diff --git a/examples/pulser-myqlm-conversion.ipynb b/examples/pulser-myqlm-conversion.ipynb new file mode 100644 index 0000000..b04dfb9 --- /dev/null +++ b/examples/pulser-myqlm-conversion.ipynb @@ -0,0 +1,3456 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 205, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import qat\n", + "from qat.core import Schedule\n", + "#from qat.qpus import AnalogQPU\n", + "from qlmaas.qpus import AnalogQPU\n", + "#import qse\n", + "from time import time\n", + "import qse\n", + "import numpy as np\n", + "import qat\n", + "from qat.core import Schedule\n", + "#from qat.qpus import AnalogQPU\n", + "from qlmaas.qpus import AnalogQPU\n", + "#import qse\n", + "from time import time\n", + "import pickle\n", + "import numpy as np\n", + "import pulser\n", + "import qutip\n", + "from pprint import pprint\n", + "from pulser import Pulse, Sequence, Register\n", + "import pulser.waveforms\n", + "from pulser.waveforms import ConstantWaveform, RampWaveform\n", + "from pulser.devices import MockDevice\n", + "from pulser_simulation import QutipEmulator, SimConfig\n", + "import matplotlib.pyplot as plt\n", + "import qse\n", + "from pulser.devices import AnalogDevice" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Testing a one atom setup with 0 amplitude and detuning" + ] + }, + { + "cell_type": "code", + "execution_count": 206, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Interatomic Radius is: 9.756753962298905µm.\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "Omega_max = 2.0 * 2 * np.pi\n", + "U = Omega_max / 2.0\n", + "R_interatomic = MockDevice.rydberg_blockade_radius(U)\n", + "reg = Register.square(1, R_interatomic, prefix=\"q\")\n", + "print(f\"Interatomic Radius is: {R_interatomic}µm.\")\n", + "reg.draw()" + ] + }, + { + "cell_type": "code", + "execution_count": 207, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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/mXTrktb7ahqkHzzfupDB/7Vjg8xSRoo0KL57spx33nndc2IAnebz+2Q2mdlWDwAAAAB6OIvZosiwSEWGRWpk0kjVN9WrorZCOwt3alfRLv3uw9/p1j/cqgRXgmalzdLS9KWaN3yeHDaH0dEBAGexgCmcrrzyytN6nslk0qpVq7o4Tc+y+kMpKky6YeGJj/38UmlMv9Y/+3zSfzwqPbVReuCS7sny+eefa+bMmd1zcgCd4vf7W7fUAwAAAACcVWzBNiW4EpTgStD0IdNVXV+tYm+xcg7naE/JHn1v7fdUXlOusSljNX/4fGVmZGp039G8BgQAnJKAKZyefvrpdu83mUzy+/0d3h8IhdNftklLx0gh7fw0pPeVpg/96vbF50jvb+u+LEVFRd13cgCd4vP7ZDr6DwAAAADg7GQ2meUMdcoZ6tQg9yA1tTTJU+fRvtJ92l6wXRv+tUE/feensofYNX3wdC0etVhL0pcoNjzW6OgAgB4uYAqnAwcOHHfb5/Pp+uuv18cff6zrr79eU6dOldvtVnFxsT788EM9+uijmjRpkn75y18alPjM2VMkXT715I5NS5Be2Nx9WcLDw7vv5AA6xef3yWQy8Qk3AAAAAOhFgi3BinHEKMYRown9Jqi2sVZl1WXaVrhNu4t2694/3qtrnrlGafFpmjNsjrIysjRl4BQFBwUbHR0A0MMETOGUkpJy3O0HH3xQn3zyib788kslJCS03T9kyBBNmzZNV1xxhUaPHq1XXnlFt9xyy5mOe0bVNEgO2/H3RYZJWx+U+v/bh1ecoa3Hd5cFCxZ038kBdIrP52N1EwAAAAD0YiaTSWHWMIVZw9Q3uq/mDZsnb51XBysOKudwjv6+9+96+m9Pq9nXrHMHnKuFIxYqMyNTA+IGGB0dANADBEzh9O9WrVqliy666Liy6ev69Omjiy66SE8++WSvL5wiwqTCyuPvM5ul4UknHlvkkVz27svy8ssvKzs7u/suAOC0tfhbWN0EAAAAAAHEYrYoMixSkWGRGpU0SvVN9SqvLdeuwl3aWbRTv/vwd7rlD7eoT0QfzUqbpaXpSzV32Fw5bA6jowMADBCwhdOhQ4dks9m+8RibzaZDhw6doUTGGZksvbtVum3ptx/77tbW4wEEnhYfhRMAAAAABDJbsE2JrkQluhI1fch0VddXq9hbrK2Ht2pPyR7913P/pfKaco1NGav5w+crKyNLGX0zeC0JAAEiYAunpKQkrV+/Xvfdd1+7xVNtba3Wr1+vpKR2lvn0MheOl1aukV7/TFo6tuPjNvxT+usO6dcrui/LsGHDuu/kADrF7/fLJGY4AQAAAAAks8ksZ6hTzlCnBrkHqamlSZ46j/aV7NP2wu1a/6/1eujth+SwOjR98HQtHrVYi9MXKzY89ttPDgA4K5mNDmCUq6++Wvv379fkyZP12muvqaysTJJUVlamDRs2aMqUKcrNzdU111xjcNKu4/e3f/9VM6QhCdJFj0l3vyLllR7/eF6pdNfL0iW/lob2ka6cfpLXO42MLpfrNJ4F4Ezw+X2UTQAAAACAdgVbghXjiNHE1Ilace4K3XHeHXp42cNaNm6ZKusqdc8f71H8TfEafvdw3fDiDdq4c6OampuMjg0A6EIBu8Lp5ptv1u7du7V69WpdcMEFkiSz2Syfzyep9ZP8V1xxhW6++WYjY3YZu92uww1mSb4THrMGS2/cLC36mXT/BunHGyRnaOuXt671yy8pLUF64wetx5+M6nrJ4Ti1PXs3b96sfv36ndJzAJwZxwonkyidAAAAAAAdM5lMCrOGKcwapr7RfTV/+Hx567w6WHFQOYdztGnPJq3atEo+n0/nDjhXC0cuVGZGplJjU42ODgDohIAtnMxms1atWqXly5drzZo12rJlizwej1wul9LT03XZZZdpxowZRsfsMgMHDtSrr/hU2yDZrSc+nhon/evH0pMfSK/8Q9p2SCqsbC2dpqZJ/zFBunqGZAs5uesVVEj5pU0aPHhwV34bAAzU4muhbAIAAAAAnDKL2aLIsEhFhkVqVNIo1TfVq7y2XLsKd2ln0U79duNvdfMrNyspIkmzhs7S0vSlmjtsrsKsYUZHBwCcApPf39FGa+gNvF6vXC6XPv/8c40ZM0bP/bd06eTuv+7P35TueDlIxcUlioyMPOnnlZWVKTo6uhuTAThdj77/qFb/bbWun329oh387xQAAAAA0Hk+v0/V9dUq8hZp6+Gt2lu8V7tLdquytlJj+47VvOHzlJWRpYy+GWzzDgBd5Fhv4PF45HQ6u+y8AbvCKdAMGDBACxfM03+tfl+JES2aObx7ruP3S+v/Kd3xkknf/e6lp1Q2SdL27ds1derU7gkHoFN8Pp9MMvELPgAAAACgy5hNZjlDnXKGOjXYPVhNLU3y1Hm0t3ivthdu1/p/rddDbz+kcFu4pg+ersWjFmvxqMWKCY8xOjoA4N9QOElqaWnRkSNH1NDQ0O7jffv2PcOJusfLr7yqxYsWatZPPtLw5CDNG9GsqDDJbO78uVt8UqlXemtLkPYVNeuC8zP1u/978pTPc+jQoc6HAdAtjs1wAgAAAACguwRbghXjiFGMI0YTUyeqprFG5dXl2np4q3YX79bdr92tq9ZcpaEJQzV32Fxlpmdq8sDJCg46yaHjAIBuE9CF02effaY77rhDH374oRobG9s9xmQyqbm5+Qwn6x5hYWF6+5339M477+jll1/WG5s3yeP1qCs2VTSbTYpwRWjm4ln6zbJlmjVrloKCTv3Hy263dz4MgG5xrHBijhMAAAAA4EwwmUxyWB1yWB3qG91XC3wL5K3zKr88X9sKtmnTnk1atWmVfD6fzh14rs4beZ6yMrLUL6af0dEBICAFbOH0xRdfaOrUqQoKCtK8efP0xz/+Uenp6YqPj9fnn3+u0tJSzZgxQykpKUZH7VJWq1VLly7V0qVLjY7SrszMTKMjAOiAz++jbAIAAAAAGMZitigyLFKRYZFKT05XfVO9ymvLtbNwp3YV7dJvPviNfvDyD5QUkaRZQ2dpafpSzR02V2HWMKOjA0BACNjC6b777pMkffLJJxo6dKjMZrPOP/983X333aqrq9NNN92kV155RU899ZTBSQPLunXrlJ2dbXQMAO3w+Y5uqUfnBAAAAADoAWzBNiW6EpXoStSMITNUXV+tQm+hcg7naHfRbl375bWqrKvU2JSxmj98vrIyspSenM528QDQTQK2cNq0aZOWLl2qoUOHtt3nP7q3XGhoqH7961/r73//u+644w49//zzRsUEgB6jxd/CCicAAAAAQI9kNpnlDHXKGerUEPcQNTY3qrK2UvtL92t74Xb94bM/6ME/PahwW7imD56uJaOWaHH6YkU7oo2ODgC9RsAWTh6PR6mpqW23g4ODVV1d3XbbbDZrxowZWrdunRHxAtbgwYONjgCgA8xwAgAAAACcLUKCQhTnjFOcM04TUyeqprFGZdVlraufinfrrtfu0pVrrtSwhGGaO2yuMkdnavKAyQqyBOzbpQDQaQH7N2hcXJwqKirabsfHx2vPnj3HHVNfX6/a2tozHS2gxcXFGR0BQAeObanH1gMAAAAAgLOJyWSSw+qQw+pQSnSK5rfMV1V9lfLL85VzOEcf7flIv9/0e/l8Pp078FwtGrlIWaOzlBLdu2a7A0B3C9jCadiwYdq1a1fb7cmTJ2vDhg3avHmzJk2apB07duill15SWlqagSkDz6ZNm5jhBPRQfvlZ3QQAAAAAOOsFWYIUGRapyLBIpSenq66xThV1FdpZuFM7i3bq1x/8Wje9fJOSI5M1K22WlmYs1dyhc2W32o2ODgA9WsAWTosWLdINN9ygwsJCJSQk6NZbb9X69es1ZcoURUVFqaKiQj6fT3fccYfRUQGgRzi2wgkAAAAAgN4kNCRUoSGhSnQlasaQGaqur1aht1DbDm/TzqKd+uOaP6qyrlLjUsZpwYgFyszI1KikUbxGBoB/Y/L7/X6jQxihqalJ5eXlioyMVEhIiCTp73//u3784x9r//79SklJ0cqVK7Vo0SKDk3aO1+uVy+WSx+OR0+k0Os63Ki4ultvtNjoGgHb8v/X/Txt3bdT3ZnxPztCe//cJAAAAAACd1djcqMraSu0v3a/thdu1t2Sv9pTskdPm1PQh07V45GItTl+saEe00VEB4KR1V28QsCucgoODTyg2zj33XL355psGJYIk7du3j8IJ6KFa/C18egsAAAAAEFBCgkIU54xTnDNOE1MnqqaxRmXVZcopyNHuot2667W7dOWaKzU8cbjmDJujrIwsnTvgXAVZAvZtVwABLGD/5rNYLLrkkku0du1ao6Pga/Ly8nTuuecaHQNAO3x+HzOcAAAAAAABy2QyyWF1yGF1KCU6RfOHzZe33qv88nzlHM7Rh7s/1O8/+r38fr8mD5yshSMWKmt0llKiU4yODgBnRMAWTk6nU8nJyUbHwL85tr0hgJ7H5/NJJrHKCQAAAAAASUGWIEWFRSkqLEoZyRmqa6xTRV2Fdhbs1M7infr1B7/WjS/dqL5RfTV76GwtTV+qOUPnyG61Gx0dALpFwBZOEyZM0Jdffml0DPybCy+80OgIADrg8/somwAAAAAA6EBoSKhCQ0KV6ErUjLQZqqqvUpGnSDkFOdpRuEOvffGaPHUejUsZpwUjFigrI0sjk0byWhtArxGwhdM999yjGTNm6JlnntHy5cuNjoOjXn75ZS1btszoGADa4ff7ZTr6DwAAAAAA6JjZZJYr1CVXqEtD4oeosblRlbWV2le6TzsKd+jlf76sn7z1EzltTs0YMkOLRy3WolGLFO2INjo6AJy2gC2c3nvvPc2YMUNXXHGFHnvsMY0fP15ut/uETxSYTCbdddddBqUMPM3NzUZHANCBFn+LzCaz0TEAAAAAADjrhASFKM4ZpzhnnM5JPUc1jTU6UnVE2wq2aXfxbt254U5d8fQVGp44XHOHzVXW6CxNSp2kIEvAvn0L4Cxk8vv9fqNDGMFsPrk3TU0mk1paWro5Tffxer1yuVzyeDxyOp1Gx/lWn3zyiSZOnGh0DADtWLlupbYd3qZrpl0jh9VhdBwAAAAAAHqF5pZmeeu9yi/P17bD27S3dK92Fe2SJE0eOFnnjTxPWRlZ6hvd1+CkAHqL7uoNArYi/+CDD4yOgHb07cv/cQI9lc/nk9lkZks9AAAAAAC6UJAlSFFhUYoKi1JGcobqGutUUVOhHUU7tKtolx57/zHd8OINSolK0ayhs5SZkanZabNlt9qNjg4AxwnYwmn69OlGR0A7Nm7cqOzsbKNjAGiHz+8TXRMAAAAAAN0rNCRUoSGhSoxM1My0maqqr1KRp0hbD2/V9oLt2vCvDfLWezW+33gtGLFAWRlZGtFnxAmjQgDgTAvYwgkAcGp8fp9MMvELLAAAAAAAZ4jZZJYr1CVXqEtD4oeosblRlbWV2leyT9sLt+vFT1/Uj9/8sZyhTs0cMlNLRi3ReaPOU1RYlNHRAQSggJn+vmDBAn366aen9dyamho9+OCDevzxx7s41be75557ZDKZjvtKS0s74znOlGnTphkdAUAH/H4/2+kBAAAAAGCgkKAQxTnjNGngJF055UrduehO/ew/fqYLRl+gkqoS3fbqbYq9IVbp96TrBy/9QB/t+UjNLc1GxwYQIAJmhVNpaanOOeccTZs2TcuXL9cFF1wgl8v1jc/5+OOP9dxzz+mFF15QXV2d1qxZc4bSHm/48OH685//3HY7KKj3/td2+PBh9enTx+gYANrh8/tY3QQAAAAAQA9hMpnksDrksDrUL6af5rfMl7feq/zyfOUcztHGXRv1uw9/J0maMmiKzhtxnrJGZyk5Ktng5AB6q97bXPybzz77TGvWrNG9996rq666Stdcc42GDBmisWPHyu12KyIiQvX19SovL9euXbv0z3/+U1VVVbJYLLrkkkt0//33q2/fvoZkDwoKUnx8vCHXPtP27dunCRMmGB0DQDtafC0UTgAAAAAA9FBBliBFhUUpKixKGckZqmusU0VNhXYU7dCuol361fu/0v+++L9KiU7R7LTZWpqxVHOGzlFoSKjR0QH0EgFTOEnS5ZdfruXLl+utt97S6tWrtXHjRj333HMnHGc2mzVq1Cidf/75uvrqq5WQkGBA2q/s2bNHiYmJstlsmjRpkh544IEOy6+GhgY1NDS03fZ6vWcqZpcwmwNml0fgrHNsSz221QMAAAAAoOcLDQlVaEioEiMTNTNtpqrqq1ToKVTO4RxtK9im9f9aL2+9VxP6T9CC4QuUNTpLwxOH82FTAKfN5Pf7/UaHMNKOHTt06NAhlZWVKTQ0VLGxsRo+fPi3brd3pvzpT39SdXW1hgwZosLCQt177706fPiwcnJyFB4efsLx99xzj+69994T7vd4PHI6nWciMoBe6rJVl6msukxXTL5CtmCb0XEAAAAAAMBpamxuVGVtpfaW7NX2wu3aV7pPe0r2KCI0QjOGzNCSUUt03qjzFBUWZXRUAN3A6/XK5XJ1eW8Q8IXT2aayslIpKSn6xS9+oauuuuqEx9tb4ZScnHzWFE6vvvqqLrjgAqNjAGjHd3//XVXUVGjF5BUUTgAAAAAA9BJ+v181DTU6Un1EWw9v1Z6SPdpTvEeFnkKN7DNSc4fNVWZGps5JPUdBloDaMAvotbqrcOJviLNMRESEBg8erL1797b7uNVqldVqPcOpus7XyzIAPQsznAAAAAAA6H1MJpMcNoccNof6xfRTc0uzvPVe5ZXlaVvBNv1l51/0xF+fkCRNGTRFi0YuUmZGppKjkg1ODqCnoXA6y1RXV2vfvn267LLLjI7SLTqaTQXAeH61LohlhhMAAAAAAL1XkCVIUWFRigqL0ui+o1XbWKvKmkptL9quXYW79MifH9H1L1yvftH9NHvobGVmZGpW2iyFhoQaHR2AwSicergf/OAHWrJkiVJSUlRQUKAf/vCHslgsys7ONjpatxg8eLDREQB0wOf3ta5wom8CAAAAACBg2EPssofYlRiZqFlps1RVX6XCykJtPbxVOYdz9Ornr6qqoUrj+43XwhELlZWRpWGJw9glBQhAFE493KFDh5Sdna2ysjLFxsZqypQp+vjjjxUbG2t0tG7x5z//udeWacDZzufzsboJAAAAAIAAZjaZ5Qp1yRXqUlpCmhqbG1VZW6m9JXu1o3CHnv/kef3ojR8pIjRCM4fM1JL0JTpv5HmKDIs0OjqAM4DCqYd74YUXjI4AAJK+WuFE6QQAAAAAACQpJChEcc44xTnjNGnAJNU01Ki0ulQ5h3O0p3iPbv3DrVr+1HKN7DNS84bNU+boTJ2Teo4sZovR0QF0Awon9CiTJ082OgKADrRtqQcAAAAAAPBvTCaTHDaHHDaH+sf0V3NLszx1HuWX5yvncI7e3/m+frPxNzKbzZo6cKrOG3WeMtMzlRSVZHR0AF2EwukbeL1eVVZWqm/fvkZHCRhHjhzh3zfQQ/n8PpllpnQCAAAAAADfKsgSpGhHtKId0Rrdd7RqG2tVWVOpbYXbtKtol3753i/1P+v+R/1j+mv20NnKTM/UzLSZCg0JNTo6gNMUsIXT66+/rtWrV+sf//iHysvLFRkZqWHDhik7O1srVqyQxWLRL3/5S/3oRz9SS0uL0XEDxq5duzRmzBijYwBoh9/vl8lM2QQAAAAAAE6dPcQue4hdiZGJmpU2S9UN1SqsLNTWw1u19dBWvfLZK6puqNaEfhO0YMQCZWVkaVjiMD74CpxFAq5wqq6u1qWXXqo33nhDfr+/7f6ioiIVFRXpgw8+0K9//WtmJwHAv2FLPQAAAAAA0BUsZotcoS65Ql1KS0hTQ3ODPLUe7S3Zq+2F2/X8J8/r3j/eq6iwKM0cMlNLRi3RwpELFRkWaXR0AN8g4Aqn7Oxsvfnmmxo3bpxuvfVWTZ06VZGRkTp8+LA+//xzPf744/rggw80c+ZMTZ8+3ei4Aefiiy82OgKADvh8PpmO/gMAAAAAANBVrEFWxTnjFOeM06QBk1TTUKOSqhLlHM7RnpI9uvkPN+uypy7TyD4jNW/4PGVmZOqc1HNkMVuMjg7ga0z+ry/z6eU2bNigCy64QN/5zne0Zs0aWSzt/4X03HPP6dprr1VDQ4MkndVb6nm9XrlcLnk8HjmdTqPjfKvXX39dS5cuNToGgHbM/+V8hdvCdenESxVkCbjPKwAAAAAAAAM0tzTLU+dRfnm+cg7naF/pPu0q3iWzyaypg6Zq0chFyszIVJ/IPkZHBc4a3dUbBNQ7hqtXr1ZsbKz+7//+r8OySZK++93vyuVyKTMzk+2jzrCamhqjIwDogM9/dIUTfy8CAAAAAIAzJMgSpGhHtKId0Rrdd7RqG2tVWVOp7YXbtbNopx5+72GtXLdS/WP6a/bQ2cpMz9SsobNkC7YZHR0IOAFVOH366adatGiR7Hb7tx67ZMkS/exnP1NOTs4ZSIZj+vThkwhAT8UMJwAAAAAAYDR7iF32ELsSIxM1M22mqhuqVVhZqK2Ht2rroa165Z+vqKaxRhP6T9CC4QuUNTpLQxOG8p4GcAYEVOFUVlamxMTEkz7+pptu6sY0aM+IESOMjgCgAz6/z+gIAAAAAAAAbSxmi1yhLrlCXUpLSFNDc4M8tR7tLt6tnYU7tfaTtbrnj/coKixKM4fM1NKMpVo4YqEi7BFGRwd6pYAqnFwul0pLS0/6+FdeeUXbt2/X3Xff3Y2p8HXvvPOOsrOzjY4BoB1+v59PAwEAAAAAgB7LGmRVnDNOcc44TR44WTUNNSqpKlHO4RztLdmrH7z0A33399/VqKRRmjdsnjJHZ2pi/4mymDsevwLg5AVU4ZSRkaE//elPampqUnBw8Dceu3nzZmVnZ8vn81E4AYC+WuFE6QQAAAAAAHo6k8kkh80hh82h1NhUNbc0y1PnUV5ZnrYVbNN729/T4xsfl8Vk0ZRBU7R41GItTV+qPpGM/ABOV0AVTtnZ2brqqqt022236eGHH+7wuA8//FDLli1TS0sLb6yeYRMnTjQ6AoAOMMMJAAAAAACcrYIsQYp2RCvaEa0xKWNU21iryppKbS/crh2FO/Tzd36u7z//faXGpmp22mxlZmRqZtpM2YJtRkcHzhoBVTgtX75cTzzxhB555BEdOHBA/+///T+NGTNGkuTz+bRlyxb95je/0Zo1axQSEqJ58+bpvffeMzh1YKmurjY6AoAO+P1+mWWWSZROAAAAAADg7GYPscseYldiZKJmps1UVX2VCisLtbVgq748+KVe/ufLqmms0cT+E7VgxAJlZWQpLSGND+MC3yCgCieLxaLXXntNixYt0oYNG/Taa6/JbrfL5XKppKRELS0t8vv9SkxM1EsvvaT33nuPwukM27Ztm0aNGmV0DADt8PlaVzjxixUAAAAAAOhNLGaLIuwRirBHaGjiUDU0N8hT69Hu4t3aUbhDz378rH74+g8VHRatmWkztSR9iRaOWKgIe4TR0YEeJaAKJ0mKj4/X5s2b9cQTT+ipp57S1q1bVVNTI0nq16+fvvOd7+jmm2+Wy+XSe++9J7/fb3BiAOgZjs1wAgAAAAAA6M2sQVbFOeMU54zT5IGTVd1QrdKqUuUcztGekj36wUs/0Hd//12lJ6Vr3vB5ysrI0vj+42UxW4yODhjK5A/wRqWhoUHl5eWKiIhQaGjocY/l5eUpNzdX06dPNyhd53m9XrlcLnk8HjmdTqPjfKumpiYFBwcbHQNAOyb8eIIGuwfr4vEXGx0FAAAAAADAEE0tTfLWeZVblqttBdu0r2SfdhXvUpA5SFMHTdWiUYuUmZGpxIhEo6MCHequ3iDgC6fe7mwrnN58800tWrTI6BgA2jHu/nEaGj9UF42/yOgoAAAAAAAAPUJtY63Ka8q1o3CHdhXt0t6Svcoty1VqbKrmDJ2jzPRMzUibIVuwzeioQJvu6g0Cbks99Gxer9foCAA6cGyGEwAAAAAAAFrZQ+yyh9iVFJm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JSUltK5nuv//+4475+OOPNWbMGIMSoqKiwugIAAAAACBJqq6oU25O65ylA21zlspUV92oqASHohIdcsWFaeCYeI1bOEDOGLusYSFtK5ZCbEEymSmWAAAAEBgCqnC68MIL9fjjj2vVqlWSpEsuuUQrVqxoe/yvf/2rvF5vj1xh8/jjj+tnP/uZioqKlJ6erscee0wTJkwwOlaXi4mJMToCAAAAgADTUNekg9uPKC+ndcVS7pZi5W8/osriGjlj7G1zlhIGRSnt3CRFuMNkCwtp2w6POUsAAACAZPL7/X6jQ+Cbvfjii1q+fLmeeOIJTZw4UY888ohefvll7dq1S3Fxcd/4XK/XK5fLJY/HI6fTeYYSn77q6mo5HA6jYwAAAADohVqafSrYW668rSU68GWxDnzZOmepJM8jqz1YMclORcaHyRVrlzM2TJHuMNmd1tbVSqFBsoYyZwkAAOBsUbCnXGmTkjR0UpLRUXqc7uoNKJz+zZ133ql9+/bphRdeMDpKm4kTJ2r8+PH69a9/LUny+XxKTk7WypUrddttt33jc8+2wmndunXKzs42OgYAAACAs5jf71fpQW/bnKX9x+Ys7SmXJMUmOxURH6YIt0PO6FBFxIfJEWGT1R4iq711xRJzlgAAAM5uFE4d667eIKC21PvRj370jY83NzfrhRdeUFFR0RlK9O0aGxv12Wef6fbbb2+7z2w2a86cOdq8efMJxzc0NKihoaHtttfrPSM5u0LpQY++fLlMtZ+/Z3QUAO0ItgYp64aJCrEF1P91AACAHq6qrE7520uVt61UuVtKlJdTosO7y9RQ23x0zlK4IuLDNGhCgkbP6y9HVKhs9pC2VUsdzVlqamgx4LsBAABAV2lqaBbrbc6sgHrX8J577vnGx499eq0nrbA5cuSIWlpa5Ha7j7vf7XZr586dJxz/wAMP6N577z3h/pdffll2u73bcnaF+pomBfWpVn7jF0ZHAdAO7+FalT6+nW1kAACAIfw+vxobmtVY16ym+mY1Hv1qafYpKNgia2iQrDHBip8fpOSlDlmCzUdf4zUe/apQjaQaSWo4+lVh3PcDAACA7uf9co++zLMZHaPHqa2t7ZbzBlTh9MEHH7R7f319vXbv3q3HH39czc3Nevjhh89wsq5z++2368Ybb2y77fV6lZycrGXLlp0VW+p98dkWxTgSjY4BoB0r0/9Pg69JVdo5LEMGAADdp6XZp8riapUe9OpIvlcleR6VHfLKW16nEFuQIuMdik6KVFyKS/GpkUocGK2oRIfsTqtCw0Nkd1oVbOUDMgAAAJBCw60K5sPTJ/B6vbr66qu7/LwBVThNnz69w8fmz5+vyy+/XCNHjtTKlSv10ksvncFkHYuJiZHFYlFxcfFx9xcXFys+Pv6E461Wq6xW65mK1+V27N6m7OxRRscA0A5LkFlWW5DszrP37xgAANBz+P1+eUpqVZLvUcmBShUdqFBpnlflRVUym0yKiHcoKsGhxEFRGjM/Vf3S3UoaHC27yyp7uFWhTqusoUHMWQIAAAB6iIAqnL6N0+nUokWL9NxzzxkdpU1ISIjGjh2r999/X1lZWZIkn8+n999/X9///veNDQcgoJjMJrHtLQAAOB01nnqV5nlUnFup4gOVKs71qOywV82NPrli7YqMdyi2r1MDxiQoZUScUkbEKjwqtHXFUrhVNkeIzO3MWQIAAADQc1A4/Zvg4GAFBwcbHeM4N954oy6//HKNGzdOEyZM0COPPKKamhpdccUVRkfrckuWLDE6AoAOmMwm+X00TgAAoGONdU0qPboNXtH+CpXkVqr0kFd13kY5Im2KjHcoJilc6bP6KSktWqkZ8Ypwhyk03Cp7eIhCw62yBJmN/jYAAAAAnAYKp69paGjQW2+91baSqKe4+OKLVVpaqrvvvltFRUXKyMjQ22+/LbfbbXS0Lrd582bNnTvX6BgA2mE2m+RjiRMAAJDU0tSisoIqleR6jq5YqlRpvkfeI3WyhQW3zlnqE64BYxM0LXuE+me4FZvsbNsKz+5kL30AAACgtwmowumZZ55p936/36+CggKtXbtWHo9HY8eOPeHY5cuXn4mIHfr+978fEFvoHTlyxOgIADpgNpskVjgBABBQ/D6/KktqVJLnUUlupYr2txZLFUXVMlvMiowPU1SCQwkDIjV63gClZsQpcVB061Z4TqtCw62y2XvWDhIAAAAAukdAFU4rVqxod6Cs/98+sb9y5crjHjOZTIYXToEiMjLS6AgAOmAym+ibAADoxaor6lWa37piqehAhUryPCo7XKWWJp8i4o7NWXJp8IREpYyIVd8RcXJE2I4WSyGyhTFnCQAAAAhkAVU4PfXUU+0WTug5ZsyYYXQEAB0wW0wSW+oBAHDWa6htUmm+52tzljw6csiruqpGOaJCFZUQpug+To2e019JQ2OUmhEvV6y9dc7S0XLJYmHOEgAAAIDj9frC6Te/+Y0yMzPVp08frVixwug4+Bbr169Xdna20TEAtMNkYoUTAABnk+amFpUdqlJJXuXX5ix5VVVWp1BHiCLiHYpJCteg8Yma8d0RGjA6XtF9nMdth8ecJQAAAAAnq9cXTt///ve1cuVKjRkzRllZWVq6dKlGjhxpdCwAOOuYLcxwAgCgJ/L7/KoorlFJXuVxc5Yqi2pkCTYrMt6hqASH+gyO1tiFAzUgI17xAyJld361YskaypwlAAAAAJ3T6wunTz/9VBs2bNDrr7+uu+66S3fffbf69evXVj5NnTpVZjPbQfQUlIFAz2Uym06YeQcAAM4cv9/fOmcpz6Pi3K9WLZUXVMvX4pMrLkxR8Q7FpriUdk4f9RvlVvKwGDkibG3b4dnCgtlmHAAAAEC3MPkD6N3D3NxcrV+/Xq+//ro2bdokn8+nqKgoLV68WJmZmZo3b57sdrvRMbuU1+uVy+WSx+OR0+k0Os632rt3rwYOHGh0DADtuKr/YxozP1XjFg0yOgoAAL1efU1ja7GU51Hx/gqV5Hl05KBX9bVNCo8KVVSCQzFJTsX1i1DysBj1T3fLFWNXaHiIQsOZswQAAACgY93VGwRU4fR15eXleuONN7Rhwwa99957qqmpkc1m0+zZs3X++edr8eLFiouLMzpmp51thdO6deuY4QT0UFcPeEzps/trwpLBRkcBAKDXaG5s0ZFDXpXkeVR8oELFBzwqzfeouqJeoc4QRbpb5yzFpUQocUi0BmTEKSrR2bYVnt1pVVAwc5YAAAAAnLzu6g16/ZZ6HYmKitLy5cu1fPlyNTQ06L333tNrr72mN954Q2+++abMZrPOOeccbdq0yeioANAjmC1mttQDAOA0+Vp8qiiqUUme5+icpQqVHvSqsrhGQSFH5ywlhit5aLQmLBmk1NHxiu8fcbRYat0OL8QWsC/fAAAAAJwFeMUiyWq1avHixVq8eLH8fr8+/vjjtrlPOLPOO+88oyMA6IDJbJLfZ3QKAAB6Nr/fr6ryuq/mLO2vVEmeR2UFVZJfcsXZFZUQrti+Tg2b2lf9R8YqaWiMwly2tnKJOUsAAAAAzkYUTv/GZDJp0qRJmjRpkh566CGj4wSczz//XDNnzjQ6BoB2mMySWOEEAECbuurWOUsleZUq2l+pktxKHTlUpYa6Jjmj7YpKCFN0klPjFg1U36Gx6pfuljM6tG07PJuDOUsAAAAAeg8KJ/QoRUVFRkcA0AGz2SwfhRMAIAA1NTS3zlnK9aj4QKWKcytVmu9VTWW97C6rIuMdik4K17DJyUfnLMUrKtHRtmIpNDyEOUsAAAAAer1eXThdeeWVp/U8k8mkVatWdXEanIzw8HCjIwDogNlsYoETAKBX87X4VF5YrZK8o8XSgQqV5nvlKalRsC3o6Jwlh1JGxGpS1hD1T3crPjVSoeEhbeUSc5YAAAAABKpe/Wro6aefbvd+k8nU7uD7Y/dTOBlnwYIFRkcA0AGzxSS/j8YJAHD28/v98h6pU2n+sWKpUiV5lSovqJYkRbjDFJXgUExfl0ZMT1H/UW4lpUV/bc5SiKx25iwBAAAAwNf16sLpwIEDx932+Xy6/vrr9fHHH+v666/X1KlT5Xa7VVxcrA8//FCPPvqoJk2apF/+8pcGJcbLL7+s7Oxso2MAaIfJ3H5ZDwBAT1ZX1aCSPI9Kco/OWcrz6Mghr5rqm+WMsSsywaGYZKcmLBmsvsNi1W9UnJzRoQoNt8rutMrmCJHZTLEEAAAAAN+mVxdOKSkpx91+8MEH9cknn+jLL79UQkJC2/1DhgzRtGnTdMUVV2j06NF65ZVXdMstt5zpuADQo5ktJslndAoAANrX1NCs0nyvSvIqj5uzVOtpUFhE65ylmKRwDZ/WV8lDotU/I0GRCWGyh4e0lUuWILPR3wYAAAAAnLV6deH071atWqWLLrrouLLp6/r06aOLLrpITz75JIWTQYYNG2Z0BAAdMJlN8rHCCQBgMF+LT2WHq1Tyte3wSvM98pTWyhoarMj4MEX1CVf/UW6de8FQDRgTr7gUl+zh1rZZS8HWgHoZBAAAAABnREC90jp06JBsNts3HmOz2XTo0KEzlAj/zuVyGR0BQAfMZrNE3wQAOEP8fr88pbUqzWstlooOVKo0z6PyoiqZTCZFuh2KTHQorp9Lo2b2U/8Mt5IGR8vusraVS8xZAgAAAIAzJ6AKp6SkJK1fv1733Xdfu8VTbW2t1q9fr6SkJAPSQZI2b96sfv36GR0DQDvMR2c4+f1+3rwDAHSpWm+DSnJb5ysV7a9om7PU3OiT62tzlgaMiVfK8FiljIhVeFSoQp2t5RJzlgAAAADAeAFVOF199dW6/fbbNXnyZN19992aMmWKoqOjVVZWpo8++kg/+tGPlJubqwceeMDoqADQ45gtJvl9/tZVTrynBwA4DY11TSo96FVJrkdFBypUkutR6UGP6ryNckTa2uYsjZyZoqQhMRowOl6uuDDZnda2WUvMWQIAAACAnimgCqebb75Zu3fv1urVq3XBBRdIat0iyufzSWrdtuOKK67QzTffbGTMgDZv3jyjIwDogOnoJ8f9fr9MNE4AgG/Q0uxTWUGVSnI9Ks6tVPH+CpUe9MpbWitbWLAi4x2K6hOu1DHxmnrxMKWOjldssrN1K7yj5RJzlgAAAADg7BJQr+LMZrNWrVql5cuXa82aNdqyZYs8Ho9cLpfS09N12WWXacaMGUbHDGjbt2/X1KlTjY4BoB1mi0k+P0OcAABf8fv8qiypUWl+65yl4gOt2+JVFFXLbDErwh2mqESHEgZEavS8VKVmuJUwMOroiqXWcskaGsRWrQAAAADQCwRU4XTM9OnTNX36dKNjoB2HDh0yOgKADpjM5tbt9AAAAammsl4leR6V5FWqaF+FSvK8KjvsVXOTT65Yu6KOzlkaOC5R/UbGqu+IODkibAoND5HdaZUtjDlLAAAAANCbBWThhJ7LbrcbHQFAByxHZzixyAkAereG2iaV5ntUkudR0f4KleR5dOSgV3VVjXJEhSoyPkwxSU5lzOmnPmkxSs1wKyIuTKHhVtmdVoU6QpizBAAAAAABKGALp5aWFh05ckQNDQ3tPt63b98znAiSlJmZaXQEAB0wmU2UTQDQi7Q0tejI4arWVUsHKlR0oFKl+V5VldXJ5ghRZHyYovuEa9C4RE3PHqEBY+IVk+RUaHhIW7kUHGIx+tsAAAAAAPQQAVc4ffbZZ7rjjjv04YcfqrGxsd1jTCaTmpubz3AySNK6deuUnZ1tdAwA7WgtnPyidQKAs4vf51dFcY1K8zwqzq1Q8f5KleR7VFlUI0uwWRHxDkUlONRncLTGLhio1Ix4JQyMbF2tdHQ7PGtosNHfBgAAAACghwuowumLL77Q1KlTFRQUpHnz5umPf/yj0tPTFR8fr88//1ylpaWaMWOGUlJSjI4KAD2O2dJaOFE3AUDP5Pf7W+cs5R6ds7S/UiV5HpUdrpKvxSdXXJii4lvnLA05p49SRsYpeVisHBE22Z3Wo3OWgmUyMWcJAAAAAHDqAqpwuu+++yRJn3zyiYYOHSqz2azzzz9fd999t+rq6nTTTTfplVde0VNPPWVw0sA1ePBgoyMA6IDZbFJLs180TgBgvPqaRpXme78qlnI9OnLQo/raJoVHhSryaLE0Zn6qkofGqH9GvJzRoUdXLbWuXLJYmLMEAAAAAOg6AVU4bdq0SUuXLtXQoUPb7vMf3RoqNDRUv/71r/X3v/9dd9xxh55//nmjYga0uLg4oyMA6IDZYlZzk8/oGAAQUJqbWnTkkFcluR4VH6hU8YFKHTnoVVV5nULDQxQZ71B0n3ANOSdRs5aP1IDRbkUlOtu2wwsNZ84SAAAAAODMCKjCyePxKDU1te12cHCwqqur226bzWbNmDFD69atMyIe1FoKMsMJ6JnMZpPk97cV9QCAruNr8X01Z+lApYoOVKo036PK4hoFhZgV6XYoKjFcyUOjNX7x0TlLAyIVGm5tK5eYswQAAAAAMFJAFU5xcXGqqKhoux0fH689e/Ycd0x9fb1qa2vPdDQA6PHMFpN8PsomAOgMv9+v6vJ6leS1boNXtL9CJfkelR+uks/nV4Q7TFEJ4YpJdmrY5CT1GxGn5OExCnPZ2rbDY84SAAAAAKAnCqjCadiwYdq1a1fb7cmTJ2vDhg3avHmzJk2apB07duill15SWlqagSkD26xZs4yOAKADJnPrm5sscAKAk1Nf3aiSfI9Kco/OWcrz6MhBrxrqmuSMtisyPkwxyU6NWzhQfYfGql+G+2tzlkJkczBnCQAAAABw9giowmnRokW64YYbVFhYqISEBN16661av369pkyZoqioKFVUVMjn8+mOO+4wOmrA2rdvn9xut9ExALTDbDHLzwonADhBU0OzjhyqUkle5XFzlqor6mV3WhUZH6boJKeGnpukPkOilZrhVnRi+HHb4QUFM2cJAAAAAHB2C6jC6b/+67900UUXKTIyUpKUnp6u999/Xz/+8Y+1f/9+jR07VitXrtSiRYsMThq48vLydO655xodA0A7zGZT6+omljgBCFC+Fp/KC6tVmv+1OUt5HnlKahRsDVJkgkNRiQ6ljIjVxKWDNWB0vOJTIxUaHtJWLoXYAurXbwAAAABAAAmoV7zBwcEnrJ4599xz9eabbxqUCP8uJCTE6AgAOmAOMsnv99M3Aej1/H6/qsrqVJJ3dDu8A5Uqya1UeWG15NfROUsOxfR1acS0vuo3Mk5JadFyRIQqNDxEdqdVVjtzlgAAAAAAgSWgCieLxaJLLrlEa9euNToKOnDhhRcaHQFAB8xmM2UTgF6nrqqhtVjK86hof4VK8jwqO+hVY32znDF2RSY4FJPs1Pglg5QyLFb9RrXOWTq2YsnmCJHZTLEEAAAAAEBAFU5Op1PJyclGx8A3ePnll7Vs2TKjYwBoh8likpjhBOAs1dTQrCMHvW3FUnFu65ylmsoG2V1WRSU4FN0nXMOn9lXSkGilZsQrMj7s6Iwl5iwBAAAAAPBtAqpwmjBhgr788kujY+AbNDc3Gx0BQAdaZzj55WeZE4AezNfiU1lBtUrzPCo6UKGSA5UqyffIU1qrEFuQohIcikoMV/9Rbp17fpoGjElQXIrraLHUuh1esDWgfkUGAAAAAKBLBNSr6XvuuUczZszQM888o+XLlxsdB+1ITU01OgKADrQWTpLomwD0AH6/X94jtSrJ9agkr1KF+ypVmu9ReWGVTCZT65ylxHDFprg0ckY/9UuPU9KQaIVF2GQ/umKJOUsAAAAAAHSdgCqc3nvvPc2YMUNXXHGFHnvsMY0fP15ut/uENxpMJpPuuusug1IGtr59+xodAUAHzBZz6wono4MACDi13mNzlipVtO/onKVDVWpqbJGrbc5SuFJHD1bKiDj1GxGr8KhQhTqtsoczZwkAAAAAgDPB5A+gvZHMZvNJHWcymdTS0tLNac4Mr9crl8slj8cjp9NpdJxvtW7dOmVnZxsdA0A7fv+D97Tn0wIt/M8xCg23Gh0HQC/UWN+sIwc9Ksn1qOhApYoPtM5ZqvU2KCzCpsj4MMUkOxWX4lJSWoxS0+MVER8m+9Gt8ELDrbIEndzvewAAAAAABKru6g0CaoXTBx98YHSENrm5ubrvvvv0l7/8RUVFRUpMTNR3v/td3XnnnQoJCWk7bsuWLbruuuv06aefKjY2VitXrtQtt9xiYHIAgcpiMcnvC5jPKADoRi3NPpUVVB2ds1Sp4gMVKs33ynukVtbQYEUmOBSV6FDqmHhNWTZUA0bHKzbF1boVntMqe3gIc5YAAAAAAOhhAuqV+vTp042O0Gbnzp3y+Xz63e9+p4EDByonJ0fXXHONampq9POf/1xSa8s4b948zZkzR0888YS2bt2qK6+8UhEREbr22msN/g66x7Rp04yOAKADZrNJ8vsVOOtiAXSW3+eXp7RWJXmVKs5tXbFUkudRRWG1zGaTIuJbi6X4/pHKmN1f/TPc6jM4WvajW+GFOq2yhgYxZwkAAAAAgLNAQBVOPcmCBQu0YMGCttupqanatWuXfvvb37YVTmvXrlVjY6OeeuophYSEaPjw4friiy/0i1/8otcWTocPH1afPn2MjgGgHWaLWSxwAtCRmsr6r+Ys7a88OmfJq+Ymn1yxrXOWYpOdGjgmQSkj45QyMk6OCJtCj26HZwtjzhIAAAAAAGezXl04LViwQPfdd5/Gjx9/ys+tqanRY489pvDwcF133XXdkO5EHo9HUVFRbbc3b96sadOmHbfF3vz58/XQQw+poqJCkZGRJ5yjoaFBDQ0Nbbe9Xm/3hu5i+/bt04QJE4yOAaAdJotJfr9fATT6D0A7GmqbdOSgt61YKs5tnbNUV9UoR6RNkfEOxSSHK31WPyUNjVFqulsR7jCFhrduhcecJQAAAAAAeqdeXTiVlpbqnHPO0bRp07R8+XJdcMEFcrlc3/icjz/+WM8995xeeOEF1dXVac2aNWck6969e/XYY4+1rW6SpKKiIvXv3/+449xud9tj7RVODzzwgO69997uDduNzGbegAJ6KovFzAwnIIC0NLXoyOHWOUvFBypUdMCj0nyPqsrqZAtrnbMUnRiuQeMSNT17hPpnuBWb7JTdaW0tl5xWBYdYjP42AAAAAADAGdKrC6fPPvtMa9as0b333qurrrpK11xzjYYMGaKxY8fK7XYrIiJC9fX1Ki8v165du/TPf/5TVVVVslgsuuSSS3T//ferb9++p3TN2267TQ899NA3HrNjxw6lpaW13T58+LAWLFigZcuW6Zprrjmt7/WY22+/XTfeeGPbba/Xq+Tk5E6d80y6+OKLjY4AoAMms0nyq/ULQK/h9/lVWVKjklxP65yl/RUqyfeqsqha5iCzIuPDFJUYrsSBkRozf4BSR7uVODDqaLHUumLJZg82+tsAAAAAAAAG69WFkyRdfvnlWr58ud566y2tXr1aGzdu1HPPPXfCcWazWaNGjdL555+vq6++WgkJCad1vZtuukkrVqz4xmNSU1Pb/lxQUKCZM2fq3HPP1f/93/8dd1x8fLyKi4uPu+/Y7fj4+HbPbbVaZbVaTyN5z/Dqq6/qggsuMDoGgHaYj65wYkc94Ozk9/u/mrOU61HR/gqV5HtUdrhKvmafXHFhioxvnbM0eGIfpYyMU9/hsXJE2NrKJeYsAQAAAACAjvT6wkmSTCaTFi1apEWLFklqXWF06NAhlZWVKTQ0VLGxsRo+fPi3brd3MmJjYxUbG3tSxx4+fFgzZ87U2LFjtXr16hO2k5s0aZLuvPNONTU1KTi49ZPD7733noYMGdLudnq9wdfnTwHoWcwW09GyicYJ6OkaaptUmn+0WDpQoeIDHh055FV9daPCo0Nb5ywlhWv0nP5KHhaj/unxcsXa27bCCw0PkcXCNrcAAAAAAODkBUTh9O+GDh2qoUOHGprh8OHDmjFjhlJSUvTzn/9cpaWlbY8dW730ne98p207wFtvvVU5OTn61a9+pV/+8pdGxe52p7qFIYAzp7V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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "delta_0 = -6 * U\n", + "delta_f = 2 * U\n", + "t_rise = 252\n", + "t_fall = 500\n", + "t_sweep = (delta_f - delta_0) / (2 * np.pi * 10) * 1000\n", + "rise = Pulse.ConstantDetuning(\n", + " RampWaveform(t_rise, 0.0, 0.0), 0, 0.0\n", + ")\n", + "sweep = Pulse.ConstantAmplitude(\n", + " Omega_max, RampWaveform(t_sweep, delta_0, delta_f), 0.0\n", + ")\n", + "fall = Pulse.ConstantDetuning(\n", + " RampWaveform(t_fall, Omega_max, 0.0), delta_f, 0.0\n", + ")\n", + "seq1 = Sequence(reg, MockDevice)\n", + "seq1.declare_channel(\"ising\", \"rydberg_global\")\n", + " \n", + "seq1.add(rise, \"ising\")\n", + "seq1.add(sweep, \"ising\")\n", + "seq1.add(fall, \"ising\")\n", + "\n", + "seq1.draw()" + ] + }, + { + "cell_type": "code", + "execution_count": 208, + "metadata": {}, + "outputs": [], + "source": [ + "sim = QutipEmulator.from_sequence(seq1)" + ] + }, + { + "cell_type": "code", + "execution_count": 209, + "metadata": {}, + "outputs": [], + "source": [ + "import qse.qbits\n", + "\n", + "\n", + "L = 3\n", + "nqbits = L * L\n", + "qsqr = qse.Qbits(positions=np.array([[0,0,0]]))\n", + "\n", + "\n", + "Omega = 1.2 # Amplitude\n", + "delta = 2.0 # detuning\n", + "C6 = 5420158.53 # interaction scale\n", + "nqbits=1\n" + ] + }, + { + "cell_type": "code", + "execution_count": 210, + "metadata": {}, + "outputs": [], + "source": [ + "H1_terms = [qat.core.Term(0.5, \"X\", [i]) for i in range(qsqr.nqbits)]\n", + "H1 = qat.core.Observable(nqbits, pauli_terms=H1_terms)\n", + "\n", + "H2_terms = [qat.core.Term(-0.5, \"Z\", [i]) for i in range(qsqr.nqbits)]\n", + "H2 = qat.core.Observable(nqbits, pauli_terms=H2_terms)\n", + "\n", + "rij = qsqr.get_all_distances()\n", + "\n", + "\n", + "def occ_op(nqbits, qi):\n", + " ti = qat.core.Term(1.0, 'Z', [qi])\n", + " return (1 + qat.core.Observable(nqbits, pauli_terms=[ti])) / 2\n", + "#\n", + "# H3 = 0\n", + "\n", + "# for i in range(nqbits):\n", + "# for j in range(i + 1, nqbits):\n", + "# H3 += (C6 / rij[i, j]**6) * occ_op(nqbits, i) * occ_op(nqbits, j)" + ] + }, + { + "cell_type": "code", + "execution_count": 211, + "metadata": {}, + "outputs": [], + "source": [ + "from qat.core.variables import Variable, heaviside\n", + "from qat.core import Observable\n", + "\n", + "def create_waveform(times, values):\n", + " \"\"\"\n", + " A Funnction allowing us to concatenate many lines, limited by heavisides,\n", + " thus creating a continuous, kinked line.\n", + " \"\"\"\n", + " assert len(times) == len(values)\n", + " # Store the final line as an ArithExpression\n", + " arith_expr = 0\n", + " t_var = Variable(\"t\")\n", + " # A line between each two points\n", + " for entry_i in range(1, len(times)):\n", + " # Create ax + b by calculating the slope and the offset\n", + " a = (values[entry_i] - values[entry_i - 1]) / (times[entry_i] - times[entry_i - 1])\n", + " b = ((values[entry_i] + values[entry_i - 1]) - a * (times[entry_i] + times[entry_i - 1])) / 2\n", + " respective_line = a * t_var + b\n", + " arith_expr += heaviside(t_var, times[entry_i - 1], times[entry_i]) * respective_line\n", + " return arith_expr\n", + "#\n", + "Omega_max = 2.0 * 2 * np.pi\n", + "U = Omega_max / 2.0\n", + " \n", + "delta_0 = -6 * U\n", + "delta_f = 2 * U\n", + " \n", + "t_rise = 0.252\n", + "t_fall = 0.500\n", + "t_sweep = ((delta_f - delta_0) / (2 * np.pi * 10) * 1000)*(10**-3)\n", + " \n", + "\n", + "# The waveform of Omega - for the sigma_x terms\n", + "omega_values = [0.0,0,Omega_max,0]\n", + "times_omega = [0,t_rise,t_rise+t_sweep,t_rise+t_sweep+t_fall]\n", + "\n", + "\n", + "omega_waveform = create_waveform(times_omega, omega_values)\n", + "# The waveform of the detuning Delta - for the 'n' terms\n", + "delta_start = -2 * np.pi * 13\n", + "delta_end = 2 * np.pi * 11 # R_blockade is taken as 7.5\n", + "delta_values = [0,0,delta_f,delta_f]\n", + "delta_waveform = create_waveform(times_omega, delta_values)" + ] + }, + { + "cell_type": "code", + "execution_count": 212, + "metadata": {}, + "outputs": [], + "source": [ + "from qat.core import Observable \n", + "Hamiltonian = Observable([\n", + " (omega_waveform, H1),\n", + " (delta_waveform, H2),\n", + " ])\n", + " \n", + "schedule = Schedule(drive=[\n", + " (omega_waveform, H1),\n", + " (delta_waveform, H2),\n", + " ], tmax=t_rise+t_sweep+t_fall)" + ] + }, + { + "cell_type": "code", + "execution_count": 213, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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fTuGd/50WFRP169hi9fggTO7d0uTFhDlTKuT49sUANHS202tfcywJkceSJIqKzJlFFBTNmzeHh4cH9uzZU9yWmZmJY8eOITg4uNRzbG1tERgYqHeOTqfDnj17yjyHiKxP0r1cPLf8MNafuC7qC2jijO2v9UT3Vq4SRGb+6tdV4bsxgVAr9X9VzN52BidK2SiNajezKSiys7MRFxeHuLg4AA/mMcTFxSEpKQkymQzTp0/Hxx9/jG3btuH06dMYO3YsvLy89CZc9u3bF0uXLi1+PWPGDPzwww/473//i/Pnz2Py5MnIyckpfuqDiKzbnvMpGLrkH5y9Jb4n/FKPZlg3KRieTnalnEkPdWzohM+f89Vr02gFvLo6BrczxPNQqPYymzkUJ06cQJ8+fYpfz5gxA8CDpzJWrVqFt99+Gzk5OZg0aRLS09PRs2dP7Ny5E2q1uvicK1euIDU1tfh1aGgo7t69i1mzZiE5ORn+/v7YuXOnaKImEVkXrU7A4t0XsWTvZVGfva0Cnz/ni2Eltu+msj3j3xDnbmXiuwMJxW2p2QV49ddorH8lGGqlZe22SjXDbAqK3r17o7wnWGUyGT766CN89NFHZR5z9epVUVtERAQiIiKqI0QisgD3sgvw+ro4HLycKupr2aAOVowORGt3h1LOpPK8Pcgb525n4p9Lj/67nryRgfc3n8HCkb4Wu+sqVR+zueVBRFRVMUn3MXTJwVKLiad9PbE1oieLCSMp5DIsDQtA0/r6q4b+L+YGVh2+Kk1QZFZYUBCRxRMEAb8cuYrQ747gdob+cvw2chlmDW2PpWGdUFdlNoOyFsnJXokfxnaGva3+LY6P/ziPw6UUcVS7sKAgIouWW1iE6evjMGvrWb3logHA3VGFdZO64eWezTkkX03auDvgq1H+em1anYCpkTG4cZ+TNGszFhREZLGu3M1GyLJD2Bp3S9TXrYULtk/rhc7NXCSIzLoN6uiB1/q21mu7n6vB5Mg4FGjLOImsHgsKIrJIf56+jWeWHsLFlGxR36tPtsTq8UFo4GD4kvlUOdP7tka/dvpPzF1IzsLaK/JyJ9iT9WJBQUQWRaPV4ZM/zmHymhhkFxTp9TmobPDdmEDMHOwNGwU/3mqSXC7DolA/tHKrq9cee0+O7/+5Kk1QJCn+xBGRxcgoBMauPIEf/kkU9Xl7OGDbtJ4Y2IFL65uKg1qJ78cEwkGtP9n1y92X8Hf8HYmiIqmwoCAii3D8ahoWnlLgxLV0Ud+znRpi85QeaO5ai/ccl0iLBnXxzQud8PicV0EAXlsbi4S74ttRZL1YUBCRWRMEAT8cSMDYldHI1Og/qWGrkOPjkI74cpQf7Gy5WqNU+ni74a2BbfXasvKLMOnXaGTlaySKikyNBQURma2sfA2mrInBJzvOQ6vTn+jX0NkOG18NxuhuTflIqBmY/GRLDOmoP0nz8p1svLH+JHQ6TtKsDVhQEJFZik/OwjNLD+HPM8mivifaNMD2aT3h19jZ9IFRqWQyGeaP6ICG9vrFw+7zKVi855JEUZEpsaAgIrOzJfYmQpYdQkJqjl67DAKm9WmBlf/pgnp1bCWKjspib2uD8W21qGev1Gv/Zs8l7CylMCTrwoKCiMxGYZEOs7aewfT1ccjT6K+Q5GynxCRvHV57qhUUct7iMFf11cDXob6i9+j/NsThYkqWRFGRKbCgICKzcCs9D6O+O4JfjlwT9fk0dMLmyd3Qvh7vxVuC4Bb18f6QdnptOYVaTPzlBNJzCyWKimoaCwoiktyhy6kYuuQg4q6ni/rCujbBxleD0aienekDI6O91KMZngtopNd27V4upq2NFU2wJevAgoKIJKPTCVj292WM+ekY0nL0/3JV2cix4HlfzH/WB2olHwm1NDKZDJ+M6Ai/Rk567f9cSsUXOy9IFBXVJBYURCSJjFwNJv5yAgv+ikfJP1ib1rfHpindMbJzY2mCo2qhViqwYkwgXOvq76ny3YEEbI27KVFUVFNYUBCRyZ25mYGhS//Bngvi5Zn7tXPDtoie6ODlVMqZZGk8neywYnQAlAr9SZpv/3YKZ25mSBQV1QQWFERkUhtOXMezyw/jelqeXrtcBrw1sC2+H9MZTnbKMs4mS9S5mQvmDu+o11ZQpMOkX04gNbtAoqiourGgICKTyNdoMfN/p/D2b6dQWKTT66tfxxarxwdhap9WkPORUKsUHtQELwY10Wu7lZGPKWtioNHqyjiLLAkLCiKqcdfTcvH8isNY9+91UV9AE2f88VovdG/lKkFkZEqzh3VAl2b19NqOJ6bh4+3nJIqIqpPFFBTNmjWDTCYT/Zs6dWqpx69atUp0rFqtNnHURLT3Qgqe/uYfnLmZKer7T/dmWDcpGB5O/NmsDWxt5Pj2xUB4lni//3vkGjaUUmySZbGp+BDz8O+//0KrfbRy3pkzZ9C/f3+MHDmyzHMcHR0RHx9f/JobCBGZjlYnYPHui1iy97Koz95Wgc+e88VwPy8JIiMpNXBQ4bsxgRi54ggKHrv19cGWM2jlXhcBTeqVczaZM4sZoWjQoAE8PDyK/23fvh0tW7bEk08+WeY5MplM7xx3d/cyjyWi6pOWU4j/rDxeajHRskEdbJ3ag8VELebbyBnzn/XRayvU6vDqr9FIycyXKCqqKosZoXhcYWEhVq9ejRkzZpQ76pCdnY2mTZtCp9MhICAAn376KTp06FDh9dPS0qDRaIpfq1QqqFSqcs4o3cNrPH4tS8ecLIOUOZ28kYFp607idob4F8PgDu74dEQH1FXZGBybtb1P1pYPYFhOw3zccfpGU6w8/Gip9TtZBXjl1xNY/XIXqGzM4+/d2vg+GZurTBAEi1sDdcOGDQgPD0dSUhK8vEr/K+fIkSO4dOkSfH19kZGRgYULF+LAgQM4e/YsGjVqVOo5mZmZcHISP/seGhqKsLCwas2ByNoIAnAoRYZNV+XQCvqFvlwm4JmmOjzpIYB3HukhrQCsOC/HxQz94iGogQ5hLXX8XpFIbm4uwsPDkZGRAUdHx0qfZ5EFxcCBA2Fra4vff/+90udoNBq0a9cOYWFhmDdvXqnHPCwoEhMT4eDgUNxelRGKqKgo9O/fH0qldTxXz5wsg6lzyi0swqxt57H15G1Rn5uDCl+H+qJz06rdG7e298na8gGMy+l+biGeXXEMN+7rr0sye6g3Rpd4zFQKtfF9yszMhKurq8EFhcXd8rh27Rp2796NTZs2GXSeUqlEp06dcPmy+J5uSS4uLgb9R6zM17aWb8SHmJNlMEVOCXezMXl1DOJL2Zo6qLkLloR3gptD9T3FYW3vk7XlAxiWk5uTEj+M7Yxnvz2st2X9Jzvi0c7LGd1a1K+pMA1Sm94nY/M0j5tUBli5ciXc3Nzw9NNPG3SeVqvF6dOn4enpWUOREdU+O88kY/jSQ6UWE6880QJrJgRVazFB1qmdpyMWjvTTayvSCZi6JgY30/PKOIvMjUUVFDqdDitXrsS4ceNgY6M/uDJ27Fi8++67xa8/+ugj7Nq1CwkJCYiJicHo0aNx7do1TJgwwdRhE1mdIq0O83ecx6uro5FdUKTX56CywYrRgXh3SDvYKCzqI4Yk9LSvJ6b2aanXdi+nEJN+OYG8Qm0ZZ5E5sahbHrt370ZSUhJefvllUV9SUhLk8kcfXvfv38fEiRORnJyMevXqITAwEIcPH0b79u1NGTKR1bmTlY+IyFgcT0wT9Xl7OGD56EA0d60jQWRk6Wb0b4vzt7Ow97FN487eysTMTaewONSfawmZOYsqKAYMGICy5pDu27dP7/WiRYuwaNEiE0RFVHscT0zD1MgY3M0Sb+g0olNDfDrCB3a2CgkiI2ugkMuw+AV/hCw9hITUnOL2rXG30NHLCROfaCFhdFQRjkcSUYUEQcCP/yQg7IejomLCViHHxyEd8dUoPxYTVGWOaiW+H9sZdVX6f+/O//M8Dly8K1FUVBksKIioXFn5GkyNjMHHf5yHVqc/QujlpMaGV4MxultTDkdTtWnlVhdfv+Cvtw6FTgCmrY3FtXs5ZZ9IkmJBQURlupiShWeWHcKO08mivl6tXbH9tV7wb+xs+sDI6vVt544Z/drotWXkaTDxlxPIKTERmMxDleZQ3L9/H7t27cLNmzcBAF5eXhg4cCDq1ePmLkSWbmvcTcz832m9tQEeeq1va7zetzUUco5KUM2JeKoVzt3OxJ9nHhW0F1Oy8X8bTuLbFwMg5/efWTF6hOKnn35CcHAwjh07Bp1OB51Oh2PHjqF79+746aefqjNGIjKhwiIdZm89g9fXxYmKCSc7JVb+pwtm9G/DYoJqnEwmw8KRfmjr7qDXvvNsMpb+XfEihWRaRo9QfPHFF4iJiUGdOvqPh82bNw8BAQEYP358lYMjItO6nZGHKWtiEJuULurr2NARy18MRGMXe9MHRrVWHZUNvh8biOFLDyEj79GmVV9FXUQ7T0f0b89dpM2F0SMUMpkMWVni1fGysrI4OYvIAh26nIqnvzlYajER1rUJfnu1O4sJkkTT+nWwNLwTSg6KvbE+DpfviH8PkTSMHqFYuHAhnnzySXTs2BENGzYEANy4cQNnz57Fl19+WW0BElHN0ukELN9/BV/uikeJhzigsnnwSOjIzo2lCY7o/+vVugHeHdwOn+w4X9yWXVCEib9EY8vUHnCys659NiyR0QXF0KFDMXjwYBw/fhy3bt0C8GBSZteuXaFQ8Fl0IkuQkavB/22Mw+7zd0R9TVzssXx0ADp4OUkQGZHYhF7Nce52JjbH3ixuS0zNwevrYvHTuC6c1yOxShcUDg4O6NSpEwIDAxEQEICAgAC0b98ewcHBNRkfEdWQs7cyMHl1DJLSckV9/dq54ctR/vyrj8yKTCbD/Gd9cPlONk7fzChu3xd/Fwt3xeOdQd4SRkeVLig+//xzREdHY+/evVi6dCl0Oh3s7Ozg6+urV2T4+flVfDEiktSGE9fx4ZYzKCjS6bXLZcD/DWiLyU+25CN5ZJbUSgVWjAnE8CUHcS+nsLh9+b4raO/piGF+XhJGV7tVuqCYMmVK8f/Py8tDnTp1MG3aNKSlpeHo0aP48ccfUVhYCK2Wu8IRmat8jRZzfz+Ltcevi/rq17HFN2Gd0KOVqwSREVVeQ2c7LB8diPAfjqLosYk/b/12Ei0a1OFtOokYNYfCzs4OABAWFgZfX18AQFFREc6dO1d9kRFRtbqelospa2L0hoofCmjijGUvBsDTyU6CyIgM17