⡆⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠲⠿⣿⣯⣭⣍⠉⠉⠉⠉⠉⠁⢲⣦⢮⡐⠊⠉⢱⣮⠀⠈⠃⢔⣢⣼⣿⣷⡦⠾⠦⠲⣶⣶⣉⣶⣶⣶⣶
⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣤⣤⣍⣙⠻⢿⣿⣦⣄⡀⠀⠘⣿⡻⣿⣿⡟⠛⠙⠀⢀⣴⣿⡿⠟⠉⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠀⠀⠀⠀⠈⠑⠨⡙⠿⣿⣶⣄⣿⣷⣿⠀⣮⠀⡀⢰⣿⡿⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⢿⣿⣿⣿⣿⣿
⡇⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣬⡻⢿⣿⣿⠃⣀⡼⠷⡽⣿⡟⠀⢀⡀⠀⢠⣥⣴⣶⣶⣦⣄⣿⣿⣿⣿⣿⣿
⡇⠀⣰⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣽⣿⣜⢿⡇⠀⢰⡟⢀⠖⠁⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⣰⡿⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢻⣷⣕⢠⡿⠑⠁⠀⠀⠀⠀⢀⣀⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⢱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⡠⠁⠀⢀⣤⣶⣿⣿⣿⣿⣿⣶⣍⠻⣿⢃⣶⣿⣿⣷⣄⠀⠈⠙⠿⣗⡀⠙⢿⣿⣿⣿⣿⣿⣿
⢻⡧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠃⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⡿⠟⠃⠀⠀⠀⠈⠻⣷⢄⠙⢿⣿⣿⣿⣿
⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡑⠄⠉⠻⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣽⣿⣿⣿⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⡀⠀⠉
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠓⠐⠒⣸⣄⣠⠀⣼⣿⣿⣿⣿⣴⡇⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣷⣶⣶⣦⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠿⠿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣉⡀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠑⠦⣤⣑⠄⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣴⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂
⡡⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠟⠉⠀⠉⠀⠀⠙⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠈⠙⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠛⠁⠀⠀⢤⣬⣤⠀⠀⣈⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠉⠑⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⣦⠀⠈⠉⠈⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⣶⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶
⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⢆⣠⣴⣾⠿⠟⠛⢛⣿⣿
⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⡠⣶⡿⣫⠾⠛⠉⢁⣀⣤⣴⣶⣿⣿⠿
