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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⡿⠓⠶⠾⠿⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⠖⠻⠷⡶⣮⡙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⢀⣚⡯⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣄⣀⣀⣀⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⠀⠀⠀⠀⠀⠀⢀⣰⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠉⠛⠿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣾⣉⠳⠄⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⡀⠉⠁⠀⠀⠀⠀⢠⣴⣤⡀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣾⠿⠁⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠀⠀⠀⠀⠀⠉⠻⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠁⢀⣼⡧⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣴⡒⠒⠶⣤⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠁⠀⢀⣠⣼⡟⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣤⠀⠀⠀⠤⠖⠚⠉⠉⣀⡠⠤⠒⢲⡆⠁⢀⡴⢩⡿⢤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⢀⣴⠞⠋⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⢽⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠋⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⢀⣤⣾⣥⠤⠴⠛⠋⠉⠙⣆⠉⠢⡄ ⠀⠀⠀⠀⠀⣠⠟⠁⢠⡾⠋⠁⠀⠀⠀⣼⡇⠀⡀⠀⠀⠀⠀⠀⢰⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⠀⠀⢠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠈ ⠀⠀⠀⠀⣴⠋⢀⡴⠋⠀⠀⠀⠀⠀⠀⣿⠿⢛⣣⣄⣀⡀⠀⠀⠀⢨⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣄⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀ ⠀⠀⠀⣼⠇⢀⡟⠁⠀⠀⠀⠀⠀⠀⠰⣿⠀⠈⠈⢻⣟⠉⠉⠉⠉⠉⠛⠻⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢠⣶⠏⢸⠛⠛⠒⢲⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡟⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⡀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠙⠿⣿⣀⢀⣀⣤⣄⠀⠀⠀⠀⣀⣀⣾⣿⣿⣄⣠⣏⠀⠀⠀⠺⣯⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠘⣷⣤⢹⣄⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣯⣤⣴⣦⣾⠷⣿⡋⠀⠀⠈⠉⢹⣿⣦⣿⠛⢷⣬⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡏⠙⢿⠟⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⡀⠀⠀⠈⢿⡷⣦⡀⠀⢸⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⡇⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⣇⠘⡆⢳⣬⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⡇⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡾⢻⣶⠿⣶⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠃⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣏⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡎⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⡀⠀⠀⠀⣠⠴⡲⠛⠉⠉⠓⠲⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣇⡴⢠⠞⢁⠞⠒⠒⠤⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡆⠰⣄⣹⢠⠃⠀⠸⡄⠀⠀⠀⠱⠀⠀⠀⠈⡇⠀⠀⢀⣠⠄ ⠀⠀⠀⣀⡴⠚⠉⠉⠉⠓⠙⠊⠂⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⢠⠇⣠⢶⠟⠁⠀ ⣠⠶⡚⠉⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡚⠁⠀⠀⡄⠀⠀⠀⢠⠞⡰⢡⠏⠀⠀⠀ ⢷⠔⠁⠀⠀⠀⠀⡎⠁⣹⡆⠀⠀⠀⠘⡖⠤⢤⡿⣄⠤⠞⠁⢰⠃⡟⠀⠀⠀⠀ ⠘⣦⠀⢠⠠⡀⠀⠙⠿⠔⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣼⠀⡇⠀⠀⠀⠀ ⠀⠈⠳⣄⣧⠙⢆⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⡿⠀⣇⠀⠀⠀⠀ ⠀⠀⠀⠈⣻⢦⢈⢧⠀⠀⠀⠀⠐⠉⢡⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⢀⠏⣸⠀⠈⠆⡀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⣸⠁⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠃⢠⠀⡴⠁⠀⠀⡆⠀⠀⠀⠈⠳⣄⣀⣠⠞⠁⠀⣰⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢶⣹⢠⡧⡀⢀⡼⠁⠀⠀⠀⠀⠀⠈⠻⡀⠀⢀⡴⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡏⠀⠈⠷⠗⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣆⠀⢄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⠋⡛⠲⢵⣦⣽⣦⣀⣀⠀⢀⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠒⠓⠒⠉⢸⣕⣠⣈⡭⠝⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠉⠙⢋⡉⠉⠉⠹⣇⣀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠄⠀⠈⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠛⣻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⣀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠠⣤⣄⠀⠀⠀⠀⠙⢷⣶⣤⣄⢹⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠘⣷⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⠿⢿⣇⠀⠀⠀⠀⠠⠿⠶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠁⢀⣠⣤⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡀⠘⠿⣿⣿⣿⣿⡿⠿⠟⠛⣉⣉⣉⣉⡉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⠿⢃⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣏⡦⠤⣤⠽⠤⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠣⢈⠇⠀⠁⣠⡿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠀⠀⠀⠀⠀⢀⡀⠈⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⡀⠀⡰⣯⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⡹⠂⢽⠎⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠃⣴⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠧⣢⠌⣁⠐⠋⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⢀⡔⠛⠒⠒⢛⣰⣶⠤⣤⡒⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⢸⡟⡁⠲⢒⠂⠹⠉⠀⠈⢥⡔⡉⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢁⠊⠓⣎⠀⠁⠀⠢⡀⠀⠀⢸⠒⢃⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠹⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡗⠀⠀⠀⣀⡠⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⡠⠔⡟⠀⠀⢀⡰⠁⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⡥⣠⠴⡗⢴⣇⠀⠀⠀⠀⠀⢀⡄⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠋⠀⠀⣱⡈⠛⠉⠉⠂⢴⠴⠞⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠁⢧⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠡⡀⠙⣇⠀⠀⡴⠁⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣉⡦⠄⡓⢰⠋⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡿⢇⡩⢀⡤⠤⠼⡄⠀⠀⠀⠀⣠⡟⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠱⣀⣀⣄⣶⠏⠙⠲⢬⣉⠫⠶⢶⣤⣄⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⡾⠁⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⢉⡻⢦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⡇⡀⢀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢼⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⢀⣀⣴⡽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠿⠻⠿⠿⠭⠭⢭⢭⠿⠛⠀

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠀⠀⠀⠀⠙⢮⣧⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣄⣤⣿⠷⠿⠟⣶⠶⠶⠛⠛⠓⢲⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠿⢿⡛⣦⠀⠀⠀⣾⡯⠀⠀⣶⣀⣾⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⠼⣴⣶⣤⣾⡟⠀⠀⠀⠈⠀⠀⢀⣿⡿⣷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠒⠛⠋⠉⠉⠁⠀⠀⠉⠉⠛⠁⠀⠀⠀⢀⣠⠖⢫⠏⡇⢻⠳⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠁⠀⠊⠀⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣶⢿⣝⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣤⣀⠈⠳⢦⡝⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠈⠙⢶⣾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⠔⠋⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣴⣖⣒⣒⣛⣛⣉⣉⣉⣤⡤⠤⠤⠔⠚⠿⠛⣷⡀⠀⢀⣤⢶⣟⠯⠤⠤⠤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠘⢧⣄⠀⠉⠛⠒⠒⠒⠶⡍⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢬⣉⣙⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⢄⠀⡚⠿⢶⣠⣴⣶⣶⣶⣶⢷⢦⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠻⢷⣽⣷⣴⣿⣿⣿⣿⣽⣿⣧⡤⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠠⠽⣿⣿⡿⣾⡟⣿⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⡾⣿⣾⡿⣿⣿⣿⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣽⣳⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣖⢒⣽⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡀⠻⣿⣿⡿⠉⠁⠀⠀⠑⠽⠷ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⢗⣷⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠀⠀⠀⠀⠚⣿⣿⣿⣿⡿⠚⢡⣴⣿⣵⣯⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⢈⣱⠀⠀⠈⢿⣿⣿⣿⣧⣤⣿⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡖⠋⠀⠀⠀⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠛⠳⠟⠛⠛⠉⠉⠉⠻⢿⡿⢿⡟⠛⠛⠉⠉⠉⠓⠚⠚⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣄⣀⣀⣤⣴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⢞⣻⣽⠿⠿⠟⠛⠳⠶⠾⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⢱⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣴⠾⠛⠉⠉⠉⠁⠈⠉⠉⠻⢷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣧⡙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⣦⣭⣉⠉⠙⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣶⣤⣤⣤⣤⣄⣀⠀⢀⣴⡶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠛⠻⢶⣤⣈⠛⠷⣤⣀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣟⠻⣦⡈⠉⠛⠻⠿⠋⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⡀⠙⠻⢶⣶⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⣿⠳⣿⣦⢼⣧⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡿⠆⠀⠀⠀⠀⠐⣿⣷⣯⠉⠀⠁⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠃⠀⢀⠀⠀⠀⠸⠟⠉⠀⠀⠀⢠⣶⣶⣄⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⣀⣤⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣧⣤⣄⠀⠀⠀⠀⠀⠀⢀⣼⠿⣤⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠸⣷⠀⢀⡴⠛⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣅⡘⠟⠻⠿⣷⣶⣴⣶⡾⣿⣿⣤⣿⣿⠁⠀⠀⠀⠀⢰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⢋⣠⠤⠖⠒⠚⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣄⠀⠘⠿⣾⣦⣤⣄⠀⠉⠙⣿⣄⠀⠀⠀⠀⠈⢻⣿⢶⣄⠀⠀⢀⣀⣠⣄⣄⣴⡿⠾⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣤⣠⣾⡿⣿⣷⡀⠀⠈⠛⢷⣤⣆⣀⠀⠈⣿⣦⣿⢻⣿⣿⣿⠿⣿⣿⣿⣤⣴⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⣿⠟⠃⠀⠀⠀⠀⠀⠈⠙⢷⣯⣭⣤⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠉⠛⠉⠉⠙⠛⠳⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣁⣤⣤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣠⡿⠖⠋⠉⠁⠉⠉⠛⠛⣗⠤⠀⠀⠀⠀⠀⠀⠈⠛⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡯⠟⠛⠉⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⣴⢛⣒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⡟⠁⠀⠀⢀⣤⣤⡄⠀⠀⠀⠈⠋⢉⣩⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⠻⠁⠀⠀⠀⠀⠙⠿⠿⠃⠀⠀⠀⠀⠀⠈⠻⡷⢯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠹⣿⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⢶⡛⠙⡿⡖⠶⠤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⣻⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠘⢿⡦⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡠⠖⡿⢧⣷⣌⠀⠻⣍⡉⠒⠤⣄⡀⠉⠙⠂⠀⠀⠻⣞⡛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⠃⠀⠀⠀⠀⠀⠸⡿⠶⣤⣄⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⡜⠁⠀⠀⠈⠉⠉⠛⢿⣦⠀⠀⠉⠳⢄⡀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠻⣦⡀⠙⢷⡀⠀⠀⠀⠀⠀ ⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡽⠋⠀⠀⠀⠀⡀⠢⣦⣿⡄⠀⠀⠀⠀⠙⣦⠀⠻⣄⠀⠀⠀⠀ ⣸⠁⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⢿⠙⢆⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣭⠿⠗⠒⠒⠒⠖⢿⡿⠟⠀⢸⡧⡄⠀⠀⠀⠀⠈⢳⡄⠹⣆⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⢀⣾⣻⡿⠦⠀⠀⢇⣈⣽⣾⣷⡀⣀⠀⠀⠀⢀⣠⣀⡀⣀⣶⡿⠛⠀⠀⠀⠀⠀⣠⡴⣏⣀⠀⠀⠸⣯⠀⠀⠀⠀⠀⠀⠀⣧⠀⢻⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡶⠟⣿⣼⢿⡏⠉⠁⠀⢙⣿⠾⡷⣴⣤⣭⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⢸⣯⡎⣩⢋⣴⡗⢸⠿⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠸⠇⢀⣴⢾⡿⡏⢠⠀⣤⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⠟⠁⢷⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣵⡞⣸⠁⣸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⢿⠋⢷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢸⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡌⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⢿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢿⢠⠊⢁⢀⡀⠑⡄⠀⠀⠀⠀⠀⠀⡤⠒⠐⢢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⢪⠆⡆⢰⠁⠀⠘⡀⠰⡀⠀⢀⣀⣠⣊⡀⠀⡰⠉⡇⠀⠀⠀⠀ ⠀⠀⣠⢎⠔⠁⠀⠱⡘⢆⡀⠀⠑⢤⡬⠉⢠⠶⣶⡄⠀⠉⠢⡠⠃⠀⠀⠀⠀ ⠀⡔⡵⠁⠀⠀⢠⠎⠈⠒⢤⠭⠭⠀⠀⠀⢺⡿⢿⡇⠀⠀⠀⠠⠓⠢⡄⠀⠀ ⢰⢹⠁⠀⠀⡰⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⣉⣀⠐⢂⡠⡀⠑⢤⣔⣁⠀⠀ ⢸⢠⠀⠀⢠⠃⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠐⡯⣔⣀⣀⣴⡡⢇⠢⠀⠈ ⠸⡼⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⣀⡀⠠⠊⠀⠀⢐⡿⠟⠀⠀⡆⠈⠀ ⠀⠙⢜⡦⢼⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠙⢆⢸⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⣛⣆⠀⠀⢸⠀⠀⠀⠀⠀⠀⡜⠀⣠⣞⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠀⠘⢆⠀⢸⠉⠐⠒⠂⠉⡝⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠾⠶⡾⠃⠀⠀⠀⠘⠼⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠄⠀⠀⣿⠀⠙⠁⠄⢰⡀⣐⠛⠬⢠⢀⠉⠄⠠⠆⣄⠄⠤⢬⡀⢀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡠⠔⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⡜⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠉⠙⡆ ⠀⠀⠀⠀⠀⠈⠀⠀⠠⣼⣧⣶⠙⡶⠶⣴⣠⣀⣄⢤⠖⢩⠎⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣆⢀⣤⣇⠙⠈⠀⠀⠀⠁⠉⠁⠃⡾⡆⡎⠀⠀⠀⠀⠇ ⠀⠀⠀⠀⠀⠀⠈⢢⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢱⠀⠀⢀⠜⠀ ⠀⠀⠀⠀⠀⠀⠀⡜⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢓⣽⣂⠤⠋⠀⠀ ⠀⠀⠀⠉⠐⠠⢙⣧⠚⠛⠀⠀⠀⠀⠀⠀⢾⣷⡄⠀⠈⣷⠀⢀⣀⣀⠀ ⠀⠀⣀⠀⠈⢐⣺⢕⠱⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠒⣹⠋⠀⠀⠀⠀ ⠈⠀⠐⠂⣈⠉⢘⣗⡈⠀⠀⠀⠀⠀⣀⣴⣾⣬⠭⠥⡤⢋⡈⠉⠁⠀⠀ ⢀⠄⠊⢀⠠⠀⠒⠙⢍⠂⠺⣜⡾⠀⠛⠛⢝⡽⢆⡽⢓⠤⡀⠈⠂⢄⠀ ⠀⠀⡠⠃⠀⠀⠀⠀⠈⠢⢤⡜⢤⣀⡠⠜⠟⢲⠉⠈⠂⡉⠂⡑⢄⠀⠀ ⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠐⠀⠁⠀⠀⠈⠂⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⠛⠁⠀⢰⡀⣐⠓⠬⢠⠀⠁⠀⠠⠆⣄⠀⡤⢬⡀⢀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⠤⠤⢤⣀⣀⠀⡇⠀⠀⠈⠑⣮⠛⠟⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣀⠀⡤⠋⠀⠀⢀⣠⣬⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠉⠉⣀⣀⠊⣱⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡔⣿⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⢒⡾⠋⠉⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡔⣣⣼⣿⠁⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣆⣤⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⢋⣼⠿⣟⢯⡀⠀⠀⠀⠀⣠⣮⠤⠖⠛⠋⠉⠓⠻⣦⡠⠀⠀⢀⣿⠯⢄⡀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⢃⡞⠁⠀⠈⠻⣝⠒⣶⣶⣮⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠺⢎⡛⣻⣶⡞⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⢸⠀⠀⠀⠀⠀⠘⠳⠼⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡨⢭⣽⣷⣶⣶⣾⠿⠿⠯⠝⠛⠿⠿⠶⣦⣄⠀ ⢣⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⢖⣒⡈⠭⠕⠒⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠇ ⠀⠑⢤⣙⡓⠂⠄⠀⠀⠒⢒⣒⣛⣉⡩⠭⠔⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀ ⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⣠⡴⠿⡶⠤⢤⡤⠟⠗⢶⣦⣤⣀⣀⣨⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣏⣀⠤⠂⠀⠀⠀⠐⢿⣿⣿⣷⠈⠛⢿⡦⠤⠼⢷⣶⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⡿⢹⡈⠘⢩⣉⡙⠓⠲⠿⠉⠁⠀⠀⠀⣦⡤⠖⠉⠉⠉⠚⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠤⠊⢁⡼⣧⣁⡷⠬⠤⠞⠉⠢⣄⠀⠀⠀⠀⠀⠀⠘⣯⣭⣽⠅⢀⣴⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⢠⠏⠀⠀⠙⣆⣄⣀⣀⡀⠀⠈⠳⣄⠀⠀⠀⠀⠈⣏⣉⣁⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠋⠀⠀⠀⠀⠈⠙⠦⡀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠂⠀⠀⠀⠀⠀⢴⡶⠾⠛⠁⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⣻⠇⠀⠀⠀⠀⠀⢰⡗⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⣴⡞⠛⠉⠀⢠⡏⣀⣀⣤⠒⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣷⡖⢫⣴⠶⢾⣇⠙⣾⣻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣿⡿⠁⠀⠀⠀⠻⡄⠈⠻⡼⠛⠛⠓⢦⣄⣀⣄⣠⣠⣿⠈⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣻⡄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠴⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢿⣿⡄⠀⠀⠀⠀⣤⡖⠉⠀⠀⠀⠀⠀⠀⠀⣾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⢹⣧⡀⠀⠀⢲⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⣀⠈⠻⣄⢠⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣤⣶⡶⣶⢾⠋⠉⠙⠂⠈⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣽⠽⠃⣠⠾⠀⣠⡶⠶⠶⢾⢧⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡛⠯⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠿⠶⢿⣷⠶⠞⠋⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⣠⡀⣿⠛⢷⣤⣈⠙⠻⢿⣳⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⢤⣤⣼⣶⣿⡟⠋⠀⠀⠉⠛⠿⢶⣦⣌⣉⠓⠚⠿⠿⣿⣶⣦⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⢱⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⠶⣦⣤⣄⣉⠙⠻⣿⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⡋⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⢄⡙⢿⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡷⢾⠆⡀⢀⢀⡆⣹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡌⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣼⡇⣿⢈⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠛⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢏⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⢾⣿⣿⣿⠿⠿⠿⠿⠿⠶⣶⣿⣿⢿⣿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠶⠶⡶⢶⠿⠛⠁⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠾⠟⠓⠚⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⢀⣄⣠⣌⣙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣴⡚⠋⠉⠁⠈⠉⠑⠺⣦⡀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⢀⡠⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠉⠉⠉⠙⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠿⠦⠑⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⠆⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠙⢶⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⣸⡇⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠇⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⡖⠴⢤⡽⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⣤⡴⡿⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⡷⠀⠀⠀⠒⠈⠉⡠⠄⠒⣲⠖⠁⣠⣣⢟⠦⡀⠀ ⠀⠀⠀⠀⢠⠞⠁⣠⠞⠉⠀⠀⡇⠀⠀⠀⠀⠀⢘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⢀⡠⠊⠁⠀⣠⠾⠛⠋⠉⠁⠀⠈⢣⠈⠣ ⠀⠀⠀⣰⠋⣠⠞⠁⠀⠀⠀⢸⠷⢶⣆⣀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀ ⠀⠀⣰⠃⢰⠃⠀⠀⠀⠀⠀⢸⡄⠈⠙⣿⡉⠉⠉⠉⠛⠳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡴⠊⡘⠛⠒⢲⣦⡀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⡟⠀⡏⠀⠀⠀⠀⠀⠀⣿⠀⣄⠠⡘⢿⣦⠀⠀⠀⠀⠈⠙⠳⣦⣶⡶⠂⡀⣠⣠⡦⠟⠻⠷⢴⣇⢠⣤⣙⢾⡷⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠙⣧⡟⢷⡵⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡋⠉⠘⢷⣤⣀⠀⢸⠙⠛⠃⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣧⢰⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⢸⡄⢆⢳⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠞⢳⠛⢿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⢣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡟⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢠⡇⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠉⠉⠻⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⡾⠀⠀⣸⢷⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⣫⠟⠀⠀⠀⠀⢹⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢲⣾⣿⣾⣿⡏⠈⣿⠿⠿⢻⣾⣧⣴⣦⣴⣦⡴⣺⠟⠉⢠⡞⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢀⡈⣇⠙⣿⠙⠁⠀⠀⠀⠀⠀⠉⠈⠙⠏⢸⠏⢰⣇⣀⠀⡿⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠐⣿⡿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⣯⠀⣇⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡏⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢹⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡧⢿⣤⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣴⠾⠤⠤⠞⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠑⠲⢤⡀⠙⣿⣠⠐⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣦⡀⠀⠀⠈⢹⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠈⠓⣿⡋⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠃⠀⠀⠀⢘⣾⡧⠤⠔⠒⠒⠒⠚⠈⠉⠉⠉ ⠀⠀⠀⠀⣀⣀⠤⠤⠤⢄⣉⣻⡧⣈⠓⢝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠊⠉⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠐⠉⠉⢀⡀⠤⠄⠒⠒⠂⠽⣗⣢⠕⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠓⠒⠈⠉⠉⣹⠏⠉⠉⠑⠒⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡠⠤⠀⠂⠀⠐⢻⡮⣧⡀⠀⠀⡀⠀⠀⢀⡀⠀⣰⣾⣿⣿⣯⣭⣭⡉⢉⢉⡿⠛⠒⠦⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⠔⠊⠁⠀⢀⠠⠐⠒⠁⠉⠻⣏⠉⠀⠘⢷⣼⣳⣾⠇⠀⠙⢯⡙⢯⡙⣿⢿⣖⣤⣿⡓⠢⢤⡀⠀⠀⠉⠓⢤⡀⠀⠀⠀⠀ ⠀⠘⠁⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⢹⣏⠀⠀⠀⠀⠀⢱⣤⣿⣇⡤⠼⠛⠣⣌⠑⠢⢌⠑⢤⡀⠀⠀⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⣟⡙⣳⡤⠤⠤⠖⠋⠹⡄⠈⢆⠀⠀⠀⠀⠑⢄⠀⠑⢆⠈⠲⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢱⠀⠈⠃⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠈⠳⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠙⣦⣤⠀⠀⠀⠀⡀⠀⠀⣼⣦⡀⢤⡀⢀⠘⠳⡄⠀⠀⡀⣄⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⢘⣿⡤⠜⢨⠀⠀⠤⠀⠤⣤⠀⣴⡉⠉⠱⠾⠀⡎⢠⠀⠀⠀⠠⠲⠿⠰⡶⠤⠆⢰⡶⠚⢤⠄⠀⢄⠀⠀⠀⠀

⠀⢀⡠⣤⣤⠤⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⡟⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⢀⣀⡠⠄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⣅⠤⢄⣀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠉⠳⢤⣀⣀⠀⠀⣀⡀⠀⠀⠀ ⠀⠀⠉⠑⠢⣕⠢⢄⣠⠜⠁⠀⠀⠀⠀⢀⠀⠀⠀⢺⣻⣫⠉⠛⠁⡧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠒⠢⢤⣀⠀⠀⠀⠀⢸⠇⡀⠀⠝⠋⠀⣤⡀⠀⢷⠀⠀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠖⢤⣤⡤⣏⣾⠃⠀⢠⣀⠀⠙⠋⠀⠘⡦⡊⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣭⣿⣦⠈⠓⠤⣀⠻⢷⣶⡗⠷⠯⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠻⠟⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠎⠉⣁⠈⠉⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡠⠖⠂⠐⡊⠀⠀⠀⠈⠲⠄⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠔⠁⠠⣤⠀⠈⠉⣵⡀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡀⠀⠀⠀⠀⠀⠀ ⣗⡆⢲⠂⠀⠠⢀⠀⢸⡆⠀⠀⠀⠀⠀⡇⠀⠀⢲⣈⠐⢄⠀⠀⠀⠀ ⠀⠈⠀⠘⠂⡀⠀⠀⠀⠁⠀⠀⠀⠀⣸⠇⠀⢀⢠⡄⠉⠢⡑⠄⠀⠀ ⠀⠀⢠⣶⡉⣏⣣⢆⡀⠀⢀⣀⡠⠞⠉⠀⣡⡋⠀⡇⠀⠀⠘⡌⡄⠀ ⠀⠀⠈⠉⠙⠹⢠⢴⡏⣩⠏⠁⠀⠀⠀⠈⠓⠗⠡⠃⠀⠀⠀⠃⡇⠀ ⠀⠀⠀⠀⠀⠀⠉⠗⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄

⠀⠀⠀⠀⠀⠀⠀⡤⢶⡴⠒⠒⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣰⢫⡶⠚⢲⠀⡹⠒⠉⠑⠲⢄⠀⠀⠀⠀⠀ ⢀⣄⣀⣀⡠⣖⠉⠁⠊⠀⢤⣊⡴⠁⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀ ⠈⢿⠀⠀⠀⠛⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀ ⠀⠀⠑⢤⣀⣀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠉⠓⢦⠀ ⠀⠀⠀⠀⠾⢥⡋⣁⡤⠮⢤⡴⠂⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠛⠒⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⣰⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⡤⠴⡤⢤⣤⠴⠠⠤⠄⠀⠆⡲⠦⠲⠠⠶⠶⠀⠀⠀

⢰⠶⡖⠒⠢⡤⢄⣴⣉⣷⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣄⠀⠀⠘⢿⣷⠀⢹⣿⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠯⡒⠀⠀⠀⠀⠻⡿⠟⠛⠓⠤⠖⠒⠒⠒⠒⠒⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢣⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢣⣇⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣴⡒⠉⣹⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣧⡏⠀⠀⡝⠀⣠⡟⠓⠢⢄⣀⠀⠀⠸⡁⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⢁⣀⣼⣥⠞⠁⠀⠀⠀⠀⠀⠉⣟⠒⢳⡄⠀⠀⠀⠀⢠⠶⡾⠉⠒⢤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠛⠟⠛⠒⠁⠀⠀⠀⠀⠰⠾⠿⠿⠿⠿⢋⣈⣢⣀⣠⠞⠋⠉⠓⠢⢄⡀⠈⠑⢄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠿⠯⠭⠤⠼⠃⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⢣⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠈⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⠤⠤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠐⠒⠢⠤⢄⣀⡉⠉⠉⠀⠒⠒⠒⠀⠉⠀⣠⠞⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⠒⠒⠒⠒⠒⠊⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠦⠰⣶⠶⠀⠀⠶⠀⠀⠲⠀

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

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠒⠂⠀⠀⠀⠀⠀⠈⠉⠐⠂⠄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⠀⠀⠀ ⠀⠀⠀⠀⠠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀ ⠀⢠⡖⡲⣅⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀ ⠀⠈⠿⣿⠧⠋⠀⠉⢇⡀⠀⠀⠦⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱ ⠀⠘⠀⠁⠀⢀⠀⠀⠀⡌⡄⠀⢀⣄⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⢶⡚⡆⠀⠀⠘⠇⠀⠀⠑⣴⡔⠉⣡⣧⡷⣃⠀⠀⠀⣀⡴⠂⠀⠀⠀⠀⢀⡴⢾ ⠀⠉⠓⢔⣤⡀⢀⠀⢀⠄⣹⠇⢠⠛⢛⡠⣊⢤⠖⠚⢧⣘⣦⢀⢀⡐⠋⣹⠀⣸ ⠀⠀⠀⠀⠈⠀⠪⢑⣤⡷⠹⠷⡾⢚⢄⢼⣻⡹⠒⠉⠀⠀⠀⠉⠙⠂⠒⡛⠄⡾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢊⠤⡼⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⣂⣻⡦⠶⠟⠊⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⡨⠓⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⡦⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣋⣄⣀⡀⠀⠀⠀⠀⠀⠉⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⣀⣀⡴⠓⠉⠉⠀⠉⠉⠻⢶⡀⠀⠀⠀⠀⠉⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠁⠀⠀⢀⠤⣀⠀⠀⠀⠀⠀⠀⠉⠛⠢⠄⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⠞⠁⠀⣀⣤⡀⠀⠀⠘⠊⢙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠋⣀⣀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠘⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⠓⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣸⣟⣄⠘⣯⠍⠍⣉⠒⠂⠤⡀⠀⢠⣾⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠙⣧⣀⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀ ⠐⢁⠎⠈⠉⠓⠒⠻⢦⡀⠉⠒⢄⡀⠀⠀⠉⠲⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⣣⠈⠙⠳⣄⠙⢦⡀⠀⠀⠀⠀ ⢀⠋⠀⠀⠀⠀⠀⠀⠀⠙⣄⣄⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣁⠀⠀⣀⣄⡲⢿⡀⠀⠀⠈⠳⣄⠹⣄⠀⠀⠀ ⡌⠀⠀⠀⠀⠀⣠⣶⣏⠉⠙⡌⢷⣼⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠋⠉⠉⠉⢉⡽⠉⠀⢸⡱⠀⠀⠀⠀⠈⡆⢹⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣯⡵⢶⣴⢿⠛⠋⠉⣺⡶⣦⣤⣙⡿⠾⠋⠁⠀⠀⠀⠀⢼⡟⣻⣃⣴⢰⠇⠀⠀⠀⠀⠀⢻⠀⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⢀⡴⣿⣿⢠⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠋⠳⠏⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣧⢧⡼⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢻⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄

⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⢞⣯⠽⠟⠚⠛⠲⠾⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⢣⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡶⠶⢤⢦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⠋⠁⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⢮⣝⣚⠒⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣦⣤⣤⣤⣀⡀⢀⣤⠤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠙⠳⢦⣍⠓⠦⣄⣀⣀⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⡻⡟⢳⡄⠉⠙⠛⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣀⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣤⠀⠀⠀⠀⣿⣜⡿⠎⠗⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠐⣾⠁⢀⡀⠀⠀⠾⠛⠁⠀⢀⣤⣄⠀⠀⠈⣿⡆⠀⠀⠀⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⣦⣤⣀⠀⠀⠀⢀⣴⠟⣴⣾⠁⠀⠀⠀⠀⠀⠀⠘⠿⢿⠇⠀⠀⠈⣧⢀⡴⠊⠁⠀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣌⠉⠙⣿⣻⡛⠛⠻⠶⢿⡇⠀⠀⠀⠀⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣹⣯⠴⠊⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⡉⣽⣿⣦⡀⠈⠻⣦⣀⡀⠀⠘⣯⣻⢶⣶⣾⣯⣿⣿⣍⣩⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⢿⠿⠃⠀⠀⠀⠉⠙⢷⣾⣭⢽⣿⣿⠛⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠒⠒⠶⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡤⠶⠦⠤⠤⠤⢤⣀⣀⡀⠸⡇⠀⠀⠀⠀⠉⢳⡌⠳⢿⠳⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣄⡀⠀⠀⣀⡼⠃⠀⠀⠀⠀⣠⣈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠆⠁⠀⠀⠀⠀⠀⠛⠿⠿⠂⠀⢉⡓⢦⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣶⣦⣤⡼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⣸⡿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⢞⣟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⢒⣿⠟⠉⠀⠠⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⣁⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⡀⣀⣀⣴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡞⢥⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⢀⣠⣤⡤⠤⢤⣤⣼⡄⠀⠄⠀⠀⠀⢸⡿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⠋⣴⠟⠉⠙⢆⠻⣦⡀⠀⠀⠀⢀⣠⠾⠗⠛⠉⠁⠀⠀⠀⠀⠀⠀⠻⣧⣌⠀⠀⡀⢸⣿⣛⡓⠒⣶⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⠃⣼⠋⠀⠀⠀⠀⠱⣮⡉⠻⣷⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⣌⣉⣿⣿⣿⡍⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⢠⡇⠀⠀⠀⠀⠀⠀⠈⠻⠦⠾⠿⣿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣉⣽⠿⣴⣶⣶⣾⣿⣿⡿⠿⠭⠽⠿⠿⠿⢿⣶⣦⣄⡀⠀ ⢧⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠴⠒⣒⣋⡭⠽⠒⠚⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣻⡆ ⠘⢆⡈⠻⢦⣄⡀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⠤⠤⠖⠒⣚⣉⣭⠥⠶⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠾⠛⠀ ⠀⠀⠙⠲⠤⣤⣉⣉⣉⣉⣉⣉⣉⣭⡤⠤⠤⠴⠒⠒⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

🐭 🐁 🐀 🐹 🐰 🐇

⠀⠀⠀⠀⠀⠀⠸⠀⢠⣿⡟⡞⣏⡇⠀⢰⣿⠀⠀⠀⣀⣀⣀⣾⡷⢷⣤⢰⡈⠂⠀⠈⠙⠲⣿⣖⠒⠒⠂⠀⠀⠀⠀⠘⠀⠀⠀⠀⡀⠀⠀⠀⠹⡄⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⢠⢧⣿⡃⠀⣬⣿⠶⠚⠉⠉⣿⣿⣿⣿⡞⢿⡧⠹⣦⡀⠀⠀⠀⠈⠙⣶⣄⠀⠀⠀⠀⠀⠀⣀⡀⢤⣄⣿⣦⠤⠀⠀⢹⡀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡏⢸⣿⢀⠐⣿⣄⡀⠀⠀⠀⣿⣿⣿⣿⡆⠀⢻⣶⣮⡻⢦⣀⡀⠀⠀⠘⣎⠙⠺⣷⣖⡲⣦⣶⡿⠿⠋⠙⢿⡄⠀⠀⠀⢷⡀⠠⢱⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃⡇⢸⣿⢸⣿⣿⣏⣙⠿⣶⣶⣿⣿⣿⣿⠇⠀⠀⠉⠛⢿⣶⣍⣛⢶⣤⡀⠈⢳⣄⢠⣾⣽⠟⠁⠀⠀⠀⠀⠀⢹⡄⠀⠀⠈⢇⠀⠀⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣷⢸⣿⠸⢸⣿⣟⣿⣷⣾⣦⣤⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⠓⢮⣉⡹⣍⠛⠶⠿⠾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣶⡃⠸⡄⠀⠀⢳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⣿⠀⣸⠙⣿⢿⡟⣿⡿⠟⠻⣿⠆⠀⠀⠀⠀⠀⢀⣠⣴⣾⣇⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠃⠀⢳⠀⠀⠀⣧⣴⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿⠀⣿⠀⣹⡘⣿⠸⣷⠀⠀⢿⠀⠀⠀⢀⣤⣾⡿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣠⣴⣾⣿⠋⢀⣼⡁⠀⠀⠸⡇⢰⠛⣥⣿⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢿⠀⣽⡇⢻⡄⢻⣇⠀⣼⡀⢀⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣀⣼⣽⣧⠀⠀⠀⢻⠀⢠⠏⢿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⠀⣿⣿⠈⡇⠘⣿⣦⢸⡷⠛⠁⠀⠀⠀⠀⠤⠴⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⣿⣿⠽⠛⠉⠹⢿⣿⡄⠀⠀⡘⠐⠏⢀⣼⡿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡇⢸⣠⣿⣿⣇⠁⠀⠉⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠼⠋⠁⠀⠀⠀⢬⡿⣿⡷⣄⢀⡇⠀⣠⠿⠟⢳⡸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⡄⠀⠀⢻⢣⢿⠀⠀⢀⣀⡀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣼⡇⠀⣏⠀⡄⠀⢱⢧ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡀⢸⣷⣿⣦⣀⡐⠿⣇⠀⠀⠈⡎⠾⣿⣭⣽⣶⣶⣿⣿⠿⠿⠿⠿⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡟⣿⠀⡀⡿⠀⡇⠀⠀⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⡟⣟⡿⣏⠉⠻⣿⠀⠐⠒⢿⡿⣿⠿⣋⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡏⠀⣿⡇⠀⡇⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⡿⢳⠀⢇⠸⡇⢹⠀⡀⣩⣿⡿⣇⠀⠀⠸⣇⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠀⠀⣹⡆⠀⠀⠀⠀⠀⠀⠠⢠⣾⡇⢸⣩⡇⠀⡇⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⢠⡇⠘⡇⢸⡆⢻⡈⣆⢻⣁⠀⢰⢿⠀⠀⠀⢿⣆⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠁⣀⠀⠀⠀⠀⠀⣠⡞⢙⡇⠘⢿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢱⠀⡇⠘⢷⡜⢿⣾⣿⣾⣞⡆⠀⠀⠘⣿⣮⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢴⣶⣿⡇⠀⠀⠀⣰⣻⡗⠈⣶⠀⢸⡷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⢹⠀⢈⢿⣦⣍⡉⠒⠀⢧⠀⢠⠀⢿⣿⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⡶⠯⠭⠖⢋⣟⣿⡄⠀⠀⢀⣾⣿⠁⠀⡇⠀⢸⡿⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠈⡀⢸⡆⠈⠀⠉⣻⡿⢶⣶⣾⠀⠀⣇⠘⣿⣧⠙⢧⡀⢠⣀⠀⠀⠀⠀⠀⠀⠈⠻⣬⣐⣀⣀⣯⣿⣻⠁⠀⢠⢾⣹⣟⡆⠘⠁⠀⣸⠃⠀⠀⠀⠰⡄ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⣷⠀⠀⠀⠈⡇⠀⠘⣿⡄⠀⢻⢠⡹⣿⣿⣦⣍⡀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠈⠙⠢⢴⡿⠃⠀⣰⠋⠺⣏⡁⢣⠀⠀⢰⡇⠀⠀⠀⠀⠀⠱ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢇⠀⢸⡇⠀⢠⢰⡇⠀⢸⣿⣧⢸⠈⡀⣷⢱⣿⢙⠿⣿⣿⣶⣶⣤⣈⣉⠀⠠⠤⢀⣀⣀⣀⣀⡀⢴⡾⠁⠀⠀⠀⠙⢾⡆⠀⢸⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠸⡇⠀⣿⢸⠁⠀⣿⣽⠿⡄⠆⡇⢹⡍⣿⣆⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷⠶⢶⣶⡶⠿⣛⠷⢦⡀⠀⠀⠀⠀⢳⡀⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⢸⡇⠀⣿⠀⡏⣸⣀⡴⢋⣀⡴⡇⠀⠇⠀⠇⣿⢿⣆⠀⠀⠀⠀⠈⠉⠛⠉⠉⠀⠀⢀⣾⠿⠶⠦⠤⢤⡄⢙⣦⡀⠀⠀⠀⠉⠳⣮⣷⣀⣀⣀⣠⣶ ⠀⠀⠀⠀⠀⠀⠀⠈⣟⣄⠀⠈⡇⠀⡸⢸⣷⠟⠁⠀⣾⢾⠀⢳⠀⣸⠀⠀⢹⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⣇⡾⠁⠻⣄⠀⠀⠐⢄⠙⢿⡿⣿⣿⣿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⣓⣀⣹⡤⠗⠉⠈⢧⠀⢸⣿⠃⠀⢸⠀⢳⠀⠄⠉⡇⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠈⢧⡀⠀⠀⠁⠈⢣⠘⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⢧⠓⠁⠀⠀⠈⡇⠘⠀⡄⠀⡇⠀⠀⠀⠉⠲⠤⠀⠀⠀⢤⠀⢻⡀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⢸⣹⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⡇⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡒⠀⢷⡀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠈⠉⠉⠛⠛ ⠀⠀⠀⠀⢀⣠⡤⣰⡾⠁⠀⢀⠄⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⢻⠀⠀⢧⠀⡙⠒⠢⠤⣤⣀⣀⣀⠀⠀⠀⠹⣄⠀⠁⠀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⣿⣿⣾⣿⣿⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢀⠈⠀⠀⢸⣦⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠋⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢧⠀⠀⠀⠀⠀⠀ ⣠⢿⣿⣹⡟⠿⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢸⠀⢰⠀⡌⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀ ⠉⠉⢏⠀⢠⠀⠀⠰⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣸⠀⢸⠀⣇⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠀⠀⠀⠀⠀ ⢀⠀⢨⣤⣼⡂⠀⠀⣿⣿⣿⣿⡷⢶⣤⣤⠤⢄⣀⣀⣀⡀⢻⡏⠀⢸⠀⡿⡌⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠃⠀⠒⢻⣿⣿⡆⠤⢄⣻⣿⣿⣀⣀⣴⣿⣯⣿⠇⠀⢸⠀⢧⡿⡘⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢳⠇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡆⠀⢀⡴⠚⠉⠉⠉⠙⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⡇⢰⠋⠀⣠⠴⠲⢤⡀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⣹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡼⢣⡞⠀⡏⠀⢰⠁⠀⠀⠀⢱⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⣠⠟⠁⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⢋⣴⠋⠀⠀⣇⠀⢹⡀⠀⠀⠀⠈⢧⠀⠀⠙⠦⠤⠴⠒⠚⣋⠉⠉⠉⠑⠒⠶⣞⠁⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⢋⣴⠟⠁⠀⠀⠀⠘⣦⡈⠳⣄⡀⠀⠀⠀⠙⠒⣲⠆⠀⠀⢠⡞⠻⣿⣷⡄⠀⠀⠀⠈⠙⢦⡴⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠞⣡⠟⠁⠀⠀⠀⠀⢠⡾⠋⠙⠦⣀⠉⠉⠉⠉⣉⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢈⣷⠤⣄⡀⠀⠀⠀⠀ ⠀⢠⠏⣼⠃⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⢹⠋⠉⠉⠀⠀⠀⠀⠀⠀⠼⢿⡉⠙⠻⠃⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⣹⠀⠀⠀⠀ ⠀⡞⢰⠇⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡉⠉⠐⠒⠤⢀⠀⠀⠳⢤⣤⣶⣋⣀⠀⠀⠀ ⢰⡇⢸⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⣠⡤⠆⣈⡉⠛⠀⠀⢀⡼⢁⡯⢄⡀⠀⠙⠒ ⠸⡇⢸⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠷⠾⠥⠤⠤⣴⣾⣿⡤⠚⠳⡀⠉⢢⡀⠀ ⠀⣷⠘⣇⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣄⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠾⣿⣽⠟⠀⠀⠀⢡⠀⠀⠉⠀ ⠀⠘⣧⡹⣆⠀⠀⢿⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠢⠤⠤⠤⠤⠤⠤⠤⠴⣾⠋⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⠀⠈⠳⣌⡳⠦⣼⡀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠓⠾⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⣷⠀⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠛⢻⡆⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢀⣼⣛⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⢻⣄⠀⠀⠀⢸⠶⠤⣤⣀⣠⣤⡤⠤⠶⢶⠟⠀⠀⣰⠟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣤⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣶⣮⣷⠀⠀⠀⠀⠀⠀⠀⢿⣤⣿⣿⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠙⣦⣤⠀⠀⢠⠀⡄⠀⠀⣸⣦⡀⢤⡀⠀⠸⠳⡤⡀⠀⡀⣄⠀⠀⢀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢐⠀⠀⠀⠁⢘⣿⡤⠜⢨⠀⠀⠦⠀⠤⡤⠀⡴⡉⠉⠱⠸⠀⡆⢠⠀⠀⠄⠠⠶⠿⠰⡶⠤⠇⠰⠶⠚⢦⠄⠀⢤⠄⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡠⠤⠄⣤⠐⡚⠉⣛⣛⠲⠤⣀⠉⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠂⣉⢄⠠⡐⢴⠋⣠⣄⠈⢢⠈⢆⠈⠳⡄⠀⠱⣄⠀⠀⠀⠀⠀⠀ ⠀⠆⣜⣯⣿⣷⡈⣠⡾⣿⣮⣦⠀⠁⠀⢂⠀⢹⣄⠀⠘⡧⠀⠀⠀⠀⠀ ⠘⢠⠝⡜⠉⠉⠉⠈⠀⠀⠀⠉⠆⠀⠀⠈⡆⠀⣏⢂⠀⠐⡀⠀⠀⠀⠀ ⡇⡌⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡀⢰⣿⣿⡀⢆⠀⠰⡀⠀⠀⠀ ⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠐⡇⡄⡅⢸⣿⢿⠁⠈⠀⠄⠱⠀⠀⠀ ⠜⠀⢰⢸⢿⣳⢆⠀⠉⠉⠛⢹⣻⡇⢿⡇⢸⠋⣸⣤⣤⣀⣘⡦⢃⠀⠀ ⢻⠀⠀⡆⠘⡒⠀⠀⠀⠀⣀⣸⣋⣰⢸⠁⢸⡓⢿⣿⣿⣿⡁⢡⠹⡄⠀ ⠈⢀⠀⢰⡉⠁⠸⠄⠀⠀⠀⠀⠀⠁⢸⠀⠘⢀⣼⣿⣿⣿⡷⡀⠆⠀⠀ ⠀⠨⠀⠀⠘⠄⡀⠠⠀⠀⠀⠀⣀⢴⡟⠀⢰⣿⣿⣿⣿⣿⣿⣧⢘⡀⠀ ⠀⠀⡀⠀⠀⠀⠈⡂⠤⠤⠶⠈⠁⡻⣄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣯⣷⡀ ⠀⠀⠁⡄⠀⠀⠀⢁⢸⠀⢰⢃⢀⠁⣽⠀⣿⣿⣿⣿⡿⠟⠛⠛⠿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠈⠄⠱⡀⡀⢎⣼⣿⢸⣿⣿⣿⡟⠀⣴⣿⣿⣦⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠑⣇⣾⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⡿⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⣿⠿⠛⠉⠉⠉⠉⠛⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢸⡇⠀⢀⠀⢀⣴⡾⠋⣠⣞⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣧⣴⡏⢠⡾⠋⠀⢰⠏⠁⠀⠀⠈⠙⢦⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣦⡀⠀⢿⠁⣧⡟⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣷⣤⣼⣿⠳⢼⡀⢻⠁⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣠⣶⠟⠁ ⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠁⠀⠀⠀⠀⠉⠛⠺⠃⠀⠁⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣠⡾⣿⡿⠁⠀⠀ ⠀⢀⣠⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⣼⠋⣴⡟⠀⠀⠀⠀ ⣰⡟⠛⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⣰⡟⠁⣼⠃⣰⡟⠀⠀⠀⠀⠀ ⣿⣄⡤⠞⠁⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠹⣶⣤⣄⣀⢀⡿⣷⠀⢀⣠⣴⠟⠉⠀⢸⡇⢀⣿⠀⠀⠀⠀⠀⠀ ⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤⣴⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⠉⠙⠁⠈⠛⠉⠉⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠹⣧⡀⠀⠀⣖⠲⣄⠀⠀⠀⠙⠻⠿⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢿⣄⠀⠸⣆⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢷⣤⣿⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⢦⣄⡀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠤⠚⠋⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⡍⠉⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠏⢀⣾⠁⠀⠀⠛⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⢀⣾⠃⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡇⠀⣸⠏⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣤⡴⠟⠋⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⢘⣷⢀⣟⡄⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠛⠃⠈⣿⢀⡇⣠⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠘⠻⠟⠉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣀⠈⠳⣄⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡾⡟⠉⠙⠻⠶⢾⣿⣶⣤⣽⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣴⣇⣀⣏⣀⣠⡴⠞⢋⡿⢋⠉⠉⠛⠛⠻⠷⣶⣾⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠘⢧⣯⣀⣼⣤⡤⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⠙⠛⠶⣦⣤⣀⣀⣠⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠀⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠀⣤⠀⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠛⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⣈⡉⠛⠛⠒⠀⠒⠛⠛⢉⣁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡤⣄⢀⣴⠆⠀⠀⠀⠀⠀⢀⣠⠴⡦⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠀⠓⣌⣏⠌⠀⠀⠀⠀⣠⢶⣋⣄⣀⡀⠀⠄⠀⠀⠀⠉⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢣⡀⢰⣷⣂⣀⣀⣀⡴⠓⠉⠉⠀⠉⠍⠻⢶⡀⠀⠀⠀⠀⠉⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠒⠒⠤⡀⣠⡷⠛⠉⢁⡀⡀⣀⣀⡤⠤⢤⡀⠀⠀⠀⠉⠛⠢⠄⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⠞⠁⠀⣀⣭⡁⠀⠀⠀⠏⢁⣀⣀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠋⣀⣀⠀⠀⠙⠛⠃⠀⠀⠀⠀⣃⡴⠋⠁⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⠓⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣸⣟⣄⠘⣯⠍⠍⣉⠒⠂⠤⡄⠀⣅⠀⣀⡴⠁⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠙⣧⣀⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀ ⠐⢁⠎⠈⠉⠓⠒⠻⢦⡀⠉⠒⢄⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⣣⠈⠙⠳⣄⠙⢦⡀⠀⠀⠀⠀ ⢀⠋⠀⠀⠀⠀⠀⠀⠀⠙⣄⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣁⠀⠀⣀⣄⡲⢿⡀⠀⠀⠈⠳⣄⠹⣄⠀⠀⠀ ⡌⠀⠀⠀⠀⠀⣠⣶⣏⠉⠙⡌⢷⣼⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠋⠉⠉⠉⢉⡽⠉⠀⢸⡱⠀⠀⠀⠀⠈⡆⢹⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣯⡵⢶⣴⢿⠛⠋⠉⣺⡶⣦⣤⣙⡿⠿⠋⠁⠀⠀⠀⠀⢼⡟⣻⣃⣴⢰⠇⠀⠀⠀⠀⠀⢻⠀⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⢀⡴⣿⣿⢠⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠋⠳⠏⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣧⢧⡼⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢻⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢄⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⣉⣶⠴⠖⣤⠤⠽⠶⠦⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢛⠻⢝⡆⠀⠀⢿⠇⠀⣴⣰⠗ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠶⠖⠋⠚⠛⠿⠃⠀⠀⠀⢀⡴⣿⠙⣣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠘⠘⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⡀⠺⢬⡳⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠈⠳⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠼⠀⣠⡄⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⢤⣶⣒⣚⣋⣉⡉⠤⠤⠺⠟⣧⠀⠀⣀⣴⠾⢉⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣆⡻⢤⣀⣉⠓⠒⠒⠎⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⣀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡉⠈⢿⡜⣺⣞⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠁⡀⠀⠙⠋⠁⠀⠉⠉⠉⠐⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣴⠁⠀⢠⠀⠀⠀⠀⡄⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣔⠏⢀⠂⡰⠏⡀⠀⠀⡞⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣙⣤⣮⠊⠀⠀⣀⢩⣇⡳⠄⠀⢀⣔⣏⠐⠠⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠶⠦⠬⠝⠁⠀⠀⠉⠢⡈⢢⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡱⢈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠒⠂⠬⠍⢉⣁⣀⣉⠠⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⡤⠀⠠⠀⠄⠀⠀⠀⠄

⣿⣿⣿⢿⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⡿⣽⣻⡽⢯⡿⣽⣫⡟⣽⣫⢟⣽⢫⡟⣽⢫⡟⣭⡻⣭⢻⡭⢯⡽⣭⢯⡽⣭⠻⣜⡣⢟⣜⡣⢟⡜⣣⢛⡜⣣⢛⡜⣣⢏⡼⣡⢏⡼⣡⢏⡼⣡⢏⡼⡱ ⣿⣷⣻⣟⣾⣳⢿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡷⣯⡽⣯⢷⣏⡷⣽⣣⢯⣟⢮⣯⢽⣚⡷⣹⢧⣻⡜⣧⣛⢧⡻⣜⢮⡳⣭⢻⡔⣏⡳⢎⡝⢮⠼⣱⢫⠼⣱⢫⡜⡱⢎⠶⡱⢎⠶⡱⢎⠶⡱⢎⠶⣙ ⣿⢿⣽⡾⣷⣟⣯⢿⡾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⣞⣯⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣽⣻⢾⣽⣻⢾⣽⢾⣯⢷⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⢯⣟⡷⢯⣟⡷⣻⣵⡻⣾⣱⢷⣫⠷⣞⢯⡞⣧⢟⡼⣏⢷⣣⢟⡵⣫⢞⡽⣎⢷⡹⣞⢣⡞⣱⢭⡛⡼⣙⡞⣥⣋⢗⣣⠳⣜⡹⢎⡳⣙⢎⡳⣙⢎⡳⣙⢮⡹⣒ ⣿⣯⣷⢿⣳⣯⣟⣯⡿⣽⢯⣿⢾⣽⣻⢾⣽⣻⣞⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢯⣷⣟⡿⣞⡿⣞⣯⡿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣾⣽⣿⣾⣿⣿⣾⣿⣷⣿⣷⣯⣟⣾⣭⢿⡹⣾⣹⢮⣏⢷⣫⢞⡵⣫⢷⡹⣎⢷⡹⣎⠷⡭⢮⡕⣏⠶⣹⢱⢣⠞⡴⣩⠞⡴⣋⠶⣙⢮⡱⣍⢮⡱⣍⢮⡱⡍⢶⣑⢣ ⣿⡾⣽⡿⣽⡾⣽⣳⡿⣯⣟⣾⣻⢾⣽⣻⣞⡷⣯⢿⡽⣯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣟⣾⣽⣻⡽⣟⣯⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣛⡾⣼⢣⡟⣮⢳⡝⣮⢳⡝⣮⠳⣭⢛⡼⢣⢞⡬⡳⣍⢎⢧⡛⡴⢣⡛⡴⣍⢞⡱⢎⡵⣊⠶⡱⢎⡖⣱⡙⢦⡍⡖ ⣿⣻⣽⣟⡷⣟⣯⡷⣟⡷⣯⢷⣻⣟⣾⣳⢯⡿⣽⢯⣟⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⣟⣯⡷⣯⣷⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣫⢞⡵⣏⢾⡱⢯⡞⡵⣛⢦⣛⡼⣍⠾⣰⠳⡜⣎⠶⡹⣜⢣⡝⡲⣍⢮⡱⢫⠴⣩⠞⣡⠳⡜⡥⣚⢥⡚⡜ ⣿⣽⣳⣯⣟⣯⡷⣟⣯⢿⡽⣯⢷⣻⢾⡽⣯⢿⣽⣻⢾⣽⣻⢯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣞⣯⢿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡽⢮⡝⣧⡛⣵⡩⢖⣣⠞⣬⠳⣥⢛⡼⣌⢳⡱⢎⢧⡚⡵⣊⠶⣉⢧⢛⡤⣛⠴⣋⠼⡱⡜⣆⢧⡙ ⣿⢾⣽⡾⣽⣳⣟⣯⣟⣯⢿⡽⣯⣟⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻⡞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣯⣟⣯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⢟⠶⣙⢦⡛⡵⢪⡝⢦⡛⡴⣋⠶⣩⢖⡹⢎⠶⡹⠴⣩⠞⡱⢎⡣⠞⡴⢋⡼⣡⠣⡵⣈⠦⣙ ⣿⢯⣷⣟⣯⡷⣯⣷⣻⣞⣯⣟⣷⣻⣞⡿⣾⣽⣻⢾⡽⣻⡞⣷⡻⢷⣛⣾⣳⣟⣾⣳⣯⡿⣽⢯⡿⣽⣳⣟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⢻⡽⢺⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢯⡹⣆⠻⣜⢣⠞⣥⢛⡴⣩⢞⡱⢎⡵⢋⡞⣱⢋⠶⣉⠷⡩⢞⡱⣘⠣⢖⡡⢓⡴⣉⠖⣡ ⣿⣻⢷⣻⡾⣽⢷⣯⢷⣻⢾⡽⣞⡷⣯⣟⣷⣳⢯⣟⢾⣳⢟⣳⣟⣯⣟⣾⣳⡽⣞⡷⣯⢿⡽⣯⣟⣷⣻⣞⣿⣿⣿⡟⢥⠲⡝⣾⣟⣿⣿⣻⣿⣟⣿⣯⢿⣞⣷⣻⣽⣚⠷⣘⢧⡚⡕⢦⢫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⢣⡭⢳⢬⢣⡛⡴⣋⠶⡱⢎⡵⢋⡜⣣⠞⡥⢫⡜⡱⢎⡱⢎⠴⢣⡙⢦⡙⢦⠱⣌⠚⡤ ⣿⣽⣻⢷⣻⢯⣟⡾⣯⣟⣯⢿⣽⣻⢷⣻⢮⣽⣳⢯⣻⣭⡟⣷⣞⣳⣞⡷⣯⢿⡽⣽⣏⣯⣟⣷⣻⣞⣷⣻⣿⣿⠫⠄⣉⣳⣽⣼⣿⣿⣿⢿⣟⣿⢯⣟⡿⣞⣷⡳⢞⡜⢢⠏⡖⡩⢞⡥⣛⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⢞⡱⢎⢧⡙⢶⡩⢞⡱⣋⠶⣩⠞⣡⠞⣱⠣⡜⡱⢊⠖⡩⢎⡱⡘⠦⡑⢎⡱⢌⡓⡔ ⣿⢾⣽⣻⣯⢿⣽⣻⢷⣻⣞⣯⢷⡯⣟⣞⡿⣼⢏⣯⢷⣳⣻⣳⣞⢷⣫⣟⡷⣯⣟⢷⣻⢮⡽⣞⣷⡻⣞⣿⣿⠁⠳⢾⣧⣽⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⡝⣮⢞⡳⣎⠳⡵⢊⡴⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢮⠳⣍⠶⣙⢦⡙⣎⠵⣊⠗⡱⢎⡱⣊⠥⡓⣬⢱⡉⢎⡱⢊⠴⣡⠣⣙⠢⡑⠦⡱⢌ ⣿⢯⣟⡷⣯⣟⣾⡽⣯⢷⣻⣞⣯⣽⣻⣼⣛⣾⣛⡾⣏⡷⣏⡷⣞⣯⢷⢯⡽⣶⢯⣛⣧⢿⡽⣳⢾⣽⣻⣿⠃⢉⡷⣿⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡿⣯⢟⡞⣞⡳⣜⣫⡑⠳⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢌⡳⢬⢳⡩⢖⡹⡸⡜⡡⢏⡕⢎⡱⣉⠖⡱⢢⠱⡘⠦⡑⣍⠲⢄⠳⣄⢣⡙⢆⡱⢊ ⣿⣯⢿⡽⣷⣻⣞⡿⣽⢯⣷⣻⢮⢷⣳⣳⠿⣜⣯⢷⣏⡿⣽⣹⢯⣞⣯⢯⣟⡾⣽⣛⣾⣫⡽⢯⣷⣫⣿⡟⢠⣯⣄⢿⣿⣿⣿⡧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡱⢦⡝⢳⡒⠦⡄⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡱⣋⠶⣙⢎⡵⢱⠱⣙⠲⡘⢎⡱⢌⢎⡑⢣⠱⣡⢣⡑⠦⡙⣌⢃⢆⠣⡜⠢⣅⠣ ⣿⣞⣿⡽⣷⢯⡿⣽⣻⣟⡶⣯⢟⣯⣗⡯⣿⠽⣞⣯⢾⣝⡧⣟⡧⢿⣜⡯⢾⡽⣞⡽⣶⢏⣿⣛⡶⣯⣿⠇⠿⢱⣿⢸⣿⣿⣡⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⠧⡝⢲⠱⣌⡠⢘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠳⣍⢞⡱⢎⠴⣋⢜⣢⡙⡱⢣⠜⡌⠦⣙⢂⠳⡐⠦⣑⢣⠱⡌⠎⡜⢢⡑⢣⠆⢣ ⣿⡾⣽⣻⡽⣯⣟⣷⣻⠾⣝⣳⣟⣞⡾⣽⢞⡿⣽⣺⣝⣮⡽⣞⡽⣏⡾⣝⣯⠾⣽⣹⢞⣟⣮⢿⣱⢯⣿⠀⣐⡊⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣜⢣⠷⢤⡡⠉⠆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡵⣊⢮⡱⢍⡲⢩⡒⢤⢣⡑⢣⠚⢬⡑⢢⢍⠲⣉⠖⡡⢎⠱⡘⡜⣠⠣⣘⢂⢎⡡ ⣿⡽⣷⢯⣟⣷⣻⢾⣽⣻⡽⣳⢾⣝⡾⣭⢿⣹⢧⢷⢾⣱⡟⡾⣵⢏⣷⢻⡼⣻⡵⢯⣾⣹⢮⣯⣻⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣭⡞⢣⢏⣬⡱⡌⢒⡠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢲⠍⣦⠱⡎⡜⣡⠚⡔⢢⡙⢢⡙⢦⡘⢥⢊⠵⡨⠜⡐⢎⠱⡐⢆⡡⢒⡡⢊⠴⡐ ⣿⣳⣟⡾⣽⢯⣟⡾⣽⣫⢷⣻⣞⣽⣳⣛⣞⢯⣞⠾⣼⢏⣷⡳⡽⣞⡽⣞⢧⡿⣱⠾⣭⡟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⢞⡩⣇⠣⠌⡑⢺⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⡑⢎⡴⢩⡒⢥⠣⣍⠲⣑⠪⡑⢎⡱⢨⠱⡌⢚⠤⢃⠲⡑⡌⢆⠓⡌⢃⠎⡱⠘⡄⢣ ⣿⡽⣞⡿⣽⣻⢾⣽⣳⢯⣟⡵⣞⣧⢷⡻⣼⢏⣾⢻⡽⣺⢧⢿⣹⢾⣹⡞⣯⠾⣝⡯⣗⢿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣖⣿⢯⢀⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡶⡷⣎⠷⣤⢓⡒⣩⢒⣿⣿⣿⣿⡟⡹⠋⢴⣆⡘⣿⣷⣏⢲⡘⢥⡙⢆⠳⣨⠱⠌⡥⣙⠢⣅⠣⢃⠍⡆⠣⠍⠦⡑⠌⡌⠱⡈⠆⡜⢠⠃⡜⢠ ⣿⡽⣯⣟⡷⣯⣟⡾⣵⣻⠾⣽⣻⡼⣳⢏⣷⢻⢮⣏⡷⣏⢿⡺⣽⣚⣧⢟⣧⢿⣹⢾⣹⢾⣹⢟⡿⢥⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⠚⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣭⡛⠿⡵⣉⠞⣩⠳⢦⡀⢎⣽⣿⣿⣿⣇⢠⣅⠮⠿⢿⠿⣿⣗⠦⣙⢢⡙⣌⠳⣄⠫⡜⡰⢡⠣⡔⢩⢊⠜⡰⢩⠘⡰⢁⠞⡄⢣⠑⡌⠔⡡⢊⠔⡡ ⣿⣽⣳⣯⣟⡷⣯⣟⣳⣽⢻⣳⣭⠷⣏⣟⡮⣟⡽⢮⣗⢯⡯⢷⡳⣏⣾⢫⣞⣳⢯⢾⣹⡞⣽⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣇⡋⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢮⡓⢦⡙⣷⡳⣬⣦⢥⡛⣤⡙⣦⣿⣿⣿⣿⣏⣿⢸⣿⣿⣿⣿⣾⣿⡜⣌⠣⣜⠰⢣⢌⡱⢢⢙⣂⠳⢌⡡⠎⢆⡑⢢⠡⡑⢊⠴⡈⢆⠱⣈⠒⡡⠎⡰⢁ ⣿⣞⣷⣻⢾⣽⣳⢯⣷⢫⣯⢷⣚⣯⡽⣞⡵⣯⢽⡻⣼⣛⠾⣯⢽⡳⣽⢻⡼⣽⡺⣏⡷⣽⢣⣟⡞⣿⣾⣥⣿⣿⣿⣯⣿⡳⢷⡈⡑⠌⢠⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣶⣍⢏⡞⣴⣙⣦⡹⢆⣿⣴⣽⣾⣿⣿⣿⣿⠐⡻⢷⢩⣿⣿⣿⣿⣿⡗⣨⠱⣌⠹⣂⠎⡔⢣⢌⠢⢃⠆⢢⠍⢢⠘⡄⢣⠘⣐⠢⡑⢌⠢⡁⢎⠰⡁⢆⠡ ⣿⢾⣳⣯⢿⡾⣽⣻⣼⣻⢞⣽⣹⢶⣻⢼⣻⢼⣳⡻⣵⣫⢟⡮⣗⣻⡼⣳⡽⣖⣻⡝⣾⡱⣟⢮⣽⡟⢻⣿⣿⣿⣟⣿⣯⢳⣦⣷⣶⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣆⢳⣎⠿⣖⣾⣿⣾⣿⣿⣿⣿⣿⡀⣟⢈⣦⣹⣿⣿⢿⣿⠓⡤⢓⣌⢣⠱⡊⢜⡂⢎⡱⢊⡜⢄⠚⡄⢣⠘⡄⢃⠆⡱⢈⠆⡱⢈⠆⡱⢈⠄⡃ ⣿⢯⣟⡾⣯⣟⡷⣯⢶⣏⣟⡮⣗⣻⡼⣏⡾⡽⢶⡻⣵⢫⣾⡹⣞⡵⣫⢷⣹⢞⡵⣻⢖⣻⡝⣾⣿⠁⠰⠟⣿⣯⢸⣿⣯⡧⣴⣠⣴⣶⣦⣄⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣮⣷⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⠃⢿⣿⠟⣽⣿⣿⠣⡙⡔⢣⠜⣢⠣⢍⠢⡙⢄⢢⠡⡘⢄⠣⡘⢄⠣⡘⢄⠊⡄⠣⡐⢄⠃⡔⢠⠃⡌⡐ ⣿⢯⡿⣽⣻⢾⡽⢯⡷⣞⢧⣟⣭⠷⣝⡾⣱⠿⣭⢗⣯⢳⡞⣵⡻⣼⣛⢮⡗⣯⡝⣧⡟⣧⢻⡞⣿⠀⠀⣦⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣛⣷⠿⣫⣾⢃⠧⡱⡘⢥⠚⣄⠳⣈⠱⡈⢆⠢⡑⢌⠢⡑⢌⠢⡑⠰⡈⢆⠡⢃⠌⡂⠜⡠⢂⠅⢢⠁ ⣿⢯⣿⣳⣟⣯⣟⣯⠷⣏⡿⡼⣞⢯⣻⠼⣏⣟⢮⣻⡜⣯⢞⣳⡽⣣⢯⣳⢻⡼⣽⢲⡟⣼⡳⣏⢿⣆⠀⢿⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢟⣿⢅⠺⡰⢡⡙⠤⢋⠤⠓⡄⢣⠘⡄⢣⠘⡄⢣⠘⠤⡑⢨⠑⠌⡄⢃⠢⡘⠄⡃⠔⣁⠊⡄⢃ ⣿⣻⣞⡷⣿⢮⡽⣞⣿⡹⣞⡽⣞⢯⣳⢻⡝⣮⢟⡶⣻⡝⣞⣧⢻⡵⣫⣗⢯⣳⡭⢷⣫⢷⡹⣎⡯⢿⣆⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⢻⡯⢌⢣⡑⢧⠘⡥⢋⠌⡓⢌⠢⡑⢌⠢⡑⢌⠢⢉⠆⢡⠂⡜⡐⢌⠂⡅⠢⡑⠌⢒⡀⠣⠌⡄ ⣿⣳⢯⡿⣽⣏⡿⣽⣲⢟⡽⣞⣭⢷⣫⢟⡼⣏⡾⣳⢧⣛⢷⡺⣝⡾⡵⣞⢯⡖⣯⡳⣝⡮⢷⡹⣞⣻⣿⡄⣿⣿⣿⡟⢛⣫⣿⣿⣿⣿⣿⣿⠟⣿⠛⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣹⡟⣌⠲⣡⠊⡕⢢⠡⢚⠰⡈⠖⡡⢊⠔⠡⢂⠱⡈⢌⠂⡅⢒⡈⢄⠣⡐⢡⠂⢍⠂⡌⢡⠒⠠ ⣿⡽⣯⣟⡷⣯⢷⣳⡽⢾⣹⡞⡽⣎⡷⣫⡽⣞⡵⣛⣮⢟⣮⢽⣣⢟⣵⢫⡾⣹⢖⣯⢳⡝⣧⢻⡜⣷⣿⣿⣿⣿⣿⣴⣿⡿⡏⢻⣿⣟⣤⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⢚⡯⣐⠣⢆⠹⣠⢃⠣⢌⠢⡑⠌⠴⢁⢊⠱⡈⢆⠘⡠⢃⡘⢄⡘⢄⠢⢑⢂⠩⢄⠊⡔⠡⠌⡡ ⣿⣽⣳⣯⣟⣷⣛⣶⢻⡝⣧⡻⣝⢾⣱⣏⢷⣹⢞⡽⣎⢿⡜⣧⣛⠾⣜⢯⣳⣛⠾⣜⢧⡻⣜⢧⡻⣜⣿⣿⣿⣿⣿⣿⡟⠳⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⡐⢫⢄⠫⡜⢠⢃⠌⡒⢌⠢⢑⠊⡄⠣⢌⠰⡐⡈⢆⠡⢂⠔⡂⠔⡈⢆⠡⢊⠰⡈⠒⢄⠣⡘⠠ ⣿⣞⣷⣻⣞⡾⣝⡾⢯⣽⢺⡵⣏⡟⣶⡹⣞⡽⣚⡷⣹⢮⡻⣵⢫⡟⡽⣎⠷⣭⣛⢮⡳⣝⢮⡳⣝⡞⡶⣿⣿⣿⣿⡿⠈⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠬⣙⠆⢳⠘⠤⣉⠆⡱⢈⢆⠡⢊⠰⡁⢆⠡⢂⠱⣀⠣⠌⢒⡈⢆⠡⢂⠱⡈⠤⢡⠉⡂⢆⠡⡁ ⣿⢾⣽⣳⢯⣟⡽⣞⡿⣜⣳⡽⣺⡝⣶⢫⢷⡹⣝⠾⣭⣳⢻⣜⡳⣽⢳⣭⣛⢶⣭⢳⡝⣮⢳⡝⣮⣝⡳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡈⠴⣈⢏⠰⣉⠒⡡⢊⠔⡡⢈⠆⡡⢒⠈⡔⡈⢆⠡⡐⢂⡑⠢⡐⢂⠅⡊⠔⡠⢃⠢⡑⠨⠄⡃⠔ ⣿⣻⢾⣽⣳⢾⣹⣳⢽⡺⣵⢫⢷⡹⣞⡽⢮⣽⣚⢯⣳⢭⣳⢭⣳⢭⣳⢮⡝⡾⣜⢧⡻⣜⢧⡻⢶⣭⢳⢧⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡐⢈⠲⢡⢎⡱⢄⡩⢐⠡⢊⠄⣃⠰⢁⠢⡑⠰⡈⢄⠃⡔⣁⠢⡑⢄⠃⡌⠰⣁⠒⡄⢃⠌⡑⢌⠰⢁ ⣿⣽⣻⢾⡽⣞⣧⢟⣞⣳⡭⣟⢮⢷⡹⣞⣳⢮⡝⣾⣱⢻⡜⣧⣛⢮⡳⣏⢾⣱⢏⡾⣱⢏⡾⣹⢳⣎⡟⡾⣴⢛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠭⡀⢡⠌⡡⢂⡅⢺⡔⡨⢔⡡⢊⡅⢒⠠⡑⣈⠒⡈⢅⠒⣈⠒⡐⢄⠒⡨⠐⡌⠰⣁⢂⠒⡈⢆⡘⠰⢈⠢⢁ ⣿⢾⡽⣯⢷⣻⢮⣛⣮⢳⣝⣮⣛⢮⢷⡹⣎⢷⣹⠶⣭⣳⣛⠶⣭⡳⣝⡞⣧⣛⢮⣳⡝⣮⢳⣝⡳⢮⣝⡳⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡁⠞⡌⠐⡤⠂⠤⢡⠘⣐⠣⣏⡐⠆⡔⣡⠈⡆⡑⠰⣀⠃⡜⢠⢊⡐⢌⠰⣈⠂⡅⢃⠌⡡⢐⢂⠱⢈⠆⢌⠡⢊⠄⠡ ⡿⣯⣟⡷⢯⢷⣫⠷⣭⢷⣚⢶⡹⢮⡳⣝⢮⣳⢭⣛⢶⣣⢏⡟⡶⣝⢮⣝⠶⣭⡳⢧⣻⣜⡳⢮⣝⡳⢮⣽⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣍⡳⢍⢦⣹⡰⢬⠑⡠⠨⠰⢀⣋⠄⠳⣼⡄⣙⠰⢠⡘⠤⣁⠣⡐⢌⡐⢢⠐⡰⢈⠢⠄⡃⠔⣈⠢⠑⡂⢌⠢⡁⢎⠠⠃⡄⢊⠐ ⣿⢷⣯⣟⢯⢷⣫⣟⢮⣳⡝⣮⣛⢧⣛⢮⡳⣝⡮⣝⣮⢳⣏⣞⡳⣝⠾⣜⡻⢶⣹⢳⡳⢮⣝⡳⢮⣝⡳⣞⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣭⢻⣌⠳⣭⢖⣦⠳⣌⢌⠡⢁⠒⢡⠈⢎⠡⠜⣷⡈⠜⣠⠘⡰⢀⢣⠘⡄⠒⡄⢣⠐⡡⢂⠱⢈⠒⡠⢁⠣⢘⠠⢂⠅⢊⠐⠡⠐⠂⠌ ⣿⣻⢶⢯⣛⡾⡵⣞⢯⢶⡹⣖⢯⡞⣭⣳⢻⣜⡳⣝⢮⡳⣞⡼⣳⢭⣛⣮⡝⣧⢏⡷⣹⢳⢮⣝⡳⣎⠷⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣽⣳⢮⡳⣎⡳⡼⡞⡴⢫⡜⠌⢦⠉⠈⠄⡐⠂⡜⢨⢽⣿⡔⢂⠱⣀⠃⢆⠱⣈⠱⡈⢆⠱⣀⠣⡘⢄⠣⡐⢡⠊⡄⠣⢌⠘⡀⢊⠡⠌⠡⢈ ⣟⡷⢯⣟⡽⣺⣝⢾⡹⣎⢷⡹⢮⣝⠶⣭⡳⢮⣝⢮⡳⣝⢮⡳⣝⢮⣳⢮⣝⢮⡻⡼⣭⣛⠾⣜⡳⣭⣛⠶⣭⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣟⡳⢞⡥⢯⡽⣭⢳⢧⡹⢜⣣⡙⢾⡀⠎⠡⠀⢄⠡⡀⠣⢎⢿⣿⣧⣖⡠⢉⠆⡒⠤⡑⡈⢆⠱⣀⠣⡘⢄⠣⡘⢄⠣⡘⠰⡈⠆⡁⠢⠐⡈⢂⠁ ⣯⣟⣟⣮⡽⣳⢞⣯⢳⡝⣮⢽⡳⣎⡟⡶⣝⢯⡞⣧⣛⢮⢷⡹⣞⢧⣛⠾⣜⢧⡻⣵⢣⣏⠿⣜⡳⢧⣏⠿⣜⡧⣏⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢾⡸⣹⡍⣞⣱⠞⣥⢻⢦⡙⣦⠧⡙⢦⡑⢎⠡⡀⠆⠰⢀⢣⠘⡼⣷⣏⡿⣿⣶⣾⣤⣵⣠⡑⣈⠒⠤⢑⠰⡈⢆⠱⡈⢆⠡⢃⠜⡠⠑⣂⠑⡠⠁⠌ ⣷⣻⡼⢶⣻⢵⣫⢞⣧⢻⡜⣧⢻⡼⣹⢳⡝⣮⡝⡶⣭⣛⢮⣳⡝⣮⣝⡻⣜⢧⡻⣜⡳⣞⡽⢮⣝⡳⣎⠿⣜⡳⣝⠾⣭⣛⠿⡿⢿⠿⣿⢿⣿⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣞⡧⢷⡩⡜⠶⣥⢯⡙⣧⣾⠵⣣⠝⣌⠣⡜⢢⠡⡁⠂⠅⣂⠢⠘⢤⢫⡝⣻⣷⣻⢞⣽⣻⣟⣿⡿⣿⣶⣮⣴⣡⣈⠆⡑⠌⢢⠁⢎⡐⠡⡀⠎⢠⢁⠂ ⣷⣳⢻⣏⣞⢧⣛⡾⣜⢧⡻⣜⣧⢻⡵⣫⢾⡱⣏⢷⣣⢟⣮⢳⡝⡶⣭⢳⡝⣮⢳⣭⢳⡝⣞⡳⢮⡝⣾⡹⢧⡻⣜⡻⢶⡍⡷⣍⣛⠮⡵⢎⣽⠀⠀⠀⠀⢮⣿⣿⣿⣿⣿⣿⡿⡞⣥⢳⡉⢳⡜⣦⢿⡻⣌⠷⣢⠝⣠⠒⡌⢠⠃⡔⢁⠂⠴⢈⡑⢎⡳⢼⢯⡷⣯⣟⣮⢷⣻⣾⣟⡿⣽⣿⣻⣿⣿⣿⣷⣾⣤⣉⡤⠘⢠⠁⡌⠂⡄⢂ ⡷⢯⣛⣞⢮⡻⣜⡳⣝⢮⢷⡹⣎⢷⡹⢧⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⢷⡺⣝⠾⣱⢏⡳⣝⢶⣹⢳⡝⣧⣛⢧⠞⡵⢎⢧⡛⣜⢣⢾⡃⠀⠀⠀⠠⣼⣿⣿⣿⣿⣟⣷⡻⣬⢓⣌⠶⣹⣯⣗⣳⣭⠳⡆⣍⠲⠠⠄⠃⡜⠐⡌⡀⢂⠬⠑⡎⡵⢋⡞⣹⢳⣻⣾⣿⢿⣟⣾⣟⣷⣿⣿⣽⣷⡿⣯⣿⣿⣿⣿⣿⣦⣴⣀⠡⠐⠂ ⣟⢯⡽⣎⣯⢳⡭⣗⢯⡞⣧⢻⡜⣯⣝⡳⢮⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⠷⣭⢻⡥⣏⢷⡹⣎⢷⣫⢞⡵⣭⠺⡭⣝⢮⢣⡝⣬⠓⡾⡇⠀⠀⠀⠐⢼⣽⣿⣿⣿⣿⣷⣿⠶⣏⢬⣛⣷⣻⣞⡷⣊⠷⣉⠦⣁⠣⣘⠐⡈⠱⣀⠖⠡⠀⡝⡘⡔⠫⡔⢣⡞⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣾⢿⣟⣷⡿⣯⣿⣿⢿⣿⣿⣿⣾⣤ ⣯⣛⢾⡱⣏⢷⡹⣎⢷⡹⣎⢷⣛⠶⣭⣛⠷⣎⢯⡳⡽⣎⢷⣫⢞⣧⢻⡵⣫⠷⣭⢻⡜⣧⢳⡝⣎⢷⡹⣎⢷⣋⠾⣜⢫⡵⣚⡬⢳⡜⢦⡛⡴⣧⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣯⡿⣜⡶⣹⣾⢯⣟⣳⡽⢎⡕⢢⠰⣁⠣⡜⢀⠡⡘⢠⠁⢆⠐⡤⢩⠓⣬⢓⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣻⣿⣿ ⡷⣭⡗⣯⠽⣎⢷⣫⢞⡵⣫⡞⣭⣛⠶⣭⢻⡼⣣⢟⡵⣫⢞⡵⣫⢞⣧⢻⡵⣻⡜⣧⢻⣜⡳⢞⡭⡞⣵⢫⡞⣭⢻⢬⡳⣜⡱⢺⡱⢎⢧⡙⡖⣿⠀⠐⠄⢀⠀⠀⠉⣿⣿⣿⣿⣿⣟⡷⣏⣷⣿⣿⢿⣻⡝⢮⡜⣡⠓⠬⣑⠜⣨⠂⡁⢃⡚⢤⡈⢠⢃⡝⢦⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣽⣿ ⣟⡵⣻⣜⡻⣜⢧⣛⢮⡳⢧⡻⣵⢫⡟⡼⢧⡻⣵⢫⡞⣵⢫⡞⣵⢫⡞⣧⣛⢶⡹⣎⢷⣪⠽⣹⢼⣙⢮⣳⢹⡜⣣⢳⣙⠦⣝⢣⡝⢎⢶⣭⡿⠛⠀⠀⠀⢹⠆⣄⣀⠿⣿⣿⣿⣿⣯⣿⡽⣾⣿⣯⡿⣧⣛⢧⡚⡥⢊⠶⣩⢎⡡⢚⠄⢃⠜⡢⣄⠣⡘⣬⢣⠿⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣯⢞⡵⣎⡷⣹⢎⣯⢳⡽⣳⡝⣮⢳⡽⣹⢧⡻⣜⢧⡻⣜⢧⣻⡜⣧⣛⢶⡹⣎⢷⡹⢶⣩⢏⠷⡮⣝⡞⣬⡓⣞⣱⢫⡜⣹⢬⣳⡾⠟⠋⠁⠀⢀⠀⠀⠀⢸⡅⣦⢉⡉⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣖⡻⢦⡛⣌⢏⡾⡵⢪⡕⢯⣌⢣⣌⡱⢎⡧⣙⣤⢏⡿⣵⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣫⢞⡵⣫⢗⡯⣞⢧⡻⣵⢻⡜⣧⢻⡵⣫⢷⡹⣎⢷⡹⣎⢷⡹⢶⡹⣎⢷⡹⢎⡗⣯⣜⢫⢷⡹⡖⣽⠲⣝⡼⢲⣍⣾⠟⠋⡁⢀⠀⠀⠀⢰⣿⠀⠀⠀⠈⡇⠸⣧⣌⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣋⢷⡙⣞⣮⡽⣽⢳⣚⠷⣜⡲⣬⡳⢯⣶⢻⣼⣻⣞⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣫⢞⡵⣫⢞⡽⣎⠷⣭⢳⡝⣮⢷⡹⢧⣏⢷⡹⣎⢷⡹⢮⡝⣧⢳⡝⡮⡝⣏⡞⢶⢎⡿⢬⡳⣝⠮⣝⣲⣽⠟⠋⠀⠠⠀⢀⡀⢀⡈⢷⣾⣿⠀⠀⢠⠀⢻⡄⢽⣷⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡍⣎⢿⣼⣳⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⣱⣏⣞⡳⣝⢮⣳⢭⡟⣼⢫⡞⣵⢫⣝⡳⣎⢷⡹⣞⢧⣛⢧⢻⡜⣳⠞⡵⣋⢶⡹⣚⢮⡜⢧⣛⡼⣹⣶⠟⢡⣀⠈⢒⠠⣇⢢⣽⣦⣿⣿⣿⣿⠃⠀⠈⢣⠀⢳⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡼⣣⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⢯⣟⡳⡽⣎⢷⣛⣾⣳⣿⣿⣿⣿⣿⣿⣿ ⣳⢯⡽⣹⢧⡻⣜⢯⡞⣵⢫⡞⣵⢫⡞⣽⢣⡟⡼⢧⡻⣜⡻⣜⢮⣓⢏⡖⢧⠻⣜⡣⢟⣬⢓⡮⢫⣵⡿⠋⠀⠈⢻⣤⣚⡤⢿⡞⣿⣻⣿⣿⣿⠏⠀⠀⠀⠈⡆⠸⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡵⣿⣿⣿⣧⣻⣾⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⡿⣟⣿⣯⣿⣟⡿⣿⣻⣿⣽⣟⣷⣿⢾⣟⡾⣽⣳⢧⣻⣼⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⢯⡞⣵⢏⡾⣱⢯⡞⡽⣎⢷⡹⣎⢷⡹⣎⢷⡹⣝⢧⡟⣼⡱⢏⡶⢭⡺⣜⢫⣝⡲⢭⣓⢮⡹⣼⡟⠃⠀⠀⠀⣐⡠⠞⣿⡽⢎⡽⣶⢿⣾⢏⡆⠀⠀⠀⠀⠀⠑⠀⣧⠀⢺⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣝⡮⣝⡾⣿⣳⣿⣟⣿⣿⣽⣷⣿⣿⣿⣿⣷⣿⣿⣿⣯⣿⣾⣟⣷⣿⣻⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣣⡟⣼⢣⡟⣼⢳⡝⣮⢳⡝⣮⢳⡝⣾⡱⣏⠾⣜⢧⡝⡞⣜⡣⢗⣎⠳⣎⣵⣫⣼⣶⠟⣉⣠⠀⠀⠀⢀⡿⣷⢍⣙⣧⣿⣾⣿⣫⣝⣾⣤⣄⣲⣤⣹⣦⠲⠤⣄⠀⠈⢿⣿⣿⣿⣿⣿⠃⢤⣿⣿⡿⢫⣙⢮⣳⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⢯ ⣞⡳⣝⢾⡱⣏⣞⢧⡻⣜⢧⡻⣜⢧⡟⣼⢣⡝⣮⣛⡼⢎⣞⡹⡲⣍⣷⡾⠟⢋⢉⣥⣶⣾⣿⣿⣿⣿⠿⡩⢞⣷⠟⠉⡐⢎⠛⡍⢯⡽⣻⣿⡻⢿⣿⣿⣿⣿⣷⣦⣜⣦⡀⠹⣿⣿⣿⣿⠏⢀⣿⡿⠉⢁⠣⣞⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣟⣿⣟⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠾⣝⢯ ⣯⣝⢾⣣⢟⡼⣎⡷⣹⢎⣯⢳⡝⣮⡝⣮⢳⡝⢶⡹⣜⣫⣖⣽⠿⢋⡡⢴⠶⣞⡾⣞⣷⣿⣾⣿⣿⣟⡶⣡⣿⠋⠀⠀⢁⠢⠕⡚⢡⢎⡱⠭⣽⠿⣟⢿⡻⣝⣮⣿⣿⣿⣷⡧⣿⣿⣿⡋⢥⣿⡏⣠⣄⣠⣔⣫⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣟⡿⣿⣾⣿⣿⡿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣯⢿⡽⣞ ⡷⢮⣳⡝⣮⢳⡝⣾⡱⣏⡞⣧⣛⢶⣽⣮⡷⠿⢛⠛⡫⢍⠋⡅⣎⢱⡙⣎⠿⣜⣻⡽⣿⣾⣿⣿⣿⣿⣿⣿⠏⢀⢠⡐⣠⠉⠒⠬⡁⢎⡰⢿⣬⡻⣜⣯⢷⣻⣿⣿⣿⣿⣿⣷⣉⡟⢦⡑⣮⢯⣴⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣻⡾⣿⣟⣯⡿⣿⣿⣯⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣯⡿⣽⢯ ⣽⢳⢧⡻⣜⢧⡻⢶⣹⢮⣽⡶⠿⠛⠉⠀⠐⠤⠣⡘⠐⢊⠒⡌⢂⠧⣜⡎⣷⣹⡾⣽⣷⡿⣿⣿⣿⣿⠿⣡⠲⣌⢶⡹⢿⣆⣙⣲⠱⣮⢙⠶⣣⢿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢷⣯⣟⣷⣿⣳⣯⢿⡽⣷⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⡷⣟⣯⣿ ⣳⢯⡞⣵⣫⢞⣽⣳⠟⠋⠁⠀⠀⠀⠀⠐⠠⠂⢀⠈⠄⢡⠘⡰⣍⡞⣴⢯⡷⣯⣟⣿⡾⣟⡿⡹⣍⢆⡳⢣⡽⣘⣮⡟⣽⣿⣿⢣⠷⣌⣯⣛⣷⣻⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣯⢷⡿⣜⢯⢾⣭⢿⡿⣿⡿⣿⣾⢿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣻⣿⣾ ⣟⢮⣽⢺⣵⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠢⡜⢢⡝⢲⣟⡾⣽⣯⣿⣿⣻⡽⣛⢥⢳⡱⢎⢎⣝⢣⡻⣵⣳⡿⣟⣿⣞⣯⢿⣝⡶⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣟⡾⣞⡯⣝⢿⣫⡗⣾⣯⣿⡽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣷⣿ ⣻⢞⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠔⣠⠒⣭⠳⡜⣧⣿⣟⣷⣯⢷⣫⢇⡧⣙⢎⢣⠳⡞⡼⣌⢷⣻⢽⣯⢿⡽⣯⣟⡞⡿⣮⣽⢳⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⢦⡈⢿⣞⣿⣿⣿⣿⣷⡿⣿⣟⡾⣽⣟⡾⣽⢣⡟⣽⣺⢷⣻⢽⣳⣯⣿⢿⣻⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢬⡸⣔⢫⢖⣻⣾⣿⠿⣝⡾⣡⠧⣍⠞⣰⠙⢎⡲⢥⣛⣼⣻⡼⢯⡟⣞⢯⣿⣱⢿⡜⣷⡝⣾⢻⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢳⣄⡆⣹⣜⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣳⢏⡷⣭⢗⣯⣛⣷⢻⣾⢯⣿⣻⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢆⡞⠶⣱⣮⣾⣿⣿⢿⡽⣛⡮⢱⡡⣚⡜⡸⢣⢛⣤⡝⣫⣼⠶⡽⢾⡹⡞⡭⢞⠶⢭⢞⡹⣞⡽⣮⢿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⣻⣽⢻⡼⣾⢿⣿⣿⢿⣻⣿⣿⣾⣳⢯⡻⣼⢛⡾⢧⣻⣼⣻⣾⢿⣽⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⡌⣞⣬⣿⣿⣿⣿⣿⣯⣿⡟⢧⠘⡅⣶⢩⠞⣱⢛⣼⢲⡝⣣⢟⡽⢞⡹⢻⡱⣛⢮⣙⣧⢫⡷⣭⢷⣯⣟⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣻⣿⣯⣿⣿⣿⣿⣿⣟⣮⢷⡏⣯⢳⣭⢻⡼⣟⣧⣿⣹⣽⣻⣯⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⡜⣰⣿⣿⣿⣻⣽⣯⢿⣿⣯⠳⡜⢠⢛⡘⢤⡃⣞⡥⢏⡞⡶⣙⢮⣟⡼⡳⣍⣳⣫⡝⣮⣝⣮⣻⡽⢯⣿⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡷⢧⣿⣿⣿⣿⢯⣟⡾⣽⢻⡯⣟⣳⡛⢾⣳⣽⡽⣞⡿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⡼⣼⣿⣻⣷⢿⣽⣿⣽⣿⣿⣦⠃⡄⠙⠦⠸⠀⡗⡌⢲⡛⣜⠶⣙⡞⣼⣱⢯⣝⣣⢿⣝⣯⣟⣾⣳⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣼⣿⣋⢿⡟⣞⣻⣞⡷⣹⢏⡷⣫⢷⣹⣛⣷⣻⣽⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⡉⣥⢻⣽⣷⢿⣷⣯⣿⣿⣿⣿⣿⣿⠂⠄⠡⠒⠐⠈⠳⢐⡚⡡⢜⡭⢻⡴⣛⢶⣭⡞⣧⣟⣯⢿⣭⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⠙⣇⣿⢫⡝⣭⣓⣮⠷⣳⢾⣱⢟⣯⣟⣯⣷⣻⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣟⡷⣯⣿⣿ ⠀⠀⣀⣄⣠⠌⢦⡱⣯⣿⣻⣾⡿⣯⣿⣿⣿⣿⣿⣿⡏⠙⠀⠀⠀⡰⣃⡤⢋⣜⣍⣫⣜⣣⣷⣻⣟⣶⡿⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡉⠁⡫⢜⠣⢯⣜⣦⠳⣬⠷⣽⣚⣷⣞⣳⣾⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣹⣿⣽⣯⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡤⠤⠴⠂⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠙⠓⠒⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀ ⠀⠀⠀⢰⣾⣭⠉⠙⠲⣄⡀⢠⣾⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣇⠀⠀ ⠀⠀⠀⠸⣿⣿⣼⡇⡶⡆⢹⡿⠿⠀⠉⠟⠧⣔⢦⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀ ⠀⠀⠀⠀⢸⠻⣿⡭⣷⡷⠟⠁⠀⠀⠀⠀⠀⠩⣆⠀⠀⠀⠀⠀⠀⠀⠿⣦⠀⠀⠀⠀⠀⠀⠀⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯ ⠀⠀⠀⣤⠇⠈⢸⠏⠉⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨ ⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⣒⠆⠀⠀⠀⠀⠀⣦⡀⠙⡆⠀⠀⠀⠀⢠⣴⠀⡀⠀⠀⢠⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪ ⡀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⢠⣿⡇⡀⠀⠀⠀⠀⠘⣇⠀⢸⠀⠀⢀⣐⡿⢫⠞⣷⡀⠀⣾⠓⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼ ⢿⢻⣍⠻⣿⡀⠀⠀⠀⠀⠀⠀⠙⢏⠀⠀⠀⠀⠀⠀⠈⢧⡘⢳⣶⠟⠉⠀⠀⣰⣟⣧⣴⣿⣆⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣶⣾⣿ ⠀⠓⠿⣶⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠢⠀⠈⢷⣾⡇⠀⠀⠀⣰⡯⣷⣫⣿⠃⠉⢹⣇⠀⠀⠀⠀⢀⣶⡶⠞⠉⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣶⣶⣾⠃⠀⠀⣿ ⠀⠀⠀⠈⠙⠻⣧⠈⠳⣤⣄⡀⠀⢠⡀⠀⠀⠀⠀⢳⡀⠀⢸⣿⡧⠀⢀⣰⡯⠿⠟⠛⠁⢀⣠⠞⠉⣃⠴⣿⡷⠟⠛⢿⣲⣤⠉⢿⣦⡀⠀⠀⠀⠀⠀⠾⠿⠋⠀⣹⡿⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠈⠙⠺⢿⣷⠟⠁⠀⣿⣦⡀⠀⠀⣶⠘⢀⣾⡏⡄⢠⡨⡟⢀⣠⣤⠖⠚⠉⣠⣶⣯⣽⣿⡁⠀⢀⣤⡤⠞⠙⠓⠛⠛⢿⣦⡦⣤⣼⠏⠁⠀⠀⢀⣿⡧⠀⠀⠲⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠑⠲⣌⡉⠻⢦⣤⣹⣤⡞⠙⣇⣿⣾⣿⢯⡿⠟⢁⡤⢀⣼⣯⠿⡿⢅⣼⠧⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠢⠤⠤⠶⠟⣿⢃⠀⠉⣶⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⠿⠿⠛⠀⠀⠘⠙⠻⢿⣏⣠⣾⣏⡴⠋⠹⠷⠖⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡃⠰⢀⣸⡼⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⣂⣠⣄⡿⠃⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢤⡞⠋⢦⡤⠔⣿⣸⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⠛⢫⢻⢨⡇⢹⣷⣾⣯⠷⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠒⠋⢅⣈⣧⣴⡶⠼⠿⠟⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⣹⡤⠶⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⣠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⡦⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠊⠁⠃⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⣰⠊⠉⠉⠉⠳⠄⠀⢠⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠐⠈⠁⠀⠀⠀⢀⠴⠂⠀⠀⠈⠙⠢⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠤⢺⡃⠀⠀⡀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠘⠛⠂⣀⣈⣑⡀⠀ ⠀⠀⠀⡠⠎⡀⠤⠞⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠳⠀⠀⠂⠈⠄⣒⠊⡠⠻⠂⠀ ⠀⢀⠜⡠⠊⠀⠀⡧⣤⣀⠀⣘⣇⠀⠀⠀⠀⠀⠀⠀⢀⠁⣠⠊⠁⠀⠀⠀⠀⡀ ⠀⡘⠸⠀⠀⠀⢠⠃⢀⢣⣄⠀⠉⠳⢆⣀⣀⠀⠀⣀⠾⣎⡆⣉⢿⡄⠀⠀⠀⠀ ⠀⡇⡇⠀⠀⠀⠀⠳⠓⠖⠋⠀⠀⠀⠀⠀⠙⢯⠉⡳⡢⡀⠉⠁⠉⠁⠀⠀⠀⠀ ⠀⣇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠔⠖⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀

⠉⠉⠉⠉⠉⢍⠉⠉⠉⠉⠉⠉⢉⡍⠉⠉⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠉⠉⠀ ⠀⠀⠀⠀⢠⡈⠻⣄⠀⠀⠀⠀⠀⣿⡀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣷⠀⠈⢷⡀⠀⡀⠀⣿⣿⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡇⠠⣄⠹⣄⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢷⡀⣿⣦⡈⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣀⣤⣾⡿ ⠀⠀⠀⠀⠀⠀⠘⣧⠸⣿⣿⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⣿⣿⠿⠛⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣠⣴⣾⣿⣿⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡆⢻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⣿⡿⠟⠁⠰⠟⠉⠀⠀⠈⠉⠉⠉⠙⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠐⠉⠀⠀⠀⠀⠀⠀⣀⡤⠤⢄⣀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⣿⣟⠻⠷⠌⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠉⠙⠒⢄⡀⠀⠐⠶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣤⣶⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⣀⣀⣄⣀⠀⠀⠀⠀⠀⠀⢀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⣴⠟⠉⣷⣾⣿⣷⣆⠀⠀⠀⠀⠀⠙⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⣼⠃⠀⢸⠉⢹⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠋⢁⡠⢤⡈⢻⣿⣿⣿⣿⣿⣿⡿⠁⣠⣴⠞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠉⠛⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⢸⣶⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠃⣰⠿⢤⡀⠙⠂⢿⣿⣿⣿⣿⣿⣿⣿⣟⡥⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⣠⡖⠒⣦⡀⠀⠀⠀⠀⠀⠀⠀⠉⡁⠀⠀⣿⣭⢿⣿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢱⡀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⣿⠀⡼⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠘⢿⣀⣀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⢸⣱⠀⣸⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⣧⠀⢤⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⢀⡼⠋⢀⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠚⠋⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡅⠀⢹⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠘⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⠲⠀⣀⠤⠖⣋⣭⣤⣤⣶⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⢿⠟⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁⢀⣠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠀⠀⠀⠀⠀⠙⢧⣶⣿⣿⣽⡿⠉⠠⠌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢘⣦⠶⠖⢋⣩⠿⠋⢁⣠⣴⠿⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠹⣿⣿⠏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠃⢀⣤⠴⠛⢉⣀⣠⠴⠛⠁⢀⣠⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⣠⡾⣫⡴⠞⢋⣡⣴⣾⠿⠋⠁⠀⣠⣴⡿⠋⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣤⣀⠀⠀⠉⠓⠶⠖⠃⠀⠀⠀⠀⢀⣠⣾⣿⠟⢉⣠⣾⣿⡿⠟⠁⠀⣀⣴⣿⣿⣿⣇⣀⣼⣿⡀⠀⠀⠀⠀⢀⣠⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣄⡀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠋⢀⣴⣿⣿⠟⠉⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⢀⣠⡿⠿⠛⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢛⣶⣤⣤⣬⠾⢻⣿⣉⣠⣾⠿⠿⠥⠤⠤⠶⢿⣭⣽⣾⣯⣥⣾⣿⣿⠟⣙⣛⣿⠟⠋⠁⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣤⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠛⠿⢿⣿⠏⠀⠀⠀⠀⠀⢀⣀⡤⠎ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⢀⡤⠞⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠟⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣬⡿⠋⠁⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠞⠁⠀⠀⠀⠀⠀⢀⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣠⡶⠛⠁⠀⣀⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⣠⣴⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⣀⣴⣿⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⣠⣴⠿⠛⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣴⣿⣿⢿⠁⠂⠀⠀⠠⣾⢿⡿⢋⣽⡝⢿⣿⠟⣿⣍⠻⣮⡠⠿⠇⠀⠂⠂⠛⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠁⠂⠀⠀⢘⢉⡿⠃⣿⣏⣿⠈⠛⢸⣿⣿⡇⢹⣷⠂⢰⠄⠀⠀⠀⠈⢿⣿⣿⠶⢦⣤⣀⣀⡀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠁⠀⢀⣼⣿⣿⣿⠃⠉⠀⠀⠀⠀⠄⡶⣾⡇⢰⡏⠿⣿⡇⠀⣿⣿⢹⣿⠀⢿⣧⢸⠀⠀⠀⠀⠀⢸⣿⣿⣧⣀⠈⠉⠉⠉⠉⠉⢉⣡⡴⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⣿⡆⠀⣠⡾⣹⡿⢻⣿⠀⠈⠀⠀⠀⠀⠀⠁⣿⠀⢸⣇⡄⣿⡇⠀⣿⣻⡯⣿⠀⢸⣧⢸⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠻⠶⠶⠶⠾⠟⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⡿⠏⠀⣿⣃⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣤⣾⣯⣇⣟⣿⣾⣿⣟⡚⣿⣦⣼⡟⢀⣀⠀⠀⠀⠀⠀⢿⣿⢹⣿⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣼⣿⢼⣿⡟⠉⠀⠀⠀⢐⣀⣤⣴⣶⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣷⣤⣍⣁⣀⠀⡀⠀⣸⣿⣾⣿⡀⣄⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⢦⣤⣀⣼⣿⣿⣟⣿⣟⣡⣤⣶⣿⣿⡛⠯⠉⠋⠁⠤⠀⠀⠀⠁⠁⠀⠈⠀⠀⠚⢉⣙⠿⠿⢿⣿⣿⣦⣤⣿⣿⡇⣿⡇⠙⣷⡘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⡿⣿⣏⣥⣿⡿⠟⣛⠋⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠉⣟⢿⣿⣿⣾⣿⡇⠀⢸⣿⡌⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⣾⠁⢻⣿⣟⡝⠛⠀⠉⠀⠀⠀⣀⣀⣤⣤⣤⣤⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣦⣤⣀⣀⣀⠀⠁⡀⢸⣿⣿⣿⣿⣷⡀⠀⢿⣿⣌⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠏⣸⡇⠀⢸⣿⣿⣿⣶⣶⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣾⣿⣿⣿⣿⣿⣧⠀⢸⣿⢻⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⡆⠀⢸⣿⣷⠻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠿⣿⣿⣿⡇⣿⡄⢸⣿⣸⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⢸⡇⠀⣼⣏⠻⣿⣶⡿⣿⣿⣿⣿⣿⠋⠁⠨⣿⣿⣄⠀⠀⠀⢻⣆⣾⡟⣁⣀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡇⣹⣇⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⢿⡄⣿⣿⣄⣉⣤⣿⣿⢿⡟⢿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣄⠀⣿⣿⣬⣶⣿⣿⣿⣿⣿⢿⣟⣿⣿⣷⣯⣾⣻⣿⠇⣨⣿⣼⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢾⣧⢻⣿⣿⣿⣿⣯⠀⢸⠛⢮⣿⣿⣿⡛⠃⠈⠙⢿⣿⡻⢷⣼⣧⡁⠘⢯⣛⣻⡛⠳⢾⣿⡏⠈⠙⢿⡿⠿⣿⣠⡿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣻⣇⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠛⠛⠒⠒⠂⠀⠀⠀⣸⡿⠀⠀⢠⡿⠀⢸⣿⡿⠁⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣟⢿⣯⣽⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏⠀⠀⣰⡟⠁⠀⢸⡸⣇⠼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣮⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠰⣄⣀⣠⠟⠁⢀⣠⣾⣿⠇⠀⠀⣿⡇⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣇⠉⠉⢹⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠙⠿⣾⣾⣿⣿⣿⣿⠀⠀⢸⣿⣿⡈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣽⣶⣾⣿⣿⣹⣿⣿⣿⣿⣝⠛⠋⠀⠀⠉⠁⠀⠀⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⢀⠀⣿⣿⡘⣧⡘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⣿⣿⣿⣿⣿⢿⣽⠇⡟⣸⣿⣿⣿⣾⣷⣜⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠳⢄⣀⠀⢀⣠⠞⠉⠀⢸⣿⣿⣿⣿⣿⣿⡏⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣄⠀⠀⠀⠉⠉⠉⠀⠀⠀⣠⡿⠉⢻⣿⣿⡾⠋⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⠷⣄⡀⠀⠀⠀⢀⣠⡾⠋⡀⢀⣿⡿⠟⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀ ⠀⣴⣿⣿⣿⡿⠟⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣴⣿⣿⣆⠀⣠⣿⣿⣦⣄⣿⣟⡉⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠻⢿⣿⣿⣿⣦⠀⠀⠀ ⣾⠛⢿⣛⣋⠚⠻⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣾⣿⣿⣿⠿⣿⣶⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡟⠲⣙⣛⡻⠉⣷⡀⠀ ⣭⠞⠛⠉⠛⠳⢦⣅⠸⣿⠿⠿⠿⢿⣯⣹⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣷⣾⡋⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⠇⣩⣴⠞⠛⠉⠙⠳⣭⡻⡄ ⠁⠀⠀⢀⣤⣶⣶⣿⣷⣄⠛⠻⣿⢆⣿⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⣿⣿⡰⣿⠟⠓⣰⣾⣿⣿⣶⣤⣄⠀⠀⠈⠳⠃ ⠀⡤⠺⢩⣽⣿⣿⣿⣿⣿⣧⡘⠋⣾⣿⡿⠿⠛⣹⡇⠈⢹⣿⣿⣿⣿⣿⠟⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⢸⣿⣿⠿⢿⣿⣷⡙⢠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀ ⢴⣶⢸⡆⢿⣷⣦⣿⣿⣿⣿⡿⠄⢉⣡⣶⣶⣿⣿⡇⠀⢸⣿⡿⠿⣿⣿⣤⣿⡿⣧⡀⣾⣿⣿⡎⠉⠸⣿⣿⣿⡇⠀⢸⣿⣿⣷⡶⣿⡿⠷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀ ⠀⠻⢛⣓⣒⣛⣶⡽⠟⣋⣡⣶⣿⣿⣿⣿⣿⣿⣿⣗⡆⠈⡟⠀⠀⢸⠛⣿⣿⣿⢿⣰⣿⣿⣿⣿⡄⠀⡹⣿⣿⡇⣰⣿⡿⠏⣇⡉⢻⣷⡤⠤⣴⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⠞⠀⡈⣿⠿⢋⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢙⠳⢧⣀⠀⣼⢸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣧⠀⡇⢹⡿⣛⡋⢿⣄⠈⢹⢇⣴⣿⣷⠀⠹⣿⣷⣦⣍⡛⠿⣿⣿⣿⣿⣿⣿ ⠀⣾⣷⣿⢀⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣾⡵⡿⠋⠀⢹⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⡆⡏⠸⠿⠿⣧⣼⣿⣿⣶⡿⠟⣯⠷⢛⣶⣿⣿⣿⡿⢃⠀⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣾⣍⣿⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠙⣷⣄⠀⠀⠀⣀⣀⣀⣀⣀⣠⡾⣱⡿⠃⢀⣀⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢼⣿⣿⣿⡟⠉⠀⠀⠀⠀⢼⣵⣿⠷⣠⣿⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢠⣼⠟⠈⠟⠀⠀⠀⠀⠀⠀⠈⠹⠁⣂⢩⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⣁⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢁⡙⢧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠁⢠⣤⣀⠀⠀⠀⠈⢀⣤⣶⡀⠁⠈⠃⠀⢳⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠊⣽⢡⣿⠀⠄⢾⣿⠟⠇⠀⠀⠀⠛⢿⣿⠏⠀⠀⠠⠀⡀⣇⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠘⣴⠏⠀⡟⡇⠀⣈⢀⣠⠀⠀⠀⠀⢠⣤⣠⠴⠊⠁⣀⠀⢀⣿⡆⠀ ⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⢠⣿⠀⠀⠳⡉⣶⣀⣼⣹⠀⠀⠀⣠⣴⣿⢿⠖⣈⠹⠛⢁⣾⣏⣧⠀ ⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠸⣿⣰⠀⠒⢻⣷⣺⣯⡙⣿⣿⣶⠗⢀⡩⣿⠒⠤⣀⣰⣿⣿⡍⠿⠀ ⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠿⣿⣆⡔⠁⠀⢉⣿⣧⣌⣽⠷⠤⣤⢿⣾⡿⣿⣿⣿⣿⠿⠸⠀⡇ ⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣖⡄⠀⡞⡜⠙⠛⠙⠽⢾⣷⣾⣿⣿⣝⡷⠛⠁⠀⠀⢰⠃ ⠀⠀⠸⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠙⢏⢰⣾⡧⠰⠀⠀⠀⠀⠀⠉⠛⢿⣿⢉⡑⢢⡀⠀⣠⠃⠀ ⠀⠀⠀⣿⡇⣄⠱⡄⠀⠀⠀⠀⠀⠀⠈⣿⡟⠀⢀⡀⠀⠀⠀⠀⠀⠓⠿⣷⣿⣿⣾⣿⡟⠁⠀⠀ ⠀⠀⠀⣿⢿⢘⣎⢹⢦⢀⠀⠀⠐⣄⡀⠘⢿⣶⣄⡙⠀⠀⠀⠙⠒⢄⣳⣾⠍⣹⣏⡁⠀⠀⠀⠀ ⠀⠀⠀⠸⣼⡎⣼⡆⠃⢸⠷⡀⠀⠈⠀⠀⠈⢿⣿⡻⣿⣿⣶⣾⣿⣾⣿⡷⣷⣼⢻⣿⠀⠀⠀⠀ ⠀⠀⠀⢀⣇⣿⣻⢿⣆⡘⣆⣷⡄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠉⠉⠁⠀⠀⠀⠀ ⢰⣶⣿⣿⣿⣇⠙⣿⣼⡿⣻⣿⣷⡀⢀⠀⣴⣦⢿⣿⣷⡿⠽⠥⠼⣿⡍⠿⠶⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠀⠈⠈⠉⠉⠁⠈⠛⠛⠙⠛⠓⠯⣰⣶⣿⣄⣩⣻⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣛⣻⡷⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠹⣷⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⣡⣶⠏⠉⠉⠉⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠈⣿⣿⢦⣀⣤⣤⡴⠶⠶⠶⠶⠶⠶⢺⠟⣺⣿⡃⠀⣠⣾⣶⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠐⢿⣶⣿⠟⠛⣰⡿⣿⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢀⣀⣼⡿⢧⢫⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⠇⠀⡟⢩⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠛⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠚⠓⠿⣏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡷⠖⠃⠀⠀⠀⢢⠀⠀⠀⢠⠃⠀⠀⠀⠀⢠⠀⣐⡆⠈⢧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⡿⠁⠀⢠⣶⣦⣦⠀⠀⠀⠀⠀⢀⣴⣿⣻⣅⠀⠀⠀⠟⠀⠀⢳⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⢋⡾⠀⣿⣁⠠⡄⣿⣿⡿⠻⣇⠀⠀⠀⠀⠓⢿⣿⣿⡟⡀⠀⠶⣀⣀⡀⡈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠰⡃⣾⠇⠀⡙⣷⠀⠀⠂⠋⠁⠀⡀⠀⠀⠀⠀⢀⣀⡀⠀⣀⡤⠖⠀⠀⠀⠈⢁⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣸⡏⠀⠀⣇⠻⣄⣀⠒⠂⣶⢿⠀⠀⠀⠀⠀⠀⢛⢿⣯⣁⣠⣤⣴⣶⣦⡄⣼⣿⣿⠀ ⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⢰⣯⡇⠀⠀⠘⢆⣈⣿⡤⣾⣥⣼⠀⠀⠀⠀⣼⢯⣿⡾⢿⠒⢠⡤⠊⠉⢁⣴⣿⣧⣽⡄ ⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣸⠀⠒⠛⢻⣷⣞⣯⢿⡘⣿⣿⣿⣾⡗⠀⣀⢭⣿⠓⠶⢄⣀⣠⣿⣿⣿⣈⠿⡇ ⠀⠀⠀⢰⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⢀⠴⠃⠈⠛⢿⣿⣀⠙⠛⣿⣅⣀⣀⣼⣷⡜⣷⣾⣿⣿⣿⣿⣿⡏⢸⠀⢹ ⠀⠀⠀⣸⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣫⠀⠀⠀⢠⠏⡿⣮⣿⡿⡭⢍⣡⣞⣁⣿⣿⣯⡹⣿⣻⣿⠝⠁⠁⠈⠀⣸ ⠀⠀⠀⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⢿⠀⢀⡏⠸⠀⠈⠉⠁⠉⠛⠿⣿⣿⣿⣿⣿⢷⣼⠋⠉⠀⠀⠀⠀⢰⠇ ⠀⠀⠀⢸⣿⢸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠈⣧⣿⡶⠀⠇⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣛⡆⡉⠙⠲⡀⠀⠀⢠⠟⠀ ⠀⠀⠀⢸⣿⣼⠀⡆⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡹⣷⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠼⢶⣿⠏⣴⣿⣿⣴⣿⣿⡾⠃⠀⠀ ⠀⠀⠀⠈⡟⣿⠘⣗⢤⢧⣤⠀⠀⠀⠀⠀⢀⠀⠀⠘⣝⡦⣄⠀⠛⣦⠀⠀⠀⠀⢧⣄⡀⢠⣌⣹⡷⠿⣿⠿⠿⠛⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡸⡄⡌⣾⡀⣏⠣⣤⡄⠀⠀⠘⣧⠆⠀⠘⢿⣮⣵⣦⣀⢀⠀⡀⠀⢀⣉⠉⢤⣽⡾⢓⠄⣿⣷⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡇⣷⢰⣇⣧⠈⠂⣜⠿⣆⠀⠀⠈⠀⠀⠀⠈⠻⣿⣟⡟⣿⣿⣭⣽⣿⣿⣽⣿⣿⡟⢾⣷⣽⠳⣽⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣹⢸⡏⣿⣿⣦⠀⠻⡄⣿⣄⡀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣾⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀ ⢀⣀⣠⣤⣾⣿⣿⠰⣿⡼⡝⣿⣦⣇⣿⣮⡁⠀⠀⠀⠀⠀⡀⢸⣿⣿⡟⣩⡯⡷⠚⠙⣛⡶⠦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠿⠿⠿⣿⠿⠿⡆⢈⣷⣧⣣⡃⢽⣽⡽⢷⣤⣠⣤⠘⣿⠿⠟⢻⣿⠿⣧⣙⣛⠛⠛⠓⠿⠖⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠛⠸⢧⣼⣾⣶⣿⣦⣀⣎⣹⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠴⠂⠀⠁⠀⠀⠀⠚⢄⠀⡨⠀⠁⣀⡢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⣤⡬⠟⠀⠀⠀ ⠀⠀⢠⣾⠇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⢒⡲⠋⠹⠁⠀⠀⠀⠀ ⠀⢰⠿⢿⡀⠀⠀⣠⡣⠄⠐⠀⢇⠀⠀⣷⢞⣁⣀⠀⠀⠀⠀⠀⠀⠀ ⠎⠃⠀⠑⠍⢲⣾⠄⠀⠀⠀⠀⠀⠁⠚⠉⢿⣏⣉⣀⣀⣀⣀⣀⡀⠀ ⠄⢄⡀⠀⠀⠀⠀⠀⢀⣀⠠⢤⡒⠠⠙⠒⠉⠉⠉⠀⠀⠀⠀⠀⢈⡽ ⠀⠀⠙⠒⠒⠊⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡴⠻⣿⣷⣦⡀⠀⣀⣤⣤⣤⣴⣦⣴⣶⣾⣤⣄⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢫⣟⡝⢦⣄⢳⡀⠀⢉⣸⣿⣿⣿⣽⣿⣿⣿⣿⣿⠿⠛⠋⢉⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⢿⣾⣆⣹⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣷⣦⣴⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⡈⠙⢿⣿⣿⣿⣿⣝⣟⢏⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠳⠾⠿⣿⣿⣟⠿⣿⣿⣧⠹⣭⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣶⣿⣿⣿⣴⣿⣻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣽⢯⣽⣿⣿⡿⣿⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣾⣿⣿⠟⣴⣛⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⢿⣿⣿⣿⣿⣿⣶⣥⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⢻⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⢀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟⢛⡋⣽⠟⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠉⢩⣽⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠉⠙⢦⡙⣼⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠙⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡟⠻⠿⣿⣿⣽⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣽⠟⠋⠉⣠⣿⣿⣿⣼⢿⣩⣽⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⠤⠴⠶⠶⠿⠖⠒⠦⣄⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⡟⠀⠠⣸⣿⣛⣿⣿⣿⣟⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠂⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣾⣥⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣾⢸⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣯⣀⡀⢀⣀⣀⣀⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠓⢒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⠛⠿⠿⠿⠛⠛⠛⠋⠉⠉⠉⠉⠙⠿⢿⣿⣿⢿⣿⡿⠛⠛⠛⠋⠉⠀⠀⠀⠈⠙⠓⠛⠛⠺⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣀⢈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠖⠒⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⠒⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀ ⠀⠀⢀⣤⡖⠲⣏⠀⠀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢦⠀⠀ ⠀⠀⠘⣿⣧⡖⡤⠍⣾⠿⠉⠻⠧⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀ ⠀⠀⠀⡸⠻⣿⣿⠟⠉⠀⠀⠀⠀⠸⢄⣀⠀⠀⠀⠀⠛⠆⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷ ⠀⠀⣴⠁⠀⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰ ⠀⠀⢹⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠈⢧⠀⠇⠀⠀⢰⡟⡦⣦⠀⢠⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢿⣯⡛⢷⠀⠀⠀⠀⠀⠙⢏⠀⠀⠀⠀⠈⢣⡘⣶⠞⠁⠀⣠⣿⣧⣾⣆⣧⠀⠀⠀⠀⠀⠀⢀⣨⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾ ⠀⠙⠻⣿⣦⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⢿⣿⠀⠀⢠⣟⣿⡿⠃⠈⡽⣄⠀⣀⣀⣴⣟⡋⢹⣦⠀⠀⠀⠀⠀⢀⣶⡶⢾⣿⠀⠀⢻ ⠀⠀⠀⠀⠉⠣⢬⣿⣶⠀⠐⣄⠀⠀⢀⡱⠀⣼⢛⢀⢰⡏⠉⣁⡠⠴⢊⣡⣶⣾⠛⠉⢀⣙⡿⠦⠽⠷⣄⣀⡀⣤⠈⠉⠀⢰⡇⠀⠠⣼ ⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⣙⠳⣤⣜⣧⡼⠻⣸⣾⣷⣷⠞⢃⠄⣰⣟⢿⣟⣹⠦⠖⠋⠁⠀⠀⠀⠀⠉⠑⠙⠧⠤⠤⠴⢿⢃⠀⢲⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠉⠙⠻⠥⠼⠧⠊⠙⠓⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠐⢤⣿⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡚⢁⣠⢶⡶⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡤⢶⢲⢺⡙⣤⣽⣿⡼⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⢩⣁⣦⠴⠶⠿⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢉⡠⠗⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⡡⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠒⢦⡀⠀⠀⢀⡀⢀⣔⡽⠃⣻⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡄⢸⡟⡟⠁⠀⠀⠘⡾⠓⣾⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢑⡍⠀⠀⠀⠀⠄⠀⢀⢀⠫⡀⠀ ⠀⠀⠀⠀⠀⡀⠤⡚⣟⠀⣼⠶⠀⠀⠴⣿⠆⠀⡀⢱⠀ ⠀⠀⢀⠔⠁⠀⢱⠁⠞⢄⢀⢴⠀⠀⣐⣦⡂⢡⡄⣸⠇ ⠀⢀⠃⠀⠀⠀⢿⡀⠘⠾⣻⡿⣶⡼⠉⡽⣊⣄⣼⡯⢳ ⠀⣼⠀⠀⠀⠀⠈⢻⣤⠀⢜⠳⠾⠭⣯⣿⣝⡿⠟⠁⢠ ⠀⢸⡇⢠⠀⠀⠀⠀⢫⣾⠂⠀⠀⠀⠈⣹⣇⣭⣦⡠⠃ ⠀⠸⣇⣳⢳⢄⠀⠠⠀⠳⣦⣑⣀⠀⣂⣰⣯⢹⣍⠀⠀ ⠀⠀⣋⣼⣦⠸⣱⡀⠀⠀⠹⣮⣿⣿⣿⠿⠉⠛⠛⠀⠀ ⠒⠿⠿⠌⠶⠏⠿⠧⢠⣰⢖⣿⠾⢓⡚⠋⠛⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀

⢠⣷⣶⡖⠒⠶⢤⣄⣀⢰⠏⢋⣷⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡧⠈⠁⠀⠀⣾⣷⣮⠉⠛⣺⣿⣿⢯⣳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢦⣄⣀⠀⠈⠛⠛⠁⠀⣿⣟⣿⣿⣿⠃⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠳⣝⠀⠀⠀⠀⠀⠀⠛⠿⠛⠉⠈⠙⠛⠛⠋⠉⠁⠉⠉⠉⠛⠛⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡇⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⣿⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠞⣿⠶⠶⠶⢾⠆⠀⢀⣷⣏⡀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣾⡇⠀⠀⢠⡇⠀⣠⢿⠃⠀⠉⠓⠦⣤⣀⡀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠛⠀⣀⣀⣾⣤⡾⠁⠀⠀⠀⠀⠀⠀⠀⠈⢹⡍⠙⠛⣦⠀⠀⠀⠀⠀⠀⢀⡿⢴⡟⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠲⢶⣿⠿⠧⠴⠋⠀⠀⠀⠀⠀⠀⣴⣶⣖⣫⣉⣿⣶⡞⠉⠳⣄⠀⠀⣠⠴⠚⠓⠾⠧⣄⡀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣀⣤⣤⡴⠲⠖⠛⠓⡾⠋⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠓⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣄⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠭⠥⠤⠤⢤⣄⣀⡀⠉⠉⠉⠒⠒⠲⠦⠤⠤⢤⣄⣀⣀⡤⠤⠴⠋⠀⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠲⠤⢤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠐⠾⢴⠂⡓⡲⣛⠀⠀⡐⠛⠂⠀⠈⠗⢃⡀⠀⠈⠀⠀⠀⠁⢐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⢻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣴⣶⣦⣤⣉⠙⠛⠿⠿⠟⢀⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣛⣿⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⣿⠛⣿⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣤⣿⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠛⠷⢶⣤⣤⣭⣿⣭⣤⣤⡶⠾⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠾⢻⣶⠾⠛⠛⠛⠛⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢀⡴⠋⢠⣤⡴⢦⣄⠀⠀⢿⣤⡤⠶⠶⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣾⠁⣼⠟⠁⠀⠀⣼⠀⢀⡿⠀⠀⠀⠀⠀⠀⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⡀⠀⠀⢀⣠⣴⡞⠉⠀⠇⠘⠇⠀⠀⣠⠞⢃⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀ ⢿⣿⠟⠛⠛⠋⠉⣬⣄⡀⠀⠀⠀⠀⠀⠀⠻⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠻⣆⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀ ⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠉⠙⠳⠶⣄⠀ ⠀⠀⠀⠀⠈⠙⣿⡶⠶⣶⣶⠟⠀⠀⢀⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠘⣧ ⠀⠀⠀⠀⠀⠀⠿⠶⣶⡏⠀⣀⣤⠶⠿⠤⣴⣶⠾⠃⠀⠀⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⢿⣥⣀⣀⣀⣠⡤⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⢀⠀⢀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠚⡟⠚⡛⣻⠟⣻⢻⣿⢻⣓⠐⠒⠒⠛⠀⠀⠘⠀⡈⠗⡛⠊⠙⠛⠲⠛⠘⠋⠀⠀⠀⠀

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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠉⠉⠉⠙⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣨⣿⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠈⡆⠻⣿⡿⢿⡟⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⢄⠀⠈⢧⢀⠀⠸⡄⠈⠁⠀⣆⠀⠀⠀⢧⠹⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢰⠃⠀⠀⠀⠀⢀⠀⠀⠀⢸⢷⡀⠀⠀⢸⡦⠀⠚⢿⡖⠒⢳⠀⠀⠀⢸⡀⠀⠀⠸⡆⠙⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢃⠀⠀⠀⡎⠀⠀⠀⢠⠀⠀⡇⠀⠀⢸⠀⢧⢰⡀⠀⢳⠀⠀⠘⣷⡀⠈⢷⡀⠀⠀⣇⠀⠀⠀⣷⠀⠸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡞⠀⠀⠀⡇⣼⠀⠀⠘⡆⢀⣷⠒⠁⢸⡀⠈⢧⣷⡀⢠⣿⣉⣩⣽⣷⣤⣴⣧⡀⠀⢹⠈⠱⣤⣿⠀⠀⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢿⡇⡀⠀⠀⣷⡏⠀⠀⢀⡷⠋⢸⡴⢒⣉⡇⠀⠈⢿⣷⡀⢳⠘⠋⣿⣿⣿⣿⣯⠀⠀⢸⠀⠀⢹⡇⠀⠀⢸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠈⣷⠃⡀⠀⢸⣧⠀⠀⠈⢹⣰⣿⣿⣿⣿⣿⡅⠀⠈⠟⠉⠉⠀⠀⢙⣿⣿⣿⢻⡆⠀⠸⡀⢠⣿⡇⠀⠀⠘⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡇⠀⠸⣾⠀⠀⣀⣿⠀⠀⠀⠸⣿⠏⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⣿⣏⣟⣿⡇⠀⠀⢿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡇⠀⠀⢻⣧⡜⠁⢸⡇⠀⠀⠀⢿⡆⣀⡈⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢁⣷⠀⡆⢸⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣧⡀⠀⢷⠀⠀⠀⢸⣿⡟⣷⣾⣿⠛⠁⠀⠀⢀⣀⠤⠀⠀⠀⠀⢀⣾⣿⠀⡇⢸⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⣿⣿⣶⣼⡄⠀⠀⠈⣿⡉⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⣴⣿⣿⣿⡀⡇⠈⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⢀⠀⠀⢻⣿⣦⣤⣄⣀⣀⡀⢀⣀⣤⣴⣾⠋⢩⣿⣿⣿⣿⡇⣿⣠⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⠈⡇⠀⢸⣿⣿⣿⣿⣿⣿⣟⣿⠿⠟⠋⠀⠀⠀⢉⣿⣿⣿⣿⣯⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡀⢻⡀⢸⡿⠿⢿⣿⣛⣯⣿⡏⠀⠀⠀⠀⠀⢀⣾⣿⣿⣶⣿⣿⣛⢿⣿⠀⠀⠀⠀⠸⣿⣿⣿ ⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⠀⢷⡀⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⢧⣿⣷⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⢹⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⣿⣿⡇⢧⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⢿⣿⣿⣿⣿⠿⠛⠉⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣠⣿⢏⠔⠉⠉⠀⠀⠀⠉⠙⠢⣽⣎⣿⣿⣧⣠⣿⣿⣽⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠉⠿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣼ ⠀⠀⢀⣀⣤⣶⣿⣿⡷⠋⣀⡠⠤⠶⠲⠶⢦⣤⣄⣿⣿⠿⣟⢛⣿⣿⣹⣻⣹⣷⣘⣿⣿⣿⣷⣦⣤⣀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣠⡾⡅ ⣿⣿⣿⣿⣿⣿⣿⡟⢀⡜⠁⠀⠀⠀⠀⠀⠀⢨⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠇⢿⢿⣽⣿⣿⣿⣶⣶⣦⣤⣤⣤⣞⣉⣤⣤ ⡟⠛⣩⣾⣿⣿⣿⡷⠋⠀⢀⣶⣤⣶⣾⣶⣶⠋⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠛⢝⣟⢿⣿⣿⣿⡻⣿⣿⣿⣿⣟ ⣷⣾⣿⣿⣿⠿⢻⠁⠀⡠⠞⠋⠀⠀⠈⡴⠁⠀⣼⠁⠀⠀⡼⠃⠀⠀⣴⠂⠀⠀⢀⣶⣧⣄⢀⠀⠀⠀⠀⠁⠈⠿⣿⣿⣿⣾⣿⣯⡀⠀ ⣿⣿⠿⠛⠁⠀⢈⡷⠊⠀⠀⢀⣤⣶⣾⠇⠀⢸⡇⠀⢀⣼⠁⣀⣀⡞⠿⠤⠤⠴⠋⠀⠈⠉⠻⡆⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⡒ ⣷⣤⣀⡀⣠⠖⢙⣧⣤⣴⣶⣿⣿⣿⣿⠀⢰⣿⡛⣃⢙⡟⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⠀⠀⠀⠀⡄⢸⣿⣿⣿⡿ ⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣻⣿⡿⠻⡟⢾⣛⣋⣉⣙⣻⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⡿⠀⠀⠀⢸⠀⠀⢠⣦⣿⣾⣿⣿⣿⠁ ⠟⠛⠛⢛⣻⣿⣿⣿⡿⣿⢿⣿⣿⣿⣾⣿⠟⣻⠋⢉⠛⢻⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡯⠀⠀⠀⢸⠀⠀⣼⣿⣿⣿⣿⣿⠃⣼ ⡆⣁⣤⣾⣿⣿⣿⣿⢡⣿⣾⣿⣏⢈⢿⡀⠀⢷⠀⠈⢄⣴⠿⠀⠀⠀⠀⠀⠀⢀⣤⣤⣬⣭⣛⠘⢿⣶⣦⡏⠀⢴⣿⣿⣿⣿⣿⠇⣼⣿ ⣿⠿⣛⣿⣿⣿⣿⣷⡯⡊⣿⡿⣿⠀⠀⠵⠄⠀⠙⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⢾⡟⠋⡘⠻⣿⣷⣔⠈⣻⣆⢀⣽⣿⣿⣿⣿⢃⣼⣿⣿ ⣶⣮⣿⣿⣿⣿⣿⡿⠇⣼⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠉⢐⡟⠙⣿⣦⡏⠈⣾⣿⣿⣿⡿⢣⣾⣿⣿⣿ ⣿⡿⣿⣿⣿⣿⣿⠁⠂⢿⣏⠛⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠑⠒⠉⠀⣀⡽⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠿⠀⢠⣿⣿⣷⣤⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡋⣰⣿⣿⣿⣿⢭⠙⣿⣿⣿⣿⣿⣿⣿ ⡿⠛⠛⠿⣿⣿⠀⣴⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠰⣟⠟⠛⠗⠶⡒⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢿⡌⣧⢰⡿⣿⣿⣿⣿⣿⣿ ⡇⠀⠀⠀⣹⣝⣻⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠈⠙⠒⠲⢤⣁⣙⢻⡇⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠟⢸⡿⣡⡿⠀⠘⣿⣿⣿⣿⣿ ⡇⠀⠀⢰⣿⣇⣾⣏⡿⢿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢀⣴⣿⣯⣿⣿⣟⣠⣴⣾⣿⡇⠀⠀⢹⣿⡹⣿⣿ ⡇⠀⠀⣸⣿⣾⣿⠋⠀⢀⣴⠿⠿⠿⠋⣻⣿⣯⣶⣄⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣷⠀⠀⢸⣿⣧⠘⢿ ⡇⠀⠀⣿⣿⣿⡏⠀⡰⣋⡟⠀⠀⠀⠈⡟⠺⡌⢿⡛⢷⣤⡤⣤⣶⣾⣿⣿⣿⣿⣿⠋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣧⠀ ⡇⠀⢸⣿⣿⣿⢁⡾⠗⢊⣉⠑⣆⡀⠀⢻⡀⣃⠀⠻⣍⠈⠛⢋⠝⢭⣿⠈⢿⡿⣨⣾⣫⣾⣿⠿⠛⠛⠋⠉⠙⢿⣿⠀⠀⠈⣿⣿⣿⡇ ⡇⠠⣾⣿⠉⠉⠉⠉⠉⠁⠀⠀⠀⢹⠀⠀⢳⣾⣀⠀⠀⠀⠀⠀⢀⡾⠃⣠⢿⣿⣿⣶⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⣿⣿⠛⠀ ⡇⣸⣿⡇⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠳⣤⣶⡟⠛⢿⣷⠶⠒⠋⠁⣠⣾⣿⣿⣟⠜⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⡏⠁⢀ ⣷⣿⣿⠇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢿⡟⠦⣌⡿⠿⡆⠀⢀⣴⣿⣿⣿⡿⠋⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣿⢧⠀⠀ ⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⣸⠋⠈⣧⣴⣫⣿⣿⣿⢟⡇⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡀⣿⠀⠉⠢ ⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⡆⠀⠀⡞⠀⢰⠋⢰⣿⣿⣿⣿⣿⠿⠁⢾⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠸⡧⠀⡀ ⡿⢃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣃⣀⣤⡞⠀⢀⣇⣴⣿⣿⣿⣿⡟⠉⠁⠀⢸⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠃⡀⠰⠀⠃

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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣼⠛⢻⣿⡀⢩⣿⠗⠂⠉⠀⣼⡃⣹⠘⣃⠀⠟⠁⢴⣦⣤⣄⡀⠙⠁⠛⠀⠸⠆⠀⣄⡀⠀⠀⠈⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣦⠀⢻⣶⡇⠀⠀⢹⣟⣿⣴⣿⣶⣶⣤⣤⣶⠌⠙⠿⣦⣄⣀⠀⠀⡇⣸⣿⣿⣦⣤⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⢀⣿⣿⣷⣶⣶⠾⠟⠛⠷⠿⠷⠬⠏⠉⠁⠀⠀⠀⠀⠙⢿⣧⣤⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣸⣿⣼⣿⠿⠛⠉⢀⠀⢀⣠⣤⠤⠴⠶⢤⣤⣀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠾⠿⠾⠿⣿⣧⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠉⠶⠤⠄⠀⢨⡶⠟⠉⠀⠀⠀⠀⠀⠈⠉⠻⣾⣦⠀⣤⡿⠋⠁⠀⠀⠀⠀⠀⠀⠙⠻⣿⣀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣤⠶⠒⢀⣀⡀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣴⡶⠶⠟⠋⠉⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠏⡾⠿⠿⠿⠛⠉⠀⠀⣉⢸⣿⡁⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⡀⠀⣿⣀⠀⠀⠀⢠⣾⣿⣿⣿⣦⠀⠀⠀⢠⣿⢃⡀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠒⢀⣀⡀⠐⠒⠂⢀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⣰⠿⢿⣧⣀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⣼⡏⠀⠹⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠄⠀⢉⡉⠉⠀⠀⠀⠀⠘⠿⣿⣷⣀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣫⡾⠋⠀⠀⠈⠙⠳⢦⣝⣿⠛⠛⠁⢀⣰⣾⠟⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⠶⠶⠾⠛⠃⠉⠉⠋⠁⠀⠀⠀⠒⠀⠀⢯⡙⠿⣷⣶⣶⣦⣦⣤⣶⣾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣶⡾⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣀⣄⣀⣀⣀⡀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠿⢶⣆⣈⡙⠻⢿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢡⣤⣤⠦⠄⠴⠀⠀⠀⠀⠄⠀⠙⠛⠿⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠘⣷⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀ ⣿⣿⣿⣿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣟⣛⣛⣁⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⣧⡀⠀⠀⠀⠀⠀⠀⣠⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣋⡉⠙⠛⠋⠉⠁⠀⠀⠀⠀⠘⠛⠂⠀⠀⠀⠀⠀⢠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⣇⠰⠶⠀⠀⠀⠈⠉⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⢛⢛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣶⡶⠆⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡉⣉⣉⣀⣀⣠⣴⣤⣤⣤⣀⣀⣀⣀⣀⣠⣠⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣶⣶⣶⡶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⠶⠾⠿⠿⠟⣉⠀⠀⠉⠉⠙⠻⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣷⡶⣶⠆⠀⢀⣹⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀⡀⢀⣀⣀⣀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣱⣆⣠⣿⡟⠁⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⠄⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⣤⣀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠘⠿⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡿⢿⡇⠀⠘⣇⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⡇⢸⣷⣖⡀⢩⣤⣤⠀⣦⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣸⡷⢸⣟⠛⠻⣆⠘⢻⡷⡉⠁⠀⣀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⠀⢢⠉⠳⡿⠛⢡⣴⡄⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⣄⠀⡀⠀⣄⣀⠀⠉⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠛⣿⠁⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⣤⡴⠶⠾⠿⠿⠶⠶⠦⣤⣄⡀⠀⠀⠀⠀ ⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⡄⠀⠀ ⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀ ⣾⠃⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⣼⣿⡆⠀⠀⠀⠀⢹⡆ ⣿⢰⠤⠤⠤⠤⠭⠭⠤⠤⠤⠤⠬⠿⠥⠤⠤⠤⠤⡌⣿ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿ ⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃ ⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀ ⠀⠀⣸⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀ ⠀⢠⣿⣿⠀⠉⠛⠻⠶⠶⠤⠤⠴⠶⠟⣿⣧⠀⠀⠀⠀ ⠀⣸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣿⠀⠀⠀⠀ ⠀⣿⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀ ⠘⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹⡇⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⢤⡞⢫⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣀⣌⠀⡆⠀⠀⠀⠀⢰⢰⠀⠀⠀⡾⠀⡇⢰⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⢺⣰⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⠇⠀⡇⠀⡆⢸⢰⣸⣷⡄⠀⠜⢀⣀⣇⡾⡀⣼⠀⢀⠀⢀⡆⠀⠀⢠⠘⡿⠀⠀⠀ ⠀⠀⠀⠀⣀⠠⠚⢡⢄⣾⠃⣄⢳⠀⠿⠿⣮⠿⣆⣀⣼⡿⠻⡟⣃⣿⢀⠆⢀⢾⢠⠀⡜⡄⢣⡐⡀⠀⠀ ⠀⠀⠈⠉⠒⢒⢞⣥⣾⠟⣴⣿⣎⠳⣜⡀⠀⠀⠈⠛⠇⠀⠉⠑⡾⣏⠜⢀⠎⡎⢸⢀⢇⠀⠈⢿⣼⣦⡀ ⠀⠀⠀⠀⣀⣼⣿⣿⡅⠰⠃⠁⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⢀⠎⠀⢀⢸⢸⠀⠱⣄⠻⣿⣦⠈ ⠀⠀⢀⣴⣿⣿⣿⡏⠓⠀⡄⠸⣿⣿⣿⣦⡀⢀⡵⠶⠤⠤⠀⠉⣸⡄⡜⢀⡇⢸⣌⣿⡄⢠⣿⣆⠘⡏⡆ ⠀⠀⣾⣿⣿⣿⣿⣿⣷⣾⡇⡄⣿⣿⣿⣿⣿⣷⣄⠀⠀⣀⣤⠖⢻⢰⣧⢸⢡⣿⣿⣿⡇⣾⣿⣿⣷⡬⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠙⣼⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠂ ⢰⣿⣟⡍⠀⠀⣇⠀⢩⠀⠈⠋⠀⢩⠀⠀⡉⠸⣿⡀⠀⠀⠀⠀⠀⠻⠿⣿⣿⡛⠋⠉⠘⣹⠀⢸⣿⡿⠀ ⢰⣿⣧⠀⠀⠀⡛⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⣿⡷⠂⠀⠀⠀⠀⠀⠀⠘⢿⣤⣀⡂⠀⠀⠀⢈⣿⡇⠀ ⠀⢿⣿⣾⡟⣀⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⢀⣴⠟⣿⣭⣿⣀⣼⣤⣿⣻⠇⠀ ⠀⠈⢻⡿⠿⠿⠟⠿⣷⣿⣦⣤⡄⠙⠂⡀⠀⠀⠀⢿⠍⠒⠢⠤⣄⡴⠛⠁⠀⠘⣄⠉⠉⠉⠉⠁⣻⡆⠀ ⠀⠀⣞⠀⠀⠀⠀⠀⠀⢠⠜⠙⠛⠳⠦⠼⠿⣤⣤⣼⠆⠀⠀⠈⣙⡉⠀⠀⠀⠀⣿⣦⣀⡀⠀⠀⠸⣇⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡶⠶⠶⠛⠛⠛⠙⠛⠉⠛⠛⠛⠿⠿⢶⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡿⠟⣯⣁⡤⠄⢀⣀⡠⠄⠀⠀⢀⡀⠀⠀⠀⢀⣀⣀⣀⣬⣽⣛⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠟⠉⠀⣀⣤⡤⠶⠚⠋⠉⠀⠀⣀⣠⡤⠴⠖⠒⠛⠉⠉⠉⠉⠙⠛⠛⠻⠿⠿⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣾⣿⣿⢟⣯⠶⠲⠶⠛⠉⠁⠀⢀⣠⣤⠶⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠳⠀⠈⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣶⣿⣿⡿⣫⡵⠋⠁⠀⠀⣀⣀⣤⠴⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣌⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢾⣿⣿⣿⢋⡾⠋⣀⣤⣶⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣙⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⢱⣿⣷⣿⣛⣉⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣯⣾⠟⠉⢿⣿⣿⣿⣿⣗⣶⠶⢿⣯⣤⣤⣄⣀⣀⣀⣀⣀⣤⣤⣤⣴⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⠁⠀⠀⣼⣿⠛⠛⠻⢿⣿⣿⣦⡄⠀⢬⡉⠻⣯⣉⣩⣭⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⠁⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠙⠻⣿⣶⡀⠙⣯⣻⣿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠀⠀⠀⠀⠀⠾⣄⣠⠶⢿⣿⡿⣶⣄⠘⢿⣟⢦⠘⠏⠛⢦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⣀⣠⣾⡟⠉⣿⢿⠙⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⠀⠀⠀⣽⣿⣧⠀⢿⡎⠀⠀⠀⠀⠈⠙⠛⣒⠶⠦⠤⠤⣴⣶⣶⠾⠛⠉⣠⣴⡴⠟⠋⠁⣿⠃⠀⡿⢸⡇⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⣿⣿⡿⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣾⣿⣿⣯⣤⠶⠞⠛⠉⠁⠀⠀⠀⢰⣿⠀⠀⠀⢸⣷⣦⣿⣅⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢮⡟⠁⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⠒⠂⠀⠀⠀⠀⠀⣀⣀⠀⠉⠓⠦⣄⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣟⢿⡉⠙⢻⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⢤⣀⠀⠀⠠⢤⣈⠙⠲⣄⡀⠀⠙⠦⣀⠀⣸⡟⠀⠀⠀⣿⣿⠹⣎⢷⡄⠀⠙⢿⣿⣦⣤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠛⠛⠿⣿⣷⣦⣌⠓⠀⠀⠀⠈⢣⣿⠀⢀⣼⣿⣯⣿⠀⠹⣄⠹⣆⠀⠈⢻⣿⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦⣄⠉⠻⣿⣷⣦⠀⠀⠀⣾⡟⢠⣾⣿⣿⣿⡛⣧⠀⢹⣆⠙⢷⣤⣤⣿⣿⣿⣿⡷⣤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡏⠀⠛⢽⣿⣿⣷⡀⠈⢿⣿⣿⣳⣾⣯⣾⣿⣿⣿⣿⢸⡟⣿⡗⡀⢹⣆⣴⣿⢟⣿⢿⣿⣿⣿⣿⣿⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⣄⠀⠙⣿⣿⡇⠀⠈⢻⣿⣿⣭⡟⠛⠻⣿⣿⡏⠀⢻⣀⣿⣇⠀⢻⣻⣿⠏⣸⣿⣿⣿⣌⢿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣹⡿⠁⠀⠀⣸⣿⣿⣿⠃⠀⠀⠮⣿⡇⠀⢰⣿⣧⣿⣆⣿⣿⣿⣾⣿⣿⣿⣿⣿⣇⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠂⠶⠚⠛⠉⢩⣿⡀⠀⠀⠀⣿⣟⢀⣼⡿⠿⢿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⣴⣿⣿⣧⠀⠀⠀⣸⣿⠋⠁⠀⠀⢸⣿⣿⣧⢹⡝⠿⣿⣿⠿⢛⣵⠟⠁ ⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⣠⣾⣿⣿⣿⣿⡄⠀⣰⢿⣧⣀⣀⠀⢀⣾⣿⣽⣿⣼⣡⣶⣶⣦⡀⣿⠏⠀⠀ ⣌⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠛⣿⣿⡿⣿⡏⣹⣿⠋⠁⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀ ⡿⣷⣌⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣴⣿⣟⠋⠰⠏⣰⣿⠟⡇⠀⠀⡇⠀⠀⠀⠈⣿⣏⣸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠞⠛⠉⠉⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣴⡶⣶⡶⠶⠶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⡿⠁⢶⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡈⠁⠉⠉⠛⠻⠿⢶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡉⢧⡀⠀⠀⣀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⢿⣿⣿⣿⣿⢼⣿⠀⠀⠈⠉⠛⠲⠶⠦⠤⢄⣀⠀⠀⠀⠀⠉⠉⠛⠛⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠛⢿⣷⢶⣤⣀⡀⠀⠀⠀⠈⢻⣄⠀⠈⠁⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣆⠈⠉⠛⠷⢶⣤⣀⡀⠉⠙⠓⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠈⠙⠛⠳⠶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠈⣉⣲⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣦⣿⣦⡀⠀⠀⠀⠀⠀ ⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⡀⠀⠀⠀⠈⢿⣟⠉⠉⠩⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣄⠀⠀⠀⠀ ⣟⠛⠛⠳⠶⠤⢤⣤⣤⣄⣠⣴⡞⣱⠋⢉⣿⣷⣶⣦⣤⣄⣛⠷⣆⡀⠀⢀⡉⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀ ⠈⠉⠉⠉⠓⢒⣶⣶⣤⡌⠉⠀⠀⠀⣴⠋⠀⠈⠙⠛⢿⣟⠙⠛⠟⠛⣻⣿⣿⣶⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀ ⠀⣠⣴⣾⣿⣿⡿⠷⠖⠛⠛⢻⡄⢸⠁⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⣰⡿⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠖⠒⠂⠀⠀⠀⠀⣷⡿⠻ ⠀⠻⡧⠥⠞⠁⠀⠀⠀⠀⠀⢸⣧⣸⣷⠀⠀⠀⠀⠀⠀⠀⠈⢻⣤⡿⠁⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠁⠀⠀⠀⠀⢀⣠⣴⣿⡿⢦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠀⠀⠀⠀⣀⣤⣶⠿⠛⠉⠓⢦⠀⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣤⣈⣉⠛⠲⠶⠤⠤⢴⣿⡇⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⣿⡟⠁⠀⠀⢠⣴⠾⠟⠋⠁⠀⠀⠀⠀⠀⢀⣿ ⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⠤⣤⡤⢴⠾⠛⠻⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⣴⡟⠳⠦⣄⡀⠀⢀⣀⣀⣀⣀⣤⡶⠾⠛⠉⠀⣼⠟⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟ ⠀⠀⠀⠀⠀⠀⠈⠿⣦⣤⠶⠶⠒⠛⢳⡄⠀⠀⢀⣀⣀⣠⣤⣀⣙⣓⣶⡾⠋⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⠟⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠒⢛⣡⠶⠛⠉⠁⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⣷⠶⠴⠾⠿⣿⣷⣤⣄⣀⣀⣀⣠⣤⡶⢟⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣯⣿⣟⡟⠛⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠉⢁⣴⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠗⠒⠛⠛⠋⠉⠉⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠿⠓⠛⠋⠉⠉⠉⠉⣿⣿⣉⣥⣤⣤⡤⠴⠶⠾⠿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢠⠟⡿⡿⢿⣿⡿⢻⣿⢏⣷⣿⣷⢈⣿⡿⣿⣾⣷⡽⢿⢿⣿⣿⣿⣿⣿⡆⠀ ⠀⠀⠁⢃⠃⢟⠃⢠⢾⣇⢞⠟⢿⢻⡿⣾⢇⠘⣷⡙⣯⠦⣤⣿⢻⡟⡇⠏⢷⠀ ⠀⠀⠀⢸⠀⠈⢎⢡⡟⡌⢸⡇⢰⢸⢻⣱⠛⡀⢸⣧⠘⣧⠘⡽⡌⠁⢡⠀⠘⠀ ⠀⠀⠀⠀⠀⣼⣦⣼⡙⠀⣼⣇⣞⠘⣟⠻⣎⣦⢸⡻⣆⠈⢶⣼⣇⡇⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⡏⣿⡀⠤⣿⢻⡇⠀⢿⡄⠙⢿⣿⠧⠽⣄⣈⣻⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢼⠉⠃⠀⠀⢸⠈⢿⡀⠰⡑⡀⠀⢸⠓⢄⠈⠢⡀⠻⠀⠀⠀⠀⠀ ⠀⡄⠀⠀⠀⣾⣀⣒⠒⠒⢂⣁⣀⠳⡀⠑⠌⢀⣎⡀⠀⠒⢒⣀⣩⡄⠀⠀⠀⠀ ⢠⣿⢠⣜⠈⣿⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠓⢹⣿⠈⠩⢰⡀ ⠀⣇⢸⢺⠀⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢫⠀⡇⢸⠇ ⠀⡟⣸⢸⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⢸⠀⡇⣾⣷ ⢠⡷⡇⣸⠀⡇⡋⢆⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⡠⠊⣿⠁⠀⢣⣿⣿ ⢸⢱⣧⢻⠰⠁⡇⠀⠑⠤⡀⠀⠀⠀⠈⠙⠀⠀⠀⢀⣠⡞⠀⠀⣏⡆⣣⣼⣿⢹ ⢹⠸⣿⣾⡄⣶⢇⡀⠀⢀⡻⣖⠤⡀⠀⠀⠀⣠⠔⢱⠏⣀⡀⢈⠻⡏⣿⣿⡇⢸ ⠀⡄⢛⣿⡇⣿⣻⢀⠤⠊⢸⠈⠂⠈⢳⢰⡿⠋⡠⠂⠀⠀⠣⢾⡆⡇⣿⡿⠀⡘ ⠀⠐⡀⣙⣧⣽⣿⠀⠀⠀⠀⠀⠀⣈⣒⡠⣐⣈⠀⠀⠀⠀⠀⠸⣷⣷⣟⣿⠐⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢴⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠟⠻⣏⡙⠲⢤⣀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⡿⠛⠓⠲⠤⣄⡀⠀⠀⠀⠀⢀⡴⢫⠞⣹⡏⠀⠀⠈⠻⣆⣀⡿⢷⡀⠀⣠⠞⢁⣠⠄⠀⠀⢹⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠀⠀⢠⣀⡀⠀⠉⠲⢄⠀⢴⣏⣰⠋⠀⡿⠀⠀⢀⣀⣤⣾⣿⠁⠀⣷⡾⠥⢴⣋⠁⠠⢦⡀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠇⠀⠀⣠⠜⠋⠳⢄⠀⠀⠑⢾⡈⢿⠻⢾⣿⠶⠟⠛⠉⠁⠀⠘⣧⢠⡯⠉⠑⠒⠬⣙⠲⢮⡀⠀⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠂⠀⠀⢉⡶⢀⣀⡈⠁⠀⠀⠀⠳⣼⣀⠈⣿⠀⠀⠀⠀⠀⢀⣠⡿⠏⠀⠀⠀⠀⠀⠀⠙⠦⣈⠓⢏⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠐⠛⡶⠋⠀⠹⢤⠀⠀⠀⠀⠀⡉⠛⠻⠦⠤⠴⠖⠛⠉⠁⣀⣀⠤⠤⠤⠤⢄⡀⢀⡘⢦⡀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⢠⣾⡀⢀⣠⠖⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⠀⡠⠴⠒⡚⢉⡠⠤⠒⠀⠀⠐⠲⡝⠀⠐⠢⠤⣀⠀⢠⡳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡀⣠⠇⠀⠉⠉⠀⠀⠀⠀⠀⠀⣀⡠⢾⡀⢇⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⢀⡄⠀⠀⠀⠑⢄⠛⠿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⠃⠀⠀⠀⠀⠀⠀⢀⡤⠴⠚⣯⠔⢺⣇⢸⡀⠈⢆⠀⠀⡀⠀⠀⠀⠀⠀⢸⣧⢀⡴⠋⣧⠀⠀⠀⠀⠀⢳⡐⢼⡄⠀⠀⠀ ⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⣸⠃⠀⡞⣿⣼⡷⠀⠈⢇⠀⢱⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⡿⡄⠀⠀⠀⠀⠀⢿⡮⣧⠀⠀⠀ ⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢸⠓⣿⡟⠀⠀⠀⠘⣆⣾⣇⠀⢀⣠⢴⡏⣩⣇⣀⣼⠁⢣⡆⠀⠀⠀⠀⠸⣷⣿⠀⠀⠀ ⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⡖⠀⠀⣠⠃⠀⣰⢃⣼⣿⣈⡳⠄⠀⠀⡿⠁⠹⠛⠉⠙⣿⠟⣋⣭⣉⡛⢷⣼⡇⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⣴⣃⠴⣾⡿⠟⣩⣥⣤⣭⡃⠀⠀⠀⠀⠀⠀⠀⠀⠉⣰⢉⣿⣽⣿⡄⠙⣷⠀⠀⠀⠀⣲⠛⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣠⠞⢹⠁⣼⠟⠀⣜⢨⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⡿⣧⠀⠸⡆⠀⠀⢴⡃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⠖⠋⠀⠀⣇⣰⡟⠀⠀⣿⠻⣿⣿⡿⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡈⠉⣠⠏⠀⠀⢱⡄⠀⠀⠈⢓⣄⠀⠀⠀ ⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⢻⣦⣈⣉⣀⣴⠇⠀⠀⠀⠀⠀⢰⣶⣦⠀⠉⠛⠛⣋⡤⠚⣇⠀⠙⣄⠀⠀⠈⣿⠀⠀⠀ ⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣇⢀⣀⠉⠝⠛⣯⠁⠀⠀⠀⠀⢀⣀⣀⣉⣀⣀⣀⣤⣄⠟⢦⣀⡟⣰⠁⢸⡄⠀⠀⢻⠀⠀⠀ ⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣿⡞⣷⡀⢀⠞⠟⣾⣿⣿⣿⠿⠿⠛⠛⠛⠛⠛⢿⡿⣿⡄⠀⠙⣷⡃⠀⢸⡇⠀⠀⠈⠀⠀⠀ ⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠠⢓⣊⢀⣸⢻⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢙⡶⠞⠋⠁⢀⡎⠀⠀⠀⠀⠤⠄⠄ ⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⠉⠛⡛⢯⡁⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣱⠋⠀⠀⠀⣠⠏⠀⠀⠀⠀⠄⣤⠖⠀ ⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢶⣾⠃⠀⠹⣮⣷⡀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡿⠁⠀⣀⠴⠊⠁⠀⠀⠀⢀⣠⠔⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢀⡤⠤⣛⣧⣄⣀⠀⠈⠻⢿⣦⣤⣤⣠⣤⣴⣾⣟⡩⠤⠒⠉⠀⠀⠀⠀⢠⡶⠿⠇⠀⠀⠀⠀⠀ ⠘⠆⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⢤⣤⡿⠥⢤⠚⠛⡷⢄⡀⠀⢀⣹⠉⠓⢞⠛⠿⣦⡀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠈⠓⠦⠤⠤⣄⠀⣀⠀⠀⢀⣾⠏⠀⠀⠈⡆⠀⠑⢦⣬⠭⡥⠼⣦⠀⠀⠳⡀⠈⢿⢦⣀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠈⠉⢒⣿⣏⠀⠀⠀⠀⢸⡀⠀⢀⡽⠀⠀⠀⠹⡦⠀⠀⢣⣀⡼⠏⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀ ⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣽⣿⣿⡼⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢠⣿⣿⣿⠃⣿⣿⡿⠀⣿⡟⢻⣿⣿⣿⣿⣿⡇⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⡿⢏⡀⢀⣾⣿⡿⠃⠀⣿⣿⡧⢒⣿⣷⣾⣿⣿⣿⣿⣿⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣼⣿⠏⠀⠀⡰⢻⣿⡿⠁⠀⢠⣿⣿⣾⣿⣿⠟⡻⣿⣿⣿⣿⣿⢸⡄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣀⣴⣿⣓⣀⣴⣎⣠⣿⡟⠀⠀⢠⣿⠛⠟⣿⣿⠿⠃⠁⣿⣿⣿⣿⣿⢸⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⢀⠿⣿⣿⣿⣿⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠋⠉⢸⣿⣿⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠜⢸⣿⣿⣿⣿⡟⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠃⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡟⠀⣿ ⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⣄⣠⣿⣿⣿⣿⣿⣿⠁⠀⡇ ⢻⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠛⠋⠀⠀⣰⣿⣿⣿⣿⣿⢻⣿⠀⢰⠁ ⡈⣿⣿⣿⣿⡈⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⠙⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢠⣾⣿⣿⣿⣿⣿⣿⢸⡇⢀⠊⠀ ⢧⠘⢿⣿⠙⣧⠹⠿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡈⠳⢤⡀⠈⠉⠓⠶⣦⣤⣤⣤⣀⣀⣴⣿⣿⣿⣿⣿⠇⣿⡏⢸⠁⠊⠀⠀ ⠈⠣⣬⡿⢷⡈⢳⣈⠙⠚⠿⢿⣿⣧⠙⢻⡿⣿⠦⠄⠉⢻⡲⢄⡈⠉⠀⠀⠀⠀⠉⠛⣿⣟⠛⠻⠯⣼⣿⠋⡜⠀⣿⡇⠉⠀⠀⠀⠀ ⠀⠀⣼⠔⠊⠉⠉⠁⠉⠉⠉⠁⠈⠛⢷⣄⠱⣜⣷⡀⢦⡀⠱⠄⠉⠲⢄⡀⠀⠀⠀⠀⢷⣉⠁⠠⣔⠉⠈⠻⢤⠜⠻⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣁⣤⣤⡤⠤⠤⠤⢤⣼⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠉⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠙⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡴⠒⢶⣄⣤⣀⣀⣀⡀⠀⠀⠀⣸⣧⠶⠞⠛⠉⠉⠉⠉⠉⠙⠛⠳⢦⣤⣼⠃⠀⠀⠀⠀⢀⣀⠀⢀⣀⡀⠀⠀⠀ ⠀⠀⢠⡟⠀⠀⠀⠉⠉⠙⠉⠉⢻⢀⣤⠞⠋⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠙⢷⣄⠀⠀⢰⡟⠙⣿⠟⠉⠻⣆⠀⠀ ⠀⣠⠾⢷⡄⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁⠀⢠⠋⢧⡀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢳⡀⠀⠀⠙⣷⡴⠟⠃⠀⠀⠀⠀⢀⣿⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋⠁⠀⠀⠘⢂⣈⣁⠀⠀⠀⠀⠀⠀⠀⣋⣉⣛⢃⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠛⠛⢻⣄ ⠸⣧⣀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⢾⢻⣷⡟⢳⠀⠀⠀⠀⠀⣼⢻⣿⠟⡟⠀⠀⠀⢹⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⢹⣧⠖⠚⠒⢄⠘⢷⣤⡴⠟⣣⡤⠤⣤⣄⠿⢦⣥⡴⢣⠖⠉⠑⢺⡷⣦⡄⠀⠀⠀⠀⢀⣠⡾⠃ ⠀⠈⠛⣶⠆⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⢈⠀⠀⠀⡴⠋⠁⠀⠀⠀⠈⠻⣦⠀⠀⢦⠀⠀⠀⠀⣿⣟⠀⠀⠀⠀⠀⠀⠈⣿⠀ ⠀⠀⠀⢻⣄⣠⡀⠀⠀⢀⣾⠙⠦⠤⢤⣮⣤⣄⢰⠁⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⣈⣶⣤⠤⠊⠀⢹⡇⠀⠀⢀⣀⣠⡴⠟⠀ ⠀⠀⠀⠀⠈⠙⠳⠦⠶⠿⣇⠀⠀⠀⡞⣡⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⢸⡷⠛⢱⣄⠹⡆⠀⠀⠈⣿⠶⠶⠛⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣇⠘⢧⡀⠀⠳⣄⡀⠀⠀⠀⢀⣴⠏⠀⣠⠞⠁⢸⠇⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠙⣦⡀⠻⢦⣀⠀⠉⠓⠒⠛⠉⢀⣠⠞⠁⠀⣰⠏⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠈⠳⣤⡀⠈⠙⠓⠒⠒⠒⠚⠉⠀⢀⣴⠞⠁⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠙⠳⢤⣀⣀⣀⣀⣠⡴⠞⠋⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣀⣀⣉⠉⠁⣀⣀⣀⣤⡶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⢨⠷⡝⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢦⣀⠀⠀⢰⠃⢠⠇⠀⠘⡎⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠈⠉⠒⡏⠀⡎⠀⠀⠀⢸⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠉⠉⠙⠲⠀⡇⢸⠁⠀⠀⠀⠘⠀⠀⠀⢹⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⢹⡈⣇⠀⠀⠀⠀⡄⠀⠀⠀⠃⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠃⠀⢀⡴⠊⠁⠀⠀⠀⠀⢣⠈⠣⢤⣀⠀⢧⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣶⣶⣶⣤⡀⠀ ⣀⠀⠀⠀⣀⣀⣼⣠⢴⣿⠃⠀⠀⠀⢠⠀⢀⡏⠀⠀⠀⠈⠉⠚⠛⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠁⠀⠰⣅⣠⣿⢤⣷⠀ ⠉⠉⠉⠉⠁⠀⠈⠀⡜⠈⢧⡀⠀⠀⠘⣦⠞⢀⠴⣄⠀⠀⠀⠀⣼⢻⣀⡠⣼⢿⡃⠀⠀⠀⢀⡠⠔⠋⠀⠀⠀⠀⡴⠖⢦⣿⣁⣠⣿⡇ ⠉⠓⠲⠤⣄⣀⠀⢀⡇⠀⠀⠙⢲⡤⣠⡏⠀⢺⣤⠏⣀⣤⡴⠀⢀⣿⠴⠒⢻⣶⡧⠔⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠳⡄⢀⣷⡋⣹⡟⠀ ⣧⡀⠀⠀⠀⠈⠉⠚⡇⠀⠀⠀⠸⣤⣬⠇⠀⠀⠀⣾⡿⠃⢀⡴⠋⠁⠀⠘⠋⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢉⡽⠋⠀⠀ ⠻⣷⢄⡀⠀⠀⠀⠀⢳⠀⠀⣠⣤⣦⣤⠀⢀⠤⣤⡤⠗⠚⠉⠀⠀⠀⠀⠀⠀⣤⠔⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠋⠀⠀⠀⠀ ⠀⠙⠳⣉⠓⠦⢄⣀⣿⣓⡀⠉⠉⠙⣿⡴⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⢀⣀⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠉⠉⠓⢲⠞⠉⠁⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣀⠤⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⢀⣆⢠⠞⠁ ⠀⠀⠀⠀⠀⠀⠀⢿⣴⡟⠁⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠉⢷⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠚⠁⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠳⢤⣀⣀⡠⠤⠔⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⠤⠤⠤⠤⠤⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀ ⠀⢠⠞⠉⣿⡛⠲⢄⡀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⡏⠻⣇⣱⠀⠀⠙⢦⡀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣛⣾⠟⢻⡄⠀⠀⠀⠙⢶⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⡴⠚⠉⠉⢉⣁⣤⣤⣀⣀⡀⠀⠉⠙⠲⣄⠀⢠⡇⠀⢸⡛⠉⠉⠉⠑⠒⠦⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣇⡀⠀⠀⠀⢸⣄⣀⣠⡶⠋⠀⠀⠀⠀⠀⠉⠙⠦⣄⣀⣨⡷⠟⠀⠀⠘⣧⣀⠀⠀⠀⢀⣠⡤⢤⣌⣉⠉⠉⠙⠲⢤⡀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠀⠀⠀⠀⢸⠀⠉⠉⠛⠓⢾⣿⡛⠋⣠⣤⡶⣶⣿⣿⣿⣗⢦⡀⠙⣆⢳⡀⠀⠀⠀⠀⢠⠟⢉⡽⠛⠉⠀⠀⠀⠀⠈⠙⢶⣄⠀⠀⠙⣆⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⢆ ⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⠛⣯⠈⠻⣿⣄⣼⣿⣿⣷⣌⡷⠽⠓⠸⣦⣧⠀⠀⠀⢀⣿⣴⢋⣀⣠⣴⠿⣽⣿⣦⣄⡀⠀⠙⢧⣄⣀⡏⠀⠀⠀⠀⠀⠀⣳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠶⠋⡧⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠉⠛⠛⠛⠉⠁⠀⠀⠀⣠⠇⡟⠀⠀⠀⢸⡏⣿⠀⠀⠻⣟⢤⣿⣟⡷⡏⣹⣷⡄⢠⣭⣩⡟⠒⠒⠒⠒⠚⠋⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠋⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⣼⠃⠀⠀⠀⠈⣷⢸⡄⠀⠀⠀⠉⠚⠫⠭⠛⠚⠉⠙⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⡿⡀⠀⠀⠀⠀⠀⠀ ⠀⢸⢻⠁⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⢤⣀⣀⣀⡤⠞⠋⢀⡼⠃⠀⠀⠀⠀⠀⢻⡀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠙⢦⡀⠀⠀⠀⠀ ⠀⠸⣿⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣱⠀⠀⠀⠀⠀⠀⠈⣧⠀⠈⠓⠦⢤⣀⣀⣠⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⡴⠋⠉⢻⠀⠀⠀⠀ ⣄⠀⢹⣦⡀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⡟⠀⠀⠀⠀⠀⠀⢰⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⢸⠀⠀⠀⠀ ⠐⠀⠀⢷⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡇⠀⢰⢳⠀⠀⠀⠀⠀⢀⡞⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡼⠀⠀⠀⠀ ⠀⠀⠀⢸⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠻⣦⣈⣳⣅⠀⠀⠀⢀⣾⠦⠤⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⠃⠀⠀⠀⠀ ⠀⠀⠀⠸⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠛⠒⠶⠒⠚⠁⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡔⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢉⡼⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣻⠀⠀⠀⠀⣀⣀⣀ ⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠭⠵⠶⠿⠿⠭⠭⣍⣙⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠏⠀⠀⠀⠀⠙⠺⢽ ⡄⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠽⣶⣤⡀⠀⢻⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠒⠒⠒⠒⠛⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⢀⣴ ⠀⠀⠙⠿⣦⣼⡆⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⢰⠇⠀⠀⠀⠀⠀⠀⣴⡵⠉ ⠀⠀⠀⠀⠈⢻⣷⠀⠀⢈⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡸⠉⠀⠀ ⠀⠀⣠⣶⡯⠖⠛⡆⠀⠀⣇⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣸⠃⠀⡼⠀⠀⠀⠀⢀⡼⠧⣄⡀⠀ ⢀⣾⡟⠁⠀⣠⠖⣷⠀⠀⠘⡆⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣰⠃⠀⢠⡿⠤⣄⣤⠖⠋⠀⠀⠀⠙⣆ ⣿⠟⠀⢀⡞⠁⠀⢸⠀⠀⠀⢹⡀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠉⠀⠀⠀⣰⠃⠀⠀⡾⣴⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘ ⠏⠀⠀⢸⠀⠀⢀⣼⠀⠀⠀⠀⢳⠀⠀⠀⠀⠈⠙⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠁⠀⠀⠀⠀⠀⡴⠃⠀⠀⣸⠁⡟⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⡴⠚⠁⢸⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⠤⣤⣤⣤⣤⣤⣤⠤⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢰⠇⢀⡇⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣟⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣠⡞⠀⣼⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣴⢿⡵⠟⠋⠉⠙⢶⣝⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⣽⠿⣦⠀⠀⠀⠀⡾⣳⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⣏⠉⠙⢷⡀ ⠀⠀⠀⠀⢀⣠⢤⢤⡀⢀⡾⠀⡼⠁⠀⣿⡇⠀⠀⢸⢧⣿⠀⠀⠀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢹⡆⠀⢸⡇ ⠀⠀⢀⡴⠋⢁⣤⠬⢿⣽⡇⠘⣧⣀⣴⠟⠀⠀⠀⣾⢸⢻⠀⠀⠀⡇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡇⠀⠀⣾⣤⣤⣼⡇ ⠀⢠⠟⠀⣴⠋⠀⢄⣼⠹⡇⠀⢸⠋⠁⠀⠀⠀⢸⣿⢸⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠚⠿⢻⠃ ⢠⡟⠀⢠⡿⠦⠶⠟⠁⠀⢿⡄⢸⣄⡀⠀⠀⠀⠈⢿⢸⣾⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣷⢳⣾⡆ ⢼⠃⢰⡏⠀⠀⠀⠀⠀⠀⠈⣿⣟⣹⡇⠀⠀⠀⠀⢹⡞⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣟⣟⣻⠁ ⣿⣛⣻⡷⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡻⡆⠀⠀⠀⠀⢻⡼⡅⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣿⢺⣿⠂ ⠉⢻⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢿⡄⠀⠀⠀⠈⢷⢻⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣿⣼⣿⡆ ⠀⠈⠻⣜⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣸⡇⠀⠀⠀⠀⢸⣇⣧⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⠀⠀⣿⠛⠛⢻⠇ ⠀⠀⠀⠈⠳⣎⡳⣄⠀⠀⠀⠀⠀⣰⢷⡟⠀⠀⠀⠀⠀⢸⢻⢸⡄⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠟⠀⠀⣿⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠈⠻⣜⣧⠀⠀⠀⣼⢯⡞⠀⠀⠀⠀⠀⠀⢸⢸⣿⡇⠀⠀⠀⠀⠀⢀⣀⣠⡤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⡎⡇⢀⡾⣣⠟⠀⠀⠀⠀⠀⠀⠀⢸⣼⣹⠁⠀⠀⣀⡴⠞⠉⠀⣷⣤⡷⡆⠈⠙⠷⣄⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣟⡾⠋⠀⠀⠀⠀⠀⠀⠀⢀⣼⣻⡟⠀⠀⣰⠏⠀⠀⠀⢀⣿⣧⣿⣗⠀⠀⠀⠈⢷⡀⠀⠀⠀⣺⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡟⣷⠟⠀⠀⠀⠀⠀⢀⣠⣤⠶⣛⣵⠏⠀⠀⣸⠏⠀⠀⢠⡾⠉⠀⠀⠀⠈⠻⣦⠀⠀⠀⢷⠀⠀⠀⢺⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⣴⠋⠀⠀⠀⣠⡶⣻⡿⠷⠞⠋⠁⢸⠀⠀⢠⡟⢀⣧⡤⡟⠁⠀⠀⠀⠀⠀⠀⠸⡇⣦⣦⣸⡇⠀⠀⢽⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⢀⣾⢹⠋⠀⠀⠀⢸⣻⡟⠁⠀⠀⠀⠀⠀⢸⠀⠀⠈⣧⠈⠋⠛⢷⡀⠀⠀⠀⠀⠀⠀⣸⡇⠋⠋⢸⠇⠀⠀⣺⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⢸⡏⡏⠀⠀⠀⠀⠘⢿⣟⣒⣲⢦⣀⠀⠀⢸⠀⠀⠀⠹⣆⠀⠀⠈⠳⣄⣀⠀⢀⣀⡴⠋⠀⠀⢀⡾⠀⠀⠀⣿⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⡝⣧⠀⢸⠀⠀⠀⠀⠙⣦⡀⠀⠀⠈⠉⣭⡍⠉⠀⠀⠀⣠⠟⠁⠀⠀⠀⢽⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠈⣧⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⡟⠀⢸⠀⠀⠀⠀⠀⠈⠛⢦⣄⣀⠀⠛⠃⠀⣀⣴⠞⠉⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠙⣏⡻⣤⣀⣀⣀⣀⣀⡴⣞⣵⠟⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠦⠤⠴⠴⠖⠛⠋⠀⠀⠀⠀⠈⠻⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠯⠤⠴⠟⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠿⠿⠟⠛⠿⠿⠶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⢾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣡⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⢧⠀⠀⢸⣧⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⣠⠀⢰⠀⠀⢰⡄⠀⠀⠀⠀⠸⣷⣤⣀⠀⠀⠀⠀⠘⢷⣄⠀⠈⢧⠀⠘⣟⠉⠙⠛⠛⠿⢿⣶⣤⣀⡀⠀ ⠀⠀⣀⣠⣤⣿⡿⠀⠀⠀⣴⡟⢀⣿⡀⠀⢸⡟⠢⣄⡀⠀⠀⠈⢷⣌⡉⠓⠲⠤⣤⣈⣿⡷⡄⢸⡇⢰⣯⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷ ⡾⠿⠛⠛⠉⢹⣧⠀⠀⣼⠏⣷⣼⠛⣷⡀⠈⢿⡀⠈⠙⠓⠶⠦⣤⣬⣛⣦⣤⠀⠀⠀⠉⠙⠻⣦⣿⣸⡛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⣿⠀⢠⡟⠀⢻⡟⠀⠈⠳⣦⡈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡈⣿⣿⣁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⣧⢸⡇⠀⠈⠃⠀⠀⠀⠈⠙⠛⠿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⣌⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣧⠙⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣧⣿⠛⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣾⣿⣶⣾⣷⣶⣦⣄⡀⠀⠀⠀⠀⢠⠀⠘⡄⠀⠀⢀⣤⣾⡿⢿⠋⠁⠀⠉⣿⠇⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠈⢟⣻⡿⣷⣦⣤⣤⣿⠀⠀⢻⣶⡶⠿⠿⢭⡵⠋⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠝⠛⠉⠀⠀⣠⣿⠀⠀⢸⠦⣤⣀⡀⠀⠀⠀⠀⠀⣼⠋⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡶⢄⠀⠀⠀⠀⠀⣠⠾⢿⣀⡀⠀⣈⡴⠏⠀⠉⠓⠦⣄⠀⠀⢻⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣇⠀⠀⠀⡼⠁⠀⠀⠈⠙⢿⠉⠀⠀⠀⠀⠀⠀⠈⢧⡀⠸⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠸⠀⠀⡸⠁⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⣾⠉⠛⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠛⣿⣄⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠞⠉⠀⠀⠀⠈⠻⣦⡀⠀⠇⢀⡴⠒⠒⠒⠶⢶⣶⠛⣉⣤⣀⡬⢷⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⡸⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠰⣄⠀⣀⡤⠴⠶⠤⢤⣠⠤⠞⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⣀⣤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⣀⣀⣀⡀⠘⠿⢶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣴⡾⠟⠉⠀⢀⣠⡴⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⢶⣤⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⡀⠀⠀⠀⠀⠀⣠⡞⢹⣶⠐⠶⡦⢶⠲⣦⠄⢲⢆⢀⡤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⣀⣠⠴⠋⠀⠈⠉⠐⠛⠓⠛⠚⠛⠿⠚⠚⠓⠓⠛⠂⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢹⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⢳⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡠⠐⣒⣲⣆⣖⠢⢤⡀⠀⠀⠀⠀⠀⠀⣀⡤⢖⣒⣢⠤⡀⠀⠀⠀ ⠀⣠⢋⠔⠁⠀⠱⠄⠀⠉⠛⢬⠷⣄⠀⣠⠔⡽⠚⠉⠀⢀⡀⠈⡙⢢⡀⠀ ⢠⢅⠂⢀⠔⠉⠀⠀⠉⠐⠠⣀⣝⡿⢟⠔⠉⢀⠤⠒⠉⠀⠀⠈⠲⠀⢱⠀ ⢸⠌⠆⠈⠀⠀⠀⠀⠀⠀⠀⣨⣿⠗⠁⢀⣶⣅⡀⠀⠀⠀⠀⠀⠀⡇⠀⡇ ⠈⣶⠀⠘⣤⢀⣀⣀⢠⣴⡿⠞⠁⢀⠴⢽⡎⠓⢌⠓⠤⢄⣀⠠⡚⠀⢠⠁ ⠀⠈⠧⡀⠈⠁⠛⠛⠈⠁⢀⡠⠔⠁⠀⠀⠑⠢⣀⠈⠁⠒⠓⠈⠀⡠⠃⠀ ⠀⠀⠀⠀⠉⠐⠒⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠒⠂⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⠁⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠳⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠘⡄⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣦⣤⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⡠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢠⢗⣿⠟⠙⠋⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⢀⣀⣹⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠈⣿⣿⠠⣒⣶⡆⠘⡿⢻⣿⠟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢸⣟⡀⠉⠋⠀⠀⠀⠀⠀⢀⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢸⢹⣧⠀⠀⠀⠪⣛⡀⠀⠸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣸⣼⢿⣧⡀⠈⠩⠖⠃⠀⣠⣾⣿⣿⣿⣿⣿⢱⣟⡉⠀⠈⢹⣿ ⠀⠀⠐⢕⣄⢹⣿⣿⣦⠀⠀⠠⠞⠻⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠺⠿⠿⣿⣿⣿⡆⠀⠀⠀⠀⠉⣻⠟⣽⠟⠻⠿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢀⠤⠂⠉⢀⠹⣿⣤⣆⠀⠠⣚⡡⢺⠋⠀⠀⠀⠀⠈⣐⠶⣶⣶ ⠀⠀⢀⠃⠀⠀⠀⢺⠰⣹⡀⢁⠉⠁⠓⠑⠁⠀⠀⠀⡰⠁⡜⡡⠂⠈⢿ ⠀⠀⡎⠀⠀⠈⡄⡿⠀⠙⡇⡎⠀⠀⠀⠂⠀⠀⠀⠀⠃⡘⠰⠳⡄⠀⠈ ⠀⠰⠀⢀⠀⠑⢠⡇⠀⠀⡿⠀⠀⠀⠀⠀⠀⡄⠀⢸⢡⠈⡆⡀⢷⡀⠀ ⢠⠃⠀⢈⠀⢀⡞⠀⠀⢰⡅⠀⠀⠀⠀⠀⠀⠀⠘⣸⢸⣾⠀⠑⠀⢧⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣲⣵⣾⣿⣊⣴ ⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣕⣷⡿⠟⠋⠀ ⠀⠀⠀⠀⢠⠌⠂⠀⠀⠀⠑⠠⣀⠀⠀⠂⠀⣀⠀⠀⠀⠀⠀⢹⠛⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⡾⠐⡇⠟⡝⠋⠉⠛⠳⠀⠀⢀⠀⢃⠀⠀⠀⠀⠘⡅⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢰⡀⡇⠀⠁⠀⠀⡆⠀⠀⠘⠀⠆⠘⠀⠀⣐⢀⢙⢄⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⣡⣃⡇⢲⣆⠀⠰⠄⠀⠀⣀⡧⡂⠈⠒⡖⣟⢺⣿⡄⠉⠺⣯⠒⢤ ⠚⠥⢆⢴⠪⡑⡌⢻⡙⠽⢻⣶⠘⢶⠫⠶⣷⠖⠀⢀⣿⣿⡝⠙⣷⠀⠀⡟⣱⣄ ⠀⠀⠀⠙⡵⣰⢰⢈⣱⡀⠀⢹⠀⠀⠀⠀⢰⠀⠀⠀⡿⣿⡇⢱⣿⠀⠀⢣⡿⠟ ⡻⡇⡏⡆⢱⣽⢼⡫⢼⠳⡀⠀⠁⠀⠀⣀⠀⠀⡠⠞⡰⠿⠃⠀⣿⡄⠀⢸⠃⠀ ⢸⣇⠑⠃⣎⠟⠁⢀⠃⠀⣷⣄⠈⡝⠓⢀⠤⠊⢀⠜⡆⠀⠀⠀⣿⡇⠀⠈⡆⠀ ⠮⢠⢳⢞⠕⢄⣀⠎⠀⣸⣿⣿⣿⠉⣯⡁⣀⠤⠊⡴⠀⠀⢻⡀⣿⣿⠀⠀⢱⠠ ⠷⡽⢁⡷⠋⣠⠋⠀⢰⠃⣿⣿⡧⠄⣱⡁⠀⢀⣾⠣⠤⠤⠘⠓⣿⣿⡆⠀⠈⢆ ⣰⡴⠊⣠⠞⠁⢀⣴⢹⠀⣿⣿⣷⠀⠀⠈⡄⠁⠀⠀⠀⠀⠀⣰⣿⣿⣿⡄⠀⠈ ⠟⣠⠞⠁⠀⣠⠟⠉⢸⠀⣿⣿⣿⢠⠀⠀⡇⠀⠀⠀⢀⡠⠋⣼⣿⣿⣿⠛⢄⠀ ⠊⢀⣀⡤⠊⢣⢰⠀⠈⠀⣿⣿⣿⠈⢆⠀⢣⡀⠀⢀⠌⠀⣠⣿⣿⣿⡏⠀⠁⠳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣳⠦⢖⣒⢲⣲⡦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⢻⣦⡲⠤⡀⠹⡋⢷⡇⣿⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢼⢠⣿⡟⠃⢀⣠⡄⠱⠀⣿⣿⠛⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⣿⣿⣛⡀⠚⠟⠛⠁⠀⠀⠙⠈⣧⣰⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⡟⠏⠀⠀⠀⠀⠀⠀⡀⠀⣸⡟⢃⠼⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⡿⢆⣀⢠⡶⠀⠀⠀⣠⠆⠐⠁⠀⠃⢀⣼⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠳⡾⡾⠛⠀⠀⠀⡎⠁⠀⠀⠀⡀⠀⠈⠁⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢣⡀⠀⣠⠖⠁⠀⠀⠀⠀⢠⡟⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⠣⠊⠁⠀⠀⠀⠀⠀⢠⠟⠇⢀⣿⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠃⠀⠀⠀⢼⡏⠘⢇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣇⡀⠀⠀⠀⠀⠀⢀⠤⠒⠁⠀⢀⡄⠀⠀⠀⢰⠊⠀⠀⣾⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡿⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡾⠂⠀⠀⠘⠉⠀⠀⣴⢻⢷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⠬⠑⠤⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⠀⠀⠐⠃⢘⣿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⡘⠁⡀⠀⠀⠀⢠⡟⠀⠀⠀⠟⣈⣻⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇⠀⠀⣸⡁⠀⠀⠀⢷⣸⠀⠀⠀⠀⣯⠀⣄⣫⣤⣺⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⣀⠤⠚⣹⡂⠀⢰⣿⣿⣦⠤⠤⠾⡟⠀⠀⠀⣼⣿⣧⣿⣿⣿⣿⣿⠟⠁⠀ ⢀⣠⠒⠋⠉⢁⣠⠴⣻⠁⢠⣼⠛⠁⠀⠀⠀⠀⣷⠀⠀⢠⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀ ⠈⠛⠛⠒⠉⠉⣀⢤⠃⢀⣿⠷⠴⠤⣄⣀⡀⠀⡿⠀⢀⣾⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⣠⠤⠒⠉⡠⠃⠀⢨⠏⠀⠀⠀⠀⠀⠉⠉⡇⠀⢸⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠧⣶⠟⢠⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠿⢴⡷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡄⢀⡀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣇⣸⡥⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀ ⢰⣿⠋⠹⣷⣤⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡀⢉⢿⣄⠀⠀ ⠸⣷⣤⠏⠀⣸⣿⣤⣴⠟⠛⢻⣷⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣿⣎⠁⡈⠿⣇⠀ ⠀⠙⣿⡄⡟⠁⡀⢘⡯⢀⢆⣿⠟⠀⠀⠀⠀⠀⣠⣼⣿⠿⠟⠿⢿⣿⡖⣦⣄⠀⠀⠀⠀⣿⡟⠁⠙⣿⣿⢧⠃⠶⣎⣿⡀ ⠀⠀⢹⡞⡄⢣⠟⠋⢁⢢⣿⠃⠀⠀⠀⣀⣴⠟⣛⣫⣥⣤⣠⡤⣶⣤⣅⣈⠹⢻⣦⡀⠀⠈⢿⡆⠡⣿⠏⠸⣤⣀⠰⣿⡇ ⠀⠀⠈⢿⣆⢉⠂⢬⣄⢒⣿⠀⠀⢀⣼⠏⡽⠞⢩⢑⢢⣄⣡⣐⣄⢢⢉⠛⢆⠣⣜⢻⣦⠀⢼⡧⢡⡆⠤⠽⢋⠉⣴⡿⠀ ⠀⠀⠀⠘⣷⣌⠰⠀⢙⣾⠟⠀⢀⣾⠋⡔⡱⠊⣴⣾⣿⣿⣿⣿⣿⣿⣶⡌⠢⡁⢆⠡⢻⣇⠻⣧⣃⠠⢀⠣⣌⣽⠟⠁⠀ ⠀⠀⠀⠀⠀⠻⠷⣭⡾⠿⠀⠀⣼⠇⡘⡖⢡⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠱⢈⠆⠡⣿⡄⠈⠻⢶⣧⠿⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠭⡐⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠡⢊⠅⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⢣⣘⣿⣿⣿⣿⡿⠟⠛⠻⠿⣿⣿⣿⣿⣿⣀⠃⠆⣼⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠂⣾⣿⣿⣿⠋⡐⡈⠄⡡⠐⡈⢻⣿⣿⣿⣧⠌⣣⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡌⢿⣿⠟⣁⠂⡅⠘⢄⠡⡁⠆⢡⠚⢿⣿⣿⢈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣈⡝⢒⡌⠱⣈⠱⡈⣴⠈⡜⢡⠘⡤⣭⣂⢭⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢷⣬⣑⣢⡑⠴⣀⡓⣌⣆⣳⣶⠟⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠍⠉⠉⠉⢻⣷⠀⠀⠀⠀⣀⡀⢀⡀⠀⠀⠀⡀⠀⠀⣿⠇⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⣀⣀⣀⣼⠿⠀⠈⣿⡾⠿⢷⢸⡇⠀⠀⠀⣿⠀⠀⣿⡾⡟⠛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠙⠻⣷⡤⡄⣿⠁⠀⢸⢸⡇⠀⠀⠀⣿⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⢠⣿⠇⠋⣿⠀⠀⠈⢸⣇⠀⠀⣶⣿⡀⠀⣿⡇⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠻⠛⠛⠉⠀⠀⠿⠀⠀⠀⠘⠿⠿⠿⠋⠿⠃⠀⠿⠇⠀⠀⠸⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⢹⣦⡀⠀⣀⡤⠖⠚⠉⠉⠉⠉⠒⠶⢤⡀⢀⡴⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⢆⣁⣽⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⡟⠦⣈⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡎⠊⢽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⣀⡤⢶⣒⠒⢦⣄⣴⠞⣛⣛⡲⢤⡀⠸⡆⠀⠛⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⢸⡇⠐⣿⣿⡇⢀⡟⢧⠀⢿⣿⣿⠀⣸⠀⠁⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠙⢦⣌⣉⣤⡾⠧⠾⣷⣤⣉⣡⠔⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡞⠄⠀⠀⠀⠀⠀⠀⠀⡄⢠⣾⣟⣉⣠⠤⢤⣼⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠟⠛⠛⢿⣶⡾⠟⠿⠟⠃⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀ ⠀⠀⢰⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀ ⠀⠀⡾⠀⢸⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣿⡆⠀⠀⠀ ⠀⠀⡇⠀⣿⡇⠀⠢⡀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⣸⠈⣇⠀⠀⠀ ⠀⣰⠃⢰⡏⢧⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⢠⣟⠀⣿⠀⠀⠀ ⠀⣿⠀⡼⠁⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⣰⠟⢸⠀⢿⠀⠀⠀ ⠀⣿⢤⡇⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠀⣀⡼⠁⠀⢸⠀⢸⠀⠀⠀ ⠀⣿⠀⡇⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⣼⠀⢸⠀⠀⠀ ⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⢸⠙⠛⢶⢤⣄⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣠⣤⣤⠶⢿⠁⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀ ⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⡾⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠉⠉⠉⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⡇⢸⠀⠀⠀ ⠀⢹⠀⡇⠀⠀⠀⠀⠀⠀⢸⠃⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⢸⡄⠀⠀ ⠀⣿⡄⠱⡄⠀⠀⠀⠀⠀⢸⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢸⠀⠀⠀⠀⠀⠀⣸⠃⠀⢻⡀⠀ ⢳⢿⡁⢀⡸⡄⠀⠀⠀⠀⠀⡇⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢓⡟⠀⠀⠀⠀⠀⢰⡏⢀⠀⠀⣷⠀ ⣿⣾⠣⡼⣷⣽⡄⠀⠀⠀⠀⡇⡀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸⡇⠀⠀⠀⠀⠀⢸⣇⣿⡆⣰⣿⠆ ⣿⡟⡇⣇⠘⢯⣱⠀⠀⠀⠀⢹⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⢹⣷⣣⣿⡇⠀ ⠩⢿⡻⣜⠲⣶⠎⠀⠀⠀⠀⢸⡧⠞⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⡇⠀⠀⠀⠀⠀⣴⣼⣫⣿⠟⠀⠀ ⠀⠀⠈⠛⠛⠫⢗⣤⣤⣤⠤⠚⠁⠀⠘⡆⠀⠀⠀⠀⠺⠀⠀⠘⠉⠀⠀⢀⡞⠈⠘⢧⣀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⢻⢸⡿⢯⢰⣶⡶⣌⣁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠂⣀⣀⡬⢛⣻⡏⡷⢤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣳⢿⠾⣤⣞⡼⢿⡇⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣸⢉⡿⣄⣿⡀⣷⣵⡾⠇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠞⠛⠲⣦⣤⠤⠤⢴⠏⣦⣈⣷⣚⠉⠻⡄⠀⠀ ⠀⠀⠀⣿⣀⠀⠈⠁⠀⠀⠀⢾⡀⢻⡿⠉⠉⣷⡞⠻⣦⠀ ⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⣤⣴⠿⠿⣠⡟⠀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡶⢻⡄⠀ ⠠⠤⡧⠤⠄⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠋⢹⡏⠁ ⠀⢀⣿⡤⠄⠘⠿⠁⠀⠠⣞⣻⠄⠀⠀⠻⠏⢀⡈⣽⠛⠃ ⠀⠀⢈⡷⣶⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠛⠂⠀ ⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠒⠒⠒⠚⠛⠛⠉⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⡤⠜⢳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⢹⡤⠒⠊⠉⢀⡠⠄⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠘⢿⡀⠀⠀⠀⠀⢣⠠⠐⠊⠘⡄⠀⡀⠈⡇⠀⠀⠀⠀⠀ ⠀⠀⢰⠁⠀⠀⢀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣄⠀⠀⠱⡀⢳⠀⠀⠀⠀⠸⡀⠀⢠⠀⠇⠀⣇⠀⢹⠀⠀⠀⠀⠀ ⣤⣶⡏⠀⠀⠀⠇⠀⠸⡀⠀⠀⠀⠈⠉⠉⠉⠉⣟⠉⠉⠙⡍⠁⠀⣿⣦⠀⠀⠹⡄⢱⡀⠀⠀⠀⢧⠀⠀⢳⣼⠀⣿⠀⢸⡄⠀⠀⠀⠀ ⢿⠁⠃⠀⠀⣾⠀⠀⠀⢇⠀⠀⠀⣆⠀⢣⠀⠀⢹⣆⠀⠀⢡⠀⠀⣿⣿⣧⡀⠀⢹⡄⢳⠀⠀⠀⢸⣧⡀⠀⢿⢸⡏⠀⢸⡇⠀⠀⠀⠀ ⣿⢰⠀⠀⢸⣿⠀⠀⢰⣿⡀⠀⠀⢻⡄⠈⣆⠀⠘⣿⣷⡀⠀⢧⠀⠸⣿⢻⣷⡀⠀⢿⡀⢣⠀⠀⢸⣿⣽⣦⣾⣿⣅⡀⢸⡇⠀⠀⠀⠀ ⣿⠈⡀⠀⠘⣿⠀⠀⠘⣿⣧⠀⠀⠘⣿⣄⠘⣧⠀⠹⣿⢿⣦⣈⣦⣠⣿⣿⣿⣷⣄⣸⣧⡸⠆⠀⢸⣍⢻⡅⢸⣿⣿⣯⣻⡷⢦⣤⣀⠀ ⣿⠀⡇⠀⠀⣿⡀⠀⠀⣿⣿⣧⡀⠀⢹⣿⢦⡘⣷⣄⣻⣷⣿⡿⠛⠛⠻⡿⢿⡿⣿⠀⠀⠀⠀⠀⢸⢿⡆⡏⠻⣿⡝⣿⣿⣿⣶⣿⡏⠀ ⣿⠀⢱⡀⠀⠸⣇⠀⢀⣸⣿⣯⣷⣤⣤⠿⠛⣛⣫⠽⠿⠛⠉⣦⡴⠖⣾⠧⠞⠁⢸⠀⠀⠀⠀⠀⢸⣾⢃⡷⢤⣼⣿⣿⣿⣿⡿⠋⠀⠀ ⣿⠀⠀⠉⠉⢻⠙⣿⣿⡿⠛⢻⣿⣿⡿⠉⠉⠁⠀⠀⠀⠒⠦⠌⠉⠋⠁⠀⠀⠀⣸⠀⠀⢰⠂⠀⣼⣏⣼⣿⡶⣤⣿⣿⡂⣿⣿⣄⠀⠀ ⣿⠀⠀⠀⠀⠈⡇⢹⠿⡌⠢⠌⠻⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡎⠀⢀⣿⠎⠉⢻⣀⠈⠳⣿⣧⠈⣿⢿⣷⡀ ⣿⠀⠀⠀⠀⠀⢣⠘⡇⠹⡄⠀⠀⠀⠀⠠⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡸⠁⠀⡸⠁⠀⠀⢸⡉⠓⢦⣹⣿⣧⡏⠈⠻⣿ ⣿⠀⠀⠀⠀⠀⢸⠀⣷⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣰⠃⠀⢠⠃⢠⠀⠀⠈⠳⢤⡀⠈⠉⣿⣧⡀⠀⠻ ⣿⠀⠀⠀⠀⠀⢸⡄⢸⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⣰⠃⠀⢀⡎⠀⢸⠀⠀⠀⠀⡸⠉⠳⣄⣾⣿⣿⡄⠀ ⣿⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⣿⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣏⣼⠏⠀⠀⣼⡇⠀⢸⡀⠀⠀⠀⣷⣄⡐⠙⣧⡟⠀⣿⠀ ⣿⠀⠀⠀⠀⠀⢸⡇⢸⠃⠀⠀⠀⣿⡆⠈⣝⠢⣄⡀⠀⠀⢀⣠⠴⠋⣠⣼⣿⠋⠀⢀⣾⣿⠃⠀⠀⡇⠀⠀⠀⠙⢿⡛⠲⣿⠅⢸⠻⣦ ⣿⠀⠀⠀⠀⠀⢸⡇⢸⣆⠀⠀⠀⣿⢷⡀⢻⡀⠈⠙⠲⠒⠋⢥⣾⣿⣿⡿⠁⠀⢠⣾⣿⣿⠀⠀⠀⣷⠀⠀⠀⠀⠀⡽⠳⣄⠀⠀⡷⣜ ⣿⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⣿⠈⣧⠀⢳⡄⠀⠀⢀⣴⣿⣿⣿⠏⠀⢀⣴⣿⣿⣿⣿⡇⠀⠀⢻⡄⠀⠀⠀⠀⣧⡀⠈⢳⣼⠁⢈ ⣿⠀⠀⠀⠀⠀⢸⠀⣸⡇⠀⠀⠀⡟⠀⠘⣧⠀⠙⢦⣶⣿⣿⣿⠟⠁⢀⣴⣿⣿⣿⣿⣿⣿⡇⡇⠀⠸⣧⠀⠀⠀⠀⠻⣿⣶⣤⠿⠀⡘ ⣿⠀⠀⠀⠀⠀⣼⠀⣿⠇⠀⠀⢸⡇⠀⠀⢸⣷⣤⣿⣿⣿⡟⢁⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⠀⠀⢿⡄⠀⠀⠀⠀⠀⡿⣧⣀⠠⢷ ⣿⠀⠀⠀⠀⠀⡇⢠⣿⠀⠀⠀⣼⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⣷⠀⠀⠀⠀⢸⠀⠘⢯⣀⠀ ⣿⠀⠀⠀⠀⢀⡇⣸⡟⠀⠀⢠⡏⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢹⣧⠀⠀⠀⢸⣷⣄⠀⢻⡇ ⣿⠀⠀⠀⠀⢸⠁⣿⡇⠀⠀⣾⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠈⢿⣧⠀⠀⠀⠙⢿⡛⠾⠷ ⣿⠀⠀⠀⠀⣸⢸⣿⠁⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠘⣿⣧⠀⠀⠀⠀⠻⣧⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⠶⠶⠶⠶⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡟⠭⣉⢉⣹⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡷⠀⠀⠀⠘⡆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠯⠽⢿⠀⠀⠀⠀⠀⠀ ⠀⠠⢾⠥⠄⠀⠀⠨⡵⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢀⣸⠀⣀⣘⣢⡄⠀⠀⠀⠀ ⢀⣀⠸⣆⠀⠀⠀⠀⡇⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠈⢹⠉⠀⠀⣹⠀⠀⢀⣀⠀ ⣯⡼⡄⢧⢩⣶⠶⠭⠇⢀⣿⡿⠶⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠦⠴⠴⠾⣟⣆⢸⣗⣶⣾⣹⣀⣠⡾⠛⠹ ⠀⢧⢱⣠⠒⠳⣷⠤⣠⡮⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢻⠉⠀⠻⠿⠉⠀⠀⠀ ⠀⠈⠖⠋⡅⠀⠈⠗⠚⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣤⡠⠤⡀⠀⠀ ⠀⠀⠀⢀⡷⠤⣶⡿⠯⢆⢣⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⣀⠬⠗⠲⣄⠱⣤⣤ ⠀⠀⠀⣎⣠⠚⠁⠀⠀⠘⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡙⡄⠀⠀⠀⠈⠢⠝⠙ ⠀⠀⠀⣨⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡯⠜⠂⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠇⠈⣿⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⠀⠀⠀⠀⠀⠈⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠿⣦⣤⡶⠟⠻⠶⢦⣤⣤⣤⣤⡶⠟⠋⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣀⡴⠟⠛⠛⠻⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢦⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣤⡾⠋⠉⠉⠙⠀⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⠈⠉⠉⠻⣆⠀⠀⠀⠀ ⢀⣀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⠀⠿⣦⠶⢾⣷ ⢿⣟⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠀⠀⠻⣧⠀⠀⢠⣤⣤⡶⠟⠁ ⠀⠙⠻⠶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡴⠿⣷⡀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣧⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡰⠊⠁⠀⠀⠀⠀⠀⠉⠁⠂⠤⢀⠘⣇⠀⠈⣿⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⠻⣷⣄⣀⣠⡄⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⡸⠁⠀⠀⢠⣶⣶⣶⣦⣄⡀⠀⠀⠀⠉⢽⣿⠛⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠻⠷⣦⣤⣴⡟⠋⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⣿⣿⣿⠋⠉⠛⠻⠶⠶⢶⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠈⠙⠻⢷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠄⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠻⠶⠶⠶⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣄⣀⣠⣤⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣷⣶⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣀⣴⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠹⠁ ⠀⠀⠀⡀⡀⠀⠀⢀⡇⠀⢀⣴⡿⣣⣾⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⣷⠀⠀⠐⡇⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠛⠿⣿⣶⣤⡀⠀⠀⠀ ⠀⠀⢸⡇⠙⠀⠀⢰⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⢻⡙⣷⡄⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠙⡇⣿⠀⠀ ⠀⠀⢸⡇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢳⣿⣀⡠ ⠀⠀⢸⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡏⢷⣀⠊⣿⠉⠁ ⠀⠀⢸⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⣿⣿⣿⣿⣿⣿⠁⢻⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⠀⠙⠀⠀ ⠀⠀⢸⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢸⣿⣿⣿⣿⣿⡟⠀⠈⣿⣿⣿⣿⣿⣿⣿⣄⣾⣿⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⢹⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⢉⣓⣒⣿⢿⣿⣿⣿⣿⠃⣀⠠⢼⣿⣿⣿⣿⡏⠀⢿⣿⠁⠀⠀⠀⠀ ⠀⠀⢸⡇⣠⣼⣧⢿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡿⡟⣛⠉⠛⢖⣹⠃⣾⣿⣿⢻⢯⠞⠀⠀⠘⣿⣿⣿⣿⡇⠀⠈⣿⡟⠆⠀⠀⠀ ⢀⠀⠛⣓⣿⣿⣟⣚⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠉⠉⠓⠤⠾⠤⠄⠀⠁⢸⣿⡿⠃⠊⠀⠦⣤⣤⣤⣿⣿⣿⣿⠀⠀⢀⣿⣷⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠉⠉⠿⠻⣿⣿⣿⡄⠹⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠘⢹⣿⣿⣿⣀⣠⣾⣿⣿⣿⣿⣿⣿ ⣀⣀⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣶⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣸⣿⢁⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠒⠢⠤⠤⠒⠤⠠⠔⢺⣿⣿⣿⣿⣿⡿⣿⣟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣿⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣶⣶⣤⣤⣤⣴⣶⣤⣰⣾⣿⣿⣿⡿⠛⠛⠙⣿⣷⣄⠀⠀⠀⠀⠀⠠⠔⠒⠊⠉⠁⠀⠀⢀⣼⡃⠀⣿⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠈⢻⣍⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣟⡛⠲⠶⠒⠚⢻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠙⢶⣄⠈⠛⠲⣤⣀⡀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠳⢤⣀⣨⡟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠐⣄⠀⠀⠀⠉⡟⠀⠀⠀⢹⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⣤⣈⣳⡄⠀⠀⠁⠀⠀⠀⣸⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⡙⠦⣉⠓⠄⠀⠀⠀⣰⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⣿⠿⠃⠀⠀⠀⣾⣾⠟⣽⡝⢿⡟⣿⣟⢻⣅⠟⠀⠀⠀⠛⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡴⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⢀⣰⡏⢸⣿⣷⠈⢰⣿⣿⡀⣿⡅⠀⠀⠀⠀⠸⣿⣿⠙⠒⠶⠤⠤⠤⠴⢂⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⠀⠀⣰⣿⡿⣿⠀⠀⠀⠀⠀⠀⣹⠁⣿⣀⣿⡄⢸⣿⣿⡇⢸⡧⠄⠀⠀⠀⠀⣿⡿⣷⣶⠦⠤⣤⠤⠾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⢿⣷⠞⠁⣿⣤⣿⡄⠀⠀⠀⠀⠀⢿⣤⣿⣿⣿⣷⣾⣿⣻⣧⣼⡇⢀⡀⠀⠀⠀⢿⣿⣿⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⡄⠀⢀⣼⣧⣿⣯⡀⠀⣀⣤⣴⣶⡾⠿⠟⠛⠛⠛⠛⠻⠿⠿⣿⣷⣶⣤⣤⣀⠀⣼⣿⢿⡇⣄⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⢳⣾⣿⡟⣻⣿⣶⠿⠟⠛⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠒⠉⠙⠛⢿⣿⣿⣿⣼⡇⠈⣷⡜⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⢿⡏⢹⣿⣿⠟⠀⠀⠀⠀⢀⣀⣤⣄⣠⣶⣶⣶⣶⣶⣤⣤⣤⣄⣀⣀⠀⠈⢸⣿⣿⣿⣷⠀⢸⣿⣼⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⢏⣿⠁⢸⣿⣿⣶⣶⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣾⣿⣿⣿⣿⣇⠀⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⢿⠀⢸⣿⣯⣛⣿⣿⣿⣿⣿⡿⢿⣿⡏⠉⠉⠹⡏⢻⡿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⡀⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣏⠸⡆⢸⣧⠘⢋⣿⣿⣿⣿⣿⣶⣾⣿⣿⣦⣤⠀⢿⣿⣳⣿⣶⣶⣾⣿⡿⣿⣿⣟⣿⣿⡇⢹⣇⣿⡿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⠷⣿⣸⣿⣿⣿⣿⠁⡟⢼⣿⣿⡟⠋⠙⢿⣿⣷⣬⣯⡉⠻⣻⣿⠛⠾⣿⠏⠙⢿⠿⣿⣧⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣽⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠀⠀⠀⠀⣸⠏⠀⢠⡟⠀⣿⡟⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣏⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⡀⠀⢀⡶⠁⠀⣠⡟⠀⢀⣿⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡙⠛⢻⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢿⣶⣶⣿⣿⡇⠀⢸⣿⡘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣷⣶⣿⣿⣿⣿⣿⣿⡛⠃⠀⠈⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣇⢀⣿⣏⢳⡸⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠳⢄⡀⠀⠀⠀⢀⠴⠋⣿⣿⣿⣿⣿⡟⣝⣾⣿⣿⣿⣷⣽⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⡀⠀⠙⠒⠒⠚⠁⠀⣠⠟⣿⣿⣿⠟⢱⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠛⢦⡀⠀⠀⠀⣠⡞⢁⢀⣿⠿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣦⡀⠀⠀⠀ ⢀⣾⣿⡿⣟⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣠⣾⣿⣆⢀⣾⣿⣦⣼⣿⣁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣆⠀⠀ ⢟⣬⠿⢦⣍⡙⢸⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡏⣰⣿⣿⣿⣿⣻⠟⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣋⣥⠼⠭⣝⢷⡀ ⠋⠀⠀⣀⣬⣽⣮⡉⠷⣦⣹⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣹⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⢵⡶⠍⣩⣾⣯⣄⣀⠀⠈⠻⠗ ⠀⠔⢻⣿⣿⣿⣿⣿⣆⠋⣾⡿⠟⢛⣿⠈⢹⣿⣿⣿⡿⢻⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⡿⠿⣿⣎⢡⣾⣿⣿⣿⣿⣿⣶⣦⡀⠀ ⠺⣿⣇⣛⣿⣿⣿⣿⠟⣃⣥⣶⣿⣿⣿⡀⢸⡿⠛⢻⣿⣾⣿⡷⢰⣿⣿⡆⠀⢿⣿⣿⠀⣸⣿⡿⢿⣿⡛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⡄⠀⢾⣷⠿⣋⣭⣶⣿⣿⣿⣿⣿⣿⣿⠿⢼⣇⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡀⢸⢻⡷⠼⢿⠉⢿⡆⣹⣿⠉⢿⣮⣝⡻⢿⣿⣿⣿⣿⣿ ⢀⣶⣾⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣴⡾⠂⢸⣿⣿⣿⠟⣿⣿⣿⣿⣧⢸⠸⠿⣧⣼⣷⣶⡾⢿⡿⢷⣾⣿⣿⡿⠂⢹⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⣠⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢿⠃⠀⠀⠀ ⠀⠀⢠⠇⡜⠚⢝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣺⠟⢳⠘⡆⠀⠀⠀ ⠀⠀⢸⠀⡇⠀⠈⠳⡙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⡜⠁⠀⢸⡆⡇⠀⠀⠀ ⠀⠀⢸⠀⡇⠀⠀⠀⢱⡀⠳⡀⠀⣀⣀⡤⢤⣀⣀⡀⠀⡞⢀⡞⠀⠀⠀⢸⠃⡗⠀⠀⠀ ⠀⠀⠘⡄⢣⠀⠀⠀⠀⢁⡴⠋⢉⣤⠀⢠⠀⠀⠀⠉⠉⢷⡀⠀⠀⠀⠀⡜⢀⠇⠀⠀⠀ ⠀⠀⠀⢳⡈⠓⠀⠐⣶⠟⠒⠊⣩⣧⠔⡏⢠⣆⢸⠳⢄⣸⠛⠷⠆⠀⠘⠁⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⣳⠀⠀⠀⠈⢠⣶⣿⡏⠀⢰⡷⠃⢸⡌⢠⣾⣾⡇⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⣿⠀⠀⠀⠀⢸⣿⣿⡗⠀⠈⠁⠀⠘⠁⢸⣿⣿⡏⠀⠀⠀⠀⢸⠀⠀⢀⠀⠀ ⠀⠙⡷⠤⠉⠀⠀⠀⠀⠀⢿⡿⠃⠀⠀⠀⠀⠀⠀⠈⢿⡿⠁⠀⠀⠀⠀⠈⠡⢴⠏⠀⠀ ⢳⣤⡘⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⣠⡶⠂ ⠀⠈⠓⠲⢄⠀⠀⠀⠀⠀⠀⠀⠩⡀⠘⢿⡿⠃⢀⡝⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠁⠀⠀ ⠀⠀⠀⠀⠈⠓⠤⣀⢀⠀⠀⠀⠀⠱⣄⣸⢇⣠⠞⠀⠀⠀⠀⣀⣀⠤⠚⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠤⢠⡦⠤⠤⠤⠤⠤⡤⠤⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⣤⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢶⡟⠒⠒⠈⠉⠉⠁⠚⠁⠀⢼⠘⢦⡀⠀⠀⠓⠀⠉⠉⠁⠐⠒⢢⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠺⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀ ⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣸⠀⢻⣧⠇⣆⡞⣏⢠⣿⠁⠀⣼⣥⣾⡿⠁⠀⣠⣾⢻⠁⠀⢀⣠⣤⠤⠔⣾⣿⢁⣾⣤⡶⠚⣡⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣄⣿⣆⣼⠛⣆⣿⠀⢻⡏⢣⠀⣴⡟⣸⡿⠃⢠⢊⣟⡬⢊⣠⡾⠋⡡⠀⣠⢊⣼⡽⠟⠋⠁⣀⣼⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠁⣿⣿⣿⣿⠀⢹⠗⠀⠈⢳⣿⣾⡹⠀⡏⢇⢠⣷⠟⠉⣰⡟⠋⡠⠊⠀⣰⣡⣿⡟⣀⣠⠔⣩⡿⠛⣈⣭⠿⠀⠀ ⠀⠀⠀⠀⢀⣀⠀⢸⣦⣧⢹⠹⣿⡆⣾⣶⣠⣄⡸⠀⡇⠁⠀⣇⡼⠛⠁⣀⡔⡹⢀⣞⣒⡼⠟⢉⢼⣿⠛⠉⢀⣴⠟⠀⡩⠞⠁⠀⠀⢀ ⠀⠀⠀⠀⣘⢻⡯⣻⡏⠫⠙⠂⣽⠿⠆⠉⠛⢻⣧⣄⠰⡀⠀⠸⣠⡴⠊⣽⡠⠗⡩⠛⠁⢀⡴⣣⡿⠃⠀⣠⣾⠃⠀⠀⣉⠩⠭⠓⠀⣀ ⠀⠀⠀⠀⣿⣤⣧⣘⡽⣄⣧⣶⡇⠀⠀⠀⠀⠀⢉⣿⠗⢋⣦⠜⢛⢀⡼⠋⢠⣮⣤⠶⠚⠋⣡⣿⣶⠴⠖⢋⣡⢧⣤⣶⠦⠦⠀⠔⠚⠋ ⠀⠀⠀⠀⢹⣹⢻⣎⠳⢤⡻⠃⠀⠀⠀⠀⠀⢀⡟⢡⠞⠉⠻⣦⣿⣟⣥⣶⣫⣤⠤⠀⢰⡯⠚⠀⢀⡠⢔⡽⠁⠉⠀⢀⠔⢂⡴⠚⡲⠋ ⠀⠀⠠⣤⣤⣽⡿⢏⣣⣻⡇⠀⠀⠀⠀⠀⠀⢸⣰⠁⠀⠀⠀⠀⠈⠈⠁⠉⠉⠹⠛⠻⠷⣤⣴⣒⡁⠐⠉⢀⣀⣂⣔⣁⠀⡠⠤⠀⠀⣀ ⠀⠀⠀⠀⠙⣍⣇⣀⣾⠏⠁⠀⠀⠀⠀⠀⠀⢸⡏⠀⠸⣯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣤⡖⠉⠁⢀⣠⣤⠿⢃⡠⢤⠶⠖ ⠀⠀⠀⢀⣾⡭⠙⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣋⡀⠤⣀⡛⠉⣀⣊⣄⠊⠁⠀⠀ ⠀⠀⠀⠘⠉⣽⣿⠃⠀⣤⣠⣄⡀⠀⠀⠀⠀⠀⠸⣲⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣥⡄⠈⠉⣉⣥⡴⠛⠨⠝⠓⠲⡶ ⠀⠀⠀⠀⡾⣿⡏⠀⠀⣿⡉⢻⣿⣶⣄⢰⡄⠀⢴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣭⣥⢍⣉⠝⠃⠡⠤⠀⢂⡺⠛⠉⠀ ⠀⠀⠀⢠⣧⣿⡇⠀⠀⠸⣷⣼⢀⡝⢿⣿⡻⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣤⠀⠐⠚⠫⠒⠤⠄⠙⠧⣀⠀⠀⠀ ⢦⣤⣹⣾⣿⡿⡇⠀⠀⠀⠈⠙⠻⠶⠯⠿⣷⡇⠀⠀⠊⠉⠁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢉⢫⣭⢭⣂⣐⣒⠲⠶⠚⠛⠁⠀ ⠉⣿⣿⣿⣿⣇⠹⡀⠀⠀⠀⠀⠀⠀⠀⠉⣹⠁⡀⠀⢠⠀⢻⡟⢻⠟⠾⢿⣶⣦⣤⠀⠀⠀⠀⢸⡻⢮⣦⡙⠷⡌⠓⠽⢤⡀⠀⠀⠀⠀ ⠀⣻⣿⣿⣿⡟⠀⢱⠀⠀⠀⠀⠀⠀⠀⢠⠃⡰⠀⠀⠀⠀⠀⠻⢾⡤⢏⣼⣁⣤⡼⠗⠀⠀⠀⠸⣷⡄⣿⣿⣷⣼⣿⣿⣧⣴⡾⠃⠀⠀ ⠀⢮⣿⣿⣿⠀⠦⠸⡄⠀⠀⠀⠀⠀⢠⠏⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣟⠿⣿⣿⣿⣿⣷⡿⠀⠀ ⠖⣾⣿⣿⣿⣿⠀⠀⠇⠀⠀⠀⠀⠈⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢿⣭⠟⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠉⠻⣿⣿⣿⡀⡀⢀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠒⣤⡤⠴⠚⢇⣠⡾⠵⢆⢀⢾⣿⣿⣿⣿⣿⣿⣿⣿⡫ ⠀⠀⠘⢯⣿⣿⡗⣿⠹⠀⠀⠈⡓⠿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⠜⠠⣠⡔⠛⠉⠈⠀⠉⣿⢠⣿⣿⣿⣿⣿⡟⢁⣽⠟ ⠀⠀⠀⠀⠉⢻⣧⡈⢦⠀⠀⠀⠈⠒⠠⠌⠉⠒⠂⠀⠀⠀⠀⠀⢀⡄⢀⣀⠴⠋⢀⡴⠉⠁⠀⢚⠀⣷⣾⣿⣿⣿⣿⣿⡿⢋⣴⣿⠟⠃ ⠀⠀⠀⡆⡆⠀⡇⢣⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⠁⠀⠈⠁⢀⠐⠉⢹⡥⡀⠂⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡛⠳⡄⠀ ⠀⠀⠀⢱⠸⠀⠡⠀⠳⡈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⣋⣀⡤⡔⡲⢊⣁⠤⠤⠁⣤⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠁⠀⠀⠀⠘ ⠀⠀⠀⠘⡄⠐⠒⠐⠀⠱⡈⠓⢦⢤⣤⣤⣴⣶⣿⣿⣿⣥⡀⡠⢂⣠⠀⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⢾ ⠀⠀⢀⠀⠀⠀⠀⠰⡄⠀⢡⠀⢸⠀⠳⢹⡙⣿⠿⠛⠋⣩⠇⠀⠉⠁⠀⡠⠂⠀⠀⠘⠛⠛⠻⠏⠉⠁⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡄⠀⠀⠀⠀⠀⠀⣠⠖⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠘⢟⢆⠀⢠⣦⡀⠀⠘⠹⠀⠀⠀⠀⣠⠞⠉⢷⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢕⠮⣦⢢⣸⡀⠙⢦⡀⠀⠀⠀⠀⡴⠋⠀⠀⢸⡇⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⣄⣑⠀⠁⠉⢧⡀⠀⠙⠢⣄⣀⡞⠁⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡖⠉⠀⠀⠀⠀⠀⠀⠉⠑⠒⠢⠿⠦⣀⠀⠈⠛⠶⣤⣀⣀⠀⣸⠃⠀⡆⠀⠀⠀⣀⣀⣀⣠⢤⣴⠖⠛⢳⡄⠀ ⠀⠀⠀⠀⢮⠀⣀⣤⡴⠖⠛⠉⠉⠀⡀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠈⠩⣟⡛⠛⠚⠛⠋⢉⡽⠋⠁⢀⡴⠛⠁⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⠉⢠⠏⠀⠀⠀⠀⡴⠋⢹⡶⠞⠉⠁⠀⠉⠙⢦⡀⠀⠠⣖⠋⠉⠀⠀⣀⡴⠋⠀⢀⣴⠿⠓⢲⡆⠀⠀⣸⠃⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣸⠁⠀⣸⢃⣠⣴⡶⠚⣻⡿⠀⢹⡄⠀⠙⠶⠶⠖⠚⠉⠀⢀⡴⠟⠁⢀⣠⠞⢀⣀⢠⡏⠀⠀ ⠀⠰⣒⠤⣀⠀⠘⣇⠀⠀⠀⣯⠀⢀⣇⡾⠁⣿⡿⠛⣉⠚⠛⠋⢷⡤⠴⠾⢶⣄⣀⡤⠞⠫⠤⠶⢾⡏⠁⣴⣿⣏⢻⠀⠀⠀ ⠀⠀⢀⡉⠲⢍⡂⠘⠳⢤⡼⠙⣦⡼⢹⢃⣴⡏⠀⢤⣍⠙⠓⠂⠀⠀⠀⢀⣾⠉⠀⡀⠀⠀⠀⢀⣠⠇⠀⣹⡌⣻⠟⠀⠀⠀ ⠀⠀⢐⡴⠂⠀⠀⠀⠀⢠⡇⠀⣿⠀⣾⣿⣯⡤⣤⣄⠈⠓⠀⠀⠀⠀⣠⣿⠭⠧⠤⡉⢻⡋⠉⠉⢀⣠⣾⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⣠⠼⣀⡴⠛⠀⠈⢛⡿⠣⣼⣿⣧⠀⠀⠀⠀⠈⠉⠉⠛⡆⠀⡻⠿⠤⠴⠚⠋⣉⡤⠖⠋⠁⠀⠀⠀⠀ ⠀⠀⣀⣀⣤⡤⣒⣯⣵⣟⡁⠀⠀⠀⣠⠟⢷⣶⣿⣍⣿⠀⠀⠀⠀⠀⢀⣠⠞⠁⣠⠇⠀⠀⠀⠴⠞⠛⠚⠓⢦⡀⠀⠀⠀⠀ ⠀⢰⠋⣡⣿⠏⢁⡤⠀⠈⢹⡄⣠⣞⣁⣀⣤⣿⢋⣽⡟⠀⠀⠀⠀⠀⢙⡇⣠⠴⠥⠤⠤⣄⡀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀ ⢀⣼⣶⡟⠁⠘⠑⠃⠀⠀⣸⢿⣥⠭⠏⠀⢸⢷⠚⣿⠁⠀⠀⠀⣠⠖⠋⠀⠀⣀⣀⣀⣀⡀⠉⢳⡖⠚⠉⠉⠉⠀⠀⠀⠀⠀ ⠾⠥⠞⠧⣄⠀⠀⠀⣠⢾⡥⠤⠽⠆⠀⠀⡼⣾⣶⠃⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠯⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⠋⠉⠉⠁⠀⠀⣀⣠⣶⢧⣴⠃⠀⠀⠀⣰⣃⡠⠤⠒⠒⠒⠲⡶⠶⠤⢤⣤⡤⠿⠋⡉⠛⠲⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠴⠒⢀⡀⠀⠀⠳⡈⣹⠟⠁⠀⠀⢀⣠⡿⣿⣃⣤⣄⣀⡀⠀⢳⡴⠚⠩⠀⠀⠀⠀⠀⠀⣴⡟⠁⠙⠳⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠁⠀⠀⠀⣿⣁⣀⣀⣠⡴⠛⢹⣤⡿⠋⠀⠀⠉⠛⠷⢮⣿⣄⡀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣁⣀⣀⣴⣋⣀⣀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣦⣶⣾⣏⣠⣤⡶⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣶⠿⠛⠻⢿⣯⡙⠛⠿⣿⣿⡻⠶⢦⣤⣀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠈⠙⢷⣄⠀⠙⠻⣦⣄⠈⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠈⠙⢷⣤⡀⠀⠈⠙⠳⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣷⣾⣿⣯⡉⠓⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⢿⢿⣿⣿⣦⡸⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣴⣾⣿⡟⠉⠉⠳⢝⡷⢿⣿⣿⡱⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⢏⣿⣿⠀⠀⠀⠀⠀⠙⣾⢻⣿⡟⠚⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣾⣿⣿⣧⠀⠀⠀⠀⢀⠟⣾⣿⡇⠀⠀⠉⠢⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⡼⠀⣾⣿⠟⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⡇⢸⢹⣿⣧⠀⡉⠛⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣗⡿⣿⣿⡁⢿⠸⣿⣯⢧⡈⠒⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⠘⡆⠉⠿⣷⣍⡲⣄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠉⠀⢈⣿⣿⣿⣿⣿⣿⡧⠹⡄⠀⠈⠙⠻⠛⠿⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠏⠀⠀⢀⣾⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣶⡾⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⡇⠙⣿⣶⣾⣷⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⡟⠿⠿⢟⣻⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣻⣿⣿⣿⠛⢿⣿⣽⣿⣿⣿⣿⣿⣾⣿⠛⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⢻⣿⣿⣟⣙⣿⣿⣿⣿⣿⣿⣿⡄⣿⡿⣾⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣿⠛⣧⣿⣿⣿⣿⣿⣿⣟⣿⣧⡼⡟⣿⣼⡿⢾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠻⡍⡻⣿⣿⣿⡿⢛⣿⠋⠀⣸⣿⣿⣯⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⣷⡀⢹⣷⣿⣿⣿⣷⣾⠁⠀⣸⡿⣿⣿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣶⣦⡤⣤⣀⣀⣤⣿⣿⡇⠛⣷⣿⣿⣿⣿⣿⣿⣿⣷⣰⢿⡇⡟⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢻⣿⡿⣿⣿⢻⡇⣆⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣼⣷⣷⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⢖⡵⢛⣷⣿⣧⣼⡟⣛⣿⣿⡋⣿⣿⡇⢹⣿⣿⣿⣿⣛⣻⣽⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠴⣫⣾⣿⣶⣿⠟⢻⣼⣿⣿⣙⣿⣿⣿⣿⣿⠇⠸⣿⣿⣿⣿⣧⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠁⠀⠸⣿⣿⣿⣿⣿⣻⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠿⣿⣿⣿⣿⡏⣿⣿⣿⠀⠀⢸⡿⣿⣿⣿⣿⡎⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⠀⠀⠀⠁⢻⣿⣿⣿⣧⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣬⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠛⠻⣸⣿⣿⡟⠀⠀⠀⠀⠀⠁⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣾⣿⣶⣿⣧⣄⠀⠀⠀⠀⠀⠀⣸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⣩⣿⣿⣿⣿⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡝⠛⣋⣭⡿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣶⠾⠛⠉⠰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠈⠀⠀⠀⠀⣼⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡖⠖⠒⣷⣄⠀⠠⡶⠖⣦⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠛⢿⣿⠓⢰⡿⠺⡇⠀⠙⠒⠁⠀⠀⠀⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢡⣿⣷⣾⣹⣷⠟⠙⣦⣅⠠⠀⠀⠀⠀⠀⠸⠉⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⠤⠤⣤⣿⣿⣏⢹⣿⠋⠉⠁⠀⠀⢛⡷⣾⡛⠋⠁⠀⣠⣶⠟⠋⣹⢦⣠⡀⠀⠀⠀⠀ ⠠⣤⣿⡥⢤⣄⡿⠛⠻⢿⠿⣯⠀⢠⡶⢶⠀⠙⢄⠠⣁⣀⣤⣾⠋⠀⣀⠼⣛⢦⣙⣿⣧⠀⠀⠀ ⠀⢻⡄⠈⠀⠘⡅⠀⣰⣿⣷⣿⣀⠉⠛⠋⠀⠀⣠⣤⣻⢻⡟⠁⡠⠊⠁⠀⠈⣷⢌⡉⠙⢆⠀⠀ ⠀⠈⣷⣤⡀⠀⣧⣾⣉⣴⣿⣿⣿⣀⠀⠀⠀⠚⠛⠋⣹⣾⣤⣎⡤⠂⠀⠀⠀⢻⡳⣷⠀⢸⡀⠀ ⠀⣰⡏⠓⠿⣷⣿⣿⣿⣿⠋⣉⣤⣌⣏⣶⠦⠆⠠⣶⣹⣿⡿⠋⠐⠚⠋⠑⢤⡀⠑⣄⠀⠀⡇⠀ ⠀⣿⣧⣴⠚⡹⣿⣿⣿⡿⣿⣿⠿⣿⠟⠁⠀⠀⠀⠀⣹⠏⠀⠀⠀⠀⢀⣀⣀⡙⣄⣸⡷⠤⠽⡆ ⠀⠀⢸⣿⣿⣀⣨⠿⠖⢉⡡⠴⢚⣩⣀⣀⣠⡤⢴⣾⣧⣤⠤⠤⠒⠒⠋⠀⠀⡄⢸⣿⡇⠀⢰⠁ ⠀⠀⠀⢻⣿⣿⡏⠀⠈⢁⠴⠊⣡⠞⠁⠁⢠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠸⢁⣾⣯⠁⠀⡏⠀ ⠀⠀⠀⠻⢿⣿⡃⠀⠀⠀⠴⢊⣹⣄⣀⣀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣾⠇⢹⠀⣼⡇⠀ ⠀⠀⠀⠀⢸⣿⣧⣀⣀⠤⠾⠿⠿⢟⡟⣻⢯⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣾⣷⡄⠀⢠⣿⠃⠀ ⠀⠀⠀⠀⠀⠻⣿⣿⣀⠀⠀⠀⠀⡎⠐⡏⠀⢷⠀⠀⠀⠀⢀⡴⠋⠀⣴⣿⢹⠃⠃⠀⡾⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⣦⡀⢻⡄⢇⠀⢸⠀⠀⢠⡶⠋⠠⣠⣾⣿⣿⣤⣤⡤⠞⢡⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣷⠈⠛⠛⢿⣾⣿⣼⣶⠃⢀⡴⠋⣀⣤⣾⣿⣿⠿⠿⠛⠁⠀⠀⡼⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠉⠉⠉⠉⠛⠛⠚⠛⠛⠛⠉⠉⠁⠀⠀⠀