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⠂⠀⠀⠐⠠⠐⠠⢂⡀⠁⠠⠁⠠⠐⠈⢂⠀⠐⠡⡀⠈⠐⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠀⠀⠀⠀⠁⣿⣿⢿⠙⠀⠀⢀⠀⠀⣶⣶⣦⣷⣾⣶⣤⣩⣉⣍⢠⡟⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⡀⠄⡈⠂⠄⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀
⠁⠠⠈⡀⠂⠄⡀⠈⢀⠀⡀⠈⠐⠠⠀⢀⡀⠄⠀⠠⠀⠠⢀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠀⠀⠀⠀⠁⡿⢿⣯⣿⣿⢿⠈⠀⠀⠏⣿⣿⢸⠆⠴⠃⣿⣿⣿⣿⠸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⢿⠙⠀⠄⠀⠤⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠄⠀
⠀⠄⠈⠀⠀⠐⠄⠂⠀⠀⠠⠄⠈⠀⠀⠀⠀⠓⠛⠛⠟⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠁⡿⣿⣿⢿⣯⣿⣿⢿⡋⢹⣇⣿⣿⣿⠹⣧⡇⣿⣿⣿⣵⢸⡆⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠄⠀
⠀⠀⠄⡈⠁⠀⠠⠐⠀⢀⠂⠀⠀⠀⠀⠀⠀⡀⣌⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠋⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⣰⡟⣯⣟⠿⣿⢿⡻⣝⣻⣿⣿⣿⠘⢦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡁⠀
⠀⠀⠀⠀⠠⠐⢈⠡⠂⠁⠀⠠⠀⠈⠀⠀⠀⠀⢸⠀⢄⣄⣿⣿⣿⣿⣿⣿⣿⣿⣴⣠⠀⠀⠀⠀⠀⠀⠉⡿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣾⣡⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⣀⣤⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠡⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠐⢂⠀⠐⠂⠀⠀⠀⢃⠀⠐⠀⡀⣤⣶⣶⣴⣠⣀⠀⠀⠀⠀⠀⠀⠀⠋⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣰⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀⡀⣀⣄⣤⣦⣶⣶⣶⣶⣶⣶⣴⣤⣠⢀⠀⠀⠀⠀⠀⠁⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠄⠈⠀
⠀⠀⠁⠀⠁⠄⠁⢂⡀⠄⡀⠀⢀⡀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣾⢃⡵⣿⢿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣷⣿⣿⣿⣼⠃⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⢂⠀⠀
⠁⡀⠈⠐⠠⡀⠀⠀⠀⠈⠀⢀⠁⡀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣰⠋⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣮⣿⢸⡇⣿⣿⣿⠿⠻⠛⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔⢀⠀⡀⠌⠀⠀
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⡀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠁⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢯⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠈⠀⠁⠀⠀⠄⠈⠀
⠄⠁⠂⠁⠠⠌⠀⠁⠀⠀⠀⠀⠀⠄⠀⡀⠀⠈⡀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠀⣸⣧⣿⣿⣿⣿⣿⣿⣿⣶⣡⢟⠿⠹⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣸⠀⠀⠀⠁⠂⠀⠀⡀⠀⠐⠀⠀⡀⠌⠂⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀
⡀⠀⠐⠀⠐⠂⡀⠈⠐⠁⠀⠀⠀⠀⡀⠀⠈⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⡽⣦⣿⣿⣿⣾⢁⡿⣿⣿⣾⢀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠁⠂⡀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠐⠈⢀⠀⠀⠀⢀⠀⠀⡀⠀⠀⡀⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⣧⢻⠀⠀⠋⡿⣿⣶⣿⢸⣿⣾⣡⠟⣿⣿⣴⣋⠸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⢐⠄⠀⠀⠁⠂⠄⡀⠁⠀⠁⠀⠀⠀⠌⠀⠀⠀⢀⠁⠀⠠⢀⠀⠐⠀⠀⠡⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠆⣿⠜⡀⠀⡇⣿⠸⠀⠀⡇⣿⠸⠀⠀⡇⣿⠛⡿⣶⣠⢀⠰⣿⢸⣇⢃⡿⣾⣡⢟⡿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢨⡇⠀⠈⡀⠀⠀⠁⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠈⠐⠠⠀⠀⠀⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠺⠀⠁⠀⡄⣿⣿⠈⠀⡄⣿⢿⠀⠀⡇⣿⢸⡀⠀⠀⠀⠀⣿⢸⡀⡆⣿⢙⣍⣭⣮⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡌⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠀⢸⡆⠀⠀⠈⠄⡀⠀⠀⠈⠐⠀⠀⠀⠁⠀⠠⢀⠀⠁⠀⠐⠀⠈⠄⠀⠀⠂⢁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⠀⠀⠀⠀⡇⣿⢿⠀⠀⣧⣿⠻⠿⣿⣿⢸⠀⠠⠀⠀⠇⣿⢡⠀⢸⣀⣤⣦⣶⣶⣿⢿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢹⠀⠀⢂⠀⢰⠀⠀⠈⠐⡀⠀⠀⠂⠀⠀⠀⠈⠀⠐⡀⠀⠀⠈⠂⠀⠀⠐⠀⠀⠄⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠃⣿⢰⠀⠀⠀⠁⠛⣿⣿⠸⠀⠀⣷⣿⠘⠄⣿⢸⠀⠐⠀⠀⡇⣿⡄⠘⢃⠀⠀⠁⠛⡿⣶⣩⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣠⢀⠀⡇⠀⢈⠆⠀⢀⠂⠀⠀⠁⠀⠠⢀⠀⠁⠂⠀⠀⠐⠀⠂⡀⠀⠀⠁⠀⠐⠀⠀⠀⠠⠐⠀
⠀⠀⠀⠀⠀⠀⠀⡏⣿⠀⠀⠀⠟⣿⣾⣠⣿⢿⠀⠀⡄⣷⢿⡏⣿⢸⠀⠀⠀⠀⡔⣢⠀⢡⡂⠃⡶⣴⣀⠟⡿⣿⣿⣽⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣠⢀⠀⡀⠀⠈⡀⠐⠀⡄⠀⠀⠀⠈⡀⠀⠁⠀⠠⡀⠀⠈⠀⠠⠀⠄⠀⠈⠄⡀⠀⠂⠀⠀⠀⠐⢂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⡇⣿⣼⠀⠁⡟⣾⠀⠀⠀⡀⣦⣾⣰⠀⠈⠐⠠⢀⠈⠀⠀⠐⠀⠀⠀⠀⠀⡄⣿⣿⣻⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠄⠀⠀⠂⠄⠀⠀⠄⠀⡀⠀⠈⠀⠀⠐⠠⠀⠀⠀⠂⡀⠐⠀⠀
⠀⠁⠀⠀⠀⠀⠗⣿⢲⠀⠀⡁⣶⣿⣿⣾⣴⢀⠀⡀⠀⠄⠀⠀⠈⢀⠀⠁⠂⠀⠀⠁⠂⠀⠂⠄⠀⢀⠀⠀⣇⣿⣿⣾⡟⣿⣿⣿⣿⣿⣾⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠄⠀⠁⠂⠄⠀⠈⡀⠀⠁⡀⠀⠐⠀⠈⢀⠀⠀⠁⠋⠙⠄⡈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠠⠈⠀⠀⠀⠠⠀⠠⠁⠀⡀⠀⠈⠀⢀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⣧⣿⢼⣿⣿⣿⣿⣿⣿⢸⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣄⣿⣿⣿⣿⣿⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣢⠀⠀⠀⠀⠀
⠀⠀⠀⠈⡀⠀⠀⢀⠀⠈⠀⠁⠄⠀⠂⡀⠄⠂⠀⠀⠀⠀⠠⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⣿⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⡙⣮⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠁⠀⠀⡇⢿⠀⠀⠁⠟⡿⣿⣿⠹⠀⠁⡿⣿⣱⢀⠌⠀⠀⠀⠀⠀
