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⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠾⠿⠿⠿⠿⠷⠀⠀⠀ ⠀⠀⣼⣆⠀⠀⠀⠀⣰⣧⠀⠀ ⠀⣼⣿⣿⣆⠀⠀⣰⣿⣿⣧⠀ ⠾⠟⠿⠿⠿⠧⠼⠿⠿⠿⠻⠷
⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤ ⠘⣿⣿⣿⣷⣦⣄⣀⠀⢠⠔⠀⢀⡼⠿⠿⢆⠀⠀⠲⣄⠀⣀⣠⣴⣾⣿⣿⣿⠇ ⠀⠈⠉⠉⠛⠛⠻⠿⢿⣿⠀⢀⣾⣷⡀⢀⣾⣷⡀⠀⣿⡿⠿⠿⠛⠛⠉⠉⠁⠀ ⠀⠀⣤⣤⣶⣶⣶⣶⣶⣿⣆⠈⠉⠉⠉⠉⠉⠉⠉⢠⣿⣶⣶⣶⣶⣶⣤⣤⠀⠀ ⠀⠀⠘⣿⡿⠟⠛⠉⣡⣿⣿⣷⣤⠀⢠⣆⠀⣤⣶⣿⣿⣬⡉⠛⠻⠿⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⡿⢋⣿⣿⠛⢠⣿⣿⡄⠛⢿⣿⡘⢿⣿⣦⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠻⠏⠀⣸⣿⡇⢀⠻⣿⣿⠟⣀⠸⣿⣇⠀⠙⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡟⠁⣿⣿⠀⠻⣆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⠉⠙⠓⠀⠘⠏⠀⠘⠟⠉⡻⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣶⣦⣼⣿⣿⣿⣿⣿⣿⡟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣠⣾⣿⣿⣿⣿⣿⣟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣿⡟⣹⡟⣴⢻⣷⠘⠿⣷⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⠐⢋⣴⣋⣯⣽⣷⣦⣤⠤⣾⣿⣿⣿⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⣿⣒⡻⠟⣿⣨⣿⠉⠉⠐⣲⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠙⠛⠻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣷⡤⣢⢹⠉⣣⣠⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣦⣤⣤⣬⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣿⢿⣡⡆⡤⣭⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠛⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣽⣿⣷⣅⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠛⠈⠙⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⠏⠙⠿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⢹⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡿⠃⠀⠀⠀⠈⠙⠋⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡆⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣄⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣧⠸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡆⠙⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡿⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⣶⡀⠀⠻⢛⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀ ⠀⠀⢠⣾⣿⣿⣿⣿⡦⣼⣯⣵⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⢹⣿⠀⠀⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣦⣀⢀⡘⣿⡇⠀⠀⠀ ⠀⣾⣿⣿⣿⣿⡟⠉⠀⠀⣾⣿⣿⣿⣿⠟⠁⠀⠉⠻⣿⣿⣿⣿⣧⣠⣶⠄ ⢰⣿⣿⣿⡿⠋⠀⠀⠀⢀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠙⠻⣿⣿⣿⡟⠁⠀ ⢸⣿⡿⠋⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠙⢻⡃⠀⠀ ⠀⠁⠀⠀⠀⠀⠀⠀⣾⣿⣿⠿⣿⡿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠙⢿⣿⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠀⠀⠀⠀
pls note the ai inflicts emotional damage (ᵕ—ᴗ—)
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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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