HomingBullet

homingbullet.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "HomingBallet",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyN2rH5pHeu3HiO5JxThqWgl",
      "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/gist/botamochi6277/17f1949d69e4bea8607aa0eac9c50543/homingballet.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JKfVV-E4nQgm",
        "colab_type": "text"
      },
      "source": [
        "[ジャンプSQ 2020年 4月号](https://jumpsq.shueisha.co.jp/sq/)の[ワールドトリガー](https://jumpsq.shueisha.co.jp/rensai/worldtrigger/)の誘導弾(ハウンド)の解説を実際に検証してみます． \n",
        "\n",
        "この解説では，誘導弾の誘導性能を調整することで弾を散らしたり集中させたりすることができると説明されています．また，基本は無し->強->弱の順に誘導性能を調整するのが標準的な使い方だとしています．\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wAyU8COAnKWV",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import pandas as pd\n",
        "from google.colab import files # to download files\n",
        "plt.style.use('seaborn-colorblind')\n",
        "plt.style.use('seaborn-whitegrid')\n",
        "\n",
        "plt.rcParams['figure.figsize'] = 800/72,600/72\n",
        "plt.rcParams[\"font.size\"] = 21"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "v_i4K1zljuLB",
        "colab_type": "text"
      },
      "source": [
        "弾の誘導を[PD制御](https://ja.wikipedia.org/wiki/PID%E5%88%B6%E5%BE%A1)で行なっていると仮定します． PD制御では目標との距離$d$に応じて力$f$を弾に加えます．力$f$は次式で決められます．\n",
        "\n",
        "\\begin{align}\n",
        "f &= k_p d + k_d \\dot{d}\n",
        "\\end{align}\n",
        "\n",
        "そして，弾の質量を$m$, 加速度を$a$とすると運動方程式は次のようになります．\n",
        "\n",
        "\\begin{align}\n",
        "ma &= f\\\\\n",
        "ma &= k_p d + k_d \\dot{d}\n",
        "\\end{align}\n",
        "\n",
        "SQで述べられている誘導性能は$k_p,k_d$のことだと思われます．ここからはこの2つのパラメーターを調整してシミュレーションを行なっていきます．"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "t6JUldpQrLzf",
        "colab_type": "code",
        "outputId": "3840c25f-df95-4b17-c092-96e5c84051b5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 860
        }
      },
      "source": [
        "mass = 1.0 \n",
        "target = np.array([30.0,0.0]) # target location\n",
        "delta_t = 0.1 # time step\n",
        "\n",
        "k_p = 0.3\n",
        "k_d = 1\n",
        "\n",
        "plt.plot(target[0],target[1],'o',markersize=10) # Plot Target\n",
        "\n",
        "v0 = 5 # magnitude of initial velocity\n",
        "acc_max = 1000\n",
        "\n",
        "for theta in np.linspace(0.1*np.pi,0.6*np.pi,num=6):\n",
        "  pos = np.array([0.0,0.0])\n",
        "  diff = target - pos\n",
        "  prev_diff = diff\n",
        "  acc = np.array([0.0,0.0])  # (initial) acceleration\n",
        "\n",
        "  time = 0.0\n",
        "  vel = np.array([v0*np.cos(theta),v0*np.sin(theta)]) # (initial) velocity\n",
        "  display(\"theta: {0}, vel: {1}\".format(theta, vel))\n",
        "  df = pd.DataFrame({\"time\":[time],\"x\":[pos[0]],\"y\":[pos[1]]})\n",
        "  # display(diff,np.linalg.norm(diff) )\n",
        "\n",
        "  while True:\n",
        "    time += delta_t\n",
        "    if time > 15:\n",
        "      display(\"timeup\")\n",
        "      break\n",
        "    if np.linalg.norm(diff) < 0.5e-0:\n",
        "      display(\"hit at {0}\".format(time))\n",
        "      break\n",
        "    diff = target - pos\n",
        "    dot_diff = (diff - prev_diff)/delta_t # \\dot{d}\n",
        "    force = k_p * diff + k_d*dot_diff\n",
        "    # print(force)\n",
        "    acc = force/mass\n",
        "    if np.linalg.norm(acc) > acc_max:\n",
        "      acc = acc/np.linalg.norm(acc)*acc_max\n",
        "    vel += acc*delta_t\n",
        "    pos += vel*delta_t\n",
        "    prev_diff = diff\n",
        "\n",
        "    # save to plot\n",
        "    df2 = pd.DataFrame({\"time\":[time],\"x\":[pos[0]],\"y\":[pos[1]]})\n",
        "    df = df.append(df2)\n",
        "\n",
        "  # Plot Trail\n",
        "  print(\"plot\")\n",
        "  plt.plot(df.x,df.y,'.',label=\"{0:.1f}\".format(theta))\n",
        "\n",
        "plt.xlabel(\"x\")\n",
        "plt.ylabel(\"y\")\n",
        "plt.title(\"v0: {0}, k_p: {1}, k_d: {2}\".format(v0,k_p,k_d))\n",
        "plt.axis('equal')\n",
        "plt.legend()\n",
        "filename = \"ballet01.png\"\n",
        "plt.savefig(filename)\n",
        "# files.download(filename) \n"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'theta: 0.3141592653589793, vel: [4.75528258 1.54508497]'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'hit at 8.899999999999984'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "plot\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'theta: 0.6283185307179586, vel: [4.04508497 2.93892626]'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'hit at 9.099999999999984'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "plot\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'theta: 0.9424777960769379, vel: [2.93892626 4.04508497]'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'hit at 9.299999999999983'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "plot\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'theta: 1.2566370614359172, vel: [1.54508497 4.75528258]'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'hit at 9.499999999999982'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "plot\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'theta: 1.5707963267948966, vel: [3.061617e-16 5.000000e+00]'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'hit at 9.699999999999982'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "plot\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'theta: 1.8849555921538759, vel: [-1.54508497  4.75528258]'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'hit at 9.799999999999981'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "plot\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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+0zWvGbruNUPXvWbouvuernnNqE3X3W8DrsFgcLrdYrE4HRcfH+/xOVUmIyOj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\nAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FxpQKkrMOgb6",
        "colab_type": "text"
      },
      "source": [
        "$k_p,k_d$を時間に応じて変えていきます．\n",
        "SQでの解説に合わせて，ゲインを無し→強→弱の順に変化させます．今回はガウス関数とシグモイド関数を使用してゲインを調整します．\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "44Z452hSv3ex",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def sigmoid(x):\n",
        "    return 1.0 / (1.0 + np.exp(-x))\n",
        "\n",
        "def gauss(x, a = 1, mu = 0, sigma = 1):\n",
        "    return a * np.exp(-(x - mu)**2 / (2*sigma**2))\n",
        "\n",
        "def gain_exp(time, final, peak, peak_time = 2.0):\n",
        "  return gauss(time,peak,peak_time,sigma=1) + final*sigmoid(time - peak_time)\n",
        "\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ptIrghiLQoF1",
        "colab_type": "code",
        "outputId": "d9f86df6-d3a4-4ef1-b16a-00b6d2c00637",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 533
        }
      },
      "source": [
        "t = np.linspace(0,10)\n",
        "k = gain_exp(t,0.3,0.3*4,2.5)\n",
        "plt.plot(t,k)\n",
        "plt.xlabel(\"time\")\n",
        "plt.ylabel(\"gain\")\n",
        "filename = \"gain.png\"\n",
        "plt.savefig(filename)\n",
        "# files.download(filename) \n"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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b7Vq3t5z5WA+UmhCp+IggiiwAoN0osvAqe8trVVRZr4l9WT/W01gsFp07KFar\ndpfKbrebjgMA8AAUWXiVlvnYiczHeqRpg2NVWFmvzKIq01EAAB6AIguvsm7vkY0Q0hIjTUdBJ0wb\nHCeJOVkAQPtQZOFV1u21alzvrgpgIwSP1D8mTP2jw9iuFgDQLvy0h9eobWzWlv2HGSvwcNMGx+rT\nnDI1NdtMRwEAuDmKLLzGxn2H1GSzU2Q93LTBsaqoa9LX+ytMRwEAuDmKLLzGl3vZCMEbnDuI9WQB\nAO1DkYXXYCME7xAfGay0xEiKLADglCiy8Ap2u13r8sq5Guslpg2OVUauVXWNzaajAADcGEUWXmFv\nea0KK+uZj/US0wbHqa7JprVH1wUGAKA1FFl4hWMbIbA1rVc4a0C0/P0sLMMFADgpiiy8QstGCMMT\nu5iOAgfoEhKo8b27MicLADgpiiy8wpd7y9kIwctMGxyrr/YdUkVto+koAAA3xU99eLzaxmZt3l/B\nfKyXmTY4Vja79FlOmekoAAA3RZGFx9t0dCMEVizwLhP7dVNooJ9WZTNeAABoHUUWHm/d0Y0QuCLr\nXYID/DWlfzRzsgCANlFk4fHW7S3XADZC8ErTBsdpe2GlCg/XmY4CAHBDFFl4tJaNELga652mDT6y\nXe1/GS8AALSCIguPls9GCF5tVM8odQ0NZLwAANAqiiw8Wst8LDd6eSd/P4umDorRyt2lstvtpuMA\nANwMRRYebd3ecoUG+ml4DzZC8FYzkuKUX16rrJJq01EAAG6GIguPti7vyEYIgWyE4LVmJsdJkpbv\nKjacBADgbvjpD4/1v40Qok1HgRMNiAnX4NhwLd9VYjoKAMDNUGThsb4uqFCTza6J/ZiP9XYzk+O0\nOrtUdY3NpqMAANyIWxTZpqYmPf/885o7d66GDx+uUaNGaf78+frwww/b/R7Lli3TFVdcoTFjxig1\nNVXnnHOO7rzzTuXk5DgxOUxal8eNXr5i5pB41Tba9EWu1XQUAIAbCTAdQJJ++ctfavny5Zo2bZqu\nueYaNTY26p133tHtt9+ugwcP6vrrrz/p63//+9/r5ZdfVmpqqn72s58pJiZGO3fu1Kuvvqrly5fr\nlVde0bBhw1z01cBV1u21qn90mLqzEYLXO2dgjIL8/bR8V4mmJ8WZjgMAcBPGi+zKlSu1fPlyzZ49\nW0888cSxx+fNm6eLL75Yjz/+uGbOnKlevXq1+vp9+/bp5ZdfVs+ePfX6668rKChIknTBBRdo6NCh\nuv322/W3v/1NzzzzjEu+HriG3W7Xur3lmjow1nQUuEBEcICm9I/W8l3FeuQHQ03HAQC4CeOjBW+/\n/bYk6dprrz3u8aCgIC1YsMv9vD8AACAASURBVECNjY1atmxZm6/Py8uTJA0fPvxYiW0xduxYSdLe\nvXsdmBjuIL+8VgcP1zMf60NmJsdp28FK7a+oNR0FAOAmjBfZLVu2KDAwUKmpqSccGz16tCRp8+bN\nbb5+0KBB8vf3V25u7gnHCgoKJEmDBw92UFq4i5aNENjRy3fMHHJkpOATVi8AABxltMhWVVWpvLxc\n8fHx8vf3P+F4jx49JB0ZH2hLYmKirr/+eu3cuVP33nuvcnNzZbVatWHDBt1///2KiorST3/6U6d9\nDTDjSzZC8DnDE7soITKYZbgAAMcYnZGtrj6yU09YWFirx0NDQyUdKbwn86tf/Uq9e/fWH//4R735\n5pvHHh82bJhee+01DRo0qM3XZmZmdjR2p9XV1bn087zZf3ce0LCYIGVn7XLp53IOzTojIUgfZxbq\n2+075O9n6dR7cA49G+fP83EOPZ87nUOjRdZiOfkPopa91U/1vH/84x/6y1/+ookTJ2rOnDmKj4/X\n3r179eKLL+qaa67RX/7yF40ZM6bV16akpHQufCdkZma69PO8VV1js3Zac3T7WQNc/s+Tc2jWD2u7\naNnur1UTmajxfTo3VsI59GycP8/HOfR8rj6HmzZtavOY0SIbEREhSaqpqWn1eMsV25bntebLL7/U\nY489pnPOOUf/+Mc/jj0+ZcoUTZ8+XbNmzdIdd9yhTz75RAEBxhdpgANsKqhQY7Od+VgfNCMpVhaL\n9PHOkk4XWQCA9zA6IxsWFqa4uDgVFxerqanphOMtN2sNGDCgzfdYs2aNJGn27NknHOvevbuGDx+u\n/fv3s3KBF2nZCGFiP7am9TWxEcEa0ytKy3cVm44CAHADxlctGD16tBobG7V169YTjm3YsEGSNGHC\nhDZfX1t7ZCme+vr6Vo/X1dUd9zx4PjZC8G2zkuO1Pv+QDtU2mo4CADDMeJGdP3++JGnx4sXHPV5d\nXa1XXnlF4eHhmjt3riSpsrJSOTk5KisrO/a8lrVily1bJpvNdtx75OXlafv27YqKilJSUpIzvwy4\nSMtGCIwV+K6ZyXFqttm1ajerFwCArzNeZCdNmqRLL71Uq1at0o033qilS5fq9ddf14IFC3TgwAHd\ne++9io4+8lfIK1as0Pnnn3/cLl0zZ87UpEmT9PXXX+uHP/yhXnvtNX3wwQd6+umnddlll6mpqUl3\n3XXXCZslwDPtO8RGCL5uQt9u6hISoI93UmQBwNe5xd1PDzzwgIYOHaq33npLixYtUmBgoNLS0rR4\n8WJNnjz5pK/19/fXs88+q9dff13/+c9/9Oc//1n19fXq2rWrxowZo+uuu+7YVVt4vpb52DO4Iuuz\nAv39NG1wrJbvKpbdbj/lqiYAAO/lFkXWYrFowYIFWrBgwUmfl56ervT09BMeDwwM1FVXXaWrrrrK\nWRHhJtYd3QhhBBsh+LSZyXF6Z1uhdhZXKaV7pOk4AABDjI8WAB2xbm+5xvbuqkB//uj6spnJ8ZLE\nLl8A4ONoA/AYdY3N2ry/ghu9oH7RYUqOC2cZLgDwcRRZeIyv2QgB3zFzSLw+zS5