+O53tp3Lt96bWqFVc3y2IcQM7MqZ3CP5eMoBcCNH25BQb+M/ec3y17xwns0vs5YHeWuL7hhHfN5Rro4PQuslZSNF21CmhPHToEO+//z6FhYWMGTOGGTNmYDab+dvf/sann35KUVERQ4cO5bXXXiM2NrapYhYt1NncUlb9nM6Xe8+RW2K0lw+LCmTcwI7c1i+M9j46J0YohBBNQ1EU9qQV8ElKGt8dvojJYvsmrXVTM7Z3KHdeE87onsG4y6Vs0UY5nFD++uuvDB8+HJPJhJeXF6tXryYtLY3y8nI++eQTbrrpJsrLy0lOTuamm25i9+7d9O3btyljFy2AoijsPJPPkm1n+P5Ytr08xFfHn4Z0YuKQznRu7+XECIUQoulUmCx8ue8cn6SkcSzzt7Hh13T2Z+KQCG7t30FmZAuX4HBC+cILL9CxY0d++ukngoODmTlzJklJSfTu3ZujR4/i7+8PQGpqKkOGDGHBggWsXLmyqeIWTma2WFl3OJMlP57h0PkiwHYbwxt6BDNpWGdu6hUig8qFEG2WvsLEyp1pLNt+1n5FxsNdzR0Dw5kyogv9wts5OUIhmpfDCeXOnTt55JFHCAkJAeCpp57io48+Yvr06fZkEiAyMpIZM2bw+eefN3qwwvmMZitf7Etn0ZZT9nvEerir+VNMBDOujyJKJtcIIdqw3BIDH/10lhU70uwLjof7ezL9ukj+FBNBOy85Gylck8MJZU5ODmFhYfbtquddu3atUbdHjx5kZ2fXKBetl9liZWe2ijff2c65Qtuda9p7a5l2bSR/Ht5F7tAghGjTispNLP7hNB/9dJYKk+3Wr91CfHjkhmjGDewoYyOFy3M4oWzfvj25ubn2bXd3d3r27Imfn1+NugUFBfj6+jZOhMKpFEVh05EsFqw7ytk8DVBBkI+OR26I5r7Yzni4a5wdohBCNJkKk4XlO1J5f+tp+x1sBnZqxyM3dmNs71DUcrtXIYA6JJT9+/dn//799u127dpx9OjRWuseOHCA6OjohkcnnOrw+SJe+fYoKWfyAPB2U5h9c0/uv64rnlpJJIUQbZeiKHx76CKvfnuUC0W2qzI9Qn2YE9+Lm3uHyK1fhfgdhxPKhx9+mEOHDl21Xk5ODsnJyTzyyCMNCkw4T2GZkde+O8bqPRkoim3Ziweu7UJkxUkmXB+Ju5yVFEK0Ycczi3nh61/tX6Y7tvMgIa4nd14TjkbOSApRK4cTyvHjxzN+/Pir1gsODiYzM7MhMQknURSF/+4/zyvfHiWv1DZr8Y8DOzLnlp6E+rizbt1JJ0cohBBNx2iB19YfZ3lKOhargs5Nzawbonl4dLQM7xHiKuROOQKAtLxSEr86xI7Ttm/k3UN8eOXO/gyLCgTAZDI5MzwhhGhSu87m8/ovGnINaQDc0jeM/7u9NxGBso6uEI6QhNLFKYrC57szePnbI5QZLejc1Dx+c3ceHNlVbgsmhGjzSgxmFqw7yqe70gEVYX46Xp3Qn5t6hTo7NCFaFUkoXVi2voI5Xx5k6/EcAGKjAnnz7oFyZxshhEv4JaOQx1ftJy2vDIBrQ628N/M6An09nRyZEK2PJJQuasuxbBL+fYCCMhNaNzVz4nsy47ooWQJDCNHmWa0K//rxDG9vPI7ZqtCxnQevTehLwbFd+HrIP4tC1EeLu6a5aNEiIiMj8fDwIDY2lt27dzu036pVq1CpVA5NHHJlZouVN9YfY/rynykoM9G3ox/fPHY9M0d2lWRSCNHm5ZYYmLpsN6+vP4bZqnBb/zC+e2IUI7q2d3ZoQrRq9Uoo09PTKS8vv+zr5eXlpKen1/m4q1evJiEhgXnz5rFv3z4GDhxIfHz8Ve+6k5qaytNPP83IkSPr/J6uJLu4gj8v3cU/t54GYOqILnz1yLX0CJVF6IUQbd+hc0X88d3tbD+Vi6e7htcm9GfRfYPldolCNIJ6JZRRUVH897//vezrX3/9NVFRUXU+7sKFC3nwwQeZPn06ffr0YfHixXh5ebFs2bLL7mOxWJg8eTLz58+v9TaQwubguUL+8I/t7DyTj7dWw7uTruHFO/qhc5OlMIQQbd+Xe89x1+IdXCiqICrIm69nX8e9wzrLAuVCNJJ6DRZRFOWKr5tMJtTquuWqRqORvXv3kpiYaC9Tq9WMGTOGlJSUy+734osvEhISwgMPPMC2bduu+j4GgwGDwWDf1uv19pgdWRqnqk5rWkZn/a9Z/PXLQ1SYrHQL9mbRpEF0DfauUxtaY7sbg7Rb2u1IfdFyWawKL397hI9+SgXg5l4hLJw4iHaeclZSiMbkcEKp1+spLCy0b+fl5dV6WbuwsJBVq1bRoUOHOgWSm5uLxWIhNLT6Ug2hoaEcO3as1n22b9/O0qVLOXDggMPvs2DBAubPn1+jfOPGjXh5OT67edOmTQ7XdRZFgc0XVHyTbjsL2dvfyv2RRRz7+Qdq/0SvrjW0uylIu12Lo+0uKytr4khEQ1SYLDyxaj8bfs0C4PGbuvHkmB4yXlyIJuBwQvn3v/+dF198EQCVSsWTTz7Jk08+WWtdRVF4+eWXGyXAyykuLmbKlCksWbKEoKAgh/dLTEwkISHBvq3X64mIiCAuLg4/P7+r7m8ymdi0aRNjx47F3b3lfsM1W6zM/d9Rvkk/D8DU4Z1JvKUHbpr6zcNqLe1ubNJuafeVVF3hEC1PfqmRmR//zL70QrQaNW/fM5BxAzs6Oywh2iyHE8q4uDh8fHxQFIU5c+YwadIkBg8eXK2OSqXC29ubmJgYhgwZUqdAgoKC0Gg0ZGVlVSvPysoiLCysRv3Tp0+TmprKuHHj7GVWq9XWKDc3jh8/TnR0dI39dDodOp2uRrm7u3ud/uGsa/3mZDBbeOqLg6z/NRO1Cub/sS9TRkQ2yrFbcrubkrTbtTjablf8bFqDjPwypi3bzZncUvw83FgydQixMotbiCblcEI5YsQIRowYAUBpaSkTJkygf//+jRaIVqslJiaG5ORk+9I/VquV5ORkZs+eXaN+r169OHToULWy5557juLiYt555x0iIiIaLbbWpNRg5uGVe9l2MhetRs0/Jl3DLf1qJuRCCNEWnckp4b4lu8jUVxDu78ny6UPpLitZCNHk6jUpZ968eY0dBwAJCQlMmzaNIUOGMGzYMJKSkigtLWX69OkATJ06lfDwcBYsWICHhwf9+vWrtr+/vz9AjXJXUVRu4v6PdrM/vRAvrYYlU4dwXTfHhwMIIURrdiq7mElLdpFTbKB7iA8rZ8YS6ufh7LCEcAn1SiirxlJeiUql4vnnn6/TcSdOnEhOTg5z584lMzOTQYMGsX79evtEnfT09DrPHncVxRUmpi7bzS8ZhbTzdGf59KFc0znA2WEJIUSzOJapZ/KSXeSVGukV5svKmbEE+dQc3iSEaBr1SihfeOGFy76mUqlQFKVeCSXA7Nmza73EDbB169Yr7rt8+fI6v19bUGowM/2jn/klo5AAL3c+e3A4vTtcfYKREEK0Bccy9Uz6YKf97l8rH4glwFvr7LCEcCn1Ot1ntVpr/JjNZk6fPs1TTz3FkCFDrnp3G9E4yo0WHvj4Z/akFeDn4cYnD8RKMimEcBlpeaVMWbqbgjITAzq147OZwyWZFMIJGu36sVqtJioqirfeeovu3bvz2GOPNdahxWUYzVYeWrmXnWfy8dG58fGMYfQLb+fssIQQollk6yuYsnQ3OcUGeoX58smMWLmNohBO0iQDEkeNGsW6deua4tCikqIoPPvlQX48kYOXVsNHMmZSCOFCispMTFm6m/T8MjoHerFixjBJJoVwoiZJKPfs2SOTZ5rY2xtP8NX+82jUKv45eTBDIwOdHZIQQjSLCpOFGR//zPGsYoJ9dax8IJYQmc0thFPVa1LOihUrai0vLCzkxx9/5KuvvmLmzJkNCkxc3ue703lvyykAXr2zHzf0DHFyREII0TwURWHOfw6y1z5ufBid2zt+21whRNOoV0J5//33X/a1oKAgnn32WebOnVvfmMQVbDmezXNrDgO2+9JOHNrZyREJIUTzeff7U3z9ywXc1CoWT4