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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡖⠉⠉⠃⠀⠀⠉⢣⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⡟⠓⠋⠙⠢⣄⠀⠀
⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⢱
⠀⣶⠒⠒⢺⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡠⠞⠁
⣰⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠒⠒⠒⠒⡏⠉⠀⠀⠀
⢣⠃⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀
⢻⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀
⠀⠓⠦⠀⡏⠀⠀⠀⠀⣮⠉⢳⠀⠀⠀⡸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⡏⠀⢘⠁⠀⠀⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠠⣃⡀⠀⢠⢼⠀⠀⡇⠀⠀⡜⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠱⠴⠋⠀⠀⠀⠸⣄⢀⡇⠀⠀⠀⠀⠀⠀
⬜➖⬜⬜⬜⬜⬜⬜➖⬜
⬜ ඞ ⬜
˚ ҉✧ෆ ҉*₊( ‾ ʖ̫ ‾)₊* ҉ෆ✧ ҉˚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⢀⣀⡀⢄⣀⣀⣀⠀⠠⠀⠒⠀⠈⠉⠛⠩⡉⢂⠑⡄⠀⠐⠒⠂⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⢢⠀⠀⠀⢀⠄⢊⠜⠋⠉⠁⠀⠀⠀⠀⠀⡠⠒⠉⠀⡠⠃⠑⠺⢄⠀⠀⠀⠀⠉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠑⣄⠈⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⢀⠀⠀⠘⠰⣆⠀⠀⠀⢢⠀⠀⠀⠂⠤⢄⡀⠈⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣸⠊⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⠊⡰⠃⠀⠀⡆⠀⣏⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠈⠁⠣⣔⡈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⢁⠀⠀⠀⠀⠀⢀⠄⢀⠞⠀⢆⡜⠁⠀⠀⢰⠅⡀⠹⡇⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠚⠦⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡡⢋⡔⠁⠀⠀⠀⡰⢀⠎⠠⡝⠀⢸⡜⠀⠀⠀⢀⢃⢡⢣⠀⢣⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢐⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠮⡎⡝⠀⠀⠀⢀⡞⠁⡞⢠⡝⠀⠀⣿⠃⠀⠀⠀⡜⡌⡜⡼⣆⠈⢣⠀⠀⠀⠀⠈⠀⣀⣀⠀⠀⠀⠠⠄⠂⢁⠔⠋⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠊⠁⡜⡌⠀⠀⠀⢒⠞⢲⠸⢧⣿⠁⠀⢀⡟⠀⢀⠆⢠⠡⡰⡇⡘⢿⣦⡀⠣⡀⠀⠀⠀⡆⢢⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡙⠀⢠⠁⠀⡌⡄⣎⡗⡡⡌⠀⠀⡼⠇⠀⡜⠀⡬⢤⠧⣇⢱⠀⠑⠱⢄⡈⠢⢄⠀⠇⢢⢣⠀⠀⡠⡪⢲⡆⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⢠⡇⠀⡜⡠⠐⢹⡌⠀⡇⠀⢰⢸⠀⢀⠇⡷⡆⠸⠀⡇⢩⠂⢄⠀⠀⠈⠁⠀⠀⠁⡎⡆⡤⢊⠔⠀⠀⣇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢣⠀⣞⠁⢰⣯⣤⣤⡘⢅⠀⡇⠀⡄⡀⠀⢸⢠⢃⢀⡇⠀⣠⢨⠀⡇⠁⡆⠀⠀⠀⠀⠀⣇⠏⡗⠁⠀⠀⠀⢹⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⢞⢰⢸⠀⡘⢈⣶⣶⣾⣵⠀⢳⡇⡇⡇⠀⢸⡎⣌⠸⠥⡀⠉⡄⠀⡇⠀⠀⠀⠀⠀⠀⠚⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⡏⢸⠀⡀⣇⢸⠉⢻⡽⢟⠁⠘⢷⢻⡅⠀⣺⣿⣭⣭⣿⣰⢤⣱⠀⠃⢀⡀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢰⡏⠀⣇⡿⡦⣃⡘⣁⠎⠀⠀⠈⢻⠱⡀⠘⠛⠿⣟⣻⣿⡷⡝⣷⠀⣸⠀⠀⢸⢀⢲⠀⡆⢰⠀⠀⡇⠀⢠⡇⠀⡸⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣀⡏⣇⢞⢼⠉⠑⠈⠀⠀⠀⠀⠉⠻⢄⣆⠸⣻⠟⠁⠹⠅⣸⢀⡋⠀⠀⡎⡸⡈⠰⠀⡛⠀⢠⠇⢀⢳⠁⢰⢁⢼⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⢠⠎⠉⠐⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⢹⠊⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣘⠢⢤⣠⡔⣎⠀⡇⡌⠃⠀⡸⢠⢣⡇⢆⢠⠁⢠⢻⠀⣌⣸⠀⢃⠎⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⢸⣆⠀⠀⠀⠀⢸⠃⠀⠀⢰⠉⠑⠤⠃⠀⡇⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢲⣿⡟⣾⣾⡦⠱⣸⣿⠘⠀⣰⡡⠁⠸⣇⢀⠇⠀⠎⡌⣼⡪⢷⠸⠃⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠙⠲⠤⠄⠀⠎⠀⠀⠀⠈⢆⢄⠀⠀⢠⠃⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠈⠉⡝⠚⠿⠃⠆⡝⡝⡆⡴⠟⢁⠂⢀⢋⣬⢀⢊⡜⡼⠋⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⣣⡘⡀⠀⡎⢀⡧⠂⡏⡰⢱⠊⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠤⠐⠂⠈⠋⡏⢱⢠⣿⡇⣬⣀⠀⢷⠁⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡉⠀⠀⡇⠀⠀⠀⠉⠀⠉⠉⠉⠉⠉⠁⣠⡔⠛⢆⠰⡼⣣⠀⠀⠀⠀⠀⠀⡠⠊⠀⡇⣿⣾⠛⠳⠇⠶⣭⣺⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠴⠿⡷⡀⠘⡄⢻⡿⠆⠀⠀⡠⠔⠁⠀⠀⣀⣿⣽⠟⠠⠠⠐⠂⠙⠋⣁⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠱⡹⡄⢱⠈⣿⠘⡆⠁⠀⠀⣠⡖⠟⠋⣉⠠⠄⡀⠒⠂⠀⠋⠁⠩⣃⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢵⣿⡄⡇⢹⠘⠀⢀⣴⠟⢉⠤⡚⠭⠐⠈⠀⣀⠀⠠⠤⠀⠐⠂⠉⠉⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠸⡀⠀⠀⣸⣿⣿⣤⢸⠀⡴⠋⣠⡾⢛⠭⠔⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠀⠀⠐⠒⠤⢄⡀⠀⠀⠐⡀⡵⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⡇⠀⠀⠀⠀⠀⠀⠀⢻⡇⠉⢻⣰⠊⣠⠾⠓⠉⠀⢀⡀⠀⣀⣤⣀⡀⠀⠀⠀⠀⠒⠂⠤⠤⢐⣣⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠸⣿⠡⠀⠀⠉⠉⠉⠉⠉⢩⣿⢼⡟⣅⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠠⠀⠀⠀⠉⢢⡀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢀⠁⠀⡄⣿⠀⠀⠀⠀⠀⠀⠀⢠⡿⣹⠀⢰⠸⡀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡰⠁⠀⠀⠀⣀⠔⠊⠁⠈⠉⠒⠠⠔⠊⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡇⠀⠀⠀⢸⠀⠀⣧⠁⠀⠀⠀⠀⠀⠀⢀⢧⠃⣿⠀⠈⡀⡇⠀⠀⠀⢀⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡜⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡇⠀⠀⠀⠘⠀⠀⣋⡇⠀⠀⠀⠀⠀⠀⡸⡜⠀⢻⠀⠀⡇⢣⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠘⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠒⠒⠒⠒⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠁⠀⠀⠀⡀⠀⢰⡿⡇⠀⠀⠀⠀⠀⠀⡇⡇⢰⢸⣰⠀⢱⢸⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡇⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⢸⣷⠁⠀⠀⠀⠀⠀⢠⢻⠀⡘⢸⣷⣀⠼⣼⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢐⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⡇⠀⠸⣯⠀⠀⠀⠀⠀⠀⠸⡾⠿⣿⡟⢽⠁⠊⢡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠤⠤⠼⠀⠀⠀⢸⠠⠤⠤⠤⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡼⡇⢸⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠆⠀⠀⠀⡆⠀⠀⠀⢇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡜⠀⠀⠀⠀⠸⡀⠀⠀⠀⠣⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣞⡘⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⢈⠓⢄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠜⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⡠⠊⡜⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠠⡀⠑⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠇⠀⠀⣸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⢀⠜⠀⠀⠀⠀⠀⠀⡠⠊⠀⡰⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⡄⠸⠀⢠⢀⠂⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡠⠃⠀⠀⠀⠀⠀⡠⠊⠀⠀⡰⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠄⠀⢣⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠄⠀⠀⠘⠈⠄⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⣄⠜⠀⠀⠀⠀⠀⡠⠊⠀⡠⢀⡌⠀⡠⢠⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠈⠄⠀⠀⢇⠈⢆⠰⡀