InvestmentMC.ipynb

investmentmc.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyM/zSYOIkYPohXzTZGVg450",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/heathhenley/d207ca2e83a7a39935f3e19435339d1a/investmentmc.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 56,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 524
        },
        "id": "L5vvCC3waybE",
        "outputId": "3a6b0ac6-d2e0-4893-92af-f5b490444d39"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Computed Future Value: 566416.06\n",
            "Iterated future value: 566416.06\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7ee67e9e4eb0>"
            ]
          },
          "metadata": {},
          "execution_count": 56
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "average_interest_rate = 8.0\n",
        "std_dev_rate = 8.0\n",
        "time_in_years = 30\n",
        "yearly_additions_usd = 5000\n",
        "starting_usd = 0\n",
        "\n",
        "def annuity_fv(cv, pmt, apr, t):\n",
        "  return cv * (1 + apr) ** t + pmt * (((1 + apr) ** t - 1) / apr)\n",
        "\n",
        "# Compute the future value (could use annuity formula)\n",
        "fv_avg = annuity_fv(\n",
        "    starting_usd,\n",
        "    yearly_additions_usd,\n",
        "    average_interest_rate / 100.0,\n",
        "    time_in_years)\n",
        "\n",
        "print(f\"Computed Future Value: {fv_avg:.2f}\")\n",
        "\n",
        "# Lets check by iterating:\n",
        "stats = {}\n",
        "accumulated_interest = 0.0\n",
        "current_value = starting_usd\n",
        "for year in range(time_in_years):\n",
        "  interest_this_period = current_value * (average_interest_rate / 100)\n",
        "  current_value += (yearly_additions_usd + interest_this_period)\n",
        "  # saving to plot\n",
        "  accumulated_interest += interest_this_period\n",
        "  stats[year] = ((year+1) * yearly_additions_usd, accumulated_interest)\n",
        "print(f\"Iterated future value: {current_value:.2f}\")\n",
        "\n",
        "bottom = np.zeros((len(stats.keys())))\n",
        "plt.bar(stats.keys(), [x[0] for x in stats.values()], label=\"Total Contributed\")\n",
        "bottom += [x[0] for x in stats.values()]\n",
        "plt.bar(stats.keys(), [x[1] for x in stats.values()], label=\"Total Interest\", bottom=bottom)\n",
        "plt.plot(stats.keys(), [x[0] + x[1] for x in stats.values()], label=\"Total\")\n",
        "plt.xlabel(\"Time (years)\")\n",
        "plt.ylabel(\"Value (USD)\")\n",
        "plt.title(f\"Classic Future Value (APR: {average_interest_rate:.1f}%, {time_in_years} years)\")\n",
        "plt.legend()"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# OK, now lets run the same \"simulation\" as above, but we will let the rate fluctuate\n",
        "# around the average rate according to the standard deviation\n",
        "\n",
        "# put it in a function so we can call it a bunch of times to see how it does\n",
        "# in different runs\n",
        "def run_mc_simulation(\n",
        "    starting_value=starting_usd,\n",
        "    yearly_contribution=yearly_additions_usd,\n",
        "    average_rate=average_interest_rate,\n",
        "    std_dev_rate=std_dev_rate,\n",
        "    years=time_in_years):\n",
        "  stats = {}\n",
        "  accumulated_interest = 0.0\n",
        "  current_value = starting_value\n",
        "  for year in range(years):\n",
        "    rate = np.random.normal(average_rate, std_dev_rate)\n",
        "    #print(year, rate)\n",
        "    interest_this_period = current_value * (rate / 100)\n",
        "    current_value += (yearly_contribution + interest_this_period)\n",
        "    accumulated_interest += interest_this_period\n",
        "    stats[year] = dict(\n",
        "        contributed=(year+1) * yearly_contribution,\n",
        "        interest=accumulated_interest,\n",
        "        rate=rate,\n",
        "        current_value=current_value)\n",
        "  return stats\n",
        "\n",
        "num_sims = 100\n",
        "results = {}\n",
        "for i in range(num_sims):\n",
        "  results[i] = run_mc_simulation() # uses defaults set to values at top\n",
        "\n",
        "# Plot the different ending values\n",
        "values = [results[i][time_in_years-1][\"current_value\"] for i in range(num_sims)]\n",
        "print(f\"Mean: {np.mean(values):.2f}\")\n",
        "print(f\"Max: {np.max(values):.2f}\")\n",
        "print(f\"Min: {np.min(values):.2f}\")\n",
        "plt.figure()\n",
        "plt.bar(range(num_sims), values, label=\"Final Value\")\n",
        "plt.hlines(fv_avg, 0, num_sims, 'k')\n",
