PWM_SineTriangle_Aligned.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/bingsen-wang/PowerElectronics/blob/main/PWM_SineTriangle_Aligned.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jAMKoELNpsK-"
      },
      "source": [
        "<center><h1><b>Pulse Width Modulation - Sine Triangle with Transitions Lined Up</h1></b>\n",
        "\n",
        "Dr. Bingsen Wang\n",
        "\n",
        "11/24/2023\n",
        "</center>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Hv0YxDrWU4h8"
      },
      "source": [
        "#Python Code\n",
        "The Python code illustrates the basic PWM.  "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 75,
      "metadata": {
        "id": "XeGsHYTt8IXU",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 905
        },
        "outputId": "f5df3dab-3959-4721-e9e6-8eb8c85959a8"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 900x900 with 2 Axes>"
            ],
            "image/png": 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Xv6a9XSIiUh6LSyISwsAVoeF8/PHHg8nyl7/85UyHFNM3v/nNwVlcN2zYEHPm2tbWVjz99NPIzc3F1772taS2ceKttrEK7zfffDOpdaaqtrYWABAKhfDHP/5xyGX279+fsau4WjKwX44dOxbzllMl9svkyZMHZ4n985//HLOgffrpp9Pe1ne+853B974+9thjMZc7cuQI/vrXv+K0007D9OnT094uEREpj8UlEQlhz549+PGPfxyzUGtubsYNN9yASCSC4uLiwZe6qyEvLw+PPfYYTCYT/vnPf+Kuu+465Tbd7u5uzJkzB52dnVi+fHnSE/pcd911gxO9rFix4qRJhADA7/fjBz/4QXq/SIK+853vDL7KY9myZafcGtnV1YXbbrtN0xP6yGXgvZFtbW346U9/esrPd+/ejU2bNikSy69+9SuYzWa0tbXhBz/4wSnH4J49e/Dcc8+lvZ0RI0bgF7/4BQBg+/bt+M1vfnPKMq2trbj++ushSRJ+/vOfG+JYICISEVtvItK10tJS2Gw2BINB3H///Xj66adx7bXX4qyzzkJubi7a2trw1ltv4Y9//CM6OzsxZswYbNmy5ZRXIgwk9B988AGA/lk9B753+eWXo6ysbPD/PR7P4NdNmzbB4XAMXln84x//iK6urlOWAYC5c+cObu/aa6/Fpk2bsHDhQqxevRq7d+/G17/+dRQVFeH999/HE088gf/93//FrbfemlIhPHHiRPzsZz/DXXfdhX/+8584++yz8a1vfQujRo3CRx99hI0bN540sdDBgwexadMmlJWV4fLLL8cHH3yA1157DS0tLYPL7Nu3DxaLBZMmTcKkSZPg8Xjw0ksvDbnMmDFjMHXqVABATk4O/vznP+PSSy/Fhx9+iM9//vP49re/jdGjR+P48ePYsGEDKisrcf3112Pz5s0n/e1nzJiB8vLypH9/AHjppZfg8XhOiu+DDz4YXPesWbOGnKl3uN8d+PR4ONHA3wLoP3Y+u62Bff8f//Ef2L17N/bv3497770Xr776Kq644grk5eXhjTfewKZNmzB27NjBq81//OMfUVJSgn/7t3/D6NGjB3+ngwcPDm77s7/Pvn378P777w+5zImxX3TRRVi3bh0WLVqEdevW4fDhw/jGN74Bm82G/fv345lnnsEzzzyDmTNnDvn3PXjwIA4ePDjk32ngOBrw3e9+F8FgEMuWLcPtt9+OP/3pT7j66qths9lw5MgRbNy4ER0dHfjZz36GOXPmDLk9IiLSAYmISOcCgYD0pz/9SVqyZIl06aWXSpWVlZLdbpfMZrPkcDikMWPGSLNnz5Y2btwoBYPBIdcBIOZ/L7/88rDLjBo1anA9o0aNirncUD7++GNpyZIl0uc+9znJ4XBIOTk50siRI6VvfOMb0q5du9L+2/z1r3+Vrr32Wqm0tFSyWCxSQUGBdMEFF0irV6+Wurq6Tolx+vTpkiRJ0oYNG2L+HitWrJAkSZJefvnlmMvMnz//lFj8fr909913S2eddZZktVqlgoICacqUKdJDDz0khcNhaf78+aes56WXXkr5d58+ffqw+/XDDz8c8nPD/e4nHg8nGu5v8dl939PTI61evVr64he/KNntdik7O1s67bTTpFmzZkkvvvjikNvfsGFD3N9p4PcZ6u84XOx///vfpeuvv15yu91STk6ONGLECOnGG2+UDh48KEUikcHPrly58qTPrVixIuZ2Bo6jz3r33XelW265RRo3bpyUl5cnWa1WafTo0VJNTY3097//fbjdSUREOmCSJBWnTCQiIiLN6ujoQGFhIQDg4YcfTvvdsEREJDY+c0lERGRAXV1dePPNNxEOh2Muc/To0cF/T5o0SYmwiIhIx1hcEhERGdDbb7+N888/Hy+++GLMZbZu3QoAOP300zFlyhSlQiMiIp1icUlERGRg9957L4LB4Cnff+ONN/CrX/0KALBy5UpkZ2crHRoREekMZ4slIiIyIJPJBKD/vZpnnXUW5s6dizPPPBPhcBj79u3Df/3Xf6Gvrw/33HMPampq1A2WiIh0gRP6EBERGdRrr72GrVu3Yt++faivr0dbWxuysrJw2mmn4eKLL8Ztt92G8847T+0wiYhIJ1hcEhERERERUdr4zCURERERERGljcUlERERERERpY3FJREREREREaWNxSURERERERGljcUlERERERERpY3FJREREREREaWNxSURERERERGljcUlERERERERpY3FJREREREREaWNxSURERERERGljcUlERERERERpY3FJREREREREaXNUMWl5ykPIsGI2mEI6amngGBQ7SiIiIiIiEgthiguJUlC/R31aNnaAnNu6r9yJBjBG194A12HumSMTt8kCbjjDmDrViA3N/X1BIPAF74AHDokW2hERERERKQgQxSX9d+tR+BQAOc8cQ5MJlPK68myZeGs352FQ185BP9+v4wR6td3v9tfED7xBJDGnxY2G/C73wFf+Qqwf7988RERERERkTKELy7/9+H/RfNTzTjnyXNgzkn/180/Px+jV43GPy7/B4IfGPs+0Icf7r8d9skngZyc9Nd3/vnAqlXA5ZcDH3yQ/vqIiIiIiEg5QheX3Ue6cezOY6h6qArW06wJfSbcFsbHD32MwDuBmMuUzSlD8ZeL8e6N7yLaF5UrXF05cgS4807goYeA005L7DNtbf3Lv/NO7GXmzAG+/GXgxhuBvj55YiUiIiIioswTurg8sugI8sbloWxuWcKfObroKN5f/D7+9fN/Dbvc6AdGo+vtLnz004/SDVOXFi0Cxo0D5s5N7jOLFwM///nwyz3wAPD228BPf5pWiEREREREpCBhi8vWv7SiY3cHzrj7DJjMiT0MKEUl+Hb4AACOyY5hl80dmYvTvnMaPl7zMXo9vWnHqyd/+Quwezdw992AOcEjKBoFduzo//fkycMvO3Ik8J3vAGvWAB5PerESEREREZEyhC0u/3X/v2ApsqB0VmnCn+n6RxciHf2vKimsLoy7/Gm3nYZoMIp/PTD8VU7R3H8/UFQEzJqV+Gf+8Q+go6P/39XV8Ze/7bb+GWQfeCClEImIiIiISGFCFpdd/+xCx6sdKL2uFGZr4r9i++52AIDFZYFj0vBXLgEgryoPBRcX4JPffoJwezjVcHXln/8EXn0VuO46wJrYY6wA+q90AoDLBUyaFH/5qirg4ouB3/4WaG9PKVQiIiIiIlKQkMVl8+ZmAEDRlUVJfa7jb/2X1gouLkj4VtrirxQj2h1F63OtyQWpU5s393+98srkPve3v/V/vfjixG+l/cpXgO5u4LnnktsWEREREREpT8jisuVPLQASu7V1gCRJ6NjTkfTnBgpY7397E/6Mnv3pT/1fE7m1dYAkAXv2JP+5gQL2v/878c8QEREREZE6TJIkSWoHEU+kJwLP4x40P92M7iPdMOeYYc41o/TrpRjxgxHILsweXDbcGsbe0r2wnmHF1IapMdfZ6+nFgQsPIBruf5VINBBFuKX/1lbrqE/v98xyZOG8t8+D2TJ0HS5FJexx7gGiwIUdF8ryLs14/vd/gW99q/91IGVlwMqVwMyZ/T/r6AD+8z+BZ57p/3c4DEybBvzkJ8D48f3LRCLApk1AXR3g9QJ+P3DWWcA99/RfWYyltRUoLQXOOANoaIi9nMcDXHhh/7YBIBAAWvrrfYwa9elyDkf/rLAWy9DriUYBp7P/a0eHPO/SJCIiIiKizND8lcv2Pe3Yf/Z+fHT/Rzj99tNxQcMFuOCDCzB5z2REuiJ4e/rbkCKf1sf+1/2ABDgmDv/MZE5ZDr5U/yVMbZiKqQ1Tcfp3TwcA5I7OHfze1IapmPLPKTELSwAwmU1wfN6BaE902HdjykWSgOuvB+66q7/AM5n6bx99/XXgzTeBSy4BCgr6n3H84APgr3/tv630/PP73y/p8fQXoocOAX/4A/Duu0B9fX/xdskln87oOpTXX+/f/sSJw8dYVta/zoaG/v+++93+748e/en3Ghr6n9+MVVgC/bfPfv7zQE/P8O/GJCIiIiIi9Wm6uGza1IR/zPgHTFkmnPv6uSj9Wulgodf+Sjs8mz0IHAyg6+2uwc90v9cNALCOTGK2GXw6mU/BRQVJx5l7Zi4AIHAw88XlX/7SP1PrpZf2F5ZjxvRfIfzpT4FbbgGefbZ/ptX8/P7lx43rX7a7G1i7Frj66v73Ta5ZA4wY0b9MXh5w4439VwjXrIm97ffe6/86cmRyMQ9M5nPRRcl9DgDOPLP/68GDyX+WiIiIiIiUM8x1I3W1/qUV7817D6YsE8558hxYy08uFo9+52j/bawmwFL86a8RfD8IAMipSPweymhvtP+KJ4DCiwqTjtU6oj+2wOHMF5fPPAPccMOn///++/1fd+0C9u8HKitP/UxeXv/XRx8FHnwQ+MY3Tl1mYObXjz6Kve2BbVVUJB5vb2//FU8gteJyoAA+fDj5zxIRERERkXI0eeUy1BjCezXvARJw+u2no+CCU68m5k/LR1Z+Fkb9ZBRslbbB74e9/Q/6WQoSr5s73+hENNj/7GXBhclfucwu7X/mc+CZzUzauRO44or+fwcCwFtv9f/7hz+MfbvqBx/0f506FbjjjqGX+d//7f9aNMwEu97/m7OoIIk/0Rtv9L+vEuh/DjNZpf/3mtKBZzaJiIiIiEibNHnl8oMffdBfJGYBI743YshlJv5x6Eoq0hUBAJhzk3+/ZbY7G3ln5SUXLIAsWxYAoK+jL+nPJiMaBX72s08LrldfBfr+b5MLFw79mWDw01tKa2pivwbktdf6v37uc7G33/V/dx/n5iYe88AtsW53/6RBybL937hBR0fynyUiIiIiIuVo7splb3PvSe+pzB2VRCUDDM7+arIk9p5KAGj/WzuA1K5aAoDZ1v9njHREUvp8wtsxA/Pmffr/L7/c/3X06NjPQb72Wv+tqUDs14AEAp/eujpjRuztD8z+OtwkPJ818H7LVK5aAiwuiYiIiIj0QnPFZevzrZD6+md/LZo5zD2aMWTl9V9FjPZEE1peikjw7+1/3jKVyXwAQAr3x5tMQSuHV17p/3rJJfGXOf10YOzYoZd57jkgFOp/7nLg3ZJDGXh2s6cnsfgiEWDv3v5/p/K8JZBaQUtERERERMpTpLg8dOgQXh64zBZH4NCnk+IUXJx8sZflTK647Hyrc/BW2lQm8wGASLD/81mOrJQ+n4rOTuDvf+//d6wrksCnVzeHK0D/67/6v86cOfzzlE5n/9dEi8u33vr0VtpUi8uB5zUdw79ZhoiIiIiIVJbx4lKSJFx22WW48sorERyoFIYRCXx6a6ntTNswSw5t4BUkAxP7xDPwvGWWIwuOL5xcwbS/2o7GDY1x1xHp7I85uyQ7iUjTc+LzlrEKx+7u/hlkh1umtbX/9SZA/+tIBvzP//S/q/JEA7feDkzsE8/A85YOB/CFL5z8s1dfBTZsiL+Ozs7+ryUliW2TiIiIiIjUkfHi8i9/+Qu8Xi96e3vxu9/9Lu7yA68QMWWbEprxteO1DvQ29w7+v21Mf0Ha83Fil9c6/tb/MF/+1HyYsk6+rfXD5R8i94z4z3yGjocAALmjk3s+NB0DVySrqvpveR3K3r2f3lYaq7h86qn+ZzILCoCvfvXT73/3u4Dff/KyY8b0f/3448RiHHjecupUIOszF3WXLwfOOCP+Oo4f7/86enRi2yQiIiIiInVktLiUJAn33HMP3G433G43Vq1aFffqZdHl/c9ZSmEJ4fbhrz52vN6Bw984jL72T2dpdXy+/+pjz4eJFZfB+v548i/IP+n7vh0+RINRuC5zxV3HQHGZNy72TLMNKxuwJ38PDkw/gL7O9GeVTeR5y4ECdNQo4Mwzh15my5b+r1//+qezwL77bv8kP1/84snLfv7z/V8//DCxGAeufF5wwcnf37Gj/3bXyy6Lv46B4nLcuMS2SURERERE6shocfmXv/wFb775Jr7whS9gxIgRaG5ujnv1smBaAQqm9z/41/LH2C83bFzfiMPXHcaEpyecVNQ5znXAbDej6x9dkKJS3Bizy/pvZR24nRYAwm1h1N9Rj7PXnx3388Cnz4l+tkAdEGoMoeEnDYh0RtDxtw40Phb/Vtvh+P2fvt9yuOctEylAfb7+rwPvzgT6ryquXHnqsueeC9jtwD/+0f9alHjKyvq/njiTbVtb/7s216+P/3kAOHSo/+tnC1QiIiIiItKWjBWXA1ctL7zwQlRUVMBms+Gmm25K6OrlOZvOQd7Zefjghx+g7ZW2we/3tvSicWMj3rrwLXif8eLcveei4N9OnoHGbDGj8OJCRANRdL/bHTfOigUVAIDu9/qXDbwXwMErD2LU3aNgn2CP+/nell6EPg4hd0wucspyhl7oM5PI+l7wxV3vcF59tX8mViB2cdndDbzxRv+/L7009rquvbb/ayjUv85Vq/q/zp596rIWC3Dxxf1XNd99N36cCxb0f33vvU+/XnklcPfdwIQJ8T/f0tJ/C+6YMZ8WqkREREREpE0ZKy737NmDN998E/fccw9Mpv7q6u6770ZzczM2b9487GdzR+Ti3P85F6d/93TU31aP1057Da+Pfh0HrziIwMEAqn5ZhUnbJ8V8B2bpN0oBAK3bW+PGWT6vHGN/Mxat21qxr3Ifjiw8gtE/G43ym8oT+j07dvc/s1k6qzTmMtZyKyr/XyWy8rNQeFkhQv8KJbTuWFyu/plbv/Md4LTThl5GkoARI4Dzzwe+9rXY6/qP/wAWLwZ+9KP+5zc/+QQYbvd84xv9X7dvjx/nvHnAb34DbNsGVFYCCxcCP/sZcNNN8T8LfDoh0KxZiS1PRERERETqMUmSFP/e0RR88skneO6553DzzTdjwYIFqK+vx6uvvoqnn34an/vc5zB+/PhMbBYA0NfRh9dOew3OLzox+W+TM7YdAHjvW++haWMTzn3jXOSfN/RtsScK+8L4x4x/4Ly3zstoXJnS0dFf0H7xi59O2JMp3/oWsHFj/xXY8/T55yIiIiIiMoyMXbk87bTTsGjRosGrlgO+8Y1vZLSwBABLgQUVCyvQ8WoHuo/GvzU2VZGeCFq2tcB5njOhwhIAehp6YD3DGn9BjSoo6L8C+eqrwNGjmdtOT0//Fc/zzmNhSURERESkBxl/FYlaRi4ZCbPVjP/9z//N2Da8/+VFn68PI384Mv7C/6f1+VYUzSzKWExKWLIEsFqB//zPzG3jv/6rf7KhH/4wc9sgIiIiIiL5CFtc5o7MxRk/PgOfPPoJej5K7LUkyZAiEv61+l9wnu9E6ddjP295omgoiubNzQkvr1UjRwI//jHw6KPARx/Jv/5IBFi9uv950a9/Xf71ExERERGR/IQtLgHgjB+dgbxxeTj2g2Oyr7tpYxO63+vGuEfHwWQ2xf8AgH898C+UzCqJPausjvzoR/3vnvzBD+Rf98aN/TPLPvooYBb6CCUiIiIiEofQqbs5x4zP/elzaH+lHY0b03u35Il6jvfg/aXvY/R9o+Gc7EzoM63Pt6L1z60YtXyUbHGoKScH+NOf+t+luXGjfOs9fhxYuhS47z5gcmbnYiIiIiIiIhkJXVwCgO1MGyZum4gPf/whOl7rSHt90XAU7859F8XXFOOMH52R8OdMFhM+9+znkGXLSjsGrTjzzP5Jd378Y+C119JfXzgMzJ0LXHNN/5VRIiIiIiLSD+GLSwAo+LcCTHphEo5+5ygigUjK65EkCe/VvIe8sXk4e/3ZSX226IoiWE/X7yyxsfzbvwEvvND/zs1AIPX1SBJQUwOMHQusXy9beEREREREpBCL2gEoxTHJgfMPnp/WOqLBKIquLEL5TeUyRSWGSZOAgwfTW0cwCFx5JXDTTfLEREREREREyjLElUu5ZOVlsbDMkLw8FpZERERERHrG4pKIiIiIiIjSxuKSiIiIiIiI0sbikoiIiIiIiNLG4pKIiIiIiIjSxuKSiIiIiIiI0sbikoiIiIiIiNLG4pKIiIiIiIjSxuKSiIiIiIiI0sbikoiIiIiIiNLG4pKIiIiIiIjSxuKSiIiIiIiI0sbikoiIiIiIiNLG4pKIiIiIiIjSxuKSiIiIiIiI0sbikoiIiIiIiNLG4pKIiIiIiIjSxuKSiIiIiIiI0sbikoiIiIiIiNLG4pKIiIiIiIjSxuKSiIiIiIiI0sbikoiIiIiIiNLG4pKIiIiIiIjSxuKSiIiIiIiI0sbikoiIiIiIiNLG4pKIiIiIiIjSxuKSiIiIiIiI0sbikoiIiIiIiNLG4pKIiIiIiIjSxuKSiIiIiIiI0sbikoiIiIiIiNLG4pKIiIiIiIjSxuKSiIiIiIiI0sbikoiIiIiIiNLG4pKIiIiIiIjSxuKSiIiIiIiI0sbikoiIiIiIiNLG4pKIiIiIiIjSxuKSiIiIiIiI0sbikoiIiIiIiNLG4pKIiIiIiIjSxuKSiIiIiIiI0sbikoiIiIiIiNLG4pKIiIiIiIjSxuKSiIiIiIiI0sbikoiIiIiIiNLG4pKIiIiIiIjSxuKSiIiIiIiI0sbikoiIiIiIiNLG4pKIiIiIiIjSxuKSiIiIiIiI0sbikoiIiIiIiNLG4pKIiIiIiIjSxuKSiIiIiIiI0sbikoiIiIiIiNJmUTsAudXX12P9+vVoaGhAZWUlFixYgLFjx6odFhERERGR4TFXF5tJkiQp0xv51re+hfr6erz66qsZ3c6GDRuwcOFCmEwmSJI0+LWurg41NTUZ3TYREREREcXGXF18whSX9fX1OPvssxGNRk/5mdlsxpEjR1BVVXXKZzhyQkRERESUnnh5dSq5OumPMM9crl+/HiaTacifmUwm1NXVnfS9DRs24Oyzz8bq1avx9NNPY/Xq1Tj77LOxceNGBaIlIiIiIhJDInl1srk66ZMwxWVDQwMGLsI6HA5UV1fD4XAAACRJQkNDw+Cy9fX1WLhwIaLRKCKRyElfa2trcezYMTV+BSIiIiIiXUk0r04mVyf9Eqa4rKysHBwNcTqdqK6uhtPpBNA/GlJZWTm4LEdOiIiIiIjSl2henUyuTvolTHG5YMECxHp8VJIk1NbWDv4/R06IiIiIiNKXaF6dTK5O+iVMcTl27FjU1dXBbDbDbO7/tQb+XVdXd9IDwhw5ISIiIiJKX6J5dTK5OumXMMUlANTU1ODIkSOYN28eAGDevHk4cuTIKVMbc+SEiIiIiCh9yeTViebqpF9CFZcAUFVVhaVLl2LixIlYunTpkKMgHDkhIiIiIkpfsnl1Irk66Zcw77lMxbFjx7B+/XpYrVaEQiEsWLCABzgRERERUZKYVxMgaHHZ19cHv9+P/Px8WCyWYZdta2vDyy+/jEsuuQQul0uR+IiIiIiIRJNoXp1Mrk76ItxtsQDg9Xqxdu1aeL3euMu6XC7Mnj2bhSURERERURoSzauTydVJX4QsLpPR19cHn8+Hvr4+tUMhIiIiItIt5tVk+OKSIydEREREROljXk2GLy6JiIiIiIgofSwuiYiIiIiIKG1CTs9UUVGBFStWqB0GERERERF9BnN1cfHKJREREREREaVNyPdctrS04E9/+hO++tWvoqSkRJFtEhERERFRfMzVxSXklctwOIzjx48jHA6rHQoREREREZ2Aubq4hCwuk9HS0oK6ujq0tLSoHQoRERERkW4xrybDF5ccOSEiIiIiSh/zahJytlijq6+vx/r169HQ0IDKykosWLAAY8eOVTssIiIiIsNjnkYiE7K4LCwsxKxZs1BYWKh2KIrbsGEDFi5cCJPJBEmSYDKZ8MADD6Curg41NTVqh0dERERkWMzT+hk5VxedkLfF2mw2TJo0CTabTe1QFFVfX4+FCxciGo0iEomc9LW2thbHjh1TO0QiIiIiQ2Ke9imj5upGIGRxGQgEsH//fgQCgbjLijRysn79ephMpiF/ZjKZUFdXp3BERERERAQYI09LNK9OJlcnfRGyuPT7/di+fTv8fn/cZUUaOWloaMDAa0sdDgeqq6vhcDgAAJIkoaGhQcXoiIiIiIzLCHlaonl1Mrk66YuQxWUyRBo5qaysHBwRczqdqK6uhtPpBNA/IlZZWalidERERETGZYQ8TaS8mlJj+OJSpJGTBQsWDI6IfZYkSaitrVU4IiIiIiICjJGniZRXU2oMX1yKZOzYsairq4PZbIbZ3L9rB/5dV1eHqqoqlSMkIiIiMibmaWQEQhaXOTk5GDNmDHJyctQORXE1NTU4cuQI5s2bBwCYN28ejhw5YqjprYmIiIi0iHlaPyPn6qIT8j2XxcXFmDt3rtphqKaqqgpLly7Fyy+/jEsuuQQul0vtkIiIiIgIzNMA5uoiE7K4jEajCIfDyM7OHrztIBZRR05cLhdmz56d8ufr6+uxfv16NDQ0oLKyEgsWLMDYsWNljJCIiIhIX+TKj9LN07Qq0bw6mVyd9MUkxXqyWEbf+ta3UF9fj1dffTXTmwIANDY2Yt26dbj55ptRUVGhyDa1pq+vD36/H/n5+bBYkhtD2LBhAxYuXAiTyQRJkga/1tXVGe62DSIiIiJA3vwonTxNBMzVxWX4oYJoNIpQKIRoNKp2KLLyer1Yu3YtvF5vUp+rr6/HwoULEY1GEYlETvpaW1uLY8eOZShiIiIiIm2SOz9KNU/TOlHzakqc4YtLj8eDVatWwePxqB2KJqxfv37wHUyfZTKZUFdXp3BEREREROpifpQY5tVk+OKSTtbQ0DD4DiaHw4Hq6mo4HA4A/e9gamhoUDE6IiIiIuUxPyJKDItLOkllZeXgyJzT6UR1dTWcTieA/pG5yspKFaMjIiIiUh7zI6LECFlcut1uLFmyBG63W+1QdGfBggWINceTJEmora1VOCIiIiIidTE/khdzdXEJWVxmZWXBbrcjKytL7VBUU1FRgRUrViQ9A9fYsWNRV1cHs9k8ODX0wL/r6upQVVWViXCJiIiINEvu/CjVPE0UzNXFJeSrSHw+H1588UVcccUVKCoqGnbZSCSCnp4e5Obm8gA/wbFjx7B+/XpYrVaEQiEsWLCAhSUREREZGvOj4SWaVyeTq5O+CHnlMhQK4ejRowiFQnGXFXXkpKWlBXV1dWhpaUnp81VVVVi6dCkmTpyIpUuXsuEkIiIiw5MrP0o3T9OqRPPqZHJ10hchi8tk+Hw+bN68GT6fT+1QZBUOh3H8+HGEw+GU1+FyuTB79my4XC4ZIyMiIiLSLznyIznyNC0SNa+mxBm+uOTISWx9fX3w+Xzo6+tTOxQiIiIiTWB+FBvzajJ8cUmxeb1erF27Fl6vV+1QiIiIiDSB+RFRbEIWl06nEzNnzhx8/xAREREREWkDc3VxWdQOIBMcDgemTp2qdhiqKiwsxKxZs1BYWKh2KERERER0AqPnaczVxSXklctgMIjDhw8jGAzGXVbUkRObzYZJkybBZrOpHQoRERERnUDUPC3RvDqZXJ30Rcjisr29HVu2bEF7e3vcZQdGThwOR+YDU1AgEMD+/fsRCATUDoWIiIiITiBqnpZoXp1Mrk76ImRxmQxRR078fj+2b98Ov9+f8joqKiqwYsUKVFRUyBgZERERkX7JkR/Jkadpkah5NSXO8MUlR06IiIiIiNLHvJoMX1xSbC0tLairq0NLS4vaoRARERFpAvMjotiELC4tFgvKy8thsQg5Ga5iwuEwjh8/jnA4rHYoRERERJrA/Ch9zNXFJeQeLS0txaJFi9QOQ1U5OTkYM2YMcnJy1A6FiIiIiE5g9DyNubq4hCwukyHqyElxcTHmzp2rdhhERERE9Bmi5mmi5tWUOCFvi21sbMTKlSvR2NgYd9mBkZPS0lIFIlNONBpFKBRCNBpVOxQiIiIiOoGoeVqieXUyuTrpi5DFJQBEIhG1Q1CVx+PBqlWr4PF4Ul5HYWEhZs2ahcLCQvkCIyIiItIxOfIjOfI0vTN6ri4qYYvLRHHkJDabzYZJkybBZrOpHQoRERGRJjA/io15NRm+uAQ4chJLIBDA/v37EQgE1A6FiIiISBOYHw2PebWxsbikmPx+P7Zv3w6/3692KERERESawPyIKDYhp3IqKSnBLbfcApfLpXYoRERERER0Aubq4hKyuMzOzobb7VY7DFW53W4sWbIEubm5aodCRERERCcwep7GXF1cQt4W297ejm3btqG9vT3usgMjJyUlJZkPTEFZWVmw2+3IyspSOxQiIiIiOoGoeVqieXUyuTrpi5DFZTAYxIEDBxAMBuMuOzBykp2drUBkyvH5fNi8eTN8Pl/K68jJycGYMWOQk5MjY2RERERE+iVHfiRHnqZFiebVyeTqpC9CFpfJEHXkJBQK4ejRowiFQimvo7i4GHPnzkVxcbGMkWVOfX09li1bhjlz5mDZsmWor69XOyQiIiKKQa/9thz5kRx5mhaJmldT4oR85jIZAyMn559/flovwxVRNBpFOBxGdnY2zGZtj0Ns2LABCxcuhMlkgiRJMJlMeOCBB1BXV4eamhq1wyMiIqIT6Lnf1lN+pDTm1cQzgmLyeDxYtWoVPB6P2qEMq76+HgsXLkQ0GkUkEjnpa21tLY4dO6Z2iERERPR/9N5v6yU/IlKDkMWl3W7HtGnTYLfb1Q6FFLB+/XqYTKYhf2YymVBXV6dwRERERBQL+21iri4uIYvL/Px8zJgxA/n5+WqHohqn04mZM2fC6XSqHUrGNTQ0QJIkAIDD4UB1dTUcDgcAQJIkNDQ0qBgdERERnYj9trHytKEwVxeXkMVlKBRCQ0NDQg9Jizpy4nA4MHXq1MHGWmSVlZWDI6BOpxPV1dWDjbXJZEJlZaWK0REREdGJ2G+Lm6clmlcnk6uTvghZXPp8Pjz++OMJTe8s6shJMBjE4cOHDTHF84IFCwZHQD9LkiTU1tYqHBERERHFwn5b3Dwt0bw6mVyd9EXI4jIZoo6ctLe3Y8uWLWlNBe12u7FkyRK43W75AsuAsWPHoq6uDmazeXDWtoF/19XVoaqqSuUIiYiIaIDe+2058iM58jQtEjWvpsQZvrjkyElsWVlZsNvtyMrKUjuUuGpqanDkyBHMmzcPADBv3jwcOXJE89OZExERGZGe+2095UdKY15Nhi8uKTafz4fNmzfrpoGoqqrC0qVLMXHiRCxdulTzI59ERERGptd+W2/5EZGShCwuzWYznE4nX2ybplAohKNHj+rq1gaXy4XZs2fD5XKpHQoRERHFocd+W4/5kdYwVxeXRe0AMqGsrAyLFy9WOwxVWSwWlJeXw2IRchfH1NfXB7/fj/z8fMP97kRERHpj1H7bqHnaAObq4jL8cIGoIyelpaVYtGgRSktL1Q5FUV6vF2vXroXX61U7FCIiIorDqP22qHmaqHk1JU7IPe/xePDggw/C4/HEXXZg5KSsrEyByIiIiIiIxJRoXp1Mrk76ImRxGY1G0dnZiWg0qnYoqmlsbMTKlSvR2NiY8jqcTidmzpw5+GJjIiIiIqOTIz+SI0/TM+bq4hKyuEyGyCMnkUgkrc87HA5MnToVDodDpoiIiIiI9E2u/CjdPE2LRM6rKTGGLy45chJbMBjE4cOHEQwG1Q6FiIiISBOYH8XGvJoMX1xSbO3t7diyZQva29vVDiVhFRUVWLFiBSoqKtQOhYiIiOLQY7+tx/yISClCFpdFRUWYP38+ioqK1A6FiIiIiIhOwFxdXEIWl1arFZWVlbBarWqHopqSkhLccsstKCkpUTsURbW0tKCurg4tLS1qh0JERERxGLXfNmqeNoC5uriELC79fj927twJv98fd1lRR06ys7PhdruRnZ2tdiiKCofDOH78OMLhsNqhEBERURxG7bdFzdMSzauTydVJX4QsLgOBAPbu3YtAIBB3WVFHTtrb27Ft27a0ngewWCwoLy+HxWKRLzAiIiIiHZMjP5IjT9OiRPPqZHJ10hchi8tkiDpyEgwGceDAgbRmMistLcWiRYtQWloqY2TiqK+vx7JlyzBnzhwsW7YM9fX1aodERESUMvZriZEjP5IjT9MiUfNqSpzhL0kNjJxMmDAB+fn5aodDOrFhwwYsXLgQJpMJkiTBZDLhgQceQF1dHWpqatQOj4iIKCns10gOzKvJ8FcuKbbGxkasXLkSjY2NaoeSsMLCQsyaNQuFhYUZ20Z9fT0WLlyIaDSKSCRy0tfa2locO3YsY9smIiKSm5r9mhL9ttz0mB8RKUXI4tJms2Hy5Mmw2Wxqh6J7kUhE7RCSYrPZMGnSpIzu+/Xr18NkMg35M5PJhLq6uoxtm4iISG5q9mtK9NuZoLf8SGuYq4tLyOKysLAQ1157ra5GweRmt9sxbdo02O12tUNRVCAQwP79+zP6gHhDQwMkSQIAOBwOVFdXw+FwAAAkSUJDQ0PGtk1ERCQ3Nfs1JfptLTJqnjaAubq4hCwuw+EwmpubE5rWWtSRk/z8fMyYMcNw97v7/X5s3749ow+SV1ZWDo7wOp1OVFdXw+l0Augf4a2srMzYtomIiOSmZr+mRL+tRaLmaYnm1cnk6qQvQhaXLS0teOSRRxJ6Ia+oIyehUAgNDQ0IhUJqhyKcBQsWDI7wfpYkSaitrVU4IiIiotSxX1OeqHlaonl1Mrk66YuQxWUyRB058fl8ePzxx+Hz+VJeR0lJCW655RaUlJTIGJn+jR07FnV1dTCbzTCb+0+hgX/X1dWhqqpK5QiJiIgSx34tOXLkR3LkaVokal5NiTN8ccmRk9iys7PhdruRnZ2tdiiaU1NTgyNHjmDevHkAgHnz5uHIkSOcrp2IiHSJ/VrimB/FxryaDP+eS4qtvb0df/vb33DxxRfr5rbhnJwcjBkzBjk5ORnfVlVVFZYuXYqXX34Zl1xyCVwuV8a3SURElClq9GtK9tty0WN+RKQUYa9cZmVlqR2C7gWDQRw4cADBYFDtUBJWXFyMuXPnori4WJHtuVwuzJ49m4UlEREJQel+Tel+Ww56zI+0iLm6mIS8cllRUYHly5erHYaqzGYznE7n4LMTRhGNRhEOh5Gdna3I797X1we/34/8/HxYLEKeTkREZCBK92tK99taYdQ8bQBzdXEZ84j+DBFHTsrKyrB48WKUlZWpHYqiPB4PVq1aBY/Ho8j2vF4v1q5dC6/Xq8j2iIiIMknpfk3pflsrRM7TRMyrKXFCFpderxePPvpoQg3jwMhJRUWFApEREREREYkp0bw6mVyd9EXI4rKvrw9NTU3o6+tTOxTVeDwePPjgg2mNBNrtdkybNg12u13GyIiIiIj0S478SI48Tc+Yq4tLyOIyGaKOnESjUXR2diIajaa8jvz8fMyYMQP5+fkyRkZERESkX3LkR3LkaVokal5NiTN8ccmRk9hCoRAaGhoQCoXUDoWIiIhIE5gfxca8mgxfXFJsPp8Pjz/+OHw+n9qhJMztdmPJkiVwu92KbK+iogIrVqzgM7tERCQEpfs1pfttOegxPyJSipDvTigsLMR1113HF9saUFZWFp8RJSIi0gn228bEXF1cQl65tNlsmDBhAmw2m9qhqKaoqAjz589HUVGR2qEoyufzYfPmzYqNJra0tKCurg4tLS2KbI+IiCiTlO7XlO63tcKoedoA5uriErK47Orqwr59+9DV1RV3WVFHTqxWKyorK2G1WtUORVGhUAhHjx5V7DmIcDiM48ePIxwOK7I9IiKiTFK6X1O639YKUfO0RPPqZHJ10hchi8vOzk7s2LEDnZ2dcZcVdeTE7/dj586d8Pv9Ka/DbDbD6XTCbBbyMCEiIiJKmhz5kRx5mhYlmlcnk6uTvhi+ahB15CQQCGDv3r0IBAIpr6OsrAyLFy9GWVmZjJERERER6Zcc+ZEceZoWiZpXU+IMX1xy5ISIiIiIKH3Mq8nwxSXF5vF48OCDD8Lj8agdSsKcTidmzpwJp9OpyPYKCwsxa9Ys4Z7ZJSIiY1K6X1O635aDHvMjIqUI+SoSq9WKcePGCfeQtNKi0Sg6OzsRjUbVDiVhDocDU6dOVWx7NpsNkyZNUmx7REREmaR0v6Z0vy0HPeZHWsNcXVxCXrksKirCnDlzDDu9M9DfOUyePFm4iYriCQaDOHz4MILBoCLbCwQC2L9/v3DPTBARkTEp3a8p3W9rhVHztAHM1cUlZHEZiUQQCAQQiUTiLivqyElhYSGuvfZaw92u2d7eji1btqC9vV2R7fn9fmzfvl242d6IiMiYlO7XlO63tULUPC3RvDqZXJ30Rcjisrm5GWvWrEFzc3PcZUUdOQmHw2hubub7FwVXX1+PZcuWYc6cOVi2bBnq6+vVDomIiJLEttx4RM3TEs2rk8nVSV+ELC6TIerISUtLCx555BG0tLSkvI6ioiLMnz9fuMJbFBs2bMDZZ5+N1atX4+mnn8bq1atx9tlnY+PGjWqHRkRECWJbrj9y5Edy5GlaJGpeTYkzfHHJkZPYrFYrKisrhbtlWAT19fVYuHAhotEoIpHISV9ra2tx7NgxtUMkIqI42JbrE/Oj2JhXk+GLS4rN7/dj586dunqe0GKxoLy8HBaLMhMh5+TkYMyYMcjJyVFkewPWr18Pk8k05M9MJhPq6uoUjYeIiJKnxbZc6X5N6X5bDnrMj4iUwuKSYgoEAti7d6+uZkItLS3FokWLUFpaqsj2iouLMXfuXBQXFyuyvQENDQ2QJAlA/zTu1dXVcDgcAABJktDQ0KBoPERElDwttuVK92tK99ty0GN+RKQUIYvLsrIy3HXXXSgrK1M7FFVlZWWpHYLwotEoQqGQ4u+6qqysHBztdjqdqK6uHnwBtclkQmVlpaLxEBFR8rTYlqvVrxmRkfM05uriErK4NJvNsFqtMJuF/PUSUlFRgeXLl6OiokLtUBTV2NiIlStXorGxUZHteTwerFq1Ch6PR5HtDViwYMHgaPdnSZKE2tpaReMhIqLkabEtV7pfU7rf1gqj5mkDmKuLS8g92traik2bNqG1tTXushw5EY8RZigbO3Ys6urqYDabBxvmgX/X1dWhqqpK5QiJiCgetuX9jNBvG0WieXUyuTrpi5DFZW9vL95//3309vbGXVbUkROv14tHH30UXq835XXYbDZMnjwZNptNxshILjU1NThy5AjmzZsHAJg3bx6OHDmCmpoadQMjIqKEsS3XHznyIznyNC1KNK9OJlcnfdHP1FwZ0traiu3bt+Oqq65SfFKWTOrr60NTUxP6+vpSXkdhYSGuvfZaGaMiuVVVVWHp0qV4+eWXcckll8DlcqkdEhERJYltub7IkR/Jkadpkah5NSXO8MUlR05iC4fDaGtrg8vlQnZ2ttrhUAwulwuzZ89WOwwiIkoD23L9YH4UG/NqEuteUJJVS0sLHnnkEbS0tKgdSsJKSkpwyy23oKSkRJHtud1uLFmyBG63W5HtDaWvrw8+n0+40U8iIiPRSluudL+mdL8tBz3mR0RKEbK4zM/Px1VXXYX8/Hy1QyGFZWdnw+12KzaSmJWVBbvdrup04l6vF2vXrhXuuQ0iIiPRSluudL+mdL9N2sBcXVxCFpd2ux1TpkyB3W5XOxTVFBYW4rrrrkNhYaHaoSiqvb0d27ZtQ3t7uyLb8/l82Lx5M3w+nyLbIyIiyiSl+zWl+22tMGqeNoC5uriELC6DwSAOHjyIYDAYd1lRR05sNhsmTJhguJleg8EgDhw4kNC+l0MoFMLRo0cRCoUU2R4REVEmKd2vKd1va4WoeVqieXUyuTrpi5DFZXt7O7Zu3ZrQKJioIyddXV3Yt28furq60lqPmrd7EhEREWlRuvmRXHma1iSaVyeTq5O+CFlcJkPUkZPOzk7s2LEDnZ2dKa+joqICy5cvR0VFhYyREREREemXHPmRHHmaFomaV1PiDF9ccuSE9K6iogIrVqzgIAARkY6xLScRMK8mwxeXFJvX68Wjjz6q+sx1ybDb7Zg2bZpitzk7nU7MnDkTTqdTke0RERFlktL9mtL9thz0mB8RKUXI4jI7OxsjRozgtNZp6uvrQ1NTk+rv3EpGfn4+ZsyYodgETQ6HA1OnToXD4VBke0NpaWlBXV0d37dFRKRjWmnLle7XlO635aDH/EhrmKuLS8jisqSkBLW1tbp6Ia/crFYrxo0bB6vVqnYoigqFQmhoaFB0lrvDhw+r+mxBOBzG8ePHEQ6HVYuBiIjSo5W2XOl+Tel+WyuMmqcNYK4uLiGLy2SIOnJSVFSEOXPmoKioSO1QFOXz+fD4448r+n6uLVu28NkCIiISgtL9mtL9tlaImqeJmldT4oQsLhsbG3HvvfeisbEx7rKijpxEIhEEAgFEIhG1QyEiIiKiE4iapyWaVyeTq5O+CFlcEtDc3Iw1a9agubk55XUUFhbiuuuuQ2FhoXyBEREREemYHPmRHHkakRYZvrjkyElsNpsNEyZMgM1mUzsUGkZhYSFmzZrFQQAiIh1jW64fzI9iY15Nhi8uKbauri7s27cPXV1daoeSMLPZDKfTCbNZmUPbYrGgvLwcFotFke0NxWazYdKkSezkiIh0TCttudL9mtL9thz0mB8RKUU/ZzIprrOzEzt27EBnZ6faoSSsrKwMixcvRllZmSLbKy0txaJFi1BaWqrI9oYSCASwf/9+BAIB1WIgIqL0aKUtV7pfU7rfloMe8yMipQhZXJaWluL2229XNeEnUorf78f27dvh9/vVDoWIiFLEtpyMhLm6uIQsLi0WC4qKilS9VVFtZWVluOuuu3Q1EigHj8eDBx98EB6PR5HtNTY2YuXKlXy2gIiIhKB0v6Z0v60VRs3TBjBXF5eQxWVbWxueffZZtLW1xV1W1JETs9kMq9Wqq2cY5BCNRtHZ2YloNKrYNkWbRpyIiIxNyX5NjX5bC0TN0xLNq5PJ1UlfxDqi/09PTw8OHTqEnp6euMuKOnLS2tqKTZs2obW1NeV1WK1WjBs3DlarVcbIiIiIiPRLjvxIjjxNixLNq5PJ1UlfxKqoUtDW1oaXX34Zl1xyCVwul9rhyKa3txfvv/8+ent7U15HUVER5syZI2NUlAk5OTkYM2YMcnJy1A7lFPX19Vi/fj0aGhpQWVmJBQsWYOzYsWqHRUQGpPX2SMttOZ1MjvxIjjxNi0TNqylxhi8uB0ZOpk6dqnYomhOJRNDT04Pc3FxkZWWpHQ7FUFxcjLlz56odxik2bNiAhQsXwmQyQZIkmEwmPPDAA6irq0NNTY3a4RGRgeihPdJqW06nYn4UG/NqEvK2WJJHc3Mz1qxZg+bmZrVDSVhRURHmz5+PoqIiRbZXUlKCW265BSUlJYpsbyjRaBShUEhTz6vU19dj4cKFiEajiEQiJ32tra3FsWPH1A6RiAxCL+2RVtpypfs1pfttOegxPyJSipDFpcPhwPTp0+FwONQOhRRmtVpRWVmp2HOi2dnZcLvdyM7OVmR7Q/F4PFi1apWmZtpbv349TCbTkD8zmUyoq6tTOCIiMiq9tEdaacuV7teU7rdJG5iri0vI4tLpdKK6uhpOp1PtUFSTn5+Pq666Cvn5+WqHoii/34+dO3cq9p6w9vZ2bNu2De3t7YpsTy8aGhogSRKA/g6kurp6sAORJAkNDQ0qRkdERsL2KDlK92tK99taYdQ8bQBzdXEJWVyGQiEcO3YMoVAo7rKijpzY7XZMmTIFdrtd7VAUFQgEsHfvXgQCAUW2FwwGceDAAQSDQUW2pxeVlZWDVwo+24GYTCZUVlaqGB0RGQnbo+Qo3a8p3W9rhah5WqJ5dTK5OumLkMWlz+fDk08+CZ/PF3dZUUdOgsEgDh48yKKHVLFgwYLBKwWfJUkSamtrFY6IiIyK7RFpkah5WqJ5dTK5OumLkMVlMkQdOWlvb8fWrVvTuq2lrKwMd911F8rKyuQLjAxh7NixqKurg9lsHnxB9MC/6+rqUFVVpXKERGQUbI9IbnLkR3LkaVokal5NiTN8ccmRk9jMZjOsVutgZ0za5Ha7sWTJErjdbrVDOUlNTQ2OHDmCefPmAQDmzZuHI0eOaGbafyIyDj20R1pty+lUzI9iY15NPCsoptbWVmzatAmtra1qh5Iwm82GyZMnw2azKbI9u92OadOmqfrMRFZWFux2uybftVVVVYWlS5di4sSJWLp0Ka8QEJFqtN4eaaUtV7pfU7rfloMe8yMipQhZXGZlZcHlcqneQOtdb28v3n//ffT29qodSsIKCwtx7bXXorCwUJHt5efnY8aMGarO9ubz+bB582bNjhK6XC7Mnj0bLpdL7VCIyOC03B5ppS1Xul9Tut+Wgx7zI61hri4uIYtLt9uNO+64w9C3lmRnZ2PEiBGqvn9RDeFwGM3NzQiHw4psLxQKoaGhQdVnC0KhEI4eParZ5xv6+vrg8/nQ19endihEZHBabo+00pYr3a8p3W9rhVHztAHM1cUlZHGZDFFHTkpKSlBbW4uSkhK1Q1FUS0sLHnnkEbS0tCiyPZ/Ph8cff1z1kWYt83q9WLt2Lbxer9qhEJHBsT2KT+l+Tel+WytEzdNEzaspcUIWlx6PB6tXr4bH44m7LEdOiIiIiIjSl2henUyuTvoiZHEZjUbR3d2NaDSqdiiqaWxsxL333ovGxsaU15Gfn4+rrrpK1ecJiYiIiLREjvxIjjxNz5iri0vI4jIZHDmJzW63Y8qUKarOhErxOZ1OzJw5M+4Li4mISLvYlusH86PYmFeTRe0A1MaRk9iCwSDq6+sxduxYXU0RruR9/mazGU6nU9V3XTkcDkydOlW17auhvr4e69evR0NDAyorK7FgwQKMHTtW7bCISAZGPb+10par0a/p7fk8veZHSmBeTYYvLim29vZ2bN26FTfffLNuGs+KigosX75cse2VlZVh8eLFim1vKMFgEB988AFGjx6tyf1UUVGBFStWyLa+DRs2YOHChTCZTJAkCSaTCQ888ADq6uo09UJ0Ikpeps9vudsjOWmlLVe6X1O635aDHvMjIqUIeVtscXExFixYgOLiYrVDIcq49vZ2bNmyBe3t7WqHknH19fVYuHAhotEoIpHISV9ra2tx7NgxtUMkohQZ/fw2UltOxFxdXEIWlzk5ORg5ciRycnLUDkU1paWluP3221FaWqp2KIryer149NFHFZtm3uPx4MEHH+SzBcNoaWlBXV2dLNPMr1+/HiaTacifmUwm1NXVpb0NIlKHEue3nO2RqJTu15Tut7XCqHnaAObq4hKyuPT7/XjxxRfh9/vjLivqyInFYkFRUREsFmPd+dzX14empibFXpAdjUbR2dnJZwuGEQ6Hcfz4cVlekN3Q0ABJkgD0P59UXV0Nh8MBAJAkCQ0NDWlvg4jUocT5LWd7JCql+zWl+22tEDVPSzSvTiZXJ30RsrgMBAJ4/fXXEQgE4i4r6shJW1sbnn32WbS1taW8juzsbIwYMQLZ2dkyRkaUusrKysErG06nE9XV1YMzK5pMJlRWVqoYHRGlg+c36YUc+ZEceZoWJZpXJ5Ork74IWVwmQ9SRk56eHhw6dAg9PT0pr6OkpAS1tbUoKSmRMTKSm8ViQXl5uXCjn0NZsGDB4JWNz5IkCbW1tQpHRERyMfr5baS2XO/kyI/kyNO0SNS8mhJn+OKSIyekd6WlpVi0aJEhntsYO3Ys6urqYDabB6fJH/h3XV0dqqqqVI6QiFJl9PPbSG05iYt5NRm+uKTYGhsbce+996KxsVHtUBJWWFiI6667DoWFhYpsr6ioCPPnz0dRUZEi29OjwsJCzJo1S7Z9UlNTgyNHjmDevHkAgHnz5uHIkSN8DQmRADJ9fsvdHolI6X5N6X5bDnrMj4iUIuS9F3l5eTjvvPOQl5endiikMJvNhgkTJii2PavVqvpzQI2Njairq0NtbS0qKipUjWUoNpsNkyZNknWdVVVVWLp0KV5++WVccsklcLlcsq6fiNSTyfM7E+2RXLTSlivdryndb5M2MFcXl5BXLgsKCnD11VejoKBA7VBU43A4MH369MGZ9oyiq6sL+/btQ1dXlyLb8/v92Llzp+rPFkQiEVW3P5xAIID9+/fLfouMy+XC7NmzWVgSCShT53em2iO5aKEtV7pfU7rf1gqj5mkDmKuLS8jiMhwOo7GxMaGpxkUdOfnsTHtG0dnZiR07dqCzs1OR7QUCAezdu1eziYoW+P1+bN++XfZEpa+vDz6fz3DT1xMZQabO70y1RyJRul9Tut/WClHztETz6mRyddIXIYvLlpYWrFu3LqGXJIs6chIKhXDs2DGEQiG1QyHKCK/Xi7Vr1xruxdtERsDzm0Qnap6WaF6dTK5O+iJkcZkMUUdOfD4fnnzySfh8vpTXUVpaittvv50z1xERERH9HznyIznyNC0SNa+mxBm+uOTISWwWiwVFRUV855bGlZSU4JZbbuH7SImIdIxtuX4wP4qNeTUZvrik2Nra2vDss8+ira1N7VASZrVaMW7cOFitVkW2Z7PZMHnyZNhsNkW2N5Ts7Gy43W5kZ2erFsNwcnJyMGbMGOTk5KgdChEZnJbbI6205Ur3a0r323LQY35EpBQhi0uTyYScnByYTCa1Q9G1np4eHDp0CD09PWqHkrCioiLMmTNH0fdzXXvttaq+n6u9vR3btm1De3u7ajEMp7i4GHPnzkVxcbHaoRCRwWm5PdJKW650v6Z0vy0HPeZHWsNcXVxCFpfl5eVYtmwZysvL1Q5FNVlZWXC5XMjKylI7FEVFIhEEAgHFpnMPh8Nobm5W9dmCYDCIAwcOIBgMqhbDcKLRKEKhEKLRqKzrraiowIoVKzT5bk8iSk+mzu9MtUdy0EpbrnS/pnS/rRVGzdMGMFcXl5DFZTJEHTlxu92444474Ha71Q5FUc3NzVizZg2am5sV2V5LSwseeeQRPlswDI/Hg1WrVsHj8agdChEZHNuj+JTu15Tut7VC1DxN1LyaEidkcen1evHwww8nNIU5R06I9KmlpQV1dXUs7IkExPObSJ8SzauTydVJX4QsLvv6+uD1eg39cnWPx4PVq1enNTrrcDgwffp0OBwOGSMjkkc4HMbx48c53TmRgHh+k5bJkR/JkafpGXN1cQlZXCZD1JGTaDSK7u7utJ4rcTqdqK6uhtPplDEykpvdbse0adNgt9vVDoWIiFLEtlw/5MiP5MjTtEjUvJoSZ/jikiMnsYVCIRw7dgyhUEjtUDRN7Yfx8/PzMWPGDOTn56saBxERpU5Lbbna/ZrWMT+KjXk1Gb64pNh8Ph+efPJJ+Hw+tUNJWFlZGe666y6UlZUpsr2KigosX75c1RlLQ6EQGhoaNNvJud1uLFmyRLhJC4hIf7TcHmmlLVe6X1O635aDHvMjIqUIWVy6XC7ccMMNcLlcaodCCjObzbBarTCbhTy0h+Tz+fD4449rtpPLysqC3W6XfSS8sLAQs2bNUvUdo0SUGZk6vzPVHslB6215phix3ybm6iIT8kzOzc3FWWedhdzcXLVDUU1xcTEWLFigyRdFZ1Jrays2bdqE1tZWRbbn9Xrx6KOP8tmCYfh8PmzevFn2hMlms2HSpEmw2WyyrpeI1Jep8ztT7ZFIlO7XlO63tcKoedoA5uriErK47Orqwp49e9DV1RV3WVFHTnJycjBy5Ejk5OSoHYqient78f7776O3t1eR7fX19aGpqYnPFgwjFArh6NGjst/qFQgEsH//fgQCAVnXS0Tqy9T5nan2SCRK92tK99taIWqelmhenUyuTvoiZHHZ2dmJXbt2obOzM+6yoo6c+P1+vPjii/D7/SmvIysrCy6XS5O3DxH5/X5s3749rWOciLSJ5zdpmRz5kRx5mhYlmlcnk6uTvljUDkBtXV1dOHDgACZPnizU+xwDgQBef/11TJo0KeWZ59xuN+644w6ZIyO5mc1mOJ1OPq+iQ/X19Vi/fj0aGhpQWVmJBQsWYOzYsWqHRTrF40nf2Jbrhxz5kRx5mhaJmldT4gxfXA6MnFRVVfEkIF0qKyvD4sWL1Q6DkrRhwwYsXLgQJpMJkiTBZDLhgQceQF1dHWpqatQOj3SGx5P+sS0nETCvJg6PUUwejwerV6+Gx+NRO5SE5efn46qrrlJsFLCwsBDXXXcdZywdhtPpxMyZM9N62bRo6uvrsXDhQkSjUUQikZO+1tbW4tixY2qHSDrC4ylxbI/iU7pfU7rfloMe8yMipQhZXObm5mL8+PHCPUeptGg0iu7ubkSjUbVDSZjdbseUKVNgt9sV2Z7NZsOECRNUnbHU4/HgwQcf1Gwn53A4MHXqVNlHMHNycjBmzBhdToawfv16mEymIX9mMplQV1encESkZyIeT5k6vzPVHslBK2250v2a0v22HPSYH2kNc3VxCVlculwuXH/99cLNAJuMvLw8nHfeecjLy1M7FEUFg0EcPHgQwWBQke11dXVh3759qs52Fo1G0dnZqdlOLhgM4vDhw7Lvk+LiYsydO1eX07g3NDRAkiQA/cludXX1YLIrSRIaGhpUjI70RsTjKVPnd6baIzlopS1Xul9Tut/WCqPmaQOYq4tLyOIyEonA7/cjEonEXVbUkZOCggJcffXVKCgoUDsURbW3t2Pr1q1ob29XZHudnZ3YsWMHZzsbRnt7O7Zs2SL7PolGowiFQqonYqmorKwcvNLkdDpRXV09eJueyWRCZWVlzM/W19dj2bJlmDNnDpYtW4b6+nolQiaFJbOf0zmetCpT53em2iORKN2vKd1va4WoeVqieXUyuTrpi5DFZXNzMx566CE0NzfHXVbUkZNwOIzGxkaEw2G1QyHKCI/Hg1WrVql+C1kqFixYMHil6bMkSUJtbe2QP9uwYQPOPvtsrF69Gk8//TRWr16Ns88+Gxs3bsxgtKS0ZPdzqseTlun5/CZKhKh5WqJ5dTK5OumLkMVlMkQdOWlpacG6devQ0tKS8jqKi4uxYMECXd52SKRlY8eORV1dHcxm8+BrBwb+XVdXh6qqqlM+w0lbjCGV/ZzK8UREqZMjP5IjT9MiUfNqSpzhi0uOnMSWk5ODkSNH6nLCFCMpKirC/PnzUVRUpHYolISamhocOXIE8+bNAwDMmzcPR44cifnaCBEnbaFTpbqfkz2eSHvYlusH86PYmFeT4YtLis3v9+PFF1+E3+9XO5SEZWdnY8SIEcjOzlZke1arFePGjYPValVke7FiqKysVDWG4VgsFpSXl8NiMfxrdU9RVVWFpUuXYuLEiVi6dOmwV5hEnLSFTpXOfk7meDIqLbdHWmnLle7XlO635aDH/IhIKSwuKaZAIIDXX38dgUBA7VASVlJSgtraWpSUlCiyvaKiIsyZM0fVkWa/34+dO3dqtpMrLS3FokWLUFpaqnYomuRyuTB79uy4z6eIOGkLnSrd/Zzo8WRUWm6PtNKWK92vKd1vy0GP+RGRUoQsLsvLy3H33XejvLxc7VBUYzKZkJOTE/P2KpJHJBJBIBBQ9dmCQCCAvXv3Gq6Tc7vdWLJkCdxut9qhpKWvrw8+nw99fX3DLifipC10qnT3c6LHk9aJcn4nQyttuRb6NSMwep7GXF1cQhaXJpMJFovFsCcs0H/SLlu2zHAnbWNjI+699140NjYqsr3m5masWbOGzxYMo7GxEStXrpR9n2RlZcFutyMrK0vW9SrN6/Vi7dq18Hq9wy7HSVuMId39nOjxpHWZOr8z1R6JROl+Tel+WyuMmqcNYK4uLiGLy9bWVmzcuBGtra1xl+XICVHmZWIE3OfzYfPmzfD