.................................................................................................... .................................................................................................... .................................................................................................... ...................................................................................................
...................................⠿⠿⠟⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠻⠿⢿................................ ...........................⡿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿........................... .......................⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶..................⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿.......................
....................⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾...........................⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿.................... ..................⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴...............................⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻.................. ................⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾.............................⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻................
..............⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾...........................⡿⠟⠋⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻.............. .............⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴..........................⠿⠛⠉⠀⠀⣀⣠⣴⣶...........⣦⠀⠀⠀⠀⠀⠀⠀⠀⠹.............
............⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴........................⠿⠛⠉⠀⠀⠀⣠⣴⣾................⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿........... ⠀⠀⠀⠀⠀⢀⣴...................⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⢀⣴......................⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘.......... ..........⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴................⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴........................⠃⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠸.........
⣼.⣷⡀⠀⠀⠀⠀⠀⢿........ ⠀⠀⠀⠀⠀⠀⠀⣰..........................⡇⠀⠀⢀⣾...⣷⡀⠀⠀⠀⠀⢸........ ⠀⠀⣠......⣷⡀⠀⠀⠀⠈........ ........⡿⠀⠀⠀⠀⠀⢀⣼................⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾..........................⡿⠁⢀⣴........⣷⡀⠀⠀⠀........ ⣧⠀⠀⢸........ .......... ...........
...............⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾............................⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾.............. ................⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾.............................⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾.................

........................................... .................................⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠻................................
...................................⠿⠿⠟⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠻⠿⢿................................
...........................⡿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿...........................
.......................⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶..................⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿....................... ....................⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾...........................⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿....................
..................⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴...............................⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻.................. ................⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾.............................⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻................
..............⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾...........................⡿⠟⠋⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻..............
.............⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴..........................⠿⠛⠉⠀⠀⣀⣠⣴⣶...........⣦⠀⠀⠀⠀⠀⠀⠀⠀⠹............. ............⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴........................⠿⠛⠉⠀⠀⠀⣠⣴⣾................⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿...........
...........⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴.....................⡿⠟⠋⠁⠀⠀⠀⠀⢀⣴....................⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿.......... ...........⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴...................⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⢀⣴......................⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘..........
..........⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴................⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴........................⠃⠀⠀⠀ ⠀⣤⡀⠀⠀⠀⠀⠀⠸.........
..........⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴................⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾.........................⠀⠀⠀⠀⣼.⣷⡀⠀⠀⠀⠀⠀⢿........ .........⡏⠀⠀⠀⠀⠀⠀⠀⢀⣴...............⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰..........................⡇⠀⠀ ⢀⣾...⣷⡀⠀ ⠀⠀⠀
⢸........ .........⠁⠀⠀⠀⠀⠀⠀⣠................⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼..........................⡿⠀⠀⣠......⣷⡀⠀⠀⠀⠈........ ........⡿⠀⠀⠀⠀⠀⢀⣼................⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾..........................⡿⠁ ⢀⣴........⣷⡀⠀ ⠀
........ ........⡇⠀⠀⠀⠀⢀⣾................⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰...........................⠟⠀⠀⣼..........⣧⠀⠀⢸........ ........⠁⠀⠀⠀⠀⣼................⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾..........................⡟⠃ ⠀⠀ ⣼............⡇ ⠀ ⠘........
........⠀⠀⠀⠀⣸.................⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶..........................⠟⠁⠀⠀⠀⣼.............⣧⠀⠀........ ........⠀⠀⠀⢰.................⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴..........................⡿⠟⠁⠀ ⠀⠀⠀⣸..............⡿⠀ ⠀........
........⠀⠀⠀⣼................⠁⠀⠀⠀⠀⠀⢀⣠⣴⣾...........................⠿⠉⠀⠀⠀⠀⠀⠀⢰...............⡇⠀⠀........ ........⠀⠀⢀................⠃⠀⠀⠀⠀⣀⣶...........................⡿⠟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⢠................⠇⠀ ⠀.......
