{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Comprehensive Wilson-Cowan Model Variants: Simulation & Comparison\n",
    "\n",
    "This notebook provides a comprehensive overview and comparison of all 11 Wilson-Cowan model variants available in the BrainMass library.\n",
    "\n",
    "## Variant Reference Table\n",
    "\n",
    "| Variant | Key Feature | States | Use Case |\n",
    "|---------|-------------|--------|----------|\n",
    "| **WilsonCowanStep** | Saturation terms | 2 (E,I) | General purpose modeling |\n",
    "| **WilsonCowanNoSaturationStep** | No saturation | 2 (E,I) | Simplified dynamics |\n",
    "| **WilsonCowanSymmetricStep** | Unified E/I params | 2 (E,I) | Parameter reduction |\n",
    "| **WilsonCowanSimplifiedStep** | 2 weights only | 2 (E,I) | Pedagogical demonstrations |\n",
    "| **WilsonCowanLinearStep** | ReLU activation | 2 (E,I) | Optimization/learning tasks |\n",
    "| **WilsonCowanDivisiveStep** | Gain modulation | 2 (E,I) | Visual cortex normalization |\n",
    "| **WilsonCowanDivisiveInputStep** | Input division | 2 (E,I) | Contrast normalization |\n",
    "| **WilsonCowanDelayedStep** | Connection delays | 2 (E,I) | Network with transmission delays |\n",
    "| **WilsonCowanAdaptiveStep** | Adaptation currents | 4 (E,I,aE,aI) | Fatigue/habituation modeling |\n",
    "| **WilsonCowanThreePopulationStep** | Modulatory neurons | 3 (E,I,M) | Attention/arousal/neuromodulation |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 1: Setup and Imports"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-21T13:55:38.071805200Z",
     "start_time": "2026-03-21T13:55:32.982031Z"
    }
   },
   "source": [
    "import sys\n",
    "\n",
    "sys.path.append(r'D:\\codes\\projects\\brainmass')\n",
    "sys.path.append(r'D:\\codes\\projects\\brainstate')\n",
    "\n",
    "import brainmass\n",
    "import brainstate\n",
    "import brainunit as u\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from matplotlib.gridspec import GridSpec\n",
    "\n",
    "# Set integration time step\n",
    "brainstate.environ.set(dt=0.1 * u.ms)\n",
    "\n",
    "# Plotting configuration\n",
    "plt.rcParams['figure.dpi'] = 100\n",
    "plt.rcParams['font.size'] = 10\n",
    "\n",
    "# Color scheme\n",
    "E_COLOR = '#3498db'  # Blue for Excitation\n",
    "I_COLOR = '#e74c3c'  # Red for Inhibition\n",
    "M_COLOR = '#2ecc71'  # Green for Modulator\n",
    "A_COLOR = '#f39c12'  # Orange for Adaptation\n",
    "\n",
    "print(\"✅ All imports successful!\")\n",
    "print(f\"   BrainState dt: {brainstate.environ.get_dt()}\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "✅ All imports successful!\n",
      "   BrainState dt: 0.1 ms\n"
     ]
    }
   ],
   "execution_count": 1
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 2: Individual Variant Demonstrations\n",
    "\n",
    "We'll demonstrate each of the 11 Wilson-Cowan variants individually, showing their unique characteristics."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.1: WilsonCowanStep (Standard)\n",
    "\n",
    "The standard Wilson-Cowan model with saturation terms.\n",
    "\n",
    "**Mathematical Formulation**:\n",
    "\n",
    "$$\\tau_E \\frac{dr_E}{dt} = -r_E(t) + [1 - r \\, r_E(t)] F_E(w_{EE} r_E(t) - w_{EI} r_I(t) + I_E(t))$$\n",
    "\n",
    "$$\\tau_I \\frac{dr_I}{dt} = -r_I(t) + [1 - r \\, r_I(t)] F_I(w_{IE} r_E(t) - w_{II} r_I(t) + I_I(t))$$\n",
    "\n",
    "where $F_j(x) = \\frac{1}{1 + e^{-a_j (x - \\theta_j)}} - \\frac{1}{1 + e^{a_j \\theta_j}}$\n",
    "\n",
    "**Key Features**:\n",
    "- Saturation term $(1 - r \\cdot r_E)$ limits maximum activity\n",
    "- Sigmoid transfer function with adjustable gain and threshold\n",
    "- 11 parameters total\n",
    "- Most versatile variant for general modeling"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-21T13:55:39.474817400Z",
     "start_time": "2026-03-21T13:55:38.120515800Z"
    }
   },
   "source": [
    "# Create model\n",
    "model_standard = brainmass.WilsonCowanStep(\n",
    "    1,  # Single node\n",
    "    tau_E=1.0 * u.ms,\n",
    "    tau_I=1.0 * u.ms,\n",
    "    a_E=1.2,\n",
    "    theta_E=2.8,\n",
    "    a_I=1.0,\n",
    "    theta_I=4.0,\n",
    "    wEE=12.,\n",
    "    wEI=13.,\n",
    "    wIE=4.,\n",
    "    wII=11.,\n",
    "    r=1.\n",
    ")\n",
    "model_standard.init_all_states()\n",
    "\n",
    "# Define simulation\n",
    "duration = 500 * u.ms\n",
    "n_steps = int(duration / brainstate.environ.get_dt())\n",
    "indices = np.arange(n_steps)\n",
    "\n",
    "\n",
    "# Input: Step function at t=100ms\n",
    "def step_run(i):\n",
    "    t = i * brainstate.environ.get_dt()\n",
    "    inp = u.math.where(t > 100 * u.ms, 2.0, 0.5)  # JAX-compatible conditional\n",
    "    model_standard.update(rE_inp=inp, rI_inp=0.0)\n",
    "    return model_standard.rE.value, model_standard.rI.value\n",
    "\n",
    "\n",
    "# Run simulation\n",
    "rE_std, rI_std = brainstate.transform.for_loop(step_run, indices)\n",
    "time = indices * brainstate.environ.get_dt()\n",
    "\n",
    "# Visualize\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 4))\n",
    "\n",
    "# Time series\n",
    "ax1.plot(time, rE_std[:, 0], color=E_COLOR, linewidth=2, label='Excitation (E)')\n",
    "ax1.plot(time, rI_std[:, 0], color=I_COLOR, linewidth=2, label='Inhibition (I)')\n",
    "ax1.axvline(100, color='gray', linestyle='--', alpha=0.5, label='Input step')\n",
    "ax1.set_xlabel('Time (ms)', fontsize=11)\n",
    "ax1.set_ylabel('Activity', fontsize=11)\n",
    "ax1.set_title('WilsonCowanStep - Time Series', fontsize=12, fontweight='bold')\n",
    "ax1.legend(fontsize=10)\n",
    "ax1.grid(True, alpha=0.3)\n",
    "\n",
    "# Phase portrait\n",
    "ax2.plot(rE_std[:, 0], rI_std[:, 0], 'k-', linewidth=1.5, alpha=0.7)\n",
    "ax2.plot(rE_std[0, 0], rI_std[0, 0], 'go', markersize=10, label='Start', zorder=5)\n",
    "ax2.plot(rE_std[-1, 0], rI_std[-1, 0], 'r*', markersize=14, label='End', zorder=5)\n",
    "ax2.set_xlabel('E activity', fontsize=11)\n",
    "ax2.set_ylabel('I activity', fontsize=11)\n",
    "ax2.set_title('Phase Portrait', fontsize=12, fontweight='bold')\n",
    "ax2.legend(fontsize=10)\n",
    "ax2.grid(True, alpha=0.3)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print(\"Observations:\")\n",
    "print(f\"  - Peak E activity: {rE_std[:, 0].max():.3f}\")\n",
    "print(f\"  - Steady-state E: {rE_std[-100:, 0].mean():.3f}\")\n",
    "print(f\"  - Response shows typical transient dynamics with saturation\")"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1400x400 with 2 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Observations:\n",
      "  - Peak E activity: 0.489\n",
      "  - Steady-state E: 0.489\n",
      "  - Response shows typical transient dynamics with saturation\n"
     ]
    }
   ],
   "execution_count": 2
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2: WilsonCowanNoSaturationStep\n",
    "\n",
    "Wilson-Cowan model without saturation terms - simpler dynamics.\n",
    "\n",
    "**Mathematical Formulation**:\n",
    "\n",
    "$$\\tau_E \\frac{dr_E}{dt} = -r_E(t) + F_E(w_{EE} r_E(t) - w_{EI} r_I(t) + I_E(t))$$\n",
    "\n",
    "$$\\tau_I \\frac{dr_I}{dt} = -r_I(t) + F_I(w_{IE} r_E(t) - w_{II} r_I(t) + I_I(t))$$\n",
    "\n",
    "**Key Features**:\n",
    "- No saturation term - activities can grow larger\n",
    "- Simpler mathematical form\n",
    "- 10 parameters (one less than standard)\n",
    "- Faster computation, but less biologically realistic"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-21T13:55:40.706010500Z",
     "start_time": "2026-03-21T13:55:39.645106500Z"
    }
   },
   "source": [
    "# Create model\n",
    "model_nosat = brainmass.WilsonCowanNoSaturationStep(\n",
    "    1,  # Single node\n",
    "    tau_E=1.0 * u.ms,\n",
    "    tau_I=1.0 * u.ms,\n",
    "    a_E=1.2,\n",
    "    theta_E=2.8,\n",
    "    a_I=1.0,\n",
    "    theta_I=4.0,\n",
    "    wEE=12.,\n",
    "    wEI=13.,\n",
    "    wIE=4.,\n",
    "    wII=11.\n",
    ")\n",
    "model_nosat.init_all_states()\n",
    "\n",
    "\n",
    "# Run simulation\n",
    "def step_run_nosat(i):\n",
    "    t = i * brainstate.environ.get_dt()\n",
    "    inp = u.math.where(t > 100 * u.ms, 2.0, 0.5)\n",
    "    model_nosat.update(rE_inp=inp, rI_inp=0.0)\n",
    "    return model_nosat.rE.value, model_nosat.rI.value\n",
    "\n",
    "\n",
    "rE_nosat, rI_nosat = brainstate.transform.for_loop(step_run_nosat, indices)\n",
    "\n",
    "# Visualize\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 4))\n",
    "\n",
    "# Time series\n",
    "ax1.plot(time, rE_nosat[:, 0], color=E_COLOR, linewidth=2, label='Excitation (E)')\n",
    "ax1.plot(time, rI_nosat[:, 0], color=I_COLOR, linewidth=2, label='Inhibition (I)')\n",
    "ax1.axvline(100, color='gray', linestyle='--', alpha=0.5, label='Input step')\n",
    "ax1.set_xlabel('Time (ms)', fontsize=11)\n",
    "ax1.set_ylabel('Activity', fontsize=11)\n",
    "ax1.set_title('WilsonCowanNoSaturationStep - Time Series', fontsize=12, fontweight='bold')\n",
    "ax1.legend(fontsize=10)\n",
    "ax1.grid(True, alpha=0.3)\n",
    "\n",
    "# Phase portrait\n",
    "ax2.plot(rE_nosat[:, 0], rI_nosat[:, 0], 'k-', linewidth=1.5, alpha=0.7)\n",
    "ax2.plot(rE_nosat[0, 0], rI_nosat[0, 0], 'go', markersize=10, label='Start', zorder=5)\n",
    "ax2.plot(rE_nosat[-1, 0], rI_nosat[-1, 0], 'r*', markersize=14, label='End', zorder=5)\n",
    "ax2.set_xlabel('E activity', fontsize=11)\n",
    "ax2.set_ylabel('I activity', fontsize=11)\n",
    "ax2.set_title('Phase Portrait', fontsize=12, fontweight='bold')\n",
    "ax2.legend(fontsize=10)\n",
    "ax2.grid(True, alpha=0.3)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print(\"Observations:\")\n",
    "print(f\"  - Peak E activity: {rE_nosat[:, 0].max():.3f}\")\n",
    "print(f\"  - Steady-state E: {rE_nosat[-100:, 0].mean():.3f}\")\n",
    "print(f\"  - Without saturation, activities can reach higher values\")"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1400x400 with 2 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Observations:\n",
      "  - Peak E activity: 0.966\n",
      "  - Steady-state E: 0.966\n",
      "  - Without saturation, activities can reach higher values\n"
     ]
    }
   ],
   "execution_count": 3
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.3: WilsonCowanSymmetricStep\n",
    "\n",
    "Symmetric variant with unified E/I parameters - reduces parameter space.\n",
    "\n",
    "**Mathematical Formulation**:\n",
    "\n",
    "$$\\tau \\frac{dr_E}{dt} = -r_E(t) + [1 - r \\, r_E(t)] F(w_{EE} r_E(t) - w_{EI} r_I(t) + I_E(t))$$\n",
    "\n",
    "$$\\tau \\frac{dr_I}{dt} = -r_I(t) + [1 - r \\, r_I(t)] F(w_{IE} r_E(t) - w_{II} r_I(t) + I_I(t))$$\n",
    "\n",
    "where both E and I use the same $\\tau$, $a$, and $\\theta$ parameters.\n",
    "\n",
    "**Key Features**:\n",
    "- Unified time constant and transfer function parameters\n",
    "- 8 parameters (vs 11 for standard)\n",
    "- Simplifies parameter fitting\n",
    "- Good for pedagogical demonstrations"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-21T13:55:41.867882900Z",
     "start_time": "2026-03-21T13:55:40.739258200Z"
    }
   },
   "source": [
    "# Create model with unified parameters\n",
    "model_sym = brainmass.WilsonCowanSymmetricStep(\n",
    "    1,  # Single node\n",
    "    tau=1.0 * u.ms,  # Unified time constant\n",
    "    a=1.2,  # Unified gain\n",
    "    theta=2.8,  # Unified threshold\n",
    "    wEE=12.,\n",
    "    wEI=13.,\n",
    "    wIE=4.,\n",
    "    wII=11.,\n",
    "    r=1.\n",
    ")\n",
    "model_sym.init_all_states()\n",
    "\n",
    "\n",
    "# Run simulation\n",
    "def step_run_sym(i):\n",
    "    t = i * brainstate.environ.get_dt()\n",
    "    inp = u.math.where(t > 100 * u.ms, 2.0, 0.5)\n",
    "    model_sym.update(rE_inp=inp, rI_inp=0.0)\n",
    "    return model_sym.rE.value, model_sym.rI.value\n",
    "\n",
    "\n",
    "rE_sym, rI_sym = brainstate.transform.for_loop(step_run_sym, indices)\n",
    "\n",
    "# Visualize\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 4))\n",
    "\n",
    "# Time series\n",
    "ax1.plot(time, rE_sym[:, 0], color=E_COLOR, linewidth=2, label='Excitation (E)')\n",
    "ax1.plot(time, rI_sym[:, 0], color=I_COLOR, linewidth=2, label='Inhibition (I)')\n",
    "ax1.axvline(100, color='gray', linestyle='--', alpha=0.5, label='Input step')\n",
    "ax1.set_xlabel('Time (ms)', fontsize=11)\n",
    "ax1.set_ylabel('Activity', fontsize=11)\n",
    "ax1.set_title('WilsonCowanSymmetricStep - Time Series', fontsize=12, fontweight='bold')\n",
    "ax1.legend(fontsize=10)\n",
    "ax1.grid(True, alpha=0.3)\n",
    "\n",
    "# Phase portrait\n",
    "ax2.plot(rE_sym[:, 0], rI_sym[:, 0], 'k-', linewidth=1.5, alpha=0.7)\n",
    "ax2.plot(rE_sym[0, 0], rI_sym[0, 0], 'go', markersize=10, label='Start', zorder=5)\n",
    "ax2.plot(rE_sym[-1, 0], rI_sym[-1, 0], 'r*', markersize=14, label='End', zorder=5)\n",
    "ax2.set_xlabel('E activity', fontsize=11)\n",
    "ax2.set_ylabel('I activity', fontsize=11)\n",
    "ax2.set_title('Phase Portrait', fontsize=12, fontweight='bold')\n",
    "ax2.legend(fontsize=10)\n",
    "ax2.grid(True, alpha=0.3)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print(\"Observations:\")\n",
    "print(f\"  - Peak E activity: {rE_sym[:, 0].max():.3f}\")\n",
    "print(f\"  - Steady-state E: {rE_sym[-100:, 0].mean():.3f}\")\n",
    "print(f\"  - Unified parameters simplify the model while maintaining core dynamics\")"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1400x400 with 2 Axes>"
      ],
      "image/png": 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GOXPmYO/evcp1V5MmTfDee+9hx44dOHDgACIjI7F8+XLY2dlBlmWlvFhxShsDEVkxNTPGRGWRkpKijBBzd3cXsiyLbt26CQDik08+Mbnt9+bNm+L5559XHhuPbCzNSNsVK1Yoy5YtWyZu3bpVZGyTJ09W2r366qvK8sTERGFnZyeA/NGbycnJhY41ZcoUpf2iRYtMjieEEF988YXJN+APkpycrDxPdnZ2JiMPX3311ULHTUhIUJYNGjRICPFvOYEWLVoIAOLs2bPiq6++UtoZ35qUnJwswsLCRJMmTYoclVywz9KetxBC3LhxQ7Rv377Yb57vvUW/oISGjY2NMlIgJCREeS6My1kY7+ePP/4QQgjx008/KcscHR1Fenq6ECK/TELB8qlTpxZ5PjNmzFCWFzxvAMTnn38uhMi/vatatWoCyB/dW2DgwIFK2w8++EAcPnxYHD58WKxcuVJZ/uSTTyrt770N7l7G39R/9tlnhdYX9Tp///33lWWdO3cutI2xQ4cOCS8vr2L75H//+59Je+ORCffedmc8ynvGjBnKue/atUtZ3rJlyyL3Zfye3rdvn8noh/v5448/lOMU/Pz111/33aa483nYkbZPP/20svyJJ55Qls+aNUtZbvwaKnjdlvb5Ks6vv/5a5Gjfgp+wsDClrfFrIzQ0VDlmdHS0cHR0FED+qJWCMh7Gry/j8yxQ1OiSU6dOKcvatm1r0jfGpWF+/vlnIYQQjz76qADyR1bHxMQUWc6BiIjIEhlfLxT3ExAQIPLy8gq1HzhwoLKfzZs3F3ntWtLr9szMTOUum969e4vffvvN5G64AqX9G14e520wGET16tWV5WfPnlX28+GHHxb5fBjv54cffih0/PuVbxLC9PrP+Jq/QF5enli2bJno0KGDqFatmvJZrOCnevXqDzzWg2IgoqqBI23JYlWvXh2NGzcGAKSkpODcuXM4efIkgPyRtN7e3qhXrx6A/NG2xhOUPexI24EDB6JGjRoAgKlTp6JmzZpwd3dH37598fXXXyvt/vjjD+X3wMBA5XcPDw9lFKAQApcuXSp0jKCgIOX3gmMBUL6xNp6BPikpSZmMrDgXL15Uvs1u0KCByT47duxYKGZPT080bdoUQP4I2zt37uDs2bOoU6cOBg8eDADKrK0FunXrBgAwGAwIDg7G0qVLceHCBWVUsrGC8yjteQNArVq1EBMTg2+//RZjx45V+rfA9u3b8cMPPyiPx40bByB/BOGWLVtw584dREVFAcifqdX4uSzg5uamTMzl7u6uLG/SpIkyMtDDw+OB52P83Brvp2CyBEmSlOXG+zB+7UyePBndunVDt27dMGHCBGX577//XuQxH6R///4lamccQ8GozeJ0794dFy5cwKpVq0zeHwWmTZtW7HN0v+MuXLhQOXfjuAtGUdzL+H1m/NxfvXr1vqM53n77beU4BT+VPQPzg14rQNGvubI8X8ZatGiBM2fOYOPGjRgxYkSh0anvv/++sh/jY65Zs0Y5Zvfu3ZGZmQkgf9TKzZs3Cx3nYV5/sbGxJn1jPHq74H1Q8D6/ceMGOnXqBGdnZzRs2BAvvPCCyb6IiIisiU6nw3/+8x9ERERAq9UWWv+ga+vSXLc7ODgod6jt27cPzZs3h6OjI9q1a4fZs2crk7SW9m94eZx3YmIibt++DQBwdHREy5YtlbZFfdYxZm9vj969ez90LEDR1zdhYWGYOnUqfvrpJ2RkZBS6Fi3ptTEREZO2ZNE6deqk/L5ixQpkZmbC0dERrVu3Nln/ww8/4NdffwUAuLi4oHnz5g91PB8fH5w8eRJvvvkmunbtiho1auD27duIiIjA8OHDsXnz5gfuo+CW/eIU3MYDADY2NsrvBX/sC25vAvIvtoyT0aVVXCwFJRLi4uLw1VdfwWAwoFOnTsrzGRMTo1x4OTs7o127dgCAo0eP4tSpUwDyb9det24doqOjsWnTJmXfsiwXecwHnXcBW1tbDBgwAGvWrMGVK1dw9uxZJckMAL/88ovy+1NPPaUkwb744gtEREQgOzsbAPD0008XGYdxIregrAGQ/7opSnEJwdLupzT0ev1Dbeft7V3mYxfFzc0N48aNw44dO5CQkIDdu3fDwcEBAHD37t0SJQ5LKi8vT+nD4jzoPWZuyus1V5SSPF9A/oecUaNGYfPmzbh58yaOHj2qvF6EEIiNjS3xMYGiX6Pl/forOMb48ePx/fff49lnn0XLli2h0+lw+fJlfPbZZwgKCuIHIyIisgp9+/bF4cOHceTIEZw+fRqpqanYsGFDoS/MCzzo2rq01+1r1qzBp59+igEDBqBBgwYwGAyIjY3F/PnzMWLEiFKdS2muZUtz3vdeAz7omtDLy6vEcRTn3uubnJwcfPbZZwDyn/dFixbh4MGDOHz4sPIlfGmu5YioamPSliyacdJ27dq1AIAOHToo3zYXrN+wYYNy0dGhQweTxEhpCCFQt25dLFq0CIcPH0ZSUhJ++uknZf327dsBQBkBDAAnTpxQfk9OTsbly5cB5F9ENGzYsNQx+Pn5mZz39OnTixxtW/ANdsOGDZULlsuXLyM5OVlpU1DH9t6YC0bOAlBqM3Xq1AmPPvooJElCVFSUcpHXuXNn5fm+ceOGst3TTz+N0aNHm+yrrL7//vtCSd+WLVuib9++yuOCOqwAYGdnh//85z8A8vth2bJlAIBq1ao9cASpWoz74eDBgxD5E0aa/BS8hgDTJF9xCfECJU1mGsewZ8+eYtulpKQU+tJAo9GgX79+Jol04z65X7zGx12zZk2R567X62FnZ1coFuP3mfHr2t/f/77nvXbt2kLHMK43bM7K8nwVkGW5UN1aIP99bVwvu6APjY85Z86cYo/ZpEmTQvt8mNdfUFBQscd44YUXAOT/u9ynTx+sX78eZ8+exZ07dzB16lQA+V88Gd8VQEREZKm8vLzQtWtXdOnSBa1bt1a+IH9Ypb1ut7GxwfPPP49vv/0Wly5dwu3bt5VrhR9++AF6vb7Uf8NL4kHn7enpCTc3NwD5yeBz584p64r7rFOguGuTslxfJycnIysrC0D+YJs333wTPXr0QP369ZGSknLffT1sDERkvWwe3ITIfBmXOSj4xtZ4WUFy0/jb3IctjQAAmzZtwooVK/DUU0+hXr16cHV1xYEDB5T1BSPaRo0ahQ8++AAA8NFHH6FWrVpo1KgRli1bprQJCQkxuRW6NN577z0EBQUhNzcXR48eRbdu3fDyyy+jdu3auHXrFnbt2oV9+/YhKSkJNWrUQEhIiDLKdPjw4XjllVdw+fJlfPLJJ8o+jSflMp6MrGCEcqdOnVC9enU0adLEZOSk8cVd3bp1ld+3bduGrl274vbt25g2bdpDnee9CibBGjFiBDp27Ag3NzecP38ea9asUdp06NDBZJtx48YpfXH06FEA+SNwy3qhW1GeeeYZZWKlZ599FjNnzkSjRo2QmJiIixcvYvfu3ejbty/mzJkDwHQUxbZt21CvXj3Y2tqiQ4cO903W3c+wYcMwbdo0ZGdn4+jRoxgyZAhGjx4NWZaxb98+dOnSBc888wxSUlKUZP6gQYPQqlUr2Nra4sCBA8rITDs7O2Xk+73xrly5Ev369YODgwMCAgLw9NNP43//+x8A4JVXXkFKSgpat26N1NRUXL58GT/88APq1q1bZPmC6dOnw8bGBk5OTpg+fbqyfODAgQ/1HFiCsjxfBWRZRt++fdGyZUsMGzYM7dq1g5OTE37++WeThH3B+2ro0KHKa2PRokWQJAmdOnVCZmYm/vzzTxw8eBB3797Fvn37Hvq82rRpg5YtW+LXX3/FoUOHMHr0aAwbNgy2tra4evUqTpw4gW+++Ua5FXLo0KGoVq0aunXrhtq1ayMvLw8///yzsr+SjDQmIiKqakp73d6gQQMMGTIEbdq0Qa1atZCQkIA///wTQP4XqNnZ2aX+G14eNBoNRo4ciRUrVgDIv5aeM2cObt++rVwvA0VPQFwc4+vViIgIdO/eHfb29mjVqlWR5dWMeXt7w97eHllZWTh79iw+++wzeHt7Y/78+aVKvpYlBiKyIuVfJpeo8hgMBmUyp4Kfb775Rlmfm5urTI5T8LNr1y6TfZRmIrINGzbctyD+pk2blO3feOONYtv5+PiIK1eu3PdYQty/AP3WrVuFk5NTscdwdXVV2l6+fFn4+PgU2/bNN98s9NzWqVNHWW9vby9ycnKEEEKEhoaabBsVFaVsk5eXJ1q3bl1o/126dFF+N56MqbTn7evre9/nv2fPnkKW5ULnEhAQYNJuz549hdoUrKtbt66yrLhJpErzmhGi+Mm3jCcJMzZ69Oj7nqfxc3LmzJlCkxsYH6e4Yzwo5pUrVyoTTtz7UzDh1sWLF+8bJwAxd+5ck+MZTwhR1HM+a9as++7P+Pk2fl6Let3VrFlTJCQkFHne5aU8JiIz3q60r6HSPF9Fyc3NfWAfjh071mSb+702SvoeL1Dce/3kyZPCzc3tvnEVeOyxx4pt4+3tbTLhIBERkSUxvl540N/0e9sbX18Ude1a2ut2rVZb7N/bkJAQpV1p/oaX13knJyeLpk2bFnu8kSNHmnxGKOoa1Jjx5NHGPwXXMvebWFcIIV5++eVC2zZq1Mhk8t4CxV0LPSgGIqoaWB6BLJpGozEpMA+YjqS1sbExmczn3vWl1alTJ0yZMgWPPPIIPDw8oNVq4erqim7dumHLli0YOXKk0nbx4sX46quvEBQUBBcXF9ja2sLf3x8vv/wyfvnll0KTaJXWkCFDcP78ebz++uto1aoVnJ2d4eDggIYNG+Lpp5/G1q1blbb169fHL7/8gkmTJikjMV1cXNC9e3ds2bIFixYtKrR/49G27du3h62trfIcFNDpdCYTQGm1WuzevRsDBw6Eq6srPD09MWXKFKxatapM51pg8+bNmDZtGjp16oTatWtDp9PB0dERbdu2xdtvv409e/YUeZtTwURFQP6ETmWdcKCirVu3DuvXr0dQUBBcXV2h0+lQp04dPPbYY/jggw8wceJEpW2rVq2wfv16NGvW7KFH1hZl/PjxOHz4MAYPHgxvb2/Y2NjAy8sLffv2Rdu2bQHkj9DYvn07XnjhBbRt2xZeXl6wsbGBm5sbevTogS+//NJkhAMAvPDCC3jzzTdRp06dIsuUvPXWW/juu+/Qp08f1KhRA7a2tvD19UXXrl2xaNEizJs3r8h4N23ahMmTJ8PT0xMODg7o27cvoqOj4enpWW7PiTl62OergI2NDfbs2YMpU6YgICAANWvWhK2tLapVq4bAwEB89NFHhd6/48ePR3R0tMlrw9vbGx07dsSsWbNMRvA/rEceeQSxsbF48cUXUb9+feh0Ori5uaFly5Z48cUXERkZqbSdOHEiRowYgQYNGsDZ2Rk2Njbw9fXFM888gyNHjnA0ChERURFKe92+cOFChISEoHbt2rCzs4OdnR2aNGmC119/3WRC5tL8DS8v7u7u+PHHHzF9+nQ0adIEdnZ2cHJyQocOHbB8+XJs3LixVHMeeHh4YMeOHWjXrt1D3Z23ZMkSZdJqZ2dnDBgwAJGRkaXaV1ljICLrIAnBKthEZN2uXbum3AL20ksvlUtSidTXo0cPHDp0CADw559/wt/fX92AiIiIiIiIiMoJa9oSkdXKzs7GnTt3lJq2ADB69GgVIyIiIiIiIiIiejAmbYnIar3wwgtYt26d8rh3795lKo9BRERERERERFQZWNOWiKyeq6srRowYgS+//FLtUIiIiIiIiIiIHog1bYmIiIiIiIiIiIjMCEfaEhEREREREREREZkRJm2JiIiIiIiIiIiIzEiVnIhMlmXcvHkT1apVgyRJaodDREREREUQQiAjIwO1atWCRsOxBg/Ca1wiIiIi81fSa9wqmbS9efMm/Pz81A6DiIiIiErg+vXrqF27ttphmD1e4xIRERFZjgdd41bJpG21atUA5D85Li4uFX48WZaRmJgIT09PjhKxQAaDAUePHkVmZiYee+wx2Nraqh0SPQS+Dy0f+9DysQ8tX2X3YXp6Ovz8/JRrN7q/yrjG5fvYurA/rQ/71LqwP60L+9O6lKU/S3qNWyWTtgW3i7m4uFRa0jYrKwsuLi58Y1ogg8EAJycnAPmvGSZtLRPfh5aPfWj52IeWT60+5K3+JVMZ17h8H1sX9qf1YZ9aF/andWF/Wpfy6M8HXeOazavk448/hr+/P+zt7REYGIgTJ04U23bt2rWQJMnkx97evhKjJSIiIiIiIiIiIqoYZpG03bJlC8LCwjBnzhz88ssvaNOmDUJCQpCQkFDsNi4uLrh165by89dff1VixERERERERERERGTxYmOBvn3z/29GzCJpu3TpUkyYMAGhoaFo3rw5VqxYAUdHR6xevbrYbSRJgo+Pj/Lj7e1diRFTVWNvbw+dTqd2GEREREREREREVJ62bQMiIoDt29WOxITqNW1zcnJw8uRJTJ8+XVmm0WgQHByMmJiYYre7c+cO6tatC1mW8cgjj2DhwoVo0aJFZYRMVYxWq0VgYCASEhKg1WrVDoeIiIioTAwGA3Jzcx9qW1mWkZubi6ysrCpbj8/W1pbXhERERNZk165////WW+rGYkT1pG1SUhIMBkOhkbLe3t44f/58kds0adIEq1evRuvWrZGWloYlS5agc+fOOHfuHGrXrl2ofXZ2NrKzs5XH6enpAPIvOmVZLsezKZosyxBCVMqxqGKwDy0f+9DysQ8tH/vQ8lV2H/K1Ur6EEIiLi0NqamqZ9iHLMjIyMqr0BHFubm7w8fGp0s8BERGRVYiPB06fzv89NhZISAC8vFQNqYDqSduH0alTJ3Tq1El53LlzZzRr1gyffvop5s+fX6h9eHg45s2bV2h5YmIisrKyKjRWIP8DR1paGoQQVXZEgqVjH1o+9qHlYx9aPvah5avsPszIyKjwY1QlBQlbLy8vODo6PlTCUQiBvLw82NjYVMmEpRACmZmZytwbNWvWVDkiIiIiKpO9ews/fvZZdWK5h+pJWw8PD2i1WsTHx5ssj4+Ph4+PT4n2YWtri3bt2uHSpUtFrp8+fTrCwsKUx+np6fDz84OnpydcXFwePvgSkmUZkiTB09OTH1ItkMFgwKlTp3Dnzh3Ur18ftra2aodED4HvQ8vHPrR87EPLV9l9aG9vX+HHqCoMBoOSsK1Ro8ZD76eqJ20BwMHBAQCQkJAALy8vlkogIiKyZLt3A1otYDAANjb5j5m0zafT6dC+fXtERkbiqaeeApD/gSAyMhKTJk0q0T4MBgPOnj2Lfv36Fbnezs4OdnZ2hZZrNJpK+9AoSVKlHo/KjxACer0emZmZ7EMLx/eh5WMfWj72oeWrzD7k66T8FNSwdXR0VDkS61DwPObm5jJpS0REZO5u3Mgvg3AvIfInIDMY8h/n5QHffw+cPAkU9eW0tzfg61uxsRpRPWkLAGFhYRgzZgwCAgLQsWNHLFu2DHq9HqGhoQCA0aNHw9fXF+Hh4QCAt956C48++igaNmyI1NRUvPvuu/jrr78wfvx4NU+DiIiIiMislcfoWCEEkjKToM/Vw1nnjBoONarcqNuqdr5EREQWbfhw4Nixotfd+zc9IwMICCi6bZcuwJEj5RvbfZhF0nbEiBFITEzE7NmzERcXh7Zt2yIiIkKZnOzatWsmIy1u376NCRMmIC4uDtWrV0f79u1x7NgxNG/eXK1ToCokI9uAa2m5yMoTkIWALNSOiEpCCBmpt/PglpsJSeLILUvEPrR87EPLV9CHHV0McHdkH1Y1qVmpWBu7Fh8e/xBXUq8oyxtUb4D/6/h/GNN2DNzs3dQLkIiIiKgooaHAiRP5I2rFPUmcBz0G8hO7Wm3+fiqRJERR0Vi39PR0uLq6Ii0trdJq2hbUvOJtfpbHYDAgOjoaGXfu4Fy1AHz7hx6GKveuISIi+td7IT7o7u9c4cep7Gs2S3e/5ysrKwt//vkn6tWr91C1gvde2oshXw1BZm4mAEDg34shCfkjVBxtHbFt+DaENAwpw1lYhrI+n+aCn1OsD/vUurA/rQv7U2U//ggMGADcvp1fBqGktFqgRg3g22+BRx9VFpelP0t6jctXCVEJ/ZYs45vz6UzYEhERUZWy99JePLHxCdzNvQvxz3/GCpbdzb2LJzY+gb2X9hazp4eTmJiIl156CXXq1IGdnR18fHwQEhKCo0ePAsgvVbBjx45yOdbVq1chSRJiY2PLZX9ERERkJh59FDh9GmjfHihpklWSgA4d8rczSthWFrMoj0Bk7mQhcDHVAPwzkKJ/k2qobq+FRpKgkQCwrJnZE0IgU6+Ho5MT69BZKPah5WMfWr6CPvRz4SVkVZGalYohXw2BEAIy5Pu2lSFDIzQY8tUQ/B32d7mVShgyZAhycnKwbt061K9fH/Hx8YiMjERycnK57L9ATk5Oue6PiIiIzEzNmkB0NDBuHPDFFw9u/8wzwOefAzpdxcdWBF5xE5VARp4GekP+zMBB/k6Y3cNb5YiotPJvXciDl5c7b0WxUOxDy8c+tHxKH7qpc+FKlW9d7Dpk5mYWGl1bHBkyMnMzsf70ekwOnFzm46empuLw4cOIiopCUFAQAKBu3bro2LEjAMDf3x8AMGjQIGXd1atXcfnyZYSFheHHH3+EXq9Hs2bNEB4ejuDgYGXf/v7+GDduHC5evIgdO3Zg8ODBWLduHQCgXbt2AICgoCBERUWV+TyIiIjITOh0yKlVC1pJgvZ+FWO1WqBePdUStgDLIxA9kFarhbZOO1x2bgEhadHa23LrlhERERGVlBACH5748KG2/eD4ByiPqTOcnZ3h7OyMHTt2IDs7u9D6n376CQCwZs0a3Lp1S3l8584d9OvXD5GRkTh16hT69OmD/v3749q1aybbL1myBG3atMGpU6cwa9YsnDhxAgCwf/9+3Lp1C9u3by/zORAREZH5SEtLQ8Lq1ZAedJ1iMAC7dlVOUMVg0paoBK7c/vd2ucY17FSMhIiIiKhyJN9NxuXbl0s8yraAgMDl25eRcjelzDHY2Nhg7dq1WLduHdzc3NClSxfMmDEDZ86cAQB4enoCANzc3ODj46M8btOmDV544QW0bNkSjRo1wvz589GgQQPs3LnTZP+9evXCq6++igYNGqBBgwbK9jVq1ICPjw/c3d3LfA5ERERkHq5evYq5L72E2klJpgnRgtJt95Zwi40FEhIqKbrCmLQlKoGkTIPyu48zq4oQERGR9buTc6dM22fkZJRLHEOGDMHNmzexc+dO9OnTB1FRUXjkkUewdu3aYre5c+cOXnvtNTRr1gxubm5wdnbG77//XmikbUBAQLnESEREROZLCIF9+/bh9ddfh9/vv5uu1GoBV1dg9uz8/2u1puv3lu8Eq6XBpC3RAxgMBmRe/x21My9DEjLcHbUP3oiIiIjIwjnrnMu0fTVdtXKKBLC3t0fv3r0xa9YsHDt2DGPHjsWcOXOKbf/aa6/hm2++wcKFC3H48GHExsaiVatWhSYbc3JyKrcYiYiIyPwkJiZizpw5+OCDD5CVlYXgnBwIjebfUbUDBgAXLgDz5uX/f8CA/OWSBGg0wJ49qsXOpC1RCeTo0+Fo0MNWI1BNx7cNERERWb8aDjXQoHoDSJAe3NiIBAkNqjeAu0PFlRZo3rw59Ho9AMDW1hYGg8Fk/dGjRzF27FgMGjQIrVq1go+PD65evfrA/er+mWzk3v0RERGRZcnIyMCGDRswceJEnDp1CjqdDuPGjEGr69chyXL+qNotW4Dt2wEvr/yNvLzyH2/Zkr9elvOTtipdF/A+bzOTnm3AF6dTcfLmXdy+a0CunF9FLL8+ctknc6DSk4QBbln5b9DqDlpI99Y4ISIiIrJCkiTh/zr+H17Z+0qpt50cOLlcrpmSk5MxbNgwPPfcc2jdujWqVauGn3/+Ge+88w4GDhwIAPD390dkZCS6dOkCOzs7VK9eHY0aNcL27dvRv39/SJKEWbNmQZblBx7Py8sLDg4OiIiIQO3atWFvbw9XV9cynwcRERFVvKysLPz222+IiorCsWPHlElMmzVrhilTpsDXxQVo0ACoVw9YseLfZO29hg8HevQAXnwRuHoVyMwEqpXfHUQlxaStGbmTIyP0m79xLS1X7VDIiCQMcP0nX+7txLcMERERVR1j2o7BzAMzcTf3LmQ8OOmpkTRwsHHA6Dajy+X4zs7OCAwMxPvvv4/Lly8jNzcXfn5+mDBhAmbMmAEAeO+99xAWFoaVK1fC19cXV69exdKlS/Hcc8+hc+fO8PDwwJtvvon09PQHHs/GxgYffPAB3nrrLcyePRvdunVDVFRUuZwLERERlY9r165h+/btuHv3LoD8O2Ru3ryJv//+G0L8O+DR398fo0aNQqdOnf79MvnnnwvXrS1Kwahbg6Fk7SsAM1BmZEPsbZOEbTWdBjqb/BvSJBSU2+Aoz8omCQlOORJsJeDpdtXVDoeIiIio0rjZu2Hb8G14YuMT0AjNfRO3GmggQcL2EdvhZu9WLse3s7NDeHg4wsPDi23Tv39/9O/f32SZv78/Dhw4YLLs5ZdfNnlcXLmE8ePHY/z48Q8XMBEREVWoq1evYsaMGcjIKHrCU3d3dzz66KPo1asXGjduXPjOn9ImYFVK2AJM2poNIQQiLuW/4LQS8MVQPzR0t1M5KgLyv7GJjr4GvV6PjrUd1Q6HiIiIqFKFNAzB7qd3Y8hXQ5CZmwkAEEZluwpq3jrYOmD7iO14vMHjqsRJRERE1u369ev473//i4yMDDRq1Ai9e/dW1nl4eKBhw4aoXt16BtsxaWsm4u7k4WZGHgCgXU0HJmyJiIiIyGyENAzB32F/Y13sOnxw/ANcSb2irKtfvT4mB07GmDZj4GrP+q9ERERU/m7cuIEZM2YgLS0NDRo0wPz58+Hk5KR2WBWKSVszcSklR/m9hRcTtuZGo9FAo9GoHQYRERGRatzs3TA5cDJeeuQlpOem407uHVTTVYO7gzsnaiUiIqIKc+vWLcyYMQOpqamoV69elUjYAgCzUGbislHSlqNszYtWq0W3bt3wyCOPQKtiLRMiIiIyLx9//DH8/f1hb2+PwMBAnDhxoti227dvR0BAANzc3ODk5IS2bdtiw4YNJm2EEJg9ezZq1qwJBwcHBAcH4+LFixV9GqUmSRJqONaAv5s/ajjWYMKWiIiIKkx8fDxmzJiBlJQU1K1bFwsWLEC1atXUDqtSMGlrJuLv5Cm/+7naqhgJERERET3Ili1bEBYWhjlz5uCXX35BmzZtEBISgoSEhCLbu7u7Y+bMmYiJicGZM2cQGhqK0NBQ7N27V2nzzjvv4IMPPsCKFStw/PhxODk5ISQkBFlZWZV1WkRERERmIyEhATNmzEBSUhL8/Pzw9ttvw8XFRe2wKg2TtmYi5e6/SdsaDhzNSURERGTOli5digkTJiA0NBTNmzfHihUr4OjoiNWrVxfZvkePHhg0aBCaNWuGBg0aYMqUKWjdujWOHDkCIH+U7bJly/Df//4XAwcOROvWrbF+/XrcvHkTO3bsqMQzK6HYWKBv3/z/ExEREZWzpKQkzJw5EwkJCfD19cWCBQvg6lq1auezpq2ZSL5rUH6vzqStWZFlGWfPnkV6ejo8PDxY25aIiKiKy8nJwcmTJzF9+nRlmUajQXBwMGJiYh64vRACBw4cwIULF7B48WIAwJ9//om4uDgEBwcr7VxdXREYGIiYmBiMHDmy0H6ys7ORnZ2tPE5PTweQf+0iy7JJW1mWIYRQfspCCAFs2wZEREAEBABt2pRpf5ao4Hks6rm2JAWvC0s+BzLFPrUu7E/rwv4suYSEBMycORPx8fGoWbMm5s+fDzc3N7N67srSnyXdhklbM5GSmZ+0ddZpYGfDpKA5EUIgJSUFer2+zB9yiIiIyPIlJSXBYDDA29vbZLm3tzfOnz9f7HZpaWnw9fVFdnY2tFotPvnkE/Tu3RsAEBcXp+zj3n0WrLtXeHg45s2bV2h5YmJioZIKubm5kGUZeXl5yMvLK7RNSQkhYDAYYLNrFyQAYtcuGGbPfuj9Waq8vDzIsozk5GTY2lpuaTNZlpGWlgYhBAcmWAn2qXVhf1oX9mfJJCQkYNGiRUhKSoKXlxemTp0Kg8FQbAkqtZSlPzMyMkrUjklbM5H8T3kEd46yJSIiIrJK1apVQ2xsLO7cuYPIyEiEhYWhfv366NGjx0Ptb/r06QgLC1Mep6enw8/PD56enoXqvWVlZSEjIwM2NjawsSnjR4D4eGjOnAEAaE6fhpSSAnh5lW2fFsbGxgYajQY1atSAvb292uE8NFmWIUkSPD09mUCwEuxT68L+tC7szwe7desWli5divT0dNSrVw8LFixAjRo11A6rSGXpz5JeOzBpawYMskBmbv4ITlc7vnGJiIiIzJmHhwe0Wi3i4+NNlsfHx8PHx6fY7TQaDRo2bAgAaNu2LX7//XeEh4ejR48eynYFtwEa77Nt27ZF7s/Ozg52dnZFHufeDw8ajQaSJCk/D0sIAc2+fSbLpB9+AJ599qH3qYaoqCj07NkTt2/fhpubW6m3L3gei3quLY21nAf9i31qXdif1oX9WbwbN25gxowZSElJQZ06dbBgwQK4u7urHdZ9PWx/lrQ9XyVm4G7uv7UsHHXsEiIiIiJzptPp0L59e0RGRirLZFlGZGQkOnXqVOL9yLKs1KStV68efHx8TPaZnp6O48ePl2qflUETEQGh/efuMBsbYPfuCj3e2LFjTRLOBT99+vSp0OMSERFR5fj7778xffp0JWG7cOFCs0/YVgaOtDUDmXn/1kl1YD1bIiIiIrMXFhaGMWPGICAgAB07dsSyZcug1+sRGhoKABg9ejR8fX0RHh4OIL/+bEBAABo0aIDs7Gzs2bMHGzZswPLlywHkj9SYOnUqFixYgEaNGqFevXqYNWsWatWqhaeeeqryT/DGDeCekcQAAFmGFBEByfDPJLp5ecD33wMnTwJFjeD19gZ8fcscTp8+fbBmzRqTZUWNMiYiIiLLcu3aNcyYMQNpaWnw9/fHggUL4OrqqnZYZoFJWzOQmfPvSFsnjrQlIiIiMnsjRoxAYmIiZs+ejbi4OLRt2xYRERHKRGLXrl0zufVNr9dj4sSJ+Pvvv+Hg4ICmTZviiy++wIgRI5Q2b7zxBvR6PZ5//nmkpqaia9euiIiIUKdm6vDhwLFjhRZLAMS9ydmMDCAgoOj9dOkCHDlS5nDs7OyKLT0hSRJWrlyJ3bt3Y+/evfD19cV7772HAQMGKG327NmDqVOn4vr163j00UcxZsyYMsdEREREZXP16lXMnDkT6enpqF+/PhYsWIBq1aqpHZbZYIbQDGTm/Zu05UhbIiIiIsswadIk/PXXX8jOzsbx48cRGBiorIuKisLatWuVxwsWLMDFixdx9+5dpKSk4NixYyYJWyA/+fjWW28hLi4OWVlZ2L9/Pxo3blxZp2MqNDS/9EERo2clIUwX3PsYyN/OxiZ/P5Vg3rx5GD58OM6cOYN+/frhmWeeQUpKCgDg+vXrGDx4MPr374/Y2FiMHz8e06ZNq5S4iIiIqGhXrlzBjBkzkJ6ejoYNGzJhWwRmCM2A8UhbR93DTwxBFUOr1SIoKAgBAQHQFtRvIyIiIrJm48cDhw8DHh75ydfS0GoBT8/87ceNK5dwvvvuOzg7O5v8LFy4UFk/duxYjBo1Cg0bNsTChQtx584dnDhxAgCwfPlyNGjQAO+99x6aNGmCZ555BmPHji2XuIiIiKj0Lly4gBkzZiAjIwONGzdmwrYYLI9gBvS5/45OcLJlHp2IiIiIzMCjjwKnTwODBgE//QTI8oO3kSSgQwfgm2+AYsoZPIyePXsq9X8LGE9Q0rp1a+V3JycnuLi4ICEhAQDw+++/m4yCBmB2k7sRERFVFWfOnMH8+fORlZWFZs2aYc6cOXByclI7LLPEpK0ZuJtrVB6BSVsiIiIiMhc1awLR0fkjZr/44sHtn3kG+PxzQKcr1zCcnJzQsGHDYtfb2tqaPJYkCXJJksxERERUaU6cOIFFixYhNzcXbdu2xcyZM9Wp3W8hmCE0A5lGSVuOtDU/sizj3LlzuHz5Mi/+iYiIqOrR6QB///yyB/ej1QL16pV7wrasmjVrppRKKPDjjz+qFA0REVHVFB0djYULFyI3NxeBgYGYNWsWE7YPwAyhGcjK+7c8gr0Na9qaGyEEkpKScPv2bYiiJtogIiIisna7dgEGw/3bGAz57SpAdnY24uLiTH6SkpJKtO2LL76Iixcv4vXXX8eFCxewceNGk0niiIiIqGLt3bsXS5YsgcFgQI8ePTBt2jTozOxLXnPEpK0ZyDH8mwi01TJpS0RERERmJD4+v7atESH9c80q3XPtGhsL/FNLtjxFRESgZs2aJj9du3Yt0bZ16tTBtm3bsGPHDrRp0wYrVqwwmcSMiIiIKs6OHTvw0UcfQQiBvn37IiwsDDalneS0iuKzZAZyjZK2OiZtiYiIiMic7N1r8lBotUC1asDkycAHHwAZGaajcPfuBZ59ttwOv3bt2vuOjC3qTqjU1FSTx08++SSefPJJk2WhoaHlER4REREVQQiBTZs2YdOmTQCAIUOGYMyYMZDu/cKXisWRtmbAZKSthi9eIiIiIjIje/YAGo0yqlb07w+cPw/MmwdcuAAMGJDfTpLy2+3Zo2KwREREpDYhBD7//HMlYfvss88yYfsQmLQ1AzkyR9oSERERkRnKywO+/x6QZcDVFWLzZhi++grw8spf7+UFbN8ObNkCuLrmt9uz58H1b4mIiMgqybKMjz76CN9++y0A4IUXXsDw4cOZsH0ILI9gBnJZ05aIiIiIzNHdu0D9+kC9esCKFYCnZ34i917DhwM9egAvvghcvQpkZuaXUCAiIqIqIzc3F0uXLsWRI0cgSRKmTJmCxx57TO2wLBaTtmYghzVtiYiIiMgcVasG/PwzoNXmPy6ifqyiYNStwfBveyIiIqoSMjMz8fbbb+PMmTOwsbHBa6+9hi5duqgdlkVj0tYMcKStedNoNOjatSsSEhKg0bCiCBEREVUxpU3AMmFLRERUpaSmpmLu3Lm4fPky7O3tMWvWLLRu3VrtsCwek7ZmgCNtzZskSdBqtdBqtazBQkRERBZNlmW1Q7AKfB6JiIjyxcfHY9asWbh16xZcXV0xd+5cNGzYUO2wrAKTtmYg13giMg2TgkRERERUvnQ6HTQaDW7evAlPT0/odLqH+jJaCIG8vDzY2NhUyS+zhRDIyclBYmIiNBoNdDqd2iERERGp5s8//8ScOXNw+/ZteHl5Yf78+ahVq5baYVkNJm3NQA7LI5g1WZZx/vx5pKWlwcPDgyUSiIiIyOJoNBrUq1cPt27dws2bNx96P0IIyLIMjUZTJZO2BRwdHVGnTh1eFxIRUZX166+/Yv78+cjMzIS/vz/mzZsHd3d3tcOyKkzamoFclkcwa0IIxMfHQ6/XQ9xv8g0iIiIiM6bT6VCnTh3k5eXBYDA81D5kWUZycjJq1KhRZROWWq22yo40JiIiAoAff/wR77zzDnJzc9GiRQvMmjULTk5OaodldZi0NQMcaUtERERElUGSJNja2sLW1vahtpdlGba2trC3t6+ySVsiIqKq7IcffsBHH30EIQQCAwPxxhtvsFxQBWHS1gwUjLTVSIANa9oSEREREREREZEZEULg66+/xoYNGwAAvXv3xssvvwytVqtyZNaLSVszkPPPRGQcZUtERERERERERObEYDBg+fLl2Lt3LwBg2LBhePbZZ1kqqIIxaWsGCkba6jjKloiIiIiIiIiIzMTdu3exePFinDx5EpIk4fnnn8eTTz6pdlhVApO2ZqAgacuRtkREREREREREZA5SUlIwb948XLlyBTqdDm+88QYCAwPVDqvKMJvZAz7++GP4+/vD3t4egYGBOHHiRIm227x5MyRJwlNPPVWxAVYgg8hP2tqYTW8QEREREREREVFVde3aNbz22mu4cuUKXF1dER4ezoRtJTOLNOGWLVsQFhaGOXPm4JdffkGbNm0QEhKChISE+2539epVvPbaa+jWrVslRVox/hloCy1rgZgljUaDTp06oU2bNpwlmYiIiIiIiIis2pkzZ/DGG28gMTERvr6+WLJkCRo3bqx2WFWOWWSgli5digkTJiA0NBTNmzfHihUr4OjoiNWrVxe7jcFgwDPPPIN58+ahfv36lRht+TP8MxEZ84HmSZIk6HQ62Nrassg2EREREREREVmtqKgozJkzB3q9Hs2aNcO7774LHx8ftcOqklSvaZuTk4OTJ09i+vTpyjKNRoPg4GDExMQUu91bb70FLy8vjBs3DocPH77vMbKzs5Gdna08Tk9PBwDIsgxZlst4Bg8myzKEEMUe65+cLTSQKiUeKr0H9SGZP/ah5WMfWj72oeWr7D7ka4WIiIiocggh8PXXX2PDhg0AgK5du+KVV16BTqdTObKqS/WkbVJSEgwGA7y9vU2We3t74/z580Vuc+TIEXz++eeIjY0t0THCw8Mxb968QssTExORlZVV6phLS5ZlpKWlQQhR5O31uYZ/PpDIeQ8sCUGVT5ZlXLt2DXq9Hk2aNIGNjepvG3oID3ofkvljH1o+9qHlq+w+zMjIqPBjEBEREVV1BoMBy5cvx969ewEAgwYNQmhoKO82VpnFZZ8yMjLw7LPPYuXKlfDw8CjRNtOnT0dYWJjyOD09HX5+fvD09ISLi0tFhaqQZRmSJMHT07PIDzgCegACOlsbeHl5VXg8VDoGgwHnz59HZmYmPD09YWtrq3ZI9BAe9D4k88c+tHzsQ8tX2X1ob29f4ccgIiIiqsru3r2LxYsX4+TJk5AkCS+88AKeeOIJtcMimEHS1sPDA1qtFvHx8SbL4+Pji6yZcfnyZVy9ehX9+/dXlhXcOmdjY4MLFy6gQYMGJtvY2dnBzs6u0L40Gk2lfWiUJKnY4xWUR9BqJH6INUNCCEiSdN8+JMvAPrR87EPLxz60fJXZh3ydEBEREVWclJQUzJs3D1euXIFOp8Mbb7yBwMBAtcOif6h+JazT6dC+fXtERkYqy2RZRmRkJDp16lSofdOmTXH27FnExsYqPwMGDEDPnj0RGxsLPz+/ygy/XBRMRKblsHMiIiIiIiIiIqpgf/31F1577TVcuXIFrq6uCA8PZ8LWzKg+0hYAwsLCMGbMGAQEBKBjx45YtmwZ9Ho9QkNDAQCjR4+Gr68vwsPDYW9vj5YtW5ps7+bmBgCFllsCIQQMBRORqZ5CJyIiIiIiIiIia3by5EksXrwYd+/eha+vL+bOnVvk3e6kLrNI2o4YMQKJiYmYPXs24uLi0LZtW0RERCiTk127ds1qb48rKI0AcKQtERERERERERFVDCEEvvvuO6xcuRJCCLRs2RIzZsxAtWrV1A6NimAWSVsAmDRpEiZNmlTkuqioqPtuu3bt2vIPqJKYJm3Vi4OIiIiIiIiIiKyTwWDAZ599hj179gAAevfujYkTJ8LGxmxSg3QP6xy+akEM4t+srVbDrC0RERGRpfj444/h7+8Pe3t7BAYG4sSJE8W2XblyJbp164bq1aujevXqCA4OLtR+7NixyuSnBT99+vSp6NMgIiIiK6fX6zFv3jzs2bMHkiThueeew//93/8xYWvmmLRVmUH+93fmbM2TRqNBYGAgWrVqZbVlOoiIiKh0tmzZgrCwMMyZMwe//PIL2rRpg5CQECQkJBTZPioqCqNGjcLBgwcRExMDPz8/PP7447hx44ZJuz59+uDWrVvKz6ZNmyrjdIiIiMhK3bp1C6+99hpOnToFOzs7zJw5E4MGDYLEEp1mjxkolclGI201fMOYJUmSYG9vDzs7O/6jRkRERACApUuXYsKECQgNDUXz5s2xYsUKODo6YvXq1UW2//LLLzFx4kS0bdsWTZs2xapVqyDLMiIjI03a2dnZwcfHR/mpXr16ZZwOERERWaFz587h1Vdfxd9//w0PDw+88847CAwMVDssKiGOg1aZwaimrQ1T6ERERERmLycnBydPnsT06dOVZRqNBsHBwYiJiSnRPjIzM5Gbmwt3d3eT5VFRUfDy8kL16tXRq1cvLFiwADVq1ChyH9nZ2cjOzlYep6enAwBkWYYsy0VuU1ayLEMIUWH7p8rF/rQ+7FPrwv60LpXdn/v378cnn3yCvLw8NGrUCDNnzoS7uztfT+WkLP1Z0m2YtFWZQeZIW3MnyzIuX76M1NRUeHh4sEQCERFRFZeUlASDwQBvb2+T5d7e3jh//nyJ9vHmm2+iVq1aCA4OVpb16dMHgwcPRr169XD58mXMmDEDffv2RUxMDLRabaF9hIeHY968eYWWJyYmIisrq5RnVTKyLCMtLQ1CCF4TWQH2p/Vhn1oX9qd1qaz+NBgM2LRpE3744QcAQIcOHfD8888jLy+v2DJOVHpl6c+MjIwStWPSVmVGOVvWtDVTQgj8/fff0Ov1EEblLIiIiIgexqJFi7B582ZERUXB3t5eWT5y5Ejl91atWqF169Zo0KABoqKi8NhjjxXaz/Tp0xEWFqY8Tk9Ph5+fHzw9PeHi4lIhscuyDEmS4OnpyQSCFWB/Wh/2qXVhf1qXyujPjIwMvPvuu4iNjYVOp8PTTz+NESNGsNRjBShLfxpf/90Pk7YqMx5pa8OsLREREZHZ8/DwgFarRXx8vMny+Ph4+Pj43HfbJUuWYNGiRdi/fz9at25937b169eHh4cHLl26VGTS1s7ODnZ2doWWazSaCv1wL0lShR+DKg/70/qwT60L+9O6VGR/Xr9+HfPnz8etW7fg4OCAsLAwdOrUqdyPQ/962P4saXu+61Vm4EhbIiIiIoui0+nQvn17k0nECiYVu9+Ho3feeQfz589HREQEAgICHnicv//+G8nJyahZs2a5xE1ERETW6cSJE3j11Vdx69YteHl54d1332XC1gpwpK3KZKPb7bXM2hIRERFZhLCwMIwZMwYBAQHo2LEjli1bBr1ej9DQUADA6NGj4evri/DwcADA4sWLMXv2bGzcuBH+/v6Ii4sDADg7O8PZ2Rl37tzBvHnzMGTIEPj4+ODy5ct444030LBhQ4SEhKh2nkRERGS+hBDYunUrNmzYACEEWrVqhWnTplVYmSSqXEzaqsxgNGEcc7ZERERElmHEiBFITEzE7NmzERcXh7Zt2yIiIkKZnOzatWsmt74tX74cOTk5GDp0qMl+5syZg7lz50Kr1eLMmTNYt24dUlNTUatWLTz++OOYP39+kSUQiIiIqGrLzs7GBx98gOjoaABAv379MGHCBNjYMNVnLdiTKjMYj7Rl0paIiIjIYkyaNAmTJk0qcl1UVJTJ46tXr953Xw4ODti7d285RUZERETWLDExEW+//TYuX74MrVaLF198EX369FE7LCpnTNqqzLimLcsjEBERERERERFRcc6cOYPFixcjPT0dLi4umD59Olq2bKl2WFQBmLRVmSz/m7VlztY8aTQaBAQEICkpiTN2EhEREREREVGlE0Jgx44dWLNmDYQQaNCgAWbMmAEvLy+1Q6MKwqStyoxH2towa2uWJEmCk5MT9Ho9JIl9RERERERERESVJysrC//73/9w5MgRAMBjjz2GiRMnQqfTqRwZVSQmbVVm4EhbIiIiIiIiIiIqws2bN/H222/j2rVr0Gq1eP7559G3b18OKqsCmLRVmVHOFhq+4cySLMu4evUqUlNT4eHhwRIJRERERERERFThTpw4gffeew+ZmZlwd3fHtGnT0KxZM7XDokrCpK3KDOLfrK2WuUCzJITAX3/9Bb1ej1atWqkdDhERERERERFZMSEENm7ciM2bNwMAmjVrhmnTpsHd3V3lyKgyMWmrMoP87+9ajrQlIiIiIiIiIqqy9Ho9lixZgp9//hkA8OSTT2LcuHGwsWEKr6phj6vMuDyCljlbIiIiIiIiIqIq6erVq1i4cCFu3boFnU6HiRMn4rHHHlM7LFIJk7YqMy6PoOFMZEREREREREREVU5kZCQ++eQT5OTkwMvLCzNmzECDBg3UDotUxKStykzLI6gXBxERERERERERVa7s7Gx8+umn2LdvHwCgXbt2eO211+Di4qJyZKQ2Jm1VJptMRMasLRERERERERFRVXDjxg0sWrQIV69ehSRJeOaZZzB8+HBInPOIwKSt6gxGNW2ZsyUiIiIiIiIisn5HjhzB//73P2RlZcHV1RVvvPEGWrdurXZYZEaYtFWZwWgmMi2/STFLGo0G7dq1Q3JyMjQajdrhEBEREREREZGFys3Nxdq1a/Hdd98BAFq2bInXX38d7u7uKkdG5oZJW5UZj7TVMh9oliRJgouLC7KysniLAhERERERERE9lKSkJCxevBiXLl0CAAwdOhT/+c9/oNVqVY6MzBGTtiozrmmrYUKQiIiIiIiIiMjq/PTTT1i0aBFyc3NRrVo1hIWFoUOHDmqHRWaMSVuVGeR/f9cyZ2uWZFnG9evXcfv2bXh4eLBEAhERERERERGViMFgwIYNG7B161bk5OSgZcuWmDZtGry8vNQOjcwck7YqMxiNtNVyJjKzJITAlStXoNfr0aJFC7XDISIiIiIiIiILkJycjHfffRfnzp0DAPTu3RtTpkyBTqdTOTKyBEzaqsxoHjIwZ0tEREREREREZPlOnDiBZcuWISMjAw4ODpg0aRIaN24MGxum4qhk+EpRmcEoa6tlTVsiIiIiIiIiIouVk5ODtWvXYteuXQCA+vXr44033kDNmjWRkJCgcnRkSZi0VZnBaKStlqVSiYiIiIiIiIgs0vXr1/HOO+/g6tWrAICnnnoKo0ePhq2tLWRZvv/GRPdg0lZlsuBIWyIiIiIiIiIiSyWEwL59+/Dpp58iJycHrq6umDp1KgICAtQOjSwYk7YqMxh90cKatkRERERERERElkOv1+Ojjz7CkSNHAABt27bFK6+8And3d5UjI0vHpK3KDMYjbVkegYiIiIiIiIjIIvz+++9YsmQJEhISoNVq8eyzz2Lw4MGQeCc1lQMmbVVmPNKW5RHMk0ajQZs2bZCcnAyNhpl1IiIiIiIioqpMlmVs3boVX375JWRZho+PD15//XU0btxY7dDIijBpqzLjmrYsj2CeJEmCm5sbcnJy+G0ZERERERERURWWnJyM9957D2fPngUABAUFYeLEiXB0dFQ5MrI2TNqqzPBvzhZaZm3NnjDk4e6RaOSePweRqYfIzQUgHrgdqU8IAWRlI83ejsl3C8U+tHzsQ8tX0Ie5T4+FXcOmaodDREREVKmOHz+O//3vf8jIyIC9vT1eeukl9OzZk9e2VCGYtFWZQTaqacv3uFmSZRk3btzA7aREaD9YCMPZU2qHRGWQrXYAVGbsQ8vHPrR8cp/+aodAREREVGmys7OxZs0a7N69GwDQoEEDvP766/D19VU5MrJmTNqqzChnCw2/mTFLQghcunQJ+rOxqPFrLLRqB0REREREREREleKPP/7A0qVLcePGDQDAoEGDMHr0aNjYMKVGFYuvMJWZlkdQLw4qget/Kr+6vjoLtg2aALa2AJPtFkHIMpKTk1GjRg1InFDOIrEPLR/70PIV9KGuQUO1QyEiIiKqUHl5ediyZQu++uoryLKMGjVqYMqUKWjXrp3aoVEVwaStykzLIzD5Z65EdhaQngYAsGnYBA49Hlc5IiotWZYBSQutlxc0TBZZJPah5WMfWr6CPpTs7NUOhYiIiKjCXL9+HUuXLsWlS5cAAN27d8dLL70EZ2dnlSOjqoRJW5WZlEfg51ezJd9OVn7XNWulYiREREREREREVBGEENi1axfWrVuHnJwcODs7Y+LEiejWrZvaoVEVxKStyjjS1jIYUv5N2to2bKJiJERERERERERU3pKSkrBs2TKcPn0aAPDII49g8uTJqFGjhsqRUVXFpK3KTGraSoDIy0Pmrq3IiomGITkRyMkGhIAQAhDF74cqjgEScqu5K49tGjBpS0RERMDHH3+Md999F3FxcWjTpg0+/PBDdOzYsci2K1euxPr16/Hrr78CANq3b4+FCxeatBdCYM6cOVi5ciVSU1PRpUsXLF++HI0aNaqU8yEiIqqKhBCIiorCp59+Cr1eDzs7Ozz33HPo27cvJA6uIxUxaasyWRiPtAVSF81C9vEjKkZE9xKSBPyTtJWcXWHjV1fliIiIiEhtW7ZsQVhYGFasWIHAwEAsW7YMISEhuHDhAry8vAq1j4qKwqhRo9C5c2fY29tj8eLFePzxx3Hu3Dn4+voCAN555x188MEHWLduHerVq4dZs2YhJCQEv/32G+ztWUeYiIiovKWnp+OTTz7B0aNHAQBNmjRBWFgYatWqpXJkRGaUtC3NSIXt27dj4cKFuHTpEnJzc9GoUSO8+uqrePbZZys56rIzyP/+bnP6R5OEreTiCo29IyABkKT8H/BbnsqmAdBEK2DQaOH64hTOeE5ERERYunQpJkyYgNDQUADAihUrsHv3bqxevRrTpk0r1P7LL780ebxq1Sps27YNkZGRGD16NIQQWLZsGf773/9i4MCBAID169fD29sbO3bswMiRIyv+pIiIiKqQn3/+GR988AFu374NrVaLUaNGYejQodBqtWqHRgTATJK2pR2p4O7ujpkzZ6Jp06bQ6XT47rvvEBoaCi8vL4SEhKhwBg/PYDzS9lik8rvrq7Pg0ONxNUKiInjIMhISEuBQxOuRiIiIqpacnBycPHkS06dPV5ZpNBoEBwcjJiamRPvIzMxEbm4u3N3z7+b5888/ERcXh+DgYKWNq6srAgMDERMTU2TSNjs7G9nZ2crj9PR0AIAsy5BluVD78iDLMoQQFbZ/qlzsT+vDPrUu7M+KkZWVhdWrVyMiIgIA4Ofnh1deeQUNGzYEAP4NpRIpS3+WdBuzSNqWdqRCjx49TB5PmTIF69atw5EjRywvaWvUT9L5/GLXkpMz7Lv2UikiIiIiIrqfpKQkGAwGeHt7myz39vbG+fPnS7SPN998E7Vq1VKStHFxcco+7t1nwbp7hYeHY968eYWWJyYmIisrq0RxlJYsy0hLS4MQAhrefWTx2J/Wh31qXdif5e+PP/7AZ599hoSEBABASEgIhg0bBp1OpyyrKOxP61KW/szIyChRO9WTtmUdqSCEwIEDB3DhwgUsXry4IkOtEAU1bV1yMiClpgAAbBs0hmSjetfQP2RZRlxcHFJSUuDh4cF/XImIiKhMFi1ahM2bNyMqKqpMtWqnT5+OsLAw5XF6ejr8/Pzg6ekJFxeX8gi1EFmWIUkSPD09eU1kBdif1od9al3Yn+UnKysL69evx+7duyGEQK1atTB16lS0bt260mJgf1qXsvRnSa//VM8MPuxIhbS0NPj6+iI7OxtarRaffPIJevfuXWRbNW4dM3a/IdMGOT9pWyf9hrJMW6ceh8ubEYPBgPPnz0Ov16NRo0b8x9VC8VYUy8c+tHzsQ8tX2X1YXsc5f/48mjZtWi77AgAPDw9otVrEx8ebLI+Pj4ePj899t12yZAkWLVqE/fv3m3xQLNguPj4eNWvWNNln27Zti9yXnZ0d7OzsCi3XaDQVer0iSVKFH4MqD/vT+rBPrQv7s+xiY2Px4YcfKiNpg4ODMWHCBDg5OVV6LOxP6/Kw/VnS9qonbR9WtWrVEBsbizt37iAyMhJhYWGoX79+odIJgDq3jhm735DpzKz8ZLJnVoqy7K6zC+5W8LB8KjmDwQC9Xo+srCwkJCTA1tZW7ZDoIfBWFMvHPrR87EPLV9l9WNJbxx6kefPm6NSpE8aNG4cRI0aU+UOaTqdD+/btERkZiaeeegpA/nMTGRmJSZMmFbvdO++8g7fffht79+5FQECAybp69erBx8cHkZGRSpI2PT0dx48fx0svvVSmeImIiKoivV6Pzz//HPv27QMAeHl5YdKkSWjXrp3KkRGVjOpJ24cdqaDRaJQi0W3btsXvv/+O8PDwIpO2atw6Zux+Q6ZtdLcA3IVbdpqyzKVOXdhzwiuzYTAYlA93Xl5eTNpaKN6KYvnYh5aPfWj5KrsPy1I6wNju3buxZs0aTJw4EVOnTsWwYcMwbtw4dO7c+aH3GRYWhjFjxiAgIAAdO3bEsmXLoNfrlTkaRo8eDV9fX4SHhwMAFi9ejNmzZ2Pjxo3w9/dX6tQ6OzvD2dkZkiRh6tSpWLBgARo1aoR69eph1qxZqFWrlpIYJiIiopI5fvw4PvnkE6Sk5A+Qe+KJJzBmzBg4ODioHBlRyametH3YkQr3kmXZpASCMbVuHTNW3JDpf6ojwD0rVVlm4866qeZECAFJkngbgxVgH1o+9qHlYx9avsrsw/I6Rt++fdG3b1+kpKTgiy++wNq1a9G1a1c0btwY48aNw+jRowuV6nqQESNGIDExEbNnz0ZcXBzatm2LiIgIZT/Xrl0ziX/58uXIycnB0KFDTfYzZ84czJ07FwDwxhtvQK/X4/nnn0dqaiq6du2KiIiIckteExERWbu0tDR89tlniI6OBgDUqlULkydPRosWLVSOjKj0VE/aAqUfqRAeHo6AgAA0aNAA2dnZ2LNnDzZs2IDly5ereRoPxfBPqbbqRiNtNdVrqBQNERERkfVyd3fH5MmTMXnyZJw6dQqvvPIKpk2bhpkzZ6Jv376YOnUqevbsWeL9TZo0qdhBBlFRUSaPr169+sD9SZKEt956C2+99VaJYyAiIqL8wVaHDx/Gp59+ivT0dEiShMGDB+Ppp5+GTqdTOzyih2IWSdvSjlTQ6/WYOHEi/v77bzg4OKBp06b44osvMGLECLVO4aHJIn+orVt2urJM4+auVjhEREREVi01NRVffPEF1qxZg1OnTqFDhw4YNGgQvv/+ewQHB2P27NmYM2eO2mESERFRCSUnJ+Pjjz/GTz/9BADw9/fH5MmT0ahRI5UjIyqbUidtp02bhnHjxpX7i780IxUWLFiABQsWlOvx1WL4pzyCY97d/F80WkissUJERERUrvbt24fVq1fj22+/hb29PZ555hmsWbMGrVu3BpB/jfv+++9j/vz5TNoSERFZACEE9u3bh88//xyZmZmwsbHBiBEjMHToUNjYmMUYRaIyKfWreMOGDXj33XfRuXNnjB8/HsOGDYOjo2NFxFYlyP8UtS1I2kqOjpAkSc2Q6B4ajQbNmjVDSkoKazASERFZoLp16+Lvv/9Gly5d8Omnn2LYsGFF1ont3r07UlNTKz9AIiIiKpX4+Hh8+OGHOH36NACgUaNGmDJlCurWratyZETlp9QZqOvXr2Pnzp3w9vbG888/j5o1a+L5559HTExMRcRn9QpG2jrkZQEAJAcmwM2NJEnw8vKCu7s7E+pEREQWaNiwYTh37hyio6Px7LPPFjuxV/v27SHLciVHR0RERCUlyzJ27tyJl19+GadPn4ZOp8Nzzz2HJUuWMGFLVqfUSVuNRoMnnngCW7duxc2bNzFv3jycOHECXbt2RYsWLfDee+8hISGhImK1SveWR9A4OqkYDREREZH1ad26NTw9PYtcl5KSgvXr11dyRERERFRaV69exZtvvomVK1ciOzsbLVu2xEcffYRBgwbxrliySmV6VdeoUQNTp07F+vXr0a1bN/z+++94/fXX4efnhzFjxiAxMbG84rRasiygETLsDTkAONLWHAkhkJCQgJSUFIh/Jo4jIiIiyxEaGorLly8Xue7PP/9EaGhoJUdEREREJZWVlYXVq1djypQpOH/+POzt7TFx4kQsXLgQNWvWVDs8ogrz0EnbtLQ0LF++HAEBAWjXrh3S09Px8ccf4+bNm1i+fDkOHz6MkSNHlmesVilP/FsaAcivaUvmRZZl/P7777hy5QpvmSQiIrJA9/vS9fbt26hWrVolRkNEREQlIYTAsWPH8NJLL+Gbb76BLMvo1KkTli9fjr59+7J8IVm9Uk9EFhkZidWrV2PHjh2wsbHBqFGj8Omnn6J9+/ZKm+eeew5+fn7o379/uQZrjWQh4PBPaQSAI22JiIiIysP333+P77//Xnn83nvvwdvb26RNVlYWDhw4gLZt21ZydERERHQ/cXFx+PTTT/Hzzz8DALy8vPDiiy+iQ4cOKkdGVHlKnbTt3bs3AgMD8eGHH2LkyJFwLGZkaOPGjTFq1KgyB2jtZBlwNBppy5q2RERERGX3xx9/YNeuXQDyJxU9fPgw7OzsTNrodDq0bNkSCxcuVCNEIiIiukdubi6++eYbbNmyBTk5ObCxscHgwYMxfPjwQn/HiaxdqZO2Z86cQcuWLR/Yrm7dulizZs1DBVWVGISAU1628liyK3o2YyIiIiIquSlTpmDKlCkAgHr16mHHjh1o06aNylERERFRcc6cOYNPPvkEN27cAJA/kehLL72E2rVrqxwZkTpKnbSdPHkyPvnkEzRt2rTQuj/++AMvvvgiDhw4UC7BVQUGAejkXOWxxG+OiIiIiMrVn3/+qXYIREREVIzbt29j9erViIqKAgC4urpi/PjxCAoKYt1aqtJKnbSNiopCenp6kevS09MRHR1d5qCqEoMsTJK2sNWpFwwRERGRldi+fTt69eoFNzc3bN++/YHtBw8eXAlRERERUQFZlvH9999jw4YN0Ov1kCQJffv2xejRo+HkxNKRRKVO2gIo9puOY8eOwcvLq0wBVTWyAGwNRiNtbW1VjIaIiIjIOgwdOhQ//vgjOnbsiKFDh963rSRJMBgMlRQZERERXbx4EcuXL8fFixcBAA0bNsTEiRPRqFEjlSMjMh8lStqGh4cjPDwcQP5Fbc+ePaHRaEzaZGdnIy8vDxMnTiz/KK2YQZiOtJV0HGlrbiRJQpMmTZCSksJbM4iIiCzEn3/+iZo1ayq/ExERkfr0ej02bNiAPXv2QAgBR0dHjB49Gn379i2UZyKq6kqUtO3cuTNeffVVCCHw1ltvYdSoUYUKQet0OjRr1gz9+/evkECtlUEGbOU85bFky5q25kaj0cDHxwcajYZ/RIiIiCxE3bp1i/ydiIiIKp8QAtHR0Vi1ahVSU1MBAEFBQRg3bhyqV6+ubnBEZqpESdugoCAEBQUByB91OH78ePj6+lZoYFWFLIRJeQRwpC0RERFRuapTpw5GjhyJUaNGoV27dmqHQ0REVKVcvXoVK1euxJkzZwAAvr6+eOmll9CmTRuVIyMyb6WuaTtnzpyKiKPKMsgwLY/AicjMjhACycnJSE1Nhaenp9rhEBERUSkNHz4cmzdvxnvvvYdGjRrh6aefxsiRI9G4cWO1QyMiIrJaaWlp2LhxI77//nsIIaDT6TB8+HAMHjwYtpzPh+iBSpS0HTBggHKRO2DAgPu2lSQJ3377bbkEVxUYhIAta9qaNVmW8euvv0Kv16NBgwbQarVqh0RERESlsGTJEixZsgTR0dHYvHkzPv74Y8ybNw9t27ZVEri8i4yIiKh85OXlYffu3di0aRP0ej2A/LKboaGh8PHxUTk6IstRoqRtRkaGMqNueno6J2MqR7IAdAYmbYmIiIgqWvfu3dG9e3d8+OGHiIyMxKZNm7BgwQJMmzYNubm5D94BERERFUsIgZ9//hmff/45bty4AQCoX78+xo8fj1atWqkcHZHlKVHS9uDBg8rvUVFRFRVLlSOEyE/aGo20BcsjEBEREVUoIQRycnKQnZ2NvLw8CCHUDomIiMiiXbt2DatWrcKpU6cAAK6urhgzZgwee+wxTuhN9JBKXdN23759CA4O5mjbcmD45/MByyMQERERVSwhBA4cOIDNmzdj+/btuH37Njp06ID58+djxIgRaodHRERkkdLT0/Hll18iIiICsizDxsYGAwcOxPDhw+Ho6Kh2eEQWrdRJ25CQEHh7e2P48OEYNWoUHn300YqIq0qQ/0nampRH4EhbIiIionI1efJkbN26FXFxcWjevDnCwsIwcuRINGjQQO3QiIiILFJeXh727NmDjRs3KnVrO3XqhNDQUNSsWVPl6IisQ6mTtmfOnMGmTZuwZcsWfPjhh/D398eoUaMwcuRI1igpJcM/WVtblkcgIiIiqjDfffcdxo4di1GjRvF6lYiIqIx+/vlnrFq1Sqlb6+/vjwkTJqB169YqR0ZkXUqdtG3ZsiXefvttvP322zhx4gQ2bdqEdevWYdGiRWjevDmefvppTJ8+vSJitTqGIkfa2qoUDREREZF1unLlitohEBERWbzr16/j888/x8mTJwHk16199tln0bt3b9atJaoApU7aGuvYsSM6duyIpUuX4rvvvsNLL72E//73v0zallDBSFsbYVCWMWlrfiRJQsOGDXH79m3WciYiIrIQKSkpcHNzg0ajQUpKygPbu7u7V0JURERElicjIwMbN27Enj17lLq1AwYMwPDhw+Hk5KR2eERWq0xJ2+zsbOzatQubN2/Gnj17kJeXh8cff7y8YrN6BTVttfK/SVtoteoEQ8XSaDTw9fWFra0tvz0kIiKyEJ6enoiJiUHHjh3h4eHxwC9eDQbDfdcTERFVNXl5efj++++xceNG3LlzBwAQGBiIcePGsW4tUSUoddLWYDBg79692LRpE3bu3Ik7d+6gS5cueO+99zBs2DB4eHhURJxWySCKGGmrLVMenYiIiIgArF69WplobPXq1bxbhoiIqISEEDhx4gTWrVuH69evA8ivWzt+/Hi0adNG5eiIqo5SZwi9vLyQmpqKtm3bYtasWRg5ciRq165dEbFZPYOc/3+N4EhbcyaEQGpqKjIyMuDp6al2OERERFQCY8aMUX4fO3aseoEQERFZkF9//RXr1q3D+fPnAQAuLi5K3Vot8xVElarUSdvJkydj1KhRaNy4cUXEU6XIBSNtjcsj2HCkrbmRZRmnT5+GXq+Hv78//1ARERFZmPr16+Obb74pcnTQr7/+igEDBnCyMiIiqtKuXLmC9evXK5OM6XQ6PPXUUxg8eDDr1hKppNQZwjlz5lREHFVSwUhbLcsjEBEREVWYq1evIjs7u8h1mZmZyq2fREREVU1cXBy++OILHDp0CACg1WoREhKCESNGcJJOIpWVKEO4dOlSPPPMM/D29sbSpUvv21aSJLzyyivlEpy1y/tnpK2W5RGIiIiIylVWVhYyMzMh/rneSk9PR0pKSqE2O3bsQK1atdQIkYiISDWpqanYvHkzIiIilMk4u3fvjv/85z+cZIzITJQoafvaa6+ha9eu8Pb2xmuvvXbftkzalpxBvqc8gkYDSaNRMSIiIiIi67B48WK89dZbAPKvT0NCQoptO3fu3EqKioiISF16vR7ffPMNvv32W2RlZQEAHnnkEYwePVqZwJOIzEOJkrayLBf5O5XNPznbf0fasjQCERERUbl46qmn4O/vDyEEnnvuOfz3v/8t9GFUp9OhWbNmaNu27UMd4+OPP8a7776LuLg4tGnTBh9++CE6duxYZNtz585h9uzZOHnyJP766y+8//77mDp1qkmbuXPnYt68eSbLmjRpokwGQ0RE9LBycnKwZ88efPXVV8jIyAAANG7cGGPGjEHr1q1Vjo6IilLqLGF0dDQeeeQRODs7F1qn1+tx8uRJdO/evVyCs3YFI221Ij8RLrE0AhEREVG5aNOmjTLxmCRJePLJJ1GjRo1y2/+WLVsQFhaGFStWIDAwEMuWLUNISAguXLgALy+vQu0zMzNRv359DBs27L53pbVo0QL79+9XHttwkloiIioDg8GAgwcP4ssvv0RSUhIAoHbt2hg9ejQeffRRSJKkcoREVJxSXwX27NkTMTExRY4iOH/+PHr27KnUQ6H7MxSMtC0oj8CkLREREVG569WrF/76668ik7a//PILvLy8ULt27VLtc+nSpZgwYQJCQ0MBACtWrMDu3buxevVqTJs2rVD7Dh06oEOHDgBQ5PoCNjY28PHxKVUsRERE9xJC4Pjx41i/fr0y4aaHhweefvpp9OrVC1rmH4jMXqmTtgWTORRFr9fDwcGhTAFVJXkFNW3/KY8gcSSFWZIkCfXr18ft27f5LSQREZEFeumll9CoUSM88sgjhdZt3LgRFy9exLffflvi/eXk5ODkyZOYPn26skyj0SA4OBgxMTFlivXixYuoVasW7O3t0alTJ4SHh6NOnTpFts3OzkZ2drbyOD09HUB+ObOKKmkmyzKEECyZZiXYn9aHfWpdHrY/f/31V6xbtw4XLlwAAFSrVg1Dhw7FE088AZ1Op+ybKhffn9alLP1Z0m1KlCX88ccfcezYMeXxxo0bceTIEZM2WVlZ+Pbbb9GsWbNShFm1Gf7pI460NW8ajQZ+fn6ws7ODhhPFERERWZzjx4/jhRdeKHJdz549sX79+lLtLykpCQaDAd7e3ibLvb29y1R/NjAwEGvXrkWTJk1w69YtzJs3D926dcOvv/6KatWqFWofHh5eqAYuACQmJiqTy5Q3WZaRlpYGIQSvi6wA+9P6sE+tS2n786+//sLXX3+NM2fOAMiv3R4SEoInnngCjo6OSE1NreCI6X74/rQuZenPgrrSD1KipO3evXuVC0JJkvDBBx8UamNra4tmzZrhk08+KUWYVZtBFNS05URkRERERBXlzp07sLW1LXKdRqMp8YVzRevbt6/ye+vWrREYGIi6deviq6++wrhx4wq1nz59OsLCwpTH6enp8PPzg6enJ1xcXCokRlmWIUkSPD09+YHTCrA/rQ/71LqUtD+vXr2KzZs3K4PtHBwc8Pjjj2PkyJGoXr16ZYVLD8D3p3UpS3/a29uXqF2JsoRz5szBnDlzAORf2MbExCAwMLBUAVFhykhblkcwa0IIpKenQ6/X37c8CBEREZmnZs2a4ZtvvkGfPn0Krfv222/RpEmTUu3Pw8MDWq0W8fHxJsvj4+PLtR6tm5sbGjdujEuXLhW53s7ODnZ2doWWazSaCv0wKElShR+DKg/70/qwT63L/frzypUr2Lx5s1KaR6PRoFu3bvjPf/6DmjVrVnaoVAJ8f1qXh+3PkrYvdZaQtTfKjzLStqA8goblEcyRLMs4deoU9Ho96tSpw4LtREREFmbq1KkYO3YstFotnnvuOdSqVQs3b97EmjVrsHLlSqxevbpU+9PpdGjfvj0iIyPx1FNPAci/XoiMjMSkSZPKLe47d+7g8uXLePbZZ8ttn0REZPkuX76MTZs24fjx4wDyE0ddu3bFyJEji62DTkSWp9RJ2y1btuDatWt4/fXXC61bsmQJ6tati2HDhpVLcNauYKQtJyIjIiIiqjijR49GfHw85s2bh08//VRZ7uDggEWLFmHMmDGl3mdYWBjGjBmDgIAAdOzYEcuWLYNer0doaKhyTF9fX4SHhwPIn7zst99+U36/ceMGYmNj4ezsjIYNGwIAXnvtNfTv3x9169bFzZs3MWfOHGi1WowaNaqsTwEREVmBS5cuYdOmTThx4gSA/GRtt27dMHLkSPj5+akcHRGVt1JnCcPDw/Hcc88Vua7gwpdJ25L5t6ZtQZ0EjuAkIiIiqgivv/46XnjhBcTExCA5ORk1atRAp06dHrr264gRI5CYmIjZs2cjLi4Obdu2RUREhDI52bVr10xufbt58ybatWunPF6yZAmWLFmCoKAgREVFAQD+/vtvjBo1CsnJyfD09ETXrl3x448/wtPT8+FPnIiILN7FixexZcsW/PTTTwDyk7VBQUEYMWIEateurXJ0RFRRSp20vXjxIlq2bFnkuubNm+OPP/4oc1BVhVLT9p/yCBInIiMiIiKqMC4uLggJCSm3/U2aNKnYcggFidgC/v7+D6yNv3nz5vIKjYiIrMCFCxfw+eef4/z585AkCZIkoUePHhgxYgR8fX3VDo+IKlips4T29vaFJl0ocOvWLdjwFv8SMwgBjZChwT8X8DYcaUtERERUUS5duoQ//vgDWVlZhdYNHjxYhYiIiIgKO3/+PDZt2oSTJ08iJycH9vb26NWrF4YPH45atWqpHR4RVZJSZ1iDgoKwaNEiDBgwAE5OTspyvV6Pd955Bz169CjP+KyaQRbQFExCBnAiMiIiIqIKkJ6ejkGDBimjXwtGvEqSpLQxGAxFbUpERFRpfv/9d2zcuBGxsbEA8meY79atG5577jmOrCWqgkqdtF24cCE6deqEBg0aYOjQocrsu1u3bkV2djZv6yqFPPnfScgATkRGREREVBHefPNNxMXF4fDhw+jatSu++eYbVK9eHV988QUOHDiATZs2qR0iERFVYefOncOmTZtw+vRpAIBWq0WvXr0wdOhQaDQaeHl5qRwhEamh1FnCpk2b4qeffsKcOXOwbds2ZSKH3r17Y+7cuSYTLtD9yUIo9WwBAKxpa5YkSULdunWRmppqMiKHiIiILENERATefvttBAYGAgBq1aqFDh06oHv37nj11Vfx3nvvceABERFVul9//RWbNm3CmTNnAOQna4ODgzFs2DB4e3tDlmUkJCSoHCURqeWhsoQNGzbEl19+qTxOTEzEV199hdGjR+PHH3/k7WUlZBCA1nikrZblEcyRRqOBv78/EhIS+KUEERGRBUpISICfnx+0Wi2cnJyQnJysrOvXrx+GDBmiYnRERFSVCCHw888/Y9u2bTh37hwAwMbGRknWclQtERV46AxUZmYmvvzySzzxxBOoXbs2Jk+ejKysLLz//vsPtb+PP/4Y/v7+sLe3R2BgIE6cOFFs25UrV6Jbt26oXr06qlevjuDg4Pu2N1cGWZiURwDLIxARERGVOz8/PyQlJQEAGjVqhJ07dyrrYmJiYG9vr1ZoRERUReTl5eHAgQP4v//7P7z11ls4d+4cbGxs0K9fP3z22Wd4+eWXmbAlIhOlyhIaDAZERERg48aN2LlzJ/R6PWrWrIm8vDxs2rQJw4cPf6ggtmzZgrCwMKxYsQKBgYFYtmwZQkJCcOHChSL/0YqKisKoUaPQuXNn2NvbY/HixXj88cdx7tw5iyrOnScDWiErjyWWRzBLQgjo9XrcvXtXmbiEiIiILEfv3r2xf/9+DBo0CK+88grGjBmD48ePQ6fT4cSJE3j11VfVDpGIiKxUVlYW9u7dix07dihfIDo4OKBPnz4YMGAAPDw8VI6QiMxVibKER48excaNG/H1118jKSkJNWrUwH/+8x88/fTTaNmyJWrUqAEfH5+HDmLp0qWYMGECQkNDAQArVqzA7t27sXr1akybNq1Qe+PSDACwatUqbNu2DZGRkRg9evRDx1HZDIVq2rI8gjmSZRk///wz9Ho9ateuDS37iYiIyKIsXrwYmZmZAIBnn30Wzs7O2Lp1K+7evYuPPvoIL7zwgsoREhGRtUlLS8OuXbuwe/du3LlzBwDg5uaGgQMHom/fvnByclI5QiIydyVK2nbr1g2SJKFnz54ICwvD448/Dpt/buVPS0srUwA5OTk4efIkpk+frizTaDQIDg5GTExMifaRmZmJ3NxcuLu7F7k+Ozsb2dnZyuP09HQA+ck4WZaL3KY8ybIMIUShY+UZ7imPoNVWSjxUOgX9V9CH7CPLVNz7kCwH+9DysQ8tX2X3YXkdx9HREY6OjsrjQYMGYdCgQeWybyIiImO3bt3Cjh07sH//fuTk5ADInwBz8ODB6NmzJ3Q6ncoREpGlKFHStlWrVjh79iwOHToErVaLpKQkDBo0CNWqVStzAElJSTAYDPD29jZZ7u3tjfPnz5doH2+++SZq1aqF4ODgIteHh4dj3rx5hZYnJiYiKyur9EGXkizLSEtLgxDCZCKr9IwcaIxG2mbl5iKLM0OaHYPBAL1ej6ysLCQkJMDW1lbtkOghFPc+JMvBPrR87EPLV9l9mJGRUeHHICIiKg+XLl3Ctm3bcPToUaWsXuPGjTFkyBA8+uijvPYholIrUdL29OnT+O233/DFF19g8+bNGDt2LF566SU88cQTePLJJyFJUkXHWaxFixZh8+bNiIqKKnYSienTpyMsLEx5nJ6eDj8/P3h6esLFxaXCY5RlGZIkwdPT0+Qfaofrt01G2jo4OaEaC4+bHYPBoNy64uXlxaSthSrufUiWg31o+diHlq+y+5AThBERkTkTQiA2Nhbbtm3D6dOnleXt27fH0KFD0aJFC1XzJURk2Uo881Xz5s2xcOFCLFy4UKlxu3XrVmzduhWSJOF///sfAKB79+6lCsDDwwNarRbx8fEmy+Pj4x9YJ3fJkiVYtGgR9u/fj9atWxfbzs7ODnZ2doWWazSaSvvQKElSoeMZAJOatpKNLT/EmiEhBCRJKrIPybKwDy0f+9DysQ8tX2X2IV8nRERkjgwGA44ePYpt27bhypUrAPL/ZgUFBWHw4MHw9/dXN0AisgolTtoa69KlC7p06YIPPvgAe/fuxaZNm/Dtt99ix44dqFu3rvKPVknodDq0b98ekZGReOqppwDkj+KIjIzEpEmTit3unXfewdtvv429e/ciICDgYU5DdQZZQCs4ERkRERERERGRucvOzsa+ffvwzTffIOGf0oZ2dnYICQnBwIED4cU7Z4moHD1U0raAVqtFv3790K9fP9y9exc7duzApk2bSr2fsLAwjBkzBgEBAejYsSOWLVsGvV6P0NBQAMDo0aPh6+uL8PBwAPkzAM+ePRsbN26Ev78/4uLiAADOzs5wdnYuyylVKoMMk/IIkk2ZuoOIiIiIiIiIyllaWhr27NmD7777TpnY3NXVFf3790e/fv3KZb4fIqJ7lVuW0MHBAaNGjcKoUaNKve2IESOQmJiI2bNnIy4uDm3btkVERIQyOdm1a9dMbo9bvnw5cnJyMHToUJP9zJkzB3Pnzi3TeVQmgxAm5RGgZdLWHEmShNq1ayM1NZX1iIiIiIiIiKqIK1euYOfOnYiOjkZubi4AwMfHB4MGDUJwcDB0Op3KERKRNTObLOGkSZOKLYcQFRVl8vjq1asVH1AlyJMBrZD/XcDyCGZJo9GgQYMGSEhIYG09IiIiC1GtWrUSf9kqSRLS0tIqOCIiIrIEsizj+PHj2LlzJ3799VdleZMmTTBw4EB07twZWn52J6JKYDZJ26oo756athJH2hIRERGVi1dffZV3yBARUYnp9Xrs27cPu3btUurVarVadOnSBQMGDECTJk1UjpCIqhpmCVWUaxCwkfP+XWDDb+vMkRACWVlZyM7OhhBC7XCIiIioBCypZBYREannxo0b2LVrFyIjI5GVlQUg/26NPn36oF+/fvDw8FA5QiKqqpi0VVGuLEzKI0i8xcIsFdweo9frUatWLd4KQ0REREREZMGEEIiNjcXOnTvx888/K8vr1KmDgQMHokePHqxXS0SqY9JWRXkyJyIjIiIiIiIiqgzZ2dk4ePAgdu7cievXrwPIr2seEBCAgQMHonXr1iytQ0Rmg1lCFeVPRGZU09aG3UFERERERERUnhITE7F7927s3bsXd+7cAQDY29ujd+/e6N+/P2rWrKlyhEREhTFLqKJcg4CdUdIWGt52T0RERERERFRWQgicP38eO3fuxLFjxyDL+aUJvb290b9/fwQHB8PJyUnlKImIisekrYpy7ymPwJG2RERERERERA8vOzsb0dHR2LNnDy5duqQsb926NQYMGIAOHTpAo9GoGCERUckwS6iiPIPpRGSsaUtERERERERUejdu3MCePXsQGRkJvV4PALC1tUWPHj0wYMAA+Pv7qxsgEVEpMUuoojxZmNS0hZblEYiIiIiIiIhKIi8vD8ePH8eePXtw5swZZbm3tzf69u2L4OBguLq6qhghEdHDY9JWRbkyWB7BAkiShFq1aiE1NZUziRIREREREaksKSkJe/fuxQ8//ICUlBQA+Z/bOnTogH79+uGRRx7hZzcisnjMEqooVxaw4Uhbs6fRaNCoUSMkJCSw9hEREREREZEKhBA4ffo09uzZg+PHjysTi7m6uiIkJAQhISHw8vJSOUoiovLDpK2Kcg0CGqOkraRh0paIiIiIiIioQEZGBiIjI/H999/j5s2byvKWLVuib9++6Ny5M2x41yoRWSH+y6aiPFnAxqg8AviHxiwJIZCTk4Pc3FwIIdQOh4iIiIiIyOpdvHgRu3fvxuHDh5GTkwMAcHBwQK9evdC3b1/UrVtX5QiJiCoWs4Qqyp+ITP53AcsjmCVZlhETEwO9Xg8fHx9o2U9ERERERETlLjs7G9HR0dizZw8uXbqkLPf398cTTzyBHj16wN7eXsUIiYgqD5O2Kso1AFrj8ghMBhIREREREVEVc+XKFezduxdRUVHIzMwEANjY2KBbt27o27cvmjZtyonFiKjKYdJWRbmygFbmRGRERERERERUtWRmZuLQoUPYu3cvLl++rCz38fFBnz59EBwcDFdXVxUjJCJSl0btAKqye8sjSFrm0ImIiIgsxccffwx/f3/Y29sjMDAQJ06cKLbtuXPnMGTIEPj7+0OSJCxbtqzM+yQisjRCCJw/fx7/+9//MHr0aHzyySe4fPmyMqp2wYIF+OyzzzBkyBAmbImoymOWUEW5sjApj8CRtkRERESWYcuWLQgLC8OKFSsQGBiIZcuWISQkBBcuXICXl1eh9pmZmahfvz6GDRuGV155pVz2SURkKTIyMnDgwAH88MMPuHbtmrLcz88PISEh6NmzJ1xcXFSMkIjI/DBpqxJZCBhk1rQlIiIiskRLly7FhAkTEBoaCgBYsWIFdu/ejdWrV2PatGmF2nfo0AEdOnQAgCLXP8w+iYjMmRACZ8+exd69e3Hs2DHk5eUBAHQ6Hbp164aQkBDWqiUiug8mbVWSaxAAABvjmrY27A4iIiIic5eTk4OTJ09i+vTpyjKNRoPg4GDExMRU2j6zs7ORnZ2tPE5PTwcAyLIMWZaL3KasZFmGEKLC9k+Vi/1pfcyhT2/fvo3IyEjs27cPt27dUpbXr18fjz/+OIKCguDk5AQgP7ErhFArVLNnDv1J5Yf9aV3K0p8l3YZZQpXk/JO01RjVtIWGI23NkSRJ8Pb2RlpaGr8FJiIiIiQlJcFgMMDb29tkube3N86fP19p+wwPD8e8efMKLU9MTERWVtZDxfEgsiwjLS0NQghoNJwew9KxP62PWn1qMBhw9uxZREVFITY2VklI2Nvbo1OnTujRowfq1asHANDr9dDr9ZUWmyXje9S6sD+tS1n6MyMjo0TtmLRVSXZeftLWpDwCR9qaJY1Gg6ZNmyIhIYH/sBIREZHZmD59OsLCwpTH6enp8PPzg6enZ4XVhpRlGZIkwdPTk9dFVoD9aX0qu09v3LiB/fv34+DBg0hJSQEA2NjYoGnTpnj88cfRtWtX2NvbV3gc1orvUevC/rQuZenPkv67yCyhSrKLKo/AmrZEREREZs/DwwNarRbx8fEmy+Pj4+Hj41Np+7Szs4OdnV2h5RqNpkI/DEqSVOHHoMrD/rQ+Fd2nmZmZOHLkCPbv34/ff/9dWe7i4oJevXrh8ccfR506dSrk2FUR36PWhf1pXR62P0vanklblRQkbbVG5REkLbvDHAkhYDAYYDAYWG+JiIiIoNPp0L59e0RGRuKpp54CkD/aIjIyEpMmTTKbfRIRlZeCScX279+PY8eOKfW0JUlCQEAAgoOD0bFjR9jw7lEionLDf1FVkpOXn6zVirx/F3KkrVmSZRlHjhyBXq9HSEgItOwnIiKiKi8sLAxjxoxBQEAAOnbsiGXLlkGv1yM0NBQAMHr0aPj6+iI8PBxA/kRjv/32m/L7jRs3EBsbC2dnZzRs2LBE+yQiqmwJCQk4cOAA9u/fb3InQO3atREcHIyePXvC3d1dxQiJiKwXk7YqUUbaGs8Yx2QgERERkUUYMWIEEhMTMXv2bMTFxaFt27aIiIhQJhK7du2aya1vN2/eRLt27ZTHS5YswZIlSxAUFISoqKgS7ZOIqDLk5OTg2LFj2L9/P86cOaPcbejo6Iju3bsjODgYjRs35iTNREQVjElblWQVNREZyyMQERERWYxJkyYVW7qgIBFbwN/fv0Rllu63TyKiiiKEwB9//IH9+/cjOjoamZmZyro2bdogODgYnTp1KrKONhERVQxmCVWSYyictOVIWyIiIiIiIqosCQkJOHjwIA4ePIgbN24oy728vBAcHIzHHnsMXl5eKkZIRFR1MWmrkuy8e8ojaDSQOHsgERERERERVSC9Xo+jR4/i4MGD+PXXX5XldnZ26Ny5M4KDg9GqVSuWPyAiUhmTtirJMRRMRPbPSFsNR9kSERERERFR+cvLy8OpU6dw4MABHD9+HLm5uQAASZLQpk0b9OzZE507d4a9vb3KkRIRUQEmbVVyb01byYZdQUREREREROVDCIFLly7h4MGDiI6ORlpamrKuTp066NWrF4KCguDh4aFilEREVBxmClWS/U9NWxv5n5G2rGdrtiRJgoeHB3Q6HW8RIiIiIiIis5aUlIRDhw7h0KFDuH79urLc1dUVPXr0QK9evVCvXj1+tiEiMnNM2qqkYCIyjSioacukrbnSaDRo0aIFEhISoGHdYSIiIiIiMjN3797FsWPHEBkZiZMnT8LW1haSJEGn0+HRRx9Fr1690LZtW2g5WIiIyGIwaauS7Lz8ZK2NUh6BfzyJiIiIiIioZAwGA2JjY3HgwAH8+OOPyMnJgRACQgi0atUKvXr1QpcuXeDo6Kh2qERE9BCYtFVJQXkErVIegV1BRERERERExRNC4M8//8TBgwcRFRWF1NRUZZ2vry969OiBli1bonnz5rxLkIjIwjFTqJLsPNPyCBJvUzFbBoMB0dHR0Ov1CAkJ4cUPERERERFVquTkZBw6dAgHDhzAX3/9pSx3cXFBUFAQevbsiYYNG0IIgYSEBBUjJSKi8sKkrUqy/knaFpRH4ERkREREREREVCArKwsxMTE4cOAATp8+DSH++QxpY4PAwED06tULjzzyCGxs/v1YX9CGiIgsH5O2Krmbmz/CVltQ05blEYiIiIiIiKq0vLw8nDp1CocOHcKPP/6I7OxsZV3z5s3Rs2dPdO3aFc7OzipGSURElYGZQpVkFiRtZY60JSIiIiIiqqqEEPj9999x6NAhHD58GBkZGcq6mjVrolevXujRowd8fHxUjJKIiCobk7YqUZK2/9S0ZdKWiIiIiIio6rh69SoOHTqEQ4cOITExUVnu5uaG7t27IygoCI0aNYIkSSpGSUREamHSViV3cwUghFLTVrJhVxAREREREVmzhIQEJVFrPKGYg4MDOnfujB49eqBVq1bQclAPEVGVx0yhSvS5slLPFgDAmrZERERERERWJy0tDUePHkVUVBR+//13ZbmNjQ06dOiAoKAgdOjQATqdTsUoiYjI3DBTqJK7uTJs5TzlsWRrq2I0dD+SJMHd3R02Nja8NYmIiIiIiB4oKysLP/74Iw4dOoRffvkFspxfFk+SJLRq1Qo9evRA586d4eTkpHKkRERkrpi0VUkmk7YWQ6PRoFWrVkhISIBGo1E7HCIiIiIiMkN5eXk4deoUoqKicPz4cWRnZyvrGjZsiKCgIHTv3h3u7u4qRklERJaCSVsVCCGQmSvgZpS0hQ2TtkRERERERJZECIHffvsNUVFROHr0KDIyMpR1NWvWRFBQEHr06AFfX18VoyQiIktkFknbjz/+GO+++y7i4uLQpk0bfPjhh+jYsWORbc+dO4fZs2fj5MmT+Ouvv/D+++9j6tSplRtwGWXnCQiAI22JiMgqGQwG5ObmFlouyzJyc3ORlZXFOxcsVHn3oa2tLSfbISKLI4TA5cuXER0djcOHDyMpKUlZ5+bmhu7du6NHjx5o2LAhy6sREdFDUz1pu2XLFoSFhWHFihUIDAzEsmXLEBISggsXLsDLy6tQ+8zMTNSvXx/Dhg3DK6+8okLEZafPza9nZCsbfaC1ZdF5c2UwGHDkyBHo9Xr07t2biQYiomIIIRAXF4fU1NRi18uyjIyMDH6ItVAV0Ydubm7w8fHha4KIzN61a9cQHR2N6Oho3Lp1S1nu4OCAzp07o0ePHmjdujU/LxARUblQPWm7dOlSTJgwAaGhoQCAFStWYPfu3Vi9ejWmTZtWqH2HDh3QoUMHAChyvSW4mysAcKStJZFlWZk8gIiIilaQsPXy8oKjo2OhJJwQAnl5eZzY0YKVZx8KIZCZmYmEhAQA+bcRExGZm1u3buHw4cOIjo7GX3/9pSzX6XTo2LEjunfvjvbt20On4yAcIiIqX6ombXNycnDy5ElMnz5dWabRaBAcHIyYmJhyO052drZJEfj09HQAlZeIk2VZGZkCAGlZ+claG5OatjZMCpqpgv4r6EP2k2W6931Ilod9aN4MBgNu374NLy+v+06wkpubC1t+UWnRyrMP7e3tIYRAQkICPDw8CpVK4PudiNSQlJSEw4cP4/Dhw7h48aKy3MbGBu3bt0f37t3RsWNH2NvbqxglERFZO1WTtklJSTAYDPD29jZZ7u3tjfPnz5fbccLDwzFv3rxCyxMTE5GVlVVuxymOLMtIS0uDEAIajQZ/J+Yna41H2t7NycXdf0aakHkxGAzQ6/XIyspCQkICkw0W6t73IVke9qF5y83NhSzL0Ol0yMvLK7KNEAIGgwEAONLWQlVEH+p0OsiyjLi4uEJ/Y40n9CEiqkhpaWk4cuQIoqOj8dtvvynLNRoN2rRpg+7du+PRRx+Fs7OzilESEVFVonp5hMowffp0hIWFKY/T09Ph5+cHT09PuLi4VPjxZVmGJEnw9PSERqOB5s4dAFkmNW0dXV3hXEQNX1KfwWCAk5MTAMDLy4tJWwt17/uQLA/70LxlZWUhIyMDtra2sLG5/+UF/x21fOXZh7a2ttBoNKhRo0ahUWscxUZEFenOnTuIiYlBdHQ0Tp8+DSGEsq5Fixbo3r07unTpAldXVxWjJCKiqkrVpG3BbXDx8fEmy+Pj4+Hj41Nux7Gzs4OdnV2h5RqNptI++EuSpBxPX0RNW43OjkkIMyWEgCRJJn1Ilol9aPnYh+ZLo9Eo/1YWNwKz4N9TgCNtLVVF9OH9/sbyvU5E5S0rKwvHjx9HdHQ0fvnlF5O7Qxo1aoTu3buja9eu8PDwUDFKIiIilZO2Op0O7du3R2RkJJ566ikA+SOpIiMjMWnSJDVDq1AZ2fn12Uxr2nLUERERkTVau3Ytpk6ditTU1ArZv7+/P6ZOnYqpU6dWyP6NjR49Go0bN8Z///vfErVPSkpC8+bN8csvv6B27doVHB0RUdEK5lKJjo7GiRMnkJOTo6zz9/dHt27d0K1bN06ISEREZkX18ghhYWEYM2YMAgIC0LFjRyxbtgx6vR6hoaEA8j8c+Pr6Ijw8HED+H9yCGkM5OTm4ceMGYmNj/7+9O4+Lqnr/AP6ZhWGHYV8URcUdcQcBRy1NzCW3TNFfLmmbS6mZbaZYmmbq19zLr2uLppXaV80yCkEcUQkUN0xFcUNEZd9n7u8P4soIKCDMDPB595pXzL3n3vsMjwNnHs49B1ZWVvDy8jLY66iM9H+LtiVH2kpMDJ4KegylUsnRPkREddT48eOxdevWUtuDgoJw8ODBpz7/yJEj0b9/f/F5SEgI9uzZg9jY2Eqdp7zi74kTJ8RpfGrSqVOncODAAaxcuVLc1qtXLxw+fLhU29dffx3r16+Ho6Mjxo4di3nz5mHjxo01HiMRUbHCwkKcOnUK4eHhUKvVyMnJEfe5ubmhZ8+eUKlUaNSokQGjJCIiKp/BK4UjR47E3bt3MXfuXCQlJaFDhw44ePCguDhZYmKiTrHs1q1b6Nixo/h86dKlWLp0KXr27ImwsDB9h18lGflFC3iULNrCRGGgaOhJZDIZ2rdvj+Tk5FKrWhMRUd3Qr18/bN68WWdbWVMrVYW5uTnMzc2r5VxlcXJyqrFzl7Rq1Sq8+OKLpRbhefXVV/HJJ5/obLOwsBC/njBhAjp37owvvvgC9vb2eomViOonrVaLM2fOICIiApGRkTqLGTo6OkKlUqFnz55o2rQpp+khIiKjZxRDB6dOnYpr164hLy8PUVFR8PPzE/eFhYVhy5Yt4nNPT08IglDqUVsKtkDZ0yNIOD0CERGRwZiamsLV1VXnYWdnB6CoL6JQKBARESG2X7JkCZydncV5+VNTU/H666/DxcUFZmZm8Pb2xr59+wAUjZBVKpXi1/Pnz8epU6fEuVyL+znLly9Hu3btYGlpCQ8PD0yePBmZmZliDBMmTEBaWpp4XEhICICivtGKFSvE2BITEzF48GBYWVnBxsYGL730ks76ASEhIejQoQO++eYbeHp6wtbWFqNGjdIpbjxKo9Hgxx9/xKBBg0rts7CwKPW9K7nQa9u2beHu7o7du3dXMBtERBUnCAIuXLiAr7/+GuPHj8dHH32EgwcPIiMjA7a2thg4cCCWLFmCTZs24ZVXXkGzZs1YsCUiolrB4CNt66OM/LKmR2DRloiI6p6xP13HvZyHv+8EAdDHZ2UHczm2DfeolnP16tUL06dPx8svv4xTp07hypUr+Pjjj7Fr1y64uLhAq9Xi+eefR0ZGBr799ls0a9YM586dK/PujJEjR+LMmTM4ePAg/vjjDwAQVyWXSqVYuXIlmjRpgitXrmDy5MmYPXs21q5di4CAAKxYsQJz585FfHw8AJQa8QoUjTIrLtgePnwYhYWFmDJlCkaOHKnzB+7Lly9jz5492LdvHx48eICXXnoJixcvxsKFC8v8Hpw+fRppaWno0qVLlb6Hvr6+iIiIwMSJE6t0PBFRSYIgICEhAREREQgPD0dycrK4z8rKCgEBAejRowe8vb15pxwREdVaLNoaQEZe8fQIBQ83smhrtDQaDdRqNTIzM9G7d2/ObUtEVAn3cgqRnKUxdBhPtG/fvlJF0A8//BAffvghAGDBggU4dOgQXnvtNZw5cwbjxo3DCy+8AAD4448/cPz4cZw/fx4tWrQAADRt2rTM65ibm8PKygpyuRyurq46+0ouJObp6YkFCxbgjTfewNq1a6FQKGBrawuJRFLquJJCQ0MRFxeHhIQEeHgUFa23bduGtm3b4sSJE+jatSuAouLuli1bYG1tDQB4+eWXERoaWm7R9tq1a5DJZHB2doZGo5vPtWvX4r///a/Otq+++gpjxowRn7u7uyMmJqbcuImIKuLGjRsIDw9HeHg4bt68KW43MzODv78/VCoVOnbsCLmcH3OJiKj2428zAyheiMxSUnKkLee0NWYFBQUoLCx8ckMiItLhYK7b1dDnSNvKeOaZZ7Bu3TqdbSXnX1UoFPjuu+/g4+ODxo0b4z//+Y+4LzY2Fg0bNhQLtlX1xx9/YNGiRbhw4QLS09NRWFiI3NxcZGdn68wR+zjnz5+Hh4eHWLAFgDZt2kCpVOL8+fNi0dbT01Ms2AJFi/KUHKn2qJycHJiampZ5S/GYMWPw0Ucf6WwrXpugmLm5ObKzsyv0GmqTNWvW4IsvvkBSUhLat2+PVatWwdfXt9z2u3btwscff4yrV6+iefPm+Pzzz3UWqStrUbzqWhCPqLa6c+eOOKI2ISFB3K5QKNClSxf06NEDXbt2hULBz1NERFS3sGhrAJn/To9gI+SL2yRmNbdACRERkaGUnKJAEAQUFhZCLpcb3XyClpaW8PLyemybo0ePAgDu37+P+/fvw9LSEgCqZZGxq1evYuDAgXjzzTexcOFC2Nvb48iRI5g4cSLy8/MrXLStKJNH7vCRSCTQarXltnd0dER2djby8/NL3XFia2v7xO/d/fv39bZgmr788MMPmDlzJtavXw8/Pz+sWLECQUFBiI+Ph7Ozc6n2R48eRXBwMBYtWoSBAwfi+++/x5AhQ/D333/D29tbbPfoonjVtSAeUW1y7949HDlyBBEREeKUMEDRAsGdOnWCSqWCn59ftf9sJCIiMiYs2uqZVhCQllt0W6E1Hk6PIDEzM1RIRERE9ASXL1/GjBkzsGHDBvzwww8YN24c/vjjD0ilUvj4+ODGjRu4ePFihUbbKhSKUlMMREdHQ6vVYtmyZWJRdOfOnU887lGtW7fG9evXcf36dXG07blz55Camoo2bdpU5iXr6NChg3iukgXGijpz5gx69epV5esbo+XLl+PVV1/FhAkTAADr16/H/v37sWnTJrz//vul2n/55Zfo168f3n33XQDAp59+ikOHDmH16tVYv3692K54UTyi+iYtLQ2RkZEIDw/HuXPnIAgCgKI/Kvn4+KBHjx7w9/fXuUuAiIioLmPRVs/ScrXQFPU/YF1ypK0pi7ZERESGkpeXh6SkJJ1tcrkcjo6O0Gg0+L//+z8EBQVhwoQJ6NevH9q1a4dly5bh3XffRc+ePdGjRw8MHz4cy5cvh5eXFy5cuACJRIJ+/fqVupanpycSEhLEaRWsra3h5eWFgoICrFq1CoMGDUJkZKROIa/4uMzMTISGhqJ9+/awsLAoNcqsT58+aNeuHcaMGYMVK1agsLAQkydPRs+ePau8iBgAODk5oVOnTjhy5Eipom12dnap752pqSns7OzE/dHR0fjss8+qfH1jk5+fj+joaHzwwQfiNqlUij59+kCtVpd5jFqtxsyZM3W2BQUFYc+ePTrbwsLC4OzsDDs7Ozz77LNYsGABHBwcqv01EBmDjIwMqNVqhIeH4/Tp02KhFiia2kWlUiEwMFD8eUJERFSfsGirZyVX0LYS8sSvOT0CERGR4Rw8eBBubm4621q2bIkLFy5g4cKFuHbtGvbt2wegaP7Xr7/+GsHBwejbty/at2+Pn376CbNmzUJwcDCysrLg5eWFxYsXl3mt4cOH4+eff8YzzzyD1NRUbN68GePHj8fy5cvx+eef44MPPkCPHj2waNEijB07VjwuICAAb7zxBkaOHIl79+5h3rx5CAkJ0Tm3RCLB3r17MW3aNPTo0QNSqRT9+vXDqlWrnvp7NGnSJGzbtg1vvPGGzvYNGzZgw4YNOttKzsO6d+9eNGrUCCqV6qljMBYpKSnQaDSl5u51cXHBhQsXyjwmKSmpzPYlC979+vXDsGHD0KRJE1y+fBkffvghnn/+eajVashkslLnzMvLQ17ew/5keno6gKKF5h433cXT0Gq1EAShxs5P+mWIfGZlZSEqKgpHjhxBTEyMzh0ELVq0QPfu3dG9e3c4OjrqxEkVw/do3cJ81i3MZ93yNPms6DESoeSfM+uJ9PR02NraIi0tDTY2NjV+Pa1Wi+TkZDg7O+PkrVxM2X8LALD+4jo0uHgcAOC0bQ9kdhxFYYw0Gg3Cw8ORlZWFoKCgUvMAUu1Q8n346HyMVDswh8YtNzcXCQkJaNKkCczKmfLHmOe0pSfLyclBy5Yt8d1336F79+4VzmG3bt3w1ltvYfTo0WXuf9y/HX332Srq1q1baNCgAY4ePQp/f39x++zZs3H48GFERUWVOkahUGDr1q0IDg4Wt61duxbz58/HnTt3yrzOlStX0KxZM/zxxx/o3bt3qf0hISGYP39+qe0XL16ssVvItVot0tLSYGtry5/FdYC+8pmbm4uYmBhERUXh9OnTOgv8NmrUCN26dYOvr2+Z80FT5fA9Wrcwn3UL81m3PE0+MzIy0KJFiyf2cTnSVs/u5zz8S7K5puT0CBxpa8ysra1RD/++QUREJDI3N8fWrVuRkpJS4WNSUlIwbNgwnUJlXeDo6AiZTFaq2Hrnzp1y56N1dXWtVHsAaNq0KRwdHXHp0qUyi7YffPCBzpQL6enp8PDwgJOTU40VubVaLSQSCZycnPiBsw6oyXwWTyMSERGBEydOiKPCpVIpmjZtCpVKBZVKhYYNG1brdes7vkfrFuazbmE+65anyWd5g1wexaKtnpUs2ppqSkyPwJWBjVbxKrXJycll3ppIRERUX/Tq1UtnhNyTODo6Yvbs2TUYkWEoFAp07twZoaGhGDJkCICijntoaCimTp1a5jH+/v4IDQ3F9OnTxW2HDh3SGan7qBs3buDevXulpu4oZmpqCtMy+pBSqbRGPwxKJJIavwbpT3Xms7CwEDExMYiIiMCxY8eQk5Mj7nN3dxcLtY0bN+YdFzWI79G6hfmsW5jPuqWq+axoexZt9azknLYmBblFXygUkLAYSERERFRrzJw5E+PGjUOXLl3g6+uLFStWICsrCxMmTAAAjB07Fg0aNMCiRYsAAG+//TZ69uyJZcuWYcCAAdixYwdOnjyJr7/+GgCQmZmJ+fPnY/jw4XB1dcXly5cxe/ZseHl5ISgoyGCvk+hJNBoN4uLiEB4eDrVajczMTHGfo6OjWKj18vJioZaIiKgSWLTVs3vZD0fayguKRtpKTCs2LJqIiIiIjMPIkSNx9+5dzJ07F0lJSejQoQMOHjwoLjaWmJioM4oiICAA33//PebMmYMPP/wQzZs3x549e+Dt7Q2g6M6e06dPY+vWrUhNTYW7uzv69u2LTz/9tMzRtESGJAgCzp49i4iICERGRiItLU3cZ2dnh+7du0OlUqFVq1Ys1BIREVURi7Z6VnJ6BGl+0UhbFm2Nm0ajwfHjx5GRkYFnnnmGtzEQERERAGDq1KnlTocQFhZWatuIESMwYsSIMtubm5vjt99+q87wiKqVIAi4ePEiIiIiEBERgfv374v7rK2tERgYiB49eqBt27bsLxMREVUDFm31rLhoK5MAyM4CAEgtrQwYEVVEbm4u8vPzn9yQiIiIiKiOEAQBV65cEQu1ycnJ4j5LS0v4+/tDpVLBx8cHcjk/WhIREVUn/mbVs/vZRXPaOim0QP6/0yOwaEtEREREREYiMTER4eHhiIiIwK1bt8TtZmZm6NatG1QqFTp27AgTExMDRklERFS3sWirR1pBwP3copG27rI8cbvUytpQIREREREREeHmzZviiNrExERxu0KhQNeuXdGjRw906dIFCoXCgFESERHVHyza6lFGnhYabdHXrtKHRVuOtCUiIiIiIn1LTk7Gvn37cPr0aSQkJIjb5XI5OnfuDJVKBV9fX5ibmxswSiIiovqJM8Tr0b0Si5C5SHLErznSloiIqHaRSCTYs2dPufvDwsIgkUiQmpoKANiyZQuUSuVjzxkSEoIOHTo8ts3Vq1chkUgQGxtbqXirIj8/H15eXjh69GiZ+1NSUuDs7IwbN27UeCxEVH3u3buHvXv3YtasWZg0aRJ27tyJK1euQCqVonPnzpg+fTq+/fZbzJkzBz179mTBloiIyEA40laP7pco2joKD4u2HGlLRERkOOPHj0dqaupji7CVFRAQgNu3b8PW1rbCx8yaNQvTpk17bFweHh64ffs2HB0dqy3W8qxfvx5NmjRBQECAuE0qlWLXrl0YPnw4HB0dMXbsWMybNw8bN26s8XiIqOrS0tIQGRmJiIgInD17FoIgACj6A1Tr1q0RFBSE7t27w8bGxsCREhERUTEWbfWoZNHWTpMtfi1l0dboWVhYQKPRPLkhERERiuaAdHV1rdQxVlZWsLJ6fJ9AJpNV+rxVIQgCVq9ejU8++eSx7SZMmIDOnTvjiy++gL29fY3HRUQVl5GRAbVajYiICJw6dUos1AJA69atoVKp4O/vj8LCQjg7O0Mq5U2YRERExoS/mfWoZNFWWZApfi21VRogGqoomUyGrl27wtvbGzKZzNDhEBFRDevVqxfeeustzJ49G/b29nB1dUVISEipdikpKRg6dCgsLCzQvHlz/PLLL+K+R6dHKLZnzx40b94cZmZmCAoKwvXr18V9JadHCAkJwdatW7F3715IJBJIJBKEhYWVOT3C4cOH4evrC1NTU7i5ueH9999HYWFhpV9PSdHR0bh8+TIGDBjw2HZt27aFu7s7du/e/dh2RKQf2dnZ+OuvvzB//ny8/PLLWLVqFWJjYyEIApo3b45XXnkFmzdvxpIlSzBo0CD+sYWIiMiIcaStHt3Lfli0tclJFb+WKtlZIiKiuillxiRoH9x/uEEQAImkxq8rtbOH43/+W+Xjt27dipkzZyIqKgpqtRrjx49HYGAgnnvuObHN/PnzsWTJEnzxxRdYtWoVxowZg2vXrpVbBMnOzsbChQuxbds2KBQKTJ48GaNGjUJkZGSptrNmzcL58+eRnp6OzZs3AwDs7e1x69YtnXY3b95E//79MX78eGzbtg0XLlzAq6++CjMzM53CbEVeT0kRERFo0aIFrK2fPO++r68vIiIiMHHixCe2JaLql5ubixMnTiA8PBzR0dEoKCgQ93l6eqJHjx7o3r073NzcDBglERERVRaLtnp0P+fhqBfz7DTxa6nSzhDhEBER1Tjtg/vQ3rtr6DAqzcfHB/PmzQMANG/eHKtXr0ZoaKhOkXP8+PEIDg4GAHz22WdYuXIljh8/jn79+pV5zoKCAqxevRp+fn4AigqprVu3xvHjx+Hr66vT1srKCubm5sjLy3vsdAhr166Fh4cHVq9eDYlEglatWuHWrVt47733MHfuXPF254q8npKuXbsGd3f3inyr4O7ujpiYmAq1JaLqkZ+fj+joaEREROD48ePIy8sT9zVs2BAqlQoqlQoeHh4GjJKIiIieBou2elRyegTTrFQUzyoltXMwTEBUIRqNBidPnkRGRgZ69uzJ+b6IiCpBavfIqFM9jrR9Gj4+PjrP3dzckJycXG4bS0tL2NjYlGpTklwuR9euXcXnrVq1glKpxPnz50sVbSvq/Pnz8Pf3h6TE9zQwMBCZmZm4ceMGGjVqVOHXU1JOTg7MzMwqFIO5uTmys7Of3JCInkphYSFiYmIQERGBY8eOISfn4cLGrq6uYqHW09NT52cCERER1U4s2upRcdFWKgFkaQ9QCABSKaTWXKXV2GVnZyM3N9fQYRAR1TolpygQBAGFhYWQy+VGX1AwMTHReS6RSKDVaivdxlhUNlZHR0fExcVV6Nz379+Hk5PTU8VHRGXTaDSIi4tDeHg41Go1MjMfrovh6OgoFmq9vLyM/ucqERERVQ6LtnpUXLRVmsmgTXsAAJDaKCHh4lZERER1XmFhIU6ePCmOqo2Pj0dqaipat25dZnuFQgGNRlPmvmKtW7fGTz/9BEEQxIJNZGQkrK2t0bBhwyrH2rFjR6xbt07nvOU5c+YMevXqVeVrEZEuQRBw9uxZREREIDIyEmlpD6dVUyqV6N69O3r06IFWrVqxUEtERFSHsWirJ4Ig4MG/RVsnU0B7/x4AQOrgaMiwiIiISE9MTEwwbdo0rFy5EnK5HFOnTkW3bt3KnRrB09MTv/32G+Lj4+Hg4ABbW9tSbSZPnowVK1Zg2rRpmDp1KuLj4zFv3jzMnDnzqabzeeaZZ5CZmYmzZ8/C29u73HbZ2dmIjo7GZ599VuVrEVHRZ4WLFy8iIiICERERuH//4QKO1tbWCAwMhEqlgre3N6fqIiIiqidYtNWTrAKg4N+7ED21qYC2qIArc+EqrkRERPWBhYUF3nvvPYwePRo3b96ESqXCxo0by23/6quvIiwsDF26dEFmZib++usveHp66rRp0KABDhw4gHfffRft27eHvb09Jk6ciDlz5jxVrA4ODhg6dCi+++47LFq0qNx2e/fuRaNGjaBSqZ7qekT1kSAIuHLlilioLTnPtKWlJbp16waVSoX27dtDLufHNiIiovpGIgiC8ORmdUt6ejpsbW2RlpYGG5uan09Wq9Ui+nISJv9ZtEjHRLNrGPJjCADAYsgo2EycUuMxUNVpNBqEh4cjKysLQUFBpeYFpNpBq9UiOTkZzs7OHKFSSzGHxi03NxcJCQlo0qRJuQtY1aY5bQk4ffo0nnvuOVy+fBlWVlYASuewW7dueOuttzB69OgqX+dx/3b03Wer7fTx/eLP4qd37do1hIeHIyIiArdv3xa3m5mZwc/PDyqVCp06ddJLn5P5rHuY07qF+axbmM+65WnyWdE+G/9kqyepeQ9r4245KeLXMhdXQ4RDRERE9Fg+Pj74/PPPkZCQgHbt2pXan5KSgmHDhiE4ONgA0RHVLjdv3kRERATCw8Nx/fp1cbtCoUCXLl3Qo0cPdOnSBaampgaMkoiIiIwJi7Z6kpr3cIVmp6y74tcyZxZtawMzMzMUFBQYOgwiIiK9Gj9+fLn7HB0dMXv2bP0FQ1TLJCUl4ciRIwgPD0dCQoK4XS6Xo3PnzlCpVPD19YW5ubkBoyQiIiJjxaKtnjzIfTjSVpmWJH4tc3E3RDhUCTKZDH5+fkhOToZMJjN0OERERERkpFJSUsQ5av/55x9xu0wmQ4cOHaBSqdCtWzdYWloaMEoiIiKqDVi01ZOS0yNY3v33liipDHL3hgaKiIiIiIiIntb9+/cRGRmJiIgInD9/XtwukUjg4+MDlUqFgIAAWFtbGzBKIiIiqm1YtNWT4qKtVNBCkVRUtJW5N4SEi1oREREREdUq6enpOHr0KMLDw3HmzBkUr+0skUjQpk0bqFQqBAYGQqlUGjZQIiIiqrVYtNWTtPyijpxL9l1ICovmRpV7eBowIqoojUaDmJgYpKenw8HBgas8EhEREdVDmZmZUKvViIiIwKlTp6DVPlyzomXLllCpVOjevTscHBwMGCURERHVFSza6knavyNtPTJuidvkjTwNFA1VVkZGBrKzsw0dBhERERHpUUZGBqKiohAZGYnY2FgUFhaK+5o1awaVSgWVSgVnZ2cDRklERER1EYu2elI8PULLHBZtiYiIiIiMVVpaGo4dO4bIyEicPn0aGo1G3Ne4cWOxUOvuzgWFiYiIqOawaKsnxSNtW2RcE7eZeDYzVDhERERERPSvBw8eQK1WIzIyEnFxceIctQDg6emJwMBABAYGwsPDw4BREhERUX3Coq0e5BRokfvvH+gb378KAJCYmUPWoJHhgiIiIiIAwPjx45Gamoo9e/bo9bpbtmzB9OnTkZqaatBzENVX9+7dw9GjR3H06FGcPXtWp1DbrFkzBAYGIiAgAA0aNDBglERERFRfsWirBw/+rdja5GfALvMuAEDerAUkMpkhwyIiIiIiqjcEQcCNGzcQFRWFY8eOIT4+Xmd/ixYtxEKtq6urgaIkIiIiKiI1dAD1wYOcoqJts9Sr4jYTr5YGioaIiIgep1evXnjrrbcwe/Zs2Nvbw9XVFSEhITptJBIJ1q1bh+effx7m5uZo2rQpfvzxR3F/WFgYJBKJzgjY2NhYSCQSXL16FWFhYZgwYQLS0tIgkUggkUhKXaPYqVOn8Mwzz8Da2ho2Njbo3LkzTp48+dhz5OXlYdasWWjQoAEsLS3h5+eHsLAw8ZxbtmyBUqnEnj170Lx5c5iZmSEoKAjXr1+vpu8ikXHQaDQ4c+YMNm3ahNdffx2TJ0/G1q1bxYJt69atMWnSJGzcuBHLli3DsGHDWLAlIiIio8CRtnpQXLRtnnZV3Maibe1iYmICuZxvFyKiqihexEcQBGg0GrHACBQVP6VSaam25ZGVuEulvLayariTZevWrZg5cyaioqKgVqsxfvx4BAYG4rnnnhPbfPzxx1i8eDG+/PJLfPPNNxg1ahTi4uLQunXrJ54/ICAAK1aswNy5c8XikZWVVZltx4wZg44dO2LdunWQyWSIjY2FiYnJY88xdepUnDt3Djt27IC7uzt2796Nfv36IS4uDs2bNwcAZGdnY+HChdi2bRsUCgUmT56MUaNGITIy8qm+d0SGlpubi5iYGERFReH48ePIyMgQ98nlcrRv3x5+fn7w9fWFg4ODASMlIiIiKh+rUHpw/9/pEZqnJojbTLxaGSocqiSZTIaAgAAkJydXSyGAiKi+iYiIAFBUtNVqtZBKpWLR1t7eHj4+PmLbyMhIaLXaMs+jVCrRoUMH8fmxY8dQUFBQql2vXr2eOmYfHx/MmzcPANC8eXOsXr0aoaGhOkXbESNGYNKkSQCATz/9FIcOHcKqVauwdu3aJ55foVDA1tYWEonkiaP6EhMT8e6776JVq1ZiPMXKOkdiYiI2b96MxMREcXX7WbNm4eDBg9i8eTM+++wzAEBBQQFWr14NPz8/AEWF6tatW+P48ePw9fV94mug+k0QBKRkpyAzPxNWCis4mDuI72tDxHLjxg38/fffiI6OxpkzZ3R+NlhZWaFr167w8/NDp06dYG5ubpA4iYiIiCqDRVs9eJCjBQQBrR5cAgBILK0gc29o4KiIiIioPCULyQDg5uaG5ORknW3+/v6lnsfGxlZ7LDNnzsSkSZPwzTffoE+fPhgxYgSaNWtWbvu4uDhoNBq0aNFCZ3teXp7OqEK5XI6uXbuKz1u1agWlUonz58+zaEvlSs1NxYa4Ddh6fisuP7gsbm9m1wzTfKdhXIdxUJopazyOrKwsnDp1SizUpqSk6Ox3cXFBt27d4OfnhzZt2vAP70RERFTrsGirBw9yNGiYlQRlftGtWYrW3pBIOZ0wERHVDyqVCkDRaLjCwkLI5XKd6RFKCgwMrPB5u3XrVn1BPsLExETnuUQiKXcEcFmKp3wouRp9WaOCKyIkJASjR4/G/v378euvv2LevHnYsWMHhg4dWmb7zMxMyGQyREdHlypUlTcFA1FF/HbpNwzfORzZBdml9l15cAUzfpuBj/78CD+99BOCvIKq9drZ2dk4f/48zpw5gzNnzuDixYs670kTExN4e3ujU6dO6NSpEzw8PAw28peIiIioOhhN5XDNmjXw9PSEmZkZ/Pz8cPz48ce237VrF1q1agUzMzO0a9cOBw4c0FOklfcgV4M29y6Kz03atDdgNFRZGo0Gp06dQnx8/BPnWiQiotJkMlm5D+kjf8R8XNtHC5AVaVOTjh07Vup58Xy2Tk5OAIDbt2+L+x8dhatQKCr8e6VFixaYMWMGfv/9dwwbNgybN28u9xwdO3aERqNBcnIyvLy8dB4lp1EoLCzEyZMnxefx8fFITU2t0Jy8VKS6+6+CIGDu3Llwc3ODubk5+vTpg3/++acmX0KF/XbpNwz4fgByCnIg/PtfScXbcgpyMOD7Afjt0m9Pdb2MjAxERUVh48aNmDFjBkaNGoWQkBD8+OOPuHDhArRaLRo0aIAXXngBISEh2L59Oz755BMMGTIEjRo1YsGWiIiIaj2jGGn7ww8/YObMmVi/fj38/PywYsUKBAUFIT4+Hs7OzqXaHz16FMHBwVi0aBEGDhyI77//HkOGDMHff/8Nb29vA7yCx7ufo0Hg/YdFW0Vbn8e0JmOUmpqKrKwsQ4dBRERGZNeuXejSpQu6d++O7777DsePH8fGjRsBAF5eXvDw8EBISAgWLlyIixcvYtmyZTrHe3p6IjMzE6GhoWjfvj0sLCxgYWGh0yYnJwfvvvsuXnzxRTRp0gQ3btzAiRMnMHz48HLP0aJFC4wZMwZjx47FsmXL0LFjR9y9exehoaHw8fHBgAEDABSNTJw2bRpWrlwJuVyOqVOnolu3bpwaoYJqov+6ZMkSrFy5Elu3bkWTJk3w8ccfIygoCOfOnYOZmZm+X6IoNTcVw3cOL5qXGo8fca6FFlJBiuE7h+PGzBsVmiohNzcXCQkJuHjxIi5duoR//vkHN2/eLNXO1dUV3t7e8Pb2Rrt27cr8PhMRERHVFUZRtF2+fDleffVVTJgwAQCwfv167N+/H5s2bcL7779fqv2XX36Jfv364d133wXwcPGP1atXY/369XqNvSJSswrQ8e6ZoicKU5g05yJkREREtd38+fOxY8cOTJ48GW5ubti+fTvatGkDoKggun37drz55pvw8fFB165dsWDBAowYMUI8PiAgAG+88QZGjhyJe/fuYd68eQgJCdG5hkwmw7179zB27FjcuXMHjo6OGDZsGObPn//Yc2zevBkLFizAO++8g5s3b8LR0RHdunXDwIEDxXNbWFjgvffew+jRo3Hz5k2oVCqx6ExPVt39V0EQsGLFCsyZMweDBw8GAGzbtg0uLi7Ys2cPRo0apb8X94itsVuRXZBdanRtebTQIrsgG9tObcNbfm+J2/Py8nDz5k1cv34diYmJuHHjBhITE3Hz5k2dqUSKNWzYUCzStm3bFo6OjtX2moiIiIiMncGLtvn5+YiOjsYHH3wgbpNKpejTpw/UanWZx6jVasycOVNnW1BQEPbs2VOToVaZy/UzsMtPBwCYduwKiYnCwBERERFRsS1btug8DwsLK9WmrD6Gu7s7fv/993LPGxgYiNOnT+tse7QwtW7dOqxbt67ccygUCmzfvr3c/eWdw8TEBPPnzxeLu+UZNmwYhg0b9tg2VFpN9F8TEhKQlJSEPn36iPttbW3h5+cHtVptsKKtIAhYdXxVlY5dcGgB0n5PQ0pKClJSUpCenl5uWzs7OzRv3lx8eHl5wdbWtqphExEREdV6Bi/apqSkQKPRwMXFRWe7i4sLLly4UOYxSUlJZbZPSkoqs31eXh7y8vLE58UdRq1WW6lFRaqi4NoVTI56+EHKNKBXjV+TqpdWq4UgCEW3BOrh3wzVjOI8Mn+1F3No3Er+rCxrxFyx4n2Pa1NbPOm1GrOnyUN15/Bxv2ON9f1eE/3X4v8bWx83JTsFlx9crvRxAgTc1dxFxN8RUGgeDliwsrJCo0aN0KhRIzRo0ACNGjVC48aNYW9vX+ocxpr/uoS/W+se5rRuYT7rFuazbnmafFb0GIMXbfVh0aJFZY40uXv3LnJzc2v24hIZLJ3sgevpEDw8kd6iLdKTk2v2mlStNBoNsrKykJubi+Tk5FIrilPtoNVqkZaWBkEQSi18RLUDc2jcCgoKoNVqUVhYiMLCwjLbCIIgLppVFxYJ0mg05b5WY1fcUaxs/DWRw8LCQmi1Wty7d6/U79iMjIxquUZdpY8+7vWM6091fP+h/dHKtRXs7e1hb28PS0vLUv92CgsLkcz+sUHwd2vdw5zWLcxn3cJ81i1Pk8+K9nENXrR1dHSETCbDnTt3dLbfuXNHZ4XjklxdXSvV/oMPPtC5HS09PR0eHh5wcnKCjY3NU76CJysMWYp7X6+Aw9TZkNvwNq/aRqPRwNLSEgDg7OzMom0tpdVqIZFI4OTkxF+QtRRzaNxyc3ORkZEBuVwOufzx3Yu68HO0to+QeOWVV/DKK69U+fjqzKFcLodUKoWDg0OpxbYMufjW49RE/7X4/3fu3IGbm5tOmw4dOpR5Tn30caVWT/fzdsyLY+Bg4VAtsVD14+/Wuoc5rVuYz7qF+axbniafFe3jGrxoq1Ao0LlzZ4SGhmLIkCEAil54aGgopk6dWuYx/v7+CA0NxfTp08Vthw4dgr+/f5ntTU1NYWpqWmq7VCrVyxtF7ugEyaS3Ibex5RuzFhIEATKZDDKZTG//ZqhmSCQS5rCWYw6Nl1QqhUQiER9lEQRB3FcXRtrWRzWRw+J/M2W9t431vV4T/dcmTZrA1dUVoaGhYpE2PT0dUVFRePPNN8s8pz76uE6WTmhm1wxXHlyp8EJkACCBBE3tmsLR0pHvdyPH3611D3NatzCfdQvzWbdUNZ8VbW8U/0pmzpyJDRs2YOvWrTh//jzefPNNZGVliavxjh07Vmehh7fffhsHDx7EsmXLcOHCBYSEhODkyZPldpKJnoZMJoNKpUKnTp0gk8kMHQ4REREZgeruv0okEkyfPh0LFizAL7/8gri4OIwdOxbu7u5iYdgQJBIJpvlOq9Kxb/m9xYItERERURUZfKQtAIwcORJ3797F3LlzkZSUhA4dOuDgwYPiQgyJiYk6VeiAgAB8//33mDNnDj788EM0b94ce/bsgbe3t6FeAhEREaFuLDBG+lVb/83URP919uzZyMrKwmuvvYbU1FR0794dBw8eNPg0EeM6jMNHf36EnIIcaPHkqUGkEinM5eYY236sHqIjIiIiqpskQm3tKT+F9PR02NraIi0tTS9z2mq1WiQnJ8PZ2ZlD4Gsp5rD2Yw5rP+bQuGk0Gly8eBHOzs5wcCh7/kpBEFBYWAi5XM7Rd7VUTeTw3r17SE5ORosWLUrd0aLvPlttV5Pfr98u/YYB3w8oWiX5MYVbKYqmSjkw5gD6NutbrTFQ9ePv1rqHOa1bmM+6hfmsW54mnxXtsxnFSFsiY6bVahEXF4f09HQ4OjryhysRURlkMhmUSqW4AryFhUWpoh6LtrVfdeZQEARkZ2cjOTkZSqWSUxAZuSCvIOwfvR/Ddw5HdkE2AOjMcStB0b8HcxNz/DzyZxZsiYiIiJ4Si7ZETyAIAu7fv4+srKxaewsnEZE+uLq6AoBYuH2UIAjQarXiomVU+9REDpVKpfhvh4xbkFcQEqcnYm3kWmw5vwWXH1wW9zW1a4q3/N7CuPbjYGtma8AoiYiIiOoGFm2JiIioWkgkEri5ucHZ2RkFBQWl9mu1Wty7dw8ODg68a6GWqu4cmpiYcIRtLaM0U2JSu0n44NkPkJqXioz8DFgrrGFvbs8/xhARERFVIxZtiYiIqFrJZLIyC3FarRYmJiYwMzNj0baWYg6pmEQigYOFAxwsyp7DmoiIiIieDnvbREREREREREREREaERVsiIiIiIiIiIiIiI8KiLREREREREREREZERqZdz2gqCAABIT0/Xy/W0Wi0yMjI4/1stpdFokJWVhezsbKSnp8PExMTQIVEV8H1Y+zGHtR9zWPvpO4fFfbXivhs9nj76uHwf1y3MZ93DnNYtzGfdwnzWLU+Tz4r2cetl0TYjIwMA4OHhYeBIiIiIiOhJMjIyYGtra+gwjB77uERERES1x5P6uBKhHg5d0Gq1uHXrFqytrSGRSGr8eunp6fDw8MD169dhY2NT49ej6scc1n7MYe3HHNZ+zGHtp+8cCoKAjIwMuLu7c0RKBeijj8v3cd3CfNY9zGndwnzWLcxn3fI0+axoH7dejrSVSqVo2LCh3q9rY2PDN2YtxxzWfsxh7ccc1n7MYe2nzxxyhG3F6bOPy/dx3cJ81j3Mad3CfNYtzGfdUtV8VqSPyyELREREREREREREREaERVsiIiIiIiIiIiIiI8KirR6Ymppi3rx5MDU1NXQoVEXMYe3HHNZ+zGHtxxzWfswh8d9A3cJ81j3Mad3CfNYtzGfdoo981suFyIiIiIiIiIiIiIiMFUfaEhERERERERERERkRFm2JiIiIiIiIiIiIjAiLtkRERERERERERERGhEVbPVizZg08PT1hZmYGPz8/HD9+3NAh0b/Cw8MxaNAguLu7QyKRYM+ePTr7BUHA3Llz4ebmBnNzc/Tp0wf//POPTpv79+9jzJgxsLGxgVKpxMSJE5GZmanHV1F/LVq0CF27doW1tTWcnZ0xZMgQxMfH67TJzc3FlClT4ODgACsrKwwfPhx37tzRaZOYmIgBAwbAwsICzs7OePfdd1FYWKjPl1JvrVu3Dj4+PrCxsYGNjQ38/f3x66+/ivuZv9pn8eLFkEgkmD59uriNeTRuISEhkEgkOo9WrVqJ+5m/+qeyfdddu3ahVatWMDMzQ7t27XDgwAE9RUoVUZl8nj17FsOHD4enpyckEglWrFihv0CpwiqT0w0bNkClUsHOzg52dnbo06cPP48amcrk8+eff0aXLl2gVCphaWmJDh064JtvvtFjtPQkVa3/7NixAxKJBEOGDKnZAKlSKpPPLVu2lOpTm5mZPdX1WbStYT/88ANmzpyJefPm4e+//0b79u0RFBSE5ORkQ4dGALKystC+fXusWbOmzP1LlizBypUrsX79ekRFRcHS0hJBQUHIzc0V24wZMwZnz57FoUOHsG/fPoSHh+O1117T10uo1w4fPowpU6bg2LFjOHToEAoKCtC3b19kZWWJbWbMmIH//e9/2LVrFw4fPoxbt25h2LBh4n6NRoMBAwYgPz8fR48exdatW7FlyxbMnTvXEC+p3mnYsCEWL16M6OhonDx5Es8++ywGDx6Ms2fPAmD+apsTJ07gq6++go+Pj8525tH4tW3bFrdv3xYfR44cEfcxf/VLZfuuR48eRXBwMCZOnIiYmBgMGTIEQ4YMwZkzZ/QcOZWlsvnMzs5G06ZNsXjxYri6uuo5WqqIyuY0LCwMwcHB+Ouvv6BWq+Hh4YG+ffvi5s2beo6cylLZfNrb2+Ojjz6CWq3G6dOnMWHCBEyYMAG//fabniOnslS1/nP16lXMmjULKpVKT5FSRVQlnzY2Njp96mvXrj1dEALVKF9fX2HKlCnic41GI7i7uwuLFi0yYFRUFgDC7t27xedarVZwdXUVvvjiC3FbamqqYGpqKmzfvl0QBEE4d+6cAEA4ceKE2ObXX38VJBKJcPPmTb3FTkWSk5MFAMLhw4cFQSjKl4mJibBr1y6xzfnz5wUAglqtFgRBEA4cOCBIpVIhKSlJbLNu3TrBxsZGyMvL0+8LIEEQBMHOzk7473//y/zVMhkZGULz5s2FQ4cOCT179hTefvttQRD4PqwN5s2bJ7Rv377Mfcxf/VPZvutLL70kDBgwQGebn5+f8Prrr9donFQxT/NZpHHjxsJ//vOfGoyOquJpP18WFhYK1tbWwtatW2sqRKqE6qgXdOzYUZgzZ05NhEeVVJV8FhYWCgEBAcJ///tfYdy4ccLgwYP1EClVRGXzuXnzZsHW1rZaY+BI2xqUn5+P6Oho9OnTR9wmlUrRp08fqNVqA0ZGFZGQkICkpCSd/Nna2sLPz0/Mn1qthlKpRJcuXcQ2ffr0gVQqRVRUlN5jru/S0tIAFP0FGgCio6NRUFCgk8NWrVqhUaNGOjls164dXFxcxDZBQUFIT08XR3uSfmg0GuzYsQNZWVnw9/dn/mqZKVOmYMCAATr5Avg+rC3++ecfuLu7o2nTphgzZgwSExMBMH/1TVX6rmq1utT7PigoiH1dI8DPInVPdeQ0OzsbBQUFYn+ZDOdp8ykIAkJDQxEfH48ePXrUZKhUAVXN5yeffAJnZ2dMnDhRH2FSBVU1n5mZmWjcuDE8PDx07iCtKvlTHU2PlZKSAo1Go/MhBgBcXFxw4cIFA0VFFZWUlAQAZeaveF9SUhKcnZ119svlctjb24ttSD+0Wi2mT5+OwMBAeHt7AyjKj0KhgFKp1Gn7aA7LynHxPqp5cXFx8Pf3R25uLqysrLB79260adMGsbGxzF8tsWPHDvz99984ceJEqX18Hxo/Pz8/bNmyBS1btsTt27cxf/58qFQqnDlzhvmrZ6rSdy0v/8y94fGzSN1THTl977334O7uXuqPLaR/Vc1nWloaGjRogLy8PMhkMqxduxbPPfdcTYdLT1CVfB45cgQbN25EbGysHiKkyqhKPlu2bIlNmzbBx8cHaWlpWLp0KQICAnD27Fk0bNiwSnGwaEtEdcKUKVNw5swZnXkYqXZo2bIlYmNjkZaWhh9//BHjxo3D4cOHDR0WVdD169fx9ttv49ChQ0890T4ZxvPPPy9+7ePjAz8/PzRu3Bg7d+6Eubm5ASMjIqLqtHjxYuzYsQNhYWH8nV2LWVtbIzY2FpmZmQgNDcXMmTPRtGlT9OrVy9ChUSVkZGTg5ZdfxoYNG+Do6GjocKga+Pv7w9/fX3weEBCA1q1b46uvvsKnn35apXNyeoQa5OjoCJlMVmqF5Tt37nBi/1qgOEePy5+rq2upSagLCwtx//595liPpk6din379uGvv/7S+QuWq6sr8vPzkZqaqtP+0RyWlePifVTzFAoFvLy80LlzZyxatAjt27fHl19+yfzVEtHR0UhOTkanTp0gl8shl8tx+PBhrFy5EnK5HC4uLsxjLaNUKtGiRQtcunSJ78N6pip91/Lyz9wbHj+L1D1Pk9OlS5di8eLF+P3330stGEqGUdV8SqVSeHl5oUOHDnjnnXfw4osvYtGiRTUdLj1BZfN5+fJlXL16FYMGDRL70Nu2bcMvv/wCuVyOy5cv6yt0KkN1/A41MTFBx44dcenSpSrHwaJtDVIoFOjcuTNCQ0PFbVqtFqGhoTrVdzJOTZo0gaurq07+0tPTERUVJebP398fqampiI6OFtv8+eef0Gq18PPz03vM9Y0gCJg6dSp2796NP//8E02aNNHZ37lzZ5iYmOjkMD4+HomJiTo5jIuL0ym+Hzp0CDY2NmjTpo1+Xgjp0Gq1yMvLY/5qid69eyMuLg6xsbHio0uXLhgzZoz4NfNYu2RmZuLy5ctwc3Pj+7CeqUrf1d/fX6c9UJR/9nUNj59F6p6q5nTJkiX49NNPcfDgQZ21OMiwqus9Wtx3JsOqbD5btWpVqg/9wgsv4JlnnkFsbCw8PDz0GT49ojrenxqNBnFxcXBzc6t6INW6rBmVsmPHDsHU1FTYsmWLcO7cOeG1114TlEqlzgrLZDgZGRlCTEyMEBMTIwAQli9fLsTExAjXrl0TBEEQFi9eLCiVSmHv3r3C6dOnhcGDBwtNmjQRcnJyxHP069dP6NixoxAVFSUcOXJEaN68uRAcHGyol1SvvPnmm4Ktra0QFhYm3L59W3xkZ2eLbd544w2hUaNGwp9//imcPHlS8Pf3F/z9/cX9hYWFgre3t9C3b18hNjZWOHjwoODk5CR88MEHhnhJ9c77778vHD58WEhISBBOnz4tvP/++4JEIhF+//13QRCYv9qqZ8+ewttvvy0+Zx6N2zvvvCOEhYUJCQkJQmRkpNCnTx/B0dFRSE5OFgSB+atvntR3ffnll4X3339fbB8ZGSnI5XJh6dKlwvnz54V58+YJJiYmQlxcnKFeApVQ2Xzm5eWJfWM3Nzdh1qxZQkxMjPDPP/8Y6iXQIyqb08WLFwsKhUL48ccfdfrLGRkZhnoJVEJl8/nZZ58Jv//+u3D58mXh3LlzwtKlSwW5XC5s2LDBUC+BSqhsPh81btw4YfDgwXqKlp6ksvmcP3++8NtvvwmXL18WoqOjhVGjRglmZmbC2bNnqxwDi7Z6sGrVKqFRo0aCQqEQfH19hWPHjhk6JPrXX3/9JQAo9Rg3bpwgCIKg1WqFjz/+WHBxcRFMTU2F3r17C/Hx8TrnuHfvnhAcHCxYWVkJNjY2woQJE9gJ0pOycgdA2Lx5s9gmJydHmDx5smBnZydYWFgIQ4cOFW7fvq1znqtXrwrPP/+8YG5uLjg6OgrvvPOOUFBQoOdXUz+98sorQuPGjQWFQiE4OTkJvXv3Fgu2gsD81VaPFm2ZR+M2cuRIwc3NTVAoFEKDBg2EkSNHCpcuXRL3M3/1z+P6rj179hT7ScV27twptGjRQlAoFELbtm2F/fv36zliepzK5DMhIaHMvlXPnj31HziVqzI5bdy4cZk5nTdvnv4DpzJVJp8fffSR4OXlJZiZmQl2dnaCv7+/sGPHDgNETeWp7O/Qkli0NT6Vyef06dPFti4uLkL//v2Fv//++6muLxEEQaj6OF0iIiIiIiIiIiIiqk6c05aIiIiIiIiIiIjIiLBoS0RERERERERERGREWLQlIiIiIiIiIiIiMiIs2hIREREREREREREZERZtiYiIiIiIiIiIiIwIi7ZERERERERERERERoRFWyIiIiIiIiIiIiIjwqItERERERERERERkRFh0ZaIiIiIiIiIdISEhEAikZT5WLx4cY1f/+rVqwgJCcGtW7d0toeFhUEikeDkyZOVOp9EIsHSpUvF51u2bMH3339fLbESEdUEuaEDICKqbSQSyRPbbN68GVu2bIGVlRX27dunh6geb82aNdiyZQtOnDhR49dauHAhwsLCcOjQoRq/FhERERHVHHNzc/z555+ltjdq1KjGr3316lXMnz8fAwcOhLu7u7i9U6dOUKvVaN26daXOp1ar0bhxY/F5cV999OjR1RYzEVF1YtGWiKiS1Gq1znN/f39MmzZNp8PXrFkz+Pr6QiaT6Tu8UrKzs7FgwQKsXr1aL9ebMmUKlixZgr/++gvPPPOMXq5JRERERNVPKpWiW7duhg5Dh42NTZViMrbXQUT0JJwegYiokrp166bzAIpGG5Tc5uTkhDZt2qBly5YGjhb44YcfUFBQgMGDB+vlekqlEsOHD8eXX36pl+sRERERkXF5//330a5dO1hZWaFBgwYIDg7G7du3S7Xbv38/AgMDYWFhATs7O/Tq1QsxMTEICwsT//jftWtXcVoGoPT0CL169cLAgQNLnXv16tUwNzdHWloaAN3pEXr16oXDhw9j//794rlDQkKwatUqWFhYID09Xedc58+fh0QiwYEDB6rvm0RE9AQs2hIR1ZBHO5AhISGwsrJCTEwM/P39YW5ujk6dOiEmJga5ubl48803YWdnh4YNG2LFihWlzqdWq/Hss8/C0tIStra2GD16NJKTk58Yx9atWzF48GDI5Q9vrtiyZYvY2e3bty8sLCzQsmVL/PHHH9BqtZgzZw5cXFzg4uKCDz74AFqtVjz2xo0beOmll+Di4gIzMzM0adIEM2bM0LnmiBEjsH//fqSkpFThO0dERERExqKwsLDU40mSk5Px4YcfYv/+/fjyyy9x9epV9OzZU+fYH374AYMGDYKzszO+//57fPfddwgMDMTNmzfRqVMnrFmzBkDRtGNqtbrU3W7FgoOD8fvvv+P+/fs627dv347+/fvD1ta21DFr165Fx44dERgYKJ570qRJ+L//+z8IgoDt27frtN+0aRMaNGiAoKCgJ752IqLqwqItEZEeFRQUYNy4cXjttdfw008/oaCgAMOGDcOkSZNgbm6OnTt3YsiQIZgxYwaOHj0qHqdWq9GrVy/Y2trihx9+wNdff40TJ048cfRsTk4Ojh49isDAwDL3jx07FgMHDsTu3bvh7u6OYcOG4e2338b169exbds2TJkyBYsXL8aOHTt0jjl9+jRWrlyJgwcPYv78+dBoNDrn9ff3h0ajQVhYWNW/WURERERkUFlZWTAxMSn1OHLkyGOP27RpE4KDg9GzZ08MHToUP/74I/755x9xflxBEDBr1iz07dsXu3fvxpAhQ9C/f38sXLgQAwcOhI2NDdq0aQMA8Pb21rnD7VEvvvgiAOCnn34St127dg1qtRrBwcFlHtOmTRvY2NhAqVSK527YsCHs7Ozw4osvYtOmTWLbwsJCfPPNNxg3bpxRTH1GRPUH57QlItKj/Px8fP7553j++ecBAFqtFoMGDYKfnx+WL18OAHj22Wexa9cu7Nq1CwEBAQCKbjHr0qULfv75Z/HWsHbt2sHb2xsHDhxA//79y7xebGwsCgoK4OPjU+b+adOm4c033wQANGjQAO3atcPJkyfFkQxBQUH45ZdfsGvXLnHO3uPHj2PRokUYOXKkeJ6xY8fqnFepVKJRo0aIiooSO9JEREREVLuYm5sjPDy81PZWrVo99rhff/0Vn376Kc6ePasz1cDFixfRt29fxMfH48aNG1i2bNlTx+jg4IDnnnsOO3bswKuvvgqgaBSvlZVVmdMmPMmrr76Knj174uzZs2jbti0OHDiA5ORkvPLKK08dKxFRZXCkLRGRHkmlUvTu3Vt83qJFCwBAnz59xG0ymQzNmjXD9evXARQtJBYZGYkRI0ZAo9GIt6W1aNECHh4eOHHiRLnXK547zMnJqcz9zz33XKlYSsZXvL04FqBoxd6lS5di3bp1uHTpUrnXdnR0LHPuMiIiIiKqHaRSKbp06VLqYWVlVe4xJ06cwAsvvAB3d3d88803UKvVOHbsGAAgNzcXAHDv3j0AgLu7e7XEGRwcjLCwMCQlJQEomhph6NChMDMzq/S5evTogZYtW2Ljxo0AikYN9+jRA82aNauWWImIKopFWyIiPTI3N4dCoRCfF3+tVCp12ikUCrFT++DBA2g0GsyYMaPUrWmJiYk6BdVHFZ/D1NS0zP0lr1uRWICikQu9e/fGRx99hObNm6NVq1b4+eefS53b1NQUOTk55cZGRERERHXP7t27YWtri507d+KFF15At27d4OrqqtPGwcEBAHDr1q1quebgwYNhamqKnTt3Ij4+HrGxseVOjVARkyZNwrfffosbN25g//79mDhxYrXESURUGSzaEhEZOaVSCYlEgo8++ggnTpwo9ZgzZ065x9rb2wMAUlNTqy0eNzc3bNq0CSkpKTh+/DhatmyJkSNH4sqVKzrtUlNTxQ45EREREdUPOTk5MDExEaf0AoDvvvtOp03Lli3RsGFDbN68udzzFA8oKDl4oDzW1tYYOHAgtm/fju3bt8PJyUnnTrbyzl/euceNG4e0tDSMGTMGFhYWnO6LiAyCc9oSERk5S0tL+Pv74/z581iwYEGljm3ZsiUAICEh4Ylzj1WWVCpF165dsWDBAvzyyy+4dOkSmjZtCqBort7ExETO/UVERERUi2m1WnFqg5KcnZ3Fft+jnnvuOaxYsQLTpk3D0KFDoVar8c033+i0kUgkWLp0KYKDgzF8+HCMHTsWpqamUKvV6Nq1KwYOHIgWLVpAJpNh06ZNkMvlkMvl6NKlS7mxBgcHY9iwYbh27RpGjBgBufzx5Y7WrVtj69at+N///gc3Nze4u7uL0zU4OTlh8ODB2LVrF15//XWYm5s/6VtFRFTtONKWiKgW+OKLL7B//36MHDkSu3fvRlhYGL799luMGzcOYWFh5R7XpEkTuLm5ITo6ulriSEtLQ7du3bBmzRr88ccfOHDgAGbPng2lUolOnTqJ7eLj45GZmQmVSlUt1yUiIiIi/cvJyYG/v3+px2effVbuMf3798fnn3+OvXv34oUXXkB4eDj27dtXqt3IkSOxd+9e3Lx5E6NGjUJwcDCOHDmChg0bAihaH2HNmjU4fPgwVCoVunbt+thY+/fvD1tbW9y+fbtCUyPMnj0bgYGBGDt2LLp27Yqvv/5aZ//QoUMBgIMQiMhgONKWiKgWCAgIwJEjRzBv3jxMmDAB+fn5aNiwIXr37g0vL6/HHvviiy/i119/few0ChVlZmaGdu3aYdWqVUhMTIS5uTm6dOmC33//HY6OjmK7X3/9FY0bN35i55qIiIiIjFNISAhCQkKqdOzs2bMxe/ZsnW2CIJRqN2jQIAwaNKjc87z++ut4/fXXdbb16tWrzHOZmpo+dkqwR49p0KAB9u/fX277X3/9Fd7e3vD19S23DRFRTZIIZf20IyKiOuP06dPo2LEjrly5gsaNG+vlml27dsWgQYMwd+5cvVyPiIiIiKg6xMXFITY2FhMnTsTatWsxadIkQ4dERPUUi7ZERPXA0KFD0aRJEyxfvrzGrxUeHo4hQ4bgypUrUCqVNX49IiIiIqLq4unpibt372L06NH46quvIJVyVkkiMgxOj0BEVA8sWbIEe/fu1cu10tPTsW3bNhZsiYiIiKjWuXr1qqFDICICwJG2REREREREREREREaF4/yJiIiIiIiIiIiIjAiLtkRERERERERERERGhEVbIiIiIiIiIiIiIiPCoi0RERERERERERGREWHRloiIiIiIiIiIiMiIsGhLREREREREREREZERYtCUiIiIiIiIiIiIyIizaEhERERERERERERmR/wdmXaZppsW6FAAAAABJRU5ErkJggg=="
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Observations:\n",
      "  - Peak E activity: 0.489\n",
      "  - Steady-state E: 0.489\n",
      "  - Unified parameters simplify the model while maintaining core dynamics\n"
     ]
    }
   ],
   "execution_count": 4
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.4: WilsonCowanDivisiveStep (Gain Modulation)\n",
    "\n",
    "**NEW VARIANT** - Divisive normalization through gain modulation.\n",
    "\n",
    "**Mathematical Formulation**:\n",
    "\n",
    "$$\\tau_E \\frac{dr_E}{dt} = -r_E(t) + \\frac{1 - r \\, r_E(t)}{\\sigma_E + w_{EI} r_I(t)} F_E(w_{EE} r_E(t) - w_{EI} r_I(t) + I_E(t))$$\n",
    "\n",
    "$$\\tau_I \\frac{dr_I}{dt} = -r_I(t) + \\frac{1 - r \\, r_I(t)}{\\sigma_I + w_{IE} r_E(t)} F_I(w_{IE} r_E(t) - w_{II} r_I(t) + I_I(t))$$\n",
    "\n",
    "**Key Features**:\n",
    "- Divisive normalization through gain modulation\n",
    "- Inhibition divides the gain of the transfer function\n",
    "- Models contrast normalization in visual cortex\n",
    "- Parameters: $\\sigma_E$, $\\sigma_I$ control normalization strength"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-21T13:55:42.792220Z",
     "start_time": "2026-03-21T13:55:41.903868600Z"
    }
   },
   "source": [
    "# Create divisive gain modulation model\n",
    "model_div = brainmass.WilsonCowanDivisiveStep(\n",
    "    1,  # Single node\n",
    "    tau_E=1.0 * u.ms,\n",
    "    tau_I=1.0 * u.ms,\n",
    "    a_E=1.2,\n",
    "    theta_E=2.8,\n",
    "    a_I=1.0,\n",
    "    theta_I=4.0,\n",
    "    wEE=6.,  # Reduced weights for stability\n",
    "    wEI=6.5,\n",
    "    wIE=2.,\n",
    "    wII=5.5,\n",
    "    sigma_E=1.,  # Normalization strength\n",
    "    sigma_I=1.,\n",
    "    r=1.\n",
    ")\n",
    "model_div.init_all_states()\n",
    "\n",
    "\n",
    "# Run simulation\n",
    "def step_run_div(i):\n",
    "    t = i * brainstate.environ.get_dt()\n",
    "    inp = u.math.where(t > 100 * u.ms, 2.0, 0.5)\n",
    "    model_div.update(rE_inp=inp, rI_inp=0.0)\n",
    "    return model_div.rE.value, model_div.rI.value\n",
    "\n",
    "\n",
    "rE_div, rI_div = brainstate.transform.for_loop(step_run_div, indices)\n",
    "\n",
    "# Visualize\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 4))\n",
    "\n",
    "# Time series\n",
    "ax1.plot(time, rE_div[:, 0], color=E_COLOR, linewidth=2, label='Excitation (E)')\n",
    "ax1.plot(time, rI_div[:, 0], color=I_COLOR, linewidth=2, label='Inhibition (I)')\n",
    "ax1.axvline(100, color='gray', linestyle='--', alpha=0.5, label='Input step')\n",
    "ax1.set_xlabel('Time (ms)', fontsize=11)\n",
    "ax1.set_ylabel('Activity', fontsize=11)\n",
    "ax1.set_title('WilsonCowanDivisiveStep - Time Series', fontsize=12, fontweight='bold')\n",
    "ax1.legend(fontsize=10)\n",
    "ax1.grid(True, alpha=0.3)\n",
    "\n",
    "# Phase portrait\n",
    "ax2.plot(rE_div[:, 0], rI_div[:, 0], 'k-', linewidth=1.5, alpha=0.7)\n",
    "ax2.plot(rE_div[0, 0], rI_div[0, 0], 'go', markersize=10, label='Start', zorder=5)\n",
    "ax2.plot(rE_div[-1, 0], rI_div[-1, 0], 'r*', markersize=14, label='End', zorder=5)\n",
    "ax2.set_xlabel('E activity', fontsize=11)\n",
    "ax2.set_ylabel('I activity', fontsize=11)\n",
    "ax2.set_title('Phase Portrait', fontsize=12, fontweight='bold')\n",
    "ax2.legend(fontsize=10)\n",
    "ax2.grid(True, alpha=0.3)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print(\"Observations:\")\n",
    "print(f\"  - Peak E activity: {rE_div[:, 0].max():.3f}\")\n",
    "print(f\"  - Steady-state E: {rE_div[-100:, 0].mean():.3f}\")\n",
    "print(f\"  - Divisive normalization suppresses responses when inhibition is high\")\n",
    "print(f\"  - Models contrast normalization effects seen in visual cortex\")"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1400x400 with 2 Axes>"
      ],
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Observations:\n",
      "  - Peak E activity: 0.434\n",
      "  - Steady-state E: 0.432\n",
      "  - Divisive normalization suppresses responses when inhibition is high\n",
      "  - Models contrast normalization effects seen in visual cortex\n"
     ]
    }
   ],
   "execution_count": 5
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.5: WilsonCowanAdaptiveStep (Spike-Frequency Adaptation)\n",
    "\n",
    "**NEW VARIANT** - 4-state system with adaptation currents.\n",
    "\n",
    "**Mathematical Formulation**:\n",
    "\n",
    "$$\\tau_E \\frac{dr_E}{dt} = -r_E(t) + [1 - r \\, r_E(t)] F_E(w_{EE} r_E(t) - w_{EI} r_I(t) - a_E(t) + I_E(t))$$\n",
    "\n",
    "$$\\tau_I \\frac{dr_I}{dt} = -r_I(t) + [1 - r \\, r_I(t)] F_I(w_{IE} r_E(t) - w_{II} r_I(t) - a_I(t) + I_I(t))$$\n",
    "\n",
    "$$\\tau_{aE} \\frac{da_E}{dt} = -a_E(t) + b_E r_E(t)$$\n",
    "\n",
    "$$\\tau_{aI} \\frac{da_I}{dt} = -a_I(t) + b_I r_I(t)$$\n",
    "\n",
    "**Key Features**:\n",
    "- 4 dynamical states: $r_E$, $r_I$, $a_E$, $a_I$\n",
    "- Adaptation currents build up with activity and suppress responses\n",
    "- Models neural fatigue and habituation\n",
    "- Slow time constants ($\\tau_a$) capture long-term adaptation"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "start_time": "2026-03-21T13:55:42.828900400Z"
    }
   },
   "source": [
    "# Create adaptive model\n",
    "model_adapt = brainmass.WilsonCowanAdaptiveStep(\n",
    "    1,  # Single node\n",
    "    tau_E=1.0 * u.ms,\n",
    "    tau_I=1.0 * u.ms,\n",
    "    tau_aE=50.0 * u.ms,  # Slow adaptation for E\n",
    "    tau_aI=50.0 * u.ms,  # Slow adaptation for I\n",
    "    b_E=0.5,  # Adaptation strength E\n",
    "    b_I=0.3,  # Adaptation strength I\n",
    "    a_E=1.2,\n",
    "    theta_E=2.8,\n",
    "    a_I=1.0,\n",
    "    theta_I=4.0,\n",
    "    wEE=12.,\n",
    "    wEI=13.,\n",
    "    wIE=4.,\n",
    "    wII=11.,\n",
    "    r=1.\n",
    ")\n",
    "model_adapt.init_all_states()\n",
    "\n",
    "\n",
    "# Run simulation with longer input period to see adaptation\n",
    "def step_run_adapt(i):\n",
    "    t = i * brainstate.environ.get_dt()\n",
    "    # Sustained input from 100-400ms\n",
    "    inp = u.math.where((t > 100 * u.ms) & (t < 400 * u.ms), 2.0, 0.5)\n",
    "    model_adapt.update(rE_inp=inp, rI_inp=0.0)\n",
    "    return model_adapt.rE.value, model_adapt.rI.value, model_adapt.aE.value, model_adapt.aI.value\n",
    "\n",
    "\n",
    "rE_adapt, rI_adapt, aE_adapt, aI_adapt = brainstate.transform.for_loop(step_run_adapt, indices)\n",
    "\n",
    "# Visualize all 4 states\n",
    "fig = plt.figure(figsize=(16, 8))\n",
    "gs = GridSpec(2, 2, figure=fig)\n",
    "\n",
    "# Time series of activities\n",
    "ax1 = fig.add_subplot(gs[0, :])\n",
    "ax1.plot(time, rE_adapt[:, 0], color=E_COLOR, linewidth=2, label='Excitation (E)')\n",
    "ax1.plot(time, rI_adapt[:, 0], color=I_COLOR, linewidth=2, label='Inhibition (I)')\n",
    "ax1.axvspan(100, 400, color='gray', alpha=0.1, label='Input ON')\n",
    "ax1.set_xlabel('Time (ms)', fontsize=11)\n",
    "ax1.set_ylabel('Activity', fontsize=11)\n",
    "ax1.set_title('WilsonCowanAdaptiveStep - Neural Activities', fontsize=12, fontweight='bold')\n",
    "ax1.legend(fontsize=10)\n",
    "ax1.grid(True, alpha=0.3)\n",
    "\n",
    "# Time series of adaptation currents\n",
    "ax2 = fig.add_subplot(gs[1, :])\n",
    "ax2.plot(time, aE_adapt[:, 0], color=A_COLOR, linewidth=2, label='Adaptation E ($a_E$)', linestyle='--')\n",
    "ax2.plot(time, aI_adapt[:, 0], color=A_COLOR, linewidth=2, label='Adaptation I ($a_I$)', linestyle=':')\n",
    "ax2.axvspan(100, 400, color='gray', alpha=0.1, label='Input ON')\n",
    "ax2.set_xlabel('Time (ms)', fontsize=11)\n",
    "ax2.set_ylabel('Adaptation Current', fontsize=11)\n",
    "ax2.set_title('Adaptation Currents Build Up During Sustained Input', fontsize=12, fontweight='bold')\n",
    "ax2.legend(fontsize=10)\n",
    "ax2.grid(True, alpha=0.3)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print(\"Observations:\")\n",
    "print(f\"  - Peak E activity: {rE_adapt[:, 0].max():.3f} (at t={time[np.argmax(rE_adapt[:, 0])]:.1f})\")\n",
    "print(f\"  - Max adaptation: {aE_adapt[:, 0].max():.3f}\")\n",
    "print(f\"  - Adaptation builds up during sustained input, reducing responses\")\n",
    "print(f\"  - After input turns off, adaptation slowly decays\")\n",
    "print(f\"  - Models neural fatigue and habituation phenomena\")"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1600x800 with 2 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.6: WilsonCowanThreePopulationStep (E-I-M Model)\n",
    "\n",
    "**NEW VARIANT** - Three-population model with modulatory neurons.\n",
    "\n",
    "**Mathematical Formulation**:\n",
    "\n",
    "$$\\tau_E \\frac{dr_E}{dt} = -r_E(t) + [1 - r \\, r_E(t)] F_E(w_{EE} r_E(t) - w_{EI} r_I(t) + w_{EM} r_M(t) + I_E(t))$$\n",
    "\n",
    "$$\\tau_I \\frac{dr_I}{dt} = -r_I(t) + [1 - r \\, r_I(t)] F_I(w_{IE} r_E(t) - w_{II} r_I(t) + w_{IM} r_M(t) + I_I(t))$$\n",
    "\n",
    "$$\\tau_M \\frac{dr_M}{dt} = -r_M(t) + [1 - r \\, r_M(t)] F_M(w_{ME} r_E(t) - w_{MI} r_I(t) + w_{MM} r_M(t) + I_M(t))$$\n",
    "\n",
    "**Key Features**:\n",
    "- 3 interacting populations: Excitatory, Inhibitory, Modulatory\n",
    "- Modulator enhances both E and I populations ($w_{EM}$, $w_{IM}$)\n",
    "- Models attention, arousal, and neuromodulation\n",
    "- Can simulate cholinergic, dopaminergic, or other modulatory effects"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {},
   "source": [
    "# Create three-population model\n",
    "model_3pop = brainmass.WilsonCowanThreePopulationStep(\n",
    "    1,  # Single node\n",
    "    tau_E=1.0 * u.ms,\n",
    "    tau_I=1.0 * u.ms,\n",
    "    tau_M=2.0 * u.ms,  # Modulator dynamics\n",
    "    a_E=1.2,\n",
    "    theta_E=2.8,\n",
    "    a_I=1.0,\n",
    "    theta_I=4.0,\n",
    "    a_M=1.0,\n",
    "    theta_M=3.0,\n",
    "    # E-I connections\n",
    "    wEE=12.,\n",
    "    wEI=13.,\n",
    "    wIE=4.,\n",
    "    wII=11.,\n",
    "    # Modulator → E/I connections\n",
    "    wEM=4.,  # M enhances E\n",
    "    wIM=2.,  # M enhances I\n",
    "    # E/I → Modulator connections  \n",
    "    wME=8.,  # E drives M\n",
    "    wMI=6.,  # I inhibits M\n",
    "    wMM=2.,  # M self-excitation\n",
    "    r=1.\n",
    ")\n",
    "model_3pop.init_all_states()\n",
    "\n",
    "\n",
    "# Run simulation with modulator activation\n",
    "def step_run_3pop(i):\n",
    "    t = i * brainstate.environ.get_dt()\n",
    "    inp_E = u.math.where(t > 100 * u.ms, 2.0, 0.5)\n",
    "    # Activate modulator from 250-500ms\n",
    "    inp_M = u.math.where((t > 250 * u.ms) & (t < 500 * u.ms), 3.0, 0.0)\n",
    "    model_3pop.update(rE_inp=inp_E, rI_inp=0.0, rM_inp=inp_M)\n",
    "    return model_3pop.rE.value, model_3pop.rI.value, model_3pop.rM.value\n",
    "\n",
    "\n",
    "rE_3pop, rI_3pop, rM_3pop = brainstate.transform.for_loop(step_run_3pop, indices)\n",
    "\n",
    "# Visualize\n",
    "fig, axes = plt.subplots(2, 2, figsize=(16, 10))\n",
    "\n",
    "# Time series of all 3 populations\n",
    "ax1 = axes[0, 0]\n",
    "ax1.plot(time, rE_3pop[:, 0], color=E_COLOR, linewidth=2, label='Excitation (E)')\n",
    "ax1.plot(time, rI_3pop[:, 0], color=I_COLOR, linewidth=2, label='Inhibition (I)')\n",
    "ax1.plot(time, rM_3pop[:, 0], color=M_COLOR, linewidth=2, label='Modulator (M)')\n",
    "ax1.axvspan(100, 500, color='lightblue', alpha=0.1, label='E input ON')\n",
    "ax1.axvspan(250, 500, color='lightgreen', alpha=0.2, label='M input ON')\n",
    "ax1.set_xlabel('Time (ms)', fontsize=11)\n",
    "ax1.set_ylabel('Activity', fontsize=11)\n",
    "ax1.set_title('Three Populations Time Series', fontsize=12, fontweight='bold')\n",
    "ax1.legend(fontsize=9)\n",
    "ax1.grid(True, alpha=0.3)\n",
    "\n",
    "# E-I phase portrait\n",
    "ax2 = axes[0, 1]\n",
    "# Color-code by M activity\n",
    "scatter = ax2.scatter(rE_3pop[:, 0], rI_3pop[:, 0], c=rM_3pop[:, 0],\n",
    "                      cmap='Greens', s=10, alpha=0.6)\n",
    "ax2.plot(rE_3pop[0, 0], rI_3pop[0, 0], 'go', markersize=10, label='Start', zorder=5)\n",
    "ax2.plot(rE_3pop[-1, 0], rI_3pop[-1, 0], 'r*', markersize=14, label='End', zorder=5)\n",
    "cbar = plt.colorbar(scatter, ax=ax2)\n",
    "cbar.set_label('M activity', fontsize=10)\n",
    "ax2.set_xlabel('E activity', fontsize=11)\n",
    "ax2.set_ylabel('I activity', fontsize=11)\n",
    "ax2.set_title('E-I Phase Portrait (colored by M)', fontsize=12, fontweight='bold')\n",
    "ax2.legend(fontsize=9)\n",
    "ax2.grid(True, alpha=0.3)\n",
    "\n",
    "# 3D phase space\n",
    "ax3 = fig.add_subplot(2, 2, 3, projection='3d')\n",
    "ax3.plot(rE_3pop[:, 0], rI_3pop[:, 0], rM_3pop[:, 0], 'k-', linewidth=1.5, alpha=0.7)\n",
    "ax3.scatter(rE_3pop[0, 0], rI_3pop[0, 0], rM_3pop[0, 0],\n",
    "            color='green', s=100, marker='o', label='Start', zorder=10)\n",
    "ax3.scatter(rE_3pop[-1, 0], rI_3pop[-1, 0], rM_3pop[-1, 0],\n",
    "            color='red', s=150, marker='*', label='End', zorder=10)\n",
    "ax3.set_xlabel('E activity', fontsize=10)\n",
    "ax3.set_ylabel('I activity', fontsize=10)\n",
    "ax3.set_zlabel('M activity', fontsize=10)\n",
    "ax3.set_title('3D Phase Space (E-I-M)', fontsize=12, fontweight='bold')\n",
    "ax3.legend(fontsize=9)\n",
    "\n",
    "# Modulator effect comparison\n",
    "ax4 = axes[1, 1]\n",
    "t_pre = (time >= 100 * u.ms) & (time < 250 * u.ms)  # Before M activation\n",
    "t_post = (time >= 250 * u.ms) & (time < 400 * u.ms)  # During M activation\n",
