.⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀ ⠙⠿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠙⣿⣿⣿⣟⠁⠀
⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠟⠁⠀⠀⡼⠟⠉⠙⠿⡄
⠀⠀⠀⠀⠀⠀⢀⣿⠟⢿⡆⠀
⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠙
⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⣤⣀⣼⣧⣀⡠⠀
⠀⠀⢹⣿⣿⡍⠀⠀
⠀⠀⠋⠀⠈⠳⠀⠀⡀⠀
⠀⠀⠀⠀⠀⠠⣀⣀⣿⣀⣀⡄⠀
⠀⠀⠀⠀⠀⠀⠈⣽⣿⣏⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠉⠂⠀⢠⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣾⣷⠖⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠋⠙⠆

⠀⠀⠀⣠⣤⡶⠶⠿⠷⠶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢄⠀
⣠⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠗⠋⠁⠃
⠉⠀⢀⡠⣄⡀⠀⠀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠋⠁⠀⠀⠀⠀
⠀⡰⢾⣿⣾⣿⠿⠿⢻⡿⢿⣿⡻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣴⣆⠀
⠀⡛⠛⣿⡇⠀⠀⢀⣿⣥⣿⣿⣷⡽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⣿⠿⠛⠀
⠈⣽⣿⣧⢙⣶⣤⣸⡇⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣽⣿⣷⣿⡀⠀⠀
⠀⠀⠙⠻⠟⢻⣿⣇⡳⣤⣈⢉⣡⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⢳⣭⣵⣿⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⣤⣤⠴⠾⠃⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣴⣾⢟⣿⣛⣻⣿⣿⣿⣿⣿⣿⡿⢿⣯⣿⣿⡉⠓
⠀⠠⢺⣴⣾⣿⣿⠗⠁⠈⠉⠉⣛⣛⣛⡛⢋⣑⣤⣾⣿⣿⣷⣷⣿
⠀ ⠀⡾⠃⣼⣿⡟⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⡛⠻⡿
⠀⠈ ⠀⢰⣿⣿⠗⢉⣉⠉⢿⣿⡋⠉⠉⣙⠛⠻⣿⣿⣿⣿⣿⢄
⠀⠀ ⣖⢿⣿⠟⣴⡧⣼⣷⢋⣿⣧⡠⣿⣉⣷⣤⣿⡿⣿⣿⣿⣆⠁
⠑ ⠀⣯⣾⣿⣾⣿⣿⣿⡇⢺⣿⣿⣿⣶⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿
⠓⣷⣿⣿⣿⣿⣿⡛⣉⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿
⢠⣾⣿⣿⣿⣽⣽⣯⣉⡉⠉⠉⠉⠛⣻⣿⣝⢻⣼⣿⣏⠈⠙⢿⣿
⣾⣿⡟ ⠁⠀⠘⡟⠿⠿⣷⣶⣶⣿⣿⣿⠿⣿⡆⣿⣿⠀⠈⠓⢶⣿
⡿⠟ ⠀⠀⠀⢀⣿⣇⡀⠀⠀⠀⠀⠀⠀⣠⡤⣽⣿⣿⠀⠀⠀⠘⠋
⠀⠀ ⠀⠀⣮⣿⡿⠿⣶⢤⣤⣴⣾⣿⣿⣷⣿⣿⣿⣆
⠀⠀ ⠀⠀⠠⠹⣿⣿⠀⠀⠀⠀⣀⣤⣿⣿⠿⣿⢿⣿⣿⡄
⠀⠀ ⠀⠀⠀⠂⠈⠃⠀⠀⠀⠀⠛⠛⠉⠁⠀⠀⠈⠛⠛⠛⠂

⠀⠀⠀⠀⠀⢀⣴⣾⢟⣿⣛⣻⣿⣿⣿⣿⣿⣿⡿⢿⣯⣿⣿⡉⠓
⠀⠠⢺⣴⣾⣿⣿⠗⠁⠈⠉⠉⣛⣛⣛⡛⢋⣑⣤⣾⣿⣿⣷⣷⣿
⠀ ⠀⡾⠃⣼⣿⡟⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⡛⠻⡿
⠀⠈ ⠀⢰⣿⣿⠗⢉⣉⠉⢿⣿⡋⠉⠉⣙⠛⠻⣿⣿⣿⣿⣿⢄
⠀⠀ ⣖⢿⣿⠟⣴⡧⣼⣷⢋⣿⣧⡠⣿⣉⣷⣤⣿⡿⣿⣿⣿⣆⠁
⠑ ⠀⣯⣾⣿⣾⣿⣿⣿⡇⢺⣿⣿⣿⣶⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿
⠓⣷⣿⣿⣿⣿⣿⡛⣉⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿
⢠⣾⣿⣿⣿⣽⣽⣯⣉⡉⠉⠉⠉⠛⣻⣿⣝⢻⣼⣿⣏⠈⠙⢿⣿
⣾⣿⡟ ⠁⠀⠘⡟⠿⠿⣷⣶⣶⣿⣿⣿⠿⣿⡆⣿⣿⠀⠈⠓⢶⣿
⡿⠟ ⠀⠀⠀⢀⣿⣇⡀⠀⠀⠀⠀⠀⠀⣠⡤⣽⣿⣿⠀⠀⠀⠘⠋
⠀⠀ ⠀⠀⣮⣿⡿⠿⣶⢤⣤⣴⣾⣿⣿⣷⣿⣿⣿⣆
⠀⠀ ⠀⠀⠠⠹⣿⣿⠀⠀⠀⠀⣀⣤⣿⣿⠿⣿⢿⣿⣿⡄
⠀⠀ ⠀⠀⠀⠂⠈⠃⠀⠀⠀⠀⠛⠛⠉⠁⠀⠀⠈⠛⠛⠛⠂

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