⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣠⠴⠿⢻⣿⣿⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣎⠁⡀⠀⣀⡀⣩⠔⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣏⡠⠀⠀⠀⠀⠘⢔⢠⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣬⣿⣿⣷⣿⠿⣿⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢧⣤⣶⢾⣤⢤⠀⢀⡈⠛⢢⠀⠀⠀⠀⠀⠀⢨⣷⣿⣿⣧⡤⠄⠀⠀⢀⣳⠀⠑⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣟⣃⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⡿⡾⣟⣋⣲⠁⠘⣿⣿⣴⡆⠀⠐⠀⠀⠀⠀⣿⣿⣿⣟⣀⣎⣁⣠⣼⣶⣿⠃⠀⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⡁⣿⣿⣿⣻⣿⣟⣛⣿⣿⣿⠱⠀⠀⠀⠀⠀⡇⣽⣻⣿⣟⠶⢶⣒⣿⣿⣿⠀⠀⠐⠀⠀⠀⠸⣿⣿⣿⣿⡛⢿⢟⣛⣿⣿⡟⠀⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠁⠀⠀⠀⠀⠀⠘⣾⡫⠿⣯⣿⠿⣿⡿⡿⣊⠀⢀⠂⠀⠀⠀⠀⢻⣿⣿⣿⣝⡿⣿⣿⡿⡟⢈⢰⡽⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣾⣏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣷⣯⣿⣴⣶⡞⢁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣥⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣦⡤⠶⠛⡳⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⣿⡗⠀⢸⠓⠢⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣇⣤⣄⣿⣷⣤⣨⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⣿⣿⣿⣏⠛⠛⠛⢻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⣷⣦⣤⣄⣀⠞⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⣿⣿⣷⣟⣶⡿⠿⠟⠁⠀⠀⡀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠈⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⠀⠀⣀⡀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠋⠙⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⣫⣽⣿⡿⠷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠉⣀⣀⣉⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⢀⣾⣟⠁⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⣀⣠⣿⠀⢸⣿⡉⠉⠉⠉⣷⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⣿⡇⠀⠸⣿⣿⣇⡀⠀⠀⠀⠐⠀⣼⣿⡆⠀⠀⠀⢸⣟⣩⣿⡄⠘⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣶⣦⣶⣠⠔⠁⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠙⢿⣿⣿⣷⣶⣷⣶⣾⡿⠁⣿⠀⠀⠀⢸⣿⣿⣿⣧⠀⠈⠉⠉⠉⠀⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⠾⡀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠈⠙⠛⠿⠟⠛⠋⠁⠀⢸⡇⠀⠀⠀⢸⣿⣿⣿⣿⣦⣀⣀⣀⣀⣼⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⢟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠈⢿⣿⡽⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