mhV5hMQhSiJahXQnn27NkaZSqVioCAAHx95Y4ETeVUdgmPfbYfi1XhrsGdeGpsD2eHJIQQzebbgxdZuOkEAC+N78e10XLjBiFainollF26dGnsOMRVFFeYeOiTPZQYzAyLDGTBhP6oVCpnhyWEEM3i4LlC/t8XBwB44PooJg2TqzNCtCT1SiirHD58mHXr1pGamgpAZGQkt956a6Pe41uA1arw9Be/cDqnlDA/DxZNHozWTSY9CSFcQ36pkYc+2UuFycqNPYP52229nR2SEOJ36pVQGgwGHnroIT755BMURbHP6LZarSQmJjJ58mQ+/PBDtFpZXLYxvP/DaTb8moVWo+b9Pw8m2FduJyaEcA1Wq8KTqw9wsaiCrsHe/GPSNWjUcnVGiJamXqe5nnnmGVasWMGsWbM4evQoFRUVGAwGjh49ysMPP8zKlSuZM2dOY8fqkn48kcNbG48DMP+OvrLWpBCt3KJFi4iMjMTDw4PY2Fh279592bpLlixh5MiRBAQEEBAQwJgxY65Yvy3659ZT/HgiBw93Nf+cPBhfD1lrUoiWqF4J5cqVK5kyZQrvvfcePXv2xM3NDY1GQ8+ePVm0aBGTJ09m5cqVjR2ry8kpNpDw7wMoCkwaFiFjhoRo5VavXk1CQgLz5s1j3759DBw4kPj4+Mveqnbr1q1MmjSJLVu2kJKSQkREBHFxcZw/f76ZI3eOHadzf5uEc0c/mdEtRAtWr4TSZDIxfPjwy75+7bXXYjab6x2UqFpr7RdyS4z0DPVl3ri+zg5JCNFACxcu5MEHH2T69On06dOHxYsX4+XlxbJly2qt/+mnn/LII48waNAgevXqxYcffojVaiU5ObmZI29+2foKHv/8AFYF/hTTiT8NiXB2SEKIK6jXGMr4+Hg2bNjArFmzan19/fr1xMXFNSgwV/fxjlS2HM9B66bmH5OuwcNd4+yQhBANYDQa2bt3L4mJifYytVrNmDFjSElJcegYZWVlmEwmAgNrvzOWwWDAYDDYt/V6PWA7CWAymRx6j6p6jtZvCoqi8P/+fYDcEgM9Q314/raeTR5PS2i3M0i7pd2O1HdEvRLKl156iXvuuYcJEybw6KOP0q1bNwBOnjzJokWLSEtLY/Xq1eTn51fb73KdoKju6EU9r353DID/u603PcNkbU8hWrvc3FwsFguhoaHVykNDQzl27JhDx3jmmWfo2LEjY8aMqfX1BQsWMH/+/BrlGzduxMurbneT2bRpU53qN6btmSq2ndXgrlKYEFbIls0bmu29ndluZ5J2uxZH211WVubwMeuVUPbubVuy4dChQ6xdu7baa4qiANCnT58a+1kslvq8nUupMFl4/PP9GM1WbuoVwtQRsuanEAJee+01Vq1axdatW/HwqP2+1YmJiSQkJNi39Xq9fdyln59j4w9NJhObNm1i7NixuLs3/wSY1LxSnl2UAliZc2sv7m+mPtDZ7XYWabe0+0qqrnI4ol4J5dy5c2VR7Sby980nOJldQpCPjjfuHiCfsxBtRFBQEBqNhqysrGrlWVlZhIWFXXHft956i9dee43NmzczYMCAy9bT6XTodDWXFXN3d6/zP5r12aehzBYrc776lXKTlWuj2/PA9dGom3mJIGe0uyWQdrsWR9tdl8+mXgnlCy+8UJ/dxFUcPFfIkh/PALBgQn+CfGS9SSHaCq1WS0xMDMnJyYwfPx7APsFm9uzZl93vjTfe4JVXXmHDhg0MGTKkmaJ1jn/9eIb96YX46tx4808Dmz2ZFELUX71mec+YMYNdu3Zd9vXdu3czY8aMegflikwWK3P+cxCrAuMGdmRsn9Cr7ySEaFUSEhJYsmQJH3/8MUePHmXWrFmUlpYyffp0AKZOnVpt0s7rr7/O888/z7Jly4iMjCQzM5PMzExKSkqc1YQmc/T/t3f3cVHV+R7APwMyII+CKI8iKKCLKSiIUatYItqaK7WZWVeJzHtbsdXl3rbYuwsv6yZq5NXUFTXN3HRlrcRSUxHBh9RECBNNWwmVFYHAYGCQYZg59w9ibqwoA/Nwhjmf9+t1Xi/n8JuZ75eHr98553d+57YCa462LxG0bNYo+A3oL3JERNQTvWoot2/fjrKysvt+vby8HB9++GGvg5KiTcfLcKWqEe6Odkifee/8UyLq++bMmYPMzEykpaUhIiICJSUlOHTokO5CnZs3b+L27du68Rs3bkRrayueeeYZ+Pj46LbMzEyxUjAJrVZA6qcXodYIiA/zwlNj/cQOiYh6yKB7ed9PZWUl+vfnp0t9XatpxHt51wAA6TNH8VQ3kRVbvHjxfU9xFxQUdHp8/fp10wdkAXZ+dQMlFfVwtu+HN2c9xLnjRH2Q3g3lvn37Ol3RvXnzZhw9evSecfX19Th69CjGjx9vnAitnFYr4PVPLqJVo8VjIwZhVoSv2CEREZlNtaIFqw613172D9NHwNut6yvYiciy6d1QXr58GXv27AEAyGQyfPXVVygqKuo0RiaTwcnJCZMmTcLq1auNG6mV+vTrWyi68SOc5LZ4+6nR/GRORJKy7PNLaFS1IXzIALwwgcukEfVVejeUqampusniNjY22Lp1K55//nmTBSYFjS1qrPhpAfPfTQmBLyehE5GE5H1bjYMXq2BrI0PGU6Nhy6u6ifqsXs2h1Gq1xo5DktYdu4baJhWGeToh6dEgscMhIjKbFrUGafsuAQBe/mUQwnz1W3idiCxTr67yJsNdq2nCtlPlAIA/zwyDvB9/FEQkHZtPfI9b9Xfh6+aAJXEhYodDRAbq1RFKGxsbveb68VaLXRMEAW/uv4w2rYApIwfjsRGDxQ6JiMhsqhpasLGgfem5N371CzjKTbLgCBGZkdFuvajRaHD9+nXk5ORgxIgRePLJJ3sV0IYNG/DOO++gqqoK4eHhWLduHaKjo7scu2XLFuzYsQOlpaUAgMjISCxfvvy+4y1F3rc1OPHdD5Db2uDPT3LNSSKSlpWHruCuWoPIoe6YOcZH7HCIyAiMfuvF27dv4+GHH0ZoaGiPXzc7OxspKSnIysrChAkTsGbNGkybNg1Xr17F4MH3HsUrKCjA3Llz8cgjj8DBwQErV65EfHw8Ll26BD8/y1wYt02jxfKD3wIAFkwMQqCnk8gRERGZT/HNH7H361sAgLQnw7iyBZGVMPrEPR8fH7zyyit46623evzc1atXY+HChUhKSkJYWBiysrLg6OiIbdu2dTl+586dWLRoESIiIjBy5Ei8//77unvjWqqPi/6J72uV8HCSY9Hk4WKHQ0RkNoIg4M3PLwMAfjPOH+FDBogbEBEZjUkmrjg5OaG8vLxHz2ltbUVRUVGn+9ja2NggLi4OZ86c0es1mpuboVar4eHhcd8xKpUKKpVK91ihUAAA1Go11Gp1t+/RMUafsf+qRa3B//50r9pXJgXBwbZ3ryMGQ/Luy5g389ZnPOlnX0klSirq4Si3xR+mjxA7HCIyIqM3lKWlpXjvvfd6fMq7trYWGo1Gd0/bDl5eXrhy5Yper/H666/D19cXcXFx9x2TkZGBZcuW3bP/yJEjcHR01Dve3Nxcvcd2OFYpQ7XCFgPkAjzuXMLBg5d6/Bpi603e1oB5S4u+eTc3N5s4EuuhatPgncPtd8RZNHk4vFx5Rxwia9KrhjIoKKjLeS/19fVoaGiAo6MjcnJyDI2tR1asWIHdu3ejoKAADg73L1SpqalISUnRPVYoFBgyZAji4+Ph6tr9OmhqtRq5ubmYOnUq7Ozs9I6vsUWN9NWnAKjx+oyHMGucZc7xvJ/e5t3XMW/m/SAdZzioezvP3sSt+rvwcrXHgl8OEzscIjKyXjWUsbGx9zSUMpkM7u7uGD58OJ577rkHnnbuiqenJ2xtbVFdXd1pf3V1Nby9vR/43MzMTKxYsQJHjx7FmDFjHjjW3t4e9vb29+y3s7Pr0X+cPR3/Qf73qL+rRvBgZ8yOCkA/27657mRP87YWzFta9M1bit+b3mhStWFD/jUAwJIpoegvtxU5IiIytl41lNu3bzdyGIBcLkdkZCTy8vKQkJAAALoLbBYvXnzf