01_sindy_uniscale.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Section 2.1 - SINDy on Uniscale Systems"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.linalg as la\n",
    "from scipy.integrate import ode\n",
    "import scipy\n",
    "from scipy import signal\n",
    "import utils\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from matplotlib import colors\n",
    "%matplotlib inline\n",
    "from IPython.display import set_matplotlib_formats\n",
    "set_matplotlib_formats('png', 'pdf')\n",
    "plt.rc('font', size=14)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def find_boundary(coefficient_matrix, data):\n",
    "    boundary_data = np.zeros(coefficient_matrix.shape[0])\n",
    "    for i in range(boundary_data.size):\n",
    "        nonzeros=np.nonzero(coefficient_matrix[i])\n",
    "        if nonzeros[0].size==0:\n",
    "            index=0\n",
    "        else:\n",
    "            index = np.max(nonzeros)+1\n",
    "        if index==coefficient_matrix.shape[1]:\n",
    "            boundary_data[i]=np.nan\n",
    "        else:\n",
    "            boundary_data[i]=data[index]\n",
    "    return boundary_data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Van der Pol oscillator\n",
    "\n",
    "### Simulate the system"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# set up parameters\n",
    "\n",
    "tau = 1\n",
    "mu = 5\n",
    "period_length = 11.45015*tau\n",
    "\n",
    "x0 = [0.0, 2.0]\n",
    "\n",
    "Xi_true = np.zeros((10,2))\n",
    "Xi_true[2,0] = 1\n",
    "Xi_true[1,1] = -1\n",
    "Xi_true[2,1] = mu\n",
    "Xi_true[7,1] = -mu\n",
    "Xi_true /= tau\n",
    "\n",
    "poly_order = 3\n",
    "coefficient_threshold = .1\n",
    "tol = 1e-10\n",
    "\n",
    "# simulate system\n",
    "num_periods_simulate = 10\n",
    "sampling_rate_simulate_exponent = 18\n",
    "sampling_rate_simulate = 2**sampling_rate_simulate_exponent\n",
    "t_simulate_full = np.linspace(0, num_periods_simulate*period_length,\n",
    "                int(num_periods_simulate*sampling_rate_simulate))\n",
    "dt_simulate = t_simulate_full[1]-t_simulate_full[0]\n",
    "\n",
    "vdp_simulation = utils.simulate_vanderpol_oscillator(dt_simulate, t_simulate_full.size,\n",
    "                                                   x0=x0, mu=mu, tau=tau)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Subsample data and apply SINDy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "test_durations = np.arange(.05,1,.05)\n",
    "test_sampling_rates = np.arange(6,19)\n",
    "test_starts = np.arange(0,1,.1)\n",
    "\n",
    "extra_coefficients = np.zeros((test_durations.size, test_sampling_rates.size, test_starts.size))\n",
    "\n",
    "for i,duration in enumerate(test_durations):\n",
    "    for j,sampling_rate_exponent in enumerate(test_sampling_rates):\n",
    "        for k,start_time in enumerate(test_starts):\n",
    "            # get subsampled data\n",
    "            initial_samples = int((5+start_time)*sampling_rate_simulate)\n",
    "            t_simulate = t_simulate_full[initial_samples:]\n",
    "            vdp_solution = vdp_simulation[:,initial_samples:]\n",
    "            \n",
    "            sampling_rate = 2**sampling_rate_exponent\n",
    "            t_max_idx = int(duration*sampling_rate_simulate)+1\n",
    "            spacing = sampling_rate_simulate//sampling_rate\n",
    "\n",
    "            t_sample = t_simulate[:t_max_idx:spacing]\n",
    "            dt_sample = t_sample[1] - t_sample[0]\n",
    "            sampled_data = vdp_solution[:,:t_max_idx:spacing]\n",
    "\n",
    "            # fit a SINDy model\n",
    "            sindy = utils.SINDy()\n",
    "            sindy.fit(sampled_data, poly_order, t=dt_sample, coefficient_threshold=coefficient_threshold)\n",
    "            extra_coefficients[i,j,k] = np.where(((np.abs(Xi_true) < tol) & (np.abs(sindy.Xi) > tol))\\\n",
    "                                                  | ((np.abs(Xi_true) > tol) & (np.abs(sindy.Xi) < tol)))[0].size\n",
    "\n",
    "boundaries = np.zeros((test_sampling_rates.size, test_starts.size))\n",
    "for k,start_time in enumerate(test_starts):\n",
    "    boundaries[:,k] = find_boundary(extra_coefficients[:,:,k].T, test_durations)\n",
    "vdp_data = [test_sampling_rates, boundaries]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot the range of data requirements for all portions of the attractor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/kpchamp/anaconda/envs/py3/lib/python3.6/site-packages/ipykernel_launcher.py:3: RuntimeWarning: Mean of empty slice\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f929f4c4240>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/pdf": "JVBERi0xLjQKJazcIKu6CjEgMCBvYmoKPDwgL1R5cGUgL0NhdGFsb2cgL1BhZ2VzIDIgMCBSID4+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\n",
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX0AAAEACAYAAABfxaZOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQh3y+/e32QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f92eb74e438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(vdp_data[0], vdp_data[1])\n",
    "plt.plot(vdp_data[0], np.nanmean(vdp_data[1], axis=1), 'k')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Show the average baseline duration on the attractor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-2.2236618198767921,\n",
       " 2.2236556197844868,\n",
       " -8.4009198354296508,\n",
       " 8.400831907459299)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/pdf": "JVBERi0xLjQKJazcIKu6CjEgMCBvYmoKPDwgL1R5cGUgL0NhdGFsb2cgL1BhZ2VzIDIgMCBSID4+\nCmVuZG9iago4IDAgb2JqCjw8IC9Gb250IDMgMCBSIC9YT2JqZWN0IDcgMCBSIC9FeHRHU3RhdGUg\nNCAwIFIgL1BhdHRlcm4gNSAwIFIKL1NoYWRpbmcgNiAwIFIgL1Byb2NTZXQgWyAvUERGIC9UZXh0\nIC9JbWFnZUIgL0ltYWdlQyAvSW1hZ2VJIF0gPj4KZW5kb2JqCjEwIDAgb2JqCjw8IC9UeXBlIC9Q\nYWdlIC9QYXJlbnQgMiAwIFIgL1Jlc291cmNlcyA4IDAgUgovTWVkaWFCb3ggWyAwIDAgMTU3LjE0\nMDYyNSAxNDcuMTY2ODc1IF0gL0NvbnRlbnRzIDkgMCBSCi9Hcm91cCA8PCAvVHlwZSAvR3JvdXAg\nL1MgL1RyYW5zcGFyZW5jeSAvQ1MgL0RldmljZVJHQiA+PiAvQW5ub3RzIFsgXSA+PgplbmRvYmoK\nOSAwIG9iago8PCAvTGVuZ3RoIDExIDAgUiAvRmlsdGVyIC9GbGF0ZURlY29kZSA+PgpzdHJlYW0K\neJztVrnOnLcV7ecp+ATU3ZdShgEB6aIULoJUsuBEsA3YApLXz7nkJ1gpVKQNUvyYmfNzubxnIXl9\ner15y+unz4vWJ/z9a/11/Q2fPy5e79ab7z/+8x8fPr5/99368PlFwH95sedmoxDHz5+//smGrxGV\nDpz+8+ffX69fX78ttV13sOROO/9k5h2LqXbK+v3j+mH9ut68lalJ1p9Qxyd8/lEXYfC714uJtqZx\nxSpAJpSJ6rq3mKrwoOycjc27toZS1creLl0qg+b2auVcia3JjXnQQIWqqCvx/1SXvChFaWGs706x\niEF9i7Aa1tUdJeFnBUMJ3bpyKozIA+qmJJS2wlECpeugvFG4ZCx0Ec3QnsKqNpcSijTBN9Q7K1Ru\nImkUqRjb4jF9rdhMqCeX+qZCBXPg8m3kjQMrCnMptkHRfExjWSq7VftUBlQzHXsATUIb58Cluxtf\n66BG1g8a3Bw86xJTm12U05Py7KYVfCqTHQkiZEjPYjK+KFWb99IA3+p6VkAfzBQLNI42RQxIOxkD\neplt7o7DJRhsFrRyOWjXJs2LQlUWurxHFn3akNNILmwMKooAnrHDqznZwraqoE8uGpozFiVWnoMB\nK5EpFlinidetqwutgfB0O4i+TcDBOnXmG76hDX1R1D26AZpSFHoblug5CAZRjnOVXyIMvQvUNa3J\nEcuhEroSx9hRMUTSD+1oCcTf0yV31UciEHcDnRroOA/TpA1GXD1NMpMpF9MIBEbDeAkVyxX0sIre\n2GKBKauc4lE0t0QBjq0iJXzlD+/aOF9qXCH8wGVYA6OVtjPTaRsshK0NTlfegoJZH7tBBiBxYGxX\nGdebODLfwVaet+jh6IjurKGWd8OCtyybz4YY4afLgD2LSFEebM9++4EucBxPQUY7YKnoC0MhPfWJ\nwTOdJyQmZtw0RIDT+HLaMDi0I4ESkF/wikN9dnBYNoWmheQjRXvGo7WOrOjhBmag4AeODsfccVEp\n3PMFdq4JN+wDz5Y+sKWDtoHFwEM8NRIIvqHnSOO2e3442FDheKYFQy7KOnkAEO70L42F9kNqotBE\nxveHm5DsniSEKuwSBnbhOmgsJ2Sq8gqkg8deCfNEUF0xtSIzeUVPQFidrRALYUG9YjKTkXlXjkBH\nhI5ZDPX0la4aTj85WJHQyRU5mDhhUSPyPgEwhmhMlMlBRUKdw04ORsASk0yI3Dz9mhzExYPkmRyE\nyE8JYz+FLPwkHtRyQwhGgsefHMR1ov7kIBLtWcHg3wdFME1+6vBkok/ioYeK+wA5aFYdDwr+cOEh\nBtnC/KYgiIZY52SICsjuiRvB3cTTBfTA+4LshVoMfOHeOPsPozxK8UAuhZwWHEINgbgCJMMOx+iT\ndkGMS2gmmZ/OTjCih+0Tdwk6nrRM+CnyZGBQ0LOqI4bBc83FJlcGR30q4BYoFs3bQsYKqOdIfLjV\n53YonDUmGK1P+J8OIo0ZcTixB16eawudxPU6uShNcnQIdDQNCiCIHJ3ZJbxwZ0AGNX6OvmORp2gm\nYgjqg86L5AqpsDOO20dSfqxX08TIeZDoLjwKpC+Ku2gyfVydiPeUb8Ovv7z+vP6bx45+/dhBDH79\nDDvPrvf/f/H8z714GjvjRDgbsiasvomOnF7/BlKxU+gKZW5kc3RyZWFtCmVuZG9iagoxMSAwIG9i\nagoxMjI5CmVuZG9iagozIDAgb2JqCjw8ID4+CmVuZG9iago0IDAgb2JqCjw8IC9BMSA8PCAvVHlw\nZSAvRXh0R1N0YXRlIC9DQSAwIC9jYSAxID4+Ci9BMiA8PCAvVHlwZSAvRXh0R1N0YXRlIC9DQSAw\nLjggL2NhIDAuOCA+PgovQTMgPDwgL1R5cGUgL0V4dEdTdGF0ZSAvQ0EgMSAvY2EgMSA+PiA+Pgpl\nbmRvYmoKNSAwIG9iago8PCA+PgplbmRvYmoKNiAwIG9iago8PCA+PgplbmRvYmoKNyAwIG9iago8\nPCA+PgplbmRvYmoKMiAwIG9iago8PCAvVHlwZSAvUGFnZXMgL0tpZHMgWyAxMCAwIFIgXSAvQ291\nbnQgMSA+PgplbmRvYmoKMTIgMCBvYmoKPDwgL0NyZWF0b3IgKG1hdHBsb3RsaWIgMi4wLjIsIGh0\ndHA6Ly9tYXRwbG90bGliLm9yZykKL1Byb2R1Y2VyIChtYXRwbG90bGliIHBkZiBiYWNrZW5kKSAv\nQ3JlYXRpb25EYXRlIChEOjIwMTgwNTE0MTYwMzQ2LTA3JzAwJykKPj4KZW5kb2JqCnhyZWYKMCAx\nMwowMDAwMDAwMDAwIDY1NTM1IGYgCjAwMDAwMDAwMTYgMDAwMDAgbiAKMDAwMDAwMTk1MCAwMDAw\nMCBuIAowMDAwMDAxNzI0IDAwMDAwIG4gCjAwMDAwMDE3NDUgMDAwMDAgbiAKMDAwMDAwMTg4NyAw\nMDAwMCBuIAowMDAwMDAxOTA4IDAwMDAwIG4gCjAwMDAwMDE5MjkgMDAwMDAgbiAKMDAwMDAwMDA2\nNSAwMDAwMCBuIAowMDAwMDAwMzk5IDAwMDAwIG4gCjAwMDAwMDAyMDggMDAwMDAgbiAKMDAwMDAw\nMTcwMyAwMDAwMCBuIAowMDAwMDAyMDEwIDAwMDAwIG4gCnRyYWlsZXIKPDwgL1NpemUgMTMgL1Jv\nb3QgMSAwIFIgL0luZm8gMTIgMCBSID4+CnN0YXJ0eHJlZgoyMTU4CiUlRU9GCg==\n",
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJ0AAACTCAYAAACULBumAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nyv0fMkhJbkGXujEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f929f3c4c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "start_idx = int(5.3*sampling_rate_simulate)\n",
    "end_idx = int(7*sampling_rate_simulate)\n",
    "end_idx_highlight = int(5.5*sampling_rate_simulate)\n",
    "spacing = 2**4\n",
    "\n",
    "plt.figure(figsize=(2,2))\n",
    "plt.plot(vdp_simulation[0,start_idx:end_idx:spacing], vdp_simulation[1,start_idx:end_idx:spacing],\n",
    "         alpha=0.8, color='#999999', linewidth=2)\n",
    "plt.plot(vdp_simulation[0,start_idx:end_idx_highlight:spacing],\n",
    "         vdp_simulation[1,start_idx:end_idx_highlight:spacing], color='#ff0000')\n",
    "plt.axis('equal')\n",
    "plt.axis('off')\n",
    "# plt.savefig('figures/02_vdp.pdf', format='pdf', dpi=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lorenz\n",
    "\n",
    "### Simulate the system"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sigma=10.\n",
    "rho=28.\n",
    "beta=8/3\n",
    "tau = 1\n",
    "period_length = .759*tau\n",
    "\n",
    "x0 = [-8.0, 7.0, 27.0]\n",
    "\n",
    "Xi_true = np.zeros((20,3))\n",
    "Xi_true[1,0] = -sigma\n",
    "Xi_true[2,0] = sigma\n",
    "Xi_true[1,1] = rho\n",
    "Xi_true[2,1] = -1\n",
    "Xi_true[6,1] = -1\n",
    "Xi_true[3,2] = -beta\n",
    "Xi_true[5,2] = 1\n",
    "Xi_true /= tau\n",
    "\n",
    "poly_order = 3\n",
    "coefficient_threshold = .1\n",
    "tol = 1e-10\n",
    "\n",
    "num_periods_simulate = 10\n",
    "sampling_rate_simulate_exponent = 18\n",
    "sampling_rate_simulate = 2**sampling_rate_simulate_exponent\n",
    "t_simulate_full = np.linspace(0, num_periods_simulate*period_length,\n",
    "                int(num_periods_simulate*sampling_rate_simulate))\n",
    "dt_simulate = t_simulate_full[1]-t_simulate_full[0]\n",
    "\n",
    "lorenz_simulation = utils.simulate_lorenz(dt_simulate, t_simulate_full.size, x0=x0, sigma=sigma, rho=rho, beta=beta,\n",
    "                                    tau=tau)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Subsample data and apply SINDy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "test_durations = np.arange(.1,2.5,.05)\n",
    "test_sampling_rates = np.arange(5,19)\n",
    "test_starts = np.arange(0,1,.1)\n",
    "\n",
    "extra_coefficients = np.zeros((test_durations.size, test_sampling_rates.size, test_starts.size))\n",
    "\n",
    "for i,duration in enumerate(test_durations):\n",
    "    for j,sampling_rate_exponent in enumerate(test_sampling_rates):\n",
    "        for k,start_time in enumerate(test_starts):\n",
    "            initial_samples = int((5+start_time)*sampling_rate_simulate)\n",
    "            t_simulate = t_simulate_full[initial_samples:]\n",
    "            lorenz_solution = lorenz_simulation[:,initial_samples:]\n",
    "            \n",
    "            # get subsamples\n",
    "            sampling_rate = 2**sampling_rate_exponent\n",
    "            t_max_idx = int(duration*sampling_rate_simulate)+1\n",
    "            spacing = sampling_rate_simulate//sampling_rate\n",
    "\n",
    "            t_sample = t_simulate[:t_max_idx:spacing]\n",
    "            dt_sample = t_sample[1] - t_sample[0]\n",
    "\n",
    "            sampled_data = lorenz_solution[:,:t_max_idx:spacing]\n",
    "\n",
    "            sindy = utils.SINDy()\n",
    "            sindy.fit(sampled_data, poly_order, t=dt_sample, coefficient_threshold=coefficient_threshold)\n",
