Dragon Hissing Emojis & Text

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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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⠤⢁⠄⠀⠀⠀⠀⠈⠙⠛⠷⣦⡄⡀⠀⠀⠀⠀⠀⠀⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⢀⣴⠟⠁⠀⠀ ⣶⢦⣦⣤⣤⣤⣤⣤⣄⣀⣀⣀⣉⠛⠳⣔⣤⡀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⡀⣠⡿⠋⣀⣴⠶⠛ ⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠈⠉⠉⠉⢛⣻⣿⣷⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⡟⣛⠁⠀⠀⠀ ⢂⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠾⠛⠉⣹⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⣀⣤⣤⣤⣶⣶⢶⣤⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢯⣍⠙⠛⠛⠛⠛ ⠀⠄⠀⠀⠀⠀⢀⣀⣤⡼⠿⠟⠃⠀⠀⠀⣠⡿⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠿⠿⢿⢻⣿⣿⢿⣿⢿⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠘⢿⣄⠀⠀⠀ ⠈⢄⣶⣶⣶⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⣼⠟⠅⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⢷⡯⢗⣻⡖⠓⢒⣃⣤⣄⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠙⢻⣦⡄ ⣼⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠰⠀⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⣻⣯⣿⣙⣾⡟⢸⠺⣿⣿⣿⡟⢉⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠙⢿ ⢡⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣇⠎⣸⢣⡟⢃⣏⣓⢷⡹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠄⠀⠀⠌ ⢢⢉⠄⠃⢄⠀⠂⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⣾⣿⣽⠨⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⢿⠀⠁⣇⠊⠠⢞⠋⠉⠉⠑⣽⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡄⠀⠀⡜⢠⡉⠖ ⠥⣊⠌⡅⢢⠈⢅⠂⠄⠂⣸⡿⢁⠀⠤⠀⠀⣿⣿⠇⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣁⡆⡟⠀⠀⢲⠀⠀⠀⠀⠈⠪⠾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣿⣿⠂⡀⡐⣌⠣⡜⣩ ⢒⡡⢊⠴⣁⠚⣄⠊⠤⣡⣿⠁⠆⡈⠔⠀⠀⣿⣿⢇⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠈⢙⣏⣴⠹⡠⢀⠠⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡐⠤⡑⣌⠳⣜⡵ ⢢⠘⣌⠲⢌⡓⡌⣍⢲⡿⡡⢎⡐⠬⠀⠐⠀⣿⣯⢧⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠹⣖⡆⠈⠢⡢⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣾⡿⣿⢀⠧⣑⠮⣝⢮⣳ ⢀⢉⡀⢷⡈⢶⢱⣈⣿⢇⡱⢆⡸⠆⠀⠁⠀⣿⣏⢿⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠈⢿⣇⠁⣀⠆⠆⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⡇⡎⢶⣉⡾⣹⡾⢷ ⢈⠢⡘⢆⡙⣆⢧⣿⣏⠞⣔⠣⡜⢡⠂⡁⠀⢿⣿⣟⡀⠄⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣬⠦⠀⢄⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⢰⣟⣾⡿⢱⡘⢦⡻⣼⣳⢟⡿ ⠀⢢⠑⡎⣵⢪⣿⣟⣬⢻⣌⠷⣌⢣⡘⠀⠀⢸⣿⣿⡷⣈⠁⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣮⠠⡵⠀⠀⠀⠀⢁⠀⠀⠀⠀⢀⠴⢋⣿⢻⢃⠧⣜⢧⣟⣳⢯⣿⠙ ⠀⢢⡙⡜⣶⣻⣟⡾⣼⢳⣎⢷⣊⢦⡙⠤⠀⣼⣿⣿⣿⣦⡑⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣷⡀⠀⠀⠀⠘⠀⠀⢀⠴⡁⣰⠞⣿⣿⢘⢮⡝⣾⡽⣫⠟⠁⠀ ⠀⢥⢪⢵⣣⣿⣻⢾⣽⣳⣻⢮⣝⡮⡵⣉⢦⣿⡿⠀⠈⠙⠻⢷⣦⣀⡅⢠⠐⠠⠄⣀⠀⣠⠄⠢⠂⠝⠋⢻⣿⡒⠠⠄⣀⠀⢐⠆⠂⠐⣴⠟⠉⠀⣿⣏⢞⣮⣽⣳⡟⠁⠀⠀⠀ ⠣⣎⢮⣳⣿⣻⣽⣻⣞⡷⣯⣟⡾⣵⡳⣕⣾⣿⠃⡄⠀⠀⠀⠀⠈⠉⠛⠿⢶⣥⣴⣠⡞⠀⠂⠀⣥⠈⡁⡢⠗⣀⠠⠀⡀⠀⢸⢘⡼⠟⠁⠀⢠⠌⣿⣏⡾⣮⢷⡛⠁⠀⠀⠀⠀ ⠀⠻⣮⢷⣿⣳⢯⡷⣯⣟⡷⣯⣟⣷⣻⢞⣿⢧⣋⠴⡩⢔⢢⡐⡀⠄⡀⢀⠀⣤⣾⢻⠄⠒⡉⠐⡬⠐⠈⠊⡀⠀⠡⠁⠒⠐⠻⣨⠇⣠⢂⡍⢦⡙⣿⣯⢷⣯⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⢫⣿⢷⣯⠿⠙⠓⠯⣟⣷⣻⢾⣽⣻⣟⣳⣎⢷⣙⣎⢦⡱⣍⣶⡷⣞⢿⣛⣬⡻⡌⠡⡀⣷⠇⠁⢀⠀⠈⠂⢁⣐⡀⡼⢨⢈⡗⣦⢳⡜⣧⣻⣽⣯⣟⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢺⣿⠋⠀⠀⠀⠀⠀⠘⣷⣯⣿⣾⣿⣽⢳⡞⣯⣾⣼⢣⣷⣾⣯⣷⠛⡏⢹⡌⡆⢱⣤⡞⡍⠈⡄⠀⠑⡄⠈⡄⠀⠀⠀⢸⡌⢹⡞⣧⡟⣷⢻⣾⢳⣯⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡿⠉⠀⠀⠀⠀⠀⠀⠀⣿⣞⡷⣿⣯⣟⣯⢿⡽⣞⣧⣿⡿⣫⣿⢶⣎⣳⡼⣷⢿⠛⢡⠀⠱⡀⢈⠢⡀⢈⠠⠐⠀⠀⠈⣟⠁⣼⡿⣽⣻⣽⣻⢾⣟⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢿⣟⣾⡽⣞⣯⢿⡽⣞⣯⣿⣟⣯⣿⡿⠿⡽⢃⠁⢃⠀⠳⠀⡑⢄⠀⠉⠐⠠⠤⠄⠐⣸⢧⣾⢿⣽⣳⣟⡾⣽⣻⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⢸⣯⣿⣟⡾⣽⣻⣞⣯⢿⡽⣿⣻⡿⣾⣿⣵⢐⢳⡘⡄⠘⡂⠄⡑⢄⠠⠑⠪⠄⢀⠀⢀⣾⣽⣻⣞⡿⣞⡷⣯⣟⣷⣻⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⣼⣻⣷⢯⡿⣽⣳⣟⡾⣯⣟⡷⣯⢿⡿⡟⣿⠘⡴⡅⠘⢄⠐⠠⢀⡂⢈⠐⢠⣐⣤⣾⣟⡽⣞⡷⣯⢿⣽⣻⢷⣻⢾⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠐⠶⣿⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣇⡀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⡿⠟⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣆⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⡿⠻⠁⡓⣚⣓⣽⣭⢯⣖⠿⣏⢯⠝⡽⠁⠮⡎⠼⠖⡰⣦⢜⢈⠀⠢⣤⢃⡪⣑⣛⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇⡧⣼⢁⣴⡿⡾⠿⡼⣯⣽⣷⣇⡟⣾⣟⢾⣷⣶⠦⣤⣶⣔⢥⡷⣅⠛⡲⣷⣭⣖⡛⡆⠞⣄⣤⡴⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⡏⢘⠂⡟⢀⡟⢧⢏⡏⡣⣿⢞⣠⢙⣤⣗⣯⠦⠏⠧⠇⡗⠟⡓⡖⢼⣸⡸⣆⡎⠿⠻⣇⣖⣦⢰⢋⡇⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⢧⣿⢠⡙⡏⡆⠒⣿⣂⡛⢁⣲⣏⣞⣠⡦⣶⡻⣛⡊⣸⡷⣝⣷⢮⠪⣉⢝⣿⡧⡬⣯⠳⣃⢷⢡⣻⣿⡏⠅⡇ ⠀⠀⠀⠀⠀⡖⢄⠀⡏⡹⣿⠘⡧⡿⡐⡄⡗⡔⠡⣉⢻⠿⣉⣟⡃⣶⣻⠿⣣⡃⠥⣃⣽⡇⢗⣶⣏⣿⡻⠮⢿⡢⢟⢿⣟⠻⢿⡳⣱⠃ ⠀⠀⠀⠀⣄⠡⡇⣕⢇⣐⣻⡀⣷⡃⡲⡛⡞⣃⠼⠫⠋⣝⠯⠎⣻⣜⡨⡂⣞⣃⠹⡎⣗⡄⡵⡇⡜⠏⣑⡃⢆⣟⣼⡳⢷⡶⣿⡽⡞⠀ ⠀⠀⠀⠀⠌⣊⣍⣫⣂⠉⡟⢖⡭⡗⠇⣺⠖⣀⠯⢤⡓⢈⠖⢆⠈⢧⡆⣊⣕⠆⣜⡊⢳⡋⢱⡟⢀⠖⠁⠑⣆⠑⡣⢃⡨⣒⠈⣿⡥⢺ ⠀⠀⠀⠀⠂⢇⡖⡓⡔⠱⣆⠚⢍⣏⡹⣹⡵⣃⡋⠂⡐⣀⡐⠀⠳⡝⣷⡼⣟⡯⢲⡇⡚⡭⠓⡔⠁⠀⠀⠀⠈⣇⠛⡇⠅⢲⡇⡀⣼⡼ ⠀⠀⠀⠀⠠⠈⣖⡑⡗⡧⢇⢐⡃⣧⣔⢈⣟⣵⠧⣅⡀⡏⡇⠀⠀⠱⣡⠢⣯⣁⡲⢏⡟⡡⠏⠀⠀⠀⠀⠀⠀⠘⡎⣗⣚⡭⣿⠔⣷⣞ ⠀⠀⠀⠀⠀⡀⢇⢪⢣⢇⡃⡏⢿⡔⣁⠮⡡⢃⣀⣀⠈⠁⠣⡀⠀⠀⢹⣆⣿⡎⡆⡷⡵⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⡩⣒⣻⠃⢗⣸⢹ ⠀⠀⠀⠀⠀⠀⠼⡘⢵⣺⡒⡟⡟⡤⠚⡕⠁⠀⠀⠀⠉⠳⡀⠑⡄⠀⠀⡋⣶⣧⡁⡔⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⣒⢚⣿⠇⠜⢡⠎ ⠀⠀⠀⠀⠀⠀⠡⣣⡹⡃⠣⡅⡅⢇⠎⡀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠸⡌⡇⣠⠃⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⡿⡰⠨⠈⡴⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⢣⡑⣗⡀⠐⠃⡏⠀⠙⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡰⠃⠀⠀⠀⠀⠀⣀⣄⣄⣧⠀⠀⠀⡟⠗⢁⠎⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠻⢶⣐⡡⠀⠀⡇⠀⢹⣿⡿⣭⣳⣆⠀⠀⠀⠀⠘⠇⠀⠀⠀⢀⣔⣟⣛⣭⣻⣻⠀⠀⡞⢁⠔⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠫⣷⡀⠉⠁⠀⠀⡃⠉⢹⣿⣿⣷⣦⣀⡀⡀⠠⣤⣶⣞⣧⣿⣿⠉⠀⡼⠈⢀⠞⠃⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⡛⣆⠀⠀⠠⣇⡀⠘⠯⠿⠿⠉⠉⣹⠋⠀⢸⠀⠀⠿⠿⠟⠀⠀⡇⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⢇⠀⠀⠈⠑⠥⡂⣄⠀⠀⠀⣇⣦⠄⠘⡆⠀⠀⢀⣀⡤⠖⢫⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠉⠙⠻⠲⣷⡟⠀⠀⠟⠋⠉⠉⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⢿⣤⢤⣤⡤⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⡀⠀⠀⣠⣤⣤⣄⠀⠀⠀⢠⠎⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠅⠉⠲⣔⡁⠀⠀⠀⠀⢀⡔⠁⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠉⠒⠢⠤⠖⠋⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⡶⠁⣠⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣴⣿⠿⠋⣁⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣿⡿⠟⠋⠉⠀⣀⣀⣀⣨⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣴⠂ ⠈⠉⠁⠀⠀⣀⣴⣾⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠛⠻⠿⠿⠿⠿⠿⠿⠟⠋⠁⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⡿⠁⠀⢀⣀⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⡿⠁⢀⣴⣿⠋⠉⠉⠉⠉⠛⣿⣿⣶⣤⣤⣤⣤⣶⠖⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⡇⢀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⡇⠈⢿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣷⡀⠀⠉⠉⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣋⣠⡤⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀

⣷⣄⡀⠀⠀⠀⠀⠀⣠⠖⠉⠉⠹⣆⠀⠀⣠⠴⠒⠉⠉⢀⣠⣤⡀⢀⣤⡶⢶⣶⣶⡦⣤⣀⠀⠀⠈⠉⠉⠳⣤⡀⠠⣄⠀⠀⠀⠀⢠⠏⠉⠉⢷⠙⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣦⣄⠀⢠⠟⠁⠀⠀⠀⠀⢈⡴⠋⠀⠀⣠⡶⠞⠛⠉⠉⢉⠛⠋⠉⠻⣦⠉⠉⠉⠛⢷⣄⠀⠀⠀⠀⠈⠻⣄⠀⠑⢦⠀⠀⠏⠀⠀⠀⠈⠒⣄⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠉⠑⣶⠏⠀⠀⣠⠞⠉⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠈⢳⡀⠀⠳⣄⠀⠀⠀⠀⠀⢀⡼⠆⠀⠱⣄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡖⠢⠤⢤⡼⠃⠀⢀⠜⠁⠀⠀⠀⡰⠁⠀⡠⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠠⡄⠘⢦⠀⠀⠀⠀⠀⠹⡄⠀⠙⣦⣀⣀⡤⠖⢻⡄⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠛⠁⠀⢀⡞⠁⠀⣠⠋⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠹⡄⠈⢳⡀⠀⠀⠀⠀⠙⡄⠀⠈⢯⠀⠀⠀⠘⢧⡀⠀⠀⠀⠘⡆⠀⠀⠀⠀ ⣿⣿⣿⣿⠿⣧⣀⡀⠀⡼⠀⠀⣰⠃⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠹⡆⠀⢳⡀⠀⠀⠀⠀⢹⡄⠀⠈⢧⠀⠀⢀⣤⠵⣄⠀⠀⠀⢹⡀⠀⠀⠀ ⣿⣿⣿⡟⠀⠀⠀⠈⢹⠃⠀⢰⠏⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠸⡄⠀⢻⡀⠀⠀⠀⠀⢹⡀⠀⠘⡆⠈⠁⠀⠀⢸⡄⠀⠀⠀⣧⠀⠀⠀ ⣿⣿⣿⡇⠀⠀⠀⠀⡏⠀⠀⡾⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢻⡄⠀⢷⠀⠀⠀⠀⠀⢷⡀⠀⢹⠂⠀⠀⠀⢠⠇⠀⠀⠀⢹⡀⠀⠀ ⣿⣿⣿⣧⡠⠤⠀⢰⠃⠀⢰⡇⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⢷⠀⠘⣧⠀⠀⠀⠀⠈⣇⠀⠈⣇⠉⠉⠀⢸⡀⠀⠀⠀⠈⡇⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⣾⠀⠀⢸⡇⠀⠀⠀⠀⣀⣿⠀⠀⠀⢸⡘⠀⠀⠀⠀⠀⠘⣗⠄⠀⠀⠀⠀⠀⣿⡟⠒⠀⢼⡆⠀⢹⡄⠀⠀⠀⠀⠸⡀⠀⢻⠀⠀⠀⢀⠇⢀⡀⠀⠀⣇⠀⠀ ⣿⣿⣿⣿⠀⠀⢀⡏⠀⠀⢸⡁⠢⠀⠀⠀⣇⣿⡆⠀⠀⢸⣵⠀⠀⠈⡆⠀⢰⣿⡴⡄⠀⠀⠀⠀⢸⣷⣠⠀⠈⣿⠀⠀⣧⠀⠀⠀⠀⠀⣷⠀⢸⠈⠉⠉⠉⣟⠛⢋⢳⠆⢹⠀⠀ ⣿⣿⣿⣿⣀⣀⢸⠁⠀⠀⢸⠅⠀⡇⠀⠀⣿⡏⣇⠀⠀⠀⣿⢠⠀⠀⠙⠢⠈⢿⣯⠠⠀⠀⠀⠀⢸⡏⢿⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠸⡄⢸⣀⣀⠀⠀⣿⡙⢿⡞⠀⢸⡄⠀ ⣿⣿⠿⣿⣯⠀⢸⠀⠀⠀⢸⣇⠀⠀⠄⠀⢿⡇⢹⡀⠀⠀⠸⣎⡇⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⢸⢷⢸⡄⠀⢸⣿⠀⠸⣧⠀⠀⠀⠀⠀⡇⣼⠁⣿⣿⠷⣌⣧⠈⣇⠀⢸⠁⠀ ⢋⣵⣿⣿⢋⣟⡿⠀⠀⠀⠀⣿⡄⠀⠀⠀⠘⣿⠀⢷⡀⠀⠀⢿⡸⡀⠀⠀⠀⠀⠹⣞⣦⡀⠀⣀⣾⣾⣼⣧⣦⣿⣴⣦⣴⣿⡀⠀⠀⠀⠀⢹⣿⠀⣿⠸⣞⣦⠽⣀⡼⠀⢸⣀⣀ ⠈⢿⣿⢃⠞⣼⡇⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⢹⣇⠘⢷⣄⣀⠈⢇⠹⣄⣀⣤⣤⠴⠛⠎⠛⠛⢿⣽⡾⢿⣿⣿⣿⣿⣯⡍⢻⡇⠀⠀⠀⠀⢸⣿⢸⡟⣦⣿⡶⢺⠉⠀⠀⢸⣿⣿ ⣷⣌⠛⢊⣴⢃⡇⠀⠀⠀⠀⢸⠻⣆⠀⠀⠀⣀⣽⣖⣀⡛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⢰⣾⣿⡿⠛⠻⣷⡄⡃⠀⠀⠀⠀⠈⣿⠀⡇⠀⠀⢻⡈⢳⡀⠀⣾⣿⣿ ⣿⣿⣷⣿⢭⣽⠃⠀⠀⠀⠀⢸⠀⢹⣦⣴⣿⠿⠛⠉⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⢹⣷⣾⠀⣽⠃⡇⢐⠀⠀⠀⠀⣿⡀⣷⠀⠀⠀⢹⡄⢳⡄⢿⣿⣿ ⣿⣿⡿⠃⣾⣿⠀⠀⠀⠀⠀⢸⢿⡉⠀⢿⡇⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠙⠉⣰⡏⠀⣿⣼⠀⠀⠀⠀⣿⡇⢹⡀⠀⠀⠀⢻⣄⣿⣿⣿⣿ ⣿⡿⢁⣾⡟⠏⠀⠀⠀⠀⠀⢸⠈⢳⡀⠀⠀⠀⠀⠘⣿⣿⠿⣿⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠶⠿⠛⠀⠀⣿⣿⠀⠀⠀⠀⣿⢳⣼⣧⡀⠀⢀⡄⠃⠉⣿⣿⣿ ⡿⠁⣼⣿⡧⠀⠀⠀⠀⠀⠀⡿⠀⠎⠻⣄⠀⠀⠀⠀⠸⣇⡀⠙⢡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡋⠀⠀⠀⠀⣿⡶⢹⠉⠹⣄⠘⡛⠀⠀⢸⡏⠉ ⠁⢰⣿⣿⡇⠀⠀⠀⠀⠀⢰⡇⠀⡄⠀⣿⢦⠀⠀⠀⠀⠈⠛⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡂⠀⠀⠀⠀⡟⣡⠟⣇⡀⢹⣧⠀⠀⠀⠀⠃⠀ ⣄⣸⣿⣿⠀⠀⠀⠀⠀⠀⣼⠀⠀⠈⢂⣿⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡟⠀⠀⠀⠀⣿⠁⠀⠈⠳⣼⣿⠀⠀⠀⢀⡃⠀ ⣿⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⣄⠀⠀⠀⠸⣿⡀⠀⠀⠅⠀⠀ ⣿⣿⡏⠀⠀⠀⠀⠀⢐⣿⣿⡄⠀⠀⠀⢼⡇⢠⡞⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠃⠀⠀⠀⢠⣿⠉⠉⡝⠉⠉⠙⠧⠠⡆⠀⠀⢘ ⣿⡟⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣦⣤⣀⡈⢻⡄⠀⣟⢳⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣽⣿⡏⠀⠀⠀⠀⢸⠛⣧⠀⣇⠀⠀⠀⠀⠈⠀⠀⠀⡈ ⣿⠁⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡎⢉⣩⣿⣶⡋⠉⠉⢻⣗⠶⡶⢤⣤⣤⣞⠉⠀⠙⢦⣀⡀⠀⢀⣀⡴⠊⠁⣠⠟⠙⢿⠀⠀⠀⠀⠀⡼⠀⠘⢷⠙⢶⣄⠀⠀⡶⠀⠀⠔⠀ ⠃⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠉⠳⣄⡀⠙⣟⣿⠷⠦⢤⣀⣙⠲⣄⠈⢳⣹⣶⠿⠋⣠⠴⠋⠁⠀⠀⡞⠀⠀⠀⠀⢰⡧⢤⣠⠼⠓⠒⠛⠛⠓⠓⠂⠄⠀⠀ ⠀⠀⠀⠀⢠⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠈⠉⠙⠓⠤⣄⡀⢙⣦⣯⣀⣀⣀⠀⠀⠈⠳⣌⠳⣄⠻⢿⣷⡏⠁⠀⠀⠀⠀⢸⠇⠀⠀⠀⢀⣼⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣤⡤⡤⠤⠤⠬⠛⠻⣥⡟⢓⠛⢛⣷⣦⡀⠀⠀⠀⠈⠀⠈⣿⣿⡀⠀⠀⠀⢀⡏⠀⠀⠀⢰⣯⣯⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋⡟⠁⠀⠀⡼⠁⢠⠃⠀⠀⠀⢀⡴⢦⣽⡾⢯⣿⡭⠜⣧⠀⠀⠀⠀⠀⠀⢿⣿⣷⠸⠆⣰⡟⠀⠀⠀⢠⢛⡞⠁⢀⣠⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⠟⠉⢀⡾⠀⠀⠀⢸⠃⠀⣾⠀⠀⠀⠀⠀⢷⡀⠉⠀⣰⠇⠀⠀⡿⠀⠀⠀⠀⠀⠀⢸⡿⣿⣷⣾⡟⠀⠀⠀⣰⢏⣾⠵⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠟⠁⠀⢀⠏⠀⠀⠀⠀⡞⠀⠀⠘⡦⢄⡀⠀⠀⠈⠻⡶⠀⡏⠀⢀⣀⡇⠀⠀⠀⠀⠀⠀⠘⡇⢹⡿⣋⠀⠀⠀⢠⣯⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀ ⠀⠀⠀⠀⡀⢀⣠⠎⠀⠀⠀⠀⠀⢹⡀⠀⠀⠘⠛⠋⠉⠛⢶⣴⣃⣸⠃⠚⠉⠈⡇⠀⠀⠀⠀⠀⠀⠀⢹⠀⣸⣯⡀⠀⣈⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠋⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣫⡞⠁⠀⠀⢀⣠⣶⡛⠩⢹⡿⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⡞⠀⠀⣀⣴⣿⠟⢁⣤⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⣿⠀⣿⣋⣉⣵⣻⣯⠴⠒⠶⣚⠓⠲⣖⠿⣿⢵⣶⣤⣤⣴⣾⠋⠀⢀⣀⣀⡤⠔⣺⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡽⣏⡤⠟⠋⠉⠀⠀⠀⠀⠀⠉⠑⠢⡀⠑⢆⠈⢧⠈⣦⠘⠆⠙⠉⡏⠫⠙⠉⠃⢸⣠⠞⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠁⠀⣠⣾⣉⣉⠶⠀⠀⠀⠀⠀⠀⠘⡄⢸⠀⡜⠀⠇⢠⠀⡄⢀⣃⣀⣰⠴⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡖⠀⠀⠀⢀⣾⠃⠀⢠⣞⡡⢋⡾⠀⠀⠀⠀⠀⠀⠀⠀⣠⡧⣾⣒⠓⢾⣒⠛⠚⢛⣩⣉⣙⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⢻⣡⣾⣴⠧⠟⣀⠄⠒⠛⠒⠚⣛⠅⠀⠀⢀⡖⠉⠁⡠⠌⠁⠀⠐⠚⠿⢶⣽⣦⡀⠀⢀⡭⠑⣢⣍⣳⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣷⣾⠿⠙⠡⠒⠉⠀⠀⢀⠀⠀⠀⢁⡤⣀⣠⠊⠀⢠⢜⡢⣄⡀⠀⠠⢄⣙⣦⠽⠮⣿⣦⡀⢹⢯⠁⠀⠀⠙⠻⢄⠀⠀ ⠀⠀⠀⠀⢀⡟⢹⠃⠀⠀⠀⠀⠀⣀⡴⣿⣿⣶⡖⢿⣠⠞⠁⠠⡀⣿⠀⠉⠪⡻⣄⡀⡎⠁⠈⢣⡀⠀⠉⠛⢦⣌⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣧⠀⣀⣀⣀⣀⣴⣾⣙⣾⣿⣿⣿⡿⠊⠀⠀⠀⠀⣷⢃⣄⢀⠀⠙⢌⢿⢧⢡⠀⠀⠱⡄⠀⠀⠀⠹⣿⢽⣦⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠹⣿⣮⣾⣯⣷⣿⡟⣿⣿⣿⠋⠀⠀⠀⠀⠀⢰⣷⣿⢿⢿⡀⠀⡎⢎⢧⣯⡇⠀⠀⠹⡀⠀⠀⢤⠘⢷⢻⠻⣦⠀⠀⠀ ⠀⠀⠀⢀⣠⣤⣤⣌⣙⣿⣿⢛⣻⣿⣿⠟⠁⠀⠀⠀⢀⡤⠚⠉⠀⠈⢣⡀⡿⠿⢿⡈⢿⣿⠀⠀⠀⠀⢳⡀⠀⠈⠁⠈⣯⣇⠈⠂⠀⠀ ⠀⠀⡴⢋⠔⠋⠉⠙⢿⣃⣉⣽⣿⡾⠋⠀⠀⠀⣠⢞⣁⠤⠤⢴⣶⡶⣀⠹⠃⠀⠀⠑⢾⣿⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀ ⠀⣞⣡⠃⠀⠀⠀⠀⠀⠀⠹⡟⠉⠀⣤⠴⣤⣿⠛⠉⠀⠀⠀⠈⢯⣿⣦⡀⠑⠦⣀⠀⠘⡇⢠⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢻⡄⠀⠀⠀ ⡸⢸⣱⣀⣀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠼⠷⠞⠛⠁⠀⠀⠀⠀⠀⠸⠇⠀⠻⣄⠀⠀⠷⡈⠀⢰⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠘⡇⠀⠀⠀ ⡇⠸⣌⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⣧⠀⠀⠀ ⠘⠒⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣯⣇⠳⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠙⢳⡖⣿⠀⠘⢆⠀⠀⢇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⡾⢹⡀⠀⠈⢆⠀⠘⢆⠀⠀⠀⠀⢸⠀⠀⠀⠀⡼⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⡴⠋⠀⢸⠁⠀⠀⠈⣆⠀⠘⡆⠀⠀⠀⠸⠀⠀⠀⢀⡇⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢞⣝⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠚⣩⣟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡏⡏⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠃⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⡀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⡇⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⣇⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣼⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡟⢹⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⡇⢸⡀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⡇⢸⡇⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢸⣇⣠⣷⡶⠶⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡽⠽⠞⠛⢉⣁⠀⢠⡈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡖⢒⡒⠉⢹⡇⠀⠈⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢸⠁⠀⠘⡇⠀⠀⢹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⡟⠀⠀⠀⣷⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⣼⠇⠀⠀⠀⢿⣆⠀⠀⠸⣿⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⣰⡿⠀⠀⠀⣀⣘⣹⣤⡤⠴⠶⣤⡈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⡭⠼⠷⠖⠚⠛⠉⠉⠉⠀⠀⠀⠀⠀⢰⣍⡓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠘⣿⣿⣶⣬⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⢠⠞⢠⡤⠄⠀⠐⠶⠶⣒⡁⠸⣆⠀⠀⠀⠹⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⠁⢀⣴⠃⣀⠥⠔⠒⠊⠉⠒⠒⠦⣤⣀⠻⢧⡀⠀⠀⠹⣿⣿⠿⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠀⢠⣮⠖⣋⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣷⣦⡁⠀⠀⠀⠘⣿⡄⠀⠙⢷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠋⠀⣠⠾⠕⠋⠁⠀⢹⡇⠀⠀⠀⠀⣠⠖⠉⠀⠀⠙⢿⣦⡀⠀⠀⠘⣿⣄⠀⠈⠻⣆⠀⠀⠀ ⠀⠀⢀⣼⠋⠀⣴⡟⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠘⢿⣄⠀⠀⠹⣦⠀⠀ ⠀⣠⡾⠁⠀⣸⡟⠀⠀⠀⠀⠀⠀⠿⠧⠤⠄⠠⠿⠄⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⠈⢿⣆⠀⢀⣸⣷⡀ ⠐⠛⠓⠂⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠧⠀⠀⠤⠾⠿⠧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣠⣶⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⢀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣟⣋⣼⣽⣾⣽⣦⡀⠀⠀⠀ ⢀⣼⣿⣷⣾⡽⡄⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣿⡿⢿⣟⣽⣾⣿⣿⣦⠀⠀ ⣸⣿⣿⣾⣿⣿⣮⣤⣤⣤⣤⡀⠀⠀⠻⣿⡯⠽⠿⠛⠛⠉⠉⢿⣿⣿⣿⣿⣷⡀ ⣿⣿⢻⣿⣿⣿⣛⡿⠿⠟⠛⠁⣀⣠⣤⣤⣶⣶⣶⣶⣷⣶⠀⠀⠻⣿⣿⣿⣿⣇ ⢻⣿⡆⢿⣿⣿⣿⣿⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⣠⣶⣿⣿⣿⣿⡟ ⠈⠛⠃⠈⢿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠋⠁⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⠀⠀ ⠀⠀⣠⣤⣤⣄⣀⣾⣿⠟⠛⠻⢿⣷⠀ ⢰⣿⡿⠛⠙⠻⣿⣿⠁⠀⠀⠀⣶⢿⡇ ⢿⣿⣇⠀⠀⠀⠈⠏⠀⠀⠀ text here ⠀⠻⣿⣷⣦⣤⣀⠀⠀⠀⠀⣾⡿⠃⠀ ⠀⠀⠀⠀⠉⠉⠻⣿⣄⣴⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⣆⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣼⣿⡗⠀⠀⠀⠀ ⠀⠀⠀⣠⠟⠀⠘⠷⠶⠶⠶⠾⠉⢳⡄⠀⠀⠀⠀⠀⣧⣿⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⣤⣤⣤⣿⢿⣄⠀⠀⠀⠀ ⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠙⣷⡴⠶⣦ ⠀⠀⢱⡀⠀⠉⠉⠀⠀⠀⠀⠛⠃⠀⢠⡟⠂⠀⠀⢀⣀⣠⣤⠿⠞⠛⠋ ⣠⠾⠋⠙⣶⣤⣤⣤⣤⣤⣀⣠⣤⣾⣿⠴⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀ ⠛⠒⠛⠉⠉⠀⠀⠀⣴⠟⣣⡴⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⡠⢉⣉⣫⠳⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⢢⠀ ⠀⠀⠀⠀⠀⢠⠛⡩⠂⢀⠠⠵⡈⢲⠤⠒⠀⠀⠂⠀⠄⣀⢄⠶⠛⢻⣋⡀⠀⠂ ⠀⠀⠀⠀⠀⡟⢘⠜⡢⠁⠀⡔⣱⠇⠀⠀⠀⠀⢀⠔⡀⠀⠣⣀⠀⠀⢴⠉⠀⢸ ⠀⠀⠀⠀⢠⠗⢡⠊⠀⠌⠌⡜⠃⠀⠀⠀⠀⠠⠁⣴⠀⠀⠀⡄⠢⡀⣨⡆⠀⢸ ⠀⠀⠀⡠⣫⠵⢡⠁⣼⠀⡜⠰⢀⡀⠀⠀⢀⣠⠎⠸⢲⠀⠄⢻⡀⠐⠙⡄⠀⠀ ⠀⢀⡾⡰⠁⠂⠇⡸⣸⣸⠔⠚⡅⠀⠀⠀⢠⠃⠈⠒⣎⡄⠰⠈⣇⠀⠀⢹⠆⠀ ⢠⡿⢱⡇⢸⡜⣠⠁⠀⠉⠀⠉⠘⢄⠀⣸⡇⠀⠂⠀⢹⠹⠀⠀⣏⠀⠀⠀⠀⠀ ⢯⠃⢨⠁⠈⠳⣙⢶⠟⣋⠙⠻⠃⠀⠉⠙⠀⠤⡽⠴⢦⣣⣁⡇⡀⢀⠀⠀⠀⠀ ⠂⠀⡄⠀⡐⡄⠈⠒⠛⣉⣩⠯⠀⠀⠀⠀⠀⠈⠘⠓⠍⠟⡻⢧⠀⡌⠀⠀⠀⠀ ⠀⢀⠁⢠⢣⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡘⠀⢀⡇⠀⠀ ⠀⣼⠀⢸⡏⡇⠀⠀⠀⠀⢠⠆⣭⣭⣐⣠⡀⠀⠀⠀⠀⢀⠎⠜⠀⠄⡈⠷⠀⠀ ⢰⢣⠀⣾⣿⢃⠀⠀⠀⠀⠸⣶⣿⣿⣿⣿⠆⠀⠀⠀⡠⠢⢊⣄⡘⠐⣡⠌⢠⠀ ⠘⢸⡇⠽⢻⠀⣦⠰⡉⢈⠀⢟⠁⠀⣀⠝⠀⠀⢀⢜⠄⠀⠉⣔⣤⠕⠁⣠⠂⠀ ⠀⠀⢳⢸⢨⡞⠉⠓⢌⠁⠀⠀⠉⢋⠀⠀⡀⢔⢵⡷⢄⠆⠚⣰⡣⠁⣐⡆⠀⠀ ⠀⠀⠈⢷⣏⠀⠀⣀⣼⣷⠀⡀⠀⠸⠤⡎⡢⠅⠒⠀⣒⠀⡐⡿⠡⣴⢺⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣶⣤⣤⣀⣀⣀⣀⣠⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠉⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠶⠛⠋⠉⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠛⠿⣿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡳⣦⡀ ⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠙⣿⣿⣇⠙⢿⣦⡀⠘⠇⠀⠙⢿⡏⠉⠻⣿⡝⠻⣿⣿⣿⣷ ⠀⢠⠞⠉⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢹⣿⣿⣆⠀⠙⢿⣄⠈⠀⠀⠈⠃⠀⠀⠘⠇⠀⠘⣿⠙⣿ ⠠⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣤⣀⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⡀⠀⠀⠈⠛⢶⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣟⡉⠀⡀⠀⠀⠉⠛⠛⠻⢭⡉⠂⠀⠀ ⠀⠀⢠⡿⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠯⠤⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀ ⠀⠀⡜⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠁⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⢯⣻⢾⢻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⢻⣽⣻⣽⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣯⣿⣿⣿⣯⣿⣻⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣠⠤⣶⣶⣤⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠟⢦⣤⡄⠒⠋⠁⠀⠀⢻⡝⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⡏⠀⢀⡀⠀⠀⠀⠀⠀⢷⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠃⠀⠀⠀⠀⠀⣸⣸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠁⠉⢳⣴⢻⣽⣟⢦⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠋⠐⠉⠙⣿⢿⡇⠀⠀⣀⡀⠀⠀⢀⡴⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⣄⠀⠀⠀⠀⠀⣰⠟⣽⠁⠀⣀⠓⠃⠀⢠⡞⣱⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣧⣦⣤⣤⡔⢋⠈⠁⠀⠀⠀⠀⠀⠀⠏⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢸⣻⣿⣿⣯⠟⠋⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣞⣳⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⢠⡀⢠⡄⠀⢀⡾⡯⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣡⡾⢋⡼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣸⢸⢠⡆⠀⠀⠀⠀⠀⠰⠞⠁⠰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡽⠛⠘⢿⣥⣤⣤⣤⣀⠀⠤⠠⢤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠶⣿⡛⠁⠀⠉⠉⠉⠙⣿⣦⢠⣰⠚⣋⣉⣁⣀⣤⠤⣶⣫⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠓⠚⠿⠯⠭⠭⠭⠤⠼⠏⢹⢾⠿⠿⠟⠓⠒⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢸⣼⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡄⢠⡏⠀⠘⣿⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⣤⠏⠀⠀⠀⡿⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡾⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡶⡦⢤⣀⡴⠋⣥⣍⡻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⢿⠀⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣥⣾⣷⣷⣶⡝⠂⠈⠀⠘⠓⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠘⣆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⣸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣔⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣆⠹⣆⠀⢠⡆⠀⢀⡀⠈⠁⠀⢸⠐⣿⣿⡀⠀⠀⠀⠀⢀⢠⣶⣟⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠫⢘⢧⣼⣷⣂⡈⠉⠀⢀⣀⡌⢧⠻⣿⣷⡀⠀⠀⠀⠨⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢉⣿⡟⠿⠥⣶⣟⣉⣁⣠⡤⠴⠖⠙⠟⣴⣀⠀⣽⡿⣳⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠃⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⢤⣈⣨⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡾⠟⠋⠙⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣴⠿⠻⠟⠿⣶⣦⣄⡀⠀⣰⣾⠛⠀⠀⠀⠀⠘⡙⢿⣧⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⡯⠄⡀⠐⢠⠀⣉⠛⢿⣿⡟⠀⠀⡀⠀⡐⢈⡒⠭⢸⣿⠀⠀⠀⠀⠀⠀ ⢤⣿⠟⢡⠀⢡⠈⠤⡑⢢⡉⢆⡿⠀⠄⡁⢠⡘⢠⠃⠜⡠⣹⣻⠀⠀⠀⠀⠀⠀ ⠛⣽⡎⠤⡉⢄⢊⠲⣉⢦⡙⠼⣧⠈⡐⣤⠻⡔⢣⡘⣌⣥⠿⠿⣶⣤⣤⡀⠀⠀ ⠀⠹⣷⡄⠑⠪⢌⡳⢩⢦⡹⣍⠿⣦⠳⣥⡛⣬⠷⠚⠉⠀⠄⠂⠄⡈⠑⣿⡆⠀ ⠀⠀⠘⣿⢆⡑⠬⣘⢃⠦⢳⢬⡳⣜⡻⣴⣻⠃⠀⠀⠂⠁⢌⡠⢡⠤⡑⠚⠷⣤ ⠀⠀⠀⣈⣿⡿⠶⠎⣍⠺⡥⢧⠽⡾⣽⣷⡷⢀⠒⡰⢊⡜⢢⡑⢆⠒⡡⢱⣶⠛ ⠀⢀⣼⡟⠃⠀⡐⠐⠈⣧⠝⣎⠷⣞⣿⠛⢃⠙⠛⠶⣥⡘⢥⡘⠦⣩⣴⠿⠀⠀ ⣶⡿⠃⠀⠀⠀⢀⠈⣸⢇⠻⣌⢳⡽⡉⠄⠂⠌⡐⢀⠈⠙⢶⣞⣿⠟⠁⠀⠀⠀ ⣷⡇⠀⡄⠂⢈⠄⠂⢀⢊⠱⡈⣾⠡⡘⠄⠃⠠⢁⠂⠌⡀⠀⢻⣿⠀⠀⠀⠀⠀ ⢧⣶⣥⣦⠈⠆⡐⠈⡀⠂⣁⣰⣏⠰⠡⠌⡡⠀⠌⣂⠐⠠⠀⢼⡿⠀⠀⠀⠀⠀ ⠀⠀⠉⠻⢷⣶⣦⣳⢶⡳⠟⠿⣿⡄⠑⡠⢡⠀⠠⢐⠂⠁⢠⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⢀⡀⣀⠀⠀⠀⠀⢹⣽⣆⣠⠀⣃⠠⣤⣉⣴⣯⡃⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡖⠋⠀⣀⠠⢤⣤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⡏⢀⣠⡾⠋⣕⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣻⣙⠧⠛⠒⠛⠃⠍⡙⢍⠫⡙⡙⡒⠞⡫⠤⠲⠒⡨⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⡧⠋⢀⢮⡭⠐⠀⠀⠀⠈⢀⣀⣃⣃⣀⣠⢡⡴⠒⠉⠀⠀ ⠀⠀⠀⢀⢺⣴⡤⢼⡡⠔⠡⢕⠁⠀⡠⠒⡀⠦⠉⠰⢮⢦⡀⠈⡒⣼⣲⣄⠀⠀ ⠀⠀⠀⡾⡟⠉⠂⠁⢀⣤⣀⣠⢒⠔⠀⡔⠱⢦⠀⡢⠱⡚⠛⢦⡙⡄⠀⠈⠃⠀ ⠀⠀⠘⢄⣀⣄⣠⣴⣿⣿⣿⠞⠁⠀⢰⣡⣀⠐⠽⣧⠄⠘⡄⠀⠘⢿⢦⡄⠀⠀ ⠀⠀⢀⣀⣙⢿⡿⢿⣽⡟⠁⠀⢀⠠⠛⠫⡛⡤⠎⣥⡗⠀⠘⡄⠈⠆⢫⡝⠄⠀ ⠀⢔⠕⠉⠙⠵⢽⡿⠋⠀⣀⡤⠅⠒⢶⣢⠝⡀⠈⢺⠇⠀⠀⠰⠀⠀⠈⡇⠀⠀ ⡌⣯⣀⠀⠀⠀⠈⠢⠼⠮⠛⠀⠀⠀⠈⠋⠣⡈⠱⠘⢸⠀⠀⠀⠇⠀⠀⢹⠀⠀ ⠇⣢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣗⡄⠀⢀⠀⠀⠀⢸⠀⠀⠘⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠻⣻⠈⢂⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⠟⢁⠀⠀⢂⠈⡄⠀⠀⠀⠀⢸⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡾⠿⠿⠟⠻⠿⠿⢿⣶⣦⣤⣴⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀ ⠀⠀⠀⣠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀ ⠀⠀⣴⡿⠃⠀⠀⠀⣀⣦⡀⠀⠀⠀⢾⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀ ⠀⢰⡿⠁⠀⠀⠐⢿⠟⠋⠀⠀⠀⠀⠀⡏⢏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀ ⠀⣿⠇⠀⠀⠀⠀⠸⣶⣶⡖⠀⠀⠰⣷⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀ ⢰⣿⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁ ⠀⢿⡆⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀ ⠀⠸⣿⡄⠀⠀⠀⠛⠳⢲⠶⠦⢤⣤⣤⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀ ⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀ ⠀⠀⠀⠙⢿⣦⣀⠀⣀⣰⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣶⣶⣶⣶⣶⠶⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣠⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡏⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡇⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⢿⣿⡇⠀⠀⢹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⣿⣷⡄⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⣿⠙⣿⣦⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⣿⡀⠈⢻⣷⣄⡈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⠋⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠙⠻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⢢⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢠⠀⢸⠀⠀⠐⡄⠀⠉⠙⣿⣄⡀⢸⣿⣿ ⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⡠⠆⠁⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⣰⡗⠀⠀⠀⠀⢀⡎⠀⣸⠀⠀⠀⡹⡆⠀⠀⠈⢳⣇⢸⣿⣿ ⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⢀⡴⠋⠀⢠⠶⠁⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⣴⠏⠇⠀⠀⠀⠀⣸⠁⠀⡇⠀⡀⠀⠀⢿⡄⠀⠀⠀⠙⢾⣿⣿ ⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⢀⡴⠋⠀⢀⡴⠁⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⢠⣞⠁⢀⠀⠀⠀⠀⢠⠇⠀⣸⠁⠀⢧⠀⠀⠀⢻⡄⠀⠀⠀⠈⢿⣿ ⣿⠏⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⢀⡜⠁⠀⠀⠀⢀⡴⠋⠀⠀⡴⠋⠀⠀⢀⣠⡴⠛⠀⠀⠀⠀⢀⡴⠛⠋⠐⢸⠀⠀⠀⢀⡞⠀⢀⡿⡆⠀⠸⡆⠀⠀⠈⢻⡀⠀⠀⠀⠈⢻ ⡙⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢠⠟⠀⠀⠀⠀⣠⠎⠀⠀⢠⠞⠀⢀⣤⠖⣿⠛⠁⠀⠀⠀⠀⣠⠞⠁⠀⠀⡀⡎⠀⠀⠀⡼⠀⠀⣸⠁⡇⠀⠀⢳⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣰⠋⠀⠀⠀⢀⡴⠁⠀⠀⣴⣋⡴⠞⠋⣠⠞⠁⠀⠀⠀⠀⣠⣾⣅⣀⣀⣀⡍⢰⠃⠀⠀⣸⠁⠀⢰⡇⠀⣼⠀⠀⠈⡆⠀⠀⠀⣽⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⢀⡞⠁⠀⢀⣼⣿⣭⣗⣶⠞⠁⠀⠀⠀⠀⣠⠞⠁⠀⠈⠁⠀⠀⠀⡟⠀⠀⣰⠃⠀⢀⡟⠀⣄⢹⡄⠀⠀⢱⡀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⢠⠟⠀⠀⢀⡾⠉⠙⣿⠟⠁⠀⠀⠀⠀⣤⣞⡁⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢠⠇⠀⠀⡼⠀⠙⠛⢈⣧⠀⠀⠈⡇⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⠄⠀⠀⣠⠏⠀⠀⢠⣾⡇⣠⠟⠁⠀⠀⠀⢀⣤⣾⣿⣾⡽⢦⡀⠀⠀⠀⠀⢀⡏⠀⢠⠏⠀⠀⡼⠃⠀⠀⠀⠘⣿⡀⠀⠀⢸⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠛⠀⢠⠏⠀⡖⣰⠋⠀⠀⢠⡟⣸⠟⠁⠀⠀⠀⢀⡴⣿⡿⡟⢿⣿⣷⣤⣽⣶⡄⠀⠀⡾⠀⣠⠋⠀⠀⣰⠃⠀⠀⠀⠀⠀⢳⣇⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡴⠋⠀⠀⣰⡏⠀⡜⣴⠁⠀⠀⢠⣯⡾⠁⠀⠀⠀⣠⠶⠋⠀⢿⠀⠱⠤⠽⣿⣿⣆⠈⠇⠀⡼⠁⣰⠋⠀⠀⣰⠃⠀⠀⠀⠀⠀⠠⣤⣼⡄⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀ ⢀⡤⠞⠉⠀⣀⡴⣿⡟⠀⣸⡝⠁⠀⠀⢠⡿⠃⠀⠀⢀⡴⠞⠁⠀⠀⠀⠈⠳⢤⣠⣴⠿⢻⠷⠀⠀⣰⠃⡴⠁⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⣳⡀⠀⢸⡆⠀⡇⠀⠀⠀⠀ ⢁⠤⠠⠶⠿⠅⠀⢹⠁⢠⠏⠀⠀⣠⠎⣾⠖⢀⣠⣶⡏⣿⡛⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠣⠞⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⡾⡆⠈⡇⢀⠃⠀⠀⠀⠀ ⠌⢀⠎⠀⠀⡀⢃⡟⡰⠋⠀⢀⡴⠃⢸⣣⣶⣻⣷⡿⡟⢆⢀⡀⠀⠉⣙⠒⠲⢦⣌⣲⡀⠀⠀⡴⠃⠀⠀⠀⣠⡞⠁⠀⠀⠀⠐⠒⠦⢤⣄⣀⠀⠀⠀⠹⡾⠀⢻⣸⠀⠀⠀⠀⠀ ⠀⠁⠀⠒⠒⠒⣸⠟⠁⠀⡠⠊⠀⢀⡿⣯⣏⡿⣯⠀⠀⠊⡳⣽⠌⠳⡘⢧⠀⢄⠈⢳⡙⢆⡾⠁⠀⠀⢀⡼⡗⠁⠀⠀⢀⣠⠤⣤⣤⣤⣤⣍⣙⢢⣀⡀⠹⡄⢸⡿⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⣀⠞⠁⢀⡠⠊⠀⠀⠀⣸⢁⠼⠏⠀⠈⠻⠧⠳⡵⣌⢳⡤⡙⢦⡱⢞⠡⣐⢯⡞⠀⠀⠀⣠⣾⠀⠀⠀⡆⠀⠈⢻⠛⡟⠿⣿⢿⣿⣿⣿⣯⣠⠄⢳⣸⠃⠀⠀⠀⠀⠈ ⣤⣤⣴⣋⣁⣤⠞⠋⡇⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠙⢿⠺⠷⡟⢦⡽⠋⠀⠀⣠⣾⡿⡻⡀⡀⠀⢷⡀⠀⠘⣦⣛⣿⣿⠿⠀⠈⠻⣿⣿⣤⣸⣿⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⢻⣿⠀⢸⠃⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣨⠞⠁⠀⣠⣾⢿⠋⡳⣜⢿⣟⢦⣀⣿⣄⠀⠈⠙⠉⠁⠀⠀⠀⠀⢘⣿⣿⣿⡏⠀⠀⠀⠀⠀⠠ ⠳⡄⠀⢤⣸⡏⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣀⡴⠟⠛⠉⢄⠳⡝⢞⢦⡹⣿⣿⣿⡍⠳⣄⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠁⠀⠀⠀⠀⢀⠆ ⠀⢹⣦⠀⢹⠁⠀⢸⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣡⡴⠊⠁⠀⠀⠀⠀⠈⠁⠀⠈⠁⠱⣝⢿⣿⢿⣆⠙⢷⠶⡶⢦⡴⠞⢉⣾⣿⣿⡇⠀⠀⠀⠀⠀⠘⠀ ⠀⣿⡟⠹⣾⠀⠀⣾⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⣺⠏⠉⠉⠙⠦⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡻⣷⡹⣷⣄⠹⣦⠶⠀⢀⣾⣿⡿⢻⠁⠀⠀⠀⠀⠀⠀⠀ ⢠⡿⠁⠀⡇⠀⢀⣿⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣀⠤⠖⠛⠉⠀⢰⣿⣍⣻⣤⡤⠤⡤⢤⣈⠙⠲⢤⡀⠀⠀⠀⠀⠀⠉⠈⠹⣞⢫⢤⡈⠓⠀⣾⢿⣿⠃⡼⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠃⠀⢰⠃⠀⢸⣿⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣿⣭⣽⢡⡆⠀⣀⣑⣀⣈⣛⣦⡄⢹⣦⠀⠀⠀⠀⠀⠀⠀⠉⠳⡿⣝⠲⠄⣿⣾⠇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠀⢀⡿⠀⠀⣼⡿⡄⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣽⣷⠈⣽⣽⣽⠶⠤⠴⠶⠝⣆⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⡼⠀⠀⡄⠀⠀⠐⠀⠀⠀ ⠀⢀⣾⠃⠀⢠⡟⣠⡇⠀⠀⢨⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠉⠀⠉⠉⠹⢶⣓⣚⠛⢶⢶⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⡇⠀⢸⠇⠀⠀⠀⠀⠀⠀ ⠀⠞⡜⠀⠀⣾⠟⠁⡇⠀⠀⢸⣯⢿⣆⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⢷⠀⠀⠀⠀⠈⡏⠉⠛⣻⣿⣃⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣻⠁⠀⢸⠀⠀⡜⠀⠀⠈⠀⠀⠀⠀ ⠌⠰⠁⠀⣸⠃⠀⠀⢹⠀⠀⢸⡿⢷⣿⣧⡀⠀⢀⣠⡶⠛⠁⠀⠀⠸⡄⠀⠀⠀⢠⡇⠀⠀⢈⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⠇⠀⠀⡜⠀⢀⠇⠀⠀⠃⠀⠀⠀⠀ ⠐⠃⠀⢀⡏⠀⠀⠀⢸⡆⠀⢸⠇⠀⠈⠙⠛⣶⣯⠋⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠋⠀⠀⠀⣼⢏⢹⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⡾⠀⠀⢸⡇⠀⢸⠀⠀⠔⠀⠀⠀⠀⠀ ⡈⠀⠀⡞⠀⠀⠀⠀⢸⡇⠀⢸⠄⠀⠀⠀⠀⣧⢹⣦⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣸⢃⣌⡁⠸⡆⠀⠀⠀⠀⠀⠀⢀⣴⡟⡟⢰⠃⠀⠀⣿⠃⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡈⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⢹⡌⢻⣿⣦⡀⠀⠀⠀⡇⠀⠀⠀⠀⣠⠾⡿⠁⠀⠘⠆⢱⠀⠀⠀⢀⣠⣶⡏⡼⢹⠁⡼⠀⠀⣼⡜⠀⢠⠁⠀⠂⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⠀⠀⠀⠀⠸⠇⠀⢸⠀⠀⠀⠀⠀⡈⡇⠀⠘⢿⣿⣦⣠⣞⠵⠛⠒⠒⡿⠣⠋⠀⠀⢀⣀⣢⠦⠴⠒⢻⠉⣿⣟⣀⡇⡸⢰⡇⠀⢠⠇⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⣷⡇⠀⠀⠀⠈⣿⣿⣧⣤⣤⣴⣫⣐⡤⠴⠚⠛⠉⠀⠀⠀⠀⠀⣾⠀⢹⡏⠙⢧⡇⣼⠀⠀⡸⢀⡇⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣀⠀⠀⠀ ⠀⣿⣁⢈⠉⠉⣉⣉⡧⠀⠀⣼⠋⠁⠀⠘⠢⡾⠋⠉⠉⢳⠀ ⠐⠛⢻⣯⠀⢠⠋⠉⠀⠀⢸⣷⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇ ⠀⠀⢸⡿⠀⢸⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀ ⢴⣯⣉⣁⣀⡈⠒⠒⡀⠀⠀⠈⠻⣧⡀⠀⠀⠀⢀⡠⠊⠀⠀ ⠈⠉⠉⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠉⠢⡠⠒⠁⠀⠀⠀⠀ ⢰⣖⠒⡀⠀⢠⣴⠒⡂⢀⣀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠙⣦⠈⢄⡾⠃⡜⣴⠟⢉⢥⡈⢢⢶⣯⢀⠁⠀⢰⡯⠉⡇ ⠀⠀⠈⢿⡬⢁⠌⢠⡿⠁⠆⠈⡇⢸⣿⣇⢸⠀⠀⢸⡇⠀⡇ ⠀⠀⠀⢸⡯⢻⠀⢸⡇⠀⡀⢸⠇⢸⣿⠃⢈⠀⠀⣿⡀⠀⡇ ⠀⠀⠀⣾⠁⠘⠀⢸⣧⠀⠈⠁⢀⠎⣿⠀⢺⠀⣰⡿⠀⢠⠁ ⠀⠀⠀⠛⠒⠃⠀⠈⠛⠳⠶⠖⠋⠀⢿⣄⡀⠉⠁⠀⡠⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣾⡿⠿⣷⣦⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠉⠉⠉⠀⠀⠀⠙⢿⣷⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢡⣦⠄⠀⠀⣴⡤⠀⠀⠀⠘⣿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⢰⠀⠀⠀⠀⠀⢠⠠⠀⠀⠀⢹⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢾⣦⣀⣤⣶⠆⠣⡀⡀⠀⣾⣿⠁ ⠀⠀⣀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠉⠉⠉⠁⠀⠀⠐⣀⣼⣿⠋⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠈⠻⠿⣶⣦⣤⣤⣤⣶⡶⠿⠟⠋⠀⠀⠀ ⢰⣶⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠛⠿⣷⣦⣤⣄⣀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⣷⣶⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡇⠹⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⡤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡏⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⣀⠴⠋⠉⠉⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⠚⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀ ⢠⣤⣶⣾⣧⣤⣤⣀⡀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡤⠴⠶⠤⢤⡀⣧⣀⣀⠀ ⠻⠶⣾⠁⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⢹⣿⣭⣽⠇ ⠀⠀⠙⠤⠴⢤⡤⠤⠤⠋⠉⠉⠉⠉⠉⠉⠉⠳⠖⠦⠤⠶⠦⠞⠁⠀⠀⠀

⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⢹⣿⡟⠻⠿⢶⣶⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⡟⠀⠀⠀⢀⣤⣤⣈⠉⠙⠛⠛⠻⠿⠶⣶⣤⣤⣤⣀⣀ ⣾⣿⡃⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛ ⠙⢿⣿⣦⡀⠀⠻⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢿⣿⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣀⣀⣀⣀⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠻⠿⠿⠿⠿⠿⠿⠛⠛⠁⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣾⣿⣿⣿⠿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⣿⣿⠟⠁⠀⠈⠻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⠀⠀⠀⠀⠀ ⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⡛⠻⢷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠪⣿⣿⣷⣀⢠⠮⠭⠭⠴⣀⣀⡜⠒⢒⠒⠓⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⢁⣷⣿⡿⠁⠀⢁⠀⠐⠀⠀⡇⠀⠉⠀⠢⣀⡐⠀⠉⠐⠠⡀⠀⠀ ⠀⠀⠀⢀⠃⣴⣿⣿⡇⠀⠀⠀⠑⠠⠄⠪⠀⠀⠀⢀⡀⠈⠐⠀⢄⠀⠀⠐⡀⠀ ⠀⠀⠀⠘⢰⣿⣿⣿⡇⠀⠀⠀⡠⠄⡀⠈⠀⠈⠉⠀⠀⠉⢐⠒⠊⠀⠀⠀⢱⠀ ⠀⠀⠀⡆⢾⣿⣿⣿⣿⠀⠀⠀⣷⣤⣀⣾⣉⣉⡆⠈⠉⢃⡈⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠈⠉⠉⠀⠀⠀⠀⠘⢟⠛⠿⣿⣿⣷⡶⠲⠬⠄⣀⠀⠀⠀⠀⠀⡆ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⡇ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢀⠀⠀⠀⢀⠂ ⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡠⠂⠀ ⠀⠀⡜⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⡠⠢⢀⣀⠠⡢⠊⠀⢠⣾ ⢠⠞⣧⡀⠈⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢀⠠⠐⠁⠀⢀⣴⠿⠋ ⠁⠀⣿⡷⠄⠀⠀⠈⠐⠠⡀⠀⠀⠀⠀⠀⢀⡀⠠⠒⠈⠀⠀⠀⢀⣴⡟⠁⠀⠀ ⠀⢸⣿⡇⠀⠢⠀⠀⡠⠒⠀⠑⠄⢰⠒⠪⡀⠀⢰⣤⣀⣸⣷⣶⣿⠏⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠉⠀⡀⠄⡒⠈⠭⠭⠥⠈⠐⣚⣛⠛⠛⠛⡲⢦⣀⠀⠀⠀ ⠀⠀⠀⣰⠃⠀⠔⡨⡢⠑⠈⠉⠁⠉⠄⠀⠀⠀⡲⠀⠀⠐⢄⠀⠈⢷⠀⠀ ⠠⣤⣿⣛⡛⠛⣻⢿⣛⣟⡻⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⢿⣿⣿⣿⡟⢦⡀ ⡴⠛⢡⡶⠒⡖⠦⢭⣿⣮⣱⣎⣿⣿⡿⠏⠀⠙⡿⠷⠿⣾⢿⣿⢭⡞⡐⣷ ⡇⠀⢺⠠⢾⡟⠲⢤⣀⡀⠠⠤⠄⡖⢂⣀⠀⠀⠙⣦⣄⠉⠉⢰⡄⠠⢃⣿ ⠹⣎⡪⠀⠀⢷⡦⣄⣯⡉⠓⠲⣤⣵⣉⣀⡀⠶⠞⠁⣀⣨⣴⢿⣷⠈⣰⠃ ⠀⠈⢳⡀⠀⠀⠻⣌⡟⠛⠷⣶⣧⣄⣀⣹⣏⣉⣻⣉⣉⣧⣸⣷⣿⠀⣿⠀ ⠀⠀⠀⠳⣄⠀⠀⠈⠳⢤⡀⣸⠉⠉⠛⡿⠻⠿⡿⠿⣿⢿⡿⣿⡟⠀⣿⠀ ⠀⠀⠀⠀⠈⠳⣅⡪⢔⡠⢉⡛⠲⠦⠤⠧⣤⣤⣧⡴⠧⠾⠖⠛⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣅⡒⠡⠶⠀⣠⡤⠤⠤⠤⠤⠤⠐⢁⠠⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣄⣀⡀⠀⠉⠉⠉⠉⠀⢀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠒⠚⠉⠁⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠻⠟⢛⣛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⡄⠀⣀⡀⠨⣙⣏⣉⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⣿⢿⣿⣿⣿⡿⣟⣿⣯⣿⣷⣿⢾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣒⡛⢫⠤⣠⢤⣤⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣻⣯⣿⢿⣿⢯⣿⣯⣿⣿⣻⣞⡷⣿⣽⣻⡽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢮⣭⣉⡓⠺⠊⢉⠓⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣻⢿⡿⣯⢿⣷⢯⡷⣯⣟⠷⣯⡗⡿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣩⣿⣿⢿⣷⣄⡙⢮⠭⡁⢠⣬⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣯⢿⣽⡿⣾⣻⣽⣳⣞⣟⡧⣟⡽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⡴⠹⢿⣿⣀⣿⣿⣯⣍⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⡿⣯⣿⡽⣟⡾⣵⢫⣾⡱⢯⡜ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣞⣰⣀⣾⡷⠘⣿⣿⣟⣩⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⢷⣟⣿⢯⡷⣏⡟⣶⡹⢇⡞ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣰⢯⣾⣿⣿⡿⠁⠀⠀⠼⢿⣿⠥⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⡾⣟⣯⢿⡼⣹⢶⡹⢣⠞ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠘⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⡽⣯⣟⢾⡱⣏⠵⣋⠎ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢬⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⣳⢯⣏⡗⣎⠳⡌⠆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⢻⡗⣮⡝⣬⢳⠉⡎ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⣯⢷⣫⢗⡭⢎⢧⡙ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣶⡆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣯⣟⣧⡟⡼⣉⢆⠣ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠹⣿⢿⡟⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡂⠭⢊⠻⡹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣻⣞⡽⣲⢍⡎⢇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⠆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⠒⠐⢀⠀⠠⠐⡆⢯⡹⡹⢛⡯⢭⡹⣿⣿⣿⣿⣿⣿⣿⡿⣾⢯⣷⣻⣜⡳⢎⡜⠦ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⢷⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡄⠠⢎⢦⡹⢄⡄⣌⣩⣝⠾⣡⢃⠡⠃⡘⢧⠿⣽⣻⣿⣿⣿⣿⣿⣽⣿⣟⣷⣻⡼⣝⢮⡙⡖ ⣿⣿⣿⣿⣿⣿⣿⠃⣾⣷⣄⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢉⣩⣁⣳⣶⣦⣤⣤⣈⣥⢛⡞⣶⣿⣜⣫⢝⣶⣫⢞⣡⣀⣒⣀⡴⣨⡽⣎⣿⣿⣿⣿⣿⣿⣿⣿⢾⣯⢷⣻⡜⣮⢱⢣ ⣿⣿⣿⣿⣿⣿⣿⡇⣿⢻⠇⠛⢧⠀⠀⠁⠀⠀⠀⠾⠛⣉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⢾⣯⢷⣻⣼⢣⢧ ⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⠀⣶⣿⠃⠀⠂⠀⠀⢰⣶⡾⠟⠫⣈⢿⡿⠟⣨⣿⣿⣿⢿⡆⠀⠈⣿⣿⣿⣿⣿⡟⢹⣯⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⢯⣿⢯⡿⣟⡾⣏⣞ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡀⢿⡃⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣉⣛⠶⣿⣿⣿⣿⠟⣿⠃⠀⢠⣿⣿⡏⢿⣯⣭⠷⣭⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣿⣿⣯⣟⣯⡿⣽⣻⢞⡵ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠱⡈⠹⡄⠀⡁⠀⠀⠀⠀⠀⠈⠙⠋⣙⣹⣿⣿⡿⠋⠀⠀⠀⠀⢺⣿⣿⣿⣆⢻⣿⣻⣶⣷⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣟⣾⢯⡿⣽⡷⣯⢿⣹ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢲⡾⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠜⡹⠟⠉⠀⣀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣞⡽⢿⣿⡿⢿⡟⢶⣡⣿⣿⣿⣿⣿⣿⣿⣳⣯⢿⣯⣟⣷⣻⣽⡳⣏ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⡀⣀⡆⡇⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣠⣾⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⡏⠱⠂⠄⣙⢣⣟⣮⣿⣿⣿⣿⣿⣿⣿⣟⣷⣻⣟⡾⣽⣞⡷⣯⡽⣳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⢈⣿⣿⣿⣿⣍⠣⡉⠴⣌⢷⣾⣻⣿⣿⣿⣿⣿⣿⡿⣞⣯⢷⣯⡟⣷⣫⡽⢶⡻⣵ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡑⢺⡿⢏⢀⣠⣀⠀⣦⣀⢻⣿⣿⣿⣿⣣⣝⡳⣎⣿⣽⣿⣿⣿⣿⣿⣿⣟⣿⡽⣯⣟⢶⡻⣵⢣⡟⣯⢳⢧ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⢰⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⢢⣏⣷⢿⣭⣻⢷⣿⣿⣿⣿⣽⣾⣳⣟⣷⣫⢯⡷⣭⢳⡝⣮⢛⡼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣞⡿⣎⡶⣿⣿⣿⣿⣿⣿⣞⡷⣟⣾⡳⣏⡷⣹⢎⡷⣙⢦⣋⠖ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣽⢳⢏⣾⣿⣿⣿⡍⣉⣛⣻⡿⢿⣾⣽⣝⣳⣝⢮⠳⣍⠶⣉⠞ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣧⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠿⠾⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣞⢿⣺⣿⣿⣿⣿⣿⡉⢿⣿⡙⠲⣤⣈⡙⠻⠮⣽⣙⡌⢣⠱⣊ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣆⠠⡀⠀⠀⠀⠀⠘⠉⠁⠀⠀⢀⣠⣶⣿⢿⡛⣴⣿⣻⢻⡽⣷⢯⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣡⡄⠀⢢⠉⠱⣄⠀⠉⠈⠐⠃⠄ ⣿⣿⣿⣿⢿⣻⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢀⠹⣄⠙⣄⡀⠀⠀⠜⢢⠳⣾⣿⣿⣿⣿⣿⣷⣯⡷⢭⡷⣯⢿⣯⣿⢾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠉⠢⠈⢦⡀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢱⡙⢧⡈⠻⣦⣄⠘⠀⠠⠀⠈⠁⠀⠀⠀⠀⠀⢌⢧⡻⡽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⡄⠀⠀⠃⠈⣷⡀⠀⠀⠀ ⣿⣿⣧⣿⣿⣧⣿⠟⠀⠀⠀⣠⠀⠀⢀⣠⠀⠀⢿⠛⠻⢤⡘⠻⣤⡀⠀⠀⠀⠀⢀⣀⣠⣤⡼⣼⢧⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡄⠀⠀⢀⠸⡇⠀⠀⠀ ⣿⣷⡿⣿⣽⠟⠁⠀⣠⡏⢰⡇⠀⠀⢸⣿⠀⠀⠘⣧⠤⠄⠙⢶⣌⠛⢶⣤⣶⣶⣿⣾⣿⣯⣟⣯⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣳⢯⣿⡄⠘⠤⢂⠙⢦⡀⠀ ⣟⡾⣽⠟⠁⠀⠀⢠⡿⠀⣾⡇⠀⠀⠹⢿⣀⣤⡀⠙⢆⡰⣳⣦⣈⡛⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣿⣿⣿⣿⣷⢫⣞⢿⡃⠄⢂⠀⢣⢳⡀ ⣯⡟⠃⠀⡰⠀⠀⣿⠃⢸⣿⡇⢀⠀⡀⠀⠈⠻⢿⣷⣮⠵⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⣿⣟⡿⣷⣿⠿⣝⡷⣎⠲⣅⠀⠀⠈⠀⠡⢓ ⠋⠀⣀⠔⠁⠀⢀⡇⠀⣾⣿⡄⠈⣆⠘⡀⠀⠀⠀⠹⢿⣿⣿⣟⣯⣙⣌⣙⡻⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣿⢯⣟⣿⣿⡿⣿⡽⣾⣽⣻⣿⡹⣌⢳⣍⡒⠈⠄⠀⠀⠀⠀⠈ ⠀⠀⠀⠠⣆⠀⢸⠀⢠⠿⣿⡇⠀⢸⣧⠑⢦⠀⠁⠀⠀⢈⠛⢿⣿⣽⣶⣯⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣿⣻⣞⡷⣿⢯⣟⣷⢳⣿⣯⡕⢎⠲⡡⠌⠐⠠⡀⠀⢀⠀⠀ ⠀⠀⠀⠀⠈⢆⡇⠠⠊⠀⣿⡇⠀⠀⣿⡷⣄⠳⣤⠀⢠⠀⠀⠀⠘⠻⠿⣿⢿⡿⠟⢉⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣟⣾⢿⣽⡻⢾⡭⣟⣿⡗⢮⡡⠂⠑⣂⠀⡲⢱⠀⠄⡁⠀ ⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⣿⣷⠀⠀⢸⡷⠜⢧⡈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡾⡽⢧⠿⣜⣿⡟⢢⠑⡤⠘⢤⠣⢌⢣⠘⠠⠀⠂ ⣾⣦⡀⠀⠀⠀⠀⢙⣦⠀⣿⣿⠀⠀⠀⠀⠆⠐⠛⣦⣄⠠⣄⠀⠰⠀⠀⠀⠀⠀⡐⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢯⡿⣷⣿⣻⠯⣷⣎⡿⡍⢦⡙⠴⡁⠎⣇⠫⢄⠊⢀⠁⠀ ⠀⠀⠉⠲⣭⣯⣿⣾⣿⣷⣽⣿⡀⠀⠀⠀⠁⠀⣨⡇⠸⣷⣄⠁⠄⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⣟⢿⣿⣿⣿⣿⣿⣿⡣⢿⡱⢎⡝⠻⠶⣾⡽⣙⠦⡙⠤⠃⢘⠀⢳⡈⡐⠀⠀⠀ ⠀⠀⠀⠀⡿⢿⣿⣿⣿⣿⣿⣿⣇⢠⠐⡁⢰⣿⠿⡷⠀⠹⡙⣶⣄⡀⠀⢠⡄⢀⣾⡿⣟⢣⠟⡼⢫⣿⢿⣿⣿⣿⡿⣿⣷⣏⠂⢜⡱⣌⡄⢣⣝⠂⡉⠒⡁⠀⠀⠂⠐⠈⠀⠠⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠔⠈⠄⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡐⠁⢠⢰⣊⣄⣤⣄⣀⠀⠀⠀⠀⠑⡀⠀⠀⠀ ⠀⠀⠀⠀⢀⠰⠐⠂⠉⠉⠉⣀⠉⠉⠛⠛⠶⣄⠀⠀⢱⠀⠀⠀ ⠀⠀⡠⢐⠕⠁⠀⣠⣶⢿⡟⠘⣿⣿⣶⣤⡀⠈⠙⢄⢸⠀⠀⠀ ⠀⠌⠀⠀⠀⢠⣾⣿⠏⢸⠇⠀⠘⣿⠹⣿⣿⣖⢄⢀⠑⠄⠀⠀ ⠸⠀⢀⡘⡀⣿⣿⢿⢀⠈⠄⠈⠀⠇⣀⢽⣿⣿⣧⠡⠀⠈⢂⠀ ⠀⠣⠈⣌⡰⢻⣿⠸⢎⡉⠣⠀⠈⠐⢡⡈⠸⣿⣿⡆⠰⠀⠀⡆ ⠀⠀⠉⠢⣐⠁⢿⡆⠢⠥⠂⡃⠀⠐⠠⠔⠁⣿⢭⡟⠺⠀⢀⠇ ⠀⠀⠀⠀⠀⠉⠊⢿⠀⢂⠤⡤⠀⠰⡀⠠⡰⠾⣋⣈⠶⠐⠊⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢀⡀⢁⣀⠬⠊⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣧⢀⠀⡀⣨⣿⣶⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠁⣿⣿⣿⣧⠀⣰⣿⣿⣿⡇⡑⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢡⠀⠀⠀⠀

