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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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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠤⠤⠄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠴⠞⢉⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⠶⠶⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠛⠉⠉⠀⠀⠀⠈⠉⠛⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡏⠀⢹⡄⠀⠀⠀⠀⠀⢠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⡄⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣆⠀⠀⠀⣿⠃⠀⠀⠀⠙⢦⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣀⡄⠀ ⠀⣿⠉⠳⣄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⣠⡴⠞⠛⠑⣿⠀ ⠀⣿⠀⠀⠘⢧⣿⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣣⡴⠞⠋⠁⠀⠀⠀⢰⡿⠀ ⠀⢸⡆⠀⢷⡈⣿⡏⠙⠳⣤⡏⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⡤⠀⠀⠀⢸⡇⠀ ⠀⠈⣿⡄⠀⢹⣿⡟⠳⣤⣽⡄⠀⠀⠀⠀⠘⣦⣠⠤⠶⠖⣛⣛⣋⣽⣽⣯⣍⣛⣳⣄⠘⣷⡄⠀⠀⠀⠀⢀⣴⠞⠋⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⣿⠁⠀ ⠀⠀⠘⣧⣸⡟⢻⡇⢸⡏⣿⣇⣀⠀⠀⠀⠀⠹⣦⣤⠖⠿⣏⠉⠀⣻⣀⣹⡇⠀⠉⠉⠓⠋⢷⡄⠀⠀⣴⠛⠁⠀⠀⢀⣴⡋⠀⠀⠀⠀⠀⠀⣴⡏⠀⠀ ⠀⠀⠀⠙⣿⡳⢹⣷⠸⣧⡻⣽⠟⠀⠀⠀⠀⠀⠈⠉⠀⠀⠘⠶⣄⣀⣉⡿⠃⠀⠀⠀⠀⠀⠘⣷⣠⡞⠁⠀⠀⠀⡴⠋⠉⡇⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀ ⠀⠀⠀⠀⠙⣧⡀⢿⡇⢈⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⢀⠞⠁⠀⣸⠇⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⣼⣧⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⣦⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢀⣰⣏⣠⠎⠀⢀⣴⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢨⡟⠁⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠛⠋⠉⠁⢀⣰⡾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⢳⡆⠀⠀⠀⠀⢀⣠⢶⠋⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⣀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⢀⣀⡤⠶⠖⢋⣁⣀⡤⠴⠒⢋⣡⠬⣷⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⢶⣚⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢀⣴⠶⠛⣿⠒⡶⢯⡉⠉⠁⠀⢀⡴⠋⠀⢀⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠉⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠇⠀⢀⣤⠶⠋⢿⣆⠀⠸⣄⡇⠀⠹⣆⠀⢀⡞⠁⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣠⠖⠋⠀⠀⠀⣨⣿⣆⠀⠈⠃⠀⠀⠘⣧⡼⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠁⢻⣧⠀⠀⠀⠀⠀⢸⣇⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠻⣷⡄⠀⠀⠙⠉⠁⠀⠀⣀⣤⠟⠀⠀⠀⠀⢀⣴⡿⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀ ⠀⠀⠀⠀⢀⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠒⠒⠖⠛⠋⠀⠀⠀⠀⠀⣰⡿⠋⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀ ⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠋⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇ ⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡄⠀⠀⠀⠀⢀⣠⡾⠛⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠤⠤⠤⠿ ⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⣤⣶⠟⠉⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀ ⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢀⣤⡶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⣀⣤⡤⠴⠖⠚⠛⠛⠓⠶⢦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢀⣠⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡧⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣤⣀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢸⡇⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⡀⠘⣧⠀⠀⠀⠀⠀⠀⡾⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⣿⡆⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡳⣄⠀⠀⢣⡀⠀⠀⠀⠑⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡳⣄⣀⣙⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄ ⠀⠀⠀⠀⠀⠀⠀⡞⣼⣿⣿⣿⡿⣿⠟⣫⣿⣿⣶⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠉⠉⠛⠻⢿⣿⠿⠛⠛⠛⠿ ⠀⠀⠀⠀⡀⡠⢖⣵⣿⣟⣩⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢀⣀⣀⣀⣀⠈⠛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀ ⠀⠠⣒⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠉⠉⢻⣿⠿⠛⠊⠉⠉⠉⠉⠉⠓⠲⢿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣄⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡁⠀⠀⠀⣀⣤⣼⡇⠀⠀⠀⣠⡴⠶⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⣼⡿⠀⡄⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠟⠉⠀⠀⠹⣿⣿⣿⣿⣷⣦⡾⠟⠋⠉⠉⢇⠀⠀⣰⡟⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠇⠀⠀⠀⠀⠀⠀⠀ ⣿⠋⠀⠀⠀⠀⠀⠈⠛⢿⣿⡿⠋⠀⠀⠀⠀⠀⠈⠃⠀⣿⣠⠴⠖⠒⠒⠚⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⣠⠔⠛⠒⠛⠁⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀ ⣿⣦⣀⡀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⡾⠁⠀⠀⢠⡴⠋⠀⣸⠇⠀⠀⣤⢖⠀⢸⠀⢀⠄⠀⣄⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀ ⠈⠙⠛⠛⠿⠿⠿⣿⣿⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠻⣤⠴⠋⠁⠀⠀⢸⡙⢿⣤⣯⠔⠋⠀⣠⣿⡄⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣠⣤⣴⣿⠏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣤⣤⣤⣶⠾⠋⠀⢳⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀ ⣶⣿⣼⣿⣿⣿⣿⠏⠀⠀⡀⢱⠀⠀⢸⣄⡀⠀⢀⣠⠴⠒⠒⠒⠲⣄⠀⠀⠀⣠⠟⠛⠓⠒⠢⢤⣸⡇⠀⠀⣰⣤⣿⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⢇⠈⢧⠀⠀⢿⠯⣍⡋⠀⣀⣀⠤⠤⠤⣼⡆⠀⠠⢧⡤⠤⢤⣀⣀⠀⢉⣥⠀⢰⡟⣿⢹⡧⠴⠾⣔⢦⠀⠀ ⠀⠉⠉⡟⢧⡀⠀⠀⠀⠀⠈⢆⠈⠣⡀⠈⢳⣄⠉⠉⠁⠀⠀⠀⠀⣿⠛⠛⢻⡿⠀⠀⣦⢀⣀⣹⠟⢹⡀⢸⣇⢡⡋⢿⣷⡀⠘⣿⢇⠀ ⠀⠀⠀⠘⠪⣛⠶⠤⠤⠶⢧⠈⢣⡀⠙⠢⢄⣉⠻⠧⠤⣄⠀⠀⠀⢹⡆⢐⣾⠃⠀⠀⠸⣆⠀⠀⠀⠀⢣⠘⣌⢦⣽⣉⣿⠇⢠⡟⣞⣀ ⠀⠀⠀⠀⠀⠈⠙⠓⠒⣿⣻⠀⠀⠙⣶⢄⣀⡀⠀⣀⣴⣿⣦⣤⣄⣘⣷⠟⠙⣶⣶⣾⣿⡛⠲⠤⠴⠻⡄⠑⢄⣉⠉⠉⢀⣠⡾⣱⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡳⣇⣀⣀⣴⠃⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⡋⡏⠀⠀⣿⣿⣿⡿⠟⠁⠀⠀⠀⠙⠢⣀⣀⣉⣩⡽⣫⣾⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠪⢭⣿⡸⡄⠀⠀⠀⠀⢀⣹⣿⣿⠛⠋⢹⠁⠀⢰⠟⠿⣿⣤⣄⣀⡀⠀⠀⠀⠀⠙⢺⠏⣿⡹⡏⠻⠋⠀⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡇⡇⠀⢠⣤⣶⣿⣿⣿⣿⣷⠖⠲⠬⣔⣋⣤⣴⣿⣿⣿⣿⠿⣤⣀⠀⠀⠀⢸⣠⣷⢡⡇⢠⣄⠀⠀ ⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠇⠀⠀⠙⠿⣿⣿⣿⠟⣿⣷⣤⣠⣾⣯⡻⣿⣿⣿⢿⣁⣀⡼⠡⠉⠓⢲⠋⠁⢹⣻⠀⠀⠀⠀⠀ ⠀⠀⢀⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠙⠛⢻⣿⣿⣿⣿⣿⡏⠈⠉⠀⠀⠀⠉⠁⢳⡦⢤⣸⣄⢀⣇⡏⢀⣠⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⢿⣛⣫⣭⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠛⠛⠻⢿⣿⣿⣿⠿⢿⣿⣷⣦⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣯⣥⣶⣾⣿⣿⣿⣿⣿⣿⠟⠉⣀⣀⣀⠈⠙⣿⣿⣿⣿⣿⠇⠀⠀⠀⢠⡿⠋⣉⠆⠀⢻⣟⢿⣿⣷⣄ ⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⢙⡿⠗⠋⠉⠉⠉⠉⠉⠓⠿⣿⣿⣿⡟⠀⠀⠀⣰⠏⣀⡼⢥⣀⣀⡀⢻⡄⢻⣿⣿ ⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢰⠏⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠉⠻⢦⡀⠀⣼⡏⡰⢁⡤⠀⢁⣄⠙⡞⣿⠘⣿⣿ ⣠⣾⣿⣿⣿⣿⡿⠟⠉⢿⣿⣿⣿⣆⣀⣤⡤⠶⢿⠀⠀⢠⠞⠋⠙⠻⣦⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿⠀⡇⢸⠀⠀⠉⢹⠀⡑⣿⣼⣿⣿ ⣿⣿⣿⣿⣿⠟⠀⠀⠀⠈⠻⣿⣿⡿⠛⠁⠀⠀⠀⠃⠀⣾⣀⣠⠤⠤⠽⣷⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣷⡀⠳⣤⠔⠋⣠⠃⣿⣿⡿⠃ ⠋⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⢐⡿⠁⠀⠀⠀⠀⣠⠴⠦⡿⠉⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠙⡄⢁⡴⠚⢁⣼⣿⠟⠁⠀ ⠀⠹⣿⣿⣿⣦⣀⡀⠀⠀⣀⣿⠁⠀⠀⠀⢀⡞⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⣟⣨⡤⠶⠛⠛⣿⠀⠀⠀ ⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⡞⠀⠀⢀⡞⠁⣀⠟⠀⢠⣖⡶⣾⠀⠀⠀⢰⠀⠀⠀⠀⠀⢸⡇⠙⠁⠀⠀⢀⣿⠃⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⠉⠛⠛⣿⣿⠃⠀⠀⠀⢠⡇⠀⠀⠈⠓⠊⠁⠀⠀⠸⣌⠛⠛⠊⠀⣠⠟⣇⠀⠀⠀⠀⢸⣷⠀⣤⣀⣹⡟⠁⠀⠀⠀⠀ ⣷⣤⣀⣤⣤⠴⠶⣾⣿⣿⡟⠀⠀⢠⠀⠘⡇⠀⠀⠀⢀⣀⡤⣄⡀⠀⠈⠛⣲⡷⢾⣁⡀⢸⠀⠀⠀⡀⣾⡏⢠⣿⡏⠁⠀⠀⠀⠀⠀⠀ ⠛⠿⣿⣿⣿⣷⣾⡿⠿⠋⠀⠀⢆⠘⡄⠀⢷⣶⠤⠚⠉⠀⣀⣀⣹⡄⠀⢼⣁⣀⣀⠀⠉⠚⡓⠀⣸⠟⢹⣧⣼⡋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠙⠛⢧⠀⠀⠀⠀⠘⡄⠱⡄⠈⢧⡉⠒⠋⠉⠀⠀⢽⠛⠒⣾⠁⠀⢠⣍⣱⡾⢃⠀⣿⠠⠚⣷⡄⠹⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠤⢶⠘⢆⠈⠢⠤⠙⠦⠤⣄⠀⠀⢸⡄⢀⡟⠀⠀⢹⡈⠁⠀⠘⣄⢻⣧⣿⣿⡟⢠⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣱⠢⢤⣀⣠⣴⣿⣶⣦⣬⣿⠋⢹⣶⣶⣿⣙⠒⠒⠻⡈⠢⢌⣉⣀⣤⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠤⠶⡇⠀⠀⠙⠻⢿⣿⣿⣿⣧⠇⠀⢸⣿⣿⠛⠉⠀⠀⠀⠈⠲⣤⣤⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢀⣠⣾⣿⣧⣀⣘⠠⢠⠏⠉⣿⣿⣶⣦⡄⠀⠀⠀⢸⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢿⣿⣿⣿⣿⣿⣉⢉⣿⣿⣿⣿⣿⣿⡉⣹⠓⠤⢄⡾⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⠉⠋⠁⠉⠙⠓⠦⣄⣘⡇⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢰⠇⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⡎⠀⠀⣰⣿⣿⣿⣿⠟⠛⢷⡄⠀⠀⠀⢠⡟⠀⡼⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣤⡤⣄⡀⠀⠀⠀⢰⠃⠀⡼⠀⠀⣰⣿⡏⣯⣿⣿⣆⡀⠀⠉⠂⠀⢠⡟⠀⢀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⠀⢈⡠⣤⢄⠈⣿⡆⢀⣠⡏⣠⠞⠀⠀⣠⡿⡻⠁⠹⣿⣿⣟⠿⢶⣦⣼⣴⠋⠀⠀⣸⠡⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⢀⣠⣤⣤⣶⣚⣋⡉⠉⠉⠉⠙⠓⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⢧⡖⢀⡤⢀⣬⡉⠁⢒⠒⠤⡀⣀⡀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠴⠖⠒⠒⠒⠲⠦⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠻⠶⣤⠏⣷⡔⠀⡠⠊⢀⠄⢈⠝⠒⠢⣄⡙⠳⣄⡀⣠⠴⠚⢋⣁⠤⠔⠒⠊⠉⠉⢫⠉⠳⡉⠑⢖⠚⠭⣷⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⠶⠾⣇⡀⠠⢒⣑⣁⣉⣿⠷⢶⣟⣇⣴⣚⣽⣠⢧⢘⡌⢢⠐⡄⠀⢣⠀⠘⡄⠈⣆⠀⢦⠈⣟⠻⢶⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠼⠛⠋⠉⠁⣀⡠⠤⠐⡒⡿⠱⢴⡿⠿⠿⣯⣯⠟⡄⢇⠘⠄⠀⢇⠀⠸⡀⠘⣄⣄⡆⠘⠀⣠⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⣀⡠⣴⠒⢏⠀⢇⠀⢦⣽⣇⠀⠀⠈⠐⠤⣀⠉⠛⠿⣼⡄⠘⠀⢸⡿⣄⣁⣤⠿⠹⠦⠖⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⢀⡠⡔⠋⢁⠀⠘⡄⠘⡄⠘⣄⣾⣿⣿⣷⣀⠀⠁⡐⠋⠑⢄⠀⠀⠙⢿⡉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⠞⠁⢀⡤⠒⢩⠀⠸⡄⠈⢶⡶⢷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⡔⠉⢀⠑⢄⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠟⣁⡤⠊⢇⠘⣤⣤⢣⠀⢱⣠⣼⣧⣾⣿⣿⣿⣿⣿⣿⣙⣻⣿⣿⢿⣦⣀⣰⣁⡀⠀⠱⡀⠀⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⠵⠞⡅⠸⡀⠈⢆⢀⣻⠻⠚⠉⠀⣰⣿⣿⣿⠿⠛⢻⡟⠀⢹⣿⡿⠻⠛⣿⡏⠻⣿⣀⠞⢁⠈⢆⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠷⠦⠦⣼⠤⠵⠖⠚⠉⠀⠀⠀⠀⢰⡿⠛⠁⠀⠀⠀⡼⠥⠖⠋⣽⡃⠀⢾⣿⠀⠀⠀⠉⠻⣥⡄⡈⢣⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢥⣀⣀⣠⡟⢷⣀⣽⠇⠀⠀⠀⠀⠀⢾⣛⡟⢟⢧⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⢀⣠⠟⣻⠁⠈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠉⠓⠿⢬⣃⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡿⠒⠚⢉⠈⣰⠇⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠳⢤⣠⣆⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⢀⣠⠴⢻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠷⠒⠋⠉⡗⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣏⡀⠀⠀⠠⠕⠂⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠉⠉⠒⣷⣦⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⣠⠴⠚⣿⠍⠉⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡴⠋⠀⠀⠐⠒⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⢠⢬⣉⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣠⡏⠉⠉⠛⠒⠚⠟⠛⠉⠁⣿⠠⠤⣀⣀⠤⠤⢄⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠒⠂⠁⠁⠀⠸⠇⠀⠀⠀⢹⣿⣷⣤⡀⠀⠘⣧⠀⠐⡇⠀⠀⢀⠳⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡒⠋⠉⠉⠑⠀⠀⠀⠀⠉⠁⠀⠀⠀⠘⠆⠀⢱⣶⣫⣥⢺⣿⣿⣧⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠾⣿⠁⠒⣊⡉⠉⠀⠤⠐⠒⠁⢀⣴⣾⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣀⠀⠀⠀⠀⠀ ⠠⠀⠀⠀⣀⠠⠔⣺⣿⣿⣿⠿⣿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀ ⠀⢠⠀⠀⠀⠀⠀⢿⣿⠏⡀⠄⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠫⠂⠀⠀⠀⠀⠈⡏⣾⠀⠀⢰⠀⡔⠁⠈⢢⠀⠈⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀ ⠉⢀⠀⠀⠀⠀⢀⠔⠃⢄⠀⣤⠛⢸⠃⠀⠀⡘⠀⣠⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⠉⠒⢄⠰⠁⠀⠀⠀⠉⠿⠇⠈⠂⠤⠐⠁⢸⣿⡟⠋⠛⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣿⣿⣿⣿⠇⠐⠀ ⠀⠄⠂⠉⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣤⣾⣿⣿⣛⣁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠁⠈⠉⠂⠀⢀⡀⡄⠀⡿⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠤⠘⢇⢲⠒⠒⠒⠛⢁⠔⠁⢀⠏⡸⠹⢭⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠞⢁⠊⡘⡌⡜⢄⣐⣒⣈⣁⠠⡔⢁⡔⡡⠃⠀⢀⠝⠲⢄⠀⠀⠀ ⠀⠀⠀⢀⠎⠀⠆⠀⡇⡟⢀⠤⢆⡄⠀⠀⣜⠴⡫⠞⠀⠀⡔⠁⠀⠀⠀⠑⡄⠀ ⠀⠀⠀⡞⠀⡸⠀⠀⢡⡡⠃⠀⠀⠙⣆⣰⡡⠊⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⡀ ⠀⠀⢠⠁⢀⡇⠀⠀⢸⠀⠀⠀⠀⠁⠒⠊⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢣

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⣶⣶⣶⣶⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡴⠛⢉⣾⣾⣿⣿⣿⣿⣿⣿⣷⣦⣉⠛⢶⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠈⠻⣦⡀⠀⠀⠀ ⠀⠀⢀⡾⠁⠀⠀⢰⣿⣿⣿⣭⣙⠙⠿⣿⡿⢿⣿⣿⣿⣿⣿⡚⣤⣈⢳⡄⠀⠀ ⠀⢠⡟⠀⠀⠀⠀⣾⣿⣾⣿⣿⣿⣿⣷⣱⣴⣤⣣⣿⣿⣿⣿⠄⢹⡟⣆⠹⡄⠀ ⠀⡾⠀⠀⠀⠀⢸⣿⢿⣽⡿⠙⠻⢿⣻⣿⣿⣿⣿⣿⣿⣿⠟⠒⣾⣷⣿⡆⢻⠀ ⢰⡇⠀⠀⠀⠀⢸⣿⡠⠆⠀⠀⠐⢎⠛⢻⣿⣿⣿⣿⣿⡟⠀⣰⢿⠿⣿⡇⠸⡇ ⢸⡇⠀⠀⠀⠀⣾⣿⡆⠈⠁⠀⠀⢤⢿⣿⣿⣿⣦⣈⡙⢣⣼⣿⣷⣷⣼⡇⠀⡇ ⠸⡇⠀⠀⠀⢀⣿⣿⣷⣻⠓⡤⢀⣼⡌⡞⣿⣟⠉⢳⣮⣍⡙⢿⡿⢿⣿⣷⢠⡇ ⠀⢷⠀⠀⠀⢼⣿⣿⣿⣯⣭⣤⣾⣜⢮⡇⡎⢿⣷⣿⣿⣿⣿⣷⣴⠊⣿⣿⣼⠁ ⠀⠘⣧⠀⢀⣸⣿⣿⣿⣿⣿⡟⡔⢹⣿⣿⡽⡄⠈⠻⣿⣿⣿⣿⣷⣅⣻⣿⠇⠀ ⠀⠀⠘⢧⣿⣿⣿⣿⣿⣿⣿⣴⠁⣿⣿⣿⡇⠈⠦⠀⠀⢉⠻⢿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠻⣿⣿⣿⢿⣿⣿⣿⣼⢳⣿⣿⣿⣆⠀⠀⠀⠀⢂⢀⣵⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠿⣾⡜⣿⡿⣻⣿⣿⣿⣿⡿⡱⡀⢀⣠⠼⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠿⠿⠿⠧⠿⠷⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠛⠋⠉⠁⠀⠀⣠⣤⠾⠟⠛⠉⠙⠓⠶⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠁⠀⠀⠀⢀⣠⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣭⡿⠷⠶⠦⢤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⢀⣴⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠞⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢲⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⢠⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⢀⣼⣯⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⣸⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠾⠃⣠⡾⠃⢀⣀⣴⡾⠟⠁⠘⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⣠⡾⠋⠁⠀⠀⠀⠀⢠⡏⠀⠀⠉⣉⣙⠉⠙⠛⠛⠛⠿⠧⠴⠾⠛⠉⢙⣿⠟⠋⢻⠃⠀⠀⠀⠛⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⠞⠉⠀⠀⠀⠀⠀⠀⢰⣿⣠⡴⠞⠛⠉⠙⠛⠷⢶⡶⠖⠂⠀⠀⠀⠀⠀⠈⢁⣀⣤⣾⡄⠀⠀⠀⠀⢹⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣩⣷⣶⣶⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⣿⣿⣏⣿⠁⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠻⣟⠁⠀⠀⢠⣾⣿⣷⣄⠀⠀⠀⠀⠀⠀⢸⡏⢸⣿⣿⡟⢻⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠙⢷⣀⠀⢸⣿⣿⣿⣉⠀⠀⠀⠀⠀⠀⢸⡷⠼⠿⠿⠃⠸⡆⠀⠀⠀⠀⡾⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠋⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⢻⡄⠀⠀⣰⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠘⣇⠀⠀⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠆⠀⠀⠀⣿⠀⢰⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠞⠛⡴⠟⠁⠀⠀⠀⢸⡏⠀⠘⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢸⡇⠀⠀⠀⠀⠀⣼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡾⠁⠀⠀⢿⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣾⠁⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣖⣛⣛⣻⣿⠟⠀⠀⠀⣼⠃⠀⠀⠀⠀⠹⣆⠀ ⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣍⡉⠉⠉⢉⡷⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠹⡄ ⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⣇ ⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡉⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿ ⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠙⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠉⠙⠓⠲⣶⣤⣶⣶⣟⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀ ⠾⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠶⠾⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠏⠀⠀

