Skip to content

Instantly share code, notes, and snippets.

@ketch
Last active March 28, 2017 01:06
Show Gist options
  • Star 0 You must be signed in to star a gist
  • Fork 0 You must be signed in to fork a gist
  • Save ketch/c9286ed82a016ae6e371ee6afae5d918 to your computer and use it in GitHub Desktop.
Save ketch/c9286ed82a016ae6e371ee6afae5d918 to your computer and use it in GitHub Desktop.
Display the source blob
Display the rendered blob
Raw
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[u'seaborn-darkgrid', u'seaborn-notebook', u'classic', u'seaborn-ticks', u'grayscale', u'bmh', u'seaborn-talk', u'dark_background', u'ggplot', u'fivethirtyeight', u'seaborn-colorblind', u'seaborn-deep', u'seaborn-whitegrid', u'seaborn-bright', u'seaborn-poster', u'seaborn-muted', u'seaborn-paper', u'seaborn-white', u'seaborn-pastel', u'seaborn-dark', u'seaborn', u'seaborn-dark-palette']\n"
]
}
],
"source": [
"%matplotlib inline\n",
"import numpy as np\n",
"from scipy.optimize import fsolve\n",
"from scipy import integrate\n",
"import matplotlib.pyplot as plt\n",
"from clawpack import pyclaw\n",
"from clawpack import riemann\n",
"from clawpack.visclaw.ianimate import ianimate\n",
"import matplotlib\n",
"matplotlib.rcParams['font.size'] = 12\n",
"from IPython.display import HTML\n",
"print(plt.style.available)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAA1AAAAEQCAYAAAC+3JV0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10697b550>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.style.use('fivethirtyeight')\n",
"\n",
"def steady_rhs(h,r,alpha,g=1.):\n",
" return h/(g/alpha**2 * r**3 * h**3 - r)\n",
"\n",
"r = np.linspace(0.5, 10)\n",
"\n",
"h0 = 1.; u0 = 2.; alpha = r[0]*h0*u0; g=1.\n",
"h = np.squeeze(integrate.odeint(steady_rhs,h0,r,args=(alpha,g)));\n",
"u = alpha/(h*r)\n",
"plt.figure(figsize=(12,4));\n",
"plt.subplot(1,3,1); plt.title('Depth'); plt.xlabel('r'); plt.ylabel('h');\n",
"plt.plot(r,h);\n",
"plt.subplot(1,3,2); plt.title('Velocity'); plt.xlabel('r'); plt.ylabel('u');\n",
"plt.plot(r,alpha/(r*h));\n",
"plt.subplot(1,3,3); plt.title('Froude number'); plt.xlabel('r'); plt.ylabel('$F$');\n",
"plt.plot(r,alpha/(r*h*np.sqrt(g*h)));\n",
"plt.tight_layout();"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAA1gAAAEYCAYAAABBWFftAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10e3b7810>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.style.use('ggplot')\n",
"\n",
"def steady_rhs(h,r,alpha,g=1.):\n",
" return h/(g/alpha**2 * r**3 * h**3 - r)\n",
"\n",
"r = np.linspace(0.5, 10)\n",
"\n",
"h0 = 1.; u0 = 2.; alpha = r[0]*h0*u0; g=1.\n",
"h = np.squeeze(integrate.odeint(steady_rhs,h0,r,args=(alpha,g)));\n",
"u = alpha/(h*r)\n",
"plt.figure(figsize=(12,4));\n",
"plt.subplot(1,3,1); plt.title('Depth'); plt.xlabel('r'); plt.ylabel('h');\n",
"plt.plot(r,h);\n",
"plt.subplot(1,3,2); plt.title('Velocity'); plt.xlabel('r'); plt.ylabel('u');\n",
"plt.plot(r,alpha/(r*h));\n",
"plt.subplot(1,3,3); plt.title('Froude number'); plt.xlabel('r'); plt.ylabel('$F$');\n",
"plt.plot(r,alpha/(r*h*np.sqrt(g*h)));\n",
"plt.tight_layout();"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAA1MAAAEUCAYAAADOemxhAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10696b8d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.style.use('seaborn-talk');\n",
"\n",
"def steady_rhs(h,r,alpha,g=1.):\n",
" return h/(g/alpha**2 * r**3 * h**3 - r)\n",
"\n",
"r = np.linspace(0.5, 10)\n",
"\n",
"h0 = 1.; u0 = 2.; alpha = r[0]*h0*u0; g=1.\n",
"h = np.squeeze(integrate.odeint(steady_rhs,h0,r,args=(alpha,g)));\n",
"u = alpha/(h*r)\n",
"plt.figure(figsize=(12,4));\n",
"plt.subplot(1,3,1); plt.title('Depth'); plt.xlabel('r'); plt.ylabel('h');\n",
"plt.plot(r,h);\n",
"plt.subplot(1,3,2); plt.title('Velocity'); plt.xlabel('r'); plt.ylabel('u');\n",
"plt.plot(r,alpha/(r*h));\n",
"plt.subplot(1,3,3); plt.title('Froude number'); plt.xlabel('r'); plt.ylabel('$F$');\n",
"plt.plot(r,alpha/(r*h*np.sqrt(g*h)));\n",
"plt.tight_layout();"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAA1gAAAEYCAYAAABBWFftAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xtc09X/B/DXNjbGNsZtoHJNRU0C72V5T/MWljfykpS3\nNO+VfQ3NyltlaGqZdpXEvKQU/jLNrKQyNTVN0bwriAqC3C8Dxi6f8/tjbWNxh41t8H4+HjzYzj6f\nz84Y++y8P+ec9+ExxhgIIYQQQgghhDQY39YVIIQQQgghhJCmggIsQgghhBBCCLEQCrAIIYQQQggh\nxEIowCKEEEIIIYQQC6EAixBCCCGEEEIshAIsQgghhBBCCLEQCrBIs/bAAw/ggQcesHU1CCGN5PDh\nw+DxeHj77bcb5fn69OkDJyenRnkuQkjjeOONN8Dj8XDs2DFbV8WmGvt86kgowCIWkZKSAh6PZ/Yj\nlUrh5+eHwYMH4+2330Zqamqj12v58uXg8Xj4/fffG/25CSF1M3HiRPB4PHz77bfVbnf16lXweDyE\nhYU1Us0sixpnpLmqrK1Q/sfd3d3WVSTEIuiyGrGodu3a4dlnnwUAqFQqZGRk4MSJE3jzzTfx9ttv\nY/Xq1XjllVdsXEtCiD2aNm0adu/ejdjYWERERFS53datW43b27tdu3ahtLTU1tUgxK6UbyuUJxaL\nbVAbQiyPAixiUe3bt8fy5csrlP/www+YOnUqFi5cCJlMhhkzZjR+5Qghdm3QoEEIDAzETz/9hIyM\nDLRs2bLCNjqdDtu3b4dQKERkZKQNalk3gYGBtq4CIXanqrYCIU0FDREkjSI8PBzx8fEAgCVLlqC4\nuNj4WFlZGdauXYvOnTtDIpHAzc0NTzzxBI4cOVLhOAMGDACPx0NpaSleffVV+Pv7QywWo3Pnzti+\nfXuFbVesWAEAePzxx41DECqbc6VUKvHSSy/B19cXzs7O6NSpU43DlAghlsXn8zFlyhRotdoKn2eD\nQ4cOIT09HU899RS8vb2N5YcPH8bw4cPh6ekJsViMkJAQrFmzBlqtttbP/+2336JPnz5wdXWFVCrF\nI488gi+//LLSbXU6HT777DM89thjkMvlkEqlCAkJwauvvoqCggLjdv+dg9WnTx+88847AIC+ffsa\nz0vBwcHgOA6BgYHw9vaGRqOp8JyMMQQHB8PT0xMqlarWr4sQR1R+fs+RI0cwaNAguLm5mX3u1Wo1\n3nvvPTz00EMQi8Xw8PDA8OHDcfTo0QrHq24+ZGRkJHg8XoWpDJmZmZg6dSoUCgVkMhn69etX6bHL\ni4uLQ//+/eHm5gYXFxd069YNW7ZsqfXr3rJlC3g8Hnbs2IEff/wRjz32GCQSCRQKBaZOnYq8vDyz\n7aubB3Xz5k3weDy88MILZuX+/v4IDg5Gbm4uZsyYAR8fH7i6umL48OFISkoCAPzzzz