*********     *****************     **********     *********************   
   **,,,,,,,**   **,,,,,,,,,,,,,,,**   **,,,,,,,,**    *,,,,,,,,,,,,,,,,,,,*   
  **,,,,,,,,,** **,,,,,,,,,,,,,,,,,** **,,,,,,,,,,**   *,,,,,,,,,,,,,,,,,,,*   
 **,,,,,,,,,,,***,,,,,***,,,***,,,,,***,,,,,,,,,,,,**  *,,,,,,,,,,,,,,,,,,,*   
 *,,,,,,,,,,,,,*,,,,***,,,,,,,***,,,,*,,,,,,,,,,,,,,*  *,,,,,,,,,,,,,,,,,,,*   
 *,,,,,,,,,,,,,,,,,**,,,,,,,,,,,**,,,*,,,,,,,,,,,,,,*****************+******** 
 *,,,,,,,,,,,,,,,,**,,,,,,,,,,,,,**,,*,,,,,,,,,,,,,,**,,,,,,,,,,,,,,,,,,,,,,,* 
 *,,,,,,,,,,,,,,,,*,,,,,,,,,,,,,,,*,,,,,,,,,,,,,,,,,**,,,,,,,,,,,,,,,,,,,,,,,* 
 *,,,,,,,,,,,,,,,,*,,,,,,,,,,,,,,,*,,,,,,,,,,,,,,,,,************************+* 
 *,,,,,,,,,,,,,,,,*,,,,,,,,,,,,,,,*,,,,,,,,,,,,,,,,,* *** *** *** ***      *+* 
 *,,,,,,,,,,,,,,,,**,,,,,,,,,,,,,**,,*,,,,,,,,,,,,,,* *,***,***,***,****** *,* 
 *,,,,,,,,,,,,,,,,,**,,,,,,,,,,,**,,,*,,,,,,,,,,,,,,****+,+**,+**,+**<,<,***+* 
 *,,,,,,,,,,,,,*,,,,***,,,,,,,***,,,,*,,,,,,,,,,,,,,**,+,,,+,,,+,,,+<<<,,<**,* 
 **,,,,,,,,,,,***,,,,,***,,,***,,,,,***,,,,,,,,,,,,******,***,***,**<,,<,,**+* 
  **,,,,,,,,,** **,,,,,,,,,,,,,,,,,** **,,,,,,,,,,** *,**+* *+* ****<,<,<<**,* 
   **,,,,,,,**   **,,,,,,,,,,,,,,,**   **,,,,,,,,**  ****,***,***,***<<<,***+* 
    *********     *****************     ****++****   *,+,,,+,,,+,,,******* *,* 
**********************************   *******++****   *+**,***,***,***,+*,***+* 
*,,,,,,,,,*,,+,,,,,,,,,,,,,,,,,,,* ***,,,,,,,,,,,*** **,***,*+*,***,***,,,**,* 
*,,,,,,,,**,,+,,,,,,,,,,,,,,,,,,,***,,,,,,,,,,,,,,,***+*+,**+,**+,**+,+*,***+* 
*,,,,,,,**,,****,,,,,,**,,,,,,*****,,,,,,,,,,,,,,,,,**,*,,,+,,,*,,,*,,,*+* *,* 
*,,,,****,,**,,****,,,,,,,,****,,**,,,,,,,,,,,,,,,,,***+*,***,***,+**,**,***+* 
*+****,,,,,,*,,,,,****++****,,,,,**,,,,,,,,,,,,,,,,,***,***,***,***,+**,,,**,**
*,,,,,,,,**,*,,,,,,,,,,,,,,,,,,,,***,,,,,,,,,,,,,,,***,,,+,,,+,,,+,,,**+,**,,,*
*,,,,,**,,,,*,,,,,,,,,**,,,,,,,,,* ***,,,,,,,,,,,*** **,***,***,***,**,**++,,,*
*,,,,,,,,**,*,,,,,,,,,,,,,,,,,,,,*   **++*********    *** *** *** **********,**
*+****,,,,,,*,,,,,****++****,,,,,*#####++#####******************************+* 
*,,,,****,,**,,****,,,,,,,,****,,*#..........#*,,,,,*,,,,,*,,*,,,,+,,,,*<<**,* 
*,,,,<<<**,,****,,,,,,**,,,,,,****#..........#*,,,,,*,,,,,*,,*,,,,*,,,,*<<**+* 
*,,,,<<<<**,,+,,,,,,,,,,,,,,,,,,,++..#....#..#*,,*++*++*++*++******+**+*<<**,* 
*,,,<<<<<<*,,+,,,,,,,,,,,,,,,,,,,++..........#*,,+,,,,,,,,,,,,,,,,,,,,,*<<**+* 
*++*******************************#..........#*,,+,,,,,,,,,,,,,,,,,,,,,**+**,* 
*++**********************##########..#....#..#****,,*,,*,,*,,*,,*,,*,,,,,,**+* 
*,,*,,,,,,,**,,,,,,,,,,,,........''..........#*,,+,,,,,,,,,,,,,,,,,,,,,**+**,* 