⠀⠁⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠈⠂⠁⠄⡈⠐⢂⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢿⠹⣌⣷⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠛⠙⠀⠀⠀⠁⠈⠀⠀⠀⠀⡇⣿⠀⠟⣿⣴⣠⠀⣿⣿⠀⡿⣾⢀⠀⠠⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢁⠂⠁⢀⠠⠀⠀⠐⠀⠂⠀⠁⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠻⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣴⠀⠀⠀⠀⣧⣿⠘⠁⠀⡇⣿⠸⠁⠉⠛⡟⣿⠀⣀⢁⠀⠀⠀⣏⣿⠀⣆⣷⢿⠿⠛⠙⠈⠀⠀⠀⠀
⠀⠀⠀⡀⠀⠀⢀⠀⠈⠠⠐⠠⠀⠀⠀⡀⠀⠀⠠⠀⠁⠀⠂⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢆⣶⣶⣴⣤⣤⣤⣶⢶⠙⠀⠀⠀⠀⠀⠀⠀⠀⠂⠛⠈⠀⠀⠀⠀⣯⣿⣼⠀⡁⣿⣿⣿⣴⣠⣇⣿⠀⠀⠈⠀⠀⠀⣿⣿⠂⢀⠁⡀⠀⣀⣏⣿⢀⠀⠀⠀
⠀⠀⢀⠀⠄⠀⠀⠠⠐⢀⠀⠀⠀⠀⢀⠀⠠⢀⠀⡀⠀⠀⠈⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣥⢀⠋⠟⡛⠿⠿⠿⠿⡿⢟⠻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠇⣿⢸⠀⠀⠃⡿⣿⣷⣿⠘⠀⡀⣷⣿⠹⠀⡇⣿⠀⠀⠀⠀⠀⠀⣿⣸⠀⢀⠠⠀⠋⡿⣶⢀⠀⠀⠀⠀
⠀⠀⠀⠈⠀⠁⠠⡐⠀⠀⠄⠀⠄⡀⠀⠐⠄⠀⢀⠀⠠⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢁⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠛⠀⠀⠀⠀⠀⡇⣿⢰⠀⠇⣿⣾⢀⠀⣧⢿⠈⠀⡀⣧⣿⠻⡇⣿⠀⠁⡀⠀⠀⠁⣶⢠⠀⠃⠛⡾⣼⣀⠐⠈⠀⠀⠀⠀
⠀⡀⠀⠀⠀⠐⡈⠀⠀⠀⠁⠂⠀⠠⠀⠂⠀⡀⠀⠄⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣶⣶⣶⣶⢶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⠀⠀⠀⡟⣿⠀⠀⣿⣿⢠⠀⠀⡏⣿⢰⠀⠀⠀⣄⣷⣿⣾⠐⠀⠀⠁⠂⠀⠁⠀⠀⢀⠀⠈⠀⠀⠀⠄⠂⠁⠀⠀
⠀⠁⠀⠐⠄⠂⠀⠀⠀⢀⠀⠀⠈⠐⠄⠀⠀⢀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠛⠿⠿⢿⣿⣿⠿⠿⠳⡛⣍⣤⣷⣿⣿⣿⢡⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠂⣿⢠⠀⠀⣆⣷⢿⠿⣾⣴⢀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠈⡀⠀⠀⠂⠀⠀⠄⡀⠀⠀⠀⠐⠀⠀⠄⠂⠀⠀
⠀⠀⠀⠁⡀⠐⠀⠀⠀⠠⡀⠁⠀⠂⠀⠄⡀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣟⠪⣄⣧⣼⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣶⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠂⠄⠀⠀⠀⠠⢀⠀⠁⡀⠀⠂⠄⡀⠀⠁⠂⠀⠀⠀⢂⠀
⠀⠈⠀⠂⡁⠀⠀⠀⠐⠄⠀⠈⠀⠐⠀⠠⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠅⡋⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⡀⠀⠈⠄⡀⠀⠀⠄⠀⠁⠂⠄⠀⠀⠈⠐⠀⠄⠀
⠀⠀⠀⠄⠈⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠄⡀⠀⠄⠀⠀⠁⠂⠄⡀⠀⠁⠀⠀⠈⠠⠀⠀⠁⠀⠀⠀
⠀⠀⠂⠄⠈⠀⠀⠠⠀⠀⠀⠈⠡⡀⠐⢈⠡⠂⠄⠂⠀⠀⠁⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢀⠀⡀⠀⠀⠁⠀⠐⡀⠀⠂⠀⠁⠀⠄⡀⠀⠀⠀⠀
⠀⠀⠀⠄⠈⠀⠀⠀⠀⠁⠠⠄⠂⡁⠄⠀⠈⠄⡀⠂⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⡍⠀⠃⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣠⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢀⠀⠈⠀⠐⠠⠀⠐⠀⠁⠂⠀⠠⢀⠀⠀
⠀⠀⠈⠄⠂⠀⠀⠀⠌⠂⡀⠐⢀⠈⠀⠐⠀⠐⡀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⢛⡯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣤⢀⠁⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀
⠀⠀⠀⠀⢂⠁⠀⠠⠐⢈⠄⠀⠀⠀⠁⠂⠀⠀⠠⡀⠂⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⠿⠃⣙⣦⣾⣶⣴⣤⣀⢀⠁⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠁⠄⠈⠐⠈⠁⠀⠀⠀⠀⠠⠀⠀
