====+====+====˜˜==˜=˜˜=˜˜˜˜˜˜:˜:˜˜˜˜˜˜:˜˜˜˜˜:˜˜˜˜˜˜:::::˜˜˜:˜::::::˜˜˜˜::˜˜˜:˜˜˜
+================˜˜˜˜=˜˜˜==˜˜˜˜˜˜˜˜::˜::::˜:˜:˜˜˜:˜˜:˜::˜˜˜::˜˜:˜:˜˜=˜:˜˜˜˜:˜:˜:
========+====+˜==˜=˜˜˜˜:˜::+==˜+˜++=+=˜::::˜:::::˜:˜:˜˜:˜:::˜˜::::˜˜˜˜˜:˜˜˜:::˜:
==+=+==========˜˜˜˜====˜˜=+I?+?IIII?I?I+=˜:˜=˜::˜:˜::::::˜˜:::˜˜˜:˜˜˜˜::::˜:˜::˜
=+˜===˜==+======˜=˜=˜=˜+??I??IIIII77II77IIIII+=+˜=::˜˜:˜:::˜˜˜˜˜˜=˜˜˜˜=˜:˜=:::˜:
==++=========˜˜˜=˜˜==:,+?????IIIIII7I777I7IIIII777I?:::::::=˜:˜:˜::˜:˜˜˜:::˜˜˜˜:
========+====˜˜˜==˜=:+==+??II??+?IIII7II7IIII7I777II?=˜:˜:::::::::˜:˜:˜˜:˜:˜˜˜::
===+=++=====˜==˜=˜==++?+?II=˜?IIIII77777777777I?7777I?=::::::::::::˜:˜˜:::˜˜˜˜˜˜
=+==+=+˜=========˜+=??III+?II7I77777777777777777I7777I?:::::::::::˜˜˜:=:˜::˜:˜:˜
+++=============˜==?II7I+IIII7I777777777777777777I7777II::::::::˜:::::::::˜:=˜˜:
=+======+=+==+==˜+?II7I?I?IIIII7777777777777777777777777+:˜::::::::˜˜:˜:˜:::˜˜˜˜
=++==+======+=+++??I?+I?+??IIII777777777777777777777777II˜:::::˜,:::˜:::˜:˜:˜:::
++=========+=˜==+I?+˜??=+??III7777I7777777777777777777777+=˜=˜::::::˜˜::˜:˜˜˜˜˜:
+=++++==+====++++?==,+?˜=???IIIII7777777777777777777I7I777II+:˜˜::::˜:::˜:::::::
+++++++====˜˜=+???+=I++:=+IIIIII77777I77777777777IIIIIII77I7I?=˜:::::˜:˜˜::˜:˜:˜
=====+=====˜˜:=++=?II=˜:˜?IIII77I7III7I7777777II7I?II77777I7III?˜:::::::::::::::
+++===+===˜˜˜:=:=?II?˜,:+++˜˜+IIIII?I?++˜+IIII7III+II777III7I??+I=::˜:::::::˜˜::
=+=++==+==˜=˜˜==+?II?˜,,,:::,..,:?+,,.,=III?++III7I=IIIII777II?I++˜::::::::::˜::
++==========+:::+II?=,=,.....:...=77=......,++=IIII?I??+IIIII7???+=::˜::::::˜:˜˜
+++++========˜˜˜=?+?I+:,.,.˜+++?˜?77II==+?III+?III??=??IIII+??????+:::˜:::˜::˜::
+++==+=+===+=˜˜˜˜=˜==˜,:˜˜=+?????I77777IIIII7777IIII?:=+?I+=?=?+?˜++::˜::::::˜::
===+=+˜=+==˜:=:=+=?++:.˜+??III???7777I777777777III=?:˜+??II==˜+?I˜˜+˜:::::::::::
++==+==+==˜+==˜˜++I+=˜,,+?IIII+++777777?I77777I7I?=+˜,˜=++???++˜+=˜:::::,˜::,:::
+===++==+˜=+˜=:˜=+I==.,,=??I?++..,=+.:I7+II77I7II+:=I+I=˜=I=˜+˜::˜::::::::::::::
+++===+==+=+?::?+,˜===,::=++?+˜....,.,=??+?IIIII?=˜III+?I=˜=+˜˜˜:˜::::::::::::::