W5C2YP74APt5wpbsvX6PDKr9HYFtETLnVsJYyudqq2pbdtbGyKiwsiMi9/x9/B0CUHSy0m/tO9GdZNCmYxQRZndFATvNBF/wmkG/fzEBEZgyKtroyzqKZwLw8iK6bVCfgq6iJeXvWv3qJAAGCnVODrF/wxZ3gH2Nrwo4Asj0wmw9xnOiCgibNe++Er9/DpjgvSBFWLVfpTZMKECVi+fDn+/fdfFBQ82L6YC1gRma9sDTDh1xh8s+cShBLrS7RoUAfbInrgGf+G0gRHVE1UNgqsGB0Id0eVXvvPhxLxv+gbEkVVO1V6DsWlS5ewceNGZGVlwcbmwWlz585F7969ERAQAH9/f9jbcxU9InNw8kYGFpxSIL3wnqhviI8HvnjeD3VVVdobkMhsuDmqsWJ0IEK/O4rCx251vLv5NFq51YUfd8Q1iUqPUOzfvx8ZGRmIj4/HL7/8gjfffBPp6emYNWsWevbsCScnJ3To0KEmYyWiCgiCgNVHryHsx+NIL9QfQVTIZfjg6XZYFh7AYoKsTqcm9fDJiI56bYVFDyZp3snKlyiq2sXgT5XWrVujdevWeOGFF4rbEhMTceLECcTGxlZrcERUeXmFWry/+TQ2PbaK4EMNHFRYFh6Ars1dJIiMyDRGdm6Ms7cyserw1eK25Mx8TFkdg8iJ3ThXqIZVy58pzZs3R/PmzTFy5MjquBwRGSgxNQeTV0fjQrJ4o6SuzV2wNKwT3BzVEkRGZFrvP90O8clZOJLw6HbfiWv3Mef3s/h0hI+EkVk/lmtEFm7nmWQMX3Kw1GJifI+miJwQxGKCag2lQo5lLwagobP+Y9CRx5Kw5tg1iaKqHVhQEFmoIq0O8/88j1dXRyOroEivr45KgZfbaDFzUFvYKPhjTrWLSx1bfD82EGql/vf+7K1n8e/VNImisn4W80kzZ84cyGQyvX/e3uVvBLNx40Z4e3tDrVbDx8cHO3bsMFG0RDXrTlY+XvzxGL7bnyDqa+vugM2vdoNffaGUM4lqhw5eTljwvP7eUkU6AZNXR+N2Rp5EUVk3iykoAKBDhw64fft28b+DBw+Weezhw4cRFhaG8ePHIzY2FiEhIQgJCcGZM2fKPIfIEvx7NQ1DvzmIY4niv7RC/L2weWp3NHetI0FkROZlmJ8XXn2ypV5banYhXvk1Gvka7jtV3Szq2TEbGxt4eHhU6tivv/4agwYNwltvvQUAmDdvHqKiorB06VKsWLGi3HPT0tKg0TxaVVClUkGlUpVzRukeXuPxa1k65iQdQRCw6kgSvvjrot6GSACgVMjw/hBvhHdpBJlMsJicDGFtOVlbPoB55jT9qRY4dysdBy49mqR56kYGZv52El8817HCBRrNMaeqqignY3OVCULJNfTM05w5c7BgwQI4OTlBrVYjODgY8+fPR5MmTUo9vkmTJpgxYwamT59e3DZ79mxs2bIFJ0+eLPWczMxMODmJd6kLDQ1FWFhYteRBZIx8LbD2ihxx98SDis62Al5qo0UzBwkCI7IAuUXAl6cVSM3XLx5CmmrRx8sifgWaVG5uLsLDw5GRkQFHR8dKn2cxIxRBQUFYtWoV2rZti9u3b2Pu3Lno1asXzpw5AwcH8SdpcnIy3N3d9drc3d2RnJxc4ddKTEzUu2ZVRiiioqLQv39/KJVKg883R8zJ9C7dyUbE2jgk3MsV9fVoWR9fjvRB/RI7K5p7TsawtpysLR/AvHPy65aNkd8dQ07ho1sd25IUCOkTiB4t65d5njnnZKyKcsrMzDTquhZTUAwePLj4//v6+iIoKAhNmzbFhg0bMH78+Gr9Wi4uLgZVZRVRKpVW8434EHMyja1xN/HuptPILRTf733tqVZ4vV8bKORlD9maY05VZW05WVs+gHnm1L5hPSwK9cekX6OL23QCMH3DKWyb2hNN6pe/dYQ55lRVZeVkbJ4WNSnzcc7OzmjTpg0uX75car+HhwdSUlL02lJSUio9B4NISoVFOszZdhavr4sTFRNOdkr8/J/OmDGgbbnFBBHpG9DBA9P7tdZrS8/VYNKvJ5BT4tFrMpzFFhTZ2dm4cuUKPD09S+0PDg7Gnj179NqioqIQHBxsivCIjHY7Iw8vfH9Eb/nghzp4OWL7tJ54yttdfCIRVei1p1pjQHv9n58LyVl467eTsJAphWbLYgqKN998E/v378fVq1dx+PBhjBgxAgqFoniy5NixY/Huu+8WH//6669j586d+PLLL3HhwgXMmTMHJ06cQEREhFQpEFXo8OVUDP3mIGKS0kV9oZ0b43+Tu6OxC3f1JTKWXC7DV6H+aO1WV699x+lkfLvvikRRWQeLKShu3LiBsLAwtG3bFqNGjUL9+vVx9OhRNGjQAACQlJSE27dvFx/fvXt3REZG4vvvv4efnx9+++03bNmyBR07dizrSxBJRqcT8O2+yxj90zHcyynU67O1kePz53zw+fO+UCsVEkVIZD3qqmzww9jOcFTrTyNcuCseey+klHEWVcRiJmWuW7eu3P59+/aJ2kaOHMkNy8jsZeRp8H8bTmL3efEHWWMXOyx/MRAdG4ofZyYi4zVzrYMl4QF4aeVxPFzWRRCA19fGYfPUHmhVYgSDKmYxIxRE1ujsrQwMX3qw1GKir7cbtkf0YjFBVEOebNMA7wzS38Ihq6AIk349gcx861nIylRYUBBJ5LfoG3j228O4VmJ9CbkMeHNAG/wwtjOc7K3rMTUiczPpiRYY7uel15ZwNwdvrIuDTsdJmoZgQUFkYvkaLd7ddApvbjyJgiKdXp9LHVv88nIQIp5qDTkfCSWqcTKZDJ8/54v2nvprD+25cAeLdl+UKCrLxIKCyISup+Vi5IojWHv8uqivUxNnbJ/WEz1bu0oQGVHtZWerwPdjA+FSYsXZJXsvY+dZTtKsLBYURCbyd/wdDF1yEKdvZoj6xgY3xfpJwfBytpMgMiJqVM8ey8IDRIvFvbPpDG7lSBSUhWFBQVTDtDoBX0VdxMur/kVGnv5ELzulAl+/4I+PnukIWxv+OBJJKbhlfXz4dDu9ttxCLX6MVyA9l5M0K8JPMKIalJZTiJdW/Ytv9lxCyUX4WrjWwdaIHnjGv6E0wRGRyLjuzTAysJFe270CGaZvOIUira6MswhgQUFUY05eT8ewJQdx4OJdUd/gjh7YGtEDbdy55ziROZHJZJgX0hF+jZ312g9duYfPd16QJigLwYKCqJoJgoA1x65h5IojuJmep9enkMvwwdPt8O2LAXBQ85FQInOkVirw3ehANHBQ6bX/8E8itsTelCgq88eCgqga5RVq8ebGU3h/8xkUlhgebeCgwtqJ3TChVwvIZHwklMiceTipsWJ0AJSKEpM0/3cKp2+IJ1YTCwqiapOYmoMR3x7C/2JuiPq6NnfBH6/1RNfmLhJERkTGCGzqgjlD9SdpFhTp8MqvJ5CaXSBRVOaLBQVRNfjrbDKGLzmIC8lZor5JT7TAmglBcHNQSxAZEVXFqM6N0NNdf7TxVkY+pqyOgYaTNPWwoCCqgiKtDvP/PI9Xfo1GVkGRXl9dlQ1WjA7Ae0PaQangjxqRpRrRTIfOTZ312o5fTcNHv5+TJiAzxU85IiPdzSrA6J+O4bv9CaK+tu4O2BbRA4M6ekoQGRFVJxs5sPQFP3g56Y8y/nr0GtYdT5IoKvPDgoLICCeupuHpb/7B0YQ0UV+Ivxc2T+2OFg24/TGRtahfV4XvxnSGqsQCdB9uPYPoa+LPgdqIBQWRAQRBwE8HE/HC90dxJ0t/UpZSIcNHz3TAolB/2NvaSBQhEdUUn0ZO+Pw5X702jVbAq6tjkJyRL1FU5oMFBVElZRcUIWJtLOZtP4eiEtsaezqpseGVYIwNbsZHQomsWEinhpjYq7le292sAryyOhr5Gq1EUZkHFhRElXD5ThaeWXoQf5y6Lerr1doV26f1RKcm9SSIjIhM7Z1B3uhVYlfgk9fT8eGWMxBKrrFfi7CgIKrA7ydvYfjSQ7hyV7zl4LSnWmHVS11Rv66qlDOJyBrZKORYEtYJTVzs9do3Rt/AL0euSRSV9FhQEJWhsEiHub+fxbS1scgt1B/KdFTb4Of/dMb/DWgr2u6YiKyfs70tfhjbGfa2Cr32j7afw+ErqRJFJS0WFESlSM7IR9gPR7Hy0FVRXwcvR/zxWi885e1u+sCIyGy09XDAV6P89Nq0OgFT18TgelquRFFJx2IKivnz56NLly5wcHCAm5sbQkJCEB8fX+45q1atgkwm0/unVnO1Qirf4cupGLrkH0Rfuy/qC+3cGP+b3B2NSwx1ElHtNKijJ157qpVe2/1cDV75NRp5hbVrkqbFFBT79+/H1KlTcfToUURFRUGj0WDAgAHIyRHf136co6Mjbt++Xfzv2rXae3+LyicIApbvu4LRPx1DanahXp+tjRyfP+eDz5/3hVqpKOMKRFQbTe/XBv3auem1nbudibf/d6pWTdK0mIfld+7cqfd61apVcHNzQ3R0NJ544okyz5PJZPDw8Kjp8MjC5RYBUyLjsPvCXVFfYxc7LH8xEB0bOkkQGRGZO7lchkWh/ghZpj95+/eTt9DByxGvPtlSwuhMx2IKipIyMh5sH+viUv7ujdnZ2WjatCl0Oh0CAgLw6aefokOHDuWek5aWBo1GU/xapVJBpTJ8Fv/Dazx+LUtnjTmduXEfX55SILVAXEz0buOKhc/7wMlOaVE5W+P7ZG05WVs+QO3OSa0Alof749kVx5D92L4+n++8gNYN7PFEicdMpVRRTsa+fzLBAsdjdDodhg8fjvT0dBw8eLDM444cOYJLly7B19cXGRkZWLhwIQ4cOICzZ8+iUaNGouMzMzPh5CT+KzQ0NBRhYWHVmgOZh+N3ZdiQIIdGp/+khgwChjTWoV9DAXyIg4gq6+x9GX64IIeARx8cdgoBM3y0cLOTMDAD5ObmIjw8HBkZGXB0dKz0eRZZUEyePBl//vknDh48WGphUBaNRoN27dohLCwM8+bNE/U/LCgSExPh4OBQ3F6VEYqoqCj0798fSqXS4PPNkbXkVKDR4uM/47Hu3xuivnr2Snw10hc9W9WXILLqYS3v0+OsLSdrywdgTg+t2J+AL3df1mtr1aAONr4ShLoq6W8MVJRTZmYmXF1dDS4opM/MQBEREdi+fTsOHDhgUDEBAEqlEp06dcLly5fLPc7FxcWg/4iV+brW8sP1kCXndD0tF1MjY3DqRoaoz7+xM759MQBezhbyp0QFLPl9Kou15WRt+QDMKaJvG1xIycEfpx+trHv5bg7e2XQWK0YHQm4mw55l5WTse2cxT3kIgoCIiAhs3rwZe/fuRfPmzSs+qQStVovTp0/D05NbStdW++LvYNjSg6UWE6ODGmP9K92sppggImnIZDIsGOkLbw8HvfZd51Lwzd5LEkVV8yymoJg6dSpWr16NyMhIODg4IDk5GcnJycjLyys+ZuzYsXj33XeLX3/00UfYtWsXEhISEBMTg9GjR+PatWuYMGGCFCmQhHQ6AYt3X8RLq/5Feq7+hCM7pRxjWmkxe2g7qGz4SCgRVZ29rQ1+GNsZzvb6f+0v3n0Jf51NliiqmmUxBcXy5cuRkZGB3r17w9PTs/jf+vXri49JSkrC7duPhpju37+PiRMnol27dhgyZAgyMzNx+PBhtG/fXooUSCL3cwrx0qp/sXj3JZScMdTCtQ5+eyUInRtY3FQiIjJzjV3ssSw8QDSxe8b6OFxKyZImqBpkMXMoKjN3dN++fXqvFy1ahEWLFtVQRGQJTl5Px5Q1MbiZnifqG9TBAwtG+kKtAMqfVUNEZJwerVzx3pB2+PiP88VtOYVaTPzlBLZO7Qkne+uZa2IxIxREhhAEAZHHkjByxRFRMaGQy/D+kHZYPjoADmrr+WEmIvM0vmdzPNupoV7b1Xu5eG1dLLQ66xkdZUFBVievUIs3N57Ce5tPo1Cr0+tzratC5IQgTHyiBWQy85hpTUTWTSaT4dNnfeDbSH+do/0X7+KLvy5IFFX1Y0FBVuVqag5GfHsI/4sRry/RtZkLdrzWE0EtLHd9CSKyTGqlAt+NCYRrXVu99u/2J2Br3E2JoqpeLCjIauw6m4xhSw/iQrJ4stPEXs2xZmIQ3By52ywRScPTyQ7LRwdCqdAfHX3nf6dw5qb4UXZLw4KCLF6RVofPd17ApF+jkZVfpNdXV2WDb18MwPtPt4dSwW93IpJWl2YumDNcfz+pfI0Or/wajXvZBRJFVT34CUsW7W5WAcb8dBzL910R9bVxr4utET0wxIcLmRGR+XgxqCnCg5rotd1Mz8PUyBhoSsz7siQsKMhiRV9Lw9Al/+BIwj1R3zP+XtgytQdaNqgrQWREROWbM6wDOjetp9d2NCENnzz2eKmlYUFBFkcQBKw8lIjQ744iJVN/iFCpkOGjZzpgcag/7G0tZpkVIqplbG3k+HZ0ADxKzOtadfgqNpy4LlFUVcOCgixKTkERpq2Nxdzfz6GoxPPbnk5qrH8lGGODm/GRUCIye24Oanw3JhC2Nvq/ij/YfAaxSfclisp4LCjIYly+k4Vnlh3C9lO3RX09W7li+7SeCGhSr5QziYjMk19jZ8wf4aPXVqjV4dXV0biTmS9RVMZhQUEWYfupWxi+9BAu38kW9UX0aYX/vtwV9euqJIiMiKhqngtshJd76O+gnZJZgFdXR6OgSCtRVIZjQUFmTaPVYe7vZxERGYvcQv0fLEe1DX4c2xlvDmwLRcndd4iILMh7Q7zRvaX+onsxSemYvfVspfayMgcsKMhspWTmI+z7o1h56Kqor72nI7ZP64V+7d1NHxgRUTWzUcixNDwAjerZ6bWv+/c6Vh9Lkigqw7CgILN0+Eoqnv7mH5y4Jp6YNDKwETZN6Y4m9e0liIyIqGa41LHF92M6w06p0Gufu+0sjpXyeLy5YUFBZkUQBCzfdwWjfzyG1OxCvT5bGzk+f84HC0b6QV3iB46IyBq093LEgpG+em1FOgFT1sTgVomdk80NCwoyG5n5GrzyazQ+33kBJXf0bVTPDpsmd0dolyaln0xEZCWG+nphcu+Wem33cgox6dcTyNeY7yRNFhRkFs7fzsTwJQex61yKqO8pbzdsn9YTHRs6lXImEZH1eXNAW/Rp20Cv7czNTMz83ymznaTJgoIktynmBkZ8ewhX7+XqtctkwP/1b4Mfx3aGs71tGWcTEVkfhVyGxS90QnPXOnrtW+Ju4aeDiRJFVT4WFCSZgiIt3t98GjM2nES+Rn9DnHr2SvzycldM69sacj4SSkS1kJOdEj+MDURdlf42Ap/uOI9/Lt2VKKqysaAgSdy4n4tRK45gTSmPQ/k1dsb213qhV+sGpZxJRFR7tHJzwKJQf702nQBERMbi2r0caYIqAwsKMrn9F+9i6JKDOHkjQ9Q3pltTbHilGxo625VyJhFR7dO/vTtm9G+j15aRp8GkX6KRU1AkUVRiLCjIZAqLdJi/4zz+s/I40nM1en1qpRyLQv0wL6QjVDZ8JJSI6HERfVphUAcPvbb4lCy8ufGk2UzStLiCYtmyZWjWrBnUajWCgoJw/Pjxco/fuHEjvL29oVar4ePjgx07dpgoUnpcwt1sPLf8ML47kICS3/vNXetgy9QeGNGpkTTBERGZOblchoWj/NDGva5e+59nkrHs78sSRaXPpuJDzMf69esxY8YMrFixAkFBQVi8eDEGDhyI+Ph4uLm5iY4/fPgwwsLCMH/+fAwdOhSRkZEICQlBTEwMOnbsWGNx6nQCFuyKh06rw5VrcpzbdQlyhcXVbqUyJqd8jRbrjl9HXinPTw/s4I4FI/3gqFZWd6hERFalrsoGP4ztjGFLDiIz/9Gtji+jLqKdpyP6tpN2KwKLKii++uorTJw4ES+99BIAYMWKFfjjjz/w888/Y+bMmaLjv/76awwaNAhvvfUWAGDevHmIiorC0qVLsWLFihqNdfm+K////8mx+5Z5PuJjvKrnZKuQ4+1BbTG+Z3PIZHyKg4ioMprWr4Ol4QH4z8rjxQsACgIwfV0cNk/tgVZudcu/QA2ymIKisLAQ0dHRePfdd4vb5HI5+vXrhyNHjpR6zpEjRzBjxgy9toEDB2LLli3lfq20tDRoNI/u8atUKqhUld8aW1dymUfS07JBHXw10gftPR1RVCT9hKKH7/Xj77mlY07mz9ryAZiTqQQ3d8ZbA9rg878uFrdlFRRh0i//YvPkbrC3Lf9Xe0U5GZurxRQUqamp0Gq1cHfXH9Jxd3fHhQsXSj0nOTm51OOTk5PL/VrNm+vvSx8aGoqwsLBKx/qgnrCY/7Qm1cNdh5CmGbgaexBXY6WORl9UVJTUIVQ75mT+rC0fgDmZgqcABNSXI+beg1vPcgjwr5uFv6N2obKDvmXllJubW2p7RfhbrxSJiYlwcHAofm3MCMW+vDPQ6XS4ffs2PD09IZdbyRwKI3NyVNtgUEd3dG3mUoPRGUej0SAqKgr9+/eHUmkdczmYk/mztnwA5mRqTxVq8cKPx3E7Ix/fhPqhW4vKfb5WlFNmZqZR8VhMQeHq6gqFQoGUFP29HlJSUuDh4VHqOR4eHgYd/5CLiwscHR2rFO/XYQHQaDTYseMmhgzxM7tvRGNZY04PKZVK5mQBrC0na8sHYE6molQq8cO4LtDpBDR2sTfq/NJyMjZPi/mz2dbWFoGBgdizZ09xm06nw549exAcHFzqOcHBwXrHAw+GeMo6vroVFBRg7dq1KCgoMMnXMwXmZBmYk/mztnwA5iSFhs52BhcTNZaTYEHWrVsnqFQqYdWqVcK5c+eESZMmCc7OzkJycrIgCIIwZswYYebMmcXHHzp0SLCxsREWLlwonD9/Xpg9e7agVCqF06dPl3r9jIwMAYCQkZFRLfGmpqYKAITU1NRquZ45YE6WgTmZP2vLRxCYk6WoKCdjfxdazC0P4MHkyLt372LWrFlITk6Gv78/du7cWTzxMikpSe++fvfu3REZGYkPPvgA7733Hlq3bo0tW7bU6BoUREREtZFFFRQAEBERgYiIiFL79u3bJ2obOXIkRo4cWcNRERER1W4WV1DUJOH/rwlt7AzXkrKysor/19wm8xiLOVkG5mT+rC0fgDlZiopyevg7UDBwjxCZYOgZVuzGjRto3Lix1GEQERFJ7vr162jUqPJ7LHGE4jEeHh44fvw43N3drWbdCCIiIkPodLpKLbFQEkcoHsMRCiIiogc4QlEFD1fHvH79epUXtgIeLAK1a9cuDBgwwGruvTEny8CczJ+15QMwJ0tRUU6ZmZlo3Lix3orRlcGC4jEPd710dHSstoLC3t4ejo6OVvWNyJzMH3Myf9aWD8CcLEVlczJ0J2hOFCAiIqIqY0FBREREVWY2tzwOHDiABQsWIDo6Grdv38bmzZsREhIC4MHwzAcffIAdO3YgISEBTk5O6NevHz777DN4eXmVec05c+Zg7ty5em1t27Ytc7tzIiJLk6/RQqPVSR0GAECjKUJ+EZCVXwSlVupoqoc55mSnVMBGYX7jAWZTUOTk5MDPzw8vv/wynn32Wb2+3NxcxMTE4MMPP4Sfnx/u37+P119/HcOHD8eJEyfKvW6HDh2we/fu4tc2NmaTMhGRQf6+cAcbTlzHzfQ83MsuRFpOIfI0ZvJbrpgN3vl3r9RBVDPzyqmuygbT+7XGhF4tpA5Fj9n8dh08eDAGDx5cap+TkxOioqL02pYuXYquXbsiKSkJTZo0KfO6NjY2Bj9LS0RkTgqKtPh4+3n8evSa1KGQGcguKMInO85jRKeGqF9XJXU4xcymoDBURkYGZDIZnJ2dyz3u0qVL8PLyglqtRnBwMObPn19uAQIAaWlp0Gg0xa9VKhVUKsPftIfXePxalo45WQbmZP4qm8+t9DxMW38Sp25Uz5YAZB0EAbiSkglHlbPB51b0vWfsz5hZLmwlk8n05lCUlJ+fjx49esDb2xtr1qwp8zp//vknsrOz0bZtW9y+fRtz587FzZs3cebMmVKfr83MzISTk5OoPTQ0FGFhYUbnQ0RkjAvpMvxySY6cIsMe36PaIaK9Fq2dqv9XeG5uLsLDw5GRkWHQEgoWN0Kh0WgwatQoCIKA5cuXl3vs47dQfH19ERQUhKZNm2LDhg0YP358meclJibqFRxVGaGIiopC//79rer5ZeZk/piT+SsvH51OwLL9CVhx9ApK/smnspFjWp+WaNmgDlzq2KKevRJqpcKEkZdNo9Hgn3/+Qa9evaziPQLMK6dnVxxFanZh8euALl3Qq5Wrwdep6GfJ2A0yLaqgeFhMXLt2DXv37jV48SlnZ2e0adMGly9fLvc4FxeXalnY6iGlUin5N2J1Y06WgTmZv5L53M8pxBsb4rAv/q7o2Gb17bF8dCDaeVbf51N10mg0qKcCmrg6WM17ZE45lSwcdYK8SjGV9bNk7DXN77mTMjwsJi5duoTdu3ejfv36Bl8jOzsbV65cgaenZw1ESERUNSevp2PokoOlFhMD2rtj27SeZltMUM2ztdH/lW0ujws/ZDYjFNnZ2XojB4mJiYiLi4OLiws8PT3x/PPPIyYmBtu3b4dWq0VycjKAB6MJtra2AIC+fftixIgRiIiIAAC8+eabGDZsGJo2bYpbt25h9uzZUCgUnA9BRGZFEAREHk/C3G3nUFjil4RcBrw9yBuvPNHC4KWQybrYllh7ouT3itTMpqA4ceIE+vTpU/x6xowZAIBx48Zhzpw52LZtGwDA399f77y///4bvXv3BgBcuXIFqampxX03btxAWFgY7t27hwYNGqBnz544evQoGjRoULPJEBFVUl6hFnM2n8WmmJuiPte6KiwJ64TgloaPyJL1KTlCUVjEgqJUvXv3RnkPnFTmYZSrV6/qvV63bl1VwyIiqjF38oBR3x/DhZRsUV+XZvWwLDwAbo5qCSIjc6TkCAUREZUUde4OvjytQL5WXExM6Nkc7wz2Fv0Codqt5C0PDUcoiIhqryKtDgt2xeO7/QkA9OdE1FXZ4IvnfTHEhxPHSUxZ8pYHRyiIiGqnO1n5mBYZi2OJaaK+tu4OWD46AC0a1JUgMrIEohEKrXmtS8mCgojIBP69moapa2JwJ6tA1PeMvxfmP+sDe1t+JFPZbG30R7QKeMuDiKj2EAQBPx1MxPw/L0Cr0/+LUiET8OHQ9hjXvTkfCaUKiUcoWFAQEdUKWfkavP3bKfx5JlnU5+mkxguNs/Fi18YsJqhSRE95mNkIBacQExHVgPjkLAxfeqjUYqJXa1dsmdwNzcR7FBKViStlEhHVMltib+LdTaeRp9GK+l7r2xqv920NnbZIgsjIkpn7CAULCiKialJQpMXH28/j16PXRH3O9kosCvVHn7ZuAACduNYgKpeKj40SEVm/m+l5mLImBievp4v6fBs5YVl4ABq72Js+MLIaJUco+NgoEZGVOXDxLl5fF4v7uRpRX3hQE8wa2l609TSRocR7eZjXMBcLCiIiI+l0ApbsvYzFey6i5HZDaqUcn4T44LnARtIER1aHIxRERFbofk4hpq+Pw/6Ld0V9zerbY/noQLTzdJQgMrJW3G2UiMjKnLyejilrYnAzPU/UN6C9OxaO8oOjWilBZGTNbBX665VwUiYRkYUSBAGRx5Mwd9s50Ye5XAa8M8gbk55owYWqqEZwhIKIyArkFWrx/pbT2BRzU9TnWleFJWGdENyyvgSRUW0hnkPBgoKIyKIkpuZg8upoXEjOEvV1aVYPS8MD4O6oliAyqk04QkFEZMH+OpuMNzecRFaBeGXL8T2bY+Zgb9FfjkQ1gSMUREQWqEirw4Jd8fhuf4Kor67KBl8874shPp4SREa1FUcoiIgszJ2sfEyLjMWxxDRRXxv3ulg+OhAtG9SVIDKqzUpuX17IdSiIiMzX8cQ0TI2Mwd2sAlFfiL8XPn3WB/a2/Ogk0+NKmUREFkAQBPx0MBHz/7wArU7/Lz+lQoZZwzpgdFATPhJKkjH3lTLNZibRgQMHMGzYMHh5eUEmk2HLli16/YIgYNasWfD09ISdnR369euHS5cuVXjdZcuWoVmzZlCr1QgKCsLx48drKAMislRZ+RpMWRODj/84LyomPJ3U2PBKMMZ0a8pigiQlvuVhXnMozKagyMnJgZ+fH5YtW1Zq/xdffIFvvvkGK1aswLFjx1CnTh0MHDgQ+fn5ZV5z/fr1mDFjBmbPno2YmBj4+flh4MCBuHPnTk2lQUQWJj45C88sPYQ/zySL+nq1dsUfr/VCpyb1JIiMSJ+tjX5Bq9UJogJYSmZzy2Pw4MEYPHhwqX2CIGDx4sX44IMP8MwzzwAAfvnlF7i7u2PLli144YUXSj3vq6++wsSJE/HSSy8BAFasWIE//vgDP//8M2bOnFlmLGlpadBoHu0aqFKpoFKpDM7p4TUev5alY06WgTlVztaTt/Hh1rPI04j/0ovo3QIRfVpCIZfVyH9HvkeWwZxykgni79Pc/AKDd7KtKCdjc5UJQsk98qQnk8mwefNmhISEAAASEhLQsmVLxMbGwt/fv/i4J598Ev7+/vj6669F1ygsLIS9vT1+++234usAwLhx45Ceno6tW7eKzsnMzISTk5OoPTQ0FGFhYVXOi4jMQ5EO2HxVjoMp4kFaexsBY1rp0L6e2X00Ui2XXgDMjtEfB/isSxHsqnloIDc3F+Hh4cjIyICjY+U3uDObEYryJCc/GIp0d3fXa3d3dy/uKyk1NRVarbbUcy5cuFDu10tMTISDg0Px66qMUERFRaF///5QKq1joyDmZBmYU9lupedh2vqTOJWSKerr6OWIJS/4oVE9u6qEWil8jyyDOeV0L6cQs2P26bX1fqov6tc17PdTRTllZop/NirDIgoKU3NxcTGoKquIUqmU/BuxujEny8Cc9B24eBevr4vF/VzxkG54UBPMGtre4OHjquJ7ZBnMISf7UlZ3F+QKo+MqKydjr2cRBYWHhwcAICUlBZ6ej1amS0lJ0bsF8jhXV1coFAqkpKTotaekpBRfj4hqB51OwJK9l7F4z0WUvMmrVsrxSYgPngtsJE1wRJVU8ikPwLxWyzSbpzzK07x5c3h4eGDPnj3FbZmZmTh27BiCg4NLPcfW1haBgYF65+h0OuzZs6fMc4jI+tzPKcTL//0Xi3aLi4lm9e2xeUoPFhNkEUrbM8ac9vMwmxGK7OxsXL58ufh1YmIi4uLi4OLigiZNmmD69On4+OOP0bp1azRv3hwffvghvLy89CZc9u3bFyNGjEBERAQAYMaMGRg3bhw6d+6Mrl27YvHixcjJySl+6oOIrNupG+mYvDoGN9PzRH0D2rtj4Sg/OKqta2ierJdCLoNCLtN7VLTAjEYozKagOHHiBPr06VP8esaMGQAePJWxatUqvP3228jJycGkSZOQnp6Onj17YufOnVCrH91UunLlClJTU4tfh4aG4u7du5g1axaSk5Ph7++PnTt3iiZqEpF1EQQBkceTMHfbOdHiP3IZ8M4gb0x6ogUXqiKLY6uQI0/3aMltc1ot02wKit69e6O8J1hlMhk++ugjfPTRR2Uec/XqVVFbRERE8YgFEVm/vEItPthyBv+LuSHqc62rwpKwTghuWV+CyIiqTqmQIe+xOcXmNIfCbAoKIqKqSkzNweTV0biQnCXq69KsHpaGB8DdsZSp8kQWwtZGAaCo+DXnUBARVbO/zibjzQ0nkVVQJOqb2Ks53h7kXeqkNiJLYqvQv03HEQoiompSpNVhwa54fLc/QdRXV2WDL573xRAfz1LOJLI8oi3MOUJBRFR1d7LyMS0yFscS00R9bd0dsHx0AFo0qCtBZEQ1o+QoG0coiIiq6N+raZi6JgZ3sgpEfSH+Xvj0WR/Y2/IjjqxLyREKzqEgIjKSIAj48Z8EzP/zgmjrZqVChlnDOmB0UBM+EkpWiSMURETVIL8ImLbuJP46d0fU5+WkxrejA+Hf2Nn0gRGZCEcoiIiq6GJKFr48rcCdfHEx0au1K75+oRNc6thKEBmR6ZTcz4MrZRIRGWBL7E28u+kU8jTi2xiv9W2N1/u2hkLOWxxk/cQjFFwpk4ioQgVFWszbfg6rjyaJ+pztlVgU6o8+bd0kiIxIGkquQ0FEZJib6XmYsiYGJ6+ni/p8Gjrh2xcD0NjF3vSBEUnowUqZj3AOBRFROQ5cvIvX18Xifq5G1PdCl0aYM7wj1EpFKWcSWTfRCAULCiIiMZ1OwJK9l7F4z0WU3CtQrZTjuSYazBneHkoWE1RLqUqulMlbHkRE+u7nFOKNDXHYF39X1Nesvj2WvOCHhJh/JIiMyHyI1qHgCAUR0SMnr6djypoY3EzPE/UNaO+OhaP8YKcAxLt1ENUuJR8b1XCEgojowaqXkceTMHfbOdFfWnIZ8PYgb7zyRAvIZDJoNOL5FES1jZKbgxER6csr1OL9LaexKeamqM+1rgpLwjohuGV9CSIjMl+iEQoWFERUmyWm5mDy6mhcSM4S9XVt5oKl4Z3g5qiWIDIi8ybavpy3PIiotvrrbDLe3HASWQVFor4JPZvjncHeoolnRPRAyRGKQq6USUS1TZFWhwW74vHdfvHUyroqGyx43heDfTwliIzIcohXytRKFIkYCwoiqnF3svIxLTIWxxLTRH1t3R2wfHQAWjSoK0FkRJZFvFKm+YxQWMy4YrNmzSCTyUT/pk6dWurxq1atEh2rVvOeLJGp/Xs1DUO/OVhqMfGMvxc2T+3OYoKokriXRzX4999/odU+Gto5c+YM+vfvj5EjR5Z5jqOjI+Lj44tfy2TcjZDIVARBwE8HEzH/zwvQ6vT/ilIqZJg1rANGBzXhzyWRAcS7jbKgMFiDBg30Xn/22Wdo2bIlnnzyyTLPkclk8PDwqOnQiKiErHwN3v7tFP48kyzq83JSY9mLAejUpJ4EkRFZNtGkTI5QVE1hYSFWr16NGTNmlPvXTXZ2Npo2bQqdToeAgAB8+umn6NChQ4XXT0tL01tER6VSQaVSGRznw2tY04I8zMkySJnTxZQsRKw9icR7uaK+nq3q48vnfeBSx9bg2KztfbK2fADmZApymf5oX2GRttp/lozNVSYIJbfgMX8bNmxAeHg4kpKS4OXlVeoxR44cwaVLl+Dr64uMjAwsXLgQBw4cwNmzZ9GoUaNSz8nMzISTk5OoPTQ0FGFhYdWaA5E1OnFXhvUJchTqxIX+wEY6DGqkg5x3OIiMdiFdhuXnH03MdFQKmNe5ep/0yM3NRXh4ODIyMuDo6Fjp8yyyoBg4cCBsbW3x+++/V/ocjUaDdu3aISwsDPPmzSv1mIcFRWJiIhwcHIrbqzJCERUVhf79+0OpVBp8vjliTpbB1DkVFOnw6Z8XEHn8hqjP2U6Jhc93xJNtGpRyZuVZ2/tkbfkAzMkUjiWmYfTPJ4pf17NX4vi7fQy6RkU5ZWZmwtXV1eCCwuJueVy7dg27d+/Gpk2bDDpPqVSiU6dOuHz5coXHuri4GPQfsTJf2xy+EasTc7IMpsjpZnoepqyOxskbGaI+30ZOWBYegMYu9tX29aztfbK2fADmVJPsVLZ6rwuLdEbHVVZOxl7PYh4bfWjlypVwc3PD008/bdB5Wq0Wp0+fhqcnF84hqi4HLt7F0G/+KbWYCA9qgg2vBFdrMUFU26lET3mYz00Gixqh0Ol0WLlyJcaNGwcbG/3Qx44di4YNG2L+/PkAgI8++gjdunVDq1atkJ6ejgULFuDatWuYMGGCFKETWRWdTsCSvZexeM9FlLxpqlbK8UmID54LLH2uEhEZr+Sy9IVaHQRBMIvHry2qoNi9ezeSkpLw8ssvi/qSkpIglz/6D33//n1MnDgRycnJqFevHgIDA3H48GG0b9/elCETWZ37OYV4Y0Mc9sXfFfU1q2+P5aMD0c6z+m4ZEtEjJdehAB6MUtjasKAwyIABA1DWHNJ9+/bpvV60aBEWLVpkgqiIao9TN9IxeXUMbqbnifoGtHfHwlF+cFRLf5+ZyFqVXCkTeLC4VWmFhqlZVEFBRNIQBAGRx5Mwd9s5FJZYmU8uA94Z5I1JT7Qwi2FXImtWWuFQWKRDHcMfRKx2LCiIqFx5hVq8v+U0NsXcFPW51lVhSVgnBLesL0FkRLVPyZUyAfNZfpsFBRGVKTE1B5NXR+NCcpaor0uzelgaHgB3R266R2QqpY1QFJjJ8ts1ctPl2LFjNXFZIjKhv84mY/iSg6UWExN7NUfkxG4sJohMrORTHoCVj1CMHDkSSUlJNXFpIqphRVodFuyKx3f7E0R9dVU2+OJ5Xwzx4XouRFKwkcsgk0Hvce2S85qkYnRBMWrUqFLbBUFAWlqa0QERkXTuZOVjWmQsjiWKf4bbuNfF8tGBaNmgrgSRERHwYBdtpUKut8uopsg8FrcyuqDYvXs3fv31V9Stq//hIggCDhw4UOXAiMi0jiemYWpkDO5mFYj6RnRqiE9GdIS9LaddEUlNVaKgKNRW7+ZgxjL606F3795wcHDAE088Ierz9fWtUlBEZDqCIODHfxLx2c4L0Or0/9JRKmSYNawDRgc14SOhRGZCaSMHHqv7Cy19hKK8zbmioqKMvSwRmVBWvgZvbTyFnWeTRX1eTmp8OzoQ/o2dTR8YEZWp5KOjFjeHwsHBAZ06dUJgYCACAgIQEBCA9u3b868WIgsVn5yFV1dHIzE1R9TXq7Urvn6hE1zq2JZyJhFJSVlimW2NmTw2WumC4vPPP0d0dDT27t2LpUuXQqfTwc7ODr6+vnpFhp+fX03GS0TVYEvsTby76TTyNPr3XmUyYNpTrfF639ZQyPnHApE5svgRiilTphT//7y8PNSpUwfTpk1DWloajh49ih9//BGFhYXQmsnkECISKyjS4uPt5/Hr0WuiPmd7JRaF+qNPWzcJIiOiyiq5FoVFr0NhZ2cHAAgLCyuegFlUVIRz585VX2REVK1upudhypoYnLyeLurzaeiEb18MQGMXe9MHRkQGUZVYLdNcVsqstmfAbGxs+HQHkZk6cPEuXl8Xi/u5GlFfeFATzBraHmqlQoLIiMhQVjVCQUSWQacT8PXuS1i856LeynoAoFbK8UmID54LbCRNcERklJL7eRRa2gjFhAkTEBgYiM6dOxePRPAJDyLzlaMBJq2Oxf5LqaK+ZvXtsXx0INp5OkoQGRFVhcWPUFy6dAkbN25EVlYWbGwenDZ37lz07t0bAQEB8Pf3h709778SmYPTNzOw8LQCaQXiYmJAe3csHOUHR7VSgsiIqKosfoRi//79AB4UFtHR0YiJiUFMTAxmzZqF9PR0KBQKtGnTBmfPnq2xYImofIIgIPJ4EuZsOwuNVn8EUSGX4e2BbTHpiRYcXSSyYOLHRi10pczWrVujdevWeOGFF4rbEhMTceLECcTGxlZrcERUeXmFWry/5TQ2xdwU9bnWVWFpeCd0a1FfgsiIqDpZ/AhFeZo3b47mzZtj5MiR1XE5IjLQ1dQcvLo6GheSs0R9XZrVw7LwALg5qiWIjIiqm1JRYqVMS5tDQUTm6a+zyXhzw0lkFRSJ+l7u3hTvPt1eNImLiCyXVY9QEJHpFWl1WLArHt/tTxD11VEpMKppId4d3JbFBJGVMdenPCzmk2bOnDmQyWR6/7y9vcs9Z+PGjfD29oZarYaPjw927NhhomiJatadrHy8+OOxUouJtu4O2PxqN/jXN4+JWkRUvUSTMs1khMJiCgoA6NChA27fvl387+DBg2Uee/jwYYSFhWH8+PGIjY1FSEgIQkJCcObMGRNGTFT9jiemYeg3B3EsMU3UF+Lvhc1Tu6O5ax0JIiMiUxDd8jCTEQqLuuVhY2MDDw+PSh379ddfY9CgQXjrrbcAAPPmzUNUVBSWLl2KFStWlHtuWloaNJpHSxSrVCqoVCqD4314jcevZemYk3QEQcDKw9fwxa5L0Or0Rx+UChneH+KN8C6NIJMJFpOTIawtJ2vLB2BOpiKH/s9/gUZrUHwV5WRsrjJBKLkgr3maM2cOFixYACcnJ6jVagQHB2P+/Plo0qRJqcc3adIEM2bMwPTp04vbZs+ejS1btuDkyZOlnpOZmQknJydRe2hoKMLCwqolDyJj5BcBkVfkOJkmHlR0thXwchstmjpIEBgRmdyemzJsS3q09057Zx1eaVd9oxS5ubkIDw9HRkYGHB0rv5quxYxQBAUFYdWqVWjbti1u376NuXPnolevXjhz5gwcHMSfpMnJyXB3d9drc3d3R3JycoVfKzExUe+aVRmhiIqKQv/+/aFUWseqhMzJ9C6mZCFi7UkkpuWK+nq2qo8vn/eBSx1bvXZzz8kY1paTteUDMCdTSTl8DduS4otfO7u4YsiQzpU+v6KcMjMzjYrLYgqKwYMHF/9/X19fBAUFoWnTptiwYQPGjx9frV/LxcXFoKqsIkql0my+EasLczKNLbE38e6m08jTaEV9r/Vtjdf7toZCXvaql+aYU1VZW07Wlg/AnGqanUo/jiIdjIqtrJyMzdNiCoqSnJ2d0aZNG1y+fLnUfg8PD6SkpOi1paSkVHoOBpGUCoq0mLf9HFYfTRL1OdsrsSjUH33aukkQGRFJzbbEwlYFZjIp06Ke8nhcdnY2rly5Ak9Pz1L7g4ODsWfPHr22qKgoBAcHmyI8IqPdTM/DqBVHSi0mfBo64feIniwmiGqxkk95aPjYqGHefPNN7N+/H1evXsXhw4cxYsQIKBSK4smSY8eOxbvvvlt8/Ouvv46dO3fiyy+/xIULFzBnzhycOHECERERUqVAVKH9F+9i6Df/4OSNDFFfeFATbHw1GI1duKsvUW1WcmErPjZqoBs3biAsLAz37t1DgwYN0LNnTxw9ehQNGjQAACQlJUEuf/QfuXv37oiMjMQHH3yA9957D61bt8aWLVvQsWNHqVIgKpNOJ2DJ3stYvOciSj53pVbK8UmID54LbCRNcERkVkoubGUuK2VaTEGxbt26cvv37dsnahs5ciQ3LCOzdz+nEG9siMO++Luivmb17bF8dCDaeVbfJGEismxK7uVBRCWdupGOyatjcDM9T9Q3oL07Fo7yg6PaPGaWE5F5UHGEgogeEgQBa49fx5xtZ0X3P+Uy4O1B3njliRaQycp+JJSIaqeSIxQFHKEgqp3yCrX4YMsZ/C/mhqjPta4KS8I6IbhlfQkiIyJLwDkURITE1BxMXh2NC8lZor4uzephaXgA3B3VEkRGRJZC9JQHRyiIape/zibjzQ0nkVVQJOqb0LM53hnsLfqgICIqqeQ6FDoB0OqEclfNNQUWFEQ1rEirw4K/4vHdgQRRX12VDb543hdDfEpfoI2IqKSStzyAB6MUdraKUo42HRYURDXoTlY+IiJjcTwxTdTX1t0By0cHoEWDuhJERkSWquQIBfBgcSs7sKAgskrHE9MwNTIGd7MKRH0jOjXEJyM6wt6WP4JEZBilQnxrwxzmUfDTjKiaCYKAnw4mYv6fF6DV6S97qVTIMGtoe4zu1pSPhBKRUUoboTCHJz1YUBBVo6x8Dd7+7RT+PJMs6vNyUuPb0YHwb+xs+sCIyGqUNnmbIxREViQ+OQuvro5GYmqOqK9Xa1d8/UInuNSxlSAyIrImpU3K5AgFkZXYEnsT7246jTyNVtT32lOt8Hq/NpI/0kVE1kEul8FGLkPRY7dUzWG1TBYURFVQUKTFx9vP49ej10R9TnZKLA71Rx9vNwkiIyJrZmsjR1Hhoz9gOEJBZMFupudhypoYnLyeLurzaeiEb18MQGMXe9MHRkRW78E8ikcFBedQEFmoAxfv4vV1sbifqxH1hQc1wayh7aFWSvtMOBFZr5JPemi0QhlHmg4LCiID6HQCluy9jMV7LkIo8fOrVsrxSYgPngtsJE1wRFRrlJyYWagVz98yNRYURJV0P6cQb2yIw774u6K+ZvXtsXx0INp5OkoQGRHVNiVHKAqLOEJBZBFO3UjH5NUxuJmeJ+ob0N4dC0f5wVGtlCAyIqqNSq6WyUmZRGZOEAREHk/C3G3nUFjiB1Yhl+GdQW0xsVcLrnpJRCYlHqFgQUFktvIKtXh/y2lsirkp6nOtq8LS8E7o1qK+BJERUW1XcrVMjlAQmanE1BxMXh2NC8lZor4uzephWXgA3BzVEkRGRFTapEzpCwrx+p1mav78+ejSpQscHBzg5uaGkJAQxMfHl3vOqlWrIJPJ9P6p1fwlQOX762wyhi85WGoxMbFXc0RO7MZigogkxVseVbB//35MnToVXbp0QVFREd577z0MGDAA586dQ506dco8z9HRUa/w4L1uKkuRVoeFu8/ju/0Jor66KhsseN4Xg308JYiMiEifOY5QWExBsXPnTr3Xq1atgpubG6Kjo/HEE0+UeZ5MJoOHh0dNh0cWLrMQGLcqGsev3hf1tXV3wPLRAWjRoK4EkRERiYnmUPCxUeNlZGQAAFxcXMo9Ljs7G02bNoVOp0NAQAA+/fRTdOjQodxz0tLSoNE8WgFRpVJBpVIZHOPDazx+LUtnjTkduXwXC04pkKkRFxPP+Hnio+HtYG9rY1E5W+P7ZG05WVs+AHMypRJ3PJBfqKl0jBXlZGyuMkEoud6f+dPpdBg+fDjS09Nx8ODBMo87cuQILl26BF9fX2RkZGDhwoU4cOAAzp49i0aNxKsZZmZmwsnJSdQeGhqKsLCwas2BpCcIwL7bMmy7JocO+rfCFDIBzzbToYe7AN4lIyJzs+ayHMfvPqoqnvLU4Zlm1XPbIzc3F+Hh4cjIyICjY+UX67PIEYqpU6fizJkz5RYTABAcHIzg4ODi1927d0e7du3w3XffYd68eWWel5iYCAcHh+LXVRmhiIqKQv/+/aFUWseiR9aSU1Z+Ed7dfAZ/Xbsj6vN0UmPJC37wayQuLi2FtbxPj7O2nKwtH4A5mdLhredw/O6N4tcNmzbDkCHelTq3opwyMzONisniCoqIiAhs374dBw4cKHWUoTxKpRKdOnXC5cuXyz3OxcXFoKqsMl/XnL4Rq4Ml5xSfnIXJq6ORkJoj6uvV2hVfv9AJLnVsJYis+lny+1QWa8vJ2vIBmJMplNx8UCvA4PjKysnYPC3msVFBEBAREYHNmzdj7969aN68ucHX0Gq1OH36NDw9OVO/ttoSexMhyw6JigkZBET0boFVL3W1mmKCiKwXHxutgqlTpyIyMhJbt26Fg4MDkpOTAQBOTk6ws7MDAIwdOxYNGzbE/PnzAQAfffQRunXrhlatWiE9PR0LFizAtWvXMGHCBMnyIGkUFGkxb/s5rD6aJOpztlMitGk+Xu/bCgo5J0wQkfnjSplVsHz5cgBA79699dpXrlyJ//znPwCApKQkyOWP/iPfv38fEydORHJyMurVq4fAwEAcPnwY7du3N1XYZAZupudhypoYnLyeLurzaeiEb0J9cerI36YPjIjISByhqILKPIyyb98+vdeLFi3CokWLaigisgT7L97F9HWxuJ8rfgwqPKgJZg1tDwV0OCVBbERExuIIBZGJ6HQCluy9jMV7LqJkLapWyvFJiA+eC3wwqVejkf4HkYjIEKoSIxQFHKEgqn7puYWYvj4O++Lvivqa1bfH8tGBaOdZfU/xEBGZGkcoiGrYqRvpmLw6BjfT80R9A9q7Y+EoPziqzefRLyIiY3AOBVENEQQBkceTMHfbOdEmOXIZ8M4gb0x6ogU3hyMiqyAeoZB+0WsWFGTx8gq1eH/LaWyKuSnqc62rwpKwTghuWV+CyIiIagZHKIiqWWJqDiavjsaF5CxRX5dm9bAsPABujmoJIiMiqjm2Cv3RVs6hIKqCnWeS8dbGk8gqKBL1TezVHG8P8hYNCxIRWYOSIxR8yoPICEVaHRb8FY/vDiSI+uqqbLDgeV8M9uHy6kRkvfiUB1EV3cnKR0RkLI4npon62ro7YPnoALRoUFeCyIiITMe2REFRcjK6FFhQkMU4npiGqZExuJtVIOob0akhPhnREfa2/JYmIuunLHHLQ8NbHkQVEwQBPx1MxPw/L0Cr0380SqmQYdawDhgd1ISPhBJRrcERCiIDZeVr8M7/TmHH6WRRn5eTGt+ODoR/Y2fTB0ZEJKGSkzI1WgGCIEj6hxULCjJb8clZmLw6GgmpOaK+Xq1d8fULneBSx1aCyIiIpFVyhAJ4MEqhslFIEM0DLCjILG2JvYl3N51GnkYr6nutb2u83rc1FHLe4iCi2qnkHArgwSiFSsLf6iwoyKwUFGkxb/s5rD6aJOpzslNicag/+ni7SRAZEZH5KHWEokgHqCQI5v9jQUFm42Z6HqasjsbJGxmiPp+GTvj2xQA0drGXIDIiIvNSWkEh9VoULCjILOy/eBfT18Xifq5G1Bce1ASzhraHWindvUEiInNSclImIP1+HiwoSFI6nYAley9j8Z6LEEpslqdWyvFJiA+eC2wkTXBERGZKqRDPIZP60VEWFCSZ+zmFeGNDHPbF3xX1Natvj+WjA9HO01GCyIiIzJtCLoNMBr0/xDhCQbXSyevpmLImBjfT80R9Azu4Y8FIPziqlRJERkRk/mQyGWwVcr1NwTiHgmoVQRAQeTwJc7edEw3PKeQyvD2wLSY90YKrXhIRVaBkQcERCqo10nML8e6m0/jzjHjVS9e6KiwN74RuLepLEBkRkeWxtZEDj21tJPUcCvE0UTO3bNkyNGvWDGq1GkFBQTh+/Hi5x2/cuBHe3t5Qq9Xw8fHBjh07TBQpPe7wlVQMWvxPqcVEl2b1sOO1niwmiIgMUHILc45QGGD9+vWYMWMGVqxYgaCgICxevBgDBw5EfHw83NzEix0dPnwYYWFhmD9/PoYOHYrIyEiEhIQgJiYGHTt2rLE4dToBEWtjoNMJSL4tx5+ZJyG3klUdjckpX6PD3/F3RE9xAMDEXs3x9iBv0Q8GERGVr7T9PKRkUQXFV199hYkTJ+Kll14CAKxYsQJ//PEHfv75Z8ycOVN0/Ndff41BgwbhrbfeAgDMmzcPUVFRWLp0KVasWFHm10lLS4NG82g9BJVKBZWq8suP6XTCY5tZyYG0lEqfaxmqnlM9eyU+eaYD+rd3A3RaaHTiJbZN5eF7/fh7bumYk/mztnwA5mRqNiX+qMsrKKxUnBXlZGyuMkEo7e9G81NYWAh7e3v89ttvCAkJKW4fN24c0tPTsXXrVtE5TZo0wYwZMzB9+vTittmzZ2PLli04efKk6PjMzEw4OTmJ2kNDQxEWFlbpWHUC8MZRi6rVTKqNkw6jW+ngxH29iIiM9sVJBW7mPioqxrTSonODqv9Kz83NRXh4ODIyMuDoWPlH9y3mt15qaiq0Wi3c3d312t3d3XHhwoVSz0lOTi71+ORk8X38xyUmJsLBwaH4tTEjFG8cjar08bWFUiHDjH6t8XL3pmZ1C0ij0SAqKgr9+/eHUmkdj6oyJ/NnbfkAzMnUfko6ipu5mcWv23X0xZDAhhWeV1FOmZmZpZxVMYspKEzJxcXFoKqsJEEQML1fa+i0Oly8dBFtWreB3ErmCBibk6Naif7t3c16Lw6lUml2HxhVxZzMn7XlAzAnU3m+c2P0apMPW4UCShsZ/Ju4GBRjWTkZm6fFFBSurq5QKBRISdG/d5+SkgIPD49Sz/Hw8DDo+Ooik8kwvV8baDQa7MiPx5CnWprdN6KxrDEnIiJLNDa4mdQh6LGYP5ttbW0RGBiIPXv2FLfpdDrs2bMHwcHBpZ4THBysdzwAREVFlXl8dSsoKMDatWtRUFBQ8cEWgjlZBuZk/qwtH4A5WYoay0mwIOvWrRNUKpWwatUq4dy5c8KkSZMEZ2dnITk5WRAEQRgzZowwc+bM4uMPHTok2NjYCAsXLhTOnz8vzJ49W1AqlcLp06dLvX5GRoYAQMjIyKiWeFNTUwUAQmpqarVczxwwJ8vAnMyfteUjCMzJUlSUk7G/Cy3mlgfw4GmLu3fvYtasWUhOToa/vz927txZPPEyKSkJcvmjQZfu3bsjMjISH3zwAd577z20bt0aW7ZsqdE1KIiIiGojiyooACAiIgIRERGl9u3bt0/UNnLkSIwcObKGoyIiIqrdLK6gqEnC/1+Sw9hHZkrKysoq/l9rmcDInCwDczJ/1pYPwJwsRUU5PfwdKBi4TJXFLGxlCjdu3EDjxo2lDoOIiEhy169fR6NGjSp9PAuKx+h0Oty6dQsODg7cPpuIiGolQRCQlZUFLy8vvXmJFWFBQURERFVmMetQEBERkfliQUFERERVxoKCiIiIqowFRRUtW7YMzZo1g1qtRlBQEI4fP17u8Rs3boS3tzfUajV8fHywY8cOE0VaeYbk9MMPP6BXr16oV68e6tWrh379+lX430AKhr5PD61btw4ymQwhISE1G6ARDM0pPT0dU6dOhaenJ1QqFdq0aWNW33+G5rN48WK0bdsWdnZ2aNy4Md544w3k5+ebKNqKHThwAMOGDYOXlxdkMhm2bNlS4Tn79u1DQEAAVCoVWrVqhVWrVtV4nIYwNKdNmzahf//+aNCgARwdHREcHIy//vrLNMFWkjHv00OHDh2CjY0N/P39ayw+QxmTT0FBAd5//300bdoUKpUKzZo1w88//2zw12ZBUQXr16/HjBkzMHv2bMTExMDPzw8DBw7EnTt3Sj3+8OHDCAsLw/jx4xEbG4uQkBCEhITgzJkzJo68bIbmtG/fPoSFheHvv//GkSNH0LhxYwwYMAA3b940ceRlMzSnh65evYo333wTvXr1MlGklWdoToWFhejfvz+uXr2K3377DfHx8fjhhx/QsGHFWx2bgqH5REZGYubMmZg9ezbOnz+Pn376CevXr8d7771n4sjLlpOTAz8/PyxbtqxSxycmJuLpp59Gnz59EBcXh+nTp2PChAlm9QvY0JwOHDiA/v37Y8eOHYiOjkafPn0wbNgwxMbG1nCklWdoTg+lp6dj7Nix6Nu3bw1FZhxj8hk1ahT27NmDn376CfHx8Vi7di3atm1r+BevwnLgtV7Xrl2FqVOnFr/WarWCl5eXMH/+/FKPHzVqlPD000/rtQUFBQmvvPJKjcZpCENzKqmoqEhwcHAQ/vvf/9ZUiAYzJqeioiKhe/fuwo8//iiMGzdOeOaZZ0wQaeUZmtPy5cuFFi1aCIWFhaYK0SCG5jN16lThqaee0mubMWOG0KNHjxqN01gAhM2bN5d7zNtvvy106NBBry00NFQYOHBgDUZmvMrkVJr27dsLc+fOrf6AqoEhOYWGhgoffPCBMHv2bMHPz69G4zJWZfL5888/BScnJ+HevXtV/nocoTBSYWEhoqOj0a9fv+I2uVyOfv364ciRI6Wec+TIEb3jAWDgwIFlHm9qxuRUUm5uLjQaDVxcXGoqTIMYm9NHH30ENzc3jB8/3hRhGsSYnLZt24bg4GBMnToV7u7u6NixIz799FNotVpThV0mY/Lp3r07oqOji2+LJCQkYMeOHRgyZIhJYq4J5v75UB10Oh2ysrLM5vPBWCtXrkRCQgJmz54tdShVtm3bNnTu3BlffPEFGjZsiDZt2uDNN99EXl6ewdfi0ttGSk1NhVarLd6Y7CF3d3dcuHCh1HOSk5NLPT45ObnG4jSEMTmV9M4778DLy0v0wSgVY3I6ePAgfvrpJ8TFxZkgQsMZk1NCQgL27t2LF198ETt27MDly5cxZcoUaDQayT8UjcknPDwcqamp6NmzJwRBQFFREV599VWzuuVhqLI+HzIzM5GXlwc7OzuJIqs+CxcuRHZ2NkaNGiV1KEa7dOkSZs6ciX/++Qc2Npb/KzQhIQEHDx6EWq3G5s2bkZqaiilTpuDevXtYuXKlQdfiCAVVm88++wzr1q3D5s2boVarpQ7HKFlZWRgzZgx++OEHuLq6Sh1OtdHpdHBzc8P333+PwMBAhIaG4v3338eKFSukDs0o+/btw6effopvv/0WMTEx2LRpE/744w/MmzdP6tCoDJGRkZg7dy42bNgANzc3qcMxilarRXh4OObOnYs2bdpIHU610Ol0kMlkWLNmDbp27YohQ4bgq6++wn//+1+DRyksv7ySiKurKxQKBVJSUvTaU1JS4OHhUeo5Hh4eBh1vasbk9NDChQvx2WefYffu3fD19a3JMA1iaE5XrlzB1atXMWzYsOI2nU4HALCxsUF8fDxatmxZs0FXwJj3ydPTE0qlEgqForitXbt2SE5ORmFhIWxtbWs05vIYk8+HH36IMWPGYMKECQAAHx8f5OTkYNKkSXj//fcNWi7YXJT1+eDo6GjxoxPr1q3DhAkTsHHjRrMZvTRGVlYWTpw4gdjY2OJdr3U6HQRBgI2NDXbt2oWnnnpK4igN4+npiYYNG8LJyam4rV27dhAEATdu3EDr1q0rfS3L+6kzE7a2tggMDMSePXuK23Q6Hfbs2YPg4OBSzwkODtY7HgCioqLKPN7UjMkJAL744gvMmzcPO3fuROfOnU0RaqUZmpO3tzdOnz6NuLi44n/Dhw8vnnlvDpvHGfM+9ejRA5cvXy4ujgDg4sWL8PT0lLSYAIzLJzc3V1Q0PCyWBAvdTcDcPx+MtXbtWrz00ktYu3Ytnn76aanDqRJHR0fR58Orr76Ktm3bIi4uDkFBQVKHaLAePXrg1q1byM7OLm67ePEi5HK5QRuDAeBTHlWxbt06QaVSCatWrRLOnTsnTJo0SXB2dhaSk5MFQRCEMWPGCDNnziw+/tChQ4KNjY2wcOFC4fz588Ls2bMFpVIpnD59WqoURAzN6bPPPhNsbW2F3377Tbh9+3bxv6ysLKlSEDE0p5LM8SkPQ3NKSkoSHBwchIiICCE+Pl7Yvn274ObmJnz88cdSpaDH0Hxmz54tODg4CGvXrhUSEhKEXbt2CS1bthRGjRolVQoiWVlZQmxsrBAbGysAEL766ishNjZWuHbtmiAIgjBz5kxhzJgxxccnJCQI9vb2wltvvSWcP39eWLZsmaBQKISdO3dKlYKIoTmtWbNGsLGxEZYtW6b3+ZCeni5VCiKG5lSSuT3lYWg+WVlZQqNGjYTnn39eOHv2rLB//36hdevWwoQJEwz+2iwoqmjJkiVCkyZNBFtbW6Fr167C0aNHi/uefPJJYdy4cXrHb9iwQWjTpo1ga2srdOjQQfjjjz9MHHHFDMmpadOmAgDRv9mzZ5s+8HIY+j49zhwLCkEwPKfDhw8LQUFBgkqlElq0aCF88sknQlFRkYmjLpsh+Wg0GmHOnDlCy5YtBbVaLTRu3FiYMmWKcP/+fdMHXoa///671J+Nh3mMGzdOePLJJ0Xn+Pv7C7a2tkKLFi2ElStXmjzu8hia05NPPlnu8ebAmPfpceZWUBiTz/nz54V+/foJdnZ2QqNGjYQZM2YIubm5Bn9t7jZKREREVcY5FERERFRlLCiIiIioylhQEBERUZWxoCAiIqIqY0FBREREVcaCgoiIiKqMBQURERFVGQsKIiIiqjIWFERERFRlLCiIyGy88cYbePbZZ6UOg4iMwIKCiMzG8ePHzW7HWiKqHO7lQUSSKywsRJ06dVBUVFTcFhQUhKNHj0oYFREZwkbqAIiIbGxscOjQIQQFBSEuLg7u7u5Qq9VSh0VEBmBBQUSSk8vluHXrFurXrw8/Pz+pwyEiI3AOBRGZhdjYWBYTRBaMBQURmYW4uDgWFEQWjAUFEZmF06dPw9/fX+owiMhILCiIyCzodDrEx8fj1q1byMjIkDocIjIQCwoiMgsff/wxVq1ahYYNG+Ljjz+WOhwiMhDXoSAiIqIq4wgFERERVRkLCiIiIqoyFhRERERUZSwoiIiIqMpYUBAREVGVsaAgIiKiKmNBQURERFXGgoKIiIiqjAUFERERVRkLCiIiIqoyFhRERERUZf8PPyRvQFGnEPkAAAAASUVORK5CYII=", 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "matrixp = sim.get_hamiltonian(0).get_data().toarray()\n", + "plt.imshow(matrixp.real)\n", + "print(matrixp)\n", + "np.savetxt('matrix-p.dat', matrixp.real)\n", + "np.all(matrixp.imag == 0)" + ] + }, + { + "cell_type": "code", + "execution_count": 216, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0.+0.j 0.+0.j]\n", + " [0.+0.j 0.+0.j]]\n" + ] + }, + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 216, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.imshow(matrixm.real)\n", + "print(matrixm)\n", + "np.savetxt('matrix-m.dat', matrixm.real)\n", + "np.all(matrixm.imag == 0)" + ] + }, + { + "cell_type": "code", + "execution_count": 217, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0.+0.j 0.+0.j]\n", + " [0.+0.j 0.+0.j]]\n" + ] + }, + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 217, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.imshow(matrix0.real)\n", + "print(matrix0)\n", + "np.savetxt('matrix-q.dat', matrix0.real)\n", + "np.all(matrix0.imag == 0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Testing a one atom setup with 0 amplitude and detuning set to fixed value" + ] + }, + { + "cell_type": "code", + "execution_count": 353, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Interatomic Radius is: 9.756753962298905µm.\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "Omega_max = 2.0 * 2 * np.pi\n", + "U = Omega_max / 2.0\n", + "R_interatomic = MockDevice.rydberg_blockade_radius(U)\n", + "reg = Register.square(1, R_interatomic, prefix=\"q\")\n", + "print(f\"Interatomic Radius is: {R_interatomic}µm.\")\n", + "reg.draw()" + ] + }, + { + "cell_type": "code", + "execution_count": 354, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "delta_0 = -6 * U\n", + "delta_f = 2 * U\n", + "t_rise = 252\n", + "t_fall = 500\n", + "t_sweep = (delta_f - delta_0) / (2 * np.pi * 10) * 1000\n", + "rise = Pulse.ConstantDetuning(\n", + " RampWaveform(t_rise, 0.0, 0.0),delta_0, 0.0\n", + ")\n", + "sweep = Pulse.ConstantAmplitude(\n", + " Omega_max, RampWaveform(t_sweep, delta_0, delta_f), 0.0\n", + ")\n", + "fall = Pulse.ConstantDetuning(\n", + " RampWaveform(t_fall, Omega_max, 0.0), delta_f, 0.0\n", + ")\n", + "seq1 = Sequence(reg, MockDevice)\n", + "seq1.declare_channel(\"ising\", \"rydberg_global\")\n", + " \n", + "seq1.add(rise, \"ising\")\n", + "seq1.add(sweep, \"ising\")\n", + "seq1.add(fall, \"ising\")\n", + "\n", + "seq1.draw()" + ] + }, + { + "cell_type": "code", + "execution_count": 355, + "metadata": {}, + "outputs": [], + "source": [ + "sim = QutipEmulator.from_sequence(seq1)" + ] + }, + { + "cell_type": "code", + "execution_count": 356, + "metadata": {}, + "outputs": [], + "source": [ + "import qse.qbits\n", + "\n", + "\n", + "L = 3\n", + "nqbits = L * L\n", + "qsqr = qse.Qbits(positions=np.array([[0,0,0]]))\n", + "\n", + "\n", + "Omega = 1.2 # Amplitude\n", + "delta = 2.0 # detuning\n", + "C6 = 5420158.53 # interaction scale\n", + "nqbits=1\n" + ] + }, + { + "cell_type": "code", + "execution_count": 357, + "metadata": {}, + "outputs": [], + "source": [ + "H1_terms = [qat.core.Term(0.5, \"X\", [i]) for i in range(qsqr.nqbits)]\n", + "H1 = qat.core.Observable(nqbits, pauli_terms=H1_terms)\n", + "\n", + "H2_terms = [qat.core.Term(-0.5, \"Z\", [i]) for i in range(qsqr.nqbits)]\n", + "H2 = qat.core.Observable(nqbits, pauli_terms=H2_terms)\n", + "\n", + "rij = qsqr.get_all_distances()\n", + "\n", + "\n", + "def occ_op(nqbits, qi):\n", + " ti = qat.core.Term(1.0, 'Z', [qi])\n", + " return (1 + qat.core.Observable(nqbits, pauli_terms=[ti])) / 2\n", + "#\n", + "# H3 = 0\n", + "\n", + "# for i in range(nqbits):\n", + "# for j in range(i + 1, nqbits):\n", + "# H3 += (C6 / rij[i, j]**6) * occ_op(nqbits, i) * occ_op(nqbits, j)" + ] + }, + { + "cell_type": "code", + "execution_count": 358, + "metadata": {}, + "outputs": [], + "source": [ + "from qat.core.variables import Variable, heaviside\n", + "from qat.core import Observable\n", + "\n", + "def create_waveform(times, values):\n", + " \"\"\"\n", + " A Funnction allowing us to concatenate many lines, limited by heavisides,\n", + " thus creating a continuous, kinked line.\n", + " \"\"\"\n", + " assert len(times) == len(values)\n", + " # Store the final line as an ArithExpression\n", + " arith_expr = 0\n", + " t_var = Variable(\"t\")\n", + " # A line between each two points\n", + " for entry_i in range(1, len(times)):\n", + " # Create ax + b by calculating the slope and the offset\n", + " a = (values[entry_i] - values[entry_i - 1]) / (times[entry_i] - times[entry_i - 1])\n", + " b = ((values[entry_i] + values[entry_i - 1]) - a * (times[entry_i] + times[entry_i - 1])) / 2\n", + " respective_line = a * t_var + b\n", + " arith_expr += heaviside(t_var, times[entry_i - 1], times[entry_i]) * respective_line\n", + " return arith_expr\n", + "#\n", + "Omega_max = 2.0 * 2 * np.pi\n", + "U = Omega_max / 2.0\n", + " \n", + "delta_0 = -6 * U\n", + "delta_f = 2 * U\n", + " \n", + "t_rise = 0.252\n", + "t_fall = 0.500\n", + "t_sweep = ((delta_f - delta_0) / (2 * np.pi * 10) * 1000)*(10**-3)\n", + " \n", + "\n", + "# The waveform of Omega - for the sigma_x terms\n", + "omega_values = [0.0,0,Omega_max,0]\n", + "times_omega = [0,t_rise,t_rise+t_sweep,t_rise+t_sweep+t_fall]\n", + "\n", + "\n", + "omega_waveform = create_waveform(times_omega, omega_values)\n", + "# The waveform of the detuning Delta - for the 'n' terms\n", + "delta_start = -2 * np.pi * 13\n", + "delta_end = 2 * np.pi * 11 # R_blockade is taken as 7.5\n", + "delta_values = [delta_0,0,delta_f,delta_f]\n", + "delta_waveform = create_waveform(times_omega, delta_values)" + ] + }, + { + "cell_type": "code", + "execution_count": 359, + "metadata": {}, + "outputs": [], + "source": [ + "from qat.core import Observable \n", + "Hamiltonian = Observable([\n", + " (omega_waveform, H1),\n", + " (delta_waveform, H2),\n", + " ])\n", + " \n", + "schedule = Schedule(drive=[\n", + " (omega_waveform, H1),\n", + " (delta_waveform, H2),\n", + " ], tmax=t_rise+t_sweep+t_fall)" + ] + }, + { + "cell_type": "code", + "execution_count": 360, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "matrixp = sim.get_hamiltonian(0).get_data().toarray()\n", + "plt.imshow(matrixp.real)\n", + "print(matrixp)\n", + "np.savetxt('matrix-p.dat', matrixp.real)\n", + "np.all(matrixp.imag == 0)" + ] + }, + { + "cell_type": "code", + "execution_count": 363, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 18.84955592+0.j 0. +0.j]\n", + " [ 0. +0.j -18.84955592+0.j]]\n" + ] + }, + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 363, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.imshow(matrixm.real)\n", + "print(matrixm)\n", + "np.savetxt('matrix-m.dat', matrixm.real)\n", + "np.all(matrixm.imag == 0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Testing one atom with Amplitude set to fixed number and detuning to 0\n" + ] + }, + { + "cell_type": "code", + "execution_count": 229, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Interatomic Radius is: 9.756753962298905µm.\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "Omega_max = 2.0 * 2 * np.pi\n", + "U = Omega_max / 2.0\n", + "R_interatomic = MockDevice.rydberg_blockade_radius(U)\n", + "reg = Register.square(1, R_interatomic, prefix=\"q\")\n", + "print(f\"Interatomic Radius is: {R_interatomic}µm.\")\n", + "reg.draw()" + ] + }, + { + "cell_type": "code", + "execution_count": 230, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "delta_0 = -6 * U\n", + "delta_f = 2 * U\n", + "t_rise = 252\n", + "t_fall = 500\n", + "t_sweep = (delta_f - delta_0) / (2 * np.pi * 10) * 1000\n", + "rise = Pulse.ConstantDetuning(\n", + " RampWaveform(t_rise, Omega_max,Omega_max),0, 0.0\n", + ")\n", + "sweep = Pulse.ConstantAmplitude(\n", + " Omega_max, RampWaveform(t_sweep, delta_0, delta_f), 0.0\n", + ")\n", + "fall = Pulse.ConstantDetuning(\n", + " RampWaveform(t_fall, Omega_max, 0.0), delta_f, 0.0\n", + ")\n", + "seq1 = Sequence(reg, MockDevice)\n", + "seq1.declare_channel(\"ising\", \"rydberg_global\")\n", + " \n", + "seq1.add(rise, \"ising\")\n", + "seq1.add(sweep, \"ising\")\n", + "seq1.add(fall, \"ising\")\n", + "\n", + "seq1.draw()" + ] + }, + { + "cell_type": "code", + "execution_count": 231, + "metadata": {}, + "outputs": [], + "source": [ + "sim = QutipEmulator.from_sequence(seq1)" + ] + }, + { + "cell_type": "code", + "execution_count": 232, + "metadata": {}, + "outputs": [], + "source": [ + "import qse.qbits\n", + "\n", + "\n", + "L = 3\n", + "nqbits = L * L\n", + "qsqr = qse.Qbits(positions=np.array([[0,0,0]]))\n", + "\n", + "\n", + "Omega = 1.2 # Amplitude\n", + "delta = 2.0 # detuning\n", + "C6 = 5420158.53 # interaction scale\n", + "nqbits=1\n" + ] + }, + { + "cell_type": "code", + "execution_count": 233, + "metadata": {}, + "outputs": [], + "source": [ + "H1_terms = [qat.core.Term(0.5, \"X\", [i]) for i in range(qsqr.nqbits)]\n", + "H1 = qat.core.Observable(nqbits, pauli_terms=H1_terms)\n", + "\n", + "H2_terms = [qat.core.Term(-0.5, \"Z\", [i]) for i in range(qsqr.nqbits)]\n", + "H2 = qat.core.Observable(nqbits, pauli_terms=H2_terms)\n", + "\n", + "rij = qsqr.get_all_distances()\n", + "\n", + "\n", + "def occ_op(nqbits, qi):\n", + " ti = qat.core.Term(1.0, 'Z', [qi])\n", + " return (1 + qat.core.Observable(nqbits, pauli_terms=[ti])) / 2\n", + "#\n", + "# H3 = 0\n", + "\n", + "# for i in range(nqbits):\n", + "# for j in range(i + 1, nqbits):\n", + "# H3 += (C6 / rij[i, j]**6) * occ_op(nqbits, i) * occ_op(nqbits, j)" + ] + }, + { + "cell_type": "code", + "execution_count": 234, + "metadata": {}, + "outputs": [], + "source": [ + "from qat.core.variables import Variable, heaviside\n", + "from qat.core import Observable\n", + "\n", + "def create_waveform(times, values):\n", + " \"\"\"\n", + " A Funnction allowing us to concatenate many lines, limited by heavisides,\n", + " thus creating a continuous, kinked line.\n", + " \"\"\"\n", + " assert len(times) == len(values)\n", + " # Store the final line as an ArithExpression\n", + " arith_expr = 0\n", + " t_var = Variable(\"t\")\n", + " # A line between each two points\n", + " for entry_i in range(1, len(times)):\n", + " # Create ax + b by calculating the slope and the offset\n", + " a = (values[entry_i] - values[entry_i - 1]) / (times[entry_i] - times[entry_i - 1])\n", + " b = ((values[entry_i] + values[entry_i - 1]) - a * (times[entry_i] + times[entry_i - 1])) / 2\n", + " respective_line = a * t_var + b\n", + " arith_expr += heaviside(t_var, times[entry_i - 1], times[entry_i]) * respective_line\n", + " return arith_expr\n", + "#\n", + "Omega_max = 2.0 * 2 * np.pi\n", + "U = Omega_max / 2.0\n", + " \n", + "delta_0 = -6 * U\n", + "delta_f = 2 * U\n", + " \n", + "t_rise = 0.252\n", + "t_fall = 0.500\n", + "t_sweep = ((delta_f - delta_0) / (2 * np.pi * 10) * 1000)*(10**-3)\n", + " \n", + "\n", + "# The waveform of Omega - for the sigma_x terms\n", + "omega_values = [Omega_max,0,Omega_max,0]\n", + "times_omega = [0,t_rise,t_rise+t_sweep,t_rise+t_sweep+t_fall]\n", + "\n", + "\n", + "omega_waveform = create_waveform(times_omega, omega_values)\n", + "# The waveform of the detuning Delta - for the 'n' terms\n", + "delta_start = -2 * np.pi * 13\n", + "delta_end = 2 * np.pi * 11 # R_blockade is taken as 7.5\n", + "delta_values = [0,0,delta_f,delta_f]\n", + "delta_waveform = create_waveform(times_omega, delta_values)" + ] + }, + { + "cell_type": "code", + "execution_count": 235, + "metadata": {}, + "outputs": [], + "source": [ + "from qat.core import Observable \n", + "Hamiltonian = Observable([\n", + " (omega_waveform, H1),\n", + " (delta_waveform, H2),\n", + " ])\n", + " \n", + "schedule = Schedule(drive=[\n", + " (omega_waveform, H1),\n", + " (delta_waveform, H2),\n", + " ], tmax=t_rise+t_sweep+t_fall)" + ] + }, + { + "cell_type": "code", + "execution_count": 236, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "schedule.display()" + ] + }, + { + "cell_type": "code", + "execution_count": 237, + "metadata": {}, + "outputs": [], + "source": [ + "matrixm = Omega_max* H1.to_matrix(sparse=False) + 0 * H2.to_matrix(sparse=False)" + ] + }, + { + "cell_type": "code", + "execution_count": 238, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0. +0.j 6.28318531+0.j]\n", + " [6.28318531+0.j 0. +0.j]]\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "matrixp = sim.get_hamiltonian(0).get_data().toarray()\n", + "plt.imshow(matrixp.real)\n", + "print(matrixp)\n", + "np.savetxt('matrix-p.dat', matrixp.real)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 239, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0. +0.j 6.28318531+0.j]\n", + " [6.28318531+0.j 0. +0.j]]\n" + ] + }, + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 239, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.imshow(matrixm.real)\n", + "print(matrixm)\n", + "np.savetxt('matrix-m.dat', matrixm.real)\n", + "np.all(matrixm.imag == 0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Testing a one atom setup with 0 amplitude and detuning checking interaction term" + ] + }, + { + "cell_type": "code", + "execution_count": 241, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Interatomic Radius is: 9.756753962298905µm.\n" + ] + }, + { + "data": { + "image/png": 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ql5WVlUEURWRkZOjUPX/+PERRRHFxsVymVqshiiJSU3VbWxcuXIAoijqtxaqqKoiiKA99bnT58mWIoqjzvE1NTQ1EUWzyt7p27RpEUZQ7B4EH14YoikhMTNSpe+PGDYiiiNzcXLmscbEoURR1RkJlZ2dDFEVkZ2fLZZIkyXUffkYqNzcXoijixo0bOsdLTEyEKIo6U5rcvn0boiji2rVrOnWTkpIgiqLOzAYFBQUQRRGXL1/WOQ83btxAYmIiqqqq5PKW/vapqakQRVFnuHlxcTFEUcT58+d16mZkZEAURZSVlcllpaWlEEURmZmZOnXPnTsHURRx9+7/XcMVFRUQRRFpaWk6dZv721dWVkIURZw9e1an7qVLlyCKIlQqlVxWXV0NURRx5swZnbpXrlyBKIo60wrV1dVBFEWcOnVKp+7169chiiLy8vLksoaGBvnv+bCbN29CFEXk5OTIZVqtVq778NDrnJwciKLYpC+4sW5rnxGNTp06BVEUdR5Uzs/PhyiKuHLlik7djnxG5Jfko6KmAnbWdrDV2MKtxg1O9U5yPaWlEhW5Fe3+jGgPvUdtHTx4sNnyDz/8EIcOHcIbb7yhdxDtUVJSAo1G0+T5FRcXlyYnv5FKpWq2/sMX7aNiY2OxZs0aveNz6OMAGysb3K+/DzSTzDWSBg599B8NQb2XQqGAv78/tFot+9ao3eyUduhj3QdVdVWAddPf19+vRz+bfp16zE7rbL958yaefPLJLps7Kj8/H4MGDcLp06cREhIil7/zzjv4n//5nybfcgHA2toaf//73zF79my57PPPP8eaNWtQWFjY7HHq6up0vimo1Wp4eHi0eWsLANYeWYs9Z/bAa4AXLC0s5Vtb5VXlUNeq8enLn+LZEc/K++atLePWNfVbW51Vl9dJ77q1pVAosCFuA7af2g5PJ08oLR/M9ScJEtQ1apRWl+L/vfT/MHnk5E67tdXhFRIfde7cOfj7+3fW7poYMGAALCwsmiSAwsLCFufXd3V11as+8GC+/uYmWbSwsND5VtjcJHqvhb6GjNwMXCq4BDulHawtrVFZ++BW1IynZiDUJ7TJPh/V0uR8zdUVBKHZclOo29z76Ml1AcP/nl1Vl9dJ19YFTO9vP+/peTh76yx+vf0r+lr3hY2VDSprK6GVtHjR70X828h/a7Lvlt5ze+jdIlm+fHmTssLCQhw+fBiRkZEYNGiQXP7JJ590KKiWBAcHIygoCJ999hmAB5l58ODBWLx4cYud7dXV1Thy5IhcNmHCBPj6+urd2d7e50gK1YX4NuVb/OvXf6G6vhoeTh54KeAlTPeb/qCVQtROkiTJ/VFct530VVxZjL0pe3Hk3BHcq7+Hxx0fx2+f+i1mPDUDVpZWbe9AD3onkueee659OxYEHD9+vENBtWTfvn2YO3cuvvjiCwQFBWHTpk347rvvcOXKFbi4uCA6OhqDBg1CbGwsgAcd5JMmTcK6desQGRmJvXv34qOPPkJ6ejpGjx7drmPqm0gaabVa1GvqobRU8gOAOqRxYAAAhIaGcmEr6pDu+CzS+yuyMefZmjVrFoqLi7F69WqoVCr4+fkhLi5O7lDPzc3VafZNmDABe/bswX/+53/i3Xffhbe3Nw4dOtTuJGIIhUIBG4VNlx+HejZHR0djh0Bmrjs+i8zuyfbu1tEWCRFRb9Gu50imTJnSZEx3cyorK/Hxxx9j69atBgdGRETmoV23tmbOnIkZM2bAwcEBU6dORWBgINzd3WFjY4OysjJcunQJiYmJOHr0KCIjI7Fhw4aujpuIiExEu29t1dXVYf/+/di3bx8SExPlJyIFQcCoUaMQHh6OhQsXYuTIkV0acHfjrS0yFo1GI88u4O/vz852Mlkd7iOpqKhATU0N+vfv32RNkp6EiYSMhaO2yFx0+MEGBweHDi2AQkTto1Ao4OvrK/9MZKr4hByRiXp4hUQiU8avOUREZBC2SIhMlCRJ8vT+Tk5OnCGBTBZbJEQmSqvV4vz58zh//rzOmhhEpkbvRDJ37lycPHmyK2Ihokf069cP/fp17toRRJ1N70RSUVGBsLAweHt746OPPsKdO3e6Ii6iXs/CwgIBAQEICAjg0F8yaXonkkOHDuHOnTv4/e9/j3379sHT0xMvvPACvv/+e51lJomIqHfoUB+Js7Mzli9fjnPnziE5ORnDhg3DnDlz4O7ujmXLljVZo5iIiHougzrbCwoKcOzYMRw7dgwWFhaIiIjA+fPnMWrUKPzlL3/prBiJeiWNRoP09HSkp6fLy6gSmSK9h/82NDTghx9+wI4dO/DLL7/A19cXS5cuxSuvvCJPIXLw4EEsWLAAy5Yt6/SAiXoTtVpt7BCI2qR3InFzc4NWq8Xs2bORkpICPz+/JnWee+45LshDZCCFQiEvwsYpUsiU6T1p465duzBz5kzY2PSO1f84aSMRUeu4QmIbmEiIiFpnNu3l0tJSREVFwd7eHo6Ojli4cCHu3bvXav0lS5Zg+PDhsLW1xeDBg/HHP/5RXkeFyNRJkoTy8nKUl5eD3/fIlJlNIomKisLFixdx7Ngx/Pjjjzh58iQWLVrUYv38/Hzk5+dj48aNuHDhAnbu3Im4uDgsXLiwG6Mm6jitVovMzExkZmZyihQyaWZxa+vy5csYNWoUzp49i8DAQABAXFwcIiIicPv2bbi7u7drP/v378err76KqqoqWFq2b5wBb22RsWg0GqSlpQEAn24nk2YWs/8mJSXB0dFRTiIAEBYWBoVCgeTkZPz7v/97u/bTmAxaSyJ1dXWoq6uT/83hl2QsFhYWCAoKMnYYRG0yi1tbKpUKAwcO1CmztLSEk5MTVCpVu/ZRUlKCDz74oNXbYQAQGxsrr/7o4OAADw+PDsdNRNQbGDWRrFy5EoIgtPq6cuWKwcdRq9WIjIzEqFGj8P7777dad9WqVaioqJBfeXl5Bh+fiKgnM+qtrbfeegvz5s1rtc7QoUPh6uqKoqIinfL79++jtLQUrq6urW5fWVmJKVOmoF+/fjh48CCsrKxara9UKqFUKtsVP1FX0mg0uHDhAgBg9OjR7CMhk2XUROLs7AxnZ+c264WEhKC8vBxpaWkICAgAABw/fhxarRbBwcEtbqdWqxEeHg6lUokffvih1zxEST1HWVmZsUMgapNZjNoCgBdeeAGFhYXYtm0bGhoaMH/+fAQGBmLPnj0AgDt37mDy5Mn45ptvEBQUBLVajeeffx7V1dU4ePAg+vbtK+/L2dm53d/uOGqLjEWSJLklPnDgQC612800Gk2vWRrDysrKoBavWYzaAoDdu3dj8eLFmDx5MhQKBWbMmIHNmzfLv29oaMDVq1dRXV0NAEhPT0dycjIAYNiwYTr7ys7OhqenZ7fFTtQRgiDAxcXF2GH0Svfu3cPt27d7zYOggiDg8ccfh52dXce2N5cWibGwRULUu2g0Gly/fh19+vSBs7Nzj28JSpKE4uJiVFdXw9vbu0MtE7NpkRD1NpIkobKyEsCDtdt7+geaqWhoaIAkSXB2doatra2xw+kWzs7OyMnJQUNDQ4cSiVk8R0LUG2m1WnlhK06R0v16U+I29L2yRUJkwjjSkMwBWyREJsrCwgLjx4/H+PHj+QxJL1BeXo5169YZO4wOYSIhIuqg3Lu5+OjoR4j4NAIzt83EjlM7UFNf06F9MZEQEfUyt0tv481/vImdp3ZCpVbhquoq1setx7sH34VGq2l126ioKAQGBsLX1xeRkZFQqVR48803UVlZCT8/P3mC2hs3biAsLAy+vr7w8/PDoUOH5H0IgoAPP/wQwcHB8PT0xKFDhxAbG4vAwEB4e3sjISEBAFBcXIznn38eY8aMga+vL+bPn9/p54J9JEQmSqvV4tKlSwCAUaNGcd12E/Nd6ne4UXQDwwYOg4Xiwa3HytpKHL98HMk3kzFh2IQWt920aZM8q8e6devw/vvvY9u2bfDz80NmZqZcLyoqCgsWLMAbb7yB69evY/z48fD398eQIUMAAHZ2dkhOTkZ8fDymTZuGLVu2IDU1Ffv378fbb7+Ns2fP4h//+Ae8vLzwyy+/AHiw6F9n45VJZKIkSUJJSQlKSkp6zYNx5iQ5Oxm21rZyEgGAfjb9UK+px8X8i61uu2fPHgQGBmL06NH46quvdJJHo8rKSqSnp8uL8Xl7e2PixIkQRVGuM2vWLABAYGAgqqqq8PLLLwMAgoKCcP36dQDA+PHj8dNPP+Gtt97C4cOHdWb56CxMJEQmShAE+Pj4wMfHp1cNRTUXjn0c0aDRnUKlcZh2X2XLH9aJiYnYvHkzjh49igsXLuCTTz5BbW1tu4756HXQOKqvcTDGw/++f/8+gAdzFWZmZiI4OBgHDhzAuHHjoNG0futNX0wkRCZKoVDA3d0d7u7uvK1lgiLGREAhKHD33l1IkgSNVoPc0lz0t+uPZ4c/2+J2ZWVl6NevH/r374/6+np88cUXAAB7e3vU1NSgvr4ewIOHUJ966ins2LEDwIP+ksTERDzzzDN6xZmdnQ07Ozv87ne/w2effYZr167h3r17HXvTLeDVSUTUAZFjIhEVHIV6TT2yirOQXZINp75OeC/yPbg7trz895QpUzB8+HAMHz4coaGh8PPzAwA4OTkhOjoavr6+cmf77t27sW/fPowdOxYvvfQSvvrqKwwePFivOBMSEhAQEAA/Pz9MmDABGzZsgIODQ4ffd3M411YbONcWGYskSfIkpH369OHtrW5SW1uL7OxseHl5tflAqCRJuKK6gnN552BjZYOJwyZiQL8B3RRp59HnPTeHo7aITJRWq8XZs2cBAKGhoXwo0QQJgoCRbiMx0m2ksUMxKiYSIhPW1oqeRKaAiYTIRFlYWODpp582dhhEbWJnOxFRM3pT97Gh75UtEiKih1hZWUEQBBQXF/eqha0EQejwrVQmEiITpdVqceXKFQDAiBEj+CxJN7GwsMDjjz+O27dvIycnx9jhdIvGpXY7OqDDbBJJaWkplixZgiNHjshrtn/66aftWmNYkiREREQgLi4OBw8exPTp07s+YCIDSZKEoqIiAMDw4cONHE3vYmdnB29vbzQ0NLRduQewsrIyaFSg2SSSqKgoFBQU4NixY2hoaMD8+fOxaNEi7Nmzp81tN23a1OObp9TzCIKAYcOGyT9T97KwsOCQ63YyiwcSL1++jFGjRuHs2bPyE59xcXGIiIjA7du34e7e8lOkmZmZ+M1vfoPU1FS4ubnp3SLhA4lERK0zi5uuSUlJcHR0lJMIAISFhUGhUCA5ObnF7aqrq/HKK69g69atcHV1bdex6urqoFardV5ERNQys0gkKpUKAwcO1CmztLSEk5MTVCpVi9stW7YMEyZMwLRp09p9rNjYWDg4OMgvDw+PDsdNZAhJklBbW4va2tpeNRSVzI9RE8nKlSshCEKrr8ZRK/r64YcfcPz4cWzatEmv7VatWoWKigr5lZeX16HjExlKq9XizJkzOHPmjDw9OZEpMmpn+1tvvYV58+a1Wmfo0KFwdXWVR680un//PkpLS1u8ZXX8+HFkZWXB0dFRp3zGjBkIDQ2Vl6F8lFKphFKpbO9bIOpSHPJL5sCsOttTU1MREBAAAPjll18wZcqUFjvbVSoVSkpKdMrGjBmDTz/9FFOnToWXl1e7js3OdiKi1pnF8N+RI0diypQpeP3117Ft2zY0NDRg8eLFePnll+UkcufOHUyePBnffPMNgoKC4Orq2mxrZfDgwe1OIkRE1DazaTfv3r0bI0aMwOTJkxEREYGJEyfib3/7m/z7hoYGXL16VV6/gYiIuodZ3NoyJt7aImPRarW4fv06AMDb25v9JWSyeGUSmShJklBQUICCggIO/yWTZhZ9JES9kSAIcn8ep0ghU8ZEQmSiFAoFhgwZYuwwiNrEW1tERGQQtkiITJQkSfI05o2LLRGZIrZIiEyUVqvF6dOncfr0aU6RQiaNLZI2NI6W4SzA1N00Gg2qqqoAPLj+uDYGGUu/fv1abREzkbShsrISADgLMBH1Wm09R8cHEtug1WqRn5/fZkZ+lFqthoeHB/Ly8vggYwt4jtrGc9Q2nqPWdcb5YYvEQAqFAo8//niHt7e3t+fF3Qaeo7bxHLWN56h1XXl+2NlOREQGYSIhIiKDMJF0EaVSiZiYGC6S1Qqeo7bxHLWN56h13XF+2NlOREQGYYuEiIgMwkRCREQGYSIhIiKDMJEQEZFBmEg60YcffogJEyagT58+cHR0bNc2kiRh9erVcHNzg62tLcLCwuTlVXui0tJSREVFwd7eHo6Ojli4cCHu3bvX6jbPPvssBEHQeb355pvdFHHX27p1Kzw9PWFjY4Pg4GCkpKS0Wn///v0YMWIEbGxsMGbMGBw9erSbIjUefc7Rzp07m1wvNjY23Rht9zp58iSmTp0Kd3d3CIKAQ4cOtblNQkICnnrqKSiVSgwbNgw7d+40KAYmkk5UX1+PmTNn4ve//327t1m/fj02b96Mbdu2ITk5GX379kV4eDhqa2u7MFLjiYqKwsWLF3Hs2DH8+OOPOHnyJBYtWtTmdq+//rq87GxBQQHWr1/fDdF2vX379mH58uWIiYlBeno6xo4di/DwcBQVFTVb//Tp05g9ezYWLlyIjIwMTJ8+HdOnT8eFCxe6OfLuo+85Ah48xf3w9XLr1q1ujLh7VVVVYezYsdi6dWu76mdnZyMyMhLPPfccMjMzsXTpUrz22mv4+eefOx6ERJ1ux44dkoODQ5v1tFqt5OrqKm3YsEEuKy8vl5RKpfTtt992YYTGcenSJQmAdPbsWbnsp59+kgRBkO7cudPidpMmTZL+9Kc/dUOE3S8oKEj6wx/+IP9bo9FI7u7uUmxsbLP1f/e730mRkZE6ZcHBwdIbb7zRpXEak77nqL3//3oiANLBgwdbrfPOO+9ITz75pE7ZrFmzpPDw8A4fly0SI8rOzoZKpUJYWJhc5uDggODgYCQlJRkxsq6RlJQER0dHBAYGymVhYWFQKBRITk5uddvdu3djwIABGD16NFatWoXq6uquDrfL1dfXIy0tTefvr1AoEBYW1uLfPykpSac+AISHh/fI6wXo2DkCgHv37mHIkCHw8PDAtGnTcPHixe4I1yx0xTXESRuNSKVSAQBcXFx0yl1cXOTf9SQqlQoDBw7UKbO0tISTk1Or7/eVV17BkCFD4O7ujl9//RUrVqzA1atXceDAga4OuUuVlJRAo9E0+/e/cuVKs9uoVKpec70AHTtHw4cPx9dffw1fX19UVFRg48aNmDBhAi5evGjQBKw9RUvXkFqtRk1NDWxtbfXeJ1skbVi5cmWTjrtHXy1d0L1FV5+jRYsWITw8HGPGjEFUVBS++eYbHDx4EFlZWZ34LqinCAkJQXR0NPz8/DBp0iQcOHAAzs7O+OKLL4wdWo/FFkkb3nrrLcybN6/VOkOHDu3Qvl1dXQEAhYWFcHNzk8sLCwvh5+fXoX0aQ3vPkaura5MO0vv376O0tFQ+F+0RHBwMALhx4waeeOIJveM1FQMGDICFhQUKCwt1ygsLC1s8H66urnrVN3cdOUePsrKygr+/P27cuNEVIZqdlq4he3v7DrVGACaSNjk7O8PZ2blL9u3l5QVXV1fEx8fLiUOtViM5OVmvkV/G1t5zFBISgvLycqSlpSEgIAAAcPz4cWi1Wjk5tEdmZiYA6CRfc2RtbY2AgADEx8dj+vTpAB4spBYfH4/Fixc3u01ISAji4+OxdOlSuezYsWMICQnphoi7X0fO0aM0Gg3Onz+PiIiILozUfISEhDQZMm7wNdThbnpq4tatW1JGRoa0Zs0ayc7OTsrIyJAyMjKkyspKuc7w4cOlAwcOyP9et26d5OjoKB0+fFj69ddfpWnTpkleXl5STU2NMd5Cl5syZYrk7+8vJScnS4mJiZK3t7c0e/Zs+fe3b9+Whg8fLiUnJ0uSJEk3btyQ1q5dK6WmpkrZ2dnS4cOHpaFDh0rPPPOMsd5Cp9q7d6+kVCqlnTt3SpcuXZIWLVokOTo6SiqVSpIkSZozZ460cuVKuf6pU6ckS0tLaePGjdLly5elmJgYycrKSjp//ryx3kKX0/ccrVmzRvr555+lrKwsKS0tTXr55ZclGxsb6eLFi8Z6C12qsrJS/qwBIH3yySdSRkaGdOvWLUmSJGnlypXSnDlz5Po3b96U+vTpI7399tvS5cuXpa1bt0oWFhZSXFxch2NgIulEc+fOlQA0eZ04cUKuA0DasWOH/G+tViu99957kouLi6RUKqXJkydLV69e7f7gu8ndu3el2bNnS3Z2dpK9vb00f/58nUSbnZ2tc85yc3OlZ555RnJycpKUSqU0bNgw6e2335YqKiqM9A4632effSYNHjxYsra2loKCgqQzZ87Iv5s0aZI0d+5cnfrfffed5OPjI1lbW0tPPvmk9K9//aubI+5++pyjpUuXynVdXFykiIgIKT093QhRd48TJ040+7nTeE7mzp0rTZo0qck2fn5+krW1tTR06FCdz6SO4DTyRERkEI7aIiIigzCREBGRQZhIiIjIIEwkRERkECYSIiIyCBMJEREZhImEiIgMwkRCREQGYSIhMrLt27fj+eef7/LjxMXFwc/PD1qttsuPRb0LEwmREdXW1uK9995DTExMlx9rypQpsLKywu7du7v8WNS7MJEQGdH3338Pe3t7PP30091yvHnz5mHz5s3dcizqPZhIiDpBcXExXF1d8dFHH8llp0+fhrW1NeLj41vcbu/evZg6dapO2bPPPqszTTwATJ8+XWfNF09PT/zXf/0XoqOjYWdnhyFDhuCHH35AcXExpk2bBjs7O/j6+iI1NVVnP1OnTkVqaioXBaNOxURC1AmcnZ3x9ddf4/3330dqaioqKysxZ84cLF68GJMnT25xu8TERJ017PXxl7/8BU8//TQyMjIQGRmJOXPmIDo6Gq+++irS09PxxBNPIDo6Gg/Pyzp48GC4uLhAFMUOHZOoOUwkRJ0kIiICr7/+OqKiovDmm2+ib9++iI2NbbF+eXk5Kioq4O7u3uHjvfHGG/D29sbq1auhVqsxbtw4zJw5Ez4+PlixYgUuX77cZDU8d3d33Lp1q0PHJGoOEwlRJ9q4cSPu37+P/fv3Y/fu3VAqlS3WrampAQDY2Nh06Fi+vr7yzy4uLgCAMWPGNCl7dHljW1tbVFdXd+iYRM1hIiHqRFlZWcjPz4dWq0VOTk6rdfv37w9BEFBWVtbmfjUaTZMyKysr+WdBEFose3S4b2lpaZctH029ExMJUSepr6/Hq6++ilmzZuGDDz7Aa6+91qQ18DBra2uMGjUKly5davK7R29H3bx5s1NirK2tRVZWFvz9/Ttlf0QAEwlRp/mP//gPVFRUYPPmzVixYgV8fHywYMGCVrcJDw9HYmJik/LDhw/jwIEDyMrKwocffohLly7h1q1buHPnjkExnjlzBkqlEiEhIQbth+hhTCREnSAhIQGbNm3Crl27YG9vD4VCgV27dkEURfz1r39tcbuFCxfi6NGjqKio0CmPjIzE+vXrMWrUKJw8eRKff/45UlJSsGvXLoPi/PbbbxEVFYU+ffoYtB+ih3HNdiIjmzlzJp566imsWrUKwIPnSPz8/LBp06ZOPU5JSQmGDx+O1NRUeHl5deq+qXdji4TIyDZs2AA7O7suP05OTg4+//xzJhHqdGyREJmYrmqREHUVJhIiIjIIb20REZFBmEiIiMggTCRERGQQJhIiIjIIEwkRERmEiYSIiAzCREJERAZhIiEiIoP8f+JD71LJhQBuAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "Omega_max = 2.0 * 2 * np.pi\n", + "U = Omega_max / 2.0\n", + "R_interatomic = MockDevice.rydberg_blockade_radius(U)\n", + "reg = Register.from_coordinates([[0,0],[2,0]])\n", + "print(f\"Interatomic Radius is: {R_interatomic}µm.\")\n", + "reg.draw()" + ] + }, + { + "cell_type": "code", + "execution_count": 242, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "delta_0 = -6 * U\n", + "delta_f = 2 * U\n", + "t_rise = 252\n", + "t_fall = 500\n", + "t_sweep = (delta_f - delta_0) / (2 * np.pi * 10) * 1000\n", + "rise = Pulse.ConstantDetuning(\n", + " RampWaveform(t_rise, 0.0, 0.0), 0, 0.0\n", + ")\n", + "sweep = Pulse.ConstantAmplitude(\n", + " Omega_max, RampWaveform(t_sweep, delta_0, delta_f), 0.0\n", + ")\n", + "fall = Pulse.ConstantDetuning(\n", + " RampWaveform(t_fall, Omega_max, 0.0), delta_f, 0.0\n", + ")\n", + "seq1 = Sequence(reg, MockDevice)\n", + "seq1.declare_channel(\"ising\", \"rydberg_global\")\n", + " \n", + "seq1.add(rise, \"ising\")\n", + "seq1.add(sweep, \"ising\")\n", + "seq1.add(fall, \"ising\")\n", + "\n", + "seq1.draw()" + ] + }, + { + "cell_type": "code", + "execution_count": 243, + "metadata": {}, + "outputs": [], + "source": [ + "sim = QutipEmulator.from_sequence(seq1)" + ] + }, + { + "cell_type": "code", + "execution_count": 244, + "metadata": {}, + "outputs": [], + "source": [ + "import qse.qbits\n", + "\n", + "\n", + "L = 3\n", + "nqbits = L * L\n", + "qsqr = qse.Qbits(positions=np.array([[0,0,0],[2,0,0]]))\n", + "\n", + "\n", + "Omega = 1.2 # Amplitude\n", + "delta = 2.0 # detuning\n", + "C6 = 5420158.53 # interaction scale\n", + "nqbits=2\n" + ] + }, + { + "cell_type": "code", + "execution_count": 245, + "metadata": {}, + "outputs": [], + "source": [ + "H1_terms = [qat.core.Term(0.5, \"X\", [i]) for i in range(qsqr.nqbits)]\n", + "H1 = qat.core.Observable(nqbits, pauli_terms=H1_terms)\n", + "\n", + "H2_terms = [qat.core.Term(-0.5, \"Z\", [i]) for i in range(qsqr.nqbits)]\n", + "H2 = qat.core.Observable(nqbits, pauli_terms=H2_terms)\n", + "\n", + "rij = qsqr.get_all_distances()\n", + "\n", + "\n", + "def occ_op(nqbits, qi):\n", + " ti = qat.core.Term(1.0, 'Z', [qi])\n", + " return (1 + qat.core.Observable(nqbits, pauli_terms=[ti])) / 2\n", + "#\n", + "H3 = 0\n", + "\n", + "for i in range(nqbits):\n", + " for j in range(i + 1, nqbits):\n", + " H3 += (C6 / rij[i, j]**6) * occ_op(nqbits, i) * occ_op(nqbits, j)" + ] + }, + { + "cell_type": "code", + "execution_count": 246, + "metadata": {}, + "outputs": [], + "source": [ + "from qat.core.variables import Variable, heaviside\n", + "from qat.core import Observable\n", + "\n", + "def create_waveform(times, values):\n", + " \"\"\"\n", + " A Funnction allowing us to concatenate many lines, limited by heavisides,\n", + " thus creating a continuous, kinked line.\n", + " \"\"\"\n", + " assert len(times) == len(values)\n", + " # Store the final line as an ArithExpression\n", + " arith_expr = 0\n", + " t_var = Variable(\"t\")\n", + " # A line between each two points\n", + " for entry_i in range(1, len(times)):\n", + " # Create ax + b by calculating the slope and the offset\n", + " a = (values[entry_i] - values[entry_i - 1]) / (times[entry_i] - times[entry_i - 1])\n", + " b = ((values[entry_i] + values[entry_i - 1]) - a * (times[entry_i] + times[entry_i - 1])) / 2\n", + " respective_line = a * t_var + b\n", + " arith_expr += heaviside(t_var, times[entry_i - 1], times[entry_i]) * respective_line\n", + " return arith_expr\n", + "#\n", + "Omega_max = 2.0 * 2 * np.pi\n", + "U = Omega_max / 2.0\n", + " \n", + "delta_0 = -6 * U\n", + "delta_f = 2 * U\n", + " \n", + "t_rise = 0.252\n", + "t_fall = 0.500\n", + "t_sweep = ((delta_f - delta_0) / (2 * np.pi * 10) * 1000)*(10**-3)\n", + " \n", + "\n", + "# The waveform of Omega - for the sigma_x terms\n", + "omega_values = [0.0,0,Omega_max,0]\n", + "times_omega = [0,t_rise,t_rise+t_sweep,t_rise+t_sweep+t_fall]\n", + "\n", + "\n", + "omega_waveform = create_waveform(times_omega, omega_values)\n", + "# The waveform of the detuning Delta - for the 'n' terms\n", + "delta_start = -2 * np.pi * 13\n", + "delta_end = 2 * np.pi * 11 # R_blockade is taken as 7.5\n", + "delta_values = [0,0,delta_f,delta_f]\n", + "delta_waveform = create_waveform(times_omega, delta_values)" + ] + }, + { + "cell_type": "code", + "execution_count": 247, + "metadata": {}, + "outputs": [], + "source": [ + "from qat.core import Observable \n", + "Hamiltonian = Observable([\n", + " (omega_waveform, H1),\n", + " (delta_waveform, H2),\n", + " ])\n", + " \n", + "schedule = Schedule(drive=[\n", + " (omega_waveform, H1),\n", + " (delta_waveform, H2),\n", + " ], tmax=t_rise+t_sweep+t_fall)" + ] + }, + { + "cell_type": "code", + "execution_count": 248, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "matrixp = sim.get_hamiltonian(0).get_data().toarray()\n", + "plt.imshow(matrixp.real)\n", + "print(matrixp)\n", + "np.savetxt('matrix-p.dat', matrixp.real)\n", + "np.all(matrixp.imag == 0)" + ] + }, + { + "cell_type": "code", + "execution_count": 252, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[84689.97703125+0.j 0. +0.j 0. +0.j\n", + " 0. +0.j]\n", + " [ 0. +0.j 0. +0.j 0. +0.j\n", + " 0. +0.j]\n", + " [ 0. +0.j 0. +0.j 0. +0.j\n", + " 0. +0.j]\n", + " [ 0. +0.j 0. +0.j 0. +0.j\n", + " 0. +0.j]]\n" + ] + }, + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 252, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.imshow(matrixm.real)\n", + "print(matrixm)\n", + "np.savetxt('matrix-m.dat', matrixm.real)\n", + "np.all(matrixm.imag == 0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Testing more atoms with 0 amplitude and detuning checking interaction term" + ] + }, + { + "cell_type": "code", + "execution_count": 255, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Interatomic Radius is: 9.756753962298905µm.\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "Omega_max = 2.0 * 2 * np.pi\n", + "U = Omega_max / 2.0\n", + "R_interatomic = MockDevice.rydberg_blockade_radius(U)\n", + "reg = Register.from_coordinates([[0,0],[2,0],[4,0],[0,2],[2,2],[4,2],[0,4],[2,4],[4,4]])\n", + "print(f\"Interatomic Radius is: {R_interatomic}µm.\")\n", + "reg.draw()" + ] + }, + { + "cell_type": "code", + "execution_count": 256, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "delta_0 = -6 * U\n", + "delta_f = 2 * U\n", + "t_rise = 252\n", + "t_fall = 500\n", + "t_sweep = (delta_f - delta_0) / (2 * np.pi * 10) * 1000\n", + "rise = Pulse.ConstantDetuning(\n", + " RampWaveform(t_rise, 0.0, 0.0), 0, 0.0\n", + ")\n", + "sweep = Pulse.ConstantAmplitude(\n", + " Omega_max, RampWaveform(t_sweep, delta_0, delta_f), 0.0\n", + ")\n", + "fall = Pulse.ConstantDetuning(\n", + " RampWaveform(t_fall, Omega_max, 0.0), delta_f, 0.0\n", + ")\n", + "seq1 = Sequence(reg, MockDevice)\n", + "seq1.declare_channel(\"ising\", \"rydberg_global\")\n", + " \n", + "seq1.add(rise, \"ising\")\n", + "seq1.add(sweep, \"ising\")\n", + "seq1.add(fall, \"ising\")\n", + "\n", + "seq1.draw()" + ] + }, + { + "cell_type": "code", + "execution_count": 257, + "metadata": {}, + "outputs": [], + "source": [ + "sim = QutipEmulator.from_sequence(seq1)" + ] + }, + { + "cell_type": "code", + "execution_count": 268, + "metadata": {}, + "outputs": [], + "source": [ + "import qse.qbits\n", + "\n", + "\n", + "L = 3\n", + "nqbits = L * L\n", + "qsqr = qse.Qbits(positions=np.array([[0,0,0],[2,0,0],[4,0,0],[0,2,0],[2,2,0],[4,2,0],[0,4,0],[2,4,0],[4,4,0]]))\n", + "\n", + "\n", + "Omega = 1.2 # Amplitude\n", + "delta = 2.0 # detuning\n", + "C6 = 5420158.53 # interaction scale\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 269, + "metadata": {}, + "outputs": [], + "source": [ + "H1_terms = [qat.core.Term(0.5, \"X\", [i]) for i in range(qsqr.nqbits)]\n", + "H1 = qat.core.Observable(nqbits, pauli_terms=H1_terms)\n", + "\n", + "H2_terms = [qat.core.Term(-0.5, \"Z\", [i]) for i in range(qsqr.nqbits)]\n", + "H2 = qat.core.Observable(nqbits, pauli_terms=H2_terms)\n", + "\n", + "rij = qsqr.get_all_distances()\n", + "\n", + "\n", + "def occ_op(nqbits, qi):\n", + " ti = qat.core.Term(1.0, 'Z', [qi])\n", + " return (1 + qat.core.Observable(nqbits, pauli_terms=[ti])) / 2\n", + "#\n", + "H3 = 0\n", + "\n", + "for i in range(nqbits):\n", + " for j in range(i + 1, nqbits):\n", + " H3 += (C6 / rij[i, j]**6) * occ_op(nqbits, i) * occ_op(nqbits, j)" + ] + }, + { + "cell_type": "code", + "execution_count": 270, + "metadata": {}, + "outputs": [], + "source": [ + "from qat.core.variables import Variable, heaviside\n", + "from qat.core import Observable\n", + "\n", + "def create_waveform(times, values):\n", + " \"\"\"\n", + " A Funnction allowing us to concatenate many lines, limited by heavisides,\n", + " thus creating a continuous, kinked line.\n", + " \"\"\"\n", + " assert len(times) == len(values)\n", + " # Store the final line as an ArithExpression\n", + " arith_expr = 0\n", + " t_var = Variable(\"t\")\n", + " # A line between each two points\n", + " for entry_i in range(1, len(times)):\n", + " # Create ax + b by calculating the slope and the offset\n", + " a = (values[entry_i] - values[entry_i - 1]) / (times[entry_i] - times[entry_i - 1])\n", + " b = ((values[entry_i] + values[entry_i - 1]) - a * (times[entry_i] + times[entry_i - 1])) / 2\n", + " respective_line = a * t_var + b\n", + " arith_expr += heaviside(t_var, times[entry_i - 1], times[entry_i]) * respective_line\n", + " return arith_expr\n", + "#\n", + "Omega_max = 2.0 * 2 * np.pi\n", + "U = Omega_max / 2.0\n", + " \n", + "delta_0 = -6 * U\n", + "delta_f = 2 * U\n", + " \n", + "t_rise = 0.252\n", + "t_fall = 0.500\n", + "t_sweep = ((delta_f - delta_0) / (2 * np.pi * 10) * 1000)*(10**-3)\n", + " \n", + "\n", + "# The waveform of Omega - for the sigma_x terms\n", + "omega_values = [0.0,0,Omega_max,0]\n", + "times_omega = [0,t_rise,t_rise+t_sweep,t_rise+t_sweep+t_fall]\n", + "\n", + "\n", + "omega_waveform = create_waveform(times_omega, omega_values)\n", + "# The waveform of the detuning Delta - for the 'n' terms\n", + "delta_start = -2 * np.pi * 13\n", + "delta_end = 2 * np.pi * 11 # R_blockade is taken as 7.5\n", + "delta_values = [0,0,delta_f,delta_f]\n", + "delta_waveform = create_waveform(times_omega, delta_values)" + ] + }, + { + "cell_type": "code", + "execution_count": 271, + "metadata": {}, + "outputs": [], + "source": [ + "from qat.core import Observable \n", + "Hamiltonian = Observable([\n", + " (omega_waveform, H1),\n", + " (delta_waveform, H2),\n", + " ])\n", + " \n", + "schedule = Schedule(drive=[\n", + " (omega_waveform, H1),\n", + " (delta_waveform, H2),\n", + " ], tmax=t_rise+t_sweep+t_fall)" + ] + }, + { + "cell_type": "code", + "execution_count": 272, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "matrixp = sim.get_hamiltonian(0).get_data().toarray()\n", + "plt.imshow(matrixp.real)\n", + "print(matrixp)\n", + "np.savetxt('matrix-p.dat', matrixp.real)\n", + "np.all(matrixp.imag == 0)" + ] + }, + { + "cell_type": "code", + "execution_count": 276, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 1.11466037e+06+0.j 0.00000000e+00+0.j 0.00000000e+00+0.j ...\n", + " 0.00000000e+00+0.j 0.00000000e+00+0.j 0.00000000e+00+0.j]\n", + " [ 0.00000000e+00+0.j 9.30527153e+05+0.j 0.00000000e+00+0.j ...\n", + " 0.00000000e+00+0.j 0.00000000e+00+0.j 0.00000000e+00+0.j]\n", + " [ 0.00000000e+00+0.j 0.00000000e+00+0.j 8.36739620e+05+0.j ...\n", + " 0.00000000e+00+0.j 0.00000000e+00+0.j 0.00000000e+00+0.j]\n", + " ...\n", + " [ 0.00000000e+00+0.j 0.00000000e+00+0.j 0.00000000e+00+0.j ...\n", + " -6.18456397e-11+0.j 0.00000000e+00+0.j 0.00000000e+00+0.j]\n", + " [ 0.00000000e+00+0.j 0.00000000e+00+0.j 0.00000000e+00+0.j ...\n", + " 0.00000000e+00+0.j -2.54658516e-11+0.j 0.00000000e+00+0.j]\n", + " [ 0.00000000e+00+0.j 0.00000000e+00+0.j 0.00000000e+00+0.j ...\n", + " 0.00000000e+00+0.j 0.00000000e+00+0.j -8.36735126e-11+0.j]]\n" + ] + }, + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 276, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.imshow(matrixm.real)\n", + "print(matrixm)\n", + "np.savetxt('matrix-m.dat', matrixm.real)\n", + "np.all(matrixm.imag == 0)" + ] + }, + { + "cell_type": "code", + "execution_count": 277, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 277, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.savetxt('matrix-q.dat', matrixm.real)\n", + "np.savetxt('matrix-p.dat', matrixp.real)\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 288, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 1. nan nan ... nan nan nan]\n", + " [nan 1. nan ... nan nan nan]\n", + " [nan nan 1. ... nan nan nan]\n", + " ...\n", + " [nan nan nan ... -0. nan nan]\n", + " [nan nan nan ... nan -0. nan]\n", + " [nan nan nan ... nan nan -0.]]