*********     *****************     **********     *********************   
   **,,,,,,,**   **,,,,,,,,,,,,,,,**   **,,,,,,,,**    *,,,,,,,,,,,,,,,,,,,*   
  **,,,,,,,,,** **,,,,,,,,,,,,,,,,,** **,,,,,,,,,,**   *,,,,,,,,,,,,,,,,,,,*   
 **,,,,,,,,,,,***,,,,,***,,,***,,,,,***,,,,,,,,,,,,**  *,,,,,,,,,,,,,,,,,,,*   
 *,,,,,,,,,,,,,*,,,,***,,,,,,,***,,,,*,,,,,,,,,,,,,,*  *,,,,,,,,,,,,,,,,,,,*   
 *,,,,,,,,,,,,,,,,,**,,,,,,,,,,,**,,,*,,,,,,,,,,,,,,*********+**************** 
 *,,,,,,,,,,,,,,,,**,,,,,,,,,,,,,**,,*,,,,,,,,,,,,,,**,,,,,,,,,,,,,,,,,,,,,,,* 
 *,,,,,,,,,,,,,,,,*,,,,,,,,,,,,,,,*,,,,,,,,,,,,,,,,,**,,,,,,,,,,,,,,,,,,,,,,,* 
 *,,,,,,,,,,,,,,,,*,,,,,,,,,,,,,,,*,,,,,,,,,,,,,,,,,************************+* 
 *,,,,,,,,,,,,,,,,*,,,,,,,,,,,,,,,*,,,,,,,,,,,,,,,,,* ****** *** *** ***   *+* 
 *,,,,,,,,,,,,,,,,**,,,,,,,,,,,,,**,,*,,,,,,,,,,,,,,* *,+*,***,***,***,*****,* 
 *,,,,,,,,,,,,,,,,,**,,,,,,,,,,,**,,,*,,,,,,,,,,,,,,*****,,,+,,,*,,,+,,,+,**+* 
 *,,,,,,,,,,,,,*,,,,***,,,,,,,***,,,,*,,,,,,,,,,,,,,**,***,***,***,***,*****,* 
 **,,,,,,,,,,,***,,,,,***,,,***,,,,,***,,,,,,,,,,,,****+,*+*,**+,**+,***,***+* 
  **,,,,,,,,,** **,,,,,,,,,,,,,,,,,** **,,,,,,,,,,**  *,,,*,,,*,,,*,,,*,,,**,* 
   **,,,,,,,**   **,,,,,,,,,,,,,,,**   **,,,,,,,,**  ***,***,+**,+**,**+,***+* 
    *********     *****************     ****++****   *,*+*,***,*+*,*+*,*+* *,* 
**********************************   *******++****   **+,+**,***,***,***,***+* 
*,,,,*,,*,,,,,,,,*,,,,*,,,*,,,,,,* ***,,,,,,,,,,,***  *,,,+,,,*,,,+,,,*,,,**,* 
*,,,,*,,,,,*,,*,,,,,,,,,,,*,,,,,,***,,,,,,,,,,,,,,,** **,***,**+,+**,+*+,***+* 
*,,,,*,,,,,,,,,,,,,,,,,,,,*,,,,,,**,,,,,,,,,,,,,,,,,* ******+*,***,***,*+* *,* 
*,,,,*,,*,,*,,*,,*,,,,*,,,*,,,,,,**,,,,,,,,,,,,,,,,,***,,,,,,**+,***,***,***+* 
*,,***,**,,,,,,,,**,,**,,,**,,,****,,,,,,,,,,,,,,,,,**,,,,,,,,*,,,+,,,+,,,**,**
*,,*,,,,,*,,,,,,*,,,,,,*,*,,*,*,,***,,,,,,,,,,,,,,,***,,,,,,,,**,**+,**+,**,,,*
*,,+,,,,,,******,,,,,,,,,,,,,,,,,* ***,,,,,,,,,,,*** **,,,,,,*****,***,**++,,,*
*,,*,,,,,*,,,,,,*,,,,,,*,*,,*,*,,*   **++*********    ********   *** *******,**
*,,***,**,,,,,,,,**,,**,,,**,,,********++***********************************+* 
*,,,,*,,*,,*,,*,,*,,,,*,,,*,,,,,,**,,,,,,,,,,**,,,,*,,,,**,,,,,**,,,,,,,,,**,* 
*,,,,*,,,,,,,,,,,,,,,,,,,,*,,,,,,**,,,,,,,,,,**,,,,+,,,+*,,,,,,,**,,,,,,,,**+* 
*,,,,*,,,,,*,,*,,,,,,,,,,,*,,,,,,++,,*,,,,*,,**,,,,*,,+*,,,,,,,,,**,,,,,,,**,* 
*,,,,*,,*,,,,,,,,*,,,,*,,,*,,,,,,++,,,,,,,,,,**********,,,,,,,,,,,**+**+****+* 
*++********************************,,,,,,,,,,**,,,,,,,,,,,,,*,,,,,,,,,,,,,**,* 
*++********************************,,*,,,,*,,**,,,,,,,,,,,,*,*,,,,,,,,,,,,**+* 
*,,*,,,,,,,**,,,,,,,,,,,,,,,,,,,,++,,,,,,,,,,**,,,,,,,,,,,,,*,,,,,,,,,,,,,**,* 
