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⠀⠀⠀⠀⣠⡴⠞⠛⠛⠛⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⡷⠶⠒⠒⠒⠶⢶⣄⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣿⠛⠛⢻⡆⠀⠀⠀⠀⠀ ⠀⢹⡷⠶⣤⣤⣤⣤⣤⡾⠃⠀⠀⠀⠀⢻⠀⠀⠈⣧⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⡴⠟⠀⠀⠀⠀⢀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣤⣤⠶⢾⡿ ⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀ ⠀⠀⠀⠈⠛⠶⠶⠶⣤⣀⠀⠀⠀⠀⢠⡶⠞⠛⠒⠛⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠴⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣶⣶⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠿⠟⠛⠋⠉⠉⠉⠉⠛⠿⠿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣷⣾⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⠿⠿⠿⠿⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⣿⣿⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⠉⠛⠿⠿⢿⣿⣶⣶⣶⣶⣶⣶⣶⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣤⣶⣶⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣯⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿ ⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣶⣶⣦⣤⣤⣶⣶⣾⣿⢿⣿⣿⠏ ⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⣠⣾⡿⠋⠀ ⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⢀⣀⣀⣤⣶⣿⡿⠟⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣶⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣶⣦⣤⣤⣴⣶⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠟⠛⠋⠉⠉⠉⠛⠻⢿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⣧⣶⣶⡶⠶⠶⠶⠾⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣧⡀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠘⣿⣷⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢻⣿⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⡇⠀⠉⠉⠛⠛⠿⠿⠿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣦⣶⣾⠿⠃⠀⠀⠀⠀⠀⠀⠀⢀⡀ ⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣤⣄⣀⡀⠀⣀⣀⣠⣴⣾⣿⠇ ⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⠛⠛⠋⣹⣿⠏⠀ ⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠁⠀⠀ ⠀⠀⠀⠀⠘⢿⣷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀⣤⣤⣶⡿⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⠿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠟⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⣤⣀⣀⣤⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

ඞ

⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡿⠋⠁⠀⠀⠈⠉⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⠇⠀⢀⣴⣶⡾⠿⠿⠿⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣀⣸⡿⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⡟⠛⣿⡇⠀⠀⢸⣿⣿⣷⣤⣤⣤⣤⣶⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀ ⢀⣿⠀⢀⣿⡇⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⠿⣿⡏⠀⠀⠀⠀⢴⣶⣶⣿⣿⣿⣆ ⢸⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣿⡇⣀⣠⣴⣾⣮⣝⠿⠿⠿⣻⡟ ⢸⣿⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠉⠀ ⠸⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀ ⠀⠻⣷⣶⣿⣇⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣀⣀⣀⣼⡿⢿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠁⠀⠙⠻⠿⠟⠋⠑⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠉⠉⠉⠉⠉⠉⠉⠙⠻⢶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⣠⣶⠛⠛⠛⠛⠛⠛⠳⣦⡀⠀⠘⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⢹⣿⣦⣀⣀⣀⣀⣀⣠⣼⡇⠀⠀⠸⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠉⠛⠿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⣿ ⠀⠀ ⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀ ⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⣠⡶⠶⠿⠿⠿⠿⢷⣦⠀⠀⠀⠀⠀ ⣿⠀ ⠀⠀⣀⣀⣀⠀⣸⡇⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀ ⣠⡿⠛⠛⠛⠛⠻⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀ ⠀⣿⠀ ⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⢀⣤⣤⣴⣿⠀⠀⠀⠀⠀⠀ ⠀⣿⠀ ⠈⠙⢷⣶⣦⣤⣤⣤⣴⣶⣾⠿⠛⠁⢀⣶⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀ ⠀⠀⠀⠀⠈⣿⣆⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠃⠀ ⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣾⣿⡿⠿⠟⠋⠁⠀⠀⠀

⣄⣤⠶⣷⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠉⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠿⠻⠛⠛⠛⡉⠈⠀⠁⠈⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⡀⣤⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡽⣿⢿⠻⠛⠟⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⣤⣤⣤⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣰⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣄⣤⣤⣤⣤⣦⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣀⣀⢀ ⠀⠀⠀⠀⠀⠁⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⠀⠀⠀⣀⢀⡀⣀⣀⣄⣷⣿⣿⣿⣿⣿⣿⣿⠹⠀⠀⠀ ⠀⠀⠀⠀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠁⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀ ⠀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⣶⢠⡷⣿⣿⣧⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀ ⡿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣾⣠⠀⠁⡟⣾⣠⡿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⢿⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⠁⠟⣿⣴⠁⡾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢻⠀ ⣿⣿⣿⣿⣿⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠚⠀⠀⣿⣁⠚⡶⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⢿ ⣿⣿⣶⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠿⣿⣿⣿⣿⣻⣛⠛⠙⠉⠉⡋⣿⠿⠻⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿ ⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⣤⣀⡀⣄⣤⣶⣶⣶⣶⣴⣤⣀⢀⠀⠀⠸⣀⣤⣶⣶⣶⣶⣶⣴⣤⣀⣦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠚⠴⣤⣸⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠻⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⣿⣿ ⠀⠀⠀⠁⠋⠛⠶⡤⣠⢀⠀⠀⠇⢸⠀⣆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⠀⠏⣼⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠘⠁⡾⣠⢧⠙⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿ ⠖⠴⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⣆⠹⠀⠀⠀⠀⠀⠀⠀⡇⢋⠖⡤⣄⢸⠀⠀⠀⠀⠀⠀⠀⡄⢁⠋⠖⣠⠀⠀⠀⣄⠳⠈⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠹⠀⠀⠀⡀⣄⠲⠓⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠒⠴⡤⣟⢀⠀⠀⠀⠀⠀⠀⠀⣦⠳⠈⡀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢶⠛⠉⠈⠀⠀⠉⠋⠛⠿⠿⣿⣿⣿⣾⣿⣿⠿⠿⠛⠙⠀⠀⠁⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠈⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣛⣿⣿⣶⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣶⣿⡽⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠦⡙⠈⡀⢄⠓⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣶⣠⢀⠉⠛⠟⠶⠴⡤⣤⣤⣦⢿⠶⠲⠓⠙⠉⠀⣇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠦⠙⠀⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⠁⠟⣿⣿⣿⢹⠉⠉⠟⠙⠀⠀⣍⠳⠟⠛⣉⣷⢿⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠛⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠻⠙⣏⣿⠉⠀⣁⠟⣿⢫⠟⡟⣼⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠙⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣼⣶⣿⣿⣿⣿⣿⡿⢿⣿⣯⣿⢻⠙⠀⣁⣯⠟⣿⣿⢿⣿⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢳⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣠⢀⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠳

⣿⣿⣿⠟⢹⣶⣶⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡟⢰⡌⠿⢿⣿⡾⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢸⣿⣤⣒⣶⣾⣳⡻⣿⣿⣿⣿⡿⢛⣯⣭⣭⣭⣽⣻⣿⣿⣿ ⣿⣿⣿⢸⣿⣿⣿⣿⢿⡇⣶⡽⣿⠟⣡⣶⣾⣯⣭⣽⣟⡻⣿⣷⡽⣿ ⣿⣿⣿⠸⣿⣿⣿⣿⢇⠃⣟⣷⠃⢸⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽ ⣿⣿⣿⣇⢻⣿⣿⣯⣕⠧⢿⢿⣇⢯⣝⣒⣛⣯⣭⣛⣛⣣⣿⣿⣿⡇ ⣿⣿⣿⣿⣌⢿⣿⣿⣿⣿⡘⣞⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣦⠻⠿⣿⣿⣷⠈⢞⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣗⠄⢿⣿⣿⡆⡈⣽⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻ ⣿⣿⣿⣿⡿⣻⣽⣿⣆⠹⣿⡇⠁⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾ ⣿⠿⣛⣽⣾⣿⣿⠿⠋⠄⢻⣷⣾⣿⣧⠟⣡⣾⣿⣿⣿⣿⣿⣿⡇⣿ ⢼⡟⢿⣿⡿⠋⠁⣀⡀⠄⠘⠊⣨⣽⠁⠰⣿⣿⣿⣿⣿⣿⣿⡍⠗⣿ ⡼⣿⠄⠄⠄⠄⣼⣿⡗⢠⣶⣿⣿⡇⠄⠄⣿⣿⣿⣿⣿⣿⣿⣇⢠⣿ ⣷⣝⠄⠄⢀⠄⢻⡟⠄⣿⣿⣿⣿⠃⠄⠄⢹⣿⣿⣿⣿⣿⣿⣿⢹⣿ ⣿⣿⣿⣿⣿⣧⣄⣁⡀⠙⢿⡿⠋⠄⣸⡆⠄⠻⣿⡿⠟⢛⣩⣝⣚⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣾⣿⣿⣄⠄⠄⠄⣴⣿⣿⣿⣇⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠛⠿⣿⣫⣾⣿

⬛⬛⬛⬛⬛⬛ ⬛🟥🟥🟥🟥🟥🟥⬛ ⬛🟥🟥🟥🟥🟥🟥🟥🟥⬛ ⬛🟥🟥🟥🟥⬛⬛⬛⬛⬛⬛ ⬛🟥🟥🟥⬛🟦🟦⬜⬜⬜⬜⬛ ⬛🟥🟥⬛🟪🟦🟦🟦⬜⬜⬜🟦⬛ ⬛⬛⬛🟥🟥⬛🟪🟦🟦🟦🟦🟦🟦🟦⬛ ⬛🟥🟥⬛🟥🟥⬛🟪🟪🟪🟦🟦🟦🟦🟪⬛ ⬛🟥🟥⬛🟥🟥🟥⬛🟪🟪🟪🟪🟪🟪⬛ ⬛🟥🟥⬛🟥🟥🟥🟥⬛⬛⬛⬛⬛⬛⬛ ⬛🟥🟥⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛ ⬛🟥🟥⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛ ⬛🟥🟥⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛ ⬛🟥🟥⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛ ⬛🟥🟥⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛ ⬛🟥🟥⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛ ⬛⬛⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛ ⬛🟥🟥🟥⬛⬛⬛⬛🟥🟥🟥⬛ ⬛🟥🟥🟥⬛ ⬛🟥🟥🟥⬛ ⬛🟥🟥🟥⬛ ⬛🟥🟥🟥⬛ ⬛⬛⬛ ⬛⬛⬛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⠶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡟⠋⠉⠀⠶⣦⠌⠙⠿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠃⡀⣀⣤⣤⡤⠶⠷⣤⣽⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⢸⡟⠋⠉⠀⠀⠀⠀⠀⠈⠉⢧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡀⠀⠀⠉⠛⠛⠿⠿⠿⢿⣿⣿⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⢶⣴⣶⣤⣀⣀⣀⣀⣀⣘⣿⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⣏⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠁⠀⢠⣄⣍⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣄⣀⣀⠀⠈⣿⣿⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢛⡛⠉⠉⠛⣿⣿⠀⢿⡇⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠄⠁⠀⠀⠀⣿⣿⠀⢸⣧⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⠀⣽⣿⠀⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢰⠂⠀⠀⠀⠀⢰⣿⡇⠀⠊⣿⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⢸⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠙⠀⠀⠄⠀⠀⢠⣿⡟⠀⠀⣸⣿⣷⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣦⣤⣤⣤⣠⣼⣿⠃⠀⠀⣿⡏⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠉⠉⠛⠛⠿⠿⠿⠟⠁⠀⠀⠀⢻⡇⢸⣆⢿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠈⣿⡿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣽⣿⣿⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠋⠛⠶⣦⣀⠀⠀ ⠀⠀⠠⢸⣿⢰⡇⠀⠀⠀⠀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠘⢃⣆⣈⢻⣷⠀ ⠀⠀⠀⢸⣿⠘⠃⡄⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⣀⣠⣴⣾⠟⠏⣺⣿⡇ ⠀⠀⠀⠈⢿⣧⣀⡀⠀⠀⣸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠿⠛⠉⠉⢀⣤⣿⡿⠀ ⠀⢀⣠⣤⡴⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣠⣤⣴⣿⣿⠟⠉⠀⠀⠀⢀⣠⣶⣿⠿⠋⠀⠀ ⢰⣿⠛⣷⠦⠀⠀⣩⣿⠿⠛⠉⠉⠙⠛⠿⠿⠿⠛⠛⠉⠁⠀⢀⣀⣴⣶⡿⠟⠋⠁⠀⠀⠀⠀ ⠘⢿⣿⣦⣤⣄⣸⣿⣷⣄⡀⠀⠀⠀⠀⠀⠂⠀⠀⣀⣤⣴⣶⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠙⠻⠿⠿⠿⠟⠿⣿⣷⣶⣶⣶⣶⣾⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠃⣿⣿⣿⣾⣶⣿⣿⣿⣴⢀⠀⠀⡡⣼⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⣼⣠⢀⠀⠀⣇⣿⣿⠘⠀⠁⠋⣰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⢀⠀⠀⠀⢻⡟⣿⣣⣿⠿⡿⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡆⢻⠀⠀⠇⣿⣿⣿⣿⣾⣶⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⢷⠿⡿⣿⣿⣩⢀⠀⠀⣄⣿⢿⠙⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣏⣿⣨⠀⢣⠀⠀⠀⠀⣿⢶⣿⠻⠈⠀⠀⠀⠀ ⠀⠀⠀⠁⠋⠟⡾⣡⣚⣷⠻⠀⢣⠀⠀⡀⣆⠺⡙⣌⣗⠹⠀⠀⠀ ⠀⠃⠿⣿⣿⣾⢽⢛⠭⣋⣼⠃⡀⠠⠀⠀⠀⢿⠈⡀⢄⣧⢿⠻⠀ ⠇⣿⣿⣿⣾⠀⠀⢀⠤⣿⠖⠤⠤⠂⠓⠚⠀⣀⢦⠺⠍⡿⣿⣿⢠ ⡀⣴⣧⣀⣄⣦⡿⣻⣙⣿⠀⠃⠈⠀⠁⢸⠀⠃⠛⣴⣤⣀⢀⣄⠀ ⠀⠀⠀⠀⠀⠀⣽⣤⣦⣿⢿⡿⢛⠛⣿⠼⠀⣀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⢤⡧⣿⣶⣶⣲⣙⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠏⣿⢞⠤⣤⠤⣦⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⣸⢲⠉⠉⠉⠋⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⢷⠈⠀⣀⠉⡞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣿⣿⡿⢼⣤⣯⠀⠀⡇⢾⠶⠶⠶⠶⠶⠶⠶⡷⣿⣰⠀⠀⠀⠀⠀⣄⣷⠶⠒⠒⠒⠓⣿⢠⠀⠀⠀⠀⠀⠀⣧⢌⠢⠒⠒⠀⡀⠀⠀⠉⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣹⢉⠀⠧⣿⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⡟⣾⠀⠀⠀⠀⠀⠀⠀⡇⢿⠉⠀⠁⡿⢰⠀⠀⠀⠀⠀⠀⠀⡇⢾⠓⠛⠛⠖⠴⡤⣠⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⣿⣾⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠃⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⣆⣸⣄⣧⣼⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠓⣿⣟⣿⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⡇⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢠⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⣠⠀⠋⡴⢀⡅⣸⠀⠀⠀⣿⠘⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠀⡞⢀⠀⠀⡇⢸⠀⠀⠋⣰⣗⠸⠀⠀⠀⠀⡿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⡇⢸⠀⠀⣧⠀⠀⣾⣤⠦⠓⠙⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⡟⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢸⠀⠀⠁⣸⠀⠀⠀⡇⠀⠏⢰⠀⠀⠀⡀⣷⢸⠀⠀⠀⠀⠀⠃⠾⣠⣀⠀⡄⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠤⠤⠠⠀⠀⡄⢹⠀⢱⠀⠀⡞⠀⠀⠀⠀⡀⢿⣤⠤⠤⠤⠤⠤⡷⢸⠀⠀⠀⠀⠀⠀⢦⠙⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⠙⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⠸⡆⠀⡇⢸⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⡀⠳⠈⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⠀⠀⠀⠀⠀⡞⠀⠁⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⠀⠀⠀⠀⡀⢀⠋⡴⣀⢤⠳⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣤⢦⠻⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⡆⣸⣆⠘⡏⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣽⢦⡟⠀⠀⠀⠀⠀⠋⡴⢀⠀⠀⠀⠀⡀⣄⠦⠓⠙⠉⠀⠀⠀⠀⠀⡀⢯⡾⣠⠀⢷⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢏⣠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣟⣶⣷⢻⠉⠁⠋⠞⣠⠀⠀⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣠⣀⣤⣤⣧⡇⣿⠈⠀⠀⠀⠀⠀⠀⠀⠃⡼⣤⣤⠀⠀⠀⠀⠀⠀⣤ ⠤⠤⠤⠤⠤⠤⠧⠤⠤⠤⠯⡿⣰⣷⣿⢿⣀⣦⣿⢀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⡟⣾⢠⠀⠀⠀⠀⠀⠀⠀⣿⠉⠈⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠟⣽⢀⠀⡆⣶⢠⠀⠀⣇⢹⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡇⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠃⣿⣿⣿⠻⠛⠛⠛⠟⠿⣿⣿⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⡇⣿⣈⣇⣾⣷⣿⣿⣿⣿⢸⣇⢰⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠈⡇⠁⡏⢸⣀⣄⣤⠶⠶⡶⣴⣤⢁⡾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠙⠉⠉⠉⠈⠀⠀⠀⠀⠀⣧⣨⣀⣀⣀⣀⣀⣀⣂⣷

⣀⣄⣦⣷⣿⢻⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠛⠛⠙⠋ ⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣴⣀⣀⣤⣤⣤⣶⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣴⣤ ⠀⠀⠏⣿⣿⣿⣾⣴⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⣿⣿⣿⢸⠀ ⠃⡿⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⠢⣿⠸⠀⠀⠀⠀⠀⡇⣿⣿⢻⠀ ⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⡖⢎⢀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠙ ⣾⣤⢀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⣛⠛⢟⣻⠙⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿ ⠀⠀⠀⠀⠀⠉⠚⠔⣀⣤⣤⣤⣠⣀⣘⣤⣦⣴⣤⢢⠈⠀⠀⠀⠀⠀⡄⣷⣿⣿ ⠉⠂⠐⠤⣀⠃⠀⢡⠀⠀⠀⠀⠁⠏⢠⠀⠀⠀⠒⠊⣤⠑⠢⠈⠀⠀⠀⡀⣦⣿ ⠀⠀⠀⠀⠀⡀⠑⠀⢄⠂⠑⠉⠋⠛⠉⠚⠀⠠⣈⠀⠀⠀⢄⡑⠄⠑⠀⠀⠀⣄ ⠀⠀⠀⠀⠀⠀⠀⣃⣾⣤⣉⠈⠒⠙⡉⣄⢦⣈⠀⠀⠀⠀⠀⠀⢄⠒⢌⠐⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⠟⣿⢻⠏⠘⠄⠿⡍⢿⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⣄⣶⣿⣿⣿⢿⠛⣟⡾⣵⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

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⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣏⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠸⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣧⠨⠀⠀⠀⠀⠀⠀⠀⠀⠏⢠⠀⢸⠀⡟⣶⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⠀⠀⠀⠀⠀⠀⠀⠇⢡⠰⠀⢰⠃⢺⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣿⠘⠀⠀⠇⠈⠀⠀⠀⠀⠆⠀⠁⡾⠒⠓⠈⠀⠀⠀⠀⠀⠃⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠁⠋⠖⠤⡀⣀⣤⢿⠀⠀⡀⠀⠀⠃⠉⠀⠀⠀⡼⠀⠀⠀⣀⠦⠑⠈⠀⠋⣠⠀⠀⠀⠀⠀⠀ ⠢⠙⠀⠀⠀⠀⠀⡀⠹⠀⠀⠀⠁⠚⡤⣀⠀⠀⠀⠀⠀⠀⣀⢳⠀⢇⠸⠀⡀⣴⠀⠁⡞⠀⠀⠀⠀⠀⠀⠀⡀⢄⢲⠙⠀⠀⠀⠁⠉⠚ ⠀⠀⣄⠦⠽⠌⠠⠀⡄⠙⠚⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢳⠀⢣⠀⠀⠀⠋⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠴⣠⢀⠀⠀ ⠀⠀⠀⠀⠀⣀⢄⠤⠶⢑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠳⠈⢦⠙⠉⠚⡶⢰⠂⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣠⠀⠀⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⢤⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⢄⠢⠑⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠊⠒⠗⠤⠠⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⡤⣋⣴⠤⠒⠒⠉⠉⠉⠀⠀⠀⠀⠀⠀⠄ ⠉⠈⠀⠀⠀⠀⠀⡀⢄⠤⠤⠤⡤⣧⣈⠀⠀⠀⠀⠀⢧⠀⠀⣆⢿⠒⠀⠀⠀⠔⠦⣸⠀⠁⡞⢒⠒⠔⠤⡠⣀⠀⠀⣀⣀⣀⢀⠀⠀⠀ ⠀⡀⣀⢄⠤⠤⠤⠲⠒⠒⠒⠒⠒⠒⣒⠒⠒⠒⠒⠒⡖⢸⠀⠀⢤⠀⠀⠀⠀⠀⠀⣆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⣾⠺⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣊⣡⠞⢀⠀⠀⠀⠀⡀⣀⣁⣞⣠⣀⣀⠋⣲⣉⡼⣁⠉⠒⠒⠚⠓⣓⢭⣳⠞⢰⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠋⡱⠖⣠⠀⠀⠀⠀⠀⠀⠁⠞⣠⠀⠀⠁⠜⢀⠀⡟⠀⣸⠀⠀⠀⢸⢸⠀⡇⡿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠞⣠⠉⠀⠀⠃⡰⠛⠉⠀⣇⠀⢳⠀⠀⡄⢘⢁⠋⡴⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠥⣾⣠⠀⠆⣶⡤⣞⠀⠀⠀⢦⡙⢦⠓⠊⣖⡠⢉⡖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠦⢁⣀⠀⠀⠀⠀⠁⠂⢄⠀⠀ ⢧⣤⠶⣒⠦⡀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠁⠢⠀⠀⠀⠀⠡⡀ ⠀⠀⠀⠀⠑⡘⡀⠀⠀⠀⡸⠢⢀⡀⠀⠀⠀⠀⢀⠼⠀⠀⠀⠀⠀⢡ ⠀⠀⠀⠀⠀⠱⠱⠀⠀⡼⢴⢖⢶⣪⡭⣄⡀⠈⠁⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠱⣕⡄⢙⣷⣻⡚⠗⢯⢶⣹⢶⡀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣗⠦⠄⡉⢖⣄⠈⠾⠿⡼⠀⠀⠀⠀⢠⢇ ⠀⠀⠀⠀⠀⠀⠀⢀⣼⠻⣿⢆⣀⢈⡿⡗⢣⠀⣠⢟⠀⠀⠀⡰⠁⡸ ⠀⠀⠀⠀⠀⠀⠀⡎⠳⣭⣑⣞⣼⠏⠯⠷⣹⣯⡿⣸⣇⠀⡞⢀⡜⠁ ⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠉⠉⠛⠛⠋⠉⠉⠀⠘⠛⢠⠃⡜⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⢨⠄⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡉⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⢀⠇⠀⡆⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠑⢄⣀⣀⡀⠔⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⡉⠖⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠟⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀ ⠙⠖⠴⣤⢦⡗⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠧⠛⠉⠀⠀⠀ ⢀⠀⠈⠀⠀⡀⣧⠸⠀⠀⠀⠁⠉⠛⠒⠒⠖⠒⠓⡉⢸⠀⠀⠀⠆⢸⠀⠀⢾⠁⠋⠒⠤⠤⠶⠶⠤⠣⠚⠛⠉⠈⠀⠀⡆⢻⣉⢾⠳⠉ ⠀⠀⢧⠈⠀⠀⠁⢮⠖⠭⣤⣀⠀⠀⠀⠀⠀⠀⡀⡐⢸⠀⡧⠸⠀⢸⠀⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢦⠒⠉⡇⣰⠀⠀⡄ ⠀⠀⠀⢯⠖⡥⢊⠔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢀⠀⢻⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠦⠑⠈⠀ ⢿⠴⣠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠀⡄⢠⠀⢀⠀⠀⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⢸⠀⠀⠀⠀⠀⠁⡞⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢇⠙⠀⠀⠀⠁⡟⢠⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡀⣻⢬⡷⣠⢃⡸⠀⡀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⡆⣟⡞⠗⣾⢀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡆⢸⡎⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠁⠉⠋⠛⠿⣿⣿⣿⣿⣿⣶⣴⣤⣤⣷⠾⠳⠛⠒⠓⠟⠶⡿⣾⣤⣤⣶⣿⣿⣿⣿⣿⣿⠿⠿⠛⠙⠉⠀⠀⢀⠀⠀⠀ ⠛⠟⠿⡿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣤⣀⢀⠀⠀⠀⠀⡗⢻⡏⢠⠀⠃⣿⠁⣿⢰⠀⠀⠀⠀⣀⣤⣶⣷⣿⣿⣿⣿⣿⣿⣿⢿⠻⠙⠈⠀ ⣷⣶⣴⣤⣯⣿⣤⣶⣤⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⠈⠀⡞⣥⡟⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣤⣤⣦⣷⣾⣶⣶⣿⢾ ⣀⠀⠀⠀⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⠛⢛⡾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣷⠸⠀⠀⢦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡾ ⣄⠲⠙⠀⠀⠆⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠓⠍⠾⡴⢀⠀ ⠀⠀⡁⣌⠤⠒⡙⢿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣴⣧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡾⢶⡤⣀⠀⠀⠀⠀ ⠀⠀⠀⢇⠸⠀⠀⠁⣀⣄⢦⠛⠉⠈⠀⠀⠀⠀⠀⠀⠀⠃⡾⢠⠀⠀⣆⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠞⡤⢁⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⢬⠓⠈⣄⢳⣈⣀⣯⢰⠀⠁⠛⠛⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠈⠴⠤⠤⡥⣾⢠⠄⡤⣒⠠⠀⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠛⠛⠛⡃⠀⠀⠀⡄⣿⣿⢠⠀⠀⡇⣹⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢰⠀⠋⠞⣿⢀⠀⠀⠃⠾⣿⢳⡿⠻⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣷⣽⠈⠀⠀⠀⡇⣼⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⠈⠀⡄⣿⢀⠀⠀⠀⡄⣤⢀⡀⣠⣀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢈⠀⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢹⣇⢈⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠞⠤⠤⠦⠓⡌⠹⠈⠀⠀⠀⠀⠀⠀⠀⡍⢻⡴⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢻⡈⣀⣀⣤⣤⠤⠤⣠⣀⣀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠉⠉⠈⠀⠁⠉⠀⡀⢹⠉⠚⠒⠴⣭⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠃⠴⣀⠀⠀⠀⠀⡀⣄⣦⢈⠀⠀⣆⢻⠒⠒⠖⣠⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠛⠈⠏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡄⣤⠀⠀⠀⠁⠄⠄⠀⡄⠘⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠋⡴⢀⠀⡀⢢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢦⠉⠀⠀⠂⠖⠀⠴⠀⠋⡴⠀⠀⠀⠀⡀⣄⠳⠉⠀⠀⠀⠀⠀⠋⢀⠀⣦⠙⠁⠉⣦⣘⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⢄⠤⠤⠤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠦⠒⠙⠙⢙⠛⠶⠴⣠⣦⣻⣄⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠁⡟⣾⣴⣁⠋⠛⠒⠴⠂⠒⠒⠛⠛⠉⣈⢤⠲⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⡟⣴⢁⠛⠾⣠⢀⣿⠀⠀⠀⠀⠀⣸⣄⣤⣶⣶⠿⠛⣙⢮⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠏⣼⢀⠋⣿⣴⠀⠀⠀⣿⠘⠀⠀⠀⠀⢸⠀⠀⠀⠀⡒⣁⣥⣬⡷⣟⢿⠻⠉⠈⠀⠀⠀⠀⠀⠀⣆⣿⢻⠈⠀⠁⠟⠿⠿⠛⠙ ⠛⠚⡟⣰⠀⡟⣾⢀⠀⠀⠀⠀⡇⢿⠀⠀⠀⠀⣿⠓⠉⠞⣴⣤⣤⣄⣤⢦⠳⣉⣿⣿⣿⢿⠿⠛⠛⠉⠈⠀⣇⣿⢿⠿⣿⣿⣿⣿⣿⣿ ⣿⢿⣸⠀⡿⣾⢄⠀⠀⠉⠛⠖⠗⣿⠸⠀⠀⠁⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⣄⢷⠸⡀⣄⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣾⠀⠇⣼⠀⠀⠋⡾⣠⢀⠀⠀⡀⢧⠙⡇⡛⣾⠀⠀⠁⠘⠀⠀⠁⠊⠒⠤⠠⠀⣇⠹⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢠⠀⡿⠀⠁⡿⣾⢀⠀⠀⠀⡇⠈⠀⣆⠻⣿⢸⠀⠃⣴⠁⠚⡤⢀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠀⡇⣼⢸⡏⣴⢦⠙⠀⠀⠀⠀⢧⠙⠀⡏⣡⢀⠉⣰⠊⣠⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⢡⠉⠋⡞⣶⣤⣤⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠀⡟⢙⢻⣿⠘⠀⡀⢄⠓⠈⠀⠀⣄⠟⢠⠸⠀⣿⡜⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣴⣀⣄⢳⠉⠛⠿⣿⣾⣴⣠⣥⣯⢽⣇⣿⣿⣿ ⣿⣾⣠⣄⣷⣿⢿⠈⠀⠀⠀⡀⢢⠀⠀⡆⠘⣇⠈⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠄⠲⠉⡀⣄⣦⣿⠀⠃⡼⣀⣄⣾⡇⣿⣿⣶ ⣼⢀⠀⠀⠀⣆⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⣆⡿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢼⠤⠤⠳⠉⣀⠤⠀⡇⠘⡇⢿⣤⣧⢿⡾⣠⠀⠀ ⠀⠀⠀⠀⠀⠋⣴⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⡄⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡿⠚⠒⠷⡽⣀⣀⢄⠿⠿⢿⠛⣿⠀⡇⣸⠀⠁⠈⠀ ⠀⠋⠞⡶⣼⣤⠥⣾⣤⣦⢿⠙⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠇⣰⠀⠀⠀⡀⢦⠉⠟⣴⠀⣄⣻⣀⢷⡿⣾⣠⣀⠀⠔ ⡴⣄⣧⠙⣿⡤⣷⠘⠀⠀⡀⣄⢶⠻⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡜⠃⢸⠀⠀⠀⠀⠀⠁⣾⠀⠀⠀⠁⡾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⡀⣀⠀⡀⣶⠹⠀⠀⠀⠀⣀⣄⢶⠙⠀⣧⠀⠀⠀⠀⠀⠀⠀⠏⢀⡽⠉⠀⠀⠀⠉⠚⣠⠀⠀⠋⡴⣦⠘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⠈⠀⠀⠀⠀⠀⣀⢧⡿⠻⠛⠛⠉⠉⠀⠂⢠⡞⣀⣀⣀⣀⣀⢁⠋⠟⠴⣠⢀⠀⠋⣴⠀⠀⠀⠀⠀⠀⠁⠋ ⠇⢸⠀⠀⠀⠀⠀⠀⠀⣆⢿⠈⠀⠀⠀⠀⠀⠀⣄⣦⣷⠘⡐⣦⣹⢧⡟⢶⠷⠾⠤⣤⣠⣁⣠⣄⣲⣛⣟⣿⢙⠉⠉⠉⠉⠒⠔⡤⣫⣾ ⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠹⠀⠀⠉⠔⠀⠀⠀⡀⣿⠘⠦⡜⢻⣿⠞⡴⣤⣀⣀⣀⣀⣀⣀⣈⣀⣤⠢⠛⠛⠛⠚⠒⠐⠄⡠⢀⠀ ⡇⢸⠀⠀⠀⠀⠀⠀⠁⠁⠉⠉⣏⣿⣈⢀⠀⠀⠀⠀⠀⡧⢿⠀⢀⡇⣼⠀⠉⠛⠞⠤⠤⠠⣀⢁⢾⠻⠈⠀⠀⣆⠹⠀⠀⠀⠀⠀⠀⠀ ⣿⢸⠀⠀⠀⠀⠀⠛⠟⣾⣀⣀⣀⣤⣦⠿⠙⠀⠀⠀⠀⠀⡃⢸⠁⣾⣆⡿⣧⣿⣿⠀⠀⠀⠀⡿⠀⡀⢸⠀⠀⠀⣇⠈⠀⠀⠀⠀⠀⠀ ⣿⣿⠘⠀⠀⠁⡟⣾⣠⠀⠀⠀⠄⡠⢀⡀⣦⠻⠀⠁⠘⠀⡇⢾⣠⠀⠀⣿⠉⢾⣡⠀⠀⠁⡼⢀⠂⠛⣾⠳⠀⠀⡇⢸⠀⠀⠀⠀⠀⠇ ⣿⣿⢿⠟⠛⣿⣴⢀⠀⠀⠀⠀⠀⠁⠋⠚⢖⡴⣦⢓⠒⡴⣠⠀⠀⠀⠀⣿⣿⠿⢀⠀⠃⣿⣹⢾⡷⣿⢠⡀⠹⠋⠟⢻⠀⠀⠀⠀⠀⡿ ⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠋⠟⡿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⣀⠀⠀⣤⣀⣄⠓⠉⡟⠿⡽⠀⠃⠻⣴⠀⠀⠀⠀⠇⣿ ⢉⡄⣤⣇⣻⠀⢀⠉⠟⡿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠷⠉⠀⠀⠀⠖⢩⠉⠞⣳⠁⣐⣻⢀⠀⠀⠀⠀⠀⣿⣸ ⣠⢀⠐⡀⣧⠻⡿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠤⠦⠶⠶⠴⡤⣤⣦⠒⣴⠀⠀⠀⠀⠀⡟⣾⠀

⠀⠒⠀⠀⠂⠀⠐⠀⠈⠀⠂⠁⠉⡀⣀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢋⠶⣽⣯⣿⣿⣿⣿⣭⠿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣴⠤⠦⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠛⣿⣶⣶⣶⣶⣶⢶⢿⠿⣿⢻⡾⣠⣀⣀⣀⣧⣾⣀⣀⣧⣿⢛⣛⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠁⠛⠛⠿⠛⠿⠻⠛⠛⠛⠛⠈⠋⡿⣽⢉⠉⠉⠛⠛⠛⠙⠉⣏⣿⣿⠀⠀⠀⠀⠁⡞⢀⠀⠁⡟⣾⣴⣤⣤⣦⢿⠛⠈⠀⠀⠀⠀⠀⣿ ⣤⠂⠐⠉⣉⣉⣀⣁⣿⣾⣷⣿⣿⣾⣴⣤⣀⣀⣀⣀⣀⣄⣦⣶⣿⣿⢿⠿⠿⠿⣿⠻⠛⠿⣿⣿⠿⠻⠛⠙⠉⠈⣄⢿⠈⠀⠀⠀⠀⣄ ⠒⠐⠀⡂⣶⣶⣶⣶⢲⠖⣿⣼⢠⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠈⣀⣄⣷⣿⠻⠈⣿⣿⣾⣤⣠⠀⠀⣀⣤⣧⣷⣿⣿⢹⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⠿⠟⣿⣿⣶⣤⣤⣤⣤⣤⣤⣶⣿⣿⢿⠻⠛⡏⣿⣿⣿⣤⠀⠀⠀⠀⠀⠁⠈⠁⠀⡇⣿⢻⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣶⣿⣿⣿⣿⣻⠙⠋⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣿⣿⣿⣿⣿⣴⣠⣀⢀⠀⠀⠀⣀⣦⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣾⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠻⠈⠀⠀⠀⠀⠀⠈⢀⠘⠀⠀⠀⠀⠃⡼⠀⠀⠀⠀⠀⠃⠴⠠⠀⠀⠀⠋⠖⣡⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣾⣴⣤⣀⣄⠢⠙⠀⠀⠀⣄⡠⢀⠀⠁⠋⠟⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⡴⢠⠀⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⣶⣶⣤⣤⣤⢦⠶⠛⡈⣀⢤⠶⠒⠒⠔⡤⣷⣿⣿⣾⣶⠲⠒⠐⠂⠒⠒⠴⣤⣀⠀⠉⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠃⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠙⠀⠀⠀⠀⠀⠀⠀⣆⣿⠀⠀⠀⠁⠉⠉⠚⠒⠔⠤⣠⣀⠀⠀⠁⠋⢶⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣀⣛⣛⣙⢈⠀⠀⠁⠉⠋⠚⠶⠤⣠⣁⠛⡿⣿⢿⠻⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠁⠞⢠⠀⠀⠀⠀⠀⠀⠀⡟⢒⠒⠶⣥⠻⣀⣦⣴⣬⣥⣉⣈⣁⢄⠤⣤⣶⣿⣬⣦⣿⢻⠀⠀ ⠻⠙⠀⠀⠀⠀⠀⣁⢿⠻⠒⠓⠛⠞⠤⣀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣿⠿⠿⠾⣠⢀⠀⠀⠃⢹⠺⡗⢻⣾⡷⠰⠀⠀⠀⣄⠳⣎⣿⢻⠀ ⣦⣿⢿⠈⠀⠀⠟⣠⠀⡀⢦⡿⠉⣄⠷⠘⠀⠀⠀⠀⠁⠋⠟⣿⣿⣉⣟⣸⠀⠀⠉⠀⠉⣿⣏⢙⣍⠉⣟⣹⠋⠈⠁⠙⠘⠀⣧⣿⣿⠘ ⠉⡛⣿⢿⠟⠿⢿⠛⠛⠛⠉⠈⣀⣍⣭⣭⠤⠤⡧⣿⣿⣿⣷⢻⣍⣤⣯⠈⠆⡿⣿⣾⣿⣶⣿⣤⣏⣤⣤⣠⣄⢀⡯⣿⢰⠀⡇⣰⣿⢻ ⣴⣤⣤⣿⣿⣀⣀⣄⣤⣶⣿⣿⣿⣿⣶⣷⣿⠻⡟⣿⣿⢹⠀⣄⣤⣶⣶⢳⠈⡀⡀⣁⣻⡋⢻⠟⣸⠇⠿⠿⠿⠿⣰⠀⠀⠋⣼⠀⣇⣿ ⠀⠀⠀⣇⣿⠸⠀⠀⠀⠟⣿⣴⣷⣿⢿⠈⣄⣷⣿⣿⣿⣿⠻⠙⠉⠉⠭⡉⣿⠻⠉⡄⣄⣴⣠⣀⢀⡶⣆⣴⣶⣴⢤⠶⡷⣿⢸⠀⡀⣿ ⠀⠀⠀⡆⣿⢸⠀⠀⠃⣿⣸⠀⠀⣆⣿⣿⠈⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⢿⠴⣀⠅⠿⠛⠿⠿⠿⠛⠖⠲⠀⣇⢹⠀⠀⣇ ⠀⠀⠀⠀⣿⢹⠀⠀⡏⣿⢰⠀⠀⠀⣇⣿⢹⠀⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠹⠎⣿⢃⣰⣤⣀⣀⣝⣾⣴⠀⡟⣿⠀⠀⡇ ⠀⠀⠀⠀⣿⣼⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠃⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢷⡿⠛⠛⠛⠛⠚⠖⡶⠶⡿⣿⠀⠀⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠛⠋⠉⣭⠙⠳⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠙⣀⣠⡤⠶⠶⠶⠾⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡇⠀⠸⣧⣀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠉⠙⠛⠛⠶⢶⣿⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣿⣶⣶⢤⣤⣤⠿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠉⢉⣛⢶⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣤⣄⣀⢸⣿⠆⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠍⠀⠀⢹⣿⠈⣿⠀⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠈⠀⠀⠀⢸⣿⠀⣿⠀⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡟⠐⠀⠀⠀⠀⣾⡇⠀⣻⡇⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣅⠀⠀⠀⠀⢀⣿⠃⠀⣿⣇⢻⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣤⣄⣀⣀⢀⣼⡟⠀⢰⣿⢿⢼⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⠟⠛⠛⠻⠿⠿⠛⠀⠀⠈⣿⢸⣆⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠋⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠷⠦⣄⡀⠀⠀ ⠀⠀⢸⡯⡄⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢂⣀⡻⣦⠀ ⠀⠀⢸⣧⠁⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⣤⡶⠿⠙⢹⣿⠃ ⠀⠀⣀⣻⣷⣦⣤⣴⣿⣷⣤⣀⠀⢀⣀⣤⣾⠿⠛⠉⠁⠀⣠⣶⡿⠋⠀ ⣴⡿⢯⠅⠉⣹⣿⠟⠛⠙⠻⠿⠿⠿⠟⠋⠁⠀⣀⣤⣴⠿⠛⠉⠀⠀⠀ ⠙⢿⣷⣤⣤⣿⣷⣤⣀⡀⠀⠀⣀⣀⣠⣴⡶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠉⠉⠙⠛⠻⠿⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣷⣿⣿⣿⣿⣾⣶⣤⣠⣀⣀⣀⣄⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⣀⣦⣼⢀⠀⠀⠀⠀⠑⠀⠀⠀⡇⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⣿⣿⣿⣿⣿⣿ ⢀⣴⣦⣿⣻⠄⠉⠋⠚⠒⠒⠒⢹⠈⢡⠀⠀⠀⠀⠋⠔⣀⣧⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣇⠻⣴⢀⠀⠀⠀⠀⡀⡱⢄⠵⠀⠤⣀⠀⠁⠟⡿⣾⣷⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⡄⣸⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠁⠟⣿⣨⢁⠍⣛⣛⣿⣿⣿⣿ ⠀⠒⠒⠓⠛⣿⠡⠊⠐⠀⠀⠀⠀⠀⠀⠀⠀⠏⣤⣦⣷⣶⣤⣤⣀⣀⢀⠀⠀⠀ ⠀⠀⡀⣀⠀⡷⡆⢁⢺⠥⠸⠀⠀⠀⠉⠔⣀⡇⠸⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡤⠓⠖⣒⠖⠎⠴⣩⠉⠭⠦⡬⠱⠀⣼⠀⠀⠀⠀⠉⠉⠋⠛⠛ ⠀⠀⠀⠛⠟⠸⠀⡇⠀⠀⠇⢴⡨⠀⠁⠔⢀⠀⣸⠀⢸⠀⠀⣿⣿⣶⣤⣦⣷⣿ ⠀⠀⠀⣿⣿⢸⠀⡆⠀⡀⡠⣢⠑⡹⠉⠈⠚⡠⠀⠀⢸⠀⠀⣿⢸⠀⠀⠀⠀⡄ ⠀⠀⠀⣿⣿⢸⠀⠁⢄⠒⠉⠉⠉⠈⠒⡸⢀⠀⠀⠀⢀⠀⠀⣿⣻⠘⠀⠀⠀⠀ ⠀⠀⠀⣫⣿⣼⡁⣓⣰⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠀⠀⣿⣿⢸⠀⠀⠀⠏

⠀⠀⠀⠀⠀⠀⡄⡽⣃⠀⡇⠀⠤⠤⡧⢀⠀⠀⣄⠝⠭⣰⠀⠀⠀⣸⠀⠀⠂⠄ ⠀⠀⠀⠀⠀⠀⠉⠃⣽⠀⠀⠀⠀⠀⡽⠀⠀⠀⠀⢣⡇⠀⠀⠀⠀⢇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡐⠃⠀⠃⠀⠊⠱⠈⠀⣼⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⡿⠀⠀⠀⠀ ⠉⠉⠉⠉⠈⠸⠁⠀⡌⠀⡇⡙⡉⢌⢸⠀⠀⠃⠄⡆⢸⠀⠀⠀⠀⡷⠈⠀⠀⠀ ⠤⠤⠤⠤⠤⡧⠘⠇⠀⠀⡆⠀⠀⠀⢆⠀⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⢹⡸⠀⠀⢊⠠⠀⠑⠈⠀⠀⠀⠱⠮⢱⠀⠀⠀⠀⠶⡎⠀⠀⠀ ⠀⠀⠁⠈⠁⠊⢿⢺⠉⡔⢀⠤⠤⠤⡤⣤⠄⠤⡠⠤⡿⠐⠀⠀⠀⡼⢠⠀⠀⠄ ⠀⠀⠀⠀⡟⢙⣌⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣖⣶⣶⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠀⠀⠀⢣⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣋⠞⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠋⠞⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠛⠿⣤⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠿⠴⣤⣀⠀⣀⣤⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠷⠙⠈⠀⠀⠀ ⠀⠀⠁⠀⠀⠀⠀⠀⣧⢸⠀⠀⠀⠀⠀⠉⠉⠛⠖⠶⠶⠶⠶⠲⠛⠉⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⡏⢸⠁⠋⠞⠴⠤⠤⡦⡶⢶⠤⠤⠿⠒⠛⠉⠈⠀⠀⠀⠀⣿⢻⡉⣿⢶⠳⠈ ⠀⠀⡄⢻⠀⠀⠀⠀⠀⣧⠛⠚⠶⡤⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⢁⣈⣿⠀⠀⠿⠘⠀⡇⠈⠀⠀⡇⣼⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⣀⢦⠻⠙⠈⠀⣧⣼⢀⠀⠀⣆ ⠀⠀⠀⡅⢻⠀⠋⠞⡤⣉⢚⠴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣿⢠⠀⡇⢸⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢦⣳⠉⠀⠀⠀⠀ ⠉⠀⠉⠛⡶⣠⢊⠔⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣇⠈⠀⡆⢸⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠲⠙⠉ ⣾⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠸⠀⡀⢀⠀⠀⠀⠀⠀⡀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣆ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡆⠙⠀⠀⠀⠀⠀⠀⠋⣾⠀⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⠀⣧⢦⠛⠋⠟⠚⡴⣯⢠⠀⡆⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⠀⡄⢿⠙⣆⣸⠁⡟⣸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⣆⡿⢸⢶⡇⣼⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡄⢾⠀⣾⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡉⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠟⠴⣤⣷⠿⠿⠻⠟⠻⠋⠟⣿⣻⣘⣦⣿⠈⠋⠖⠠⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠋⠛⠛⠛⠛⠛⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀ ⣾⣴⠇⣾⣶⢠⣁⣉⠏⣿⣿⣿⣿⣻⢈⠀⡄⣿⢀⠀⠁⠟⠿⠿⠛⠋⣿⣿⣿⣿⣼⣤⢷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠿⣶⣶⣶⣶⣷⣿⣿⣶⣥⣩⣉⣀⣥⢿⠻⠈⠀⠀⠀⠀ ⠚⠖⠤⡤⣤⣀⣀⣀⣀⣀⣄⣦⣿⣿⢿⠛⠛⣼⠀⠀⡿⣿⣿⢸⡄⣿⣿⣿⣿⣾⠀⠀⡀⣷⠸⠀⠀⠀⠀⠀⠀⠀⠇⣿⢀⠀⠉⠟⡾⣤⣀⠀⠃⣿⣶⣴⠀⡦⣷⣿⣷⠹⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣿⣿⣶⣤⣀⠀⠀⠇⣿⣿⣿⢠⠏⣿⣿⣿⣿⢠⠀⠀⠀⡆⢻⠉⠛⠛⠛⠛⠛⠛⡟⣿⠛⡾⣠⢿⣿⣿⠘⠀⠀⣄⠢⠀⠀⠀⠀⠉⠀⣷⠘⠀⠀ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡋⣟⢛⠛⠛⠛⠛⠛⡿⣿⣿⣿⡿⣿⣿⣿⣼⢀⠀⠀⠀⠀⠀⣿⣼⣀⢉⣿⣾⣠⢀⠋⡛⣟⣤⠷⡛⣈⣀⢀⠟⣿⣿⣶⠀⠀⡶⣿⣿⢾⡄⢿⠟⡴ ⣄⢦⠙⠉⠉⠋⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⢀⠀⠀⠀⠀⠀⠀⠀⡄⢿⠟⣴⣁⠉⠉⠌⣤⣤⣠⠀⠀⡅⢺⠀⠀⣀⣉⠉⠋⠛⠛⡿⣿⢾⠷⠿⣿⣿⠹ ⠠⠀⡇⣾⣠⢀⠀⠀⠀⣀⣄⣶⣿⣿⣿⣿⣿⣾⣴⣤⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢻⠀⡦⣷⣿⢸⠀⠟⣿⢶⠉⠋⠛⠶⡶⣤⣠⣀⣀⠏⣴⢻⠁⠀⠀⡇⣿⣟⣿ ⠀⠟⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠿⠾⣶⣿⣾⣷⣿⣾⣿⣿⣽⢿⣶⣷⣿⠻⠛⠟⡿⣾⣧⣾⣿⠿⢸⡇⢸⠀⠀⣯⣿⣿ ⠻⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣾⣶⢀⠀⠀⠀⡟⢰⠀⣄⣿⣤⣀⣀⣤⣤⠶⠶⠻⠛⠛⠛⠛⠿⣿⣿⣿⣾⡄⢻⠀⠈⣧⣿⣿ ⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠸⣦⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢈⠀⠀⠁⠟⡿⣴⠀⠀⠀⣧⠸⠀⠀⠁⡿⣤⣶⠶⠶⠶⠶⣿⣿⣿⣽⣉⠀⠀⣷⡘⡯⡈⣿⣿ ⣤⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⠃⢰⠀⠀⠀⠁⠋⠙⠋⣿⢿⡛⢻⠛⠛⡾⣴⣠⠀⠀⠀⠀⡆⢿⠀⠋⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣷⠹⡇⢻⡏⢸⣿⣿ ⠀⣿⣿⣿⣿⠻⠉⠀⠀⠀⠀⠀⠀⠀⠁⡟⣰⠀⠀⠀⠀⠁⠟⣿⣤⢀⠀⠀⠁⣿⣽⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⢻⣿⣿ ⠀⣸⣷⣿⣿⣿⣿⣿⠷⠻⠛⠛⠛⠿⣼⣀⠀⠀⠀⠀⠁⡿⣿⣧⣴⢿⠶⠿⣾⣥⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠇⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡿⣰⠁⣿⣸⡏⣿⣾ ⠀⢸⡇⣿⣿⣿⣿⢰⠀⠀⠀⠁⠛⠾⣶⣶⢿⠘⠀⠋⣿⣠⣦⡷⠹⣿⠈⣇⣿⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢸⠀⠀⠀⠀⠀⠀⢿⠙⠈⠀⠉⠋⠟⡶⣤⢀⠀⡟⣾⠃⣿⣾⢠ ⠀⢸⡇⣸⣧⣿⣿⠀⠀⠀⠀⣴⢀⠁⠞⣶⣉⣏⠶⣿⢀⠀⠀⠀⣀⣄⢶⡶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠻⠙⠉⠛⠟⡶⣠⣀⣄⣤⣀⣀⠀⠀⠀⠋⡿⣰⠃⡿⣿⢀⠀ ⠀⢸⡄⢸⡀⣼⣦⢷⠛⠙⠉⠈⠀⡉⢯⠾⢦⣽⠅⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠘⠀⣀⣆⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠏⣿⣠⡇⠀⠀ ⠀⢸⠀⢸⠀⢸⠀⠀⡀⣀⣤⣤⣤⣤⣤⢦⡤⣀⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣶⠠⠀⡀⣤⢷⠻⠉⠀⠀⠀⠀⠀⠉⠋⠟⣿⣠⣇⠀⡇⠀⠀ ⠀⢸⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣤⣤⣤⣤⣤⣀⠀⣿⠀⡇⠀⡇⠀⠀ ⠀⢸⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⡇⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣤⣀⣀⣀⣀⣄⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣤⣀⣀⣀⠀⡀⣀⣦⣷⣿⣿⣿⣿⣾⣴⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠆⠉⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠋⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣀⠀⣾⣶⣿⣿⣿⣿⢀⠦⠈⠀⠁⠋⠛⠚⠒⠒⠓⠟⢹⠀⠀⣆⠘⠀⠀⠀⠀⠀⠀⠀⠁⠋⠞⣠⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢀⠀⡀⣄⣦⣷⠸⠀⢫⡿⣾⣤⠀⠀⠀⠀⠀⡀⣄⣽⠦⠓⣟⠀⠀⠀⠀⠁⠋⠶⣠⢀⠀⠀⠁⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠐⡇⣿⠟⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠹⠀⡀⣦⣬⠤⡤⣀⠀⠀⠀⠀⠉⠟⣿⣿⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣀⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⣄⠰⠀⠀⠀⠀⠋⡿⣿⣾⣤⣀⢀⠚⡴⣤⣦⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣿⣿⣿⢻⠉⠋⠟⠿⣛⣟⣿⣿⣿⣶⣶⣶⣶⣴ ⠉⠉⠛⠟⠻⠛⠙⠛⡟⣾⢧⠈⠋⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣤⣤⣶⣷⣿⣶⣶⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠖⠤⣤⣤⣀⢸⡇⢿⢠⠃⢠⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠋⠖⣠⣇⠘⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠀⠀⠀⡄⢿⡀⣰⠀⣾⡤⢁⠚⢰⠀⠀⠀⠀⠀⠋⠖⡠⢀⠀⠀⡇⢸⠀⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⢦⣳⠉⠉⠽⣬⢤⠯⠚⠓⠞⠶⣲⠒⠒⠒⠒⠓⠾⡶⠻⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠋ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡃⣸⠀⠀⠀⠀⠟⣠⠉⠖⠤⣤⣤⣤⣭⣚⠴⠢⡟⣼⠀⡇⢸⠀⠀⠀⠋⠛⠛⠿⠿⡿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠃⠿⠿⣿⠀⠀⠀⡇⠀⠀⠀⠀⡇⣼⣤⢘⠀⠀⠀⠋⠔⢀⠀⠀⠀⡞⠀⠀⡇⢸⠀⠀⠀⣿⣿⣿⣾⣴⣤⣀⣤⣶⣷⣿⣿ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⡇⠐⠀⠀⠦⡕⢿⠼⢠⠁⠜⣠⠀⠀⠀⠀⠉⡞⢀⠀⠀⡇⢸⠀⠀⠀⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⡀⣧ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⡀⠳⠀⠀⠀⠀⣠⣀⢤⠶⢶⠒⠒⠔⠧⣾⢀⠀⠀⠀⠀⡇⢸⠀⠀⠀⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⡀⢦⠓⠈⠀⠀⠀⠀⠀⠀⠉⠚⡷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢙⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣞⣷⣿⣿⢻⠂⠒⠶⢳⠈⠀⡀⣀⠄⠤⠤⡠⣀⢀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠏⡿⣿⣿⣸⠄⡼⡴⣶⠠⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⡟⠈⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⣿⣿⣿⣿⢹⠀⠀⠀⠀⠀⠋⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⣿⣾⣠⢀⠉⠛⠛⠚⠒⠓⠛⠛⠛⠉⠉⠀⡀⣄⢦⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠟⡿⣴⣀⢁⠋⠾⣴⣇⣿⡀⠀⠀⠀⠀⠀⣿⣶⣷⣿⣿⠿⠻⠙⡈⣤⠶⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠄⠋⡿⣴⢀⠃⡿⣾⣠⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⣿⠀⡀⠀⡄⣀⣤⣶⣿⣿⠿⡙⣌⢿⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠉⠇⣾⢠⠁⠟⡿⣴⢀⠀⠁⠀⡆⣿⠘⠀⠀⠀⠀⠀⣿⠘⠘⠀⠀⠂⠈⠤⠂⠘⣂⣄⣶⢶⡿⣿⢿⠛⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⠻⠀⠀⠁⠛⡿⣿⣿⢿⠻⠛ ⠛⠉⠋⣏⣼⠀⠃⡿⣽⢠⠀⠀⠀⠀⠂⠀⣿⢻⠀⠀⠀⠁⠀⣿⢹⠻⠉⠋⠟⠶⣴⣤⣤⣤⣤⢶⢿⢙⣄⣮⣿⣿⣿⢿⠿⠛⠙⠉⠈⠀⠀⠀⣇⣿⣿⢻⠛⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣽⡏⣼⠀⠃⣿⣾⡪⡈⠀⠀⠄⠌⠁⠉⡇⣿⢹⠀⠀⠀⠀⡇⣿⠟⣾⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣧⣛⢚⣀⣴⣷⣿⣿⣿⣿⣿⢿⠿⠻⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣾⠀⠀⣿⣸⢄⠀⠀⠐⠋⠿⣶⣠⣀⣤⣶⣿⠀⠀⠳⠇⣡⣿⣠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣌⣷⢙⡀⠀⡬⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢠⠀⠇⣼⢀⠀⠐⢋⡾⣰⠀⠀⠀⠀⠘⠀⡄⢿⠁⡆⠾⡿⢸⠀⠀⠁⣏⠀⠀⠀⠀⠉⠖⠴⣠⣀⢀⠀⠀⣷⢛⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣸⠀⠀⡿⢀⢀⠠⢿⣽⡰⠀⠀⠀⠀⠀⢿⠀⠀⡀⣷⠛⣏⣿⠀⠀⠁⡾⢠⠀⠋⡴⣠⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⠂⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢸⠀⡏⣺⢭⠀⣿⣻⣳⠈⠀⠀⠀⠀⠀⡄⠱⠀⠀⠀⣁⣼⣤⢀⠀⡞⢀⠋⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⠶⠐⠀⠀⡟⣿⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢸⠀⣿⢸⣿⠇⣿⠀⠀⣄⠳⠉⠀⠀⠀⠀⡆⢜⠸⠁⣼⠇⠀⠇⠟⢀⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⠛⠻⠿⣴⣤⣀⠀⠉⠛⡟⢿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿ ⣿⢸⠁⣿⠹⣿⡏⣿⠘⠀⠀⠀⡀⢦⠓⠈⠀⠀⡀⣇⡿⠀⡇⠀⡀⣸⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⠀⡀⣌⢶⠛⠿⣿⣿⣿⣾⣠⢀⠁⠉⡉⣿⣸⣇⣿⣽⣿⣿ ⣿⣿⣾⣠⣆⣷⢽⣧⡾⠘⠀⠀⠀⠀⠀⣄⠳⠀⠀⠀⣇⠈⡇⠘⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣤⠀⠀⣳⠉⠀⠀⣀⣤⣷⣿⢀⠀⠟⣴⣀⣀⣇⢸⣇⣿⣿⣿⣶ ⣿⣠⠀⠀⠀⠀⣆⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⡝⣽⢿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠚⠛⠙⡀⣄⠦⠒⠀⠀⣷⠈⠀⣿⠛⠿⠷⡟⢹⡿⣾⣠⢀⠀ ⢠⠀⠀⠀⠀⠀⠀⡄⣿⣿⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣸⠀⠀⠀⣉⣿⠾⠓⠛⠉⠉⡄⢻⠀⣇⣻⠀⠀⣿⣾⣠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠉⡟⣠⣏⣿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⢼⠤⣤⣦⣻⠉⠀⠀⠀⣇⣿⣿⣿⢿⡿⣻⠈⡇⣿⠙⠀⠉⠛⠀⠀ ⠀⠀⠋⠾⣶⣿⣤⣤⡅⣿⣴⣤⣷⣯⠳⠈⠀⠀⠀⠀⠀⠀⠀⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡏⣢⠀⠀⠀⠀⠀⡀⢷⠈⠋⡾⢠⠀⡀⣷⡘⣄⢷⡟⣿⣴⣀⢀⢄⠢⠔ ⠋⣴⣷⢿⠈⣿⠾⠶⣿⢈⠀⠀⠀⡀⢤⣷⠻⠑⠈⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢰⠇⣸⠀⠀⠀⠀⠆⠀⠀⡇⣿⢀⠀⠀⠀⠀⡇⢸⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠄⡦⣦⣴⠰⠀⡖⢷⠘⠀⠀⠀⠀⠀⣀⣶⣷⠯⠙⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠁⡼⠠⣀⣄⣠⢀⠀⠀⠁⡾⢠⠀⠀⠀⠋⠟⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⣧⠹⠀⠀⠀⠀⠀⠀⠀⣀⢦⢻⠈⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⡟⢻⠛⠉⠉⠉⠉⠚⠴⣠⠀⠀⠁⠛⡴⣠⠀⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠻⠈⠀⠀⠀⠀⠀⠀⠀⢄⣧⢯⢿⠻⠛⠛⠛⠉⠈⠀⠀⡆⢠⡏⣰⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⡴⣀⢀⠀⠀⠋⡾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛ ⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡍⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⣾⣿⢉⡁⣀⣿⣽⠶⠹⠟⢹⠛⠛⠛⠚⠶⠶⡶⣤⣶⣰⣷⣭⢭⠤⠿⣿⣀⠀⠀⠀⠀⠀⠀⠁⠋⠖⡶⣭⢿ ⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡤⣿⠙⠀⠀⠀⠀⠀⠁⠘⠀⠀⡀⡄⣿⡈⠀⠩⣎⢻⡇⣺⠀⠉⣿⠛⠒⠒⠒⠖⠶⠶⠶⠶⡲⣖⣿⣹⣌⣤⣤⣤⣤⣤⣤⣀⢀⠁⠋⠖⣤⢀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⣦⠻⠊⠙⠉⠖⣠⠀⠀⠀⠀⠄⡞⣿⠘⡀⢧⣆⠿⣿⡾⣠⢀⠀⠀⠀⠀⠀⠀⠉⠈⡆⠸⠀⠀⣀⣄⢶⠿⠾⠶⠴⠤⡤⣀⣀⠀⠀⠀⠀ ⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠨⠁⠉⠛⣿⣿⣙⢀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢷⠀⡃⠀⣿⣸⠀⠁⠛⠛⠾⠤⡤⣠⣀⣀⣀⣋⢿⠿⠙⠀⠀⠀⡀⢷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣻⠀⠀⠀⠀⠀⠀⠀⠉⠋⠟⣷⣈⣄⣤⣤⣦⣶⠿⠹⠀⠀⠀⠀⠀⠀⠀⣀⡆⠸⡀⠇⣼⣧⠟⣿⣾⣿⣿⠸⠀⠀⠀⠀⠁⣿⠀⡀⣧⠀⠀⠀⠀⡀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠘⠀⠀⠀⠀⢀⡃⡿⣿⣴⢀⠀⠀⠀⠉⠊⠖⡀⣦⢿⠘⠀⠀⠀⠀⠀⠀⢷⢹⡏⣶⢀⠀⣿⢸⣆⣹⣟⢠⠀⠀⠀⠃⡞⣰⠀⠀⡇⠻⠈⠀⠀⠀⣇⢸⠀⠀⠀⠀⠀⠀⠀⠁ ⣿⣿⣿⠸⠀⠀⠁⠿⣿⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣄⣧⠹⠉⠚⡠⠀⠙⡟⣤⢀⠀⠀⠀⣿⢿⠞⣠⠏⠠⠀⠀⠋⣳⠉⠀⣍⣿⣿⣠⢧⠀⠁⠀⡇⢿⠀⠀⠀⠀⠀⠀⠀⡟ ⣿⣿⣿⢿⠝⠻⠟⣿⣴⠀⠀⠀⠀⠀⠀⠀⠉⠁⠋⠛⠶⠴⣤⣤⣶⠻⠖⡴⣠⢀⠀⠀⠀⠀⠀⢻⣿⣿⣾⠀⠀⠀⠏⣻⢻⡛⣾⣿⣿⣸⠀⡁⢻⠛⠛⡟⣿⠀⠀⠀⠀⠀⠀⠁⣿ ⣿⣿⣿⣿⣿⡿⣷⣰⠀⠀⠀⠀⠀⠈⠭⠟⠿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡈⣀⢤⠤⠠⠤⣤⣠⣄⠳⠈⠀⡁⢿⠛⡴⢀⠀⠏⠉⣿⠀⠀⠀⠀⠀⠀⡟⣿ ⣰⣄⣿⣿⣷⣾⢠⠆⠠⠀⠀⡉⠟⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠻⠋⠈⠀⠀⠀⠀⠁⠟⣠⣀⣀⣟⣠⢤⠶⠿⣶⣠⢀⠀⠀⠀⠀⠀⠇⣿⣾ ⠻⠙⠀⠀⡪⣮⠘⠀⠁⠟⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠳⠙⠉⠀⠀⡄⢤⠲⠖⡥⣉⢻⠚⡠⡇⢸⠀⠀⠀⠀⠀⠀⠀⡿⣿⢠ ⢀⠀⢄⠑⠀⣅⣿⠿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣄⣤⣤⣤⣤⣤⣤⣀⣀⣦⠶⡶⢀⠀⠀⠀⠀⠀⠀⡏⣿⣸⠀

