Sheep Dot Art

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡴⠊⠙⠚⠉⠁⠑⠦⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⣹⡀⠀⠀ ⠀⠤⠊⠑⠐⣠⣀⡀⣤⡤⠇⠂⠉⢱⣀⡠⠐⡨⣤⠀⢨⣵⢺⡁⠀⢁⡆ ⣞⠀⢀⡠⠊⠀⠀⢎⡁⠀⠀⠀⡠⠊⢠⠁⠘⠿⠿⠁⠈⠛⠋⡎⠉⠁⠀ ⠹⡀⡇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⡆⠀⢈⢠⠃⠀⠀⠀ ⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠲⠀⣻⠗⠁⠀⠀⠀⠀ ⠀⠈⡆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠱⡄⠀⠀⠀⠀⣜⡇⠀⠀⠀⠀⢀⠀⠀⠠⢀⡅⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠱⣀⣀⢀⡔⠘⣷⠀⠀⠀⠀⡮⡄⠊⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⠤⠴⡀⠠⣋⢦⠤⢤⠔⠀⢓⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠣⢄⣠⠥⠀⠀⡘⠀⠘⡄⠀⠢⢀⣈⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣀⣤⣤⣶⣦⣄⠀⠀⢀⣤⣴⣶⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣤⣴⣿⡟⠉⠛⢿⣿⣿⣿⠟⠋⠛⠻⣿⣷⣾⣿⠟⠉⠉⠉⠙⠛⢿⣿⣦⣴⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠉⠙⠿⢿⠇⠀⠀⠀⠙⠿⠃⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠿⠏⠉⠙⠻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣶⣶⣿⠏⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⢶⣶⣿⣿⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⡾⠟⢉⣡⣴⠿⢿⣿⡀⠀⠀⣸⣷⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⣤⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⣠⣿⣇⠠⣄⡉⠛⢷⣬⣉⠻⢶⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⡟⠃⣠⣾⠟⢉⡴⠞⢈⣿⣿⣷⣾⠿⠻⣆⠀⠀⠀⠀⣰⣿⣿⣧⠀⠀⣼⣿⣷⣤⣤⣤⣤⣿⠟⠻⣶⣾⢿⣿⢿⣦⡈⠻⣦⣄⠈⢿⣷⡄⠙⢻⣦⡀⠀⠀ ⠀⠀⣴⡿⠃⠀⣰⡿⣣⡾⠋⣀⣤⡿⣱⣿⣿⠏⠀⠀⠈⠙⠶⠶⠿⠿⠿⠛⠿⣷⣾⣿⠿⠋⠉⠛⠛⠉⠀⠀⠀⠀⠀⠘⣿⣦⡙⢿⣷⣄⣙⠃⠀⢻⣿⡆⠀⠹⣷⡀⠀ ⠀⣴⡿⠁⠀⢸⣿⣠⣼⣶⠾⠟⠉⣰⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣿⣦⡈⠙⠻⠿⠿⠿⠿⠇⠀⠀⢻⣷⠀ ⢰⣿⠃⠀⠀⠈⠉⠉⠉⠀⣀⣴⣾⠟⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡆⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠛⢿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⣿⡇ ⢸⣿⠀⢀⣀⣀⣤⣤⣶⡿⠟⠋⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠉⠛⠛⠿⠿⣿⣷⣶⡾⠿⠛⠁ ⠀⠙⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟⠁⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⣿⣿⡄⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⠉⠙⠛⠁⠀⠀⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠻⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⡃⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠸⣿⣿⣦⣄⠀⠀ ⠀⠀⠀⠀⣀⣤⣿⣷⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣶⣤⣄⣀⣀⣀⣠⣴⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⠀⠈⠙⠿⣿⣆⠀ ⠀⠀⢀⣾⣿⡿⠛⠋⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⠀ ⠀⠀⢸⣿⡏⠀⠀⠀⠀⠠⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⣰⣿⡏⠀ ⠀⠀⠈⢿⣿⣦⡄⠀⠀⢀⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠙⣿⣿⡄ ⠀⠀⠀⠈⠻⣿⣿⠏⠀⣸⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⢸⣿⣧ ⠀⠀⠀⠀⠀⢸⣿⡀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⠏⠀⢀⣠⣼⡿⠟ ⠀⠀⠀⠀⠀⠀⠻⣷⣦⣌⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠁⣀⣼⡿⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠿⠿⠿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄⣀⣀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣤⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡿⠿⠿⣿⣷⣄⡀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⣀⣴⣿⣿⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠹⢿⣿⣿⣶⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⠟⠛⢶⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠁⠀⠀⠈⠁⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⡄⠀⠀⠀⠀⠀⠀ ⢀⡾⠛⠛⠀⢶⣤⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⡶⠞⠛⠛⢳⡄ ⠈⣷⡀⠀⠀⠀⠈⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣼⠃ ⠀⠈⠻⣦⣤⣤⣤⡿⢷⡦⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⢿⣤⣤⣤⣴⠾⠃⠀ ⠀⢠⡾⠋⠁⢸⠏⠀⠈⢷⣤⣤⣦⠀⠀⣰⣤⣠⡼⠃⠀⠘⣧⠈⠉⢻⡆⠀ ⠀⢈⣷⡄⠀⣿⠀⠀⠀⣴⡄⠀⠙⠛⠛⠋⠀⢠⣦⡄⠀⠀⣿⠀⢠⣾⡃⠀ ⠀⣾⠁⠀⠀⣿⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣼⠀⠀⠈⣿⠀ ⠀⢘⣿⠆⠀⢻⡄⠀⠀⠀⢀⠀⠈⣳⣾⠃⠀⡀⠀⠀⠀⢀⣿⠀⠰⢾⡋⠀ ⠀⠘⣧⣀⡀⠈⣷⡀⠀⠀⠈⠛⠛⠋⠉⠛⠛⠉⠀⠀⢀⣼⠃⢀⣀⣸⠇⠀ ⠀⠀⠈⣿⠃⠀⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠾⠁⠀⠈⣿⠁⠀⠀ ⠀⠀⠀⠘⠷⢶⡖⠀⠈⠛⠶⣤⣤⣤⣤⣤⣤⠶⠛⠁⠀⢰⡦⠾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢷⣤⣴⡆⠀⠀⡀⠀⠀⢀⠀⠀⢠⣦⣤⡾⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠾⢻⣤⣤⡾⠷⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡠⠒⠈⠛⠊⠋⠑⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡎⠀⡀⠀⠀⠰⡀⠀⠐⣪⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡧⠀⠉⣓⠴⠊⠉⠉⢫⠀⠀⠉⣉⣲⠀⠀⠀⠀⠀⣄⠀⠴⠄⡀⡀⠀⠀⠀ ⠀⢀⡿⠓⠊⠀⠠⠾⠟⠁⠘⡖⠐⠚⣇⣀⢀⣀⠤⠖⠒⠒⠠⢄⡀⠀⠈⠑⡄⠀ ⣠⠯⠀⠀⠀⠀⠀⠀⠀⣠⠜⠀⠀⠀⢸⢆⠀⠈⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠄ ⢷⡤⠂⢀⠀⠀⣀⡠⠔⠁⠀⠀⠀⠀⡜⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠈⠻⠭⠶⠚⠛⡄⠀⠀⠀⠀⠀⠀⠈⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣵⠠⠤⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠻⡤⠄⢀⡠⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⡸ ⠀⠀⠀⠀⠀⠀⠀⢱⠖⠮⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠞⡞⠀⡀⡅ ⠀⠀⠀⠀⠀⠀⠀⠈⣗⠂⠤⠀⠀⠀⠀⠀⠀⢀⠀⠤⡔⠁⠀⠀⡠⡾⠠⠮⡾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢱⡩⠁⢄⠀⠀⠀⣀⠄⠂⠀⡴⠓⢶⠚⢹⡇⡇⠀⢀⡷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠀⣽⠉⠙⣦⠄⠀⣾⠁⠀⡼⠀⠈⡇⢹⠀⢸⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⡿⠀⠀⢻⠀⠀⢯⠀⠀⡇⠀⢠⡇⢸⠀⠈⢇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠂⠀⡇⠀⠀⢸⡆⠀⣾⠀⠀⠓⠓⠋⠀⡏⢀⠀⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⡿⠀⠀⢸⠇⠀⡏⠀⠀⠀⠀⠀⠈⠓⠚⠚⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢼⣰⣀⡼⠃⠀⢀⡞⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣰⣀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢴⢺⠳⣭⢟⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡔⠉⠀⡰⠺⣍⡿⢞⣖⢓⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⠀⢊⣄⢀⡈⠓⢺⡀⡾⢼⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠙⠀⢰⡀⡀⡠⠘⣭⣽⢿⣯⡖⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢡⢠⡀⠀⠀⣩⡞⡇⠀⣟⣖⢹⢭⣏⡏⣽⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡆⡛⣶⣲⣪⡟⡿⢍⣾⣞⣩⡟⠷⠔⢈⣄⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣻⣌⣖⡿⢮⢗⢵⣻⠧⣾⣮⣭⡽⡦⣼⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠦⠓⣔⣣⠭⣞⣳⠾⢏⣧⣛⠏⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⡏⡇⡵⠋⠁⠈⡍⡏⡏⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠇⠷⡦⠀⠀⠀⠷⠇⠱⠾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣀⡠⠤⣄⢀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠴⠦⡏⠀⠀⠉⠀⠀⠘⠋⠀⣷⣤⡀⠀⠀⠀ ⢀⡔⠉⠁⢀⣉⡲⠴⠒⠣⢄⠀⢀⡠⠄⣀⡀⠀⠀⠀⠀⠀⢀⣟⣀⠀⠀ ⠈⠓⠒⠂⣹⡟⠋⡑⣤⠤⠤⣻⡵⢤⣀⠀⠈⡆⠀⠀⠀⠀⠀⠀⢸⠇⠀ ⠀⠀⠀⣰⠃⠑⠬⠗⢟⠇⢀⠇⡇⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⢻⡄ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠁⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀ ⠀⠀⠀⢧⠰⠂⡦⠀⠀⢀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠟⠀ ⠀⠀⠀⠈⠓⠦⠤⠴⠒⢯⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡼⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢶⠂⢠⡀⠀⡀⠀⡀⠀⣄⠀⣦⣤⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⡟⠓⠚⠧⠜⠙⠒⣿⡛⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣟⢼⢃⠀⠀⠀⠀⢠⣔⠿⠃⡏⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⢁⡸⢸⠀⠀⠀⠀⠀⠀⣠⣒⡯⠓⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠓⠊⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿ ⣿⣿⣿⣿⠿⠿⠿⢿⠏⠁⠀⠉⠿⠋⠁⠀⠉⠿⠋⠀⣰⡿⣿⠶⣦⣤⡶⢿⣿⣿ ⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⣿⠰⠆⠀⠐⢺⡏⣿ ⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣇⣰⠿⣆⠀⣄⣠⣸⣷⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠙⢧⣭⣭⣿⣿⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿ ⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿ ⣿⣿⣄⠀⢀⡄⠀⠀⣠⡾⠃⠀⠀⠀⣀⠀⠀⠀⣄⠀⢴⡄⠀⣤⣤⣴⣿⣿⣿⣿ ⣿⣿⣿⣷⣾⠃⠀⣼⣯⡀⠀⠀⣀⣼⣿⣦⣄⣀⣿⠀⢸⣧⣾⠻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡿⠀⢰⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⣿⣿⡀⢻⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠇⢀⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣧⣨⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣠⣶⡿⠿⣷⣦⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠟⠻⢿⣿⠁⠀⠀⠀⢻⣿⠿⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣾⠿⠿⠿⠇⠀⣠⣄⡀⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⣠⣤⣶⣾⠿⠿⠿⣿⣦⠀ ⣿⡇⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠈⣿⡇ ⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃ ⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⢻⣷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⡿⠃⠀⠀⠀⠀⠀⣀⣼⡿⠃⠀ ⠀⠀⠙⢻⣿⣷⣶⣶⣶⣾⡿⠿⠛⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠻⠿⣿⣶⣶⣶⣶⣿⣿⠋⠁⠀⠀ ⠀⢀⣴⡿⠛⠛⠃⢀⣿⡟⠀⠀⠀⢻⣿⣄⠀⠀⢀⣀⠀⠀⠀⠀⢀⣄⠀⠀⢀⣼⣿⠁⠀⠀⠹⣿⡄⠈⠛⠛⢿⣷⡄⠀⠀ ⠀⢸⣿⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠙⠿⠿⠿⠿⣿⣦⣀⢀⣠⣾⡿⠿⠿⠿⠛⠁⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⣿⣿⠀⠀ ⠀⠈⣿⣷⣄⠀⠀⣿⡟⠀⠀⠀⠀⢠⣶⣦⡀⠀⠀⠈⠛⠻⠟⠛⠋⠀⠀⠀⣴⣶⣄⠀⠀⠀⠀⢸⣿⡀⠀⢠⣴⣿⡋⠀⠀ ⢠⣾⡟⠋⠁⠀⠀⣿⡇⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⠀⠀⠈⣿⡇⠀⠈⠉⠻⣿⡆⠀ ⢸⣿⡄⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⣿⡇⠀ ⠀⠻⣿⣶⡄⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣴⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⢠⣶⣾⡟⠁⠀ ⠀⢰⣿⠋⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⣴⣤⣀⣀⣴⣿⣿⣧⣄⣀⣠⣤⡀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠙⣿⣧⠀⠀ ⠀⠸⣿⣄⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠁⠀⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⢀⣿⡟⠀⠀ ⠀⠀⠙⠿⣿⣿⡇⠀⠀⠹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⣿⣿⡿⠛⠀⠀⠀ ⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠈⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠙⠋⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣦⣤⣤⣤⠀⠀⠈⠻⢿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⠟⠁⠀⠀⢠⣤⣄⣤⣾⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠛⣿⡇⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⢸⣿⡟⠋⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣤⣤⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣤⣤⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⢿⣷⣄⡀⣀⣼⣿⡀⠀⠀⠀⣾⣷⣄⡀⣀⣼⣿⠋⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠟⠋⠻⣿⣶⣶⣿⠟⠙⠛⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⣉⣷⠤⣶⡒⠦⣤⡴⠒⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠴⠚⠉⠉⠓⢦⡀⢠⠞⠁⠀⠀⠀⠉⢢⡀⠀⠀⠀⠀⠘⠒⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠏⠀⠀⠀⢀⣀⡀⢹⡏⢀⣀⡀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⢤⡀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⢧⠀⠀⠀⠻⣿⠏⡿⣇⠻⠿⠇⠀⠀⠀⠀⡞⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀ ⠀⠀⣰⠋⠀⠈⣿⠶⠤⠤⠔⠋⠁⠘⢦⡀⠀⠀⠀⣠⣾⡁⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣀⠀⠀ ⠀⣼⠁⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠁⣿⡇⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀ ⢰⠇⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣀⠀⣿⡇⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃ ⢸⡄⠀⠀⢀⡏⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢻⣿⡏⢷⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢾⡁⠀ ⠀⠙⠢⢶⣞⠁⠀⢳⡀⠀⠦⣄⣀⢀⣀⣠⠀⠀⢀⡿⠀⠈⠓⠦⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⢨⡗⠀⠀⠑⢤⡀⠀⢹⠉⠁⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀ ⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠉⠙⠚⠓⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡏⠀⠀ ⠀⠀⠀⠀⠀⠙⠦⠤⠤⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠦⠤⠴⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡾⠉⣽⡀⠀⠀⠀⣰⡄⠀⠀⠀⢀⣶⡀⠀⠀⢀⣼⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⣰⢫⠟⣲⠖⠚⠁⠙⠲⠤⠔⠋⠀⣟⠓⡞⣏⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡾⢠⣇⣼⢠⣯⣀⣤⣤⣤⣤⣤⣤⣄⣀⣼⡀⣧⣸⡀⣇⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⠶⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀
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໒꒰ྀི ˶• ༝ •˶ ꒱ྀི১
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
૮꒰˵• ﻌ •˵꒱ა
⣿⣿⣿⢿⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⡿⣽⣻⡽⢯⡿⣽⣫⡟⣽⣫⢟⣽⢫⡟⣽⢫⡟⣭⡻⣭⢻⡭⢯⡽⣭⢯⡽⣭⠻⣜⡣⢟⣜⡣⢟⡜⣣⢛⡜⣣⢛⡜⣣⢏⡼⣡⢏⡼⣡⢏⡼⣡⢏⡼⡱ ⣿⣷⣻⣟⣾⣳⢿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡷⣯⡽⣯⢷⣏⡷⣽⣣⢯⣟⢮⣯⢽⣚⡷⣹⢧⣻⡜⣧⣛⢧⡻⣜⢮⡳⣭⢻⡔⣏⡳⢎⡝⢮⠼⣱⢫⠼⣱⢫⡜⡱⢎⠶⡱⢎⠶⡱⢎⠶⡱⢎⠶⣙ ⣿⢿⣽⡾⣷⣟⣯⢿⡾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⣞⣯⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣽⣻⢾⣽⣻⢾⣽⢾⣯⢷⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⢯⣟⡷⢯⣟⡷⣻⣵⡻⣾⣱⢷⣫⠷⣞⢯⡞⣧⢟⡼⣏⢷⣣⢟⡵⣫⢞⡽⣎⢷⡹⣞⢣⡞⣱⢭⡛⡼⣙⡞⣥⣋⢗⣣⠳⣜⡹⢎⡳⣙⢎⡳⣙⢎⡳⣙⢮⡹⣒ ⣿⣯⣷⢿⣳⣯⣟⣯⡿⣽⢯⣿⢾⣽⣻⢾⣽⣻⣞⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢯⣷⣟⡿⣞⡿⣞⣯⡿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣾⣽⣿⣾⣿⣿⣾⣿⣷⣿⣷⣯⣟⣾⣭⢿⡹⣾⣹⢮⣏⢷⣫⢞⡵⣫⢷⡹⣎⢷⡹⣎⠷⡭⢮⡕⣏⠶⣹⢱⢣⠞⡴⣩⠞⡴⣋⠶⣙⢮⡱⣍⢮⡱⣍⢮⡱⡍⢶⣑⢣ ⣿⡾⣽⡿⣽⡾⣽⣳⡿⣯⣟⣾⣻⢾⣽⣻⣞⡷⣯⢿⡽⣯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣟⣾⣽⣻⡽⣟⣯⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣛⡾⣼⢣⡟⣮⢳⡝⣮⢳⡝⣮⠳⣭⢛⡼⢣⢞⡬⡳⣍⢎⢧⡛⡴⢣⡛⡴⣍⢞⡱⢎⡵⣊⠶⡱⢎⡖⣱⡙⢦⡍⡖ ⣿⣻⣽⣟⡷⣟⣯⡷⣟⡷⣯⢷⣻⣟⣾⣳⢯⡿⣽⢯⣟⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⣟⣯⡷⣯⣷⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣫⢞⡵⣏⢾⡱⢯⡞⡵⣛⢦⣛⡼⣍⠾⣰⠳⡜⣎⠶⡹⣜⢣⡝⡲⣍⢮⡱⢫⠴⣩⠞⣡⠳⡜⡥⣚⢥⡚⡜ ⣿⣽⣳⣯⣟⣯⡷⣟⣯⢿⡽⣯⢷⣻⢾⡽⣯⢿⣽⣻⢾⣽⣻⢯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣞⣯⢿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡽⢮⡝⣧⡛⣵⡩⢖⣣⠞⣬⠳⣥⢛⡼⣌⢳⡱⢎⢧⡚⡵⣊⠶⣉⢧⢛⡤⣛⠴⣋⠼⡱⡜⣆⢧⡙ ⣿⢾⣽⡾⣽⣳⣟⣯⣟⣯⢿⡽⣯⣟⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻⡞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣯⣟⣯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⢟⠶⣙⢦⡛⡵⢪⡝⢦⡛⡴⣋⠶⣩⢖⡹⢎⠶⡹⠴⣩⠞⡱⢎⡣⠞⡴⢋⡼⣡⠣⡵⣈⠦⣙ ⣿⢯⣷⣟⣯⡷⣯⣷⣻⣞⣯⣟⣷⣻⣞⡿⣾⣽⣻⢾⡽⣻⡞⣷⡻⢷⣛⣾⣳⣟⣾⣳⣯⡿⣽⢯⡿⣽⣳⣟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⢻⡽⢺⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢯⡹⣆⠻⣜⢣⠞⣥⢛⡴⣩⢞⡱⢎⡵⢋⡞⣱⢋⠶⣉⠷⡩⢞⡱⣘⠣⢖⡡⢓⡴⣉⠖⣡ ⣿⣻⢷⣻⡾⣽⢷⣯⢷⣻⢾⡽⣞⡷⣯⣟⣷⣳⢯⣟⢾⣳⢟⣳⣟⣯⣟⣾⣳⡽⣞⡷⣯⢿⡽⣯⣟⣷⣻⣞⣿⣿⣿⡟⢥⠲⡝⣾⣟⣿⣿⣻⣿⣟⣿⣯⢿⣞⣷⣻⣽⣚⠷⣘⢧⡚⡕⢦⢫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⢣⡭⢳⢬⢣⡛⡴⣋⠶⡱⢎⡵⢋⡜⣣⠞⡥⢫⡜⡱⢎⡱⢎⠴⢣⡙⢦⡙⢦⠱⣌⠚⡤ ⣿⣽⣻⢷⣻⢯⣟⡾⣯⣟⣯⢿⣽⣻⢷⣻⢮⣽⣳⢯⣻⣭⡟⣷⣞⣳⣞⡷⣯⢿⡽⣽⣏⣯⣟⣷⣻⣞⣷⣻⣿⣿⠫⠄⣉⣳⣽⣼⣿⣿⣿⢿⣟⣿⢯⣟⡿⣞⣷⡳⢞⡜⢢⠏⡖⡩⢞⡥⣛⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⢞⡱⢎⢧⡙⢶⡩⢞⡱⣋⠶⣩⠞⣡⠞⣱⠣⡜⡱⢊⠖⡩⢎⡱⡘⠦⡑⢎⡱⢌⡓⡔ ⣿⢾⣽⣻⣯⢿⣽⣻⢷⣻⣞⣯⢷⡯⣟⣞⡿⣼⢏⣯⢷⣳⣻⣳⣞⢷⣫⣟⡷⣯⣟⢷⣻⢮⡽⣞⣷⡻⣞⣿⣿⠁⠳⢾⣧⣽⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⡝⣮⢞⡳⣎⠳⡵⢊⡴⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢮⠳⣍⠶⣙⢦⡙⣎⠵⣊⠗⡱⢎⡱⣊⠥⡓⣬⢱⡉⢎⡱⢊⠴⣡⠣⣙⠢⡑⠦⡱⢌ ⣿⢯⣟⡷⣯⣟⣾⡽⣯⢷⣻⣞⣯⣽⣻⣼⣛⣾⣛⡾⣏⡷⣏⡷⣞⣯⢷⢯⡽⣶⢯⣛⣧⢿⡽⣳⢾⣽⣻⣿⠃⢉⡷⣿⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡿⣯⢟⡞⣞⡳⣜⣫⡑⠳⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢌⡳⢬⢳⡩⢖⡹⡸⡜⡡⢏⡕⢎⡱⣉⠖⡱⢢⠱⡘⠦⡑⣍⠲⢄⠳⣄⢣⡙⢆⡱⢊ ⣿⣯⢿⡽⣷⣻⣞⡿⣽⢯⣷⣻⢮⢷⣳⣳⠿⣜⣯⢷⣏⡿⣽⣹⢯⣞⣯⢯⣟⡾⣽⣛⣾⣫⡽⢯⣷⣫⣿⡟⢠⣯⣄⢿⣿⣿⣿⡧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡱⢦⡝⢳⡒⠦⡄⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡱⣋⠶⣙⢎⡵⢱⠱⣙⠲⡘⢎⡱⢌⢎⡑⢣⠱⣡⢣⡑⠦⡙⣌⢃⢆⠣⡜⠢⣅⠣ ⣿⣞⣿⡽⣷⢯⡿⣽⣻⣟⡶⣯⢟⣯⣗⡯⣿⠽⣞⣯⢾⣝⡧⣟⡧⢿⣜⡯⢾⡽⣞⡽⣶⢏⣿⣛⡶⣯⣿⠇⠿⢱⣿⢸⣿⣿⣡⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⠧⡝⢲⠱⣌⡠⢘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠳⣍⢞⡱⢎⠴⣋⢜⣢⡙⡱⢣⠜⡌⠦⣙⢂⠳⡐⠦⣑⢣⠱⡌⠎⡜⢢⡑⢣⠆⢣ ⣿⡾⣽⣻⡽⣯⣟⣷⣻⠾⣝⣳⣟⣞⡾⣽⢞⡿⣽⣺⣝⣮⡽⣞⡽⣏⡾⣝⣯⠾⣽⣹⢞⣟⣮⢿⣱⢯⣿⠀⣐⡊⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣜⢣⠷⢤⡡⠉⠆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡵⣊⢮⡱⢍⡲⢩⡒⢤⢣⡑⢣⠚⢬⡑⢢⢍⠲⣉⠖⡡⢎⠱⡘⡜⣠⠣⣘⢂⢎⡡ ⣿⡽⣷⢯⣟⣷⣻⢾⣽⣻⡽⣳⢾⣝⡾⣭⢿⣹⢧⢷⢾⣱⡟⡾⣵⢏⣷⢻⡼⣻⡵⢯⣾⣹⢮⣯⣻⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣭⡞⢣⢏⣬⡱⡌⢒⡠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢲⠍⣦⠱⡎⡜⣡⠚⡔⢢⡙⢢⡙⢦⡘⢥⢊⠵⡨⠜⡐⢎⠱⡐⢆⡡⢒⡡⢊⠴⡐ ⣿⣳⣟⡾⣽⢯⣟⡾⣽⣫⢷⣻⣞⣽⣳⣛⣞⢯⣞⠾⣼⢏⣷⡳⡽⣞⡽⣞⢧⡿⣱⠾⣭⡟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⢞⡩⣇⠣⠌⡑⢺⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⡑⢎⡴⢩⡒⢥⠣⣍⠲⣑⠪⡑⢎⡱⢨⠱⡌⢚⠤⢃⠲⡑⡌⢆⠓⡌⢃⠎⡱⠘⡄⢣ ⣿⡽⣞⡿⣽⣻⢾⣽⣳⢯⣟⡵⣞⣧⢷⡻⣼⢏⣾⢻⡽⣺⢧⢿⣹⢾⣹⡞⣯⠾⣝⡯⣗⢿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣖⣿⢯⢀⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡶⡷⣎⠷⣤⢓⡒⣩⢒⣿⣿⣿⣿⡟⡹⠋⢴⣆⡘⣿⣷⣏⢲⡘⢥⡙⢆⠳⣨⠱⠌⡥⣙⠢⣅⠣⢃⠍⡆⠣⠍⠦⡑⠌⡌⠱⡈⠆⡜⢠⠃⡜⢠ ⣿⡽⣯⣟⡷⣯⣟⡾⣵⣻⠾⣽⣻⡼⣳⢏⣷⢻⢮⣏⡷⣏⢿⡺⣽⣚⣧⢟⣧⢿⣹⢾⣹⢾⣹⢟⡿⢥⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⠚⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣭⡛⠿⡵⣉⠞⣩⠳⢦⡀⢎⣽⣿⣿⣿⣇⢠⣅⠮⠿⢿⠿⣿⣗⠦⣙⢢⡙⣌⠳⣄⠫⡜⡰⢡⠣⡔⢩⢊⠜⡰⢩⠘⡰⢁⠞⡄⢣⠑⡌⠔⡡⢊⠔⡡ ⣿⣽⣳⣯⣟⡷⣯⣟⣳⣽⢻⣳⣭⠷⣏⣟⡮⣟⡽⢮⣗⢯⡯⢷⡳⣏⣾⢫⣞⣳⢯⢾⣹⡞⣽⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣇⡋⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢮⡓⢦⡙⣷⡳⣬⣦⢥⡛⣤⡙⣦⣿⣿⣿⣿⣏⣿⢸⣿⣿⣿⣿⣾⣿⡜⣌⠣⣜⠰⢣⢌⡱⢢⢙⣂⠳⢌⡡⠎⢆⡑⢢⠡⡑⢊⠴⡈⢆⠱⣈⠒⡡⠎⡰⢁ ⣿⣞⣷⣻⢾⣽⣳⢯⣷⢫⣯⢷⣚⣯⡽⣞⡵⣯⢽⡻⣼⣛⠾⣯⢽⡳⣽⢻⡼⣽⡺⣏⡷⣽⢣⣟⡞⣿⣾⣥⣿⣿⣿⣯⣿⡳⢷⡈⡑⠌⢠⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣶⣍⢏⡞⣴⣙⣦⡹⢆⣿⣴⣽⣾⣿⣿⣿⣿⠐⡻⢷⢩⣿⣿⣿⣿⣿⡗⣨⠱⣌⠹⣂⠎⡔⢣⢌⠢⢃⠆⢢⠍⢢⠘⡄⢣⠘⣐⠢⡑⢌⠢⡁⢎⠰⡁⢆⠡ ⣿⢾⣳⣯⢿⡾⣽⣻⣼⣻⢞⣽⣹⢶⣻⢼⣻⢼⣳⡻⣵⣫⢟⡮⣗⣻⡼⣳⡽⣖⣻⡝⣾⡱⣟⢮⣽⡟⢻⣿⣿⣿⣟⣿⣯⢳⣦⣷⣶⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣆⢳⣎⠿⣖⣾⣿⣾⣿⣿⣿⣿⣿⡀⣟⢈⣦⣹⣿⣿⢿⣿⠓⡤⢓⣌⢣⠱⡊⢜⡂⢎⡱⢊⡜⢄⠚⡄⢣⠘⡄⢃⠆⡱⢈⠆⡱⢈⠆⡱⢈⠄⡃ ⣿⢯⣟⡾⣯⣟⡷⣯⢶⣏⣟⡮⣗⣻⡼⣏⡾⡽⢶⡻⣵⢫⣾⡹⣞⡵⣫⢷⣹⢞⡵⣻⢖⣻⡝⣾⣿⠁⠰⠟⣿⣯⢸⣿⣯⡧⣴⣠⣴⣶⣦⣄⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣮⣷⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⠃⢿⣿⠟⣽⣿⣿⠣⡙⡔⢣⠜⣢⠣⢍⠢⡙⢄⢢⠡⡘⢄⠣⡘⢄⠣⡘⢄⠊⡄⠣⡐⢄⠃⡔⢠⠃⡌⡐ ⣿⢯⡿⣽⣻⢾⡽⢯⡷⣞⢧⣟⣭⠷⣝⡾⣱⠿⣭⢗⣯⢳⡞⣵⡻⣼⣛⢮⡗⣯⡝⣧⡟⣧⢻⡞⣿⠀⠀⣦⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣛⣷⠿⣫⣾⢃⠧⡱⡘⢥⠚⣄⠳⣈⠱⡈⢆⠢⡑⢌⠢⡑⢌⠢⡑⠰⡈⢆⠡⢃⠌⡂⠜⡠⢂⠅⢢⠁ ⣿⢯⣿⣳⣟⣯⣟⣯⠷⣏⡿⡼⣞⢯⣻⠼⣏⣟⢮⣻⡜⣯⢞⣳⡽⣣⢯⣳⢻⡼⣽⢲⡟⣼⡳⣏⢿⣆⠀⢿⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢟⣿⢅⠺⡰⢡⡙⠤⢋⠤⠓⡄⢣⠘⡄⢣⠘⡄⢣⠘⠤⡑⢨⠑⠌⡄⢃⠢⡘⠄⡃⠔⣁⠊⡄⢃ ⣿⣻⣞⡷⣿⢮⡽⣞⣿⡹⣞⡽⣞⢯⣳⢻⡝⣮⢟⡶⣻⡝⣞⣧⢻⡵⣫⣗⢯⣳⡭⢷⣫⢷⡹⣎⡯⢿⣆⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⢻⡯⢌⢣⡑⢧⠘⡥⢋⠌⡓⢌⠢⡑⢌⠢⡑⢌⠢⢉⠆⢡⠂⡜⡐⢌⠂⡅⠢⡑⠌⢒⡀⠣⠌⡄ ⣿⣳⢯⡿⣽⣏⡿⣽⣲⢟⡽⣞⣭⢷⣫⢟⡼⣏⡾⣳⢧⣛⢷⡺⣝⡾⡵⣞⢯⡖⣯⡳⣝⡮⢷⡹⣞⣻⣿⡄⣿⣿⣿⡟⢛⣫⣿⣿⣿⣿⣿⣿⠟⣿⠛⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣹⡟⣌⠲⣡⠊⡕⢢⠡⢚⠰⡈⠖⡡⢊⠔⠡⢂⠱⡈⢌⠂⡅⢒⡈⢄⠣⡐⢡⠂⢍⠂⡌⢡⠒⠠ ⣿⡽⣯⣟⡷⣯⢷⣳⡽⢾⣹⡞⡽⣎⡷⣫⡽⣞⡵⣛⣮⢟⣮⢽⣣⢟⣵⢫⡾⣹⢖⣯⢳⡝⣧⢻⡜⣷⣿⣿⣿⣿⣿⣴⣿⡿⡏⢻⣿⣟⣤⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⢚⡯⣐⠣⢆⠹⣠⢃⠣⢌⠢⡑⠌⠴⢁⢊⠱⡈⢆⠘⡠⢃⡘⢄⡘⢄⠢⢑⢂⠩⢄⠊⡔⠡⠌⡡ ⣿⣽⣳⣯⣟⣷⣛⣶⢻⡝⣧⡻⣝⢾⣱⣏⢷⣹⢞⡽⣎⢿⡜⣧⣛⠾⣜⢯⣳⣛⠾⣜⢧⡻⣜⢧⡻⣜⣿⣿⣿⣿⣿⣿⡟⠳⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⡐⢫⢄⠫⡜⢠⢃⠌⡒⢌⠢⢑⠊⡄⠣⢌⠰⡐⡈⢆⠡⢂⠔⡂⠔⡈⢆⠡⢊⠰⡈⠒⢄⠣⡘⠠ ⣿⣞⣷⣻⣞⡾⣝⡾⢯⣽⢺⡵⣏⡟⣶⡹⣞⡽⣚⡷⣹⢮⡻⣵⢫⡟⡽⣎⠷⣭⣛⢮⡳⣝⢮⡳⣝⡞⡶⣿⣿⣿⣿⡿⠈⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠬⣙⠆⢳⠘⠤⣉⠆⡱⢈⢆⠡⢊⠰⡁⢆⠡⢂⠱⣀⠣⠌⢒⡈⢆⠡⢂⠱⡈⠤⢡⠉⡂⢆⠡⡁ ⣿⢾⣽⣳⢯⣟⡽⣞⡿⣜⣳⡽⣺⡝⣶⢫⢷⡹⣝⠾⣭⣳⢻⣜⡳⣽⢳⣭⣛⢶⣭⢳⡝⣮⢳⡝⣮⣝⡳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡈⠴⣈⢏⠰⣉⠒⡡⢊⠔⡡⢈⠆⡡⢒⠈⡔⡈⢆⠡⡐⢂⡑⠢⡐⢂⠅⡊⠔⡠⢃⠢⡑⠨⠄⡃⠔ ⣿⣻⢾⣽⣳⢾⣹⣳⢽⡺⣵⢫⢷⡹⣞⡽⢮⣽⣚⢯⣳⢭⣳⢭⣳⢭⣳⢮⡝⡾⣜⢧⡻⣜⢧⡻⢶⣭⢳⢧⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡐⢈⠲⢡⢎⡱⢄⡩⢐⠡⢊⠄⣃⠰⢁⠢⡑⠰⡈⢄⠃⡔⣁⠢⡑⢄⠃⡌⠰⣁⠒⡄⢃⠌⡑⢌⠰⢁ ⣿⣽⣻⢾⡽⣞⣧⢟⣞⣳⡭⣟⢮⢷⡹⣞⣳⢮⡝⣾⣱⢻⡜⣧⣛⢮⡳⣏⢾⣱⢏⡾⣱⢏⡾⣹⢳⣎⡟⡾⣴⢛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠭⡀⢡⠌⡡⢂⡅⢺⡔⡨⢔⡡⢊⡅⢒⠠⡑⣈⠒⡈⢅⠒⣈⠒⡐⢄⠒⡨⠐⡌⠰⣁⢂⠒⡈⢆⡘⠰⢈⠢⢁ ⣿⢾⡽⣯⢷⣻⢮⣛⣮⢳⣝⣮⣛⢮⢷⡹⣎⢷⣹⠶⣭⣳⣛⠶⣭⡳⣝⡞⣧⣛⢮⣳⡝⣮⢳⣝⡳⢮⣝⡳⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡁⠞⡌⠐⡤⠂⠤⢡⠘⣐⠣⣏⡐⠆⡔⣡⠈⡆⡑⠰⣀⠃⡜⢠⢊⡐⢌⠰⣈⠂⡅⢃⠌⡡⢐⢂⠱⢈⠆⢌⠡⢊⠄⠡ ⡿⣯⣟⡷⢯⢷⣫⠷⣭⢷⣚⢶⡹⢮⡳⣝⢮⣳⢭⣛⢶⣣⢏⡟⡶⣝⢮⣝⠶⣭⡳⢧⣻⣜⡳⢮⣝⡳⢮⣽⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣍⡳⢍⢦⣹⡰⢬⠑⡠⠨⠰⢀⣋⠄⠳⣼⡄⣙⠰⢠⡘⠤⣁⠣⡐⢌⡐⢢⠐⡰⢈⠢⠄⡃⠔⣈⠢⠑⡂⢌⠢⡁⢎⠠⠃⡄⢊⠐ ⣿⢷⣯⣟⢯⢷⣫⣟⢮⣳⡝⣮⣛⢧⣛⢮⡳⣝⡮⣝⣮⢳⣏⣞⡳⣝⠾⣜⡻⢶⣹⢳⡳⢮⣝⡳⢮⣝⡳⣞⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣭⢻⣌⠳⣭⢖⣦⠳⣌⢌⠡⢁⠒⢡⠈⢎⠡⠜⣷⡈⠜⣠⠘⡰⢀⢣⠘⡄⠒⡄⢣⠐⡡⢂⠱⢈⠒⡠⢁⠣⢘⠠⢂⠅⢊⠐⠡⠐⠂⠌ ⣿⣻⢶⢯⣛⡾⡵⣞⢯⢶⡹⣖⢯⡞⣭⣳⢻⣜⡳⣝⢮⡳⣞⡼⣳⢭⣛⣮⡝⣧⢏⡷⣹⢳⢮⣝⡳⣎⠷⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣽⣳⢮⡳⣎⡳⡼⡞⡴⢫⡜⠌⢦⠉⠈⠄⡐⠂⡜⢨⢽⣿⡔⢂⠱⣀⠃⢆⠱⣈⠱⡈⢆⠱⣀⠣⡘⢄⠣⡐⢡⠊⡄⠣⢌⠘⡀⢊⠡⠌⠡⢈ ⣟⡷⢯⣟⡽⣺⣝⢾⡹⣎⢷⡹⢮⣝⠶⣭⡳⢮⣝⢮⡳⣝⢮⡳⣝⢮⣳⢮⣝⢮⡻⡼⣭⣛⠾⣜⡳⣭⣛⠶⣭⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣟⡳⢞⡥⢯⡽⣭⢳⢧⡹⢜⣣⡙⢾⡀⠎⠡⠀⢄⠡⡀⠣⢎⢿⣿⣧⣖⡠⢉⠆⡒⠤⡑⡈⢆⠱⣀⠣⡘⢄⠣⡘⢄⠣⡘⠰⡈⠆⡁⠢⠐⡈⢂⠁ ⣯⣟⣟⣮⡽⣳⢞⣯⢳⡝⣮⢽⡳⣎⡟⡶⣝⢯⡞⣧⣛⢮⢷⡹⣞⢧⣛⠾⣜⢧⡻⣵⢣⣏⠿⣜⡳⢧⣏⠿⣜⡧⣏⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢾⡸⣹⡍⣞⣱⠞⣥⢻⢦⡙⣦⠧⡙⢦⡑⢎⠡⡀⠆⠰⢀⢣⠘⡼⣷⣏⡿⣿⣶⣾⣤⣵⣠⡑⣈⠒⠤⢑⠰⡈⢆⠱⡈⢆⠡⢃⠜⡠⠑⣂⠑⡠⠁⠌ ⣷⣻⡼⢶⣻⢵⣫⢞⣧⢻⡜⣧⢻⡼⣹⢳⡝⣮⡝⡶⣭⣛⢮⣳⡝⣮⣝⡻⣜⢧⡻⣜⡳⣞⡽⢮⣝⡳⣎⠿⣜⡳⣝⠾⣭⣛⠿⡿⢿⠿⣿⢿⣿⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣞⡧⢷⡩⡜⠶⣥⢯⡙⣧⣾⠵⣣⠝⣌⠣⡜⢢⠡⡁⠂⠅⣂⠢⠘⢤⢫⡝⣻⣷⣻⢞⣽⣻⣟⣿⡿⣿⣶⣮⣴⣡⣈⠆⡑⠌⢢⠁⢎⡐⠡⡀⠎⢠⢁⠂ ⣷⣳⢻⣏⣞⢧⣛⡾⣜⢧⡻⣜⣧⢻⡵⣫⢾⡱⣏⢷⣣⢟⣮⢳⡝⡶⣭⢳⡝⣮⢳⣭⢳⡝⣞⡳⢮⡝⣾⡹⢧⡻⣜⡻⢶⡍⡷⣍⣛⠮⡵⢎⣽⠀⠀⠀⠀⢮⣿⣿⣿⣿⣿⣿⡿⡞⣥⢳⡉⢳⡜⣦⢿⡻⣌⠷⣢⠝⣠⠒⡌⢠⠃⡔⢁⠂⠴⢈⡑⢎⡳⢼⢯⡷⣯⣟⣮⢷⣻⣾⣟⡿⣽⣿⣻⣿⣿⣿⣷⣾⣤⣉⡤⠘⢠⠁⡌⠂⡄⢂ ⡷⢯⣛⣞⢮⡻⣜⡳⣝⢮⢷⡹⣎⢷⡹⢧⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⢷⡺⣝⠾⣱⢏⡳⣝⢶⣹⢳⡝⣧⣛⢧⠞⡵⢎⢧⡛⣜⢣⢾⡃⠀⠀⠀⠠⣼⣿⣿⣿⣿⣟⣷⡻⣬⢓⣌⠶⣹⣯⣗⣳⣭⠳⡆⣍⠲⠠⠄⠃⡜⠐⡌⡀⢂⠬⠑⡎⡵⢋⡞⣹⢳⣻⣾⣿⢿⣟⣾⣟⣷⣿⣿⣽⣷⡿⣯⣿⣿⣿⣿⣿⣦⣴⣀⠡⠐⠂ ⣟⢯⡽⣎⣯⢳⡭⣗⢯⡞⣧⢻⡜⣯⣝⡳⢮⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⠷⣭⢻⡥⣏⢷⡹⣎⢷⣫⢞⡵⣭⠺⡭⣝⢮⢣⡝⣬⠓⡾⡇⠀⠀⠀⠐⢼⣽⣿⣿⣿⣿⣷⣿⠶⣏⢬⣛⣷⣻⣞⡷⣊⠷⣉⠦⣁⠣⣘⠐⡈⠱⣀⠖⠡⠀⡝⡘⡔⠫⡔⢣⡞⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣾⢿⣟⣷⡿⣯⣿⣿⢿⣿⣿⣿⣾⣤ ⣯⣛⢾⡱⣏⢷⡹⣎⢷⡹⣎⢷⣛⠶⣭⣛⠷⣎⢯⡳⡽⣎⢷⣫⢞⣧⢻⡵⣫⠷⣭⢻⡜⣧⢳⡝⣎⢷⡹⣎⢷⣋⠾⣜⢫⡵⣚⡬⢳⡜⢦⡛⡴⣧⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣯⡿⣜⡶⣹⣾⢯⣟⣳⡽⢎⡕⢢⠰⣁⠣⡜⢀⠡⡘⢠⠁⢆⠐⡤⢩⠓⣬⢓⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣻⣿⣿ ⡷⣭⡗⣯⠽⣎⢷⣫⢞⡵⣫⡞⣭⣛⠶⣭⢻⡼⣣⢟⡵⣫⢞⡵⣫⢞⣧⢻⡵⣻⡜⣧⢻⣜⡳⢞⡭⡞⣵⢫⡞⣭⢻⢬⡳⣜⡱⢺⡱⢎⢧⡙⡖⣿⠀⠐⠄⢀⠀⠀⠉⣿⣿⣿⣿⣿⣟⡷⣏⣷⣿⣿⢿⣻⡝⢮⡜⣡⠓⠬⣑⠜⣨⠂⡁⢃⡚⢤⡈⢠⢃⡝⢦⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣽⣿ ⣟⡵⣻⣜⡻⣜⢧⣛⢮⡳⢧⡻⣵⢫⡟⡼⢧⡻⣵⢫⡞⣵⢫⡞⣵⢫⡞⣧⣛⢶⡹⣎⢷⣪⠽⣹⢼⣙⢮⣳⢹⡜⣣⢳⣙⠦⣝⢣⡝⢎⢶⣭⡿⠛⠀⠀⠀⢹⠆⣄⣀⠿⣿⣿⣿⣿⣯⣿⡽⣾⣿⣯⡿⣧⣛⢧⡚⡥⢊⠶⣩⢎⡡⢚⠄⢃⠜⡢⣄⠣⡘⣬⢣⠿⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣯⢞⡵⣎⡷⣹⢎⣯⢳⡽⣳⡝⣮⢳⡽⣹⢧⡻⣜⢧⡻⣜⢧⣻⡜⣧⣛⢶⡹⣎⢷⡹⢶⣩⢏⠷⡮⣝⡞⣬⡓⣞⣱⢫⡜⣹⢬⣳⡾⠟⠋⠁⠀⢀⠀⠀⠀⢸⡅⣦⢉⡉⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣖⡻⢦⡛⣌⢏⡾⡵⢪⡕⢯⣌⢣⣌⡱⢎⡧⣙⣤⢏⡿⣵⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣫⢞⡵⣫⢗⡯⣞⢧⡻⣵⢻⡜⣧⢻⡵⣫⢷⡹⣎⢷⡹⣎⢷⡹⢶⡹⣎⢷⡹⢎⡗⣯⣜⢫⢷⡹⡖⣽⠲⣝⡼⢲⣍⣾⠟⠋⡁⢀⠀⠀⠀⢰⣿⠀⠀⠀⠈⡇⠸⣧⣌⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣋⢷⡙⣞⣮⡽⣽⢳⣚⠷⣜⡲⣬⡳⢯⣶⢻⣼⣻⣞⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣫⢞⡵⣫⢞⡽⣎⠷⣭⢳⡝⣮⢷⡹⢧⣏⢷⡹⣎⢷⡹⢮⡝⣧⢳⡝⡮⡝⣏⡞⢶⢎⡿⢬⡳⣝⠮⣝⣲⣽⠟⠋⠀⠠⠀⢀⡀⢀⡈⢷⣾⣿⠀⠀⢠⠀⢻⡄⢽⣷⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡍⣎⢿⣼⣳⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⣱⣏⣞⡳⣝⢮⣳⢭⡟⣼⢫⡞⣵⢫⣝⡳⣎⢷⡹⣞⢧⣛⢧⢻⡜⣳⠞⡵⣋⢶⡹⣚⢮⡜⢧⣛⡼⣹⣶⠟⢡⣀⠈⢒⠠⣇⢢⣽⣦⣿⣿⣿⣿⠃⠀⠈⢣⠀⢳⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡼⣣⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⢯⣟⡳⡽⣎⢷⣛⣾⣳⣿⣿⣿⣿⣿⣿⣿ ⣳⢯⡽⣹⢧⡻⣜⢯⡞⣵⢫⡞⣵⢫⡞⣽⢣⡟⡼⢧⡻⣜⡻⣜⢮⣓⢏⡖⢧⠻⣜⡣⢟⣬⢓⡮⢫⣵⡿⠋⠀⠈⢻⣤⣚⡤⢿⡞⣿⣻⣿⣿⣿⠏⠀⠀⠀⠈⡆⠸⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡵⣿⣿⣿⣧⣻⣾⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⡿⣟⣿⣯⣿⣟⡿⣿⣻⣿⣽⣟⣷⣿⢾⣟⡾⣽⣳⢧⣻⣼⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⢯⡞⣵⢏⡾⣱⢯⡞⡽⣎⢷⡹⣎⢷⡹⣎⢷⡹⣝⢧⡟⣼⡱⢏⡶⢭⡺⣜⢫⣝⡲⢭⣓⢮⡹⣼⡟⠃⠀⠀⠀⣐⡠⠞⣿⡽⢎⡽⣶⢿⣾⢏⡆⠀⠀⠀⠀⠀⠑⠀⣧⠀⢺⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣝⡮⣝⡾⣿⣳⣿⣟⣿⣿⣽⣷⣿⣿⣿⣿⣷⣿⣿⣿⣯⣿⣾⣟⣷⣿⣻⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣣⡟⣼⢣⡟⣼⢳⡝⣮⢳⡝⣮⢳⡝⣾⡱⣏⠾⣜⢧⡝⡞⣜⡣⢗⣎⠳⣎⣵⣫⣼⣶⠟⣉⣠⠀⠀⠀⢀⡿⣷⢍⣙⣧⣿⣾⣿⣫⣝⣾⣤⣄⣲⣤⣹⣦⠲⠤⣄⠀⠈⢿⣿⣿⣿⣿⣿⠃⢤⣿⣿⡿⢫⣙⢮⣳⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⢯ ⣞⡳⣝⢾⡱⣏⣞⢧⡻⣜⢧⡻⣜⢧⡟⣼⢣⡝⣮⣛⡼⢎⣞⡹⡲⣍⣷⡾⠟⢋⢉⣥⣶⣾⣿⣿⣿⣿⠿⡩⢞⣷⠟⠉⡐⢎⠛⡍⢯⡽⣻⣿⡻⢿⣿⣿⣿⣿⣷⣦⣜⣦⡀⠹⣿⣿⣿⣿⠏⢀⣿⡿⠉⢁⠣⣞⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣟⣿⣟⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠾⣝⢯ ⣯⣝⢾⣣⢟⡼⣎⡷⣹⢎⣯⢳⡝⣮⡝⣮⢳⡝⢶⡹⣜⣫⣖⣽⠿⢋⡡⢴⠶⣞⡾⣞⣷⣿⣾⣿⣿⣟⡶⣡⣿⠋⠀⠀⢁⠢⠕⡚⢡⢎⡱⠭⣽⠿⣟⢿⡻⣝⣮⣿⣿⣿⣷⡧⣿⣿⣿⡋⢥⣿⡏⣠⣄⣠⣔⣫⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣟⡿⣿⣾⣿⣿⡿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣯⢿⡽⣞ ⡷⢮⣳⡝⣮⢳⡝⣾⡱⣏⡞⣧⣛⢶⣽⣮⡷⠿⢛⠛⡫⢍⠋⡅⣎⢱⡙⣎⠿⣜⣻⡽⣿⣾⣿⣿⣿⣿⣿⣿⠏⢀⢠⡐⣠⠉⠒⠬⡁⢎⡰⢿⣬⡻⣜⣯⢷⣻⣿⣿⣿⣿⣿⣷⣉⡟⢦⡑⣮⢯⣴⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣻⡾⣿⣟⣯⡿⣿⣿⣯⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣯⡿⣽⢯ ⣽⢳⢧⡻⣜⢧⡻⢶⣹⢮⣽⡶⠿⠛⠉⠀⠐⠤⠣⡘⠐⢊⠒⡌⢂⠧⣜⡎⣷⣹⡾⣽⣷⡿⣿⣿⣿⣿⠿⣡⠲⣌⢶⡹⢿⣆⣙⣲⠱⣮⢙⠶⣣⢿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢷⣯⣟⣷⣿⣳⣯⢿⡽⣷⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⡷⣟⣯⣿ ⣳⢯⡞⣵⣫⢞⣽⣳⠟⠋⠁⠀⠀⠀⠀⠐⠠⠂⢀⠈⠄⢡⠘⡰⣍⡞⣴⢯⡷⣯⣟⣿⡾⣟⡿⡹⣍⢆⡳⢣⡽⣘⣮⡟⣽⣿⣿⢣⠷⣌⣯⣛⣷⣻⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣯⢷⡿⣜⢯⢾⣭⢿⡿⣿⡿⣿⣾⢿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣻⣿⣾ ⣟⢮⣽⢺⣵⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠢⡜⢢⡝⢲⣟⡾⣽⣯⣿⣿⣻⡽⣛⢥⢳⡱⢎⢎⣝⢣⡻⣵⣳⡿⣟⣿⣞⣯⢿⣝⡶⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣟⡾⣞⡯⣝⢿⣫⡗⣾⣯⣿⡽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣷⣿ ⣻⢞⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠔⣠⠒⣭⠳⡜⣧⣿⣟⣷⣯⢷⣫⢇⡧⣙⢎⢣⠳⡞⡼⣌⢷⣻⢽⣯⢿⡽⣯⣟⡞⡿⣮⣽⢳⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⢦⡈⢿⣞⣿⣿⣿⣿⣷⡿⣿⣟⡾⣽⣟⡾⣽⢣⡟⣽⣺⢷⣻⢽⣳⣯⣿⢿⣻⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢬⡸⣔⢫⢖⣻⣾⣿⠿⣝⡾⣡⠧⣍⠞⣰⠙⢎⡲⢥⣛⣼⣻⡼⢯⡟⣞⢯⣿⣱⢿⡜⣷⡝⣾⢻⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢳⣄⡆⣹⣜⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣳⢏⡷⣭⢗⣯⣛⣷⢻⣾⢯⣿⣻⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢆⡞⠶⣱⣮⣾⣿⣿⢿⡽⣛⡮⢱⡡⣚⡜⡸⢣⢛⣤⡝⣫⣼⠶⡽⢾⡹⡞⡭⢞⠶⢭⢞⡹⣞⡽⣮⢿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⣻⣽⢻⡼⣾⢿⣿⣿⢿⣻⣿⣿⣾⣳⢯⡻⣼⢛⡾⢧⣻⣼⣻⣾⢿⣽⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⡌⣞⣬⣿⣿⣿⣿⣿⣯⣿⡟⢧⠘⡅⣶⢩⠞⣱⢛⣼⢲⡝⣣⢟⡽⢞⡹⢻⡱⣛⢮⣙⣧⢫⡷⣭⢷⣯⣟⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣻⣿⣯⣿⣿⣿⣿⣿⣟⣮⢷⡏⣯⢳⣭⢻⡼⣟⣧⣿⣹⣽⣻⣯⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⡜⣰⣿⣿⣿⣻⣽⣯⢿⣿⣯⠳⡜⢠⢛⡘⢤⡃⣞⡥⢏⡞⡶⣙⢮⣟⡼⡳⣍⣳⣫⡝⣮⣝⣮⣻⡽⢯⣿⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡷⢧⣿⣿⣿⣿⢯⣟⡾⣽⢻⡯⣟⣳⡛⢾⣳⣽⡽⣞⡿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⡼⣼⣿⣻⣷⢿⣽⣿⣽⣿⣿⣦⠃⡄⠙⠦⠸⠀⡗⡌⢲⡛⣜⠶⣙⡞⣼⣱⢯⣝⣣⢿⣝⣯⣟⣾⣳⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣼⣿⣋⢿⡟⣞⣻⣞⡷⣹⢏⡷⣫⢷⣹⣛⣷⣻⣽⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⡉⣥⢻⣽⣷⢿⣷⣯⣿⣿⣿⣿⣿⣿⠂⠄⠡⠒⠐⠈⠳⢐⡚⡡⢜⡭⢻⡴⣛⢶⣭⡞⣧⣟⣯⢿⣭⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⠙⣇⣿⢫⡝⣭⣓⣮⠷⣳⢾⣱⢟⣯⣟⣯⣷⣻⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣟⡷⣯⣿⣿ ⠀⠀⣀⣄⣠⠌⢦⡱⣯⣿⣻⣾⡿⣯⣿⣿⣿⣿⣿⣿⡏⠙⠀⠀⠀⡰⣃⡤⢋⣜⣍⣫⣜⣣⣷⣻⣟⣶⡿⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡉⠁⡫⢜⠣⢯⣜⣦⠳⣬⠷⣽⣚⣷⣞⣳⣾⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣹⣿⣽⣯⣿
⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
໒꒰ྀི´ ˘ ` ꒱ྀིა
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣾⠿⣿⣆⠀⢀⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⠀⢹⣿⣾⣿⣿⣄⣦⣄⡀⣰⣿⡿⠛⠋⠛⠿⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⠏⠀⠀⠀⠀⠀⢹⣇⣀⣀⡀⠀⠀ ⠀⠀⠹⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣯⣍⣹⣷⡀⠀ ⠀⠀⠀⠹⡇⢸⣿⣿⣿⠿⠟⠋⣼⣿⣿⣿⣿⣿⠋⠉⠉⢹⠉⠉⠁⠈⣧⡀ ⠀⠀⠀⠀⠹⣸⣿⣴⡿⣷⣤⣴⡏⠈⠻⣿⣿⣿⣧⠀⠀⣼⡄⠀⠀⠀⠈⠁ ⠀⠀⠀⠀⠀⣇⠙⠋⠀⠙⠛⠋⠀⠀⠀⠈⣻⣿⣿⠀⠀⢻⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠀⠀⠈⠻⠷⢄⡀⠀⠀ ⠠⡠⡠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⢵⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠾⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⠀⢰⣿⣿⡟⠙⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠛⢿⣿⣿⣿⣶⣶⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡿⠃⠀⠉⠉⠛⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣽⣏⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣯⠿⠁⢻⡌⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⢩⣭⣻⡶⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣵⠟⠀⠀⠈⣷⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣸⡄⠉⠙⠶⣭⡓⣦⣄⠀⣀⣠⣤⣤⣄⣰⣟⣼⠋⠀⠀⠀⠀⢿⡈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⡿⣧⠀⠀⠀⠀⠙⠓⠛⠋⠁⠀⠐⠐⠂⠀⠉⠉⠀⠀⠀⠀⠤⣬⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣝⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀ ⠀⠀⠘⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣜⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠟⣟⣉⢻⡄ ⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⣤⡀⠀⠀⠀⠀⠀⠘⣧⣻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⢛⡟⠁⣠⣤⡉⠙⣿⡇ ⠀⠀⢸⡟⣧⠀⠀⠀⢀⣤⢤⡄⠀⠀⢀⣀⣨⣧⣤⣤⣤⣤⡓⠀⠀⠀⠀⠀⠀⣨⡷⣸⡷⠄⠀⠀⠀⠀⠀⢀⣤⡶⠛⠋⠀⠀⣸⠟⠋⠁⠈⣷⢀⣿⠃ ⠀⠀⢸⡇⠘⠀⠀⡾⠋⣠⣤⣶⣶⠟⣿⣫⣅⡀⠀⢳⡄⢹⣧⠀⢠⡶⠒⠛⠛⢿⡽⣿⡓⠶⣦⠀⣠⣤⠾⠋⠁⠀⠀⠀⣠⡞⠁⠀⠀⠀⣰⣇⡾⠋⠀ ⠀⠀⣼⠇⢀⣤⣾⠟⠛⠁⠀⢠⡿⠀⠀⠀⠈⢻⡆⠀⢻⢸⣿⡿⡿⠀⠀⠀⠀⠀⠹⡄⢀⢠⣿⣿⠉⠀⠀⠀⠀⠀⣠⡼⠋⠀⠀⣠⣤⣤⡿⠋⠀⠀⠀ ⠀⣼⣯⣼⠟⠉⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣿⢀⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢱⡚⣸⡟⠃⠀⠀⠀⢀⡴⠚⠁⣀⣤⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⢛⣿⠟⠁⠀⠀⣠⡤⠞⠉⠀⠀⠀⢀⣠⣤⣤⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣳⡿⠁⠀⢀⡤⠞⠋⢀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣯⣠⠶⠚⠉⠁⠀⠀⣠⣴⡶⠟⣿⠿⠙⠉⠉⠉⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢁⡤⠖⠋⣀⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⢀⡀⠀⠀⠀⣰⡾⠋⠀⢀⠀⠙⣦⣀⣤⣤⣤⣧⡄⠀⠀⣆⠀⠀⠀⠀⠀⠀⣼⣿⠖⠋⣀⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⡌⠉⠑⠒⠾⠿⣄⡀⠀⢾⠀⠀⠿⣿⣿⣿⣿⡟⠁⠀⠀⣿⠀⠀⠀⠀⢀⡞⠉⢀⣰⠞⢉⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢻⣆⡀⠀⠀⠀⠀⠁⠀⠘⢧⡀⠀⠈⢩⡟⠻⣄⣀⣀⡼⠋⠀⠀⠀⠀⠈⠀⢠⡞⠁⠀⣸⢻⡇⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⣀⣀⠀⡀⠀⠀⠀ ⠀⠀⠀⠹⢷⣆⠀⠰⡆⠀⠀⠀⠀⠉⠛⠚⠫⢥⡤⠼⠉⠉⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⣿⢸⣷⠀⠀⣀⣴⠞⠋⠉⠁⠀⠈⠉⠙⠿⣶⣿⣦⡀⠀ ⠀⠀⠀⠀⠀⠉⠻⠶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⣿⠸⣿⠀⠀⣹⠟⠁⣀⡤⠤⠤⢄⣀⠀⠀⠀⠛⠘⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢻⢀⣿⠀⢰⠏⣠⣾⡿⠶⢶⣿⣇⢯⣷⡀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢹⠸⣿⠀⣿⠞⠋⠁⠀⠀⠀⠉⢻⣷⣿⣷⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢘⠀⣿⠀⠛⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹⣿⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠄⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯⣫⠇⠀⠀⢀⣾⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣯⠟⠀⠀⣠⣾⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⡇⣿⡄⢀⣀⣤⣴⡿⢿⣿⣿⡝⠃⠀⣠⣾⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⣿⠸⣿⠛⣭⣭⣤⠬⠽⠛⠁⣀⣤⡾⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⣄⠀⠀⠀⠘⣧⢻⣷⢶⣤⣤⣴⡶⠾⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠈⢷⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⢟⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⢳⡹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡟⣾⣿⠀⠀⠀⠀⠀⠐⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢳⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢀⠁⠙⢢⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠈⣏⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠹⣆⠀⠀⠀⢠⠆⣠⡴⠞⠁⠉⠙⠛⠛⠛⠛⠛⠶⣦⣤⣄⠀⠀⠀⢸⡀⠀⠀⠀⣿⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠙⣦⠀⠀⣷⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⡗⠄⠈⣧⠀⠀⠀⠻⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣴⠋⠀⠀⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡎⠀⠘⣦⡀⠀⠀⣀⣸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡏⣄⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠈⠛⠶⠚⣉⠉⢈⣛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⣿⣋⡾⠋⠀⠀⠀⠀⢸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠦⡀⠀⠀⠈⢳⡄⠻⣎⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠒⠒⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠶⠶⠶⠶⠿⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⣮⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣁⡀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣯⡁⠀⠀⠀⠀⠀⢀⡔⠁⠀⣤⣼⠓⣄⠀⠀⡴⠋⠑⢤⡀⠀⠀⠀⠀ ⠈⢻⣿⣿⣝⣿⣿⣆⠀⠀⠀⣠⡏⠀⣤⣠⣿⡏⠃⠘⡦⠊⠀⠀⠀⠀⠉⠢⡀⠀⠀ ⠀⠀⠙⢿⣿⣿⣿⢿⣷⣄⡜⠁⠹⣄⠿⠿⠞⠃⣠⠞⠁⠀⠀⠀⠀⠀⠰⢷⣼⢦⡀ ⠀⠀⠀⠀⠙⢿⢧⡑⠝⢿⡷⣄⠀⠀⠉⠒⢒⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢛⣿ ⠀⠀⠀⠀⠀⠀⠑⢌⠂⣾⢓⠚⠢⡀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠓⢿⣏⡇⠀⠙⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠋⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡀⢰⠁⣑⣄⠀⠀⠀⠀⠀⠀⠀⣠⠎⡠⢊⠴⣯⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡳⣦⣽⣷⣄⣀⣠⣇⡤⣞⢕⡫⢖⡵⣪⠔⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢺⣿⣿⢿⡻⣄⣩⡚⠕⣩⣶⡧⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣟⢾⠋⡰⣟⠽⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡯⠞⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⠤⠐⠒⠒⠢⠄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⠊⠀⠀⢀⠀⢠⠀⠀⠀⠑⠄⠀⠀⠀ ⠀⠀⡘⠀⡀⡠⠇⠘⠒⠒⠂⠼⡀⡄⠘⡄⠀⠀ ⠀⠀⡇⠠⠃⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⡇⠀⠀ ⠀⠀⣇⢃⣰⣾⣷⣆⠀⢀⣚⣿⣿⣒⣡⡇⠀⠀ ⠀⢴⢿⠈⠸⢿⡿⠙⠀⠘⠹⠿⠿⠊⠸⢏⠄⠀ ⠀⢈⣽⣃⠀⠀⠀⢀⣤⣤⠄⠀⠀⢠⣿⣅⠀⠀ ⣎⠀⠹⢹⠑⠠⣀⠀⠉⠉⠀⡀⠔⢹⠛⠁⢈⡆ ⠀⠁⠒⠓⠃⢀⠤⣔⢛⢝⣛⡶⢤⡘⠒⠊⠉⠀ ⠀⠀⠀⠀⡰⠁⡇⠈⠒⠒⠚⠁⡎⠈⠄⠀⠀⠀ ⠀⠀⠀⢐⠣⢤⡇⠀⠀⠀⠀⠀⣣⠤⠺⡀⠀⠀ ⠀⠀⠀⣈⠿⡾⠉⠋⠹⠁⠋⢹⠙⣇⣻⡇⠀⠀ ⠀⠀⠀⡇⢸⠇⠀⠀⠀⠀⠀⠀⠀⢹⡄⢸⠀⠀ ⠀⣤⣜⣗⣾⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣩⢗⡶ ⠀⠀⠀⠈⠙⠠⡤⠤⢀⣤⡀⠤⢤⠔⠃⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⣗⣤⣾⠀⡗⠒⢺⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⠀⢸⠀⡇⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⡇⠀⡂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⣇⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⠿⢿⠀⡿⠿⢇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠓⠤⠜⠁⠢⠤⠜⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⣤⣶⣦⣤⠠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⣾⠘⡄⠀⠀⠀⠀⠀⣀⣤⣤⣤⠀⢠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀ ⠀⠀⢠⡞⠋⠓⠤⢍⠛⠿⠶⣿⣿⣿⣿⡿⠆⠀⠀⠀⢸⣿⣆⡗⠀⠀⠀⠰⢿⣉⠉⢉⡙⠒⠚⠛⠻⠿⣿⣿⣷⡄⠀⠀⠀ ⠀⠀⠈⠉⠉⠉⠲⢄⠀⠀⠀⠀⠀⡹⠁⠀⠀⠀⣀⣴⣾⣿⣿⣿⣦⣄⠀⠀⠀⠈⢧⠀⠈⠉⠁⠒⣶⠖⠋⠉⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⢣⢀⣤⣶⢿⣿⠃⣿⠃⠀⢷⡈⢻⣟⢷⣤⣀⣼⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠈⣿⣿⠃⣿⠇⠸⡞⠀⠀⢸⢳⠈⣿⡌⣿⣿⠃⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣶⣦⣼⡏⢸⣿⠀⣦⡇⠀⠀⠘⠘⡀⢸⣵⢸⣏⢀⣀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⢿⡇⡇⠀⡇⡇⠀⠀⠀⠀⡇⢸⣽⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡤⠤⠤⣀⠀⢸⣿⣹⣯⡲⠲⣻⣷⣼⡇⣧⣤⣤⣴⣄⣧⣾⡿⡴⢦⣫⣝⣿⣿⠀⢀⡠⠤⠤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡟⠛⠒⠶⢤⣿⣿⠛⠳⣌⠣⣄⣙⣿⣿⡟⢻⣍⣯⡙⠻⣯⣿⣋⣀⡴⢋⠾⠛⢻⣿⣧⠶⠒⠒⠺⣇⠀⠀⠀⠀ ⠀⠀⣠⠟⠀⢼⣿⠂⠀⣸⡟⠛⣶⣾⡷⣌⠻⠿⢼⣷⣾⣿⣿⣿⣿⣧⠾⠟⢋⠴⣷⣶⠛⠹⣏⠀⠀⢿⣽⠀⠙⣦⠀⠀⠀ ⣠⣾⣏⣓⠒⠢⢤⣀⣤⣽⡇⢷⣿⡿⠀⠈⠑⠒⠂⠛⠿⣿⠿⠿⠟⠀⠒⠊⠁⠀⣿⣿⣷⢨⣿⣵⣀⡠⠤⠒⣒⣛⣳⣄⠀ ⣿⣽⠟⠙⠻⢷⣾⣿⣿⣿⣿⢮⡛⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠟⣡⣾⣿⣿⣿⣧⣶⠿⠛⠛⣯⣿⠇ ⠈⠁⠀⠀⠀⢠⣿⣿⣿⡿⣷⣴⠻⣷⣦⣬⣉⣑⣒⣒⣐⣒⣒⣒⣒⣒⣪⣉⣭⣤⣶⠿⢧⣼⢿⣿⡿⣿⣇⠀⠀⠀⠈⠁⠀ ⠀⠀⠀⠀⢀⣏⢿⡇⢹⣿⣤⡇⠀⠈⢿⣿⣿⡟⣛⠛⢿⠧⠨⢿⠟⣛⡻⢿⣿⡿⠃⠀⢸⣧⣾⣿⠀⣿⢻⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢾⣿⣦⣑⡼⢿⣿⣧⣀⣀⣨⣿⢻⣿⣿⡋⠈⠀⠀⠁⠚⣻⣿⣿⣿⣧⣀⣀⣤⣿⣿⢸⣔⣷⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣯⣿⣷⣸⣿⣿⡛⣛⣋⣵⣿⡏⢻⣿⡶⣤⣤⣴⣿⣻⢿⣿⣦⣍⣛⢛⣿⣿⣿⣼⣿⣯⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⢿⡏⠸⠉⣿⣿⣿⣿⣿⢿⡿⢻⣗⠀⠹⠿⠶⠴⠾⠟⠁⢸⡟⢻⡟⣿⣿⣿⣿⣿⡇⡀⠉⣿⢻⡀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣦⡱⢄⡂⢿⣿⣿⣿⣿⣿⣷⣿⣿⣑⡒⣤⠤⡤⢤⠔⡊⣿⣟⣦⣿⢿⣿⣿⣿⣿⠃⣁⢼⣡⣿⡷⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣻⣶⣷⢹⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣸⣧⣾⣻⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⡿⣿⡟⢸⠟⣿⡿⠋⠀⢻⣿⡉⢿⣿⣍⣋⣻⣾⣷⣟⡉⢡⣿⡿⠋⣼⣿⠀⠈⠻⣿⡏⡏⢻⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⡙⣧⠀⡆⢿⠀⠀⠀⠈⢿⣷⣤⣯⣿⡿⢟⣻⣛⡻⠿⣿⣥⣤⣾⡿⠃⠀⠀⠀⣹⠀⡆⢸⢟⡸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⣦⣱⢈⢷⠀⠀⠀⠀⠙⠢⠄⣠⠴⠟⠁⠈⠙⠷⢤⡠⠤⠋⠁⠀⠀⠀⣼⣇⣸⡠⣫⡞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣭⣋⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣫⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣆⢸⣇⠈⢿⡆⠀⠀⠀⣇⠀⠸⣇⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠉⠙⠲⣄⣄⡀⠀⢀⡈⠙⠻⣿⡇⠀⣿⡎⠻⣾⣿⣇⠀ ⢻⡀⢿⠀⢸⣿⣄⠀⠀⢸⣆⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⠙⠲⣤⣤⠚⣏⠛⠓⠒⠒⠚⠩⠗⢶⣄⡀⠀⠀⠈⠙⢯⣦⣌⠻⢤⡀⠈⠛⢦⣿⡇⠀⢸⣿⣿⣆ ⠈⣧⠸⡇⠀⢿⣿⡇⢘⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⢠⡀⠀⠀⠢⠈⠳⣶⠖⠛⠛⠙⢶⣌⠳⢄⠀⠀⠐⠢⡀⠀⠈⠙⠶⣄⠀⠀⠀⠈⠻⣶⣄⠳⣤⡀⠀⢹⣷⠀⠸⣏⣽⣿ ⣀⣽⣦⣿⣄⣸⣿⣿⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⡏⣧⠀⠻⣄⠀⠀⠀⠀⠈⢻⣶⡄⠀⠘⢾⡳⣄⠹⣦⡀⠀⠈⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠈⠻⣷⣎⢿⣶⣄⠻⣤⠞⠋⠉⠙ ⣿⠈⢿⠹⣿⣿⡿⠃⠀⣠⠏⠀⠀⠀⠀⠀⢀⠀⣸⠀⣼⡆⠀⠙⣟⢦⣀⠀⠀⠀⠙⢮⣦⡀⠀⠻⣌⢳⣌⢻⣶⡀⠱⣄⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠈⠻⣿⢿⣼⠟⠁⠀⠀⠀⠀ ⣿⣦⣸⣀⣽⠏⠀⠀⢰⠏⠀⢀⠀⠀⣀⣰⠿⠄⣿⢀⡏⠹⡄⠀⠈⣳⡉⠳⣤⡀⣀⠈⠻⡽⣄⠸⣟⢧⡙⢀⣿⣬⣷⣧⣿⣦⣀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠈⠳⡤⢤⡀⠀⠀⠀⠀ ⣿⣿⡟⢿⡟⠀⠀⢠⡏⠀⠀⣏⣴⠿⠟⠃⠀⣇⣿⣸⠀⠀⠙⣄⠀⠹⣟⣦⣀⠙⡿⠿⢶⣽⣽⣆⠘⣇⣷⡿⠟⠛⠛⠛⠛⠛⢿⣿⣆⠀⠀⠈⢳⡄⠀⠀⠀⠀⠙⢮⠻⣄⠀⠀⠀ ⣿⢿⣇⡿⠁⠀⠀⡞⠀⠀⣼⠋⢀⡄⠀⢠⣔⣿⣿⠏⠀⠀⠀⠘⢷⣄⠈⠻⣎⠿⠷⠂⠀⠈⠻⣿⣿⣿⣯⣤⣤⣤⡀⠀⠀⠀⠀⠉⠻⣷⡀⠀⠀⠹⡄⠀⠀⠀⣄⠈⠃⠈⠳⠄⠀ ⢻⣾⣿⠃⠀⠀⢰⠇⠀⣾⡇⠀⢸⠀⠀⣸⢸⢹⣿⡆⠀⢠⡀⠀⠀⠉⠓⠒⠊⠛⠀⠀⠀⠀⠀⢱⢫⣿⠋⠁⣤⡍⢿⡆⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠻⡄⠀⠀⠘⣦⠀⠀⠀⠀⢤ ⠺⣿⡟⠀⠀⠀⣼⠀⠀⣼⠀⠀⡾⠀⠀⣿⣼⢸⢹⣷⠀⠈⠙⠓⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢾⣷⣿⡇⢀⣿⠀⠀⠀⠀⠀⠀⡀⢱⡀⠀⠀⠹⣦⠀⠀⠈⢧⠀⠀⠀⠀ ⣿⣿⠃⠀⠀⠰⡇⠀⠀⡇⠀⠀⡇⠀⣸⣏⡏⢸⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠈⡟⢦⣭⣭⣵⠟⠁⠀⠀⠀⢀⣤⢮⠄⠀⠳⡄⠀⠀⢻⣷⣄⠀⠘⢧⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⡇⠀⢠⡇⠀⣰⡇⢰⣧⡿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠿⠀⠀⠀⠀⠀⠹⡄⠀⠈⣿⣿⣷⣄⠘⡆⠀⠀ ⣿⠀⠀⠀⠀⢸⣇⠀⢸⠀⠀⣿⣇⡿⠛⠁⠀⣀⣶⣖⣊⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠞⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠸⣿⣿⣿⣷⣿⡀⠀ ⡿⠀⠀⠀⠀⠘⣿⠀⢻⠀⠀⣿⡿⢀⣠⣴⣿⠟⢋⣡⣤⣭⣽⡳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢿⣿⣿⣿⣿⣧⠀ ⢧⠀⠀⠀⠀⠀⠹⡄⢸⡀⠀⡿⣷⣾⣿⠏⠁⢴⠟⣁⢠⣿⡏⢻⡀⠙⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠸⣿⣿⣿⣿⣿⡄ ⣾⠀⠀⠀⠀⠀⠀⣇⠈⡇⠀⡇⢻⣿⠇⠀⠀⢸⡀⠿⣿⣿⡇⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⢻⣿⣿⣿⣿⡇ ⣿⠀⠀⠀⠠⡀⠀⠸⡆⢧⠀⡇⢸⣿⡄⠀⠀⠈⠻⠤⣤⣤⠴⠋⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⡜⣿⣿⣿⣿⣿ ⣿⠀⠀⠀⠃⣷⠀⠀⠙⠸⣷⣿⡆⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣰⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢷⣿⣿⣿⣿⣿ ⣿⡆⠀⠀⠀⠸⡇⠘⣇⠀⠈⠻⢿⡈⠻⣆⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢞⣽⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢸⣿⣿⣿⣿⣿ ⣿⣇⠀⠀⠀⠀⢻⡀⠹⡄⠀⠀⠀⣇⠀⠈⠀⠠⠶⠶⡞⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢞⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⣿⣿⣿⠏⢻ ⣿⣿⠀⣠⡀⠀⠀⢧⠀⢹⡄⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⢸ ⣿⣿⠀⣿⡇⠀⠀⣌⣧⠀⢻⣆⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸ ⣿⡞⣸⠁⢻⡀⠀⠸⣟⣆⠀⢻⣦⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣅⣉⣻⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⡎ ⣿⣿⣿⠀⢸⣧⠀⠀⠹⣾⢧⡈⢻⣷⣄⠀⠈⠳⣤⣀⣀⣀⣀⣠⠤⣤⡀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡳⡇ ⣿⣿⣿⢠⠘⣿⣧⡀⠀⢻⡗⢿⣆⡻⣿⡷⣤⡀⠀⠈⠉⠉⠉⠀⢀⡼⣋⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⢣⠇ ⣿⣏⣿⢸⡇⣿⡏⠳⣷⡌⢻⡀⠀⠉⠙⢿⣮⢿⡲⣴⣶⣤⣴⣾⡽⠞⠉⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢀⣾⣿⣿⣿⠟⠁⣸⢀ ⢿⣿⣿⢰⣿⢹⣧⡀⢻⠙⡶⣷⡄⠀⠀⠈⠻⣯⡳⣄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢠⣿⣿⣿⣿⠃⠀⣸⢿⠸ ⠀⠙⠿⣧⣯⣟⡿⡇⠘⡆⢹⣹⡿⣆⠀⠀⠀⠈⠻⣮⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⣰⣿⣿⣿⡿⠁⠀⢠⠇⣸⠃ ⠀⠀⠀⠘⠻⠾⢿⣿⣤⣽⣄⣷⡳⡜⢧⡀⠀⠀⠀⠈⠙⢾⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢾⣿⣿⣿⢿⠃⠀⠠⢾⠃⠁⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠿⢿⣦⡀⠀⠀⠀⠀⠀⠛⠻⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⢤⣀⣠⠞⠁⣠⣴⣿⠿⠟⢛⠠⣿⠇⢠⣾⡿⠀⡆⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣗⣦⣀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣷⣤⣤⣤⣀⣀⣀⣀⣀⣀⡀⣀⡀⠀⣀⣀⣠⣤⣴⣿⣿⠏⣁⡴⠊⢁⣠⡿⢶⡟⠉⠁⠀⡇⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣛⡲⠶⣦⣀⠀⠀⠀⠀⠉⠋⣙⡙⡛⠛⢿⣟⠛⠛⠿⠿⠿⣿⣿⣿⠻⣿⣿⡿⠋⠀⢁⡐⠚⠋⠉⡓⠸⠀⠀⠀⢀⡇⠀

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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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