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      =~~~:~~~~~=I=+::::,,,,,,.......,,,,~~++??++=++?????II?7I?=~~===+==~~~~~~~~~~:~~~
      +~~::~~~~~~++=~,,..,.,,,........,.,,:~~~++?=+??????III7?+~~~==+=~=~~~~~~~~~~~~~~
      +~~~~=?+?:=,:,:,,.....,,...,.......,.,,:++?=+?????III7I+=~~===+==~~~~~~~~~~~~~~~
      +~~:,:.,:==,,,.,..:,........,........,,:~++=+?????III7?=~~~====~=~~~~~~~~~~~~~~~
      ?=~=~=~~:,,,,,.,...,.,............,....,~++=??????II7I+=~~~===~=~~~~~~~~~~~~~~~~
      ?=+=~::,:,.,,,,,..,,,,.,...............,:==+?????II77?=~~~~=====~~~~~~~~~~~~~~~~
      ?~~~~:,,::,,,,,,,........,...............:=+?????II7I+~~~~~==~=~~~~~~~~~~~~~~~~~
      I:=+~::,.,..,,,..,......,.................,,+???II77?=~~~~~=~=~~~~~~~~~~~~~~~~~~
      7+??==:,,.,,...,,...,...........,....,,,,,..:~??II7I+~~~~~=~==~~~~~~~~~~~~~~~~~~
      II~=?=::+:,,..,,..,........,.,,,,,,,,,:::::~,.:?I77?=~~~~~=~=~~~~~~~~~~~~~~~~~~~
      II=~+~=,,,,,,,.,..,,,,,,,,,,,,,,,,::::::::::::,,+7?+~~~~~~~===~~~~~~~~~~~~~~~~~~
      I7==:::=,,,.,,.,,,,::,::::::::::::~~~~~~~~~:::::,,+=~~~~~~~==~~~~~~~~~~~~~~~~~~~
      I~~~~::,,,,,,,,,,:::~:~~~~=~~=~~~~~~~~~~~~~~:::::,,~~~~~~~===~~~~~~~~~~~~~~~~~~~
      I=~+~==:~,,,,,,~:~~~+===+=+++=======~=~~~~~~::::::,,~~~~~===~~~~~~~~~~~~~~~~~~~~
      I++=~:,,,,,,,::~==++??+++??+++=========~~~~~~~~~:::,,~~~~===~~~~~~~~~~~~~~~~~~~~
      I~~~~=::,,,,:~=????IIII?????+++++=+++=========~~~~~~:~~~===~~~~~~~~~~~~~~~~~~~~=
      ?+~=~,::,,,:==?IIIIIII?III??+++++++==+=========~~~~:,::~===~~~~~~~~~~~~~~~~~~~==
      I=?~~,,,,,,:~??II7IIIII7I???++?++++++==++=+=====~:,,,,,~==~~~~~~~~~~~~~~~~~~~~==
      I7~~~:,,,,::~+IIII7IIIIII??++???++++=+===+===~~~:,,,,:,,==~~~~~~~~~~~~~~~~~~~===
      II+=~~~:,,::~=?IIIIIIII??I?I???????++========~~:,,,:::,,,=~~~~~~~~~~~~~~~~~~~===
      777?=~~~::::~=+IIIIIIIII?I?I???????++=~~~~~~~~~:,::~~:,,,:~~~~~~~~~~~~~~~~~~===~
      7777?~+~~:::~=+?IIIIIIIIIIIIII??+?++=~~~~~~~~~~::~:.,,,,,::~~~~~~~~~~~~~~~~~~==~
      7IIIII+I=~~~=+=+?I???III?IIIII???++==~~~~~~~~~~::...,,::::::~~~~~~~~~~~~~~~~===:
      777I+?7I~~~=++++??????IIIIIII?+++==~~~~==~~~~~::,~:::~:::::::~~~~~~~~~~~~~~===~:
      777?+==~~~==++?+++???IIIIIII+=~~~~~~~~====~~~::,,:::::::::::::~~~~~~~~~~~~~===~:
      7III?==~~~~=+++??????IIIII+==~============~~::,,:::::::::~~:::~~~~~~~~~~~~~===::
      77II?=~~~~~==++++++??IIII?+?+++==~~~~~~~====~::,::::::::~~~:::~:~~~~~~~~~~===~::
      IIII?=~~::::==+++++?IIIIII????++==:,,,::~=+===~:::::::::~~~~:::::~~~~~~~~~===:::
      7III?=~~::::~=++=++IIII7III???+=,,.:,,:::==++++=~:::::::~~~~~:::~~~~~~~~~===~:,,
      IIII?=~=++????+==+?IIIIIIII??+==+,~~:::~~=++???++==::::::~~~::::~~~~~~~~~===~,,,
      IIIIII7777777II?+++?IIIIIII?+~+??+==~~~~~=+???II??+=~~::::::::::~~~~~~~~~===:,,,
      IIIII77777777??I??++III7II?++?I??+=~~~~~~=+??III??+=::~::,,::::~~~~~~~~~===~:,,,
      7IIII77III???I+?I?=+?IIIIIIIIII?++===~~~==++??I???+~::,,,,,,,~:::~~~~~~====~,,,,
      7IIIII7II?????I?I+==?IIIII77IIII??++=====~+?II?+??==~,,,,,,,:~::~~~~~~~====:,,,,
      7IIIII7I????????II+=+?III77IIII?I??+===~~~=???+~~~=::::::,,,::::~~~~~~~===~,,,,,
      77IIII7I?????????I?I7IIIIIIIIIIII?++===~~~==++~~=~~~~::::,,,::::~~~~~~~===:,,,,,
      77IIII7I???????????777IIIIIIIIIII??+==~~~~===++==~~~~:::,,,,:::::~:~~~~===,.,,,,
      77IIII77I???I???????I7II?IIIIIIII??++===~===++++==~~~~,,::,,:::::::~~~===~...,,,
      77IIIII7II????????????I77IIIIIII?I??++======+++++=~:::~~::,,,::::::~~~===,......
