⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⣀⣤⠰⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠗⠛⠇⠋⣰⣶⠈⠹⠿⠑⠿⢿⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠛⠈⠀⠀⠀⠀⠀⣼⣷⠀⠀⠀⠀⠀⠈⠈⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⢀⣤⢶⡟⠙⡆⣄⡀⠀⠀⠀⠀⠐⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠔⠛⡁⠐⠤⠉⢻⣧⣦⡿⠉⡠⠖⠊⠙⠂⠄⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⠠⠎⠀⠀⠈⠃⠀⣼⣾⣿⣷⡀⠐⠃⠀⠀⠘⠂⠁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠈⠍⠀⠁⣤⣾⣿⣿⣿⣿⣿⣦⡈⠁⠌⠉⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⣿⣶⣶⣶⣿⣿⣿⠿⣿⣿⣿⢿⣿⡙⢷⣶⣶⣿⣮⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣿⣿⣿⡿⣿⣟⣛⣛⣿⣻⣷⣎⡻⢷⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⠟⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⡟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣮⢻⣿⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡜⣏⣛⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢸⣜⣏⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣟⠿⢟⣩⣿⣿⣿⣿⣿⣯⣿⣿⡿⣽⣟⣻⣿⢻⣿⣽⣶⣽⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣛⡷⡿⢿⢾⣾⣵⣿⣿⣿⢾⣿⣿⡟⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡟⣼⣿⣿⣿⣿⡽⢿⡏⠵⠊⢻⡼⡉⡯⡽⣿⢿⣽⣷⣛⣿⣷⡜⣿⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢰⡿⣿⣿⣿⣽⣟⣿⠊⢐⣿⡾⠓⣰⣼⢿⢷⣟⣯⢿⣿⣿⠙⣷⠠⠑⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀
⡶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣹⠁⢿⣿⣿⣟⠏⣠⣾⣿⣿⣿⣿⣿⢿⣛⣶⣿⣿⣻⡟⡷⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠄⠀⠙⠛⠛⠾⠿⠿⠿⠿⠿⠯⠷⠾⠿⠿⠿⠋⠛⠋⠁⠀⣼⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢁⠀⠀⢴⣶⣶⢢⢶⠰⢰⠶⢶⠶⣰⣶⣶⣦⠀⠀⢠⠁⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠤⢶⣶⣶⣶⣶⣶⣴⣶⣶⡶⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⡀⠲⣶⣶⣶⣶⣶⣿⣷⣶⡶⠶⠒⠒
⣛⣛⣙⣩⣭⣿⣿⣯⣭⣿⣷⠆⢠⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⡤⠈⣽⣿⣿⣿⣿⣯⣭⣭⣻⣛⣛