{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tutorial 5: Molecular crystal packing images\n",
    "\n",
    "This tutorial discusses how to convert the crystal packing into spherical images.\n",
    "From the image representation, we will show how to measure the crystal packing similarity.\n",
    "More details about this approach can be found in https://arxiv.org/abs/2207.12548\n",
    "\n",
    "Created by Qiang Zhu (2022/07/27)\n",
    "\n",
    "Last updated: 2022/08/11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load the crystals\n",
    "from pyxtal import pyxtal\n",
    "from pkg_resources import resource_filename\n",
    "\n",
    "cif_ben = resource_filename(\"pyxtal\", \"database/cifs/benzene.cif\")\n",
    "cif_naph = resource_filename(\"pyxtal\", \"database/cifs/naphthalene.cif\")\n",
    "cif_anth = resource_filename(\"pyxtal\", \"database/cifs/anthracene.cif\")\n",
    "\n",
    "\n",
    "#benzene\n",
    "ben = pyxtal(molecular=True)\n",
    "ben.from_seed(cif_ben, ['benzene'])\n",
    "\n",
    "#naphthalene\n",
    "naph = pyxtal(molecular=True)\n",
    "naph.from_seed(cif_naph, ['naphthalene'])\n",
    "\n",
    "#anthracene\n",
    "anth = pyxtal(molecular=True)\n",
    "anth.from_seed(cif_anth, ['anthracene'])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute and display the image describing benzene's crystal packing\n",
    "sph_ben = ben.get_spherical_images()\n",
    "sph_ben.align()\n",
    "sph_ben.plot_sph_images()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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jhxNeQXjXF77FlfMH0CK+r6sfDJppOnsO9U+kkgN+oKz8rzZfboKUCnlNyCYc2ZSjNeFguVnM7Inr+hoAtIpQAxHpvMqCQhFwglYKh4hkJS/DI9q7LHWjFlyLwiIwgACuFVMGZNiaFtAltK0lCXzxhzt52bs/HWnPMAzDOFY5oZcYvvXja7jwc18uzf09M2Fnxu5OpOLL8t65VYtQxtB061pKutJd428vKwC43JNmDr9pqtBDhGIyb2XIUoJrZoXCUsY7+noNnapBUupzOrCRUuTpP2lAPhE4oIBnberhYNMikCiag7ii/f/8xg8559RtPOEhd1tDg4ZhGMaxwAmrIPy/y67hqe/8EFTpiVIYYWb3DDkgSk5w50RUqR0IHSiozLe61oh2k4mAJkitCrV+5x6tJpD2OLe0oxmaSubLsQ8gQLqs5BPha3IZ+JAP0aAS1PZjkECdIuSC1pxw4Ye+SDPL+N2H/0Lkqg3DMIxjiRNSQfj8dy7nee/9OH6Cwnog2j8J9jrrqUKmuBY4Xzovlk/g6aH2ZkSlkgEdx0TX0v5wxxLX8Lgs7GUqgeiFUbiGH2kFSFc8jazHitF2WPCKW4F8rvSLKF/FCoOsblkQ6YnwEHxFySbgNRf9LwtLDZ792PuNdR2GYRjGxuOEUxDe+fFv8Mb/+l8qKPV9IC1FUwpHw5zC8a/9uVxWyOpShihqRxGQPseBHhSSZV8eL+uXLwXSQ62AoyOFU2PmR7hIMuQX4XKozGfkVVd0UY5X6L4nK75QYgYQr8j1PdfSTvswAbX9WVdxSKQIPcr6LShZrbx4V+wT4UtJescnvsmlP7qBN/zVb426EuMw0EpCtm2WvBrX4Or7w0pm+v2YJSm0BgUuj4dSTgXkCeIhlulyPOwqmwif5LaF99nQNHztvha/J9VD4f6Ty8P1JRYDOILYtWtkWC6wq2mb5lw4DE3yzWOOqgyFDlDbH74nWyJykrTCclKMKywrU2m4LT/i9lYispIFIrYA3PZNwXKNyChAXg/fk5iczF0RbQoZdTHBcUXKR/zwx2SlNRuWE3fKCDnxiu6OJ3sb5IRSEHZeu5d3vvPLTGhnzi5DALpP+wpoq3/eT1rdkMHeyV2F4cleteMzCP2TL15JWjosDG1lopIMO0dC0bf33SWQsj4iVA9mZJNJsQwRaNZ5RSOhi72hl20qS4rkhfLRbiVdZmiZoXKIYvmi7RYBeAc45dvfuYYHP+KVfPaiF5JEsrAZhmEYG5sTKorhyc/+V8QrTrU71/VuFkQ56fecE3v2KeoFnszzQOXOsUJz6DEqdIMPeh0jh170+0cMfJZI+s6OAhQcvwxrB30n9laOVOtZKhEoMlSWClILeNj9Xx7pwDAMw9jonDAKwnve95XCvNM70Q48rSvDFoGo6Sc2aebxZQJp+REaR6S8OHPkkZiCABEnyrJDH2l20OIQqiaUCk+wU0ErQnOmyiv+/qLo2AzDMIyNywmhICwuNXjb+79SfGiHCMIqk3LJ4NN7T/EQqiMtCG6Uj0GvVWNMRvXZbnvonIgzYrFUsLaRFD4P/VaE3rHkNcenPv8jrrrqpjW1ZxiGYWwcTggF4cm/97ZO6uNBhkp6DQzBCiMYpXCojniaL0zzh8soC0LR99oPiUgwbLKoHFA0QspJWwlzkE8k/P5T3jZ6fIZhGMaG47h3UrzooovZs7hcqEKq3UmuPam237x20hxL6bio2l1Txxe7IhZmdSlCEksHxM5av/c47THRt8MGpTzWzLtKSq9lQgRa7Zk25NfgSw9ABsaunTMq5ec+v4N2NZFuOGbZnwrgQPPiujV1xbiT7pbQq+lGAkjm0aQ4Qcp7BD3e5qpkdcfD7v9yPvWlv1ilRWMUknuSxSbVJK7XJ83wP+lkJWxmSm86GO5raSVYDqCzU8Hy1vZwEhwfiTwASA81g+VusRE9J0Q9i2vf1QORn7mIYu1aI0xyEUXeV8N9+Fose1a8i2Q57LaeHArfEx2xf0tMVmKh1slSuO/K7rCcAMjCUnhcm8JJnJo74onAfCTyobLQCpZH5WTEA1dMVsaVExghK+slJxCVlXHlpNPcGOH0x7WCcNOuA7zhZR9l0lOEd1STjo9BXnF9/gbeSfG5/WWUkQI9uwqX5VokLAp12I6O6Fubb3foIVd6M8j1idCIHzhx0iekIR9Cl/VEOQyNS+mkb+7pWQHJciQbuCAFWW4WVg2RQnGQ4ofe5dqN/CiVIa2mXWfK8nxfScrNn4q6We75/ce9gbf/5x9Gr9MwDMPYOBzXSwx//ez3kLZ88VTrhO4TdRH+1wl1hE5kQye1QU+4Yt+0e7grAQEfg04UQ48lIPQaPLZeCBTpP+m97vJgpVCmxCsu87iWJ1nOcM28+JyXFpXMI82srw0Al+V9909y5Zqf7uHKH9+4jldgGIZh3FoctwrCzitv4uorCuc4BXDS3R3Ydf0R4s/lYVQjNVfzIbgFPgZr4nDbl2GdR6BIIhWwSITqSuYLC0nv+eWyTIfEQZpwwWPfcHjjNAzDMI4ox62CcMFjXt+/3t/GyepGANUec3x/+WE/wY90YBx96pr6XO2iRikQkaiFwc2XepdZBsul0RqOaGjlXYfFpMxGWa3wR7/95lUGaxiGYRxtjksF4b/e+1V821lOpHh6bTvmCZ0tgzvTWTC64bA2LIiccitbD25JHyKFk2GgvLAiDBTTds8Y3DCCHkfLHnodYhIHieOHP7iO73/zysMbr2EYhnFEEB09sRyBmW19ybKMR5z/ks4yQuGZ7/Ai+Im0cKrrLObLsCKQedLlrH8CbO9omOWd3RAH0XLyC6EC+Qgv1cJBsoiQ6D6lt9+LrZJdy0f7LtYJdPhaej6qc3EnRgFNe8JA29feXibwvuOXURzWIqrDDV+vOukr74SKtttuFb4JbqXJJ3/wd7hAGxuM9XT7uEXM1U/We5/xuzBi+2o/XQuWB5VAwDXCntAywpNfI57YWomMa4QDrluKeFznkf4jMjzSMzvSllbDe9nnm8NRGgB+IhIlEvH+dwuRaJBsRKREGrmPMW96P+LaKxGv+clQKtfhTdLaxOQE4rISkxMf2Ba+01bke3RL4WiXkfdxzD7GlROIy8q6yQnEr3FcOQHIc752zXuYX9m1pt+14yqKIcs8j3nIK4ttkJsZ6j3MTqIi5FMVfL28oWVuA1FQ6f/hTJZbxeTXW6iKqsetZNEndZ2p9XgU9t/7rJ6i9WRklIHKiKUPVWjkJM0RPwStPLqzoQLifXRiUQWcCy41qCokaWGJWYuVwiuSDdy/Vl7030Ygm6vzq7/ySj75mT89FpQEwzCME47j5pf5J5fv4mG//Aqa+5YLT/rcdzQsTaVQDtqWAF/GMw5O2F5xzfBuh4XjXTfyYSiqoDd3wgBaG6EcrBcjdj9cU8+jnsDahwZzRITKXDsssudVxsG3IzYEcE1Pq5nzSw+5kB//ZNdaRmgYhmEcQY4LBeFNb/4fLvj9d5DsXy7M4M3SjFOvoiK0ZqpD5vPQpOmWw5txAKPNNiM2gmnvIXCrcwv6aIchBo8NLjv0ELR6iEA6UB5RnJLlFpJ5LnjWO3n5Kz9+OEM3DMMwbiWOaQVh900H+c0nvokPv/8bpPMrxRyZ+2IySwqTeT5o2u9ZS+9DlWQli8+zI9b5/Iid7fLKEbrFt9RCUW5oFGxatWtF6C0f1dTAjmidzyIdSwwKrpGDwuc++X0e8muvYv/+xcO8AMMwDGM9OWZ9ED580cW86Q2fQ1s5lfnlzvbItIpJ3tcrqCt8DzqTp9du2N0ArpGNdMnscyAcpBJeQlCgOZOgNUFT8AloQvm3oAk0pxWXCUlTEA+SU7x77fyNh/SgUFUpxhHbyXE1ItfeN+Dg+kqPFWHg/HZUg/RVL0q9gNPyfOdQ+pdvhHIHyFaOVhLyxRa/8fjX84LnP5xff8T5Y1+eYRiGsX4ccwrCvqUlHv2Kf+XgniXqm5Xpa5v4RHCZIlnxNOqdoJWE5W11fM0VXvoixTbBbXqiBASo72t1ikP7H6BlyOSg24IIKydVyasOX3FoRfCpoImQ1+DAHYvJPqR8qICvljsV9e5i2HH9L/7WFOp7U2p7pev44HsVCSVpKrNXrnQTQmnvRZZtlxEEIYRiH3Rf6xGJXmVAIHfQ3BwWGdfyqGtvX11YHFyuVPe1St8DQVNHUu6NoCgkSRFRkivNTdCaTshrwks+/ln+/pIv8dnnP5PZej08YMMwDONW5ZhSEF73ta/yxv/9BjqpVLY4pvbAyintMBNl+sf7IU3QiSpaceRTSd/Tr/qeNfUOUiRq6nkqH5pDFaSSdMo7ewEItGZTlnfUgk6CKycVM/+gub2n2eL/bmBfhqGK2k241KZtjShHndeVfCIlbUYiGbTcFnmEL4W0l2Zix4WoM6SvOrqbJpRj8oqfSEgavtzBMoGVrFOjsbXaqSsqLJyeolUHqjQOZtztjW/ijx94X/7gHveMjulEIpuqsO+eO5i9ajlaJ50Ph0tlc2FFa/HUcOKcvBqXg8piOOyqflO4b9eMh8g1T50Nls/fNhyumU2E5W92Z7yP6R/uDh+ILKk1ToorpSubw5FAUzeG71d9bzjJkZ+aiPYxf6dNwfKl7ZE+9seXP2evDMtKVE42hce1eEp8vHktPK5x5QRAGuFzGqfE5CQcrpnX45bSmKyMKycQl5X1khOIy8q4cgJQ3+fJbo6HbQ5yTPggXLJ7Nz//pn/hDV/6Buqhtk/Z/BNFtPCaxwmV+SaIFApA6sjrad+MK3ncLO9a/Tb7oUiF0gIh7fbbfyO0ZivhfRFQGlsZGV1QVlwDa1hQ0NIaMaKbYeVogFWSfIlnvA2ZBLKqG4p8kPJ/kmnn+xMPc1dmxTKQCKJCdZ/wmk98hbu85Q38eO+etfdrGIZh3GI2tILQzDL+4KKLePS73se+hWVQZfKGnLkrFdc7mXmluqfwQyieVIVsIhDXH5kgXXOVzTZGzImtTZVgu62ZVU6kUCLWLcJBwFdGNCYM7Yo4VGVUpEa7TuxBrZ0re6DMD2ry7e9EKfaV6A6PdAVmdnb3mhAVkhVo7Wzxq+9+D8/91MfJRm0KYxiGYawbG1ZBuOjSSznvdW/ic5cVW/KKwuxVnukbSse3HtIDK93JrTSRZ707Wa3y1CsNH12bL84Pz+O+ItFc9ytbhz35hztm/fZHEMhHKQisoa9VrQNFZsdRYxhsQRPpKiba3alNgGSlXzEThdq8MrGrWy4U1oTazcKnv/lj7vjm1/KpKy5fZZyGYRjGLWXD+SDsXljgKf/5Ia7YvQ9FEQRyZfPlnsqhYeUAr9T3rHQmeE0ceTrgTOjL9fXIBJlE1r1WozWTBo0EPlFas0qaeJIkJ008afne+ewyts0e4uDyBLl35N7hvSNX6XzuvHKhmdRRkuJ+hBAhG7HuJsgttiAIQtJU8vhy5DAKeVVIG4WWpYlA1tNf7vv8HkRharcnr+c0e9bxRIVkGZLr4P989CJ+5tTtvOeRj+OkqckxBmMYhmGslQ2lIOxv7OHpX/t7ktOV229PaDZTGvNVGl+dg9yR1xXNS3+C0qegsn+578lXK46sPpCF0EPw8RZAFdfKu8dGPGX3b/4DizsqNOcEXwFfgbx8337GPn7xvCtRFbwW/XaGWOopFZexubZMnguqQm8QZV8khUDiPBdfcxaX3HB6cX5OofRk4LLyvSX4FKZvlDLks7i23sgIiflD9OZeWM3a0hqxVCHl+b7foSOrOtKVjE5ujB6SlYx8qtrpHgF1MH29Z37W09oOmiqaKlQ9WlGSVGlUvsdrfvQR/uz8dzJb2TxyzIZhGMb4bCgF4Z9+/GomphrFZDlZhB3uvvEkGnMJzMCQJ6FXTr0yQytpd14TRzaddierNpGdAMkVaY1e1/aT1aCz4YE7VvFpOZae45vnFkqfPMVF/BBS8agX0rQ9m8cpggt8x2tSywdurfX4FaonmxHyK3qUo4Fm3YqQHuh6NQ9ekQK0fJGXIdKIQ1DRiPNluXyQ9Zflkw65uRypSF/WR7eoLJwx2T+YUkOq7VNW7r5cLIQNrOTcIDOklYx/v+pvueDc1wTGcvzhN+csPX6e/KJN0TrbvrIQLE8Ww8luslrYHNSYiyvKSTPiyxNJOBNN4gTcdLewF/iOX702WH7ObNhZ9dNfOT/ax+33bQqWV67fFyyPJSwCyGvhY1HrWyvstLN0VtgrH2D3I8IJrB79s98Lln/mmjtE28o/Ohcsj8rJQrjv/LR4ZEdMVsaVE4jLyp67hqNaxpUTiMvKuHICcVlZLzmBuKyMKycAn732Z/BfW7vFfMP4IHx731e5bOFA35O0z4T5a+aAbrRC5yVCuqzdff/bOQBUiy9htZwBUhjrXTkZDUUu0DNnDeYWEEGlsByQyNBkOTsdD0PrNLneiTJFIGnbHsrX0JgD1zbUjAzcg/7/isEPtz3qXve117MXhUARtTDYXvlZWoI0JSiluQpf3nU2y/kl/Gj+W7f49hmGYRj9bAgFIfcZb7ji3xhMk3Tg6tmRFu/qfFjr0nEc/8YJ2+shr0nUsXF6akTqzhIRRUZ6Ro6PrvZtrpM/5Li6Td/3MTAGF8kB0e6nem3MyOXYtTTHjYtzfOL6l+MtusEwDGNd2RAKwnt3vp2FrH8PQ/Ww7ydbwMeHWN2f9Yc70g5z7C1YZU09tr1wp0K4OJ+QcH4CUaq1EUmfSpwqss53/0gpCKvpNUOHR/XriSbCEhVqO+OrYJkmfOGGcxEO8bEb3jl6UIZhGMZYHHUFYW9jF5+48bv4gaEcvH4an48eXu1AZN3mCFgQYju6TdQb+BFKTZt1X2JgLQrCOmgIwtgWhJG4cqOq2OEVwR2Kj3spq3L5/HauOPRB5lvxtULDMAxjPI66gvDqy1499CCuCjdfthUdpSDkSrIyuDFPz6u/xcMfYGRSzSYkOCFPTa2ga7B2u3VeXgBYdTOko7TEMKpfhdFOogrVa0ZbEb6y6/bkXnnvVS8dc2CGYRhGjKMaxfDfN3yYnywuMKinHLpumtbi6P2iq/vjZvy+Ne/VJrNcR24xHDt9Zc7150Yo2Tx3iDRdXUNIBtdGVqGSxL1ce/EJxKqO5ZsRQwtP3BG5LYcTXonEE0V6SJZz8unw9y0q1K6qsPKzraii0fQpX7rhHH759B/xpZs+zv23P2KNF3PrIiLPBv4EOAX4IfB8Vf1yeewc4O3AOcAHgBeqjlYtt9SWeMLtvs37T/qleKVYyu6lsMezy+LLOzFcJN+HLEWiGDaH8z0ALJ0cbutPzvxUsPy+9XA68K/f7sxoH62ZcP+VLOzNPcqiJXnYyz66G2sW/sfY2BR/+PnFs38aLH/1Kd8Olr+8Ek+RHpWVMeVERvkKRf5hjisnEJeV9ZITiMvKuHICcVlZLzmBuKyMKydQyMq/1Jaixwc5qhaEq5d2ln91AvdRhWapHGjkP7TIXoj2ntlDO8RRtXug87n7UrphJxp7Sf8I2/ialDH//a9qtQgn02z45fPuC8D7njIffylQTXIEP/IFoEknzWP/q50aSgKv3mvzvnuP2tfVc89Etb/O4Kt9twbuv29/BzKsdEnm299s4FWkvSbvNBJ4wf7GBCKwazn8j+ZIIyK/BbwOeDlwV+CrwH+LyBlllTcBHwQeDtwBeMLRGKdhGEaMo6ogPOt2z2NrZ3vgMqhOYOu5+3EVPxRi1wm1E2FlW2UoPLFNX5hj+wojYY6aOnDxMMf2zo2DfUzsLWfugfDLvTdvJs8ckjL0ckn35b3DuZ4yF38JsNisUeyqEH8BJE1XOCMMvhCk3Dhp6NVzbX1hju1b1Xv9QrHz4Ygwx/Z31DlZy9FJoR30PW84yKcrnSDKwRdA87SssHU5AjWERDwPO+NSWnoSv3nm89YiekeCPwLepapvU9VLVfUPgRuBC8rjm4GLgUuAq4FNR2OQhmEYMY6qguCc43nnPmPIYU8cbDlnH0MhCj1oxQ0nJwqaE2DkIvhqVveIZS1d9sWT7QCLS/U1rfXnq+17fJisllNiPRi1kUys35GBDJW4GGoCjdvGzW+J5Jy35XqmKk1+4/SXjDeuWwkRqQJ3Bz4zcOgzwH3Kv/8S+CSwAtwJePcRG6BhGMYaOOpOineauyt3mduOG3AE2HTbg6s63TfnIju0jZWSOGDz7m8sWJouh8sXl+q4ZHX/An8rKAghhaWPw4zY6G/jljfRhx+tIJBAviV+P1Px3G3bNcxW78ntZu64zoM7bE4CEmAwwfxu4GQAVf0MsAM4XVXvr6rBRVMReaaIfEtEvrW4P7wbomEYxlpZ3N+k/ZtSvp4Zq3vUFQSA5537R0P+fknFM3fW/MhH4sbmtG/bfyifVMeYxFadp6MWhPBjsfeOLItvLdtp1sm6zNe9yBHaK2i1cMqRQSRDDggEnT2Lqkrj9LhzYio5v3jyT0nE8Ttn/vnoQW1AVLWpqoNKxGCdt6rqPVT1HlObq0dqaIZhHKdMba7S/k0pX2+N1d0QCsJMZRO/dfr9hqwIW8/eP3K3weamNHgFfRPlamaIw3yQT1YUjegBi4vxfcvbeJU1hUOOw6oKwnopJGPeMxmhCflRKbETaJ4ZX16YqjQ4Z+4m7rb196mnU+MN6tZlL4Vb5Y6B8h3AriM/HMMwjPHZMMmaHnXaE/n07q+yp+lpz0DpRM7UyQss3DBTlPVmHQRaU64Iv+lxJNQy58DQ43ksWVPZ3qpz58D5oiAZaCA679DCBJs3x8NsgHJb6XXedahviWHw+lnTdapqserSc0/7WGuoZG+Gzd7R9FgLtLdu78DaX0ui+LnwiBPJedApPwHZzoN3PHZtYzpCqGpTRC4GHkIRqdDmIcCHDrfdfY1J3v/Tu1PfO+JbjHw/OhG2PmjEejMKX430MRlRjEdsgz25K9zWq3Y+LFj+X5EkPPNXbo72cdKhSG6UNKzhr+YTEzynGjmQhn9iawfi9+QrV9w+WP7CajjB0mev/ZloW1FZGVNORinyMSvs2HICUVlZLzmBuKyMKycQl5X1khOIy8q4cgJFYq99jXgY5NCw1lzzVsY5x/PPfRZ//v23IKJ4L+RZwtSORVYun8ZlRbiby4uYXFemfM4mhMqBVme6zasJSSMnq7mefwQa/AchAImgiRuI2x+ot9QqTu8kIyqUi+mdOc0tCXm1SPPsS0/7+YVJ8lzwuZSnFJOuS7TThEe6IRIDtCMMtYxDFFeEf3YUgB7dQvIykjGD6s2CNHPwpWFFoZPyWUEa2cjMeoqglWR4RWBw8vaDhQMnDGyd7Jq+iBaRYgyk3X9Ufiqlti8DVypsUgZeiLC4PUf2JmhFoaKFtCYKDjbLCtvqCzz+jAuj13OU+Sfg30Tkm8BXgD8ATgXefFRHZRiGsUY2jIIAcIfZ83ji1qfzkk99mVbPJhvJdmXLpR4XWI5ubZuiOn+g66rQykkXc7KZSvdJ1PWEPg6SOLTqkMiGMQBCe5LVvrLZqxsstSb6sjmqwP4bT+LrjQnS1JMkOWniSZOcJPFUkoxKklGrtMjmDrKwWCfPHS2fkPukfHd9L++F3ddtZmp3UigEWakYDNyN6nxGZXnEOoPXgVTOQxcaSePcJU9HBJeoFgrNQFllWYt2VYtlkJ7vwderRXs9SocKLG2DVq1GevVAF6K0ZjwHTqpy+/TlnDF19sjxHi1U9QMishV4McVGSZcAv6qqO4/uyAzDMNbGhlIQAH7zjnfn0efchRf893/z6R9dgaLkdWHvnR1bLvMkK/0P3po6mptqVPc3ivkt9ySDu1u5zh49QfJqghuxk1WMyqFs6EFaFNJDCQd2TZNPjZ5sveiqEzIACrV5ob40oq4qSSSyomhCR0WNFnVWWT5QdHTEQQTX9O0GkF4TooAOmC5VoDktLJ3aL5pK4fPR2OZ5zB3vxIW//FDSUcrOBkBV/xn456M9DsMwjMNhQ/7CVtOUNz3ykXz0ab/N1tlJALQi3HwnR3OWociF5kkT3dk/K1b3k8ZgzF988vO1VVInRSIhkxUfdcCr7xUYYZUAOksA64JC0lqtv1WOr6qsyPDeE0M1BvA9Fgehb8vWvJb0WRMUyKtw8HZpf7ko2bQyc7s6n3ny03j1rzx8wysHhmEYxzob+lf2Z7dv55sX/AHPf8C9i9TIDg6c61jeNpAFOnU0t9RRaYc5KslS3l0L7zgjhidIX0tGe+ZHjgmQHgpbHmoHWHXClZjmcZi4UQpCcAOpgSprkIaos1K5vDBYljQGzBa+u4zg6wNWggTmz6l07puieKesbPf82a8+kG8+/dmcvWXr6oM0DMMwbjEbbokhxHPudS+edN55PO3DH+aH1+/h4FmOvOqZuV47aQaam2tUb15BVSHzpMs5zR5nVXXxjYR8JRk9ebaf9AMm+OqBFq25ypAyICpU9yvNzassI6zJiVxXr7iKBUEYHW4IrKrQ6Bp8FIbG1KsglPexiDKRYrmiHJM6Yf7stGOhUFGySeUOt9/Ov//G45mprR46erzj9idMfWiW2StHJFuphP9J59O1YPmQAldSm49rizFF1E+HvyNZjidW2/adcHKg/QdOD5Z/rX6bYPnpO+NLhJUbDwTLNXKvxMf/nSSNiGNx7N9FpI/Jqw9G+9jx8U3B8v/55r3Cbe2Lrx3OXhWRlZicTIWjGNKInADIgbCsjCsnAG4pvBnY9m+HEzwd2B+Rk4mwnEBcVsaVE4jLynrJCcRlZVw5AZja73H7V9+np80xoSAAbJmc5KLf+R0+e8UVPP89H6U1I7QqGVM3tHCZ4jKPR3FZjiw2cInDZVpEFvR+J6FJspTvUdOnywf+gUjxv8r+JulJNXzVoYkU4S3l03p9LzQ3g2TlpDgwwa4pyLEjgGXSovZHodsmRSSDa/iBzJQ94YMKOuKHr3tKT53eeEco7lOkjcIJdKCsrSD4st3cl3kcioiJdCmDMix1ZbPDrSSk6vEpLJ2uvPuxj+O+Z561+pgNwzCMdeeYURDaPOTss/nOi5/LX/zVf/Ltm65GMkgXijBH0gRaOZJ7yDwTu1ZozVU7zneqitP+p/H2X/lESrKchZ/TnYDX4BN4msHMzqVOdIACuMIUn6dCZaGKVgrFQVPwTjshkT6F5jQ4ryTN/pBFKcM4nS9M7bX9UJv3RYhnVkzIkpfperWwDshKK2pnUOgmWYoeT/qeKAfDHV0CE3ta/TeuXU9L59H2qo4q5D2OkapIq1QQVBERkqYvoiJToX7QUTvYRB3c+fwzeM1zn0SabugVMMMwjOOaY05BAKhWU/7xwifwhf97KX//9x8jB5KFJiJFHL+0clhp4pzgGnnpY9AOvyuyGg5OlH6iQrIcN1NqUjgdBqfXzEPVla0DHpJmkZLaXZN1+g+22/7/qAiCci0/aY4OQxh/y5sBBubjTnvl/RJkwELRXfwI9d23s6MO75qtZSdaLfZe0FR46Ut+gwfcL77xi2EYhnFkOKYf0R70gDvykQ8/lzN+9lTy6WoxWZW7XkkrB4V0sdVjlpfOJkdDOMHXkrjJP4nfKsl81AHSNfN1dUSMspZoiFFKiMSPa2/a7N7ynlMHxyK9ylR7eSEwzqyeoiLU52p84qMvNOXAMAxjg3BMKwgAM9N13vm23+MZz/8V8qliOaGzW2CjiXglWWh1J6YREQ35ZGDf5DYjnPMki6dR7A3ru1VZi39BhPaySPjgwH0bOBZSDvDD1oI+Zx6RMqTRQSI86nH34JMXvZDJSUtGZBiGsVEQHf3keYRmt/Xhxl0HePKjXke63IKVZjH42UlUpPBFSF3X8a5ctx+c+NIDy8W6fgBZbkaTS+Yzteguha3JFK2OWmZYhyWGVobL4sfbPgaxY1p1QSuJqhb5EwbHF1McVJHWsPXA5dpdTkHQRMjrKe981zM466xt8es6+tzilZv1Yq5+st77zKeM9Hj2ESUr5j3tGuFlNWnFlV6thvuP7TMvgw6+vf1HvNYZoXSP2wd5uC2thh8I8s3xxF9+InztyVL4PrqFsPf9yOuL7f0fewiIXF8xsEi+iUhUi0YspTE5gbisxORk1HbvRH7D3FI42iV67SN+T6OyMqacQFxW1k1OIC4r48oJgPd8bee7mV+JJLcY7GItlY4VTjl5Ex/42Av47V9+JdSrRZRA7pHEkR5qkU1Xih/K9q1pe9f13M+8VkGyyI9WNYHBXRo7J3aTTHUoPybLGVniiOpbRQxi4QjZW95jw5fMd830Q1+tDF7GUPOr7ZJYVOppoT3/e1/mhCgKO1tOZ4omMvzv0CsibqjMJxT/aH15uYsNPvTxF7D5pJnR4zIMwzCOCseVggCwdfss93nQHfjqFy4rrQVFufNK5VCzWCpoRzW0T+qd5VTRahp8bFRN0GpkTwINTPAlSeZJblqMP4p6RSPnFoOXkT4QhQUgQWthTdf7vDg/tkziFReK4GhHRgxopJ07MLALoiauzAbXtRXgQNsbInnFqYdmxuN+5z6mHBiGYWxgjnkfhBB//brf6Q+3K1IjdsqGllUGY/9DdboV1new68RIC4FLuorR4AsgjygnXoPKARA04YUUFG3nbtCyLVXSXHnmn/3aqtdkGIZhHD2OSwUB4E9f8bjuh3KSE+ibDEdO9aEJdzUz/Tht9R0fffjWdgQZ2gQKigm92b9eFotaKCwYaX9WSyg2jeo4hVIoHM2MD37lL9dn4IZhGMatxnGrIDz4186nXi+eaAWKpQNK5cAXf3eOQedzUTiwBNFDZzl+kFuoBNxiVu1/lBNkqEyDzi7BpQUnYcejtMd6kHvEK0+74MFMjdhq1TAMw9gYHLcKAsCLX/MEvCtC6shL7/nO3FaU925XrD2vGIdrRGiH9t1qjBpX5JhCJ/tl+3NHAWpmbd/HbnnFFWGk9N8nP1E4f2pv/VQGFAmBPOcJz3zQYV+iYRiGceQ47pwUe7nHfc7l3o8+ny988/KioL0OLlJYE1S6k2PpcyBKGcdfWBlcXsbwa7m9sS9N5+NEYQngBPFlToY+RQUQh2hWTKIB+3178pXBPRyGgw6CRI9J0XZeKfNIpMW+BD4RkuUy5bIb2FyqJ0wUVXwiaNWV96br76Ht0EgBzRXnPJ/72t+u6XYZEZxDa1XyubgFJpsaL7wq2b8YLJeFEQmhNoWdS/NN4XFFM4AClUjIW3IwEvYV8Q3K5yajffha5GcuEg7mRoR4JgvhCCcfCenLdkQccUco9LEdXZNDkVC/WLgbkM2Gv5N8MiInK+Frl4icAMhS5LuaDYcAZnPhEEsAH9lePa2Ey5NDI8IDI8RkZVw5gbisrJucQFRWxpYTQCWNhuOHOK4VBICX/NWj+cIj/xFtZwls732gPd74Je2tf3s/962jdw4M7FvQ/tHKPEmzyDMQOqcyH8+VQCLRPRY0dZDGd3lUlNamas+giz9Ei+v1KZAUT/+dfZHLid61AvKXK4zYM6oz8SNotVAQ2mPrWGWSUpHIIV3K+dCH/nBEg4ZhGMZG47heYgBwzvHO1z2l1/2+761v0h1YX4hO5oNZDtsKQeoK7Szm4Djibq+6T8EItDdCwUkxOScOTR1aSYoQyNI60BvmCZFrjGnMociF0NNhz3W6hucpT7w3Wyyk0TAM45jiuFcQAM4+ewd3PffU4sPghkC9hGbLdojkWhBBR9xRP2Ivg/Z6/+GgyWE6KIb2fFLFrXXb5nLppHMqbZ8OKaMglB21Kk97+gPW1p5hGIaxYTghFASA17/qt7sTovRaEbqToXT+10V0wF+gJPbEry4+0Wsl3FbfmMakHUUQPT7CQTG2pBHd+2CgzIcWqBydpYXKgQYf+MjzomMzDMMwNi4njIIA8KcXPAQVwdMb1ij9myIFtiyO+gaEykY8zfukqz1o4FUc0MArUt4m0mfniT6AqEavK2hZCLXf41DUiXQoLSHS9Lzx7U/HjeEQYxiGYWwcjnsnxV4e+fDz+bcvf4erdu4l8YLLQPJiUk9a0KMz9E2uPimUhD6nxsFAgvbEmAi96ge9x5PiqTvoGCgCMe/ptn9DwPHR1xx5xZVLJ4FzXXkdA8faRYNLIiqCS0o/zFJz0RQ07+8+r7QdOIvPPi3uU14Vqk348of/LHwtxmGjTvDTVZpzcQ/S5a3hf9J5JOFMcruJYPmoLKSxqISgRQmoLI9YsopYv2L9xxTwxta4Z/zylsg9iZwia1SQe9FIIEFMQU9HON9P7A03Fr3CEUuCzU3h5F0rW8N9ZLVwfXd2WE4AXOS78rEHlxG5mtKIrEzEHnQi166RaAiIy0pUTkYkmY0+ZEWIysmI56h0OVw+tpx0+lq7tfqEUhAA/uPlT+PC93+ef7v4e+R1QMA7hXa0QrlBkMsFyQsFQjKPawmunDDFA16pLICvtsMAi/ZVhLSqpMs9E2rPzJqpUp3PAmaKwrEwmGmsva4/gDpheUd1OKKinNw1V1Y2Syc8sj3h4wslpTVX+EyoKwRXnZCnCkm1DHtsC25AoPLiHkFxL5Ll4kfvtrUZ/uvVzxj9JRiGYRgbnhNOQQD4syc+mJmJKm/8xv9DE0W8oEk5Y0sRBeBFodqe9RNcc3iabM5CsjJcntcTkt0++CSSTyTooQwJGQsSV2SfXON15FVXLAf0KpKdEETIa0I2E0jhDOR18IEQaXWBaItBZcYX96zTpQrJinL+9u28+69/Z42jNwzDMDYyJ+wC8bMffV+e8Qt3B8rNkjwDoYv0/a1OhxYOtELw4RoRGnMRh0QRWjNp6Xeghf9De3MhB3gPrax4ZRlkeWFVaNfzXa0jr8VDJxWlFbcK4gMW58F9ILqFg9fQU66QLsK9TjvVlAPDMIzjiBPSgtDmBY+5P5fsuomvXn9tYUVwA1sT9lruU0Gawwv5eRWSRsiKIPhUcS1tqyDl7o2Q1x15BdL9K7gsR7K8UAQUdKVR/N3TlpucQKcnwRW7HWriIHX4Svn1DW7cVA4ur4+wRQQVi8GtoyJt+24AiGvCGW6St/75E+J9GYZhGMccJ6wFoc07LngcNXXFckD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      "text/plain": [
       "<Figure size 648x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# One can rotate the image and using different lmax as well\n",
    "sph_ben.rotate(0, 0, -40)\n",
    "sph_ben.plot_sph_images(lmax=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of neighboring molecules 30\n",
      "[-2.041 -2.041 -2.041 -2.041 -1.325 -1.325 -1.325 -1.325 -1.127 -1.127\n",
      " -1.127 -1.127 -0.363 -0.363 -0.224 -0.224 -0.075 -0.075 -0.075 -0.075\n",
      " -0.067 -0.067 -0.067 -0.067 -0.067 -0.067 -0.061 -0.061 -0.061 -0.061]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "==============================\n",
      "*** Open Babel Error  in LoadAllPlugins\n",
      "  Unable to find OpenBabel plugins. Try setting the BABEL_LIBDIR environment variable.\n"
     ]
    },
    {
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       "\t\tviewer_1660223545840034.getModel().setStyle({},{\"sphere\": {\"colorscheme\": \"greenCarbon\", \"scale\": 0.5, \"opacity\": 0.65}});\n",
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       "\t\tviewer_1660223545840034.getModel().setStyle({},{\"sphere\": {\"colorscheme\": \"greenCarbon\", \"scale\": 0.5, \"opacity\": 0.65}});\n",
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       "\t\tviewer_1660223545840034.getModel().setStyle({},{\"sphere\": {\"colorscheme\": \"greenCarbon\", \"scale\": 0.5, \"opacity\": 0.65}});\n",
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       "\t\tviewer_1660223545840034.getModel().setStyle({},{\"sphere\": {\"colorscheme\": \"greenCarbon\", \"scale\": 0.5, \"opacity\": 0.65}});\n",
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       "\t\tviewer_1660223545840034.getModel().setStyle({},{\"sphere\": {\"colorscheme\": \"greenCarbon\", \"scale\": 0.5, \"opacity\": 0.65}});\n",
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       "\t\tviewer_1660223545840034.getModel().setStyle({},{\"sphere\": {\"colorscheme\": \"greenCarbon\", \"scale\": 0.5, \"opacity\": 0.65}});\n",
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       "\t\tviewer_1660223545840034.getModel().setStyle({},{\"sphere\": {\"colorscheme\": \"greenCarbon\", \"scale\": 0.5, \"opacity\": 0.65}});\n",
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       "\t\tviewer_1660223545840034.getModel().setStyle({},{\"sphere\": {\"colorscheme\": \"greenCarbon\", \"scale\": 0.5, \"opacity\": 0.65}});\n",
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       "\t\tviewer_1660223545840034.getModel().setStyle({},{\"sphere\": {\"colorscheme\": \"greenCarbon\", \"scale\": 0.5, \"opacity\": 0.65}});\n",
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       "\t\tviewer_1660223545840034.getModel().setStyle({},{\"sphere\": {\"colorscheme\": \"greenCarbon\", \"scale\": 0.5, \"opacity\": 0.65}});\n",
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       "\t\tviewer_1660223545840034.getModel().setStyle({},{\"sphere\": {\"colorscheme\": \"greenCarbon\", \"scale\": 0.5, \"opacity\": 0.65}});\n",
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       "\t\tviewer_1660223545840034.getModel().setStyle({},{\"sphere\": {\"colorscheme\": \"greenCarbon\", \"scale\": 0.5, \"opacity\": 0.65}});\n",
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       "\t\tviewer_1660223545840034.getModel().setStyle({},{\"sphere\": {\"colorscheme\": \"greenCarbon\", \"scale\": 0.5, \"opacity\": 0.65}});\n",
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       "\t\tviewer_1660223545840034.getModel().setStyle({},{\"sphere\": {\"colorscheme\": \"greenCarbon\", \"scale\": 0.5, \"opacity\": 0.65}});\n",
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       "\t\tviewer_1660223545840034.getModel().setStyle({},{\"sphere\": {\"colorscheme\": \"greenCarbon\", \"scale\": 0.5, \"opacity\": 0.65}});\n",
       "\tviewer_1660223545840034.addSurface(1,{\"opacity\": 0.5, \"color\": \"#f9fdc5\"});\n",
       "\tviewer_1660223545840034.addModel(\"12\\nH6 C6\\nC -6.882632 -4.143336 -6.099585\\nC -6.023860 -3.144144 -5.658375\\nC -7.794688 -4.713240 -5.214300\\nC -6.045312 -2.726760 -4.335700\\nC -7.816140 -4.295856 -3.891625\\nC -6.957368 -3.296664 -3.450415\\nH -6.797516 -4.446144 -7.111885\\nH -5.320096 -2.699976 -6.332605\\nH -8.454856 -5.512296 -5.533270\\nH -5.385144 -1.927704 -4.016730\\nH -8.519904 -4.740024 -3.217395\\nH -7.042484 -2.993856 -2.438115\\n\",\"xyz\");\n",
       "\t\tviewer_1660223545840034.getModel().setStyle({},{\"sphere\": {\"colorscheme\": \"greenCarbon\", \"scale\": 0.5, \"opacity\": 0.65}});\n",
       "\tviewer_1660223545840034.addSurface(1,{\"opacity\": 0.5, \"color\": \"#f9fdc5\"});\n",
       "\tviewer_1660223545840034.zoomTo({\"model\": []});\n",
       "viewer_1660223545840034.render();\n",
       "});\n",
       "</script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<py3Dmol.view at 0x7fe3dcaae890>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# view the molecular packing at the real space \n",
    "sph_ben.plot_real_image(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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UoXWs/QKp4tSIlDrhDYk6iDFvQ6lka32e9ftv5F/e9F+bN9BxHMc56XEPgsGz/+zfeP8/f5LQK+Jc/9hAORQQVjqcUhCAoohz+vUxJoyDwSALUFVoCHEwrhSqitCLSxDRqGcIEJ/mB26uiYMNTlAP5CEaF3H5ZL2fjLwZwkC7INGbUO8qxOvSooRQQZ5HA0cVMkEkDE+qEtfOiipZr+Rvn/VWrrx8H0944o/fbH3uOI7jbC3cQGjw0B99LjdefgAp+nEQb7ViXALqJ/8aGVoK8cl7OGWlGlcz1IMxTKxUjP/PsrFpCoEsEOr5MoU4oTi+NHKw//i0mE4GllFVKMtRHVUo4pxpY7XkyGgZTDFU9b55qA2Tev52sJKiNny0jOcM3ZK3/d0H+c93XsZr3/l7R9/JjuM4zpbHDYSa/dcf4he/98+g14+egRDiEsQ8i0/g9TJFUYVyJErUskQrHQYxoihHosW6bGJVQwij6QSt5/4tkdQUjA/60eAIUQNBHOA1y6JnYbwtw3PXhkwejZXB1Ii06vYUZRR0ZfH6FUEy0NqzIL2CG79xAz92uyfxjx/6I3bv2X5M1+BMjxQl2Q2H7I1WWuSmmMsSJFrpZQ0RIIYI0Jyg7E8XHU6sCI5WmlxDBDe4pyfKVtIof7qalg2M5ol9W+k5dCGNatgUb+pcGr5QDIGaea2GqjA7nIY+XLgy3XXmQNpeM91z34i4uZwqF7MlI+Si0T7ZmX7H1RK0zqWCOW2IQ61rlcOG6HPdqJcb9+dcKvA0BYSW+LBI7yftG/esdV6jn7RjRRg1yozvmZlSutk+Q/Qqq0Y/GWUEQYzr3QjXIAD/8Px38Iv3ekZUeatGo6DdgjwfrgCIbvwKyjjgD8V/48ZBWU7egMP4BYMlj4YxEFI5oqm+TupMvpf6WBPvm+cbaCYGVNXw5hOIN16/GBk1Zb0Esp5eGLSXVoZ28miAVMov3udZ/N1z33bENjuO4zgnD6e1B6G73uPn7vkMeodWhgI97bShlUWLr14qCIOpgfr/qlDJMOa2xkLQfLQyYchIRxCXK+rEPlJVk6HgVZHepJVvmQvRIAiJMTHwSAxDJrTykahxYLAMjQSpvSOhYbjUx5B6+1BdKcPNtGrPSinQK/iXl72fN1/6H/zLJ/+EmZn0CcJxHMc5uThtPQhvuvQ/eNB3PzUaB/VTtLZbtXEQRsbBWC6E4RO5Nt7X/5cQ4r71KgIGSwdr4eD4U/3A1T8cexmJGKVZ1ng/HMrrJ/2JMojHHpxnsHMI0egZtCeL1zl0iY57OwaBmAbLLXXQ0HFvhNQRGGWo0ajW+zzoLk/nza/+6LF9KI7jOM6W4bQzEFZW1nnQPZ7Oy5/11jhHUwcP0lYOnVY9wIfRU/W4noA66MmEWHBy+2jlQWOqoelZaO53lIz5LhplBmNLG5vnn9hvos1MTj/UsRFMIyHPoB2dUaHX52V/9m88+F7PoNs1gn44juM4JwWn1RTDpS95D6978XujaKjfj0/JIcQBbqYVB7xxd3vt/k8G0KHGUGtvw8DLoHEJY/zvCGEYb2B4jGF45nHjQUFDalyMM77css7WOH4eDYKGbLRCQgbljXZJvURz0C6p5xLKMSEjRF2FjMVU0Pqadeyk9XSDSB3euShZ27/MA+/yJzzmSQ/gIY/4XuvjcI6FSm1h4ZwRNa3d+Hpb2hYr5ayBqYu5mctMwdu2VAhYGREcMyMFdLDEZ5aY0xIpGkK7cmGyTK3oeGUqbgxGRD8ryl8wIk5m+9LohflVRohEQ7hpRv6bSfvYipxZ7lpM920Z6bM7ab9XRr2m+C43Pv9srZuU0bXSKRsizW2pSLE0vhOhn/aT9ZRsPmxZ4SqN76IZrdNAZ4z7zoh+mHxXpoxWKlZ/WmmnN+G0MBCqquIn7vkMquX1qKguy/iDN9uOH3BDTTrUB4zrBQbI2I9lPliuODZoN4WBqqNBdZxeUR8s9TSocQMYP2vxPM0fyzoxlKWQtdqmVTVpAAWN6ahjJwwFmMPzl7XJNJy7YHg+DRWSZWivXyeGKvi75/w/Xn3JB3jLf/yxdQWO4zjOFuW0mGL4mfv/BeV6HdcgBDTPYW4musWtpSYwHBQn5vdr7cBwbLRWJTSxphdgtPphTC8wDKg0OM9Aq9B4Pywfa9eE5sBaKmNaGKRTBkGGDoXBuZN+KMuxdwP1pcRokUGg00azLBoOZcXa4TV+6SEv2ryfHMdxnC3FKW8g/MJPvoCVfctItxitFe/kcfAac8E1VxJA6maaeJ9NKv9N78Fgv2bRRkaDNbAfCfM46bHiDIIxXTEuwhwcznKlDXYZVhythBiFZ5RhSGna+TDokvRKrvnqdTzh0S+f9qocx3GcE8wpbSD86s+/lH2X74/zM4O51nYdPbA2DuLYNunmb7r4h+9q3YAOwiQXdRyBfhmDT1RVfLoevIoSKRUt49z+8FVUGysKmx6F8aWFzfIgtoEg8cl9/JzDNhTlZBurKra9X0JRxakBrXNKVNXQqEpO05zzLHVkgI0bCVkMLiW9ki998ls85Ymv2+DCHcdxnK3EKatB+JWH/DVX/s81MQmREFPTzrQZ5FEYjtC9/qTAo6piHIKxEVGaQpTZmTRiXCczx/wJkeOwUMcfxcdOJHYEsw2uMVnfuMmJJS0aEUKdOnqsLWUFdbrg4ZRKrxh7L3HVxyCyIlB1WsP0rxpCXALZypH1HlKUSLfPJ97xOf5ovcuzXvqoja7K2QiRGB3OmBarDEFWU0AmhkAvGJH1ghGBTa2IcVbEvKYwciPSbMIbTI1N51VTK92zEemQ2bTNVuS/cs6Kwjf51kyTbIgFrbTYpuAvGEJLKwqjpVEyBJlWVEdLuFjNpOe1Pm8xBG75UiqEs663bEQXLI1zsmMhKQqWINcSuFrXOu0SMWNfNe4TS0RrRU0007GvGoJB63M0YshUC5P3oiWODcb9HyxBbi06n5ZT0oOwfHiNq/7n2pFx0M6jIDFITGg06DdVpFdMxhLoF4iO3k88wNe7DXQIm43P8fgbbB+GX8bUH9gehLR8GKMgKcdWukLyIzfawMQ1DX5chtdY6cR1oxr7arxfev3RebX2KEhU62ori9fdL/n0+75EYYS8dRzHcbYOp6SB8Kzfe/1oOUcrH602GDD4f9M6V02Wfak0QiFblqph0Z10WNfQ6LNxy11gIj00EI2Puk9lEHCpNmC0lQ9jJVBWvPwv334zX4DjOI5zc3LKGQhVVfHpD30lDmB5iK7HgbusnNQaDLwHYzunwsSmO8YS8FmDqw7/2WJs0CbrGsbckdGrMFknehaqyTq9YlLkOTDUskBVG2sCvOXSjxxj+x3HcZzjwSmnQXjlX70bKasYMKiVjbwH3f5YQCCg1xst16td/dovUtf8YDpgMOBLGAtwVNct60ROY3kXYvKmRuTBAYMlgE3yLM6lJZs28FAocYBeT+eRZZDCuUmlMTOfyJi4oJ5zHBhQw+mKEI8/iPMwfs0D+kWcjhiuzNCY9KrVGvadlmUtWKwzZJYVFBXvfPMn+dEH382+NsdxHOeEcsoZCG980TvjGLYwO4pyVY2yMA5C/sjy2mQAINWhKG+IkWp2PPXmcC6+UFOIGNNAG0KULDOSOtWDtGVQDJYQNomP9YgRHUyxRUXD8ubxijJqGiaWPWoaeausYhTK8WMWxcTxpN+HxW0TzazyaiTC7OSwvMYLf/d1biAcDSLxnjT0JWE5FUGF1YbhaAnZltIUu9XhNHqfJW4LZ+5OyooztiVlGMJFWTOMWqMtmSGYzKwgYNOKGQ3hYtU2rs1IW53tOzy533U3pMc3jPKwY3vakG3zaZl1XYbHstqZRjm0ovdZAdcsAV1ynwBihElX6145eCjd17iO9p4zJ94XZ04XqdGKVGilMc6MlOLZQeM300p1bEQT1XkjffSsEfnQOEU4ZChwr9+f7mvosMJi+v2RbuNesaI3WoJEi3br9BUp/vtrPhKV9q08zpcPXkXDDV6nZZ4QGlqiuRAmBv44sI/2Gz/m1BzFh3OTOYpTNa9HIEZjbkwzmFMsZSPBVFkhY0mnIHo0pPZaqBAjQHb7fPw9lx3NFTmO4zjHiVPKQHjJH74hPoW3W9GNPqBsaAu6kxazqqaWpRljOzMGeLVn9Y9SfrBZdTMO/lT7bjI1Mc0xxuJFTNAss6Yyxix6AWT8iSwL0G6jWeDpv/R3dhsdx3GcE8opYyD8+2s+Et2MnVZ8Qh0kXRokIxqgCv1+Ik5MyPMknPFGw7Rdbkw7HOE4oz3HXvUTd1X/Hd+2GWPyginaOlQibHCcsekDEdMVqs3VHw0jbLTsUWK4a2HoLv/IOz634XU4juM4J4ZTRoPw4j98Q3yyzVtxzf5AlFiUk+NeWU1mA9MYZEXnZ2IeghCoZnJ0Lj7hkgkaBJEM6Vdj2oE44GWH1whr/WTg1V4/CiGbqxnabdDWSA8x0DWGgO6c33RaoDl8D3WTS6ujOSgBGSgf+r2xJ/mxYAftDtLI6qYiVHNtyu31HO1AmBigykNM6jTQclQVstojWytiWRU9MJnKoAHDmBKD3A4AsloNPTOqVZwK6vV5xq++gndc+VcbX7jjOI5z3DklDIRf+4W/gcW5GA2wrJAgw6hxWk0+yWsWkNYoWlXZyUepckUoOhnV7OQqA+mWUCi088kszut9Qq+0I5atd21dQ5YNpyombIFMosEgxrE2DIEIaIWEgFTlqC71aoOiTGM9DGiItQQI633KHbNoMwKfxmufEHPtVKr1krxbjgRiyz2y7uh8WlXDoFMQp3JGwkmNQas6HWhn/M5j/p7nXfLoDS7SgWhEVvMdwuG1dOMUIihLLKeGWC5YkerWjHOupWKxsGpELzQEdGKmYjYi0FniQ2vKzfICGlNf1nfVikIn3fR7ow3xphrfrbCQ9qfMGn1iiQAPHk7KpGNE1jt7Z1JWLKb18iUjSub+A+l519PPkbk0bbUYAs9g/MZVS6nItXltmSEAb/7ugC2WbE4RxwMaU6HW73Lf6HdDzC1G+8yUymV6f1ppls3oh9sNoaYhjpTGKjU9lN4n5vWflYqIq/mOHXVyA07qKYaqqviFn3gB3/zcVdE4aEYRVMPNH0bixaqVofOd6PIOgWI2o5pLjQMpNY2HAGSH1zb29VfGvPzgmNYP3CbBliyl7HT7blBuaQYAFLKD6UAgIrEPemP7BaGayShm66WZIVBt61C1xlJgN27Eyc9mTCDaK7nsY1/nlx7yIirrh95xHMc57py0BkJvveDB93s2+67Yn1h2G46nYfTUrkGots0Ml/WVcxlVpyFCLCqkjC77hKIkrBfmuXQw325heQigPu8xrnAwM0jKxoczLGbqs4e1/sSqj9E2IZSNZVJBqDoZxVw2zGZZLs7EHAyk+oXmuWBkX0k/Znz8mR95Lj3DUnccx3GOLyflFMONB5Z56I8/H13r1VkUNxiMN0hvXAbo7ZmlmA/0FwLLFwlZHzQomsVH2zITwnKgfQiyAkKhSAGhgFAq+Q29qFGoRZBHFD2Ot8FqamhETBiuDxQqxp62x57Ah/tuJHzcyBihdv+PPeFrfU7NAgVdih1zVLmgOVQ5VLlQtqC3KJQLJZkqUoFUQAVlK2P+W9A+WNGan6Vz9SpZJdEEnYhgyURnidSXVClSlKxcv8RP/cCf8/q3/w6L21M3p+M4jnN8OOkMhM9fsZdHPe3VzOxpE1YDMzd0CXlA1vp1quKqfik6XO4o9BbbdPfMUs0EbrxNoJwVVJTirAIyJn0pfSHflyNtobeLaIBojAswGOA0284tPtwjDGyBSuP5B4K9XMn3GQFn8qjgFyaf8Kv5DuVimi1swKarFvp9wnigEK0FkK0MeuncVHHWdsqztkfBYIgizME0RZnBtfdpIYPkjoO4BYGRcJFA94w+tMdaVcHa+ZDtayOlELoz7Pyykq1VzFy7SvtwPx6wKKOmA6IBU3s6qrk2KsLaWR10Jud+T3wJr3vGo7jtOZMBVhzHcZzjw0llILzqg5/i+W/4IO1+RrEYmD9UonNtqqIkqyPJaVGMhE1zMzG8r8DaBfNoHjh4kVDMgrag3FVA0Mk5/IJoHIxP/IfGIkBVZm6oCDo2yGeCDsbiTk61OIfcaETUqufrEwZtPppIijA0XiYTKzHK9Gild90xH7UXBlkFMzdUrJ8RNtQ2CEK2v0V5Rh9adbsDgFKeVRBujIGqbvxOYedXA2u3XKD1pUOjFSBr3eGUhOTxFtR2jrYyWn1h9awWWU/4uWe9mj962P35uXvfyb720wzNhe7uGWasyJnLaZS70BA8rdzhFkmdA/8rFWMFY4Znx9dTcdfcNw6m+xrR9qx7V404I9V5qTG4flbqRSrm0+9Pazn12s3sNfrk0HRlZpvPnmzf+vdclNQ59B1pf1ZGQNadXzL682NfScrKQ+lDhuxOxW2VEYXQEtWV112flFnCypU7TneviHmvpIXzjXtFVgytUzOSLdi/X2en4rv1s9Nr6C+kfZKvWPdJ+judWffJweW0fQa6mLZl9U7nJmWHLjLuFWNE3vnlyXtl7mPpPVEZ33+5ZfoZdnfPoPn0U9knhQahqioe87I38YLXfZD24Xql3oFedPuLIOvjT8/16gUYDnDdnR0U4dCFtXHQ0Ti4BSYHwRLyfa0jBxmoYPs3NxYhUlVkVv5vNoyOEJ/SjyXKorDhQL6RuDGsrKfTL2Ps+EZ1xD4QFbJ9LSgahlSAamdBNVtRduDgRVAF6O6svSNjaaTHTyLdPiJC1lfaN8Zlo+1D8Oevfg+/9cq3unjRcRznOLPlDYR9h5e579Nexic/dTmtlTiwZGslnUPl8Ik0rKdxCIbucIH1s2Y4/B1Cf4E4cO0qauNgrH4VPQdUG4gSB6gys68iN1YGjepgxpqP7dpgn6NYejJ5PNlklYO9Iaz2No3dna/D7D4jMVMTheyGFjQfGALo9pJqvqSYhYO3DazdYo5BmITxUBKDVoa1aOSJQudQQbZeIkBrGT70sa9y/2e8nBuXDY+M4ziO821hS08xfPiL3+Txr3gLrRuVvFcL9Upldm935K4uK1uVnwVQWNvVoX9xn23ndDl39/Xc7sy9YzkCNNoRqnx19Sy+Ob+HqghUhaBVhpaCVkJVBrQStBDKQznbrijRQG1MGIgMB7yp2WSZ45H33WhlxAbV13obblNicKRtl5f0dwn5zoKQV4RMCaFCMiVkVXzlUWtx3o59XLxwBSEoWlsrWusXvnX4DC7be0u6u2ZY29dm7tpu/GysJFBlBVlAFGb3dlm+YBYJQr4Kh65c5n5Pv4RLHvsQ7nHr84+pmxzHcZzp2bIGwpVLN/KI/3w9M/MtenMhDsYV7LqsoFjI41N6peQ3jM1lDaL9qaKzbcq5Fis/LVx48VVQKT++5/PM5enAfUN3gY+v3or5M0bH0lrvOP7IK6L0vjnH+pk7WR8fYKv45BtTLEPnuhVmWjmaDyIl6thj88i5PrYYkHKmNQqmkbpD7E4aLGiYadEaWzg45rhHB2GRpf6nFgV22wW9M2chq1dQDISIY8c+8+z9zF20PBz040pMHYY5GLDEDJ3ZglvPpdntbrdzL73ZnPUL21y+bQ/F37bIVgPS648tYahP2e1RnDE/bGNruc+B27fREI0WsoKf//Br+M9zfoMz5xbsPnEcx3FuFrasgfCbH/lXQKiyEAWDGXXK5oDW09nKaF3+cD19HQSoauf0zupw5i33ETJlz+whWmLrBr68chZlY7ZFBCQbPzJoCeXBdvq0n9VP3vUg3dvdQazIVjDMMtkc8qVSM9pW3GkDkeLAnqjGt8uEqWBFBAPondGmmt1kWkOgvLEDukKWbz7VUBH4/PK5poFABbeZu47/WT+Pc261n71nncfscg6razHcdFWOdAllic6MbsmgtcBrIBKVgAb47Y++ldfc/6GbtulURDOht5jROpR+ppmVZfOcPRNvr75v+nV/wA9/Ij0WqUfuzR+/e1J2wdt2JGXzn74yKVNLfHbOWUnRwe9MU93uv2N63xdnpEZ+a1/aJ7s/m4r5dn7WUNVdty8pkm2pAbp0ux0T76/6kfR78TP3+FhS1jWUZ+94d5rm/NZfPyMp0698PW1bUgJVyyg1HKtWimHOSs9r3Ss/+yP/kZR1DEXrKz/xvUnZeW/fOfF+8VOpSNES2rInbdvB/5V+rvvvlF5//8z0Psn3G/fJ59L7btdnjH66JhV4ykwq9l69w9lJ2RU/mn4/f+xen07KSmO++P3vvXji/a0v35PUkW9ckZRVM+ln2FvMhnFqpmFLahAuX7qRz+y/luzGbEIs1z6s8UlyDKkaaZsH5XnG+kXK/M54I95udi+tLP3GVApfWzkL+2vXrCyUN268FHF4biOX/LcTMxztEbDy3Tfp7bdXOlhc19vOapl++fJMud38XgIVrXZB/3uqiZTRUhtLcfqokfBJoLU8eW3ZoYyP7P0W160aS0gdx3Gcm40taSD85n+8BUrIlrIJwWDngI7iDtQEY8kXxIA/M3dfAZTFbI3tLVvgdvX6jukblimV8fTWJPQ2HnxvgtJgQzYSKW52rs3aOKBcaiEynfEhKF9ZSZ8KAVC4cGYfISi773wActtx1TSspILOwbEJExWyQ3F66bc/8tap2uU4juMcG1vOQPj6of187sBeskMNF70q7cOalGEkywCo5jN2n3eQkMFtZ/YSNli396XlPfTVng5IjrmcT5EYAbL14x0q+OjNjtDdZJnm2HH7h47sMQEoyfjCynnmtlZW8V2zVyNB2XHGMuUtxto75v1oJvARYObG5mcOYSnwsesu59oVI2mJ4ziOc7Ow5QyER7739dF7cONksKLWUgztO85E8iCIIY4H4ZQf0KPVKpgPq5w/t58sVAiTr34pXLE2CLqhR3wVB6aQbKiaGb4G2zbc7SatYth8WabFtNMg/f2t+hhHfh0uZ7mhu0BGlbzmsy7fMXMdWSjpPGxsrnG8fUrMQDl+aX0Ia6O2igp5/Tn84ntfN9U1nChE5HEi8k0RWReRT4nIfca23UZEPigi14jIC0Q2iYvtOI5zAthyIsUD3XoqQIlJj4iyu9CLKwWGwQuVofdgKFAUasGb0trdJ88q5rMerVBRlVGpP+4yL7UFkoqyrGBGqkKIsrrhOTeKl1AFiamNrbFZK9sLURGTJA1WGzSR8ZUQo5YOx2crkNAgaVTjcCq1WHJC3GicjzggD/t7fLMojewRKMJK2SajHL4fdG0elJ1hlauyis6OLutj5504SpWWhR5UM2PrM8q47w1rhqhpiyAi/wf4K+BxwH/Uf98uIt+lqlcALwHeCHwYeDbw88Brj3hgVYKRTEsNQ7BabKTnvSAVhj1rz0eTsrmQeo0+dZsLkrLVM9NIbfPG9JEWxufUSr123Z2pjaQXpFODt92Tigq/PpeK2dauTqMw7mgbKYWtlOjG0unutsn2nX3LVLT25LPS/lw1Mrv+v/PvkJ5yh5Fi2Uj3rJ10mrM/l/bdzKwR+dA4XrkrjfzH+em98uQzP5mUWffK+29526RsdbFxrxhxWLRnLA03Pq/13em1Vrc89vtk/aq039W4P8XKgmvc76tnpGV7bpPeK39+i/en+xr3ynvO/86J9+VC+hlaOjTzQfUo9Wpb7qnlpd//0xCg3B47ajAId3cJGqKyXQZjXq3SHAoUhw9hQve929FKOFgtcKg3Q8iULCiDtANBYFury5ntJZQw8RodcfQSgWx7f/R+I7e+CEKdl0GNV1nFwbzxCr2CUEEoYzKo8ZeUSig0KQ8lcZ9uP6Zwbr4GRkOjDVLpRG4Fk2hFkG/vDZc1jr+i6mCy39pScNu564b9m4mSZfFVInypey5lGTj4vrFQqWMixRgZaRRpUYihR4ttgwWh0Tosd8Uf9H/4wZ/b/GY6sTwReKWq/p2qflFVfwO4Fvi/9fadwKeAy4BvATtORCMdx3E2YssZCD9w7kXsmV2g3FE0liUI3e3NjIcSMyoa5FdWrByOT1Bf6+6hX9r1vnN+L7kVUNwgWywwHuMTSsNyPxJTagFtjmHf0lgCY9HeMW3Ap4rb1MZBsqWCK9d2U5BRlQH5+MQHO/yf5pPpthXo7pTEkCm3l9xy2w7ueqateTjRiEgbuCvwrsamdwH3rv//x8DbgHXg9sClx62BjuM4U7DlDASA597rJyCHaqGcCPuzvluSZY7atgWGosoNV+2kLISruzs3fFj+jrl9VM2DbogS5o8s7qtmjqFbj2Gp4k3Zt+ocWZgZZgokn06r0JKK75q/1j4Xga/0zqYqYe/VuyZXoox9LlXjs9QA67vGU1Jr9CwFeMG9HzhVu04QZxAjd1zXKL8OOBtAVd8F7AHOU9XvV1VzvkREHiMinxSRT/a70yWLcRzH2Yh+d5nBb0r9esxGdbekgXCfc27FLea2UewqJwaQ3jZJnrStLGZxg9L93BwicYC6Ym2XOU0/m/U5oz39mvps1wY5FibaNN2qiEluioGwUfkmosj2kT/61q4eWk0nngwo57QPmttWyjYHy3kU4cYvbJ+cfxyPpGh8lv3x6VGBckfBhdt28t1nptnRTjZUtaeqTSOiWecSVb2bqt6t1fHokY7j3DRanQUGvyn165KN6m45keKA59/7J3nou16LSAVlGE5Kl1lF3pNanKdQCwKjfnAkL5R+Ret6OHxgjh1nrvCN3llcMLvfXO74nfN72dfbRnUkeymDbNc6/cvrNLqjeMmjvwphvYxtair0UQjBVC9oCBuvONi8VTEylrGvQtQiIMl0TVgv4xO7jFceuyaB1q51JJvGcFFuM7fX9NL0y8CXulGg1F1vEb6SQ399OG0wcfSQ1ULNWmvQVmKYyrpWq4IAL/zeLe09ANgHlEQPwTh7gL3HelCplNZqhRh5PqpuGq0wO9BwSlyZxql45g1pRD8rOt7ll6epmM87bFjcxhyTGc3TSEU8sz893srls0nZV1bTSHVWhLyZA+nxxIqbYkU9NSIOzu2bLLviq6ng7Q/PuF9SZkXHy66cScuW9ydlanypKisSnlUvT3/PMqNeOGxknrsiTan8R9fdOymzom5e8dU00t/5+xr9bvSvWPFRjM+rc2N6zuUrprtPrIibs/uM+8S4P2kZ7TOmuDtL6fGuujztz2fuSfvTirrZvFeyg6ngsTS+/6FrRBxdraIGbUq2rIFwz7Nvyf/Ob8f7Vr/J3PVK1o+Bc6pORuu61ZGbOsuBesWAgGZZzPi4tM72LyvXf+Rs1u52gPmFdb4uZ3Le/MFEfX+L9iHaUrDcnRklZyqFqpI6eVN8UQT6BzrMHyhjquk6P4RU9RLMgXiyErTbTSIDAjCb/jBATKA0rk4eb+FwlcZY2fj/N0wMpQpGmFtt58zvA24s6rTYDPMdDPIyVDksHZyje0UgtCqyvKyTNlVkWUzeJFlFCEon7/Ods3vplqPbadDm5X6H/9l/LoeWF9j/2d0sfnGFbKULeR5tkSwf1g9ZTudg9NBUAbrnz7L9azF6ZtmG1bOEhy5ezJ3POMe+3i2CqvZE5FPADxNXKgz4YeBNJ6ZVjuM4R8eWNRAAXvKwn+aDF3+d33zFvyEHKrJefFpe2zPD3N71aBRkYZQdUEbLEKUooVIWPtLn4P6zufwi5QvZLakWC2hrMrkiXSE70JqIvWCiSr6zZPGKTaywOlmULG+WEzrdZ6I9jc0btqrpqdjkmAOq2TbDfoJhIqx6JwAOnx9Ylg7stQ2aYW1RdHufy65uuPwr4jP0wQ70YfFbwq7PrhCU2qvRYPA5EhdQrO3pQP2kVLWg3Bm49NEP4R7GcrstyvOBV4vIJ4CPAL8GnAP87QltleM4zpRsSQ3COPf9rot411N+hZlzZylm6/AHcxm9xXwYTqCaaacTB2UJIrSWCjoHCrZ/DaSEcDiH1dH6/AHaUcod/QlRpEkmLF+QUW0mM5DBIGywweFlMGVyHKhm22NLQo3tGSxdGIYD9EYoii72YaEZsAroCdxYGwffgLlr+rSW65UpjWBIClQz0XuiAt3FnHI2i3GTZmHhgnne+yePPZmMA1T1n4DfAp4MfAb4PuB/q+rlJ7BZjuM4U7PlDQSAPTu28aE//TUuvusF9Ofr5W+721R5PVkwY8xxVjp0+c9dvU5rFbZ/XZASstUWshRSI2FWKXcURzQSVGDp/E26LgR0IwNho2NvYhxsmoxpM8Nio+L5zqbRF5fOD0eMKD00DrYZxsFKgENtKGD7N4TOYZi7pvamVGNhqMbnQ2da0VDIhd6u+P/eAtz73rfmfU99DLu3pcFMtjqq+lJVvVBVO6p6V1X90Iluk+M4zrRs6SmGcUIIvOL//iyveO8neMnrPkxnSVnbkbNwTR3xKwhaKZKF4SCk/T60cvLVitaBLkiH7V+DwxcpWT+jKoVqR0kUD9aiubmKUvtkh1qbBEOClfMzFr9V1K55GZbHg2zi9s8CA03lODoQSh3ldEEUXBgR6LDLoY6wNQhLPahcN6oKsHxBfgTTUdFtfVg0jIPDGbKSg8D2r0FrRWlfv0a2VtSWXX94Xgm1ZDTEqI7SL1k7o4OUSne78HsP/0Ee9n3fvVlDTi8UQj+dHoMNBF7XT0aSO/eDu5Iq/37996XHMvRZF3w9LZz/xo0bt3X8eAtGpL71dDXQji+muTVmbkz37S+k7rt8xRA97k2j68makXp6cbrVIXPfODjx/oK370jqfOwrd0nKDN0Z53zZ0A1dky5oUUPHFIxcL+3D6bRdZmiTrOOJcd5zP7g9KXvf9fdI22LeK+l5m32HIVyVTvpQpV3jPvlSuups5kD6AFHMp/dJa9m6T9IVxuZ9Yt3HBtu+fDApu+V6mqL6PZfdKymrjGfdc77U6M/G9xpAWtPlzAl9KyLvxpw0BsKAX/6he3Dn+d380eNfFXMx9AukqKICfjw6oEjM9FirUbd9dR39RqBqZ2z7Spvu2W2KeWHtDGH9AiHUYn8NgCjaKQjLGfkaSKGEInZu1oNQKPmhHq3ru3WkwyoOcFUd2rgo4PCS/ZSeZZM/5oNw0pWiFdgBG8aXSzSoFCqBwZdrMPhShy412tC64gZah7pRvR0k5oHIAhqEKhd2/XdJf3ubqgVVW+LfllDlUM4IulCQ5SUsx6ZJFX8EW1dlzOxV2ks9Zq5dp7OvR1gvJ8WaWYCZzuia6usPS+toFth2eYG2My55xS9zxzufPFMKjuM4pxonnYEAcLd7XsTL/ulxPPb/vDS638vKtopkcvmfVErWLZnbu87svh7VtpkYjVGgmG/F5YJjA7T0e3GVgnXorpKv9MwIiBo2efxuegLGBnRRtQ2ETewDBpkjNjQsNmCw3HJg2NTx/YPAwrUddH/6RKLUKx1aApKPrqdUWssFohWokh1ajUbbIBeEcb3JNQmQB7Sd8Q9veQLnnpc+7TqO4zjHj5NCg2Bxq4v28Pp3/h7azk13lclEauEKWVqPsRMU8uU+oVdOBu7JQxwQrUN18g3DPMvRGAjDcjhyxINjOaaBCLJBaEnNs9inyaF0zDgYDPKK9CpaS8VQZJkdWovGweD0GxhECa0c7eT883uf5MaB4zjOFuCkNRAAdu1e4N8+8sdUnXy0RI6xcVGaEQ9Aq2qY+S4UFbLcHWoWsrWSsFaMBjWRaCQIdra8bZ2Nn9E3EgFuGvXw2FYxbChi3FC3sIFxIFBuTwOOqCoqkhgHYbUgXy2HnohoHJTDfcYDcmh9/In3gzeZwGyLf//oU1jcfvKJER3HcU5FxBr4xjg+6+5uIkVR8BO3e1JcutfKUGQ0aJbV5ECpCv3+aPpBoUKhncU5+SxQdlroQgfN6mRQEt3xoWoKPJTWdUtQVKnocGUVekZY5oV5M0WotjKqXYZYatDOsYG5Sdi/PByYGx0Dyw0BjkS9gsxOGgIKaDujf+a2SQOiFi4qOpzOkbIiLHUJ3aLOHFkh3YIw3K+OR9Fujw4OSawDQaBfQFXytq/9JWEzz8uJ4xjdOjc/i4vn6d3u/uvkS+l9lV17ICnT9ck4HDJnGF+GIauH05wP1VIqDAvbtqXHOzP1/qixyihYMULWjDLrnrDK+lMK8hbSPqgWjX4xUuWGGydFlLpiiNtmDQN7Pi0TI8qdHkpFmmaUx7PSqHzVYnqOcDhN2cz1RrRGI6ph2JGKFHUmFcLJcioE1bX0vM1+qXbvSNtmLKsOS+mxdMUQn1oPPS1rdZsRvM6KyzKX9me1kMaEka6h0tyXfhcr4zsVDNGjbDe+U4372OxfK4332TuTsmKxwyf/6yUcPnzVVL9rJ6UGoUme59zl3rfhv//jK9E9nmdoHoaDq6z0Jn7ldXU1Dkw1ogo3jn50c0BmZyanCoJAp2M8fYv5RC6dDsykN5Tm0QhpDvgqQLeAvPmDMPBmbKA+LUo0CNLOGeZMlvq4QZDFVD2LahLqVADp9+msrKd117qTUy9liTaNn057sh/abWTsx00BXeiMDJ6igqJEioIf+um7b1XjwHEc57TllPlVfualj6m9A7XLezCeiaRPSQ1rSyQd5LXfn5xWqNScZoANyhsCyVH12hsweIUQBYMhICJ12ObGq6yQ0iivNO4zeDIPIV7r4Nhmc+2pjI08SVpNLtlU1fSJo277BO3G00Y2MtiGOTP6BVTKE//y581zO47jOCeOU8ZACCFwx3tdhNQu7/FYBJo3UjRZrqfmk7vpsi/tQX8juYG5IuEoBYU3BSuB00YiwQ32F8P9mLjpLDdoazIvg45nuKzqqYp+yQ88+K7uPXAcx9mCnFK/zM/+x8eBVsMn0yGN9MsSQmoQjA9SgyfwspoYt6Usbvo4vkm8o2NlkxWQN6kBChOGkhKnFwbZHuNL0oBMeZ56FMYzyykxPoUqv/eCX9io9Y7jOM4J5JTQIAwIIXDre9yar/73FUiljIIcSjQSygodLPHbtgC9/nAKQkTQXoFs9HQ88EjkeQzFHNfwxb9ZhlZ2LIbhTMewQCf/TlTexPzYbKXCJtsG4QbGa0zUHjQsZFHUVadaHm4YaAsG8RrKEmQk6tI8xMBPg6mIqkLb7egx0Chs1CxEz0XdkKDxv3d7wMXuPTgKpKhoHVizPUPbDYHrYkMEZQnjllKhXdUUtgLSnDICZEeqbyl2TLcKxUq7LJZYzPJ4TekFkywVpKmRstdc1muddr0hBFsyxJyG0DBYn9c2IyrfQpomOYkjsgFhxYj8Z62kMgSOYglVDQ+qWPfK4VS8ankUpZHFtpozIilaP4mJJmuDZeSWF9PYN0bCa2DdE4YgszLEttJJy7JeKjQUQ4BbraZiy2At2W/eKwuGEDbdC+mmn2HrwGgZ+jScUgYCwPMu/VUeePFToxYhBLQTkw5p3karscFytoWsdBsPzpL+SEmY/EEaeB8mymQ09z9AozZhUDKMCaAKvdIWNh5anXzyHosphDQCPw/tDLVDKqvCfGdi/8H/k6f7QUAjbZT1iwktgRjnkjybmLJRiLkexs439FOVihR96BVoFnjKC9174DiOs1U55R7f2jNt9lywOz709ooYjnmMoRhPJFlWI1lILLHEMrMsemuBwUZPPrWQcMJLX79ilGcdvWohYqhfE+LEuk4wjiMwKVY8whPXhs8ojScfs2+a1vy4oTTe1zr4PAoEuNXtz6FtPLk5juM4W4NTzkAAeO6lvxqnEjQmABoaCeO5GojuxolBz3R3N4ZFax3tmKdgnA2HZSOAk3GmI9IMPjTNcTZsp7XTNO7NsT5TGi5BkdjnqkPjAI1t/tOXPvLIx3Ycx3FOGKekgXDWLXYwu3MuBuPpFTEoSa8htlONSYoG76kV/vXgPSob/R/S+fzxYyZsYAgwft56KmLo2Rj8/wgvrT0INI6hjXMcsY2bXI803o/3xXCf5vLQVjZsx7BOv0TW+1DPO8/unufMPds3aI3jOI6zFTglIilaVFXFg77/WfQOriLrfUQ1hmTutEdBlESiSr/S0UBXllBV9Tz9YCAOg4MCoFmW6gGEVAswPqhPNg7plXGA18lyyuLIvT4eECnPR0/xA8++SHySbxoJY5kum+2ZMAeEmDq7qoYrFXT8nIOLHugxhsGeJAapquMdhKKC9R7ZWj8aF+0Ws2du41/e/6STSZx4UxaY3Kxsb52l99r1M4ghZFIrQuDCpKjOyh0iVrRBI4qgtlLBV9kxRGAG2UoqjgzLRpQ/Yyqsmk+DjVWz6dRU6KWCrLBkRGY0PIBqpRk2rq0p7pJVQxhoCRJn0ih31YJxTsOoD0akvrBsnNcSeBriu2rOEN910npieA/DchrBM6ymfWzdZzrXuBeN6UXppddq9rF1n2wz7hPjHME4h9mf1uc4Z0QrNMSW1u+3laLbEuVa37Nmf1rfWetelxUjCmWvz8cO/DOH+tdP9bt2yk4ChxB48wf+iAfd588oANb7hPUCLRVmapV9LpM3qghons69DwR849MTzcyL4wGAxun107J6CWWClf3QQof/QDZmgOiogjRutOGmxpcmChjzxpdOx4yC2C5tLGeM0wkNvYHWQsZKY5rntR6h20dDQFs5rV1z/PN7TyrjwHEc57TllP6lzvPAm9//h8h8B51pRUusXyBrvahLKKs00dHYNMNkmXGC8X03ypWQZbaA0VqCdDRBjDbbp7miYkBueDiaxxiWjRU12huTN7GJcVAQVrqE9ZFxkO2Y5V/e8wfkzTY4juM4W5JT/te6PZPzpvc+CTo55BKf0FdWkaVlZK0fEy01pwIGS/Sag6VlEIwjkkYq3CirY2PFxPicvR7Nq2HM6GbnbOoFrBUOwgYGw/gUxNgKkIHnpDYSwlpBOLQCy6uoVtHrMNvije/6Pdozp6zDynEc55TjtPjFnl+Y4e3/9TSe/LhX8+n3fQFBYb2HdPtUnTYszEE7ix6GMFwoWKv7G8//1vumi6AaH+qBIHFOf3y3PIv5l2rvxFAg2cri4Ds+IA80AoOBfzDFUGnUICig1fDcmmeJwJAgY0aQDNuVXNNgScNg1mIY4GhUR8f3U2Lmu1IJS2tkB+vgMe022s65+w99F09/0S/6tILjOM5JxmlhIEDUJDzrbx/Jlz5/Jb/1f14ao3Gtdwnr3Rj9b3YGOq1aaDceFlgn/18LlYbGQwWJ5r+pT4B00A/EqG7NejNGmXW8QbmOVkQMyxpCLFGFQifzS6imAZMGQsuxIEeah9gfQyEiiApS1AZKEXMqhOW1GC2sTietnRZ//c+P57bfdW7abufYkDowlXUvGIKnpjDKEm1pKzXcyjlD3GbUS6bnwE5FfTCNOKhGmmAxxHwym4rqppZOG4JEWUsFadKzUkUbmVib+h1DtGbnajHEh4ZozdrXFO51jTTylqbJErOltezIeubUZVpkpUBWK6phM+bMlIJE6af1LFHp1NE1jWsVS2i5nrYlrBmfd5VGMC0XDDHjvBGFsTRElFb7+pNlltDSXH5vBePLs6OSXZ92j3Xfecfzedtlf8Zdf+xO6NxsVOH3+lHxudaL6t3xMLBN13ptPOjgfYBk8aOVyVGZKPt2SuMnV1gYHg7L4BgzDpR6mWI7Q/IwGgiCIIMVHEUFRUXoFmSHVqJxkGXobIfvfeBdeNtlf+bGgeM4zknMaeNBGCeEwDNf+kg+8aGv8NTH/n1c1jVwv3d7SLuF9ss6hbIxH59FLcNw2kCIj9ZNjcL4+yrmJEgG78RbwPTWgzXwG9EPrSVLE9oCYXK6QQRth+H7oUhxcE1FFaM5rvWQoozLqVo5mgX+4jWP4U53vdWUF+A4juNsVU5LA2HAPb7/trztC8/i5773mazsX6nHeQGtkEpi5sJaDSgCWhQxP8FAsV+UUJYjDWOdCGooVJybibEC6lDD2glR51BWMTHJeGAjafxn3Clh5GdoLrscvBcqqsGAHqjzH9QuKdXoijbcrMPVG1lAOi2kG6LNM0jGVJ9b66kJKXUU1lmEXefu4NXv+X3XGjiO45winNYGAkRvwj9/7Kn81Z+8mXe87uNIpTFWQkYccAcCvQpCloMEtJ6zlFYeVyMM3tdP5YNBk7UuzI9l3lKNGcHqp/UqE3rb4pyylDHHAlWJZqAhIFXcJ/RiwKKqHUbxCSpFSmJCqjBaVdA+2Iv7EetkS+sTsY0s42Bo0GQZIc9qvWOFtDJEQowDARCIuoWiQsoqzucp/NQv34fH/v4DbupH4TiO42whTnsDYcATnv5g7vvjd+QPHvny0SqEXIYJiURqwyEE6LSRfj+mRw4B6bSh158IfzxkbT0KIEUI68WEpkVKHbruNcRzlXlG1WkIGq2piErJukpWTJYxrlVRRXolg/TUsm6IcagP3WrFmAUDT0JnZMhorU8QjasVoiGjqCjPe+2vcfu7XHgUPe0cK9Vsm9U7nUfoG+JAI8pd1oiulh1IUxFbmJEFDUGeNoRnAGEtFfxhCM2Gq24m6hkRF5fSaHCWwA0rPbFlDBvnEDV+Bo3jmSmFk7YZxzfKzOObB5xyvtFa2myJNI0IlkmK+40w0idbUSKZNSIpWtOhR6xkl1kiTSuldrAih66n+2rPEH1Wxudj3TuGsDI3IpGan4XRFvO70rgOnU/TPZdnpCmmC0MYWeVC9VFD5LkBbiCMcfE9b83ff+BJ/PzD/4asKJGiQkollPUAXUHol3EqYbYVRY29oo4LkEVjYGAkDL7YlaJVFb0NGuftda7NIH2zlBojEtbIIMDBFL8LzfzpUlT1isTa/b/Wj9MCIYvainEtwmB6QySmdB6sXMgEnR196as8DL0TSjRoqpZQZoE3vvbX2bNnx9F1suM4jnNS4BPGDc65xU7+8ZW/RrmtQ7Fzlv6uOXq7ZykWOpTb2hQ7ZiEPaAgwP4POtIcDrdSeAmCUt4FoKWoIaLsFlVJ0AmXtnZB+Q1g4rUixsXACVaSIEQ6rdqA/k0XdQ7sVl8d1+2P6hZFAUWY6DBNUtXN0YRbNM7SVUeyYoVxsU25r09vdoXdm3RfbOrz+NY9z48BxHOcUxg0Eg/PP28UrXviI4TJGDYGyE4ZTAeV8Oz6ZA8y2Yxhn6rn82khQqEWO9WC8FNd9B41TDeVsRn8xp2pBf0Yo89qVPwhQNFxsCOMpncfLUagEihb0ZoWqE+gvtihnc/LVguGaifrcKKOMjyIw0xlGYtSZFjo/MwyMVC60ogs5CEVHokFU86oX/RLn3GLnzd7vjuM4ztbBpxg24DYXnc0Lnv6z/PafvBFCHInLTiDrVkMjIVvpxfF/ts4QWSq0Mtg5P3TvS53oScoK7fbRmTbZckGxrQ15QBCKuTCaZigUbSmaCaJEIWI/Dtqa11MA9eqEficg9dyj9BVZifMTUiphtRh6L6TdjmJKIQoaa7GkKNAvqbIAgwyBA+OgPu7AMBp4LF765w/lVheeeXw/DMdxHOe44wbCJtz1uy/kFx52T171ho8TCoVSKDoBqZSqFah2zJJ1K5AQl/71SlrLBaCQZ1FvIBoH4hAHfC0rpJ2RH+xS7OggmdBaqehtq2Mu5EIxy2TkMUOkKAVk5Sh2QWul9laUSn6wi2QCvSJGjKxXZGgd70Bn20PPQf+MObQVYt4JrShnMkKpSFGL0Or9NMDjHvX93PH25x2XvndSillh/x3aZEYW47nr06/ywuWT7/OlNHqhHl5KD2akkw5FKoKqFtMU0+ViGlkPo8xKKW0Kuax6VrQ5K5KgIaoTQ7hmig+tfY207UkdS2RmlVnCQCuNtyECVCO6pBpJ0MyogWupME6MqIFY0RoNzEiHRppppNGf1nJo6/qnFWka9ayIjrp9Pi3bkUZDbEZ+3OgcpojSiJJppsU+lIqG1Yp+uX1x4r31HVs+PxUurp5lpGifgeK/pw/T5wbCEXjsz9+HB/3InfmRP42rG0IZoFLydQglFKrkq2X80W5n9LcLrcP94fQD6/065Gn8UEJZUXWVXFpkB7r0tndolSXFrFANHuIL0M0E0xoH8MHNGXpKvlwhBbQPdWMQo24Rl2wOnv6FGINhpjUs6y22IYuGQjEbKOdyVIQqh2IGEKHKKhDh/c94LLsX0y+X4ziOc2riBsIUnL1rkc+98In8yovfyCe+dhVSCMWcErqQ94T+fE6VV7SWKzQLdLe3aS33kUqotrVHKyE0LhGUfpxuEKDdKyhnWuRrJeu7W1SzGVJAH6JCJAyCN1HHRQCphNaqkvUhWyvp7O8j/ZJstT964soC1UwYpmWuMkHzQCijZ6A/n9dLLKG/LVDWsfaLGahacRpDA9z/jrfm+b/yoBPS747jOM6Jww2Eo+Dlj/9Z/vvrV/HIF78RLQU60G8p+Vqcq69yIV8rUcnob8sIJWTrJaEPpSqhX5J1yxitsCiRQgm9kmy1h5YV7SsVLUt0vk139wzaiW6EYi6DCvL1EiQQ1vu0b+wiy91hlEPJsqgzyDM0k7g8MQhlJ6NqxWBMVQvKmYwq1NoGKvpzWZx2CNCfJS5jzAGBN/7uL3C78846cR3uOI7jnDDcQDhKvvui8/jM857A9z35b1ha6xEKobugSAWiQm+hBapkfSXrQZXncUqiV6HrcT4/9CskE6QFUpZIkcXwy91+DPix3CU/vB7DIo/nVxCJc3eh1itkWdQSdFpoFoWOmmX1079QtTKqdkbZkaHYsGpB2Y4BMwgZVdA6VkI8fpXDmdvneM9Tf9XDJjuO45zGuIFwDIQQ+Oizfh2A1V6Pl777Y7zuY59lvVfGJ/NSqAqhmInpO1vLQlkIOh8o5zOoqmhQ9CtaS30kqxAydDaPKxdWezGU8cAwGE4bDCIbxpwJOteupxACoGgr0F9oU7XqPAz1AF8RDYJiPqbtrTKo8rgqAhHmZ9v88v3uzqPvczdyQ+zkbBEkGndi6NvKTio8aqaYzbalosIk5TfE5FvNY+1M9SfdM9PjdXek4pn+rCX4SouCoeXL11MRWGs5jXLXWkl3zlasqIZGmmFLCGmRiBTT/dQQN1qCR6uPq/lUkFgspMK9Yi49XpWnHRoKI+Lmaipws1J0h9Upo/wZiJF6PMEQAWrL6CcjRXnVNq5/Nq3Xn7fK0t+3woj8WFkjo3GbtNbSws6NaT919qVtzowHMFP02fjeFnPGPTFjXIMRMLFsM12cnRo3EG4ic+02v/uA+/K7D7gvAEVR8ddv+zCf//pezplfYM/ObexYmGH7tll2L84z12lx/hnbOXP34hGOfNM4dHiVvQeXWV5d58DSGgeX1zm0vMq1Ny5x7dISd77Nufzq/e/hXgLHcRzHxA2Em5k8Dzzxgfc90c1g++Ic241laI7jOI4zDf746DiO4zhOghsIjuM4juMk+BSD45wkZF3Y+ZXSFp+tpMKwbG1S8KSG4Et3pRESy7lU3dTbmZat7U6P192ZKqD6RnwtNR5NLPFlvpYer7WUlnUOpwfsHEqFYflyKlzMVg0xY3eKFM1WemJL02MJEo0+ttLzWoJES5Bm9aclXDTRtC25IV4Nq8bxpowcKc2+s1JHd9LrL2eNPtmWlvUW0+N1F9NO6W1Lr6EwZmKtQHViaC9bK4Y42IoIaXwWbeP7mFni0Aa5cb/OX5vW6xy2xaxXGoEzN8I9CI7jOI7jJLiB4DiO4zhOghsIjuM4juMkuIHgOI7jOE6CixQd5yQhW+mz/VOGGmkjGkIzKw2vzhnphI1omhpSkZUYkQQzQwBl7WtmK7U0f4YGTqzAh4aorrKi9VltMfY15X0NUaKZYtqKrmgd3xBBWj/GVsrmfPXYPx/pG+mEe6n6zoo4mYg0McSHYIs3m/fitAHarM9ryrJp7yf7np1u39Az+njKe8D6nln3saxONjA/nKZtz6817kULETPC6Ea4B8FxHMdxnAQ3EBzHcRzHSXADwXEcx3GcBDcQHMdxHMdJcJGi45wslAV64KC9zRAgSmsyoptY+V8NUVRmlHUM4VW+lioNSyvtbGs6AaGFFV0x9A1xZC+tmHVTAV0wRH8mloiuUTZlkmgw0h/LWtoOWU/FYyGbTshmllliQavM+GypjH4y9jXFgXLkvjMjKVoCPUMImq8ZkRqt+9MQc1r3oiVItLDuReu+C12rzca9aEXwXEsjKUq3UdZ8D2jfEB5ulJ67nC5tN7gHwXEcx3EcAzcQHMdxHMdJcAPBcRzHcZwENxAcx3Ecx0lwkaLjnCxkGbJ90d5misUaZZbwzhCjhdU0tFwwIv9l1vHM6IWWaC0tukkYAjIxBXlW9MMpz9EUDE4rDLSYVkBoRSo8HkwrhLTKprkXrVP2DTGndX+upyI7S1i7le4xKaf8bK37M2sIOmfS6KfSMQTIlvgUwBAXb4R7EBzHcRzHSXADwXEcx3GcBDcQHOcoEJE9IvJKEblGRFZF5B0icptGnY6IvEhE9onIioj8m4ic16jzABH5ooh8Q0QeeXyvwnEc58i4geA4UyIiArwFuA3wU8B3A5cD7xGR+bGqLwQeAjwUuA+wCPy7iGT1cTrA3wK/BTwCeKqInH88rsFxHGdaXKToONNzG+CewMWq+lkAEfm/wF6iMfByEdkO/DLwS6r67rrOw4mGxP2BdwJtoAT+G1gHDgLbjnj2ENC5mZv3iqbFiGhnpjs2ArpNFzPxFGEKMd5R1TsZMcVxRxZvmj0yZWbiU6Y3DUHv1Kmxb8I5Nqx6857ZcU5pBvLh9UGBqlZAF/i+uuiuQAt411idK4EvAveu3y8BLwOuBg4AH1LV//l2N95xHOdoEN18Wc7U4cYd5xRl+HAiIi3ga8AngV8FloHfBp4NvEtVf1REHga8Cmjp2JdLRN4HfFVVHztWtg3IVPXghicXeQzwmPrt7YAv30zX5WzOGcC+E92I0wjv7+NH83fkElW9xKroUwyOswkisjz29seBnwZeAewnThO8B3g7x+DlrD0JR6pzCWB+eZ1vHyLySVW924lux+mC9/fWxA0Ex9mci8f+f7WqrgEX11qDtqreICL/SfQqQNQjZMQnohvG9t0DfPg4tNdxHOdmwTUIjrMJqvq1sdfaWPmh2ji4DXA34F/rTZ8iSqt+eFC3XuL4v4CPHsemO47j3CTcg+A4R4GI/CxxrvRy4I7AXwFvUdV3QTQcROQVwF+IyPXEqYjnA58jTkc4Jwc+rXN88f7egrhI0XE2Z0JbICK/CfweccrgWqIg8Rmq2hur0wH+EngYMAu8F3hcvZrBcRznpMANBMfZnFNmibXjOM7R4BoEx3Ecx3ES3EBwHOeURES+v86DcbWIqIg8amxbS0SeIyKfq/NlXCsirxWRCxrH8LwaUyAifygi/yUih0XkBhF5q4jcYZP6L6s/k99tlHt/byHcQHAc51RlAbgMeAKw1tg2B9wF+LP674OA84F3iMi4ePuFeF6NafgB4KXEaKE/CBTEHCW7mhVF5GeAewDXGMd5Id7fWwZfxeA4zimJqr4NeBuAiLyyse0QY0tR6zqPBb5AXJL6+W9rXo1TDFX90fH3dT8dAr4XeOtY+S2JK3/uTwwwNr6P9/cWwz0IjuM4kcX67431X8+rcexsI44vg76k9sy8Dnimqn7R2Mf7e4vhHgTHcU57RKQNPA94q6peVRefTXxabeYIuK7eBoCq/rmIvJgj5NU4zfgr4DPAx8bKng7sU9W/2WAf7+8thhsIjuOc1tRPtq8BdgAPPJZjTJNX43RBRJ5PzG76fapa1mU/ADyKydDlx4z39/HBpxgcxzltGXN73wn4IVXdP7Z5PK/GOHvqbU4DEXkBUWD4g6r6jbFNPwDcArhWRAoRKYBbAs8RkYHHxvt7i+EGguM4pyV1+u5/IhoH91PV5iDkeTWOAhH5K0bGwZcam19K7OeLx17XAC8Afqiu4/29xfApBsdxTklEZAG4df02ABeIyMVEcds1wBuBuwM/CaiIDOa5D6nqmufVmB4ReQnwcOCngBvH+nJZVZdV9Xrg+sY+fWCvqn4ZPI/JVsRDLTvO5nio5ZOUet77/camS4GnAd/cYNdfUtVX1sfwvBpTICIbjRVPV9WnbbDPt4AXq+pfjpV5f28h3EBwnM1xA8FxnNMS1yA4juM4jpPgBoLjOI7jOAluIDiO4ziOk+AGguM4juM4CW4gOI7jOI6T4AaC4ziO4zgJbiA4juMcJSLyKBFREbn1kWsfP0TklXV8gcH7C0XkaSLyHd+Gc32rmUbbObVwA8FxHOfU4RnAg8feXwj8CXCzGwjOqc+RQi17kBjHcZyTBFX9+olug3Pq4B4Ex3GcmxkRaYnIM2s3fK/++8w6QdSgzoX1NMVjReRPReRaETkoIm+tkxSNH29ORP5GRPaLyLKIvFlE7l3v/6ixesMphkao6XfXdbUup/7/0xrnubB5zLr8CfU1rIvIJ0XkPhtc961E5B9F5AYR6YrIZ0TkwVZdZ+vjBoLjOM7Nz6XAHwCvAn4CeCXwpLq8yR8Sk0o9GngCcC/gNY06l9Tb/5I4hfBl4B+P0IZPA79e//836+Peqy6fGhH5ZeCFRGPjp4jX8jpgZ6Pe+cB/AncGfht4YH2uN4nIA4/mnM7WwLM5Oo7j3IyIyB2IaY/HExW9S0QK4Bki8mxV/dzYLt9S1YeN7X8m8FwROUdVrxGR2xGTF/2Bqv5FXe3dIjIH/MZG7VDVwyLyP/XbL6rqx4/hWgIxsdU7VfWXxspvAF7fqP404rT0fVV1f132ztpw+FPg3472/M6JxT0IjuM4Ny/fX/9tegEG7+/bKH9b4/3n678X1H+/hzjwvrFR75+PtYFHwXn16w2N8jcBRaPsx4jXckhE8sELeCdwZxFZ/La31rlZcQ+C4zjOzcuu+u+1jfK9je0DDjTed+u/M/XfW9R/r2/Uu+6YWnd0DM49cS5VLURkf6PuWcAj6pfFbuDwzds859uJGwiO4zg3L4MB/2xgfFXB2Y3t0zIwNM4CvjlWvufomzZBF2g3ynZvcO6Jc9WegWbd/cCHgedscL5rjqGNzgnEpxgcx3FuXj5U//35Rvkv1H8/cJTH+wSgwM82ypvvLQbeiFlj2+XAHRplD2i8vwq4Evi5RvlDSB8w3wHcCfiCqn7SeHVxTircg+A4jnPs/JiI7G2UHSKq/J9WP2l/lLh64CnA61T18xwFqvolEXktUeAYgE8BPwj8ZF2l2mT3rxC1Ao8WkQNEg+HLqrpEFBk+WUT+GPg4cB+iuHL83JWIPB14uYj8Q73PrYkrNJrTBU8lGjMfEpEXA98irnS4A/Adqvroo7lu58TjBoLjOM6x8yKj7AvAXYBvEJcmPpnoXn8O8PRjPM9jgCXg94nTAu8jLmH8d6JBYqKq+0Xk8cQllh8EMuB+RC/GnwM7gMcTB/y3AQ8nLlUcP8YrRGQBeCLRgLis/vuaRr0rRORuxNUMzwLOJE47XIa9vNPZ4oiqnug2OI7jOEeJiPwu8BfAhap6xYluj3Pq4R4Ex3GcLY6I/ATRVf8Z4pTCfYDfBd7gxoHz7cINBMdxnK3PEjGK4R8A88DVwF8TEzE5zrcFn2JwHMdxHCfBlzk6juM4jpPgBoLjOI7jOAluIDiO4ziOk+AGguM4juM4CW4gOI7jOI6T4AaC4ziO4zgJ/x+VG/9y7UVorQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 648x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute and display the image describing naphthalene and anthracene\n",
    "sph_naph = naph.get_spherical_images()\n",
    "sph_naph.align()\n",
    "sph_naph.plot_sph_images()\n",
    "\n",
    "sph_anth = anth.get_spherical_images()\n",
    "sph_anth.align()\n",
    "sph_anth.plot_sph_images()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Similarity between benzen and naphta 0.7145885464284113\n",
      "Similarity between antcen and naphta 0.9742268926829936\n"
     ]
    }
   ],
   "source": [
    "# One can clearly see the strong similarity between naph and anth\n",
    "# To further comfirm it, one can simply compute the similarity as defined in\n",
    "# https://arxiv.org/abs/2207.12548\n",
    "\n",
    "s1 = sph_naph.get_similarity(sph_ben)\n",
    "s2 = sph_naph.get_similarity(sph_anth)\n",
    "print('Similarity between benzen and naphta', s1[0,0])\n",
    "print('Similarity between antcen and naphta', s2[0,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "@webio": {
   "lastCommId": null,
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  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}