⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⡆⠀⠀⠀⠀⢀⠈⠉⠲⡄⢀⡼⠁⠀⠀⠀⠀⣾⣆⠀⠀⠀⠀⣀⣤⠤⠒⠒⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠑⠒⠢⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠓⠀⠀⠀⠀⢀⡀⠁⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢀⣿⣟⣄⡠⠖⠻⠷⠦⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⠀⠀⣀⡰⠋⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⢸⠿⠋⢁⣀⣀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀
⠉⠀⡰⣛⡓⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣠⡮⠖⠋⠉⠉⠉⠉⠓⠲⠤⣀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠉⠉⠉⠐⠒⣩⣤⣤⣤⣤⠶
⠒⠊⣸⠟⠁⡄⠀⠀⠀⠀⠀⠀⢀⡜⠀⢠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⡀⠀⠀⠀⠈⠲⣄⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀
⠉⠉⠉⠑⢾⣇⠀⠀⠀⠀⠀⠀⡟⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠈⢦⣰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⢠⣿⣿⣿⣿⠃⠀
⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⢀⣠⣶⣾⠏⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⢀⣾⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢣⢀⡴⠋⡰⢟⠏⠀⠀⣰⠃⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢠⣾⡿⢋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⣿⣿⣿⣍⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢏⠀⡼⢃⡞⠀⠀⢰⠇⠀⠀⡼⠃⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣘⣙⠛⠋⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣗⣾⠋⢻⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⠣⣸⠀⠀⢠⠏⠀⠀⢰⠇⠀⠀⡀⠀⢠⠃⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠈⠉⠉⢳⣠⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣼⣛⢿⣷⢸⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢶⡇⠀⠀⡿⠀⡴⢀⡏⠀⠀⢠⠃⠀⡞⠀⠀⠀⡠⢰⡇⠀⠀⠀⣼⠁⠀⠀⠀⠀⢷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠉⠉⢸⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⣸⠃⠀⢸⠁⢠⡇⢸⠇⠀⠀⡟⠀⢰⠃⠀⠀⢰⢳⡿⠀⠀⠀⢰⠇⢠⡇⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⠃⠀⠀⠀⠘⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠐⡇⣧⣿⠀⠀⣿⠀⡼⢤⣸⡄⠀⢸⠁⠀⡿⠀⠀⢠⢧⡿⠁⠀⠀⢀⡏⡼⡜⠀⢠⡆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣬⣄⠀⠀⠀⠀⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢿⡀⠀⣿⢦⣧⡀⡝⡇⠀⣼⠀⢰⠃⠀⠀⣞⣮⠇⠀⠀⠀⡞⣸⣱⠁⢀⣾⡀⠀⠀⠀⢠⠏⠀⠀⠀⡰⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡄⠀⠀⠀⢇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠸⣷⠀⣿⡌⡏⣿⣧⡇⢸⢿⠀⢸⣴⡀⢰⣽⡟⠀⠀⠀⡼⣱⢇⡏⠀⢸⢻⠁⠀⠀⢀⡎⠀⠀⢀⡼⠃⠀⠀⠀⡀⢀⣿⣯⣝⡛⣿⣇⠀⠀⠀⢸⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⢸⣦⣿⠃⢷⣿⢹⣿⡿⢀⠀⡾⠀⢈⣿⡟⠳⠤⢄⣼⣱⡿⡞⡇⠀⡏⡇⠀⠀⠀⡼⠁⠀⡄⣸⠃⠀⠀⠀⣼⠀⠈⣿⢿⡟⠛⠿⣾⣯⣗⡦⣌⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⢸⠏⢽⠀⠈⠛⠶⠟⠇⠸⡶⡇⠀⢸⣟⣤⠀⠀⡰⡹⢻⠕⢠⡇⣸⣻⠀⠀⠀⡸⠁⠀⣾⣤⡏⠀⠀⠀⢸⠃⠀⣶⣿⣾⡇⠀⠀⠀⠀⠀⠙⠳⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠘⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠉⠉⠙⠛⣿⣧⣁⡊⠀⠸⣷⢷⠇⠀⠀⣴⠃⠀⣼⣿⣿⠧⠀⠀⢰⡇⠀⠀⣿⣽⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣴⣇⠸⠋⣹⡗⠲⣿⡎⠀⠀⡰⠁⠀⣼⠛⢳⣿⠃⠀⠀⣾⠆⠀⣧⣿⣟⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⣠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⣸⣾⠁⠀⡼⠁⠀⡼⠁⠀⣾⠇⠀⠀⣸⠏⠀⢀⣿