,,,,,,,,,.,,,.,,,,,,,,,,,.,,.,,,,.:,:ZOZO888DDDDDDDDDDDD8DD8D8DDDDDDDDDDDDDDDDD:,:,,,,,,,,,,,,,,,,,,,,,,::,,,,::::::::::::::::::::::::::::::
,,,,.,,,....,.,.,,,,,,,..,,,,,,,,,:=:88ID88DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD,.:,,,,,,,,,,,,,,,,,,,,,::,:,::,:::,::::::::::::::::::::::::
,,,,,,,,,,,,.,.,,,,,..,,,,,,,,,,,:++~DDOODDDDDD8DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDI,,,,,,,,,,,,:,,,,:,,::,:,:::::::::,::::::::::::::::::::::
,,,,,,,,,,,,,.,,,,,,,,,,,,,,,,,,,:~7D8888DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD:,,,,,,,,,:,,,,,,,:,:::,,:,:::::::::::::::::::::::::::::
,,,,,,,,.,,,,,,,,,,,,,,,,,,,,,,,,,7DOD88DDDDDDDDDDDDD88DD8DDDDDDDDDDDDDDDDDDDDDDDDDN=,:,,,,,,,,,,,,,,,,,,,,:,,,::::::,,:::::::::::::::::::::
.,,.,,,,,,,,,,,,,,.,.,,,,,,,,,,,,:7ODDDDDDDDDDDDDDDDO$I?++?$O88DDDD8DDDDDDDDDDDDDDDN=::,,,,,,,,,,,,,,,,:,,,::,,:,:::::,,:,::::::::::::::::::
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,DN8DDDDDDDDDDDD8$I+===~~==I$OZZ$$O88DDDDDDDDDDDDD$I:,,,,,,,,,,,,,,,:,,,::,,:,::::::::::::::::::::::::::::
,,,,,,,,,,,.,,,,,,,,,,,.,,,,,,,,,,:$NDDDDDDDDDDDD8$I==~~~~~===+?III?I7Z8DDDDDDDDDDD$7I?,,,,,,,,,,,,,,,,,,,,::::,::::::::::::::::::::::::::::
,,..,,,.,,,,,,,,,,,,.,,,,,,,,,,,,,,,8DDDDDDDDDND8$+=~=~~~~~~====+++??7$$O8DDDDDDDDN$I7+::,,,,,,,,,,,,,:::,,,:,:::::::::::::,::::::::::::::::
,.,,,,,,,,,,,,,,,,,,,,,,,,,,,,:~OD8$D8DDDDDDDDD$?=~~~~~~~~~~====+=+++?77$O8DDDDDDDDD~~~::::,,,,,,,,,,,,,:,,:,:::::::::::::::::::::::::::::::
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,:ZOOOD88DD8DDDDDDI+===~~~~~~~~======+=++?II$$O8DDDDDDDN::::::,,,,,,,,,,,,,,:,:::,::::::::::::::::::::::::::::::
,,,,,,,,,,,,,,,,,,,,,,,,,,.,:DDDDD88D88DDDDND7====~~~~~~~~~~=====+=+??I$$$ZODNDDDDDDO:::::,,,,,,,,:,:,::,,::::::::::::::::::::::::::::::::~~
,,,,,,,,,,,,,,,,,,,,,,,,,,+OO8DDD8DDDDDDDDNDI?===~~~~~~~~~~========++?I77ZOODDDDDDDDD=~::~,:,,,,,,,,:,,,:::::::::::::,:::::::,:::::::~::::::
,,,,,,,,,,,,,,,,,,,,,,,,,,I8888DDDDDD8DDDDDZI8D7=~=~~~~~~=~~~~====+++?I77ZZ88DDDDDD8D~~::,::,,,,,,,,,::,:::::,::::::::::::::::::::::::::::::
,,,,,,,,,,,,,,,,,,,,,,,,,=DOD88DDDDDDDDDDN8OOODDDDZ+=======~=~=====++??I7ZZO8DDDDDDDDO:~:,:,,,,,,,,,:,,:,::::::::,:::::::::::::::::::::::~::
,,,,,,,,,,,,,,,,,,,,,,,.:8ODDDD8DDDDDNDDDD7?+==+DDDDD87+++=====++=+???I77ZOODDDDDDNDDD+~::,:,:,:,:,,,,,::::,:::::::::::::::,::::::::::::::::
,,,,,,,,,,,,,,,,,~,,,,,:?8D8DDDDDDDDDDDDN7??IO8Z$$8NDDDO?++==++I7I7III77$7$ODDDDDDDDDD~~~:,::::,:,,,:::,:::::,::::::::::::::::::::::::::::::
