################################################################################################################################
#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.
##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..
#..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..#
####....####....####....####....####....####....####....####....####....####....####....####....####....####....####....####....
#.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.#
##....####....####....####....####....####....####....####....####....####....####....####....####....####....####....####....##
#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.
########........########........########........########........########........########........########........########........
#.#.#.#..#.#.#.##.#.#.#..#.#.#.##.#.#.#..#.#.#.##.#.#.#..#.#.#.##.#.#.#..#.#.#.##.#.#.#..#.#.#.##.#.#.#..#.#.#.##.#.#.#..#.#.#.#
##..##....##..####..##....##..####..##....##..####..##....##..####..##....##..####..##....##..####..##....##..####..##....##..##
#..##..#.##..##.#..##..#.##..##.#..##..#.##..##.#..##..#.##..##.#..##..#.##..##.#..##..#.##..##.#..##..#.##..##.#..##..#.##..##.
####........########........########........########........########........########........########........########........####
#.#..#.#.#.##.#.#.#..#.#.#.##.#.#.#..#.#.#.##.#.#.#..#.#.#.##.#.#.#..#.#.#.##.#.#.#..#.#.#.##.#.#.#..#.#.#.##.#.#.#..#.#.#.##.#.
##....##..####..##....##..####..##....##..####..##....##..####..##....##..####..##....##..####..##....##..####..##....##..####..
#..#.##..##.#..##..#.##..##.#..##..#.##..##.#..##..#.##..##.#..##..#.##..##.#..##..#.##..##.#..##..#.##..##.#..##..#.##..##.#..#
################................################................################................################................
#.#.#.#.#.#.#.#..#.#.#.#.#.#.#.##.#.#.#.#.#.#.#..#.#.#.#.#.#.#.##.#.#.#.#.#.#.#..#.#.#.#.#.#.#.##.#.#.#.#.#.#.#..#.#.#.#.#.#.#.#
##..##..##..##....##..##..##..####..##..##..##....##..##..##..####..##..##..##....##..##..##..####..##..##..##....##..##..##..##
#..##..##..##..#.##..##..##..##.#..##..##..##..#.##..##..##..##.#..##..##..##..#.##..##..##..##.#..##..##..##..#.##..##..##..##.
####....####........####....########....####........####....########....####........####....########....####........####....####
#.#..#.##.#..#.#.#.##.#..#.##.#.#.#..#.##.#..#.#.#.##.#..#.##.#.#.#..#.##.#..#.#.#.##.#..#.##.#.#.#..#.##.#..#.#.#.##.#..#.##.#.
##....####....##..####....####..##....####....##..####....####..##....####....##..####....####..##....####....##..####....####..
#..#.##.#..#.##..##.#..#.##.#..##..#.##.#..#.##..##.#..#.##.#..##..#.##.#..#.##..##.#..#.##.#..##..#.##.#..#.##..##.#..#.##.#..#
########................################................################................################................########
#.#.#.#..#.#.#.#.#.#.#.##.#.#.#.#.#.#.#..#.#.#.#.#.#.#.##.#.#.#.#.#.#.#..#.#.#.#.#.#.#.##.#.#.#.#.#.#.#..#.#.#.#.#.#.#.##.#.#.#.
##..##....##..##..##..####..##..##..##....##..##..##..####..##..##..##....##..##..##..####..##..##..##....##..##..##..####..##..
#..##..#.##..##..##..##.#..##..##..##..#.##..##..##..##.#..##..##..##..#.##..##..##..##.#..##..##..##..#.##..##..##..##.#..##..#
####........####....########....####........####....########....####........####....########....####........####....########....
#.#..#.#.#.##.#..#.##.#.#.#..#.##.#..#.#.#.##.#..#.##.#.#.#..#.##.#..#.#.#.##.#..#.##.#.#.#..#.##.#..#.#.#.##.#..#.##.#.#.#..#.#
##....##..####....####..##....####....##..####....####..##....####....##..####....####..##....####....##..####....####..##....##
#..#.##..##.#..#.##.#..##..#.##.#..#.##..##.#..#.##.#..##..#.##.#..#.##..##.#..#.##.#..##..#.##.#..#.##..##.#..#.##.#..##..#.##.
################################................................################################................................
#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#..#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.##.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#..#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#
##..##..##..##..##..##..##..##....##..##..##..##..##..##..##..####..##..##..##..##..##..##..##....##..##..##..##..##..##..##..##
#..##..##..##..##..##..##..##..#.##..##..##..##..##..##..##..##.#..##..##..##..##..##..##..##..#.##..##..##..##..##..##..##..##.