⠀⠀⠉⠉⠀⠀⠀⠀⠀⠻⡛⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⣹⣛⣟⣤⣴⣥⢿⡿⣿⢾⠀⣤⠻⡤⢀⠉⠉⠉⠀⠟⠿⠿⠺⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠟⠿⠿⠿⠿⠾⠶⠶⠛⠉⠀⠀⠀⠀ ⢊⠒⣔⠤⠤⡠⣀⣤⣦⣿⣿⠻⠋⣼⠀⠇⣿⣿⣄⣿⣿⣿⣿⢀⠀⣧⠸⠀⠀⠀⠀⠀⠃⡾⣀⠁⠋⠖⣤⣀⠃⡾⣶⠀⡷⣿⢿⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣶⣤⣀⠀⠀⣿⣿⣼⠋⣿⣿⣿⢠⠀⠀⡀⢻⠛⠞⠷⠿⠿⠶⢶⠿⣨⣶⣿⢺⠀⠉⢍⠨⠀⠉⠉⠈⢷⠈⠁ ⠳⠈⠀⠀⠀⠉⠛⠟⠿⡿⠿⠿⠿⠿⡿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⣇⢹⠏⣶⣠⠀⠗⠾⡰⣀⢦⠘⠀⡦⣴⣤⢀⡉⣏⣿⣭⡏⣿⢸ ⠐⡀⣿⣴⣀⣀⣀⣤⣦⣿⣿⣿⣿⣾⣶⣤⣤⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢘⡆⣶⢿⠀⠟⠾⠑⡉⢛⠖⠴⣤⣤⣃⣴⣘⣈⣀⣇⣹⣿ ⠀⡿⢀⠀⠀⠀⠀⠀⠀⡀⣆⣻⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣶⣦⣿⣶⣿⣿⣿⣿⣽⣿⢶⠶⠒⡶⣴⣇⣿⡿⢘⢹⠀⡁⣿⣿ ⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⠈⠙⠀⠀⠀⠀⠀⠀⠀⠇⣰⢀⠀⠁⠏⣰⠀⡀⣹⠀⠀⡁⣛⣛⣭⢭⠭⣿⣿⣿⣶⢠⣇⠈⡙⣧⣿ ⣧⣿⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⡆⠀⠀⠀⠉⠙⠏⠿⡙⢩⠋⠟⣶⣠⠀⠀⠀⣧⠈⠋⡼⢀⠀⠀⠀⠀⣀⣀⣄⢦⠻⡈⢻⣟⡇⣿ ⡇⣿⣿⣿⠻⠙⠈⠀⠀⠀⠁⠋⣴⠀⠀⠀⠃⡿⣽⢈⠈⠁⡟⣹⢈⠀⠀⠀⠀⠀⠀⡇⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⣿⣾⡟⣿ ⡇⡀⣿⣿⣿⣾⣤⣤⣤⣥⣯⢛⠛⠈⠀⠏⣼⣳⣹⣇⣀⣿⢛⣶⢠⠀⠀⠀⠀⠀⠀⣿⢀⠀⠀⠀⠀⠙⠀⠀⠀⠁⠋⠞⣠⠁⣿⢫⣿⣼ ⡇⠀⣼⣷⣿⢸⠀⠀⠖⣠⢁⠞⡡⢯⠷⣸⠀⠀⣄⣤⠲⣶⢀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠻⠉⠉⠋⠞⣤⢤⠤⣤⣠⢀⠀⠋⡾⢃⣿⣸⠀ ⡇⠀⢸⡀⣀⢦⠳⠛⠉⠉⡋⢿⢥⣻⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⣈⣆⠻⠈⠀⠀⠀⠀⠀⠀⠀⢁⠋⣿⢀⢸⠀ ⡇⠀⢸⠀⠀⠀⠀⠀⡀⣀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⣄⢦⠲⠛⠛⠛⠞⠴⣤⢸⡇⠀⢸⠀ ⡇⠀⢸⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⠀

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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⣤⣠⣀⣀⣀⣤⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣤⣤⣤⣤⣤⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣷⣿⣿⣿⣿⣾⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠻⠈⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⠁⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⡀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣀⠀⠇⣴⣶⣷⣿⣿⣿⣿⡘⡀⣄⠸⠀⠀⠉⠛⠛⠚⠶⠶⠲⠒⠛⡟⣿⠈⠀⠀⡄⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡾⣠⣀⣀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣀⠀⠀⠀⣄⣶⣷⣿⢻⠀⠀⣵⠟⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⢦⠳⠙⡊⠹⠀⠀⠀⠀⠀⠀⠁⠛⡾⣤⢀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡆⣿⠹⠁⣿⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⠀⡀⣄⠷⠿⠻⠛⠛⠖⡤⣠⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠐⣠⠇⣿⣿⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠀⠀⠀⣄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡿⣿⣿⣿⣾⣴⣠⣁⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠁⠟⡿⣿⣿⣴⣀⠀⠀⠁⠾⣤⣤⣤⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣿⣿⣿⡉⠀⠁⠋⠞⠿⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⠀⠀⠀⠀⠉⠉⠉⠈⠀⠀⡀⣿⣟⠙⠈⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣠⣀⣀⠠⠀⠀⠀⠀⠀⠇ ⠒⠒⠶⣶⣶⣶⣶⣶⠵⣿⣿⣿⣸⡀⢸⠇⣾⣄⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡾⣿⠀⠀⡀⣀⣤⣿⣤⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂ ⠀⠀⠀⣀⠀⠤⣤⣠⣀⣀⢀⡇⢸⠀⢿⣼⠀⠇⢰⠁⠋⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡶⣠⠀⣇⢘⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⡇⢻⠀⣿⠀⠁⣿⡶⣠⢀⠋⣾⠀⠀⠀⠀⠀⠀⠀⠀⠋⠞⣤⢀⠀⠀⠀⡇⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣄⠳⠮⠐⡒⢰⠉⠞⣶⢒⠓⠈⠀⠀⠉⠋⠚⠴⣠⢀⠀⠀⠀⠉⠉⠉⡟⢈⠐⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣄⢦⠒⠛⣲⠒⠒⠒⠒⣴⣥⣾⣴⣠⣄⣬⣭⣭⣭⣩⣉⣋⣴⣠⣀⣧⠹⠈⠀⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠛⠛⠛⠿⠿⡿ ⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣸⠀⠀⠀⠀⠀⠏⣼⠀⠁⠞⣤⣀⣀⣀⣀⣀⣋⠞⡴⣤⢦⡿⣾⢀⠀⠀⣿⠀⠀⠀⠀⠁⠟⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠛⠟⠿⠿⢿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣴⡦⣘⠀⠀⠀⠀⠀⠋⡴⣀⠀⠀⠀⠀⡏⢠⠀⠀⠀⣿⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣶⣤⣤⣤⣶⣷⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⠀⠀⠂⠒⠉⠀⢿⠉⠉⢶⠀⠀⠋⠖⡤⢀⠀⠀⠀⠀⠀⠋⣰⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⡀⣤⣦⣿ ⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⠀⠀⠀⠀⣧⣈⠀⠀⠀⡀⢦⣝⣷⢙⠈⠀⡷⢀⠀⠀⠀⠀⠀⠉⠋⡶⢠⠀⠀⠀⠀⠃⣿⠀⠀⠀⠀⡇⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄ ⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⠀⠀⠀⠀⡀⢷⠈⠀⠀⠀⠀⡀⠀⡀⣀⣤⡤⢤⠤⠤⠤⡤⣋⣾⢠⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⡇⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡇⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡀⣦⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⡿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡆⣶⣿⣿⣿⣿⠐⠀⠀⠂⠒⠒⠑⠀⣀⢤⠲⠒⠛⠛⠛⠚⠖⡴⣤⣀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⣨⣍⣟⣿⣿⣞⡀⣑⣌⣁⣏⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠿ ⠀⠀⠀⠀⠀⠀⠃⠟⣿⣿⣿⣿⢘⡀⣙⣔⣥⣦⠠⠁⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠁⣽⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⢻⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠉⠛⣿

⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⠀⠀⠀⠀⠀⠁⠁⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡤⢱⠀⠀⠀⠀⠀⠂⡇⠀⡚⠰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⡷⠈⠀⠀⠀⠀⢤⠀⠏⢩⠀⠀⠀⠀⠄⠀⠀⠀ ⠀⠀⠀⠀⠠⠀⠀⠀⠀⠊⠐⠤⣄⢳⠀⣍⠀⠓⠐⠂⢀⠀⢄⠢⠉⠀⠀⠀⠀⠀ ⢀⠢⠓⠐⡀⠐⠊⠔⣀⠀⠀⠀⠀⡘⠡⣆⠀⡀⠁⢀⠀⠀⠀⠀⠀⣀⠣⠒⠤⡠ ⠀⠀⠀⣀⠄⣢⠀⠀⠀⠀⠀⠀⠀⡄⠐⢠⠐⠤⢠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⠤⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⠄⠒⠀⠉⠂⠚⠐⠤⠦⠈⠦⠙⠀⠀⠁⠋⠔⡃⣠⢉⠤⠒⠒⠒⠐⠀⠀ ⣀⠄⠤⠀⠂⠒⠒⠒⡒⠒⠒⠒⢓⠀⡄⠀⠀⠀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠄⠠⠁⠊⠀⠀⠀⠒⠒⠐⠀⡋⠣⠐⠥⠭⠩⠚⠝⣸⢀⠀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠕⣔⠀⠀⠀⠀⠊⡠⠀⠐⠀⡐⡄⠀⠀⢧⡀⢏⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡳⠼⠀⠞⢥⠠⠄⡝⠑⠉⠲⡫⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣠⠀⠀⠀⡰⣿⣠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⣿⣿⣶⣤⢀⠀⠀⣷⣿⣿⣿⠀⠀⠀⠀⠁⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣾⢀⠀⠀⠀⠁⠈⡇⣿⣿⣷⠻⠈⠀⠿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⢹⠀⠀⠀⠀⡇⢻⡿⣿⣸⡇⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣷⠘⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣷⠻⠛⠛⡿⣿⣿⣾⣤⢀⠀⠀⡄⣷⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⣿⣴⣤⠿⠀⠀⠀⠀⠀⡀⣿⣽⣿⠽⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣿⢻⠙⠀⡄⠳⠀⠀⠀⠁⠈⣿⣤⢶⣿⢷⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠋⠟⡿⣾⣠⠋⡴⣯⠻⠈⡀⠸⠀⠀⠀⠀⣧⢿⠻⡙⣈⣷⢿⠙⠀⠀⠀ ⠀⠀⠋⠿⣿⣿⣿⣿⢴⣩⠚⡤⣉⣾⢡⠈⣄⠒⠀⠀⠀⠀⢿⢸⡀⣀⢤⣷⣿⠿⠙⠀ ⠁⠟⣿⣿⣿⣿⣺⢐⣤⣤⣡⣏⣼⢁⠋⢉⠈⠀⠀⠀⠀⠀⣦⢷⠙⠈⠁⠛⣿⣿⣿⢸ ⡆⣿⣿⣿⣿⣿⢉⠉⠉⠉⠉⡟⣾⣠⠀⠀⠀⡀⣄⡷⣈⠀⠀⠀⣇⣛⠟⣿⣿⣷⣿⢠ ⠀⣤⣤⣶⠀⡀⣄⣧⣿⣿⠻⡟⢹⠀⠀⠛⠀⠀⠀⡞⢀⠀⠋⠛⡾⣠⣀⢀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⡆⣿⣴⣤⣿⣿⢿⠻⣹⠉⠋⣿⢿⠴⡠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣆⠳⠛⡿⣿⣿⣿⣿⣿⣶⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣾⣠⢉⣉⠉⣉⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣤⣀⢀⡀⣀⣀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢹⣄⠻⠉⠈⠀⠉⠋⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠘⠀⣀⣀⣀⣀⣏⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠲⠓⠛⠖⡴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠹⠒⢦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠃⢰⠚⠉⠉⠉⢣⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⡀⠸⢤⣤⣀⣠⡼⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⣒⣦⡤⠤⠽⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣏⡀⢰⡎⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⠉⠀⢹⢸⡇⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠀⠀⠀⣾⠘⡇⣯⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣗⣀⠀⢠⡇⢰⣿⢹⠀⠀⠀⠀ ⠀⠀⠀⢀⠞⠉⠉⠛⠋⠀⠘⡟⣼⡄⠀⠀⠀ ⠀⠀⣰⠃⠀⠀⡀⠀⠀⠀⠀⠑⠛⠓⠤⡀⠀ ⠀⠀⣯⠃⠀⣸⠃⠀⠀⠀⠀⣰⣇⣠⡶⣸⡆ ⢀⣠⡼⠷⣶⡿⢷⣤⣤⡴⠞⠋⢁⣠⠶⠋⠀ ⠘⠷⢥⣼⣧⣄⣀⣀⣀⡤⠴⠚⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠄⠂⠄⠄⠂⠀⠠⠀⠈⠛⠛⠛⠛⠙⠋⠕⣺⣶⣷⣿⣖⠱⠀⠀⠀⠀⠀⡄⢀⣧ ⠊⠒⠓⠻⠛⠛⠛⠋⡿⢉⠛⠛⠛⣙⣿⣹⠀⠀⠊⢠⠁⡞⣤⣤⢦⠙⠀⠀⠀⡇ ⠀⢄⠦⠶⠖⣢⣟⣴⣁⢉⠉⠉⠉⡉⣄⣤⣿⣹⣧⣿⣶⣴⣤⢦⠷⡛⢿⠉⠉⠉ ⠀⠀⠀⠀⠀⠇⢿⡿⣾⣠⣀⣀⣀⣤⣦⢷⠿⣿⣿⣰⠁⠉⠛⠛⠛⡟⢿⠘⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣴⣠⣀⣀⣀⣦⣿⢸⠀⠀ ⠀⠀⠀⠀⠀⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⣼⢀⠀⠀⠀⠀⠀⠀⡎⢀⠀⠀ ⠀⠀⠀⠀⠀⡿⣿⢻⠀⠀⠀⠀⠂⠈⠀⠀⠀⡜⠀⠀⠀⠉⠀⠀⠁⠔⢀⠀⠀⠀ ⠀⠀⠀⠀⡇⣿⣽⣭⢄⠢⠉⠀⢤⢠⠉⠛⡿⠈⠀⠀⡀⠁⠊⠔⢠⡇⠀⠀⠀⠀ ⠀⠀⠀⠃⡠⣀⢀⡀⣀⢤⠘⣀⣀⣀⡀⣷⣰⣀⢁⠉⣈⢂⠐⠤⠀⡏⠐⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡏⣉⣿⠪⠃⠛⠒⠶⡰⣉⠟⣿⢿⠘⠀ ⠛⠈⠀⠀⢍⠳⠚⠛⠌⡠⠀⠀⠀⠀⠏⢿⠿⠴⢀⠀⠙⣳⢻⢯⠐⠀⢄⡑⣿⠘ ⡉⣿⠛⡟⢉⠉⣈⠤⡛⠲⠒⠛⠿⣿⣭⠶⢸⠓⠿⠿⣷⠴⠾⢴⠴⠗⠾⠀⣾⢻ ⣠⣀⣿⣀⣀⣅⣿⣿⣽⣦⢿⣿⣿⠈⣀⣥⢦⡈⡀⢿⢶⡶⠏⠾⠿⢩⠉⡟⢀⣷ ⠀⠀⣷⢸⠀⡟⢰⡀⣷⢹⡄⣿⣶⣶⣶⣶⣶⣶⢶⠷⠠⠋⠛⠻⢻⠙⡘⣯⠀⡇ ⠀⠀⡇⢸⠀⣿⠀⠀⡀⣿⠈⣯⢸⠀⠀⠀⠀⠀⠀⡀⡦⠻⢹⠉⠉⡂⠒⣿⠀⡆

