Skip to content

Instantly share code, notes, and snippets.

@hannorein
Last active February 29, 2020 23:00
Show Gist options
  • Save hannorein/db7eb7801c1753067a0865ee56d0d769 to your computer and use it in GitHub Desktop.
Save hannorein/db7eb7801c1753067a0865ee56d0d769 to your computer and use it in GitHub Desktop.
Display the source blob
Display the rendered blob
Raw
{
"cells": [
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"import rebound # install rebound with \"pip install rebound\"\n",
"import numpy as np\n",
"%matplotlib inline\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Query data from NASA Horizons"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"human_labels = [\"Sun\",\"Earth\",\"Moon\",\"2020 CD3\"]\n",
"horizon_labels = [\"Sun\",\"399\",\"301\",\"2020 CD3\"]\n",
"# 399 is the object code for Earth [Geocenter]\n",
"# 301 is the object code for Moon [Luna]\n",
"# The search for 2020 CD3 will output a warning because the mass is unknown. That's ok."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Searching NASA Horizons for 'Sun'... Found: Sun (10).\n",
"Searching NASA Horizons for '399'... Found: Earth (399).\n",
"Searching NASA Horizons for '301'... Found: Moon (301).\n",
"Searching NASA Horizons for '2020 CD3'... Found: (2020 CD3).\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/rein/git/rebound/rebound/horizons.py:140: RuntimeWarning: Warning: Mass cannot be retrieved from NASA HORIZONS. Set to 0.\n",
" warnings.warn(\"Warning: Mass cannot be retrieved from NASA HORIZONS. Set to 0.\", RuntimeWarning)\n"
]
}
],
"source": [
"sim = rebound.Simulation()\n",
"sim.add(horizon_labels)\n",
"sim.save(\"init.bin\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Integrate simulation"
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {},
"outputs": [],
"source": [
"# this avoids having to query NASA Horizons all the time\n",
"sim = rebound.Simulation(\"init.bin\")"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {},
"outputs": [],
"source": [
"year = 2.*np.pi \n",
"Nsamples = 5000\n",
"times = np.linspace(-5.*year, year, Nsamples)\n",
"xyz = np.zeros((Nsamples,sim.N,3))"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {},
"outputs": [],
"source": [
"for i, t in enumerate(times):\n",
" sim.integrate(t)\n",
" for j, p in enumerate(sim.particles):\n",
" xyz[i][j] = p.xyz"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Plot orbits in inertial frame"
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(1,1)\n",
"ax.set_aspect(\"equal\")\n",
"for j in range(sim.N):\n",
" ax.plot(xyz[:,j,0],xyz[:,j,1],label=human_labels[j])\n",
"ax.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Plot orbits in corotating frame centered on Earth"
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {},
"outputs": [],
"source": [
"earthsun = xyz[:,1,:]-xyz[:,0,:]\n",
"phi = np.arctan2(earthsun[:,1],earthsun[:,0])\n",
"c, s = np.cos(phi), np.sin(phi)"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAASgAAAD8CAYAAADE3zmUAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAgAElEQVR4nOydd3gVVdfFfyedFnrvJVTpXUGaIB3BBjYUFLu+rxVfC9i7Ip+KDRVRQUUBlaJIE1B67zVA6CSkAOn3fH/smczcmgAJSWDW8+SZe6fdmSSz79n7rL2W0lrjwIEDBwURQfl9AQ4cOHDgD06AcuDAQYGFE6AcOHBQYOEEKAcOHBRYOAHKgQMHBRZOgHLgwEGBRa4EKKVUb6XUDqXUbqXUaB/bw5VSPxjbVyilahnryyqlFiqlTiulPvQ4prVSapNxzHillDLWl1FKzVNK7TKWpXPjHhw4cFDwcMEBSikVDHwE9AEaA8OUUo09dhsJnNJa1wPeB9401qcAzwNP+Dj1BOAeIMr46W2sHw3M11pHAfON9w4cOLgEkRsjqHbAbq31Xq11GjAVGOSxzyBgkvF6GtBDKaW01me01kuRQJUFpVRlIFJrvVwLk/Qb4Dof55pkW+/AgYNLDCG5cI6qwEHb+xigvb99tNYZSqkEoCxwMsA5YzzOWdV4XVFrfcR4fRSo6OsESqlRwCiAYsWKtW7YsGGObsaBg/yDhsMbZFm5BUhVo9BgzZo1J7XW5XPznLkRoPINWmutlPLZq6O1/gz4DKBNmzZ69erVF/XaHDg4L4xrBvH74aGpUC4qv6/mnKCU2p/b58yNFO8QUN32vpqxzuc+SqkQoCQQm805q/k55zEjBTRTwePnfeUOHBQ0lK4py/gD+XsdBQS5EaBWAVFKqdpKqTBgKPCrxz6/AsON1zcAC3SALmUjhUtUSnUwZu/uAGb6ONdw23oHDgo/ipaTZfKp/L2OAoILTvGMmtJDwB9AMPCl1nqLUuolYLXW+ldgIjBZKbUbiEOCGABKqWggEghTSl0H9NJabwUeAL4GigBzjB+AN4AflVIjgf3ATRd6Dw4cFBgUMVgzZ+Py9zoKCHKlBqW1ng3M9lj3gu11CnCjn2Nr+Vm/GrjCx/pYoMcFXC4A6enpxMTEkJKSkv3ODnKEiIgIqlWrRmhoaH5fSuGFGaCcERRQyIvkF4KYmBhKlChBrVq1UIVstqQgQmtNbGwsMTEx1K5dO78vp/AioqQsUxLy9zoKCC7bVpeUlBTKli3rBKdcglKKsmXLOiPSC0WwMfp0ZeTvdRQQXLYBCnCCUy7D+X3mAlSwLHVm/l5HAcFlHaAcOChwCDIeSZcToMAJUPkKpRS33XZb1vuMjAzKly9P//798/GqHOQrMlJlGRKRv9dRQOAEqHxEsWLF2Lx5M8nJyQDMmzePqlWrZnOUg0saaWdkGVY0f6+jgMAJUPmMvn37MmvWLACmTJnCsGHDsrbFxcVx3XXX0axZMzp06MDGjRsDrh87diwjRoyga9eu1KlTh/Hjx1/8G3JwYcgKUMXy9zoKCC5bmoEdtUbPypPzRr/RL9t9hg4dyksvvUT//v3ZuHEjI0aMYMmSJQCMGTOGli1bMmPGDBYsWMAdd9zB+vXr/a4H2L59OwsXLiQpKYkGDRpw//33O7ykwgST/2TSDS5zOAEqn9GsWTOio6OZMmUKffv2ddu2dOlSfv75ZwC6d+9ObGwsiYmJftcD9OvXj/DwcMLDw6lQoQLHjh2jWrVqOCgkSDKEOkpUzt/rKCBwAhQ5G+nkJQYOHMgTTzzBokWLiI0N1EOdPcLDw7NeBwcHk5Hh8GkKFRKdAGWHU4MqABgxYgRjxoyhadOmbus7d+7Md999B8CiRYsoV64ckZGRftc7uASQaIh2OAEKcEZQBQLVqlXjkUce8VpvFr2bNWtG0aJFmTRpUsD1Dgo5zsRCchyEFYcSlfL7agoEVADVk0sGvgTrtm3bRqNGjfLpii5dOL/XC0D0Mvi6L1RpBaMW5vfVnDOUUmu01m1y85xOiufAQUHBie2yLO/IU5twApQDBwUFx7bIsoIToEw4AcqBg4KCmJWyrJqrWVKhhhOgHDgoCEhNkhFUUAhUaZnfV1Ng4AQoBw4KAg6tBe2CSk2dPjwb8tX63Nj2jLF+h1LqWmNdA6XUettPolLqP8a2sUqpQ7ZtfT0/z4GDQof9y2RZ3dNS8vJGvlqfG/sNBZog1uYfK6WCtdY7tNYttNYtgNbAWWC67Xzvm9sNPfRCh4MHD9KtWzcaN25MkyZN+OCDD7K2xcXF0bNnT6KioujZsyenTkl/1nfffUezZs1o2rQpV155JRs2bMg6Zu7cuTRo0IB69erxxhtv+P3cd955h4YNG9KiRQvatm3LN998A0DXrl1p0KABzZo1o2HDhjz00EPEx8cDoj7arl07mjdvTpMmTRgzZkxe/EoKBlJPw4kdcHg9HFoDsXsk/cpr7P5LlnW65f1nFSZorS/oB+gI/GF7/wzwjMc+fwAdjdchiKOw8tzXvp9tXS9gme39WOCJc7nG1q1ba09s3brVa93FxOHDh/WaNWu01lonJibqqKgovWXLFq211k8++aR+/fXXtdZav/766/qpp57SWmu9bNkyHRcXp7XWevbs2bpdu3Zaa60zMjJ0nTp19J49e3Rqaqpu1qxZ1rnsmDBhgu7Vq5dOSEjQWmudkJCgv/76a6211l26dNGrVq3SWmudmpqqH3vsMX311VdrrbV2uVw6KSlJa611Wlqabteunf7333993ld+/17PGXHRWi/7P62/H6b1W/W0HhPp++f9K7SeepvWa77R+vSJ3L2G0ye1HlNS65fKaZ16OnfPfRGBuDhdcEyx/+S39XlVYLnHsZ6CSEOBKR7rHlJK3QGsBh7XWhc6C4zKlStTubK0M5QoUYJGjRpx6NAhGjduzMyZM1m0aBEAw4cPp2vXrrz55ptceeWVWcd36NCBmBhxh1+5ciX16tWjTp06gCgkzJw5k8aN3Qeyr732GosWLcpqi4mMjGT48OF4IiwsjLfeeot69eqxYcMGmjdvTvHixQFxw0lPTy/c8r4uF+yYBf9+BAf+dd8WHA4lqwqbWylIjoeko2KkGX8Atv0KQaHQeCBc+XDuFLT3LAA01LzSkVnxQIFudTGMQAciIy0TE4CXAW0s3wVG+Dh2FDAKoEaNGoE/aGweSVuMzZkzR3R0NOvWraN9e4nrx44dywpelSpV4tixY17HTJw4kT59+gBw6NAhqle3zJ2rVavGihUr3PZPTEwkKSkpK4hlh+DgYJo3b8727dtp3rw5mZmZtG7dmt27d/Pggw9mXWuhw95FMOdpixQZWhQa9IF6PaFGeyhVy5LdNZGZAbG7Yf9S2DFHAsrmn+Xniuuh58sS1M4XO+fKsu4Fu6ldcsiNAHUu1ucxHtbn2R3bB1irtc56Qu2vlVKfA7/7uiit9WfAZyCtLud2SxcPp0+f5vrrr2fcuHE+G36VUl6jlYULFzJx4kSWLl2ap9embW1QwcHBrF+/nvj4eAYPHszmzZu54gov28KCi5REmP0EbPxB3pesLiOgFrdCePHAxwaHCHmyQkNoezfEH4QVn8DKzyVI7foL+r4FzYcGPo8vpJ2VoAfQaMC5H3+JIzcCVJb1ORJchgK3eOxj2pX/i836XCn1K/C9Uuo9oAoQBay0HTcMj/ROKVVZizU6wGBg8wXfQQ5HOrmN9PR0rr/+em699VaGDBmStb5ixYocOXKEypUrc+TIESpUqJC1bePGjdx9993MmTOHsmXLAlC1alUOHrSy7JiYGC/p4MjISIoXL87evXtzNIrKzMxk06ZNXn11pUqVolu3bsydO7fwBKhjW+HH22UUFBIBVz8pwSkkPPtjfaFUdbj2VWh/nwS9nXNh+r1wcCX0edOyjsoJds+D9DOSKpZx/AQ9ccGzeFrrDMC0Pt8G/KgN63Ol1EBjt4lAWcP6/DFgtHHsFuBHYCswF3hQa/HbUUoVA3oCv3h85FtKqU1KqY1AN+C/F3oP+QGtNSNHjqRRo0Y89thjbtsGDhyYpVAwadIkBg0aBMCBAwcYMmQIkydPpn79+ln7t23bll27drFv3z7S0tKYOnUqAwcOxBPPPPMMDz74YJa43enTp7Nm8exIT0/nmWeeoXr16jRr1owTJ05kzeglJyczb948GjYsJO0Y+/+Fib0kOFVoAvctg6ufOP/gZEep6jBsKgwYL7Wr1RPhuxtkVJRTbDb+vZsMCbzf5YrcrroXxJ+COIu3ZMkSDeimTZvq5s2b6+bNm+tZs2ZprbU+efKk7t69u65Xr57u0aOHjo2N1VprPXLkSF2qVKms/e33NWvWLB0VFaXr1KmjX3nlFZ+f6XK59Jtvvqnr16+vmzRpolu0aKEnT56stZZZvPr16+umTZvq+vXr6wceeECfOnVKa631hg0bdIsWLXTTpk11kyZN9Isvvuj3vvL79+qGvX9r/UolmYX74Q6tU8/k3WcdXGXNAn7ZV+uUpOyPSUnU+uWKcsypA3l3bRcJ5MEsniO34iBXUWB+r8e3w8SekJoIzW+BQR9CUHDefubJXTBpgMj21rgSbp8OoQHso9Z8Db89KvuOmJO313YR4MitOHCQE5yJhe9vkuDUeBAM+ijvgxNAuSi4cxaUqAIH/oGZDwilwR/WGEKDrb2pHg4EToBycGlBa/j1IYjfL4Xn6z7xpg3kJcrWhVt/FB7V5p9h4au+9zu6CQ6vhfCS0Mi7XuhAcFkHqMshvb2YKBC/zw1TYcdsCI+EmybnT+NtpaZw4yRQwbDkHYtGYMdaY3Ki2U1Oc3AAXLYBKiIigtjY2ILxUF0C0FoTGxtLREQ+WnafPiEkTJDp/lLVA++fl4i6Bq4xehan3ycsdBMpibDeYM+0uuPiX1shQoFmkuclqlWrRkxMDCdOnMjvS7lkEBERkb8efIvfgNQEqHcNNB+W/f55jY4Pi874rj9g2kgYMVdqYeu+hbQkqHkVVG6W31dZoHHZBqjQ0FBq13aIcZcMTu6C1V+BCoJer0gfXX4jKAgGfwITrhK1zH8/hA4PwooJsr3jg/l7fYUAl22K5+ASw6I3QGdCy9ugQgGgOZgoWgYGjpfXC16Fpe9JulemDtTvnb/XVgjgBCgHhR8JMbBluhSluzyd31fjjaieEjgzU61ZvQ4PXBzqQyGHE6AcFH6s/FxGT02ug5L5WAMLhF4edIMWnu2qDnzBCVAOCjfSk4WRDTIqKaiI8JD0cWXkz3UUMjgBykHhxs65kBIPlVtAtQJs17Rvsfv7RW/mz3UUMjgBykHhxqZpsmx2U/5eRyBoLUV8MFjjSvSkTu7O18sqDHAClIPCi5QE2DUPUAVbrmTvQpEWjiglfYEtb5Oa2aLX8vvKCjycAOWg8GLHHJkZq9UJIivn99X4hssF816Q11c9AhGRMtMYHCa9ekc35e/1FXBctkRNB5cATKumhv1ytn/yKTiwAmJWwbHNQk9IPAyZaVK0Di8BRctB6ZpQ8Qqo2hpqd5b154tNP0kQiqxqFfFLVYc2I4WwueBVuGXq+Z//EocToBwUTrhcYoAAgc0GUpMkSGydCfuWSGrlDxkpcOYEnNhmGRkEhUKtq0RTqtGAc2vsTU+BBS/L627PQmgRa1vnx2DtJNg5B2LWQLXWOT/vZQQnQDkonDi2WYJJZFXRYfJEQgwsGw/rv5e+NxAiZ82roFpbkWIpXQsiq4hOeVCI6EedOQEnd8LRzRC9FA6tlkC4dxHMKQlt75GRULGy2V/jys8g4aBIDXsaKhSvAO1GwbJxsOx9uPnbC/yFXJpwApSDvEdKovjJ7V0s6c6ZExIQileQQNGgL9TrcW5mA3sWyLJuN/e+u7Nx8PfbsOoLSd1AglLL26S1pGgZ/+cMKwolKolcyhXXW+fbOgPWThb9piXvwPKP4ar/iPGCvxHV6ePw9zvyuudLvlnjHe6Xc237XRyMy9bN+f1fJsiVAKWU6g18AAQDX2it3/DYHg58g9iYxwI3a62jjW3PINbomcAjWus/jPXRQJKxPsOUElVKlQF+AGoB0cBNuhAad14WOBsnvWerJkK6DyOB00fh6EZJdSKrQtdnhGGdkxaQA4bfa+0ustRaUrm5o+FsrKxrMkRSqUpNz/8eipaBNiPk58ByWPIu7PpTZuDWfgP934P613ofN2+MoazQU4KvL5SoJPSIdd9KI3H/98//Oi9RXLAmuVIqGNiJOLDEIDZUw7TWW237PAA001rfp5QaCgzWWt+slGqM2Eq1Q2yn/gLqa60zjQDVRmt90uPz3gLitNZvKKVGA6W11gEbsHxpkjvIAySfkpFAwkEZceyZb20rWR2ufASqtxVJXFeGNM3uXyYic7G7ZL9anWHIZ5J6+YPW8E59OHMcHl4LRUrDjPutulGtzmILVbl53txn9FIJhOYMXMvb4drXZIYOxEnmq94yU/fA8sAjoxM74KN2kmb+ZzMUL58313wRkBea5LkRoDoCY7XW1xrvnwHQWr9u2+cPY59/DePOo0B5LPup133sF43vALUD6Kq1PqKUqgws0lo3CHSNToDygzOxcHA5HF4PcXsgbp8EmZQE0C6xZoooCaVqSPd99fZiz20GD5dL+D2bf4Z9f1tBxh+KloUaHYWs2LCfZZjpcsHmafDH/yT9K14Rbp8BFRv7Pk/8QRh3hfCKbv0JfroLEmPkWnu9KulcXsutuDIlPZv/slAdStaAm76GSs3hsy5SI7v6Kej+bPbn+n6oFMu7Py+WWIUUBTVA3QD01lrfbby/HWivtX7Its9mY58Y4/0eoD0wFliutf7WWD8RmKO1nqaU2gecQizOP9XiFIxSKl5rXcp4rYBT5nuP67Jbn7fev3//Bd3nJYMTO6WmsnWmPETng8rNISMNkuPgtLctuxuuuB6Sjkrh+YxNHDC0GLS+U+o4Jofp9HEJNvuXSvC5cxZU8mEOumUG/GQYDQSFgisdqraBG7+++Cqax7eLaeeR9eKNV64+HNskQf2BFTmb9dv1F3x3PZSqCY+sv7ga6rmIvAhQBblI3klrfUgpVQGYp5TarrX+276D1lorpXxGWF1IrM8vClwu+YZePgGil1jrQyLkwa7eVh6sMnWgWHnR8w4Klmn3s3GSsh3fKqnNngVwZEPOPjeyKmSkQtMbpBCenixp36ZpMvJa/pGYXXZ5StQni1eA236Gn+6U650yFO6eDyUqup/38FrbvaWLHfm1r0NI2AX/qs4ZFRrCyHmS8q2eKMEJZCSXU0pC3W6SAsfvl569ut3y7noLGXIjQB0C7F9b1Yx1vvaJMVK8kkix3O+xWmtzeVwpNR2pU/0NHDPtz40U73gu3MOli31L4M9nraASWkxkSRpfB3W6ZO+wG1lFRjEpCdbMWU4QWhQSD8nP9t9h1hOii9ThfrhrjhTH/34btv0G818Sh92bvpF6zY1fi79czEqYNgKG/+Y+qlj2gfW650tS28pPBc2QMOj3rgQoExumyv3auU/+EBQs2uQLX5UJAydAZSE3xpKrgCilVG2lVBgwFPjVY59fAdP86wZggeFE+iswVCkVrpSqDUQBK5VSxZRSJSDLAr0XsNnHuYYDM3PhHi49JMfDz3fDpP4SnEpUkULu49vguo+hfq+c2X/vXQRjS0oaY0fnx6Fhf+/975oLYxPgmRh4aA30Hwf1+0gA2TkXvhkEX/WFtDPC/bl9BpSuLenm592EHR4aAUO/g2IVJN1b8Yl1/pWfu1/DVY8WDHnf9d+5v98xS+71bFzOjm9xq8gVb/sdzpzMfv/LBLniLKyU6guMQ2gGX2qtX1VKvYRYIf+qlIoAJgMtgThgqNZ6r3Hss8AIIAP4j9Z6jlKqDjDdOH0I8L3W+lVj/7LAj0ANYD9CMwj4X3DZFckPLBeR/sQYGcl0ekz0r8+FBX18mxStPUdNd893lzXZOhN+tDmTPL5Dps89cfoErP0a/vlQ5FEAWtwGvV4WTtT0++ShDgqVkVTDvrB9NkwdJqnow2ukReWnO61zPh8LwQWgSpF4BD5qL7SCwZ+K9Mu318vvv1IzuGNmYP6Vie9uFApDv/eg7ci8v+5cRoEskhcGXFYBast0+GWUkBSrtpEp+3MhAKanCMdn2XhkfsLANS9Cp/+475uZAV/2gkNrrHVVWsFds/2nNimJ8O9Hwo/KTJOa1+BPoU43SUWXfyxBatgUSZF+ulPuqXILKbSbfKryjeDB5Tm/r7yC1jBlmNTMoq6FW36QEV3CIUlT4/bIpMIdM4UOEQgbpspItVZnuPP3i3P9uQjH+txBYKz+SmbBMtOkcDxi7rkFp5g18Glno8ZjC063z/AOTiDB5NAaKYY/vFZmrg6vhd987GsiIhK6PQP3LYMaV8rM3rfXCwGy16vQ8SEpfE8bIXpJPQwlgCPrJTgp41/WV3tLfmDtNxKcwkvCgHFWulmyqgSZMnUkxZ48WPoCA6FBX5kJjF4qozIHToC6ZLBlBvz+X0DDNWOh7zs5bx3RWmo7X14roxQTIUXkm99X0fb0cVhsqEL2HyeBcNhUKcJvnCpF70AoX18e4K7PyPuFrwh1oPvzwpNKTYSpt0gdyg5TEaB8QOrbxcGJHZZRaL93vMmlkVVg+O/S83d4Hfw4HDLT/Z8vIlJGjWhpDXJQoGkGDnKKgyvhl3sADd2fg07/zfmx6Snw26MSVEBGQfEHAAU3TIQ6XX0ft/A1SDst/W31e8m6ik2kpjTrMZj1uKQqgZjRQcHQdbTUtH4aIQ/ld6ckLT25E05shwkd3Y8xbcSLV/Q+38VEeoqM8jKSxSTUn6Jnyapw2y/wf62EYvFyORklJsdLLS7ttHxBgHyhmBIyc54ySLI1hcqQXXp4icKpQRV2JJ+CTzoLV6nt3TJyyumsVooxSoleIsX0rs9IM2xKQmBWc+we+LANoOCBf91HM1rL7NW+xdD6Lkl7coKjmyXVO31U3tfoKFypQAgtBmVqS8NxtTYyW+jJmcorzH4KVn4qKdy9f7trRmWmw8EVMsEQswoOrbMUFc4XpWpILatmJ/nSKN+gYMxe2nC5ETUdZAet4ddHJDhVbS1kxZz+054+Ad8OET5S8Upw2zRRfkxJkGJv58f9H7tsnLTCtLzNO9VSCvq+DR93FE5P+3uzN9KM3SMUBO2y1mUXnADSzwg94dhmWDcZ1H9FuaD1ndBkcN75zu2YI8EpKBSunyjBKTNDAtLGqTIKSklwP6ZEFUg6bL1vMlh+wopbdbXMNDnul3vkfVgJqbUd3yaj2vgDwhsDqfs1HiQN0dXaFLhglVtwAlRhxo45khaFlZAHJadM6pQEKziVqQO3T5deuj0LoEgZGPh//v/hEw/D+imAgqv8pJLlG0Cbu0TyZMErwmnyRNoZYZQveVcY1Nnh5m8lpTIlVJ47Lkz349vg0FoZse1ZIKPB6CWSgnYdDU1vzN2HN26vxQnr8YLUmea/JLpTSbbCdtkoiOolvYvV2ljUi4WvSe1u72Lo+bLv1pzYPbD4DdGQ6veOBL/Y3TIa2/e3cNMSD8kkxfKP5bPajpRUs4hX11ehhpPiFVakJwv3Jn4/9H4TOtyXw+NSJJXav1SC011zhRg5vhWcPQlDvoBmN/o/fv7LkgY2Ggg3T/a/X9IxGNdUGmkfXGmNtE6fEIrB8o9zfq++MDbBe11yPGz5BZaOs4Jerc5CTC1V48I+DyD1NEzsKW0/Fa8Q4bv138s9gvw+W9wqIyN/s6euTOE77Zkvx98115vLFb0Mvu4rn3H/Mh/ncMns6Zbpcr9mYAwtKrIwVz0qbUMXGQ7NwIGF5RPkIazQRGpPOYHWMPNBCU4lKgt9oERFaTk5e1LqPk1v8H98ZoZoF4G0rARCiYrQ8lZ5vewDqZX9+Ry8U887OFVtI+0qfd4WTlSnx7K/l51/WsVlE0VKyQP68FoY+KGoJ0QvkRrdrnnZnzMQtIZfH5LgBJJWrvlKglOjAdK+8/BaqdsFonYEBcP1X0iKFrNK0mVPVG0l6eOxLd6pIkjbT/W20Ps1kWi5+VvRxUo/K7pS45rBn8/7PraQwRlBFUaknZHRydlYSc/qds/Zccs/gblPS91j5DyRM0k8Ah80k9Rp1CIpOPvD9llSVC9XX0ZF2aVOcXthfIDzDRgvagem7IqJmQ9agTAQqreX9h1/hp1nYmHmA1LfUsEw4ANodXv25/WFJe/B/BdtKxQ0u1lmTCs0PPfz7Z4vaXZQKIxa6C2q90VP6UW89WeIuiZn5zy8Dha/LYx8EBJs9+eg5R0XRSHBGUE5EKz5WoJT1TbCwM4Jjm4SpjaIN5uptfTP/0lwajwocHACSWdAGltzUtfJSPW9/trXpU2l9XDv4JR8yjLjfHitmBX4w8EV8MU18Ptjkn55olhZGDoFrn5SzBJ+fUjY2ueKfz92D041roR7F8OQT88vOIGobLYZKaTU6ffL6NSOGh1keXBFzs9ZpSUM+x7uWQDVOwgJ9rdHDUb73vO7znyGUyQvbHBlygMDkk7kJFBkpsOMB0TFss1IUTMAGWGs+UpeB5q1AwkAJkfH1Ov2e40u+Ge8dOfbUaw8DPshsIPJhh+k+F2nm6RKfd6UNC3hoPt+vV6VB/DfD0VFIHoJ3DjJW+QuKEhGEeGRMO95KXD/+5HwipJPCbs7vISkvBUaicJDjSulLgcwZ7TYQ5m4fqLcf24U3nu9LL/TY5tg9ZfQfpS1zfyyOB/NrqqtpYtg888w9xlJ6SdcJQTetvcUKr0pJ0AVNuxZIE2opWsLHSAnWPm5zNiVqiHyJCbWfSN1i3o9s5fH3fWnBI7q7QPL8Z6NkyCw60/vbX3fyd5eab2R2rW5S5YRkTLi+2ag+34JByV4NbkOJg0UYueEjhKAm90kJMfiFSUw7f7LfSRydKP35x7dCLv+kJpQkTKijb53kXuAeGJX7hafw4pB79clbV74igQ+0y2mYhNZnq+ooFJST6zbHWY/KYqlc56CnX/AkM9z5kpTAOAEqMKGtd/IsuVtOfsmTD5ltaT0edtdZne1MXpqN8r3sXbsmC3LRgP973NiB3x3g/B1ipSWYvf8F2XkBkIJMO1RtkgAACAASURBVEdvvhC7R1LRsBLCUDdRp4s3cXPFJ1IT8xxZrZ7orsvkD0GhMPJPGT2lJgp94uBKqQ0d3yIjMzueP3lurjM5RYO+EkT2LBAPPZPYWqau9OXFHxBCral3fq4oWkY6AppcJ5y5PfPh06tFMaIQePE5AaowITleuE8qSL7hAyF2j4waZthm236+2zejedk42Gh04QeHS3tKapLUpkKLitzJpp9k38rNZEbLM8WJXiojgZQESU9u+kb61FwZVvvM1pnSKOwPZv9Zgz6WVlVGmgRHV4b3/p7B6VzgSpeisilrUrW1zMY1HwoTrnTft3ILGRnmBUtdKej9hkFs/UYkkMvWFepB+foSsI9vgxrtL+xzGg2Qv8uPw8Xr78trZQRawGVdnABVmLD7L3mwanX2nWYd2yrCaTvmiMyHJ/y1W+z3wbXxh0kDxCCgfi9JMWt3toJTZho06CfT6PEHJLCEFBGuz0ftxLE34ZD0p/nCDsOVpdEAmV1c/pEU5k0bKX+o3kGabGteJemMKbsLUKGx6E35SutmPSZpXOfHoUoLGUF91ddjJyVKCl/0kMbpvPCuK99ASJbrv5XZwus+kvVl60mAit9/4QEKoGQ1oUP8+Zww4Wc9JsXzni8X2LqUE6AKE8xGWXv6o7UEgmUfuNdZIkpZwnAg9kfFK8r6HbPhh1vP7xrCS0LCAWGJr/rCfVubEVJnCgqW1hOA5jdLQKrVSab79y6y+FF2pJ6Wb3YQieCf77YIkBUay8zh3NHux1RrJ1K7lZtB2lmpsdiDE0C7e+S6tBYW9uK3pGhsYtuv8uPZilKsgkz/B4XAD7cJZ+nL3vKAl6t3zr+2bHH147Bhivxc/YT0GJasJtviD+Te54SEQd+3JCD/+rCksvH7YfBn5yZoeJFQMMOmA2+4MmG3QTZs0EeW+5aIxdHUWyQ4hZWQIvFdc+DJPUJDAJl5qtBIUqJvBroHp+a3iEzKs0eFnT02QVQxB4yX+kiIh/Bcy9vgpsnQxYcVYeJhKepqm1yISRMw6RB7F/q+v+glVhq38QeDADlQFDzv/8e3+WafNyU4JR0T5vW6yZKO9n9fJGBAVBV2/SWpVJ0ucNcsuOUn73PZg1ORMjILVrKatKjcPkOIkGeOi/vK6RPex18oytSR4r7OlBlQkJEqXFgq6w8tbhGVhfCS0t83aUDO5YkvIpwAVVhwYrvUd0rWkAL0L6MsvfHiFaWO8cQOcbqteaX8Ux9aLR3/9XrAX2Phs67uri5XPQqDJ0jAsytglqgkHKVhU+BJD6+75R/BzyOl/82O4HAZIX3aRdpB4g8Ik7taW9le+2pZHvDB69n/rzi4GJiT2ZZeqW9Sa91Q7pzn4sTm+fB1P+/jTu2TWtvEa6SeVLqWcIDajJBZwC5PSwPyL3eLl56J+r2EY+UPdbtLwDARXhyGfi+1qFPR8PMI+cLIbVxlCP1t+EEK42afXnweBCiQgD3yT/mfOrQavu4vOl8FCLkSoJRSvZVSO5RSuw23X8/t4UqpH4ztK5RStWzbnjHW71BKmeaf1ZVSC5VSW5VSW5RSj9r2H6uUOqSUWm/8eBYNLk0cXCnLjBQp4m78QUYLXf8Hj26Q1pOwYtb+pstuhUbw9QBYathqt7/fGhU1DdBz5wYlLrkj/pDu+cw0azQHMv3+3y3Q4UFJiWJWyfqzsVYxvXwDCZYJB1izZTu1Rs+i3uiZfPjcHWR+2SfrVJMzruH+9P+yU8vDeXTnGopO8zMh8MezErjiD0iRe+Rf1vQ8QJfRQqFIPiVieBlp1raydeWefGHzNAno9i6L8OIi51usvKSKS9/L4e/uHFChocippJ+BTT9amldn8mDEZv/MEXOl4fj4FqnBJXiaMuUfLjhAGdbnHwF9gMbAMMPS3I6RiMFmPeB94E3j2MaIC0wToDfwsXG+DOBxrXVjoAPwoMc539datzB+Zl/oPRQKmA/9mePSHFq9vWgxdX3at/73PmOkdGi11GVK15ZidavbRWSteEVpRs0OJ3cBWv6Ba3SAG76UmpAdH3eQgHXtq/DQKvdtU4bB2TjWHExgeaqkLB999xMVieOnsJd4KGQm9vnALzKt75syJPJF2DsUU6lscNXBC0lHIOkIp8q3gzt+9RbHCwoS8buS1aW59u+3rG1HNlrKCHZUby9Bdtk4dzcZkJHlkM/k9eK3ZfSW2zD5X6u+tJQJ7LXEvEDJqqIjX/EKcYf+qnfu1r0uALkxgmoH7NZa79VapwFTgUEe+wwCJhmvpwE9DFfgQcBUrXWq1nofsBtop7U+orVeC6C1TgK2AX6mfi4DuFzutkadn4A7Z7unIXZobfVjgcy23btYZoJ2z5d1dbvnjA1ttkiUNT5r7SRpmA0rLsGqVmcZKc24X1KEzDTp5jexcw5H3mzNy59MZqMRZG4Pnsdv4c/RMmg3h3RZHkiXAfJpHcEBbRIhNW+Efk41dZJ1rnq8lO67h26jqzYdD95PrTGLqTV6lvcORcsIMRFkFHl0k2idf9rZfT9TevjgCmsS4s/nRKfdjrrdpa6WmSozhrndy9poABQtJ6MZM0gkX4Sm3+IVxH+wamv53EkDC4Quem4EqKqAPUmOwTuYZO2jtc4AEoCyOTnWSAdbAvbixUNKqY1KqS+VUj61UJVSo5RSq5VSq0+cyMMhcl7D5YLfH7Xe930Hejwf2G7J/s3f7l6pJUWUlPdmDSqnDcbmKKFMXfnH/cPo5+s/TpjPw38TBYKi5ayWii3iGPZE+r2scUVRWcXxQ9jLNFIigdIteAMVVDz/Zjamf+qrxGlRo9ylq6GNf8kbgv+mV/AaEnURHkx7hFDlu+bzRUY/UrD8/WqNnsWobzwaw2t2lBYPV4bMyH3oQVBUQaIdde3r8n7PAgm8rgz4/T/yN7Cj50vy+9wz/8JVEjwREg6NDTLs3sWyTE3Im5qXJ4qWkcJ55eZS35t8Xb579BXoIrlSqjjwM+KXl2isngDUBVoAR4B