Candy Dot Art

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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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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣹⣿⠇⠀⢀⡤⠞⢻⣀⣤⠼⠛⠙⣠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢉⣉⣉⡻⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣿⡟⠀⡴⠋⢀⣠⣼⠊⣦⠀⣴⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡿⢁⡼⠃⠀⠀⠹⡿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣇⠀⢀⣴⣿⣿⣷⡄⣧⠈⠙⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡷⣤⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠋⠀⠚⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣶⣿⣿⡿⠋⠀⢻⣹⡄⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠛⢿⢢⠼⠙⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠁⠀⠀⢠⣦⣄⡀⢠⣤⡀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣿⣿⣿⣿⣁⣀⠀⠈⣀⠀⠀⢀⡀⠀⠀⣠⣖⣓⣶⣦⣤⡠⣖⣋⠥⣶⠚⠀⠀⠀⠀⠀⠀⠘⠛⠿⠟⠀⠀⠀⠠⣾⠁⠀⠁⠀⣻⡇⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⠟⠁⠀⠉⠙⠲⣬⣆⠀⠸⣇⠀⢘⡹⠟⠋⠉⠉⢉⡄⠗⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢀⣯⡇⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⠃⠀⣠⣶⣿⣿⣿⣿⢻⠀⠀⠈⠀⠀⠙⠦⠤⠤⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡤⠚⠊⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠳⣤⢾⡿⠋⠀⢀⣀⣼⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠋⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣾⣗⠖⠚⠉⡵⠋⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢨⡟⠁⠀⢀⡜⠁⣸⠁⠀⠀⠀⠀⠀⣤⠤⣼⠛⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⢴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⠀⠀⢀⡞⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠀⠀⠙⠢⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⢸⠃⠰⡟⡤⡀⠀⢀⣴⠖⠒⠒⠲⠋⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣇⠀⠀⢿⣠⡄⠛⠛⠛⠂⠈⠙⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⢧⢹⡄⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣆⠀⢸⡇⠀⠀⠀⠀⢀⣠⠤⠴⣖⣛⣫⣭⣽⣿⣿⣽⣷⣦⣄⣸⡇⡇⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣄⠈⢧⠀⠀⡴⣞⣍⣁⣴⢶⠿⢿⠏⡟⠁⣿⢸⣅⣿⣼⣏⡇⡇⡇⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣆⠘⢦⡀⣧⣿⣿⡋⠙⠀⣂⣸⣧⣿⣿⣿⣿⣿⣿⣿⣿⠁⠃⡇⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠙⣮⢿⠻⣿⣾⣿⣿⣿⣿⡿⠛⣿⣹⠿⠛⣰⠃⠀⠀⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠈⢿⣳⡌⠻⠿⠯⠥⠼⠗⠋⠉⢀⣀⠴⠃⠀⠀⢸⢇⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢳⡙⠲⠤⠤⠤⠤⠖⠒⠚⠉⠁⠀⠀⠀⢠⡏⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠘⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡝⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⣀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢯⠙⠲⣖⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠉⠳⢄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠘⣇⠀⠈⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠈⠲⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠰
⠀⢀⡔⠛⠒⠒⢛⣰⣶⠤⣤⡒⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⢸⡟⡁⠲⢒⠂⠹⠉⠀⠈⢥⡔⡉⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢁⠊⠓⣎⠀⠁⠀⠢⡀⠀⠀⢸⠒⢃⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠹⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡗⠀⠀⠀⣀⡠⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⡠⠔⡟⠀⠀⢀⡰⠁⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⡥⣠⠴⡗⢴⣇⠀⠀⠀⠀⠀⢀⡄⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠋⠀⠀⣱⡈⠛⠉⠉⠂⢴⠴⠞⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠁⢧⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠡⡀⠙⣇⠀⠀⡴⠁⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣉⡦⠄⡓⢰⠋⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡿⢇⡩⢀⡤⠤⠼⡄⠀⠀⠀⠀⣠⡟⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠱⣀⣀⣄⣶⠏⠙⠲⢬⣉⠫⠶⢶⣤⣄⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⡾⠁⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⢉⡻⢦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⡇⡀⢀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢼⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⢀⣀⣴⡽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠿⠻⠿⠿⠭⠭⢭⢭⠿⠛⠀
