"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mass, wcs = lt.g_mass(3, 100, 0.3, 1.0)\n",
"\n",
"fig = plt.figure()\n",
"ax = fig.add_axes([0.15, 0.1, 0.8, 0.8], projection=wcs)\n",
"plt.imshow(mass)\n",
"plt.colorbar()\n",
"\n",
"for row in lt.get_sources(): \n",
" ellipse = Ellipse((row['x']/3600.,row['y']/3600.), #conversion from arcsecs to degrees\n",
" width=row['b']/3600, \n",
" height=row['a']/3600,\n",
" edgecolor='pink',\n",
" facecolor='none',\n",
" angle =row['theta']+90,\n",
" transform=plt.gca().get_transform('world')\n",
" )\n",
" \n",
" ax.add_patch(ellipse)"
]
},
{
"cell_type": "markdown",
"id": "1415c18c-2d06-4664-85b6-74de81c5cf23",
"metadata": {},
"source": [
"Here we have displayed the source in pink and the cluster of galaxies that acts as a lens in yellow.\n",
"The colorbar indicates the mass repartition of the cluster in $10^{12}$ Msun/pixel."
]
},
{
"cell_type": "markdown",
"id": "368dd590-3255-4880-aed8-d39ebe3334d5",
"metadata": {
"tags": []
},
"source": [
"## Modelling gravitational lensing\n",
"Using the data from the above source, one or more images can be created corresponding to the gravitational lensing under study."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "e8e1174c-fc31-4b84-a6b1-0acae72441f2",
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Compute multiple images for source 0...images found 3, not found 0\r"
]
},
{
"data": {
"text/html": [
"
Table length=3\n",
"
\n",
"
n
x
y
a
b
theta
z
mag
\n",
"
str2
float64
float64
float64
float64
float64
float64
float64
\n",
"
1a
-0.1439036032657953
2.0560154188542463
3.5000000009029875
0.7418610444825656
274.0036883033475
1.0
21.684363693981073
\n",
"
1a
-0.14387454674726022
2.057052271183944
3.500000000902991
0.7423114188365738
274.00087143112734
1.0
21.683704757410105
\n",
"
1a
1.5017408667543064
-21.45605858938671
7.741844354807153
3.5000000009029857
184.0036860228906
1.0
19.13805902100179
\n",
"
"
],
"text/plain": [
"
\n",
" n x y a b theta z mag \n",
"str2 float64 float64 float64 float64 float64 float64 float64 \n",
"---- -------------------- ------------------ ------------------ ------------------ ------------------ ------- ------------------\n",
" 1a -0.1439036032657953 2.0560154188542463 3.5000000009029875 0.7418610444825656 274.0036883033475 1.0 21.684363693981073\n",
" 1a -0.14387454674726022 2.057052271183944 3.500000000902991 0.7423114188365738 274.00087143112734 1.0 21.683704757410105\n",
" 1a 1.5017408667543064 -21.45605858938671 7.741844354807153 3.5000000009029857 184.0036860228906 1.0 19.13805902100179"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lt.e_lensing()\n",
"lt.get_images()"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "7a46324b-9e47-46e9-a62e-e53e1d3fb808",
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/var/folders/mm/6xbl_6k14pn5zn23cltp9rzc0000gn/T/ipykernel_24111/310927048.py:27: MatplotlibDeprecationWarning: Unable to determine Axes to steal space for Colorbar. Using gca(), but will raise in the future. Either provide the *cax* argument to use as the Axes for the Colorbar, provide the *ax* argument to steal space from it, or add *mappable* to an Axes.\n",
" colorbar = plt.colorbar(cmap)\n"
]
},
{
"data": {
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juroa169fN7r8b7/9Fp9//jnc3Nzg5uaGRx99VFXX+fPnq8rVdV1AuyWxPqNHj0ZQUJBqCw8PN+l8IqLGJjw8XPK9OXr0aFtXSSIoKAi+vr6qTVcrnDGZK30CAwPh4eGBPn36YOrUqaqWPwDo3r07srKysHPnTmzevBmenp6IjY3FmTNn5HlxZFfssuXO3d0dUVFRyMnJwZ/+9CfV/pycHIwZM8bguSEhIfD390dOTo7qL5Lq6mrk5eVhyZIlAICoqCg0adIEOTk5GDduHACgrKwMP/74I5YuXaqz3G3btuHOnTuqx0eOHMHzzz+Pffv2oUuXLgCAmJgYvPHGG6iuroa7uzsAYO/evQgICNBK19Zn586dWi13Th/gMRVrHrnTqHJjmtd2GtmqFidPnoS3t7fqsSWtdkDt5MNypGXrJjG+ePGipE6arXbqzMk+7du3D7du3cKhQ4fw+uuv44EHHsAzzzwDAIiOjkZ0dLTq2NjYWPTu3RsrV67EihUrTH5NFmNa1qrsMrgDgLS0NCQlJaFPnz6IiYnB+vXrUVJSgsmTJxs8TxAEpKamYvHixQgNDUVoaCgWL16Mpk2bYvz48QAAX19fTJgwAS+//DJat26NVq1a4ZVXXkHPnj0xdOhQneXWBXB1rly5AgAICwtDixYtAADjx4/HggULkJKSgjfeeANnzpzB4sWL8be//c3ktKxmOkGzOZ+IiKQ6dOhgcUCnTim6QCnDBMR1ZRiTJrYkcxUSEgIA6NmzJy5duoT09HRVcKfJxcUFffv2Zcudk7Lb4C4xMRFXr17FwoULUVZWhoiICOzatQvBwcH1njtr1izcuXMHU6ZMwfXr19G/f3/s3btX8hfd8uXL4ebmhnHjxuHOnTt49NFHkZWVBVdXV7Pr7Ovri5ycHEydOhV9+vRBy5YtkZaWhrS0NLPLJCKixsOSzJU6URRRVVVl8Pni4mL07NnTovqSfRJETsDmECorK+Hr64s4jIGb0MTW1ZEH07Da7D3F6qiYytXmRF/9NeI95CIbFRUVsrTc1X3fvvmfR+DZ3PI2kLu3ajCv37dG12/r1q1ISkrCunXrVJmrDz74ACdOnEBwcDBmz56N0tJSbNy4EQCwevVqdOzYEd27dwdQO+9damoqpk+frhpUsWDBAkRHRyM0NBSVlZVYsWIFPv30Uxw4cAD9+vWz+DUaq+7e3ngX8PGSobw7QIuXIdt77yzstuWOiIjIluROyxqrvsxVWVmZZM47pVKJ2bNn49y5c3Bzc0OXLl3w9ttv48UXX1Qdc+PGDUyaNAnl5eXw9fVFZGQk8vPzGzSwo4bDljsHwZa7RoItd9bBljttTvTVb62WuwWHh8rWcje//zdsXQJb7hoKW+6IiIh0UABQyDAcs/4Vyxshjpa1KgZ31LDYWleLLXQNS9/9bswteo1smhRz2CotS2QpfuKIiIiInAhb7oiIiHRQiC5QyNDqJkcZTodpWaticEfW15hSsUy3OhZj3y9nT98yRauTCAFKGaIHkREINTD+JiIiIiJyImy5IyIi0oFpWStiWtaqGNyRdThzKpap18bH0HvubClbpmhVlKIApWj5d5kcZRCZgr+liIiIiJwIW+6IiIh0UMAFChnaQOQow+kwLWtVDO5IHs6chgWYiiX91D8bzpyiBRpdmpZpWXJU/I1FRERE5ETYckdERKSDEi5QytAGIkcZzkYQ5En4OHvSyFwM7oiIiHRQiAIUMqRU5SiDyBQM7sh8zvgnE/vWSQgu5r3HorJx9c1S0ff5cZa+eJwmhcghMLgjIiLSgQMqrIijZa2KwR0REZEOougCpQyrS4hcoUIbgzurYnBHpnG2VKwTpmHNTaXaax2cIsWr+TlzhjQtU7REdovBHRERkQ4KCFDI0DQkRxlEpmBwR0REpINSlKe/nDM0PsuOaVmrYnBHjY+DpmLtId1qC8a+bodK3zrzqhZEZHMM7oiIiHRQyjSgQo4yiEzB4I6IiEgHJQQoZcj7yVGG02Fa1qr45wQRERGRE2HLHdXPGaY/seN+do21L53cHLZvnjP0v3PSaVG4/Bg5KgZ3REREOrDPnRUxLWtV/MQRERERORG23JE2R03D2nHqFWD61V7oex/sIl1r6DPsKClbze8PB07TKiHT2rJsXqIGxuCOiIhIB1Gm0bIigzttTMtalX03dRARERGRSRjcUS1BuL85EsHl/mZnBBdBsjkM9Xsqx+Yg7P79csB7CsBxv1tQu/SYXBvZXkZGBvr27Qtvb2+0a9cOY8eOxenTpyXHbN++HQkJCWjTpg0EQUBxcbFRZW/btg3h4eHw8PBAeHg4duzYYYVXYDwH+5YgIiJqGHWjZeXYyPby8vIwdepUHDp0CDk5OaipqUF8fDxu376tOub27duIjY3F22+/bXS5BQUFSExMRFJSEn744QckJSVh3LhxOHz4sDVehlHY546IiIic3u7duyWPN2zYgHbt2qGwsBCDBw8GACQlJQEAzp8/b3S5mZmZGDZsGGbPng0AmD17NvLy8pCZmYnNmzfLU3kTMbgjspDdpfDsLW1naX1sNErUrkfVUoOQK6XKtKwOMg+oqKyslOz28PCAh4eHwVMrKioAAK1atbKoCgUFBXjppZck+xISEpCZmWlRuZaws98CRERE9qFubVk5NrKuoKAg+Pr6qraMjAyDx4uiiLS0NAwcOBAREREWXbu8vBx+fn6SfX5+figvL7eoXEuw5Y6IiIgc2sWLF+Hj46N6XF+r3bRp03Ds2DHs379flusLGgOGRFHU2teQ2HJHRESkgy1Hy65ZswYhISHw9PREVFQU9u3bp/fY/fv3IzY2Fq1bt4aXlxe6d++O5cuXax1nVyM6BRk3AD4+PpLNUHA3ffp07Ny5E9999x0CAwMtfin+/v5arXSXL1/Was1rSAzuGjNHnaLAxlNC2GzKDCebesRodva67WLKFEd9vx3sO8dWwd3WrVuRmpqKOXPmoKioCIMGDcLw4cNRUlKi8/hmzZph2rRpyM/Px6lTpzB37lzMnTsX69evVx1jjyM6G5ooipg2bRq2b9+Ob7/9FiEhIbKUGxMTg5ycHMm+vXv3YsCAAbKUbw5BFB14bZhGpLKyEr6+vojDGLgJTeQp1EG+YLXY+BeaTX+hk342Gnhh8wEWjrIsmSYZf/XUiPeQi2xUVFRIUnPmqvu+Hb77BTRp5m5xefduV+Prxz4wun79+/dH7969sXbtWtW+sLAwjB07tt6+ZHWeeOIJNGvWDJ9++ikAIDExEZWVlfj6669Vxzz22GNo2bJlg47orLu3FesBHy8ZyrsD+E6CUfd2ypQp2LRpE7Kzs9GtWzfVfl9fX3h51Vbm2rVrKCkpwa+//orHH38cW7ZsQbdu3eDv7w9/f38AQHJyMjp06KB6Lw4ePIjBgwfjrbfewpgxY5CdnY25c+di//796N+/v+Uv0gz8bUFERKSD3C13lZWVkq2qqkrrmtXV1SgsLER8fLxkf3x8PA4ePGhUvYuKinDw4EEMGTJEta+goECrzISEBKPLtAqZUrLGWrt2LSoqKhAXF4f27durtq1bt6qO2blzJyIjI/H4448DAJ5++mlERkZi3bp1qmNKSkpQVlamejxgwABs2bIFGzZsQK9evZCVlYWtW7faLLADOKCCHIEdtFg1WGudHbxWh2Xo3lmxdUv9s2GTVjzN1+2oLXl2SO6pUIKCgiT758+fj/T0dMm+K1euQKFQmDX6MjAwEL/99htqamqQnp6OiRMnqp6zxxGdDc2YRGVKSgpSUlIMHpObm6u176mnnsJTTz1lZs3kx+COiIioAZgyotOc0Zf79u3DrVu3cOjQIbz++ut44IEH8Mwzz1hUJjkmBndEREQ6iIAsc9TVtRfVjeQ0pE2bNnB1dTVr9GXdAIGePXvi0qVLSE9PVwV3djeiU+ZJjEmKOaDGRH2kmr3/tWaj0YCaIyGtNiLSHka6ugi23RpSA93vBvv8GK6EY4ykdYDvI1uMlnV3d0dUVJTW6MucnByTRl+Koijp02ePIzrJethyR0REZEfS0tKQlJSEPn36ICYmBuvXr0dJSQkmT54MoHbt0tLSUmzcuBEAsHr1anTs2BHdu3cHUDvv3TvvvIPp06erypw5cyYGDx6MJUuWqEZ0fvPNN7JN4kv2hcEdERGRDrZaWzYxMRFXr17FwoULUVZWhoiICOzatQvBwcEAgLKyMsmcd0qlErNnz8a5c+fg5uaGLl264O2338aLL76oOqZuROfcuXMxb948dOnSxbYjOpmWtSrOc+cgZJnnzk5THzrZcILiBrpQw1zHEFvN11fH1vPDAQ02stRmc+E50shZC34VWWueu8FfToFbM8PLWBlVv9tVyB+1Rrb6OTLVPHcfAj5NZSjvd8B3onHz3DUmbLkj+2GDgKfBV5hoCLYO2oxlbD2tGRipvycNNF1K7aUaKNhroNdHRPaFwR0REZEOtkrLElmKwR0REZEOoihAlCEwk6MMp8M+d1bF4M7ZOVI/O2cjdxrWUdKtcmuo9C1XerAt9e8qdgUnsgiDOyIiIh2UEGSZxFiOMohMYQdD9hxDRkYG+vbtC29vb7Rr1w5jx47F6dOnJceIooj09HQEBATAy8sLcXFxOHHihOSYTp06ITc3F7m5uejUqVMDvgIiIjKFLSYxbjQEGTfSwuDOSHl5eZg6dSoOHTqEnJwc1NTUID4+Hrdv31Yds3TpUixbtgyrVq3CkSNH4O/vj2HDhuHmzZs2rLkds9HqDLKvHCDn6gdWXNFBEAS73iwm972z4qoWNlm9wparoRBRg2Ja1ki7d++WPN6wYQPatWuHwsJCDB48GKIoIjMzE3PmzMETTzwBAPjkk0/g5+eHTZs2SSaTJCIi+8cBFeSo+OebmSoqKgAArVq1AgCcO3cO5eXliI+PVx3j4eGBIUOG4ODBgzapIxERmY9pWStiWtaq2HJnBlEUkZaWhoEDByIiIgIAUF5eDgDw8/OTHOvn54cLFy6oHp8/f17n/2VlzyNknWHlCTsfBStLitMG9NVblkV01O+xnY2qVf9sNuhKFvY8wTFHzhJZhMGdGaZNm4Zjx47pXHBZ8xeUKIpm/bKtrKxEZWWl6jH77RERGVZaWir53vTx8bFoSSqmZclRMbgz0fTp07Fz507k5+cjMDBQtd/f3x9AbQte+/btVfsvX76s1ZpnjNGjRyMvL8/yChMRNRLh4eGSx0OGDEFubq7Z5YkypVQZ3OnASYytisGdkURRxPTp07Fjxw7k5uYiJCRE8nxISAj8/f2Rk5ODyMhIAEB1dTXy8vKwZMkSk6+3c+dOrZY7zS8uIiK67+TJk/D29lY95kLy1FgxuDPS1KlTsWnTJmRnZ8Pb21vVx87X1xdeXl4QBAGpqalYvHgxQkNDERoaisWLF6Np06YYP368ydfTTCeoB3pUP9mnmLCzfnay96tzaaC+kErT+3YZeq1m9ceTs/8dIGvfNc3PbYP2wXMCHTp0kDWgEyFPlz++i9TQGNwZae3atQCAuLg4yf4NGzYgJSUFADBr1izcuXMHU6ZMwfXr19G/f3/s3btX8pckERE5BiUECFyhwjqYlrUqBndGMqaFQBAEpKenIz093foVIiIiItKBwZ2zsOfpLzgbfi0zUrEWp18bKt1qLGPrY2T61uLpU+RO0ToqTouiE0fLkqNicEdERKSDUhQgyBCYcRJjamh29mc9EREREVmCLXfkNOxuhGxDpWHNTb3aOpVvKMVm6DUZkbLVNZl4vTTfL3PStDKnN222egUBqP2IyjJalm+dNg6osCoGd0RERDqwzx05KqZliYiIiJwIW+6IiIh0YMudFTEta1UM7sihOWo/O6v2rbO36VP09ZEztp6aHZb01c9AXzyzpkyxdJoU9r9zeBwtS46KaVkiIiIiJ8KWOyIiIh04WtaKmJa1KgZ3jsrW01jUx1FWpZCjnrZOxRpbrq1Wq7B0VQrN16fvN6X6dcxY4aLBUrSA/a0Coc5RVqsArB411QZ3cvS5k6EyRCZwkN/ARERERGQMttwRERHpwNGyVsS0rFUxuCOHI/sIWVNZ8/qGUpgyp1/NShPLSCsNauwoWH31Vi9Psywj07RGkWMlCwtx5GzDEP/Y5CiHqCExLUtERETkRNhyR0REpAPTslbEtKxVMbgjeTjK6FjAvLqakYo1Ou1pTipWjtSrOellfffOjFGVgoFTREMpVnXq6Vb112oo5asnRat5rwyOnpWUbcZIWnsekarOkUb5WgPzsuSgHOg3MhERERHVhy13REREusiUlgXTstTA2HJHRESkQ90KFXJsplqzZg1CQkLg6emJqKgo7Nu3T++x27dvx7Bhw9C2bVv4+PggJiYGe/bskRyTlZUFQRC0trt375peOTkIMm6khcEdkYzUvzQNcnG5v0kLkG5GnKPrC1tVBxcDm+BS/+bqKt30laV5nDFlG6ibwddkpfto9ntJJLOtW7ciNTUVc+bMQVFREQYNGoThw4ejpKRE5/H5+fkYNmwYdu3ahcLCQjz88MMYNWoUioqKJMf5+PigrKxMsnl6ejbES6IGxrQsERGRDrYaLbts2TJMmDABEydOBABkZmZiz549WLt2LTIyMrSOz8zMlDxevHgxsrOz8eWXXyIyMlK1XxAE+Pv7m/4CyOGw5Y6IiEgXUZBvA1BZWSnZqqqqtC5ZXV2NwsJCxMfHS/bHx8fj4MGDRlVbqVTi5s2baNWqlWT/rVu3EBwcjMDAQIwcOVKrZa9BMS1rVQzuHI2uNJOTE1wEyWZmIfc3Y6mnCuVgTArRyHMMpgyNTb3qTbG63N8005vGbuplmJMWNnDvTU7RGrrHRqZojWbOZ8acz6bkdBl+PhyVoZ8dOxQUFARfX1/VpqsV7sqVK1AoFPDz85Ps9/PzQ3l5uVHXeffdd3H79m2MGzdOta979+7IysrCzp07sXnzZnh6eiI2NhZnzpyx7EWRXWJaloiISAdzB0PoKgcALl68CB8fH9V+Dw8PvefomnfRmP6fmzdvRnp6OrKzs9GuXTvV/ujoaERHR6sex8bGonfv3li5ciVWrFhh7EshB8HgjoiISBeZJzH28fGRBHe6tGnTBq6urlqtdJcvX9ZqzdO0detWTJgwAZ9//jmGDh1q8FgXFxf07dvXdi13cqVUHaPRtsGZlQfIyMjAxx9/rLX/448/xpIlSyyuFJEjkXVUpXqa0NhUrKF0p750q2bK1cX1/qY58tXSTb1sfalbzfStofSxUfdE/300B0fOUkNxd3dHVFQUcnJyJPtzcnIwYMAAvedt3rwZKSkp2LRpEx5//PF6ryOKIoqLi9G+fXuL60zykmN6GrO+9d5//310795da3+PHj2wbt06iytFRERka3WjZeXYTJGWloYPP/wQH3/8MU6dOoWXXnoJJSUlmDx5MgBg9uzZSE5OVh2/efNmJCcn491330V0dDTKy8tRXl6OiooK1TELFizAnj17cPbsWRQXF2PChAkoLi5WlUm2pVQq8eabb6JDhw5o3rw5zp49CwCYN28ePvroI5PLMyu4Ky8v1xntt23bFmVlZeYUSUREZH9EGTYTJSYmIjMzEwsXLsRDDz2E/Px87Nq1C8HBwQCAsrIyyZx377//PmpqajB16lS0b99etc2cOVN1zI0bNzBp0iSEhYUhPj4epaWlyM/PR79+/UyvoBw4WlZi0aJFyMrKwtKlS+Hu7q7a37NnT3z44Ycml2dWn7ugoCAcOHAAISEhkv0HDhxAQECAOUWSIzJzdF+jYSgdaGR6T28aUD09qfk+SJ4z7jjJdeROPQr3f7tJWjCUmr/11BalV6+qUrPeaseplaH+GkRDveDVX5/6cZrvl1IJ0qD+GRJ5f6xpypQpmDJlis7nsrKyJI9zc3PrLW/58uVYvny5DDUja9i4cSPWr1+PRx99VNKa2qtXL/z3v/81uTyzgruJEyciNTUV9+7dwyOPPAIA+Pe//41Zs2bh5ZdfNqdIIiIiu2KrSYyp8SktLcUDDzygtV+pVOLevXsml2dWcDdr1ixcu3YNU6ZMQXV1NQDA09MTr732GmbPnm1OkURERPZF5tGypIajZSV69OiBffv2qVLvdT7//HPJKiPGMiu4EwQBS5Yswbx583Dq1Cl4eXkhNDTU4Jw9RERERKRt/vz5SEpKQmlpKZRKJbZv347Tp09j48aN+Oqrr0wuz6J57srLy3Ht2jUMHjwYHh4eRk+ySFQfi2faN7c/oBHXNfszrrf/nJF11dfPTrPOevrZCa46VsbQVQc5+t+p92VT+7+g3o9NkDZniAr1R3r63wHSPnh6+t9pUX99kjro6X9ngK7JZXVf01D/Qn2Fa7xYM/q1qf/siMZel/Rg8xI1jFGjRmHr1q1YvHgxBEHA3/72N/Tu3Rtffvklhg0bZnJ5ZgV3V69exbhx4/Ddd99BEAScOXMGnTt3xsSJE9GiRQu8++675hRLRERkP5iWpQaUkJCAhIQEWcoyq3njpZdeQpMmTVBSUoKmTZuq9icmJmL37t2yVIyIiIiITGdWy93evXuxZ88eBAYGSvaHhobiwoULslSMyCFZuBqCztUnVE/qScVqnqMvFat5nKur2v+NTMvqS9Nqpib1pGWhUDtfIcnDSuqqN0UL6J8mRS1FK2icYnBqFH30pXKp8WDLnfUw442WLVsa3c3n2rVrJpVtVnB3+/ZtSYtdnStXrnBQBREROQdRqN3kKIdIQ2Zmpur/V69exaJFi5CQkICYmBgAQEFBAfbs2YN58+aZXLZZwd3gwYOxceNGvPnmmwBqWxuUSiX+/ve/4+GHHzanSCIiIqJG49lnn1X9/8knn8TChQsxbdo01b4ZM2Zg1apV+Oabb/DSSy+ZVLZZwd3f//53xMXF4ejRo6iursasWbNw4sQJXLt2DQcOHDCnSCK7JvsocEsXszew8oTeVKx6GhYA3NQeq9VHVD9fs576RhNrjspUS2MKCj2jUzWppWn1p2gBaZrW9ulWo1fGIIcjikYPoq63HNKBDZoqe/bswZIlS7T2JyQk4PXXXze5PLN+w4SHh+PYsWPo168fhg0bhtu3b+OJJ55AUVERunTpYk6RRERE9kWOdWXl6rdHTq1169bYsWOH1v4vvvgCrVu3Nrk8s+e58/f3x4IFC8w9nYiIiIgALFiwABMmTEBubq6qz92hQ4ewe/dufPjhhyaXZ3Rwd+zYMaML7dWrl8kVISIisiscUGE9Nhgtm5GRge3bt+O///0vvLy8MGDAACxZsgTdunVTHSOKIhYsWID169fj+vXr6N+/P1avXo0ePXroLTcrKwvPPfec1v47d+7A09PTqLqlpKQgLCwMK1aswPbt2yGKIsLDw3HgwAH079/f+Bf5B6ODu4ceegiCIGitQlHXx0R9n0Kh1UmGyD5ZuhKGIUb205P059NabcLAShR6z9HTz85N2udOVH+s5zjRTdpzQ9TTV1DQ6Lsm1Nx/LNaofR+o96vTWZL2cVqvT/3rRbIKhJ6VKyCdGkVvvzjN90vOjlKar4ErRzgEQdRaSMXscsj28vLyMHXqVPTt2xc1NTWYM2cO4uPjcfLkSTRr1gwAsHTpUixbtgxZWVno2rUrFi1ahGHDhuH06dPw9vbWW7aPjw9Onz4t2WdsYFenf//++Oyzz0x/YToYHdydO3dO9f+ioiK88sorePXVVyVDdt99910sXbpUlooRERERyUVzkYUNGzagXbt2KCwsxODBgyGKIjIzMzFnzhw88cQTAIBPPvkEfn5+2LRpE1588UW9ZQuCAH9/f7PrVlJSYvD5jh07mlSe0cFdcHCw6v9//vOfsWLFCowYMUK1r1evXggKCsK8efMwduxYkypBRERkdziJsfXInJatrKyU7Pbw8Kh33t2KigoAQKtWrQDUNmKVl5cjPj5eUs6QIUNw8OBBg8HdrVu3EBwcDIVCgYceeghvvvkmIiMjjX4ZnTp1Mjgrg6kZUbMGVBw/fhwhISFa+0NCQnDy5ElziiRyXJZOa2IO9VUotFa1UKuPoWlN1FKxosf9rwLR/f7/lR7Srwhlk/tl/ClgP65W+yD/Si+43JOmQV2qau7Xr/p+/YQq9cI0fuO56l7VQtBIj4rqqWrteVKsg6tVNE7sc+cwgoKCJI/nz5+P9PR0vceLooi0tDQMHDgQERERAIDy8nIAgJ+fn+RYPz8/g6tvde/eHVlZWejZsycqKyvx3nvvITY2Fj/88ANCQ0ONqn9RUZHk8b1791BUVIRly5bhrbfeMqoMdWYFd2FhYVi0aBE++ugjVU65qqoKixYtQlhYmDlFEpEDeaRtEaY8sAuiCDxR8AB+v2da3xIiIjldvHgRPj4+qsf1tdpNmzYNx44dw/79+7We0/yDWXOsgabo6GhER0erHsfGxqJ3795YuXIlVqxYYVT9H3zwQa19ffr0QUBAAP7+97+r0sTGMiu4W7duHUaNGoWgoCBVhX744QcIgoCvvvrKnCKJyIEkB/8bQO0YhNHtD2HL2TjbVojIGpiWtR6Z07I+Pj6S4M6Q6dOnY+fOncjPz0dgYKBqf12fufLycrRv3161//Lly1qteYa4uLigb9++OHPmjNHn6NO1a1ccOXLE5PPMCu769euHc+fO4R//+Af++9//QhRFJCYmYvz48aoRJ+SkBBukII1lz3UD5F2VQn30peZflILu5yQrTwDSUbFqqdia5u6q/99rLv2KqGlaW4af1w2cvhuArh6/IqjVb6i67i45rsmt+9dyu6VWHcX933Ki5ghbpZ6VLLTSzmqPJeku269WITtJCtrO6mfPdZMLgzunIooipk+fjh07diA3N1ere1lISAj8/f2Rk5Oj6i9XXV2NvLw8natHGLpOcXExevbsafQ5mn0GRVFEWVkZ0tPTjU7tqjN7EuOmTZti0qRJ5p5ORA7qAfdSuAlKHL3VFQ94lKF1k5u2rhIRUb2mTp2KTZs2ITs7G97e3qo+dr6+vvDy8oIgCEhNTcXixYsRGhqK0NBQLF68GE2bNsX48eNV5SQnJ6NDhw7IyMgAUDsBcXR0NEJDQ1FZWYkVK1aguLgYq1evNrpuLVq00JkODgoKwpYtW0x+rWYHd7qUlZXh3r17Jg/ZJSLH0d3rFwDAibv8OScnx5Y7p7J27VoAQFxcnGT/hg0bkJKSAgCYNWsW7ty5gylTpqgmMd67d69kjruSkhK4qLX637hxA5MmTUJ5eTl8fX0RGRmJ/Px89OvXz+i6fffdd5LHLi4uaNu2LR544AG4uZkeqska3D3yyCP46aefOIkxmUWw5oTCjsqce6IvpamRFlafoFh9VKx6Kva2v3Ti41tBAtoorwAi8H1QewiiiMqm7lrHNStXu6zaSFrhntokxjUaaWJDqVhjqN8rfgUBkP5MiZw42XQcLWs9NlihQu8E5urFCQLS09MNjrTNzc2VPF6+fDmWL19ufEX0XHfAgAFagVxNTQ3y8/MxePBgk8qTNbjbuHEjfv/9dzmLJCI700K8DQC4DF8IAG6A/WyJiCzx8MMPo6ysDO3atZPsr6iowMMPP2xyo5msPdD79u2LIUOGyFmk3VmzZg1CQkLg6emJqKgo7Nu3T/WcKIpIT09HQEAAvLy8EBcXhxMnTkjO79SpE3Jzc5Gbm4tOnTo1cO2JLNcMdyECCMZVCABKhVa2rhKRVdQtPybHRmSIvulWrl69atZAVVlb7pzd1q1bkZqaijVr1iA2Nhbvv/8+hg8fjpMnT6Jjx45mr0lH5EjEP/4m7IOfAQD/RYAtq0NkPexzZz02SMvao7r56wRBQEpKimR+PoVCgWPHjmHAgAEml2tWcNeyZUuDE/qpu3btmjmXsEvLli3DhAkTMHHiRABAZmYm9uzZg7Vr12Lx4sVmr0lHpCL3dC76pk8BIKr1wVNfeaJuuhOgto+duv++sAbiwSvAMWBOm6+B34AVE/YhbIN0Ak6PyvtlqE+Lot4JWauPpTn97PTRuo/shEdE9sfX1xdAbcudt7c3vLy8VM+5u7sjOjoaL7zwgsnlmhXczZs3D4sWLUJCQgJiYmIAAAUFBdizZw/mzZunWqfNmVRXV6OwsBCvv/66ZH98fDwOHjxo0Zp0RA6lzR9z2v1WBXi5QnCz8/kFiYjs1IYNGwDUdtl65ZVXZJsr2Kzg7sCBA1i4cCGmTZum2jdjxgysWrUK33zzDb744gtZKmdPrly5AoVCoXPNufLycqPXpDt//rzO/xM5jC7Nge8u16aaHmxh69oQWY0AefrLOXjm0DqYlpWYP3++rOWZFdzt2bNH52zNCQkJWi1bzqa+NedMXZNOn8rKSsmM1TdvcqJYsg+CqwvEx9sDV6ohPNTS1tUhUiktLZV8b5qyJBVRQ+vduzf+/e9/o2XLloiMjDQYK3z//fcmlW1WcNe6dWvs2LEDr776qmT/F198gdatW5tTpN1r06YNXF1dVS10derWnJNrTbo6o0ePRl5enmWVJrISIbAZEMgpUMi+hIeHSx4PGTJEa04yk3CeO7KiMWPGqAZQjB07VtayzQruFixYgAkTJiA3N1fV5+7QoUPYvXs3PvzwQ1kraC/c3d0RFRWFnJwc/OlPf1Ltz8nJwZgxY2Rbk67Ozp07tVruNL+4iIjovpMnT0pmJrC41Y6jZa1HgDyDqBx4nhn1VKxdpGVTUlIQFhaGFStWYPv27RBFEeHh4Thw4AD69+8vawXtSVpaGpKSktCnTx/ExMRg/fr1KCkpweTJk41ek85YmukEzUWFyUlpLcDuqvMw48tT++LTWKFAUN6/lvoqEm6/3/9/84vSL9/uH0zReZnmF6Vlq5chWaFC7Zqa9YERs8cbzVkXsieDOnTowDQsObTq6mpcvnwZSqX0O8zUZV3Nnueuf//++Oyzz8w93SElJibi6tWrWLhwIcrKyhAREYFdu3YhODgYgHFr0hERkYNgy531cECFxE8//YQJEybg4MGDkv11/fZNXaHC7ODu559/xoYNG3D27FlkZmaiXbt22L17N4KCgtCjRw9zi7V7U6ZMwZQpulsvjFmTjoiIHINcq0s4cOaQGshzzz0HNzc3fPXVV2jfvr1ZAzHVmRXc5eXlYfjw4YiNjUV+fj4WLVqEdu3a4dixY/jwww/xz3/+06JKERERETUWxcXFKCwsRPfu3WUpz6zZR19//XUsWrQIOTk5cHd3V+1/+OGHUVBQIEvFqPERlaJqoz8oxfubsURR96ZUSjah5v7mUlWj2prcur81K1dIttYnlDo3zePUy1AvW/2amvXRW29r3isnx58pC4kybiYytI65pu3bt2PYsGFo27YtfHx8EBMTgz179mgdt23bNoSHh8PDwwPh4eHYsWOH6RWTiyDItzmB8PBwXLlyRbbyzArujh8/LhkxWqdt27a4evWqxZUiIiKyORsFd3XrmM+ZMwdFRUUYNGgQhg8fjpKSEp3H5+fnY9iwYdi1axcKCwvx8MMPY9SoUSgqKlIdU1BQgMTERCQlJeGHH35AUlISxo0bh8OHD5tWObkIMm5OYMmSJZg1axZyc3Nx9epV1Vy3mnPeGsustGyLFi1QVlaGkJAQyf6ioiJ06NDBnCKJiIgIhtcxz8jI0Do+MzNT8njx4sXIzs7Gl19+qZqaKzMzE8OGDcPs2bMBALNnz0ZeXh4yMzOxefNm674gqtfQoUMBAI8++qhkf4MOqBg/fjxee+01fP755xAEAUqlEgcOHMArr7yC5ORkc4okR6E+xYTci9xbyp7rBtSmHuu4mFE/fdOaaPbWVj9O7f+CQjq0Xqy5/2UhVN//89ftllo170nPaXJLd701j3OpqlEr+/7/oX5Njfroq7dWalZp4DlTKe18yhR7ntLFnusmE7kHVGi2wHh4eKgmsa1T3zrmxlAqlbh586ZknfeCggK89NJLkuMSEhK0AsOGI2ezm+N3O/juu+9kLc+s4O6tt95CSkoKOnTooJrjTqFQYPz48Zg7d66sFSQiIrIJmVeoCAoKkuyeP3++1uwK9a1jbox3330Xt2/fxrhx41T7ysvLLSpTdpwKRWLIkCGylmdWcNekSRN89tlnePPNN/H9999DqVQiMjISoaGhslaOiIjIWVy8eFEyybJmq506c9cp37x5M9LT05GdnY127drJUiZZ37Fjx3TuFwQBnp6e6Nixo8HPiyaz57kDgM6dO6Nz586WFEHk+CxNt5pDLSUmarQsSFaBUKg9p/klrtaHQ6hSO0yhlsq9J+3n4aLn9Qka6U2hRu2xWipW/ZpaKVH1NK1S/fVppp1tkA609/QtWYfMkxhrrjykS33rmBuydetWTJgwAZ9//rmqD1cdf39/s8q0GrbcSTz00EMGA+0mTZogMTER77//Pjw9PestT9bfRNnZ2di4caOcRRIREdlEXZ87OTZjqa9jri4nJwcDBgzQe97mzZuRkpKCTZs24fHHH9d6PiYmRqvMvXv3GizTujhcVt2OHTsQGhqK9evXo7i4GEVFRVi/fj26deuGTZs24aOPPsK3335rdNc3i1ruNL322ms4c+YMB1UQERGZydA65kDtSNfS0lJVY8rmzZuRnJyM9957D9HR0aoWOi8vL/j6+gIAZs6cicGDB2PJkiUYM2YMsrOz8c0332D//v22eZEk8dZbb+G9995DQkKCal+vXr0QGBiIefPm4T//+Q+aNWuGl19+Ge+880695cka3P33v/+Vszgi69Oc3NVFxr8CNdOJeprc1dOOgmb2z0U9VanW0O6qVpbma1BvJjAwfF5SG7UyRLUUpFAjbdwX9N0fzTqol6En3SpJ12rWVd/IYEPXVU/XapyjldrVxdKRt4ZwEmHHZKO1Zetbx7ysrEwy593777+PmpoaTJ06FVOnTlXtf/bZZ5GVlQUAGDBgALZs2YK5c+di3rx56NKlC7Zu3Yr+/ftb/PLMwrSsxPHjx1Xvr7rg4GAcP34cQG3qtqyszKjyZA3uiIiInIZMU6GYEyAaWse8LmCrk5uba1SZTz31FJ566inTK2MNcq0u4STBXffu3fH2229j/fr1qpW/7t27h7ffflu1JFlpaanRfSTNCu52796N5s2bY+DAgQCA1atX44MPPkB4eDhWr16Nli1bmlMsERERUaOzevVqjB49GoGBgejVqxcEQcCxY8egUCjw1VdfAQDOnj2rN+DXZNaAildffVU1GePx48fx8ssvY8SIETh79izS0tLMKZKIiMi+2HBtWWpcBgwYgPPnz2PhwoXo1asXIiIisHDhQpw7dw7R0dEAgKSkJLz66qtGlWdWy925c+cQHh4OoHYh4pEjR2Lx4sX4/vvvMWLECHOKJLJrkn5xcqQS5FytAhorT6h1XRNc1co2tHyNq3q/P/WVPjReq77XrjVdiZ5VJNT732nWR+04Uf04zalP7GxVCqP685FjslGfu0aBaVktzZs3Vw2asZRZwZ27uzt+//13AMA333yjGh3bqlUrsxa4JSIiImrsTp48iZKSElRXV0v2jx492qRyzAruBg4ciLS0NMTGxuI///kPtm7dCgD46aefEBgYaE6RREREdkXutWVJDUfLSpw9exZ/+tOfcPz4cQiCoMoI1GWKFIYyLzqY1edu1apVcHNzwz//+U+sXbsWHTp0AAB8/fXXeOyxx8wpksg5KJX3NzOIoijZoFTbROX9TbJfc7t/nKi4v2kdp1Dc32qM3O7V6N6MPV/9mhr1kdZVfdOotxH3ROs+2uC9JCIy1syZMxESEoJLly6hadOmOHHiBPLz89GnTx+jR0OrM6vlrmPHjqrRG+qWL19uTnFEREREjVZBQQG+/fZbtG3bFi4uLnBxccHAgQORkZGBGTNmoKioyKTyzJ7nTqFQ4IsvvsCpU6cgCALCwsIwZswYuLq6mlskERGR/eCACuvhgAoJhUKB5s2bA6hdX/jXX39Ft27dEBwcjNOnT5tcnlnB3f/+9z+MGDECpaWl6NatG0RRxE8//YSgoCD861//QpcuXcwplkhFVJvRX++qCIYLkD4WjOyBoL6SgJ7raqb5jB49q36e+jnGjpyV1E3PyhWARmeL+8eJml021F6foK9uclAfBWto5Qn198zY44xd+UFfatWMlK3RaV5zVqXQ/NyaQeRqGLJhnzsrc5LATA4RERE4duwYOnfujP79+2Pp0qVwd3fH+vXr0blzZ5PLM6vP3YwZM9ClSxdcvHgR33//PYqKilBSUoKQkBDMmDHDnCKJiIiIGqW5c+dC+ccfoYsWLcKFCxcwaNAg7Nq1C++9957J5ZnVcpeXl4dDhw6hVatWqn2tW7fG22+/jdjYWHOKJCIisj9sdbMSuYbLOoeEhATV/zt37oyTJ0/i2rVraNmypVlzq5oV3Hl4eODmzZta+2/duqVaE42IiMihsc+d9XAqFADA888/b9RxH3/8sUnlmhXcjRw5EpMmTcJHH32Efv36AQAOHz6MyZMnmzzRHjkw9f5BxvZpa0w0+3mp96czso+b3pUx9PW/A6R98PT0vwMAqPXBE9XfP3P6OBqiXldDfcr09bPTPEdPnzKj+8LpO45TntRPhj6BRHRfVlYWgoODERkZKetqN2YFdytWrMCzzz6LmJgYNGnSBABw7949jBkzxqzcMBERkb3hgAorYssdAGDy5MnYsmULzp49i+effx5//etfJV3ezGVWc0uLFi2QnZ2Nn376CZ9//jk+//xz/PTTT9ixYwd8fX0trhQREZHNiTJuJFU3FYocmwNbs2YNysrK8Nprr+HLL79EUFAQxo0bhz179ljUkmf2PHcfffQRli9fjjNnzgAAQkNDkZqaiokTJ5pdGSJHpDd1ag4DqVyjUrSAgWlSNI9TK0OU5GiNrKyR9KZBDXxxGTndid4vP5lTrHKmS4iI1Hl4eOCZZ57BM888gwsXLiArKwtTpkzBvXv3cPLkSdX8d6YwK7ibN28eli9fjunTpyMmJgZA7ezKL730Es6fP49FixaZUywREZHdYFqWGpogCKq1ZZUW/JFqVnC3du1afPDBB3jmmWdU+0aPHo1evXph+vTpDO6IiMjxcbSs9XCFCpWqqips374dH3/8Mfbv34+RI0di1apVeOyxx+BiaGJ7A8wK7hQKBfr06aO1PyoqCjU1NWZVhIwk/vFt4+D9DEyhOeO+xStWyLhahUn0rURhaOSsnnMMpoINjaSVHKfvPsjwuo1ZJcHQyEu5U7ENNULWBqtSNOoVKereV6bNyUFNmTIFW7ZsQceOHfHcc89hy5YtaN26tcXlmhXc/fWvf8XatWuxbNkyyf7169fjL3/5i8WVIiIisjm23FkPR8sCANatW4eOHTsiJCQEeXl5yMvL03nc9u3bTSrXogEVe/fuRXR0NADg0KFDuHjxIpKTk5GWlqY6TjMAJCIicgTsc0fWlpycbPlAPB3MCu5+/PFH9O7dGwDw888/AwDatm2Ltm3b4scff1QdZ40KE9kzo0fOGpOirS2k3nMMjeQUDGX8DKVs6yg0HutLaZuTWjQn9apVhp7rGjrfyFQsR8gSkbVlZWVZpVyzgrvvvvtO7noQERHZF6ZlrYcDKqzK7LQsERGRU2NwZz3sc2dVXBCUiIiIyImw5Y7kodnnytjpRmyhgaZF0eyzpbcPnr7+d7WFqBeg+xxNcvTH00uzE575LO5Xp12gRWWY3cfOBtOfNBhHqaeVcECFNcnVdEe6MLgjIiLShWlZ62Fa1qrsuHmFiIiIiEzFljtyOOoz8pu1WoWlNNNwctZBM31oaJqUOoZWtdBXFuxwqg850q+mlmUOO1gRolGvStGAmJa1IrbcWRWDOyIiIl2YlrUi9rmzJqZliYiIiJwIW+4claGVDOyBOSNSbUGOUb5GjqQ1evUKSdkGRtLeL1j62JhRuYbou465LE2Ryj2qVlK0sWVb2PTiSKNO7bmuDd2VgC131sO0rFUxuCMiItKB8YcVcYUKq7LjJhUiIiIiMhVb7sihyT5y1tJ0shkpWnUG07VGjoI1OnVlafrWUmZPGmzF9KvkOvaViuUIWRtgWpYcFFvuiIiIdKibCkWOzVRr1qxBSEgIPD09ERUVhX379uk9tqysDOPHj0e3bt3g4uKC1NRUrWOysrIgCILWdvfuXdMrJwdBxo20MLgjIiKyI1u3bkVqairmzJmDoqIiDBo0CMOHD0dJSYnO46uqqtC2bVvMmTMHDz74oN5yfXx8UFZWJtk8PT2t9TLIhhjcERER6SLKuJlg2bJlmDBhAiZOnIiwsDBkZmYiKCgIa9eu1Xl8p06d8N577yE5ORm+vr56yxUEAf7+/pLNZuoGVMixkRYGd+Q0RKWo2mQq8P5mDqUo3Yy5pChKNuOuo9S/Gb6YbTdrvCaL7qPp75f2hS38zGgVJ/NnmkwnY2BXWVkp2aqqqrQuV11djcLCQsTHx0v2x8fH4+DBgxa9lFu3biE4OBiBgYEYOXIkioqKLCqP7BeDOyIiogYQFBQEX19f1ZaRkaF1zJUrV6BQKODn5yfZ7+fnh/LycrOv3b17d2RlZWHnzp3YvHkzPD09ERsbizNnzphdJtkvjpYlIiLSQe61ZS9evAgfHx/Vfg8PD/3naKQbRVE0fvJzHaKjoxEdHa16HBsbi969e2PlypVYsWKF2eWajfPcWRVb7pyFsekuW5A5VeWwzEj5aaYXTUozAobTmyamOmUhc30svz8WpmGdhT3/jNryu03mPnc+Pj6STVdw16ZNG7i6umq10l2+fFmrNc8SLi4u6Nu3r+1a7mwwWjYjIwN9+/aFt7c32rVrh7Fjx+L06dOSY0RRRHp6OgICAuDl5YW4uDicOHGi3rK3bduG8PBweHh4IDw8HDt27DC+YlZgl8GdMTf39OnTiI2NRWBgIBYuXCh5rqqqCtOnT0ebNm3QrFkzjB49Gr/88ovkmOvXryMpKUnVPJ6UlIQbN26onj9//rzkr6Tc3FyMGTMG7du3R7NmzfDQQw/hs88+06p7Xl4eoqKi4Onpic6dO2PdunWS59PT05GSkgKgthNsbm6uGXeIiIickbu7O6KiopCTkyPZn5OTgwEDBsh2HVEUUVxcjPbt28tWpr3Ly8vD1KlTcejQIeTk5KCmpgbx8fG4ffu26pilS5di2bJlWLVqFY4cOQJ/f38MGzYMN2/e1FtuQUEBEhMTkZSUhB9++AFJSUkYN24cDh8+3BAvSye7DO6MublTp05FUlISsrOz8eWXX+LAgQOq51JTU7Fjxw5s2bIF+/fvx61btzBy5EgoFArVMePHj0dxcTF2796N3bt3o7i4GElJSXrrdPDgQfTq1Qvbtm3DsWPH8PzzzyM5ORlffvml6phz585hxIgRGDRoEIqKivDGG29gxowZ2LZtm8x3iIiIrM1W89ylpaXhww8/xMcff4xTp07hpZdeQklJCSZPngwAmD17NpKTkyXnFBcXo7i4GLdu3cJvv/2G4uJinDx5UvX8ggULsGfPHpw9exbFxcWYMGECiouLVWU2vIZvutu9ezdSUlLQo0cPPPjgg9iwYQNKSkpQWFgIoDbgzczMxJw5c/DEE08gIiICn3zyCX7//Xds2rRJb7mZmZkYNmwYZs+eje7du2P27Nl49NFHkZmZadotkZHd9bnTvLkA8Mknn8DPzw+bNm3Ciy++CAC4ceMGIiMj0atXLwQEBKCiogIAUFFRgY8++giffvophg4dCgD4xz/+gaCgIHzzzTdISEjAqVOnsHv3bhw6dAj9+/cHAHzwwQeIiYnB6dOn0a1bN616vfHGG5LHM2bMwJ49e7Bjxw6MGjUKALBu3Tp07NhR9YaGhYXh6NGjeOedd/Dkk0/Kf7NIL83RhRavXmHpyhWajFzJQm91DKSozOqX05CpWROZtbqEIXKnYGVMZXJUrJ0xYxoTveWYIDExEVevXsXChQtRVlaGiIgI7Nq1C8HBwQBqJy3WnPMuMjJS9f/CwkJs2rQJwcHBOH/+PIDa35mTJk1CeXk5fH19ERkZifz8fPTr18+il2Y2mRfurayslOz28PAw2KcRgCpuaNWqFYDaBpry8nLJSGUPDw8MGTIEBw8eVMUfmgoKCvDSSy9J9iUkJNg0uLO7lrv6bm6dhQsXYtiwYWjatClcXFyQkJAAoPZDfe/ePcn5AQEBiIiIUJ1fUFAAX19fVWAH1HY29fX1NWmoeUVFhepDUVeu5vD1hIQEHD16FPfu3TO6XCJbc20CtAl2RWBEE7Tr7AZffxe42t2fgkTOa8qUKTh//jyqqqpQWFiIwYMHq57LysrS6tKjq+9pXWAHAMuXL8eFCxdQVVWFy5cvY8+ePYiJiWmgV2N9xoxEVieKItLS0jBw4EBEREQAgKqfo6kjlcvLy2Uf3Wwpu/u6NnRzL1y4oHo8YsQI/Pbbb6isrETbtm0l57u7u6Nly5Za59eVXV5ejnbt2mldu127dqpjOnXqZLDF4J///CeOHDmC999/X3JtXfWuqanBlStX0L59e6Snp6ueU//BI7KVZi1d8OBwL0QM80SbTm5oHeQKX39XuGi0KCqVIm7+pkT5mXv4b14VTn53F2ePVEHBv1vISck9WpbUyNxyZ8pIZACYNm0ajh07hv3792sXacZIZblHN1vK5sHdZ599Jmnq/Ne//gXAuBvl4eEhCewM0Txf10039s3Izc1FSkoKPvjgA/To0UPynK5667ueIXWTXNYx1JmTyBwdwptg+Es+6PfnpnBzF3D2SBV+/e89nPj3XVz7pQbXLipwp1KJJp4CPJsL8GnnihYBrujYyx1Dp3hjzBxf3L2lxE8HqvDd+pv44WsbrVFJ9IfS0lLJ92bdqFSz2Sgt2zjIuzCsKe/19OnTsXPnTuTn5yMwMFC1v27FjvLycslAk/pGKvv7+1t9dLOpbB7cjR49WpIerZux29SbW8ff3x/V1dW4fv26pPXu8uXLqpFG/v7+uHTpkta5v/32W73XyMvLw6hRo7Bs2TKtDq363mA3Nze0bt263rqrGz16NPLy8kw6R0W9xdHelmaRu++a0Ze9f09k7X9XW6Bl5VnY/06TvhZn9T8weo/2wqQNrVFxSYlt82/g8P/9jhtlCp3n6SzLBej4YBOEDfFE7zFNMXNbO1worsaml6/jTIH2rPuW1FsWcvZlk3m6EJv1s7PHaU/qmPlZCA8PlzweMmQIZyQgFVEUMX36dOzYsQO5ubkICQmRPB8SEgJ/f3/k5OSo+jBWV1cjLy8PS5Ys0VtuTEwMcnJyJP3u9u7dK+voZlPZPLjz9vaGt7e36rEoimbd3DpRUVFo0qQJcnJyMG7cOAC1nU9//PFHLF26FEDtG1FRUYH//Oc/qs6khw8fRkVFhcE3Izc3FyNHjsSSJUswadIkredjYmIko2eB2je4T58+aNKkSb11V7dz506tljvNLy4iczw4wgtTNrXB0e2/48MXrqLGjFhMVAIXiu7hQtE97M68ia4DPTDurRaY/W8/fLmkAjsWVMhfcaJ6nDx5UvL7xKJWO4Atd9bWwG0PU6dOxaZNm5CdnQ1vb29VY4yvry+8vLwgCAJSU1OxePFihIaGIjQ0FIsXL0bTpk0xfvx4VTnJycno0KGDql/fzJkzMXjwYCxZsgRjxoxBdnY2vvnmG50p34Zi8+BOk7E3Vx9fX19MmDABL7/8Mlq3bo1WrVrhlVdeQc+ePVWjZ8PCwvDYY4/hhRdeUPWZmzRpEkaOHKlzpCxQG9g9/vjjmDlzJp588knVh8Ld3V01qGLy5MlYtWoV0tLS8MILL6CgoAAfffQRNm/ebPJ90Gxi1hwJRGSuJ9N9cfLbu3j/2auyzQv70/4qvBV3CSNe8cGTC1rgRpkC362/JU/hREbq0KGD5QGdGva5syIBMq1QYfzNXbt2LQAgLi5Osn/Dhg2q+WdnzZqFO3fuYMqUKbh+/Tr69++PvXv3Sv5oKCkpgYvL/YzNgAEDsGXLFsydOxfz5s1Dly5dsHXrVklWsqEJolVzIeYRRRELFizA+++/r7q5q1evVo1oqc/du3fx6quvYtOmTbhz5w4effRRrFmzBkFBQapjrl27hhkzZmDnzp0AatOgq1atQosWLXSWmZKSgk8++URrv2azf15eHl566SWcOHECAQEBeO2112SZR6iyshK+vr6Iwxi4CSa0AtpbWtaQBkzT3r+kFe+P3K9HhroKLsDHt4ORNfUq8j62TvA1/p2WeORFb6Q98AsqLzXk6hf2O8WJdtG2WG3BjtOwmkz8tVQj3kMuslFRUSFLcFf3ffvgs4vh6u5pcXmK6rv44ZM3ZKufI6u7txVFLeHjbfl3ZOVNJXwjr/PearDL4I60Mbiz1iUbV3AHAEtOBODnw1VY//xVWcrT1LSFC1aWBiJryjXs+6QBW+8Y3NV30Ya/prnsJbhLljG428jgDmBw11Dsbp47IrKuvStvIuaZ5hiU3Mwq5bu5Ay4uAifkJYcniKJsG2mwwdqyjYnd9bkjmdnzyFlnZ81RtYbU08L373U3EdijCZ5d3RptOrnhq6WVuHdXnl8+bu5A8orW+L1CiaJ/3ZGlTNlb5PRxpJYtZ8QAiEg2DO6IGqFPU6+h4rICI172xcDk5tidWYn9G2/hTqX5v2ADI5ogKbMVOvV2x/spV3D7GoMlcnAcLWs9giDTgAo2WujC4I6oEVIqgC/erEDBptsY9bovEjNaIjGjJc5/X42T393Fqdy7+N+hKoMtep7NBbTu6IbwRzzR509N0XWAJ65erMHS4Zfw8+HqBnw1RNbB0bLkqBjckf2wwQTHmv3CrDrAoqFenwnp20s/1+DDF65iW/oN9Iz3QvjDnhjyXHOMes23drmxy0rcKKvB7xUiqn5XQhCAlh1qlyhr1tIVAHCvSsSJf9/Bmr/+hu+zf4eiRuZ6WlMDpWI5UTERNSQGd0SE66UK5G+4hfwNtyAItUuTde7rgRbtXdGivSu8fFzg3lSAIAD/K6jC4c9rcO1iDa7+osDFY9W4e9MOAjUiuTEtaz1My1oVgzsikhBF4JcT9/DLiXu2rgqRTTEta0VyjXRlbKcTp0IhIiIiciJsuWtMNKcasOfmbBv0v6u9rO4/sWXvi6evL1RDTuRsD33eGoqz962TVsLWNTCOI0x9wrQsOSgGd0RERDowLWtF7HNnVUzLEhERETkRttyR/ZN7pQezqnD/T+8Gmy5Fkw1et0OxUTrS5qlYR0nDOiKmZa2HAyqsisEdERGRHkypWgujO2tiUwARERGRE2HLXWOmPlrNkTql2mgk7f3LN+CqFtILG3ecs6Vv7SztaPM0bG0lbF0D8zjCCFl1oihPnR3tdTcENtxZFYM7IiIiHTha1ooY3FmVk/2JT0RERNS4seWOiIhIF46WtSI23VkTgzsiCzXYqhbGsrQ/ltx99hy0f5hd9K0jmxKUtZsc5ZAGxnZWxbQsERERkRNhyx0REZEuTMtaD5cfsyoGd1SL06LIzmZTpljKQdOolrL7NKyjvi8OPA0IR8uSo7Kv34ZEREREZBG23BEREenCSYythwMqrIrBHWnT/CJylDStobSVHaRs7W5UbSNl1+lXR029qnOiQIZpWStinzursv1vPCIiIiKSDVvuiIiIdOFoWStiXtaaGNxR/Rx1JK06BxpVqw/Tt4bZdbrVEKZi7RbTstYjCi4QZfguFvm1qJN9/ZYjIiIirFmzBiEhIfD09ERUVBT27dun99iysjKMHz8e3bp1g4uLC1JTU3Uet23bNoSHh8PDwwPh4eHYsWOHlWpPtsbgjoiISJe60bJybCbYunUrUlNTMWfOHBQVFWHQoEEYPnw4SkpKdB5fVVWFtm3bYs6cOXjwwQd1HlNQUIDExEQkJSXhhx9+QFJSEsaNG4fDhw+bfFvkIci4kSYGd0RERDrUpWXl2EyxbNkyTJgwARMnTkRYWBgyMzMRFBSEtWvX6jy+U6dOeO+995CcnAxfX1+dx2RmZmLYsGGYPXs2unfvjtmzZ+PRRx9FZmamiXdFHiJcZNtIG+8KNT6i8v7mQESlaNTmbJzydTvoZ5Csr7q6GoWFhYiPj5fsj4+Px8GDB80ut6CgQKvMhIQEi8ok+8UBFURERLrIPFq2srJSstvDwwMeHh6SfVeuXIFCoYCfn59kv5+fH8rLy82uQnl5uexlWoTz3FkVW+6IiIh0kDstGxQUBF9fX9WWkZGh/9oaQYsoilr7TH49VijTfC4ybqSJLXdkGmeYFkWdZlrMzqZJMYecKUpzp19xuDSptTlj+tVJpz+xposXL8LHx0f1WLPVDgDatGkDV1dXrRa1y5cva7W8mcLf31/2Msl+Of5vMiIiImtQivJtAHx8fCSbruDO3d0dUVFRyMnJkezPycnBgAEDzH4pMTExWmXu3bvXojItIUKQbSNtbLkjIiLSxUYrVKSlpSEpKQl9+vRBTEwM1q9fj5KSEkyePBkAMHv2bJSWlmLjxo2qc4qLiwEAt27dwm+//Ybi4mK4u7sjPDwcADBz5kwMHjwYS5YswZgxY5CdnY1vvvkG+/fvl+EFmkEQ5MmUcIZonRjckfmcLUUL6E+fOUG61hxMr5rIGdOv6piKbRCJiYm4evUqFi5ciLKyMkRERGDXrl0IDg4GUDtpseacd5GRkar/FxYWYtOmTQgODsb58+cBAAMGDMCWLVswd+5czJs3D126dMHWrVvRv3//Bntd1HAY3BEREekgQKblx8w4Z8qUKZgyZYrO57KysrT2iUYE3k899RSeeuopM2ojP7lSqkzL6sbgjoiISBczVpfQWw5JCS5My1pR48w1ERERETkpttyRPDT/MnWWPnh11PtSNdL+d6SHM/eza+QtTuYsHaavHJJiWta6GNwRERHpYqPRso2DXBMQ8+bqwiYIIiIiIifCljuyDmecJqWOoTQcU7bOyZlTr5oaeSpWnSCKEGS4H3KU4XxkWluWaVmdGNwRERHpovxjk6MckhDhAlGG5KHItKxObGYgIiIiciJsuSPrc+YUrSZj03dM39qHxpRuNYRpQ52YlrUmAfKkVJ38d4qZGNwRERHpwtGyViMKLhBl+CNX5DwzOrH5gIiIiMiJsOWOGlZjStEaoi8dyHStdTD9qo2pwvpx+TErYlrWmhjcERER6cAVKqyHo2Wti80ERERERE6ELXdERES6MC1rPYJMkxg35u49BrDlzkwZGRkQBAGpqamqfaIoIj09HQEBAfDy8kJcXBxOnDghOa9Tp07Izc1Fbm4uOnXq1LCVtjd1X5xyfYE6A1Fp+tbY8B6Zhz9vJhOU8m2kScD99WUt2Rjc6cLgzgxHjhzB+vXr0atXL8n+pUuXYtmyZVi1ahWOHDkCf39/DBs2DDdv3rRRTYmIiKixYXBnolu3buEvf/kLPvjgA7Rs2VK1XxRFZGZmYs6cOXjiiScQERGBTz75BL///js2bdpkwxoTEZFZNFs7LdlIQoQg20baGNyZaOrUqXj88ccxdOhQyf5z586hvLwc8fHxqn0eHh4YMmQIDh482NDVdEz8IjSPOWnKhkxh2nv9nBl/piwjyriRlOAi30ZaOKDCBFu2bMH333+PI0eOaD1XXl4OAPDz85Ps9/Pzw4ULF1SPz58/r/P/miorK1FZWal6zNQuEZFhpaWlku9NHx8f+Pj42LBGRLbB4M5IFy9exMyZM7F37154enrqPU7QGLkjiqLWPmOMHj0aeXl5Jp9HRNRYhYeHSx4PGTIEubm5ZpfHtWWtR66UKtOyujG4M1JhYSEuX76MqKgo1T6FQoH8/HysWrUKp0+fBlDbgte+fXvVMZcvX9ZqzTPGzp07tVruNL+4nJqhL0MOfbcupj4dCwMHlZMnT8Lb21v12OJWO06FYj1ypVSZltWJwZ2RHn30URw/flyy77nnnkP37t3x2muvoXPnzvD390dOTg4iIyMBANXV1cjLy8OSJUtMvp5mOkE90CMiIm0dOnRgGpYIDO6M5u3tjYiICMm+Zs2aoXXr1qr9qampWLx4MUJDQxEaGorFixejadOmGD9+vC2qTERElhAByNGQzYY7Hbi2rDWxPVNGs2bNQmpqKqZMmYI+ffqgtLQUe/fulaQJSAYcAUiNHX8GGkRdnzs5NpKqW1tWjs0U+fn5GDVqFAICAiAIAr744gvJ85cuXUJKSgoCAgLQtGlTPPbYYzhz5ozBMrOysiAIgtZ29+5dU2+LbNhyZwHNjrqCICA9PR3p6ek2qQ8RERHpd/v2bTz44IN47rnn8OSTT0qeE0URY8eORZMmTZCdnQ0fHx8sW7YMQ4cOxcmTJ9GsWTO95fr4+Kj63tcxNPjS2hjcERER6SJCpgEVlhfhdGy0tuzw4cMxfPhwnc+dOXMGhw4dwo8//ogePXoAANasWYN27dph8+bNmDhxooFqCPD39zepLtbEtCwREZEuXKHCauROy9bNDVu3VVVVmVynunPUW9xcXV3h7u6O/fv3Gzz31q1bCA4ORmBgIEaOHImioiKTry8nBnfk2PjlSY0FP+tEegUFBcHX11e1ZWRkmFxG9+7dERwcjNmzZ+P69euorq7G22+/jfLycpSVlRk8LysrCzt37sTmzZvh6emJ2NjYevvqWRPTskRERLooIc9gTE4dqYO8o2UvXrwomQbHw8PD5JKaNGmCbdu2YcKECWjVqhVcXV0xdOhQvWncOtHR0YiOjlY9jo2NRe/evbFy5UqsWLHC5HrIgcEdERGRDlyhwnpEwQWiDBMQ15Uh11JzUVFRKC4uRkVFBaqrq9G2bVv0798fffr0MboMFxcX9O3b16Ytd0zLkvNgfxdydPwME9kFX19ftG3bFmfOnMHRo0cxZswYo88VRRHFxcWS1aoaGlvuiIiIdOHyY1Zkm0mMb926hf/973+qx+fOnUNxcTFatWqFjh074vPPP0fbtm3RsWNHHD9+HDNnzsTYsWMRHx+vOic5ORkdOnRQ9etbsGABoqOjERoaisrKSqxYsQLFxcVYvXq1DK/PPAzuiIiIdGFwZ0UC5EkemhbcHT16FA8//LDqcVpaGgDg2WefRVZWFsrKypCWloZLly6hffv2SE5Oxrx58yRllJSUwMXlft1v3LiBSZMmoby8HL6+voiMjER+fj769etnweuyjCCK/NQ5gsrKSvj6+iIOY+AmNLF1dZyHHPMsEZmKX7uyqhHvIRfZqKiokKXfVd337aPhr8DN1fSO+Vr1U1Th3yffka1+jqzu3v5SOgw+Ppb/LqusvIfADjm8txrYckdERKQLW+6sRhQEiDL8cS1HGc6IAyqIiIh0Ucq4mWjNmjUICQmBp6cnoqKisG/fPoPH5+XlISoqCp6enujcuTPWrVsned7+1j91kXEjTbwrREREdmTr1q1ITU3FnDlzUFRUhEGDBmH48OEoKSnRefy5c+cwYsQIDBo0CEVFRXjjjTcwY8YMbNu2TXKcj48PysrKJJst1z8l62Falho3Q+kSNveTJZiKc3i2mudu2bJlmDBhgmot08zMTOzZswdr167VufLCunXr0LFjR2RmZgIAwsLCcPToUbzzzjt48skn79fDjtY/ZVrWuthyR0REpIvMa8sas/5pdXU1CgsLJVNvAEB8fDwOHjyos5oFBQVaxyckJODo0aO4d++eap99rX/KtKw18a4QERE1AGPWP71y5QoUCgX8/Pwk+/38/FBeXq6z3PLycp3H19TU4MqVKwDsc/1Tsh6mZYn00ZdKYRqA1DH96ryUIiDI8P4qa8swZf1TQeN7RhRFrX31Ha++397WPxUhQJRhEmM5ynBGDO6IiIh0kXkqFGPWP23Tpg1cXV21WukuX76s1TpXx9/fX+fxbm5uaN26tc5zbL7+qeBSu8lRDmnhXSEiIrIT7u7uiIqKQk5OjmR/Tk4OBgwYoPOcmJgYreP37t2LPn36oEkT3RMF28P6p2Q9bLkjMhVH2DY+TL02UjK13MG0MtLS0pCUlIQ+ffogJiYG69evR0lJCSZPngwAmD17NkpLS7Fx40YAwOTJk7Fq1SqkpaXhhRdeQEFBAT766CNs3rxZVab9rX9qm7VlGwsGd0RERLrYaIWKxMREXL16FQsXLkRZWRkiIiKwa9cuBAcHAwDKysokc96FhIRg165deOmll7B69WoEBARgxYoVkmlQ7G39UxEuEGVIHspRhjPi2rIOgmvLOgi23Dknfk3aNWutLTs0ZDrcXGRYW1ZZhW/OreT6p7h/b8+X/0m2tWU7+e/gvdXAljsiORkbBDAItA8M2sgQpQhTU6r6yyEJQZDne5DfpToxuCMiItJFVNZucpRDEkzLWhfvChEREZETYcsdERGRLjYaUNE4cLSsNTG4I7IFc77s2bfEMP4CJbmxz531CAJEWSYx5veiLkzLEhERETkRttwRERHpwrSsFTEta00M7hxE3XSEn15cxbl8iIjUVFZWIigoG7JP2ypCpuDO8iKcDteWtSoGdw7i5s2bAICgoCAb14SIyD7dvHkTvr6+tq4Gkc0xuHMQAQEBuHjxIry9vSE08g6kpaWlCA8Px8mTJ9GhQwdbV6dR4ntge3wP7hNFETdv3kRAQIDcBTMtayUiBIgypFTlKMMZMbhzEC4uLggMDLR1NexCZWUlAMDb25spahvhe2B7fA+krNJip1QCkGECYiUnMdbmAnnGdDItqwvvChEREZETYcsdERGRLkzLWo0oCBBl6GIkRxnOiMEdORwfHx8MGTKEqSgb4ntge3wPGgCDOytiWtaaGNyRw/Hx8UFubq6tq9Go8T2wPb4HRKQPQ16S3fnz59GnTx9bV4PILvHnw4EoRfk20iDIuJEmttwRERHpIIpKiKLlI13lKMPZiIKLLGvLyrI+rRPiXSGruHfvHp599lmEhYUhMTFR9pnjz58/jwcffBApKSkIDw/H//t//w9ffPEF+vfvjx49euDMmTOyXu/WrVt47LHH0LNnT/Ts2RN79uyRtXxnwntVP2v+fPBng4gY3JHZ1qxZg5CQEHh6eiIqKgr79u1TPXfq1CnMnj0bJ0+exKVLl7B//36jzzX2mLprHD9+HLm5uThw4AAOHz6M6dOnY9WqVSaVlZGRgb59+8Lb2xvt2rXD2LFjcfr0adXze/bsQevWrXH8+HEcO3YMMTExZt83R1Df/TL0vLPfq/o+K2vXrkWvXr3g4+MDHx8fxMTE4Ouvv5aUYejnIz09HYIgSDZ/f3/V8zdv3kRqaiqCg4Ph5eWFAQMG4MiRIzrLr+9no75rAUBNTQ3mzp2LkJAQeHl5oXPnzli4cCGUf8zd5tTvtyhTSpYDKnRgWtaaGNyRWbZu3YrU1FTMmTMHRUVFGDRoEIYPH46SkhIAQLdu3dC9e3cIgoDIyEicP3/e6HONPaZbt27o1q0bXF1dERYWhqFDhwIAevXqZfL18vLyMHXqVBw6dAg5OTmoqalBfHw8bt++DQDo2bMn9u3bh1mzZuHQoUNOPUKxvvtV3/POfq/q+6wEBgbi7bffxtGjR3H06FE88sgjGDNmDE6cOKEqw9DPBwD06NEDZWVlqu348eOq5yZOnIicnBx8+umnOH78OOLj4zF06FCUlpZKyjfmZ6O+awHAkiVLsG7dOqxatQqnTp3C0qVL8fe//x0rV64E4OTvd91oWTk2khDhIttG2nhXyCzLli3DhAkTMHHiRISFhSEzMxNBQUFYu3YtAMDDw0N1rKurKxQKhdHnGnuM+jVcXFxUj11cXEy+3u7du5GSkoIePXrgwQcfxIYNG1BSUoLCwkIAQNeuXVFUVISIiAjMnDlTq2XQmdR3v+p73tnvVX2flVGjRmHEiBHo2rUrunbtirfeegvNmzfHoUOHVGUY+vkAADc3N/j7+6u2tm3bAgDu3LmDbdu2YenSpRg8eDAeeOABpKenIyQkxKyfDUPXqlNQUIAxY8bg8ccfR6dOnfDUU08hPj4eR48eBeD87zeRI2JwRyarrq5GYWEh4uPjJfvj4+Nx8OBBi8+1pHy56lpRUQEAaNWqFQDg119/RbNmzZCcnIyZM2eiuLjYpHo4ivrulzH3s7HcqzqanxV1CoUCW7Zswe3bt01KV545cwYBAQEICQnB008/jbNnzwKoTZEqFAp4enpKjvfy8tLq+mDpteoMHDgQ//73v/HTTz8BAH744Qfs378fI0aMAODk77dSKd9GUoIg30ZaOFqWTHblyhUoFAr4+flJ9vv5+aG8vNzicy0pX466iqKItLQ0DBw4EBEREQCA48eP45VXXoGrqyu8vLzw0UcfmVQPR1Hf/TLmfjaWewXo/qwAtfcgJiYGd+/eRfPmzbFjxw6