........⡀⠀⢸...............⠃⠀⠀⠀⣠⣾...........................⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠................⡟⠀⠀⠀........ ........⡇⠀⢸.............⡿⠃⠀⠀⣠⣾...........................⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠.................⠃⠀⠀⠀........
⢠........ ........⣷⠀ ⠀⣰................⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀.................⠏⠀⠀⠀⠀⢸........ ... ⠀⠀⠀⠀⣾........ ⢰........................⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴................⡿⠃⠀⠀⠀⠀⠀⢀.........
⢀⣴.................⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⣼.........................⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾.................⠛⠀⠀⠀⠀⠀⠀⠀⠀⢠..........
..............................⠀⠀⠀⢀⣠⣤⣶.....⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰........... ...........⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾........... ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼............
...........................................⣷⡄⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿.....⡿⠿⠿⠿⠛⠋⠉⠁⠀⠀⣀⣴⣾..........................⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾.............
..........................................⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾............................⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾.............. ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾................
⣠⣶.................. ⠀⠀⠀⠀⠀⠀⠀⣀⣴..................... ................
.............................. ⠈⠉⠛⠿⢿............... ⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾.......................
.......... ⠀⠀⠀⠈⠉⠛⠻⠿⠟⠛⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣶⣶............................
.......... ⠉⠛⠻..................⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣶⣶............................
.......... .................... ⠀⠈⠉⠿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣶⣶............................
.......... ⠀⠀⠤⣴..............................⡿⠋⠀⠈⠀⠀⢀⣀⣀⣤⣶⣶......................
⠤⣴.....................⡿⠋⠀⠈⠀⠀⢀⣀⣀⣤⣶⣶..........
⢠.....................⡟ ⠀⠀ ⠀⠀⠀⠤⣴...............⡿⠋⠀⠈⠀⠀⢀⣀⣀⣤⣶⣶.....
.......................................................................................... ⢠⠤⠤.....................⠿⡟⠋ ⠀⠀ ⠀⠀⠀⠤...............⡿⠋⠀⠈⠀⠀⢀⣀⣀⣤⣶⣶.....
..............................⠀⢠⠤.....................................⠿⠿⡟⠋ ⠀⠀ ⠀⠀⠀⠤...........⡿⠋⠀⠀⠀⢀⣀⣀⣤.......
⢠⠤......................................⠿⠿⠿⠿⠿⡿⠋ ⠀⠀ ⠀⠀ ⠤........⡿⠋⠀⠀⢀⣀⣀⣤......
⢠⠤....................................................⡟ ⠀⠀ ... ⠤......⡿⠋⠀⠀⢀⣀⣀⣤....
⢠⠤⠤............................................................⠿⡟ ⠀⠀ ⠤⠤⠤⠛⠉⠉⠀⠀ ⠀⠀⠤......⠋⠀⠀⢀⣀⣀⣤....
⢠⠤..........................................................⠃⡟ ⠀⠀ ⠈⠉⠛⠟⠛⠉⠉ ⠀ ⠀ . ⠀⠀⠀⠀⠀⠀⠀⠤......⠋⠀⠀⢀⣀⣀⣤....
⢠⠤......................................⠃⠿⠿⡟ ⠀⠀ ⠈⠉⠛⠿⠿⠿⠿⠿⠟⠛⠉⠉⠤⠀ ⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤........⡿⠋⠀⠀⢀⣀⣀⣤.....
⢠⠤..................................⠃⠿⡟ ⠀⠀ ⠤⠈⠉⠛⠻⠿⠿⠿⠿⠿⠿⠟⠛⠉⠉⠀⠀ ⠀ ⠀⠀⠀⠀⠀⠀⠀⠤...............⡿⠋⠀⠈⠀⠀⢀⣀⣀⣤⣶⣶......
⢠⠤...........................⠃⠿⡟ ⠀⠀ ⠈⠉⠛⠻⠿⠿⠿⠟⠛⠉⠉⠀ ⠀ ⠀⠀⠀⠤⣴.....................⡿⠋⠀⠈⠀⠀⢀⣀⣀⣤⣶⣶⣶.........
⢠⠤..........................⣷ ⠀⠀ ⠈⠉⠛⠻⠿⠿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣶⣶............................