⠀⠀⠀⢀⠠⠀⡀⠀⠀⠀⢠⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡐⢱⠈⡗⡜⡀⠀⢀⣸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠱⣜⠂⢚⣡⠠⣴⣿⡏⠙⠛⣿⡂⠀⡔⡨⡭⡑⠄ ⠀⠀⠀⠀⠉⡝⠁⣤⣿⢦⡁⠀⢘⣛⠻⢢⡄⢆⣈⡿⠸ ⠀⠀⠀⠀⣰⠃⡼⠿⠏⠀⡇⢰⣿⠉⠳⡄⣿⠒⠀⠂⠁ ⠀⠀⠀⣴⠋⣢⣑⣤⣠⣴⣇⣿⡉⠀⢀⡇⡿⠀⠀⠀⠀ ⠀⠀⢸⠹⠶⡟⠁⠀⠀⠉⠒⠛⠙⠻⣍⠔⢺⠀⠀⠀⠀ ⠀⠀⠸⡆⢰⡟⠷⣤⣀⠀⠀⠀⠀⠀⣸⢦⢾⠀⠀⠀⠀ ⢀⢔⢢⠙⢾⣹⣦⣀⣉⠈⡛⠛⠛⢫⠇⢀⡞⠀⠀⠀⠀ ⢸⠁⡠⠥⣆⠈⣹⣿⠿⢿⣿⣷⡿⠷⠖⠋⠀⠀⠀⠀⠀ ⢸⣿⣁⣠⡞⡏⣾⣿⣷⣿⣿⣿⣿⡇⠂⢄⠀⠀⠀⠀⠀ ⠀⠙⠛⣿⠋⢠⠿⠟⠋⡉⡈⠓⠛⡌⡄⠀⢆⠀⠀⠀⠀ ⠀⠀⢸⠁⠀⠏⠀⠀⠘⠿⠟⠀⠀⠸⣸⢀⣀⠀⠀⠀⠀ ⠀⠀⢸⡄⠀⡆⠀⠀⢰⣿⣷⠀⠀⢠⡏⠉⣻⣷⠀⠀⠀ ⠀⠀⠈⢻⣧⡘⠦⣀⣀⠉⣁⣠⠴⣫⢷⡾⠉⢹⠀⠀⠀ ⠀⠀⠀⢰⠉⠛⠷⣶⠼⢭⡥⠖⠋⠀⡌⢧⣠⠏⠀⠀⠀ ⠀⠀⠀⡸⠤⠤⠤⠬⡄⢸⠤⠤⠤⠤⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣅⡀⠀⠀⢀⡷⣇⠀⠀⠀⣀⣸⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢀⣀⣀⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠁⣠⠖⠉⢀⣀⣧⣈⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣷⣄⠀⠀⠀⠀⠀⠀⣠⢾⠛⣿⡁⣠⠞⠉⢀⣯⣀⣈⣇⠀ ⠀⠀⠀⠀⠀⢀⣼⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠀⣀⣘⣏⠛⣷⢤⣀⣀⡤⠞⠁⣸⠟⠀⡷⠃⣠⣶⣟⣏⣀⣀⣘⣆ ⠀⠀⠀⠀⠀⣾⡿⠛⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⣠⠖⠉⠉⠉⣏⠙⡿⢾⣄⣀⣀⣠⣼⣽⣠⠞⠀⡰⠃⢨⠟⠋⠀⠀⠀⠉ ⠀⠀⠀⠀⢰⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⠞⠁⣠⣴⣾⣿⠏⠉⠓⢾⣦⣀⡀⢻⡿⠟⠁⢀⠞⠁⡴⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡇⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⡸⢀⠏⢠⠞⠁⣨⠟⠋⠉⠉⠉⢻⡧⢤⣈⣁⣀⣠⠖⠋⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣤⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⢳⡇⡸⢠⠏⢠⠞⠁⣠⠔⠊⠉⠉⢻⠗⠦⣄⣀⠀⢀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⠤⠔⠒⠚⠉⠉⠛⠒⠺⡗⢿⣤⣀⣀⣤⠀⠀⠀⠀⠀⠀⢸⣀⡞⣷⠇⡜⢠⠏⢀⡞⠁⠀⠀⣰⢞⣻⠇⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⣿⡿⣏⠀⣀⡤⠔⠒⠒⠒⠒⣲⣶⡗⠾⠤⢤⣈⣿⢿⡖⠦⠤⣀⣠⣴⠏⢘⡟⢀⠃⡜⢠⠏⠀⠀⠀⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⣿⡿⠋⠀⢻⡉⠀⣀⣤⠤⠒⠒⠚⠛⠛⠒⠢⠤⢤⣀⣏⠙⢻⠲⠤⢿⣿⣋⠤⠊⢀⣾⣠⠃⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⡟⠀⢀⣴⣿⣿⣿⣿⣦⣀⠤⠖⠒⠒⠒⠒⠲⠤⣤⣀⣯⣉⠛⠒⠦⠤⣀⣀⣀⡤⠚⢹⣿⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡿⠀⠀⣿⠟⠛⣿⠟⠛⣿⣧⣠⠤⠔⠒⠒⠒⠒⠰⣿⠿⣯⣈⡉⠑⠒⠦⠤⣀⣀⣀⡤⢿⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⡀⠀⢿⡀⠀⢻⣤⠖⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⠤⢄⣀⣀⣀⣼⠟⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢷⣄⠈⠙⠦⠸⡇⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠛⠶⠤⠶⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣾⣿⣆⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⣿⡿⠃⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣙⠓⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣾⣿⣷⣶⣦⣤⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡾⣿⣿⣿⣿⣿⡿⠟⠛⠻⢿⣿⣿⣿⣦⡀⠀⠀ ⠀⠀⠀⢀⠃⠀⠀⠹⣿⡿⠃⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⠀⠀ ⠀⠀⠀⢸⢀⣀⡀⠀⣿⡇⠀⠀⣀⣀⠀⠀⠀⠈⣿⣿⣿⡇⠀ ⠀⠀⠀⡏⠀⠉⠀⠘⠁⠛⠀⠀⠉⠃⠀⠀⠀⠀⢹⣿⣿⠇⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠀⠀ ⠀⠀⠀⢈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡀⠀⠀ ⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⡄⠀ ⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷ ⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢉⣽⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢐⣾⣷⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠡⠤⣮⣿⣵⠆⠠⠤⣀⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠏⠀⠐⢾⣽⣛⠟⠚⠛⠓⠒⠈⠱⡄ ⠀⣀⣀⣤⣀⣤⣄⠠⡜⠃⠀⢀⣀⣼⣿⣿⠿⢦⣶⣶⣦⣿⣿⡟ ⣾⣿⣿⠻⢿⣿⡇⠀⢫⣣⡱⣾⡿⣿⣿⣿⣆⣄⢀⢉⡉⣩⣿⠀ ⢻⢻⡿⡎⠀⠀⢇⣀⣬⣷⠉⠙⠉⠙⣻⣿⠙⠓⠛⠿⣿⣿⠟⠀ ⢸⣄⠈⢧⠀⠀⠸⡀⢀⣿⣤⣀⠀⠀⣺⡟⠿⣶⢦⣦⣤⡿⠀⠀ ⠀⢻⣷⣼⡄⠀⠀⢱⣿⡿⠿⠾⠷⣶⣿⣷⣦⣌⢉⣻⠏⠁⠀⠀ ⠀⠀⢧⣿⣷⡤⠒⠓⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⣚⡻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⡴⠑⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡇⠀⠿⡀⠀⠀⠀⣀⡴⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⢄⣠⠾⠁⣀⣄⡈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⠁⠀⠀⠈⠙⠛⠂⠈⣿⣿⣿⣿⣿⠿⡿⢿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⣁⣀⠀⠴⠂⠙⣗⡀⠀⢻⣿⣿⠭⢤⣴⣦⣤⣹⠀⠀⠀⢀⢴⣶⣆ ⠀⠀⢀⣾⣿⣿⣿⣷⣮⣽⣾⣿⣥⣴⣿⣿⡿⢂⠔⢚⡿⢿⣿⣦⣴⣾⠁⠸⣼⡿ ⠀⢀⡞⠁⠙⠻⠿⠟⠉⠀⠛⢹⣿⣿⣿⣿⣿⣌⢤⣼⣿⣾⣿⡟⠉⠀⠀⠀⠀⠀ ⠀⣾⣷⣶⠇⠀⠀⣤⣄⣀⡀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠉⠈⠉⠀⠀⢦⡈⢻⣿⣿⣿⣶⣶⣶⣶⣤⣽⡹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠲⣽⡻⢿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣮⣭⣽⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⢳⣆⡀⠀⠙⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣻⡀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⣠⡴⠒⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣦⣀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠺⠓⠊⠉⠉⣲⠀⠈⡇⠀⠀⠀⠀⠀⣿⣿⡉⠉⠉⠑⠦⣳⡄⠀⠀⠉⠉⠉⠉⠛⠻⠿⠿⣿⣿⣿⣿⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⢻⠲⠿⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⣴⣿⡄⠀⠀⠀⢀⡏⠛⠃⠀⠀⠀⠀⠀⠙⠀⣠⡤⣤⣀⣠⠦⠀⠀⠀⠀⠀⣍⠻⣿⣄⠀⠀⢻⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⣼⣿⣿⣷⡀⠀⠀⢸⣇⠀⠀⠀⠀⠠⠄⠀⣰⡟⢉⣤⣤⡉⠁⠀⠀⠀⠀⠤⠀⠙⠁⢹⣿⣆⠀⢸⣧⡀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣴⣿⣿⣿⣿⣧⡀⠀⢘⡟⠁⠀⠀⠀⠀⢀⡾⢻⡄⠸⣤⣌⣿⠀⠀⠀⠀⡄⠀⠀⣤⠀⣿⣿⣿⣆⢸⣿⣿⣦⡀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⡜⢹⣿⣿⣿⣿⣿⣷⡀⠐⣧⡀⠀⢀⣴⠀⠈⠙⠲⠿⠶⠴⠾⠋⠀⠀⠐⠺⠆⠀⠀⠈⠀⣿⣿⣿⣿⣾⣿⣿⣿⣟⢦⡀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⢸⣿⣿⣿⣿⣿⣿⣷⡄⣟⣁⣀⣀⣠⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⣴⡖⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢹⢦⡀⢸⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣸⠀⠙⢦⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⡿⢻⡏⠉⠉⠈⠙⠲⢬⣗⡦⣄⠀⠀⠀⣠⠄⠀⠀⣹⠉⠉⢉⣟⣿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣆⣀⣠⣽⣦⣤⣤⣴⣶⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡛⡄⠀⣸⠀⠀⣴⠞⢻⡽⢿⣾⣍⢾⣿⣦⠞⠁⠀⠀⠀⢿⣤⣶⡾⢛⣾⣿⣷⠶⣄⡀⠈⠉⢹⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣷⣿⠀⣿⠀⠀⢿⡄⢿⡴⢆⡷⠹⣎⢻⠅⠀⠀⠀⠀⢀⣴⣿⠏⣴⠏⣾⢰⠎⣳⢀⣿⠂⠀⢸⠀⠀⣾⣹⡟⢹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⢱⣿⡇⡟⠀⠀⠈⠳⢤⣉⣉⣤⡤⠟⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠻⣄⣉⣓⣚⣣⡾⠃⠀⠀⢸⠀⢸⣿⠻⠃⡟⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣿⡿⢻⡇⠀⠀⠀⠀⣀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⢿⣿⡀⣰⠃⠈⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣷⡈⠃⣠⠤⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡄⠰⢤⣀⠀⠀⠀⠀⢸⣿⣿⢟⣵⠏⠀⠀⠸⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠉⠙⣇⠀⠀⠀⠀⢀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⢤⡀⠀⠌⠙⠲⢤⡀⡼⠋⠁⣹⠋⠀⠀⠀⠀⢻⣿⣿⣄⡀⠀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⣿⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⢀⣤⣀⢀⣀⣀⡀⠀⠀⠀⠈⠀⠈⠳⢆⡀⠀⠀⢙⣧⣀⡞⡇⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣻⣹⣦⣉⣤⣤⣤⣾⣄⠀⠀⠀⠀⠈⠻⣽⣵⣟⡿⠃⠀⠀⠀⠀⠀⢧⡀⠀⠙⢦⣠⠟⢀⡿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠈⠛⠋⡀⢀⣀⠀⢤⡀⠀⠀⠙⢆⠀⢠⡟⠀⣸⡁⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠲⠶⣶⣉⣉⣉⣉⣉⢉⣉⣭⠭⠟⠛⠀⠀⠀⠈⢳⡟⣶⠋⢸⣿⣿⣿⣿⣶⣶⣤⠀⠀⠀⠀⠀⠀⠈⠻⢿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⣹⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢞⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⡉⡳⢦⣀⣀⠀⠀⠀⠀⣀⣠⣴⣾⢟⣵⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠊⠀⠀⠈⠉⢟⡿⣻⣿⢿⣿⣽⡷⣿⣿⢞⡵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⠂⠀⢀⢴⢵⡿⣺⢟⣷⡷⣻⣾⣾⢟⣵⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢄⣶⣿⣷⡊⢘⢼⡵⣫⣠⢾⣝⡷⡻⠃⠀⠘⣯⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠔⢹⠃⠈⠳⣞⡿⢻⠞⣵⣫⣫⡾⠁⠀⠀⠀⣸⡿⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣽⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⣠⣤⣾⠧⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⠋⠩⣍⡉⠀⠀⠘⢠⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀ ⣾⠁⠀⠀⠀⠉⠑⢦⣄⣈⣇⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀ ⣿⡄⠀⠀⠀⠀⠀⠀⢻⠁⠉⢳⡀⠀⠀⠀⢹⠛⠶⣄⠀ ⡏⠙⠶⣄⡀⠀⠀⠀⠘⠂⠀⢀⡇⠀⠀⠀⢸⠃⠀⢹⡆ ⣇⠀⠀⠈⠛⢦⡀⠀⡔⢀⣠⠾⣆⠀⠀⠀⢸⠀⠀⠀⣷ ⢸⣆⠀⠀⠀⠀⠙⠛⠛⠋⠁⢀⡟⠛⠓⠋⠀⠀⠀⠀⡏ ⢸⡏⠳⣄⠀⠀⠀⡇⠀⢀⣠⠞⢻⡄⠀⠀⡄⠀⠀⢰⠇ ⠈⢧⠀⠈⠻⢶⣾⠷⠾⠋⠁⠀⣸⠁⠀⣸⠁⣀⡠⠋⠀ ⠀⠈⢷⡀⠀⠀⠀⠀⠀⣀⣤⠞⢁⣠⠞⠉⠛⠉⠀⠀⠀ ⠀⠀⠀⠉⠛⠒⠒⠚⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⠛⠿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠿⢿⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⣿⠛⠉⠉⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⣿⡿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⠿⣿⠇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣿⠛⠲⢦⣤⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⠟⠁⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠹⣧⡀⠀⠀⠀ ⢀⣼⠟⠅⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠑⠿⠃⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠹⣧⠀⠀⠀ ⣾⠏⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⢽⣧⠀⠀ ⣿⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⣿⣆⠀ ⣿⣆⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀ ⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠈⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇ ⠀⠀⠀⠙⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀ ⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠈⠹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠁⣀⣠⣤⣤⣄⠀⢠⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢾⣽⣿⡇⠈⠉⢿⠿⠻⠁⠀⢿⠙⠋⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣏⢿⣷⠀⠀⠀⠀⠀⢠⣦⣸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⣷⡀⠀⠀⣀⣀⣬⣭⡴⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣿⣿⣆⠀⠀⠘⠛⠛⣳⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣍⡿⣿⣶⣦⣷⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣼⣻⣿⣿⣿⣦⡝⠻⣿⣿⣷⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣤⣶⠿⢻⣟⣯⡬⠿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣛⠛⣯⣿⣷⣄⠀⠀⠀⠀ ⠀⢀⣾⣿⣿⣿⣿⣦⣿⣿⢳⡠⠝⣿⣿⣿⣽⣿⣿⢿⣿⣾⣆⢿⣯⣿⣿⣦⠀⠀⠀ ⠀⣸⣿⣿⣟⣯⡿⣿⣿⣿⣞⣿⣾⠿⢻⡟⢿⣿⡟⢿⣿⣿⣿⣿⣿⢫⣹⣿⠀⠀⠀ ⢠⣿⢿⡜⢿⡟⢷⣹⣷⣿⣿⢿⡿⣶⡌⡇⣿⡇⡝⣿⡛⣻⣿⣻⢿⣯⣿⣟⡆⠀⠀ ⢸⡿⣷⣧⢸⡏⠋⠙⣿⣿⣇⣾⣿⣿⣇⢻⣽⣷⢰⣿⣧⣿⢸⣿⣿⣿⣏⢹⣿⡇⠀ ⢸⣧⢿⣿⣧⣿⣠⣀⢹⣿⣏⣿⣼⣷⢹⢸⣿⣝⠘⢁⠈⣿⡾⢱⢃⣿⣿⣼⣭⣁⡀ ⣸⣿⡼⣯⣗⢾⣤⣜⣫⣿⣴⡿⢿⠛⢼⣻⣿⣿⣀⣤⣸⣟⣇⡿⠼⠼⠷⠆⠀⠨⢿ ⣿⣟⣳⣿⠟⠛⠛⠛⠻⢿⡏⠀⠈⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⣾ ⢻⣿⣿⣷⠀⠀⠀⠀⠀⠈⠁⠛⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇ ⢾⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠦⣄⣀⠀⠀⠀⠀⠀⣀⣠⡤⠞⠁ ⠀⠉⠙⣿⣿⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠛⣓⣶⣶⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣶⣴⣦⣄⣀⣀⣀⣀⣤⣄⣤⣶⣶⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⣿⣿⠛⠻⠻⡿⣿⣿⢿⣿⠉⣿⣿⡏⢹⢻⢻⡟⢸⣻⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣿⣝⡄⡀⢰⣃⠈⣿⠈⡿⠀⣟⢹⡇⠈⣼⣿⣧⣾⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣽⣦⣽⣼⣟⣺⣯⣬⣧⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡏⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣦⣄⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢾⣷⡀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠉⠉⠻⢿⣿⣿⣿⣿⣿⣿⡿⠃ ⠀⠀⠀⠀⠀⠀⠿⣿⣿⡿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢔⣒⠂⣀⣂⣤⣄⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⢠⣟⣼⣷⠼⣞⣽⢏⣿⣆⠱⣄ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⣆⠛⠢⠐⡍⡉⣾⣾⣽⣟⡰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣿⣦⠀⠤⢶⣿⠿⢋⣴⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣺⡙⢻⣿⣿⣧⣽⣉⣁⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣷⡔⡉⣩⢋⡋⠩⠯⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣘⣶⣁⢙⢐⣄⡴⠪⠓⠁⠉⠃ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢻⣿⣿⣿⣿⠻⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠫⣿⠉⠻⣇⠘⠓⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⣿⠂⠁⠀⠀⠀⠀⠀⠀ ⠀⢶⣾⣿⣿⣿⣿⣿⣶⣄⠀⢐⢝⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣧⠈⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠻⢿⣿⣿⠿⢛⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⣢⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡟⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⠀⠀⠀⠀ ⠀⠀⢀⣼⡟⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⠀⠀⠀ ⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⠀ ⠀⣼⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀ ⠀⡿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⡇⠀ ⠀⣿⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⣷⠀ ⢸⣿⠁⠀⠀⠀⢀⣾⣿⣿⣿⣿⣟⣿⣶⠀⠀⠀⠀⠴⣿⣭⣭⣿⣯⣴⡯⢿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⠀ ⠸⣿⠀⠀⠀⠀⠘⠛⢫⣿⡟⠉⠙⠷⣤⠀⠀⠀⠀⢀⣴⡶⡟⣉⣍⣹⣷⣟⢹⣿⠖⠂⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀ ⠀⣿⡄⠀⠀⠀⠀⠛⠛⢻⡿⠯⢿⢒⣿⡏⠀⠀⠁⣿⡿⠞⢻⣿⢼⣯⣽⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠀ ⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠀⠀ ⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡯⠀⠀ ⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇⠀⠀ ⠀⠀⠈⢧⠀⠀⠀⠀⠀⢀⣠⣴⣶⠿⣿⣷⣶⣶⣶⠾⣿⠟⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀ ⠀⠀⠀⠸⡆⠀⠂⠀⣶⣿⣯⣏⣿⣧⠽⣿⣿⣯⣿⣿⣿⣶⣶⣿⡟⣿⣿⣷⣦⣠⠀⠀⠀⠀⡄⠀⠀⣾⡇⠀⠀⠀ ⠀⠀⠀⢀⣧⠀⢣⢸⣿⣿⣿⣿⣿⠿⠿⣮⣿⣧⣿⠿⠤⠿⠷⢿⣿⣿⣿⣿⣿⡀⢰⠀⣀⠀⠃⠀⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⠈⣻⣆⠈⡏⠿⠛⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣽⠟⠋⠹⠇⣼⢰⡟⠀⠀⠀⣼⣿⣻⡀⠀⠀ ⠀⠀⠀⠀⣏⣿⣇⠀⠀⠀⠐⣆⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⣴⡟⠀⠀⠀⢠⡏⣼⡇⠀⠀⣸⣿⣿⢫⢧⠀⠀ ⠀⠀⠀⠀⣿⣸⣿⡆⠀⠀⠀⣈⢷⣦⣀⣀⣀⣠⣤⣤⣤⣶⣿⠋⠉⠀⠀⠀⢰⢟⣼⠏⠀⠀⢀⣿⣿⣿⠂⣿⠀⠀ ⠀⠀⠀⠀⠇⠀⢹⣧⠀⠀⠀⢿⠀⠈⠙⠛⠛⠛⠿⠟⠋⠉⠛⢷⡄⠀⠀⠀⠈⠛⠉⠀⠀⠀⣸⣿⣿⣿⣼⢿⠀⠀ ⠀⠀⠀⠰⡄⠀⠀⢻⣦⣀⠀⠘⣧⠀⠀⢹⡄⠀⠀⣠⣦⡀⠀⠘⣷⠀⠀⢠⣤⣴⣤⣀⣀⣶⣿⣿⠿⠋⢁⣼⠀⠀ ⠀⠀⠀⠀⢧⠀⠀⠀⠻⣿⣧⣀⣿⡄⠀⢸⣿⠀⠀⢹⣿⡇⠀⠀⣿⣇⣠⣾⣿⣿⣿⣿⣿⠿⠋⠀⠀⢠⡜⠃⠀⠀ ⠀⠀⠀⠀⠀⢧⡀⢀⠴⠁⢈⢿⣿⠇⠀⠈⣿⡆⠀⠈⣿⣧⠀⠀⠸⣿⣿⣿⣿⣿⡿⠟⠁⠀⢀⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⠋⠀⣠⣮⠞⠛⠓⠒⠶⣼⣷⣤⣤⣬⣿⣤⣤⣴⡟⠛⢻⡟⠛⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⣠⣯⣿⠃⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠿⠿⠿⢿⡇⠀⠈⢧⠀⢀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠛⣿⣿⡇⠀⠀⠀⢀⡤⠔⠊⠉⠁⠀⠀⠀⠀⠀⠀⢱⠀⠀⠈⢷⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⡀⣀⣀⣀⣠⣴⡿⠀⠀⠀⠀⠀⠀⢀⣷⣀⣠⡈⢿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⢭⣷⡶⠟⠋⠉⠀⠀⠀⢀⠀⠀⢠⣾⣿⣿⣿⣿⠄⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⠀⠀⠀⠀⠀⣀⣀⣤⡶⣀⠁⣠⣾⢟⣫⠟⢹⣿⢸⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠷⠶⠶⠶⠾⠟⠛⠋⣴⣿⣧⣾⣿⣾⡏⠀⢸⣿⣾⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣆⡀⠀⢀⣠⣾⣿⣿⣍⣹⣿⣿⣴⡇⠀⠈⣿⣿⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⠿⠟⣩⡿⢿⣯⣿⠉⠉⠀⠀⠰⣿⣿⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡙⠻⠶⠟⢻⡇⠀⠉⠁⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡇⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣤⠀⠀⠀⣿⣷⡄⠀⠀⠀⠀⠀⠀⣻⣿⣿⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣛⠶⣄⣩⣷⣶⣴⣿⣿⡇⠀⠀⠀⠀⠀⣰⣿⣿⣿⣟⣿⣶⣮⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡴⠿⠟⠓⣊⣿⠿⣯⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠐⢹⡿⠮⠀⢾⡛⣛⣛⢻⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠒⠛⠛⠒⠶⣦⣴⡉⣿⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣾⣷⠀⠲⢾⣭⣭⣿⡭⣿⣿⡄⠀⠀⠀ ⠀⠀⣴⡿⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢹⣿⡀⠀⢀⣤⣤⣤⣬⣿⣿⣿⡆⠀⠀ ⠀⣼⣟⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⡀⠀ ⠀⢿⣿⣷⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀ ⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⠿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⠄⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⡇ ⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣛⡻⠿⠿⠿⠿⠿⠿⠟⠛⠀

⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⢀⣀⣤⡤⣤⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⠉⠀⠈⣉⡓⠒⠚⠉⠴⢶⠀⠈⠉⠉⠂⠉⠉⠀⢠⡶⠶⣌⠙⠒⠒⠒⠋⠉⠉⠙⢷⣆⠀⠀⠀ ⠀⠀⠀⢿⠀⢀⡀⠘⠿⠃⠀⠀⣠⡾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣦⠀⠀⠀⠀⠀⠘⢿⡆⠀⢀⡿⠀⠀⠀ ⠀⠀⠀⠈⢣⡈⠁⠀⢀⣠⣴⣾⣏⣈⠉⠒⢄⡀⠀⠀⠀⠀⣀⡤⠖⠛⣳⣦⣄⣀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⢠⠟⢉⣿⣿⣿⣿⣿⣿⡿⢿⣦⡀⠱⣄⠀⢀⠜⢁⣠⣾⣿⣿⣿⠿⣿⣿⣏⠛⢻⡉⡇⠀⠀⠀⠀ ⠀⠀⠀⢠⡏⢰⣿⢋⣿⣿⣿⣿⠋⠁⢾⣿⣿⡀⠸⣄⡎⣰⣿⢻⣿⣿⣿⣿⠛⠻⣿⢻⣷⡀⠹⡇⠀⠀⠀⠀ ⠀⠀⠀⣾⢀⣿⡇⣿⣿⣿⣿⣿⣦⣴⣿⣿⢻⡧⠀⡿⠀⣿⡇⣾⣿⣿⣿⣿⣄⣠⣿⡟⢻⡇⠀⢻⠀⠀⠀⠀ ⠀⠀⠀⣿⠸⣿⣤⢿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡇⢀⣇⠀⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⡇⠀⣾⠀⠀⠀⠀ ⠀⠀⠀⢹⡄⠙⣿⣦⠿⣿⣿⣿⣿⡿⣏⣳⡟⢀⣼⢿⡀⠹⣿⣉⣿⣿⣿⣿⣿⣿⠟⣩⣿⠁⣰⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣄⡈⠛⠷⣼⣯⣭⣥⣴⠟⠋⣠⠞⣿⢸⡷⣄⠘⠻⣷⣬⣟⣏⣹⣿⡷⠟⢁⣴⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠙⠲⠤⣤⣤⣤⣤⣤⠴⠛⠁⠀⡟⢸⡇⠈⠓⠦⣤⣈⣉⣉⣉⣁⣤⠶⠋⣱⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠸⡇⠀⠀⠀⠀⠀⠉⣉⡍⠁⠀⠀⠠⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⢴⡄⠀⠀⠀⠀⠀⢀⡴⣿⡇⠀⡷⣄⠀⠀⠀⠀⡼⠙⢳⡀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣄⠀⠀⣀⡀⠀⠀⠀⢠⠏⠀⢈⡇⠀⡇⠈⢧⠀⠀⡼⠁⠀⠈⡇⠸⠃⣼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⢻⠀⠘⢿⡿⠆⠀⢴⠛⡄⠀⢸⡇⠠⡇⢠⣈⡼⠀⢧⡘⢾⡷⠃⠀⢸⠛⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡁⣈⡷⠖⠒⠲⠶⠤⢼⡛⠓⠶⣾⠃⠀⣷⡤⠭⢤⣶⠦⢬⣤⠤⢤⣀⡼⠀⣻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⡟⢻⣤⣤⣤⣤⣀⣀⣈⣓⣊⣽⠀⠀⣇⣙⣖⣋⣀⣀⣀⣀⣀⣀⣹⣿⠛⠉⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⢀⣀⣀⣇⢸⠙⠛⠛⠛⠁⠙⠿⠿⠿⣿⠀⠀⣿⠿⠿⠏⠉⠿⠿⠿⠿⠋⡟⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠸⣦⢤⣄⣀⣀⣀⣀⣤⡤⣬⣿⣾⣁⣀⣀⣀⣀⣀⣀⣠⣤⣀⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠣⡄⡇⠀⠿⢦⣄⣀⣀⣸⡆⠀⠀⠀⠀⠀⠸⣿⣿⣍⣿⣿⠈⢸⢃⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣧⢻⠇⠀⠀⠀⣧⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠁⠀⠀⢸⣾⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⠀⣿⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠸⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣷⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣦⣾⣧⣼⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⣿⣇⣠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣘⣻⣿⣟⢛⣻⣟⣁⣀⣀⣀⣀⣀⣀⣀⣈⣻⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠈⠻⣮⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠋⠀⠀⠀⠀⠙⣿⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣠⣤⣤⣀⡀⠀⠀⣀⣴⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⠀⠀ ⢀⣤⣾⡿⠟⠛⠛⢿⣿⣶⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣦⣀⣀⣤⣶⣿⡿⠿⢿⣿⡀⠀ ⣿⣿⠏⠀⢰⡆⠀⠀⠉⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡿⠟⠋⠁⠀⠀⢸⣿⠇⠀ ⣿⡟⠀⣀⠈⣀⡀⠒⠃⠀⠙⣿⡆⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀ ⣿⡇⠀⠛⢠⡋⢙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀ ⣿⣧⠀⠀⠀⠓⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⢸⣧⣤⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀ ⣿⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠻⣷⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀ ⠈⠛⠻⠿⢿⣿⣷⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣷⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣷⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣷⣶⣶⣤⣤⣀⡀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣷⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢸⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣤⣄⣀⡀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣻⣷⣶⣾⣿⣿⡿⢯⣛⣛⡋⠁⠀⠀⠉⠙⠛⠛⠿⣿⣿⡷⣶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⠿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⢷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣄⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⣰⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠿⠁⠀⠀⠀⠀ ⠀⠀⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠊⠉⠙⣦⠀⠀⢰⣶⣦⣄⠀⠘⣿⣿⣿⣿⡇⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⣠⠟⠀⠀⠈⢻⠿⠟⠀⠀⢿⣿⣿⡿⠃⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⣤⠟⠀⠀⠀⠄⠠⢍⠉⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣤⣤⣄⡀⠀⠤⠋⠀⠀⠀⠀⠀⣀⢸⡿⠀⢀⡄⠀⠀ ⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⢀⣴⣿⣾⣧⣾⣿⠁⠀⠀ ⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣿⢳⣿⣿⣿⡿⠃⠀⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣿⣿⣿⣿⣿⡿⠄⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠹⣿⡻⣦⣀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣹⢷⣍⡛⠷⣌⡛⠚⠿⠷⠄ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠉⠙⠛⠚⠓⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡲⠖⠲⢌⡭⠭⣅⠒⢤⠤⢤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣏⣏⣙⣛⡟⠒⠶⢺⡇⠀⠀⠀⠱⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⡴⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠔⠊⠀⡄⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⢀⣾⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢀⡇⠀⠀⠀ ⠀⠀⢀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡇⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠒⠒⠢⠤⠤⢤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⣀⣷⠀⠀⠀⠀ ⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⣤⣤⣤⣤⣤⣤⣶⣿⣿⠿⢆⠀⠀⠀ ⠀⢫⣉⣛⣻⣷⣶⣤⠀⠀⢀⠴⠋⠉⢻⠿⠿⠿⠿⠿⠿⠟⠛⠉⠀⠀⠈⡆⠀⠀ ⠀⢴⢻⡿⠷⢾⣋⣀⠤⠚⠁⡆⠀⠠⣿⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⠀⠀ ⢀⣸⠛⠤⡤⠀⠀⠀⠀⠀⣸⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠘⡀⠀ ⠣⣀⣹⣏⣉⣁⠀⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀ ⠛⠭⣅⣙⣅⠈⠉⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⡅⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣘⠦⠬⢶⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⣉⡢ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠁⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⢠⠃⠀⠀⠀⣜⠄⢀⡄⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠒⠻⠦⣸⣀⣀⣀⣀⠤⠤⠔⠃⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔ ⢧⣄⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡟⠀ ⠘⠿⣿⣗⣦⣀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⣀⡀⠀⣀⣤⡶⣻⣿⡿⠏⠀⠀ ⡄⠀⢿⣿⣟⢦⣽⣶⡶⠟⠍⠉⠉⠙⣿⣿⠏⠙⠚⡯⠯⠕⠒⠿⢯⡿⠁⠀⠀⢠ ⣅⡤⠈⢻⣿⠉⠉⠉⢉⠀⣄⡀⠀⠀⢻⢷⠀⠀⠈⡗⠀⠀⠀⠀⠈⣇⡀⢀⣂⢰ ⢅⠀⠀⠘⠃⠀⠀⠆⢸⣧⠃⢰⠀⠀⠨⠐⠀⠀⠀⠈⢷⡄⡄⠀⠀⠀⠐⢶⣾⠁ ⢸⣇⡀⠀⠀⠀⠸⠀⣿⡏⠀⠈⣆⡄⠀⠀⣦⠀⠀⠀⠈⣷⡏⠀⠀⠀⣀⠀⠹⡃ ⣼⣯⡷⡶⣶⣶⣾⣷⣶⣍⠀⢠⢿⣇⣆⠠⠳⢀⠀⢠⢀⣽⣾⣿⣿⣿⡿⡀⠀⠘ ⣿⠃⠁⠧⡘⢿⣿⣿⣿⣿⡂⠀⠃⠻⢿⣟⣴⠁⠀⠁⣿⣿⣿⣿⣿⠟⣠⠇⠀⠀ ⣿⣄⡄⠀⠈⠑⠌⠙⣿⣿⣷⠀⠀⠀⠀⢱⠁⠀⠀⣰⣿⣿⠛⠋⠡⠒⠁⠀⠀⠀ ⣇⠃⠙⢾⡀⢀⣀⣠⠟⢿⣻⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⢀⠀⠀⣄⣤⠀⠀⠀ ⠸⣇⡀⠈⠙⠻⣿⡗⠀⢲⣿⣻⣖⣀⣀⣀⣀⣠⣾⣿⡯⢧⣰⢿⡿⠛⠀⠀⠀⣠ ⠀⠈⠳⡀⠀⢰⡎⠋⠀⠀⠙⢿⣿⣿⣿⣽⣿⣿⣿⠟⠁⠀⢭⣯⣀⣀⣤⣶⣿⣿ ⠀⠀⠀⢉⣦⣜⣧⣣⠀⠀⠀⠀⠙⣿⣿⣿⡿⠋⠁⠀⠀⡶⢲⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⡷⠖⣶⠒⣬⣿⡟⠤⣶⣶⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢠⣾⣿⣿⣿⣿⡟⠓⠢⣄⡉⠉⠈⠉⠉⣁⣴⣾⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀ ⠀⠀⢿⣿⣿⣿⣿⣿⡇⠀⠄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠭⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⣿⡿⠟⠋⠁⢠⣿⣿⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡿⠿⠛⠋⠉⠀⢀⣶⣦⣴⣿⣿⠟⠻⠿⢿⣿⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠛⠉⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⢿⣶⡄⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⢰⣿⠟⠀⡀⠀⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⠀⠀⠀⠀⢀⡤⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣄⣀⣥⣴⣿⠟⠀⠀⠀⠀⠘⠿⠿⠿⠃⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢸⣿⡇⠀⠀⠀⠀⠰⠚⠁⠀⠀⠘⠻⠿⠿⠟⠀⠀⠀⠀⠀⠀⠸⣿⣿⠛⠛⢻⣿⡆⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣴⣾⣿⣿⣿⣷⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣮⣿⣿⠁⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⢸⣿⣿⣿⣿⣶⣦⣄⠀⠀ ⠀⠀⣾⣿⠟⠋⠁⠀⠉⠛⠻⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⢸⣿⣿⠁⠀⠉⠻⣿⣧⠀ ⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢿⣿⣆⠀⠀⠀⢹⣿⡇ ⢀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⣼⣿⡇ ⠸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣀⣴⣿⡟⠀ ⠀⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠋⠀⠀ ⠀⣿⣿⠈⠻⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡏⠀⠀⠀⠀ ⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀ ⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠈⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣶⣶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣶⣾⣿⠿⠿⠛⠉⠻⣿⣷⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠈⡄⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣧⠀⠀⢹⡀⢸⡉⠻⠒⠦⡄⠀⢀⣠⡤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣚⠛⠛⠀⠉⠙⢾⣧⠀⠈⡇⢸⡇⡄⠀⣠⣧⠞⠉⠀⡀⠀⠐⠛⠒⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣿⣿⣷⢦⣀⠈⠓⠦⣽⣷⣦⡿⣾⡷⣇⣰⠟⢁⡤⠒⠉⠀⠀⢀⣀⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠷⠒⠀⠀⠉⠙⠛⠿⣶⣾⣿⡏⠙⣷⠉⣾⡏⣿⣾⡇⠀⣀⣤⣶⡾⠭⠥⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣄⣀⣠⠤⠤⠤⠤⣤⣴⡾⣿⣟⠉⠒⠂⠘⠃⢾⡟⡛⣳⣯⠭⠶⠶⠒⠂⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⣁⣠⠤⠶⠖⠒⠚⣿⣽⠟⠁⠀⠀⠀⣀⠀⢀⠀⠙⢿⣿⣶⣶⣶⡶⠦⠤⢶⣶⣶⣒⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⣽⠃⠀⠀⢁⣀⣠⡤⠶⠒⣻⣿⣧⡄⣄⡈⡷⠄⣩⡔⠻⢶⣶⣿⠷⠶⠤⢭⣉⠛⠒⠦⣄⠈⠉⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡴⣋⠁⠀⢸⡇⣀⣴⡾⣿⠟⠁⡠⠒⠉⢀⡠⣟⡿⡟⢀⢶⠆⣺⣷⣤⣐⣾⣛⠒⠦⣄⡀⠀⠁⠀⠀⠀⠙⢶⣒⣀⡈⠙⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣉⡀⠈⢭⣷⣾⠟⣿⢁⡞⠁⠀⠀⠀⣠⡖⢉⡼⠁⠀⣹⡟⢻⠳⣿⠙⢿⠳⣄⠀⠉⠲⢄⡙⠲⣄⠀⠀⠀⠀⣘⣯⣄⣠⡶⠾⠟⢦⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⡉⠀⣠⣴⡟⣿⡇⠀⣇⡟⠀⠀⠀⡴⣺⠏⠀⠎⠀⠀⣰⣻⠁⢾⠀⢹⡀⠈⢧⠘⣦⡀⠀⠀⠙⠆⠈⠻⡶⣄⡀⢸⡇⠈⡟⢦⣄⣀⣈⣳⡄⠀⠀⠀ ⠀⢠⠯⠀⣹⠟⠁⣿⠁⢸⡇⠀⢿⡿⠁⢠⠞⢠⡏⠀⠀⠀⠀⣸⠃⡏⠀⢸⠀⠈⡇⠀⠘⡆⢸⣏⠳⣄⠀⠀⠀⠀⠹⣎⡟⠻⠀⠀⣇⠀⠟⢷⣾⢅⣹⡄⠀⠀ ⢠⡏⢠⠞⠁⢰⠀⠁⠀⡤⡇⠀⢸⡇⢠⣿⢀⣼⠀⣤⠀⠀⢠⡏⢠⡇⠀⢸⠀⠀⣿⠀⠀⠀⠀⢻⣯⣽⣦⡀⠀⠀⠀⠘⣿⠀⠸⡇⠻⠀⠀⠸⢮⡷⣬⢿⡄⠀ ⣼⢰⠃⠀⣾⢺⠀⠀⠀⢻⡀⠀⣀⣳⣾⡽⠋⣿⠀⡇⠀⢀⡾⠀⣼⡇⠀⠈⠀⠀⢹⡀⠀⠀⠀⠸⡏⣷⡊⠳⣄⡀⠀⢀⣹⠒⠶⠿⠶⢤⣤⣄⣀⣧⡈⠂⢻⡀ ⠿⠚⠋⠉⠉⠉⠉⠙⠛⠛⠉⠉⠁⠀⠀⠀⠀⣿⠀⣇⠀⣼⠃⡼⢻⡇⠀⢀⠀⠀⠘⡇⠀⢸⠀⠀⣿⡿⠻⣄⣈⣹⡶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢾⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠿⠴⢃⡼⠁⠈⣧⠀⢸⡄⠀⢰⣇⠀⢸⡆⣰⠟⠁⠀⢻⡠⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⢠⡞⠳⠚⠳⠤⠟⠙⠳⢾⣛⠁⠀⡼⡀⠀⣧⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣧⡀⢸⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠞⠻⢷⡿⣏⡛⠲⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠛⠉⠉⠉⠓⢤⡙⠆⠑⢀⣀⡬⠿⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠥⠒⠚⠉⠉⠓⠲⢄⠑⠄⠀⣨⡶⠿⣿⡯⢿⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⢀⣀⠤⠤⢤⣀⠀⠀⠀⠃⢀⣾⣍⣉⠉⠲⢄⠐⢌⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢁⠴⠚⠁⠀⢀⣠⣤⣀⠙⢦⠀⠀⠈⠀⠀⠈⠑⠦⠀⠳⡀⠑⢄⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⡔⠁⠀⠀⢀⠔⣡⣾⣿⣉⣦⠀⢀⡈⠉⠑⠦⡀⠀⠀⠀⠀⠙⡄⠈⠣⡈⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠋⠀⠀⠀⡠⢃⡴⠋⠁⠀⠁⠉⠉⠉⠙⢣⡀⠀⠈⢳⣄⠀⠀⠀⠘⢆⠀⠑⡜⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⡴⢁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠙⣷⡀⠀⠀⠈⢆⠀⠘⣾⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⡜⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠈⢷⡀⠀⠀⠈⢆⠀⠸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⡼⠁⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠳⡀⠀⠀⠘⡆⠀⢻⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⠁⢀⣿⢠⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣦⠀⠀⠘⣄⠀⠀⠸⡀⠸⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢀⠇⠀⡼⣿⠀⢀⣠⣤⣤⣭⠉⠛⠀⠀⠀⠀⠘⠋⢉⣥⣤⣬⢷⣄⠀⠈⣆⠀⠀⢇⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡼⠀⢠⠃⣿⠶⣿⡻⣿⣿⣿⠷⠀⢠⠀⠀⠀⠀⢸⣿⣿⣿⣟⣿⡿⢦⡀⠘⡄⠀⢸⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢠⠇⠀⡎⠀⣿⠄⠀⠉⠛⠛⠉⠁⠀⠘⠀⠀⠀⠀⠀⠉⠙⠛⠋⠁⠀⠈⣷⡀⢱⠀⠀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⠀⣸⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢳⠈⡆⠀⣷⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠇⢠⠇⠀⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡇⠀⠀⡇⠀⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⡞⠀⢰⣿⠃⣇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⢰⠃⡇⠀⠀⢸⠀⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣸⠁⢀⣾⡏⢸⣿⡀⠀⠀⠀⠀⠀⣠⠔⠢⠤⠒⢄⡀⠀⠀⠀⠀⠀⣼⡆⢇⠀⠀⢸⠀⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡟⢠⠃⠀⣼⣿⠀⣿⠁⣷⡀⠀⠀⠀⠺⡗⠈⠉⠉⠉⠘⡿⠀⠀⠀⠀⣼⡇⣧⢸⡀⠀⠸⡄⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⢡⠏⠀⡸⢹⠇⣸⡏⠀⡜⢿⢦⡀⠀⠀⠈⠒⢲⠶⠒⠋⠀⠀⠀⣠⣾⠁⡇⢸⣧⢳⡀⠀⡇⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣷⠏⠀⢠⠃⣼⢠⣿⠀⠀⡇⣸⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⡏⠀⡇⠘⡏⢷⡷⡄⢻⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⡎⠀⣿⣾⠃⠀⢸⠁⣿⡆⠀⠀⠈⠓⠢⠤⠤⠴⠒⠉⠀⠀⢠⡇⠀⡇⠀⡇⠀⠻⡜⢾⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡟⠁⠀⠀⢸⠁⠀⣿⡏⠀⢀⠇⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⡇⠀⡇⠀⠀⠹⡎⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠟⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⡜⢀⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢹⡀⢳⠀⠀⠀⢻⡸⡇⠀⠀⠀⠀⠀ ⠀⠀⣰⢿⠀⠀⠀⠀⢀⣾⡇⠀⣿⠀⢰⠁⣸⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣧⡘⣆⠀⠀⠘⡇⢻⡄⠀⠀⠀⠀ ⠀⢰⡏⠈⣆⠀⠀⣠⡎⣹⢻⡄⠹⣦⡼⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠺⠦⢄⣸⣁⣀⣻⣄⡀⠀⠀ ⠀⡿⣄⠀⠈⢑⡸⠋⣰⡟⠋⠻⣦⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒ ⢸⠃⠀⠉⣉⣡⡤⠾⠋⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⠀⠤⠤⢀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡷⣦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠆⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠰⣧⠀⣀⡀⢰⠆⣀⡀⠀⠀⢀⣤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣖⢀⣴⣦⣴⣶⡆⠀⢸⣿⠿⣿⣾⣿⠿⣿⢸⣟⣹⠇⠀⣼⣧⣼⡿⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣤⣶⡿⣧⣿⣼⣿⣫⠴⣽⡿⠀⠈⠷⠀⠿⠙⠷⠛⠹⠸⠟⠉⠀⠀⣿⠁⣼⢿⣏⢨⣿⣾⢷⣦⣤⡀⣴⠄⠀⠀⠀⠀ ⢠⡄⢾⣆⣾⠛⣷⢿⡸⣧⣹⣟⠃⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠛⠹⠇⣾⢃⣿⣱⢏⣤⣤⡄⠀⠀ ⠸⣷⠟⢻⡿⠷⠟⠈⢁⣿⠋⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠈⠙⠿⢸⣟⣛⢳⣾⢶ ⠀⠹⠗⠈⠁⠀⠀⠀⣸⠃⠀⠀⠹⠷⠶⠶⠶⠶⢦⣤⣀⣀⡿⠉⠉⢿⡆⣀⣴⡾⠿⠛⠛⠉⠉⠙⠛⠛⠶⣄⡀⠀⠀⠀⠀⠉⠉⢷⣿⠆ ⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⢸⣿⠛⠁⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⢀⣤⠶⠒⠒⠒⠒⠲⠦⣤⡀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⡼⠉⠀⠈⢻⣷⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⠋⠀⠀⠐⠟⠀⠀⠀⠀⠀⡙⢳⡄⢠⡟⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⢀⣼⡿⠀⠻⣶⣶⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⠀⣿⠀⠀⢀⣶⡦⣄⡀⠀⠀⠘⠋⠀⢹⣸⣷⠋⠉⠻⣦⡤⠒⠛⠛⠛⠿⣟⠋⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⠀⠘⣆⠀⠈⣿⡿⠿⣿⣽⣿⣿⠆⠀⢸⠻⣷⡀⠀⣠⡏⢠⣶⣿⣿⡆⠀⠀⠱⡄⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠈⠛⠦⣌⡛⠶⠦⠿⠟⠋⣀⡴⠋⠀⢳⡉⠉⠹⡅⠈⢹⣭⣥⣿⣶⡤⠾⠃⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⡀⠀⠉⠉⠛⠛⠛⠉⠁⠀⢀⣠⠞⠻⣦⡀⠳⠤⠞⠻⠿⠴⠚⠀⢀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⣶⠶⠶⢶⣶⠶⣶⠛⠋⠁⠀⠀⠈⠛⠷⣦⣤⣤⣤⣤⣴⡶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣷⠀⣿⠃⢸⡏⢸⡇⢸⡇⣰⡿⣦⢹⣇⠈⣿⢿⡿⠿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⢿⣇⣿⠀⠘⣷⣼⣧⣼⢿⣿⠶⣿⡎⢻⣾⠋⢈⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⢛⠋⠛⠛⠓⠙⠃⠹⠋⠸⠷⠀⢾⠇⢸⠏⠀⠹⣶⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠃⠀⠀⠀⠀⠀⣠⡾⠟⢛⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀ ⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠛⣦⣄⠀⠀⠀⠀ ⣿⣧⠀⠀⠀⠀⠀⠀⣠⡞⠃⢀⣼⠋⡀⠀⠀⠀⣴⠃⠀⠀⠀⢠⡄⠀⠀⢠⣄⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⠉⠉⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⢀⣤⣾⣿⡄⠀⣾⠃⢸⡇⠀⠀⣿⠃⢀⣠⠾⢻⣿⠀⣠⣾⡟⣸⡟⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢷⡀⠀⠀⠀⠀ ⣿⡟⠀⠀⠀⠀⠀⢠⣿⠁⣸⠇⠀⢸⡇⠀⣼⣟⣠⡟⣡⠴⣿⣧⡴⠋⢹⣷⢏⡠⣾⠛⣷⠀⣰⠄⠀⠀⠀⠀⠀⠀⠈⣿⠛⠻⠄⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⢀⣾⣥⣾⣿⠀⣰⡾⣧⡼⢻⣿⠿⠛⠁⣰⡿⠋⠀⠀⣾⢏⣼⣷⣞⣯⣿⣾⡟⠀⢰⡆⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⣼⡿⢁⣿⡇⣰⡏⢀⣹⠃⠘⠁⠀⠀⠔⠉⠀⠀⠀⠀⡟⠈⠹⣿⣿⣇⣽⠏⢻⡀⢸⡇⠀⢸⡇⠀⣿⣿⣿⠀⠀⠀⠀⠀ ⣿⣇⠀⠀⠀⠀⡟⠀⢸⣧⣿⣿⡇⣿⠛⠻⠷⣦⣄⢲⣄⠀⠀⠀⠀⠀⣀⠀⠀⠉⠀⠙⠋⠀⠀⣿⣾⣧⠀⣼⣿⢸⣿⣏⠻⡇⠀⠀⠀⠀ ⣿⣿⠓⠒⠒⠚⠓⠒⣿⣿⢿⣸⡇⣿⠀⣠⠖⠚⠻⣷⠁⠀⠀⠀⠀⠺⢋⣴⠿⠿⣟⠛⠛⠻⣶⣿⢻⣿⣷⡟⢙⢻⣿⣿⠀⠁⠀⠀⠀⠀ ⣿⣿⡆⠀⠀⠀⠀⢸⠟⠁⢸⣿⢻⢻⡀⡇⠀⠀⠀⠸⡆⠀⠀⠀⠀⢠⡿⠁⠀⠀⠈⢆⠀⢀⡿⠉⢸⣿⠻⡟⠁⠈⣿⣿⠃⠀⠒⠒⠒⠒ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⠏⠈⠓⠿⠦⠤⢤⣼⡧⠀⠀⠀⢠⣿⣇⠀⠀⠀⢀⠞⢀⡼⠁⠀⢸⡏⠘⢳⡶⣰⠏⠹⠀⠀⠀⠀⠀⠀ ⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠒⠛⠚⠉⠀⠀⠀⠈⠀⢀⡜⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣾⣿⣥⣤⣄⣀⣀⣀⣀⣀⣀ ⡿⠃⠀⠀⠀⣀⣤⠴⠖⠋⠁⠈⠳⣄⠀⠀⠀⠀⠀⠀⢀⡤⡾⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠉⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠁⠀⣤⣶⣿⣯⣤⣤⣤⣀⣠⠄⠀⣀⡙⠲⣤⣀⡀⢀⠈⠀⢙⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠋⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢾⠿⡿⠁⠈⡏⢹⡏⠉⠉⠉⣿⠙⠛⠛⣛⣿⢿⣿⣿⠛⠉⠙⣶⣶⣶⣶⣶⣿⣿⠿⣿⣿⣷⣾⣟⣶⣒⣢⣤⣄⣦⣤⣤⡄⡀⠀⠀⠀ ⠀⡾⠀⡇⠀⠀⡇⢸⡇⠀⠀⢀⡇⠀⠀⠀⡇⠀⢰⡿⣷⣀⠀⣼⠋⠀⠙⣿⣿⠛⠁⣠⣿⣧⠀⠀⠀⣿⠇⠀⠀⠉⠹⣯⠉⠉⠉⣿⠛⡿ ⢰⡇⠀⡇⠀⠀⡇⢸⡇⠀⠀⢸⡇⠀⠀⠀⡇⠀⣿⣿⣏⣿⣿⣿⣄⣀⡔⠋⠁⠉⢺⣿⣿⣿⡆⠀⠀⣿⠀⠀⠀⠀⠀⡏⠀⠀⠀⡿⠀⡇ ⠘⢷⣀⣷⣤⣤⣷⣾⡇⠀⠀⣸⣧⠀⠀⢠⣇⣴⣿⣿⡿⠿⠿⠿⡿⠛⢷⣀⠀⠀⠀⣿⣿⣿⣷⡄⠀⣿⠀⠀⠀⠀⠀⠃⠀⠀⠀⡇⠈⠃ ⠀⠀⣿⣿⣀⡀⠀⠈⠉⠛⠉⠙⠛⠶⠾⠞⢻⣿⣿⣄⡇⢀⢐⠚⠧⠀⠄⠈⣷⡷⠺⣿⣿⣿⣯⣀⣰⣿⣀⡀⠀⢀⣀⡀⠀⠀⠀⡇⢀⡀ ⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⣱⠀⠨⣟⣶⣆⡤⠁⠀⢧⢹⣾⡿⡿⠉⠉⠀⠀⠈⠉⠉⠉⠉⠙⠓⠷⠒⠒⠛⠺⠷ ⡋⠉⣉⣩⡉⠛⠒⠒⠒⠒⠒⠲⢶⣤⣤⣼⣿⣿⣿⣿⣦⣖⣳⡤⠧⠼⠀⠸⣏⣡⣤⣴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⣾⠿⣯⣩⣷⣄⠀⠀⠀⠀⣴⡿⠟⠋⠻⢿⣿⣿⣌⣻⠿⢿⣿⣿⣶⣶⡶⠶⠞⣉⣴⣿⣟⠉⠓⠒⠒⠒⠲⠶⠲⠦⠤⠤⠤⠤⠤⠤⣀ ⠀⣿⠀⠀⠀⢸⣡⡴⠶⠶⣾⢷⣿⣿⣤⣴⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣷⣦⣴⡴⠶⠶⢦⣄⠀⠀⠀⠀⢀⡀⣀⣴

⠀⠀⠀⢰⠒⢲⠒⠒⣶⠖⠖⠒⠒⠒⠒⠲⣖⠲⡒⠒⠒⣶⠐⠒⢲⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⡌⠀⢰⢇⡇⢠⠀⠀⠀⠀⠀⠈⠢⡘⢆⠀⠸⣆⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠇⢰⠇⠀⡾⣿⢳⠘⡄⠀⠀⠀⠀⠀⠀⠈⢪⣷⣄⣻⡄⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⢀⣿⠀⢠⣿⡇⢸⡀⢣⠀⠀⠀⠀⠀⠀⠀⠘⡀⠙⢻⣷⡀⠀⠘⡄⢰⡀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⠀⠀ ⠀⠀⢸⣼⣿⡆⢸⣿⠇⠸⣇⠈⢇⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⡿⣷⡀⠀⢿⡄⠹⣦⡀⠀⠀⢀⡀⠸⣼⠀⠀⠀⠀ ⠀⠀⣾⣿⣇⣇⢸⣿⠀⠀⢹⡀⢸⣆⡀⠀⢤⠀⠀⠀⢈⣇⠀⢣⡘⣷⡀⣸⣿⣆⠚⢿⣎⠉⠀⠀⠀⢻⡀⠀⠀⠀ ⠀⠀⣿⣿⣿⢻⠹⡟⠒⠒⠒⢷⠚⣿⣷⣄⠈⢳⡀⠀⠀⢸⡍⠹⣏⠉⣿⡀⢧⠙⢧⡀⠻⣦⡀⠀⠀⠘⡇⠀⠀⠀ ⠀⠀⢸⣿⡇⠈⣆⣇⣀⣤⣴⣾⣧⣽⠙⢿⡦⡀⠻⣦⡀⠀⣿⣄⢿⠚⠛⠻⡌⡗⠒⠿⣄⣻⡿⣦⠀⠀⡇⠀⠀⠀ ⠀⠀⢸⣿⠁⠀⠺⣿⠁⠀⠀⠀⠈⠻⣇⠈⠙⢿⣷⣜⣿⣦⣸⠙⢆⣇⠀⠀⠘⢿⣀⠀⣈⡙⣧⠘⢷⣤⠇⠀⠀⠀ ⠀⠀⢸⣷⣴⣶⣶⣿⣶⣶⣦⣤⣴⣤⣼⡆⠀⠀⠙⠈⠛⠛⠻⠇⢴⣿⣷⣷⣾⣿⣿⣿⣿⣷⣿⣷⣾⣿⣇⣀⢠⠀ ⠀⠘⢻⣿⣟⠁⠀⠀⣏⣭⡟⠻⣿⣿⡿⡄⠀⠀⠀⠀⠀⠀⠀⠰⣟⡉⠀⠀⠀⣤⣽⡏⢉⣿⣿⡇⡸⢻⠉⠁⣿⠀ ⠀⠀⠀⡇⠈⠑⠂⠀⠛⠛⠛⠛⠛⠛⠓⠁⠀⢀⣀⠄⠀⣤⣤⡄⡨⠹⠓⠒⡚⠛⠛⠛⠛⠛⠉⠁⠀⣼⠀⢰⣿⠀ ⢣⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠃⡼⠱⠉⡉⠀⠁⠀⢀⠀⠁⠀⠀⠀⠀⠀⠙⠀⢰⠇⢠⡟⢹⠀ ⠈⢧⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣠⢿⠃⡾⠀ ⠀⢸⣧⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡾⠁⢸⠀⡇⠀ ⠀⠘⣟⢳⣄⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠀⠀⣿⣼⠃⠀ ⢸⡀⢿⠈⡟⢳⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀ ⠀⢧⠸⣇⣿⠈⣷⡈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠇⠀⠀ ⠀⠸⡄⢻⡜⣧⣿⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣖⣂⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣿⡟⠀⠀⠀ ⠀⢠⠹⡄⢻⣿⣿⠀⠈⠓⣦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⣰⡿⠀⠀⡠⠀ ⠀⠸⡄⠙⣆⠻⣿⡄⠀⠀⢸⡟⡷⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⣠⡿⠁⠀⣰⡇⠀ ⠀⠀⢷⡀⠈⠳⣝⢿⣄⠀⠀⠻⣷⠈⠉⢳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉⠀⠀⠀⠀⢠⡿⠁⠀⣴⣿⠁⠀ ⠀⠀⠘⣿⣄⠀⠈⢻⣝⠷⣄⠀⠘⠲⢤⣾⣿⣏⠈⠑⢦⠤⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⣠⣾⣿⠃⠀⣠ ⡀⠀⠀⠹⣟⢶⣄⠀⠻⣏⠈⢷⣤⠀⢰⣿⣿⣿⣄⠀⠈⡇⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡟⣁⣴⣾⣿⡿⠃⢀⣴⠏ ⠘⣄⠀⠀⠘⢦⢙⣷⣦⣌⡳⢦⣤⣤⣾⣿⣿⣿⣿⣿⡆⢹⡀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣟⣩⣴⣶⣿⠋⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢻⣿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡶⣀⣀⣀⠘⣿⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢸⡇⠀⠀⠀⠀⠀⣤⡀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣁⠀⠀⡡⢿⡿⠿⠇⠑⠢⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣾⡇⠀⠀⠀⠀⠀⣿⡆⠀⠀⢱⠀⢸⡀⠀⠀⠀⠀⠀⡄⠘⡇⢀⡀⠀⠈⢻⡷⠤⠤⠔⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡀⠀⣿⡇⡄⠀⠀⠀⠀⣿⣷⡀⠀⢸⣇⠀⡇⠀⠀⠀⠀⠀⡇⢀⣷⣶⣦⠀⣀⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢠⠇⡇⢠⡇⣇⠅⠀⠀⠀⢸⣹⠛⢳⠀⢸⠘⡇⣿⠆⠀⠀⠀⢠⡇⢨⣾⣿⠏⠘⠁⠀⢀⢀⠁⡀⠀⠀ ⠀⠀⠀⠀⠀⡜⣟⠀⠀⢰⠀⡗⢺⣦⣑⠸⡇⠘⡼⠀⠀⠀⠈⣿⡀⠈⠃⢸⣠⠟⠛⣧⠀⠀⣀⡾⡇⢸⣿⡃⠠⡀⢶⣄⠄⡛⡄⠈⠀⠀ ⣄⠀⠀⠀⠀⢻⣹⡄⠀⠘⡄⢱⢸⡄⠹⡙⠛⠶⣵⣧⠀⠀⠀⢸⣁⣠⣤⣞⣀⣀⣠⣿⢤⠴⣛⡸⠀⣼⣿⣿⠖⠀⠀⠈⡦⠒⢄⠀⠀⠀ ⢹⣆⠀⣠⣤⣞⠁⢳⠀⡀⣣⠘⣸⡟⣦⠹⠦⠤⠍⠛⢧⡀⠀⠘⣿⠛⠹⡉⠉⣩⢃⣴⠃⠀⢠⢿⣸⢹⣿⠏⠀⢀⣄⡞⠀⠀⠈⠀⠀⠀ ⠘⣿⡄⠘⡏⠛⣧⠀⣧⣘⡍⢇⣿⣿⡄⣀⠀⠀⠀⠀⠲⡞⢦⣄⣹⡛⠷⠚⠋⠈⠉⠉⠋⠠⣧⣿⣿⣼⠉⠀⠄⣗⣾⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣧⠰⣄⢹⣶⣿⡿⠀⠀⢹⣿⣿⡟⠃⠀⠉⠉⠀⠇⠀⠈⠉⠃⠀⠀⠀⠀⠀⢠⠀⢀⡞⣧⠏⣧⢀⢨⠆⢹⣏⣀⣀⣀⣀⠀⠀⠀ ⠀⠀⠘⣿⣧⢻⣿⣿⣿⡅⠀⠀⠈⠹⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣇⣤⡞⠀⣸⠀⡟⣌⣻⣆⢻⡇⠉⠉⠉⠉⠀⠀⠀ ⠀⡀⠀⠘⣿⣷⣻⣿⣿⡇⠀⠀⠀⠀⢹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀⠙⠀⣿⠀⡇⣯⣿⣿⣎⡇⠀⠀⠀⠀⠀⠰⢳ ⡀⠀⠀⠀⠘⢿⣷⡻⡾⢧⠀⠀⢆⠀⠀⢿⣾⣷⣄⠈⠙⠛⠛⠓⠦⠀⠀⣀⠴⢛⣽⣿⠀⠀⠼⡏⢀⣿⣾⡿⣟⣿⢿⠀⠀⠀⠀⠀⠀⠀ ⠱⠦⠀⠀⠀⠀⢻⣷⡹⣿⠄⠀⠀⠀⠀⠈⠻⣿⣿⣷⣄⠀⠀⢀⣠⠴⢊⣡⠴⠛⠉⣸⢰⠀⣼⠃⣸⡿⢋⡾⠋⢙⠂⠣⣄⠴⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⣤⣭⣭⣷⣾⣭⣵⣶⣷⣶⣾⣿⣸⠀⣿⣡⣿⡵⡹⠓⣠⡏⠀⠀⠀⠀⠀⠂⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠑⠲⣄⠤⠶⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠋⠁⠀⠀⠀⠀⠀⣀⣀⣀⣼⡷⠚⠒⠲⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⣠⣤⢿⣿⣿⣟⠛⠃⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠂⠀⠀⠀⢀⣴⣿⣿⡟⣿⣿⡿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⢾⣏⠀⠀⠀⠀⠀⣾⣿⣿⡟⠀⢀⣀⣀⣬⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀ ⠀⢷⠲⠜⡄⠀⠀⣦⡞⠁⠀⠀⠀⢠⣾⣟⣷⣿⡇⠀⠛⣿⣯⣿⡿⣿⣦⢀⠀⠀⠀⠀⠀⠸⢿⡶⠀⠀⢐⡾⠇ ⠀⠀⠉⠲⢧⠀⠀⢻⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠀⣿⣿⣍⣳⣿⣿⣿⣇⢀⡄⠀⠀⠀⢈⣿⠀⠐⠉⠀⠀ ⠀⠀⠀⠀⠀⢀⠀⣬⣿⣶⣧⠀⠀⢹⣿⣿⢿⡿⠋⠀⠀⠉⠉⠉⠀⠙⠻⣿⣿⣿⣿⣤⣴⣄⣼⣧⡀⠀⣼⠇⠀ ⠀⠀⠀⠀⠀⠘⣾⣿⠦⣼⣿⣶⣢⣿⣿⡅⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠔⣻⣿⡯⠉⠛⢿⣿⣿⣿⣿⣄⠘⢿⣦⣶⠞⠁⠀⢀⣰⣿⣿⡏⢿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀ ⢀⣦⣴⣿⡥⢾⣿⣿⠁⣴⣦⣬⣏⡉⠛⣿⣿⢷⣤⣀⠀⣀⣠⣴⠋⠁⢙⣿⣇⠀⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀ ⠒⣤⡀⢈⠀⠙⠒⢢⠄⠹⣿⣾⣿⡟⣦⡈⠙⣛⡿⣿⢻⣿⣿⠁⢀⡤⢺⣿⢟⣚⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣟⢻⡒⠤⢄⣉⣴⠐⠀⠉⠙⢿⡿⣯⣼⡿⣧⣤⣿⣿⢾⣯⣀⣼⡧⢞⣿⡿⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠻⢧⣙⠲⠤⣀⠉⠉⠒⠒⠀⠀⠈⢫⣹⣿⣿⣿⣿⣥⠀⢉⡿⠿⠞⠋⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⢿⠻⣧⡏⡏⢀⡴⠋⠀⣠⠊⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣮⡟⢧⡉⠙⡒⡿⢶⡤⠀⠘⣄⠛⢋⣠⢋⡴⡁⡰⠑⠀⠀⢀⣀⠠⠤⠤⠤⠘⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡹⣿⣿⡾⠻⣄⠀⠙⠺⣷⡄⠀⠘⣆⠈⡵⢋⣾⡰⠁⣰⠖⠛⠥⡄⠀⠀⠀⣀⣀⣳⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⢻⠀⠀⢸⡊⠢⡀⢻⣿⡀⠀⠈⢿⠁⢸⣿⡗⠒⠋⣰⣁⣴⣃⡀⠀⣼⠁⠈⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢠⡿⢷⣤⣹⣄⢻⣷⠀⠀⡸⠛⣾⣧⣬⣴⠚⠋⠉⠁⠈⠉⠙⠺⢷⣄⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠈⡇⠀⠀⠘⣏⢿⠹⣆⣻⣧⡴⠁⠀⠘⣇⡈⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻⡄⠀⠀⢻⠘⡇⢻⣯⡅⢸⡀⠀⣰⡿⣯⡳⢤⡙⠂⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⢳⣄⣼⠀⡇⠈⡇⢿⣦⠭⠛⠁⠀⠈⢻⣦⡙⢦⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠉⣿⠀⣧⠀⠇⢸⠛⡆⠂⠀⠀⠀⠈⣿⣷⡌⢣⡀⠀⠀⣠⠟⢹⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⣿⠀⣿⠀⠀⢸⠀⢳⡀⠀⠀⠀⠀⣸⣿⡟⣆⠳⠀⠀⢳⡀⠈⠀⠀⠀⠀⠀

⠛⠉⠉⠀⠈⠁⠀⠀⠀⠀⠀⠉⠛⠉⢻⣿⣿⡛⢻⣅⡄⢰⣷⣾⡟⢋⣾⠃⣾⣿⠇⣾⣿⠟⣁⡞⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠀⣠ ⠀⣤⣤⡀⠀⠀⣶⣶⣶⣿⣿⣶⠀⠀⠀⠀⠀⠈⠁⠸⠀⢨⣿⡃⡰⣿⣿⣶⡿⠃⢸⠏⢀⣜⣼⡇⣤⢾⡅⠀⠀⠀⢠⣾⣿⣿⠿⠅⠀⠁ ⠀⠈⠟⣷⢄⡀⠸⣿⣿⣿⣿⣿⠀⣴⣶⣶⣦⣶⣾⢰⣰⢸⣿⡇⡧⢇⣿⣯⠇⣄⣧⢸⣾⠿⠋⣱⣳⣿⡃⠀⠀⡴⢿⣿⣿⠃⠀⠀⠀⣠ ⣦⠀⠀⠨⣼⡷⠴⠚⢛⣿⣻⢟⠀⢹⣌⣉⡽⠿⢿⣿⣿⣆⡟⢣⡇⢸⣿⠇⣸⣹⣿⣾⡵⢪⡾⠙⠛⣿⡇⠀⠀⠀⡼⢻⡏⠀⠀⠀⣾⣿ ⣿⣆⠀⠀⠘⢇⣥⣄⣸⣿⠃⠈⢰⣟⠓⠒⠚⠭⣿⣿⡿⣿⡀⠀⢻⣸⣿⣶⣿⠏⢻⣿⡾⢋⡴⢃⣴⣯⣷⠄⠀⣼⣿⡟⠀⠀⠀⣼⣿⣿ ⣿⣿⣇⡀⠀⠀⠙⢿⠏⢹⡄⠀⣿⣾⣶⣦⣵⠖⠺⢇⢻⣿⢻⡆⢦⢿⣦⡘⣿⢳⣼⣿⣿⣿⣶⣿⣻⣿⡇⠀⡼⢽⡞⠀⠀⢀⣼⣿⣿⣿ ⣿⣿⣿⣧⠀⠀⠀⡞⠛⡟⢃⣸⢫⠋⢘⡿⣿⢷⡀⠸⡜⣿⡎⢿⣮⡀⣋⣵⣷⣾⣟⣿⣿⣿⡟⣻⡿⠿⢁⡜⠀⣼⡀⠀⠀⣿⣿⣿⣿⣿ ⣿⡿⣿⡿⠀⠀⡈⢀⣠⣷⡟⢻⣇⣰⣋⣠⠾⣷⣿⣶⣇⢹⣷⡄⢉⠉⠉⢉⣿⣿⣿⠿⣿⣿⣉⣿⢧⣾⡿⠀⢠⣾⡇⠀⣸⣿⣿⣿⣿⣿ ⡋⠀⠸⡇⢀⣴⡿⠍⢛⣵⣃⠜⠛⠁⠀⣩⣿⣿⣿⣿⣿⣦⣿⣾⣮⣉⣡⣾⣿⣿⣄⣼⣿⣿⣿⠯⣽⣿⣭⡤⠟⠛⠁⢀⣉⣉⣾⣿⣿⣿ ⣧⠀⠀⣰⡟⢁⣔⠋⠛⢻⡿⠷⠖⡒⠪⢄⣸⣿⣿⣿⣿⣿⣿⠀⠀⠨⠵⢜⠉⠉⣿⣿⣿⣿⣿⡈⠉⠁⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿ ⣿⢳⣾⠋⣷⣿⣷⡿⣓⡁⠂⠀⠀⠳⡄⠈⢹⣿⣿⣿⣿⣿⣿⡀⣀⠀⠀⣦⣀⣾⣿⣿⣿⣿⣿⣿⣿⣾⢿⣷⣴⣿⣿⣿⣿⣿⣟⣿⣿⣿ ⣿⣿⣿⣦⣿⣿⣷⡶⣦⠴⣆⣀⣸⣿⣿⡟⢻⠙⣿⣿⣿⣿⢯⣳⠤⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡗⠦⠭⣀⠈⠉⢙⣿⣏⢋⣼⡟⢿⣿⣿⣫⣿⣦⣾⣿⣾⣿⣿⣇⡈⠻⢿⣿⣿⣿⡿⠧⢄⢸⣿⠃⣸⣿⣿⣿⣿⡿⠛ ⣿⣿⡟⢿⣿⣿⣿⣿⡿⣿⣿⠶⠿⠞⣻⣿⣿⣿⡇⠸⡿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⢿⣿⣭⣿⣿⣿⣿⣶⣼⣿⣿⢿⣿⣿⣿⣿⣿⣦⣾ ⣿⣿⣿⣄⠈⣿⣿⣿⣿⣶⣿⣿⢿⣞⣹⠟⣿⣿⠁⠀⡇⠟⢿⢻⡿⣿⣛⡸⠋⢭⡄⢿⣿⡍⠉⣽⡿⣿⣿⣽⣿⣥⣿⣿⡿⣿⣿⠟⠻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠒⠒⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠔⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠔⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⢹⠉⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡏⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠴⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⣰⢧⣞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠋⠀⠀⠁⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⢀⣠⠿⢤⣀⣤⣴⣞⡁⢠⢹⡍⠑⠒⢤⡀⠀⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⠞⠒⠲⠦⠤⠔⠒⠋⠀⠀⠀⠀⢰⠿⡝⣟⣯⠚⣷⠤⠤⣄⠈⢦⡀⠀ ⠀⠀⠀⠳⡀⠀⠀⡤⠤⠴⠚⠁⢀⣴⡶⣶⠲⣤⠀⠀⠀⠀⠀⠀⣿⣧⣾⢸⢸⠀⢹⡄⠤⠴⢳⡴⠇⠀ ⠀⠀⠀⠀⣸⠴⠚⠋⠀⠘⠢⣠⣾⣿⣧⣄⣧⠹⣳⡀⠀⠀⠀⠀⢻⣿⠟⣸⡏⠀⢸⠓⠒⠛⠉⠀⠀⠀ ⠀⠀⢠⠞⠁⠀⠀⢀⡄⠀⠒⠒⢻⣿⣿⣿⣿⠀⡏⣷⠀⠀⠀⠀⠐⠣⠞⠋⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠋⠀⠀⣤⠞⢡⠃⡆⠀⠀⠘⠻⣿⠿⠋⣠⢃⡼⠀⠀⢀⡠⠔⡖⢲⠃⢀⡜⠁⢀⣀⣠⡴⠚⣻⡆ ⢰⡏⠀⢀⡞⠁⡰⢛⡜⠈⠢⣀⠀⠀⠈⠉⠉⠉⠁⠠⣴⢦⣀⣉⡮⠤⡊⣠⠞⠉⠛⠁⠀⠀⢸⠊⢀⡇ ⠈⡇⠀⢸⢒⣉⠴⠋⠙⢏⠀⠈⠙⠦⢄⣀⠀⠀⠀⢀⡈⠲⡒⣺⢠⡶⠛⠑⠲⢤⡀⠀⠀⠀⠘⣤⠎⠀ ⠀⠈⠉⠉⠁⠀⠀⠀⠀⣠⠛⠒⠒⠀⠀⠀⠉⠉⠉⠙⠙⠦⠬⠯⠎⠀⠀⠀⠀⠀⠙⣄⠀⢀⡴⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠒⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣀⣸⠁⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠋⠀⢰⠓⢲⠖⠢⣄⣠⠞⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣸⡆⠀⠘⠲⢾⡤⠤⠚⠁⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢯⠉⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢀⣀⣀⣤⡞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⠲⢶⠀⢀⡸⢦⡀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢀⣀⡴⠊⠁⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡴⠋⠂⠀⠀⠀⢀⡴⠋⣏⠉⠉⠀⠀⠤⢖⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠈⠁⠙⢦⡘⢦⡀⠀⠀⠀⠀⣙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⡀⢀⡠⠔⢶⣓⡄⠙⠦⣴⣊⣉⣹⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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