⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⣿⣿⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠷⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⠏⠀⠀⠀⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⠀⠀⣰⢛⣥⣤⣤⣀⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⢀⣤⠶⠚⠛⠉⠉⠉⠛⠛⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣤⣀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣤⣟⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣄⣀⡈⢛⣿⣿⡿⠋⡠⣴⣿⠋⠉⠙⠻⣷⡌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣹⣿⣿⡿⢿⣿⣿⡿⠛⠛⠛⠿⣿⣿⣿⣷⣦⣾⠿⢧⡀⠀⡀⠀⠀⠀
⠀⠉⠻⠿⢿⣿⣿⢣⠎⢠⣿⠁⠀⠀⠀⢀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⠝⣳⣿⡿⠃⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣶⣶⡷⣞⠁⠀⠀⠀
⠀⠀⠀⠀⠈⣿⡏⡆⠀⢸⡇⠀⠀⠀⢀⣾⠋⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠃⠀⣿⣿⠃⠀⠀⠀⠀⠀⢀⣼⠟⠻⣿⣿⢿⣿⣿⣶⣤⣀⣀⠀⠀
⠀⠀⠀⠀⠀⠘⣿⡅⠀⢸⣷⡀⢀⣴⣿⠟⠛⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢀⣤⣿⣿⣶⣾⣿⣿⠈⢻⣿⡿⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠘⢧⠀⠘⣿⣿⣿⣿⠃⠀⠀⣼⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⣤⣤⣶⣿⡟⠁⠀⠀⣿⢿⡟⠀⠸⣿⣷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠹⠁⠙⣿⣷⣤⡾⡟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠙⢻⣿⡿⢿⠀⠀⢀⣴⠻⣾⠇⠀⢸⠏⠹⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡴⠶⢾⣅⣠⣥⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⣸⣿⠤⠈⣶⣖⣹⣿⡾⠃⢀⠰⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣷⣿⣤⣌⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣾⡷⠞⢛⠻⣿⠿⢒⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣷⣷⣮⣭⣭⠿⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⠋⠉⠘⠁⠀⠀⠀