⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀
⠉⣿⠉⠁⠀⠀⢠⣴⣶⡄⣿⢰⣆⣶⢰⣆⣴⣶⣦⣶⡀⣴⣦⣶⣶⠀⠀⠀⣠⣶⣦⢠⣶⣦⣰⣶⣶⣶⣦⢠⣶⣶⡄⠀⠀⢸⣷⢶⣄⢠⣴⣶⣄⣴⢶⡄⣿⣠⡶
⣤⣿⣦⡄⠀⠀⢻⣧⣿⡇⣿⠸⣿⢻⣿⠹⣯⣼⣧⠘⣿⠟⢸⣽⣷⠄⠀⠀⢿⣤⣤⢿⣧⣾⢻⡏⢸⡇⣿⡻⣿⣯⡇⠀⠀⢸⣧⣴⡿⢿⣤⣿⡼⣧⣤⡤⣿⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠁⠀⠀⠀⠉⠰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⣤⣤⣤⣤⣤⣤⣤⣄⣤⠀⠀⠀⠀⠀⣠⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⢸⣏⠉⠉⠙⠻⢷⣤⣄⡀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠈⣿⡄⠀⠀⠀⠀⠈⠉⠻⣷⣄⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣆⠀⢘⣿⡄⠀⠀⠀⠀⠀⠀⠈⠻⣷⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡿⠟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⣷⣤⣤⣤⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠶⠶⣷⣶⣶⣶⣶⡶⠿⠇⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠈⠉⣿⣿⣿⣿⣿⠋⠈⠉⠉⢻⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⢹⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣤⡿⠏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣄⣀⣀⣀⠹⣷⣄⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠠⣶⡿⠿⠿⠿⢶⣶⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⣏⠉⠛⠛⠛⠿⠀⡀⣸⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠁⢿⣿⣿⣿⣿⣿⣷⣄⣀⣼⠇⠀⠀⣀⡀⠀⠀⠀⠀⠀⠘⠷⠶⠿⠿⠿⠿⠿⠿⣿⡏⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠆⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣤⣾⠟⠛⠛⠻⠷⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣤⣴⡶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠿⠷⠶⠶⠶⠾⠟⠛⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛?