**********************************************************************
*,,,,,,*,,,,*,,**,,,,,,,,,,,,,,,,**,,*,,,*,,*,,,,*,,,*,,*,,,,*,,,*,,,*
*,,,,,,*,,,,*,****,,,,,,,,,,,,,,****,*,,,*,,*,,,,*,,,*,,*,,,,*,,,*,,,*
*,,,,,,*,,,,*,****,**+***,,,,,,,****,*,,,*,,*,,,,*,,,**'*,,,,*,,,*,,,*
*****+**,,,,*,,**,,*,,,,******,,,**,,',,,*+**,,,,*,,,+,,*,,,,*,,,*,,,*
*,,,*,,*,,,,*,,**,,*,,,,*,,,,*,,,**,,*****,,*,,,,*****,,*,,,,**+**,,,*
*,,,*,,**+***,****,******,,,,#.,***#........#,,,,*,,,,,,',,,,*,,,*+***
*,,,*,,,,,,,,,****,*,,,,*..,,#..**##........##+##*,,,,,,******,,,,,,,*
*,,,*,,,,,,,,,,**,,*,,,∩*...,#...*#..............,,,,,,,,,,,,,,,,,,,,*
*,,,*,,,,,,,,,,**,,*,,,,###'##...*#.....................,,,,,,,,,,,,,*
***+*,,,,,,,,,****,***+*#.......####..88..88..88..88..88,,88,,88,,88,*
*,,,,,,,,,,,,,,**,,,,,,,.........##.............................,,,,,*
*******,,,,,,,,++,,,,≈≈≈≈≈≈≈≈....''..............................,,,,*
*,,,,,*,,,,,,,,++,,,,≈≈≈≈≈≈≈≈....''..............................,,,,*
*,,,,,+,,,,,,,,**,,,,,,,.........##..............................,,,,*
*,,,,,*,,,********,**'**#.......####..88..88..88..88..88..88..88..88,*
*,,,,,*,,,*,,,,**,,*,,,,#........##...............................,,,*
*,,,,,*,,,*,,,,**,,*,,,,#.####.).##..........)....................,,,*
*******,,,',,,,***,*,,,∩#.#,,#..####.........)....................,,,*
*,,,*,,,,,*,,,,***,*,,,,#.#,,#..##*#.............................,,,,*
*,,,*,,,,,*,,,,**,,***###.',,#[..##............########.........#+****
*,,,',,,,,*******,,,,,,...#,,#...##....#######.#.)....#.....#####,,,,*
*,,,*,,,,,,,,,,**#..,,,,..#,,#..####...#.....#.'......####..#...#,,,,*
******'**,,*****##..**+*#.#,,#[.##*##'*#.....'.#......#..'..#...#,,,,*
*,,,,,,,*,,*,,,*#...#,,,#.####...#*,,,,#.....#.#......#..#..'...#,,,,*
*,,,,,,,*,,+,,,*#...#,,,#.)..)...#*,,,,#.....#.#......#,,#..#...#,,,,*
*,,,,,,,*,,*,,,*##..#,,,#.)####.##*****#######################'##*****
*,,,,,,,*,,*****#...#####..#..#.##*,,,*,,,,,**,,,,*,#.....#.#..#...#,*
*********,,,*,,*#..........'..#..#*,,,*,,,,,**,,,,',#.....#.#..#...#.#
*,,,,*,,,,,,*,,*#..........#..#..#*,,,*,,,,,**,,,,*,#.....#.'..#...#.#
*,,,,',,,,,,',,*##...#####.####.##**'**,,,,,**#####,#.....#.####...#.#
******,,,,,,*,,*##...#...'......##**,,*,,,,,*,......#.....#....##'##.#
*,,,,,,,,*******#....#...##'##...#*,,,**'****,......###'###...)).....#
*,,≈≈≈,,,*,,,,,*#....#...#...#...#*,,,,,,,,,,,..........)............#
*,≈≈≈≈≈,,*,,,,,*##.÷.#...#...#..##**,,,,,,,,,,*#'##..................#