TbWOz6SgAAEM6\nPCPb1NSkzZs3q6ioqNVNDFpcdNFFpxUM+L51e7nRC/8zMzlOf12TqzV7ynTe0VEDAIBv6VCRzcrK\n0o033qiioqI2n9NyFzFFFo62bm+5+kWHKqFLiOkocANnD4hRcICflu8qocgCgI/qUJF98MEHVVhY\nqHHjxmnEiBEKCaFQwDXsdrvW5ZXr7IExpqPATYQHB+jM/tFavqtEj5oOAwAwokNFduvWrbr44ov1\nhz/8wVl5gFbtO1SrA4frmI/FcWYmx+uO93eo4FCtenUNNR0HAOBiHbrZy263a9y4cc7KArQpI/fI\nfOwkdvTCd8wcEieJZbgAwFd1qMgOGjRIxcUsdwPXW5tnVXiQPxsh4DipCZHq0SWEZbgAwEd1qMj+\n5Cc/0auvvqqSEq5+wLUy8qya0KebAtgIAd9hsVg0MzlOK7NK1Wyzm44DAHCxDs3IWiwWTZw4UTNn\nztT555+vvn37Kjg4uNXnsl0sHKWyrklbDxzWXdMGm44CNzQzOU4vfLVPX+07xNJsAOBjOlRkb731\nVlksFtntdr399tuyWCwnPKdl+S2KLBxlQ365bHZpcv9o01HghqYnxclikT7eWUyRBQAf06kiC7hS\nRl65LBY2QkDrYsKDNK53Vy3fVaJFM5NNxwEAuFCHiuxtt93mrBxAmzJyrRrWPVJdQwNNR4GbmpUc\nr9+vzFJ5TYO6hQWZjgMAcBHunIFba7bZ9WV+OWMFOKmZyXGy2aWVu0tNRwEAuNBJr8heddVV+tnP\nfqaxY8ce+317WCwWvfTSS6efDj5ve2GlDtc1aTLrx+IkxvfpqqiQAC3fWaJLR/QwHQcA4CInLbIb\nNmyQ1Wo97vftwRwtHCUj78ifv0n9uCKLtgX4+2l6Upw+3lV87IZTAID3O2mRXbVqlWJiYo77PeBK\na/Os6h4ZrAExYaajwM3NTI7Tv785qB1FVRqWEGk6DgDABU5aZHv27HnS37cmJydHO3bsaNdzgVPJ\nyC3X5H7duMKGU5qZ3LJdbTFFFgB8hMNv9lqzZo0WLVrk6LeFDzp4uE651hrGCtAufbqFKaV7hJbv\nZOdBAPAVHVp+S5I2btyol19+Wfv371dzc/Nxx+rq6rR3715FRUU5LCB819qj87GsWID2mpkcp6fX\n7lVNQ5PCgjr8rzcAgIfp0L/p169fr+uvv15NTU1tPic6Olp33HHHaQcDMnLLFRLgp9E9+Q8jtM/M\n5Hg98XmuPt9j1awh8abjAACcrEOjBc8++6yioqL05JNPaunSpZKkxx57TMuWLdNvfvMb9e3bVw89\n9JDmzZvnlLDwLRl5Vo3r01VBASx3jPY5e2CMQgP99J/tRaajAABcoEMN4dtvv9WPfvQjTZ8+Xb17\n95YkxcXFaciQIbruuuv01FNP6Te/+Y02btzolLDwHbWNzfq6oEKT+jJWgPYLDfTXrCHxWvZtoWw2\nu+k4AAAn61CRraqqOlZgW+4ib2hoOHZ84MCBuvzyy/X3v//dgRHhi77KP6Qmm12T+7MRAjomPS1R\nBw7X6at9h0xHAQA4WYeKbEREhMrLy4/9OiAgQAcOHDjuOQMGDNCOHTsclxA+qWUjhIl9KbLomDkp\n8Qrws2jptoOmowAAnKxDRXbo0KF6/fXXtXfvXklH1pX997//fdxV2S1btjg2IXzS2rxyJceFKzYi\n2HQUeJhuYUGaOihG72wrlN3OeAEAeLMOFdkFCxYoJydHd999tyRp1qxZ2rJliy6++GLdd999uuGG\nG/Taa69pxIgRTgkL32Cz2bU2z8qyW+i09LRE7S6t1o6iKtNRAABO1KHlt2bMmKE///nP2r17tyTp\nlltu0TfffKN169Yde6xXr15auHCh45PCZ+wqqZK1plGT2QgBnXRhaoJuWbpNS7cdZJcvAPBiHV4x\n/IILLjj26+DgYL3wwgv65ptvVFBQoLi4OI0YMUJBQUEODQnfsjbvyBz2pH7Mx6JzEruE6Iw+3fTO\ntoP67Ywk03EAAE7SoSK7atWqNo8FBwfr8OHDWrNmjfz9/RUdHa0hQ4ZQatFhGblWxYQFKjk+wnQU\neLD0tETd8f4O5Vlr1C86zHQcAIATdKjI3nrrrceW3WqPLl266Oc//7kWLFjQ4WDwXRl5Vk3qF92h\nP2vA981LS9Ad7+/QO9sO6vazB5qOAwBwgg7d7HXttdfq7LPPlt1uV9euXXXWWWfpggsu0DnnnKOY\nmBjZ7XZNnTpVF154oaZMmaK6ujo98MADWrlypbPyw8uUVtUrq6SasQKctoGx4UpLjNQ73xaajgIA\ncJIOXZG95JJLdOWVV+qee+7R5ZdfLn9//2PHbDab3nzzTS1evFivvPKKEhISVFBQoCuvvFJLlizR\n9OnTHR4e3qdlPpYVC+AI6WmJun9Floor6xUfyVJuAOBtOnRF9pFHHtHs2bN15ZVXHldiJcnPz0+X\nX365zjzzTD366KOSjqxgcOWVVyozM9NxieHVMvKsCvS3aGzvrqajwAvMS0uQ3S69t52rsgDgjTpU\nZDdu3KjRo0ef9DkjRozQunXrjv2+e/fuqq+v71w6+JyMXKtG94xSaKD/qZ8MnMLwxC7qHx2mpdso\nsgDgjTpUZG02m3Jyck76nH379qmysvLY77OzsxUXF9e5dPAp9U3N2lhQwVgBHMZisSg9LUGrdpfq\ncF2j6TgAAAfrUJEdNmyYXnzxRS1duvS4bWklqbm5WcuXL9dLL72kgQOP3CH88ccf6+WXX9a4ceMc\nlxhe6+uCCtU32dgIAQ41Ly1RDc02fZhZbDoKAMDBOnSz1y9+8Qtde+21uvvuu/W73/1OiYmJCg0N\nVX19vQoLC4+NENxyyy2SpH//+9/y9/fXj3/8Y8cnh9fJyGUjBDjexL7d1D0yWEu3HdT8UT1NxwEA\nOFCHrsiOGTNGb7zxhqZPn66QkBDl5+dr165dysvLkySdccYZ+uc//3lshYJLL71Ub7zxxrErtMDJ\nrN1r1YCYMCV0CTEdBV7Ez8+ii1IT9NHOYtU1NpuOAwBwoA5vUTt06FD97W9/kyRVVFSotrZWQUFB\nio4+8a+DzzvvvNNPCJ9gt9uVkWvVzOR401HghealJugf6/Zq5e5SDWSfDQDwGh26Ivt9UVFRSkhI\naLXEAh2RU1aj4qoGxgrgFFMHxSoqJEBLvzloOgoAwIFOq8gCjrI2zyqJjRDgHEEBfrpgaHe9t71Q\nTTa76TgAAAehyMItZORa1SUkQMO6R5qOAi81Ly1BZTWN+rqw1nQUAICDUGThFjLyyjWxbzf5+THA\nCOeYlRyvkAA/rcirNh0FAOAgFFkYd6i2UdsLKxkrgFOFBwdoZnKcVu2tlt3OeAEAeAOKLIxb1zIf\ny0YIcLJ5aYkqrG7SpoIK01EAAA5AkYVxGXnl8vezaHyfrqajwMv9YFh3+VukpdtYvQAAvAFFFsat\nzbNqRI8uigju8LLGQIdEhwVpXGKo3tlWaDoKAMABKLIwqrHZpvX5hxgrgMtM7xeuncVVyiyqNB0F\nAHCa3KLINjU16fnnn9fcuXM1fPhwjRo1SvPnz9eHH37Y7vew2Wx69dVXddFFF2nEiBEaP368rr76\naq1Zs8aJyXG6th44rJqGZjZCgMtM6xshSVyVBQAv4BZF9pe//KUefvhh9erVS4sWLdKdd94pSbr9\n9tu1ePHiU77ebrfrV7/6le6//3716dNH9913n26++Wbl5+frxhtv1EcffeTsLwGdtJYbveBi3cMD\nNKFPV73zLXOyAODpjA8lrly5UsuXL9fs2bP1xBNPHHt83rx5uvjii/X4449r5syZ6tWrV5vv8e67\n7+rDDz/UDTfcoDvuuOPY4zNmzNAPf/hDrVy5UrNnz3bq14HOycgtV++uIerdLdR0FPiQeWmJuvOD\nTOWX16hPtzDTcQAAnWT8iuzbb78tSbr22muPezwoKEgLFixQY2Ojli1bdtL3WLJkicLCwnTrrbce\n93ivXr20du1aPfroo44NDYew2+3KyLNqEldj4WLz0hIkScu+ZbwAADyZ8SK7ZcsWBQYGKjU19YRj\no0ePliRt3ry5zddbrVZt375d48ePV1jYkSsrTU1NamhocE5gOMy+Q7XaX1HHWAFcLikuQsMSIpmT\nBQAPZ7TIVlVVqby8XPHx8fL39z/heI8ePSRJ+/bta/M9srKyJEl9+/bV8uXLddFFFyktLU1paWk6\n//zz9dZbbzknPE5bRm65JGlyf270guvNS03Q53vKVFpVbzoKAKCTjM7IVlcf2fO85Urq94WGHpmb\nrKqqavM9ysuPlKENGzboo48+0nXXXacBAwYoPz9fzz33nO655x6VlZXppptuavX1mZmZp/MldEhd\nXZ1LP8/dvb+5RKEBFgVWHFBmpWfceMM59Hwt53BkRJ1sdumZlVt0cXIX07HQTnwPej7Ooedzp3No\ntMhaLJaTHm/ZD/1kz2sZIcjNzdU777yjAQMGHDt27rnnavbs2Xrqqac0f/58de164s5RKSkpnYne\nKZmZmS79PHe35T+FOnNArNKGDTUdpd04h56v5RwOsdvV97MyrS+z6B7Oqcfge9DzcQ49n6vP4aZN\nm9o8ZnS0ICLiyHqONTU1rR5vuWLb8rzWhIeHS5JGjhx5XImVpJ49e2rSpEmqr6/Xli1bHBEZDlJc\nWa8dRVWaOijGdBT4KIvFoouHJ+qTXSUqq2amHgA8kdEiGxYWpri4OBUXF6upqemE4wUFBZJ0QkH9\nrt69e0tSq6+XpLi4OElSZSW7+LiTT3PKJElTB8UaTgJfdvXY3mpotunVrwtMRwEAdILxVQtGjx6t\nxsZGbd269YRjGzZskCRNmDChzdcPHDhQXbt2VXZ2dqsrFbTcKJaYmOigxHCE1dmligj215heUaaj\nwIcN79FFY3tHafH6fcdGmQAAnsN4kZ0/f74knbCDV3V1tV555RWFh4dr7ty5ko5cVc3JyVFZWdmx\n5wUEBCg9PV2HDh3SCy+8cNx77NixQ+vXr1d8fLxGjBjh5K8EHbE6u1Rn9o9RgL/xP4LwcdeP76Nv\nDh7WpoIK01EAAB1kvEVMmjRJl156qVatWqUbb7xRS5cu1euvv64FCxbowIEDuvfeexUdfWSd0RUr\nVuj888/XM888c9x73HrrrUpOTtZjjz2me+65R++++67++te/6kc/+pH8/Pz0u9/9ToGBgSa+PLTi\nQEWddpVUMx8Lt3D5qJ4KDfTT4vX5pqMAADrI+Ba1kvTAAw9o6NCheuutt7Ro0SIFBgYqLS1Nixcv\n1uTJk0/5+oiICL322mt65plntHz5ci1btkxhYWEaN26cbrrpJo0cOdIFXwXa69OcUknMx8I9RIUG\n6pLhPfTa5v16dO5QhQW5xb8WAQDt4Bb/xrZYLFqwYIEWLFhw0uelp6crPT291WMRERH69a9/rV//\n+tfOiAgHWp1dpqiQAI3qyXws3MP1E3rr5U0Fevubg7pqbG/TcQAA7WR8tAC+59OcMp01IEb+fidf\nRxhwlbMGxGhQbDjjBQDgYSiycKmCQ7XKLmU+Fu7FYrHouvG99fkeq3aXtL2TIADAvVBk4VKrs5mP\nhXu6emxv+Vmk5zfsMx0FANBOFFm41OrsMnULDdTwRPa2h3vpERWiOSnd9dLGfWpqtpmOAwBoB4os\nXGp1TqnOHhgjP+Zj4Yaun9BHBw/X66OdxaajAADagSILl8mz1ijPWst8LNzW+Snx6h4ZzE1fAOAh\nKLJwGeZj4e4C/f109dheej+zWIWH60zHAQCcAkUWLvNpTpliw4M0rHuk6ShAm64b30fNNruWbCww\nHQUAcAoUWbiE3W7X6uxSncN8LNxccnyEpvSP1uIN+bLb7abjAABOgiILl9hTVqN9h+oYK4BHuH58\nH2WVVCsj12o6CgDgJCiycIn/zcdyoxfc36UjEhUZHKDFrCkLAG6NIguXWJ1dpoTIYA2JjzAdBTil\n8OAAzR/VQ//aekCH6xpNxwEAtIEiC6ez2+1anXNkPtZiYT4WnuH68X1U09CsN7ccMB0FANAGiiyc\nLqukWgcP1+scxgrgQcb36aphCZGsKQsAbowiC6dj/Vh4IovFouvH99b6/EPaXlhpOg4AoBUUWTjd\npzll6tElRINjw01HATrkR2N6KdDfwlVZAHBTFFk4ld1u16c5ZZo6iPlYeJ7YiGBdOCxBL28qUEOT\nzXQcAMD3UGThVJlFVSqqrGesAB7rhgl9VFrdoPe2F5qOAgD4HoosnIr1Y+HppifFqXfXEP2T8QIA\ncDsUWTjV6pwy9ekWqv7RYaajAJ3i72fRteP66JOsEuWX15iOAwD4DoosnMZms+vT7FJNZf1YeLhr\nx/eWJL34VYHhJACA76LIwmm+LaxUWU0j87HweP2iwzRtUKxe+CpfNpvddBwAwFEUWTjNpzlH5mPP\nGch8LDzf9RP6KM9aq1W7S01HAQAcRZGF06zOLlP/6DD1ZT4WXuCi1AR1jwzWn1Znm44CADiKIgun\nsNns+uzo+rGANwgJ9Nf/TR2olbtL9cWeMtNxAACiyMJJth44rPJa5mPhXX4ysa+6RwZr0SdZpqMA\nAESRhZOszmH9WHifsKAA/d/UgVq1u1RruCoLAMZRZOEUq7PLNDg2XD2jQk1HARzqpkn9lBAZrEXL\nuSoLAKZRZOFwTc02fb6H+Vh4p9BAf/3fuYP03+xSfZ7DVVkAMIkiC4fbvP+wDtc1MR8Lr/WTiX2V\nEBms+5iVBQCjKLJwONaPhbfjqiwAuAeKLBxudXaZhsRHKKFLiOkogNO0XJVd9Mku01EAwGdRZOFQ\njc02rcllPhbeLzTQX3eeO0irs8v0WQ67fQGACRRZONSmggpV1TczHwufcCOzsgBgFEUWDrU6m/lY\n+A6uygKAWRRZONTq7FKlJkQqLiLYdBTAJW6c2FeJXVhXFgBMoMjCYRqabMrIK2esAD6l5arspzll\n+jSbq7IA4EoUWTjMF7lW1TQ0a9pgiix8y4/POHpVlllZAHApiiwc5v0dRQoO8NN0iix8TGigvxae\nO1ifcVUWAFyKIguHeX9Hkc4dFKvw4ADTUQCX+/EZfbgqCwAuRpGFQ2SVVGl3abUuGNrddBTAiJDv\nXJVdzVVZAHAJiiwc4v0dRZKkOSnxhpMA5vz4jD7q0SVEi5bvkt1uNx0HALweRRYO8Z/tRUpLjFTf\n6DDTUQBjQgL9tXDaIH2+x6pPc8pMxwEAr0eRxWk7VNuoNblWxgoASTdM4KosALgKRRanbfnOYjXb\n7LoghSILfPeq7OpsrsoCgDNRZHHa3s8sUkxYoCb07WY6CuAWbpjQRz2jQvTbj3dyVRYAnIgii9PS\nbLPrw8xinZ/SXf5+FtNxALcQEuivReclaW1euZ7KyDMdBwC8FkUWp+XLveWy1jTqB8MYKwC+6/oJ\nfTQzOU53vL9DWSVVpuMAgFeiyOK0vL+jSAF+Fp2XFGc6CuBWLBaLnr9spEIC/HXVa5vV1GwzHQkA\nvA5FFqflPzuKdNaAGEWFBpqOAridHlEhevriNK3PP6SHV2ebjgMAXsctimxTU5Oef/55zZ07V8OH\nD9eoUaM0f/58ffjhh516P7vdriuuuELJycn629/+5uC0aJFbVqPthZW6YCibIABtuWxUT80f2UOL\nlmfp64JDpuMAgFdxiyL7y1/+Ug8//LB69eqlRYsW6c4775Qk3X777Vq8eHGH32/JkiXauHGjo2Pi\nez7IPLKbF+vHAif394vTFB8RrB+9tll1jc2m4wCA1zBeZFeuXKnly5dr9uzZeuqpp5Senq7LLrtM\nS5YsUVJSkh5//HEVFBS0+/3y8/P1+OOPKzU11YmpIR2Zj02KC9fguAjTUQC3Fh0WpOcvG6EdRVW6\n56OdpuMAgNcwXmTffvttSdK111573ONBQUFasGCBGhsbtWzZsna9l91u1913363w8HDddNNNDs+K\n/6mqb9Lq7DKuxgLtNHNIvG6e1FePfb5Hn+WUmo4DAF7BeJHdsmWLAgMDW72COnr0aEnS5s2b2/Ve\nr732mjZs2KBFixapS5cuDs2J463MKlFDs40iC3TAIxcM1cCYcF39+hYdrms0HQcAPJ7RIltVVaXy\n8nLFx8fL39//hOM9evSQJO3bt++U71VQUKA///nPmjNnjmbMmOHwrDje+zuKFRUSoCn9o01HATxG\neHCAllw+UvsO1er2d7ebjgMAHi/A5IdXV1dLksLCwlo9HhoaKulI4T2ZlpGC0NBQ3XPPPR3KkJmZ\n2aHnn466ujqXfp6z2Ox2Ldu2X5N6hCo7a5fpOC7lLefQl5k+h10l3TC8m57dsE+jo5p0bt9wY1k8\nkenzh9PHOfR87nQOjRZZi+XkW5q27FF+que98cYb+vLLL/WXv/xF0dEdu0KYkpLSoeefjszMTJd+\nnrN8lX9IZbU5WnDGYKWk9DIdx6W85Rz6Mnc4h38bbNOGkjW6f12ZfjglTXERwUbzeBJ3OH84PZxD\nz+fqc7hp06Y2jxkdLYiIOHK3e01NTavHW67YtjyvNfv379cjjzyimTNnatasWY4PiRO8v6NIfhZp\nVjK7eQGdERTgp5cXjNKh2ib95O1vjv1HOwCgY4wW2bCwMMXFxam4uFhNTU0nHG9ZdmvAgAFtvsdv\nf/tbBQQE6Oabb1ZhYeGx/1mtVklHxhIKCwtVUVHhnC/CB72fWaSJfbsplqtIQKelJnbRH2YP0Tvb\nCvXypvYvMQgA+B+jowXSkZUJli9frq1bt2rMmDHHHduwYYMkacKECW2+PiMjQ5J00UUXtXr8xRdf\n1Isvvqh58+bpoYceclBq37W/olZfF1TowfOHmI4CeLzbzx6g93YU6rZ3vtU5A2PUp1vr9wsAAFpn\nvMjOnz9fy5cv1+LFi48rstXV1XrllVcUHh6uuXPnSpIqKytVXFysrl27KiYmRpL0zDPPtPq+WVlZ\neuyxx3TBBRfoggsuUGJiovO/GB/wYWaxJHbzAhzB38+il+aP0vBHP9U1b2zRyp9MlJ/fye8JAAD8\nj/EiO2nSJF166aV66623dOONN2rWrFmqr6/XG2+8oQMHDuihhx46dgPXihUrtHDhQl111VW6++67\nJUlTp05t9X1bVkLo169fm89Bx72/o0h9u4VqWEKk6SiAV+gfE6YnLkzVDf/aqt9+vFO/nz3klDe4\nAgCOMF5kJemBBx7Q0KFD9dZbb2nRokUKDAxUWlqaFi9erMmTJ5uOh6NqG5u1IqtE143vww9awIGu\nG99b6/PL9cdV2fKzWHT/rGS+xwCgHdyiyFosFi1YsEALFiw46fPS09OVnp7ervecMGGCdu3yrTVO\nnW11dqlqG236AWMFgENZLBY9c/FwSdLvV+6WzW7nyiwAtINbFFl4hvd3FCk8yF9nD4wxHQXwOn5+\nR8qsRdIfV2XLLukP24WsHQAAH59JREFUlFkAOCmKLNrFbrfr/R1FmpEUp5DAE7cTBnD6/Pwsevri\n4bJYLHpwVbbsdumP51NmAaAtFFm0y7aDldp3qE6/O4+xAsCZ/Pwseio9TRZJD/33SJl9cA5lFgBa\nQ5FFu7y/o0iSdH5KvOEkgPfz87Po7+lpslikh1dny2a36+ELUiizAPA9FFm0y/s7ijS2d5QSu4SY\njgL4hGNlVhY98mmO7JL+RJkFgONQZHFKxZX1+jK/XL+bkWQ6CuBTLBaLnkxPlcUi/fnTHNntdj3y\ng6GUWQA4iiKLU/poZ7HsdnbzAkywWCz627xUWSQ9+tke2SX9mTILAJIosmiH93cUqUeXEI3uFWU6\nCuCTLBaL/jovVRaLRY99tkc2u12PzR1GmQXg8yiyOKmGJpuW7yrR/FE9+KEJGGSxWPSXi4bJYpGe\n+DxXDU12PXbhUAUHsBweAN9FkcVJrdlTpsr6Jl2QwlgBYJrFYtETFw5TgN+RK7Orc0r1z0tHaFL/\naNPRAMAIP9MB4N7e21Gk4AA/TRscazoKAB0ps4/OHaYPbxiv6oZmTfl7hn66dJsO1zWajgYALkeR\nRZsam216Y/N+nZ8Sr/BgLt4D7mR2Sndtv+Mc/WxKfz21Nk9D//Sp/rO90HQsAHApiiza9MmuEhVX\nNejqsb1NRwHQiojgAD1xUarW3TZF3UIDNff5r3TZkk0qqqw3HQ0AXIIiiza9tHGfYsICNXsIu3kB\n7mxC327adPtZemBWspZ9W6iUh1frhQ35stvtpqMBgFNRZNGq8poGvbe9SAtG91JQAH9MAHcXFOCn\ne2YkaeuvzlJqYqSue3Orpj/zpXJKq01HAwCnoaGgVf/aekD1TTZdNbaX6SgAOmBI90h9evMkPXNJ\nmv6/vXuPq6rO9z/+3nuzMS6G9wtIFCqWoil4m5wZcrxRkqZmFiWlndImtWl+U2M5p6s2drPJcR5m\naaPmDCYeNZs6oSJaXookb6dMvAuiYYQKm4tc1u8PBN0CaiqsveT1fDx4sNf3+11rf3ALvPfiu75r\nS8YJdX5znV5fu1enS8rMLg0ArjqCLKq1cEuGOrb0VyQ3QQAsx263adyvbtT3z9yugWHN9edPd6nN\nK6v1/1Z+p++O5ZpdHgBcNQRZVLH3J5c2HcxRXPdgboIAWFhQgI+Wj+mhxMd66Tc3NdHMLw8o/I11\n6vXOl3pv8yGdLGDJLgDWxppKqGLhlnTZbNKDkUFmlwLgCtlsNg3s0EIDO7TQ8bwiLUrN0LyUdI1b\nukN/+Pj/dE+XQI3tGayotk154wrAcgiycFNWZujD1Az1b99MQQE+ZpcD4Cpq7t9AT0W11R9+G6pv\n0k/og5R0xW89og9TM9S2qa/G9AzWQ92D1aYR3/sArIEgCzcbDvysgz8X6JXom80uBUAtsdls6nlD\nY/W8obFmDOmo/9lxVB+kpOsv/7tbz3++W1Ftm+q2G5uoR3Aj9byhkVpff53ZJQNAtQiycLNgS7r8\nGzg0LLyV2aUAqAO+3l4a3T1Yo7sHa99PLv3zm3R9+v2Pmr52r0rLytehbRNwnXre0Eg9b2isHsGN\n1D04QNdf5zS5cgAgyOIc+adLlLD9qO7pEsgtaYF6qG0zP02942ZNveNmFRSXamvGSX2TfkIph08o\nJf2Elu0svwWuzSbd3MJfPYIbqUdwI7Vr5qfA669T4PUN1NTPm7m2HqiszFCpYai07MyH22O5tZed\n6Ss7015mnGkvU5X+sjPbZcbZ5zjbXt5Wdl5bRkauthUcUZlhyFB5u3FOv3HOeEOq7DPc2irGSobO\n7lcx3lDF+OrbK45R2X7m3iHV9auafSvbzjnGufuXP64Y536cc4/n1nbOePfts8fWeW3V7X/uMaq2\nn/O4huNd6FiS5LDbFBvqpVvkGUgrqLTi/44pt6hED7F2LFDv+Tgduu2mJrrtpiaVbdmu09qSfqIy\n3H7+Q5YWbslw28/psKn19ddVBtuzj69TYEADNfdrIF9vh3ycdvk4HfJ1OuTjdMhuNzf8GoahkjJD\nxaVlKi498/m87dOVn8vbyj/X1H7OvmXVb5ec017+3OVt1T8+O77kTOg8+7nMra26x57nR9Oe2WaT\nbCqfYmOr3Lad1+feL5WPOXff8jZVbTuzrWrGVRyn6riq41XDPpVfh9vXZKum7cJjLzSmyrhz2r3s\nNuUGN5SnIMii0sItGbqhsY9+G9rU7FIAeKCmft4adHMLDTpz22rDMHTkZKEO5xQo81Rh+cfJIh3N\nLVTmyUL9kJWntXuzdeISlvnydtirDbgOu/sv6MKCAvmsya4aFGzlZ5XOBrgylZbpgiHv/LBa22w2\nyWm3y8thk9Nuk9Nhl9Nx5rPdJq8zbV5225kxZ8Y6bPJ1OuTlKB9T/mGXw352u/rHdjns5WfQHLby\n9pofy63dbivvs9t0dtvuvm23le9jP9Ne3nZ2XMUYu608ADpsNtlsNh3Yv1/t27WVraJPZ8fazhl/\nbt+57ee2VYRL+3nB0yZb1Tb+UnDV7Nq1y+wSKhFkIUnKPFmo1WnH9Wy/9qafGQFgDTabTW0a+Vx0\nlYP80yU6eqpImacK9ZPrtAqKS5V/ulQFxWUqKC4t3y6ubrtUZWXn/Qm22CYfp+Psttz/ROrjtF9S\nyHPYzwbIikDp7bCfDZf2c0LmmW1vr7NjvN32sbm1lY+tehwHP1slSfYcb3Vo4W92GbhGEGQhSfrX\ntxkqM8QtaQFcdb7eXmrbzEttm/ld8bF27dqlW27xlNl5AMzGnb0gwzC0YEuGeoc0Vlhz3iUDAABr\nIMhC246c0nfHcrnICwAAWApBFlqwJV3eDrvu7RpodikAAACXjCBbzxWXlunfW4/ork4t1cTX2+xy\nAAAALhlBtp77/IcsHc87zbQCAABgOQTZem7hlgw19/dW9Jl1IQEAAKyCIFuP5eSf1srvflRstyA5\nHfxXAAAA1kJ6qcc+2pap06VlrB0LAAAsiSBbjy3ckqHwVg3VLSjA7FIAAAB+MYJsPbXneJ42H8pR\nXPc23H8aAABYEkG2nlq4JUN2m/RABNMKAACANRFk66GyMkMfpmZoQFhzBQZcZ3Y5AAAAl4UgWw99\nsT9bh3IKuMgLAABYGkG2Hlq4JUMNG3jp7vBWZpcCAABw2Qiy9UxeUYkSdmRq5K2t5evtZXY5AAAA\nl40gW8+899Uh5RWV6tHeIWaXAgAAcEUIsvVIYXGp3kjep9+1a6beIY3NLgcAAOCKEGTrkX9+k65j\nuUWa0r+92aUAAABcMYJsPVFcWqbX1u5V75DG6tuuqdnlAAAAXDGCbD3x72+P6FBOgab0b8+dvAAA\nwDWBIFsPlJYZ+mvSHt0aeL0G39LC7HIAAACuCoJsPbBs51HtPu7Sc/04GwsAAK4dBNlrnGEYmrZm\njzo099OILq3NLgcAAOCq8YgV8UtKSrRw4UKtWLFCBw8elMPhUIcOHRQXF6c777zzko6RkpKiOXPm\naMeOHcrPz1eTJk3Uq1cvPf7442rbtm0tfwWe67NdWdqeeUr/HNVVDjtnYwEAwLXDI4LsH//4RyUm\nJqpfv356+OGHVVxcrOXLl+upp57S0aNH9cgjj1xw/zlz5mjGjBkKCQnRY489pubNm2vHjh1asmSJ\n1q5dq8WLFyssLKyOvhrPUXE2NqSxjx6IDDK7HAAAgKvK9CC7Zs0aJSYm6o477tDf/va3yvZhw4Zp\nxIgRevvttzVo0CC1adOm2v3T09P1zjvvKDAwUEuXLtX1118vSbr77rvVtm1bvfzyy3r33Xc1Y8aM\nOvl6PMm6fdnafChH/xjeWU4Hs0gAAMC1xfR0s3TpUknSmDFj3Nq9vb0VGxur4uJirVixosb9T5w4\noZiYGI0bN64yxFbo27evJGnXrl1XuWprmLZmj1o1bKCxPYPNLgUAAOCqM/2M7LZt2+R0OhUeHl6l\nLyIiQpK0devWGvfv3LmzXn/99Wr7cnNzJUkNGza8CpVay9eHcpS05ye9eVdHXed0mF0OAADAVWdq\nkM3Ly1NOTo6CgoLkcFQNW4GBgZLKpw9cjg8//FCSNHTo0BrH1OXZ2sLCwjp7vmdXZSqggV1RTeru\nOeuDunwNUTt4Da2N18/6eA2tz5NeQ1ODrMvlkiT5+vpW2+/j4yOpPPD+UgsWLFBCQoIiIyN13333\n1Tjulltu+cXHvly7du2qk+fbnnlSyYf36uXoDurepf5d5Fab6uo1RO3hNbQ2Xj/r4zW0vrp+DVNT\nU2vsMzXIXmxxfsMwLmncuUpLS/Xaa69pwYIFCg8P1+zZs6s923ste3XNXjVs4KUJfW40uxQAAIBa\nY+rFXv7+/pKk/Pz8avsrzthWjLuYU6dOady4cVqwYIH69++vRYsWKSAg4OoUaxG7s/KUsCNTT/S5\nUY19vc0uBwAAoNaYekbW19dXzZs3V1ZWlkpKSuTl5V5ORkaGJCk0NPSix8rOzlZcXJz27dunCRMm\naMKECfXydqzT1+7VdV52PfXbi/+bAQAAWJnpy29FRESouLhY27dvr9KXkpIiSerVq9cFj3HixAk9\n/PDDOnTokN58801NnDixXobYQz/na1Fqhh7tHaIWDRuYXQ4AAECtMj3IVlyINW/ePLd2l8ulRYsW\nyc/PT0OGDJFUvpzWvn37lJ2d7TZ28uTJSktL0+uvv66YmJi6KdwDvZ68Tzab9PTt9feWvAAAoP4w\nfR3Z2267TSNHjlRCQoIee+wxRUdHq6ioSIsXL1ZmZqamT5+uJk2aSJJWr16tZ599VnFxcZoyZYok\naf369UpOTlZYWJjsdrs+//zzap8nKiqqchWEa9HRU4Wal3JYD3UPVptG1+7XCQAAUMH0ICtJr7zy\nijp27KiEhAS9+OKLcjqd6ty5s+bNm6c+ffpccN8dO3ZIktLS0vTkk0/WOC4pKanG29xeC2as36/i\n0jL9+XftzC4FAACgTnhEkLXZbIqNjVVsbOwFxw0fPlzDhw93a5s4caImTpxYm+V5vGzXac3edFD3\ndwtSu2Z+ZpcDAABQJ0yfI4sr99b6fXKdLtWz/dqbXQoAAECdIcha3I7MU3ojeZ8ejAxSp1YNzS4H\nAACgzhBkLayktExjP9qmJr5O/W1ouNnlAAAA1CmPmCOLy/Pmun1KzTiphLhINfXjLl4AAKB+4Yys\nRe36MVcvrkrTiC6tdc+tgWaXAwAAUOcIshZUWmbokY+2y8/boX8M72x2OQAAAKZgaoEF/X3DAW0+\nlKNFsd3UklvRAgCAeoozshaz7yeXnvtsl2I6tlRsRJDZ5QAAAJiGIGshZWWG/mvJdjkddr17T2fZ\nbDazSwIAADANUwss5L2vDmndvmzNvfdWBQX4mF0OAACAqTgjaxGHfs7X0//5Xv3bN9PYnsFmlwMA\nAGA6gqwFGIahxxJ2yDCk9++9lSkFAAAAYmqBJcz/Jl2r0o5r1rBw3djE1+xyAAAAPAJnZD1c5slC\nPfXxd/ptaBM9ftuNZpcDAADgMQiyHswwDI1fukOnS8s0b1RX2e1MKQAAAKjA1AIPtnhrpj75/ke9\nNaSj2jXzM7scAAAAj8IZWQ+VlVukict3qtcNjfTkb0LNLgcAAMDjEGQ9kGEYmrB8p3KLSvXBqK5y\nMKUAAACgCoKsB5q+dq8Sth/VCwPD1LFVQ7PLAQAA8EgEWQ8ze9NBPffZD4rtFqTJv2tndjkAAAAe\niyDrQf79bYaeWLZTd3Vsqfn3s0oBAADAhRBkPcQn3x1TXPw2RYU21UdxkXI6eGkAAAAuhLTkAdbt\n/UkjF6YqIihAK8f2lI/TYXZJAAAAHo8ga7JvDp/QXR+kqG1TX/3vo73U8DqW9gUAALgUBFkTfXcs\nV9Hvf6Xmfg20alxvNfXzNrskAAAAyyDImuRAdr4GzvlK3g67Vo/rraAAH7NLAgAAsBT+jm2Co6cK\n1X/OZhUUl+qLJ25TW24/CwAA8IsRZOtYtuu0Bsz5Sj/mFilp/K8U3vp6s0sCAACwJIJsHXKdLtOd\nc7/W3p9c+uy/eqlXSGOzSwIAALAsgmwdKSwu1YQ1R5V6rFD/81B3/a59M7NLAgAAsDQu9qojb3+x\nX19nFmj+fV01NLyV2eUAAABYHmdk60hstyAF2XL1YGQbs0sBAAC4JnBGto6ENPFVj9YssQUAAHC1\nEGQBAABgSQRZAAAAWBJBFgAAAJZEkAUAAIAlEWQBAABgSQRZAAAAWBJBFgAAAJZEkAUAAIAlEWQB\nAABgSQRZAAAAWBJBFgAAAJZEkAUAAIAlEWQBAABgSQRZAAAAWBJBFgAAAJZEkAUAAIAlEWQBAABg\nSQRZAAAAWJLNMAzD7CLMkpqaanYJAAAAuIjIyMhq2+t1kAUAAIB1MbUAAAAAlkSQBQAAgCURZAEA\nAGBJBFkAAABYkpfZBVzrSkpKtHDhQq1YsUIHDx6Uw+FQhw4dFBcXpzvvvNPs8nAReXl5mjt3rj77\n7DNlZmbK6XQqNDRUw4YN0/333y+Hw2F2ifiFNm7cqLFjx0qSdu/ebXI1uFQHDhzQrFmztHnzZuXm\n5qpFixYaMGCAJkyYIH9/f7PLw0UcOXJEc+bM0YYNG5SVlSVvb2+1b99eQ4cO1ahRo/hZ6oGWLVum\nadOmKS8vT0lJSWrTpk2VMRkZGfrHP/6hjRs36ueff1ajRo3Uu3dvTZw4USEhIXVSJ6sW1LJJkyYp\nMTFR/fr1U//+/VVcXKzly5dr69ateuaZZ/TII4+YXSJqkJWVpfvuu0/Hjh3TkCFD1KNHD7lcLi1d\nulS7d+/W8OHD9de//tXsMvEL5OXl6a677lJmZqYkgqxV7NixQw899JD8/PwUFxenFi1aaNOmTfr4\n448VHh6u+Ph4eXt7m10manDw4EGNGjVKhYWFGjlypDp16qTTp0/r448/VmpqqmJiYvTWW2+ZXSbO\nyM7O1vPPP6+kpCT5+PgoPz+/2iCbnp6uUaNGqaCgQHFxcWrXrp3S09M1f/582Ww2xcfHKzQ0tPYL\nNlBrVq9ebYSFhRlPPvmkW3tRUZERExNjdOrUyUhPTzepOlzM5MmTjbCwMOODDz5wa3e5XEbfvn2N\nsLAwY9++fSZVh8vx3//930bXrl2N6OhoIywszOxycAmKi4uNQYMGGT179jSOHj3q1vf8888bAwYM\nMFJSUkyqDpfimWeeMcLCwozFixe7tZeUlBgxMTFGWFiYsXPnTpOqw/luv/12o0+fPsYXX3xhPPjg\ng0ZYWFi1WeXxxx83wsLCjHXr1rm1p6amGmFhYcaYMWPqpF7myNaipUuXSpLGjBnj1u7t7a3Y2FgV\nFxdrxYoVZpSGS9CyZUsNGjRII0eOdGv39fVVr169JEk//PCDGaXhMmzevFlLlizR+PHj1axZM7PL\nwSX68ssvdeDAAY0ePVqtWrVy63vppZe0atUq9ejRw6TqcCkOHjwoSerevbtbu8PhULdu3SRJhw8f\nruuyUIOuXbtq5cqV+s1vflPjmOzsbK1bt06hoaGKiopy64uIiNCtt96qTZs26ciRI7VdLhd71aZt\n27bJ6XQqPDy8Sl9ERIQkaevWrXVdFi7RH/7wB82cObPa+Xd5eXmSxNw8i3C5XJoyZYo6duzIdB6L\n+fLLLyXJ7ZdlYWGhWeXgMoSFhUkqn+d8voyMDElSu3bt6rQm1Oztt99WkyZNLjhm586dKi0trXwj\ncr6IiAgZhqFt27bVRoluuNirluTl5SknJ0dBQUHVTmIPDAyUVD7HBNZy+PBhrV+/XoGBgZVnZuHZ\n3nzzTWVlZWn27Nny8uLHnpWkpaVJkgICAjRlyhQlJiYqNzdXvr6+6tu3r55++mm1bt3a5CpxIePG\njVNycrKmTp0qSerWrZvy8/P16aefatOmTRo5cmRl2IU1VGSXiixzvorvybo4085P9Fricrkklf8Z\nujo+Pj6Szp7ZgzUcP35c48ePV0lJiV588UU1aNDA7JJwEV9//bXi4+M1YcIEdejQwexy8Avl5ORI\nKr9wNiQkRNOmTZNhGEpKStLKlSu1ZcsWLV++XE2bNjW5UtSkTZs2Wrp0qZ5++mk98cQTle1Op1OT\nJk3S448/bmJ1uBwVGaciy5yvIvvURcYhyNYSm812wX7jzGIRFxsHz/HDDz9o/PjxysrK0tSpU6vM\nC4LnKSgo0JQpU3TzzTdr3LhxZpeDy3D69GlJ0i233OK2Skh0dLT8/PwUHx+vDz74QE8//bRZJeIi\n0tPT9fvf/15Hjx7VxIkT1alTJ5WWlio5OVkzZ87U4cOH9eqrr8puZ7ajVXhSxiHI1pKKuZP5+fnV\n9le8m2GOpTUkJiZq8uTJstvtmj17NiHWIt566y0dO3ZMCQkJcjqdZpeDy+Dn5ydJGjFiRJW+kSNH\nKj4+Xl999VVdl4Vf4LnnntOePXu0ZMkSdenSpbK9f//+8vf31/z58xUZGVnlwlp4rkvNOA0bNqz1\nWnj7U0t8fX3VvHlzZWVlqaSkpEp/xQT3OlljDVdk4cKFevLJJ9WiRQslJCQQYi1iy5YtWrRoke6/\n/341btxYx44dq/yoOMtXsV1aWmpytahJcHCwJKm4uLhKX8XqE0zR8lz5+fn65ptvFBQU5BZiKwwY\nMEBS+Y1KYB033HCDJFWuyX2+usw4BNlaFBERoeLiYm3fvr1KX0pKiiRxsZCH++ijjzRt2jRFRkZq\nyZIlvPGwkM2bN8swDC1cuFBRUVFuHxVX0lZsHz161ORqUZPIyEhJ0vfff1+lr+KCEy728lyFhYUy\nDENFRUXV9hcUFFSOg3V06dJFTqdTqamp1fanpKTIy8urcoWm2sTUglp03333KTExUfPmzav8YSyV\nn3JftGiR/Pz8NGTIEBMrxIVs375dL7/8sjp37qz333+/xgv34JliYmKqXfpOkmbMmKG0tDS9++67\nksS6sh4sJiZG77zzjhYsWKBhw4ZVLgtkGIYWLFgg6exZPXieJk2aKDQ0VPv379eGDRv061//2q3/\n008/lVR1jVl4toCAAEVHR+uTTz7R6tWr3b4Hk5OTlZaWpjvvvLNOLsLkFrW17C9/+Uvln6Ojo6NV\nVFSkxYsXa/fu3Zo+fbruvvtus0tEDe655x7t3LlTkyZNUtu2basdExQUpM6dO9dxZbhSo0ePVkpK\nCreotYhly5bpueeeU5s2bfTwww/L6XRq1apV2rBhgyIiIrRgwQJuUevBNm7cqHHjxslutys2Nlad\nOnVSUVGR1qxZo+TkZHXo0EHx8fGV86FhniNHjmjnzp2V23//+9+1d+9evfDCC5VvIit+72VlZene\ne+9VTk6OHnroIbVv31779+/X/PnzFRAQoI8++kgtW7as9ZoJsrXMMAzFx8crISFB+/btk9PpVOfO\nnfXoo4+qT58+ZpeHC7iUpZqGDRum6dOn10E1uJoIstazefNmzZ07V9u3b1dhYaGCg4M1ePBgPfro\noyyDZwG7d+/W3LlzlZKSouzsbDkcDoWEhGjgwIEaO3Ysf/HyEMuWLdOzzz57wTHn/t7LysrSrFmz\ntH79emVnZ6tp06aKiorShAkT1KJFi7oomSALAAAAa+JiLwAAAFgSQRYAAACWRJAFAACAJRFkAQAA\nYEkEWQAAAFgSQRYAAACWRJAFAACAJRFkAcBDjR49Wh06dFBGRobZpQCAR+KGCADgIRYvXqybbrpJ\nvXr1kiSlpKTo559/VlRUlHx8fEyuDgA8D0EWADxAaWmpunfvrrFjx2rixIlmlwMAlsDUAgDwAGlp\nacrPzze7DACwFM7IAoDJJk+erOXLl7u1TZgwQSkpKUpJSVFSUpLatGmjjIwM9evXT7fffrv+/Oc/\n69VXX9XWrVtls9nUvXt3vfLKK2rYsKFmzJihxMREnTx5UsHBwRo7dqyGDRvmdnyXy6X33ntPq1ev\nVnp6upxOp2688UYNHTpUDzzwgLy8vOrynwAALgtBFgBMtnPnTi1fvlz/+te/FB0drTvuuEPt2rXT\nSy+9VG2QjYyMVFZWlgYPHqyQkBCtWrVKycnJioqKkiQ5nU717dtXP/30k95//325XC4tXbpU4eHh\nkqS8vDzFxsbqwIEDGjFihLp27SqXy6WkpCRt3LhRgwYN0syZM838JwGAS8JbbgAwWefOnbVnzx5J\nUrt27RQdHX3B8ampqXrjjTc0ZMgQSdLgwYPVp08frV+/vtoQ+vbbbyspKakyyL777rvavXu3Zs6c\nqUGDBlWOe+CBBzRp0iQlJiZq/fr1lcEYADwVc2QBwGJ8fX01ePDgyu0GDRooNDRUknTvvfe6je3Y\nsaMk6fjx45Vtn3zyiRo3bqxf/epXOnXqlNtHxXGTk5Nr+8sAgCvGGVkAsJhWrVrJ4XC4tTVo0ECS\nFBQUVG17SUmJJCk3N1fHjh2TJPXo0aPG52DtWgBWQJAFAIvx9vausc/pdF5wX5fLJUlq3bq1Xnvt\ntRrHBQQEXF5xAFCHCLIAUI/4+/tLkvLz8ytvvAAAVsUcWQCoR/z9/RUYGKiTJ08qLS2tSn9+fr4K\nCgpMqAwAfjmCLAB4gIo5r4WFhbX+XDExMZKkOXPmVOl744031Lt3b3377be1XgcAXCmmFgCABwgO\nDpYkrVy5Uo0bN1ZgYGCtPde4ceO0bt06/ec//5HL5dLAgQNVUlKitWvXVq5H27Vr11p7fgC4Wjgj\nCwAeICIiQrGxsXK5XJo1a5ZSU1Nr7bn8/f0VHx+v8ePH69ChQ3rhhRc0depUZWZm6k9/+pNmzZol\nu51fDwA8H3f2AgAAgCXxlhsAAACWRJAFAACAJRFkAQAAYEkEWQAAAFgSQRYAAACWRJAFAACAJRFk\nAQAAYEkEWQAAAFgSQRYAAACW9P8Bdcd0/n06DiUAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "S6WDuKBHQ3Ta",
        "colab_type": "code",
        "outputId": "e0ed7790-e25e-4686-82d1-1e9901f5f755",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 860
