⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣀⡀⠀⣀⣤⣄⣠⣴⣿⣿⣿⣿⣿⣄⣠⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣶⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣭⣀⣼⣿⣿⠿⠿⠛⠋⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠉⠛⠳⠦⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣶⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⣶⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀
⡇⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣸⠇⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠃
⠀⠀⠀⠀⠀⢠⡟⢀⠙⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣽⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀
⠀⠀⠀⠀⢀⣾⠁⠈⡴⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⣼⠃⠀⡿⠁⠀⠀⠀⢰⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⣸⠏⠀⣸⠁⠀⠀⠀⠀⢸⠀⠀⠀⡴⠋⡼⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠻⡄⢀⠀⠀⢠⠀⡇⠀⠀⠈⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⣰⡏⠀⢰⠃⢀⡄⠀⠀⠀⢸⠀⢀⡜⠉⠲⣇⡰⢲⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢀⡤⠿⡅⠀⠀⣸⡀⢿⠀⠀⠀⠀⠉⠁⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣴⠏⣀⠀⣯⡖⠉⡇⠀⠀⠀⢸⢀⡞⠀⠀⠀⠟⠳⣌⢧⢸⠀⠀⠀⠀⠀⠀⠀⣼⣡⣾⣋⣤⣀⣱⡀⠀⡟⠹⣼⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⡾⢋⣴⠏⠈⠁⡇⠀⢹⡄⠀⠀⠘⣾⠀⠀⠀⠀⠀⠀⠘⠯⢻⡀⠀⠀⠀⠀⢠⠾⢿⡿⠿⠛⠛⠛⠿⢧⣸⠁⠀⣿⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡵⢏⡟⠀⠀⠀⡇⢠⠇⠈⠂⠀⠀⡇⠀⣶⣵⣄⠀⠀⠀⠀⠀⠙⠦⣀⢀⡴⠃⠐⠋⠀⠀⣀⣤⣀⡀⠈⠛⢷⣄⢸⠀⠀⠀⠀⠀⢸⡟⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣾⠃⠀⠀⠀⣧⠏⠀⠀⠀⠀⢸⡇⠀⠀⠙⣿⣧⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣦⡀⠀⠹⣼⠀⠀⠀⠀⠀⢸⣷⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⡟⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢻⠀⠀⠀⠀⠀⢸⡀⠘⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣯⣤⠀⠀⢸⠀⠀⠀⠀⠀⢸⠙⡄⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⣸⠃⠀⠀⠀⠀⢀⡼⠁⠀⠀⠤⠒⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⡇⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⣠⡿⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠟⠋⠀⠀⠀⢸⠀⠀⠀⣰⠚⢹⡤⠃⣰⡇⠀⣼⣆⠀⠀⠀⠀⠀
⠘⣇⡾⢻⡇⢀⣶⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢠⠇⠀⢸⣤⡾⢻⡇⠀⣿⣿⡆⠀⠀⠀⠀
⠀⠛⠃⣾⠁⣸⢿⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠔⠒⣶⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⣼⠀⠀⡟⠈⣷⢸⡇⢰⣿⣿⣿⡄⠀⠀⠀
⠀⠀⠀⢿⣠⡿⢸⡇⠀⠈⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠞⠁⠀⠀⠀⡠⠃⠀⠀⠀⢀⣤⣾⢿⡇⠀⠀⡇⠀⠀⢧⣼⠃⢸⣧⣿⣿⣿⣿⣷⠀⠀⠀
⠀⠀⠀⢸⣿⡇⠈⢿⡀⠀⢸⡇⠉⠳⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠻⠿⣏⣀⣠⠤⠖⠋⠀⢀⣠⣴⢾⠟⠋⠀⣼⣁⡤⠤⠧⢄⠀⢸⠻⣧⣸⡿⠁⠿⢿⠀⣠⣴⡀⠀
⠀⠀⠀⠀⢻⡇⠀⠈⢿⣄⠈⣷⠀⠀⠀⠀⠉⢉⣿⠷⠲⡦⣤⣤⣤⣄⣀⣠⣤⣤⣤⣶⠾⠟⠋⠁⢸⠀⢠⡟⠉⠁⠀⠀⠀⠀⠀⠀⡇⠈⠻⠀⣠⣦⡀⠀⢸⣿⣇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⡆⣠⣤⡶⠞⠋⠁⠀⠀⡇⣾⠈⠉⠉⠉⣿⣯⣻⡉⠀⠀⠀⠀⠀⣿⠀⢘⡧⠤⠒⠂⠁⠀⠀⠀⠀⠸⡀⠀⠀⢹⣿⣿⣦⡀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⢠⡇⡟⠀⠀⠀⣼⣿⣧⡤⡇⠀⠀⠀⠀⠀⡏⠀⢹⡀⠀⡠⠄⠂⠀⠀⠀⠀⠀⢣⠀⠀⠀⢿⣿⡿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⢸⠠⠇⠀⠀⠀⠙⣝⣋⡡⠇⠀⠀⠀⠀⢰⠇⠀⠀⢳⡉⠀⠀⢀⡀⠀⠀⠀⠀⠈⡆⠀⠀⠘⣿⣧⠈⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠔⠉⠉⢆⠁⠀⠀⠉⠒⡄⠀⡸⠒⠉⢲⡀⣳⡀⠈⢯⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢹⣿⣆⠀⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠋⠉⣿⠀⠀⠀⠀⠀⠀⠀⣼⠦⢄⡉⠀⠀⠀⢸⠆⠀⠀⠀⠀⠸⡼⠀⠀⠀⠀⣧⢻⠙⠒⠚⣦⣀⣀⣀⣀⣠⣿⣄⠀⢠⡀⠹⠿⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠄⠹⣧⡀⠀⠀⠀⠀⠀⡇⡄⠀⠈⡇⠒⠢⠤⠤⠀⢀⣀⣀⣀⣁⣀⣀⣀⣀⣈⣸⠀⠀⢰⠛⠻⢿⠿⠟⠋⠁⠈⢲⡟⠁⠀⠐⢶⡀⠀