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++++++++=+++======++===+===++NMMMNMNNMMNNMNMMNMMNMMMMMNMMNM=+??==~~~~======+=++=
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?+++++++++++++=+=++++==+=+====MMMNNNNNNNMMMMMMMMMMNNNMMMMM++==+====~===~==++==++
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++?++++++++++====+=+=====+==~==+MMMNNMNNDNNNMMMMMMMMMMNMN==+++=====~+~=====+====
++++++++=++==+=========+==~=====NNMMMMMNNMMMMMNMMMMMMMMMN====+==+=====~=+=======
+=+++=++++===+======~=+===~===~==MNNMMNMMNMNMMMNMNNMNMMM=~~?+=+==~=~====~=======
+++++++++++=++====++========~=+=+NNNNNNNMMMMMMNMMMNNNMMM~==++=========~=====+===
+=++++=+=+====+===+==============OOOO8N$NMMMNNDZZOO88DDN+=+=+++====~~======+====
++++++=+=+==+======+==============OOOODONMNMDNDOZZO8D8D~?++=++=+===~==========+=
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+++=+++===+===++===========~====+ZOOOOOZ888ZO8O8OOOO88N==++=========+========+==
+++==++++++====================+$$$7$$$$77$$ZZZZZOOO88N=?+==+~+~=~~=~=~=========
++++++=+==++===+=======+~+====$$77777$$Z$Z$$$777$$$ZZON+++??+=========~~=======+
++++=+=++======+============7$$77IIIII$ZOZ77II77777$$ZON=+++++=~+========+=+===+
++++++=+=+==+=+============7$777III?II$O877IIIIII77$$ZO8N+++++========+=========
+++++++=++=+=+=++====+++===$$77II????I7OZ7I????III77$ZZO8D+=+~===+====~+=~~====+
++=+=+=+=+++++++========++Z$$7III????I7O$II??????I777$ZO8D=++===+=~~=====+===~+=
+=+++++++=+++++=====+==+=+Z$77III??+?I78$7I??+??III77$Z88DD++=++===+=+=====+====
+++++++++=+++=++==+==++==+ZZ$777III?I778$7II????II77$ZZO8DD++=+===========~===+~
+++++++++++++++=+++++++++:,,,,,,,,,?I7$DZ77IIIIIII7$$ZZ8DDD===+====+========+==+
++++=+=+++++++=+==+++=+=~:,,,,,,,..,,..,,:,,,,,,,,:+$OOO:~8+=====+====+===+=+===
++++++++++=++++++==+++++:,,,,,,,,:,..,,,,,,,..,,.,:,,,,,,~~8=+========+====~+=+~
+++++++++++=++++=++++++=:,,,,,,,,,,,:::::::::,,,,,,,,,,,::~8+~=====++==+++=++===
++++=++++++=+++++++++++:,,,,,,::::::::::::::,,,,,,,,,,,,:::8Z+=====+~==~+++=~===
+++++++++++++==++=+++++:,,,,,,,::::::::::::::::,,,,,,,,,,,:?O==+===++++==+===+==
++++++++++++=++++=+=++:,,,,,,,,,,,:::::::::::,:,,::,,:,,,::=O=+++=++=+++===++++=
+++=++++++++++++++++++:,,,,,,,,,,,,:::~~~~::::,::,:,,,,,,,:~8==+++====++=+++++==
++++++++++++++++==+?++:,,,,,,,,,,,:,::?NII~::,:,:::,,::,,::~8+++=++==++=+=+=++++
++++++++++++++++++++++:,,,,,,,,,,,,,:~8DIII::,,,::,,,,,:,::=8+==+++===+==++++=+=
++++++++++++++++++++++~:,,,,,,,,,,,::~D$?I?~:,,:,,,,,::,:::=8++++++=+=++=+++++++
++++++++++++++++++++++~:,,,,,,,,:,:::+DII?I?,,,,,,,:::,::::=8+++++==+++=++++=++=
++?+++++++++++++++++++~:,,,,,:,,::::~DDII?II:,,,,,,:::::::~=D++++++++=++++++++++