        }
      },
      "source": [
        "mass = 1.0 \n",
        "target = np.array([30.0,0.0]) # target location\n",
        "delta_t = 0.1 # time step\n",
        "\n",
        "k_p_final = 3\n",
        "k_p_peak = 6\n",
        "t_peak = 2\n",
        "k_d0 = 6\n",
        "acc_max = 10.0\n",
        "\n",
        "plt.plot(target[0],target[1],'o',markersize=10) # Plot Target\n",
        "\n",
        "v0 = 10 # magnitude of initial velocity\n",
        "\n",
        "for theta in np.linspace(0.1*np.pi,0.6*np.pi,num=6):\n",
        "  pos = np.array([0.0,0.0])\n",
        "  diff = target - pos\n",
        "  prev_diff = diff\n",
        "  acc = np.array([0.0,0.0])  # (initial) acceleration\n",
        "\n",
        "  time = 0.0\n",
        "  vel = np.array([v0*np.cos(theta),v0*np.sin(theta)]) # (initial) velocity\n",
        "  display(\"theta: {0}, vel: {1}\".format(theta, vel))\n",
        "  df = pd.DataFrame({\"time\":[time],\"x\":[pos[0]],\"y\":[pos[1]]})\n",
        "  # display(diff,np.linalg.norm(diff) )\n",
        "\n",
        "  while True:\n",
        "    time += delta_t\n",
        "    if time > 15:\n",
        "      display(\"timeup\")\n",
        "      break\n",
        "    if np.linalg.norm(diff) < 0.5e-0:\n",
        "      display(\"hit at {0}\".format(time))\n",
        "      break\n",
        "    k_p = gain_exp(time,k_p_final,k_p_peak,t_peak)\n",
        "    # k_d = gain_exp(time,k_d0,2.5)\n",
        "    # k_d = k_d0 - k_d0*sigmoid(time - 4)\n",
        "    k_d = k_d0\n",
        "    diff = target - pos\n",
        "    dot_diff = (diff - prev_diff)/delta_t # \\dot{d}\n",
        "    force = k_p * diff + k_d*dot_diff\n",
        "    # print(force)\n",
        "    acc = force/mass\n",
        "    if np.linalg.norm(acc) > acc_max:\n",
        "      acc = acc/np.linalg.norm(acc)*acc_max\n",
        "    vel += acc*delta_t\n",
        "    pos += vel*delta_t\n",
        "    prev_diff = diff\n",
        "\n",
        "    # save to plot\n",
        "    df2 = pd.DataFrame({\"time\":[time],\"x\":[pos[0]],\"y\":[pos[1]]})\n",
        "    df = df.append(df2)\n",
        "\n",
        "  # Plot Trail\n",
        "  print(\"plot\")\n",
        "  plt.plot(df.x,df.y,'.',label=\"{0:.1f}\".format(theta))\n",
        "\n",
        "plt.xlabel(\"x\")\n",
        "plt.ylabel(\"y\")\n",
        "plt.title(\"v0: {0}, k_p_final: {1},k_p_peak: {2}, t_peak: {3}, k_d: {4}\".format(v0,k_p_final,k_p_peak,t_peak,k_d0))\n",
        "plt.axis('equal')\n",
        "plt.legend()\n",
        "filename = \"ballet02.png\"\n",
        "plt.savefig(filename)\n",
        "files.download(filename) \n"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'theta: 0.3141592653589793, vel: [9.51056516 3.09016994]'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'hit at 4.4'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "plot\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'theta: 0.6283185307179586, vel: [8.09016994 5.87785252]'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'hit at 4.200000000000001'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "plot\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'theta: 0.9424777960769379, vel: [5.87785252 8.09016994]'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'hit at 3.2000000000000015'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "plot\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'theta: 1.2566370614359172, vel: [3.09016994 9.51056516]'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'hit at 3.2000000000000015'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "plot\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'theta: 1.5707963267948966, vel: [6.123234e-16 1.000000e+01]'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'hit at 6.5999999999999925'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "plot\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'theta: 1.8849555921538759, vel: [-3.09016994  9.51056516]'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'hit at 6.499999999999993'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "plot\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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AhdPyvf3228WeI/Rv0s2bN7FlyxYAUJpNRWhinDeeP3+OI0eOACjsu1/0rqaVlRW++eab\nEi/YmjVrpjiWlStXVuv1kpKSAACVK1fGuXPn0KNHD8yZMweRkZHYt28fli1bhl69egl6QS0WJqxa\nIG/ZOnz4MGQymdK2Y8eOITMzE/b29oovc3Z2NgDA0tKy1HLlV9ny52ubPsR59OhRzJo1CzY2Nli5\nciXq1q0r+Gt4enqidu3axR738vJSnMDE7O6gDhcXF5U/FHXq1AFQ2G+w6AXD22+/jW+//RYLFixQ\nWZ78/T558kSEaFU7cuQI3Nzc0LJlSwQHB+P69esIDQ3Fzp07yzVgZuvWrVi9ejWcnJwQERGhuIAS\nUqdOnVS2HnXs2BFA4fRdmvTLfB1N6qRUKsXx48cBFPbnVKVu3bqK1v2///5b8bhQ9eTatWsYP348\nAGDx4sVo3rx5qc9XV9GLgEmTJuHNN9/E1q1bcfHiRRw9ehSjRo2CiYkJfvvtN/z000+CvKaYqlev\njlatWhV73MXFRdECVvRcI2/seO+991SWJ+/CAUAp0W3YsCFmzZqF5cuXq0yO1P1cHzx4gJEjR+LF\nixeYPn16iX3RhXT//n2MGDECubm56Nixo6KhR2hinTdiY2MhlUohkUgU54eibGxs0LlzZ0FeC/jv\nOyKVSjFu3Di888472LNnDy5duoRDhw5hwIAByM/PR3h4OHbu3CnY64qBXQK0wMfHB9bW1khOTsbF\nixfRokULxTZ5d4AePXoUuyX/anKrr3QVZ3x8PMaPHw8TExP88MMPik74QnN1dVX5uHxi8hs3buD+\n/fuivLa6SkrUi15MqBqEdv36dRw7dgwPHz5ESkoK8vLyAEAxYEKbo2+dnJzg4+ODrKws3L17Fw8f\nPsTKlSuRmZmJESNGlKlP8vHjxxEWFgY7OzusWrXqtQtglFVJK/84ODjA1tYWWVlZgtYRTepkYmKi\n4mJx8eLFKgddAP9NqXbnzp1i28pTTx49eoQRI0YgOzsbs2fPRpcuXdR7k2rIzc1V/Lt69epYtWqV\nopXR2toan3/+ObKzs7F27VpEREQgJCREr0dCl/S5AoVJ5K1btxSfa05OjuKzWr9+Pfbt26dyP/mc\n2qo+13v37uHPP/9EUlISnjx5orgLIx/EVNrnKv9epqSkYNSoURg4cOBr3195xcfH49NPP0VycjKa\nNm2KxYsXK81MIxQxzxvyLizVqlUrsS42bNhQsNeTf0cyMzPx/vvvK00RWLduXYSFhSE1NRWHDx9G\neHg4/P39RTmmQmDCqgU2Njbo0qULDhw4gEOHDikS1tzcXPzxxx8AoHSVKG8hKW3UbtHtQvbX1IQu\n40xNTcWIESOQlZUFS0tLwaasUaXobddXyQeMaDpSWmiarvaSm5uLqVOnYvfu3SJFpDlPT0+lPoEX\nLlzAV199hfDw8DLNo3n79m18/vnnyMvLg7m5uairhJV2e65SpUrIysoStI5oUiflXXcA5dbTkshH\n7QPlryc5OTkYPnw4kpOTIZFIyj0Q51VFWwcHDhyosmtSSEgI1q5di+zsbJw7d07Q1iuhlfVzvXDh\nwmvLLvq5AoX9/tesWVPmi9KxY8cqkmFNBuuW1alTpzBmzBhkZGTAy8sLP//8sygXH2KfN+SfQ2mx\nq3u7Xx1FvyMfffSRyueEhITg8OHDuH//Pm7dulXubl1iYZcALZF3Czh06JDisePHjyMzMxO1atVS\nGmUvH3H6/PlzRUuGKvLbNWLc4lSHLuNMSEjAo0ePUKdOHeTk5GDixIlKrS1CKq1/rvxkX9pz9FF4\neDh2794NU1NTDBs2DLt378b58+dx/fp1XL9+HXPnztV1iGjRogWWL18OExMTREVFlTqtjyqxsbF4\n+fIlXFxckJ6ejtDQUNHuBpQ2SlmMOqJJnSzaWnLkyBHFZ1zSf7Nnz1Y8v7z15MmTJ7h+/Trq1q0L\nmUyGKVOmaDQdz+sUHWxTUtLk7OysuLjW9Z2Q1ynr57pu3brXfq5r1qxRPH/Lli2IiIhAQUEB+vfv\nj23btuHs2bOIj4/H9evXFfMjl+bEiROKOzvffvutypkIhLJ3714MGzYMGRkZ6N69O9asWSPayndi\nnzfkZZXWiilkf+ui3xEXFxeVzynan/zBgweCvbbQDOtX1oB17NgRlSpVQlJSEq5duwbgv+4APXv2\nVKq88qubgoICRYdpVe7evQug5NuRYtNlnObm5vjuu++wZcsWODo64saNG5g/f75g5RdV2mAZ+TZ9\nvs34qoKCAsWAhZCQEHzxxRd46623lN7DixcvdBWekvr16yta5dRpRSrKzs4OK1euxKpVq2BlZYXj\nx49j3bp1YoRZrPWqKHkdEfIHVpM6WfQHKzk5We3XEKKeSCQSTJgwAXv27EGDBg2QkpKCqVOnqh3D\n67i4uCi6OJR2TOTdSfT1VqecJp9rlSpVFO9Hk88VgGLmB19fX8yaNQvNmjVD5cqVFeW9fPnytWUE\nBQVh//79aNOmDbKzszFp0qRyz32tyqFDh/Dll19CKpVi8ODBWLp0qaAzkbxK7POG/E5jaZ910dbz\n8io6+r+k85Smd+h0hQmrllhYWCg6pP/xxx9K3QF69+6t9NxKlSopksFz586pLO/hw4eK0byqBtto\ngy7jbNGiBfz9/eHo6KiYdmXjxo2KORmFVNIMAPn5+YoWG1UDYPRVenq6YjLxkm6P/vPPP6LHceTI\nEfj7+6NHjx6ltmDIT+yatlB269YN77zzDho0aIAvv/wSQOEo5vj4+LIHXYKS6khKSoqi/6iQ/eA0\nqZO1a9dWtDDKb+GqQ4h6UrNmTYwYMQJWVlZYuHAhzM3NER0djc2bN6sdR2kkEomii1VJsTx//lyR\nAJTUwqQvSpttRH7hL/9cLSwsFFMcafK5Fi2rpM9VnbsZM2bMUDQcVKlSBVeuXMHSpUs1iuN1zp49\ni0mTJqGgoACTJk3ClClTRL/oEPu8UXRAW0kXfJp+nqWpVq2aoiW8pO9I0ZlB9Pk7woRVi+TdAo4d\nO4bTp08jIyMDTZo0UTn/Wc+ePQH8Nw/lq3777TcAQOPGjXXa30Qf4uzcuTOCgoIgk8nw1VdflWmF\nltKcP39e5UTOZ8+eVSQjJS2coI9sbW1LbUm5efMmoqKiAKDUrh7l5ezsjLi4ONy+fVsxiv1VcXFx\nimSjtAEpr/PRRx+hc+fOyM3NxcSJE9VqQdJETEyMyjL/+usvAIXJhbu7u2Cvp0mdNDU1RYcOHQAU\njnxW1WcxNzcX/fv3R1hYmGI2CaHrSZMmTTBu3DgAhXO6yudxLi8/Pz8AhecaVTORyPvfWllZCfI9\nlR8TMb4biYmJuHr1arHH7927pxg0VXTQrjzh3L17d4nJz7BhwxAaGqp0F0zeSqvqc01JSVGct4HX\nv88aNWogLCwMQOFyqqdOnSr1+epKT0/HuHHjkJOTg//973/49NNPBSlXE2KcN5o1awYTExMUFBSo\nPO9lZmYqzhtCkX9H1q1bp7JxQP4deeONN/R6PlYmrFrUtm1bODg44NKlS4olWEuakuPjjz+Gk5MT\nLly4gMWLFyv9yBw9ehSrV68GAMVUMUX5+vrC19e3xCRASOWJ85NPPoGvry927NhR7jgmT56M+vXr\n48mTJ4ItnSdnbW2NKVOmKN3CSUtLU7TstmrVyqBaWK2srBRX3Js3b1a6jXfu3DkMHToU/v7+AAoH\nt6lze+rx48eKeqfucrVNmzZF69atAQBTp04tNjVYQkICJk+eDKBwTfhXF1LQtJ5/++23cHR0xK1b\ntzBv3jy19lGXVCpFWFiYUj/qxMRERYuTn5+foLcxNa2Tw4cPh6mpKa5du1YszvT0dIwfPx6xsbE4\ne/asYsCHGPVkyJAh8Pb2xsuXL4v1Oy9LHQIAf39/1KtXD0+fPsUXX3yhNLjt8uXLWL58OQDgww8/\nLNYtoyznSvnAqH///VfwwZaVK1fG1KlTlS5GsrOzMWPGDMhkMtSuXVvxnQEKl3C2tbVFcnIyJk6c\nqFQf5PsdO3YMMTExSqtxvfXWWwAKGxqKvofr169j8ODBStNT3b59+7Vx9+jRAwEBASgoKMDkyZOL\nzbldluO8dOlSPHnyBJ6enor5jNUl5G+g0OcNR0dHxRSW33//fbHPurQuM5cuXVK8t9KW3H1VSEgI\n7O3tkZCQgLCwMKXv8tGjRxVdRIYOHarX3WY4S4AWmZqawtfXF5s2bcKBAwdgYmKitPpQUXZ2dli6\ndCmGDRuGFStWYNeuXWjUqBEeP36suF0wevRolUutyTu/azJR+f79+5WW7yx6JTl9+nSlH9vg4GDF\nil3liTMxMRH3798XZEEBKysrfP/99+jfvz+OHj2KDRs2IDg4uNzlAkC/fv0QHR2tWG/bxMQEFy9e\nRHZ2NipVqoSZM2cK8jraNHbsWEyYMAF//PEH3nvvPTRo0AAPHjxAQkIC+vfvj4kTJ2LPnj3IyclB\nnz590LZt21KXJJRKpYp6p0krxKJFizB06FBcv34dAwYMQOPGjeHk5ITHjx/j1q1byMvLg6OjI5Yu\nXVpsWitN67mjoyPmzJmDkSNHYvPmzejYsSO6du2qdqylGTZsGNauXYuOHTuiadOmyM3NxYULFyCV\nSuHs7IxJkyYJ8jpymtZJd3d3hIWFYcaMGdiyZQsOHTqEJk2aICsrC/Hx8Xjx4gWqVq2KhQsXKnW9\nELqemJiYYP78+ejduzfi4uKwaNEiTJkyBUDZ65C5uTl+/PFHfPLJJzhy5Ai6dOkCDw8PPHv2DFev\nXlUsQzthwoRi+5blXCnv2pSeno6uXbvCwcEBwcHBCAoKUruMknTt2hVJSUnw8fFBs2bNYGlpiStX\nruDp06cwNzfH7NmzlQb4OTs7Y9GiRfj8888V9cHDwwN5eXm4fv06nj9/DmtrayxcuFBplpYxY8bg\nxIkTuHLlCt577z289dZbSEtLw7Vr19CpUydMnz4dMTExSElJwZAhQ+Dh4fHaeWynTp2Ks2fPIikp\nCdOmTUN4eLhim6bH+dmzZ4qGjJycnNeuolb0N6ksr1caMc4boaGhiI2Nxb///otu3brB09MTJiYm\nuHLlCkxNTTF27FilwY9yL168ULw3TVr47e3tsXz5cowYMQKbN2/GkSNH8NZbbyE5ORnXr18HUHi3\nVKjfTLGwhVXL5Amq/CRa2nRMLVu2xN69e9GvXz+Ympri1KlTSElJQadOnfDLL79g7NixgsV1+/Zt\nREdHK/6Trz0MFI4GLbpNPveiUHEKtQ50kyZNFFfiCxYsEKwfkLW1NbZu3YqAgAAkJSXh3LlzsLKy\nwvvvv48dO3YIOmeetrz//vuYN28e3nrrLTx58gSXLl1C5cqV8d1332HWrFmwt7fHjBkz4OTkhOTk\nZEEHARTl5OSE7du3Y/r06WjVqhUePHiAEydOICkpCW5ubvjf//6Hffv2KVqEVNGk/nTp0kUxX+RX\nX32l8WCVkjg5OWHHjh3o0qULbt26hQsXLqBq1aro378/tm/fDicnJ0FeR64sdbJfv36IjIyEv78/\nrKyscPr0acTFxaFWrVoYNmyYyuMsRj2pUaOGIqFeu3at0rmmrBo0aIB9+/Zh2LBhcHBwwNmzZ3H7\n9m14enpixowZ+OWXX0pt4dakDjVu3Bhff/01atSogaysLGRnZws2A4pEIsEvv/yCIUOG4MmTJzh7\n9iyAwnq7ZcsWxSIARXXu3Bn79u3DwIED4ejoiH/++QexsbFwcHDAwIEDsXfvXrRv315pnxYtWmDF\nihVo0aIFMjMzcfHiRUgkEnz99df48ccfYWFhgTlz5sDFxQXPnj1TawEROzs7LFiwAKampjh06BC2\nbdtW5uOQkZGhaH2Pj49X+v1R9d+rv0lyQv22CH3eqF+/PrZt24ZevXrB1tYW58+fx61bt+Dj44Md\nO3YorVgolLfffht79+7FwIEDYWlpidOnT+PRo0fw9vbG999/X+xiVS/JiHSoS5cusq1bt+o6DJU+\n/vhjmaurq+yHH37QdSikQn5+vqxx48ayEydO6CyGLl26yFxdXWU7duzQyuuxTgpLH+qQTCaTTZ48\nWebq6iqbPHmyTuMwFvryuZKw9DydJmOWnp6OBw8eiLKcKhm/+Ph45Ofns/5QmbEOGSd+rsaJCSvp\nzJ49e2BnZyfYuuJUsezatQtvvvmmXk/DQvqNdcg48XM1Thx0RToj7ycl1qTF06ZNK9MUV46OjqUO\nHCnJ4sWLNRrdXFTRJUnp9STS/HcAACAASURBVGQyGapVq4YZM2aUq5xRo0aVab9GjRqpnPnidbRd\nJ6lkQtUhgN99fSLk51oSbZ83qBATVtIZeSd2sZw4caJMSzGW9ar8n3/+wZkzZ8q0L2lGIpFg+PDh\n5S4nOjq6TPuVtrJVabRdJ6lkQtUhgN99fSLk51oSbZ83qJBEJhNpcW09o+k65ERERESkfS1btiz2\nWIVqYVV1AHQhLi4OjRs31nUYRovHVzw8tuLi8RUPj624eHzFVZGOb0kNjBx0RURERER6jQkrERER\nEek1JqxEREREpNeYsBIRERGRXmPCSkRERER6jQkrEREREek1JqxEREREpNeYsBIRERGRXmPCSkRE\nRER6jQkrEREREek1JqxEREREpNeYsBIRERGRXmPCSkRERER6jQkrEREREek1JqxEREREpNeYsBIR\nERGRXmPCSkRERER6jQkrEREREek1JqxEREREpNfMdB0AEREREQkrLy8P69evx65du3Dnzh2YmprC\nzc0NgwYNgp+fn1plxMTEYNOmTYiPj0daWhrs7e3h5eWFoUOHwtPTU+R3oIwJKxEREZGRmTBhAqKi\nouDj44OQkBBIpVLs3LkT48ePx8OHDzF06NBS91++fDl++OEHuLq6YsiQIbC3t8f169exefNmHDly\nBCtXrkSHDh209G6YsBIREREZlSNHjiAqKgo9evTAkiVLFI8HBASgT58+WLx4Mbp3745atWqp3D8h\nIQHh4eFo1KgRtm3bBisrK8U2T09PfP755wgPD9dqwso+rERERERGZPv27QCAwYMHKz1uYWGBoKAg\nSKVS7Nq1q8T9JRIJJkyYgClTpiglqwDQsWNHAMCDBw8Ejrp0bGElIiIi0sDJ5DuIeZSAzjUaoG31\neroOp5iLFy/C3Nwc7u7uxbZ5eXkBAC5cuFDi/vXr18fw4cNVbrt16xYAoEmTJgJEqj4mrERERERq\nOpl8Bz6/r0RuQR4sTMwQ7TtCr5LWzMxMpKenw8XFBaampsW216xZEwCQmJioVnn5+fnIyspCRkYG\nzp49iwULFsDZ2RmTJ08WNO7XYcJKREREpKaYRwnILchDvkyG3II8xDxK0KuENSsrCwBgY2Ojcru1\ntTWAwsRWHTdu3IC/vz8AwMTEBIGBgZg4cSIcHBwEiFZ9TFiJiIiI1NS5RgNYmJgpWlg712ig65CU\nSCSSUrfLZDK1nidXp04drF+/HllZWbh06RK2bt2K48eP4/vvv8fbb79d7njVxYSViIiISE1tq9dD\ntO8Ive3DamdnBwDIzs5WuV3eAit/3uvY2trC29sbANC1a1cEBgYiMDAQ48aNw+HDhxUttmLTq4Q1\nMjISc+bMQWZmJqKjo4tNt9C1a1fcv3+/xP0//PBDfPPNN2KHSURERBVY2+r19C5RlbOxsYGTkxOS\nk5ORl5cHMzPlVC8pKQlA4cCqsqhTpw7atWuHqKgoXL16VWutrHqRsKampmL69OmIjo5+babu4OCA\nGTNmqNxWp04dMcIjIiIiMhheXl6IiopCbGwsWrZsqbTtzJkzAKBoNVVl1apV+OWXX/DFF18gMDCw\n2Pbnz58DKByQpS16kbD27dsXUqkUq1atws8//6w4mKpYW1vD19dXi9ERERERGY4BAwYgKioKERER\nSglrVlYWNm7cCFtbW/Tu3RsAkJGRgeTkZNjb28PR0REA0LRpU6SlpWHdunXo2bMnLCwsFGXcvn0b\n//zzD6ytrVVOmyUWvVg4oHnz5tizZ49WV0wgIiIiMkbt2rVDv379EB0djeHDhyMyMhKbN29GUFAQ\nHjx4gOnTpytG+R8+fBh+fn5YsWKF0v69e/dGfHw8/P39ERERgV27dmHx4sUYMGAAcnJyMHHiRNja\n2mrtPelFC+vixYvLtN/Lly9hbm6ucp4xIiIioopq1qxZaNKkCbZt24aZM2fC3NwcHh4eiIiIQPv2\n7V+7//z589GuXTvs2LEDP/30E7Kzs1G5cmV4enpi0KBBWm9k1IuEVRMvX75EWFgYfv/9d6SlpUEi\nkaBJkyYYMmQIevbsqevwiIiIiHROIpEgKCgIQUFBpT5PPupf1f4BAQEICAgQK0SNGFzCmpqain//\n/Rdffvklqlativj4ePzyyy+YOHEikpKSMHLkyBL3jYuL02KkJXv58qXexGKMeHzFw2MrLh5f8fDY\niovHV1w8vgaWsM6ZMwcSiQRt2rRRPNa5c2f4+vrigw8+wLJlyxAYGIjq1aur3L9x48baCrVUcXFx\nehOLMeLxFQ+Prbh4fMXDYysuHl9xVaTje/78eZWP68WgK3W1bdtWKVmVq1evHt59911IpVKcPn1a\nB5ERERERkVgMKmEtjbxVNSMjQ8eREBEREZGQDCZhvXfvHnbu3Ilr166p3J6QkAAAcHFx0WZYRERE\nRCQyg0lYHz16hClTpmD69OmQSqVK2y5cuIBjx47B0dGx1JUbiIiIiMjw6HzQ1f3793H58mXF32lp\naQCAv/76SzGprYuLC1q3bo3AwEBERkaib9+++OCDD1C1alXExcVhy5YtMDMzw9y5c2FlZaWT90FE\nRERE4tB5wnr69GmEhoYWezwsLEzx74CAAMybNw+zZ8+Gh4cHdu/ejfDwcEilUjg6OsLX1xfDhg2D\nq6urNkMnIiIiIi3QecJa0oS1qpiamqo1CS4RERERGQ+D6cNKRERERBUTE1YiIiIi0mtMWImIiIhI\nrzFhJSIiIiK9xoSViIiIiPQaE1YiIiIi0ms6n9aKiIiIiISVl5eH9evXY9euXbhz5w5MTU3h5uaG\nQYMGwc/PT60yCgoKsHnzZmzbtg3//vsvLC0t0bhxYwwbNgwdOnQQ+R0oY8JKREREZGQmTJiAqKgo\n+Pj4ICQkBFKpFDt37sT48ePx8OFDDB06tNT9ZTIZJk6ciAMHDqB79+4ICQlBeno61q9fj+HDh2PR\nokXo0aOHlt4NE1YiIiIio3LkyBFERUWhR48eWLJkieLxgIAA9OnTB4sXL0b37t1Rq1atEsvYvXs3\nDhw4gGHDhuGLL75QPN6tWzf0798fR44c0WrCyj6sRERERBrIvnUST/bORfatk7oORaXt27cDAAYP\nHqz0uIWFBYKCgiCVSrFr165Sy1i/fj1sbGwwevRopcdr1aqFv//+G99//72wQb8GW1iJiIiI1JR9\n6yTufucDWV4uJGYWqDs5GjYN2+o6LCUXL16Eubk53N3di23z8vICAFy4cKHE/dPS0nD16lV07twZ\nNjY2AAr7xBYUFMDCwkKcoF+DLaxEREREasqOi4EsLxcoyIcsLxfZcTG6DklJZmYm0tPTUb16dZia\nmhbbXrNmTQBAYmJiiWXcuHEDAFC3bl1ERUXB398fHh4e8PDwgJ+fH7Zt2yZO8KVgCysRERGRmmwa\nd4bEzELRwmrTuLOuQ1KSlZUFAIqW0VdZW1sDKExsS5Keng4AOHPmDA4ePIghQ4agfv36uHfvHlat\nWoWpU6ciNTUVI0eOFDj6kjFhJSIiIlKTTcO2qDs5GtlxMbBp3FnvugNIJJJSt8tkstc+Lzc3FwDw\n77//YufOnahfv75iW9euXdGjRw/8+OOPGDBgAOzt7QWI+vXYJYCIiIhIAzYN26Jar1C9S1YBwM7O\nDgCQnZ2tcru8BVb+PFVsbW0BAM2bN1dKVgHAxcUF7dq1Q05ODi5evChEyGphwkpERERkJGxsbODk\n5ITk5GTk5eUV256UlAQAxRLRomrXrg0AKvcHACcnJwBARkZGecNVGxNWIiIiIiPi5eUFqVSK2NjY\nYtvOnDkDAPD29i5x/wYNGsDe3h63bt1SdA8oSj5gy9nZWaCIX48JKxEREZERGTBgAAAgIiJC6fGs\nrCxs3LgRtra26N27N4DCVtKEhASkpqYqnmdmZobAwEA8ffoUa9asUSrj2rVrOH36NKpXrw5PT0+R\n38l/OOiKiIiIyIi0a9cO/fr1w7Zt2zB8+HD4+voiJycHW7ZswYMHDzBv3jw4ODgAAA4fPozQ0FAM\nGjQIX3/9taKM0aNH48SJE1i0aBESExPRqlUr3L17F+vWrYOJiQlmzJgBc3Nzrb0nJqxERERERmbW\nrFlo0qQJtm3bhpkzZ8Lc3BweHh6IiIhA+/btX7u/nZ0dNm3ahBUrViAqKgq7du2CjY0NWrVqhZEj\nR6J58+ZaeBf/YcJKREREZGQkEgmCgoIQFBRU6vMCAwMRGBiocpudnR0mTZqESZMmiRGiRtiHlYiI\niIj0GhNWIiIiItJrTFiJiIiISK8xYSUiIiIivcaElYiIiIj0GhNWIiIiItJrTFiJiIiISK8xYSUi\nIiIivcaElYiIiIj0GhNWIiIiItJrTFiJiIiISK8xYSUiIiIivcaElYiIiIj0GhNWIiIiItJrZroO\ngIiIiIiElZeXh/Xr12PXrl24c+cOTE1N4ebmhkGDBsHPz0+tMo4ePYr169fj0qVLePHiBVxcXNCr\nVy98+umnsLS0FPkdKGPCSkRERGRkJkyYgKioKPj4+CAkJARSqRQ7d+7E+PHj8fDhQwwdOrTU/deu\nXYu5c+eiWrVqCAkJgYuLC06cOIHw8HCcP38eq1evhqmpqZbeDRNWIiIiIqNy5MgRREVFoUePHliy\nZIni8YCAAPTp0weLFy9G9+7dUatWLZX7P378GAsXLoSNjQ0iIyPxxhtvAAD8/f3h7OyMlStXIjIy\nEv369dPK+wHYh5WIiIjIqGzfvh0AMHjwYKXHLSwsEBQUBKlUil27dpW4//HjxyGVSuHn56dIVuWG\nDx8OKysr7NixQ/jAS8GElYiIiEgDmfee4GHMNWTee6LrUFS6ePEizM3N4e7uXmybl5cXAODChQsl\n7p+SkgIAqFOnTrFtdnZ2qF27Nq5cuYK8vDyBIn49dgkgIiIiUlPmvSe4EfEnZHn5kJiZwnVoF9jV\nqabrsBQyMzORnp4OFxcXlX1Ma9asCQBITEwssQw7OzsAQFpamsrtFhYWkEqlePz4MVxcXASI+vXY\nwkpERESkpozbyZDl5QMyQJZXgIzbyboOSUlWVhYAwMbGRuV2a2trAIWJbUlat24NiUSCQ4cOITc3\nV2lbfHw84uPjAQDZ2dlChKwWJqxEREREaqpUvzokZqaARAKJmQkq1a+u65CUSCSSUrfLZLLXPs/V\n1RUBAQF48OABRowYgfj4eDx+/Bj79+/HyJEjFa205ubmwgX+GuwSQERERKQmuzrV4Dq0CzJuJ6NS\n/ep61R0A+O92fkmtn/IWWPnzSjJ9+nQAwO7du/HBBx8AAJycnDBu3DicOnUKiYmJsLe3Fyrs12LC\nSkRERKQBuzrV9C5RlbOxsYGTkxOSk5ORl5cHMzPlVC8pKQkAUL9+/VLLsba2xty5czF58mTcuXMH\nNjY2aNCgAUxNTbFp0yY4OTlpNWFllwAiIiIiI+Ll5QWpVIrY2Nhi286cOQMA8Pb2Vqsse3t7NG/e\nHK6urjA1NcWjR48QFxeHDh06CBrz6zBhJSIiIjIiAwYMAABEREQoPZ6VlYWNGzfC1tYWvXv3BgBk\nZGQgISEBqampiue9ePECPXv2hJ+fX7FBV/PnzwcAfPzxx2K+hWKYsBIREREZkXbt2qFfv36Ijo7G\n8OHDERkZic2bNyMoKAgPHjzA9OnT4eDgAAA4fPgw/Pz8sGLFCsX+1tbW6NSpExISEvDxxx/jt99+\nw/bt2xESEoL9+/dj7NixaNq0qVbfE/uwEhERERmZWbNmoUmTJti2bRtmzpwJc3NzeHh4ICIiAu3b\nt3/t/pMmTUKNGjWwfft2zJs3DwDQtGlTLFu2DN26dRM7/GKYsBIREREZGYlEgqCgIAQFBZX6vMDA\nQAQGBqrcPzg4GMHBwWKFqBF2CSAiIiIivcaElYiIiIj0GhNWIiIiItJrTFiJiIiISK8xYSUiIiIi\nvcaElYiIiIj0GhNWIiIiItJrTFiJiIiISK8xYSUiIiIivcaElYiIiIj0GhNWIiIiItJrTFiJiIiI\nSK8xYSUiIiIivcaElYiIiIj0GhNWIiIiItJrTFiJiIiIjFRkZCRatmwJNzc3JCUlqb1fQUEB9uzZ\ng+DgYLRv3x7u7u7o3LkzJk+ejISEBBEjVs1M669IRERERKJKTU3F9OnTER0dDWtra433nzZtGrZv\n346WLVti1KhRsLa2xsWLF7Fjxw4cOnQImzdvxltvvSVC5KqxhZWIiIjIyPTt2xexsbFYtWoV3N3d\nNdr3r7/+wvbt29GuXTts3LgRH330EQIDA/HNN99gwoQJyM7OxsqVK0WKXDUmrEREREQayMu5ipcZ\nm5CXc1XXoZSoefPm2LNnDzp06KDxvvb29hg/fjzGjx8PExPlVLFjx44AgIcPHwoSp7rYJYCIiIhI\nTXk5V5GV+gUgkyJHYg5bxwUws2yq67CKWbx4cZn3bdasGZo1a6Zy282bNwEAjRs3LnP5ZcGElYiI\niEhNebmxgEwKoACQSZGXG6uXCatQpFIpXrx4gadPn+LYsWNYuHAhXF1dMXr0aK3GwYSViIiISE1m\nFp7IkZgXJq0Sc5hZeOo6JFEdPXpUkZxaWFggODgYo0ePhq2trVbjYMJKREREpCYzy6awdVxQ2LJq\n4WnUrasA4OXlhfXr1+P58+c4f/48Nm/ejJiYGCxduhSNGjXSWhx6NehKnbnCkpKSEBoaio4dO8Ld\n3R3vvPMOJk2ahLt372o5WiIiIqqIzCybwqpSkNEnqwDg4OAAb29vdOvWDVOmTMHatWtx584dTJo0\nSatx6EULq7pzhSUmJuLDDz/EixcvMGjQIDRs2BCJiYlYu3Ytjh07hs2bN6N+/fpajJyIiIio4vD0\n9ETjxo1x5coVPHr0CDVq1NDK6+pFC6u6c4XNnTsXqampWLJkCcaPH49evXph1KhRWLFiBZ4+fYrZ\ns2drMWoiIiIi4zN79mx4e3vj1KlTKrc/f/4cAJCXl6e1mPQiYVVnrrDU1FTExMSgfv366NSpk9I2\nLy8veHp64u+//8b9+/fFDpeIiIjIKKSlpSEhIQHPnj1TPObm5oanT58iIiICMplM6flnzpxBYmIi\natasiVq1amktTr3oEqDOXGGXL19Gfn4+WrRooXK7l5cXYmNjcfHiRbi4uAgdIhEREZFBuH//Pi5f\nvqz4Oy0tDUDhClYODg4AABcXF3h4eODXX3/FsmXLEBoaipCQEACAv78/9u7di7/++gsDBgyAn58f\nKleujPj4eGzZsgUSiQRff/21Vt+TXiSs6khMTAQA1KxZU+V2Z2dnAMC9e/e0FhMRERGRvjl9+jRC\nQ0OLPR4WFqb4d0BAAObNm6dyf3Nzc0RERGDTpk3Yu3cvlixZgtzcXFStWhWdOnXC0KFD4emp3em8\nDCZhzcrKAoASB2XZ2NgAADIzM0ssIy4uTvjAyuDly5d6E4sx4vEVD4+tuHh8xcNjKy4eX3Fpenwb\nN26MXbt2vfZ5cXFxePfdd/Huu+8q/i6qdevWaN26dYn7apPBJKwSiaTU7fI+FqU9T9vLiJUkLi5O\nb2IxRjy+4uGxFRePr3h4bMXF4yuuinR8z58/r/JxvRh0pQ47OzsAQHZ2tsrt8hbYSpUqaS0mIiIi\nIhKfwSSsderUAQA8ePBA5Xb5QgOch5WIiIjIuBhMwtqsWTOYm5uX2FR85swZmJmZwcvLS8uRERER\nEZGYDCZhrVKlCnx9fXH37l0cPnxYaduff/6JGzdu4L333oOjo6OOIiQiIiIiMeh80JUmc4V9+eWX\nOHfuHCZNmoRPPvkEjRo1wu3bt7F27Vo4OztjypQpOnkPRERERCQenSesmswVVr16dWzduhXLli3D\n7t27kZqaCkdHR/Tq1QtjxoxB9erVtRk6EREREWmBzhPWwMBABAYGqv386tWr45tvvhExIiIiIiLS\nJwbTh5WIiIiIKiYmrERERESk15iwEhEREZFeY8JKRERERHqNCSsRERER6TUmrERERESk15iwEhER\nERmpyMhItGzZEm5ubkhKStJo39zcXPz444/o0aMHPDw80LZtW4wcORKXLl0SKdqSMWElIiIiMjKp\nqakYPXo0vvrqKxQUFGi8f05ODoYMGYLw8HC0bNkSs2fPxqBBg3DhwgUEBwfj/PnzIkRdMp0vHEBE\nREREwurbty+kUilWrVqFn3/+GWfOnNFo/9WrV+Ps2bOYMWMGgoKCFI97e3tj1KhROHLkCFq2bCl0\n2CViwkpERERkZJo3b45p06bBwcEBP//8s0b75ufnY9OmTahTpw4GDhyotM3LywunTp0SMlS1sEsA\nERERkQZupEux81YWbqRLdR1KiRYvXgwHB4cy7Xvt2jU8efIEHTp0gEQiAVDYnzUvL0/IEDXCFlYi\nIiIiNd1Il2LWqXTkFQBmJlmY1qYqXKua6zosQd24cQMAUKdOHWzZsgVr1qzB3bt3AQBNmjTB6NGj\n4ePjo9WYmLASERERqelqai7yCoACAHkFhX8bW8Kanp4OANi1axdevHiBkJAQ1KxZE9evX8eqVasw\natQoLFiwAL1799ZaTExYiYiIiNTU1NECZiZZ/9/CWvi3scnNzQUApKSkYM+ePXB0dAQAdOrUCd7e\n3ujfvz/mz5+Pnj17wsREO71LmbASERERqcm1qjmmtamKq6m5aOpoYXStqwBga2sLoDBBlSercp6e\nnnB1dcWNGzeQkJCARo0aaSUmDroi0rGTd9IwN/omTt5J0+sytVE2EZEhcK1qjoCGtkaZrAJA7dq1\nAaDEQVZOTk4AgIyMDK3FxBZWIh06eScNPitOIjevABZmJoge2RZt65VtVKeYZcpdfPwCQ38Xp2wi\nItIPzZs3h6mpKa5du6Zye2JiIgCgZs2aWouJLaxEGhKyhTEmIRW5eQXIlwG5eQWISUjVyzLlzjx8\nIVrZcmzBJSLSnrS0NCQkJODZs2eKxxwcHPDuu+/i5s2b2Ldvn9Lzo6Ojce/ePbi7u6NGjRpai5Mt\nrEQaELr1snMDR1iYmSjK69zA8fU76aBMudbO1qKVDYjbOkxEVFHcv38fly9fVvydllbYAPDXX38p\n5mZ1cXGBh4cHfv31VyxbtgyhoaEICQlR7BMaGopLly7hyy+/xNWrV+Hm5obr169jw4YNsLGxwYwZ\nM7T6npiwUoVx8k4aYhJS0bmBY5mTIFWtl+VJqNrWc0D0yLbljkvsMuWav2EtWtmA8MeXiKgiOn36\nNEJDQ4s9HhYWpvh3QEAA5s2bV2IZzs7O2L59O5YtW4aDBw9iw4YNqFy5Mrp164YxY8agQYMGosRe\nEiasVCEI1XInRutl23oOgidlYpSpjbLFbB0uSoiLFyIifRUYGIjAwEC1nvvZZ5/hs88+U7mtWrVq\nmDlzpoCRlR0TVqoQhGq5E7P1krRzfNntgIjI8DBhpQpByJY7MVsYSfzjy24HRESGhwkrGYTy3sJl\nyyjJaavbARERCYcJK+k9oW7hsmWUAF68EBEZIiaspPd4C5eEpq2LFw7uIiISBhNW0nu8hau/bqRL\njXo97fLg4C4iIuEwYSWtKWtrE2/hCkPo5PJGuhSzTqUjrwAwM8nCtDZVBU1aDT0Z5p0BIiLhMGEl\nrShva1NF639qCMnl1dRc5BUABQDyCgr/FiqxFDsZLvo6YiXFvDNARCQcJqykFWxtUp+hJJdNHS1g\nZpL1/3EW/i0UMZNhObGTYt4ZICISDhNW0gq2NqnPUJJL16rmmNamqigtlGImw3LaSIq1fWeAg7yI\nyFgxYSWtqCitTULcYjak5NK1qrkot+rFTIbltJEUA9rri8tBXkRkzJiwksbKM3jKmH9AhbrFbGjJ\npVjEjlcbSbG2+uIC7HZDRMaNCStphK04JRPyFrOhJZeGSuzjrI1uB3LsdkNExowJK2mErTgl09Yt\nZjIc2qwTFaXbDRFVTExYSSPG2oojRD9DbdxiJsOi7Tph7N1uiKjiYsJKGjHGVhwh+xnyVj69Slt1\nwtAXWiAicURGRmLOnDnIzMxEdHQ0atWqpfa+e/bswW+//Ya4uDjk5eWhXr166NevH4KCgmBqaipi\n1MUxYSWNGVsrjjb7GRKJQZuDu4jIMKSmpmL69OmIjo6GtbW1xvvPmTMH69evR926dTFy5EhUr14d\nBw4cwOzZs3Ht2jXMnTtXhKhLZqLVVyO9dPJOGuZG38TJO2m6DkUnCvsZFn4Z2PeUDJGqiy6xVfTz\nBpG+69u3L2JjY7Fq1Sq4u7trtO+VK1ewfv161KxZEzt37sTw4cPh7++PlStXomfPnoiMjMTJkydF\nilw1JqwVnHzU/7SD8fBZcbJC/vjI+xn2d7NlyxQZJG1fdPG8QRWdIVywNW/eHHv27EGHDh003veP\nP/4AAPTr1w+2traKxyUSCT777DMAwPbt24UJVE3sElDBGcuo/6L998qCfU/JkGl7cJexnDeIysJQ\npndcvHhxmfdNSUkBANSpU6fYtnr16sHGxgYXL14sc/llwYS1gjOGUf+v9t8LrmGGxroOikjLtHnR\nZQznDaKyqggXbHZ2dgCAtDTVLcgWFha4f/8+ZDIZJBKJVmJil4AKTj7qf1aPt/T2KvF1Xu2/d+cF\nr8OIxORYpRKm92yBzzs3MtjzBlFZyS/YTCUw2gu2Nm3aAAD2799fbNvRo0fx9OlTyGQyvHjxQmsx\n8ZedDH7U/6uTs9ezztN1SERG6787GmYwM3WAY5VKug6JSKuMcXrHV3Xq1Ane3t44ffo0Jk6ciDFj\nxsDCwgLHjx/H0qVL4ezsjIcPH8LcXHtd6ZiwksF7tf9e/qNUXYdEZLQ4DRyR4Tf0qGPJkiX46quv\nsG/fPuzbtw8AULt2bcyZMwc///wznj9/zoSVyu/knTSDu/orz8TnRfvvxT0SIzoiArgEMVFF4eDg\ngBUrViAlJQVJSUmoUqUK3nzzTUgkEoSGhqJRo0ZajYcJqxEylBGMRXHicyLDwCWIiSoWJycnODk5\nKf6+cOEC0tPT8fHH2MjYUQAAIABJREFUH2s1Dg66MkKqRjDqO11MfE5EZeNa1RwBDW21mqwawryX\nRIYoLS0NCQkJePbsmeKxhw8fomvXrhg0aBBkMpnicalUioULF8LGxgb9+vXTapxsYTVChjjlDG8z\nElFJDPGuEZEu3b9/H5cvX1b8LZ+e6q+//oKDQ+F3x8XFBR4eHvj111+xbNkyhIaGIiQkBADg7OyM\nZs2a4eDBgxg2bBj8/PyQm5uLbdu24dq1a/juu+/wxhtvaPU9MWE1QoY4gpG3GYmoJBVh3ksiIZ0+\nfRqhoaHFHg8LC1P8OyAgAPPmzSuxjAULFqBhw4bYv38/vvnmG1hYWKBZs2bYsGEDWrVqJUrcpWHC\naqQMcQQjV5siolfdSJdCYmkLc1MTIN9w7hoR6VJgYCACAwPVeu5nn32mWG61KHNzc4wZMwZjxowR\nOrwyYcJKRER6qeicr52av4WmlaTo617d4C7Giaj8mLAaIEOYsqo8U1QREQHKgzGrVq6Ed9xs0bae\nra7DIiIdYMJqYAxh8AGnqCIiIXAwJhHJMWE1MIYw+IAr4RinvJyrsLM4jLycAphZNhW03LzcWJhZ\neApaLhk+DsYkIjkmrAbGEKasYquI7gmdBOblXEVW6heoZJmLrNRDsHVcIGi5kEmRIzEXrNxXX4MJ\nseHiYEwiApiwGhxDmLKKrSK6JUYSmJcbC8ikkEhkgExamAAKkbD+f7lAgaDlKsrXQkJMRETiY8Jq\ngAxhyiq2iuiOGEmgmYUnciTmkBVIITExh5mFpyCxysuFTApIhCtXTuyEWPE6bMU1GoYwqJWoImLC\nSqQHhEx4xEgCzSybwtZxAR4mHYZzrW6CJWXycsVK9sROiAG24hoTQxjUSlRRMWEl0jGhEx6xkkAz\ny6bIzDWBmWVjQcorWq5YCZ7YCTGgvVZcEp8hDGolqqiYsJJaOK+qeES5hS9iEmhoxD4W2mjFJfFx\nRS0i/caEVQ/pWx8qzquqmlC38ZnwGDZttOLKsa+sOLiiFpH+Y8KqZ/SxDxXnVS1OyNv42kx4SBza\naNFmX1nxcEUtIv1nousASJmqPlS6VjivamFl4byqhVTdxi8PM8umsKoUxASESiR0naP/8BxHpP/Y\nwqpn9HFhAM6rWhxv45O2sc6Jh+c4Iv3HhFXP6OvCAJxXVRlv45O2sc6Ji+c4Iv3GhFUPGcLCAIZO\niMErHIlP2qbNOscBXkSkT5iwUoXDwStEpeN3hIj0DQddUYXDwStEpeN3RDwn76RhbvRNnLyTputQ\niAwKW1gruIq4IAAHrxCVjt8RcejjtIVEhoIJqw7peoGAirogAAevEJWO3xFxbL+SjJy8AhRw6Vci\njTFh1RF9uNKuyAsCcMAUUen4HRHWjXQprmaYQyIxgURWAHNT/Zi2kMhQMGHVEVULBGg7YS2cLDvr\n/1tYDW+ybI5iJiJDcTU1F1UrV0KnFm/hSfpzDPR8g62rRBowuIQ1PDwcy5YtK3G7hYUFLl++rMWI\nykYfFggw5MmyOYqZyHhUhItPeQNB9SqVULNqJQQ2rarrkIgMisElrHKfffYZGjZsWOxxU1NTHUSj\nOX1ZIMBQJ8tWNYrZWH/oiIxZRbn4NOQGAiJ9YLAJa6tWreDt7a3rMMqFCwSUHUcxExmHinTxaagN\nBET6wGATVqrYOIqZyDjw4pOI1GHwCWteXh7y8vJgZWWl61BIyziKmcjw8eKTiNQhkclkMl0HoQn5\noKv+/fvj0qVLuH79OmQyGZycnODn54exY8fCzs6u2H7nz5+HjY2NDiIu7uXLl0ywRcTjKx4eW3Hx\n+IqHx1ZcPL7iqkjHNzs7Gy1btiz2uMG2sMbExCA4OBgTJkxAcnIyduzYgXXr1uHMmTPYvHkzrK2t\ni+3TuHFjHURaXFxcnFZiMZRVrIQeIayt41sR8diKi8dXPMZ+bHW9EI2xH19dq0jH9/z58yofN7iE\ntWfPnnB3d4eXlxeqVKmieLxPnz749NNPcfz4cWzZsgWDBw/WYZS6ZyirWFWUEcJERGLRh4VoiMRm\nousANPXmm2+iS5cuSskqAJiYmGDIkCEAgGPHjukitFKdvJOGudE3cfJOmlZeT9UqVvpI1QhhIiJS\nX0xCKnJeWYiGyNgYXAtraZycnAAAGRkZOo5E2atXvxG+zhC7Zd9QVrHiCGEi0hZjXaCgfvUqiiVf\nITFB/epVXr8TkYExqIQ1NzcXf/75J/Ly8vD+++8X256QkAAAcHFx0XZopXp1GdYzD19goMivaSiT\nVHOEMBFpg7npbWSlLjfK7kcW1rb/1969x0dR3/sff+9uNkBCuIWLIkIMGIyAaPAWrQoHi4gtKKhc\nqqBYLfahFa217XkcL8WieDznp0dsFSu2RbwgCKhoixYFL2DBCAgIchdigEgIkotJdrPz+yNsTMgG\ndpOZnZnN6/lPy8zu7DfjJPue73y/n6+GnHOGDhQfUbeO7ZTcJtXuJgGmc1Vg9fv9evzxx1VQUKBe\nvXqpf//+tfsqKyv13HPPSZJGjBhhVxMjOnYZ1vNPbjghzApuKVJNeSoAVmvl25awCxT0S0/WSR3T\n1Ll9mqOfqAHN4arA6vF4NG3aNN12222aOHGixo4dq6ysLB08eFCvv/66du3apauvvlrDhg2zu6n1\nHLsMa4fvD9jdJABoUSqrT5cSdPiRW56oAc3hqsAqSRdddJFeeuklzZ49W2+99ZaKi4vVpk0bZWdn\na8qUKbr66qvtbmJEdZdh3byZwAoA8RSozkzo4UdueaIGNJXrAqskDRw4UE899ZTdzUAEiTqpAYD7\nMfwIcC9XBlY4EzVVAQCAFVxXhxXORU1VAEgc8a4fDhxP1IH1X//6l0KhkJVtQRNsLQ5o0fYybS0O\n2N2UmkkMHr8kb8JNakCN6m/LtG/5lyrdc9DupgCwULh++P3/2KKhz64itMJ2UQ8JuOOOO9S1a1eN\nHj1a1157rXr06GFluxAFpy2/Sk1V5yjdc1AlOwuVltlVbXt2Nu2Yle/tUEHIkCfJp6xbhph27PDx\nzW4zEG+JMo4/vHpWqM7qWSz3CjtF3cN6/fXXq7KyUs8++6yGDRumW265Re+++66CwaCV7XM1qx+n\nOHH51aRW/dQ6bYKr/1DHW+meg6b2WpbuOaitsz9QwXtfaOvsD0w7bsnOQqnakAzJCIZq/m0Sq9oM\nxFN4HH/lkb+qrOg3ClZusrtJTVa7epbE6llwhKh7WKdNm6YHHnhAK1as0JIlS7R8+XKtXLlSnTp1\nqu117dWrl5VtdZVjl2NdNiXX9LtTtyy/isaFg5oRrDat17JkZ6GMYHW9YGlGj2VaZlfJ55FCkifJ\nW/Nvk1jV5rrowYXVIo3jd+vNO6tnwWliqhKQlJSkoUOHaujQoSovL9d7772nt956S7Nnz9bzzz+v\n8847T+PGjdOwYcOUlNSyCxAcuxyrFY9TKBbtflYEtbTMrvIk+WQEQ6YGy7Y9O6vVj3srPZRieuiz\nqs1hVtwYAMdKSh6oygRZnIDVs+A0TU6VKSkpGjVqlEaNGqU9e/bot7/9rdasWaM1a9aoS5cumjx5\nsiZNmiSPx2Nme13j2OVYB/dOt+RzKBZtD7N666wIam17dlbWLUMs6U30dUnVydnZph0vzMo2S/Hp\nwQUSaRw/HSJwmmZ1g37++edauHCh3n33XR05ckRt2rTRlVdeqS1btmjGjBlaunSpZs2apXbt2pnV\nXtc4djlWtw5WT5QJBGYys7fOqqDWtmdn1wUyK9tsdQ9uXQw9aNkSaXECOkTgJDEH1uLiYr3xxhua\nP3++du7cKcMwdPrpp+uuu+7SqFGj1LZtW0nSvHnz9PDDD+uRRx7RjBkzTG+4G9RdjtWNWAggMrN7\n69wYLt3G6h7cMIYeAIA1og6sK1eu1Pz587Vs2TIFAgH5/X5dddVVGj9+vAYNGtTg9WPHjtW2bdu0\nePFiUxuM+EmkCQRmimdvHcwTjxsDhh4AgDWiDqyTJ0+WJJ166qkaO3asxowZo44dOx73PTk5OXr5\n5Zeb10LYJpEmEISZ8bg2Xr11cB9uZoDIVu0+5PohcrBX1IF16NChGj9+vH70ox9FffALLrhAc+fO\nbVLDYL9EmkAgmT/2lKCKY8X7Zobxsi2LW+cUxKPMIxJf1IH1T3/6U8wHT09PV3q6NbPjER+JNIGA\nx7WIh3jdzDBetmVx85yCumUeK4MhLdhYSGBFzKJe6Qr22Voc0KLtZdpaHLC7Ka4Wflwrj4fHtXC9\nSDdgSFyR5hS4xeDe6fL7albN8ni82lTi5/sMMWvZ1f1dYGtxQA9/Wnx0Nasy3X9hR8qMNBFjT5FI\nGC/bsrh5TkFuRic9+NNz9Mr6A+rcsZ06tkvTpqIqvssQEwKrBcwcXL6pqErBkBSSFAypxf+SN3fM\nHmNPkSi4AWtZ3D6nYHS/LtpUksRS4mgyAqvJzB5c3i89WUneMn7JxZg94FjcgLUsbp5TwMpZaC4C\nq8nqDi6vCoa0fEdRswIrv+Q/YNIUYC+qEqA5WDkLzUFgNdng3ulKTvLW9rAO7t38Kglm/5K7tTQK\nY/YA+/CEA4CdCKwmy83opGVTch1bINnNpVEYswfYhycccAIWIGi5CKwWyM3o5NhfJLcvt8qYPcAe\nPOFITG564sYCBC0bgbWFcUJpFMbBAe7DE47E47YnbmbPEYG7EFhbGLtLozAODnAvnnAkFrc9cas7\nR8Tn8yqza3u7m4Q4YqWrFiipVT+1Tptgyx8mVucBEI3SPQe1b/mXKt1z0O6mJKyk5IGSxy/J64rF\nCHIzOumvPztPAzJ76NKBZ2hJvlgxqwWhhxVxxTg4ACfCk5j4sPuJW1Mkt0nVGb1OYTGdFojAirhi\nHByAE6EiQfy4bTECFtNpuQisDrO1OJDwiwQwDg7A8fAkBo1hMZ2Wi8DqIFuLA3r40+Kjd45luv/C\njvwyAmhxeBKD42HFrJaJwGqBphY23lRUpWBIrhibQ2kqAFbiSYz7OL2mK4sOuBuB1WTNKWzslrE5\nTIgAANTl9+1UWdGfHFvTlUUH3I+yViaLVNg4WuGxOdf3TW3ycIBg5SZVlLysYOWmmN8bLUpTAXA7\nymaZq5VvW4Oark7SnO9mOAM9rCarW9g4Ocmrwb3TY3p/c8bmxGvVEiZEAHAznhKZr7L69Jqarjau\nong8db+b/T6vPK1StbU44Nhhd2iIwGqy3IxOWjYl15ZxMvFatYQJEQDcjLJZ5gtUZzq6pmv4u3nB\nxkJtKvFr/XdJ2vRpMZObXYTAaoHcjE62jI1JSh6oyjjd4TIhAoBb8ZTIGk6v6Zqb0Un7g61U8FWZ\nKyY3oz4CawJx46olABBvPCVqudwyuRkNEVgTjNPvcAHACXhK1DKx8IB7EVgBADAZtaqbzup6rrFO\nbqZ+qzMQWMEf1mYq375K5ZuXKyV7sFL65Dr2mFYeF8APqELQdPGqdhMt6rc6B4G1hWupf1jNCm7l\n21fp68eGyghWyZOUrF6/XdbsIGjFMa08LoD6qELQdPGqdhOtSPVbCaz2YOGAFq4lLgIQDm6FC+/X\n148NVfn2VU0/1ublMoJVUqhaRrBK5ZuXN799FhzTyuPW+4ztq3TwrUebdU4BtwtXIZDHQxWCGCUl\nD6yp5yqvI+q5huu3+jxScpJXmV3ba9H2Mm0tDtjarpaIHtYWzm3lXczoGY0U3Jp6rJTswfIkJdf2\nWqZkD27Scaw+ppXHDaMHF6hBFYKmc1q1m7q11TO7tteSfCkYKlOSt4warnFGYHWArcUB22YsuukP\nq1mByMzgltInV71+u8zUcaFWHNPK44aZeSNw3M9hHC5cwIoqBC1lvoHTqt2Ea6sv2l6mYIgarnYh\nsNpsa3FAD39afLQmnD13bG4p72JWIDI7uKX0yTU9OFlxTCuPK1nfgyvRi4uWq6XON3ASarjai8Bq\nkWjLYGwqqlIwpKju2Kwu9eF0ZveMEnTMZXUPrhS/Xtzaz6M3Fw7BRC77xVLDlVJY5iOwWiCWMhjR\n3rE5rdRHUzT3yz8egQjNY/WNQDx6ccPozYWTuG2+gd2s6uCJpoYrpbCsQWC1QCxlMKK9Y3NaqY9Y\nmTb+lJ7RFi2eNy3x7s0FjsdN8w3sZncHD6WwrEFgtUC4DEb47mpw7/Tjvj6aO7ak5IGq9PhrQqsD\nSn3Eii9/mCVeNy3x7M2Vam7qjFWvqdx/Pb8biMjs+QaJOonL7g6euhnA7/PK0ypVW4sDTNBqJgKr\nBeqWwTBr/IrTSn3EKt5f/kBzxbU39+gTCAUq9fWqWQw/gOUSeRKX3R084QywYGOhNpX4tf67JG36\ntJgyWM1EYLVIuAyGmaIp9eHUO2bGn8KN4tWbW/sEwgjxBAJxkciTuJzQwZOb0Un7g61U8BVlsMxC\nYE0gVt8xmzFpii9hoKHaJxCB+A0/4OaxZUv0SVxOqOVKGSxzEVgTiJV3zMyYBqwTfgKx+8PX1OtS\na8ew8rsMiUlcjTGzukC0k6opgRUdAmsCsfKOmUlTgLVS+uTKE+iglD7Zln4Ov8sIM2sSV+megwps\nOKDS1C6uDr5WVBc40aRqSmBFz2t3A2Ce8B1z9x8PMH04QPiRpbw+Jk0BLhbP3+Xy7at08K1HVb59\nlWWfAXuFh6IF1u3X1tkfqHTPQbub1GSRqgtYLVIJLERGD2uCsWqZVSZNAYkhXr/LDD1oGWqHosn9\nk7fsqC5wbBnMzK7ttWh72QlX0mqJCKyIGpOmgMQQj99lhh60DD8MRat2/eQtO6oL1C2Dmdm1vZbk\nS8FQmZK8ZZTBOgaBFQBgunjVXqbigb3CQ9F2frpRmRf2b1LvqpPKMdpRXSBcBnPR9jIFQ5TBagyB\ntYXhjzuAeIjH0AOGHThD256d5S/r1uSw6vYFDMyqLHC8MljrDnyvxQXbWnQlAQKrTbYWB05Y6sJs\n/HEHEE9WDz2wctgBN/fx4fYFDMysLNBYGaxVuw9p8jsFCoSMFl1JgMBqsUj11fZWJOnFT4uP3kX9\nME7FzPpvkTCmDEAisWrYATf38eP2BQwiVRZozvd3pDJYy3cUqSpkKFSnkgCBFaZqrL7a7u+TFAyp\n3jiVzJStptd/O1a8xpQBQDxYNezAqpt7em0bau4CBnaPf41HZYHBvdOV7PXU9rAO7p1u+me4AYHV\nQpHqq+VmdFJGm6CSvlO9cSpm36VFQmkqAInGimEHVtzc02vbuKaWY3TC+Nd4VBbIzeikF0Z01+7q\ntNqntXYMK7QbgdVCx9ZXC98Vndo62GCcSrAy8l2a2XePlKYCgOOz4ubeil7blt5j65Txr/GoLHB2\ntzYan326pJo5MA8fM6yw6LuShF/elcBqobr11Y69iI4dpxLpLs0Jd4/xsKpwt5bv36HBJ/VWbteM\nZh8no8KnbDV/eUuz2gXAfcy+uTe715YeW3eOfzVjrsqmoqp6wwoXbvpW05asTfjlXQmsFgvXV4vG\nsXdpTrl7PJ7mhrpVhbs19J+zVBUKKtmbpGXDf9Hs4/g9XmVkZDQ7/JrRrkjHJQQDLY/ZvbZm9di6\nuZe2qeNf7Rr3alZFgWPLX317+EjE4YeJhsDqYE6/ezQj1C3fv0NVoaCqDUNVoaCW79/RpCBX9zgy\nQk0+jtntqsuqEFz3+FaH4XUlB7T4iwICN9AEZvbamtFjmwi9tLGOf7XzyaVZc1WOLX9V9F2Snvl4\nR4Phh4mGwOpgke4ezb4bbk7IMSPUDT6pt5K9SbUhbvBJvWN6f6Tj+D3eJh/H7HbVZUUIDrM6DIc/\nY/LmfyhghCz7jPDn0AsNHJ8ZPbZm9NKGv5OMNhlSdvOHYlnNzieXZlYUqDessGPD4YfhSVlV35dp\nZ+F3CTG2lcDqcHXvHs2+G25uyDEj1OV2zdCy4b9odkCpe5yMCl+zg45Z7arLihAcZmUYrv8ZIYVk\n3WfEI3jX/SyCMdysuT22ze2lrfudJK9f5RkZju+hjfXJpZnDB6ysKFB3+GF4Utb+4hJ9sHaLDCOk\nVgkwtpXA6iJmzzJtbsgxM2yaERjCx9m8eXOzj1X3eGaxIgSHWRmG63+Gt7aH1YrPiEfwlhIzGBPA\nEavm9tLW/U6SoZi+k+waOxvLuFcrhg9EW1GgOZOzwpOyDhQfUXUoJCkxxrYSWF3E7FmmZvWQ8uUY\nPavOl5VhuO5nvJB9pXa3rrbsM+IRvKXEC8bx/BxCcWJpTi9t3e8kef1Rfyc15WmhmQE32nGv0Q4f\nMHsSV6TJWZI36veHJ2V169hOX3q9kpEYY1sJrC5S9254Z7e++r/ycg0u3G3KY3S+gNwvHjcPZ6d1\n03gLx6nF65pMtGAcj88hFONYdb+TCttEPxwg1qeFsQZcs8JtNMMHrOiFjTQ5Szon6vf/MCkrVT8f\nkNZgDGukJePdgMDqMil9crW+3cmmfXHQQwqnicc1mWjBOB6fkwih2Iow3NIDdriH9tsYhmLF+rQw\nloAbbbiNJtRGM3wgml7YWHtgzZic9cOkrFRJPwTteRsKNXHuGgWr3Teu1ZWBNRgMas6cOVq8eLF2\n794tn8+nvn37auLEiRoxYoTdzbNcvHptgESWSME4Hp/j9lC8ruSAblmz1NQwbEXANnshFScG6VjH\nzsYScKMJtycKtXXDbNs+ubUVeg6+9ZcG7T1RL2xTemAjT86qf0PQlDGuW4sDmvHRN6oK/jCudc5n\n+a7pbXVlYL3nnnu0dOlSDR06VDfddJMCgYAWLVqku+++W/v27dMtt9xidxMtFa9eGwDNF6+nGFZ/\njttD8eoj+00Pw2YHbCsWUmnqcZoaeKN9XyxjZ2MJuNGE2+OF2khhVlLEbeH2ZN0yRIfWfCZf5Zfy\nVm2T9EMgPV4P7PF6XpNa9dPXJRn633d3aG7eP1RaGVTbVrt1w6BT9NtLAuoQvD/mBQg2FVWpc4d2\n8nm9CoVC8ng9+uuavQpWu2OFLNcF1n/9619aunSprrzySj355JO126+55hqNGTNGTzzxhK644gr1\n6NHDxlZai7GnAOzg5lB8fruTTA/DZgdsKxZSacpxmhp4m/O+E/03DwfcVYW7tfyLZY2+NqVPrkpu\nnas9699Wz4FXNQi3qwp3a72/rS7x+eWRGoTaSGFWUr1t3308R4c/+XttgO32sydV9s+pNfuW+dTh\nksnq8KOJkqSqzYslnaWaSVPVKl/z/1Sw26/krLHas/TbBj2v4RC70Zukq9/ZrkB1SIGQIUkqqQzq\n+U/3KC20Rr/PDcjjiW0Bgn7pyTqpY5qGnHOGDh4+ojPaS/PX5qvakCoCId339hb991VnODa0ui6w\nLliwQJJ0880319uenJysCRMm6