⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣷⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⡟⢋⠛⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⠋⣹⣦⠉⠃⣀⣶⣆⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣖⢿⡼⠀⣀⠀⢩⠏⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⣷⣾⠷⠸⠀⣼⣶⠶⠾⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⣁⣤⡤⠞⠋⠁⠀⠀⠀⠙⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣀⡀⠀⠀⣠⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠁⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠙⢦⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⢾⡿⠋⠉⠙⠛⠐⠦⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾⠃⠀⣀⠀⠀⠀⠻⣄⠀⠀⠀⠠⡄⡆⠀⠀⠀⢻⡀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡴⠉⠀⠀⠀⠀⠀⢠⣴⠏⠀⠀⢰⡇⠀⠀⠀⠀⢻⣆⠀⠀⠀⠁⢻⡀⠀⠀⠈⡇⠀⠀⠀⢹⣷⣄⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⣀⣴⠾⠋⠁⠀⠀⢠⠟⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠉⢦⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣤⠤⠖⠛⠉⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⢨⢻⣇⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⢡⠀⠀⠈⠙⢦⣤⡀⠀⠸⣯⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣤⣶⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣠⠇⠀⠙⣷⣄⣠⣾⣍⣁⡀⠀⣀⠀⠀⠈⠳⣄⠀⠀⠀⠈⠉⠻⠶⢬⣀⠀⠀⠀⠀
⠀⠀⠀⠀⣰⣿⣿⣧⣴⣶⡶⢶⣶⠀⠀⠀⠀⠀⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣠⡾⠟⠉⠀⠀⠀⠈⠻⣦⣽⣀⠀⠀⠀⠙⠶⢄⡀⠀⠀⠀⠀⠀⠿⣷⣄⠀⠀
⠀⠀⠀⣼⣿⡿⡟⠛⠋⠉⠛⠷⣿⣄⣀⣤⠄⠻⣤⣀⠀⠀⠀⠀⠀⣠⡄⠁⣠⡴⠛⠁⠀⠀⣠⠊⠀⠀⡆⠀⠀⠉⠙⢶⣄⠀⠀⠀⠀⣁⣤⣤⣴⠾⠿⠶⢦⣹⡆⠀
⠀⠀⢰⡿⣡⠟⢷⡀⠀⠀⠀⠇⠘⠋⠉⣷⠀⠀⠀⠀⠉⠀⠀⠉⢁⣩⡿⠟⣉⣀⣀⣀⣀⣉⡁⠀⢀⣀⣻⡶⠒⠉⠁⠀⠉⣿⡶⣶⠶⠟⠁⢸⣷⡄⠀⣿⠀⠙⣿⡄
⠀⠀⠀⢠⡏⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠈⠿⠶⠦⠤⠤⠤⢶⣿⡏⠉⠿⠛⠿⠿⠭⠉⠉⠉⠉⠉⠉⠉⢿⡅⠀⠀⠀⠀⠀⢿⣷⡀⠀⠀⠀⠀⠈⢁⣼⣿⠀⠀⠿⠃
⠀⠀⠀⣾⠁⠀⠰⠀⠀⠙⠳⣤⣀⣀⡀⠤⠤⠤⠤⠤⣄⣀⣸⣯⠀⠀⠀⢰⣦⠀⠀⠈⠳⣤⣦⢀⠀⠀⠈⠛⠓⠒⠶⢤⣀⢘⣿⠟⢦⣀⡀⠀⢀⣺⣧⡿⠀⠀⠀⠀
⠀⠀⣸⠏⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠙⠷⢄⡀⠀⠈⢻⡟⠀⠀⠀⠀⠀⠀⠀⣰⠾⠿⣿⡄⠀⠻⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀
⠀⣰⠏⠀⠀⠀⣰⠟⠁⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⢿⣀⣠⡾⠻⣦⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀
⣴⠏⠀⢀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡞⠇⠀⠈⢻⡄⠀⠀⠀⠀⠀
⣿⣸⡿⠋⢁⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣠⣄⣿⡄⠀⠀⠀⠀
⢻⣿⠀⠀⡈⠘⠛⠲⠤⢄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣶⣿⣿⠇⠈⣿⠀⠀⠀⠀
⠈⠙⣆⠀⡁⠀⠀⠀⠀⣠⡟⠉⠉⠉⠛⠻⠶⢬⣀⣀⡀⠀⠀⠘⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠭⠉⠹⣶⣷⣾⠟⠀⠀⠀⠀
⠀⠀⠹⣧⣠⡄⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⣻⠟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠛⠳⣆⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣴⡖⠶⣶⢶⣺⣿⠿⠋⠙⠿⣔⠶⠀⠠⠄⠀⢠⢄⣶⣿⠟⠁⠀⢀⣤⠚⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠛⢧⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠉⣩⣹⣿⣿⡉⠁⠀⠀⠀⣠⡌⠙⠓⡒⠒⠒⠿⠟⠉⠀⢀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠋⠈⠛⠻⠄⠀⠀⠀⠀⡠⠟⠙⠂⡇⠀⠀⠀⢸⡇⠀⠀⠀⠙⣧⠀⠀⠀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡞⠀⠀⠀⣰⠁⠀⠀⠀⠘⢧⠀⠀⠀⠀⠘⡄⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢠⡟⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⢻⡄⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠴⠊⠀⢀⡞⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠙⣄⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⡠⠊⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⠈⠓⠦⣤⣀⡈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