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠉⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⡀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠁⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣧⠀⠹⣆⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⢤⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠈⠳⢦⣀⠀⠀⠀⠈⠳⢦⣀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡔⠚⠋⠁⠀⠀⠀⣀⣀⣠⣤⠖⠚⠋⠀⡼⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠈⠙⢷⡦⣤⣀⠀⠉⠙⠛⠦⠤⠤⣤⣀⠀⠀⢀⣴⣿⡅⠀⠀⠀⢀⡴⠞⠉⢉⣥⠞⠁⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠙⢦⡉⠓⢦⣄⡀⠀⠀⠘⣿⣿⣷⣶⣿⣾⣯⢞⣦⣤⣦⣿⡤⠖⠛⠉⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠙⠲⣄⣨⠷⣄⡀⢀⣷⣿⣛⣿⡯⡿⠿⠿⠋⣿⠏⠁⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡄⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣀⣀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢹⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠘⠋⢷⠀⠀⠀⠀⠀⠀⠀⣀⣼⠁⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⠓⠒⢿⣠⡀⠀⠀⠀⢀⠀⣿⠧⠤⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠸⣿⢳⠀⣀⠀⡿⣿⠃⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⣷⣿⣾⡇⠉⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠈⠿⢇⣽⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢾⠃⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⣻⠉⠁⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠙⢯⡓⠒⠲⠶⠶⠦⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠊⠁⠀⢠⡇⠀⠀⠀⠀⠈⠑⠦⣀⣀⣀⣀⣀⡀⠀⢀⣠⠖⠁⠀⠀⠉⢳⡀⠀⠀⠀⠀⠀⠈⠉⠙⠲⠦⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠋⠁⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀ ⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀ ⠀⢀⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇ ⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⢀⣀⠴⣶⠲⠶⠀⠀⠀⠀⠈⣿ ⢸⡇⠀⠀⠀⠀⠙⠻⡶⠶⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣓⣦⣄⣀⣠⠴⠟⠉⠳⠤⣀⣀⣠⣴⣋⣀⣠⠤⠶⠚⠋⠉⠀⠀⣿⠀⢀⣀⣀⣀⣠⣐⣿ ⠘⢿⡀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠉⠙⠛⠛⠒⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣭⣿⣷⣿⣷⣤⡟ ⠀⠈⣷⠶⢦⣤⣶⣒⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⣛⣿⣿⣿⠿⣾⡇ ⠀⠀⠸⣿⣻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⢸⠃ ⠀⠀⠀⢿⡉⠉⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⡼⠀ ⠀⠀⠀⠀⢧⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⡇⠀ ⠀⠀⢰⡶⣜⣧⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣸⢻⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣾⣿⣿⣿⣿⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⣿⣿⣿⠏⡩⠭⢛⡿⠿⣿⣿⣿⠿⢿⣛⣛⣛⠛⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⢻⣿⣿⡟⠠⠥⣤⣥⡚⠡⠴⠶⠤⠍⠒⣨⣽⠟⢅⢻⣿⣇⣠⣀⠀ ⢀⣠⠤⠬⣿⣿⠁⠂⠀⠈⠉⠉⢄⠀⠀⠀⢀⠌⠉⠁⠀⠸⢸⠟⣡⠤⠈⡇ ⡎⢠⠶⠦⢌⠻⡄⠀⠠⠂⠉⠁⢢⢃⠀⠀⡬⠂⠉⠁⢢⠀⡏⠜⢁⠔⣰⠁ ⠹⣄⠢⢀⠀⢀⢳⠀⢇⠛⠃⠀⢀⢸⠀⠰⢇⠙⠃⠀⣠⢀⡰⠂⣡⠞⠁⠀ ⠀⠈⠙⠲⠬⡽⠁⠀⠀⠐⠒⡶⠤⠈⠀⠀⠀⠱⡖⠁⠤⡀⠀⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡀⠀⠀⠖⠺⢦⣀⠀⠀⠀⢀⣴⠏⠊⠍⠀⢠⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⠤⢌⡂⠤⠈⢣⢄⣤⠊⠤⠐⢁⡤⠚⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠀⡇⢠⠼⢏⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠋⠎⢱⡈⡧⠘⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠄⠘⢔⠃⠐⠄⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠻⣿⣿⣿⣿⣿⣤⣷⡀⢠⣤⣄⠀⠀⠀⠀⡈⠻⠶⢦⣼⣤⣿⣿⠋⣨⣤⠆⢠⣠⡾⢋⡤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡙⢿⣿⣿⣿⣿⣿⣿⣦⣬⣿⣿⣿⣷⣀⠁⣄⢀⣤⣉⣸⣿⡟⣀⢠⡟⣣⣾⣫⡶⠛⠁⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⡏⠉⠙⠛⠛⠋⠛⠟⡿⠿⠿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣀⣩⣟⡿⣿⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⣤⠀⣲⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣏⣈⠀⠉⢀⠀⠀⠀⢀⠀⢰⡀⣠⠗⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣟⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠏⠈⠙⠲⠀⠳⠄⠐⣮⠒⠼⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⠛⣽⣿⣿⣿⣿⣿⣿⡿⣾⡶⢆⠀⠀⠀⠀⠀⠀ ⣿⡆⠐⠶⡀⠀⠈⢢⠈⠉⠲⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣧⣤⠊⠀⠀⠀⠀⠀⢠ ⡿⠀⠀⠀⠀⢠⡀⠀⣲⣶⣾⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠂⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⠀⠀⠸⣿⢼⣿⣿⣿⣿⣿⡿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢠⣾ ⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⡟⣋⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣹⡿⣿⣿⣿⣿⣷⢹⣿⠻⣿⣿⣿⣿⣿⣿⣶⣠⣼⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠙⣿⡿⣿⣿⣿⣿⣿⣏⣼⠏⠀⣼⣿⣿⣿⣿⣿⣿⣿⣅⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠈⠁⠀⠀⠉⠉⠉⠉⠀⠀⠾⢷⣿⣿⣿⣿⣿⣿⣿⣿⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣏⣩⣄⠀⠀⠀⠀⠀⠀⠸⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⢸⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⡿⠃⠀⠀⠀⣾⣷⠶⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠈⠛⣆⠀⡀⢤⠞⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠿ ⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡀⠒⠢⠤⠄⠀⠀⣨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠛⠷⠾⣿⣷⣾⣶⣿⡿⣧⣧⣴⣦⣠⣄⣀⣀⣀⣀⣀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠙⠳⠦⠀⠀⢀⠁⣉⠭⠍⠉⠩⠟⠛⠇⠀⠀⠀⠘⡗⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀
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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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