Eh4cbVWb//v2xceNGdO3aFZcuXcKiRYswYMAAnDhxAq1bt0ZMTAzefPNNhIWFwc/PD5s3b8bhw4cRGhpqcv3ruxYAvPbaa6ioqED37t1VrYxvvfUWnnnmGdVrddr3WxQBcBJjaxAhyJJSFdnnTicGd2Q2QeMvJlEUIQgCOnXqpErZAMA777xj9LnGHqN5jX/+85+q/0dHR+Orr74y+Xp1pk2bhmPHjklaQhISEpCQkKDzeGdU3/0y9Hxjule6PitAbZ+34uJi3LhxA9u2bcOzzz6LvLw8hIeH1/vzMXz4cNX/e/bsiZiYGHTp0gWffPIJ0tLS8Omnn+L5559Hhw4d4Orqit69e2P8+PH4/vvvAZj2s1HftYDaPpb/+Mc/sGnTJvTo0QPFxcVITU1FQEAAnn322Ub1fhM5CgZ3ZLI2bdrA1dVVq+Xr8uXLWi065pxrSfmW1nX69OnYuXMn8vPzERgYaNK1nEF990vO98bRGfqsuLu744EHHgAA9OnTB0eOHMF7772H999/3+TrNGvWDD179lRNYdKlSxfk5eXh9u3bqKysRPv27ZGYmIiQkBCLX5PmtQDg1Vdfxeuvv46nn34aQG0QeOHCBWRkZODZZ5+1+Jr2TFQqIQqc58465BrpypY7Xdjnjkzm7u6OqKgo5OTkSPbn5ORgwIABFp9rSfnm1lUURUybNg3bt2/Ht99+K8svSkdU3/2S871xVOZ8VkRRRFVVlVnXq6qqwqlTp9C+fXvJ/mbNmqF9+/a4fv069uzZgzFjxphVfn3X+v333+HiIv1V4erqqpoKxalxtKz1CC7ybaSFLXdklrS0NCQlJaFPnz6IiYnB+vXrUVJSgsmTJ8tyriXlm3O9qVOnYtOmTcjOzoa3t7eqZcrX1xdeXl4mX9OR1Xe/5HxvHFF9n5U33ngDw4cPR1BQEG7evIktW7YgNzcXu3fvNqr8V155BaNGjULHjh1x+fJlLFq0CJWVlapWsj179kAURXTr1g3/+9//8Oqrr6Jbt2547rnnTH4t9V0LqB39+9Zbb6Fjx47o0aMHioqKsGzZMjz//PMmX4+IGgaDOzJLYmIirl69ioULF6KsrAwRERHYtWsXgoODZTnXkvLNuV7dNBJxcXGSczds2ICUlBSTr+nI6rtfcr43jqi+z8qlS5eQlJSEsrIy+Pr6olevXti9ezeGDRtmVPm//PILnnnmGVy5cgVt27ZFdHQ0Dh06pLq/FRUVmD17Nn755Re0atUKTz75JN566y00adLE5NdS37UAYOXKlZg3bx6mTJmCy5cvIyAgAC+++CL+9re/mXw9h6MUAYEDKqyhdkCF5SlVDqjQTRDlXheKiIjIgVVWVsLX1xePuP8ZboLpQbOmGvEevq3+HBUVFc41ybMZ6u7t6RvT4e3jUf8J9bhZWYVuLVby3mpgspqIiIjIiTAtS0REpIOoFCHKkJZlgkwb07LWxeCOiIhIF1EJQIZRwZwKRQcXyJM8ZAJSF94VIiIiIifCljsiIiIdmJa1HlEQIMqwLqwcZTgjBndERES6MC1rRUzLWhODOyIiIh1qcA+QodGtBvcsL8TJ3Kw0b8UWa5XjbBjcERERqXF3d4e/vz/2l++SrUx/f3+4u7vLVp6jqru3/YJWyVYm7602TmJMRESk4e7du6iurpatPHd3d3h6espWniPjvbU+BndEREREToQ9EYmIiIicCIM7IrI79+6xAzoRkbkY3BE5sLi4OEybNg3Tpk1DixYt0Lp1a8ydO1c1r9b169eRnJyMli1bomnTphg+fDjOnDmjOv/ChQsYNWoUWrZsiWbNmqFHjx7YtUt/J/Lq6mrMmjULHTp0QLNmzdC/f3/k5uZKjsnKykLHjh3RtGlT/OlPf8K7776LFi1a6C3z/PnzEAQB//d//4e4uDh4enriH//4B65evYpnnnkGgYGBaNq0KXr27InNmzdbdL+IiBoDBndEDu6TTz6Bm5sbDh8+jBUrVmD58uX48MMPAQApKSk4evQodu7ciYKCAoiiiBEjRqhaxqZOnYqqqirk5+fj+PHjWLJkCZo3b673Ws899xwOHDiALVu24NixY/jzn/+Mxx57TBUwHj58GM8//zymTJmC4uJiPPzww1i0aJFRr+O1117DjBkzcOrUKSQkJODu3buIiorCV199hR9//BGTJk1CUlISDh8+bOEdIyJybhxQQeTA4uLicPnyZZw4cQLCHzO1v/7669i5cyeys7PRtWtXHDhwAAMGDAAAXL16FUFBQfjkk0/w5z//Gb169cKTTz6J+fPn13utn3/+GaGhofjll18QEBCg2j906FD069cPixcvxvjx43H9+nV8/fXXqueffvpp7N69Gzdu3NBZ7vnz5xESEoLMzEzMnDnTYB0ef/xxhIWF4Z133qm3vkREjRVb7ogcXHR0tCqwA4CYmBicOXMGJ0+ehJubG/r37696rnXr1ujWrRtOnToFAJgxYwYWLVqE2NhYzJ8/H8eOHdN7ne+//x6iKKJr165o3ry5asvLy8PPP/8MADh16hRiYmIk52k+1qdPnz6SxwqFAm+99RZ69eqF1q1bo3nz5ti7dy9KSkqMKo+IqLHiJMZEjYwoiqpgcOLEiUhISMC//vUv7N27FxkZGXj33Xcxffp0rfOUSiVcXV1RWFgIV1dXyXN1qVxLEgHNmjWTPH733XexfPlyZGZmomfPnmjWrBlSU1NlnR+LiMgZseWOyMEdOnRI63FoaCjCw8NRU1Mj6aN29epV/PTTTwgLC1PtCwoKwuTJk7F9+3a8/PLL+OCDD3ReJzIyEgqFApcvX8YDDzwg2fz9/QEA4eHhOutjjn379mHMmDH461//igcffBCdO3eWDAYhIiLdGNwRObiLFy8iLS0Np0+fxubNm7Fy5UrMnDkToaGhGDNmDF544QXs378fP/zwA/7617+iQ4cOGDNmDAAgNTUVe/bswblz5/D999/j22+/lQR+3bt3x44dOwAAXbt2xV/+8hckJydj+/btOHfuHI4cOYIlS5aoRtjOmDEDu3fvxtKlS/HTTz9h1apV2L17t6S+//nPf9C9e3eUlpYafF0PPPAAcnJycPDgQZw6dQovvvgiysvL5bx1REROicEdkYNLTk7GnTt30K9fP0ydOhXTp0/HpEmTAAAbNmxAVFQURo4ciZiYGIiiiF27dqFJkyYAavu1TZ06FWFhYXjsscfQrVs3rFmzRlX26dOnUVFRoXq8YcMGJCcn4+WXX0a3bt0wevRoHD58GEFBQQBq+/99+OGHWLlyJR566CHs3bsXc+fOldT3999/x+nTp+udy27evHno3bs3EhISEBcXB39/f4wdO1aOW0ZE5NQ4WpbIgcXFxeGhhx5CZmamrauiV1ZWFlJTU/WOliUiInmx5Y6IiIjIiTC4IyIiInIiTMsSERERORG23BERERE5EQZ3RERERE6EwR0RERGRE2FwR0REROREGNwREREROREGd0REREROhMEdERERkRNhcEdERETkRBjcERERETmR/w9GEf/bsV/BuAAAAABJRU5ErkJggg==",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def plot_images():\n",
" fig = plt.figure()\n",
" ax = fig.add_axes([0.15, 0.1, 0.8, 0.8], projection=wcs)\n",
" plt.imshow(mass)\n",
"\n",
" norm = Normalize(min(lt.get_images()['mag']), max(lt.get_images()['mag']))\n",
" for row in lt.get_images(): \n",
" ellipse = Ellipse((row['x']/3600.,row['y']/3600.),\n",
" width=row['b']/3600,\n",
" height=row['a']/3600,\n",
" facecolor = 'none',\n",
" angle =row['theta'] + 90,\n",
" transform=plt.gca().get_transform('world')\n",
" )\n",
" # Assign color to the ellipse based on the magnification\n",
"\n",
" color = cm.ScalarMappable(norm=norm, cmap = 'Wistia').to_rgba(row['mag'])\n",
" ellipse.set_edgecolor(color)\n",
"\n",
" ax.add_patch(ellipse)\n",
"\n",
" # Creating a ScalarMappable object for colorbar\n",
" cmap = cm.ScalarMappable(norm=norm, cmap = 'Wistia')\n",
" cmap.set_array(tab['mag'])\n",
"\n",
" # Adding the colorbar\n",
" colorbar = plt.colorbar(cmap)\n",
" colorbar.set_label('Magnitude')\n",
" plt.colorbar()\n",
" plt.show()\n",
"plot_images()"
]
},
{
"cell_type": "markdown",
"id": "3f292095-6882-4a17-bf7c-09a36b7e7562",
"metadata": {},
"source": [
"As we can see, three images are displayed whereas in the SIS model only two images should appear. This happens because due to numerical resolution limits, Lenstool finds two radial images, whereas only one should exist in theory. Note that depending on the grid.number, and grid.polar parameters, this third image is not always detected."
]
},
{
"cell_type": "markdown",
"id": "de9995ed-ffd0-4ab8-b3a8-6ef4391aafc4",
"metadata": {},
"source": [
"### With another source"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "9c7c9a90-ddaa-46a0-84c0-4ad8be109ba5",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/html": [
"
\n",
" n x y a b theta z mag \n",
"str2 float64 float64 float64 float64 float64 float64 float64 \n",
"---- ------------------ ------------------ ----------------- ------------------ ------------------ ------- ------------------\n",
" 1a 19.003780153858134 19.041315591211987 6.228466685230651 3.5000000004546004 135.05652820048417 1.0 19.374217246134503"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"lt.e_lensing()\n",
"display(lt.get_images())"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "aa541b4d-1242-44c0-8ccc-8d3423695536",
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/var/folders/mm/6xbl_6k14pn5zn23cltp9rzc0000gn/T/ipykernel_24111/310927048.py:27: MatplotlibDeprecationWarning: Unable to determine Axes to steal space for Colorbar. Using gca(), but will raise in the future. Either provide the *cax* argument to use as the Axes for the Colorbar, provide the *ax* argument to steal space from it, or add *mappable* to an Axes.\n",
" colorbar = plt.colorbar(cmap)\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"
\n",
" n x y a b theta z mag \n",
"str2 float64 float64 float64 float64 float64 float64 float64 \n",
"---- ------------------- ------------------- ------------------ ------------------ ------------------ ------- ------------------\n",
" 1a 10.033094210747203 10.033094210747207 20.656397190255532 3.5000000004537077 134.99999999105756 1.0 18.072533671216917\n",
" 1a -6.6330663752945656 -6.6330663752945656 13.65607183861927 3.5000000004537037 134.99999999408797 1.0 18.521855628870078"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"lt.e_lensing()\n",
"display(lt.get_images())"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "3f6198c4-50b5-450c-9f33-cdc06f70ddd1",
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/var/folders/mm/6xbl_6k14pn5zn23cltp9rzc0000gn/T/ipykernel_24111/310927048.py:27: MatplotlibDeprecationWarning: Unable to determine Axes to steal space for Colorbar. Using gca(), but will raise in the future. Either provide the *cax* argument to use as the Axes for the Colorbar, provide the *ax* argument to steal space from it, or add *mappable* to an Axes.\n",
" colorbar = plt.colorbar(cmap)\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_images()"
]
},
{
"cell_type": "markdown",
"id": "7e773a81-fe5d-47c6-a351-178d04685b73",
"metadata": {},
"source": [
"By moving the source closer to the lens, the flux can be amplified.\n",
"The second colorbar represents the magnitude values of the obtained images. "
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "a2abbc1e-c704-4d03-8a4b-3685e1efc69d",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/html": [
"
\n",
" n x y a b theta z mag \n",
"str2 float64 float64 float64 float64 float64 float64 float64 \n",
"---- -------------------- ------------------- ------------------ ------------------ ------------------ ------- ------------------\n",
" 1a -0.25707791557222537 3.672954994000554 5.500000001342866 2.0826060496906016 94.00372378931525 1.5 21.054388909410584\n",
" 1a 1.6149036200952676 -23.072957535127333 13.082585562250514 5.500000001342866 184.00367029497949 1.5 19.059172764025583"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"lt.e_lensing()\n",
"display(lt.get_images())"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "a92f6e72-5018-487b-a07b-ae02112e62ec",
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/var/folders/mm/6xbl_6k14pn5zn23cltp9rzc0000gn/T/ipykernel_24111/310927048.py:27: MatplotlibDeprecationWarning: Unable to determine Axes to steal space for Colorbar. Using gca(), but will raise in the future. Either provide the *cax* argument to use as the Axes for the Colorbar, provide the *ax* argument to steal space from it, or add *mappable* to an Axes.\n",
" colorbar = plt.colorbar(cmap)\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_images()"
]
},
{
"cell_type": "markdown",
"id": "7cafac7c-f48f-4617-affe-ad3cceaab38f",
"metadata": {},
"source": [
"The image obtained for the first source studied is modelled again and the size of the source is increased; it can be seen that the size of the image is also increased. "
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "ee69d2ce-729b-482d-888a-c8d6c78cd349",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/html": [
"
\n",
" n x y a b theta z mag \n",
"str2 float64 float64 float64 float64 float64 float64 float64 \n",
"---- ------------------- ------------------- ----------------- ----------------- ------------------ ------- ------------------\n",
" 1a 1.8173670426662405 -25.965958656690344 9.369170222656104 3.50000000232949 184.00362385225992 15.0 18.93091728652996\n",
" 1a -0.4595568468859513 6.565971489067192 3.50000000232949 2.369165693006243 274.0036418742858 15.0 20.423681522252945"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"lt.e_lensing()\n",
"display(lt.get_images())"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "2475403e-f1b8-44a0-b2d5-56ff1bbec8be",
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/var/folders/mm/6xbl_6k14pn5zn23cltp9rzc0000gn/T/ipykernel_24111/310927048.py:27: MatplotlibDeprecationWarning: Unable to determine Axes to steal space for Colorbar. Using gca(), but will raise in the future. Either provide the *cax* argument to use as the Axes for the Colorbar, provide the *ax* argument to steal space from it, or add *mappable* to an Axes.\n",
" colorbar = plt.colorbar(cmap)\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_images()"
]
},
{
"cell_type": "markdown",
"id": "01b71fb7-b19f-4f6a-89ca-48ba0fee378d",
"metadata": {},
"source": [
"When the redshift is increased, the distance between the images is also increased. "
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "ff7599c5-5c19-4fbb-be58-74330f6df5ef",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/html": [
"