⠀⠀⠀⠂⠀⠠⡀⠄⠀⠀⠁⠀⠠⢀⠀⠀⠈⢀⠀⢀⠂⢀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢖⣶⣤⣤⡀⣀⠀⠁⠀⠂⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢈⠠⠈⠐⠠⠄⠈⠡⠀⠀⠀⠀⠀⠀
⠀⠂⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠈⠄⡀⠀⠀⠀⡐⠀⠀⢈⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣦⣶⣶⣶⣤⣤⣤⣤⣤⣀⣀⢀⠁⠂⠀⠐⠂⢀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⡈⠐⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⢀⠀⠀⠀⠂⠄⡀⠀⠈⠐⢂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠⢀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢈⠠⢀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠄⠀⢀⠀⠈⠄⠀⠌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠟⡠⠐⠀⠀⠀⠀⢀⠀⠀⠀⡄⡀⠀⠐⡀⠀⠀⠀⠀⠀⠉⠋⠈⠙⠈⠂⠅⠩⠚⠋⠉⠀⠀⠐⠁⠠⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠠⠀⠀
⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠟⠿⣿⣿⣿⣿⢸⠀⠀⠈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⢀⠈⠀⡀⣧⣿⣿⢻⣇⣿⣿⣿⣾⢃⣿⣿⣿⣼⠌⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⡀⠀⠀⠈⠀⠁⢂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣾⣥⣀⣐⣄⣷⣿⢿⠀⠀⠀⠐⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⣄⣤⢀⠀⣀⣋⢛⠿⠿⣄⣦⣴⢂⠁⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠐⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠉⠀⠀⠁⠀⠀⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⡀⡉⠒⣡⡌⠘⡀⣦⣶⢰⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠠⠀⢀⠀⠀⣦⣶⣠⠀⡀⠐⠈⠠⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠄⠂⠀⠀⠀⠀⠀⠋⠈⠓⠛⡛⠿⣿⢸⣿⣿⣿⣸⠂⠄⠀⠀⠀⠀⠀⠀⠉⠋⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣾⣡⡔⠎⡁⠰⢩⠤⡘⠁⠿⠿⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠈⠀⠐⡀⠀⠈⢀⠀⠀⠀⠂⡁⠄⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠛⠘⠀⠀⠀⠋⠈⠀⠀⠁⡀⠂⢀⠀⠄⣋⠟⣿⢿⡈⣷⣿⣿⣾⢠⣤⣴⣤⠀⠀⠀⠀⠁⠋⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠙⢉⡠⠔⢃⡡⠒⢌⠠⡟⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠛⠉⠀⠀⠂⡀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠁⠀⢀⠀⠀⠄⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠋⡈⠀⠀⠀⠀⣿⣿⠀⠇⢻⠀⠀⠁⠿⠸⡄⣷⣿⣾⢣⠻⡛⠟⠿⠹⠀⠈⡀⠀⠀⠃⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⡙⠉⢉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠐⠀⠀⡀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠇⣿⢘⠀⠀⠀⠀⣿⣿⠀⡇⣿⠀⠀⡅⣿⢹⠉⠉⣀⠈⠀⡀⣀⣄⣤⢠⠀⠀⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