*,,*,,,,,,,**,,,,,,,,,,,,,,,,,,,,++,,,,,,,,,,*****++***,,,,,,,,,,,*****++***+* 
*,,*,,,,,,,**,,***********+****,,**,,*,,,,*,,**,,,,,,,**,,,,,,,,,**,,,*,,,**,* 
*,,*,,,,,,,**,,**,*,*,*,*,*,*,*,,**,,,,,,,,,,++,,,,,,,,**,,,,,,,**,,,,+,,,**+* 
*,,+,,,,,,,**,,*,*,*,*,*,*,*,**,,**,,,,,,,,,,++,,,,,,,,,**,,,,,**,,,,,*,,,**,* 
*,,*,,,,,,,**,,**,*,*,*,*,*,*,*,,****++****++*******************************+* 
*,,*,,,,,,,**,,*,*,*,*,*,*,*,**,,****++***#++###############################+# 
*,,*,,,,,,,**,,**,*,*,*,*,*,*,*,,**,,,,,,*#.......o..........................# 
*************,,****************,,**,*+**,*#......4...........................# 
****#######**,,,,,,,,,,,,,,,,,,,,**,*,,+,*#..##############o'##############..# 
*__________**,,,,,,,,,,,,,,,,,,,,**,+,,*,*#..#,,+,,,+,,*,,,.....*,,+,,,+,,#..# 
*__________***********++***********,*,,+,*#o.#,,*,,,*,,*,,,.....#,,*,,,*,,#..# 
*,#####+##############++##########*,+,,*,*#.4#***,,,*******..####***,,,***#..# 
*_#)))+.+..##................##..#*,**+*,*#..#,,,,,,,,,*,,,...,,*,,,,,,,,,#..# 
*_#).)#.#?(##......#..#......##..#*,,,,,,*#..#,,,,,,,,,,,,,ooo.,,,,,,,,,,,#..# 
#######+#####................''..#********#..#,,,,,,,,,*,,,oo.o,*,,,,,,,,,#..# 
#..)..).).))'................)'..##########o.#*+***+**,****.o****,**+***+*#..# 
#'#####+#####......#..#......##........).oT..#,,,,*,,*,*,,****,,*,*,,*,,,,#..# 
#.#...#.#[[##................##.........oo...#,,,,*,,*,+,,*  *,,+,*,,*,,,,#..# 
#.#...#)#))#####'#####''######################*************  *************#++# 
#.#..)'.#.)##.......##''################   ############   *****************++* 
#.##'####))##.......##....##..'...##...### #..........#  **,,,**,,,,,,,,**,,,* 
#.#.....#..##.......##...##...#[.##......###....#####'#  *,,,,,**,,,,,,**,,,** 
#.#.....#'###...<...##..##...##..#........##.####.....## **,**,,***++***,,,*** 
#.#........##.......##..#...##...'.........###.........# *,,,*,,,,,,,,,,,,**,* 
#.#........##.......##..'..##....###.......##..........##*,,,**,,,,,,,*,,,*,,* 
#'###########.......##.##([#.....).###......#...........#*,,,*,,,*,,,***,,+,,* 
#.......#..#############...'.........##.....#...........#**,***,***,,,*,,,*,,* 
#...#...#.#############....#....####..##....#'..........#*,,,*,,,*,,,,,,,,**,* 
#...#...#)#....#...[##..#..##..##..##..'..(.(#'........##*,,,**,,,,,,,,,,,,*** 
#.##.##.#)#....#....##.###..##.'....+..#.....)##'.....## *,,,*,,**++**,,,*,,** 
#...#...#.'....'..).####.##..#.##..##..#........######'##**,**,**,,,,**,***,,* 
#...#...#'#....#..))###...)..)..####...##...#######))).(#*,,,,,*,,,,,,*,,*,,,* 
#.......'.#....#..))##....#..##...))....##.##....=.(...=#**,,,***,,,,***,,,,** 
######################################################### ***** ****** ******