561atQpvv/02Dh8+jKioKKPHZQw/NKqw9adFzP8rPrTPNpNERL2x9WQ56pStCBzoiNlR/mKHQ0QmYNAcSqVSCYVCARcXFzg7OxscTEpKChITExEVFYXo6GisWbMGSqUSSUlJAID58+fDz88PGRkZAICVK1ciLS0Nu3btQmBgIKqqqgAAzs7ORonHWDYdL0Nzqwbh/m6YNurBR1uJiKzJHWUrtpz8HgDwn/EjYMcP1ERWqcd/2devX8eiRYswdOhQuLq6wt/fH25ubggICEBycnKPr+7+uTlz5iAzMxNpaWmIiIhASUkJDh06pLtQ5+bNm7h9+7Zu/MaNG9Ha2opnnnkGPj4+ui0zM7PXMRjbj8pW7PzqJgBg6dRQrrlGRJLyl/xraFK1YZSvK2aM5iLmRNaqR0co9+3bh3nz5qGpqQmBgYGYOXMmXFxc0NjYiG+++QYbN27Ejh078NFHH2HWrFm9Cmjx4sX3PcVdUFDQ6fH169d79R7m9MGX5bir1mCUrysmhw4SOxwiIrOprL+LHWdvAAD+MH0kbGz4gZrIWundUF6+fBlz5szBsGHDsGnTJkycOPGeMSdPnsQrr7yC5557DkVFRQgLk/ZtBRtb1Nh++joAIPmxYB6dJCJJWZ9/Da1tWkwI8sCkEE+xwyEiE9L7lPfy5cvh6emJU6dOddlMAsDEiRNx8uRJDBw4UDfPUcr+evYGFC1tGD7ICdM5d5KIJORW/V3sOV8BAEjhdB8iq6d3Q5mfn48FCxZ0uxyQh4cHXnrpJRw7dszg4Pqyu60abD3ZPp900eRgnuohIknJKiiDWiPg4WEemDBsoNjhEJGJ6d1Q1tXVITAwUK+xQUFBqKur621MViG78CbqlK3wd++PX0f4ih0OEZHZ3G64i+zC9qOTS6b07K5pRNQ36d1Qenp66n0Fd3l5OTw9pTtfprVNi80n2pfJ+I/Y4Vwmg4gkJaugDK0aLaKDPBAznEcniaRA705n8uTJ2Lp1K+7cufPAcXfu3MHWrVsxefJkQ2Prsw5crERlQwsGudhjdiQX8SUi6ahWtOBvPx2dXDolRORoiMhc9G4o//jHP6Kurg6TJk3C6dOnuxxz+vRpxMbGoq6uDqmpqUYLsi8RBEF3V5zEmKFwsOMtxohIOjYWlKG1TYvxge48OkkkIXovGxQWFoZdu3Zh/vz5mDhxIgIDAxEeHt5pHcry8nI4ODjgo48+wqhRo0wZt8UqvP4jSm8pYN/PBs9PGCp2OEREZlOjaMHfzrXfyOF3U0J4ZTeRhPRoYfOnn34aERERWLVqFfbv34+cnBzd13x8fPDyyy/jtddeQ3BwsLHj7DO2nmqfO/n0OH94OMlFjoaIyHw2nfgeqjYtxgUMwC+DpTuPnkiKenwv72HDhiErKwsAoFAo0NjYCBcXF7i6uho9uL7mZl0zjlyuBgAs+GWguMEQEZnRD40q7Pyq/a44S+K47iSR1PS4ofw5V1dXNpI/s/30dQgCEBs6CMGDXcQOh4jIbDafKEOLWouIIQN4VxwiCeJ6NkZyt1WDj4var2x88dFAcYMhIjKj2iYV/nq24+gk504SSREbSiP5/EIlFC1tCPBwRGzIILHDISIymy0nvkeLWotwfzdMDmX9I5IiNpRG0vHp/IUJAbzNIhFJRm2TCjvO8OgkkdSxoTSCCxX1uHirAfJ+NpgdNUTscIiIzGbT8TLcVWsQPmQAHhsxWOxwiEgkbCiNoOPo5IzRPlwqiIgko6axRVf/fs+jk0SSxobSQA3Nanx+oRIA8G8PcyFzIpKOrIL2uZNjAwYglnMniSSNDaWBPrtwC6o2LUZ6u2BcwACxwyEiMosaRYtu3cnfc91JIsljQ2mg7PPtSwU9GzWEBZWIJOMvBWVQtWkRNdQdE7nuJJHksaE0wKXKBpTeUsDOVoaEsX5ih0NEZBZVDS3Y9dM9u38/lUcniYgNpUH2nP8nACA+zJsX4xCRZKw6fAWtbVpEB3ngkeEDxQ6HiCwAG8peUrVpkVNyCwAwO8pf5GiIiMyjpKIenxa3177//tUveHSSiACwoey1Y1dqUN+shrerAybyzjhEJAGCIODNzy8BAJ4e54fwIQPEDYiILAYbyl769Ov2pYJ+E+kHW94Zh4gk4LMLlSi+WQ9HuS1enz5S7HCIyIKwoeyFJjVw6lodAOCpsTzdTUTW70dlK/7nwLcAgEWTh8PL1UHkiIjIkrCh7IWSOhnatAIe8nNF8GBnscMhIjIpQRCQ/tkl/NCowvBBTnh54jCxQyIiC8OGshfO17Z/2xIiuFQQEVm/v569gc8uVMJGBrz7bAQc7GzFDomILIzFNZQbNmxAYGAgHBwcMGHCBJw7d+6B4/fs2YORI0fCwcEBo0ePxsGDB00a3z9/vIvyRhlkMuDJMb4mfS8isj6WXuP+1aHS21j2+WUAwOvTRyKCF+IQURcsqqHMzs5GSkoK0tPTUVxcjPDwcEybNg01NTVdjj99+jTmzp2LBQsW4Ouvv0ZCQgISEhJQWlpqshj3f3MbAPBwkAe83TiHiIj01xdqXAdVmxbr8v6BRTuLodEKeHqcH/59Ek91E1HX+okdwM+tXr0aCxcuRFJSEgAgKysLBw4cwLZt2/DGG2/cM37t2rWYPn06XnvtNQDAW2+9hdzcXKxfvx5ZWVldvodKpYJKpdI9VigUAAC1Wg21Wv3A+ARBwL4L7Q3lr0YN6na8NenIVUo5A8ybees3Xl+mrnGG1DcAuFrViA/P3MDlchv8+esCKFraAACzI/3w1q/D0NbW1qN8+xL+zjNvKTBljbOYhrK1tRVFRUVITU3V7bOxsUFcXBzOnDnT5XPOnDmDlJSUTvumTZuGnJyc+75PRkYGli1bds/+I0eOwNHR8YEx3lIC137oB1uZgH5Vl3Dw4KUHjrdGubm5YocgCuYtLfrm3dzcrPdrmqPGGVLfAOAfDTLsuWyL9pNXbXCzE/DroVpE2t3A4UM3un2+NeDvvLQw7wfrSY2zmIaytrYWGo0GXl5enfZ7eXnhypUrXT6nqqqqy/FVVVX3fZ/U1NROBVqhUGDIkCGIj4+Hq6vrA2NUqtrgHnQbJ4tLMeuJqbCzs+suLauhVquRm5uLqVOZtxQwb/3y7jgCqA9z1DhD6hsA1DSqIAy6gdqKMjw5KQrjgzwls84uf+eZtxSYssZZTENpLvb29rC3t79nv52dXbff3AF2dngmaggcay7qNd4aMW9pYd7dj7MkhtQ3APDzsMPSuFAcPHgNDw8fZHH5mQN/56WFeXc/Tl8Wc1GOp6cnbG1tUV1d3Wl/dXU1vL29u3yOt7d3j8YTEYmFNY6IrJnFNJRyuRyRkZHIy8vT7dNqtcjLy0NMTEyXz4mJiek0HmifF3C/8UREYmGNIyJrZlGnvFNSUpCYmIioqChER0djzZo1UCqVuisi58+fDz8/P2RkZAAAlixZgtjYWLz77ruYMWMGdu/ejfPnz2Pz5s16v6cgCAD0nyegVqvR3NwMhUIhqcPkzJt5S0FP8+6oGx11pDvmrnE9rW8Af/bMWxqYtwlqnGBh1q1bJwQEBAhyuVyIjo4Wzp49q/tabGyskJiY2Gn83//+dyE0NFSQy+XCqFGjhAMHDvTo/SoqKgQA3Lhx49brraKiwiJrHOsbN27cjLHpU+NkgqDnR2srpdVqUVlZCRcXF8hk3V/N2HHVZEVFhV5XTVoL5s28paCneQuCgMbGRvj6+sLGxmJmEOn0tL4B/Nkzb2lg3savcRZ1ylsMNjY28Pf37/HzXF1dJfVL2IF5Swvz7p6bm5uJo+m93tY3gD97qWHe0mKKGmd5H6mJiIiIqE9hQ0lEREREBmFD2UP29vZIT0/vcvFga8a8mbcUSDXvn5Pq94B5M28pMGXekr8oh4iIiIgMwyOURERERGQQNpREREREZBA2lERERERkEDaURERERGQQNpQ9sGHDBgQGBsLBwQETJkzAuXPnxA7J5E6cOIGZM2fC19cXMpkMOTk5YodkFhkZGRg/fjxcXFwwePBgJCQk4OrVq2KHZXIbN27EmDFjdIvexsTE4IsvvhA7LLNasWIFZDIZli5dKnYoZscaJ40ax/om3foGmK7GsaHUU3Z2NlJSUpCeno7i4mKEh4dj2rRpqKmpETs0k1IqlQgPD8eGDRvEDsWsjh8/juTkZJw9exa5ublQq9WIj4+HUqkUOzST8vf3x4oVK1BUVITz58/j8ccfx6xZs3Dp0iWxQzOLwsJCbNq0CWPGjBE7FLNjjZNOjWN9k2Z9A0xc47q92zcJgiAI0dHRQnJysu6xRqMRfH19hYyMDBGjMi8Awt69e8UOQxQ1NTUCAOH48eNih2J27u7uwvvvvy92GCbX2NgohISECLm5uUJsbKywZMkSsUMyK9Y46dY41jfrr2+CYPoaxyOUemhtbUVRURHi4uJ0+2xsbBAXF4czZ86IGBmZS0NDAwDAw8ND5EjMR6PRYPfu3VAqlYiJiRE7HJNLTk7GjBkzOv2dSwVrnLSxvll/fQNMX+P6meRVrUxtbS00Gg28vLw67ffy8sKVK1dEiorMRavVYunSpXj00Ufx0EMPiR2OyV28eBExMTFoaWmBs7Mz9u7di7CwMLHDMqndu3ejuLgYhYWFYociCtY46WJ9s/76BpinxrGhJOpGcnIySktLcerUKbFDMYsRI0agpKQEDQ0N+Pjjj5GYmIjjx49bbdGtqKjAkiVLkJubCwcHB7HDITIr1jfrrm+A+WocG0o9eHp6wtbWFtXV1Z32V1dXw9vbW6SoyBwWL16M/fv348SJE/D39xc7HLOQy+UIDg4GAERGRqKwsBBr167Fpk2bRI7MNIqKilBTU4Nx48bp9mk0Gpw4cQLr16+HSqWCra2tiBGaHmucNLG+WX99A8xX4ziHUg9yuRyRkZHIy8vT7dNqtcjLy5PM3AupEQQBixcvxt69e3Hs2DEEBQWJHZJotFotVCqV2GGYzJQpU3Dx4kWUlJTotqioKLzwwgsoKSmx+mYSYI2TGta3/2ft9Q0wX43jEUo9paSkIDExEVFRUYiOjsaaNWugVCqRlJQkdmgm1dTUhGvXrukel5eXo6SkBB4eHggICBAxMtNKTk7Grl27sG/fPri4uKCqqgoA4Obmhv79+4scnemkpqbiiSeeQEBAABobG7Fr1y4UFBTg8OHDYodmMi4uLvfMHXNycsLAgQMlMaesA2tcOynUONY36dQ3wIw1zqjXjFu5devWCQEBAYJcLheio6OFs2fPih2SyeXn5wsA7tkSExPFDs2kusoZgPDBBx+IHZpJvfTSS8LQoUMFuVwuDBo0SJgyZYpw5MgRscMyOykuGyQIrHFSqXGsb9Kub4JgmhonEwRBMF57SkRERERSwzmURERERGQQNpREREREZBA2lERERERkEDaURERERGQQNpREREREZBA2lERERERkEDaURERERGQQNpREREREZBA2lCR5L774IhISEsQOg4jIJFjjyBx4L2+yajKZ7IFfT09Px9q1a8EbRhFRX8QaR5aCt14kq1ZVVaX7d3Z2NtLS0nD16lXdPmdnZzg7O4sRGhGRwVjjyFLwlDdZNW9vb93m5uYGmUzWaZ+zs/M9p4MmT56MV199FUuXLoW7uzu8vLywZcsWKJVKJCUlwcXFBcHBwfjiiy86vVdpaSmeeOIJODs7w8vLC/PmzUNtba2ZMyYiKWGNI0vBhpKoCx9++CE8PT1x7tw5vPrqq/jtb3+L2bNn45FHHkFxcTHi4+Mxb948NDc3AwDq6+vx+OOPY+zYsTh//jwOHTqE6upqPPvssyJnQkR0L9Y4MjY2lERdCA8Px5/+9CeEhIQgNTUVDg4O8PT0xMKFCxESEoK0tDTU1dXhm2++AQCsX78eY8eOxfLlyzFy5EiMHTsW27ZtQ35+Pr777juRsyEi6ow1joyNF+UQdWHMmDG6f9va2mLgwIEYPXq0bp+XlxcAoKamBgBw4cIF5OfndzlXqaysDKGhoSaOmIhIf6xxZGxsKIm6YGdn1+mxTCbrtK/jykqtVgsAaGpqwsyZM7Fy5cp7XsvHx8eEkRIR9RxrHBkbG0oiIxg3bhw++eQTBAYGol8//lkRkXVhjaPucA4lkREkJyfjzp07mDt3LgoLC1FWVobDhw8jKSkJGo1G7PCIiAzCGkfdYUNJZAS+vr748ssvodFoEB8fj9GjR2Pp0qUYMGAAbGz4Z0ZEfRtrHHWHC5sTERERkUH4sYKIiIiIDMKGkoiIiIgMwoaSiIiIiAzChpKIiIiIDMKGkoiIiIgMwoaSiIiIiAzChpKIiIiIDMKGkoiIiIgMwoaSiIiIiAzChpKIiIiIDMKGkoiIiIgM8n8bzFTFccw7gQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_step = fom.step_resp()\n",
    "fig, ax = plt.subplots(fom.dim_output, fom.dim_input, sharex=True, constrained_layout=True)\n",
    "for i in range(fom.dim_output):\n",
    "    for j in range(fom.dim_input):\n",
    "        ax[i, j].plot(np.linspace(0, fom.T, y_step.shape[0]), y_step[:, i, j])\n",
    "for i in range(fom.dim_output):\n",
    "    ax[i, 0].set_title(f'Output {i + 1}', loc='left', rotation='vertical', x=-0.2, y=0.2)\n",
    "for j in range(fom.dim_input):\n",
    "    ax[0, j].set_title(f'Input {j + 1}')\n",
    "    ax[-1, j].set_xlabel('Time')\n",
    "_ = fig.suptitle('Step response')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d171398",
   "metadata": {},
   "source": [
    "## Transfer function evaluation\n",
    "\n",
    "The transfer function {math}`H` is the function such that\n",
    "{math}`Y(s) = H(s) U(s)`,\n",
    "where {math}`U` and {math}`Y` are respectively the Laplace transforms of\n",
    "the input {math}`u` and the output {math}`y`,\n",
    "assuming zero initial condition ({math}`x(0) = 0`).\n",
    "The expression for {math}`H` can be found by applying the Laplace transform\n",
    "to the system equations to obtain\n",
    "\n",
    "```{math}\n",
    "\\begin{align}\n",
    "    s E X(s) & = A X(s) + B U(s), \\\\\n",
    "    Y(s) & = C X(s) + D U(s).\n",
    "\\end{align}\n",
    "```\n",
    "\n",
    "using that {math}`s X(s)` is the Laplace transform of {math}`\\dot{x}(t)`.\n",
    "Eliminating {math}`X(s)` leads to\n",
    "\n",
    "```{math}\n",
    "Y(s) = \\left( C (s E - A)^{-1} B + D \\right) U(s),\n",
    "```\n",
    "\n",
    "i.e., {math}`H(s) = C (s E - A)^{-1} B + D`.\n",