3fR2rtf5Ma91Ga92mfPkAutgFGVpLcDLZ45C9tMr+f9yn4/u8aSlLag0xxsNbvV3OriExRpalaohbS9ppmV0zNaOUEnLjQ6ug1XDhaRlI0yHcnPY832X0IFyl0znYatv4JqMnt6eP5hSRVFIye3RIlwMgktP8L0RGjGPTh3OYchQj2efl1Q/yLiD/ufUYtUbPIjnN9lBfM0YkTk5FW+uqGw252iU6WR3ul9FR+llhxYcVF/7UFg8DiOLlrd7FJe/k/iiqsZGAbPtNrgFEweJioEgpuG262Hqd2C5uNMl5nGIGQG4EqHOxPien1udKqVAkOH2ntc76D9FaH9NaZ2qtXcDnSIp5aeLvd9yDU/mGgdOy49vcZsNoNdx9/1PRkBwno51SNXN2DWcMkuT+f2TEEFFKRnGeKFqGkXG3MzTtuaxV48M+om/QCp7NGMFh7W5cOSZjOBmEsHFsL8b3lbSuf6c2RL/Rj41d11NGnYaanXjv1TeIfqMfE4f6Vg1oE7TT53qARi/MpeVLRk9gaDFRoTRRubm4yoQZWuKZqfK76v++zNadOS7BGEQ9wuuDR8hs6sEV7jOjuYGanYTqELvLugZfTPq8QrGyQkotU1cC9Hc3+FaLuAgoqNbnCpgIbNNau02XKKUq294OxrJEv7SwdaY0kKLEBQTkn9YfUpOsVhMTno2tpsFm1dY578Y/awzxNxsSKD1e8NnyUWv0LOZvP85yV2OiXdb28WEfER1xK1WUO8dmX9uZRL/el8iIUOFPgbDjEw4Z9uZKGmnN6zSVFDzQQAWegj91Np3Go3+GlzwqAXV7SG+deX5zFBQaITWrkAhr3+gl3vWY8BLQ3lAxXflZwGs4ZwSHWFw3ExczQIH8jYf/KhSEmFUw7S5vSZiLgAsOUEZN6SHgD6SY/aPWeotS6iWllNlZOhEoq5TaDTwGjDaO3YLYmG8F5gIPaq0zgauA24HuPugEbymlNimlNgLdgHPwWCokOLlLrMABer4ojbJg1ZE8obWkX3F7ZSam9Z2y3tOqyOQu+RN48wU7ea98QxmVecCzOH0M+dxfM90to3T35603m36S5liwSJIlKosUiitdmlsrN7OuYeMPPi+vtDpNKfw7plRXx9gaMcJaEW403S6fIIRL06fObrBQvr5lGGrisA/eVKvhUr/aMdcaaeYWTN6YiYsdoECIqnfMkC/GXX/C7MdzP53NBrlSg9Jaz9Za19da19Vav2qse0Fr/avxOkVrfaPWup7Wup3Weq/t2FeN4xporecY65ZqrZXWupknnUBrfbvWuqmxbaDWOv+nGnITmRkiV5J+Fq64QaRwTZdffy4l676VEU5oMbjxa8sdJdSjdeHENlnmhF5gIjXRen3Ni17FeV8zZ6eMonemx7+XWv2le5Bd8q606Jjpg3ZZ6ZTd22+2zf6qqndwXf9gXba86C090ydoBUvCrfOsd9VBP71fZukykiVAZiTLNdlto0D4YvbPOrbF6/xEVpaRmCvdaqbOLdS8yv19fgQoEL7YLQbnbs3X8je7iCjQRfLLEkvft+zE+70rKYhpS6Rd3vsnHbXNrL0nNkVBhiyI5z/1yd2yLFc/59dz+pgsi5aD+u5BwOe0PnDEqDcNDjaakNveLfyixENWClrvGkCJ1ZXZ/rLtVyEp1ulq6VNtmSHCayY8FTgBko5QLDyE6DeEbR5OGi+GfMWEsA+ydtnnqsjNaS9Q+39zrAL3WoP5UrqW9zmDgqCPnTe1wee90nyode25iVLV3euEQXkg9ZJTVG8nDeAoCeobfI9m8wJOgCpIOBVtkQmv+9gi6pmM54wU72PmPC3T0PV7i0Y2WLpF9gCVdlaafINCoHQOC+T2qe2uo93qVv6CE0C6vQe9+TApqg//DZrZCvhnY93F80DqbgAtDc7TmVjpuAerJmR/UIsZs7M2ImP0kw1ZWPp1hodY0/8ndSS3pD1HKvJ7rPXRCaERmChd2/eN2PWStv/ue59614je+YHluW9SYMr+giU/k19oNEDaqUA046PPQQHjAuAEqIKEeS8I0bHZze6W4+aD6Nmkuusv2DpDUrm+b1sBxExXkk9Z+5ryK6Vr51x4zSR1gpuCQqDgFEIGo0Js2weMl+sKCYfBNn7W4XUSLFvc5n6CiJLQsL+8/usFCWS1r7b0r+ztKebIJzleuEorP4dPOlEleYfbKb/K6I0L90mBu3baHv6qAYTbGtsE9o5v895epJSMDnUm7PHTCH2+sKfieSGWd67ocJ+0M7nS4cfbLwrb3AlQBQUHlssIIqQI9Bjjvs00fbQbQ7pcEtBARjd237dIg+tq76mK2yfLsucgFbL6S+u1MXo7luhjFGfDpBpz3FfYHyylRB/cxB/PeI/mGg+SmbQDy6W2FhwG/d5376MzUcbQZjq5E95tILWq9LNeuz0Z+iMrIh5iafgjPBvyLVU5wRKXTR0hUH3HPipa9IbvfUzSa07ckM8Fdn314HweQZno9bLU3c7GShtTHvOznABVUPC3wS268iFvQbdi5eUf9OxJizS3eZq0Q0RWE7a4HSUNapldpsOsJUVWJkc4fVw0uk0Y/4jtX5vv5wDoFrSOq45PkZGRiZMeaggm7yikCKC8jRVi90pqOcuoE131H9FfMtNbe5pb1NDVXjdZeEs+sKlYR9a4okjURammTnJPyGwWhD/OzDDbjKLZiO2JjDSLmgHyBeKr/65qK1l6KjxcKOxfJgVhBAUyUXPDl3JtxzbLbLMn0z43Py7Pzuwg5zi6WZptQ4rI7JEngoKtLv2jG2Wmz3ywuz1jOZCYMPvmjm+1poXNAFXcm8PkE1tnuhflUxICpnZlSOSr0kbRuccLVj+eXRwOrAet+VC4boI1AWBi/1JDFXOzcHA6GzUoMzCZ9wEi/WJHfRt3qFo7eO44TZ+cy/VpL9I89TOGpI5lRuaVhJJJkyCb3fquP323dOyZL7OYFRobqag2OFoeMB1Yjm60aAu5AfuoKTtV0YuJIqVEQyw8UiYH/n47zz7KCVAFAcsNW6NWd/h326jSQpaH1so/xaloSXHshWcTpWvL6OLMCcsCPCtA5dCVxOinM6GTArE5NGtb/C6jmJqdoOPDoqAJlqqCiSxipAtaDINBPizQTdODa8ZYSg2mx54/l5P/HbFGniUqiy27UViOfqMfmiDW6vr8J/0h7kn3cC7WmV73C1gEzObDoL0xSl33rWg12VG0jIxaM1Jyty5jVzFIPOx/v/xAuSgRQkTBotfELSYP4ASo/EbaGevhaH+v//2qG5rU+xZbjiMdH/DdNKyUxeExe++SzmEEdTZOWluCw7KImW/+6L8A/PPVx2SWK6yECOAFBYkCJYjEr52BnDViMkZ2LYb5v44mQ6zXvmYwTQz6WHhIq76Qa775W6tuZ2D+412yXvcIWud9Dk8XlwMrpGk4rLioiFZuJtyktCR32oMJs2Bv7/W7UCQX4AAFIvzXw0iVf8mBM9B5wAlQ+Y1tvwn3p3r7wIL8Jm9ozwKpixQpHdh115yi3rNAlmax15Nd7gt7FwFazlG+AQCVle8UowRnab3VsLXq9ZJVrC9bT36S4+DAP9YBgThdnjhlFPbj9vrudzPZ1gkHLTJn//d9MuXrlhf+VEN1gJuCF5GpFX1TX2OLyyjSn4q2lCtdmTDnSXnd/j4ZIYFFf9gwxftaStvOk1uwz8KaTdsFDVf9V2Z480izyglQ+Q3T5tvkMPlDsXLu7OJWdwQWuW9gdAbtmCMjmAxDDSAkwv8xJvYukmWdblkcoTrKd4q35sp/JH2s3h5a3WltUMqiC2yzcYiyApQxggrU3/XLPfDn8zDehyV782FCUgVY9LrQM9qNktGOH+x+5VpeCf2SEOVicmZPtupajEh70vZ5xihg6ftCzIys5s5obzxQRlQHV3gXyyMNg4OAqfA5ItnWZlTApHizEBQk9BH7LHJunj5PzuogZ0hPFssmsB7mQGhqsxz35A95onwDUcFMjpNir1nDyS5AaW0xu+t2y5rqbhDk/Q3eUB0gbO1XQlTs/763dZFp8rl1hhWIzABlkkBP+lcj4NAay0DAE3W6ugeJmp3g2tf8nwsIWf4hbYJ2ckKX5N2MmwA4RhlWuwxm/YF/ZMS50DjPwA/cmethxSwpFPOLxYTZwuNZn7oQ2BuUL5bcyvmgSGnxQcwDOAEqP7H/HxnZVGqWM1NIZevFy87pQylrNLFmkgRDyJ6RnBAjhd6IUlCpGeklqnFGh1NBxVMa94fvhzqzAS3WTnYtcBNVW0mad/qYBMmko5ZV1cap8OMd8NcY7+NygtK1pbgNUqC+aVLgqfiDq7Kak59Ov4ckrNHng2mPWPtNHiznvepRI632gBl0d3goTZsBKjU3A5TtSyEtf+ROcowqPka5uQAnQOUn9v0ty5yqW9qNCha+mj3/pMUt0hqyc441m5fdCMrsOavSEoKCiXrujywDA/vUfOegjZQ89LfYFl39lO9zKQUtDIur72+Ccc28eUW7/gx8PSY8i/tzbKnZzd9KCuwP8QdFSdOVAR0eZIGrldvmY3jI2DQe5E2WNVGnizD3j6x3J8Ka6XZujnTs5y/II6g8hBOg8hOHjdmknKhbpqfA7gXW+0NrLHNMfyheQYKUvSCdXXHaDFBmsy6wxhUFQJsgs4VE80TIj/Ky82P+qREgD7QJ04gTZMbPl/AdePfogXfqZG/eXfm5jMZ+uksMP6ffJ6aU818Sc4NxV8Dpo9LScs1Yr1NfG+Rh9NDnLf/KEaFFrC+UnTbWvFlT8+R1XQgS7CMoJ0A5uJjQWr6FQRQcs0P0Epntq9TU4J8A857P3jOt82PuqaEvJxM7fASoVS5Rs2yrJEB1DdpA86C9wnBvF2B6OekoTLNpMdXtDkOMFC8tCf75P9/H+VKwNIv8vrD+WxmNbflF6AYbpogS6ZJ3DdE/A4fWwIQr2dniR24LnkeUimF0yBQ+DXvf/XzZWcGbYnI7baM/M/DnZoCyK4B69BJeLnCsz/MLpvRI0bKiJJkdzEbUqGvFrGDTT+J9N22EWAb5q7+UriX8quUGITIj1fd+Jo4a1uGVm5PpklGBWURuGbSbUDJ4OMTgbV35sP+ZxMx0+OF292n3PQusnkCw0k5PmE4yOUG3Z4XzFFZcgoQrU2pI8QeFQGgirLjU4WJ3ERa7i1c8fl1/ZbbkmmBjRLvvb/kd+0OdrrI8sFzS7KAgK/DnVktK8in3epbnBMRlgsvzrgsCThkPZ5k6OZPfNblEtTrJ/oM+hhJVIGalqGkGUjrsajNRCCQ4lp4s6pYqGErVZPK/0QDEUpLtruoUVak8EDyT1kG7RGWxzUj/51r0hlxbZFXxrDNxyhagbvza//E5QZPB0OUpoVxcMQSa3gDNbxbKwyYjBS1bT0xF/3cInj0izsM+7LqyghP4HsHZUbKaFOZTEywRQFN5NJAs87nA1O4yofyknJc4nACVXzBbInLCH0k9LUaTKtiyEi9W1mjnKCIpzl9j/Acpu4rl5mn+m1rNdLFkNQgOYexvW7M2LXDJLM1/Qw0WdZsRvsXjAI5vF7cTkDTvm4G+9/vpTt/rc4oTO2HjT+5p7o458Fk3iN0NFZuKWWlJg6N0cAXMeCBrhPZLZifuTHuSLzN6c0JHup976bjAdR+TCGsqGJicpaIB6nHnAk/6hb+a2CWOAml9HuichjnDCmP9D4ZRQ+GDWV8wH55AOLJe0pZKTd2DQrU2wj9RwSKdO/tJ/zN7V9xgvf7hdt/21mbK5UNhcn6mNY2coYMkQPnCyd3wcXvrvUkFOB+ERPg3JwVRc/jlbimCf9wRxpYUV5vUBBFYu2u2WEQd3QTf3QSTBoiVUpk63Jn2FI+lP8AiV0teyriDK1M/5J9Mm7zJX2Pgw7bCd/IV+LMC1HJZmr2OgSYMzgVmgDKlc0y7+ssMBdL6PJtzvolYn9cDThnnLnwwW08iSmW/r6mHXamp97b6vSRVCg6DVZ/DW7UlWP3xrMxmTb0VvrnOcmUB4de831gaX2P3WKTJrADlrbi5TkdlvT6gK7hLwqQmwfop4izsaYp5IchIsXoIPVG+kdAbTAWD41vdt1dqLkXxaSPgk84iHRNWHLo9B/f/yyKX+8REOiG8nGFzLy5ZXb5Efh4pFAVPU4QqBlXhmPG5Zm3Nl3zw+cAMUCZ9omgOWpQuQeRGkTzL+hxAKWVan9v/YwYBY43X04APPa3PgX2G64s55+51TqXUNqA7YDahTTLOOyEX7uPiwiyARkQG3g+sAOVJhjSNOA+usIq0KfGWkF12mPmgLIPDxcnELJCnJ3uNGuyKlKmEShF8zwLY+CNsnxV4lu1CkH4GyjWAk+4qmQz5VLTVF7/pPt1vwj57ByJj0/lxGVEBnaPKsWSXu8TKHm2brLjlR7Fb+vM5aYSOWS2N0CbFwNR1j90lLHm7A3NuICtAGWqqOemhvASRGwHKl315e3/7aK0zlFJ26/PlHseaX82+zlkWiDesrjz3d4NSahQwCqBGjbzpE7ogpBnKj2F+6jh2nDAezgqNZJl6GtZ/JzIt9qKzJyKriWRJ0TKwebrUqkBMDExGNwg/yQxOIDOE+//h9ZD6LHY1Z5nrCuopKyVsFHQQ3q7n3iBaurb3tTS/BQ6tth62Ck0gqicsG5f9PdtRt7t3gPr0akn/4vYChrtxuSipSZmFaztSE90UEYqHe//rp2GbgYvfD62Hy4zd9Hul1jR5MPR6RWYvw4vLKCvhIBzdIDyr4PCcpezZIe2M3JcKtmpal2mAumSL5JeE9bkJk7BXqoakUuNbwJynJCCUqCI60XfOhmePwbNHrfpQYoy0d6SdhbZGJlyhsbjFPLnH3Vap5e3un5l4iGEhC/kkbBybIu5mergHszolXkY23Z8XMX3PbvZbp4k0zMmdUqTv+w7c+7f4/IUWO7f7X+FngGzSEcrWEx7U/JckOBUrD11Gw6hF0PYeUfhc/x38X2tpBM7MYMH2bJpvY41ZtNI14c5Z0PV/8v7P5yR9drmylB5Yb6gbVGqaO8Xso5uFMlGhsWXJlVuzg4UMuTGCOhfr85icWp/7WR8LlFJKhRijKF+fVTjg6WjrD5kZlrHlrCekpw2EFX3Vf6BhP++Hov/70PQmkSA5tlkE7k0Z4BPbJT0rVk6cVmbcJw+3nZXe61V5+E3hOH+4b6mkk6YBp4nwSPj+ZimQV2sHN37lPrIY8qnUdQKhSGlp0/Ej5euGWENWuPbV0PouabwOMeZOqrQU3awFr4iO019jYcsMqmXeyh7fg2+BXX8pKBi6Pi0jthn3i3ZUSryRzv0lBFEIbL5wLjA7DKq0sF7nkVpAQUeBtD73d07jmIXGOTDOOTMX7uHiw9TtdmUjEXv6mMVS3jNfiurXfQJ3zxf5D3/f2DU7wqjF0OdtGWWZzcXaJdP7sXuEZHnjJOj9pvuxfz6bfXACeKW8Nbq59nUpXIOkUzpTLNvvmu2d9pzwSNdM3PITPB9r6EidsmSDs0PXZ+DhtRJwrxhiBScTZeqIjvZtP0ugPrKemWHP0ydohdtuwdhmHH0J5DW7EW79UXrx1n1rpcmmHG/VVt7HnA/sAeqU/5nVywEF0vrc3zmNcz0NPGacq6xx7sIHc/YuOy81e+oUWQ1GLRQVypyQO4NDoP0oeHQ9DLS1lWz/Hf6vlUzLv1gK5j7t8/CkkLIMSn2JV9NlTuLnzE60SfGTbh3f4l77ufFruPZV38zq7T60zW+fITOSCQetmbuVn2Z/j2XrwdVPBhb7M1HvGnjgX2gyhOIqhQlhH/Bw8C+Y6p5l7GoN/mYP63aXoK6CvSkUpszxhcJsgSpVU1qCwiMv2xpUrrS6GLbksz3WvWB7nQLc6OfYV4FXfaz3Oqexfi/WTF/hhfkPZ1dN9IVUm8xGlycD84I8kZkhqdqJ7Za42zmgREYsv4SNIVjJA7zDfzGCvQAAIABJREFUVZ2TRLLHVZm6QYZWUZHScg/rvrUOHPyZ/9HP6RNw2AdRdPJ13ut8YcB4+O0RqX9lpEitaMt0YZHnBOEl4IYveWl9MZ4L+ZbHQ6dRRiXxYsYdVFc238HEAJWD+r1gwAfw60PWunL1c6dAnpokI8ygUNGfAglUOflCugTh9OLlF0zX4LNxgfdLS7Jez31GHF2rtBBjgLBigJKp+LQzorqYdETqJ3H7jClwP83BtTrLZ6fESxBM9T2SM4MTwP9Cp/C/UA+52/p9JKWzO+9OHyVT9C2GiQpDSrw8dIfXXZhFeJPBMls39xmZ1ev2rMjOLH5LtuWwQJ2Wqfkysw+HdVk+CP2Iu0L+II0Qd5pBdn+XVrfDik8sE4fqnhPX54mDKwAtGuhmob78OVjVX2JwAlR+wdS5PnMi8H52Znj6WekxM/vMcoJSNaB8Q/kpFyUyJAA3fJXFCUJrqUnZSZbB4e7yKP6w4Xvf61d9Lj/nikfWSxuQr/aY5FMiuFe9rcgSl6svNaWTO8QFuX6vHH1E/eeENzXX1Y770kP5LPQ97g2ZxRltE/PzE7Dd0P99mNhTXttpGhcCU2G1VieZzQMRNLxM4QSo/EKWC4ifjn4TpnxH3R6iU7RngdR6zsYKodKVKSOpsGKGMkJVUUcoVV3SIM9+uU3G9P++xVZapJSYYzYZIjNSQ76QYvOpaH56/z/cGPJ3rt56wHtNPOzfwcV0qKncXALUsS1Cn/hrrATDHAYoOxa6WvJU+ijeD5tAMWULyKlJErgDpVZ2vaajGyXI56QWFgjRhtRLzU6w9D157auD4DKBE6DyC4YZAXF7Az8I5mqdKUGk3DlYl/tCVC8JTttneddtwg3X39QESZfK1qVfj26w+G8O6zJUUXEc16XokfoOp4lgX4SNKlC7i5y30QDo9JgEziXviCQMSJNz19HwrSFj0m6U5TtnQrvEKMFuVGCHKXtr6mcd2SDmnwtfh13zJK0tUzvg7adnevcqTnd1pk3GTm4Nsbkma5ekzf4aokEIrfb9570AQ78L+PkBkXZG6nMqSCgLh89BL+wSxSVL1CzwKFpGZvLSzwRO80INvaX0XGolaWSYM+ya560NZXrJ2QrqRZOiAaiipCYzPmMwSRRlUNA/7sfuWyzLGlfKdHv1tnDLD0KHiKwmNalvbRpL5ijJfPga9hfOVOIhy0LKhElfMGGamB5ZL825TQYDOnuFUSDqWR9tMcD0zKu8VwZqdM5Ic9clDw6XOpw/CkVOEL1UZIkrt5D6YUaypOa51YBcCOEEqPyEmQ4EcjbJmu3LJd+x0rVEhiQtyRLBM2F2ztuVDmxpzAkdyY+ZXYkgladDpwKgOz1mcbrAm9dVrQ3ct0QsrOwwuT6m3dapaDE+KObhfNzvXffGZJDRZ2hR4YilJEBLQ/d8y/Tsia9+0CnYh2NxIHnkHTaqRMWm1jUs8+NCkxOYo83611q1qJo+AudlBCdA5SfM2oI5lPcFky+VHR3hXHCF4di7/lv39WYgsDvG2HhaMzI7kUYoNwYvprKKY7OrFnX+aiXtJCbSfdSPipaB/u+5rzu6SVIZ81pid4sxgqd9UZuR7tP3ZjpsD6Y1r5L2lri97lrlHqg12gf/ysCj1Y0+wvINrZWBTCnsonYRJYWUCsJWPx/rKa0tCeGoXlL0h9zjVhVSOAEqP2Fa9Rxe53+fomUBBWdPSotKbqDFLUI03DHH3RDSfDiPbbFGIjai6NzMtihc3BMsD/qHGdehCeJkO5vDyt9v+/7M7V6UNhmhlKgklImMFGnQ9WRjRy+xamNgBWozaCXESL3M9KvzQ2NIzfCfrpUnHnVknehPDf/N2hCz0vcBJ3ZY5qYglJGydSVQZiSfH5Xi+FbpnSxeUe7t4HLhQvmyvrqM4ASo/EROAlRImMzKaVdg8uC5oEQlSSNcGdJEayKyqozYkuOsXjSTi4NoQnUI2kaNoBMcdJXnT5c0G7d5e7kUx0FSPF8zk0ttxgR2SZIjG61p9ENrxZ3Fjqm3uY+KvAKUMdqLMrQO9y72ecsNnpvrcz3A4gEG16z21Za8CYifoC/Y7wUsyoiZrm6Z4fez/MJk10f1hJ1/yN+7TpecyfFcwnACVH6ifCMprsbtCUwMNBtFs6MknAtMxYMVn1rFcqVsaadH0CxTFxdBDDSK47+4OuGy/fvcscGmUTj9PksED+TezhraS7U6uzvBTBlmCeRFL7HqMCCpTmqC5R8IVsppypCYI7yaHWVUeHidUARsCJTaARTdaszGNb3Jndi66w9hvttxar9oYKlgoWWAZXte3wiS0Ut9p7r+oLXlVNx4sDU7mBO36UscToDKT4SEWZ54+wJwjcrkoJh+rqh3jch5JB2RB86EWZS1pzAA5aKIfr0vXYJlNPNHZlu3zQe0rbh94B9YYqs57bONamp0sIIVSFpj0g3sdZ3IalKP8mRomwEp1JDANQNBeAlJD3WmzBgaWB0dmBG+7/Eo0awKKy7KEPbWIu1yL4aDWGXpTHeKhhlgS1SSAJ+RLClaTnFss5BNi5aVc+1bLBK/OW2WvoThBKj8hmlsuc93agJI2wMELACfM5QSuRYQAblMQwPQVIzcs8B9//AScGofVVQcJ3Uk27S7/McBXZEUbWsMXvQ6HDDUAvYtsdaXqWt1/3d5WpQWfKFqKwlCt/7kvt7UgMoKUGetbebo77g0LSckp3PDJ//6Pj8wsHkVlMmEb3ydqDt4yrtss9Wk4g+I3x7I78601LJLodToKEt/xhS+YI6YGl8H643raXKd1Q51GcMJUPmN2l1l6ad2Alg1mtwMUCAzaKVrSZ3J5BBVbS125nF7xJ3FRGpS1udvdNVBe/zruAjK6mVLrdJeRhk/3gGJRyR1M1HWFqDKNxRtKF+mlBWMlDGipPXQA8x6XOpjwYakin3iwORLHd/G2bQMmr8Y2FZ9/PUNrFFbK0Owz6zzmRMGB5Zb6eqCV6T954obRKzOCIRuM385qSvakZlhpXcN+sCar4zrGe7/mMsIToDKb1RpKXIacXvcTS3tqHQFoOSByM5481wQHAo9DKXMha9JehMcIt/e4E5DSDqSNXrp3sn31PcOLaJ4r+9vQHyF9iKD++W17qlp6Vo2D7nSUpguXsH7ZBVs5MwwDwXOr/qIQgO4G4caLPLkkwdo/MIffm8bIPqNfuJAnHxKgrKZSiYaKg2VW0DJGsJeP75NgvPGHyQw9ngeThpEypI1rCI5WCqb/v6Wntg5V4JimbpCvUg+BdU7WK4xlzmcAJXfCA6RmRtwVwSwI7yE/OO70nP+zZxTNBks0r9njluzU6b874ap1n5HNlgaSZFV2fd6X69TrXWJ80vLoN10O3AXB13l3d2Dg0KhaDlrRBIcJgHhtA/tJXv/mWdQPhVtjXzs8sGGLO6u/QcC3DDsfa2vcJxMt+WOD1qtRub1lqwKVY3R0LHN8Ofz8rrdKAmyRzfK+8oejbwljXQvIfA1ZMEUvWs+FP79SF53eeqylVfxhBOgCgLM2ZptfgIUyEgDAqeC5wOl4FrDInzZOOFAVWsj6ZJnC47JEg8JQynFntfcg9QKl4x62gdt4xQluCf9cffji1cUC2+Toa0z4dPOvq/LrntlD1A3fCWNtCYOWqqYPT5aA0Ax/M+gbX+5N0FBSgiVsbtFDaHRIGsHe9pmXsPS96VGGFFSnGHA+qKo3Nz9A4qVkwJ3SkL2YoQnd8PehbJ//H6ZPKjWzqoDOnACVIFAVE+hGxxc4V/JsbZRTPecXcsN1GgvjG1XBvz6iASQzo9772dyowwb7uAgJaMRA7t0VWJ1CSqpU9RSR9mua5CsbfK7iUbbjBmg/vifFQRNHpMv2GVfSteE23+x3u+ex/jXHqPW6N8JNSR70/30wO94pTcRocFSt1poaCR2eVpGsSbMXrryDd113AF6vmSlc2bh33OWUSkrZT3jbmvlBVMuuUIjMV5QQdD3bWf0ZIMToAoCwksY35pa+sl8oVYn+QeOWenF88kVXDNGZtQOrZaR1BVDxCbKjp1GXcc2ogkKUlLPAUDxr0uK292CpH3nuHafiXrv2ZHWA2jXUBr8SVbgA2CXrcBtH0EVKS2aULbC9CNpE3kvdAIVlZA4zxDhdXv7Xu9LeIhx/nWTxRGnbBQ0H2btlHbWsHsKEq0pu2V89Q7Q0iCRnjkJxzYJ89yXUJ05wxioXph42JoRPL5NRpNt77EaoR0AFxiglFJllFLzlFK7jKVP4WSl1HBjn11KqeG29a2VUpsMG/PxhpknSqm3lVLblVIblVLTlVKljPW1lFLJSqn1xs8nF3L9BQrNDRayPwG4IqWkVuTKsPq0chMRJS3d8gWvCpeo37seOxntL/ZePQNmkPrT4Ef1Dl5FEVKoGeQ+bf9Y6DS3tAwQi6qIUu7F5u9vsmpVtgd9/v506o+eQdrxXbi04sn0UZzV4QwJXsqkMDF/OKjdbcai3+iHMoPi2Ti5P4Duz7qPng6vlUBR8QoIjbC0wQEGjJP0FCzOWvX2sp8nQox1/nStQNyfTVKoWWzv/qz//S9TXOgIajQwX2sdBcw33rtBKVUGGIMYb7YDxtgC2QTgHsTNJQqxPweYB1yhtW4G7ASesZ1yj9a6hfFz3wVef8FB/T7ykB7ZYCkpesJsJ9l6Hq0UOUHUNXDlI/KQThsphfkOD3rvZ/J/PBD9Rj/uuOMeUnUIbdUOWgftctueoIt6HfNlRm9qTUxj4LMfetW8nnx+NLVGz+J4nNUoffcPO2mk9hOmMtmjq/BTZlcGp73IHlflrH1aq12A5vn+jW2jOwN/jZFaT81Owjuy44DBmarRUdQj/rEZTdhnFU3rL5PD5oksx54M39uTjrqTUlUw3DDRfcTmALjwADUIsR/HWPpSvr8WmKe1jtNan0KCT2+lVGUgUmu93LCT+sY8Xmv9p809eDnif3dpIzTCYiev9zOKMhtid/5hORPnNnq8IOJyiTHiXdftf977xKzyK2vSpmEtwuv3IEhp7g3+zW1bSeV9zd9l9gCgZ7AUuOdlWs3Cr4VMJIJUKiirYVkTRNsgqRNt0MKw36FrcF2a5c1XPegE0Y0+ZWQTj1rO/n8krQoKFblez1rPfjNAtYffbaJ5ZksLSP3KbHyu3xufMLW7Qr0DMiCUDvvoqs+bVkeBAzdcaICqqLU2iCMcBSr62MeXNXpV4yfGx3pPjADsKmO1lVLrlFKLlVJ+poDE+lwptVoptfrEiWx0vwsKWhiaQuu/E3VFT5SuCVVaCXt697y8uYbgULFVKlEZ9i+D2U/CCA/C4+ljwgPyByNd7exLY8kD08NeoF/QcnoGSYCalHktf2XK9H6oymRYsMVo3+6SonX3IJlBW5xpTfF3DbKlY0XLShr2cUdpuclIkxHR9Htle6f/ehsRpJ2R+0VB/EHLjBPcRzbRS6WZumyURSb1hKn86cnfApHWWWtrQu74ELS7x3s/B0AOApRS6i+l1GYfP4Ps+xmjoPNTC/P/2c8CGYDZcn8EqKG1bon4632vlPLZ7l0orc+rtpLRS0q8OwfJjiwtpym+t+cGSlaFYVNkBLDheylYe06nf9RWlAh8oWH/HKcrkSqZj8LG0zBIvsNWuBrxacaArO3/DZmW9XqHrk45EmgXtJ0MHcRilwSoSE7zf+UN/9b/b++8w6Mq0z58PxAiEIr03lQUaYKgoChroVuwixVFYBVxXdF19XN3RezYURcF1AXsgiuIIAIqKgoICoiFulQRNEE6JIT3++M5xzkzmRQySTgJz31dc2XmzDlnzjvll/d96rlPw83zddaTsRtm3QcjT4HhR2mqSp020DmmYido8b79e3V59unDus2vxXVkoMn1D97rtLgge2/bPq8eVLBMDGjs1ajAsvCkAdDtgezfHCN3gXLOdXHOtYxzmwRs9pZqeH/j9anOrr35RqKXblFtzEXkOuBc4CpP/HDO7XPOpXr3FwKrgJLVk6eDZ1ab92L8ZVTrPrpEWTE9uvJlQVO3LVz8ktpHPn880rwhyIunw/MdNTRh9mNqs/noH/DWNdnGALlK9fhHxvUAzDvQ7I/7PrclTWCFq8eCA/qxVpJIqeNlBxpwcenPSJIDfHygLQsfvJQ193VmSbPxariv21aDTFOqa7v1a/6rM53UlZHyvW2ujKTJBPHL9x7IUKFqe00kxcaPh9q/LyJQzXtnPQfoTGzPVn2NcgGj/95tMCzgQzqpv4UU5IFEl3jBlubZtSGfDnQTkSqecbwbMN1bGm4XkY6e9+5a/3gR6QHcCZzvnPvDcCEiNUTUFy0iR6GG9dUJjiFcNO+ty6vflmnd8Fgq1NCse3cgupZTYdCsF1w0SsUpuwj2X3/UJcsnD6g4ffmsimc2SP+ZPDBEW191qLyd+4c9HvX8oKTJzD1iMHUkNcuxf+vTnburqQet21W3U2blRzDqDM31q1BbuxkHvXJHn6VpKUGm3alLv29f06UfqD1v6cTIPvVPVg/mZq+ZdXXvf+BPU3R5V6uVevri4ZdIrlzfC0p1KmqPBBKKm52r5zdxypVEBeoRoKuIrAC6eI8RkfYiMgbAOZcG3A987d2GedsABgFjgJXobMi3NT0HVARmxIQTdAaWiMgiYAJwY+BcJYPSZaDjTXp/9qPxZ1HtvP8J34yLVCEoLFpdAhe8QNyE3liqNNYl6tFnxe/l1uRPWnyvSmNdPu74GfE9klUaa4OFY7pSVjKoF0egZGK/SDLvlNvgjct1dlTjeLh+aqSVl8+aOVqbCtTW03WYiv+vP8KkQfB0KxXVWfdFjNYV68Dl49XOtm2dJk77MVd+Abt2fbMXF9/DWame/oN5pVd0Eb7arRLr/HKYIS6fReaLE+3bt3cLFiw41JeRd9J3wdOt1R1+1UR1/wc5cECbbKathktehpYXxz9PQfL9e/DuwLw188yO+idB/5l6f/RZsHGh5tJl7IKz/hmxDf22Er4dp7FCOVH1aGh/vebHJR0R/dz/PoPXL1c7VNur4fznVFT2p8PSCTrT2/JD1nN2f0ij6pdOVBE7tidc+aa+1yPaalrKHcuyt7FNujm6DXyQCrXhpi9LbJcWEVnonGtfoOc0gQopc0bAjH9qpn3/WVn/Yy94WWcRdU6AgbOLZrmw9kt49RIVlCBn3qOxPds26NKzfFW97p+mRBfiq1Bbf9ygHY79SOqksnDbD/F/uEPjCEHvf0Ot5mrwjjfuJW+rUGSmq2f0/GeztkV3TkupvBInVCDYVbn6sdDjEc3HW/M5HNdLz5exW5sj/L5Oo9I3LdYwhWCScMW6uiTftFiN79dPK9HhBIUhUNa4M6ycdAN8OUJnGUsnZm2yecIVGk+zabEmsh51RuFfU6NT4c+z1e6THqg8+c04GDQ3a5PL1JXRArXzF50dJqeonccXqNaXZT+rqFQ/ksMH8Nel0V61IJkZ8PH9kZnXSf2h52ORCPAgzulMKkjHQSpCwRSc35bDq4E4qGVT4bE4DSBiOesfOmN87VJ93O3BEi1OhYXl4oWV5BQNmgQt9REbF1WmHHTw4no+izY0FyrVm8IdyzXtxmfbejUCx+ae+TlpQfwmDEGRiRetDio4QXGC+N5E0CTfl7qpOEkp6PEo9Ho8vjjt36cxUX6pE9AZXI+H4cYvoMNNke2xhePKVtY4q8pea/ljumi4QK/Hoc8bkX2O7am2p8x0XYL6n5VxUJhAhZk2V+syZsfP0TW+fU4aoD+GNZ9nbcJZmCSnwIBZ8KdAZpPLhAdqapCjT0Uv/SQYiT3NO2ZpIBAyXvhcxl54Ps6M46nm0Q0Z9m6HGffCyE6aS1e5AVw3FTreGH/5t3MLjD0PvgvUYW97TaQn4L6dWpgOoO8UtUn54QJ9p8Bd6+DO1XDbUhg8H66eCOc8rsGWfseZskfCuPM1tOC4c3SJaB67fGECFWZKlYKew/X+nGeilx6gCcR+XfFZ9+W7q26+OfNuGLwwetvTLVUsdvyiHYBBA0/9qOt1X8IPk6MNycti2pGvmQMvdIrUH49l9nBN+p39mHri5jyteW8n9tUZUKNT4h+3fr4a54PJymXKR6fzfPGUhhLUP1krSHz1fPTjnPCj+39fq2WNj+miToxY+5eRZ8xIXhz44HZdjtRsAQM/ifZYpe+GEW3ULX7p2Ei53qLEOXWnr/sy/vNlK2vQ52sxdrQKtdUu1aADXPOeJuHOfQHWfpH1HKWTo1tCBWl4qkZk128X//nM/fDFk/DpIzrTq+O9Xzs2aT0oX6B+WwEjT9XXuWGGBmg+c4La2677IGeBytgDD9aOPG7aDS4bH7/aQQmlMIzkNoMqDnQdpj+WLd+rYTxIcnktEQueraqQkohzQgT6TVNDeTz2bssqThCpzrB+HjxUR5OT134ByRWjm3tC9uJ07WSNgcpOnDYsgNFnaoE6lwmdbtXmBDs2qQH+1L/ofhl7YML1+jptr1aD9mePqzg17ZazODkH4wPL2NaXw+WvHlbiVFiYQBUHklM0WFJK6XImto34iddpdPO2dTpTOFTUPB7+labesLzw9ej422u10CYSuZHkGeHj2Xe2roH3BsGYLlo/vHJDnaWdcCV87tW56v2seh6dgylDdAldpYnanbb85BnRJdJYIh6707T5qD97TK4AF76YNS7LyBcmUMWFhh0iXr13B0ZK04Kmd/jF5eY8A6l5+HEXFqVKqzfspq8iddQPluyaXnb2ZorHnwcnXquF3l69WNNWfDZ/r7mBz7bTVKBSpbV6wc1zdVb0znU6Szqxr0a8OwfT79Gk6KRycNlY7bLzwe2al9fuOq+rThyWTVN72/KADe3WxWYQL0BMoIoTnf6quXrpO/SHGUwWbthBvX6Z6TBpcLSn61BQq7kuv/zk57zQuo+6631OGRwxwldpElkSbvlJqxZ0vFlFZNIgeKgejDpTbUjfjNWA0dZ9tLJBl6FqDJ/8F01zqX4sdH9QwxgmD4a5z2sCdp9XNfB18Zu61CxfXUshx7L9Z02IfqOPelh9Wl6sicpGgWECVZwQgQtGqkdp23oNINwZKCDR7X41PK/7Mroa5KEi2