Ankha Dot Art

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

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