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⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⢁⣀⣀⣀⡈⠉⠛⢿⡿⠿⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠏⢀⣴⣾⣿⣿⣿⣿⣿⡟⠃⢀⣀⣤⣤⣄⠉⢿⣿ ⣿⣿⣿⣿⣿⡏⠀⣾⣿⣿⣿⣿⣿⣿⠏⠀⣴⣿⣿⣿⣯⣻⣧⠀⢻ ⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠈ ⣿⣿⣿⣿⡏⠀⣼⣿⣿⣿⣿⣿⣿⣿⣧⠀⠹⢿⣿⣿⣿⡿⠟⠀⣼ ⣿⣿⣿⡿⠇⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡈⠉⠀⠀⣴⣿⣿ ⣿⡿⠁⣀⢠⢤⣤⠀⠀⠉⢀⠀⠀⠈⠉⠻⢿⣿⣿⣿⡇⠀⣿⣿⣿ ⡟⠀⣴⣽⣷⣷⠆⠀⣴⣾⣿⣔⡳⢦⡄⣄⣠⣿⣿⣿⡇⠀⣿⣿⣿ ⠀⢰⣿⣿⣿⠇⠀⣼⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⠀⢻⣿⣿ ⠀⠸⣾⣿⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿ ⣧⠀⠻⢿⣿⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿ ⣿⣷⣤⣀⣈⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠟⠙⣿⣿⣿⡏⠀⣼⣿⣿ ⣿⣿⣿⣿⣿⡇⠀⣄⠀⠙⠛⠿⠿⠛⠁⢀⣼⣿⣿⣿⡇⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⡀⠘⠿⠶⠀⢀⣤⣤⡀⠙⢿⣿⣿⡿⠁⢰⣿⣿⣿ ⢻⣿⣿⣿⣿⣿⣿⣦⣤⣤⣴⣿⣿⣿⣷⣄⣀⠈⠁⣀⣠⣿⣿⣿⣿ ⣹⣿⣿⣿⡿⢋⣩⣬⣩⣿⠃⣿⣿⣿⣿⢸⣿⡿⢋⣡⣬⣩⣿⣿⣿ ⡗⣿⣿⣿⣧⣈⣛⠛⠻⣿⠀⣿⣿⣿⡿⢸⣿⣧⣈⣛⠛⠻⣿⣿⣿ ⣿⣿⣿⣿⠹⣿⣿⡿⠂⣿⣇⠸⣿⣿⠃⣼⣿⠻⣿⣿⡿⠀⣿⣿⣿ ⣿⣿⣿⣿⣶⣤⣤⣴⣾⣿⣿⣶⣤⣤⣾⣿⣿⣶⣤⣤⣴⣾⣿⣿⣿

ඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞ

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡑⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣣⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠱⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⠀ ⠀⠀⠀⠀⢀⣀⣀⣸⢧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣩⡤⠶⠶⠶⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⡇ ⠀⠀⠀⣰⣫⡏⠳⣏⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣄⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀⡅⡇ ⠀⠀⢰⡇⣾⡇⠀⠙⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⠿⠛⠻⢿⣶⣤⣍⡙⢿⣿⣷⣤⣾⡇⣼⣆⣴⣷⣿⣿⡇⡇ ⠀⠀⢸⡀⡿⠁⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣯⠴⢲⣶⣶⣶⣾⣿⣿⣿⣷⠹⣿⣿⠟⢰⣿⣿⣿⠿⣿⣿⣿⠁ ⠀⠀⠈⡇⢷⣾⣿⡿⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⣌⠳⣼⣿⣿⣿⣻⣿⣿⣿⣿⡇⠈⠁⢰⣿⣿⣿⣿⣶⣾⣿⣿⠀ ⠀⠀⠀⣷⠘⠿⣿⡥⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠌⠉⣿⣿⣿⣿⣿⣿⠟⠃⠀⢀⡿⣿⣿⣿⣿⣿⣿⣿⡞⠀ ⠀⠀⠀⢸⡇⠀⠹⠗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠟⠉⠉⠀⠀⠀⠈⢃⣿⣿⣿⣿⣿⣿⡻⠀⠀ ⠀⠀⠀⠈⢧⠀⠀⠏⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠁⠀⠀ ⠀⠀⠀⠀⠈⢳⠶⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⠀⠀⠊⠁⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣼⣿⣀⡰⠀⠀⣤⣄⠀⠀⠀⠀⢹⣿⣿⣿⣿⢻⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⢠⣤⣶⣤⣀⠀⢀⣶⣶⣶⣿⣿⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠻⣿⣿⣥⣤⣯⣥⣾⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠠⠀⠀⠀⠀⠈⣿⣿⣼⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⣠⣰⣄⡀⠀⢀⣀⣀⣛⣟⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠾⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠠⣄⣉⣉⣻⣿⣿⣿⣿⣿⣿⡟⠧⢄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠅⠀⠀⠀⠀⠘⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠉⠓⠢⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⡄⠀⠀⢀⡑⠢⠄

⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ 𐙚 -`♡´-˙✧˖°📷 ༘ ⋆｡˚˙✧˖°📷 ༘ ⋆｡˚˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆˚‧｡⋆🌻⋆｡‧˚⛷🧚‍♀️🛖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣀⣀⣠⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠛⠋⠉⠉⠛⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣀⡤⣤⢤⡤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⣀⣤⣶⠿⠛⠋⠁⠁⠀⠀⠀⠉⠛⣯⣳⡀⠀⠀⠀⠀⠀⠀⢠⡿⠃ ⠀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⠀⠀⠀⠀⠀⣠⡿⠃⠀ ⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⢹⡆⠀⠀⢸⣿⠀⠀⠀⠀⢠⡿⠁⠀⠀ ⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⢀⣮⠏⠀⠀⠀⠀⠘⣷⡀⠀⠀ ⠀⠙⠿⣶⣤⣀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀ ⠀⠀⠀⠀⠉⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣄⣀⣀⣤⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠈⠉⠉⠙⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⣠⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢺⠋⠀⠉⠛⠞⠁⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⢾⢹⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⠀⣠⠴⠒⠋⠉⠙⠓⠒⠤⣄⠤⠷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡴⢴⣿⣣⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠸⣏⠀⠀⠀⠀⠀⠀⠀ ⣤⣴⣷⠞⣼⠁⠀⠀⠀⠀⠀⣀⣠⠤⠤⢤⣀⡀⠀⠈⢧⠀⠀⠀⠀⠀⠀ ⠈⢛⡟⢺⠇⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠈⠑⢆⠈⡆⠀⠀⠀⠀⠀ ⠀⡞⠀⡞⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⡇⢀⠀⠀⠀⠀ ⠀⡇⠀⡇⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣿⠀⠀⠀⠀ ⠀⠇⠀⡇⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣏⣹⣦⡀⠀⠀ ⠀⡆⠀⡇⠀⠀⠀⠀⠀⠀⠉⠢⠤⣀⣀⣀⣀⠤⠞⠁⠀⣏⢳⣿⠇⠀⠀ ⠀⣇⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢒⡶⠖⢤ ⠀⠹⡄⢸⡀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠢⢄⡀⠀⠀⠀⠀⠀⡏⠀⠀⢸ ⠀⠀⠙⠲⡷⢦⣀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠙⣖⠒⠦⠤⢼⠀⠀⢀⡟ ⠀⠀⠀⠙⠳⣰⣍⠀⠀⡀⠘⠁⠀⠀⠀⠀⠀⠀⢸⠢⠤⣀⣸⣀⣀⡞⠁ ⠀⠀⠀⠀⠀⠀⠸⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠈⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠙⠒⠒⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣷⣶⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠁⣰⣿⣿⣿⡿⠿⠻⠿⣿⣿⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠏⠀⣴⣿⣿⣿⠉⠀⠀⠀⠀⠀⠈⢻⣿⣿⣇⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣼⣿⣿⡏⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀ ⠀⠀⢰⣿⣿⡿⣿⣿⣿⡇⠀⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⠁⠀⠀ ⠀⠀⣿⣿⣿⠁⣿⣿⣿⡇⠀⠀⠻⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⢰⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⢸⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⢉⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣇⠀⣿⣿⣿⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⢸⣿⣿⣿⣷⣦⠀⠀⠀ ⠀⠀⢻⣿⣿⣶⣿⣿⣿⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⡀⠀⠉⠉⠻⣿⣿⡇⠀⠀ ⠀⠀⠀⠛⠿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠈⠹⣿⣿⣇⣀⠀⣠⣾⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣦⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠛⠋⠉⠉⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠞⠉⠉⠁⠀⠀⠀⠀⠉⠉⠙⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⣯⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣤⡀⠀⠀⠀⠀⠀ ⣶⡄⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠋⠉⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠢⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀ ⢹⣷⢤⡤⠶⣾⣿⠻⠿⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀ ⠀⠉⠛⠛⠉⠉⠉⠉⠓⢦⡉⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠹⡄⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠉⠓⠶⢤⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⢻⡀⠀⠀⠀⠀⢰⢏⣠⡤⣶⡒⢲⣶⠦⣤⣤⣍⡉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⢧⡀⠀⠀⠐⣿⠋⣠⡟⢹⣷⡞⠉⣷⡾⠛⣦⣹⣿⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣌⠳⣄⡀⠀⠙⢿⣿⣧⠟⣿⣧⡾⣿⣦⡾⡟⢀⣼⣷⠉⣻⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣮⣝⠒⠶⣾⡿⢿⣶⣿⣥⣄⣈⡉⠀⠹⠟⠋⣧⡴⢿⠋⣻⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢻⢿⣤⣦⣀⠀⠀⠈⠙⠛⢦⣤⡀⠀⠀⠸⣶⣿⢖⣻⣧⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⣠⡏⠈⠉⠲⢦⣀⣀⢹⣌⣿⣦⡀⠀⠉⠿⠛⠛⢾⡆⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠻⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢻⣿⣿⠙⣇⠀⠀⠀⠀⠙⢯⣫⣏⣯⣎⢷⡀⠀⠀⠀⠀⣼⣴⣶⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⢀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⣿⠈⢻⣿⣿⢻⣇⢀⣤⠀⣠⣼⡟⢻⡛⠉⠉⣣⡀⠀⡀⣰⣿⠁⣿⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⢀⣾⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠹⣤⡈⠳⠶⠛⣇⠀⣿⡟⢻⣷⠛⢿⣷⡟⣿⣠⠟⣿⣷⡾⣿⣿⡏⢠⣿⡦⠀⠀⠀⣀⣴⠋⠀⠀⣰⡿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠻⠯⣗⣶⠤⣌⣏⣁⣷⡞⠹⠦⠜⠛⠶⠟⢻⣄⣽⣏⣿⣿⠟⡇⣼⣿⣧⣄⠀⠀⣿⠁⠀⢀⣼⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠙⠛⠓⠿⢿⣿⣿⣿⣿⣶⣶⣦⡤⠿⠼⠟⠛⠋⠀⠙⢻⣧⣿⣿⠀⢠⣼⠂⠀⣼⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⣾⠁⠀⢸⡧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣸⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⠞⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⢦⡤⢤⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⣀⡼⠁⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠦⠤⠤⠤⠤⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

.　 +⠀ ⠀ ⠀˚⠀ ⣴⠟⠉⠉⠛⢦⡀⢀⣴⠛⠉⠈⠙⠻⣄ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠹⣦ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆ ⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃ ⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⣠⡴⠛ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⠶⠋ ⠀⠀⠀+. *

