⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣴⠶⠟⠛⠛⠛⠛⢛⣛⣻⣷⣶⣶⣶⣤⣀⡀⢀⣀⣀⣤⣄⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠉⠉⡙⢳⢦⣄⠀⢀⣴⣿⣿⣍⠉⠁⠉⠛⢷⣬⡙⣿⡿⠟⠉⠁⢀⣽⠿⢿⣿⡿⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⣰⣧⠶⢞⣿⠟⠐⢯⣓⠒⠂⠽⢷⣄⠀⠀⠀⠈⢿⣍⠀⠀⠀⠀⣾⠃⠀⢀⣬⡿⣦⡙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⣠⡾⠋⠀⠰⠟⠁⠀⠀⠀⠙⠆⠀⠀⠀⠹⣷⠀⠀⠀⠀⠹⣧⡀⠀⢸⡇⢀⣴⣿⣥⣄⡘⢷⡜⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠘⢷⡄⢸⣁⡾⠋⣇⣠⣼⣿⣎⣿⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠘⣷⠀⠀⠀⠀⠈⣷⡘⢿⣇⠀⠻⣿⣺⡏⣿⣿⣸⠟⠛⠛⣿⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⣼⠁⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢀⡀⠀⠸⣇⠀⠀⠀⠹⣇⠀⠀⠀⠀⠘⣧⠀⠙⠻⢦⣬⣭⣽⠟⣿⡿⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢰⠇⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⣿⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠠⠍⣣⡼⠟⠿⣿⠓⠶⣿⣄⠀⠀⠀⠀⠀
⠀⣠⣴⡿⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⣼⠋⣷⠀⠀⢠⡄⠀⠀⠀⠀⡇⠀⠀⣿⣄⠀⠀⠀⠸⡇⠀⠀⠀⠀⠘⣷⡴⠖⠒⣲⣟⣹⣶⣒⣶⣏⠀⠀⣼⡏⠀⠀⠀⠀⠀
⠸⢿⣥⣤⣴⡟⠀⠀⠀⠀⡏⠀⢘⣿⣿⣶⣿⣇⠀⠈⣧⠀⠀⠀⢰⡇⠀⣸⠃⠻⣦⡀⠀⠀⣇⠀⠀⠀⠀⠀⣿⢷⣴⣿⢿⠿⣿⣎⠻⢦⣽⣧⣰⣿⣦⡀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣇⡴⣿⠏⠣⠄⠼⠛⢷⣄⢹⣇⠀⢀⣾⣷⣾⡿⢿⣿⣾⣿⣦⣄⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⠀⢿⡙⣧⣠⠟⠈⢻⡍⠻⣿⣦⡀⠀⠀
⠀⠀⠀⠀⣿⠀⠀⠀⣠⡾⠋⠀⣿⠒⠒⠒⠦⠤⢌⡿⠻⠿⣦⠾⢹⣽⢫⡾⢻⢛⠿⢿⣍⠋⡇⠀⠀⠀⠀⠀⣸⠀⠀⠀⣿⣀⣸⡇⠀⠁⠀⢀⡿⠀⠀⠈⢿⣷⡄⠀
⠀⠀⠀⠀⣿⡄⠀⣴⠋⠀⠀⠀⠙⣦⣀⠀⢀⣠⡾⠃⠀⠀⠀⠀⠉⠀⣾⠃⠈⠉⠀⠀⣿⣸⠇⠀⠀⠀⠀⠀⣿⠀⠀⢠⡟⢹⡏⠁⠀⠀⣠⡟⠀⠀⠀⠀⠈⣿⣷⠀
⠀⠀⠀⠀⢸⣇⠀⣿⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢠⡟⠀⢀⡼⠃⠈⣷⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⢹⣿⡀
⠀⠀⠀⠀⠈⣿⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⣠⣾⣇⣀⡀⠀⠈⠻⢦⣤⡤⠞⣹⠏⠀⠀⠀⠀⠀⣸⡇⣠⡿⠁⠀⠀⠸⣧⣰⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⢹⣇⠀⠙⠷⣦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⣴⠏⢀⡀⠀⠀⠀⢰⣿⡾⠋⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡅
⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠙⠻⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡾⣁⣴⣿⡇⠀⠀⢠⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⣿⣤⡀⢻⣆⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠙⠛⠛⠛⠉⢀⡿⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣾⣿⠛⠷⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⣀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡟⠀⠀⠀⠀⠀⢀⣾⡿⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠘⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠈⣿⣟⠻⠿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣾⣿⡿⠛⠉⠀⣿⣟⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣀⠀⢀⣿⡿⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠉⠉⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⢨⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣿⡿⠃⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⡀⠀⠀⣀⣼⣿⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣶⣿⠿⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣤⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