⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠉⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠈⠉⠳⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⠀⠀⠉⠙⠲⠦⣄⣀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⠦⠤⣤⣄⣀⣀⣀⣀⡀⠀⠀⢹⣆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠈⠉⠻⣦⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠦⠴⠧⠤⡤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠶⠖⠒⠒⠒⠛⠻⠛⢻⡄⠀⠀⠀⠀⠀⠘⢧⡀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⠤⢤⣤⣤⣄⣀⣀⣟⣀⣀⣀⣀⡤⠴⠶⠖⠚⠋⠉⠉⠉⠙⠛⠒⠲⠶⠶⠦⠤⢤⣤⣿⣀⣀⣀⣀⣴⡶⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣀⡀⠀⠉⠉⢉⠉⠉⠉⢀⣀⣀⣀⣀⣤⡤⠤⠤⠶⠶⠶⠶⠦⢤⣤⣠⣀⣀⣄⣀⣀⣠⠴⠟⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⡿⠛⡟⠛⠋⠉⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡏⠙⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢰⡇⠀⠀⠀⠀⢠⡿⣷⡄⠀⠀⠀⠀⠀⠀⣰⠾⡆⠀⠀⠀⢸⡇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣸⡇⠀⠀⠻⠷⢶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⣽⠀⢸⡄⠀⠀⠀⠀⢿⣼⠟⠀⠀⠀⠀⠀⠀⠀⣿⣴⡏⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀
⣠⣶⣿⣯⣽⡆⠀⠀⠀⣶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⡇⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢸⡇⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠉⠉⣹⠃⣴⣤⡀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣇⠀⠀⠀⢀⣠⡤⠞⠛⠛⠛⠛⠓⠲⠶⣤⣤⣀⡀⠀⢀⣿⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⡴⢻⡇⠹⡷⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣇⠀⠸⣦⠶⠛⠉⠀⢤⣀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠈⠙⠛⠿⠁⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠿⠇⠈⣷⠀⣧⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠤⠤⠶⠞⠛⠁⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⡄⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⢹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⡇⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣾⣷⣤⡀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⢸⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⣿⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣬⣤⣤⠉⢳⣤⠀⠀⠀⣴⠟⠀⠀⠀⠀⣸⠀⠀⠀⠉⠳⢤⣄⡀⠀⣀⣤⠞⠋⠀⠀⠀⠀⣿⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣶⣿⠀⣰⡟⠙⠛⠚⠃⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⣿⣇⣿⠁⠀⠀⠀⠀⠀⠀⠀⣸⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡆⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡉⢿⡷⣤⣤⣀⡀⠀⠀⢀⡾⠃⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢷⠀⠀⠈⠙⠛⠲⠟⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⢸⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠷⠶⢶⡖⠛⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣤⣿⠄⠀⠀⠀⠀⠀⠀⡜⠈⠙⠓⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠛⣿⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣤⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡇⠉⠉⠙⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠉⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠶⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