8IDw+Hu7s7\n3N3dMXXqVCiVyirr/euvv6JPnz6QSqVQKBSYPHkyMjIyKt3277//RkREBHx8fODs7Iy2bdvi9ddf\nN2sb/ve1VfU/YK8owCKNpm/fvujXrx9ycnKQkJAAQD+McPDgwXjttdfg7OyMmTNnYty4cbhw4QIG\nDRqEvXv3VnqsZ555BvHx8Rg3bhxeeOEFpKen4/nnn8eGDRuM20yZMgX9+/cHAEyePBnLli3DsmXL\n8PLLL5sdS6PRYMiQIfj5558xduxYREZGIikpCePGjcPPP/9spb8GIaQyU6dOBY/HQ2xsbKWPVzY8\n8IMPPsDgwYNx7tw5jBo1CnPnzoVUKkVUVFSlw5Aq8+677+KZZ57BjRs3MHnyZMycORMZGRmYPn06\nXnrpJbNtdTodRo8ejVmzZiEjIwPPP/885syZg/bt2+OTTz7B3bt3q3yeadOmoW/fvsbXajgvLViw\nAHw+H9OmTUN2dja+//77Cvv+/vvvSEpKQmRkJA2lIs3GH3/8gSeeeALOzs6YNWsWnn76aQAAx3EY\nOXIklixZAj6fjwULFmDs2LE4evQoHn/88QZfJC0qKkK/fv0QGxuLTp06Yf78+fD29sbgwYPx119/\nVbrPK6+8gvHjx+Pu3buYMGECZs6cCZVKhRkzZmDRokV1ev69e/di1KhR8Pf3x5w5c/DAAw8gNjYW\no0aNatDrMigrK8MTTzyBs2fPIjIyEgMHDsShQ4cwePBg/PPPP+jTpw8YY3jhhRfQrl07xMbGVjgX\nGhw7dgzDhw9Hy5Yt8dJLL6FLly746quv0KdPnwoB4bfffovHHnsMP//8M4YOHYoFCxYgMDAQq1ev\nxpAhQyq9uFTV/4BdY4RYwK1btxgAFh4eXu12b775JgPA3nzzTcYYY4sXL2YA2OrVq822y8zMZEFB\nQUyhULCSkhJjef/+/RkAFhISwoqKiozlaWlpzMfHhzk7O7O0tDRj+bJlyxgA9ttvv1Van6CgIAaA\njRw5kpWVlRnLDx8+zACwoUOH1vpvQAixjIEDBzIA7NSpU2bl2dnZTCQSMV9fX6bVahljjJ0/f54J\nBAL22GOPsYKCAuO2HMexWbNmMQDs//7v/4zlv/zyCwPAVq1aZSy7evUqEwgEzN/fn2VkZBjLCwoK\n2IMPPsgAsGPHjhnL161bxwCwp556yuy8wRhjeXl5TKlUGu/37t2bCQQCs22WLl3KALCjR49WeO13\n7txhAoGADR8+vMJjkyZNYgDY+fPnK//DEWLnDG2Fdu3asWXLllX4uXLlinFbw2cVANu5c2eFY33x\nxRcMABs+fDjTaDTG8gsXLjBnZ2fm4eFh1k6o7LNoYPhs3b1711i2ZMkSBoC98sorZtt+9tlnxnqV\n/wwfOHCAAWBjxoxhKpXKWF5WVsZGjBjBALCzZ8/W+DcyvC6hUMhOnDhhLNdqtaxPnz4MADt9+nSF\nv1P5c5rBjRs3GAA2ffp0s3I/Pz8GgEVGRjKdTmcsN5wz3d3d2WeffWYsV6vVLCwsjAmFQpaZmVnh\nuQGwbdu2mT2HoX338ssvG8syMjKYVCplbdu2Zenp6Wbbv/vuuwwA27BhQ6XHr+x/wJ5RgEUsorYB\n1ieffMIAsNmzZzOdTsfc3d1ZSEhIpdt+9NFHDADbv3+/scwQYFX2QXvnnXcYALZ+/XpjWW0DrOTk\n5Eof8/T0rPb1EEIsb8eOHcbzRHkbN25kANjixYuNZbNnz2YA2N9//13hOLm5uQwAGz9+vLGsssbI\nG2+8wQCwjRs3VjjG119/zQCwGTNmGMuCg4OZSCRit2/frvG11DXAYoyx8PBwJhAIWGpqqrEsLy+P\nicVi1qNHjxqfkxB7ZWgrVPVT2cWQnj17VnosQ7Bx4cKFCo+9+OKLFdoKdQ2wAgICmIuLC8vJyTHb\nVqfTsbZt21b4DA8fPpzx+XyWlZVV4fjnzp1jAFhUVFQVfxkTQ4A1bdq0Kh/7+OOPjWUNCbDu3btn\nVv7bb78xAKxDhw4VjmVoT/3xxx8VnjskJIRxHGe2fWFhIZPL5czLy8tYFh0dzQCw+Pj4CsfXarXM\n09PT7P2u6X/AnlGSC2Iz165dQ35+PgIDAyud7Hrjxg0A+pTMI0aMMHvMMMSmvD59+gAAzp8/X6d6\nuLu7o3Xr1hXK/f39ceLEiTodixDScGPGjIGbmxt2796NDRs2wNnZGUDlwwNPnToFPp+Pffv2VTqs\nTiwW4+rVq9U+n+GcYRhSXN6AAQPMtsnPz8fNmzcRFhZmtQQWM2fOxA8//IDY2FgsXboUgD4boUql\nqjCXghBHFB4ejgMHDtRq2x49elRafv78eXh4eFS6XMOAAQPw2Wef4fz587UeJlxeXl4e7t69i+7d\nu8PT09PsMT6fj169ehnnKhmcOnUKcrkcmzZtqnC8srIyAKjxXFRe9+7dK5T5+/sD0J+HGsrb2xut\nWrUyKzPc79SpU4XtDUmH7t27V+GxPn36gMfjmZW5urqic+fOOHr0KFJTU+Hv749Tp04BAI4ePYoL\nFy5UOI5IJKr0b1TV/4A9owCLNCrDB9Pb2xu5ubkAgAsXLlT6QTP476RHAPDx8alQ1qJFCwAwm2Be\nG25ubpWWOzk5geO4Oh2LENJwLi4umDhxIj799FN89913GD9+PC5cuIBz586hT58+aNeunXHb3Nxc\ncByHlStXVnm8ys4h5RUWFgIwnUPK8/HxAY/HM25jOL/4+vrW+XXVVnh4OPz8/LB161a8/vrr4PF4\niImJgUQiwcSJE632vITYo8o+l4wxFBUV4cEHH6x0H0MwYPjc1pXhc15VMoXK6pSXlwfGmDG5VmVq\nOheVJ5fLK5QZknTodLpaH6cuxxcIBDU+d2VzpCprkwHm7TJ/f39ju++DDz6osl6VJSKp7O9t7yjJ\nBWlUhsyAPXr0MH6Ax48fD6Yfrlrpz7JlyyocJzMzs0LZ/fv3AVQdMBFCHIehl8qQ7KKqta/kcjkE\nAgFUKlWV5xBDb3hVDOciwzmkvKysLDDGjNsYzi+VXcW1FIFAgGnTpiEpKQlHjhxBYmIizp49i2ee\neabShg8hTdl/e0YMZa6urpV+ZgHTZ7n854XP54MxVumF0/9emDV8zrOysqo9fnmurq7w8/Ortj3z\nyy+/VPEq64/P1zflK8uYWtcLzvVVWZsMqNguM7wfN27cqPJvVFkAV9n/gL2jAIs0mqNHj+KPP/6A\nQqHAwIED0bFjR7i6uuLMmTN1vhpTWZrUY8eOAQA6d+5sLDNcjbHE1R5CSON5+OGHERoaip9//hkp\nKSnYuXMnZDIZxo0bZ7bdI488Ap1Oh9OnT9f7ubp06QJAn6nqvwwXhQzbuLu7o127drh27Rru3LlT\nr+erzXnphRdeAJ/PR0xMDGJiYoxlhBC9Ll26IC8vDxcvXqzw2H8/twDg4eEBjuOQnp5utq1Op6sw\nisbDwwMBAQG4cuWKsdfFgOO4SqcPPPLII0hLS6s2i6g1eHh4AADS0tIqPHbu3LlGqcPx48fBGDMr\nKyoqwoULF+Dl5WUc2vjII48AAE6ePNko9bIlCrBIozh48CDGjh0LQJ8OWSqVwsnJCbNmzUJSUhKW\nLFlSaWPj1KlTKCkpqVD+zjvvmK3HkJ6ejg8//BDOzs5mDTDD2OnGPuERQhpu2rRp4DgOkyZNQlZW\nFsaNGwepVGq2zZw5c8Dn8zF37twKDScAyMjIqHHew6RJkyAQCLB27VpkZ2cby4uKiozDfZ5//nlj\n+ezZs6FWqzFv3jyo1WqzYxUUFNQ4DKg256XAwEAMHToU8fHx2LFjBzp06GCcZ0oIMX0m/9t+uHTp\nErZu3QoPDw889dRTxvKHH34YACosAbF27dpKL5ZERkaipKSkwvpSW7Zswc2bNytsP3/+fADA9OnT\nK+05unXrFm7fvl3LV1d7HTt2hFQqxb59+8zmZqWnpxvX3LO2S5cuVVi78N1330VBQQGee+45Y9m0\nadOMS2hUNrIgPz8fiYmJVq9vY6A5WMSirl+/bkxYUVZWhoyMDPz555+4fv06nJ2dsX79esyYMcO4\n/cqVK3HmzBmsXbsW33//Pfr27QtPT0+kpqbi77//xrVr15Ceng6JRGL2PK1bt0ZoaCjGjh0LtVqN\nPXv2ICsrC+vXr4efn59xO8MCw6+//jouXboENzc3uLu7Y968eY3y9yCE1F9kZCSioqLw559/Aqg4\nPBAAunbtig8//BAvvfQS2rdvjyeffBKtW7dGbm4ubty4gaNHj+K9996rcq4GAHTo0AErV67E0qVL\nERYWhmeeeQZOTk6Ij4/HnTt3sGDBAvTu3du4/YIFC/Drr79i//796NChA0aMGAEXFxckJyfj0KFD\nOHnyJEJDQ6t8PsN5KSoqCufPn4ebmxs8PT0xZ84cs+1mzJiBH3/8EaWlpXj99dfr+ucjpEmbNm0a\n4uPjceDAAXTr1g3Dhg1Dbm4udu/eDY1Gg+3bt0Mmkxm3nz59Ot5//3288cYbOHv2LFq3bo3Tp0/j\nypUr6Nu3b4WRMUuWLMHevXuxYcMGJCYm4tFHH8W1a9fwww8/YPDgwRWG+z399NNYtGgR1q5di3bt\n2mHIkCHw9/dHZmYmrly5glOnTiEuLg5BQUEW/TuIxWLMnTsXa9asQdeuXTFy5EgUFhbi+++/x4AB\nA5CSkmLR56vM0KFDMWPGDOzfvx/t2rXDX3/9hYSEBLRt2xZvvfWWcbtWrVph+/btmDhxIkJDQ/Hk\nk08iODgYxcXFSE5OxpEjRzB9+vRKE4U4nEbIVEiagcpSr7q4uDBfX1/2xBNPsLffftss/Wl5Go2G\nbdq0ifXs2ZO5uroysVjMWrduzUaOHMm2bdtmtr6FIU17SUkJW7hwIfPz82MikYiFhoZWWIPBIDY2\nloWFhTFnZ2cGgAUFBRkfCwoKMrtfnuG5CCG2M2bMmCrTBpd37NgxNmbMGNaiRQsmFApZixYt2KOP\nPspWrVpldu6pLqVxXFwc69WrF5NKpczFxYV1796dbdmypdLn02q1bNOmTax79+5MIpEwmUzGQkJC\n2Kuvvsry8/ON21WVGjomJoaFhoYaz0tt27atsI1Go2EeHh5MKBSarc9FiKOq7ZIujFX/WTUoKytj\nq1evZh07dmTOzs7Mzc2NDR061CyVeHlnz55lAwcOZC4uLszNzY2NHj2aJSUlVZqmnTH9uk2TJ09m\nnp6eTCKRsD59+rA//vij2qUWDhw4wIYNG8a8vLyYUChkvr6+rH///mzdunUsOzu7xtdtSMW+ffv2\nWv9NtFote+utt1hAQAATiUSsQ4cO7KOPPqo2TXtl55yqtq+qXuXrk5CQwHr16sUkEgnz9PRkzz33\nXIW1rgz