*********     *****************     **********     *********************   
   **,,,,,,,**   **,,,,,,,,,,,,,,,**   **,,,,,,,,**    *,,,,,,,,,,,,,,,,,,,*   
  **,,,,,,,,,** **,,,,,,,,,,,,,,,,,** **,,,,,,,,,,**   *,,,,,,,,,,,,,,,,,,,*   
 **,,,,,,,,,,,***,,,,,***,,,***,,,,,***,,,,,,,,,,,,**  *,,,,,,,,,,,,,,,,,,,*   
 *,,,,,,,,,,,,,*,,,,***,,,,,,,***,,,,*,,,,,,,,,,,,,,*  *,,,,,,,,,,,,,,,,,,,*   
 *,,,,,,,,,,,,,,,,,**,,,,,,,,,,,**,,,*,,,,,,,,,,,,,,**************+*********** 
 *,,,,,,,,,,,,,,,,**,,,,,,,,,,,,,**,,*,,,,,,,,,,,,,,**,,,,,,,,,,,,,,,,,,,,,,,* 
 *,,,,,,,,,,,,,,,,*,,,,,,,,,,,,,,,*,,,,,,,,,,,,,,,,,**,,,,,,,,,,,,,,,,,,,,,,,* 
 *,,,,,,,,,,,,,,,,*,,,,,,,,,,,,,,,*,,,,,,,,,,,,,,,,,************************+* 
 *,,,,,,,,,,,,,,,,*,,,,,,,,,,,,,,,*,,,,,,,,,,,,,,,,,* ****** *** *** ***   *+* 
 *,,,,,,,,,,,,,,,,**,,,,,,,,,,,,,**,,*,,,,,,,,,,,,,,* *,+*,***,***,***,*****,* 
 *,,,,,,,,,,,,,,,,,**,,,,,,,,,,,**,,,*,,,,,,,,,,,,,,*****,,,+,,,*,,,+,,,+,**+* 
 *,,,,,,,,,,,,,*,,,,***,,,,,,,***,,,,*,,,,,,,,,,,,,,**,***,***,***,***,*****,* 
 **,,,,,,,,,,,***,,,,,***,,,***,,,,,***,,,,,,,,,,,,****+,*+*,**+,**+,***,***+* 
  **,,,,,,,,,** **,,,,,,,,,,,,,,,,,** **,,,,,,,,,,**  *,,,*,,,*,,,*,,,*,,,**,* 
   **,,,,,,,**   **,,,,,,,,,,,,,,,**   **,,,,,,,,**  ***,***,+**,+**,**+,***+* 
    *********     *****************     ****++****   *,*+*,***,*+*,*+*,*+* *,* 
**********************************   *******++****   **+,+**,***,***,***,***+* 
*,,,,*,,*,,,,,,,,*,,,,*,,,*,,,,,,* ***,,,,,,,,,,,***  *,,,+,,,*,,,+,,,*,,,**,* 
*,,,,*,,,,,*,,*,,,,,,,,,,,*,,,,,,***,,,,,,,,,,,,,,,** **,***,**+,+**,+*+,***+* 
*,,,,*,,,,,,,,,,,,,,,,,,,,*,,,,,,**,,,,,,,,,,,,,,,,,* ******+*,***,***,*+* *,* 
*,,,,*,,*,,*,,*,,*,,,,*,,,*,,,,,,**,,,,,,,,,,,,,,,,,***,,,<<<**+,***,***,***+* 
*,,***,**,,,,,,,,**,,**,,,**,,,****,,,,,,,,,,,,,,,,,**,<<,,<<,*,,,+,,,+,,,**,**
*,,*,,,,,*,,,,,,*,,,,,,*,*,,*,*,,***,,,,,,,,,,,,,,,***<,<,<<,,**,**+,**+,**,,,*
*,<+,,,,,,******,,,,,,,,,,,,,,,,,* ***,,,,,,,,,,,*** **<<,<<<*****,***,**++,,,*
*,<*,,,,,*,,,,,,*,,,,,,*,*,,*,*,,*   **++*********    ********   *** *******,**
*,<***,**,,,,,,,,**,,**,,,**,,,***#####++#####**************************** *+* 
*,<<<*,,*,,*,,*,,*,,,,*,,,*,,,,,,*#..........#*<<+,,+,,+<<+,,+,,+,,+,,+,,* *,* 
*,<<<*,,,,,,,,,,,,,,,,,,,,*,,,,,,*#..........#*<<+,,+,,+<<+,,+,,+,,+,,+,,* *+* 
*,<<<*,,,,,*,,*,,,,,,,,,,,*,,,,,,++..#....#..#*++*++*++*++*++*++*++*++*++* *,* 
*,,<<*,,*,,,,,,,,*,,,,*,,,*,,,,,,++..........#*,,+,,+,,+,,+,,+<<+,,+,,+,,* *+* 
*++*******************************#..........#*,,+,,+,,+,,+,,+<<+,,+,,+,,* *,* 
*++************####################..#....#..#*++*++*++*++*++*++*++*++*++* *+* 
*,,*,,,,,,,**,,..................''..........#*,,+,,+,,+,,+,,+,,+,,+,,+,,* *,* 