++++++++++++++++++++++~:,,,,,,,,::::=D?I??II~,,,,,,:::::::~=D?+++++=++=+++=++=++
++++++++++++++++++++++~:,,,,,,,::::~DD?II????::,,,,,:,,:::~=D??+++++++++++++++++
++++++++++++++++++++++~:,,,,,,::::~=D?I??III?~:,,,,,,,::,:~+D?+?++++++++++++=+++
++?++++++++++++++++?+++:,,,,,,::::~OD????I?II?:,,,,:,:::::~+D???+++++++++++++++=
?+++++++++++++?++++++??:,,,,::,:::=DII???I?II?:,,,,,,:::::~OD?????++++++++++++++
++?+++++++++?+++++++?+?:::,,,::::~8D?III?I??II:,,,,,:::,::~DD???+?++++++++++++++
++++?++?+++++++++++??+=:,,,,:::::~DII??I?I?III~,,,,,:::,,:~DZ??+??++++++++++++++
?+++?++++?+++?????+?++:,,,,,,,,::ZD??III??III?I:,,,,,,,,,:~DII????++++++++++++++
?+?+??+?++++++???+???+:,,,,,,,,,~D8II????IIII?I:,,,,,,,,,,:D7?????++++++++++++++
?+?+???+++?++?+?+?+???:,,,,,,,,:=D???I?I??IIIII~,,,,,,,,,,:DOII??++++++?++++++++
???++???++?++???+????:,,,,,,,,:~8$IIII????II?III:,,,,,,,,::DD?I????+++++++++++++
?+?+?????++?++?+???+?,,,,,,,::~8OIIIII?I??IIIIII::,,,,,,,::8D??I??+??+?+++++++++
?++?+?????+?????????:,,,,,,,::88IIIIII??IIIIIIIII:,,,,,,,,:+DI?I????++++++?+++++
????+???????+???????:,,,,,,,:=8IIIII?III?IIIIII7II:,,,,,,,:~D7III???++++++++++++
????+??????+???????:,,,,,,,,:O8II?III?I?IIIIIIIIII,,,,,,,,,~DDI??I???++++++??+?+
??????????+??+?????:,,,,,,,,:88IIIIII?IIIIIIIIIII7:,,,,,,,,:+DIIII???+????++++++
???????????????????,,,,,,,::~8OIIIIIIIIIIIIIIIII7I:,,,,,,,,:=DZIIII?+??+???++?++
??????????+????????O,,,,,,,:~8I?IIIIIII?II?IIIIIII=:,,,,,,::~DDII?I????++?+++++?
?????????????+?????OOOZZZZO888IIIIIIIIIIII?IIIIIIII:,,,,,,,:~8DIIII??+????++??++
????????????I??????OOOOOOO888IIIIIIIIIIIIIIII?IIIII:,,,,,,::~?DIIIII???????++???
????????????????+??OOZZZ888OI?IIIIIIIIIIIIIIIIIIIII~:::,,,,::+NIIIII????????????
~:~::::::::::::::::OZZZZ88??~=?I7I7IIIIIIIIIIIIIIIII~:,,,:::=8D7III??II?????????
:::::::::::::::::::8OZZZO8+=::~~~~~~~~~~~~:::::::::::8OZZZO888Z~::~~??I?????????
+??????+?+?+?++?+++8OZZO8$I=~+::~~:~~:::~:~::::::::::8OOOO88D8Z::~~~~:::::::,:::
???????+++?++???+++8OZOO87I??II7III?77III????++++???+IOZOZO8888~:~::::::::::::::
?????+?????+++??+++8OZO8D7????I7?$?77II?II??++I?+??+?I8OZOO8D8D$77II???++?++++?+
?????+???????++???+8OZO87I?I777I777III?I??+?I++??+???II8ZOO888D7IIIII???II???++?
II+?????++???????+I88Z88Z??IIIIII777I+?I+???+?++?++?+IIOZOO88DZ77I??IIII?????++?
???+????????+??????8OZODO?IIII777I?I?????++++???++?+??I8ZO88DD77III?+??II?I???++
?++?????++?++????++O$ZODO?IIIIII??+?++?++++++?????+????IOZ88DD7IIII???I??+??????
++?????+++?++++++++$II$88II?77II+++++?II?I???+++++?++=?IOZO88D7$7II???+??I++I???
+?+?+?+?+??=+?++?+??++?$O$III??+?++++???+???+++++++++++$$$ZD8D?I7I???????III????