Harga_Harap_Atom_Hidrogen.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Harga Harap Atom Hidrogen.ipynb",
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# Harga Harap Posisi Atom Hidrogen\n",
        "\n",
        "Sebuah atom hidrogen H memiliki elektron yang tereksitasi pada orbital 4f dengan $n=4$ dan $l=3$.\n",
        "\n",
        "Di bawah ini adalah program untuk menentukan harga harap langsung $\\bar{r}$, harga harap $r_{rms}$, nilai $r$ maksimum $r_m$, dan harga harap harmonik $r_h$."
      ],
      "metadata": {
        "id": "PfB5q5d0aaVS"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#Import libraries\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from IPython.display import display, Latex"
      ],
      "metadata": {
        "id": "VbTImdDcaZR-"
      },
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "id": "yAasEbO6aWdY"
      },
      "outputs": [],
      "source": [
        "def integrate(r, to_integrate):\n",
        "\n",
        "  xmin = min(r)\n",
        "  h = 0.5\n",
        "  dx = 1\n",
        "  result = 0\n",
        "\n",
        "  for i in range(len(r)-2):\n",
        "    result = result + (to_integrate[i] + 4*to_integrate[i+1] + to_integrate[i+2])\n",
        "    xmin = xmin + dx \n",
        "    \n",
        "  result = result * h/3\n",
        "\n",
        "  return result"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Import data\n",
        "\n",
        "data = np.loadtxt('uas43.out')\n",
        "r = [] #Position\n",
        "R = [] #Radial position\n",
        "rR = [] #Wavefunction\n",
        "\n",
        "for i in range(0, len(data)):\n",
        "\tr.append(data[i][0])\n",
        "\tR.append(data[i][1])\n",
        "\trR.append(data[i][2])\n",
        "\n",
        "rrR2 =[]\n",
        "rms = []\n",
        "rr = []\n",
        "rh = []\n",
        "\n",
        "for i in range(0, len(r)):\n",
        "\trrR2.append(r[i]*(rR[i])**2)\n",
        "\trr.append((rR[i])**2)\n",
