⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣿⣿⣿⣿⣿⣯⣛⢿⣷⣿⣧⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣉⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⢹⡿⢨⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⡿⠟⢿⣾⠿⢿⣧⣼⣿⠻⢻⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣿⣿⣿⣿⣿⣿⡇⢰⠟⠁⢶⣾⣿⢿⣿⠟⢠⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⣿⡿⠉⠉⠀⠘⣇⠀⠀⠀⠈⠘⠛⠀⢸⡷⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣈⣽⣿⢿⣿⡀⠀⠀⠀⢻⡄⠀⠀⠀⠀⢀⣀⣄⣱⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠙⡇⠀⠀⠀⢸⠇⠀⠀⠀⠀⠙⣿⡏⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠏⠀⣷⠀⢷⣄⡀⠀⢺⡀⠀⠀⢰⣟⠛⢻⠇⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡶⣾⠛⠉⢩⣿⠀⠀⣿⠀⣠⠉⠛⠶⣬⣷⣄⠀⠈⠉⠛⢃⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣮⣄⠀⠈⠁⠀⠀⣿⠀⢹⡆⠀⠀⠈⠙⠻⢦⣤⣀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢸⡇⠈⣧⠀⠀⠀⢀⡶⣟⣻⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣧⡙⢿⣄⠀⠀⠀⣿⠀⢻⠀⠀⣠⣾⣵⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠟⠋⠀⠀⢸⡄⠀⠈⠻⣿⣿⣿⣿⣿⣥⣬⣿⣦⠀⠀⣹⡄⢸⣦⣾⡿⢋⣽⠃⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣟⣿⣿⠁⠀⠀⠀⠀⠀⢹⣄⠀⠀⠈⢿⣿⣿⣿⣿⡟⠻⢿⣧⣾⣿⠁⢸⠃⡟⠀⣿⣇⠀⢠⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣾⡟⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⢹⣿⣿⣿⣿⠟⣬⡹⢷⣤⡉⠻⡟⢀⣤⠾⠿⢿⣿⠇⠈⠋⣿⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⡿⢱⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢻⣿⣿⣿⡇⠙⢡⠀⠉⠻⣶⣤⠈⠀⣀⣠⣿⣷⣄⠀⠀⢻⡄⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⠃⣾⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣇⠀⠀⠂⠀⠀⢻⠀⣸⡿⢿⣿⣿⣿⣷⡀⠘⣷⠀⠀⠤⠌⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢃⣿⡆⠀⠸⣧⡀⠀⠀⠀⠐⠢⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢾⣰⣿⠁⠀⢻⣿⣿⣿⣿⣰⣿⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣿⡿⢸⣿⣇⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⠁⠤⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⠃⣤⠸⣿⡀⠀⠀⢰⣶⣽⣿⣦⣀⣀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡅⣤⡄⠀⠀⠉⠀⠀⠀⠀⠀⠹⣿⣿⣧⣿⣀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣇⣯⣄⠘⣿⣦⠀⠈⣿⠀⠀⠉⠉⠛⠻⢦⣄⠀⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⡿⠿⠶⠦⣤⡀⠀⢹⡄⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣍⠋⠀⠈⣿⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠘⢷⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣷⣄⠀⣿⡀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠈⢿⠀⢤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠠⠀⣿⠇⢸⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠙⢦⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⣼⢷⣄⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⡀⠀⣸⣿⣆⠀⢷⡀⠀⠀⢀⡴⠞⠉⠀⠀⠀⠀⠈⢳⡀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠞⠋⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣡⡾⠋⠀⠹⣇⠀⠹⣦⡐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣠⣤⣄⣀⡙⢷⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⠋⠀⠒⠲⠤⠜⣧⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠉⠉⠉⠻⠇⠈⢷⡀⠀⠀⠀⣆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢆⣸⡏⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠈⠻⣆⠀⠀⠀⠀⠀⠀⣠⣾