\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "RuntimeWarning: invalid value encountered in divide\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "p = np.loadtxt(\"matrix-p.dat\")\n", + "q = np.loadtxt(\"matrix-q.dat\")\n", + "plt.imshow(p == q)\n", + "\n", + "pd=p.diagonal()\n", + "qd=q.diagonal()\n", + "print(p/q)" + ] + }, + { + "cell_type": "code", + "execution_count": 291, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. -0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. -0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. -0. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. -0. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. -0. 1. 1. 1. 1. 1. 1. 1. -0.\n", + " 1. 1. 1. -0. 1. -0. -0. -0.]\n" + ] + } + ], + "source": [ + "print(pd/qd)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 290, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 1.11466037e+06 9.30527153e+05 8.36739620e+05 7.37296384e+05\n", + " 9.30527153e+05 7.47717221e+05 7.37296384e+05 6.39176429e+05\n", + " 8.36739620e+05 7.37296384e+05 5.69405121e+05 5.54651862e+05\n", + " 6.53283927e+05 5.55163972e+05 4.70639405e+05 4.57209427e+05\n", + " 7.33555469e+05 5.60008503e+05 5.40324700e+05 4.51467711e+05\n", + " 5.60008503e+05 3.87784819e+05 4.51467711e+05 3.63934004e+05\n", + " 5.40324700e+05 4.51467711e+05 3.57680178e+05 3.53513167e+05\n", + " 3.67455254e+05 2.79921547e+05 2.69500710e+05 2.66656979e+05\n", + " 8.36739620e+05 6.53283927e+05 5.69405121e+05 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8.66907777e+04 6.77519816e+02 1.32328089e+03 -8.36735126e-11\n", + " 6.39176429e+05 4.57209427e+05 3.63934004e+05 2.66656979e+05\n", + " 4.57209427e+05 2.76565706e+05 2.66656979e+05 1.70703235e+05\n", + " 4.57209427e+05 3.59932402e+05 1.92553249e+05 1.79966201e+05\n", + " 2.75919945e+05 1.79966201e+05 9.59537440e+04 8.46899770e+04\n", + " 3.63934004e+05 1.92553249e+05 1.73381555e+05 8.66907777e+04\n", + " 1.92553249e+05 2.24957751e+04 8.66907777e+04 1.32328089e+03\n", + " 2.66656979e+05 1.79966201e+05 8.66907777e+04 8.46899770e+04\n", + " 9.59537440e+04 1.05862471e+04 6.77519816e+02 -8.36735126e-11\n", + " 4.57209427e+05 2.75919945e+05 1.92553249e+05 9.59537440e+04\n", + " 3.59932402e+05 1.79966201e+05 1.79966201e+05 8.46899770e+04\n", + " 2.76565706e+05 1.79966201e+05 2.24957751e+04 1.05862471e+04\n", + " 1.79966201e+05 8.46899770e+04 1.05862471e+04 -2.54658516e-11\n", + " 2.66656979e+05 9.59537440e+04 8.66907777e+04 6.77519816e+02\n", + " 1.79966201e+05 1.05862471e+04 8.46899770e+04 -1.70985004e-10\n", + " 1.70703235e+05 8.46899770e+04 1.32328089e+03 -2.54658516e-11\n", + " 8.46899770e+04 -6.18456397e-11 -2.54658516e-11 -8.36735126e-11]\n" + ] + } + ], + "source": [ + "print(qd)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Testing more atoms with fixed amplitude and 0 detuning checking interaction term" + ] + }, + { + "cell_type": "code", + "execution_count": 314, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Interatomic Radius is: 9.756753962298905µm.\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "Omega_max = 2.0 * 2 * np.pi\n", + "U = Omega_max / 2.0\n", + "R_interatomic = MockDevice.rydberg_blockade_radius(U)\n", + "reg = Register.from_coordinates([[0,0],[10,0],[20,0],[0,10],[10,10],[20,10],[0,20],[10,20],[20,20]])\n", + "print(f\"Interatomic Radius is: {R_interatomic}µm.\")\n", + "reg.draw()" + ] + }, + { + "cell_type": "code", + "execution_count": 325, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "delta_0 = -6 * U\n", + "delta_f = 2 * U\n", + "t_rise = 252\n", + "t_fall = 500\n", + "t_sweep = (delta_f - delta_0) / (2 * np.pi * 10) * 1000\n", + "rise = Pulse.ConstantAmplitude(10,\n", + " RampWaveform(t_rise, 0.0, 0.0), 0.0\n", + ")\n", + "sweep = Pulse.ConstantAmplitude(\n", + " 10, RampWaveform(t_sweep, delta_0, delta_f), 0.0\n", + ")\n", + "fall = Pulse.ConstantDetuning(\n", + " RampWaveform(t_fall, Omega_max, 0.0), delta_f, 0.0\n", + ")\n", + "seq1 = Sequence(reg, MockDevice)\n", + "seq1.declare_channel(\"ising\", \"rydberg_global\")\n", + " \n", + "seq1.add(rise, \"ising\")\n", + "seq1.add(sweep, \"ising\")\n", + "seq1.add(fall, \"ising\")\n", + "\n", + "seq1.draw()" + ] + }, + { + "cell_type": "code", + "execution_count": 326, + "metadata": {}, + "outputs": [], + "source": [ + "sim = QutipEmulator.from_sequence(seq1)" + ] + }, + { + "cell_type": "code", + "execution_count": 327, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "10.0%. Run time: 0.07s. Est. time left: 00:00:00:00\n", + "20.0%. Run time: 0.15s. Est. time left: 00:00:00:00\n", + "30.0%. Run time: 0.23s. Est. time left: 00:00:00:00\n", + "40.1%. Run time: 0.31s. Est. time left: 00:00:00:00\n", + "50.0%. Run time: 0.37s. Est. time left: 00:00:00:00\n", + "60.0%. Run time: 0.43s. Est. time left: 00:00:00:00\n", + "70.1%. Run time: 0.49s. Est. time left: 00:00:00:00\n", + "80.0%. Run time: 0.55s. Est. time left: 00:00:00:00\n", + "90.0%. Run time: 0.61s. Est. time left: 00:00:00:00\n", + "Total run time: 0.66s\n" + ] + } + ], + "source": [ + "\n", + "results = sim.run(progress_bar=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 328, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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AIOd1+KioqNDYsWPVs2dPtW/fXpJUXFysiIgIxcbGuhzbpEkTFRcXu32c7OxslZaWVm5FRUXelgQAAEKARx+7/FhmZqb++te/6vPPP7+qAux2u+x2+1U9BgAACB1eXfl4/PHH9eGHH+qzzz5T06ZNK/fHx8frwoULOnXqlMvxJSUlio+Pv6pCAQBAzeBR+LAsS48//rjef/99ffrpp2rZsqXLeHJysq655hrl5eVV7tu/f7+OHj2q1NRU31QMAABCmkcfu2RmZionJ0crV65U/fr1K+/jiImJUWRkpGJiYjRixAiNHz9ecXFxio6O1hNPPKHU1FS3M10AAEDt41H4mDNnjiSpd+/eLvsXLlyohx56SJI0bdo0hYWFKSMjQ06nU2lpaXrzzTd9UiwAAAh9HoUPy7J+9pi6detq9uzZmj17ttdFAQCAmovvdgEAAEYRPgAAgFGEDwAAYBThAwAAGEX4AAAARhE+AACAUYQPAABgFOEDAAAYRfgAAABGET4AAIBRhA8AAGAU4QMAABhF+AAAAEYRPgAAgFGEDwAAYBThAwAAGEX4AAAARhE+AACAUYQPAABgFOEDAAAYRfgAAABGET4AAIBRhA8AAGAU4QMAABhF+AAAAEYRPgAAgFGEDwAAYBThAwAAGEX4AAAARhE+AACAUYQPAABgFOEDAAAYRfgAAABGET4AAIBRHoePjRs36u6771ZiYqJsNptWrFjhMv7QQw/JZrO5bHfeeaev6gUAACHO4/BRVlamm2++WbNnz67ymDvvvFPHjx+v3P7nf/7nqooEAAA1R7inv5Cenq709PRqj7Hb7YqPj/e6KAAAUHP55Z6P9evXq3HjxmrdurXGjBmj7777rspjnU6nHA6HywYAAGoun4ePO++8U4sXL1ZeXp6mTp2qDRs2KD09XeXl5W6Pnzx5smJiYiq3pKQkX5cEAACCiMcfu/ycQYMGVf53hw4d1LFjR91www1av369+vTpc9nx2dnZGj9+fOXPDoeDAAIAQA3m96m2119/vRo1aqQDBw64Hbfb7YqOjnbZAABAzeX38PH3v/9d3333nRISEvz9VAAAIAR4/LHLmTNnXK5iHD58WIWFhYqLi1NcXJxefvllZWRkKD4+XgcPHtSzzz6rVq1aKS0tzaeFAwCA0ORx+Pjyyy/161//uvLnH+7XGD58uObMmaNdu3bpnXfe0alTp5SYmKg77rhDv/vd72S3231XNQAACFkeh4/evXvLsqwqx9euXXtVBQEAgJqN73YBAABGET4AAIBRPl/nAwBgXovncwNdQkAcmdI/0CXAC1z5AAAARhE+AACAUYQPAABgFOEDAAAYRfgAAABGET4AAIBRhA8AAGAU4QMAABhF+AAAAEYRPgAAgFGEDwAAYBThAwAAGEX4AAAARhE+AACAUYQPAABgFOEDAAAYRfgAAABGhQe6AAD4sRbP5wa6hIA4MqV/oEsAjOHKBwAAMIrwAQAAjCJ8AAAAowgfAADAKMIHAAAwivABAACMInwAAACjCB8AAMAoFhnDFWHhJ8/V1p5JLJiF0FFbz9NAn6Nc+QAAAEYRPgAAgFGEDwAAYBThAwAAGOVx+Ni4caPuvvtuJSYmymazacWKFS7jlmXppZdeUkJCgiIjI9W3b1998803vqoXAACEOI/DR1lZmW6++WbNnj3b7fgrr7yimTNn6q233tLWrVt17bXXKi0tTefPn7/qYgEAQOjzeKptenq60tPT3Y5ZlqXp06frhRde0IABAyRJixcvVpMmTbRixQoNGjTo6qoFAAAhz6f3fBw+fFjFxcXq27dv5b6YmBilpKRo8+bNbn/H6XTK4XC4bAAAoObyafgoLi6WJDVp0sRlf5MmTSrHfmry5MmKiYmp3JKSknxZEgAACDIBn+2SnZ2t0tLSyq2oqCjQJQEAAD/yafiIj4+XJJWUlLjsLykpqRz7KbvdrujoaJcNAADUXD4NHy1btlR8fLzy8vIq9zkcDm3dulWpqam+fCoAABCiPJ7tcubMGR04cKDy58OHD6uwsFBxcXFq1qyZxo4dq9///ve68cYb1bJlS7344otKTEzUwIEDfVk3AAAIUR6Hjy+//FK//vWvK38eP368JGn48OFatGiRnn32WZWVlemRRx7RqVOndOutt2rNmjWqW7eu76oGAAAhy+Pw0bt3b1mWVeW4zWbTpEmTNGnSpKsqDAAA1EwBn+0CAABqF8IHAAAwivABAACMInwAAACjCB8AAMAowgcAADCK8AEAAIwifAAAAKMIHwAAwCjCBwAAMIrwAQAAjCJ8AAAAowgfAADAKMIHAAAwivABAACMInwAAACjCB8AAMAowgcAADCK8AEAAIwifAAAAKMIHwAAwCjCBwAAMIrwAQAAjCJ8AAAAowgfAADAKMIHAAAwivABAACMInwAAACjCB8AAMAowgcAADCK8AEAAIwifAAAAKMIHwAAwCjCBwAAMMrn4WPixImy2WwuW5s2bXz9NAAAIESF++NBb7rpJn3yySf/9yThfnkaAAAQgvySCsLDwxUfH++PhwYAACHOL/d8fPPNN0pMTNT111+voUOH6ujRo1Ue63Q65XA4XDYAAFBz+Tx8pKSkaNGiRVqzZo3mzJmjw4cP65e//KVOnz7t9vjJkycrJiamcktKSvJ1SQAAIIj4PHykp6frN7/5jTp27Ki0tDR99NFHOnXqlP70pz+5PT47O1ulpaWVW1FRka9LAgAAQcTvd4LGxsbqF7/4hQ4cOOB23G63y263+7sMAAAQJPy+zseZM2d08OBBJSQk+PupAABACPB5+Hj66ae1YcMGHTlyRF988YX+/d//XXXq1NHgwYN9/VQAACAE+fxjl7///e8aPHiwvvvuO1133XW69dZbtWXLFl133XW+fioAABCCfB4+lixZ4uuHBAAANQjf7QIAAIwifAAAAKMIHwAAwCjCBwAAMIrwAQAAjCJ8AAAAowgfAADAKMIHAAAwivABAACMInwAAACjCB8AAMAowgcAADCK8AEAAIwifAAAAKMIHwAAwCjCBwAAMIrwAQAAjCJ8AAAAowgfAADAKMIHAAAwivABAACMInwAAACjCB8AAMAowgcAADCK8AEAAIwifAAAAKMIHwAAwCjCBwAAMIrwAQAAjCJ8AAAAowgfAADAKMIHAAAwivABAACMInwAAACj/BY+Zs+erRYtWqhu3bpKSUlRfn6+v54KAACEEL+Ej6VLl2r8+PGaMGGCtm/frptvvllpaWk6ceKEP54OAACEEL+EjzfeeEOjRo3Sww8/rHbt2umtt95SVFSUFixY4I+nAwAAISTc1w944cIFFRQUKDs7u3JfWFiY+vbtq82bN192vNPplNPprPy5tLRUkuRwOHxdmiSpwnnWL48b7K62n/TNc7W1ZxJ98wbnqHfom3f88R77w2NalvXzB1s+9o9//MOSZH3xxRcu+5955hmre/fulx0/YcIESxIbGxsbGxtbDdiKiop+Niv4/MqHp7KzszV+/PjKnysqKvT999+rYcOGstlsAazMtxwOh5KSklRUVKTo6OhAlxMy6Jvn6Jl36Jt36Jt3amLfLMvS6dOnlZiY+LPH+jx8NGrUSHXq1FFJSYnL/pKSEsXHx192vN1ul91ud9kXGxvr67KCRnR0dI15oZlE3zxHz7xD37xD37xT0/oWExNzRcf5/IbTiIgIJScnKy8vr3JfRUWF8vLylJqa6uunAwAAIcYvH7uMHz9ew4cPV9euXdW9e3dNnz5dZWVlevjhh/3xdAAAIIT4JXzcf//9+uc//6mXXnpJxcXF6tSpk9asWaMmTZr44+lCgt1u14QJEy77iAnVo2+eo2feoW/eoW/eqe19s1nWlcyJAQAA8A2+2wUAABhF+AAAAEYRPgAAgFGEDwAAYBThAwAAGBXw5dUBd0pLS1VcXCxJio+Pv+JV8wBv/PDllrV12qM3OEdxNbjy4Sd79+7VY489ps6dOyshIUEJCQnq3LmzHnvsMe3duzfQ5QWtt99+W+3atVNcXJzatWvn8t/z588PdHlBq7i4WCtXrtTcuXM1d+5crVy5svKNAe6tW7dO/fr1U4MGDRQVFaWoqCg1aNBA/fr10yeffBLo8oIW5yh8gSsffrB69WoNHDhQXbp00YABAyoXVyspKdG6devUpUsXrVy5UmlpaQGuNLi8+uqrmjhxop588kmlpaW59O3jjz9WVlaWTp48qaeffjrAlQaPsrIyPfroo1qyZIlsNpvi4uIkSd9//70sy9LgwYM1d+5cRUVFBbjS4PLOO+9o5MiRuvfeezVt2rTLXmv9+vXT/Pnz9eCDDwa40uDCOeofly5d0rFjx9SsWbNAl2LOz37vLTzWsWNH68UXX6xyfMKECVaHDh0MVhQamjVrZi1durTK8SVLllhJSUkGKwp+I0aMsG688UZrzZo11qVLlyr3X7p0yVq7dq31i1/8who5cmQAKwxON954ozVr1qwqx2fPnm21atXKYEWhgXPUPwoLC62wsLBAl2EUK5z6QWRkpAoLC9W6dWu34/v371enTp107tw5w5UFt8jISG3fvl1t27Z1O75371517dpVZ8+eNVxZ8GrQoIFyc3PVo0cPt+ObNm3SXXfdpZMnTxquLLjVrVtXO3fu5Bz1EOeof+zcuVNdunRReXl5oEsxho9d/KBFixbKzc2t8n9subm5at68ueGqgl+3bt00ZcoUzZ8/X+Hhri/N8vJyTZ06Vd26dQtQdcGpoqJCERERVY5HRESooqLCYEWh4aabbtL8+fP1yiuvuB1fsGCB2rVrZ7iq4Mc56p0uXbpUO14bQy5XPvxg2bJlGjJkiNLT09W3b1+Xz0Xz8vK0Zs0a5eTkKCMjI8CVBpddu3YpLS1NFy9eVK9evVz6tnHjRkVEROjjjz9W+/btA1xp8Bg6dKj27dun+fPnq3Pnzi5jO3bs0KhRo9SmTRu9++67AaowOK1fv1533XWXrr/+erfn6KFDh5Sbm6tevXoFuNLgwjnqnbp162rQoEFq2bKl2/Hjx49r3rx5terKB+HDT7744gvNnDlTmzdvdpmOlpqaqqysLKWmpga4wuB0+vRpvfvuu9qyZctlfRsyZIiio6MDXGFwOXnypIYMGaK1a9eqQYMGaty4sSTpxIkTOnXqlNLS0pSTk6PY2NjAFhqEjhw5ojlz5rh9rY0ePVotWrQIbIFBinPUc127dtWIESM0ZswYt+OFhYVKTk4mfAAILfv27XP7ZtCmTZsAVwYgKytLNptN06dPdzt+8OBBjRw5Up999pnZwgKI8OFnLMTjOxcvXtTx48dr13Q0IIRwjuJKccOpn7z99tt64403tH//fkmSZVmy2Wxq3bq1nnrqKY0YMSLAFYaevXv31ro7wq/EhQsXtGLFiss+4uvRo4cGDBhQ7Q2pcK82zj7wBc5RXClWOPWDV199VVlZWRowYIDy8vL017/+VXv27FFeXp4GDhyorKwsvfbaa4EuEzXAgQMH1LZtWw0fPlw7duxQRUWFKioqtGPHDg0bNkw33XSTDhw4EOgyQxIXhWFKWVmZNm7cGOgyjOJjFz9o3ry5Xn31Vd13331ux5cuXapnnnlGR48eNVxZcLuS6Whff/01f1X9yO23365rr71WixcvvuxGP4fDoWHDhuncuXNau3ZtgCoMTvfcc0+146WlpVq/fj2vtZ/gHPWP2niljY9d/ODEiRPq0KFDleMdOnTQt99+a7Ci0LB3796fnY729ddfG64quG3atEn5+fluZxhER0frd7/7nVJSUgJQWXBbtWqVbr/99sqpoj9Vm94EPME5Cl8hfPgBC/F4p3379kpJSal2Otq8efMMVxXcYmNjdeTIkSrXVThy5AjTbN1o27atMjIyqrz3qrCwUB9++KHhqoIf56h3fvjOparUxrBL+PCDWbNmKS0tTfHx8dUuxANXPXv2rLxB15369euz6NNPjBw5UsOGDdOLL76oPn36XLZY1u9//3s98cQTAa4y+CQnJ2v79u1Vhg+73c6MDTc4R73jdDo1ZsyYKq+I/+1vf9PLL79suKrA4p4PP2EhHpgydepUzZgxQ8XFxbLZbJL+dbNkfHy8xo4dq2effTbAFQYfp9Op8vJyvu0XRvTs2VP33XefsrKy3I7Xxns+CB9ADXH48GGXoFvV5/IAzPqv//ovXbx4URMmTHA7XlRUpJdeekkLFy40XFngED78qLi4WFu3bq18Q0hISFD37t0VHx8f4MpCU1lZmQoKCrisC5/56TkaHx+vlJQUztGfkZ+f7/arI7p37x7gyhAqCB9+UFZWpkcffVRLliyRzWarvNno+++/l2VZGjx4sObOncslXw/VxkuTV6uoqEgTJkzQggULAl1KUOEc9c6JEyeUkZGhTZs2qVmzZi73GB09elQ9e/bUn//858rvGAKqwiJjfpCVlaX8/Hzl5ubq/PnzKikpUUlJic6fP6+PPvpI+fn5VX72B/jS999/r3feeSfQZQQdzlHvPPbYYyovL9e+fft05MgRbd26VVu3btWRI0e0b98+VVRUKDMzM9BlBqULFy7oT3/6k8aNG6fBgwdr8ODBGjdunJYtW6YLFy4EujzjuPLhBw0aNFBubq569OjhdnzTpk266667dPLkScOVBbcrmY525swZrnz8yAcffFDt+KFDh/TUU0/Rs5/gHPVO/fr1tXHjRnXu3NnteEFBgXr37q3Tp08briy4HThwQGlpaTp27JhSUlJcrhht3bpVTZs21erVq9WqVasAV2oOU239oKKiotrv04iIiFBFRYXBikID09E8N3DgQNlstmqXAv9hBgz+D+eod+x2uxwOR5Xjp0+flt1uN1hRaPjh/2s7duyociXizMzM2rUSsQWfGzJkiNW5c2dr+/btl41t377dSk5OtoYOHRqAyoJbjx49rOnTp1c5XlhYaIWFhRmsKPglJiZaK1asqHJ8x44d9MwNzlHvPPbYY1bz5s2t5cuXW6WlpZX7S0tLreXLl1stWrSwHn/88QBWGJwiIyOt3bt3Vzm+a9cuKzIy0mBFgcc9H34wa9YsNWnSRMnJyWrYsKHatm2rtm3bqmHDhuratasaN26sWbNmBbrMoNO/f3+dOnWqyvG4uDgNGzbMXEEhIDk5WQUFBVWO/9xVkdqKc9Q7b7zxhtLT0zVo0CA1aNBAkZGRioyMVIMGDTRo0CClp6fzpZlu/LAScVVq40rE3PPhR/v27XO7yFibNm0CXBlqir/85S8qKyvTnXfe6Xa8rKxMX375pX71q18Zriw0cI56x+FwqKCgwKVvycnJLJ5YhZdeekmzZs362ZWIJ06cGNhCDSJ8AADgZ6xE7Irw4ScXLlzQihUrLluIp0ePHhowYEC1N7vVZvQNpvBa872SkhLNnTtXL730UqBLCVqHDh1SSUmJpNq9EjHhww+YVuUd+uZ7Bw8e1KhRo/Tpp58GupSgwmvNP1gIEFeK8OEHt99+u6699lotXry4ymlV586dq13Tqq4AffM93gzc47XmnV27dlU7/tVXX2nw4MG83tzYu3evZs2a5XZZ+scff1zt2rULcIVmET78ICoqSvn5+Wrfvr3b8d27dyslJUVnz541XFlwo2+emzlzZrXj//jHP/Taa6/xZvATvNa8ExYWVuUMqh/222w2Xm8/sXr1ag0cOFBdunRRWlqay5W2devWqaCgQCtXrlRaWlqAKzWHRcb84IdpVVX9j602Tqu6EvTNc2PHjlVCQkKV9yfUxmWbrwSvNe/ExcXplVdeUZ8+fdyO79mzR3fffbfhqoLf888/r+eee06TJk26bGzixImaOHGinnnmGcIHrs7IkSM1bNiwn51WBVf0zXPNmzfX1KlTdd9997kdLywsVHJysuGqgh+vNe8kJyfr2LFjat68udvxU6dOsa6MG19//bWGDh1a5fjgwYM1depUgxUFAePLmtUSU6ZMsRISEiybzWaFhYVZYWFhls1msxISEqypU6cGurygRd88k5GRYT377LNVjhcWFlo2m81gRaGD15rnli9fbv3xj3+scvz777+3Fi1aZLCi0NCmTRvr9ddfr3L89ddft1q3bm2wosDjng8/O3z4sMvNRbV1WpWn6NuV2bt3r86ePauuXbu6Hb948WK1f6mCqY/wv2XLlmnIkCFKT09X3759L7vStmbNGuXk5CgjIyPAlZpD+AAAwM+++OILzZw50+1sl6ysLKWmpga4QrMIHwFQVFSkCRMmaMGCBYEuJaTQN/gSUx+9Q9/gC4SPAGDtBe/QN8/t27dP/fv316FDhwJdSlBh6qN36Bt8hfDhBx988EG144cOHdJTTz3Fm+hP0DffI7C5d/PNN2vAgAFupz5K/5r+uHz58p9dVKu2oW/+URv/SCB8+EF1C/H8gIV4LkffPDd+/Phqx//5z38qJyeHnv1EZGSkCgsL1bp1a7fj+/fvV6dOnXTu3DnDlQU3+uYftfGPBNb58IOEhAS9+eabGjBggNtx1l5wj755bsaMGerUqVOVX2V+5swZwxWFhhYtWig3N7fKN9Hc3FxmCLlB37xzJX8k1DaEDz9ITk5WQUFBlW+iP/fXfW1F3zzXqlUrjRs3Tg888IDbcQKbe5MmTdKQIUO0fv36aqc+whV98w5/JFyO8OEHzzzzjMrKyqocb9WqlT777DODFYUG+ua5rl27qqCgoMrwQWBz7ze/+Y3+3//7f5o5c6Zef/31y2ZtrF+/vtZNfbwS9M07/JFwOe75AEJYcXGxnE4nl7qBIDZ06FA1btxY06ZNczu+c+dOde7cWRUVFYYrCxzChwFOp1OSZLfbA1xJaKFvMKG0tNTlL/iYmJgAVxQa6NuV44+Ey4UFuoCaat26derXr58aNGigqKgoRUVFqUGDBurXr58++eSTQJcXtOgbTHn77bfVrl07xcXFqV27dmrbtm3lf8+fPz/Q5QUt+ua5+Ph4gsdPcM+HH7zzzjsaOXKk7r33Xk2bNs3lpqyPP/5Y/fr10/z58/Xggw8GuNLgQt98rzZO4bsSr776qiZOnKgnn3zyssWyPv74Y2VlZenkyZN6+umnA1xpcKFvV+fSpUvas2ePyxWjdu3a6ZprrglwZQFg9Gvsaokbb7zRmjVrVpXjs2fPtlq1amWwotBA33yPb7V1r1mzZtbSpUurHF+yZImVlJRksKLQQN+8U15ebv32t7+1YmNjLZvN5rLFxsZaL7zwglVeXh7oMo3iyocfHD16VH379q1yvE+fPnrqqacMVhQa6Jvn7rnnnmrHS0tLZbPZDFUTOk6cOKEOHTpUOd6hQwd9++23BisKDfTNO88//7wWLVqkKVOmuL1i9OKLL+rChQuaOnVqgCs1h3s+/OCmm26q9rPPBQsW8OVLbtA3z61atUrnz59XTEyM261evXqBLjEodevWTVOmTNGlS5cuGysvL9fUqVPVrVu3AFQW3OibdxYvXqw//vGPevTRR9WiRQtFRkYqMjJSLVq00COPPKLFixdr0aJFgS7TKK58+MHrr7+uu+66S2vWrHG7EM+hQ4eUm5sb4CqDD33zXNu2bZWRkaERI0a4HS8sLNSHH35ouKrgN2vWLKWlpSk+Pl69evVyea1t3LhRERER+vjjjwNcZfChb945ffq0EhMTqxxPSEiodo2jmoiptn5y5MgRzZkzR1u2bLlsIZ7Ro0erRYsWgS0wSNE3zzz88MOKiorS7Nmz3Y7v27dP/fr10+HDhw1XFvxOnz6td9991+1rbciQIVWuRlnb0TfP9e/fX5cuXdJ7772nRo0auYx9++23evDBB1WnTp1a9YcC4QMIYU6nU+Xl5YqKigp0KQCqUFRUpH79+umrr75Shw4dXK4Y7d69W+3atdOHH36opKSkAFdqDuHDj346rSohIUFt27atndOqPEDfYEpxcbG2bt3q8lrr3r274uPjA1xZcKNvnquoqNDatWvdXjG64447FBZWy27BDORUm5qKaVXeoW++d/HiRetvf/tboMsIOmfOnLGGDh1q1alTxwoPD7caN25sNW7c2AoPD7fq1KljPfDAA1ZZWVmgyww69A2+UsuilhnPP/+8/vCHP2jKlCk6dOiQysrKVFZWpkOHDmnq1Kn6wx/+oOzs7ECXGXTom+/t2bNHLVu2DHQZQScrK0v5+fnKzc3V+fPnVVJSopKSEp0/f14fffSR8vPzlZWVFegygw59uzr5+fmaMWOGsrOzlZ2drRkzZmjbtm2BLiswAp1+aqImTZpYa9asqXJ8zZo1VuPGjQ1WFBrom+8VFhZaYWFhgS4j6MTGxlqbNm2qcvzzzz+3YmNjDVYUGuibd0pKSqxbb73VstlsVvPmza3u3btb3bt3t5o3b27ZbDbr1ltvtUpKSgJdplFMtfUDplV5h755rkuXLtWOnzt3zlAloaWiokIRERFVjkdERNSqbxi9UvTNO4899pjKy8u1b98+tW7d2mVs//79+o//+A9lZmZq2bJlAarQPG449QOmVXmHvnmubt26GjRoUJUfrRw/flzz5s3ju11+YujQodq3b5/mz5+vzp07u4zt2LFDo0aNUps2bfTuu+8GqMLgRN+8U79+fW3cuPGynv2goKBAvXv31unTpw1XFjhc+fCDt956S/369VNCQkK106rgir55rn379kpJSdGYMWPcjhcWFmrevHmGqwp+s2bN0pAhQ5ScnKwGDRqocePGkv61fPipU6eUlpamWbNmBbjK4EPfvGO32+VwOKocP336tOx2u8GKAo8rH37CtCrv0DfPZGVlyWazafr06W7HDx48qJEjR+qzzz4zW1iI+Oqrr7R58+bLXmtt2rQJcGXBjb55JjMzU7m5uZo2bZr69OlTuRCbw+FQXl6exo8fr7vuukv//d//HeBKzSF8AADgR06nU2PHjtWCBQt06dKlyvtmLly4oPDwcI0YMULTpk2rVVc/CB9+lJ+ff9lfBz169OCLl34GfUOgnTx5UqtWrdKwYcMCXUpIoW/VczgcKigocPl/W3Jycq1ckp7w4QcnTpxQRkaGNm3apGbNmrncu3D06FH17NlTf/7znys/L8W/0DfvuQtsqamp6t69e4ArC007d+5Uly5duFHXQ/QNV4obTv2AaVXeoW+eqy6wjRs3jsBWhepu/pNUq2YdeIK++UdJSYnmzp2rl156KdClGMOVDz9gWpV36Jvn7r33Xh07dkwLFy6sMrAlJiYS2H4iLCxMNputynHLsmSz2fgL/ifom3/UxitGXPnwA6ZVeYe+eW7t2rXauHHjZcFDklq3bq2ZM2eqd+/e5gsLcvXr19dvf/tbpaSkuB3/5ptv9OijjxquKvjRN+/s2rWr2vH9+/cbqiR4ED784P7779fw4cOrnVY1ePDgAFcZfOib5whs3vlhZdhf/epXbsdjY2PFReHL0TfvdOrUSTabzW1vfthf3RWlmojw4QdvvPGGKioqNGjQoCqnVb322msBrjL40DfPEdi8M2TIEJ09e7bK8fj4eE2YMMFgRaGBvnknLi5Or7zyivr06eN2fM+ePbr77rsNVxVY3PPhR0yr8g59u3KsHwAEv7S0NP3yl7/UCy+84HZ8586d6ty5c636XhzCh598++23WrBggdv1Kh566CFdd911Aa4wONE37xDYPMdrzTv0zXPvv/++ysrK9MADD7gdP3nypD744AMNHz7ccGWBQ/jwg23btiktLU1RUVHq27evy/THvLw8nT17VmvXrlXXrl0DXGlwoW/e4c3Ac7zWvEPf4CuEDz+45ZZbdPPNN+utt9667CYiy7I0evRo7dq1S5s3bw5QhcGJvnmONwPv8FrzDn3zj6KiIk2YMEELFiwIdCnGED78IDIyUjt27KjyS5a++uorde7cWefOnTNcWXCjb57jzcA7vNa8Q9/8g3U+4BPx8fHKz8+v8gTNz8+v/AsV/4e+eW7nzp1atGiR22l6NptN48aNq3LRttqM15p36Jt3Pvjgg2rHDx06ZKiS4EH48IOnn35ajzzyiAoKCtSnT5/LLoXPmzePKaNu0DfP8WbgHV5r3qFv3hk4cGCV63z8oLat8yELfrFkyRIrJSXFCg8Pt2w2m2Wz2azw8HArJSXFWrp0aaDLC1r0zTOzZs2y7Ha79eSTT1orV660tmzZYm3ZssVauXKl9eSTT1qRkZHW7NmzA11mUOK15h365rnExERrxYoVVY7v2LHDCgsLM1hR4HHPh59dvHhR3377rSSpUaNGuuaaawJcUWigb1du6dKlmjZtmgoKCio/M65Tp46Sk5M1fvx43XfffQGuMLjxWvMOfbty//Zv/6ZOnTpp0qRJbsdZ5wNAyOLNAAhOf/nLX1RWVqY777zT7XhZWZm+/PLLKpetr4kIHwAAwKiwQBcAAABqF8IHAAAwivABAACMInwAAACjCB8AAMAowgcAADCK8AEAAIz6/ybACauJg3DMAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "count = results.sample_final_state()\n", + "\n", + "most_freq = {k: v for k, v in count.items() if v > 10}\n", + "plt.bar(list(most_freq.keys()), list(most_freq.values()))\n", + "plt.xticks(rotation=\"vertical\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 329, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#Define Rydberg state observable\n", + "obs = qutip.basis(256*2, 0).proj()\n", + "plt.figure(figsize=(6, 6))\n", + "k = results.expect([obs])[0]\n", + "\n", + "plt.plot(results._sim_times,k)\n", + "plt.xlabel(r\"Time ($\\mu s$)\")\n", + "plt.ylabel(r\"Population in $|r\\rangle$\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 341, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "crank = 0, prank = 2\n", + "rcut is 10.0\n" + ] + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import qse.qbits\n", + "\n", + "\n", + "L = 3\n", + "nqbits = L * L\n", + "qsqr = qse.Qbits(positions=np.array([[0,0,0],[10,0,0],[20,0,0],[0,10,0],[10,10,0],[20,10,0],[0,20,0],[10,20,0],[20,20,0]]))\n", + "\n", + "\n", + "Omega = 1.2 # Amplitude\n", + "delta = 2.0 # detuning\n", + "C6 = 5420158.53 # interaction scale\n", + "\n", + "qsqr.draw()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 331, + "metadata": {}, + "outputs": [], + "source": [ + "H1_terms = [qat.core.Term(0.5, \"X\", [i]) for i in range(qsqr.nqbits)]\n", + "H1 = qat.core.Observable(nqbits, pauli_terms=H1_terms)\n", + "\n", + "H2_terms = [qat.core.Term(-0.5, \"Z\", [i]) for i in range(qsqr.nqbits)]\n", + "H2 = qat.core.Observable(nqbits, pauli_terms=H2_terms)\n", + "\n", + "rij = qsqr.get_all_distances()\n", + "\n", + "\n", + "def occ_op(nqbits, qi):\n", + " ti = qat.core.Term(1.0, 'Z', [qi])\n", + " return (1 + qat.core.Observable(nqbits, pauli_terms=[ti])) / 2\n", + "#\n", + "H3 = 0\n", + "\n", + "for i in range(nqbits):\n", + " for j in range(i + 1, nqbits):\n", + " H3 += (C6 / rij[i, j]**6) * occ_op(nqbits, i) * occ_op(nqbits, j)" + ] + }, + { + "cell_type": "code", + "execution_count": 342, + "metadata": {}, + "outputs": [], + "source": [ + "from qat.core.variables import Variable, heaviside\n", + "from qat.core import Observable\n", + "\n", + "def create_waveform(times, values):\n", + " \"\"\"\n", + " A Funnction allowing us to concatenate many lines, limited by heavisides,\n", + " thus creating a continuous, kinked line.\n", + " \"\"\"\n", + " assert len(times) == len(values)\n", + " # Store the final line as an ArithExpression\n", + " arith_expr = 0\n", + " t_var = Variable(\"t\")\n", + " # A line between each two points\n", + " for entry_i in range(1, len(times)):\n", + " # Create ax + b by calculating the slope and the offset\n", + " a = (values[entry_i] - values[entry_i - 1]) / (times[entry_i] - times[entry_i - 1])\n", + " b = ((values[entry_i] + values[entry_i - 1]) - a * (times[entry_i] + times[entry_i - 1])) / 2\n", + " respective_line = a * t_var + b\n", + " arith_expr += heaviside(t_var, times[entry_i - 1], times[entry_i]) * respective_line\n", + " return arith_expr\n", + "#\n", + "Omega_max = 2.0 * 2 * np.pi\n", + "U = Omega_max / 2.0\n", + " \n", + "delta_0 = -6 * U\n", + "delta_f = 2 * U\n", + " \n", + "t_rise = 0.252\n", + "t_fall = 0.500\n", + "t_sweep = ((delta_f - delta_0) / (2 * np.pi * 10) * 1000)*(10**-3)\n", + " \n", + "\n", + "# The waveform of Omega - for the sigma_x terms\n", + "omega_values = [10.0,0,Omega_max,0]\n", + "times_omega = [0,t_rise,t_rise+t_sweep,t_rise+t_sweep+t_fall]\n", + "\n", + "\n", + "omega_waveform = create_waveform(times_omega, omega_values)\n", + "# The waveform of the detuning Delta - for the 'n' terms\n", + "delta_start = -2 * np.pi * 13\n", + "delta_end = 2 * np.pi * 11 # R_blockade is taken as 7.5\n", + "delta_values = [0,0,delta_f,delta_f]\n", + "delta_waveform = create_waveform(times_omega, delta_values)" + ] + }, + { + "cell_type": "code", + "execution_count": 343, + "metadata": {}, + "outputs": [], + "source": [ + "from qat.core import Observable \n", + "Hamiltonian = Observable([\n", + " (omega_waveform, H1),\n", + " (delta_waveform, H2),\n", + " ])\n", + " \n", + "schedule = Schedule(drive=[\n", + " (omega_waveform, H1),\n", + " (delta_waveform, H2),\n", + " ], tmax=t_rise+t_sweep+t_fall)" + ] + }, + { + "cell_type": "code", + "execution_count": 344, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "matrixp = sim.get_hamiltonian(0).get_data().toarray()\n", + "plt.imshow(matrixp.real)\n", + "print(matrixp)\n", + "np.savetxt('matrix-p.dat', matrixp.real)\n", + "np.all(matrixp.imag == 0)" + ] + }, + { + "cell_type": "code", + "execution_count": 348, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 7.13382634e+01+0.j 5.00000000e+00+0.j 5.00000000e+00+0.j ...\n", + " 0.00000000e+00+0.j 0.00000000e+00+0.j 0.00000000e+00+0.j]\n", + " [ 5.00000000e+00+0.j 5.95537378e+01+0.j 0.00000000e+00+0.j ...\n", + " 0.00000000e+00+0.j 0.00000000e+00+0.j 0.00000000e+00+0.j]\n", + " [ 5.00000000e+00+0.j 0.00000000e+00+0.j 5.35513357e+01+0.j ...\n", + " 0.00000000e+00+0.j 0.00000000e+00+0.j 0.00000000e+00+0.j]\n", + " ...\n", + " [ 0.00000000e+00+0.j 0.00000000e+00+0.j 0.00000000e+00+0.j ...\n", + " -4.88498131e-15+0.j 0.00000000e+00+0.j 5.00000000e+00+0.j]\n", + " [ 0.00000000e+00+0.j 0.00000000e+00+0.j 0.00000000e+00+0.j ...\n", + " 0.00000000e+00+0.j -1.11022302e-14+0.j 5.00000000e+00+0.j]\n", + " [ 0.00000000e+00+0.j 0.00000000e+00+0.j 0.00000000e+00+0.j ...\n", + " 5.00000000e+00+0.j 5.00000000e+00+0.j -4.88498131e-15+0.j]]\n" + ] + }, + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 348, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.imshow(matrixm.real)\n", + "print(matrixm)\n", + "np.savetxt('matrix-m.dat', matrixm.real)\n", + "np.all(matrixm.imag == 0)" + ] + }, + { + "cell_type": "code", + "execution_count": 349, + "metadata": {}, + "outputs": [], + "source": [ + "np.savetxt('matrix-q.dat', matrixm.real)\n", + "np.savetxt('matrix-p.dat', matrixp.real)\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 350, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 1. 1. 1. ... nan nan nan]\n", + " [ 1. 1. nan ... nan nan nan]\n", + " [ 1. nan 1. ... nan nan nan]\n", + " ...\n", + " [nan nan nan ... -0. nan 1.]\n", + " [nan nan nan ... nan -0. 1.]\n", + " [nan nan nan ... 1. 1. -0.]]\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "RuntimeWarning: invalid value encountered in divide\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "p = np.loadtxt(\"matrix-p.dat\")\n", + "q = np.loadtxt(\"matrix-q.dat\")\n", + "plt.imshow(p == q)\n", + "\n", + "pd=p.diagonal()\n", + "qd=q.diagonal()\n", + "print(p/q)" + ] + }, + { + "cell_type": "code", + "execution_count": 351, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. -0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. -0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. -0. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. -0. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 0. 1. 1. 1. 1. 1. 1. 1. -0.\n", + " 1. 1. 1. -0. 1. -0. -0. -0.]\n" + ] + } + ], + "source": [ + "print(pd/qd)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 352, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 7.13382634e+01 5.95537378e+01 5.35513357e+01 4.71869686e+01\n", + " 5.95537378e+01 4.78539021e+01 4.71869686e+01 4.09072915e+01\n", + " 5.35513357e+01 4.71869686e+01 3.64419277e+01 3.54977192e+01\n", + " 4.18101713e+01 3.55304942e+01 3.01209219e+01 2.92614033e+01\n", + " 4.69475500e+01 3.58405442e+01 3.45807808e+01 2.88939335e+01\n", + " 3.58405442e+01 2.48182284e+01 2.88939335e+01 2.32917762e+01\n", + " 3.45807808e+01 2.88939335e+01 2.28915314e+01 2.26248427e+01\n", + " 2.35171363e+01 1.79149790e+01 1.72480454e+01 1.70660467e+01\n", + " 5.35513357e+01 4.18101713e+01 3.64419277e+01 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5.54820978e+00 4.33612682e-02 8.46899770e-02 -8.43769499e-15\n", + " 4.09072915e+01 2.92614033e+01 2.32917762e+01 1.70660467e+01\n", + " 2.92614033e+01 1.77002052e+01 1.70660467e+01 1.09250070e+01\n", + " 2.92614033e+01 2.30356738e+01 1.23234079e+01 1.15178369e+01\n", + " 1.76588765e+01 1.15178369e+01 6.14103961e+00 5.42015853e+00\n", + " 2.32917762e+01 1.23234079e+01 1.10964196e+01 5.54820978e+00\n", + " 1.23234079e+01 1.43972961e+00 5.54820978e+00 8.46899770e-02\n", + " 1.70660467e+01 1.15178369e+01 5.54820978e+00 5.42015853e+00\n", + " 6.14103961e+00 6.77519816e-01 4.33612682e-02 -1.33226763e-15\n", + " 2.92614033e+01 1.76588765e+01 1.23234079e+01 6.14103961e+00\n", + " 2.30356738e+01 1.15178369e+01 1.15178369e+01 5.42015853e+00\n", + " 1.77002052e+01 1.15178369e+01 1.43972961e+00 6.77519816e-01\n", + " 1.15178369e+01 5.42015853e+00 6.77519816e-01 2.22044605e-15\n", + " 1.70660467e+01 6.14103961e+00 5.54820978e+00 4.33612682e-02\n", + " 1.15178369e+01 6.77519816e-01 5.42015853e+00 -6.66133815e-15\n", + " 1.09250070e+01 5.42015853e+00 8.46899770e-02 -3.99680289e-15\n", + " 5.42015853e+00 -4.88498131e-15 -1.11022302e-14 -4.88498131e-15]\n" + ] + } + ], + "source": [ + "print(qd)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Testing more atoms with fixed amplitude and detuning Pauli term fixed checking interaction term" + ] + }, + { + "cell_type": "code", + "execution_count": 394, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Interatomic Radius is: 9.756753962298905µm.\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "Omega_max = 2.0 * 2 * np.pi\n", + "U = Omega_max / 2.0\n", + "R_interatomic = MockDevice.rydberg_blockade_radius(U)\n", + "reg = Register.from_coordinates([[0,0],[10,0],[20,0],[0,10],[10,10],[20,10],[0,20],[10,20],[20,20]])\n", + "print(f\"Interatomic Radius is: {R_interatomic}µm.\")\n", + "reg.draw()" + ] + }, + { + "cell_type": "code", + "execution_count": 395, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "delta_0 = -6 * U\n", + "delta_f = 2 * U\n", + "t_rise = 252\n", + "t_fall = 500\n", + "t_sweep = (delta_f - delta_0) / (2 * np.pi * 10) * 1000\n", + "rise = Pulse.ConstantAmplitude(10,\n", + " RampWaveform(t_rise, 10.0, 0.0),0)\n", + "sweep = Pulse.ConstantAmplitude(\n", + " 10, RampWaveform(t_sweep, delta_0, delta_f),0\n", + ")\n", + "fall = Pulse.ConstantDetuning(\n", + " RampWaveform(t_fall, Omega_max, 0.0), delta_f, 0.0\n", + ")\n", + "seq1 = Sequence(reg, MockDevice)\n", + "seq1.declare_channel(\"ising\", \"rydberg_global\")\n", + " \n", + "seq1.add(rise, \"ising\")\n", + "seq1.add(sweep, \"ising\")\n", + "seq1.add(fall, \"ising\")\n", + "\n", + "seq1.draw()" + ] + }, + { + "cell_type": "code", + "execution_count": 396, + "metadata": {}, + "outputs": [], + "source": [ + "sim = QutipEmulator.from_sequence(seq1)" + ] + }, + { + "cell_type": "code", + "execution_count": 397, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "10.0%. Run time: 0.07s. Est. time left: 00:00:00:00\n", + "20.0%. Run time: 0.14s. Est. time left: 00:00:00:00\n", + "30.0%. Run time: 0.22s. Est. time left: 00:00:00:00\n", + "40.1%. Run time: 0.30s. Est. time left: 00:00:00:00\n", + "50.0%. Run time: 0.37s. Est. time left: 00:00:00:00\n", + "60.0%. Run time: 0.43s. Est. time left: 00:00:00:00\n", + "70.1%. Run time: 0.49s. Est. time left: 00:00:00:00\n", + "80.0%. Run time: 0.55s. Est. time left: 00:00:00:00\n", + "90.0%. Run time: 0.62s. Est. time left: 00:00:00:00\n", + "Total run time: 0.68s\n" + ] + } + ], + "source": [ + "\n", + "results = sim.run(progress_bar=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 398, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "count = results.sample_final_state()\n", + "\n", + "most_freq = {k: v for k, v in count.items() if v > 10}\n", + "plt.bar(list(most_freq.keys()), list(most_freq.values()))\n", + "plt.xticks(rotation=\"vertical\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 399, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#Define Rydberg state observable\n", + "obs = qutip.basis(256*2, 0).proj()\n", + "plt.figure(figsize=(6, 6))\n", + "k = results.expect([obs])[0]\n", + "\n", + "plt.plot(results._sim_times,k)\n", + "plt.xlabel(r\"Time ($\\mu s$)\")\n", + "plt.ylabel(r\"Population in $|r\\rangle$\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 400, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "crank = 0, prank = 2\n", + "rcut is 10.0\n" + ] + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import qse.qbits\n", + "\n", + "\n", + "L = 3\n", + "nqbits = L * L\n", + "qsqr = qse.Qbits(positions=np.array([[0,0,0],[10,0,0],[20,0,0],[0,10,0],[10,10,0],[20,10,0],[0,20,0],[10,20,0],[20,20,0]]))\n", + "\n", + "\n", + "Omega = 1.2 # Amplitude\n", + "delta = 2.0 # detuning\n", + "C6 = 5420158.53 # interaction scale\n", + "\n", + "qsqr.draw()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 418, + "metadata": {}, + "outputs": [], + "source": [ + "def occ_op(nqbits, qi):\n", + " ti = qat.core.Term(1.0, 'Z', [qi])\n", + " return (1 + qat.core.Observable(nqbits, pauli_terms=[ti])) / 2\n", + "#\n", + "H1_terms = [qat.core.Term(0.5, \"X\", [i]) for i in range(qsqr.nqbits)]\n", + "H1 = qat.core.Observable(nqbits, pauli_terms=H1_terms)\n", + "\n", + "# H2_terms = [qat.core.Term(-0.5, \"Z\", [i])+qat.core.Term(-0.5,\"I\",[i]) for i in range(qsqr.nqbits)]\n", + "# # H2_terms_Z = [qat.core.Term(-0.5, \"Z\", [i]) for i in range(qsqr.nqbits)]\n", + "# H2 = qat.core.Observable(nqbits, pauli_terms=H2_terms)\n", + "H2=0\n", + "for i in range(qsqr.nqbits):\n", + " H2 += occ_op(qsqr.nqbits,i)\n", + "H2=H2*(-1)\n", + "rij = qsqr.get_all_distances()\n", + "\n", + "\n", + "\n", + "H3 = 0\n", + "\n", + "for i in range(nqbits):\n", + " for j in range(i + 1, nqbits):\n", + " H3 += (C6 / rij[i, j]**6) * occ_op(nqbits, i) * occ_op(nqbits, j)" + ] + }, + { + "cell_type": "code", + "execution_count": 419, + "metadata": {}, + "outputs": [], + "source": [ + "from qat.core.variables import Variable, heaviside\n", + "from qat.core import Observable\n", + "\n", + "def create_waveform(times, values):\n", + " \"\"\"\n", + " A Funnction allowing us to concatenate many lines, limited by heavisides,\n", + " thus creating a continuous, kinked line.