####....####....####....####........####....####....####....########....####....####....####........####....####....####....####
#.#..#.##.#..#.##.#..#.##.#..#.#.#.##.#..#.##.#..#.##.#..#.##.#.#.#..#.##.#..#.##.#..#.##.#..#.#.#.##.#..#.##.#..#.##.#..#.##.#.
##....####....####....####....##..####....####....####....####..##....####....####....####....##..####....####....####....####..
#..#.##.#..#.##.#..#.##.#..#.##..##.#..#.##.#..#.##.#..#.##.#..##..#.##.#..#.##.#..#.##.#..#.##..##.#..#.##.#..#.##.#..#.##.#..#
########........########................########........################........########................########........########
#.#.#.#..#.#.#.##.#.#.#..#.#.#.#.#.#.#.##.#.#.#..#.#.#.##.#.#.#.#.#.#.#..#.#.#.##.#.#.#..#.#.#.#.#.#.#.##.#.#.#..#.#.#.##.#.#.#.
##..##....##..####..##....##..##..##..####..##....##..####..##..##..##....##..####..##....##..##..##..####..##....##..####..##..
#..##..#.##..##.#..##..#.##..##..##..##.#..##..#.##..##.#..##..##..##..#.##..##.#..##..#.##..##..##..##.#..##..#.##..##.#..##..#
####........########........####....########........########....####........########........####....########........########....
#.#..#.#.#.##.#.#.#..#.#.#.##.#..#.##.#.#.#..#.#.#.##.#.#.#..#.##.#..#.#.#.##.#.#.#..#.#.#.##.#..#.##.#.#.#..#.#.#.##.#.#.#..#.#
##....##..####..##....##..####....####..##....##..####..##....####....##..####..##....##..####....####..##....##..####..##....##
#..#.##..##.#..##..#.##..##.#..#.##.#..##..#.##..##.#..##..#.##.#..#.##..##.#..##..#.##..##.#..#.##.#..##..#.##..##.#..##..#.##.
################................................################################................................################
#.#.#.#.#.#.#.#..#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.##.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#..#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.##.#.#.#.#.#.#.#.
##..##..##..##....##..##..##..##..##..##..##..####..##..##..##..##..##..##..##....##..##..##..##..##..##..##..####..##..##..##..
#..##..##..##..#.##..##..##..##..##..##..##..##.#..##..##..##..##..##..##..##..#.##..##..##..##..##..##..##..##.#..##..##..##..#
####....####........####....####....####....########....####....####....####........####....####....####....########....####....
#.#..#.##.#..#.#.#.##.#..#.##.#..#.##.#..#.##.#.#.#..#.##.#..#.##.#..#.##.#..#.#.#.##.#..#.##.#..#.##.#..#.##.#.#.#..#.##.#..#.#
##....####....##..####....####....####....####..##....####....####....####....##..####....####....####....####..##....####....##
#..#.##.#..#.##..##.#..#.##.#..#.##.#..#.##.#..##..#.##.#..#.##.#..#.##.#..#.##..##.#..#.##.#..#.##.#..#.##.#..##..#.##.#..#.##.
########................########........################........########................########........################........
#.#.#.#..#.#.#.#.#.#.#.##.#.#.#..#.#.#.##.#.#.#.#.#.#.#..#.#.#.##.#.#.#..#.#.#.#.#.#.#.##.#.#.#..#.#.#.##.#.#.#.#.#.#.#..#.#.#.#
##..##....##..##..##..####..##....##..####..##..##..##....##..####..##....##..##..##..####..##....##..####..##..##..##....##..##
#..##..#.##..##..##..##.#..##..#.##..##.#..##..##..##..#.##..##.#..##..#.##..##..##..##.#..##..#.##..##.#..##..##..##..#.##..##.
####........####....########........########....####........########........####....########........########....####........####
#.#..#.#.#.##.#..#.##.#.#.#..#.#.#.##.#.#.#..#.##.#..#.#.#.##.#.#.#..#.#.#.##.#..#.##.#.#.#..#.#.#.##.#.#.#..#.##.#..#.#.#.##.#.
##....##..####....####..##....##..####..##....####....##..####..##....##..####....####..##....##..####..##....####....##..####..
#..#.##..##.#..#.##.#..##..#.##..##.#..##..#.##.#..#.##..##.#..##..#.##..##.#..#.##.#..##..#.##..##.#..##..#.##.#..#.##..##.#..#
################################################################................................................................
