⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡹⠾⠿⠟⠉⢁⣀⡀⢄⠀⠀⠉⠙⠢⢈⠻⣻⣿⣿⣿⣷⣿⣿⣿⣷⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⢐⣾⣲⣭⠐⠂⠀⢲⣝⠛⢆⡀⠀⠀⡀⠀⠀⠑⣌⡻⣿⣿⣿⣿⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⣴⣿⠟⠓⠀⠀⢰⡾⣫⠛⠀⠀⠀⠀⢤⡈⠀⠎⠐⢸⣿⣯⣻⣿⣿⣷⣿⣿⣿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣱⣿⠷⠂⠀⢠⣴⡏⢛⠀⠁⠀⠀⠀⠀⠀⠹⢦⣈⡢⢑⠽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣕⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡿⠁⠀⡠⣘⣿⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠹⣮⡶⣝⣂⡱⢝⣿⣿⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡔⠀⣨⣾⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⡈⠛⠢⢕⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢰⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠙⠛⢿⣿⣻⠿⣿⡞⠿⣿⣿⣦⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⡀⠀⠀⠐⠒⠀⠈⢉⡉⠉⠉⠉⠉⠉⠂⢻⣄⠀⢹⣿⣷⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠢⠀⠀⠸⣦⣤⣄⣢⣀⣀⠀⠀⠉⠐⠂⠬⢣⣖⢠⠃⠐⠀⠘⢿⣯⢆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢻⣿⡌⠉⠉⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⠏⢳⠀⠀⢠⢟⠘⡟⠀⠀⠀⢰⡘⡿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣄⢻⣿⣦⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠘⠖⠀⢸⣼⣿⠀⠀⠀⣰⣣⣿⠑⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣧⣬⣿⣿⣿⡿⠀⠀⠀⠀⣶⣤⣤⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢇⠀⠀⠀⠀⣸⣿⣿⡄⠀⢀⣿⣿⣿⠮⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⢹⣻⣿⣿⣿⡿⠀⠀⠀⠀⢻⣿⠿⠀⠀⠀⢸⢹⣿⣿⣿⣿⣿⡏⠀⠀⠘⣤⢿⣿⣿⢯⣢⣼⣿⣿⡇⢄⠢⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣟⣀⠀⠀⠀⠀⠀⣿⡟⠀⠀⢠⠏⠀⠨⢿⣿⣿⠟⠀⠀⠀⠀⠀⠙⢿⣿⣷⣯⣿⣿⣿⣿⣿⣷⣧⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢴⣿⣿⣿⢻⣿⣿⣤⠀⠀⠀⠀⠈⠁⠀⡤⠊⠀⠀⠀⠘⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⢈⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣋⡽⠿⠋⠀⠀⠻⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣱⣿⡯⣿⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠂⠠⠀⠀⢀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⡿⡏⣓⢃⠾⠛⡹⠿⠟⠿⢻⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢹⣷⢛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡟⣿⡿⣼⣿⣷⣶⣶⣄⠀⢰⠃⢠⡄⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