\n", + " \"\"\"\n", + " assert len(times) == len(values)\n", + " # Store the final line as an ArithExpression\n", + " arith_expr = 0\n", + " t_var = Variable(\"t\")\n", + " # A line between each two points\n", + " for entry_i in range(1, len(times)):\n", + " # Create ax + b by calculating the slope and the offset\n", + " a = (values[entry_i] - values[entry_i - 1]) / (times[entry_i] - times[entry_i - 1])\n", + " b = ((values[entry_i] + values[entry_i - 1]) - a * (times[entry_i] + times[entry_i - 1])) / 2\n", + " respective_line = a * t_var + b\n", + " arith_expr += heaviside(t_var, times[entry_i - 1], times[entry_i]) * respective_line\n", + " return arith_expr\n", + "#\n", + "Omega_max = 2.0 * 2 * np.pi\n", + "U = Omega_max / 2.0\n", + " \n", + "delta_0 = -6 * U\n", + "delta_f = 2 * U\n", + " \n", + "t_rise = 0.252\n", + "t_fall = 0.500\n", + "t_sweep = ((delta_f - delta_0) / (2 * np.pi * 10) * 1000)*(10**-3)\n", + " \n", + "\n", + "# The waveform of Omega - for the sigma_x terms\n", + "omega_values = [10.0,0,Omega_max,0]\n", + "times_omega = [0,t_rise,t_rise+t_sweep,t_rise+t_sweep+t_fall]\n", + "\n", + "\n", + "omega_waveform = create_waveform(times_omega, omega_values)\n", + "# The waveform of the detuning Delta - for the 'n' terms\n", + "delta_start = -2 * np.pi * 13\n", + "delta_end = 2 * np.pi * 11 # R_blockade is taken as 7.5\n", + "delta_values = [10,0,delta_f,delta_f]\n", + "delta_waveform = create_waveform(times_omega, delta_values)" + ] + }, + { + "cell_type": "code", + "execution_count": 420, + "metadata": {}, + "outputs": [], + "source": [ + "from qat.core import Observable \n", + "Hamiltonian = Observable([\n", + " (omega_waveform, H1),\n", + " (delta_waveform, H2),\n", + " ])\n", + " \n", + "schedule = Schedule(drive=[\n", + " (omega_waveform, H1),\n", + " (delta_waveform, H2),\n", + " ], tmax=t_rise+t_sweep+t_fall)" + ] + }, + { + "cell_type": "code", + "execution_count": 421, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "matrixp = sim.get_hamiltonian(0).get_data().toarray()\n", + "plt.imshow(matrixp.real)\n", + "print(matrixp)\n", + "np.savetxt('matrix-p.dat', matrixp.real)\n", + "np.all(matrixp.imag == 0)" + ] + }, + { + "cell_type": "code", + "execution_count": 425, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[-1.86617366e+01+0.j 5.00000000e+00+0.j 5.00000000e+00+0.j ...\n", + " 0.00000000e+00+0.j 0.00000000e+00+0.j 0.00000000e+00+0.j]\n", + " [ 5.00000000e+00+0.j -2.04462622e+01+0.j 0.00000000e+00+0.j ...\n", + " 0.00000000e+00+0.j 0.00000000e+00+0.j 0.00000000e+00+0.j]\n", + " [ 5.00000000e+00+0.j 0.00000000e+00+0.j -2.64486643e+01+0.j ...\n", + " 0.00000000e+00+0.j 0.00000000e+00+0.j 0.00000000e+00+0.j]\n", + " ...\n", + " [ 0.00000000e+00+0.j 0.00000000e+00+0.j 0.00000000e+00+0.j ...\n", + " -1.00000000e+01+0.j 0.00000000e+00+0.j 5.00000000e+00+0.j]\n", + " [ 0.00000000e+00+0.j 0.00000000e+00+0.j 0.00000000e+00+0.j ...\n", + " 0.00000000e+00+0.j -1.00000000e+01+0.j 5.00000000e+00+0.j]\n", + " [ 0.00000000e+00+0.j 0.00000000e+00+0.j 0.00000000e+00+0.j ...\n", + " 5.00000000e+00+0.j 5.00000000e+00+0.j -4.88498131e-15+0.j]]\n" + ] + }, + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 425, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.imshow(matrixm.real)\n", + "print(matrixm)\n", + "np.savetxt('matrix-m.dat', matrixm.real)\n", + "np.all(matrixm.imag == 0)" + ] + }, + { + "cell_type": "code", + "execution_count": 426, + "metadata": {}, + "outputs": [], + "source": [ + "np.savetxt('matrix-q.dat', matrixm.real)\n", + "np.savetxt('matrix-p.dat', matrixp.real)\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 427, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 1. 1. 1. ... nan nan nan]\n", + " [ 1. 1. nan ... nan nan nan]\n", + " [ 1. nan 1. ... nan nan nan]\n", + " ...\n", + " [nan nan nan ... 1. nan 1.]\n", + " [nan nan nan ... nan 1. 1.]\n", + " [nan nan nan ... 1. 1. -0.]]\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "RuntimeWarning: invalid value encountered in divide\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "p = np.loadtxt(\"matrix-p.dat\")\n", + "q = np.loadtxt(\"matrix-q.dat\")\n", + "plt.imshow(p == q)\n", + "\n", + "pd=p.diagonal()\n", + "qd=q.diagonal()\n", + "print(p/q)" + ] + }, + { + "cell_type": "code", + "execution_count": 428, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1. 1. -0.]\n" + ] + } + ], + "source": [ + "print(pd/qd)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 390, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[26.33826339 5. 5. ... 0. 0.\n", + " 0. ]\n", + " [ 5. 24.55373778 0. ... 0. 0.\n", + " 0. ]\n", + " [ 5. 0. 18.55133566 ... 0. 0.\n", + " 0. ]\n", + " ...\n", + " [ 0. 0. 0. ... 35. 0.\n", + " 5. ]\n", + " [ 0. 0. 0. ... 0. 35.\n", + " 5. ]\n", + " [ 0. 0. 0. ... 5. 5.\n", + " 45. ]]\n" + ] + } + ], + "source": [ + "print(q)" + ] + }, + { + "cell_type": "code", + "execution_count": 389, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[-18.66173661 5. 5. ... 0. 0.\n", + " 0. ]\n", + " [ 5. -20.44626222 0. ... 0. 0.\n", + " 0. ]\n", + " [ 5. 0. -26.44866434 ... 0. 0.\n", + " 0. ]\n", + " ...\n", + " [ 0. 0. 0. ... -10. 0.\n", + " 5. ]\n", + " [ 0. 0. 0. ... 0. -10.\n", + " 5. ]\n", + " [ 0. 0. 0. ... 5. 5.\n", + " 0. ]]\n" + ] + } + ], + "source": [ + "print(p)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "def occ_op(nqbits, qi):\n", + " ti = qat.core.Term(1.0, 'Z', [qi])\n", + " return (1 + qat.core.Observable(nqbits, pauli_terms=[ti])) / 2\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 416, + "metadata": {}, + "outputs": [], + "source": [ + "qubits=qse.Qbits(positions=np.array([[0,0,0]]))\n", + "H2=0\n", + "for i in range(qubits.nqbits):\n", + " H2 += occ_op(qubits.nqbits,i)\n", + "H2=H2*(-1)\n", + "rij = qubits.get_all_distances()" + ] + }, + { + "cell_type": "code", + "execution_count": 417, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[-1.+0.j, -0.+0.j],\n", + " [-0.+0.j, 0.+0.j]])" + ] + }, + "execution_count": 417, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "H2.to_matrix(sparse=False)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "pulserenv", + "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": "3.1.-1" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/examples/qbits-tutorial.ipynb b/examples/qbits-tutorial.ipynb new file mode 100644 index 0000000..4cc5d05 --- /dev/null +++ b/examples/qbits-tutorial.ipynb @@ -0,0 +1,258 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Overview of the Qbits object" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "#import matplotlib.pyplot as plt\n", + "#from mpl_toolkits.mplot3d import Axes3D\n", + "import numpy as np\n", + "import qse\n", + "#from qse.utils import squarelattice, triangularlattice, hexagonlattice, kagomelattice" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Square Lattice\n", + "\n", + "We have several functions in the `qse.utils` submodule to directly generate known lattice objects." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "crank = 2, prank = 2\n", + "rcut is 10\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "square_reg = qse.utils.squarelattice(1, N1=6, N2=6)\n", + "square_reg.translate(displacement=-square_reg.get_centroid())\n", + "qse.draw(square_reg, radius=10)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Triangular lattice" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "crank = 2, prank = 2\n", + "rcut is 1.1\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "triangular_reg = qse.utils.triangularlattice(1, N1=6, N2=5)\n", + "qse.draw(triangular_reg, radius=1.1)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "rmin is 1.0099999999999998\n" + ] + } + ], + "source": [ + "rij = triangular_reg.get_all_distances()\n", + "\n", + "ib = np.logical_not(np.eye(triangular_reg.nqbits, dtype=bool))\n", + "rmin = rij[ib].min()*1.01\n", + " \n", + "print(f\"rmin is {rmin}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Hexagonal cricket" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "crank = 2, prank = 2\n", + "rcut is 1.1\n" + ] + }, + { + "data": { + "image/png": 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D/ffDtdcVGB+zYXyIrVBASBoAtXE4rHhhhWSkZbSaHTlncmTdO+tazF5XYHzMhvEhtsKdAdIAlB316RC6tS/OGlPjUtXfa207cKaJnxdNO0wD/sZ3qK9lNzk+wLfx6cj4EPtgMkAaUFVZJXPu1F+b2xi9sKxasKrVRUf491H+FPxzG595/sfs//Cd+Kn6ZrXMrZlrfHzArzN+7bv43L1zVxbUfXOxlMnx+Zfp/+K7+JDQMBkgDdi8ebMMqx0mS2SJJHRMaPA9vGmsXbI2YvXJ+Dn4eclxyfeosWFfz4qe4je2bdsmQ+4OUf433iEwLT5xpf6rPMKdGQNvDVT+N95hMy0+Xc52iYgdxA5YWkg8ioqK5A9/+IMaJycny09++hPJK86Leuey4A5qfTr1kcOfHJbKQKW0adNGli9fLj17+iMpOHfunLz55puCjyxuylv24jLZWbrTqPjEd46XoxuOyuVLl1VPhJdeekm1jfYDly5dkt/+9reqO2T37t3lpV+8JLvLdxsVn8SuiXJi0wk5V35Ofe9nP/uZpKamRtwmEjnCfX4zGSAKTIO33nrL66e+dOlSSUlJERM5evSo/O1vf/M68j333HPih/igze2ZM2fUn3/0ox/JoEGDxEROnjwpf/rTn9Q4LS1Nnn/+eZUYuM5f/vIXOX78uBo/++yzMnLkSDGR4uJiefvtt9UYV0svW7bMF/HxKwH2GSAPAy7/0YnA6NGjjU0EANq99u/fX42x+J46dUpcp6CgwEsEkACZmgiAwYMHe62IYfOxY8fEdTAHdSKABAhz1FSwE4DPuL74Kz8/P9omEQNgMkDk1q1b6lpg0K5dO+Pvn8dbDC6E0W8zGzduVFuzrnLnzh3ZtGmTdxkOLisyHdioL5HKzs6Wu3fviqvU1NSoOQgwJ3FBk+lv2viM47OudUJYA4i/YTJAlOjp+vXrapyenm7FUVBiYqJ3ffGFCxdk//794iq7du2Sq1evqvGkSZOs0Ej06tVL2QpgO3xwFcw9zEGAOYm5aTr4jE+bNk2N8dnPzWUnQr/DZMDnXL58Wfbs2aPGED1NnjxZbGHmzJnSoUMHT2V/48YNcfG8Ly8vT427dOki06dPF1uArbAZ4GFTWVkproE5l5OTo8aYi5iTtoDPOs6Swe7du9VaQPwLkwGfgy1cbHOCuXPnWnX/PB40M2bMUOPq6mpvUXYJHN/gmEBv7erkxwZg66xZs9QYPuijKJfAnMPcAxkZGV7yYwM4JtBHTlgD9FEU8SdMBnyMTaKnUEyYMEFtSevt2vPnz4srlJSUyOHDh9U4KSlJnnzySbEN2AzbAYRq8MkVKioqvOOp3r17y/jx48U2gsW4EHqePn062iaRKMFkwIegTM1G0VNToNcAbNd+ZWVlqf/bDOzXvmiCBZM2AREhbNe4EB8AH/D50b5gDmIu2kZjMS7i47IYl4SGyYAPwQf/iy++kM6dO6sFzBbRUyiGDBmi/sO2JxYyvdthc3ywI4AjG/z3+OOPS79+/cRWYDt8wFzDf19++aXYDt6ikVC3b99ezT2UU9qKFuMicevUqZMcOHAg2iaRKMBkwIdA9LR161Y5e/as9OjRQ4mebH5bg+04+8QZNXyyvZTt9u3bqtwLvnTt2lXmzGn6rgibgN6hW7duqsslfIOPtoK5hfN1+IJkAHPP9s8P1gBUqcAniHFv3rwZbbNIhGEy4EOCRU/jxo2zSvQUCpzZ4u0TXLlyxauQsBEo76uq6u+jHzNmjKf4thlUqsAXgKoCXSFhI1DeY44BzDnMPWBzQoA1QJfqIhFwUYxL7g+TAZ8BgV1Toicbz6M12nZUFuDoQ/dO0A9Um8BDRtfkoxZ86tSp4grwRfew2Llzp/dAtQkkMromH3NNV7NgDtr6GdJ2B4tx9+3b55QYlzwYJgM+orHAzlbRUyg6duzolbJhG9rGUjZsPweXeuoucS4AX+CTzaVsOF7TRxyYa5hzrtBYjBsskCTuw2TAR0BYV1hYqMa2i55CMXbsWO+WPNy3gN7rtoDY4A4CLbobNWqUuAZ80rfkBd+3YAOlpaVqTmnRHeaaawSvCygzPHHiRLRNIhGCyYBPgOgJwjqb+tv7qZQNVRC61NPmUsJwS9k0tpSyNVXqqe9ecA3sDvjlXgnyDW7OZnIPENTpM1qcDWrRk4uggZK+PhbXtR45ckRMB6WeaGID8MapG/W4CK7N1Q2U4DN8Nx3MId0wCXNLN+pxEawNWCMatysnbsNkwAdASAdBXWPRk8vgbFrrIUwvZYN6G2fRAKVqWvfgMig1hK8Avptcyoa5o/UN6PugdQ8u44IYlzwcTAZ8AIR0roqe7lfKNmXKFO+yH6jXTWX79u3ewxCLMHoLuA581JcuwXf8Dkxlx44d3iVLmFOYW66DNUJfumSrGJc8HEwGHAcCOi16grDORdFTKHBFKxrd6AX92rVrYhq4+nbv3r1qjKYvEydOFL8AX/V1zChlu3jxopgGrl/WiSTmkkulng8CfQdsFeOSh8eeK+osoKa2RnKLcqW8slySuiVJer90aRPbJmp2lFWWyaHcQ9JJOkmsxDotemoKbEOje98HH3ygRFBZ2VmSMD7BqPh8tfsraVvXVsUHok6XSj0fBLbc4fNf/vIXJSLckLVBUqelGhMf2HHiixNSe7dWxQdzSR9t+AEtxn3nnXfUnz/b8JkMmjVIzlWdMyY+0bTDNZgMtBDrC9bLyqyVUhL45la2lLgUWb1gtSwasSiqdsRJnLyY8qIS1vmNJ554Qr11ZpdkS+bRTAkcDRgZn58k/ESGDh0qfgM+Dxw4UD49/alknsqUwCkz4/PDXj9Uc8lv6NtM1xWsk8ySTAm8a158omGHi/jnNbGVJ+jiNYsbTFBQGihVX8f3o2lHQALqgxwpO0wrZasdVitrZI36PZgan9cqXpMPjn0gfozP3SF3jY/P/1z6H1/GB1QPqDY6PpG2w1Vi6sIowoYAC/3Rceaq24mSb7as0lan3TNBg8GbxavyqtpqbC1qpVZWyap7PrCaGIlRGXThykJfbakxPmbD+JgN42M/4T6/uTPQTHB2db8PCsAEPitnW9UO/PuhPiigTuqkOFCs7PUTjI/ZMD5mw/j4ByYDzQQilnCoktat0w333w/XXldgfMyG8TEbxsc/UEDYTKBmDYcVL6yQjLSMVrMj50yOrHtnXYvZ6wqMj9kwPmbD+PgH7gw0E5S19GnfJ+T3cZaVGpeq/l5r24EzM/y8aNphGvA3vkN8yO8zPgbEp6P58QF+jU9Cp/peA03B+LgDk4FmUlVZJXPuzmnye3rirlqwqtVFLfj3UV4T/HMbn6n9Zs5vfCeuqb5ZLXNr5loRn/+Y/R++i8+d23dkQd03FxeZGh/w64xf+y4+tTW18q2Yb1kRn3+Z/i++i09LwmSgmaDv/bDaYbJElkhCx4YZNDLZtUvWRqz+FT8HPy85LvketS/sS7ySKH4Dfe+H3B2i/G/8BmpafHpW1Hfj8xPoez/w1kDlf58OfYyOT1yp/yqpdu3aJf1v9Ff+927f2+j4dD5Tf5cCeTRYWtgMzp49K3/84x/VOCUlRV74yQuSV5wX9c5YwR26enXoJfkf58uN6zekXbt2smLFCt/E8Ny5c/K73/1Ojfv06SMv/vxF2VGyw6j4xHeOl8OfHJbAtYDq+LZ8+XLp1auX+IFLly7Jb3/7W9V9EP3+f/HyL2RX2S6j4pPQJUGObjgqly5eUj0Rfv7zn0tioj+Saqz7r7/+uty5c0fdJfHy8pdlb8Veo+KT2DVRvt78tZSX1QsHf/rTn0q/fv0ibpPJhPv8ZjLwiGABe+utt9QDByxbtkySkxtmrKZw8OBB+fjjj9V49OjR8r3vfU9cB9MabVSRsIEf//jHqtOdiRw9elT+9re/qfGwYcPkueeeEz/w/vvvy4kTJ9R4yZIlqtOdiZw+fVree+89ryPf888/rxID11m/fr18+eWXavyd73zHu3baNHC19O9//3s1xtXfL774oi/iEy7sM9DK4OIOnQiMGTPG2EQA4EOMDwk4fPiwdy+7yxQUFHiJwPDhw41NBAAegrpV9PHjx+XUqVPiOidPnvQSAfiOGJkK5g6SNHDmzBk1t1ynuLjYSwT69u2r1jhTwa4sXnJAeXm5dzEbeTiYDDwCt27d8u6fx9Y77mY3GWTJCxcu9P6clZWl3pxdBdua2dnZaoyLf0y/fx7xmT9/vvc2s3HjRqmpqRFXgW/wEcBnXIZj+pscLlTSl3xt2rRJzTFXwdqANUJjQ3ywBmMtBrhuGWs0eTiYDDyi6On69etqnJ6e7l2TazKpqaneRSulpaVqh8Bl0ZO+rnjSpEneNbkmg3NoXBmrrzXev3+/uAp809cVjxs3zrsm12QwhzCX9LXGmGOukp+f711XjDUDa4fpYPsbazHA2ow1mjwcTAYeQfS0e/duNYboafLkyWILuIJVZ8+ognAxe8b5WF5enhpD9KQXCBuYOXOmdOzYUY1zcnLkxo0b4hrwCb4B+AqfbWH69OnSpUsXNcYcw1xzDawJeLMGWCuwZtgC1mKsyQBrNNZqEj5MBh4SbD9DPKi3DnEnuy0ge546daoaV1VVeQ9Nl8BCprdwsXXYoUMHsQU8aGbMmKHG1dXV3kPTJbZt26Z8A/C1c2d7ysEwl/SRIOaYfmi6RG5urlobANYKmwTjWIv1kSDWaBznkPBhMvAQQNhli+gpFFOmTFHKUoCtzitXrohLoid9/GG66CkU48ePl969e3vb6RUVFeIK8OXAgQNqDB/hq224LMbFWqB3PbFGYK2wDT+KcVsKJgMOi56aAlt/OnuGT65kzzaKnpoCgkeICbVPmHMuiD11fLQv8BG+2ob+7LsoxsWupxauYo3QR4o20ZQYV+/kkvvDZCBMvvjiC+nUqZOaZLaInkIxcuRI1ZgD22o4w0Udte3gLQ3+QPFti+gpFIMHD5YhQ4YoX7CQ4Q3Hdo4dO6Z8QQIwdOhQ5aOt4LPz+OOPq7UA/ugSPJvBGoC1AAlA//791RphK8FiXKzZejeK3B8mA2GADwlKCYuKilQSkJHRerdzRQqUGkLAhVp827NniJ4giER8oPrGua7tb2vQo6BKBfHBG9vdu3fFVmA7fEB8IOo0vdTzQWBuQViHTpHwCbtrt2/fFlvBZx9rAHyBLsLWXbVgIExFUgCfsHa7KMZtaZgMhAGEXFr0hHNorSi2FXzQ8UHB2yc4f/682vmwFQghtegJb2xaE2EzOFPXHfmCz3JtBLajHA/gjVNrImwGc2zUqFFqjLkH4Z2t4M0ZawDAro0L7ZaxRmvNkKti3JaGyUAYoidd822r6CkUs2bN8tT2yJ5v3rwptoEHpa75DhY92f5m01htj4dNZWWl2AZs1jXf8AXlebaj51aw2t5WMS4+86jwAFgLsCa4QmMxrk54SNMwGbgPjQVctoqeQoEtW704Y1HYvn272IYLoqdQ4BhHL87YhtZdL20u9dR9FFzABTEu3pj1SwCST9t3Pe8nxnVJ7NkaMBm4DxBuFRYWqrHtoqdQTJw40evQt3fvXtX9zibRE4RpWtRls+gpFGPHjvW2bdFzHd0jbQG2opsdgA+mXnTTHHBUoG/Jw50Fer2wAXzW9+3bp8bQP0yYMEFcQ4txAWLjghi3tWAy8ADRE4CqG4IuF7G1lE2LnjQuiJ6aAnPPxlK2pko9dW9/l2iq1NAGMa7ru57BwDc992wX47Ym7n06W1D0pM8A8fbs8h3zyJwHDRqkxmjS8fXXX4tNoie8PetGMC4SXOqFJjdHjhwR00G5nW7Ig7dn+OAqmHuYgzaJcfEZ1w15gt+eXSR41wNr+p49e6JtkpEwGQghetLqYFdETy7dmuey6CkUOJvWra9NL2WDbSj1BLDZpv72jwrmYPv27a0Q4wY3UHN51zOUGBeCVl19RL6ByUAT4MOsF1vXRE+h6NOnj5c9X7582ejsOVj0hEQNQkjXwQUsulICyeqOHTvE5FJPXfkAm/XlMS6DOajvlTBdjIvPNj7jWnGPz77rNBbjunivRHNhMtCE6AlCLZdFT6HAYoaOXSZnz8GiJwgfcYTjF1DKpq/L3rlzp1e7bxKwCbY1vhjLD9ggxsVnWicqeFPWCYwfsFmMGwmieuVeTW2N5BblSnlluSR1S5L0funSJrZN1OwoqyyTg58flM7SWWIl1lnRUyiQCCB7/vvf/666+m3askl6jOlhVHyO7Doi7eraqfi4LHpqCmxD47hg/fr1SgS1MXujJExIMCY+sOP4geNSV1On4oPjAb117ge0GPf9999XwrwNWRskdVqqnKs6Z0x8Th8+rd6MER906dPJvx/QYtw//vGP6s+fbfhMBs8ebFR8kqJoR9SSgfUF62Vl1kopCXxz61dKXIqsXrBaFo1YFFU74iROfp76c6dFT6FAT2+8eeecz5HMQ5kSOBQwMj4/SfiJ06KnUKDDIt46s0uyJbMgUwIFZsbnR71+pGz1G1qM+8mpTyTzdKYETpsZn+cee87r3+8ntBh37dG1klmaKYF3zYtPShTsAFF57cUvYPGaxQ1+AaA0UKq+ju9H046ABOQ/i/8zYnaYhNoJGSGyRtao34Op8Xmt4jX54NgH4jcg8qwdVmt8fN649IZv43Nn8B3j4/PWtbfkw+Mfih+pHlBtdHxKI2yHJqYujKLlQCCgWr1eu3bNa7/ZnC2RtNVp9/wCPIMkRmVGhSsLW3WrxBQ7TMOU34spdpiGKb8XU+wwDVN+L6bYYRqm/F5qImhHuM/viB8T4Gwk1C8A1EmdFAeKZemvlsoAGdBqdhRKoZTIg+2AvRlp9t9SGC6Mj9kwPmbD+JgN42PQMQFEEuFQJa2rZA/33w/XXldgfMyG8TEbxsdsGB8xZ2cAaslwWPHCilbNiHLO5Mi6d9a1mL2uwPiYDeNjNoyP2TA+Bu0MoGwCZyE4E2kKfD01LlX9PT/YYRrwN75DfMjvMz4GxKej+fEBfo1PQqeEkN9nfKIL/E3sXN9rwOT4xERhfYt4MgAxBMomQONfhP7zqgWrWl3Ucj879JlN5rxMX4lrQPXNaplbU38ta2NMi89v5vzGd/G5c/uOzK+tv1jK5PiAf5/1776LT21NrXwr5ltWxOfXGb/2XXykTuTbbb5tdHxiImhH1EsLUT+5dslaSY5LbvB1ZEr4eqTqK0PZgTrcJbJEUqtSxY+tmIfcHaL8b/wGalp8Ei6HfgNzFXSGHHR7kPK/T4c+RsenZ0V9Nz4/ge6L/W/0V/73bt/b6Ph0K6nvZukn0EMlpTKlPj7tzIxPSoTtiFppoYmdl4Lt6NGuhxz88KDcvnVb9bN+5ZVXvAsuXKe8vFzefPNNNY6Pj5dlLy6THSU7jIpPrw69JP/jfLlx/Ya6BGfFihVqbvqBixcvyhtvvKGuyO3Ro4e89IuXZFfZLqPiE985Xg5/clgC1wKqZ8Xy5cudvvEzGKyPr7/+uuoOibsKXl7+suyt2GtUfBK6JEhBVoFcvHBRfe+ll17yWvS6zvXr1+W1115T3VWxti//5XI5cPGAUfFJagU7wn1+RzUZMPkiD30X+9NPPy3PPPOMuA6mAdp0FhUVqT8///zzMmBA65XWNAf0Ff/oo4/U+IknnpBFiyKbQUeLP//5z9710t///vdl+PDhYiIFBQWyZs0aNR46dKj84Ac/ED+wbt0673rp7373uzJmzBgxkdOnT8t7773ndeR74YUXvBtLXebTTz9VV5+DhQsXehezuU4gzOe3fxrvPwRIAHr3rt9CwuSpqKgQ1zl69KiXCOAhY2oiALDI9u3bV42//PJLKS4uFtc5efKklwggNsOGDRNTwfxJS0tT4xMnTijbXQefHZ0IJCcny+jRo8VUBg4c6CWSZ8+eVcmb62AN/+KLL9QYtzRijScNYTJwnwtH9BszdgnC2ECxljt37simTZs8302/3xxvMbhwRON6fILvn4fvmJsmv8np+GgbYTt8cBW9RmhMjw/AhVf6kq/s7Gy1BrhK4zUc8fHTBXThwt9ICAYPHqy2OMGZM2fk2LFj4rLoCVtIYPLkyeo82nRSU1PVEQEoKyuT/Px8cVn0BL0AGDdunCQkmC+chI2wFcD2/fv3i6vg2Ap6G4AdAcxN08FVy5MmTVJjfPZ37dolroK1G2s4wI4aLpIi98Jk4D7gDVlnkMieIQxyDSwEeXl5agzR07Rp08QWcEVuu3bt1Hjz5s1KGOSi6CknJ0eNIXrCtbO2AFthM4APN27cENfAnNuyZYsaYy7Onj1bbCE9PV195gHWAJwtuwbWbKzdAGu56bue0YTJwH2AClpnz1evXnUye8ZCppMcPFw7dOggtgAxjE5e8NDMzc0V19i2bZuX5GRkZFhV2QJbYTOorq5WvrhY6om5BzAXbRJY47OukxccEyChdg2s2Vi7AdZy7IiQpmEy8ACmT58uXbp0UWM8bCorK8UVILyDAM8G0VMocKyhSwt3794tly9fFhdFTxC02ih6clmMi7mGyiOAOYi5aBsui3GxVusXBKzhWMtJaJgMhJE9z5o1y8ue9Zag7dgoemoKbM1CDAUgUoMQEr7ZLihsSvSkBV824aoYFz5g+1kLI7H9rI+sbMJlMS7Wai2MxA6ITbue0YDJQBg8+eSTkpSUpBY2bDmVlIS+etIWDh8+7D1cbBE9hWLkyJGqXhoLG86lCwsLrUxsGoue0FwIfkDICkGrC2Jc+HT8+HGxHdTq37x5U51DY+6NGDFCbCVYjIs1AWuD7WCHA2s1GpNh7cYaTu4Pk4EwwAceTSpwBoq6XNuzZ5xB4w0aHxiovm0SPTWFLrfDeS3qvREfPHRsFz3BF5xxuiB6wu4NNDjwCaWGNotxMbfgA3zBnAsuo7QV6IWwFmBNsF2Mi7UZ8cFa3alTJ7V22x6fSMBk4CGyZ7wBgNLSUu+s3UZwjqZFT3irtkn0FApk/7pk6MKFC1aXsgWLnlAK5UI7X+gG9O6A7WJczC3MMYA550I7X6wBWAtAVVWV1WJc7GxgjQZYs23e9YwkTAYeMnvGthNA9nz79m2xUfQEoZ3NoqdQQNuhzwVRyoZtXNtwWfQEX3Q1hK1iXBxD6aoIzDWbSj0fVox75coVsQ2syVrXhbUaazYJDyYDDwE+KFOnTlVjLGS6Pt8mcDxgu+gpFHh4zpgxQ42RCOj6fFtFT8HJjQug50BwKZuNYlzMKZRJAsw1XWnkAo3FuLo+3yawJuskE2u1Xy4xawmYDDwkmGB6Wx2d+/R2ri2iJ91J0XbRUyhw+YjeVkfnvvPnz4stQJiqOym6KnqCT3pbHb7q7VwbwFzSx0+YYy5edKPFuABrBdYMW8BOBtZkgDVav7iR8GAy8AjZs9560qVstoiegksJXRA9hVPKBiGRDWLPxqWeiI+L/dPhU3Ap24YNG6yJT/BcsrXUM1wxrgY+2yLGDd71xA6HS7uekcC91SYCPP74454oBbf96b7XtoiennrqKSdET6EYMmSIV4qHNxvcnGeT6Anzq1+/fuIqePMcNWqUVWJczCH9loz5hf9cBbtSWCP0boi+9tdkUE6sb1/E2qznFwkfJgMt1KjD5Ow5+Pw8uImSywTfTGb6vRIQPelWsH4RPeHNzRYxLuaOvjXSL/3tg/UqEEyaLMbVpZ6u73q2NkwGHhG08NRnumixevDgQTGVYGW9a6Kn+5WyjR8//p62saaKnlDO5SfRE3ycMmWKFWJczB2trIdOQLdXdhmbxLho2a3bXI8dO9Zrr0weDiYDzQDK6Pbt26vx1q1bPZWxSWCbD0I6l0VPocBipkvZcKGMfuCahJ9FTzaIcTFnMHcA5pJ+QPqBxmJcfcxoEkhUsPYCrMV+2PVsLer36cgjges/UTuNbU7UH2/N2Sqdh3eW8spySeqWJOn90qVNbORFRjW1NZJblCtllWVyZNcRaVfXTmIl1lnRUyjQfQx14H//+9/VNvSmLZukx5gexsQHdhzbf0ykBll5rO9ET1i8cSSyfv16JfzamL1REiYkGBWfU/mn5M7tOyo+eNDoK5n9ANYKHIm8//77Sjj52YbPpF96PzlXdc6Y+BQXFMv1m9dVfLAW6yuZycPDZKCZTJw4UQlsdlzZIZl7MiWw55s7wVPiUmT1gtWyaMSiiNmzvmC9rMxaKSWBb+5PiJM4+WniT50WPYUCQiiIJ7dVbJPMQ5kSOGRmfH7U60e+FD1BLIm3zo3FGyWzIFMCBWbG57nHnlNb0H5Di3E/PvmxZBZmSqDQzPg82/VZtRaTR4fHBM0EIqiYkTGyRtZIQL75oIDSQKksXrNYTeBIgJ+Dnxf8QQGw6/+d+38Rs8MklIhwhBgfnzcuvSEfHPtA/AaEXrXDao2Pz1vX3pIPj38ofozP7UG3jY/P21Vvy8dffxwRO1wlpi6MIt9AIKAEP9euXXOij31Lb1mlrU67Z4JqYiRGZdCFKwtbdUvNFDtMw5Tfiyl2mIYpvxdT7DANU34vpthhI+E+v3lM0ExwdhVqgoI6qZPiQLEs/dVSGSADWs2OQimUEnmwHbA3Iy1D/ALjYzaMj9kwPv6BxwTNBCKWcKiS1lWyh/vvh2uvKzA+ZsP4mA3j4x+4M9BMoKoNhxUvrGjVjDXnTI6se2ddi9nrCoyP2TA+ZsP4+AfuDDQTlNfgrApnVk2Br6fGpaq/5wc7TAP+xneMD/l9xie6wN+ETgnGxwf4NT6JnRONj49fPz8tCZOBZgKxCsprQOOJqv+8asGqVhe13M8OfaaWOS/Td+Ia1IjPr/3m4hWT4/ObOb/xXXxqa2ploSw0Pj7g32f9u+/iI3Uiz8Q+Y3R8ImmHyzAZaAFQZ7t2yVpJjktu8HVksvh6pOpwQ9mBOtwlskRSKlPEb2zfvl0G3R6k/O/ToY/R8Um4HPoN2VV27NghaTfTlP+92/c2Oj49K3qK39i7d6+kVqXWx6edmfGJtB2uwtLCVuqMZUqHrh7tesjBDw/K7Vu31cUjr7zyii/uJgAXL16UN954Q11k0qNHD3npFy/JrrJdRsWnV4dekv9xvty4fkP1rFixYoUv7iYAWE9ef/11dREQOsct/+Vy2XNuj1Hxie8cL19++qVcu3pN9ax4+eWXfXE3Abh+/bq89tprcuvWLdXNE/HZf2G/UfGJph22EO7zm8mAT7J73BsPxo0bJ9/+9rfFD/z5z3+Wr7/+Wo2///3vy/Dhw8VE8vPz5cMPP/Q68v3TP/2T+IF169bJkSNH1Pi73/2ujBkzRkzk2LFj8te//tXryPfP//zP4gc++eQTdQkQWLhwoa/uNXGJcJ/fPCbwAU8//bT06VO/RY4P97lz58R1kAToRGDgwIEybNgwMZXRo0dLcnL91icejkVFReI6Z8+e9RIB+I7fgalg7gwYMOCeeeUyWCN0IoC1A2sIcRsmAz4A25u4pAhgIwh3f4exIWQt6tKb/7vfHO1U4bvJ95vDNtzBrsnKynI6Pji2gY+23D+v46NtxNzCHHMVzL3G8VFtvYnTMMI+YdCgQd7b8ZkzZ6SgoEBcPha5dOmSGuONJj4+dGmhKaSkpHhvx+Xl5XLo0CFxFfimd6fgM3w3Hcwh/XaMuaWvBXcRrA3YuQFYM7CzRtyHyYCPwHWkOsPftGmT3LlzR1wUPaGCAOC62YwMe1qTzp4927vCeMuWLUq45RrwSd8/D1/hsy1gLukrjHNyctRccw2sCdnZ2Q2uMCb+gMmAj+jZs6dMmjRJja9evSq7du0S19i2bZv3EJ05c6Z07txZbAHinmnTpqkxHjSff/65uAZ80g/R9PR0qwTJmEs6ucQcw1xzDawJEJoBrBVYM4g/YDLgM6ZPn+6VFubl5SmlqStg6/nAgQNWi54mT54s3bt3V+Pdu3d7xx0uAF/gE4CP8NU2XBbjYi3AmgBQ6olkjfgHJgM+A70G9NYstgSxHQ3BkO2CNVdET9g6nzt3rie0w3EOfMPY5hjBdmw/ww8AH9FXwTawdd6UGNfm2ADYj7VAHx3OmjVLrRXEP9i3WpJm8+STT0pSUpJSR2NLsKSkxGg1d7iiJ/2gsV30NGLECOnfv78a37x5U06dOqUSG5tjdPr0aamurlY+pKWlKR9tFuMOHTpUjVFVgD4ENscGYA3AWgA/sDZgjSD+gsmAD8EHHk1E0IgCqmHbSw216Km4uFipvvWbte3x6dWrl+o5EPxGbSN4YGLXBr7gDNr0Us9wgLAOcw1zDvFBF0Xbd9WwFmBNwNyzPT7k4WEy4EPw4Uc5ly7pKi0tlcOHD4sLoqfBgwerh6jt8cGDBm/Q4MKFC7J//36xFdiO1tAAPiUkJFi/tY45hrnmghgXn/2ysjI1Tk1NVeuC7fEhDw+TAR+CrB//zZkzxzu33bx5s9y+fVtsFj1BGAmBpCvxQTWEPreFcv3GjRtiG7AZZXgAZXnwSftn+9tnsBg3NzfXSjEuqiLw2dd6FawJrsSHPBxMBnwMtgR1KVtVVZVa0GwjWPQEYaRLoic8aHQpG87b9UPVJpDEwHYwY8YMpy7JakqMaxtIpPHZB1OnTrWq1JO0LEwGfM6UKVO8BQBbnVeuXBFbwHmtPt5wVfQ0fvx479gD2+0VFRViC7BVl3ripj/44qoYF2AuQohnC/is6+MNvBhgLSD+hcmAzwkuZYPQC6VstpYSuritGaqUzZb4aFvhA3xxDZvvlYDwUd+xgDVAd78k/oTJAJFRo0ZJv379vBK9wsJCMR1c+6tFT7j2V9vvIrg2F/8BxOb48eNiOii3wx0YALZrsZ2LYO5hDtokxsU8Qoy0/SNHjoy2SSTKMBkg97zd4O3T5FI2iJ70+SwEkBA9+eleCdNL2WCb3mEKvjHTZWwS49p2aySJDEwGiALnnmPHjvXOevVd5qaLniCAxHmn6+DMfcKECd5Zr27rayKwTWtPJk6caH2pZzhgDkKAZ4MYFzqO8+fPq/FTTz3laR6Iv2EyQDyCW5DiZjl0vzMNP4ueoMbXFy/hYVNZWSmmAZv0BUuw1YVSz3AJVuObKsbFZ1pfsITPOj7zhAD7moOTVgOXk2DxxhYvFo2tOVuly4guUl5ZLkndkiS9X7q0iY28CKymtkZyi3KVHQX7CiSmJkZiJdZ3oifU6WPx/vTTT9U29KYtm6Tnkz2Nis+p/FOqzA7xQdmdvvLXT2LcdevWKWHexuyNkjgx0aj4FB0tkhs3b6j4uFbqSZoHkwHSAGzrYhsx73KeZO7NlMDebxqppMSlyOoFq2XRiEURs2d9wXpZmbVSSgLflGzFSZz8uPePfSl6wlHOvn37ZFvFNsnMz5RAvpnx+UH3HzhZ6hmOGBfxySrKksxjmRI4ZmZ8nu36rHfsRAjgMQFpAMq/YkbGyBpZIwFp2FGtNFAqi9csVgtMJMDPwc8LXsgA7Prtxd/KB8c+EL+hRIQjxPj4vHn1Tfnw+IfiNyDEqxlaY3x83q56Wz468VFE7CB2EFMXRlEs2mzifBb939mhym2wpZi2Ou2eBUQTIzHqDadwZWGrbnmaYodpmPJ7McUO0zDl92KKHST6hPv85jEBaQDOFkMtIKBO6qQ4UCxLf7VUBsiAVrOjUAqlRB5sB+zNSKtv2esHGB+zYXyIrfCYgDQAIqNwqJL60r7WItx/P1x7XYHxMRvGh9gKdwZIA6B6DocVL6xo1TeKnDM5su6ddS1mryswPmbD+BBb4c4AaQDKn3CWiDPFpsDXU+NS1d/zgx2mAX8TOiWE/D7jE13gb2KnxJDfZ3yIqTAZIA2AmAjlT6DxQqL/vGrBqlYXHd3PDn3mmTkv03fip5q7NbJQFjb5PdPi85s5v/FdfKRO5Jk2zxgdn0jaQeyByQC5B9RBr12yVpLjkht8HW8a+Hqk6qRD2YE66SWyRJIDDb/uB3bs2CFpN9OU/33a9zE6PvGX4iNih0ns2bNHUqtSlf+92/c2Mj6RtoPYAUsLSVidy0zpoNazfU85+OFBuVV9S7VTfeWVV3zTRe3q1avy3//93+oioG7dusnLy1+WPef2GBWf3h17S/7H+XK96rq6uGfFihW+uDtC30nw+uuvq4u0OnXqJMt/uVz2X9hvVHyiaQeJDuE+v5kMEOtAh7fPPvvMu2jlH/7hH8QPrF27Vr766is1/t73viejR48WE8EVvh988IHXkW/x4sXiBz7++GM5ePCgGn/rW9+S8ePHR9skQiTc5zePCYh1jBs3TuLj67egcbviuXPnxHXOnj3rJQIpKSnyxBNPiKnAtuTk+q1p2AzbXae8vNxLBDA3MUcJsQkmA8TKlrzz58/3/oy72cPY4LIW2+6fh22wUQPb4YOrYO4FxwdzU7WNJsQiOGOJlQwcOFCGDx+uxnjzPHr0qLjKoUOHvN2PMWPGeG/dJoPdC9gKYDt8cBXMvaKiIjXGnMTcJMQ2mAwQa8F1sbhYCeDaZVyd6xrV1dWyZcsWNW7fvr26FtgWYKu+Ynrr1q3KF9fAnMPcA5iL8+bNi7ZJhDwSTAaItfTs2VMmTZqkxhDH7Ny5U1zj888/lxs3bqhxenq6qiKwBdgKm8H169eVL66BOYe5ByZPniw9evSItkmEPBJMBojV4GHTtWtXrwYfyllXuHTpkqpbB927d/cSH5vAAxK2A/gCn1wBSUBeXp4aYw5OmzYt2iYR8sgwGSBWg14DeuscW7abN29Wgi4XBIXZ2dme8A7bz6jbtw3YrLfO4Qt8cgHMLxzfoOcDwBzEXCTEVpgMEOuBUK1v375eY56SkhKj1fbhcPLkSe94YMCAAZ5Y0kZge1pamhrDJ/hmO8XFxd7xAOaeFksSYitMBoj16FK23r17q0Xa9lLDmpoa2bhxo0pqEhISVKmazckNbIcP8AU+wTf4aHspISoIMOcWLlxodXwIAUwGiBOkpqZKUlL9daxlZWWSn58vNndYvHjxoucXHqK2k5iYqHwB8G3//v1iKyiTRJMhvSuAMkpCbIfJAHGGOXPmeKVsOM9Fj3jbwDb69u3b1bhjx44yc+ZMcQX4Ap9ATk6OdwxiE5hTutQTc82mUk9C7geTAeIM6Ls9depU79KY3NxcsY1t27Z59fgZGRnSuXNncQX4MmPGDDWGj/DVNjCnUCYJUD3Au1qIKzAZIE4xZcoU75a83bt3y+XLl8UWKioq5MCBA2qMs+inn35aXAOX98A3AF/hsy1gLmFOAcwxlE0S4gpMBohTYOsWnQkBRGq6O5wtojQtfITgTndXdAn4pO+VaOyz6aAsUgsfUS6pj6QIcQEmA8Q5Ro4cKf3791fjY8eOyenTp8V0YOeZM2fUeOjQoTJ48GBxFfgGHwF8hu+mgzl0/PhxNcbcGjFiRLRNIqRFYTJAnKPxrXkoZTP51jw0rtHNeHDbnR/628NHfbMffNfNe0y/NVLPLZYSEtdgMkCcBKVsTz31lBqfP3/eO4s3kV27dqlmSWDixInSq1cvcR34CF8BfNdn8SaCMsgLFy6o8dixY9XcIsQ1mAwQZ5k1a5bXIhbK9Zs3b4ppVFZWelUPXbp0kenTp4tfgK+6WgKXGOF3YRqYMyiDBJhLmFOEuIh9zc4JCRM8XFHKhm1oLOpbtm2RriO7SnlluSR1S5L0funSJjbyIr2a2hrJLcpVdpzKP6XuVIiVWPWg0XX4fgC+ok7/k08+Ub+D7M3Z0mtsL6PiU3S0SG7cvKHig7mEOUWIizAZIE4zYcIEdUSQeylXMvdlSmDfN7capsSlyOoFq2XRiEURs2d9wXpZmbVSSgIl3tfiJE5+0P0H8uSTT4rfgM/ouLj13FbJPJwpgcNmxufZrs+quUSIq/CYgDiNKs8bKbJG1khAGl5vXBoolcVrFqsHQCTAz8HPC37QANj15tU35cPjH4rfUCLCEebH5+2qt+WjEx9FxA5CokFMXRhFvrgjHk02cEsXO24Rm8CWb9rqtHsWeE2MxKg30MKVha26JW2KHaZhyu/FFDsIaWnCfX7zmIA4Dc5+Qy3woE7qpDhQLEt/tVQGyIBWs6NQCqVEHmwH7M1IyxC/wPgQYgY8JiBOAxFYOFRJVavaEe6/H669rsD4EGIG3BkgTgNVejiseGFFq77x5ZzJkXXvrGsxe12B8SHEDLgzQJwG5Wk468WZb1Pg66lxqerv+cEO04C/iZ1CN/FhfAiJDEwGiNNA7IXyNNB4odd/XrVgVauLwu5nhz6TzpyX6T9xWp3IM22eafJbpsQnknYQEi2YDBDnQZ362iVrJTkuucHX8SaIr0eqjj2UHahjXyJLpO+1vuI39uzZI6lVqcr/3u3rrzY2LT6RtoOQaMDSQuIbgjvLmdLhrmf7nnLww4Nyq/qWane7YsUK6dq1q/iBqqoqee211+T27dvSqVMnWf7L5bL/wn6j4hNNOwhpCVhaSEgjsKCbUBbW2I6es3rKZ599Jrdu3ZKtW7fKP/7jP4ofgK9IBABaMXft0lUyupgXH0L8AI8JCIky48aNk/j4eDU+ePCglJe7X74GH+ErSEhI8G6YJIREByYDhBjQknfBggXen7OysiSM0ztrgW/wUTN//vz6tsSEkKjBTyAhBjBgwAAZPny4GhcVFcnRo0fFVb766ivlIxgxYoTynRASXZgMEGII8+bNq79YSUQ2bdqkrvV1DfgE3wB8nTt3brRNIoQwGSDEHHr06CGTJ09WYyh/d+7cKa6xY8cOpW4G8BU+E0KiD5MBQgxi2rRpXmlhXl6eSgpcAb4gGQDwMT2d3fwIMQUmA4QYBHoNzJ49W43v3r0rmzdvVoI72wWFsB++wCcwZ84cad++fbTNIoT8H0wGCDGMMWPGSN++9d0Ir1y5IiUlJRIT03TPfFsoLi6Wq1evqnFycrKMHj062iYRQoJgMkCIYeDBv3DhQlV/X1paKhs2bLB6Z0CXEiKpgU8oo7Q9uSHENZgMEGLgwxNvz3hw6gY9hw4dEluB7bqREnyCby4cfRDiEkwGCDEMvDXjP2gH2rVrp762ZcsW1a7YNmAzbAfwBT5p/7g7QIg5MBkgxFBwqQiqC8D169fl888/F9uAzbAdoHqAF50RYiZMBggxGNTi48Yxfd3v5cuXxRYuXboku3fvVuPu3bt7PRQIIebBZIAQg8HWOjoTgpqaGsnOzhZbQKfB2tpaNUanwbZteUkqIabCZIAQw0H//v79+6vx8ePH5dSpU2I6sBG2grS0NOUDIcRcmAwQYjgQ2gWX423cuNF74zYR7GDARgCbcSshxYKEmA2TAUIsIDExUZ566ik1vnDhguzfv19MBbbBRgCbYTshxGyYDBBiCTNnzlTtisG2bdvkxo0bYhqwKScnR41hK2wmhJgPFT2EWEKXLl1kxowZSkRYXV0tW7ZtkW6jukl5ZbkkdUuS9H7p0ia2/grkSFJTWyO5RbnKjrNfnZWb1TclVmIlIyND2UwIMR8mA4RYxIQJE+TAgQOSeylXMvdnSmB//XXAICUuRVYvWC2LRiyKmD3rC9bLyqyVUhIo8b4WJ3GypNsSGT9+fMTsIIQ0Dx4TEGIRbdq0ERkpskbWSEC+SQRAaaBUFq9ZrB7QkQA/Bz8vOBEAsOv3lb+Xj058FBE7CCHNh8kAIRaBLfl/y/+3Jr9XJ/W9/l/NelX9vda2AzsC+mc2RSTsIIS0DDwmIMQicDbf+E08GDyciwPFsvRXS2WADGg1OwqlUErkwXbA3oy0jFazgxDSMnBngBCLgEgvHKqkqlXtCPffD9deQkh04c4AIRaBqoFwWPHCilZ9I885kyPr3lnXYvYSQqILdwYIsQiUD6JqIEaa7uiHr6fGpaq/5wc7CCEtA5MBQiwCfQRQPggaP4j1n1ctWNXq/QZMsYMQ0jIwGSDEMtBHYO2StZIcl9zg63hTx9cj1WfAFDsIIc0npq6uLnRt0P8RCATUnerXrl2TuLi4FvixhJCW7PxnSgfCaNpBCHn05zcFhIRYCh64JpTtmWIHIeTR4TEBIYQQ4nOYDBBCCCE+h8kAIYQQ4nOYDBBCCCE+JywBoS44gCqREEIIIXagn9sPKhwMKxmorKxU/09NTW0J2wghhBASQfAcR4lhs/oM1NbWSllZmXTr1k1iYppuP0oIIYQQs8AjHolA3759JTY2tnnJACGEEELchQJCQgghxOcwGSCEEEJ8DpMBQgghxOcwGSCEEEJ8DpMBQgghxOcwGSCEEEJ8DpMBQgghRPzN/wcKyk509+unAwAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "hexagonal_reg = qse.utils.hexagonlattice(1, N1=5, N2=5)\n", + "\n", + "qse.draw(hexagonal_reg, radius=1.1)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Kagome Lattice" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "crank = 2, prank = 2\n", + "rcut is 3\n" + ] + }, + { + "data": { + "image/png": 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3iJP4GwBOSD1rMwEPQujr/N3gApyAG9M466LvDYQD57FATldgjTH3R1dS170yc+bMtMcee1QulK4m4FKEfe5mKhUDYm6mQvp+de6VVREYBd6J9yNToAknuTDdFoxbB3ngZe5mKrmLwB/CDTjh32hxK7lXosDovhykBsANN9xQuRF1JdVZS0qAkMS6dVUyXk7ohYEe1gngYOZBT4MQeIB6AxBQfIODQE7oIWh8IEK5vzs3d+tLL5mHYcJEYHcJhKuDPOgpx0kuDOR44R40Z3Lw20zAbYSed+Gd6vzdMcAzx5eCATgVv2ZOgPtBGB7vR6Q397Lmo9kr7DHmwJ4bBHhHAy9hWuAEoaDOXRSFvhh9H90rMDnGuPvuu0ctMAJkBfCJrqQ633juPgHQmmfPnj2QkJTH4/BunGHw4vlpyo4ouVcUDBBAxa8CYylzogmWL19e7RVcSayZUBc8mANzBZ8InlasXFOhFwZ6WCeAw4+vE8Zl0FMXYha1G7479thj0+9///u0cOHCgZ6vpgBRg/lBpGNp1i7FZhQMuBamyf3GKFjIZlCAkE2dOnUo6CnOtzSfEuMjnoLKe4MKST6HuWuS5Z14N4s4tWlW0W8MLrkf3FrwR7wPAqwtcRCsdR5x7zObtGCA92GvsedKAZNNIO59B4QsTPo8o+teESeAJYRhdHZUHBQnPBurGqm4uIdK820TBgC0Z96lKRi3BK4jmj64ZT6sNYIO71kKjmw6PwgC3M89CEYIC6M5PxdffHEloERXkvPtKoAiJBFr0iXO5OWEXhjoYZ0AiDJEoMT0gBIxKzE+TKSkmHWJAi6Zu9VyYMBoaGqyeSpV3XiaSiFsMGC1pdHkYGOuRXMlKjxnunWR0CXGx3cEk1GVkECqNihlR9gXgXcCR02Bl3WZE+ASnIJbg74GLW6kK4k1jq6kOmtJE+NDSAI37L02qMuOgPGBE0zeMPWmwMsIjGWBHBgoY8D0tBgMWtwIVxLrYdBgCS9d9graM5koXYJx62pp8D4IJGjyupma4nFKmROMS3xM6fx0TWtdtmxZJQxo6s/n3bVqIu9EXY8bb7wx3X777WlNhV4Y6GGtB/yv5MRjus19gXXant+VCCXaDeZF/J+jKQYkkTDCnn/rUqnqAuFivvNocrBj/nwMeoq/D4ITgqesx1CHky7pXYNE2MfMiYhLcTKa4kasKc8kQG4QnPiOEdrqMbTVAtACEAs5tQVexkA4/o6BcKNJawXQon/5y19WriTLcguxvHMJL6Xx2oJx81oaQCk7Ig+8BC91gXgx1VY3jJaT0RY3Ovvss6vnE3ibwyCWAYBxUFS6BuO+HNALAz2s9WDQExpJDk1BPiXNBoCYoCFhYpf4dCVgObQResb3u7ZAuEFysDHTEvSU+3/FieOVnhGvicBYmNg1AcfgyEHSu9oIfSkQrqlATtcSt4zPmmIpYY1zaNL26kzv7Dn2nvUY6qxFdcWA2gIvYyGnQTIn8riLpiBVcAJ+cREMwvTqhIFSPYYupaPb4nG4Lq/v0SQwlqCrYL1w4cIqJTBmJUWcDCoMALgaEOQGjTN5qaAXBnpYqwHfL7nwsX76qhIzgPr8EAtK8g5KwLoQesztFLtBo2SsQQPhmrRANL2zzjqrMm/GoCehlGpZl0oXgbEYk7F5RtdiQE3vEAk9uAAn4Ga0gXBNWiAxD4zF2q6uvcL31mPADNy1GFAT2GXSQk64e/iMNnOiqXcEAiPuH96htJ+bcKKAVMILgZnMk70ySDGgLoGX7DmCJcEJwlEXgXEQwfqpp56qmlJRnIsiXSWcOKdBgJgOslfYh13chi819MJAD2stQBTQyDDj5UFP8ZomrQOIxEwNhu+Q5DEBQ4RHQ8BKwBgQBQikjUxMLxwt5Fog/l+IGtaNknm4TavJGV/0dzMmY/OMtmJAXcG0QgCc8Bz+v0uBnLZxJfasIWuJCds1jgJPW3R4SUDSWoTQQlc/GB+4aLMWdQX3HBYBgy4Ze1VwnUffM+cdd9yxYnoxb3+050drEWNhHbDC42iExRIwd/YGz9DCZvfM0UIuGFx//fWVm5C9Mprz0wTQKoI8ccusadALAz2stWDQE0SnBF0IfCx2k5u7iQAmyAzf4aoQMEEfOVo1wgs+eLQZA8G6BFy1AfigFDO+bCPLc/NwXoa4jvGV/N2MiXbDM1ZHV7bYKQ5cgBNwY22F1aFB8T6sIeZ81rTkXtGc36QFA+6V3FpEnAkMm94PqwrMjbEMhINRw7B1M4H31eF3/u1vf1uZw4877rhhcRfRvdJFcHSv5MGRBGlSrwCBY3WAFRV5f6wOpDFiLYgdNFcVnnnmmcoaiNCray/vHeFeGQ0wHlZMBFMbI60p0AsDPayV0BT01EUYiL5diEzJ3G0hFVINyb8eLeSd4izbK3ONrZK7RtjXQQx6qsvBhsFK1HLwe68pmbupSoi5tmu1uRKAbzMnYqc4rQSWiV0dhJ61Yw0tJVtyr8gA63pH8D3XwBA0d0d3EXuQvUhmgS2MV1VgxEViIFzsoBmvGS3A9C3FDO5LcReW/VWALJ0fxnGvlGppGIxLV8jVITCalWI2ifE4PC/voDka+OUvf1nhggZnuXtFwUCcjLbbJG2fd9tttzUu1bAXBnpYK6Ep6KnOxJmnd/E3hz0yhlxwIGUL/+eghVQG6RRXIvRdUqlyaAp6ktjzrjIwtcD44TvN6zKhUo0GnsGz8DkPClHrr+sUt7oIvfnzrCEpifkzogDIHNwfpdr3CkR5MSCBvcicR1OPoU5grAu8jBX7RlPqluA+7qN+fg5x/fO4Cz+xd0TT+SkF43aFmGoL1JUQNh6nqYNmF3jggQeqSptYGnMXVRQMPBPRmljXsbEOyGahV0ip9fPLBb0w0MNaBwSYEfQUm4aUQGLQlN7VpZgPJnf8k9Rs7wIx3xmC0TUQbpBUqtIzYXqYZUtBT/E6tWO1YnCjWdjv2wrX0NGQZw3Slc3MCQg8TLNLIFwMvBwNoWfNeF5elTIHtX33k37v2Duibf20JF1xxRVVgFsXGLS18CAdNOuAvUXaH+6eJvzrLst7RxhTo4DptXVAwCbjDOInb0q1XdUOmnXwi1/8onILUmq6TcGIQaol90obsKcRklAyBhUkXizoXqC5hx5eJnj2uWfThXdemJY+sjRNnTQ13Xb+bVXeO58SQJiMrFei9wA3lVWtI8AwZwgavsT5u89Pv77n10NzOXT7Q9O4sS8wCQgCxJbxIEpdG8TE+fA87rMKoZXlcmYU8fLY3Y+lu+6+K51wwgm1Y4sTYxPABQRNnMQ4gagN1wlcaDdf+cpX0oKrF6Rlmy2rxQljwpAh7DAxmN2gwXWWNoZJMBbWBfCbM7OIky033jJdcd4V6dWHNruStAZEBmfUPTgRL5EJ1jXFIeaBfQmRP+k9Jw3btxEvjMM7sMasK8LOoKWmrU4JTtlzME9wm2el5Ofnvivvq56Hu6cOdJ04V+aoa8vzpZnccyZjzIHv0bZ/9KMfpb332Ttd/+j1tXuFsXgXxuZdunQUzIGzw1zBLa4F8AqecmEi4iU9mtLvbvxd+sOP/GHj8/LCVO4Fe2l4fgAFqbq9Dk2h7sVll1+Wnpn6TC1OXirohYEe1mg487dnppN/dnJatOwFc/TkNDmd+rpTR1zrYTTwCYBZNGl0XYQBgApi/+uy/5VmnTIr3ffMC4E/MybPqObypl3fVBExiJmNZVY1wr6J0JfwsvVGW6f5S+ant0152whmJ04seSuzy58ZLQIStqgZx3vQbpbvujwd+X+PTA+veHgETt6621srDQ2ibLrcIA1iBiX0JZxsNmaztOtmuw4bQzz4kcGXIvUjMef9EWhynOTEHuvAv/nKv0n/4XP/Id39xN0j8PL6nV6/SgJjDhZyYm4KSgiPjFt3fj57+GdHvGs8P+IJXJdcOFqQcsHA33JhieZhX7/g62m3r++WHlj+wAicvHn2m1dZYMznaLlnrWxx3BJettxwy7TXw3ult0174fwMmmoZA021utUJBpXwNzel1//i9enhNPL8vG1u/TxeDBizooO9DWTi+8Gcldd976GHFws4sMefcXxakQr53WlM+uEJP0xvmfOWYQQsmnM5iF3ysSXuTYyqbi7MA/jm0d+sDi/nY1XSnOpAQs9xPXfpuendP3p37Vx+8I4fVMQ1Mjo/vKuEvAkMkEJwiIwzMsF//t0/N+LkW6/9VnrDzm+oiPKgDWK6APODNqHBnr347PS+f3lfI07YK6X3kJF1SWXkWV5X2ncymref8fYR98a9csIeJ6yywFgCLQ7slZ/f+fP0gZ9+oPX8yMzjezAvBNuS0JiDFhNjLkr7rm2vgBOER/bKqqaUliBaHDg/J/34pNq5/PCEH9YyYsbpcn7qBM9Bzk/TPAaBrvy7FwZ6WCMBE96sU2cNk9zzAzN90vR048dvTBtu8EL0f87MupheJWZ1RKjrXG7/5O0vqnmPOS57ZFma+425aeljSxvn8vs/+n3aaMOVJv5o/ehK4EvXRi1w+bPL0+yvzU6LH1lcO49pk6al20++PW0w7sU1QD7x5BNply/vkpY8tqR1r4iTuFe6CINNzCBq1OyVOV+bkxY90rBXJk+v8PJi7pWnn3k67filHdOSR5d0Oj+560O3SBdhunTWIgPssldeqvPz6GOPpjl/P6fx/MyYPCPddvJtxbkoDI7GahEFg2eWP9OKk6Z5DAJd+XcfQNjDGgn48uqYL4A0DcH91V2/Kh7OQRuJNMnEXefCdS8mMM8FDyyoJWQ5XnKzflvdhfxZ8Z48+p7x6wiZ8+D3ixa++H3cmUudIBBxcvndlxezI9rqLnRp5KTr5dIll9YKAkNzWfbi75VLFl9SKwiUzk9pr6zK+YmxF5ctvax1r7xU5+eK+65oPT8Lly0szmWQ81P3fLMvupyfunm8WNDHDPSwRkIV1NMBvvLtr6QL0gUv6lyuTdd2uu7Lp305/TL9cr2Yy5oyj34uqzaP/vy8PHO5tuM8utLB1QG9m6CHNRLOv/38dMRpI3Ogczjv/eelw2cdvsrmvKbrz7vtvHTkt49sHePs95ydjtjxiFUuQ1sCzdDM5bX/e2TzoS54GcQc3uY+6bo+Z510VoWTFyOOQpMrODnm+8eMCicGeXWt9d92/Tm3nJNe893mNEb3ypE7HfmixAwwx3NvPXfUOBnN+WnypXc9P3VzWR2gK2dVzs/yFnfiS0nfBoHeTdDDWg2k1+AzM5im6JOeMC3tvfnexYpxwCBMua45D6lsu226W5o6YWrjXJjrITMOKXYQHC3ETok2vzl8x8Mr/2rte+B/nTg9HTTtoBG/DVpTvc59wlzmT5zfCSes46A52E1Q6pR42KzDKpw07pWJ09L+W+8/4rdBXARATMPM50XQ3pxN5nTCy8HTD25tLdwVSp0SX73Dq9OMSe3nZ6/N9iq+S3XNatgrrPvc8XNbcTJz8sxqr6xOKHVK9PyMZi4rVqEnQQTWZ4/Je7wsOGmCXhjoYY0EgmZIr6mLhAY+e8Rn09NPPT2iYt9oDm1eZMeKcEjTm26yafriMV8c9uwcPv+az6eNN9q42Ed+EMGgqdVrNcfnVqS/Oexvivc6t7869K/Sgw88OKxV8mjarkrgnfuw1sJjxlbv3ISTzx31uSo4bdA+8k0CQN4psSqRnMZUc2naK+Ds0UceHVHaeBDfeI6XvEAO/06ZPCWd8tpTGvHyhaO/UO2pttbCbTgptUoeKh09boP0udd8rjz/5+f1t0f+bXrm6WeGShv73NEIA3ksha2FqxLCG21cvXMTTk553SmrJXgwPz+xdHRlEVuR0t8d+XeNe+WUmrkMEodUAgXGqufEs89V5yM+t+s8XizohYEe1lggLe19G78vbbXRytr9Alre99/y/fTOPd85lKcNk5LQj0YYkMBDVK2Hb/U78pNJ8Tnt9adVEfIRyNn+2hFfq1K0Yk5xrNEeBYO62vd1BExTrVYCxpu8eHL6wPgPVJpfjpczjj8jnbjXiRVeeJ6EfjTWkqgFW0KYMRmbtDjS4779hm9Xz41Abv+ndvhUevu8tw9ZA2LVtthHvk4wyEtHRwFAvALi66DNDkonpBPSduOHd69kbv/0tn+q9opVIC37G3PjR7NXFBjZe+xB8EIKJTUnKrxke2XKmCnVvuV3LT2l3hFNgoH7oK5VsmVy+YD/D036UNpyg+FtrJnX9978vaHzw/627K99OkYrIEWBke8wT1Mb4x27v6P2/HzhoC+sUgpdyVoU8RrPIHPa7sHt0kkbnDTCwjZj8ozadL5VDR6MFRVJnwTv4P87b/rOiPPTNI8XE/qYgR7WWKCKG/XvP/FvPlFF315/5/Vp1+12rUxnWAQ4VPoCIV4wLA4dhIB9OkhFN8ZBizGdDmYXo6KtFDd23Nj0/675f+neJ+9N82bOS3deeGd68okn04c//OFh+eo50ciL/+TaZczJzu81zYt5QGS//vWvp7e97W1p7ry56UcLfpQeG/tYla62zxb7pAnjJ1TPNz6Af5k7YDGkQcAiNgD3Wr7ZZ0DcNh2/aTr/tvPTzXffXOFks2WbpR//84/Txz72sarQkHPP/cl5DrYgbuqKHXmv78jv//AP/1AxtXe9+10VTgi82m3GbunA7Q6stEHmHoUOcOJaU+p2EOZnzjrjIQTwXIUVxuE3viOl7l+v+9e0fJPlaatNtkpX/vOVae+99q6a98T4jVLxn5j7n0NdsSNA4auKWP/Vr6qqmX/4sT9M1y67duj84EJgz3J+APtRcHZYa8YetDaEZZURJngn7ve9mIt7aIMNN0g/vurH6b6n7qv2yoNXP5juvP3O9IlPfGKgglT5eepyfngv3vHLX/5y1VTqlQe9storT2/0dGvlv0FjSwTuYT/wLzhhv7k+zIuiXBMmTkgXL7r4RatA2JV/99kEPayRgMZFXXnaq2JSJYhm9kazq5K0HKhnl6/srGe5Ug47zI7/h2HyYePnpVmbCvpAyKjkBhFUC4dAqZkyFs85eNrBFdGh8c19E+9LX/3qV6uubHQKVGvLg69kWoCam9+r0ZUIme11He+nP/1p1YqXim4Ac4HhGvMAsVN7Zi7cx+8QArRhvutSGInnghOIFTiFmMicFLIqQWDTTSuXAUGCe0zaY6gZ0IIrFlRz/YM/+IMhoUSNLeJEHKnd6cM3GK0kCEiYtTbQp4JeAB//+McrIgpOuIba/TyP9+B65i0+bQqFKZtruzA/e05AXJmTeLfhFXOF6dnMiOsPmX5I1ewK2OKoLdJPfvKTtP/++1f7zLLPufCY10AQ76allUrcKhy5PuzlCy64oGqetOUWW6bDtzg8zdl4TvXcihEtf7baKxY+4l7WmQ9nj48WoLbzo3AEPtknlSAUrBb2eVB4Z314F/bKE9s+kU499dSqV8LhhzcHynWtdlgnSHMt/Qd4J/oCcA9zyRtYlWBQawnPReAEx5wRrFIKLp4ffmPP4Up7sQInB4HeTdDDGmsVgJjDYEu57xwwTaUSSYmEjYEgzAgFEKkSQKBs8sJ4Mg++51/N2R7aqLEKMIQDDjhgqCubZslo5s3N3VwDwUS4sN57NHNKNBxDBnD99denO++8s2rQFMF56YPmfWOteMbgWbwfgLmyrlVy3imOe7g3+qT5l2fY8Klkaqck7x133JFuuOGGIaYd67bn5m6uARfWo7fyYe5ecQzXnN/QflkDW0FHnPAv47KGCiNxjXk/1p49wF5QSMuB9wUnthZmjzkf19w1ZLySWZleANtss03V3Cni0n2huyiau8GvFh200pJ7JQoCjnnWWWdV99KKt7RXmKNM2nV0DjB0hO62Dpq8O9Y08Mb9Nk6KZ9LzY1nwPGCTeRx22GFVF0X2XWk/NjUaKwmLgkK360NXz+uuu67am4Oa+1d0dCflTcpsnJRbDe37MKil4cWEXhjoYY2Dm2++uWrteeyxxxZrxUf/sYRKAqEmIHMvEfrYKY777BRn1b3YolbGKtMD8jnR/Y0x6WUPSKA0uzYRsLo+8pqxox8YAr/XXnsVW/E6N97XfuuR4fAdz21qlVzqFMc93JsLF3xnTf0SoUQb3nPPPStNTGavlQWibzfGGEeg5hWLG8UgO91A0coCznl+3oo3Co5WUVQojIIEv9sqmefA8GPgpYFwUWCUkVp1z3lrlZHplZpiIcixv/loFZKBgFP+jm2V870S4wO4lnvYK1onuBYryYIFC6pOjaVWvM4tCkmubzSH13XQjIFw/G1rYSAK0u5lxuRZdecH6wX3s7+bgiPdDyXXSgSFIwVvg4MRwnbeeec0e/bs2ntXRRhQYGQtFahYv7yRk02gVDDWFOiFgR7WKODQYRWoa8UbGR+HSe3R3yRCakqR0EO8aH8MseT32FpY4hGZkocW4l+yCggQTkyc9EJnfOcTGX8bAQNkmAoOmlg1+UJs8DeX7jPqXxN1ZPKa22VgOaFfunRp9eFvvrO1cPS1RrcCY/MMGVJdRD6Mj2tpXasmKzOL79oEEXcySQAcs46XX355pVmWNKy4ZgpJMZDSTnNaGtT4HZu1ZM9EgTHurbimkekBdXuF1s+77bZb5UJhPtwXmyTVxUjk7xXN4zJImSdj17XijVkz4kwtNbqsFJS0KLFuCEXghI8CI/jiHq0Uca9wv66kmLqbv5tCEvFBWJPqgiO7auZaVaKrju6AzDu3qnWBFQ17vElgjHsruoLASdzLawr0wkAPaxTAUNHaaY9bgigM5NqNIGGNUeiabhlbU65mTAlf3rVOpqd2VdL21GDQgmGiZ5999hAB4xNNu22xujHimfscg3mAFzonytTzgDsgWgc0Afu976HpVPM536FZos3wt9pKNLGKJ4AxtbzEZ0a8ae5mrvhmmXuMZcjXpwki7iJOmBOuGbQvmF6phkFMd/M9opAknuMe4BpdUOwVTep5RHoUPqIrKcZARJxEdxHCC2NfccUVQ+/jJ8aTNIGCmpYV9xwWNVxJWKtK2Svx/LgHopAknqOAzDu53sYGcJ/WMt1ZCnmOH11Jjl0qBc39xMHstNNOlSUppgIO4qd3rKiFA+Dh3HPPrWI1oiupK6yosWgMS7UNAqPWs9xKAkRX0poGvTDQwxoDEA+DntDSShC1YEATsNpNTGMzehh3AL5NApgwEXJoYYBoffwr8YgWAZlpDCqTwMdUQBkr8yDY8ZZbbkm33Xbb0D2O3SYQ5L7weD9Mj7nj/7VtbDSh5tkJuZAUg60UCMCHZt5Zs2ZVGit/8x2/RV+rYzcxvcjsfE/uZc7MHWIciWkeW9FFy4v3g2MYHzh3D+S+9IgTwMDQKExFrS3uCXz77BXmDj7YQ7x7DOJzDN0okenFvZL7u7fddttqj7PX3beuWx5b0cUXHvcQwijCEesZaxjkgpd/a73SheK8ZWJ8z7uj+cLAdtlll5WBf088ke65556h2JOY7uleiK6kuvMTYx1YS7R3LASDQh5UGvcKlil+R0AaDawoCHYx1TZaGOP6lDJooitpTYNeGOhhjYG6oKcIuRasCRiiJVOR4HBgMd1xMDFpmu5EgJr+PDQ0fa785r0x6KkU8Fbyd8NUMQHjm8y1MRlWSRuOxCNPr4pBT5qQ1QKjtqrwUjIBR4uGGi+4wQRsdDkf/uY7ftOCAsj48qAnmbXaTozlkFFxrybgRYuGN/DxfUvacNTC8y6L+n/nzp07xPTyuIs8IBNgPlzD2sZANiO/eWfGYm9o2mbPsHcYh71kzYZ4bzSF+2wzBerM3bo20IQjxKBMrRXxvfOg0ghE5PNuWNVk6HnchXOKhbC0hMQaHQp+vDO/4QPno6CJhs0cwJlplnGvRFdSXM+41rEWgHiPwbhdoU4LBxBimlxJXeC5cH44A1gCEILYG+Ahmvvj+uQMP3clrWnQCwM9rBGAllEX9JRDrvFJdDB1S8SQ2jm4HFaj6CVCtlyFuG233coiNR7wyEA123KIDe6SeNWZMPHpo0lCgHKI2rAMqol4NAU9RU1fJpNX6YP4GUzIbxbbgeGj3fG7DEBGw3f8xjUWXzLWgLH4Pa+umBd4yc2pzB0TML7s3DISM0HyTIPcSiKQP8/cSq4kBQPxYpCdczVq3vWMmRPsBTQ890fcM1gK2EvcFwMv2XNqgFomooYaiwHle+Goo46q9jx7P19btdt8fWLWSATe49JLL63cMnktCQUDhT7uVbCN6YjWAojFqhAQsWR4T1wfgv4IFGVsq3UqxIA3mF7ckzGmRZzle4VAUMZHm+8CTVo4gLDFOyBkjBZWPG/p4FxXFRU33riiKSgV8RrfsbQ+xk9Eq9qaBmvmrHpY7wCmVxf01Fb6VO0GwpxL7ZbxleFAxKMWwSdG2EOY+eib19wdtfGmQCbGOfDAA6t0t1JKo8+EcPB7HfEYJOgpEvuoBQK8K2NYUVG/ZjSnMo+YNcFvBl5asY8xZAaau2UuXYK7eAeCFGF+uUAQtWHmYRZFqQhNdCWB6yac5FYKxjezgTXOMyfinuBd2StRCzfwkr3FHgMnWhOiuTuuQxMQZ4KvnL1fmn/MBMkzOnLAPcCavepVr2p8ZgxOdSytF1hHWCMELRgd6y/zcn3ASVwfAy/R6hkHnIJbx9Va1HWvgGMEAgQ+tPomaBKkgVtvvTXdeOONxaykrvDc83EBnAHAzIm4tgpqQN36aFVb04IGI/TCQA8vO/zud7+rorcxhXeB3DIAQYA4Q8wsNmMxIsHI62jOFGT4HHKuQajgA0RC05WgkFlgMGEJfLbBTqVxIbhoRwQNQmjbIPrwFQwYw3dB0+fjNb6PrgaJdsQJwD0KWnxMvYyMuoumw5qgtV544YVFf7h48Le6MXEloelRQa4LiNtoZYCh8S78ZgGmuJ98tkwy3ysQdO6zuqNVL2MaW9e9wp6HgcK0SsDctFTUFdfB/cL9WKW6rIXnJ1pREIrAicWBYiqg93h+8kBA/5/7mK8BqTGWoCkaP4f99ttvKJiwBG1aeMxKIhUX991o4Inn4yLADWdQgbGrOytek7uS1kTohYEeXlaAuHBoCUyaPr2+G1+JmHHIhhp/PPdcZd6GIOXMJkruMDdzf3OzuvEH+KEhhpgErWE/SAUyiCtmSbRg5lYiHszBMralwEIEAa4jfqIrAREv+jUhZjBOtE9/j750P7yrwXV+YnoX780YjMWY1rAfhOkBvItCTml9wAU4cX1y64+uJHDb5krKrUj2nNDMyxrHlLfo9nB9FJ7EV/Sr8xG3jGHgYSyP2wXY8zA+zkD+vrpOXJ9SbAXPwv2CuX7OnDmdnuma8TwL5PAszo/R9q6JAZm6zsAJDFF3SAyOBJgnKcG6mazvMche4bpDDjmkEnBiMG6cV5MWDuCmQ5vvKjRG4H2sN6GFpBRvUBf0m0MUFtdk6IWBHl5WuPjiiyvfZF0qYQkgtFFqx0yJ1G5amOZ3IPpazYsHNAMDBllBBDj0fDC5QhghgFbsGwQwAUNcIdRC7gvXjJ1nGkBAMZNiYRgk6AniZOYERFkzrxHdxhGYUWAgnUzGwK+YsiaDYow4ppXn6jIBSsB4EGcItSbg3BcecZOnC2JOh+mh7Q0CZgkwFmtqNT8+9ieIJWJlXj4/1gOIOf1WSmTvsQfjnhxESGLvcwYIAKzzhZdiK4BrrrmmMu0Pkj9vICtzRRjAymEgHO/kHnU9fP+4VgZOWtgnVh60kiR7hWfJWNtSa0v1GGIwbhctHGC+FKPCXYfA1hWefV5gjBUVTSvNoSnoN78OnK2JqYQ59MJADy8bwGARBvBzdm2gw8GC4XEvhAsiFk2a+jglVDGHWh+jGQXWHpBJmz+vhs0hh5gQaGh1sbrSrDkwBr7K22+/vdJw6iKeS8FiEEAjqwfxa8pgIWJmTlhICcYnTqIWJ15kMH6nNcSgJwv0GGHPM5grz4wV+9rgFa94RcU8MQHLXEq+8Oi7Zy64ktASwWlX0IpRtRaeMmWoQI5aaqzHoKtEBihO4ncKCebPxwJDRtizr2IHzS7A3kcTpiQvgkudLzz67tXIiby3zHEXiAVyDISL5ZMVdtznMUPEcxKFBc+PKYy8f6wSajwG5xCcxFbJbWAwLj1KumrhupK4pq3XgcB8Hs0ERuMCShaN2C+kLUUwz0pak6EXBnp42YBDKyFsA9O/ICgQKyKcow8umvH1cSMwyPxL0d2R4XCtgkQek8A9VuwjYIxPl8IwmIBpKARzz8scR4jM8Pe//32VP4+m16ZdypjMd0aAgOnFfG/Ht6KgneX0AVv7no/alkFrukiiFuaYPMOSq0afR4tMm5CEgGRJ3jpzbywbjBkda0sXVxJr4zpp4YmBWxJ4gwLzlEH2BEyNe9kTBo0am8LeUtOLwawKGOxNI+x1HbQBZ4B71YTrfOGxbgVBquxdMnDaQJeArYURHmITIt/dd4CJmV4qrvLeETEFEaad16UQTFuFwYI/xu0iKBmMi5YPHtu0cIB9SOMqghC7mOXdu0888cRQBcr4jCgMRGtRlwBRFZE1NZUwh14Y6OFlgcWLF1e55+bP1wEHMPo1I8PLc7CjxhTNc03VzAygM0CrlK2gDzhG2MNAIGpNhJ770E5gNGg3bcSDORJ0SPxEqRRzBN5RTQtNHbzE/P+IE7U2hQerAEbiHVMVrfRnXEAsbhRNtgDX8mzmwFyYU1uOOO9GuiTCYBtxB2e4TNgD4LJJ2GBOCgFmTiDkxKp4gO+iNUjGxF7JS9/GGgaxJ0EeP5AHoyoocb3m+Ka58zxSDWlGZTR+07UwR/YUQkRThHoskGMJbl1q+R4328J0VF0h7pVS7wgFaPeI+8zYCcfmGv3v1idAgGhzMxF0Cv5xoXTRrnHL4Z7be++9R2VhjBCFvOgiaYpVKKUSrslBgxF6YaCHlwU4tDvuuGNj0FPe+IOP0n4MIoSAcW0stcvhhoi0EZuYMw1ERhaJWYxKRyhAizCVqkToJR5cS0aAJuAmwJcOgcQ8WleWNu8UxzzMnPBj9HnECf/PXAywbGM2RpVzj3UKxLMuhPhM5sBcmBNzqyP0joMQqAm4CcCZ+fMw9lKwZRQYGZt9wrxjFkgUiqKwyH6CaUfmVQfcz5hcbzBm3HuOIW4ZG5wwH7XyUrqpvnDOAmcCK0gbmFWB5lwqxRwFRlNtmYeCg3N0beNeARjbNthtYEtohIYoLCkg5II268j14Kqug6bnB3wjJKHtWw+iDgw4bEolVGDUwsg86to0rwgFmPJmQ22gK2lN6krYBr0w0MNLDldffXVasmRJbdBTXeMPIfooY4U9K95pCbDaXBORj4c2Vq/LteBcq2d825PmhD73hRM0B7O0K1tb0JPaUwwWq+sUF1MKvT52LVTLNUgOPKoR10G0qnhfHMsCRPq2xRNzMRitROijL5x3JH7AJkZ1AM7AHTjMYytygZFnsybR2uBeMTDQtWOvuEesRVHX6lr8WorZ++Kei4GGCktCUwfN3BfOmeBscEbqAIZHDAXXmuYZyzqXAuFiqm0uGMU0w9izgn/bXD+unb0KPEOuQSzbHYVD3lcrRd5BM9fCcQ8ROBqDcXMA3whRuOWoV9KltbAVFZvWfEUQSroKAqVSzGsD9MJADy8pcLAIetpnn31GBD01Nf6IBEwGabqOpn6ZngfcwMI6s3UMegJilHJesrWOCEjoeRYE2J73UYtgPmj7uEVwj5QAnPA+Bj3FYDFwYpR67BQXgx9lQvpVY3BX9LXGkrxdg568X81XU7qWl1j2NwZexkJOVqeL60OJWP6mb0EJwBXR8rqSIk7BMbgG52Y5xKyJKLB4n1px3CuuqyV56yxJsZlVXB+DNGUWsWtm3jsib5WMZSQvsMSZ4GyAk5JWboDprrvuWqUkuqY8m+vtOVEKhIsplGYBKBjFXgWuT5uQlOfPi+fowosuuigYRDdT7KCppS2uNR8EH4QgYmpKoOWt1NXTVNsoMHaJJ3jmeQGrS6xCBHCS1+JYG6AXBnp4SQFNkEMWUwmj1B4bf5QarcSqcjJE075yyd1gKKPoc6hrGuLYUfBoM6tjhmXeamWm7QmkSeErL5mAee/f/OY3VSOVSKQgmhBIPswTIsa/pV7vMjvv1xReimTOWz93CXpSiDAPXzz5TC0G4sxWyc4ZC0GsYQ/wPYFedO8rmYBhepjNwZ1g+qNuCHAO7qO/WyFODV4G59xLOd8KUCUhqa5ojHjXZ+4zS70jYqMi9jZMydr/xmYIBASCQyot5oBbBRN3blUz4BMhCaEDQcyCRfH5nh8FOp4bq+Pl+9zWzyUhqS5/Pha9sjRzjFMB8rVCGLC4Fu8BPYjnh8BRqpOW6jFwLTEFuJLYC7mFMabadtXWlz9vHRu0qZDZFmubVQBYu0SXHtY6ePa5Z9OFd16Ylj6yNE1ME9NVl12Vjn7N0UPMBoJgahoH2T7gEleDlWInwgj2Bs/bDwsGwnFdrCUucYzfRTDAShNhG0jU0HIYVy3Hd2JudGX7+te/nhZcvSA9POXhCidTJ01Nt//y9mFBT0aty4BgeMwDQi8u8hKvEfI88Rw0BdtMJpqPm4KeHFM/sISd+cTyxMZxRBxjkuWdYGSMb7U6tGCEAUzA7z7p3UN75fF7Hk93LrozfeLjnxiaG/NlDO5Dg+aZMhTxIiNy3wi50FgC5sX41h4Q8la8OS6tVyDu/D6WsdZaoaDEeLwD95mhgIDAWIyBWwTrwF5775Wue+S6CidbbrxluvK8K4flzzOeQpaVAxkz7pW4X3KcgD8FodKai09wH9N/ZZaR+eb3lbovukZe4xnTgmK3Us8Pz0RQYG4oEF/+8pfThRdfmFbMXDF0fu678r7qnFiKmTGxEoADhYBBGfqzHVMHI7hHtaisbdALAz28aHDmb89MJ//s5LRo2Qvd6jYbu1maN3leRUwggvrWZMoxlampD4CBT9HXWQeMD3FQS5bpNR1an697wgIjJdBErpZokJnMy4h/iP/jOzyejvjxEenhFQ8P3T85TU6fO+pz1d/Mk4/FbMx5ByRMMbI7gtqx82/CiUWWFDjamF7ES8RJbo2R+VjYxjnzDhB1iLM53RJ6Ar7+9Ft/mv7D5/9Duuvxu4bG2nLDLdNe9++VXj/l9UNpotyjC0RNV7N/DC6NoL/a/dS05tZjyK0dTXUwjKcQ/+6B+LuMOe5vGQ6MnT1idUT2Cgz/W5d8K835+znpgeUv1OifMmZK+sZ23xgmMIJTA2B9vlDn544ZNM6tDtgfMGcDLrvkz7sPxEm8V7CYksw3riXCoym/4Ib3Yw2W77o8vfncN6eH0/Dz8xcH/0V1P9cqMBoE2RVWhOqGsa5GV1CBWVtSCXPohYEeXjRB4Pgzjk8r0vDgo4efezi94wfvSN88+pvpzbPfPBTEYxBTHaOrK/phsFaTfy6agCEoeSveEkRtWW1YM7AgofOa3ISMgCPzg9D/YuEv0mdv++wInCxLy9IfnvOH1djHzjq2mqOE0yAqcRKLF0VCrIYlQ5NRN72fQpIEE7zURVYLNuURd9ZPiGumoBAtE7HYEc+Idf0vuv+idHo6PaWVTfOG4IFnHqj2EHvlbXPfNix+RAYW077ES74+5oWbadL0fmr54ELriSb1Jly6B2NxojyQUUYdYw38GICnu+zcpeembz3yrZHnZ8XD6cQzT0zffOSb6U27vmmot0KMW4i9L5rWJwo8Te/nntItoPDbxvR8x+iWyvdkHCvGNiioQB90C3F+/tt1/614fj55yScrXHB+ojWuK6wIQb9aNQa5f23pP9AEa58to4e1wjWARSA/tIDf/dmlf5bGT1hZvCQvBtTVhBeD6Nrus7a7LoOuh1Yin5cN7pp3bIT95ltsnj59waeLOBE+c/Fn0qTJk4aCrmKvd0GCH9PA8jLHEuG294tNaroGPcWxS2WDnVepel5cZ96xMgmPSenfnfXvis8SV39+2Z+nTTZdGcWvvztajWIhntL6+MwuOIlxJqZRtjE9swlizEA0kUdBLe4VrVqxi2Bl6t90k/Spcz/VuFc4PxMmThi6r1RLI65PbMmct/yN6ZB1YDAu58esii649GzmmSC6bfKg0ljDwHWrCkBNmpj+8wX/uREn//Wi/5q22HKLEU3K2iCWOd4wFFMaZIwuVrU1HXphoIfVDvh9o2sgBw704kcXp8vvvryTAFDSwgf1yVlBDQ2jS0lTIBKFSCjUHPOI9Ca4dMmlacmjSzrhJBYDqnsXGY7pbDHiWW2vy7ysNsenS9BTPrbPFSex5W/d/bG40TUPX5OWPra0ES+LHlmUfnXXrxrdQXEtDJjLI9Lb6ggI4p8MiNH4f2MmSGl96u5RSFrwwIJWnMS90jQ/nxuLCUVBravgqJAEToAuTC+OXTo/QJMgHQWD39z7m7Tksfbzc/Gii9MgUFfm+LkBGpPpSlobgwYj9G6CHlY7ENjTBW6+++a092bNlcIAtTx8gbkZWwLXVvUOMPXKALg2cOwYAW/REubAfLoSDN61C9xyzy1pn8336XQt72MthiiUMGd8p10EAnDLGECTABKvt35+1CzBP+MQA9BF0BJuu294V7pV3SumpzKnvO88JviYYtgEXMv7tNUfEBCm8mtdH4TQugDXEtx6762r/fywPuz9fH1Ke7wOuI7ofMboIljFmhd169M1QI9zsTppT3Q35i63FS3pxDlw1tbGVMIc1u7Z97BGAhG+XWDHrXasfIJNhy6aWK10FsG0wbqsgAgwb1KUuD5nFCUwNUqzo0TTojq2c20iaLoxdthih9QFZm05q3Vu0RcOsSVQKror7CdgKd4m0MIBWLq5i9vEVsOx0qKVHLsEdeoXnjFlZIGY0e4V14fgzXx9xE8XYUCXB+/Eu9RFzEfQWhWbP7k+Vjhs0+INitx+8+ZS1BEnXfaKwZtWZ9Qvzr9mY3QxrSMgUfyHMc0G6SIMmA3g+rBfrbtg8aem+YM7zsXqpD2uT+n8rhhAGNAFY7vrtRl6N0EPqx0O3f7QNGPyjDQGh3AB+H7ahGlpv632G5YDnWsbuS+8DrqYgK1TABGDAHTR9uLY0RduBLbm11KP+VgLAIK4x+Q90tQJU1txsvfmew/dE4uzxLGjLzwGjfmOBpO1Ncgx6AlGwKeuHkN+j2Pra41pn6WWzPFezdXch4Vh/sT5adrEafX4By8Tp6VXbPuKYTUM8rGjLzym0sXiUV01PfDAODDaunoMEeLYuS88pvSVygbn1QCxMOw+afdOe4XzE3txlPAdW/66TnF9urpQDNA0m6Nr907jKfJYhejqKhVXys/PnlP2bMXJzMkzK9rTBPn5KQlSz3V0EcSqlGtjKmEOa/8b9LDGwbix49Kprzu1Mdjnb4/82/TkE08O1fXPi6OYjtTka+1KzOKh1fcpAW26xwwH51QXzBfzx3PizHMxi2680cYVTprg80d/Pj337Eo3hPfH8Rw/+l+F2IHRvPs2Ah+DniSMbUKSkfx16xPnJk6sOSARtqsg/7/1VlunLxz9heKzJPx//eq/To89+thQaek4XsR9XdCie8to9Sa8OLYBpmYUtO0v1yIWZGpan3y/W3iLz6SJk9KXjv1S8/k5auX5wdoVBbP8/OSCdFwfTfhteyXmz3OtwbhtfQsUHOP5ydcnCo+xnLZn0zok0JRTXntK4/NOed0p1XVN79El6HdFR8GxS1bS2gS9MNDDiwK7j9s9nZBOSNuN327Y9+QEf+u130on7XtSZW7n0OHLtPiJhWTwwwl1hMrgpDYtGAandgSowTZpNzINzdlNQYuMzTOcs6lJvBfEx57ub5nzlvT+Td9f5c9HIHf8v+z6X9KJe5041GnPin2+H+PBKEyPK4HWilgaeJCgp7aSvOJFi02Ti0RhgDnHHH/eiXfjHS3jPGXJlPS+jd+Xpk+cPgIvp7/99PS+A95X4S/GfCiAgHPXtwQyHFNQ24SBvCqlsRhNQpL7MGqc+XziM5kze1x3Cn/zXtzDmcB6dfDmB6d3pnembTfZdsT5+dKrvpRO2uekCn/cb8XL/Pw4r/x9FQhME/UduubP6w5pEpLEs3ivOz8yXs+PjJp/wQnfk3WCq+Udu78jfWTKR9IW41YWXBI2H7t5+tQOn6rST5vWqGuzoRUdhIF1IZUwhz5moIfVDhwmyoa+fe7b02lvPq2K8F3yyJI0bdK0tOjiRWnczeNSeuVKpgmRV/q3T7w513lxobwrXBfLgBH3eeBhXbU5QdOmvtV4r5qYmgFzw8zusyxFnOc7X3jhhWnOc3PSqX98arps6WXp3ifvTVtvsnWa/NDkdNbPz6pK8sIMmCv3MT+bzfD/fIydMDgw1r4HJHaAed0lYlXKn8/rMZTW1UJC+bjRuuN8zC/XEsBvfAdxl9nyzpRi/uPX/XH62vyvVXhZ9PCiCi8LfrQgbXH3Fint/kINews5uVfUVhVQSoV39JFrVajLYNHNEt9dSxLPq6voGAPR8joHzisKru4VxuR9+M6ufwLn57XbvzaddtJpVXbOXY/dlbabsF2674r70r033JtWHLnSQgMurUIILq1gaJBf0/mJli1jGkprXmJ6eT2GHNTyS4WgSueH8c2+YK9YYMp4A4DOhTMemZGu+8h16dpl16b7n7q/ihGY+dzM9L3vfq/qZUFMUA7R3dgW5LciWAS7uJIGCZZd06EXBnpY7UDTEAj2+973vjR2zNh0+KyVzXequv2veyj9/d//fdVwZPbs2dX31rBXa4TIxHarEg9NuPqE9e2ZwlSCuvz5qN3kjE2pXwuCxFwrQax8KHMwgt9Kh3n3PAjcZZddVjXnGb/p+HTEjkcMpeRtuMuG6aorr6oYwEknnVRdL6FnTO5lPuAkBu5F87CMRjM+78RcIK55JLumaqvWRQAnebU5QEKthhitDwokmoVjMSDmbfYF75OnX/HOMPl99923GhO8aP2Y/OrJVS+L/ffffyjwjfdnTdAa0Yhty+xcYz49843V9TRJGycRCX7uSopg4CH35YFimstNQYzWJPds1MQB1gscK6TmQYDXXXddWrhwYfrwhz9cuUrAie/2xNZPpK985SvVGTvkkEOG5kdQHmcnnh+Fi7h3PT+xAmJTRLxZErnAnAtJcf4y+tL5icWXFMo8v87fPhxx/zHv8847Lx1wwAFpm623SYdvcfiwOdG/gl4WH/zgB4etX6we2iVzYUWH4EHpUJfA0rUJejdBD6sVIB5owK985SsrIqeULXOgJO9+++1XMQEJtxobhJYa/RAxWxhbiSwWZwEgMBaFcYzcOtDWNKRkAlaj0d8ss5URqg3EKHVbC3PtdtttV2l5efoi71uZfw8+eJhFw7nTeObmm29ON91007D584xtt922GtNWyWYAxNr3EvcYeJgHi3UJeiqZgHNfawwEdH1cG90BsVMcc+cdolka4F15Z8oRR5y4V2w884tf/GLY+phVAq6ZS2yVrPYXi1IZsBgj+mMhnpIrKQcFoDj/PCiuYtZPPDF0TV5MK7YWZo+z143yF9f8ffbZZw+17RUvChqcKUoVc8bylr/MkTHZ7whLtkr2/CjUMF5sFKSw4vs5l7b8eXEcz09eYCk/P+7ZyJytush90AezL+L6IAhwP42tSmZ8+hbcddddVWfQfH0G6TGwooOLoK7B2doOvTDQw2oFCDeE7tBDDx0mZUfGd9RRR1WaCJpy7svjgEHw0BYl9Gi4jhUr2eWELUZrx6CnJl+/XdlkcBJyhYIoAOTFgBif+enXtLVwLPTCOHfeeWf67W9/W7XizYu8SORnzZpVaTd2Zcurs8VWyZHQ+x4KS9Z7l2mqqfqOXYKe/C3eE60AxgCo+cU0wrpOcTFYTMbMu86dOzftsMMOI1wd/j84u+GGG9Idd9wxTMvzY4dL1oC1kEFGYSkKBlEI0ELiOzb5fxnLkrwyPBlp/DvuTfcdz7UfQ2wtHN0t4gQmz7vw3nXnhyZGzCXulWh9QIAC73yHQGYjMPebe8V1k2nqdnLfazVrMq3HYFyFhzimAphnKJ6fvLUweIkZGI7BNXRrxKrGe5ei/REOUUBoBR6DS7uUNx8kk+Dp59dpbe0/0AS9MNDDagMk86uvvrpqwapWGgm8jJCDhIQP4UNTKqUORkIv05WRAZqkjYRXCzH63qI7bYdWQgXzUhtWg+HeEjGEQDFvzN9odhCxUstfta2f/OQnVe953CJRqBEvfod2w5gXX7yyilruvuDvnNDnrV4jQ1LLlcjDkNCg24Ke9PdzLffE4kUR37lrRcsF3zNH5prP33Wm5SzvaivruFdi1D84A3d0NdR1kWtkzJU1YC0Yk7XJM0VkRlyrRUeGx/Vd/L9G0fMM96LMLmZkxPXgOoWUKDBG8J3o6HjppZdW3ffs3hkFAfcK1yNQc9YWLVpUjOEwDoHncR4UWqO1x54Dtnn2t+jGaKuq57MNYow+d8fN35f9xPhNrYVjJgjmf6wFuAjyvRJBBQTXUhSkB4EVDZaBNqva2g7r3hv18LIBBHvGjBlV3/GSlB0ZH61rYRb0bG/SPCT0+HhhTBDMmCPtuDHPnWfGpiqlHOwY8KZlgeujABCZk2ZLmQ2/Y9KMAU45cB/+XwgxAlJ0ZeRjAzAL/OMIA00lYiOh5/0Y3+jxOHbU3iG2MT2xlPPumokzP1Y4dLz4DK7n2Zp5mZPdFkugQIjPG+KObzvfK1EL5gPuGB9cNll5WAvWxAh71ko/dRw7Cgb8zV6JLZdLe8U9YjyJTNSxckEGXLBX2bN1AmMExjn//POrGALcAD437oG4V+bPn18Fy6EJN50f/e+cNdaJOcUgz/h8rR/M05oTno+6+ghq4ApH8fzkAi9jKAQAJYExAvdjVbvllluqPeBzHTMHnov14PLLL68E00Gj/Fe0BA+2uZLWduiFgR5WCxj0hO9byAmOREFGxLVoN0uXNpcQ5T6IJEwGIgNBg9hHoh1NyxAwiJoVzqLf0lxsiZzMDkasNlnSDjTzcg3XWp2uCXgGBJ4YCQiyhDMXkABdFJiAITaYgNuA62CmEFTjFqxDAEQztQyReWjGNadbfOhq0WQMA4tR6HFMzeP665lDDPpsAt6N69DkfF7EhX8rmDBncAgu2woAMT/WxvW85557qrWLEIVSrmFfKSwpFEScRIbIO1atdJ/HUb5X+H/2JnvUbJkmgVGA6eEOOeaYY4beu+78OE/Oj/c1gYGX4AS868bJLUo+zzPBu0b3WX6GFCoVOHS/lJQABBHWwuDGLqWImQ9uxzlz5lRuNM9PtJYInnEUEWJJiLsYFFY0CBpdXElrO/TCQA+rDAY9cRAJeopSdk7MDCSCgOy8886VGRgzYF1qYAQIDIRExgrBtWiRGlleNEZtNo8t0PdtcxjNsvoEJWZoAzzHnup5lkATGPSESTcWesmFGDUsxmUemoDvvvvu1mdI6NGyNNeai+/vmjc175tdIA5isRqJLddo/tb861paQ4FncQ3P7topjnfi3XhH3lXrTamPgpqYZnHWBZx2AcZlrVgzNWID3RRwXGtTFK0PkRe/0bogTowz0eLk3mMvarni2bbnbgPu5QzgDiFuJDY5ys+PggnzwApHoCEMs0tvAeaib553ZK4GXsa1NV2QefDOWgFisScFRM+Pe0pXhONxPcKHfUXyLIEmIKaIPUb8RN35cc4G2zJnhCRidIgzWV0ugieetzSuS6mEOfTCQA+rDAY95VaBXDuVeEYTPAcdv+f111/f+XnGE0BsY4R9TJEyYlyibRAeGqwEznlJ3Phe86hNWSBGMttBKo1BaGPQUwzwimZX/44m+L322qsSqnC7dAUDx+yboMYOaN5mHrF8ssTPcsS5xszHgC0ZqRYIrrNAziD+U94J8zbvCPjeaqBATD+TCTAPcAlOwW1X4D6FFSP5TfvjnayFkGdc8L0pi3GtYqS8RaZiIBx7shQX0AQLFiyohCTPj66MeGbi3zEojpgL3oMz2BUY2/gFAy8VvHinUqlt92jVYvl5nCkQeH743gwT/t9AVxi0wa9dtWrmgwsRl4n9SOL5iSmkMagUYH+hmLDXuigZbcGDy59f97W9K2Eb9MJAD6sE+ABj0FNJylYLK+UrQ5CIAsay0FbeNI4NyKQhMhB6zJDMJ6awqQnH9C4DC7k/ZiSoeREICcPhesbXJTAIYcEUHoOenLfaC88xNbJUsY50OzQbNJyuAJ4ZS7+9hB68RCFE3zDvb60DLRN8Fwv5yJQZR6ZhvALPqqvvUALeBbN2FBoB/bDggvEtBJWXyX3FK15RPbeLC0VQc2cNWUv+Zm1Z45g5orDG+xsoqJbLvnavAAoECEbg1s6ECh0+twuYP48bhPsjGP8Cg40tsyPwXtQb4Ayy97uAaxYDL7kXgcQW3zGThvfX1QFOrKvAdzGtVXcUuEU4UmDEGqFw0xXOOuusoRiACNIQ1gdtvVTmGMCSxLtcccUVq2wZeCKUYl6XoRcGelglgDCT22wBFMEAuFj9S8k+ZyAceDQqIswHleAl1hAcNDP8wxYaytOKSnnHMdUKwmwEfSSAQNSa24DceaqhwdBzfzIQu/1ZQCkfG+0GBgFR7MJwo79TIm5RId4JjU9mottEN4om4Px7hRTu1coQCXsM9OvqSqK4UF4lTiFJIc7/z8fmeccdd1xasmRJheMukAeasqYWy4nFlWLAWwwCtECP38fcevaJ7iMr6HldVyEJQYA5wbxKezxfn9LYnD3OYKzH0AUn4gVGx/lD4PCdYoMlcWecSFwfrRgyaDNWtKyM5vwglCA46l6L8wZ8tgJ8SZtnTQ4//PAqGDdmIXXBSwStautiKmEOvTDQw6jB4CWKw+SHSNNm3symRBQgJHvvvXcVYU4EeBvEamoSJz5EksNo+M0I+ziPurxjzbxcjyaDL9ZrdDVEM3YX/+/MmTOroKf8N8dUC/ddYqZBFJJgWqRKdcVJjIoH1zAp8vgNHLOQU/S1QugsqhN/06zOvYxhHEbMwtAk3AaYsWESuabnezuO1gq19hwn4JT1QQjtKoQY/OWYrC1uGNY6dzNFIcD1iXuMPcL1zJcx0ObjHhP3XXCChYLIdzJrcheUWrZaOLiP84jAXDmDuNoI4h3k/Bg3wZhYXcAtwDvG+h66AmwL7X3+ZuYE7oftt99+GMPWdVDK1CgB54e56EqKONFdomDn80vjYpXjui5xJs9lmTg+T1fSuho0GKEXBnoYFcj0dtxxxyraN4e6TnJ1GgLCAIQVTbjueRKwWM1MTRcCYalaU6lgPvpyDVrMLQWYEvN8Z5kAoIvBd4I4lFKt8qAnosJz0DKhhun8gUhcBd4BFwomYDXzOoYRA7cM/DPSm3cz+FFBiTnGZkOxyRG/cQ3XGoRnQJlj6l6RYDY1R0IDR9CzomAEXUhA3pI5+qwjgFvW7Fe/+lUjs3Ne0V3k71oIjAVhPANFowXFYD4YHXvJzAnwwm/sFbX26Now6r6JAepKwv1Rd34UpPMOmTkYcV/nJ3ev6J4CnDPj8r0uIut7mAFgkGFsg8y9jIOwaOZEPD/i2aBLrQpt5weLwO233z7ClQTE4kjukVKVTYE5kZJI74u2OJMVmbUkdvVcV7oStkEvDPQwKiDoiZTA/NBKCOs6/cWCMhE4hIwVtZsoAMQo/1g8Rj+mfnDvgyCZGgdzs3iOvysoADEQjmdYb8Ao+ljcKGo8eR955oEWT9ATBDWC75EXMZKwGa9Qsg7AuKKQFIsrSRyN6tbcHYOeZNo8B+bDeODDNsICf/OdufFGfkso1U5jiVufadxFjDYXmDu+bdIm871S10nOyO1SF0VwCwMF1zK2mEkSo/xjMSCzKqwv4H5C2CEOQuEwFuexWBN7yHRL9pa/uw8NwIvFqmLWQi4YkDtPOWb2fK51+g65n9r3MeI/3yu4pTiTV1111bDzEy0Wnh/HNkLfIE3vM57ADBUEuhh4yvvabRTBwcwJ8W6tAv8/nlnPT8zWcF8jIBH8p4Ui7nneIa/rkJ+fXMiYN29eZaVrizNZkbkIxPG6HjQYoRcGehgYOHTnnntuVSAH07yQR+aXAm6a/MyYFymmgnYTCWisfW+fg5ifH1MJZXya9SFS5B3zPcwfTYePgXDWLohzioQx5rVLPGNpVRkaH+bNb/gqSxpNXdc0xoRQOlYkaLwvmjA119GYork71r7PtZoY9BRrBViDARM3DB9Cj4/WQDi+4ze70olL/deW5I1zj37jGGTHXG+77baqBgVZI1EwlLjLeEpmWDXikoWACpb8BpEX/wpuMQYg7sFYijnuQ8eG+aHdsjfcJ1ZUxCdv7QJx6RixJG/ESSydbZBd3Cu77LJLlU5YOj91te9dgzwDAuAsEpNBISK0+uguystpx+De2JXQveL4CMm8u/U9xAvjIyzSc0JB0Hfw/DBW7Fvg2c17RyisUEcCK55VKev6hZTOj+9WKqaFwIXw1RRn8lyWSdClFPO6Br0w0MPAwKHlgFoVDPBQe9ib0s1yV0HUYNCEMVHD/HJm57U504uEU8IUYxX4wOQ48Jg1uYf/z81/0W8ogzbVMJ+3WqBzhGlcc8011fx9nxiroCm+qYKezM97FGhgGAhKBIip1eW179XASkFPMZAT8F7dKmh9WAQ0e0eiK3EV56aVxfaz0dITNU/eB2bN3HEnyUhjXnhc2xxk5gbRyfzELbhGC4ZJ5Y2S8r3inBU8/F4rlvcaJW99iegnj+ujRQbQcpQLSXGvRGGJ9Ej2IQJNXOsYwd90frTKxIA+7wcnzI20vHh+HM+1dO55/rwxITHol99tAc68EQR0KcSywVorfJb1GPKaF6Xzw5i4w7CqmQKroGbqYNP5AVyjGPsCILAQl2EvhxKsCHvF9V2frAJALwz0MBBAIPHVov1GH6ypg5qV24hZ1D6iuRttA98yQT8lf3GU4EtNQ6I5USZiIBwEbdddd620P90EUfPP561Gp3YjU82B7zGFo1FjLdFMj3mZ8fMSviWQUPp8iKNuCt5FE3DsyhbnHcfIg560CPhOsVMc70NwIB/+5jt+i9dG90UUkiIBLVl6mCtWB+auFsg7mZ+vINGGFwAcGu2um4JsC3COkFQaIwox+n99pxi06DrznsYFYCWgIBaCQAy8lOHkFhyFJPFcl1HAfidrhlgQLVbc43tpbWo7P1pBuIf5aupnj3M2ETgs+xsh4ruUPx/Pj64UhEXwwnnn/DBvAyl5rnhVeHUvKGTE5lGlfcL3WBrBtRYfcM0+tIVyvh/qIG9yJBx55JHVeKU4k/z8PLEO9x9ogvXrbXtYZbBpiEFPuZYHNBF4CUYpuEsNhpoF/F2Konfs0qFVi3Wc2CnOQDjmCdGxYl8k9KV5awKOZYRzgmbQk6mEaqf6q9VKjb7P74/BXRLXGBPBvxBgtJtSPYY47zzoKXb6k6GWOsXxMSc8RtjHAjRqW7kJuETkmSPmagJDmbsCkT518+djNHv+Ts49Fk0y3VEtEZyD+9/97ncj7geieT7WABCHMjwFRisqskd4hhUvFZTYU2rm0doizqOQVGJ8CC7cC9MzbdH1lok1BdnlwZH64jXB868xKyU/edwref68z9TqoMAI7gwq5Nq8g6YVLz130X1hmWfN/L5DBIqOITjiSnJdNf3rPrMmR5eMhGitcC6sPeWvsZgo7EacjnneWqLgu74EDUbohYEeOoN+N1vxlqp/RSk7FwD0d+dm01wCt/wskfkQaEFzdAx6im1xPcT8jV8zdorLfY08U0JvhD0aUC4MOE/GKmnBBj3tvvvuVdCTTF2/qWZQzd157fsYHKkm5Sf3DRM7wN+4aUrWkjzoKa6PJt6mTnFAqVWy6xUFgmgCLmnBWHaYq614fQdx4kemWsKJmnKMetffL87AObjPTcBxH6LFugZxfRgvFxhLJYS5LnbQtMa+lSxzBuLezJkW91155ZWVIBCZVTwL0S2W944wONN9KQ69J0bbIyQRoHjrrbcW90p0JUV3lhkjWoiiwBiBZ1jxErBVch7Mp6CTl7TOFQwyIWhnHd2NESfSiZhS3CQYaK2Iew8hCcsJVogIzuu5LH5ifYNeGOihE3BgOLSYCekpUJc6qJQdo7ujL9R6520V/WSuUbuJ13togagpw8AgSkZDd2lhLBOAYEHUYtATwBgSoXzeaBowG4Kecl9rBBlqDJrKhaM8WEmG5fWW5MXUmQtJXBuDnmTczAWizvVcZ+ZEm2k+Enp7QMRgvmgCzhkfzyJ/3lLMrn+eMQD43pH5xf1SiimIwWK8I7hnfqxFxImmf5leLIBluWnWzhLCbXXn456K3ffiHmRPxv0TBRTOD8F4WHhKBbDivGM75DyYNu4jIU89JM6EAMXY9yM/P54N8c3YxI7wsYxzm9/cZkzgT6uTVgDXJwbj5q42Yj4o0EWQXy6oldY9prVG+pJnnABxHM8ZwinPpEpixPmY57OSoitpfYP1J1Syh4Hh2eeeTRfeeWFa+sjS9ODCB9N999+X3vnOdw7zP8cDGzUMiUs0+0WoM6PG3zm43/zmN9Pvb/p9WrLhknTdHdelOY/PSQdud+CQ2du5cJBhTGq2TYFpJYBgQeghMDbgQStSI9EEvNHGG6VLllyS7nvqvjTrwVnpyouvTIccfEhlVo7m+IiTaK6MKXkSxtgKFohV7yRoEj7cM5RYxdz8jhPekS5efHF6/K7H09SJU9O+W+6bNpuy2ZC7xHdhPhBrn90VrGLIWGjQ4BfNyveCmVT+6qefShctvCjdfNfNad5T89KSS5dUDIK5KkDl6xH962qQrJ3CliZh3yM2nHJuMgRwf9BBB1UBaHvvs3e1PuzZ3Z7cLe231X5p001WVgfUn21KJe+igNoVeKbBp+bZM29wEVNHK1/3uLHVXJY/sDw98+Az6Zbbbkkf+sCHhszxuVXM86NgoXYczesKNI4Rz5aMzDgczs/Xvva1dOmvLk1Pb/d0uv7O69Ouj+6aDp5+8LBreS6MHMFIISDiugtoPWHN2BO641w7rQMbb7JxhZP7n74/zX5sdlpw9oLKlcTZy92NES8xjsLzoVXJPWIsSQw09PyIE4QklBmUjPe89z3VXB6767E0bdK0tM8W+6Qpk1e21F4foRcGeijCmb89M538s5PTomWLhr7baqOt0tylc9NbJr9lWNEZibZ/S2DbtE/uaar3TXDYE7OeSAf+04HpoeceeuH7idPSF4/5YnrTrm+qiBhEmWeaFx+DmLqCc4FoQdwhaGjEsbnRD6//YfpP5/+ntPjRxUP3TRkzJc3eavaQliczk0j5idpehMj4o2YMSNT0gUrwIPL/9fv/Nf3bz//bdNfjL2g40ydNT184+gvpuB2Pqwgvz2Xuaneas7sSeXFohULGBC8ybt7np3f8NP3p2X+aljy6ZOi+yWly+qtD/2pEOqW4UOiJRWkiaCmJ9ygsRT+7DIvfKMn7nd98J+3ylV3S/c/cP2KvvHGXN1b7xIwC/d8KToMEi2m1YAzux0pgfwJ+Ay+nX3N6+vQFn06LH3lhr2y5wZZp/sPz01u2e8vQ+XCvKEC7j0rnR4HIdVFAjDEUkfkhyD29y9PpuJ8flx5OD4/AyZtnv7nCiRoxAhzroSA2CESXAHvDOhYWvWJO/3LLv6T/eN5/HH5+0pT0le2/UhSkI76B0r7NBYNYlKl0fviNLKiTv35y+o+f+4/p7ide6Aw6feL09KXjvpTeNvdtaX2EMSs6UE02O6Y0Ftd65z2s24LA8Wccn1akrDBQWnkYf/COH6S3zHnLsKA7D57aURtxleA0aWVt8/jm0d+siHxkeIDMY5AgoGiuj99ZbOWcJeek9/zf9zTi5K27vXVYKdo8x7/NDK3/WdeAjNDAMH3eCCUn/vOJI+6PeHnH7u8YarAkwAi7rE0THrUSYJb/2R0/Sx/6+YdG4MS5nHH8Gent894+TFiUOMvE24TGuDbiMlpQZB4VTs48sXGvsGe19gixE2BXKOFRQYn5nb347PS+f3lf7VzAC3ultL5qx01CclwbA1RLZ/EH1/2gESf/cMw/pNfv9Pqh8xPTMLuuTRMe+Y7zA75+sfAX6QM//UDjXjl+/vGjphWle8QvIE6YY9v5+eEJP1ynBIKu/LsXBnoY4RqYdeqsYRaB/MCggf7+j36fNtxgZF63HefaiEgbw+4yD0x7t598e9pg3EizYtd5CKYAlojwo489mmZ/bXZa+tjSRpzc+PEbh3ASGUVJ0Og6j1xzfG7Fc2nXr+46TOMcMZfJ0yu8jBs7/F0GmUcbo8Q1sNP/2GmYRaAOJ6xP7i4ahMCX5iFOqn+fe7Zan0acTJqebv/kSJwMymia9lblglj2cJr3zXmte8XzEy1DgwhspXlEK93yZ5e34gQLwW0n31bNI4dBBcfoDsrh8Sceryw2TTiZMXlGNZd8fUazbyOMsNJ1OD8zGuayNkJX/t0HEPYwDIgRqGPAAJL9okcWpV/d9asRfuAmc14OUQsZ7Tw40Piq68bu6irIfZI5/Obe39QSsoiTy+++vEhABzFD57EUanqm/12y+JJaQjY0l2WLKvy1jd0GTS6FS5dcWisI5PskdkrsMnYOpWwFTb8Ik5ctvawdJ4+UcaK2OMheAUpz57urHryq017x/MR9EYtbtUFpj8csnS44wVx/8aKLa8cfdK/U7XHORRtOFi5bWFwfxx5tdL/nR9dLl/OzsGEu6zL0MQM9DAMCr7rAl0/7cvplau+mN1q4Nl27Rsyjn8uqzeMr3/5KuiC9EOX/cs6lX5+Xfh5r61yWdqSD6xL0boIehsH5t5+fjjjtiNbrznv/eenwWYevkjmv6fqu8zj7PWenI3ZcWcAlwiC+4DpTsWbX8247Lx3z/ZFdCLvgZND4hbbrz7nlnPSa775QBroJL0fudOQIbbyr+6TuWs2u4OTo7w2vId8VJ6MxQzddz1yO/PaRo8JJm4uo657VDH3ureem1/7v144KL4PGLzRdvyrneFD3SdP5EScv1flpA+Zy1HeOGtVc1lbo3QQ9jAoO3f7QymdWB5XPc+L0dMiMQ1bZnFdXshXCsvuk3dPUCVOHgnpK82CezCOWNI6m1q5mzmjGVwCIxYAOm3VY5edtmgs4IeWxaewuUOfi4P8J3JuzyZxOeDlo2kEjOggO4j7JzeF56ehqn0ya0TiPaROmVemOpXeJY6/KXmE+8ybM64QTUupKHQTrxi5BLHFsSluspeFeqQP3CnNZHXultJaMs+eUPVtxMnPyzGodBxm7BPHc5+eHv1+9w6tb90rdXFbFRZCPQ+pkl/MzswEv6zL0wkAPw4Cgmb85/G+Kv3mA/uKQv0gP3P9AFVEeC5o0+Q27NiwiIpvqZyueW5E+d9Tnhj03h8+/5vNp441Wlqg15UqGpabWhaB5balTYqUZpzHVs+oioQFS6R5+6OGh0qyjJWaWRY3MidQvSwhPmjipSgsr4cX/5/fxm44fVnAlFvPpKgyUiiMNlY4et0H63GtWrk8dTv7miL9JTzw+spBTLP86CF7ivMGxFRIJgPv80Z8v4kRg/ag3UOogGKPOu+DEvSI+jemoYmjSmPS3R/xtp/PDXs/3/6ACUlxP/mWPUOnw2eXPpr876u8acXLK606pDZJri+mJENM/S+eHZ7BXms5P3VxWhzDAnEgTRkOeMH5C6/k5pQEv6zL0wkAPI2D87ePTB8Z/oJLmIxC9TwrQu/d5d1VQxBr2sf/7oAQe4F5SsxACGItUJ8xZJ+xxQvr2G75dRT1HIDf5M7t9pkrPylvXRsHAWv91/QDMSbY0ayRgmoEd/8DJB6YT0glpu/HbDcfJxGnp9Lefnt6197sqU5w17CX0UZMcBC/mnNs7AQbM+NRYJz+8wsukDC9jplRzId3SAiwWONKUzDuD66ba9/zGNQo1ee8I6x2QNvjBiR9MW2ywxQicfP8t308n7nliNWfutfa/pu3R4EThToGR/2d8UijfMf8d6bTXnzYCJ9Q8+MphX6nSCi1yZJBdrPKnwNO0VywNHAWAvJU189z2gW3TSRucNMJC4F7h/LDH2eu8h6V6fc9BcOL8osAIPjg/4P87b/rOiPOz2ZjN0qd2+FRj+pzCWpPg6Pmxs6fCYjw/4vSI7Y5IJ445MW2zyQstzwEsNk2pfINaS/L5DQmMG25Y1YWAbrEXTnvDaVXWzSBzWdehjxnoYRhQGvRb3/pWOv7449Oc3eakHy34UXps7GPVwdl7873T5Ekrm/1YchRCYKlaDprNYLoCpm/Md2xDiJg59hZOqcqmbrpJuuCOC9JNd92U5s2cl8YtHpcuOP+C9Md//MfV8yyLnBMN2+xK1OoyH7g/L7uqVgxA2L7xjW9UBPzEd51Y4YQAo7kz56YDtjmg0iKYh9dDwMw5l4kPQuRhKtzPeBRsYWwZEO9YaTgTJqRnlj+T/vW6f03LN1meJo2ZlK785yvTUUceVVXjq+v/Hts7lwQVrTsWv8l947od+I2KfzST+tjHP5auefialRXuttu1Mgs/+cSTQ9ULwS/PYZ1ZT+4Fl4PkjVs50EZO3O96M56dEDfYcIP046t+XFWIZK/ceeGd6fHHHk8f/ehHh7rYlUrdwpBjQZ9S5oP/5vOOZY5ZN6r+UYr5lQe9storj499PE2bvLLCHZqpe1urDWeAv1lnKzx2Bd6b8weO2ROWXbY0Mb9tOn7T9Mvbf5luvvvmCidbPrZlOvOHZ6aPfOQjVWGvQeIjYkon4F6JXTLFWWxE9v3vf796zw99+EPV+tz9+N3VXDDHN2nhg8aW+GxrYbBW4NR9zbtYrpy9YoXVqZOmts5lbYWu/LvPJuhhGFCmc+bMmWnevHnV/x887eCqsp8CAEQTQixBs+JY1PzyYjclsGwpH4ggUruaqA1G7D/AWATz7D5x96q2+4odVqSrrryqKsmL0CJRzSuYSdytqR+rzZXqu+fEXWb6m9/8ptK6eBbEApww12222WaIAcg8bRRDaVYItR0R82I3TX5NDi9/U6JVk7bvBoGL7WUPmX7IEEHfeOnGVX3+fffdt1oXS9vGFNBYvQ+IzYesFmhxo7xUrlo968PaXHjhhVUr3i023yIdvvnhafZGs6u9wu/Ln1nZfY+1tWww+4L/t3U0BKpLUxiLP4Eb9gljiGf7MFhxj7/BCXNnr9w74d6KOdMgiPbSmrJzBhPrIOR7RaFIoSbfx7F6Hq2sOR+04eZa9grrqGXD/hGWAuZvfmefoMUyFvd3KToEw4t9OLREKezY1ROXDudnj0l7VDgBrvj1FdVZ/8AHPlD7DPdeXjlSnGhVyYVKBQHXh+ZmfHgWcwEngHOpg9FYSyz+xD1UVHR/uLftpWFg7LoSJLg6oHcT9DAEV199ddVOlI5nEdSKYle22BXMsrcwAggtpk+1/TqpnWsgLjbOiSbpvGlIrtXzN41Nrr/++nTnnXcWe5jnrV65x9LC/Guzmry1cN5siN/pwAcjsXFPxAnXgRd7tms2Zky+R2CACOGzVDAogU1ewA1MDVwCsRlU7D9f8rvTx55n0pxGk62EOfd38zwZOxolH3GdtxaOY7g+MBIYzatf/ephOJHp2fpZQqymCthOGqJtq+QScD04A3fgEFzyfnHM2Iq31PyKOvv0SKBTnUJAbHLkmttV0+ZOca8obNpGV604bzbEXqSdtV09872iW4JxXB/f08ZQdtBkH9SdH86WrYXBJfe6Vj5DnNr5MmeonB/mS+vgEuTnh7Gjyyn2S8hrJcRmQwB7hY6E22+/fRoEBoktYY5DcQETJlS49MxE4dmunqsjKHFdg14Y6GHoMEEw99prr6r/fAQ1AA4QDCD3EQKmoUmcrO0fCb0+UjU8ewlIHJXWDe7SdF/yG9o90a5sars8D0Iaa7bnrZK1DOSthZlX1WAmVFJDEGCcI488stZfa0366JPm4//nrZIjoee59oS3tbAuB9479jNgbjEmIidovCMd/K655pq0dOnSIc1MLdJ1s+NgLAaU48r7uId7vY/rlixZUj2DNtOlTovRp66QpGCn1YV35F1hLr6/glwuMNpV0n0WOzzqw3cN4toIrp2ta419YG6sed4qORYDUguOuOKZzI+9Fsvc/uQnP6ka4cyePbt4fgCFJK0M7nndJ7wrZ0OGHwMvFRg5Wwrf3O8+U1Bz3WR6pcBezjhn/eyzzx4y52v9qWuVXNc3QHyXunbiSoJBsy8HhS6xJbnAyJ6yQVLeVVWrzCClp9cn6IWBHirA5AuxOeaYkfnAMZBIYimRkuFoXuU6CT3XQuQhakQ4c2j9zbbAeTObyPSiGb9EFNBuYHqY8SWwHn4FlegHLoHXxYYmahCM/etf/7rSuEv93CW8Wh1iIKXv5DuWCD0fiDsQWwtryYhV+9TUFZDqCOUee+xRtX7+6U9/OuQm8L1cqzr3iKAW6LqKH8dDAOMZPKtpr+i/llnFd/IdsRBocQEX7pVcYJS4R1dQzvTqNEnWDoGA1s+sqQGjvpfMq4nxxCBV30NrB+/HPmHu7MkSTiJeo5AE+E6+YxQKOTPgg7E5S3YVNI4kukt8jo27ZHp1ewULBteef/75Q5kVUZDLz2AdXjz7UQsHeEddSZjsV6cwUCcwKqxFKwng3m1rab4+Qy8M9FARmcsuuywdeuihxf7leZpRNAEDHrxofuUQ4iNWICB4hYOI1B6Jh1qoBMf2rB7auoAuroGR7LfffhUxs+iJXdJkXnGMHDSBK8RwH8RWUyhaE4xq9913L0bf50KS2qZj87td4DS18gzwArNTELCVbjSxRuHDbIsYpFXy6fscGN/ChQsrk7VarZ3juqQXRtcA93CvFoMbbrihciXxjFL0fdSC7WIXo+XFlURbi4OBc+DEVslq+z7Hts+OlfefLzEPsyNYQ5goPn2zI/gosLgHmvYKoHAlTvgwNwIpacULQ8q7ZkZhAOBeXT5+L/P2XHCPAYGcHc4QvxuPE7Vw3TuAmn20qsU5xL3CvXR7REgy2C4K0/ker9snFh3KrQfE9DAmdGU0UJdJYOZELjDmQYsR77qSuhSWWl+hFwZ6GBb01CXNKDcB50F5HEgImOlfs2bNqvyFfG/aXSQesbOfTC/3SUp0Ym4499KOlN/QQCIBkxjEOIIc1NqBXDO85ZZb0q233lrFT0RCowVCLTQSymgCznHF/0NwfX8YE64O3hUTJ8Res3NshQxEN0ouIOXFgPhuhx12qLT2c845Z5gAE7VZiWYJZL45ca8qD553Xtpzzz2r9RS/sbhRzviiGdzvtVTo1uHdwQG4ACfgxvRBa1kobDpG7krye3Hi7zHWgbW87bbbqrWNe1sNOgZT5hCZdNwr/EvQJoAp3ODLuE995zohyT0e18f3Z/7gmjPEtXzH2TIwVIuAY0dXUsSJ+z2vBfCqV72qEmDYKyUtvEkYiFafvD33XXfdVcUgITSOxixfUgJiqi3rroUxziW6XoToSuqhHnphYD2HuqCnNqIQTcCR4HBgIVYQMw4smjWHE6lcHye/2xo4jh2DngC1dhlOXgsAgsc8jjjiiEq7gaFE0Oog8YugKyCa0AWea9ATRLhUwyDOS7yo3UnkoxYPU4OI8R04QevjejQbiDH3KBDIPGR6edBTJOpRmIm1AGB8MGA01gjiz3HjmroGWllyrQyBizHZK6UaBlEwEN+6UGK9B99NQYB3BwfggjENAONefgd3eWVJ/b+apI3ZcF2iuVvBY8cdd0y77bbbUJxJ3NsKYLoQIihYRNO7gIaKi4BUQvZiNLHH4kZxXnGPuwbx/HA2OCPG4HAtf4MTcMnZ4nfXXnx6RqJVLT8/MssYGxGDcXOoq87o83LhSADH06dPr+ISRgNxvfkbnIBr5oMQgIWkKVYhzjO6knqoh14YWI+hKeipjShE7UZNDKkd4o0/k3Q309uiOZ7fSCmCGCnlx8hlhYzI7GRgEv/8UBvpDwPPIUbix0wDfdalOv11QU/6imUKMUJZgUMTMN9xvX5N3p+gLc3IMSKd9+M3/KoWclLjwhQa34FxoxCTB0cKED/Ms7h/eJcIZkCIh+gWsDZCbk6F+YAXNMnclVSai/OMkf/WAuDdLJDDO/Pu5qu7PvwNrvhNjdh8fMc17sTsiBgcqR8+X1vWlD3Hu+RrKwOPJZzdNyVGoykchn3AAQeMGC8Gavp+0YoCnmOGgum5XM8ZMYXS9eFe3pmzxW8GXnq/VrVoxbLvgoFzpfOTB+Pm7wHE76MSkNcXAHAlIViU4ie6ggKS1jSeR7ouAmPcmzG1s9TjJHcl9VAPvTCwngKHjdzruqCnLuZCNUzGQCvnGqR2C8JoXpcxxKC+GGHPvXffffeQSTUGRUlM26wWaMI33XRTlc8cQfOrqYSmSsksciZq0NOBBx7YGPTk/CIDlDDxt4FwjAcBg5D5PjwX4iYj8P5o+jTwEkYug4q+5ZLmngNuH9YCISlfOzV7ffdqeXlbXYB7YXqMhY+5CXLBTcbE95q+Y+aEdSQ0j7s+kYHJBMClwXQyV83drkWJ2UVgLALaMO3HSH3n7lgxldD9k+OFvcaeY++17c9cmFXwYXzeiTPA/jcQLgYren4A94qpiAD3MoZWhujOqBMWc4AGYNpfsGBBY7xD1MJLuObZuB1xU2EZGC2AewQjhAGDTHOGnqd25hCtaj20Qy8MrKfAgZbpQZTbICcKmmqtIAjj5BMPpcxFop1ravw/B51DjlbEWAaKRULTxbyHOX+fffapfJ8l7YZPDCqsGxvtCMIT8+ebQBOtzIjxwIvaOIRdoSi+d2SSJa0eYg8hZJwYHS5+u+CEcTHpE0xI0F9p3gZ9SuA140fg/jvuuKPKNOnyXK+RoZl9gnWh6q/wfP5+Pp+olcd9pM/f9ELGicVj1Ai7VqkjO4Q9n1uS8qA516eUocDvBJgSNMje64oTz4SBpeCD9+H/82JDWqKi9hvnoVCAlYB9wvnhulwo6rJm7HmEx4svvnhEPIlWwbzAUilgE7cUzyeWZzRgqi2CQBQYI8Sg0iZBJ3cl9dAMvTCwngKBYGiD+Dq7gARREyHaCJoeGhvFYEqBV2oRHGaInZkCmrtjLjNBUhB7iBpjqwkP4ufDLM69xA/kc9dnakW83FcLoBmRP4/boWvQk4yDsSHqmnmp4mhp5hjMFssB87v4zIMjjS1Au+Ieo6djQFoXmDNnTjUOqYa5xudcILq6dNQqBe5BQGKNGasLKGgwV7MmeD/eJVbji42h4vqomTu/GPPB7+wV1gdcg3Nx0nWvcC9rzFpjkcrXUjdMXJ98bNwvvNcgkfJRyLBADnuevaIQYK8Mz4ntezlDCm3x/PjeuA7ALcIFY8d91BUvvIuphvm8fW6erhv3Ie8DXqheipAyCMS4AMaOqYIRxJ9BpXXnwPn2VoHu0AsD6yFw4GCYVqwb5MAqtXMQNWlXdfKfP3xCzDuOgT4WeVE7kqjY14AxITZW7BsEsExg6YgmYM2mBsUZ4OUcYxyE+fODBj0ZF8B4VtfjXUwV01TLXHh//a0+G8IefZumAIITcGQNAiv2lZhTmwkYpocJWMhrPOS57gKuJHLzB/H/KnzFAjmY53kXCypFVwfvrhlcxs79VrH0WpkRY+hm4jszNAbBCWsMA0VIEoxVAOJeEVcxuwMNmL3Gew0CFshhbOsFKDQyvlYxi2CJjxgXoDCpJYrvTcW0vofxO6Xgvzrg2dAEAiINxo1BiFELLwlfuAeYx6CphNbdYA9whg0krRME6oIW43V5VlIP7dBjaj0EzKMQjTzoqQ44XFYUtIQwDC+ayGNJ3qhhxhx7rrHOgEFRHtrYR8Dc4RhoVpfelAPmfeaDCTeaenPiEtMgIZgEPWEKH4TpQbz0a1oRTqZvFL1BkDJ/o++NGbBssSlpgIJBjApXUOJeGEpTaeMc0OoxZ2sNitUNI040u8cATksxM0YXsCIcH+YqwxOMEVBY0yVgmWG+t2ywQY4yJFMJ3T8WcgL3MJS84mUbWJKXbBrfOQ9E06yvdmymCc+GcXYB00oV5Cw+Ffd8TDUsZRzETJs8lVABQouRPnau0YLX9fyw1gg4xpnUMd9cGMCVdN111w1lmnSBXGBkzq55PoYWmlL2Tw55VlIP3aAXBtYzsGkIhLCLJsXBsiyqgVwxnQtgHKPoTY8T8vSuPJcakClFQsgzeB4aYB5h3wSMTZlcNFo6MMaMgTwiWt8qBBXi1zXoiblj0uRdTZ+MOcx53jiM0awL/cAwyFj7PnYrrDrNPW/ejPO2kBMMlrGaekDkgL+f9TGmIqZJCjEdj7+5lnft4v/V6mFtCdO/Spok78Y78q6xOqGxEuDG+BK1YYWLWJdCsFEP97MmMW21CVjr+fPnV2vPM9S249jOWyZM7MVVV11V7bEurqQo0LKXDSR1bBm4ODcewufaO8ICXuKQMwZOzKrIY3p4hs+zDHgXQSkG4954442N5yeuLRYWUzfbgHtZ+2hh1H0XcS6oUNRlDORj856lLIcemqEXBtYj0P+L75eD2wT6NSFi5n3nVQElmtHvDeGxulus5x5BTZ1Dmwd/xQBFgGfrjoDI2xmxCSDwpKTBzNQiojYVhRjmh58TRka9gi5+TesFmDkRtXrHj0FOasFWrSvVvtcvHP3FscJjHDtG2CusxfK2JeC5ZAJcccUV1TuIk3xsv+cazMWkEralZfFsmY2ZE3nQpH/HdzPSO29+E7MD3HNG9pcqKGpdYC1YE+bPGvEObWZyiuIw/8svv3zYXo17XJxYlZK0v1Ip5ggWyIHpab5nL8exfY+Y4sk+9L3rekd4vph3jLdwvvEZCko8G3eW8ThNQEwG6Ya8q1aRur0C4H7ClYRVoAm4hzkgsPF3tDDm1zl2dDd2qR7YpxKOHnphYD0CmB5EstR/oK7xB8Rd074HNK/wpluAg40GkwehlcCaArZylQBEQhmjoSH0+BP5G02rjtDr80a7weyPduMYuaAh0wMvRFLrz8417aj18s68Z4z8jkGE5ryLF4vFxOp8JVBYkdHrv9Z0bnxDDB4Ef64PGmUdoXdedO8