#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#..#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#
##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##....##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##
#..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..#.##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##.
####....####....####....####....####....####....####....####........####....####....####....####....####....####....####....####
#.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.#.#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#.
##....####....####....####....####....####....####....####....##..####....####....####....####....####....####....####....####..
#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##..##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#
########........########........########........########................########........########........########........########
#.#.#.#..#.#.#.##.#.#.#..#.#.#.##.#.#.#..#.#.#.##.#.#.#..#.#.#.#.#.#.#.##.#.#.#..#.#.#.##.#.#.#..#.#.#.##.#.#.#..#.#.#.##.#.#.#.
##..##....##..####..##....##..####..##....##..####..##....##..##..##..####..##....##..####..##....##..####..##....##..####..##..
#..##..#.##..##.#..##..#.##..##.#..##..#.##..##.#..##..#.##..##..##..##.#..##..#.##..##.#..##..#.##..##.#..##..#.##..##.#..##..#
####........########........########........########........####....########........########........########........########....
#.#..#.#.#.##.#.#.#..#.#.#.##.#.#.#..#.#.#.##.#.#.#..#.#.#.##.#..#.##.#.#.#..#.#.#.##.#.#.#..#.#.#.##.#.#.#..#.#.#.##.#.#.#..#.#
##....##..####..##....##..####..##....##..####..##....##..####....####..##....##..####..##....##..####..##....##..####..##....##
#..#.##..##.#..##..#.##..##.#..##..#.##..##.#..##..#.##..##.#..#.##.#..##..#.##..##.#..##..#.##..##.#..##..#.##..##.#..##..#.##.
################................################................................################................################
#.#.#.#.#.#.#.#..#.#.#.#.#.#.#.##.#.#.#.#.#.#.#..#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.##.#.#.#.#.#.#.#..#.#.#.#.#.#.#.##.#.#.#.#.#.#.#.
##..##..##..##....##..##..##..####..##..##..##....##..##..##..##..##..##..##..####..##..##..##....##..##..##..####..##..##..##..
#..##..##..##..#.##..##..##..##.#..##..##..##..#.##..##..##..##..##..##..##..##.#..##..##..##..#.##..##..##..##.#..##..##..##..#
####....####........####....########....####........####....####....####....########....####........####....########....####....
#.#..#.##.#..#.#.#.##.#..#.##.#.#.#..#.##.#..#.#.#.##.#..#.##.#..#.##.#..#.##.#.#.#..#.##.#..#.#.#.##.#..#.##.#.#.#..#.##.#..#.#
##....####....##..####....####..##....####....##..####....####....####....####..##....####....##..####....####..##....####....##
#..#.##.#..#.##..##.#..#.##.#..##..#.##.#..#.##..##.#..#.##.#..#.##.#..#.##.#..##..#.##.#..#.##..##.#..#.##.#..##..#.##.#..#.##.
########................################................########........################................################........
#.#.#.#..#.#.#.#.#.#.#.##.#.#.#.#.#.#.#..#.#.#.#.#.#.#.##.#.#.#..#.#.#.##.#.#.#.#.#.#.#..#.#.#.#.#.#.#.##.#.#.#.#.#.#.#..#.#.#.#
##..##....##..##..##..####..##..##..##....##..##..##..####..##....##..####..##..##..##....##..##..##..####..##..##..##....##..##
#..##..#.##..##..##..##.#..##..##..##..#.##..##..##..##.#..##..#.##..##.#..##..##..##..#.##..##..##..##.#..##..##..##..#.##..##.
####........####....########....####........####....########........########....####........####....########....####........####
#.#..#.#.#.##.#..#.##.#.#.#..#.##.#..#.#.#.##.#..#.##.#.#.#..#.#.#.##.#.#.#..#.##.#..#.#.#.##.#..#.##.#.#.#..#.##.#..#.#.#.##.#.
##....##..####....####..##....####....##..####....####..##....##..####..##....####....##..####....####..##....####....##..####..
#..#.##..##.#..#.##.#..##..#.##.#..#.##..##.#..#.##.#..##..#.##..##.#..##..#.##.#..#.##..##.#..#.##.#..##..#.##.#..#.##..##.#..#
################################................................................................################################
#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#..#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.##.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.
##..##..##..##..##..##..##..##....##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..####..##..##..##..##..##..##..##..
