Neutron_Star_TOV.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/ad0711/neutron-stars/blob/main/Neutron_Star_TOV.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Y29HBYNyjfy5"
      },
      "source": [
        "#Using TOV equations and a Polytropic Equation of State to plot Mass-Radius curve for a typical neutron star.\n",
        "#### Bharath Variar, 2019B5A70930H\n",
        "#### Adit Danewa, 2019B5A71372H\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fqllo3NfjdWI"
      },
      "source": [
        "## Initialization\n",
        "Importing relavant libraries"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "oLDBNRPFeX3z"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import math\n",
        "from scipy.interpolate import interp1d\n",
        "plt.style.use('seaborn-whitegrid')\n",
        "plt.rcParams[\"figure.autolayout\"] = True\n",
        "plt.inline = True\n",
        "PI = math.pi\n",
        "E = math.e\n",
        "km = 6.7426e-1 # 1 km -> M.\n",
        "kg = 5.02785e-31 # 1 kg -> M.\n",
        "mevfm = 2.9092e-6 # 1 MeV/fm^3 -> M.^-2\n",
        "mev = 8.896e-61 # 1 MeV -> M. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9N3X0uqnjatI"
      },
      "source": [
        "##Equation of State\n",
        "Using a polytropic Equation of State (EOS) to find pressure ($p(r))$) from energy density ($ϵ(r)$) using two parameteres $(Κ, γ)$ \\\\\n",
        "\n",
        "$$ p(r) = Κϵ(r)^γ $$\n",
        "\n",
        "Using $Κ = 0.00119224$ and $γ = 1.82059886$\n",
        "\n",
        "$ 1 \\ MeV/fm^3  = 2.9092 × 10^{-6} M_\\odot ^ {-2} $ \\\n",
        "$ 1 \\ km = 6.7426 × 10^{-1} M_\\odot $"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ZGG3rMbFehKg"
      },
      "outputs": [],
      "source": [
        "def EOS(p, K_inv = 838.75729718, gamma_inv = 0.54926981):\n",
        "    '''\n",
        "    Arguments: p (in mev/fm^3)\n",
        "    Returns: epsilon (in MeV/fm^3)\n",
        "    '''\n",
        "    epsilon = np.power(p * K_inv, gamma_inv)\n",
        "    return epsilon\n",
        "\n",
        "def EOS2(epsilon,K = 0.00119224, gamma = 1.82059886):\n",
        "    '''\n",
        "    Arguments: epsilon (in MeV/fm^3)\n",
        "    Returns: p (in MeV/fm^3)\n",
        "    '''\n",
        "    p = K * np.power(epsilon, gamma)\n",
        "    return p"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YH3pmEQBipS-"
      },
      "source": [
        "## The TOV Differential Equations\n",
        "Now that we have the pressure, we will use it to solve the Tolman-Oppenheimer-Volkoff (TOV) equations to find equilibrium conditions of non-rotating stars in General Relativity.\n",
        "The TOV equtations are:\n",
        "$$ \\frac{dM(r)}{dr} = \\frac{4\\pi r^2 \\epsilon (r)}{c^2} $$\n",
        "$$ \\frac{dp(r)}{dr} = -\\frac{G\\epsilon (r)M(r)}{c^2 r^2}\\left(1 + \\frac{p(r)}{\\epsilon (r)}\\right)\\left(\\frac{1 + 4\\pi r^3 p(r)}{M(r)c^2}\\right){\\left(1 - \\frac{2GM(r)}{c^2 r}\\right)}^{-1}  $$\n",
        "\n",
        "Using $G = c = M_{\\odot} = 1$ the pressure equation can be simplified to:\n",
        "\n",
        "$$ \\frac{dM(r)}{dr} = {4\\pi r^2 \\epsilon (r)} $$\n",
        "\n",
        "$$ \\frac{dp(r)}{dr} = -\\frac{(\\epsilon (r) + p(r))(M(r) + 4\\pi r^3p(r))}{r(r - 2M(r))}$$\n",
        "\n",
        "We use initial energy density $$ϵ = 463.27 \\ MeV/fm^3$$ and boundary condition for pressure $$p(r = R) = 0$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "NOZ0TFwVe_4l"
      },
      "outputs": [],
      "source": [
        "def TOV(r, y_array):\n",
        "    '''\n",
        "    input: r, y_array (p0, m0)\n",
        "    output: values after applying differential equation on y_array\n",
        "    '''\n",
        "    p0, m0 = y_array\n",
        "    p0 = p0*(1/mevfm) # P in M.^-2 to MeV/fm^3 for EOS\n",
        "    epsilon = EOS(p0)\n",
        "    epsilon *= mevfm # Converting epsilon from MeV/fm^3 to M.^-2\n",
        "    p0 *= mevfm # Reconverting p0 from from MeV/fm^3 to M.^-2\n",
        "    dy0 = -(epsilon+p0)*(m0 + 4*PI*p0*(r**3))/(r*(r-2*m0))\n",
        "    dy1 = 4*PI*(r**2)*epsilon\n",
        "    return np.array([dy0,dy1])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 314
        },
        "id": "HaGep9UCfC_x",
        "outputId": "02fb716e-7b6e-48bc-f768-f65b3d4c8b31"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f501a632350>]"
            ]
          },
          "metadata": {},
          "execution_count": 4
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "p_min = 1.0e-8 # Min. Pressure in MeV/fm^3\n",
        "p_max = 2000 # Max Pressure in MeV/fm^3\n",
        "num_points = 1200 # number of points to divide array into\n",
        "pres_array = np.linspace(p_min, p_max, 1200) # Pressure array in MeV\n",
        "epsilon_array = np.array([EOS(pres) for pres in pres_array])\n",
        "plt.plot(epsilon_array, pres_array, 'r--')"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Fourth Order Runge-Kutta Method\n",
        "To solve equations of the form\n",
        "$$\\frac{dy}{dx} = f(x, y) \\nonumber $$\n",
        "with initial condition $y(0) = y_{0}$, we use the fourth order Runge-Kutta method by defining the following variables: \n",
        "\\begin{align}\n",
        "    k_{1} &= hf(x_i, y_i) \\nonumber \\\\\n",
        "    k_{2} &= hf(x_i + \\frac{h}{2}, y_i + \\frac{k_1}{2}) \\nonumber \\\\\n",
        "    k_{3} &= hf(x_i + \\frac{h}{2}, y_i + \\frac{k_2}{2}) \\nonumber \\\\\n",
        "    k_{4} &= hf(x_i + h, y_i + k_3) \\nonumber\n",
        "\\end{align}\n",
        "For a given range of $x$ and step size, $h$, $[x0, x]$, we divide the interval into $\\{x_0, x_1, \\dots, x_i, \\dots, x\\}$ where $x_{i+1} = x_{i} + h$.\n",
        "The solution is then given by: \n",
        "\\begin{equation}\n",
        "    y_{i+1} = y_{i} + \\frac{k_1}{6} + \\frac{k_2}{3} + \\frac{k_3}{3} + \\frac{k_4}{6} + O(h^5)\n",
        "\\end{equation}"
      ],
      "metadata": {
        "id": "WodXoupom-74"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "_YfAyMcUgLe_"
      },
      "outputs": [],
      "source": [
        "def rungeKutta4(funct, y0, x_min, x_max, n):\n",
        "\n",
        "    # Count number of iterations using step size or use fixed number of points.\n",
        "    # step height h\n",
        "    # y0 are the initial conditions.\n",
        "    rad_arr = np.linspace(x_min, x_max, n+1)\n",
        "    y = np.array((n+1)*[y0])\n",
        "    h = rad_arr[1] - rad_arr[0]\n",
        "    # Iterate for number of iterations\n",
        "    for i in range(n):\n",
        "        # \"Apply Runge Kutta Formulas to find next value of y\"\n",
        "        k1 = h * funct(rad_arr[i], y[i])\n",
        "        k2 = h * funct(rad_arr[i] + 0.5 * h, y[i] + 0.5 * k1)\n",
        "        k3 = h * funct(rad_arr[i] + 0.5 * h, y[i] + 0.5 * k2)\n",
        "        k4 = h * funct(rad_arr[i] + h, y[i] + k3) \n",
        "        \n",
        "        # Update next value of y\n",
        "        y[i+1] = y[i] + (1.0 / 6.0)*(k1 + 2 * k2 + 2 * k3 + k4)\n",
        "\n",
        "        # check stop condition\n",
        "        if(y[i][0] <= 1.0e-13):\n",
        "            return rad_arr[:i], y[:i],\n",
        "            break\n",
        "        \n",
        "    return rad_arr, y"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "JwRCZKEtqj7z",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "35a661c8-b023-49fd-b350-2dcde85c11b6"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:6: RuntimeWarning: invalid value encountered in power\n",
            "  \n"
          ]
        }
      ],
      "source": [
        "p_min = 1.0e-8 \n",
        "p_max = 2000\n",
        "r_min = 0.01 # minimum radius in M.\n",
        "r_max = 30 * km # max radius in M.\n",
        "mass_arr = np.zeros(num_points)\n",
        "rad_arr = np.zeros(num_points) \n",
        "epsilon_init = 463.27 # MeV/fm^3\n",
        "m0 = (4/3)*PI*(r_min**3) * epsilon_init * mevfm # Mass in M.\n",
        "p0 = EOS2(epsilon_init) * mevfm # initial pressure in M.^-2\n",
        "y0 = (p0,m0) # (MeV, MeV/fm^3)\n",
        "rad_arr, y = rungeKutta4(TOV, y0, r_min, r_max, num_points)\n",
        "p_arr, m_arr = y.T"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Edpz4mjKHwCD"
      },
      "source": [
        "## Visualisation"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "F8APScfTIKcG"
      },
      "source": [
        "### For a single star"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 211
        },
        "id": "fF8EbzCUBzVU",
        "outputId": "eabba7b8-ca77-477b-fbe5-3e2ee2ce9be3"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1152x360 with 2 Axes>"
            ],
            "image/png": 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wgIEDB1KvXj3rKPRHPdpGD/tP0dHRSX4vdnZ21gTTo27fvs2XX37JhAkTAMuUrb8nwuDp+nL/1A9V/0mMpASPyDMKDAxk4sSJODs7W0d5PLR+/Xp++uknFi5ciIuLCz/88ANr1qwBIEeOHHTr1o1u3bpx+vRp3n33XSpXrkyNGjWS3f5P83abN2/OnDlz2LRpE76+vly5coUhQ4awbNkyPDw8OHPmDH5+foDlBvvofO4bN24ke85Hp1VFR0cn2RcUFERQUBBXrlzhww8/ZOXKlbRs2dK638nJiZiYGOv3h3Ou/27AgAF07NiR1q1bYzKZrE9oHB0dk7zN4klvjHhSO6eGF154gZs3b1oXIr558yYvvPDCP5ZzcHCgX79+9OvXj0OHDvHuu+9SvXr1p7rm3+uf3EgjV1dXHBwcnmrBxddee43JkycTFxfHrFmzGDp0KEuXLk1yzPDhwylbtixTp07F1taWoKCgp4pVRESyvkcXJX4SV1dXSpQoQUhISLL7n6XvY2NjkySJ8Pe+yN+vO3XqVEqVKvXYvie92MHFxYX27dszduxYvv32WyDl++HD/1GPiYkhb9681gdSf/ekuJ/mfvz3flpUVBTFihVLcsz8+fM5c+YMISEhODg4MHHiROuIGgcHhyR9iMjISIoXL/5YnA8ePKBPnz58/fXXeHl5pZjkeF4P+08PPW3/CbCOUL958yaDBg1i9uzZT9WHcnR0xGw2c+/ePXLnzk18fHyyfVBXV1e6dOlC3bp1n3i+p+nLpXU/VOTf0Nh7kWdUsWJFrl69yvHjxx8bQnv9+nVefPFFXFxcuHHjBhs2bODOnTuAZX2ch8NUixcvzgsvvIDJZEpx+z/JkSMHH374IePGjePBgwdERUWRJ08eSpQoQXx8vHUx4Tt37lCxYkX2799PVFQUCQkJrF69OtlzFixYkD///BOAFStWWIdBT506leXLlwOWp0Jubm6PxVi8eHFsbW2tT5ZCQkKSrcf169d5/fXXMZlM/Pjjj9y7d4+7d+/y8ssvEx8fby2/ZMmSFNvhSe2cGurUqWNtv6ioKDZt2pTitKxHde/e3bp4YqlSpXB0dHyq3yVYnl7t3r2bqKgo4uLiWLly5WPHvPjiixQuXNia4ImKiqJfv36Pveb16NGj9OrVi7i4OOzt7a3tDZa/m4edyOvXr+Ph4YGtrS07d+7kr7/+eq5XxoqISPZVvnx5IiMjOXjwIADnzp1jwIABmM3mZ+77uLq6cuzYMRITE4mKiuJ///tfitd9+NICsKwPNGrUKI4cOfJUMXfu3JkDBw6wZ88eIOX7Ya5cuShTpoz1BRvr1q3j/v37j53v0f7TuXPnrC8neNL9+FEVKlRg8+bNAJw9e5b9+/c/dsz169cpUaIEDg4OXLhwgW3btlnv2eXKlbP2DSIiIqwjwP/uYZ/r9ddfByxJIzs7u1S799epU4dNmzZZHyQuXbrUOvX+SVasWMHUqVMByyjpEiVKPPU1HRwcKFmypHXh5uDg4GTb2Nvbm2XLlpGQkIDZbGbatGnJ/n2l1Jf7e/8pLfuhIv+GEjwiz8hkMuHr60v16tUfW5+kYcOG3Lx5E19fX/r370+fPn24fPkyo0ePJigoiIkTJ1qHBVesWBFPT88Utz+Nhg0bkjNnTpYuXUqZMmWoXbs2fn5+tGrVinr16lGhQgXat2+Ph4cHQUFBNG3alLfffjvFRXP79u3LsGHDaNy4Mblz57YOSW7cuDGrVq3Cz88Pf39/7OzsaNy4cZKydnZ2jBgxgkGDBhEQEIDJZLJOjXpU79696dmzJ40aNeLu3bu0atWKzz77jMuXLzNs2DA+/fRTGjdujLu7OzY2NsnepJ/UzqmhT58+3Lp1y7p4YLdu3Z7qCVe7du3o378/AQEBNG3alDZt2jz1HOxy5crRtGlTmjZtSocOHZJ9wmQymZgwYQKLFi2yxubp6flYO5cqVQo3NzcaNmxIgwYN+Oabb6xvIfHz86Nfv37MnTuXHj168NVXX9GwYUP27NnDBx98wJQpU5LtWIqIiCQnV65cTJ48mREjRhAQEEDPnj3x9/fHZDI9c9/H39+fPHny4OPjw8cff5xk2tff9enTh9u3b+Pn50eDBg1ITEx8bOpTShwdHenWrRtfffUVZrP5iffDYcOGMXPmTPz8/Dh06BAlS5Z87HwtW7bkwoUL1K9fn/Hjx1tHUD/pfvyo9957jwsXLlCvXj1GjBhB/fr1HzsmKCiIvXv34ufnx1dffcUnn3xCeHg48+bNo0ePHpw+fRpfX1/mzJmDt7d3sv2nfPny8c4779CkSROaNGlC8eLF8fHxoXv37qmS5ClXrhzdunWjbdu2+Pv7c/v27ad6Db23t7f1TVgBAQGcOHGCzp07P/V1hw4dyvTp02nQoAF3796lUKFCj9W/TZs2FC1alAYNGuDv78/JkyepXLnyY+dKqS9Xo0YNfvnlF5o1a5bm/VCRf8NkTm4VKhERg929e5eKFSuyb9++JHOuszKz2WztkPz88898/fXXyY7kEREREXnUo32IXr16UblyZTp27GhwVOnn0fq/+eabzJs3jzJlyhgclUj60wgeEckwmjVrxvr16wHL/OaSJUtmm+ROVFQUb775JhcuXMBsNrNhwwYqVKhgdFgiIiKSwS1cuJAePXqQmJjI9evX2bNnj/UV8NlBr169mDlzJmB5FbvZbNZbrCTb0ggeEckw9u3bx/Dhw7l//z4ODg4MGzYsVRf/y+iWLFnCnDlzMJlMlChRgpEjRyb7JggRERGRh+7cucOnn37KH3/8gY2NDc2bN6dbt25Gh5VuTp48yaeffkp0dDR2dnYMGDDgqdb+EcmKlOAREREREREREcnkNEVLRERERERERCSTy2F0AE9Lb3URERHJvpJ720l2p76RiIhI9pVc3yjTJHgg7Tp3EREReHh4pMm5Mwu1gdogu9cf1AagNsju9YeM2QZKZKRMfaO0kd3rD2oDUBtk9/qD2gDUBpAx2yClvpGmaImIiIiIiIiIZHJK8IiIiIiIiIiIZHJK8IiIiIiIiIiIZHJK8IiIiIiIiIiIZHJK8IiIiIiIiIiIZHJK8IiIiIiIiIiIZHKZ6jXpIiIiIulp1KhRHDx4EJPJxKBBgyhXrpx1365du5gwYQK2trbUrl2bnj17pljm0qVLfPzxxyQkJFCwYEHGjh2Lvb0969evZ86cOdjY2ODp6Unfvn0JCQlh0qRJFC9eHIDq1avTo0cPQ+ovIiIimYcSPCIiIiLJ2LNnD3/99RfBwcGcPHmSQYMGERwcbN3/xRdfMHv2bAoVKkS7du3w8/MjKioq2TKTJ0+mTZs2BAQEMGHCBJYvX07Tpk0ZN24cq1evxsHBgZYtW9KoUSMAAgMDGThwoFFVFxERkUxIU7REREREkhEeHo6Pjw8AJUuWJDo6mpiYGADOnTuHk5MTRYoUwcbGBi8vL8LDw1Mss3v3bry9vQGoW7cu4eHh5M6dm9WrV+Po6IjJZCJ//vzcvHnTmMqKiIhIpqcRPCIiIiLJuHbtGmXLlrV+d3FxITIyEkdHRyIjI3FxcUmy79y5c9y4cSPZMvfu3cPe3h6AAgUKEBkZCYCjoyMAR48e5cKFC5QvX56zZ8+yZ88eunbtSnx8PAMHDuS1115LNsaIiIhUrzdAbGxsmp07M8ju9Qe1AagNsnv9QW0AagPIXG2gBI+IiIg8s0RzIgmJCSSaEzFjJleOXEaHlObMZnOqlPn7tjNnzvDRRx8xfvx47OzsKF++PC4uLtSpU4cDBw4wcOBA1qxZk+z5PTw8njmmpxFx8CAeZcqAyZQm58/oIiIi0qxtMwu1gdogu9cf1AagNoCM2Qb79+9PdrsSPCIiItnQ/fj7XIq5xMXbF7lw6wKXYy5zI/YGJy6cwHTUxI17N7gRe4Nb928RGx9r/dx7cI/Y+FgeJD5Icr7vGn7Hu5XfNag2acPV1ZVr165Zv1+9epWCBQsmu+/KlSu4urpiZ2eXbJk8efIQGxtLrly5rMcCXL58mZ49ezJmzBhr57FkyZKULFkSgIoVKxIVFUVCQgK2trZpXmcAhg/HY+hQy8/29pZPrlzg7AwuLlCggOVTqBAULw4vvfT//+nsnD4xioiIyGOU4BEREcmCzGYzl2Iucfz6cU5EneB41HGORx3n1I1TnL91nmt3ryVbziGHAwUcCuCcyxnn3M68nP9lcufITW673OSyzUWuHJZPzhw5yWGTAxuTDTlscuD/in861zDt1ahRgylTphAUFMSRI0dwdXW1Tqlyc3MjJiaG8+fPU7hwYbZu3cq4ceO4ceNGsmWqV69OWFgYjRs3ZuPGjdSqVQuAwYMHM2zYsCTTumbOnEmRIkVo2LAhx44dw8XFJf2SOwCtWnE1KgpXJye4f9/yiY2FGzcgKgouX4YjRyz/vH8/admCBeG11yyfsmXh9dehcmX4v3YTERGRtKMEj4iISCZ3+/5tDl89zMHLBzl05RAHrxzk8NXDxMTFWI+xs7GjhHMJSrqUpGrRqryY70VezPsiRfMW5cV8L1LYsTDOuZw5cexEhhuGbJRKlSpRtmxZgoKCMJlMDB06lJCQEPLmzYuvry/Dhg2jf//+gOWtV+7u7ri7uz9WBuDDDz9k4MCBBAcHU7RoUZo0acLp06fZt28fkydPtl6zU6dONGrUiAEDBrB06VLi4+MZOXJk+la8dGmuv/cerv/0d2A2Q2Qk/PUXnD0LZ87An39akj+LF0N0tOU4Gxvw8ICqVS2fWrUsCaBsOv1LREQkrSjBIyIikokkJCbwR+Qf7Dq3i/Dz4YSfD+fY9WPW/flz5adcoXJ0Kt8Jj4IevOLyCq+6vEoxp2LksNFt/1l99NFHSb6XKVPG+nOVKlWSvDY9pTJgmdI1d+7cJNvc3d05ePBgstddsGDB84SbvkwmcHW1fKpUSbrPbIZLl+DAAdi7F/bsgdWr4WEbuLpC3bqWj48P/N+UNBEREXl+6umJiIhkYPGJ8ey9sJfNpzaz/ex2fjn/C7fjbgPg6uCKp5sn7cu1p3yh8pQvXJ5i+Yph0sgIMZrJBEWLWj4NGli2mc1w6hT8/DNs3Wr5PEyQlSkDb70FjRqBpyek55Q0ERGRLEIJHhERkQzEbDZz9PpRNp/azOZTm9l6Ziu37t/ChIlyhcrRrlw7qherjqebJyWcSyiZI5mHyWQZqVOyJHTtakn4HD8OoaGwZg1MmABjxsALL1iSQkFBltE9OdRdFREReRq6Y4qIiBgsPjGeHWd3sOrPVaw6uorTN08DUMK5BEFlg/Ap4UM993oUyFPA4EhFUpHJBKVKWT69elnW7AkLs0zlWrkS5s+3LNrcqhW0bQvVqmndHhERkSdQgkdERMQAdx/cJfREKCv/XMm64+uIuhdFTtuceJfw5uMaH1O/ZH1KOJcwOkyR9OPkBC1bWj7378P69ZbFmmfOhG++gRIloEsXy6dIEaOjFRERyXCU4BEREUkn8YnxbDm1hcW/LyYkIoSYuBiccznTsFRDGpdujN8rfjja63XSIuTMCU2bWj7R0fDjj/D99zBkCAwbBo0bw3vvgbe35S1dIiIiogSPiIhIWjKbzey+sJtFhxbxwx8/cPXOVZxyOtGqbCtav94ar5e99HYrkSdxcoJOnSyfY8fgu+9g3jxYscKynk/PnvDOO5A3r8GBioiIGEs9ShERkTRw/e51FhxawMxfZ/JH5B/ktM1Jo9KNaPN6GwJfDSRnjpxGhyiS+ZQqBePGwRdfQEgIfPst9OtnGdXz3nuWtXzc3IyOUkRExBBK8IiIiKQSs9nM//76H9/9+h0r/ljB/YT7VH2xKjMbzaTFay1wyuVkdIgiWUOuXNCmjeWzdy+MH2/5TJxoWZT544+hXDmjoxQREUlXmrQsIiLyL92Ju8O3e7/FY6oHdebXYd2xdbxb6V0Odj/I7nd2806ld5TcEUkrVarA0qVw8iR88AGsWgXly0OzZnDwoNHRiYiIpBsleERERJ7TuehzDNw0ELeJbry//n3y5czHvMbzuNj/IlMCp1CukEYQiKSbl1+2jOA5exY+/xw2b4YKFZToERGRbEMJHhERkWe098JegpYH4T7JnXHh41bEQvoAACAASURBVPAt4cvOLjvZ/c5uOlboSB67PEaHKJJ9OTvDf/8LZ87A0KGwZYsl0dO8ORw9anR0IiIiaUYJHhERkadgNpvZdmYbvgt8qTqrKqEnQun7Zl9O9TrFDy1+oHqx6phMJqPDFJGHnJ0tiy8/TPSEhUHZstCjB1y+bHR0IiIiqU4JHhERkScwm81sOL6BWnNrUWd+HQ5fOcwYnzGc63uOsfXH8lL+l4wOUUSeJH9+S6Ln5ElLcmfWLHjlFcu2mBijoxMREUk1SvCIiIgkw2w2s/roat6Y+QaBiwM5G32WbwK+4XTv0wyoMYC8OfMaHaKIPAtXV5gyBf74AwIDLdO4XnkF5s+HxESjoxMREfnXlOARERH5m59O/4TnbE8aL23Mrfu3mP3WbE70OkHPqj3JbZfb6PBE5N949VX44Qf45Rdwd4dOnaBGDdi/3+jIRERE/hUleERERP7PwesH8fneB+/vvbl4+yKzGs0iomcEXSp2wd7W3ujwRCQ1VasGO3fCvHlw+rTldevdukFkpNGRiYiIPBcleEREJNuLiIygydImtN7SmkNXDvG139cc+/AYXSt1JYdNDqPDE5G0YmMDHTta3q7Vty/MnQulSpF/2TJN2xIRkUxHCR4REcm2rt29xgfrP+A/3/6HrWe20uv1XpzsdZLeb/YmV45cRocnIunFyQnGj4dDh6B8eYoMHQp16+q16iIikqkowSMiItlOXEIcE8In8MrkV5i+bzrvVX6PEx+eoPtr3bV4skh25uEBW7dyccQIS7KnXDkYMQLi4oyOTERE5B8pwSMiItmG2Wxm5Z8rKTutLP039sezmCeHehxiaoOpFHQoaHR4IpIRmExEN2sGERHQtCl8/jlUqgTh4UZHJiIi8kRK8IiISLZwIuoEAYsCaBrcFDsbOza03cCGtht4reBrRocmIhlR4cKwdCmsXQu3blnetDVgAMTGGh2ZiIhIspTgERGRLC02PpZhPw/j9Wmvs+vcLr72+5pDPQ7h/4q/0aGJSGbQoAEcOWJ5w9a4cfDGG/Drr0ZHJSIi8ph0S/CMGTOGVq1a0axZMzZu3Jhk365du2jevDmtWrVi6tSp6RWSiIhkcaEnQnl92uv8d9t/edvjbY5+cJTeb/bWm7FE5NnkzQvTp8OGDXDjhuUV68OHw4MHRkcmIiJilS4Jnl9++YXjx48THBzMrFmzGDVqVJL9X3zxBVOmTGHJkiXs3LmTEydOpEdYIiKSRZ2/dZ4Wy1oQsCiAHDY52Nx+M4ubLaZI3iJGhyYimZm/P/z+O7RqBUOHQvXqlrV6REREMoB0SfBUqVKFSZMmAZAvXz7u3btHQkICAOfOncPJyYkiRYpgY2ODl5cX4VrETkREnkOiOZEZ+2bw2tTXWHtsLV/U/YKD3Q/iXcLb6NBEJKtwdoaFC2HZMjh9GipXhu++A7PZ6MhERCSbS5cx6ra2tuTJkweA5cuXU7t2bWxtbQGIjIzExcXFeqyLiwvnzp1L9jwRafSEJDY2Ns3OnVmoDdQG2b3+oDaAzN0GZ2POMnTfUHZf3U0112oMf2M4xRyLcer4qac+R2auf2pRG4g8pebNoWZN6NgR3nsPNm6EmTMtCSAREREDpOsiBJs3b2b58uXMmTPnucp7eHikckQWERERaXbuzEJtoDbI7vUHtQFkzjZISExgyp4pDNoyCDtbO75r+B3vVHoHk8n0zOfKjPVPbRmxDfbv3290CCLJK1zYsi7PhAnw6aewZw8sXmxJ/IiIiKSzdFtkefv27UyfPp2ZM2eSN29e63ZXV1euXbtm/X7lyhVcXV3TKywREcnEIiIjqDW3Fn3D+lLPvR5H3j/Cu5Xffa7kjojIc7GxgY8+gl27wN4evLwsCzD/33IEIiIi6SVdEjy3b99mzJgxzJgxg/z58yfZ5+bmRkxMDOfPnyc+Pp6tW7dSo0aN9AhLREQyqURzIhPCJ1BhRgWOXj/KwqYLWdN6DW753IwOTUSyqypV4MABaNPGsgCzjw9cuWJ0VCIiko2kyxSt9evXc+PGDfr06WPdVq1aNUqXLo2vry/Dhg2jf//+AAQGBuLu7p4eYYmISCZ0NvosnVZ2YuuZrTQu3ZgZDWdQyLGQ0WGJiFhep75ggSW506MHVKwIP/ygKVsiIpIu0iXB06pVK1q1apXi/ipVqhAcHJweoYiISCZlNptZfHgxPdf3JMGcwOy3ZtO5QmdNxxKRjKdjR0typ1kzqFMHxo6FPn1A/70SEZE0lG5r8IiIiDyvqHtRtF7RmnY/tqOsa1kOdj9Il4pdlNwRkYyrXDnYtw8aNYJ+/aBlS7h1y+ioREQkC1OCR0REMrQtp7ZQ7ttyrIhYwch6I/lfp/9RwrmE0WGJiPwzJycICbGM4PnxR8s6Pb//bnRUIiKSRSnBIyIiGVJ8YjxDfhqC7wJf8ubMyy9df2FQrUHY2tgaHZqIyNMzmSxv2dqyBaKjoVo1WLbM6KhERCQLUoJHREQynHPR56gzrw4jt4+kS8Uu7Ht3H5WLVjY6LBGR5+flZXnLVvnylulan38OiYlGRyUiIlmIEjwiIpKhrD66mgozKnDwykEWvb2IWW/NwsHeweiwRET+vSJFYOtW6NwZRoywLMJ8+7bRUYmISBahBI+IiGQI9+Pv0ye0D42XNubl/C/za7dfafOfNkaHJSKSunLmhNmz4euvYc0a8PSEU6eMjkpERLIAJXhERMRwp2+cpsacGkzaPYleVXuxq8suXi3wqtFhiYikDZMJeveG0FC4eNGy+PJPPxkdlYiIZHJK8IiIiKE2HN9A5e8qcyLqBD+2+pFJAZPImSOn0WGJiKQ9Hx/YswcKF4b69WHaNKMjEhGRTEwJHhERMUSiOZHh24bTYHEDijsVZ3+3/TQp08TosERE0tcrr0B4OAQEQM+e0K8fJCQYHZWIiGRCOYwOQEREsp8b927Q7sd2rD++nvbl2jO94XTy2OUxOiwREWPkywcrV1qSOxMnWtbkWbQIHLTAvIiIPD0leEREJF0duHSAZj804/yt80wLnEb3N7pjMpmMDktExFi2tjBpEpQsCX37Wl6rvmaN5c1bIiIiT0FTtEREJN3M/20+1edUJy4hjv91/h89qvRQckdE5FG9ellG80REQLVqcPiw0RGJiEgmoQSPiIikufjEeHpt6EWnVZ3wdPPk1/d+5U23N40OS0QkY2rUCLZvh/h4qFEDwsKMjkhERDIBJXhERCRNRd2LImBRAFP2TKHvm33Z2H4jrg6uRoclIpKxVaoEu3fDyy9DgwYwc6bREYmISAanNXhERCTNRERG8NbStzgbfZY5b82hc8XORock8kxGjRrFwYMHMZlMDBo0iHLlyln37dq1iwkTJmBra0vt2rXp2bNnimUuXbrExx9/TEJCAgULFmTs2LHY29uzfv165syZg42NDZ6envTt25cHDx7wySefcPHiRWxtbfnyyy8pVqyYUU0gRipWDHbsgJYtoVs3uHQJPvsMNLVVRESSoRE8IiKSJtYdW0e1WdW4ff82WztuVXJHMp09e/bw119/ERwczMiRIxk5cmSS/V988QVTpkxhyZIl7Ny5kxMnTqRYZvLkybRp04bFixfz0ksvsXz5cu7du8e4ceOYN28ewcHB7Nq1ixMnTrB27Vry5cvHkiVL6N69O+PHjzei+pJR5MtnWWy5Y0cYOhTef1+vURcRkWQpwSMiIqnKbDYzZucYGi1pxCsur7D33b1UL1bd6LBEnll4eDg+Pj4AlCxZkujoaGJiYgA4d+4cTk5OFClSBBsbG7y8vAgPD0+xzO7du/H29gagbt26hIeHkzt3blavXo2joyMmk4n8+fNz8+ZNwsPD8fX1BaB69er8+uuvBtReMhQ7O5g7FwYOhOnToUULiI01OioREclgNEVLRERSTWx8LN3WdGPBoQW0LNuSuY3nkscuj9FhiTyXa9euUbZsWet3FxcXIiMjcXR0JDIyEhcXlyT7zp07x40bN5Itc+/ePezt7QEoUKAAkZGRADg6OgJw9OhRLly4QPny5Zk2bZr13DY2NphMJuLi4qzlHxUREZH6FQdiY2PT7NyZQYatf8eOOJtMFB49mrs1a3Ju6lQS8+VLk0tl2DZIR9m9DbJ7/UFtAGoDyFxtoASPiIikimt3r9F4aWN2ndvFiLojGFxrsF6BLlmK2WxOlTJ/33bmzBk++ugjxo8fj52d3TNd18PD45ljehoRERFpdu7MIEPX/8svoXx58nToQOl33oHQUHjxxVS/TIZug3SS3dsgu9cf1AagNoCM2Qb79+9PdrumaImIyL927Pox3pz1Jvsv7ueH5j8wpPYQJXck03N1deXatWvW71evXqVgwYLJ7rty5Qqurq4plsmTJw+x/zel5uGxAJcvX6Znz56MHj3a2nl0dXW1jvB58OABZrM52dE7ko0FBcH69XDmDFSvDpnkybKIiKQtJXhERORf2f7Xdjxne3Lr/i22dtxKi7ItjA5JJFXUqFGDsLAwAI4cOYKrq6t1SpWbmxsxMTGcP3+e+Ph4tm7dSo0aNVIsU716dev2jRs3UqtWLQAGDx7MsGHDkkzrqlGjBqGhoQBs3bqVatWqpVudJRPx8YFt2yxr8dSqBSk8zRURkexDU7REROS5LT68mM6rOuOe3531bddTwrmE0SGJpJpKlSpRtmxZgoKCMJlMDB06lJCQEPLmzYuvry/Dhg2jf//+AAQGBuLu7o67u/tjZQA+/PBDBg4cSHBwMEWLFqVJkyacPn2affv2MXnyZOs1O3XqRGBgILt27aJ169bY29szevRoQ+ovmUClSrBzpyXZU7curF0LtWsbHZWIiBhECR4REXlmZrOZkdtH8tnWz/B6yYuQViG45Hb554IimcxHH32U5HuZMmWsP1epUoXg4OB/LAOWaVdz585Nss3d3Z2DBw8me90vv/zyecKV7OiVV2DHDvD1BT8/+PFH8Pc3OioRETGApmiJiMgziUuIo8vqLny29TPal2vPxvYbldwRETGSmxv873/g4QFvvQXLlxsdkYiIGEAJHhEReWrRsdEELApg3m/zGOY1jPlN5mNvq8VfRUQMV7Ag/PQTVK0KrVrB30aMiYhI1qcpWiIi8lQu3r5IwKIAIiIj+L7J97Qv397okERE5FH580NYGLz9NnTpArduQe/eRkclIiLpRAkeERH5R0evHcVvoR/X711nXZt1+Jb0NTokERFJjoMDrF4NbdpAnz4QHQ2ffQYmk9GRiYhIGtMULREReaLd53dTY04N7sXf4+eOPyu5IyKS0eXMCcHB0LEjDB0KH38MZrPRUYmISBrTCB4REUnR+uPrabGsBUUcixDWLoySLiWNDklERJ5GjhwwZw44OsK4cfDgAUycqJE8IiJZmBI8IiKSrHm/zeOd1e9QvnB51rdZTyHHQkaHJCIiz8LGBqZMATs7+PpriIuDb76xbBcRkSxHCR4REUnCbDbz1c6v+HTLp/iU8CGkZQh5c+Y1OiwREXkeJhNMmAD29jBmjGUkz4wZSvKIiGRBSvCIiIhVojmRPqF9mLxnMq1fb828JvP0GnQRkczOZILRoy0jeUaOhPh4mDULbG2NjkxERFKREjwiIgJAfGI8g/YMYvVfq+lTrQ/j/cZjY9ITXhGRLMFkgi++sIzkGTrUMpJn3jzLWj0iIpIl6L/oIiJCbHwsrVe0ZvVfqxlRdwSDaw3GpIU4RUSyns8/tyR1Bg+2jORZsMAyskdERDI9JXhERLK5mLgYmixtwpbTWxhUcRBDag8xOiQREUlLgwZZRvIMGGAZybNkieW7iIhkakrwiIhkY1H3omiwuAF7L+xlfpP5VLGvYnRIIiKSHj76yDJyp08faNECli1TkkdEJJPT4goiItnU5ZjL1JlXh18v/crylsvpUL6D0SGJiEh66t0bpk6F1auhZUvLa9RFRCTT0ggeEZFs6MzNM/h878PlmMusa7MOnxI+RockIiJGeP99MJvhgw+gdWtYulRr8oiIZFJK8IiIZDMRkRH4LvDlzoM7bGq/Cc9inkaHJCIiRurZ07Lgcp8+0LYtLF5sdEQiIvIclOAREclGDlw6QP2F9bE12bKt0zbKFSpndEgiIpIR9O4NCQnQvz/Y2FjesiUiIpmKEjwiItnE3gt7qb+wPnnt87KlwxZeLfCq0SGJiEhG0q+fJcnz8ccUjYmBVavA1tboqERE5ClpkWURkWxg17ldeH/vjXMuZ7Z33q7kjoiIJG/AAPjyS5zWrYPOnS0JHxERyRQ0gkdEJIvbdmYbDRY3oGjeovzU8Sfc8rkZHZKIiGRkn3zC1UuXcJ082TKCZ/Zsy7QtERHJ0JTgERHJwjaf2sxbS97i5fwvs6XDForkLWJ0SCIikglc794dVxcXGDbMktyZOVNJHhGRDE4JHhGRLGrD8Q00DW5KqQKl2NxhM64OrkaHJCIimcnnn1vervXFF5aRPNOnK8kjIpKBKcEjIpIFrT66mhbLWlC2YFk2td9EgTwFjA5JREQyG5MJhg+3rMPz5ZeQOzd8/bVlu4iIZDhK8IiIZDHL/1hO6xWtqVSkEqFtQ3HO7Wx0SCIiklmZTDByJNy7Z0nu5MkDo0YpySMikgEpwSMikoUsPryYDj924E23N1nfdj35cuYzOiQREcnsTCaYMMGS5Bk9GhwcYMgQo6MSEZG/UYJHRCSLmP/bfDqv6ozXy16sab0GR3tHo0MSEZGswmSCadPg7l347DNLkqdvX6OjEhGRRyjBIyKSBcz7bR5dVnXBu4Q3q4JWkccuj9EhiYhIVmNjA3PmWEby9OtnWZOne3ejoxIRkf+TrgmeY8eO8f7779OpUyfatWuXZF+9evUoXLgwtra2AIwbN45ChQqlZ3giIpnS/N/m02VVF3xK+LAqaBW57XIbHZKIiGRVOXLAokWWJE+PHpY1eTp0MDoqEREhHRM8d+/eZcSIEXh6eqZ4zMyZM3FwcEivkEREMr3vD35P51WdrSN3lNwREZE0Z28Py5dDw4bQubNlJE+LFkZHJSKS7dmk14Xs7e2ZOXMmrq6u6XVJEZEsbeGhhXRa2Yl67vWU3BERkfSVKxesWgWentCmDaxda3REIiLZXroleHLkyEGuXLmeeMzQoUNp3bo148aNw2w2p1NkIiKZz6JDi+i4siN13euyuvVqrbkjIiLpz8EB1q2DChWgeXPYvNnoiEREsrUMs8hyr169qFWrFk5OTvTs2ZOwsDD8/f2THBMREZEm146NjU2zc2cWagO1QXavP2SeNlj711o+2fMJVQpWYWzFsfx14q9UO3dmaYO0kt3rD2oDEXlGTk4QFgZ16kDjxpafa9Y0OioRkWwpwyR4mjRpYv25du3aHDt27LEEj4eHR5pcOyIiIs3OnVmoDdQG2b3+kDnaYMnhJXyy5xNqv1Sbta3X4mCfuuuWZYY2SEvZvf6QMdtg//79RocgIk/i4gKbNoGXFwQGwk8/wRtvGB2ViEi2k25TtJ7k9u3bdO3albi4OAD27t3Lq6++anBUIiIZS/DvwbT7sR21itdKk+SOiIjIcytUyDJFq0AB8PeHP/4wOiIRkWwn3Ubw/P7773z11VdcuHCBHDlyEBYWRr169XBzc8PX15fatWvTqlUrcubMyWuvvfbY6B0RkezshyM/0DakLTWL12Rdm3VK7oiISMbj5mZJ8tSsCb6+sGMHuLsbHZWISLaRbgme119/nQULFqS4v2PHjnTs2DG9whERyTSWHVlGmxVtqF6supI7IiKSsZUsCRs3WqZr+frC9u1QpIjRUYmIZAsZYoqWiIgkb8UfK2i9ojWexTxZ33Y9jvaORockIiLyZP/5D2zYAJcvQ/36EBVldEQiItmCEjwiIhnUmqNrCFoRxJtub7K+jZI7IiKSiVSrBqtWwbFjloWXY2KMjkhEJMtTgkdEJAPafGozLZa1oGLhiqxvu568OfMaHZKIiMiz8faGpUth3z5o0gTu3zc6IhGRLE0JHhGRDGbn2Z00XtqYUgVKEdoulHw58xkdkoiIyPNp2hTmzIEtW6B1a4iPNzoiEZEsSwkeEZEMZP/F/QQuDsQtnxub2m/CJbeL0SGJiIj8Ox06wKRJ8OOP8M47kJhodEQiIllSur1FS0REnuz3q79Tf2F9nHM5s7n9Zgo5FjI6JBERkdTRqxfcvAlDh0L+/DBxIphMRkclIpKlKMEjIpIBHL9+HN8FvuS0zcmWDlso5lTM6JBERERS12efwY0b8PXX4OxsSfaIiEiqUYJHRMRgZ6PP4rPAh/jEeLZ12kZJl5JGhyQiIpL6TCYYP94ykmfYMMtInt69jY5KRCTLUIJHRMRAl25fwvt7b6Jjo9nacSuvFXzN6JBE5BGjRo3i4MGDmEwmBg0aRLly5az7du3axYQJE7C1taV27dr07NkzxTKXLl3i448/JiEhgYIFCzJ27Fjs7e2Jjo6mX79+ODg4MHnyZABCQkKYNGkSxYsXB6B69er06NEj/SsvkhZsbGDmTLh1C/r0AScn6NTJ6KhERLIEJXhERAxy/e51fBf4cun2JTa130TFIhWNDklEHrFnzx7++usvgoODOXnyJIMGDSI4ONi6/4svvmD27NkUKlSIdu3a4efnR1RUVLJlJk+eTJs2bQgICGDChAksX76cNm3aMHToUCpXrsyff/6Z5NqBgYEMHDgwvasskj5y5IDFi6FRI+jaFfLlg7ffNjoqEZFMT2/REhExQHRsNH4L/TgRdYLVrVfjWczT6JBE5G/Cw8Px8fEBoGTJkkRHRxMTEwPAuXPncHJyokiRItjY2ODl5UV4eHiKZXbv3o23tzcAdevWJTw8HLAkiSpXrmxA7UQMljMnhIRA1aqW16dv3mx0RCIimZ4SPCIi6exO3B0aLG7AwSsHWdFyBfXc6xkdkkiWd/fuXRISEp6pzLVr13B2drZ+d3FxITIyEoDIyEhcXFwe25dSmXv37mFvbw9AgQIFrOdxdHRM9tp79uyha9eudOzYkT/++OOZ4hbJNBwdYf16KF0aGjeGX34xOiIRkUxNU7RERNJRbHwsTYKbEH4+nKXNltKgVAOjQxLJkhITE1m3bh1r1qzh8OHD2NvbExcXh7OzM15eXgQFBfHSSy890znNZvMzx5FcmX86T/ny5XFxcaFOnTocOHCAgQMHsmbNmmSPjYiIeOaYnkZsbGyanTszyO71h/RtA9tvvuHldu2w9fPjrwULuP/qq+ly3X+S3f8Osnv9QW0AagPIXG2gBI+ISDp5kPCAlstasvnUZuY1nkeLsi2MDkkky+rQoQOenp7069ePUqVKYWNjGbR88+ZNdu/ezbhx4/Dx8aFx48YpnsPV1ZVr165Zv1+9epWCBQsmu+/KlSu4urpiZ2eXbJk8efIQGxtLrly5rMempGTJkpQsaXmbXsWKFYmKiiIhIQFbW9vHjvXw8HjKFnk2ERERaXbuzCC71x/SuQ08PGDbNqhZkxLdu8OOHVCiRPpc+wmy+99Bdq8/qA1AbQAZsw3279+f7HZN0RIRSQcJiQm0/7E9a46tYWrgVDpW6Gh0SCJZ2ty5c+nZsydlypSxJncA8ufPj5+fH1OmTCEwMPCJ56hRowZhYWEAHDlyBFdXV+uUKjc3N2JiYjh//jzx8fFs3bqVGjVqpFimevXq1u0bN26kVq1aKV535syZrF27FoBjx47h4uKSbHJHJEtxd4eNG+H+ffD1hUuXjI5IRCTT0QgeEZE0lmhOpNuabgQfCWaMzxjer/K+0SGJZHl2dnb/+phKlSpRtmxZgoKCMJlMDB06lJCQEPLmzYuvry/Dhg2jf//+gOWtV+7u7ri7uz9WBuDDDz9k4MCBBAcHU7RoUZo0aUJCQgKdOnXi1q1bXLlyhfbt2/P+++/TqFEjBgwYwNKlS4mPj2fkyJH/vkFEMoOyZS1r8nh7Q/36llE9j6x1JSIiT6YEj4hIGjKbzfQN7cuc3+bwee3PGVBjgNEhiWR5S5Ys4cCBA3h5ebF69Wq8vLxo06bNc53ro48+SvK9TJky1p+rVKmS5LXpKZUBy5SuuXPnPrZ9wYIFyV43pe0iWV61arByJTRoYPls3gwODkZHJSKSKWiKlohIGhry0xAm75lMvzf7MazOMKPDEckWfvnlF7766itWrVrFjBkz+PPPP40OSUSehY8PLFkCe/bA229bpm2JiMg/UoJHRCSNjNo+ilE7RtGtUjfG1R+HyWQyOiSRbCF//vyYTCaCgoIArK8nF5FM5O23YeZMy7o87dtDQoLREYmIZHiaoiUikgYm757M4J8G0/Y/bZnWYJqSOyLpqEOHDgDUq1cPgPr16xsZjog8ry5d4OZN6N8f8ueHGTNA91MRkRQpwSMikspm/zqb3qG9aVqmKfOazMPWRm+/EUlPD18x/lDFihUNikRE/rV+/SAqCkaOtCy4PHq00RGJiGRYSvCIiKSiJYeX8O6ad/Er6ceSZkvIYaP/zIoYaciQIfz888/Y2tri6upK6dKlKV26NO3btzc6NBF5WiNGWJI8X30Fzs4wcKDREYmIZEj6Pw8RkVSy6s9VtP+xPbVeqkVIqxBy5shpdEgi2d7evXvZtm0btra2XLlyhT///JOjR48aHZaIPAuTCb75Bm7cgE8+sYzkefddo6MSEclwlOAREUkFm05uouXyllQuWpm1rdeSxy6P0SGJCFD+/7F353FR1fsfx1/DpoKKQoJ7IrnhmrsS4gKKqFfNXQE128yl0q6a5VKZ6XWp7Kct7ksaSWYuKeaaC7lnaqamXcM0BXFDRbb5/TFXksQQhTnAvJ+Pxzxmzjlzhvf5dpi+fDzn+61dmytXruDu7o6npyeenp74+/sbHUtEssrODhYuhKtX4YUXwNUVunc3OpWISK6S5Vm0bt68SYpGsRcRSbPj9x10/KIjVR+ryro+6yhSoIjRkUTkK64Z+wAAIABJREFUf3r06EFISAhz585l3759XL9+3ehIIvKwnJwgIgKaNoWQEIiMNDqRiEiukukVPKmpqaxdu5bVq1dz+PBhnJycSExMpHjx4vj7+9OzZ08ef/xxa2QVEcl19p3bR7ul7SjnWo4NIRtwK+RmdCQRucu///1vevToQUpKCkuXLuX48ePcvn2bjRs3Gh1NRB6GszOsWQPNm1umUv/uO0vBR0REMi/whIWF0aRJE4YNG0blypWxs7Nc9HPlyhV2797N1KlTCQgIoGPHjjkeVkQkNzly8QhtlrTBrZAbm8I24VnY0+hIIvI3JUuW5IUXXki3LjEx0aA0IpItihWzXL3z1FPQrh1s2wa1ahmdSkTEcJkWeObPn4+jo+M964sVK0abNm1o06YNSUlJORJORCS3OnnpJAGLAijoUJCNoRspW7Ss0ZFEJAPVqlVj4cKF9O3bN22dk5OTgYlEJFt4elqu3nnqKWjTBnbsAG9vo1OJiBgq0wJPRsWdh3mPiEh+cebKGVotakWKOYUtoVvwdlOHUiS3io2NZdeuXcyePZvq1atTtWpVqlatStu2bY2OJiKPqkIF2LABmjWDwEBLkad0aaNTiYgYJsuDLAMkJyfzyy+/cOXKlezOIyKSq52/fp5Wi1pxPfE634V+R7US1YyOJCIZmDBhAgCTJk1i3bp1bN68maFDh1KhQgV++ukng9OJSLbx8YF16yAmBlq3hrg4oxOJiBgmywWeixcvMmrUKKKjo/n000/57rvvciKXiEiuE3szloDFAfwZ/yfr+qyjTsk6RkcSkfvYt28fAH369AEst2VVr16dzp07M3LkSCOjiUh2a9AAVq2CX3+F4GCIjzc6kYiIIbJc4Jk/fz6vvvoqnp6ejBw5klWrVuVELhGRXOVKwhVaL27N6cunWdN7DY3LNjY6koj8g8aNG9OjRw9iYmKIiIjgyJEjGlxZJD9r0QLCw2HfPujcGW7fNjqRiIjVZbnAk5CQQKFChfjll19yIo+ISK4TnxhPu6XtOHLxCF91/4rmFZobHUlEMjFq1CimTJmCvb09Z8+eZdasWbRv35527drxyiuvGB1PRHJCx44wdy5s3Ai9e0NystGJRESsKtNBlv8uLCyMKVOm0LdvX+bPn0/Tpk1zIpeISK6QkJxAxy868sPZHwjvGk5wpWCjI4nIAzh48CB16tRh/vz5eHl5pa2/ceMGJ0+eNDCZiOSovn3h8mV49VV44QWYMwdMJqNTiYhYRZYLPF5eXowYMYJ9+/bh6+tL5cqVcyKXiIjhklKS6La8G5t/28zCTgvp6tPV6Egi8oBWrlzJ22+/TYUKFfDz88PPz48SJUrg4uJCnToaP0skX3vlFctgy++8A8WLw5QpKvKIiE3IcoEHoHjx4gQGBmZ3FhGRXCMlNYWQr0NYc2INs4JnEVY7zOhIIpIFb731FgCnTp1i+/btjBo1ivj4eBo1aoSfnx9169bF3t7e4JQikmPeestS5Jk2Ddzd4fXXjU4kIpLjMh2DJyoqijhNNygiNiTVnMqzq5/ly6NfMiVwCgMbDDQ6kohk0alTpwDw9vamX79+zJ07l4ULF1KvXj3Wr19Pt27dDE4oIjnKZIIZMyxj8YweDZ9+anQiEZEcl+kVPP3798fd3R2TyUTlypWpXLkyVapUoXLlylSqVAknJydr5BQRsQqz2czL615mwY8LGOc/jteavmZ0JBF5CM8//zwNGzZk6NChlCpVCoCCBQvi7++Pv7+/welExCrs7GDBArh6FQYOhGLFoEcPo1OJiOSYTK/gGTNmDB4eHoSFhTFw4EAqVqzI0aNHmTRpEi1atLBGRhERqzCbzby+6XX+b+//MbzJcMb5jzM6kog8pHXr1uHj40OfPn2YMGGCrkYWsVWOjrB8Ofj5QUgIrF9vdCIRkRyTaYGnT58+LFu2DICJEyfi4ODAG2+8weLFi9m5c2eOBxQRsZZPj33K5J2TebHei0wJnIJJAzKK5FlOTk6Ehoaybt06SpUqRdeuXfnggw+Ij483OpqIWFuhQrBqFdSsCU8/DfobRkTyqUwLPGC5pPn5559n0aJFnDlzhq5du3Lo0KGcziYiYjUf/PABM47MIKRWCDPbzVRxRySfKFCgAAMGDGDNmjUULFiQp59+mrlz5xodS0SszdXVcvVOuXLQrh3obxkRyYcyHYNn7969nD59mtOnT3Pq1Cni4uJwcXHhypUr1sgnIpLjZu+fzauRrxJQJoD5HedjZ3qg2reI5AFnz57l9OnT/Pbbb5w7dw4XFxfef/99BgwYYHQ0EbE2Dw/47jvw9YU2bWD7dqhUyehUIiLZJtMCT2hoKNWqVSM4OJjQ0FDKli1rjVwiIlax9PBSXljzAkFPBDGp9iQc7DL9WhSRPKBDhw5cvHiRUqVKUbFiRSpWrEiTJk0ICQmhQoUKRscTEaOUL28p8vj5QWCg5XatMmWMTiUiki0y/Utm/PjxnDx5km3btjF//nyKFSuWNptW5cqVCQgIsEZOEZFs980v3xD2dRjNHm/GV92/4syvZ4yOJCLZZNasWZQtW1a3W4rIvapWtdyu1aKFpcjz/ffw2GNGpxIReWSZFnh69uyZbvnPP//k+PHjHD9+nMjISBV4RCRP2nBqA90julO/dH1W91qNs6Oz0ZFEJBuVK1cOgP/+97989tlnFCxYkLFjxxqcSkRyjXr1LAMvBwVBcDBs2gRFihidSkTkkWQ60ITZbE63XLJkSfz9/Xn++eeZMmVKhu8REcnNtp/ZTqcvOlHtsWqs67OOIgXUoRPJr0aMGEGbNm3Yu3cvACdOnGDEiBEGpxKRXKF5c/jySzhwADp1goQEoxOJiDySTAs8YWFhLF68mHPnzqVbn5iYSFRUFCNHjuTrr7/OsYAiItlp7x97abe0HeVdy7MhdAPFCxU3OpKI5KDU1FT8/f2xt7cHoHLlypw8edLgVCKSa/zrXzB/PmzeDL16QXKy0YlERB5aprdozZkzh4iICIYNG8bZs2cpWrQoCQkJmM1mfH196du3Lz4+PtbIKiLySH668BNtlrTB3dmdjWEb8XDxMDqSiOQwDw8PoqOj08biMZvNJOhf6UXkbqGhcPkyvPwyPPcczJ0LdppRU0TynkwLPAUKFKBPnz706dOHpKQkLl++TMGCBSlatKg18omIZItfYn8hcHEgzo7ObArbRNmimhFQxBaMHj2aN998k5iYGL766iu2b99OJU2LLCJ/N3SopcgzfjwULw7TphmdSEQky7I0H7CjoyMeHvoXbxHJW05fPk3AIsuA8JvCNlGxeEWDE4mItZQtW5Y5c+awceNGfvnlFxo0aEDXrl2NjiUiudHYsRAXB++/D+7u8PTTRicSEcmSLBV4RETymuir0bRa1IqbSTfZ2m8rVR6rYnQkEbGCqKgoqlSpgpubGw4ODgQFBREUFGR0LBHJzUwmS3Hn8mV4802K374Nb79tdCoRkQeWaYHn7g7Sozpx4gQvvfQS/fr1IyQkJN22Xbt2MX36dOzt7WnWrBmDBg165J8nIrbtQvwFAhYHcOnmJTaFbaKWZy2jI4mIlfTv3x93d3dMJhOVK1emcuXKVKlShcqVK1OpUiWcnJyMjigiuZGdnWUMnitX8JwwAapWhd69jU4lIvJAMi3wZFcH6ebNm7zzzjs0adIkw+0TJkxg7ty5eHp6EhISQps2bXjiiSeydjQiIv9z6eYlAhYHcPbaWSJDImlQpoHRkUTEisaMGUNERARt27blySef5LfffuPo0aOsWLGC06dPs3PnTqMjikhu5egI4eHc9PfHpW9fcHWFdu2MTiUikqlMh4cfM2YMHh4ehIWFMXDgQCpWrMjRo0eZNGkSLVq0eOAf5OTkxOzZszMcwyc6OhpXV1dKlSqFnZ0d/v7+REVFZe1IRET+52rCVdosacPJSydZ1XMVT5V/yuhIImJlffr0YdmyZQBMnDgRBwcH3njjDRYvXqzijohkrlAhzs6cCbVqQdeusH270YlERDKV6RU8ffr0oUuXLixatIiJEycSGhrKG2+8kTbd6AP/IAcHHBwy/nExMTHpbgFzc3MjOjr6nvcdO3YsSz/zQSUkJOTYZ+cVagO1QX45/htJN3j+++c5HHeYj3w/ovTt0g98XPmlDR6FrbeBrR8/5K82KFiwIM8//zy9evVizpw5dO3albFjx1K7dm2jo4lIHpBauDCsXw9+ftC+PWzdCk8+aXQsEZH7eqBBlnNLB6latWo58rnHjh3Lsc/OK9QGaoP8cPy3km7Rfll7DsUd4osuX9Ctercs7Z8f2uBR2Xob2PrxQ+5sg/3792d5n71793L69GlOnz7NqVOniIuLw8XFhStXruRAQhHJt0qUgO++A19faNMGduyAypWNTiUikqFMCzzW6CB5eHgQGxubtnzhwgVNxy4iWZKYkkjX5V3Z8tsWFnZamOXijojkL6GhoVSrVo3g4GBCQ0MpW7as0ZFEJK8qV85S5PHzg8BA+P57ePxxo1OJiNwj0wKPNTpIZcuWJT4+nrNnz1KyZEm2bNnC1KlTs/3niEj+lJyaTO+vevPtyW/5pN0nhNYONTqSiBhs/PjxnDx5km3btjF//nyKFSuWNllE5cqVCQgIMDqiiOQlVapAZCS0bAmtWsG2bVCmjNGpRETSybTAk10dpCNHjjB58mT++OMPHBwciIyMpGXLlpQtW5bAwEDGjx/P8OHDAQgODsbLy+vRjkxEbEKqOZX+3/Tnq2NfMb31dF6o/4LRkUQkF+jZs2e65T///JPjx49z/PhxIiMjVeARkax78knLmDyBgX8VeTw9jU4lIpIm0wJPdnWQatSoweLFi++7vUGDBoSHhz/QZ4mIAJjNZgauGciSn5YwocUEXm3yqtGRRCSXMJvN6SaEKFmyJCVLlsTf3/++7xERyVSjRrB2LQQFQUAAbNkCjz1mdCoREeABB1m+W0YdJBERazObzbwa+SqfHfiM1596nTeavWF0JBHJRcLCwmjdujWtWrWidOnSaesTExPZv38/K1eupFGjRjz99NMGphSRPMnPD1avhnbtoHVr2LQJihc3OpWISNYLPCIiRjObzbyx+Q0+3P0hQxsO5d2W7xodSURymTlz5hAREcGwYcM4e/YsRYsWJSEhAbPZjK+vL3379sXHx8fomCKSV7VsCV9/Df/6F7RtCxs2QNGiRqcSERunAo+I5Dnjt47nvR3v8Vzd5/gg6APdYiEi9yhQoAB9+vShT58+JCUlcfnyZQoWLEjRLP4BNnHiRA4dOoTJZGL06NHUqlUrbduuXbuYPn069vb2NGvWjEGDBt13n/PnzzNixAhSUlIoUaIEU6ZMwcnJiatXrzJs2DBcXFyYMWMGAElJSYwaNYpz585hb2/Pe++9R7ly5bKvcUQkewQFwfLl0LWr5Wqe9evBxcXoVCJiw+yMDiAikhUTvp/A29+/Tf86/fmk/Scq7ohIphwdHfHw8MhycWfPnj2cOXOG8PBw3n33Xd59N/3VghMmTOCjjz5i2bJl7Ny5k19//fW++8yYMYPevXuzdOlSHn/8cSIiIgAYN24c9erVS/e5a9asoWjRoixbtowXX3yRadOmPcLRi0iO6tgRPv8cdu2yXM1z65bRiUTEhqnAIyJ5xqQdkxizZQyhtUKZ3WE2diZ9hYlIzomKikqbTMLb25urV68SHx8PQHR0NK6urpQqVQo7Ozv8/f2Jioq67z67d++mVatWALRo0YKoqCjAUiT6e4EnKiqKwMBAAJo2bcqBAwescrwi8pC6d4cFCywDLnfpArdvG51IRGyUbtESkTxh2q5pvL7pdXrV6MX8jvOxt7M3OpKI5GJff/01kyZNwmw207x5c8aOHUvhwoWz9BmxsbFUr149bdnNzY2YmBgKFy5MTEwMbm5u6bZFR0dz+fLlDPe5desWTk5OALi7uxMTEwOQYabY2Ni0z7azs8NkMpGYmJi2/92OHTuWpWN6UAkJCTn22XmBrR8/qA0gi21Qvz7Fxo+n1LhxXA8O5uz774OjY84GzGE6B9QGoDaAvNUGKvCISK734Q8f8tp3r9HNpxuLOi9ScUdEMjVr1izmz5+Pp6cnixcv5v3332fMmDGP9Jlmszlb9snq5/zT+6tVq5blTA/i2LFjOfbZeYGtHz+oDeAh2mDsWHBzo8iQIVSbMAGWLgWHvPvnls4BtQGoDSB3tsH+/fszXK/7G0QkV5u1dxavRL5C56qd+fzpz3Gwy7sdJRGxnsKFC+Pj44O7uzuvvPIKP/30U5Y/w8PDg9jY2LTlixcvUqJEiQy3XbhwAQ8Pj/vu4+zsTEJCQrr3/tPPvXOFT1JSEmazOcOrd0QkFxo8GKZMsQy+3L8/pKQYnUhEbIgKPCKSa322/zMGfTuIDpU78EXXL3C0z9uXOouI9cTExBAeHs7evXuJi4sjOTk5y5/h6+tLZGQkAEePHsXDwyPtlqqyZcsSHx/P2bNnSU5OZsuWLfj6+t53n6ZNm6at37BhA35+fv/4c9evXw/Ali1baNSoUZazi4iBXnsN3nkHliyBAQNU5BERq9E/hYtIrjTv4DxeWPMCwZWCWd5tOU72+tdrEXlwQ4YM4cSJE6xevZoTJ05w8+ZNnnvuOapWrUqVKlVo3759pp9Rt25dqlevTs+ePTGZTIwbN44VK1ZQpEgRAgMDGT9+PMOHDwcgODgYLy8vvLy87tnnTp6RI0cSHh5O6dKl6dSpEykpKfTr149r165x4cIFQkNDeemllwgODmbXrl306tULJycnJk2alKNtJSI54M03LYWd8eMty3Pngr1uMReRnKUCj4jkOosOLeLZVc/S2rs1X3X/igIOBYyOJCJ5TI8ePdIt//nnnxw/fpzjx4+zbdu2ByrwALz22mvplqtWrZr2ukGDBoSHh2e6D1huu5o/f/496xcvXpzhz33vvfceKJ+I5GL/K/CqyCMi1qICj4jkKksPL6X/N/1p4dWClT1WUtChoNGRRCQfKFmyJCVLlsTf39/oKCJiS1TkERErUoFHRHKNL49+SdjXYTxV/ilW9VxFIcdCRkcSEREReTQq8oiIlajAIyK5whdHviBkRQhNyjVhbe+1uDi5GB1JREREJHvcXeQxmWDOHBV5RCTbqcAjIoZbengpoV+H4lvOl2/7fEthp8JGRxIRERHJXn+/kkdFHhHJZirwiIihlvy0hL4r++JX3o81vdeouCMiIiL5l4o8IpKDVOAREcMsOrSIfiv70bxCc1b3Wq3bskRERCT/U5FHRHKICjwiYogFPy7gmW+eoaVXS1b1WoWzo7PRkURERESs4+4iT2oqzJunIo+IPDIVeETE6uYdnMezq54loGIA3/T8RrNliYiIiO0ZNw7s7GDsWLh9GxYvBkdHo1OJSB6mAo+IWNWcA3N4bvVztPZuzcoeK1XcEREREds1ZgwULAgjRliKPF98AQUKGJ1KRPIoO6MDiIjt+Gz/Zzy3+jmCngjSlTsiIiIiAP/+N3z0EaxcCZ06wa1bRicSkTxKBR4RsYpP9n3CC2teILhSMF/3+JqCDgWNjiQiIiKSOwweDLNnQ2QktGsH8fFGJxKRPEgFHhHJcTN2z2Dg2oG0r9yeFd1XqLgjIiIi8nfPPguLFsG2bRAUBFevGp1IRPIYFXhEJEe9t/09Xl7/Mp2rdiaiWwQFHHRfuYiIiEiGQkIgPBx274bAQIiLMzqRiOQhKvCISI4wm82M2TyG0ZtH07tmb77s9qWKOyIiIiKZ6doVVqyAQ4egZUuIiTE6kYjkESrwiEi2M5vNDN8wnAnbJ/Dsk8+yqNMiHOw0aZ+IiIjIA+nQAVavhhMnwN8fzp83OpGI5AEq8IhItko1p/LS2pd4/4f3GdJwCJ92+BR7O3ujY4mIiIjkLa1bw7p18Pvv4OcHv/1mdCIRyeVU4BGRbJOcmky/lf34ZP8njPIdxYdBH2Jn0teMiIiIyEPx94eNGy1j8fj6wpEjRicSkVxMf3mJSLZITEmk11e9WPzTYt5p8Q4TW03EZDIZHUtEREQkb2vcGL7/3vK6WTP44Qdj84hIrqUCj4g8soTkBJ4Of5qInyOY3no6bzZ7U8UdERERkexSowbs3AlubhAQAN99Z3QiEcmFVOARkUdyI/EGHZZ1YO3JtXzc7mNebfKq0ZFERERE8h8vL9ixA7y9oV07iIgwOpGI5DIq8IjIQ4u7FUfA4gA2/7aZBR0X8GL9F42OJCIiIpJ/lSwJW7dCgwbQowfMnm10IhHJRVTgEZGH8se1P2g2vxkHzh8golsEfev0NTqSiIiISP5XvDhs2GCZZev552HyZKMTiUguoQKPiGTZyUsneWr+U5y5eob1fdbTuVpnoyOJiIiI2A4XF/jmG+jZE0aNghEjwGw2OpWIGMzB6AAikrccPH+QoM+DSDWnsqXvFuqXrm90JBERERHb4+QES5ZYruiZMgUuXIA5c8DR0ehkImIQFXhE5IF9f+Z7OizrgGsBVzaEbqDqY1WNjiQiIiJiu+ztYeZMKFUKxo6FP/+0DL5cpIjRyUTEALpFS0QeyOrjq2mzpA2li5Rm5zM7VdwRERERyQ1MJhgzBubOhU2bwN8fzp83OpWIGEAFHhHJ1KJDi+gc3pkaHjXY3n875VzLGR1JRERERO72zDOwejUcPw5NmsAvvxidSESsTAUeEflH70e9T9+VffGv4M/msM085vyY0ZFEREREJCNt28K2bXDrFvj6wq5dRicSEStSgUdEMpRqTmV45HCGbRjG09WeZm3vtRQpoPu5RURERHK1+vUthR03N2jVClauNDqRiFiJCjwico/bybfp/VVvpv8wncENBvNl1y8p6FDQ6FgiIiIi8iC8vS1Fntq1oUsXmDXL6EQiYgUq8IhIOlcSrtBmSRvCj4YzOWAyM9rOwN7O3uhYIiIiIpIVJUrA5s3Qrh0MGgSvvgopKUanEpEcpGnSRSRN9NVo2n7elhOXTvD505/Tu2ZvoyOJiIiIyMNydoavv4bhw+GDD+DXX2HpUk2jLpJP6QoeEQHgxJUTNJnbhOhr0awPWa/ijoiIiEh+YG9vKe7MnAnr1oGfH0RHG51KRHKACjwiwpbfthCyJQQzZrb3305Lr5ZGRxIRERGR7PTSS7B2Lfz2GzRsCHv3Gp1IRLKZCjwiNm7p4aUEfR6EZyFPogZEUcuzltGRRERERCQntGljGXy5QAHw94cVK4xOJCLZSAUeERtlNpsZv3U8fVb0oUnZJixpuYTyruWNjiUiIiIiOal6ddi9+68ZtiZNArPZ6FQikg1U4BGxQQnJCfRZ0Ye3tr1F/zr92RC6AVcnV6NjiYiIiIg1eHpaZtjq2RNefx3694eEBKNTicgj0ixaIjbm4o2LdPqiE1Fno3iv1XuM9B2JyWQyOpaIiIiIWFOhQpYZtapWhfHj4dgxyy1bZcoYnUxEHpKu4BGxIT/H/EyjOY348c8fiegWwainRqm4IyIiImKrTCYYN85S2Dl6FOrXt4zRIyJ5ktWu4Jk4cSKHDh3CZDIxevRoatX6ayDXli1bUrJkSezt7QGYOnUqnp6e1oomYhM2nNpAt+XdcHZ0Zlu/bTQo08DoSCIiIiKSG3TuDD/8AB07QvPmMGsW+PoanUpEssgqBZ49e/Zw5swZwsPDOXXqFKNHjyY8PDzde2bPno2Li4s14ojYnE/2fcLgbwdTw6MGq3utppxrOaMjiYiIiEhuUqOGZer0nj3huefw7NULFi4ER0ejk4nIA7LKLVpRUVEEBAQA4O3tzdWrV4mPj7fGjxaxaUkpSQxaO4iBawcS9EQQ2/tvV3FHRERERDLm5gbffgvDh+O2bBkEBMDFi0anEpEHZJUCT2xsLMWLF09bdnNzIyYmJt17xo0bR69evZg6dSpmTdMn8shibsQQsDiAWftm8e+m/+abnt9QpEARo2OJiIiISG7m4ABTp/LH5MmwZw/Uq2e5fUtEcj1DZtH6ewFn6NCh+Pn54erqyqBBg4iMjCQoKOie/Y4dO5YjeRISEnLss/MKtUH+aoNjl48xeOdg4m7HMbnRZDqU7cCJ4yf+cZ/8dPwPS22gNrD14we1gYiIWFzr0IEyAQHQpQs0awbTpsHgwZaBmUUkV7JKgcfDw4PY2Ni05YsXL1KiRIm05U6dOqW9btasGSdOnMiwwFOtWrUcyXfs2LEc++y8Qm2Qf9og/Eg4/bf0x93ZnZ19dlKvdL0H2i+/HP+jUBuoDWz9+CF3tsH+/fuNjiAiYpvq1oUDByAsDIYOhZ07YfZsKKKrwkVyI6vcouXr60tkZCQAR48excPDg8KFCwNw/fp1BgwYQGJiIgB79+6lUqVK1oglkq+kpKbw+sbX6flVT+qVrse+5/Y9cHFHREQyNnHiRHr06EHPnj356aef0m3btWsXXbt2pUePHsycOfMf9zl//jyhoaH07t2bl19+Oa3fs2rVKrp06UK3bt1Yvnw5ACtWrMDf35/Q0FBCQ0P5+OOPrXS0IiIZKF4cvvkGJk6E5cuhYUPLlOoikutY5QqeunXrUr16dXr27InJZGLcuHGsWLGCIkWKEBgYSLNmzejRowcFChTAx8cnw6t3ROT+riRcoc+KPnx78lteqPcCM9rOwMneyehYIiJ5WmazgE6YMIG5c+fi6elJSEgIbdq0IS4uLsN9ZsyYQe/evWnbti3Tp08nIiKCTp06MXPmTCIiInB0dKRr164EBgYCEBwczMiRI406dBGR9Ozs4PXXoXFjyyxbDRtaruTp3dvoZCJyF6uNwfPaa6+lW65atWra6759+9K3b19rRRHJV37880e6fNmF36/+zsftPubF+i8aHUlEJF+43yyghQsXJjo6GldXV0qVKgWAv78/UVFRxMXFZbjP7t27eeuttwBo0aIF8+bNw8vLi5o1a1Lkf7c61K1blwMHDhhwpCI4EbmlAAAgAElEQVQiD6hFCzh4EHr0gD59YMcOy9g8hQoZnUxEMGiQZRHJHvMOzmPQt4NwL+TO9/2+p0m5JkZHEhHJN2JjY6levXra8p1ZQAsXLkxMTAxubm7ptkVHR3P58uUM97l16xZOTpYrK93d3YmJiSE2Nvaez4iJicHR0ZE9e/YwYMAAkpOTGTlyJD4+Phlm1AQUOcPWjx/UBqA2+MfjnzkTjw8+wP3jj0nYtIk/pk4l8YknrBvQCmz9HAC1AeStNlCBRyQPupV0iyHrhjD34FxaebViWZdllHApkfmOIiLy0P4+C+jD7nO/z7mzvnbt2ri5udG8eXMOHjzIyJEjWb16dYb7aAKKnGHrxw9qA1AbZHr88+ZB164U7NcP7x494MMP4dln89UsW7Z+DoDaAHJnG9xvAgqrDLIsItnn9OXT+M7zZe7Bubzh9waRIZEq7oiI5IB/mgX079suXLiAh4fHffdxdnYmISEh0/d6eHjg7e1N8+bNAXjyySeJi4sjJSUlJw9VROThBAfDoUPg6wvPPw/du8Ply0anErFZKvCI5CGrj6+m3mf1+O+V/7Km1xomtJyAvZ290bFERPKlf5oFtGzZssTHx3P27FmSk5PZsmULvr6+992nadOmaes3bNiAn58ftWvX5vDhw1y7do0bN25w4MAB6tevz+zZs1mzZg0AJ06cwM3NDXt7fdeLSC5VqhRERsLkybByJdSpA7t2GZ1KxCbpFi2RPCAxJZE3N7/JlF1TqFuqLhHdIvAq7mV0LBGRfC2zWUDHjx/P8OHDAcusV15eXnh5ed2zD8CQIUMYOXIk4eHhlC5dmk6dOuHo6Mjw4cMZMGAAJpOJQYMGUaRIETp06MC///1vvvjiC5KTk3n33XeNbAYRkczZ2cGIEeDvD716QbNmMG6cZeYtB/3JKWIt+m0TyeVOXz5Nz4ie7D23lxfrvcj7Qe9T0KGg0bFERGzCP80C2qBBg3TTpt9vH7Dc0jV//vx71gcFBREUFJRuXcmSJVm8ePHDRhYRMU6jRpZZtgYOhLFj4dtvYdEiqFTJ6GQiNkG3aInkYssOL6POJ3U4GXeSiG4RfNz+YxV3RERERCT3cnWFpUth2TL45RfLLVuzZsFDDFQvIlmjAo9ILhSfGM8z3zxD7xW9qeVZix9f+JEuPl2MjiUiIiIi8mB69oQjR+Cpp2DQIAgKgj/+MDqVSL6mAo9ILvPjnz9S/7P6LPhxAWOajWFrv608Xuxxo2OJiIiIiGRNmTKwfr3lCp4dO6BGDcuVPbqaRyRHqMAjkkukmlP54IcPaDSnEdcTr7MpbBNvt3gbBzsNlSUiIiIieZTJZBmT59AhqFYNeveGLl3g/Hmjk4nkOyrwiOQCv1/9ncDFgbwa+SptvNtw6MVDtPBqYXQsEREREZHs8cQTsH07TJpkGXzZxwfmz9fVPCLZSAUeEQOZzWYWH1pMzY9rsuePPczpMIdven7DY86PGR1NRERERCR72dvDyJHw009QsyY88wy0aQO//WZ0MpF8QQUeEYPE3oyl6/KuhK0Mo5ZnLQ69eIgBdQdgMpmMjiYiIiIiknMqV4atW2HmTIiKsozNM2MGpKQYnUwkT1OBR8QAa0+spcasGqw5sYbJAZPZ2ncrFYtXNDqWiIiIiIh12NnBSy/B0aPg7w8vv2yZcevQIaOTieRZKvCIWNGlm5cI+zqM9sva41nYk73P7WWE7wjs7eyNjiYiIiIiYn3ly8PatbB4Mfz6K9SrB8OGwfXrRicTyXNU4BGxArPZzPKjy/GZ5cOyI8sY02wMe57dQy3PWkZHExERERExlskEISFw/Dg8+yx88AFUrQpffqlBmEWyQAUekRx2/vp5unzZhe4R3SlXtBz7n9/P2y3epoBDAaOjiYiIiIjkHm5u8MknlnF5PD2hRw8ICoKTJ41OJpInqMAjkkPMZjPzD87HZ5YP635dx+SAyfzw7A+6akdERERE5J80agR79lgGXv7hB8sgzG+8odu2RDKhAo9IDvgl9hcCFgfwzKpnqOFRg0MvHmKE7wgc7ByMjiYiIiIikvs5OMCQIfDLL9C9O0ycaJl9a8ECSE01Op1IrqQCj0g2upl0kzc2vUGtj2ux/9x+ZgXPYlu/bVR2r2x0NBERERGRvKdUKcsAzFFR8Pjj0L8/NGwIO3YYnUwk11GBRySbrD2xluqzqjNxx0R61ujJ8cHHGdhgIHYm/ZqJiIiIiDySxo1h1y5YsgT+/BP8/Cxj9Jw5Y3QykVxDf3mKPKLfr/5O5/DOtF/WnkIOhdjadyuLOi/Cs7Cn0dFERERERPIPOzvo08cy29a4cbB6teW2rWHDIDbW6HQihlOBR+Qh3Uy6yVtb36Lq/1Ul8tdIJrWaxI8v/oh/BX+jo4mIiIiI5F8uLjB+vKXQExICH34IFSvCO+9AfLzR6UQMowKPSBaZzWaWHl5Klf+rwvht4+lQpQPHBh1j5FMjcbJ3MjqeiIiIiIhtKFcO5s6Fw4ehVSsYOxaeeAJmzoTERKPTiVidCjwiWbD77G6azmtKnxV98HTxZHv/7YR3DefxYo8bHU1ERERExDb5+MDXX1sGYq5aFQYPhmrVLDNuJScbnU7EalTgEXkAv1/9ndCvQ2k8tzH/vfJf5necz57n9vBU+aeMjiYiIiIiImAZiHnLFvj2W3B1tcy4VaUKzJsHSUlGpxPJcSrwiPyDmBsxDIscRqWPKrH86HJGPzWak0NO0q9OP82OJSIiIiKS25hM0LYt7N8P33wDxYrBgAGWQs+cOSr0SL6mv1BFMnD99nXe3vY23jO8+XD3h4TWCuXkkJO82+pdCjsVNjqeiIiIiIj8E5MJ/vUv2LfPMtuWuzs89xxUqgSffAK3bhmdUCTbqcAjcpfbybeZsXsG3jO8Gbd1HK29W3Nk4BHm/GsO5VzLGR1PRERERESywmSC9u1hzx5YuxY8PWHgQHj8cZgwAeLijE4okm1U4BEBEpITWPbrMip9VImX179MTc+a7H52NxHdI6hWoprR8URERERE5FGYTBAcDD/8AJs3Q/36MGYMlC8PL78M//2v0QlFHpkKPGLTbiXd4sMfPsR7hjfvHHiHcq7l2BCygU1hm2hYpqHR8UREREREJDuZTNCihWUg5p9+gi5dYNYsy/TqvXtbrvQRyaNU4BGbdCPxBtN2TcPrQy9eiXyFSm6VmOc/jx39dxDoHWh0PBERERERyWk1a8LChXD6tOUqntWroVEjaNgQFi3CdPu20QlFskQFHrEpMTdieHvb21T4sAKvffcaNT1rsq3fNrb220pjz8aYTCajI4qIiIiIiDWVKwfTpsEff8BHH8G1a9C3L0+0agVvvAHR0UYnFHkgKvCITThx6QQvrnmR8h+UZ9zWcTQs05Cdz+zku9DvaPZ4M6PjiYiIiIiI0YoWhcGD4dgx+O47btWpA5MmgZcXdO5sGaQ5OdnolCL35WB0AJGcYjab2fH7DqZGTWX18dU42jsSViuMYU2GaeBkERERERHJmMkEAQGcLVOGaoUKwccfw4IFsHIllC4N/fvDM89AxYpGJxVJR1fwSL5zM+km8w7Oo8HsBjRb0Iydv+/kzWZv8vsrvzP7X7NV3BERERERkQdToQJMngxnz8KKFVCnDrz3Hnh7Q8uW8PnncPOm0SlFAF3BI/nI8djjfLzvYxYeWsiVhCv4lPBhVvAs+tbpi7Ojs9HxREREREQkr3J0tNym1bmzpdizYAHMmwchIeDiYlnfuzcEBoKD/swWY+jMkzwtMSWRVcdX8fG+j9n822Yc7Rzp4tOFgfUH4lfeT4Mmi4iIiIhI9ipbFt58E0aPhu+/h6VLYflyWLIESpSAHj0sxZ7GjS23e4lYiQo8kueYzWYOnD/AwkMLWXp4KZduXaK8a3nebfkuA54cgGdhT6MjioiIiIhIfmdnB82bWx4ffQTr11tu2ZozB/7v/6B8eXj6acujaVOwtzc6seRzKvBInnH++nk+P/w5C35cwNGYoxSwL0DHqh3pW7svbbzbYG+nL0wRERERETFAgQLQsaPlce0afP01fPWVZYDmDz4ADw/o1MlS7GnRApycjE4s+ZAKPJKrxd2KY+UvK/ny6Jd8d/o7Us2pNC7bmI/bfUyP6j0oXqi40RFFRERERET+UrQo9O1reVy/DuvWWQZoXroUPvsMXF0hOBjatoU2bSzFH5FsoAKP5DqXb122FHV+/pKNpzeSnJpMxeIVGeU7irDaYVR5rIrREUVERERERDJXpAh07255JCTAxo2WYs+338KyZZYxeurXtxR72raFBg10K5c8NBV4JFeIvhrN2pNr+eb4N2lFHa9iXgxvMpxuPt2oW6quBkwWEREREZG8q2BBaN/e8khNhYMHLVf3rFsHEybA22+Du7tlJq4WLSyPJ57QQM3ywFTgEUOkmlPZ+8deVp9YzZoTazh04RAAFYtXZFjjYXSr3o16peqpqCMiIiIiIvmPnR3Uq2d5vPkmxMXBhg2WK3s2boQvvrC8r0yZv4o9LVqAl5exuSVXU4FHrObstbNsOr2JTb9tIvJUJBdvXMTeZI9veV/+E/AfOlTpQBX3KirqiIiIiIiIbXFzg549LQ+zGU6cgC1bLI/ISMsU7GCZmatJk78edepowGZJowKP5Ji4W3Fs/e9WNp7eyKbfNnHi0gkASjiXIKBiAO0rtyfoiSDcCrkZnFRERERERCSXMJmgShXL48UXLQWfn3+2FHu+/x527oTwcMt7Cxa0XAV0p+DTsKHlqh/9o7lNUoFHsoXZbObXuF/ZFb2LndE72RW9i6MxRwFwcXTBv4I/L9R7gYCKAdTwqIGdyc7gxCIiIiIiInmAyQTVq1segwdb1p09Cz/8AFFRlseMGTB1qmXbY4/Bk09C3bqW5yeftIzlY6e/wfI7FXjkocTciOHA+QMcOH+A3X/sZlf0LmJuxgDgWsCVpuWa0rNGT1pUaEHDMg1xtHc0OLGIiIiIiEg+UbYsdO1qeQDcvm0ZtHnfPsvzwYMwfTokJVm2Fy4MtWtDzZrg4/PXo2RJXe2Tj6jAI//IbDYTfS2any78xP5z+znwp6Woc/ba2bT3eBf3pm2ltviW86Vpuab4lPDRFToiIiIiIiLWUqAANG5sedyRmGi5tevAgb+KPl98AVeu/PWeYsX+KvZUqwaVKoG3t2Uw50KFrH8c8khU4BEAklOTOXnpJD/H/Myx2GNpz8dijnEj6QYAJkxUeawKzR5vRt2Sdalbqi51StaheKHiBqcXERERERGRdJycLIMw16nz1zqzGS5csBR+7n6sXAlz5qTfv0wZypcqBbVqWYo+3t5QoYLl6qGSJcHe3qqHI5lTgcdGmM1mLt26xG+Xf+P05dP8diX98+9XfifZnJz2/jJFyuBTwocBTw7Ap4QP1T2qU6dkHQo7FTbwKEREREREROShmUyW4kzJktCyZfptsbFw6hT8+qvl+dQpTEeOWKZu//PP9O+1t4fSpaFcOUvB5+7nUqXA0xM8PCy3hukWMKuxWoFn4sSJHDp0CJPJxOjRo6lVq1batl27djF9+nTs7e1p1qwZgwYNslasPC8hOYFLNy9x6dYlYm/Gcu76Oc5dP8f56+c5F38ubfnc9XMkJCek27eEcwm8invRsExDWnm2oknlJviU8KHqY1VxLehq0BGJiIjkHg/Tf8lon/PnzzNixAhSUlIoUaIEU6ZMwcnJiVWrVrFw4ULs7Ozo3r073bp1IykpiVGjRnHu3Dns7e157733KFeunFFNICIituKxxyyPRo3SVp05doxq1arBjRtw+jScOWMZ4Dk6+q/ngwdh1SpISLj3MwsW/KvY4+GR/rWbm+UWseLF0z+rKPTQrFLg2bNnD2fOnCE8PJxTp04xevRowu9M6wZMmDCBuXPn4unpSUhICG3atOGJJ56wRjSrSjWncjv5NokpidxO+d9z8m0SkhOIT4xPe1xPvP7X69t/vb5y+0paMefO882kmxn+LBdHF8oULUOpwqVoVKYRpYuUpmzRsngV86Ji8Yp4FfdKdzXOsTu/uCIiIgI8XP8lLi4uw31mzJhB7969adu2LdOnTyciIoJOnToxc+ZMIiIicHR0pGvXrgQGBrJlyxaKFi3KtGnT2LFjB9OmTeODDz4wsCVERMTmubhYBmiuWTPj7WYzxMVZCj5//gkXL1puBbt48a/X587Bjz9alu8M/pwRe/v0BZ+iRS0/v3Bhy/PfX9+9XKiQZTyiAgUst6jdef33ZUfHfFlEskqBJyoqioCAAAC8vb25evUq8fHxFC5cmOjoaFxdXSlVqhQA/v7+REVFWa3Ak5yazPCo4VyNuorZbCbVnIqZ/z2bzele39n2IO9LNaemFXHuFHJSzCkPldHF0YUiBYrgWsAVd2d3yhYtS23P2rgXcsfd2T3dc+kipSldpDRFChTJ5pYSERGxLQ/Tf4mLi8twn927d/PWW28B0KJFC+bNm4eXlxc1a9akSBHL/7Pr1q3LgQMHiIqKolOnTgA0bdqU0aNHW/vQRUREssZkAnd3yyMzZrNloOfLly2PO6/v93ztGly6ZLmK6MYNiI+3PKemPlrmOwUfR0fLFPL29n893/W6YkqK5UqkjLbfmXr+TrHIZLI8atSATz55tHwPwSoFntjYWKpXr5627ObmRkxMDIULFyYmJgY3N7d026KjozP8nGPHjmV7tuTUZOzN9qQmpmJnssMBB0wmEyZMmEwm7LDDZPfXsglT2gxRdiY7TNy77c6yk50TjnaOONn/79nub893rXd2dMbFwQVnB2ecHf56Xcih0IPPSJUAqQmpnI05m/l7/75rQkKOtG9eYuttYOvHD2oDUBvY+vGD2uBuD9N/uXz5cob73Lp1CycnJwDc3d2JiYkhNjb2ns/4+3o7OztMJhOJiYlp+98tp/5b2fp5YOvHD2oDUBvY+vGD2gCs0AbOzpZH6dJZ289sxpSYiN3Nm5hu3sTu1i3L68RE7BITMSUmYkpKsjxntJyU9NdycjKm1FRISbF87t3PqamkJiVx+87P/N86U2qqpcBkNlsed7b/r+h0Oz6eCwacO4YMsmy+0wBZlFO3EP3H7j82f3uSbtFSG9j68YPaANQGtn78kDvbYP/+/UZHAB6u/5LRPvf7nKyuh5zrG+XG88CabP34QW0AagNbP35QG4DaAB6uDVwAt0zf9fDu1zd6wEtDHo2HhwexsbFpyxcvXqREiRIZbrtw4QIeHh7WiCUiIiJyXw/Tf7nfPs7OziT8b/DJf3rvnfUxMTEAJCUlYTabM7x6R0RERORuVinw+Pr6EhkZCcDRo0fx8PCgcGHLAL9ly5YlPj6es2fPkpyczJYtW/D19bVGLBEREZH7epj+y/32adq0adr6DRs24OfnR+3atTl8+DDXrl3jxo0bHDhwgPr16+Pr68v69esB2LJlC43ums1ERERE5H6scotW3bp1qV69Oj179sRkMjFu3DhWrFhBkSJFCAwMZPz48QwfPhyA4OBgvLy8rBFLRERE5L4epv/i5eV1zz4AQ4YMYeTIkYSHh1O6dGk6deqEo6Mjw4cPZ8CAAZhMJgYNGkSRIkUIDg5m165d9OrVCycnJyZNmmRkM4iIiEgeYbUxeF577bV0y1WrVk173aBBg3TTjoqIiIjkBg/Tf/n7PmC5pWv+/Pn3rA8KCiIoKCjdOnt7e957772HjSwiIiI2yiq3aImIiIiIiIiISM5RgUdEREREREREJI9TgUdEREREREREJI9TgUdEREREREREJI9TgUdEREREREREJI9TgUdEREREREREJI9TgUdEREREREREJI8zmc1ms9EhHsT+/fuNjiAiIiIGqVevntERch31jURERGxXRn2jPFPgERERERERERGRjOkWLRERERERERGRPE4FHhERERERERGRPE4FHhERERERERGRPM7B6ADWNnHiRA4dOoTJZGL06NHUqlUrbduuXbuYPn069vb2NGvWjEGDBhmYNGf85z//Yf/+/SQnJ/PCCy/QunXrtG0tW7akZMmS2NvbAzB16lQ8PT2Nipojdu/ezcsvv0ylSpUAqFy5MmPGjEnbbgvnwPLly1m1alXa8pEjRzh48GDacvXq1albt27a8oIFC9LOibzuxIkTvPTSS/Tr14+QkBDOnz/PiBEjSElJoUSJEkyZMgUnJ6d0+/zTd0ZelFEbvP766yQnJ+Pg4MCUKVMoUaJE2vsz+53Ja/5+/KNGjeLo0aMUK1YMgAEDBtC8efN0++T3c2Do0KFcvnwZgCtXrlCnTh3eeeedtPevWLGCDz/8kPLlywPQtGlTBg4caEh2yX623i8C9Y1svW+kfpH6RbbcLwL1jSCf9Y3MNmT37t3m559/3mw2m82//vqruXv37um2t23b1nzu3DlzSkqKuVevXuaTJ08aETPHREVFmZ999lmz2Ww2x8XFmf39/dNtb9GihTk+Pt6AZNbzww8/mIcMGXLf7fn9HPi73bt3m8ePH59uXcOGDQ1Kk7Nu3LhhDgkJMb/55pvmxYsXm81ms3nUqFHmb7/91mw2m83Tpk0zf/755+n2yew7I6/JqA1GjBhhXrt2rdlsNpuXLFlinjx5crp9MvudyUsyOv6RI0eaN2/efN99bOEcuNuoUaPMhw4dSrfuq6++Mk+aNMlaEcWKbL1fZDarb2Q2q290N/WL1C+ypX6R2ay+kdmc//pGNnWLVlRUFAEBAQB4e3tz9epV4uPjAYiOjsbV1ZVSpUphZ2eHv78/UVFRRsbNdg0aNODDDz8EoGjRoty6dYuUlBSDU+UetnAO/N3MmTN56aWXjI5hFU5OTsyePRsPD4+0dbt376ZVq1YAtGjR4p7/3v/0nZEXZdQG48aNo02bNgAUL16cK1euGBUvx2V0/JmxhXPgjtOnT3P9+vU8/69w8uBsvV8E6htlxlbOgzvUL1K/yJb6RaC+EeS/vpFNFXhiY2MpXrx42rKbmxsxMTEAxMTE4ObmluG2/MLe3h5nZ2cAIiIiaNas2T2XmI4bN45evXoxdepUzGazETFz3K+//sqLL75Ir1692LlzZ9p6WzgH7vbTTz9RqlSpdJedAiQmJjJ8+HB69uzJ/PnzDUqX/RwcHChYsGC6dbdu3Uq79Njd3f2e/97/9J2RF2XUBs7Oztjb25OSksLSpUvp0KHDPfvd73cmr8no+AGWLFlCWFgYr776KnFxcem22cI5cMeiRYsICQnJcNuePXsYMGAAffv25eeff87JiGJFtt4vAvWN7lDfSP0iUL8IbKtfBOobQf7rG9ncGDx3y6//k87Mxo0biYiIYN68eenWDx06FD8/P1xdXRk0aBCRkZEEBQUZlDJnVKhQgcGDB9O2bVuio6MJCwtjw4YN99xfbAsiIiLo3LnzPetHjBjBv/71L0wmEyEhIdSvX5+aNWsakNC6HuT7IL9+Z6SkpDBixAgaN25MkyZN0m3L778zHTt2pFixYlSrVo3PPvuM//u//2Ps2LH3fX9+PQcSExPZv38/48ePv2db7dq1cXNzo3nz5hw8eJCRI0eyevVq64eUHJdfz+8Hob5R/v2ef1DqF6WnfpFt9otAfaM78mrfyKau4PHw8CA2NjZt+eLFi2lV+r9vu3DhQpYuVcsrtm/fzieffMLs2bMpUqRIum2dOnXC3d0dBwcHmjVrxokTJwxKmXM8PT0JDg7GZDJRvnx5HnvsMS5cuADYzjlwx+7du3nyySfvWd+rVy9cXFxwdnamcePG+fI8uMPZ2ZmEhAQg4//e//SdkZ+8/vrrPP744wwePPiebf/0O5MfNGnShGrVqgGWwVT/fr7byjmwd+/e+15+7O3tnTa44pNPPklcXJxuYckn1C+yUN9IfSNQvwjUL7rDlvtFoL7RHXm1b2RTBR5fX18iIyMBOHr0KB4eHhQuXBiAsmXLEh8fz9mzZ0lOTmbLli34+voaGTfbXb9+nf/85z98+umnaaOi371twIABJCYmApYT+s7o8PnJqlWrmDt3LmC57PjSpUtps2HYwjlwx4ULF3BxcbnnXxtOnz7N8OHDMZvNJCcnc+DAgXx5HtzRtGnTtO+EDRs24Ofnl277P31n5BerVq3C0dGRoUOH3nf7/X5n8oMhQ4YQHR0NWDr3fz/fbeEcADh8+DBVq1bNcNvs2bNZs2YNYJllws3NLd/MIGPrbL1fBOobgfpGoH7RHeoXqV8E6hvdkVf7RiZzfr2m6j6mTp3Kvn37MJlMjBs3jp9//pkiRYoQGBjI3r17mTp1KgCtW7dmwIABBqfNXuHh4Xz00Ud4eXmlrWvUqBFVqlQhMDCQhQsXsnLlSgoUKICPjw9jxozBZDIZmDj7xcfH89prr3Ht2jWSkpIYPHgwly79f3v3ExJFH4Bx/OvqqkWxlGAQXpYQ04hYKiI8WLYRRNTFSyR0CILAIqsFK4jwsoSxBB4K6RDUoUtQCUHHThUUHTLY3aiLRAZFhwrc0WXfgzTvK/b+MXV9V7+fk6O/mZ3fss4+PjvjfFk2r4GfRkZGuHbtGjdv3gRgaGiI7du3k0gkGBgY4NmzZ0QiETo7O/8/t/ybo5GREa5cucKHDx+oqalh3bp1XL16lb6+PgqFAuvXryedThONRunt7SWdTlNfXz/jmPF3B/pK8Kvn4MuXL9TV1YVvzBs2bODy5cvhczA5OTnjd6ajo2ORZ/J7fjX/7u5uhoaGWLFiBStXriSdTtPQ0LCsXgODg4MMDg6ydetW9u/fH449ceIE169fZ2xsjFQqFf6BsxRuh6o/LedcBGYjMBuBuchctDxzEZiNYOllo2VX8EiSJEmSJC01y+oSLUmSJEmSpKXIgkeSJEmSJKnCWfBIkiRJkiRVOAseSZIkSZKkCmfBI0mSJEmSVOEseCRJkiRJkiqcBY8kSZIkSVKFs+CRVDZ3796lvb2dgwcPkkwmue0u9WEAAAM7SURBVH///owx4+PjdHd3UywWAXj69CmpVOq3Hi8IAo4cOcLk5OSc9luSJGm+mYskzTcLHkllk8/n6enp4eHDh2QyGdLp9Iwx9+7dY+/evVRXVwOQzWZpa2v7rcerra1l586dPHr0aE77LUmSNN/MRZLmmwWPpLLJ5XLE43EAmpqaiEajM8YMDw+zZ8+ecDmbzdLa2koQBPT19ZHJZCiVSpw6dYr+/n4OHz7M7t27efHiBalUin379nHhwoVw/WQyyfDw8MJPTpIkaRbMRZLmW81i74Ck5SOfzxOPxymVSty5c4fe3t5pPw+CgNHRUZqamsLv5XI5GhoaOHbsGF1dXRw6dCjcViKR4NKlS9y4cYOLFy9y+/Zt1q5dS0dHB0EQUFtbS3NzM69fvy7rPCVJkv6NuUjSfLPgkVQWHz9+5MePHxw/fpxPnz7R0tLCyZMnp435+vUrq1evDpcnJiYYHR3lzJkz9Pf3k0gkACgUCnz79o2jR48CUFVVRVdXF42NjQBEIpHwU7Dq6mqi0Sjfv39n1apV5ZiqJEnSPzIXSVoIXqIlqSzy+Tzbtm3jwYMHPH78mPfv3/Pq1atpY+rr6wmCIFx+9+4dmzdvpqamJrz2HODt27e0tbURiUwdwrLZLFu2bAFgbGyMxsZGqqqqwvFBEFBXV7eQ05MkSfrPzEWSFoIFj6SyyOVy4T8FjMViHDhwgCdPnkwbE4vFKBaLFAoFYCqgJBIJMpkM58+f5/Pnz8BUKNq4ceO0bbe0tITr/Pwapj79WrNmzS+va5ckSVoM5iJJC8GCR1JZ5HI5Wltbw+XOzs4ZQQagvb2dly9fhus0NzcTj8c5d+4cp0+fZmJignw+H26rUCgwPj5OLBYL1/lrkHn+/Dm7du1awJlJkiTNjrlI0kKoKpVKpcXeCUn66c2bN9y6dYuBgYF52V5PTw9nz54N71IhSZJUKcxFkmbDM3gk/a9s2rSJHTt2UCwW57ytIAhIJpOGGEmSVJHMRZJmwzN4JEmSJEmSKpxn8EiSJEmSJFU4Cx5JkiRJkqQKZ8EjSZIkSZJU4Sx4JEmSJEmSKpwFjyRJkiRJUoWz4JEkSZIkSapwfwDJTM6eIq0/hQAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "r_arr = [np.linspace(r_min, r_max, num_points+1)][:len(m_arr)][0]\n",
        "plt.figure(figsize=(16, 5))\n",
        "plt.subplot(1, 2, 1)\n",
        "plt.title('Mass-Radius diagram for single star')\n",
        "plt.plot([r/km for r in r_arr], list(m_arr), 'g-', label = \"mass\")\n",
        "plt.xlabel('$R$ $(km)$')\n",
        "plt.ylabel('$M$ $(M_\\odot)$')\n",
        "plt.savefig('mass_single_star.png')\n",
        "plt.subplot(1, 2, 2)\n",
        "plt.title('Pressure-Radius diagram for single star')\n",
        "plt.plot([r/km for r in r_arr], list(p_arr), 'r-', label = \"pressure\")\n",
        "plt.xlabel('$R$ $(km)$')\n",
        "plt.ylabel('$P$ $(MeV/fm^3)$')\n",
        "plt.savefig('pressure_single_star.png')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### For multiple stars"
      ],
      "metadata": {
        "id": "ASwa0SwHrysp"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "RMWcJAjgIWl8",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0145dbbc-5ef1-4a6f-db46-c5aff4e2d456"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:6: RuntimeWarning: invalid value encountered in power\n",
            "  \n"
          ]
        }
      ],
      "source": [
        "e_min = 1.0 #0.017 #MeV/fm^3\n",
        "e_max = 1500.0 #Mev/fm^3\n",
        "tot_stars = 100\n",
        "e_span = np.linspace(e_min, e_max, tot_stars)\n",
        "\n",
        "rmin = 1e-2 #solar mass\n",
        "rmax = 30*km #solar mass\n",
        "div = 20000\n",
        "\n",
        "R_plot = []\n",
        "M_plot = []\n",
        "P_plot = []\n",
        "\n",
        "for star_index, ec in enumerate(e_span):\n",
        "    \n",
        "    S_0 = (EOS2(ec)*mevfm, (4/3)*np.pi*((rmin)**3)*ec*mevfm)\n",
        "    t,u  = rungeKutta4(TOV, S_0 , rmin , rmax , div)\n",
        "    p_sol,m_sol  = u.T\n",
        "    \n",
        "    if len(m_sol) > 0:\n",
        "        r_span = list(np.linspace(rmin, rmax, div+1))[:len(m_sol)]\n",
        "        R_plot.append(r_span.pop()/km)\n",
        "        M_plot.append(list(m_sol).pop())  \n",
        "        P_plot.append(list(p_sol).pop())"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "max_mass = max(M_plot)\n",
        "index = np.where(M_plot == max_mass)[0][0]\n",
        "R_plot.append(R_plot[index])\n",
        "M_plot.append(M_plot[index])\n",
        "dict = list(zip(M_plot, R_plot))\n",
        "dict = [tup for tup in dict if not np.isnan(tup[0])]\n",
        "radius_at_max_mass = [tup[1] for tup in dict if tup[0] == max_mass][0]"
      ],
      "metadata": {
        "id": "sn5f8bApWYEQ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 441
        },
        "id": "DEDQEu8RYohP",
        "outputId": "e10f5cf2-51d4-4989-f41a-f882d8753e66"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x432 with 1 Axes>"
            ],
            "image/png": 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y/f3vf9c777yjGTNmKC0tTWvWrNGNN96ocePGqbCwUJGRkXrwwQeVnJyssWPH6vbbb9eGDRt08uRJu23NmjW7ujeMy6rzp6jei0xRhqWVLlg8lGFppfciGc8EgNro0CHH2iurQ4cOslgsatasmdq2bStPT081bdpU58+fV35+vuLi4vTkk08qLy9PkhQTE6PJkydrwYIFCgsLU7Nmzey2oWbV6YDzXmSKYjcmKlgZ8pChYGUodmMiIQcAaqGgIMfaK8vLy8vu37OysvTtt99q6dKlWrp0qXx8fCRJ999/v5YsWaLGjRvrz3/+s/bv32+3DTWrTgecvhsnqL7KjmfWV4H6bpzgoooAAFU1bZrk61u2zdfX2l4Tdu3apRYtWsjb21sbN25USUmJioqKNH/+fHl5eSk2Nlb9+/fX/v377bahZtXpOTg3yP64ZUXtAAD3VTrPZsIE62mpoCBruLma+TeX0717d2VkZGjw4MGKjIxUr169lJSUpC5duujRRx+Vn5+f/Pz89Oijj+rMmTPl2lCzLIZhGK4uojJ27typzp07V+tzZlhaKVgZ5dsVrGDjoMPPl5aWprCwsKsvrI6gvxxDf1UefeUY+ssx9Jdjarq/KsoHdfoU1ca+03RGZcczz8hXG/vW0HgmAABwijodcB77Il4r+y5UhoJ1QRZlKFgr+y7UY1/U0HgmAABwijo9B0fS/8KMNdAES3rMpdUAAIDqUKdHcAAAgDkRcAAAgOkQcAAAgOkQcAAAqEBWVpbatm2r//znP2XaBw4cqLFjx7qoqpqTnZ2tRx55RIMHD9Yjjzyi3NzccveZNWuWYmNjNXDgQG3YsEGSNGLECCUkJCghIUH33nuvJk2aZHu+UaNGaebMmbbHr127VrfffruKiopsbfn5+erQoYPWrl1bbe+FgAMAwGXccMMN+uSTT2zH2dnZ+u9//+vCimrO66+/rj/+8Y9KTk5WVFSUFi9eXOb2b7/9Vvv27dPKlSv17rvvavr06ZKkN99807ZlRYcOHfTggw9KksaPH6+OHTuWe51GjRpp06ZNtuMNGzaoRYsW1fpe6vwqqtouJcV5V+0EgLrolltu0ZYtW1RSUiJPT09t3rxZ4eHhKiwslCR9/PHHSk5OloeHh9q0aaOpU6dq/vz5qlevnh5//HG99dZb8vLyUmJiou05x44dq4CAAO3evVsnTpzQk08+qbVr1yovL0/JycmyWCwaNWqUCgoKVFhYqEmTJqljx45auHChPv/8c3l4eKh379566qmn7LaV2rVrV5nRE0nq06dPhVdSnjx5sq655hpJUuPGjbV79+4yt3fp0sUWWPz8/HT27Flbv0jSgQMHdOrUKdt95s2bp/fff19nzpwp8zwRERFat26doqKiJEn//Oc/1b17d8d+MVfACE4tlpIiJSZKGRmSYVh/JiZa2wEA1cPb21u33HKLtm3bJkn67rvvFBERYbv97Nmzevfdd7VixQodOHBA6enpevLJJ/XZZ58pPT1d//rXv+wGCi8vL33wwQcKDQ3V999/r/fff1+hoaHatm2bcnNz9eCDD2rp0qV6/vnntWjRIknSe++9p+XLl2vFihXy8/OrsK1Uhw4dbCMrpX8ut02Er6+vPD09VVJSomXLlunee+8tc7unp6d8/7fh1+rVq9WzZ09buJGkJUuWaPDgwbbjBg0a2H2d9u3ba//+/Tp9+rSOHTum8+fPV/sO64zg1GITJkgFZfcKVUGBtZ1RHACoPjExMfrkk0/UtGlTBQQE2P6RlyR/f389/fTTkqT9+/fr5MmT8vHx0fPPP6/4+HgtWLBA3t7e5Z6zdJQjMDBQv//97yVJTZs21alTp9S0aVO99dZb+tvf/qaioiLb60VHR+vRRx/VPffco/vuu6/CtqtRUlKiF198UV27