KGHHtLixYt1xx132NG8uGHsKYBEZNXftrPTupkehs0O2FYspNKU\n4zQ18DblfbGE3Gheu6pwt4ZuWaMqfyclb1mjZRk5ta+p+/5BA6/TM11O0hnnXvNDEN6/Q0O79VXa\n0R5aw+fXAn9b5XQ6pd62z4vylRGolMcIqTpQqb2fzFXS0X8boWoVfzBLRR/OloyQvKFqJSefrlDy\nmfJWfamK/G2qkBRYs0+hdtfJ4/HJCARUsOA5dbrwotoQmxqSfhVK0ttGkjbIV/vzBUKGPvi6u+4+\nz6vWfskTwxjXupOx+qX3VNF3JVr8RYGqgyEZkj7eWaTBf16p5b+8yJGh1XWBdd26dfL7/erfv3+D\nfTk5OZKktWvXxrtZUfvfhfP0YYF06eYv9OvRY+1uDgC0GFaEYTOPacVCKk05TlMDb1PeF0vIjea1\nx3tN3X15ad209MwrlHM0rIaD7MPeJC2/da6Sdn6q27/dr7z9e5RcWFBvWyBUrec9XiUZhgIerx73\ntNF9Hq/8RkheSR4ZUnWgpgdXkq9qm7xV2+Sp005f1ZeqNoI1/zCCqtz8N32zK09Gu+skQ0qWNNoX\n1E98Qd0eaK0Nxg+hdc2+7hq9cIymXlSq0edcoRc+T9X/ffSBDpVXqVWSTx3bJKmy2lArn0eV1Ya6\npCarU0pyxHN6Wuc0bfu2RMHqo+Naqw3N+SyfwNpcpaWlKi4u1imnnCKfz9dgf/fu3SVJe/fujXfT\novK/C+fpt6tSVR0y9PbXHknzCK0AgFpmL6TS1Pc2JfA25X2xhNxoXnu81zS279iQu6x1e+nMK5T3\n+T8b3XbLwOt03uG9Wt3hVH3Rvru+SknXT/dv0jX7N8lnhFTt8cpjGPIrVPv5Rp12+qq2Kbloem3P\nq69qW83+dmNULa+8krweKcmQBnmrtaG6fuZZ9c3J2vRWkg4bqfrFgg319n1dXP+cxLqUzuHKai3a\nXqZ+6ck/LP/qAK4KrGVlZZKklJSUiPvbtGkjqSbYRmLWCkhN9WGBVH10LEooZOjDAmmEzW1KRBUV\nFbb/t05UnFtrcX6tw7mNTQdJV/u7S0Xfa3PRic9b+PzG+r4OkmafcYVWH9mv89udpA7HeV80rz3e\naxrbl1Hhk99TU2Df7/Eqo6ImHB5v25cdeujLDj1UbRjyezz6skMPfdG+u948qZ/OPxpkPZJ+un+T\nPJK+TOum7JIDyiwrUs6Rb+ST5D3a8yrVhNnqwE79+7R87d16mn7qq5bPkIKS8kINO+gkqaQiqJkf\n7TzhOY6F1yMVedM076tS+TzSpJOP6NTWQVM/o6lcFVg9Hs9x9xuGcdzXZVtY8Dwal27+Qm9/7VEo\nZMjr9ejS7va3KRFt3ryZ82oRzq21OL/W4dxaqznnN1vZGm/ia4/3mkj7spWtjIyMBj3DJ9omqcH/\nT2+VoqLKcp179H/D//5xqxStLfpGG74v0effblefze+r3aG96hj8Xof9bbQjJV3vdB+gmSOv1++e\n3Ky3qyo1yFutvJCv3nCAutJaJ6l3j5O08cCOE5+4KPg80q2X9NXhpHYKSao2pDVVnZWR0TauPa15\neXkRt7sqsLZt21aSVF5eHnF/uAc2/DqnqXn8f3QMa3cxHAAAAAeINIQimm2N/f9orCrcrf/e8IG+\n+u5b9W3fRTNKHVGZAAAVdUlEQVQHDFFu1wzdMOiInv90T4NhAHX5vR7dOOgUXX3uacovrdbWvftV\nFQjK5/XKn+RTyDDk9XgUMgy18vuV7G8Y9zySOrSq6eBr2zpZg/uepMtP76y/bypRIFTT6/vFwYA2\nFRVrcv80Xd6zTUw/n9lcFVhTUlLUpUsXFRYWKhgMKimpfvPz8/MlSZmZmXY0Lyq/Hj1WI7jTBwCg\nRcvtmqFFQ29usP3Xl/XW39fkKxCqbvS9fp9Xd1/aW707t9GM4X00/6uTdLjKaPT10dhVIb2wsURZ\nHZJ0oLxahyprjldt1GzvmZZk65hWr22f3EQ5OTkKBAJav359g32rV6+WJF1wwQXxbhYAAECz9e6c\nqgWTBinF75PfW3+Io9/rUYrfpwWTBql351RJ0uU922jWj7vo1gFpOqWtT51be9UrzadTUn3qldZ4\nL20k1Ya0uThYG1brbt9UVNW8H6yZXNXDKknjxo3T0qVLNXv2bA0aNKh2e1lZmebOnavU1FSNHDnS\nxhYCAAA03ZXZ3fTFvZfpiQ936MW8b1RSEVRa6yTdOOiUoz2rqQ3ec3nPNhEf228tDujNHWUqKK1W\nWrJHbZNr+irXFlapOspOWZ+nZuEBO7kusF500UW67rrrNH/+fN12220aPny4Kisr9eqrr6qgoEAz\nZsxQp07Oqx8GAAAQrd6dU/X06LP09OizmjWpLaujX/ee26HB9q3FAa3I/16HK38ovRUpxPo80uT+\nabaXuHJdYJWkhx9+WGeeeabmz5+vhx56SH6/XwMGDNDs2bN18cUX2908AAAAR8vq6G8QQsMhVpJO\na+9XSVXIMfVYXRlYPR6PJkyYoAkTJtjdFAAAgIQQKcQ6hesmXQEAAKBlIbACAADA0QisAAAAcDQC\nKwAAAByNwAoAAABHI7ACAADA0QisAAAAcDQCKwAAAByNwAoAAABHI7ACAADA0QisAAAAcDQCKwAA\nAByNwAoAAABHI7ACAADA0QisAAAAcDQCKwAAAByNwAoAAABHI7ACAADA0QisAAAAcDQCKwAAAByN\nwAoAAABHI7ACAADA0QisAAAAcDQCKwAAAByNwAoAAABHI7ACAADA0QisAAAAcDQCKwAAAByNwAoA\nAABHI7ACAADA0QisAAAAcDQCKwAAAByNwAoAAABHI7ACAADA0QisAAAAcDQCKwAAAByNwAoAAABH\nI7ACAADA0QisAAAAcDQCKwAAAByNwAoAAABHI7ACAADA0QisAAAAcDQCKwAAAByNwAoAAABHI7AC\nAADA0QisAAAAcDQCKwAAAByNwAoAAABHI7ACAADA0QisAAAAcDQCKwAAAByNwAoAAABHI7ACAADA\n0QisAAAAcDQCKwAAAByNwAoAAABHI7ACAADA0QisAAAAcDQCKwAAAByNwAoAAABHI7ACAADA0Qis\nAAAAcDQCKwAAAByNwAoAAABHI7ACAADA0QisAAAAcDQCKwAAAByNwAoAAABHI7ACAADA0QisAAAA\ncDQCKwAAAByNwAoAAABHS7K7AdH697//rYkTJx73NfPmzdPZZ58dpxYBAAAgHlwTWMOGDx+uK6+8\nMuK+jIyM+DYGAAAAlnNdYO3Tp4+GDx9udzMAAAAQJ4xhBQAAgKO5NrCGQiGVl5fb3QwAAABYzGMY\nhmF3I6IRnnQ1ZMgQVVRUKC8vT1VVVUpJSdEll1yiu+++W6eddlqj78/Ly1NKSkocW9y4iooKtW7d\n2u5mJCzOr3U4t9bi/FqHc2stzq+1WtL5LS8v16BBgxpst3UM67PPPqtAIHDC111zzTW1/3/VqlW6\n/vrrdeONN6qiokLLly/Xm2++qZUrV2revHnq3bt3o8fJzs42pd3NtXnzZse0JRFxfq3DubUW59c6\nnFtrcX6t1ZLOb15eXsTttgbWWbNmRfVY//zzz1dWVpaeffZZZWZmqlevXrX7rrrqKmVmZurJJ5/U\n448/rmeffdbKJgMAACDObA2sa9eujen1Q4YMibh98uTJmjlzpj755BMZhiGPx2NG8wAAAOAArp10\nVVerVq2UlpamqqoqVVZW2t0cAAAAmMg1gXXVqlV6+eWXVVVV1WDfoUOHdPjwYaWnp7eYQckAAAAt\nhWsWDnjzzTe1cOFCBQIBTZo0qd6+p556SpI0YsQIO5oGAAAAC7kmsE6dOlUrV67UjBkztHHjRp13\n3nkKBAJ6//339fHHHysrK0u/+tWv7G4mAAAATOaawNqtWze99tprmjVrlj788EP94x//kM/nU0ZG\nhu666y7ddNNNjqmzCgAAAPO4JrBKNaH1gQcesLsZAAAAiCPXTLoCAABAy0RgBQAAgKMRWAEAAOBo\nBFYAAAA4GoEVAAAAjkZgBQAAgKMRWAEAAOBoBFYAAAA4GoEVAAAAjkZgBQAAgKMRWAEAAOBoBFYA\nAAA4GoEVAAAAjkZgBQAAgKMRWAEAAOBoBFYAAAA4GoEVAAAAjkZgBQAAgKMRWAEAAOBoBFYAAAA4\nGoEVAAAAjkZgBQAAgKMRWAEAAOBoBFYAAAA4GoEVAAAAjkZgBQAAgKMRWAEAAOBoBFYAAAA4GoEV\nAAAAjkZgBQAAgKMRWAEAAOBoBFYAAAA4GoEVAAAAjkZgBQAAgKMRWAEAAOBoBFYAAAA4GoEVAAAA\njkZgBQAAgKMRWAEAAOBoBFYAAAA4GoEVAAAAjkZgBQAAgKMRWAEAAOBoBFYAAAA4GoEVAAAAjkZg\nBQAAgKMRWAEAAOBoBFYAAAA4GoEVAAAAjkZgBQAAgKMRWAEAAOBoBFYAAAA4GoEVAAAAjkZgBQAA\ngKMRWAEAAOBoBFYAAAA4GoEVAAAAjuYxDMOwuxHxkJeXZ3cTAAAAcAKDBg1qsK3FBFYAAAC4E0MC\nAAAA4GgEVgAAADgagRUAAACORmAFAACAoyXZ3YCWIhgMas6cOVq8eLF2794tn8+nvn37auLEiRox\nYoTdzXO1mTNn6umnn250f3JysjZs2BDHFrnbwoULNX36dJWWlmrZsmXq0aNHg9fk5+frT3/6kz75\n5BMdOnRIHTp00IUXXqg777xTvXr1sqHV7nGi8/sf//Ef+uabbxp9/9ixYzVt2jSrm+kqpaWlev75\n5/XOO++ooKBAfr9fmZmZuuaaazR+/Hj5fL56r+f6jV4s55Zrt2kOHjyoF198Ue+//77y8/NlGIYy\nMjI0fPhw3XzzzWrVqlXtaw8dOqQ///nP+uCDD3TgwAGlpqZq0KBB+uUvf6n+/fvb+FNYj8AaJ/fc\nc4+WLl2qoUOH6qabblIgENCiRYt09913a9++fbrlllvsbqLr3XnnnerTp0+D7cd+WSGyoqIiPfDA\nA1q2bJnatGnT6Ov27t2rsWPH6vvvv9fEiRPVp08f7d27V3/729/00Ucf6ZVXXlFmZmYcW+4O0Z5f\nSerUqZMefPDBiPt69uxpRfNcq7CwUOPGjdP+/fs1cuRI/eIXv1BZWZkWLFighx9+WJs2bdKjjz5a\n+3qu3+jFem4lrt1Y7du3Tz/72c9UWFioa6+9VpMnT1ZZWZmWLFmiJ554Qh9//LHmzJkjr9erI0eO\naNy4cSooKNC4ceN01lln6eDBg5ozZ44mTJigF154Qeeee67dP5J1DFjuvffeM7Kysoy77rqr3vbK\nykrjJz/5idGvXz9j7969NrXO/Z566ikjKyvL+PTTT+1uiqsNHjzYuPjii40PP/zQuOGGG4ysrKyI\n1+Xtt99uZGVlGcuXL6+3PS8vz8jKyjJuvvnmeDXZVaI9v0OGDDGGDBliQwvd6Xe/+52RlZVlvPDC\nC/W2l5WVGUOGDDGysrKMHTt21G7n+o1erOeWazd2U6dONbKysoxFixbV2x4IBIyRI0caWVlZxooV\nKwzDMIw//vGPRlZWlvHSSy/Ve+2ePXuMAQMGGMOGDTNCoVDc2h5vjGGNgwULFkiSbr755nrbk5OT\nNWHCBAUCAS1evNiOpgG1zj77bL355pu65JJLGn1NUVGRli9frszMTF122WX19uXk5GjgwIFauXLl\ncR8LtlTRnF/Erlu3brriiit03XXX1duekpKiCy64QJK0ZcsWSVy/sYrl3KJpLrnkEt1555266qqr\n6m1PSkrSRRddJKmmFzYYDOqNN95Q27ZtG/z3OPXUUzV06FDt3r1bn332WdzaHm8MCYiDdevWye/3\nRxxfkpOTI0lau3ZtvJuVsILBoILBoFq3bm13U1zliSeeOOFrNmzYoOrqap1zzjkR9+fk5Gj9+vVa\nt26dTjnlFLOb6GrRnN9IKioq5Pf7GdrSiKlTpza6r7S0VJLUtm1bSVy/sYrl3EbCtXtio0ePbnTf\njh07JEnZ2dnatWuXvvvuO1144YXy+/0NXpuTk6N33nlHa9eu1XnnnWdZe+1ED6vFSktLVVxcrK5d\nu0b8pe3evbukmnFVaJ4lS5Zo1KhR6t+/vwYOHKgf/ehHeuSRR2r/sKL5wtdp+Lo91sknnyxJ2rNn\nT9zalIgqKir0hz/8Qbm5uRo4cKD69eun0aNHa8mSJXY3zTX27NmjFStWqHv37rW9gVy/5oh0bsO4\ndpuuvLxchw4d0hdffKH77rtPK1as0OTJk3XWWWdx7YoeVsuVlZVJqnmEEkl48gWhqvmWL1+uG2+8\nUffcc48KCwv1+uuv6+9//7tWr16tV1555YQTXXBi4eu5sXMZvs65npunqKhIu3bt0n333aeOHTtq\ny5YteuGFF/TrX/9a+fn5mjJlit1NdLRvv/1WU6ZMUTAY1EMPPVQ7y5rrt/kaO7dhXLtNd++992rZ\nsmWSah7zz5w5U8OGDZPEtSsRWC3n8XiOu98wjKheh8b95Cc/Uf/+/ZWTk6P27dvXbh8zZoxuvfVW\nffzxx3r11VcbjCFG7LierTd9+nR5PB5deOGFtdsGDx6s4cOHa9SoUXr66ac1evRode3a1cZWOteW\nLVs0ZcoUFRYW6o9//GO9sapcv81zvHMrce0219SpU3XDDTdo//79+uc//6k777xTY8aM0bRp07h2\nxZAAy4XH95SXl0fcH75rOt44IBzfaaedpiFDhtQLq5Lk9Xo1efJkSdJHH31kR9MSTrTXc1paWtza\nlGhyc3PrfeGHZWRk6PLLL1cgENC///1vG1rmfEuXLtX48eNVUlKiZ555psH4QK7fpjvRuZW4dpsr\nKytLF110kUaPHq3nnntON9xwg15//XXNnTuXa1cEVsulpKSoS5cuKiwsVDAYbLA/Pz9fkqj7Z5Eu\nXbpIkkpKSmxuSWII11EsKCiIuJ/r2Vrhnimu54bmzJmju+66S127dtX8+fMb9P5JXL9NFc25PRGu\n3diNGzdOUs1wt/C121gFi5Zw7RJY4yAnJ0eBQEDr169vsG/16tWS1GDgOqJTVVWlpUuX6u233464\nPzzLkhm/5jjrrLPk9/uVl5cXcf/q1auVlJRUW/0CsdmzZ48WLVqkL7/8MuJ+rufI5s2bp+nTp2vQ\noEF67bXXGv3S5vqNXbTnlms3duXl5frxj3+s4cOHR9z/3XffSZKqq6uVkZGhzp07a+PGjaqqqmrw\n2nCWOP/8861rsM0IrHEQvkuaPXt2ve1lZWWaO3euUlNTNXLkSDua5np+v1+PP/64fvOb32jjxo31\n9lVWVuq5556TJJa/NUn79u01fPhwff3113rvvffq7fvggw+0detWDRs2TOnp6Ta10N3279+v3/3u\nd3rggQcUCATq7Vu7dq0++ugjpaenc4Nbx/r16zVt2jQNGDBAf/nLXxoMDaqL6zc2sZxbrt3YpaSk\nqHPnztq1a1fETpfXX39dknTuuefK6/Xq2muvVXl5uV5++eV6r9uyZYs+/PBDDRw4UGeeeWZc2m4H\njxEeqQtL/dd//Vfto5Thw4ersrJSr776qr766ivNmDFDV199td1NdK2VK1fqtttuU3JyssaOHaus\nrCwdPHhQr7/+unbt2qWrr75ajz32mN3NdLRvvvlGGzZsqP33zJkztX37dj344IPq1KmTpJqekQED\nBqiwsFDXX3+9iouLNWnSJJ1++unauXOn/va3v6l9+/aaN2+eunXrZteP4kixnN/f//73Wrhwoc44\n4wyNGjVKHTt21ObNm/Xqq6/KMAw9/fTTTXokm6iuvfZabdiwQb/61a/Uu3fviK8Jn1tJXL8xiPXc\ncu3GbtOmTZo4caIqKio0ZswYnXXWWaqsrNT777+vjz/+WL169dJrr72mDh06qLy8XOPHj9e2bds0\nbtw4nXPOOdq3b5/++te/KhgMau7cuerbt6/dP5JlCKxxYhiGXnnlFc2fP187duyQ3+/XgAEDdOut\nt+riiy+2u3mut379es2ePVuff/65iouL1aZNG2VnZ2vMmDHcDERh4cKF+v3vf3/c11xzzTWaMWOG\npJov/aefflorVqxQUVGR0tPTddlll+mOO+5gBnAEsZzf6upqzZs3T2+88Ya2bt2qQCBQ2zP185//\nXFlZWXFqtTtE8wVd99qVuH6jFeu55dptmvz8fD333HP65JNPdODAAXm9XvXo0UNDhw7Vz3/+83o9\n26WlpXrmmWe0dOlS7d+/X+3atVNubq7uuOMOnXbaaTb+FNYjsAIAAMDRGMMKAAAARyOwAgAAwNEI\nrAAAAHA0AisAAAAcjcAKAAAARyOwAgAAwNEIrAAAAHA0AisAAAAcjcAKAAAARyOwAgAAwNEIrAAA\nAHA0AisAuMBnn32m7OxsjR07VqFQqN6+d955R3379tXtt99uU+sAwFoEVgBwgXPPPVe33nqr1q1b\npxdffLF2++HDhzV9+nR16dJF06dPt7GFAGAdAisAuMSdd96pfv366cknn1R+fr4k6bHHHtPBgwf1\nyCOPqFOnTja3EACsQWAFAJfw+/36n//5HxmGoQcffFCffPKJFi5cqBtvvFGXXnqp3c0DAMt4DMMw\n7G4EACB6L7/8sv7whz8oNTVVJ598shYuXKhWrVrZ3SwAsAw9rADgMiNHjlRKSorKysr005/+lLAK\nIOERWAHAZaZPn66Kigr16dNHs2bN0u7du+1uEgBYisAKAC7y7rvvauHChZo0aZKeeeYZGYahe++9\nV8Fg0O6mAYBlCKwA4BKFhYW6//77lZGRoalTp6pnz566++67tWHDBs2cOdPu5gGAZQisAOAS//mf\n/6kjR47o0UcfVevWrSVJN954o3JycvSXv/xFeXl5NrcQAKxBYAUAF3jppZf00UcfadKkScrJyand\n7vV69cgjj8jv9+s3v/mNSktLbWwlAFiDslYAAABwNHpYAQAA4GgEVgAAADgagRUAAACORmAFAACA\noxFYAQAA4GgEVgAAADgagRUAAACORmAFAACAoxFYAQAA4Gj/H3I6Kmq/xbuBAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6eN_Zk53U4Fg",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mIf8R-btbF3u",
        "colab_type": "text"
      },
      "source": [
        "[【Unite Tokyo 2018】誘導ミサイル完全マスター](https://www.youtube.com/watch?v=t_4MbV2zIwg)版\n",
        "\n",
        "この講座では弾の着弾時刻をあらかじめ決めて，加速度が一定の時に目標時刻に着弾するように加速度(力)を調整しています．\n",
        "\n",
        "講座の中でも語られていますが， 次式は残り時間$t_r$の時に加速度一定($a(t)$ = const)で距離$x$を移動することを表しています．\n",
        "\n",
        "\\begin{align}\n",
        "x &= \\frac{1}{2}a(t) t_r^2 + v(t)t_r\n",
        "\\end{align}\n",
        "\n",
        "これを加速度$a(t)$について解くと，\n",
        "\n",
        "\\begin{align}\n",
        "a(t) &= \\frac{2}{t_r^2}x(t) + \\frac{-2}{t_r}v(t)\n",
        "\\end{align}\n",
        "\n",
        "となります．\n",
        "\n",
        "実際には相手が移動することによって$x$が想定通りに減っていかないので，加速度を更新することになり，加速度は一定になりません．もし，相手が動かない場合は加速度は一定となります．また，位置ベクトルの各成分は放物線を描きます．"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YZTEypW8c_EZ",
        "colab_type": "code",
        "outputId": "b94c59d8-cb9c-43b0-a200-4efd9202b489",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 860
        }
      },
      "source": [
        "mass = 1.0 \n",