5fLKvW6s4aYsxcD9n9vzmFTmizEk0r04mVyd9EbK47O3txUcffYTe3t64y4o6cuL1evHwww+nNXqdl5eH8847D3l5eTJGRiSPUCiEo0ePIhQKqR2KojhpizEYfT8b9fwmfZAjP5IjT9OiRPPqZHJ10hchi8tkiDpy0tfXB6/Xm9ZzNwUFBbj66qtRUFAgY2QkN5vNhsmTJ8Nms6kdCimEk7YYA/ezsbAt1w858iM58jQtEjWvpsQZvrjkyEls4XAYjY2NCIfDaodCwygsLMS1116LwsJCtUMhhYgyaQsNj/vZWNiW6wfzo9iYV5Phi0uKraWlBevWrUNLS4vaoSSstLQUt99+u2LTzJeVleGuu+5CWVmZItsbSjgcRnNzs2Y7uZKSEtxyyy26mmZeSRUVFVixYgUqKioS/owok7YMpb6+HsuWLcOcOXOwbNky1NfXp7WcnqWyn1M5noxEy+2RVtpypfs1pfttOegxPyJSipDFZUFBAa655hrezmlAFosFRUVFir0g22w2w2q1Ds7qqIaWlhY88sgjmu3ksrOz4Xa7ZX9BttPpxMyZMwffAUj6t2HDBpx99tlYvXo1nn76aaxevRpnn302Nm7cmNJypF+ZOr8z1R7JQSttudL9mtL9NmkDc3VxCVlc5uXl4dxzzzX0RDQulws33HCD4Z7VaWtrw7PPPou2tjZFttfa2opNmzbx2YJhtLe3Y9u2bWhvb5d1vQ6HA1OnToXD4ZB1vUpraWlBXV2d6gml2urr67Fw4UJEo1FEIpGTvtbW1uLYsWNJLWdUohxPmTq/M9UeiUTpfk3pflsrjJqnDWCuLi4hi8vu7m689dZb6O7ujrusqCMnubm5OOuss5Cbm6t2KIrq6enBoUOH0NPTo8j2ent78f777/PZgmEEg0EcOHAAwWBQ9vUePnxY9vUqLRwO4/jx46rfCqe29evXx5xd0GQyoa6uLqnljEqU4ylT53em2iORKN2vKd1va4WoeVqieXUyuTrpi5DFZUdHB5577jl0dHTEXVbUkZOuri7s2bMHXV1dKa/DZDIhJydHuNe0kBja29uxZcsWXoEQRENDAyRJAtB/1aq6unrwqpUkSWhoaEhqOdI3nt+kZXLkR3LkaVqUaF6dTK5O+iJkcZkMUUdOOjs7sWvXLnR2dqa8jvLycixbtizui3BJfVlZWWqHQAoScdKWysrKwUTN6XSiurp68Hk7k8mEysrKpJYTgYj7mYbHtlwf5MiP5MjTtEjUvJoSZ/jikiMnpHcVFRVYvnw5E1DStQULFgxekfwsSZJQW1ub1HJEesO2nETAvJoMX1xSbF6vFw8//LCuXnfgcDgwffp0xSZ5yc/Px1VXXYX8/HxFtqdHdrsd06ZNg91uVzsUTSosLMSsWbOSeredKJO2nGjs2LGoq6uD2WwenKVy4N91dXWoqqpKajkRpLKfUzmejITtUXxK92tK99ty0GN+RKQUIYvLnJwcjBo1Cjk5OWqHomt9fX3wer26eoH3Z2+TyzS73Y4pU6aomqh4vV48+uijmu3k8vPzMWPGDNkTFYvFgvLyct1PX2+z2TBp0iTYbLaEPyPKpC2fVVNTgyNHjmDevHkAgHnz5uHIkSOoqalJaTm9S2U/p3I8aVGmzu9MtUdy0EpbrnS/pnS/LQc95kdaw1xdXEIWl8XFxaipqUFxcbHaoagmNzcX48ePF24WsnhCoRCOHTuGUCikyPaCwSAOHjyo6syDfX19aGpq0mwnFwqF0NDQIPs+KS0txaJFi3T14u2hBAIB7N+/H4FAQO1QNKGqqgpLly7FxIkTsXTp0phXIhNdzmhEOZ4ydX5nqj2Sg1bacqX7NaX7ba0wap42gLm6uIQsLiVJQl9fX8znck4k6siJy+XC9ddfb7j3J/l8Pjz55JPw+XyKbK+9vR1bt27ljIbD8Pl8ePzxxxXbJ3rj9/uxfft2+P1+tUPRDJfLhdmzZ8dtvxJdzkh4PA2P7VF8SvdrSvfbWiFqnpZoXp1Mrk76ImRx2dTUhPvuuw9NTU1xlxV15CQSicDv9yMSiagdClFGNDY2YuXKlWhsbFQ7FJJZX18ffD5f3Cs4iS5H+sPzm0Qnap6WaF6dTK5O+iJkcZkMUUdOmpub8dBDD6G5uTnldbhcLtxwww3CjaqROETrlBMl+qQtXq8Xa9eujfvsWaLL6ZXo+zkeo57fpH1y5Edy5GlaJGpeTYkzfHHJkZPYcnNzcdZZZxn2eQC9KCwsxHXXXWfYBNSIRJm0hYbH/WwsbMv1g/lRbMyryfDFJcXW1dWFPXv2oKurS+1QEpaVlQWXy6XYi6izs7MxYsQIZGdnK7K9odhsNkyYMEGzCajZbIbT6Rx8bQSdLCcnB2PGjEnquW9RJm2h4aWyn1M5noxEy+2RVtpypfs1pfttOegxPyJSivZaV9KMzs5O7Nq1C52dnWqHkjC324077rgDbrdbke2VlJSgtrYWJSUlimxvKF1dXdi3b59mO7mysjIsXrwYZWVlaoeiScXFxZg7d25Sz31z0hZjSGU/p3I8GYmW2yOttOVK92tK99ty0GN+RKQUIYtLt9uNO++8U1cNFVGqOjs7sWPHDsN1ciUlJbjllltULezlEI1GEQqFEI1G1Q6FBCDK8STK+Z0Mo7blZEzM1cUlZHGZlZWF/Px8Xd1iIbfy8nLcfffdKC8vVzsURXk8HqxevRoej0eR7TU2NuLee+/ljIbD8Hg8ePDBB2XfJ9nZ2XC73arekiwHj8eDVatWKXbM6kFFRQVWrFiBiooKWZYzElGOp0yd35lqj0SidL+mdL+tFUbN0wYwVxeXkMVlW1sbnnnmGbS1tcVdVtSRE5PJBIvFApPJpHYoiopGo+ju7tb9qL1IotEoOjs7Zd8n7e3t2LZtG98xSiSgTJ3fmWqPKHVG7bdFzdMSzauTydVJX4QsLnt6evDOO++gp6cn7rKijpy0trZi48aNaG1tTXkdubm5GD9+PGdDI00KBoM4cOAAgsGg2qEoTvRJW1paWlBXV4eWlhZZltMr0ffzcIx8fpP2yZEfyZGnaVGieXUyuTrpi5DFZTJEHTnp7e3FRx99hN7e3pTX4XK5cP311/M9lxpntVoxbtw4WK1WtUMhhYg+aUs4HMbx48cRDodlWU6vRN/PdDK25fohR34kR56mRaLm1ZQ4wxeXHDmJLRKJwO/380XWGldUVIQ5c+agqKhI7VBIIaJM2kLD4342Frbl+sH8KDbm1WT44pJia25uxkMPPYTm5ma1Q0lYcXExFixYoNhIf2lpKW6//XaUlpYqsr2hRCIRBAIBzXZyRUVFmD9/PhOmGNxuN5YsWZLUc9+iTNpCw0tlP6dyPBmJltsjrbTlSvdrSvfbctBjfkSkFCGLS6fTiUsvvRROp1PtUEhhOTk5GDlypGLPKFksFhQVFcFisSiyvaE0NzdjzZo1mu3krFYrKisrZb/Vy263Y9q0abDb7bKuV2lZWVmw2+3CPfdN6hDleMrU+Z2p9kgOWmnLle7XlO63SRuYq4tLyOLS4XDgoosugsPhUDsU1RQUFOCaa65BQUGB2qEoyu/348UXX1Ts5fJtbW149tln+WzBMPx+P3bu3Cn7PsnPz8eMGTOQn58v63qV5vP5sHnzZvh8PrVD0YzCwkLMmjULhYWFsixnJKIcT5k6vzPVHolE6X5N6X5bK4yapw1gri4uIYvLnp4eHDlyJKH7vUUdOcnLy8O5556LvLw8tUNRVCAQwOuvv45AIKDI9np6enDo0CE+WzCMQCCAvXv3yr5PQqEQGhoaEAqFZF2v0kKhEI4ePar730NONpsNkyZNgs1mk2U5IxHleMrU+Z2p9kgkSvdrSvfbWiFqnpZoXp1Mrk76ImRx2dbWhqeeeiqhUTdRR066u7vx1ltvobu7W+1QiDLC5/Ph8ccf1/0VGjpVIBDA/v374yabiS5H+sPzm0Qnap6WaF6dTK5O+iJkcZkMUUdOOjo68Nxzz6GjoyPldZSXl+Puu+9GeXm5jJERUbpEn7TF7/dj+/btcW+TS3Q5vRJ9PxPplRz5kRx5mhaJmldT4gxfXHLkJDaTyQSLxQKTyaR2KDSMsrIy3HXXXSgrK1M7FFKIKJO20PC4n42Fbbl+MD+KjXk1Gb64pNhaW1uxceNGtLa2qh1KwvLy8nDeeecp9gyDw+HA9OnTVb2t2mw2w2q1wmzW5ulss9kwefJkPhcXg9PpxMyZM5N67luUSVtoeKns51SOJyPRcnuklbZc6X5N6X5bDnrMj4iUos1sNE0WiwWlpaWqvh5CBL29vfjoo4/Q29urdigJKygowNVXX63Y7GtOpxPV1dWqJnKtra3YtGmTZju5wsJCXHvttbLP6Gk2m+F0OlVPxNLlcDgwderUpBI5USZtoeGlsp9TOZ60KFPnd6baIzlopS1Xul9Tut+Wgx7zI61hri4ufWdlMZSWluLWW29V9cX2asvJycGoUaMM996ocDiMxsZGhMNhRbYXCoVw7NgxVZP83t5evP/++5rt5MLhMJqbm2XfJ2VlZVi8eLHubyELBoM4fPgwgsGg2qFoRk5ODsaMGRO3/Up0OSMR5XjK1PmdqfZIDlppy5Xu15Tut7XCqHnaAObq4hKyuEyGqCMnxcXFqKmpQXFxsdqhKKqlpQXr1q1DS0uLItvz+Xx48skneXviMFpaWvDII48otk/0pr29HVu2bEF7e7vaoWhGcXEx5s6dG7f9SnQ5I+HxNDy2R/Ep3a8p3W9rhah5mqh5NSVOyOKyqakJ999/P5qamuIuK+rIiSRJ6OvrgyRJaodClBEejwcPPvggPB6P2qGQzKLRKEKhEKLRqCzLkf7w/CbRiZqnJZpXJ5Ork74IWVxKkoTe3l7hTthkNDU14b777kvrpC0oKMA111yjq+cgyDii0Sg6OzsNWViIPmmLx+PBqlWr4hYWiS6nV6Lv5+EY+fwm7ZMjP5IjT9Mz5uriErK4TAZHTmLLy8vDueeeq6sZ3IwoPz8fV111FfLz89UOhRQiyqQtNDzuZ2NhW64fzI9iY15Nhi8uOXISW3d3N9566y10d3erHUrCTCYTcnJyFHv3VFZWFlwul6rvobPb7ZgyZQrsdrtqMcTD9/TFZrFYUF5entTzKaJM2kLDS2U/p3I8GY1W2yOttOVK92tK99ty0GN+pBTm1WT44pJi6+jowHPPPYeOjg61Q0lYeXk5li1bhvLyckW253a7cccdd8DtdiuyvaEEg0EcPHhQs4VGRUUFli9fjoqKCrVD0aTS0lIsWrQoqee+OWmLMaSyn1M5noxEy+2RVtpypfs1pfttOegxPyJSipDFZUlJCW6++WaUlJSoHQpRxrW3t2Pr1q2GKzSKioowf/58FBUVqR0KEcnMiOe3UdtyMibm6uISsrjMzs5GRUUFsrOz1Q5FNW63G3feeaeqV9TU4PV68fDDD8Pr9SqyPY/Hg9WrVws7oYgcvF4vHn30Udn3idVqRWVlJaxWq6zrVVpjYyNWrlyJxsZGtUPRDLfbjSVLlsRtvxJdzkhEOZ4ydX5nqj0SidL9mtL9tlYYNU8bwFxdXEIWlx0dHXj++ecTul1B1JGTrKws5Ofna/bZkkzp6+uD1+tFX1+fItuLRqPo7u7mjIbD6OvrQ1NTk+z7xO/3Y+fOnfD7/bKuVw2RSETtEDQlKysLdrs9bvuV6HJGI8LxlKnzO1PtkUiU7teU7re1QtQ8LdG8OplcnfRFyOKyu7sbb775ZkIPWos6ctLW1oZnnnkGbW1tKa8jJycHo0aNQk5OjoyREckjEAhg7969CAQCaoeiONEnbfH5fNi8eXPcl7gnupxeib6fh2Pk85u0T478SI48TYsSzauTydVJX4QsLpMh6shJT08P3nnnHfT09KS8juLiYtTU1KC4uFjGyEhu2dnZGDFihHADJBSb6JO2hEIhHD16FKFQSJbl9Er0/UwnY1uuH3LkR3LkaVokal5NiTN8ccmRk9gkSUJfXx+nk9a4kpIS1NbWCndrNxGRkbAt1w/mR7ExrybDF5cUW1NTE+677z5dvQjX5XLhhhtugMvlUmR7xcXFWLBgAa/uDqOwsBDXXXcdCgsL1Q5Fk0pKSnDLLbcklVCKMmkLDS+V/ZzK8WQkbI/iU7pfU7rfloMe8yMipQhZXNrtdlxwwQWqv4iYlJebm4uzzjoLubm5imwvJycHI0eOVPW51MbGRtx7772aLTRsNhsmTJgAm80m+3onT54s+3qVlp2dDbfbnfStcCJM2kLxJbufUz2etCZT53em2iM5aKUtV7pfU7rfJm1grq4dH3zwAf74xz/KNqmWkMVlfn4+rrjiCuTn56sdimqcTicuvfRSOJ1OtUNRVFdXF/bs2YOuri5Ftuf3+/Hiiy8KMWNppnR1dWHfvn2y75PCwkJce+21ur8C0d7ejm3btvHddidwOp2YOXNm3PYr0eWMRJTjKVPnd6baI5Eo3a8p3W9rhVHztAHM1bVjz549mDVrFsaPH48nnngi7SJTyOKyt7cXH3/8MXp7e+MuK+rIicPhwEUXXQSHw6F2KIrq7OzErl270NnZqcj2AoEAXn/9dc5oOIzOzk7s2LFD9n0SDofR3NyMcDgs63qVFgwGceDAAQSDQbVD0QyHw4GpU6fGbb8SXc5IRDmeMnV+Z6o9EonS/ZrS/bZWiJqnJZpXJ5OrU2bNnz8ff//733HOOedg3rx5aReZJinJp5FXrVqF1157LamNvP322+jq6sKFF16Y1OdSZbPZMH78eLzzzju672BTlZWVBYfDga6urpRvn9Pj31HpmLXwN9JCDMPJVHxa/70TlcrvIcrvHktWVhacTic6OzuHbb8SXU6vjHxsGLHd0EpsRuxHkyVHzHLkaXqmx/1uBO3t7Th69Cg8Hg8cDgd27tyJL33pS0mtQ8grl8kwm82w2+0wm8X6U+Tk5KCqqiqtZyZ6enpw8OBB4abJJtK7np4eHD58WNhzMycnB2PGjInbfiW6nF6Jvp+J9EqO/EiOPE2LRM2rKQmSAmpqaqRp06YpsSlJkiTpk08+ke655x7pk08+kXVZPRH194pH6d9bC3/ncDgstba2SuFwWLUYhpOpv5EW/vZyEOX3kFOifxP+7U4lyt/EiO2GVtpyI/ajahD192b7rU9///vfpWuvvVYCII0dO1Z64oknUm6LOKxAMbW1teGZZ55BW1ub2qEkLDc3F+PHj1ds1rm8vDycd955yMvLU2R7Q7FYLCgqKoLFYlEthuFYrVaMGzcOVqtV7VA0yW63Y9q0aUk99y3KpC00vFT2cyrHk5FouT3SSluudL+mdL8tBz3mR0SxPP744/jiF7+Id999F0888QTeeecdzJ07N+W2SMji0mw2Iy8vj5fk09TT04N33nlHV7dkuVwuXH/99Yq9L6ugoABXX301CgoKFNneUNra2vDss89qtpMrKirCnDlzUFRUJPu6s7KyZF+n0vLz8zFjxoykZswTZdIWGl4q+zmV40mrMnF+Z7I9SpdW2nKl+zWl+2056DE/0hrm6tpx8cUXY+vWrWkXlQOE3KNlZWVYunQpysrK1A5FNRaLBaWlpaqPgCotEonA7/cr9nB8OBxGY2OjqjOW9vT04NChQ5rt5CKRCAKBgOz7pKKiAsuXL0dFRYWs61VaKBRCQ0MDQqGQ2qFohsViQXl5edz2K9HljESU4ylT53em2iM5aKUtV7pfU7rf1gqj5mkDmKtnVltbGx566CG88847cZc988wz8bWvfU22Y1HI4jIZoo6clJaW4tZbb0VpaanaoSiqubkZDz30EJqbmxXZXktLC9atW4eWlhZFtqdHzc3NWLNmjWL7RG98Ph8ef/xx+Hw+tUPRjNLSUixatChu+5XockbC42l4bI/iU7pfU7rf1gpR8zRR82q9WbRoERYvXoyf//znim9byD3f3NyMX//61wk1VBw5IdInr9eLRx99FF6vV+1QiEhmPL+J9CnRvDqZXJ2SE41GsWPHDgDA5MmTFd++kMVlJBJBW1ub4W6xOFFTUxPuv/9+NDU1pbwOp9OJSy+9FE6nU8bIiOTR19eHpqamlF/yq2eiT9rS2NiIlStXorGxUZbl9Er0/TwcI5/fpH1y5Edy5Gl6xlw9c/7xj3+go6MDAFBdXa349oUsLpMh6siJJEno7e2FJEkpr8PhcOCiiy6Cw+GQMTKSm8PhwPTp07mfDESkSVtiSTThEDkxMcJ+pk+xLdcPOfIjOfI0LRI1r9aT3bt3A+ifLGvSpEmKb9/wxSVHTmLr6enBkSNHVJ9cQMtMJhNycnJgMplUi8HpdKK6uppXmHXKbDbD6XQm9XyKKJO20PBS2c+pHE+kDVppy7XQr2kd86PYmFer729/+xuA/llg1egL2PtQTG1tbXjqqadUnxY9GeXl5bj77rtRXl6u2PaWLVum2PaGEgqFcOzYMc0WGmVlZbjrrrv4XHMMZWVlWLx4cVJ/H07aYgyp7OdUjicj0XJ7pJW2XOl+Tel+Ww56zI/IGCRJwp49ewCoc0ssIGhxWVRUhBtvvFGT77GizDKZTLBYLIYacfX5fHjyySc1W2iYzWZYrVbZR88KCwtx3XXXobCwUNb1EpH6MnV+Z6o9koPW2/JMMWK/TczV5eLxeDB27FhUVlaisrISbrd7cKbnX/7yl4Pf/9znPqfYM+zaa11lYLVaUVVVBavVqnYoqikpKcHNN9+MkpIStUNRVGtrKzZu3IjW1lZFtuf1evHwww9zRsNhtLa2YtOmTbLvE5vNhgkTJsBms8m6XqV5PB48+OCD8Hg8aoeiGSUlJbjlllvitl+JLmckohxPmTq/M9UeiUTpfk3pflsrjJqnDWCuLo+ysjLU19ejoaEBDQ0N