{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "intro02",
   "metadata": {},
   "source": [
    "# Models and Dynamics\n",
    "\n",
    "brainmass ships a library of neural-mass models, from simple phenomenological oscillators to\n",
    "biophysical mean-field models. This tutorial gives you a **map of the families** and the two\n",
    "tools you need to understand any of them:\n",
    "\n",
    "- the **phase portrait** — the trajectory in state space, and\n",
    "- the **bifurcation** — how changing one parameter qualitatively changes the behaviour.\n",
    "\n",
    "By the end you will be able to orient yourself with {func}`brainmass.list_models`, recognise\n",
    "the main model families, and read a bifurcation diagram.\n",
    "\n",
    ":::{note}\n",
    "This is a guided *tour*, not the full catalogue. For a runnable demo of **every** model — and\n",
    "help choosing one — see the {doc}`/gallery/index` and {doc}`/howto/choose_a_model`.\n",
    ":::"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "imports02",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-19T06:45:24.682151Z",
     "iopub.status.busy": "2026-06-19T06:45:24.681943Z",
     "iopub.status.idle": "2026-06-19T06:45:29.917014Z",
     "shell.execute_reply": "2026-06-19T06:45:29.915985Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "An NVIDIA GPU may be present on this machine, but a CUDA-enabled jaxlib is not installed. Falling back to cpu.\n"
     ]
    }
   ],
   "source": [
    "import brainmass\n",
    "import braintools\n",
    "import brainstate\n",
    "import brainunit as u\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "brainstate.environ.set(dt=0.1 * u.ms)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "md-catalog02",
   "metadata": {},
   "source": [
    "## Orient yourself with `list_models()`\n",
    "\n",
    "{func}`brainmass.list_models` returns a typed catalogue of every public model: its name, its\n",
    "**category**, how many state variables it integrates, and a one-line use case. It is the\n",
    "fastest way to see what is available."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "catalog02",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-19T06:45:29.920871Z",
     "iopub.status.busy": "2026-06-19T06:45:29.920234Z",
     "iopub.status.idle": "2026-06-19T06:45:29.925437Z",
     "shell.execute_reply": "2026-06-19T06:45:29.924615Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "name                     category          #states  use_case                                 \n",
      "-----------------------  ----------------  -------  -----------------------------------------\n",
      "HopfStep                 phenomenological  2        Oscillation onset, rhythm generation     \n",
      "VanDerPolStep            phenomenological  2        Nonlinear relaxation oscillations        \n",
      "StuartLandauStep         phenomenological  2        Amplitude-controlled oscillations        \n",
      "FitzHughNagumoStep       phenomenological  2        Excitability, spike generation           \n",
      "ThresholdLinearStep      phenomenological  2        Fast linear E-I responses                \n",
      "Generic2dOscillatorStep  phenomenological  2        Flexible planar dynamics (TVB)           \n",
      "LorenzStep               phenomenological  3        Chaos, coupling test fixture             \n",
      "LinearStep               phenomenological  1        Baseline node, coupling sanity checks    \n",
      "WilsonCowanStep          physiological     2        E-I population firing-rate dynamics      \n",
      "JansenRitStep            physiological     6        EEG generation, alpha rhythms            \n",
      "WongWangStep             physiological     2        Decision making (perceptual choice)      \n",
      "WongWangExcInhStep       physiological     2        Resting-state BOLD/FC, E-I balance       \n",
      "MontbrioPazoRoxinStep    physiological     2        Exact QIF mean-field (theta neurons)     \n",
      "CoombesByrneStep         physiological     2        Next-gen mean-field, conductance synapses\n",
      "LarterBreakspearStep     physiological     3        Conductance-based limit cycles / chaos   \n",
      "EpileptorStep            physiological     6        Seizure onset/offset, epilepsy           \n",
      "KuramotoNetwork          network           1        Phase synchronization                    \n",
      "HORNStep                 network           2        Single coupled-oscillator step           \n",
      "HORNSeqLayer             network           2        Sequential HORN layer                    \n",
      "HORNSeqNetwork           network           2        Multi-layer HORN sequence network        \n"
     ]
    }
   ],
   "source": [
    "print(brainmass.list_models.to_table())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "md-families02",
   "metadata": {},
   "source": [
    "The catalogue groups models into three families:\n",
    "\n",
    "| Category | What it is | Examples |\n",
    "|---|---|---|\n",
    "| **phenomenological** | Minimal models capturing a *behaviour* (oscillation, excitability) without biophysical detail | {class}`~brainmass.HopfStep`, {class}`~brainmass.StuartLandauStep`, {class}`~brainmass.FitzHughNagumoStep` |\n",
    "| **physiological** | Population firing-rate / mean-field models with interpretable biology | {class}`~brainmass.WilsonCowanStep`, {class}`~brainmass.MontbrioPazoRoxinStep`, {class}`~brainmass.JansenRitStep` |\n",
    "| **network** | Models that are intrinsically a network of units | {class}`~brainmass.KuramotoNetwork`, the HORN family |\n",
    "\n",
    "We will visit one model from each of the first two families and a fourth next-generation\n",
    "mean-field model, and watch a parameter move each one between regimes."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "md-osc02",
