⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠉⠀⠀⠀⠀⠉⠙⠛⢿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣀⣤⣶⣿⣿⣿⣿⠓⣀⡤⠀⠀⠀⠈⠛⣿⣦⣴⠶⠛⠛⠛⠒⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣥⣉⠉⠉⠩⣟⣿⠛⠈⢴⣽⣿⣿⣾⣽⣿⣦⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣶⡄⠈⣿⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢡⠭⠛⢟⣤⣤⣿⣯⠀⠀⢀⣤⣭⣙⡛⢿⣝⡙⢛⣢⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣴⠉⠹⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣽⣾⣿⣿⠂⠀⠀⠙⢿⡟⣡⡥⣉⣉⠛⣿⠈⣭⣬⣤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⢰⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣼⣿⣿⣿⣿⢀⣀⣀⠀⠀⡿⣦⢻⣾⣼⣷⣿⣀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⢻⣿⣿⣧⢠⣀⣐⣾⣿⣶⣿⣿⠸⢈⣶⣶⣤⣤⣤⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣿⣿⣿⣛⣭⣤⣀⠀⠻⣿⣆⣿⣿⣾⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣿⣿⣿⣿⢋⠀⠉⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢶⣶⠛⠛⢤⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠋⣀⣠⡤⠀⠀⠀⠀⠀⠀⠈⠀⠀⣾⣿⠛⣶⣄⣀⠀⢀⣶⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣰⢰⣿⣿⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣝⠉⠁⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠉⠀⠀⠀⠀⠀⠀⠠⣤⣤⣴⡝⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣠⣤⣤⣤⣴⣴⣤⣀⠀⠀⠀⠀⠀⠀⣠⣶⠾⢛⣛⣛⣭⣭⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣫⣽⣶⣿⣿⣿⣿⣿⣷⣦⣝⢻⣶⣤⣶⢛⣵⣾⣿⣿⣿⣿⣿⣿⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠻⣿⣦⠩⣴⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⣛⢫⣭⢠⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠈⣨⣛⠛⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠈⢻⣬⠻⠿⠛⠁⠀⠀⠀⠀⠀⢸⠉⠀⣨⡛⡟⡈⣤⣀⣠⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣶⣙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⡀⠀⠀⠀⠀⠀⠀⣴⠀⢸⣟⣾⢸⣶⣿⣿⣿⣿⠉⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣷⣙⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣰⣀⠀⠀⠀⢰⠁⠀⢸⡟⡜⣆⢻⣌⢿⣿⠁⣠⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣭⠻⠿⠿⣛⣛⣛⣛⠿⣶⣶
⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣸⣀⢰⢠⡔⠀⢸⣬⣣⣜⣷⣝⣄⢀⣾⡿⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣴⣤⣄⣀⠀⠈⢛⢈⢸⡀⠀⢠⣿⣤⢿⣷