      77IIIII7IIII????????III7IIIIIIII????+++=~~==+=~~=====~~~~::,,::::~::~~==~...,,..
      777IIII777777IIIII77777?II?IIII????++++=~=~=++++++++=~~~~::,,,::::::~~==:....,,,
      777IIIIIII777777777777?III??II???????+++=~~=+++++++++==~~:::,,:::::::~~~,....,,,
      777IIII??I77+===++++I??III??????????+++++++=++++++++++==~::,,,:::::::~~:......,,
      777IIII??+======+++???IIII???++?++==+++++++++++++++++====~,,,,:::::::~~,........
      7777III??+======++??+IIIII++=+++++==~~~~=+++++++++++=~~~,,,,,,,::::::~~.........
      7777III??+=~::~~~+?=?IIIII?=~==+====~~~~~:::::~===+==,,,,,,,,,,:::::~~:......,,,
      7777III?++=~~~~==I=+II?????+:+~===~~~~,::::::,,,,,,,...,,,,,,,,,::::~~,.......,,
      7777I7II?+=~~===I?~??I??+???++::~===~~~~::..,.,,,,,....,,,,,,,,,::::~:..........
      7777IIII?+==+++II+~?II?+=+???++::~~=~~~::::::,.,,,,...,,,,,,,,,,::::~:.......,.,
      7777777I+=+???III+~?III+~=?+~=+=~,:=~:~~~:::::::::,,,,,,,,,,,,,,::::~,,,,,,,,,,,
      777777I?++??IIIII?=+?I??=~=+~=++=~,~===~::::,,,,,,,,,,,,,,,,,,,,:::::,,,,,,,,,,,
      777777I++?IIIIIIII?=???++=:?=:=+++~,:===:::,,,,,,,,,,,,,,,,,,,.,:::::.,,,,,,,,,,
      77777I??II77IIII?II?++?+++=?+=+=+++~,:~~~,,,,,,,,,,,,,,,,,,....,,:::,,,,,,,,,,,,
      7777I???I77IIIII???II??+++??I??+~+++~,,:~~,,,,,,,,,,,,,,....,,.,,,::,,,...,,,,,,
      7777I??I777IIII?????II??==?+==~====+=~,::~:,,,,,,,,,,,,,...:,.,.,,::,..,,,,,,,,,
      777I??I7777IIIIIIII?????=+::::::~~~~==:,,,~:,,,,,,,,,,,,..:,,,.,,,:,,,.,,.,,,,,,
      77II?II777IIIIIIIIIIIII?:=:~~=~~~~~~~~~:,,,~,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,....
      77I??I7777IIIIIIIII??++++======~~~~~~~::,,,,:,,,,,,,,,,,.:.,,,,,,,,,,,.,,,,,,,,,
      7I??II7777IIIIII?????????+++=~~====~~~~:,,,,,,,,,,,,,,,,,..,.,,,,,,,,,,,,,,,,,,,
      II?II77777III+=~~~~~~~~:~=++++==++=~==~~:,,,,,,,,,,,,.~~.,,.,.,,,,,,,,,,......,.
      I??I77777II?=~~=+++?????++=~~====~,,,,:~~:,,,,,,,,,,,,:~,..,.,,,,,,,,,,,........
      ??I777777I+==????????????+++=~::==::,,,,,,,,,,,,,,,,,,::..,,,,,,,,,,,,,,........
      ?II777777?=?IIII??????????+++=~~:,~~,,,,,,,,,,,,,,,,,.::.,,,,,,,,,,,,,,,,.......
      II7777777+IIIIIIII???????+++++=~~:,:~:,.,,,,,,,,,,,,,.::..,,,,,,,,,,,,,,,,......
      I77777777?IIIIII?I???????+++===~::,,,~:,.,,,,,,,,,,,,..,.,,,,,,::,,,,,,,,,......
      I77777777IIIIII?I???????+?++++=~:,,,,,:,,,,,,,,,,,,,,,...,,,,,:::::,,,,,,,,.....
      777777777IIIIIIII????????+++++===:,,,,,:,,,,,,,,,,,,,,...,,,,,::::::,,,,,,,.....
      7777777777IIIIII?I?I???++++~~~~~~~:,,,,,:,,,,,:,,,,,,..,,,,,,,::::::,,,,,,,,....
      7777777777IIII?I????+++++++===~~:::,,,,,,,,,,,::.,,,..,,,,,,,,,:~~:::,,,,,,,,...
      7777777777III?III???+??+++====::,,,::,,,,,,,,,::,.,,.,.,,,,,,,.,~~~::,,..,,,,...
      777777777III??I?I?????+??+++==~~=~,,,,,,,,,:,,:::,,..,.,,,,,:,..,~~~::,...,,,,..
      777777777IIIIII???++===~====~+=,,,,,,,:,,:,:,,,:~,,,..,,,:,,:,,.,,:~~:,....,,,,,
      777777777IIIIII?+++=+++=+~=~:~~~,,,,,,::,~~:,,,:~~~~,,,,::,:,,,,,..,,:,....,,,,.
      777777777II?????I??+=+?++=~~=::,::,.,,:::~~~:,,,,:~,,,,::,,:,,,.,,,,~,,,,,,,,,,,
      77777777III????++++++=++~+=====,,,:,,,,:~==~~,,,,,,..,::,,:,,,,,.,,,~~~~:,,,,,,,
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