+O53vwsAGD169OD3Ghoa8M9//lOxd6oKWVx2dnbilVdeQWdnZ9xlRR05yc7ORkVFBbKzs9UORVG9vb346KOP0Nvbq8j2+vr64PV6OaPhMHp7e/H+++/Lvk+6urqwb98+dHV1ybpepUWjUXR2diIajaodimZkZ2fD7XbHbb8SXc5IRDmeMnV+Z6o9EonS/ZrS/bZWiJqnJZpXJ5OrU+IGJvO56KKLVItByOKyq6sLu3fvTqhTEnXkpKOjA88///zgVMSpsFgsKC0tVWykgygZnZ2d2LFjhyE7JtEnbWlvb8e2bdvQ3t4uy3J6Jfp+Ho6Rz2/SPjnyIznyNC1KNK9OJlenxPT29uL1118HwOJSVaKOnHR3d+PNN99Ed3d3yusoLS3FrbfeitLSUhkjI7llZWXB5XIhKytL7VBIIaJP2hIMBnHgwAEEg0FZltMr0fcznYxtuX7IkR/Jkadpkah5tR688cYbg/3hhRdeqFochi8uOXJCeud2u3HHHXfA7XarHQoREaWIbTmJgHm1egZuiXW73TjrrLNUi8PwxSXF1tTUhPvvvx9NTU1qh5KwgoICXHPNNSgoKFBkey6XCzfccANcLpci29Oj/Px8XHXVVXwRfAxFRUWYP39+Us99izJpCw0vlf2cyvFkJGyP4lO6X1O635aDHvMjEt/A+y3VvGoJCFpc5ubmYuLEicjNzVU7FF2TJAm9vb2QJEntUBKWl5eHc889F3l5eYpsLzc3F2eddZaqx5rH48Hq1as1W2jY7XZMmTIFdrtd1vVarVaMGzdO989LW61WVFZWJvV7iDJpCw0vlf2cyvGkRZk6vzPVHslBK2250v2a0v22HPSYH2kNc3V5RSIR7N27F4C6z1sCghaXLpcLs2fPNvTVJLvdjgsuuECTHWgmdXd346233lLsGYauri7s2bNH1ds/otEouru7NVtoBINBHDx4UPbn4oqKijBnzhzdX6Hx+/3YuXMn/H6/2qFoht1ux7Rp0+K2X4kuZySiHE+ZOr8z1R7JQSttudL9mtL9tlYYNU8bwFxdXm+99dbgOcviMgP6+vrg8/kSmkZb1JGT/Px8XHHFFYa79aejowPPPfecYrOvdXZ2YteuXXxwfRjt7e3YunWr7DN6RiIRBAIBRCIRWdertEAggL179yIQCKgdimbk5+djxowZcduvRJczElGOp0yd35lqj0SidL+mdL+tFaLmaYnm1cnk6hTfwPOWDocDX/jCF0762auvvooNGzYoFouQxaXX68XatWsTegGwqCMnvb29+Pjjjw333igyjubmZqxZswbNzc1qh0IyC4VCaGhoQCgUkmU50h+e3yQ6UfO0RPPqZHJ1im/gecupU6eeMuP08uXLccYZZygWi5DFZTJEHTlpbW3F+vXr0dramvI6SkpKcPPNN6OkpETGyIgoXaJP2uLz+fD444/D5/PJspxeib6fifRKjvxIjjxNi0TNq7Wuvr4eAHDBBRec9P0dO3YgGAzisssuUywWwxeXHDmJLTs7GxUVFcjOzlY7FBpGcXExFixYgOLiYrVDIYWIMmkLDY/72VjYlusH86PYmFerY+B9yCNHjhz8XltbG+644w6sX79e0VgMX1xSbB0dHXj++ed19RxETk4ORo0ahZycHEW2l5ubi/Hjx6v6zG5OTg5Gjhyp2O+crOzsbIwYMYKdcAw2mw2TJ0+GzWZL+DOiTNpCw0tlP6dyPBmJltsjrbTlSvdrSvfbctBjfkRiW7BgAQDgvffeG/x65ZVX4u6778aECRMUjYXFJcXU3d2NN998U1czuBUXF6OmpkaxkV+Xy4Xrr79e1Wd2/X4/XnzxRc0WGiUlJaitreXt1TEUFhbi2muvRWFhYcKfEWXSFhpeKvs5lePJSLTcHmmlLVe6X1O635aDHvMjEtu8efPwm9/8Btu2bUNlZSUWLlyIn/3sZ7jpppsUj8Wi+BYVUFFRgRUrVqgdhqrMZjPy8vJgNhtr/ECSJEQiEWRlZcFkMmV8ewMzGtrt9lMeoFZKIBDA66+/jkmTJgk369xwysrKcNddd2nyCkQywuEw2tra4HK5dP+7yMVsNsPpdMZtvxJdzkhEOZ5EOb+ToZW2XOl+Tel+WyuMmqcNYK4uv9tuuw233Xab2mEoc+VyypQpqr9zxWjKysqwdOnSwXuwjaKpqQn33XcfmpqaFNlec3MzHnroIc5oOIzGxkbce++9aGxslHW9ZrMZVqtV9x1zS0sLHnnkEbS0tKgdimaUlZVh8eLFcduvRJczElGOp0yd35lqj0SidL+mdL+tFUbN00h8imRlt9xyC+6//34lNgWgv3Otq6tLqHMdGDmpqKhQIDIikktrays2bdok3Ex7RMTzm0ivEs2rk8nVSV/0PeQfQzgcxvHjxxEOh9UORTXNzc349a9/ndbIo91uxwUXXAC73S5jZETy6O3txfvvvy/cO8ISIfqkLR6PBw8++CA8Ho8sy+mV6Pt5OEY+v0n75MiP5MjT9Iy5uriELC6TIerISSQSQVtbGyKRSMrryM/PxxVXXGGo5/j0KC8vD+eddx7y8vLUDoUUIvqkLdFoFJ2dnYhGo7Isp1ei72c6Gdty/ZAjP5IjT9MiUfNqSpzhi0uOnMTW29uLjz/+mCPHGldQUICrr74aBQUFaodCKUp20oxwOIzm5ma2W4JLdT+rNbkYpYdtuX4wP4qNeTUZvrik2FpbW7F+/XpdPfPidrtx5513wu12K7K98vJy3H333SgvL1dke0MJh8NobGzUbENeWlqK22+/HaWlpWqHokkVFRVYvnx5Us99izJpCw0vlf2cyvFkJFpuj7TSlivdryndb8tBj/kRkVKELC4LCwsxa9Ys3kpkQFlZWcjPz1ds5N5kMsFisag6fXpLSwvWrVun2ULDYrGgqKgIFou8bz7Kz8/HVVddxdu2iQSUqfM7U+2RHLTSlivdryndb5M2MFcXl5DFpc1mw6RJkww5CcKAoqIi3HjjjSgqKlI7FEW1tbXhmWeeQVtbmyLba21txcaNGzl6OYy2tjY8++yzsu8Tu92OKVOm6H7CKa/Xi0cffRRer1ftUDSjqKgI8+fPj9t+JbqckYhyPGXq/M5UeyQSpfs1pfttrTBqnjaAubq4hCwuA4EA9u/fj0AgEHdZUUdOrFYrqqqqYLVa1Q5FUT09PXjnnXfQ09OjyPZ6e3vx0Ucf8bmLYfT09ODQoUOy75NgMIiDBw8iGAzKul6l9fX1oampCX19fWqHohlWqxWVlZVx269ElzMSUY6nTJ3fmWqPRKJ0v6Z0v60VouZpiebVyeTqpC9CFpd+vx/bt2+H3++Pu6yoIyednZ145ZVX0NnZmfI6zGYz8vLydP+SehJTe3s7tm7divb2drVDUYXIt5D5/X7s3Lkzbhue6HJ6JvJ+Ho7Rz2/SNjnyIznyNC1KNK9OJlcnfTF81SDqyElXVxd2796Nrq6ulNdRVlaGpUuXoqysTMbISG4mkwk5OTmqPvdJyhJ90pZAIIC9e/fGbZcTXU6vRN/PdDK25fohR34kR56mRaLm1ZQ4wxeXHDkhvSsvL8eyZctUnbGWiIjSw7acRMC8mgxfXFJszc3N+PWvf43m5ma1Q0mY0+nEpZdeCqfTqcj2CgoKcM011/C9ZMNwOByYPn06HA6H2qFoUmFhIa677rqknvsWZdIWGl4q+zmV48lI2B7Fp3S/pnS/LQc95kdEShGyuMzJycGYMWOQk5Ojdii6FolE0NbWhkgkonYoCXM4HLjooosUSxzy8vJw7rnnIi8vT5HtDcXr9eLhhx/WbKHhdDpRXV0te+KQnZ2NESNGIDs7W9b1Ks1ms2HChAlJPfctyqQtNLxU9nMqx5MWZer8zlR7JAettOVK92tK99ty0GN+pDXM1cUlZHFZXFyMuXPnori4WO1QVJObm4uJEyciNzdX7VAU1dPTgyNHjig261x3dzfeeustdHd3K7K9ofT19cHr9Wq20AiFQjh27BhCoZCs6y0pKUFtbS1KSkpkXa/Surq6sG/fPuGeu0mHzWbD5MmT4xZIiS5nJKIcT5k6vzPVHslBK2250v2a0v22Vhg1TxvAXF1cQhaX0WgUoVAI0Wg07rKijpy4XC7Mnj0bLpdL7VAU1dbWhqeeekqx92V1dHTgueeeQ0dHhyLb0yOfz4cnn3wSPp9P7VA0qbOzEzt27BBuxsB0FBYW4tprr417a2eiyxkJj6fhsT2KT+l+Tel+WytEzdMSzauTydVJX4QsLj0eD1atWgWPxxN3WVFHTvr6+uDz+VQfASXKlMbGRtx7771obGxUOxSSWTgcRnNzM8LhsCzLkf7w/CbRiZqnJZpXJ5Ork74IWVwmQ9SRE6/Xi7Vr16b17EZRURFuvPFGFBUVyRgZEaVL9ElbWlpa8Mgjj6ClpUWW5fRK9P1MpFdy5Edy5GlaJGpeTYkzfHHJkZPYrFYrqqqqYLVa1Q6FhuFyuXDDDTcId2sNxSbKpC00PO5nY2Fbrh/Mj2JjXk2GLy4pts7OTrzyyiu6enbHYrGgtLQUFotFke3l5ORg1KhRqj6zm5ubi7POOkuzkwJkZWXB5XIhKytL7VA0yWq1Yty4cUklKaJM2kLDS2U/p3I8GYmW2yOttOVK92tK99ty0GN+RKQUFpcUU1dXF3bv3q2rBLa0tBS33norSktLFdlecXExampqVH1mt6urC3v27NHsfnK73bjjjjvgdrvVDkWTioqKMGfOnKRur+KkLcaQyn5O5XgyEi23R1ppy5Xu15Tut+Wgx/yISClCFpdutxtLlizRZOdBYpEkCX19fZAkSbUYOjs7sWvXLsMVGqWlpbj99tt1lZAMJRKJIBAI8H1pn5HolSUtXoFSkyjHkyjndzK00pZroV8j8TFXF5eQxWVWVhbsdruhk46KigqsWLECFRUVaoeiqKamJtx///1oampSbHv33XefYtvTI4/Hg9WrV8v+/IXFYkFRUZGubqUaSnNzM9asWYPm5ma1Q9GMiooKLF++PG77lehyRiLK8ZSp8ztT7ZFIlO7XlO63tcKoedoA5uriErK49Pl82Lx5c0LvseLIiVgkSUJvby9HXDUkGo2iu7tb9pnj2tra8Oyzzxru3WhERpCp8ztT7RGljv22WBLNq5PJ1UlfhCwuQ6EQjh49ilAoFHdZUUdOWlpaUFdXl9YU/bm5uZg4caLqkwsQDaWnpweHDh1CT0+P2qEoTvRJW7xeLx599NG4U/Qnupxeib6fh2Pk85u0T478SI48TYsSzauTydVJX4QsLpMh6shJOBzG8ePH03q5uMvlwuzZszktusbl5uZi/PjxHAQwENEnbenr60NTU1Pcl4snupxeib6f6WRsy/VDjvxIjjxNi0TNqylxhi8uOXISW19fH3w+n7CJmyhcLheuv/56DgIYiCiTttDwuJ+NhW25fjA/io15NRm+uKTYvF4v1q5dq6tbzkpKSnDzzTejpKREke253W7ceeedqj6zG4lE4Pf7NZuAFhcXY8GCBaq+rkXLysrKcNddd6GsrCzhz4gyaQsNL5X9nMrxZCRabo+00pYr3a8p3W/LQY/5EZFShCwunU4nZs6cCafTqXYopLDs7GxUVFQgOztbke1lZWUhPz9f1Wd2m5ub8dBDD2m20MjJycHIkSNlfyG3w+HA9OnT4XA4ZF2v0sxmM6xWK8xmIZtjUpgox1Omzu9MtUdy0EpbrnS/pnS/TdrAXF1c+u59YnA4HJg6daruk850FBYWYtasWSgsLFQ7FEV1dHTg+eefR0dHhyLba2trwzPPPMMZS4fh9/vx4osvwu/3y7pep9OJ6upq3XdMra2t2LRpE1pbW9UORTMKCwtx3XXXxW2/El3OSEQ5njJ1fmeqPRKJ0v2a0v22Vhg1TxvAXF1cQhaXwWAQhw8fRjAYjLusqCMnNpsNkyZNgs1mUzsURXV3d+PNN99Ed3e3Itvr6enBO++8wxkNhxEIBPD6668jEAjIut5QKIRjx47p/rmO3t5evP/+++jt7VU7FM2w2WyYMGFC3PYr0eWMRJTjKVPnd6baI5Eo3a8p3W9rhah5WqJ5dTK5OumLkMVle3s7tmzZgvb29rjLijpyEggEsH//fnagJCyfz4cnn3ySM9IJqKurC/v27UNXV5csy5H+8Pwm0YmapyWaVyeTq5O+CFlcJkPUkRO/34/t27endetPRUUFVqxYgYqKChkjI6J0iT5pS2dnJ3bs2IHOzk5ZltMr0fczkV7JkR/Jkadpkah5NSXO8MUlR05I78rLy3H33XejvLxc7VBIIaJM2kLD4342FrblJALm1cQei2JqaWlBXV0dWlpa1A4lYXa7HRdccAHsdrsi23M6nbj00ktVfWbXZDLBYrHAZDKpFsNw8vLycN555yEvL0/tUDQpPz8fV111FfLz8xP+jCiTttDwUtnPqRxPRqLl9kgrbbnS/ZrS/bYc9JgfESlFyOLSYrGgvLwcFotF7VB0LRwO4/jx4wiHw2qHkrD8/HxcccUViiVWDocDF110karP7La2tmLjxo2aLTQKCgpw9dVXo6CgQNb1ZmVlweVyqfoaGDnY7XZMmTIlqcRKlElbaHip7OdUjictytT5nan2SA5aacuV7teU7rfloMf8SGuYq4tLyOKytLQUixYtQmlpqdqhqCYnJwdjxozR5Lu8Mqm3txcff/yxYkl3T08Pjhw5oupssb29vfjoo480W2iEw2E0NjbK3gm73W7ccccdir3oO1OCwSAOHjzI51NOYLVaMW7cOFitVlmWMxJRjqdMnd+Zao/koJW2XOl+Tel+WyuMmqcNYK4uLiGLy2SIOnJSXFyMuXPnori4WO1QFNXa2or169crNvLb1taGp556iu+5HEZLSwvWrVvH24diaG9vx9atW/l8ygmKioowZ84cFBUVybKckfB4Gh7bo/iU7teU7re1QtQ8TdS8mhInZHHZ2NiIlStXorGxMe6yoo6cRKNRhEIhRKNRtUMhygiPx4PVq1fD4/GoHQrJLBKJIBAIIBKJyLIc6Q/PbxKdqHlaonl1Mrk66YuQxSUAwycbHo8Hq1atSqtjLiwsxKxZs1BYWChfYEQyiUaj6O7uFq5jToTok7Y0NzdjzZo1aG5ulmU5vRJ9Pw/HyOc3aZ8c+ZEceZreGT1XF5WwxWWiOHISm81mw6RJk2Cz2dQOhYZRUFCAa665RpMTVFBmiDJpCw2P+9lY2JbrB/Oj2JhXk+GLS4AjJ7EEAgHs378fgUBA7VASZjabkZeXp9h74SwWC0pLS1V9tiAvLw/nnnuuJqfWB/qn18/JyVF9en2tys7OxogRI5CdnZ3wZ0SZtIWGl8p+TuV4MhItt0daacuV7teU7rfloMf8SEnMq41NP2cyKc7v92P79u3w+/1qh5KwsrIyLF26FGVlZYpsr7S0FLfeequqz+x2d3fjrbfeQnd3t2oxDKe8vBzLli3ji8FjKCkpQW1tLUpKShL+DCdtMYZU9nMqx5ORaLk90kpbrnS/pnS/LQc95kdEShGyuCwpKcEtt9zCzpUMoaOjA8899xw6OjrUDkVRxcXFWLBggXAz7RGRMc9vo7blZEzM1cUlZHGZnZ0Nt9tt6NuC3G43lixZovt3ACarubkZv/71rxWb4KOpqQn3338/mpqaFNmeHnm9Xjz88MPwer2yrjcnJwcjR47U/TvCGhsbce+99/L5lBOUlZXhrrvuinslI9HljESU4ylT53em2iORKN2vKd1va4VR87QBzNXFJWRx2d7ejm3btiV0K5GoIydZWVmw2+3IyspSOxRFRSIRtLW1KXa/vyRJ6O3thSRJimxPj/r6+uD1etHX1yfrev1+P1588UXeliQgs9kMq9Ua9xmsRJcj/cnU+Z2p9kgkSvdrSvfbWiFqnpZoXp1Mrk76ImSPHAwGceDAgYQmQRB15MTn82Hz5s3w+XwpryMnJwdjxozR/ZUhElMgEMDrr79uyAkVRJ+0pbW1FZs2bYr7UvVEl9Mr0ffzcIx8fpP2yZEfyZGnaVGieXUyuTrpi5DFZTJEHTkJhUI4evQoQqFQyusoLi7G3LlzDfXMix7l5ORg1KhRHAQwENEnbent7cX777+P3t5eWZbTK9H3M52Mbbl+yJEfyZGnaZGoeTUlzvDFJUdOYotGowiFQnyJtcYVFxejpqaGgwBERDrGtlw/mB/FxryaDF9cUmwejwerVq2Cx+NRO5SEFRUV4cYbb0RRUZEi2yspKcHNN9+s6pUFSZLQ19en2ec+XS4XbrjhBrhcLrVD0aTS0lLcfvvtSU37L8qkLTS8VPZzKseTkWi5PdJKW650v6Z0vy0HPeZHREoRsri02+2YNm0a7Ha72qGQwqxWK6qqqmC1WhXZXnZ2NioqKlR9JqqpqQn33XefZmeszc3NxVlnnYXc3FxZ15uXl4fzzjtP9ReOp8tisaCoqEixF5aT2EQ5njJ1fmeqPZKDVtpypfs1pftt0gbm6uISsrjMz8/HjBkzkJ+fr3YoqnE6nZg5cyacTqfaoSiqs7MTr7zyCjo7OxXZXkdHB55//nm+l2wYXV1d2LNnD7q6umRdb0FBAa6++moUFBTIul6ltbW14dlnn0VbW5vaoWhGfn4+rrrqqrhteKLLGYkox1Omzu9MtUciUbpfU7rf1gqj5mkDmKuLS8jiMhQKoaGhIaGHpEUdOXE4HJg6dSocDofaoSiqq6sLu3fvVixx6O7uxptvvonu7m5FtqdHnZ2d2LVrl+yJQzgcRmNjI8LhsKzrVVpPTw8OHTqEnp4etUPRDLvdjilTpsRtlxNdzkhEOZ4ydX5nqj0SidL9mtL9tlaImqclmlcnk6uTvghZXPp8Pjz++OMJTe8s6shJMBjE4cOH+UA1