        "target = np.array([30.0,0.0]) # target location\n",
        "delta_t = 0.1 # time step\n",
        "\n",
        "k_p0 = 0.0025\n",
        "k_d0 = 0.01\n",
        "acc_max = 100.0\n",
        "\n",
        "plt.plot(target[0],target[1],'o',markersize=10) # Plot Target\n",
        "\n",
        "time_target = 5.0\n",
        "v0 = 10 # magnitude of initial velocity\n",
        "\n",
        "for theta in np.linspace(0.1*np.pi,0.6*np.pi,num=6):\n",
        "  pos = np.array([0.0,0.0])\n",
        "  diff = target - pos\n",
        "  prev_diff = diff\n",
        "  acc = np.array([0.0,0.0])  # (initial) acceleration\n",
        "\n",
        "  time = 0.0\n",
        "  vel = np.array([v0*np.cos(theta),v0*np.sin(theta)]) # (initial) velocity\n",
        "  display(\"theta: {0}, vel: {1}\".format(theta, vel))\n",
        "  df = pd.DataFrame({\"time\":[time],\"x\":[pos[0]],\"y\":[pos[1]]})\n",
        "  # display(diff,np.linalg.norm(diff) )\n",
        "\n",
        "  while True:\n",
        "    time += delta_t\n",
        "    if time > 10:\n",
        "      display(\"timeup\")\n",
        "      break\n",
        "    if np.linalg.norm(diff) < 0.5e-0:\n",
        "      display(\"hit at {0}\".format(time))\n",
        "      break\n",
        "    diff = target - pos\n",
        "    dot_diff = (diff - prev_diff)/delta_t # \\dot{d}\n",
        "    force = k_p * diff + k_d*dot_diff\n",
        "    # print(force)\n",
        "\n",
        "    if time < time_target:\n",
        "      acc = 2*diff/((time_target-time)**2) - 2*vel/(time_target-time)\n",
        "      if np.linalg.norm(acc) > acc_max:\n",
        "        acc = acc/np.linalg.norm(acc)*acc_max\n",
        "    else: \n",
        "      acc = 0\n",
        "    vel += acc*delta_t\n",
        "    pos += vel*delta_t\n",
        "    prev_diff = diff\n",
        "\n",
        "    # save to plot\n",
        "    df2 = pd.DataFrame({\"time\":[time],\"x\":[pos[0]],\"y\":[pos[1]]})\n",
        "    df = df.append(df2)\n",
        "\n",
        "  # Plot Trail\n",
        "  print(\"plot\")\n",
        "  plt.plot(df.x,df.y,'.',label=\"{0:.1f}\".format(theta))\n",
        "\n",
        "plt.xlabel(\"x\")\n",
        "plt.ylabel(\"y\")\n",
        "plt.title(\"v0: {0}, time_target: {1}\".format(v0,time_target))\n",
        "plt.axis('equal')\n",
        "plt.legend()\n",
        "filename = \"ballet03.png\"\n",
        "plt.savefig(filename)\n",
        "files.download(filename) \n",
        "\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'theta: 0.3141592653589793, vel: [9.51056516 3.09016994]'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'hit at 4.999999999999998'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "plot\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'theta: 0.6283185307179586, vel: [8.09016994 5.87785252]'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'hit at 5.099999999999998'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "plot\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'theta: 0.9424777960769379, vel: [5.87785252 8.09016994]'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'hit at 5.099999999999998'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "plot\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'theta: 1.2566370614359172, vel: [3.09016994 9.51056516]'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'hit at 5.099999999999998'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "plot\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'theta: 1.5707963267948966, vel: [6.123234e-16 1.000000e+01]'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'hit at 5.099999999999998'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "plot\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'theta: 1.8849555921538759, vel: [-3.09016994  9.51056516]'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'hit at 5.099999999999998'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "plot\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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q1Cj07dsX69evF/1+vr6+ACoD4dWrV+s5+rp78cUXAVRu0/nf//7X5HPn5eVh4sSJOHPm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\n",
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wH20GkMrmHNm",
        "colab_type": "code",
        "outputId": "9a0cd636-84c0-461e-e7c2-f550b7ee8d7b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 546
        }
      },
      "source": [
        "distance = np.sqrt( df.x**2 + df.y**2)\n",
        "plt.plot(df.time,df.x,label=\"x\")\n",
        "plt.plot(df.time,df.y,label=\"y\")\n",
        "plt.xlabel(\"time\")\n",
        "plt.legend()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f5dd6983390>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 193
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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oaCjS0tJw7NixZ7adOnUKKSkpGDBgACwsLJqenIiIiFrM/eJKTNweg3atjPDv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\nuJKfAXMdfSzx64s323ZBK31joeMRCe7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GE6Q7owkaqZT7tDP+LI1++ojZJ6P5V8NObAt9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\nm0qliIiIiOTb/wH4YFKLIhRdbgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_d2aDlPQoHwV",
        "colab_type": "code",
        "outputId": "566bafa1-58fa-4829-b9a4-486e31cd15af",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 860
        }
      },
      "source": [
        "mass = 1.0 \n",
        "target = np.array([30.0,0.0]) # target location\n",
        "delta_t = 0.1 # time step\n",
        "\n",
        "acc_max = 100.0\n",
        "\n",
        "plt.plot(target[0],target[1],'o',markersize=10) # Plot Target\n",
        "\n",
        "time_target = 5.0\n",
        "time_start = 0.01*time_target\n",
        "time_end = 0.95*time_target\n",
        "v0 = 3 # magnitude of initial velocity\n",
        "\n",
        "for theta in np.linspace(0.1*np.pi,0.6*np.pi,num=6):\n",
        "  pos = np.array([0.0,0.0])\n",
        "  diff = target - pos\n",
        "  prev_diff = diff\n",
        "  acc = np.array([0.0,0.0])  # (initial) acceleration\n",
        "\n",
        "  time = 0.0\n",
        "  vel = np.array([v0*np.cos(theta),v0*np.sin(theta)]) # (initial) velocity\n",
        "  display(\"theta: {0}, vel: {1}\".format(theta, vel))\n",
        "  df = pd.DataFrame({\"time\":[time],\"x\":[pos[0]],\"y\":[pos[1]]})\n",
        "  # display(diff,np.linalg.norm(diff) )\n",
        "\n",
        "  while True:\n",
        "    time += delta_t\n",
        "    if time > time_target*1.2:\n",
        "      display(\"timeup\")\n",
        "      break\n",
        "    if np.linalg.norm(diff) < 0.5e-0:\n",
        "      display(\"hit at {0}\".format(time))\n",
        "      break\n",
        "    diff = target - pos\n",
        "    dot_diff = (diff - prev_diff)/delta_t # \\dot{d}\n",
        "    force = k_p * diff + k_d*dot_diff\n",
        "    # print(force)\n",
        "    acc_max = gain_exp(time,4,8,0.5*time_target)\n",
        "\n",
        "    if (time < time_end) and (time > time_start) :\n",
        "      acc = 2*diff/((time_target-time)**2) - 2*vel/(time_target-time)\n",
        "      if np.linalg.norm(acc) > acc_max:\n",
        "        acc = acc/np.linalg.norm(acc)*acc_max\n",
        "    else: \n",
        "      acc = 0\n",
        "    vel += acc*delta_t\n",
        "    pos += vel*delta_t\n",
        "    prev_diff = diff\n",
        "\n",
        "    # save to plot\n",
        "    df2 = pd.DataFrame({\"time\":[time],\"x\":[pos[0]],\"y\":[pos[1]]})\n",
        "    df = df.append(df2)\n",
        "\n",
        "  # Plot Trail\n",
        "  print(\"plot\")\n",
        "  plt.plot(df.x,df.y,'.',label=\"{0:.1f}\".format(theta))\n",
        "\n",
        "plt.xlabel(\"x\")\n",
        "plt.ylabel(\"y\")\n",
        "plt.title(\"v0: {0}, time_target: {1}, time_start: {2}, time_end: {3}\".format(v0,\n",
        "                                                                          time_target,\n",
        "                                                                          time_start,\n",
        "                                                                          time_end))\n",
        "plt.axis('equal')\n",
        "plt.legend()\n",
        "filename = \"ballet04.png\"\n",
        "plt.savefig(filename)\n",
        "# files.download(filename) \n",
        "\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'theta: 0.3141592653589793, vel: [2.85316955 0.92705098]'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'hit at 5.099999999999998'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "plot\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'theta: 0.6283185307179586, vel: [2.42705098 1.76335576]'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'hit at 5.099999999999998'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "plot\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'theta: 0.9424777960769379, vel: [1.76335576 2.42705098]'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'hit at 5.099999999999998'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "plot\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'theta: 1.2566370614359172, vel: [0.92705098 2.85316955]'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'hit at 5.099999999999998'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "plot\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'theta: 1.5707963267948966, vel: [1.8369702e-16 3.0000000e+00]'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'hit at 5.099999999999998'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "plot\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'theta: 1.8849555921538759, vel: [-0.92705098  2.85316955]'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'hit at 5.099999999999998'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "plot\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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hwoVK65RNb+Tk5KTSQIIePXqgRo0aSE1NVfij/+zZM/Epi7qfWKjzkWFZyUZa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\n3dqrUp0Pna6MPp2UdW2WSnYVyrP/HR19N79etbbDxXfWfh2zq3N//b/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+WNOnT1dhYWHQ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\n",
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "buGwxytqpkay",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}