⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠈⠉⠻⢶⣄⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣯⣥⣄⣀⣤⣄⣤⣽⣿⣶⣞⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⡿⠟⠛⣻⣟⣭⣿⠿⠿⠿⡿⠟⣟⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢨⣞⣿⡿⠉⠉⣳⡀⠻⣷⣿⣿⠀⠀⢠⠇⠀⣿⡼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠻⠿⢥⠤⠒⡟⠳⣀⠈⠛⠦⠴⠚⠁⠀⠀⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⡠⠤⠤⠼⠦⣤⡇⠀⠈⠳⣄⣀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣴⣞⣉⡀⠀⣀⣀⣀⣀⠀⠀⠠⠤⠤⠤⠉⠻⡆⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠉⠉⠉⠁⠀⠈⡟⠓⠲⠤⠤⠤⠤⠶⠚⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡴⢾⡋⠉⠀⠀⠀⠀⠀⠈⠉⠓⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⠋⠀⣀⡹⠶⡖⠊⠉⠉⠉⠉⠉⠉⠉⢉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⢀⡼⠋⠁
⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⢀⣀⡀⠽⢦⠤⣠⠔⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠦⣄⠀⠱⡄⠀⠀⠀⡼⠋⠁⠀⠀⠀⠀⠀
⠀⠀ ⠀⣠⣤⣴⣶⣤⠏⢀⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠳⣄⠘⣆⣤⢿⡶⠀⠀⠀⠀⠀⠀⠀
⠀ ⠀⢀⣝⣻⣿⢿⡟⢠⠏⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡖⠒⢂⣈⣿⡿⢿⣯⣤⣄⣀⠀⠀⠀⠀⠀
⠀⠀⠛⠛⠻⣿⠀⣩⠏⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹⡿⣿⡿⠳⢶⣤⣿⣝⠛⠚⠃⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣼⣰⠋⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣻⠎⠀⠀⠀⠈⢹⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀ ⠀⠀⠘⢿⠃⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡴⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀ ⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀ ⠀⠀⠀⠀⢿⠀⠀⠀⠀⣤⣤⠤⠤⠤⠤⠤⠤⠤⣤⣄⣀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀ ⠀⠀⠀⠀⠳⡀⠀⠸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡆⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀ ⠀⢀⣀⠤⠤⠒⠛⢦⣤⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢀⣴⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀ ⠀⠞⠯⣄⣀⠀⠀⢀⡠⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣉⠙⠋⠉⠉⠉⠓⠢⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀ ⠀⠀⠀⠈⡉⠓⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⣤⠤⠔⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