++ecf9txzzzF/f38mFAqZQqFg3bp1Y4sXL2ZXr16t8fU6Ah5j/xk0SYgdGzBgAI4cOVJh\nrC8hhDQ1ycnJCA4OxqhRo7B3715bV4cQQkgt0RwsQgghxA5t2LABjDHMmjXL1lUhhBBSBzQHixBC\nCLET+fn5+PTTT5GcnIyYmBg8+uijGDJkiK2rRQghpA4owCKEEELsRHZ2NpYsWQIXFxc88cQT+Pzz\nz21dJUIIIXVEc7AIIYQQQgghxEJoDhYhhBBCCCGEWAgNEazCvXv3bF2FZk+hUACA2cKfxHZq+374\n+vo2RnWaHDrn2B6dc+xHXd4LOufUHZ1vbI/ON/bF0m0c6sEihBBCCCGEEAuhAIsQQgghhBBCLMSm\nQwRzcnKwb98+JCUl4fbt21Cr1di0aRN8fHxq3JfjOOzbtw+HDx9Gfn4+fH19MXbsWDz66KONUHNC\nCCGEkLqpTbsnKSkJhw8fxpUrV5CdnQ1XV1d07NgREyZMqFX7iBBiezbtwcrIyMCJEycgk8nQsWPH\nOu27Z88efPPNNxg6dCiWLFmCdu3aYcOGDTh79qyVaksIIYQQUn+1afccP34cqampGD58OF5//XVM\nmjQJt27dwuLFi2m+DiEOwqY9WB07dsQXX3wBAEhISMD58+drtV9BQQH279+PUaNG4emnnwYAhIaG\nIiMjA7t27UK3bt2sVmdCCCGEkPqoTbtn1KhRkMvlZmUdOnTAvHnzkJCQgPHjxzdKXQkh9WfTHiw+\nv35Pf/78eWi1WvTt29esvG/fvrhz5w4yMzMtUb0q5RTycfmOE05eEaFYxbPqcxFCCCFNGWOASg3k\nK3nIyOPjVoYAF2/xcPoqD8npAltXz6Jq0+75b3AFAN7e3pDL5cjNzbVGtQhp1hgD9h3nIeGs5dr0\nDpmm/e7duxAKhWjZsqVZeUBAAAAgNTW1zuOUo6KijLejo6ON6Ror8+Z2Ab78UX/SP/6RBkH+tFaz\nNTg56f89q3svSOOh94OQ5qtMAxSreChR8VFcxtPfLuOhRMVDSRm/3G3TT6nhR13J739vq/69zVjl\nDZtn+rnig1n5jfxq7U9qaioKCgrg5+dXr/3r0sYhjYO+U+3Dycs8LPlCgD8v8dHen+Hs5woILRAd\nOWSApVQqIZFIwOOZn5BlMpnxcWtyl5lu51v3qQghhJB60XFAUQkPRaV8FJbwUFTCR1EpD8p/7ytL\nDfd5UKr4+t+lfChVPBSX8vSBVCkfxSoeNDrbjNZQqWmUiE6nwxdffAG5XI6BAwfaujqENAnX7gJv\nbXXCd8dMvcrXU3n4v6N8jHuca/DxHTLAsobo6Giz+9VNJBXxZQD0Xfh30ouQna2yZtWaLVqEz77Q\nQsOEND6OAwpKeMhX8pGn5CPf8FPMR0Ex79/f+tsFxXwUFvNRUMJDYQkfylL7XIlFLOLgImIQiwAX\nZwaxiEEs1P92cdbfdpeLIBYBD/qV2bq6NhcTE4Pr169j8eLFxgvJdVWXNg5pHNTGsY2sAj427HXF\njgQJdJzpAk4bX4ZVU3XoH5KJ6t6S2rZxHDLAkkqlKCkpAWPMrBfL0HNV3xNQbcklpsi2sNg+v8AI\nIYTYH61OP483u5CPnEIBsgsMt/nILTL9zi0yBVRcFcPnrEnkxCAVc5CKGWQuDBJnBqlYXyYRM0j/\nvS9xZpA4c3Ax3jb9uBh+i/S/xSL9T22mX5sanyVWfqX2befOnUhISMDcuXPRuXNnW1eHEIdVWsbD\nZwel+Hi/DMUq00nI01WHV8Yo8fI4F4iEqDa4qguHDLACAgKg0Whw//59s3lYqampAAB/f3+rPr+b\n1DTnqrCEAixCCGnuVGogM1+AjFwB0vP4uJ8nQFaB/ndmvv52VoE+cKpqvpEl8HkMcgmDm5SDXMJB\nLmWQSzi4ujC4unBwlTC4/ntf5sJBJmb62xL9bZlYf1vkkK2DpmXv3r3Yt28fpk2bhn79+tm6OoQ4\nJB0HfPuHC9Z8I0dGnilpjljEYcbwYsx9SglXCYNI6GLR53XIU2iXLl0gEAhw9OhRPPPMM8byo0eP\nIiAgwOoL8ZXvwSoopvHhhBDSlHEckFnAR2qWAGnZAqTlOCEtW4B7uXzcyxHgXo4AuUWWzXbnLGTw\ncOXgISv348rBXaq/7S7j4CZlcJfpAyl3qT6okooZePS15PAOHjyI3bt3Y8KECRg2bJitq0OIQ/rj\nHxFW7XLD5dtCYxmPxzCuXykWPVOIVp4Nn2tVFZsHWCdPngQAJCcnAwASExMhl8shl8sREhICAJgw\nYQL69++P2bNnAwDc3NwwYsQIfPfdd3BxcUHr1q3x559/4uLFi3jttdesXmezIYLUg0UIIQ6vVA1c\nTuHh5j3gnxtSpNx3wp1MAe5k6YOpMk3DohYBn0Eh56Bw4+Dtpvv3NweFXAdPOQeFnIOnKwevf39L\nnClQaqpqavccP34c27ZtQ5cuXRAaGorr168b95VIJFYfpUOIo7ue6oRVO+X49bzYrHxAJxWWPluI\nkECt1etg8wBr/fr1Zve3bNkCAAgJCcHy5csBABzHgePMo8yJEydCLBbj4MGDyM/Ph6+vL1555RV0\n797d6nU2HyJI34CEEOIIGAOyC/m4nuqEG2lOuHnPCUnpTkhOd0JajqDc0D23Oh3X202HVp76nxYe\nHFp66tDCXX/bx12HFu76oKmeSz+SJqamdk9iYiIYY0hMTERiYqLZtuXbRoQQc9kFfKyLd8XOX80T\nWHQM0ODNSYXo36nxkubwGGO0iFMl7t27V+Vj9/P46DZXP/drYGcVtkfRwn/WQBl27AtlEbSu6s45\npO5KVDxcueuEK3eEuHJHiKt3nXA1VYh8Zd2iHJETg59Ch0BvLfy9dfBT6OCv0MHPSwdfLx1aeupo\nvpIV1OX8T+ecuqPzje1RG8dyyjRAzCEZNn4nQ1G57Kk+7jq89kwRxvUvgaCGU7+l2zj0tVAPblJT\nb1o+ZREkxCGcPHkSx44dQ3JyMgoKCqBQKNCzZ0+MHj0aLi61n9z63XffYdeuXejQoQNWrVplxRqT\n2iot4+HCLSESk4S4mCLEPylCJN1zqnX2PYkzhzattHgwSIC2vkAL10IEtdAh0EeLlh7U80QIIfaI\nMeCHv8R4Z5ccd7JMIY1YxGH2iGLMHqGEVGybfiQKsOpBLNJPQC7T8GiIICEOYv/+/fDy8sLEiRPh\n5eWFW7du4ZtvvsGlS5ewatUq8GvRir5//z7i4+Ph5la3IWTEstKyBTh1VYTT10U4e1PfQ1V+OEhV\nvOQ6tPfXor2fFu39NAj206JtK30QxeOVv4JZau2XQAghpAH+uSXEsu1ynLrqbFYe0bcEUeMK4etl\nvQQWtUEBVj3JJRyyCgSU5IIQBxEVFQW5XG68HxISAplMhs2bN+Py5csIDQ2t8RhbtmxB3759ce/e\nPeh0OmtWl5STlsPHsYvOOHbJGaeuipCWXf1XF5/H0N5fi4eCNAgJ0iAkUIuOgRp4u9n2C5cQQkjD\nZObzER3nij1HJGZLXjzSoQzLnytE5zYaG9bOhAKsejIGWDREkBCHUD64Mmjbti0AIDe35nmUhuGF\nL730Et5//32L14+YqNTAn5edkXBOjD8uOiM5vfqvqtYttegWrEbXtmp0bqtBxwAtXJxpejEhhDQV\nZRpgy48ybNwng7LcPKtAby2WPluI8EdUdpV5lQKsepL/m0lQpeFBpdYPGySEOJbLly8DAPz8/Krd\nTqlUYtu2bYiMjIRMJrPIc0dFRRlvR0dHG4enNVfZBcD3f/Jx4AQfv57jobSs8m9KkZChR3uGXqEM\nvUM5PNqRwVMO6L/OGvaV5uSk37+5vxf2gN4LQgign2f1y1lnrNjhhpT7pnO8VMxhwSglXhimtMs2\nOAVY9eRWbi2solI+xCIaekKII8nNzUVcXBzCwsKMPVlV2bFjB1q1aoUBAwY0TuWaiZxC4LtjfMT/\nwcfvibxK51Hx+Qzd2zE83pXh8a4cHgthcHGu5GCEEEKalOupTli+XY4j/5jWszIsFBw1rhAtPOy3\n7U0BVj2VzyRYUMyDN815J8RhqFQqrFmzBgKBAHPmzKl22ytXruDIkSOIjo4Gz4LjD6Kjo83uN5dU\nvVod8Nt5Z8T9IcEvf4uh0VX8m3rIdHi8Sxme6KpC/7AyuMtMw/2Ki/Q/1kBpk+0HpWknpPkqLOFh\nXbwrtv4kNbvw1qO9GiufL7CbeVbVoQCrnuQS0xd+QTEfAE14J8QRqNVqREdH4/79+1ixYgW8vLyq\n3f7zzz+gnbdgAAAgAElEQVTHwIED4eXlheLiYgCATqcDx3EoLi6GSCSCUChsjKo7tLQcPr76RYo9\nRyTIKhBUeLyVpw7hPUsR/rAK3dura1yzhBBCSNPCcUDcHy5YvVuO7ELT90RLTx3emFiIUb1K7Wqe\nVXUowKqn8j1YlEmQEMeg1Wqxbt06JCUl4Y033kBgYGCN+6SlpSEtLQ2//PJLhcemTp2KyZMnIzw8\n3BrVdXiMAaeviRDzkxQ/nhZXGALoIdNhdO9SjHysFN2CNbTeFCGENFPnbgrxRqwbEpNNE6qchQwv\nhisx/2klJDZaz6q+KMCqp/I9WIXFDhJOE9KMcRyHjRs34uLFi1i8eDHat29fq/2WLVtWoSw2NhYc\nx2HatGlo2bKlpavq8BgDjlxwxvq9rvj7hvnsYwGf4fHOZRjfvwRPdFNBRN9ChBDSbOUU8rF6tyu+\n/l1qVj60eymWReoXfXdE9NVWT/Lyc7CoB4sQuxcTE4OTJ09izJgxcHZ2xvXr142PeXl5wcvLC1lZ\nWZg/fz4iIiIQEREBAHjooYcqHEsqlUKn01X6WHPGmH5+1fq9rjh30zyw8pDpMGlgCZ4fXAw/Gy8A\nSQghxLa0OmD7YQnWfiM3a0e3baXByucLMaBzmQ1r13AUYNWTXEJDBAlxJImJiQCAvXv3Yu/evWaP\nRUREYNy4cWCMgeM4cBwFAHV1+Y4T3vrKDScum6f4a9NKizkjlBjVuwQudphKlxBCSOM6fV2IpVvd\ncem2af6yxJnDwjFFmD68uEmMbGgCL8E23KU0RJAQR7J58+Yat/Hx8UFcXFyN2y1fvtwCNWoacgv5\nWPONK3b+KgHHTOfCYF8NXh6txNOPlVLCCkIIIcgu4OOdr+WI+0NiVj6qVwneeLYQrTybzsVNCrDq\nqXwPVn4xtR4IIc0LY8A3R12w/Cs3s+EdfgotlowvosCKEEIIAEDHATsSJIjeYz4csIO/Bm9PKUCv\nELUNa2cdFGDVk5yyCBJCmqnsAj6iYtxw6IyLsUws4jDvaSVmjVDSUEBCCCEAgPPJQiz50g3ny2UH\nlIo5vDq2CNOGFkPYRCORJvqyrM+NsggSQpqhH0+L8doWN+QWmdYoCX+kFMueK6DkFYQQQgAABcU8\nrImTY9thCVi54eNPP6r/vmjp0bS/LyjAqidXSnJBCGlGdBzw9i45Pj8oM5a5Szm8OzUfI3upbFgz\nQggh9oIxYN8JFyzfLjdbVL5NKy3emZKPfmFNbzhgZSjAqidnoX5IjErNpzTthJAmraCYh7mbPPDb\nebGxbGBnFdbOzG/yVyEJIYTUTnK6AK9vdcfRi6ZssmIhw4LRRZgVroSzsJqdmxgKsBrAXcqQoaYh\ngoSQpispXYCp73siKV3/zcjnMbw5qRAzhheDR6c+Qghp9so0wMf7ZfhonyvKNKYvhoGdVXh7SoHD\nLhbcEBRgNYBcwiEjT4DCEj4YAzU2CCFNSmKSEM+u9jL20rtJOHyyIA/9Ozn2ApCEEEIs4+QVEaJi\n3HDznql7qqWHDisnF+DJh1XNtm1MAVYDyP9dC0ut5UGl5sHFmdWwByGEOIbzyUJMXO1lnGPatpUG\nW/+Xi7atmt+VSEIIIebylDy8s0uOr3+XGst4PIZpQ4qx6JkiuEqad5uYAqwGKL8WVkEJBViEkKbh\nQrIQE981BVc92qvx1aIcuEnpHEcIIc0ZY8D3J8R46ys3ZBeakliEPqBG9PQCdGmrsWHt7AcFWA3g\nVj6TYDGfJnsTQhzehWQhJrxrGhbYvZ0aO17LafZXIwmxhJycHOzbtw9JSUm4ffs21Go1Nm3aBB8f\nH7Pt1Go19uzZg6NHj6K4uBgPPPAAJk2ahJCQEBvVnBAgNUuAJV+64ddyCY9cnDksiijC9GHFcBJU\ns3MzQ+nvGkBe7mpuQUkzHWRKCGkybt8XYOJ75sHVzigKrgixlIyMDJw4cQIymQwdO3ascrtPP/0U\nCQkJGDduHBYvXgwPDw+88847SElJabzKEvIvHQfEHJLi8de8zYKrgV1U+H1NFl4Mp+Dqv2zag5Wd\nnY1t27bhwoULAICwsDBMmTIFCoWiVvvu3r0bly5dQmFhIRQKBR577DGMGjUKYrG4xv0twU1q3oNF\nCCGOqkTFw/QNnshX6s9l3YIpuCLE0jp27IgvvvgCAJCQkIDz589X2CYlJQXHjh3D7Nmz8fjjjwMA\nQkJCsHDhQuzZswdRUVGNWmfSvF2964T/feGOczdFxjJvN30Si6d6Nt8kFjWxWYBVVlaGlStXQigU\nYu7cueDxeNi9ezdWrFiBtWvXVhskqVQqrFq1ClqtFuPHj4dCoUBSUhLi4uKQnp6OV155pVFegxst\nNkwIaQIYAxZtccOVO/osUEE+WnxFwwIJsTg+v+a2wpkzZyAQCNCrVy9jmUAgQO/evfHdd99Bo9FA\nKGxGCwoRm1BrgY++c8VH+2TQ6ExR1IQBxXjj2UJ4yOj7oTo2C7ASEhJw//59fPjhh2jZsiUAICgo\nCAsWLMDhw4cxYsSIKve9du0a0tPTsXTpUnTu3BkAEBoaCqVSif3796OsrAzOzs5V7m8pZkMEaS0s\nQoiD+vygFN/9KQGgH0+/ZWEufXkSYiOpqanw8fGp0I7x9/eHVqtFRkYGAgIC6nTM8r1e0dHRtRop\nRKzLyUnfBLfH9+L0VR5mrhPg8m3TBYHWrRg+flmLgV2FALxsVzkrsfT7YbNulzNnzqB9+/bG4AoA\nfHx80KFDB5w+fbrafbVaLQDAxcXFrFwqlYIxBsYap2FgnkWQerAIIY7n2CUR3t4lN95fNzMfIYFa\nG9aIkOZNqVRCJpNVKDeUKZXKxq4SaSZKy4DFnwvQ72UnY3DF5zO8HKHD2c80GNiVLrzVls16sO7e\nvYuHH364QnlAQABOnDhR7b5hYWFo1aoVdu7ciRkzZkChUODmzZs4ePAgBg8eXK85WPW5uhPQytRr\npeGkUCgaZ+5Xc2HPV3eaI3o/mp58JQ/zNnmAY/pz2axwJUY+prJxrQghlhYdHW12Pzs720Y1IQaG\n71J7eS/+uirCws/dcSvDlK3iwQAN1s3MR5e2GpQogZImHNvX9v3w9fWt1fFsFmAplUpIpdIK5TKZ\nDMXFxdXuKxKJsHLlSqxbtw4LFy40lg8cOBDTpk2zeF2r4l7uAlNB9VUmhBC7s3qPHFkF+i/TXiFl\nWDKh0MY1IoRIpVJkZWVVKDf0XFXWu0VIfZWoeHhvjyu+/FkK9u/FNqGAYcGoIswbqYSIFnSqF4f8\ns6nVanzwwQcoKCjAvHnzjD1Y8fHxEAgEmDFjRp2PWZ+rO0wjANACAHA/R43s7Lw6Py+pmr1d3Wnu\nLH11h9jWmetC7EjQX+QSizisfzGf0uwSYgcCAgLw119/VZhPnpqaCicnJ7OpFYQ0xMkrIiz8zB23\nM03hQKfWaqx/MR8daah4g9gswKqqp6qqnq3yfv31V1y6dAkbN240nmhCQkIgkUjw+eefY/DgwXjg\ngQesUW0zcsoiSAhxQBotsPhLd+P9V8cqEeCts2GNCCEG3bt3R1xcHE6cOIEBAwYAAHQ6HU6cOIFO\nnTpRBkHSYIZeq5ifTL2hIieGVyOKMCtcSRfbLMBmAZa/vz/u3r1boTw1NRX+/v7V7nvnzh1IpdIK\nV3GCg4MBAGlpaY0UYJkm+xXSQsOEEAcR85PUmJK9g78GM4Y34YH1hNiZkydPAgCSk5MBAImJiZDL\n5ZDL5QgJCUHr1q3Rq1cvbNu2DTqdDj4+Pvj555+RmZmJ+fPn27LqpAn466oIr3zmjpT7phCga1t9\nr1V7f+q1shSbBVg9evTA9u3bcf/+fbRooR9ml5mZiWvXruHZZ5+tdl93d3cUFxcjIyPDLMi6efMm\nAMDT09N6FS/HSQBIxRyKVXwU0ELDhBAHkJYtwPvfuhrvR08vgNAhB4sT4pjWr19vdn/Lli0A9CNx\nli9fDgCYM2cOvv76a+zevRslJSUICgrC66+/jjZt2jR2dUkToVIDa7+R47ODprlWIieG/0UU4UXq\ntbI4m32tDho0CIcOHcKaNWswYcIE8Hg87NmzB15eXhg8eLBxu6ysLMyfPx8RERGIiIgAAAwYMAA/\n/PADVq9ejdGjR0OhUCA5ORnx8fFo06YNOnTo0GivQy5hKFbROliEEMewYoccpWX6C0LPPl6Mhzuo\nbVwjQpqXuLi4GrcRiUSYPHkyJk+e3Ag1Ik3dhWQhXvrEHdfTTMNLO7dRY8OsfHSgXiursFmAJRaL\nsWzZMsTGxmLTpk1gjCE0NBRTpkwxS7POGAPHceA403wnHx8fvPPOO4iLi8OePXtQWFgIhUKBQYMG\nYcyYMbVaKd1S3KQc0nMFKCzhgzGAR3EWIcRO3Uhzwg9/6dcP9JDpKGsgIYQ0YRot8NE+GT74P1fo\nOH0D1UnA8MqYIsx7mnqtrMmmA0MUCgX+97//VbuNj49PpVd7/P39zVK024oh0YWO46GkjAepmBZh\nI4TYp08OmCY0zxpRDE9XOl8RQkhTdDPNCS994o7EZJGxrGOABh/MzkPoA9RrZW008r6B3KSmBkpB\nMQVYhBD7lJ7Lx95j+t4rqZjDc4No8T5CCGlqOA6I/UWKd3bJodLoe634PIY5TymxcGwRnCkJZaOg\nAKuB/puq3deLq2ZrQgixjS0/yqDR6b9sIweVmF0cIoQQ4vgy8vhY+Kk7jvxjmmoT5KPFh3Py8HB7\njQ1r1vxQgNVAblJTQEWZBAkh9qigmIcdv0oAAEIBwwvDKC07IYQ0JQf/EmPRFnfkK01t0UmPF2PZ\nc4U0usoGKMBqoPJrYVEmQUKIPdqeIIWyVP+lO7p3KfW0E0JIE6Es5eGtr9yw54jEWKaQ6/D+zHwM\n7lZmw5o1bxRgNdB/hwgSQuzTyZMncezYMSQnJ6OgoAAKhQI9e/bE6NGj4eLiUuV+WVlZ2Lp1K1JS\nUlBQUACxWAx/f3+MHDkS3bp1a8RXUD8qNRBzSGq8P3sE9V4RQkhTcPamEPM3e5gtGjy4mwrvz8iH\nwo0upNkSBVgNVH6IIAVYhNiv/fv3w8vLCxMnToSXlxdu3bqFb775BpcuXcKqVauqXN5BpVLB1dUV\nEyZMgKenJ0pLS5GQkID33nsPr776Knr27NnIr6Ru4o9JkJmvz8U7uJsK7WnNE0IIcWg6Dtj0vQzr\nvjWlX3dx5rA8shCTBpbQkkF2gAKsBvpvFkFCiH2KioqCXC433g8JCYFMJsPmzZtx+fJlhIaGVrpf\nQEAAZs+ebVbWrVs3zJs3D7/99pvdB1i7fjUNG5lDvVeEEOLQ0nL4WLDZAyevOhvLOrVW46O5eQj2\n1dmwZqQ8CrAaiIYIEuIYygdXBm3btgUA5Obm1ulYAoEAEokEAoF9r9KYmiUwroHSzk+DRx5U27hG\nhBBC6uvH02L873N35P+bVI3HY5g9QolFzxRBRC16u0JvRwOZDxGkHixCHMnly5cBAH5+fjVuy3Ec\nGGMoKirC4cOHce/ePUyZMqXezx0VFWW8HR0dDYVCUe9jVWX776aLPuMe51vlOZoSJyf9VyL9nWyP\n3gtCTErVwModbvjqsGk+bUsPHT6YnYe+oXThzB5RgNVA5lkEqQeLEEeRm5uLuLg4hIWFGXuyqrNj\nxw4cOHAAACAWi/Hyyy8jLCzM2tVskP87ajonje1LE54JIcTRXE91wuyPPHD1rmmF4MHdVFg/Mx+e\ncjqv2ysKsBqo/BBBCrAIcQwqlQpr1qyBQCDAnDlzarVPeHg4evfujfz8fBw5cgQbN27EwoUL0b17\n93rVITo62ux+dnZ2vY5TlbQcPk5daQkAaNtKAx9ZFiz8FE2OobfE0u8Fqbu6vBe+vr7Wrg4hjY4x\nIO6IC16PdYNKrW9fipwY3pxUiKlDiimRhZ2jAKuBXMv1YNEQQULsn1qtRnR0NO7fv48VK1bAy8ur\nVvt5eXkZt+3evTuWL1+O7du31zvAsrYf/zKlng/vqaIvY0IIcRDKUh6WfOmGvcdNSYrattLg4/l5\nCH2AMsE6AupyaSAB39SLVUg9WITYNa1Wi3Xr1iEpKQlLlixBYGBgvY/Vpk0bZGRkWLB2lnXglNh4\nO/yRUhvWhBBCSG1dvuOE4W94mwVXz/QrwY/vZFNw5UCoB8sC5BIOhSV8yiJIiB3jOA4bN27ExYsX\nsXjxYrRv375Bx7p27RpatGhhwRpaTnouH6ev61P4PtBCi4eC6EuZEELsGWPA179L8GasG1Qa09pW\n704twLh+dJHM0VCAZQFyKQOy9UMEOQ6oYr1SQogNxcTE4OTJkxgzZgycnZ1x/fp142OG4X9ZWVmY\nP38+IiIiEBERAQCIi4uDUqnEgw8+CHd3d+Tn5+PXX3/FzZs3sWDBAlu9nGodOm3qvRrRs5SGBxJC\niB0rUfGw+Es3xB8z9Vo9GKDBZwvyEOxHF8gcEQVYFuD27