        "\trms.append((r[i]**2) * (rR[i]**2))\n",
        "\trh.append((1/r[i]) * (rR[i]**2))\n",
        "\n",
        "#Integration\n",
        "r1 = integrate(r, rrR2)\n",
        "r2 = integrate(r, rr)\n",
        "Rms = integrate(r, rms)\n",
        "rH = integrate(r, rh)\n",
        "\n",
        "#Normalized\n",
        "r_norm = r1/r2\n",
        "rms_norm = np.sqrt((Rms/r2))\n",
        "rh_norm = (rH/r2)**-1\n",
        "max_P = rR.index(max(rR))\n",
        "rm = r[max_P]\n",
        "\n",
        "print(\"Harga harap langsung: \", r_norm)\n",
        "print(\"Harga harap rms: \", rms_norm)\n",
        "print(\"Harga harap harmonik: \", rh_norm)\n",
        "print(\"Nilai r maksimum: \", rm)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2C0Oo2VDcDci",
        "outputId": "e610a5a2-570a-4467-82ca-ce1746ba3b96"
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Harga harap langsung:  15.999999994662932\n",
            "Harga harap rms:  16.970562738608994\n",
            "Harga harap harmonik:  14.000000001999494\n",
            "Nilai r maksimum:  15.958634009794029\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Peluang\n",
        "rR2 = []\n",
        "for i in range(len(rR)):\n",
        "\trR2.append(rR[i]*rR[i])\n",
        "\n",
        "norm_coeff = np.sqrt(np.sum(rR2))\n",
        "rR = rR / norm_coeff\n",
        "P = []\n",
        "\n",
        "for i in range(len(rR)):\n",
        "\tP.append(rR[i]*rR[i])\n",
        " \n",
        "prob = sum(P)\n",
        "print(\"Peluang (0<=x<=100): \", prob)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Y-knLD7OeyO0",
        "outputId": "9a626b27-9b08-4102-9b20-c633c57acc0d"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Peluang (0<=x<=100):  0.9999999999999996\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Grafik Fungsi Gelombang dan Peluang"
      ],
      "metadata": {
        "id": "RguexowffRGZ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(r, rR)\n",
        "plt.title('Grafik rR(r) untuk n=4 dan l=3 (Numerik)')\n",