        "plt.xlim([0, num_sims])\n",
        "plt.xlabel(\"Simulation Number\")\n",
        "plt.ylabel(\"Final Value (USD)\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 534
        },
        "id": "p0yBiEYClrP2",
        "outputId": "ec6984cb-07cb-4e24-d2ae-b56642c0edb2"
      },
      "execution_count": 57,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mean: 557679.67\n",
            "Max: 1012118.07\n",
            "Min: 230715.74\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'Final Value (USD)')"
            ]
          },
          "metadata": {},
          "execution_count": 57
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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FI0aM0BtvvKFjx47pvvvuU/v27a3r33rrLQ0aNMjpRQIAALhSjZ9DtH37dm3atEmhoaEaM2aMzfq+fftqwIABTi0QAADA1Wr8XWY9evRQjx497K576KGH6lwQAABAfatRIHr22WfttgcGBqpr166KjY11SlEAAAD1qUaBaMGCBXbbS0pKVFpaqoEDB+qdd95R69atnVIcAABAfajRbfcFBQV2X6dPn9bXX3+t6upqzZgxw1W1AgAAuESNAtGVdO7cWXPnztXGjRudtUsAAIB64bRAJEkREREqKipy5i4BAABczqmB6IsvvlDHjh1rtM2iRYsUGRkpX19fxcTEKDc394r9S0pKNGnSJLVv314+Pj7q2rWr1q9fX5eyAZhc5LR1Ni8A5lOjSdVlZWV220tLS5WXl6c///nPSkhIcHh/q1evVnJysjIzMxUTE6OMjAwNGzZM+/fvV3Bw8CX9Kysrdcsttyg4OFj//Oc/1aFDB33zzTcKCgqqydsA6p2ZnvYKNHT8PMKeGgWioKAgWSwWu+ssFosefPBBTZs2zeH9paena/z48UpMTJQkZWZmat26dVq6dKnd/SxdulSnTp3Sp59+qmbNmkmSIiMja/IWAAAALlGjQLR582a77QEBAerSpYv8/f0d3ldlZaXy8vI0ffp0a5uHh4fi4uKUk5Njd5t33nlHsbGxmjRpkt5++221a9dOd999t6ZOnSpPT0+721RUVKiiosK6fLlRLgAAYF41/uoOZzl58qSqqqoUEhJi0x4SEqJ9+/bZ3SY/P18ffPCB4uPjtX79en399dd6+OGHdeHCBaWmptrdJi0tTbNmzXJa3QAAoOlxOBAVFhYqIiLC4R0fOXJEHTp0qFVRl1NdXa3g4GC9+OKL8vT0VP/+/XXkyBE988wzlw1E06dPV3JysnW5rKxM4eHhTq3LlbjWjaaKP9sAGhKH7zK77rrr9Ic//EHbtm27bJ/S0lItXrxYPXv21L/+9a8r7q9t27by9PRUcXGxTXtxcbFCQ0PtbtO+fXt17drV5vJY9+7dVVRUpMrKSrvb+Pj4KCAgwOYFAADwYw6PEO3Zs0dz5szRLbfcIl9fX/Xv319hYWHy9fXV6dOntWfPHn355Zfq16+fnn76ad16661X3J+3t7f69++vrKwsjR49WtL3I0BZWVlKSkqyu82gQYO0cuVKVVdXy8Pj+yz31VdfqX379vL29nb0rQCNHqMrAOBcDo8QtWnTRunp6Tp27Jief/55denSRSdPntSBAwckSfHx8crLy1NOTs7PhqEfJCcna/HixXr55Ze1d+9eTZw4UeXl5da7zsaNG2cz6XrixIk6deqUJk+erK+++krr1q3TU089pUmTJtXkPQMAANio0aRqSfLz89Odd96pO++8s84HHzt2rE6cOKGUlBQVFRWpb9++2rBhg3WidWFhoXUkSJLCw8P1/vvv65FHHlHv3r3VoUMHTZ48WVOnTq1zLQAAwLxqHIicLSkp6bKXyLKzsy9pi42N1datW11cFQAAMBO3ByKgIWKODgCYi1O/ywwAAKAxYoQIAIAGjlFr1zNtICovL5enp6eqK89f0l4XDX1/zj6uq+uzt39H2xzdX12O6yhn11wf9dWlX22P6a6fH3f9nNnT0P+s1Ja7anP0GN1nbrBp2zt7uMP7q8txHdWQPitn7r8mXP3n1GIYhlGbDV999VVlZmaqoKBAOTk56tixozIyMtSpUyfddtttzq7TacrKyhQYGOjuMgAAQC2Ulpa65CHLtZpD9MILLyg5OVm33nqrSkpKVFVVJUkKCgpSRkaGM+sDAABwuVqNEPXo0UNPPfWURo8erZYtW+q///2vOnfurN27d+vGG2/UyZMnXVGrU/wwQnT06FEFBAQ4PEzqqIa+P2cf19X12du/o22O7q8ux3WUs2uuj/rq0q+2x3TXZ+KunzN7GtLn4kzuqo2/Qxzn6mPU9TMuKytTWFiYy0aIajWHqKCgQFFRUZe0+/j4uPXae020aNFCLVq0kIe37yXtddHQ91eX49qb1Ofq+uzt39E2R/dXl+M6ytk110d9delX22O66zNx18+ZPQ3pc3Emd9XG3yGOc/Ux6voZ/3A1ylVqFYg6deqkXbt2qWPHjjbtGzZsUPfu3Z1SGADAvbizqfHhnNVerQJRcnKyJk2apPPnz8swDOXm5ur1119XWlqalixZ4uwaAQAAXKpWgejBBx+Un5+fZsyYoXPnzunuu+9WWFiYFi5cqN///vfOrhEAAMClav0covj4eMXHx+vcuXM6e/asgoODnVkXAAA1wuUi1EWdH8zYvHlzNW/e3Bm1AAAAuEWtJ1VbLJbLrs/Pz691QUB941+VAIBaBaIpU6bYLF+4cEE7d+7Uhg0b9NhjjzmjLgBuRlBEQ8GfRdSHWgWiyZMn221ftGiRtm/fXqeCAAAA6lutvrrjckaMGKF//etfztyly/RMfd/dJQAAgAbCqYHon//8p1q3bu3MXQIAALhcrS6ZRUVF2UyqNgxDRUVFOnHihP7+9787rTgAAID6UKtANHr0aJtlDw8PtWvXTjfeeKO6devmjLpQj5iwCAAwu1oFotTUVGfXAQAAmojG+A9thwNRWVmZwzsNCAioVTEAAJhdYwwTTYHDgSgoKOiKD2OUvp9LZLFYVFVVVefCAAAA6ovDgWjz5s2urANAE8a/eAE0dA4HoiFDhriyDgAAALep05e7njt3ToWFhaqsrLRp7927d52KAoAfMLoEoD7UKhCdOHFCiYmJeu+99+yuZw4RAMAszBbam+r7rdWTqqdMmaKSkhJ99tln8vPz04YNG/Tyyy+rS5cueuedd5xdIwAAgEvVaoTogw8+0Ntvv63o6Gh5eHioY8eOuuWWWxQQEKC0tDSNHNk00iIAADCHWo0QlZeXKzg4WJLUqlUrnThxQpLUq1cv7dixw3nVAQAA1INaBaJrrrlG+/fvlyT16dNH//jHP3TkyBFlZmaqffv2Ti0QAADA1Wp1yWzy5Mk6duyYpO+/xmP48OFasWKFvL29tXz5cmfWBwAA4HI1CkR33nmnHnzwQcXHx1ufWt2/f39988032rdvnyIiItS2bVuXFAqg8fjpXSgA0NDVKBCdPn1aI0eOVFhYmBITE3Xfffepc+fOat68ufr16+eqGgEAQBPUkG7hr9EcoqysLOXn5+uBBx7Qa6+9pi5dumjo0KFauXKlKioqXFUjAACAS9V4UnXHjh31xBNPKD8/X5s2bVJYWJjGjx+v9u3ba9KkScrLy3NFnQDQaEROW2fzAtDw1eousx8MHTpUr732moqKipSWlqZVq1YpJibGWbUBAADUizp9l5kkFRQUaPny5Vq+fLlKS0sVFxfnjLoAAADqTa1GiM6fP6/XXntNQ4cOVZcuXfTKK6/ogQceUEFBgTZs2ODsGgEAAFyqRiNEubm5Wrp0qVavXq3z58/rt7/9rTZs2KCbb77Zehs+YE9DupOgIeNzanw4Z0DTUKNAdP3116tPnz6aPXu24uPj1apVK1fVBSfgL2r34HMHgManRoFo+/btPG/IherjF6mZflmb6b0CdcXPC8yuRnOICEMAAKApqtNt9wAAAE0BgQgAAJhenZ9DBACNCXNlANjDCBEAADA9h0eIoqKiHH7W0I4dO2pdENCYMNoAAE2Dw4Fo9OjRLiwDAADAfRwORKmpqa6sAwCaNEYTgYaNOUQAAMD0anWXWVVVlRYsWKA33nhDhYWFqqystFl/6tQppxQHAABQH2o1QjRr1iylp6dr7NixKi0tVXJysm6//XZ5eHjoiSeecHKJAGorcto6mxcAwL5aBaIVK1Zo8eLF+vOf/ywvLy/dddddWrJkiVJSUrR161Zn1wgAAOBStbpkVlRUpF69ekmS/P39VVpaKkn69a9/rZkzZzqvuiaCyZRA48PPLWAutQpEv/jFL3Ts2DFFREToqquu0saNG9WvXz9t27ZNPj4+zq4RQANGcADQFNQqEP32t79VVlaWYmJi9Mc//lH33HOPXnrpJRUWFuqRRx5xdo1ogvglCgBoSGoViObOnWv9/7FjxyoiIkI5OTnq0qWLRo0a5bTiAKAp4x8GQMPhlOcQxcbGKjk5udZhaNGiRYqMjJSvr69iYmKUm5vr0HarVq2SxWLhKdoAALhJU7mbtdbfdn/gwAFt3rxZx48fV3V1tc26lJQUh/ezevVqJScnKzMzUzExMcrIyNCwYcO0f/9+BQcHX3a7Q4cO6dFHH9XgwYNr+xYAAAAk1TIQLV68WBMnTlTbtm0VGhpq86WvFoulRoEoPT1d48ePV2JioiQpMzNT69at09KlSzVt2jS721RVVSk+Pl6zZs3SRx99pJKSktq8DQAAAEm1DERPPvmk5syZo6lTp9bp4JWVlcrLy9P06dOtbR4eHoqLi1NOTs5lt/uf//kfBQcH64EHHtBHH31UpxrQcDCfAmga6uNnmb8v4Gy1CkSnT5/WmDFj6nzwkydPqqqqSiEhITbtISEh2rdvn91tPv74Y7300kvatWuXQ8eoqKhQRUWFdbmsrKzW9QIAgKapVoFozJgx2rhxoyZMmODseq7ozJkzuvfee7V48WK1bdvWoW3S0tI0a9asOh+bf40AAJoKfqddqlaB6Oqrr9bMmTO1detW9erVS82aNbNZ/6c//cmh/bRt21aenp4qLi62aS8uLlZoaOgl/Q8ePKhDhw7Z3M32w4RuLy8v7d+/X1dddZXNNtOnT1dycrJ1uaysTOHh4Q7VBwA/xi8RoOmqVSB68cUX5e/vry1btmjLli026ywWi8OByNvbW/3791dWVpb11vnq6mplZWUpKSnpkv7dunXTF198YdM2Y8YMnTlzRgsXLrQbdHx8fHh6NvAj/FIHgEvVKhAVFBQ4rYDk5GQlJCQoOjpaAwYMUEZGhsrLy613nY0bN04dOnRQWlqafH191bNnT5vtg4KCJOmSdgAAAEfV+jlEzjJ27FidOHFCKSkpKioqUt++fbVhwwbrROvCwkJ5eDjl+ZEAAAB2ORyIkpOTNXv2bLVo0cJmTo496enpNSoiKSnJ7iUyScrOzr7itsuXL6/RsQAAAH7K4UC0c+dOXbhwwfr/l/PjhzTCnJijAgBobBwORJs3b1Z+fr4CAwO1efNmV9YEAABQr2o0OadLly46ceKEdXns2LGX3DIPAADQ2NRoUrVhGDbL69evV1pamlMLAgCgIeDyv7m4/S4zAEDjQUhAU1WjQGSxWC6ZNN0UJ1HzAw8AgLnU+JLZfffdZ33y8/nz5zVhwgS1aNHCpt+bb77pvAobMIITAABNQ40CUUJCgs3yPffc49RiAAAA3KFGgWjZsmWuqgMAANPhSkPDwXdiAAAA0yMQAQAA0yMQAQAA0yMQAQAA0+PBjAAANGFM3HYMI0QAAMD0CEQAAMD0CEQAAMD0CEQAAMD0mFTdCDFBDgB/DwDOxQgRAAAwPQIRAAAwPQIRAAAwPQIRAAAwPQIRAAAwPQIRAAAwPQIRAAAwPQIRAAAwPQIRAAAwPQIRAAAwPQIRAAAwPQIRAAAwPQIRAAAwPQIRAAAwPQIRAAAwPS93FwDniJy2zmb50NyRbqoEAIDGhxEiAABgegQiAABgegQiAABgegQiAABgegQiAABgetxl5ibcFQYAQMPBCBEAADA9AhEAADA9AhEAADA9AhEAADA9AhEAADA9AhEAADA9AhEAADA9AhEAADA9AhEAADA9AhEAADA9AhEAADA9vssMAFAnP/1uRqAxYoQIAACYHoEIAACYHoEIAACYHoEIAACYHoEIAACYHoEIAACYXoMIRIsWLVJkZKR8fX0VExOj3Nzcy/ZdvHixBg8erFatWqlVq1aKi4u7Yn8AAICf4/ZAtHr1aiUnJys1NVU7duxQnz59NGzYMB0/ftxu/+zsbN11113avHmzcnJyFB4erl/96lc6cuRIPVcOAACaCrcHovT0dI0fP16JiYnq0aOHMjMz1bx5cy1dutRu/xUrVujhhx9W37591a1bNy1ZskTV1dXKysqq58oBAEBT4dZAVFlZqby8PMXFxVnbPDw8FBcXp5ycHIf2ce7cOV24cEGtW7e2u76iokJlZWU2LwAAgB9zayA6efKkqqqqFBISYtMeEhKioqIih/YxdepUhYWF2YSqH0tLS1NgYKD1FR4eXue6AQBA0+L2S2Z1MXfuXK1atUpvvfWWfH197faZPn26SktLra/Dhw/Xc5UAAKChc+uXu7Zt21aenp4qLi62aS8uLlZoaOgVt/3b3/6muXPn6j//+Y969+592X4+Pj7y8fFxSr0AAKBpcusIkbe3t/r3728zIfqHCdKxsbGX3e7pp5/W7NmztWHDBkVHR9dHqQAAoAlz6wiRJCUnJyshIUHR0dEaMGCAMjIyVF5ersTEREnSuHHj1KFDB6WlpUmS5s2bp5SUFK1cuVKRkZHWuUb+/v7y9/d32/sAAACNl9sD0dixY3XixAmlpKSoqKhIffv21YYNG6wTrQsLC+Xh8f8DWS+88IIqKyt155132uwnNTVVTzzxRH2WDgAAmgi3ByJJSkpKUlJSkt112dnZNsuHDh1yfUEAAMBUGvVdZgAAAM5AIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKZHIAIAAKbXIALRokWLFBkZKV9fX8XExCg3N/eK/desWaNu3brJ19dXvXr10vr16+upUgAA0BS5PRCtXr1aycnJSk1N1Y4dO9SnTx8NGzZMx48ft9v/008/1V133aUHHnhAO3fu1OjRozV69Gjt3r27nisHAABNhdsDUXp6usaPH6/ExET16NFDmZmZat68uZYuXWq3/8KFCzV8+HA99thj6t69u2bPnq1+/frp+eefr+fKAQBAU+HWQFRZWam8vDzFxcVZ2zw8PBQXF6ecnBy72+Tk5Nj0l6Rhw4Zdtj8AAMDP8XLnwU+ePKmqqiqFhITYtIeEhGjfvn12tykqKrLbv6ioyG7/iooKVVRUWJdLS0slSdUV51RWVqbqinM2/Wmrn7afaki10cb5po3zTVvDOt8//q9hGFc8fq0ZbnTkyBFDkvHpp5/atD/22GPGgAED7G7TrFkzY+XKlTZtixYtMoKDg+32T01NNSTx4sWLFy9evJrA6+DBg84JIT/h1hGitm3bytPTU8XFxTbtxcXFCg0NtbtNaGhojfpPnz5dycnJ1uWSkhJ17NhRhYWFCgwMrOM7QF2UlZUpPDxchw8fVkBAgLvLMT3OR8PBuWg4OBcNR2lpqSIiItS6dWuX7N+tgcjb21v9+/dXVlaWRo8eLUmqrq5WVlaWkpKS7G4TGxurrKwsTZkyxdq2adMmxcbG2u3v4+MjHx+fS9oDAwP5w91ABAQEcC4aEM5Hw8G5aDg4Fw2Hh4drpj+7NRBJUnJyshISEhQdHa0BAwYoIyND5eXlSkxMlCSNGzdOHTp0UFpamiRp8uTJGjJkiObPn6+RI0dq1apV2r59u1588UV3vg0AANCIuT0QjR07VidOnFBKSoqKiorUt29fbdiwwTpxurCw0CYNDhw4UCtXrtSMGTP0l7/8RV26dNHatWvVs2dPd70FAADQyLk9EElSUlLSZS+RZWdnX9I2ZswYjRkzplbH8vHxUWpqqt3LaKhfnIuGhfPRcHAuGg7ORcPh6nNhMQxX3b8GAADQOLj9SdUAAADuRiACAACmRyACAACmZ7pAtGjRIkVGRsrX11cxMTHKzc11d0lNXlpamq677jq1bNlSwcHBGj16tPbv32/T5/z585o0aZLatGkjf39/3XHHHZc8gBPON3fuXFksFpvnenEu6s+RI0d0zz33qE2bNvLz81OvXr20fft263rDMJSSkqL27dvLz89PcXFxOnDggBsrbpqqqqo0c+ZMderUSX5+frrqqqs0e/Zsm6+I4Fy4zocffqhRo0YpLCxMFotFa9eutVnvyGd/6tQpxcfHKyAgQEFBQXrggQd09uzZGtVhqkC0evVqJScnKzU1VTt27FCfPn00bNgwHT9+3N2lNWlbtmzRpEmTtHXrVm3atEkXLlzQr371K5WXl1v7PPLII/r3v/+tNWvWaMuWLTp69Khuv/12N1bd9G3btk3/+Mc/1Lt3b5t2zkX9OH36tAYNGqRmzZrpvffe0549ezR//ny1atXK2ufpp5/Ws88+q8zMTH322Wdq0aKFhg0bpvPnz7ux8qZn3rx5euGFF/T8889r7969mjdvnp5++mk999xz1j6cC9cpLy9Xnz59tGjRIrvrHfns4+Pj9eWXX2rTpk1699139eGHH+qhhx6qWSEu+UKQBmrAgAHGpEmTrMtVVVVGWFiYkZaW5saqzOf48eOGJGPLli2GYRhGSUmJ0axZM2PNmjXWPnv37jUkGTk5Oe4qs0k7c+aM0aVLF2PTpk3GkCFDjMmTJxuGwbmoT1OnTjVuuOGGy66vrq42QkNDjWeeecbaVlJSYvj4+Bivv/56fZRoGiNHjjTuv/9+m7bbb7/diI+PNwyDc1GfJBlvvfWWddmRz37Pnj2GJGPbtm3WPu+9955hsViMI0eOOHxs04wQVVZWKi8vT3FxcdY2Dw8PxcXFKScnx42VmU9paakkWb+PJi8vTxcuXLA5N926dVNERATnxkUmTZqkkSNH2nzmEueiPr3zzjuKjo7WmDFjFBwcrKioKC1evNi6vqCgQEVFRTbnIjAwUDExMZwLJxs4cKCysrL01VdfSZL++9//6uOPP9aIESMkcS7cyZHPPicnR0FBQYqOjrb2iYuLk4eHhz777DOHj9UgHsxYH06ePKmqqirrE7B/EBISon379rmpKvOprq7WlClTNGjQIOvTxYuKiuTt7a2goCCbviEhISoqKnJDlU3bqlWrtGPHDm3btu2SdZyL+pOfn68XXnhBycnJ+stf/qJt27bpT3/6k7y9vZWQkGD9vO39ncW5cK5p06aprKxM3bp1k6enp6qqqjRnzhzFx8dLEufCjRz57IuKihQcHGyz3svLS61bt67R+TFNIELDMGnSJO3evVsff/yxu0sxpcOHD2vy5MnatGmTfH193V2OqVVXVys6OlpPPfWUJCkqKkq7d+9WZmamEhIS3FydubzxxhtasWKFVq5cqWuvvVa7du3SlClTFBYWxrkwEdNcMmvbtq08PT0vuVumuLhYoaGhbqrKXJKSkvTuu+9q8+bN+sUvfmFtDw0NVWVlpUpKSmz6c26cLy8vT8ePH1e/fv3k5eUlLy8vbdmyRc8++6y8vLwUEhLCuagn7du3V48ePWzaunfvrsLCQkmyft78neV6jz32mKZNm6bf//736tWrl+6991498sgj1i8V51y4jyOffWho6CU3R128eFGnTp2q0fkxTSDy9vZW//79lZWVZW2rrq5WVlaWYmNj3VhZ02cYhpKSkvTWW2/pgw8+UKdOnWzW9+/fX82aNbM5N/v371dhYSHnxsluvvlmffHFF9q1a5f1FR0drfj4eOv/cy7qx6BBgy55/MRXX32ljh07SpI6deqk0NBQm3NRVlamzz77jHPhZOfOnbP5EnFJ8vT0VHV1tSTOhTs58tnHxsaqpKREeXl51j4ffPCBqqurFRMT4/jB6jwlvBFZtWqV4ePjYyxfvtzYs2eP8dBDDxlBQUFGUVGRu0tr0iZOnGgEBgYa2dnZxrFjx6yvc+fOWftMmDDBiIiIMD744ANj+/btRmxsrBEbG+vGqs3jx3eZGQbnor7k5uYaXl5expw5c4wDBw4YK1asMJo3b2689tpr1j5z5841goKCjLffftv4/PPPjdtuu83o1KmT8d1337mx8qYnISHB6NChg/Huu+8aBQUFxptvvmm0bdvWePzxx619OBeuc+bMGWPnzp3Gzp07DUlGenq6sXPnTuObb74xDMOxz3748OFGVFSU8dlnnxkff/yx0aVLF+Ouu+6qUR2mCkSGYRjPPfecERERYXh7exsDBgwwtm7d6u6SmjxJdl/Lli2z9vnuu++Mhx9+2GjVqpXRvHlz47e//a1x7Ngx9xVtIj8NRJyL+vPvf//b6Nmzp+Hj42N069bNePHFF23WV1dXGzNnzjRCQkIMHx8f4+abbzb279/vpmqbrrKyMmPy5MlGRESE4evra3Tu3Nn461//alRUVFj7cC5cZ/PmzXZ/RyQkJBiG4dhn/+233xp33XWX4e/vbwQEBBiJiYnGmTNnalQH33YPAABMzzRziAAAAC6HQAQAAEyPQAQAAEyPQAQAAEyPQAQAAEyPQAQAAEyPQAQAAEyPQAQAAEyPQASYiMVi0dq1a11+nMjISGVkZDSY/TR0N954o6ZMmeLuMgBTIxABTcSJEyc0ceJERUREyMfHR6GhoRo2bJg++eQTa59jx45pxIgRbqzSvuXLlysoKOiS9m3btumhhx5y6bGzs7NlsVh07bXXqqqqymZdUFCQli9f7tLjA2gYvNxdAADnuOOOO1RZWamXX35ZnTt3VnFxsbKysvTtt99a+4SGhrqxwppr165dvR0rPz9fr7zyihITE+vtmK5UVVUli8Vyybe4A7CPnxSgCSgpKdFHH32kefPm6aabblLHjh01YMAATZ8+Xb/5zW+s/X58yezQoUOyWCx64403NHjwYPn5+em6667TV199pW3btik6Olr+/v4aMWKETpw4Yd2Hvcs7o0eP1n333XfZ+tLT09WrVy+1aNFC4eHhevjhh3X27FlJ34/QJCYmqrS0VBaLRRaLRU888YSkSy+ZFRYW6rbbbpO/v78CAgL0u9/9TsXFxdb1TzzxhPr27atXX31VkZGRCgwM1O9//3udOXPmZz/DP/7xj0pNTVVFRYXd9T98Xrt27bK2lZSUyGKxKDs72/peLBaL3n//fUVFRcnPz09Dhw7V8ePH9d5776l79+4KCAjQ3XffrXPnztns/+LFi0pKSlJgYKDatm2rmTNn6sdfNVlRUaFHH31UHTp0UIsWLRQTE2M9rvT/o2zvvPOOevToIR8fHxUWFv7s+wbwPQIR0AT4+/vL399fa9euvewv9MtJTU3VjBkztGPHDnl5eenuu+/W448/roULF+qjjz7S119/rZSUlDrV5+HhoWeffVZffvmlXn75ZX3wwQd6/PHHJUkDBw5URkaGAgICdOzYMR07dkyPPvroJfuorq7WbbfdplOnTmnLli3atGmT8vPzNXbsWJt+Bw8e1Nq1a/Xuu+/q3Xff1ZYtWzR37tyfrXHKlCm6ePGinnvuuTq9V+n7YPb888/r008/1eHDh/W73/1OGRkZWrlypdatW6eNGzdecpyXX35ZXl5eys3N1cKFC5Wenq4lS5ZY1yclJSknJ0erVq3S559/rjFjxmj48OE6cOCAtc+5c+c0b948LVmyRF9++aWCg4Pr/F4A0zAANAn//Oc/jVatWhm+vr7GwIEDjenTpxv//e9/bfpIMt566y3DMAyjoKDAkGQsWbLEuv711183JBlZWVnWtrS0NOOaa66xLg8ZMsSYPHmyzX5vu+02IyEhwbrcsWNHY8GCBZetdc2aNUabNm2sy8uWLTMCAwMv6ffj/WzcuNHw9PQ0CgsLreu//PJLQ5KRm5trGIZhpKamGs2bNzfKysqsfR577DEjJibmsrVs3rzZkGScPn3ayMzMNFq3bm2UlJQYhmEYgYGBxrJlywzD+P/Pa+fOndZtT58+bUgyNm/ebLOv//znP9Y+aWlphiTj4MGD1rY//OEPxrBhw6zLQ4YMMbp3725UV1db26ZOnWp0797dMAzD+OabbwxPT0/jyJEjNrXffPPNxvTp062foSRj165dl32vAC6PESKgibjjjjt09OhRvfPOOxo+fLiys7PVr1+/n50U3Lt3b+v/h4SESJJ69epl03b8+PE61faf//xHN998szp06KCWLVvq3nvv1bfffnvJZaMr2bt3r8LDwxUeHm5t69Gjh4KCgrR3715rW2RkpFq2bGldbt++vcP1P/DAA2rTpo3mzZvncF32/PQzbd68uTp37mzT9tOarr/+elksFutybGysDhw4oKqqKn3xxReqqqpS165draOB/v7+2rJliw4ePGjdxtvb2+bYABxHIAKaEF9fX91yyy2aOXOmPv30U913331KTU294jbNmjWz/v8Pv5B/2lZdXW1d9vDwsJnbIkkXLly47P4PHTqkX//61+rdu7f+9a9/KS8vT4sWLZIkVVZWOv7mHPTj2qVL678SLy8vzZkzRwsXLtTRo0dt1v0wOfnH7/1y7/unn19dapKks2fPytPTU3l5edq1a5f1tXfvXi1cuNDaz8/PzyZUAXAcgQhownr06KHy8nKn7rNdu3Y6duyYdbmqqkq7d+++bP+8vDxVV1dr/vz5uv7669W1a9dLwoa3t/clt7z/VPfu3XX48GEdPnzY2rZnzx6VlJSoR48etXw3lxozZoyuvfZazZo1y6b9hzvefvzefzzBuq4+++wzm+WtW7eqS5cu8vT0VFRUlKqqqnT8+HFdffXVNq/Gducg0FARiIAm4Ntvv9XQoUP12muv6fPPP1dBQYHWrFmjp59+WrfddptTjzV06FCtW7dO69at0759+zRx4kSVlJRctv/VV1+tCxcu6LnnnlN+fr5effVVZWZm2vSJjIzU2bNnlZWVpZMnT9q9lBYXF6devXopPj5eO3bsUG5ursaNG6chQ4YoOjraqe9x7ty5Wrp0qU2Y9PPz0/XXX6+5c+dq79692rJli2bMmOG0YxYWFio5OVn79+/X66+/rueee06TJ0+WJHXt2lXx8fEaN26c3nzzTRUUFCg3N1dpaWlat26d02oAzIxABDQB/v7+iomJ0YIFC/TLX/5SPXv21MyZMzV+/Hg9//zzTj3W/fffr4SEBGsY6dy5s2666abL9u/Tp4/S09M1b9489ezZUytWrFBaWppNn4EDB2rChAkaO3as2rVrp6effvqS/VgsFr399ttq1aqVfvnLXyouLk6dO3fW6tWrnfr+pO9D39ChQ3Xx4kWb9qVLl+rixYvq37+/pkyZoieffNJpxxw3bpy+++47DRgwQJMmTdLkyZNtHkq5bNkyjRs3Tn/+8591zTXXaPTo0dq2bZsiIiKcVgNgZhbjp5MBAAAATIYRIgAAYHoEIgAAYHoEIgAAYHoEIgAAYHoEIgAAYHoEIgAAYHoEIgAAYHoEIgAAYHoEIgAAYHoEIgAAYHoEIgAAYHoEIgAAYHr/B7jtJptfS2ZIAAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "4kIPWKVWq89x"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}