xBBjvGgVPHMMgsSQuxDYmIiAGDv3r3Y\nu3ev2WMREREYN24cGGPgOA4cZ0pe06ZNG/zwww/4888/UVJSAnd3dwQFBWHFihV48MEHG/U11NYP\n5edfPaKyYU0IIYRU50aaE2Z+4IHraaYsgRMGFOPtyYVwcab2pKOiAMsCPGSmxlh2AR9yCa2kTYi9\n2bx5c43b+Pj4IC4uzqysR48e6NGjh7WqZXGZ+XycvKpfXDjAW4uw1hob14gQQkhlvvmdj5nrFCgp\n0w99Eos4rJ5GQwKbAgqwLMBPYQqoUrOd0KYVBViEENv48bQYjOnHBI6g7IGEEGJ31Fpg4ccCbP5O\nYCwL9tXg85fz0MGfhgQ2BRRgWUCgjymgupMpqGZLQgixrmOXnI23h/Wgq6CEEGJPMvL4ePFDT5y5\nbmovPv1oKdbOyIfMhYYENhUUYFlAgLfpasPdLAqwCCG2c+6mfnigWMjQuQ0NDySEEHtx8ooIszZ6\nIKtA31Z0EjAsi6SFg5siCrAswLwHi/6khBDbuJfDR3qu/ou7Uxs1hHQ6IsQhXb16Fd9++y1SUlKg\nVqvRqlUrDB06FAMHDrR11Ug9MAbEHJJi5U45dJw+kvL1Yvj6TS2CfYptXDtiDfT1awEB5eZgUQ8W\nIcRWziWJjLe7BlPvFSGO6Pbt21i1ahXat2+PF198Ec7Ozjh58iQ+/fRTaLVaDBkyxNZVJHVQWsbD\na1vczBYOfvTBMsSt4KGFB5CdbcPKEauhAMsCJGIGhVyH7EIB7lCARQixEcPwQADoFqy2YU0IIfV1\n/PhxcByHqKgoiMX6Ne06deqE27dv48iRIxRgOZDULAGmrffEpdumFOwzhiuxdGIhWngobFgzYm02\nDbCys7Oxbds2XLhwAQAQFhaGKVOmQKGo3T9damoq4uLicOnSJahUKigUCgwdOhRPPvmkNatdqQAf\nfYCVUyhAsYoHqZgmKhJCGtfZm6YvcQqwCHFMWq0WTk5OEIlEZuUSiQTFxTSczFEcv6Sfb5VbpL/w\nLhZxWDezAKN6UfKh5oBvqycuKyvDypUrce/ePcydOxfz5s1Deno6VqxYAZWq5oUxk5KSsHTpUmg0\nGrz44otYsmQJnnrqKbMFQhtTICW6IITYkEYLnE/WB1gtPXTw9bLNuZAQ0jADBgwAAHz55ZfIzc1F\ncXExDh8+jIsXLyI8PNy2lSM1Msy3mrjayxhc+Su02Lc8m4KrZsRmPVgJCQm4f/8+PvzwQ7Rs2RIA\nEBQUhAULFuDw4cMYMWJElftyHIdNmzYhNDQUixYtMpaHhoZavd5VCfA2T9X+YACtY0AIaTzXUp2g\nUuuvmVHvFSGOKzAwEMuWLcP777+Pn3/+GQAgEAgwY8YM9O7du17HjIqKMt6Ojo6u9UghUjdlauCl\nTQJsPWS60D6gC4edSzko3NzNtnVy0jfB6b2wD5Z+P2wWYJ05cwbt27c3BlcA4OPjgw4dOuD06dPV\nBliXL19GWloaZs6c2RhVrZXymQTvZjkBKLNdZQghzc7fN2j+FSFNQXp6OtatW4eAgADMmDEDIpEI\np0+fxhdffAGhUIi+ffvauoqkEpl5wPiVTvjzkmlw2PzROrw3UwcnGtjU7NgswLp79y4efvjhCuUB\nAQE4ceJEtftevXoVAKDRaLB06VIkJydDKpWiV69eiIyMrDBuuTGUXwuLEl0QQhrb2fIJLtpRBkFC\nHNXXX38NJycnREVFGa+qh4WFQalUIjY2Fr179wafX7cZHtHR0Wb3syl1nUVduu2Eqes8kZatf19E\nTgzvTcvH+AGlyM+rfB9DTwm9F/ahtu+Hr69vrY5nswBLqVRCKpVWKJfJZDVO4szNzQUAbNiwAcOG\nDcOzzz6LpKQkxMXFIScnx2zYYG01tPu8cwfT7fv5EigUjR/kNTXUfW5f6P2wb4YAS8Bn6NSaAixC\nHNWdO3cQFBRkPOcaBAcH49ixYygsLIS7u3sVe5PG9vPfzpi7yQMlZfrgSiHXYcvCXDzcns7DzZlD\npmlnTJ+hr2/fvhg/fjwA4KGHHgLHcdi1axdSU1Ph7+/fqHUK8Ab4fAaO4yHlfqM+NSGkmctT8pCc\nrj+ddwzUwMWZspgS4qjc3d2RkpJizCZocOPGDQiFQshkMhvWjhgwBnx2UIq3d8nBmH7x4IeCNNj6\nai78yq2PSponmwVYVfVUVdWzVZ6rqysA/boQ5XXu3Bm7du1CSkpKnQMsS3Sft/Twwb0cJ9xKB7Ky\nssHj1fkQpBzqPrcvlu4+J5aTmFR+/hVdNSXEkQ0bNgzr169HdHQ0hgwZApFIhDNnzuD48eMIDw+v\n0LNFGp9aCyzd6oZdv5naq8N6lOKjOfmQ0DI9BDYMsPz9/XH37t0K5bXpfarpcZ6NIptAbx3u5ThB\nWcpHnpIHT1f6kBFCrO8sJbggpMl49NFHsWTJEuzbtw+ffvopNBoNWrRogenTp2Pw4MG2rl6zV1DM\nw4wPPHH8krOxbN7TRYgaV4Q6To0jTZjNAqwePXpg+/btuH//Plq0aAEAyMzMxLVr1/Dss89Wu2/X\nrl0hFApx/vx59OjRw1iemJgIAGjbtq31Kl6NAB8dTurzb+BulhM8XelKMiHE+s4lmRYY7koBFiEO\nr2vXrujatautq0H+406mAM+v9cSNNP05VyhgWDMjH+P60fpWxJzNAqxBgwbh0KFDWLNmDSZMmAAe\nj4c9e/bAy8vL7ApNVlYW5s+fj4iICERERADQDxEcNWoU4uPj4eLigtDQUCQnJ+Pbb79F//79zVK/\nN6byiw3fyRSgcxsKsAgh1sVxwLl/E1y4Szm0aUlj/wkhxNLO3hRi6vueyC7UZ4p2l3KIWZiLRzvS\nRS1Skc0CLLFYjGXLliE2NhabNm0CYwyhoaGYMmUKxGKxcTvGGDiOA8dxZvtHRETAxcUFP/30E/bv\n3w8PDw88/fTTGDt2bGO/FKPyiw3r18IihBDrSs4QIL9YPy6la7CahqgQQoiF/XRGjDmb3I2LuQf5\naPHVazkI9qULWqRyNo0CFAoF/ve//1W7jY+PD+Li4iqU83g8jBgxotoFiRtb+cWG72TSWliEEOs7\nd5PmXxFCiLXE/iLBm7Fu4P7NFNijvRpfLsyFl5yrYU/SnFE3iwWVX2z4Li02TAhpBEnpptP4Q0Ha\narYkhBBSWxwHvLfHFZv3uxrLnnykFBvn5MGFljolNaAAy4JaenAQOTGotTzcoSGChJBGkFruYk6A\nDwVYhBDSUGot8Orn7th7TGIse2G4EssmFdIwbFIrFAVYEJ8P+Cl0uJXhhNQsATgO9EEkhFhV+Ys5\ngd40H4AQQhqiWMXDzA888PsFUz6AZZEFmPlkxbVbCakKNf8tzJBJUK3l4X4+/XkJIdZlGI7sIdNB\n5kJr7xHSEFevXoVGQxmAm6ucQj7Gve1lDK5ETgwfz8+l4IrUGUUAFhZQLtHF3UzqICSEWE+pGsjM\n1wdYAdR7RUiDLVu2DKdOnbJ1NYgNpGYJMGqFAonJ+glWMhcO26NyMPIxlY1rRhwRBVgWVn6Izh1K\ndEEIsaK0csMDKcAixPJKSkrw4YcfIjMz09ZVIVZ0PdUJI5crkPxv0iBvNx3i38xGn4coMyupn3p1\nsWRmZuLw4cPIyMiAUqkEY+bDUng8Ht566y2LVNDRlJ9kTpkECWmYjz/+uMZteDweZs+e3Qi1sT/l\nL+KUXyaCEGIZOp0Of/75JwYNGgQfHx9bV4dYwflkISa954k8pf58GuSjxa4lOXigBZ1TSf3VOcA6\nc+YM1q9fD51OB7FYDJlMZo16OSyzHiwaIkhIgxw5cqRW21GABfh7UwZBQgipixNXRJjyvieUpfoB\nXR0DNNi1JAc+7rTGFWmYOkcAX3/9Ndzc3LBo0SK0adPGGnVyaOUDLOrBIqRh9uzZU6GM4zhkZmbi\nwIEDuHXrFpYuXWqDmtmHVMogSAgh9XL4nDNe/MATKo1+AeFuwWpsfy0H7jJKFkQars4BVkZGBiZO\nnEjBVRU8XDlIxRyKVXyag0WIFfD5fLRs2RIvvPAC1q5di6+++gqzZs2qcb+TJ0/i2LFjSE5ORkFB\nARQKBXr27InRo0fDxcWlyv2SkpJw+PBhXLlyBdnZ2XB1dUXHjh0xYcIEmw8ZupNZboggBViEWMT1\n69cRGBgIf39/W1eFWMmBU2LM3eQBrU4fXPUNLUPMwlxIxRRcEcuoc4Dl4eFhjXo0GTwe8EALHS7d\n5uNejgCFJTzIJfSBJcQaOnfujD179tQqwNq/fz+8vLwwceJEeHl54datW/jmm29w6dIlrFq1Cvwq\nFq07fvw4UlNTMXz4cAQEBCA3Nxfx8fFYvHgx1qxZA4VCYemXVWvle8n9aIggIRbx008/4aeffoJI\nJDIGWZcvX4ZcLoefnx8EArp46sj2HnPBS5+4g2P64Gr4w6XYPC8PzkIbV4w0KXUOsAYPHozjx4/j\nySefrLJB0tx1bqPGpdtCMMbD+WQh+oZSFhpCrCEnJwdqde0+X1FRUZDL5cb7ISEhkMlk2Lx5My5f\nvpRXsKYAACAASURBVIzQ0NBK9xs1apTZfgDQoUMHzJs3DwkJCRg/fnz9X0ADGQIsH3cdXEQ2qwYh\nTcbHH3+MW7dumf0AQHx8POLj4+Hk5ARfX18EBAQgKCgIQUFB6NKli41rTWrr698kWLTFDezf4Gp0\nrxJ8MDsfThQzEwurMcC6fPmy2f3g4GD89ddfWLp0KYYMGQJvb+9KA62QkBDL1dLBdA3WYNdv+tvn\nbooowCKknrKzsystVyqVuHjxIg4ePIj27dvX6lj/DZIAoG3btgCA3NzcOu3n7e0NuVxe7X7Wpizl\nGbNeUYp2QizDy8sLXl5e6NGjh7GssLAQKSkpSE5ORkpKCm7duoXjx4/j+PHjACqfK0rsT+wvEizd\n6m68P2FAMda8UAAB9RUQK6gxwFqxYkWVj3366adVPtacTzhd25oCqsQk6nMmpL7mzp1b7eMtW7bE\n9OnT6318wwUkPz+/Ou2XmpqKgoKCOu9XXlRUlPF2dHR0nYcapifzjLfb+QtsOlSxqXBy0n8l0t/S\n9uzpvZDL5ejUqRM6depkLFOpVMaAi9i/rT9J8MY2U3A1eXAx3p5cABqIRaylxgCruaY/boj2/lpI\nnDmUlPFxLkkExvRzswghdTN27Fjw/vPh4fF4kMlkaNmyJTp16lTvocq5ubmIi4tDWFiYsSerNnQ6\nHb744gvI5XIMHDiwXs9tCbcyTLeDWtqsGoQ0S2KxGCEhIc16tI6j+PInKd7c5ma8P/NJJd6aVEjt\nMmJVNQZYAwYMaIRqNC0CPtC5jQYnrjgjM1+AezkC+CloCA8hdTVu3DirHFelUmHNmjUQCASYM2dO\nnfaNiYnB9evXsXjx4gatAxgdHW12v6rhkFW5nCQFoG80KGRFyM4uqXddiJ6ht6Su7wWxvLq8F76+\nvtauDnFQMYekeOsrU3A1K1yJN56l4IpYH3WOWknXYNMwwbM3aZggIfZCrVYjOjoa9+/fx9KlS+Hl\n5VXrfXfu3ImEhATMnj0bnTt3tmIta1Z+GYgAyiBICCFmtv4kMQuu5jxVRMEVaTQUYFlJl7Ya4+3E\nJErvRYg90Gq1WLduHZKSkrBkyRIEBgbWet+9e/di3759mDp1Kvr162fFWtbOXbMAi3rICSHEYEeC\n+ZyruU8V4fUJRRRckUZDAZaVlE90cY4SXRBicxzHYePGjbh48SIWLVpU6+yDAHDw4EHs3r0bEyZM\nwLBhw6xYy9q7m6Uf4c3nMfh5UYBFCCEAEPeHC6JiTMHV7BFKLKHgijQyCrCsxNeLQ0sPfaPnwi0h\ntNT+IcSmYmJicPLkSTz11FNwdnbG9evXjT85OTkAgKysLEyYMAHffvutcb/jx49j27Zt6NKlC0JD\nQ832S01NtclrYczUg9XKSwdhnVc0JISQpue7P13w6mem4Gr6UCWWTqRhgaTx0deyFXVpq8ahMy4o\nLePjWqoTHgqieRKE2EpiYiIA/VC/vXv3mj0WERGBcePGgTEGjuPAcZzZfowxJCYmGo9hEBISguXL\nl1u97v+Vp+RBWaq/PhZACXQIaZLOnj2Lffv2ITk5GXw+H61atUJkZGSVi6I3d4dOi7HgY3dw/y4i\nHDmoGCuep+CK2AYFWFbUNViDQ2dcAOgXHKYAixDb2bx5c43b+Pj4IC4uzqxs7ty5Na7H1dhSs0yn\n7gAfCrAIaWp++eUXfPnllxg6dCjGjh0LjuOQkpKCsrIyW1fNLh29KMLsjzyg4/TR1Lh+JVg9tYCC\nK2IzFGBZ0X/nYUUOsmFlCCFNRvkMgoGUQZCQJiUzMxOxsbGIjIxEeHi4sbxLly42rJX9+vuGENPW\neUKt1UdTI3qW4v2Z+bSIMLEp+vezok6tNeDxGAB9DxYhhFjC3UzKIEhIU/Xbb7+Bz+dj8ODBtq6K\n3btyxwnPr/FCSZm+Oft4ZxU+mpsHAbVuiY3ZtAcrOzsb27Ztw4ULFwAAYWFhmDLl/9u78/CoyrN/\n4N/ZktkySZhkAiQhYWkoSUDUIArYV8ANxVqRYjS0gtpaVt+qNIq+hYD8aqD2FYSfFrUlFRVQA0qL\ngtAqBkNNagkKCJiAJixZyDqTzH7ePyaZJM0OkzlnJt/PdeVi5syc4Q4nuTn3eZ5zP/O8Cwz21q5d\nu/DWW29h9OjRWL16dX+EelnCtAKSYp04WabCqXNKmJtk0GsEscMiogBXWtVmiiALLKKg8s0332Do\n0KH4/PPP8d5776GyshLR0dG48847L7uLaWZmpvdxdnZ2n8+zpOjMBWDuWhVqLZ6Rq8mpbuSulkOr\nDozvTan05PFgOBbBwNfHQ7Qa32azYdWqVTh//jwWLVqExYsX48KFC8jKyoLVau3155SXl+O9995D\neHh4z28WQcuCw4IgQ1EJ27UT0ZVrN4Jl4hRBomBSU1ODixcv4o033sDdd9+NZ599FuPGjcOf/vQn\n7NmzR+zwJKGyFpi5XIWL1Z7iavwoN3audkKrFjkwomaijWAdOHAA5eXlWL9+PQYPHgwASEhIwNKl\nS7F//37MnDmzV5/z2muv4cYbb8T58+fhcknvSu74kQ5s+8Tz+N/FIZicYu/2/UREPWm5B0ulEDA4\n0t3Du4kokAiCgKamJjzxxBOYOHEiACA1NRWVlZXYuXMnZsyYAVkfuzdkZ2e3e15VVeWzeP3NYpVh\nznNGfHvO82+QGONEzhNVcDS5UdUkcnB90DJSEsjHIpj09ngMHTq0V58n2ghWYWEhkpKSvMUV4Ong\nNXr0aBQUFPTqM/Ly8lBSUoIHHnigv8K8Yu0aXXzLESwiujKC0NpFMDbKxXsNiIKMXq8HAIwbN67d\n9nHjxqGurg41NTVihCUJDifwq/WROFLiua89yuDCW09dQlQ4LzSRtIg2glVaWooJEyZ02B4fH4/8\n/Pwe9zebzcjJycHcuXO9yehK9Nf85CmRgE4twGKV4fA3aoRHRHFR0F7i/GRp4fGQhso6OawOz5Vb\n3n9FFHzi4+Nx+vTpLl+XD9D2eIIA/Oa1CPy9yDMPUKd2Y2tmNRJimAdJekT7LTWbzdDpdB226/V6\nWCyWHvffunUrhgwZgptuuqkfovMdpQK4Nc3T2KLWLMOnRVyUgYgu3/cVbNFOFMyuu+46AEBRUVG7\n7UVFRTAajYiIiBAjLNG9uFOPHQe1ADzTo1/7dQ3GDneIHBVR5wJyLOXEiRP49NNPkZ2d3ed5yF3p\nz/nJ08ZpsDMvEgCwbb8d4xPqfPbZwYzzk6XF1/OT6fJU1LYWWEOMvHJLFGyuvvpqpKSkYPPmzaiv\nr0dMTAzy8/NRVFSEhQsXih2eKN7L0+D37xq8z//waC1+NJaLLpN0iVZgdTVS1dXIVlubN2/GtGnT\nYDQavZ/hcrngdrthsVgQEhIClUo69ztNv9oKlUKAwyXD3n+p8f/m13EBPCK6LA2NrReVDFou+0AU\nbGQyGZYtW4a33noL77zzDsxmM2JjY7F06VJMmTJF7PD87vCJEDy5uXXUbtlP6zFrSgB1s6ABSbQC\nKy4uDqWlpR22l5WVIS4urtt9z507h3PnzuHjjz/u8Nr8+fPx4IMPtlv9XGzhOgFTUm34R5EaFbUK\n/OtbFSYkcVibiPquvqn16kyYljd2EwUjrVaLRx55BI888ojYoYiq5IICD//vINidngtLP/1RIx77\niVnkqIh6JlqBlZaWhjfeeAPl5eWIiYkBAFRUVODkyZM9dgVcsWJFh21btmyB2+3GQw891K4zoVTc\nnmbFP5pvzPyoQMMCi4guS7sRLC5cTkRBqtYsw8/XGVFr9lxUuiHZhrWP1MJHd4YQ9SvRJqpNnz4d\n0dHRWLt2LQoKClBYWIh169bBaDTilltu8b6vsrIS6enpePfdd73bUlJSOnzpdDpotVqkpKTAaDSK\n8S1167Y0K2Qyz8nQhwVqCDwvIqLLUN/YmrYNOo5gEVHwcbqABS9F4sxFzzjAyCEOvPbf1QgJyM4B\nNBCJVmCp1WqsWLECQ4YMwcaNG7FhwwZER0fjt7/9LdTq1qW4BUGA2+2G2x3YJxLR4W5MSPKsifVd\nhRInSpkliKjv2hVYnCJIREHoubcMOPiV51wwQudGzrJqROh5ZZoCh6hn+VFRUXjyySe7fY/JZMKO\nHTt6/KyVK1f6KKr+M2OCFV+cDAUAfFSgRvIwziMmor5pO0UwjFMEiSjIbP9Eg1c/9KxvqpALeOWx\nagwfzI6pFFjYy86PZkyweh/vKdCIGAkRBaq2I1hsckFEwaTwlApP/am1Y+DKn9XjxlS7iBERXR4W\nWH4UH+1CaqInUZz4XoWz5Yoe9iAiaq+hiSNYRBR8Kmrl+OWLrR0DH5hqwfxbOy7nQxQIWGD52e1p\nraNYHxWou3knEVFHLSNYmlA3VLyVk4iCgMMJLNgQifLmhdQnJNmwZn4dOwZSwGKB5Wd3XNdaYG37\nVIsA791BRH7Wcg8WW7QTUbD43XYDDn/juUfdFOHCHx+rYcdACmgssPxsdJwT14zyTBM8fU6FT46G\nihwREQWSlhEstmgnomDw13+q8ce/tTa1eHlJDWIimd8osLHAEsEv7mjtHvjqhzoRIyGiQGK1w3t/\nAu+/IqJA9+05JR7/Y2tTi+X31+P6MWxqQYGPBZYI7phgRWyUEwBw8Cs1TnzPcXAi6llDE9fAIqLg\n0GQHHt0QCYvVk9fuvK4Jj97BphYUHFhgiUCpAB66rTWJvPYRR7GIqGf1bdfA0nIEi4gC16qt4fim\nVAUAGDHEiRd+WcumFhQ0WGCJ5IGpjdCpPVegdx7SorKOh4KIutfQZg0sg4YjWEQUmPZ8ocZf9nsu\nLocoBby8pJoXjSio8KxeJAatgPT/agQA2Bwy/OVjjmIRUfc4gkVEga6sUoEnN7fed/U/GfVITXSK\nGBGR77HAEtHDt1sgk3lOknL2a2HlfZ1E1I1292CxiyARBRinC1i8KQJ1zaPxt17bxMWEKSixwBJR\nQozLu/DwpXoF3vlMK3JERCRl9RZOESSiwLV+ZxgKTnmWpxk8yMX7rihosX2dyH45w4IPCzQAgHXv\nhOHH1zchXMepP0S+dvjwYeTl5aGkpAR1dXWIiorCxIkTcc8990Cj0XS771tvvYWSkhKUlJTAbDZj\n4cKFuOmmm/wTeBucIkhEgepIsQrrd3nWu5LLBGxcVINBYcxjFJw4giWy635ox63XNgHwjGL9ITdM\n5IiIgtPu3bshl8tx//3345lnnsGtt96Kffv24bnnnoPb3f1o0EcffQS73Y5rrrnGT9F2jm3aiSgQ\nNdmBx16OgMvtuUi08C4zbuB6VxTEOIIlASvn1uPTo2rYHDL8ea8OGVMbkRTHGz6JfCkzMxMGg8H7\nPDk5GXq9Hps2bcLx48eRmpra5b5btmyBXC7HxYsXcfDgQX+E2ymOYBFRIMrebsC35z0t2ccMc+Dx\nextEjoiof3EESwISYlx49E4zAMDlluF/csIh8NyJyKfaFlctRo4cCQCorq7udl+5XBqpsm2b9jDe\ng0VEASD/RIh3vU+VQsD6BTUIVYkcFFE/k8ZZA2HJj80YPMgFAMg7FooPC9QiR0QU/I4fPw4AiI2N\nFTmS3mloah3BMnAEi4gkztwkw69fiYAgeHLX4/c2ICWBM3Qo+HGKoERo1QJ++0AdFm4cBADI2mrA\n1PFWaEJEDowoSFVXV2PHjh0YO3asdyTLnzIzM72Ps7OzERUV1eM+TfbWlD08PhKRvGXTp5RKz79v\nb44F9S8ei+Dw/PYwlFZ6juU1o+xYeJdZ5IiI/IMjWBLy4xusuP6HNgBAWZUSq7aGixwRUXCyWq1Y\nu3YtFAoFFi5cKHY4vVbXZrkYA1d1IBow1qxZgzlz5mDbtm1ih9Jr/zqtwpaPPVMDQ1UCXlxQA6VC\n5KCI/IQjWBIikwHPzavDHc9Gw+6U4S/7dbh+jA1332AVOzSioGG325GdnY3y8nJkZWXBaDSKEkd2\ndna751VVVT3uU9NgAiCHTu1GTU3P76e+aRkt6c2xoP7Vl2MxdOjQ/g5HVHl5efjuu+/EDqNPHE7g\nN6+1Tg3873saMHKIS+SoiPyHI1gSM2aYEyt+Vud9vuzVCJRc4CUfIl9wOp144YUXUFxcjKeffhrD\nhg0TO6Q+aekiyA6CRAOD2WxGTk4Ofv7zn4sdSp/8cY8e35R6Oln8MN6BX83k1EAaWFhgSdCDNzdi\n5kTP2lgWqxyPbhgEK5eLILoibrcbGzZswNdff41ly5YhKSlJ7JD6RBBauwga2EGQaEB48803MWzY\nMEyZMkXsUHrtzEUF/vc9zw2iMpmA7IdrEcL5UjTA8EdegmQyYN0vavH1WRXOlitx/DsVVrwRjuyH\n63remYg69frrr+Pw4cOYNWsWQkNDcerUKe9rRqMRRqMRlZWVWLJkCWbPno3Zs2d7Xz9+/Djq6+tR\nW1sLACguLoZa7en0ef311/slfqsDcLg4gkU0UHzzzTc4ePAg1q1bd8WfdTlNdS6HIABz1ylhdXhy\n1aN3uXH7JN5P3hk2cpEWXx8PFlgSZdAK+ONj1bjrt577sbYe0GH4YCd+dael552JqIMjR44AAHJz\nc5Gbm9vutdmzZ2POnDkQBAFutxtud/sRoh07dnhbugPA3r17sXfvXu9r/lBvaZ1wYNByBIsomDmd\nTmzevBl33XVXQN1j9s4ncvzj355cFRslYPV83ndFA5OoBVZVVRVycnJw9OhRAMDYsWMxb968HqvH\n4uJi7N+/HydOnEBVVRXCwsIwZswYpKenw2Qy+SN0v0hNdGLVg3V46vUIAMDqN8MRrhVw/9RGkSMj\nCjybNm3q8T0mk6nTgmnlypX9EFHftF1kmAUWUXB7//33YbfbMWvWLJ983uU01emrJpsMmZujvc9X\nzK2BvcmKqiaf/1VBgU11pKW3x6O3FzxEuwfLZrNh1apVOH/+PBYtWoTFixfjwoULyMrKgtXafde8\nQ4cOoaysDDNmzMDy5cuRkZGBM2fO4Kmnngq6H9SfTW/EkrsbvM9/81o4dh/mIsREA019m0WGOUWQ\nKHhVVVUhNzcX9913HxwOBywWCywWz+yVluf/OcouBa/8TYfzlzzX7Sen2HDHBHZApoFLtBGsAwcO\noLy8HOvXr8fgwYMBAAkJCVi6dCn279+PmTNndrnvT37yExgMhnbbRo8ejcWLF+PAgQO47777+jV2\nf8uc04D6RjlyPtbBLciwZFMk9JpqTL3KJnZoROQnHMEiGhjKy8vhcDjw0ksvdXht9+7d2L17N9au\nXYvExET/B9eF85fk2LRbDwCQywRk/awOMlkPOxEFMdEKrMLCQiQlJXmLK8AzPWf06NEoKCjotsD6\nz+IKAKKjo2EwGFBdXd0v8YpJJgOee7AO9RYZdn6uhcMlw8N/GIT1C2pw1/W8QkQ0ELS0aAeAMA1H\nsIiCVWJiIlasWNFhe1ZWFm688UZMmzat3bmTFPxumwFNNs9FoIxpjRgzzClyRETiEq3AKi0txYQJ\nEzpsj4+PR35+fp8/r6ysDHV1dYiNjb2sePzVYedKvPEscN8qN/52WA6bQ4ZfbRiEOqsTj93rDsor\nReywIy08HuJqaOIIFtFAoNPpkJKS0ulr0dHRXb4mln+dViH3kBaAJzct+2lDD3sQBT/R7sEym83Q\n6XQdtuv1eu9c495yuVx49dVXYTAYMG3aNF+FKDkqJfD2s06kT23typO5WYknXlbAxUY9REGt3sJ7\nsIhIWtxuYMVfWtuw/3pWA4wGXgAiCoo27a+//jpOnTqFp556Cnq9/rI+wx8ddnxl3cNAVFgYNn7g\nWchv0y4FTpx1YP2vajEoiBIbO+xIi6877FDf1PMeLKIBzV9LQvTFh4Vq/Ls4BAAwYogT827lUjJE\ngIgjWF2NVHU1stWVN998EwcOHMCCBQtw1VVX+TJEyZLLgafTG/C7h2ohl3muZP/9iBq3PB2N/BMh\nIkdHRP2hoU0XQQNHsIhIZC438MK7Yd7nz6TXIyQoLtsTXTnRCqy4uDiUlpZ22F5WVoa4uLhefUZu\nbi7ef/99zJ8/Hz/60Y98HaLk/fzmRmx5shoROs/V7Is1Csx5zogX3g2Dk1MGiYJK2xGsMI5gEZHI\ndh/W4GSZCgAwbrgdt6Wx6RZRC9EKrLS0NJw+fRrl5eXebRUVFTh58iTS0tJ63H/Pnj3Ytm0b0tPT\ncfvtt/dnqJI2/Wob9v2uEteN9rRsdwsy/CE3DD9eEYWvz/JSElGwaGjTRdDALoJEJCKnC3jhvdbR\nqydnNwRlsy2iyyVagTV9+nRER0dj7dq1KCgoQGFhIdatWwej0YhbbrnF+77Kykqkp6fj3Xff9W47\ndOgQcnJyMH78eKSmpuLUqVPer7KyMjG+HVHFRrnwzrOX8OtZDZA1TxksKgnBjGeisfINAyxWZj2i\nQFffxBEsIpKG3EMalFzwXMS9ZpQd08ZzXU6itkQb4lCr1VixYgW2bNmCjRs3QhAEpKamYt68eVCr\n1d73CYIAt9vdbtXyI0eOQBAEHDlyBEeOHGn3ucnJyVi5cqW/vg3JUCo8V5Amp9iw7NUInLmohFuQ\n4dUP9fjrPzV4Or0e90xqgly0kpqIrkTbESw9R7CISCQOJ/Bibuvo1bKf1nP0iug/yARB4P/UnTh/\n/rzYIVw2qx3Y9EEYNn6gh93ZmvXGDHPg6fvqMW28LSCSIbsISgu7CPavnnLODY+Z8H2lEnqNGydf\nv+inqAYW5hzp6MuxYM7puys5x3nz71r85rUIAMD1P7Th3f+5FBDnFFLDfCMtvj7H4XhGEFKHAE/M\nbsDHz1dgckrrsP2J71X4+Toj7l1txKdHQ8HSmihwtEwRZIt2IhKLwwms39W6HM6yn/LeK6LOsMAK\nYqOGurB9+SW88ZtLSE5weLf/85tQPPC8Ebctj8auzzXsOEgkcYLQOkWQLdqJSCx7CtQ4V+W5u2RK\nig3Xj7GLHBGRNLHACnIyGTBtvA1711TipYU1GBbt9L527DsVFm2MxORfm/DS+3pU1vHHgUiKmmwy\nuNyeAitMwxEsIhLHax+2jl79aqZZxEiIpI1n1AOEXA7MmtKEgy9U4KWFNRgzrHVEq6xKiee3GzBh\ncQwWbIjEZ1+HwMVzOCLJqG+zyHAYR7CISARffqvCl9+GAABGDXXgv8aycyBRV7hQ0gCjUnoKrXsm\nN+GTo6F4+a96HDoWCgBwuGT44LAGHxzWYPAgF+6Z1IRZUxqRPMzZw6cSUX9qaLPIMO/BIiIxvP6R\nzvv44dst7EpM1A0WWAOUTAZMvcqGqVfZ8O05Jbb+XYt3DmpRa/FkzIvVCrz8Vz1e/qseP4h14I4J\nVsyYYEVqooM3tBL5WZ2lzQgWW7QTkZ9dqJbjr//UAADCtW7MntIkckRE0sYCizAq1omVP6tH5n31\n2POFBrl5Ghz8KhRuwXNSd/qcCuvPqbB+Vxjio524+Worpl5lw6RkOzShPNkj6m8NTRzBIiLx5Hys\ng9PlOSfImG6BVs3/+4m6wwKLvDQhwL1TmnDvlCZU1Mrxfr4Guw5pcKQkxPue0kol/rxPjz/v00Ot\nEnBDsg1TUm2YkmJD8jAnpwwQ9YP6NosMG3Q8sSEi/2myybD1gBYAoJALmHdLo8gREUkfCyzqlCnC\njV/MsOAXMyw4d0mOvYUa7ClQ458nQrwjW1aHDP8oUuMfRWoAQITejUljbJj4QzsmjLYjJcEBpULM\n74IoOLS9B4tdBInIn3IPaVBj9vxnPmOCFbFRXNuFqCcssKhHsUY3HrrNgodus6DGLMPBo6H4e5Ea\nnxSFoqq+tYKqNcuxp0CDPQWeedraUDeuHuXA1SPtuGaUA+NH2hETyZNDor5qaDuCxS6CRORHWz5u\nbW7xyAy2ZifqDRZY1CeRegF3T7Li7klWuN3A8e+VOHQsFIeOh+LwiRBYrK1X2httcs9rzV0KAWDI\nIBfGDrcjNcGJscPtSElwYqjRxcYZRN2ob3MPVhjvwSIiPzlVpsTx71QAgJQEB9J+4OhhDyICWGDR\nFZDLgdREJ1ITnXj0TgscTs/ixV+cDEHByRB8cTKk3QgXAFyoVuBCtQb7/tW6zaB144fxDowZ5sTo\nOAeS4pxIinUiKsrP3xCRRNVb2jS5YBdBIvKTDw5rvI/vmdTIi6FEvcQCi3xGpQTGj3Rg/EgHfnmH\nBYIAlFYq8O9iFf79bQj+XRyCY98p0WRr3wmjvlGOL06G4ouToe22Gw0CRscLGBYdjpFDXBgx2Inh\nQ5wYZnJCEwKiAaP9QsMcwSKi/icIwAf5au/zu663ihgNUWBhgUX9RiYDhplcGGZy4e4bPInZ5QZK\nLijx9VkVvjqrwonvlTjxvQqVdR27YVyql+HzYzJ8Dl2H14YMciExxolhJhfio51IMLkQb3IiLsqF\nmAg3uxlSUGm30LCOBRYR9b/j3ytRfMEzPfCaUXbERbO5BVFvscAiv1LIgR/EOvGDWCfumdy6UGFV\nnRwnSpU4fU6FU2VKnD6nxLcXQlBV1/l8BM9UQwXyT3R8TaUQEBvlwlBj+68hg1wYHOnCkEFuDApz\nc6oDBYx2TS44RZCI/OCD/NbpgT++gQsLE/UFCyyShKhwN24Mt+PGVHvrtqgoVNcDBcfqUHxBiZIL\nSpwtV+LsRQXOlCthbup8mMrhknneV971j3eoSoApwgVThBsxkS7END82RbgQHe6GKcKNqHAXjAY3\nQvhbQiJraXIhkwnQcYFPIupnggDsbr7/SiYTMHMiCyyivuCpI0naIANw7Q8cuPY/OhcJAlDdIMf3\nFQp8X6nA9xVKlFYqcK5KgbLmL6u963mCNocMpZVKlFb2HEO41g1juBtRBk/BNSjMDaPBDWOY53HL\nV2SYG5F6N3RqgaNjEnT48GHk5eWhpKQEdXV1iIqKwsSJE3HPPfdAo9F0u6/dbsf27dvx2WefwWKx\nIDExERkZGUhOTvZL7C0jWGEagdNfiYLcleQqXzl6RoXvKjyniNeNtmPIIE5NJuoLFlgUkGQyca3N\nXgAADpBJREFUeIocg2etrf8kCEBNgxznq+U4f0mB85cU3mmFF2sUuFgtR3mtostRsLbqGuWoa5Sj\n5ELvfl1UCgERek+xFdH8Fa4TEK5zI0LX+tigdSNcK8DQ/NigFVic9aPdu3fDaDTi/vvvh9FoxJkz\nZ/DOO+/g2LFjWL16NeTdVC6vvPIKvvzyS8ydOxcxMTHYu3cv1qxZgzVr1iAxMbHfY2+5B4sNLoiC\n35XkKl9pNz3weo5eEfUVCywKSjIZMMjgxiCDG6mJzi7fZ7HKUF7jKbYq6+SorFWgolaOyjoFqurl\nqKqTo7JOjqo6BezO3lU+DpcMlXWKTht39EQhFxCmERCmdSNMK8CgcUOvEWDQev4M07ih03jeo1O7\nm//0PNZrBOjVArTNjzm1sb3MzEwYDAbv8+TkZOj1emzatAnHjx9Hampqp/udPXsWeXl5WLBgAaZO\nnerd9/HHH8f27duRmZnZr3ELAlDfPILF+6+Igt/l5ipfEQRg9z893QPlMgF3TmT3QKK+4ikYDWg6\ntYARQ1wYMaT77kiC4CnGqurluNT8VWOWo7pejksNCtSYZag1e7bVNMhRa/H86XD1bTjK5Zah1iJD\nreXKr1CqFAJ0zYWYNlSALlSARi14H2ubt2tDBWhCBWhCBGibX9eEtN+uCRVgcQGaEMDl9LTkDzRt\nT1hajBw5EgBQXV3d5X6FhYVQKBSYNGmSd5tCocDkyZOxa9cuOBwOqFQq3wfczGKVwS00TxHkCBZR\n0LvcXOUr/zqtwrkqT5K/IdmO6HDmHaK+CsDTJCL/k8ngGSHSuJAY07tWtYIANNlkqDHLUWuRoc4i\nb/5qfVzfKGv+U46GJhnqLXLUNcpgbvI8F4TLny/ocMlQ21z4+dLWzFBMvcrm088Uy/HjxwEAsbGx\nXb6nrKwMJpMJoaHt12mLi4uD0+nExYsXER8f3+e/u+3IV3Z2NqK6WFnb2uY+wagIVZfvoyunVHr+\nS+S/sfh4LNrrTa7qTm/zDQB8/E7r7IsHblbwGPQT/oxLi6+PBwsson4ik8EzIqR2IfYyfl/dbs/o\nRX2TDJbmgquhUQ6zVQZLkwwNTc2PrZ6CzNL82GL1bG+0yrx/NtrksDl8c3OXJiQ4pqlVV1djx44d\nGDt2rPfqcGfMZjP0en2H7S3bzGZzv8UIAPWW1uMWrguOf3si6r3e5ipfcLuB3IOei3IKuYCfTOHo\nFdHlYIFFJFFyORCmFRCmFQBc+X9yTpenYGu0eb6abDI0WuXe5y1fVnvr6012GazNf7qghsUKRBkC\n/z9cq9WKtWvXQqFQYOHChaLEkJ2d3e55VVVVp+9rsihw9w1haGiUY9QQG6qqLP4Ib0BquXLZ1bEg\n/+nLsRg6dGh/hyMaX+Wq3uYbhxN44l4NPsjXQKkE4KgGfx36B/ONtPT2ePQ237DAIhoglAo0dzC8\nvFGQ1uTTddOQQGC325GdnY3y8nJkZWXBaDR2+36dTofKyo79/FtGrjob3fKlhBgX/v+S2n79O4hI\nevqaq3xBpQTSb2pC+k1NcAX+tTQi0YhaYFVVVSEnJwdHjx4FAIwdOxbz5s3r1fxHsdelIaLA43Q6\n8cILL6C4uBjPPvsshg0b1uM+8fHx+OKLL2Cz2drdh1VWVgalUonBgwf3Z8hENABdTq7yNQXX3CO6\nbKL9+thsNqxatQrnz5/HokWLsHjxYly4cAFZWVmwWntuCfrKK6/gwIEDmDNnDp566ilERkZizZo1\nOHv2bP8HT0QBx+12Y8OGDfj666+xbNkyJCUl9Wq/a6+9Fi6XC/n5+d5tLc/HjRvXrx0EiWjgudxc\nRUTSIdoI1oEDB1BeXo7169d7rwAnJCRg6dKl2L9/P2bOnNnlvmKvS0NEgef111/H4cOHMWvWLISG\nhuLUqVPe14xGI4xGIyorK7FkyRLMnj0bs2fPBgAMHz4ckyZNQk5ODlwuF0wmE/bt24eKigosWbJE\nrG+HiIJUb3IVEUmbaAVWYWEhkpKS2k2vMZlMGD16NAoKCrotsMRel4aIAs+RI0cAALm5ucjNzW33\n2uzZszFnzhwIggC32w23u/3NBwsXLsTbb7+Nbdu2obGxEQkJCVi+fDlGjBjht/iJaGDoTa4iImkT\nrcAqLS3FhAkTOmyPj49vNxWnM/2xLk1f1ogg/+AaEdIS6Mdj06ZNPb7HZDJhx44dHbaHhITgwQcf\nxIMPPtgfoRERefUmVxGRtIl2D5bZbIZOp+uwXa/Xw2Lpvg2x2OvSEBERERERdYZt2pu1rBHRMpIV\nEhIiZjjUBo+FtPB4+E5LvsnOzg7qtXwCDY+FdPBY+FZmZibzjcTwWEiLr46HaCNYXY1UdTWy1ZZO\np+t0lMpX69KwSYY0ZGZm8lhICI8HBTv+jEsHj0X/4b+rNPBnXFp8fTxEK7Di4uJQWlraYXtZWRni\n4uK63Tc+Ph4VFRWw2Wwd9uW6NEREREREJBbRCqy0tDScPn0a5eXl3m0VFRU4efIk0tLSut2X69IQ\nEREREZEUyQRBEMT4i61WK5YtW4aQkBCkp6dDJpNh+/btaGpqwu9//3uo1WoA6HRdGgB48cUXUVRU\nhLlz53rXpfnyyy+xevVqtk4mIiIiIiJRiFZgAUBVVRW2bNmCr776CoIgIDU1FfPmzYPJZPK+p6Ki\nAosXL+6w9oPdbsfbb7+NvLw877o0GRkZSElJEeNbISIiIiIiErfAIiIiIiIiCiai3YNFREREREQU\nbFhgERERERER+QgLLCIiIiIiIh9hgUVEREREROQjLLCIiIiIiIh8hAUWERERERGRj7DAIiIiIiIi\n8hEWWERERERERD7CAouIiIiIiMhHlGIHIBVVVVXIycnB0aNHAQBjx47FvHnzEBUVJXJkA8+xY8eQ\nlZXVYbtWq8WWLVv8H9AAcenSJbz//vsoLi7Gd999B7vdjo0bN8JkMrV7n91ux/bt2/HZZ5/BYrEg\nMTERGRkZSE5OFinywMN8Ix3MN+JhzvEf5hxpYL4Rj7/zDQssADabDatWrYJKpcKiRYsgk8mwbds2\nZGVlYd26dVCr1WKHOCDNnz8fI0eO9D5XKBQiRhP8Ll68iPz8fIwYMQJjxoxBUVFRp+975ZVX8OWX\nX2Lu3LmIiYnB3r17sWbNGqxZswaJiYn+DToAMd9IE/ON/zHn+AdzjvQw3/ifv/MNCywABw4cQHl5\nOdavX4/BgwcDABISErB06VLs378fM2fOFDnCgSk2NhZJSUlihzFgjBkzBq+++ioAz+9EZ8nn7Nmz\nyMvLw4IFCzB16lQAQHJyMh5//HFs374dmZmZfo05EDHfSBPzjf8x5/gHc470MN/4n7/zDe/BAlBY\nWIikpCRv4gEAk8mE0aNHo6CgQMTIiPxHLu85HRQWFkKhUGDSpEnebQqFApMnT0ZRUREcDkd/hhgU\nmG+IPJhz/IM5h8j/+YYjWABKS0sxYcKEDtvj4+ORn58vQkQEAC+99BLq6+uh0+lw1VVXISMjg/PF\nRVZWVgaTyYTQ0NB22+Pi4uB0OnHx4kXEx8eLFF1gYL6RJuYbaWLOuXLMOdLDfCNNvsw3LLAAmM1m\n6HS6Dtv1ej0sFosIEQ1sWq0WM2fORHJyMrRaLc6cOYOdO3fimWeewdq1axEeHi52iAOW2WyGXq/v\nsL1lm9ls9ndIAYf5RlqYb6SNOefKMedIB/ONtPky37DAIskZPnw4hg8f7n2enJyMMWPGYPny5fjw\nww+Rnp4uYnREFEyYb4jIX5hvBg7eg4Wur+J0ddWH/G/EiBEYMmQIiouLxQ5lQNPpdJ1ewWnZ1tmV\nH2qP+Ub6mG+kgznnyjHnSBvzjXT4Mt+wwIJnbmVpaWmH7WVlZYiLixMhIiJpio+PR0VFBWw2W7vt\nZWVlUCqV7W6ips4x3xD1HnPOlWPOIeodX+YbFlgA0tLScPr0aZSXl3u3VVRU4OTJk0hLSxMxMmpR\nXFyM8+fPY9SoUWKHMqBde+21cLlc7W6Mbnk+btw4qFQqEaMLDMw30sd8Ix3MOVeOOUfamG+kw5f5\nhvdgAZg+fTo++ugjrF27Funp6ZDJZNi+fTuMRiNuueUWscMbcDZs2ACTyYThw4dDp9PhzJkz2LVr\nFwYNGoQZM2aIHV5QO3z4MACgpKQEAHDkyBEYDAYYDAYkJydj+PDhmDRpEnJycuByuWAymbBv3z5U\nVFRgyZIlYoYeMJhvpIX5RlzMOf2POUc6mG/E5c98IxMEQfD5dxCAqqqqsGXLFnz11VcQBAGpqamY\nN28eTCaT2KENODt37sShQ4dQWVkJu92OiIgIjB8/HnPmzEFkZKTY4QW1OXPmdLo9OTkZK1euBADY\n7Xa8/fbbyMvLQ2NjIxISEpCRkYGUlBQ/RhrYmG+kg/lGXMw5/sGcIw3MN+LyZ75hgUVEREREROQj\nvAeLiIiIiIjIR1hgERERERER+QgLLCIiIiIiIh9hgUVEREREROQjLLCIiIiIiIh8hAUWERERERGR\nj7DAIiIiIiIi8hEWWERERERERD7CAouIiIiIiMhHWGBRQHM6nbDb7WKHQUQDBHMOEfkL803gYoFF\nAeOTTz7BnDlzUFRUhG3btmHhwoXIyMjA6dOnxQ6NiIIQcw4R+QvzTXBRih0AUV9t3boVAHD77bdD\nqVQiMjJS5IiIKJgx5xCRvzDfBAcWWBRwXC4Xnn/+eYSEhIgdChENAMw5ROQvzDfBgVMEKeDcfPPN\nTDxE5DfMOUTkL8w3wYEFFgWcwYMHix0CEQ0gzDlE5C/MN8GBBRYFnNDQULFDIKIBhDmHiPyF+SY4\nsMAiIiIiIiLyERZYREREREREPsICi4iIiIiIyEdYYBEREREREfmITBAEQewgiIiIiIiIggFHsIiI\niIiIiHyEBRYREREREZGPsMAiIiIiIiLyERZYREREREREPsICi4iIiIiIyEdYYBEREREREfkICywi\nIiIiIiIfYYFFRERERETkIyywiIiIiIiIfOT/AFzyXKFMjQxnAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10f0371d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.style.use('seaborn-poster');\n",
"\n",
"def steady_rhs(h,r,alpha,g=1.):\n",
" return h/(g/alpha**2 * r**3 * h**3 - r)\n",
"\n",
"r = np.linspace(0.5, 10)\n",
"\n",
"h0 = 1.; u0 = 2.; alpha = r[0]*h0*u0; g=1.\n",
"h = np.squeeze(integrate.odeint(steady_rhs,h0,r,args=(alpha,g)));\n",
"u = alpha/(h*r)\n",
"plt.figure(figsize=(12,4));\n",
"plt.subplot(1,3,1); plt.title('Depth'); plt.xlabel('r'); plt.ylabel('h');\n",
"plt.plot(r,h);\n",
"plt.subplot(1,3,2); plt.title('Velocity'); plt.xlabel('r'); plt.ylabel('u');\n",
"plt.plot(r,alpha/(r*h));\n",
"plt.subplot(1,3,3); plt.title('Froude number'); plt.xlabel('r'); plt.ylabel('$F$');\n",
"plt.plot(r,alpha/(r*h*np.sqrt(g*h)));\n",
"plt.tight_layout();"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.13"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment