{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculate path propagation/attenuation according to ITU-R P.452 (16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## License\n",
    "\n",
    "```\n",
    "Calculate path propagation/attenuation according to ITU-R P.452 (16).\n",
    "Copyright (C) 2015+  Benjamin Winkel (bwinkel@mpifr.de)\n",
    "\n",
    "This program is free software; you can redistribute it and/or\n",
    "modify it under the terms of the GNU General Public License\n",
    "as published by the Free Software Foundation; either version 2\n",
    "of the License, or (at your option) any later version.\n",
    "\n",
    "This program is distributed in the hope that it will be useful,\n",
    "but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
    "MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n",
    "GNU General Public License for more details.\n",
    "\n",
    "You should have received a copy of the GNU General Public License\n",
    "along with this program; if not, write to the Free Software\n",
    "Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from astropy import units as u\n",
    "from pycraf import pathprof\n",
    "from pycraf import conversions as cnv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Doing generic studies"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For spectrum compatibility studies on the ITU-R level, it is often necessary to do so-called generic studies. These are analyzing compatibility for the smooth-Earth scenario, i.e., assuming the terrain to be completely flat."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Producing the zero-height profile\n",
    "This is obviously trivial. We just produce a zero-filled numpy array and an appropriate distance vector."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "distances = np.arange(0., 100., 0.05)  # 100 km in steps of 50-m\n",
    "zero_hprof = np.zeros_like(distances)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As for the [terrain-based height profile](https://github.com/bwinkel/pycraf/blob/master/notebooks/03a_path_propagation_basic.ipynb), we first create a `PathProp` instance and call the `loss_complete` function afterwards. Since we use a custom height profile, the Tx/Rx coordinates are not relevant, but since the constructor wants to have a number, we will just feed in dummy values. We will also provide values for $\\Delta N$ and $N_0$, the radiometerological parameters, as the P.452 algorithm needs them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "lon_t, lon_r = 0 * u.deg, 0 * u.deg\n",
    "lat_t, lat_r = 50 * u.deg, 50 * u.deg\n",
    "h_tg, h_rg = 10 * u.m, 50 * u.m  # Tx will be within clutter\n",
    "G_t, G_r = 10. * cnv.dBi, 0. * cnv.dBi\n",
    "\n",
    "frequency = 10 * u.GHz\n",
    "temperature = 293.15 * u.K\n",
    "pressure = 1013. * u.hPa\n",
    "\n",
    "time_percent = 2 * u.percent\n",
    "DN, N0 = 38. * cnv.dimless / u.km, 324. * cnv.dimless\n",
    "\n",
    "zone_t, zone_r = pathprof.CLUTTER.URBAN, pathprof.CLUTTER.UNKNOWN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pprop = pathprof.PathProp(\n",
    "    frequency,\n",
    "    temperature, pressure,\n",
    "    lon_t, lat_t,\n",
    "    lat_t, lat_r,\n",
    "    h_tg, h_rg,\n",
    "    30. * u.m,  # dummy height resolution\n",
    "    time_percent,\n",
    "    zone_t=zone_t, zone_r=zone_r,\n",
    "    delta_N=DN, N0=N0,\n",
    "    hprof_dists=distances * u.km,\n",
    "    hprof_heights=zero_hprof * u.m,\n",
    "    hprof_bearing=90 * u.deg,  # have to provide dummy bearings\n",
    "    hprof_backbearing=-90 * u.deg,\n",
    "    )\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next step is to feed the `PathProp` object into the attenuation function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L_bfsg:   153.89 dB - Free-space loss\n",
      "L_bd:     200.98 dB - Basic transmission loss associated with diffraction\n",
      "L_bs:     197.07 dB - Tropospheric scatter loss\n",
      "L_ba:     174.22 dB - Ducting/layer reflection loss\n",
      "L_b:      174.22 dB - Complete path propagation loss\n",
      "L_b_corr: 190.32 dB - As L_b but with clutter correction\n",
      "L:        180.32 dB - As L_b_corr but with gain correction\n"
     ]
    }
   ],
   "source": [
    "tot_loss = pathprof.loss_complete(pprop, G_t, G_r)\n",
    "(L_bfsg, L_bd, L_bs, L_ba, L_b, L_b_corr, L) = tot_loss\n",
    "print('L_bfsg:   {0.value:5.2f} {0.unit} - Free-space loss'.format(L_bfsg))\n",
    "print('L_bd:     {0.value:5.2f} {0.unit} - Basic transmission loss associated with diffraction'.format(L_bd))\n",
    "print('L_bs:     {0.value:5.2f} {0.unit} - Tropospheric scatter loss'.format(L_bs))\n",
    "print('L_ba:     {0.value:5.2f} {0.unit} - Ducting/layer reflection loss'.format(L_ba))\n",
    "print('L_b:      {0.value:5.2f} {0.unit} - Complete path propagation loss'.format(L_b))\n",
    "print('L_b_corr: {0.value:5.2f} {0.unit} - As L_b but with clutter correction'.format(L_b_corr))\n",
    "print('L:        {0.value:5.2f} {0.unit} - As L_b_corr but with gain correction'.format(L))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is also interesting to study the attenuation effects as a function of distance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# have to avoid the first few pixels, as each profile needs to have at\n",
    "# least 5 or so values for the algorithm to work\n",
    "\n",
    "# store attenuations in a numpy record for convenience (without units!)\n",
    "attens = np.zeros(\n",
    "    distances.shape, \n",
    "    dtype=np.dtype([\n",
    "        ('LOS', 'f8'), ('Diffraction', 'f8'), ('Troposcatter', 'f8'), \n",
    "        ('Ducting', 'f8'), ('Total', 'f8'),\n",
    "        ('Total w. clutter', 'f8'), ('Total w. clutter/gain', 'f8')\n",
    "        ])\n",
    "    )\n",
    "attens[:5] = 1000.  # dB; initialize to huge value \n",
    "\n",
    "for idx in range(5, len(distances)):\n",
    "\n",
    "    pprop = pathprof.PathProp(\n",
    "        frequency,\n",
    "        temperature, pressure,\n",
    "        lon_t, lat_t,\n",
    "        lat_t, lat_r,\n",
    "        h_tg, h_rg,\n",
    "        30. * u.m,  # dummy height resolution\n",
    "        time_percent,\n",
    "        zone_t=zone_t, zone_r=zone_r,\n",
    "        delta_N=DN, N0=N0,\n",
    "        hprof_dists=distances[:idx] * u.km,\n",
    "        hprof_heights=zero_hprof[:idx] * u.m,\n",
    "        hprof_bearing=90 * u.deg,  # have to provide dummy bearings\n",
    "        hprof_backbearing=-90 * u.deg,\n",
    "        )\n",
    "    \n",
    "    tot_loss = pathprof.loss_complete(pprop, G_t, G_r)\n",
    "    attens[idx] = u.Quantity(tot_loss).value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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GCFwNgQC7O0AwKSZmlwGr+3lqbKx6r8R+fj88+KAVvKqrrbJjjrGGKx5+uL11i3KaQyYi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\n7Rsb7TXtvoYqYMw3Ej5XFV8blY0svnQxQaFSfElGh8bGRh5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Bnj17qKio8Lby8vJBeblS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vz9739n4sSJTJ8+naFDh97W8xxdZmYmGzduZPXq1axdu5b169dz5op5eu7u7oSFhdGlSxc6d+5M\nx44dqVGjhkURXy0vD2Jj4bffYMuWiwXY8eNXX2sYtu6FrVpBy5a2X1u1gqAgxyu8zLw8jh/aQVzM\nRuISdnLoxO/EnTtMXNYJDjmfI8Ezm6wr/zi657/yueZCvQsu1MupTKBLdQI9/QmsFkxg7TuoF9iC\neiHtNLIlIiIiFcrNqpl7yiSKYiiJEbL0uHRO/nASJw8nQr8LvaoYA/jggw+YOHFiud8M2CqZmZls\n2LCBqKgooqKiWL9+PRkZGZddU6dOHbp06VJYgLVq1arcTD3My7NtmvzbbxcLsC1bIDX16murVLEV\nXQWFV25uFMOG2RpvOAIzL4/khL3ExWzkUPw24k7EEJeawKGsJOKczhHvkXX1dMIrNjOukW4QlOlB\nIFUJdK9FPe8AAmuGEBgQSmCjdtQKbo6Tc5k3d3VYWjshVlMOitWUg+IIbvg3I9M04wEMw5hhmuZl\nQ0OGYcwALBsumhISwtigIILdr94stSiyTmSx8x7bDMzq91SnSpsq17zu8ccf5+uvv+aVV15hwIAB\nxY7XURSlAGvevDndu3cvLMACAwPLxV5LubkQE3N58bV1K5w7d/W1/v7Qrh20bQtt2tiKsOBgcLqk\nmURUFHZXjKUmHyF292piYzcTd+J3DqXEE5eVRJyRSpxHJheurJOv2GurRrpBcKYHwYYv9T3qEFyt\nAcH+TanfsB1Bd3TEs2r5GekUERERsQdF7bK4xTTNtpccOwM7TdNsVprB3SCeGy0vK5IDLx7gyOQj\neDbzpNWvrXDzv36nPtM0y0VBYQXTNNm1axdLlixh6dKlrF69+poFWEREBBEREYSHh+Pn52dRtJdL\nTIQNGyA62vbr5s2Qlnb1dXXr2oqvggKsXTtbQWaPCqYVxu5dR2z8VmJP/E5sWgKxeSeJdbvASY8b\n/7nxzTCon+FOsOFLsLs/9X3rE+zflOD6bQi6owNVqtcpo28iIiIiYh9KtcuiYRhjsO0b5mEYRsEk\nLgPIAj4t7kOtlpOaQ/L3yQA0/k/jGxZjQIUrxpKSkvj1119ZunQpS5cu5fgVi6fKYwGWnm4b8Soo\nvqKj4fDhq6+rV+/ywqtdO1uHQ3uSnXGB+L3riY2JJvbITmJPHSA2/SixxhkOXjnK5QRc0v/CIxsa\nXHCjoelLA3d/gn2DCa59B/XrtyWoSRhVawaW9dcRERERqdCKOkI2wTTNMWUQT5Hc7gjZvif3cfyL\n43g09qD9rvY4uV6ch/bOO+/Qv39/QkNDSyJUu5CTk8P69etZuHAhS5YsYdu2bZe97+/vT+/evend\nuzc9e/akZs2aFkVqY5pw6BCsXWsrvKKjbU03rti2jCpVoH176NgROnSwvUqy+CrNees5WRnE7V5L\nzN41xBzeRszp/RzITOSASyoJlXNuuA9X9XSDhpmeNHSqQUOvejT0a0LDoNY0vKMz/g1bYzgVYRMv\nsQtaOyFWUw6K1ZSDUh6UyT5kpmmOMQzDFwjhkp5ppmmuKu6DrWLmmZz88SQAod+EXlaMAfj5+dGv\nXz/27NlD5cqVr3ULh5CamsqSJUtYsGABP//8M6dOnSp8z93dne7duxcWYaGhoZaOEubm2gquNWts\nr9WrbdMRL+XkZFvn1aHDxQLsjjugPPdiMfPySIzdRszuVcTEbSYmeR8xF44Q43SG2MpZ5Fwa+yVr\nuQwTAtOcaZhdhYautWhYNZiG/s1oWL8dDZt30yiXiIiIiB0p6gjZU8DzQACwDegIrDdNM7J0w7tu\nPMUeITvy0REO/PUAboFudIzreM1C48SJE5aPApWGuLg4FixYwIIFC4iKiiL7kg20GjVqxIABA+jb\nty/dunXDvZjNUkpCejps3GgrvNasgXXrrm68UaMGdOkCnTrZiq877yy/DTZSkuKJ2b6cmNiNxBzf\nTcy5OGLMk8R4pnP+Bs0mA9OcaZxdlSbudQmp1oiQgFY0DAkjuFkX7cMlIiIiUk6UyQgZtmKsPRBt\nmmYPwzDuAN4q7kOtkrYrjdgXYwFo+E7D6476OFIxFhsby7x585g3bx5btmwpPO/k5ETXrl0ZOHAg\nAwYMoEmTJpaNgl24YCu6VqywvTZvvnqz5QYNoGtX6NbN9muTJuVrny8zL49jB7awd8dy9h7ayJ6T\ne9mbeZS9bqmcuHQzZCeg6sXDGukGjTO8aOxSi8Y+DWhcpyWNG3ekUcseeHhXK/PvISIiIiJlq6gF\nWYZpmhmGYWAYhptpmvsMw2hSqpGVglM/nsLMMak1pBY1H7YVXXl5eTg52JqaAwcOFBZhW7duLTzv\n5eVF3759C0fCrNqMOSvL1nhjxQpYvhzWr7edK2AY0Lr1xeKra1eoU06a++VmZxG3ew17d0WxYMUS\nsnxPszc3kb0e50m9tDfMJVMMPbKh8Xl3Ghs1aFIlmMa1QmncsD0hLSKoVqehFV9DHITWTojVlINi\nNeWgOIKiFmRHDMPwAX4AfjEM4wwQX3phlTzTNDm95DQA1fpdHHl44YUXyMjI4P3338fDw8Oq8G7b\n0aNHmTVrFnPmzLmsKUeVKlUYMGAADz30EH369LFkKmJurq0D4vLltteaNbZRsQKGYet6GBkJPXrY\npiJWrXr9+5WF3OwsDmxbxs4dv7LnyFb2psayJ+8EMZUzLm6OnAtcsn1dtXSDZhlVaFqpDk2rNaFp\n8J00a3kXAU3aazNkEREREbmmIq0hu+wDhtEd26SrxaZpZt3s+tJQnDVkJ74+wZ6H9+Di40LY/jAq\n1ajE999/zwMPPICrqysbNmygTZs2pRRx6UhLS+P7779nxowZ/PrrrxT8TKpUqcLAgQN58MEHLSvC\nEhNhyRJYvBh++QVOn778/dBQWwEWGQnh4VDNotl5BY01dm5ZxK6D0ew8tZeducfYUzn9YuF1hbpp\nTjTN9qGpewDNaobStGEHmrbqiV9gU3UwFBEREalgSnsfMnfgT0AjYCfwuWmaK4v7MCslf2fbdyzo\n1SAq1bB1Uli4cCEA7777rt0UY3l5eURFRTFt2jS+/fZbzp8/D0ClSpUYMGAAQ4YM4e677y7zIiwr\ny9aGfvFiWyG2ffvl79evD7162QqwiAhr9v46d+oYuzb+xM7fV7Hz+A52ZiSw0z2V05dulnzJiFe9\nNGda5FQj1DOYZv4taRrSiTva9FIXQxEREREpMTccITMM4ysgG1gN9AXiTdN8voxiu65bHSEzTZMN\nIRvIiM3gzm134tXKq/D8r7/+Ss+ePcv95s8nT57kyy+/ZOrUqRw4cKDwfOfOnRk6dCgPPfQQ1cp4\nmOnYMfjpJ9tr+XLIrw0B8PS0TT+8+27o0wcaNSq7JhxmXh5Hft/E1s3z2XpwHVtT9rHd+SRxVXKu\neb1PhkGL9Cq0cAukRa0WNG/clebt++NTK+iGz9G8dbGaclCsphwUqykHpTwo7S6LzUzTbJH/oM+B\njcV9kJXO/HKGjNgMXHxd8GzmWXjeMAx69eplYWQ3Zpomq1evZurUqXzzzTdk5Xe+CAgI4IknnmDo\n0KGEhISUYTywaxf8+CPMnw+bNl3+fvPmtuLr7rttjTjKYpAuNzuLmC1L2bp1EdsOb2Lr+Vi2up/h\n1KWjXj62XyrlQNM0d1o4+dOi2h20aNCRFm37UjeknaYaioiIiIglbjZCtsU0zbbXO7bKrYyQmXkm\nv7X7jbRtaTR4uwGBL5X/6Wbp6enMnDmTyZMns2fPHsBWPPbt25c//elP9O3bFxeXsmkSkZ1t2w+s\noAiLi7v4nru7bRrigAHQty8EBJRyLBkX2Lnue37bsYStiVvYmhXPDs80LlxjL69q6QZtMnxoXbkB\nbeqF0bplHxq37YWru+fVF4uIiIiIFNPtjpDdrCDLBQomohmAB3Ah//emaZqW7E57KwXZud/O8dud\nv1GpdiU6HOzA0eSjBAaWz6LsxIkTfPzxx3z88cckJ9vWvNWuXZvhw4fz9NNPExR04yl0JSUrC5Yt\ng3nz4Icf4MyZi+/5+dkKsHvvhZ49bVMTS0Nebg77t/zCps3z2Ri/jk2ZB9nqlUbmNerQwDRnWuf4\n0aZqE9o06EybOwdQ744OGvUSERERkVJXqlMWTdN0Lu6Ny4vzu2z1ZNXwquS55NGnTx9CQ0OZM2cO\nrq7XaaNXxvbv388777zDjBkzyMzMBKBt27aMGjWKBx98sEzivLQI+/57SEm5+F7TprYCbOBACAsD\n5xLOCjMvj6P7f2PT+m/YGLuKTed+Z7PHGc4WTHn0yH8BjVNduZM6tKnRnDaNu9O6w31UDyi7aZuX\n0rx1sZpyUKymHBSrKQfFETj85kjntp4DoHJoZVxdXdmyZQuLFi0qF8XY77//zptvvsns2bPJy8sD\nYMCAAYwaNYrw8PBSbzSSm2srwubOvboIa94cHnzQ9mratGSfm5GWwm8r57Bu+0+sS97KBtckEivb\nvj8ugK/tt3XTnGifU4v21ZoT1rQn7bo8iK9//ZINRkRERETEQre8D1l5UNQpi7npuayvt56cUzm0\nWduGqp0t3m043969exk/fjxz587FNE1cXFwYNmwYL7/8Mo0bNy7152/fDjNmwOzZtv3CCpRWEZZ0\naBfrVs5g3f7lrD2/j9+qpJF1xT8F+GQYtE/3Jcy7Ke0bhdO+02DqhFi+XFFERERE5IZKu8uiXTs1\n/xQ5p3LwaueFdydLlrtd5siRI4wbN44vv/wS0zRxdXXliSee4JVXXqF+/dId+Tl2zFaATZ8OO3de\nPN+oEQwZAg89VDJFmJmXx96NP7F6/VesPRrNOjOBWO/8dvOVbC/DhOZn3eji0oDOQV3p2GEQIW17\nac2XiIiIiFQ4Dl2QFawfq963uqX7jJ09e5aJEycyefJkMjIycHFx4amnnmLMmDGl2mAkO9vWGfG/\n/4VffoH8WZFUqwaPPAJDh0KHDre3P5iZl8ee6AVErZtF1LF1rHQ9RrJn/uhl/ibLlbOg43lfOldt\nTuemvenYY+hN9/iyB5q3LlZTDorVlINiNeWgOAKHLsjSD6QD8Nra12g0vhHPP/883t5lN1KWm5vL\n1KlTGTduHKdOnQLgwQcf5K233qJRo0al9twDB+Czz+CLL+DECdu5SpXgnntsRVi/frbj4rhhAZY/\nI9T/vBPdcwPoUjuMLu0foEXn+3GpVAabkomIiIiI2BmHXkO24Y4NxP8ezx+c/4BhGBw6dIiA0t4s\nq+DZGzYwcuRItmzZAkC3bt1499136dChQ6k8LyvL1pjjv/+1NeooEBoKzzxjm5ZYrVrx7n00ZjO/\nLP0PSw79wjKXwxcLsHx1zjsRkVuPiHrhRHQbSqM2d2n6oYiIiIhUCFpDdh3nd58n/fd0lngsITc9\nl0ceeaRMirFTp04xZswYPvvsM0zTpF69evz73//mgQceKJVpk8nJMHUqfPzxxQYdHh7w8MO2Qqxj\nx1ufknjh7ElWLfoPS3d8z9KM3eyuamvFT/7gogowEREREZGS4bAF2YmvbHP1XnjkBXr17sUdd9xR\n6s/88ccfGTFiBElJSbi4uDBq1CjGjh1L5cqVS/xZ27fD++/bGnXkb11Gs2YwciQ89hj4+BT9XgWN\nOBYun8qSE+tZXeWMrQuim+1VOQsiL9Sid51u9Ip4ksbt+qgAQ/PWxXrKQbGaclCsphwUR+C4BdnX\ntoKs7qN1adGrRak+6/Tp0zz//PPMnDkTsE1PnDp1Kk1LeAMv04RFi+DddyEqynbOMGxrw55/Hu66\nq+ijYdkZF1i1cAoLNs9mQfYuDlbJ74Toa+uCeGeKJ72rtKZ3u4fo1Hs4lTy8SvS7iIiIiIiIg64h\nyzmXwxrvNTi5O9H1XFecXEpvNGfZsmUMHTqUxMREPDw8mDhxIs8++yxOJTiClJsL33wDEybYRsYA\nvLzgySfhr3+1ta4vitPHYlk0fxILYn5isdthzl7SZ6N6ukH/nPr0bdyfnn3/Qo16TUosfhERERER\nR6U1ZNeQmWCbw+dWz63UirHc3FzeeOMNxo8fj2madO7cmS+//JKQkJASe0ZWltMvickAACAASURB\nVG0D57ffhv37bef8/eFvf4Onn4aqRdjnOjlhL99/90/mxS1iRdXT5DpR2A2x2Vk3Bni2ZkCnP9Kx\n93CcXYvZelFERERERIrFIQuyjMMZ7GEPIbVKrji6VGJiIo899hgrVqzAMAxeffVVxo4di7Ozc4nc\nPzsbvvwSxo+Hw4dt5xo0gJdfhmHDwP0mHeSTE/by3bdvMi9+EVFVz9iKMF9wyYXIM74MrBPBPb2f\npWHryBKJt6LSvHWxmnJQrKYcFKspB8UROGZBFpvBBjYwZuMYftn4C2FhYSV27w0bNnDfffdx/Phx\natWqxaxZs7jrrrtK5N65uTB3Lrz6KsTG2s6FhsLf/w4PPQQuN/ivdfZEAt/MHcecg/NZUfUMeZcU\nYX1T/HiwwT3cO+gfVKvTsERiFRERERGR2+eQa8h2P7Kb5K+SCZgcQPBfgnG5USVzC+bMmcMTTzxB\nZmYmERERzJkzh9q1a9/2fU0TfvwRxo6FXbts5xo3to2QDR4M11uOlpOVwdJv3mb65s/50fMwGa62\n86650POcijARERERkdKmNWRXME2TlKgUAPz7+JdIMWaaJq+99hpvvPEGACNGjODDDz/E1dX1tu+9\nZQu88AKsXm07DgyE116DoUOvPyK2beVXTFv8NrPztnHC0yxcE9bjjA9DGtzH/Q+Ow9e//m3HJiIi\nIiIipcvhNpNK359OdlI2rrVc8Wziedv3y83N5ZlnnuGNN97AycmJ999/n08++eS2i7Hjx2H4cLjz\nTlsxVqMGfPABxMTAE09cXYydP3OC/33wBGEvetEm6hEmu2/lhKdJk9RK/NOpF3GD17B88hmefO4L\nFWNlJKpg7wERiygHxWrKQbGaclAcgcONkGUcygDAq4UXRlE35bqOrKwshgwZwrx58/Dw8GDevHn0\n79//Nu8J//43vPkmpKWBqys895xtuuK1uibuWvs9Uxe8ygxjp61NvQ/4ZBg8Zjbnj3eN4s67hmqT\nZhERERERO+Vwa8hm/W0W0f+OZtADg4j4NqLYz8jIyOCBBx5g0aJFeHt789NPP9GtW7di3w9g7Vp4\n5hnYs8d2PGAATJoEV3bKz83O4seZ/8fk7VNZ7ZtaeL5jihd/avQIDw6ZgGfVGrcVi4iIiIiI3D6t\nIbvCjCUzWMISaqfVJoKIYt0jOzubhx9+mEWLFlGjRg2WLFlC27Ztix1TSgqMGQP/+Y/tOCQEPvoI\neve+/Lq008f54vNnmZz0Iwer5IAvVMmEIbmhjOg/jlbhDxU7BhERERERKX8caq5bXl4e0bHRAES0\niyjWPXJzc/njH//I/Pnz8fX1ZdmyZbdVjP3wAzRrZivGXFzg//4Pduy4vBg7fnAHr/xfR+q9W4fn\nLnzLwSo5NDjnwoeegzk2OpGP396lYqwc0rx1sZpyUKymHBSrKQfFETjUCFl2djZ/bvRndu7eSUjr\nW98U2jRNRo4cyZw5c/Dy8mLx4sW0bNmyWLGkpsLzz9s2eAbo3Bk+/dS2r1iBY/u38M7/hjPVeZut\nZb0rdDlThVGt/8zAx8bj7FqpWM8WERERERH74HBryNb5ryPreBZh+8PwbHRrXRbfffddXnrpJdzd\n3Vm8eDHdu3cvVnyrVsGwYRAfD+7u8Pbb8OyzF/cTO/L7JiZ+MZzPXHeSmV8S35fizyt3j6dDn+HF\neqaIiIiIiJQ9rSG7RNaJLLKOZ+FcxRmPBh639NkffviBl19+GYAZM2YUqxjLyYFx42DiRNtmz+3a\nwYwZ0LSp7f3Tx2J5a8rDfOj0G1n54Q06W5ex9/1LUxJFRERERCogh1pDdn73eQA8m3liOBW9SN25\ncyePPfYYpmny1ltvMXjw4Ft+dmIi9OwJEyaAYdjWiq1fbyvGMtJSeG/CPTT8MIRJlX4jywUePBvA\nzp7f8c2/jqgYs1Oaty5WUw6K1ZSDYjXloDgChxohKyjIKodWLvJn0tLSePDBB7lw4QJDhw7llVde\nueXnRkXBI49AUhLUrg1z50L37mDm5TH30xd4ef/HJHjlgjtEnvHlnQEf0O6uIbf8HBERERERcSwO\ns4Zs4cKFfPjch3Q52IXHJz1Ovb/Vu+l9TNPkj3/8IzNmzKB58+Zs2LABT8+irzszTfjwQ3jxRcjL\ng4gImDPHVpTt3fATz84ZxnLfMwC0OOvOO2H/oM9Df9dGziIiIiIiDkJryPK1bduWbq7dcMW1yCNk\n06ZNY8aMGXh6evL111/fUjGWk2Provjxx7bjMWPgjTcg89wJxoy9l0lGNNm+UC3dYGLtITz598/U\nNVFERERERC7jMEM1/v7+3JVzF2GE4V7f/abXJyQk8NxzzwHw8ccf07Sg80YRnD0L/fvbijE3N5g1\nC956C9b9/CEt/1mXiS7RZDvDU2lN+P0ve3n6hekqxhyQ5q2L1ZSDYjXloFhNOSiOwGFGyAByzuQA\n4FLtxl/LNE1GjBjBuXPnuP/++xk2bFiRn3H0KPTpA7t3g5+fbePn1qEneWFMLz5w24ZZBVqmuDO1\nz4d0vPup2/o+IiIiIiLi2BxmDZmZZ7LSdSXkQXh2OE4u1x/8mzZtGo8//jjVqlVj9+7d1K5du0jP\nPXjQ1knx0CFo1gwWLoSTB6bzh0VPsd87G+c8+IcRzj9eXkglD6/b+o4iIiIiIlL+aQ1ZvpzUHMgD\n5yrONyzGzpw5w+jRowGYPHlykYux3buhVy9be/uwMFj4Ux6zv3iQ0Wnfke1ta9rx5T2f0TbysRL5\nPiIiIiIi4vgcYg3ZRx99RM++PVnFqptOV3zjjTc4efIk3bt3Z8iQorWe374dwsNtxVhEBMybeYhn\n3grg+fTvyHaGv6a3ZNP4JBVjFYzmrYvVlINiNeWgWE05KI7AIQqy6OhoVkWvIo00XH1dr3vd3r17\n+eijj3BycmLy5MkYxs1HFvfutY2MnT5ta+Qx6dUfiZjamO99EvHOhG/qjeaDidtxq+xdkl9JRERE\nREQqAIeYsrh7924AggnGtdb1C7KXXnqJnJwcRowYQevWrW963wMH4K67IDnZ1shjxMNvELH0Vc5V\ngbYpHsx7/GcatIooqa8hdiYiIsLqEKSCUw6K1ZSDYjXloDgCh2jqERcXx6p3VuH3iR8NnmpAk/82\nueozmzZtIiwsjMqVK3Pw4EFq1qx5w2ckJkKnThAfD+HheQzsM5iXMr8nzwkePBvAl69uxbNqjRL/\nbiIiIiIiYj9ut6mHQ0xZDA4OpmvVrnjggVug2zWvef311wF49tlnb1qMnT8PAwfairH27fNo37kT\no7Ntxdg4M5y57x5SMSaaty6WUw6K1ZSDYjXloDgCh5iyCJBxOAMAt3pXF2SbNm1i4cKFVK5cubDD\n4vXk5sJjj8HmzdCgfhYturZikvs+XHLhC/8/MeTPn5RK/CIiIiIiUvE4TEGWmZAJgHs996veGz9+\nPAB//etfqVHjxiNbL70EP/4I1XwyaHvPHfyvajzu2fBN01fp/9hrJR632C/NWxerKQfFaspBsZpy\nUByBQ6whA4iuH01GXAZhMWF4hngWnt+/fz+NGzfGzc2Nw4cP4+fnd937zp0Ljz4Kri453PtME76p\neZAqmfBTxw8IH/jXUvs+IiIiIiJin8r1GjLDMD43DCPJMIwdl5x7xzCMvYZhbDMM41vDMLwveW+M\nYRj789/vXZRnPPnkk7Rp04ZNhzcB4BZw+ZTFKVOmAPDYY4/dsBjbuxeeegogj/sfb803NQ9SOQsW\nd/2PijG5Js1bF6spB8VqykGxmnJQHEFpN/X4AuhzxbmlQKhpmq2B/cAYAMMwmgEPAU2BvsDHRhE2\nCps0aRKf/PsTAnMDcfZyxtnDufC91NRU/ve//wG26YrXk5YGgwbZmnk88HBnvg7YjVsOzG/3Hp37\njbiV7ysiIiIiIlJkpVqQmaa5BjhzxblfTdPMyz+MBgLyfz8QmGuaZo5pmnHYirWwmz3D19eX1o1a\nU5WqOFdxvuy9WbNmce7cObp163bDfcdGj7aNkN0TOYTvmm7AJRe+aTKWyAdGFfWrSgWkeetiNeWg\nWE05KFZTDoojsLrt/ZPAz/m/rwscvuS9o/nnbio3LRfgqoJs+vTpAIwYcf1RrkWLYOpUuLPRuyzu\nMguAqTUe554hbxTl0SIiIiIiIsVmWUFmGMY/gGzTNOfc7r0KCzKviwVZTEwM0dHReHl5cd99913z\nc6dOwfDhEFhtGQcGv0yOM7yUHcaTz31xuyFJBaB562I15aBYTTkoVlMOiiOwpO29YRiPA/2AyEtO\nHwXqXXIckH/umh5//HGCg4MBqJRcCU886V6lO2D7w/n5558DMHjwYDZtsjX8KBjWLvjD+9lnEZxK\nTqF2v36kJJrc61ubCe+tLXz/yut1rONLjwuUl3h0rGMd67isj7dt21au4tFxxTvetm1buYpHxxXj\nOCoqii+//BKgsB65HaXe9t4wjGBggWmaLfKP7wYmAeGmaZ665LpmwCygA7apir8AIVf1t+di2/uv\nv/6aUaNGMajjIO775j6q9a9Gy59aYpom9evXJz4+nuXLl9OjR4+r4lq2DHr2hO79W7Cy/S4anHNh\ny0uxVK0ZWAo/BRERERERcUS32/a+VEfIDMOYDUQA1Q3DSABeBf4OVAJ+yW+iGG2a5kjTNPcYhvE1\nsAfIBkZeqxi7VEJCAkeOHOFC2gXg4pTFLVu2EB8fT506dejevftVn8vMhJEjoUOzUaxsv4tKOfB1\n3y9UjImIiIiISJlyKs2bm6b5B9M065im6WaaZqBpml+YphlimmaQaZpt818jL7l+gmmajUzTbGqa\n5tKb3T8xMRGAmp41AXCpYqsv58+fD8DAgQNxcrr6K773Hpw+uouYe/5tO/YeRLu7htzu15UKpmDo\nWsQqykGxmnJQrKYcFEdQqgVZaXvzzTeJjY1lUItBwMUuiz/++CMA995771WfSUqCiROhUb+7OeNp\n0utMNZ4d9XXZBS0iIiIiIpKv1NeQlYaCNWQFYl+J5fDbh6n/Vn3MR23rx7y8vDh58iRubm6Xffav\nf4VNy0ex4aF/4ZUFu/6whqDQLmX9FURERERExAHc7hoyux4hK5CdnA2Aaw1XFixYAMDdd999VTEW\nGwvTPztO3N2TAXin2iMqxkRERERExDKOUZCdvFiQLV68GIB77rnnquvGjoU2nQeT5J1H+5TKjHhh\nRpnGKY5F89bFaspBsZpyUKymHBRH4FAFmeFjsHr1agB69ux52TUHDsDaxVFEd14LwPu9/4WTsyXb\nsImIiIiIiAB2vIYsKSmJxo0b07hxYz5M/ZD039NhDvR4tAchISHExMRc9pk//Qm2n65HdOgRhqTW\nZ8akgxZFLyIiIiIijqJc70NWmvz8/Dh48CCpqakc7XgUgNXbbaNjV24EnZgIK+d/y74RR3DLgQnP\nfFXm8YqIiIiIiFzJbqcsGoZBtWrVCA4OJvdsLgCrNq4Cri7IJk8Gn67PAzAipxUBTdqXbbDikDRv\nXaymHBSrKQfFaspBcQR2W5AVyMvKIy8jjzynPDZu3ghAeHh44fvp6bDkm2+JDj2KWw68/OT/rApV\nRERERETkMna7hqwg7qzkLNbVXMfRqkcZcnYIdevW5ciRI4XXTpsG/1loWzv2XEYr3p+wzaqwRURE\nRETEwVT4fchyzuYA8Lvr7wCEhYVd9v7MqevZ2PQILrnw0hOflXl8IiIiIiIi12O3Bdk///lP/Pz8\n+OCTDwD4HVtB1r79xfVh27ZBduUXyXOCwWlB1G18pyWximPSvHWxmnJQrKYcFKspB8UR2G1Blpyc\nzMmTJ8m5YBsh25u5F7h8hGzaZyfZ0da2ruyFPmPLPkgREREREZEbsNuCLCUlBQBvZ29yyGHf+X0A\ntGvXDoDcXNi95SXOeJrceaoyHfoMtyxWcUwRERFWhyAVnHJQrKYcFKspB8UR2G1BNnXqVI4fP06/\n5v04ylGy87KpX78+Pj4+AKxcCSeafAfAiIaDrQxVRERERETkmuy2IHNzc6NWrVq4Z7oTRxwAoaGh\nhe9//b81bA8+i0c2PPSHNy2KUhyZ5q2L1ZSDYjXloFhNOSiOwG4LsgI5Z3MKC7JmzZoBkJ0NBxJf\nA+Ce1CC8/QIsik5EREREROT67L8gS8khnnjgYkG2elUesaGrABje5WnLYhPHpnnrYjXloFhNOShW\nUw6KI7D/guzs1QXZT3O+J656Nn7nDe66f5SV4YmIiIiIiFyX3RdkmecyOcxhAJo2bQrAviP/AaDn\nhRBcKrlbFps4Ns1bF6spB8VqykGxmnJQHIHdF2QJpxPIJpt6fvXw8vJi/36ID1wPwEN3qruiiIiI\niIiUX3ZfkB06cwiARgGNAPhh9hb21D2PRzb0vv9FK0MTB6d562I15aBYTTkoVlMOiiOw+4LsyLkj\nAATVCQLgt98mAdD1ZG08q9awLC4REREREZGbsfuC7Nj5YwAEBQSRmwtxXssB6B/Y28qwpALQvHWx\nmnJQrKYcFKspB8UR2H1BdvTCUQCCA4P5bXMW+wKTALh3oNrdi4iIiIhI+WaYpml1DLfMMAyzIO7G\nHo3Zn7GfqJlRrNp6mHFVhhKY4kL8v7MtjlJERERERBydYRiYpmkU9/N2PUJmmibHsmxTFoMbBLPr\n4FwA2l+ob2VYIiIiIiIiRWLXBdnZs2c5n3ced9ypUdOPuMobAehR/y6LI5OKQPPWxWrKQbGaclCs\nphwUR2DXBdmxY7bRsRrUIOmUQUzdkwDcM2CYlWGJiIiIiIgUiV2vIVu2bBk9e/akFa14fsI7PJnZ\nh5ppThx/OxvDya5rTRERERERsQO3u4bMpSSDKWuJiYkAVKc6W/fMh4YQmuKnYkxERERELBccHEx8\nfLzVYUgJCwoKIi4ursTuZ9eVS8GUxepU51D6OgCauzW3MiSpQDRvXaymHBSrKQfFauU9B+Pj4zFN\nUy8He5V0kW3fBdnRiwVZgvcBALq07GFlSCIiIiIiIkXmEAWZr4sv+/3PAdCz/yNWhiQVSEREhNUh\nSAWnHBSrKQfFaspBcQR2XZAlHrOtITOrQror1D3rTPW6DS2OSkRERESkfFm5ciVjx44tPD558iSD\nBw+mR48e9O/fn0OHDgGwfft2wsPDiYiIIDw8nOzsbKtCrjDsuyA7bivI0qrZRsfqp1azMhypYMr7\nvHVxfMpBsZpyUKymHLw1hnGxEeBzzz3HqFGjWLFiBe+//z7PPPMMAG+++SbTpk0jKiqKn3/+GVdX\nV6vCrTDsuiA7deoUAKdrJgMQTKCV4YiIiIiIlHt5eXkkJibSqVMnABo1akSdOnU4fPgwlStXZunS\npWRkZODl5WVxpBWD3RZk2dnZpKSm4IQTx2vZ1pI1rtHC4qikItG8dbGaclCsphwUq9ljDhpGyb9u\nVXJyMjVr1rzsXN26dTl+/DjvvPMOW7ZsoXnz5vz5z38uoW8tN2K3Bdnp06cB8Mabw34JALRr2cXK\nkEREREREyj0/Pz+SkpIuO3fkyBH8/f2pWbMmU6dO5cABWwfzpUuXWhFihWK3BdnJkycBW0GWUMM2\nQtb5rt5WhiQVjOati9WUg2I15aBYzR5z0DRL/lX0Z9sudnJywt/fn3XrbPv47t+/n2PHjhEQEEBs\nbGzh9X5+fuTl5ZXo95eruVgdQHEVFGTuLu5kumbjn+qETy2tIRMRERERuZbZs2ezYcMGAJ555hne\ne+89Tp8+jYeHB59++ikAM2fOZNGiRXh4eBAUFMTrr79uZcgVgmHeSlldThiGYX7//ffcf//9NK3c\nlL3/by8djvgS/d/TVocmIiIiIgLYuhra49+15cau/O+af1yM1Xw2djtlMSUlBQDT3fbDqJ1dy8pw\nREREREREbpndFmRnzpwBILdyLgB13DRdUcqWPc5bF8eiHBSrKQfFaspBcQR2W5AVjJBlemUCEFSj\niZXhiIiIiIiI3DK7L8guVL0AQOOQllaGIxWQPe59Io5FOShWUw6K1ZSD4gjsviA753sOgLYdO1oZ\njoiIiIiIyC2z24IsIyMDgEzvTNyzXQhs3MziiKSi0bx1sZpyUKymHBSrKQeLbuXKlQQHB9OrVy8i\nIyOZO3cuSUlJTJgwAYDPPvuMsLAwFi1axGuvvUaXLl3YunXrLT8nPj6eFStWAFx2f7k+uy3Ivvrq\nK2YPmwshUOOcF4aT3X4VEREREZFSN2zYMH755Rd+/vlnZs2aRWJiImPGjAFg3rx5rFmzhr59+7J8\n+XLWrl1LmzZtCj9b1Pb9cXFxLF++HIBatWoV3l+uz66rmBPnjoIz1DjvbXUoUgFp3rpYTTkoVlMO\nitWUg8Xj7u7O6NGjmT9/PkOHDuXbb79l48aN9OnThylTprBjxw4iIyPZvXs3kZGRPPTQQ0ybNo2J\nEycSERFBp06d2L59OwDr1q2ja9euREZGMm/ePD799FNmzJhBr169iI+PZ+jQoYBtw+lOnTrRrVs3\ndu7cCUCnTp145plnaNu2LUuXLrXs52E1F6sDuB0nso4CUC3dx+JIRERERESKwCj2/sHXV4zNp/39\n/YmOjqZGjRoMGjSIKVOmsGzZMgzD4KuvvmL58uXEx8eTnJxcOOKVkZHBK6+8QmxsLK+++iozZ85k\nzJgxLFiwAF9fXwBq1qxJw4YNeeONN4iPj8cwDPLy8vjwww9Zv349hw8f5tlnn2XBggWcPn2aCRMm\nkJWVxV/+8hd69+5doj8We2HXI2QnSQKgelY1iyORikjz1sVqykGxmnJQrKYcLL6jR4/SuXPnwmPT\nNK85LbFVq1aFv582bRrdu3fnqaeeIjExsfBzBcXY9SQnJxMUFISTkxNBQUGkpqYC4OfnR/Xq1fH3\n9+fs2bMl8bXskl0XZKddTgJQzfSzOBIRERERkSIwzZJ/FfnRtmszMjKYPHkyAwcOvOF1AMYlI3qf\nfPIJK1eu5L///W/hNU5OTpw+fbrwc66uruTk5Fx2Pz8/PxISEsjJySEuLo6qVatede+8vLwifw9H\nY9dTFk+7nwKglqu/xZFIRaR562I15aBYTTkoVlMO3pqZM2cSHR1Nbm4uzzzzTGFhBJcXR9f7fYcO\nHQgPD6dbt26F59566y0GDBiAu7s7f/rTn+jTpw9jxozh0UcfZeLEiYCtaBs5ciTdunXD2dmZjz/+\n+IbPqWiMonZMKU8MwzBN06TNkyFsCzrAx0ff5c+fjrY6LBERERGRQoZhFLk7odiPK/+75h8Xu6K0\n7ymLlW1zTQP8gq0NRCokzVsXqykHxWrKQbGaclAcgV0XZCmV0wAIqhdsbSAiIiIiIiLFUKpTFg3D\n+By4B0gyTbNl/jlf4CsgCIgDHjJN82z+e2OAJ4Ec4HnTNK+5IYFhGGZqSjrekz0wTIPjYYnU7Fer\n1L6HiIiIiMit0pRFx2RvUxa/APpcce4V4FfTNJsAy4ExAIZhNAMeApoCfYGPjRus7ju0LxaAKulV\nqFTZreQjFxERERERKWWlWpCZprkGOHPF6XuBafm/nwbcl//7gcBc0zRzTNOMA/YDYde7d/wBW0FW\n9UJVDLeK25VFrKN562I15aBYTTkoVlMOiiOwYg1ZTdM0kwBM0zwO1Mw/Xxc4fMl1R/PPXVPi0XgA\nvC944+Ru10vhRERERERKTWpqKj169KBHjx74+PgQGRnJ8OHDLY1p69at7NixA4BDhw6xcuVKS+Ox\nUnnYh6xYE2tPpySCG1RNr4qTmwoyKXva+0SsphwUqykHxWrKwaLx9vZmxYoVAISHh7N8+XKLI4It\nW7bg4uJCy5YtOXjwIGvWrKF79+43/Zxpmg63Z5kVBVmSYRi1TNNMMgyjNnAi//xRoN4l1wXkn7um\nWd/Ng9pwPOk4U2ZOIaxXWOEfyoLhax3rWMc61rGOdaxjHevYyuPyauzYsSQmJnL48GG+/vpr/vGP\nf7Bz5058fHyYNWsWSUlJPPHEE/j4+HDq1Cnmzp1LvXr1mDBhAgsXLsTDw4Np06bh5ubGoEGDcHZ2\npnXr1kyaNIlvv/2W9957D09PT8aPH4+7uzt/+9vfyMzMZNCgQYwePZpPP/2Uc+fOsWLFCtLT09m4\ncSPr169n8eLFvPrqq6xatQoXFxe++OILMjMzGTFiBL6+vgwcOJChQ4da/ePj8ccfByA4OPi271Xq\nG0MbhhEMLDBNs0X+8dvAadM03zYM42XA1zTNV/KbeswCOmCbqvgLEGJeI0DDMMyRw+/n43rfc/+G\n+5k1ZRYe9T1K9XuIXCkqKqrwf7oiVlAOitWUg2K18p6D1+qyaJRCoWbews8gPDycVatWMXbsWHx8\nfBg1ahTR0dFMmzaNTz75hOnTp3Pq1CkGDhzI/fffz44dO1i/fj2zZ89mzJgxPP300yxcuJBVq1bx\nzTffMGDAADZt2sTf//53AHJzc+ncuTNr1qzB1dUVgMzMTNzcbE34unfvzrJly5g2bRqurq4MGzaM\nZcuWsXbtWsaNG8e2bdv47LPP+Oijj9i1axf/+c9/ePHFFxk8eDBbt24t8Z9dcdhVl0XDMGYD64DG\nhmEkGIbxBDAR6GUYxu/AXfnHmKa5B/ga2AP8DIy8VjFWIC37NGDrsmi4ONawpYiIiIhIaWvXrh0A\nsbGxtG3btvDcgQMHAGjZsiUArVq14sCBA8TFxdG6devC62JjY+nRowfp6ekMGTKEOXPmkJSURMOG\nDQuLMYADBw7Qt29fIiIiiImJITk5+box7d27l2XLlhEZGclzzz1HampqYQyOqlSnLJqm+YfrvNXz\nOtdPACYU5d5peWcB8MrwwnBWQSZlrzz/i5xUDMpBsZpyUKxmjzl4K6NZpfL8S8Y7nJxsYzMNGzbk\nyy+/5Omnn2bz5s00bNgQgJ07d2KaJtu2baNRo0YEBQUVjlJt2rSJhg0bkpuby/jx4wFo06YNDz/8\nMIcOHSIrK4tKlSphmiZTpkxh7NixdO7cmU6dOmGaJq6uruTk5ABc9vsm2D1gFQAAGZlJREFUTZrQ\nr18/Jk2aBNhG3OLi4hxu3dilykNTj2K5wDkAqmRUUUEmIiIiIlIEBYXNpQVOx44dmTZtGt27d8fb\n25vZs2dz4sQJatSowcCBAzl16hRz5syhbt26dO7cmS5duuDu7s706dNZv34948aNIysri759++Lk\n5MTo0aMJDw/Hy8uLN954g3vuuYcRI0YQGhqKp6cnAJ06dWL48OHs3LmTV199lbFjxzJkyBBmzpzJ\nwoULiYyMxMnJiccee4zw8HCHLshKfQ1ZaTAMw+wxvDYr6h1n/NzxvLT6JSrVqGR1WFLBlPd56+L4\nlINiNeWgWK285+C11pDZi9jYWP75z3/yv//9z+pQyp2SXkNmtyNkSz6KZXHQr1Q67aY1ZCIiIiIi\nYpfsdoTMNE1Wea0i73weXVO74lLFbmtLEREREXFA9jxCJtdnV10WS12u7RetIRMREREREXtk1wWZ\nmWurTDVlUaxQ3jd8FMenHBSrKQfFaspBcQSOUZBphExEREREROyQ3RZkpmlCXv6B3X4LsWfluauT\nVAzKQbGaclCsphwsupUrVxIcHEyvXr2IjIxk7ty5Rf7sjz/+SEpKCgDTpk0r3ItMSobdljIFo2M4\n4dD7EoiIiIiIlIRhw4bxyy+/8PPPPzNr1iy2bdtWpM/98MMPnDp1CoA//vGPtGnTpjTDrHDstiAr\nbOih9WNiEc1bF6spB8VqykGxmnKweNzd3Rk9ejTz589n3LhxgG3ka/r06QCMHTuWbt260bNnTw4f\nPszixYsZMmQIkyZN4vXXX2f58uWsXLmSfv36MXDgQLp168aFCxfIysri3nvvpV+/fjz66KOF95Mb\ns9te8Vo/JiIiIiL2JsqIKvF7RpgRt/wZf39/5s6dy+DBgy87v23bNg4dOsTq1asLz/Xt25exY8dS\nv359Xn/99cLzbm5ufP/990yYMIFff/2VjIwMunTpwksvvcTIkSOL/X0qGvstyHJUkIm1NG9drKYc\nFKspB8VqysHiO3r0KI8++ijZ2dmArT+DYRjExMTQuXPny641TfOa+6k1b94cgDp16pCSkkJiYiKt\nWrUCoHXr1qX8DRyH/RZkankvIiIiInamOKNZJaWgqMrIyGDy5MmMHz+eDz74AICdO3fSqlUrmjRp\nwoIFCy4b4apUqRK5ublX3e/KPg4NGjRgx44d3H333ezYsYOwsLBS/DaOw27XkBU29XC2Ng6puDRv\nXaymHBSrKQfFasrBWzNz5kx69epFv379+MMf/kCLFi04duwY/fv3Jzk5GYBWrVoRFBRE165d6dmz\nJ6mpqfTu3ZuRI0fy6aef3rCZ3r333svatWvp27cvSUlJuLq6ltVXs2t2O0JW2NRDUxZFRERERG6o\ne/fuHDp06KrzP//881Xn3nzzzcuOBw0axKBBg655T7B1Xizw3Xff4ezszMiRI2nQoMHthl0hGNea\nD1reGYZhZhzJYH3Aeir5V6Lzsc43/5CIiIiISBkyDOOaa68c2d13301aWhohISF88cUXVodTKq78\n75p/XOxRIrsdIdMaMhERERGR8mXx4sVWh2B37H4NmaYsilU0b12sphwUqykHxWrKQXEEdl+QqamH\niIiIiIjYK7tdQ5a2N41NTTfh0diDDr93sDokEREREZHLVMQ1ZBVBSa8hs9sRssIui1pDJiIiIiJy\nXampqfTo0YMePXrg4+NDZGQkw4cPv+q6FStWkJCQcN37fP7550yfPr00Q62Q7LYg0xoysZrmrYvV\nlINiNeWgWE05WDTe3t6sWLGCFStW0LJlS5YvX87nn39+1XXLly+/Zmt8KV0qyEREREREKpj4+Hgi\nIyPp2rUr//rXv8jIyGDGjBm8+OKLvPLKK2zZsoWIiAg6derEe++9Z3W4Ds1+297nqO29WCsiIsLq\nEKSCUw6K1ZSDYjV7zEHj9ZL/u6v56q2vU5swYQITJ04kLCyMPn36MHToUIYNG0bPnj0JDw8nMzOz\ncASye/fuvPDCCyUctRSw34JMXRZFRERERIolNjaWNm3aANCyZUvi4uIua1Rx4MABRo8eTXp6OjEx\nMSQnJ1sVqsOz24KssKmHpiyKRaKiouzyX+bEcSgHxWrKQbGaPeZgcUazSkOjRo3YvHkzHTt2ZNu2\nbfy///f/cHV1JTfX9pfsKVOmMHbsWDp37kynTp3ULbIU2W1BpjVkIiIiIiLF8/LLL/P444+Tk5PD\nfffdR82aNenRowfjxo0jOjqaAQMGMGLECEJDQ/H09LQ6XIdmt/uQnV52mu13bccnwofWK1pbHZKI\niIiIyGW0D5lj0j5k+QpHyNTUQ0RERERE7JTdF2Rq6iFW0d4nYjXloFhNOShWUw6KI7DbgkxNPURE\nRERExN7Z7Rqy5B+T2XXvLqoPqE6L+S2sDklERERE5DJaQ+aYtIYsn7osioiIiIiIvbPfgixHa8jE\nWpq3LlZTDorVlINiNeVg0aSmptKjRw969OiBj48PkZGRDB8+/KrrVqxYQUJCwnXv8/nnnzN9+vQS\njW3o0KHXfebWrVvZsWMHAIcOHWLlypUl+uzywv73IVOXRRERERGR6/L29mbFihUAhIeHs3z58mte\nt3z5cpycnAgMDCzL8K5ry5YtuLi40LJlSw4ePMiaNWvo3r37TT9nmiaGYT81gt2OkKmph1gtIiLC\n6hCkglMOitWUg2I15WDxxcfHExkZSdeuXfnXv/5FRkYGM2bM4MUXX+SVV15hy5YtRERE0KlTJ957\n773r3qd///4APProo0yZMoX0/9/e/QdXWd15HH9/gaSIFrrUpQxEQ51UStGgMIkSEkhoKIir290J\nBbaS4tiG2SpioF0IMzQ7zrQJxfqjW7o7sS7pam1nYduCnV1kIQk/SpCmEJXfAgIlQaXsCtIimuS7\nf9wn2QvcQAjhPtzwec3c8T7PPc85516/3Mz3nvOcc+YMBQUF7ZZfuHAhOTk55Ofnc/r06bbzixYt\nYsOGDUBk1KyhoYGKigoWL17MzJkzqaiooLKykkmTJgFQWlpKXl4eEyZM4OjRoxw4cID8/HymTJnC\nSy+91BUfUdwk/giZEjIRERERSSDRozexFv1obzGQS113OcrKyigvLyczM5OJEycyY8YMCgsLyc/P\nZ+zYsZw9e7ZtSui4ceN44oknYtbTu3dvzp49C8Drr7/O1q1byczMjFm2rq6OxsZGNm7cGPM9RZ8z\nM4qKikhKSqKwsJB169YxfPhwvvOd71BfX8+JEyeorq5mx44dlJeXU1xczIkTJ1i7du0VfS5hSNgR\nMiVkEjbNW5ewKQYlbIpBCZtisPMOHDjA3XffDUB6ejqHDh06J8nbv38/9913H7m5uezbt4/jx4/H\nrCcjI4MVK1aQlpZGU1MTmzdvZsyYMTHL7tu3j6ysrJivRSdmLS0tF+377t27WbduHePHj+fxxx/n\n1KlTAIwYMeKi112rEj4h06IeIiIiIpJI3L3t0d7rnbnucqSlpVFXV4e7U19fT2pqKklJSTQ3R+4L\nWrp0KYsWLaKmpoYhQ4a022brlMbs7GwGDx7MypUrycjIiFl26NCh1NbWXvCeAPr160djYyPuzq5d\nuwBISkqiqanpgudDhw5l8uTJVFVVUVVVxbJly4DYo22JIGETMt1DJmHTvHUJm2JQwqYYlLApBjtv\n/vz5lJSUkJOTw8SJExkwYAB5eXk8+eSTlJWV8cADDzBr1iymTZtGnz592q0nMzOTvXv3kpWVxZgx\nYzAzkpOTaWlpYe7cueeUHTVqFAMHDiQ7O7vtHrLWJKqgoIAlS5YwdepU+vfvD0SSvcrKSoqLi0lP\nT2f9+vU89NBDjBw5sm21yPz8/LaVHxM1IUvYjaGP/ugobz32FoP+fhC3//j2sLskIiIiInIObQzd\nPWlj6IDuIZOwad66hE0xKGFTDErYFIPSHSR+QqZ9yEREREREJEEl7JTFw0sOc/DbB0mZl0LaU2lh\nd0lERERE5Byastg9acpiKy3qISIiIiIiCS5hEzLdQyZh07x1CZtiUMKmGJSwKQalO0jchKxJCZmI\niIiIyKWcOnWKvLw88vLy2paLf+SRRy4oV11dzZEjR9qt54UXXmhbYr6rzJgxo902t2/fzhtvvAHA\n22+/zfr16y+r7qKiorZNoztizpw5l1V/V+kVSqtdQBtDS9i094mETTEoYVMMStgUgx3Tt29fqqur\nARg7dixVVVUxy1VVVdGjRw9uvfXWeHavXdu2baNXr16kp6dz8OBBNm3axLhx4y55nbtjZpw8eZK+\nfft2uL3nnnvuSrrbaYk7QqYpiyIiIiIinXL48GHGjx9PdnY2Tz/9NB9++CEvvvgixcXFLFiwgG3b\ntpGbm8vo0aN56qmn2q3n/vvvB2D69OksXbqUM2fOUFBQ0G75hQsXkpOT07YxdKtFixaxYcMGIDJq\n1tDQQEVFBYsXL2bmzJlUVFRQWVnJpEmTACgtLSUvL48JEyZw9OhRDhw4QH5+PlOmTOGll15iz549\nDBs2DICSkhLy8vKYPXs2RUVFAMyePZu8vDxyc3NpbGwEICcnp639Rx99lJycHL73ve919iPusIRN\nyLSoh4RN89YlbIpBCZtiUMKWiDFoZl3+6IyysjLKy8vZtGkTr776Kh988AGFhYU8++yzlJeXM3z4\ncGpqaqitreWVV16hqakpZj29e/fm7NmzALz++uts3bqVzMzMmGXr6upobGxk48aNrF27lptuuilm\n/1vfV1FREQsWLKCyspKioiIefvhhVq9eTX19PSdOnKC6uppnnnmG8vJyAE6cOMHy5cuZMWMGa9as\naUvWdu3aRXV1NaNHj25rY8mSJVRXV1NSUsLzzz/f1m6ryZMns3HjRlatWtWpz/dyJPyURe1DJiIi\nIiJyeQ4cOMDdd98NQHp6OocOHTpnKff9+/fzrW99izNnzrBv3z6OHz8es56MjAxWrFhBWloaDQ0N\nbN68mbFjx8Ysu2/fPrKysmK+Fp0MtbS0XLTvu3fvZt26dYwfPx6AlJQUAEaMGNFWZsuWLTz22GPU\n1tZy5513AnDXXXe1JfHf/e532bBhAx999BHp6ekXtHHHHXcA0KdPn4v2pSsk7AiZpixK2DRvXcKm\nGJSwKQYlbIkYg+7e5Y/OSEtLo66uDnenvr6e1NRUkpKSaG6OTENbunQpixYtoqamhiFDhrTbTuuU\nxuzsbAYPHszKlSvJyMiIWXbo0KHU1tZe8HkA9OvXj8bGRtydXbt2AZCUlNQ2Mhf9fOjQoUyePJmq\nqiqqqqpYtmwZ8P9JXVNTEz169KBHjx6kpqayc+dOgLYFQt577z22bNnC+vXrKS0tbevD+XuLnX/u\nakn4hEyLeoiIiIiIXJ758+dTUlJCTk4OEydOZMCAAeTl5fHkk09SVlbGAw88wKxZs5g2bdpFR4ky\nMzPZu3cvWVlZjBkzBjMjOTmZlpYW5s6de07ZUaNGMXDgQLKzs9vuIWtNfAoKCliyZAlTp06lf//+\nQCTZq6yspLi4mPT0dNavX89DDz3EyJEj21aLzM/Pb1v5sbWuzZs3t01PTElJYdiwYeTm5lJTU0NS\nUhI333wzycnJTJgwgdWrV7f1r/X66NG6zk4JvRyWiLuHm5nvfXQvjUsbSfthGimzU8LuklyHampq\nEvKXOek+FIMSNsWghO1aj0Ezi8sIi5zrtdde45ZbbmHQoEEANDc307NnT15++WWOHTvGvHnzrqj+\n8/+/BsedztwS9h4yLeohIiIiIiLnu+eee845XrBgAVu3biUpKYnly5eH1Kv2JewI2Z5v7OHY88e4\n/V9uZ9CsQWF3SURERETkHBoh6566eoRM95CJiIiIiIiEJLSEzMyKzWyHmb1hZj8zs2Qz+wszW2Nm\ne83sVTPr1971WmVRwpaIe59I96IYlLApBiVsikHpDkJJyMxsEDAbGOnu6UTuZZsOLADWuvtQoAoo\nabeS1nvItA+ZhKS+vj7sLsh1TjEoYVMMStiu9RhMTU29KhtB6xHuIzU1tUvjJMxFPXoCN5pZC3AD\n0EAkARsXvP5ToIZIknYBb9IImYTr/fffD7sLcp1TDErYFIMStms9Bg8dOhR2FyQBhDJC5u6NwA+A\nI0QSsZPuvhb4jLu/G5R5BxjQbh2asigiIiIiIgkulBEyM/sU8NdAKnASWG5mXwXOX4am3WVpPv3g\np/nErZ+gz+fb36hO5GrSr14SNsWghE0xKGFTDEp3EMqy92ZWAEx0928ExzOAe4HxQK67v2tmA4Fq\ndx8W43qtHyoiIiIiIteERNwY+ghwr5n1Bs4CXwR+B5wGZgKLga8BK2NdfCVvWERERERE5FoR2sbQ\nZlYKTAM+BrYDXwc+Cfw7cAtwGPiKu1/bd2uKiIiIiIh0UmgJmYiIiIiIyPUutI2hO8vMJpnZHjPb\nZ2bzw+6PdH9mlmJmVWa208zeNLPHg/Md3shcpCuYWQ8z22Zmq4JjxaDElZn1M7PlZrY7+E68R3Eo\n8WRmxWa2w8zeMLOfmVmyYlCuJjN7wczeNbM3os61G3NmVmJmbwXfk1/qSBsJlZCZWQ/gR8BEYDgw\n3cw+H26v5DrQBMx19+HAaODRIO46vpG5SNeYA+yKOlYMSrw9B/xnsODWCGAPikOJEzMbBMwGRrp7\nOpG1EKajGJSraxmR3CNazJgzsy8AXwGGAfcBPzazS659kVAJGZAJvOXuh939Y+AXRJbPF7lq3P0d\nd68Pnp8GdgMpRGLvp0GxnwJfDqeHcj0wsxRgMvCTqNOKQYkbM+sL5Lj7MgB3b3L3kygOJb56Ajea\nWS/gBiL72SoG5apx903A/553ur2YexD4RfD9eAh4i0j+clGJlpANBv4QdXw0OCcSF2Y2BLgL2MJl\nbGQu0gWeAb7NufszKgYlnj4L/NHMlgVTZyvMrA+KQ4kTd28EfkBkte4G4KS7r0UxKPE3oJ2YOz9X\naaADuUqiJWQioTGzm4AVwJxgpKzDG5mLXAkzux94NxipvdjUB8WgXE29gJHAUncfCfyJyLQdfRdK\nXJjZp4iMTKQCg4iMlH0VxaCE74piLtESsgbg1qjjlOCcyFUVTI1YAbzo7q37471rZp8JXh8IvBdW\n/6TbGwM8aGYHgZ8D483sReAdxaDE0VHgD+5eFxz/B5EETd+FEi/5wEF3/x93bwZ+BWShGJT4ay/m\nGohs39WqQ7lKoiVkvwPSzCzVzJKJ7GO2KuQ+yfXhX4Fd7v5c1LlVRDYyh4tsZC5ypdx9obvf6u63\nEfneq3L3GcArKAYlToLpOX8ws9uDU18EdqLvQomfI8C9ZtY7WCjhi0QWOlIMytVmnDtDpb2YWwVM\nC1b//CyQBmy9ZOWJtg+ZmU0isspTD+AFdy8PuUvSzZnZGGAD8CaRIWkHFhL5B6aNzCWuzGwcMM/d\nHzSz/igGJY7MbASRhWWSgIPAw0QWWVAcSlyYWSmRH6Y+BrYDXwc+iWJQrhIzexnIBT4NvAuUAr8G\nlhMj5sysBHiESIzOcfc1l2wj0RIyERERERGR7iLRpiyKiIiIiIh0G0rIREREREREQqKETERERERE\nJCRKyEREREREREKihExERERERCQkSshERERERERCooRMREREREQkJErIREQkrsys2cy2mdkOM9tu\nZnOjXhtlZs9e5NpUM5sen57GbPuMmW2LOn7zCur7vpkdi37/IiJy/ekVdgdEROS68yd3HwlgZjcD\nPzezvu7+j+7+e+D3F7n2s8DfAT+PQz9jeau17wHvbEXu/g9mdroL+iQiIglMI2QiIhIad/8jUAQ8\nBmBm48zslajn24PRtN+b2Y1AGZAdnJsTjFJtMLO64HFv1LXVZrbczHab2YutbZpZhpn91szqzWyL\nmd1oZj2CEavXgvPfuJz3YWa3BX0aZWZfM7NfmdkaMztoZo+aWXHw+mYz+1T0pVf4EYqISILTCJmI\niITK3d8OEqK/bD0V/Hce8E13rzWzPsCHwAJgnrs/CGBmvYF8d//IzNKIjJxlBNffBXwBeAf4rZll\nAb8DfgFMcfdtZnZTUO8jwPvufo+ZJQfl17j74Uv138xuD+osdPcdZnYHMDxovw+wH/i2u480s6eB\nQuCHnf7ARESkW1FCJiIi14JYI0W/BZ4xs58Bv3T3BrMLiiUDPzKzu4Bm4HNRr21192MAZlYPDAFO\nAY3uvg3A3U8Hr38JuNPMpgTX9g3qulRCNgD4NfC37r4n6ny1u/8Z+LOZvQ/8Jjj/JnDnJeoUEZHr\niBIyEREJlZndBjS5+/HohMvdF5vZb4D7iYxYfSnG5cXAO+6ebmY9gTNRr52Net7M///Ni5X8GTDb\n3f/7Mrt/EjgC5ADRCVl02x513IL+9oqISBTdQyYiIvHWlhAF0xT/GfinCwqZ3ebuO939+0SmGn4e\n+IDI6FWrfsCx4Hkh0PMSbe8FBprZqKCNm4JE7lXgm2bWKzj/OTO7oQPv5SzwN0BhWKs/iohIYtOv\ndCIiEm+9g6Xjk4GPgX9z92dilHvCzPKIjG7tBP6LyGhTs5ltByqBpcAvzawQWA38qZ02HcDdPzaz\nqUSmOd4A/BnIB35CZErjNosM070HfLkjb8bdz5jZXwFrzOyD9toWERGJxdz1d0JERORSzCwV+I27\nd9k9YGZWCnzg7k93VZ0iIpJYNGVRRESkY5qBfq0bQ18pM/s+8FXaH9UTEZHrgEbIREREREREQqIR\nMhERERERkZAoIRMREREREQmJEjIREREREZGQKCETEREREREJiRIyERERERGRkPwfrRX/gVj6mSIA\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f53c6282160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.close()\n",
    "fig = plt.figure(figsize=(14, 8))\n",
    "ax = fig.add_axes((0.1, 0.1, 0.8, 0.8))\n",
    "for (name, style) in zip(\n",
    "        attens.dtype.names, \n",
    "        ['b-', 'r-', 'c-', 'm-', 'g-', 'k-.', 'k-']\n",
    "        ):\n",
    "    ax.plot(distances[5:], attens[name][5:], style, label=name, lw=2)\n",
    "\n",
    "ax.legend(\n",
    "    *ax.get_legend_handles_labels(), \n",
    "    loc='lower right', fontsize=8, handlelength=3\n",
    "    )\n",
    "# ax.set_xlim((0, 300))\n",
    "# ax.set_ylim((80, 199))\n",
    "ax.set_xlabel('Distance [km]')\n",
    "ax.set_ylabel('Path attenuation [dB]')\n",
    "ax.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "With this, it is easy to see at which distance diffraction kicks in (at about 58 km), because the `L_bd` term shows a sharp bend at this point."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [Root]",
   "language": "python",
   "name": "Python [Root]"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}