⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣧⣴⡀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣼⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⠿⠿⣿⣿⣿⣷⣶⣶⣿⣶⣿⣾⣿⣿⡿⠿⠿⠿⠿⣿⣿⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣼⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⠈⠙⠿⠿⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⢹⣿⣿⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠿⠿⢿⣿⣷⠂⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠏⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣷⡀⠀⢠⣶⣆⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣾⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⢸⣿⡯⠅⠀⠀⠀⢀⣴⣿⣿⣿⡿⠆⠘⢿⢿⠋⠀⣀⣨⣿⣿⣿⣦⣀⡀⠀⠉⠉⠁⠀⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⢿⣿⣿⣿⡀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⠀⠀⠀⢠⣼⣿⡇⠀⠀⠀⠀⢸⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⠀⠀⠀⠀
⠀⠀⠀⢀⣠⣤⣤⣴⣶⣶⣾⣿⣿⣿⠀⠀⠀⠈⢹⣿⣷⣀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣶⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⠀⠀⠀
⠀⠀⣴⣾⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠉⣿⣿⣿⠀⢀⣰⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀
⢀⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄⠀⠀
⣿⣿⣿⠋⠀⢰⣿⣿⣧⣼⣧⣤⣴⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀
⣿⣿⣿⠀⠀⠈⠿⢿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀
⢿⣿⣿⣷⣶⣀⡀⠀⠀⠀⢉⣻⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀
⢀⣿⣿⣿⡿⣿⣿⣿⣶⣶⣾⣿⣿⣯⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀
⢸⣿⣿⣧⡄⠉⠛⠛⠻⠿⠿⢻⣿⣿⡇⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⢠⣴⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣇⠀
⢸⣿⣿⣿⣿⣷⣶⣤⣤⣤⣴⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⡟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇
⢸⣿⣿⣏⡋⠻⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣤⣶⣿⣿⣿⡿⠟⠋⠀⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁
⠈⢿⣿⣿⣷⣦⣤⣤⣤⣤⣤⣿⣿⣿⡀⠀⠀⠀⠀⢸⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣤⣴⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠹⢿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣾⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠉⠟⠛⠛⠛⠛⠏⠉⠙⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