   "metadata": {},
   "source": [
    "## An oscillator: the Hopf model\n",
    "\n",
    "The {class}`~brainmass.HopfStep` is the normal form of an oscillation **onset**. Its\n",
    "bifurcation parameter `a` controls everything: for `a < 0` the origin is a stable focus (any\n",
    "perturbation decays to rest), while for `a > 0` a **limit cycle** appears whose amplitude\n",
    "grows like `sqrt(a)`. The transition at `a = 0` is a *supercritical Hopf bifurcation*.\n",
    "\n",
    "We run the model across a range of `a` and record the peak-to-peak amplitude of the settled\n",
    "trajectory — this traces the bifurcation diagram directly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "bif02",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-19T06:45:29.928613Z",
     "iopub.status.busy": "2026-06-19T06:45:29.928223Z",
     "iopub.status.idle": "2026-06-19T06:45:31.470824Z",
     "shell.execute_reply": "2026-06-19T06:45:31.469865Z"
    }
   },
   "outputs": [
    {
     "data": {
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3b9+Gv78/VCoVjh07hjZt2mDkyJF47733IJfL0aVLF3z++edISkrCqlWr4ODgoO5FzuLj44MVK1bghx9+gKenJxwcHLL1hAGZYyVnz56NQYMGoVWrVvj444/VU2J4eHgY7DJSRDnSz0OfRCXT/v37xeDBg0W1atVE2bJlhVwuF56enmLUqFEiJiZGo25KSooYMmSIsLKyEhYWFqJ3794iNjY21ykxwsPDRa9evYSFhYWwsbERI0eO1JgCIMsff/whmjdvLsqUKSPKlCkjqlWrJkaMGCFu3ryprpPTtAivx/Xtt9+KihUrCmNjY+Hk5CR69eolIiIihBD/TZMwZ86cbPvmNIWCQqEQo0aNEvb29kIikWhM0fDmtQohxP3790X//v2Fvb29MDExEZUqVRIjRowQaWlpQojMKTG+/vpr4ezsLMzMzESzZs1EaGioaNWqlcYUCtpOibFt27YcXx8wYIDGlBhZli5dKqpVqyaMjY2Fo6OjGD58uHjx4oVGnax2PnfunPD19RWmpqbC3d1dLF26NNvxoOWUGHPmzBHz5s0Trq6uwsTERLRo0UI9PUqW/E6JIYQQT58+FT179hTm5ubCxsZGfP755+Lq1as5TomRU3sIkfmznjNnjqhWrZqQy+XC3t5edOzYUYSFhanr7N69W9SuXVuYmpoKDw8PMXv2bPVULJGRkep60dHRonPnzsLCwkIAUP9sc5u+Y8uWLaJevXrCxMRE2Nrair59+2pMGZJX7Dm1E5E+SIQo4D0JIioSWROVPn36tEjGTJHutG7dGs+ePXvrODkiIoBjyoiIiIgMApMyIiIiIgPApIyIiIjIAHBMGREREZEBYE8ZERERkQFgUkZERERkAErd5LEqlQpPnjyBhYVFvpfxICIiIiooIQQSExPh4uKS57qxpS4pe/LkCVxdXfUdBhEREZUyDx8+RIUKFXJ9vdQlZRYWFgAyG8bS0lLP0RAVrvT0dMybNw8A8PXXX0Mul+s5IiKi0ichIQGurq7qHCQ3pS4py7plaWlpyaSMSrz09HSYmpoCyHzPMykjItKftw2b4kB/IiIiIgPApIyIiIjIAJS6yWMTEhJgZWWF+Ph43r4kIiKiQpff3KPUjSnLL6VSiYyMDH2HQaQVY2NjyGQyfYdBREQFwKTsDUIIREdH4+XLl/oOhahArK2t4eTkxHn4iIjeQqkSOBMZh9jEVDhYmKJRRVvIpPr77GRS9oashMzBwQHm5ub8w0bFhhACKSkpiI2NBQA4OztDoVBg586dAIAPPvgARkb8lSciAoADV6MwfU84ouJT1WXOVqYI7OIN/5rOeomJn9CvUSqV6oSsXLly+g6HSGtmZmYAgNjYWDg4OEClUiE8PBwA0K1bN32GRkRkMA5cjcLw387jzUH10fGpGP7beaz4tL5eEjM+ffmarDFk5ubmeo6EqOCy3r8cE0lElJ1SJTB9T3i2hAyAumz6nnAoVUX/HCSTshzwliUVZ3z/EhHl7kxknMYtyzcJAFHxqTgTGVd0Qf0/JmVERERUakQn5J6QvS42MX/1dIlJWQnRunVrjBkzJs86Hh4eWLhwoXo7OjoaHTp0QJkyZWBtbV2o8RWURCLBrl27iuRcLVu2xO+//14k5yqo8PBwVKhQAcnJyfoOhYioWLn/PBnz/r6JH/66lq/6DhamhRxRdkzKSpGzZ89i2LBh6u0FCxYgKioKFy9exK1bt/QYGTBt2jTUrVs3W3lUVBQ6duxY6OffvXs3YmJi8NFHHxX6ufKSmpqKESNGoFy5cihbtix69uyJmJgY9eve3t5o0qQJ5s+fr8coiYiKh5R0BbaHPUKfn0LRas4RLPnnDp4nZyCvQR4SZD6F2aiibVGFqcanL0sRe3t7je2IiAj4+PjAy8urwMcUQkCpVBbaVAtOTk6Fctw3LV68GIMGDYJUqt//U8aOHYu9e/di27ZtsLKywsiRI9GjRw+cOHFCXWfQoEEYOnQoAgICOMUFEdEbhBAIu/8C2849wl+XnyA5XQkAkEiAFl72+NCnAoQQGL35Ymb91/bNStYCu3jrZb4y9pSVIAqFAiNHjoSVlRXs7OwwZcoUvL6K1uu3Lz08PPDHH39g/fr1kEgkGDhwIO7duweJRIKLFy+q93n58iUkEgmOHDkCADhy5AgkEgn2798PHx8fmJiY4Pjx41CpVPjxxx/h6ekJExMTuLm5YcaMGerjTJw4EVWqVIG5uTkqVaqEKVOmqJ8OXLt2LaZPn45Lly5BIpFAIpFg7dq1ALLfvrxy5Qratm0LMzMzlCtXDsOGDUNSUpL69YEDB6J79+6YO3cunJ2dUa5cOYwYMSLPJxGfPn2Kf/75B126dNEonz9/PmrVqoUyZcrA1dUVX375pca5dC0+Ph6//vor5s+fj7Zt28LHxwdr1qzByZMncerUKXW9Dh06IC4uDv/+++9bj2lsbIyAgAAEBATA2Ni40GInItK36PhULAu5g3bz/kWvlaHYcu4hktOV8ChnjvHvVcGJiW2xfnAjdKnjgq51y2PFp/XhZKV5i9LJylRv02EA7CnLt/T09Fxfk0qlGj0WedWVSCQafxxzqyuXy7WOcd26dRgyZAjOnDmDc+fOYdiwYXBzc8PQoUOz1T179iz69+8PS0tLLFq0CGZmZnjx4kW+zzVp0iTMnTsXlSpVgo2NDQICArBq1SosWLAAzZs3R1RUFG7cuKGub2FhgbVr18LFxQVXrlzB0KFDYWFhgQkTJqBPnz64evUqDhw4gMOHDwMArKyssp0zOTkZfn5+8PX1xdmzZxEbG4vPPvsMI0eOVCdxABASEgJnZ2eEhITgzp076NOnD+rWrZtjOwDA8ePHYW5ujurVq2uUS6VSLF68GBUrVsTdu3fx5ZdfYsKECVi+fHmu7dKxY0ccO3Ys19fd3d1x7VrO4xnCwsKQkZGB9u3bq8uqVasGNzc3hIaGokmTJgAy3xt169bFsWPH0K5du1zPBWS+3wryXiIiKg7SFEocDo/FtrCHOHrrKbJmsTCXy9C5ljM+bOCKhh42OT6V7l/TGR28nTijf3EUFBSU62teXl745JNP1Ntz587NtWfG3d0dAwcOVG8vWrQIKSkp2eoFBgZqHaOrqysWLFgAiUSCqlWr4sqVK1iwYEGOyYi9vT1MTExgZmamvkWoTVL23XffoUOHDgCAxMRELFq0CEuXLsWAAQMAAJUrV0bz5s3V9SdPnqz+3sPDA+PHj8fmzZsxYcIEmJmZoWzZsjAyMsrzduXvv/+O1NRUrF+/HmXKlAEALF26FF26dMHs2bPh6OgIALCxscHSpUshk8lQrVo1dO7cGcHBwbkmZffv34ejo2O2W5evPzjh4eGBH374AV988UWeSdkvv/yCV69e5fp6Xr1V0dHRkMvl2R66cHR0RHR0tEaZi4sL7t+/n+uxiIhKsquP47E97BF2XXyMlyn//b1t5GGLXg0qoHMtZ5QxeXuKI5NK4FvZcCaLZ1JWgjRp0kTjvwFfX1/MmzcPSqVS54tUN2jQQP399evXkZaWlmevzZYtW7B48WJEREQgKSkJCoUClpaWWp3z+vXrqFOnjjohA4BmzZpBpVLh5s2b6qSsRo0aGtfr7OyMK1eu5HrcV69ewdQ0+1M2hw8fRlBQEG7cuIGEhAQoFAqkpqYiJSUl1wmGy5cvr9U1FZSZmVmOyfybFAoF/vrrLwDA+++/zzFoRFRsxSWn48+Lj7H13CNcj0pQlztZmqKnT3n08nFFRbsyeRzB8PETOp8CAgJyfe3NHpbx48fnWvfNLtTRo0e/W2A6lHUdr49Dy63H7/XEKGtpn9yEhoaib9++mD59Ovz8/GBlZYXNmzdj3rx5Oog6uzd7oyQSCVQqVa717ezssvUS3rt3D++//z6GDx+OGTNmwNbWFsePH8eQIUOQnp6ea1L2LrcvnZyckJ6ejpcvX2r0lsXExGTrQYyLi0PlypVzPU8WlUqFS5cuAQA6der01vpERIZEoVTh6O2n2HbuEQ5fj0GGMvPvk1wmRYcajujdwBXNPe30estRl5iU5ZM243IKq+7bnD59WmP71KlT8PLyyncvWdbTmVFRUahXrx4AaAz6z42XlxfMzMwQHByMzz77LNvrJ0+ehLu7O7799lt12Zu33uRyOZRKZZ7nqV69OtauXYvk5GR1UnjixAlIpVJUrVr1rXHmpl69eoiOjsaLFy9gY2MDIHN8l0qlwrx589TJ6tatW996rHe5fenj4wNjY2MEBwejZ8+eAICbN2/iwYMH8PX11ah79epV9OrV663xEBEVRxFPk7Dt3CPsOP8IsYlp6vKa5S3Ru4ErutZxgbV5yRsvq9ek7OjRo5gzZw7CwsIQFRWFnTt3onv37rnW37FjB1asWIGLFy8iLS0NNWrUwLRp0+Dn51d0QRuwBw8eYNy4cfj8889x/vx5LFmyRKveKDMzMzRp0gSzZs1CxYoVERsbqzEWLDempqaYOHEiJkyYALlcjmbNmuHp06e4du0ahgwZAi8vLzx48ACbN29Gw4YNsXfvXuzcuVPjGB4eHoiMjMTFixdRoUIFWFhYwMTERKNO3759ERgYiAEDBmDatGl4+vQpRo0ahX79+qlvXRZEvXr1YGdnhxMnTuD9998HAHh6eiIjIwNLlixBly5dcOLECaxcufKtx3qX25dWVlYYMmQIxo0bB1tbW1haWmLUqFHw9fVVD/IHMnvxHj9+rPFAABFRcZeYmoG9l6OwLewRwu7/d/fCtowc3euWx4cNKqC6s3bDXoobvU6JkZycjDp16mDZsmX5qn/06FF06NAB+/btQ1hYGNq0aYMuXbrgwoULhRxp8dC/f3+8evUKjRo1wogRIzB69GiNyWLzY/Xq1VAoFPDx8cGYMWPwww8/5Gu/KVOm4Ouvv8bUqVNRvXp19OnTB7GxsQCArl27YuzYsRg5ciTq1q2LkydPYsqUKRr79+zZE/7+/mjTpg3s7e2xadOmbOcwNzfHwYMHERcXh4YNG6JXr15o164dli5dqtU1vkkmk2HQoEHYuHGjuqxOnTqYP38+Zs+ejZo1a2Ljxo15PuyhKwsWLMD777+Pnj17omXLlnBycsKOHTs06mzatAnvvfce3N3dCz0eIqKCUqoEQiOe48+LjxEa8TzHBb5V/19n3JaLaDQjGJN2XEHY/ReQSSVoV80BKz+tj1MB7TC1i3eJT8gAQCJeH0CkRxKJ5K09ZTmpUaMG+vTpg6lTp+arfkJCAqysrBAfH59toHlqaioiIyNRsWLFHAd+U8kVHR2NGjVq4Pz58wad7KSnp8PLywu///47mjVrlmOd19/HUqlUnUwGBARwegwiKhIHrkZh+p5wjYW/na1MEdjFG/41nfHoRQr+CHuM7ecf4mHcf0M+KtuXwYcNXNGjXnk4WJacv8N55R6vK9ZjylQqFRITE2Frm/tSCGlpaUhL++9+dEJCQq51qfRycnLCr7/+igcPHhh0UvbgwQN88803uSZkRET6duBqFIb/dh5v9vhEx6fii9/Oo5qTBW7GJCKrS6isiRG61HHBhw0qoJ6rdY5zipUWxTopmzt3LpKSktC7d+9c6wQFBWH69OlFGBUVV9r20uqDp6cnPD099R0GEVGOlCqB6XvCsyVkwH/LGd2ITgQANK1cDh82qAD/Gs4wk+t22qbiqtgmZb///jumT5+OP//8Ew4ODrnWCwgIwLhx49TbCQkJcHV1LYoQifTO2NhYPUULl1kiosJ2JjJO45ZlbhZ/VBdd6xbNvI7FSbFMyjZv3ozPPvsM27Zte+sTaCYmJtme4iMqLSQSicacckREhen8g/ytDGMQg9kNULFLyjZt2oTBgwdj8+bN6Ny5s77DISIiKtVepSux5/ITbDx1H5cexedrHweLkjOIX5f0mpQlJSXhzp076u2seapsbW3h5uaGgIAAPH78GOvXrweQectywIABWLRoERo3bqxeD9DMzCzHBawLKq/Z34kM3evvX4VCgYMHDwIA/Pz8uMwSEenMndhEbDz9AH+EPUJCqgIAYCQFjGRSpGbk/HdUAsDJKnPhb8pOr5/Q586dQ5s2bdTbWWO/BgwYgLVr1yIqKgoPHjxQv/7zzz9DoVBgxIgRGDFihLo8q/67ksvlkEqlePLkCezt7SGXy0v1UyBUvAghkJ6ejqdPn0IqlUIul0OhUODcuXMAoF5AnoiooNIVKhy8Fo2Np+/j1N04dbmrrRk+aeSODxtUwLl7cRj+23kAmrcps/6aBnbxLjHLIumaXpOy1q1bI69p0t5MtI4cOVKo8UilUlSsWBFRUVF48uRJoZ6LqLCYm5vDzc0t25qsREQF9TAuBZvOPMDWcw/xLCkdACCVAO2qO6JvYze09LKH9P8TLf+azljxaf1s85Q5vTZPGeWM9zLeIJfL4ebmBoVC8da1GIkMjUwmg5GREXt4ieidKVUCITdisfH0fRy59VQ9r5iDhQk+auSGjxq6wsXaLMd9/Ws6o4O3E85ExiE2MRUOFpm3LNlDljcmZTmQSCQwNjbmFAJERFTqxCakYsvZh9h05gGevNbT1cLLDn0bu6FddUcYy97eEy+TSuBbuVxhhlriMCkjIiIq5YQQOBnxHBtP38ff12Kg+P91Km3MjfFhA1d83MgNFe04vU5hY1JGRERUSr1MScf2sEf4/fQD3H2WrC5v4G6Dvk3c0LGmM0yNOdt+UWFSRkREVIoIIXD+wUtsPH0ff12OQroic/qKsiZG+KBeeXzS2A3VnXNfNJsKD5MyohLM2NgYo0ePVn9PRKVXUpoCuy48xsbTD3A9KkFd7u1siU+buKNrXReUNWFaoE9sfaISTCKRwNraWt9hEJEeXY9KwG+n7mPXhcdITs+cVcDESIoudVzQt7Eb6rpa84ltA8GkjIiIqJhRqkSe002kZiix93IUNp6+j/MPXqrLK9mXQd/G7uhZvzyszeV6iJzywqSMqARTKpUIDg4GALRr1w4yGQfsEhV3B65GZZuY1fn/J2at6mSJjafuY/v5R3iZkgEAMJJK4FfTCX0bu8G3Ujn2ihkwJmVEJZhSqURoaCiAzBU0mJQRFW8HrkZh+G/n8eZaOFHxqfji/5c2ylLe2gyfNHbDhw0qcAHwYoJJGRERUTGgVAlM3xOeLSF7U9uq9vjU1x2tqjhwBv1ihkkZERFRMXAmMk7jlmVuhraszJn0iymuWExERGTgFEoV/r4Wna+6sYlvT9zIMLGnjIiIyEAlpGZg69mHWHPiHh6/fJWvfTh+rPhiUkZERGRgHsalYM2Je9h67iGS0hQAMtehzFCqkJSmzHEfCQAnq8zpMah4YlJGRERkAIQQCLv/Ar8ej8TBa9H4/zXB4eVQFkOaV0T3euVx5GYshv//U5avD/jPGs4f2MWbg/uLMYkQ4m0PcpQoCQkJsLKyQnx8PCwtubYXlWxCCDx9+hQAYG9vz/mJiAxQhlKF/Vej8evxSFx6+FJd3sLLDp+1qISWXnYav7t5zVPmX9O5KEOnfMpv7sGeMqISTCKRwMHBQd9hEFEO4l9lYPOZB1h78p46wZIbSfFB3fIY3LwiqjpZ5Liff01ndPB2ynNGfyqemJQREREVoXvPkrHmRCS2hT1Cyv+vRWlXVo5+TTzQt4kb7MqavPUYMqmE016UQEzKiEowpVKJY8eOAQBatGjBGf2J9ESIzLUqfzkeicPXY5A1cKiqowWGtKiIrnVcYGrM38/SjkkZUQmmVCrx77//AgCaNm3KpIyoiKUrVNh75Ql+PR6Jq48T1OVtqtpjSPNKaObJtSjpP0zKiIiIdOxlSjo2nn6A9aH3EJOQBgAwMZKip08FDG7mAU+HnMeLUenGpIyIiEhH7j5NwuoTkfgj7DFeZWSOF7O3MMEAX3d80tgdtmXkeo6QDBmTMiIioncghEBoxHP8ejwSwTdi1eXezpYY0rwi3q/jDBMjDh2gt2NSRkREVABpCiX2XIrCr8cjcT0qc7yYRAK0q+aAIc0roUklW44XI60wKSMiInqNUiXynAMsLjkdG0/dx/pT9/E0MXO8mJmxDL18KmBQMw9Usi+rr9CpmGNSRkRE9P/ymi2/sn1ZrD4RiR3nHyNNoQIAOFmaYkBTD3zcyBXW5hwvRu9Gr8ssHT16FHPmzEFYWBiioqKwc+dOdO/ePc99jhw5gnHjxuHatWtwdXXF5MmTMXDgwHyfk8ssUWmiUqkQFRUFAHB2doZUKtVzRESG68DVKAz/7Tzy80exVnkrfNaiIjrVcoaxjL9XlLdiscxScnIy6tSpg8GDB6NHjx5vrR8ZGYnOnTvjiy++wMaNGxEcHIzPPvsMzs7O8PPzK4KIiYoXqVSK8uXL6zsMIoOnVAlM3xP+1oSsQ3UHDG1ZGQ09bDhejHROr0lZx44d0bFjx3zXX7lyJSpWrIh58+YBAKpXr47jx49jwYIFTMqIiKjAzkTGadyyzM3g5pXQqKJtEUREpVGB+lwVCgUOHz6Mn376CYmJiQCAJ0+eICkpSafBvSk0NBTt27fXKPPz80NoaGihnpeouFIqlThx4gROnDgBpVKp73CIDNb9uOR81YtNfHviRlRQWveU3b9/H/7+/njw4AHS0tLQoUMHWFhYYPbs2UhLS8PKlSsLI04AQHR0NBwdHTXKHB0dkZCQgFevXsHMzCzbPmlpaUhLS1NvJyQkZKtDVFIplUocPnwYANCwYUMus0T0hpcp6Vh94h5+ORqRr/oOFqaFHBGVZlr3lI0ePRoNGjTAixcvNJKgDz74AMHBwToNTheCgoJgZWWl/nJ1ddV3SEREpGfPk9Lw44EbaD47BIuDbyMlQ6Ux7cWbJMh8CpO3Lqkwad1TduzYMZw8eRJyueajvx4eHnj8+LHOAsuJk5MTYmJiNMpiYmJgaWmZYy8ZAAQEBGDcuHHq7YSEBCZmRESlVGxiKlYdvYvfTj1QL4NUzckCo9p6QQJgxO/nAUBjwH9WqhbYxTvPxI3oXWmdlKlUqhzHpjx69AgWFoW7wKqvry/27dunUXbo0CH4+vrmuo+JiQlMTEwKNS4iIjJs0fGpWPlvBDadeaCeY6xWeSuMauuJ9tUdIf3/ZGuFtH62ecqc/n+eMv+aznqJnUoPrZOy9957DwsXLsTPP/8MAJBIJEhKSkJgYCA6deqk1bGSkpJw584d9XZkZCQuXrwIW1tbuLm5ISAgAI8fP8b69esBAF988QWWLl2KCRMmYPDgwfjnn3+wdetW7N27V9vLICKiUuDRixSsOBKBbeceIV2ZmYzVc7PGV2290LqqfbZpLfxrOqODt1OeM/oTFRatk7J58+bBz88P3t7eSE1NxSeffILbt2/Dzs4OmzZt0upY586dQ5s2bdTbWbcZBwwYgLVr1yIqKgoPHjxQv16xYkXs3bsXY8eOxaJFi1ChQgX88ssvnA6DiIg03H+ejGUhd7Dj/GMoVJk3IxtVtMVXbb3QzLNcnnOMyaQS+FYuV1ShEqkVaEZ/hUKBzZs34/Lly0hKSkL9+vXRt2/fXMd1GRLO6E+lSXp6OoKCggBkjq98cywoUUkT8TQJy/65gz8vPYHy/5OxZp7lMKqtF5pUYqJF+pHf3EOvyyzpA5MyKk1UKpW6t9nNzY3LLFGJdTM6EUv+uY29V6KQ9VetdVV7jGrrBR93G/0GR6WeTpdZ2r17d75P3LVr13zXJaLCJZVK4eHhoe8wiArN1cfxWPrPHRy4Fq0ua1/dEaPaeqKOq7X+AiMqgHwlZW8uEi6RSPBmB1vW/XnOGk5ERIXt4sOXWBJ8G8E3YgEAEgnQsaYTRrbxgrcL74JQ8ZSvexkqlUr99ffff6Nu3brYv38/Xr58iZcvX2L//v2oX78+Dhw4UNjxEpEWlEolzpw5gzNnzvAfJioRzt2LQ//VZ9B92QkE34iFVAJ0reOCg2NaYnlfHyZkVKxp/fTlmDFjsHLlSjRv3lxd5ufnB3NzcwwbNgzXr1/XaYBEVHBKpRL79+8HANStW5fLLFGxJITAqbtxWBx8G6F3nwPIfEKye93yGNGmMirZl9VzhES6oXVSFhERAWtr62zlVlZWuHfvng5CIiIiykzGjt1+hiX/3MbZey8AAMYyCXrWr4AvW3vCrZy5niMk0i2tk7KGDRti3Lhx2LBhg3px8JiYGPzvf/9Do0aNdB4gERGVLkIIhNyMxeLgO7j48CUAQC6Tok9DV3zRujLKWxv+9EtEBaF1UrZ69Wp88MEHcHNzU68h+fDhQ3h5eWHXrl26jo+IiEoQpUrkOlu+SiXwd3gMlobcxtXHCQAAEyMpPmnshs9bVoaTlak+QycqdFonZZ6enrh8+TIOHTqEGzduAACqV6+O9u3b5zlDMhERlW4HrkZlW1fS2coUUzp7QykElv5zBzdjEgEA5nIZ+jVxx2ctKsHegusXU+mgdVIGZE5/8d577+G9997TdTxERFQCHbgaheG/ncebs5VHxafiy9/Pq7fLmhhhYFMPDG5eEbZluAIFlS5aJ2Xfffddnq9PnTq1wMEQEVHJo1QJTN8Tni0he50EwKh2nhjSrBKszI2LKjQig6J1UrZz506N7YyMDERGRsLIyAiVK1dmUkZkQIyMjPDxxx+rvyfShzORcRq3LHMiAPhWsmNCRqWa1p/SFy5cyFaWkJCAgQMH4oMPPtBJUESkG1KpFFWqVNF3GFTKxSbmnZBpW4+opNLJ6sSWlpaYPn06pkyZoovDERFRCXEnNgnrTt7PV10HCz5dSaWbzu5nxMfHIz4+XleHIyIdUCqVuHLlCgCgVq1anNGfisyzpDQsPHwLm848hFKV12iyzPFkTlaZ02MQlWZaJ2WLFy/W2BZCICoqChs2bEDHjh11FhgRvTulUok///wTAODt7c2kjArdq3QlVp+IxIojEUhKUwAA2ld3RDPPcvhuTzgAaAz4z5pIKbCLt3q+MqLSSuukbMGCBRrbUqkU9vb2GDBgAAICAnQWGBERFR8qlcDOC48x9++b6kH9tcpb4ZtO1eFbuRyAzDnJ3pynzMnKFIFdvOFf01kvcRMZEq2TssjIyMKIg4iIiqkTd55hxt7rCI/KnIW/vLUZJvhXRZfaLpC+1vvlX9MZHbydcp3Rn6i00zopGzx4MBYtWgQLCwuN8uTkZIwaNQqrV6/WWXBERGS4bsUkImjfdYTcfAoAsDA1wog2nhjY1AOmxjnfKpdJJeqeMyLSpPXTl+vWrcOrV6+ylb969Qrr16/XSVBERGS4YhNTEbDjCvwXHkXIzacwkkowsKkH/v1fG3zRqnKuCRkR5S3fPWUJCQkQQkAIgcTERJia/vfoslKpxL59++Dg4FAoQRIRkf6lpCuw6mgkfjoagZR0JQDAv4YTJnashop2ZfQcHVHxl++kzNraGhKJBBKJJMfJKCUSCaZPn67T4IiISP+UKoE/wh5h7t83EZuYBgCo42qNyZ2ro6EHp7Eg0pV8J2UhISEQQqBt27b4448/YGv73y+iXC6Hu7s7XFxcCiVIIioYIyMj9OrVS/09kbaO3nqKmfuu40Z0IgDA1dYME/yq4f3azpBIOECfSJfy/SndqlUrAJlPX7q5ufGXkagYkEqlqFGjhr7DoGLoelQCZu67jmO3nwEALE2N8FU7L/TzdYeJEceMERWGfCVlly9fRs2aNSGVShEfH6+eITwntWvX1llwRERUtGISUjHv75vYFvYIQgDGMgkG+HpgZFtPWJvL9R0eUYmWr6Ssbt26iI6OhoODA+rWrQuJRAIhsi+bIZFIoFQqdR4kERWMSqXC9evXAQDVq1eHVKqT5W6pBEpOU+Cno3ex6uhdvMrI/BzvXNsZE/yqwr0cB/ETFYV8JWWRkZGwt7dXf09ExYNCocD27dsBAAEBAZDL2dNBmhRKFbaFPcK8v2/hWVLmIH4fdxt806k6fNxt9BwdUemSr6TM3d09x++JiKh4EkLgyM3MQfy3Y5MAAO7lzDHJvxr8azpx3DCRHuQrKdu9e3e+D9i1a1etAli2bBnmzJmD6Oho1KlTB0uWLEGjRo1yrb9w4UKsWLECDx48gJ2dHXr16oWgoCCNedOIiCh3Vx/HI2j/dZy48xwAYG1ujNHtvNC3sTvkRrzFTaQv+UrKunfvnq+DaTumbMuWLRg3bhxWrlyJxo0bY+HChfDz88PNmzdznIj2999/x6RJk7B69Wo0bdoUt27dwsCBAyGRSDB//vx8n5eIqDR68vIV5v59EzsvPIYQgFwmxaBmHviyjSeszIz1HR5RqZevpEylUhXKyefPn4+hQ4di0KBBAICVK1di7969WL16NSZNmpSt/smTJ9GsWTN88sknAAAPDw98/PHHOH36dKHER0RUnChVIsfFvhNTM7Dy3wj8ciwSaYrMz/NudV0w/r2qcLU113PURJRFb7NJpqenIywsDAEBAeoyqVSK9u3bIzQ0NMd9mjZtit9++w1nzpxBo0aNcPfuXezbtw/9+vXL9TxpaWlIS0tTbyckJOjuIoiIDMSBq1GYviccUfGp6jInS1O0rmaPQ9di8Dw5HQDQqKItvu1UHXVcrfUUKRHlpkBJWXBwMBYsWKDxqP2YMWPQvn37fB/j2bNnUCqVcHR01Ch3dHTEjRs3ctznk08+wbNnz9C8eXMIIaBQKPDFF1/gm2++yfU8QUFBXP6JiEq0A1ejMPy383hzoqLohFRsPvMQAFDJrgwmdayGDt6OHMRPZKC0HtG5fPly+Pv7w8LCAqNHj8bo0aNhaWmJTp06YdmyZYURo9qRI0cwc+ZMLF++HOfPn8eOHTuwd+9efP/997nuExAQgPj4ePXXw4cPCzVGIkMik8nQrVs3dOvWDTIZZ2EviZQqgel7wrMlZK+zNDPCvtEt8F4NPlVJZMi07imbOXMmFixYgJEjR6rLvvrqKzRr1gwzZ87EiBEj8nUcOzs7yGQyxMTEaJTHxMTAyckpx32mTJmCfv364bPPPgMA1KpVC8nJyRg2bBi+/fbbHCfGNDExgYmJSX4vj6hEkclkqFu3rr7DoEJ0JjJO45ZlThJeKXDhwUv4Vi5XRFERUUFo3VP28uVL+Pv7Zyt/7733EB8fn+/jyOVy+Pj4IDg4WF2mUqkQHBwMX1/fHPdJSUnJlnhl/fef0woDREQlXWxi3gmZtvWISH+0Tsq6du2KnTt3Ziv/888/8f7772t1rHHjxmHVqlVYt24drl+/juHDhyM5OVn9NGb//v01HgTo0qULVqxYgc2bNyMyMhKHDh3ClClT0KVLF96aIcqBSqXCrVu3cOvWrUJ7ipr0Jz4lA3+cf5Svug4WnMuRyNBpffvS29sbM2bMwJEjR9Q9WqdOncKJEyfw9ddfY/Hixeq6X331VZ7H6tOnD54+fYqpU6ciOjoadevWxYEDB9SD/x88eKDRMzZ58mRIJBJMnjwZjx8/hr29Pbp06YIZM2ZoexlEpYJCocCmTZsAcJmlkubgtWhM3nUVTxPT8qwnAeBklTk9BhEZNonQ8r5fxYoV83dgiQR3794tUFCFKSEhAVZWVoiPj4elpaW+wyEqVOnp6QgKCgLApKykeJaUhsDd17D3chQAoLJ9GfSoXx5zD94CAI0B/1lD+ld8Wh/+NZ2LNlAiUstv7qF1TxkXJCciKnpCCOy+9ATTdl/Di5QMyKQSfN6yEr5q5wVTYxkq25fNPk+ZlSkCu3gzISMqJvQ2eSwREeVPdHwqvt15BcE3YgEA1Z0tMadXbdQsb6Wu41/TGR28nXKc0Z+IigetkzIhBLZv346QkBDExsZmGzy8Y8cOnQVHRFSaCSGw5exDzNh7HYlpChjLJPiqrRe+aF0ZxrLsz2nJpBJOe0FUjGmdlI0ZMwY//fQT2rRpA0dHzgxNRFQYHsalIGDHFRy/8wwAUMfVGnN61UYVRws9R0ZEhUXrpGzDhg3YsWMHOnXqVBjxEBGVaiqVwPrQe/jx4E2kpCthYiTF//yqYlCzirwVSVTCaZ2UWVlZoVKlSoURCxHpmEwmQ8eOHdXfk2GLeJqEidsv49z9FwCAxhVtMbtnbXjYldFzZERUFLSeEmPdunU4cOAAVq9eDTMzs8KKq9BwSgwiMjQKpQqrjkViweFbSFeoUEYuw6RO1dG3kRuk7B0jKvYKbUqM3r17Y9OmTXBwcICHhweMjY01Xj9//rz20RIRlVLXoxIwYftlXHmcuUxdyyr2COpRC+Wti98/vUT0brROygYMGICwsDB8+umnHOhPZOBUKhUePHgAAHBzc8u2dizpT7pChaUhd7A85A4UKgFLUyNM7VIDPeuX5+cqUSmldVK2d+9eHDx4EM2bNy+MeIhIhxQKBdatWweAM/obkksPX2LC9su4GZMIAPCr4Yjvu9WEgyXXpyQqzbROylxdXTkWi4ioAFIzlFhw6BZWHbsLlQDKlZHju2410amWE3vHiAha38uYN28eJkyYgHv37hVCOEREJdOZyDh0XHQMPx3NTMi613XBoXGt0Lm2MxMyIgJQgJ6yTz/9FCkpKahcuTLMzc2zDfSPi4vTWXBERMVdUpoCPx64gfWh9wEAjpYmmPlBLbSr7qjnyIjI0GidlC1cuLAQwiAiKnmO3nqKgB1X8PjlKwDARw1dEdCpOqzMjN+yJxGVRgV6+pKIiHIXn5KBH/aGY1vYIwBABRszzO5ZG8087fQcGREZMq2TstelpqYiPT1do4wPARBRafb3tWhM3nUVsYlpkEiAAb4e+J9fVZQxeaePWyIqBbT+lEhOTsbEiROxdetWPH/+PNvrSqVSJ4ER0buTyWRo3769+nsqPM+T0jBtTzj2XHoCAKhkXwY/9qyNBh62eo6MiIoLrZOyCRMmICQkBCtWrEC/fv2wbNkyPH78GD/99BNmzZpVGDESUQHJZDI0a9ZM32GUaEII7LkchWm7ryEuOR0yqQTDWlbC6HZeMDVmIkxE+ad1UrZnzx6sX78erVu3xqBBg9CiRQt4enrC3d0dGzduRN++fQsjTiIivVKqBM5ExiE2MRUOFqZoVNEWz5LS8O3Oqzh8PQYAUM3JAnN61UGtClZ6jpaIiiOtk7K4uDhUqlQJQOb4sawpMJo3b47hw4frNjoieicqlQpRUVEAAGdnZy6zVEAHrkZh+p5wRMWnqsuszIyRplAiNUMFY5kEo9p64YtWlSE3YhsTUcFo/elRqVIlREZGAgCqVauGrVu3AsjsQbO2ttZpcET0bhQKBX755Rf88ssvUCgU+g6nWDpwNQrDfzuvkZABQPyrDKRmqOBezhx/jWqBr9p5MSEjonei9SfIoEGDcOnSJQDApEmTsGzZMpiammLs2LH43//+p/MAiYj0RakSmL4nHCKPOukKFTwdyhZZTERUcml9+3Ls2LHq79u3b48bN24gLCwMnp6eqF27tk6DIyLSpzORcdl6yN4UFZ+KM5Fx8K1croiiIqKS6p0nznF3d4e7u7suYiEiMiixiXknZNrWIyLKCwdAEBHlIjE1f+PwHCxMCzkSIioNOMU0EVEO9l6Ownd7ruVZRwLAySpzegwionfFnjIiotcIIbAk+DZG/H4e6UqBmi6WkCAzAXtd1nZgF2/IpG++SkSkPb0nZcuWLYOHhwdMTU3RuHFjnDlzJs/6L1++xIgRI+Ds7AwTExNUqVIF+/btK6JoiYoXmUyGVq1aoVWrVlxmKR9SM5QYu+Ui5h26BQAY3Kwi/hzZHCs+rQ8nK81blE5WpljxaX3413TWR6hEVAIV6PZlREQE1qxZg4iICCxatAgODg7Yv38/3NzcUKNGjXwfZ8uWLRg3bhxWrlyJxo0bY+HChfDz88PNmzfh4OCQrX56ejo6dOgABwcHbN++HeXLl8f9+/c5PxpRLmQyGVq3bq3vMIqFZ0lp+HxDGMLuv4BMKsF33Wqgb+PMh5j8azqjg7dTthn92UNGRLokEULkNQVPNv/++y86duyIZs2a4ejRo7h+/ToqVaqEWbNm4dy5c9i+fXu+j9W4cWM0bNgQS5cuBZA5+7irqytGjRqFSZMmZau/cuVKzJkzBzdu3ICxsbE2YaslJCTAysoK8fHxsLS0LNAxiKhkuRmdiCHrzuLRi1ewNDXC8r4+aO5lp++wiKiEyG/uofXty0mTJuGHH37AoUOHIJfL1eVt27bFqVOn8n2c9PR0hIWFoX379v8FI5Wiffv2CA0NzXGf3bt3w9fXFyNGjICjoyNq1qyJmTNnQqlUansZRKWCEAKxsbGIjY2Flv9/lRohN2PRc8VJPHrxCh7lzLFzRDMmZESkF1rfvrxy5Qp+//33bOUODg549uxZvo/z7NkzKJVKODo6apQ7Ojrixo0bOe5z9+5d/PPPP+jbty/27duHO3fu4Msvv0RGRgYCAwNz3CctLQ1paWnq7YSEhHzHSFTcZWRkYMWKFQCAgIAAjX+kSjshBNaevIfv/wqHSgCNK9pi5ac+sCnDNiIi/dC6p8za2lq9wPHrLly4gPLly+skqNyoVCo4ODjg559/ho+PD/r06YNvv/0WK1euzHWfoKAgWFlZqb9cXV0LNUYiMnwZShUm77qK6XsyE7LeDSpgw5DGTMiISK+0Tso++ugjTJw4EdHR0ZBIJFCpVDhx4gTGjx+P/v375/s4dnZ2kMlkiImJ0SiPiYmBk5NTjvs4OzujSpUqGk+RVa9eHdHR0UhPT89xn4CAAMTHx6u/Hj58mO8YiajkiX+VgUFrzmLj6QeQSIBvOlXD7J61uZg4Eemd1p9CM2fORLVq1eDq6oqkpCR4e3ujZcuWaNq0KSZPnpzv48jlcvj4+CA4OFhdplKpEBwcDF9f3xz3adasGe7cuQOVSqUuu3XrFpydnXO9LWNiYgJLS0uNLyIqne49S0aP5Sdw/M4zmMtl+LlfAwxrWRkSCZ+iJCL90zopk8vlWLVqFSIiIvDXX3/ht99+w40bN7Bhwwat50EaN24cVq1ahXXr1uH69esYPnw4kpOTMWjQIABA//79ERAQoK4/fPhwxMXFYfTo0bh16xb27t2LmTNnYsSIEdpeBhGVMqfuPkf35ScQ8TQZzlam2PaFLzp4O759RyKiIlLgZZbc3Nzg5ub2Tifv06cPnj59iqlTpyI6Ohp169bFgQMH1IP/Hzx4AKn0v7zR1dUVBw8exNixY1G7dm2UL18eo0ePxsSJE98pDiIq2baee4hvd15BhlKgTgUrrOrfAA6WXK+SiAxLvuYpGzduXL4POH/+/HcKqLBxnjIqTdLT0xEUFASgdD59qVIJzD54Az/9excA0Lm2M+Z9WAemxlzdgIiKTn5zj3z1lF24cCFfJ+W4DCLDIpPJ1GM0S9syS8lpCozZchGHwjMfJvqqnRfGtPOClLPwE5GB0npG/+KOPWVEJV9U/CsMWXsO4VEJkBtJ8WPP2uher3Cn7CEiyo1Oe8peFx8fD6VSCVtbW43yuLg4GBkZMdEhIr269PAlhq4/h9jENNiVleOnfg3g426j77CIiN6qQPOUbd68OVv51q1b8dFHH+kkKCLSDSEEXr58iZcvX5aKZZb2Xo5C759CEZuYhqqOFtj5ZTMmZERUbGidlJ0+fRpt2rTJVt66dWucPn1aJ0ERkW5kZGRg0aJFWLRoETIyMvQdTqERQmBJ8G2M+P080hQqtK3mgO3DfeFqa67v0IiI8k3r25dpaWlQKBTZyjMyMvDq1SudBEVElF+pGUpM+uMydl18AgAY0rwivulUHTIO6CeiYkbrnrJGjRrh559/zla+cuVK+Pj46CQoIqL8eJaUhk9WncKui09gJJVg5ge1MOV9byZkRFQsad1T9sMPP6B9+/a4dOkS2rVrBwAIDg7G2bNn8ffff+s8QCKinNyMTsTgtWfx+OUrWJoaYcWnPmjmaafvsIiICkzrnrJmzZohNDQUrq6u2Lp1K/bs2QNPT09cvnwZLVq0KIwYiYg0hNyIRc8VJ/H45St4lDPHzhHNmJARUbFXoGWW6tati40bN+o6FiKiPAkhsObEPfywNxwqATSpZIsVfX1gU6Z0rVRARCWT1j1lrVq1wvr16zmon4iKVIZShcm7ruK7vzITsj4NXLF+cGMmZERUYmidlNWrVw/jx4+Hk5MThg4dilOnThVGXESkA1KpFA0aNECDBg0glWr9624w4lMyMHDNGWw8/QASCfBtp+qY1bMW5EbF95qIiN5UoGWWFAoFdu/ejXXr1mH//v3w9PTE4MGD0a9fPzg6OhZGnDrDZZaIipd7z5IxeN1Z3H2aDHO5DIs+qocO3ob9OUNE9Lr85h4F+jfTyMgIPXr0wJ9//olHjx7hk08+wZQpU+Dq6oru3bvjn3/+KXDgRERZTt19ju7LT+Du02S4WJli+xdNmZARUYlVoIH+Wc6cOYM1a9Zg8+bNcHBwwMCBA/H48WO8//77+PLLLzF37lxdxUlEBSCEQEpKCgDA3NwcEonhzd+lVAmciYxDbGIqHCxM0aiiLWRSCbaefYhvd11BhlKgjqs1VvX3gYOFqb7DJSIqNFrfvoyNjcWGDRuwZs0a3L59G126dMFnn30GPz8/9Qf+8ePH4e/vj6SkpEIJ+l3w9iWVJunp6QgKCgIABAQEQC43rEHxB65GYfqecETFp6rLnCxNUauCFQ6FxwAAOtd2xrwP68DUWKavMImI3kl+cw+te8oqVKiAypUrY/DgwRg4cCDs7e2z1alduzYaNmyo7aGJqBQ5cDUKw387jzf/K4xOSEV0eGaS9lU7L4xp5wUpZ+gnolJA66QsODj4rZPEWlpaIiQkpMBBEVHJplQJTN8Tni0he521uTFGMyEjolJE64H+FSpUwO3bt7OV3759G/fu3dNFTERUwp2JjNO4ZZmTlykZOBMZV0QRERHpn9ZJ2cCBA3Hy5Mls5adPn8bAgQN1ERMRlXCxiXknZNrWIyIqCbROyi5cuIBmzZplK2/SpAkuXryoi5iIqITL71OUfNqSiEoTrZMyiUSCxMTEbOXx8fFQKpU6CYqISrZGFW3hbJV7wiUB4GyVOT0GEVFpoXVS1rJlSwQFBWkkYEqlEkFBQWjevLlOgyOidyOVSlGnTh3UqVPHoJZZkkkl+LZz9RxfyxrWH9jFGzIO8ieiUkTrpy9nz56Nli1bomrVquqnMI8dO4aEhATO5E9kYIyMjNC9e3d9h5Gje8+SAQASCfD6bIlOVqYI7OIN/5rOeoqMiEg/tE7KvL29cfnyZSxduhSXLl2CmZkZ+vfvj5EjR8LWlrcaiOjtbsckYnHwHQDA3F614WJtnm1GfyKi0qZAyyy5uLhg5syZuo6FiHRMCIGMjAwAgLGxsUEss6RUCUz44zLSlSq0qWqPHvUrGERcRET69k6DTGrVqoWHDx/qKhYi0rGMjAwEBQUhKChInZzp29qT93DhwUuUNTHCjA9qMSEjIvp/75SU3bt3z2A+6InI8D14noK5B28CAAI6VYOLtZmeIyIiMhwG8TjWsmXL4OHhAVNTUzRu3BhnzpzJ136bN2+GRCIx2IHMRPQfIQQm7biMVxlKNKlki48buuk7JCIig/JOSVmLFi1gZvZu/+lu2bIF48aNQ2BgIM6fP486derAz88PsbGxee537949jB8//q3rcBKRYdhy9iFORjyHqbEUs3rU5pqWRERv0DopO3r0KBQKBQBg3759cHbOfGxdoVDg6NGjWgcwf/58DB06FIMGDYK3tzdWrlwJc3NzrF69Otd9lEol+vbti+nTp6NSpUpan5OIilZ0fCpm7L0OAPi6Q1V42JXRc0RERIZH66SsTZs2iIvLvkhwfHw82rRpo9Wx0tPTERYWhvbt2/8XkFSK9u3bIzQ0NNf9vvvuOzg4OGDIkCFvPUdaWhoSEhI0voio6AghMHnXFSSmKVDH1RqDm1fUd0hERAZJ66RMCJHj01LPnz9HmTLa/ff77NkzKJVKODo6apQ7OjoiOjo6x32OHz+OX3/9FatWrcrXOYKCgmBlZaX+cnV11SpGIno3uy89weHrsTCWSTCnV23OQUZElIt8z1PWo0cPAJlrXw4cOBAmJibq15RKJS5fvoymTZvqPsLXJCYmol+/fli1ahXs7OzytU9AQADGjRun3k5ISGBiRqWGVCqFt7e3+vui9jwpDdP3hAMARrbxQhVHiyKPgYiouMh3UmZlZQUgs6fMwsJCY4C/XC5HkyZNMHToUK1ObmdnB5lMhpiYGI3ymJgYODk5ZasfERGBe/fuoUuXLuoylUqVeSFGRrh58yYqV66ssY+JiYlGAklUmhgZGeHDDz/U2/mn7wlHXHI6qjlZYHjrym/fgYioFMt3UrZmzRoAgIeHB8aPH6/1rcqcyOVy+Pj4IDg4WD2thUqlQnBwMEaOHJmtfrVq1XDlyhWNssmTJyMxMRGLFi1iDxiRATkcHoPdl55AKgFm96wNuZFBzMBDRGSwtF5mKTAwUKcBjBs3DgMGDECDBg3QqFEjLFy4EMnJyRg0aBAAoH///ihfvjyCgoJgamqKmjVrauxvbW0NANnKiUh/4l9l4Ntdmf9ADW1RCXVcrfUbEBFRMZCvpKx+/foIDg6GjY0N6tWrl+eyKOfPn9cqgD59+uDp06eYOnUqoqOjUbduXRw4cEA9+P/Bgwd6GQtDVBKkp6cjKCgIQOb4SrlcXiTnDdp3HTEJaahoVwZjO1QpknMSERV3+UrKunXrph6XVRiz548cOTLH25UAcOTIkTz3Xbt2rc7jIaKCO3HnGTafzVwTd1aPWjA1luk5IiKi4iFfSdnrtyx1ffuSiEqOlHQFJu24DAD4tIkbGlcqp+eIiIiKD63HlL0uKSlJ/fRjFktLy3cKiIiKr7kHb+Fh3Cu4WJlion81fYdDRFSsaD1YKzIyEp07d0aZMmVgZWUFGxsb2NjYwNraGjY2NoURIxEVA2H3X2DNyUgAwMwetWBhaqzniIiIihete8o+/fRTCCGwevVqODo65jnon4hKhzSFEhP/uAwhgB71y6N1VQd9h0REVOxonZRdunQJYWFhqFq1amHEQ0TF0NJ/7uBObBLsysox9X1vfYdDRFQsaX37smHDhnj48GFhxEJEOiaVSuHl5QUvL69Cm1om/EkCVhyJAAB8160mrM2LZtoNIqKSRuuesl9++QVffPEFHj9+jJo1a8LYWHPcSO3atXUWHBG9GyMjI3zyySeFdnyFUoUJf1yCQiXgX8MJnWo5F9q5iIhKOq2TsqdPnyIiIkI94z6QuUi5EAISiQRKpVKnARKR4fr52F1cfZwAKzNjfNe9hr7DISIq1rROygYPHox69eph06ZNHOhPVIpFPE3CwsO3AQBT3veGg4WpniMiIiretE7K7t+/j927d8PT07Mw4iEiHUpPT8fcuXMBAOPHj9fZMksqlcCkPy4jXaFCyyr26Fm/vE6OS0RUmmk98rdt27a4dOlSYcRCRIUgIyMDGRkZOj3mhlP3cfbeC5SRyzDzg5rsMSci0gGte8q6dOmCsWPH4sqVK6hVq1a2gf5du3bVWXBEZHgexqVg9oEbAICJHauhgo25niMiIioZtE7KvvjiCwDAd999l+01DvQnKtmEEPhm5xWkpCvRyMMWnzZ213dIREQlhtZJ2ZtrXRJR6bE97BGO3X4GEyMpZvWsBamUty2JiHSlcGaTJKISJzYhFd//FQ4AGNuhCirZl9VzREREJUu+esoWL16MYcOGwdTUFIsXL86z7ldffaWTwIjIcAghMOXPq0hIVaBWeSt81ryivkMiIipx8pWULViwAH379oWpqSkWLFiQaz2JRMKkjMiASCQSuLu7q78vqH1XonHwWgyMpBLM7lkbRjJ2shMR6Vq+krLIyMgcvyciw2ZsbIyBAwe+0zFeJKcjcPdVAMCXrSvD28VSB5EREdGb+O8uEeXp+7/C8SwpHV4OZTGiLSeNJiIqLPnqKRs3bly+Dzh//vwCB0NEhiXkRix2XHgMiQT4sVdtmBjJ9B0SEVGJla+k7MKFC/k6GGf1JjIs6enpWLRoEQBg9OjRWi2zlJiagW92XgEADG5WEfXcbAolRiIiypSvpCwkJKSw4yCiQpKSklKg/Wbtv4Go+FS42Zpj/HtVdRwVERG9iWPKiCibU3efY+PpBwCAWT1rwUzO25ZERIWNSRkRaXiVrsSkPy4DAD5u5Iamle30HBERUenApIyINCw4fAv3nqfAydIUAZ2q6TscIqJSg0kZEaldevgSvxy7CwCY2aMmLE2N9RwREVHpwaSMiAAA6QoVJmy/DJUAutV1QdtqjvoOiYioVDGIpGzZsmXw8PCAqakpGjdujDNnzuRad9WqVWjRogVsbGxgY2OD9u3b51mfqDSTSCRwcXGBi4vLW6esWX7kDm7GJKJcGTkCu9QoogiJiCiL3pOyLVu2YNy4cQgMDMT58+dRp04d+Pn5ITY2Nsf6R44cwccff4yQkBCEhobC1dUV7733Hh4/flzEkRMZPmNjYwwdOhRDhw6FsXHutyJvRidiWcgdAMC0rjVgWyb/85kREZFuSIQQQp8BNG7cGA0bNsTSpUsBACqVCq6urhg1ahQmTZr01v2VSiVsbGywdOlS9O/f/631ExISYGVlhfj4eFhacg0/IoVShZ4rTuLSo3h08HbEz/18OBE0EZEO5Tf30GtPWXp6OsLCwtC+fXt1mVQqRfv27REaGpqvY6SkpCAjIwO2traFFSZRibb6RCQuPYqHhakRfuhekwkZEZGe5GtG/8Ly7NkzKJVKODpqDih2dHTEjRs38nWMiRMnwsXFRSOxe11aWhrS0tLU2wkJCQUPmKiYycjIwLJlywAAI0aMyHYL896zZMz7+xYAYHLn6nC0NC3yGImIKJPex5S9i1mzZmHz5s3YuXMnTE1z/mMSFBQEKysr9Zerq2sRR0mkP0IIxMfHIz4+Hm+OVFCpBCb+cRlpChWae9qhdwP+bhAR6ZNekzI7OzvIZDLExMRolMfExMDJySnPfefOnYtZs2bh77//Ru3atXOtFxAQoP6jFB8fj4cPH+okdqLi7vczD3A6Mg5mxjIE9ajF25ZERHqm16RMLpfDx8cHwcHB6jKVSoXg4GD4+vrmut+PP/6I77//HgcOHECDBg3yPIeJiQksLS01vohKuycvX2HW/swhAhP8q8LV1lzPERERkV7HlAHAuHHjMGDAADRo0ACNGjXCwoULkZycjEGDBgEA+vfvj/LlyyMoKAgAMHv2bEydOhW///47PDw8EB0dDQAoW7YsypYtq7frICouhBD4ZucVJKUp4ONug/6+HvoOiYiIYABJWZ8+ffD06VNMnToV0dHRqFu3Lg4cOKAe/P/gwQNIpf916K1YsQLp6eno1auXxnECAwMxbdq0ogydqFjadfExjtx8CrlMitk9a0Em5W1LIiJDoPekDABGjhyJkSNH5vjakSNHNLbv3btX+AERlVBPE9MwfU84AGB0ey94OljoOSIiIspiEEkZERUOlQDKWNlCqVLhTGQcfj/7GC9TMuDtbIlhLSvpOzwiInoNkzKiEurA1ShM3xOOqPjM5GvFmjAAgFQC/NirNoxlxXpGHCKiEoefykQl0IGrURj+23lExadme00lgEcvUvQQFRER5YVJGVEJo1QJTN8TjtwWtZUAmL4nHEqVXpe9JSKiNzApIyphzkTGqXvIZFCiu8lVdDe5ChmUAAABICo+FWci4/QYJRERvYljyohKmNjE/25ZSgDYSFPV3+dWj4iI9I89ZUQljINF/hYVz289IiIqGuwpIypBElMzsPvS4zzrSAA4WZmiUUXbogmKiIjyhUkZUQlx5GYsvtlxBU/iNW9fvi5rO7CLN2fyJyIyMEzKiIq5+JQMfL83HNvDHgEA3GzNMatnLSS8ysAPu68AGf/VdbIyRWAXb/jXdNZTtERElBsmZUTF2N/XovHtrqt4mpgGiQQY1LQixvtVgbk881e7lactfpwdCgBYM6gRmno5soeMiMhAMSkjKoaeJ6Vh2p5w7Ln0BABQyb4M5vSqDR93zXFiRjIprKysAABNKpVjQkZEZMCYlBEVI0II/HU5CoG7ryEuOR1SCfB5q8oY3c4LpsaybPWNjY0xZsyYog+UiIi0xqSMqJiITUjFlD+v4uC1GABANScL/NirNmpXsNZvYEREpBNMyogMnBACO84/xnd/hSP+VQaMpBKMaOOJEW08ITfiVINERCUFkzIiA/bk5St8s/MKjtx8CgCoWd4Sc3rVQXVny3ztn5GRgbVr1wIABg4cCGNj48IKlYiI3hGTMiIDJITApjMPMXPfdSSlKSA3kmJMey8Ma1EJRrL8944JIfDkyRP190REZLiYlBEZmAfPUzBpx2WcjHgOAKjvZo0fe9WGp4OFniMjIqLCxKSMyECoVALrQu/hxwM38SpDCVNjKf7nVw0Dm3pwKgsiolKASRmRAYh4moSJ2y/j3P0XAIAmlWwxu2dtuJcro+fIiIioqDApI9IjhVKFX49HYv6hW0hTqFBGLkNAp+r4pJEbpOwdIyIqVZiUEenJzehETNh+CZcexQMAWlaxR1CPWihvbabnyIiISB+YlBEVsQylCiuORGDJP7eRoRSwMDXC1Pe90cunAiQS3feOmZub6/yYRESkexJRyp6TT0hIgJWVFeLj42Fpmb+5noh05erjePxv+2Vcj0oAALSv7oAZH9SCo6WpniMjIqLCkt/cgz1lREUgNUOJJf/cxsp/70KpErAxN8a0rjXQtY5LofSOERFR8cOkjKiQnX/wAhO2X8ad2CQAQOfazpjetQbsyproOTIiIjIkTMqICsmrdCXm/X0Tv56IhBCAXVkT/NC9BvxrOhdZDBkZGdi4cSMAoG/fvlxmiYjIgDEp0zGlSuBMZBxiE1PhYGGKRhVtDW7iT8aoG3nFeOruc0z84zLuP08BAPSoXx5T3/eGtbm8SGMUQuD+/fvq74mIyHAZRFK2bNkyzJkzB9HR0ahTpw6WLFmCRo0a5Vp/27ZtmDJlCu7duwcvLy/Mnj0bnTp1KsKIc3bgahSm7wlHVHyquszZyhSBXbyLtHckL4xRN3KLcYJ/NZy//wIbTt1Xl838oBbaVHPQV6hERFRM5H9l40KyZcsWjBs3DoGBgTh//jzq1KkDPz8/xMbG5lj/5MmT+PjjjzFkyBBcuHAB3bt3R/fu3XH16tUijlzTgatRGP7beY0/0gAQHZ+K4b+dx4GrUXqK7D+MUTdyizEqPhVjt1xUJ2QfN3LDwbEtmZAREVG+6D0pmz9/PoYOHYpBgwbB29sbK1euhLm5OVavXp1j/UWLFsHf3x//+9//UL16dXz//feoX78+li5dWsSR/0epEpi+Jxw53RzKKpu+JxxKlf5uHzFG3cgrxiwyCbBhcCME9agFS1OO4SIiovzR6+3L9PR0hIWFISAgQF0mlUrRvn17hIaG5rhPaGgoxo0bp1Hm5+eHXbt25Vg/LS0NaWlp6u2EhIR3D/wNZyLjsvWavE4gsxfly41hcLbSz2ztUfGvSk6Mv4XByUo/83pFx6fmGSMAKAVgJNP7/ztERFTM6DUpe/bsGZRKJRwdHTXKHR0dcePGjRz3iY6OzrF+dHR0jvWDgoIwffp03QSci9jEvP9IZzl4LaZQ49CFYhFjuOHHmN/3BBERURaDGOhfmAICAjR61hISEuDq6qrTczhY5K/XpntdF1Sw0c+SN49epGDXxSdvrVccYvygnn5j3Hnh7THm9z1RFDgNBhFR8aDXpMzOzg4ymQwxMZo9HzExMXBycspxHycnJ63qm5iYwMSkcCfpbFTRFs5WpoiOT81xrJEEgJOVKeb1rqu3aR2UKoHTkXElIsa5H+o3xlN33x5jo4q2RR1ajuRyOb755ht9h0FERPmg14EvcrkcPj4+CA4OVpepVCoEBwfD19c3x318fX016gPAoUOHcq1fFGRSCQK7eAPI/KP8uqztwC7eep1nizHqRnGIkYiIiie9j0YeN24cVq1ahXXr1uH69esYPnw4kpOTMWjQIABA//79NR4EGD16NA4cOIB58+bhxo0bmDZtGs6dO4eRI0fq6xIAAP41nbHi0/rZBqA7WZlixaf1DWJ+LcaoG8UhRiIiKn4kwgCm+V66dKl68ti6deti8eLFaNy4MQCgdevW8PDwwNq1a9X1t23bhsmTJ6snj/3xxx/zPXlsfldqL6jiPhO9oWCMuqFQKLB161YAQO/evWFkVOKHkRIRGZz85h4GkZQVpcJOyogMSXp6OoKCggBkPvQilxftMk9ERJT/3EPvty+JiIiIiEkZERERkUFgUkZERERkAJiUERERERkAJmVEREREBqDUPR+f9bBpYSxMTmRo0tPTkZqauQ5nQkICn74kItKDrJzjbRNelLopMR49eqTztS+JiIiI3ubhw4eoUKFCrq+XuqRMpVLhyZMnsLCwgERSOBN9Zi16/vDhQ86F9g7YjrrBdtQdtqVusB11g+2oG0XRjkIIJCYmwsXFBVJp7iPHSt3tS6lUmmeWqkuWlpb8RdEBtqNusB11h22pG2xH3WA76kZht6OVldVb63CgPxEREZEBYFJGREREZACYlBUCExMTBAYGwsTERN+hFGtsR91gO+oO21I32I66wXbUDUNqx1I30J+IiIjIELGnjIiIiMgAMCkjIiIiMgBMyoiIiIgMAJMyIiIiIgPApExH4uLi0LdvX1haWsLa2hpDhgxBUlJSnvVHjRqFqlWrwszMDG5ubvjqq68QHx9fhFEbHm3bEQB+/vlntG7dGpaWlpBIJHj58mXRBGtAli1bBg8PD5iamqJx48Y4c+ZMnvW3bduGatWqwdTUFLVq1cK+ffuKKFLDpk07Xrt2DT179oSHhwckEgkWLlxYdIEWA9q05apVq9CiRQvY2NjAxsYG7du3f+t7uLTQph137NiBBg0awNraGmXKlEHdunWxYcOGIozWcGn7GZll8+bNkEgk6N69e+EGmEWQTvj7+4s6deqIU6dOiWPHjglPT0/x8ccf51r/ypUrokePHmL37t3izp07Ijg4WHh5eYmePXsWYdSGR9t2FEKIBQsWiKCgIBEUFCQAiBcvXhRNsAZi8+bNQi6Xi9WrV4tr166JoUOHCmtraxETE5Nj/RMnTgiZTCZ+/PFHER4eLiZPniyMjY3FlStXijhyw6JtO545c0aMHz9ebNq0STg5OYkFCxYUbcAGTNu2/OSTT8SyZcvEhQsXxPXr18XAgQOFlZWVePToURFHbli0bceQkBCxY8cOER4eLu7cuSMWLlwoZDKZOHDgQBFHbli0bccskZGRonz58qJFixaiW7duRRIrkzIdCA8PFwDE2bNn1WX79+8XEolEPH78ON/H2bp1q5DL5SIjI6MwwjR479qOISEhpTIpa9SokRgxYoR6W6lUChcXFxEUFJRj/d69e4vOnTtrlDVu3Fh8/vnnhRqnodO2HV/n7u7OpOw179KWQgihUCiEhYWFWLduXWGFWCy8azsKIUS9evXE5MmTCyO8YqMg7ahQKETTpk3FL7/8IgYMGFBkSRlvX+pAaGgorK2t0aBBA3VZ+/btIZVKcfr06XwfJz4+HpaWljAyKnVLkgLQXTuWJunp6QgLC0P79u3VZVKpFO3bt0doaGiO+4SGhmrUBwA/P79c65cGBWlHypku2jIlJQUZGRmwtbUtrDAN3ru2oxACwcHBuHnzJlq2bFmYoRq0grbjd999BwcHBwwZMqQowlQrnX/9dSw6OhoODg4aZUZGRrC1tUV0dHS+jvHs2TN8//33GDZsWGGEWCzooh1Lm2fPnkGpVMLR0VGj3NHRETdu3Mhxn+jo6Bzrl+Y2Lkg7Us500ZYTJ06Ei4tLtn8eSpOCtmN8fDzKly+PtLQ0yGQyLF++HB06dCjscA1WQdrx+PHj+PXXX3Hx4sUiiFATe8ryMGnSJEgkkjy/dPGBnZCQgM6dO8Pb2xvTpk1798ANTFG1IxEVf7NmzcLmzZuxc+dOmJqa6jucYsfCwgIXL17E2bNnMWPGDIwbNw5HjhzRd1jFRmJiIvr164dVq1bBzs6uyM/PnrI8fP311xg4cGCedSpVqgQnJyfExsZqlCsUCsTFxcHJySnP/RMTE+Hv7w8LCwvs3LkTxsbG7xq2wSmKdiyt7OzsIJPJEBMTo1EeExOTa5s5OTlpVb80KEg7Us7epS3nzp2LWbNm4fDhw6hdu3ZhhmnwCtqOUqkUnp6eAIC6devi+vXrCAoKQuvWrQszXIOlbTtGRETg3r176NKli7pMpVIByLxzc/PmTVSuXLnQ4mVPWR7s7e1RrVq1PL/kcjl8fX3x8uVLhIWFqff9559/oFKp0Lhx41yPn5CQgPfeew9yuRy7d+8usf8VFnY7lmZyuRw+Pj4IDg5Wl6lUKgQHB8PX1zfHfXx9fTXqA8ChQ4dyrV8aFKQdKWcFbcsff/wR33//PQ4cOKAxrrS00tV7UqVSIS0trTBCLBa0bcdq1arhypUruHjxovqra9euaNOmDS5evAhXV9fCDbhIHicoBfz9/UW9evXE6dOnxfHjx4WXl5fGVA6PHj0SVatWFadPnxZCCBEfHy8aN24satWqJe7cuSOioqLUXwqFQl+XoXfatqMQQkRFRYkLFy6IVatWCQDi6NGj4sKFC+L58+f6uIQit3nzZmFiYiLWrl0rwsPDxbBhw4S1tbWIjo4WQgjRr18/MWnSJHX9EydOCCMjIzF37lxx/fp1ERgYyCkxhPbtmJaWJi5cuCAuXLggnJ2dxfjx48WFCxfE7du39XUJBkPbtpw1a5aQy+Vi+/btGp+FiYmJ+roEg6BtO86cOVP8/fffIiIiQoSHh4u5c+cKIyMjsWrVKn1dgkHQth3fVJRPXzIp05Hnz5+Ljz/+WJQtW1ZYWlqKQYMGaXygREZGCgAiJCRECPHf9A05fUVGRurnIgyAtu0ohBCBgYE5tuOaNWuK/gL0ZMmSJcLNzU3I5XLRqFEjcerUKfVrrVq1EgMGDNCov3XrVlGlShUhl8tFjRo1xN69e4s4YsOkTTtmvRff/GrVqlXRB26AtGlLd3f3HNsyMDCw6AM3MNq047fffis8PT2FqampsLGxEb6+vmLz5s16iNrwaPsZ+bqiTMokQghRuH1xRERERPQ2HFNGREREZACYlBEREREZACZlRERERAaASRkRERGRAWBSRkRERGQAmJQRERERGQAmZUREREQGgEkZUSnRunVrjBkzJs86Hh4eWLhwoXo7OjoaHTp0QJkyZWBtbV2o8RWURCLBrl279B0GEdE744LkRKR29uxZlClTRr29YMECREVF4eLFi7CystJjZMC0adOwa9cuXLx4UaM8KioKNjY2+gmqmBs4cCBevnzJpJbIQDApIyI1e3t7je2IiAj4+PjAy8urwMcUQkCpVMLIqHA+bpycnArluEUhIyMDxsbG+g7jnaWnp0Mul+s7DKJij7cviUoRhUKBkSNHwsrKCnZ2dpgyZQpeX2nt9duXHh4e+OOPP7B+/XpIJBIMHDgQ9+7dg0Qi0eitevnyJSQSCY4cOQIAOHLkCCQSCfbv3w8fHx+YmJjg+PHjUKlU+PHHH+Hp6QkTExO4ublhxowZ6uNMnDgRVapUgbm5OSpVqoQpU6YgIyMDALB27VpMnz4dly5dgkQigUQiwdq1awFkv3155coVtG3bFmZmZihXrhyGDRuGpKQk9esDBw5E9+7dMXfuXDg7O6NcuXIYMWKE+lw5mTZtGurWrYuffvoJrq6uMDc3R+/evREfH6+uc/bsWXTo0AF2dnawsrJCq1atcP78eY3jSCQSrFixAl27dkWZMmUwY8YMKJVKDBkyBBUrVoSZmRmqVq2KRYsWaeyXFfPMmTPh6OgIa2trfPfdd1AoFPjf//4HW1tbVKhQAWvWrNHY7+HDh+jduzesra1ha2uLbt264d69e+prWrduHf788091m2b9DPPa7/V4ZsyYARcXF1StWjXHdouIiEC3bt3g6OiIsmXLomHDhjh8+HCu7UxU2jEpIypF1q1bByMjI5w5cwaLFi3C/Pnz8csvv+RY9+zZs/D390fv3r0RFRWVLVF4m0mTJmHWrFm4fv06ateujYCAAMyaNQtTpkxBeHg4fv/9dzg6OqrrW1hYYO3atQgPD8eiRYuwatUqLFiwAADQp08ffP3116hRowaioqIQFRWFPn36ZDtncnIy/Pz8YGNjg7Nnz2Lbtm04fPgwRo4cqVEvJCQEERERCAkJwbp167B27Vp1kpebO3fuYOvWrdizZw8OHDiACxcu4Msvv1S/npiYiAEDBuD48eM4deoUvLy80KlTJyQmJmocZ9q0afjggw9w5coVDB48GCqVChUqVMC2bdsQHh6OqVOn4ptvvsHWrVs19vvnn3/w5MkTHD16FPPnz0dgYCDef/992NjY4PTp0/jiiy/w+eef49GjRwAye+H8/PxgYWGBY8eO4cSJEyhbtiz8/f2Rnp6O8ePHo3fv3vD391e3adOmTd+6X5bg4GDcvHkThw4dwl9//ZVjmyUlJaFTp04IDg7GhQsX4O/vjy5duuDBgwd5tjVRqVUky54Tkd61atVKVK9eXahUKnXZxIkTRfXq1dXb7u7uYsGCBertbt26iQEDBqi3IyMjBQBx4cIFddmLFy8EABESEiKEECIkJEQAELt27VLXSUhIECYmJmLVqlX5jnfOnDnCx8dHvR0YGCjq1KmTrR4AsXPnTiGEED///LOwsbERSUlJ6tf37t0rpFKpiI6OFkIIMWDAAOHu7i4UCoW6zocffij69OmTayyBgYFCJpOJR48eqcv2798vpFKpiIqKynEfpVIpLCwsxJ49ezRiHTNmTN4XLoQYMWKE6Nmzp3o7K2alUqkuq1q1qmjRooV6W6FQiDJlyohNmzYJIYTYsGGDqFq1qsbPOy0tTZiZmYmDBw+qj9utWzeNc+d3P0dHR5GWlvbWa3lTjRo1xJIlS7Tej6g0YE8ZUSnSpEkTSCQS9bavry9u374NpVKp83M1aNBA/f3169eRlpaGdu3a5Vp/y5YtaNasGZycnFC2bFlMnjxZ6x6V69evo06dOhoPKzRr1gwqlQo3b95Ul9WoUQMymUy97ezsjNjY2DyP7ebmhvLly6u3fX19NY4bExODoUOHwsvLC1ZWVrC0tERSUlK2a3i9XbIsW7YMPj4+sLe3R9myZfHzzz9n269GjRqQSv/7yHZ0dEStWrXU2zKZDOXKlVNfx6VLl3Dnzh1YWFigbNmyKFu2LGxtbZGamoqIiIhcrzO/+9WqVeut48iSkpIwfvx4VK9eHdbW1ihbtiyuX7/OnjKiXHCgPxHlW1ZSIF4bh5bbWKzXEyMzM7M8jxsaGoq+ffti+vTp8PPzg5WVFTZv3ox58+bpIOrs3hxcL5FIoFKp3umYAwYMwPPnz7Fo0SK4u7vDxMQEvr6+Grf8AM12AYDNmzdj/PjxmDdvHnx9fWFhYYE5c+bg9OnTb405r+tISkqCj48PNm7cmC3WNx/oeF1+93vzOnIyfvx4HDp0CHPnzoWnpyfMzMzQq1evbG1CRJmYlBGVIm/+oc8a+/R6r1Fesv4oR0VFoV69egCQbYqKnHh5ecHMzAzBwcH47LPPsr1+8uRJuLu749tvv1WX3b9/X6OOXC5/a49e9erVsXbtWiQnJ6uThhMnTkAqleY6GD2/Hjx4gCdPnsDFxQVAZtu9ftwTJ05g+fLl6NSpE4DMwfLPnj1763FPnDiBpk2baoxPy6snK7/q16+PLVu2wMHBAZaWljnWyalN87Nffp04cQIDBw7EBx98ACAz4Xv9gQEi0sTbl0SlyIMHDzBu3DjcvHkTmzZtwpIlSzB69Oh8729mZoYmTZqoB/D/+++/mDx58lv3MzU1xcSJEzFhwgSsX78eEREROHXqFH799VcAmUnbgwcPsHnzZkRERGDx4sXYuXOnxjE8PDwQGRmJixcv4tmzZ0hLS8t2nr59+8LU1BQDBgzA1atXERISglGjRqFfv34aDxUURNZxL126hGPHjuGrr75C79691VNyeHl5YcOGDbh+/TpOnz6Nvn37vrWHMGu/c+fO4eDBg7h16xamTJmCs2fPvlOsQGZb2NnZoVu3bjh27BgiIyNx5MgRfPXVV+qHATw8PHD58mXcvHkTz549Q0ZGRr72yy8vLy/s2LEDFy9exKVLl/DJJ5+8c48kUUnGpIyoFOnfvz9evXqFRo0aYcSIERg9ejSGDRum1TFWr14NhUIBHx8fjBkzBj/88EO+9psyZQq+/vprTJ06FdWrV0efPn3U45+6du2KsWPHYuTIkahbty5OnjyJKVOmaOzfs2dP+Pv7o02bNrC3t8emTZuyncPc3BwHDx5EXFwcGjZsiF69eqFdu3ZYunSpVteYE09PT/To0QOdOnXCe++9h9q1a2P58uXq13/99Ve8ePEC9evXR79+/fDVV1/BwcHhrcf9/PPP0aNHD/Tp0weNGzfG8+fPNXrNCsrc3BxHjx6Fm5sbevTogerVq2PIkCFITU1V94ANHToUVatWRYMGDWBvb48TJ07ka7/8mj9/PmxsbNC0aVN06dIFfn5+qF+//jtfG1FJJRGvDw4hIqJscltNgIhIl9hTRkRERGQAmJQRERERGQDeviQiIiIyAOwpIyIiIjIATMqIiIiIDACTMiIiIiIDwKSMiIiIyAAwKSMiIiIyAEzKiIiIiAwAkzIiIiIiA8CkjIiIiMgAMCkjIiIiMgD/B8CklF5tOVT4AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 700x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def limit_cycle_amplitude(a):\n",
    "    \"\"\"Peak-to-peak amplitude of the settled Hopf trajectory for bifurcation param a.\"\"\"\n",
    "    node = brainmass.HopfStep(\n",
    "        in_size=1, a=a, w=0.3, init_x=braintools.init.Constant(0.1)\n",
    "    )\n",
    "    r = brainmass.Simulator(node, dt=0.1 * u.ms).run(\n",
    "        400.0 * u.ms, monitors=[\"x\"], transient=200.0 * u.ms\n",
    "    )\n",
    "    x = np.asarray(r[\"x\"][:, 0])\n",
    "    return x.max() - x.min()\n",
    "\n",
    "a_values = np.linspace(-0.2, 0.4, 13)\n",
    "amplitudes = [limit_cycle_amplitude(a) for a in a_values]\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(7, 3.5))\n",
    "ax.plot(a_values, amplitudes, \"o-\")\n",
    "ax.axvline(0.0, color=\"grey\", ls=\"--\", label=\"bifurcation (a = 0)\")\n",
    "ax.set_xlabel(\"bifurcation parameter a\")\n",
    "ax.set_ylabel(\"limit-cycle amplitude\")\n",
    "ax.set_title(\"Supercritical Hopf bifurcation\")\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "md-bifread02",
   "metadata": {},
   "source": [
    "The amplitude is flat at zero while `a < 0` (the unit is silent), then rises smoothly once\n",
    "`a` crosses zero. A single number turned a quiet node into a sustained oscillator — that is a\n",
    "bifurcation, and it is the reason these models are useful for studying rhythm generation."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "md-excite02",
