Coupling-MDCM-Dirchelet-Adaptive-endpoint-matching-Cubic.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "be27c3a6",
   "metadata": {},
   "source": [
    "This file is part of https://github.com/diehlpk/reusommer21.\n",
    "\n",
    "Copyright (c) 2021 Patrick Diehl\n",
    "\n",
    "This program is free software: you can redistribute it and/or modify  \n",
    "it under the terms of the GNU General Public License as published by  \n",
    "the Free Software Foundation, version 3.\n",
    "\n",
    "This program is distributed in the hope that it will be useful, but \n",
    "WITHOUT ANY WARRANTY; without even the implied warranty of \n",
    "MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU \n",
    "General Public License for more details.\n",
    "\n",
    "You should have received a copy of the GNU General Public License along with this program. \n",
    "If not, see <http://www.gnu.org/licenses/>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b5441b8f",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import Symbol, simplify, lambdify\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from functools import reduce\n",
    "import operator\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import sys\n",
    "from matplotlib.ticker import FormatStrFormatter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c18283b1",
   "metadata": {},
   "outputs": [],
   "source": [
    "def interpolate_lagrange(x, x_values, y_values):\n",
    "    \"\"\"\n",
    "    x : value at which to evaluate y, should be between min and max x_values\n",
    "    x_values: list or numpy array containing values of x\n",
    "    y_values: list or numpy array contaning values of y\n",
    "    \"\"\"\n",
    "    def _basis(j):\n",
    "        p = [(x - x_values[m])/(x_values[j] - x_values[m]) for m in range(k) if m != j]\n",
    "        return reduce(operator.mul, p)\n",
    "    assert len(x_values) != 0 and (len(x_values) == len(y_values)), 'x and y cannot be empty and must have the same length'\n",
    "    k = len(x_values)\n",
    "    basis = []\n",
    "    for j in range(k):\n",
    "        basis.append(_basis(j))\n",
    "    #return sum(_basis(j)*y_values[j] for j in range(k)) \n",
    "    return basis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3c932c81",
   "metadata": {},
   "outputs": [],
   "source": [
    "example = \"Quartic\"\n",
    "save_results = False\n",
    "has_condition = True\n",
    "con = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "0102259b",
   "metadata": {},
   "outputs": [],
   "source": [
    "#############################################################################\n",
    "# Solve the system\n",
    "#############################################################################\n",
    "\n",
    "def solve(M,f):\n",
    "    return np.linalg.solve(M,f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b7c775d1",
   "metadata": {},
   "outputs": [],
   "source": [
    "#############################################################################\n",
    "# Loading\n",
    "#############################################################################\n",
    "\n",
    "def f(x):\n",
    "    \n",
    "    if example == \"Cubic\":\n",
    "        return -( 2/np.sqrt(3)) * ( -6 + 4*x )\n",
    "    elif example == \"Quartic\":\n",
    "        return  -32/9 + 64/9 * x - 64/27 * x * x\n",
    "    elif example == \"Quadratic\":\n",
    "        return 8/9\n",
    "    else:\n",
    "        print(\"Error: Either provide Quadratic, Quartic, or Cubic\")\n",
    "        sys.exit()\n",
    "\n",
    "def forceFull(n,x):\n",
    "    \n",
    "    force = np.zeros(n)\n",
    "   \n",
    "    for i in range(1,n-1):\n",
    "        force[i] = f(x[i])\n",
    "    \n",
    "    force[n-1] = 0\n",
    "    \n",
    "    return force\n",
    "\n",
    "def forceCoupling(n,x):\n",
    "    \n",
    "    dim = n\n",
    "    \n",
    "    force = np.zeros(dim)\n",
    "   \n",
    "    for i in range(1,dim-1):\n",
    "        force[i] = f(x[i])\n",
    "    \n",
    "    force[dim-1] = 0\n",
    "    \n",
    "    return force"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ebed63f7",
   "metadata": {},
   "outputs": [],
   "source": [
    "#############################################################################\n",
    "# Assemble the stiffness matrix for the finite difference model (FD)\n",
    "#############################################################################\n",
    "\n",
    "def FDM(n,h):\n",
    "\n",
    "    M = np.zeros([n,n])\n",
    "\n",
    "    M[0][0] = 1\n",
    "\n",
    "    for i in range(1,n-1):\n",
    "        M[i][i-1] = -2\n",
    "        M[i][i] = 4\n",
    "        M[i][i+1] = -2\n",
    "\n",
    "    M[n-1][n-1] = 1\n",
    "\n",
    "    M *= 1./(2.*h*h)\n",
    "\n",
    "    return M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "97eb7677",
   "metadata": {},
   "outputs": [],
   "source": [
    "#############################################################################\n",
    "# Assemble the stiffness matrix for the coupling of FDM - VHM - FDM\n",
    "#############################################################################\n",
    "\n",
    "def CouplingMDCM(n,h,nFD,hFD,x1,x2,x3):\n",
    "\n",
    "    fVHM = 1./(8.*h*h)\n",
    "    fFDM = 1./(2.*hFD*hFD)\n",
    "    \n",
    "    dim = 2*nFD + n + 4\n",
    "    \n",
    "    M = np.zeros([dim,dim])\n",
    "        \n",
    "    M[0][0] = 1 \n",
    "\n",
    "    for i in range(1,nFD-1):\n",
    "        M[i][i-1] = -2 * fFDM\n",
    "        M[i][i] = 4 * fFDM\n",
    "        M[i][i+1] = -2 * fFDM \n",
    "    \n",
    "    # Same end node and start node\n",
    "    M[nFD-1][nFD-1] = -1 \n",
    "    M[nFD-1][nFD+2] = 1  \n",
    "    \n",
    "    # Interpolate the first PD node\n",
    "    weights = interpolate_lagrange(x2[0], [x1[nFD-4],x1[nFD-3],x1[nFD-2],x1[nFD-1]], [\"u1\",\"u2\",\"u3\",\"u4\"])\n",
    "    M[nFD][nFD] = -1\n",
    "    M[nFD][nFD-1] = weights[3] \n",
    "    M[nFD][nFD-2] = weights[2]\n",
    "    M[nFD][nFD-3] = weights[1]\n",
    "    M[nFD][nFD-4] = weights[0]\n",
    "    \n",
    "    # Interpolate the second PD node\n",
    "    weights = interpolate_lagrange(x2[1], [x1[nFD-4],x1[nFD-3],x1[nFD-2],x1[nFD-1]], [\"u1\",\"u2\",\"u3\",\"u4\"])\n",
    "    M[nFD+1][nFD+1] = -1\n",
    "    M[nFD+1][nFD-1] = weights[3] \n",
    "    M[nFD+1][nFD-2] = weights[2]\n",
    "    M[nFD+1][nFD-3] = weights[1]\n",
    "    M[nFD+1][nFD-4] = weights[0]\n",
    "         \n",
    "    mid = nFD+n+1\n",
    "    \n",
    "    for i in range(nFD+2,mid+1):\n",
    "        M[i][i-2] = -1. * fVHM\n",
    "        M[i][i-1] = -4. * fVHM\n",
    "        M[i][i] = 10. * fVHM\n",
    "        M[i][i+1] =  -4. * fVHM\n",
    "        M[i][i+2] = -1. * fVHM\n",
    "    \n",
    "    # Interpolate the first PD node\n",
    "    weights = interpolate_lagrange(x2[len(x2)-2], [x3[0],x3[1],x3[2],x3[3]], [\"u1\",\"u2\",\"u3\",\"u4\"])\n",
    "    M[mid+1][mid+1] = -1 \n",
    "    M[mid+1][mid+3] = weights[0]\n",
    "    M[mid+1][mid+4] = weights[1]\n",
    "    M[mid+1][mid+5] = weights[2]\n",
    "    M[mid+1][mid+6] = weights[3]\n",
    "\n",
    "    # Interpolate the second PD node\n",
    "    weights = interpolate_lagrange(x2[len(x2)-1], [x3[0],x3[1],x3[2],x3[3]], [\"u1\",\"u2\",\"u3\",\"u4\"])\n",
    "    M[mid+2][mid+2] = -1\n",
    "    M[mid+2][mid+3] = weights[0]\n",
    "    M[mid+2][mid+4] = weights[1]\n",
    "    M[mid+2][mid+5] = weights[2]\n",
    "    M[mid+2][mid+6] = weights[3]\n",
    "    \n",
    "    # Same end node and start node\n",
    "    M[mid+3][mid+3] = -1\n",
    "    M[mid+3][mid] = 1\n",
    "    \n",
    "    for i in range(mid+4,dim-1):\n",
    "        M[i][i-1] = -2 * fFDM\n",
    "        M[i][i] = 4 * fFDM\n",
    "        M[i][i+1] = -2 * fFDM\n",
    "\n",
    "    M[dim-1][dim-1] = 1\n",
    "    \n",
    "    if has_condition:\n",
    "        con.append(np.linalg.cond(M))\n",
    "        \n",
    "    return M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "323c7f42",
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute(amount):\n",
    "\n",
    "\n",
    "    hFD = 1./ amount\n",
    "    h = hFD / 5\n",
    "    nFD = int(1 / hFD)+1\n",
    "    n = int(1 / h)+1\n",
    "    \n",
    "    x1 = np.linspace(0,1,nFD)  \n",
    "    x2 = np.linspace(1-2*h,2*1+2*h,n+4)\n",
    "    x3 = np.linspace(2*1,3*1,nFD)\n",
    "    xFull = np.linspace(0,3*1,3*nFD-2)\n",
    "    xAll = np.concatenate([x1,x2,x3])\n",
    "    \n",
    "    forceFD = forceFull(len(xFull),xFull)\n",
    "    MFD = FDM(len(xFull),hFD)\n",
    "    \n",
    "    uFDM = solve(MFD,forceFD) \n",
    "\n",
    "    forceCoupled = forceCoupling(len(xAll),xAll)\n",
    "\n",
    "    forceCoupled[nFD-1] = 0\n",
    "    forceCoupled[nFD] = 0\n",
    "    forceCoupled[nFD+1] = 0\n",
    "\n",
    "    forceCoupled[nFD+n+2] = 0\n",
    "    forceCoupled[nFD+n+3] = 0\n",
    "    forceCoupled[nFD+n+4] = 0\n",
    "\n",
    "    MCoupling = CouplingMDCM(n,h,nFD,hFD,x1,x2,x3)\n",
    "    #np.savetxt(\"m.csv\", MCoupling, delimiter=\",\")\n",
    "    uCoupled = solve(MCoupling,forceCoupled) \n",
    "    \n",
    "    return xAll, xFull, uCoupled, uFDM , nFD, n\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "2c4aace4",
   "metadata": {},
   "outputs": [],
   "source": [
    "xAll = []\n",
    "xFull = []\n",
    "uCoupled = []\n",
    "uFDM = []\n",
    "nFD = []\n",
    "n = []\n",
    "for i in range(5, 9):\n",
    "    \n",
    "    res = compute(i)\n",
    "    xAll.append(res[0])\n",
    "    xFull.append(res[1])\n",
    "    uCoupled.append(res[2])\n",
    "    uFDM.append(res[3])\n",
    "    nFD.append(res[4])\n",
    "    n.append(res[5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "88cb2acb",
   "metadata": {},
   "outputs": [
    {
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     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xSlice = []\n",
    "uSlice = []\n",
    "\n",
    "for i in range(0, len(xAll)):\n",
    "    xSlice.append(np.concatenate([xAll[i][0:nFD[i]-1],xAll[i][nFD[i]:nFD[i]+n[i]+4],xAll[i][nFD[i]+n[i]+5:]]))\n",
    "    uSlice.append(np.concatenate([uCoupled[i][0:nFD[i]-1],uCoupled[i][nFD[i]:nFD[i]+n[i]+4],uCoupled[i][nFD[i]+n[i]+5:]]))\n",
    "    plt.plot(xSlice[i],uSlice[i],label=\"m=\"+str(i+5))\n",
    "    \n",
    "plt.plot(xFull[0],uFDM[0],label=\"FDM\")\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.axvline(x=1,c=\"#536872\")\n",
    "plt.axvline(x=2,c=\"#536872\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "cf67aba8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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SJUto1KgRfn5+AIwePTrSDQ6YEwmijBIlSrB169ag+++//546derw+PFjJ2plMBjeNQICAujfvz/169cPMjgjRoygR48eUVK+MTpRSNmyZdm4cWPQ/YoVKyhWrFhQ19ZgMBgik0ePHlG7dm2GDh0aFDdkyBB6937tQJhIwxidKKZixYqsXv3/6yVOnjxJwYIF2bVrlxO1MhgMsZ2LFy9SvHhxVq1aFRQ3YMAA+vfvH6V6GKPjBKpVqxa0Fj4gIID79+9Trlw5/ve//zlZM4PBEBvZsWMHhQsX5s8//8QyVQ69evVi8ODBUa6LMTpOolatWixYsACAly9f4urqytdff03nzp2DxlkNBoMhvEybNo3y5cvz5MkTXr58CUCXLl0YNWqUU/QxRseJeHl5MXPmTACePXuGm5sbEydOxNPTk7t37zpZO4PBEJN5+fIlHTp0oE2bNiROnJgnT54A0LZtW8aNG+c0vYzRcTJfffUVU6ZMAeDx48ckTpwYX1/foK6wwWAwvCm3b9/Gw8ODn3/+mTRp0nDv3j3g1d8bZ2GMTjSgbdu2jB8/HrCsLokfPz63b9+mSJEirF+/3rnKGQyGGMXJkycpXLgwu3btIl26dNy8aTkJrEGDBsyYMcPJ2hmjE23o3LkzI0eOBCyG59mzZ6RNm5YqVaowZsyYoMk/g8FgsMeaNWsoVqwYDx48IEWKFFy7dg34/zlkEVvnHkctxuhEI7799lsGDRoEWI7M+fvvv/niiy/o2bMnX331Fc+ePXOuggaDIVqiqowcOZLq1auTOXNmXFxcuHHjBgCenp4sXbo0WhgcMEYn2jFw4EC+/fZbwDIRuGfPHurVq8ecOXMoW7Zs0D8Xg8FgAMsf1MaNG9OnTx8qVqzItWvXuHXrFqpKhQoVWL16dbQ6biv6aGIIYuTIkXTu3BlVJSAggGXLltG+fXuOHz9OoUKFOHjwoLNVNBgM0YArV65QqlQpFixYQKtWrdi9ezf37t1DVSlZsiTr1q3D1dXV2Wq+gjE60ZRx48bRunXroBOrf/75Zzp06ICrqyslS5Zk0aJFzlbRYDA4kf3795M5c+agP6HTp0/n4cOHBAQEECdOHDZv3kzcuHGdrOXrGKMTTRERpk6dSrNmzVBVXFxc+OGHH2jQoAEFCxbEy8uLfv36ERAQ4GxVDQZDFDNv3jxKlSpl9/vv5+dH/Pjxo1grxzBGJxojIsyYMYN