⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣤⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠛⠛⢻⡇⠀⠀⡤⣤⣄⠀⢰⡆⠀⢰⡄⢰⠶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⡇⠀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣷⠋⢨⢿⠀⣿⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢶⣹⡇⠀⢠⡾⠟⠒⣶⡆⢠⡖⠋⠹⣇⠀⣾⠛⢻⡇⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⢿⣦⡤⠼⣿⠀⠈⠳⠞⠋⠀⠸⠷⠶⠟⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⣷⠀⠀⣧⠀⠀⢸⡇⢰⣇⣀⡀⣀⡇⠀⣧⣀⣸⡇⠀⣿⣇⠀⢀⣠⣷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠃⠃⠀⠈⠛⠛⠛⠋⠀⠉⠉⠉⠉⠃⠀⠉⠉⠉⠁⠀⠈⠉⠉⠁⢸⡿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠽⠿⠕⠚⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⠀⢀⣀⣀⣀⣀⡀⠀⣀⣀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⠙⣿⡇⠀⢸⣿⢫⣿⣷⠀⠀⢸⣿⣿⠁⠀⠀⢸⣿⣿⠻⣗⡀⠀⢸⣿⠀⠀⠀⠀⣿⠀⢸⡇⣿⣻⣿⡇⠀⢸⣿⡇⠀⢸⣿⣧⠀⠀⠀⠀⠀⢸⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣼⡇⠀⢸⡏⠀⠘⢿⡇⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠹⣿⠀⠘⣷⠀⠀⠀⣿⠇⠀⣿⣻⠉⠉⠉⠀⠀⣿⣿⡇⠀⢸⣿⣯⣆⠀⠀⠀⢰⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠸⣷⠀⠀⣝⡏⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢸⣿⡟⣿⣄⠀⠀⡟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⢿⡇⠀⣹⡃⠀⢸⣿⣿⣿⡇⠀⠀⢸⣿⣿⠀⠀⣿⣿⠀⢸⣻⠀⢸⣽⡟⠀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⢿⡇⢸⣟⠇⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢸⣿⡇⠀⢻⣧⢸⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⢸⣿⠀⢸⣧⠀⠀⣸⡇⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⠄⠀⢀⣿⠀⠀⠀⢻⢀⣿⡇⠀⠀⣿⣾⠀⠀⠀⠀⠀⢸⣟⣿⠀⠀⣿⣿⠀⠀⠸⣿⣿⡿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⣾⣿⡇⠀⠸⣿⣴⣿⡿⠀⠀⢸⣿⣿⣄⣠⠀⣿⣿⣾⣷⣟⠉⠀⠀⠀⠀⢿⣿⠃⠀⠀⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⠀⢸⣿⡇⠀⠀⢹⣇⡟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠈⠛⠛⠋⠀⠀⠀⠋⠉⠉⠉⠀⠀⠋⠛⠛⠛⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠉⠉⠁⠀⠈⠉⠁⠀⠀⠈⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠀⠀⢀⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠯⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣀⠀⠀⠀⣠⡖⠲⢤⠀⠀⣶⠶⠶⡆⠀⢠⠶⠒⠲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⡴⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢤⡄⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠙⣷⠀⢸⣅⣠⠜⠀⠀⢸⠇⠀⠀⠀⠀⡯⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠸⠇⠘⠧⠤⠤⠀⠀⠘⠇⠀⠀⠀⠀⠘⠶⠶⠒⠀⠀⠘⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