CaulpQXr1q1DS0uL2qGQzILBIA4ePBi3/Up0OdIfnt8kOlHztETz6mRyddIXIYvLZIg6ctLe3o4tW7akNRW02+3GkiVL4Ha75QuMiNIm+qQt7e3t2Lp1a9z2K9Hl9Er0/UykV3LkR3LkaVokal5NiTN8ccmRk9iysrJgt9uRlZWldig0DLfbjTvvvJODAAYiyqQtNDzuZ2NhW64fzI9iY15Nhi8uKTafz4fNmzfrqoHIzc3FxIkTFZsJ0G6344ILLlD1ma+srCzk5+drtpPLzc3F+PHjNTk7oxY4HA5Mnz49qeduRJm0hYaXyn5O5XgyEi23R1ppy5Xu15Tut+Wgx/yISClCFpdmsxlOpxNms5C/nmJCoRCOHj2qq1sbXC4XZs+erdg7zPLz83HFFVeo+sxuW1sbnnnmGc0WGi6XC9dff73s+8RkMiEnJwcmk0nW9SrN6XSiuro6qRkDRZm0hYaXyn5O5XjSokyd35lqj+SglbZc6X5N6X5bDnrMj7SGubq4hNyjZWVlWLx4McrKytQORTUWiwXl5eWGu52qr68PPp8PfX19imyvt7cXH3/8MXp7exXZ3lB6enrwzjvvaLbQiEQi8Pv9iEQisq63vLwcy5YtQ3l5uazrVVooFMKxY8eYpJwgOzsbI0aMiPuevUSXMxJRjqdMnd+Zao/koJW2XOl+Tel+WyuMmqcNYK4uLiGLy2SIOnJSWlqKRYsWGW4iCK/Xi7Vr18Lr9SqyvdbWVqxfvx6tra2KbE+Pmpub8dBDD6G5uVntUDTJ5/PhySef5O1VJygpKUFtbS1KSkpkWc5IeDwNj+1RfEr3a0r321ohap4mal5NiRNyz3s8Hjz44IPweDxxl+XICZE+eb1ePPzww4ZLSIiMgOc3kT4lmlcnk6uTvghZXEajUXR2diIajaodimoaGxuxcuVKNDY2prwOp9OJmTNn6v7ZHRJTX18fvF6v4W6lAsSftKWxsRH33ntv3PYr0eX0SvT9PBwjn9+kfXLkR3LkaXrGXF1cQhaXyRB55CTdZ0ocDgemTp1qyMRGT5xOJy699FIOAhiIKJO20PC4n42Fbbl+yJUfafHZ33SJnFdTYgxfXHLkJLZgMIjDhw8jGAyqHYpmmc1m5OXlqfpsgcPhwEUXXcRBAJ3KysqCy+VK6vUDokzaQsNLZT+ncjyRNmilLddCv6Z1zI9iY15NbDkopvb2dmzZsgXt7e1qh5KwiooKrFixAhUVFYpsr6ysDEuXLlX1md2enh4cOXJE9RkGYykvL8fdd9+t+1ldk3HPPffAZDLF/c9ms+GCCy7AG2+8gfr6+pPW8corr8T83Jlnnhlz0pZrrrkGJpMJU6dOjRlfdXX1kOttaGjAxo0bh/zZhRdemNLf4vvf//6Q63vllVdSWh8AfPLJJ/jpT3+KhQsXAgC+9KUvIS8vDyNGjMDFF1+M2267DRs3bkRDQ0PMdTz22GMoKCjANddcg3A4nHIsmZTK5Dxutxt33HEH3G734PeG2t/D/W1EpuX2SCttudL9mtL9thz0mB8RKUXI+Y+Lioowf/58FBUVqR0KUca1tbXhqaeews0336zJztlkMmVkqnWXy4UbbrhBk+9Gmz17NqqqqgAAd955J1paWlBSUoKHHnpocJlIJIJ//etf2Lx5MzZt2oRNmzbhtttuw69//WuYzWacc845eOKJJ/DJJ5/gRz/6EQBg8uTJWLx4MUKhEI4fP37KdsPh8GDR9sYbb6C9vR2FhYWnLHf33Xdj4cKF2Lp1K7Zu3Yrf/e53sFqtKC0txcUXX4wnnngCALBu3Trs2bMHALB3717s2bMHF110UcJ/h9bWVjz22GOD/z9r1izMnj0bAHDOOeckvJ4T/eEPf8CiRYvQ1dWFiy++GADwwx/+EFarFf/617/wwgsv4OGHHx5c/qGHHsL3v//9U9bzq1/9Cn6/H3/+859x6NAhnHvuuSnFowcD+3vPnj1Yt26d2uEkJFPnd6baIzlovS0nkhNzdYFJBvfJJ59I99xzj/TJJ5+oHYqsent7JY/HI/X29qa8Dj3+bbxer/TYY49JXq9Xke15PB7pV7/6leTxeBTZ3lC0vp9aWlqkDRs2SC0tLWqHoopRo0ZJAKRRo0YN+fPjx49Ly5cvl8rKyiQA0rJly076eSQSkVwulwRAcrvdUjQajbnPd+/eLQEY/G/Lli3DxnbllVdKn//852P+fP78+Set78orr0zodx5wzz33nPT5FStWJPS5cDgstba2SuFw+KTv79y5UzKbzRIA6be//W3M5X73u99JJpNJAiDdf//9Q27jt7/9reR0OqUrrrhCCoVCSf1eSknl3G5qapIeeOABqamp6ZSfbdiwYXBffPjhhzJGqh9abo+00pYr3a8p3W/LQY59JUeepkVaOY5JPULeFuv3+7Fz5074/f64y4o6cpKdnQ232224l4uHw2EcP35csdvcIpEI2trahHwoXy69vb346KOPZH8hd1dXF/bs2YOuri5Z16s0s9kMi8UCu90OAFizZg3+9a9/nfTzSy+9FED/O/oOHjwYc10vvfTSSc9J7dixI+ayvb292LNnD2bOnBk3xvHjxwMAXnjhBbz99ttxlweA7u5urF27dvCzybBYLCgqKjrlCtNPfvITRKNRXHbZZVi0aFHM5RYuXIibbrpp2G0sWrQIfr8fL7zwAnJycpKOUaui0Si6u7t1/7xTps7vTLVHIlG6X1O639YKUfO0RPPqZHJ10hchi8tAIIC9e/ciEAjEXdZqtaKyshJWq1WByJTT3t6Obdu2pfU8gMViQXl5uWZvISJj6+zsxK5du9DZ2al2KLK44IILAPQnWtu2bTvpZ5dffvngv1966aWYk7bs2LEDl112GUaMGDG4bCyvvfYaAoHASeuO5Yc//OHgv3/2s5/F/2UA/O53v0NbWxsWL16c0PInamtrw7PPPou2trbB7wWDQezbtw8AcP7558dcbkC84lIPjDw5j2jnN4lFjvxIjjxNixLNq5PJ1UlfhCwukyHqyEkwGMSBAwfSmsmstLQUixYtQmlpqYyRkdwsFgtKS0s5CKBzI0eOHPz30aNHT/rZZ4vLoSZtaWtrw5tvvonLL798cPkPP/zwlImCTlyPzWZL6BnKb37zmzjjjDMAAP/93/99Snyf1dfXhwcffBCzZ8/GmDFj4q7/s3p6enDo0KGTJjbx+XyQJAkA4PV6Yy434Etf+hJWr149eNVXj4bazyQutuX6IUd+JEeepkWi5tWUOMMXlxw5Ib0rLS3FrbfeykEAnTvx6tRnbw8bPXo0Ro8eDQDYs2fPkK+m+Otf/4poNHpScQnEvjX2pZdewkUXXYTc3Ny4sWVnZ+MHP/gBgP7bLn/+858Pu/wf/vAH/Otf/zrpime6CgsLYTKZAADPP/88Ojo6hl3e6XRiyZIlmDJlyknfH2om340bN8ZcT2dnJ5YvX45zzjkHNpsNLpcLX/rSl/DLX/4SfX19qKmpOWV9f/zjHwEAI0aMOOVnAPDuu+/ipptuwmmnnQar1YpRo0bh1ltvRXNzc8w4otEodu7cidtvvx3nnnsuCgoKkJ2djdLSUlx22WVYt24db/XUObblJALm1WT44pJia2xsxMqVK9HY2Kh2KAkrLCzErFmzhpwhMxOKiopw4403CvfMrpwGXvdQUFCgdiiaVFxcjAULFpx0np14FXPAQMEYDAbxwgsvYPXq1Se9pHrgiubnP/95XHbZZYOFzFDFZVtbG/7+978ndEvsgIULF6KkpAQAsGnTpiFnqwUASZLwwAMPoLq6evD2VTnY7XZ8/vOfBwA0NTXhy1/+csyrssOZPXs2nnjiiZNm7o2loaEBkyZNwn333Qefz4fFixdjzZo1uOqqq/DLX/4SM2bMGCzoSkpK8MQTT+CJJ57AeeedBwBYu3YtnnjiCcyaNWtwnbt378aMGTNQUVGBlStX4u6770YoFMIjjzyCadOmnXQbqMfjGdzP99xzDy6//HL85je/QXFxMf7jP/4Da9euxU033YS3334bixYtwoUXXgiz2YwFCxaguLg46b+NEbA9ik/pfk3pflsOesyPiJQiZHFps9kwefJk2Gw2tUPRPb1NVGOz2TBp0iTF9r3VakVVVZWqz+w2NTXh/vvvR1NTk2oxDCcvLw/nnnsu8vLyZF1vbm4uxo8fn9CVNy3LycnB6aefjr/+9a+D3xuq6Dvxe/v27Ttl0paXXnoJM2bMgMlkGiwyAeDll18+5Urorl27EI1GE5rMZ0BeXh5uv/12AP2ToqxZs2bI5f785z/j8OHDsl61HHDiOl977TXccMMNAIBnn332pEJ7OJMmTcLcuXPxta99bdjlent78ZWvfAUNDQ0YOXIk3n77bdx3332ora3FPffcg0OHDqGzsxNPP/008P/bu/couao6X+C/vDqPTjrvToIEorxMAgG8vKIgTADBURjDhbmwjATwCoiKA4IDghLmAoKXKyCDDDi8VAZGUBBGuJAsIJMwgQBRkPc7A3OTTuedzqM7nfT9o6ymQzrd1b2rq6uqP5+1sqpTfeqck1TVPvt7zj6/HZnwO2PGjJgxY0bzPa/Tp0+PGTNmxJQpU5rXe/bZZ8ecOXPiJz/5SZxxxhnxox/9KJ588sno06dPvP3223HTTTc1L9uyOE82xF5xxRUxe/bsuOCCC+Lss8+On/70p/Hmm2/GpEmT4rnnnovvfOc7MX78+JIvUtRV3++uao/yoVja8kIf1wp93M6XUusfFRt99fJVluFy2LBhcfzxx5fUWbB8q6ysjM997nPNFSh7ivXr18fChQsLNhxj3bp18dRTT3Vr0YmmpqZoaGhovh+t2GzYsCEWLVoUGzZsyOt6hw8fHieddFJRznPZEWvXro2f/OQnzUUdjjnmmFav+E2bNq25Euyzzz67ze/efvvteO+997YJoNmf161b11wIJ2v27NkxduzYbUJPLr797W/H4MGDIyJTsGf58uXbLXPNNdfEPvvsE1/84hc7tO6WBg8eHIcffnjztrJOOeWUuOKKK5qHEGe/fxdddFGMGzcuDj744Ljqqqvivffe6/S2s26++eZ45ZVXIiLi6quv3m7ewSFDhsRNN93U4Q7mCSecsN0cnxMnTozPfvazERHx8MMP7/C1I0aMaJ7ztKWRI0fGT3/604iIeOyxx+K+++4r+fuduur73VXtUT4US1te6ONaoY/bxaKn9tOy9NXLV1mGy82bN8eyZctyKmtdrmdOqqqq4qijjoqqqqru3pWCWrt2bTz66KMF61jV1dXF3LlzS346jK60Zs2aePjhh9u9R66jtmzZEmvXri2Zs8dbt26N5cuXN/+pqamJ559/PmbNmhX19fVRWVkZkyZNil/96letvn748OHNwy3feOONbX6XHfraWrhs+fus7FXOjhoxYkR84xvfiIhMJ/2GG27Y5vfz58+Pp59+Oi688MIOr7ulIUOGxBFHHBFDhgzZ7neXXHJJPPfcczF9+vTYtGlTPPXUU1FXVxdNTU2xcOHCuOSSS2K33XaL6dOnx7vvvtvpfbjtttsiInMVp+Ww1pYOOeSQ5kJHufqbv/mbVp/PTtny+uuvt/r7H/zgB/H666/vsNhL9t7SysrKePXVV0u+o95V3++uao/KSaGPa4U+bheLcu2n5dqv7khfndJSluFy+fLlcfPNN7d6Vv3jyvXMSX19fbz//vutFv6AcrBs2bK47rrr2iyCUkw++OCDGD16dPOfsWPHxoEHHhj33ntvREScccYZsXDhwjaLeezoHsnZs2fHpEmT4hOf+ETzcy2L9bQMl++++268++67HRoS29L3vve95iGX//iP/7jN1Y2rr746dtlllzjllFM6te6s+vr6ePvtt3fYfu2///7xu9/9LhYvXhw/+9nP4rjjjttm+GRTU1M8+OCDsf/++8fTTz/d4e2vXr06Xn755YiI+PSnP91mJ2nvvffu0Lr32muvVp/PXqHbUeipqqra5rOxefPmWLVqVfPJilI5yZKrUvt+Q0eVaz8t1351R/rqlJayDJcdUa5nTlauXBl33XVXrFy5stPrGDVqVHzzm99sLuIBdN6YMWNi9uzZ2/yZN29ePPDAAxER8a1vfavd4VHZcLlixYpYunRpjBw5MhobG+PJJ5/cLngOGDAgDj300IiIeOGFF5rbguzclx0p5tPSJz7xiZgxY0ZEZELYzTffHBERL7/8cjzyyCNx3nnnJU+lsHLlyrj77rvbbb969eoVK1eujFtuuSWWL18ev/nNb+LYY49t/v3atWvj5JNP7nAV1ffff795aOJOO+3U5rIdHbbZ2tXYiGi+v61lSMwWe8oW53nhhRdi5syZscsuu0RFRUWMGDFimxMWQGHko3+Uj35aMSrXfjW56/Hh8u67nTnZkX79+kV1dXX069evu3eFNowaNSrOPPNMJwGK3IABA+Koo47a5s+hhx7aoWGVU6dOjcrKymhoaIg//OEPUVFREQsXLow1a9a0WQQoO41FRMScOXNin332ibFjx3b63/L973+/+f7P6667Lurr6+Oaa66JYcOGNQ+bLbTKyso46aST4tFHH405c+Y0X2388MMPmwN1rloOB2yvoExHg3T2/y0XFRUVzcV5brzxxjjooIPil7/8ZYwcOTJuuOGG+P3vf7/NyQpKm7a8dOgf7ZgrkpRUuNy6NSJfJ0KamiLOPTfiySfT1rNxY8R++0X8+c952a2isnr16njooYeaC42UgoqKithtt90KVilxwIABsc8++3RrxdJ+/frFuHHjivYgV1FREbvuumvJV6/sKoMGDYoDDjggp+qVFRUVcfjhh0dVVVVMmjQp/vjHP8bjjz/e/PzHffy+y61bt8YTTzzR6SGxWXvttVdztdWlS5fGZZddFvfee2+cc845RVGc4sgjj4xzzz23+e+vvvpqh17fspDQpk2b2ly2K4ejrl27Nh577LF49tln47zzzmuu8Lto0aI499xz4/jjj9/mZEVE5l7YpqamoqyGWgyKuT0qlra80Me1Qh+386EU+0dQKEUdLv/pnyKOOCJi8uSI6uqIfv0icq0T0XJC8tZ8+9uZQPi//lfaPg4cGPGLX0R8+csRCxemravYbNy4Mf74xz/Gxo0bu3tXcjZy5MiYMWNGweZ4Gz58eJxwwgndWrF0zZo1OU0q311GjhwZp512mnn3dmDo0KHxpS99Ked5944++uiorKyMqVOnxty5c2P27NkxderU7SqrRkTst99+zcMlZ8+e3Tw8NjVcRkRcdNFFzT9fc8010bdv320CXVc48MAD40tf+lJOy06dOrX5545W35wwYULzPKH/7//9vzaXXbVqVYfW3RHr16+PZ555Jv7whz80h9jzzz+/ed9ak20HzOPYumJuj4qlLS/0ca3Qx+18KMX+UTFqr69OaSrqcDlqVMQBB0T07x9RW5u5crn//u2/bty4cXHppZduVzo+6+c/j7j33oi7784E1lQHHhhx9dURRx8dkVCcMK969+4dQ4YM6dAQrHKwdevWqK+v32b+v67U2NgYK1eujMbGxoJsrzUbNmyI559/vihL60dkOvaNjY15L68/duzYuOSSS5KGdxaDzZs3x5IlS3K+P6Xl1cg5c+bEwoULd3j/ZK9eveLII4+MiIj//M//jBtvvDEGDBgQhx12WPJ+H3jggc3rjoiYOXNmVFdXJ683ItPhGD58+HYdj9ra2njhhRfaXS5i20C56667dmj7w4YNi3322SciMtVb2/puZQv/dKUVK1Y0/zx+/PhWl8kO5c1e9Sr1+5266vvdVe1RPhRLW17o41qhj9vFoqf207La66tTuor6E33iiRHXXhtx+eUfPfeX+hSd9sYbEeedF3HddRHZOg3tnTlZtSqzfFsjq045JeKv/zriq1+N6Mac0WzMmDFx/vnnx5gxY7p7VwqqpqYmrr766pwnVE9VW1sbN954Y9TW1hZke6Vo6dKlceWVV+Z9YvBevXpF375927yKUwqWL18et956a873p0yePLn5nqxFixZFY2Njm8V5Wv7u7rvvjkMPPTRvUy9lr1727t07LrjggrysMyKiuro6zj333FbDak1NTTzxxBPtLvfoo49GRGbIXcsQnKuvf/3rEZGp6Pjggw+2uszChQtj8eLFHV53R7W8B29HU5U8//zzzcv26tWr5O936qrvd1e1R+Wk0Me1Qh+3i0U599NckezZijpcZmWHm44bF7Hbbu0vX1tbG7fcckurDeNZZ0XsuWfEX4od5nTm5KyzIs4/P+Kaa9re7k9+EvGnP6UPtQXat2LFirjzzju3uarTUxx88MHNP48YMaJ5/svWtAyX2Xv28uWoo46KjRs3xoYNG2L33XfP23rbc8YZZ8Rrr722w9//8pe/bJ6n8vvf/36nCqScffbZMXny5IiIuPjii7cLI3V1dfGtb30rb1dr23LkkUc2X9247LLLtpvcfu3atfG9732vy/ejkHry9xtKWa5XJNvqq1Pa0urFF8jcuZnHXK9aNjY2xtKlS7cb0vHII5l13XNPRK6jELZujchOEdfekNzx4yPOPjtztfWccyK682RUTU1N3H333fHVr36102fFKisr43Of+1xRFOiAj2toaIjFixd3eJqJQnjppZfipZdeiohonsx+/fr18etf/7p5mex0Hp3x2c9+Nu6///7YsGFDHH300W0Oqxo/fnzstdde8cYbb0RE+1OQ1NTUNFceffcv4/yz+73bbrttcy9jxI6rqc6ePTtqamq2CYEvvfRS87qmT5++w7alpqYmfvnLX8app566Tfs1YcKEWLx4cSxevDj23XffOOGEE2LixIkxbty46N27dyxevDgeffTReOGFF6J3795x/vnnxz/8wz9ss+7se9Pyyt6CBQuib9++MWbMmOb/n4qKivi3f/u3mDZtWrz33nux7777xje+8Y341Kc+FR9++GHccccdcdRRR8XkyZPjrrvuavP/IPtZaPl/mf33L1iwIN55551WlznkkEPigAMOiH333TeuuuqquOiii+Lll1+OT3/603H66afHrrvuGosXL44777xzuylOHnnkkdhll13i6KOPbt6PBQsWNP/+wQcfjFGjRsWUKVNiypQpre5/dyrm7zfko3+Uj35aKdtRX53SV/ThctOmj65cpt4m9OMfR4wYETF9+kfP1dbWxu9+97s44YQTWp0n7MUXI7L31h9xRPvb+Na3Im64IXMV8//8n7T9TbF169ZYt25d0j0MVVVVzRUIKV6VlZVxyCGHOAlQRH73u9/F5S3H80dm+OvXvva15r+nhMsvfvGL8fWvfz2amppymq/y6KOPjjfeeCOqq6tj3333bXPZ1157bZv9jIjmv8+cOXO7cLkjV155ZczNnhn8iwceeKB5Xs/33ntvh5/ZrVu3xoYNG7Zrv5566ql47bXXYvbs2bFgwYJYsmRJTJw4Ma644opYunRpDB06NPbYY4+48MIL49RTT4299957u3W39t7ceuutceutt8bhhx++zf/nhAkT4sUXX4xrrrkm7r///rj22mujsrIyJk2aFLNmzYqZM2fGqaeeGhHRaoXP1v4Psv+X2X//Lbfcsl04zS7z5JNPNhcw+vu///s48MAD44YbbogFCxbENddcE5WVlTFx4sT4u7/7u/jmN7+5TVGnH/7wh7HnnnvG0Ucf3ep+nHfeeRGRuRJajOGyJ9KWl4589I/y0U8rRu31qyl/RR8un3kmor4+83PK/ZYvvxwxf37EmWdmCgRltXfmJHs8Hj48Ipfj7+67R3z+85lKtz/8YcSwYZ3f5+5WX18fS5YsiXHjxjVP8E3xqaqqimOOOaa7d4MWZs2aFbNmzcpp2V69ekVFRUWH7i0bOXJk/Nd//VeMGjUqp2kLbrzxxrjxxhtzWvcRRxyRl2InTz31VPI6WjNx4sSYOHFinHvuubFkyZK49dZb49lnn825KERH3puIiCFDhsQVV1wRV1xxRau/zw5RHTFixHa/y+X/4M4774w777yz1d9liz1l3+dp06bFtGnTdriupqamWLp0adxxxx2xaNGi5mI4XfVekF/a8tKhf7RjrkhS9PdcZsNdVVVEOyfc23TPPZnHY4/t2Ov+/d8zj5//fO5Dab/85YgNGyIefrhj2yo2K1eujLvuuitWrlzZ3buSs+rq6rjgggsKch9URObegssuu6xbq501NDTEBx98ULTDx6qrq+O8884r2HtSasaOHRsXX3xxh6pidrQIEJ3z8ssvx5IlS9pc5s0334yI6JKrf515nzvzeepJirk9Kpa2vNDHtUIft/OhFPtHUCglEy6nTs093A0bNixOPPHEGNbisuHvf595zGVoa1ZTU8S8eR1/XTbA/va3ub+G/OjTp09UVlb2qEplK1asiNtvv71oC1/06dMnqqqq8v6eDB06NI477jjz+dFlvvKVr8R3vvOdHf7+zTffjFf/UkZ8esv7LUjWVd/vrmqP8qHY2/Ku0hOP27TeV6c8FHW4bGjIDIuNyNxvuXFj5l7G//bfMsNPR4+O+MIXIp59dtvXDRw4MCZPntxcbn/Fisw0IrvumhneuiM1NRF77BExYULmT3V1RPaE8fXXf/T83nu3Pd3IpEkRgwZFPPZY5t/QHUaMGBEzZ85sdahWOVu5cmXcc889BTubuHz58rjttttcQWrDqlWr4r777sv7ZPODBg2Kz3zmMzFo0KC8rrfQamtr4+c//7mKeS2MHDkyzjjjjHYnVc91uRQPP/xwPP3009s9v2HDhjjzzDMjIjOU+K//+q+7bB86olw+T131/e6q9qicFPq4VujjdrHoqf20rI/31SkfRR0un3suEygjMpVXDz44E9Yeeyzi7bcjXnstM2/lX/3VtnNQ1tXVxYIFC5onlX7mmcxVyL/Mib2NlmdOxoyJeOutiPffz/z59rczy3zqUx899/77mfs3+7Zxt2rv3pkhvJs2tT03Zlfq379/TJgwocfdC1BfXx9vvvlm1Gdv1O1imzdvjg8//LDkJyzvSps2bYpXX301Nm3alNf1btiwIRYtWtTtE46namxsjNraWventFBRURHjx4+PioqKvCzXWb169YqGhoaYNm1azJw5M2644Ya47bbb4gc/+EFMnDgx5s6dGwcffHD85je/6ZLtd0a5fJ666vvdVe1ROSn0ca3Qx+1iUa79tFyvSH68r075KOpw2bK43eWXR9x4Y8Sll0ZkpywbNSriK1/JBNCbbvpo2XXr1sXjjz/eXGghO+f0+PHbb6OtMyfZ7XemSu0nP5l5bFFdvqDWrl0bc+bMibVr13Z6Hb17944hQ4a0Oc0BdJc1a9bEww8/HGuy5Zx7kM4UASola9eujccee6zd9ivX5Tpr7ty5cf3118cxxxwT8+fPj4svvjjOPvvs+Od//uf49Kc/HbfddlvMmzevyyoilvv73Jae/P2m+OWjf5SPfloxyvWK5Mf76pSPoq4W2zJc3nRTxOGHb79M9oT1O+/seD3Z37V2b3pdXV38+c9/jn322WebMu4fH5LbUTvvnHl85ZWOvzYf1q9fH08//XRMnjw5qqqqOrWOMWPGxPnnn5/nPSPfevfuHYMGDXISoAfJFm0pV+vXr49nnnkmpkyZ0mb7letynbXTTjvFd7/73fjud7+b93XnotzfZ7alLS8d+egf5aOfVox21K+m5yjaFqyxMeI//iPz84wZEccf3/py//Vfmce27qXM3nrSWl2AHZ05aTkktzNToGRPZLsVj642ZsyYuPDCC3vkJMwA5UJbTjlwRZKiDZcvvBCRHYb9l5oJrVqwIPPYylzZzbLrGTAg9+1nr5pWV0fstVfur8vKjgYo5RE9NTU18dOf/jRqamq6e1dyNmTIkPjCF74QQ4YMKcj2hg0bFtOnT1ftrA1DhgyJadOmFew9KTXDhw+Pk08+OYa3dYbsY8qlaAtt68z73JnPU0+iPWpfoY9rhT5u50Mp9o+gUIo2XGbD3cCBmUI+rXn77UyBnYiIo4766Pn+/fvHnnvu2XyTdPae9LaK8Hxcdn7Lzly1jCiPcLl169ZYt25dbN26tbt3JWeDBw+OqVOnFmwoxsCBA2PKlCndWu1s2bJl8bOf/SyWLVvWbfvQlsGDB8dhhx2W9/ekoqIidt111y4r5lIoAwYMiL322isGdODsV7kUbaFtnXmfO/N5KkZd9f3uqvYoH4qlLS/0ca3Qx+18KMX+UbH5eF+d8lG04TIb7qZO/ei+yo+7777M4047RRx44EfPjxgxIk455ZTm8s7ZSua5FofbsiUiW3m+M/dbRnQu0ObTwIEDY//99+9xJZ43btwYr7zySmzMjmnuYuvXr4+FCxfG+vXrC7K91mzZsiVWrVoVW7Zs6bZ9aMumTZvijTfeyHt1xpEjR8Zpp53WpdNQFEJdXV3MmzdPxbwWBg0aFAcccEC701DkulxPUi6fp676fndVe5QPxdKWF/q4VujjdrHoqf20rI/31SkfBQmXf/7zn+PJJ5/MefmtWyPmz8/8fMQRO17uX/8183jiiZnpP7K2bNkS69evb26gsyMtWjuWtHbmZNGij4bSdjZcZtvI7joRN2zYsDj++ON73HDN1atXx/333x+rV68uyPbWrl0bjz76aNlVe8unVatWxb333pv3eeWampqisbExmpqa8rreQlu3bl088cQT7k9pYejQofGlL30phrZ2o3wnlutJyuXz1FXf765qj8pJoY9rhT5uF4ty7aflekXy4311ykeXh8umpqY48sgj49hjj835rNSf/vTRcNK/+qvWl3nppYgXX8z8PGPGR8/Pnh3x+uvL4tprr20eWpKdgqS121ZaO3OSHZI7eHDEfvttu/z8+RF33NH+vyF7XM9Om1JomzdvjmXLlpl/kbK1dOnSuPLKK2Pp0qXdvSvk2ebNm2PJkiXttl+5Lkfp8f2m3JVrPy3XK5LLlm3bV6d8dHm4fOSRR6K2tjYaGhriF7/4RU6vyYa7QYMiDjqo9WWyAW/SpI+GxG7dGnHaaREfnxJst90yjx98sP16Wjtz0nJIbp8+2y5/6aURu+zS/r/hww8zj5/6VPvLdoXly5fHzTffHMsTytWOGDEiZs6cacgCFJlyL9qyfPnyuPXWW9ttv3JdrlSV+/sMpSof/aN89NOKkSuSdGm4bGpqilmzZkV1dXVUV1fH1VdfndPVy2y4bOt+y9/+NvP48auWkydvPy3JvvtmHt97b/v1tHbm5K23Mo+HHLLtso8/nhnueuSR7f4TmsPlnnu2v2yx6t+/f0yYMMHN1kVuxIgR8dWvftVJgB6kXIq20Dbvc8+iLS8d+kc75ookXRouH3nkkXj++edjv/32i5133jmWLVvW7tXLpqaIefMyP7d1v2V22Gy2SuzWrRE//GHERRdtv+xnPhNRWZkZRptLYa/sFFPZ4bQREatWRZx7bsTtt7f/+oiIP/858/jxgFpK1q5dG3PmzCmp+wn79u0bY8eOjb4FqqRUUVERu+22W7dWLO3fv3/svvvuRXuQ69u3b4wePbpg70mpGTBgQEyaNKlDAaJcirbQts68z535PPUkxdweFUtbXujjWqGP2/lQiv0jKJQuC5fZq5aHHnpojBs3LgYOHBhf+9rX2r16+corEStXZn7e0f2WERHHH595rK/PFOr5znciDjggYtq07Zft2zfi85+PWL8+4rXX2t/3M87IPL7++kePxx4bccklmSuj7Vm+PDMEd7fdPgqqpWj9+vXx9NNPd2sl1I4aPXp0nHXWWTF69OiCbG/kyJExY8aMbq1Yum7dunjqqaeKtoDH6NGj45xzzinYe1Jqhg8fHieddFKHhj6WS9EW2taZ97kzn6eepJjbo2Jpywt9XCv0cTsfSrF/BIXSZeFy3rx58fzzz8esWbOi119ugrzkkkti2bJlcc899+zwdVVVEdXVEccckxkWuyP/+I+Z+ytPOikz7HXcuMxzERFjxoyJiy66KMa0SHZ/+7eZx0cfbX/fTz01s66HHoqYMCHif/7PiKuuivja19p/bcRHw3qnT89t+a7S5+M3jJJ3W7dujfr6+m6d66quri7mzp3b465iVVdXx3nnnRfV1dXdvStJtmzZEmvXrnV/Sgu9evWKioqK5mNH6nI9Sbl8nsrl+90RxdKWF8Nxrafoyf201vrqlIcuC5e77757/NM//VNMa3Epcffdd49/+Zd/iUPaGCu6yy4RNTUR//f/bju9yMcNHZop6rNkScQbb2QK7WSX7927d/Tv3z96t1jB9OmZAkEPPZTb/n/rW5l7L99/P1MhNpf7LLP+7d8yj//jf+T+mnwbN25cXHrppTFu3Lju24lusGTJkrjiiitiyZIlBdleTU1NXH311VFTU1OQ7ZWipUuXxo9//OO8V33s06dPVFVVlfzBedmyZXHddde5P6WFsWPHxsUXXxxjx47Ny3I9Sbl8nrrq+91V7VE5KfRxrdDH7WLRU/tpWa311SkPXfaO7rTTTnHWWWdtd0b5b//2b2PSpEldtdmIiFixYkX8+te/jhUrVjQ/N3Ro5grk/PkRb7750bL5PnOyaVMmwB5wQOYPhVfqZ+zLTVNTUzQ0NHTJfHX33Xef+eqgDHXV97ur2iPSOG6Xj1z71a311SkPZXm6oKGhId55551oaGjY5vkLLojo3z/ipps+ei7fZ07+9V8z94x+//t5WV2n1dbWxi233BK1rU3umaOBAwfG/vvvHwMHDszjnkF+bNq0KV599dXYtGlTd+9KwZV70Zba2tr4+c9/3m77letyparc3+e29OTvN8UvH/2jfPTTilGu/eod9dUpfWUZLndk/PiIH/wg4pZbIhYvzjyXzzMnW7ZE/O//nZl387//9+TVJWlsbIylS5dGY2Njp9cxbNiwOP7442PYsGH52zHybsCAAbHPPvv0yA5oT1XuRVsaGxujtra23fYr1+VKVbm/z2xLW1468tE/ykc/rRi5IkmPCpcREX//95m5J7/3vczf83nm5M47M5Vlb7ml7ftFS8XmzZtj2bJlsXnz5u7eFdowfPjwOOGEE3RAe5ByKdpC27zPPYu2vHToH+2YK5KUQQTqmIqKiN//PuKppzJhMF8+/DDiwgsjrrwyYv/987fe7rR8+fK4+eabY/ny5d29KzkbNWpUfPOb34xRo0YVZHvV1dVxwQUXdGtFw8bGxli5cmXRnv0cNWpUnHnmmQV7T0rN2LFj45JLLulQUZpyKdpC2zrzPnfm89STFHN7VCxteaGPa4U+budDKfaPoFDKMlxWVVXFF7/4xaiqqmr195/8ZKbozg9+EPHii+nb27w5YsaMiOOOy1wZpfv069cvqquro1+/fgXZXp8+faKysrJbK5bW1tbGjTfeWLT3bfTr1y/GjRuX9/dkyJAhMW3atBgyZEhe11tovXr1ir59+5pOg7wol89TV32/u6o9yodiacsLfVwr9HGb4tBeX53SVZbhsrKyMg466KCorKzc4TKf/WxmupOrrkrbVlNTZr7NPfaIuP32tHXl07Bhw+LEE0/scfdLrl69Oh566KFYvXp1Qba3cuXKuOeee2LlypUF2V4pWrNmTfzhD3+INWvW5HW9gwcPjsMOOywGDx6c1/UW2ooVK+LOO+90f0oLw4cPj5NPPrnd4YG5LteTlMvnqau+313VHpWTQh/XCn3cLhY9tZ+WlUtfndJUluFy48aN8dJLL8XGjRvbXG7KlIhHH007c7JxY8Sxx0b84hcRxTTd3sCBA2Py5Mk9rtLrxo0b449//GO7732+1NfXx5tvvhn19fUF2V4p2rBhQzz//POxYcOGvK5306ZN8cYbb5R8NcmGhoZYvHix+1NaGDBgQOy1117tFjbJdbmepFw+T131/e6q9qicFPq4VujjdrEo135arlckc+2rU3rKMlyuXr06HnjggZzOgqWeORk0KOJrX+vUS7tUXV1dLFiwIOrq6pLWU+oT1FO+Vq1aFffee695LstQXV1dzJs3r932K9flKD2+3xS71P5RvvppxSbXfnVH+uqUlrIMlx1RrmdO1q1bF48//nisW7eu0+sYN25cXHrppTFu3Lg87hmQqtyLtqxbty6eeOKJdtuvXJcrVeX+PkOpykf/KB/9tGJUrv1qctfjw6UzJ5S6cePGxWWXXeYkQA9SLkVbaJv3uWfRllMO9Kvp8eGSHautrY1bbrml2yvXdURlZWV87nOfK9gN4kOGDIkvfOELJV+xtCtVVlbGIYcc4qb9HRg6dGgcd9xxMXTo0JxfUy5FW2hbZ97nznyeehLtUfsKfVwr9HE7H0qxfwSFUpbhsl+/frHzzjsra52osbExli5d2u1zbnVEVVVVHHXUUQUrbT148OCYOnVqt1YsXb58edx2221FO99WVVVVHHPMMXl/T/r27RujR4+Ovn375nW9hTZo0KD4zGc+E4MGDcr5NeVStIW2deZ97sznqRh11fe7q9qjfCiWtrzQx7VCH7fzoRT7R8VGX718lWW4HDVqVHz9618vqQl5861///6x5557Rv/+/bt7Vwqqvr4+3n///YJWuXvllVe69d6CzZs3x4cffhibN2/utn1oS0NDQ3zwwQd5D0KjR4+Oc845J0aPHp3X9Rbahg0bYtGiRapXtjBgwICYNGlSTtVic1muJymXz1NXfb+7qj3Kh2Jpywt9XCv0cbtY9NR+Wpa+evkqy3DZEeV65mTEiBFxyimnxIgRI7p7Vwpq5cqVcddddxV0fq7777/fvQVtWLFiRdx+++2GcO7AmjVr4uGHHzbvXgvDhw+Pk046Kad5LnNZrifxeWqb9qh9hT6uFfq4XSzKtZ9Wrv1qcleW4XLJkiVx+eWXx5IlS9pdtlzPnGzZsiXWr18fW7Zs6e5dgS6xdOnS+PGPfxxLly7t7l0hz7Zs2RJr165tt/3KdTlKj+835a5c+2m59qs70lentJRluCRi2bJlce2118ayZcs6vY5hw4bFiSeeGMOGDcvfjkGeNDU1RUNDQzQ1NXX3rhRcuRdtWbZsWVx33XXttl+5Lleqyv19bktP/n5T/PLRP8pHPw2KUY8Pl86c7NjAgQNj8uTJMXDgwO7eFdowbNiwmD59upMAPUi5FG2hbd7nnkVbXjr0j3ZMv5oeHy7Zsbq6uliwYEHU1dV1967krHfv3jFkyJDo3bswH+2+ffvG2LFju7Vi6cCBA2PKlClFe5Dr3bt3DBo0qGDvSampqKiIXXfdNSoqKnJ+TbkUbaFtnXmfO/N56kmKuT0qlra80Me1Qh+386EU+0dQKKVdw38HBg8eHIcffnhOZbQ7smwpyce/q6mpKerr60tqWNKYMWPi/PPPL9j2Ro8eHWeddVbBtleKxowZExdeeGHe11su392RI0fGaaed1qHXlPu9hrm+t+XyGdiRzrzPnfk8FaOuem+7qj0qJ4U+rhX6uJ0P+egflWv7pf2mV1MBksPpp58eb731VsyfP7+rNwUAAEA3KJ0xCAAAABQt4RIAAIBkwiUAAADJhEsAAACSCZcAAAAkEy4BAABIJlwCAACQTLgEAAAgmXAJAABAMuESAACAZMIlAAAAyYRLAAAAkgmXAAAAJBMuAQAASCZcAgAAkEy4BAAAIJlwCQAAQDLhEgAAgGTCJQAAAMmESwAAAJIJlwAAACQTLgEAAEgmXAIAAJBMuAQAACCZcAkAAEAy4RIAAIBkwiUAAADJhEsAAACSCZcAAAAkEy4BAABIJlwCAACQTLgEAAAgmXAJAABAMuESAACAZMIlAAAAyYRLAAAAkgmXAAAAJBMuAQAASCZcAgAAkEy4BAAAIJlwCQAAQDLhEgAAgGTCJQAAAMmESwAAAJIJlwAAACQTLgEAAEgmXAIAAJBMuAQAACCZcAkAAEAy4RIAAIBkwiUAAADJhEsAAACSCZcAAAAkEy4BAABIJlwCAACQTLgEAAAgmXAJAABAMuESAACAZMIlAAAAyYRLAAAAkgmXAAAAJBMuAQAASCZcAgAAkEy4BAAAIJlwCQAAQDLhEgAAgGTCJQAAAMmESwAAAJIJlwAAACQTLgEAAEgmXAIAAJBMuAQAACCZcAkAAEAy4RIAAIBkwiUAAADJhEsAAACSCZcAAAAkEy4BAABIJlwCAACQTLgEAAAgmXAJAABAMuESAACAZMIlAAAAyYRLAAAAkgmXAAAAJBMuAQAASCZcAgAAkEy4BAAAIJlwCQAAQDLhEgAAgGTCJQAAAMmESwAAAJIJlwAAACQTLgEAAEgmXAIAAJBMuAQAACCZcAkAAEAy4RIAAIBkwiUAAADJhEsAAACSCZcAAAAkEy4BAABIJlwCAACQTLgEAAAgmXAJAABAMuESAACAZMIlAAAAyYRLAAAAkgmXAAAAJBMuAQAASCZcAgAAkEy4BAAAIJlwCQAAQDLhEgAAgGTCJQAAAMmESwAAAJIJlwAAACQTLgEAAEgmXAIAAJBMuAQAACCZcAkAAEAy4RIAAIBkwiUAAADJhEsAAACSCZcAAAAkEy4BAABIJlwCAACQTLgEAAAgmXAJAABAMuESAACAZMIlAAAAyYRLAAAAkgmXAAAAJBMuAQAASCZcAgAAkEy4BAAAIJlwCQAAQDLhEgAAgGTCJQAAAMmESwAAAJIJlwAAACQTLgEAAEgmXAIAAJBMuAQAACCZcAkAAEAy4RIAAIBkwiUAAADJhEsAAACSCZcAAAAkEy4BAABIJlwCAACQTLgEAAAgmXAJAABAMuESAACAZMIlAAAAyYRLAAAAkgmXAAAAJBMuAQAASCZcAgAAkEy4BAAAIJlwCQAAQDLhEgAAgGTCJQAAAMmESwAAAJIJlwAAACQTLgEAAEgmXAIAAJBMuAQAACCZcAkAAEAy4RIAAIBkwiUAAADJhEsAAACSCZcAAAAkEy4BAABIJlwCAACQTLgEAAAgmXAJAABAMuESAACAZMIlAAAAyYRLAAAAkgmXAAAAJBMuAQAASCZcAgAAkEy4BAAAIJlwCQAAQDLhEgAAgGTCJQAAAMmESwAAAJIJlwAAACQTLgEAAEgmXAIAAJBMuAQAACCZcAkAAEAy4RIAAIBkwiUAAADJhEsAAACSCZcAAAAkEy4BAABIJlwCAACQTLgEAAAgmXAJAABAMuESAACAZMIlAAAAyYRLAAAAkgmXAAAAJBMuAQAASCZcAgAAkEy4BAAAIJlwCQAAQDLhEgAAgGTCJQAAAMmESwAAAJIJlwAAACQTLgEAAEgmXAIAAJBMuAQAACCZcAkAAEAy4RIAAIBkwiUAAADJhEsAAACSCZcAAAAkEy4BAABIJlwCAACQTLgEAAAgmXAJAABAMuESAACAZMIlAAAAyYRLAAAAkgmXAAAAJBMuAQAASCZcAgAAkEy4BAAAIJlwCQAAQDLhEgAAgGTCJQAAAMmESwAAAJIJlwAAACQTLgEAAEgmXAIAAJBMuAQAACCZcAkAAEAy4RIAAIBkwiUAAADJhEsAAACSCZcAAAAkEy4BAABIJlwCAACQTLgEAAAgmXAJAABAMuESAACAZMIlAAAAyYRLAAAAkgmXAAAAJBMuAQAASCZcAgAAkEy4BAAAIJlwCQAAQDLhEgAAgGTCJQAAAMmESwAAAJIJlwAAACQTLgEAAEgmXAIAAJBMuAQAACCZcAkAAEAy4RIAAIBkwiUAAADJhEsAAACSCZcAAAAkEy4BAABIJlwCAACQTLgEAAAgmXAJAABAMuESAACAZMIlAAAAyYRLAAAAkgmXAAAAJBMuAQAASCZcAgAAkEy4BAAAIJlwCQAAQDLhEgAAgGTCJQAAAMmESwAAAJIJlwAAACQTLgEAAEgmXAIAAJBMuAQAACCZcAkAAEAy4RIAAIBkwiUAAADJhEsAAACSCZcAAAAkEy4BAABIJlwCAAD0QO+++248+OCD0djYmJf1CZcAAAA90Lx582L69OkxadKk+NWvfpUcMoVLAACAHmjmzJnxwgsvxMSJE+PUU09NDpm9mpqamjrygquvvjr+4z/+o0Mb+dOf/hR1dXVx6KGHduh1AAAAdL3Vq1fHm2++GTU1NTF48OCYM2dOHHzwwR1ahyuXAAAAJOvwlcvOOP300+Ott96K+fPnd/WmAAAAyNGiRYvi8ssvj4ceeij22GOP+NGPfhQnn3xy9O3bt8Pr6vgrAAAAKHl33XVXnHbaabHHHnvEr371q06HyizhEgAAoAf6/Oc/Hw888EB8+ctfTgqVWe65BAAAKBOrVq2K6667Ll599dV2l/3kJz8ZX/nKV/ISLCOESwAAgLJx1llnxfnnnx/XXHNNwbctXAIAAJSBrVu3xuOPPx4REfvvv3/Bty9cAgAAlIEXX3wx1qxZExERRxxxRMG3L1wCAACUgblz50ZExPDhw2PKlCkF375wCQAAUAb+/d//PSIyVWB79y581BMuAQAASlxTU1PMmzcvIrpnSGyEcAkAAFByampqYo899ogJEybEhAkTorq6OpYvXx4REddff33z83vvvXc0NjYWZJ/yM6EJAAAABTNmzJh46623mv9++eWXx6xZs+JTn/pUvPPOO92yT65cAgAAlLhsMZ/DDjus2/ZBuAQAAChhDQ0N8cwzz0SEcAkAAEAnPffcc7Fx48aIiDj00EO7bT+ESwAAgBKWHRJbXV0de+21V7fth3AJAABQwrLzW3bnVcsI4RIAAKBkbdmyJZ5++umI6N77LSOESwAAgJK1aNGiqKuriwjhEgAAgE7K3m85ePDg2G+//bb53fz58+OOO+4o2L4IlwAAACUqe7/l1KlTo0+fPtv87tJLL41ddtmlYPsiXAIAAJSot956KyIiDjnkkG2ef/zxx2Pjxo1x5JFHFmxfhEsAAIASNWbMmIiIGD9+fPNzq1atinPPPTduv/32gu6LcAkAAFCizjjjjIiIeP3115sfjz322Ljkkkti8uTJBd2XvgXdGgAAAHlz6qmnxrp16+L666+P3/72t7HzzjvHVVddVdDhsFm9mpqamrp6I6effnq89dZbMX/+/K7eFAAAAN2gIFcuDzrooBg7dmwhNgUAAEA3KMiVSwAAAMqbgj4AAAAkEy4BAABIJlwCAACQTLgEAAAgmXAJAABAMuESAACAZMIlAAAAyYRLAAAAkgmXAAAAJBMuAQAASCZcAgAAkEy4BAAAIJlwCQAAQLL/D0ArG8x025cFAAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "import matplotlib\n",
        "from os import linesep\n",
        "from numpy import linspace,cos,pi,sin,random,arccos,heaviside,array\n",
        "from scipy.optimize import fsolve\n",
        "import matplotlib.pyplot as plt\n",
        "from matplotlib import animation,rc\n",
        "rc('animation', html='jshtml')\n",
        "plt.rcParams.update({\"font.family\" : \"serif\",\"mathtext.fontset\" : \"cm\"})\n",
        "\n",
        "#functions\n",
        "def carr(f,t): #carrier\n",
        "  return 1/pi*arccos(cos(2*pi*f*t))\n",
        "\n",
        "def m(MI,f,theta,t): #modulation function\n",
        "  return (MI*cos(2*pi*f*t + theta) + 1)/2\n",
        "\n",
        "def h(ct,mt): #PWM switching function\n",
        "  return heaviside(mt-ct,0)\n",
        "\n",
        "# draw dotted line between two points in two different plots\n",
        "def l2Ax(fig,p1,p2):\n",
        "  transFigure = fig.transFigure.inverted()\n",
        "  p1_g = transFigure.transform(ax_lst[0].transData.transform(p1))\n",
        "  p2_g = transFigure.transform(ax_lst[1].transData.transform(p2))\n",
        "  line = matplotlib.lines.Line2D((p1_g[0],p2_g[0]),(p1_g[1],p2_g[1]),\n",
        "                      transform=fig.transFigure,ls='--',color='gray', lw=1)\n",
        "  fig.lines.append(line)\n",
        "  return\n",
        "\n",
        "#parameters\n",
        "Nf = 2500 # number of frames\n",
        "fc = 12 # carrier frequency\n",
        "fm = 1 # signal\n",
        "MI = 0.7 # modulation index\n",
        "theta = 0\n",
        "\n",
        "#time series\n",
        "t=linspace(0,1,Nf)\n",
        "ct = carr(fc,t) #carrier time-domain signal\n",
        "mt = m(MI,fm,0,t) #modulation function time series\n",
        "ht = h(ct,mt) #pwm signal time series\n",
        "\n",
        "#intersection points\n",
        "def y(x):\n",
        "  return m(MI,fm,theta,x) -carr(fc,x)\n",
        "ts=[] #list for intersection points\n",
        "for k in range(fc):\n",
        "  ts.append(fsolve(y,1/fc*(0.25+k))[0])\n",
        "  ts.append(fsolve(y,1/fc*(0.75+k))[0])\n",
        "mts = m(MI,fm,theta,array(ts)) #m(t) values at intersection points\n",
        "# print(len(ts))\n",
        "#set up figures\n",
        "fig = plt.figure(figsize=(9,9))\n",
        "fig.tight_layout()\n",
        "ax_frame = [[[0, 0.5, 1, .4], [-.02,1.1], [-.1,1.1]], #sine & triangle\n",
        "            [[0, 0,   1, .4], [-.02,1.1], [-.1,1.1]], # pwm\n",
        "            ]# [pos-boundary, xlim, ylim] for subplots\n",
        "ax_lbl=[['$c(t),$', '$t$'], [r'$h(t)$', '$t$'],] #yx axes labels\n",
        "clst=['m','b','b'] #colors of lines\n",
        "ax_lst=[] #axis list or the list of subplots\n",
        "lines = [] #array for all lines\n",
        "for k in range(len(ax_frame)):\n",
        "  xn,xm,yn,ym = ax_frame[k][1]+ax_frame[k][2]\n",
        "  ax=fig.add_axes(ax_frame[k][0],xlim=[xn,xm], ylim=[yn,ym],fc='none') #no fc\n",
        "  ax.axis('off') #turn off axis frames\n",
        "  ax_lst.append(ax)\n",
        "  ax.annotate(\"\", (xm, 0), (xn, 0),arrowprops={'arrowstyle':\"->\"}) #x-axis\n",
        "  ax.annotate(\"\", (0,ym), (0,yn),arrowprops={'arrowstyle':\"->\"}) #y-axis\n",
        "  if k==0:\n",
        "    lines.append(ax.plot([], [], clst[k], lw=1)[0]) #triangle carrier\n",
        "    lines.append(ax.plot([], [], clst[k+2], lw=2)[0]) #sine reference\n",
        "    lines.append(ax.plot([], [], color='k', ls='',marker='o',markersize=5)[0]) #sine reference\n",
        "    y_text=ax.text(0.1,ym,'$m(t)$',size=24,va='center',color=clst[k+2]) # addtional ylabel\n",
        "  else:\n",
        "    lines.append(ax.plot([], [], clst[k], lw=1.5)[0]) #pwm\n",
        "  ax.text(xm-.02,0,ax_lbl[k][-1],size=24,va='top',ha='right') #x-axis label\n",
        "  y_text=ax.text(0.01,ym,ax_lbl[k][0],size=24,va='center',color=clst[k]) #y label\n",
        "ax_lst[0].text(0.5,ax_frame[0][2][1]+0.1,'Sine and Triangle',va='bottom',ha='center',size=20)\n",
        "ax_lst[1].text(0.5,ax_frame[0][2][1]+0.1,'PWM Signal',va='top',ha='center',size=20)\n",
        "\n",
        "# for k in range(len(ts)):\n",
        "#   l2Ax(fig,[ts[k],mts[k]],[ts[k],1])\n",
        "# animation function. This is called sequentially\n",
        "def animate(i):\n",
        "  k = int(t[i]*fc) # the kth carrier period\n",
        "  if k==fc:\n",
        "    return\n",
        "  if (t[i] - ts[2*k]>=0) and (t[i-1] - ts[2*k]<=0):\n",
        "    l2Ax(fig,[ts[2*k],mts[2*k]],[ts[2*k],1])\n",
        "    lines[2].set_data(ts[:2*k+1], mts[:2*k+1])\n",
        "  if (t[i] - ts[2*k+1]>=0) and (t[i-1] - ts[2*k+1]<=0):\n",
        "    l2Ax(fig,[ts[2*k+1],mts[2*k+1]],[ts[2*k+1],1])\n",
        "    lines[2].set_data(ts[:2*k+2], mts[:2*k+2])\n",
        "  lines[0].set_data(t[:i+1],ct[:i+1])\n",
        "  lines[1].set_data(t[:i+1],mt[:i+1])\n",
        "  lines[3].set_data(t[:i+1],ht[:i+1])\n",
        "  return\n",
        "\n",
        "anim = animation.FuncAnimation(fig, animate, frames=Nf, interval=50)\n",
        "# anim #uncomment to generate animation in the output area\n",
        "# to save the animation, uncomment the following three lines\n",
        "fn = r\"PWM_sineTriangle_aligned.mp4\"\n",
        "writervideo = animation.FFMpegWriter(fps=100)\n",
        "anim.save(fn, writer=writervideo,dpi = 120)"
      ]
    }
  ]
}