#..##..##..##..##..##..##..##..#.##..##..##..##..##..##..##..##..##..##..##..##..##..##..##..##.#..##..##..##..##..##..##..##..#
####....####....####....####........####....####....####....####....####....####....####....########....####....####....####....
#.#..#.##.#..#.##.#..#.##.#..#.#.#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#.#.#..#.##.#..#.##.#..#.##.#..#.#
##....####....####....####....##..####....####....####....####....####....####....####....####..##....####....####....####....##
#..#.##.#..#.##.#..#.##.#..#.##..##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..#.##.#..##..#.##.#..#.##.#..#.##.#..#.##.
########........########................########........########........########........################........########........
#.#.#.#..#.#.#.##.#.#.#..#.#.#.#.#.#.#.##.#.#.#..#.#.#.##.#.#.#..#.#.#.##.#.#.#..#.#.#.##.#.#.#.#.#.#.#..#.#.#.##.#.#.#..#.#.#.#
##..##....##..####..##....##..##..##..####..##....##..####..##....##..####..##....##..####..##..##..##....##..####..##....##..##
#..##..#.##..##.#..##..#.##..##..##..##.#..##..#.##..##.#..##..#.##..##.#..##..#.##..##.#..##..##..##..#.##..##.#..##..#.##..##.
####........########........####....########........########........########........########....####........########........####
#.#..#.#.#.##.#.#.#..#.#.#.##.#..#.##.#.#.#..#.#.#.##.#.#.#..#.#.#.##.#.#.#..#.#.#.##.#.#.#..#.##.#..#.#.#.##.#.#.#..#.#.#.##.#.
##....##..####..##....##..####....####..##....##..####..##....##..####..##....##..####..##....####....##..####..##....##..####..
#..#.##..##.#..##..#.##..##.#..#.##.#..##..#.##..##.#..##..#.##..##.#..##..#.##..##.#..##..#.##.#..#.##..##.#..##..#.##..##.#..#
################................................################................################################................
#.#.#.#.#.#.#.#..#.#.#.#.#.#.#.#.#.#.#.#.#.#.#.##.#.#.#.#.#.#.#..#.#.#.#.#.#.#.##.#.#.#.#.#.#.#.#.#.#.#.#.#.#.#..#.#.#.#.#.#.#.#
##..##..##..##....##..##..##..##..##..##..##..####..##..##..##....##..##..##..####..##..##..##..##..##..##..##....##..##..##..##
#..##..##..##..#.##..##..##..##..##..##..##..##.#..##..##..##..#.##..##..##..##.#..##..##..##..##..##..##..##..#.##..##..##..##.
####....####........####....####....####....########....####........####....########....####....####....####........####....####
#.#..#.##.#..#.#.#.##.#..#.##.#..#.##.#..#.##.#.#.#..#.##.#..#.#.#.##.#..#.##.#.#.#..#.##.#..#.##.#..#.##.#..#.#.#.##.#..#.##.#.
##....####....##..####....####....####....####..##....####....##..####....####..##....####....####....####....##..####....####..
#..#.##.#..#.##..##.#..#.##.#..#.##.#..#.##.#..##..#.##.#..#.##..##.#..#.##.#..##..#.##.#..#.##.#..#.##.#..#.##..##.#..#.##.#..#
########................########........################................################........########................########
#.#.#.#..#.#.#.#.#.#.#.##.#.#.#..#.#.#.##.#.#.#.#.#.#.#..#.#.#.#.#.#.#.##.#.#.#.#.#.#.#..#.#.#.##.#.#.#..#.#.#.#.#.#.#.##.#.#.#.
##..##....##..##..##..####..##....##..####..##..##..##....##..##..##..####..##..##..##....##..####..##....##..##..##..####..##..
#..##..#.##..##..##..##.#..##..#.##..##.#..##..##..##..#.##..##..##..##.#..##..##..##..#.##..##.#..##..#.##..##..##..##.#..##..#
####........####....########........########....####........####....########....####........########........####....########....
#.#..#.#.#.##.#..#.##.#.#.#..#.#.#.##.#.#.#..#.##.#..#.#.#.##.#..#.##.#.#.#..#.##.#..#.#.#.##.#.#.#..#.#.#.##.#..#.##.#.#.#..#.#
##....##..####....####..##....##..####..##....####....##..####....####..##....####....##..####..##....##..####....####..##....##
#..#.##..##.#..#.##.#..##..#.##..##.#..##..#.##.#..#.##..##.#..#.##.#..##..#.##.#..#.##..##.#..##..#.##..##.#..#.##.#..##..#.##.