dlW3bt3s3ueLL77Q6tWr9d5779naioqKtHPnTiUlJVXqdSIiIvTFF1/o9OnT6tu3r06dOnXVtV+MEZxa7FAFe4JW1A4AqJpu3bpp27Zt+vTTT8ucSikqKtKUKVM0d+5cJScn65ZbbrHdlpubKz8/Px05csTuc1488nHx3w3D0AcffKDmzZtr+fLlZQLDyy+/rKSkJOXm5iohIUHFxcV220rt2rXLNvm39M+l82ouNW7cOAUHB2v48OF2b9+8ebMWLFigRYsWqWHDhrb27du3251vU5GYmBh99tlnSk1NVXR0dKUfV1mM4NRiQUHW01L22gEA1cfHx0ddunTRmjVr9Prrr6ukpESSdObMGXl6eqpZs2bKzs7Wrl27dP78eZ06dUoffPCBVq1apSeeeEIRERFlwsCV5OXlqW3btpKsoyUXP+fw4cM1fPhw7dixQzk5Ofrwww/LtJ0+fVqNGjWS9Nspqsr6+OOP5e3trREjRti9/dSpU5o1a5bef/9922uU+umnn9SuXbtKv1bHjh11+PBhNWjQQNdee22lH1dZBJxabNo065ybi09T+fpa2wEA1SsmJkYnTpxQ/fr1bauoGjdurPDwcA0cOFDt2rXTE088oRkzZuiOO+7Qo48+qqZNm2rw4MGaM2eOJk+eXOnXGjBggMaMGaPPPvtM8fHx+uSTT7Rhwwbl5eVp0KBB8vX1VadOnXT99deXa7s0eDhi2bJlOnfunBISEiRJrVu3VlJSkkaOHKkZM2Zo/fr1ysvL03PPPWd7zMyZM3XdddcpNzdXQRf9H3ZOTo5Gjx6tw4cPq6SkRLt27SrXBz169FCTJk3K1VH6evXq1avye7EYhmFU+dFOVNF26O6kpreEt6c2r6JyRX/VZvRX5dFXjjFVfznhS9FU/eUENd1fFeUDRnBqufj42hNoAKBGlS4tLR3WLl1aKvFFWQcxyRgAYA6XW1qKOoeAAwAwB5aW4iKcogIAmEMNLC3NysrSvffeqw4dOkiyLgtv1qyZ3njjjTJLuyvy1VdfKTU1VaNGjdK8efM0ZcqUKtfiiOzsbA0bNkx33nmnxowZI0maOnWq9u7dK8l6cUI/P78y17HZtm2bnn32WbVp00aSFBoaqkmTJmns2LHavXu3bfLy448/rhtvvFEjRoyo1r2jqhsBBw6rzRObAZhYDS0tDQkJKbPU+qmnntK6det0//33V/o5mjVr5rRwI1n3gOrWrZsuXLhgayvdAFOS/vrXv6p169blHnfHHXfozTffLNf+/PPPq3fv3rbjrKysaq64+hFw4BDm8AFwW6VfQjX8f2ChoaHK+N9I0YwZM/Tjjz/q3Llzeuihh/Tggw8qPT1dY8aMkb+/v23ZdFZWlm3Eo0+fPlq3bp3q16+vmTNnqk2bNuratateeOEFeXh4qKSkRLNnz9b1119ve82LR19KzZs3r8Il4fPmzdOGDRu0b9++crfl5+dr69atGjZsWLX0x6ZNm5ScnGwb7QkKCtL333+vhx56SOnp6fruu+/02GOPKd7J/0gQcOAQtocA4NZqeGnp+fPn9d133+mJJ57QuXPndP3112vcuHEqLCxUZGSkHnzwQb311lsaPny4IiMjK33tm9TUVHXv3l3Dhg3T7t27lZubWybgXDz6UhkV7QElSatWrdIf/vAHWSyWcrf9/PPPeuqpp5Sfn6/hw4crPDxckpScnKzFixerSZMmZWrJyMjQ22+/rUWLFik/P19paWmaP3++8vPzdc8992jjxo3avXu33njjDQIO3Btz+ADUNb/88ovtwnfp6ekaMGCAIiMjJVlHQ+Li4uTt7a28vDxJ1v2obrvtNknSnXfeqX//+99XfI3w8HANHz5cp06dUnR0tDp16lRD70b65JNPtHLlynLtrVq10vDhw9WvXz9lZmZqyJAh2rBhgwYMGKBGjRopLCxMCxcu1F//+lc99thjOnv2rIYNG6aZM2eqYcOGys/PV1BQkBo3biwfHx8FBASoefPmOnz4cLXvM1UZBBw4hO0hANQ1F8/BGTFihK677jpJ1l3Fv/32Wy1dulTe3t62UGIYhm105OI5MPacP39ekvW01z/+8Q998803mjNnjgYOHFhmjo+jp6gqcvDgQTVu3NjuFYKbN2+u/v37S5KCgoLUtGlT5eTklNlws0+fPra9sY4cOaL77rtPy5Yt07T/zXO6eOK1l5drIwbLxOGQadOsc/YuxvYQAOqKF154QUuWLNHZs2eVl5enFi1ayNvbWxs3blRJSYmKiooUEhKiXbt2SbKuTLpUgwYNlJubq5KSEv3www+SpE8//VT79u1TZGSknn32WdvjS02aNElLly4t86cqWzJcbr+ojz/+WH/7298kWTcKPX78uJo3b65nnnlGmZmZtvdTusoqJCRESUlJOnTokL7++muHa6lpjODAIU6awwcAbumGG25Qt27d9Pbbb+vJJ5/UokWLNHjwYEVGRqpXr15KSkrSn//8Z40bN05LlizRDTfcYBulKTV48GA99dRTCgkJ0Y033ijJenpo8uTJ8vX1laenpyZOnFjlGkv3gMrNzdXZs2dte0DdeOONys3NVUBAQJn7l+771KdPH40ePVobN27U+fPnlZSUJB8fH8XHx+u5557T7373O/n6+mrGjBk6e/asJMlisWjatGl66qmnNHfu3CrXXBPYi6oasT+JY+gvx9BflUdfOYb+cgz95RhX7UXFKSoAAGA6BBwAAGA6BBwAAGA6BBy4tZQUqVUrycPD+jMlxdUVAQBqA1ZRwW2xLQQAoKoYwYHbuty2EAAAXA4BB26LbSEAAFVFwIHbqmj7h0vbmacDALiU0wLOrFmzFBsbq4EDB2rDhg1lbtuyZYsGDRqk2NhYzZ8/31klwc1VZluI0nk6GRmSYfw2T4eQAwB1m1MCzrfffqt9+/Zp5cqVevfddzV9+vQyt//lL3/RvHnztHz5cn3zzTf6+eefnVEW3Fx8vLRwoRQcLFks1p8LF5adYMw8HQCAPU5ZRdWlSxd17NhRkuTn56ezZ8+qpKREnp6eyszMlL+/v6699lpJUkREhLZu3WrbnwN1W3z85VdMMU8HAGCPUwKOp6enfP93rmH16tXq2bOnbUv1Szf+CggIsO1aeqm0tLSaL/YqFBYWun2N7qQ6+qtFi9bKzvax016ktLT9V/Xc7obPV+XRV46hvxxDfznGVf3l1OvgfPHFF1q9erXee++9Kj3e3Tc3YwM2x1RHf82eXfZaOZJ1ns7s2T7lnjslpXbvgs7nq/LoK8fQX46hvxzjjM027XHaJOPNmzdrwYIFWrRokRo2bGhrDwwM1LFjx2zHOTk5CgwMdFZZqOUqM09HYjIyANQ1Tgk4p06d0qxZs/TOO++oUaNGZW5r2bKlTp8+raysLBUXF+urr75SeHi4M8qCScTHSwcPShcuWH/aG5VhMjIA1C1OOUW1fv165eXl6bnnnrO13XnnnWrbtq2ioqKUlJSkUaNGSZL69++vkJAQZ5SFOoTJyABQtzgl4MTGxio2NrbC27t06aKVK1c6oxTUUUFB1tNS9toBAObDlYxRJ1TmooEX4+rIAFC7EXBQJ1R2MrLEhGQAMAMCDuqMykxGlpiQDABmQMABLsGEZACo/Qg4wCUqu4s5AMB9EXCASzg6IRkA4H4IOMAlHJmQLLHiCgDckVP3ogJqiyvtYl6qdMVV6aTk0hVXpc8BAHANRnCAq8CKKwBwTwQc4Cqw4goA3BMBB7gKrLgCAPdEwAGuAiuuAMA9EXCAq+DoiiuJVVcA4AysogKuUmVXXEmsugIAZ2EEB3AiVl0BgHMQcAAnYtUVADgHAQdwIlZdAYBzEHAAJ2LVFQA4BwEHcKKqrLoCADiOgAM4WXy8dPCgdOGC9Wdl97zq27c1S8sBoJJYJg64ud+WlvtIYmk5AFQGIziAm2NpOQA4joADuDmWlgOA4wg4gJtjaTkAOI6AA7g5lpYDgOMIOICbK11afu21RSwtB4BKYhUVUAvEx0u33bZfYWFhri4FAGoFRnAAE0tJsV43h+vnAKhrGMEBTOq36+dYj7l+DoC6hBEcwKS4fg6AuoyAA5gU188BUJcRcACT4vo5AOoyAg5gUlw/B0BdRsABTKr0+jnBweL6OQDqHFZRASYWH0+gAVA3MYIDwC6uoQOgNmMEB0A5XEMHQG3HCA6AcriGDoDajoADoKpBDJ8AABrlSURBVByuoQOgtiPgACiHa+gAqO0IOADK4Ro6AGo7Ag6AcriGDoDajlVUAOziGjoAajNGcAAAgOkQcADUCC4UCMCVOEUFoNpxoUAArsYIDoBqx4UCAbgaAQdAteNCgQBcjYADoNpxoUAArkbAAVDtuFAgAFcj4ACodlwoEICrsYoKQI3gQoEAXIkRHAAAYDoEHAAAYDoEHAAAYDoEHABujS0fAFQFk4wBuC22fABQVYzgAHBbbPkAoKoIOADcFls+AKgqAg4At8WWDwCqioADwG2x5QOAqiLgAHBbbPkAoKpYRQXArbHlA4CqYAQHAACYDgEHAACYDgEHAACYjlMDzt69exUZGank5ORyt/Xp00cPP/ywEhISlJCQoJycHGeWBqAOYNsHoO5w2iTjgoICTZ06Vd26davwPosWLVL9+vWdVRKAOoRtH4C6xWkjOD4+Plq0aJECAwOd9ZIAYMO2D0Dd4rQRHC8vL3l5Xf7lJk+erMOHD6tz584aNWqULBZLmdvT0tJqssSrVlhY6PY1uhP6yzH0V+XZ66tDh9pJspS776FDhtLS9jipMvfEZ8sx9JdjXNVfbnMdnBEjRuiuu+6Sv7+/hg0bptTUVMXExJS5T1hYmIuqq5y0tDS3r9Gd0F+Oob8qz15fBQVZT0tdKijIUuf7lc+WY+gvx9R0f+3cudNuu9usorr//vvVpEkTeXl5qWfPntq7d6+rSwJgImz7ANQtbhFwTp06pccff1xFRUWSpO3bt6tNmzYurgqAmbDtA1C3OO0U1a5duzRz5kwdPnxYXl5eSk1NVZ8+fdSyZUtFRUWpZ8+eio2N1TXXXKObbrqp3OkpALhabPsA1B1OCzgdOnTQ0qVLK7x96NChGjp0qLPKAQAAJuYWp6gAAACqEwEHAACYDgEHAACYDgEHAACYDgEHAACYDgEHAK4Su5QD7sdttmoAgNqIXcoB98QIDgBcBXYpB9wTAQcArsKhQ461A3AOAg4AXIWgIMfaATgHAQcArgK7lAPuiYADAFeBXcoB98QqKgC4SuxSDrgfRnAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAAIDpEHAAwM2xWzngOK6DAwBujN3KgaphBAcA3Bi7lQNVQ8ABADfGbuVA1RBwAMCNsVs5UDUEHABwY+xWDlQNAQcA3Bi7lQNVwyoqAHBz7FYOOI4RHAAAYDoEHAAAYDoOB5yCggKVlJTURC0AAADV4opzcC5cuKBPP/1U69at008//SQfHx8VFRWpcePGioiIUFxcnIKDg51RKwAAQKVcMeAMGTJE3bp10/PPP6/Q0FB5eFgHfU6ePKlt27bp1VdfVWRkpAYMGFDjxQIAAFTGFQPO4sWL5e3tXa69UaNGio6OVnR0tM6fP18jxQEAAFTFFefg2As3VbkPAACAs1RpFVVxcbH27NmjkydPVnc9AAAAV83hgHP06FGNHTtWmZmZeuedd/T555/XRF0AAABV5nDAWbx4sUaOHKnmzZtrzJgx+vjjj2uiLgAAgCpzOOAUFhbqd7/7nfbs2VMT9QAAXCwlRWrVSvLwsP5MSXF1RYDjHA44Q4YM0ezZs9WxY0ctXrxY3bt3r4m6AAAukJIiJSZKGRmSYVh/JiYSclD7OBxwQkJC9OKLLyozM1Ph4eF66KGHaqIuAIALTJggFRSUbSsosLYDtUmVdhNv3LixoqKiqrsWAICLHTrkWDvgrq44grN161adOHHCGbUAAFwsKMixdsBdXXEE59FHH1WTJk1ksVgUGhqq0NBQtW3bVqGhoWrTpo18fHycUScAwAmmTbPOubn4NJWvr7UdqE2uOIIzadIkBQYGasiQIfrzn/+s3//+99q9e7deeeUV9e7d2xk1AgCcJD5eWrhQCg6WLBbrz4ULre1AbXLFEZz4+HgNHDhQS5Ys0fTp05WQkKAJEybIYrE4oz4AgJPFxxNoUPtVahVVvXr1lJiYqCVLligjI0ODBg3SDz/8UNO1AQAAVMkVR3C2b9+uAwcO6MCBA9q/f79OnDih+vXrsw8VAABwW1cMOAkJCQoLC1P//v2VkJCgli1bOqMuAACAKrtiwElKStK+ffu0adMmLV68WI0aNbKtpgoNDVVkZKQz6gQAAKi0KwacuLi4MsdHjhxRenq60tPTlZqaSsABAABu54oBxzCMMiumWrRooRYtWigiIqLC+wAAALjSFVdRDRkyREuXLtWvv/5apr2oqEhbt27VmDFj9OGHH9ZYgQAAAI664gjOu+++q9WrV+v5559XVlaW/Pz8VFhYKMMwFB4erqFDh+qmm25yRq0AAACVcsWAc8011yg+Pl7x8fE6f/688vLyVK9ePfn5+TmjPgAAAIc5tJu4t7e3AgMDa6oWAACAalGpKxkDAADUJlcMOFu3btWJEyecUQsAAEC1uOIpqkcffVRNmjSRxWKxXdyvbdu2Cg0NVZs2beTj4+OMOgEAdUxKijRhgnTokBQUJE2bxiagqLwrBpxJkyZp9erV6tevnzp16qRffvlFu3fv1tq1a3XgwAF98803zqgTAFCHpKRIiYlSQYH1OCPDeiwRclA5VzxFFR8fr+XLl0uSpk+fLi8vL02YMEFLly4l3AAAasSECb+Fm1IFBdZ2oDIqNcm4Xr16SkxM1JIlS5SRkaFBgwbphx9+qOnaAAB11KFDjrUDl7riKart27frwIEDOnDggPbv368TJ06ofv36OnnypDPqAwDUQUFB1tNS9tqByrhiwElISFBYWJj69++vhIQEtWzZ0hl1AQDqsGnTys7BkSRfX2s7UBlXDDhJSUnat2+fNm3apMWLF6tRo0a21VShoaHsJg4AqHalE4lZRYWqumLAiYuLK3N85MgRpaenKz09XampqQQcAECNiI8n0KDqHNqqQZJatGihFi1aKCIioibqAQAAuGpO3aph7969ioyMVHJycrnbtmzZokGDBik2Nlbz5893ZlkAAMBknBZwCgoKNHXqVHXr1s3u7X/5y180b948LV++XN98841+/vlnZ5UGAABMxmkBx8fHR4sWLbK7G3lmZqb8/f117bXXysPDQxEREdq6dauzSgMAACbj8BycKr+Ql5e8vOy/XG5urgICAmzHAQEByszMLHe/tLS0GquvOhQWFrp9je6E/nIM/VV59JVj6C/H0F+OcVV/OS3gVIewsDBXl3BZaWlpbl+jO6G/HEN/VR595Rj6yzH0l2Nqur927txpt92pk4wrEhgYqGPHjtmOc3Jy7J7KAgAAqAy3CDgtW7bU6dOnlZWVpeLiYn311VcKDw93dVkAAKCWctopql27dmnmzJk6fPiwvLy8lJqaqj59+qhly5aKiopSUlKSRo0aJUnq37+/QkJCnFUaAAAwGacFnA4dOmjp0qUV3t6lSxetXLnSWeUAAAATc4tTVAAAANWJgAMAAEyHgAMAAEyHgAMAAEyHgAMAAEyHgAMAwFVISZFatZI8PKw/U1JcXRGkWrZVAwAA7iQlRUpMlAoKrMcZGdZjSYqPd11dYAQHAIAqmzDht3BTqqDA2g7XIuAAAFBFhw451g7nIeAAAFBFQUGOtcN5CDgAAFTRtGmSr2/ZNl9faztci4ADAEAVxcdLCxdKwcGSxWL9uXAhE4zdAauoAAC4CvHxBBp3xAgOAAAwHQIOAAAwHQIOAAAwHQIOAAAwHQIOAAAwHQIOAAAwHQIOAAAwHQIOAAAwHQIOAAAwHQIOAAAwHQIOAAAwHQIOAAAwHQIOAAAwHQIOAAAwHQIOAAAwHQIOAAAwHQIOAAAwHQIOAAAwHQIOAAAwHQIOAAAwHQIOAAAwHQIOAACoUEqK1KqV5OFh/ZmS4uqKKsfL1QUAAAD3lJIiJSZKBQXW44wM67Ekxce7rq7KYAQHAADYNWHCb+GmVEGBtd3dEXAAAIBdhw451u5OCDgAAMCuoCDH2t0JAQcAANg1bZrk61u2zdfX2u7uCDgAAMCu+Hhp4UIpOFiyWKw/Fy50/wnGEquoAADAZcTH145AcylGcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOkQcAAAgOl4OeuFpk+frh9++EEWi0Xjx49Xx44dbbf16dNHLVq0kKenpyTp1VdfVfPmzZ1VGgAAMBmnBJzvvvtOGRkZWrlypfbv36/x48dr5cqVZe6zaNEi1a9f3xnlAAAAk3PKKaqtW7cqMjJSktS6dWvl5+fr9OnTznhpAABQBzllBOfYsWNq37697TggIEC5ublq0KCBrW3y5Mk6fPiwOnfurFGjRslisZR7nrS0NGeUW2WFhYVuX6M7ob8cQ39VHn3lGPrLMfSXY1zVX06bg3MxwzDKHI8YMUJ33XWX/P39NWzYMKWmpiomJqbc48LCwpxVYpWkpaW5fY3uhP5yDP1VefSVY+gvx9Bfjqnp/tq5c6fddqecogoMDNSxY8dsx0ePHlWzZs1sx/fff7+aNGkiLy8v9ezZU3v37nVGWQAAwKScEnDCw8OVmpoqSdq9e7cCAwNtp6dOnTqlxx9/XEVFRZKk7du3q02bNs4oCwAA1JCUFKlVK6l9+3Zq1cp67ExOOUV12223qX379oqLi5PFYtHkyZO1du1aNWzYUFFRUerZs6diY2N1zTXX6KabbrJ7egoAANQOKSlSYqJUUCBJFmVkWI8lKT7eOTU4bQ7O6NGjyxy3a9fO9vehQ4dq6NChzioFAADUoAkTSsPNbwoKrO3OCjhcyRgAAFSrQ4cca68JBBwAAFCtgoIca68JBBwAAFCtpk2TfH3Ltvn6WtudhYADAACqVXy8tHChFBwsWSyGgoOtx86afyO56EJ/AADA3OLjrX/S0va45MKIjOAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAADTIeAAAIBql5IitWoltW/fTq1aWY+dycu5LwcAAMwuJUVKTJQKCiTJoowM67Ekxcc7pwZGcAAAQLWaMKE03PymoMDa7iwEHAAAUK0OHXKsvSYQcAAAQLUKCnKsvSYQcAAAQLWaNk3y9S3b5utrbXcWAg4AAKhW8fHSwoVScLBksRgKDrYeO2uCseTEgDN9+nTFxsYqLi5OP/74Y5nbtmzZokGDBik2Nlbz5893VkkAAKCGxMdLBw9Ku3fv0cGDzg03kpMCznfffaeMjAytXLlS06ZN07RLxqj+8pe/aN68eVq+fLm++eYb/fzzz84oCwAAmJRTAs7WrVsVGRkpSWrdurXy8/N1+vRpSVJmZqb8/f117bXXysPDQxEREdq6daszygIAACbllAv9HTt2TO3bt7cdBwQEKDc3Vw0aNFBubq4CAgLK3JaZmWn3edLS0mq81qtRWFjo9jW6E/rLMfRX5dFXjqG/HEN/OcZV/eWSKxkbhlGlx4WFhVVzJdUrLS3N7Wt0J/SXY+ivyqOvHEN/OYb+ckxN99fOnTvttjvlFFVgYKCOHTtmOz569KiaNWtm97acnBwFBgY6oywAAGBSTgk44eHhSk1NlSTt3r1bgYGBatCggSSpZcuWOn36tLKyslRcXKyvvvpK4eHhzigLAACYlFNOUd12221q37694uLiZLFYNHnyZK1du1YNGzZUVFSUkpKSNGrUKElS//79FRIS4oyyAACASTltDs7o0aPLHLdr18729y5dumjlypXOKgUAAJgcVzIGAACmQ8ABAACmQ8ABAACmYzGqelEaJ6tonTsAAKjbOnfuXK6t1gQcAACAyuIUFQAAMB0CDgAAMB0CDgAAMB2XbLZpFnv37tXTTz+tRx55RIMHD9b27ds1Z84ceXl5ydfXV7NmzZK/v7+ry3Qbs2bN0s6dO1VcXKw//elPuvnmm/Xiiy+qpKREzZo10+zZs+Xj4+PqMt2Cvb4aN26ciouL5eXlpdmzZ9v2c0P5/rr77rslSZs3b9YTTzyh9PR0F1foXi7tr969e2vs2LHKyMhQ/fr19eabb/LddZFL+6tx48Z811fg7NmzGjt2rI4fP65z587p6aefVrt27VzzXW+gSs6cOWMMHjzYmDhxorF06VLDMAzjgQceMPbv328YhmG8/fbbxjvvvOPKEt3K1q1bjSeeeMIwDMM4ceKEERERYYwdO9ZYv369YRiG8dprrxkpKSmuLNFt2OurF1980fj0008NwzCM5ORkY+bMma4s0a3Y6y/DMIzCwkJj8ODBRnh4uAurcz/2+is5OdmYOnWqYRiGsWLFCuOLL75wZYluxV5/8V1fsU8//dRYuHChYRiGkZWVZdx9990u+67nFFUV+fj4aNGiRWV2Pm/cuLFOnjwpScrPz1fjxo1dVZ7b6dKli9544w1Jkp+fn86ePatt27apb9++kqTevXtr69atrizRbdjrq8mTJys6OlpS2c8Z7PdXSUmJFixYoIcffphRwUvY66+vvvpK9913nyQpNjbW9t8l7PeXv78/3/UV6N+/v5588klJUnZ2tpo3b+6y73oCThV5eXmpXr16ZdrGjx+vYcOGKTo6Wjt37tQDDzzgourcj6enp3x9fSVJq1evVs+ePXX27FnbPz5NmjRRbm6uK0t0G/b6ytfXV56eniopKdGyZct07733urhK92Gvvw4dOqQ9e/aoX79+Lq7O/djrr8OHD+vf//63EhISNHLkSAL0Rez118SJE/muv4K4uDiNHj1a48ePd9l3PQGnGk2dOlV//etflZqaqs6dO2vZsmWuLsntfPHFF1q9erVeeumlMu0Gl2Mq59K+Kikp0YsvvqiuXbuqW7duLq7O/VzcXzNmzNC4ceNcXZJbu7i/DMNQSEiIli5dqjZt2uidd95xdXlu5+L+4rv+ylasWKG3335bL7zwQpnvd2d+1xNwqlF6errtaordu3fXrl27XFyRe9m8ebMWLFigRYsWqWHDhvL19VVhYaEkKScnp8zpvrru0r6SpHHjxik4OFjDhw93cXXu5+L+Kigo0IEDBzR69Gj98Y9/1NGjRzV48GBXl+hWLv18NW3aVF26dJEk9ejRQz///LOLK3Qvl/YX3/UV27Vrl7KzsyVJYWFhKikpUf369V3yXU/AqUZNmza1fTH89NNPCg4OdnFF7uPUqVOaNWuW3nnnHTVq1EiS9YshNTVVkrRhwwbdddddrizRbdjrq48//lje3t4aMWKEi6tzP5f2V/PmzfXFF19o1apVWrVqlQIDA5WcnOzqMt2Gvc9Xz549tXnzZknS7t27FRIS4soS3Yq9/uK7vmI7duzQe++9J0k6duyYCgoKXPZdz1YNVbRr1y7NnDlThw8flpeXl5o3b66RI0dq1qxZ8vb2lr+/v6ZPny4/Pz9Xl+oWVq5cqXnz5pX54nzllVc0ceJEnTt3Ttddd51mzJghb29vF1bpHuz11a+//io/Pz81aNBAktS6dWslJSW5qEL3Yq+/Zs6cqeuuu06S1KdPH3355ZeuKs/tVNRfr7zyinJzc+Xr66uZM2eqadOmLqzSfdjrrxEjRui1117ju96OwsJCTZgwQdnZ2SosLNTw4cPVoUMHjRkzxunf9QQcAABgOpyiAgAApkPAAQAApkPAAQAApkPAAQAApkPAAQAApkPAAQAApkPAAQAApkPAAeASK1asUHh4uO677z5FRkbqo48+KnefwsJCDR48WCUlJZKkrVu36oUXXqjS6xUVFSk+Pl7FxcVXVTeA2oGAA8Al9u7dq+HDh+vjjz/WnDlzNGPGjHL3WbNmjaKiouTp6SlJ2rNnj2666aYqvZ6Pj4+6deum9evXX1XdAGoHAg4Al0hPT7dd/r5ly5Z2L92+bt069e3b13a8Z88ehYWFqaioSGPHjtWcOXNkGIZGjBihKVOm6KGHHlLv3r21Y8cOvfDCC4qOjtb48eNtj4+MjNS6detq/s0BcDkvVxcAoG7au3evQkJCZBiGkpOTNXLkyDK3FxUVKTMzUy1btrS1paenq0mTJnr88cc1aNAgDRgwwPZcnTp10ksvvaQFCxZowoQJWrp0qQICAhQREaGioiL5+PioTZs2+umnn5z6PgG4BgEHgNNlZ2frzJkzSkxMVE5Ojtq2batnnnmmzH3y8vLUsGFD2/H58+eVmZmp559/XlOmTFGnTp0kSefOndOpU6c0dOhQSZLFYtGgQYMUGBgoSfLw8LCNDnl6esrb21unT5+2bVwKwJw4RQXA6fbu3avbb79d//jHP5SamqoDBw7o+++/L3OfevXqqaioyHa8f/9+3XzzzfLy8rLNyZGkffv26aabbpKHh/XrbM+ePbrlllskSUeOHFFgYKAsFovt/kVFRbrmmmtq8u0BcAMEHABOl56ebpss7O/vr3vuuUebNm0qcx9/f3+VlJTo3LlzkqzBpVOnTpozZ47GjRunY8eOSbKGpXbt2pV57rZt29oeU/p3yToq1LhxY7vzfQCYCwEHgNOlp6crLCzMdtynT59yAUeSwsPDtXPnTttj2rRpo5CQEI0ePVrPPfeczp8/r71799qe69y5cyosLJS/v7/tMRcHnG3btqlXr141+M4AuAuLYRiGq4sAAHt2796t999/X7Nnz66W5xs+fLhGjRplW70FwLwYwQHgttq3b68777zTdqG/q1FUVKTIyEjCDVBHMIIDAABMhxEcAABgOgQcAABgOgQcAABgOgQcAABgOgQcAABgOgQcAABgOv8fIk78yEp7SWoAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "plt.figure(figsize=(8, 6))\n",
        "plt.title('Mass-Radius diagram for neutron stars')\n",
        "plt.xlabel('$R$ $(km)$')\n",
        "plt.ylabel('$M$ $(M_\\odot)$')\n",
        "plt.savefig('mass_multiple_stars.png')\n",
        "plt.plot(R_plot, M_plot, 'bo', label = \"mass\", )\n",
        "plt.plot(R_plot[index], M_plot[index], 'ro', label = f'Max mass = {max_mass: .3f}M.\\nRadius = {radius_at_max_mass: .2f}km')\n",
        "plt.legend(loc='upper right')\n",
        "plt.savefig('mass_multiple_stars.png')"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print (M_plot)\n",
        "mass_fn = interp1d(R_plot,M_plot) # M(r)\n",
        "pressure_fn = interp1d(R_plot[:-1],P_plot) # P(r)\n",
        "E_plot = []\n",
        "for p in P_plot:\n",
        "    E_plot.append(EOS(p))\n",
        "ep_fn = interp1d(R_plot[:-1], E_plot) # epsillon(r)\n",
        "lamb = []\n",
        "nu = []\n",
        "for index, mass in enumerate(M_plot):\n",
        "    lamb.append(-np.log(1 - 2*M_plot[index]/R_plot[index]))\n",
        "    nu.append(np.log(1 - 2*M_plot[index]/R_plot[index]))\n",
        "lamb_fn = interp1d(R_plot, lamb) # R(lambda) \n",
        "nu_fn = interp1d(R_plot, nu) # R(nu)\n",
        "for r in R_plot:\n",
        "    print (mass_fn(r))"
      ],
      "metadata": {
        "id": "bL3M4PZ22O-N"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Boundary conditions for the pertubation functions\n",
        "def initial_conditions(l,omega):\n",
        "    nu0 = 0\n",
        "    K_0 = [epsilon_init+p0,-(epsilon_init+p0)]\n",
        "    W_0 = 1\n",
        "    H1_0 = (l*K_0 + 8*PI*(epsilon_init + p0)*W_0) / (l+1)\n",
        "    term = ((4*PI*(epsilon_init + 3*p0)/3) - (omega**2)*np.power(E, -nu0)/l)*W_0\n",
        "    X_0 = (epsilon_init + p0)*np.power(E, nu0/2)*term + K_0/2\n",
        "    X_R = 0\n",
        "    return\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "1Yx-4AA3LbTb"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def taylor_expand(r_final,l,omega):\n",
        "    p2 = -(4*PI/3)*(epsilon_init + p0)*(epsilon_init + 3*p0)\n",
        "    epsilon_2 = p2*(epsilon_init + p0)/(nu0 + 0.001)*p0\n",
        "    nu2 = (4*PI/3)*(epsilon_init + 3*p0)\n",
        "    e_nu = E ** (-nu0/2)\n",
        "    p4 = -(2*PI/5)*(epsilon_init + p0)*(epsilon_2 + 5*p2) - (2*PI/3)*(epsilon_2+p2)*(epsilon_init + 3*p0) - 32*PI*PI*(1/9)*epsilon_init*(epsilon_init + p0)*(epsilon_init + 3*p0)\n",
        "    v4 = 2*PI*(1/5)*(epsilon_2 + 5*p2) + 32*PI*PI*(1/9)*epsilon_init*(epsilon_init + 3*p0)\n",
        "    e0 = epsilon_init + p0\n",
        "\n",
        "    c1 = 32*PI*e_nu/((l-1)*(l+2))\n",
        "    c2 = -4*(1/((l-1)*(l+2)))*(8*PI*(1/3)*epsilon_init + omega*omega*e_nu)\n",
        "    c3 = -4*(1/((l-1)*(l+2)))*(2*PI*(1/3)*l*(l+1)*(epsilon_init + 3*p0) - omega*omega*e_nu)\n",
        "    c4 = 2*e_nu*(1/(l*(l+1)*(nu0+0.001)*p0))\n",
        "    c5 = 3*(1/l*(l+1))\n",
        "    c6 = 8*PI*epsilon_init*(1/3*l)\n",
        "\n",
        "    d1 = -0.25* e0\n",
        "    d2 = 0.5 * (p2 + (e0 * omega**2 * (l*(l + 3) * (e_nu**2)) / (l*(l+1))))\n",
        "    d3 = 0.5 * e_nu\n",
        "    d4 = 0.25 * nu2 * e_nu\n",
        "    d5 = 0.25 * (p2 + rho2)\n",
        "    d6 = 0.25 * e0\n",
        "    d7 = 0.5 * (omega ** 2) * (e_nu ** 2) * e0\n",
        "    d8 = -p4 + (4/3)*PI*epsilon_init*p2 - (((omega ** 2)/(2*l))*(epsilon_2 + p2 - e0*nu2))*(e_nu ** 2)\n",
        "    d9 = 0.5 * (l + 2)\n",
        "    d10 = -0.25 * l * (l + 1)\n",
        "    d11 = 4*PI*e0\n",
        "    d12 = (4/3)*PI*(e0 + (2*p0))\n",
        "    d13 = 0.5\n",
        "    d14 = - (4 * PI)  * (epsilon_2 + p2 + ((8/3)*PI*epsilon_init*e0))\n",
        "    d15 = 0.5 * (l + 3)\n",
        "    d16 = -(8*PI*e0*(l+3))/(l*(l+1))\n",
        "    d17 = 4*PI*((((2*l) + 3)*epsilon_init)/3 - p0)\n",
        "    d18 = 8*PI*(epsilon_2 + p2)/l\n",
        "    d19 = -8 * PI * e0\n",
        "    d20 = 0.5\n",
        "    d21 = 0.5 * (l+2)\n",
        "    d22 = 0.125 * (l * (l+1) * e0)/e_nu\n",
        "    d23 = -(e0/e_nu)*((0.25*(l+2)*nu2) - (2*PI*e0) - (0.5*(omega**2)*(e_nu**2)))\n",
        "    d24 = 0.5 * (epsilon_2 + p2 + (0.5*e0*nu2))*(l/e0)\n",
        "    d25 = 0.5 * e0 / e_nu\n",
        "    d26 = 0.25 * e0 / e_nu\n",
        "    d27 = 0.5 * (omega**2) * e_nu * e0\n",
        "    d28 = -0.25 * (l*(l+1) * nu2 * e0)/e_nu\n",
        "    d29 = omega*omega*\n",
        "\n",
        "    d30 = -1\n",
        "\n",
        "    T = np.array([0,d1,d2,d3],[d10,d9,d11,0],[d15,d30,d16,0],[d22,0,d23,d21])\n",
        "    U = np.array([0,d5,d8,d4,d6,d7],[0,d12,d14,0,d13,0],[d17,0,d18,0,d20,d19],[d27,d25,d29,d24,d26,d28])\n",
        "\n",
        "    return"
      ],
      "metadata": {
        "id": "SQGvXR9QIdps"
      },
      "execution_count": 3,
      "outputs": []
    }
  ],
  "metadata": {
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}