        "plt.xlabel('r')\n",
        "plt.ylabel('rR(r)')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "VHohQ1lvfQMz",
        "outputId": "4e223756-7e05-49c2-ddd8-0c2a79aac33b"
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(r, P)\n",
        "plt.title('Grafik P(r) untuk n=4 dan l=3 (Numerik)')\n",
        "plt.xlabel('r')\n",
        "plt.ylabel('P(r)')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "qRMj8slsfZuB",
        "outputId": "e1e5896d-5dbb-4f97-837e-c3669ca7ceb3"
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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oyXNupoLg+hxFBXnqIBeRMVFwZKjYiKrFs8+tmQqgqCCPZVXlvBSeTCgiMhoFR4Y6cDwYUXX+rHM/4oDgzPMdDScYGhpxbIKICKDgyFjjNaIqZkVNBSd7B9h/vHNctici2UvBkaH2HQs+4M+rnDwu24vNrrtNzVUicgYKjgy1/1gns8uLz3lEVczi2VMoKshja72CQ0RGp+DIUAeOdVI3Y3yONgAK8/NYWlV+arZdEZGRKDgy1IHjnSyYOX7BAbC8upzt6iAXkTNQcGSgjp5+jp3so26cgyPWQf5KS9e4bldEsouCIwMdOBZ8sI9nUxW82kGu5ioRGY2CIwPFhsyOd1PV+bPLKMrP08gqERmVgiMDHQiH4s6fMWlct1tUkMeSqjKNrBKRUSk4MtCBY51UV5RQUpg/7tteXlPBtoZ2RpndXkRynIIjA+0/3jnuHeMxF1aX09EzQH2rplgXkcQUHBnowLHUBcfSqnIAdjTqGuQikpiCI8N09PTT2tXPvOnj278Rs2ROGWawU8EhIiNQcGSYWBPS3GmpCY5JRQXUzZis4BCRESk4MkwsOGqnpe5KfUurytjZ2JGy7YtIZlNwZJhD4Vndc1PUVAWwdE45B1u66OjpT9lziEjmUnBkmPrWbiYV5TNtUmHKniPWQb67SUcdInI6BUeGOdTaxdxpkzCzlD3H0uogONTPISKJKDgyTH1rd0r7NwCqK0ooLylgh/o5RCQBBUcGcXfqW7pS2r8BYGYsrSrXEYeIJKTgyCAnugfo6B1I+REHwLLqcnY3dTCoa3OIyDAKjgxyqDUYUVWbonM44i2tKqe7f5BXwpl4RURiFBwZJDYUd0KOOKpiHeTq5xCR10ppcJjZajPbbWZ7zeyuBI8Xm9lj4eMbzKwu7rG7w+W7zeytccv/p5ltN7NtZvaImZWkch/SyamzxlPcxwGwaNYU8vNM/RwicpqUBYeZ5QNfAW4AlgG3mtmyYcXuAFrdfRHweeD+cN1lwC3AhcBq4Ktmlm9mNcDHgJXuvhzID8vlhEOtXZSVFFBRmrpzOGJKCvNZWKmpR0TkdKk84lgF7HX3fe7eBzwKrBlWZg3wcHh7LXCdBScorAEedfded98P7A23B1AAlJpZATAJaEjhPqSV+tbulM1RlYhGVolIIqkMjhrgUNz9+nBZwjLuPgC0AzNGWtfdDwOfAw4CjUC7u/8s0ZOb2QfNbLOZbW5ubh6H3YneoZauCenfiFlaVU5Dew/tXZp6RERelVGd42Y2jeBoZAFQDUw2s/clKuvuD7j7SndfWVlZOZHVTAl3D444JqB/IyY29cjOJh11iMirUhkch4G5cfdrw2UJy4RNTxXA8VHWvR7Y7+7N7t4PfA+4KiW1TzPHO/vo7h9k7kQeccwpA2CXmqtEJE4qg2MTsNjMFphZEUEn9rphZdYBt4e3bwae9OBi1+uAW8JRVwuAxcBGgiaqK8xsUtgXch2wM4X7kDYOhyOqqqdOXHBUlhUzfXIRuzTZoYjEKUjVht19wMzuBH5KMPrpG+6+3cw+C2x293XAg8C3zWwv0EI4Qios9ziwAxgAPuLug8AGM1sLPB8u3wI8kKp9SCeN7RMfHMHUI2XsVHCISJyUBQeAu68H1g9bdk/c7R7gXSOsex9wX4LlnwE+M741TX8NbT3AxAYHwJI55XxnwysMDjn5eambkVdEMkdGdY7nssb2booL8lJ6HY5Elswpo6d/SFOPiMgpCo4M0dDeQ/XU0pRehyOR2Mgq9XOISIyCI0M0tnVTVTHxs6to6hERGU7BkSEa2nqoqpjY/g0Iph45b+ZkTXYoIqcoODLAwOAQRzt6qJ4azXyOS6rK2aWTAEUkpODIAEc6ehlyIjnigKCDvL61mxM9mnpERBQcGaGxLXYORzRHHLFrc+xWB7mIoODICA3t0ZzDEbOkSlOPiMirFBwZIHbEEcWoKoA55SVUlBbqDHIRARQcGaGxvYey4gLKSib25L8YM2PJnDINyRURQMGRERrauqmKqH8jZmlVObubOhga8kjrISLRU3BkgIb27shGVMUsrSqjq2+QQ61dkdZDRKKn4MgAjW3RncMRs2ROeFEnnQgokvMUHGmup3+Q4519kR9xnD+7jDxD/RwiouBId03hUNyoRlTFlBblUzdzss4gFxEFR7prCC/gVBPRORzxls4p1yy5IqLgSHeN4QWcqtIgOJbMKeOV412c7B2IuioiEiEFR5qLXTI26qYqCCY7BE09IpLrFBxprqG9h+mTiygpzI+6KiyZE049on4OkZym4EhzDRFdwCmR2mmllBUXsEtDckVymoIjzTVGdAGnRMyMJVWaekQk1yk40lxDe3fkJ//FWxKOrHLX1CMiuUrBkcZO9g7Q0TOQNkccEEyxfrJ3gPrW7qirIiIRUXCksagv4JTI0nBklc7nEMldCo401nDqrPH0OeK4YHYwskr9HCK5S8GRxtLxiGNycQHzZ0zSkFyRHKbgSGMN7T2Ywezy9AkOCM7n0JBckdyV0uAws9VmttvM9prZXQkeLzazx8LHN5hZXdxjd4fLd5vZW+OWTzWztWa2y8x2mtmVqdyHKDW2dVM5pZjC/PTK96VV5ew/3klXn6YeEclFKftEMrN84CvADcAy4FYzWzas2B1Aq7svAj4P3B+uuwy4BbgQWA18NdwewBeBn7j7EuBiYGeq9iFqTSd60mKOquGWzCnHHfYcORl1VUQkAqn8KrsK2Ovu+9y9D3gUWDOszBrg4fD2WuA6M7Nw+aPu3uvu+4G9wCozqwCuBh4EcPc+d29L4T5EqqGtm+o0OWs83tKqcOoRdZCL5KRUBkcNcCjufn24LGEZdx8A2oEZo6y7AGgGvmlmW8zs62Y2OdGTm9kHzWyzmW1ubm4ej/2ZUO5OY3sPc9IwOOZOm8TkonwNyRXJUUkHh5lNjms2mmgFwGXA19z9UqATOK3vBMDdH3D3le6+srKyciLrOC5O9AzQ1TeYNvNUxcvLMy6YU8YOHXGI5KQzBoeZ5ZnZbWb2IzM7CuwCGs1sh5n9vZktGmHVw8DcuPu14bKEZcysAKgAjo+ybj1Q7+4bwuVrCYIk6zSl4Tkc8ZZUlbOz8YSmHhHJQWM54ngKWAjcDcxx97nuPgt4I/AscL+ZvS/BepuAxWa2wMyKCDq71w0rsw64Pbx9M/CkB59E64BbwlFXC4DFwEZ3bwIOmdkF4TrXATvGurOZJJ2uw5HIhdXldPRo6hGRXFQwhjLXu3v/8IXu3gI8ATxhZoUJHh8wszuBnwL5wDfcfbuZfRbY7O7rCDq5v21me4EWgnAhLPc4QSgMAB9x98Fw0x8FvhOG0T7gA8ntcmZobE+fK/8lsry6AoBth9uZO31SxLURkYl0xuBw9/6wT2N7OAQ2YZkRlq8H1g9bdk/c7R7gXSOsex9wX4LlLwArz1TvTNcYnvw3q6w46qokdMGcMvLzjG0N7dywoirq6ojIBBpT53j4bX+3mc1LcX0klK4n/8WUFOazeNYUth1WB7lIrhlLU1XMNGC7mW0kGM0EgLvfNO61krQ9+S/e8poKnt59FHcnOP1GRHJBMsHx6ZTVQk7T2N7DosopUVdjVMury1n7XD1HO3rTbj4tEUmdMwaHmZkHfnmmMuNbtdzl7jS2dfOmxTOjrsqolte82kGu4BDJHWMajmtmHx3ev2FmRWZ2rZk9zKtDamUcdPQO0JmmJ//FW1pVjhnq5xDJMWNpqloN/DfgETM7D2gFSglC52fAF9x9S+qqmHsa24KhuHPS9OS/mMnFBZw3czLbGtqjroqITKCxDMftAb5KMENtITAT6M7myQWjFjv5Lx0nOBxueU0Fm/a3RF0NEZlAY5lypMTM/tTMvkxwsl2zQiO1Yif/peMEh8Mtr66gob2H4yd7o66KiEyQsfRxPExwwt1W4G3A/0lpjeTUyX+Z0OF8YU05ANsb1M8hkivG0sexzN1XAJjZg8DG1FZJmtrT++S/eBfGph5paOfq8zNvFmIRSd5YPplOTScSXjNDUqyxPf1P/oupKC1k3vRJbNfIKpGcMZYjjovNLPapYEBpeN8Ad/fylNUuR2XCyX/xlteUs/WwRlaJ5IozHnG4e767l4c/Ze5eEHdboTHOYif/ZULHeMxFtVM52NJFS2df1FURkQmQ/o3oOSZ28l/11MwJjotrpwLwYr0G24nkAgVHmmlqz4yT/+JdVFtBnsELBxUcIrlAwZFmGtoy5+S/mMnFBZw/u0xHHCI5QsGRZpoy6OS/eBfXTuXFQ226BrlIDlBwpJmGDDr5L94l86bS2tXPwZauqKsiIimm4EgzmXTyX7xYB/kLh9RcJZLtMuvTKQc0tvek/XTqiZw/ewqlhfkKDpEcoOBIM0FwZM6IqpiC/DxW1FQoOERygIIjzTS192Rcx3jMJfOmsr3hBH0DQ1FXRURSSMGRRk709HOydyAjm6og6OfoGxhiV5PmrRLJZgqONBIbipspExwOd8m88AxyNVeJZDUFRxo5nIEn/8Wrrihh5pRitig4RLKagiONHG4NgqNmWmYecZgZl8ydqg5ykSyX0uAws9VmttvM9prZXQkeLzazx8LHN5hZXdxjd4fLd5vZW4etl29mW8zsh6ms/0RraOumIM+YVZaZRxwAr5s/jX3NnbqUrEgWS1lwmFk+8BXgBmAZcKuZLRtW7A6g1d0XAZ8H7g/XXQbcAlwIrAa+Gm4v5uPAzlTVPSqHw+nU8/Ms6qqctdfXTQPguVdaI66JiKRKKo84VgF73X2fu/cBjwJrhpVZQ3BNc4C1wHVmZuHyR9291933A3vD7WFmtcDbga+nsO6RaGjrpiZDO8ZjVtRWUFSQx2YFh0jWSmVw1ACH4u7Xh8sSlgkvS9sOzDjDul8A/gwY9WQBM/ugmW02s83Nzc1nuw8T6nBr5gdHcUE+l9ROZeP+lqirIiIpklGd42Z2I3DU3Z87U1l3f8DdV7r7ysrKygmo3bnpHxyi6URPxnaMx1tZN41th9vp7huMuioikgKpDI7DwNy4+7XhsoRlzKwAqACOj7LuG4CbzOwAQdPXtWb2r6mo/EQ7cqKHIYfqDD/iAHh93XQGhlyjq0SyVCqDYxOw2MwWmFkRQWf3umFl1gG3h7dvBp704IIO64BbwlFXC4DFwEZ3v9vda929Ltzek+7+vhTuw4Q5NRQ3C4LjsvnTMIPNB9RcJZKNClK1YXcfMLM7gZ8C+cA33H27mX0W2Ozu64AHgW+b2V6ghSAMCMs9DuwABoCPuHtWt3s0tGf2ORzxKkoLuWB2GRsVHCJZKWXBAeDu64H1w5bdE3e7B3jXCOveB9w3yrafBp4ej3qmg9gRR3UGzoybyOvrpvO95+sZGByiIMOuLSIio9NfdJo43NbNjMlFlBbln7lwBlhZN43OvkF2NXVEXRURGWcKjjRxuC07RlTFXHHeDACeeflYxDURkfGm4EgTh1u7sqaZCoJrpi+aNYXf7j0edVVEZJwpONKAu9OQZUccAFctnMGmAy26sJNIllFwpIHWrn66+wez4hyOeFctnElX3yAv1ut8DpFsouBIA9l0Dke8K8+bgRn8dq/6OUSyiYIjDcQu4FSbZU1VFZMKWV5dwTPq5xDJKgqONHDqyn9ZdsQBcNWiGWw51EpX30DUVRGRcaLgSAOHWrqYUlzAtEmFUVdl3L1h4Uz6B51NBzTNuki2UHCkgYMtXcybPongUiTZ5fV10ynMN55RP4dI1lBwpIFYcGSj0qJ8Vs6fzi/3ZMY1UUTkzBQcERsa8iA4ZmRncAC8eUklu5o6TvXliEhmU3BE7GhHL30DQ8zN0iMOgGuXzALgyV1HI66JiIwHBUfEDrZ0AWRtUxXAwsopzJs+iacUHCJZQcERsVwIDjPj2iWzeOblY/T0Z/VlVURygoIjYgdbusiz7DtrfLg3L5lFT/8Qv3tZJwOKZDoFR8QOtXRRVVFKUUF2vxSXL5hOaWG++jlEskB2f1plgGweihuvpDCfNyyayZO7jhJcVl5EMpWCI2KvHM+N4AC4buksDrd166qAIhlOwRGhrr4Bjp3szepzOOJdv3Q2ZvDjbU1RV0VEzoGCI0KHWoIT4rL5HI54lWXFrKqbzo+3Nm6i0bQAAA9GSURBVEZdFRE5BwqOCO0/1glAXY4ccQC8bUUVvz96kt8fUXOVSKZScERo37GTACyYOTnimkyc1cvnqLlKJMMpOCK0v7mTWWXFlJVk33TqI5ldXsLK+dNYr+YqkYyl4IjQvmOdOXW0EXPjRdXsaupgV9OJqKsiImdBwRGhfc0nOa9yStTVmHA3XlRFQZ7xb1sOR10VETkLKQ0OM1ttZrvNbK+Z3ZXg8WIzeyx8fIOZ1cU9dne4fLeZvTVcNtfMnjKzHWa23cw+nsr6p1JrZx+tXf2cl4NHHDOmFHPN+ZX8YEsDQ0M6GVAk06QsOMwsH/gKcAOwDLjVzJYNK3YH0Orui4DPA/eH6y4DbgEuBFYDXw23NwB80t2XAVcAH0mwzYywLxxRdV5l7gUHwDsuraHpRA/P7tPcVSKZJpVHHKuAve6+z937gEeBNcPKrAEeDm+vBa6z4Pqpa4BH3b3X3fcDe4FV7t7o7s8DuHsHsBOoSeE+pMy+5mBEVS42VQG8ZdlsphQXsPb5+qirIiJJSmVw1ACH4u7Xc/qH/Kky7j4AtAMzxrJu2Kx1KbBhHOs8YfYf66Qgz6idlt2z4o6kpDCfmy6pZv3WRtq7+6OujogkISM7x81sCvAE8KfunnBojpl90Mw2m9nm5ub0u971y80nmTdjEoX5GfkSjIvbVs2jp3+I76uTXCSjpPJT6zAwN+5+bbgsYRkzKwAqgOOjrWtmhQSh8R13/95IT+7uD7j7SndfWVlZeY67Mv72HDnJBbPLoq5GpJbXVLCipoLvbjioGXNFMkgqg2MTsNjMFphZEUFn97phZdYBt4e3bwae9OATZB1wSzjqagGwGNgY9n88COx0939IYd1Tqqd/kAPHOzk/x4MD4LbL57H7SAfPH2yNuioiMkYpC46wz+JO4KcEndiPu/t2M/usmd0UFnsQmGFme4FPAHeF624HHgd2AD8BPuLug8AbgP8KXGtmL4Q/b0vVPqTK74+cxB0umKPguOniasqKC/jmbw9EXRURGaOCVG7c3dcD64ctuyfudg/wrhHWvQ+4b9iy3wA2/jWdWLvDCf4UHDC5uIBbL5/Hg7/ZT31rF7XTcmfCR5FMlbs9sxHac6SDooI85ufIdOpncvtVdQA8pKMOkYyg4IjArqYOFlVOoSCHR1TFq5layttXVPHopkOc6NHQXJF0p0+uCOxp6mCJmqle44/fdB4newf41jMHoq6KiJyBgmOCtXT20XSih/MVHK+xoraC65bM4l9+vZ8OHXWIpDUFxwTbergdgItqKiKuSfr5+PWLae/uV1+HSJpTcEywbWFwXKjgOM1FtVO5fuks/uXX+2jv0lGHSLpScEywl+rbWDBzMhWluXPVv2R84i0X0NE7wJee/H3UVRGRESg4JtjW+nZW6GhjRMuqy3nPyrk8/MyBUzMIi0h6UXBMoOaOXhrae7ioVsExmk/8p/MpLsjjb9bvjLoqIpKAgmMCbT3cBgST+8nIZpWV8NHrFvMfO4/yk21NUVdHRIZRcEygTQdaKcgzLq6dGnVV0t4db1zAsqpy7vnBNl2vQyTNKDgm0Mb9LayoraC0KD/qqqS9wvw87v8vF3HsZC/3/WhH1NURkTgKjgnS0z/IS/VtrFowPeqqZIwVtRX8yTULeXxzPT96qTHq6ohISMExQbYcbKN/0FlVp+BIxifecj6XzJ3KXU+8xMHjXVFXR0RQcEyYZ/cdxwxWzldwJKMwP49/vPVSzODD332Orr6BqKskkvMUHBPk6T3NXFw7lYpJOvEvWXOnT+ILt1zCjoYTfPzRFxgc0mVmRaKk4JgAx0728lJ9G2++YFbUVclY1y6ZzT03LuPnO47w1z/aoWuUi0QopVcAlMCv9jTjDtcuUXCci/e/YQEHW7r5xm/3U1SQx12rlxBchl5EJpKCYwL8fMcRZk4p5sLq8qirkvE+feNS+gYH+edf7mNoyLn7hqXk5Sk8RCaSgiPFTvT084tdR7lt1Tx9wI0DM+Ov1iwnz4x/+fV+Gtt7+Ny7LqakUOfGiEwUBUeK/WRbE30DQ6y5pDrqqmQNM+Mvb7qQ6qml/O2Pd1Hf2s0/3nopc3UNd5EJoc7xFFu7uZ66GZO4ZK6mGRlPZsaHrlnIP73vMvYePcnbvvRr/v3FhqirJZITFBwp9FJ9GxsPtPC+K+arEzdFVi+vYv3H3sTCyil89JEt3PHQJg616ERBkVRScKTQP/9qH1OKC3jP6+dGXZWsNm/GJP7vh67kL962lGf3Hef6f/gl9/1oB80dvVFXTSQrKThS5IVDbfzopUbef1UdZSU66S/VCvPz+OOrz+M/PnkNb7+oigd/s5+r/+4p7vnBNn5/pCPq6olkFcuFE6lWrlzpmzdvnrDn6xsY4p1f/S1HTvTw9P96M1OKNQZhou1rPslXnnqZf3+xgb7BIV43fxo3LJ/DDSuqqJlaGnX1RNKemT3n7isTPqbgGF/uzv/3/W18Z8NBHvivr+M/XThnQp5XEjt+spfHNh9i3QsN7GoKjjwuqq3gyoUzWFU3nZXzp2saGJEEIgsOM1sNfBHIB77u7n877PFi4FvA64DjwHvc/UD42N3AHcAg8DF3/+lYtpnIRAVH78Ag967bwSMbD/In15zH3TcsTflzytjtP9bJj7c18oudR3mpPpit2AzOmzmZC+aUcf7s4Gfe9ElUTy1l2qRCDWqQnBVJcJhZPrAHeAtQD2wCbnX3HXFlPgxc5O4fMrNbgHe6+3vMbBnwCLAKqAb+Azg/XG3UbSaSyuDoGxjileOd/HJPMw//7gCHWrr50DUL+fPVF+hDJ4119w3ywqE2Nh1oYdvhdvYc6eCVli7i/xyKC/KoqiihqqKUmWXFVJQWMLW0iIrSQipKCykvLaC4MJ/SwnxKwv+D23kUF+STlwcFeXnk5xkFeaYTQCWjjBYcqWx8XwXsdfd9YSUeBdYA8R/ya4B7w9trgS9b8Gm7BnjU3XuB/Wa2N9weY9jmuLnxH39NV+8gg+4MDjlDQ37qduyns2/w1GytF9dW8DfvXMGbFlemojoyjkqL8rly4QyuXDjj1LLuvkFebj5JfWsXDW09NLZ309DeQ2NbN1vr22jv7qe9u59zmZy3IM/Ij/sJ7ucRy5TYdw3D4m7zmi8hNsayduqf07chuWH6pCIe/9CV477dVAZHDXAo7n49cPlIZdx9wMzagRnh8meHrVsT3j7TNgEwsw8CHwSYN2/eWe3A4lll9A8OBX/kFnxjjH1zzLfgD7+spIC6GZNZWTeN+TMmn9XzSHooLcpneU0Fy2sqRiwzNOSc7BugvaufEz399PQP0ds/SHf/ID39Q/SEt3sHhl7zRWNg0BkcGmLQnYEhZ3Dw1cf6Bx3wU0c77uB43O3Tl8f/F2s18LBMouVkf1emJFBWkpqP+Kwd7uPuDwAPQNBUdTbb+Px7LhnXOknmy8szyksKKdcQa8lhqTyP4zAQf+ZbbbgsYRkzKwAqCDrJR1p3LNsUEZEUSmVwbAIWm9kCMysCbgHWDSuzDrg9vH0z8KQHx9frgFvMrNjMFgCLgY1j3KaIiKRQypqqwj6LO4GfEgyd/Ya7bzezzwKb3X0d8CDw7bDzu4UgCAjLPU7Q6T0AfMTdBwESbTNV+yAiIqfTCYAiInKa0Ybjaq4qERFJioJDRESSouAQEZGkKDhERCQpOdE5bmbNwCtnufpM4Ng4VicTaJ9zQy7uM+Tmfp/NPs9394TzJ+VEcJwLM9s80siCbKV9zg25uM+Qm/s93vuspioREUmKgkNERJKi4DizB6KuQAS0z7khF/cZcnO/x3Wf1cchIiJJ0RGHiIgkRcEhIiJJUXCMwMxWm9luM9trZndFXZ9UMLO5ZvaUme0ws+1m9vFw+XQz+7mZ/T78f1rUdR1vZpZvZlvM7Ifh/QVmtiF8vR8Lp+3PKmY21czWmtkuM9tpZldm+2ttZv8zfG9vM7NHzKwk215rM/uGmR01s21xyxK+rhb4UrjvL5nZZWfznAqOBMwsH/gKcAOwDLjVzJZFW6uUGAA+6e7LgCuAj4T7eRfwC3dfDPwivJ9tPg7sjLt/P/B5d18EtAJ3RFKr1Poi8BN3XwJcTLD/Wftam1kN8DFgpbsvJ7gUwy1k32v9ELB62LKRXtcbCK5vtJjg0tpfO5snVHAktgrY6+773L0PeBRYE3Gdxp27N7r78+HtDoIPkhqCfX04LPYw8I5oapgaZlYLvB34enjfgGuBtWGRbNznCuBqgmvg4O597t5Glr/WBNccKg2vMDoJaCTLXmt3/xXB9YzijfS6rgG+5YFngalmVpXscyo4EqsBDsXdrw+XZS0zqwMuBTYAs929MXyoCZgdUbVS5QvAnwFD4f0ZQJu7D4T3s/H1XgA0A98Mm+i+bmaTyeLX2t0PA58DDhIERjvwHNn/WsPIr+u4fLYpOAQzmwI8Afypu5+Ifyy8lG/WjNk2sxuBo+7+XNR1mWAFwGXA19z9UqCTYc1SWfhaTyP4hr0AqAYmc3qTTtZLxeuq4EjsMDA37n5tuCzrmFkhQWh8x92/Fy4+Ejt8Df8/GlX9UuANwE1mdoCgCfJagrb/qWFzBmTn610P1Lv7hvD+WoIgyebX+npgv7s3u3s/8D2C1z/bX2sY+XUdl882BUdim4DF4eiLIoIOtXUR12nchW37DwI73f0f4h5aB9we3r4d+MFE1y1V3P1ud6919zqC1/VJd38v8BRwc1gsq/YZwN2bgENmdkG46DpgB1n8WhM0UV1hZpPC93psn7P6tQ6N9LquA/4oHF11BdAe16Q1ZjpzfARm9jaCtvB84Bvufl/EVRp3ZvZG4NfAVl5t7//fBP0cjwPzCKajf7e7D+98y3hm9gfAp9z9RjM7j+AIZDqwBXifu/dGWb/xZmaXEAwIKAL2AR8g+PKYta+1mf0l8B6CEYRbgP9O0KafNa+1mT0C/AHB1OlHgM8A3yfB6xoG6JcJmuy6gA+4++akn1PBISIiyVBTlYiIJEXBISIiSVFwiIhIUhQcIiKSFAWHiIgkRcEhIiJJUXCIpIHwhCz9PUpG0BtVJCJmVhde8+VbwDZeOxWESNrSCYAiEQlnJN4HXBVOcS2SEXTEIRKtVxQakmkUHCLR6oy6AiLJUnCIiEhSFBwiIpIUdY6LiEhSdMQhIiJJUXCIiEhSFBwiIpIUBYeIiCRFwSEiIklRcIiISFIUHCIikpT/B2KWAE4LW4wyAAAAAElFTkSuQmCC\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}