Dh/h2gVzDjtoe2rL585HZNHWKYy4y7xhEGN/B91Bg6IIXXVPuFYPsYoW/mMHA2qAVN3XQVFhjzQ866KChegylrBm/w52AWwGmV1fZMgbCcR/4tudEXOc8qJQPOOTatvNj8CfX2rZZvMQKmV7Lh7Ft6cuasV+agn6hEbyHwbhxr8Tzw7W4ksjk2XbbbVsFRlugM++Slh+tJXWVMOtAnEa3VA/doRcG1hNoC3qqa/wRNXZrkKulAWoOWgJitbk6kHgZZGfAGRAJTk4QIQgQNOZfIvSReBChTT16mFpeOjgyPYOeyKrQVBsFgpg5EeMChFgwSV+8xMtYiuj7rYMYP6FmqDYoIc4ZICChj62SI6FX61SrREj6/e9/X5Vajowvjke5XlxJXBt7Trg2jK3wETvFxfGiYBTdJrqUfMe8b0EO1qcQj2qIChKxHkAUWGI8gfEu7rE8Ip04E+ZfEpLch/y/riTKPedlnXOBkT3KXo1ar4KR1h+tPIBVARVIm6xfMX9eS4GxDf4uTmJpbOaSB17mHTTVwhG+YjBufn4UMhAEuKdOwVBgZL9oYWzS2qNVrS1jIAetKn3/gdFBLwysJ9AU9FTX+AMoVQOMvlUDCCVEsSRvHeRNQ+qqBNYRAcu0xgj7WMPe+6g2xzuRO10i8HnQUwyUsuhJya+Za3Yy7Vh8KI6lP9wWwl2CnmLRplhZz7zzmJanJpUTejS7vOUv1SYxAeMuEnKzO79xDde6ppZ1tueEmRMKjFEAcF7iRDeKzM/18V3rYkG4J5aSjTi12FBsrFPqHRE7aLqeMjfHYhyYGXuBmICS4AhTZC9ZlTL6+Y1pyVsLx/Ojtci4Gd9dF4fr429t5yfmz8dOlDEWplT10PMWO2g691wLj8G4rrEfcASTx73CdXndf1NtFRgRVqPAWAcxo6MtUDBCXoq5h8GhFwbWAyCtrBT0VNf4IxKwWM1M366afEzXi8BYav85qCnmh1Zmp1ZUsgxEkNCbt857oOVEZgthxgSMMADBzhlfXdATzEKTOxoeJk1NszE7INahjw1qfJc4f4l3icjXBT1BgKNVQUIfa9/7TK0iPANCD+G1xn2+Dgg/+G0xATuGTI/vwGXu/7X5FEyDsXmGLZrz5jdxjs4P4F2igKeVoE5IMqgv7ln3osKJzDSuQ8w+cP+yhlqUWNu8+iB7gOJBphrGfcK+uuSSS6q9FPPneTa/gS/ei70YWwt7flz/eH48H6WiOJ7BkiWpLn8+pkHGngH5MxVKPIPMmedb9Cu3rkAziAlAABQv7hWqUmL9oKKjoHBERcRcYGwDhT/fpasgwDONVepTCUcPfWmmdRCefe7ZdOGdF6aljyxNUydNTbedf1uVU016WSRiaAUGN6ltaV6O9ebzVCvrndeZ5GLfgpjS56Gti/SV8FsQqC0ISC0CYsPHcrdGX/MMcp7pnoZ289rXvTade+u5afGyxenJe59Mi5cuTn/0sT8aGo/5mq8OTqLfUstB3tM+ziUywxLYZEZTbJegJ6O5JfIKUZqFLdkrLiTWzI1ANyPxGUM/rbEAaLvz5s9Ll999eVr66NK01cZbpavOv6oyD3MNwJhaGMCpbiD2To6TEmOLe6W05nxvnYXo65VZ1hWviYJG9MerZSusuae1TPBe+vX1X8tYybD5xje+kRZcvSA9OOnBdO8T96atN906PXztw9XcLNClS822vwSrRkamtSGuT1zP6M4qZSREISniLbqSSkwvCgR8xKfVHc3qiYGYzNssDt4JKwH3mQlCh0oCSbEWveOEd6TzbjuvOj/jHh9XuZve9573Dc2P+ZrGyHkcpOBPLOU9aPBfn0q4eqAXBtYxOPO3Z6aTf3ZyWrTshfKzk9Pk9LmjPjfk1+TQm8+vdqepWfNiiXCr8XhtkxTOwdTH7SGV6dUd2ugjNyCqzlQYfeEyIDQ/npkTekzAf376n6dP3PyJtPTxpUNjbLnhlmmvB/ZKb9j8DdU94MEe8mrLmowVjpxnBIPiYuR3CaIJWCYnk2+q2KbQIRHPce//2xLY76xhwEdTtoQed9H3F3w/7fQ/dkr3P/NCt8cpY6akb0z9xgiBMQoH0eVSx+RdH+ff5MdljXhWdB219Z93rxjLkgtY/m68g64b1xSNlv3IuvOO4J8AuMd3eDwd/a9Hp4dXPDzs/PzFwX9RvXcUGD0/4kK8xHlH3OgLFydNmi9jWItCpmqxqiamp4UqFgrKrU26stwreeEiY4f4f/YLsSP//h/+ffoPX/oP6e4nXqjYuMW4LdJeT++Vdli+wzCBsYs7IEK+foPcqxA26DN7GAm9MLCOCQLHn3F8WpGGB2QtS8vSH57zh9VhO27H46oDbvU/Nag6ASAn7tFX2mbGh4jp3+R6iA/EogkkTGoHJYEgr5EewYp9EHgJ/TXPXJNOT6entLJp3hA88MwDFb6+efQ301t3e+sQQ84D3nx355ILR85Xk3QTXkyRBBcKBm1BT1pt9OfGRktxLgpHsTCNWrHBZhB6nnnOknPSaU+eNuJZMMETzzwx/cOj/5DesPMbKmuCDEaBSP9xNHXXrY+Mpyk/3BgU5sX+qHMl5TgR1IaNX4kQTeLOW5wwbxi6JXzPXnx2+uxtny2en09e8slK233t9q+tcOncFAI9P747UFof59sUE5MLSQpcXVrxKrx6jwWc4rOco1Y/LQQKSqw5a6AweNH9F608P5mH68FnHxw6P2+f9/ah6qGDgNk/8VwNYuovuZJ6GB30DpZ1yDWARSAnZBE+c/Fn0sRJE4c0l1gMqIsgEAPC1LSaIJab7do0RI02mpZjaltbp7IYYV+5P8aOSZ/8+SeL14mrP7vsz9Km4zcder+80UsUgNTO8ojnyDCbIJqAzbpoC3qKAW0Gi+XBlqXe8rGGgQQThrbBhhukPz3nTxuf+d8u+W/VXnHN8loA8Vml9YkEuk1wBGxHrMugS9EYBY1YKCnWIXCtYlCp7pW49ysNeML49B/P/4+N5+e/XPhfKpzAkB0jr6XhHqpbH6/XwtIEMRi3a/68Akk8q3kmiOsTNfG49xUo2Svg49/+4t8WnyWu/vyyP0+TJg9vstQGrpWCtILaINq9wmjff2D1QC8MrCNAjEB0DZQO7uJHF1f+4bpiQE2CQF79qwvjAzioaBddW4lGUy4QCZpBal1asgJcc83D16Slj73gGiji5ZHF6Vd3/arYvjfOS+amlSCPSM+j8utAIcdudV0EiGquz48dqzgaPOh3dRCJ/VUPXtWOk0dX4qQtx7tufbwnpiw2ge4jcGIqYRvEnPS4Fq6P86t7dsyMueK+Kzrh5Nf3/Lr1/CiE1a1PvsebwBiNWJWyCfLaEbHstgGVbYJ0LG507bJrW/Gy6JFFFf3pCtHdGNdnUGGgzZXUw2DQuwnWESBYsAvccs8taZ/N9+l0LQfWTIPIsPieg9iluBAHnGjrNr+xACGD8EXNSRcDc0HjH6Ql6c1339z5ur0327vT/IjEZ264FSJe9Ht3MVnanjjW6W8CBCrwF6+FwDMX4wK6EtLb7rttte4VtXDmYu0IQetHl1LSrDlxDZip61IwI5jGGHPyTWnj33x9muDWe2990c5Pvj6lPd4E1o0oNe/JweDGWN0zro/uoq7Qda90pT9NqYO6XLqAgmeb27GH7tALA+sIkDXQBXbcasdiCdAI0RcOUcmLFHEIbTrURsy432wFGEUbITJdEaJlgBhMz8qGVv7rUqOcz8zNZqYusNPWO1X+47a5MQdiEpiXgonzjOb0trkB3M+1lqltgmiuBzSxxvVpy8vWN7zDFjukrnul1EY2H9MOi/zr3hIHptd1eUeYGFkvQNseBUx/NXjM9REfcX2aAJzM2nJWWl3nJ/rCCbzkE7XgfI83QSyUZKxP27vYHjueH9fHNL8ue5TP9ptvn1YX/YlxRyXLSlfLgFkVbfETPQwGvZtgHYFDtz80zZg8I41J5cPB99MmTEv7brnvMJNhXZnWpupfSvBtJvEY6aufvO0ezb6xiI0m4GgeL5UNVutQY4S5zJswr3rvOgAv0ydOT6/Y9hXDcrBzyGukR999zMbo4iYw6AmmEk3aXXBSilUoxVbEe2MtAJ49f+L8NHXC1Na9sv/W+w+rYVDCd+4LL/nuu+AllrSuq8fQhJc8qNQ1aiobrDDBZ88pe3bCyd6b7z3MIlHCd15GN4+t6IqTmIrLGWoqWhXvMX6ldH7y2Jf83likCGsU56cNLzMnz6zoTxPEZkMlAairOwno+w+8ONALA+sIjBs7Lp36ulMbr/m7o/4uPf3U00NpdHnFOAlkHoiWg8SsjTDFQ9ulJG8c2+Cg3Bceg/lk3JGASdBMddpqy63SF475QvFZEri/fNVfpscefWyIQMaCS+KkVCM9BouZT99G4GPQk37ytpK8MT7DOZaKGsU0urwYEGOYVjpxwsT0pWO/1Bgs99kjPpueePyJ6p684mIcP18f944MxzVr2itqesZPgJu2krzex/PrfOG58OheUehzjpW7ZszYdMprT2l83ueO/lx6dvnKjpUK0lGwdq+UBOm4ProH2vZKzJ+PwbhN4F7J1yfWYoixFXFtFVbsysmabL7Z5rV7xfNzyutOqehPHXRpNmQMRZswEEsx91aB1Qu9MLAOwRt3eWN63ybvq/LnI0xJU9Lf7Ps36d37vLsy2RuopR/avH4YhWa8OlDbMyWpDiQwsRVvW0lewN/yMro5OGd8r0ZP8x054BAyKypWBVUWTUrv3+T9lQUgwmZjN0s/eMcP0h8c+AeVRgrxAy++nwwU4lOHE02u0ULQhJc86AmtLzLOEjie19Tl9pt1AE6s6W+lvrxT3EGbHZTemd6Ztt10eHMZcuq/ftTX03v2e8+QO4R7XQ/GNKCtzqyrpSDOuQknCjhmVajBNlkHxLMWgaagUr63UJJm9NguGHzwru/Y/R3pw5M/XOXPR9hszGbp0zt/Or1rr3cN7Sn2GHtNkzfzACdN5yeWdQbazkGeSsjfCndNeBGnTe600pnnenBkYKs9J7Z7cLv07nHvTtMmDrewUZPi9Lefnt4292218+nabKiriwCcdMlK6mFw6DG6DgGNiOamuelLf/ylKhL8nsfvSduM3yZtuHTD9KtLf5WePHqlyRHiZzU8ArZsIyvhidXANGvmEe1qH3Vg/nw8tLEkb8mHHHPlc+Iu4ZdxGHGuJYB3sSRpzHemeApte//k9X+Svjr3q+mypZelRQ8vShNXTEzX/su1afvHVvpEzR2HOFqxj/+XiDk38ZMX/YlVAOuEmFL99LweQ4mRRIaXE1S1URmLz+YexuRjgZz4XCrKkTP/j+/+x3TRwouqCoRTJ05Nd1xwRxrz+zEpvWrlWPjfrSwHozBAUGav1lfS/qPlxLl1YXquh9adkjlYnNTtFa1eWppMXeQe1pjfYqVKgEp77IfrPnxdFUV/75P3pq032Tpttmyz9POf/rzaS7atBg/Mj/oEjM2+Mx1S7dq9Es+Pe8V9WyfYlfLn83oMJZCx55kx4sS9Es+Pgoxn1hLFzuOiiy5KHzr4Q+kfDv6HdMniSyq6suXGW6YFP1pQCQolyOsqdAl8bLtGlxr0q4fVD70wsI6Atebpzz5+0/Hp8FmHD2khY2eNTddcdU0699xz03HHHVddD5GB0EMY1ZAiw9DnKAOOVe+iOa+UYqj2UmolWleSN/oxmUPeo91PDD7SvKw2T1W5PP0KpkdlOUoxQ0iO2PGIIYFj/D3j0/nnn5/22muvIYIFoYdIgk8r0xmVHouziJcYCMV9MLb8+7yUbE706krylsyi+RxiZLbrwPtp5oVw5gFvlGdevHhx+uhHP1qZx8GJz3rguAfS17/+9XTttddWHfoAuwyCZzJDmAt7ReEuzoW5aqXRneG7l8zEdf5f6zEoJOW4dE+CcxlcjI8wRc60QyP42Xs26smzHhCm999//7TN1tukw7c4vPrdoj0LrlhQ7aX3vve91fWMzX5jfuwV/rUEr5aH6IqL58f3VSjJmWVTKWaLVpWEpFi3QiHEOUQBJe4V8I/wy2/MPxcyaHDGeJT1ZowjdzpyaK5bHLlF1emR8xMZdBQEujYbsghUV1dSD6sfeqyuI0DTEAg0TUOUsmMhFEry/uY3vxlqOAJYPY7a6hABiIINetQurJ/OWKYURm2nFITU1DSkZAKOQVfcJ+GyDasETOZjMJathSFidEUz1kC48cYbq1a91JyPOFGLRXACEJIEmQrMgjGZl62Snb9z0Txs2eXoy8+D+eyU19S3IDcBxwp/WmJslawrw+I5vpOd4vieyHyEixgoyr28LwScdY944W++ox49vRwk6GqxaNKMydi2pY2VCWNFO+MuYnfBPA4gdyXlECvvxfXRzB5jE3xWvj6ArYV5Pmtqf4K4PrTi5VnsCd8p4oU9xF6iHn9cH65jTHtj2CpZF008P3FPW7a4FAzbVJVSK0cMxhUHjhnPamw05vnRRcBcOfOcfdbdNRKWLFmSrrnmmvSa17ymWF55v/32qwSic845Z8T6uNe7ZgfkY7e5knpY/dALA+sA3H777el3v/td1WlOLShq8RwiurLRoQ9JvxSRDkHQvB4JPaBgYCU7g4/y1qhdm4ZY+18Cllf1y1slR5MnxBNNLG8tLOGNxBUBaf78+Wn77bcfZoYUJ9x/xBFHVOZhmEWMePbZsVWyhN4x8iqOascydJm7AoMtkEsQTcARD9EUHyvF5YV90Hrz1sKxe6I4ufDCC6t5IRy6brmlB8bHfGlkFN0jMpO8VbLxA0Ccnww1RvQr4Kjp5a6kCLpQZPSxI58umSgA5MWAosAYWwvHQjzcj6uMPcBeyEttu1d22GGHNHfu3GHnR1+4qXyxVTJ7NDb9yvdyxENk5v7bVGAoBuPGQNpoSs/PrOcnCox8z5w5+6VMEN515syZaffddy+a8fl/9gpWJCxNdUGlbRD3Yd3vXUox97Bq0AsDazlwSGm7ussuu1SfXMqOvlwYwC233JKuv/76YkQ6hxjrQiT0eaS7Er+FVCQAasdoYW2HVu1GP3TUFh27ZBpWw4uBcLnvXoIGI2N8+8/Him/RooF2A0GE8JX88tZHiITe3u9xbrFtb2SsujGagiEF3SP2LnAMGV1JW+R6mBkMGXzk5u8YPU5b2UsvvTS96lWvqtYoWgWiFsxvmIUvu+yyqv21mn2evcCzeKZNkPIgSBmMApP70GZSsQtjHchsdWXFGJaI87hHWRvWKBcY871uPAPnh2v23XffofWMe8V5I2wzrkJSnjHA3wYj8rsWpfz8WCI6WomYB9cyflspZoUk3Ay6Gpyn5zLXyhW+coEx3+taW2h5vnDhwqFW1nUVR2n7jKIBDkuVSruAcR110KcSvjTQCwNrOWD6R8r30ObCQGR8ELx99tmnMuuptZUgEnoICITe5jFxbKOV1XgkfJqVSxHkanQxxcuqaJGQxLx6iRjXY5Yk1qFJm2RsmB5tevVlRoITtSQAMyhCEhaWpoj0SOgxr9quNTKPWINAom4Ue10Ng+jrNvBPoh5dI3E9eUcFE9tQN2mTjIMpHA2ZFsU+N+6BuFe4hmvxozcRd7M2FO6Yk2sf56yVwvfS3VRXw8D18XdwaByBY0XTtevAHFibOoExX1PWHPN/FBr9zX+dG2Oxp9hbTdU3Dbxkr7Jno1Ad92G0QJlOCePzfNTtFX/XOhfPT27OtzAVZ9gYklxgjKBQyF7Bqob7wOfWvS8WFYRGrJOjKQ3cNHabK6mH1Qe9MLAWA4ecADiCniB8JQleQinhxScKwUHrawMOIAQNAozZE6EjNijKNQ9AbUPTp66E6FbQ7AzBzLMU4thcBxFDi8RfjdWiS8163APMGQ04+uFzxiezwY2AdsN9JaYUwWJBMErwKKGPY8tA9BPznhBr8aEVJceLRXfQYvOWuxFgduCF54AT5tJmPr3jjjuqGAqsQ7oz8r2iFUnzO9dC4Lm3CQy8ZC6MwdyYY35NxAnvyLtGphbxIY5sgQ0OxUlJiFFgZE2Yi8WLmkBXEmuPOTxG2sexI1M65JBDqvlgSWoDrgMn7F32MHhx78ex496HUbv3S3iJ9TTASV7bIo7NnDmznF3OQynAtgTRlRSFtXyP6VLgzBOrhADRVkCrBHVWB6Brg7MeVh16YWAthhj0JOSH1sAz88TxDyLJky6EebcNJPSWFEbzg7DFIiGaw6N2EtvX2qFPBqSGZ+qeWlMkvDATiBhjme/cxV8Yg54s96pVI78/VmdDM+S90Pq6gClYpsAxVwmhDMtYCFM3Da7zNzMP/E6t2XoM0eesm8S4BRgBjKaLJqYraeedd64YX2yikzO+2GyIa3faaafq3jYhKbqZmJv+eq1FsVKg/l/f1wyJEk70e+vWiKmlADgH99aWYE26mpNZaywJML0Y+BlBpmqWBEIMe4s9dtddd7U+I3bQ5H7mavS+v2v9Yg6eixgXYaaJgYeeH90Buk/ieQQfnFX+33TILucHdwyKAoI095iRlKfTxtgC5v3qV796SJAYBJqCBxWQe6vASwO9MLCWQh70JORMTy0vmhA1nxMx3hW4VxMjxCFG2Mf+87GamX7VqkXs8ylzEkHnZWqYjAkfqMF8EPZBms0AMegJ8L0NQBNHedc0GBimcfzBXRoH5fEEPMfAy5zpadr1/U3/Ai+WzJUhmjsfS/LmgXBoeIMEaF155ZUVTgn2ynPdYxBbJO7inHu4lzG6Avczx1LgZUwxVDgUXwqr7qO4VxSqZIq6amIgXFOAZg7MA8aFRstco788muhlwLGADymX7DGEpK4APsEHe5oxwSl7XQEE3BuDE/cKwHvF/gviJGbfGGNiXA1j6uobxHRPqiDzxAIC+N5xXnmZY/896qijKgELgWdVhQEFJPZCn0r40kCP5bUQOCjkPMegJ78H1MI08eXBREYBEySEJj3IcyE+eYQ9GojpSmoQecCbwXkQNdMOJfialhUwDGLMA8PagKjmGPQkOJ8Yp1AKdDrssMOq68DtIDjhHWOEPe+CDzWWrJVgwuwk+hJwiH3emIm/NS1DXA2Es0hOV7xAtLEgRVeS8449DWI6WBybZxJkyRhNVRJznDCWGSqMyTvwLuwZy/KKO95dYdHMAXDE/Xk2BP8SCMlYXBcD4QbZK7gHmBeBkhFipoHWrFKPDvbYnXfema677rrOzxTnzJk9LuPmk58HG4GZ7meGQH5+zLzhDOaZE1pdugLvQ3AxlpKcXjDvmEablzlWSCLGAIGi63PrXARdspJ6WL3QCwNrIdx0000VMTz22GOLfnsgpg5aGCYCaYYEE2Id6HJwcwlef6iBbGhsRo/HgLeSFmFAmRYNzd88w2I2eRBhGzAPgt2wekydOryDmiVoZXyan3Ocqd3cdtttnUzAOTFTKLDcM5qfjC2md9lIRqZvMGdMy7Nls1kC0U0yiDAAE2dO0ZXke5t+JrNxjvnY3MscYj2GJsiDB5m7WQe8E+8W0yO5xmJS+u0VImOKnJXybAsco+Hb+h9EYG0JGuS9ooXF99adY7Gg0vmh3gICFnuurYeCY8fgQZ7LXtfCoZUtnh/3hOsjruL54Ts0aM4g18S4mjwmoW1+CEjz5s1Ls2fPLp4f+0AoxOWgkgFtaoszic/NrQJaOtqyKnpYvdALA2sZcHgwhUOMCHyLoIsgaqISjxJBwC/Ioe2i3VikxaY8RlOj0TEPtXsj7IGmvGPzndV6SVHSzKsGH83IbQBR5tmHH374CHwBauk8IxYnyok8BXdgXF1NwDH/PWq7M2bMqJiVvlufFzV/AwUjMzF7g2umT58+FFAW3S95wZw6YByqUlphMceLAol+6ljJLwLMhQqOl19+eTVmF5woBOpvNjiOfWtgaCw8pdnb1ruxEI8CJ7gEp5jooxUl1nPoAqwta8xax3cVp2rbzMU9L84iIEwwJ1xLbRDdQO7teH60nsT6Hvn6xBoWZk6AR3DBGAqM8Yx23Su4gagVgHWsNHfxa02PvFCSwPoijGNd6yqE5Aw/KhY9vHTQCwNrGVxyySUVASLgLT9EsRRr3qkMyKOO8ZPjMyXVsC4KWIKUVwPU1w+RMuuAjxH2seRwXnbYAjnczxwg8BIZ7jGlDuD/TbeqI2oGPWHyzWscOH9ATSqannMGwveagG+44Ybi8ySOuhyASLz4HRO3gWMxwj5WInQulsoFJ2ZOwDhtXWtJXM3VjG8lwiZhCaGR52MtyfeK97o+fiK+Ik4Yw3oMdTjxXovh6J6xrK+trHk3I+wtWmQ9hdiS2VK5Zk4YSMrHd46uqFj1sA4nrClriwaroFx3fuKa5mmhXGM9BvzkvEsJFADcw4Dnx/PB3ucMcBaseGkdhnx97MNh5oTnzt4axh7kVQ/r0lqjK4k1pppi6fzE9amrsilesK6xbvQEGcRaAijI9EGDLz30wsBaBAY9EegGAYgQMwZyLTxGGeeAJsABJLtAyDUYwLz5vIKaAT4WPDGaG2Jgq2TBfGdN316rRSNWmzPIzVa/BnZFi4GAeTMGPQncY/e+UhtXI6VzvKDV4//E9xm1wtgq2Tkb0S1DMuhJzdUIe4g9pmA0XE2tjgs+jPwGJ7GJk+VlFSLySpDRKhGZ4M0331x9ZHqlKO28iJHMz7XN9xBjOa5zl4FGC0A+R+ce/b+8I+9qhkqsYqiJnu/BGbgzc0Kc2rcgzltcycDUjqOFgb3C2mJ1iaAlI1ZtjHuFfxVyIrDn2HuMW3d+ZHjs5VhaOvac4B4zVGyChJCbl2/mOxtpca0BhBbyyit4emZ9/9L5IT2ZsWHipfPjPoxMW8GgJFBztsELAkZTy/JS8GBTKeYeXlzohYG1CDC9cVByU57Eu8m0Vucq4HqIABYH/Pax13usfQ9IDIz0tRWvY8swIWbWsDewyUC4UoGc6L821TDOW8FABh7Nw/h+0fZyphdr2MskSu8eAx8jYHmBEWECjub5vNxuJJA54RQnCjc0TLI5FJoduOFfxuU3mJ4mds2nUUiKRZ98dt47wrliCrcEdcSzzCKvtFiqzJebghlrzpw51dg+J69977xizEhkeu4VGSbvzLvz/+CCvaK1AFzxm8wzapKxJK+Q48TYDOcK02NNLTAkKNDUVbmLgkwuPGpJIvCOWJPoLoq9CfIiXzF/PsZpcC9zwNTOOTLwkg/7hXnkPSfcK7yvBZ1iMDFQ1zuCQFesarjXorDmNZ6T0vmJ1oo8buKggw6qxkMg6OoiELd9/4GXB3phYC0Bgp7IbYZxR81fRmaAT13ATSnASuZN0BBaBu6CKADE2veAY+eHNmpjpqZxLxoTY0nITKcrpRH5HUwjaqZRiIlBdjJyBCTqxhNzEFP0FI5iMGMOjmeam/eb+veKV7yiMgHDvGN2RHS75EzPoCe/z5kv7wdeYHYGKcIQY8OhqN0BMg2FpDwOJAbZcS1xAmiPWn0ULiKTairi4u/xHnHKmIxN/IDm7hgcGYWYUiveaFWKawkOAJgTuAFHZlhE4SS+P7jOhaR8r7hurCFMDyYVu/q57u6Dpr3iGYvuGe5FSGL/4UKJrpG6vZLnz3t+Yjqu/UKYK2eHM8T34EWcuD4xnTj2/YhnVrxEnPM+WL8QuogJiefHoF/xUgeOp0AV9xBCFxVS6+JMYvCtCkafSvjyQY/1tQRgepivCQYDIqFWcm+KvM2191gLgIOLZv3b3/62CiIqMes4RqlpiBpazBCwXgCEkgAn6xPkXegcG9DcqXaTlw6O70MrXsYjq0ItkPtgJmrPuU8yH8N/uYZ5ca/mbhgfBNniTk3ELA96iowmMnk0X0zAWEd23XXXipkaeBl9+LkGarlaNbA6Sw/3XXzxxVUsCP5fTe5mNpS6z9XhxfoM1r8H0NQZG7dSKdUwMj0ZeLQCRXO8MQoGwoELcAJubKajxq5AEM3+Mk33U11GAfMhEwJGio9f9wprbd37/N1ziHuJa7jXYj/MgfNDyiMCeyk6Po5RYnrRL69rxXoBnB0EDusTxMyD3DqikGRXw1K8kNdRipky3Jwf18LzI10oBfiVcJM3OQJo7MTcm+JMHFt3Xh80+PJBLwysBYAZnKh/i8bEQyfxaCrpGaV9Nam84x7aNbXIS1HAOdOL5tS8UE5eIEe/pu4BzJuxVXKuSQK5CbjE+GLQEwzKFL3chNwUZMf3BlgZ86DG7PtgAibbYtGiRSNw6tzyoCfXR20SkLlZUdEc+jzwEkKvNhYzDaIJuInxQXgZF7Ov6XqAmqB+Y90RdTjRtxxTQMUxY/OM6Ccv7ZXoSgJil0E+CowxEM5aDHkHTUArT2Q4tn6OvQLytab2BGZ81jIW39KaolWnDid5cGR0BYlj9iD1GBA6ciEpZ3reL75ygcfWwha0stqgRbhiIae8gFOcW5OQxJw466QRUpkyPz/8a02BLhk9uopygQCc48ojHbqEV2lX35Xw5YdeGFjDIQ96iia86MvLJfg8uCtWUcvN3QJmPYgzxYgiOHYMegIcXzNxqbVwfAZ/lwh9SWuJJuCSMBCDnvICS7FTXizHnNe+jwxbE7tEWoKG3x3LRl6SNwoDMegpCgKMl7cWLpUQltCDGwg9Gqb1CaL5VROwWlSOE0zsrB3lcqPp1vfK/del2vfOPfrevVcc8zfPWLBgQfXM0l6JVSnFZ3wn3jEXGOtKG4M74wjyIkQKtbE/RL5OrB2aNWsZfeFxzaOgUeodEYNa4x4Tx4wLTvh/9mYJJ7krKabe8nyF5Cgw5uen1Co51osw9iUG45b2Cq4k7qXAUFyf+G4KGtKcPEg1hxhsKc1BSKKeCTQsCiTRWpK7knp4eaAXBtZwIHuAwwKjjr7w/OB4QEvR3ZE5NgF+W6KAiR2I2o3ELAY9abK1W6FNjNo6xeWEHoLFvTGaHDAmQEtEJCRcDzFDQ+W66C7J66fHIi68E+/gu0nYI0QhS4KGRYZKjbgl4tg8K8ZPSDSdr1HybZ3ifK6piFxnNoYChnPWBJyvO4Cmh8CIKymuTy58uH+0PjCeqaPxt/yeuO48g2fFao1xLoynIBAL1fBOvBvP6FJC2Ip9Fi0Cp1of6nAf54HAsnTp0moN6wTp+CwtOXGvKDDm1Rlz8zh/syfZm+xRwflGq1qMVfAMmGrb1nOCMczGsQYDZzA/lwbj5sIA86AuBzExpjOWzg8QhR8FmCbBQIEgxlZQj4G1Ay9xr2hVy11JPbw80LeCWsPg2eeeTRfeeWFa+sjSNHns5HTlxVemw159WEU01cJzQqEGI0jQ84Nd52fOCxGhXaLdHPWao9LFiy9Oj9/1eJo6cWrad8t902ZTNhs65BxkNHvG1cQ7SHcxCIyaH8QCggaRU0vkndEex44bmy6444J08903p3lPzUsLL1pYMQhcBFG7j8RdwSlG3uunjWZfffs5XmPQGkSXss8ISbvN3S1dsuSSan12e3K3CicTxq/Me9ekb4645WQH8YMyP7Rl4ybwpTOOQo/dDytz85hUrc/y+5enpx94Ot16+63pIx/6yDD/cy4c5YF4NscBNJPX1avQmiTeYLDf+ta30nXXX5fum3Bfuv7O69Psx2ang6YdNMT0vJY5s8amxJX2ZxNoPWE8C1WBF8+EQtJGG29Urc99T91XzeXKc66sNFP2S9TCI0TtPgapqs3HXHuFGucujsQre5L8eoSkE991YjWXx+56LE2bNC3ts8U+w84PH/YKYyKIR5dMF+B6zh3jcXbYL6alMqZtpZ9+5umKptx818rz8+DVD1b3Iri4F/LSwo4R42rEm3N3v+sqiesZLS2sHY2MEEDm7z5/2PnZf+v9h7mSenj5oBcG1iA487dnppN/dnJatOwF//RmYzZLczafMywQDZBo+68mzCYCaxBbE3CIMXf+1Zl/lT5w7QfSkkdf6F0wfdL09IWjv5Bev9PrK8LDnGBcMO3oK+zq91Mw4X4+BKpJ6G1B+9Pbf5r+9Jw/HTaPyWly+u+H/vcRxF3XiMQqxgHk5tZYZlaffyRq/q72QkOoM649I838wsx039MvREdPmzgtffGYL6Y37vLGoe6MPFNXSKwp0BXMObcxDwTdoDPGYvzTrzk9ffqCT6fFjyweum/LDbZM8x+cn96yzVuGNDkFn0jAZTr5OkU8xvUUH35k8gQoPjrz0XTo/zk0PbTioRE4efPsNw913ONZaLx5E6Ku4Dzcb3aKNB6Fuf/fm/5v+k/n/6e0+NEXcDIlTUlfnfnVEQKf+IhxAiXN2PgGBanoXnK/5AIBfvL//N3/nP7083+a7nr8hbLW0ydOT1845gvpDTu/oVpProV54w4A8o6MXXDCx94OCATsFd7TmgY/veOn6U/PHnl+PrP/Z4ZwWpdxo0CZQzwfUVjyN89QFB4Rpv/npf8z7fQ/dkr3P3P/sL3ypWO/lN4+7+2d3rmHFw/GrOhAqSwDihYIke7hxREEjj/j+LQiZWY31L+U0hnHn5HeNvdtQwQM8MCpsbS5AdTQ6vKGhf9zw/9Jx//g+BHfO5dvHv3NdPz840d0FLTmfFeNT6YQtSErrDHW2YvPTu/7l/eNwIlzAScQEXESNTvH6tLoJBIyiVu0KAA/uO4H6cR/PrERJzA/zkd8nzyQsAvkeOS90KoRlvjurMVnpff+3/fW7pUfvOMH6S1z3jL0LoAEOqbRdVkbCX7cc34qnJx5Yu08vvXab6VjZx07xMDdczKPQZrQmEUQ9zh7GdrEWGctOiv9wU/+oHGveH48L76HOOris2ZtXMt8zxmfwvlp2yvMJe8oaAOgrlpyCY9mZyAY/PzOn6cP/uyDtTg5/e2np3fs/o5VohX5fKJwFa0F7JV3/fO7avfKD0/4YYWTHlY/dOXfvTCwhrgGZp06a5hFID8waOU3fvzGtOEGIwu7DEJE2hh2p7lMnp5uP/n2NG7s8OcNSsxKBF544skn0i5f3iUteWxJK042GLdS44s4KQkaXeeRa9PPrXgu7frVXYdp4aW53HbybdVcIgwyjzYiXFWgW/Zw2v1bu6eljy1txctGG67UdKNQYWnjNoFNRhPnEbVp9snsr81uxAla361/cms1j67vWAd1e4uxHn3s0TTn7+d0wknp/AwisOXzcK8oGHTdK7d/cuT5GVRwbNpbTz71ZNr5yzsPswjk85gxeUa1Z/N5jFZgE0Zzfprm0sOqQVf+3QcQrgGAP6+O+QJI04seWZR+ddevRhQzqX4fwLRYl5I20FyWLaquy0Efa1domjfvWicI5DgpZUcMgpM8liL6jRn7ksWX1BKyOJeLFl7UOnYbaJUozZ05XfPwNbVML87l8rsvH1YMqPotq0rXBFGAiN+ZeXHZ0stacYK5Htzl4Putjr3Cd1fcd0UnnKyO81O3Vwyy67pX6s7PoHulbi1ZnzpBwHksXLawOI+2sdtgNOenaS49vDTQxwysAUAwTRf4yre/ki5I7R3SVgWuTdd2uu7Lp305/TL98mWfx/qEkzVpLmvKPAaZy/q0V9aUeQwyl650sIcXB3o3wRoA599+fjritCNarzvv/eelw2cdvkpm6Lbrz7313HTUd4Y3LCnBOe89Jx2505GjNi02mYoZh3kc/b3hNeS74mQ08QtN13ddn7Pfc3aFk/x9BnGf1JmKDY4877bz0jHfX5kbPiheBjVDx0jz1Y2TJhdR1z2rORqcjHavDGoOb7ueuRz57SNHNZdB3Sd1e3Z1nJ9BXX4vFn3rYdWhdxOsRXDo9odWPjODaYp+xonTq5StHAYxcQKm1uUyoEFqczaZk6ZOmNo4F+b6yqmvHNEBLfqW2yAW7fEeC77w76tmvirNmNSME3zSpCblkM+nC9SZaJnLvAnzOuHk4OkHF3OwBzH/5vXa89LRr97h1ZXPufY9nt8rh8wY3sFxVfZKaY57bbZXJ5wwj9jUKLoquroJ4rzzYlr8zfkBJ23nhz3bNHYXqKtyCJAhsNumu7XiZebkmdWcBxk7h9KZi9kOXc5P3TykD6ujRwBzmj9x/qhx0sNLB70wsAYAQTOnvu7U2qhf4C9f9ZfpwQcerKS8SERXBzGztTBRyOTMkxYWn53Phd833WTTER0EY2e5NvAdIgEDhirebbBh+txrPld+h+fn8dev/uv06COPDhVsyXEyKOOLeOVdrAhHUODnj/58EScCKZfgJO8gGBv9tIG4szhOrBw5VDwpjUl/e8TfNuLlLw75i/TA/SsL0eTV+FZFQOJvSwg/8/Qz6e+O/LtGnHz+NZ9PG2/0Qovn/L0G3Svus9gpsRp77LjqWU3n568O/av00IMPVWsa0xoH9Y2X4h3sOYHmtcnGm7Sen1Ned0ptoFxXIUncxSJA/L9powRttp2funnkgvpowBoK0BWex/rEZ3edSw8vHfTCwBoC+266bzohnZC2G7/dsO/RfkkBetfe76pStGz2I6EfTaCPRB6iSq62uf2Yksh7JkXu22/4dlUoJcLm4zav5kJOvUxqiCBnudhRC4wQNRiviZ0STc/iN1KNPjDhA1X+fI6T//3W/13hxGptEuOY7jUanFTR6c+3GGYOmNXIAz9+3vHptNefNgIn5GyTKvamXd80VGM+ljcGrPJnsZkcJOqxFrz5/BG3VsPb5v5t0ns3eu8ICwFzI4UOvFiwybbUo7WWAJbRtecEY4OXE/c6MX3nTd+p1iMCuf3/dfZ/TW/d7a3Dqg/6PjI8BYO6Erdai8CdBW7yTolaYQ7f9vB04pgT0zabbDMcJxOnpX962z9VOGHOljZmjV3v0e6VKDBaVZO9QlrnaW8YuVemjJkylOLYNnYdlM5Y3mdEvJF2+7EtP1ad2whYbJpS+UaDk5LAyNpCs/iQwljCSdtcenjpoI8ZWAOAJfj7v//7ipic8M4T0o8W/KgKppk7c27ab6v9KinfrnUA/5pzXtcWuAm4v6pM9vTTFWGFuAOm57HeVXW35c+kf73uX9PyTZanjZ/ZOF39/65Ob3/r26uGRrE5UYTYnlaiEl0Tmh8tolS63/r3dMajA9/HPv6xdPVDV6+scDd1dmV6RjOVuMvowIn+XAjQILn95mfbSMZWsYA9Bqoo6Q3Gpf93zf9L9z55b5o7Y2763c9/lyZOmJje85731FZz453taliK6DeDIAoB+dzEKWvzta99rSrx+ooDX1HtlcfGPlale1LhjrnYuIYxea6lai3uNAhwLx/G414LH1lkpyqGtOkm6Ze3/3JlhciZ89IGSzZI551zXvrEJz5RrZHrmQutUfDJzdJReLGldI7TiO/vfve71Vw++KEPph9f9eOVFe5m7JZese0rKo3TCp4A47HWliXO62W0gedPn71FgxQEWaOquNJzzw6dnynjpqQr//nKdMThR1QlvweJj8jTF8VJ0/nhexps/fjHP04f+vCH0k1P35RuWHhDtT6Y45u08NHUxoh1H3i+jbgAyyLz/fgJ44cqrE6dNLV1Lj2sOnTl3302wRoA9IZHuzjhhBOqg3HwtIOrg0OTDw4lhCc2i+FfSrNC0NDq1WC7BPtwKNFmICqUaLWeudXZYHqxQcmrZrwqTZ06tbp33MJxVUleWpM6lzwIzBxuG+Wo+QHWS1czjPNV43E85nHJJZdU/ec332zzdPhmh6fZG80eqvG//JnlQ53OJIAIU3ZN5F8OgKV2uwhH4JkxEIRkprHeu8IH68M7gJedjt0p/eM//mP6/e9/X3WAUxiKAoGpVrn1BBzYypePvSQiaCVxTWj4whxpI8y1zAWcWAsenMDcXB+r09lESkLdJjxqIYGAWApYphTb7FZa+rgNqsCvPSbtUeFkxQ4r0lVXXpXOOuus9M53vnOoCl1e8tlcf4UXruFfmWqsjFcSBFwfcE9nvA984APVXDw/VEiUOSt8KsSCM/aYbgNx1ga8MzixTHUck2dxvtz/6ZmUDpl+SJo2baU2vOndm1a9RqjGV1eLX0FZN0oUAGJVP/ZPLsDEMtTcx1mtekhMm574b87Gc4bOctvaDyIc8SxwzJzYa5wfzzxz0QrEvoO+9UGCayb0boKXGThAF1xwQdU0BAIlqClqQrfhSPRJ28GMw4tZDoZWZ+jhMOK/49ByKOkJEDX0SJAhVCVTIR3OnG/epCX3d8vsuIbnqSloco613uMYCgtnn312NQ96JUScCLy7XdlkHDJNiLStkmGAmphz4Pm2FuaZ4FLhIjaDshVvKaDO1s/2bM+7tvkcxrQZkFo6DIhxZZb+7jPyZkP0n7/xxhurcrcRFwpXsXVzXB9+Q5BhzW2VbCvkEvCbrYW5h3tdK838sRVv7qpibszxd7/7XTXnvMkRIKPTfcI9WnTAjcKRLoKIS90lrg8CEmuw/fbbD5uDTC22fnZ/MSZrzZrz/7qZ6vz1NgSytTB7zDMThbnY1TPfs4ceemj1W2zuFMG1MpDWMuOxi2B0I8T4n7zZEGfU0siDwCCuE66D5rBX+NvOmwrSZkXY1XNQS0MPLy30wsDLDEjvHF6ahkSIBx3tVkYtEbTuPf9CsGlYUiL0+jVja2EPbN7vIPafLxEECBkNRy677LJqzKg5Y0pWAIitkiVgXut3xgZwD/dGjXPx4sXp2muvrYSPnIBEIYnr7eAn89aHDFOR0CsESejNnKgC4UKnOJm4xB3Q521nPCDXmugoyfhYMgDfA3zyblGLjf7uWJwldgq0qU/sV28r3l133TXtsssuI3DietnPQNeDDFOXEAQbzc3grtidMgqMXGNr4ch8S/3nS3uFee68884V49OvzbvEd4vrFosBxbiL2PDGZjzxvXAjwZBsxSvEHh66Nnym6+t72UGTZ9gqWYYbA+EUGNlbsT206wZONN2XYnn4nnlec801VRfMuuwI3z+en7rCVLkgzXdYgegQiPDRxTIWoeTGahMYoT0qF3lXVa09g86jh5ceemHgZQQOEx3OaIJTaqULqN3Yxc7DKkPRRF4i9AgAPAPiYWthCSsQBYHYDhaoC0zEbA8xRBuzW6KuAYMBu5hbJXQyChkx48FA0PJwR+QQtXPmGjs2DplnnydC/L+E3sBLcWJrYfBiS1nfOTazaWN6AO4IzPZ0ZTPuwPcC+LdLHruBYL6Lmidz15VU0vRi8KPMSCEpMnGZRmyVDD4Ylw9/21qYa3JzvO8e+883aZJ0Nbz77rvTr3/966EsgFiv3uDINohd7RSMwDG4Jq6EPVnyhdYJSY6jRYV52U3RVsnsEZiqgXAKjLHZVzw/7kOtAnU4YU9jTWKP12VHtNUMcezcSuLzcM/wHuBlUGizCtQJjAo0UZBmLBtsrY40xR5eXOhX6GUECAJxAbRYbUsziiZgQGbD92r5HGIOKMyawwoh5jvbo0biHnuzx0MbhZCSRsJz6Gr429/+Ni1cuHAoutsuadFlUAfRHMo8eK4xEVgEsAwQIBfNw0I0k/r+UUgCcvcF/w8hZyx629sqWcKtNSHvWhf7z9fhxBiAgw8+uHoPhCS1Ov7fLn3RPF4CtT3XR5zYIRBBg31iQF4cJy8dzHvJZBxb4ct35R7bRUPc+fA332m1kbhzb0wFzZlenIPfcT/7br/99kvnnXfe0FrbZTC+a51pPrpLDCLk47uAa8Y78MADi9krca+4tgpJzpnvfVdxBw7YI+wV5sbeKe2pOM/oSmo7P0cddVR1dq6//voR2RH5vOvw4lxiu2XgjjvuqM5m7krqCu7DHKKFMQqMuiyju1GIrqQe1nzohYGXCfD9EvSE9lR3aHP/YNRuIkM0YAgCptRO8BRmWogM2o0BPmrPMbK9xPR8Zl7MBNhtt90qUzUaSJx79J3WtUqWiOk7j8SD72B6BD3NmDFj6NpY3CgvmpSbgGPKo0FuEDHwwrWYr4nNkLCZohm1VJkZY0b/b3y+v2tRgeAhJBHBfddddw3hJeK1LrXQd4+CWgycM0YDJmIkuVYU90IuJBln4vuo3evWMX2SMdBU+Wgm57foC49j6/+NuPJ3BTzN3XwPTnyH+E6+o3uhBI4HREGN+8AxzBSzu3ELeapinrOvkBSFKXHF/7MXjAtgj7BX2DPsHb6zFXNM4ctdSeIkPj+eH76fPn162nvvvSshqfTu0dJTgnh+ohtNVxJnk7mPBvLgQQNJ2Rc8E7wg5HkOnEueLZJb1XpY86EXBl4G4BCVgp5yyDWEaALOzfgQaUy9MZAHIsfh1VJg5kEcOwY9eWjVxGLVuKFiQM8fejQPLA8LFiwYNmeJqxpkDhLjaPoViLTmd8ZWaInuhBhxHlPPchOw78G1vDNEHgKGb9NUMvBisRjulakpAOVBT/H5MuGYO8/fe+65Z7WerG2+jgonuhAiiOuSiwVG9Jvf/KZyJcFsYk0GtTLXKQZKghMZZNRS9YFHDU+NO7oOYoyFe0XBJwpIPrdk7maujIsQg5sDhhLB/RwzTgRdAbkJXCBgc+bMmdUZytdBIcK9El1rCkm53509YPEqzwzPZc+wd3AdgBf3dMRnzvQUAOLz81oaMRi3S5MowTFLLhZcjuyXQYMGc7z7HsYgcX6wjpjJUxe0GIF7u7oMe1gzoBcGXgYg0KwU9NSldLDajURJ/6apiJrDo4mVQ7nddttVBM4iKTIODnrMJlC7AjzMpRxxBA4yIM4999xhQWiAmrkE0XeIWnQ+HkybwMQ86KkuyM4CPTEIUk1YJg+OwQdWEk3fAHPggx+Y3xhLomfsAuNGX6jR3aWAtwis6Z133lm5OyKoDQMx0yDWZSj5inElMUfS0fK9kTMYszjEuXEmvreZE1xPupsplK4Pf/Mdv3GNEfYAY+hKihYbnpkLbvnaMnf2phkXEWRqMjnXxz1VqtMPbhctWpSOPfbYETjO10dhVw1Wt5q+dgvkcA14Zk+4P3xv3of5IxhYyMnzx/2+v+NqHm/aK3kwbpsiIM5L5nj31Pnnn5/233//6myOBuKe5B3NnFBgzOdSJ6iJh7r0yR7WTOhzPV5igKCiAdcFPUUo+e9lGjBPA/ei/xvQVCvILLAWcB0EzZxzK6dJ1CUyMae5DtBWIcwQoVywiRq1c5FYl4KJugQ9eb9mYYm974E2K64gYryvzzLwS4YTCyZBPCHq4EVGYE2BGN0u0W/CCSbgPfbYo0qNJFgsmnHjONFqUldjgPz5W265pcqfb3qmrgiJswKMDJ73UrAraXdxfXw/9gS/GYxqRDi4NzgzFpVpChBjPNxhp512WrrpppuGmbBdU9dSQTZmFkRgHuAWKwwCbtMzDXB0DN0DVqx0LyIk55axuD6+n5YOzOacH5k1lgOFi0HOD3sdbZ73Of7440fM3z3uOgF16XkI5VzHmRwtWC/A+Ayre0bQ6hLXP4fcldTD2gG9ZeBlChqM+fNNkGsIECqLpUAYzI2PIHMx9TASVIkfGiBaHx+uixpM7jesAxgDxId8cohrPm8gan0Sj5xAkotOqlXXoKdcMGLcWC4XRm5wU3zvaKaPhEpXgwxQ14FMVgLc1feJxsrzEfoixEp7CkkyjFJgIj5lfMuYw7viBFBLt6oijIu1gmnl7+36aJ2I4/D/3MO9jAETNBgxMoIueCEmgXdBcCwF+jkX16dUlRDgfnDb1RTu3LSiGERo/QnWPK9uGDMWFLjjeDyfPaa7xUqEkQF23ccISQQqYk2qswpGLbw0NsIaMUikJ48mWI9nQFPuueeeim6YOZEzc4XMmDqYQ56V1MPaA70w8BICUfLkGGPK61qAwyCkmO/MYaSSWOlASjwYHwbnAY4Bb9H0yUd/afRnd2V8mIAhgrkJOEYZGwEeA8vifBGQ0M67Bj3lAW1qrmjlELI8yC5qyhByNfPoApDg8jt+fwvRWMO+Lsq6BLzvvHnzKhOwZvY4b60wWC+cZ870cCXxXpiSu+Ik7zlhGVKCMaOGqRvELAdjBuJ3sfkN9zIGY8XYkxhn0QV4F0zy1mMQdHFU5WrHjx/6/zwiH1ySP0+cQFdmE4PxWEsLTLHGPMsgxuhKUPNlL6gJ57UAuA8rC3gBF6xVHrDZBdjzuB8I/ItCUtzD0WJTGpvzgxBA5sagYJMyhAEsaSgXJXdVLIBVR7vMquhTCddO6FfsJQSDnjAjDxJha1yA+c4QZQlZTJWqyzvmgEZNV/8mxM4qbBxgiLzxBF3nx5howph/MWkLMfVJE7WEN0Z4YyZFIxkk6ElmbpYE7wFh5l2qngrPF4OJFQSNBJepgyczCQyONE5AKwEfi6tYZrYLMD7155lLDCaM0fFaYVyLGOimK4mUORhF17Xgfhhm1SluzJihAlMyNeMWtAawr+Ja8DffxRgGccYYMgu+4xk8qykFLscJ78I7URvAfavwEn3hsVZEnB+4RCMnjXOQ/en5Aa+uK2sc11yXAnvCMyTOmGusYGgKLTjh3LD3tLSZoTEIM8Q6wH0xGNe9Ei0CMUtB8NwZdNsVrKjImTd4NLeQCDFjoMn07xlrq5PQw5oJvTDwEgG+dXKLB2F6ECUOLKZeI+A1/3IoIWhW/cvT+WKRFwiVxA6QsUWTohX7ALXKujS4kgmYdEOrzalh5r7kmAap9okp/IADDhh6dhtwL0SXOTKe+c6CGqOR6DGSm2fy7vwWi+bkQU+aaBnL0sY8M0aTdzUB33DDDdW6S9zzYLK8UJKWEuZ72GGHdXqWTEzrjhUptQZYzS/XXMUV3/ubDCHuFfPgtRJYcY5nxfTMrtYBLUnRFx73SgwEVCAgfx5cDpI/z71mRlhC2ABInpXXY1Aw5F15N97dyH3fX1eTuBLYgwQgMm/2ph00uwDzwlrIWYhWm5z55lY79wpnb8cdd+z0rGhhVGDk7Au51a4pYyAfN89K6mHtgl4YeAkgBj1hym6DmP4lQyoVBJJwcW2MGvc3ibiE1RSqeGjVgKKPOFbsM+2uDQggJI4BE7B+5VjLwHnLhJkrOOE7Cgx1ZXi2FkYwskBOxIlMjmvtYggo/Fj7XoasgAAOnXNkhsYTmHan66CLoETjIoj0T37yk2GpgxEnap/2KCBKHlcS6Xhd0rJi5gT4MH1SnMj4LH7Ee8Y15Rmxd4T3cU0MJsszW3gGzwKfeYR9E/AM1vvqq6+u3jW+e8RpZMzgDjM6uASnbcA4ugQYg/MTmZR7ReuH50eLGN/H3hGxyiDjsrc8j3GvGMzL3mQsrRFdzg+xN1xHefLYkTA/P5HRXnrppZXQQTnsNnBNo4VRgVGcRZdPFATagmYB3jNa43pY+6AXBl4CoJAOBxFNsQk4eHYiBCyPWmKqauASPplgXs1M0Hynebau2pmpf+Zaq3Hm6YM5YHpFw8e8rU81L/pibQQ+EGDy50klbDMrMmc0Gf5FWGFuZhTEsWXuail8YnXDGKGusCST5D21WBgjEPENTn22PvlYw74OINTUY8AyFAUN74tCDHMiq4LUPlxJTcBcteDYc8KgyTi276KGzZytBFjXO8LfuFaLk1H++bwtbcz1WmzaNGLejZgX3lVGU5q3jBncgcM2pmcgnHOwQE5JAAPUwF37uFcMOFWQdq/EJlwKD/k+9PzwbGNaojuvBOCPoGLcZtAAz0np/ACMR40C3C4w9iawkyfvGS2MOe5k+NHdWErtzMHsiz5ocO2GXhh4kQECaf58U95tbPzBgUUIiFHsEnWJkWZtCJW50W0+wxgkJ4HPiTAgIUQ7shSrldlKhN55Qcy4Fu0mzrtEcPD/wkQIQFQDaeoUB+7QZMRhZKoxl9z3AifRtFsHarxcb/OnGHwYGRMAvsEJmjSMp4nQcz/jEtgF4Y6BgjlTBXQpYAqvq8yXd4pjLlpIoqVHgSgW39HvbwBpE05sdWxTK8cxWjxqkmrEzKWtg6bCBe+IZYDSufleifsw5s/bTKhJYDQQTiEg3ysxgDI2+iplLkRwDK+PhY2sQZHvlbhnmzpoOi/KTcOojTNpOj+4B3i/vMFZjmtbV1uS21ij0hzcO20ZA/l9scFZD2sv9MLAiwwcbJg7AWVNUnts/JHXPbfKmYxObc68Z6vN6ctsi/SNdeqjFpz7JAEJPfPiupzQR+IBoaH8LIFQBAVGIhzHvvnmm6sPlhJNxHnL37xTHAQ+mjB9roKRWpwmcbXbpla9MegJHPLRqqJWxrzyEtAA4xt0lRN6rjManjmAE+7HJywOIv54FveyV9CaiXTPW/7WdYqLBFht1b0STbxqt7H1cx0oXHGtmrJjiPe8tTDAnJs6aMaIdN5x9913r96Z76IWHJkeOON7cGjZYHGbC4wGwsVYmHh+3GOurxk3uhDatHfz5xlf90F0N+WtuV1rAy9LHTSjFs6Yxx133FBQYNzv0eVDKWbcLOCkLqMoby0cXWolcM5mInXNdupTCdcd6IWBFxHIHUbbK/UfiI0/rBcQzbwxFRAwE0CiGQvg6CJo8u/nTUPyYD6JZp0WXSL0+uQj8SAuAjM3mkvUguPYedCTJnzeVSIWO8XpJom178VBjIdwLJ9r2+E6F0ce9BQjt8V5rL2Q177n+rxVMpagvIwuOCdwDrcIgl+uBfP/WA5gNhZvyntO5AKj65jXvldIjH74qOUZt9AkJOn/dU3FQYxviK2FY+8I91jsoKmJOg+Kw+zPs8guKOGE+yhjjD/d94llnc2cUGBkLXIrmoKDOIgMMZ6fGIzbhelFnCp0xU6Iee8Ii3vFeBz2utYJx4rBuIBrGIULgi+JPaKHR2ntcoGxjbHrcuySMZDfx3PqshB6WLugFwZeJDDSNw96qmv8UWpAU6q5boGTPKhHTaWk3XhffmgVMHxuF1eDhJ5/jZrOCSjCD4WEKIQSrQP8bfnV3P9rloAlULWQRAEgr30vAVXQySOetRLUCUmxFa/g+Nwrc7DqYRTGNBFrcjdlDTN1KZiO0s0QZgi5YzgnmALBYFiP0CLjXlEQAGSwEu/YOyL6+wHnF4smCTC+ut4RuhRKhayM7ve+GHdQmpOCC38rEMR1gHmTJsi7gwPf2X3I+eF8EIuSz5HxwLV417WRr4s4iecnVmwUFH5KQlK0quX7SyueezDuTS0G8UzbKpk9zl4vud4QCK2pkJ8f3CqcrTz+SJyUBMYmUMgtde1sA9OV+66E6wb05YhXIzz73LPpwjsvTEsfWZqWLVmWlixdkj7x8U8M/W6ENgABMwgu+u+jxp+bgCE4Tb48CDiCRl4KlOfW1b6XYarZdTH3WagGoiPz4/8h7jwHrQUTMIzvIx/9SLrgzgvS0keXpq023iotOH/BsKAny+XybtYLAB8xr1+clBhbW6AT38dgwvgOPCemVQmO530xdiNmBCjARcsKRNh3MmBLrRYC/u1vfzvddPNN6c4xd6Z7n7g3bTN+m/Tg1Q9WQoBVKQ2EYy15FoWh+M71Fyex9n2EWC62pBW65gpD0RzdVDTGmgiRsblPnUtsFASAH2NgtPpY+4B7eeerrrqqyiw57vXHpXNvPTctXrY4jX1sbIWn97/3/UPz4/01saP16krR1ZOfn/zdoyBQAkt168qI97kn6vaKTN9rdEUoGMTUX119BFGyRxCqzXThe+sxYC2aO29u+vU9v67Oz3YTtkvX/uzaypVEsSPxy5xtlsS9XRm6boGYMdIVdCVF4bWHtRt6YWA1wZm/PTOd/LOT06Jli4a+22rDrdJe9++V3rj5GysiZqESDq0SuQQsb1sbQRNejPwuQTQBe0glUiWmJ8hYrFdQV1Nd4gE4Xwsg8X6R0KPdfOzUj6W//OJfpnuffqFb3ZQxU9I3tvvGkIUEpgchRDhQuwOiZleai+bxaKItgSZgo+gNGGwLeoo4kTnkpXxlGNFq4Xx4H54RCT1WooemPpQOOuOg9NBzLzSnmZwmp7845C+GLDsKjOBWy00MlozzjrhRO9dS0ASMYTBqrM3gb3UQG0WJl7hvY58BK1oqONkDQ0EJAYFns1f+7PQ/S//m1n+T7nr8rqFnbbHBFmmvp/ZK2y/ffkhgZK9ptdAipXlbRlxyyRmXkJcXzt/NegyeF+MN8vLWJZzE2h65BSGWoPaMWXERHBiMapAnbqXv/OY7aecv75zuf+b+YXvlq7O+OkJgjD0nuoBn2X08aMXA3JXUw9oP/UquJkHg+DOOTyvScFM0h5jvv3n0N9Nb5rylIoZqkyUfZgmiFiaDbPLPQSgVPBQM2pqGRCZmBHc+tygI5C4KiRHPgmjz7zlLzknfW/69Ec9atmJZOvHMEytCdtyOxw21ipVpRMKkyTd/nsTda9W06iCagCG2XYKeIoNT8ysxWQP1LFZkpL1Mm2fD+CD04OTUpaeO2CfL0rL0yYs/maZMnpKOmXnMEIPwXaO2axCeQmRpfey22MQcjDNxfwBdisZY/ZFn+Mx8fRSgogvBhlLcj5ADg1VQuuaZa9IZ6YyUHh/+rAeXPzjs/HCfOI4pf9Ftk7+zgrTnJ65tCcAJ5wdcKBi0teLVr++ZMY4mLxgUs3nEk+4ivmOOMPfq/Cw9J337yW8X98p7/997qz38+p1eP9RbYRCIQb/WcRjE568rqa3RWg9rF/QxA6vBNYBFID+0gN/92WV/ljYdvzJSPRYDahIE8oh0rm8K8CuZgPV5txGLGMmtlh1T27rmHVucZ6ONN0r/7qx/V36v53HymYs/kyZOmjgkqGhOjY17YgnjGD2uIGB0e1v6oHOTYQwS9KSgEU29MU3N9YkuDQP4FELQ9DbeZOP0qXM/Vdwnwn++8D9XOGGuMV4kat8Ga9atjwypy16JjXuaXEklxhcFlJgJIo5iUKnaZ4x/4R1h7s8sfyZ98uefLD5r6Pxc2nx+tCDFNYkmcNehS6GoGIzrfmlrxRv9+j4rZoJEQSAGLSrQxDNQNZPaYFz692f9+8a98plLPpO22HKLgQWB2GxIQa0trTJCmyuph7UX+tVcRSBGILoGcuBAL35kcbr87ss7m+M09wKloixtoLaEhtPl0Ergc4YT88u75h0zxoIHFqSljy1txsmjK3GSl+fNx4oMRxNrdAuIlzbGpwnY1s9dgp4iXnKG06U6W4x1uPL+K1txsuTRJZV/OBcASu8S/fdxfdwrXYQBACuE5Yi79J+PY7s+Co+aydvcNgoG7M3rHrluoL1St5edS74+CjyD4MRgXC0XbdH1+dmMmSDu27iXS/dHS8dVD17VjpNHFqeLFl6UBoFoUYstxp1DF1BB6YMG1z3o3QSrCAQLdoGb77457b3Z3q3XQbBIN4QYYV6OgAlRjbMNMNdzPeO05doDmO2j3zX2RpBwdwXetQvccs8taZ/N92m9TisJc8Gcmgd3SXTbwO5yaF9d6sYbBR5z/U0JBXBxdNWObrvvtk7X3XrvrWnfLfYdqPa+EfMSdNMRuzacYgygS0qZVQxNiYvrA/NEuBjEd90VL4OcH9cHi0x8p9IerwPbhJtV0gYGvMZsHitVWpegK8PtipOutAeIVpLcvdR1XuCW96wrXNTD2g29MLCKMHXS1E7X7bT1TpV/r4vkbm59vF5/dRdhQHNoZZ5+vtBMG2jejKlpNnIx8r+tRrkR9bO2nJW6wI5b7TiUVtk0poGXRv9r4gSs/d7lHRGOiOC2kFIbQTNILvp4mQPxEfp5u8R9cB/vurpwEn3hNiaK66OP3HbNTcD6kgEBgMM2Rqlv3P4O+fpYPrtLbjvz3H7z7dPqOj+uj/iw34I4yPd409zAo4JNl4h53WdaV1wfcPtinZ8utCeP9cn3Q5d0YqGrK6mHtRN6N8EqwqHbH5pmTF6Z5lOCMWlMmj5xejpwuwOH5WDnEH3hJQ2tq4kTMOgJxqlpvQmi2Tf3hectZfO5S9Q1E0Mw5k+cn6ZOmFq9ex1Opk2clg7Y5oBhOdileUUTazS/SuC6ulDU8A1Ca6s2F8c2IDAGhvlvXdngWAyIz55T9mzHyYRpad8t9x1R3ChC7guP7oHoLzd6vUvRGKvwdWlKFcfOfeH5+tTtFd8P60WXvcL5ecW2rxhR3KjJF57HVsQ93jV/nr1SV48hf684dt36xNiKCLGWBs/efdLurTiZOXlmRXva5lUX9JvPvQ1cty6upB7WTuiFgVWEcWPHpb878u+Kv3mYSRt79JGV1fpiJTsFgy7Vv7QMtAVBSbwsrdulJK8EXuab+8Jj4GCsTR/9xBbIwT0xftPx6UvHfqkxAOqvX/3X6fHHHh8q9WslOwWDvEa6c4m+e10DbcJAHvRktbkmISkyVQWJfH1ibEVcyyjg8DcFZNgLXzzmi43r8LdH/W166smnKhwafe9YMrRS0GIeW6FQ2bZXYiqh2nKbSdyASt8z94XnsRVRkFLAMTee/UIGRd1eyc+Pey/fd1GQjhaJPLaii4CktcXsEINx2/ZXrIVQtz4Kj3F/xz1vNs7GG22cTn3dyKyTCKe87pSK9jStU1vQb0z7bAOzTvpUwnUXemFgNcCEOyek92/y/kqDiUCe9A9P+GH6gwP/oDKjctAJ6jNgCMKDb1LzW5sJMZb3rYM8f96ufE0+dQmC19RpEebdY25Xs5Yx4BvlNysqvnLKK9M70zvTtptuO2yMKWlK+l/H/q/0vgPeVxVI4ZlWYdMCwdg8AyiZMCWuMX+8ifHlQU9GpTdZBySUavh17gCD08C7XQzFPWttPj14OWGPE9KHJ3+42hc5Tv6/3f+/dNI+J1XZGMwPAYIxY+17xvd9SyDD8X2b9on587EUs9aBJlw6bl5Gt4SXOGf3PO/Eu1mCu6rbf9/W6d0bvLuyFkXYbOxm6Qfv+EF1fsAhuLQGgy4KxmfMPNUyzkOBwMyTpvfL8+dNoWw6P5rafUbd+XF+8fy4jzkDCAWcCT5HTTsqvWvsu9LWG289bAzqDPzDMf+Q3jb3bbXziVaSJpei+6OLK8nCRD2su9CLeasINOShgtqfvP5P0lfnfjVduuTSqoLapss3Tdf95Lq098Z7V4QBomeFMwK2OFh8YiqYrX9LXeUkMk2pdKVUQiPnIT51REoipmZVyhlXi/YaNRsZIMQ6mhApJXvsrGPTP574j+niRRenJY8sSVMnTk03/PSGtPGtG6f0ihdKG2tR4F/8tGrvgGbonOHn0eN1zVVypldXj6F0nwVk8iIyMhSZroxUrRdib4Ec1t17KS+7/WPbp+s/cn265uFr0r1P3pu23mTrNHbR2PSby39T4RKhEd8487Kuv75r3TYxZz9nbJrJ3U91a17Kn8/rMbQVqsmtWLGaJhALJjEm68t9sUAO637JJZekjxzykfTNA7+ZLlt6WVr08KI0KU1K1/7LtWnmozOH/Pfsa3BrUB44j1UP1YTz82O6ZywgVWKApfx511YhoXRfFErrai54bt3bMmwEI6s0xj1KA6dDtjgk/c8P/88qa4BqlcQILLxoYVpx04qUDhoxjWFzqXM35uvZZhXQlWSGRQ/rLvTCwCoCTG+77barmoZwCI/a+agXtKbFG1a/f/zjHx/SjCD0FlyB+KNF5w2Komk1FhmKTDE/mB7aUv58qdpcnS9Q36qmzFhsx7nk5XYtpiQgHC1ZsiT94R/+YRo7Zmw6fNbhQxrlrGNnpe9973tVffVZs2ZV91mVEZwQ7W8L2tigyLnYBtjfYm+FErHW/5sHPSkk5SV5xaXPiQWH4rq4Fmruukkg7qWKcOCe8rL0KNhqy63SEVscMVTwZeyOY9N111xXMYC3vvWt1fWOAfNDa7R1bhTGJPyW2RUnXsO9jJ8HzDWVYq4ryRs1RNsau1fcs7F3hOtgG13+tfVzBMoQw+hp8c39R+x4xNA44+8ZX7Uv5mzJjBQ6EZJ4P/aJZXzrzo9zscS05zNfc61q+R7yPvZSHqjq3lNQc59HnGgt8vzoJmH+7H0bXQn29TjppJMqVwDnx7W4b+J96e///u+rBmjz5s0bsa6ljIE66BKH1KUqZQ/rBvSi3ioAB/a2224bahoSmTYEgGY8aHe//vWvRxxACADE3ep01j9XW5NB5a1R6/zjTU1D6kzAMoWoXfksCZi17yV0tha2tjrEMQZFcu+5555b9WbfZptthrQhhZhddtml+iAkeY9+X4g6YwJ2RQTyeagFGvAWzeMxDqAt6AnBKDcBR40/+r6NMVD7i2tkpziuYV1h4gowwjnnnFPdS//5POCMuVOS95prrkmLFy8etj48B2ETJmpv+qiFxoZNFlQSB7E6X9wzTaWYY0leIfr/3V88w8I8gHNRaLS1MHNm7ryD5nqBd7322murd49nxz1Ot0LGAndxfXRHgWtwbqvkeH5iZkXc0zHeJK6Pa15nCjezJt9f0RyvQO7Y+b4FbFIGsNfZ8/H88O9Pf/rTtOuuu1bnJBf8saTtv//+6ayzzhpR1GgQQcD7mq6ts6r1sG5CLwyMEjgoNOKhIc/MmTOHmdwkZkj9NGKhJ7tEOpq0rdgHAYqEPq9kp6lazTgnZDHoqQ6iCRiI+fMx+lttOBYDUuvNWwvLAGIGwi9/+ctqXAShWNBE3PDda1/72kqgoKVvHpHOx/Flss5Z64rzU8CQEBpR73u1BT3lQlLMUogEVq07LwZU6hSn6ycGi/EOV1xxRcXcxFcMuOMatDza17KnHDtWz7NVMveBOxv2OEZ0I8T1jdkekQk2+X9j6+eIhzgWkK+F50KBUaFXzT3PBEEg3H777dPcuXOHMT33HGODM3AHDvOgUuZpJ0csMrFbpIKBOGHsPMshBma2Mb08GFdBWoHDtc7XwvHiXraVcRRanBeKA+/BGYnnJwI44Xq6PebZP4OY8tvcBF1KMfew7kAvDIwSLr744srMbyveSMyiL/eggw6qiAzm0FJEOocxJ/SMW/KPG/UtUTfVymIqbZG+RtHb9MV5S9QVPKIWKcPjHuaJRhZN7jGanPgJ/OKYfNW6o4AE8J3aDSZgxs0j0oESoY9aJaCwFFs8q50ZD9AW9CQB5XqIn0zPKGzrOuR+YDQ85mQgXN7IJqa2oenReRBrScxSEC/iGwvTwoUL04IFC4rEnXe0Rz3rb9/6XOgSJ2qrMhsb27SVYuY3/fPcI9PTBRGLHMV1ZS5RYGSuca/HTIMrr7yysgxoVcsFJPG07777VhYmcFiKDdHNxDV8r/ug7vwYWa9gw5qz9iVXUg7gxFgO8Z6fn/wMsmeZE3s4Coz53PiXs4AwTctma1l4TQSeg4XpoosuqhSI0vlpA/FTd0/MSuph/YBeGBgFcGgRBl75ylcOBRvVMT4IxVFHHVURP0vhliASeg4hfmL7v8exYz1zfc5WP6vLwZbwqcEwroJF1E6iiVZfL0SMZ8Hw6iqPSYywgODDxS8O5CbOKCQddthh1b8XXnhhreYhoTfCHpwwH03FkaGKDwk+TEyfeilf3/n5O2tqKllu2hUnfAxg4x4zJ5rWFDcSH4TGyPhzKxKAwEB7WvAYr8mB9+PZCGesJcxGLd771Ixj6V/93lpBSjjRZaO2zLjcK37zzpkKpszBGJJcYMzXFEAQxKrGOzedH/4Gd+Kxqcska8Gz3bsGt0bfeDTdm2rKmrpXms6PKYy2CZf5x9Q99zgf9ip7tk5gjMB8OAsAHQvbCgIhWGJhQHgYVBCIuK27r0uDsx7WLeiFgVEAWj4SMxpwScr2X33W+P9oX4ufrw1sVgLjhUEZTxCJggxEAQACHM31sYxu/H8+jB219hLBsR0xgICCwNNmfjToCcIdGXAkNs5bnzcCAUKSz6oDCBLzhvhxLxYI4wlKOOGdjOTPcSBBN5DMADuEMHGRz9vS0KwF/xrg2GY+ZRzWHBfAtGnThsV9xLFlNszlNa95TfWvjKEOqgC78eMrnLD2aIh8dJd4jfMQj7ynDDzWu4guKM3OtpWOY8SxeZbPZQ7MpUupWjRansFeicWV8j2uW2D69Olpt912q3BZEmAisCasDWtkW2CF5bq9wh43yDZa3Ep7h7MGU6/bKwB7kz1qNVGDYZuAeXIW0Pg913VmfAUTXAnXXXfdsDiT1eEi0JXUWwXWL+iFgQHBoCcIWWz2kUvZ/B2LsnBw0Wx+97vftT5DMy3aBPei5ZiLD+QFguxyp6tArQ7GFVO9IHimNEIgcyGG79Dw+Nd85y6aQQx6mjNnzrAmRyWc6AvHHMo76idvA9PSIK4QeuZqvrYE3nc3FU0NVQYITjTxavbmOnDonCPDtoYCWp5r0jWyGusRAh1rr7BmoGjEiWsJrhG8EDIvu+yy6rltYIQ95mfGgTHzzLgnNeGrDesmiKby3EUSU1/FVxzPFFmeybO7CIwA78S78Y6Wlpb55HiJBXxwJ5iG2AVYI+NxWDueq5spChp8x9pzXezi5/mJFhctLOwtLSyRqfIde9IsIfZq1yI9xE/g6sB9ZmxFqbVwLLC00047VfEWMRi3K9RZHWKBrj5ocP2CXhgYEAx6imk9uZQtoQE04XnQSR/r0iQH4LBCMCG2PAMNGoIYo7khZGrbajQQWLQXia3mzzz3PAYTGpSGRoVGOEgqUQx6Agx41DUhjgzWMuCMORx77LHplltuSTfddFPn50GoILQQZYQkmRIAIY6VAWO1N54LTrhf64U4cdwoJBkIx7uwBoM0aGEcNGBiRuyDoCUhRo+r5cV6/gcffHB1TxdLksC9aKEIcPrujbBXs7UAlUzfPcp7mTKnVcDr9JPLmAyE4xk8i2cOUpWOd+LdwIvzdo/GvZJ37YS5HnjggZXFpEvjrWg9QSjgGe5xgDWW6bkOMV2T79krPD9WDYyVDtlrjsUeZC9y7tibgxToYe9zBjgLzNkgxNydk5c5BlBK7rrrrioTZXVYBlhX3W49rF/QCwMDwNVXXz0s6KkkZeuXL5UWPvLIIysCRBRwV2BsDqYBWRxWiBrMNxJ1/jVISmYrQTWPP0ZUQ8wgjDJT7rEiXPRjtwECCH5LBB2IoGAgm9pwrG4YgQh6TMBYB7o+U0IGUzFHW5xAoKO2yd+8O0whRsZDrG00FDMa7L7HeHnmxCDaF+/DM3QliRNT76KJPu9ox98IVr/97W/THXfc0fmZZgkYeMn6mt7nfjCHn2fa1c/v+dvmVlzj99xrtkueOTEITu68887qnXi3/H15ZnRVKBzF63ArcR0CeVfQ+mMEP2OztryLAk48P7ybQpPfs3e0vkUrDnuNcRgPHJk5Mcj54Tr2Cho+SkYEz4qui1JQKe+FYEU6b1sPhfhMIBcGTC3uUwnXT+iFgY7AQcPsC9MjZ7rEnKIJz4MciQJEBp/w9ddfP8Ln3UWC1y/L+GhnBkjl6V2ldCMZkdca9IUJFaaqEOCnFEhVAogQQgqCTj5vU/JivfxSfXjyzPmtq5CUR55DgPkYsKUwFtO7TC/T5C2jiQGZBhKCW5iOQgAwCIFHYITxsdZRa46V+XRnxGJBEXC5YH0Cv12e6zWuNQSd+YN7/NfGnRj0FvdE3LdqpgZj8jf3MgZjMabMIkb9d5kfVoH58+dX+fP5b3F9tB5FnAHMCU140aJFaenSpQPvFcZk/ryXdSxY8zyVVndBXB/3iteyx3Qfuf9KGSJtgNuD52lVyxWM2AeirmQ5AifCWVucSRy7FDxolcU+lXD9hF4Y6Ahov2hF5PhG8NDnzYby4C2BVCmuIwixC2gqVGMCeAa1DdBijLCPJtao6eQHXssCYxHUBiNXa4zBY12IGQQVF8Hee+89wqwoEdcny+9qLrmgwRxgfuC4SzfBaBExBoH3RDNDUIOoobHFpju6DGzrG33B/AYeWV+YBXgx9kK8azrvAmh6CFdEy0eI5l72CBpnNAXnOCeYjFRDAsvawHiJWGQH4H3ROMGPaXc+R/cJa+P6uDZmTnAP9zKG0fCxCJN+8zagVgBCklkkcd7RhWRr5FjvIQI4ZR5drQPiNtbnYG0JSsT1oHUsFvCx+qSBgjGllfc2roa9BhM2mDKeny57hTFg4AhHzCXHC+D6GNNSEtI551RpRJjuEmdSchEYYNz3H1h/oRcGOgAHzPz5PMJWHyOQm/BKteP1k+NyoGRvCWIgnAJA7CPO7zAbG+AwBxgzhM0AtVwQsF4AhA+CqynZPvRqPFo4rC7XZCGA6RELsd9++434Le8kp5Dk9zmQToXG1hRMKPOSEfmeamq6QxAKeB9N2wbHOYdofjUuAAAn4BUtz2JDrqmCgc+uY4AEl8LAc03P+ceSveIlCnCCwg1BllgH6hrlOKZFrbR6aOlgfN5J/77Fo6wfkFfJsx4B13CtcQiMYQVB0wz17fPsOkYlnkmXNGA07stceBUn7sPSmOAWywu4bjo/uqfUsl1LewHwTqw5YDxBFLhjS2YFTPsimGrr+amreth0fhBomFMuIAHRdSNeYkvmHEhJRTjpEmeSCwMGDdZVpexh/YBeGBgg6InArghqEUBJC68zF5JmSNR99JPH9LJYUS8W1QEMelJztYY984OYmQPvXMx3RhBgDOMCBJinjE6zpP5RIAYmRsJm0BPxEyUtQ6aRt/xVA80FAt6Degz0NSAgqiQAeI8ZAJq7DXoy6NF4AvBicGSM4pdgW0wJrQyGF3FqtTnNxrFgjXOKlfnEFRafPffcs9I8Iyjc1bVkBvQLR8D9wnfWHnCvaMkxGFEXQF6yWZM+15gNwfOsnBifx982R7K2RExDtSRvLLVrrn5pToKujpIrSetNXcvfUhdFcAuOLeQVz09cFwPhdI0YAKngq5WAtWcPmMqbp2cyR77nWZ41fze+QpdC3Jvx/OSCgUF/uJJys7xZLXn1zNiSOT8/zIGzSLYSab6DZBK0lWLuYf2AXhhoAQ4WQU8505PYAnX9wpt8h/jJ8X1CEKK5O9a+z7vlxaYhcWzu41o0AzQetH/jAdDwIBwGwsmcJQgS+bySnYRNrSSa5fkXrYagJ5oNCV4jIStpGY5ZEggwdc6YMaNKU4xEFIgxALH5TAx68n00XfPhvWMNe3CiFggDwLKhthjfP5bkFXx27EsQ3SuWnc4DTGPTnFKUtkyrZCGw2tzll18+5Lcv1b6POMlb8ca9otuGuvj8zj5BgOTD33zHb5qlXVeFIn6P0fw+N+7Z6F65++67K6sa7xAzVHxXA2RL50cBoaQNg2NwjWvJfanVxXnq7xdiKeboxvPcsRc4I1qLPD/2nEBocF/pd+c+K3vK7MVJjDEAolDLHmevI9REiP1CSlka4jovrayQhIWgKdUwDx40NqIPGuyhFwYagIPCwdp5550rn7YQa6T7KUFdgJVmSsymNGGxTHFe+z5K8Hn9dK+RqUo8dB8gEOCj5TqIWM6E8sBENeycUORBdvyNbxJCiXlTLTA39zaZG2ObXe/R3I11wKjzGPAYgyMj0cqDnqL/Vg0T4g8OGB8BzG53ZhPEIDrHsBoh40cCGgP1tBgwBgwEpkdkt++Wm3vz6PgSTsxoUKDhXRCSEGqwJMlgYnCk+BdHMX/euYqTGHAKDpg/QgZMm/e1mFIUTmSWQKzHkO/xGGTn/LCqYYrnHRS4FBaiBaAEMvbcvaRGD66pWYBGbyZNbE8c94qmcC0Zfp8H/bInwAF7hL3Cb+wday64PtF64P6LQlK+V+L5puMge5y9rsUtCkdt5yeWdc4FAsbk7BOj0UUYqOvq2cP6B70w0AAcKAhl9P/G1LxYrrYEkRDl5m5+s4MdBK2uAEg8tHnTkKhFGARo+hdaDkIM38fMg9LYgNpNXtgofx8IIRHQ5Hxb6Ib7LP+rNtOkZfiu+kC5V0ZFYCTajablUvpTFITyoKeY+qU/HsKOpsd1CHUQdwimhZy8Nm8ApcaaFzYqvQ/ztWCQc+O54EamXYrgjrjV3w/grzfWgfuPO+64dOutt1aFq/IxcmElMj0hDyrV9M33BAeS4mnaXYw7iTUzfNcoJNUFyvI9czV/3roT3Me7uf6lNY5j+OF+5gVOnY+Fi8B9l/OjBSbfKzJf5ue+MKiVdwUnBl56bb5XrMeQFzYqrTHzZY/b4IyxjOEQJ20FnGJcUBQI2IOHHHJIZaWKAbR1adBtDc56WH+gFwZqIA96ilqEBCGXsnMwujtv9aoGAwFBkoe5omlHiGNrivbQqhE4HlDqFMdzrA5naVb90jnByU3AdYzPoCcEmVgoR+GIecUKfzmo7eoCiGNoZSF9DIZRSpVy3qWgJ7UstfZSpzjLPdtm2BSzmFImcdWFogm4ztJDLQC0PUzXvo9mYk26BviVAsqisCjTktA7nnEmJRNwZHp5/3nHdUzr9vMxhoB3zDtoGnsSGU6sZBmfVdor/D+mcGpIUCnP/RHfLQaplvZKPD8xANT15W8EdVJ1CdrMn+9eyfPn4xprjbG1MNda5dL6HrGDpkK548r8Y+vnuEdzuOCCC6pr3Cvu3Xh+2oJUhYjLKJxgMWEuMc6ktFeiK6mHHnphoAZi0FM0l0aTdamkpwRCZqfJORYDioD5FC2eyoSlQxuDnhRAHNeGPE2d4oC6Vsm5EBNNwCUCb9ATAkz0WyrY5K2F834AMU1P06QlkrUScB+CDMGauCOsGJfjJQ96cn3M4dfna+ZEHhzFPCX0RtizZrn5VWJpMKFziPPBfA+znj179rB7xUneWlj/tviL8SKxK6CFeGQ4xJmgtWJJyvecOIdZ6RN3fIUS7o2ZExbIEfjbipcA13JPzDTQMmPjo/jsCLqS7Orpe/hemsyjC8M1jHEYQHQ9GNAojhGQwD2CR74uvlN0JcV7Gc9Ykry1cAQLOVnxErwY6xBbMsc4k9L5YS+DF9qam1Yaz494UZDwvLQJBnF9tM6Bd1qEu975+cldST300AsDBeAAEbBl//m8gE9+sPg3z9OXqLf1GDcKWD+iINGNQU85oYGx17UWLj0nlja2hn0k4tEEHH3RAlopQU8IMHnqYATfXddFrH2vBpUX2slTpzAB47+NqVJxrsZPABHnaHi8W8ycaHJZRO1YE7H4kvnxm8QzJ/LUAEBIwhQe1ycGxSnUaRGSaese8fo8IyUPFkPQwz2T12NwH6q1yqSMVbDAFIxPgbFJGzTCno959bpeotBltH+OE75DA2aujBF94XnDIH3p7nVwYgaBMRnRvRJx69ng/LAGtH7OcaJwm58fwPVmfUsCYwTuYS9Z8ZI9xl6L1iTAYNzSnmUvcwYx40dBOq4FY4FXBcmSsFQSDGIJbj5WNIypujG2o+RK6mH9ht4+hO/suWfThXdemJY+sjRNnTQ1LbxoYXXoyZ9XS86Dv6KGrlanCTPXttrMffgOKaYCs/3ghz6YLllySVryyJI096m5ad8t900Txk8YEjgAfdEQHmvtd40E5j0wgXIvGrFtZ61NH7u3PbfiuXTx4ovT8vuXp6fufyrddsdt6aMf/mgtcY8WlBggFk3W1ry3zG28P5r7NQGffvrpaf8D9k+3PXdbuv7O69Psx2eng6YdNMQoFQSMPeD9IOyDtF9lnggeMk4IvaZzYzI0AW+08UbV+tz31H1p10d3TQvOXTBUijl3ewi+bx5kp19ZfMk4YtEqLSjGRxC0iXUGS9Lr3/D6ai6P3fVYmjpxarVXNpuysrOjTMO4CDtbDhIoZjdH5obgaLli3wX88P2YsWOq83Pz3TeneU/NSw9ctbK8NXON7qzS+XFfaG1QK444U9uN62mKHWOw3pxVrHlz582tcMJZ3u3J3dL+W+8/JFB4Xo3HUOMf5PzYTEqhGcXBQFT3CmezcqGMSdVclj+wPI17Yly6/rrr07ve+a6hNc/fSbxEwce9xD3eF89OpDfuG88E5+cb3/hG+t2Nv0t3bXxXdX7Ys4fMOGRofXvoQVjvhYEzf3tmOvlnJ6dFyxYNfTc5TU5//eq/HkoH02yobzc2NTEnv46YNLkUIpBv/Ef/44/SZz73mXTPk/cMfT9t4rT0xWO+mN6065sqjYMPBB0iBqGIaWZdQRM2AgAEDYIOgYTIaYo9/drT06d/+em0+JEX2qNuueGWaf4D89Nbtn7LMM034kRtp+QS0QyeM8AoSEWCRgDkfVvfl/Y5bZ/04HMPjsDJm2e/uRrDGAXmr6ujTQAr4YS5gROebc0GG0HxPj+84Yfp0+d/Oi1+9AWcTElT0temfW1EUKnEW7eRY+TCon5jmaOFcnJiL/PjOtw0f/3jv04f+/3H0tLHXijLO33i9PSFY76Q3rDzG4YKVtnKObpWujI+ccj9MDyEUIQL9whz+sltP0mfOvdTacmjS4adn/92wH+r/o6CtOcn4kX3WS5AKxREt5tuBT+OC96w4v3T1f+Utv/i9um+p+8btldOee0p6Y27vLF6f/Y79yG8GTQ6mr0CDuL5Mb6E33in0685PX36guHnZ/Nxm6f5z8xPOz67Y/F8OHZpffJ02hivEM9PFB4R5J6Y9UQ66IyD0kPPPTTi/JywxwkDvXcP6zaMWdHhJJiTbR37dUkQOP6M49OKNBIFY9KYdPrbT0/Hzz9+GAGTUGmC7CJda2JtYtjM5e1nvL04D+CbR3+zEgjAf3xmtFx0BQhrHvsAoUcggMifvfjsdMIPTxiBF+fyg3f8IL11t7cOC4iTIKnVtwknWgiYdxwnWld+cN0P0olnnlg7j2+99lvp2FnHVowqugPUngbRfEp4lNAzN3Dyvn95X+1eOeP4M9Lb5719WIleibPvlvuic9BPbBR/Po4m4/9zw/9JJ/7zicV5uFdYH/ZKfJ983dtA4S7iEbxa6fIXC3+RPvDTD4zq/Fg/oK7GQISYxpiPoyBV7ZUWnCAQYCGJfvIoqHWFHI9mrNgk66xFZ6X3/N/3NJ4f9spoaUWEKIiLIwXqtvPzwxN+mN42922d37uHtRO68u/1VhjANTDr1FnDLAL5gZk+eXq68WM3pg3GvRAdHhmOvtM2aGPYneYyaXq67eTbqrlEGJSYlQh8HOvBhx5Me/3jXsM0ztJcbvz4jWnDDYYXRpKZdSHw+TxyrREXxa5f3XWYZpXPAw3n1j+5NW204cgaCl3n0UaEGevhZQ+ned+c1wknrE/uLhpEYMvnEc3D1XzSirTLV3ZpxAtzuf2Tt6dxY8etEqMxO6O0xx97/LFqfRpx8vz5YR55sahBzk++x6OFrvq7y16ZNC3dfvLtI87PIPNo21tVauLDD6U9/ucejXiZMXlGdZbz9RmNwBZhmNXyuWfT7K/NbsRJ0zx6WHegK/9eb6NH8HHWMV+JLr9ftvSyEcWAupj9I5SirQeeyyOL0kULLxp47BFjNZiJecfrH72+lpDFufzqrl8VYwaALgw4j8zXl25A2SWLL6klZM4Dcz3XtY3dBjGwqjTWVQ9e1RknsRjQaPZKHmOSFze6eNHFrXhhLuyp1bFX6ub963t+3Y6T589PXgzIsbsKavm8Y9xF573yyOLi+SkFyjZB0x5nTtcuu7YVLwuXLSyuzyDnpwSxuNGlSy5txUndPHpYP2G9jRkgwKgLfPU7X00Xphf3wFybyg1XcvjyaV9Ov0y/XCPm8pVvfyVdkC542eexPuFkTcJL13n05+flmUvXeXSlgz2s+7DeugnOv/38dMRpw9sRl+C895+XDp91eK1vt4vG12a27jqXc957Tjpyp+HNXgY1LTaZw9G+zr313HTM948ZFV4GjV9our4rTs5+z9kVTnK8DuI+aTIV8/15t52Xjv7eynz5QXHS5JYpQdv1zOXIb4/cA132imN3cZ807VnGYR6v+e5rRoWT0ZjDm65flbM8qPukbs+ujvMzmviFOlhVnPSw7kDvJmiBQ7c/tPKZGUxT9HlOnJ4O3O7AEb8pPw1i+jWNLAcIwPyJ89PUCVMb58JcXzn1lcUOgoOYf6N51rStWNzk1Tu8uvI5174Lc5k0I71q5qsax+4CdWmXfLf35nt3wsnB0w8u5mB3SekslTj2/2PpaPYKOGnbK8ylNPYg/t8mFwcZAnPHz+28V/IOgjG2ow1yk3VeS4P0NPZB0zyI6ThgmwNax+4CdXucNd990u6tOJk5eWa1jsXfB9grpfMTC0d5fkYzl0HPT9McSTNdFZz0sP7BeisMEDRz6utOLf7mAfqrQ/8qPfTgQ0OlWVfl0OYEB8I2VEI4jUmff83nhz07B1KBxm86flgVNZlVV5+n18nsYuW7oaI3aUz62yP+thEvf/7KP08PPvDgiMI3TT7mrgTesq9PPfnU0DzqcALONtn4hQYysTiL7zkI4yt1SqwKJI0dVz2rLmoe+ItD/iI9cP/KQk55JbxBBaQ4J+dF7QP2IcGS7IUSXvx/ft90k5UprxbaUTDIx+6Ck7xTYuWr33Cj9LnXfK78Ds/P478f+t/TsoeXDVW8zMdeFcGRv8E1e2XFcyvS5476XONeOeV1p9QGynUVpuOeiufH1M/KcjFmbOteqZvLoIJjCTiT0JTHH3s8ffaIzw57btd59LB+wnorDABvmfOW9IEJH6jy5yOg0fzT2/4pvWvvd1XmFWvYS+hzTbILxEAlSwjDeEh14kMK1mmvP22EVk4e+3fe9J0qLcpiI7EDmhpbFAxyUIOJfdVj9TdNnppAt75v6/Tejd47Yi78P+liJ+17UnUfOecS+tESeOdnkxwEJLvnnbjXiek7b/xOtR4RqjoQ+/x1tX7RbBur+EWLRx2hN1cbAhpNtLF0tBaHw7c9PJ045sS07SbbDhuDuYGTd+/z7modGcvytr7boHslptDFnhOUyyWFkvoKp73htCpaP8Jm4zar5sJeGca4nw9qjO9bV8nOvSJO6sYBL6THfWzLj1X58zlOvv+W71fnhzkzd9fW9xqU6UVhIPYJAOeYPsmZBydkDeR7hRTUphS6LpaBKFRFASAGFyuEznpiVnrX2HeN2LdYbOrS+VY1eFCBkTPJ/gXv79rrXem7b/ruQPPoYf2F9TZmAKCsK02C/ugTf5QWPLAg3bDwhjRv5ryqatlzzz5XEd7YdlVhgMPGb4MU+jGX30ZB3C8ThqggIFRV2DbdJP1owY/S3Y/fneZMm5Ou/Zdr046zdkxvfOMbRxRBimNbilbmY2qbxBfwt9wfLXHnHt7xa1/7WlUEicp/zOXpjZ5O24zfpjLdT5k8ZajGgtXceDZjkr/dVNK1BN5vIyYLt1h/AMI/fsL4Kore9XnixifStVdfm/7kT/5kiDmV/Ml5S2ZT23KrAc/JS7PGCnmM/d3vfrdau/+/vTMP1qys7/wDNOigNIsKdLdAyyogNDsSNWljsUUTjSIhWowYMaVmJkwqlUqRqpR/GKvyx0TBJVoxRpnRioXoqDNJJVEM+6Ky2c3SLAJCdwMuIA2IyjL1Oe3n8utfP+e85226m9vc50vdou9733POc57lty9nvPuM8vXrv96tD2NhTtCSrVYILKtrWVnqIExD5K2maMdDayiYWaDANG/beTPr88InXliu/8b15W2//7Zy8MEHz5SKzntUTT92x4tCmYIi34uCorCGA58vX768fP3rXy/v/eP3lhWPr5hZn2N2O6b86pe/6mhFbNHL/ud69opV+8bC623iw/XGeNhgi8/ZK56fA19+YLn1m7d2FrXTTz996viInMPvfsl7PJ4fvv/xj3+8HHbYYeW33/DbM+tDZVNM8n2a+LSxJfG6WCOEQkieH+eMOSHjwgqrQ+NoeP5hLP+es9kEHBIEARriwOCWzl9aDnjBAWXBggXdIWICPZxqn1T0gsEggUM8kL7HEDQLtfBMtTuZaawnzkJBUH5j4VrfM2NZdOKiriTvMcccU3bfffcZ82Ss2mYNhFgnXaFDrc7n1HKjLRTEd6ifznvyPL7LWBgHsMeADW54Du8CAWJOIEjUorc73BC0kGD6Zo6pCAdk7FzP3zstfd62XZCT6/PLhb8sNy67sevKRk+A3MpZOB/2PIhukditTUbbJwjceuutXfvg97znPV2eelwfns26ak0wQI85YM21nDBnY4RH1o054RrWwWZFrg/zb+MrENdnm3u2Kd/61re6uvSxVHNk6LGbovtOE76VIy3kk4UryxzbL4Hyv4cffnhZsPuCwn+uD1jzxJqZ/hFeZ68D5oS/8fsY5se1CKnMJ/PIdbrtLNDE2nYC+tbbrLM++/3OfuWzn/1sWbFiRdfUaFJMTywR7XxFK1EtmDKWoWb++S6lmB2LczKEaa0lrI9FsXg2e0VhxPHyt6750bbbtSDBhomYs24CmB7ahf3nIywtasMUCaTaEqWA+YwGLtZ+ryGbeWF4apCaGcFQ0xBawC5evLhrOOI10STpc6Jpl7HybrYxVvPJrYVzs6G77rqr3HLLLR2DrTHz2OwlNtHhuxBohBkIkK2S+6ApXeEBAclx2Zwlt+KN4DuU5P3ud7/b3Sc3OYparuV9HT8MgzWwiZKaptpfbGZjB0P6ANB/niZNGbonbO7k+nBvnsWac39bJfcZ4rqCT79uHYxwZeOpuD6T+s/T1ZCxY/EyDkRm5XMVdOLeZq+oqeeW2/EaCxBxbxoR8ZldCTNs/WyVSYVRrufdeEffN8YTRKjZMnfch+uiIO1c29WzlpXCmrF2nJ8hd1F0oylAxS6cjieei9xsiH1Pp0A6nU7TA6J27yEwTp4Vm5TpGnO8scFZQ8MYzElhYOXKlV2zF4hnnzQu0dPUHBkOBxcGNkToY1tcO8DZCEfNDMiohjQkmDMdDZctWzZDBHmWJvbYKjkSsOxL1xfNM7lWc7GaIG1g0Z4QPmro3Bi/btCi5ijDtA4+DZ54lxqhZ5wKUH6X+zkHEnfdHkMWBsywWErsyqZmxnz7bmp60d8dNWPNwgpXWj6iK+ayyy7r1raP6QHeITdn4hmmw7FPYqvkHHipAAUQNBGqZOLea0z/ecaxdOnSrsUxc+9YGJt7xbgTCxnFev/5M4UGrpXRcE/uzTN+8zd/s5fZaGUwdsI5V6jgHWOr5Bx4GQVGz5pNgLwXY9HaM8T0WDvWkPbBcd5zq2T3inOe915k2ArScX1oNMaeZG9OizFxSFFgZJ3stpm7qmo1mKYBU0PDnBQGOLT0QEfrHgIHTWITGU4k1JHQGyQVpXYInqZeW/jGTmSx/3wfdt11184ciwmSQy7zlLnrCshNcCKitiPUjnmXq6++ujPfIiANIQtJVoNTM+H/mdDjq0IAQBCIrYUlyCC6PWwmM+SC4bu0rr3jjjs6E7AthiWGCi66CvruoUATTeMKTIwbV9Jxxx3XrWUfNNtreQEKWa67rZIRggy85P4PPPDAjMlcgTFqpwqrY/vP2zYYa4bMznd1nnNjoNq8+L3IAM1I4N62Ux6CLoLYWyCeH97V95b5c35qAmN2ZwHGZrzKkImdtWMNsWYgFNSyI7xH37zE2v9aoKLVAFcSe5E9OS0DnpSq3CcwKsRGKwlgTtzXDQ1jMeeEgRtuuKGzDHBoJyGagCMgTppO+T+/2+oVDV7zN8TMA2vgVCQUYw6t0d1oYWhFl19++QwBg9hyT4vmDKUYStQlHgb72bkNQnnEEUd0hHMozcprNQGL3GOeuUNI4vNVq1Z1TI/r+IzxRxOrTAfIPCYxPa7HF4tAp3WA+xhEBWSEQ3PivWTYPFeB58ILL+w+I36iL/peaNmJ7hEtDGqRzA9CkME89957bzdXxgbEPRUtRWp6k5ie5m7M1Lh77r777hltnznRsuV3h+4DFHi5VosB9+TePCO6V4aEJC1JfefHVsnc75577unmhjkycDJq4fH9h1xJce64L4ILz2Wv5OwIrUN+v+8+wC6H7hH/xn1pQ0478mkxlEkQMycUnBSooiXKa6MrqVkFGqbBnBIGID4GPaFtjwEEJGo3ao8yMHu9I7VzAPfbb79OalfzM5BPwuM9NCvXmF78u5YJfLoEJX3nO9/ptBsPuibTSFxrkPlqCo3BhwgC3Ic2sM5TrbiRkIFrHVDQ0GTK9VpKuMdee+1VFi1aNJMDDYGLvnBdA0CmVwu2y8WAuI6e7cw/8QMS5+y772NYaps5G4HrEF6IlsdSwnzFGga1+gU5ziR2Koy+eDRe9gUWJVo08zctSZG4a+GIDKhmCs/mbn7ff//9u3sbzOZaR999n5++Fkvi+3EvYm3Y4/zEfPu+tFYZfxTMPD8Kj+xn5oDPGDear9Yk0yCdR/fBkCvJeJEYNMoaspas6f3337/eNTGIsAbTMjPzBbgfeIdJVrVpggdjqi1nXwtjPMvR3SiYkyFXUkNDH+aUMDAp6KkGDql+cgmFhAPigEmTA4sAoIaH9osEbz2BbKpV04tBTwoAjE+Go9XA77361a/uNCYIch6j1oVaf3YD6Wqm9xj0pKVALTDXMIiEUl9lHKvQVcI9NI1D0Pg3c8CcMDdx/DKMHPQkEXYMII6RudYEHC04UTiRQUdEBhW1vOhKQog56KCDqjUMfPdoMZAIqwm73jI9NTwEAfYL7wmRRwOG+SFA6js2910hIjK9LABEc7fvTJwJAs211167znvFTIIYJCh0R0RfuGCfsK5Y1WLcRaw9kAWDKCQ5V5Hx4v+G6TMHzAVzwtwwR6y55yfOpecn7ud8fmq1AEi5ZE21JGV47wwFjxirIBgHe4+zOeRKGkLcK13nw1+7kXgWZyamptYEtbh2Y6xqDQ1zWhgYE/TUByVyI8ajEABzxsogQQT+n4MMUVNLhrjpb9dtkMuZGvQnY4mER034xhtv7MypEWr83i+awA0UrLkj+oKeJHyOI2uBPE8TsJpyFAIw4SMExKp3jAWiv9tuawv3GHjpnBn0FIWQoehu4ZrWiLyMPmcayAhrtfcJLsWEn11J+rzj2mSmHIUkI90VAmB2CIzRnWO0PWvA3BggFi0lMXMj+7sjQ47vwb7DvYElLGd2OJeOU/h7LTKfe5ClwD15h7jvsiCSC/S4ZgprCgH8wOh4d7MlXB9+EKiZM+MJ+L+uLpleFkLy+cl7xWBc1niMMOB56nPnET/B3qtlJY2FzzRzgndi/aAtcfwxVqHWW2SMK6mhoQ9zxpaENj0m6KkGtRskdk2Q/M79Yn92iYaEWqIEseCgQ/zMBTZFCkjUvdfQYd533307Ey1M/Mwzz1yHARgEpyYqcZPQZqZn0NMf/dEf9foXJfbeW7+0+fq6BADPgVFINKMA4bhkvgbcIUBgJeC+Cl3Oo8R8ku+T71Ek6Stf+UqnocFc4vhzMJ/1F2rNaXg2sQK4khRaanB8+m9df5/JXnEvsNZRu3NO4vowDjRL9pVuJ6+HKfh9syGiptwH3D4wPeoxZMEmrqnCgpp0DdyDv5Ot0Ie8V9wnarJYP3wn1hpGH90QcX1iRgfnhz3inJq26fmJtQD8vQ+sKYIva2w9hrimUTiKQb+1uV69enUXg/T2t799g83yZgWpKGDpysqKwrHuxtqaD7mSGhrGYE6IkOTPYzJFq96QoBpNyjBzDm5NajdtTe0nEgeeCTPgGogahN4Uw1qv90ngPSCo11133TqfR99wNG2CfH/eyaDBsUFPUQs0hx1mztzqHonEVUas1pYtHVxjBD1+XNMzh9K7+kDwFsGEEPk8Zn+0yigMxDkTl156acdopnUlzfQx+HX6KO9jWqmBpMJCOQaQRoGEf2MmZwxYn9hzBlrG0rdjwPdx/1AwyUj0OC/AoEKfUZsTrr399ts74WJshLpr75i5P+/CO/FuvGN+b9fHGI54L+bQokW6Djw/NWvREPDtMwaCcWtzohAb0yljkKFgr5GKi1CxIeAZZlAYF1ATBLSO9WWBjEnFbWgoc10Y4BChRaOxEpw0LQx6g4nHlJ4MfepGsktMorkbgsX1BNPxNwijWvU0QBihFgDamn5voKZpLjZjcQx5zKTMwcSHNL0+6Nc06nvhwoXrmId9d7Xlrgrar83Sfq4ZWeZPcRgIIve1hv20wFSLpQM3SoSmZdfHoiy50AvPxpWEb3laDYt7sUdYU+7JGsdsEgUi3931MSYim7v5O+uMJouACSONaz0WCHvcK7tQYlop62OlTdMzIzg/MDmCeQAAADJYSURBVCKsJdNCIZp34F04Q1pponslnh8FKveu31MoYG4Bc82cD2V51ADTZI05A6x5Pj85Y6BWEIiaH+y1DXEP8J6cnZxqm5/RlzGQ0VIJGzYGnvfCgEFPaNMb2vgD4gERg1npJxdZi7CAi8VvTLOzmpx12SH0mIU1CU9L6GHiPBs/bh430GdqoZeYBsj40YAn5c/35Tt3neKefrqbE66HkMUgNt0UEuoYMMZn0Qfr5whJBo7xDgYZTkPoEUoOPfTQLoo+RsvH1DTnJKZjRlcSY2BeNlRg5Ho0WObF58QgOwsiRU2TzxQKjQGw1LOBl3zmfuyreFkDz8BPjmbPT62evrEhmsmjIHbbbbdtUP58DIRj7AbC8WNcgtp/fH/nxcJYcV95xixJzFxraRuqeFkDa8z1MRg3ujYi880FgdhL7DHcDey5aQVG9jb3MJC05pqJtRiGBIGhrKSGhmnwvBYGIBAXXXRRF/Rk7ftJiCWEIY5K7cKgJbWHGE0fI7TRLPWBGydg0JMH26IqG0LouTcCgcWCHJOxCtGnHAMAzYmeNugp5ztjadEdIWE3wNLnWp0Qoq4AZYElvxdTCTWFSiQ3hNAj9HFPKgeq5TkHMXXQ3w3GI3/+pptumorpRYHRokI2WuLe1mNQIPL9TMvk/biHWRyOzfeN1gkLOeUOmmOw5557dqZsNHz9zwYuZlO98SX6qLmGjAqi8KcVGBmr1jThO/GOzrNxNTyTOTE9LhY9MiPGUtJ8zr8tSoT1IbdKHoLBuKw5AYWxzHZ2xbieAkGasUyTSmgJYQVGKyrWrA65zPEQhkoxNzRMg+e1MEAk9aSgJ8GhNGoZogCzs0AOkOGbasih5iDKYPVDyxi1BkQtOZbEjRXNMqGHeY4h9EceeWRHDCHYahH68uN7WfyFf5OFQNAThGwMAYmZEznfOaeP8V0YgX55zZtquBI/MweMEVBAiO+8oYSe6xByMAFzDXAd8py6HqwPc0hwJj+ToIUjCow2b/Lvvjs/zJ1d9YxdQBBkXuJcak3iR6YXx22AJvvSvTpWUGK9GQdCUszbj3tFX70WDb7Leo61qunPzwKj7+e7826+p8ISsBuorhy+b+dKxhGrJ8a9x9yzBlwjwx3jZiIQl/X+13/91xlBOpvac0Eg5pC6AmSwjNHGGT/7kD0cBcZ4/2x16EvtzNCt04IGGzYGnrfCgPnzY4KelNohTjb+6CMKVl2zjr3+1lp6F5Cw8gzvWWNMkdDbuS5XPszgPgS6YcqFyavRxHtHMz1jwbxJwOCkoKcYF2C9gNyK1+eobSoMWN61r/a9lgDurb9YRCIeCb0R+mPiCcgogKkgDMYaAl6n8OaY8P8SP0FGwhC0cjAOCHEWGPOc6wdX6HGfSOh9fpwvGaQZCnGehfUJWA/ujbBWqxkQQWwHFjKC5hRs+/aKliy+e/TRR090JdlzAiacBcZ473h+FHzi+XGvxJRJ/hbn0PiXvAe4hrVgTRgPazRGqGbNEWAoRuTzY+pnrC1iKqHljcdYGBkH12aBMd7bZ9bKHPfBVMK+BmcNDdPiebuL0PTI/yeAamzjD4hJjvzWj2gQk2ZlmcCk1DcPOcwpBvP1ESkON/dGezDIqI/Q8znBVETRQ6SilhGJmcQCgofQYHe7GlPlutgpDiaSMye8b5wT/q9PuFZRLULiB3G0UZH3yD5rYA17U+yGrCfOMe948803d/UC4jPj3Gi1Ie7iqKOO6ua9z/rA91gLhB32CGOpCYwx4E1t066MQ3slCmyOw2DCXPrZ7zPXlqdlbOyXmpvJPQgDY5/rJ8/7MPrG+Q7vR4vvvsqWPMs9agGoLDD6PYtG+U5mntSi9OM7um58X7fOUNVDxszasEasFWPri8dxHKw9eyAWN4p7xb2MO4Hg1CFXkgKjFkZjSGpafnQf5WZDkzCmFHNDQ5nrwsCkoKe+xh/xEMZiQDJjmb/17602NwQLpcDcY+Aa6NNw/T7aRCT0UbONEc+YcdFAKFUcg/WylmrQE5H7lg2OzMNAuNgpLroS1OJz5TtgrwT95EPau8IVjIO51Iw/VMkOGE9g4GUm9DGnHQGJZlR0YoxEN84JICOD30nBc31yrrluCgPhYmOpKCw6L1HrZz4UkCYFier/tW9ETDuMWSlxbvkOzC8GXsYOmjEinT2LJoybiNTHqAX7fT7jb9dff333XYXjKDxGgdFAuCww5tLR+fzYA2LS+XGfM4dcEy1N7hMzD6KQp0neeBzWMBedUgtn7fmMveD1ea/wf/bS3nvv3bkXJgmMWhiHmm35jFqzoSGYSti6EjZsTDzvhIFJQU99jT/6at9rrvTgRl+e1eb6tMkY9KSW472GauYLnhMJPaZsu645Fu4L48Y0jnaj8JGJWQ56inXquSZmTsjw+mrfR98qv8eysLpLYpve2hrEKn6xFr+Bh7mSnYKBTC0Tetcsrg9R9DA26jHEOA0tFxBuBChcSVZuc324n4GkWWA07iFWjvTa2CUxar6W5O2zCOVSzLHnhPPqHNd6RygosV+seMn/c0T6IYcc0lmTYGxRoImMlL/hSiIzo6/nBP93b8aeAVFocVxxr8T14V2HhCTjeDw/jkXoYtGtkXtHxHgcfjenP6cOsvb0/aC/BXuitlfYQ5w/9lQGz84CY7Yw1hAbWI0VBABz0ldRtKFhQ/G8EwYI7qkFPfU1/phU+z5Gd2cTnkVPcle2zPRyARV/r/URqCFqxKZr5XQngub4HoVQFAYkaPZyz0FPfA+iDpGDoMXMiUm179XCa5HMtn6uCUkKTzn4SuEgt5at1b6PrZKZFz7jHWKEOmCNCbJE45M5yfj4nq4kvhPnhPGxV5g3+0zETot9te8VImIjnr7Wz2P8vwoYCpWxuFFf7wiFOa5zv2dwNjB540bRiuR+IrqezIpa0KDCkQzPzJo4BoXDWAxIS1E+P1oJ+s5PLX8+Co8GH07qHcHaGd9hU6RcewNXAfuFTBvPT9TciT/xO0OpttnC2IdYJnzIepDhuWyphA0bG1t8PsqTTz1ZLv3hpWX1mtVll+12KddcfE2nJZvOxKEzwp0DZF31aK6PgVzxYGpOtHxqTXKHmKltRP+daYa14CvNmIyJ68YEDJkKRuEWu98xXt5TgoJZ92tf+1o5/IjDy/I1y8uPfv6jsuv2u5afXv/TdYKe9GtCGCGUlt2NVg7N9lGzy+/W1x1NRg6Rj+8/KegpNtCRyDuOWLI5xl7wb33yrrNlfQEmYGIlsJq89nWvLd/+wbfLyodXlq0f3brcdvtt5d3vevfMurIWrKX3jMGf8d00VWcXiubevr3CmJjz2MESaM2paXpqrjIBGV6cE1M8fb77lf4QZj2YvcD9sAyg9RNncuZ7zyxXrrqyrH5kddlt+93K8n9fXpYsWTJT2MfgPfaL8SzOiVYS5yILvvn81Nacd+Zens+43/k8pvUK59hsnljfQ4FJ4SYKpDJsrmGv8E6cH91UaP2f//znu33xw61+2J2fl/2Xl5Un71wb9MheEmY4cB3C4jS++9hsaBpBwOfm/dPQUOa6MPDVm79azvq3s8q9D68NEgM7brVj+YeX/UN38CGEEl+EAGsBRALWF9SVi7L0MevI2GMK21ArXq8zzzsStBqiL1wGYIBUJPSYgD998afLqz77qvLgkw/OXD+/zC8fft2HZ6wcMDwD+LSO+Ay1tZiTL9REdRUMmTW5h215ZXKTgp6cE5m8ZuX8d6A26ucGGdrvQEKvCficfz+nnPH9M8rqR1fP3G+XebuUJT9fUvZ4co91BEaFCzVmm0o5lrxOzl1fiWMh8WdvyOTU+muBdyLmvrtX/G4UDLRMOBZ+5zn2O0CDNXUPwfF9576vfPjcD5cf/fJHM8/asexYPvWKT60nMGod0QSvcBoFn7xXFE6Gym3rQuGsRoEhupLGnJ9cM8E5sxSyViMtDViUeCZWNvYqZwG34sOLHi7HnX9ceeiph9Y5P391+F9147Nluf0RxrgDIqKlbVLwcYZWM/ZKQ8PGxrwtWRA45fxTytNlXfPiw08/XE776mndQX/j3m/sDqx+YJnYpEMYibt56EPfl0jITGqteDO8n0y1RtCABWKysGCUutoshP7bq79dPvWTT60/J+Xh8qeX/mmZv8P8cvzLj+/GCBGTqEsg1UBrwonEPWrwQ3MSTcD6vmP8xNC8qCXHmvk5JUsGrVbsZ0bjw8jw/zKGu7e/u/zzU/9cyjNdkzs8+MSD3R76zPGfKb+33+/NBME5J5rk3Q8KZLX1iULM0Pvx/qyXc5xb8fbNpZUMdZX0rQ+fySxieiKCEfOvRsxe+eITX1zvWT8rPyvv/No7y+M/f7ycvPjkmaqbCkcKo8D1yS6RLEhrReiDTJ+5sEIh8xqLFWX4PM9ydFFERPeJwoxWQYNXDYa8cPWF5aMrP1o9P2dfd3ZXbdDzE5uUjUEUpK2mOA1aKmHDpsbWW6prAItAPrTAz/768r8uL3rxi2ZMamOb30QtPAaDTTqARtEbkDeW6UUCK8Pp3mNk3rFazvYv2r78+bf+vDon4uxLzu7mxII20d8tUY3BYjGIKkc8x4j8Pmgp0QxcK+pSmxfvrRARU9tq1dliDQPnSmvJYz9/rNsrNThXH7zyg928eM/cKtn1yZkGuaXspJTKLCTJTCf5f2OgX1yfHB0f10eLgXEXuhsQeMpWpfzZf/zZ4DM5Py/eYW1RJIXFWEsjPqu2PjkActJeia2fxzI9A/3Gro/XxH3PT2dBeuELyl9c+BfD5+fis8tOO+9UTbUdQtzD05yfCC0bLWiwYVNhixQGiBGIroEMDvTKR1aW79z/nd5iQDXUqn+NPbRqd7YpHnNoY9S/RCoGP43NO+Y+1/z4mnVM4LU5WfXIqvK9H31vYqfEaF7VUhCD4rSyjBmXfvLsE+5DjOSODMdgxugu6btejR6B4KZHb5o4L+yVq++7elBYjJkGaud5fcbuFTVt4j6GXEk1YSBngjiWoYh0TeqMFSb7/Z99f9ScfPeB7w52Shxan1h5ML5DHwzGJYXWOZr2/Lg+MfOl7/zkmJhrf3LtqDm5avVVZRr0NRsaIzjGe7SuhA2bGlukm4BgwTG444E7yuE7Hz7ahAchwkwZD2k0jU8C3yWqHU19jBlQE2YUHPgdPyaHHj/mWIJx+/3PNKEZwg9+9INyxC79hZhqleV0IcQx2u1uDHifsW2aJea5b7vpj9Z3GIu7fnLXRt0rrg/I62ORoTHBXZjr+TEqfhKi/z1+ZjrbNCVp7/zxnRt1TuL6WE9DaBofc344M5jrmdcx5YQ19+fzg0DOXBkwuTHnZCztcSy6G+O6jRWQxBhXUkPDnBQGFuywYNT39n7Z3p3/eAjRF26J2YhpCDwa8O67794d2lx6tIbMVP3dpkoQszH5x1z3ipe+oowB38PMOSYHGkILkbf6W/SLZyLcB+bPdCzeZwwjhznG2gPMCUKA2RlDlgGhj3vPnfcsY7DPrvtM3CuuD3uEebDfguOsCTF9Y+M7vJPxG5OQmarrw1w5nj4NPr/D4pcsLhvz/DAW3kE/f2R+NSGmD8QykNnC9X2twvOz45zH82OhorGlfceen7G0J7sb8/PAWGtlX1ZSQ0OZ626C1+35uvLy+S8vW+H8rIDPF714UTlmt2PWK84SUfO11r4z5tBqIjUSfUxL4mj+zb5wCftQ2WDTzfhZstOSsuBFCwbnZOGLFpajXnbUjBm1z3oRfa2al6Pfc6yJ06Anq8dNqjaXXQU5aFHtKMZW5OfFypEwl4NedNDEeXGv5Ep2EdkXHiPZHWt3vxF7xfx5A0DHWJGiSTz7wmuxFRGxFgDPftUOrxo1J0fvevSo8xNjGbLvfuz5cS/rjx8qWhXnxGcoCCiI1GIr8tjN9ecdD9v5sIlzssf8PTraM427sXZOpnERTMpKamiY08LANltvU8496dxqsI+H+W9e+zflkTWPzBQ8ySVu9eXVCsSI3KRkTKQvh9Zqc5NMnQZiOa6s8WaCFgmYQgL/x73x9FNPl48c/5HB5/3t6/+2/Pyxn890dcslbhVisq81B4vlgkdjgp6sNjfGJK71QV9r1LZzbIXR4bEgkbUleM8d5+9YPnbyxwb3yode86Hy6CNr2wnH+XXOYyZB1PJybMWYOVGbN7qdd0NoGSsgTVof90VtfU273G7b7XrPjyAVlTlxH+eqh32+8Oy7H8v4Yv68wbhjhSS15771cf3y+VF772pLPPFk+bvj/27wWeecdE5He/owNuh3rIAk7WpdCRs2B7ZIYQAct9Nx5bStTiu7b7/7Op9TZ+BLb/1SOePYMzotA2LWMctfpxVyuCA8MAowJHF7aCcd3Jw/P1RtLmNSy1ID2mz5akU1PoPh4ZrA/I4p/g8O/YPyxzv9cXnJti9Zd07KjuWjx320nH7k6TMuCPyqElAAceRe+jjzO0eiH9vOjg16ivUYxlzLM2IaW4QuC1tDa92xDDKBefzbTnGLHl5UTt/u9E7bjaDOwAWnXtDtFVP+uJ/Fa5hrfleTrxF3x9hnwcnI+fOTSvJGyNRrwqumeOtrxOp8dqDkGXb2O2GPE8o7tnlH2fWFu663V85703nlXce8a8ZywbWmT5oiyjNiYag8Fgv/xOj+PuRU3FiPYRKcu77z47qxhozZtFF++J01t2rjHy75w3LWgrPKztvsvN6cfHjJh8tbD3xr7ziilWRS0O8YYZr7tP4DDZsTW2TMAAeFUrJv3v/N5QunfmGmAiHV9pb9v2Vlt5+urahnwxeYnJHbptVFJigjyUxqjASf+w8Io+j7THzZBJ5zxmP1Nu5rcSCFGX5yvvO1115b9npsr3LbB24rNzx0Qzcn+Dgfu+WxctvNt5Unfnut0AEzgNCYc44woZZqYSaFgszgjJ8wn75PmKoFPeV6DDWoedbiAtR21Rhj6hprYIEc3s94Bgj+JZdcUj7w+g+Uzx3zuZm98oJfvaDbK0u2WzITrGlxHoIm3TuOQ01XDT2utftJ5tfnu6/lz5vyx5wMWajM6Mj31nIR6/HHQlLWNGCNY2Ejmlb91q6/Vc57z3nlsnsu6+Zk9xfvXlb8x4qy/V3bl3LkWkGFe8k0GZ/3UPD1/Bg3kYUTNfE+TVmmlysU5noMteviXhlzfrT08D6a3xEC3Gc0N9vl/l3KsvcsK7f98raZ8zNv1bxy+aWXd2elFt+RCywN0YyxqcoKoK0rYcPmwhYpDFA/fdWqVeX9739/Z7ZbunjpzN8WnbiofOUrX+m68xkoJ6En2hliDzGOTWc0LZvSp+ZgDvMQ+vLn9bXHanM1QcBCP7HinYRFDctxQsTQ6GXo8ZkwQ+qn03J25512Lkt3emZOfrHgF+Wm5TeVK664outPACT01pvndwQLGWw0NcsEZYpqYUOFXvqCnvpK8npdLK4jUY8VEn2+xNROcfyN8edKfswJ83/MMcd018S9Mu/eeV0t+ve9730zjNYqhswze8VSswaoOSdAH7VrJcOpFeIZKhqjkMQaZpNw9IU7/3FOahXt+B1rGONnPiLDA7SxphXvu9/97jJvm3nrzMk+J+/TleQ99thju+6WRuWzbgjUZMuwrvr281gMuPVvMrO+Kpt9VSljPYaaAJTPj3MV4xXy+WFsrKsCY86QQcGAbixauKjw38zf9nyq3HDdDd1eetOb3lRdH91XkzAmtmSoFHNDw6bCFucm4ODTa/3oo49eL/IfHHDAAWXPPffsGvYICRZmTxrTcHhJYdJXW2t0Ev3yfWZtv9en5ULM/I6IvlaZefTHql1oStbEaac4zPy+dxwXtfe55jWvec1644Do0Znv8ssvX6dxjVXYyIBgLLZK1qVirfmoGevLzb77sUFPNRNw1OJiZDjvHfsUOB5N+HaKg+ERha5pWtx3331dK16a7tQ0sTe84Q0dw6RbXVwfns88IwgguNgqWYEhNmdifI6zrxAP0Ndf0/Ssx5DjTGJQae7iGNcgClYIjOxtvsucwFDiHo5dPelMmMHZ4W+2fvYa7sG9uCf/5hnR1RYLNeXzY1BfDuablD9vPYZ4fmpBvxYqch/GNWI8CoysJWuqqyzONd0r+XvsPyC4B3uIzoV0wczr0+fOqmFMDMWkUswNDZsCW5wwcNlll3WHcOnSZ7SZCIgDBxfNh85s2RwP88O/jnajSVhiE4uzxDS62L0vAuY81DQkmoBjpLuEL3ZKtIJeNHnyt9xaGDOlDFNiayte6s33EZAjjjiiEyIUkmKZY+6HoGSrZAm9bpJYnMWxG/QYOwrqT54U9MS7xIZE0Zyrdun85cqRfZ3iXLOYaYDWv88++5R99923Og6ECLo9IkixllEL535q1bZK1neeixvFvgEKejGAbkzRmFiS1/VR41QIcP/FCnreT4GRdbObI2PLmSAIR8zd8ccf37s+/I3v8N3sC+ee3Jtn2AQp9ojIDb9yIKGukjH581lIigGUsdCRz40VKIGxErG1MGvqmXXfsfa4ktgLfXX/2UPsJQQp16cvdXAIk1yPzk/rStiwubFFCQNorZi60XKHctxtS8vBjRHtHkJzvPsIvVB4iBqI0dkSqEmRvmqCVuGLqWsyk6wtcl9brULYbC0ciUjMNIDpYdJFo+sD15500kll2bJl5a677prRwqOWwj0zoY9amb5hmUxMAWReIO52txsieN7DbnjRJZBL6Mb78AyYFPOIhodwEwlxTG37/ve/35nDa614IzCHsxcwAdci0hkD84HQoUbMmLN/3DHHEtaMw+52Y6pS2tfCoEU1crVgYxgiosDI320tHMfm/uW+upK6ssQ94G90uKT1M9fUUm8VTnmmFpqc7hkZtNYeYwQM/JzE9NwHzCFzGUswK3jk2g78jTXSQlJrLRwzQRCQEQLodjoE9hJ7ir2VyxxvDGFgyJXU0LCpsUXtOIKeONiHHz65Khq+cYgUFoI+zSMTeggqREfGFNOlImHjbzAyoMZSgz5Mvo8gExlp1GDUJCVijBvCag/2PoLDmLB+3H777Z02NynYERMwbhTcLEOBTpHQMx8S+ujvjFog76R/V822L19fCwngXW397LxoAdDPq2aqmReizXr1BVYZ7wHTQyCsuZIieB4WFUzAvOfQXHMvhBCEEtbId1XrzVYUx2iXyDiHGTEugu87J9la5F7h+3yPPavA2FfoSmaOm4jv2sp6CAgMXMc1Q2WOeSbP5r6MhTHJ9Gvnxx+DA3nnvvMT50z3Vjw/ca94D9aEtWGNagJjBNez5lhAcBlNYsDciz2FkNSXXTIE93PfdUOupIaGTY0tRhgw6Ime45OYnlI7rWs5uJNy2yX0EDa0FrW/2nMkPEZWy6w0m0vQ9ZlaIQ2hQ/9pLRVLM69BX2hnkzRJ7kdPeoKeYJC1Qjzxu4wFnyhBYGg3Q5DQI4zwb8YGsa9pNgoHdlKM76/ZMwaYaTY2EyJbALyncQEIAgb3DbX6FVdeeWX3zNe+9rW9hXgEf3/FK17R/SAkTQKEmnc02l03U238xlrwfcbPPow+f/eKnxt0yb2HmIZd9izSMyQwCpje9773vRmf+FAOv3/ju1xj+eU+uO6MhTExNsbYd354N96Rd3VP6DJzXpwnPmfuLObVd36MCzBVkO+PYaqsues/lAbpOXdPscemxVDw4BhXUkNDmevCwKSgp768fSLIMQHjDxwDmC9MFYYD4zMXv3ZorZFvUBsw/zoGgvEdtObYmjWPF6sBz9KvOTa32KAntJoYzJeZX/SFc380QzTnMbnt9rJHWOL9ILjZTB6DnpgXzZxqdnyfeVHL42+W4a3VY9DywrN4J1wXYzvFwQzQZnElqSnXagDoy9YXjgvl7rvvLjfffPPEZ+jLNkofZtkVrkkMVqZvBcaYqWGtC+sBOA7mzmqNeY61SCAw8m7My9jANYRGWvAeeuih68VWRERfON9dsGBBd+0Y6GYyHod5yXtMU7ipm7G9uOeHv2td4J58lznMwbjA9EmtOrpJxpwfspKwrLH2sVBS7fwo8PFutWDcZ+siMJWwdSVseK6wRQgDY4KeYiCaJnh+OOhXXXXVRO1GxHgC7mOEfTRD6m+MwYUA4oZvH41Exq9Z3IOuadlAODRuo9enaUyUg55i5bdJLX+5hmdeeumlZSy4t9aTHHgZg550m0QCypzwk4Pq+NFPLiONmRMIIWh40zRowZXEOAmYzLEVrmEtIh0h8Kijjuo0xSELSwRzLlO2yQ5CjMzN/HmtHD7XLA57NcSxxep1CkmMByGAHwP42KNjNcgf/OAH5bbbbuvOQnRlTGr5a5wJ13KPac6PAYycO91eken5fBDrMzAnZuG4j61pEYNxFRiZcwXGac4P42GvsOasfV8mSBSk3YcG43L9NOjLJJiUldTQsDkw64UBDgmm/qGgp8gAcy7z3nvvXfbbb79OuxkyF+f7WTveCHtM61gLFAZielfs9Q5kcjBpi9GYf804uU8MhIv5/WPHh2afg54yQZNJ18ocY01ASIJQT/NciHUMvFQr9t1i/rdBj7FcLAQ7Ci3OIQJXzpzQXD52bPfee29Zvnz5DNOrBYvFiP/sC0fjQztlXqZ5Lu+j9QIhBmGG9zFVVAFIZsf3dREAGxYpNDhXaMnMB/cDMC0tJGOqHcb8+SVLlnRavshlg2tljoHWBIJUx86JTI+xMmau083EO8U0Q60sFvOJtSYUlqJgqSVNgZFnMPe+y9g1w8zPWrPmIu4JhfxaUKlCEnuNPfdsLQOWYm6phA3PJWa9MID2CkGp5c+DvhrpESeccEJ38MdqN1GC118JsSLHGManGyKnd2UtXC1MYUGT5urVq7vfEQI0C05D4BkHRZd4r6xpOA9Gsvd1XDzkkEM6IQnrwhgNM/o7eSaEmnlBO2M8ak8xvUsNMPZeyEF2asC8j8KRcQEGy40F70Jw6V577bXe3yyEo/m9Zm1AI8VPfsstt3TWj2n3CtfbQXDlypUzdSyisOj66G5yfWINA5sxIRzB9JhrmJ7zN828XHPNNd24EP4yDAJVGOgLKiXAknsQPzAN0/P+7BPeAQHYYNR4fixoZTnpWHI5nh/AnLJX+BtzbTaP2QpjwNqyxqx1La5AwZy94tgy2GPsNfbcNEJInl8F9tZ/oOG5xqwWBiAcpBJilqsR72zC62NqEI1FixZ12s0YghGj2CMjQ1vlx/LG0Zwcfa2ZeMCY0WYQBGB2tmlVkNFMPJaY8R4wTJh5bexaIRBgDMjKYK4IhrrhhhvKnXfeOXpOomtEFwBpjXzOesViQq6PxDxG05s5wTUQXGJB1I5zwacx8+J74AKpwdK1PqMvsJC9xnexvIxBrBrpmNmL7DfmRh9/dlH0rQ/3YE6YGzR5gyxjWqtrMQkwVt6DDJJa/nxen1otDcC1+++/f7noootG9duI58cx8w6cQ97JdY/+f+eBOdHKFE31zCFzyZxirVCgci+O3SeAVEKepSspj929rdurz23EXiNNl703CY4tl01uqYQNswWzegdi2oeoHnzwwev9reYLHwIHFyI0pN1IHCF4EgA1GD6HKMZUKrQ2GLxV+XLecfRrcm9NydzDxi+x6qFR5UNEjaAnAt1q+fMSMsedu7ZljDEBGwTonMRaAL6z6ZnMjxH2VuXL1el4PwhgLJBjHrgCklq06+H89o2Re0LgcSWhhWZEX7jrmWMrsgmYbAu0+745idUAYy0AAyfNxIABxgh7zfGuj1YA3tECOXxmqiDMkb/HQj5affpaCwvmhOtr+fO5wFIuxJPBPWBaQ0KSjDPWA3C++ZyxeH74XLeQmQRxThRqY+aEqbbcQ1derGEwpmooZn3WNruSXNdYYMn9UquyCRgL8zImGLdmFegrxdzQ8Fxg1goDNA1ZsWJF9dAOaeF94MBhKiX+ILaMlYBJkDi03Nfob83YMdLXVCq0Nsu/5ha2pihCGGUKEnOJjGbI+DyZb63qYSzFDAONyGWOHUtfsJhgTiDIUUjKFgBN4boAolXDoCeeZ8U+/k2MRS29DGGBeZHhxeutNhcFjhiApw83CwZUEGR8WDqGiHvM1e8rGwwWL15cXvnKV3a+9vg3GWgMDnWMmrtjK96coWJxHoUHx8Lew9XCu7NPYuYEDFjGGKsemrboXsmCAfdjTREaa5aqmiAdYyuyNYl74JbC7cDaxjmJY3DtortIAUhTuPEEZqgwVouDOSdW1tQawBzG82cwbqxhoJBnjEo+P2YlHXjggd0a1/ZKdjf2BeaKscG4WRhoqYQNsw2zUhjg4KCt4pNDe43IEc/TgHx8GDjmzshwFQBiP4AYB1DrSujhthCNFQNNiYPBoglBxGr+QD7LqYbWcM+17xVUSGfi37l++qQa6TlYLBI0tCyYKHNiVbha7XtjBSYFPZlKhysEwPgRAAz64vv8jfmsVXzk79EUrT+91juCsXJPAv7wa8d3z0Gltdz0GCyWtWEyV+htgBYZzd3ANcrxGN4nR4XrOrBXgGmrar28L4JRredEFpJcT/dK7B0R3VqWYsa8P23LbK0V2ZqEu4F8fO6dz4/XKaC7V/qYnu/C2eHdFZ6ZE+aGOWJvMmcGEUZowo8auetROz/8H3M+a5qzkrxPtDTU9kpNIMjBuGMzCXjfoVLMDQ2bG7NSGKBxDMwjBj3lvPANqf4FE4FpoN2gjUQTdqx9nzX83DQkauFoJDA/XAB8hg/Rhii5hHCE2lPMJ4+BYZER82zmg74MVFaMrYXH1kiXoIHod2ZOqKrGc7CaaFmIwZFxTH1BT1kL593srIi5HSJsy2W1xpq1wlRDGVF8vgFpUTDAlUSjJRhVTFWbFFQqYuphvB5GhAUGUzt/UyOP2Spxr0T/b3xe1MIZtx3/YByWhUZg1DJUs1a4343HMDhPC0MMyOTfBMcRP4HQqBUlZm/kjJuM3IQq7hWi7xk3z6idH8fkHNTy57MWzrtzfrgWFxiCgO4092G2VnCtVS+Hzo9rZtlhao9w35jKqSA95vzUhEeCcdmDQ0Wr4l5RkGqphA2zCbNOGIB4wJRi05DsCx9rVovmbg8wUcAUL4Iw1CrfRQleU2M8tFkL5xlo1FgDIE5oY/i/DRwbCvTi+1G7qWUUSOyJWoa5khftfFi0Zqy7REbPMyyOpJaItkRJXghxzZfq9bWgp5oWbkU4PqcMMhYervOzPmtFNAH7zDgGwfVUpSQHnqqU/K6/2uqRY/dK7A4ZeyUYjIjWV2Oeca9wrfPbp4XzfYQ6flhL0l75PFa87GM4uR5DLaPAz/Bhs0/o0aFly6JPkwSBOL9aCNxn3AtN3ZK8cX1qTK+WP18T1EzHZC6wPCAwOk9W7axZK7RYaUnqy8jhc9YQIEy7X3muwsqYuCPHnGMr+Jw9qBCWEc8PyK6khobZgFknDMCkIR7WT+/zhY8VAGq1ALAOwEiISahdH5kemoXEM2vhEMjcKU7tl58YN1BDNgH3pYyhWWOuhuDEtEWJmJrGUJBdDMZTwwbeDwEJQQkTcO1a5yAHPWXizu+1TnEGjjH/sVVytlZkISlqwXmdzJ8nmyFaRmwWpHtlUu37WAfAdVFjRbsmJ513ytf63exKylo4n8XYEvaJ6apYBbAgWYCKsdSsFZqUo5BUW2vGyn7CqhYDVDXd98VdxPeK8Rm6JJwT7smc8AwZbL4+Mz3nNQvSvKsluI0LYE6MsYkdNH1+tFZ4fuyU2Sc4IpiTlWSKZBQSYx2Dod4REbXYiqFg3Ggtca+1VMKG2YZZJQzkoKex/cIjAasJADl/GhMkfnJMzFHT0BzqoY1BT5G487mV1Wqd4mSWMcI+dwAUMde+Rsz4N73lDXqKVhKeHRv8ZCEo1r6PlhUbCxnlLUFj3qnFcOutt643vzLk6P+NEenMccycqHWKM/ASQs91asRZG+aaaAKuMT72CQwaAh8FtfhuCgXRl55r36t56tpwHV1/hA204WwCjsKArqTsVzYLJQuMcS/HwMvYQVOBLWrDsfVzTQtm/nElYcqPApXln2MHwejzd07i+ZH5OicGAsrI6PtB0JwNu4Trl11JUZDm3jWBMZ5RCznFDpqmQWZLlEJSnzDA2mHGh1lriXI+4/mJGQlDgrV7OVsrasG48fzUrGoNDbMFs2pHwpwxneL/HeMLjwTMaP5aMaAaSEPj8EftJh5+mR6IQYa5tXBfp7hM6GMqVQ6cy9pNHActhw166vOFq/n53rH2fbSqZBNxJmgwPXKvWYc4RolZDHqKvnAZO3+X2Q+ZXY2wj4RepixziibgPCe6khDo7PmQfeHRly7zjbXvZSSxGJDXRWsFIKOFngX4yuOcRE3bqH994fxYQrhPYIyotUq22qVzHYWk2p6lPC7zj4ugT5CO0ff8TTeAboS4j+JeydYK4ikQqrHk1cYSmZ7XcE8+HxIYM3KrZH6cX89lDMY1tVOwZqwdaxjXtO/89AnWNcEgx1Zg3TAYNwbBxvOTXUkNDbMFz2n9yyeferJc+sNLy+o1q8uvHvxVp5V+4P0fmNHgav5NiAh/UyuS2E0raesn/8Y3vlEOOfSQct1PryvL715eDnjsgPLqBa+eOegSHOvD8zwD48bCVCpMoJhEIYYQDrWhaAKet+28cvnKy8uPf/Hjsv+j+5frv3n9TCnmvkAnLSPmV0cGwO9RQ8xdAqNvmPsvXbq06w559dVXl2NffWw3lsfue6ws3GFhOXyXw8tOO67tSqiwgHDDdebEj43nADarMYIcBmVevemWMKmtt9m6XHzXxeX2+28vB/3ioLLmxjXddeR4S9xrPe0tCKSQpcsnWpJ0t2SBQK2eecMETJAYbokz33tmuWLVFd2efeXjryxHvvTI8sIXrA0aVOM09oDn6RoZCztocg/2CvcxEJX7M64Zq8bTT3Xr88RPnijzHp9Xlt+wvJzxX8+Y0fRrsSTOR3Q/6PLxOn50K8RzpYCt0ACD/cIXvlCOOPKIcscTd5Qbf3hj2e+R/cprXr62Wqhj9d64hrgegWUaMznXuL+sY8G/GbduFYNxt91u2259OD8HPn5gufnfbu4sAqxhzBgYepZZCe4TLWx958e9ws+xxx5brr322k5YPeHEE7qxPHrfo2XR/EXlsJ0PK/N3mD/VGWloeN4LA1+9+avlrH87q9z78DO1vV+67UvLQfcfVN6y01vWIe6ZgHmgn62pDT/5py76VNnnE/uUn/zqJzOfL3zxwvLREz5a3rz/m2e67hlh/mzyghlzJvRoRnaq++K1XyxnX3J2WbnmmWI3O261Y/n0Sz49o4VL3LMAEP3CtfE5h5o0ZYCxbLBR85iAP3HhJ8qpV55aVj7yzFgWvXhR+cgJHylv2udNnZatn9wqeRsCCT33scqc7g/G8i93/kv5y2//5TrjmF/mlw/9xodm3jtmPWQBoG+vSOzdV5rG4xxGIQnT+5988k/KB//nB8sDjz+wzl4558Rzyu/u+7szBZU2RGDMcA4QhmCACkeAz89ffn45++J198ou83YpBz9ycFn45NoKfTG9b8z58Xf3lYJW3CcKTfyNWI2HFjxUlnx+SXnwyQfXmZOPHP+R8vuv/P3uexZI2hCBsdZBk3lmTux+qJXngpsuKGdfdPZ6e+XjR318VMZARoytiXNYEwzcK4wF19WHLvhQOfPGM8uqR1etc34+9jsfK2898K0b9P4NDZsSWz09ImKGg4dmimQP89oYgsAp559Sni4pGrqsJRJffvuXO0KSCVhfnfBNNY7PnvjZcvLikzsChna2Mf18ZiGgFUNILlx1YTntq6etNxbHc/4p55e3HfS2mTkZIwD0IVtXIpGHoEFU3/G1d1THAT5z/GfKWw54S7cXNnaeNAIGQgHE+1srv1Xe9S/v6p2TL731S+XUQ06tWouyVjsJWbiKxJ7PLrjxgnLa/zmtOg7wjyf8Y3nj3m981gJjDYyLfaLb4Jsrv1ne+bV3Dp4fGE7f+0yTjVMTrjyDX17+5eqedRyfO/lz5cQ9T+zmg/OzMc+u/nd7SLBXTv+/pw+en1MOPmWjPLsmXMUATejK0F654NQLmkDQsNkwln9vdmEA18DicxevYxFYZ0Blq7Joh0VlxftXlG3nPdPwZmOb1saMAw3njv9+R3nBdpuuXCgE5aGfPVQO+adDyupHV/eOBTPjivetKPO2eaaxy8aYk8xIoVdYSqLGud5YdlhU7vofd5Vttt40qVFsyUcefaQc8OkDRs0J44gE+dkiMsAuqLQ8Xfb95L6Dc8JeufOsO7s9u6kAo3nwoQfLYecdNjwvm+D8ZMEAF8V+f7/fxDm5/b/d3rlRNhW6dM2Hf1YO/seDB+fk5fNf3q3Pxt6z+fyM2SubaiwNDc+Gf2/2AEJiBPoYsIfp3jX3lqvvu3qdYibPxTgwN1656sqyKcH7LXt4WS8hcyyM9arVV40KjpwGubgR89JHyGbGsube7nubCrzbNT++ZvSc5GJAzxYG2Rl0efm9l0+cE/YK39uUYCw3PXrT5HnZBOcnBmQyL1esvGLUnLA+mxKs1Q0P3TBxTu55+J5NsmdzcaPL7rls4rxsqrE0NGxRMQMEXo3BJ//XJ8sl5ZJNNo5lZdmo733ivE+Ui8vFm2wc04zl7//335dLy6YlIrNlXtqcPLuxtPMzu8cylg42NGwubHY3wUV3XVRef97rJ37vP9/1n2Xp4qXP6llbwjjaWGb3ONpYZvc42lgaGrZQN8Hr9nxd5zMzmCaDz/eYv0f3vbkwjjaW2T2ONpbZPY42loaGjYPNLgwQNHPuSed2/84Hxt/POemcTR5cM1vG0cYyu8fRxjK7x9HG0tCwBVcgJK2G9BqiwSOQqDdn2s1sGUcby+weRxvL7B5HG0tDwxZaZ6BWgXDBDgs609lzITHPlnG0sczucbSxzO5xtLE0NGxBdQYaGhoaGhoa5ngAYUNDQ0NDQ8PsQhMGGhoaGhoa5jiaMNDQ0NDQ0DDH0YSBhoaGhoaGOY4mDDQ0NDQ0NMxxNGGgoaGhoaFhjmNUoyKzD0lRaGhoaGhoaNgyIN+eVEVglDCwZs2a7v977LHHxhhbQ0NDQ0NDw2YEfJx6A8+q6NBTTz1VVq1aVXbYYYeN0hu9oaGhoaGhYdMDFo8gsHDhwrL11ls/O2GgoaGhoaGh4fmLFkDY0NDQ0NAwx9GEgYaGhoaGhjmOJgw0NDQ0NDTMcTRhoKGhoaGhYY6jCQMNDQ0NDQ1zHE0YaGhoaGhomONowkBDQ0NDQ0OZ2/j/Ls0lo6JUv1QAAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "kagome_reg = qse.utils.kagomelattice(1, N1=5, N2=5)\n", + "kagome_reg.translate(displacement=-kagome_reg.get_centroid())\n", + "qse.draw(kagome_reg, radius=3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Qbits attributes\n", + "\n", + "# Available methods\n", + "\n", + "# manipulating Qbits\n", + "\n", + "- Using supercell to generate lattices." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "36\n", + "72\n" + ] + } + ], + "source": [ + "print(square_reg.nqbits)\n", + "nn = square_reg + square_reg\n", + "print(nn.nqbits)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.10" + }, + "orig_nbformat": 4 + }, + "nbformat": 4, + "nbformat_minor": 2 +}