DEmL6ycEamhdERl6Py3QH3vvZGk3dQVWrvdBUQ4faeGGYAGaA6ap01Bq3m2rC+e0sDM5ApqH9qdpuEG377qzZzGqddtx2b4yCu92+0BrYHusytVc/dGtIUfJ2uazpn36LUCtO93cO+PkSsmUMWN5BS48i1NYP31J21i6WfQl68Kvb3eah8/kH29pqJkc0zRunMCNjKJcb/vToX3vCDJfdvgpa4afAlq1H4yUHZ34g0wL5uS9Bl7o4NEvxmnYRgInPeMtnV/4TQt8VuhlnromvXS5d6kQXodR52hvepAvXvT/q4evS+fVbFs3htunqfn3LdNS7M06nRw742RKxZmUFzZuQXGX6gCUKk+XPF6pKicH5ZQ9WgY8LHGSx0Kfl4E43prHBR4OXffw3/OUXHt/rDad1Z9HGkamldqtVSRaHCyppQAzLpfDe8H9uuS7fhz1Z7kV7Cs2Vy9dVu9rr/NzoXzRkTSbOaPhql36Kzp6olaYuaHSdHpOkefrSVc6rbVKp3PtFYvZd/3829zKyFYsnA+KZECBRq5/Prl6qZPKgfnj9C8tvTdOvPY/J26yK94s+iDBdfP19CCvds0wTZ9p/7QTxuiQvpOX10a3TwPKtWJJEfHUv8krYEOMORHnfnsToU7VsRvmZ66SitiLp0Y6b8Xj97Pq0AdyFQBXf6h9umLR1I5aH2pRu4HOwlPvRPmvwiNT4frcmi6ephgApVPSqxAgeaVTRkCi7zI7JYXq6F53w5N6t2Tpl6sLkOL7poW/kdrmWemqwhc8oomNb/URSsF3LJAn1/+IRzTVasDjD4rYnAuX13TZDbHRM4HE4fPeVL3SU7RGdP+fSo0v6/TEIPFCZZETioHx5ytxQGP6xltiwKdHY4+ExBNoA62aj9MMYHKJyVaoEBtJ9+MhQ//T0uh+N6nyg3U2+cyNWWmsBNWd6dFXPagSbLdH9IifAAT+unMpmk39cKNPCW6NHByRfVQlkrSukmZ6br/wS7/Yml7tebHZezRpeWOX1S4D2TqLVg+puswdULUOUGDYOORsUc9hr/+qJ7EHgfhCCjBmEDlkxIvUD6pq7TO0to5+rhWS51l+DliF4zUmtwFzYFM+G6Cer92/aqzpPOezvpa23/Wcrt7f9cZ0JGN4LVAsb3bl8OnD+kMrF57uOEjXZqOv0jTYI6orAZpgFaXaXOCfTtVAJOOgJUzo3vRXfEWHJdNayjQFJh3+mrdqkr1YOCn8ZeNsfg2vmpNdfYUr3vLYYjVgzJyptrR6pFaOhFm/EsN6EEv2ns3admWgmpztD9dm4h+9rjWUAf1ZJ33jJZliaVSXTj3SZ1JfTBEDdhBpt2pM7/lH2kL9i+e1FCDWi1UoHxx6vkYdBgYOe7nRVoHyhenhqdo7p9foSAeBzK15MpPUzRX8Io38yZOC15RcSpVBi4eY+JUyIS19flQEdkYaHHeK3DM3d7+y0SkeyLXXyIR0eJ2t3yjtqhKMT1Pp94BjzaBX5fnr/pBxl5YPRs+uAOeOBbeHaDiVLmBGp77TokvTj4tL4509PXbM531T41P+uE9GNNVBQk073DVx9F5cEdUUoP1/nRtYDr+Im3ltHKmCs25T2u5lZzEaX+6irUfF3X1u9HG7+xY/pG+f6BCW7dN7scYCZHQEk9EhgNpzrlHROQuoIpz7u8x+1QFFgDt0cI/C4F2zrmtIjIf+AswD5gKjHDOTRORocBO59zjMedqDryBtlCvC8wEjnXO5Rg2fdgs8eKRmaE/5IWv6I84SOlkbWRQ4zhNRk6pocXYSidr3l/GbvWY7dysqTVbftQKn8G65DWba7T4CVdAUpx2TrGsnKlt1f3QA9BQiLJHwvu3am2rWE67DeaPUftUnTa6HFsxqOAPAAAL/klEQVQ7J3KOMilam7zTrbnPgvZu10Jyqz/R6PKrJkDjPMQvLf8I3rpK7WKdblVblRFF6GxQIrIMOMM5t8nri/epc+64mH2u8Pb5s/f4ReBT7/aJc65Z7H45CNTdAM65h73H04GhzrmvcrrOw1qgguxKhQ//Dt+9k9h5arWCo89QO1DtVnnLPdudBrOGqX0JB41O01y6jQs1Pur853R2tWwqfPWcBlHmRo1m0OpSjeAuXzX3/X/5Dt7uq4nIKTXgyre1WWpuLHhZZ4wuUw3/PYdbvl0cwmiDKszW54NF5Fp09nW7c26r9/zcHI75AxEZCAwEaNiwYbxdDj9Sqqnd5Mx7dGnmxxeBBhkmV9QZ04H9GkOUVFZ/+CnV1SBc4zgNUDyYfLP0XRrJPftRjdsqlaSVOE+/XX/wHwzR59/tr7Or7g9qgOW2DZqM6y+pAFJqalv1GsdrUTq/oWZuZGbA3H/Dxw/q7K9mC239VLVJzsft2wEf3hUprtfprxquYeJUZOQqUCIyE6gd56l7gg+cc05ECsolOBLtpee8v08AB5Xo5JwbBYwCnUEV0HWVDKo2gX7TNW3j04c1dWPtV1rH6My7CyamZ+saWPS6Rmfv8VoXNvmTdtOt4U+yS2kkd502Gp6w5E2dQXX+m+bTnTxAQwQm9ldj9u5UtTOd0CdvgafOaW+6mUO1lhZoFYOej8avlx48bvmHmt7y+1r1Sp77FLS9KoE3xMgPoVzixRzfGJjinGtpS7xCYNsGnVksfoM/aoPXaQPNz9cgyprNo7v1ZkdmhnrT1nyuM58N8yPP1WsPpw/RiPLsZh+/rdTlp28nK1dFS6q0uVq9kzOHapcb0BilnsOhYcf459q7XZN554+GTYt0W5XG0OuJrD0GgzinRvk5T0fSW2q3gotGa60rI0fCaIN6DEgNGMmrOufujNmnKmoY9xf736BG8rQ4RvJnnXNTRaSOv3QUkduADs65PiLSAnidiJF8FtDUjOQFQOoqmPei1lAKtpQqk6L5cpUbqGesTHmNO8rYq0GWO39RcUlbFenOC7pfs3O0nlKjTnlfFq2Yod47vzIB6FLu6LO1ken3/41sb3iKzrRqt9ZifZuWqPF8zRy1b4EuC0+9RWdj2c2atm1UQfv21UhYRtnKuhQ9eUAk0NTIkTAKVDXgbaAhsBa4zBOe9mhb8v7efv0AP9HpQefcK9729sB/gHJo2/NbvKXieKAN+i99DfDngGDdgy739gN/dc7FVNzPignUQZCxR2cRP76vhmq/lXdeqNZUQwKadIZjuycWI7RhgRqnl02NdEs5GBp10iVrq0ujI8Iz92upms1LtXHnuq/UUO9ToZYawvNqeDf+IHQCVVwwgUqAnVs0xGDbei15krFXDc1J5bRKQvlqugSr1hTKVsr9fAdL5n5dLq6fp164X5fBrt905pYTRzbS60muqAb/jF269Nu+MTraHNQZcEwXaHGhFsWzcr35IoxePKOkU6Fm3iKsC4vSSdrRuNGp8Z93TmdDqz7R5d2WHzVh+Pe12Z+zYl2ofox2k2nYERp0zNoV2QgFJlBG8UZEDdm1W0GnQIeW7T9rmMC+HerxK1Neo8Yr18vZg2eEChMoo+RRplyk1K9RrLGSv4ZhhBYTKMMwQosJlGEYocUEyjCM0GICZRhGaDGBMgwjtJhAGYYRWkygDMMILSZQhmGEFhMowzBCiwmUYRihxQTKMIzQYgJlGEZoMYEyDCO0mEAZhhFawtr6/K1A2/M1IrLI295YRPYEnnshkes3DCPcJDqDuguY5ZxrinZYuSt2B6+ry71AB7Qby70BIRsJDACaerceAM65y51zbZxzbYCJwLuBU67yn3PO3Zjg9RuGEWISFajewFjv/ljggjj7dAdmOOfSvO7AM4AeXh+9Ss65uU47N4yLPd6bUV0GvJHgdRqGUQxJVKAKs/U5wOnAZufcisC2JiLyrYjMFpHTE7p6wzBCTVhbn/tcQfTsaRPQ0DmXKiLtgPdEpIVzbnvsgSIyEBgI0LBhwwK+LMMwioJcBco5l22vaBHZ7HcB9pZsW+LsthE4I/C4Ptr2fKN3P7h9Y+DcScBFQLvAtewD9nn3F4rIKuBYIEvTO+fcKGAUaF+8HAdpGEYoSXSJNxnwvXJ9gUlx9pkOdBORKp5xvBsw3VsabheRjp6t6dqY47sAPznn/lgGikgNESnt3T8KNayvTnAMhmGElEQF6hGgq4isQAXlEdCW5iIyBsA5lwbcD3zt3YZ52wAGAWOAlcAqtP25Tx+yGsc7A0u8sIMJaHv1NAzDKJFY63PDMAqEwmh9bpHkhmGEFhMowzBCiwmUYRihxQTKMIzQYgJlGEZoMYEyDCO0mEAZhhFaTKAMwwgtJlCGYYQWEyjDMEKLCZRhGKHFBMowjNBiAmUYRmgxgTIMI7SYQBmGEVpMoAzDCC0mUIZhhBYTKMMwQosJlGEYoSUhgRKRqiIyQ0RWeH+rZLNfX2+fFSLSN7D9QRFZLyI7Y/Y/QkTeEpGVIjJPRBoHnrvb275MRLoncv2GYYSbRGdQdwGznHNNgVne4yhEpCpwL9ABOBm4NyBk73vbYrkB2OqcOwZ4CnjUO1dztNtLC6AH8G+/DZVhGCWPRAWqNzDWuz8WuCDOPt2BGc65NOfcVmAGKi445+YGWqdnd94JwNle77zewJvOuX3Ouf+h7ariCZxhGCWAXDsL50KtgMD8AtSKs089YH3g8QZvW078cYxzbr+IbAOqedvn5uVcwdbnwD4RWZrLaxZXqgO/HeqLKARsXMWP4wr6hLkKlIjMBGrHeeqe4APnnBOR0DTZC7Y+F5EFBd2vKyyU1LHZuIofIlLgzSdzFSjnXJfsnhORzSJSxzm3SUTqAFvi7LYROCPwuD7waS4vuxFoAGwQkSSgMpAa2B4818bcxmAYRvEkURvUZMD3yvUFJsXZZzrQTUSqeMbxbt62vJ73EuBjpy2QJwN9PC9fE6ApMD/BMRiGEVISFahHgK4isgLo4j1GRNqLyBgA51wacD/wtXcb5m1DRIaLyAagvIhsEJGh3nlfAqqJyEpgCJ530Dn3PfA28APwIXCzcy4zD9c5KsFxhpmSOjYbV/GjwMcmOjExDMMIHxZJbhhGaDGBMgwjtBRrgToUqTZFQQGMq52IfOdd/wgvyBURGSoiG0VkkXfrVYRj6uGlJ60UkXgZBwed3pTbOYuCQhrXGu/zW1QYrvu8kN9xiUg1EflERHaKyHMxx8T9XuaIc67Y3oDhwF3e/buAR+PsUxVY7f2t4t2v4j3XEagD7Iw5ZhDwgne/D/BWMRvXfG9sAkwDenrbhwJ3HILPqTSwCjgKSAYWA83z8p4Dzb39jwCaeOcpnZdzFsdxec+tAaoX9edUQONKAU4DbgSeizkm7vcyp1uxnkFR9Kk2RUW+x+XFo1XyxuaAcdkcX5ScDKx0zq12zqUDb6JjDHKw6U15OWdhUxjjCgP5Hpdzbpdz7gtgb3Dn/H4vi7tAFUmqDeCn2hQViYyrnnc/drvPYBFZIiIvZ7d0LATy8hlk957nNM6D/VwLmsIYF4ADPhKRhaIpW0VNIuPK6Zw5fS/jkmguXqFTXFNtcuMQjWskGpPmvL9PAP0K6NxGwXGac26jiNQEZojIT865zw71RR0KQi9QLlypNgVGIY5ro3c/uH2j95qbA68xGpiS3+s/SPKSopSf9KZDnfZUKONyzvl/t4jIf9ElV1EKVCLjyumccb+XOVHcl3hFnWpTVOR7XN7ScLuIdPRsHdf6x3ti53MhUFQVHr4GmopIExFJRo2qk2P2Odj0prycs7Ap8HGJSIqIVAQQkRT0cy3qShyJjCsuOX0vc+RQeQoKyNtQDS2UtwKYCVT1trcHxgT264caIVcC1we2D0fXwge8v0O97WWBd7z95wNHFbNxtUe/1KuA54hkDIwHvgOWeF+wOkU4pl7Acu+a7vG2DQPOz+09R5e9q4BlBDw/8c55CL6DBTou1HO22Lt9X0zHtQZIA3Z6v6vmOX0vc7pZqothGKGluC/xDMMowZhAGYYRWkygDMMILSZQhmGEFhMowzBCiwmUYRihxQTKMIzQ8v933/zxjyHzsgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(1,1)\n",
"scale = 0.01\n",
"ax.set_ylim([-scale,scale])\n",
"ax.set_xlim([-scale,scale])\n",
"ax.set_aspect(\"equal\")\n",
"xearth = xyz[:,1,0]-xyz[:,0,0]\n",
"yearth = xyz[:,1,1]-xyz[:,0,1]\n",
"xearthrot = c*xearth+s*yearth\n",
"yearthrot = -s*xearth+c*yearth\n",
"for j in range(2,4):\n",
" x = xyz[:,j,0]-xyz[:,0,0]\n",
" y = xyz[:,j,1]-xyz[:,0,1]\n",
" xrot = c*x+s*y\n",
" yrot = -s*x+c*y\n",
" ax.plot(xrot-xearthrot,yrot-yearthrot,label=human_labels[j],lw=2)\n",
"ax.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Estimating the apparent magnitude"
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {},
"outputs": [],
"source": [
"H = 31.72 # absolute magnitude, ignoring correction for phase angle"
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {},
"outputs": [],
"source": [
"x = xyz[:,3,0]-xyz[:,0,0]\n",
"y = xyz[:,3,1]-xyz[:,0,1]\n",
"xrot = c*x+s*y\n",
"yrot = -s*x+c*y\n",
"x2020 = xrot-xearthrot\n",
"y2020 = yrot-yearthrot\n",
"dis = np.sqrt(x2020**2+y2020**2)\n",
"m = H + 5.*np.log10(dis)"
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAYgAAAEGCAYAAAB/+QKOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAgAElEQVR4nOydd3wc1bX4v0e76tWyJbnIvRtwwcZUA3ZogQQCoYaQEJJAEvgleeElL6Tykpf2SCUvjQRCIIRAEgiETsBgwMa2bNx7tyRbzeq93N8fO7NeSbvau5JWq3K+n89+pJ29M3NmZveee8o9V4wxKIqiKEpX4mItgKIoijI4UQWhKIqiBEUVhKIoihIUVRCKoihKUFRBKIqiKEHxxlqA/mTMmDFmypQpsRZDURRlyLBhw4ZyY0xOsM+GlYKYMmUKBQUFsRZDURRlyCAih0N9pi4mRVEUJShRUxAikiQi60Rks4hsF5H/drZPFZG1IrJPRJ4QkYQQ+9/jtNktIpdGS05FURQlONG0IJqBFcaYBcBC4DIROQv4EfAzY8wMoBL4ZNcdRWQecCNwCnAZ8GsR8URRVkVRFKULUVMQxked8zbeeRlgBfB3Z/ufgA8F2f0q4K/GmGZjzEFgH7A0WrIqiqIo3YlqDEJEPCKyCSgFXgX2A1XGmDanSSEwIciuE4CjAe9DtVMURVGiRFQVhDGm3RizEMjHZwHM6e9ziMjtIlIgIgVlZWX9fXhFUZQRy4BkMRljqoCVwNlAloi46bX5QFGQXYqAiQHvQ7XDGPOAMWaJMWZJTk7QVF5FURSlF0QziylHRLKc/5OBi4Gd+BTFtU6zjwPPBNn9WeBGEUkUkanATGBdtGS9/7W9FBw6Ea3DK4qiDEmiaUGMA1aKyBZgPfCqMeY54L+AL4nIPmA08CCAiFwpIt8BMMZsB54EdgAvAXcaY9qjIWR1YyuPrT3Mtb9dw6f+tJ79ZXXhd1IURRkByHBaMGjJkiWmNzOpG1va+ePqg/zmjf00t3Vw98Wz+NSyaXjiJApSKoqiDB5EZIMxZkmwz3QmNZCc4OFzF87gtbsv4MJZOfzgxV185PfvUl7XHGvRFEVRYoYqiABy05P43S2L+fF1C9h0tIoP/vJtthZWx1osRVGUmKAKogsiwrWL8/nHZ88hToSbfv8u7x6oiLVYiqIoA44qiBCcOiGTf3z2HMZmJvHxh9bxxu7SWIukKIoyoKiC6IGxmUk8ecfZzMhN445HN7BeU2EVRRlBqIIIQ3ZqAo/ctpQJWcnc9vB6dh6ribVIiqIoA4IqCAtGpyXy6KfOJDXBy6f+VMCJ+pZYi6QoihJ1VEFYMiErmQc+tpiyumbu+stG2to7Yi2SoihKVFEFEQHz87P43odOZfX+Cu57ZXesxVEURYkqqiAi5LolE/nImZN4YNUBVu8rj7U4iqKMcLYXV/PE+iNRObYqiF7wzSvmMXVMKl96cjPVDa2xFkdRlBHIgbI6bn+kgCvuf5v7Xt5NU2v/l6tTBdELkhM8/PyGhZTXNfOtZ7fFWhxFUUYQ9c1t/PDFXVz681Ws3l/BFy+ayWt3X0hSfP+vyuwN30QJxvz8LO5cPoNfvLaXD5+ez/mzdC0KRVGiy7qDJ/jSk5sorGzk2sX5fOWy2eSmJ0XtfGpB9IHPXjidqWNS+eYz26Ji3imKogC0dxjue3kXNzywBk+c8PfPnM2Pr1sQVeUAqiD6RFK8h+996FQOVzTw65X7Yi2OoijDkOrGVm57eD2/Wrmf6xbn8/znl7FkSvaAnFsVRB85Z8YYrlo4nt+uOkBRVWOsxVEUZRhxuKKeq3/9Du/sK+f7V5/G/167gLTEgYsMqILoB75y2RwAfvKyzo1QFKV/2FtSy3W/XcOJ+hb+/Kkz+ciZkwZcBlUQ/cCErGRuO3cqT28qYluRrh+hKErf2FZUzQ0PvIsBnrj9bM6aNjomcqiC6Cc+t3w6Wcnx/PDFXbEWRVGUIczeklo++uBakrxxPHnH2cwemx4zWaKmIERkooisFJEdIrJdRL7gbH9CRDY5r0MisinE/odEZKvTLvKFpgeYjKR47lw+g7f3lVOgZcEVRekFhZUN3PLgOuI9cTx++1lMHZMaU3miaUG0AXcbY+YBZwF3isg8Y8wNxpiFxpiFwD+Ap3o4xnKnbdAFtQcbN585mdGpCdz/umY0KYoSGZX1Ldzy4DrqW9p45LalTB4dW+UAUVQQxphjxpiNzv+1wE5ggvu5iAhwPfB4tGQYaJITPHz6/Gms2lPGpqNVsRZHUZQhQlt7B3f+ZSNFlY08dOsZzB2XEWuRgAGKQYjIFGARsDZg8zKgxBizN8RuBnhFRDaIyO09HPt2ESkQkYKysrL+ErnXfPSsyWSlxPPL10JdlqIoSme+98JOVu+v4PvXnMYZAzTHwYaoKwgRScPnSvqiMSZwObab6Nl6OM8YczrwfnzuqfODNTLGPGCMWWKMWZKTE/tyF2mJXm47dyqv7SplT0ltrMVRFGWQ8/cNhfzxnUN84twpXLs4P9bidCKqCkJE4vEph8eMMU8FbPcC1wBPhNrXGFPk/C0FngaWRlPW/uSjZ00m0RvHH985GGtRFEUZxOw6XsPXnt7KOdNH8/XL58ZanG5EM4tJgAeBncaYn3b5+CJglzGmMMS+qSKS7v4PXAIMmbKp2akJXHN6Pk9tLNLlSRVFCUpjSzuff/w9MpLiuf+mRXg9g2/WQTQlOhe4BVgRkNZ6ufPZjXRxL4nIeBF5wXmbB7wtIpuBdcDzxpiXoihrv3PbuVNobuvgL2sPx1oURVEGIf/z/A72lNTx0+sXMCYtMdbiBCVqRT2MMW8DEuKzW4NsKwYud/4/ACyIlmwDwcy8dM6flcMjaw5z+/nTSfAOvtGBoiix4ZXtx3ls7RHuOH/aoF4qQHutKHLrOZMprW3m9V0lsRZFUZRBQlVDC197ehtzx2Vw9yWzYy1Oj6iCiCIXzMplXGYSj687GmtRFEUZJHznuR1UNbRw37XzB71nYXBLN8TxxAnXLZnIqr1lFFY2xFocRVFizOu7SnhqYxGfvXA6p07IjLU4YVEFEWWuX+LLa/5bQdCELUVRRgg1Ta187altzMpL464VM2ItjhWqIKJM/qgUls3M4W8FR2nvMLEWR1GUGPGLf++lpLaJ/712AYleT6zFsUIVxABw4xkTKa5uYtXe2JcCURRl4NlTUsvDqw9x4xmTWDgxK9biWKMKYgC4aG4emcnxPPNeUaxFURRlgDHG8O1ntpOe5OXLlw7urKWuqIIYABK8cVx+2lhe2VFCQ0tbrMVRFGUAeW7LMdYcqOA/L5lNdmpCrMWJCFUQA8RVCyfQ0NLOqzt0ToSijBTqm9v43vM7OWV8BjctHfg1pfuKKogBYumUbMZlJvHspuJYi6IoygDxmzf2c7ymie9cdQqeuKCFJQY1qiAGiLg44coF43lzT5kW8FOUEcDx6ib+8PYBrlwwnsWTB88aD5GgCmIAuXLheNo6DC9sPRZrURRFiTK/eG0P7R1myAWmA1EFMYDMG5fBtDGpvLTteKxFURQliuwrreOJ9Uf56FmTmZidEmtxeo0qiAFERLj01LGsOVBBVYO6mRRluHLfy7tISfBy1/KhMWM6FKogBpjLThlLe4fh3ztLYy2KoihRYMPhE7y8vYQ7zp/G6EG6zoMtqiAGmPn5mYzPTOKlbRqHUJThhjGGH764i5z0RD65bGqsxekzqiAGGNfNtGpvOXXNOmlOUYYTK3eXsv5QJV+8aCYpCVFbj23AUAURAy47ZSwtbR28sVvdTIoyXDDG8PN/72VidjLXL5kYa3H6BVUQMWDJlGxGpyZoNpOiDCPe2FPGlsJq7lo+g3jP8Ohao3YVIjJRRFaKyA4R2S4iX3C23ysiRSKyyXldHmL/y0Rkt4jsE5GvRkvOWOCJEy45JY+Vu0ppbmuPtTiKovQRYwy/+PdeJmQlc/Wi/FiL02+EVRAiMktEXhORbc77+SLyDYtjtwF3G2PmAWcBd4rIPOeznxljFjqvF4Kc0wP8Cng/MA+4KWDfYcFFc/Oob2ln7YETsRZFUZQ+8tbecjYdreJzy6cP+mVEI8HmSn4P3AO0AhhjtgA3htvJGHPMGLPR+b8W2AlMsJRrKbDPGHPAGNMC/BW4ynLfIcE508eQ6I3j9V0ah1CUoYwxhl+8tpfxmUlcu3j4WA9gpyBSjDHrumyLKP1GRKYAi4C1zqa7RGSLiDwkIqOC7DIBOBrwvpAQykVEbheRAhEpKCsbOgvyJCd4OHv6aFbuLsUYXWlOUYYqq/dXsOFwJZ+9cPqQWSnOFhsFUS4i0wEDICLXAtZJ/CKSBvwD+KIxpgb4DTAdWOgc5yeRCh2IMeYBY8wSY8ySnJycvhxqwFkxJ5fDFQ0cKK+PtSiKovQCN/YwNiOJ688YHplLgdgoiDuB3wFzRKQI+CLwWZuDi0g8PuXwmDHmKQBjTIkxpt0Y04HPfbU0yK5FQODdzne2DSuWz84FYKW6mRRlSPLugROsO3SCz1wwbdhZD2ChIJw4wEVADjDHGHOeMeZQuP1ERIAHgZ3GmJ8GbB8X0OxqYFuQ3dcDM0Vkqogk4It5PBvunEONidkpzMpLY6XOh1CUIcnvVu1nTFoCNw7BxYBsCDnVT0S+FGI7AIGdfgjOBW4BtorIJmfb1/BlJC3E57I6BNzhHHc88AdjzOXGmDYRuQt4GfAADxljttte1FBi+ZxcHnr7IHXNbaQlDv2Zl4oyUthTUssbu8v40sWzSIofftYD9KAggHTn72zgDE6O4D8IdA1ad8MY8zYQbAmlbmmtTvti4PKA9y+EajucWDE7l9+9eYC395Zx2anjwu+gKMqg4A9vHSApPo6PnjU51qJEjZAKwhjz3wAisgo43UlVRUTuBZ4fEOlGAIsnjyIjycvru0pVQSjKEKG0tol/vlfM9Wfkk52aEGtxooZNkDoPCFy8oMXZpvQDXk8c58/KYeXuMjo6NN1VUYYCj6w+TGtHB588b1qsRYkqNgriEWCdUyLjXnxzGf4UValGGMtn51JW28z24ppYi6IoShgaWtr489rDXDIvj6ljUmMtTlSxyWL6HvAJoNJ5fcIY8/1oCzaSuHB2DiLorGpFGQL8fUMhVQ2tfHrZ8LYewK4W0ySgHHjaeVU425R+YnRaIgvys3hd010VZVDT3mF48O2DLJqUxeLJwYpADC9sXEzPA885r9eAA8CL0RRqJLJiTi5bCqsor2uOtSiKooTg3ztLOFzRwKeXTfOn/A9nbFxMpxlj5juvmfhmPq+JvmgjixVzcjEG3tw9dOpJKcpI49E1hxmfmcQl80ZGnk7EdWmdCq1nRkGWEc28cRnkpCeqm0lRBikHyup4e185HzlzEt5hsiBQOMJO3e0yozoOOB0ojppEI5S4OGH57Bxe3Hac1vaOYbMilaIMFx5be4R4jwzLonyhsOmF0gNeifhiEsNqbYbBwoo5udQ2tbHhcGWsRVEUJYDGlnb+VnCUS08ZS256UqzFGTBsiv/sMMb8LXCDiFwH/C1Ee6WXnDczh3iPsHJXKWdNGx1rcRRFcfjXlmJqmtq4ZRiX1QiGjQVxj+U2pY+kJXpZOjVb50MoyiDjz+8eZlZeGkunZsdalAGlp2qu78dXPG+CiNwf8FEGEa4op9izfHYu//P8To6eaGBidkqsxVGUEc+2omq2FFbz31eeMiJSWwPpyYIoBgqAJmBDwOtZ4NLoizYyWT7HWURIs5kUZVDwxPqjJHrj+NDCoKseD2t6qua6GdgsIo8ZY9RiGCCmjUll8ugUVu4q5WNnT4m1OIoyomlsaeefm4q4/LRxZKbEx1qcAacnF9OTxpjrgfdEpFuZUWPM/KhKNkIREZbPzuXxdUdobGknOWF4LkSiKEOBF7cdo7apjRtGUGprID1lMX3B+fuBgRBEOcmKObk8vPoQq/eX8765I2PGpqIMRv66/ihTRqdw5ggLTruEjEEYY445fw8Hew2ciCOPM6dlk57k5V+bdT6iosSKA2V1rDt4ghvOmDTigtMuNtVcrxGRvSJSLSI1IlIrIrpwQRRJ9Hq4csF4Xtx2nJqm1liLoygjkicKjuKJEz68eOQFp11s5kH8L3ClMSbTGJNhjEk3xmSE20lEJorIShHZISLbReQLzvb7RGSXiGwRkadFJCvE/odEZKuIbBKRgsgua+hz3ZKJNLd18NzmY7EWRVFGHG3tHTy9sYjls3NG1MzprtgoiBJjzM5eHLsNuNsYMw84C7hTROYBrwKnOkHuPfQ86W65MWahMWZJL84/pFmQn8msvDQeffcwxuhSpIoykLy1r5zS2mauXTwyg9MuNgqiQESeEJGbHHfTNSJyTbidjDHHnMqvGGNqgZ3ABGPMKwFps+8C+b2WfhgjInx62TR2HqvRORGKMsD8Y0Mho1LiWeHMSxqp2CiIDKABuAT4oPOKKLNJRKYAi/CtZx3IbYRefMgAr4jIBhG5vYdj3y4iBSJSUFY2vNZS+NCiCeSPSuZHL+6mua091uIoyoiguqGVV3aUcNXCCSR4R3ZV5bDF+owxn+jLCUQkDfgH8EVjTE3A9q/jc0M9FmLX84wxRSKSC7wqIruMMauCyPcA8ADAkiVLhpUvJt4Tx3euOoXbHi7gP/+2ha9fPpeMZC+tbb7LTIyPIyle50koSn/y3NZiWto6uHaxOjds1oO4P8jmaqDAGPNMmH3j8SmHx4wxTwVsvxWfFfI+E8LBbowpcv6WisjT+Fay66Yghjsr5uTx5Utnc9/Lu7ulvcYJvP+0cfzPVacyKjUhRhIqyvDiyfVHmZ2Xzinjw+biDHtsyn0nAXM4Wd77w8BBYIGILDfGfDHYTuJLHH4Q2GmM+WnA9suArwAXGGMaQuybCsQZY2qd/y8BvmN5TcOOO5fP4KK5eazZX05T28nFhIqrGnl0zWEKTzTwxB1nqzWhKH3kvSOVbC6s5rtXjbzCfMGwURDzgXONMe0AIvIb4C3gPGBrD/udC9wCbBWRTc62rwH341t46FXnAbxrjPmMiIwH/mCMuRzIA552PvcCfzHGvBTpxQ0nZo9NZ/bY9G7bz5yaze2PbuDXK/fxpUtmx0AyRRk+/Gn1IdISvVx9urqXwE5BjALS8LmVAFKBbGNMu4g0h9rJGPM2EEwFvxCifTG+8uIYYw4ACyxkG/FccspYPrRwPL998wA3nzWZvIyRm7OtKH2hrLaZ57ce4+YzJ5OWaNM1Dn9sJ8ptEpE/isjDwHvAfY7r59/RFE6x4z8unkVbRwcPvXMw1qIoypDl8XVHaG03fOzskbVqXE+EVRDGmAeBc4B/Ak/jyy76gzGm3hjz5WgLqIRn8uhULpk3lr8XFNLW3hFrcRRlyNHa3sFjaw9z/qwcpuWkxVqcQYNtkm8TcAyoBGaIyPnRE0npDR9aNJ6K+hbWHjwRa1EUZcjx0rbjlNQ0c+s5aj0EYlOs71P40ktfBv7b+XtvdMVSIuXC2bkkx3t4ZfvxWIuiKEOOR9YcYlJ2ChfMGtkzp7tiY0F8ATgDOGyMWY5vRnRVVKVSIiYp3sPiyaPUglCUCNleXM36Q5V87OzJeOI0tTUQGwXRZIxpAhCRRGPMLkDzKQchZ07NZtfxWirrW2ItiqIMGf60+hDJ8R6uG+GF+YJhoyAKnZLc/8Q3d+EZQBcMGoQsnjIKgK1F1WFa9o7W9g7e2VdOaU1TVI6vKANNZX0Lz2wq5kOLJozINafDYVOL6Wrn33tFZCWQCYzoSWuDlXnjfKUBdh6r4fxZOf167Oa2dj76h7WsP1RJaoKHP35iKUtH6DKMyvDh6feKaG7r4JazNDgdDKssJhEZJSLzgVqgEDg1qlIpvSIrJYFxmUnsOl7b78d+dM1h1h+q5Kvvn0NeRhKfe2wjZbUh50kqyqDHGMOTBUeZn5/JPK27FBSbLKbvAluAXwI/cV4/jrJcSi+ZMzadncf6d0VYYwwPrz7EmVOz+cwF0/n1R0+npqmV7zy3o1/PoygDyf6yOnYdr+XDWlYjJDYWxPXAdGPMBcaY5c5rRbQFU3rHtJw0Dlc09OsqdLuO11JY2cg1p/vW5p0zNoPPXTidf20u5u295f12HkUZSN7Y7Vs/5qJ5eTGWZPBioyC2AUHXjVYGH5OyU2hsbae8rv8ymVwlcOHskznin7lgOpNHp/CtZ7bpYkbKkOSN3WXMzE1jQlZyrEUZtNgoiB8A74nIyyLyrPuKtmBK75iY7fuyHzkRtJJ6r9heXM3YjKROhQCT4j1856pTOVBez0NvH+q3cymdqahrZltRNUf62SqMJtUNrTxZcJQ/v3uYl7YdZ+ORykFXAqatvYOCwyc4d8aYWIsyqLEpWfgn4Ef4SnsPrqesdGNSdgoAR080sHjyqH455s5jtcwd173U+AWzcrh4Xh6/fH0v15w+QSvJ9iPNbe3c/eRmnttyzL/ttAmZfOOKuZw5bXQMJeuZ49VNfPg3qymqauy0/Zzpo3nktqV4PdFdwnNfaR1PFhxl3rgMrlo4PuSaDntK6mhq7WDRJHWO9ISNgmgwxgRbVU4ZhOSP8imI/rIg2jsM+8vqWDE3eAmCb14xj4t+9iY/eGEnP79xUb+cMxrUNbfxxb++x67jtdx27lQ+ce6UQb0gzK9X7ue5Lce44/xpLJo0imPVjfzhrYPc8MC73HzmJL5+xVxSEgauJPXbe8vZUlTFNYvyGZsZeiDw7We3caK+hcc/fRbTclIpq23mzT1l3Pfybv66/igfjWI66baiam564F1qm9sAOFBWF3KNlC2FvmIQp03IjJo8wwGbb9hbIvID4FnAn9dojNkYNamUXpMU72F0agLH+2kyW1ltM20dhvxRwf20k0ancPuyafzfyn3kpCfyxYtmkToIa+n/4IWdvL6rlPn5WXznuR2s3l/Oj69bQFbK4Fuqtam1nT+tOcSlp+Rxz+Vz/dtvOGMiP31lDw++cxBPnPCdqwYm2/ylbcf5zJ83APDHdw7x1GfPYaJjqQay81gNL28v4e6LZ3H2dJ+Vk5eRxCnjM3h5+3EeXXM4agqivcNw95ObSU308tJ/nM/PX93DL1fu44LZOSye3H2+ztaiatKTvEwZnRoVeYYLNvbeIuAs4PtomuuQICc9sdsche3F1azaUxbxsY5V+1wF43oYNf6/983gI2dO4vdvHWTFT95g9T67zCbXHdDQ0haxXJFQUdfM3woKuXHpJJ7+3Dnc+8F5vLmnjCvuf5uD5fVRPXdveHNPGVUNrdx8ZufONCXByzc+MI9rT8/nbwWFNLZEPzmgtb2De5/dzqkTMnj2rnNpbGnnnqeCLyT5ZMFREjxx3ZSAiHDVwgnsLqmlsLL/YmOBvLmnlN0ltXztirlMyErm3itPISctkf99aXfQ9gfK6pmRm0ac1l7qEZv1IJYHeWma6yCmq4KorG/h6l+t5mMPrWPjkcqIjnW82meJjM0InemR6PXw/atP4x+fPYe0RC+f+8tGToSpB3WkooGrf/UOX/n7Fu76y3sRyRQpK3eX0dLewUeWTkJEuPXcqfztM+fQ2OqbHW5Tu8oYw5t7yvo8x+S9I5U8vu4Ie0pCT2Zcs7+C5HiPfxTelQ8uGE9jazvrD0W/MOOL245zvKaJuy+ezfz8LL540Uze3lfOe12+R8YYXt52nAtn5zAqtbtVdo5zLevCFJNctaeMN3aXRizns5uKyU5N4P2njgUgNdHLHRdMZ+3BE91kBThcUa/WgwXRjRgpMSEnrbOCWLXX10EC/GXtkYiOdcxRED1ZEC6LJ4/i1zcvpqqhlUfWHOqx7e9W7ae5vYOblk7k9V2lfp9wNFi5u5Tc9EROCZgtu3BiFg/degaltU1845ltYY/xyJrDfPyhdVz1q3c41Eur4+F3DnL1r1dzz1Nbueznq3hmU1HQdu8eqGDJlFHEhwjoLnQCq5uPRr+o8j/fK2JCVjIXOKVbblo6iaT4OP75XmfZD1c0UFzdxLIQJV5m5qYR7xH2lNSFPNfu47V87KF13PrH9RFbdusPVXLWtOxO9+z6JfkkervL2tTaTnF1kyoIC6KmIERkooisFJEdIrJdRL7gbM8WkVdFZK/zN2iqjYh83GmzV0Q+Hi05hyM5GT4F4aZFbi+uIcETxxXzx/HG7lI6OuzTJU/UtxAnkGVZyGz22HTOnjaaF7eGXpeiuqGVpzYW8aGF4/mvy+bgjRNe3Ba9dSw2HanizGmjuwWlF07M4s7lM3h+yzG2FoYucNjS1sEvXtvLrLw0Wts7+NuGoxHLUFrTxA9f2sXy2Tm8fvcFLJ48im/8cxvVja2d2jW1trOnpJZFE0Nn12QkxZM/Kpl9ZaE7W/C5h7705Ca+86/ezXhvaGnjnX3lXDwvz++KSU30smxmDq/uKOmUdrv2YAUAZ4fIsPJ64pgyOpV9paFlfmL9yfv62s4SaznLapspqmrk9Emdu5L0pHjeNzeX57ce7ySrm8AxZUz3OIrSGZtSG4k224LQBtxtjJmHL4Zxp4jMA74KvGaMmQm85rzvevxs4NvAmcBS4NuhFInSnZy0RFraO6hp9Pn2D5bXM3l0Cstn51Je18LuHtwbR080cPYPXuOWB9fS0WGoaWolIzk+ooyfC2fnsLukNmStpr+uP0Jjazu3njOVrJQETsvPZMOhyFxfLo+vO8I9T21lf4jOsqaplaKqRuaM7Z6mC3DbeVNJio/j7z10+m/uKeNEfQtfff8clkwexTv7KiKW85+bimhq7eCbH5jHtJw0vv3BU6htaus2uj1UUU+HgRl5weV1mTgqhaNhMtWeWH+UpzYW8dA7B9leHHmF34JDlTS3dbBiTucMtvNmjKG4uoni6pOJELuO15Ic72HamNCj8qljUjlcEdoyeHNPKefPymF8ZhLbi+1dee4xpwdZKvSCWTmU1zV3UkyuVTxeJ8iFxcaCWGO5rRPGmGNuppMxphbYCUwArsI3twLn74eC7H4p8Kox5oQxphJ4FbjMQlYFXwwCoKzO10EfKq9nyphUTndcEz25c+57eTfHqpt4a285mwurqGlsJSMpsjLIp+X7UgeD+evb2jt4ZM1hzpya7S+QdtqETH3P+bcAACAASURBVLYXV0dk2QC8tO0Y9zy1lcfXHeG6367plnsPPrcFEHQeB/hG4+dMH8NbPZQMefq9QkanJrBsZg6njM9kb0ltxJPWXt5ewvz8TP96x6dOyGR2Xjovd1kBcK/jgpkRZl3kidnJHDnR/XoD+fsGn9xw0ve/4fAJfvLK7rAxIjhZNn5BF2vGnTsQ6NvfW1IXNuibl5Hk/052pbSmif1l9SybMYZpOWkcCGMdBXLUCXwHy6w6c6rPonk3IPZR7gxcxqTZjHNHNiEVhIiMFZHFQLKILBKR053XhUBEtpmITMGXDbUWyDPGuLN/jgPBCqFMAAKHdIXOtmDHvl1ECkSkoKws8iyd4UhGsq9Dd90Xx2uaGJ+ZxJTRqWQkedl0NPhosrqhlZe2H+eK+eMA2HC4ktqmNjKSI0tbne2MfoO5E17afpyiqkZuO2+qf9usvHTqW9opjbA67INvH2TqmFRe/Y/zaWpt595nt3dr48YLpo0J3eEunJjFgfL6oNlU1Y2t/HtnKR9cMJ54TxwzctOob2n3j0JtaGnrYGtRNWd1cb9cOCeH9YdOUN988rz7y+oQgWk5PfvH8zKSOFHfTHsIpVpc1cimo1V8ctlURqXEs6+0jpa2Dj79yAZ++fo+PvbQWppae86C2lpYzdQxqWQmdx4gzB2XQbxH2FZ0cgCwt7SWmXk9K7Wc9ESqGlqDlmZxLYYFE7OYmJ1MUZX9/T3qKMpgqdiTR6cwOjWBrQGDoop6V0EMvhTnwUZPFsSl+NJZ84GfcjLF9UvA12xPICJpwD+ALxpjOg0pjW8Y1qf6AcaYB4wxS4wxS3Jy+ncNhKGK+4OuaWylpa2D2qY2RqclEhcnzM/PYmtRcAvijT2ltLR18KnzppKR5OXIiQZqmlpJT4zMgshOTSDRG9dtLoYxhgdWHWDqmFQumntyXDDB+WEXVdmnQJ6ob2H9oUquXjSBmXnp3HH+dF7dUcK+0s7uM1fp9DS5a5bTsQVVaNuO0dLWwdWLJnSStScFcay6kZ++uscvy67jNbS0dbAgv/NI/Kypo2ltN50WeCquaiQ3PZGkeE/I44OvtHuH8T3jYLgWw4WzcpkwKpmiqkY2HK7kRH0LNy2dyLaiGn813uKqRr729Fb+96Vd1AUoq31ldf57E0i8J45J2Sn+UX5LWwclNc3+WfyhcC3biiB1wnY41uaccenkpCX2qPy6UlHXTGZyfNB7JiLMGZfeqQR+eV0Lid440gbhfJ3BRkgFYYz5k7MG9a1dUlyvNMY8ZXNwEYnHpxweC9inRETGOZ+PA4LltBUBgev/5TvbFAsyAyyIygbfjzHbcTXMzEtjf2l9UHfOmv0VZCR5mZ+fxcRsn4+7pjFyC0JEGJuZ1K0TXbO/gi2F1Xxq2dROa//mO77gwsqeXSaBuO6NM51Fi24+axIi8K/Nxzq1O17dFLLzcHFdE8VdXFTGGB599zDTclKZ77jNchy3RFltcAVhjOEzj27g/tf28omH19PW3uHP3Om65oB7zECXX0lNs1XJkuxU3zN2n29XNh2tIjnew6y8NMZlJlNc1ehXWJ9/30zuuGAaf1l7hB+9tIurf/0Ofys4ym/e3M8tD66lpa0DYwxFlY3+mfldmZ6TxgHHOnPdRuHkdr+Dwdxb24urmZSdQkZSPGPSE+kwwdu5NLa0s2Z/BR0dhurG1m5WTiCz8zLYU1LrVzjltc2MSUsc1DPpBws2MYjnROQjIvI1EfmW+wq3k/ju/oPATmPMTwM+ehZws5I+DjwTZPeXgUuchYpGAZc42xQLAhWEO1pzfdHTc9JobG3nWJCZ1qv3V3DWtNF44sTvL65paiU9whgE+DqL484ku7b2Dhpb2vn+izsZl5nUrf5+rtOxhApqP7H+COf+8HVueXCtf4T73pEqvI5FBD5/8umTRvHars7ZL8drmhgbpuPKTfd9XlrbTGFlA595dAP3vbyL//7XDrYV1fC5C2f4O5PcjER/22Cs3F3K5sJqls0cw9ETjRQcrqSwsgERGJ/VWY7RaYnkj0pmc4DLr6SmyS9PT7gzwCsbWnhuSzH3v7a304h709EqTsvPxOuJIzslgaqGVg6U15OS4GFsRhL/eclslkwexW/e2E+cCP/6f+fx8xsW8t6RKp7aWMiJ+hYaW9tDzqD3lZWvp629g5Iad65Mz3KnJ/kGGrVN3V15O4/V+ldEHJ3qWBr1oV2OX/77Zm76/bs8tvYwVY2tPWbZzR6bRlNrh3+SXkV9C6PVvWSFjYJ4Bl9guQ2oD3iF41zgFmCFiGxyXpcDPwQuFpG9wEXOe0RkiYj8AcAYcwL4LrDeeX3H2aZY4AaVqxtb/aMwd/Q2I9fnMtjfxZ1SWd/CkYACfxlJXqobW2lsbSc1oWd3RzBGpcRT3dhKSU0T5/7odeZ+6yW2FdXwjSvmdRvNpyd6iROoaujuLvnT6kP81z+2kpkcz1t7y/n9qgMAHKyoZ2J2CskBsp07fTQ7ims6xRJKa5r8nXooRqcm4IkTSmqa+Omre3hp+3F+/cZ+Hl59iOsW53PNopPhr1FOx1wdRFZjDD//914mZifzixsXIQJrD5ygsLKRvPQkEr3d7+O8cRmdsspKaprICyNvoBzHq5u56y/v8dNX9/DclmLAV+hvR3GNP1U203kWFXUt5Kb7Rs7xnjj+dNtS/vCxJbzw+WXMGZvBlQvGMzM3jX9uKgqb6ZM/KpnWdkN5XYt/jfJw99l16QTGXMCXjnvkRAPTc31xl7Sk4O1ciqsaeWGrz1J8fVcpVQ09WxCTsn3HdWMVdc1t6l6yxOYu5RtjIs4gMsa8DYSy4d4XpH0B8KmA9w8BD0V6XgUSvHEkx3uoaWz1j8LcEZOrIPaV1nVat9rNOJrrjOIyk+Opbmiltd2QGMYfHoz0pHhqm9r4W8FRSmqa+eR5U1k6NZtLTxnbrW1cnJCVkkBVY2eXQmV9C99/YScr5uTy+48t4dY/ruNfm4v5j4tncfREQ7fR7cJJWXQY2FZU418vu6apjUlhJkTFxQlZyb5OdNWeMj60cDzf+MA8Glvau2XGxHviSPTGUdfcxr7SOnYdr+GK08YhIryxu4wthdX88JrTyE5NYEKWb65CRV1zN+vBZVpOGit3l9LW3kGHgcqGVisLIi3R90zWHTyZcvv0e0VctXACO4/V0tLewUJXQSTH09zmG+kHdqSpid5Oi+WICCvm5PLg2wcpdVxo2UFmRcNJa+F4TZPfmgont9sp13Xp+AsrG2nvMP6Ja+611TS18f0XdnLO9NGd1iJ5bWcJHQZOGZ/BgfJ64kRCWjpwsgS+m+1U39zG6FSdA2GDjQWxWkROi7okSr+S6XR4rjnvWhWjUxNIT/R2y0ff6U8HPakgapvbaGxtJ9Eb+XzK9CQvtU1trDtUyey8dL75gXlBlYNLVnJ8NwviL+uO0NzWwVffPwdPnK/zOlBeT3FVI0dONHTrvN0gcOAM49qmNr9roydSE70cq2qivK6FOeMyGJOWGDRt0n9tzW187MG13PWX93jBmYj189f2kj8qmWscF5qbrlnZ0Bqyo52Wk0pru6GwspHaJt/120xKTHYqubrP7aK5uazeV0F9cxubnPiMO+PazWo7eqKBzDDFCeeNz6Ctw7DpiO8ehhqZu0H/49VN/kB5uFiVaxnUdlEQh5zv4pQxroLwnfOtPeU8sOoAn3h4faeY2aq95eSPSmbZzByKKhvDPuOxGUl448Q/b0QtCHtsfvnnARtEZLeIbBGRrSKyJdqCKX3DVRCuuyXF+UGIiJPV0jkGsfNYDWPSEv2ZJhnJ8bip/r1TEPHUNbdxuKKeGWHSHwHSHXldWts7eHTNYc6bMYZZTtqsW5p5w+FKqhpau60ENtqRf29AJlNdcyvpFp1BWqLXn+kyMURg1iU10cue47X+iWL3v7aXN/aUsfloFXcun0GCc78mZCX7O9CMEB3tdCed9UB5nV+Z2yi0FMeqO1Lh6/SuXzKRlvYO3j1QwaajVeRlJDIu03d/MpzjFVc3kdWDKwZgZq7vXhcc9imZcAqipKaJ2uY2ErxxQV1ogbjZcHVdYhBuKrJrQaQ6FsTq/b65KcbAHueZdnQY3t1fwbKZY8hOjaetw3CivrnHc3s9cYzLSvInQdQ3tw3KisODEZu79P6oS6H0O6mJHhpa2qlr9uWcpwS4iSZkJXebVHakoqFT7n2gbz/cDz8Ybqd0uKKB980Jv+ZvSrynU16+WyTu+9ecLGk9x7Fu1hzwuVWCjcqnjUllf5mvw2lt76CptcNqtJiW5PWnWk7owV0BPmXipqbesGQiTxQc5RN/XE/+qOROAfjRqQlUNrSQFO8J2dFOdeZnHCxv8LtobOR1n8/xmiZSEjxcMDuH5HgPq/aUselold+9BHSK+fTkq4eTgXQ38ypU++yUBOI9wrHqJt9cGQullhTvU5yNre00tbb75Tpc0UBqgsc/L8FVJIcCrNz1B08wZ2wGByvqqW1uY9HEUX4HdoeBxPieBzGB3/n65nZVEJbYVHM9jC/ldIXzf4PNfkpsSUnw0tDSRkNzGykJnk4zXCeMSqaoS9nloqrGTiPypAClEO7HF+r8LmMzwwddkxM8NDoKwhjDg2/55ktcOOuk7zkt0cvo1AR2OJOqgo2Gp+emsa+0DmOMf6SaZtF5BVoZ4TrR1EQvzW2+4oe3nTfVbwV88wPz/NYD+OI+HQYaWtpDzkYflRLvmzNS3UiN42KyyRpL9MbhZmmOSkkg0eur/vqPjUUcqmjoVJcoUEGkJPas7DOT40nwxlFe10yCNy5kenBcnDDGma9Q12TnshERErxxFBw6wWn3vsyzm31B9YPOTH83U8xVfk2tHeSmJ5KVEs+OYz4Lwp1Qd8qEDH+g3nc/er6u3PQkyuuaaWnroKW9wx/nUHrGphbTt4H/Au5xNsUDf46mUErfSU7wWRD1Ld3N6fFZydQ0tfl93u0dhpKapk4VWwM7ht64mAI7SpuSBskJHhpb2jl6ooEv/30Lmwur+fSyad1KN+RlJPlLZWcG8dVPz0nzZ2+5wVCbDjfwHoXr7ALvzdjMJJ656zxWfXl5txhLoIUTSumICOOcOSN1EbiYRMRvFbod6gWzcvzXvGRKgIIIeBZJYTpSEfHP9Qh3HzKduFFdc5uVEgbfd2n1/gpa2w2PvXsY8FkKgZVV4z0nn3l2agKz8tL9z3x7cTXxHmFmbjopCfbf0TFpiZTXNp90uQ7ganxDGZtf/tXAlTiprcaYYqDnSmJKzElxFURz9zRV11JwTW531bjAlMbAH1xvXEyB+9v8GJPjfQri1j+u45lNRdx4xkSuX5LfrV1eRiINzkI5wTrdaX6ffj31Tmdgk6YbKG+4DjrB6cC8cUJGkpe0RC+TRnePW6RZKp2xmUkcd1w1Nud3cQPVKQEKAnyunMBZ24EKLcFC2bv3NSHM+tFZKY6CsLQgoPN3aX+Zbx5FUWUjkwPun2tpuLLMGZvOnuO++lc7imuYlZfuxDwCFF+YTLuc9ETqW9r9iRC9sYpHIjZPtcUYY0TEAIiIFlEfArgKoqGlrVsH7SqC4qpG5ozNoNiZ0BaYitlXCyJwn2SLDjo53uMP+n7v6lO7rabmEphKGUxBTHTLdlQ2+qt72nSKbhtvnIS9Xrdtcrynx9m4gdfdkwzjMpNZd/BERBYPnLzHyc6zmjImlQc/voTc9CS8nuD33+ZZup19uE40KzmBA+V1xImEzPgKJTNAeV0zu47X0tZhupXpSPTE0dLWQVK8h1l56dQ2t1FU1cjOY7VcONtVhPbX5SZfuPM74uNUQdhgc5eeFJHfAVki8mng38DvoyuW0ldSErw0trQFTelzFYH7Y3FLTARaEEkBnUNvRlsJnSwICwUR0GbRxNCV3QNH18lBRo3jA6wjd5GkUAvvBOK2SUvyhi3B4I6sw80PCVTMPSmI3IxESmub/BaPzf3yydzZZw/wvrl5/mq6Lp3jSeGP7WYR2VoQDS3t1jJ37cjd1eO6KQjnO5fgjfNX4l29v4LyumZ/6fZO39GwLiafu8/9rsd7tcyGDWEtCGPMj0XkYqAGmA18yxjzatQlU/pESoKHhlafi6lrWYGctETi5ORyoseq3FXjAhVE37KYAvcJ1pF3xRsQa+ipsF6grztYp5uS4CU7NYHCykZaI1AQbgdjM8JOsGwb2Gn21NlmpyTQ2m787g8beQPbheucA+9TosWx0xwLJpzl5Zvc2Eq2SFhl0lWW6Tm+bLPXd/kURFcLxK+EvXH+NOd/OUFt931iBIrPjYO5BSRt7/FIp0cFISIe4N9O0T5VCkOI5AQPxil41nV05vXEkZueRLGjGIqqGklL9HZKVfQGBAptXDRdCbQ6wvmHXZkA3+p1PWQRBVpDoeSakJVMYWUDLU6mUYLFaNHtMLwWrgf3vElhLKtkS9+/m41TWtOEJ046FTLsCfeehbu/gc/Sxhp0YzbhFUQ8LW0d1DS1Wn9H3I586phUiqoa2ejU1Opa0uOkEvaQnhTPxOxk/5odsx0LotN3LMz5XXekW3rG5jkrYVxMxph2oENEMntqpww+3AyXE/UtQTuFcVlJHK/xmdvHqhsZl5nUybUS+AOy7bACSYzQxRTvnCMjOb7HRWcCXUyhRq35TnnrSCyISJRgvOdk59UTtjEId+Z0aW2z9UgcTgbLw1logdaZzfFdWcO1dZV1Q0u79YjclTnBG8fssb55LROzU7p9x/wyOH/nOG1HpcST68QTIrEg3DTjCqfyrM2gQbGLQdQBW0XkQRG5331FWzClb7j+b1+pjO4/nnEB5biLq5q6jeACO5W4XpRFDuxcbFxM8e6oPEynG3gtoWIFE7J85a1dCyISBdHW0WHdNpwFERgI7dGCcNJhS2ubO6V4hsO9rnDXFxiwtrEg7GMskScyuN8lT1wc85zYQrDlYLu68eY7s+jn52f5n3vgOcMqM2dgUaEWRETYZDE95byUIUQnv3OQH++4zGRW7irDGMOx6kZOndB5rYJAt4SnFwoi0AqIt+g8XIUUzlixGelPGJVMU2tHRP5mt017eP3g9+OHsyA6uel6kGGUY0GU1DRFlDHmHj+cAg9U9jbxpHhLCyIwCG9rQXgDUoRXzMnj8XVHed/c7jPt3Q7cVWgfOXMSu0tq+dyFM/xtAq0ObxjF6okT0pO8lDvl7zUGYYdNkPpP4doog4/AjjRYpzouM4nG1nbKapspr2thfGZXC+LkPr0ZbHW2QMK3d3+wthlEPeHO83Br/ETiVmm3sCA8zg0Jp/g6+f57dDH5LIjapjbSegjQd8UfNwnTOQY+CytryuO6d3o+bmqinQstEPfexYlw8bw81tyzIug6Em7n7yrj