    "            extra_coefficients[i,j,k] = np.where(((np.abs(Xi_true) < tol) & (np.abs(sindy.Xi) > tol))\\\n",
    "                                                  | ((np.abs(Xi_true) > tol) & (np.abs(sindy.Xi) < tol)))[0].size\n",
    "\n",
    "boundaries = np.zeros((test_sampling_rates.size, test_starts.size))\n",
    "for k,start_time in enumerate(test_starts):\n",
    "    boundaries[:,k] = find_boundary(extra_coefficients[:,:,k].T, test_durations)\n",
    "lorenz_data = [test_sampling_rates, boundaries]\n",
    "lorenz_data2 = [test_durations, extra_coefficients]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot the range of data requirements for all portions of the attractor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/kpchamp/anaconda/envs/py3/lib/python3.6/site-packages/ipykernel_launcher.py:3: RuntimeWarning: Mean of empty slice\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f929f166240>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/pdf": "JVBERi0xLjQKJazcIKu6CjEgMCBvYmoKPDwgL1R5cGUgL0NhdGFsb2cgL1BhZ2VzIDIgMCBSID4+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\nbyAyNCAwIFIgPj4Kc3RhcnR4cmVmCjYwNjYKJSVFT0YK\n",
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX0AAAEACAYAAABfxaZOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd8VFX+//HXmZbMpJLeSA8daSFIlSKg2Ltid1f3u7rl\n93XVXfu6uvp1Lbvu6rp9ray6VrAhIDXSpdeQkN57MpNk2v39MRgIBElCCsx8no/HPIDMLecGeOfO\nOed+jtI0DSGEEL5BN9ANEEII0X8k9IUQwodI6AshhA+R0BdCCB8ioS+EED5EQl8IIXyIhL4QQvgQ\nCX0hhPAhEvpCCOFDDAPdgONFRERoycnJA90MIYQ4q2zdurVa07TIU213ytBXSj0IXAkMBdqADcCD\nmqbt/p59koHDnbx1oaZpX37f+ZKTk9myZcupmiWEEOIYSqmCrmzXle6dmcCfgSnAbMAJLFdKhXVh\n3wuA2GNeX3elUUIIIfrGKe/0NU2bf+yflVI3Aw3AVGDJKXav0TStvOfNE0II0Zt6MpAbdGS/ui5s\n+6FSqlIpla2UuroH5xJCCNGLehL6LwHbgfXfs00zcB9wLbAAWAG8q5S6qbONlVJ3KaW2KKW2VFVV\n9aBJQgghukJ1p56+UupF4HpgmqZped06kVKvANM1TTvn+7bLzMzUZCBXCCG6Rym1VdO0zFNt1+U7\nfaXU74EbgNndDfwjNgEZPdhPCCFEL+nSPH2l1EvAdcAsTdP29/BcY4GyHu4rhBCiF3Rlnv4rwM3A\n5UCdUirmyFvNmqY1H9nmGSBL07Q5R/58K+AAtgFu4BLgHuCXvX4FRzgcDRQVv0FE+HkEB39vD5IQ\nQvisrtzp333k1xXHff0J4NdHfh8LpB33/iNAEuACDgJ3aJr2Vs+aeWpK6Th8+A/odCYJfSGEOImu\nzNNXXdjmtuP+/Drwes+b1X0GQxAmUyQ2a25/nlYIIc4qXlVwzWJJxWbryRizEEL4Bi8L/RSsts5K\n/gghhAAvC/0ASxpOZz12e+1AN0UIIc5IXhX6FksKgHTxCCHESXhZ6KcCEvpCCHEyXhX6ZnMCSpmw\nSugLIUSnvCr0ldJjsSRhk8FcIYTolFeFPsi0TSGE+D5eGfotLYW43Y6BbooQQpxxvC70AywpaJqT\nlpaigW6KEEKccbwu9GUGjxBCnJyEvhBC+BCvC32jMQSjMVxm8AghRCe8LvQBAiypMldfCCE64ZWh\nb7GkSPeOEEJ0wjtDPyAVh6MWh6N+oJsihBBnFO8MfRnMFUKITnll6AccCX3p1xdCiI68MvT9/Qej\nlBGbVUJfCCGO5ZWhr9MZMJsTpXtHCCGO45WhD7J0ohBCdMZrQz/AkkpLSwFut3OgmyKEEGcMrw19\niyUNTXPQ2lo80E0RQogzhveGfoCslyuEEMfz2tCXaZtCCHEirw19o3EQRuMgudMXQohjeG3ow3c1\neGQGjxBCfMfLQz9N7vSFEOIYXh36AZYU7PZqHI7GgW6KEEKcEbw69KXwmhBCdCShL4QQPsSrQ99s\nHoxSegl9IYQ4wqtDX6czYTYnSg0eIYQ4wqtDHzxdPDZb7kA3Qwghzgg+EPoptLQUoGmugW6KEEIM\nOB8I/VTcbjutrSUD3RQhhBhwPhH6IDV4hBACfCD0A9qnbcpgrhBCeH3oG41hGAwh2KwymCuEEF4f\n+kopLJZU6d4RQgh8IPTBU4NHuneEEMJHQt9iScVur8TpbBropgghxIA6ZegrpR5USm1WSjUqpaqU\nUkuUUqO6sN9opdRqpVSLUqpEKfWYUkr1TrO7xxIgg7lCCAFdu9OfCfwZmALMBpzAcqVU2Ml2UEoF\nA8uACmAi8HPgfuDe02xvj8i0TSGE8DCcagNN0+Yf+2el1M1AAzAVWHKS3W4ELMCtmqa1ALuVUsOA\ne5VSL2qapp1es7vHYk4EdFJ4TQjh83rSpx90ZL+679lmMrD2SOB/ZykQByT34Jyn1GazsmPZ51QX\nFZzwnk7nh9mcIN07Qgif15PQfwnYDqz/nm1i8HTtHKvimPc6UErdpZTaopTaUlVV1YMmgdvtZvk/\n/kzu1k2dvi9LJwohRDdDXyn1IjANuErrxQpmmqb9TdO0TE3TMiMjI3t0DHNgEKHRsVTk5nT6foAl\nFZvtMJrmPp2mCiHEWa3Loa+U+j1wAzBb07RT3TKXA9HHfS36mPf6RHRaBuUnCX2LJQW3u43W1tK+\nOr0QQpzxuhT6SqmXOBr4+7uwy3pgulLK/5ivzQVKgfzuNrKrYtIyaKqpwlp/4nCDLJ0ohBBdm6f/\nCnA7sBCoU0rFHHkFHrPNM0qpFcfstgiwAa8ppUYppa4EfgX06cydmNQMACryDp3wnoS+EEJ07U7/\nbjwzdlYAZce87jtmm1gg7bs/aJrWgOfOPg7YArwCvAC82CutPomo1DSU0lGee/CE90ymCAyGIFk6\nUQjh07oyT/+UT9FqmnZbJ1/bBczoWbN6xuRvJiw+odN+/e8Kr8nSiUIIX+Z1tXdi0oZQnptDZ71I\nFim8JoTwcV4Y+hm0NDbQVH3ifH+LJZW2tnKcTusAtEwIIQaeV4Y+QHneiV087YO5LXK3L4TwTV4X\n+hFJKej0hk779duXTrTKDB4hhG/yutA3GI1EJiVT0ckMHrM5GVAybVMI4bO8LvTB08VTnnsIzd2x\n5IJe74e/f4KUWBZC+CyvDP3otAzsLTbqyk8suSBLJwohfJlXhn5M2hCATvv1LVJ4TQjhw7wy9MPj\nB2Pw8+v0yVxLQBpudwttbX1W900IIc5YXhn6Or2e6JQ0KnI7q8GTAsjSiUII3+Q1oV9RUcFdd93F\nunXrAIhOzaAyPw+3q2PZ/wApvCaE8GFeE/qBgYG8/vrrfPLJJ4BnBo/T3nbC8okmUxR6fYCEvhDC\nJ3lN6AcEBDBlyhSWLVsGHPNk7nGDuZ7CaynYrDKDRwjhe7wm9AHmzp3Ljh07qKioIDQmDr+AgE6X\nTwyQ9XKFED7K60IfYMWKFSiliE7tfPlEiyWF1rZSXC5bfzdRCCEGlFeF/vjx4xk0aBDLly8HPF08\n1UX5OO32DtsdXUUrv7+bKIQQA8qrQl+v1zNnzhyWLVuGpmnEpGbgdrmoKujYfy9LJwohfJVXhT7A\n+eefT3FxMQcOHCC6fTC340NaFksygCydKITwOV4X+t/16y9btoyg8AgsIaEn9Ovr9Wb8/ePlTl8I\n4XO8LvRTU1NJTU1l2bJlKKWOVNw8WQ0eWS9XCOFbvC70wXO3v2rVKhwOBzFpQ6gtLcbe0nGmjme9\n3PxO19IVQghv5bWh39TUxKZNmzwPaWkaFYc73tVbLKm4XFba7BUD1EohhOh/Xhn6s2bNQinFsmXL\njhnM7djFI0snCiF8kVeGflhYGJmZmSxbtgxLcAjBkVEnhP7RaZsyg0cI4Tu8JvQdTc18+YfXqNjn\nCfe5c+eyceNGGhoaiEnNOGHNXD+/GPR6C1YZzBVC+BCvCf3i8jqS/vIsy15ZBHhC3+VysXr1aqLT\nMmiorMDW2NC+vVIKizlFpm0KIXyK14R+SsZg6hNSMW3byPaieiZPnozFYmHZsmXtyydW5HVcVMUi\n6+UKIXyM14Q+wOD5sxleW8DT723CaDQxY8YMz2Buajoo1cmTuam0tpbgcrUOUIuFEKJ/eVXoh82c\ngUFzY9jxLe9tKWLu3LkcOHCAypoawmLjT7zTD0gFNGwt+QPSXiGE6G9eFfrmsWPRBQRwQUs+z365\nn0nTZgK0T9086bRN6dcXQvgIrwp9ZTRimXwumZUHabDZ+bLUSExMDMuXLycmLQNrXS1NtdXt23+3\nSLrM1RdC+AqvCn2AwGnTUBVl3J1u5O2NhWROmcHy5cuJSkkDOj6kpddb8POLkcFcIYTP8LrQD5g2\nDYAbKCXUYqI8MIOqqirKmqzo9PoTlk/0FF6TO30hhG/wutA3JSRgSk7GtWk9v7xgKGWBnjIMq1at\nJnxwUif9+mlYbXlSeE0I4RO8LvTBc7dv27SZq0ZFMWF4Gv5RSXyx9Cti0jKoyM3pEPAWSwouVzN2\ne9UAtlgIIfqH94R+Yxksuh6KNhM4fRpaayut327lN5eNwpg4hrVr1zIoIYlWazMNFeXtu8nSiUII\nX+I9oe8XBCVbYMUTWDIzUUYj1rXrGDM4lPlz5+K0t7G5wFNG+diHtL4LfauEvhDCB3hR6AfCjPsh\nfy268o1YJmZizV4HwHM/vR50el75ZA16o6lDv76/fyw6nb/M4BFC+ATvCX2ACbdBSCKs+A0BU6fS\nlnMIR1kZybERDBk9nkPb12OKSugQ+krpjtTgkWqbQgjv512hb/CDWQ9C6TYC4pwAWLOzAVh4xcXY\nK/PYVG+g4nAubrerfTeLJQWbVe70hRDez2tC3+6yszR/KaWp0yFyGH6H/o4hOormtZ4unvnz54Gm\nsa2kGmdbK7XFRe37WiyptLQW43a3DVTzhRCiX3hN6Ne21nL/6vv5OG8JzH4EVZNDwPBYrOvXozmd\nZGZmEhISgmbzTM3cvWNP+76eGjxubLaCAWq9EEL0D68J/ZiAGLJis1iSuwRt6EUQP4FAw07cjY20\n7NyFwWBg1qxZ1BXspU0ZWLZmc/u+snSiEMJXdCn0lVIzlFKLlVIlSilNKXXbKbZPPrLd8a8LeqXV\nJ3Fp2qUUNxezvXoHzHmMgKBSUArrOk8Xz9y5cykuKsRqDsFRXsiKfZ4pnO2F12QwVwjh5bp6px8I\n7AZ+DrR04/gXALHHvL7uVuu66fzE8zEbzCzOXQypM9EPm4E5wkXzmtWAJ/QBrG4XEY4anly8i1aH\nC4MhED9TtMzVF0J4vS6FvqZpn2ua9pCmae8D7m4cv0bTtPJjXvaeNbNrLEYLcxLnsDR/KW2uNpjz\nOAHRzbTu2YOzro709HSSkpLYW1CEXnNhKy/iH2s9QS9LJwohfEFf9+l/qJSqVEplK6Wu7uNzAXBJ\n6iU02ZtYXbQaEiYQOGkiaGBd+RVKKc4//3w2btuOy+1mVngrL688REl9C5YAT7VNKbwmhPBmfRX6\nzcB9wLXAAmAF8K5S6qbONlZK3aWU2qKU2lJVdXqFzybFTiLSHMmSvCUA+N/0W3QmN9aP/wV4unga\nGxupanMyKcgGwNOf7cNiScXpbMThqDmt8wshxJmsT0Jf07RqTdNe0DRtg6ZpWzRNewz4C/DASbb/\nm6ZpmZqmZUZGRp7WufU6PRelXsS64nXUttaiYkcSMDQa6658tPpi5syZg1KKohYHTcWHuWdmOp/t\nKiO/PgIAq6yiJYTwYv05ZXMTkNEfJ7ok7RKcmpMvD38JQOClN+Ns0dH27qNEREQwbtw4DpSUUVNU\nyG1ZcSSGWXhptefBLKm2KYTwZv0Z+mOBsv440ZBBQxg6aChLcj1dPAHzLgXA+vUyqD7E3Llz2ZOT\nS6vdTkNJPo9fMoJvi/1wY5TQF0J4ta7O0w9USo1VSo09sk/ikT8nHnn/GaXUimO2v1UptVApNVwp\nNVQpdR9wD/CnvriIzlySdgm7a3aT15CHMToav/RUmivMsPK3nH/++TicTnKraqjIzWHO8GhmDYuh\nvDmSusZD/dVEIYTod129088Eth15mYEnjvz+N0fejwXSjtvnEWALsBm4HrhD07Tfn26Du2pBygJ0\nSsenuZ8CEDBjJrYqE+7tHzEtLRh/f3/yG6ztFTcfu3gEZdZoymoOft9hhRDirNbVefqrNE1Tnbxu\nO/L+bZqmJR+z/euapo3QNC1A07TgI4O0b/XNJXQu0hLJ5LjJfJr3KW7NTeD0aeByY60fhH/275g+\nfTo5lTVU5HlCPzkigLiIIZh1FWw6XNGfTRVCiH7jNbV3OnNJ6iWUWcvYWrEV84QJKLMZq3sCHFrG\n3MwMiioqyc/Lo9XaDMD04ePR69y8tHQVLrfM1xdCeB+vDv3ZibOxGCwsyV2CzmQiICuL5txGCIxh\nrvFbAHIqqqnI9fTjhwZ7JhfZrHks2igVN4UQ3serQ99sMDM3aS5fFXxFi7OFgGnTcBQWYR92F+ew\nh8hBIRysqG5fMzfgSLXNSYnNPLf0ADXNUl9fCOFdvDr0wVN50+qwsqpoladfH2iuj0IXlsqcNCO5\nVbWUHfKEvsEQhMkUycy0Fmx2F89/dWAgmy6EEL3O60M/MyaTmIAYFucuxpiUhDEhAes3G2DWw8yN\na6bB1sK3WzrW1je4C7ltSjLvbC5iR1H9ALZeCCF6l9eHvk7puCjlItaXrqemtYaA6dOwbdiANuQS\n5maNBGDHgRys9XWAp9qm1XaYn5+fQXiAH48t3oNbBnWFEF7C60MfPA9quTQXXxz+gsBp03DbbNh2\n7GTw1U+RFmY40q/vmboZYEnF6azHT9fEQwuGsaOonve/LR7gKxBCiN7hE6GfFprGiPARLMldgmXS\nuWAwYF23FobMZ97oWPKqaincswM4dunEPK4YF09m0iCe/WI/DS2OgbwEIYToFT4R+uAZ0N1Xu488\nRymWceNoXpcNSjF/4d3YXS7Wfv4+0DH0lVI8cdlI6mx2fr9MntQVQpz9fCb0L0i+AL3SsyRvCQHT\np9O2bx/OqipmXvdjdErxze5DaLY6zOYElDK1L504Mi6EGycl8cb6fPaVNQ7sRQghxGnymdAPN4cz\nLX4an+V9hnnKZACas7MJCQlh9JBU9pbV0vjVCyilx2JJ6rB04i/mDSHEbOTxxXtkZS0hxFnNZ0If\n4OK0i6m0VbIztAF9RATWtesAOH/ehRTX1XNgxX+hufLIerlHSyyHWkzcP38Ymw7XsnhH6UA1Xwgh\nTptPhf7MhJkEGYP4NP9zAqdOwZqdjeZycfGVV6FpsPSgHdY8j8WSSktLIW730cHb6yYOZnR8CE9/\nvo/mNucAXoUQQvScT4W+v8GfecnzWFawDOPkLFz19bTu3cvUqVPxN5lYU6pgy78I0ELQNCctLUXt\n++p1nkHdisY2/vR1zgBehRBC9JxPhT545uy3OFvYlGgHpbCuW4fRaGTs8KFsL6hEQ4dl70rgxKUT\nxycO4qrxCfw7O5/S+paBaL4QQpwWnwv9cVHjiA+M55PqlfiPHEnzkX79mdOnU91kZdugS7HsWgp0\nvl7uvfOGgAYvLZe7fSHE2cfnQl+ndFycejEbyzfCpLG07NiBq7GRS6+4EoDFuX4YlQWj29BhBs93\n4kPN3HhuIv/dWkRuVXN/N18IIU6Lz4U+eLp43JqbrclucLmwrt9A1nnnEWIxszJ7A0z5KZamFqz1\nOzvd/55Z6fgb9bz4lTywJYQ4u/hk6CcFJ3FO5Dn8R78VXWAg1nXr0OsNjM1IY+vuvbiyfkSA3Yit\nufMunIhAP344LYXPdpWxu6Shn1svhBA955OhD56lFA825eLOHEXzunVomsa0yedibW1ly879WGJn\n4NC7cOR82un+P5yRSqjFyO+WSs19IcTZw2dD/4LkCzDoDOxM0eEsK8Oel8f8BQsAWPzhB1iGXAuA\nbf0z0MlTuMH+Ru6emcaag1VsyKvp17YLIURP+Wzoh/qHMiN+Bu+Gevrlm9euZdTEScSGBLFs2TIC\ngocBYLXmwP7O7/ZvmZxMTLA/v/tyv5RnEEKcFXw29MFTeTPHvx5nYgzWddmERscyPCGO7bt343aH\noZQBW3gkfP0UuF0n7O9v1POzORl8W1jPin2VA3AFQgjRPT4d+tMTphNsCuZAhhnb5s1obW1MzhyP\nw+li3br1mM1J2OLToWo/7Hy302Nck5lAcriF5786ICtsCSHOeD4d+ia9iQtTLuTzqDK0tjZsm7cw\nc9Ys9DodXy1d6lk6Ud8CsWNh5TPgbDvhGEa9jnvnDWV/eZMUYxNCnPF8OvQBLk69mO3xDtwmz2pa\nSSNGkRIxiC+/+IKA7wqvzX4YGgph62udH2N0LCNig3lx2UHsTnf/XoAQQnSDz4f+mMgxxIYlUZAa\nSPO6bGJSM8iIjmDfgQNYrWFomoPWuAxIng6rfwdtJz6Fq9Mp7p8/lMJaG+9uKerkLEIIcWbw+dBX\nSnFx2sWsiW/EnpuLX2sbY9I9SyZu3FgOgK0lH+Y8DrZq2PBqp8eZOTSSicmD+NOKHFrsJw76CiHE\nmcDnQx+OdPGkKgCs2dlMyMoiwN+Pdev2eb5my4XBE2HoAvjmj2CrPeEYSikeuGAYlU1tvPZNfn82\nXwghusww0A04EwwOGkz08PHUh2wjcO064mdOJi0yjK9XrOYHP4w5Wm1z9qPw6hR49yYITz/hOBOB\n1yKqqF7Vhr0uDpP+NH6mWsJh+i/AL7DnxxBCiONI6B9xSfqlbE3eQsg32UTfeiNDoiJ4f+suKitH\nERh4pNpm9AiYfA/seh9qcjs9zlS3m1rNjn3vDkx+p/HttVZCyVZY+B4Y/Xt+HCGEOIaE/hHzkufx\nQPqTzNlhI6SljYzoCAC2fesiJuaYuvrzf+t5nYQReOo/21i+t4LVP5tJVFAPA3v7f+Dj/4H/3gbX\nvQl6Y8+OI4QQx5A+/SOCTcEMmnoeLh04tm4lJSWFmPAwNm2qxG6vxuFo7PKx7p07BLvLzStfH+p5\ng8beAAueh4NfwEc/6vSJYCGE6C4J/WPMH30lOXFQ+fVSYtIyGBoTxYYNh3A6tU5X0TqZlIgArs0c\nzKJNhRTV2nreoKw74fwnYPcH8On/67TwmxBCdId07xxjavxUXsiwMHRVAVEL40kOsbDa2sK+fW2c\nMzqPkJCxVBU10WZ1nPJYNyRFsWlDCX95bw8/npnWvYZoGlS1gMsNXAlxwfDNKij5q2cGkerJ1XVG\nETQ0lODYQJTqtYOK0+BobaXs0EFAfsD7IpPZQkxaRp+eQ0L/GEadkZAZM1ErP8e/vp60qAh0Oh3f\nftvKJRd77vQ3fJRL4d4Tp2x25kpMsL2JT7Zv71Y7Rpt1pPrpj/lKhudVABQUdOtYp1L3pcZeTWGL\nDSB4yCCik4OJSg7GP0DGEAbCin/9hT2rlw90M8QAiU0fysLfvtCn55DQP86M2bfS+LvPcWzPxuJn\nYlhqCtu+rcJ6ZL3cKVelM+HCU9/pAzS1OPnpf7YxMi6Y+y8Y2qV9tJw6tDUlMCwMlRrS8c1d/4Xi\nzZ67/dSZ3biqk5zL6ca1p4b40mZ0FVaqSprY0uam3KERHGkmKjm4/YdA5OBADCb9qQ8qeqyxqpJ9\n61YyYsZsRs+aN9DNEQPAaDb3+Tkk9I8zImo0/xkSSMbWvYRNn8qIygY+WpNHZeV+AMLjuzdv/uKq\nFF5cdpCb/WB84qDv3dZe0kzlN2X4pYYQcfMIlP64LpdpP4MP74Td98CI5z19/qdrdiIuqwPblnJ0\n68uIrG/D5aenymwgJ6eOnM0VgKfURFh8QPsPgejkYAbFBqDTSbdQb9m85ENAMfW6mwmOiBzo5ggv\nJaF/HKUUAdOmEbjjS4JCgxgc4I/LpbF+/QHmzHahVPfudu+YlsLr3+Tz3JcHWHTnpJP2nbusDmre\n2os+wEDYwmEnBj6ATg9X/BUcLfD5fWAK9MzyOU36ACNB5w0mcHoCrftraV5fSkxOPTF6hWlqDNbY\nQCqa7FQUNJGzpZI9az3VRA1+eqISg9p/EEQlBxEU5i/jAz1gra9j99dfMWLGLAl80ack9DuReckP\naHzlS1pqioj2M2Cx+LF1SxOtrSWYzYndOlagn4F7ZqXzm0/3su5QNdMzTvwPrbk1at/Zj6vRTtT/\njEEfaDr5AfVGuPrfsOha+ORuMFlgxGXdvcROKZ3CPCIc84hwHFU2rOvLsG6twLinhpT4QEZPi8X8\n49E01LVRWdBERX4jlfmN7FhZhNvpGXg0Bxk7fBqQ8YGu+faLxTidDiZeetVAN0V4OXWmLfOXmZmp\nbdmyZaCbweo5E6gw6ykKiOKToiIOF+1j2/aviAif2e1jtTldzH5+NeGBJj65Z+oJd8INXx6maVUx\ng67KIGBiTNcOarfCm1dAybdww38gY26329UV7jYXtm2VNK8vxVlhQ2cxYJkYQ+CkWAxhngfPXE43\nNSXNVBz2/BCoyG+krsLWPgHFL8Agd//fQ3O30VD6Z4z+KQREXD7QzREDKCoxiEt+NrZH+yqltmqa\nlnmq7eRO/yT052Yy5OO1FJ8TwznpGaxdv5OcnC09Cn0/g56fn5/BA+/v5Mvd5Vw4Orb9PduuappW\nFROQFdP1wAcwBXhKNLx+iacW0E0fQPK0brftVHR+egLPjSVgUgxteQ1Y15fSvLaY5jXF+A8LI3By\nHH7poUQlBROVFNy+n73FSWVhExWHG2iuO3HxGXFU2cEVNJTYyZi0AEto1EA3RwygoPC+L7nSpdBX\nSs0A7gMmAHHA7ZqmvXaKfUYDLwNZQC3wV+BJ7Uz7aHESwy68gaoP1qCz6EmxeAZgVyxfxeRz7+vR\n8a4cF89fV+fy/FcHmDsiGoNeh6PCSt1/D2IaHETopd2cyw9gDoWbP4J/L4BF18EtiyFhQo/adypK\nKfzTQvFPC8VZ34Z1YxnWzeVU79uNIcJMwORYAiZEo/P3/JMymQ0kDB1EwtDvH7z2dY62Vv7+k2yS\nx07gwh/PGejmCB/Q1SdyA4HdwM+BllNtrJQKBpYBFXiKT/4cuB+4t2fN7H/hWVNw+OnBVoepqYGI\nCH/WrtvV4+MZ9DrumzeU3CorH24rwd3qpObNfSiTjrCbhqMMPXw4OiACbvnE8+tbV0L57h63sasM\noX6EzE8m9ldZhF03FJ3FQMOSPMqe3kjdx4dwVFj7vA3eYvfKZbQ0NjDpsmsGuinCR3QpaTRN+1zT\ntIc0TXsf6Mp6gDcCFuBWTdN2H9nvWeBedZZ07iqTCW38KBKqbNhbbEzKSmTjhlLc7p4vh3jBqBjO\nSQjhj8tyqH73AM7aFsIXDscQ4nd6jQ2O9dzlGy3w5uVQfRo1f7pBGXRYxkURdfdYon4yFvPoSKxb\nyqn4/bdU/W0ntl3VaK6z4oPdgHA5nWxe8iFxQ0cQP3zkQDdH+Ii+6tOfDKzVNO3YTwVLgSeBZOBw\nH523V8WffzGtzz1HQThkjk3ns88PsnXrN0yc2LO+c6U8yyou/+d27A21hFycit/xD2ABlZWV7Nu3\nj0mTJuGBr2dHAAAgAElEQVTv38U+vkFJnjv+f18Ib1wKt3/h+Vo/MSUEEXZNECELUrBtKad5fRm1\nb+9DH