⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠴⠶⠾⠷⠶⠶⠤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⢀⣤⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣯⡴⠀⠀⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠈⠀⠀⠀⠉⠛⢷⣦⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣿⠋⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡙⢿⣄⠀⠀⠀⠀⠀
⠀⠀⠀⢠⡿⠁⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠒⠀⠀⠀⠀
⠀⠀⠀⣾⠃⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀
⠀⠀⣼⠇⠀⠀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀
⠀⣸⡏⠀⠀⣰⣿⠇⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀
⢠⡿⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⣿⣉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⢶⣶⣦⣄⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀
⣸⡇⣠⠀⠀⣿⡏⠀⠀⠀⠿⣽⣿⣿⡟⡤⠔⠒⠒⠒⠒⠲⢤⣄⡀⠀⢺⣧⣴⣿⣿⣿⡆⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⢻⣿⣿⠀⠀⣿⣧⠀⠀⠀⠀⢈⡽⠋⠀⠀⢀⣴⣶⣦⣤⠀⠀⠀⠉⠲⣼⣿⣿⣿⣿⣿⠃⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣼⡇⠀⠀
⠀⠀⣿⣀⠀⣿⣿⡀⠀⠀⡰⠋⠀⠀⠀⠀⠘⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⠳⡍⠉⠁⠀⠀⠀⠀⡟⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⠇⠀⠀
⠀⠀⠹⢿⣇⠸⣿⣷⡀⠀⡇⠀⠀⠀⠠⣤⣀⣠⣿⣅⣀⠀⣀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⣠⣼⡏⠀⠀⠀⠀
⠀⠀⠀⠈⠛⠷⠶⠿⠿⣶⣝⣂⠀⠀⠀⠈⠉⠁⠀⠉⠛⠛⠋⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⢻⣈⣿⣦⠀⠀⢀⣀⣰⣿⡿⠁⢀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠁⠀⠀⠀⣀⣤⣴⣾⠟⢛⣻⣿⣶⣾⣷⠟⠋⠀⠀⢸⠿⣦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢫⡉⠙⠛⠿⠷⠶⢶⣶⣶⣤⣴⣶⣾⣶⡶⠶⠿⠛⠛⣉⣡⠶⠛⠉⠁⠀⠀⠈⠻⣦⡀⠀⣰⡿⠀⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⢷⡿⠋⠀⠀⠀⠀⠈⠑⠒⠦⢤⡄⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡾⠋⠀⢠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢡⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷⠀⠀⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣴⠟⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠐⠆⣿⡀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⣿⠋⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢙⢿⣄⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⣴⡟⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠈⠙⣿⢿⣶⣤⣀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⡇⢠⡄⠀⢻⣄⢸⣿⠉⢛⣿⢃⡀⢀⠀⠀⠀⠀⠀⢀⣿⣿⡿⢀⡀⠀⣀⠀⢤⠾⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⣄⣸⣀⣀⣨⣿⣾⡇⠀⢾⡇⣿⠀⣿⠀⠀⠀⠀⠀⣼⣿⣿⣧⣸⣀⣀⣿⣠⣼⣴⠟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠛⠛⠓⠻⠷⠶⠞⠛⠛⠋⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