    "E_pre_mean = rE_3pop[t_pre, 0].mean()\n",
    "E_post_mean = rE_3pop[t_post, 0].mean()\n",
    "ax4.bar(['Before M\\nActivation', 'During M\\nActivation'],\n",
    "        [E_pre_mean, E_post_mean],\n",
    "        color=[E_COLOR, M_COLOR], alpha=0.7, edgecolor='black', linewidth=2)\n",
    "ax4.set_ylabel('Mean E Activity', fontsize=11)\n",
    "ax4.set_title('Modulatory Enhancement Effect', fontsize=12, fontweight='bold')\n",
    "ax4.grid(True, alpha=0.3, axis='y')\n",
    "for i, v in enumerate([E_pre_mean, E_post_mean]):\n",
    "    ax4.text(i, v + 0.02, f'{v:.3f}', ha='center', fontsize=10, fontweight='bold')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print(\"Observations:\")\n",
    "print(f\"  - Mean E before modulation: {E_pre_mean:.3f}\")\n",
    "print(f\"  - Mean E during modulation: {E_post_mean:.3f}\")\n",
    "print(f\"  - Enhancement: {((E_post_mean / E_pre_mean - 1) * 100):.1f}%\")\n",
    "print(f\"  - Modulator enhances both E and I responses\")\n",
    "print(f\"  - Models attention, arousal, and neuromodulatory effects\")"
   ],
   "outputs": [],
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 3: Side-by-Side Comparison of All Variants\n",
    "\n",
    "Now we'll compare all variants with identical input to see how they differ in their responses."
   ]
  },
  {
   "cell_type": "code",
   "metadata": {},
   "source": [
    "# Create all variants with compatible parameters\n",
    "print(\"Creating all 11 Wilson-Cowan variants...\")\n",
    "\n",
    "# Common parameters for fair comparison\n",
    "common_params = {\n",
    "    'tau_E': 1.0 * u.ms,\n",
    "    'tau_I': 1.0 * u.ms,\n",
    "    'a_E': 1.2,\n",
    "    'theta_E': 2.8,\n",
    "    'a_I': 1.0,\n",
    "    'theta_I': 4.0,\n",
    "}\n",
    "\n",
    "# Create all models\n",
    "models = {}\n",
    "\n",
    "# 1. Standard\n",
    "models['Standard'] = brainmass.WilsonCowanStep(\n",
    "    1, **common_params, wEE=12., wEI=13., wIE=4., wII=11., r=1.\n",
    ")\n",
    "\n",
    "# 2. No Saturation\n",
    "models['NoSaturation'] = brainmass.WilsonCowanNoSaturationStep(\n",
    "    1, **common_params, wEE=12., wEI=13., wIE=4., wII=11.\n",
    ")\n",
    "\n",
    "# 3. Symmetric (uses unified params)\n",
    "models['Symmetric'] = brainmass.WilsonCowanSymmetricStep(\n",
    "    1, tau=1.0 * u.ms, a=1.2, theta=2.8, wEE=12., wEI=13., wIE=4., wII=11., r=1.\n",
    ")\n",
    "\n",
    "# 4. Simplified\n",
    "models['Simplified'] = brainmass.WilsonCowanSimplifiedStep(\n",
    "    1, **common_params, w_exc=12., w_inh=11., r=1.\n",
    ")\n",
    "\n",
    "# 5. Linear\n",
    "models['Linear'] = brainmass.WilsonCowanLinearStep(\n",
    "    1, tau_E=1.0 * u.ms, tau_I=1.0 * u.ms, wEE=12., wEI=13., wIE=4., wII=11.\n",
    ")\n",
    "\n",
    "# 6. Divisive (Gain)\n",
    "models['Divisive (Gain)'] = brainmass.WilsonCowanDivisiveStep(\n",
    "    1, **common_params, wEE=6., wEI=6.5, wIE=2., wII=5.5, sigma_E=1., sigma_I=1., r=1.\n",
    ")\n",
    "\n",
    "# 7. Divisive (Input)\n",
    "models['Divisive (Input)'] = brainmass.WilsonCowanDivisiveInputStep(\n",
    "    1, **common_params, wEE=6., wEI=6.5, wIE=2., wII=5.5, sigma_E=1., sigma_I=1., r=1.\n",
    ")\n",
    "\n",
    "# 8. Delayed\n",
    "models['Delayed'] = brainmass.WilsonCowanDelayedStep(\n",
    "    1, **common_params, wEE=12., wEI=13., wIE=4., wII=11., r=1.,\n",
    "    delay_EE=0.5 * u.ms, delay_IE=0.5 * u.ms, delay_EI=0.5 * u.ms, delay_II=0.5 * u.ms\n",
    ")\n",
    "\n",
    "# 9. Adaptive\n",
    "models['Adaptive'] = brainmass.WilsonCowanAdaptiveStep(\n",
    "    1, **common_params, wEE=12., wEI=13., wIE=4., wII=11., r=1.,\n",
    "    tau_aE=50. * u.ms, tau_aI=50. * u.ms, b_E=0.3, b_I=0.2\n",
    ")\n",
    "\n",
    "# 10. Three-Population\n",
    "models['ThreePopulation'] = brainmass.WilsonCowanThreePopulationStep(\n",
    "    1, **common_params, a_M=1.0, theta_M=3.0, tau_M=2.0 * u.ms, r=1.,\n",
    "    wEE=12., wEI=13., wIE=4., wII=11.,\n",
    "    wEM=2., wIM=1., wME=4., wMI=3., wMM=1.\n",
    ")\n",
    "\n",
    "# Initialize all models\n",
    "for name, model in models.items():\n",
    "    model.init_all_states()\n",
    "\n",
    "print(f\"✅ Created {len(models)} variants\\n\")\n",
    "\n",
    "# Simulate all variants with identical input\n",
    "duration = 500 * u.ms\n",
    "n_steps = int(duration / brainstate.environ.get_dt())\n",
    "indices = np.arange(n_steps)\n",
    "time = indices * brainstate.environ.get_dt()\n",
    "\n",
    "results = {}\n",
    "\n",
    "for name, model in models.items():\n",
    "    print(f\"Simulating {name}...\", end=' ')\n",
    "\n",
    "\n",
    "    def sim_func(i):\n",
    "        t = i * brainstate.environ.get_dt()\n",
    "        inp = u.math.where(t > 100 * u.ms, 2.0, 0.5)\n",
    "        model.update(rE_inp=inp, rI_inp=0.0)\n",
    "        return model.rE.value, model.rI.value\n",
    "\n",
    "\n",
    "    rE, rI = brainstate.transform.for_loop(sim_func, indices)\n",
    "    results[name] = (rE, rI)\n",
    "\n",
    "    # Re-initialize for next simulation\n",
    "    model.init_all_states()\n",
    "\n",
    "    print(\"✓\")\n",
    "\n",
    "print(\"\\n✅ All simulations complete!\")"
   ],
   "outputs": [],
   "execution_count": null
  },
  {
   "cell_type": "code",
   "metadata": {},
   "source": [
    "# Plot all variants in a grid\n",
    "fig, axes = plt.subplots(4, 3, figsize=(18, 16))\n",
    "axes = axes.flatten()\n",
    "\n",
    "for idx, (name, (rE, rI)) in enumerate(results.items()):\n",
    "    ax = axes[idx]\n",
    "\n",
    "    # Plot E and I\n",
    "    ax.plot(time, rE[:, 0], color=E_COLOR, linewidth=2, label='E', alpha=0.9)\n",
    "    ax.plot(time, rI[:, 0], color=I_COLOR, linewidth=2, label='I', alpha=0.9)\n",
    "    ax.axvline(100, color='gray', linestyle='--', alpha=0.4, linewidth=1)\n",
    "\n",
    "    # Format\n",
    "    ax.set_title(name, fontsize=12, fontweight='bold', pad=8)\n",
    "    ax.set_xlabel('Time (ms)', fontsize=10)\n",
    "    ax.set_ylabel('Activity', fontsize=10)\n",
    "    ax.legend(loc='upper right', fontsize=9, framealpha=0.9)\n",
    "    ax.grid(True, alpha=0.3, linewidth=0.5)\n",
    "    ax.set_xlim([0, 500])\n",
    "\n",
    "    # Add metrics as text\n",
    "    peak_E = rE[:, 0].max()\n",
    "    ss_E = rE[-100:, 0].mean()\n",
    "    ax.text(\n",
    "        0.02, 0.98,\n",
    "        f'Peak: {peak_E:.2f}\\nSS: {ss_E:.2f}',\n",
    "        transform=ax.transAxes, fontsize=8, verticalalignment='top',\n",
    "        bbox=dict(boxstyle='round', facecolor='white', alpha=0.7)\n",
    "    )\n",
    "\n",
    "# Hide extra subplots (we have 10 variants but 12 subplot positions)\n",
    "for idx in range(len(results), len(axes)):\n",
    "    axes[idx].axis('off')\n",
    "\n",
    "plt.suptitle('Side-by-Side Comparison: All Wilson-Cowan Variants\\n(Identical Step Input)',\n",
    "             fontsize=16, fontweight='bold', y=0.995)\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print(\"\\n📊 Comparison Summary:\")\n",
    "print(\"=\" * 70)\n",
    "print(f\"{'Variant':<20} {'Peak E':<12} {'Steady-State E':<15} {'Rise Time'}\")\n",
    "print(\"-\" * 70)\n",
    "\n",
    "for name, (rE, rI) in results.items():\n",
    "    peak_E = rE[:, 0].max()\n",
    "    ss_E = rE[-100:, 0].mean()\n",
    "\n",
    "    # Find rise time (time to 90% of final value)\n",
    "    target = ss_E * 0.9\n",
    "    rise_idx = np.where(rE[:, 0] > target)[0]\n",
    "    rise_time = time[rise_idx[0]] if len(rise_idx) > 0 else 0\n",
    "\n",
    "    print(f\"{name:<20} {peak_E:>10.3f}   {ss_E:>13.3f}   {rise_time:>8.1f} ms\")\n",
    "\n",
    "print(\"=\" * 70)"
   ],
   "outputs": [],
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 4: Choosing the Right Variant - Decision Guide\n",
    "\n",
    "### Decision Tree\n",
    "\n",
    "```\n",
    "What is your primary goal?\n",
    "\n",
    "┌─ General exploratory modeling or teaching\n",
    "│  └─> WilsonCowanStep (Standard) - Most versatile\n",
    "│\n",
    "├─ Need simpler/faster computation\n",
    "│  └─> WilsonCowanNoSaturationStep - Simpler dynamics\n",
    "│\n",
    "├─ Reduce parameter space for fitting\n",
    "│  └─> WilsonCowanSymmetricStep - Fewer parameters\n",
    "│\n",
    "├─ Pedagogical demonstrations\n",
    "│  └─> WilsonCowanSimplifiedStep - Minimal complexity\n",
    "│\n",
    "├─ Optimization/gradient-based learning\n",
    "│  └─> WilsonCowanLinearStep - ReLU activation\n",
    "│\n",
    "├─ Model visual cortex normalization\n",
    "│  ├─> Gain control: WilsonCowanDivisiveStep\n",
    "│  └─> Input normalization: WilsonCowanDivisiveInputStep\n",
    "│\n",
    "├─ Include realistic axonal delays\n",
    "│  └─> WilsonCowanDelayedStep - Connection delays\n",
    "│\n",
    "├─ Model neural fatigue/habituation\n",
    "│  └─> WilsonCowanAdaptiveStep - Adaptation currents\n",
    "│\n",
    "└─ Model attention/arousal/neuromodulation\n",
    "   └─> WilsonCowanThreePopulationStep - Modulatory neurons\n",
    "```\n",
    "\n",
    "### Feature Comparison Table\n",
    "\n",
    "| Feature | Standard | NoSat | Sym | Simp | Linear | DivG | DivI | Delay | Adapt | 3Pop |\n",
    "|---------|:--------:|:-----:|:---:|:----:|:------:|:----:|:----:|:-----:|:-----:|:----:|\n",
    "| **States** | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 3 |\n",
    "| **Parameters** | 11 | 10 | 8 | 9 | 7 | 13 | 13 | 15 | 15 | 18 |\n",
    "| **Nonlinear** | ✓ | ✓ | ✓ | ✓ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ |\n",
    "| **Delays** | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ | ✗ | ✗ |\n",
    "| **Adaptation** | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ | ✗ |\n",
    "| **Modulation** | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ |\n",
    "| **Normalization** | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ |\n",
    "| **Complexity** | Med | Low | Low | Low | Low | Med | Med | Med | High | High |\n",
    "| **Stability** | Good | Good | Good | Good | Good | Med | Med | Med | Good | Good |\n",
    "\n",
    "### Use Case Recommendations\n",
    "\n",
    "**Cognitive Neuroscience:**\n",
    "- Working memory: **Standard** or **Adaptive** (for fatigue effects)\n",
    "- Attention: **ThreePopulation** (modulator = attention signal)\n",
    "- Decision making: **Standard** or **Symmetric**\n",
    "\n",
    "**Sensory Processing:**\n",
    "- Visual cortex V1: **Divisive** variants (contrast normalization)\n",
    "- Auditory cortex: **Standard** or **NoSaturation**\n",
    "- Somatosensory: **Standard**\n",
    "\n",
    "**Network Modeling:**\n",
    "- Large-scale brain networks: **Delayed** (realistic transmission delays)\n",
    "- Small local circuits: **Standard** or **Simplified**\n",
    "- Whole-brain models: **Standard** or **Linear** (for speed)\n",
    "\n",
    "**Machine Learning:**\n",
    "- Training recurrent networks: **Linear** (gradient-friendly)\n",
    "- Reservoir computing: **Standard** or **NoSaturation**\n",
    "- Neuromorphic computing: **Adaptive** or **ThreePopulation**\n",
    "\n",
    "**Clinical Applications:**\n",
    "- Epilepsy modeling: **Standard** (captures seizure dynamics)\n",
    "- Fatigue/habituation: **Adaptive**\n",
    "- Arousal disorders: **ThreePopulation**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## References\n",
    "\n",
    "**Original Wilson-Cowan Model:**\n",
    "- Wilson, H. R., & Cowan, J. D. (1972). Excitatory and inhibitory interactions in localized populations of model neurons. *Biophysical Journal*, 12(1), 1-24.\n",
    "\n",
    "**Divisive Normalization:**\n",
    "- Carandini, M., & Heeger, D. J. (2012). Normalization as a canonical neural computation. *Nature Reviews Neuroscience*, 13(1), 51-62.\n",
    "- Heeger, D. J. (1992). Normalization of cell responses in cat striate cortex. *Visual Neuroscience*, 9(2), 181-197.\n",
    "\n",
    "**Spike-Frequency Adaptation:**\n",
    "- Benda, J., & Herz, A. V. (2003). A universal model for spike-frequency adaptation. *Neural Computation*, 15(11), 2523-2564.\n",
    "- Wang, X. J. (1998). Calcium coding and adaptive temporal computation in cortical pyramidal neurons. *Journal of Neurophysiology*, 79(3), 1549-1566.\n",
    "\n",
    "**Delay Models:**\n",
    "- Robinson, P. A., Rennie, C. J., & Wright, J. J. (1997). Propagation and stability of waves of electrical activity in the cerebral cortex. *Physical Review E*, 56(1), 826.\n",
    "- Jirsa, V. K., & Haken, H. (1996). Field theory of electromagnetic brain activity. *Physical Review Letters*, 77(5), 960.\n",
    "\n",
    "**Neuromodulation:**\n",
    "- Deco, G., Ponce-Alvarez, A., Mantini, D., Romani, G. L., Hagmann, P., & Corbetta, M. (2013). Resting-state functional connectivity emerges from structurally and dynamically shaped slow linear fluctuations. *Journal of Neuroscience*, 33(27), 11239-11252.\n",
    "- Shine, J. M. (2019). Neuromodulatory influences on integration and segregation in the brain. *Trends in Cognitive Sciences*, 23(7), 572-583.\n"
   ]
  }
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