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⣴⠞⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⣷⠀⠀⠀⢀⡾⠃⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡇⠀⠹⢦⡤⢤⣄⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣾⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡴⠞⠋⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢧⣄⡀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠇⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⢀⣀⣀⣀⣱⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣤⠶⠋⠀⠈⠉⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠘⠳⠛⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⠃⠐⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠐⠀⠀⠂⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⢀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠊⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠋⠙⣧⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠻⡧⠀⠀⢻⣄⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠁⠀⠀⠘⠛⠳⢦⣀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⣤⣤⣤⡄⠀⢹⡆⠀⠀⠀⣽⡷⣿⡋⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠸⣇⡀⣀⡤⠀⢸⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠈⠛⠉⠀⣠⠞⠛⢳⡶⢤⣤⣤⣴⡶⠶⠶⠚⠛⢩⡿⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢻⡁⠀⠀⠀⠙⠳⠶⠖⠛⠀⠀⠀⠀⣴⣋⣠⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⠙⠳⢶⡶⠶⠶⠞⣫⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡞⢻⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠛⠛⠶⠶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠉⠉⠀⠈⠳⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂⠀⠀⠀⣤⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⠶⢤⣀⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠛⠋⠉⠉⠉⠉⠉⡿⠛⠻⠷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉⠀⠙⣦⣀⣀⣀⣠⡤⠴⡿⣄⡀⠀⠀⠉⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⣰⠋⢧⠀⠀⠀⠀⠀⡇⠀⠉⠙⠓⠒⡶⢯⣙⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⢀⠞⠁⠀⠈⣳⡤⠤⠴⠚⣟⠛⠒⠒⠒⣺⠳⢤⣀⣉⣻⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠶⠶⣤⣾⡁⠀⠀⢀⡜⠉⣧⣠⣤⣴⣾⣶⠶⠶⠶⠷⣶⣶⣶⣬⣭⣙⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⣿⠀⠙⢲⣞⠁⣠⡾⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⡇⠀⠀⢸⠏⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀ ⠀⠀⠀⢀⣠⣴⣶⣶⣦⣾⠃⠀⠀⢠⡇⠀⠀⣸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄ ⠀⠀⣠⡿⠿⡄⠀⠀⠈⣿⡀⠀⠀⡼⠀⠀⣴⣃⣤⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⣰⡿⠁⠀⠹⡄⠀⠀⣿⠿⣶⣴⡷⠒⠋⠻⡄⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃ ⢀⣿⠁⠀⠀⠀⢹⣀⣴⡏⠀⠀⠙⢿⣦⠀⠀⢹⡄⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠋⠀ ⢸⡿⢧⠀⠀⢀⡼⠯⣼⡇⠀⠀⠀⠀⠙⣷⡄⠀⣇⡤⠞⠉⠻⢷⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣶⣿⣿⣿⠀⠀ ⣿⡇⠈⢧⣠⠎⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⣿⡞⠛⠢⣄⠀⣠⠏⠈⠉⡿⠛⠛⠛⢻⠛⠛⠛⠛⢿⠉⠁⣴⠟⠁⣿⠀⠀ ⣿⠃⠀⡼⠧⣄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠘⣶⣁⡀⠀⡼⠁⢀⡀⠀⠘⡇⣀⣠⣤⣬⣷⣾⠏⠀⠀⣿⠀⠀ ⣿⣀⡞⠁⠀⠈⢣⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⡼⠁⠀⠉⣹⠛⠉⠉⡉⠉⢙⣏⠁⠀⠀⠀⣼⡏⠀⠀⠀⣿⠀⠀ ⣿⡿⣄⠀⠀⠀⠀⢳⣼⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⡾⠁⠀⠀⢀⡇⢠⠂⣜⣠⣤⠸⡟⢣⠀⠀⢰⡿⠀⠀⠀⠀⣿⠀⠀ ⣿⡇⠈⠳⡄⠀⠀⣨⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⠒⠲⢤⣸⠀⣸⣄⣿⣿⣿⣷⣿⣞⣠⣤⣿⠇⠀⠀⠀⠀⣿⠀⠀ ⢸⣇⠀⠀⢹⡀⡰⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣹⢉⡽⣿⢿⣿⣿⣿⣿⣅⠀⠀⣿⠀⠀⠀⠀⢀⣿⠀⠀ ⠘⣿⡀⠀⠈⡿⠁⠀⢸⣷⣦⣤⣤⣄⣀⡀⠀⠀⢸⡇⠀⠀⠀⡟⠘⡅⢇⢸⣿⣿⠇⡇⡸⠀⠀⣿⠀⢀⣀⣠⣼⣿⠀⠀ ⠀⢻⣇⠀⣰⠛⠒⠦⣼⡇⠀⠀⠉⠉⠙⢻⣷⣦⣼⡏⠉⠓⠦⣿⠤⠵⠾⠾⠿⢿⣸⣯⠧⠖⠚⣿⡾⠟⠋⠉⣹⡇⠀⠀ ⠀⠈⢿⣶⠇⠀⠀⠀⢸⣿⣶⣤⣤⣤⣀⣼⣀⣈⣙⣃⡀⠀⠀⢹⡀⠀⠀⢀⣀⣀⣸⣁⣀⣀⣤⣤⣤⣶⠶⠿⣿⡇⠀⠀ ⠀⠀⠈⠻⣷⣄⠀⠀⢘⣧⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢉⡉⠉⠉⠀⠀⠀⢀⣿⠁⠀⠀ ⠀⠀⠀⠀⠈⠙⠛⠿⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠶⠶⠶⢶⡶⠿⠿⠿⠛⠋⠀⠀⢀⣀⣤⣾⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⢸⣧⣤⣤⣤⣶⣶⠶⠿⠛⠋⠁⣼⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡍⠙⠛⢿⠿⠷⠶⠶⠾⠿⠿⠟⢻⡇⠀⠀⠀⢸⡏⠉⠁⠀⣀⣀⣀⣀⣄⣀⣀⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠲⢦⣼⣀⣀⣀⣤⣤⣀⣀⡀⢸⡇⠀⠀⠀⢸⣷⠖⠚⠉⠉⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⡏⠁⠀⠀⠀⠀⠀⠈⠉⣿⠇⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣀⡇⠀⠀⠀⠀⠀⢀⣠⣾⠟⠀⠀⠀⠀⠀⠈⠻⢷⣶⣶⣶⣶⡶⠿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⡇⣿⣴⣤⣿⣼⢀⠀⡜⢀⠀⠀⠀ ⠀⠀⡷⠀⠀⠛⣿⣧⠛⡜⠀⠀⠀⠀⠀ ⠀⠀⡄⠹⠉⣿⣿⣴⣤⢿⠈⠀⠀⠀⠀ ⠀⠀⠀⡀⣯⣸⣆⠀⠀⡇⣴⠻⠀⠀⠀ ⠀⠋⠿⣾⢜⣗⠱⢀⠈⡀⢾⠢⢷⠙⠀ ⡷⣿⣽⡀⣁⣺⠄⠠⠒⠐⣄⠙⡯⣿⢰ ⡀⢀⡀⣇⢶⢻⠟⠡⠛⠂⠴⣀⢀⠀⠀ ⠀⠀⠀⡀⠥⣾⣴⣷⢈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡟⣱⢈⣉⢎⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⠐⠈⠒⢠⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠋⠴⠤⠤⠤⠓⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢦⠚⠀⠀⠃⡼⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠉⠉⠀⡀⢹⠀⠀⠁⢸⠀⠁⠀⠀⠀⠀⠀ ⠏⣰⠀⠀⡀⢿⣨⣦⠛⠟⡾⣀⠧⡿⣀⣰⣀⠧⠈ ⡆⠈⠀⠀⠀⡇⢀⠀⠀⢠⠀⠀⡷⢈⠀⠀⠀⠃⢰ ⠀⣄⠳⠉⠋⡴⠀⠀⠀⠀⠀⠀⠀⢳⠈⠉⠞⣠⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠁⠉⠈⠉⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⢧⠀⠃⡴⣠⠀⠀⡀⣀⠧⠀⠇⢠⠀⠀⠀ ⠀⠀⠀⡀⠱⡀⢦⠒⠉⠉⠈⠒⡤⠁⡴⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⢦⠑⠈⠀⠀⠀⠉⠖⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠐⠶⣿⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣇⡀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⡿⠟⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣆⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡏⠛⠷⣶⣄⣴⠟⠛⠉⠙⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⢈⣙⣁⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠾⡇⣿⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠟⠒⠛⠛⠶⠦⣤⣀⣀⣀⢾⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⣴⣿⣁⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢯⡀⣽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢼⡋⢹⡛⣷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢾⣿⣿⢷⠋⣺⠃⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠖⠒⠶⠦⢤⣄⡀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠙⣿⠛⢻⠏⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠇⠀⡾⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⠀⢀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⣤⣷⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢸⢿⣿⠀⠀⠀⠀⠀⠀ ⠀⡏⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⣾⣤⡿⢷⣄⠀⠀⠀⠀ ⠀⣧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣄⣀⣀⣀⣀⣀⣤⠴⠛⠁⠀⣿⠙⣷⣿⡇⠀⠀⠀⠀ ⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠮⠤⣤⣶⣤⡀⠀ ⠀⢹⡇⠀⢹⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⣻⡄ ⠀⠀⠻⣴⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠉⠉⠉⠳⣄⡀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⣾⠀ ⠀⠀⠀⠈⣙⡿⠿⢦⣄⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠈⢻⡙⠛⠒⠒⠶⡿⠀⠀⠀⣰⡏⠀ ⠀⠀⠀⠀⠙⠾⣆⣾⡉⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠦⣄⣀⡀⢷⡀⢀⣰⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⢻⡦⢶⣿⢷⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠈⠉⠉⠙⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⠾⠧⢤⣤⣀⣀⣀⣤⣤⠴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣅⣁⢈⣭⣿⣷⣾⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣖⣦⣤⣲⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⡿⠟⠋⠉⠻⡟⢟⡽⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⢞⢝⣍⢿⣹⡿⠳⣛⣋⣓⣩⣲⡤⡀⠀⠀⠀⠀⠀⣰⡿⣣⠟⠁⠀⠀⠀⠀⠀⠘⢑⡻⣟⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⣿⣽⡿⣿⣟⡁⠀⠀⠀⠉⠉⢻⣟⠋⠝⢓⢤⣠⡴⣶⡿⣟⣭⣓⠖⠢⣤⣀⣀⣀⣬⡶⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣹⣫⢿⡇⣃⠴⡀⣀⡠⠤⠶⠒⣺⠿⣟⢸⣯⣃⣳⡾⡲⠷⣮⣥⣼⣮⣤⣥⣾⣿⣿⣻⡿⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⠣⣿⣿⣶⣾⣿⣷⣶⡂⢩⡭⢊⣽⣿⡿⠿⠿⢿⣦⣴⣙⠈⠙⠏⠉⠋⠉⠀⠩⠀⠂⠀⢀⣤⢤⣤⣤⣂⣅⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠉⠙⠟⡟⢛⠋⡵⣻⣿⠏⠀⠀⠀⠘⢿⢯⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣀⠖⣫⠵⢏⣽⣿⣿⡧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣩⢅⡏⠀⠀⠀⠀⠀⠈⠫⣳⠄⢹⡆⠀⠀⠀⠀⣢⣴⣿⣿⣿⠟⠁⠈⢿⢿⡿⠄⠀ ⠀⠀⣰⣾⣏⣩⣉⠰⣄⠀⠀⠀⠀⣠⢖⣴⢟⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣾⣿⡀⠀⢠⣾⣿⣿⡿⠟⠁⠀⠀⠀⣸⣾⠣⠂⢀ ⠀⣰⡇⠈⠙⠤⣽⣿⣹⣷⣤⣈⣴⣩⡤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⡫⠁⠀⠀⠀⣀⣴⣾⡿⠃⠁⠀⠘ ⢰⣿⣹⡄⠀⠀⠀⠉⠛⠻⠿⠛⠋⠉⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡀⣤⡶⠁⢼⣿⠃⠀⠀⠀⠀ ⢹⡇⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⡆⠡⣬⣧⣀⡜⠁⠀⠀⠀⠀⠀ ⠀⠱⡄⢂⠣⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⠃⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠢⢀⣙⠿⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⡄⠀⠀⠀⣀⣀⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠈⠑⠊⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢿⣿⣿⡶⡤⣕⡤⠀⠂⠀ ⠀⢀⠀⣤⠔⠆⢶⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠄⠀⠀ ⠁⣠⡎⠀⣀⣠⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠀ ⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀ ⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⋆౨ৎ˚⟡˖ ࣪⋆୨୧⋆⋆ ˚｡⋆୨♡୧⋆ ˚｡⋆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣬⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⢸⠀⠀⠄⠠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇⣿⠀⠀⠀⠀⠀⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣄⣤⣤⣤⣤⣤⣧⣾⣤⣦⣶⣶⣶⣶⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⣷⣿⣿⣿⣿⣿⣶⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⣇⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣰⣀⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣶⣶⢶⠶⠶⠶⠿⡿⢿⠿⠿⠻⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⣧⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠙⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⣇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣘⣦⢻⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠿⢈⠀⠁⡟⢻⠹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⣇⢸⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣤⣀⠀⠀⣀⢤⠳⠉⠀⠀⠀⠀⠀⠀⡇⢸⠀⡄⢹⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⡇⢸⠀⠀⣿⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠈⠀⠀⡇⢸⠀⠀⣿⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⠀⡇⢻⠀⠀⣿⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⡇⣿⠀⠀⣿⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡇⣿⠀⠀⣿⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀ ⠉⠈⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠙⠉⠛⠒⠒⠒⠶⠶⠲⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡟⣿⠀⠀⣿⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣶⣶⢶⠶⠿⠿⡟⣿⠛⠛⠉⠉⠉⠈⠀⠀⠁⡿⣠⢀⠀⠀⠀⠀⠀⠀⠉⠈⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣴⠠⡇⣸⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣀⣀⣀⣤⣤⣤⣤⣷⣿⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠈⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠞⡶⢠⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⣆⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠋⠞⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣴⣶⢶⠶⠷⠿⠻⠛⠛⡿⢻⠉⠉⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢦⠶⠓⠛⠛⠟⡶⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡾⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⣇⣸⣄⣤⣬⣭⣶⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠛⠉⠉⠉⠉⠉⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢀⣀⣤⣤⣤⣤⣽⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠃⠀⠀⣸⠏⠉⠁⠀⠀⠀⠀⠈⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⡶⢶⡿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡿⠁⠀⢸⡇⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⢀⣠⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠉⢹⡿⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⡴⠛⠉⠁⠀⠀⠈⠉⠉⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣇⣠⡤⠶⠶⠶⠤⣄⣀⠀⣀⣽⣄⡀⠀⠀⠀⠀⠀ ⠈⣿⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣠⢾⣩⡵⠖⠚⠛⠓⠲⢦⣍⠻⣧⡀⠀⠙⢶⡤⠤⣄⠀ ⠀⠈⠻⠶⢾⡇⠀⠀⠀⠀⢠⣤⣄⣀⣀⡤⠄⠀⣿⠀⠀⢠⡿⠿⢷⠶⠛⠋⢻⡀⠀⠀⠈⠳⡌⢷⡀⠀⠀⠀⠀⢸⡆ ⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⢸⡇⠀⢹⡇⠀⠀⠀⡏⠀⠀⢹⣄⣠⠟⠀⠉⢳⡟⠀⠀⠀⠀⣠⠇⢸⠇⢀⣴⣀⣠⠾⠁ ⠀⠀⠀⠀⠀⢿⣄⡀⠀⣀⣼⠇⠀⠘⠷⣤⣤⣼⣃⡴⠖⠛⠉⠙⢧⣄⣀⣴⠧⠤⠴⠶⠛⣁⣴⣿⠶⢋⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠾⣅⣀⣀⣀⣀⣀⣠⣦⠈⠉⠛⠓⠒⠛⢛⣉⣥⠴⠞⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠳⠶⠒⠒⠒⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠁⠚⠔⠤⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠁⠋⠿⠿⠿⠿⠿⠿⠻⠿⠬⠀⠓⠙⠀⠀ ⡄⢠⠀⠁⠟⡿⣿⣿⣿⣿⣿⣿⢿⠘⠀⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠺⠐⣀⠀⠀ ⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀ ⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀ ⠀⠀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀ ⠀⠃⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣶⣤⣤⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠀ ⠀⡿⣿⣶⣿⢀⠀⡏⣿⣿⣬⢿⠘⠀⠁⠉⠉⣀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢨⠀⠀ ⠀⣧⣿⠸⣿⣿⣤⣿⣿⣿⢿⣼⣦⠻⠀⠀⠁⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀ ⠀⡀⣷⣿⣿⣯⣿⣿⣿⣿⣿⣿⢿⣿⠛⠙⠈⠄⠹⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀ ⠀⠀⠀⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠃⡿⣿⣾⣤⣤⣀⣀⣀⣀⣀⣇⣿⣿⣿⣿⣿⠘⠀⡇⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀ ⠁⡿⣿⣸⠀⠶⠰⠀⠀⠀⠀⠁⠀⣿⣿⣿⣿⣿⢸⠀⡀⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀ ⡇⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣷⣿⣿⣿⣿⢸⠀⠃⣿⣿⣿⣿⣿⣿⣿⢹⠀⠀⠀ ⡇⣿⣷⠸⠀⠀⠐⠀⠀⠀⠀⡁⠀⡇⣿⣿⣿⣿⢸⠀⡇⣿⣿⣿⣿⣿⣿⣿⣷⣿⠠⠀ ⡇⣿⡏⢸⠀⠀⠀⠀⠀⠀⠀⡧⠸⡟⣿⣿⣿⣿⢸⠀⡇⣿⣿⣿⣿⣿⣿⣿⢠⣷⢸⠀ ⠀⣿⣿⢻⠀⠠⠹⠉⠉⠀⠀⡄⢁⣿⣿⣿⣿⣿⠠⠀⡇⣿⣿⣿⣿⣿⣿⣿⠴⡇⢸⢸ ⠀⡆⣿⣍⣶⠿⠻⠛⠛⠿⠶⣶⣥⣉⣟⣿⣿⣀⠀⠀⡇⣿⣿⣿⣿⣿⣿⢸⠀⡇⢸⢰ ⠀⠀⣄⣦⣷⢿⣶⣷⣾⣶⣶⣶⣶⣤⣤⢠⢀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⢀⠁⡿⢠⠀ ⠀⠀⠀⠀⡇⣿⠘⡇⢹⠂⠘⠀⠀⠐⠒⠀⠀⠀⠀⠂⠀⡄⣿⣿⣿⣿⣰⠋⡾⢀⠀⠀ ⠀⠀⠀⠀⠀⣷⢿⡈⣷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⠾⣿⣟⣿⣾⡴⣠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⣿⢿⡙⣤⢷⠙⡈⣄⠰⠀⠀⠁⠟⣴⣁⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣶⣿⢿⠛⡍⣦⠶⠻⠙⠏⣿⣿⡿⣿⣾⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣶⣷⣿⣿⣿⣿⣿⣶⣴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡤⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢤ ⢣⡀⠀⠉⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠉⠀⢀⡜ ⢸⡉⠒⠄⠀⠀⠀⢉⡙⢢⠀⠀⡔⢋⡉⠀⠀⠀⠠⠒⢉⡇ ⠀⠉⢖⠒⠀⠀⠀⣇⠀⣸⠀⠀⣇⠀⣸⠀⠀⠀⠒⡲⠉⠀ ⠀⠀⠀⠉⠙⠫⠤⠚⠉⠀⠀⠀⠀⠉⠓⠤⠝⠋⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠒⠒⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⡾⣀⠀⠀⠀⠀⡀⢦⠘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⢦⠛⠈⠀⠀⠀⠟⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠄⢼⠀⠀⠀⠀⣄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠉⠉⠁⠀⠀⣷⠀⠀⠀⠈⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠏⡴⢀⠀⣀⣧⠛⡾⣧⢹⡄⠁⢹⣼⠦⠓⠏⣾⣧⣤⣤⠳⠈⠀ ⠂⣸⠀⠀⠀⠀⠀⣧⢰⠀⣦⣖⣼⣴⢀⠀⠇⣼⢀⡀⠀⠀⠀⢧⠀ ⠀⢷⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠀⠀⠀⣦⠸⠀⠀⠀⠀⠁⡜⢀ ⠀⠀⣄⠳⠉⠉⠟⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠀⠁⠺⣴⠀⠀ ⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⢀⠀⠀⠀ ⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⣧⠀⠀⠀⠀⠁⠛⠛⠛⠛⠙⠈⠀⠀⠀⡇⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⢨⠀⡇⣼⣠⠀⠀⠀⠀⠀⣀⢧⠘⠀⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⠀⡄⠳⠉⠈⠀⠀⠀⠁⣋⡶⢠⠋⢰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⢧⠘⠀⠀⣀⣀⣀⣀⣀⢀⠁⠞⣠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣄⢦⠓⠉⠈⠁⠉⠋⠴⣠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠛⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⡶⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣽⡗⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠯⠭⣉⠙⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠟⠉⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢠⡏⡇⡘⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣀⠀⠀⣈⠆⢹⣦⠀⠀⠀⠀⠀ ⠀⠀⢠⡾⠋⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢀⣾⡞⢠⣿⣢⣌⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠏⠉⡉⠁⠀⣸⢹⠇⠀⠀⠀⠀ ⠀⢠⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⡇⢸⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⠤⠒⡎⢀⣠⠴⠯⣞⡀⠀⠀⠀⠀ ⠀⡾⠁⠀⠀⠀⠀⢿⣦⡀⠀⠀⠀⠀⣠⠞⠁⡎⣰⣇⠀⠙⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠛⠛⠓⠒⠦⣄⠙⠳⣄⠀⠀ ⢰⡇⠀⠀⠀⠀⠀⠀⠙⠿⣶⣶⣶⠿⠋⠀⢠⠀⡿⠛⣛⣿⠿⣿⡖⠒⠒⠲⠦⠤⣀⡀⠀⠀⠙⢷⣤⣀⣀⣀⣤⣤⣤⣤⣀⠑⠀⠘⢦⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⡜⠙⠾⡋⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠉⠒⠶⣦⣿⣿⣾⠛⠀⠀⠀⠀⠹⣟⡆⠀⠘⣧ ⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⡶⢦⣴⠿⠆⠶⣿⡛⢿⡖⠦⣤⣀⡀⠀⠀⠀⠀⠈⠉⠛⠧⠄⣀⣀⠀⣀⣼⡟⠁⠀⠀⣿ ⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢠⠟⠦⡀⠙⠳⠤⣀⠈⠛⠾⣷⡀⢧⡜⠛⢷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⢀⣿ ⠀⠀⠀⢹⣷⣦⣀⠀⠀⠀⠀⠀⠀⢠⠃⣼⣷⣶⡿⣶⠀⠀⢀⣷⡀⠀⠘⣿⣿⣧⠀⠈⠾⣏⠛⠻⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿ ⠀⠀⠀⢸⣿⠀⠉⠛⠶⢤⣄⣀⢀⡇⣼⣋⠭⣿⢃⠙⡟⢉⣿⠀⢳⡀⢰⣿⠉⢿⠇⠀⣰⠙⣆⠀⠘⣮⠉⠛⠻⠶⢶⣶⣶⣾⠿⠟⠋⠀ ⠀⠀⠀⠀⠻⣦⣄⠀⠀⣀⢀⠝⢙⣧⣌⡉⠛⠛⠿⠴⠿⠿⠷⠆⣀⣷⣼⣇⣆⡈⣧⣴⣿⣃⣘⣆⠀⢸⠀⣠⠖⠊⠉⢱⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⢿⣿⠷⠋⢠⠞⣿⠁⠙⢦⡼⠛⠉⠑⠒⣶⢰⡖⠲⠴⠠⠔⠫⢭⡄⠀⣠⣠⡌⣷⢸⡀⡏⠀⠀⠀⠻⠼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣮⡥⠔⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⠁⠀⠀⠀⠀⠀⠀⢳⢀⡇⠀⠻⣿⢸⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⢻⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠘⠦⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⣀⣀⣀⣀⣀⣠⣼⠇⠀⠘⣧⣄⣀⣀⣀⣠⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠇⠠⣀⠁⠋⠛⠛⠛⠛⠙⠀⠀⠁⠿⣿⣿⣿⣿⣿⣿⣙⡀⠦⠀ ⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⢸⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⢹⠀⠀ ⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀ ⠀⣿⣿⣿⣠⣇⣿⣿⣷⢈⠀⠀⡀⣄⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀ ⠀⣿⢻⣿⣿⣯⣿⣿⡿⣬⠻⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⢸⠀ ⠀⡀⣷⣿⣟⣿⣿⣿⣿⣿⣿⠿⠻⠈⠐⡆⣿⣿⣿⣿⣿⣿⢸⠀ ⠀⠃⡿⣾⣶⣴⣤⣤⣤⣧⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⢀⠀ ⠁⣿⣼⠀⠠⠀⠀⠀⠀⠀⣿⣿⣿⣿⠸⠀⣿⣿⣿⣿⣿⣿⠀⠀ ⡇⣿⠘⠀⠀⠀⠀⠀⠀⠠⣧⣿⣿⣿⢸⠀⣿⣿⣿⣿⣿⣿⠙⠀ ⡇⣿⢹⠀⠀⠀⠀⠀⠀⠘⡏⣿⣿⣿⢠⠀⣿⣿⣿⣿⣿⣿⣧⠘ ⡀⣿⣿⠈⠀⠀⠀⠀⠀⢡⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⢾⡀⢻ ⠀⣦⣻⣽⢿⠿⠿⠭⣭⣛⣛⣿⣶⢀⠀⠀⣿⣿⣿⣿⣿⢠⠇⣸ ⠀⠀⡀⣇⣿⣇⣸⣁⣀⣀⠀⠀⠀⠀⠀⠈⡆⣿⣿⣿⣼⠋⣼⠀ ⠀⠀⠀⡄⣿⠸⣧⠈⠀⠀⠀⠀⠀⠀⠀⠋⠾⣿⣿⣾⡴⣠⠀⠀ ⠀⠀⠀⠀⡄⣿⠻⣍⠲⠙⣈⠀⠀⠋⡽⣫⣿⣿⣴⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣤⣷⢿⡻⣛⣿⠿⣿⣾⣶⣠⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⡆⠸⠀⠀⠀⠀⠀⠀⠀⣷⣄⣿⣿⣿⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⡀⢻⣿⣿⣿⣿⣿⣿⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣤⣦⣷⢶⠶⠶⠶⡶⢹⠀⠀⠀⠀⠀⠀⠀⣄⣦⣿⣿⣿⣿⣾⣴⠀⢀⠀⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⣆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⣤⢤⠦⠶⠶⣿⠶⠶⠶⠶⠶ ⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⣆⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⣿⢶⠙⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠃⠟⠀⠀⡟⠛⠈⠀⠀⠀⠀⠀⠀⠀⣧⠸⣇⠘⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⢀⠀⡀⢄⠲⠈⠀⠀⠀⠀⡇⠀⡀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⠈⠀⠀⡇⠀⠀⢿⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠹⠀⡇⠘⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⡇⢸⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⡇⠘⠀⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇⢸⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⣦⠶⠶⠶⠳⠛⠛⡟⢹⠉⠉⠉⠈⠀⠀⡏⣴⣀⣀⠀⠀⠀⠁⣀⢤⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⢢⠃⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⣸⣀⣀⣀⣤⣤⣧⢴⠀⠀⠀⠀⠀⠀⠀⣀⠣⡁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠶⡤⢀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⡆⠹⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢻⠛⠛⠙⠉⠉⠈⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⣀⢦⠲⠓⠉⠉⠚⠴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣰⠀⠀⣀⣀⣀⣀⣄⣿⣤⢤⠷⠾⠷

