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