,,,,,,,,,,,,,,,,,:IZ?~,=Z8888D88DDDDDDDDI==IZDD8DDDDO$O$I+==?I$Z8DNDDDDDDDDO8DDDDDDDD8:=:::::,,,,,,::,:,::::::::::::::::::::::::::::::::::::
,,,,,,,,,,,,,,,:,,,,OOD8D8D88DD8DDDDDDDN=~==+7$,DDNODDZI===??$O8DDDDNDDDDDDDDDDDDDDDDD7,+:~,:,,,,,::::::,:::,:::::::::::::::::::::::::::::::
,,,,,,,,,,,,,,,,,,..:,O888DDD8D8DDDDDDD$=~~~=+7ZO77Z$777=~=+?O888888OZOOZZO888NDDDDDDD$,+::::::,,::,::::::::,:::::::::::::::::::::::::~:::::
,,,,,,,,,,,,,,,,,,,,,=I~OZ88D+D8DDDDDDD==~:~~=~?II77??+?~~~+Z8D88DD8NDDD8888DDDDDDDDD8Z:~=:::,,:::,,::::::,:::::::::::::::::::::::::::::::::
,,,,,,,,,,,,,,,,,,,,,++I:D8DN+NDODDDDDD=~~::~~~~==++===~~~=I$8ODDD?DDDODNDDDDDDDDDDDDDD+,=,::,,::::,,:::,,::::::::::::::::::::::::::::::::~~
,,,,,,,,,,,,,,,,,,,,:~+,~88D88NINDDDDND=~~:::~~~~~~~~~~~~~=$$Z8ZZZO88NDDDD88DNDDDDDDDDD~~=::~,::::::,:::,::::::::::::::::::::::::::::::~::~~
,,,,,,,,,,,,,,,,,,,:::++:8DZ7DN~DDDDDDD~=~:~:~~:~~~~~~~~:~+$$$7$777$ZOD8OOZ8DDDDDDDDD8N:+=::~,,:::,:,:::::::::::::::::::::::::::::::::::::::
,,,,,,,,,,,,,,,,,,,:,~??+ODOO7Z8DDDDDDN+=~~~~:~~~~~~===~~=+$$$$I?II??777$7Z8DDDDDDDDDDD::+::~,,:::,,::::::::::::::::::::::::::::::::::::::::
,,,,,,,,,,,,,,:::::~~:~~,IDOOO8ONDDDDDD?==~~~~~~~~=+=~~~~=+$$$7I?????I?+?7ODDDDDDDDDD8D~:=::~::::::::::::,:::::::::::::::::::::::::::::~::::
,,,,,,,,,,,,,,,,,~~::,~~~:=O878ODDDDDNN?==~~~~~~~=====~~~=?7OO$I?++++++IIZ8DDDDDDDDDDDD~::,::::::::::::::::::::::::::::::::::::::::::::~::::
,,,,,,,,,,,,,,,,:::::::~~~::I:$DDDDDDDNI===~~~~~~~++DO++?$Z$$O$I?++++??7$8DDDDDDDDDDDDD+:::::::::::::::::::::,::::::::::::::::::~::::::~:~::
,,,,,,,,,,,,,,,,,:,::~+:~=~=~IN88DDDDDNI++=~~~~~~~=I+II7ZZD8ZO7I?+++?I7ZO8DDDDDDDDDDDDDZ=~::::::::::::::::::::::::::::::::::::::::::::::::::
:,,,,,,,,,,,,:,,::,,:=:~=~:8DDDDDDDDDDNI?+==~~~~~~~~==?IZZ88O$7I???IIIZ88DNDDDDDDDDDDDDI~::~::::::::::::::::::::::::::::::::::::~:::~~:::~~~
,,,,,,,,,,,,~??I7O88ZZDDDD88DDD8DDDDDDNI?+=====~======?I+7$7I77??II7I$8DDDDDDDDDDDDDDD8I::::::::::::::::::::::::::::::::::::::::::~::~:::~~~
,,:,,:~====+=~~=I$7$I?DOZ$8DD8D8DDDDDDD$??====++=~?ZZ$+=?I$$I77I$777Z88DDDDDDDDDDDDDDDDZ,::::::::::::::::::::::::::::::::::::::::::::~::::~~
,~~~~=~======+???=+?$ZO7$D88OZ8DDDDDDDD8II+++?7DN88OO8DDODDZ$$$$7$7$8DDDDDDDDNDDDDDDDDDO~:::::::::::::::::::::::::::::::::::::::::::~~::~~~~
~~=======+=++?+?III??I7$O88888D8NDDDDDN8$7????II7??$ZOD88DDDOZZZZ$O88DDDDDDDDDDDDDDDDDDO~::::::::::::::::::::::::::::::::::~::~::::~~~~~:~::
~===+=+=+??+???I??777??777IZ8ODDDDDDN8O8O7I????+I7I=?7II$8DDDOZZ8ZO8DDDDDDDDDDDDDDDDDDDD::,:::::::::::::::::::::::::::::::::::~:::~::::~::~~
