#####**************#################****************************
#....,,,,,,,,,,,,,,.................,,,,,,,,,,,,,,,,,,,,,,,,,,,*
#....,,,,,,,,,,,,,,..........C......,,,,,,,,,,,,,,,,,,,,,,,,,,,*
#....###########*###########T.......**********************,,,,,*
#...'#.........###.........#'..C....,,,,,,,,,,,,,,,,,,,,,,,,,,,*
*,,##...'##+....'....+##'...##......,,,,,,,,,,,,,,,,,,,,,,,,,,,*
*,,#....#.8#{,,,#....#..#....#....#.,,,,,,,,,,,,,,,,,,,,,,,,*,,*
*,,#....#..#....#....#))#....#,...#,,*********************,,*,,*
*,,#....+##+....'....+##+(...#,...#,,*,,,,,,,,,,,,,,,,,,,,,,*,,*
*,,##..........###...{{.8...##,,..#,,*,,,,,,,,,,,,,,,,,,,,,,*,,*
*,,*#'##'##'##+# #'##+##'##'#*,,..#,,*********************,,*,,*
*,,*#....8...,,*##......c...##,,,,*,,,,,,,,,,,,,,,,,,,,,,*,,*,,*
*,,*....'##'.,,,+....+##'....#,,,,*,,,,,,,,,,,,,,,,,,,,,,*,,*,,*
*,,*,...#,,#..,,#...)#..#....#,,,,*,,*********************,,*,,*
*,,*,,..*,,*8.,,#....#$.#....#,,,,*,,*,,,,,,,,,,,,,,,,,,,,,,*,,*
*,,*,,,,'**',,,,#....'##{8...#,,,,*,,*,,,,,,,,,,,,,,,,,,,,,,*,,*
*,,**,,,,,,,,,,*##..c.,.....##,,,,*,,*********************,,*,,*
*,,**'**'**'**+* #+##'##'##'##....#,,,,,,,,,,,,,,,,,,,,,,*,,*,,*
*,,**,,,,,,,,,,***,,......,.##....#,,,,,,,,,,,,,,,,,,,,,,*,,*,,*
#..*,...'**+,,,,+,,,.'**'....#....#..#********************,,*,,*
#..#,...#,,*,,,,*,,..#,,#...,#....#..#,,,,,,,,,,,,,,,,,,,,,,*,,*
#..#,...*,,*,,,,*,,..*,,#...,#....#..#,,,,,,,,,,,,,,,,,,,,,,*,,*
#..#,..,+**+,,,,',{,,'**'...,#....#..#####****************,,*,,*
#..##.,,,,,,{{,***,,,,,,,C.'##....#......,,,,,,,,,,,,,,,,,,,,,,*
#...'#********** **********#..[[[.p.....,,,,,,,,,,,,,,,,,,,,,,,*
#....#######################.)[[))...######***************,,,,,*
#............................[c<<..[.......,,,,,,,,,,,,,,,,,,,,*
#...........................[[<(.<8[.......,,,,,,,,,,,,,,,,,,,,*
#............................[[<<.[C.......,,,,,,,,,,,,,,,,,,,,*
#)............................[[[[.........,,,,,,,,,,,,,,,,,,,,*
#....#######################..[(....#######****************,,,,*
#.......)).....,,,,,,.......[...........,,,,,,,,,,,,,,,,,,,,,,,*
#..#.).)C)pC...,,,,,,........#....#..##.#**,***,***,***,**,,*,,*
#..#.(.###{....,,,,,,........#..[.#8##*,* *,* *,* *,* *,***,*,,*
#..#...# *''H#.,,,,,,........#....#.#**,***,***,***,***,***,*,,*
#..#...##*,,,*'''*,,,........#....#..,,,,,,,,,,,,,,,,,,,,,,,*,,*
*,,#....#*,,,*,,,*,,,........#....#,#**,,*************,,***,*,,*
*,,#....#*,{{*,∩,*,,,........#....#,* *,**,,,,,,,,,,,**,* *,*,,*
*,,#....#*****,,,***,........#....#,***,*,,****,****,,*,***,*,,*
*,,#....#####*******,........#....#,,,,,*,**,,,,,,,**,*,,,,,*,,*
*,,#........#*,,,,**,........#e...#,***,*,*,,,,,,,,,*,*,***,*,,*
*,,#......⌠.#*,∩⌠,**,⌠.......#....#,* *,,,*,,,,∩,,,,*,,,* *,*,,*
*,,#........#*,,,,**,........#,,,,*,***,*,*,,,,,,,,,*,*,***,*,,*
*,,#........#**'''***###.....#,,,,*,,,,,*,**,,,,,,,**,*,,,,,*,,*
*,,#........###,,,*****#.....#....#,***,*,,****,****,,*,***,*,,*
*,,#..........#,∩,',,,*#.....#....#,* *,**,,,,,,,,,,,**,* *,*,,*
#,,#..........#,,,',∩,*#.....#....#,***,,*************,,***,*,,*
#.,#..........#'''*,,,*##....#....#,,,,,,,,,,,,,,,,,,,,,,,,,*,,*
#.,#.............,*'''* #...)#....#,***,***,***,***,***,***,*,,*
#..#.............,,,,.###....#....#,***,* *,* *,* *,* *,***,*,,*
#..#.............,,,,........#....#..**,***,***,***,***,**,,*,,*
#................,,,,............)...,,,,,,,,,,,,,,,,,,,,,,,,,,*
#...)#######################........#**********************,,,,*
#......)).................†..........,,,,,,,,,,,,,,,,,,,,,,,,,,*
#....................................,,,,,,,,,,,,,,,,,,,,,,,,,,*
#####################################***************************