################################################################
#......^.......................................................#
#.............................(..................[.............#
#....#######################...(....#######################....#
#..)......,,,,,,,,,,,,,...........(.....,,,,,,,,...............#
#..#......,,,,,,,,,,,,,......#....#.....,,,,,,,,.......)....#..#
#..#..#########,,,*****####..#....#..#..*,,******###..#..#..#..#
#..#..#?""....#,,,*,,,,,,,#..#....#..#..*,,*,,,*,,,#..#..#..#,.#
#..#..#))....(#,,,*,,,,,,,#..#....#..#,,*,,*,,,*,,,#..#[.#..#,,*
*,,#..#[.(..T.#{,,*,,,,,,,#..#....#,,********,,*,,*#######..#,,*
*,,#..#.....c)#*,**,,,,,,,#..#....#,,,,,*,,,,,,*,,,,,,#.....#,,*
*,,#..#.(..()cD...,,,,,,,,#..#....#,,,,,*,,,,,,*,,,,,,#...).#,,*
*,,#.)########c...,########(.#....#,,****,,**,,*,,**,,####p.#,,*
*,,#.....{,,,*..c.,#....).().#....#,,****,,**,,*,,**,,####).#,,*
*,,#......,,,*....,#.........#....#,,,,,,,,*,,,,,,,*,,o..)C)#,,*
*,,#......,,,*,,,,,#.........#....#,,,,,,,,*,,,,,,,*,,..o...#,,*
*,,#..####****,,,,,########..#....#,,****,,**,,*,,**,,####).#,,*
*,,#..#,,,,,,,,,,,,,,,,,,,#..#....#,,*,,*,,**,,*,,**,,*,,#..#,,*
*,,#..#,,,,,,,*****,,,,,,,#..#....#,,*,,*,,*,,,,,,,*,,*,,#..#,,*
*,,#..#,,,,,,,*,,,*,,,,,,,#..#....#,,*,,***************,,*,,*,,*
#..#..#,,,,,,,*,,.*,,,,,,,#..#§...#,,,,,*,,,,,,*,,,,,,*,,,,,*,,*
#..#..#{{,,,{{*,..*,,,,,,,#..#....#,,,,,*,,,,,,*,,,,,,*,,,,,*,,*
#..#..#########...****#####..#....#,,****,,*********,,****,,*,,*
#..#...).)).).....,,,,...)...#....#,,,,,,,,,,,,,,,,,,,,,,,,,*,,*
#...........).....,,,,...............,,,,,,,,,,,,,,,,,,,,,,,,,,*
#....#######################........##*********************,,,,*
#..)..............).))................,,,,,,,,,,,,,,,,,,,,,,,,,*
#.................)............<<.....,,,,,,,,,,,,,,,,,,,,,,,,,*
#.............................<..<}...,,,,,,,,,,,,,,,,,,,,,,,,,*
#..........(................)..<<.....,,,,,,,,,,,,,,,,,,,,,,,,,*
#....######################)).......##*****************,*,*,,,,*
*,,,,,* *,,,,,,,,,,....()))).........#*****,,,,,,,,,,,,,,,,,,,,*
*,,*,,* *,,,,,,,,,,......##......)#...**,,,,,,,****,,,,****,*,,*
*,,*,,* *,,,,,,,,,,....#####.#....##.,,,,,,,,***,,,,,***,,,,,,,*
*,,*,,****,,,,,,,,,###.*  *#.#....#**,,,,,,,**,,,,,,**,,,,,,*,,*
*,,*,,,,****,,,,*****#+****,.#,,,,***,,,,,,,*,,,,,,,*,,,,,,,*,,*
*,,*,,,,,****,,*****,,,,+,,,,*,,,,**,,,,,,,**,,,,,,**,,,,,,,*,,*
*,,*,,,,,,*******,,,,,,,**,,,*,,,,**,,,,,,,*,,,,,,,*,,,,,,,,*,,*
*,,*,,,,,,,* ***,,,,,,,***,,,*,,,,**,,,,,,,*,,,,,,,*,,,,,,,,*,,*
*,,*,,,,,,****,,,,,,,,***,,,,*,,,,*,,,,,,,**,,,*****,,,****,*,,*
*,,*,,,,,,***,,,,,,,,,**,,,,,*,,,,*,,,,,,,*,,***  *,,***,,,,*,,*
*,,*,,,,,***,,,,,,,,,***,,,,,*,,,,*,,,,,,**,**   **,**,,,,,,*,,*
*,,*,,,,***,,,,,,,,,***,,,,,,*,,,,*,,,,***,,*  ***,,*,,,,,,,*,,*
*,,*,,,,***,,,,,,,,***,,,,,,,*,,,,*,****,,,*****,,,**,,,,,,,*,,*
*,,*,,,,**,,,,,,,,** *,,,,,,,*,,,,*,,,,,,,,*,,,,,,,*,,,,,,,**,,*
*,,*,,,**,,,,,,,**** **,,,,,,*,,,,*,,,,,,,,*,,,,,,,*,,,,,,,**,,*
*,,*,,,,+,,,,,****,*****,,,,,*,,,,*,,,,,,,**,,,,,,**,,,,,,,**,,*
*,,*,,****+******,,,,****,,,,*,,,,*,,,,,,,*,,,,,,,*,,,,,,,***,,*
*,,*,**  *,***,,,,,,,,,****,,*,,,,*,,,,,,**,,,,,,**,,,,,,,***,,*
*,,*,*****,,,,,,,,,,,,,,* *,,*,,,,,,,,,***,,,,,***,,,,,,,,,**,,*
*,,*,,**,,,,,,,,,,,,,,,,* *,,*,,,,*,****,,,,****,,,,,,,**,,,*,,*
*,,,,,,,,,,,,,,,,,,,,,,,* *,,,,,,,,,,,,,,,,,,,,,,,,,******,,,,,*
*,,,,***********************,,,,,,,,*,*,*******************,,,,*
*,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,*
*,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,*
****************************************************************