************************#################***********************
*,,,,,,,,,,,,,,,,,,,,,,,.................,,,,,,,,,,,,,,,,,,,,,,*
*,,,,,,,,,,,,,,,,,,,,,,,........C.......,,,,,,,,,,,,,,,,,,,,,,,*
*,,,.******#######******####........###********************,,,,*
*,,,....####.(...#####   ##...X...T..# *,,,,,,,,,,,,,,,,,,,,,,,*
*,,*c.pp.............#####...#....#..# *,,,,,,,,,,,,,,,,**,,*,,*
*,,*.............c..........##....#..# *,,,,,,,,,,,,,,*****,*,,*
*,,*#......................#*#....#..###*,,,,,,,,,***,*  **,*,,*
*,,*#.....................## #....#....##**,,,,***###+##**,,*,,*
*,,*#...........c.........## #...?#...§.##***,*###.....+,,,,*,,*
*,,*#........###p###.......###....#...§H§## *###((.....#*,,,*,,*
*,,*#.......###(.(###....W..##....#.§§.§C§# ##}|(....(#*,,,,*,,*
*,,*.......###.cXO.###......##....#..§§§C§###φ(.....$##*,,,,*,,*
*,,*,,,,,,,*#§(C.$..##......#*,,,,#..§.§§###$.......(#**,,,,*,,*
*,,*,,,,,,,*#..p∩..φ##.......#,,,,#.....###$.......[##*,,,,,*,,*
*,^**,,,,,,*#.......##.......#,,,,#.....##[..)....$##*,,,,,,*,,*
*,,**,,,,,,*##.....###.......#,,,,#...C###).[C..$(##**,,,,,,*,,*
*,,**,,,,,,,*########D......##,,,,#...###"(....%### *,,,,,,,*,,*
*,,***,,,,,,,******#........#*....#...##(.()(C!##**#**,,,,,,*,,*
*,,* **,,,,,,,,,,,..........#*....#....+...)####*..#***,,,,,*,,*
*,,* **,,,,,,,,,,,..........##.%..#..####'######....****,,,,*,,*
*,,***,,,,,,,,,,,,,,,,......##....#.#*  #.###.......,,****,,*,,*
*,,**,,,,,,,,,,,,,,,,,.....c%#.%..#.##**#.........C.,,,* *,,*,,*
*,,*,,,*****,,,,,,,,,,.......#.....(%##.............,,,* *,,*,,*
*,,,,,**   *****,,,,,***#.%....%.[.%(%%.............,,,* *,,,,,*
*,,,,*********************##...%[p[%.###############*******,,,,*
*,,,,,,,,,,,,,,,,,,,,,.......%c<c[[[..%.%.,,,,,,,,,,,,,,,,,....#
*,,,,,,,,,,,,,,,,,,,,,........c[[Q[[(...s.,,,,,,,,,,,,,,,,,.c..#
*,,,,,,,,,,,,,,,,,,,,,.......%[<<c[....%..,,,,,,,,,,,,,,,,,...O#
*,,,,,,,,,,,,,,,,,,,,,.......%%)[[[..%....,,,,,,,,,,,,,,,,,....#
*,,,,*****************######%...[[(O######################*....#
*,,,,,**,,**,,,,,,,*,,,**,D%%........##.§##..##..##..##..#*....#
*,,*,,**,,,,,,,,,,,**,,**,...#....#.C##.X##..##.§##§.##..##....#
*,,*,,,,,,,,,,,**,,**,,,,,...#....###.O##c.##..##§§##..##..#*,,*
*,,*,,,,,,,******,,,*,,,,,..,#....#*#..##..##..##§e##§.##..##,,*
*,,*,,,**,,**,,,,,,,*,,,**,,**,,,,#..##.O##c.##..##§§##..##.#,,*
*,,**,,**,,,*,,,,,,,**,,**,,,*,,,,#C.*#..##OO##..##§§##..##)#,,*
*,,**,,,,,,,*,,,******,,,,,,,*,,,,###..##c.##.e##O§##§.##E.##,,*
*,,*,,,,,,,,**,,**,,,,,,,,,,,*,,,,**#..*#..##..##(.##..##.X##,,*
*,,*,,,,******,,,,,,,,,,,**,,*,,,,*..##..##..##§.##..##e.##[#,,*
*,,***,,**,,,*,,,,,,,******,,*,,,,#..**..*#..##[.*#..##XD##9#,,*
*,,***,,,,,,,*,,,*****#[..,,,*,,,,##*,,**..##.[#*).##..##.C##,,*
*,,*,,,,,,,,,******,,)#?...,,*,,,,***,,**..**.}*#%.*#O.*#O.#*,,*
*,,*,,,,,**,,**,,,....#/..#*##,,,,*,,**,,**,,**..#*O.#*..##)#,,*
*,,*,******,,,,,,,,..)##y.##.#,,,,*,,**,,**,,**..**O.*#D.**?#,,*
*,,*,**,,,*,,,,,,,*#e*##.....*,,..#**,,**,,**,,**,,**OC#*,,**,,*
*,,*,,,,,,*,,,*#####........,*,,..#**,,**,,**,,**,,*#OO**,,**,,*
*,,*,,,,,,**,,*#......p....#**,...#,,**,,**,,**,,**^.#*,,**,*,,*
*,,*,,**,,**,,,#.......##..###,...#,,**,,**,,**,,**,,**,,**,*,,*
*,,*****,,,,,,,#D.)##..##....#....#**,,**,,**,,**,,**,,**,,**,,*
*,,*,,,,,,,,,,,##).##(e*.....#....##*,,**,,**,,**,,**,,**,,**,,*
*,,,,,,,,,,**,,*#..)(...D...........,**,,**,,**,,**,,**,,**,,,,*
*,,,,**********#############........,**********************,,,,*
*,,,,,,,,,,,,,,.......).D...........,,,,,,,,,,,,,,,,,,,,,,,,,,,*
*,,,,,,,,,,,,,,..........*..........,,,,,,,,,,,,,,,,,,,,,,,,,,,*
***************#####################****************************