⠀⠀⠀⠀⢞⠉⠳⡎⠁⢹⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡁⠬⠯⢉⡁⠠⡀⠀⠀⠀⠀ ⠀⠤⢾⠖⠁⠀⠀⠀⠀⠈⠂⢎⠀⠀⠀⠀ ⠻⠯⠏⠀⠀⢀⠔⠀⠀⠐⠢⢄⢁⠀⠀⠀ ⢠⠘⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣎⡄⠀⠀ ⠸⠠⠀⠀⠀⠡⠀⠀⠀⠀⠀⢀⢿⣧⡀⠀ ⢰⢰⠀⠀⠀⠀⠁⠒⠒⠒⠂⠁⠸⢛⣃⡀ ⠘⡈⠀⠀⠀⠀⠀⡠⠄⠠⡀⠀⠀⠐⠁⢸ ⠀⠨⢏⡖⠀⠀⠶⠀⠀⠀⠘⣍⡁⡇⢀⠎ ⠀⠀⠀⠘⢶⡿⣀⣀⣀⣀⠜⠀⠀⠉⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠴⠶⠶⢤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⣦⠀⠀⠤⠾⢄⣀⠉⢳⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠟⠀⢀⠔⠁⢣⡀⠠⢴⠤⠤⢤⠏⣒⣻⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡟⠒⠲⠧⣀⠄⢉⡧⠶⠚⠒⠒⠛⠒⠒⠶⢽⣆⠀⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⡀⠀⠸⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄ ⠀⣠⢾⠋⠙⣿⠀⢀⠇⢀⣆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⢰⠇⠀⢣⠀⡟⠓⢾⡈⠉⠆⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏ ⡟⢆⠀⡸⠯⡇⠀⠀⠙⣆⢸⠤⠚⢳⣤⣄⣀⣀⣀⣀⣀⣠⡤⣾⢿⠀ ⡇⢈⢎⠀⠀⡇⠀⠀⠀⠘⡇⠉⢦⣊⢀⠌⠀⠀⠇⣀⣀⣣⡼⠃⢸⠀ ⣧⠃⠀⠑⡄⡇⠀⠀⠀⠀⢻⣠⠃⠀⡝⡉⡉⡉⡽⡀⠀⣸⠃⠀⢸⠀ ⣇⠑⡄⠀⡼⡇⠀⠀⠀⠀⠸⡗⠂⢄⣇⣇⣿⣿⣾⡧⠤⡏⠀⠀⢸⠀ ⢿⠀⢸⡜⠀⣧⣀⣀⡀⠀⠀⡇⠀⢰⠰⢹⣿⣿⠋⡆⢀⡇⢀⣀⣾⠀ ⠸⣆⡜⠁⠲⣇⣀⠈⠉⡟⠶⠏⠉⠺⡒⠛⠚⠓⡗⠒⠘⢟⣋⣩⡿⠀ ⠀⠙⢧⣀⣀⣏⠉⠉⠙⠛⠛⠛⠒⢒⠓⠒⠚⢛⣛⣋⠉⠉⠁⢠⡇⠀ ⠀⠀⠀⠈⠉⣿⣀⠀⠀⠀⠀⠀⠀⣸⠉⠉⣿⣉⣉⣤⡤⠴⠞⢻⠁⠀ ⠀⠀⠀⠀⠀⢹⣍⡙⡟⠓⠚⠛⠋⢹⠀⠀⢻⣀⠠⠤⠀⠀⠠⡟⠀⠀ ⠀⠀⠀⠀⠀⠸⡆⢸⠉⠉⠉⠉⠑⡾⠀⠀⠸⣆⠀⠀⠀⢀⣸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠾⠤⠤⠤⠶⠚⠁⠀⠀⠀⠈⠉⠛⠋⠉⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⡴⠋⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀ ⠀⠀⢀⡴⠋⡟⠀⠀⠀⠀⢀⠿⡱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠉⠑⡌⣆⠀⠀⠀ ⠀⣰⠋⠀⣸⠀⠀⠀⠀⢀⣮⢡⠷⠮⠆⠀⠀⠀⠀⠀⠀⢠⠀⣉⠍⢀⢧⠀⠀⠀ ⢠⠃⠀⠀⢻⣄⠀⠀⣠⠞⡜⣜⣑⣤⡀⠀⠀⠀⠀⠀⢰⠋⠁⠐⠚⠂⢌⠲⣄⠀ ⢸⠀⠀⠀⠀⠉⠛⠛⠁⠠⡹⢭⠟⠛⢯⠉⠉⠀⠒⠠⢈⣱⣶⡶⠒⠒⠲⢄⠈⢦ ⠘⡄⠀⠀⠀⠀⠀⠀⢀⢃⡗⢶⡓⠒⢏⣷⠲⢤⣄⡀⠀⠈⠙⠀⠤⠄⠴⠊⠀⢸ ⠀⠈⣦⣄⡀⠀⠀⠀⡌⣾⣬⢦⠈⣑⡄⠉⣷⣿⠈⢟⡓⢦⣄⣀⠀⠀⠀⠀⣠⣾ ⠀⠀⢻⣀⠉⠑⢒⢼⡸⠷⢾⣎⣧⣯⠘⣄⣟⠘⣅⣼⠱⡀⢡⠉⡩⠿⣿⠛⠉⠀ ⠀⠀⠀⠉⢳⣞⣁⢚⡇⠱⠔⠋⠐⠂⡖⠃⠋⠛⢭⠉⠭⣽⢸⢸⠀⠀⠿⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⡏⠉⡇⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠚⠀⠙⢸⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⡘⢹⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣀⣀⣀⡇⠈⣇⣀⣀⣀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠃⡔⣡⢚⠿⠠⠄⠧⠶⠛⢙⠨⠑⠈⠀⠀⠀⠀⠀⣆⢿⠈⠀⠀⠀⠀⠀ ⠀⠁⡜⢃⡞⢠⠀⣧⠀⠀⡇⠈⠀⠉⣋⣯⡾⠷⠛⠉⠀⠀⠀⡄⢿⠈⠁⠟⠻⠛ ⢿⣼⠃⣼⠐⠁⠉⡏⢹⠀⡁⣻⡴⣀⠀⠀⡀⢤⣿⣤⣷⢿⠿⠻⣟⣿⣿⣿⣿⣿ ⣿⠀⡸⠁⠟⣠⠀⠁⡄⠑⠿⢠⠃⠰⠉⠐⠠⡀⡀⢺⠀⣆⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⡇⢁⡼⢢⠈⠀⡀⠒⡁⣠⠁⠡⡠⠀⠀⠀⠀⠀⢿⠉⠚⣴⣥⣿⣿⣿⣿⣿⣿ ⢻⡴⡷⣿⠈⠀⢄⠐⠀⢡⠁⡇⢠⠀⠀⠀⠀⠀⠃⢠⠑⢌⡦⣷⣠⠞⡤⢸⣿⣾ ⢠⠀⠀⣇⢿⠈⠀⠀⠀⡀⡧⣼⠀⠀⠀⠀⠀⠀⡜⡉⠌⡒⢑⡍⠙⣿⣅⣼⣀⠀ ⠁⠞⠷⢡⡾⣦⠳⠈⠀⠀⡀⢸⠀⠀⠀⠀⠃⠃⣠⠀⣀⠣⠞⣠⣆⣄⡶⢴⡀⠀ ⢀⣄⡤⡀⢣⠈⠀⣀⢦⠑⠀⢸⠀⠀⠀⠀⠱⠼⠀⠀⠈⡰⠀⠊⡡⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⢇⠘⠀⠀⡀⢆⢷⠼⠢⠛⡉⡝⠉⠉⠂⠒⠷⣐⠋⡔⠀⠀⠀⠈⠗ ⡇⠀⠀⠀⠀⠀⣄⠱⠉⠂⠠⠀⡆⠜⡦⡿⠚⢤⠤⠀⢁⠁⣄⢠⣓⣒⣒⠀⠤⢀ ⡿⠀⠀⠀⠉⠟⠤⡤⢶⠙⠀⠀⠀⣧⠁⣼⠟⡿⣸⠀⠀⡘⢆⠀⠀⢣⠀⠀⠀⠀ ⣿⠹⠈⠟⣴⢀⠀⠀⢀⡉⢫⠚⠩⡞⡠⠀⣿⠝⢐⠁⡚⢉⠿⢤⠀⡇⠈⠀⠀⠇ ⣾⣿⣿⢡⠀⠁⠋⠾⣠⠀⠀⡀⠀⠀⠀⠀⣢⣌⠀⡤⣄⢚⣖⠜⣉⣺⢠⠀⠀⡿ ⠠⠀⣧⠋⠿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠒⡒⠖⡒⠶⣏⠀⠀⠀⠏⢰

⠀⠀⠀⠀⡇⠀⠀⢹⠀⠀⠀⠀⣣⣿⣿⣿⣿⣹⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀ ⠤⠤⠤⠤⡷⠶⠲⡖⠘⠀⠀⠀⡀⣦⣷⣿⣶⢨⢠⠀⠀⠀⠀⡸⠀⠀⡏⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⢆⠈⠀⠀⠀⠀⠀⠀⠁⢠⠀⠀⠀⠀⡟⢙⠀⡀⣇⣀⣀⣀ ⠀⠀⠀⠀⡇⠀⠀⠀⠁⢨⠀⠀⠀⠀⠦⠒⡔⠢⠑⠀⠀⠀⡇⡆⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⡇⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠑⠀⡇⠀⢸⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⠀⢸⠀⡇⠀⠀⠀ ⠉⠉⠈⠀⡏⠀⠀⠀⠀⢣⠊⠒⠒⠒⠑⠀⠀⠀⠀⠀⠀⡀⡇⠁⢰⠀⡇⠀⠀⠀ ⠀⠀⠀⡀⣇⣀⣀⣤⠧⢠⠀⠀⠀⠀⠂⢏⠀⠀⠀⠀⠀⠀⣾⡤⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠢⠑⠉⠉⠒⠀⢀⠀⠀⠀⠀⠀⠎⢠⠤⠤⠤⡧⠲⠒⠛

⠀⠀⠀⠀⠁⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠅⢀⠀⠀⢅⠀⠀⠀⠀ ⠀⠀⠀⠀⢆⠀⠄⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⢸⠀⠀⠀⠀ ⠀⠔⠤⠳⠖⠙⠿⠢⠏⠤⠂⠀ ⡀⠑⠀⡆⠀⣀⢀⠄⢸⠀⠂⠠ ⠀⠀⣀⢀⠀⠀⠀⠀⡀⠧⢀⠀ ⠀⠀⠁⠁⠊⠐⠂⠑⠀⡀⠀⠀ ⠀⠀⡀⠐⠂⠐⠀⠔⢡⠠⠀⠀ ⠀⠀⠀⡀⠠⠒⠒⠠⢀⠀⠀⠀

⠋⠓⠙⠉⠉⠟⠺⠓⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠈⠀⠀⠀ ⣂⣐⢤⡤⣤⣷⢻⠊⢠⡟⣿⣧⣿⣾⣀⢧⠀⠀⠀⠃⡸⣋⣟⣠⣇⠴⡆⢶⠘⠀ ⠉⠀⠀⠁⠋⣛⢛⠛⠛⣿⣻⣿⣴⢀⠀⡄⣸⣞⣴⣋⣞⡢⣌⢂⠶⠠⠇⠿⡯⠜ ⠁⣼⣀⣀⣀⣤⣷⣴⣠⣀⣀⠀⠀⠀⠁⠉⣟⠛⣿⠚⠿⠛⢭⠩⣚⣟⣸⣘⣇⣟ ⡿⠈⠀⠀⠀⠀⡀⠳⠀⠀⠀⠀⠀⠄⣤⠁⡞⢀⣇⣀⣁⠾⡶⣶⠿⣿⢨⢳⡗⣿ ⣇⢿⠙⠈⠀⠀⠁⡔⠀⠀⠋⠽⡬⢯⠬⣠⢀⠀⡀⠺⣠⠀⠀⠀⠀⠀⣇⡇⣿⣿ ⡇⣿⣿⣸⣀⣊⢖⠾⠉⡼⢦⣷⣏⣼⢀⠀⠀⠀⠆⠈⠀⠁⠻⠉⠋⠖⣠⡎⣯⣰ ⡇⢸⣠⢦⠒⠛⡞⠯⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡉⣄⣱⠈⠀⠀⠀⡁⠞⣧⠀ ⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⣀⣀⠀⠀⠀

⠀⠀⠀⠈⠀⡠⢀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠚⠄⣤⢳⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠙⠈⠀ ⠀⠃⠀⠀⢫⠓⠆⠀⠀⠀⠀⠤⢸⠃⠀⠘⠀⢴⠠⡀⣀⣀⡀⠀⠀⠂⠉⢮⣠⠄ ⠉⡂⠴⣀⠠⢀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠢⠁ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠁⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⢭⠓⠤⡼⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠄⢿⡾⢀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠁⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡞⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠯⣥⣀⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⠛⠁⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡇⢠⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠈⢳⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣿⠟⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⡼⠁⣾⡀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠶⠦⠤⠶⠞⠀⢸⡏⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⡿⠁⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣽⠁⣰⣿⣍⡭⠤⠽⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠾⠆⢀⣠⠀⠀⠀⣼⠀⡿⠀⠀⠀⠀⠀⠀ ⠀⣴⡟⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⣻⠀⣿⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣇⡤⠶⢲⡏⠀⣀⡤⠶⠯⣼⣁⠀⠀⠀⠀⠀⠀ ⢰⡿⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⣼⠃⣰⠏⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠀⠀⠀⠼⠓⠛⠓⠶⢤⣄⠀⠉⠳⣦⡀⠀⠀⠀ ⣾⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⣄⡀⢀⣀⣴⣾⠏⠀⠀⡇⢰⣿⣿⣤⣤⣶⣿⣿⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠈⢻⣆⠀⠀ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠟⠋⠁⠀⠀⡼⠁⣼⡍⢉⣴⡾⠟⠛⢿⣯⠉⠉⠉⠉⠉⠙⠓⠲⢦⣄⡀⠀⠀⠙⠻⣷⣶⠶⣶⣶⠖⠒⠒⠒⢶⣶⣤⡈⠀⠀⠙⣷⡀ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⡼⠁⠙⢿⡉⠀⠀⠀⠈⢻⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣷⣦⣿⣿⣟⡏⠉⠀⠀⠀⠀⠀⠘⣷⢙⡆⠀⠀⢹⣧ ⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⣷⣖⣦⣤⣽⠦⢠⢴⣶⠛⢷⣷⠦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠻⢿⣁⡀⠀⠀⠀⠀⠀⢀⣿⡞⠀⠀⠀⠀⣿ ⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢀⣼⣍⠉⠙⢿⣤⡀⠀⠀⠹⢷⣄⣻⣆⠀⢹⡉⣛⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠶⠞⠛⠋⠀⠀⠀⠀⠀⣿ ⠀⠀⠹⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⡀⠉⠳⣄⠀⠈⠙⠓⠦⣄⠀⠉⠙⢿⣧⣜⣧⡇⠀⠙⣏⢻⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿ ⠀⠀⠀⠈⣿⡿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢠⣿⣿⣭⣿⢻⣷⠄⠀⢀⣠⡾⡇⠀⠀⠘⣿⣾⣿⣷⡀⠀⠙⢫⣦⠉⠙⠿⣷⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿ ⠀⠀⠀⠐⣿⠁⠀⠙⠛⠷⣦⣤⣀⣀⠀⢠⡏⣠⢟⣉⣠⣼⡿⡀⠻⣟⠛⢻⡟⠀⢻⡄⠀⢰⣿⡏⠹⣾⡗⠀⠀⣼⠛⣧⠀⠀⠘⣧⠉⠛⠛⠿⠿⣷⣶⣶⣶⣾⣿⣿⠿⠟⠋⠀ ⠀⠀⠀⠀⢿⣧⡀⠀⠀⠀⠀⠈⠉⢛⡿⢿⣇⠙⠛⠷⢤⣿⣷⣇⣀⣹⣶⣿⣣⡆⠀⢻⡄⢸⡿⢀⠀⠹⣦⠀⣼⢏⠇⠘⣧⠀⠀⢸⡇⠀⠀⣀⡤⠴⠚⢲⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠿⣷⣤⣀⣠⠞⣰⠋⠀⣼⣿⡟⠻⣦⠀⢀⣤⣤⣤⣀⣀⣉⡙⠛⣻⣛⠛⠛⠷⠿⠤⠤⠿⠿⠿⠿⠶⠶⠿⠷⣄⠈⡇⢠⡾⠃⠀⠀⠀⣸⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡷⠛⠀⢀⡞⠉⣿⡇⠀⠘⠦⠾⠋⠀⠀⠀⠀⠙⡇⢸⡟⠉⠛⠛⠛⠛⠛⠛⠲⣶⠀⠀⣴⠦⢶⡄⣿⠀⡇⢸⡇⠀⠀⠀⠀⠻⠾⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣋⣉⡤⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢀⡇⠀⠸⠿⣿⠀⡇⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠾⠁⠀⠀⠀⢿⢠⡇⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⣇⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣤⣀⣀⣀⣀⣀⣀⣀⣤⣾⠟⠀⠀⠘⣿⣦⣤⣤⣀⣀⣤⣤⣴⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠉⠉⠉⠉⠉⠙⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⢀⣴⣶⠿⠿⠿⠟⠛⠛⠛⠻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣤⣶⡾⣾⡏⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡿⠋⠀⠀⣾⡇⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠇⡀⠀⠀⣿⠁⠀⠀⠀⠀⠘⢿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣶⢿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⡾⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⠀⠀⣀⣀⣤⣤⣄⣀⣀⠀⠀⠀⠀⠈⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⡇⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⢀⣿⠾⢟⣉⣁⣤⣤⣄⣉⡉⠛⢶⣴⡶⠟⠛⠛⠶⣤⡀⠀⠀⠀⠀⠀ ⠸⣷⡄⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣴⠟⣧⡾⠛⠉⢉⣀⡀⠉⠉⠙⠳⣦⣌⠻⣦⡀⠀⠀⠈⠿⠞⠛⠻⣦⠀ ⠀⠙⠿⠿⠶⣿⡇⠀⠀⠀⠀⠀⠀⣤⣤⣄⣀⣀⣠⣤⠆⠀⢸⡿⠀⠀⠀⣼⡿⠿⠿⣶⠶⠛⠋⠉⣿⡄⠀⠀⠀⠀⠙⣧⠈⢷⡄⠀⠀⠀⠀⠀⠀⢹⡆ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⡅⠉⢹⣿⠁⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⣴⠗⠀⠐⠶⣴⠟⠁⠀⠀⠀⠀⠀⣼⠃⢸⡇⠀⢀⡤⠀⢀⣠⡿⠀ ⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⣿⠇⠀⠸⣿⡀⠀⠀⠀⣼⠁⠀⣀⣤⣽⡷⢶⣯⠀⠀⠀⠀⣹⠀⠀⠀⢀⣠⣴⠞⠋⢀⣾⢃⣴⠿⣷⠛⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣦⣤⣀⣀⣤⣾⠟⠀⠀⠀⠙⠛⠿⠿⠟⣫⡶⠟⠉⠁⠀⠀⠀⠙⠷⠦⢤⣶⣟⣛⡛⠛⠋⣉⣀⣤⣴⡿⠟⠋⣡⣼⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣤⣀⣀⣀⣀⣀⣤⣤⣬⣧⠀⠀⠉⠉⠉⠉⠉⠉⢉⣡⣤⡴⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠸⣷⣶⡶⠶⠶⠶⠖⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⢀⣠⣾⣿⣿⣿⣿⣷⠀⠀ ⠀⠀⠀⢀⣠⣤⣠⣠⣤⠀⣾⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣏⣉⣉⠁⠀⠀ ⠀⢀⣴⣿⣿⣿⣿⣿⡿⢁⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⣼⣿⣿⣿⣧⣤⣤⣀⢸⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠀⠈⠉⠛⢛⣿⣿⣿⡟⠀ ⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣀⣼⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠁⠀ ⠀⠀⣀⣀⣀⣈⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⠟⠀⠛⣻⣿⣿⣛⡏⢡⣤⣄⠀ ⠀⣾⣿⣿⣿⣿⣿⡿⠛⠀⣀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠈⢙⣻⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠛⠁ ⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠉⠉⠁⠀⠀⠀⠀⢀⡀⣀⡀⠀⠀⠀ ⠹⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀ ⠀⠀⠉⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⢿⣻⣿⣶⣼⣿⣿⣿⡿⠿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⢯⣿⣿⠟⣻⢭⡛⠁⡀⠠⠐⠀⠉⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⣿⣻⣿⣿⢏⡚⢥⢊⠇⠀⠄⡁⠄⠀⢀⠀⡀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⡝⣢⠏⣶⡌⠀⠄⠂⢁⠂⠐⢠⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⣿⣿⡄⠠⠁⢊⡽⠿⢶⣶⣥⡶⢶⣻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣷⣤⣌⣀⢌⣍⣒⣲⣃⣮⣵⣿⡟⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣿⣿⣿⣿⣿⢿⣳⡿⣿⢿⣿⡿⣿⢿⣟⡿⣽⣻⣿⣿⢯⣟⡿⣽⣿⡋⢻⡿⣿⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣻⡾⣽⣟⡿⣾⣻⢯⣿⣿⣿⣿⢯⣟⡿⣞⣿⢿⣽⢯⣿⣿⣿⣿⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢿⡽⣯⣟⣿⣻⣽⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣟⡾⣟⣷⣿⣻⢿⡿⣿⣿⡿⣯⣟⡿⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠑⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣽⢾⣟⣯⣿⣻⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣯⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣞⡷⣯⣧⡼⣿⣿⣦⡄⠀⠀⠀⠀⢄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠁⡀⠐⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⢿⣽⡾⣶⡿⣾⣻⣾⣿⣿⣿⡿⣿⣻⣽⣿⣿⡿⣟⡿⣯⣟⡷⣏⣠⣿⣻⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣽⣻⣽⣻⡽⣟⡟⠛⣿⣿⣟⣷⣯⢿⣳⣟⡿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠄⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⣯⢿⡾⣽⣷⣿⣿⣿⢿⣻⣽⡾⣽⡷⣟⣿⢯⣷⢿⣻⣽⣷⣻⣟⣿⣿⣿⡿⣟⡿⣽⢯⡿⣽⣻⣿⣿⣿⣿⣿⣟⣾⢯⣿⣳⣯⣟⣿⣻⢿⣿⣿⣿⣷⣿⣻⣟⡿⣽⣻⣿⣿⣾⣟⡿⣞⣿⡽⣿⣷⡄⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡤⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⣽⣻⣯⢿⡿⣟⣿⡽⣾⣻⣽⣾⣻⣽⣻⣽⡾⣿⣽⣻⣽⣾⣷⣿⡿⣟⡿⣾⡽⣿⡽⣟⣯⣿⣻⣷⡈⢻⣿⣿⣿⣿⣞⣿⣳⣯⡷⣿⢾⣽⣻⣿⠿⢿⣿⣿⣿⣿⣽⣟⣷⢯⣟⡿⣞⣿⢯⣷⢿⣯⣿⣿⡀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣽⣻⢷⣻⣯⣟⡿⣞⣿⣽⣻⣞⣷⣯⡷⣟⣷⢿⣳⣯⣟⡾⣷⢯⣷⢿⣻⣽⡷⣿⣳⣿⣻⣽⡾⣽⣻⣿⣿⣿⣿⣿⣷⡿⣾⣽⣳⡿⣯⢿⣞⡿⣿⣶⣤⣾⡿⣯⣟⡿⣿⣿⣿⣽⣻⣟⣾⣿⣯⣿⣞⡷⣿⣧⣄⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣟⣾⡽⣟⡿⣾⣽⣻⢯⣷⣯⣷⣿⣿⣾⡽⣟⣾⣟⡿⣾⣽⣻⣽⢿⣾⣻⡽⣷⣻⢷⣟⡷⣯⣷⣟⣿⣳⣟⣾⣽⣿⣿⣿⣽⢷⣯⡷⣿⣻⢯⣿⡽⣯⣟⡿⣽⣻⢷⣻⣽⢯⣟⣿⣿⣷⣿⣿⣿⣿⣷⣻⣽⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡾⣟⣯⣿⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⡿⣽⡷⣯⣟⣾⣟⣾⡽⣿⡽⣯⣿⢾⣻⣽⡾⣽⣾⣻⢾⣽⣻⣿⣿⣿⢯⣿⢾⣽⡷⣟⣯⣷⢿⣻⢾⡿⣽⣯⢿⣯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣷⣿⣳⣯⣿⡽⣷⣟⡿⣞⣿⣽⣳⣿⣻⢾⣽⣻⡽⣿⣿⣿⣿⢿⣽⣻⣾⡽⣿⡽⣾⣻⢯⣿⡽⣷⣻⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⡿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡷⣟⣯⡿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣞⡿⣯⣷⣻⣽⣞⣯⡿⣽⢯⣟⣿⣿⣿⣿⣟⣾⢷⣯⢿⣳⡿⣯⣟⣯⣷⢿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣞⡿⣿⣿⣿⣿⣿⢯⣿⣿⣟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣯⣟⡿⣿⣽⣻⢷⣟⣿⡿⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣿⣾⣿⣽⣯⣟⣷⣯⣟⣾⣽⣳⣿⣯⣿⣿⣿⣿⣿⣿⣿⣾⣻⢾⣟⣯⢿⣳⡿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣽⣇⡙⢿⣿⣽⣻⢷⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⣾⣽⣻⢷⣯⣟⣿⣾⣏⣴⣿⡿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣶⣿⢿⣽⣻⣞⣿⣿⡿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⡿⣾⣽⣞⡿⣿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣯⣿⣯⣿⣿⣻⣽⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣾⣯⡷⣿⡽⣾⡽⣿⣳⣟⡿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢷⣻⣾⣻⢷⣿⣿⣿⣿⣿⣿⣷⣿⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣟⡿⣿⢿⣿⣿⣿⣿⣿⣟⡿⣽⣻⣾⣽⣷⣿⣟⣿⣿⣿⣿⡿⢿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣽⣿⣿⣽⣻⣽⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢾⣿⣿⣿⣿⣿⣿⣟⣿⠃⢹⣿⣿⣯⢿⣻⣾⣽⣿⡿⠋⠹⣿⣿⣿⣿⣽⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣽⣾⣯⣷⣯⣷⣿⣿⣿⣿⣯⢿⡽⣟⣾⡽⣥⣽⣿⣿⣿⣻⣿⣿⣿⣽⣻⣽⣿⣿⣿⡟⠀⠀⠉⠻⢿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣻⣏⠛⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣿⣿⣿⣿⡿⣞⣿⣷⢾⣿⣿⣯⣿⣿⠿⠛⠁⠀⠀⠀⠹⣿⣿⣿⣽⣿⣿⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣯⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢿⣿⣿⣿⣿⣿⢯⣿⣿⣿⣻⢿⣶⣀⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⣿⣿⣿⣿⣿⢯⡿⣽⡶⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣽⣿⣯⢿⣿⣿⣿⣿⣿⣿⣯⡿⣿⢿⡿⣿⣟⡿⢻⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣳⣿⣻⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣯⢿⣿⣿⣿⣟⣯⣿⡟⢻⣿⣷⣻⣿⡆⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣽⢯⣟⣷⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣻⢾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣷⣯⣿⣿⣽⣿⣿⣻⣽⣟⣾⣳⣿⣾⣜⣿⣿⣿⣟⡷⣯⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢯⣿⣿⣿⣿⣿⣟⡾⣟⣯⣟⣷⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⣾⣻⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣟⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⡷⣿⣿⣿⣿⣿⡿⣽⣻⢾⣳⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣞⡿⣿⣿⣿⣿⣿⣿⢷⣻⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣯⣿⣻⣿⣿⣿⣿⣿⣿⣿⢿⡿⣟⣟⠻⣿⣿⣿⣟⣿⣻⢿⡿⠿⣟⣿⣿⣿⢯⣟⡿⣞⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣻⢟⣿⣿⣿⣿⣿⣿⣽⣻⣟⣾⣿⣿⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣯⣟⣯⣟⡿⣿⣿⣿⣿⢯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣯⣿⣿⣿⣿⣿⣿⣟⡾⣷⣻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣯⣿⣷⣿⣿⣿⢯⣟⣯⢿⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣽⢯⣟⣿⣿⣿⣿⣿⣾⣟⡾⣷⣿⣯⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⣿⣷⣿⣿⣞⣿⣳⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡽⣷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣯⣟⣿⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣾⣽⢿⣿⣿⣿⣾⢿⣽⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠙⢿⣿⣿⣿⣿⣿⣞⣯⡿⣞⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣟⣷⣻⣾⣿⣿⣿⣿⣽⣟⣾⣽⣦⣽⣿⣿⣿⣟⣿⣻⢿⣋⣻⣿⣿⡷⣯⢓⣿⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣯⢿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣿⣿⣿⣿⣿⢾⣽⣿⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣞⡿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣯⣿⣿⣿⣿⡽⣷⣾⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣳⣿⣆⠙⣿⣿⣿⣶⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢿⣽⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⡿⣽⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣯⢿⣻⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣻⢿⣷⣿⣳⣯⢿⣻⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣿⣿⣿⣿⡿⣿⣿⣿⣾⣿⣿⣿⣿⣻⣿⣾⣷⣻⣾⣷⣻⢶⣻⣞⣷⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣯⡟⢻⣿⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣽⣻⣽⢾⣯⣟⡿⣽⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣻⣿⣯⣿⣿⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣽⣻⣿⣿⣿⣿⣿⢿⣾⣿⣿⣿⣿⣟⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⢿⡽⣷⣌⣿⣿⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣳⡿⣽⣻⡾⣽⣻⣿⣈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⢿⣾⣿⣿⣟⡷⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⢯⣿⣳⣟⡿⣿⣿⣿⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣟⣯⣷⣿⣯⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣿⣿⣿⣽⣿⣿⣿⡿⣯⡿⣾⣻⣿⣿⣟⡾⣟⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⣽⣻⣟⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣯⣷⣿⣿⣿⣿⢯⣟⣾⣟⣿⣿⣿⣿⣿⣿⡿⣿⣿⣯⣿⣿⡿⣯⣟⣷⢿⣽⣿⣿⣿⡽⣏⣿⢾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣟⣷⣿⣿⣿⣷⣿⣷⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣻⣿⢿⣿⣿⣯⡿⣾⣽⢾⡻⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⣽⣷⣻⡽⣿⣿⣿⣿⢷⣟⡿⣾⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡷⣯⡿⣧⣸⢿⣿⣿⣿⣿⣻⣿⣿⣽⣷⣯⣿⣿⣿⣿⣿⣟⡿⣾⣻⢷⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣷⣿⣿⣿⣿⣷⡿⣽⢯⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡾⣟⣷⢿⣻⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⣽⣻⢯⣟⣿⣿⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣟⡾⣟⣯⣟⣯⣷⢯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣻⡽⣟⣯⣿⡿⠀⠀⠀⠀⣿⣿⣿⣻⣿⣿⣯⣟⡿⣽⣾⣻⢾⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣿⢿⣷⣿⣿⣟⣾⣽⣻⢯⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⢿⣿⣷⣻⣽⣟⣾⡽⣿⢾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣻⣿⣿⣿⣟⣾⣻⢾⣽⣟⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⢷⣯⡷⣿⢯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⣟⣿⣿⣿⣳⡿⣯⡷⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⣿⣿⣟⣾⣽⣟⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢷⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣯⣿⣿⣿⣿⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣯⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⢿⡿⠿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠋⠛⠑⠋⠟⠿⠻⠙⠀⠁⠋⠛⠛⠛⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⡿⣿⣿⣿⣿⣿⢿⡿⣼⣀⣀⣀⣿⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⣿⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠉⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣼⢠⠀⠀⠀⣇⣿⣶⣷⠻⠀ ⠀⠀⠀⠀⠉⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⡇⣿⠀⠀⣿⠸ ⠀⠉⠁⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣠⠀⠀⠀⠀⠀⠀⠀⡇⣿⠘⠀⣿⢸ ⡟⣻⠿⠿⠿⣝⣮⣾⣴⣠⣀⡇⣿⠀⠀⠀⠁⠉⠈⠀⠀⠀⠀⠀⡇⣿⢸⠀⣿⢸ ⣆⣿⣿⣿⣶⣶⢴⠀⠀⠀⠀⡏⣿⠿⣿⣿⣿⣿⣿⢿⠻⠀⠀⠀⡇⣿⢀⠀⣿⢀ ⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣶⣶⣤⣤⣤⣤⣷⣿⣿⢸⠀⠀⡇⣿⠛⡟⣾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠙⠀⠀⠀⠀⠀⠀⣇⣿⢸⠀⠀⡿⣸⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⢿⠿⠿⠿⡾⣶⣴⢀⠀⠇⣿⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⠻⠙⠉⠈⠀⠀⠁⠋⡿⢰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣤⣤⣤⣤⣠⠀⠀⠀⠀⠀⠀⠀

⣀⢤⣦⣷⣿⣿⣿⣿⣿⢹⠉⠋⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠻⡛⠙⠀⠙⠉⠀⠀⠁ ⠀⠀⠀⠀⡀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿ ⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⠀⠀⠀⡀⣀⣀⣄⣤⣤⣦⣶⣴⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣠ ⠀⠀⠀⠀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣦⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠀⠀⣀⢀⡀⣀⣄⣿⣿⣿⣿⣿⣿⠸⠀⠀ ⠀⠀⠁⡿⣿⣿⣿⣿⣿⣿⣾⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⢻⠀⠀ ⠀⠏⣿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠿⠴⡇⣿⣾⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⠀⠀ ⡿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣾⢀⠁⡟⣼⣏⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⠸⠀ ⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠟⣶⣩⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⠙ ⣿⣿⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠿⠿⡿⣭⣩⠈⠀⢧⣻⣙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿ ⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠚⠷⣠⠀⠀⣀⣄⣤⣤⣠⣀⠀⠀⠁⢠⣀⣤⣤⣤⣤⣠⢀⡄⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿ ⠀⠀⠀⠁⠉⠚⠖⡤⣀⠁⢸⡄⠘⠀⠀⠀⠀⠀⠀⠀⠁⠔⠁⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢶⠘⠢⠉⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿ ⠒⠤⡠⣀⠀⠀⠀⠀⠀⡇⢀⠀⣄⠑⠀⠀⠀⠀⠀⠆⢊⠔⣤⢰⠀⠀⠀⠀⠀⠄⣉⠚⡤⢀⠀⣄⠳⡈⢤⠑⠈⠀⠀⠀⠀⠀⠀⡀⣧⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠈⠀⠀⣄⠦⠒⠐⠉⠉⠉⠉⠉⠉⠋⠒⠒⠔⠤⣁⣼⠀⠀⠀⠀⠀⠀⣄⠳⠈⣄⠢⠈⠀⠀⠀⠀⠀⠀⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠤⠯⠿⠿⡶⣴⣤⣠⣀⣀⣀⣤⣤⣶⢿⠛⠒⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠢⠙⡀⢤⠑⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣶⣠⢁⠋⠚⠒⠶⠤⠤⠷⠲⠒⠙⠉⣄⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠳⠈⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢹⠋⡿⣿⣿⢻⠒⠗⠸⠀⡗⠣⠿⠒⣷⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⢿⡿⢿⠨⠀⣦⣽⡯⣿⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠣⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣄⣦⣶⣿⣿⣿⣿⣿⣿⢿⡿⣿⣶⣤⣥⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳

⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⠉⠀⠀⣀⣙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⠁⠀⡞⠉⠉⠉⠉⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡞⠋⡏⠀⠀⣇⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡇⠀⡇⠀⠀⠈⠙⠛⠋⠉⢹⠂⠀⠀⣀⠤⠤⠤⠤⣀⠀⠀⠀⠀⠀ ⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⣁⠤⠤⠤⣀⢀⣹⣀⠀⠀⠀ ⠀⢳⣀⡇⠀⠀⠀⠀⠀⠀⠀⣼⠀⢠⣾⣗⡩⢍⠉⠒⢝⢦⠀⠑⠒⠆ ⠀⠀⠀⣧⠀⠀⠀⡏⢹⠉⠀⡇⠀⣫⣠⠂⠐⠎⠀⠀⡸⢈⢇⣤⡠⠎ ⠀⠀⠀⠘⠦⠤⠖⠁⠈⠙⢺⡗⠉⠀⢈⣓⠲⠯⠭⠭⢔⣛⠭⠊⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠘⠒⠒⠒⠉⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣿⡿⢴⣃⢸⠀⣇⠤⠤⠤⠤⠤⠤⣿⣸⠀⠀⠀⠀⣄⢽⠤⠢⠔⡿⢠⠀⠀⠀⠀⡀⢸⠤⠤⠀⠀⠁⠋⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠲⠙⣿⢸⠀⡇⠀⠀⠀⠀⠀⠁⣿⢀⠀⠀⠀⠀⠀⡆⢺⠓⡟⢸⠀⠀⠀⠀⠀⠀⣽⢤⠤⡤⣀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡟⣯⠘⠀⡇⠘⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀⠀⠀⢇⠐⣿⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣠⠁⠔⣠⡇⢀⠀⡂⢹⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⡄⢿⣰⠀⠀⠀⠀⠀⠀⠀⡌⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠃⢰⠀⠀⡇⠀⠀⡞⣆⢻⠉⠀⠀⡿⢸⠀⠀⠀⠀⠀⠀⠀⠇⣿⠰⠀⠀⠀⠀⠀⠀⠀⢿⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⡇⠀⠀⠀⡼⠀⠀⢇⠀⣼⡀⣄⠦⣿⢸⠀⠀⠀⠀⠁⠚⠔⡦⣿⠀⠀⠀⠀⠀⠀⠀⡆⣿⢀⠀⠀⠀⠀⠀⠀ ⠒⠒⠒⠒⠒⠒⠐⠀⡀⢹⡄⠘⠀⡌⠀⠀⠀⡇⡞⢒⠒⠒⠒⣗⢸⠀⠀⠀⠀⢣⠈⠀⠀⣇⠐⠀⠀⠀⠀⠀⠀⠀⣦⠻⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⢰⠇⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⣄⠑⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⡆⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠀⡏⠀⠀⠀⠃⢰⠁⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⢀⡏⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢺⠉⣸⠀⠀⠀⠀⠞⣠⠀⡀⢄⠲⠙⠈⠀⠀⠀⠀⠀⢢⠓⣾⣦⠘⠀⠀⠀⠀⠀⠀⡄⠒⢣⣰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡷⢹⠀⠀⠋⡴⠀⠇⠤⠤⠤⠤⠤⣤⣤⠤⠤⠦⠶⠤⣤⠤⠧⣇⠸⠀⠀⠀⠀⠀⠀⠞⣤⠤⠀⠤⠤⠤⠤ ⠤⠤⠤⠤⠤⠼⠤⠥⠿⣰⣷⢿⡰⣦⣹⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⡟⢠⠀⠀⠀⠀⠀⡇⢺⠀⠀⠀⠀⠀⠀⠂ ⠀⠀⠀⠀⠀⢸⠀⡿⢙⠈⡄⣠⠀⠉⣏⠘⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡇⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⣾⣦⣿⣿⣿⣿⣿⣼⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠈⢀⡏⣀⠤⢶⡒⣒⣶⣴⢃⢰⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠉⠉⠉⠀⠀⠀⠀⢇⠬⠤⠤⠤⠤⠤⠿

⠀⠀⠀⠀⢀⣴⣶⠿⠟⠻⠿⢷⣦⣄⠀⠀⠀ ⠀⠀⠀⠀⣾⠏⠀⠀⣠⣤⣤⣤⣬⣿⣷⣄⡀ ⠀⢀⣀⣸⡿⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠙⣷ ⢸⡟⠉⣽⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿ ⣾⠇⠀⣿⡇⠀⠀⠘⠿⢶⣶⣤⣤⣶⡶⣿⠋ ⣿⠂⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃ ⣿⡆⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⢿⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀ ⠘⠻⠷⢿⡇⠀⠀⠀⣴⣶⣶⠶⠖⠀⢸⡟⠀ ⠀⠀⠀⢸⣇⠀⠀⠀⣿⡇⣿⡄⠀⢀⣿⠇⠀ ⠀⠀⠀⠘⣿⣤⣤⣴⡿⠃⠙⠛⠛⠛⠋⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠒⠒⠒⠲⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣚⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀ ⣶⡀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠁⠀⠈⠉⠉⠉⠓⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀ ⠘⢷⣶⡾⠿⠭⣙⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣄⠙⡆⠀⠀⠀⠀⠀⠀⠈⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢹⡀⠀⠀⠀⠀⢀⠞⠁⠈⠑⠢⠤⣀⣀⡀⠀⠀⠀⠀⣀⠴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⢳⠀⠀⠀⢠⣯⢴⣶⣖⣺⣿⢲⣦⡬⣍⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣈⢧⡀⠀⠸⣷⣾⣡⣿⣇⣼⣏⣨⡷⢛⣯⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣯⣓⠂⣼⡿⢷⣾⣉⣀⣉⠉⠳⠟⣿⠴⡿⢻⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⣷⣶⠤⣄⠀⠉⠙⣲⢄⠀⠀⠻⣿⣿⣿⡜⣷⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⠀⠀⠉⠲⣤⣼⣾⣷⡄⠀⠈⠁⢈⣇⣁⠀⠀⠀⠀⠀⠀⣰⠋⠈⣳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡟⠻⣿⡿⣆⢀⣄⢀⣼⠿⣟⠛⠛⡄⠀⠀⣸⡏⣹⠀⠀⠀⠀⢀⡴⠁⠀⣰⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⣦⡙⠒⠻⣄⡽⡏⣻⡟⢻⣿⢻⣤⠻⣿⣾⣿⣿⢁⣿⡆⠀⠀⣠⡞⠁⢀⣾⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠛⠿⠶⣾⣤⣿⣧⣟⣎⣉⣉⢙⣶⣿⣿⡿⠹⣾⣿⣿⡆⠀⢻⠀⢠⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠋⠉⠁⠀⠀⠀⠀⠛⠛⠃⢰⠋⠀⣾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⢹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⡀⠀⠀⠀⣀⡼⠁⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