⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⣼⣟⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⢠⠞⢩⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⣸⡿⢻⣷⣦⡙⢿⣦⠀⠀⠀⠀⠀⢿⡀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⢠⣿⣳⡿⠃⠹⣷⡄⢻⣷⠶⠶⠶⢶⣾⣷⣽⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣮⠏⠀⠀⠀⠀⠀⠀⠀⣼⡏⣸⣿⢀⣀⣸⣷⠘⣿⠀⠀⠀⠀⠀⠀⠉⠙⢻⣿⣶⣶⠾⠿⠟⣿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣱⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣤⣿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢁⣠⣴⣾⡿⠻⣿⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⢀⣾⠟⠋⠁⠀⠀⠀⣠⡆⠀⠀⢀⣤⠀⠀⠀⠀⠀⠿⠋⠀⣴⡿⠋⠁⢻⣧⠀⢹⣷⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⢠⣿⠃⠀⢰⡿⠃⠀⠀⢀⠀⠀⠀⠀⠀⢿⣦⣀⠘⢿⣯⠀⠀⣿⣧⡄⠀⠀
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡜⠁⠀⠀⠀⠀⠀⢀⣴⡿⠏⢀⣠⣴⣶⣦⣤⣶⠿⢿⣇⠀⣿⠇⠀⣠⣾⡿⠀⠀⠀⠀⠀⠀⠙⢿⣷⣿⡏⠀⢰⣿⠙⣿⡄⠀
⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⢀⡤⠽⠛⠁⠀⠀⠀⠀⠀⢀⣴⣿⣿⡾⠀⣾⡏⠁⠀⠀⠉⣿⣷⣜⢿⣆⣿⡀⣰⡿⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣧⣠⣿⠇⠀⢹⣷⠀
⠀⠀⢠⣬⣥⣤⣤⣤⣴⣏⣊⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⣿⠇⠀⢹⣧⡀⠀⢸⣿⡇⠈⠙⢿⡿⢿⣷⣿⣡⣼⣿⣤⣤⣀⣴⡶⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⢸⣿
⠀⢰⣿⠃⠙⠛⣿⣿⣯⣟⠿⢿⣿⣷⣶⣶⣤⣤⣄⣀⣀⠀⠀⠀⢠⣿⠀⠀⠀⠙⣿⣶⣿⣭⣀⣀⣀⣹⡟⢠⣿⠿⠉⠉⠉⠉⢩⣿⣿⡿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⢰⣿⠃⠀⠀⠀⠈⠙⣿⣿⣷⣦⡀⠀⠀⠀⠉⠉⠙⠛⠿⣿⣿⣶⣾⣿⣤⣄⣀⡀⣿⡆⣭⣿⣿⣿⡟⠛⠁⠘⢿⣦⡀⠀⠀⠀⢸⣿⣿⡇⠀⠙⢿⣶⠀⠀⠀⠀⠀⢰⣿⠃
⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⡀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣍⠉⠛⠛⠿⠿⢷⣿⣄⣀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣄⣸⣿⣿⠁⠀⠀⣠⣿⠃⠀⠀⠀⠀⣿⠇⠀⠀
⠸⣿⡄⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄⠀⠀⠀⠀⠈⠛⠛⢻⣿⠀⠀⢀⣴⡇⠀⠀⠈⠉⠛⣿⡿⠿⠿⠟⠛⠁⠀⣶⠀⠀⠀⣿⠀⠀⠀
⠀⠘⣿⣄⠀⠀⣀⣤⣿⣟⣠⣤⣤⣤⣴⣿⣿⣶⣶⣶⣶⠾⠿⠿⠿⣿⡿⠿⠿⠿⣿⣿⡿⠿⠿⢿⣿⣷⡶⠿⠋⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⢻⣿⡄⠀
⠀⠀⠈⠛⠿⠿⠟⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠿⠟⢻⡏⠀⠀⣀⠀⠀⠀⠀⣿⣄⠀⠀⢻⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⢠⣿⣆⠀⠀⠀⢿⣿⣦⡀⠛⢿⣇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⢀⣴⡿⠃⠻⣷⣄⠀⠘⣿⡝⠿⣷⣬⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⢉⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣵⣿⡋⠀⠀⠀⠈⠙⢷⣦⡘⣿⡄⠈⠉⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠉⣿⣿⠇⠀⠀⠀⠀⠀⠙⠻⣾⣿⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠙⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⣠⣴⣶⠾⠷⣶⣶⣴⡿⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣅⠀⠀⠀⠉⠛⠿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⠟⠉⠀⠀⠀⠀⠈⠙⣿⣆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⣄⡀⠀⠀⠀⠀⠉⠙⠛⠿⠿⢷⣶⣶⣶⣤⣤⣴⣶⣼⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠛⢿⣶⣦⣤⣤⣤⣤⣴⣿⠟⢿⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠈⠻⣿⣦⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣴⣶⡶⠿⠿⠛⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠛⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