0WmJ/N9HTu/cRiL7jmUkxftdTJFYaiOZsE9VRGaKyN9FZIeIHHBfAyGc0nsCO8VgHaSbKbTRqdo5rouLKXB01psYRJxE5qLyj4bDfCNtOiI3G+topX1Ko9uJ2ixyGTgK7glbF1NgGY7exELCPZ/OzzL8cV0ZJGS1fh+BLiZrCyKu870bl5kcdFDQ4VSK7MnNFRehGzQjOd7vYlILwg6bu/RH4Df4FgxaDjyCltoY9IS3IHyd6EanNHTX9QoCR1i9iUF4I9zf7UzDubNsOtA8p/aTW97ZpjNwz2tzpbb3I85y5J7gjfPf70g6LnefcPdMIlTWCX53W8/q0naeRyCusvKEGcG757Yd6dsMYjKTvf7jhrO6FB82TzXZGPMaIMaYw8aYe4EroiuW0ldsXEzgK50NdHMxefoYpA7stGx+vLb+dJuOaExqIt444UgECsLtzG3WKXYPZ4yNvYGVDG5nG4mC8FpaEIFYKWvnWbSFURCpgQrCtiMXO+vL397Sv2llQQRaampBWGFzl5pFJA7YKyJ3icjVQPgC/0pMSQiT4ZGb7pss5yqIrpPT+prm6okwBuG2Dzeys/lhxzlrarsVV232iaS/cDsje/UQvkNMsZx7EEyOSJ6PTVvb49mm8XY6ticymW0H+jYKInAOjbqY7LC5S18AUoDPA4vxrTP98WgKpfSdTjGIID9ed7Ic+GaZdp1s1dlFFPn5AzsAm1G5+EeWPX8lba2ZQIVn0xlFYiX1NSYTDL+CiMD14Vow/W1BnHxePavAwDTf3sYgQsrg/O1pTkwgNvcgKUCh9eYZjkRsspjWAzhWxOeNMbVhdsFp/xDwAaDUGHOqs+0JfOU6ALKAKmPMwiD7HgJqgXagzRizxOacykkSw7iYwKkiWtPkX7M3EE+Efutu+0f4A/RYjoZtjxuYGWMjfm9G4RF4mJAw/adbbrw3+fm27hroXwsiUCl4LRWEe+ywHb8bE7KN91g0C1w0y1bxjHRsspiWiMhWYAu+CXObRWSxxbEfBi4L3GCMucEYs9BRCv+g5/kVy522qhx6Qbh5EHAyDhFsic3AH1BfXUw22Da39QwEWhA2Ci6SILV7bR0RaIhwMriTCXuhiyNUbuHbuIcLd3mBVqqtCJFaELZzcGw6/MCsK1UPdthMlHsI+Jwx5i0AETkPX2bT/J52MsasEpEpwT4T37DgemBFJMIq9oSLQcDJ+jRuWexQDIQFYTuis3YxBVoQ/Xh+6N3EwXB7uBZEJPfa7b/728XUmyytcCmxLv4spjCWkiuC9cDBQuYky4qzyklsxmPtrnIAMMa8jS/ltS8sA0qMMXtDfG6AV0Rkg4jc3tOBROR2ESkQkYKysrI+ijV8CFQKocorXHJKHpnJ8Vw0Lzfo5y69mSgXaSd6MvDb87DV2sWUGaGLKQJ5e+OesI1BRN+CsFcQkQTh7eWOLIvJVlnZXFegi6k393kkYmNBvOmsB/E4vu/MDcAbInI6gDFmYy/Oe5NzvFCcZ4wpEpFc4FUR2WWMWRWsoTHmAeABgCVLlkTynR7WdLYggo+cVszJ471vXhy2w+vNiDniGIQ/dbTndr0JUtulrkZuQUQUgwhzeJt6VSHl6W8LohcDgki/IeFkduW0VcY2X4vAeRu2Fs9Ix0ZBLHD+frvL9kX4FEZEbiIR8QLX4MuICooxpsj5WyoiTwNLgaAKQglOuHkQLjY/wN64mGyDi13bh+t0exOktuHkPIjwbf1B6gjG2LbzOyK6b87pIwlSD5bnbZ3FZB2bCt/QZmVDpTM2WUzL+/mcFwG7jDGFwT50ljSNM8bUOv9fAnynn2UY9oRLc42Egcj4sLVSbBWEu8SkLScPa29tRGJB2BYh7M2djihFN4IYRCQTASPVKdbzIKznS1goCHUxRYxNFtNop8T3Ricm8AsRGW2x3+PAGmC2iBSKyCedj26ki3tJRMaLyAvO2zzgbRHZDKwDnjfGvBTJRSmdR3R9nTU6EDnjtn5v287QZpGiQCJxo/VOQdhZEL251ZGUjbBxH/XmeUcaWg93Dvd22VomNu00iylybFxMf8Xn3vmw8/5m4Al8lkBIjDE3hdh+a5BtxcDlzv8HOOnWUvqBvloQvYlBRIqt3ztayioSK8k2oB5IuFvoVi2N1FUTKI8NdhaE729kQWo7GYylW8yNEUTNxaQawgobBTHOGPPdgPf/IyI3REsgpf+JZI2BYAyEOW7r1oiWMePpRQwiEsJ1oO6ks3D1j4LR37PAIzmeiK/Tt70l7uMNW2PJOZ6169HGxaQxiIix6TleEZEbRSTOeV0PvBxtwZT+o691ZwbSxRSOaGWfRNIpurejP2Xxr2hns2KRg2vBRKLAIwlS27jQvBEoVjgpc7ivpHs4axeTxVc8cLVCzWKyw6bn+DTwF6DFef0VuENEakWkJprCKf1DXxdHGQgXk/UpomxB2NCbLJ9wuAqiNQIF0RtsnmVv7oVth+saSOHaR2OiXOB8IA1S22GTxdR9wVhlSNHXGMRA/JhsR4zRkiUugg4pGjK4z6ilPXIXUySjYSvlFkEMwn+8CF1MtvewP7OdbJZbVTpjE4NAREYBMwF/cnmoiWvK4KOvLqbeBE4jP4fzN1y7KJ0/kpFwNCwIfwwiyhZEbybB9cTJkb5tkNp1i9m1t3Y9WjQLjMWpAWFHWAUhIp/CV/I7H9gEnIUvfVXrKA0RhsbiKHa+7Ggpq5NpleHbRiMmk+iPQdhbEJGk2brYuGIiubqTitUOV+Rw7SO2NGxcTIEKQn1MVtiuB3EGcNiZNLcIqIqqVEq/MhRKG9t20NG6lEg6umiI4CrxqMcgIriBNhPlIlGsgccM1z7SQoR2qxaqBREpNgqiyRjTBCAiicaYXZxc00FR+gV/DCJc8DLKWUw2I8toFPw6GYOIroKIZPEmGyINUrv3zrpibD9OlFMixyYGUSgiWcA/8RXOqwQOR1csZaQh/g46XLvonD8uwpFwfxPfCwsiUjeM/XEjnwBoa5h02MocpWtzUX1ih00W09XOv/eKyEogE9DSF0q/EuvfayTB1qi4mHoRg3Dpb3n8cYJI1o6I2MXU8w7++RLRijnF/Bs3NLDKYnIxxrwZLUGU/ufFLyyjrLY51mJYYdstRm9EaT/hKxouJnfCWSSr1EVS6qM32NzqSCcN+q0e23Y61I8pESkIZWgxd1wGc8fFWgo7/CPLMO2iPfKLtMxEf+EGWdsjKLURLRdTJHonEsXqO/QgWbJF9Y4VQyH/URkB+LuNGE2Usx3ZBtunP/A6ExQiKcX04cX5AJwyPrP/BCGyEh5uE/t5EJG11xhEbFELQhkU2HbQ0ftd22uIaMjgTmCLxMV06SljOfTDK/pdlkiUZVykFoSl1RNtO0P1gx1qQSiDBLtRa7R80pF0itGJQfh+ipG4mKJNJEu12k+U811fuKwnW5ejEl1UQSiDinAdQrQmynVE6PqA6MQg+tNt1Vt6s9a27b04qf9i7WJS1WODKghlUBGub4qaBdGL0tn9G4NwgtSDQEPYlsOAQAVhd+PGZ/rKuWUmx1vJEC1UPdihMQhlUBGrH+5JF1NsyVzHmQAADXdJREFUJOhNFlMk3PvBeWw8Ylchx7YcBkRei+mey+eyZEo2Z0/vedViE6GlESlqQNihFoSiAHkZvpHt1adPsN6nPzuZSNaV7g23njuV+29aZNXWDZTbuNsiKVECvrXCP7hgvFVb33F7/vyK04ZIHvcQJWoKQkQeEpFSEdkWsO1eESkSkU3O6/IQ+14mIrtFZJ+IfDVaMiqDh1h7VrJTE9j13cu44/xpMTn/QCzKZIu77KlNmfgIJ1JbY/t1+NXNp/cqk0tnUtsRTRfTw8D/AY902f4zY8yPQ+0kIh7gV8DFQCGwXkSeNcbsiJagyuAhlsHDpHi7BWXGpCUCcOqE8PMP3vrKcmqaWsO2G4hlXW3JTk0AYHpuWti2kc6DsCXaWUyDSB8PaqKmIIwxq0RkSi92XQrsM8YcABCRvwJXAaoghhiPf/os0hKHX5hr9th0nr3rXOaNywjbdmJ2itUxvf29kk8fOGf6GB795FLOntZznAAinwdhy7c/OI9vPbOd2WN1QctYEotf710i8jGgALjbGFPZ5fMJwNGA94XAmaEOJiK3A7cDTJo0qZ9FHdn830cWUdkQfvQbinCByKHM/Pysfj2eJ8oxiEhZNjMnpudfPDmb5z+/LKYyKAMfpP4NMB1YCBwDftLXAxpjHjDGLDHGLMnJie2XerjxgfnjueWsyQN6zkhKTQ8nvIPIxRQJkc6DGCwMNXljxYAqCGNMiTGm3RjTAfwenzupK0XAxID3+c42RRm2DKYYRG+Ixjrd0USD1HYMqIIQkcCctKuBbUGarQdmishUEUkAbgSeHQj5lNgzUme4DqYspt4wxMVXQhC1GISIPA5cCIwRkULg28CFIrIQXxbbIeAOp+144A/GmMuNMW0ichfwMuABHjLGbI+WnIoyGBgK64YHwx2JDzXPoCo0O6KZxXRTkM0PhmhbDFwe8P4F4IUoiaYoSj8xVDvaISr2gDN4cusUJQJm52n642BiqFkQih3DL0ldGZLMGptOvEf4fytmhG278j8vZHRawgBIpQxXRmqsK1JUQSiDgoykePZ+L2jllW5MHZMaZWmU4Y6qBztUQSjKICHBE8cnl02NtRi9YtCsNW2JGhB2qIJQhi3LZo5h3cETsRbDmj3fe3+sRYgYddUMb1RBKMOWRz8ZskKLMsJRxWaHZjEpitJnNItpeKIKQlGUXqPj8OGNKghFURQlKKogFEXpNerKH96oglAURVGCogpCUZQ+o0Hq4YkqCEVReo26mIY3qiAURek1P7luIZefNpY547R44nBEJ8opitJrZo9N59c3L461GEqUUAtCURRFCYoqCEVRFCUoqiAURVGUoKiCUBRFUYISNQUhIg+JSKmIbAvYdp+I7BKRLSLytIhkhdj3kIhsFZFNIlIQLRkVRVGU0ETTgngYuKzLtleBU40x84E9wD097L/cGLPQGLMkSvIpiqIoPRA1BWGMWQWc6LLtFWNMm/P2XSA/WudXFEVR+kYsYxC3AS+G+MwAr4jIBhG5vaeDiMjtIlIgIgVlZWX9LqSiKMpIJSYKQkS+DrQBj4Vocp4x5nTg/cCdInJ+qGMZYx4wxiwxxizJycmJgrSKoigjkwFXECJyK/AB4GZjgpf4MsYUOX9LgaeBpQMmoKIoigIMsIIQkcuArwBXGmMaQrRJFZF093/gEmBbsLaKoihK9IhmmuvjwBpgtogUisgngf8D0oFXnRTW3zptx4vIC86uecDbIrIZWAc8b4x5KVpyKoqiKMGJWrE+Y8xNQTY/GKJtMXC58/8BYEG05FIURVHs0GquiqKMGP5113lsOloZazGGDKogFEUZMZyWn8lp+ZmxFmPIoLWYFEVRlKCoglAURVGCogpCURRFCYoqCEVRFCUoqiAURVGUoKiCUBRFUYKiCkJRFEUJiioIRVEUJSgSoqDqkEREyoDDvdx9DFDej+LEkuFyLcPlOkCvZTAyXK4D+nYtk40xQddKGFYKoi+ISMFwWd50uFzLcLkO0GsZjAyX64DoXYu6mBRFUZSgqIJQFEVRgqIK4iQPxFqAfmS4XMtwuQ7QaxmMDJfrgChdi8YgFEVRlKCoBaEoiqIERRWEoiiKEhRVEAGIyL0iUuSsl71JRC6PtUx9QUTuFhEjImNiLUtvEZHvisgW53m8IiLjYy1TbxGR+0Rkl3M9T4tIVqxl6g0icp2IbBeRDhEZkmmiInKZiOwWkX0i8tVYy9NbROQhESkVkW3ROL4qiO78zBiz0Hm9EGtheouITAQuAY7EWpY+cp8xZr4xZiHwHPCtWAvUB14FTjXGzAf2APfEWJ7esg24BlgVa0F6g4h4gF8B7wfmATeJyLzYStVrHgYui9bBVUEMX34GfAUY0lkIxpiagLepDOHrMca8Yoxpc96+C+THUp7eYozZaYzZHWs5+sBSYJ8x5oAxpgX4K3BVjGXqFcaYVcCJaB1fFUR37nJcAA+JyKhYC9MbROQqoMgYsznWsvQHIvI9ETkK3MzQtiACuQ14MdZCjFAmAEcD3hc625QueGMtwEAjIv8Gxgb56OvAb4Dv4hulfhf4Cb4f8qAjzHV8DZ97aUjQ07UYY54xxnwd+LqI3APcBXx7QAWMgHDX4rT5OtAGPDaQskWCzXUow58RpyCMMRfZtBOR3+PzeQ9KQl2HiJwGTAU2iwj43BgbRWSpMeb4AIpoje0zwdehvsAgVhDhrkVEbgU+ALzPDOJJSBE8k6FIETAx4H2+s03pgrqYAhCRcQFvr8YXjBtSGGO2GmNyjTFTjDFT8JnPpw9W5RAOEZkZ8PYqYFesZOkrInIZvrjQlcaYhljLM4JZD8wUkakikgDcCDwbY5kGJTqTOgAReRRYiM/FdAi4wxhzLKZC9REROQQsMcYMybLGIvIPYDbQga+U+2eMMUNytCci+4BEoMLZ9K4x5jMxFKlXiMjVwC+BHKAK2GSMuTS2UkWGk8L+c8ADPGSM+V6MReoVIvI4cCG+ct8lwLeNMQ/22/FVQSiKoijBUBeToiiKEhRVEIqiKEpQVEEoiqIoQVEFoSiKogRFFYSiKIoSFFUQyqBARLJE5HMB78eLyN+jcJ5EEfm3Ux32hv4+/kAhIreKSJmI/CFG539MRE6IyLWxOL8yMKiCUAYLWYBfQRhjio0x0eh8FjnHX2iMeSLwA6fK51DiCWPMp6J1cBEJWWnBGHMzOrls2KMKQhks/BCY7ozs7xORKW6Ne2e0/E8ReVVEDonIXSLyJRF5T0TeFZFsp910EXlJRDaIyFsiMifwBCKSC/wZOMM5z3TneD8SkY3AdSKy0Dmmu2bDKGffN0TkZyJSICI7ReQMEXlKRPaKyP8EuyARqXMKDW52jpnnbJ8iIq8753hNRCaJiEdEDoqPLBFpF5HznfaruswoD3auVSKyMOD92yKyQERSncKT65z7dVWADG+JyEbndY6z/UJn+7PADmf/551r2DaUrS4lclRBKIOFrwL7nZH9l4N8fiq+NQj+f3v3F9pjFMdx/P1VskKUKytyJRe0zJ8im1xQ5E64EJuQxNoNUS7In1zsbkr+ZsNEuxIXJH8XMk2ztQuEC0VNmlnmX9vHxTk/nvHYz5Zp+/m+rp7feZ7nnPN7+tX5nXN6vt9ZwH6gU9J04B6wJl5zFCiTNAPYChxKViCpFVgP1MV2nsVTbyUVSjoHnAK2x5wNzfSM+/RF0kzgMHAB2Bz7VWpm41L6PJLwtnQBIXfChlh+EKiObdQAlZK6gMeE/ATzgIdAkZmNACZIetrr04MTQCmAmU0G8mI0353AdUmzgQVAhZmNBFqBhZIKgZVAZaKuQqBc0mRCroFXkgokTQUuZ+mHyyE+QLih4oakDklvgHbgYixvBiaZ2ShgLlBrZo3AEWB8elW/OA9gZmOAsZJuxfJqoDhxXWZJpRlokfRa0mfgOT2Dv2V84UfAxwZgUjyeA5yNx6cJAwJAXWyvGDgQy2cRYgdlUwssNbPhhAjEVbF8EbAjPpObQB4wERgOHDOz5nhvMmFOvaQXie+6MM6yiiS1/0FfXI7476K5uiHrc+K4O/G5m/A7Hga8i5nn+upDH/uQbD/Zh599TURs7frNNUm3gU1APiHvxTZCnJ26bB2T1GlmVwkBDVcAM+IpA5b9nODHzHYTYvcUEJ7dp8Tp789D0hMzKwSWAPvM7JqkPdn643KDzyDcYNEBjO7vzTHz3AszWw4Q1/IL+lhHO9BmZkWxaDVwq5db+usuIYIohCRImQGgnjAL6pb0CWgENvLnqT2PE5aKHkhqi2VXgDKzEPvdzKbH8jHAa0ndhO+ZukFvIQd4p6QzQAVh+cn9J3yAcIOCpLfAnbgRWtHPalYB68zsEdBC/9JIlhDW6ZsIkX0H4t9yGbA2trEaKAeIy1UvCelIIQwcownLPFlJagDeAycTxXsJy0lNZtYSP0PYnymJz2oKv59FTQPq4xLVLiB1Q97lJo/m6twQZCHx0ExJWxJl+YR9hilxZjDQfagCLkn66++ruMHBZxDODU0fgcWZF+XMbA1wn5AS9F8MDjXAfHruXbgc4zMI55xzqXwG4ZxzLpUPEM4551L5AOGccy6VDxDOOedS+QDhnHMu1TdkbQxxhS4XUQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig,ax = plt.subplots(1,1)\n",
"ax.set_ylabel(\"apparent magnitude\")\n",
"ax.set_xlabel(\"time from now [years]\")\n",
"ax.plot(times/year,m);"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.0"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment