⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣦⣤⡀⢰⣿⣿⢿⣧⠀⣠⣶⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣦⢻⣿⣿⣏⣾⣟⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠶⠷⢶⣤⡀⠀⠀⠀⠀⣠⡶⠛⠒⠒⠤⠀⢈⣛⣻⠾⣇⡙⢟⢸⣿⢿⣯⣥⣀⠀⠀⠔⠒⠓⢶⣦⠀⠀⠀⠀⠀⣠⡴⠾⠶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣠⣤⣤⣀⠀⢠⣿⠃⠀⣤⡀⠈⠻⣦⡀⠀⢰⡟⠀⠀⣀⠀⠀⣴⣿⣿⣿⣯⣖⡱⠟⡋⢮⣽⣿⣿⣿⣷⡄⠀⢀⡀⠀⢹⣧⠀⠀⣠⡾⠋⢀⣠⡄⠀⢿⣇⠀⢀⣠⣤⣤⣀⠀⠀
⣰⡿⠋⠉⠉⠙⣇⠀⢻⣧⣀⣸⡟⠀⠀⠈⠻⣦⡈⣷⡀⣾⠁⠀⠘⠛⠻⢿⡿⠿⢫⢸⣷⣝⣷⣌⠙⠛⠛⠉⠙⠀⠀⢹⡄⣸⠇⣠⡾⠋⠀⠀⠸⣯⣀⣠⡿⠃⢠⡟⠉⠈⠉⠻⣷⠀
⢹⡇⠀⢸⣀⣸⠇⠀⠀⠈⠉⢉⣀⣰⣶⣶⣆⣸⣿⣾⣿⣿⡆⠀⠀⠰⣀⡀⠀⠀⣿⠸⣿⣿⣿⣿⠀⠀⣀⣀⠆⠀⢀⣾⣿⣿⣾⣿⣰⣶⣶⣆⣀⣈⠉⠉⠀⠀⠈⢷⣆⣾⠀⠀⣿⠆
⠘⢿⣤⣀⠀⠀⢀⣀⣤⣶⢿⣿⠟⠉⠀⠀⠀⠀⠉⠉⠛⠿⢿⣦⣀⠀⠈⢿⣷⣄⢹⡄⠈⠻⣿⠋⣴⣾⡟⠁⢀⣤⣾⡿⠟⠋⠉⠁⠀⠀⠀⠈⠙⢿⡟⠷⣦⣄⣀⠀⠀⢀⣠⣼⠏⠀
⠀⠀⠈⠙⠛⠛⠛⠉⠁⠀⣾⡇⠀⢠⠶⣦⡄⠀⠀⣀⣤⣴⣶⣬⣿⣷⣦⣈⠻⣿⣇⢻⡄⠀⠁⣼⡿⣋⣤⣶⣿⣯⡵⢶⣤⣄⠀⠀⠀⣴⡶⢦⠀⠈⣿⡄⠀⠉⠛⠛⠛⠛⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⣸⡇⠀⢠⡟⠁⣀⡀⠀⠀⠈⠉⠛⠳⢦⡙⠶⢷⠀⣜⣡⡾⠛⠉⠁⠀⠀⢀⣀⠀⠹⣧⠀⠘⣿⡀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠿⣄⣨⡿⠀⠀⢠⠶⠛⠛⠻⢿⣆⢸⣠⣿⠿⠛⠛⠳⣄⠀⠀⠸⣯⣠⡼⠃⠀⠀⠈⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢹⣾⠟⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