   "metadata": {},
   "source": [
    "## An excitable unit: FitzHugh–Nagumo phase portrait\n",
    "\n",
    "The {class}`~brainmass.FitzHughNagumoStep` we met in tutorial 01 has two variables, so its\n",
    "dynamics live in a 2-D **phase plane** `(V, w)`. Driven steadily it settles onto a closed\n",
    "loop — the limit cycle — which {func}`brainmass.viz.plot_phase_portrait` draws by plotting\n",
    "one variable against the other."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "phase02",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-19T06:45:31.475255Z",
     "iopub.status.busy": "2026-06-19T06:45:31.474961Z",
     "iopub.status.idle": "2026-06-19T06:45:32.112005Z",
     "shell.execute_reply": "2026-06-19T06:45:32.111036Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x350 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fhn = brainmass.FitzHughNagumoStep(in_size=1)\n",
    "r = brainmass.Simulator(fhn, dt=0.1 * u.ms).run(\n",
    "    400.0 * u.ms,\n",
    "    inputs=lambda i, t: (1.0,),   # steady drive -> sustained spiking\n",
    "    monitors=[\"V\", \"w\"],\n",
    "    transient=100.0 * u.ms,\n",
    ")\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 3.5))\n",
    "brainmass.viz.plot_timeseries(r[\"V\"], ts=r[\"ts\"], labels=[\"V\"], ax=ax1)\n",
    "ax1.set_title(\"time series\")\n",
    "brainmass.viz.plot_phase_portrait(r[\"V\"][:, 0], r[\"w\"][:, 0], ax=ax2)\n",
    "ax2.set_xlabel(\"V (activator)\")\n",
    "ax2.set_ylabel(\"w (recovery)\")\n",
    "ax2.set_title(\"phase portrait (V vs w)\")\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "md-ei02",
   "metadata": {},
   "source": [
    "## An E–I rate model: Wilson–Cowan\n",
    "\n",
    "The {class}`~brainmass.WilsonCowanStep` is a *physiological* model: two coupled populations,\n",
    "excitatory (`rE`) and inhibitory (`rI`) firing rates, with interpretable connection weights.\n",
    "Depending on its parameters it can rest at a fixed point or oscillate. Here we run it from a\n",
    "small perturbation and watch the two populations relax together."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "wc02",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-19T06:45:32.114816Z",
     "iopub.status.busy": "2026-06-19T06:45:32.114512Z",
     "iopub.status.idle": "2026-06-19T06:45:32.350764Z",
     "shell.execute_reply": "2026-06-19T06:45:32.349998Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x320 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "wc = brainmass.WilsonCowanStep(\n",
    "    in_size=1, rE_init=braintools.init.Constant(0.3)\n",
    ")\n",
    "r = brainmass.Simulator(wc, dt=0.1 * u.ms).run(60.0 * u.ms, monitors=[\"rE\", \"rI\"])\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 3.2))\n",
    "brainmass.viz.plot_timeseries(r[\"rE\"], ts=r[\"ts\"], labels=[\"rE (excitatory)\"], ax=ax)\n",
    "brainmass.viz.plot_timeseries(r[\"rI\"], ts=r[\"ts\"], labels=[\"rI (inhibitory)\"], ax=ax)\n",
    "ax.set_title(\"Wilson–Cowan E–I dynamics\")\n",
    "ax.set_ylabel(\"firing rate\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "md-mpr02",
   "metadata": {},
   "source": [
    "## A next-generation mean-field: Montbrió–Pazó–Roxin\n",
    "\n",
    "The {class}`~brainmass.MontbrioPazoRoxinStep` is an *exact* mean-field reduction of a network\n",
    "of quadratic integrate-and-fire neurons. Its state is the population firing rate `r` (a\n",
    "unit-aware quantity in `Hz`) and the mean membrane potential `v`. The coupling strength `J`\n",
    "moves it between a low-rate fixed point and self-sustained oscillations.\n",
    "\n",
    "We compare two coupling strengths and plot the firing rate over time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "mpr02",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-06-19T06:45:32.353429Z",
     "iopub.status.busy": "2026-06-19T06:45:32.353181Z",
     "iopub.status.idle": "2026-06-19T06:45:32.691373Z",
     "shell.execute_reply": "2026-06-19T06:45:32.690706Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x320 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 3.2))\n",
    "\n",
    "for J in [14.0, 21.0]:\n",
    "    mpr = brainmass.MontbrioPazoRoxinStep(in_size=1, J=J, eta=-5.0)\n",
    "    r = brainmass.Simulator(mpr, dt=0.1 * u.ms).run(\n",
    "        80.0 * u.ms, monitors=[\"r\"], transient=10.0 * u.ms\n",
    "    )\n",
    "    # r['r'] is unit-aware (Hz); viz strips the unit for plotting.\n",
    "    brainmass.viz.plot_timeseries(r[\"r\"], ts=r[\"ts\"], labels=[f\"J = {J:.0f}\"], ax=ax)\n",
    "\n",
    "ax.set_title(\"Montbrió–Pazó–Roxin: coupling J shifts the regime\")\n",
    "ax.set_ylabel(\"firing rate r (Hz)\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "md-next02",
   "metadata": {},
   "source": [
    "## What you learned\n",
    "\n",
    "- {func}`brainmass.list_models` (and `.to_table()`) is your map of the model families:\n",
    "  **phenomenological**, **physiological**, and **network**.\n",
    "- A **phase portrait** ({func}`~brainmass.viz.plot_phase_portrait`) shows the trajectory in\n",
    "  state space; for a 2-D model a limit cycle is a closed loop.\n",
    "- A **bifurcation** is a qualitative change of behaviour as a parameter crosses a threshold —\n",
    "  the Hopf `a`, the MPR coupling `J`.\n",
    "- The same `Simulator`-driven workflow applies to every model, so swapping models is cheap.\n",
    "\n",
    "## Next steps\n",
    "\n",
    "- {doc}`/tutorials/03_noise` — real activity fluctuates; add stochastic dynamics.\n",
    "- {doc}`/howto/choose_a_model` — pick the right model for your question.\n",
    "- {doc}`/gallery/index` — the full model zoo, one runnable demo each."
   ]
  }
 ],
 "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": "3.13.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