⣿⣿⣴⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠐⠄⠀⠀⠀⠙⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⡐⠈⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⣿⣿⠀⠀⠀⠉⠛⣿⣿⢀⡇⣿⠛⠟⡟⣿⣾⣶⣷⣿⠻⠀⠀⠁⠋⠛⠰⠀⠐⠀⠀⠀⣦⣿⣿⣿⣾⠀⡀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣁⡿⣾⣠⠀⠀⣤⣤⣤⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣿⢸⠀⠀⠁⠂⠀⠀⠀⣿⢻⠀⠀⠀⠠⠀⢀⠁⠀⠀⠄⠀⢀⡀⠀⢀⠠⡐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡟⣿⢠⠀⠁⡟⣿⣾⣯⣿⠀⡇⣿⣸⣀⡟⣿⢠⠀⠀⡇⣿⢻⡿⣽⣉⢉⠀⠀⠀⡀⠀⠂⠀⡀⣤⣠⠀⠀⠉⠉⠉⠉⠉⠉⠉⠛⠚⠐⠀⠁⠟⣶⣠⠀⠀⠁⠻⠈⠀⠀⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⢸⠀⡀⠀⠀⠈⠀⠀⣗⣿⢸⠀⠁⠂⠄⠀⠈⠀⠀⠁⠀⠀⠐⠠⠀⠀⠀⠀⢀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡏⣿⣸⠀⠀⡇⣿⣸⠀⡏⣿⠀⡇⣿⢸⠃⣿⣸⠀⠈⠀⡏⣿⢂⣄⣥⣶⣷⣿⣿⠿⠛⠈⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣴⣀⠀⠉⠟⣴⢀⠀⠂⠀⠀⡇⣿⣿⠻⠈⠀⡀⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢀⠀⠀⠐⢀⠀⠀⠀⣿⣿⢼⠀⠀⠀⠂⠀⠀⠁⡀⠀⠀⠠⠀⠄⠀⠀⠠⠀⠀⠀⡐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡄⣶⣢⠀⠀⠀⡆⣿⢿⡿⣿⣨⠀⡀⣿⣿⡿⣾⢈⠄⠀⠁⣿⣸⠀⢀⠠⠄⠀⠋⠟⣿⣿⣠⠀⠀⠀⠐⠀⠀⠇⣿⣿⣶⣤⢀⠀⠁⠋⡿⣴⢀⠀⠀⠄⠀⠀⠀⡿⣿⣿⣿⣿⠻⠉⠀⠀⣀⣤⣷⣿⣿⣿⣿⣿⣟⢰⠀⡀⠁⠀⡀⠀⠀⠃⣿⣿⢰⠀⠈⡀⠁⠀⡀⠀⠈⡀⠀⠐⡀⠀⠈⢀⠀⠠⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⣀⠠⠀⠀⠀⣄⣿⣿⢤⠀⠀⠁⡟⣿⢀⠀⠉⠛⠿⣿⣴⣠⢀⠀⠀⠀⠀⠀⠂⠀⠀⡀⣀⠀⠀⠀⠋⠟⣿⣿⢠⠀⠀⠀⠂⠀⠠⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⠛⠀⠀⠀⡀⣄⣤⣤⣤⣀⠀⠀⠀⠀⠀⠠⠀⠀⡟⣿⣼⠀⠀⠀⠂⠀⠀⠄⠀⠀⠀⠐⠀⠄⠀⠀⠀⠂⠄⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡄⣿⣰⠀⠆⣴⣠⢄⠀⠀⠠⠈⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣠⠀⠀⠀⠀⠀⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⠚⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠐⠀⠀⠆⣶⣴⢀⠀⠁⠂⠀⠀⠄⠀⠂⠀⢀⠀⠄⠀⠀⠠⡀⠀⠈⠀⠠⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⡁⠄⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⣥⣦⣷⣿⣿⣿⢰⠀⠀⠀⠀⡀⠀⠐⠀⠀⡄⣿⣿⣿⣿⣿⣿⣯⢟⣴⣠⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠈⠂⠀⠀⠀⠂⠀⠀⠈⠂⠀⠁⠀⢀⠀⠠⠀⠁⡀⠀⠐⠄⠀⠂⠄⠀⠀⠄⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠠⠀⠈⠐⠀⠀⡀⢿⠻⡈⣧⣰⠀⠀⠀⠀⠂⠄⠀⠀⠐⠀⡀⣿⣿⣾⣿⢟⣾⣰⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠄⠀⠀⠐⠀⠀⠀⠀⠂⠀⠁⠀⠐⠀⠁⡀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⢀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠠⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠀⣆⣿⢿⠘⠀⠀⠀⠀⠂⠀⠀⠐⠠⠀⠀⠀⣿⣯⡿⣿⣴⢀⠀⠀⠁⡀⠀⠀⠠⡀⠀⠀⠠⠀⠀⠈⠠⠀⠈⠀⠠⢀⠀⠈⠀⠀⠈⠂⠀⠀⠐⠀⠀⠀⠂⠁⠠⠐⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠈⡀⠀⠄⠀⠀⠀⣧⣿⢠⠀⠀⠀⠀⠈⠀⠠⠀⠄⠀⠀⠀⣿⣿⣾⢀⠀⠐⢀⠀⠈⠀⡀⠀⠈⢀⠀⢀⠂⠀⢀⠁⠀⠐⠀⠄⠀⠀⢀⠁⠀⢀⠀⠁⠀⠠⠀⠀⠀⠐⢈⠠⡀⠀⠀⢀⡐⠈⠀⠀⠀⢀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠄⠀⠀⡇⣼⠀⠀⠂⠀⠄⠀⠁⠀⢀⠈⠀⠀⢀⠀⠐⠀⠠⠀⠀⠁⠂⠀⠄⡀⠀⠈⠀⠐⡀⠀⠀⠄⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠄⠀⡀⠀⠈⠀⡄⠀⠀⠠⠀⠄⠀⠂⠀⠀⠐⠀⠈⢀⠀⠠⠀⠠⠀⠄⡀⠀⠀⠈⠐⠄⠀⠀⠀⠈⠂⠄⡀⠀⠀⠀⠂⡁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠈⠀⠀⠀⠀⠀⠁⠠⠀⡱⠜⠀⠐⠈⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠁⡀⠀⠈⢀⠈⠀⠀⠀⠀⠠⢀⠀⠀⠀⠁⠈⠐⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠆⠀⠀⠀⠀⠀⠠⠂⣑⡰⠀⠐⠌⠀⠊⢠⠀⠀⠂⡀⠐⠀⠀⠀⠀⠀⠀⠀⠁⡰⠁⠠⠀⠃⠡⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠂⠂⢁⡠⠒⠄⠀⠁⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⢁⠠⠀⠂⡁⠁⢎⡠⠀⢀⠠⠀⠜⢀⠀⠀⠀⠀⡀⠄⠀⠀⠂⠀⠀⠀⠉⣰⠈⠠⠀⠎⢠⠂⠄⡀⠌⠀⠂⠀⢀⠠⡐⠄⠀⢀⠈⠀⠂⠌⠠⠒⢁⢂⠡⢂⠡⢀⠂⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠆⠹⠀⠻⠀⡿⢷⠀⣿⢻⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⡀⠃⢀⠐⠀⠀⡀⢈⣀⠄⠠⡤⠀⠐⠀⠁⠀⠡⠠⠐⠌⠠⠐⠀⠐⠌⡐⠠⠀⠁⠴⢈⡐⠈⠡⢂⠀⠎⢀⠀⠀⠀⠈⠆⡀⠄⠂⣀⠔⠃⣀⠘⡠⠆⠂⢁⠠⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠶⣷⠸⣇⢹⣄⣤⠀⣾⡀⣠⡄⢶⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⡐⡈⡐⠂⠀⠀⢄⠂⠀⠐⠈⠀⠄⠐⡌⠂⡐⠀⠂⣀⠑⠠⠀⡄⠠⠴⠂⢤⠒⠂⠐⠘⠉⠉⠡⠉⠐⠀⠀⢀⠀⠀⠐⡀⠀⠀⠀⠈⠄⠂⣀⠒⢈⠠⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡆⡶⢠⡀⣠⠀⠀⠀⠀⠀⠀⠀⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⢀⡘⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⢁⠤⡈⠀⠀⢀⠠⡐⢈⠰⠈⠀⠀⠁⠀⠐⠈⠈⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⠀⠀⠠⢀⠈⠀⠂⠀⡀⠄⠀⠂⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠧⠘⠧⠸⠇⠸⢿⠈⣧⠸⠇⡿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠈⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠐⢀⠀⠀⠄⠀⠀⠠⠀⡀⠄⢂⠌⠀⠄⠀⠀⡂⠄⠀⠈⠀⠀⠠⠀⠄⠀⠀⠀⠈⠐⠠⢀⠂⠀⠀⠄⠀⠀⠀⠀⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡗⢿⡠⣦⡴⣠⡁⢘⠀⣿⡿⣄⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠂⠄⡀⠀⠀⢀⠀⡀⠀⠀⠄⠀⠁⠂⠀⠠⠀⠐⢀⠁⠀⢀⠈⡀⠀⠀⠠⢀⠀⠂⠀⠠⠁⠀⢀⠀⠀⠀⠐⢈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⠃⠈⠀⠿⠈⠀⠀⡀⢀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠈⠐⡀⠀⠐⢀⠀⠠⢀⠀⠂⠀⠀⠀⠀⠀⠈⠂⠀⠁⠀⠀⠁⡀⠀⠐⡀⠀⠀⠈⠐⠀⠀⠀⠀⠐⢈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⠛⠃⠾⠻⠉⡏⢿⠁⡟⢻⠅⣿⢿⠘⡆⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠠⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⡀⠀⠈⠂⠀⠄⠀⢀⠀⠀⠀⠂⠁⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠛⣿⢻⡿⣿⣴⢷⣟⣆⢶⣴⡆⢶⣴⠋⠾⣷⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⢀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠻⡏⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠐⠌⠂⠁⠀⠈⠁⠀⠈⠁⠀⠈⠠⡐⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