    "Note that {math}`H` is a matrix-valued rational function\n",
    "(each component is a rational function).\n",
    "\n",
    "The transfer function of a given {{ LTIModel }} is stored as the attribute\n",
    "`transfer_function`.\n",
    "It can be evaluated using its\n",
    "{meth}`~pymor.models.transfer_function.TransferFunction.eval_tf` method.\n",
    "The result is a NumPy array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a1ceee5b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.56266667 0.61333333]\n",
      " [0.620175   0.50166667]\n",
      " [0.564075   0.38833333]]\n",
      "[[0.35516035 0.42800414]\n",
      " [0.39053974 0.30625375]\n",
      " [0.35602872 0.21798312]]\n",
      "[[0.41916591-0.24498821j 0.49022668-0.21786001j]\n",
      " [0.46133002-0.27112399j 0.36609293-0.23081817j]\n",
      " [0.42019995-0.24562591j 0.26612665-0.20191321j]]\n"
     ]
    }
   ],
   "source": [
    "print(fom.transfer_function.eval_tf(0))\n",
    "print(fom.transfer_function.eval_tf(1))\n",
    "print(fom.transfer_function.eval_tf(1j))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0b9a5131",
   "metadata": {},
   "source": [
    "Similarly, the derivative of the transfer function can be computed using the\n",
    "{meth}`~pymor.models.transfer_function.TransferFunction.eval_dtf` method.\n",
    "The result is again a NumPy array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "d98c16bc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.32905051 -0.28965578]\n",
      " [-0.36417571 -0.31024153]\n",
      " [-0.32990749 -0.27380581]]\n",
      "[[-0.13086074 -0.11936496]\n",
      " [-0.14479475 -0.12300531]\n",
      " [-0.1312008  -0.10527819]]\n",
      "[[-0.1198173 +0.21367653j -0.11093146+0.18362116j]\n",
      " [-0.13256763+0.23652374j -0.11255455+0.20186916j]\n",
      " [-0.12012849+0.21423385j -0.09488566+0.18167128j]]\n"
     ]
    }
   ],
   "source": [
    "print(fom.transfer_function.eval_dtf(0))\n",
    "print(fom.transfer_function.eval_dtf(1))\n",
    "print(fom.transfer_function.eval_dtf(1j))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "055d1d8e",
   "metadata": {},
   "source": [
    "To evaluate the transfer function over a sequence of points on the imaginary\n",
    "axis,\n",
    "the {meth}`~pymor.models.transfer_function.TransferFunction.freq_resp` method\n",
    "can be used.\n",
    "A typical use case is plotting the transfer function,\n",
    "which is discussed in the next section.\n",
    "\n",
    "## Magnitude and Bode plots\n",
    "\n",
    "It is known that if the input is chosen as\n",
    "{math}`u(t) = a e^{\\xi t} \\sin(\\omega t + \\varphi) e_j`\n",
    "(where {math}`e_j` is the {math}`j`-th canonical vector),\n",
    "then\n",
    "\n",
    "```{math}\n",
    "\\lim_{t \\to \\infty}\n",
    "\\left(\n",
    "  y_i(t)\n",
    "  - a \\lvert H_{ij}(\\xi + \\boldsymbol{\\imath} \\omega) \\rvert e^{\\xi t}\n",
    "  \\sin(\\omega t + \\varphi + \\arg(H_{ij}(\\xi + \\boldsymbol{\\imath} \\omega)))\n",
    "\\right)\n",
    "= 0.\n",
    "```\n",
    "\n",
    "In words, if the input is a pure exponential,\n",
    "the frequency is preserved in the output,\n",
    "the amplitude is multiplied by the amplitude of the transfer function, and\n",
    "the phase is shifted by the argument of the transfer function.\n",
    "In particular, if the input is sinusoidal, i.e., {math}`\\xi = 0`,\n",
    "then the output is also sinusoidal.\n",
    "\n",
    "It is of interest to plot the transfer function over the imaginary axis to\n",
    "visualize how the LTI system responds to each frequency in the input.\n",
    "Since the transfer function is complex-valued (and matrix-valued),\n",
    "there are multiple ways to plot it.\n",
    "\n",
    "One way is the \"magnitude plot\", a visualization of the mapping\n",
    "{math}`\\omega \\mapsto \\lVert H(\\boldsymbol{\\imath} \\omega) \\rVert`,\n",
    "using the {meth}`~pymor.models.transfer_function.TransferFunction.mag_plot`\n",
    "method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "bc401577",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "w = (1e-2, 1e3)\n",
    "_ = fom.transfer_function.mag_plot(w)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d561c6ba",
   "metadata": {},
   "source": [
    "Note that {meth}`~pymor.models.transfer_function.TransferFunction.mag_plot`\n",
    "computes the Frobenius norm of {math}`H(\\boldsymbol{\\imath} \\omega)` by default,\n",
    "just as `scipy.linalg.norm`.\n",
    "Likewise, the choice of the norm {math}`\\lVert \\cdot \\rVert` can be controlled\n",
    "using the `ord` parameter.\n",
    "\n",
    "Another visualization is the Bode plot,\n",
    "which shows the magnitude and phase of each component of the transfer function.\n",
    "More specifically,\n",
    "{math}`\\omega \\mapsto \\lvert H_{ij}(\\boldsymbol{\\imath} \\omega) \\rvert`\n",
    "is in subplot {math}`(2 i - 1, j)` and\n",
    "{math}`\\omega \\mapsto \\arg(H_{ij}(\\boldsymbol{\\imath} \\omega))`\n",
    "is in subplot {math}`(2 i, j)`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "f96a6b26",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x1000 with 12 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(6, 2, figsize=(8, 10), sharex=True, constrained_layout=True)\n",
    "_ = fom.transfer_function.bode_plot(w, ax=axs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8f90cfa",
   "metadata": {},
   "source": [
    "## System poles\n",
    "\n",
    "The poles of an LTI system are the poles of its transfer function.\n",
    "From the form of the transfer function\n",
    "it follows that the poles are eigenvalues of {math}`E^{-1} A`,\n",
    "assuming that {math}`E` is invertible.\n",
    "Conversely, the eigenvalues of {math}`E^{-1} A` are the poles of the system\n",
    "in the generic case\n",
    "(more precisely, if the system is minimal, i.e., controllable and observable;\n",
    "see {cite}`A05`).\n",
    "\n",
    "The poles of an {{ LTIModel }} can be obtained using its\n",
    "{meth}`~pymor.models.iosys.LTIModel.poles` method\n",
    "(assuming the system is minimal)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "472da6af",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "poles = fom.poles()\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(poles.real, poles.imag, '.')\n",
    "_ = ax.set_title('Poles')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb60109d",
   "metadata": {},
   "source": [
    ":::{note}\n",
    "\n",
    "The {meth}`~pymor.models.iosys.LTIModel.poles` method uses a dense\n",
    "eigenvalue solver,\n",
    "which is applicable only up to medium-sized problems.\n",
    "\n",
    ":::\n",
    "\n",
    "## System Gramians\n",
    "\n",
    "The controllability and observability Gramians of an asymptotically stable\n",
    "system with invertible {math}`E` are respectively\n",
    "\n",
    "```{math}\n",
    "\\begin{align*}\n",
    "    P & =\n",
    "    \\int_0^\\infty\n",
    "    e^{t E^{-1} A} E^{-1} B\n",
    "    B^{\\operatorname{T}} E^{-\\!\\operatorname{T}}\n",
    "    e^{t A^{\\operatorname{T}} E^{-\\!\\operatorname{T}}}\n",
    "    \\operatorname{d}\\!t, \\text{ and} \\\\\n",
    "    E^{\\operatorname{T}} Q E & =\n",
    "    \\int_0^\\infty\n",
    "    e^{t A^{\\operatorname{T}} E^{-\\!\\operatorname{T}}}\n",
    "    C^{\\operatorname{T}} C\n",
    "    e^{t E^{-1} A}\n",
    "    \\operatorname{d}\\!t.\n",
    "\\end{align*}\n",
    "```\n",
    "\n",
    "From this,\n",
    "it is clear that {math}`P` and {math}`Q` are symmetric positive semidefinite.\n",
    "Furthermore,\n",
    "it can be shown that {math}`P` and {math}`Q` are solutions to Lyapunov equation\n",
    "\n",
    "```{math}\n",
    "\\begin{align*}\n",
    "    A P E^{\\operatorname{T}}\n",
    "    + E P A^{\\operatorname{T}}\n",
    "    + B B^{\\operatorname{T}}\n",
    "    & = 0, \\\\\n",
    "    A^{\\operatorname{T}} Q E\n",
    "    + E^{\\operatorname{T}} Q A\n",
    "    + C^{\\operatorname{T}} C\n",
    "    & = 0.\n",
    "\\end{align*}\n",
    "```\n",