2LCf1gYyHz+E9SWFpPhHkNqYhb1izsv1S18i2GQP0EzEvr2HH103Big+LivVRzzXofQV0rd\nBdwFkJjYvSmRfSl4+gwCn/wtGm6GxHsGX7/44oMehz5ApktHEv6s0ru4LLPjoJ3D4WDNmjVkZ2fj\ndrvZs2cPN9xwA4MGdbFfPHII3PIxvHYRvHEZ3PElBHVjcLgXdDbnv2VXdb+24WygaaBsTpKDR2Eo\nUbSUVg10k8QZwBgfeNaGfrdomvY34G/gmbI5wM1pZ0pMRJcQi8llp6mqmeRkI8tXrOSxx3p2PGdN\nC7XvHMQV7s+TNZXUZufzszme4kqHDx9myZIl1NbWMmbMGIYMGcLixYv5xz/+wfXXX8/gwYO7dpKY\n0XDjB57Qf+MyuO1zCAjvWYNPw7Fz/sWJcjZ+w+IX/8BFP3+AlCmTB7o5wof0VWnlciD6uK9FH/Pe\nWSN0xixi6ttozGli/AQLGzfsoaXllGPZJ3DbXdS8uRcUDL5jFDNGRPP3NXmUVtfz8ccf8/rrr6Np\nGjfffDNXXHEFI0eO5Ic//CEmk4nXXnuNnTt3dv1kgyfCwnegLh/eugJaG7rdXtF3NE1j48fvERoT\ny5Bzpw50c4SP6avQXw9MV0od2yE9FygF8vvonH0icPo0wppb0Tl0ZE6MwW53kp2d3a1jaJpG3Qc5\nOCpshF8/FEO4mV/MHUKUs5y//eVVdu7cybRp07j77rtJSzs6dTMyMpI777yThIQEPvzwQ77++uuu\nDySnzIBr34CKPfD2tZ6HucQZoWDXdiryDjHx0qvR6aSInehfXZ2nHwh8txK4DkhUSo0FajVNK1RK\nPQNkaZr23UTjRcDjwGtKqaeAIcCvgCfOlnn63wnIyiLE7gQgOS0Ug0Hx2WefMWfOnC4/Zdq8rpSW\nHVUEz0/Cf2gYtbW1bFr2KdONh6l2BPDjm29kZPrRsQzNbsdRVoYpKQmLxcLNN9/Mp59+ypo1a6ip\nqeHyyy/HaOxCaYMh8+Gqf8D7d8A7N8IN73jlersut8ae0gbszp7PrOqqjOggQsynV1Zi00fvETgo\njBEzZvdSq4Touq726WcCK4/58xNHXq8DtwGxQPstqqZpDUqpucArwBagDngBePH0m9y/dAEBRI4e\ng95WSVOTk7FjLfzhD39g0aJFTJ06tf01fvx4TKYTa+a05tbT8EUe/iPDsUyPY926daxatQqdTsfk\n887np8sbCNrZwDPp4KiopP6996h7711cVdXEv/gCwQsWYDAYuOyyy4iIiGD58uXU19dz/fXXExQU\ndOoLGHkF2G2eOj3v3wHXvu416+3WWe28u6WIN9cXUFLf/S63nvA36rhiXDw3n5vMiLjgU+9wnNKD\n+yjau4uZt/wQQ1d+cAvRy6T2ThfU/OMfLPnwP1inNxM3vIKS4h+zefNesrOzyc31TLXz9/cnKyur\n/YfAlClTCFIWKv+0DZ3FgOPKKD798jMqKioYNmwYF154ISEhITz28S62fb6a540Hca9eCS4XATOm\n46qto+3QIZLfeQf/oUPa27Jv3z4+/PBDzGYzCxcuJCami7NzNv4NvrgfRl/jqdR5Fncr7C5p4PVv\n8lm8o5Q2p5tzU8O4fmIi4d9XqK4XOF0aS/eU8/H2ElodbrKSw7hlShLzR8Zg1Hetp/Sj3/2G0gP7\nuPOVf2Hy7/va6cJ3dLX2joR+F7QeOMAX/3MHFWNMZFxayNgx/yY8fAYA5eXlZGdnk52dzbp169i2\nbRtOp6c7aGhsGuNjRxA7NR2ncjF48GAuuugihg8fjrulhYZPP6Xqjbdw5Ryk1d9C3A3XMeiG6zEl\nJuKorCT/qqtRZjMp7/8XffDRu8qysjIWLVpEa2srV199NUOHdm2BFta+ACt+A+NvgUv+CGfHc3KA\np2jdF7vKeWN9Pt8W1mMx6bliXDy3TE5maEwXPvH0onqbnf9uKebNDQUU1tqICvLjxklJ3JA1mKjg\nk3efVRXm88b9P2HKNTcy+erTL4ktxLEk9HuRpmmsmTeH7fEmRt2SQ2rag6Qk/bDTbW02G5s2bWLZ\nXz9hxabV7CjdR2trKwAxMTFMGT+esUrH8Lw8hrhcBA4fzqYxs3ncmsCH985mZNzRh7Vs326j4NZb\nCZgymcGvvorSHb2bbGxs5J133qG0tJR58+YxefLkro0xLH8C1r0I594D8397xgd/WUMLizYW8p9N\nhVQ320mJCOCWyUlcNSGBYP+B7R5xuTVWH6zkjfUFrDpQhUGnuHB0LLdOTmJC0qAT/j4+++Nz5G7d\nxJ2v/AtzYP/+oBLeT6ps9iKlFHHnjGNL8X7anIpDVdknDX2LxcIwlUB+ejrGoSHcFHEHGenp7Pvq\nK1YvWcKGr5bxodOz3KLF359J8XFMaCvDXt7I0x+F8PY9Rwf3LOPHEf3gr6j4zZNUv/JnIn/6k/b3\ngoODue222/j444/56quvqK6uZsGR/v/vNecxz0yeDa+AXyDMeuj0v0G9TNM0NuTV8sb6fL7aW4Fb\n05gzLIpbJiczLT3ijFmtS69TzB4Wzexh0RyutvLWhgLe21LEkh2ljIgN5pbJSVw2Nh6zSU99eRkH\nvlnLhIsvl8AXA0ru9Luo/tNPefNfr5CwsAAtVDFj4vtEhAzvsI3b7Wbj8my+zl6FW2nMmHIuw0tK\naPzPOzgKC9FHRjDouuuxTp/GpgMHWLduHdnZ2Wzfvv3IVExF+rARzJ01g6lTpzJp0iRSU1Mpf/gR\nGj76iIQ//5mg2bNOOOfKlStZu3YtycnJXHvttVgslu+/GLebus9u5JArm5BWP1LL9BjcAx+kbjRa\n7C5sdhdOt4ZOgdmox2IyYDhDgv5U3Gi02l1Yj7uG9WWx7KsO5odjCgg0uQa6meJMFXsOLHy3R7tK\n904vc9bVsWjhVTBeETYrH6NSxAy+k9Hp96LTGamsrGTxx4spLi0mToUx3VGH+vRjtNZWzBMmEHbj\nQoLOPx/VyQyf5uZm1qz7hjufextn2T5sRftobm4GICwsjMwJExhaWMQIp5OL/rOIwRMnnnCMHTt2\nsHjxYkJCQli4cCERERGdXofD0cCh3GcpLX0XI2YctODn9mdY60giXANTy72x1cmhymYOV1txuNwM\nCjCRERVIYpjlrAn742lAVVMbOZXNFFTZKDvsIjLCwNysCGJC/Dk7r0r0uUHJMKNn5dsl9PvAZ9de\nwX7l4Nzf3sXWg79ipH8bOr9E3G03kr2uFJNbR1ZbGnFf/wvaqgm55GIGLVyI//Dhpz448OaGAh79\neDf/uGkcEc5KNm/ezKZNm9i0aRO7d+9ufzArKTGRrEmTyMrKIisri/HjxxMYGEhhYSHvvPMObreb\na6+9ltTU1PZja5pGZeVnHMx5EoejjsGDbyc15ec0Ne1l/4FHsFpziIpawJCMR/Hz6/vwd7k1Vu6v\n5PX1+azNqcaoVywYHcstk5MZnxjqVSttff7Pv7Fv2RKWZNxKvsNMcriFm85N4prMwac951+I70jo\n94Ftv36Ur/dt45r7H8WVEcVflv4PM4KK8TO1Yi0YxrDcH2M8tJKQ+aMIvfIK9KGh3Tq+3enm/BdX\nE+Bn4LOfTuvQd221WvnmjTdY/usn2Bcawm6Hg8OHPXXrdDodI0eOJCsri5EjR1JRUYGfnx+XXnop\nEyZMoKWlhAMHH6OmZhVBQaMYPuxpgoKOlvJ1u+0UFP6d/PyX0en8SE/7JXFx16FU7z+wXWe1896W\nIt7cUEBxXQvRwX7cNCmJ67MSiQw6zRLTZ6CW5ib+fvftpGVOYu7dv+CL3WW8ub6ALQV1mI16Lh8X\nzy2Tkxge2/05/0IcS0K/D1SvXcvrLz/LuMwp1IVFs6uoiKDWOsbH7MA9uhiDM5Th454mKmpej8/x\n8bYS/t+72/njDeO4dEzcCe/X/POfVD73PFH334f70ks7fBrYtGkTNTU1ABiNRmJiosnMjGbEyAqG\nDzczbdqvGJxwCzpd54O9Ntth9u1/mPr6jYSETGDYsN8SGJDR42s51u6SBt5Yn88n2z1z6yelhHHr\nlGTmjoju8hz3s9H69//DN/99m1uee5nIxOT2r+8uaeDN9QV8vL2ENqebrJQwbp2czLyR3v39EH1H\nQr8PuB0Ofv+j27HFJuLWGxiWd5hzh0xAax3D/oh1tIz9kGAaiYycz5Ahj+Hv1/2yxm63xoI/rqWp\n1cmC0Z3sr2lkvfkC8Ts3su6uR6gaMuaYtzTqKoopPrCLipy1VOasIu9QE21tnr9jc1AICUNGkzBk\nNOFDRtE6fATJwRHEuI8NGY1I/QqSjP9ERyulzqspcV6DRs8efNI02FZUz9Yjd7ZXjPfc2Q6L8f47\nW3trC3+/5w7ihg7nigc6L81abzv6yaeo1vPJ5/yh4Rhw4XI6cTkduJ1OXC7P749+zdHJ17q3XX9Q\nSqE3GtHrjegMBgwGIzq94cjXDOgMBvQGz++P3a7j175/O51ej/KSUZK4UDM/mJF+6g07IVM2+4DO\naEQfHY/mtDM9OJAZL71C1T8PoBnc1M1I4dk9Tq6LTmBS9Spqa7NJT7uf+PiF3eom0ekUD180nHve\n/pa3NxZ2us0HqZfxzOHDjPn3Czww916qAsLa3zPp2lgw8iA/nL+HZkcKq/fPwbavmbzSaraXNFFQ\nmkvOt9+A5hkf0EVG45eQjiUoCf/oVPyj0zCGZhBkeoQr0z9gYvQ7GB0reefADRxq6Nldf2yIP49d\nPIKrJiT4VB/2rhVLaW1uYtLl13b6fn19PXv27IH9exhXvBvb5u3s3LuHTY21fdswnQGl10N/BKXm\nRnM52/+9ie8XljKSH+T17ZKncqffTc1NjXz24v9Run8PV068D32NIvJH5+CXGMzKwpX8cu0vSfQ3\n8/8GR9DWvJ2Q4HGebpLALj4120X2/HwOX30NpsREkha9jc7fn+qaVRw48BitrSXExV1PetoDGI0h\n7DqYwzNrN7IzJolqSxDBjjam1pQQefggX2zcxP4dO3AW5cORgeKQkBDGjh3LuHHjSE83Exj0FTEx\ntSQOvo709F9hNJ642pfoyOlw8M+f/oBBsfFc8L8PsnfvXvbs2cPu3bvZs2cPe/bsobS0tH37gIAA\nRowYwciRI0lJScHf3x+j0YjJZMJoNHb4/fG/dvVrJpMJvV4/IIPkbrcbh8OBw+HAbrd3+PV0v+Zw\nOPr9evpKfHw8d9xxR4/2le6dPmRvbWHLE2+TqA3FNdFE0lWT2t87UHuAn3z9Exra6nlmzOUY6z7C\n6WwiKfFOkpN/gl7fe1Uum1aupPjHdxNw7QU0XOumsvJTLJZ0hg17ikGhEzlsa+O1kmr+U15Do9NN\nVEszI4sPce+545l4zjntx9nWaON/dxxk167dDK0oIL2sgJxdu9ixY0f72gFGo57kZAMZGUFMnXol\n06ffxNixY7tW9M1HNDc3t4f7qi8+Y+PaNTShp7T86BISZrO5PdyPfSUmJqLTSV++6DkJ/T7Usrua\nmrf2Uarlsb50MVc99AQJw0e1v1/dUs3Pvv4Zu6t384txPyLTcJjy8o8wm5MYNvQpwsKm9Eo7NE3j\n4Fs/pmTQMjDrSU79KYmJd7Kyro1/l1TzdW0TBgUXR4ZyR3wEIwzw3nvvUVhYyMyZMznvvPPa7/oc\nbo2/FVfx/OEydErxYGost8QMIu/QIbZt28a2bdvYsiWbbdu2UF9vb29Deno648aNa/9kMHbsWGJj\nY3vl+s5UNpuNffv2td+xf/fKz89v38ag1xMfHsa0ufM6hHtKSoqEu+gTEvp9ZFdhHa1v7WdwsD9B\nNyTx3lMP0VxXwzWPPk1M2tE+71ZnK49kP8LS/KVckX4FPxl6PodyHqelpZDYmKvIyHgQo7GLa992\nwmrNZf+BR6iv34S5MhT3G3q+ffSvvI0fBa12ok0GbomL4Ka4cKL9jvajO51OlixZwo4dOxg1ahST\nJ3dcqq/E4eKZiibW2xyM9DfwaHQQGX5Hh37cbicHDv6bjRv/Te6hFgoLY8jJaaCw8Oj4Q2RkJCNG\njGDUqFGMHDmS1NRUzGYzTqezyx/fu/v+d0Xu+pLb7aawsJDDhw/z3f8bk8nE0KFD20N91KhR+LfZ\n2PX+21x+38NkTOqdH/C9yel0Ul1djcvV908GBwUFERzs/YP2ZwIJ/T6gaRpXfrqD9YEQbtAzLiSA\nEQao/+BNIkvzuf3Bx4k4ZlqeW3Pz6o5X+cuOv5AZnckL05+htvwtCgv/jsEQTEbGw8REX9atPla3\nu438gr+Rn/9n9Hp/3Am/5pPmkXxUXkub0USWxcQPUmJZEBGK8SRPs2qaRnZ2NsuXL+/8feBQVALZ\naaOxG4yMKT7EhIL9GI5ZtcvPz0pa+kbCw0toagpj185x5ObaKS8vb39VVVV1faWvkzCZTF3quzYY\nDP3SVx0XF9fhzj09Pb1DvSNN03jzgZ/icjq57YU/dyiSNxDcbje1tbWUlJS0v8rLy/sl8L8TFBRE\nfHx8+ysuLg5/f+9bzGegSej3kR1FdWyut7LL4GZbo40cWyvffQcHNdUxJT6GrKhwxgVZGBVkwaLX\n8Wnepzye/TjRAdG8POdlovQO9u1/iMbG7YQNmsawYU9iNid+73kB6uo3s3//wzTaCjgY/GOWMo8t\nTXbMOsXl/nrOf+IhRoYGkfTavzst93C88vJyGhpOvn5ug1vj1QYHX7S4iNMr7g0xMtH/aB1+TdNo\nac2mvv5V3O4GAgMvIzjoJnQ6T514u91OTk4ORUVFNDQ0UFdXR2NjI3q9Hp1OR2hoKHFxccTHxzN4\n8GDi4+MJCgpqD/OBGnQ8HXnfbuajZ5/ggrv/l5HnzTn1Dr2sqampQ8CXlJTQ1tYGeJ7d+O77HRsb\n2+miP72trq6uvR21tUdnJUVERHT4QRAdHX3qYoHie0no95Mmp4udTTayi8r4Yts2SiPiaLB4Bjf1\nCoYHmBkXbCGcGj7e9X8oexEvznyec2OzKC5ZRG7u82iak9SUnzF48B3odCdOaXQ4GjmU+yx7Spey\nxnAVX6v5VDt1JJtN3B4fwXUxYYQaDTR+8QUl/3svgxYuJOaxR3vtGtfVNfHAgWLyWtq4OnoQv06P\nJ8J09D+ow9FIbt5zlJQswt8/nqFDniAiYlanx7Lb7ZSVlXUIpfr6esAzpzsyMrJDGERFRaHXnx0L\nvmiaxjuPPUBTbTU/eOnv6Ps4xFpbWyktLW3/PpaWltLY2Ah4ntKOjo7ucHcdGRk5oOMJNputvb2l\npaUUFxdjtXrWbtbr9cTExHT4uw8LC5Pxj26Q0B8AFYdz+e9vHsIZFUvK3fezz6VjW6ON7U02Gpye\nj9M6zY6+LY/p4VFcnzyeEX7NWPOforpmGYGBwxk+7GmCgz0zazRNo6LyCxYfWMRnzilsUefiRsfs\nsGDuSIhgVlgQuuPuhCt+9xy1//oXsc88Q+gVl/fatbW63LxUUMGfCisINuh5PC2ea2M61oyvr9/C\nvv0PY7MdIjrqYjKGPIqfqfPCb8eyWq0dwqukpASbzQaAwWDoNAzOxE8AxXt38+4Tv2L27T9i3AWX\n9OqxnU4nFRUVHb5H1dXV7e+HhYV1+B7FxMR0bR3lAaRpGo2NjR2uqbS0FLvdM1HAz8+v/ZPJdy8Z\nHzg5Cf0BUnJgHx/89lFComO49vFnMAcG4dY0Dre0sa3Rxub6BpaUHqSWQaA8H68jjAZG+FuJtX5F\nkmsH02InkBx3Jf/c/zkfWVMoVMkE62FhXCS3xUeQbD55jRrN6aTwh3fSsm0bSYvexjxy5Em37Yn9\n1hbu31/M5kYr00IDeW7oYFIsR9vjdrdRUPA3Dh8Zc0hP/xVxsdd06wE1TdOor68/IQy+G6w1m80n\nhEFgYGCvXmdPfPDM41TkHeLOl/+J0a/nfdan6ocPCAg4oY/8lOW0zxJut5vq6uoO115RUdE+NiTj\nAycnoT+ACnZt56NnnyAyMZmrH/ktfsf9h3S5XTy7+QXeyF1LcvR80mIuZFezo8P4gFFrw6H8yDDZ\nuCs5natiIrB0sSaLs7aWw1ddDQpSPvgAw6CezxLqjFvTeLO0hqdyS3FoGvcmx/DjwVEdBo6t1rwj\ns4s24meKRqc/vWJqmgZulwuny4nT6cLpdHYYjPQUpxvIu38Nt8uF0ulOu1Cdpmnts4OUAr3egMFg\nwGDQYzAYfK7LQ9PAdczfu9Pp7DBBwLu+HwksuHBxj/aU0B9guVs3sviFp4kbMpwrH/x1p3d+7x14\nj6c3Pk1KSAovz3mZYP8YdjTZWF+Zw+GGAq5PGsv0qOQedWW07NpNwY03Yp4wnsS//x3VB/3L5W0O\nHs4p5rOqBoYF+PPC0MFMCAlof1/TNMrLP6S2NrvXzw3gcrtpaWmhxWajtbWVgfy3bGtswGlvIyg8\n8rS7nnR6HRaLBbPZjL+f/xnZlTXQnC4nLbYWbC02z0D1mRVjPWbyS2DO7D/0aF8J/TPA/uzVfPan\n50keM57L7nsEQyd9rOtL1/OLVb/AqDfy0qyXGBs1ttfOX//Bh5Q9/DDhP/wBUff1bGGGrlha3cCD\nB4spa3NwW3wED6XGEmQ4OwZfe0NtaTH/vvfHZF12NdNvuHWgmyN8VFdD35s+F51xhk09j3l3/ZT8\n7Vv57KXf4e5kbvTkuMm8ddFbBBgD+MHSH/BZ3me9dv7Qq64k9PrrqPnHP2n88steO+7x5keEsCZr\nGD9IiOC1kmqmb9zP51X1fXa+M83mxR9gMBiZsOCygW6KEKckod/HRs+ex6xb7+TQ5vUsffUPaJ08\nrJQaksqiBYsYHTmaX639FS9vexl3L1UljHnoIcxjx1L60MO05eT0yjE7E2jQ81RGAp9NyCDMqOeO\n3fncvuswpa32U+98FmusrmLvmq8ZNXselpDuLZojxECQ7p1+suHDd8l+903GzL2QOT+4u9N+WofL\nwZMbnuSjQx8xPX46w8KG9cq5/eqsTHrovzjNJjY9dRVOS9+uUOXSFJvs8axtTUKHxhhTOUblnaV1\ntcM1aBWN6MYlgN+ZPUVSnPkS/P344/j5PdpX6umfYSZdcS321hY2f/I+Rn8zM268/YTgN+qNPDHl\nCVJCUnh1x6usL13fa+dfeambh99uIPjZ13jxaiNaPwwODtJH0jjoJjZrI/r8XANFFxOPFuMZtKZ1\noFsjznYhtoo+P4eEfj9RSjH9hltxtLawZcmHmMxmJl91Q6fb3T7qdm4fdXuvt6E26W0MTz3FUutd\nRN59d68f39dkv/smGz56j9ue/zPhCYMHujlCdImEfj9SSjH7th/haG3lm/fexuRvYcJF/Tf4N+jG\nhbTu2kn1n17GPHIkgeed12/n9jZtNhvbvvyUjImTJfDFWUUGcvuZ0umY96OfkTFpCqve+Ds7Vyzt\nv3MrRcwTT+A3bBgl992PvaCg387tbXYs+5w2m5Wsy68Z6KYI0S1ypz8AdHo9F/3sfj557imW/f1l\njP7+DJ/aP3fdOn9/Ev70J/Kvuorin/yUuN89CzrfmVPfG5wOO1sWf8DgtCGEOjVaDxwc6CYJL6Hz\n98OUlNSn55DZOwPIYW/jw2cep2T/Xi79xcOkZ0469U69pDk7m6I772pfF1d0XUF4MHsSIpl0qIRw\nq4zeit7jP+YcUt59t0f7yhO5Zwl7i43/PvUIVfl5XPHLX5N0Tu89kXsqrfv2YS8s6rfzeQO328W7\n77+JxWzh0ouvkRIJolfpQ0IIOLdnN38S+meRluYm/vvEg9RVlHH1Q08SP8x7pzie7fau+ZovXnmR\nyx94lLQJ/ffJTIhTkTIMZxFzYBBXPfwkQWERfPh/v6Yi79BAN0l0QnO72fTJ+0QMTiJ13MSBbo4Q\nPSKhf4YICB3E1Y88hX9gIO8//RjVRTKz5kxzaOtGaooLybr8mgFf+1aInpLunTNMXXkp7z7+Sxxt\nbQSFn3rVKdF/mutq8A8M4o7f/xXdWbKEo/AdUobhLDUoJo5rHn2ajR+/h8vu3cXKzjbh8YMZff4F\nEvjirCahfwYKTxjMgp/8YqCbIYTwQtIxKYQQPkRCXwghfIiEvhBC+BAJfSGE8CES+kII4UMk9IUQ\nwodI6AshhA+R0BdCCB9yxpVhUEpVAadTeCYCqO6l5gwkb7kOkGs5U3nLtXjLdcDpXUuSpmmRp9ro\njAv906WU2tKV+hNnOm+5DpBrOVN5y7V4y3VA/1yLdO8IIYQPkdAXQggf4o2h/7eBbkAv8ZbrALmW\nM5W3XIu3XAf0w7V4XZ++EEKIk/PGO30hhBAnIaEvhBA+xCtCXykVq5R6XSlVpZRqVUrtVUqdN9Dt\n6i6llF4p9aRS6vCR6zislHpKKXXGL3ajlJqhlFqslCpRSmlKqduOe18ppX6tlCpVSrUopVYppUYO\nUHO/1/ddi1LKqJR6Vim1UyllVUqVKaUWKaUSB7DJnTrV38lx2/71yDb39WMTu6wr16KUGqKU+lAp\nVa+UsimlvlVKDR+A5n6vLvxfCVRK/UkpVXzk/8oBpdT/9tb5z/rQV0qFAtmAAi4ChgM/BSoHsl09\n9EvgHuBnwDDg58DdwIMD2aguCgR242lzSyfvPwD8As/fzUQ8fz/LlFJB/dbCrvu+a7EA44H/3875\nhFhVhmH89wwYGhWt0hZWRv8QixGihVDNJNJCxloEVmC4a2MuQizGFglpWuYfGGwVZaZprWKmGFoE\nUyqEQWal5qIZpBwNU6KBkRp5W7xn6HJj5t575jTfPfe+Pzice99zufd5+e55znfe7+VsyfZPAAuB\nwSa8ONcaEwAkPQU8BJyfJV15mDYXSYtwHxgGHgOWAK8AY7OosV5qjctO3MvW4H62BdgmaU0hv25m\npd6ArcDR1DoKymUA2FcV2wcMpNbWYB5jwNqK9wJGgU0VsXnAn8DzqfU2kssUn1kMGHB/ar2N5gHc\nDpSJCh0AAANPSURBVPyamcsIsCG11jy5AAeBA6m1FZTLD8DmqtgQ0FfEb5Z+pg88CXwt6bCk3ySd\nkLROklILy8ERoFvSfQCSFuOzls+Sqpo5i4AFwOeTATMbB74ElqUSVSA3ZfsrSVU0SHZn8iHwmpmd\nTq0nL5I6gB7glKTBrMx7XNLq1NpycgTokbQQQNIyoBMYLOLLW8H078RLID8DjwN7gG14maRsbAf2\n43/ev4Ef8Zn/3rSyZsyCbH+xKn6x4lgpkXQd8BbQb2a/pNbTIJuBS2b2dmohM+QWvGTSi08sVuAX\nswOSVqYUlpP1wHfAucwHhoCXzGygiC9vthpkHjqAb8xssu79raS7cdPvSycrF6uB54BnccPvBPZI\nGjazd5IqC/5DNlP+ALgZWJVYTkNI6gLW4v+xsjM5ef3EzHZmr09IehBYB3yaRlZuXsDvgFfhD598\nBNghacTMZjzbb4WZ/ihwqip2Gmi6boo6eBPYYWaHzOx7M9uPL+qUYSF3Oi5k+/lV8fkVx0pFRWnk\nAWC5mf2eWFKjdAG3AqOSJiRN4PX97ZLKdsdyCZigBXxA0jzgdWCjmfWb2Ukz6wMOAYV0VrWC6R8F\n7q2K3cPMHs+ciuuBa1Wxa5R/nIZxc18xGZA0F3gYOJZKVF4kzQEO44bfbWZlvHDtxfV3VmzngV3A\n8oS6GsbM/gKO0xo+MCfb/jcfaIXyzi7gmKRN+Im4FK+J9SZVlY9+4GVJw3h5ZynwIvB+UlV1IOkG\n4K7sbQdwm6RO4LKZnZO0G+iVdAY4y7/tdAeTCJ6G6XLBjfFjvO20BzBJk+sSf2QL1E1BrTGhqq05\nqx9fMLOfZldpberI5Q3gI0lfAV8A3cDTeKNHU1HHuTKEt2iO4RetR/Gy78ZCBKRuWSqo7WklvvBx\nFTeU9WTPFSrTBtwI7M4GehxfnN4KzE2trQ7tXXjbYvX2XnZcwKt4Oe4qvji1JLXuRnMB7pjimFGj\ntbOZ8pji8yM0actmPbngaxRns3PnJPBMat15csGbG97FW2nHgTN4aacQT4sHrgVBELQRZa8VB0EQ\nBA0Qph8EQdBGhOkHQRC0EWH6QRAEbUSYfhAEQRsRph8EQdBGhOkHQRC0EWH6QRAEbUSYfhAEQRvx\nDxJW2fwHfldZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f929f3a5fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(lorenz_data[0], lorenz_data[1])\n",
    "plt.plot(lorenz_data[0], np.nanmean(lorenz_data[1], axis=1), 'k')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Show at what sampling rates/durations the system is and is not correctly identified"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/kpchamp/anaconda/envs/py3/lib/python3.6/site-packages/ipykernel_launcher.py:5: RuntimeWarning: Mean of empty slice\n",
      "  \"\"\"\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f929f3f7278>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/pdf": "JVBERi0xLjQKJazcIKu6CjEgMCBvYmoKPDwgL1R5cGUgL0NhdGFsb2cgL1BhZ2VzIDIgMCBSID4+\nCmVuZG9iago4IDAgb2JqCjw8IC9Gb250IDMgMCBSIC9YT2JqZWN0IDcgMCBSIC9FeHRHU3RhdGUg\nNCAwIFIgL1BhdHRlcm4gNSAwIFIKL1NoYWRpbmcgNiAwIFIgL1Byb2NTZXQgWyAvUERGIC9UZXh0\nIC9JbWFnZUIgL0ltYWdlQyAvSW1hZ2VJIF0gPj4KZW5kb2JqCjEwIDAgb2JqCjw8IC9UeXBlIC9Q\nYWdlIC9QYXJlbnQgMiAwIFIgL1Jlc291cmNlcyA4IDAgUgovTWVkaWFCb3ggWyAwIDAgMjI5LjEw\nNjI1IDE3NC4zNDY4NzUgXSAvQ29udGVudHMgOSAwIFIKL0dyb3VwIDw8IC9UeXBlIC9Hcm91cCAv\nUyAvVHJhbnNwYXJlbmN5IC9DUyAvRGV2aWNlUkdCID4+IC9Bbm5vdHMgWyBdID4+CmVuZG9iago5\nIDAgb2JqCjw8IC9MZW5ndGggMTEgMCBSIC9GaWx0ZXIgL0ZsYXRlRGVjb2RlID4+CnN0cmVhbQp4\nnJVUTW/bMAy961fwuF4YkZRE6digXbDdsgXYYdgpTbsFTYeswPr3R8WOISdelhkwbD2J7/FLJNi6\n2S3B0yt42Nr7Bl/hm30fgGABs7vN7x/rzafFHNavzhu+c8wFySeOtnpuVqQBJaSs0WA/Xn537sWZ\nipksjPjJOZbejBW1O2bUlDGcoM8NSkkwDfCRYYSa0qPbwwQ9lYgCJBEL/NrAF3iB2S3XyMkipyZy\nc9KNI9+bdYIaP0maIl/vYPaB4O4nLN0S9kdmbyFXdo95zF93nHgUKTHLKAkNGpCPcbm5G7x9c/MV\nzN4TUIDVo+OIOadgFvYA+d651YN7F29gtYX71dH24Icjz5iUC+lIuIWvUy6CmvpHx8rkp6U1oj+r\ne4NeJ0wpIZ0ITsc61EoLapGUQ9UrmE7Ai3KKDNbOQUWUvPF1ipcFSRQTS1BqFRv0n5IkjOKFYuYQ\n9KDJR83aZP/V5AwfD63IFxvdhYC5c9RIS46kYu7Hgtx1hiYsnqnUjKmVv+vU+scUYzI0Z+QuuZYQ\nsbJWsOmtZPusygeYFKmjMDhSX3kS6tM1QkNC33vRUiePsXeDkKiYIxUeemqE5mJlPONgL1h6jhYe\nJk+Lus/tFa957a63PxuY00Nucm4Z6dT02/1t+tXz14/Q9nRDc4l96f4AvSJCuQplbmRzdHJlYW0K\nZW5kb2JqCjExIDAgb2JqCjUwMwplbmRvYmoKMTcgMCBvYmoKPDwgL0xlbmd0aCAyMTAgL0ZpbHRl\nciAvRmxhdGVEZWNvZGUgPj4Kc3RyZWFtCnicNVDLDUMxCLtnChaoFAKBZJ5WvXX/a23QO2ER/0JY\nyJQIeanJzinpSz46TA+2Lr+xIgutdSXsypognivvoZmysdHY4mBwGiZegBY3YOhpjRo1dOGCpi6V\nQoHFJfCZfHV76L5PGXhqGXJ2BBFDyWAJaroWTVi0PJ+QTgHi/37D7i3koZLzyp4b+Ruc7fA7s27h\nJ2p2ItFyFTLUszTHGAgTRR48eUWmcOKz1nfVNBLUZgtOlgGuTj+MDgBgIl5ZgOyuRDlL0o6ln2+8\nx/cPQABTtAplbmRzdHJlYW0KZW5kb2JqCjE4IDAgb2JqCjw8IC9MZW5ndGggODAgL0ZpbHRlciAv\nRmxhdGVEZWNvZGUgPj4Kc3RyZWFtCnicRYy7DcAwCER7pmAEfiZmnyiVs38bIErccE+6e7g6EjJT\n3mGGhwSeDCyGU/EGmaNgNbhGUo2d7KOwbl91geZ6U6v19wcqT3Z2cT3Nyxn0CmVuZHN0cmVhbQpl\nbmRvYmoKMTkgMCBvYmoKPDwgL0xlbmd0aCAyNDggL0ZpbHRlciAvRmxhdGVEZWNvZGUgPj4Kc3Ry\nZWFtCnicLVE5kgNBCMvnFXpCc9PvscuR9//pCsoBg4ZDIDotcVDGTxCWK97yyFW04e+ZGMF3waHf\nynUbFjkQFUjSGFRNqF28Hr0HdhxmAvOkNSyDGesDP2MKN3pxeEzG2e11GTUEe9drT2ZQMisXccnE\nBVN12MiZw0+mjAvtXM8NyLkR1mUYpJuVxoyEI00hUkih6iapM0GQBKOrUaONHMV+6csjnWFVI2oM\n+1xL29dzE84aNDsWqzw5pUdXnMvJxQsrB/28zcBFVBqrPBAScL/bQ/2c7OQ33tK5s8X0+F5zsrww\nFVjx5rUbkE21+Dcv4vg94+v5/AOopVsWCmVuZHN0cmVhbQplbmRvYmoKMjAgMCBvYmoKPDwgL0xl\nbmd0aCAyNDcgL0ZpbHRlciAvRmxhdGVEZWNvZGUgPj4Kc3RyZWFtCnicTVG7bUQxDOvfFFzgAOtr\neZ4LUl32b0PJCJDCIKEvKaclFvbGSwzhB1sPvuSRVUN/Hj8x7DMsPcnk1D/muclUFL4VqpuYUBdi\n4f1oBLwWdC8iK8oH349lDHPO9+CjEJdgJjRgrG9JJhfVvDNkwomhjsNBm1QYd00ULK4VzTPI7VY3\nsjqzIGx4JRPixgBEBNkXkM1go4yxlZDFch6oCpIFWmDX6RtRi4IrlNYJdKLWxLrM4Kvn9nY3Qy/y\n4Ki6eH0M60uwwuileyx8rkIfzPRMO3dJI73wphMRZg8FUpmdkZU6PWJ9t0D/n2Ur+PvJz/P9CxUo\nXCoKZW5kc3RyZWFtCmVuZG9iagoxNSAwIG9iago8PCAvVHlwZSAvRm9udCAvQmFzZUZvbnQgL0Rl\namFWdVNhbnMgL0ZpcnN0Q2hhciAwIC9MYXN0Q2hhciAyNTUKL0ZvbnREZXNjcmlwdG9yIDE0IDAg\nUiAvU3VidHlwZSAvVHlwZTMgL05hbWUgL0RlamFWdVNhbnMKL0ZvbnRCQm94IFsgLTEwMjEgLTQ2\nMyAxNzk0IDEyMzMgXSAvRm9udE1hdHJpeCBbIDAuMDAxIDAgMCAwLjAwMSAwIDAgXQovQ2hhclBy\nb2NzIDE2IDAgUgovRW5jb2RpbmcgPDwgL1R5cGUgL0VuY29kaW5nIC9EaWZmZXJlbmNlcyBbIDQ4\nIC96ZXJvIC9vbmUgL3R3byA1MyAvZml2ZSBdID4+Ci9XaWR0aHMgMTMgMCBSID4+CmVuZG9iagox\nNCAwIG9iago8PCAvVHlwZSAvRm9udERlc2NyaXB0b3IgL0ZvbnROYW1lIC9EZWphVnVTYW5zIC9G\nbGFncyAzMgovRm9udEJCb3ggWyAtMTAyMSAtNDYzIDE3OTQgMTIzMyBdIC9Bc2NlbnQgOTI5IC9E\nZXNjZW50IC0yMzYgL0NhcEhlaWdodCAwCi9YSGVpZ2h0IDAgL0l0YWxpY0FuZ2xlIDAgL1N0ZW1W\nIDAgL01heFdpZHRoIDEzNDIgPj4KZW5kb2JqCjEzIDAgb2JqClsgNjAwIDYwMCA2MDAgNjAwIDYw\nMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAKNjAw\nIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCAzMTgg\nNDAxIDQ2MCA4MzggNjM2Cjk1MCA3ODAgMjc1IDM5MCAzOTAgNTAwIDgzOCAzMTggMzYxIDMxOCAz\nMzcgNjM2IDYzNiA2MzYgNjM2IDYzNiA2MzYgNjM2IDYzNgo2MzYgNjM2IDMzNyAzMzcgODM4IDgz\nOCA4MzggNTMxIDEwMDAgNjg0IDY4NiA2OTggNzcwIDYzMiA1NzUgNzc1IDc1MiAyOTUKMjk1IDY1\nNiA1NTcgODYzIDc0OCA3ODcgNjAzIDc4NyA2OTUgNjM1IDYxMSA3MzIgNjg0IDk4OSA2ODUgNjEx\nIDY4NSAzOTAgMzM3CjM5MCA4MzggNTAwIDUwMCA2MTMgNjM1IDU1MCA2MzUgNjE1IDM1MiA2MzUg\nNjM0IDI3OCAyNzggNTc5IDI3OCA5NzQgNjM0IDYxMgo2MzUgNjM1IDQxMSA1MjEgMzkyIDYzNCA1\nOTIgODE4IDU5MiA1OTIgNTI1IDYzNiAzMzcgNjM2IDgzOCA2MDAgNjM2IDYwMCAzMTgKMzUyIDUx\nOCAxMDAwIDUwMCA1MDAgNTAwIDEzNDIgNjM1IDQwMCAxMDcwIDYwMCA2ODUgNjAwIDYwMCAzMTgg\nMzE4IDUxOCA1MTgKNTkwIDUwMCAxMDAwIDUwMCAxMDAwIDUyMSA0MDAgMTAyMyA2MDAgNTI1IDYx\nMSAzMTggNDAxIDYzNiA2MzYgNjM2IDYzNiAzMzcKNTAwIDUwMCAxMDAwIDQ3MSA2MTIgODM4IDM2\nMSAxMDAwIDUwMCA1MDAgODM4IDQwMSA0MDEgNTAwIDYzNiA2MzYgMzE4IDUwMAo0MDEgNDcxIDYx\nMiA5NjkgOTY5IDk2OSA1MzEgNjg0IDY4NCA2ODQgNjg0IDY4NCA2ODQgOTc0IDY5OCA2MzIgNjMy\nIDYzMiA2MzIKMjk1IDI5NSAyOTUgMjk1IDc3NSA3NDggNzg3IDc4NyA3ODcgNzg3IDc4NyA4Mzgg\nNzg3IDczMiA3MzIgNzMyIDczMiA2MTEgNjA1CjYzMCA2MTMgNjEzIDYxMyA2MTMgNjEzIDYxMyA5\nODIgNTUwIDYxNSA2MTUgNjE1IDYxNSAyNzggMjc4IDI3OCAyNzggNjEyIDYzNAo2MTIgNjEyIDYx\nMiA2MTIgNjEyIDgzOCA2MTIgNjM0IDYzNCA2MzQgNjM0IDU5MiA2MzUgNTkyIF0KZW5kb2JqCjE2\nIDAgb2JqCjw8IC96ZXJvIDE3IDAgUiAvb25lIDE4IDAgUiAvdHdvIDE5IDAgUiAvZml2ZSAyMCAw\nIFIgPj4KZW5kb2JqCjMgMCBvYmoKPDwgL0YxIDE1IDAgUiA+PgplbmRvYmoKNCAwIG9iago8PCAv\nQTEgPDwgL1R5cGUgL0V4dEdTdGF0ZSAvQ0EgMCAvY2EgMSA+PgovQTIgPDwgL1R5cGUgL0V4dEdT\ndGF0ZSAvQ0EgMSAvY2EgMSA+PiA+PgplbmRvYmoKNSAwIG9iago8PCA+PgplbmRvYmoKNiAwIG9i\nago8PCA+PgplbmRvYmoKNyAwIG9iago8PCAvSTEgMTIgMCBSID4+CmVuZG9iagoxMiAwIG9iago8\nPCAvVHlwZSAvWE9iamVjdCAvU3VidHlwZSAvSW1hZ2UgL1dpZHRoIDE5NiAvSGVpZ2h0IDEzNgov\nQ29sb3JTcGFjZSAvRGV2aWNlUkdCIC9CaXRzUGVyQ29tcG9uZW50IDggL0ZpbHRlciAvRmxhdGVE\nZWNvZGUKL0RlY29kZVBhcm1zIDw8IC9QcmVkaWN0b3IgMTAgL0NvbG9ycyAzIC9Db2x1bW5zIDE5\nNiA+PiAvTGVuZ3RoIDIxIDAgUiA+PgpzdHJlYW0KeJzt3cEJwzAQAME4pBL335JcS1pQYI2INfPW\nw4/lDgcUH2OM15zzPCdPsqf36gfgOcRERkxkxERGTGTEREZMZMRERkxkxERGTGTEREZMZMRERkxk\nxERGTGTEREZMZMRERkxkxERGTGTEREZMZMRERkxkxERGTGTEREZMZMRERkxkxERGTGTEREZMZMRE\nRkxkxERGTGTEREZMZMRERkxkxERGTGTEREZMZMRERkxkxERGTGQ+80ev65o86TvjezKZyIiJjJjI\niImMmMiIiYyYyIiJjJjIiImMmMiIiYyYyIiJjJjIiImMmMiIiYyYyIiJjJjIiImMmMiIicwPlzDv\nMH+xc54roKuYTGTERGbxmrOSnsRkIiMmMovX3L+4463zeUwmMmIis/Wa85Npy2QiIyYyf7Pm7vh7\n1p1X0h1MJjLHGGP1M/AQJhMZMZERExkxkRETGTGRERMZMZERExkxkRETGTGRERMZMZERExkxkRET\nGTGRERMZMZERExkxkRETGTGRERMZMZERExkxkRETGTGRERMZMZERExkxkRETGTGRERMZMZERExkx\nkRETGTGR+QJxnRYVCmVuZHN0cmVhbQplbmRvYmoKMjEgMCBvYmoKNDM4CmVuZG9iagoyIDAgb2Jq\nCjw8IC9UeXBlIC9QYWdlcyAvS2lkcyBbIDEwIDAgUiBdIC9Db3VudCAxID4+CmVuZG9iagoyMiAw\nIG9iago8PCAvQ3JlYXRvciAobWF0cGxvdGxpYiAyLjAuMiwgaHR0cDovL21hdHBsb3RsaWIub3Jn\nKQovUHJvZHVjZXIgKG1hdHBsb3RsaWIgcGRmIGJhY2tlbmQpIC9DcmVhdGlvbkRhdGUgKEQ6MjAx\nODA1MTQxNjM3NTgtMDcnMDAnKQo+PgplbmRvYmoKeHJlZgowIDIzCjAwMDAwMDAwMDAgNjU1MzUg\nZiAKMDAwMDAwMDAxNiAwMDAwMCBuIAowMDAwMDA0NjEwIDAwMDAwIG4gCjAwMDAwMDM3MTggMDAw\nMDAgbiAKMDAwMDAwMzc1MCAwMDAwMCBuIAowMDAwMDAzODQ5IDAwMDAwIG4gCjAwMDAwMDM4NzAg\nMDAwMDAgbiAKMDAwMDAwMzg5MSAwMDAwMCBuIAowMDAwMDAwMDY1IDAwMDAwIG4gCjAwMDAwMDAz\nOTggMDAwMDAgbiAKMDAwMDAwMDIwOCAwMDAwMCBuIAowMDAwMDAwOTc2IDAwMDAwIG4gCjAwMDAw\nMDM5MjMgMDAwMDAgbiAKMDAwMDAwMjU5MyAwMDAwMCBuIAowMDAwMDAyMzkzIDAwMDAwIG4gCjAw\nMDAwMDIwNzIgMDAwMDAgbiAKMDAwMDAwMzY0NiAwMDAwMCBuIAowMDAwMDAwOTk2IDAwMDAwIG4g\nCjAwMDAwMDEyNzkgMDAwMDAgbiAKMDAwMDAwMTQzMSAwMDAwMCBuIAowMDAwMDAxNzUyIDAwMDAw\nIG4gCjAwMDAwMDQ1OTAgMDAwMDAgbiAKMDAwMDAwNDY3MCAwMDAwMCBuIAp0cmFpbGVyCjw8IC9T\naXplIDIzIC9Sb290IDEgMCBSIC9JbmZvIDIyIDAgUiA+PgpzdGFydHhyZWYKNDgxOAolJUVPRgo=\n",
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOUAAACuCAYAAADJVsq5AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f929f3adc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cmap_shading = colors.ListedColormap(['white', '#dddddd'])\n",
    "norm_shading = colors.BoundaryNorm([0,1,10], cmap_shading.N)\n",
    "\n",
    "plt.figure(figsize=(3.5,2.5))\n",
    "plt.plot(lorenz_data[0], np.nanmean(lorenz_data[1],axis=1), '-k', linewidth=2)\n",
    "plt.imshow(np.mean(lorenz_data2[1][::-1,:,:],axis=2), cmap=cmap_shading, norm=norm_shading, interpolation='nearest',\n",
    "          aspect='auto', extent=[lorenz_data[0][0]-.5, lorenz_data[0][-1],lorenz_data2[0][0],lorenz_data2[0][-1]])\n",
    "# plt.savefig('figures/02_sampling_lorenz.pdf', format='pdf', dpi=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Show the average baseline duration on the attractor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-18.711907266995201,\n",
       " 19.491577301761811,\n",
       " -24.585989380467449,\n",
       " 26.012622436875088)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/pdf": "JVBERi0xLjQKJazcIKu6CjEgMCBvYmoKPDwgL1R5cGUgL0NhdGFsb2cgL1BhZ2VzIDIgMCBSID4+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\nUiAvSW5mbyAxMiAwIFIgPj4Kc3RhcnR4cmVmCjE2ODAwCiUlRU9GCg==\n",
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAASwAAADuCAYAAACDKjp+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nDzpY0Pmsmg02AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f92627746a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_periods_simulate = 30\n",
    "sampling_rate_simulate_exponent = 12\n",
    "sampling_rate_simulate = 2**sampling_rate_simulate_exponent\n",
    "t_simulate_full = np.linspace(0, num_periods_simulate*period_length,\n",
    "                int(num_periods_simulate*sampling_rate_simulate))\n",
    "dt_simulate = t_simulate_full[1]-t_simulate_full[0]\n",
    "\n",
    "lorenz_simulation = utils.simulate_lorenz(dt_simulate, t_simulate_full.size, sigma=sigma, rho=rho, beta=beta,\n",
    "                                    tau=tau)[0]\n",
    "\n",
    "start_idx = int(5*sampling_rate_simulate)\n",
    "end_idx = -1\n",
    "end_idx_highlight = int(5.85*sampling_rate_simulate)\n",
    "spacing = 2**6\n",
    "\n",
    "# find the max index at which to plot the solution\n",
    "sample_max_idx = int(0.85*period_length/dt_simulate)\n",
    "\n",
    "fig = plt.figure(figsize=(5,4))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "ax.plot(lorenz_simulation[0,start_idx:end_idx:spacing], lorenz_simulation[1,start_idx:end_idx:spacing],\n",
    "        lorenz_simulation[2,start_idx:end_idx:spacing], alpha=0.8, color='#999999', linewidth=2)\n",
    "plt.plot(lorenz_simulation[0,start_idx:end_idx_highlight:spacing],\n",
    "         lorenz_simulation[1,start_idx:end_idx_highlight:spacing],\n",
    "         lorenz_simulation[2,start_idx:end_idx_highlight:spacing],\n",
    "         color='#ff0000')\n",
    "ax.axis('off')\n",
    "# plt.savefig('figures/02_lorenz.pdf', format='pdf', dpi=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Duffing\n",
    "\n",
    "### Simulate the system"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "alpha = 1\n",
    "beta = 4\n",
    "tau = 1\n",
    "period_length = 3.179*tau\n",
    "\n",
    "x0 = [1.0,0.0,0.0]\n",
    "\n",
    "Xi_true = np.zeros((10,2))\n",
    "Xi_true[1,1] = -alpha\n",
    "Xi_true[2,0] = 1.\n",
    "Xi_true[6,1] = -beta\n",
    "Xi_true /= tau\n",
    "\n",
    "poly_order = 3\n",
    "coefficient_threshold = .1\n",
    "tol = 1e-10\n",
    "\n",
    "num_periods_simulate = 10\n",
    "sampling_rate_simulate_exponent = 18\n",
    "sampling_rate_simulate = 2**sampling_rate_simulate_exponent\n",
    "t_simulate_full = np.linspace(0, num_periods_simulate*period_length,\n",
    "                int(num_periods_simulate*sampling_rate_simulate))\n",
    "dt_simulate = t_simulate_full[1]-t_simulate_full[0]\n",
    "\n",
    "duffing_simulation = utils.simulate_duffing_oscillator(dt_simulate, t_simulate_full.size, x0=x0, alpha=alpha, beta=beta,\n",
    "                                                 tau=tau)[0][0:2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Subsample data and apply SINDy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "test_durations = np.arange(.1,1,.05)\n",
    "test_sampling_rates = np.arange(5,19)\n",
    "test_starts = np.arange(0,1,.1)\n",
    "\n",
    "extra_coefficients = np.zeros((test_durations.size, test_sampling_rates.size, test_starts.size))\n",
    "\n",
    "for i,duration in enumerate(test_durations):\n",
    "    for j,sampling_rate_exponent in enumerate(test_sampling_rates):\n",
    "        for k,start_time in enumerate(test_starts):\n",
    "            initial_samples = int((5+start_time)*sampling_rate_simulate)\n",