~==+++???I?IIIII7III?7$7II$7$ZDDDDDNNZZ$ZOI???I$ZOZ$77I7OD88OO8OO8DDDDDDDDDDDDDDDDDDDDDD,:::::::::::::::::::::::::::::::::~:~:~~::::~~~~~~~:
==++++??I7II7II7I77I?I???7$Z$Z8DDDDNNI7$$$ZI++=?I7$88DDDDD88OOO8DDDDDDDDDDDDDDDDDDDDDDDD:::::::::::::::::::~:::::::::::::~:~::::::~:~:~~~~~~
+++???II7$7777$I$7$7II++??I$ZODDDDDDN77$$ZO$?====++?7ZZ88DO88D8DDDDDDDDDDDDDDDDDDDDDDDDO::::::::::::::::::::::::::::::::::~:::~::~~~~~~~~:~~
+++???II7$$$$$$7$$$ZII+=~=I7ZODDDDDDD?7$ZZZZZ??===?+?IIIZZOO8DDDDNDDDDDDDDDDDDDDDDNDDDD8:~::::::::::::::::::::::::::::::::~:~~~~:~~~~~~:~~~~
????IIII$$$$ZZZZ$$$$$I?++==+$8NDDDDNO777$OZOZ8Z$I77II7$$ZOO8DNDDDDDDDDDDDDDDDDDDDDDDDDD8:::::::::::::~:::::::::::::::::::~~~~~~:~~~~~~~:~~~~
??III777$$$$ZZZZZZZ$77?++==?IDDDDDDD7?I7IZZOOO88D88OOZDD88DDDDDDDDDDDDDDDDDDDDDDDDDDDDD7~::::::::::::~::::::::::~::::~:~:~:~:::~:~~~~~~~~~~~
7777$7$$$$$Z$ZZ$$Z$Z$7I?++=?+DDDDDDD7?I77$7ZOO8OOO888DDDDDDNDDDDDDDDDDDDDDDDDDDDDDDDDDDD7::::::::::::::::::::::::::::~::~~~:~:~~~~~~:~~~~~~~
$$ZZZZZ$ZZZ$Z$$Z$$$7II?+++=??DDDDDDN$7I777$$ZZO8O888DDDDDDDDDDDDDDDNNDDDDDDDDDDDDDDDDDDO$7=:~:~~:::::::::::::~:~~:::::~~~:~~~~~~~~~~~~~~~~~~
ZZZOOOOZZZZ$Z$Z$$$77II??++???DD8DDDN$$7$77$ZZZZO8OO8O8DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDO$7$7::::~~:::::::::~~::~~::::::~~~~~~~~~~~~~~~~~~~~~
8O8888OOOOZ$$$$$$$7$77??+?+?$DDDDDDN7$7$$Z$7$7$$$Z$$88D88D8D888DDDDDDDDDDDDDDDDDDDDDDDDZ$$77$~~~::::~:::~::~~~~:~:~~::~~~~~~~~~~~~~~~~~~~~~~
DDD8DDD888OZ$$$$$Z$777I????IODDDDDDD7777$77$$$$7$$$O8OO8OO8888DDDDDDDDDDDDDDDDDDDDDDDDNOZZ$7I77:~:::::::~~~:~~:~~~:::~:~~~~~~~~~~~~~~~~~~~~~
NDDDDDDD88OO$$$ZZ$$777I???I7NDNDDDD7$$77$$$$$$77$$OOZOOOOOO888888DDDDDDDDDDDDDDDDDDDDNN8ZZ$7IIII::~~~:::~~~:~:~~:~~~~~~~:~~~~~~~~~~~~~~~~~~~
8DDDDDDDD8OZZZZZZ$$$77III?7?NDDDDD8II7I77777$$$7$7ZOZZZZZZZOO8OO888O8D8DDDDDDDDDDDDDDDN8O$$$7II77:~~~~~~~:~~~~~~:~~~~~~~~~~~~~~~~~~~~~~~~~~~
8888DDDDDD88ZOOO$Z$$77II?I$$NDDDDDD+$I7777II777$7$$$$ZZ$ZZZZOOOZOOOOOO8O8DDDDDDDDDDDDDDOOO$Z777II7=~~~~~~~~~~:~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
8D8DDDDDDD8OOZZOZ$Z$$7IIII7I7DDDDDDNI$7II77I77777$$$$ZZZZZZOOZZOOOO88O888DDDDDDDDDDDDDDDOO$$77I7I7+~~~~~~~~~~~~:~~~~~~~~~~~~~~~~~~~~~~~=~~~~
DDDDDDDDD8OZOZZZ$Z$$$7II??I?ODD8DDDOI7777777$$Z77$$ZZZOOOOOOO8OO88D888DDDDDDDDDDDDDDDDD8ZZ$77I7I$:~~:~~::~~::::~~~~:~~~:~~~~~~~~~~~~~~~~~~~~
DDDDDDD8O8Z$$$$Z$$77II??+??DDDDDDDO7$77$$$$$77777ZOO8OOOOOOO8888DDDDDDDDDDDDDDDDDDDDDDOZ$$7I7$?:~~:~~~::~~~~:~~~~~~~~:~~~~~~~~~~~~~~~~~~~~~~