    "\n",
    "The Gramians can be used to quantify how much does the input influence the state\n",
    "(controllability) and state the output (observability).\n",
    "This is used to motivate the balanced truncation method\n",
    "(see {doc}`tutorial_bt`).\n",
    "Also, they can be used to compute the {math}`\\mathcal{H}_2` norm (see below).\n",
    "\n",
    "To find the \"Gramians\" {math}`P` and {math}`Q` of an {{ LTIModel }},\n",
    "the {meth}`~pymor.models.iosys.LTIModel.gramian` method can be used.\n",
    "Although solutions to Lyapunov equations are generally dense matrices,\n",
    "they can be often be very well approximated by a low-rank matrix.\n",
    "With {meth}`~pymor.models.iosys.LTIModel.gramian`,\n",
    "it is possible to compute the dense solution or only the low-rank Cholesky\n",
    "factor.\n",
    "For example, the following computes the low-rank Cholesky factor of the\n",
    "controllability Gramian as a {{ VectorArray }}:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "fc923326",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "NumpyVectorArray(\n",
       "    NumpyVectorSpace(101, id='STATE'),\n",
       "    [[-9.67050759e-01 -9.49603788e-01 -9.37818152e-01 ... -5.08356138e-01\n",
       "      -5.03442167e-01 -4.98481264e-01]\n",
       "     [-1.13133419e+00 -9.59580542e-01 -8.43810516e-01 ...  1.94699113e-01\n",
       "       1.92880555e-01  1.91000976e-01]\n",
       "     [ 9.08538963e-01  4.58145972e-01  2.24375612e-01 ...  9.25753046e-02\n",
       "       9.17614570e-02  9.08841977e-02]\n",
       "     ...\n",
       "     [-4.48720858e-17  1.95466800e-15 -3.87392910e-14 ... -1.84179333e-10\n",
       "       3.10420349e-11 -2.87160762e-12]\n",
       "     [ 3.97648476e-18 -1.92190365e-16  4.26024322e-15 ... -2.24465928e-11\n",
       "       1.75879252e-12 -8.24288506e-14]\n",
       "     [-1.85127015e-17  7.70480426e-16 -1.45373940e-14 ...  1.65200046e-10\n",
       "      -3.71100064e-11  4.41382006e-12]],\n",
       "    _len=101)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fom.gramian('c_lrcf')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6784cd1",
   "metadata": {},
   "source": [
    "## Hankel singular values\n",
    "\n",
    "The Hankel singular values of an LTI system are\n",
    "{math}`\\sigma_i = \\sqrt{\\lambda_i(E^{\\operatorname{T}} Q E P)}`,\n",
    "where {math}`\\lambda_i` is the {math}`i`-th eigenvalue.\n",
    "\n",
    "Plotting the Hankel singular values shows us how well an LTI system can be\n",
    "approximated by a reduced-order model.\n",
    "The {meth}`~pymor.models.iosys.LTIModel.hsv` method can be used to compute them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "a48bfe2c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hsv = fom.hsv()\n",
    "fig, ax = plt.subplots()\n",
    "ax.semilogy(range(1, len(hsv) + 1), hsv, '.-')\n",
    "_ = ax.set_title('Hankel singular values')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5416c99c",
   "metadata": {},
   "source": [
    "As expected for a heat equation, the Hankel singular values decay rapidly.\n",
    "\n",
    "## System norms\n",
    "\n",
    "There are various system norms,\n",
    "used for quantifying the sensitivity of system's outputs to its inputs.\n",
    "pyMOR currently has methods for computing:\n",
    "the {math}`\\mathcal{H}_2` norm,\n",
    "the {math}`\\mathcal{H}_\\infty` norm, and\n",
    "the Hankel (semi)norm.\n",
    "\n",
    "The {math}`\\mathcal{H}_2` norm is\n",
    "(if {math}`E` is invertible,\n",
    "{math}`E^{-1} A` has eigenvalues in the open left half plane, and\n",
    "{math}`D` is zero)\n",
    "\n",
    "```{math}\n",
    "\\lVert H \\rVert_{\\mathcal{H}_2}\n",
    "=\n",
    "\\left(\n",
    "  \\frac{1}{2 \\pi}\n",
    "  \\int_{-\\infty}^{\\infty}\n",
    "  \\lVert H(\\boldsymbol{\\imath} \\omega) \\rVert_{\\operatorname{F}}^2\n",
    "  \\operatorname{d}\\!\\omega\n",
    "\\right)^{\\frac{1}{2}}.\n",
    "```\n",
    "\n",
    "It can be shown that\n",
    "\n",