    "            t_simulate = t_simulate_full[initial_samples:]\n",
    "            duffing_solution = duffing_simulation[:,initial_samples:]\n",
    "            \n",
    "            # get subsamples\n",
    "            sampling_rate = 2**sampling_rate_exponent\n",
    "            t_max_idx = int(duration*sampling_rate_simulate)+1\n",
    "            spacing = sampling_rate_simulate//sampling_rate\n",
    "\n",
    "            t_sample = t_simulate[:t_max_idx:spacing]\n",
    "            dt_sample = t_sample[1] - t_sample[0]\n",
    "\n",
    "            sampled_data = duffing_solution[:,:t_max_idx:spacing]\n",
    "\n",
    "            sindy = utils.SINDy()\n",
    "            sindy.fit(sampled_data, poly_order, t=dt_sample, coefficient_threshold=coefficient_threshold)\n",
    "            extra_coefficients[i,j,k] = np.where(((np.abs(Xi_true) < tol) & (np.abs(sindy.Xi) > tol))\\\n",
    "                                                  | ((np.abs(Xi_true) > tol) & (np.abs(sindy.Xi) < tol)))[0].size\n",
    "\n",
    "boundaries = np.zeros((test_sampling_rates.size, test_starts.size))\n",
    "for k,start_time in enumerate(test_starts):\n",
    "    boundaries[:,k] = find_boundary(extra_coefficients[:,:,k].T, test_durations)\n",
    "duffing_data = [test_sampling_rates, boundaries]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot the range of data requirements for all portions of the attractor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f929f094358>]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/pdf": "JVBERi0xLjQKJazcIKu6CjEgMCBvYmoKPDwgL1R5cGUgL0NhdGFsb2cgL1BhZ2VzIDIgMCBSID4+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\nIDI0IDAgUiA+PgpzdGFydHhyZWYKNTY2NgolJUVPRgo=\n",
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYYAAAEACAYAAAC3adEgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f929a6ac390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(duffing_data[0], duffing_data[1])\n",
    "plt.plot(duffing_data[0], np.nanmean(duffing_data[1], axis=1), 'k')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Show the average baseline duration on the attractor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.1000798934242517,\n",
       " 1.1000758892108191,\n",
       " -1.9054745551801413,\n",
       " 1.9054841127883311)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/pdf": "JVBERi0xLjQKJazcIKu6CjEgMCBvYmoKPDwgL1R5cGUgL0NhdGFsb2cgL1BhZ2VzIDIgMCBSID4+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\nMiAwIFIgPj4Kc3RhcnR4cmVmCjI4ODMKJSVFT0YK\n",
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJ0AAACTCAYAAACULBumAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n/R9fGQky23xNPQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f929f050668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "start_idx = int(5*sampling_rate_simulate)\n",
    "end_idx = int(7*sampling_rate_simulate)\n",
    "end_idx_highlight = int(5.25*sampling_rate_simulate)\n",
    "spacing = 2**4\n",
    "\n",
    "plt.figure(figsize=(2,2))\n",
    "plt.plot(duffing_simulation[0,start_idx:end_idx:spacing], duffing_simulation[1,start_idx:end_idx:spacing],\n",
    "         alpha=0.8, color='#999999', linewidth=2)\n",
    "plt.plot(duffing_simulation[0,start_idx:end_idx_highlight:spacing],\n",
    "         duffing_simulation[1,start_idx:end_idx_highlight:spacing], color='#ff0000')\n",
    "plt.axis('equal')\n",
    "plt.axis('off')\n",
    "# plt.savefig('figures/02_duffing.pdf', format='pdf', dpi=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Rossler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = 0.1\n",
    "b = 0.1\n",
    "c = 14\n",
    "tau=.1\n",
    "\n",
    "x0 = [0.0, 10.0, 0.0]\n",
    "\n",
    "period_length = 6.14*tau\n",
    "\n",
    "Xi_true = np.zeros((20,3))\n",
    "Xi_true[0,2] = b\n",
    "Xi_true[1,1] = 1\n",
    "Xi_true[2,0] = -1\n",
    "Xi_true[2,1] = a\n",
    "Xi_true[3,0] = -1\n",
    "Xi_true[3,2] = -c\n",
    "Xi_true[6,2] = 1\n",
    "Xi_true /= tau\n",
    "\n",
    "poly_order = 3\n",
    "coefficient_threshold = .1\n",
    "tol = 1e-10\n",
    "\n",
    "num_periods_simulate = 10\n",
    "sampling_rate_simulate_exponent = 18\n",
    "sampling_rate_simulate = 2**sampling_rate_simulate_exponent\n",
    "t_simulate_full = np.linspace(0, num_periods_simulate*period_length,\n",
    "                int(num_periods_simulate*sampling_rate_simulate))\n",
    "dt_simulate = t_simulate_full[1]-t_simulate_full[0]\n",
    "\n",
    "rossler_simulation = utils.simulate_rossler(dt_simulate, t_simulate_full.size, x0=x0, a=a, b=b, c=c, tau=tau)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Subsample data and apply SINDy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "test_durations = np.arange(.1,2,.05)\n",
    "test_sampling_rates = np.arange(5,19)\n",
    "test_starts = np.arange(0,1,.1)\n",
    "\n",
    "extra_coefficients = np.zeros((test_durations.size, test_sampling_rates.size, test_starts.size))\n",
    "\n",
    "for i,duration in enumerate(test_durations):\n",
    "    for j,sampling_rate_exponent in enumerate(test_sampling_rates):\n",
    "        for k,start_time in enumerate(test_starts):\n",
    "            initial_samples = int((5+start_time)*sampling_rate_simulate)\n",
    "            t_simulate = t_simulate_full[initial_samples:]\n",
    "            rossler_solution = rossler_simulation[:,initial_samples:]\n",
    "            \n",
    "            # get subsamples\n",
    "            sampling_rate = 2**sampling_rate_exponent\n",
    "            t_max_idx = int(duration*sampling_rate_simulate)+1\n",
    "            spacing = sampling_rate_simulate//sampling_rate\n",
    "\n",
    "            t_sample = t_simulate[:t_max_idx:spacing]\n",
    "            dt_sample = t_sample[1] - t_sample[0]\n",
    "\n",
    "            sampled_data = rossler_solution[:,:t_max_idx:spacing]\n",
    "\n",
    "            sindy = utils.SINDy()\n",
    "            sindy.fit(sampled_data, poly_order, t=dt_sample, coefficient_threshold=coefficient_threshold)\n",
    "            extra_coefficients[i,j,k] = np.where(((np.abs(Xi_true) < tol) & (np.abs(sindy.Xi) > tol))\\\n",
    "                                                  | ((np.abs(Xi_true) > tol) & (np.abs(sindy.Xi) < tol)))[0].size\n",
    "\n",
    "boundaries = np.zeros((test_sampling_rates.size, test_starts.size))\n",
    "for k,start_time in enumerate(test_starts):\n",
    "    boundaries[:,k] = find_boundary(extra_coefficients[:,:,k].T, test_durations)\n",
    "rossler_data = [test_sampling_rates, boundaries]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot the range of data requirements for all portions of the attractor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/kpchamp/anaconda/envs/py3/lib/python3.6/site-packages/ipykernel_launcher.py:3: RuntimeWarning: Mean of empty slice\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f929a6fc2e8>]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/pdf": "JVBERi0xLjQKJazcIKu6CjEgMCBvYmoKPDwgL1R5cGUgL0NhdGFsb2cgL1BhZ2VzIDIgMCBSID4+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\nRgo=\n",
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYYAAAEACAYAAAC3adEgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\noYlBKaXUGP8fkzQ/bzQMa/IAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f929a6e4f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(rossler_data[0], rossler_data[1])\n",
    "plt.plot(rossler_data[0], np.nanmean(rossler_data[1], axis=1), 'k')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Show the average baseline duration on the attractor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-21.57888607236643,\n",
       " 24.240539051986286,\n",
       " -23.104101652193023,\n",
       " 20.02789328035928)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/pdf": "JVBERi0xLjQKJazcIKu6CjEgMCBvYmoKPDwgL1R5cGUgL0NhdGFsb2cgL1BhZ2VzIDIgMCBSID4+\nCmVuZG9iago4IDAgb2JqCjw8IC9Gb250IDMgMCBSIC9YT2JqZWN0IDcgMCBSIC9FeHRHU3RhdGUg\nNCAwIFIgL1BhdHRlcm4gNSAwIFIKL1NoYWRpbmcgNiAwIFIgL1Byb2NTZXQgWyAvUERGIC9UZXh0\nIC9JbWFnZUIgL0ltYWdlQyAvSW1hZ2VJIF0gPj4KZW5kb2JqCjEwIDAgb2JqCjw8IC9UeXBlIC9Q\nYWdlIC9QYXJlbnQgMiAwIFIgL1Jlc291cmNlcyA4IDAgUgovTWVkaWFCb3ggWyAwIDAgMzAwLjQg\nMjM4Ljg0IF0gL0NvbnRlbnRzIDkgMCBSCi9Hcm91cCA8PCAvVHlwZSAvR3JvdXAgL1MgL1RyYW5z\ncGFyZW5jeSAvQ1MgL0RldmljZVJHQiA+PiAvQW5ub3RzIFsgXSA+PgplbmRvYmoKOSAwIG9iago8\nPCAvTGVuZ3RoIDExIDAgUiAvRmlsdGVyIC9GbGF0ZURlY29kZSA+PgpzdHJlYW0KeJxtncvObEtS\npOfnKfIJ/or7ZQhCKolZ0wMGiBFU05QOSFASvH7bZ+6Ru1tqENTeUbkz14qLu7m5uUf9/Pm3P/xV\n/fzLXz7l82f9339//uHzj/rPf/7Uzx8/f/ibP/3Xv/7Tn/7uj3/9+ae//FY0/m+/9VJ+hv70e/6p\n9fNzhv5afv3xf//227//pm/Vx/6oL/qX32r52R//v3/7rZ37/vJ7/qW181P5hx79/k1f879++4/P\nr3/c9v20un/G+Pznnz5///n3zx/+qvHw7fO3+p0/6z9/vUD5Wf/PK/ymV/itrvFz9j67fq5+ucze\nrp6pTv2ljlqqfqjo12cZh+eZQz82djke7+vszmPXcX9qbWOvGN9tlevx/rOXhuLz+ufjVMY1M6OP\ncY9/tnY9gYf7T9173MVwmXWVzrAmoPSxdv9cTcUua3lyWtdnytyfu3/Knj2+o56ftm4fnzt/9q7n\n+gerHkQ/uObnDv33p5Tl+b0/45zB67efufX2zcNTf9E76PE0bfeWHp9uP6WtWdvnnJ81T5sa1SOd\ns8/8nPWj71+TZ7vrp956hz45fvR6y9N3+8/Vy877OVVf29ri2fTLbU697GdrFsf1zN2qVyqt389e\nP1OPFaPaYV3vUT+7/5ypl58x2veoeoRdNcel+ZU1em5vu30Wk31X7/FjpdSjB1uannFWfINmp9Sp\nXba0AqXPyftqAu/ZV3O2ys/sRS+U7zvL0vdOLYvm7ObU6Kf0aJ+p7y2350Sun9bLXusz+48mbl8v\naGVW9ab1M+vPuC1+r9b5s9o55360n/QL+SWt/LAEdX+GfnGPEWejLS1puWN9hv5Uzyn+dG8/W7Os\nCR98XZ/VP9k1t70MnZihLV9Gaf40n1lHU6NRPX71Fprth72yPVqGNo+/Qoei3HJmY1gPu4Y/rYk8\nffW7Gdbsr9iHWxuqXJ0I/UQrp/j8aIVL13aZPHPTN8fDnfmj52y8ytYzN20thrUJtNpldOZjlK45\n8LC2e5tscc3eLqMdvqSxBGz3+9EpPZoHH82mJThN03c+ev5++F+GWYJ5+rifpQ/op0b1cNerz1s2\nm3FP7wmGNTtajt50jrV19X13eVy/qXXUeWTe9enqo8mPLs2a5rjOzcnj3Xh0bcWmA149rgms+aZs\nCD3j1Pfo4ded8+bEVM0Wv6sHvlqC5rXX+ZlXm1rHWfO4tYAe3kc7Vks3PtjRovPsX9URWndpYs7+\n0RdzJhiVLWMfH4ZlXjSPHq7s+r4aw0dzHk+oWVoYCH+1tuTwwi3sm47OYnRNbVN/h87LnuNgx8pP\nOa3EsF95Hk2pj6w2eH9GVWsxO8NzlG2noclkh+hweHjdU6Z37OEEy5IyPFbTr3t4yNo1rQzDTRMa\nBm5oojQ7mKyrt7naqM/+Ls3AZLjr/MX89SlLodXvNnCnsKnjSM3euydKW+POsMqa4lNZQA0XrXYc\nnra13WXODgaxlLbj3ZuWtWsGJhbxaJFitlv74fjpHU7XSdTuvHnktah8h46ifrt5tF622NVDHW0G\nnZPlpZEH1PHSn7VlZ9GMxYdlFJbOn3aynvrI8/QcLuPuczCsQ7511Wd6VtGHPpsHLet+LVItmlcM\nbtP/1JnD2vSaSm2WVXUKZn613rvoxbZWXUuUxk6bTrOq1cMQy0fGhFT8RmlxAK+wQuv55lqNuw4G\nWidxxDpqnjR85OzksfV0fdc3qzLh+qEls6eZrDXXQEeL47S0/vIjttyyf5rMwmnVBpXfyxWT1x3a\nO5o2WQjthHP8kx3DMYf8mQz9lsEITzrw+2O2EfZfvzly/xXtKM3E5JDpz34d2bNzMEsMt69fwHCd\n2/QkGtYRGze2PD5J/mB7eMgQ1zS8W/Mq68eXyNCdmYdPD7KxbPrJPXaeVP2lepfoAeXM6nrnWnux\nyI9q+BThjJ5W4Bz9l52XXzj3mpakV3mJw1StM/GCaXealm4xsXLA3b+oHS1c03Gqcp9LaxrDW38R\nMKms2bzyBmHsmWTtJNZdbqnE410Wqm4WWAZTeCiHte3mAUgsuQD5tdglAjFzb4yQX0uGx/Mnjy13\nx3dru8pE83UMa8/LvsgL622vYF0cYEynHBNoQmdFxjWOJG5fwIttLCMgNxJQTsPaL2xeHb6BcVv5\nJFoO7QGd1Cb/HvZFMONsLffgWMuYC2PmSxa9jPzm4WA9ly1jc3Wuuw20lldv7OHFviza0lgjPV9M\nCYZCG0YuCuO607PooeYVMGkfvKYszfFT6+y30fFWeqTBbg3bz9ZZQCZNMJAqlmZhI3USWqDEniYX\nDz/0mcGwdueNU7ZqIJ0D1MSUxGxrM2pX6q9GoEPbKIy/toa89vSwMGc8tqw5XlZbm9Eh45+HqQuM\nD4PYJWez8+QVuRJMvCAFOHKm0RYKx5fo6bT5dg5XfJ1dJFhxnbTaOh0CRTLxmpCr/Xcfll4ygDrs\nmj6djhNf0vjJpr/bBzVtypaWTkANi3rARPfGzqlgPAFgOwrtJrnURHvAMzzqxKS0EbENQH1yxHR+\n9FozQbZOhbyAfLR2lNBeAGqdRW3/e/C/BdgZXq/oeMg/YM1l5NeSpUk0OvRY+vDmF3Xqaw7Lpck0\ncDyWZjh2pYY1idoqHCZthgg6NKolwPRrV7SBPc9flGs3bpKJAj54ohQxaF8ARnXWNesZuRRtv81j\nYZ8VJYxAnQo7du+cGlmXK38UG15oasn8VhtiGZ8SQABvo7VeNq2Cg/nY8obr6JAcQ25Zw/lWUocG\neyVc0a7MVQwfIhKg0SRskmUY6drl7uWqPgK9WvYdzrPLbPOFC4ip05xmR+GcPBbmb2o7CGvGc2sT\n623kjhkGe8SX6IdkzW1xQUHaACutuUyPlsefxgMGjNbm1Zbu098NxAwYrX+qXYA1r8R+GYppXeWb\nmDeeW9h0z7QCMlgyiLylPO+IsweMnAefDtaaRCppiTVT2lqfKQvZ9nYwhM3V1qnhV84IkCHQrf+6\n8Nmrc6N/FeiaiKtjELTAbe0VUFwbWsGETBC7obWI6UDFgplCgOydKx9jg9Y4CAIk1fGbrM60y2/E\npkJ98kxYbR1NQyOAu7bzEKLDPOOXR35aUEYTfxxO3u934IAU9WgKdGKHLVfTttwVH8lBxZTGc+is\n6PF0mI6xyU0sr7PSJjEc8zVkOmKWtKEWET/29hBvpM/Ttq42ck3HNeyFTHaXp1NgJJ/DC+YiEkpW\ngOUFao9E6wqu8P3z41BzjUApiwBOAeuAG9DGH3HU5XEF+eV5zDC0u2/gvInL0PmMcc3jDl+jfdGu\nTQPjh9DhC1S03zUlHtdoWPMhAHrlnYIJmYvdnehIvyV87vEiaxIxrMwusSBmV8haQVsQJw2wCSmi\nd5IjOTUiW6aua2cyAcI3+ndfIAkkwSfMk06hVsLgg6vA58qttTQx2s76H1MYbIyTdkorKAsW0cPM\nUIg50lIullhIa3kSL0DFVupgfOVKTCAIYziiw4dv4YTr8B9APvTVcBgC4KeaKsDEa99eb0qdS6Nq\nYiIhZsWhG0zRYmPbZcylPWdMre/qMVqxq2DnIZSRY/ohnkbnRae3GH0DIhRzadtzuOZayWvgmEue\nwyvc+jGD0fFCI8BdjR1NENoFiHy+5cUT8uEdtKn0tDISGxvenz+6UFIyNFqphCw6hVoZmw6mV2+8\nn6m+Nl127C0DqIYvHrAj2maAzUDYwPQrgz7gCOQbNNufwOM6s9qaEAoCtTPcwGDpCngcrF0ehTUW\nB0DW+iPrLCBR+jO+WkjBFob7klsOhMNCadmXPy3bMOrDzNdk0ICjmnmadRT7AcL4SfQP90PBQmXC\nejz31dutnWdfk6bARC+p8C4jKwDWgn9KEmOFP7pE0efcMODdjjYsp7Y2kFNOTTtj3pomcmuvapOD\nu4XoW7AVsE6CSbKFoLvRZgzrS2RjOBL6tH5jBFmBIQNDf+wkhXbWfkaymYxjegR05as8Xow/9eTg\nxcOsPBSrl8f3wBStLqsfZIVmSzEWZKcWXDis5Lzg/W4YEEbrQ6aKo9a6EfW3GhgFx6Zv53xpYftI\nfm3DjF6WhSNKmOyVkMOQL5fhYlixFYzq7yYruuIr7TIzHiWOGLZSuwnDciDSTkKrhQ9rht9He+Jh\nZFlQBaVAU9yBrFOgUK2LTvQOjoXIMoA2MzHahmTRyuKhYnfKZWhuu/mHglXLPStMOYNngD3tJ+GF\n5kyhmR9EW6nExufAy/YPhnVAZ3kcRtNZ057VS66pk9ETDgtoQJVBSwg7xJToUEHdbfO0rZ8YNA+5\nMXyyFOvu/vhmLby+jhW9Nw+rLLieH++IN1vpfxSBL79IM1MVBwRmGvZkJlEx4kW0Kzaw00yF3u7U\nL9khVLQccAm+ZBwmfMdW1BptdkLNEFTD2kREvdoqE3LpDSv4J2TYROLjvO8Q3JnYZa2PZnx/v1ou\ni+9gL2t9Vj7IkpHaDja3wE7E8Dy2PIG+cen5ZNF3vmMF9A0DYf1nMHMwEgqBYCQczPf0dAuyaMqs\nEwsrBA3WoGlT6CQcR846vj3wGrFLgdfAmgvJt/iSDgupILma1hAQDiQisKrYEL+HdWv51JjL5cBu\n4Z+FBEbuMXyhcDhkx5TBac+Kym4MQ2+5wBWwXsZdyP9AGch35O/JtN4h3DrNJAhMBCkECVE0k+Yd\n5AVmzPXiiMJ88c2apQibmQVB8OpRuY8a/gNcqJOx/CrEz/Ud8yYAs/wugM8AFTuyMSxMhf0bAUE2\n5rcSYJoU0rYcaYaE3OETsQPEIkFHNBIwOhEsmEDGShsv37qHPI9sCYmaGUBO0zRstfWkByPo80x8\nLsOg07PgmPdjadnBB4Mop64/3f7IXp0JkBwc+d4rvuTCpWk2jXch5gKxaJhMifYCsZwOQdgbLPva\neEO9rkDAeqYZN6BzpROmPTkiQLnB4QxzF0f7KqYVJmYdYlpNwsAOjHwbzcMI4IPziL2KhZVhKTYW\n+hVB4pwobUoQrT5wFD6GXZCPhF8btp4Ks1tYJ1I88rRBuypsCJuPRXK4AKUrmxpmCA5n82EQtiBj\nsl6RmhvGezpRLckIuQWZLOCxIk3ts0i0cX7Ogce4xuDrmfZlzk2Dgsarv+Qe3C5wvDPTGZVOpgyW\nhbhIXiCYb0z4Ubxb/eHy0imN4PfieYEXLWPpTtpDu4LRQnD8iIsGY+g3EW69D0BPwIWdt/ZATbui\nk0HAZ5JcLiozhg0i7JKlYDF1NB7e0tGCsNHkC1+X+ihXgVgIffaxQqrYShWUPY6Wk4W9dyWBDJsB\nPGQbaDp6eLRKxmr22DRCN3W9kP4o+tB8QI9pO+SwHBkPMLHtAJT2eIHVTUGSm2gGvjGso3hkWXQE\n1pJtWTlcZOmHDwxRTXmf7tBPm+O1iQzeT4Lm9WmZa0XA674HlIer3Sf6yCAm50Bybc8kLvR851E5\nZXRIXChNzOujIrRtFka/AvZGThUEQB8RHAtXlJgqYC/xTcUi9iIUF+z0lHe0l1PYLSzantPV0hDe\nQGdsZ6zSb5MINZ0hoLWC/OhkvQsEo60x7G/uP3n8CXzUdpfJu8+6bxlQ/VPBlKOYIRJpE1jORgK8\nHNC6RzF4CwKK4VtzonjhoXiqMnydO4lj11iZ4x9cPZ0P9k4hqgyvnrrI5q8H7lZ1fHGLQudnlgln\nmt/73hcDHvOqMg3mvOU627NNsjYYKkh5Abj9MoX6sEyHmf0+bjIZWPRj2CykfEqeA8V7Ogac0sWv\nnMAhxrt681HD5s+dCURso7Z27Cehc0dA0AJ3AcuMIYrG40uG95McvcyX4MFpQSJMCEF2P6GgIvD5\nHdYpJEkDG9hvfrd2iM4S6XMgs47P+24h9HKdFlJA1fMn8XLT+JAE7JeE0RrIr93AxuucpKZhTQ5W\nDMMs11cfGS5gLrCEIYH+SYeitd5QjLZGetuAbBgbhSxh0YDuEaLLfghuwvhDxR7C4/QFMnO2laTE\n9CPt8yIAB0zXCKYFYNi8jqIK8x86HMESGRrMhlmBFhFarCsNvL7CjAt8EXnOBCNHx6CZhjiKjJN7\nA6XrU/60lvTGlh9YkkrYw3AZL9UIMSqoa3GIHPzNNNIiE4vdI4grfHsabliCHhyHj30Cvy0j2XnJ\nAbs00zRcIeHr/O1FmmE7oueQGzpWaQiYz0g9KMy7Yf8IJgtAPQ3dka2812sjTxnGqED2LRwIfBXD\nYUThtacNNOyXAxFmUgZF7vaQOVEEYdaA6AlMhuGv+EmPDrAvPlF7cmsOQ/3R8B3bvIdgRzfU4jRu\nGFs2u4zlcGgHNhGWIDnTgBUtxuapLVKGXYClJJkhbKATYN5DW8G7C496KnoXAbUivJAajTGJmYyU\nBfQNsaDTbu9lmaxcNZYTXktHtqzIl9WVGhhQJHn7SYaH/O9zXAqiri2p7E1PLro7farzQHr6Kt4Z\n6QBwF3oMBXyTrPCLEaAcYRv0ARnNDHiuHSeCDiDTSjoEPKAlGKYVjrDgeOHf7JDkDGsHJ5PBN1ay\nDeYmMLw7QcyEwDBloTBwfHM1QMqbTIas+uM9tFGJ31FpaEkTkA0AFwmJ4dRZgo1DuAjXEzTO7pkU\nxJ/KvJj0UZRQvqZDBmNCURdgxQ73fBEzaTbtRw4LOtOIgfxlf+CitY5pCTfJrNF75CHvtEODBNaf\nNRHrONO8gxoG4hl5HIIfGdMn3iik11pQlTJWN8bBL5rC++GUVpIrjx3WSsmofDAM2j0tCDJsg/Ct\nXprJFwQtEVpjI/X+ej1nmGXlM1GHlkXx7rJ4Q7jvxIY7lkEdze61NqWPxyrJqZj31asKasTh18Ha\nMuNhr+UFk1YCM8tATA934syRmHk1p+ZhFjYL8Gud+aeoIwQWYuXIOSjiCJ3GIUW7c7PIt8gDGnlr\nLsqjlHXS4NewN30nxNaOW9XiKM59NZAMcEEQUQ3ftcnPNyEui9WL4a0MY+4hKD3FNgH29eESm0VB\nrI6/IbmZnswfdbKaB5II7qjUDPw6LnnM4GAOiqkY1rvpzF3L1mQAznjs45Fnw22CB3Ym8UBnjiTB\nyEUPGugMENB5WDK3t6RJaYop5ZzJL2Aed2YTMQd4XPy04GJKG+oil21exXm2hFCVsKOx9xQcHbRu\nOy3NmshebFrLHGmAGkkKEuII48p9gwMRiRPcOt0jVl3D8hWyNE6H95rMG2k2iC2nW5jpmb8n690i\n0z7ffqoOsZ3fYQvJWT+e91yL4Bx37RV2Q/5ro2YIlkO/kWTxJRuOYEtgWv/qfLUvEGx8upo0f/Ov\ng5zKg076eCY87gofdhAUckSBB3G6AxrGYoemtzppSqGE9dWgR/3DHL5QX2g5J5N3nvvvZvKXSVe5\nrRLvbhq3gcLg/KzeyY29kIuEw1C0FKedf+qY0qM3GCVeQXvoGNwqAJ8RuXh2Ds7O/6qmLBB8Cey7\nfjwUbiMBESHssvxDpqCnUAvd2j6h80DSmVo62NTFilnvNhMnkWPWlgySaEFzpYlqZH5NlWh/pPO7\naFUP9CMaE5mLeBsZOlIty+LJ7in43QoI2VZUfwvDqdPaElDihuSftJ9A+LH5nDZDn8Luk2UtEeuD\npGRFjoVGBZ3FG5Zra9OJ7NJwIjksVAhY3chn9vhy6hPobSUp390e4j0KeU6wkdqgsaOuYZBhc6g1\nUl2oDa2jC/sx+MAO5udaAbiClx5Ew0+2ohVgRUDTCuC+GheFRRBCYDCd1vk8ZSXTaeOno7fCgvL7\n3UIxfGbfKfeCKxFG7SMUDOUXQ64pgR1i5vUdiaZlb+EhpmUXes37ArRj0KX3QtyTTDhHb5PFR0w5\nRlLKaBXPIfTTMMHoeTlDcNcwUJ9wOSMRiJwb3CnQ9o6y32kiA9isS9buyhxoJ76dxD14PQUMsZR9\nkNJHN8jE7x4Rv7V1aAJ5GR3jnRw0OhOy4by6PFRyTQ2l4CKjdhGZtKQ6QdPaM4g3sBIzuQenQXRA\nmn0hUXnwGoWM+jnhZ7UZ2uMeGvZos+6LxNyTYwjZnDD865gS/D1kwNdbRmu65EcixiWyXAR6jue0\nTOYY0XjrkAkUyMJrkudNfbGwAXyTtRsnyDA2K2JRm3KUO6ZuwLmLZBZnyQmd+AIBA70h4GgJ/Uc2\n8xoNalVIjnQb+ogKmrCZJVrIrb8iDxlgK7cIagI9A8sOKSMztiU/qY1eQa3YJseHT8mBVQvTuV8G\nTw7wTET2Ji3uTWUQy3dtZoHwVs1G4KQIgDUDSZSdyySD35BBTJD2hfT1qNamoGVglMxOyu+RBGvN\nJshUTiDt7IBlPnBpgOjWS1hlUobETf1j1V6/96u+u0yYPy2Xn/EoOm/T+waDJfPoO9D6drqvBJf9\ne+iwFD4Ng2Fn206efE4heo2Ka5rBjgNI9OqRdN19ngSgkDf7LiucZ3+H2YFlnyHjWCulCEgzJsS1\ng6DWDCWCW9AEgIaWtaXjK8KocLreH4q+hnEPQHusVkPqifmrMUz4WgnBNhKRmqgcrcBBWQNIkgP+\nfpjw/3I6N9r0oCeItDuoJpPyYwQlAhcgtICwAOptzUiMkhuDNrcCW3NQy9OlEArqEEH23CdrlH2o\nyNlNUNSQn/6e1Psc0MHNwtDk72XWNFHTHG9p9YxnaS/qOZus6tDrLbGsybI5JI33pcIubLrN4dZa\npkCjUQJgK4nOpSQywJXDybumA8IwvDdHQB4eAhncH6tgJNLRNvjD8ySZPgClzlXDOCCCW4mOBaaQ\nuWIfBH3DVfWG3cPAQbco2Am73KxQRckJFfH1SQpdO0yDxXayWMk5VKy4sE74JB2isHuVmoI1TlLZ\nfe1X53CBe9Zqe4WfZIM41z4TTudZVC06UZfJ6Zq8vnexDJvJLQj3E8ZM+yTwtU5sOEbvhGKFNRLd\nFigONad8PMQbCrkWCEejRTF/v5FELFE7A2mlM33MM8PiGWhdBNFyDKaZFTmFL0dqOixFMzF1Q66F\nayMXeK1elnG6SbPICLVlMhl8nMoKkkLTKmVi2xYULsKVXjnaE5t1QwpiPwR1uvBpCSMrctKzq7nh\n3jJhBEddrYhFsaGo/yVZtRWp9Jik0HqS/KDtQyRv4gLCOOxpsXRNWxwnP0lppJkdgs/bBMAgwpnf\nfcg5cCUKtuVpOyc0nYs9+u0p6XWaxWwB+20l9CBNqEON8UUl9uTgC0Zs4AWcodT6PzmAdgKZaSL0\nozV5iAlyb/ixd6IXlF/ye8XCOr3f3g/jEn7CwpM8JEvtYaiXRfSDOxg7/D1k6twLNT30uEDiiWGH\nW3e7uEQA6Z4n1+jeSUEw69d3GkLwpIDZRmK1bw5DYfab6EAHun3ZDAKNG1mqldoOq6AgqaGoyEel\nts6+HlvgfLqc4Wz5hGgGqSxpFrz2WDPAh7aDIiSL/EkOzjScDsWwsxPJ/3oEewFiBWCc2j5P8iIn\nr71t5Cq38WIN+PWI8eUKTxxlRb2CpdD+KEhk6lJkA5Hv+gXANM/08CxprhWpNJ2q9TLEZ5DTNwSs\nPT09Kd1R4ak4rlerO5/vLmiZjCN1cDKtzeFcWGKOcb9ZNgDQOJGnI1pDYuZ9DIQmA2Cd897JtA1z\n8Fa6TXKP8e5WZdRrcK4FOeehXGEiMqaXOKy1zOIg5cVo2Uth/GZCH3sVeykoqvrlIDrBhqdVTjnl\nxRjRCWxBb3aFOl+ITlxyrGpR6NJ/8QdIPc1vLL1EUgUIfxYyQpenlGQbCutbiRoPlmsGvxtYcELh\nIoW6APQHiq9iH2efC5VZz6JNKo2ss0esmF4AydrFlVCDIKRSX5EhlUHzONl3boKzQh7sIqbdKLHL\nGG/4TBNu1mY8mhaQU2x9l+vMXtrRITOU6AIftNQFcZBYs+MoWP7kvEynvLJOhMUIp8ZuqGQmXVQx\nT0iyn2OsaCNNLRwqWF4KUDiT/A20AOr0B24xPdrz5McoCXv7AbBVWuTYykO3RNsy3VYjwyL2J4jT\nNBH7Ah4XoM7DLoKwALqQexhPySE8Pmz+YfqzDmUBBoF35mh7ck/IS2owDmhzxvkinCOHUkMVvc+s\nj58opCANYo8eKDgi+VuO4YykI7TWC3YLFjZeXe8YeOi4mnFvq7mJl8sTRRTWqbkihn3R0koX4ERo\nTSh9feSCLBlYC3eiB+wzkfABty+rbLTp+0unDZf+wmG1GqV4Ubo3carmLU4NIAw+1g4FCDuVOM6T\nHSM5LZHqIP1wcnggjR8+CbPe/YYr4pDInS9K/vK78WxJOcyT6j52K9vVoScWPdOUeveKdNWUgw5C\ne2nKLXd7nMAjqI1NQoyruK66pKML8gYcsAgM7UyUCWfixiZaIQ2WZyPa628lqQctxplEUfOt+yz3\nhiK5IqNYaaFHFAdDmGfRCiiY7F0UQsvnJyNHBpzCz56y4zqCKaEuVlB1BWcvS53WgXwEzHSoCQ+q\n/zwKgu/6gRAZrq+O37kwClOgjOSqIsXYLkqV0CiXO7M8AinbBqvzmlRe+FwjttYRcKbuUKn1SNtL\npBoExWU8zehAqG4mYqOKfXanRQiJmkcPPZ7iFuVTZOrk1ONQmhawwPG4dDQcy409WpyqG1SGG8da\n0olKCqZZD3oyq7YU1Eb2uGb1JZweXIGB8F6hfWSrKNhCnqFdNcey1QKWNwVPNsH6ovJ0yxCVgJpL\nLUyf+bWoV6kIo+CwRaAFia8YLTLsWuziYA1HrtO3XJYHAg319YJhIZNBSl/7ZibE165AUQ3k5ei1\ntPeKwlpNCmGFhNV6klIodcYEje9y4DGHsebFMt1ICNSQjGtaBq0FOAefCHmGllSLoF22hKtibzUK\nzxZS52G+9663tQhwLVIeqLke46D32zrhlP7LiX9loDr14OJhmr3Gbsb8NmbPw+U8O4uvXSWGNWM7\njPVik5gcpP66P8SGgoYUSeX5NAeZOjmIyy8GC/QNvfTVfGmLUwcOySAf/pQS+jri+An323sG49WV\nSZhfy2D2s0CKeHoWHsqO7FdSXa1rd1OFFWWywNjWzEuSx9AS7BAjD0gT/DLHoPc7n6JZoSHVDJTo\naj9/jTLht9YJaYkcVq4kJDNy4erxPm4qOdH3Umwv8zGs7j1fsV9Dsqvvcek2EfbDoIUA7NqKz2+K\n7VLzZUZQgdZ6onABQxbNiji4krSGsu/o4Kn7HY+VdW0Eh9XtEcYNgwB/HmJhcoQ9ATJyReGh40SV\nHjBrFtBvUk1jZlJbMabbDAJVYxZ5bVj6YLGGZRDVw1eOYH+1Ptf1/w66R9LxZGyvJipqXtbM7UAC\nupLrjE4PY7UX6OnIlRimznI9qSnaOzkLSsbXfYV5VOEWBFWkGRSQ3qdiPXrYEoxqzboe6AlqN1qP\nKrmWRVSdDBscBr5RrjNPNnI4MjLXGsUusHwTVxV25janLwOynki5a2c249VHcECmIdOIqKuv8chI\nmVEsgrtRjJwQYipt1uNqaojN8lozkDWJbNwoKaDAaWwaKLiaGkHMefXbJKWXkxxzyoa/QrY7egoj\nqg9tfvcsi7DH8rZMZlIyI2sriIXUtMz7UmkznD9sBMeg5XsXHIghzhozQ4M2XeK4TFLQTeRVRlLs\nhYaKHY4y5y0AKSLLZnVQesrM0YbdE5gZCng9DQOBuVCaTbzmJlbR/U4owYTqEMJoX2kDBQbLGuXo\nT/K7k8EHa2SJshBsiubBHsYB8JlrvbpSqlD7CppTFmWUF+LhVE7UEt6TTNo0L8CCWY28sm7FJB0p\noFBFl6DXOaboppsjALnRFTATYNiG14BM/a6ZqceiUADqd6fRSZgAIk8yB1GaMzOggfPfh2O4KMnS\nTAU8Lm66MF06R2VuDne/fHHqDWVqfdwGHTK6NegyBfeb1ZOZulasUfCRZLNrbYncXZ/fgsOwShlZ\nr7MIE4D/+BE9yHTCocrT9m9LjknvAsdsZZ1v8XZzYweOAfHgG6bPAZDDfraXp38mhllO08kdpIzC\nujNiTA5p3zZK8dSyZifSdHLJJaIcissVL0xXz+qrs+zNZM9ldo79c4ZyRK+KF8qICuu+zq+i6YY9\njXKwVK5s18KBb/CWQo9fVYxwJYAWgYbs03iMv2LbNVwJSKo8eV/Y3qAe2BfWk/zu1K/sPuWLsPnE\nXrGliOgn8Rk6ZTbDq6VuaN6MJyEZ68tUdMj6gJl9fZsQCQrqGz1KZPVavAgwlfiwIud8mxHq4hIM\nuYvD0mgrzEbmB6MzThaWdsLUDdq+Zt8THXfUlhUZN5SOYG1qWSkO1Ma03ESA79uvCPonCinRK43H\nTOoDpNvAu0JgXy3B2d2AdxF+ZHaxEkZ3ThxEheYmAurKOxQoJ04KbjE+TWqpUpmL5OKMrCco3ncm\neoH3K5kHyv3NR7IB2jsfBYL8QI2QD9BmTYEYbS0m+G5bdpJlmiDRSvyPMYdYbk9OpphBDoijN1Y6\nTiqvtOGrU3WViu0XRVB6f62uEIDKFk4NfzSXxRV9W6EbkYh19ta4LopqXzMOAG83uXyp3H2VL6cd\nShkn1WgyBm9p5BWq21HckwoepIsjKc9dX26qe7nA1NPNQTLEwasPq4LRA+3EWxZcXCAIcD20lL87\nRXxQHZhk7QdBUFp4TQbemxptud6Iy/gMG2AFKzJKeSJ+kDEJQtj6m7Hdsn4AVdn0SUpqha4S110l\nXBnIXKfNHhQBWqg8Seu0hH5ybkiWYCOgXILurKAeKuKm/WkGg0Rkeqg3fZr0lQatIuM2OTybWzX9\nHrq4aaUdorxeHiE7HTCWGz2oVnbpue6ZAlqiPKWPr7Z3w1+5DkWAIVqWwAHQwayFhkco8AY1QL3L\nwFbT3Ac3FvyCTFGDM3bBCcUuMYz4uJBDJ7LQ8Wzv05ftZRxPMc55w/JzZINdFUmVSf6kkDOVvScU\nkzUekFIqNxYDzdEz5JHR7lnlAly69MyX2xukr6MBxiBV72FKzhad1K4Pygnzcl00pf/AcrlLwMvt\naRowQTahNVtd0JdsYs2B/CUav4VHIKO3rc3Tg0bS1ML1YvaALBM49StzZ3wEMTKyXiH4JGz1haLP\nxA5lhlr2abpk0KoodjfCa2phohXc+0WqTtoiM3zdZyilVPTrgtuxIrmTVfoEAB/FuQwyYwpqfhWY\nCEdNP8e6I4vOQHTI303yXHn+lLiRCnJRPEzHnQ8WuiEPojpiI9a3pn0hDTBMuLed2kkM7kFvZe8h\nQPBtA0GXhWLJxX2gla0D+b1Clzda0Ny0FEDg5pAJfURwB2iqN2V/CC76+ebbCmJt4joq9rNuG05j\nhZ6ur8jxItK0jYbMKpb9eRAGqbveRH4xuvPh4TpZeZtw5N2vTd3a0JnLfjYy+PjO7Y4QbiNW53uE\n3KFA6foSlJjR6uKxai2rjQpl8grudK6MSE9mLjjKWplm66sTfQJpwSQJQEKTovp93YfgnQqvj15A\n4e5+TZ0KCNeiAyRN5QUWlQJyiyU0Vfs84R0c8jQzcEhIPYVd6k2izVzbL7hz16yR3d9eAetZznkg\nJyZP3HIvO9pdEBcy4L089oNMw3CbOboh7VelK8u6o4GdOyoF5Ja5gF7X4Ib13mmnu2viTNnMmRpC\n0sJyudvpQVSw7bECE+BioER/lrQmMs0FPrpyLHd/JmkgJbb+m8xMeZ0t6nL6ifD7RhcRE7jLyfqo\n14zRCioe7sLinlGB2SFE5nGbw0PNJ02jcliLOc2EuvLqfRzgsvEd7gPZRrTVam4t2Gilh1EoTgnG\nczc25P24fEGYsqXT2U6+fQgKqWdJvEzyWqAHnnVFn4ST5nFAMPnUD5rJ3HSA8qdYVpvePsP0bufj\nV1QoH6Lxtzp0BxstxMh6/tfpZNKKwKJevWj2ZMM+yvwEwpSJSC8Ps2eU2pzjiO3g1MGqAa4xHBHY\nstEiePfw2gH32Lh6pOj5Ay0UJNGwWIz8Or+oU7CeSJS03jamlbN6xbcYPGEFa44vLYQis4cCoVuN\nV2wKypc0lGFpTso1cv8vs4emYkRSbo5HMXbX7dRoJadXT1RGg46OQzAl8iRGLuPbhJ8OfWrdzyJT\noTuDCx41AT35Kud4HFatluEJgFlhQVhJWooGHqrNjEEoK4WAsscjOHrTsQxMQFK4vKwhsX7wHKM9\nk1Gj0GKZ0JCPOtl6Ds0j9sGEBq2Znkq5QJgusnDrK34mXTDdZYja0ORzKa6+zt8R1CStHK3uJhaS\nNPApNX0RScg7ojmcvHDYZpdzR63GYn7rq8jBnm4+4y5wzyhayY3AmxK+npIQdzmp6LKiOm0kpxT9\nA90FFMVDzXx4h8s+kQOU4e1f1fHapjw0rA2T2VKLzNy8EgsvwPrtL0Cmx9IvAozM6pE+ueZnh4VB\nATFdnHjoyEIrTG3tICPdqXO6Km/yMmGGN3XRY8XjEba1b3F1qeTIsdOlJwW4waME/m4OJCsUuaDj\nriOQQNAtFYV8ImN6c0xHIYqFsnoRZFyt3lwA0pXZZnAb/QG8jjKt2QzR3nTSBMyy43rrExhTJNMD\nA+8nRQLqgFONgdtO0ANipii1WHdMf7QEpCiCXfKPpKT1zAzi87yo28FzlOZaUQcw9uGYCBjfp2ux\nQd9WRgZTx1c3uF0fvCWj+K2/U4iAQv9A7o/UJKKVvRvnQzTRLW6OqKChOYzWcGyuN1MbEXwgpx09\nkJhWHa8ecisy8am7IEFQrcIiU+sk9e/mRITPcKRUlQmZrFeh3RunKRUMKbl2w6mK3JFARbMXhwkE\n7CYh0dkI7jwR8JhYMYuybtYwIya9NL61ME3fkVub/gmDQM7i8PNEGuTi6TJrcE2F8tPC0S1qWU8n\nd5eKf/oUHRKwAWplJPqDKR1rRSxBl4/X0BNVyjTKp0fytwRXT0o2DBVQSsXcGg5RDvNB7+H9ahq0\nFbMCctBU5ImvqDYIKbeg6xzP9E0sYnY+HVH0ZFZgu3olMgzf7styeGW5VceaO0saiz0dMelxO8U5\nXkcjTSzyQYr4tU7jwWWa9tD0YNSQR1mtaMoMDvvIxrVApZVsoOkNnI3DPSYgmGOkcHWapbruEnYh\nqi1UKiu/gKxFta2W74ryGlKojToum2r3dw2we0jABJkseNVe92RyNNfFCZTj39dUjtZ11Vn+RXe0\nV/eoR6PYlzIJzdp6rgtoVhzKg9z61y02akRME5SdCeaGcOXQ/2lWl5mcr/RG6xogUec06TlAMAVs\nFvsiN0t7v2ni40K+SKZF4E+aZE/KJygsHXe8VIsml4jNLYvmCUg1qQZ3ze5w2JVstwv2TO0OMvGW\nofweejgh/eGvJuH97efoYPBar0dLnHeWEf5Wv43mrGeZLkSmw+ZJx5N9sryj4Go9T7198STnvphO\ngWiiGChhpk4k4rBplihq763ShSoyvUQsEc2W4cqqZSs0DBbOiq5G1QU+AAJMNQ2iLNcgM6dNQFTG\njIwbCmVKL1Fg2BTWxPROGJoDcOirqDaYEOuZJjkzSDZm9aupmNdt4Awm+nrV3G55TbjlxGAZvT9v\ngiCnbsvhaLx0XtHL1GuETheQXZ9cRaG81cjd5VLzNfhsVhkANPnR5xxlGMhKWfhG08mHsQ+HCAxL\nEcR+7rjfEd3Pvg1jt/nXEe3mSE/1tL6Nnp5OZ97iFrGxpSjaqi61GFDM336dNKLsNob9lPrMrwI5\n16oQhitg/mZh3OIiihfb+LaV2YIt4QfoaRKfpuv4aPHVKBVjo3WHx4iYo2FrwpNulRUZa3ue274V\n1PShDPl4eTx6o+1hJTuGkpvGYK8TA516p4sREa6NLwim6MP9nhdl2jPN8qiWujth/K35AGAX15G6\nf3t+mrQ3wq/oi6QnqK8H56YJVrQepLJ+pE0zjW9VJ9Lb8Bswd6VTWmE98ogsuY+Te+dvt48PLpMY\nVKdMSw04kaX4FnLQezL6DjwBH2gDdslCOLmMU558mq4NQKrldnbfdvUuhBohUK3ZgB6DC1qfFsLV\nJ/CC075ubU4ajJzAa51BzQltL6lu7nU9aQxkYjFzoT+19aIWfNoN8yz7O7+NnZsbdLtBrEKVsMNI\n1PeIOmt5oiy6cJN1m4/phGy2Ie/bZbfHRSHIfNoTYxzs3zDRsVPK6nKNiTZwRCOBlMIN1/KfaF1H\n07fX9P7QaMFakVte4gOntpAh2LKWmdEqFZXFEAH3IeOcuT4zP/MmDzOz/Q5bmHy/W8C5BsDD26ru\n4Mwn3YC/DX+obTUlTWozFgGakkhqR2/oGiSzwSedmKPN0wr9I+aZhNOdERH1NtMm0gRgOx+88PUx\n7Bq6kXofUnNpWNfykd5R8brC3hoaIz+GdNvZWtvkBVSxk/prpyafL5ndbebIBeLmXg2Km8b1aD+8\n6jPZAwNlplYzkFI6El8kuSz4HaetB/MFbGpL1fBKMQx4c8AMBC/5Do27VJButRE52dEII14m3abc\n3GK/JlRWJNXtnvvUM4bFIcO/iD5c9