⠀⠀⠀⠀⠀⣠⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣽⣿⠏⣿⡟⠿⣿⣿⣿⣯⣿⣯⢮⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⣏⣠⣼⣷⣴⣍⣻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⣿⣿⣿⣿⠘⢧⣛⣿⡿⠻⣿⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣇⡥⠩⡀⠀⠙⠶⠓⠂⠸⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⡄⠀⠀⣀⠀⠀⠀⣠⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⣿⣶⣄⠀⣠⣴⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠇⣿⠘⢿⣿⡿⠷⢟⣽⣿⠏⠻⢿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠠⠊⠀⣸⠔⣷⣿⡠⣺⣿⡏⡟⠀⠀⠀⠙⠫⡳⣄⡀⠀⠀⠀ ⠀⠀⢠⠎⢀⣿⣿⢋⣾⣿⣿⠘⡇⠀⠀⠀⠀⠀⠈⢦⡉⠓⠂⠤ ⠀⢀⠏⠀⢺⣿⣿⣿⣿⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⠀⠀ ⠀⣼⠃⣀⣿⣿⣿⣿⣿⣿⡇⠘⠀⠀⠀⠀⠀⠀⢀⠔⠚⣿⣷⢄

⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⢀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣿⣯⣀⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⡧⠁⢘⣿⢿⣿⣿⣿⣿⣿⣿⡇⢠⠅⣿⣿⣿⡗⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣄⣠⣴⣾⣿⡿⣿⣿⣿⣿⣿⣿⣧⣄⣴⣿⣿⣿⡓⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⢿⣮⣿⣿⣿⣿⡿⣧⡀⠈⠉⢿⣿⢿⣿⣿⣿⣿⣿⣿⣷⡄⠀ ⠀⠀⠒⠦⢤⣀⡀⠸⣿⣿⣿⡯⢿⣇⣀⠉⡂⢀⣀⣻⣾⡬⣍⢻⣿⣿⣛⠋⢠⠄ ⠀⠀⠀⠉⠢⢉⣗⠻⢿⢿⣿⠟⠶⢿⡿⠑⠀⠈⢚⣑⣿⠦⠂⠸⢿⠧⠒⣣⡾⠄ ⠀⠀⠀⠀⠀⠀⠈⠒⢤⡹⠟⠧⡀⠀⡀⠀⠀⠀⠀⠀⠀⢄⣈⠖⣛⠬⠋⠁⠀⠀ ⠀⠀⠀⣀⡤⡤⠂⠁⠈⠛⢷⣀⠀⠀⠀⠀⠂⠀⣀⡀⠀⠀⣹⣿⡛⠆⠀⠀⠀⠀ ⠀⠀⠈⠉⠉⠉⠀⠒⠐⠒⠀⠽⡢⣀⠀⠿⣫⣜⠋⠛⡠⡜⠉⢡⠈⢫⠂⢄⠀⠀ ⠀⠀⠀⠀⢀⠀⠀⠠⠄⠤⢄⠀⠈⢆⠑⠢⢄⣠⡔⠉⣴⠀⠀⠘⠀⢨⠀⠀⠀⠀ ⠀⠀⡐⠈⠈⠉⠑⠠⢀⠀⠀⠢⣀⠀⣢⠀⠐⠅⢄⠰⢹⡇⢀⠃⠀⠘⠀⡆⠄⠀ ⠀⡐⠀⢀⠀⠀⠀⠀⠀⠑⡤⠊⡑⠀⠀⠳⢢⢀⣀⣷⣿⣿⠊⠀⢀⣤⣊⠀⠀⠀ ⡨⠕⠨⠤⠤⠤⣄⠀⠀⠀⠃⢈⠀⡌⢠⠀⠁⠒⠊⠙⢭⠑⠀⠉⡀⠀⢀⠙⠦⡀ ⠀⠀⢀⣀⡀⠀⠀⠁⢂⠘⢉⡹⠶⣤⣄⢀⡖⡄⠀⠀⠀⠃⠠⠄⠑⣀⣀⠀⠀⠼ ⠉⠀⠀⠀⠀⠈⢄⠀⠈⠀⡘⠁⠀⠀⠈⣱⣼⣽⢷⣶⣶⣮⣉⠃⠀⠐⢤⠄⠐⠒

⠀⠀⠠⠰⠥⡴⡠⡪⣳⣺⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⣄⠀⠀⠀⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⠻⢿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⠀⠀⢀⡾⠃⢿⣿⣿⣿⡟⣏⢿⣿⣿⣿⠈⢿⡤⠊⣣⡜⢿⣿⣿⣿⡿⢻⣿⣧⠃ ⠀⠀⠈⠀⠀⢸⣿⣿⣿⣿⠘⣼⣧⠹⣿⣧⠊⢇⠡⠌⡁⠐⢙⣿⣿⡧⢠⣿⣿⡄ ⠀⠀⠀⠀⠀⠘⡟⢻⣿⣿⡅⠈⠙⢄⠙⢿⣆⠈⠀⠀⠑⠂⠁⠈⠸⡧⢺⠻⠟⣦ ⠀⠀⠀⠀⠀⠠⠃⠈⢟⣿⠳⡀⠀⠨⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡍⢠⠊⢀⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠾⡆⠩⣀⠀⠈⠀⣠⡴⣾⠿⣛⠝⢲⡠⠪⡆⠀⢡⡿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠭⠝⠑⠢⠄⡈⠁⠀⠑⢂⠄⢎⠈⠢⠀⠑⠂⠃⣾ ⡀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠒⢰⠨⡂⠈⠑⣲⠒⠉⢆⠀⠂⠀⠀⠀⠀⠀⣿ ⣧⡀⠄⠀⠀⣀⣀⣾⡟⠠⠔⠊⠀⣟⢉⠔⠁⠀⢡⠀⠀⡎⡄⠀⠀⠀⠀⠀⢀⣿ ⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠡⠀⢊⠣⠁⢀⣾⣤⡀⠆⠰⢸⡇⠀⠀⠀⠀⠀⣼⣿ ⠀⠀⠀⠀⠀⢀⣾⢻⠃⠀⠀⠑⣘⣁⣠⣾⣿⣿⠟⣶⣇⣾⡇⠀⠀⠀⢀⡤⣿⣿ ⠀⠀⠀⠀⣠⣿⣷⢰⠀⣤⠀⠉⣠⣿⣿⣿⣿⡿⠀⢹⣵⣺⢙⡀⠀⠀⠡⢊⣼⣿ ⠀⠀⣠⣶⣿⣿⣿⡈⡾⠁⢀⢞⣿⣿⣿⣿⣿⠃⠀⢸⣿⡇⣾⣷⠔⢁⣴⣿⣿⣿

⠀⠀⠀⠀⢀⠠⢴⣁⣀⣄⠈⠠⣜⣴⣧⣤⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠉⠀⠉⠁⣿⣋⣼⡁⡎⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⣠⡀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⠁⠀⠀⠀⠀⢸⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⣿⡇⠙⢿⣯⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⣸⣿⠋⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⢻⣿⣿⣿⣿⣿⣷⠀⠻⣿⣇⢀⡴⠛⣆⢀⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡇ ⠀⠀⠀⠀⡼⠟⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⡈⣿⠈⣿⣏⢿⣿⣿⣿⡆⠀⢹⣿⠋⣨⠴⢾⣿⠆⠘⢻⣿⣿⣿⣿⣿⣿⠀⠹⣿⣿⣿⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣏⣙⣷⢼⣿⣄⠹⣿⣿⣿⡖⠋⢹⡋⠀⠤⠤⠔⢀⠔⠉⠉⢻⣿⣿⣿⣿⡆⣸⣿⣿⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⠄⠉⠻⠿⣇⠀⠺⣿⣿⣷⠀⠀⠛⠀⠀⠀⢾⡁⢀⡠⠖⠙⠻⠹⣿⠋⢠⣿⣿⣿⣧⡝⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⢻⣿⣿⣿⣿⡄⠀⠀⠀⠙⠲⠀⠈⠻⣿⣧⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢿⡗⠉⢻⠁⣻⠁⢻⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠈⣿⣿⣿⣿⣷⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢀⡞⠁⠀⢨⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢧⠹⣿⠈⣷⣄⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⢀⡴⠓⠊⠳⡄⠀⣠⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣿⡄⠈⢣⡀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⠿⢋⡠⠛⢛⣇⡴⠯⢄⡆⠀⠀⠹⣴⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣵⠖⠒⠿⡷⢤⡀⠀⠀⠈⠻⠿⠲⠋⠁⠐⢊⠁⠀⢀⡴⠋⠠⡀⠀⠙⠢⣀⡀⠹⡇⢀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣩⠟⠁⠐⠒⠘⠥⢄⠈⡟⠢⢄⡀⠀⠀⠀⠉⠉⠀⢀⡎⠉⢢⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⢸⣿ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠇⠀⠀⠐⠂⠤⢄⠘⠀⢙⠇⠀⠈⠓⠢⡤⡤⠤⠒⠋⢇⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿ ⣆⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠀⢰⣿⡿⠀⢠⠤⠤⣤⠀⢸⠀⣄⣘⠲⢄⡀⠄⠀⢰⠇⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿ ⣧⣀⡀⠠⢀⡀⠀⠀⠀⠀⢀⢀⣿⣿⡇⠀⣤⠔⠚⢩⠃⢸⣾⡏⠀⣠⠊⢩⠀⠀⠘⡄⢀⠀⠀⣌⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿ ⠟⠁⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⢻⣿⡇⠀⠸⡄⠀⠸⣀⡞⡟⡷⠊⠀⠀⣼⡀⠀⠀⢱⠀⠀⢠⠇⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠘⣄⠀⠉⡸⢱⠁⠀⠀⣴⣿⣿⣦⣀⠈⡇⠀⡎⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠁⠀⠀⠀⠈⢦⣀⡵⠃⠀⢀⣾⣿⣿⣿⣿⡿⢷⣷⢰⠁⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠋⢸⠁⠀⠀⠀⠀⢀⣀⠤⠔⣶⣶⣿⣿⣿⣿⣿⣿⠇⠈⣿⢿⠖⠛⣿⣧⠀⠀⠀⠀⠀⣠⠾⠛⣻⢿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⢸⠀⠀⣸⡽⠉⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿⣬⣯⣽⡿⠈⡆⠀⠀⠀⠚⢁⠴⠊⢀⣴⣿⣿ ⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣇⠘⡀⣴⡟⠁⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢸⣿⣿⣿⠃⣸⣿⡄⠀⢀⠔⠁⣠⣴⣿⣿⣿⣿ ⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⠀⣟⠋⠀⡀⣠⠞⣱⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣼⣿⣿⡇⢰⣿⣿⣿⠖⠁⣀⣼⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣠⣴⠃⠀⢀⡀⠨⠃⣄⡘⣐⣇⢠⣤⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⠀⠀⠀⠤⠴⠶⠧⠡⠞⠚⢛⣿⠟⢠⡷⢀⠳⢏⣸⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣰⣿⣶⣸⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆ ⣴⣄⣀⣀⡀⠀⠀⠀⢐⣾⣿⣾⣿⣿⣏⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣹⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠻⣿⣿⣿⣿⠙⢿⣿⣯⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠹⣿⣿⣿⠀⠀⠙⢿⣧⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠹⣿⣿⡆⣠⡾⠃⠹⣇⣀⡴⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡀⢻⠀ ⠀⠀⠀⠀⠀⣠⡿⠛⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⡆⢹⣿⣯⠻⣿⣿⣿⣿⣿⠀⠀⠹⣿⡿⠋⢈⣠⠶⣿⣿⡇⠀⠟⠻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠙⢿⣿⣿⣿⣇⠈⠄ ⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠚⢷⣀⢿⣿⡄⠙⣿⣿⣿⣿⣇⣠⠾⠻⣿⠒⠉⠀⠀⢉⣉⡡⢀⣠⠞⠏⢿⣿⣿⣿⣿⣿⣇⣠⠀⣾⣿⣿⣿⣿⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠒⠬⢭⣽⣿⣷⠄⠈⢻⣿⣿⣿⡄⠀⠀⢹⣄⣀⡉⠉⠉⢁⡴⠋⠀⠀⠀⣠⡿⣿⢹⣿⣿⡿⠃⣸⣿⣿⣿⡟⢿⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⣿⠣⠀⠀⠙⠿⢿⡄⠀⠙⢿⣿⣿⣿⡀⠀⠀⠃⠀⠀⠀⠀⠻⣆⠀⣠⠴⠋⠀⠉⠹⠀⢿⣿⠀⢠⣿⣿⣿⣿⡷⣶⣉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠈⣿⣿⣿⣿⣿⣿⡆⠀⠈⠉⠀⠚⠻⢶⠀⠀⠙⢮⡻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⢛⠉⢸⡏⠈⢻⠃⠸⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠹⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠙⠈⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡼⠀⠘⢁⡴⠋⠀⠀⢹⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠃⠀⠀⠀⢻⣇⢻⣿⣿⠻⣷⡀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣃⣠⣴⡛⠀⠀⠀⣠⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠹⣿⠀⠹⣕⢤⠀⠀⠀⠀⠈⠓⢤⠀⠀⠀⠀⠀⠀⢀⣠⡤⢒⣺⣽⣷⡲⣦⠀⡀⠀⠀⢀⡼⠋⠁⠀⠀⢳⡀⠀⣠⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⣿⡇⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣪⣿⣾⣿⣿⡿⠏⢁⡴⠋⠛⢹⢀⡴⠿⢤⡸⡀⠀⠀⠀⢳⣼⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣤⣤⣤⣽⣷⢤⡀⠀⠀⠀⠀⠙⢿⡿⠧⠤⠟⢛⡉⠥⠔⠛⠁⠀⠀⢈⡵⠛⣄⠀⠀⠙⠳⣄⠀⠀⠀⢻⡟⠁⢹⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⡄⠀⠠⠤⣤⠟⠁⣀⠀⢀⡝⠉⠙⠲⡤⣀⠀⠀⠀⠉⠉⢉⡁⠠⠤⠤⠔⠀⢀⡤⠴⡏⠀⠀⠈⠳⣄⠀⠀⠈⠙⠒⠂⠀⠃⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠃⠀⠀⠉⠉⠉⠁⠒⡆⠀⢿⣈⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠙⣆⠀⠀⠀⠈⠓⠆⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠁⠀⠀⠉⠑⠲⠦⢄⡀⢸⠀⠘⠙⡄⡼⠀⠫⠑⠲⡤⣤⠤⠶⠚⠉⠹⡄⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿ ⡦⠀⠀⠀⠐⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠇⠀⣄⣀⣀⣀⣀⠀⠀⡇⠸⡀⠀⡷⣄⡀⠀⢰⠀⠀⢧⡏⠀⠀⣀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⣿⣿⣿⠀⠀⠸⠀⣉⡴⠿⡆⠀⡇⢰⣿⠒⠋⢀⣹⢶⡄⠃⠀⢸⡇⠀⠀⠟⠀⠀⡏⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⡦⣤⡄⠘⠠⠤⠀⠀⠀⠀⠄⣀⠀⡦⢼⣿⣿⣿⠀⠀⣶⠋⠉⠀⢸⠁⠀⣇⣟⣿⠀⣠⠞⠁⢸⡇⠀⠀⠀⢳⠀⠦⠀⠀⢠⠧⢜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿ ⠛⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠉⣿⣿⣿⠀⠀⠘⣆⠀⠀⠸⡄⣼⢻⠏⣿⠞⠁⠀⠀⣸⣇⠀⠀⠀⠈⣇⠀⠀⠀⣾⠐⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠘⣆⠀⠀⠉⢁⡏⢰⠃⠀⠀⠀⣰⣿⣿⣷⣆⠀⠀⢻⡀⠀⣸⠃⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⠀⠀⠀⠀⠈⢧⡀⠀⠸⣰⠏⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣦⡈⣇⠀⡇⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⢫⠞⠁⠀⠀⠀⠀⠀⠀⠙⠤⠞⠁⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣰⠇⣠⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠀⡿⠀⠀⠀⢀⠀⠀⠀⣀⣠⡴⠒⢒⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⢻⠛⠛⢛⣿⣿⡄⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⣹⠿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⠀⣿⠀⠀⠀⣼⣩⠉⠉⠉⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⣿⡀⣷⣛⢾⣿⠁⢳⠀⠀⠀⠀⠠⠞⠁⢀⡴⠋⠁⣠⣼⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠀⢹⠀⠀⣼⡿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣿⣿⣿⣷⣿⡇⢀⣿⣆⠀⠀⠀⠀⣠⠖⠁⠀⣠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⡇⠘⣆⣾⡟⠁⠀⠀⠀⣠⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣻⣿⣿⣿⡟⠀⣼⣿⣿⣆⠀⣠⠞⠁⠀⣰⣾⣿⣿⣿⣿⣿⣿ ⠐⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣏⠋⠀⢀⡀⣠⡾⣋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢀⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠟⢁⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠀⡄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣰⡄⣠⠀⠃⠀⠀⠀⢠⠆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣷⣶⣾⣷⣶⣾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢹⣿⢿⢻⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⢾⣏⡇⢸⣿⣿⡿⠹⣿⡃⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡏⢻⣿⣿⣿⡟⠛⠄⠘⣟⠉⠻⣿⣿⣟⣷⢾⢿⡶⢉⣿⣿⣿⡿⠿⠿⠿⠿ ⣿⣿⣿⡼⣻⣿⣿⠁⠀⠀⠀⠀⠉⢉⢏⠏⢨⠀⠈⠉⠉⠁⢹⣿⣿⣷⣦⣤⣤⣤ ⣿⣿⣿⣿⣦⣿⡃⠁⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⡼⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢇⠀⠀⠀⣴⣮⢉⠐⠠⠄⠁⢀⠀⠀⠀⠀⡞⠉⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡿⢻⠿⢏⠢⡀⠘⣿⡿⣟⠉⠉⣉⣷⠇⠀⠀⡠⠎⠀⠀⣿⣿⣿⣿⣿⣿ ⣿⠿⡟⠀⠀⠣⠀⠱⡄⠑⢌⡢⠌⠩⠉⠭⠘⢀⡔⡏⠣⡀⠀⠈⣿⣿⣿⣿⣿⣿ ⠁⢠⡇⠀⠀⠀⠈⠂⢜⢦⠀⠈⠒⠤⠤⠤⡲⡝⠁⡇⡠⢾⠤⣀⣿⣿⣿⣿⣿⣿ ⠀⠸⠘⡀⠀⠀⠀⣰⠉⡇⠑⢄⠀⠀⠀⡠⢱⢹⢀⠗⠁⢸⠀⠀⠉⠙⠛⠻⠿⣿ ⠀⠀⠀⠐⠀⢀⠼⣿⣿⣍⠐⠠⡑⠤⠰⠥⢊⠎⠼⢧⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣄⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡙⢆⠀⠀⠀⠀⠀⠀⠘⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣶⣄⠀⣼⡄⠀⢠⠀⠀⠹⠈⠀⠀⠀⠀⠀⢠⣼⠇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣇⠐⣆⣀⢘⣀⣢⣤⣄⣀⣁⣼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⠃⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣧⣀⣿⣿⠏⡞⠀⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⣟⣿⣯⣀⠃⢀⣿⣿⣿⣿⣿⡏⠀⢻⣿⣧⠔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠋⢯⣿⣿⣿⣿⣿⣿⣿⠿⢿⡀⠀⢼⣿⡿⠛⠻⣿⣾⣿⣿⣿⣿⢿⣥⣴⣾⣿⣤⡶⠚⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣇⠘⣿⣿⣿⣿⣿⣿⠏⠀⠀⠉⠒⠂⠙⠒⣀⣀⣈⣿⣿⣿⣿⢛⠘⠟⢉⣟⣻⣿⣃⡀⢺⣿⣿⣿⣿⣿⡟⠉⠉⠉⠙⠛⠛⠛ ⣿⣿⣿⣿⣿⣆⣟⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠊⡼⢃⡾⠉⢠⠀⠀⠉⠁⠀⠀⠀⠀⠘⢹⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣤ ⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢀⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⣴⡒⠒⠒⠤⠄⣀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣇⠀⠀⠀⠀⣼⣿⣿⣧⣠⣦⣤⣤⣄⣈⣉⡐⢢⡶⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣇⠈⠳⣄⠀⠀⢻⣿⣿⣿⣿⠉⠉⠉⠀⠀⠉⣿⣿⠁⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠏⠀⠈⢷⡇⠈⠳⣄⠈⠓⢤⡀⠻⣉⠁⠹⠧⠤⠤⠴⠾⠟⠹⡇⠀⠀⢀⠴⣾⠁⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠟⢿⠃⠀⠀⠀⠈⠣⡀⠀⠘⢶⡀⠀⠙⠢⣌⠑⠒⠀⣐⣂⣀⡒⠒⠈⠀⣠⡖⠙⡆⠈⠳⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠀⢀⣿⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠻⣄⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⣀⡴⢋⡿⠁⠀⡇⠀⢀⣜⣧⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢈⣲⡌⠳⡀⠀⠀⠀⠀⠉⠉⠉⠉⢁⠏⣹⣇⠀⢀⡇⣠⠋⢹⡏⠉⠓⠦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⠇⠘⡄⠀⠀⠀⠀⠀⠀⣠⠋⠀⢧⠀⠈⢣⡀⠀⠀⠀⠀⠀⢠⠌⢸⡏⣿⡇⣸⠟⠁⠀⠘⡇⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⣿⣿⣿ ⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⢀⣼⣿⣷⣤⠾⠤⣀⠀⠙⠦⣀⠀⠀⢠⡟⢀⣾⣦⡿⢰⣿⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙ ⠀⠀⠀⠀⠀⠀⠡⠀⠀⢠⠾⠿⣿⣿⣿⣦⡀⠀⠈⠑⢄⠈⠓⠦⠿⠖⠋⢁⠾⠇⢸⠛⠻⠠⣄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡽⠇⠀⣀⡀⠀⣀⣀⣀⣀⣀⠀⠀⠈⠉⠿⣦⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣠⣾⣿⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⢻⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡙⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢹⣿⣿⣿⣿⣿⣿⠋⠛⣿⣇⢸⣿⣿⣿⣿⢃⣿⣿⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣄⣀⣿⠀⢹⡿⢿⣿⣿⠋⠙⡟⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢿⣿⣿⡟⡇⠀⣶⡟⠙⢼⠃⠘⣿⣿⠀⠚⢩⣯⠍⠉⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⢺⣿⣿⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⣿⠀⠀⠈⠋⠀⠐⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⠀⣀⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡸⠉⢿⡄⠀⠀⠀⠀⠀⠀⠀⣄⠀⠈⠃⠀⠀⠉⠀⠀⠀⡿⣿⠿⠟⢹⣿⠏⠀⠼⠟⠛⠓⢾⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡈⠳⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠟⣀⠔⠓⠿⠂⠀⠚⠀⢀⠈⢀⣿⣿⣿⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣤⣀⠀⠀⢀⣶⡞⠏⠓⠢⣴⣔⡶⢶⣤⡀⢉⣿⡿⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⢻⣿⡟⠙⣦⡀⠀⠘⠻⠿⠿⠶⠶⠞⠓⠻⠛⠁⠀⣀⣾⠋⡇⠀⠀⢀⢀⠈⠛⠷⠷⣾⣷⡿⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⢸⡟⠁⢨⡏⢸⠷⣄⠀⠀⠀⠠⠤⠄⠂⠀⢀⡠⠞⣩⠃⠀⢷⠀⢀⣿⣿⠇⠀⠀⢀⣻⣿⡇⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⣿⣧⢀⣾⠃⠈⣧⡌⢳⠢⢄⣀⣀⣠⠤⠒⠉⢀⡴⠃⠀⠀⣾⠀⣼⣿⠇⠀⠀⠀⠀⣿⣿⠃⠀⠢⣀⣄ ⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⣿⡇⣼⣿⠀⢀⣼⣷⡈⢳⠀⠀⠀⠀⠀⢀⡖⢹⣷⠀⠀⠀⠙⡖⠛⡟⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠈⠁ ⠀⠀⠀⢠⠖⡇⠀⢀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠙⢻⡟⢷⡄⠀⠀⠀⢀⣰⡿⠖⣻⣿⣷⡀⢀⠀⠻⠦⠇⠀⠀⠀⠀⣯⣽⠁⠀⠀⠀⠀⠀ ⠀⠀⢠⢏⣾⠀⠀⠘⡀⠀⠀⢰⣿⣼⣿⠁⠀⠀⠀⢣⣄⡙⠦⠤⠴⠋⠁⣡⣿⣿⡧⠆⠝⠈⠀⠀⠀⠀⠀⠀⠀⠀⢉⠁⠀⠀⠀⠀⠀⠀ ⠀⣴⠃⠸⡌⣇⠀⠀⢳⠀⠀⣾⣿⣿⠇⠀⠀⠀⠀⠀⢹⣿⣷⠀⠀⢠⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀ ⡶⠃⠀⠀⠹⣾⡄⠀⠈⢆⣸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⠀⠀⠀⠀⠈⠛⠆⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⢣⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢳⡀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠛⠶⣤⣀⣿⣿⣿⢣⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡷⣼⣧⡀⠀⠀⠀⠀⠀⠀

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