    "```{math}\n",
    "\\lVert y \\rVert_{\\mathcal{L}_\\infty}\n",
    "\\leqslant\n",
    "\\lVert H \\rVert_{\\mathcal{H}_2}\n",
    "\\lVert u \\rVert_{\\mathcal{L}_2}.\n",
    "```\n",
    "\n",
    "Additionally, for systems with a single input or a single output\n",
    "(i.e., {math}`u(t) \\in \\mathbb{R}` or {math}`y(t) \\in \\mathbb{R}`),\n",
    "\n",
    "```{math}\n",
    "\\lVert H \\rVert_{\\mathcal{H}_2}\n",
    "=\n",
    "\\sup_{u \\neq 0}\n",
    "\\frac{\\lVert y \\rVert_{\\mathcal{L}_\\infty}}{\\lVert u \\rVert_{\\mathcal{L}_2}}.\n",
    "```\n",
    "\n",
    "The computation of the {math}`\\mathcal{H}_2` norm is based on the system\n",
    "Gramians\n",
    "\n",
    "```{math}\n",
    "\\lVert H \\rVert_{\\mathcal{H}_2}^2\n",
    "= \\operatorname{tr}\\!\\left(C P C^{\\operatorname{T}}\\right)\n",
    "= \\operatorname{tr}\\!\\left(B^{\\operatorname{T}} Q B\\right).\n",
    "```\n",
    "\n",
    "The {meth}`~pymor.models.iosys.LTIModel.h2_norm` method of an {{ LTIModel }} can be\n",
    "used to compute it."
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    "The {math}`\\mathcal{H}_\\infty` norm is\n",
    "(if {math}`E` is invertible and\n",
    "{math}`E^{-1} A` has eigenvalues in the open left half plane)\n",
    "\n",
    "```{math}\n",
    "\\lVert H \\rVert_{\\mathcal{H}_\\infty}\n",
    "= \\sup_{\\omega \\in \\mathbb{R}}\n",
    "\\lVert H(\\boldsymbol{\\imath} \\omega) \\rVert_2.\n",
    "```\n",
    "\n",
    "It is always true that\n",
    "\n",
    "```{math}\n",
    "\\lVert H \\rVert_{\\mathcal{H}_\\infty}\n",
    "=\n",
    "\\sup_{u \\neq 0}\n",
    "\\frac{\\lVert y \\rVert_{\\mathcal{L}_2}}{\\lVert u \\rVert_{\\mathcal{L}_2}},\n",
    "```\n",
    "\n",
    "and, in particular,\n",
    "\n",
    "```{math}\n",
    "\\lVert y \\rVert_{\\mathcal{L}_2}\n",
    "\\leqslant\n",
    "\\lVert H \\rVert_{\\mathcal{H}_\\infty}\n",
    "\\lVert u \\rVert_{\\mathcal{L}_2}.\n",
    "```\n",
    "\n",
    "The {meth}`~pymor.models.iosys.LTIModel.hinf_norm` method uses a dense solver\n",
    "from [Slycot](<https://github.com/python-control/Slycot>) to compute the\n",
    "{math}`\\mathcal{H}_\\infty` norm."
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    "The Hankel norm is\n",
    "(if {math}`E` is invertible and\n",
    "{math}`E^{-1} A` has eigenvalues in the open left half plane)\n",
    "\n",
    "```{math}\n",
    "\\lVert H \\rVert_{\\operatorname{H}}\n",
    "= \\sigma_1,\n",
    "```\n",
    "\n",
    "i.e., the largest Hankel singular value.\n",
    "Since it is independent of {math}`D`,\n",
    "the \"Hankel norm\" is only a seminorm in general.\n",
    "\n",
    "It can be shown that the Hankel norm is the norm of the Hankel operator\n",
    "{math}`\\mathcal{H} \\colon \\mathcal{L}_2(-\\infty, 0) \\to \\mathcal{L}_2(0, \\infty)`\n",
    "mapping past inputs {math}`u_-` to future outputs {math}`y_+`\n",
    "\n",
    "```{math}\n",
    "y_+(t)\n",
    "= \\mathcal{H}(u_-)(t)\n",
    "= \\int_{-\\infty}^0 h(t - \\tau) u_-(\\tau) \\operatorname{d}\\!\\tau,\n",
    "```\n",
    "\n",
    "where {math}`h` is the impulse response\n",
    "{math}`h(t) = C e^{t E^{-1} A} E^{-1} B + D \\delta(t)`\n",
    "(i.e., {math}`H` is the Laplace transform of {math}`h`).\n",
    "Thus,\n",
    "\n",
    "```{math}\n",
    "\\lVert H \\rVert_{\\operatorname{H}}\n",
    "=\n",
    "\\sup_{u_- \\neq 0}\n",
    "\\frac{\\lVert y_+ \\rVert_{\\mathcal{L}_2}}{\\lVert u_- \\rVert_{\\mathcal{L}_2}},\n",
    "```\n",
    "\n",
    "The computation of the Hankel norm in\n",
    "{meth}`~pymor.models.iosys.LTIModel.hankel_norm` relies on the\n",
    "{meth}`~pymor.models.iosys.LTIModel.hsv` method."
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  {
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   "id": "f04cf711",
   "metadata": {},
   "source": [
    "Download the code:\n",
    "{download}`tutorial_lti_systems.md`,\n",
    "{nb-download}`tutorial_lti_systems.ipynb`."
   ]
  }
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