*,,*,,,,,,,**,,........o.........''..........#*,,+,,+,,+,,+,,+,,+,,+,,+,,* *+* 
*,,*,,,,,,,**,,#######o########..##..#....#..#*++*++*++*++*++*++*++*++*++* *,* 
*,,+,,,,,,,**,,**,*,#)#[#,*,*,#..##..........++,,+,,+,,+,,+<<+,,+,,+,,+,,* *+* 
*,,*,,,,,,,**,,*,*,#W#S#D#,*,*#..##..........++,,+,,+,,+,,+<<+,,+,,+,,+,,* *,* 
*,,*,,,,,,,**,,**§#:#,#m#$#,*,#..####''####''#**************************** *+* 
*,,*,,,,,,,**,,*,#.#,*,#Y#†#,*#..####''####''###############################+# 
*,,*,,,,,,,**,,*#.#,*,*,#m#Y#,#..##..)...##..................................# 
*************,,*##*******####*#..##.#'##)##..................................# 
############*,,,,,,,,,,,.........##.#.['.##..##############++##############(.# 
#_________.#*,,,,,,,,,,,.........##.+.÷#.##..#,,,*,*,*,*,,,,,,,,*,*,*,*,,,#(.# 
#_________.#**********++###########.#.:'.##..#,*,*<*,*,*,*,,,,*,*,*,*,*,*,#()# 
#_______...###########++###########.+)[#.##..#,,,*<*,*,,,,,,,,,,,,*,*,*,,,#o.# 
##########'##................##..##.##'#.##).#*,**<*,*,*,*,,,,*,*,*,*<**,*#..# 
#.?(.')))'.##......#..#......##..##.,....##..#,,,*+*+*,,,,,,,,,,,,*+*+*,,,#..# 
##########.##................''..#**#######..#,*,*,,,*,*,*,,,,*,*,*,,,*,*,#).# 
#...........'................''((##########).#,,,*,,,,,,,,,,,,,,,,,,,,*,,,#..# 
#'#####'#####......#..#......##.((.).........#+***,*,*,*,*,,,,*,*,*,*,***+#..# 
#.#..#..#..##................##..............#,,,,,,,*,,,*,,,,*,,,*,,,,,,,#..# 
#.#..'..'..#####'#####''######################****************************#++# 
#.##'####'###.......##''#####  ##########################*********** ******++* 
#.#.....†..##.......##......#  #.........##...oo'...'..=#*,,,,,,,,,***,,,,,,,* 
#.#........##.......##......#  *#.......#*#(..oo##.##[[/#*,,,,,,,***,,,*,,,,,* 
#.#####[#####...<...###....##  ####)..###########...#####*,,,,,***,,,,***,,,,* 
#.#...)))..##.......# ##')## ###.((...+..##..##.......## *,,,***,,,,,,,*,,,,,* 
#.#...)))[.##.......###.)))###....##'##.....##.........##*,+**,,,,,*,,,,,,,,,* 
#'###########.......##......#....##...##....#)..........#***,,,,,,***,,,,*,,,* 
#)))....#..*##########......'.ooo'.....'.)))()..........#**,,,,*,,,*,,,,***,,* 
#..#.#..#.############......#....##...##)...#[).........#*,,,,***,,,,,,,,*,,,* 
#.##.##.#.#....#....###....###....##'##()...##.........##**,,,,*,,,,,,,,,,,,** 
#.......#'#....#..[.# ##''## ###..'..)'))##..##.......## *****,,,,,,,*,,,,**** 
#.##.##.#())...'..))###...)##  ####...###########...#####*,,,***,,,,***,,*+,,* 
#..#.#..#'#....#..))##......#  *#.......#*#...oo##.##.!.#*,,,,,+**,,,*,,**,,,* 
#.......).#....#.!))##......#  #.........##....o'...'...#*,,,,,,,***,,,***,,,* 
#############################  ##########################********* ***** *****