⠀ ⢸⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⣤⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⢀⣾⣿⠛⠉⠛⠿⣿⣦⣀⣀⣀⣀⣀⣀⣀⣠⣶⡿⠛⠻⣿⣦⣠⣤⣶⣶⣾⣷⣶⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⣾⡿⠁⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⣿⡿⠋⠀⠀⠀⠈⢿⣿⠋⠉⠀⠀⠈⢿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⢰⠾⢿⣷⣿⣿⣶⡀⠀⠀⠀⢸⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠀⠀⢻⣆⣴⠋⠉⠉⢿⣿⣶⣶⣶⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣤⣀⣬⣿⣿⡀⠀⠀⣸⡟⣿⡄⠈⠙⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⣤⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠉⠻⣿⣷⣿⣿⣤⠾⠁⠀⢠⣿⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣀⢀⣠⣴⣿⡇⠀⠀⠀
⠀⢀⣴⡿⣷⣤⡀⠀⠀⠀⠸⢿⣿⣿⣿⡿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠛⠉⣿⣧⠀⠀⠀
⢴⣿⡏⠀⠈⠛⢿⣶⣤⣀⣀⣀⣿⣿⣿⣇⡀⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀
⠀⠙⢿⣦⣄⠀⠀⠈⠉⠙⠛⠛⢿⣿⣿⣿⠉⠀⠀⠀⠀⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡆⠀⠀⠀⠛⣿⣿⠻⠷⠦
⠀⠀⠀⠉⠻⠿⣶⣦⣤⣄⣀⣀⣹⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠛⢶⡀⠀⠀⠀⠀⠀⠿⠿⠃⠀⠀⢠⣤⣿⣟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⡟⠙⠻⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⢿⣦⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⠿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⡿⠟⠁⠀⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠟⢋⣹⣿⣿⣿⣿⠏⠀⠀⠀⣠⣿⠟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣟⣩⣤⣶⡿⣿⡿⢿⣿⡟⠀⠀⠀⣰⣿⢃⣤⣤⣄⣾⠉⢻⡆⠀⠀⠀⣿⠃⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁⠀⣿⡇⣸⣿⠿⣶⣦⣼⡿⠁⠸⣇⣀⣹⡿⢶⣾⠟⠛⢷⠀⢿⣇⠀⠀⢀⣠⡾⠟⢷⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⠀⠀⢸⣿⠁⠀⠀⢈⣿⢿⣇⣰⣿⣶⣶⠿⠀⠈⣿⣆⣰⡿⠉⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠘⢿⣷⠀⣿⡏⠀⠀⠀⣿⣀⣠⣿⡏⠈⢻⡄⠀⠀⠀⠈⣿⡏⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠀⠀⢸⣿⣼⣿⠀⠀⠀⠀⠈⠙⠉⠀⠙⠛⠋⠀⠀⠀⠀⠀⢿⣧⣀⣀⡀⠀⢀⣼⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⣿⣤⣤⣤⣤⣤⣼⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⡟⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⢿⣿⠏⠉⠉⠉⠉⢹⣿⠟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⠿⠿⠿⣿⣦⣀⡀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠿⠿⠿⣿⣷⣶⣶⣶⣶⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