*,≈≈≈≈≈,,*,,,,,*##..)#####...#..#***,,,,,,,,,,*,,,#.............##'###
*,≈≈≈≈≈,,',,,,,*#...))...#...#...**,,,,,,**'***,,,######.##'###.#....#
*,,≈≈≈,,,*,,,,,*#...[.)..#...#...#*,,,,,,*,,,,*,,,**,,,#.#....#.#....#
*,,,,,,,,*,,,,,*##..)....#####..##**,,,,,*,,,,*,,,**,,,#.#....#.#....#
*****,..1#########..####........#***,,,,,*,,,,*,,,**,,,'.#....#.#....#
*,,,*,,........##...#,,*..###**,,**,,,,,,*,,,,*,,,**,,,#.#....#.#....#
*,,,',,........##...#,,#..#,,,*,,**,,,,,,****######################'##
*,,,*,,.......#*##..#,,+..#,,,*.#***,,,,,,,,,#.......................#
*#####*#......####..#,,*..+,,,*.##**,,,,,,*'*#.......................#
*.....,#2......##..######.#,,,*..#*,,,,,,,*,,#.......................#
*......#ZZ.....##..#.∩).#.#####..#*,,,,,,,*,,#.......................#
*......#......#*##.#.)).#.......#***,,,,*****#......##############...#
*.....zzAC.#######.####'#.......##**,,,,*,,,,#......#............#...#
*......#..A#...##.....[).[.......#*,,,,,*,,,,#......#............#...#
*#######...'...##^....#######....#*,,,,,',,,,#..#####..#########'###.#
*...'......#...###....#,,,,,#...##**,,,,*,,,,#..'.#....#...))......#.#
*...#......#######....#,,,,,+...##**,,,,*,,,,#..'.#....#...........#,#
*,,,#..........##.....#,,,,,#....#*,,,,,*,,,,#..#....###..#######..#,*
*####..........##.....#,,,,,#....#*,,,,,*****#..#....#....#.....#..#,*
 #....#..#....####....#########.##**,,,,,,,,,#..#....#....#.|.).#..#,*
*#............#*##.......#....#.##**,,,,,,,,,#..#....#....'.}.=.#..#,*
#...###''###...##........'....#..#*,,,,,,****#..#....#....#..)).#..#,*
#...#......#...##........#....#..#*,,,,,,*,,,#..#....#....#.....#..#,*
*#.,#......#,.####.......######.##**,,,,,',,,*,,#..4.###..#######..#,*
**,,#......#,,#*##.##'##........##**,,,,,*,,,*,,'.#....#...........#,*
*,,,#......#,,,*#..#...#.........#*,,,,,,*,,,*,,',#....#...........#,*
*,,,###..###,,,*#..#...#.##'##...#*,,,,,,*****,,****#.1#########+###,*
**,,#))))(.#,,**##.#...#.#...#..##**,,,,,,,,,*,,,,,,#............#,,,*
**,,#).[)[.#,,**##.#####.#...#..##**,,,**+****,,,,,,#............#,,,*
*,,,#[=.|.:#,,,*#........#...#...#*,,,,*,,,,,*,,,,,,##############,,,*
*,,,#(..().#,,,*#........#####...#*,,,,*,,,,,*,,,,,,,,,,,,,,,,,,,,,,,*
**,,########,,**##..............##**,,,*,,,,,*,,,,,,,,,,,,,,,,,,,,,,,*
**,,,,,,,,,,,,**##..............##**,,,*,,,,,*,,,,,,,,,,,,,,,,,,,,,,,*
*,,,,,,,,,,,,,,*#................#*,,,,*,,,,,*,,,,,,,,,,,,,,,,,,,,,,,*
****************##################************************************