⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⡶⢶⣤⣀⠀⣸⣇⠉⠉⠉⢉⣿⡀⠀⣀⣴⠶⣶⠀⠀⠀⠀⠀
⠀⠀⠀⣿⢻⡷⠀⡈⠻⣿⣟⣁⣀⣀⣀⣀⣌⣿⡿⠏⡈⠹⣟⣻⡇⠀⠀⠀
⠀⠀⠀⢻⡿⣇⣀⡘⢤⡟⢻⠛⡟⣛⣛⡇⢻⢛⡿⠣⣄⣠⡿⣿⠃⠀⠀⠀
⠀⠀⠀⠈⠳⣾⣯⣀⡠⣿⢹⠀⣧⣾⢬⡇⢼⢸⡷⣤⣹⣿⡶⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠻⣿⣧⣿⣼⣤⣷⡾⣶⣧⣾⡼⣧⣿⡿⠛⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣾⡇⢀⡴⠋⢰⠄⠉⠈⠻⡄⠲⣿⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣴⡿⠃⠀⠁⠀⠀⠁⠀⠀⠀⠀⠙⠆⠙⢿⣷⣄⠀⠀⠀⠀⠀
⠀⠀⣠⣴⣿⡟⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡷⣄⡀⠀⠀
⠀⣰⣿⣵⠋⠀⣰⡎⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠐⣦⠀⠀⠈⢳⣽⣷⡀⠀
⠺⣿⣿⣿⣇⣰⠧⠀⠀⠀⠀⠀⢯⡇⠀⢠⡄⠀⠀⠈⣟⣦⣠⣶⣷⣼⣿⠆
⠀⠹⢿⣿⢷⡿⣿⢧⡄⠀⣰⣾⣽⠇⢀⣼⣷⡀⠀⣴⣿⡿⣿⢿⣿⠿⠀⠀
⠀⠀⠀⠀⢸⡟⠿⠟⠛⢾⡿⣿⣹⣿⣿⣟⣯⣿⠾⠛⠿⠟⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠻⢦⣾⣇⠀⣤⣭⢩⣿⣏⢩⣭⡄⢐⣿⣷⡿⠟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣾⢁⣿⠛⢯⡉⠻⣿⡿⠉⢩⠟⢻⣏⠙⣦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⠋⠻⠶⠾⠏⠛⢻⡟⠙⠻⠶⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣻⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠻⠿⠿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⡿⠀⠀⠀⠸⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⠁⠀⠀⠀⠀⠉⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠐⠀⠐⠐⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡀⠃⢀⣁⣤⣤⣤⣀⠀⠀⣤⣾⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⢿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣟⠿⠿⠃⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠄⠀⠀⠀⠀⢠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠁⢸⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡀⠒⠠⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⢸⣿⣿⠻⡙⠛⠿⣿⡏⣿⣿⣿⣿⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⡘⣿⣿⠄⠀⠀⢀⠈⠀⠻⣿⣿⡿⢾⣿⣿⣟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠀⡀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⢷⢿⣿⠷⣀⠀⠿⠏⢀⠎⣿⣿⠀⣿⣿⡿⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣀⣼⣿⡧⠞⠈⢿⣇⠈⢱⣶⣴⢿⢠⣿⠋⢐⣿⣿⣤⣰⢆⠀⡀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠓⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⣻⣿⣿⠟⠑⠀⢀⡈⠿⠦⠯⢥⣧⣬⡟⠥⣀⡂⠈⠻⣿⣧⣬⡵⢃⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠙⠛⢛⡯⠡⠄⠤⣾⣷⣄⠀⠀⠀⢸⣤⣇⠀⠀⠀⢸⣿⠀⠉⠉⠱⠀⠈⠑⢄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀
⠀⠀⠀⠀⠀⠀⠢⠀⣀⠠⠀⠀⠀⠀⠀⢰⠃⠈⠡⢄⠀⠀⠈⢿⣿⣄⠀⠀⣼⣿⣿⡆⠀⠈⣼⡇⡀⢀⡢⠁⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⢢⠤⡀⠀⠻⣿⣦⣼⣿⣿⢿⣿⣄⣴⣿⣅⠩⢧⡀⡁⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡎⠈⢨⠒⣾⣿⣿⣿⣾⣯⣿⣯⣿⣿⣿⡖⠀⠀⡇⢠⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⡸⠁⣈⡞⠠⢿⣿⣛⣿⣿⣿⣿⣿⣿⡟⣻⡷⡂⠀⢸⡄⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⣰⠇⣀⡞⠀⡜⠘⣿⡻⣿⣿⣿⣿⣿⣿⡿⢿⡇⠹⣆⠀⢣⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠋⠀⡿⠀⠀⡇⠀⢻⣙⣽⣿⣿⣿⣻⣿⣑⣽⠁⢠⣧⢀⠈⢧⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