=+++==+====+==+++???++:=˜=+,˜,:.:=˜=,:,˜+˜˜+II?IIIIII==˜::˜::=:˜::::::::::::::::
++++====+=+=+=˜=˜III?+=::˜˜.,,,.......,.˜˜˜:?+?+?I+?7I??˜=˜+:˜::::::::::::::::::
+=+=+===+=====+˜=?=˜=˜:::................:˜=˜???==?I?II?˜:,˜:=˜:::::::::::˜::,:,
++++=+=======?+˜++˜=??˜˜,,......::,:˜:,...,.:+:I????II+I+=,.::::::::::::::::::::
++=+=====+=+++=+I++=++?˜:..,,=,=++:˜˜::,,˜:.˜˜:?III???III?,.:˜˜:::,::::::˜::::::
++===+==++==++++==++?I=++,:˜==+??+=++?˜?=??+=I???I?7IIII?=I+:˜::::::::::::::::::
+++===+===˜==+++˜+I+I?+II???II???+?IIII?7III??+IIIIII?77II??::::::::::::::::::::
+=+=+=+====+˜˜+=??II?????I++?II???II?II77I?I?+??7I7III77III??:::::::˜:::,:::::::
+++++==+=++===++II??=?II?II?III?+?+??I77IIIIIII?+777II7777II?:,::::::˜::˜:::::::
++++=+=+======?II?I+++++???IIII?II??7I7IIIII?IIIIII77I7I7I7=:I:::::,::::::::::::
++==++=+=+=˜=+???++?I+?????II?I+?+??II77IIIIIIIIIII77777?I?=++::::::˜:,:::˜:::::
+++===++=+=+˜,..˜˜?I?I=????II????I7?IIIIIIIIIIIIIIII7777I7+˜..˜:::::::::::::::::
+++++++:,........˜?++????IIII?+???+IIIIII7II7I7I7II7I7I77I:˜,...,˜::::::::::,:::
=:::,,,,,..........:+?????I?II˜???I?I?I?I7IIIIII7?III,+˜:I.....,,.,::::˜::::::::
.:::,,,,.............˜+??I?I???+????II7?III7I7I7I=I+?::˜.,:,,,.,,,.,,,:˜::::::::
,,:˜::,,,.,..........,????I?I?+??+I+II?I?I?I?I??,,,:?˜:.,..,,,,,,.,...,,,:,:,:::
,,˜::,,,............+????I?I??+I++??I?I7˜?=::,:,::::˜˜.....,,.,,,,:,:˜,,,.,,˜,,,
,:˜:,,,,..,,.......?7I7˜II?????I??III77==˜.,,,,::::˜˜:...,,,:,,,,,:˜˜:,,:::.˜+==
,:˜˜,,,.,,.,..,,..I7777:77IIIIII?I7777,,,,,,,::::˜:˜=....˜::,,,,,˜==˜,.,:::˜=,:=
˜˜:=:,,,.,,,.,:,,777777=7777777777777,::::::::˜::˜˜==,,:˜=::,,,:˜+++::..˜˜==,=+=
˜˜::˜::,,,,,:::,777 7777777777777777˜˜˜˜::˜:˜:==˜˜˜˜=:==˜˜:::::=++==:,.˜+++=˜:,˜
:˜:::˜,,,,,:,˜,777777777777777 7777+=˜˜˜˜˜˜˜˜::=˜˜˜˜=˜==˜˜˜,:˜=++==˜.,=++?+˜˜˜+=
:˜:˜˜:,,,,:˜:˜777777 777 7  77777 =˜˜:˜˜˜:˜˜=˜,˜:˜˜==++˜˜=˜:˜˜++˜˜=,:=+++?++=+=˜
˜˜˜˜:,,,:::˜?I77 7 7 77 7777 7  7+˜=˜==˜˜:=====˜=˜˜˜=+=˜˜˜::+===:˜::=++==˜::˜,,=
˜˜˜:,,,,::˜?77777777 77  7 7   7?====˜˜˜,˜˜+===++=+++==˜˜:˜=++=˜˜::===+˜,,:˜==+˜
=˜:,,,,::˜? 7 777  7 77   77   7˜=+=˜:˜:˜=+=++==+=++==+=:˜˜++=˜,::===+˜::==++==,