⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⢳⡀⠙⢦⣽⣦⡀
⠀⠀⠀⠀⠀⠸⡟⣿⣷⡄⠀⠀⢳⣄⠀⠙⣟⡙⣦⣀
⠀⠀⠀⠀⠀⠀⢳⠈⢿⣿⣦⢀⡴⣟⢒⣖⣡⣀⣀⣀⡉⠑⢦⣀
⠀⠀⠀⠀⠀⠀⠀⢷⣠⠋⢹⣿⠋⣸⣿⣿⣿⣿⣿⣿⣿⡿⠾⠛⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠟⢢⡆⠙⣾⣿⡿⣿⣿⠿⢿⣿⣿⣷⣄⣀⣀⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠓⣀⣹⣿⣇⠱⡽⠳⣿⣿⡿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠏⠀⠰⠛⢿⣿⠇⣿⣀⣀⣀⣸⣿⠉⡆⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡼⢿⣿⣿⡿⠟⠋⣀⣀⠀⠀⠉⠁⣴⣿⣿⣿⣿⣿⣿⣦⡇⠀⠀⣴⣿⣿⣿⣿⠳⡄
⠀⠀⠀⠀⠀⠀⠚⠀⠘⣿⣿⣧⣀⡾⢿⠟⠀⠀⠀⠀⠈⠉⣹⣿⣿⣿⣿⣿⠃⠀⣸⣿⣿⠿⠿⢿⠀⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡑⠉⠀⡊⠉⠀⣠⠞⠻⣿⡼⠋⠉⠙⢢⠀⠰⡏⠁⠀⠀⠀⠈⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⢿⣶⣤⡤⠐⠒⠚⠷⣄⠀⠀⠀⠀⠀⠀⢹⠀⢇⠀⣀⣀⣀⠀⢸⣿⣿⢷
⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠛⢿⣿⡟⠉⠀⠀⠀⠀⠀⠈⠀⢀⣤⠀⠀⠀⣸⠀⠘⣿⣿⣿⣿⡟ ⢹⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣈⠩⡇⠀⠀⠀⠀⠀⢀⣀⡴⣚⣿⠃⠀⠀⢸⠀⠀⠀⠘⠛⠛⠟ ⠀⢸⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠋ ⠀⠀⢇⠀⠀⠀⣠⣾⠉⠀⢀⣼⠃⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠈⣳⣾⣿⣿⣿⠶⠋⠁⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⢀⣴⣿⣿⣿⠟⡏⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⠾⣿⣿⣿⣿⢏⡿⠷⠤⠤⠶⠒⠛⠟⠑⠒⠒⠒⠒⠒⠢⠤⣘⠀⠀⡞⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠛⠛⣫⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉ ⠉⠈⠉⠉⠉⠒⠒⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⡠⠔⠛⢧⠀⠀⢇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠈⠑⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠐⠛⠒⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠑⠒⠦⣄⠀⣠⡤⠶⠛⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣠⡴⠛⠋⠁⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⣀⣀⣀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⡟⠁⠀⠀⠀