*,,*,,,,,,,**,,,,,,,,,,,,........''..........#*,,+,,,,,,,,,,,,,,,,,,,,,*<<**+* 
*,,*,,,,,,,**,,***********#####..##..#....#..#*,,*++*++*++*++******+**+*<<**,* 
*,,+,,,,,,,*#..#*,*,#.*,*,*,*,#..##..........++,,,,,*,,,,,*,,*,,,,*,,,,*<<**+* 
*,,*,,,,,,,*#§.#,*,#k#,*,*,*,*#..##..........++,,,,,*,,,,,*,,*,,,,+,,,,*<<**,* 
*,,*,,,,,,,*#§§#*,#[#,*,*,*,*,#..####++####''#******************************+* 
*,,*,,,,,,,*#§§#,#e#,*,*,*,*,*#..#***++***#''###############################+# 
*,,*,,,,,,,*#§§##§#,*,*,*,*,*,#..#*,,,,,,*#.....)...(........................# 
************#§.#'##############..#*,*+**,*#..).)(......)).(.......)..(.......# 
***##########§§d§.§..............#*,*,,+,*#..##############)'##############).# 
*__________##.§§.................#*,+,,*,*#).#))#))#))))#....).#[<[[#[.#[[#..# 
*__________###########++##########*,*,,+,*#.(#))#))##''##......##''##[[#[[#..# 
*____#####'###########++##########*,+,,*,*#..#.....#....#......#....#.....#..# 
######)))#.##................##..#*,**+*,*#(.#..####..).###).###....####..#..# 
#.?(.')))'.##......#..#......##..#*,,,,,,*#..#..'..)............)......'..#..# 
##########.##................''..#********#..#..####..).............####..#..# 
#.....).....†................''..##########).#.....#).####....####.)#.....#..# 
#'#####'#####......#..#......##.........)..(.#))#))#..#((#....#((#.)#[[#[[#..# 
#.#..#.....##................##...))...).....#))#))#..'((##..##(('..#[[#.[#..# 
#.#))#####)#####'#####''#########################*#########################++# 
#.#))#.....##.......##)'############ ########## ######   ******************++* 
#.#))#.....##.......##......'..'...###........###....####*,,,,**,,,*,*,*,,,,,* 
#.#[[###'####.......##......'..'.....##......##....###..#*,,,,*,,*,,,,,,,*,,** 
#.##'#.....##...<...##.....##..##.....##....##..#.##....#*,,,+*,***,,,,,***,,* 
#.#........##.......##.).###....###....#....#.....#.....#*,,**,,,*,,,,,,,*,,** 
#)#........##.......##..##........###.###).##.#.#.#.....#*****,,***,,*,,***,,* 
#)###########.......##''#...#..#...#...(#..#......###'###*,,,*,,,*,,***,,*,,,* 
#.......#..*##########..)..........'...))).)......'.....#*,,,+,,,,,,,*,,,,,,,* 
#÷###...#.############''#...#..#...#....#))#)...).###'###*,,,*,,,*,,***,,*,,,* 
#.#.....#.#....#..[[##.)##........###.###..##†#.#.#[(.}.#*****,,***,,*,,***,,* 
#.#...#.#'#....#..[.##...###....###....#....#.....#.}...#*,,**,,,*,,,,,,,*,,** 
#.....#.#†'....'..))##.....##..##.....##....##.)#.##.[(.#*,,,+*,***,,,,,***,,* 
#...###.#)#....#..))###.....'..'.....##......##....###..#*,,,,*,,*,,,,,,,*,,** 
#.......'.#....#..))# ###...'..'...###........###....####*,,,,**,,,*,*,*,,,**  
#####################   *##########* ########## ######   *******************