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