lHu+nZAaSQILCaj2cB4IZiieMhSuyvtpqBE3NswaV1q/vqD\nBqSbrF67Y6bRZ48L3aPFdglUbmuDQhtVXG/NWgtZYBrGFftHSnKyHdywM3OVCUmg15egIMk1bIfi\nuE8Xp8+6KwWeoP1qrdZPD2m1jsL4hug8aXP4UFfN0qVqtf0e2aXzZEf2Yk2d2y67t0D2xys9ONpp\naUu5SX4b6k43O8LJ1O6wAmQvezhNh9AA1SjRLaIphSf6utSGfczWKkSlqzqLWXeUIkEKIQ+xPvkI\nQNpd3qjygTGOtmuGVKR4qzuWbjcsj4Zybj9j/hISA8FPssvU0I5I402X6pobHssFYtTWTmKSANHM\nYGgHau1ZZMKSRXcdAPBN0WTxpQErtMY9kpAxmfTDW+aG5ScfXeR2rgTERFSpzfFVI+an4MzG/DbA\no5jruNSNvXlfOpe+XjXwLFWhM42xZoIGjcOGPuVK/aCggAcbRLJ9r3dBw512ObC9O+kz338ysEhu\nV3ESoZLbkzGNFqCLXsQBigdY81oAd6MFZRhdttaacePJyQ5C2x2L6zSw5mhkYyF0g4WWJMNdQnLy\n3KvN5DyFMDRL7gl/qQuDBnaPlT6fmaF5zDHvMuhCFVbXpd9uoXqs6Vg3LWnX+S/O3CLvHt9yuWMp\nPu01n8AcnEuFRzVWud0dEGNYcQwqIdgxuePWXotj9ixK2X5tP7+2vkdZBZNMQe63uz3SsvOxbIuQ\n5b2/wlIUEr6ZQa9U3g0k2hHT/YVRd9P8Np2XIDJu+Vq1lr26IRPxqc7xa+tltGwFMUKA4D13ihHJ\nuly3BCT+ndRLeZlpQTj4i2dg5hU2TqspwLPXoAN6e9qdGxpAt9dfa77SD1l/qHh3lKBZsYfp9EFX\nNRcF15brTN7EDARS8ZpKNVCD5nGbqBbGy4shhtuNW2dRiQJibw6rPKaforVvTxdah05zzFjA14cI\novBuBAY3Okj0d6K0fcne0B+PPGOaZQGaUP+13b+BKne23Li95dKy0cP0sT8rMqkoM+trCEcXUjKp\nw2KFrw0vOrXL1xTQMzuL/AhrHR4gU2/9fvvEkb4sbkEvX5l3YvluHCIPbp+ZN00JDO5x7E7p6zn/\nd++JTqsFmLU9U7hv2SeSVh+Fftq3jHiiuAgxBeLXL3ctAxrNkvvr4syDlNJOqCkWtUGvEAbjFLUg\nlBt+6fJb3SUOl1xSkUYxTSXdFpFqmfN1LqVkfAaVXJEe5mxfwYrttmMXteGLWK7vBnMUrH/47baK\nLr+4HZxO6S7v+pFNIsXqgcX/nMS0dPve5pJp9ZhXIzhJ5U+zwDOLlF304UuMKLg+JSUcbj9LL1f3\nn9BoTPf0TNmBUGzBdQ1pdWm3UT0Mior9h66kUErsnsTt/uL4CHbAqQiMb3YSdeu30aIaGd1Y4iHy\n/ZTCmTeeK/EQwtt73Tnv+L6u+7Uu1x3iiDiEceq3v1j31Sa0qMGmRxLrmCgvhrUCpCmQtRxrwxbT\n56aMpypwmTdJIirh5/plGNFzF4vm9PjZr8bo4joG00nVRprfShN62VuyWWpWUxKwof9yPoR7xLIT\nErYV8LkpIy7pgoF60y1ltu9pKfl49HmvVvuiHZ6vLo/6k+hRDoewWrBHDsIRvLtJo/xWfWISBBrT\nvTrX6jvvMMFU+gYNG413d4i7blak0wizuO/rVaGjTRppb7knz8Ok7SnTN5shJxibx8JF3xsFaoa4\nrWn56bU4XPnW7+tCR5ePqCKkfmKN5LEWrqe6BAPF9ytLWSHxW8HX0hbtmXg5+xFFiXK+qUEgPqLZ\n6mu5tvZTVExEDe5LMc7NORnusnCCOMalnXfO0LsH2pcFyrbiVMBOWlCaQxk9U5odaqVlOQiBdbw8\nDc6X4/br66lqtjbowTC57E/uaq+nA+aVr5Oa+O7XctJ9sqNH082uhBZa0LzVPpI+o/erYZNXQ0RJ\nFfjK6l+uNhgxTCublX3ZwQjU3YX9B+xGvI/+0o2jUc3RAS7ZCEq+EPK7f1l04XS6hVRXkHWZhTH7\nyzAHgU6FAWd3NLu2sEIbJlyZCbRLioXWrvcE1QxxtH1LEJXGNTtIFItR6HKKGup7TQvUOGII3zLS\nXzVdIfd1T7ERWXCUXz2fYEm3GaY4KBuBErqTrLS2q5685QsNxbBEmVSaAtj7PGdzCwJYCz18e3nc\nS4zryzr2XOPbu0jvDcxhD7aT0i5iMMqVfd3fbHn9QyeHdEgtuoX+vkmwTRdJRM1KG9T3Jn6uhBvN\nDLRsVnm9mCEUZg6vpzKF9nGbzOFJD6bKh24gpIQQKS5LDItNTtWcyqo7a84hs1CNOXDYZXwNM461\n1KAyVhbDOg1VuAeOu1BqSgVvCKLriHzoE7W6x6Jji+kU6Gmv8QO3Zu5I17YbHUZgBXZ3s95lMm70\n+qD2caHIstI7Wq7CQ+CGl/cjQPQ88pgmaiPkoVwxd3O4cpWOk/ejZZdXWAuaXvTsYLPmetV7pCdX\n3A0IKf7V0WGv66twqa+9HLC/krJzVD9SLMGOD24GBjVSJ4nXtY71RsOFlp22AN374A4gNO7Oxr/H\n93m62ySoPFt7nenkhCmRPlpeM+I2uTT8IH6/WWO0nUAH7hORPiECpQYCFe1Gp5+sfo/2cWhJnIoj\na/g1y3Kwy/k8WjIGSUfX176sDWOb9ZRyQJQNbjbxMDgi8nnDDMS+0fKi/iKUEWzX6KaxWnviUzoK\nhA1fCDMf4OK+vGVvcl4bSJoILe7diOtF5k6Wo7ioqUTec2Z9MTc9UWJrQt874VVRr23xFbV237pC\nCom3L2FyOJnkLtZ3Vb7cNDPin3fv0hq+uYeKIXqTPxtXdijd3PYpkiUwMnM5JjLxcGfSBh1o5nbf\nSFBtfOnwAgzyvWaI97KNBQ1Ri3vEyT8G+Qcb4ZZ+2934IgURHS94+OW7ikLWwWwRT0UxyYZriufq\nNNdybEsPLb/EtUSOjmTO+bb3voUm8qE93i3b/9NmoFxqsmAwhVrKm8vjnlO489LW00Aj1LkW99JF\nN2CDrxikVzV2d3JnyivxmcWU2HST4VSpufEfhFYwva/DF9cATk4ENpN2yUFnd19jA5oYvpDihsUb\nvvKMJiv0qygvYpm+/oZlGgCYk6X76IIxmtXDN+/SWtE6PRmKuLguEDRuwQRFxYs+DnlyC0X0EiVv\nthIpc41J9Btq4wUV7u27ThR2Ix8Ol+gKgI5LoRPuRMqV4FIoyq3khu+KbM9SXWgkaz24tOdXWTKw\nz+INSLbXkpNCrYnDzrDOyblqvIl03pP3SSpjhTgYVHseG+JWqM36N7che4Rzi2wfwdmiqPSZV0UO\n9F/mRNOI9T7me9GsbPgWEjm71Cq5KxrGmKxjdenu78mqc0thdCFSwNpfn+kZxLDbPKfIwG2N1g3l\nGq25As8dX5WG/NJtbmp+GjVIMyLn06QLXn9jd8Y3zIMqKU/hWAnJsnS4Z1nhQsNLwsr4WQu9n5SC\nPtgn2O81f7n969ybbcDJ3jFu+t1LaDe4LfFX7d846NOdPXzt/4cv/ejR14La37xgFbaoBd8+U5KA\nJk5mP8A9Fyin6CKukG0RCqySLfPRUqFiM7ylV/irUaN/YyRHZZUTpUFF9pZkjyzUrI+aEIgHevrO\nhZK3VNXh+rcZArp9XozPJQmDTupBY0V5MxnhSUOxuHR10IoxgSFXNNMDg44wtc5v2o9CVVcE0q+2\nv7bBW3OzoyJQzjG5Wdc5rKioRr/97YFBY45lnZEs1GqvnNnxuZuIj9Bqx3cLIblvOWocWc6XnrPW\nPlRxXFT1eN8zXTsMKEazPp4Bbe4dYq3FfRUgNe6p9PFt65EkXJrSQ741kKr+6qC386aoTW/2JwnH\nqUefSqiu9hR0OmA8dajO7njF9nqMlRgwLx0y66Goqs2QLK88Sp1WSe6Yj22hYbX3HrPnprFQmVr/\n9hoQ7hllJDVaSYQN7m7n6v4X5iJHopK2LQv3h29mv30di+Y0dCBIFmqeRuoEi3nfi/RxJSamXXXU\nnNBTIhskWLnvikVfLTK/gbIcTXGljDtNPtMis8siEWjgFl5sfqLcir4itHN7KrdJMtoKOq5E3I8l\nIAMwTHmY3H4FIPIcvvScfpnzXY0dJQ57xkViPcgXW3Luy4qeKodLcBPQFo7y9jWRVKauHMbKlR6w\nwjnsHF4ukdumkHv99rQYN68wln8c99vd7Y4bIibgTF4jOK0IGHmPUynZ2Z6rTk2lUlg82rexHfrI\na5a0cuHdQ8oIlsOuFi9pTCs3eK6ofuMqiucfaZ+3bRJLy3oAd0ldFE2HRKKc9fpKreZU5/Wt3fM8\niSSAKhpG0O5m5dbBhU6n+IgBx+u1fCAzo3MFpdNftEzmcUTrijVfFzdurywuRY+L+kpeycOmXy4e\n8fhCpZVnhEazOzpp6ANnPx7xuAv8J/JnNy905FJrLq9yYnDQXeZ1RebYzQDvXGA0E0q1QrOK4FR2\nBhEYiG63Cl9TTmkPpm2q2p3IpRDie+OpImL3hSIzj5I8rR0y+JvVITvz4Lwd15jF/Vu0JtuBNxdX\nhN/IAY6YdHdCRdfDtqLV90vAUVm4bNBpxhRaC1svrtkh3dm7iTSnP7hvzRWsWhxPnq8659JcnwQd\nkJaNMAp3H7uNF3fz9GylQYlSXBNBO4vo8Vlc2XSjIVx5lSRk74dvd6Lip2ReUDZp7aiF1nrvR5ks\nO31aLehP69XI0EYuug3X/b0RwN3wiVDRuvV3/7u7j/t+YesP2reHs+IBRCzDaYAUr1Hvc2g+6R5v\n8OyRQaB9AeSvW8JTfvhtKrjN3xKw9SckQfezKNt3qwr9oT6WmlR9XNVH6cdTGgllumqEutan57Nw\ngb4HDFNXnV0wzMDhjl1tMlP9zl2K3AYaecQ1vzl7kj3TZSPu6huADeL3wPIDseWyzguqhy8SdG+0\nVIATZyLfj9iiZ/msaQnFVtMrULhv7bVhE+jK0vDJ1XsBhNF0WaZrXUA7WSHCPamNfDR1GFG5lxnA\nxQq4CHbt/ZVe6NO0RKlWjJ+5nnaNS0H0b60Sm22UV/MhJIra14196WfyUCxtzqgcQe5Y1jiv9JyM\n2YrOm/Tin68cmkTZNuFrlcSra9fkU3lhafJIPSpSpcOFtL6pb9w8+9tXfbq9LjFr/ZaCoFd2q5t7\nSv9eGUbb6tki5TVbe0nhzD64kv1dKOBrY66ZccLv/VpbuWHJiDSqDlNPLGyUD3L2hXwlVeOoio/b\n5PElpedtbmDhg2TfcLO/EiVfyYAWxOnMfrObW/B1xxOy28qTA0jWcWlZ3LGy4VWnyMc9LNmMfX+F\npmjJDVhneeJrCMTlBotIf1EovDPJLbVxUcevnkrgMKJKu16Zhnzz5gt6mJ1DS5T9bpBi96wdHAIN\nhL6X8t263r1Nr4do9Ltnv9Dda576vYpZ0RwUE/K1UX5d1aefp2AMrVBxJVAMj+lOnztuDynvS46r\n0IHC9bXjxhxt3yZuv0prOA9X48S4kw8xdH1uCmI6epHT/609BQtXpMXVIdoqeS0SNu1g4j4hLHjS\nQjh0cz4oNGoWVLMycUEOiOvAwDwcy4VfhtOknuJBuqEdeQormmsmG8jQE3jYPNTXUYZrpbnP1MQI\n/VUy1cc9LJ3rPqbr9O63zP90SihdaTFefxffcuqKZdq+zJfSc5aTGrS8lC8z7KYYRnxzXXmb+Iq7\nT6Ne+dKx36Pb/Ebxq9QnRN4W9JRoXopqs73Tf2U91oie/vkUlFOT3e1Ro57NU4yaKWl3rrW8q2VR\nUW6cERdyVarRE5nRCmS50JIj119tA8L64pBoIc94GcHOalUzWONl7XzhNQItd1RZqZJ20O7eR7S7\ncpdUD6Nd8yXvLvCnUWMOH3JePS+3eTk0Ewk32mu9fMB17Z41RMdX+LRHi2/YW+fREVm+6g2k0z3v\n0swbWvwmxw2EiBVXsBx+b2CdE3wtyp5zltxf3KUD5UmAfFObPHbYWa1df2INSqBtIWvr38v4HCtu\nt0ev78JGwtYdrSrdaD5rse3OdqqVSfdn8wtE4dWyB7iRktUi///h3/7nb//j8x8fJGLx/1DqCKQI\nZ37+80+fv//8++cPf9U///KXT/v87ad+/vyR+f389+cfPv/4KZ9/1kjR//7dH3/7w9/86b/+9Z/+\n9Hd//OvPP/3lt4Dc2x3+yF1Fjfe/RVPQCjsZiJiSgdeYlpaCJXrUOYH/DpwQLVd9e3y3110c4W8t\n+XnuHs2qADe7wYi7ovtd1dcpFd4jALcCrLziwBVmw6JHOLvyq1mGvNN0stLe63WZRLEyomtfPdkZ\nAgWBK8msm3w3IxcnA8au0ewaeJEgkfLoYFbWvXkZOSiiLepcTvaY/sQFUcSz0b1qRrHXNYVJc3fA\nNldFZSU0rb3nTbAdjO31beykg9xOKS6Cd1NHus37DpOGnQyoTL+b4Y4zwtdRIxP1MlRnIHfGJdYY\nRSywXTXI5co9hXxc8TZa3L16Ih8RsnFUg26s0AOiklc5+0ZcLVgXnJivivC9JuSg5v6qpaGFurEe\nOCon0uLwHcwGzNF9ejtqnIoB48AUv8og2L3I9tFn8L4OUixBtexYsU9eZdHcDhMxb1Rdp23sLRol\nBJ5V2Fpfmw2UC9vCOOHqdxslGSii44Ek+7WUcaUD+407d0j2P51zudwQbMRO2VUAtCzv3gxr9ldW\nI7j14/ZNVbIE5fGddLvY7vfcxmtbS4+iSYMo92pubZ5vJyG94uh5L/a7foNiMGcm3dhpPAaDJlP0\n9TW3FPWRyWA0X5Xoy056XKSMQfnt/wCluLM+CmVuZHN0cmVhbQplbmRvYmoKMTEgMCBvYmoKMTcz\nMDcKZW5kb2JqCjMgMCBvYmoKPDwgPj4KZW5kb2JqCjQgMCBvYmoKPDwgL0ExIDw8IC9UeXBlIC9F\neHRHU3RhdGUgL0NBIDAgL2NhIDEgPj4KL0EyIDw8IC9UeXBlIC9FeHRHU3RhdGUgL0NBIDAuOCAv\nY2EgMC44ID4+Ci9BMyA8PCAvVHlwZSAvRXh0R1N0YXRlIC9DQSAxIC9jYSAxID4+ID4+CmVuZG9i\nago1IDAgb2JqCjw8ID4+CmVuZG9iago2IDAgb2JqCjw8ID4+CmVuZG9iago3IDAgb2JqCjw8ID4+\nCmVuZG9iagoyIDAgb2JqCjw8IC9UeXBlIC9QYWdlcyAvS2lkcyBbIDEwIDAgUiBdIC9Db3VudCAx\nID4+CmVuZG9iagoxMiAwIG9iago8PCAvQ3JlYXRvciAobWF0cGxvdGxpYiAyLjAuMiwgaHR0cDov\nL21hdHBsb3RsaWIub3JnKQovUHJvZHVjZXIgKG1hdHBsb3RsaWIgcGRmIGJhY2tlbmQpIC9DcmVh\ndGlvbkRhdGUgKEQ6MjAxODA1MTQxNjU3MDQtMDcnMDAnKQo+PgplbmRvYmoKeHJlZgowIDEzCjAw\nMDAwMDAwMDAgNjU1MzUgZiAKMDAwMDAwMDAxNiAwMDAwMCBuIAowMDAwMDE4MDIwIDAwMDAwIG4g\nCjAwMDAwMTc3OTQgMDAwMDAgbiAKMDAwMDAxNzgxNSAwMDAwMCBuIAowMDAwMDE3OTU3IDAwMDAw\nIG4gCjAwMDAwMTc5NzggMDAwMDAgbiAKMDAwMDAxNzk5OSAwMDAwMCBuIAowMDAwMDAwMDY1IDAw\nMDAwIG4gCjAwMDAwMDAzOTAgMDAwMDAgbiAKMDAwMDAwMDIwOCAwMDAwMCBuIAowMDAwMDE3Nzcy\nIDAwMDAwIG4gCjAwMDAwMTgwODAgMDAwMDAgbiAKdHJhaWxlcgo8PCAvU2l6ZSAxMyAvUm9vdCAx\nIDAgUiAvSW5mbyAxMiAwIFIgPj4Kc3RhcnR4cmVmCjE4MjI4CiUlRU9GCg==\n",
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAASwAAADuCAYAAACDKjp+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3XtMW1l+B/Dv9RtjsDHYBvMMDxMSQhKGvJhMks4j+2h3\nZmf6R1upVdXuP6uuVm23Urt9/NHZVaWqav9oVbVSd6VqpVb7R1czO4/ddnYymWTygAx5T0KAhPBI\nwIAxfkBsbGPf/mF8517bvGaA5JrvR0LYl2tzyQxfzjn3nN8RRFEEEZEaaJ72BRARrRcDi4hUg4FF\nRKrBwCIi1WBgEZFqMLCISDUYWESkGgwsIlINBhYRqYZug+dzWjwRbQVhPSexhUVEqsHAIiLVYGAR\nkWowsIhINRhYRKQaDCwiUg0GFhGpBgOLiFSDgUVEqsHAIiLVYGARkWowsIhINRhYRKQaDCwiUg0G\nFhGpBgOLiFSDgUVEqsHAIiLVYGARkWowsIhINRhYRKQaDCwiUg0GFhGpBgOLiFSDgUVEqsHAIiLV\nYGARkWowsIhINRhYRKQaDCwiUg0GFhGpBgOLiFSDgUVEqsHAIiLVYGARkWowsIhINRhYRKQaDCwi\nUg0GFhGpBgOLiFSDgUVEqsHAIiLVYGARkWowsIhINRhYRKQaDCwiUg0GFhGpBgOLiFSDgUVEqsHA\nIiLVYGARkWowsIjWMDc3B7/f/7QvgwDonvYFED2rZmdn0dvbi3g8Do1Gg69+9aswmUxP+7J2NLaw\niFZw584dxONxAEAqlcLIyMhTviJiYBHlMTc3h7m5OcWx0dFRpFKpp3RFBACCKIobOX9DJxOpzczM\nDCKRCK5fv5736xqNBi6XC8XFxdi3bx8EQdjmKyxY6/qH5BgW0TKfz4eLFy+uek4qlYLX6wUA1NTU\nwG63b8el0TJ2CYmWTUxM5BwrLi6Gx+NRHCsqKgIABIPBbbku+hxbWEQARFHE1NRUzvHTp09DEARY\nrVb09fUBAKLRKAAG1tPAFhYRgPn5eUQiEcWxkydPSmNUNTU1OVMaGFjbj4FFBEjjUnLl5eXSY0EQ\ncOLECcXXw+Ew7xpuMwYWEXID6/Tp0znnWCwWWK1W6XkqlUI4HN7ya6PPMbBox4vFYggEAopjFosl\n77knT55UPGe3cHsxsGjHm56ehnw+4le+8pUVz9XpdHA4HNLzR48ebem1kRIDi3Y8+XQGQRBQXFy8\n6vldXV3SY5/Phw1OvqYvgYFFO5p8IigAvPTSS2u+pqioCDabTXo+Ojq6FZdGeTCwaEeTt640Gg1K\nS0vX9bp9+/ZJj2/cuMFW1jZhYNGOlpkMCgDHjh1b9+sqKioUzzOTSWlrcaY77VihUEjx3Ol0AkhP\nIh0cHEQymZRaTqIoKj40GuXf+kgkArPZvD0XvoMxsGjH6u/vlx4fOHBAmtV+9+5dTE5Obui9vF5v\nTquLNh8Di3Ys+WB7XV0dACCRSGB6ehqCIKCzsxM6nU4KMkEQIAgC4vE4rl69qniv+/fvK8a1aGsw\nsGhHSiaT0mODwQCdLv2r4PV6kUwmUVFRgfr6+ryvFUURn332GWKxWM57arXarbto4qA77UzyqQjy\nNYKPHz8GkF7svBJBEFBWVpZznAPvW4+BRTvSrVu3pMeZqQzxeBwzMzMQBAFut3vV1+cr3Le4uLi5\nF0k5GFhEyyYnJ5FKpeBwOHJKycTjcXi9XumuYb7Ayi5PQ5uPgUU7jjxYuru7pceZ7mB1dbXifFEU\n0dPTg56eHjx48ABAOrCy67lnb1pBm4+BRTuOfIMJl8sFIF2xwefzQRCEnMAaHh6WNlIdGBhAPB6H\nTqdDSUmJ4jwuhN56DCzacWZmZqTHmVbS5OQkRFGE0+mEwWAAAPj9fvT39+P27dsA0msIE4kE7t27\nB0BZ4A9IT4mgrcVpDbRjyWerZ98djEQi+OSTTxRrBDN3AYeHhzE9Pb2NV0oZDCzaURYWFqTHR48e\nBZC+uzc7OwuNRoOqqioAwPj4uCKsdDqdYqmO/H1o+zCwaEe5efOm9DgzfjUxMQFRFFFZWQmDwQBR\nFBXLdo4ePQq32w1RFBEKhXD27NkV318URW6uuoU4hkU7Sr7xq0yJmcxgu/ycmpoaaU5WKpXKWTCd\njTXetxZbWLRjLC0tSY8z41fRaBR+vx9arVYKpkuXLknnHThwAAsLCxgZGcHY2Bji8fiq32NiYkKx\nUQVtLgYW7RjyltPevXsBfN4ddLlc0Ol0irlUTqcTfX19igH2srIyWK3WFauMjoyMYM+ePVvzAxAD\ni3aOzKRPAGhoaACgvDsoiiLOnTsnnZMJOK1Wi5qaGjQ2NqKsrAzxeBxjY2N5q4xmL4imzcXAoh1B\nFEXMzs5Kz/V6PSKRCObm5qDValFZWYmHDx/mvK69vR0NDQ3S3CwgXd3B4XAoWmy0PTjoTjtCvnV+\nmdZVVVUVRFFULIgGAIfDAY/HowirjMz0h3zYyto6DCzaEeQbnmaK9cm7g/kmgmbOy2e1wFrrTiJ9\ncQws2hEyawEBoLm5GQsLCwgGg9DpdHC5XFJ4ZWi12pw1hXJms1mx1ZccA2vrMLBoR5APuNtsNimg\n3G43NBpNTg13t9stVSFdyUqtLK4p3DoMLCp4+e7mySeLyruLGat1BzNWCixWHt06DCwqePIB99LS\nUszPzyMUCkGv18PlcmFoaEhxvslkgsPhWPN9rVYrjEZjznHePdw6DCwqeIFAQHrs8XikQKmsrIRG\no1Hs/gwAtbW1OfsO5iMIQt7a72xhbR0GFhU8+az06upqaQC+oqIib7ispzuYsVbtd9pcDCwqePIu\nmlarlQKrvLwcN27cUJxrtVo3tBYwu4gfbS0GFhW07AH3SCSCaDQKvV6PkpISTE1NKb6+kdYVkF5E\nzR2ftw8DiwrakydPpMfNzc3S4ma73Z6zLZcgCKitrd3w92hqavpyF0nrxsCigibvDjY1NUnrCcvL\nyzE4OKg41+l05mzvtR6ZQoC09RhYVNDk6wOLi4ulFlZ5eXnOYueVtqZfS74JpvLaW7R5GFhU0ORj\nWEtLSwiFQnm3mtfpdKuuD9woVh7dGgwsKljysLJYLJibm4MoirDZbDnr/aqrq6HVatd8z2QyiQcP\nHuRsmpoddvJSNrR5GFhUsOQD7vv27VNMZ/jss88U566nOxiLxXDx4kXcvn0bly5dUgzaZ09v4DZg\nW4OBRQVLPkbldDqlwLLb7YoWktlsXnM+1fz8PM6dOye9RyKRUOzAk/16n8/3pa+fcjGwqGDJKzRo\nNBoppLLHryorK1fdmsvn8+Hjjz+WWmwejwdarRaTk5NSlYfi4uLNvnzKg4FFO0I4HMbS0hLMZnPO\nZNHVpiWMjY3h0qVLirt+Q0NDSCaTAIAbN24gkUjkXQRNm4+BRQVJPuAu7w6Wl5fjzp070tcEQVhx\nprrX68W1a9eQSqWkYy0tLTCbzdLzWCyG8+fPc/PUbcLAooIkH3Bva2tTBFamdQSkx7P0en3e98ie\nWNrc3Ix9+/bh9OnT6Orqko6Hw2HeFdwmDCwqSPfv35ce2+12KbCyZ7I7nc68r/f7/YqB+ZKSEmkv\nQ41Gg7q6Orz66qvS13t7ezft2mllDCwqSCMjI9LjxcVFRCIR6HS6nPGrlQJLPmAvCAK6urpy5mnp\ndDqpO7nWjtC0ORhYVPDkC57ltbH0en3OHUMg3Z2UF/XbvXt33vOA9B1G2j4MLCo4qw24yzkcjryV\nRYeHh6XHNpsNra2tK34vBtb2YmBRwVlYWJAeywfcswfX83UHE4mEojvY1dWlCDVRFPH48WN88skn\nmJqaQklJyWZfPq2CW9VTwZEPuFutVgSDQQiCkLM5RL7AkncZ6+rqUFpaKj1fWFjAzZs3pfcJBoN4\n8cUX4Xa7c7YJo63BwKKCIw+dQCAgLXiWD7ibzWZYLBbF61KplGIHnUxhvszxwcFBJJNJqVrp3Nwc\nPv30UzQ3NzOwtgkDiwqafP2gfP/BfLPbJycnEYvFAKSX72QG2q9fv47x8XEA6VZXe3s7NBoNzp49\ni2AwyHWD24hjWFRQ5APuLpdLukOYPbierzsoH7vKtK5mZ2cxPj4OrVaL48ePo6urCyaTCQaDAYcP\nH4YgCBgbG9uKH4XyYGBRQZEXzmttbZVaWPLxK0EQcjZKnZubk8JNq9WiuroaoihKFUtbWlpyQs5u\nt0uTSWl7MLCooMgH3HU6HRKJBMxmsyLIbDYbDAaD4nXyca+mpiZotVqMjIwgFArBbDbD4/Hk/X4t\nLS0rztGSLwGizcHAooKSGWsCPq/6mb24OXv8amlpSRFYjY2NiMfj6O/vB5Au/pevbjuQbq2tNFue\ndd03HwOLClYmsLKDIztgHj9+LD2uqqqC2WxGf38/4vE4HA7Hmrs7r9TCSiQSX+SyaRUMLCoY8mBy\nu91SYMnLFet0OtjtdsXr5OsOm5qaEAqFMDIyAkEQsH///jVLx6wUWGxhbT4GFhWM7GkL8XgcRUVF\nirEkl8uluGMYDocRCAQAAEVFRXA4HLh9+zZEUURjY6Ni4uhKioqKUFRUlHOcLazNx8CigiEfcM8U\n3ctuTWXvbiMfu/J4PPD5fPD5fDAYDGhra1vxe6VSKUULymaz5ZyTvbM0fXmcOEoFw+v1So8z3cH5\n+XnpmCAIisXKmS27Murr63HhwgUA6fDKvpMoiiL8fj9u3bqFUCgEvV6P7u5ulJeXo6ysTPH9AWUR\nQdocDCwqSJnAkk9ncDgcihCSB4zH48H09DQCgQBMJhMaGxsV7xeNRnH27FlpJjyQ7vKdP38eR48e\nzWnJAcpF2LQ5GFi0qsXFRXi9XkxNTWF6elpR31xOWFqCNhaDLh6HkG/sRqNB0mDAktGIlMEArDCQ\nbbfbUVNTg+rqaphMpnXXSpd3v5xOJ2ZmZmA0GhUBk90dvHfvnvR4165duHz5MoB0/Sv5NIbFxUX8\n7//+74rfu7e3FydOnMg5znlYm4+BRYjH43jw4AEGBgY+P5hKwRQMwjwzg+KZGZTMzqIiFIIxHIZx\n+bMhHIYuGoUuHodmA3fERI0GSwYDkiYT4hYLYlYrYqWl6c9WK6abm3G7szPndYIgYPfu3Whubs4p\nFSNf2Gy1WjEzMwODwbBiYM3Pz0vdRafTCZ/Ph/n5eRQXF6OhoUE6LxaL4Ze//KXivbu7u2EymRAI\nBHDu3DkAwCeffJJzvevZSZo2hoG1w0SjUdy6dUuqLqCJx1EyOYnS8XHsHR9H6fg4LJOTMPt80GaF\nUMJkQnw5WKJ2O0INDUgUFSFpMmHJaERyOYRSWm1OC0pIpaCNxdKtsFgM2sVF6BYXYZifhzEchnVs\nLB2CCwsYffFFTOcJLFEUce/ePUXLCEh35+RVFqLRKADl+JXNZlPsdiPf+Xn37t24evUqgHT9rMxd\nxHg8jl/84hfSeZlNKDKtPrvdjra2Nul6tFqtolW10mRT+uL4L1rgwuEwLl68mO4ypVIomZiAfWgI\nB4eGYB8aQsnjx9Asd/NSWi3mq6sRamjA5JEjiDgciDideOJ0IupwILkNe+8JS0vQbHA6gDysAOVE\n0Ax56yoYDEotsqKiIvh8PkQiEZSWlqK2thZAOqzef/996TV79uzB7t27c963ublZCqzsLmD2hhf0\n5TGwCkwqlcLt27fT27SLIkomJlB98yZct26hfGAA+kgEABAvLsacxwPvoUMI1dcjXFuLhaoqiCts\nebVdRJ0OyS1omchnq8v3JayqqsLAwAAEQUBHRwcEQcDS0pIirDweT96wAtJVTM1mMyLL/65y2XcZ\n6csT5OU41mFDJ9P2SCaT6OnpwczMDDTxOFw3b6Kqrw/OW7dgXq5WMF9VBd++fZjzeDDn8WChqgrI\nU8+80D333HO4du2a9DwzMN/a2oq9e/diaWkJ7777rvT1Xbt24eDBg9LzRCKBQCCASCSCyspKmEwm\nhMNhnDlzJud7HT58GDU1NVv7AxWOdd1dYQtLpURRRH9/PwYHB6GJxVB58yYOXb6MyqtXoV9cRLy4\nGDMdHRjYvx8z+/cjssIC3Z1GHlaZQfnMWNTs7Kxi8DwTVktLS3j06JFUvSHzR16r1aKpqWnFSg4c\ndN98bGGpzOLionTXyjoygl0ffojaCxegj0QQKynB5JEjmOjuhm/vXogc9F2XpqYmjI6OKsag2tvb\nUV5ejsnJSYyNjUn7Dmo0GthsNuh0OqnGlt1uV2y6mnH8+PEVKzlQjnW1sBhYKjEzM4OLFy9CE4uh\n7sIFNHz4IewPHiBpMGDi6FGMnzrFkNokJpMJoigqpkSUlZWhpaUFVVVVUsspEAjg8uXLivPkGFgb\nwi5hIfB6vejp6YEuGkXLBx+g5b33YAoGEaqtxa0//EOMnziBBLea2lSZSahGoxG1tbWoqanJO5O9\nrKwMra2tuH37dt73WWmSLX1xDKxnVDAYxNmzZ6GLRrH7vffQ/ItfwLCwgOn9+/Hpn/wJZtvbV5wt\nTpsjFothdHQUZrMZRqMRxcXFOefs2rULQ0NDeRc6r3eWPq0fu4TPmGQyiXfeeQdIpVB37hza//u/\nYQoGMXnoEAZ/8zcRaGl52pdYMAwGgzQ2tR5msxkNDQ2or69XlJMZGhpSTJXIeOmll2C1WjflWncA\ndgnVpr+/HwMDAygbGsKBH/8YZcPD8Hs86PmLv0BghTtRtD56vT6nPlUmrGw2m6KW1koikQj6+/vR\n39+Puro67N+/H3q9Pm93EUh3KWlzMbCeAalUCj//+c8hLC1hz//8D1rfeguLNhv6/viP8ej48R05\nX2ozmM1mNDY24v79+9LAeL5wCgaDKCoqQkVFBR49eqT4Wk1NTd6Z8+Pj45ibm8PRo0dXLPKXvbUY\nfXnsEj5lfr8f58+fh+XxYxz6l39B2fAwxk6dwq1vfQtLsrVvzzKTyQSXy4Xy8nJYrVYYjUZotVrp\nF1YURang3cLCAubm5jAzM5N3KsCX0dLSoijil9He3o5UKiXt3GwwGFBeXp5TvwpIryt8+PChoqt4\n+PBhTE1NKTa4yLBYLHjppZfw4Ycf5sx2f+211zgXa/04reFZNzg4iLt378J14wYO/+M/IqXT4ca3\nv43JY8ee9qXl1djYiNbW1g2VfdmIRCKBsbGxFe+65WOz2XD06FHFwuaVZp6//PLL+Oyzz6Qa77t2\n7VLUc89obGyEXq/H4OCgdOyFF15AKpVCX19fzrhXW1sbAoGAomIEALzxxhvr/jmIgfVM+/TTT/H4\n8WPs+tWvsP9HP0K4rg49f/VXiJaXP+1Lk7S3t0t79D0NoihiZmYGvb29eWtLnT59GhaLZcXXT0xM\n4MqVKzmv8Xq9uHPnDkRRRHV1NbRabU7radeuXaisrERPT4907MSJE7BYLLhw4YKiEgQANDQ0KMot\nAwysDWJgPasuX76MqakptP7sZ9j7059iqrMTn37ve1jKs5HBWqxWK0Kh0IZeo9PpVtzRpaurC7W1\ntQVzS1666ypz6tQppFIp9PT0IJFIoKqqCk6nU9rlOWPPnj2w2+24ePGidOzrX/86kskkzp07p5gw\nWlpaqqhuCjCwNmhd/8NxVHCb3b17F1NTU9j1wQfY+9OfYuzUKfR8//tfKKxsNpsirFZrbQCQit5l\nh5VWq8Vv/MZv4I033kBdXV3BhBWQ/tneeOMN7Nq1Szp27tw5GI1GvPDCCzAYDPB6vYhGo+jo6FC8\ntr+/HxqNBl1dXdKxjz/+GGazOWeL+uywoq3BwNpGPp8Pg4ODcPf24sCPfgTvc8/h+h/9EcQNdrms\nVmvO3S6Xy7VqDfHKysq82069+uqreO211wq+FMrBgwfR3t4uPf/www9htVpx5MgRCIKAoaEhWCyW\nnF2hr1+/jurqamnzimg0iunpadTV1RX8v9mziIG1TVKpFC5cuICimRk896//irmWFnz6Z3+24bBy\nOp0oKSlRhFVNTY1is1Dg8zlAGo0G7e3tOQPCL7/8Mt54440dVRXT4/Eoyr188MEHcDgcUmvp9u3b\nOJZ1w2NhYQHj4+PolFVA7evrg0ajQXV19fZcOEkYWNvk5z//OZBK4bl/+zdAFNH3p3+6ZgXP7Hk8\nVqs1Z15QW1tbzjwhh8OBWCwGg8GAo0ePKmZhC4KA119/fV0bhBaiQ4cOSY8jkQgSiQSam5thsViw\nsLCAx48f54TW8PAwjEYj6uvrAaTvZkYikbx7EdLWYmBtg8z4Rv3Zs3B+9hk++/3fX7M+VXFxcc7i\n2UOHDuH69evS8+PHjys3jgDQ2toKn88HnU6H7u5uaScYIN0tfP311wtqjGqjBEHAr/3ar0nPe3p6\noNFo0NzcDAB49OhRzu464XAYCwsLUvlkIF2pYbUxQy7J2RoMrG1w5swZIJlE69tvY665GaOvvLLq\n+YIg5IyPdHd3K+YnnThxQro1n7F//35pY9DOzk7FJMri4mJ0d3dvxo+jemVlZdLjzP6Fme6dz+eD\nKIo5YRQMBlEum3ISDAax2h32Fq753BIMrC2WuSPnvnoVlqkp3H/ttTWrLFRVVSEQCEjPKyoqYLPZ\npIJxZWVlSKVSinEsQRDw5MkTJJNJuN1uVFdXY2JiQvr66dOnN/PHKjhGoxEmkwmpVArRaFRRAx5I\nj2XJ56PF4/FVy8dkD97T5mBgbbFMyd36jz5CpKICk0eOrPma7D33WlpaFBMbDx48mDNJ8ZVXXsHY\n2BiA9PISeeuqu7t7R3cD88m3YDnTqo3H4zkLlwVByGlRrVS4D+DC563CwNpiwWAQSCZRce8epg8e\nhKjV5vz1ljObzTnzpFwuF4aHh6XnVqtV6spkxONxJBIJWCwW2Gw2xUA7/9rnyjfZNrPkxmg05syr\n0mq1ioAqLi7e9LWQtDYG1jawPnoEfSSC2bY2AMg7HyrDZrPB5/NJzysqKqDRaKTNQW02G+LxuKJg\nXKY7mPl6NraucmUv9YlEIlhcXIROp4PRaJRaqxnZ897sdnvedYi0tRhY26B4uSpAePm2eCZ88rFY\nLIrFteasig0WiyVn7KSoqEj6BWRJk7XJW0+ZAfjMTthOpzMn4DUaDcrKyqQbGgA3SX1a+H/3Fsp0\n7TTLn5PLY1MbqfWd3RJYWlrKCaVIJCJVwMy3oecG14sWPHklh+7ubiSTSWnMr7a2Fnfv3lWcn+nC\nZ2562Gy2nLpZcgcOHNjsS6ZlDKwtlAmWTGBlZrWvNrs8kUgopjRk1wqfmpqC0WhUlOgFPp/3EwgE\nEI/HFctQMq0HSq8PzBAEAUajEYODg4hGo7BarXC5XBgaGlK8pqWlRTEm2NHRIW1Pn09dXd3mXzgB\nYGBtqUxgLS7fkTIv/4XO7ubJBQIBxdZQfr8fS0tL0ixrID04XJ5VhiYcDsPpdCKZTGJ0dFSaCAkA\nV65c4Q4uSIe9fKLtq6++ipmZGQwODkpb1b/33nuK17jdbhgMBjx8+BBA+r/pWtUxdtJyp+3GwNoG\nweVKAbblQdrVZkiHQqGcZTNerxeNjY3S8wcPHiieA8DFixelkBoYGMDi4qJiZnZm89Wdanx8XDHr\n/9SpUwiHw7hy5QpEUURrayvGxsYU3WeDwYCOjg588MEH0rHu7u6cMjS0fRhY2yBeWopIRQUqlrsj\nq3XRsjfwBNIlaeR3/wYGBlBSUpIzl8jr9cLtdmNpaQlXrlzBwYMHP7+GeBxnz57dceNZoiji8uXL\nuHr1qnSsq6sLoiji4sWLSCQSqK6uRiKRUMx1EwQBnZ2d6Ovrk441NTXljG9lk69VpM3HwNpiTU1N\nAIBHx4/Ddf06ivx+RCKRVbsNjx49UoyDRCIRjI6O4oUXXpCOnT9/Hp2dnYoB+JGREVRUVMBsNiMQ\nCODKlSv42te+Jn09GAzi7bffzlu9sxBFIhG8/fbbikoVzz//PJLJJC5cuIBEIiEFvHyeG5Be5uT1\neuH3+wGk78TqdDrFCoR85K1a2nwMrC22b98+AMDIK69AEEU0fPghAKxaLSEej+fUDb9x4waMRqM0\nvrWwsICHDx/mFJ27ffs2ampqYDAYMD09jZ6eHrz88suKc9555x3pjlchSiaTOHPmDP7v//5PcfzU\nqVMYHR3FjRs3kEql0NDQgMnJyZzSPHv37oXX61XMxWptbVXUeKengyWSt8Fbb70FADj6938Px507\nOPPP/7yu2u1ut1vRfdTpdHjppZcUYyoejweCIOT8MpWVlSEej+PJkycwGAw4cOAAPv3005zv8bWv\nfS3njqNaJZNJXLp0KWcVQElJiXSnLx6PQ6fTweFw5Oyao9Fo0NHRIY0BZnR0dKxrY4zGxkZOafji\nWNP9WbG0tIR3330X5qkpvPy978G3bx96vv/9NRdB63Q6mEwmRSVRvV6PkydPKuYSVVZWorS0NOd2\nPKCs+V5VVQW9Xp93uyo171K8sLCAX/3qV3m/1tHRgdHRUWmy6Eo18IuKitDU1KSYvpApO5Pv3zWf\nX//1X+cawi+OgfUs6e3txeTkJJrffRcdP/kJrn3nOxh78cU1X5epEJA97nT8+HHF5ghAuivT39+f\nd2Bdq9UimUxCEATU1dXlLD3JqK6uxnPPPffM35pfXFxET0/PimNK9fX1CAQCUlCtti292+1GMplU\ndA0dDgcEQdhQ15mbTnwpDKxnzVtvvQUhmcTzP/gBKu7dw6W//mv49u9f83WZsMnW2dkpdXMy6urq\nEA6H19x6XRAEOJ3OnPEbudLSUhw+fBglJSVPfT1iMpmE1+vN262Vc7lcCAaDq1ZSyDCbzbDZbDl3\nbZubmxXLcNbjq1/96qrz62hNDKxnTaZrqH/yBCf+5m9g9vnwyQ9/iJBsR5eNqqqqgtFozCk343Q6\nMTs7u64Jo2azOe+SnmwajQb79+9HdXX1lm7AkKn1NTQ0tO5Z+vm22VqJTqdDaWlpTrUFg8EAu92e\nU/9+Pdi6+tIYWM+iUCiEjz76CEV+P07+5V9CF4uh58//HP6sbaM2aqVWwUb3LVyt67TW6yoqKmC3\n21FaWgqz2QydTqdomYmiiGQyiVgshnA4jEAgAL/fv+puP6sxGo3rakllZCoxZCpbyFVVVeXdun4l\nJY8eIeKfUPO1AAAGpUlEQVR0Imk04sSJE6ioqFj3aykvBtazyu/34/z58zBPT6P77/4OxdPTuP6d\n7+DRiRNf+r1dLlfebt5K3Uo1yVdEbz30ev2KJX3KysrWnFuVzTY8jOM/+AG8XV249t3vsnW1ORhY\nz7JAIICPP/4Y+oUFHP2Hf4Dj7l0MfvOb6P/t34aYVXH0i8jsAkP5rbcbnM324AGO/+AHSJjNuPDm\nm/jKt7/91Mf3CgQD61m3uLiIX/7ylxASCRz48Y+x68wZBBsacPW730W4oWFTvsdqrQvamLIHD/D8\nm28iYbHgwptv4tjv/I5qp4I8gxhYaiCKIt5++20AQGVfHzr//d9hePIE/b/1W3jwjW8gtQmtLfry\nyoaGcPyHP0TcYsEnb76Jmuefl1Yx0KZgYKnJwMAA+vv7YQiFcPA//gPVvb1YcLlw93d/FxPHjq05\nyZS2jvPmTRz5p39CrKQEF958E5Y9exTrOmlTMLDUJjPtAUj/kuz7yU9gHR+Hv7UVd37v9+BfrglP\n26PI78e+//xP1PT0YN7txsW//VuYPR6cPHnyaV9aIWJgqdXk5CR6e3uBZBL1585hz09/iqJAALNt\nbbj/jW/A29UFyPbIo80lJBJoef997P7ZzyCkUhh8/XUMffOb6OzuZjXRrcPAUru7d+9icHAQ2sVF\nNHz0EZrffx/FMzOYr6rCg298A+MnTiBZIAuXnwVCMonKq1fR/l//hZLJSUweOoTbf/AHiLhc+PrX\nv86NJ7YWA6tQ3LhxAyMjIxCSSbh7e+F55x2UDQ9jyWTCxNGjGD91Cr69ewHumPOFmObm0HDmDBrO\nnIHZ78dCZSVufetbmO7shNvtxpEjRzh1YesxsArN6Ogorl+/Dogi7IODqP/4Y9Rcvgx9JIJIRQXG\nT5zA5LFj6ZLM/AVbXTIJ55072PXBB6jq64MmlcL0/v0YOX0a3q4uiDodXn311Wd+EXgBYWAVqkgk\nIhWn08RicPf1oe7cObhu3YKQSiFqt2OqsxNTXV2Y6ehAkiVPAAD6J0/gvHkTVVevwnXjBozz84iV\nlGDsxRcx8soreFJVBQAMqqeDgVXoRFHE+Pg4rl27BgAwhEKovH4dldeuwXXzJvTRKJIGA2Z374a/\nrQ2zbW0IeDw7JsCERALWsTE47t5F5bVrKL93D5pUCjGLBdOdnfB2dcF76BBSBgO7fk8fA2snEUUR\nw8PDUmVMIZFARX8/qq5dQ8WdO7COj0MQRaS0WgQbGzHb1oZgUxNC9fVYcLulPRPVrMjvR9nQEOzL\nH2UPH0K7vJA7VFeHqa4ueJ97DnMtLYBWC61Wi1deeYVlYZ4NDKydLBQK4fz589Lu0/qFBdgHB1Ex\nMIDye/dQdv8+tLIdqcO1tQjX10sB9sTlwhOHA6lnrTWWSsHs86FkYiL98fix9Ni4XF4mqdcj2NiI\nOY8n/dHaKpWkLi0txfPPP18wZaELCAOL0kRRxPT0NHp7e6X6WEIigZKJCVjHxmAdHU1/HhuDKavw\n36LNlg4vpxPR8nLErFbES0sRKylB3GpFbPlx0mT64gP9yST00Sj0kQh0kQj0kQhMwSBMc3Mo8vtR\nNDeXfrz8XCtbGxkrLcV8dTXmq6sRqq9HwONBsL5eWkCu1Wpx7Ngxxea09ExiYNHKEokEBgYGcP/+\nfcVxQygEy9QUzDMzKJ6eRvHMDMzLn4vm5qBZbpXlkzQYlB96PVJ6PQRRhJBMQkilIKRSgChCSKWg\nTSTSISXb8CHnPfV6RO12LNrtiNrtiJaXY8HtxnxNDearqxHP2n2ovr4ee/fu5Zwp9WFg0cbNz89j\neHgYIyMjubWnRBG6SATGcFj6MCx/1i4uQhuPKz40iQS0iQREQYCo0Sg/tFqkdDokzGYkiouRMJux\nVFSU/mw2I2a1IlpejrjFkrfl5na74fF4UFZWxoHywsDAos0Xi8Xg9/sxOzuLQCCAYDC4qYUBrVYr\n7HY7ysrK4HA4YDabGUg7AwOLiFRjXYHFtRxEpBoMLCJSDQYWEakGA4uIVIOBRUSqwcAiItVgYBGR\najCwiEg1GFhEpBoMLCJSDQYWEakGA4uIVIOBRUSqwcAiItVgYBGRajCwiEg1GFhEpBoMLCJSDQYW\nEakGA4uIVIOBRUSqwcAiItVgYBGRajCwiEg1GFhEpBoMLCJSDQYWEakGA4uIVIOBRUSqwcAiItXQ\nbfB8YUuugohoHdjCIiLVYGARkWowsIhINRhYRKQaDCwiUg0GFhGpBgOLiFSDgUVEqsHAIiLVYGAR\nkWr8P0ed5BN7l1PcAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f929f4047f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_periods_simulate = 30\n",
    "sampling_rate_simulate_exponent = 12\n",
    "sampling_rate_simulate = 2**sampling_rate_simulate_exponent\n",
    "t_simulate_full = np.linspace(0, num_periods_simulate*period_length,\n",
    "                int(num_periods_simulate*sampling_rate_simulate))\n",
    "dt_simulate = t_simulate_full[1]-t_simulate_full[0]\n",
    "\n",
    "rossler_simulation = utils.simulate_rossler(dt_simulate, t_simulate_full.size, x0=x0, a=a, b=b, c=c, tau=tau)[0]\n",
    "\n",
    "start_idx = int(5.1*sampling_rate_simulate)\n",
    "end_idx = -1\n",
    "end_idx_highlight = int(5.8*sampling_rate_simulate)\n",
    "spacing = 2**6\n",
    "\n",
    "# find the max index at which to plot the solution\n",
    "sample_max_idx = int(0.85*period_length/dt_simulate)\n",
    "\n",
    "fig = plt.figure(figsize=(5,4))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "ax.plot(rossler_simulation[0,start_idx:end_idx:spacing], rossler_simulation[1,start_idx:end_idx:spacing],\n",
    "        rossler_simulation[2,start_idx:end_idx:spacing], alpha=0.8, color='#999999', linewidth=2)\n",
    "plt.plot(rossler_simulation[0,start_idx:end_idx_highlight:spacing],\n",
    "         rossler_simulation[1,start_idx:end_idx_highlight:spacing],\n",
    "         rossler_simulation[2,start_idx:end_idx_highlight:spacing],\n",
    "         color='#ff0000')\n",
    "ax.axis('off')\n",
    "# plt.savefig('figures/02_rossler.pdf', format='pdf', dpi=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot results for all systems"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/kpchamp/anaconda/envs/py3/lib/python3.6/site-packages/ipykernel_launcher.py:2: RuntimeWarning: Mean of empty slice\n",
      "  \n",
      "/home/kpchamp/anaconda/envs/py3/lib/python3.6/site-packages/ipykernel_launcher.py:6: RuntimeWarning: Mean of empty slice\n",
      "  \n",
      "/home/kpchamp/anaconda/envs/py3/lib/python3.6/site-packages/ipykernel_launcher.py:8: RuntimeWarning: Mean of empty slice\n",
      "  \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(0.15, 1.5)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/pdf": "JVBERi0xLjQKJazcIKu6CjEgMCBvYmoKPDwgL1R5cGUgL0NhdGFsb2cgL1BhZ2VzIDIgMCBSID4+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\n",
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPoAAAC1CAYAAAB24uKEAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nK/D/AUfN5STMAAAAA0lEQVSKYFuMLDMvAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f929efca080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(3.5,2.5))\n",
    "plt.semilogx(2**lorenz_data[0], np.nanmean(lorenz_data[1], axis=1), 'k', linewidth=2, label='Lorenz', basex=2)\n",
    "\n",
    "plt.semilogx(2**duffing_data[0], np.nanmean(duffing_data[1], axis=1), 'k--', linewidth=2, label='Duffing', basex=2)\n",
    "\n",
    "plt.semilogx(2**vdp_data[0], np.nanmean(vdp_data[1], axis=1), 'k-.', linewidth=2, label='Van der Pol', basex=2)\n",
    "\n",
    "plt.semilogx(2**rossler_data[0], np.nanmean(rossler_data[1], axis=1), 'k:', linewidth=2, label='Rossler', basex=2)\n",
    "plt.xlim([2**6,2**18])\n",
    "plt.ylim([0.15,1.5])\n",
    "\n",
    "# plt.legend()\n",
    "# plt.savefig('figures/02_sampling_all.pdf', format='pdf', dpi=300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}