69eoREBCAq6srP/zwAwULFqRFixYMHz6cWrVq8fDhQ2erajAYogB/f3++/fZbmjRpQtGiRZ2tzlthjE40x8XFhQULFvDll1/i7+9PnDhxGD9+PCLCuHHjWLt2LcWLF+fixYvOVtVgMEQiDx48oHr16vzwww+0bduWGjVqOFult8IYnRiAq6sry5cvx8PDAz8/P+LGjcv//vc/9u7dy5o1a7h8+TKFChXC19fX2aoaDIZI4Ny5cxQtWpQNGzbw888/kyFDhihxuBYZ2PUcKiLdQhNU1bERr47BHnHixGHVqlV4eHiwbds24sWLx+LFi3n48CE7duygXr16uLu7M2nSJNq2bRt2hgaDIUbg4+ND3bp1ERE2bdrE+vXrGTNmDIkTJ+bRo0fOVu+NCa2nMwZoDKQEEgNJQgRDFBMvXjzWrVvHF198wYsXL4gfPz7r16+nY8eObNq0iYoVK/LNN9/Qrl27oNNkDQZDzERVmTRpEpUqVSJ9+vTs3buXRYsWMWbMGJIlS8ajR4/s7r9JmzZtFGvrOKEZnfzAJqAKkAX4HRiiqoNVNVxOGEQkhYhsFpGz1tfkdtJ5iMhfInJORHo7Ii8ifazp/xKRSsHifa1xR60hTXjq4CwSJEjApk2bKFSoEM+fPydBggT8/vvv1KpVixkzZtCrVy+mTJlCpUqVuH37trPVNRgMb8GLFy9o06YNnTp1wtPTk+3bt9O/f3+mT59OihQpuH//PmnSpOHixYtB2yqCh+vXrzu7Cnaxa3RU9aiq9lbVvMD/gOrAKRH5MgLK7Q34qGp2wMd6/woi4gr8DFQGPgW8ROTT0OStzxsAuQAPYLI1n0AaqWpea7gZAfVwCokSJcLHx4c8efLw9OlT4sePz/HjxylXrhydO3dmzpw57N69m0KFCnHixAlnq2swGN6AW7duUaFCBaZPn06fPn1YuHAhzZo1Y/HixaRJk4Y7d+6QMmVK9uzZQ+bMmZ2t7hsT5kICEUkN5AM+By4DEfFjXR2Ybb2eDdSwkaYwcE5VL6jqC2CRVS40+erAIlV9rqoXgXPWfGIdSZIkwdfXl5w5c/L48WPixYvHpUuXKFGiBF988QXbt2/n6dOnFCtW7BX32AaDIfoSeOrIgQMHWLBgAb1796ZKlSqsW7cu6MTo9957j127dvHBBx84W923QuydXiwizYH6QAJgGbAkonoHInJPVd8Ldn9XVZOHSFMH8FDVr633TYAiqtrBnryI/ATsVdV51vj/AetVdZmI+GKZn/IHlgND1U7lRaQ10Bogbdq0Bd529/+jR49InDjxW8k6yv379+nQoQOXL18mUaJEiAgJEyZk9OjRuLm50b9/f86cOUPLli1p2LDhWx/6FxV1iWy8t+7G39+fuu4lna1KhBAb2gRMuwSyc+dOhg8fTuLEifn+++9Jly4dvXv35syZM6RMmZJbt26RMGFCfvrppygxOOH9fJUtW/aQqhZ87YGt8UDrb3EAcAxYYw2rgwd7csHktwAnbITqwL0Qae/akK8L/BrsvgkwyXptUx7LcFzjYPH/A2pbrzNYX5NgmatqGlYdVJUCBQro27Jt27a3ln0Trl27plmzZlUR0WTJkmnq1Kk1ZcqUevDgQX3y5Il6eXkpoF5eXvrkyZO3KiOq6hKZ9P/xZ+3Yf5iz1YgwYkObqJp2CQgI0CFDhiighQsX1qtXr+rVq1c1V65cGj9+fM2aNasC6ubmpocOHYocpW0Q3s8XcFBt/KbaXTINlH0TqxYSVa1g75mI3BCRdKp6TUTSYXvI7jKQKdh9RuCq9dqevF0ZVb1ifX0oIguwDLvNeYuqRTvef/99du7cSbFixbhy5QrJkycnYcKElC1blrVr1zJ//nxy585N3759OXPmDCtXriRjxozOVttgeOfZtm0bnTp14sSJEzRp0oRp06Zx7do1KlSowI0bN8iYMSPnz58nQYIEbN68mfz58ztb5XAT2kKC7YEBOAWcChEXHlYDzazXzYBVNtIcALKLSDYRiYdlgcDqMORXAw1EJL6IZAOyA/tFJI6IpAIQkbhAVSy9rlhDxowZ2blzJ2nSpOHu3bs8ffqU1KlTU6lSJdavX0/v3r1ZtWoVf/31F4UKFWLfvn3OVtlgeKdZuXIl5cuX58SJE8SNG5e2bdty4cIFSpQowZ07d8iUKRPnz58nXrx4bNiwgWLFijlb5QjBrtERC4NE5D/gT+CMiNwSkQERUO5IwF1EzgLu1ntEJL2IrANQVT+gA7AROI1lTulkaPLW50uwGMkNQHtV9QfiAxtF5DhwFLgCTI+AekQrsmbNys6dO0mZMiX37t3j4cOHfPDBB1SvXp0lS5ZQrVo19u7dS6JEiShdujTz5s1ztsoGwzvJ7t27ady4cZBH4ICAABYsWECpUqXw8/Mjffr0/Pnnn8SJE4c1a9ZQunRpJ2sccYQ2vNYF+AIopJaVYIjIB8AUEemqquPetlBVvQ2UtxF/FfAMdr8OWOeovPXZMGBYiLjHQIG31TcmkT17dnx9fSlZsiS3b99GRMibNy9eXl48fPiQli1bsn//furWrUuTJk04fvw4I0aMiHY+NwyG2MrMmTNp27YtqVOnxt/fn5cvXxInThxmzpxJqlSpeO+99zh+/Diurq54e3tTsWJFZ6scoYS2ZLop4BVocABU9QKWUwqaRrZihrcnV65cbN26FTc3N/777z8uX77MF198wddff824ceNImTIlGzdupF27dowePZovv/yS+/fvO1ttgyFW4+fnR7du3WjRogWlSpXi+PHjbN26lSZNmqCqZMiQgRQpUvDHH3/g4uLCwoULqVatmrPVjnBCMzpxVfW/kJGqeguIfp6BDK+QN29etmzZQsKECbl58ybnz5+ncuXKdOvWjUGDBhEnThx+/vlnpkyZwqZNmyhWrBjnzp1zttoGQ6zk3r17VK1alXHjxtGpUyfWr19PihQpuHLlCvPnz+eTTz4hWbJkHD16FIBZs2ZRt25d5yodSYRmdF685TNDNKFw4cKsX7+eePHicePGDY4dO0bdunUZPHgw3bp1IyAggLZt27J582Zu3rxJ4cKF2bJli7PVNhhiFX/99RdFihRh69atTJ8+nQkTJgQNp9WvX58CBQqQIEGCIA+gv/zyC02aNHGy1pFHaEYnj4g8sBEeYjmdwBADKFmyJGvXrsXV1ZUbN26wZ88emjdvzvjx4/n666/x9/enTJkyHDhwgAwZMuDh4cHEiRODJjgNBsPbs3HjRooUKcLdu3fx8fHh66+/BmDChAm0aNGCsmXLIiIcOHAgKL5Vq1bOVDnSCW3JtKuqJrURkqiqGV6LQZQvX54VK1YgIly7do2ZM2cClgnNOHHiICJ88MEH3Lhxg6pVq9K5c2dat27NixemQ2swvA2qytixY/H09CRRokRMmDCBkiVLoqoMHjyYLl26kDNnTp49e8aePXtQVUaOHEmnTp2crXqkE9qS6VrBrm2eAm2IOXh6erJ48eJQ09y6dQtvb2/69evHr7/+SoUKFbh161YUaWgwxA5evHhBixYt6N69OzVq1ODXX3+lU6dObN26le7duzNo0CDix49P3Lhx+f333wEYOHAg3377rZM1jxpCWzL9HeBtvfbB4urAEIOpVasWc+bMoVGjRnbTuLi4MHToUD7//HO++uorChUqxKpVtvbuGgyGkFy/fp1u3bpx8uRJBg4cyIABA4JWolWpUoVnz56RIEECPv74Y44fPw5Ar169GDhwoJM1jzpCm9MRO9eGGEzDhg1DfR7Ys6lfvz67du3Cz8+P4sWLs2PHjqhQz2CIsRw+fJhChQpx/vx5li5dyqBBg3BxceHFixdMnz6dZ8+eARYHa4EGp2PHjowcOfKtD+KNiYRmdBKKSD4RKQAksF7nDwxRpaAhailVqhRXrlwBoECBAhw4cIDcuXMzcOBAhgwZQkBAgJM1NBiiH4sXL6ZEiRKICBMnTqROnToAPHnyhBo1arBkyRLc3NzImjUrf//9NwBff/0148ePf6cMDoRudK4BY7G4rb5uvf7RGsZEvmoGZ3DlyhVKlCjB+fPnAUiXLh3btm2jYsWKDBw4kPr16/P48WMna2kwRA8CAgLo378/DRo0IH/+/Bw4cIDs2bMD8ODBAzw8PFi/fj2JEycmR44cXLp0CYD48eNTv359u+6mYzOhrV4rG0ooF5VKGiIWe/7TXVxcWLx4MQ8fPqRkyZJBXkcTJEhA7969GTNmDN7e3pQoUYJ//vknKlU2GKIdjx49onbt2gwdOpQWLVrg4+MT9N3677//KFeuHHv27KF+/frkyJGDw4cPA1CnTh3Wrl0bdP+u8e6ZWQPXr18P8m0REBBAnz59AHB1daVz584sW7YMgNKlSwftHxARunfvztq1a7lw4QKFChUKWnljMLxrXLx4keLFi7N69WrGjx/Pr7/+Svz48QHLvGjp0qU5efIkS5Ys4d69exw6dAiAqlWrMn/+fCpUqECvXr2cWQWnYYzOO46IMGzYMLp06cLLly+5dOkSbdq0wdvbm/fee49y5crh6+sblL5y5crs27ePZMmSUbZsWWbMmOE85Q0GJ7B9+3YKFy7Mv//+y/r16+ncuXPQvMyFCxfo3Lkz//zzD6tXr2batGls3LgREcHd3Z2lS5cSL148J9fAuRijY0BEGDt2LG3atOHly5dcvHiR5s2bs3z5cjJnzoyHhwd79uwJSv/JJ5+wb98+ypQpQ8uWLenatSt+fn5OrIHBEDVMmzaNChUqkDJlSvbt2/fKCdAnT56kRIkSPH78mA0bNjBu3Dg2bNiAi4sLJUuWZOXKlSRIkMCJ2kcPwjQ6IuLjSJwhZiMiTJ48mWbNmvHy5UsuXLhAw4YNWbp0KZ9//jn9+/dn0aJFQemTJ0/OunXr6Ny5M+PHj8fT05O7d+86sQYGQ+Tx8uVLOnToQJs2bahQoQL79u3j448/Dnp+4MABSpUqBcDo0aMZMWIE69evx9XVlUKFCrF27VoSJUrkLPWjFaGdSJBARFIAqUQkuYiksIasQPoo09AQZbi4uPC///2P+vXr8+LFC86dO0fdunVZuHAhuXLlomHDhkybNi0ofZw4cYLGs319fSlSpAh//vmnE2tgMEQ8t2/fxsPDg59//jloXjNZsmRBz7dv30758uVJliwZPj4+zJo1i99++424ceOSO3duNmzYQJIkSZxYg+hFaD2dNsAh4BPra2BYBfwc+aoZnIGrqytz586levXqvHz5knPnzlG9enX69OlD5cqVadOmDWPGvLpivmXLlmzdupV79+5RpEgR1q9f7yTtDYaI5eTJkxQpUoRdu3Yxa9YsxowZ84rDw3Xr1uHh4UHGjBnp1KkTBQoUCBqKTpMmDZs2beK9995zkvbRk9CWTE9Q1WxAD1X9QFWzWUMeVf0pCnU0RDFx48Zl8eLFeHh48PLlS86ePUufPn2YNm0a9evXp2fPnvTv3/+Vk6hLlCjBwYMHyZYtG1WrVuXHH380J1UbYjRr166lWLFiPHr0iO3bt9OsWbNXni9evJjq1auTK1cu2rVrR48ePXj69GnQ8zt37rBx48aoVjvaE+acjqpOChknIu9HjjqG6EL8+PHx9vamTJky+Pv7c/nyZSpXrhzkEmHo0KF07tz5lRMKMmfOzO+//07NmjXp0aMHX331VdDRHwZDTEFVGTVqFF9++SXZs2fn4MGDFC1a9JU006dPx8vLi+LFi7NhwwZ69eqFv7//K2mePn1Kv379olL1GMHbrl77X3gKtc4NbRaRs9ZXm6dYi4iHiPwlIudEpHdY8iKSUkS2icgjEfkpRF4FROQPa14T5V07e+ItSJgwIatXr6Zo0aIEBATw559/UrFiRYYPH0737t2ZNGkSLVq0eGXlmpubG0uWLGHQoEHMmTOHsmXLcu3aNSfWwmBwnKdPn9K4cWN69+5NvXr12LlzJxkzZnwlzY8//kjr1q3x8PBg9erVtG7d+pUeTnDMJurXCdXoiIiriLzmSlJVq4Sz3N6Aj6pmx3KCde+QCUTEFcvcUWXgU8BLRD4NQ/4Z0B/oYaPMKUBrILs1eISzDu8EiRMnZt26dUFHe/z5559UqFCB3r17M2TIEGbPnk39+vV5/vx5kIyLiwsDBw5k2bJlHD9+nEKFCgV5RTQYoitXrlyhdOnSLFiwgKFDh7Jw4cJXVpypKgMGDKBHjx7UrVuXpUuX0rJlyyBfVbbInDlzVKkfYwjV6KiqP/BERJKFlu4tqA7Mtl7PBmrYSFMYOKeqF1T1BbDIKmdXXlUfq+ouLMYnCBFJByRV1T1qmWiYY6dMgw2SJUvGDz/8QM6cOXFxceH06dO4u7vTrl07JkyYgLe3N19++eVrZ7LVrl2b3bt34+rqSsmSJV9Zcm0wRCf2799PoUKFOHXqFCtXrqRfv36vGJKAgAC6dOnC999/T8uWLZkzZw5fffUVy5cv57333sPNze21PTiJEiVi2LBhUV2VaE9o/nQCeQb8ISKbgaBfFVUNj4u7tKp6zZrPNRFJYyNNBuDfYPeXgSJvIB8yr8sh8spgL7GItMbSKyJt2rSv7Mh/Ex49evTWstENFxcXBg0aRJcuXbh+/Tp//PEHxYoVY8yYMXz77beMHj2aIkWKMHLkSBInTvyK7Pjx4xk4cCBeXl6sXbuWFi1aOOWgw3v37uHv7x9r2iS2fL6c3S6bN29m9OjRpEyZkokTJ5IsWbJXdPH392fMmDFs2LCBunXr0qBBAzw8PNi+fTtJkybFz8+PsWPH8vfff/Prr79y8+ZN0qRJw9dff02GDBlibBtF2ucr8AwuewFoZis4ILcFOGEjVAfuhUh714Z8XeDXYPdNgEnW61Dlga+An4LdFwK2BLsvCawJqw6qSoECBfRt2bZt21vLRjcC63LlyhX98MMPNXHixBo3blzNly+f3r59W5ctW6Zx48bVvHnz6o0bN16Tf/78ubZs2VIBrV69uj548CCKa6Da/8eftWP/YVFebmQRWz5fzmoXPz8/7dWrlwJaunRpvXXr1mtpnj17prVr11ZABw8erC9evND69esroKlTp9YkSZLo3r17X5GJLe0S3noAB9XGb2qYPR1VnR1WGjtyFew9E5EbIpJOLb2UdMBNG8kuA5mC3WcErlqvHZEPmVfw2cDgeRnegPTp0+Pj40OpUqW4d+8ef/zxB+7u7mzZsoU1a9ZQs2ZNSpUqxebNm8mU6f+bL168eEyfPp08efLQtWvXoMMSs2XL5sTaGN5VHjx4QMOGDfntt99o06YNEydOfO1MtMePH1OrVi02bdrE+PHjad++PU2aNGHx4sWkS5eO+/fvs2HDBooUKWKnFIMt3mqMQ0QGhbPc1Vh6TFhfbflDPgBkF5FsIhIPaGCVc1Q+CLUMxT0UkaLWVWtNw5Ix2CdLliz4+Pjg5uZG4sSJgwxPkSJF2LRpE9euXaNEiRKcPXv2FTkRoWPHjmzYsIErV65QqFChGDv0YIi5nDt3jqJFi7JhwwYmT57M1KlTXzM49+/fJ3ny5GzatAmALl26EDduXBYtWoSLiwt37txh1apVlCxZ0hlViNG87cD6oXCWOxJwF5GzgLv1HhFJLyLrAFTVD+gAbAROA0tU9WRo8tY8LmFxOPeViFwOtuLtG+BX4BxwHjDb5sPBRx99hI+PD3HjxiVZsmQcO3YMd3d3PvvsM7Zt28aTJ08oWbJkkFve4ASeXZU6dWrc3d2ZOnWqE2pgeBfx8fGhcOHC3Lhxg82bN/PNN9+8lubWrVuULVuWly9f2swjICCA5cuXU6GC3cEcQyg4cuDneRGZLyJtA3/AVXVNeApV1duqWl5Vs1tf71jjr6qqZ7B061T1Y1X9UFWHhSVvfZZVVVOoamJVzaiqp6zxB1X1M2teHaxjjoZwkDNnTrZs2YK/vz8pU6bk6NGjVKpUiQ8//JAdO3YQJ04cSpcuzd69e1+TzZ49O3v37qVixYp88803tGvXzu6X3GAIL6rKTz/9RKVKlUiXLh379++nbNmyr6W7fPkypUqVCvMMwSpVwrtr5N3FkZ7Op8AvQEpgjIhcEJEVkauWIaaQO3duNm3axNOnT0mbNi2HDx+mUqVKpE+fnl27dpEyZUoqVKjA1q1bX5NNliwZq1evplevXkyZMoWKFSty+/ZtJ9TCEJt58eIFbdu2pWPHjnh6erJnzx4+/PDD19KdO3eOEiVKcPXqVXN8TSTiiNHxB15aXwOAG4Q9cW94hyhYsCDr16/n3r17pE+fnoMHD+Lh4UGKFCnYuXMnWbNmxdPTk9WrV78m6+rqyqhRo5gzZw579uyhUKFCQW6yDYbwcuvWLdzd3Zk2bRq9e/dm5cqVJE2a9LV0f/zxByVLluTx48ds27aN4sWLO0HbdwNHjM4DYDxwEctS6WKq2iZStTLEOIoXL86aNWu4efMmWbJk4cCBA3h4eODm5sb27dvJkycPtWrVYsGCBTblmzRpwvbt23n27BnFihWzaaAMhjch8DSM/fv3s2DBAkaMGGFzf9j+/fspXbo0Li4u7Nixg7x58/L11187QeN3A0eMjhewA2gHLBKRwSJSPnLVMsREypYty4oVK7h8+TIffPAB+/fvp3LlysSLF48tW7ZQsmRJGjduzJQpU2zKFylShAMHDvDJJ59Qo0YNRowYYU6qNrwVK1asoHjx4rx8+ZIdO3bg5eVlM922bdsoX748KVKkYNeuXeTIkYOvv/6aWbNmESeO7R0ladOmjUzVYz2OnDK9SlV7YvGvsw7Lxsu1kayXIYbi4eHBkiVLuHjxIjly5GDv3r1UrlwZsPgeqVKlCu3atWPkyJE25TNkyMCOHTto0KABffv2pVGjRnYPUzQYQqKqfP/999SqVYtcuXJx8OBBChUqZDPtmjVrqFy5MlmyZGHnzp1kyZKF1q1bM3PmTPLnz4+fnx9Dhgx5bXPj9evXo7hWsQtHVq8tF5HzwATADcseF5unQhsMANWrV2fevHn8+eef5MqViz179uDp6Ym/vz/e3t40aNCAPn360KdPH5s9mYQJEzJ//nyGDx/OokWLKFWqFFeuXHFCTQwxiSdPnlC/fn0GDBgQNFybLl06m2kXLlxIrVq1yJ07N9u3bydt2rS0adOG//3vfxQuXJjDhw/Tp08fvvvuuyiuRezHkbPXRgKH1XL4p8HgEPXr1+fZs2d89dVX5M+fn927d+Pp6cm6deuYN28eSZMmZeTIkTx48IBJkya9NtYuIvTp04dcuXLRqFEjChYsyMqVK83ub4NN/v33X6pXr87Ro0f54Ycf6NGjh92Tn6dNm0bbtm0pVaoUa9aswc3NjW+++YZff/2V4sWLs3v3brp06cKwYcPs5mF4exwZXjtgDI7hbWjWrBlTp07l8OHDFCxYkN9//50qVarw7Nkzpk6dSs+ePZk8eTLNmjV7xSdPcL788kv27t1LokSJKF26NPPmzYviWhiiO7t376ZgwYKcP3+etWvX0rNnT7vGYvTo0bRp0wZPT0/Wr1+Pm5sb7dq1Y9q0aZQqVYrdu3fTpk0bxo4dawxOJBH1R/0a3inatGnD+PHj2b9/P8WKFWPnzp1UrVqVJ0+eMGrUKIYNG8a8efOoU6eOXS+juXLlCpJv0qSJTS+NhneTmTNnUrZsWZImTcrevXvx9PS0mU5V6devH7169aJBgwasWLGCBAkS0KFDB3755RfKlSvHjh07aNq0KZMnTzYGJxIxRscQ6XTu3Jnhw4fz+++/U7p0abZv3061atV4+vQpffv2ZdKkSaxatYqqVavy6NEjm3mkTJmSTZs28c033zB69Gi+/PJLNm/ezIgRI9izZ08U18jgbPz8/OjWrRstWrSgVKlS7Nu3j5w5c9pMGxAQQKdOnRg+fDitWrVi3rx5xIkThw4dOjBlypSgzcv169dnxowZTnG78U5h6+jp4AGLh84w42JrMK4NLEREXfr376+Auru7q4houXLl9PHjx6qqOnv2bHVxcdGiRYvqnTt3Qs1n8uTJ6urqqiKiLi4umjBhQt29e3fY5RvXBtGSN22XO3fuaKVKlRTQjh076suXL+2mffnypTZt2lQB7dGjhwYEBGhAQIC2b99egaB8qlevri9evIiI6sSadoks1wZ2TbqIJBCRFEAqEUkuIimsISuQPpJtoSEWMnjwYLp3787mzZupXLkyW7du5csvv+TJkyc0bdqUZcuWcfjwYcqUKcONGzfs5vPNN9/QvHlzVJWAgACeP39uTqt+R/jrr78oWrQoW7duZdq0aUycONHufprnz59Tt25d5syZw9ChQ/nhhx8AS8/7559/xtPTk02bNuHh4cHixYuJGzduVFblnSW0fmQbLKdJf2J9DQyrgJ8jXzVDbENEGD16NO3bt2fdunXUqFGDrVu3Ur16dZ4+fUrNmjVZu3Yt586do2TJkvzzzz9282rRokWQe+CAgABu3rxpNpLGcjZu3EiRIkW4e/cuPj4+tGrVym7ax48fU7VqVVauXMnEiRPp168fYHFRMGnSJKpWrcrGjRspU6YM3t7exI8fP6qq8c5j1+io6gRVzQb0UNUPVDWbNeRR1Z+iUEdDLEJEmDhxIi1atGDlypXUqVMHHx+fIMPj7u7O5s2buXnzJiVKlODMmTM28ylWrBhbt25l4MCBlChRgvHjx9O6dWtevHgRxTUyRDaqytixY/H09Aw6Yik0Pzb37t3D3d2drVu3MmvWLDp27Iiq0rVrVyZOnEj16tWDDNjq1atJmDBhFNbG4NC8BlAcaIhlY2hToKkjcrEhmDkdCxFdFz8/P23YsKEC6uXlpSKilSpV0qdPn6qq6pEjRzR16tSaJk0aPXr0aKh5+fv7a79+/RTQEiVK2HSXrWrmdKIrobXLs2fP9KuvvlJAa9WqpQ8fPgw1rxs3bmiePHk0bty4unz5clVVDQgI0K5duyqgNWvW1Pjx42vBggX13r17EV4X1djTLlE+pxOIiMwFxgAlgELWUDAyDKDh3cHV1ZXZs2dTq1YtFi5cSJMmTdi0aRM1a9bk2bNn5M2bl507dxI/fnzKlCnD7t277ebl4uLC0KFDWbhwYdCxJ8eOHYvC2hgig+vXr1O2bFlmzZrFwIEDWbp0KYkTJ7ab/t9//6VkyZKcOXOGtWvXUqtWLVSVnj17Mm7cOGrXrs2GDRvIkSMHGzduJFmyZFFYG0MgjqwNLAh8oartVLWjNXSKbMUMsZ84ceKwcOFCPD09mTt3Li1atGDDhg3UqlWLZ8+ekSNHDnbt2hXkYXTLli2h5tegQQN27tyJv78/xYsXZ/ny5VFUE0NEc/jwYQoVKsTRo0dZsmQJgwYNCnUp85kzZyhRogTXr19n8+bNVKxYEVWlV69e/Pjjj9SpU4eNGzeSJUsWNm/eTIoUKaKwNobgOGJ0TgDvR7YihneTePHisXz5csqVK8fMmTNp3bo169evJ2HChIgIWbJk4ezZszx58gR3d3e+//77V+S3bdsWtCoJLL59Dhw4wOeff06dOnUYPHgwAQEBUV0tQzhYvHgxJUqUQET4/fffqVu3bqjpjx8/TsmSJXny5Am+vr588cUXqCq9e/dmzJgx1K1bly1btpA2bVp8fHxIkyZNFNXEYAtHjE4q4JSIbBSR1YEhshUzvDskSJCAVatW8cUXXzBjxoxQ0w4YMIA+ffoAFoNTr169104RTpcuHb6+vjRt2pRBgwZRv359Hj9+HGn6GyKGgIAA+vfvT4MGDciXLx8HDhwgX758ocrs3buX0qVLEy9ePHbu3Em+fPlQVfr06cMPP/xA/fr12bp1K0mTJsXHx4f06c1uD2fjyIGfgyK6UOv+n8VAVuASUE9V79pI54HldGtX4FdVHRmavIikBJZhmXeapaodguXlC6QDAs/Jr6iqxgNqNMHNzY21a9fi7u7O/v377abLly8fI0eO5OjRoxw8eJAlS5bY9HWfIEECZs2aRe7cuenVqxfnzp2jYr0mkVkFQzgICPCndu3arFy5khYtWjB58uQwlzEHrnpMly4dW7ZsIUuWLKhajrsZNWoUDRo0YNu2bcSLFw8fHx+yZMkSRbUxhIYjB35ux/LDHtd6fQA4HM5ye2M51SA74GO9fwURccWyH6gy8CngJSKfhiH/DOgP9LBTbiNVzWsNxuBEM5ImTcqGDRtCTbN7924+/vhjNmzYwOeff27T4AQiInTv3p21a9dy4cIFDh06xOPHto/ZMTiPZ8+ecvbsOVavXs348eP59ddfwzQ4q1atwtPTk2zZsgX5wlFV+vfvz4gRI2jQoAG7du0iICAAHx8fPvrooyiqjSEsHFm91gpL7+EXa1QGYGU4y60OzLZezwZq2EhTGDinqhdU9QWwyCpnV15VH6vqLizGxxADSZ48dFdNe/bs4c6dO3z++eds27YNLy+vMDeFVq5cmb179xInThzOnz8fak/KELXcuHGDI0eO8PLlC9avX0/nzp3DPGxz3rx51K5dm7x587J9+3bef/99VJUBAwYwbNgwvLy82LdvH48fP2bLli12z2QzOAdHhtfaYzEA+wBU9ayIhHcmLq2qXrPmd81OfhmAf4PdXwYCnak4Im+LmSLiDywHhqqdXysRaQ20Botr2rc9YuXRo0ex5niW6FKXmjVrMnDgQPLkyUP//v1ZtGgRf//9N99//z2urq6hyn74wYf8deYM1atXZ/r06aEuv40JRJc2eVsCAgL49ttvccvwIR9++AHx4sULsz4rV65kwoQJ5MuXj4EDB3L8+HEAZs2axezZsylfvjw7d+7k7t27/Pjjj9y5cyfK36OY3i6BRFo9bG3eCR6AfdbXI9bXOMBxB+S2YFn5FjJUB+6FSHvXhnxdLPM4gfdNgEnW61DlsbjU/ilEXAbraxJgEw5ucDWbQy1EZV3Spk2rgM0QL148nT17tqpaNv0FbjBt2LBhmAc29v/xZ23Zva/GiRNHa9WqpQEBAVFRnUgjpn++hg4dqoB+3aOfQ5t2R4wYoYBWq1YtaBOxquqgQYOCPgO5cuVSNzc3/f333yNT9VCJ6e0SiNM2hwLbRaQvkFBE3IGlwBoHjFkFVf3MRlgF3BCRdADWV1vzK5eBTMHuMwJXrdeOyIfU54r19SGwAEvvzRANuX79etAHNKQzrRcvXtCiRQvmzJmDiDB//nxGjhzJggULqF27tl2fPIEkSuTGiBEj8Pb2ZvLkyZFdFYMddu7cyYABA/Dy8rLrUjoQtS5/7tOnDw0bNmT58uVB5+4NGTKEQYMG4eXlxenTpzl//jxr1qyhePHiUVENw1vgiNHpDdwC/sByCOg6ILyOw1cDzazXzbAcIhqSA0B2EckmIvGABlY5R+WDEJE4IpLKeh0XqIql12WI5kyYMOG1ORt/f3+++eYbXr58CcC3337L5MmTWbt2LZ6enjx8+DDUPLt160aVKlXo1q0bhw+Hd02M4U3577//8PLy4oMPPuCXX34B7M/hBAQE0K5dO0aNGkXbtm2ZO3du0GnQQ4cOZeDAgTRs2JDz589z8uRJVqxYEeriEoPzcWT1WoCqTlfVuqpax3od3uN8RwLuInIWcLfeIyLpRWSdtVw/oAOwETgNLFHVk6HJW/O4BIwFvhKRy9YVb/GBjSJyHDgKXAGmh7MOhijA3knTT548oXHjxkFurr/55hvmzp3Ljh07qFChAnfu3LGbp4uLC7NmzSJ16tTUq1ePBw8eRIruhtcJCAigadOm3Lp1iyVLlpAkSRK7aV++fEmTJk2YOnUqvXr1YvLkyUGnEgwbNoz+/fvj5eXFP//8w+HDh1myZAkeHh5RVRXDWxLmQgIRqQp8D2SxphdAVTXp2xaqqreB8jbirwKewe7XYelZOSRvfZbVTrEF3kZXg3PJnDkzf//992vxyZIlY8mSJYhIkCfIRo0akSRJEurVq0fp0qXZtGmT3aGbVKlSsWjRIsqUKUPr1q1ZuHChcVEcBYwZM4b169fz888/h7rx89mzZ9SvX5/Vq1czfPjwoA3BACNGjOC7777Dy8uLmzdvsnv3bhYsWED16tXt5meIPjgyvDYeyxBWSlVNqqpJwmNwDIY3YdiwYSRKlOi1eDc3NwYOHMjixYtp0qRJUI/nyy+/5LfffuPixYuULFmSS5cu2c27RIkSfP/99yxevJjp003HN7LZvXs3ffv2pU6dOnzzzTd20z18+JAqVaqwevVqfvrpp1cMzqhRo+jbty8NGjTg/v37+Pj4MGPGDOrXrx8VVTBEAI4YnX+BExEwpGYwvDGNGjVi2rRpZMmSJegstu+++467d++yYsUKBg4cyKJFi2jWrBn+/v4AlC9fni1btnD79m1KlCjBn3/+aTf/b7/9looVK9K5c+eg5beGiOfOnTt4eXmROXNmfv31V7u9yjt37uDu7s727duZM2cO7du3D3r2ww8/0Lt3bxo0aMCLFy9Yt24dU6dOpVmzZjbzMkRPHNmn0wtYJyLbgeeBkao6NtK0MhiC0ahRIxo1avRKXKlSpahatSq//fYbAwcOZPDgwYgIs2fPxtXVlaJFi7J9+3YqVqxIyZIl2bhxo828XVxcmDt3Lnnz5qVevXocPHgwxu/fiW6oKs2bN+fatWvs3r3brkuB69evU7FiRf766y+WLVtGjRo1gp6NGTOGb7/9lnr16iEieHt7M27cONq0aRNFtTBEFI70dIYBT4AEWPa4BAaDwWm4u7uzbNkyjh49ypYtWxg4cCDz58+nefPmQT2e3Llzs3PnThIlSkTZsmW5f/++zbzSpEnDggULOHv2LN98802YJxwY3owJEyawevVqRo8eTcGCtl1xvXjxgpIlS3L+/Hl+++23VwzO2LFj6dmzJ/Xq1cPNzY2FCxcyfPhwunTpEjUVMEQstjbv6KubKm1u8HlXgtkcaiG61mXp0qXq4uKiZcuW1YEDByqgTZs2VT8/v6A0//zzj3788cdapkZ9/arLt3bzGjx4sAI6Y8aMqFA93ETXNgnO/v37NW7cuFqjRg27m3G7fz9ay9duqO+9957u3r37lWdjx45VQOvUqaPt2rVTQPv37x8Vqr81MaFdHMGZm0O3iEjFyDN7BsPbU6dOHWbPno2vry/79u1j4MCBzJkzh5YtWwb1eDJlyhTU47l48SInT560mVe/fv0oV64c7du3t5vG4Dj37t2jXr16pE+fnhkzZticx3n48CHHjx1DVfH19aVYsWJBzyZMmEC3bt2oXbs2mTNnZvLkyXTv3p3BgwdHZTUMEYwjRqc9sEFEnonIAxF5KCJmY4Mh2tC4cWOmTZvGhg0bOHbsGAMGDGD27Nm0atUqyIFbmjRpyJ07Ny4uLnTp0sXmEJqrqyvz588PWnZtfPC8PapKy5YtuXz5MosWLbJ7kOvQoUN5/uI52bJlI0+ePEHxEydOpEuXLtSuXZucOXMyduxY2rdvz+jRo83S9hiOI5tDk6iqi6omULNk2hBN+frrr5k4cSIrV67kzJkzDBgwgJkzZ75ieOLGjcf777/Pli1bWLXK9iEW77//PvPnz+f06dN06mS8sr8tkydPxtvbmxEjRlC0aFGbac6ePcu4ceNIm/Z9EiVyC4r/6aef6Ny5MzVr1iR//vwMHTqUFi1aMHHiRGNwYgGOuDYQEWksIv2t95lExJxbZoh2dOzYkVGjRgWdPN2/f39mzJhBmzZtggxPqpSpyJUrF926dbN7TluFChXo168fM2bMYN68eVFZhVjB4cOHXzlqyB7dunUjfvz4fPBBtqC4n3/+mY4dO1KjRg2++OIL+vXrR8OGDZk2bVrQaQSGmI0jrTgZKAY0tN4/wuJczWCIdvTq1YtBgwYxe/Zsbt68Sb9+/fj1119p27YtoCDChAkTuHjxImPH2l/1P3DgQEqVKkXbtm1D3edjeJUHDx5Qr1490qRJw+zZs+0aig0bNrB27VoePXrEnj17OHbsKCJChw4diB8/Pu7u7vTo0YNatWoFLYM3xA4cMTpFVLU9VsdoanErHS9StTIYwsGAAQPo1asXv/zyC48fP6Zv375Mnz6dM2fOAkr58uWpWbMmw4cP58qVKzbziBMnDgsWLCBhwoRUr17dbjrD//P06VPq1avHpUuXWLhwISlTprSZ7sWLF6Eud37+/DkdOnTA09OThQsXEieOI9sJDTEFR4zOS6vraAUQkdRAQKRqZTCEAxFh5MiRdOrUifHjx6Oq9OnTh2vXrnL58hVUlR9//BE/Pz++/fZbu/lkyJCBlStXcu3aNUqVKhXqkTrvOo8ePaJKlSps2rSJadOmUaJECbtpf/rpJ/76669Q8ytXrhzLly8nXjzz/za24YjRmQisANKIyDBgFzA8UrUyGMKJiDB+/HhatWrFiBEjSJQoERkzZuL27f84ePAg2bJlo2fPnsyfP5/du3fbzeeLL77Ax8eHu3fvUqpUKc6ePRuFtYgZ3L9/n0qVKrFjxw7mz59PixYt7Ka9ceMGgwcPpnLlyqHmuWrVqiCfOYbYhSOr1+ZjOQpnBHANqKGqSyNbMYMhvIgIU6ZMoXHjxvTv3584ceIgWI5QAejduzcZM2akU6dOQXt6bFGoUCG2bdvG06dPKVWqlNnDE4zbt29Tvnx5Dhw4wJIlS/Dy8go1fb9+/Xjy5Anjxo0LNZ2bm1uozw0xF0dWrxUFrqjqz6r6E3BZRIpEvmoGQ/hxdXVl5syZ1K1bl0uXLhIvfny8vb1RVdzc3Pjhhx84dOgQM2fODDWfPHnysGPHDkSEMmXKcOTIkSiqQfTlxo0blClThpMnT7Jy5Upq1aoVavqDBw8yY8YMOnfuTI4cOaJIS0N0w5HhtSlYVqwF8tgaZzDECOLEicP8+fNJmTIlz58/48yZM5w+fRqABg0aUKJECfr27cu9e/dCzSdnzpzs2LGDRIkSUa5cOfbt2xcF2kdPLl++TKlSpbhw4QK//fYbnp6eoaZXVTp16kTq1Knp378/AGnTprWZ1l68IXbgiNERDbZ9W1UDcOx0aoMh2hA3blw++eQTRCwf+RUrVgCWIbiJEyfy33//MWTIkDDz+eijj9ixYwcpU6akQoUK7NixI1L1jo5cvHiRUqVKce3aNTZt2kS5cuXClJk/fz579uxhxIgRQadMB+9dfvRR9qCzua5fvx5puhucjyNG54KIdBKRuNbQGbgQ2YoZDBFNnDhxSZEiBSLC4sWLg+Lz5cvH119/zaRJk4J6QKGRJUsWduzYQaZMmfDw8GDTpk2RqXa04syZM5QqVYp79+7h4+PDF198EabMo0eP+PbbbylYsCBfffVVUPzy5csREZIkSYKb2+uO+gyxE0eMTlugOHAFuAwUAVpHplIGQ2SROnUqVJU//vjjlSXQw4YNw83Nja5duzrk2iB9+vT4+vry8ccfU61aNdasWROJWkcPTpw4QalSpXj+/Dm+vr4UKlTIIbnhw4dz9epVJk2aFLRZ1N/fn6VLl6KqZMyYCTDH27wrOLJ67aaqNlDVNKqaVlUbqurN8BQqIilEZLOInLW+2jwNUEQ8ROQvETknIr3DkhcRdxE5JCJ/WF/LBZMpYI0/JyITxRzi9E4SP34CSpcuDcCyZcuC4lOnTs2gQYPYuHEja9eudSivNGnSsHXrVvLkyUOtWrVYsmRJpOgcHTh8+DBlypTB1dWVHTt2kDt3bofkzp8/z48//kiTJk1eOYPt999/58GDB6RMmZLUqVNFltqGaIgjq9cSiEh7EZksIjMCQzjL7Q34qGp2wMd6H7JcVyzH7VQGPgW8ROTTMOT/A6qp6udAM2BusCynYOmhZbcGj3DWwRBD6devHwDTp09/Jb59+/bkzJmTrl278vz5c1uir5EiRQq2bNlC0aJF8fLyYs6cORGur7PZu3cv5cqVI3HixOzYsYNPPvnEYdnu3bsTN25cRo4c+Ur8L7/8AkCnTp2C5tkM7waOtPZc4H2gErAdyAg8DGe51YHZ1uvZQA0baQoD51T1gqq+ABZZ5ezKq+oRVb1qjT8JJBCR+CKSDkiqqnusiyLm2CnT8A5QoUIF0qRJw5kzZ16ZtI4bNy4TJkzg/PnzjB8/3uH8kiZNyoYNGyhbtizNmjUL+kGN6ezZs4fWrVtTrlw5UqdOzY4dO/jwww8dlt+8eTOrVq3iu+++I3369EHxqsqqVatwdXWlY8eOkaG6IRrjiNH5SFX7A49VdTZQBfg8nOWmVdVrANbXNDbSZAD+DXZ/2RrnqHxt4IiqPrfKXbaTl+EdQ0Ro164dAKNHj37lmbu7O9WrV2fo0KFcvXrVlrhN3NzcWLt2LVWqVKFt27Z07tyZu3fvRqjeUcmOHTsoXbo006dP59mzZ4wdO5bMmTM7LP/y5Us6d+7Mhx9+SNeuXV95tnnzZh4/fkzp0qXt+tkxxF4cWfr80vp6T0Q+A64DWcMSEpEtWHpIIennoG625lwccl4vIrmAUUCgx9M3yktEWmNdLJE2bVp8fX0dKfY1Hj169Nay0Y3YUJd79+7h7++Pr68vRYoUwcXFhRkzZlCtWrVX0tWtW5d169bx1Vdf0bdv3zcqo3Pnzri6ujJp0iRmzZpFy5YtqVKlSqSckhxZbbJ3715GjhzJy5eWr76IsHr1apIkSeJwHsuWLeP06dMMGzaMPXv2vPKsR48eANSuXRtfX99X2iU2EBu+KxCJ9bDlwzp4AL4GkgOlsSyVvgm0DUsujDz/AtJZr9MBf9lIUwzYGOy+D9AnLHksw39ngC+CxaUD/gx27wX84oiuBQoUsOsDPCxii6901dhRl/4//qwd+w8Lui9WrJgCeujQodfS9unTRwHds2fPW5V15MgRLV26tAKaO3du3bp161vrbY+IbpNTp06ph4eHApopUyaNFy+eurq6asKECXX37t0O53Pz5k1NliyZVqpUSQMCAl559vTpU3V1ddWUKVMGxYVsl5hObPiuqIa/HsBBtfGb6sjqtV9V9a6qblfVD9Syim1qeAwdsBrLRD/WV1tuHA8A2UUkm4jEAxpY5ezKi8h7wG9YjNPvwepwDXgoIkWtq9aa2inT8A4RuKCgd+/X1rHQt29f0qdPT6dOnYIcwL0JefPmZdu2bSxdupT79+9Trlw5ateuzcWLF8Otd0Rz9+5dunTpQu7cudmzZw9jx47l3Llz+Pr68v333+Pj40OxYsUczq9fv348fvyY8ePHv+bpc8yYMfj7+9OwYUM70oZYjy1LZDFSdAst2JNzJAApsaw6O2t9TWGNTw+sC5bOE0uv5TzQzwH577Ac03M0WEhjfVYQOGHN6ycsJy2Yno6DxIa6hPxH7e/vrwkTJlRXV1e9c+fOa+nnzp2rgM6YMSNc5T558kSHDh2qiRIl0vjx42vfvn314cOH4cpTNfxt8vLlS50yZYqmTJlSRUTbtGmjN2/eDFeehw4dUhHRrl27vvYsICBA06ZNq4D++++/QfGmpxM9cUZPJ0kY4a1R1duqWl5Vs1tf71jjr6qqZ7B061T1Y1X9UFWHOSA/VFXdVDVvsHDT+uygqn5mzauD9U0xvMO4uLhQrVo1/P39mTLl9eMEGzVqRLFixejTpw8PHjx463ISJkxIv379OHPmDHXr1mX48OF8/PHHzJkz5616URHB1q1byZ8/P9988w2fffYZhw8fZurUqaROnfqt81Tr+WqpUqViwIABNsu8ceMG2bJlI2PGjOFR3xCDsWt0VHVwaCEqlTQYIovWrS2Ha4wbNw4/P79XngWey3bz5k2+//77cJeVIUMG5s6dy549e8iUKRPNmjWjWLFi7N27N9x5O8qFCxeoVasW5cuX5+HDhyxbtoxt27aRN2/ecOe9aNEifv/9d4YPH85777332vPhwy1uuFq2bBnusgwxF0c2h34gImtE5JaI3BSRVSLyQVQoZzBENqVKlcLNzY3//vuP5cuXv/a8YMGCtGjRggkTJnDmzJkIKbNo0aLs2bOH2bNn8++//1KsWDHq16/PzJkzOXbsWNCqsYggICCAM2fOsHjxYjp27EjOnDnZtGkTQ4cO5dSpU9SuXfu1eZe34fHjx/Ts2ZMCBQrQvHnz157/9ddfbN26FYB69eqFuzxDzMWRJdMLsJwMUNN63wBYiOUMNoMhRhM3blxq167NvHnzGDduHPXr138tzfDhw1m6dCmNGzfG19eXRInCfzili4sLTZs2pVatWowYMYKJEycGHaMTL148PvvsM/Lly0e+fPnInz8/uXPnDtOx2YsXLzh16hRHjhwJCkePHuXRo0dBdW3QoAEjRowgQ4aI26amqrRr144rV66wZMkSm8vDJ06ciIiQI0cOsmfPHmFlG2IejhgdUdXgx8nME5EOkaWQwRDV1K5dmzlz5rBv3z727t37yhlhYDljbe7cudSsWZOGDRuyfPnyCNt3kzhxYoYNG8aQIUM4d+4cR44c4fDhwxw5coSVK1fyv//9DyDoBzu4ITp9+jQnT54MMjAnTpzgxYsXgGWzat68efnqq6+CZHLlykW8ePEiRO/gDB48mDlz5jBkyBCKFy/+2vM7d+4wc+ZMVNX0cgwOGZ1t1sM2F2HZUFkf+E1EUgAETuIbDDEVd3d3EiVKhJ+fH+PGjXvF7UEgX375JRMmTKBjx45069aNCRMmRKgOrq6u5MiRgxw5ctCgQQPA0oO4fPlykBE6cuQIu3btYuHCha/IpkyZknz58tGlS5cgA/PRRx9FyobUkMyaNYvBgwfTokULvvvuO5tppk+fztOnTwGoWbOmzTSGdwdHjE7geEObEPEtsBghM79jiNEkTJgQT09P1q9fz/Lly/nnn39sHvnSoUMHLl68yNixY8mWLRtdunSJVL1EhEyZMpEpUyaqV68eFP/ff/9x5MgRDhw4QJMmTciYMWOEzMu8KVu2bKFVq1a4u7szdepUmzq8fPmSSZMmkTJlSpImTUqePHmiXE9D9MKRzaHZQgnG4BhiBTVr1uTx48cA/PTTT3bTjR49mtq1a9OtWzebCw+iglSpUuHu7k7x4sXJlCmTUwzOH3/8Qe3atcmZMyfLli0jbty4NtMtX76cK1eucP/+fWrVquUUXQ3RC0dWr9UVkSTW6+9ExFtE8kW+agZD1FGlShXixo3LRx99xLRp04Im30Pi4uLC3LlzKVq0KI0bN37tXLF3gStXruDp6UnixIlZt24dSZMmtZlOVRk3bhzvv/8+fn5+ZmjNADh2ynR/VX0oIiWwuDeYDYT3GByDIVqRLFkyKlSowKNHj7h//z6zZs2ymzZhwoSsWrWKDBky8OWXX3Lu3LmoU9TJPHz4kCpVqnDv3j1+++23UDd57tmzh/3795MuXTref//9NzpKxxB7ccTo+FtfqwBTVHUVEPFLYAwGJ1OzZk2uXLnC559/zoQJE0I9LSB16tSsX78eVcXT05P//vsvCjV1Di9fvqRevXqcOHGCZcuWhbmhdNy4cbz33nv89ddf1KhRI8hVteHdxpFPwRUR+QWoB6wTkfgOyhkMMYrq1asjInz88cecO3eO3377LdT02bNnZ/Xq1fzzzz/UqFGDZ8+eRZGmUY+q0r59ezZs2MDUqVOpVKlSqOn//vtvvL29KVeuHE+ePDFDa4YgHDEe9YCNgIeq3gNSAD0jUymDwRmkSZOGkiVLcubMGTJlysS4cePClClevDhz587l999/p2nTpk47Sy2yGTlyJNOnT6dv3758/fXXYaafNGkSIoKrqyvvvfceZcqUiXwlDTECu0ZHRAJnBxMAvsBt696c58DByFfNYIh6atasyR9//IGXlxfbtm3j6NGjYcrUrVuX0aNHs3TpUr799tvIVzKKWbBgAX379qVhw4YMHTo0zPQPHz5k+vTp1K5dGx8fH6pVqxYpm1INMZPQejoLrK+HsBiZQ8GCMTqGWEngMJCbmxuJEiVi/PjxDsl1796ddu3aMWbMGCZPnhyJGkYtO3bsoHnz5pQuXZoZM2Y4tOR55syZPHjwgFKlSnHnzh0ztGZ4hdBOma5qfc2mFudtZn+OIdaTJUsW8ufPz4YNG2jevDkLFy7k+vXrYcqJCBMmTKBq1ap07NiRNWvWRIG2kcuff/5JjRo1+OCDD1ixYgXx48cPU8bf35+JEydSrFgxTp8+TcKECcOc/zG8W4Q2vJY/tBCVShoMUUmtWrXYs2cPDRo04MWLFzZ97dgiTpw4LFq0iHz58tGgQQMOHoy5AwI3btygcuXKxI0bl3Xr1pE8eXKH5NauXcv58+fp3LkzK1asoHLlyhFyQKoh9hDa8NqP1vAzsA+YBky3Xk+MfNUMBudQq1YtwLLrvmrVqkyZMsXhlWlubm6sXbuW1KlTU7VqVS5duhSJmkYcP/zwA9u2bQMsbgqqVavGtWvXqFevHtmyZXM4n3HjxpE5c2YyZszI1atXzdCa4TVCG14rq6plgb+B/KpaUFULAPmAd2c3nOGdI2fOnOTIkQNvb2+6du3KrVu3mD9/vsPy77//PuvWrePZs2d4enpy9+7dSNQ2YihUqBD16tVjy5YteHl5cfDgQeLHjx9kgB3hyJEjbN++nY4dO7J69WrixIlD1apVI1FrQ0zEkSXTn6jqH4E3qnoCyBtpGhkM0YBatWqxbds28uTJQ+7cuRk/fjxv4uH8008/ZcWKFZw7d47q1as7NC/kTMqWLcvs2bOpVq0aa9aswc3NjZUrV1K2bFmH8xg/fjxubm60bNkSb29vypcvb9ODqOHdxhGjc1pEfhWRMiJSWkSmA6fDU6iIpBCRzSJy1vpqc8BYRDxE5C8ROWd1rxCqvIi4i8ghEfnD+loumIyvNa+j1pAmPHUwxG5q1aqFv78/v/32G127duXEiRP4+Pi8UR5ly5Zl1qxZ7N27l+zZszNy5MhouYFUVZk/fz6tW7cO0q9r165vZHCuXbvGwoULadGiBVeuXOHcuXNmaM1gE0eMTnPgJNAZ6AKcssaFh96Aj6pmB3ys968gIq5Y5pMqA58CXiLyaRjy/wHVVPVzoBkw99VcaaSqea3hZjjrYIjFFChQgEyZMuHt7U2DBg1IkyaNQ5tFQ9KwYUNOnTpF+fLl6dOnD59++inLly9/o15TZLJv3z6KFy9O48aNcXNzI1myZPTv358pU6YEzfE4wuTJk/Hz86NTp054e3sjIq+4YzAYAnHEtcEzVR2nqjWtYZyqhvfvWnUsB4difa1hI01h4JyqXlDVF1icyAV+im3Kq+oRVb1qjT8JJLAe22MwvBEiQs2aNdm4cSP+/v60a9eOdevW8eeff75xXh999BErV65ky5YtuLm5UadOHcqWLevQxtPI4sqVKzRp0oSiRYty6dIlevXqxZ07d1ixYgVDhgxhyZIl1KtXzyHD8/TpU6ZOnUq1atX46KOP8Pb2pnjx4rz//vtRUBNDTMMRJ26RQVpVvQagqtfsDHVlAP4Ndn8ZKPIG8rWBI6r6PFjcTBHxB5YDQ/Ut/26+fPmSy5cvhzlUkixZMk6fDtdIpFNIkCABGTNmtOsj5V2hZs2aTJw4kQ0bNvDNN98wYsQIJk6c+NabP8uXL8+RI0eYPn06/fv3J3/+/Hz99dcMHTqUNGmiZrT36dOnjBkzhpEjR+Lv70+fPn3o06cPU6ZMYcmSJUFDamXLlmXJkiUcOHAgzGG2+fPn899//9G1a1cuXLjAsWPH+PHHH6OiOoYYSKQZHRHZAtj6q9PP0SxsxDlkJEQkFzAKqBgsupGqXrH6BloONAHm2JFvDbQGSJs2Lb6+vq88T5w4MWnTpiVDhgyh7tD29/ePEpfBEYmqcv/+fY4dO/aKT5lHjx699j7ENO7du4e/v7/D9fD39ydZsmRMmTKFlClTUq5cOWbOnImHh4ddHzKOkDNnTmbOnMmcOXOYMWMGCxYsoEmTJtSqVeuNDP2btImqsm3bNqZNm8aNGzcoVaoUbdu2JV26dBw6dIjChQsDvJKfiFC4cOFQy1BVhg0bxkcffYSqMmbMGADSpUvnsG5v2i7RndjwXYFIrIeqRnkA/gLSWa/TAX/ZSFMM2Bjsvg/QJyx5ICNwBvgilPK/An5yRNcCBQpoSE6dOqUBAQGvxYfkwYMHYaaJjgQEBOipU6deidu2bZtzlIlA+v/4s3bsP+yNZFq2bKlJkybV58+f6/HjxxXQESNGRJhOp0+fVk9PTwX0o48+0pUrVzr02VJ1vE0OHjyoJUqUUEDz5Mmjvr6+4dD4VTZu3KiAzp49W1VVixcvrnnz5n2jPN6mXaIzseG7ohr+egAH1cZvqiOeQz8WkekisklEtgaGcNq61Vgm+rG+rrKR5gCQXUSyiUg8oIFVzq68iLwH/IbFOP0erA5xRCSV9TouUBU4EZ4KxGa3u7G5bm9KzZo1efDgAVu3buXzzz+nfPnyTJo0ya5n0Tflk08+4bfffmP9+vXEiROHGjVq4O7uzh9//BG2cBhcu3aN5s2bU6hQIc6cOcP06dM5dOgQpUuXjgDNLX9YR40aRdq0aalfvz7Xrl1jz549b7S3x/Du4cjw2lIsnkKn8/8O3cLLSGCJiLQE/gHqAohIeuBXVfVUVT8R6YDFrYIrMENVT4YmD3QAPgL6i0h/a1xF4DGw0WpwXIEt1voYDKFSvnx5kiRJgre3Nx4eHgwaNIjSpUvToUOHUL2LvikeHh6UL1+eKVOmMGjQIPLmzUubNm2oWbOm3T8Bx44dw8/Pz+az/fv3M2LECJ4/f06PHj3o168fyZIlizB9weK+YOvWrfz000/Ejx+fVatWoarG6BhCx1b3R18dijoUVprYHOwNrznCgwcPNG3atIplLuqVkDZtWofyiGguXryoCRIk0Dx58miePHm0TZs2NtOZ4bX/p0GDBpomTRr18/NTVdUBAwYooHPnzo1oFVVV9b///tMOHTqoq6urzc+Oo6F69ep69uzZSNHx8OHDGi9ePK1WrVrQcGDFihU1e/bsDg8PBmKG16InkTW85khPZ42ItANWYPGlE2is7oTb4r0D3Lhx443io4IPP/zQqct1Yxo1a9Zk0aJF7N69m5IlS9K/f3+2bdvGN998Q5EiRciePXuElpcyZUomTZpEjx49+Pfff+2mO3LkCPny5bP5LHny5OTKlStC9Qrk0aNH1K9fn1SpUgW5O7h79y5bt26le/fuZnjWECqOGJ3AuZPg3kIVMO4NgC5dutj9Aff3D3000p43xbx584bpx+XSpUtUrlyZEiVKsHv3bjJkyMCqVatImDChA1ob3oTKlSsTP358vL29KVmyJHHixGH+/PnkyZMHLy8vdu/eHSlOyrJkyUKWLFnsPvfz86NEiRIRXm5YdOjQgfPnz7N161ZSpUoFWE6X9vPzM0NrhjBxZHNoNhvBGJxowNmzZ2nfvj0nT57kvffeY/ny5YwePZq8efO+Fjp16hQkd/HiRfLly0fp0qXZuXOnE2sQM0iSJAkVK1ZkxYoVgUPOZMqUiZkzZ3Lo0CH69OnjZA2jjvnz5zN79my+++67VxYkrFixggwZMlCwYEEnameICdjt6YhIOVXdKiI2/7qoqnfkqRVzCK1H8vDhw1D3c4R3DXy2bNnImzcvYDm25dKlS3z33Xf07NnTrky6dOn4559/SJkyJYcOHaJGjRqcPHkyXPtO3gVq1qzJmjVrOHLkCPnzW9xJVa9enfbt2zN27FjKly+Pp6enk7WMXM6dO0fbtm2DhhgDefz4MRs2bKBly5a4uDhyspbhXSa04bXSwFagmo1nChij42SCe3J0dXXl6dOnjB492uYx/KVKlWLixInEjx8/SK5AgQJ8+OGHnDlzxvxDDYNq1arh6uqKt7d3kNEBGDNmDDt37qRZs2YcO3aM9OnTO1HLyOPFixc0aNCAuHHjMn/+fOLE+f+fjo0bN/L06VMztGZwCLtGR1UHWl/De7jnO03atGltLhpImzZtpJTXs2fPUHs6t27dIkWKFLi6unLhwgXOnj3LBx+Y0dKwSJUqFaVKlWLFihUMHTo0KD5BggQsXryYAgUK0KRJEzZt2hTjTqFwhD59+nDo0CFWrlxJpkyZXnm2YsUKUqZMScmSJZ2knSEmYfrCkcz169dtLsV2ln+VHTt2kDt3bvLkyUOdOnWYOnUqKVKkcIouMY1atWpx6tSp1w79/OSTT4L2rIwaNcpJ2kUe69atY+zYsbRv3/61k6NfvHjBmjVr+PLLL1/p/RgM9jBGJ4aSNWtWTpz4/0MVevTowaBBg8KUq127NidPnuTYsWMcPnyYatVsjZ4abFGjRg3A8s8+JM2bN8fLy4sBAwawe/fuKNYs8rh69SrNmjUjd+7cQeeqBWfbtm3cv3/f+M4xOEyoRkdEXESkeFQpYzBEZzJmzEjhwoVtGh0RYerUqWTJkgUvL68Y4aI6LPz9/WnSpAlPnjxh8eLFJEiQ4LU0K1aswM3NDXd3dydoaIiJhGp0VDUAMGeUGwxWatWqxYEDB2xu2kyaNCkLFy7k6tWrtGrVKmh5dUxl1KhRbN26lUmTJvHJJ5+89tzf35+VK1dSpUoVmwbJYLCFI8Nrm0SktphtxgZD0DDSypUrbT4vXLgww4cPZ/ny5fzyyy9RqFnEsnv3bgYMGECDBg1o3tz2WqK9e/dy48YNM7RmeCMcMTrdsBz6+UJEHojIQxF5EMl6GQzRko8//phcuXLh7W1/x0D37t2pVKkSXbt2fWXeLaZw9+5dvLy8yJIlC1OnTrV7rI23tzfx4sWL9fuTDBGLIycSJFFVF1WNq6pJrfdmJ6HhnaVWrVrs2LGDW7du2Xzu4uLC7NmzSZYsGfXr1+fJkydRrOHbo6q0atWKq1evsnDhQrsnU6sq3t7euLu7m43FhjfCodVrIvKliIyxhqqRrZTBEJ2pWbMmAQEBrFmzxm6atGnTMnfuXE6dOkWXLl2iTrlw8ssvv7B8+XKGDx8e5E3UFseOHePSpUtmaM3wxjjixG0k0Bk4ZQ2drXEGB5k/fz5Zs2bFxcWFrFmz2jwxICo5fvw4xYoVI1euXHz++ec8e/bMqfrENPLmzUvWrFlDHWIDcHd3p3fv3kyfPp2lS5dGkXZvz4kTJ+jatSuVKlWie/fuoab19vbGxcWFL7/8Moq0M8QWHOnpeALuqjpDVWcAHtY4gwPMnz+f1q1b8/fff6Oq/P3337Ru3dpphsfPz4/GjRszdepUTp48ia+vL3HjxnWKLjEVEaFWrVps3ryZBw9Cn94cMmQIRYsWpVWrVly8eDGKNHxznjx5Qv369UmWLBmzZ88O8ww1b29vSpUqRerUqaNIQ0NswdEtxO8Bgf5zItb9YAwnLNcGBw4c4Pnz56/EP3nyhJYtWzJ9um3npZHp2mDTpk1BJxKAxXeL4c2pWbMmY8eOZf369dSvX99uurhx47JgwQLy5s2Ll5cXO3fujJZGvkuXLpw6dYpNmzaFeUTTmTNnOHnyJBMmTIgi7QyxCUd6OsOBIyIyS0RmA4escQYHCGlwwop/E97GtcGZM2cQESpVqkT+/Pn54Ycfwq3Hu0idOnUAaNCgASISFN5///3X0mbLlo1ff/2Vffv2MWDAgKhWNUyWLl3K9OnT6d27t0ObPAM3x5r5HMPbEGpPR0RcgACgKFAIEOBbVXXOwWHRkLBcG3z++ef8/fffrz3LkiWLU1wb+Pn5sWvXLg4cOECiRIkoX748BQoUoHz58uHS5V3jTT3C1q1bl1atWjFq1CjKlSvn9B388+fPp1+/fvzzzz+AxZvskCFDHJL19vamUKFCrx38aTA4giMnEnRQ1WuqulpVVxmD82YMGzaMRIkSvRKXKFEihg0bFu68Q7o28PPzC7OnkzFjRkqXLk2qVKlIlCgRnp6eHD58ONy6GMJm/Pjx5MyZkyZNmjjVXXnIeUZV5erVqyxZsiRM2YsXL7J//37TyzG8NY4Mr20WkR4ikklEUgSG8BRqzWOziJy1via3k85DRP4SkXMi0jsseREpLCJHreGYiNQMJlNARP6w5jUxqk5YaNSoEdOmTSNLliyICFmyZGHatGk0atQoUsrr2bMnR48efS1MnDgRgEqVKnH8+HGePHmCn58f27dv59NPP40UXQyvkihRIhYtWsT9+/epXbu23bnAyKZfv36v7R16+vQp/fr1C1VOVenSpQsJEyaMtM+vIfbjiNFpAbQHdmCZzzkEHAxnub0BH1XNDvhY719BRFyBn4HKwKeAl4h8Gob8CaCgqubFssruFxEJHEKcArQGsluDRzjr4DCNGjXi0qVLBAQEcOnSJad+YZMnT063bt0oVKgQefPmJX/+/FSpUsVp+rxrfP755/z6668cO3aMfPny4e7uzqZNm6LsnLajR4/aHO4Fgoba7OHt7c3q1asZMmQImTNnjgz1DO8AYZ4yDfRW1WwhQni9flUHZluvZwM1bKQpDJxT1Quq+gJYZJWzK6+qT1TVzxqfAIuHU0QkHZBUVfeo5ds9x06ZMYa3dW0A0LhxY06ePMmJEyfMQgIn0KhRI/79919GjRrFqVOnqFSpEnnz5mXu3Lm8ePEiwstTVTZt2oS7uzv58uWze6xNaIbk3r17dOjQgXz58sWoza6G6EeoCwlUNUBE2gOLI7jctKp6zVrGNRFJYyNNBiD4Ub6XgSJhyYtIEWAGkAVooqp+IpLBKh88rwz2lBOR1lh6RaRNm/a1Cf9kyZLx8OHDMCvp7+/vULroyLNnz16p96NHj8K98MHZ3Lt3D39//wipR/LkyW26L0iePLnD+RcuXJhZs2bh4+PDkiVLaNq0Kd26daNOnTpUrVoVNze3UOXDapOXL1+ybds2Fi9ezIULF0iVKhWtW7cmSZIk/PTTT6+soIwfPz6NGze2m9+PP/7IzZs3GTRoELt27XKofo4Ske0SHYgN3xWIxHrY8moZPAD9gR5AJiBFYHBAbguW4a6QoTpwL0Tauzbk6wK/BrtvAkyyXjsinxPYj6XHUwjYEuxZSWBNWHVQVQoUKKAhOXXq1Gtxtnjw4IFD6aIjIeu4bds25ygSgfT/8Wft2H9YpOQ9f/58BXTixIlvJR8QEKDr1q3TcuXKKaBJkybVHj166L///mtXxl6b3L9/X0ePHq0ZMmRQQD/77DOdNWuWPn/+PCjNvHnzNEuWLCoimiVLFp03b57dcnbs2KGAdu/e/a3qFhaR2S7OIDZ8V1TDXw/goNr4TY20OR1VraCqn9kIq4Ab1iGvwKGvmzayuGw1dIFkBK5ar8OUV9XTwGPgM2teGe3kZTCEGy8vLypVqkTfvn1t+toJCxGhcuXK+Pj4cPDgQTw9PRk3bhzZsmWjadOmHD9+PMw8Ll++TM+ePcmUKRM9e/YkR44crFu3juPHj9OsWTPixYsXlNbRecbnz5/TunVrsmbNyuDBg9+4XgZDSBw5ZTrkfE5EzOmsBppZr5sBq2ykOQBkF5FsIhIPaGCVsytvTRvHep0FyAFcUstQ3EMRKWpdtdbUTpkGw1sR6Dk0ICCAdu3ahWthQIECBVi4cCHnzp2jffv2eHt7kydPHjw8PNiyZctreR8/fpymTZuSLVs2xo0bh6enJwcPHsTHx4fKlSvbncNxhBEjRvDnn38yderUMIf7DAZHsGt0RKRXsOu6IZ6F90SCkYC7iJwF3K33iEh6EVkHoJYFAR2AjcBpYImqngxNHigBHBORo8AKoJ2q/md99g3wK3AOOA+sD2cdDIZXyJo1K99//z1r165l2bJlEZLf+PHj+ffffxk+fDjHjh3D3d2d/PnzM3/+fA4dOoSHhwd58uTB29ub9u3bc+7cORYuXEiBAgXCXf6pU6cYPnw4jRo1olKlSuHOz2CA0BcSNAAClzb1weLILRAPoO/bFqqqt4HXtsCr6lWCHSaqquuAdW8gPxeYa6fMg1iG2gyGSKNTp04sWLCAjh07UqFCBZInt7kF7Y1Injw5ffr0oVu3bsyfP58xY8bQuHFjAN5//32GDx9O27ZtI6SsQAICAmjVqhVJkiRh7NixEZavwRDa8JrYubZ1b7DDDz/8wLZt216J27Ztm9OWKs+fP/+VkwpcXFyctkkxNhInThymT5/Of//9x7fffhuhecePH58WLVpw4sQJ1q1bx3fffcelS5fo06dPhBocgGnTprF7927Gjh1LmjS2FpcaDG9HaEZH7VzbujfYoVChQtSrVy/I8Gzbto169epRqFAhp+jTqFGjoFMK5s6dS9asWYPObzNEDPny5aNr165Mnz6d7du3R3j+Li4uVK5cmfLly79yFFJEceXKFb799lvKly9P06ZNIzx/w7tNaMNreUTkAZZeTULrNdb7BJGuWQwhLNcGrq6upE+fnkqVKpEuXTquXbtGzpw5GTx4sN3VQJHp2iA4CxcuxMvLy+H0BscZPHgwy5cvp02bNhw9epQECWLOV6ZTp068ePGCqVOnhmsRgsFgC7s9HVV1VdWkqppEVeNYrwPvo59DkGhM8uTJSZcuHf/88w/p0qWLsKGQt3FtEJzFixcboxNJJEqUiKlTp/LXX38xfHjM8QSycuVKvL29GTRoEB999JGz1THEQhx14mawQ1iuDZIkSRI0pNa/f3+mTJnCwIEDKVu2bLjLfhvXBoHs27ePRIkS8dlnZm1FZFGxYkUaN27MyJEjqV+/Prly5XK2SqFy//592rdvT548eejWrZuz1THEUhzZHGoIB4EGZ8mSJQwZMoQlS5a8MscTHt7GtUEgixYtMr2cKGDs2LEkTZqUVq1aERAQ4Gx1QqVv375cu3aN6dOnR0vvpobYgenpRDIHDhxgyZIlQT2bsmXLsmTJEg4cOBAhvZ2Q9OzZM8yeTkBAAEuXLmXHjh0RXr7hVVKnTs3YsWNp1qwZU6dOpV27ds5WySa7d+9mypQpdOrUyWmLXAzvBsboRDK9evV6La5s2bKRYnAcZceOHWTMmJEPPgjvwRIGR2jSpAnz5s2jd+/efPnll2TMmDFsoSjk+fPntGrVikyZMjF06FBnq2OI5RijE0Ox5drAUcqUKcPevXsjQy2DDQKPyPnss8/o2LEjK1ascLZKr/DDDz9w6tQpfvvtNxInTuxsdQyxHDOnYzBEAR988AGDBg0KWh0WXfjzzz8ZOnQo9evXx9PTM2wBgyGcGKNjMEQR3bp1I2/evHTo0IH79+87Wx0CAgJo3bo1iRIlYsKECc5Wx/COYIyOwRBFBB6Rc+PGDXr3fs1De5Tzv//9j507dzJmzBjSpk3rbHUM7wjG6BgMUUjBggXp3LkzU6dOjXAPnG/CtWvX6NmzJ2XKlKFFixZO08Pw7mGMjsEQxQwZMoQsWbLQunXrV1xGRyWdO3fm2bNn/PLLL+aoG0OUYoyOwRDFJE6cmClTpnD69GlGjhwZtkAEs2bNGpYuXUr//v35+OOPo7x8w7uNMTrvGC9fvqRZs2Z8/vnn5MyZkxEjRjhbpXeSypUr4+XlxfDhwzl9+nSUlfvw4UPatWvHZ5995tBxSQZDRGOMThSxZ88eRowYwZ49e5yqx9KlS3n+/Dl//PEHhw4d4pdffuHSpUtO1eldZdy4cbi5udG6desoOyKnX79+XLlyhenTpxMvXrwoKdNgCI7ZHBpOHHFtcP/+fY4fP05AQAAuLi7kzp2bZMmS2c0zMl0biAiPHz/Gz8+Pp0+fEi9ePJImTRpWNQ2RQNq0afnxxx9p0aIF06dPp02bNpFa3t69e/npp59o3749RYsWjdSyDAZ7mJ5OFHD//v2gf7IBAQERtkfjbVwb1KlTBzc3N9KlS0fmzJnp0aMHKVKkiBB9DG/OV199RdmyZenVqxdXr16NtHJevnxJq1atSJ8+PcOGDYu0cgyGsHBKT0dEUgCLgazAJaCeqt61kc4DmAC4Ar+q6sjQ5EWkMDAtUBwYpKorrDK+QDrgqfV5RVW9Gd66OOLaYM+ePZQvX54XL14QL1485s+fT7FixcJb9Fu5Nti/fz+urq5cvXqVu3fvUrJkSSpUqGDOYXMSIsIvv/zC559/TqdOnVi2bFmklDN69GhOnDjBqlWrTM/W4FSc1dPpDfioanbAx3r/CiLiCvwMVAY+BbxE5NMw5E8ABVU1L+AB/CIiwQ1rI1XNaw3hNjiOUqxYMXx8fPj+++/x8fGJEIMDb+faYMGCBXh4eBA3blzSpEnDF198wcGDByNEH8PbkT17dgYOHMjy5ctZtWpVhOT5/vvvIyJBoV+/fgC0bt06QvI3GN4WZ83pVAfKWK9nA77AtyHSFAbOqeoFABFZZJU7ZU9eVZ8Ek08AaIRr/pYUK1YswoxNaITl2iBz5sxs3bqVxo0b8+TJE/bu3UuXLl0iXS9D6PTo0YOFCxfSvn17ypYtG+7eyI0bN94o3mCIKpxldNKq6jUAVb0mImlspMkA/Bvs/jJQJCx5ESkCzACyAE1U1S9YHjNFxB9YDgxVVZtGSURaA63BMtnr6+v7yvNkyZLx8OHDMCvp7+/vULq34dGjRwQEBATl//z5c54/fx5meU2bNqVdu3Z8+umnqCqNGzcmW7Zsr8k9e/bslXo/evTotfchpnHv3j38/f2jbT3atm1Lhw4d+Oijj0iUKFGY6QMXprwp0a3+0b1d3pTY8F2ByKtHpBkdEdkCvG/jUT9Hs7ARF2bPRVX3AblEJCcwW0TWq+ozLENrV0QkCRaj0wSYYyePaVjnhgoWLKhlypR55fnp06dJkiRJmBUInNOJDD777DNOnToVdB84fBIWSZIkceho/QQJEpAvX76ge19fX0K+DzGNrYdPce/evWhbjzJlypAwYULWrVvnUPpbt26ROnVqm8/+/vvvUMuJTkT3dnlTYsN3BSKvHpFmdFS1gr1nInJDRNJZeynpAFvzK5eBTMHuMwKBy3vClFfV0yLyGPgMOKiqV6zxD0VkAZbhO5tGx2BwFs2bN6d58+YOpQ3tR8EcbWOIrjhrIcFqoJn1uhlga/b0AJBdRLKJSDyggVXOrrw1bRzrdRYgB3BJROKISCprfFygKpZFBwaDwWCIQpxldEYC7iJyFnC33iMi6UVkHYB1LqYDsBE4DSxR1ZOhyQMlgGMichRYAbRT1f+A+MBGETkOHAWuANPDUwE700Gxgthct3cFe64KjAsDg7NxykICVb0NlLcRfxXwDHa/DnhtgDsU+bnAXBvxj4EC4dP6/0mQIAG3b98mZcqUsW4YQ1W5ffs2CRIkcLYqhnBw/fp1Z6tgMNjEHIPzFmTMmJHLly9z69atUNM9e/YsRv54J0iQgIwZMzpbDYPBEAsxRuctiBs3LtmyZQszna+v7ysrwAwGg+Fdx5y9ZjAYDIYowxgdg8FgMEQZxugYDAaDIcoQszw2dETkFmB/e3fopAL+i0B1nElsqUtsqQeYukRXYktdwluPLKr62pEZxuhEIiJyUFULOluPiCC21CW21ANMXaIrsaUukVUPM7xmMBgMhijDGB2DwWAwRBnG6EQu08JOEmOILXWJLfUAU5foSmypS6TUw8zpGAwGgyHKMD0dg8FgMEQZxugYDAaDIcowRicCEBEPEflLRM6JSG8bz0VEJlqfHxeR/M7QMywcqEcZEbkvIketYYAz9AwLEZkhIjdFxKbPpJjSHuBQXWJEmwCISCYR2SYip0XkpIh0tpEm2reNg/WIEe0iIglEZL+IHLPWZbCNNBHbJqpqQjgC4AqcBz4A4gHHgE9DpPEE1mNxwV0U2Odsvd+yHmWAtc7W1YG6lALyAyfsPI/27fEGdYkRbWLVNR2Q33qdBDgTQ78rjtQjRrSL9X1ObL2OC+wDikZmm5ieTvgpDJxT1Quq+gJYBFQPkaY6MEct7AXes7rZjk44Uo8YgaruAO6EkiQmtAfgUF1iDKp6TVUPW68fYnHOmCFEsmjfNg7WI0ZgfZ8fWW/jWkPI1WUR2ibG6ISfDMC/we4v8/oH0JE0zsZRHYtZu+LrRSRX1KgW4cSE9ngTYlybiEhWIB+Wf9bBiVFtE0o9IIa0i4i4Wr0t3wQ2q2qktonxpxN+bLkODflPwZE0zsYRHQ9jOU/pkYh4AiuB7JGtWCQQE9rDUWJcm4hIYmA50EVVH4R8bEMkWrZNGPWIMe2iqv5AXhF5D1ghIp+pavA5xAhtE9PTCT+XgUzB7jMCV98ijbMJU0dVfRDYFVeLK/G4IpIq6lSMMGJCezhETGsTEYmL5Yd6vqp620gSI9omrHrEtHYBUNV7gC/gEeJRhLaJMTrh5wCQXUSyiUg8oAGwOkSa1UBT6yqQosB9Vb0W1YqGQZj1EJH3RUSs14WxfH5uR7mm4ScmtIdDxKQ2ser5P+C0qo61kyzat40j9Ygp7SIiqa09HEQkIVAB+DNEsghtEzO8Fk5U1U9EOgAbsawAm6GqJ0WkrfX5VGAdlhUg54AnQHNn6WsPB+tRB/hGRPyAp0ADtS5viU6IyEIsq4dSichlYCCWCdIY0x6BOFCXGNEmVr4AmgB/WOcQAPoCmSFGtY0j9Ygp7ZIOmC0irlgM4xJVXRuZv1/mGByDwWAwRBlmeM1gMBgMUYYxOgaDwWCIMozRMRgMBkOUYYyOwWAwGKIMY3QMBoPBEGUYo2MwGAyGKMMYHYPBYDBEGcboGAwxDKsvF3fr9VARmehsnQwGRzEnEhgMMY+BwBARSYPlhOMvnayPweAw5kQCgyEGIiLbgcRAGatPF4MhRmCG1wyGGIaIfI7lzKznxuAYYhrG6BgMMQirx8b5WLw5PhaRSk5WyWB4I4zRMRhiCCKSCPAGuqvqaeB7YJBTlTIY3hAzp2MwGAyGKMP0dAwGg8EQZRijYzAYDIYowxgdg8FgMEQZxugYDAaDIcowRsdgMBgMUYYxOgaDwWCIMozRMRgMBkOU8X8eQJJogg5DHgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.clf()\n",
    "markers = ['s','o','x','.']\n",
    "level = [2,5,6,7]\n",
    "\n",
    "for i in range(0, len(xAll)):\n",
    "    xClean = np.concatenate([xSlice[i][0:nFD[i]-1],xSlice[i][nFD[i]+1:nFD[i]+n[i]+1:5],xSlice[i][nFD[i]+n[i]+3:]])\n",
    "    uClean = np.concatenate([uSlice[i][0:nFD[i]-1],uSlice[i][nFD[i]+1:nFD[i]+n[i]+1:5],uSlice[i][nFD[i]+n[i]+3:]])\n",
    "    plt.plot(xClean,uClean-uFDM[i],color=\"black\",marker=markers[i],markevery=level[i],label=\"n=\"+str(i+5))\n",
    "    \n",
    "#plt.gca().yaxis.set_major_formatter(FormatStrFormatter('%0.6f')) \n",
    "plt.xlabel(r\"$x$\")\n",
    "plt.ylabel(r\"Error in displacement w.r.t FDM\")\n",
    "plt.title(r\"Example with \" + str(example).lower() + \" solution for MDCM with m = 2\")\n",
    "plt.grid()\n",
    "plt.axvline(x=1,c=\"#536872\")\n",
    "plt.axvline(x=2,c=\"#536872\")\n",
    "plt.legend()\n",
    "plt.savefig(\"MDCM-d-adaptive-endpoint-matching-cubic-\"+str(example).lower()+\".pdf\",bbox_inches='tight')\n",
    "\n",
    "if has_condition :\n",
    "    np.savetxt(\"con_mdcm_d-cubic-matching.csv\", con, delimiter=\",\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1cff5cdd",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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