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⢀⠠⠀⢁⠔⡙⠀⠌⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⡄⠀⠈⠀⠀⠘⡄⠀⢂⢣⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠂⠁⠀⡠⠂⠰⠁⠌⠀⠀⠀⠀⡼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢡⠀⠀⠀⠀⠀⢇⠣⠀⠊⠆⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⢀⠃⡜⠀⠀⠀⠇⢜⠠⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⡄⠀⠀⠀⢸⠘⡀⠡⡀⠨⡄⠀⡘⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⡌⠰⠁⠀⠀⢠⠌⡜⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠆⠀⢃⠀⠀⠀⠘⡄⢃⢀⠘⢄⠈⢲⠁⠀⠀⠀⠀⠄⠊⠀⠠⠐⠈⠀⡸⢠⠁⠀⠀⡠⠊⠰⠀⠀⠀⠀⡗⡄⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠄⠈⡄⠀⠀⡀⣇⠘⡀⠑⢄⠑⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⢃⠂⠀⠀⠔⠁⡰⠁⠀⠀⠀⠀⡇⠘⡄⠀⠀⠀⢀⠔⠁⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠄⠘⡀⠀⠀⡇⢀⠰⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⡠⠊⢀⠔⠁⠀⠀⠀⠀⠀⡇⠀⠘⠄⢀⠔⠁⠀⠀⠀⢈⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢂⠀⠀⠀⢸⡄⢂⢁⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠊⠀⠐⠁⠀⠀⠀⠀⠀⠀⢀⠀⠠⠠⡈⠅⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⢸⢁⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠑⡈⠄⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠺⣏⠳⣄⠀⠀⠀⠀⠀⠀⣘⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⠜⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠁⠀⠀⡇⠉⠺⣛⢦⠤⠤⢶⣟⣽⡙⡵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠪⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠁⠈⡟⣻⡿⠑⢼⢞⢢⡀⠀⠀⠀⠀⠀⠀⠀⢁⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢧⡂⠄⢀⠀⢀⣼⢰⠋⠀⠀⠀⠑⠍⣚⡷⠶⢲⡶⠶⠶⢿⡛⣿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⢪⠋⠀⠀⢠⣖⣢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢓⠢⠤⠤⣬⢞⢆⠀⠀⠀⠀⠀⠀⠈⠁⠀⠛⠒⠀⣡⣾⠘⣦⣕⠤⡀⠀⠀⠀⣶⡆⠀⣶⡦⠀⠀⠀⠠⢐⣤⢶⢾⢿⡔⠁⠀⠀⣰⡟⠀⠀⠈⠁⠘⠲⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠀⢰⢰⢡⠂⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⡱⢡⠊⠁⠀⠁⡈⢆⠀⢀⣀⡀⠀⠉⠀⠀⠀⣀⡴⠛⢹⠀⠀⠸⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠈⠑⢏⠡⠶⠤⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣸⠈⣼⢁⠂⠄⢀⠙⢢⣀⣀⣀⣀⣀⠀⠀⠠⠤⣧⠇⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠻⢆⠴⠛⠁⠀⠀⡏⠀⢠⠃⢒⡮⠋⠁⠙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣿⣰⠂⠄⠎⣠⡏⣰⣟⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡰⠁⢀⠊⠀⠀⠀⠀⢘⡌⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⡜⣼⣿⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡪⠁⡴⠃⡀⣀⢄⡐⠠⠅⠒⠒⠂⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠳⣠⠄⡀⠀⠀⠀⣀⠀⡀⠀⠐⠒⠊⢉⣉⣻⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠊⢁⠩⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠪⠤⡤⠥⠔⠒⠒⠒⠒⠈⠁⠀⠀⣼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⢤⡤⢶⠒⣰⣨⣧⡧⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠐⣦⡷⢟⣫⢷⡝⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡠⠄⠂⠀⠀⢀⡠⠜⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⢁⣀⣀⡀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢀⣀⣀⡀⠀⠀⠀⢀⣈⡰⠤⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀
⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠾⠟⠻⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠟⠛⠓⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀
⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠉⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀
⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣠⣴⣶⣦⡄⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⢠⣶⣶⣶⣦⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀
⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢰⣿⣿⣿⣿⣿⡄⠀⠀⣿⠻⠟⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⠁⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀
⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠿⣿⣿⣿⠟⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠙⢿⣿⣿⠿⠁⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⢧⡀⠀⠀⠀⠉⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀
⠀⡞⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠙⠢⢤⣄⣀⣀⣤⣶⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣷⣦⣤⣀⣠⠤⠔⠋⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⢸⡀
⠀⡇⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⡇
⢠⠃⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣷
⢸⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢻
⣼⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⢸
⢻⡀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⣼
⠀⢳⡀⠀⠀⠀⠀⠀⠉⠳⢦⣀⣀⣀⣀⣠⡴⠞⠋⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠙⠶⣄⣀⣀⢀⣀⣤⡴⠛⠁⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀
⠀⠀⠀⠀⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠲⠤⠤⢤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⡤⠤⠴⠒⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣠⠴⠞⠛⠉⠉⠉⠉⠉⠉⠛⠒⠾⢤⣀⠀⣀⣠⣤⣄⡀⠀⠀⠀
⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢭⡀⠀⠈⣷⠀⠀⠀
⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⢀⡟⠀⠀⠀
⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡅⠀⠀⠀
⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣀⠀
⣾⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠸⡇⠉⣷
⣿⠀⡰⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢆⠀⠀⠀⠀⠀⠀⣧⡴⠋
⣿⠸⣀⣈⡻⠋⠀⠀⠈⠓⠶⠶⠖⠛⠀⠀⠀⠙⢟⣁⣀⠇⠀⠀⠀⠀⢰⡏⠀⠀
⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣄⠀⠀
⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢸⡇⠀
⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠒⠚⠋⠀⠀
⠀⠀⠀⠀⠈⠛⠶⢤⣤⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⡤⣴⠚⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠩⣉⠉⠉⠉⣩⠍⠁⠀⢷⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡟⠐⠦⠤⠼⠂⠀⠸⠥⠤⠔⠂⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣧⡟⠳⠒⡄⠀⠀⠀⡔⠲⠚⣧⣀⣿⠿⠷⣶⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠻⣄⢀⠀⠀⡗⠀⠀⠀⡇⠄⢠⠀⣼⠟⠀⢀⣨⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⢶⠬⠴⢧⣤⣤⣤⣽⣬⡥⠞⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