Nsfw Dot Art

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠶⠶⠶⠤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⢣⡶⠀⠀⠀⠀⠀⣠⠖⠉⣀⡴⠶⠊⢷⡆⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⠃⡼⠁⠀⠀⠀⣠⠞⣡⡴⠋⠁⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⣇⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⡏⢠⡇⠀⠀⠀⣼⣣⠞⠃⠀⠀⠀⣀⣠⣤⣄⣿⡇⢧⡀⠀⠀⢻⣄⡀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⢸⡇⠀⢠⣼⣿⣏⡀⠀⠀⢠⢾⠛⠉⠁⢀⣿⡉⠛⣷⣄⠀⢸⣿⠻⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⡇⠀⣇⡴⢿⣿⡉⠉⠉⠁⠀⠀⠀⣀⣶⠾⢿⡛⠟⢶⣼⡇⠀⢸⢻⡀⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣧⠀⢸⡆⣿⣛⠩⣿⣷⠀⠀⠀⠀⠙⠉⣷⢾⣿⡇⠾⠀⢻⠀⢸⠇⣽⠛⢹⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡄⠀⠻⣏⠛⠳⡿⢿⡞⠀⠀⠀⠀⠀⠾⠿⠿⠇⠆⠀⠀⣆⣼⣱⡇⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⠀⠀⠙⡄⠀⠙⠉⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠁⢿⡀⠀⢸⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢧⠀⠀⢻⡄⠀⠀⠈⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢰⠘⡇⠀⠈⢿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢷⡀⠘⡟⠦⣀⠀⠀⠒⠒⠋⠉⠁⠀⠀⢀⣠⠆⠀⣹⠀⣈⡇⢹⡄⠀⠸⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠱⣄⣷⠀⢹⡳⣄⡀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⣿⠀⣟⢿⠈⡇⠀⠀⣹⣻⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠻⣧⣿⠇⢰⡍⠳⠤⣴⠛⠁⠀⠀⠀⠀⢰⣿⠀⡿⢸⠀⢸⡀⢀⣿⡇⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠇⢀⡼⠋⢀⣮⡇⣀⠴⡟⠀⠀⠀⠀⠀⠀⣿⠃⠻⣅⣼⠀⢸⡇⢸⣹⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠏⢀⡞⢀⣀⡸⠟⠋⠁⠘⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠳⢄⣸⣧⣧⣟⡼⠉⠀⠀⠀ ⠀⠀⠀⠀⢀⡤⠿⠤⠚⢲⣟⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⡀⠀⢀⣀⠙⠛⠿⢾⣄⠀⠀⠀⠀ ⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠓⠀⠴⠒⠒⠚⠒⠛⠛⣿⡉⠉⠉⠀⠀⠀⠀⠀⠀⠙⢢⡀⠀ ⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄ ⠀⢸⢹⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⢸⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⣼⠛ ⠀⠀⠸⣇⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⢀⡏⠀ ⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⣼⠀⠀ ⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣰⠃⠀⠀ ⣼⢃⣴⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢳⠀⠀⠀⢠⠏⠀⠀⠀ ⣿⠈⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⠀⠀⢸⠀⠀⠀⣾⠀⠀⠀⠀ ⢹⡆⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠉⠈⠀⠀⡼⠀⠀⢰⡇⠀⠀⠀⠀ ⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣸⠃⠀⠀⣼⠀⠀⠀⠀⠀ ⠀⠀⠈⠳⢤⣀⣀⣀⣀⣀⡴⠖⠋⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠁⠀⠀⢰⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⢻⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠒⠋⠉⣿⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢽⣼⠀⠀⠄⠀⠀⠀⠀⠀⠀⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⡿⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⢹⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡼⣇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣧⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣹⠃⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠈⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠦⣄⣠⠤⡦⢤⣞⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣦⠞⣻⠀⢱⣄⡈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠ ⠀⠀⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⣿⣧⣀⣿⠿⡎⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⡀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣏⢈⠻⠛⠙⢄⢹⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠂⠁⠀⠀⠀⠀ ⠙⢄⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣻⠷⣶⠶⠊⣇⣼⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠑⢤⣀⠀⠀⣠⠞⢆⠀⠈⠲⢄⠀⠀⠀⢀⡴⠿⠟⠛⠿⢷⠀⠾⠛⠛⠛⢲⠽⡄⠀⠀⠀⠀⢀⠴⠋⠀⢰⣆⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠑⢆⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠆⢀⡠⠊⠁⠀⠀⠀⠀⠙⠓⢦⡴⠒⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢀⠴⠀⠢⣀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣱⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠒⠋⠁⠀⠀⠀⠀⠉⠙⣲⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠤⠤⠄⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠬⡅⠀⡇⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢰⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣬⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⠤⢤⡴⠎⠀⠀⠀⠀⠱⣦⣀⣀⡀⠤⠔⠚⢿⣼⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⡴⠚⠉⠙⠲⣄⠀⠀⠀⡴⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡞⠀⠀⠗⠐⠆⠈⡆⠀⠀⠙⣦⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢳⠰⣶⣤⣤⣶⢠⠇⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠓⠮⢭⡭⠵⠋⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⡿⣿⣿⣿⣿⡝⠓⠒⠦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢧⠈⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⡄⠀⠈⠻⣿⣧⠀⠀⠀⠀⠀⢠⠟⠳⣄⠀⠀⠀⢀⢄⡠⠢⠦⢄⠀⠀ ⠀⠀⠀⠀⠙⠦⣄⡀⠙⢿⡄⠀⠀⠀⢠⠏⠀⠀⠈⢦⠀⡸⠁⠀⢀⡤⡀⠀⠱⡀ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⢾⠓⠛⢯⣹⣿⣶⣶⣶⣤⣬⣾⠀⠀⡎⠉⠀⠀⠑⢄⡱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠤⢾⢯⡉⠛⠿⣿⣿⣿⡏⠀⡜⠁⠭⣦⡀⣀⣀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢸⠀⠀⠳⡈⠢⣄⠀⠈⠛⡇⠀⠙⣄⣶⡄⠀⠉⣡⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢸⠀⠀⠀⠱⡄⠈⢳⠀⢘⡄⠀⣺⠀⢉⠖⣲⡞⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣼⠀⠀⠀⠀⡇⠀⢸⠀⢸⢦⡤⡯⠀⢼⢢⢿⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⡏⠀⠀⠀⢸⠁⠀⢸⠀⢺⡿⠣⠃⠀⠊⠋⠚⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠀⠀⠀⣸⢁⣀⠀⠀⡏⠀⠀⠸⡇⠀⠙⢦⡀⠀⠀⣀⣀⠀⠀⠀ ⠀⠀⠀⠘⢯⡉⠓⡄⠰⣟⣉⣉⡷⢸⣁⣀⡀⠀⢷⣟⣉⣳⠉⠲⣎⠉⠈⡇⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠈⠉⠀⠈⠳⢤⣹⠀⠀⠈⠉⠁⠀⠀⠈⠉⠉⠀⠀⠀

⢴⣤⣶⣾⣟⣇⠀⠐⠒⠂⠿⠛⢻⠳⡖⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠳⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠉⠛⠓⠲⠦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠴⠂⠀⠀⠀⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠒⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠁⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⣀⠀⠀⠀⠈⠓⢦⠀⠘⢻⠀⠀⢠⡇⠀⠆⠀⠤⣤⡀⠤⢤⠤⠖⠚⠉⠀⠀⠈⢳⡀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⣤⡤⣶⣷⣄⣸⣦⠀⢸⠀⣀⡤⣾⣿⣶⣾⣧⠄⠀⠀⢀⣀⡤⢾⡁⠀⠉⣻⠗⠋⠁⠀⠀⠀⠀⠀⠀ ⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣸⣏⠁⠈⠛⢻⣯⣿⣾⠟⢁⠀⣿⣿⡏⠟⠛⠋⠉⠁⠀⠀⢈⣻⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣄⣙⣻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⠹⣟⣚⣻⢦⣄⠀⠀⠉⠛⠂⠀⠑⠙⠋⠀⠀⠀⠀⠐⠦⠖⣻⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠻⠿⠿⠿⠿⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠁⠀⠀⠀⠀⣿⠿⠷⠶⢿⣰⠂⢀⡶⣄⠐⠂⠀⢻⣆⢀⣴⣒⣶⣶⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⢶⣶⣤⣤⣴⣶⣶⠙⠉⠻⠿⢶⣶⡶⠖⠒⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠉⢡⡟⠀⣽⠖⠒⠀⠉⠉⠛⢦⡴⠛⠁⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣦⣬⣭⣽⡛⠛⠻⣿⣯⣧⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠀⠀⠀⠀⠀⠀⡞⢀⡞⠁⠀⠀⠀⢀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠙⠳⢤⣄⡀⠀⠀⠀⠀⢀⣠⣤⣾ ⠛⠿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⣀⣤⢤⣖⣒⣲⣷⣿⣒⠲⢤⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢩⡽⠛⣿⣿⣿⣿⣿⠙ ⡀⠀⠉⢿⣭⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⠀⠀⠀ ⣿⣶⣦⣤⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣀⣀⠀⣀⣀⣀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉ ⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠚⠁⠀⣠⠞⠋⠁⠀⠈⢹⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⠀⠀ ⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⡼⠁⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣀⠀⠀ ⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣸⠁⠀⠀⠀⠀⣰⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠃ ⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣯⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡻⣷⣦ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣾⡇⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠜⢷⡙⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⣿⣯⣀⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠈⢷⠈ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠲⢾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀ ⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀ ⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀ ⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀ ⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀ ⣿⣿⣿⠟⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀ ⠛⠉⠀⠀⣀⣤⡿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠀⠀⠀⠀⠀⠀ ⠀⣀⡴⠞⠉⠀⠀⠈⣙⡷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠈⠁⠀⠀⠀⠀⠀⠀⠀⠸⡄⣹⣿⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⢈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣺⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠟⠛⠋⠁⠀⠀⠀⠈⣉⣽⠿⠛⠉⣩⣿⢿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⠀⠤⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋⠀⣠⡴⠟⠋⠀⠀⠈⣋⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢛⡉⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⣠⡶⠞⠋⣀⣠⠶⠟⠋⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠉⢠⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⢃⢸⠀⠀⠀ ⠀⠀⠀⣀⣤⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣼⣿⠿⠧ ⠀⢠⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⠏⠀⢀ ⠹⣿⣿⣿⡏⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢆⠀⠀⣸⠃⢀⡔⠁ ⠀⠘⢿⣿⣧⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠏⠀⢀⣿⡶⡡⢀⠀ ⢠⠐⡀⢻⣿⣦⡀⠀⠀⠀⣀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⢀⢼⣿⠡⠁⡎⠀ ⡀⠇⢱⡀⣿⣿⣿⣦⣤⣀⡤⠞⠀⠀⠀⠀⠙⢦⣀⣀⠀⣀⡤⠋⣾⣿⣅⢼⠁⠨ ⡇⠘⢠⢇⢹⣿⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠁⠀⢸⣿⣿⣷⡘⠀⠀ ⢃⢀⠌⠀⠼⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⠛⠚⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠉⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⡉⠛⠿⡷⣦⣤⣴⣶⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠈⢱⠀⢠⡀⢠⣬⡟⢙⣻⢁⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠣⢽⡇⢠⡿⣌⠻⣿⣃⣸⠟⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣼⠃⢸⢻⠈⢳⠃⢙⣹⣴⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣇⢸⡀⠀⡄⠀⠈⠓⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠛⡫⠛⠓⠶⣶⡒⣚⣛⣿⡀⢀⠀⠀⠀ ⠀⠀⠀⠀⢀⡖⠑⣄⠀⡇⠀⣸⠀⠀⠀⣄⠀⡇⠀⠀⠀⠻⣽⠃⠀⠀ ⠀⠀⠀⠀⠀⠳⠚⠁⡆⠑⠦⣹⡄⠀⢠⡏⠣⢹⣄⠀⠀⠀⡟⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠧⠔⠧⠄⣀⠀⡇⠐⠛⠛⠓⠾⠿⣷⠔⢈⠀⠀⠀⠀ ⠀⠀⠀⣰⣡⣇⣀⣀⣀⣰⡁⠉⣳⣄⣀⣀⣀⣀⣀⡍⣇⣠⠇⠀⠀⠀ ⠀⠀⢀⠹⠋⠉⠀⠀⠀⠀⡩⠛⠉⠁⠀⠀⠀⠉⠙⠛⠿⢀⠀⠀⠀⠀ ⠀⠔⠁⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀ ⡌⠀⠀⠀⠀⠀⠀⣰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀ ⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆ ⢡⠀⠀⠀⠀⠀⠀⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⠶⡇ ⠸⡓⠤⣀⠀⠀⢀⣀⣹⡂⠄⠀⠀⠀⠀⠀⢀⣀⠤⠊⠀⠀⠀⠀⠙⡇ ⠀⢣⣠⣤⠼⠟⠛⠛⠉⢹⠛⠓⠒⠒⠚⠛⠷⠤⠤⣤⣀⡀⠀⠀⠰⠁ ⠀⢀⠁⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢳⠁⠀ ⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀ ⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⡨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀ ⠀⠀⠈⠢⢀⣀⣀⣀⡀⠔⠁⠈⠢⠀⣀⠀⢀⣀⠀⠤⠊⠀⠀⠀⠀⠀

⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣟⠉⡿⢿⣿⣿⣀⡿⢿⣛⠻⣟⠛⠛⠛⠛⣿⣚⢿⣶⣴⣂⣠⣤⣠⣥⣴⣥⡆⢀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⠞⢩⣧⡨⠿⠿⢿⡝⠯⠛⠶⣤⢾⠀⠀⠀⠀⠉⠀⠛⢉⠉⠟⣉⣉⢉⣙⡏⣉⣁⣘⣈⠀⠀ ⣶⣤⣤⣤⣤⣤⣤⣄⣤⡴⠶⣶⣶⠟⠍⠁⢒⠿⡠⠖⠉⠉⢙⣷⠀⠀⠀⠈⠩⣳⣖⢶⠒⠒⠒⠒⢶⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⡖⣲⣿⣿⣞⣁⣀⠴⢚⣿⠛⣷⡈⣆⠀⠱⡌⠉⢧⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⠛⠛⠟⠛⠛⠛⠋⠉⢻⡿⢛⣶⣿⣿⣿⠋⣹⣟⣁⣴⣾⠃⢀⡏⠇⠸⡀⠀⢱⠀⢈⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡘⣾⣿⣿⡇⣸⡯⠽⠟⢋⣉⠑⡞⠀⡼⢠⢧⠀⠀⡇⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⢰⢁⡟⠀⠉⣰⠙⡿⣷⣶⢦⡄⢰⠁⢰⠃⣸⡌⠀⢸⠃⢀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣤⣤⣤⣶⣷⢸⢸⢧⡰⢼⣿⡀⠉⠀⠈⠀⠀⠀⢧⢇⣸⣳⠁⡰⢃⠀⣸⣿⣤⣶⣦⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡏⠀⣠⠆⠘⢿⣿⡸⣼⡝⢦⠣⠁⠀⠀⠀⠀⠀⠀⠘⠙⠻⢥⠞⢁⠜⣰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣿⣿⠏⡼⡰⠁⠀⠀⠈⢿⢿⣼⣇⠘⣧⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣼⣧⣾⡷⠛⢿⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡿⠀⠈⠰⠁⠀⠀⠀⠀⠸⠺⣿⣿⣇⣿⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⡀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠇⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠿⢿⣿⡇⠀⠀⠈⠓⠤⣤⡤⠖⠊⠉⠀⠀⠀⠀⠀⠙⡄⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠙⠓⠤⠄⣀⡀⠀⢸⣷⣦⡤⠤⠖⠒⠒⠢⢤⡀⡇⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢀⢆⡀⠀⠂⠒⠒⠒⠻⠦⣄⡀⠀⢀⠢⠤⠤⢄⡹⣯⣀⠻⢸⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⡸⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠈⠉⠳⣤⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⢬⣳⣤⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣴⡿⡄⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣗⣷⠀⠀⠀⠀⠈⡦⣀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠖⠋⠈⠳⣄⠀⠀⠀⠀⠀⠀⢠⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⣽⣿⡄⠀⠀⠀⠀⢸⠈⠉⠒⠒⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠈⠳⣆⡀⠀⢀⡴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀ ⠀⠀⠀⠀⠀⢸⣷⣿⣿⣧⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠛⠉⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠉ ⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⡄⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣧⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⠀ ⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣷⠀⠀⠀⠀⡹⣿⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠛⢧⡀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀ ⠀⠀⠀⠀⠀⢸⣿⣟⣿⣿⣿⠄⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣟⣿⡛⠭⠄⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⢸⡇⢿⣁⣵⣾⡆⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⢸⣿⣦⣽⣯⣿⣿⣄⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡱⡄⠀⠀⠀⠀⠀⠀⠂⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠀⠁⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠙⡄⠀⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠹⡄⡇⠀⠀⠀⢠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⢸⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠋ ⢠⠀⢄⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢧⠀⠳⠀⠀⠀⣿⣿⠂⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠀⠀⠀⣟⣿⣿⡆⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⣀⢀⣠⣤⠴⠶⠚⠛⠉⣹⡇⠀⢸⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠈⢦⢰⠀⠀⠀⠀⠀⠈⢳⡀⠈⢧⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠀⡏⠀⢰⠃⠀⠀⠀⣿⡇⠀⢸⡀⠀⠀⠀⠀⢸⣸⡆⠀⠀⠀⠰⣌⣧⡆⠀⢷⡀⠀⠀⣄⢳⠀⠀⢣⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠘⠀⠀⠀⢀⣿⣇⠀⠸⡇⣆⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⢹⣾⡇⠀⢸⢣⠀⠀⠘⣿⣇⠀⠈⢧⠀⠀⠘⠀⢠⠀⠀ ⠀⠀⠀⠀⠀⢀⡇⠀⡀⠀⠀⠀⢸⠈⢻⡄⠀⢷⣿⠀⠀⠀⠀⢹⡏⣇⠀⣀⣀⠀⣿⣧⠀⢸⠾⣇⣠⣄⣸⣿⡄⠀⠘⡆⠀⠀⠀⠀⠆⠀ ⠀⠀⠀⠀⠀⣾⢿⠀⠇⠀⠀⠀⢸⠀⠀⢳⡀⢸⣿⡆⠀⠀⠀⣬⣿⡿⠟⠋⠉⠙⠻⣽⣀⡏⠀⠙⠃⢹⡙⡿⣷⠀⠀⢹⠀⠀⠀⠀⠰⠒ ⠀⠀⠀⠀⢸⣿⣿⣇⢸⠀⠀⠀⢸⣦⣤⡀⣷⣸⡟⢧⣀⡴⠶⠿⠻⡄⣀⣤⣴⡾⠖⠚⠿⡀⠀⠀⠀⠈⣧⠁⠹⠆⠀⠀⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⢸⣀⣼⣿⣼⡆⠀⢀⡘⡇⠀⠀⠹⡟⢷⡜⢉⣠⣠⣠⣀⣤⡿⣛⣥⣶⣾⡿⠛⠿⠿⣶⣦⡤⢹⠀⢀⠀⠀⠀⢹⡄⠀⠀⠀⠀ ⠀⠀⠀⢸⢸⡛⠁⠀⠙⢿⠋⠉⠉⠻⠀⠀⠀⢿⣄⠈⠁⠀⠀⠀⢉⢟⣴⡿⠿⠟⢁⠇⠀⠀⠀⠀⠹⣿⠻⡇⢸⠀⠀⠀⠈⣷⠀⠀⠀⠀ ⠀⣀⣀⣘⣿⡇⠀⢀⣠⣤⣶⣶⣶⣾⣦⡀⠀⠈⡿⠀⠀⠀⠀⠀⠀⣿⠟⠳⠦⡤⠊⠀⠀⠀⠀⠀⣸⠇⠀⡇⣼⠀⢰⠀⠀⢹⣇⠀⠀⠀ ⠛⠁⠈⣿⣷⣧⣴⣿⠿⠛⣿⠿⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⣴⣶⠿⠿⠿⡷⢛⠕⠷⡄⣧⣿⠀⢸⠀⠀⠸⣿⡄⠀⠀ ⠀⠀⢠⣿⢿⣿⣿⠁⠀⠀⠈⠳⠤⠶⠃⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⣱⠒⡠⢆⡴⣣⣯⢞⣴⡟⢿⡄⡏⠀⠀⠀⡏⢷⡀⠀ ⠀⠀⡌⣿⠀⠙⣿⡦⢀⣤⡴⣶⠖⣲⠆⢀⠞⠁⠱⠀⠀⠀⠀⠀⠠⣾⠟⠛⡡⠞⠁⢀⡴⢋⢎⣽⡿⣫⠋⠀⠘⢷⠃⡄⠀⠀⡇⠈⣿⡀ ⠀⠀⣇⢹⣦⠀⠼⢃⡾⢋⣶⢃⡼⣹⡳⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠠⠋⠀⡰⠋⠀⢘⣇⡇⠀⢠⠟⠀⡇⠀⠀⠀⠀⢹⡵ ⠀⠀⢻⣌⢿⡆⠀⡝⣼⠟⣩⢏⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠈⠀⣠⠏⣠⣾⡇⠀⠀⠀⠀⠘⣷ ⡀⠀⢸⣿⣿⣷⠆⢠⠏⡴⠃⡡⠋⠀⠀⠀⠀⠀⠀⣀⣠⠤⠔⠒⠤⣄⣀⠀⠀⢀⣰⠏⠀⠀⠀⠀⢀⣠⡾⠗⠋⢰⠏⡇⠀⠀⠘⠀⠰⢻ ⣇⠀⠘⣿⣿⣟⠻⣄⡞⠀⠐⠁⠀⠀⠀⠀⠀⣠⠞⣩⣤⣶⣶⣾⣷⣶⣬⣿⣿⣿⡏⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢸⡆⡇⠀⠀⠀⠀⠀⠀ ⠹⡄⠀⠹⣿⣿⡄⠀⠉⠉⠀⡀⠀⠀⠈⢻⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⣧⠀⠀⠀⠀⠀⠀ ⠀⣿⢦⣀⠘⢿⣷⡀⠀⠀⡀⢦⠀⠀⠀⠀⠹⣿⣿⠏⠙⢻⣿⡿⠛⠉⠀⠸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠀⠀⡆⠀⠀⡀ ⢼⣿⠀⠈⢳⣤⣉⣻⣤⣀⣉⣩⠆⠀⠀⠀⠀⠹⡿⠀⠀⠈⡿⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠓⠂⠀⣠⣾⣿⣿⡿⢿⡄⠀⣧⠀⠀⠹ ⣾⠃⠀⣠⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢠⠴⣿⡄⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⣧⣀⠧⣰⣻⢄⠀⠀ ⠛⠶⢾⣿⣽⣭⣽⣭⢹⣷⠀⢹⣦⣀⠀⠀⠀⠀⡄⠀⠀⣸⡀⠀⠀⠁⣰⣧⣽⠀⠀⠀⠀⢀⣴⣾⣿⣿⡟⣻⣿⣿⣿⣿⢠⣿⣧⡸⣷⣄ ⠀⠀⠀⠈⠙⠿⣿⣿⣿⠏⠀⣾⣿⣿⣷⣦⣀⠀⢇⠀⠀⠈⠁⠀⣠⠔⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⣼⣿⠏⣷⡈⠉ ⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣾⣿⣿⣿⣿⣿⣿⣷⣾⡆⠀⠀⠀⡾⠁⠀⠀⠀⣀⡴⠞⠛⣛⣿⡿⠿⠛⠛⠉⠉⠀⠀⠀⢰⣿⡿⠂⠈⠻⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢎⠉⠛⠻⠿⠿⠿⠿⠿⣇⠠⠸⣇⣀⣤⣴⣾⡭⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⡀⠀⠀⠀⠀⠀⠈⣳⠀⣿⠛⠻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡯⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡀⠠⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠁⠢⠀⠀⠀⠀⠀ ⠀⢠⢪⠀⠀⡠⣂⠄⠒⣄⠀⠀⠀⢡⠀⠀⠀⠀ ⠀⡏⡄⢀⣼⠊⢀⣤⠄⡿⣆⠀⣦⣸⠀⠀⠀⠀ ⠀⠃⢡⣿⢭⡁⠀⠰⢖⣿⡞⡀⡟⡼⡄⠀⠀⠀ ⠀⠸⡈⢏⠹⠧⡀⠀⠘⠛⠀⢰⠿⡀⢣⠀⠀⠀ ⠀⠀⠡⠈⡆⡀⠣⠤⠀⠀⡀⢸⢰⢃⠈⣇⠀⠀ ⠀⠀⠀⢑⢧⡟⡆⢤⠔⠈⠀⣼⡸⡈⡀⡜⡆⠀ ⠀⠀⠀⠎⣌⠠⠗⠘⠀⠀⠀⡇⠑⠄⣷⡧⠃⠀ ⠀⡐⠈⠉⠁⠀⠒⠂⠀⠀⠒⢳⡒⠀⠈⠁⠢⡀ ⠀⡇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠓⡀⠀⠀⠀⣹ ⠀⡣⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢀⠃ ⡈⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠸⠀⠀⡌⠀ ⡏⠃⠄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠒⢀⠀⢸⠀⠀ ⠈⠢⣀⣀⡀⠔⠀⠐⢄⠀⠀⠀⣀⠌⠀⡆⠀⠀ ⠀⠀⢰⠀⠀⠀⠀⠠⡀⠀⠉⠁⡈⠀⢰⠀⠀⠀ ⠀⠀⢸⡆⠀⠠⠀⠀⠈⠠⠀⠀⠃⠀⡆⠀⠀⠀ ⠀⠀⠀⣇⠀⢠⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⠀⢸⠀⠀⠀⠀⠀⠸⠀⢰⠀⠀⠀⠀ ⠀⠀⢀⠃⠀⢸⡄⠀⠀⠀⠀⠀⠑⡃⠀⠀⠀⠀ ⠀⠀⡌⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀

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⠶⠶⣶⣿⣆⠀⠐⠙⠛⠛⠳⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠈⠙⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠑⠒⠲⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣠⠔⠉⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠤⢄⡀⠀⠀⠀⠤⡀⠀⢶⡏⠀⡰⠁⠄⢀⣀⠀⣀⣀⡤⠤⠂⠀⠰⣄⠁⠀⠀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣠⣤⣼⣦⣀⣧⠀⡇⢀⣤⣾⣯⣽⣄⠀⢀⣀⡠⢶⡀⠈⣳⠖⠊⠁⠀⠀⠀⠀ ⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⣧⡀⠉⠹⠿⣿⡏⠠⣸⣿⠟⠉⠁⠀⠀⣀⡠⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⣷⣶⣾⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⣿⣶⣟⣻⣀⠀⣀⡁⠀⠀⢠⡀⠀⣄⣀⣉⡹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢥⣤⣤⣤⣤⣬⠹⠛⢶⣦⣤⠤⠤⠴⠖⠒⠉⠁⠀⠀⠀⢀⠟⠉⠉⠉⠙⢠⠋⣹⠆⠀⠘⠓⠾⡩⠟⠉⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣦⣭⣽⣛⣛⣿⣿⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⢀⡇⡴⠃⠀⠀⣀⠴⠊⠀⠀⠀⠀⠀⠙⠳⢤⣀⣀⣀⣀⣠⣤⣾ ⠉⠻⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠤⠖⠶⠟⠻⠛⠻⢶⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢹⣿⠟⠛⠉ ⣦⣄⣈⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠒⠲⠤ ⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⢁⡬⠛⠉⠉⢑⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀ ⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⠎⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣄⡀ ⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣸⠀⠀⠀⢠⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣁ ⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⡏⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠹⡿⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡸⣿⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠹⠌ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀ ⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀ ⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀ ⣿⣿⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀ ⠿⠋⠁⢀⣹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀ ⢀⡤⠖⠉⠀⠀⠹⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣬⣿⠷⠶⠶⠤⢤⣤⣤⡤⣤⣹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡠⠤⠒⠋⠉⠀⠀⠀⠀⢀⡴⠞⠋⣀⡴⠞⠋⠻⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠒⠁⠀⢀⡀⠀⠀⠀⠀⣠⡴⠞⣉⣠⠴⠚⠁⠀⠀⢀⣴⣿⣿⣿⣿⣶⣦⣤⣤⣀⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⠄⣀⢤⢴⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⡼⡀⣦⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡀⠀⠀⠁⠢⢄⠀⠀⠀⠀⠀⢀⡷⣩⠛⢣⡱⣾⠄⠀⠀⠀⠀⠀⢀⠠⠐⠀⠀⠀ ⠈⠢⡀⠀⢀⢄⠑⠄⡀⠀⢀⣼⠿⢿⡅⠥⠶⢷⢂⠀⠀⠀⡠⠒⢡⠀⠀⠀⠀⠀ ⠀⠀⠀⠩⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⢀⠀⠀⠀⠁⢡⠀⠀⠀⠀⠁⠓⡒⠊⠀⠀ ⠀⠀⠀⠀⣂⡀⠀⠀⠀⠀⠙⢤⠄⠂⠁⠁⠒⢠⠔⠁⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⡏⠀⠀⠀⠀⠀⠀⢑⡄⢒⠒⡔⠁⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⢁⢸⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⢀⡤⠚⢄⠀⠀⠀⠀⣠⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣡⠋⠀⠀⠀⢣⠀⠈⠁⠈⢛⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⣠⠶⠟⠿⠿⠿⢿⢿⣶⣶⣶⣶⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠓⠀⠀⠀⠠⠿⠖⠒⠻⣯⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢠⣺⣿⣿⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⣿⠟⠃⠀⣧⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡰⠃⠀⡀⠀⠀⡀⣠⠀⠀⣶⣵⣷⣿⣿⣿ ⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢸⡏⢻⣤⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡿⠧⠦⠄⠠⢀⣤⣿⣿⣿⣿⠏⠈⠙⠛⢻⣿ ⠀⠀⠀⠀⣼⣣⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⠀⢸⠀⠐⢿⣿⣿⣿⣛⣛⣻⣗⣖⣒⣲⣶⣶⣶⣶⣾⣿⡧⠤⣤⣤⣤⣤⣄⣀⣀⣀⣘⣧⣠⣶⣶⣦⣽⣿⡿⢿⣻⣏⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⢀⣿⠙⢷⣄⠀⠀⠀⣠⡶⠋⠁⡏⢀⡟⠀⠀⠀⠻⢿⣿⢀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⠓⠒⠶⠖⣤⡿⠿⣟⢿⣇⠉⣿⠟⠿⢤⣀⣈⠃⠀⠀⠠⣤⢿⣿ ⠀⠀⠀⣸⠟⠂⢤⠈⠛⠒⠛⠁⠀⠀⣰⠇⣼⣅⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⠾⠋⢀⣠⣿⡷⠟⢾⡏⠀⠀⠀⠈⠉⠀⠀⣤⣄⣠⣾⣿ ⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⢠⡄⠀⠘⣿⠀⡏⣿⣷⡂⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⡞⠁⠀⣰⣾⢟⠩⠤⠤⢼⣇⠀⠀⠀⠀⠀⠀⠰⠉⢠⣿⣿⡿ ⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢸⠀⣷⣿⣿⣿⣦⣀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⠃⢀⣾⢿⠋⠀⠀⠀⠀⠀⠀⠙⠲⢤⣾⣿⠟⢀⣠⣿⣁⣠⣤ ⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⡆⠻⣿⣿⣿⣿⡿⠗⠓⠒⠒⠲⠽⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⠟⢹⡇⡼⣿⡟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠿⢿⣿⣯⣠⡇ ⠈⠳⣆⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⡇⠸⢽⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣾⣿⣿⣿⣿⣿⡿⠋⠘⢸⣧⡇⣿⠀⠣⠀⠀⠀⠖⠉⠓⠶⢤⣄⠀⠀⠀⠀⠀⠀⠈⠙⠻⠇ ⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⡸⠀⠀⠘⡇⢀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⠿⠋⣠⠞⠀⠈⢿⣇⠙⠲⠀⠀⣠⠖⠋⠉⠙⢶⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠔⠁⠀⠀⠀⢀⡬⠔⠚⠉⠉⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠙⠃⠀⣴⠞⠁⠀⠀⠀⠀⠈⠀⢸⣿⣿⣶⣦⣤⣤⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠰⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⠄⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢰⢋⣠⠴⢚⣉⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡴⠚⠱⡄⠀⠀⢨⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠈⠓⢤⣠⣄⡀⠀⠀⠈⢱⠞⠉⠀⠰⢏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠏⠀⠀⠀⡆⠀⠠⣯⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛ ⠀⠀⠀⠀⠀⠈⣕⡯⠳⠦⢄⡀⠀⠀⠀⠀⢀⣀⣉⣉⣉⣉⡽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠉⠀⣤⡤⠚⠁⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠙⠲⡄⠀⠀⠀⣄⣀⣉⣥⣤⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⢧⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣸⡍⠳⣄⠀⠠⣄⣉⣁⣉⡴⠋⠀⠀⢀⣠⡴⠊⠀⠀⠀⠀⢀⣠⠴⢦⡖⠒⠒⠋⠁⠀⠀⠈⠳⢤⣄⣤⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⢧⠀⠀⠉⠓⠒⠦⠞⠋⠀⠀⠀⠀⠉⠀⢀⣀⣀⡤⠴⠚⠉⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠈⠸⠶⠒⠒⠋⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣄⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣠⣴⡶⠿⠿⠿⠷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡿⠁⠀⠀⢠⣾⡆⠀⢰⣶⠀⠀⢻⣧⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠛⠁⠀⠈⠋⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⢻⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⡇⠀⣶⣤⣄⣀⣀⣀⣀⣀⣠⡄⢀⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⢃⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢿⣦⣈⠛⠻⠿⠿⠟⣛⣵⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠻⠿⠶⠾⠿⣛⣉⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢶⣶⣤⣤⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣯⠻⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⠉⠙⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⢀⡴⠶⣦⣴⠛⠉⠹⠏⠙⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣄⡀⠀⠀⠀⠀⠘⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣄⡀⠀⠀⠻⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⣴⠇⠀⠀⠀⠀⠀⢠⡶⠶⢦⣀⠀⠀⠀⠙⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣽⣿⣴⣾⣿⣿⡻⠿⢷⣿⣧⣤⣤⣄⣀⣀⣀⣀⡀⠀⢻⣧⣸⠃⠀⠀⠀⣸⡟⠛⠛⠀⠀⠀⠈⠙⢦⡀⠀⠸⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠁⠀⠀⠀⠙⣿⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⣰⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⣄⣀⣀⣠⣿⣟⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢀⣾⠋⠈⠛⠳⣆⠀⠀⠀⠀⠀⠀⠘⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⠛⠛⠻⣿⡙⢿⣦⡀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢻⡁⠀⠀⠚⠳⠿⣷⡄⢀⣀⣤⠶⠦⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⣿⠀⠀⠀⠘⢿⣄⠈⠻⣦⣀⠀⠀⠀⠀⠉⠛⠿⣿⣷⠀⠀⠰⡿⣷⡀⠀⣀⣀⡀⠀⠀⠈⠉⠙⠷⢀⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⣿⠀⠀⠀⠀⠈⢻⣦⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢨⡿⣦⣛⠿⠿⠆⠀⠀⠀⠀⣠⣾⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⣿⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠈⠹⣷⣄⠀⠀⠀⢿⠀⠀⠀⠀⢰⡟⠁⠈⠛⠿⣶⣤⣤⣤⣴⠾⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠸⣿⠀⠀⠀⣸⣿⠀⠀⠀⣴⣿⠀⠀⠀⣤⠗⠀⣨⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⠀⣿⠀⠀⠀⣻⣦⠀⢀⡀⢿⡏⠀⠀⠀⣻⡆⣐⣿⣹⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⣿⠀⠀⠰⣿⠋⣸⡾⢧⣾⠇⠀⠀⠸⣯⠙⣿⠛⢿⡉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⣿⡄⠀⢠⣾⣿⣏⣷⢈⣷⠀⠀⠀⣴⠟⢴⠛⢠⡾⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⣿⡇⠀⠈⣿⣿⠛⠁⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⢹⡇⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⣼⡟⣀⣀⣤⣄⡀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⢀⣈⠻⣷⣤⡀⠀⠀⠀⢀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⠛⠛⠿⢷⣦⡄⠀⠀⣼⣿⡿⠟⠛⠉⠙⢿⣆⠀⣾⡇⠀⠀⠀⠀⠀⠀⠘⣿⣤⣶⡿⠿⠻⢿⣦⠙⠿⣶⣤⣶⠿⠛⠉⠉⠙⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠈⣿⠀⠀⠛⠿⣶⣤⣤⣀⣠⣾⠟⢰⣿⣶⣶⣶⣶⣤⡀⠀⠀⠻⢿⣧⣤⣀⣀⣼⣿⠀⠀⠈⠙⢷⣄⡀⠀⠀⣀⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢷⣾⠟⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠻⣿⣄⡀⠈⠉⣿⡄⠀⠀⠀⠈⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠙⠛⠿⠿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢢⣀⡀⠀⠀⢠⣾⣙⣷⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⡶⣶⣤⢿⣿⣿⣿⡿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⣿⡿⣰⡾⢭⡝⣿⣾⣿⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠿⣿⣟⡓⠋⠀⠹⣿⡿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣇⣀⠠⠞⠛⠛⠛⠓⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠁⠀⢀⠀⠀⠀⣀⠀⡘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢧⠀⢢⣸⡵⣁⠽⠐⠒⠚⠓⠳⡤⠀⠀⠠⠄⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣧⢀⡨⠋⠁⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠉⠢⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⢡⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⡀⠀⠀⠀⠀⠘⠄⠀ ⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⡄ ⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⡅ ⠀⠀⠀⠀⠀⠸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢹⡀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠍⠉⠒⠀⠀⠀⠀⠀⠰⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢢⠀⠀⢀⣀⢀⣌⡀⠀⠀⠀⣀⠠⠒⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠈⠸⣽⡏⠁⠀⠙⠧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠒⠠⠀⢠⠛⡔⡤⠐⠀⠙⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡘⠁⠀⠈⠣⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡐⠁⠀⠀⠀⠀⠐⠄⠀⠘⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣄⠜⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⢡⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣄⢽⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⠜⣣⣼⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠇⠠⢾⠀⠀⠀⠀⠀⠀⠀⠴⡭⢤⡞⢻⠿⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⢉⣀⠤⠤⠭⢟⣦⣯⣇⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠁⣠⠒⠉⣠⠒⠁⡠⠚⢻⡿⣿⢿⡣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⢀⠎⠁⡰⠊⠀⣠⠊⠀⠀⣼⠇⢋⢇⣷⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣠⠏⣠⠞⢠⢎⣴⠃⡠⠀⢠⣿⠀⢸⢸⣿⠞⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⣼⡟⡴⢁⡴⡣⠛⡿⢠⠃⢀⢿⡇⠀⢸⢈⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⡟⡇⡼⢸⡟⢁⣾⣿⣧⣰⣧⠇⢀⣾⠏⣇⠀⢸⢸⣿⡆⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠁⠁⣇⢇⣸⢃⡞⠀⠫⠿⢹⡟⣠⢾⠏⠀⢸⡇⡆⡸⡌⣷⡼⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡏⣼⡇⠀⠀⠀⢸⠵⠋⠃⢸⣟⢿⣧⢣⡇⣿⡘⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⣿⣿⣿⣾⣸⢰⣿⣣⠀⠀⠀⠀⢀⣀⣀⣀⣠⣾⣧⣾⣷⣿⣿⣾⣯⣣⡀⠀⠀⠀⠀⠀ ⠀⢠⣾⣿⣿⣿⣿⣿⣿⡿⠿⢧⣙⣆⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡹⣦⡄⠀⠀⠀ ⢀⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⠁⠀⠀⠀ ⢸⣿⣿⣿⣿⣧⢀⡀⠀⢀⡄⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⢣⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣇⣤⣴⣿⣷⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀⣄⡌⣇⠀⠀ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣌⡀⢸⣣⠸⡄⠀ ⠀⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠉⠙⠻⣄⡧⠀ ⠀⢈⣿⣷⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠉⠉⠛⠛⠻⢿⣿⣿⣿⣀⡒⠢⡠⠴⣮⡇⠀ ⠀⠀⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣷⣀⣈⣴⡟⠃⠀ ⠀⠀⢼⣿⡟⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠏⢙⡇⠀⠀ ⠀⠀⣾⣿⣷⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⣀⡜⡇⠀⠀ ⠀⠀⠘⣿⣿⣧⠀⠀⠘⠢⠤⣄⣀⠀⠀⠀⣤⠞⡟⠢⡀⠀⠀⠀⠀⠀⣠⣿⢁⡖⣠⢾⣫⠃⡇⠀⠀ ⠀⠀⠀⠈⠿⣿⣗⠄⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⡇⠀⠈⠛⢲⣶⡶⢾⣿⡇⣼⡾⣽⣯⠃⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣾⡄⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠐⣾⣿⣷⠏⣿⢠⡟⣰⣿⠇⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⠀⣿⡞⢀⣿⡟⠀⠀⡜⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠈⣿⠀⢸⠏⢣⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡾⡼⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠳⡀⠀⢿⠀⢸⠀⠈⠀⠀⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠹⡄⠈⢇⠀⠀⠀⠀⠀⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⢀⠀⠀⠱⡀⠈⠳⢤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⢀⡿⢹⣄⠀⠀⠀⠀⠀ ⠀⠀⡶⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⡞⠀⠀⠀⠀⠀⣠⡾⠁⡜⢇⡀⠀⠀⠀⠀ ⠀⣴⢧⣈⠓⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⡜⠀⠀⠀⠀⢀⠔⢱⣣⠊⠀⠈⢧⢠⡀⠀⠀ ⠰⠃⠀⢸⠋⠒⠢⢤⣉⠉⠒⠢⢤⣄⡀⠀⠀⠀⢹⡟⠀⠀⠀⠀⣰⠇⢀⡏⠘⣄⠀⠀⠈⢧⠙⢄⠀ ⠀⠀⠠⠋⠀⠀⠀⣼⠀⠉⠉⠒⠦⠤⣈⡉⠓⢶⢄⣇⠀⠀⠀⢠⠧⠤⢸⠀⠀⠈⠢⡀⠀⠈⠳⡀⠳

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⠤⣤⣤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⣉⡤⠴⠀⣀⣈⣭⣁⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠗⠋⣀⡤⠤⠒⢘⡥⠤⡀⠙⢦⡀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁⡤⠚⠁⣠⠖⠛⠻⠧⢤⡈⠳⣄⠑⡄⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢻⣿⠋⣠⠞⠁⢠⠎⠀⡖⢀⠀⢀⡄⡵⡄⠘⢦⢣⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢫⡿⠃⣰⠏⠀⣳⡏⠀⣴⠁⠀⣸⣇⠙⡘⢿⡄⠈⠋⢧⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⠁⢰⠏⠀⣠⣿⣟⢺⣟⣚⣿⡟⠘⣦⣷⡈⣿⡄⢀⡞⣧⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢀⡿⠀⢸⣿⣿⣿⣿⡿⣶⡿⠁⠀⠈⢿⣷⣿⣷⠴⣷⣽⣇⣿⢇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣸⣇⢰⣿⢿⣾⣭⣿⠿⠋⢠⣐⡒⠀⠀⣹⣿⢃⠂⢸⣿⣿⣿⠎⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣤⣿⣿⣿⡏⠀⠚⠉⠇⠀⠀⠙⢹⡿⡷⠦⡿⠙⢸⢠⣾⣿⣿⣿⣰⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣏⣿⣧⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠞⠀⣰⣶⣿⣿⡧⠟⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⣟⢻⣿⣹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣿⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⣿⡟⠙⢦⡀⠀⠀⠀⣀⡤⢞⢏⡟⢼⡿⣿⣇⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠀⠀⠀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣦⡼⣿⠓⣶⠟⠋⣠⣟⣉⣀⣤⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⠒⠉⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠉⢣⡤⠊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀ ⠀⢀⣈⡗⠀⣰⣾⡿⢿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣿⡿⣿⣿⢭⣭⣄⣆⠔⠬⢍⠉⢛⠛⠿⣿⣿⣿⣿⣿⡏⡀⠘⠿⡋⠙⢿⣿⡇⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣷⣧⣼⣾⣿⡻⠿⠿⢭⣭⣾⣽⣿⠃⠀⡠⠟⢠⣿⣿⣿⠀⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⠞⠋⠐⠂⢭⣙⠛⠛⠿⣿⣿⣿⣿⣷⣶⣶⣦⣶⣾⣿⣿⣿⣶⣼⣁⣀⣼⣿⣿⣿⣇⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠙⢷⣶⣤⣤⣤⠤⠬⠉⠉⢭⣝⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠈⣿⣿⣿⣿⣿⣧⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⠀⠀⠀⠘⢿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⣠⠎⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⡊⠛⠶⠶⠖⠋⠁⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠁⢀⣤⠏⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⠶⠶⠾⠉⠁⢀⡞⠁⠻⣿⣿⣿⣿⣿⣿⣿⣿⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠙⢿⣿⣿⣿⣿⣿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⡿⢱⠏⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⡿⠀⡇⣠⠗⢄⠉⠲⠦⠤⣀⣀⣀⣀⣀⣀⣀⡤⠶⠻⠋⢻⠀⠱⡹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⣾⠇⣸⠁⠃⠀⠀⠉⢒⠦⠄⣀⣀⣀⠀⠀⣀⣀⣠⠴⠺⡀⠈⡇⠀⢻⡻⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣽⣿⢠⠃⠀⠀⢀⡆⠀⠈⠀⠀⠃⠀⠀⠃⠉⡏⠀⠀⡀⠀⡇⠀⢸⡄⠀⢳⠙⢆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡿⢃⡇⢸⠀⠀⠀⣸⠀⠀⠀⠀⠘⠀⠀⠀⠀⠐⡇⠀⣄⡇⠀⢸⡀⠀⢣⠀⠈⢷⠈⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠃⣼⠁⡜⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⣧⠀⠈⢧⠀⠘⣆⠀⠈⣧⠘⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡟⠀⢻⠀⡇⠀⠀⣼⠀⠀⡇⠀⠀⡆⠀⠀⠀⠀⠀⡇⠀⠀⢹⡄⠀⢸⡀⠀⠹⡄⠀⢸⣦⠹⣇⠀⠀⠀⠀ ⠀⠀⢀⣿⠁⢸⡏⢰⠃⠀⡆⣿⠀⠀⠀⠀⠀⡇⠀⠀⡄⠀⠀⠇⠀⠀⠸⣷⠀⠀⣷⡀⠀⢷⠀⠀⣿⣆⣿⡄⠀⠀⠀ ⠀⠀⠈⣿⠿⢿⡇⣾⠀⠀⣇⣯⠀⢸⠀⠀⠀⡇⠀⠀⠃⠀⠀⢸⠀⠀⠀⣿⠀⠀⢸⡇⠀⢸⣦⣠⣼⡟⠋⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⢸⣷⣿⣦⡀⣿⡇⠀⢸⠀⠀⠀⡇⠀⠀⡇⠀⠀⢸⡀⠀⠀⣿⡆⠀⠸⣧⣤⣤⣿⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣷⣭⣿⣷⡀⢸⠀⠀⠀⡇⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⡇⡤⣺⣿⠿⠻⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡇⠙⢻⠿⣬⣿⣯⣍⣒⣿⢦⡀⣿⡦⣄⢸⣿⣉⣐⢾⣿⣿⠟⠁⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠙⠛⠈⠛⠿⢿⣿⣬⡿⣿⣶⣼⠿⡿⢿⠋⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⣀⣁⣿⣿⣇⣈⣉⣇⣀⣆⡀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡠⠤⠒⠒⠒⠙⠒⠒⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠅⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⢣⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡄⢹⡄⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣀⣀⣀⠿⠀⠀⠀⠈⠷⠤⣄⣀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⡇⠀⠀⠀⣠⠊⢠⡀⠉⠲⡄⠀⠀⠀⠀⠀⠀ ⠘⢯⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣉⣒⣦⣄⠀⠈⢦⡀⠀⠀⠀⠀⣇⢰⠇⠀⠀⡜⠁⣴⣿⣿⣶⡄⠘⢦⠀⠀⠀⠀⠀ ⠀⠀⠉⠲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⠛⣿⣿⣿⣿⣦⡀⠳⡀⠀⠀⠀⣿⡟⠀⠀⠀⠸⡀⠙⢻⣿⡿⠀⠀⣸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⡷⠖⠀⠀⠀⠀⠀⢚⠻⣿⣿⡿⣿⠏⠘⢷⣶⣷⡄⠀⢸⡟⠁⠀⠀⠀⠀⠱⡀⠈⠛⠀⠀⡠⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠾⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠈⠙⣏⢀⣤⣾⡴⢻⠂⠀⠀⠀⠈⠉⠒⠤⠤⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣻⡉⠉⣽⠃⠀⠀⠀⠲⠀⣀⣠⡄⠀⠤⠤⠄⠈⣡⣾⠟⠁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⠹⣤⡧⠤⠶⢾⣍⣉⠍⠀⣰⠧⣤⣤⡤⣶⠿⢋⣡⣄⡞⢁⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠣⣌⠑⢢⣤⡤⠤⣖⣠⡜⠁⠀⢻⣧⣍⣉⣉⣭⣶⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡟⠁⠀⠀⠀⠀⠉⠉⠁⠺⢿⣿⣁⣴⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣼⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⠟⠉⠉⠁⠒⣒⠤⢄⣀⠀⠀⠀⠀⠀⣠⣴⡶⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢯⡀⠀⠀⠀⠀⠀⠀⢠⡀⠈⠑⠢⢄⠀⠀⠋⣹⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢹⣆⠀⠙⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢿⣧⡀⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡒⠤⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠈⠶⠼⢿⣷⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠐⡇⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢹⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⢣⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠙⠲⣤⣀⣀⣀⣀⣀⣀⣤⣾⣿⠛⣧⡉⠓⢶⣤⣤⢤⡴⣶⡎⠁⠀⢴⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠘⢦⡈⠙⠛⢻⠉⠀⣼⠟⠀⡇⠈⠓⠤⣀⠀⠀⢣⣼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠀⠉⠉⢁⣧⠀⠀⠀⠀⠀⠙⢦⡀⠸⠀⣸⣇⠈⠀⡇⠀⠀⠀⠈⠑⠦⣈⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⢀⠞⠁⠘⡆⠀⠀⠀⠀⠀⠀⠈⠓⠚⠁⠈⢳⠀⡇⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⡀⠀⠀⢀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⣧⡀⣿⣷⡆⢯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢧⢿⣿⡿⠟⠻⢻⢹⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⢘⣧⢣⡀⠀⠀⣸⣴⡏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣽⣼⢿⣆⣋⠕⢉⡜⡈⠧⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠹⠩⡿⠉⡏⡆⠚⠇⣆⠂⡄⢀⠇⠀⠀⠀⣠⠖⠈⠑⢆ ⠀⠀⠀⠀⠀⠀⠈⡄⢡⡁⣳⡿⠁⠀⠈⠛⠀⠛⠎⡆⢀⡠⠊⠀⠀⠀⠀⠸ ⢀⠤⠤⢀⡀⠀⠀⢡⠀⢣⡁⠀⢀⠀⠀⠀⠠⠴⠗⡩⠊⠀⢀⠎⠀⠀⠀⠇ ⡇⠀⠀⠀⡀⠉⠐⠠⢄⡀⢱⡀⠁⠀⠀⠁⠀⡠⠋⠀⠀⢠⠂⠀⠀⠀⢠⠀ ⠡⡀⠀⠀⠈⠂⢄⠀⠀⠈⠙⠠⡀⢀⣤⢀⡔⠁⠀⠀⠀⡆⠀⠀⠀⠀⠎⠀ ⠀⠈⢄⠀⠀⠀⠀⠠⡀⠀⠀⠀⠈⣉⣳⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠊⠀⠀ ⠀⠀⠀⠁⢀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠘⠔⠀⠀⠀⠀⢠⠩⠦⢠⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠄⡀⠠⠈⠢⢀⠀⠀⠀⡸⠄⣀⣀⣠⡇⠀⢀⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠈⡗⠖⠊⠀⠀⠀⠀⢦⠘⡶⢻⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣍⡆⣸⠀⠀⠀⠀⠀⠈⠳⣸⠫⠑⠙⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠅⠐⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⠶⠦⠞⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠦⠶⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⢈⣧⠀⠀⡀⠀⠀⢀⠇⠀⠀⠀⠀⣀⠀⢀⣘⣷⢄⡀⡀⠀ ⠀⠀⠀⢠⠃⠀⣠⣴⠯⠋⠀⠀⠤⣌⡉⠓⢤⡀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⣸⣿⣧⠤⠓⠐⢤⠾⠤⣤⠋⠒⢤⣿⠉⠁⠀⠀⠀⠹⣇⠀ ⠀⠀⠀⠸⣤⠞⢁⠔⠀⠀⠀⠀⠀⠈⠙⢦⡀⠙⢦⡀⠀⠀⠷⣤⡀⠀⠀⣰⠟⠉⠀⠀⠀⢶⡁⠀⠀⠈⠦⠀⠀⠙⠒⡶⠲⡀⠀⠀⢿⡄ ⠀⠀⢀⣼⠃⠀⣇⡤⠊⠀⠀⠀⠀⠀⡼⠀⠙⣢⣤⣝⣒⣉⠦⣬⣝⣦⠞⠁⠀⢀⣀⠤⠴⠈⢓⣤⡤⠀⠀⠀⠀⠀⠀⠸⣤⠑⠀⠀⡀⠃ ⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢀⡤⠊⠉⡤⠊⠀⠀⠀⠀⠀⠉⠓⢶⡞⠉⠀⠀⠀⠀⠀⠀⢈⡓⠦⢄⡀⠀⠀⢰⡇⠑⠄⢸⣿⡀ ⠀⢠⠃⠀⠀⠀⠀⠀⠀⣀⣴⣾⠕⢺⠏⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢦⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠈⠑⢤⡀⡇⠀⠀⠘⢹⠇ ⠀⢸⠰⢤⣀⣀⠤⢔⣾⠿⠃⡄⢀⡏⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡳⡀⠀⢀⠼⠇⠀⠀⠀⠀⠀⠀⠀⢹⠣⢴⡆⠀⠸⠀ ⠀⢸⠀⢀⣠⠔⠊⠡⠖⠀⠀⡿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠱⡐⠋⠀⢆⠀⠀⠀⠀⠀⢀⠀⠈⣆⣀⠈⢓⣁⠀ ⠀⠼⠖⠉⠀⠀⠀⠀⢀⠤⢆⡇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠓⠲⠀⣀⠞⢁⣠⡒⠉⡀⠀⢀⣈⡿ ⠀⠀⠀⠀⠀⢀⣠⠔⠃⣠⢾⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⡤⣴⠶⠒⠛⠛⠺⠯⣄⢠⣀⠈⠉⢿⡀⠀ ⠀⠀⣀⡤⠖⣉⡤⠖⠊⠹⢺⡷⣘⡆⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡠⠴⠚⠀⣀⣀⣈⣷⣯⠑⢤⡀⢃⠀ ⠀⣀⣤⠖⠋⠁⠀⠀⠀⠀⡜⠀⠈⢻⡀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣠⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠋⠀ ⠚⣿⣿⣿⡄⠀⠀⠀⢀⡞⠀⠀⠀⠈⢧⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢍⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⣿⣿⣤⠤⠖⠋⠀⠀⡠⠄⠀⠈⣆⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠁⠀⠀⠀⠀⠀⠈⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⡥⠀⠀⠀⠀⣠⠴⢀⣠⠤⢦⡀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡞⢸⠁⠀⠀⣠⢚⡥⠚⠉⠀⠀⠘⣗⡄⠀⠀⢰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢾⠇⡎⠀⠀⣰⡳⠋⠀⠀⣠⣤⠶⠢⡿⣸⣆⠀⠈⣧⣄⢸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡄⢳⣠⣾⡟⠓⠆⠀⠘⠙⢀⣤⣶⢿⣤⣹⡅⠀⣿⠈⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠸⡇⣾⡛⣶⡦⠀⠀⠀⠛⢱⢼⣷⠸⠋⢣⠀⡇⣹⠛⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢱⠀⠹⣏⠉⢟⣻⣀⠀⠀⠀⠐⠛⠛⠐⠀⠘⣴⡽⣇⠀⢸⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢇⠀⠘⡄⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⢹⡀⠈⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢦⠀⢻⢦⡀⠈⠰⠶⠒⠂⠀⠀⢀⡤⠀⡇⢘⡆⢇⠀⠸⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠳⡼⡀⣟⡶⢄⡀⠀⢀⡠⠖⠁⠀⢀⡇⢸⢻⠸⡀⠀⣿⢇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠏⢳⠟⢀⠷⠈⣹⡇⠀⠀⠀⠀⣼⢣⡞⢸⠀⡇⢰⣼⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠎⣠⠋⢀⡼⠟⠊⠟⠀⠀⠀⠀⠀⣿⠀⠑⢯⣀⣇⣎⢏⡞⠀⠀⠀ ⠀⠀⠀⢀⡠⠾⠔⠓⢞⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⣀⡈⠛⠿⠯⣀⠀⠀⠀ ⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠉⠉⠉⠉⠉⣧⡀⠀⠀⠀⠀⠀⠀⠑⡄⠀ ⠀⠀⢻⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠀⠀⠀⠀⠀⠀⠀⢹⡆ ⠀⠀⢸⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⡼⠃ ⠀⠀⠘⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⢠⠇⠀ ⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⡎⠀⠀ ⢠⠇⣠⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⡄⠀⠀⡸⠀⠀⠀ ⢸⡀⠛⠄⢀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⠵⠀⠀⡇⠀⢀⠇⠀⠀⠀ ⠀⢷⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣰⠁⠀⣾⠀⠀⠀⠀ ⠀⠀⠑⢤⣀⠀⠀⢀⣠⠴⠋⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣀⡴⠁⠀⢠⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⢻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠉⡽⠀⠀⠀⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣾⠀⠐⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡄⠀⠀⢠⡀⠀⠀⠀⠀⠙⣄⠀⠀⠀⢰⠁⠀⠀⣼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡜⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣻⠁⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠃⠀⠀⠸⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠏⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠔⡆⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠈⠀⠀⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣼⡆⡄⢀⠃⠀⢸⠀⡀⡇⠂⠤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⣼⠡⠇⢻⠀⢠⠸⡄⡇⢹⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⢀⢢⡇⢦⠀⣸⡀⢰⠀⣷⣷⠈⣇⠀⠀⢸⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣆⣼⡿⠤⣼⣠⣏⣇⣼⣶⣹⣾⠧⠼⢦⣀⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠙⠹⢿⠋⠁⠀⠀⠀⠀⠉⠣⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⢢⢄⠀⠀⠀ ⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⢢⠀⠀ ⠀⢠⠃⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⣁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⢡⠀ ⠀⣼⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠐⣦⢹⣆⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⡄ ⠀⣿⠀⠀⢷⠀⠀⠀⠀⠀⢀⡀⢀⡏⠀⣿⠀⡏⠑⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠃ ⠀⢹⡆⠀⠸⡄⠀⠀⠀⠀⠀⠀⠙⣷⠀⣗⢠⡿⠛⠁⠀⠀⠀⠀⢈⡇⠀⠀⢀⠀ ⠀⠀⢿⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠙⣷⣿⡿⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡎⠀ ⠀⠀⠘⣇⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⣿⣽⡇⠀⠀⠀⠀⠀⠀⢰⡿⠀⢀⡞⠀⠀ ⠀⠀⠀⠹⡇⠀⠸⣆⡀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⢰⣿⠃⠀⣼⠃⠀⠀ ⠀⠀⠀⠀⢿⣦⠀⠹⣆⠀⠀⠀⣀⣤⣿⣿⣷⣄⠀⠀⣀⣴⣿⡧⣀⣼⡏⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⣷⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⢁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢻⣿⣿⣿⠏⣿⣿⣿⡟⠻⣿⣻⣿⡇⢰⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣼⣿⣿⣿⠀⣿⣿⣿⡇⠀⢹⣿⣿⣠⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣇⣀⢸⣿⣿⣯⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⣿⠇⣿⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣯⢸⣿⡷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡾⡏⠀⣿⣿⣿⣿⣿⣿⠁⠀⠀⢻⣿⠿⠃⠐⢻⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠁⠀⢸⡏⠁⠀⠹⣿⠀⠀⠀⠘⡇⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠻⠀⠀⠀⠀⢷⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀ ⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠓⠒⠒⣒⣒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡫⠡⠀⡨⠭⡙⠦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⡡⠒⡠⠥⠆⡐⢌⢢⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡿⢃⠞⣠⠊⠐⠀⡀⡸⡄⠲⣄⢹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣻⢁⠎⣠⣿⣰⡷⣾⠱⣴⣹⡄⠈⡆⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡇⣼⢠⣿⣿⣿⠿⢃⠀⠈⣿⠟⢹⣿⣾⢂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡧⣿⣿⠁⠉⠁⠀⠉⠿⢒⠏⣙⣾⣿⡧⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠙⣿⣿⣦⡀⠀⠀⠀⠀⢁⡴⣿⣿⣁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣌⡦⢤⡴⢊⠗⢁⣻⣿⣤⣀⠀⠀⠀⠀⠀ ⠀⢀⠐⣈⣾⣿⣿⣿⣿⣿⣿⣬⣹⣄⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀ ⢰⣾⣶⣿⣿⣿⣿⣿⣿⣯⣭⣍⢛⠛⣛⠻⣿⣿⣿⣏⠹⢟⠻⣿⠀⠀ ⣸⣿⣿⣿⣿⣿⡫⠿⢟⡿⠿⣿⣿⣾⣿⣿⣥⣾⣿⣯⣠⠊⣸⣿⡇⠀ ⠹⣿⣿⣿⣿⡏⠀⠀⠀⠀⠑⠶⠤⠄⠈⠉⠩⢝⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠘⣿⣿⣿⣄⠀⠀⠀⠀⡄⠐⡀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⡀ ⠀⠀⠈⠛⠛⠛⠑⠒⠒⠉⠀⠀⠱⣄⡀⠀⣀⠴⢙⢿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⡆⠀⠹⣿⣿⣿⠟⠀ ⠀⠀⠀⠀⢀⣴⡷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⠀⠀⠈⠉⠁⠀⠀ ⠀⠀⠀⢀⣾⢱⠡⠂⠁⠂⠠⠤⠤⠤⠤⠐⡚⢳⠑⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⡇⡌⠀⢀⠀⠉⠑⠐⠂⠰⠂⠉⠰⠀⡆⠸⡷⡀⠀⠀⠀⠀ ⠀⠀⢸⢣⢃⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⣴⠀⡆⠸⡀⢱⡰⡀⠀⠀⠀ ⠀⢀⡏⣸⠸⠀⣈⠀⡄⠀⠄⠀⠀⢰⠀⠘⡄⢰⠀⢡⠀⢧⢱⠀⠀⠀ ⠀⢸⣤⡟⡄⠀⣿⠀⡄⠀⠀⠀⠀⠈⠀⠀⡇⠀⡇⠈⣆⣸⡟⠃⠀⠀ ⠀⠀⠀⢿⣗⣦⣇⠀⠀⠀⡀⠀⠀⠀⡇⠀⢷⠀⣽⣶⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠸⣯⠙⠿⣵⣷⣦⣇⢀⣆⠄⣷⣄⣾⠿⠋⠀⣼⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⡄⠀⠀⠀⢈⣻⣿⣙⣻⣉⡉⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⣿⣿⣧⠀⠀⠀⠀⠀⠐⣾⣿⡿⠀⠈⣿⣿⣿⣧⢀⣠⡀⠀⠛⠺⠶⠤⠶⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢶⣿⣿⣾⠃⠸⣿⣿⣷⢶⡄⠀⣄⢰⣿⣿⠇⠀⠀⠈⢿⣿⣿⣿⡏⠁⠀⠀⣦⣀⢀⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⢻⣿⣿⡀⢹⡶⠋⣿⣿⣿⠀⠀⠀⠀⠈⢿⣿⣿⣷⠀⠀⠀⢈⣤⣤⣈⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠘⣿⣿⣿⣿⣦⣤⣿⣿⡏⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡀⠀⠘⠿⠹⠏⣧⠀⠀⠀⠀ ⠀⠀⠀⣀⡄⠀⠀⠀⠲⠛⠀⢰⠀⠀⢀⣿⣿⣿⠁⠀⠀⠀⠀⢹⣿⣿⡇⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⡀⠒⠿⠿⠷⣿⠀⠀⠀⠀ ⠀⠀⠀⠉⠀⠀⠀⠀⣤⣤⠀⢸⠀⠠⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠛⣿⣷⡀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠛⠛⠛⠛⢿⠀⠀⠀⠀ ⠀⠀⠀⡀⠀⠀⠀⠀⣿⠀⠀⢸⡇⢰⠟⠉⠋⠁⠀⠰⠆⠀⣀⣴⢾⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣶⣶⣶⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⢸⣆⣼⢶⡇⠀⠀⠀⣠⠖⢸⠿⠟⠉⣹⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣀⣀⠀⠀⢹⣿⣿⣿⣿⣥⣀⣽⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⣹⠀⢸⣿⡿⠶⠿⣦⣤⡾⠃⠀⠋⠀⠀⢠⣿⣿⣿⣛⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⡿⠟⠛⠀⠀⠀⠀ ⠀⠀⠀⢀⡈⠀⠀⠀⣾⠋⠀⢸⣿⣿⡀⠀⠸⠉⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣽⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⡀⠀⠀⠣⣤⣰⣿⣿⣿⣷⢦⣤⠀⠀⣰⣿⢩⣾⣿⣽⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠇⠀⠀⣠⣿⣿⣿⣿⣿⣿⣾⣟⠆⠀⢏⣴⣿⣿⣿⣿⣿⡇⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⠒⠒⠒⠒⠚⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⡿⠿⠇⠀⠀⠻⠛⠋⠉⠉⠉⠩⢅⣀⠀⠀⠁⠉⠉⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣽⠏⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⣠⠖⠂⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢸⣿⡿⠿⢿⣿⣿⡀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠏⠠⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣽⡆⠀⠀⠈⣿⣿⠀⠀⠀⠙⢧⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⡋⠐⠒⠀⠈⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⣀⣤⡤⠖⠒⠛⠉⠉⠉⠁⠀⣷⠀⠀⢸⣿⣿⠀⠀⠀⠀⠸⣧⠀ ⠀⠀⠀⢰⣿⣿⣿⣿⣿⠏⡼⠁⠀⠀⠀⠀⠀⠀⠛⣆⠀⠀⠀⠀⠀⠀⡷⢖⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⢀⣼⡃⠀⢰⣿⣿⣿⣦⣤⣀⡀⠀⢹⠀ ⠀⠀⠀⣾⣿⣿⣿⣿⡟⡰⠀⠀⠀⠀⣀⣀⣀⣤⡤⣾⡄⠀⠀⠀⠀⠀⢻⣾⣿⣿⣿⣿⣿⠿⠦⠤⠴⠞⠋⠈⠛⠛⢋⣿⣿⣿⣿⣿⣿⣟⣷⣾⠀ ⠀⠀⠀⠛⢡⣿⣿⣿⠃⢿⡤⠴⠚⢻⣿⣿⣿⣷⣄⣼⣧⡄⠀⠀⠀⠴⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⠛⠛⠿⢿⣿⣿⡀ ⠀⠀⠀⠀⠸⠋⣿⣿⠀⠘⣧⡀⠀⣿⣿⣿⣿⡿⠟⠃⠈⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⠀⠀⠀⠉⠻⣇ ⠀⠀⠀⠀⠀⠀⣿⣿⠀⣆⣸⡏⠛⠛⠋⠉⠀⠀⠀⠀⢀⡴⠋⠉⠙⠳⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿ ⢀⣀⣀⡀⠀⣠⣿⣿⡆⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣦⣤⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⣴⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀ ⠀⠀⠀⠀⣹⡟⠁⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⣿⣿⣿⣿⣷⠁ ⠀⠀⠀⠀⠋⠀⠀⠀⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⢿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⡗⠀⠀⠀⠀⠀⣿⡿⠿⠿⠛⠛⢋⣽⣿⣶⣄⡐⠀⠀⢼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠻⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣷⣄⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⣽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣽⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣦⡀⠀⢀⣤⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡧⠾⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠚⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣯⣿⣿⡟⣁⡀⠀⢀⠀⠀⠀⠀⣀⣤⣤⣤⣶⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣠⣶⡟⣥⡤⠤⠤⠤⠤⣀⣀⠈⠉⠳⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⠋⣁⣷⠞⠉⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠐⠈⠛⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣟⣷⣿⡿⣾⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠰⣬⡓⢄⡀⠀⠨⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣽⣿⣿⣿⣴⠟⠀⣤⣤⣀⠀⠀⠀⠀⠀⠙⠂⠀⠙⢦⡘⢦⡀⠀⠈⠻⣿⢷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡼⠋⠉⠀⠀⠀⣿⠀⣼⣿⣾⡿⠛⠳⢄⡀⠀⠀⢦⡀⠀⠀⠻⣶⣿⣧⣀⢠⣘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡇⠀⠀⢰⣦⣤⣄⣀⣻⣿⠿⠖⠒⠒⠒⠿⢷⣄⡈⠳⣄⠀⠀⠘⢧⡙⢿⡀⣿⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠈⢿⣿⣿⣿⠛⠁⠀⠀⠀⣀⣀⣀⣀⣈⣻⣷⣜⣷⣦⡀⠘⣧⡗⣿⡸⣟⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠈⣯⠀⡟⠀⠀⣀⠀⠀⠉⠹⠍⠉⡁⣀⣤⣟⣿⣿⣿⣦⣸⡅⣿⣿⣿⣦⣙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣧⡀⠀⠀⠀⠈⣧⡇⠀⠀⣿⡀⠀⠀⠀⠀⢈⡿⣿⣿⡿⠋⠻⣿⢿⣿⣿⣿⣿⡿⠻⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣧⡀⠀⠀⠀⠈⣷⠀⣸⠃⡁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠈⢿⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣾⣿⣄⠀⢦⡀⠘⣷⣣⣴⢶⣳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⡟⠃⠐⠊⠉⠉⠉⠑⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⠙⣾⡀⠈⠙⢦⡉⠿⣌⠛⠉⠀⠀⠀⠀⠀⣀⠀⢀⣠⡄⠀⠀⡾⣿⠈⠓⠀⠀⠀⠀⢀⡄⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠃⠈⠳⣄⠀⠀⠙⢦⣙⣦⡀⠀⠀⠀⠀⢙⣡⡴⣿⣽⡇⢀⣼⠃⡿⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠉⢻⣿⣤⣀⠀⠀⠘⠻⠗⠚⠃⣠⣾⡏⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⢰⡀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣄⠙⣿⡙⠛⠛⠒⠲⠖⠒⢛⡽⠋⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⠀⢸⣷⡄⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠀⠀⠠⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠛⠻⠿⣄⡰⠶⠶⠶⠾⠋⠁⠀⠀⠀⠀⣴⢫⠟⠀⠀⠀⠀⠀⠀⠀⠈⣧⣷⡀⠀⢱⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠤⠶⠖⠦⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣇⠀⢸⡆⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡏⠁⠀⠀⠀⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠸⡇⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⢠⣤⡄⠀⠀⣷⠀⢳⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠘⢿⣦⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⠀⠀⠘⣿⣦⡀⠀⠀⠘⠛⠋⢀⣼⣿⡀⠈⢧⠀⢠⡟⠀⠀⠀⠀⢰⠟⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠙⢧⣙⠻⠟⠒⠾⢟⣻⢿⡀⢧⡀⠈⠇⣸⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠹⣇⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠉⠹⠶⠖⠚⠋⠁⠸⡇⠀⢣⡀⢠⡟⠀⠀⠀⠀⠶⢿⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠹⣄⠀⠁⠸⢿⡆⠀⠀⠀⣠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣀⣈⡳⣼⠁⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠈⠳⢄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠘⠁⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠑⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⠙⠻⣷⡛⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⠹⣝⠶⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡔⣆⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⣆⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⠔⠒⠒⠒⠠⠤⠼⣿⢧⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⢻⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⡳⣄⠀⠀⠀⠀⠻⡮⣷⣄⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⣀⣀⣀⡀ ⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣬⠳⣄⠀⠀⠀⠳⡌⠻⣦⡀⠀⠀⠀⠀⠀⢀⡘⠦⠀⠀⣀⣠⣶⣛⣁⠀⠈⠉⣭⡉⠁⠀ ⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠦⠤⣤⠀⢀⡀⠀⢀⣀⣠⣤⡴⠶⠒⠂⠀⠈⢳⡝⣦⠀⠀⠀⠹⣄⠈⣹⠶⣄⡀⢠⣶⣾⠯⣴⣷⡟⠉⠀⠙⣿⠛⠛⠛⠻⢛⢻⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣶⣾⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⣮⣦⠀⠀⠀⠘⢳⣍⣘⢷⣄⣸⣿⣯⣧⣬⣿⣦⣀⣀⣠⣿⠛⠛⠃⠾⠀⢸⡇⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀⠀⠙⡎⢷⡀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡤⠀⠀⠀⣿⣆ ⠀⠀⠀⢧⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⠛⠶⣤⡀⣴⡇⢘⡇⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿ ⠀⠀⠀⠸⢧⡐⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⣀⣼⣿⣟⡆⡼⠃⠀⠀⣀⣀⣀⣀⣀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠙⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠋⠜⠁⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫ ⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠦⠴⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣾⣿⣿⣿⣿⣿ ⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠚⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠉⠻⢿⣿⣿⣿⣿⣿⣿⣾⡷⠀⠻⣏⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠠⣾⡟⢿⣦⡀⡀⣿⠃⠙⣿⣦⠂⢉⡐⡀⠀⠀ ⠀⠀⠀⣀⠀⠀⣸⣿⠀⠘⣿⡾⢽⡿⠀⠀⠘⣿⣆⠐⣷⢢⠀⠀ ⠐⠁⠀⡤⢸⢠⣿⠇⠀⠀⣛⣧⣾⡇⠀⠀⠀⠹⣿⣖⣛⣻⠀⠀ ⠀⠀⠀⢧⢸⣜⣆⢀⠔⠞⢋⣿⣿⣷⣶⣦⣤⣄⣹⣿⣯⡽⠀⠀ ⠀⠄⠀⣊⣸⣷⣀⠁⣠⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⠀⠈⢠⣾⣿⣿⣿⣤⣽⣿⡿⠇⠹⠟⠛⠛⣛⠛⠛⢿⣿⣷⡀⠀ ⠀⢠⣿⣿⣿⠹⠛⠋⠁⠀⠀⢀⠊⠀⠀⣀⣀⢡⠀⢸⡏⠙⢃⠀ ⢀⣿⣿⡏⠃⠀⠀⠑⡄⠀⠀⢄⣶⣿⣦⠀⣀⢼⣠⣾⣧⣤⣈⡆ ⠘⡹⣿⠰⡒⣲⣿⣯⠧⠀⠀⠊⠉⠉⠁⠀⠀⠀⢠⣿⠙⠛⠿⡇ ⠀⠀⣿⠠⠋⠉⠁⠀⢠⠊⠉⠒⠀⠀⠀⠀⠀⠀⣾⣏⣀⠀⠀⠀ ⠀⡾⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢛⣿⣿⣶⡄ ⠀⠁⢠⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⡿⠋⠀ ⠀⠐⢿⣿⣿⣿⣿⣶⣶⣦⣤⡶⠀⠀⠸⠟⠛⠻⣿⣅⡀⡇⠀⠀ ⠀⠀⢀⣈⠉⠉⣉⠟⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀ ⠀⣰⣿⣿⠓⠛⠁⠀⣀⣀⣤⣴⠂⠀⠀⠀⠀⠀⣰⠛⠛⠉⠀⠀

⢀⡿⠁⠀⠀⠀⢠⠏⠉⠹⣄⠀⠱⡴⠃⠀⢀⣾⣿⣿⡷⢫⡶⠋⠁⠟⠿⣿⠁⠀⣿⠀⢸⡞⡄⠀⢳⠀⢡⠀⠑⣆⠀⠀⠀⠈⠻⡧⡈⢆ ⢸⠁⠀⠀⠀⠀⡎⠀⠀⠀⠀⠑⢢⡄⠀⠀⡼⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣸⠀⢰⣿⠀⠀⡇⡇⠀⠈⡆⠀⡆⠀⠈⢷⡀⠀⠀⠀⠹⡌⠪ ⠆⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢸⠈⠢⣸⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡜⢿⠀⠀⡇⢧⠀⠀⢹⠀⢁⠀⠀⠀⠻⣄⠀⠀⠀⠹⣄ ⠀⠀⠀⠀⠀⠂⠀⢀⡆⠀⠀⡄⢸⠀⠀⠈⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢰⠃⢸⠀⢀⡇⣼⠖⠒⠺⡄⢸⠀⢱⡀⠀⢼⢷⣄⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡄⢸⠀⣀⣀⡀⣸⣀⣀⠀⠀⠀⠀⠀⠀⢸⢠⠇⠀⣸⠀⣸⠁⢸⠀⠀⠀⡇⠘⠀⢸⣧⠀⠸⣄⠈⠲⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢰⣧⣼⠿⠋⠉⠁⢸⠉⠙⠛⠄⠀⠀⠀⠀⣼⠏⠀⠀⡇⠀⠁⠀⢸⠀⠀⣀⡇⠀⠀⢸⠙⡄⠀⡿⡆⠀⠈⠑ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⢻⠸⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⢰⠃⠀⠀⠀⡾⠊⠉⣩⡇⠀⠀⣾⣙⣇⠀⣇⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⢧⠀⠀⣼⡄⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⡼⢁⣴⣿⣿⠃⠀⣸⣿⣿⣿⠀⣸⣽⡆⠀⠀ ⠆⠀⡀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠈⣣⡀⣿⣷⡀⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣠⣾⣴⢗⣿⣿⣿⣿⣏⣉⠉⠀⠈⣏⠀⣿⣿⣧⠀⠀ ⡆⠀⠀⠀⠀⠀⠀⣷⡄⡜⢻⣆⣬⣴⣿⣿⣿⣿⣿⣿⢷⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⣿⣿⣿⣿⣿⣷⡄⠀⠉⠙⠛⣿⣿⠀⠀ ⠘⠄⠀⠀⠀⠀⠀⣿⡷⢿⣿⣻⣿⡿⠛⠋⣩⣯⣿⣟⡛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠉⠙⠁⢸⣿⣿⠀⠀⠀⢀⣿⣿⠀⠀ ⠀⠀⢀⠀⠀⠀⠀⣟⣡⣾⣿⡿⠋⠀⢀⣾⣿⣿⣿⠿⣿⣦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠳⢄⣀⡾⠛⣿⠀⠀⠀⢸⡟⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡏⠀⠀⠀⣼⣿⡇⠈⠁⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣤⣴⠞⠁⠀⠀⠀⠉⠁⠈⠀⠠ ⡄⠀⠀⠀⠀⠀⢀⠈⣿⣿⡇⠀⠀⠀⠹⣇⠑⠤⣄⣠⢟⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷ ⠃⠀⠀⠀⡄⠀⠸⡄⠘⣿⣿⣆⠀⠀⠀⠙⠷⢦⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣷⠀⠸⣿⠿⣷⡄⠀⠀⠀⠀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃ ⠀⠀⠀⠀⠀⠀⢀⣿⣷⡀⠘⣆⠈⠁⠀⠀⠀⡠⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠠⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀ ⠀⠀⠰⠀⠀⠀⢸⠏⢻⡟⢦⠈⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⢠⠤⣔⣊⡡⠤⠖⠒⠒⠲⣀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠀⣾⣦⠀⠱⠘⣷⣔⠳⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀ ⠀⠀⠀⠀⠀⠀⣿⡎⢧⠀⠀⠘⣆⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣇⠀⠀⠀⠀⠀⢀⣀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⢠ ⠀⢀⠀⠀⠀⠀⡇⠙⢌⣣⠀⠀⠸⣆⠀⠀⠉⠓⠀⠀⡀⠀⠀⠀⠀⡄⡴⠉⠉⠉⠙⠋⠉⠉⠙⣇⠀⢸⠇⠀⠀⠀⠀⠀⣠⣾⠏⠀⠠⠄ ⠤⠞⠀⠀⠀⢀⡇⠀⠀⠉⢇⠀⠀⡟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠈⠀⠀⠀⠀⢸⣄⡞⠀⠀⠀⠀⣠⠞⠁⡟⠀⠀⢀⠀ ⠀⠀⠰⠀⠀⢸⠀⠀⠀⠀⠈⣆⠀⣷⠀⢻⡷⣦⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⠇⠀⢀⡴⠊⠀⠀⢸⠃⠀⡄⠠⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡀⣿⠀⠀⢻⣏⠻⣿⠶⣄⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⡼⠏⠀⣀⡴⠋⠀⠀⠀⠀⣾⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣇⠇⠀⠀⠀⠹⣷⣌⢱⡜⣄⣽⣛⣚⣷⠀⠀⠀⠀⠀⣠⠞⠀⠄⣸⠋⠀⠀⠀⠀⠀⠀⣿⠀⠆⠀⠀⠀

⠀⠀⠀⠠⠂⠀⠀⠙⠉⠀⠀⠀⣠⠀⢀⡀⠀⠀⠀⣀⠣⡀⠀⣸⡀⠀⠀⠀⠀⠀ ⠀⢀⣀⠠⣴⢄⣀⣀⠀⢀⣴⡞⠙⣑⠔⠀⠀⠀⠌⡰⠁⣸⣢⣍⡎⢘⠈⠁⠀⠀ ⠀⠀⢀⣼⢁⡾⠋⠉⣹⢻⢯⡇⠸⡟⠀⠀⠤⡎⡔⠁⠀⢻⣷⢻⣷⠀⣱⢁⠀⠀ ⠀⠀⢹⣁⡞⠁⠀⢠⠃⡜⢸⠘⣠⡇⠀⠀⡼⢸⠀⠒⡄⡎⠻⣿⠹⢸⠭⠉⠀⠊ ⣰⢅⢸⣝⡡⠠⢠⣿⢖⠁⣾⡀⠘⣝⠀⠃⣧⠛⡄⠀⢱⡱⡀⢻⠶⡁⠀⠁⠃⠁ ⢡⠸⢌⣇⡀⡗⢯⢻⡜⠀⡇⢇⡤⠋⠀⠀⢻⣢⢛⢼⡀⢻⣽⣌⡇⠑⠦⡄⠀⠀ ⡄⠀⠀⠈⡆⠀⢸⢸⣇⢧⡗⠈⢒⡀⠀⠀⠄⢇⠙⢄⠙⠣⣣⡙⡇⠀⠀⡹⠂⠀ ⣧⠈⠰⠤⣇⠀⠸⠙⣡⣾⢿⣿⣿⡿⣄⠀⠀⠈⢆⡴⣤⠷⠾⠿⣧⠀⣸⠁⢠⣀ ⣷⣿⡍⢿⣷⡈⠒⠧⣟⠱⠞⠻⠙⠄⡆⢱⠤⠄⣈⠣⡀⠀⠀⢠⡉⣱⣡⣤⡾⣿ ⣿⣻⣿⣾⢷⢫⠁⠐⠌⡫⡀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⢀⠂⣠⠹⠧⠻⠋⠀ ⣿⣿⣿⣿⣄⣉⣣⣄⡀⠈⢌⠂⡀⠀⠀⠀⠀⠀⠀⢀⠀⣰⢉⠅⠋⣀⡴⠋⠀⠀ ⠹⣿⡻⣷⣾⡉⠂⠐⠯⡟⠶⢧⢹⡀⠀⡾⠓⠚⠙⠛⡟⡧⠁⡰⠚⢁⢴⡆⠀⠀ ⣶⡵⠉⠀⣠⣞⣄⠀⠀⢺⠷⣦⡷⡽⣄⠁⠀⠀⡀⢠⠀⡑⠝⠮⡏⠀⡼⣷⣴⣷ ⢛⡀⠀⢰⢿⡿⡟⢤⣦⢌⢪⠀⢀⣽⣄⠻⡓⣲⠖⢁⣸⣀⢤⡄⣧⠀⣇⡉⡿⠻ ⢄⠠⠔⡡⣫⡊⡄⣠⣞⣗⣩⢟⠟⡿⡽⣔⢼⡟⣰⣟⣿⣿⣷⣿⣾⡀⣿⠁⠀⠀

⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⠯⡽⣿⣧⣼⣯⣙⡏⠉⠉⠫⡷⠶⡴⠦⢶⠶⠆⠤⠀ ⣤⣤⣤⣤⣤⣤⣤⡴⠋⣑⢞⠍⠀⣸⣆⠀⠀⠗⣶⠀⠀⠰⠀⠈⠁⠁⠀⠉⠀⠀ ⠿⠿⠿⠿⠿⢻⡿⣽⣿⡿⢳⡖⣨⠏⠸⡜⡀⢡⠈⡆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠁⡻⢿⢣⣟⣛⠉⢡⠃⠇⡇⠀⠀⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣼⠀⣇⠄⣆⠉⠉⠉⠘⣜⣼⢇⠜⢀⣿⣤⠤⠤⠄⠀⠀⠀⠀⠀⠀ ⣿⣿⢇⡐⠃⠙⣷⣻⠑⡄⠀⠀⠀⠀⠀⠑⢪⣪⡾⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠁⠐⠁⠀⠀⠘⢿⣧⡏⠢⣀⠀⠀⣀⡰⠟⠁⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡃⠀⠀⠀⡠⠊⠉⠉⠙⠥⠀⣀⢙⣯⡥⠤⠤⠤⣀⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⠀⠀⠀⡤⠀⠀⠉⠉⠐⠢⠀⠐⠂⠒⠳⢌⣀⠀⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠈⡄⠀⠀⢰⠀⠀⠀⠀⠓⠀⠀⠈⠆⠀⠀⠀⠀⠽⣴⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⣀⣵⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⡆⠀⠀⢱⠤⠀⠀⠀⠤⠐⠊⠈⠢⣀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣧⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠊⠹⠀⠀⠀⠀⠀⠀⢻⠟ ⠀⠀⠀⣿⣿⣿⡆⠀⠀⣷⡠⠀⠀⠀⠀⠀⠀⠘⠀⠳⡀⠀⠀⡆⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⣽⣿⣿⡗⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡆⡇⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⣾⠿⣱⣷⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠇⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠓⠛⠛⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠑⣸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠹⠀⠀⢋ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⢀⠀⠀⢀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠢⠁⢠⣿⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⡀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡎⢸⣷⡄⠀⠀⠀⠀⠀⢠⣾⡇⢱⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡗⠚⣿⣿⡆⢠⠤⣤⢰⣿⣿⠓⣻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢹⣿⣿⣿⣄⣿⣿⣿⡏⠀⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣲⣿⣿⣿⠿⠿⠿⣿⣿⣿⣖⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣹⣿⣥⣤⡄⠀⡠⣤⢬⣿⣏⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⠀⠀⠈⢉⠁⠀⠀⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⣀⠀⠀⠁⢀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡀⠙⠻⣇⡏⠑⠒⠊⢇⣸⠟⠋⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⢂⡩⠀⠀⠉⠉⠑⠂⠢⠠⠖⠒⠋⠉⠁⠀⠠⡁⠢⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠢⡀⠀⠸⠀⠀⠀ ⠀⠀⠀⠀⡧⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢇⠀⠀⠀ ⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂ ⢰⠀⠀⠀⠠⠤⡄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠄⠀⠀⠀⠘ ⢸⡄⢀⠀⢠⣩⠁⠀⢣⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠊⠀⢈⣁⣄⠀⠀⢸ ⠀⢋⠈⢄⠑⠛⠀⢀⡼⠀⠀⠀⡠⢺⠻⠢⡀⠀⠀⠀⢦⡀⠈⠛⢋⠔⠀⡌ ⠀⠀⠢⣀⠈⠉⠉⠉⠀⠀⠀⠉⠠⡞⠀⢳⢄⠁⠒⠀⠀⠉⠉⠉⠁⡠⠊⠀ ⠀⠀⠀⠀⠁⣲⠤⠤⠄⠀⢂⠠⠊⠀⣧⠀⠁⠍⣐⠂⠠⠤⠠⢖⠈⠀⠀⠀ ⠀⠀⠀⢀⢾⠃⠉⠉⠉⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠉⠉⠀⠈⠱⡀⠀⠀

⠀⠀⠀⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠉⠉⠀⠐⠇⠈⠋⠉⠉⠉⠛⢀⡈⠃⠉⠐⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣿⣿⣾⣿⣿⣿⣿⣷⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣠⣀⣀⡀⢠⣶⡄⠀⠠⢼⡦⢹⣷⡀⠄⠠⠷⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠈⣷⡉⢹⣿⡀⡆⢸⣷⠀⢿⣧⠀⠠⣤⠈⢲⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⡿⣿⣿⣿⣿⣿⣷⠀⠀⢻⣿⡀⢻⣷⠀⠘⣿⣆⢸⣿⣦⠀⢻⣧⣸⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣼⣿⡿⣿⣿⣿⣿⣿⣿⣿⠈⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣾⡿⣰⣿⣿⡇⢹⣿⣿⣧⡀⠈⣿⣧⢸⣿⣷⡀⢸⣿⡈⢿⣿⣴⣷⣿⡟⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠃⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⠿⣦⢷⣄⣼⣿⣿⣿⣿⣿⣿⠿⠋⠿⠿⠋⠸⣿⣿⣿⡇⠀⢿⣿⣿⣷⡸⣿⣿⣿⣿⣿⣷⢾⣿⣷⢸⣿⡄⣿⣿⡇⢿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠈⠻⣿⣿⠋⠀⠈⠓⠶⠾⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠸⣿⣿⣿⡷⡶⠚⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠴⠟⣿⣿⣿⣿⣿⣿⣿⣼⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠋⣿⢈⣷⣀⣀⡀⠀⠀⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⢀⣴⠿⣿⣿⣧⠁⠀⠈⢻⣽⣞⣿⣿⠻⢿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⣿⣿⠀⣠⡾⠋⠉⠉⠉⠉⠉⠉⠙⢦⣸⣿⣿⠀⠀⠀⠀⠀⢀⣰⠟⠁⣶⠟⠉⠻⢀⠀⠀⠀⠹⢿⣌⣿⠀⠀⠹⣏⣠⠾⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡟⣟⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠀⠀⢀⣀⣵⠟⠁⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⠻⣿⣿⣿⣿⣿⣿⢃⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠶⠼⠿⢷⣀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠉⠳⣤⡀⠀⠘⢷⠒⠀⠀⠀⠀⠀⠈⠁⠀⠀⣠⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠙⠷⣤⡸⣦⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠸⣿⣋⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠙⠻⣤⣤⡤⢒⣻⣿⣿⡄⠀⠀⡀⠀⠀⠀⠀⠀⢀⡟⠉⢹⣓⣲⠀⠀⠀⠀⣠⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⣠⣴⣾⣿⣿⣿⣿⣟⣁⣀⣀⣀⣀⣀⣀⣀⣀⡴⠋⠀⠀⠀⠉⠙⢶⣄⠀⠀⠹⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡃⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀ ⣼⠀⠀⠀⠀⠀⣿⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀ ⣿⡀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣀⣀⣀⣠⣤⣴⠶⠞⠛⠉⢡⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇ ⢻⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⣐⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠈⣿⣀⣀⣀⠀⣺⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⠚⠃⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣉⢙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢰⡎⣧⢻⡌⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿ ⣤⣶⣦⣼⣿⡸⣎⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⣛⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁ ⣟⢸⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀ ⣿⣎⣿⠿⣻⢉⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀ ⣏⣿⡏⣀⣫⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀ ⣿⠃⠁⣼⠁⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⣿⢡⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⢠⣤⣤⣤⣴⣿⡻⠍⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀ ⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣱⣄⠀⠀⠀⣴⣯⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀ ⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣦⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⠒⠠⠬⠟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣯⣻⢿⣟⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣝⢳⣬⡻⣿⣿⣿⣿⣿⣿⣿⣿⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣮⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣻⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣽⠁⠀⠀⠀⠀⢸⡇⣀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠋⠀⠀⠀⠀⠀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠦⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡀⠀⠀⠀⣠⠞⢁⣀⡤⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⣤⣾⣿⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣶⠶⠒⠋⠉⠉⠉⠉⠀⠈⠉⠉⠉⠁⠒⠂⠀⠠⣄⡀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⣀⣠⠴⠶⠀⠀⠀⣀⣴⠞⠋⠀⢀⡴⠋⢁⣤⠶⠒⠚⣻⡛⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠋⠁⠀⠀⠀⣠⣾⣿⠁⠀⠀⢠⠊⢀⣴⠟⠁⢀⣠⣾⢻⡶⣽⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠛⣯⣳⣄⡠⠴⠛⠉⡜⡇⠀⠀⢰⠏⢠⡟⠁⣠⡴⣻⡟⣱⡏⢠⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⢹⠁⠠⠀⡞⣠⢏⣴⡯⣿⡿⣻⠟⡹⣱⡿⠀⠀⠀⠀⠀⡔ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠸⣧⠀⠀⠀⡌⣼⠀⡄⢸⡿⣿⣿⣿⣍⢁⡾⠃⣼⣿⡿⠁⠀⠀⠀⠀⢰⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢘⡆⠀⠀⣧⣿⠀⣿⢸⣧⡀⢉⡽⠟⢋⣤⣾⠿⢻⠇⠀⠀⠀⠀⠀⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠘⣿⡀⠀⢹⢻⠀⢹⠈⡏⠻⠃⠀⠀⠀⢸⠻⣿⡏⠀⠀⠀⠀⢀⡼⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠸⣷⣰⣾⣾⡇⣴⠀⡿⡄⠀⢀⣀⡄⠙⡀⣿⠀⠀⠀⠀⠀⢨⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠈⠟⢿⣿⠇⢻⡀⣿⣎⠀⠀⠙⠀⠀⣻⠃⠀⠀⠀⠀⢀⣾⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⣹⠀⢨⣧⣸⡓⠹⣶⣶⡾⠋⡇⠀⠀⠀⠀⢀⢿⢱⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠄⠀⠀⠀⡴⠃⣴⡿⢻⡿⡷⠶⠛⠋⠁⢸⠀⠀⠀⠀⢠⠋⣾⠈⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣦⣴⡶⠯⣖⣚⣭⠤⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠈⢰⡟⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡤⠔⠊⠉⠉⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⣴⣿⣿⠀⣷⡀⠀ ⠀⠀⣠⣤⠔⠊⠁⠀⠀⠀⠀⢠⠔⠉⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⣠⣰⣿⣿⣿⣿⠀⡇⡇⠀ ⢰⠟⠓⠂⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⢰⣿⣿⡟⢸⠃⣿⠀⡷⢳⠀ ⢸⠀⠀⠀⠀⠀⠠⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢀⣾⣿⣿⠀⣿⠀⣿⠀⣇⠈⡆ ⠘⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⢠⣿⣿⣿⡇⢀⣿⢀⣿⠀⢸⠀⠀ ⣇⡄⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠞⢁⣴⣿⣿⣿⣿⡇⢸⡿⢸⢻⠀⢸⡀⠀ ⠸⣳⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣶⣿⣿⣿⣿⣿⣿⡇⢸⡇⣾⠸⠀⢸⡇⠀ ⠀⠙⢧⣀⠀⠀⠀⠀⠀⢀⣼⡷⠦⢄⣀⣀⣀⣀⣀⣠⡤⠖⠛⠉⣼⣿⣿⣿⣿⣿⣿⣹⣿⡇⠸⣇⡏⢰⠀⠈⠁⠀ ⠀⠀⠀⠈⠛⠒⢶⢴⡞⣽⠟⠀⠀⠀⠈⠻⣍⣁⠂⢻⢦⠀⠀⠀⡽⣿⣿⣿⣿⣻⡟⣿⣿⣷⢨⢹⠀⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⠀⡷⡄⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠲⢤⣀⠱⢿⣿⣿⢸⣿⡇⣿⠋⠀⡖⡌⢰⠰⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠁⢱⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣿⣿⣼⣿⠇⣿⠀⣶⢹⡇⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⣿⣿⣷⡏⢰⣿⡸⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠘⢤⠀⠀⠀⠀⠀⠀⠀⠀⢻⣠⣀⣹⣿⣻⣿⣃⡀⢸⠇⠀⠘⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡄⠀⠀⠈⢟⠀⠀⠀⠀⠀⠀⠀⠰⠿⣷⣘⣿⣿⣿⣿⣿⣾⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣎⢹⣿⣿⢀⡙⠟⣧⣴⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣿⣿⣿⣿⣿⣧⠀⠻⠻⣴⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⢿⣋⣏⣤⣴⢤⣤⣽⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⢿⣿⣹⣿⣿⣿⣿⣻⣺⣿⣿⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣍⠼⢿⣿⡿⠿⠛⢉⣻⣄⣹⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣿⠗⣟⣹⡮⢛⣂⣼⠖⢉⢙⣺⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡬⡿⠖⣿⠽⡤⠿⠟⠓⢦⣀⣾⡟⢾⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡿⣴⣯⢤⣀⡈⠀⢀⣤⠀⢀⣿⣛⡟⠻⢻⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡒⢤⠤⡤⢤⠽⢍⣩⣳⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡒⢖⠒⡈⡘⠦⢘⣎⢶⠁⢻⣠⣄⡉⡡⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⢄⢣⢸⢌⠳⠒⡀⡸⢦⠚⠫⠳⢿⢿⣶⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⣤⠌⢒⠻⣿⣏⣀⣀⣠⢺⣦⠹⣿⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⠐⡫⠋⢈⠫⣊⣽⡫⠖⠁⠀⠀⠀⠀⠀⠀ ⣠⡔⠂⣨⢩⠝⠁⠂⢄⠀⠀⠀⢀⡞⢲⠀⠀⠀⠹⡀⠀⡑⡄⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠺⡏⠀⠀⢄⡶⠁⢂⠄⠒⡓⠚⠶⡂⠀⠀⠓⠄⠈⢾⣷⡀⢠⠀⠀⠀⠀ ⢘⢟⡠⠄⠚⠂⠀⣳⣡⡔⠁⠀⠃⠀⠀⠀⠈⠔⠢⢤⠘⢦⡞⣻⣤⡪⡇⣀⠀⠀ ⢸⣾⡇⠁⠀⢀⠌⠀⠀⣇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢈⠖⣡⠆⠀⣰⡄⠀⠀⠀ ⠈⢿⣇⡄⠀⣎⠀⠀⠀⢩⠁⠀⡈⠀⠀⠀⠀⠀⠀⠀⡆⠀⠻⣆⠀⢩⣡⠀⠀⠀ ⠀⠐⠛⢇⠀⡇⠀⠀⠀⢼⠹⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠢⡀⠀ ⠀⠀⠀⢀⢆⢧⡀⠀⠀⠀⠁⠝⣷⠤⡏⠐⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡇⠀ ⠀⣀⡼⢋⠜⢋⠁⠀⠀⠀⠀⠀⡈⠰⡷⠀⠀⠀⠈⠁⠐⠠⠄⣠⣀⣠⠏⠙⡇⠀ ⠒⠂⠎⠁⡀⠘⡦⠀⠀⠀⠀⢀⢧⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢸⣇⠀ ⠓⠈⠁⠀⠀⢻⡅⠂⠄⠀⠀⠌⠈⡄⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠼⡀ ⠀⠀⠀⢀⣀⣘⡁⠀⠀⢀⠎⠀⠀⢰⠀⠹⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠉⠙⣟⠻⣶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⣤⠤⠄⠚⠳⠈⢢⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣊⣁⠀⠀⠘⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠉⣠⠟⠁⠀⠀⣀⠠⣵⡀⠉⢉⣭⡽⠛⠉⠁⠀⠁⠑⠒⠲⠤⣀⠀⢀⠤⢲⡿⠫⠟⢋⡟⠁⠀⠀⠀⠸⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢠⡞⣥⢄⡤⠒⠉⠀⠀⢀⡭⢤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠉⠥⡔⠁⠀⠀⠀⠈⠉⢉⡽⠆⠀⠀⢇ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⡠⠛⡪⠂⠀⢀⠀⡰⠃⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢠⠀⠀⠀⠙⢤⡄⠀⠀⠀⠸⣷⠄⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⠊⢠⠞⠀⠀⢠⠋⡸⠁⡼⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⣠⠃⡄⠀⠀⠀⢄⠘⣦⡀⠀⠀⠘⡆⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⣰⢟⠅⡠⠃⡄⠀⢠⠇⠀⠁⡜⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢹⠀⡃⠀⠀⠀⢸⡄⠀⠙⢆⢢⣸⠇⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⢀⠜⢡⣫⡾⠁⡜⠀⢀⣾⠀⠀⡜⠐⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠈⡾⣇⠀⠀⡄⠐⣿⡀⠀⠈⠉⠙⣆⠀⠀⠀⢄ ⠀⠀⠀⠀⡴⠋⣰⠟⢡⠃⢰⠁⢠⠏⢹⠀⡼⠀⣀⣨⡟⠉⠀⠀⠀⠀⠀⠈⣻⠟⠲⢤⡀⣇⣿⡀⠀⢱⠀⢹⣧⠀⠀⠀⠀⢻⣆⠀⠀⠀ ⠀⠀⢀⣾⠟⣿⠏⠀⡎⢀⡇⠀⡞⢂⣼⣼⡗⠛⠉⠀⢧⠀⠀⠀⠀⠀⢰⢠⠃⠀⠀⠀⠈⢻⣧⣧⠀⠈⡆⠘⣿⡀⠀⠀⠀⠀⠏⠆⠀⠀ ⠀⣠⣿⠏⣰⡏⠀⠀⣇⡾⡁⡸⠀⠀⠀⠙⠓⠀⠐⠒⠺⣧⡀⠀⠀⢠⣿⡏⠀⠀⠄⠀⠀⠘⣿⠘⡆⠀⡇⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⣿⡏⠀⢿⡇⠀⠀⣿⢀⣷⡇⠀⢀⣀⡀⣀⣀⣀⢀⡀⠈⠛⢄⡀⡼⣿⠀⠠⠤⢀⣀⠀⠀⠹⡇⠹⡀⢃⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⡼⠀⠀⣸⠁⠀⠀⠙⣺⣈⣳⣶⣞⣛⣋⣉⠉⠻⡿⠋⠀⠀⠀⠈⠉⠩⠄⢠⣴⡾⠷⠾⣵⣄⡹⣄⣣⣾⠀⢸⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⣸⠁⠀⠀⡇⠀⠀⢀⠄⡏⠻⢯⣈⣦⣤⡽⣍⠤⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣙⣦⣄⡠⠭⣿⣿⣿⢹⡄⠂⠀⢰⠃⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⢸⠀⠀⠀⡜⢸⡇⠀⠀⠉⠉⢉⣀⢤⡴⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⣀⡛⠁⠽⠿⡇⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡞⠀⠀⣰⢃⣾⠆⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡼⠀⢀⠎⠀⠀⠀⡞⠀⠀⠀⠀ ⠀⠀⢠⡇⠀⠀⣟⣼⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⠎⠀⠀⠀⢸⣧⠀⠀⠀⠀ ⠀⠀⣾⠁⠀⢠⣿⡏⢹⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣥⣤⣄⣉⡓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢠⠏⠀⠀⡄⢀⠋⠻⡇⠀⠀⠀ ⠀⢰⣿⠀⠀⢘⣿⣿⣼⡀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⣿⣿⣿⣿⣿⣷⣟⣦⠀⠀⠀⠀⠀⠀⠀⣰⠃⡰⠃⠀⠀⡜⠀⡾⠀⢀⡆⠀⠀⠀ ⠀⡿⢻⣄⢰⣿⡟⣿⠈⢧⠀⠀⠀⠀⢀⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢀⠞⢁⠞⣡⣶⣄⡜⠀⣘⡠⣾⠏⠀⢰⠀⠀ ⠀⠇⢸⣿⠀⢹⡿⢿⠂⠈⣧⠀⢀⠖⠉⠈⢱⠀⢿⡿⠉⠀⠈⠁⠀⣹⠇⠀⠀⠀⠀⢀⡴⢋⠀⠀⠀⠛⠓⡶⠀⡘⢁⡔⠁⠀⢠⠃⠀⠀ ⠘⠀⠈⣿⡦⢼⡅⠘⡆⣀⣾⣷⡀⠳⢄⣠⠎⠀⠈⢳⣦⣤⣤⡰⠞⠁⠀⠀⠀⢀⡴⢋⣰⠋⠀⠀⠀⢀⡾⢧⣿⠟⡁⠀⢀⢾⠇⠀⠀⠀ ⠀⠀⠀⠘⣿⡈⡇⠀⣟⠛⠉⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠈⣇⡀⠀⠀⠀⢀⡤⠋⡠⣾⣿⡤⣴⡶⠀⠛⠀⣼⣃⡜⠁⢀⢞⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣧⣱⠼⠛⠁⠀⠀⠀⠀⢹⣦⣄⠀⠀⠀⠀⠀⢸⡇⠀⣠⢖⣩⠔⠋⣠⡋⠁⣀⢋⠀⠀⢀⣾⣿⠏⠀⢀⣞⣾⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣿⣆⠀⠀⠠⠀⣤⣶⣿⣿⣯⠀⢀⣀⠀⠀⠐⠒⣛⣻⠭⡔⠒⢉⠉⠁⠀⢨⢉⡀⢀⡞⣼⠏⠀⢦⣿⠏⢸⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣯⣿⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢶⡀⡀⠀⠀⠀⠀⠀⠀⣰⣿⣃⣛⡗⣼⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢷⣬⣷⣤⣤⣴⣢⣶⣿⣿⣿⢿⣗⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣿⠿⣿⣿⣷⠿⡿⣿⣷⣿⣿⣿⡟⠻⣿⡧⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣹⣿⡿⡿⡀⣧⣼⣟⠉⠙⢾⣷⣣⢘⣿⣿⡿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣿⣷⣧⣳⢿⣏⠁⣿⡿⠀⣿⣿⣿⣯⣿⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣿⣿⣿⣿⠟⣻⠖⠋⠀⠀⠉⣿⣿⣟⣽⢿⣿⣟⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠛⢯⣷⣿⠀⠀⠐⠀⢀⣬⣶⣿⣬⣽⣿⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣏⡀⠀⣠⠖⠛⠉⠛⠹⠋⠙⠛⠉⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⠟⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠐⢮⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡸⠥⠀⠀⠀⢀⣇⠀⢀⠀⢀⣀⠤⠆⠤⢄⣙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣷⡆⠈⠢⣀⠀⣿⣠⠎⠀⣩⣤⠤⠖⠒⠒⠚⠧⠼⣦⣀⣠⠤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠘⠷⢿⣻⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠉⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠀⡀⢠⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⢦⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡽⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⣰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠚⠉⢻⣞⡹⠛⠳⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡤⠤⠤⠤⣄⡀⡀⢀⣴⣁⣀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠲⠭⡛⣹⣯⠝⠛⠉⠉⠉⢷⣶⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⢹⣿⢿⠀⠀⠀⠀⠀⠀⠉⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠤⠤⠤⣀⡀⠀⠀⡸⠻⣇⠱⣄⣤⠴⠛⠉⠉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠀⠀⠀⠀⠀⠙⢦⡴⠃⠀⠘⢦⡞⠁⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⣺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠖⢺⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣤⠟⢳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢳⡀⡠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣠⠞⢙⣣⣼⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠉⠙⢓⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠟⠋⠁⣠⣿⣿⡒⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⠤⠤⠞⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢒⡒⢚⣛⠋⠀⢿⠿⠃⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿ ⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⠟⠋⠉ ⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢟⣽⠟⠁⡱⢸⣷⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣶⣿⣿⡿⠟⠀⠀⠀⠀ ⣿⣿⡟⠀⠀⠀⠀⣀⣀⣤⣤⣤⣶⠾⢿⣧⠈⠻⣷⣀⣤⣶⣿⡟⠸⠀⠀⠘⠓⢦⣄⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣋⡵⠞⠛⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣶⣶⣿⣿⡿⢛⣻⠟⠋⠁⢦⠸⣇⢧⠀⣹⣯⣿⣿⣟⣤⠴⠦⠤⠤⠷⠦⢭⣓⠀⠀⠀⣾⡿⣿⡄⠀⢀⣴⣴⣾⣿⡿⣿⡟⠛⢛⡟⢻⡙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡉⠉⠉⠁⠀⠀⠡⠴⠛⠁⠀⠀⠀⠈⢧⣙⣴⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢨⣙⢳⣾⣿⣿⣏⣿⣾⣿⣿⡿⠥⠄⣿⠋⠀⠈⠀⢧⠃⣷⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⢀⣠⣴⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣽⣿⣿⠛⢻⣿⣿⠁⠀⠀⣠⣿⠀⢀⣠⣄⣬⣷⣧⣶⣶⣿⣿⣷⣶⣶⣦⣄⣀⡀⠀ ⠀⠀⠀⢀⣴⠋⠁⠀⣠⣴⣶⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠿⣿⣿⣿⣿⣮⣿⣿⣿⣛ ⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢹⡏⠍⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣴⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⡀⠀⡾⠀⢈⡗⠰⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠯ ⠀⠀⠀⣠⣶⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢡⡾⠁⣸⠇⠀⢸⡅⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⢀⣴⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢀⣿⠃⠀⡏⠀⠀⣻⡇⠀⡀⠀⠀⠀⣿⢩⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⣣⠀⠀⢻⣷⠀⡳⠀⠀⣰⣿⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣴⣆⠀⢠⣿⣿⠀⠁⠀⣰⣿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣤⣼⣿⣿⣦⣠⣿⣿⡏⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠿⢿⣿⣿⣳⡌⠋⠿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠏⣀⠀⢰⠟⠛⠁⠀⠀⠸⢿⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡌⣿⣿⣿⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠩⠰⠾⠛⢦⡼⠀⠀⠀⠀⠀⠀⠘⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣶⣭⣟⡳⣾⣭⣝⣛⡲⠶⠶⠶⠤⣤⣤⣤⣀⣀⣄⣀⣀⣤⣖⠋⠑⠲⠆⣀⡤⢖⡿⠃⠀⠀⠀⠀⠀⠀⠀⠉⢻⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣟⣿⣿⣽⣿⣟⣶⡶⠶⢶⣤⣤⣤⣀⣤⣬⣭⣥⣈⣉⣐⣒⡒⠒⠒⠋⠀⠀⠤⠴⠞⢋⡀⠀⠀⠀⠀⠘⢿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣅⠉⠛⠛⠿⣿⣿⣷⣾⣿⣿⣿⣿⡶⠶⢤⣤⣉⡉⠙⠛⠚⠛⠿⢶⣛⡻⠿⢷⣖⡒⠲⠤⣤⣄⣈⣉⠉⠙⠛⠠⠬⢿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠹⣿⣿⡻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡇⠹⣿⣷⡞⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠜⠿⣿⠿⡄⠀⠨⢿⣶⡟⠟⡿⢻⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣶⠄⠀⠀⠀⠀⠈⠓⠃⢠⡇⠀⣿⣿⣿⣿⣿⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣤⣿⣿⣿⣿⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡱⠦⣀⠀⠀⠀⠀⣠⠶⠳⠾⣿⣿⠟⠛⠏⣿⣷⡎⠀⠀⠐⣀⠤⠀⡀⠀⠀⠀ ⠻⠁⢀⡠⠉⠘⠳⡼⠁⢆⡀⠀⠀⠉⠲⠄⡀⠈⠢⠉⢆⡀⠀⠀⠀⠀⠈⠂⠀⠀ ⢀⠔⠉⠀⠀⡄⠀⠣⠤⠄⢉⠁⢐⠦⠀⠀⢬⡗⠀⠑⠌⢟⡒⠒⢄⡀⠀⠀⠀⠀ ⠉⠒⠤⢀⠀⢳⠢⠤⠤⡵⠋⣠⠁⠀⠀⢸⠉⠪⢣⣦⡀⠚⢏⠉⢩⠠⠈⠁⠀⠁ ⠀⠀⠀⠀⠉⠒⠧⡀⢎⡠⠊⣥⠘⡀⠀⠆⡠⣂⣉⠉⢺⡶⠼⡄⠀⠑⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠺⢄⠀⢹⠀⢁⣰⠪⠤⠤⠀⠱⠄⢱⡤⣸⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠫⣉⢡⠆⠀⠀⠀⠀⠀⠀⠈⢷⣈⢇⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢣⢻⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠣⣦⡈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⣿⡜⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠟⠸⠿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⢀⠉⠁⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⢀⣀⣤⣐⣀⣀⣀⣀⣀⣀⣠⣂⡆⠀⠀⠀⠀⠀⠀⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠿⣿⣯⣭⣉⠚⡩⠧⣄⠘⣇⠀⡀⡠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⣠⣿⠛⢻⠿⢿⣶⣦⣀⠙⡿⠳⣌⠶⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠴⣿⡟⣧⡀⣦⣀⠙⠻⢿⣷⣌⡞⠁⠀⠀⠀⠀⣠⠀⠀ ⠀⢀⠤⠂⠙⣀⢿⡿⡈⠙⢧⣽⢿⡷⣛⣋⡟⠀⠀⣀⡴⠞⠉⠀⠀⠀ ⠀⠀⠀⠀⠰⡇⠸⠣⡉⠂⠀⠉⢁⠐⢠⠉⢳⡤⠈⠉⠀⠀⠀⠀⠀⠀ ⠀⡀⠔⠉⠠⠃⣜⡆⠸⠂⠄⡀⠐⠙⡗⠶⢦⣧⣀⡀⠠⠄⣶⠊⠀⠀ ⠈⠀⠀⠠⢁⢀⢀⠶⠀⠀⠀⠀⠀⠘⠀⠒⠉⠁⠀⠀⡠⠒⠕⠀⢀⠆ ⠀⡀⠒⠁⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠟⠋⠩⡑⡢⢄⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠑⢤⢀⢌⡹⠂⢝⢅⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠎⢰⢧⠇⢠⠜⣒⠜⢦⣕⣳⠶⠤⢀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡄⠸⢸⠀⠈⢸⢀⠑⢢⠹⡌⠈⢩⢻⠀⣿⣿⣿⠍⠀⠀⠐⠂⠀⠀⠀⡴⢶ ⣼⠀⣰⠀⠀⢰⠘⡄⠳⡀⠑⢜⠣⢥⡇⣼⣿⡟⠁⠀⡀⠀⠀⠀⠀⠀⣐⣿⣿ ⢡⣆⢱⢸⠀⠈⡆⢱⠀⠘⣦⣀⣱⠀⢠⢿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⡾⣿⣿ ⠈⡾⡀⢆⠣⡀⢸⠈⠋⢨⣽⠟⡝⢀⣾⠋⠈⢿⢿⠿⡿⠶⢿⣿⣷⣶⣿⣷⣿ ⠀⠘⢷⣄⠁⢀⡼⠠⠀⠠⣧⡾⠀⣾⠁⠀⠀⡜⡸⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠛⠛⠈⠰⠶⠾⠁⠀⣸⠇⠀⠀⡰⠕⢁⠜⠁⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⣁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢸⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⢵⡯⠯⠯⠼⠥⠧⠟⠨⠯⠖⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⡼⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣆⠈⡜⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⠸⡇⣿⣿⡇⢻⡈⣿⣿⣿⣇⢻⡀⢻⣿⡈⠁⠈⠘⢻⡿⢿⣿⣿⣿⣧⠀⠸⣷⡀ ⣿⣿⣿⣿⣷⢿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠘⡎⢿⣿⣿⣿⢈⣷⢸⣿⣿⣿⣸⡗⠉⢻⣷⠀⠀⠀⠈⣷⣾⣿⣿⣿⣿⣆⠀⠹⣧ ⣿⣾⣿⣿⣿⣟⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⡟⡇⢹⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⢷⢸⣿⣿⣿⡄⢻⡄⣿⣿⣿⠁⠃⠀⠈⣿⣇⠀⡰⠂⠘⠿⣿⣿⣿⣿⣿⡆⠀⢿ ⣿⡯⣿⣿⣿⣿⣹⣧⠀⢹⣿⣿⣿⣿⡿⣿⠀⢻⠘⣿⣿⡿⣿⣿⣇⠀⡄⠀⠀⠀⣠⣾⣿⣿⣿⣼⡟⣿⣿⣿⡟⠛⣏⠙⣿⡇⢀⣀⣀⣠⣾⣿⣾⣇⠀⠀⠀⢻⣿⣿⣿⣿⣷⡀⠈ ⣿⣇⢹⣿⣿⣿⣇⠗⠀⠈⢿⣿⣿⡿⣿⡛⠀⠀⠀⢻⣿⣧⠹⣿⣿⣠⠃⠈⣠⣼⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⡇⠀⢹⣤⣟⣻⣿⣿⣿⣿⣿⣿⣧⢿⣦⠀⠀⠨⣿⣿⣿⣿⣿⣇⠀ ⣿⣿⠀⢻⣿⣿⣿⡆⠀⠀⠀⢿⣿⣧⢻⣇⠀⠀⠀⠘⣿⣿⣥⣿⣿⣧⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣇⡴⢫⣶⣿⣿⡿⠟⠛⠉⢿⣿⣿⡸⣿⣧⠀⠀⢹⣿⣿⣿⣿⣿⠀ ⣿⣿⡄⠈⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⠀⣿⡄⠀⠀⢀⣿⣿⡿⣏⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣏⣴⣿⣿⣿⡇⠀⠀⠀⠀⠘⣿⡞⣇⣿⡿⣷⠀⠛⣿⣿⣿⣿⣿⡇ ⣿⣿⡧⣄⢸⣿⣿⡿⡆⠀⠀⢨⣿⢹⡇⢸⣧⠀⠀⣸⣿⣿⣿⠹⣸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣾⣾⣿⠃⠀⣿⠇⠀⠀⠀⠀⠀⣿⣀⣻⣿⣷⣾⣧⠀⢿⣿⣿⣿⣿⡇ ⣿⣿⡗⣿⠈⣿⣿⣿⢻⡀⠀⢸⣿⡌⣧⠀⣿⡀⣠⣿⣿⣿⣿⠀⡇⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⡜⣼⡿⠿⠃⢀⡿⠀⠀⠀⠀⣀⣴⣿⡏⠺⣿⣿⣻⣿⣖⢸⣿⣯⣀⢹⣿ ⣿⣿⣇⣿⠀⣿⢿⣿⠘⣇⠀⣿⣿⡇⠿⠀⣹⡟⣿⣿⣿⡿⢸⠀⢱⢹⣿⡇⢹⣿⣿⣿⣿⣿⠟⠁⠀⠸⢁⣿⣧⠒⣠⠞⠁⠀⠀⢠⠞⣭⠈⣟⡀⢋⣿⣿⣿⣿⡿⠦⣿⣿⣿⠀⠛ ⣿⣿⣿⣺⡄⠹⢸⣿⠀⢸⣸⣿⣿⡧⠖⠋⠉⣿⣿⣿⣿⠃⢸⠀⢸⠀⣿⡇⢸⣿⡿⠟⠉⠁⠀⠀⠀⠀⢸⣿⠉⠼⠁⠀⠀⢀⡴⣫⠞⢁⣼⠁⠀⠀⢽⡟⣿⣿⣷⡆⣿⣿⣿⠀⢶ ⣿⣿⣿⣾⡇⠀⢸⣿⣄⡼⣿⣿⣿⠴⠖⠒⠒⢿⣿⣿⣏⠀⢸⠀⠀⠀⢻⡇⣘⠃⠀⠀⠀⠀⠀⠀⢀⠀⠠⠏⠀⠀⠀⣠⠞⣡⠞⢁⡴⠛⣎⡃⠀⠀⢸⢆⢿⣿⣿⡇⣿⠟⢿⠀⠨ ⣿⢿⣿⣿⣇⠠⢾⣿⠇⣠⢿⣿⣧⣤⣶⣶⣶⣾⣿⣷⣶⣯⣁⡀⠀⠀⢸⠀⠈⢣⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⢧⣄⡠⠴⠫⠀⠀⠈⢂⠀⠸⣿⢸⣿⣿⣿⡇⣿⣷⡇⠀⢩ ⠸⡿⣿⣿⣯⠀⢸⣿⣟⣥⣾⣿⣿⡿⠛⣉⡙⠿⠏⠈⣹⡟⠳⠦⣄⠀⠈⠀⠀⠈⣧⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢹⡇⠘⡟⣿⣿⡇⣿⣿⡇⠀⡇ ⡄⢻⡹⣿⣿⣤⣼⣿⣿⣿⡿⠛⠉⢻⠟⠉⣷⢀⣠⡼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢣⣿⣻⣇⣿⣿⠀⠀⠀ ⡇⠀⠀⢻⣿⣿⣿⣿⣿⠋⠀⠀⠀⠉⠀⠊⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⣿⣿⢹⣿⡟⠀⠀⠀ ⢿⡄⠀⢠⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣸⡿⣿⣿⣿⣿⡆⠀⠀ ⡶⠿⣟⠛⡙⣿⣿⣿⣷⣄⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢠⣿⠀⢸⣿⡟⢿⣿⣦⡀ ⠀⠀⢸⣆⢰⡈⣿⣿⣞⠛⢿⣾⠋⠀⢀⣈⡙⢦⣤⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⣼⣿⠀⣸⡿⠀⠀⠈⠛⠻ ⡗⠒⠘⠙⢷⣷⡼⣿⣿⣦⢦⠙⠓⠒⠮⢁⡤⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⡿⠁⠀⠀⠀⠀⠀ ⣿⣼⣷⣦⣌⣻⡿⣬⣿⡿⣇⠱⣄⠀⠉⠉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢘⣶⢶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣸⠃⠀⠀⠀⠀⠀⠀ ⢁⣾⣧⡙⣿⣿⣿⣿⣿⣿⣿⢧⡘⢧⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠛⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⡏⠈⠻⣿⣾⠉⠈⠻⣿⣿⣻⣯⣳⡌⢦⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⣀⣀⣀⣠⣴⣾⣻⠟⠁⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡇⠹⣧⠀⠀⠀⠀⠀⠀⠀ ⣦⡀⠀⠈⠻⣤⣀⣤⣽⣿⣿⣿⣿⡿⣦⡘⡆⠀⠀⠈⢳⣄⠀⠀⠀⠀⣟⣯⢺⢹⡿⠛⠛⠛⠛⠛⢿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣼⢿⣿⣿⣿⣿⣿⡀⠹⣆⠀⠀⠀⠀⡀⠄ ⣿⣿⣶⣶⣦⣬⣿⣿⣿⣿⣿⣿⣿⣿⣮⡓⢾⣤⡀⠀⠈⠿⠂⠀⠀⠀⣿⡟⡸⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢠⣾⠃⠀⠙⠛⠿⢿⣿⣧⣀⣨⡤⠔⠒⠉⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠷⣄⡙⠳⣄⠀⠀⠀⠀⠀⠀⢻⡷⣅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⡆⠀⣰⣿⡟⠀⠀⣀⣠⡤⠶⠚⠉⣉⣀⡤⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠋⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⣦⣈⠳⣄⠀⠀⠀⠀⠈⠣⣈⢻⠄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠃⣰⡿⣿⣠⠞⠉⠁⠀⠀⣠⡴⠞⠉⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣦⣤⣾⡙⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠛⠷⠦⣤⣄⣀⣀⠈⠓⠤⣌⣙⠦⣤⣀⣀⣀⣀⡤⠖⠋⠀⠀⣰⡿⣴⡟⠁⠀⠀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣻⣿⣿⣿⣿⡍⣿⣷⣄⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠙⠢⣤⣀⠈⠉⡉⠉⠓⠒⠒⠯⢭⣭⣍⣉⣉⣱⡀⠐⠂⢠⡾⣋⡼⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠻⡽⣿⣿⣿⠘⣯⣿⡱⣤⡹⣝⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠉⠓⠾⣤⣀⡀⠀⠀⠀⣀⣠⡴⠥⠟⠛⠓⠦⠴⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⢽⠘⢿⣿⡇⠘⡏⢿⠝⢞⣎⢯⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢙⣥⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⠀⠀⢧⠨⣿⣿⣄⢼⡞⣦⢫⣯⣳⡻⡜⣿⣿⣿⣿⡿⠀⠀⠀⣄⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠳⣀⠈⡃⠈⢿⣏⠋⢳⡏⠣⡻⣷⡷⡼⣌⢿⣿⣿⠇⠀⠀⠀⢈⣠⠞⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⡄⠀⠀⠀⢀⣼⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣄⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣿⣿⠟⠉⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀ ⠀⠀⣰⡿⠋⢡⡔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀ ⠀⣰⠋⠀⣀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠈⢆⠀⠀ ⣰⠃⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠋⠉⠉⠀⠒⠂⠀⠀⠠⣌⡇⠀⠀⠀⠀⠀⠈⢆⠀ ⠃⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠈⢦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠚⠉⠁⣀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠁⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣮⣿⣿⣿⣷⣾⣵⣦⡖⠀⢀⣼⠀⠀⠀⠀⠀⣠⣾ ⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⣶⣖⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⢻⡛⠛⠿⠉⠉⠙⠛⠻⣿⠯⢿⠀⠀⠀⢀⡴⢻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣶⣿⣿⣿⠛⠿⠶⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀⠁⠀⣾⣆⠀⢀⣾⣽⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣾⠟⠋⠙⠯⢍⣀⡀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠘⡄⢸⣿⠁⣿⢡ ⠀⠀⠀⠀⠀⠀⠤⣴⣿⢋⠀⠀⢀⡤⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠸⣼⣿⣼⣣⣿ ⠀⠀⠀⠀⠀⠐⠚⠛⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢣⢀⢿⣿⣿⣿⣿ ⠀⠀⢀⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⢸⣼⣿⣟⣻⣿⣿ ⠈⠻⣅⡀⣀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⢸⡏⠉⠉⠁⠈⠉ ⢆⠀⠈⠳⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⢁⣀⡌⣿⣄⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⢸⠇⠀⠀⠀⠀⠀ ⠈⠓⢤⡀⠀⢿⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢻⣦⠀⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢃⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⢿⢻⣿⡇⠀⠀⠀⠀⠀⠀⡼⠁⠀⢀⡄⠀⠀⠀⠀ ⠀⠀⠀⢙⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠉⠀⠨⣿⡀⠀⠸⢿⡇⠀⠀⠀⠀⠀⡜⠁⠀⣠⡞⠀⠀⠀⠀⠀ ⣆⡀⠀⠀⠉⠛⠀⠐⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠈⢷⠀⠀⠀⢃⠀⠀⠀⢀⡞⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀ ⠀⠙⠒⠤⢤⣀⣀⣀⣈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠈⡆⠀⠀⢸⠀⠀⢠⠎⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠾⡇⠉⢻⣷⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⢸⠀⠀⡀⠀⢠⠏⢀⠼⠋⠄⠀⠀⠀⠀⠀⠀⠀⠘ ⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡀⠉⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠘⠀⠀⡇⢀⡎⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠙⢿⣶⣤⡀⠀⡀⠀⠀⠀⠀⠀⠙⡀⠀⠀⢰⢁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠻⣿⣷⣀⣽⣷⣶⣦⡤⠤⢄⣵⠄⠤⠞⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀

⠀⠀⠀⠐⣩⣕⢟⢦⡌⣟⣿⢳⡴⡱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿ ⠀⠀⠐⣿⣞⣢⡄⢛⢻⣿⣿⠇⣏⡪⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⠀⠀⠀⢃⠛⠏⢱⡔⠈⠉⣿⠎⣿⣆⠘⣥⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠐⠄⢹⠀⠀⣰⠻⡄⣧⠣⠱⣌⢳⢽⠀⣴⣹⣷⡄⠀⠀⠀⠀⠀⢸ ⢠⠤⡄⠀⠀⠈⠈⠀⠈⣾⡜⣧⢹⣄⢑⣈⡳⣧⣻⠀⠈⢹⡇⠀⠀⠀⠀⠀⣾ ⠀⠑⣸⡢⡀⠀⠀⡇⢠⣿⡗⢼⠋⢁⡤⠂⠁⠉⠙⣆⣠⡋⡁⠀⠀⠀⠀⠀⣿ ⠀⠀⠨⠛⣊⡀⠀⡇⢈⠟⠀⠈⣕⡏⠀⠀⠀⠀⢀⠗⠁⠀⠣⡐⢤⡀⠀⠀⣿ ⠀⠀⠀⠀⠠⡄⠁⠇⡈⠀⠀⡘⠟⠃⠀⠀⠀⢀⡎⠀⠀⠀⠀⢱⠀⣷⠀⠀⣿ ⠀⠀⠀⠀⠀⠈⠢⢴⠁⠀⣸⣹⠀⠀⠀⠀⢠⣾⡇⠀⠀⠀⠀⣞⣴⠙⡆⠀⢻ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡉⡏⠀⠀⠀⢠⢣⢹⢱⠀⠀⠀⠀⠹⡏⠀⣧⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠘⡕⠊⠁⢣⠀⠀⠀⠀⡿⠊⠀⠀⠀⠀⠀⢆⠁⠀⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠑⡤⢀⢰⡅⠀⠀⠀⠀⠀⡼⡎⠀⣸⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠒⠒⠢⡀⠀⡌⠃⡀⠀⠀⢀⡰⡙⠀⢠⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⡗⣼⢀⠀⠘⠓⠊⠁⠑⢣⡴⠋⠀⠀⠀⣤ ⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⠀⠀⠠⡑⠹⡎⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠠⣿ ⠀⠀⠀⠀⠀⠀⠀⢀⠪⠀⠀⠀⠈⠀⡆⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⢻ ⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⡰⢰⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠇⠃⠀⠀⠀⢈⡏⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡱⠡⠀⠀⠀⠀⠣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⣾⡟⠀⠀⠀⠀⠀⢀⡞⠉⠉⢷⣀⠀⠈⢧⣠⠞⠀⠀⠀⣼⣿⢏⣿⣫⠞⣽⡴⠟⠉⠾⢟⡿⢿⡏⠀⠀⣿⡄⠀⢹⡌⡇⠀⠈⢳⠀⠘⡄⠀⠙⣦⡀⠀⠀⠀⠀⠘⢞⡷⡄⠘⡄ ⢰⡟⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠈⠳⢤⡀⠃⠀⠀⠀⣼⣹⣿⠛⠋⠁⠀⠉⠀⠀⠀⠀⠈⠀⢸⡇⠀⢠⣿⡇⠀⢸⠁⡇⠀⠀⠘⣆⠀⢻⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠻⡜⢦⡹ ⠸⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⢹⠦⡀⠀⢰⠋⢽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣸⣿⡇⠀⢸⡇⢸⠀⠀⠀⢻⡀⠀⡇⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⢱⡄⠝ ⠃⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠈⠢⣞⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢠⡏⢹⠀⠀⢨⡇⢸⡆⠀⠀⠘⡇⠀⣧⠀⢀⠀⠀⠈⢧⣀⠀⠀⠀⠀⠹⣆ ⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⡞⠀⠀⠀⢰⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡼⠁⢸⠀⠀⢸⠀⣸⡷⠞⠛⠓⢧⠀⢸⠀⠘⣇⠀⠀⢰⡻⣷⡀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡇⠀⠀⠀⣾⠀⣟⠀⠀⠀⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣰⠃⠀⢸⠀⠀⣸⠀⢸⡇⠀⠀⠀⢸⠀⢸⠀⠀⢿⡆⠀⠈⣧⠀⠙⢦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⣿⡀⣷⢤⣲⠿⠷⠒⢺⡯⠽⢷⣂⡄⠀⠀⠀⠀⠀⠀⣿⣴⠃⠀⠀⣿⠀⠠⠇⠀⢸⡇⠀⠀⠀⢸⠀⠀⠀⠀⡾⢳⠀⠀⢸⣧⠀⠀⠘⠲⢄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⣯⣿⠉⠀⠀⠀⠀⠸⡆⠀⠀⠈⠉⠀⠀⠀⠀⠀⢰⡷⠃⠀⠀⢀⡏⠀⠀⠀⠀⢸⠇⣀⡤⣤⣼⠀⠀⠀⢀⣇⣸⡇⠀⢸⠹⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⠉⣧⠸⠀⠀⠀⡀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⡼⠛⠁⢀⣀⣽⠀⠀⠀⣼⣧⣍⣧⠀⢸⣆⣿⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢸⠀⠸⣆⠀⠀⢀⣷⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣼⠃⣠⣶⣿⣿⡟⠀⠀⢰⣿⣿⣿⣿⠀⠀⣏⣻⡆⠀⠀⠀ ⣇⠀⠀⠀⠈⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠹⣆⠀⢸⡟⣧⠀⢹⠤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢰⣆⣰⣫⢞⣵⡿⠿⣿⣷⠖⠒⠛⠉⠉⠉⣿⠀⢸⣿⣿⣿⠀⠀⠀ ⡇⠉⠒⠄⠠⠀⠀⠀⠀⣿⠀⠀⣴⡈⡇⣀⠤⠞⣷⣼⣿⣿⣷⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠋⠟⠛⢱⡾⣫⣾⣿⣿⣿⣿⣶⣄⠀⠀⠀⡿⢤⣼⣿⣿⣿⡄⠀⠀ ⢇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⢀⣏⣙⣿⣶⣾⣿⣿⣟⣻⣿⣿⣿⣯⣻⣓⡾⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣿⣿⣿⣿⣿⠿⣿⣿⣿⡄⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀ ⠘⠦⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢓⣿⢋⣽⣿⡿⠟⠋⢉⣠⣶⣮⣿⣝⡛⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠉⠁⠀⢸⣿⢿⡇⠀⠀⠀⠀⢸⣿⢿⡇⠀⠀ ⠀⡀⢜⡀⠀⠀⠀⠀⠀⣾⠟⣡⣾⣿⣿⡿⠋⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣦⡀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⢦⡀⠀⠀⡾⡿⢻⡇⠀⠀⠀⠀⣾⡿⠘⡇⠀⠀ ⠀⠃⠀⠸⠀⠀⠀⠀⠀⢸⣾⣿⣿⡽⠛⠀⠀⠀⢠⣿⣿⠟⠛⠿⠋⠈⢹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠉⠛⠚⢁⣠⡿⠃⠀⠀⠀⠠⠿⠃⢰⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣻⣻⡇⠀⠀⠀⠀⢸⣿⠿⣄⠀⠀⠀⠀⣸⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⡌ ⡆⠀⠀⠀⠂⠀⠀⠀⢣⠀⢹⣿⣽⣇⠀⠀⠀⠀⠘⢻⣆⠉⠓⠦⣄⡴⢋⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠄⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⣴⣧ ⢣⠀⠀⠘⡀⢠⠀⠀⢸⡆⠀⢻⣿⢾⣶⡀⠀⠀⠀⠈⠛⢷⣦⣤⡤⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⡀⠄⢻⣿⣧ ⠀⠀⠄⠀⠠⠋⠀⠀⠀⣿⠀⠀⢿⣯⡿⣿⣦⡀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢸⣿⠇ ⠀⡄⠀⢀⠀⠀⠀⠀⠀⣽⣧⡀⠈⢳⣍⠙⠻⡷⠀⠀⠀⠀⠀⢀⡠⣶⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀ ⠠⠁⠀⣸⠀⠀⠀⠀⢀⡿⣿⣷⣄⠀⠹⡄⠀⠀⠀⠀⠀⠀⠠⣋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠒⠒⠓⠚⠛⠒⠲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀ ⠀⠀⠀⢿⠀⠀⠀⠀⣸⡇⠘⢷⠙⢧⡀⠈⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⣖⣛⣁⡤⠴⠞⠛⠛⠛⠛⣦⣰⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠉⠀⠀⢸⠀⠀⠀⠀⣿⣧⠀⠈⢷⠈⣿⣤⡐⢦⣄⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡤⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀ ⠀⠀⠀⡌⠀⠀⠀⠀⣿⡎⢷⡀⠀⠁⠘⣿⡙⠦⣝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡅⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀ ⠀⠀⢀⠁⠀⠀⠀⠀⡏⢷⡈⢷⡀⠀⠀⠘⣧⠀⠈⠛⠯⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⣥⠤⢤⣤⣀⣀⣤⣤⢴⣶⣦⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠁⠀⠀⠜ ⠀⠀⡜⠀⠀⠀⠀⢸⠇⠀⠙⢦⣳⡀⠀⠀⠸⣧⡀⠀⠀⠀⠉⠉⠀⠠⣤⡀⠀⠀⠀⠀⣿⢠⠟⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠹⡇⠀⢀⡏⠀⠀⢀⠀⠀⠀⠀⣠⠞⣿⠃⠀⢀⠜⠀ ⣠⠾⠊⢠⠀⠀⠀⢸⠀⠀⠀⠀⠈⢧⠀⠀⠀⡏⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⢷⣀⣸⠃⠀⠀⠀⠀⠀⣠⠞⠁⢰⠏⠀⠀⠈⢰⠀ ⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⣧⠀⠀⣧⠀⠹⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢟⡿⡧⠀⠀⠀⢀⡴⠊⠁⠀⢀⡿⠀⠀⡴⠀⡌⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⡆⠀⣿⠀⠀⠹⣬⡟⣿⣳⣤⣀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠣⡄⠀⠀⣠⡶⠋⠀⠀⠀⠀⢸⡇⠀⢠⠇⠀⡇⠀ ⠀⠀⠀⠀⠄⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢻⠀⡟⠀⠀⠀⠙⣝⣌⠛⢿⣛⠻⡄⠠⣄⣀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠆⠀⣶⡞⠋⠀⠀⠀⠀⠀⠀⣼⡇⠀⡜⠀⠀⣤⠀ ⠀⠀⠀⠀⠠⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⢸⣦⠇⠀⠀⠀⠀⠘⣮⣳⣄⡉⣇⢳⣀⣼⣙⣟⣻⣷⡀⠀⠀⠀⠀⠀⢀⣠⠟⠀⠀⡀⣸⡋⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⡇⠀⠀⠁⠀

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⡏⠉⠉⠉⠉⠉⠉⠉⠁⠀⣄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣻⣿⠿⣿⣿⣿⡍⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠈⢹ ⡇⣠⠶⠒⠲⠶⣿⣶⣦⣄⣈⣳⣀⠀⠀⠀⡠⣼⣟⣾⣾⣩⢷⣄⠀⣠⠤⢤⣧⣾⣿⣧⠀⢀⠀⠀⠀⠀⠀⠀⢀⣤⡖⣁⣀⣀⣠⣄⣀⣸ ⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠒⠻⢤⣿⣿⣿⣿⠁⣰⡟⠀⢹⣆⣠⣿⣸⣿⣿⡿⡁⠉⠒⠒⠒⠒⠈⠙⠛⠛⠿⠛⠋⠉⠉⠻⣿ ⣧⠀⠀⠀⠀⠀⢀⠀⠀⠒⠒⠶⠶⣶⣶⣶⣦⣀⣸⣿⣧⠀⠀⣠⣀⣤⡀⠀⣾⡏⣿⣿⣷⣈⣑⣶⠶⠶⠒⠉⠐⠀⢀⡠⠄⠀⠀⠀⠀⢹ ⡿⣧⣀⠀⠠⡀⠀⠉⠒⠒⠠⠤⢀⣀⠀⠉⠙⠫⣌⠻⣿⣧⣄⠉⠉⠋⣠⣾⣿⣿⣿⢿⠿⠋⠉⠀⣀⡠⠤⠒⠚⠉⠀⡀⠀⠀⠀⠀⠀⢸ ⡇⣿⣿⣧⡀⢱⡀⠀⠰⣤⣀⠀⠀⠀⠉⠓⠢⣄⠈⠑⢬⣉⣭⣭⣷⣿⣉⣉⠙⣫⠖⠁⣠⠔⠚⠉⠀⠀⠀⢀⣠⡴⠊⠀⢠⠀⢀⠀⣠⠃ ⡇⢹⣿⣿⣍⠙⣿⡄⠀⠹⣿⡿⠷⣶⣤⣄⣀⠈⠙⢶⣤⡈⣻⠁⢰⡏⠀⢀⣟⣱⠖⠉⠀⣀⣠⣤⣴⡶⣿⡿⠋⠀⣠⣶⡟⠀⣾⣴⣿⠀ ⡁⠀⠻⣿⡏⡀⣿⣿⣄⠀⠙⣦⠀⠈⣿⠉⠙⠳⢦⣤⣌⢻⡇⠀⡾⢳⠀⢀⣏⣡⣶⣴⣾⣿⠉⣼⣃⣤⠏⠀⣤⣾⣿⣿⠄⢰⣿⣿⡿⠀ ⡇⠀⢸⣿⡇⡇⢸⡟⠻⣦⡀⠈⠳⣆⡏⠀⠀⠀⠀⠙⢿⠙⠻⣖⠧⠼⣳⠟⠋⣹⠋⢀⣿⡇⣼⣿⠟⢁⣠⣼⠿⢻⣿⡟⠀⣿⣿⡇⡇⢀ ⡇⠀⢸⣿⡇⡇⢸⡇⠀⠈⠛⢦⡄⠘⡇⠀⠀⠀⠀⠀⠈⠳⡀⠈⠙⠚⠁⠀⣴⠁⠀⣸⠘⣿⣿⣧⣤⣾⠟⠁⠀⠘⣿⣡⣰⣿⣿⡇⢰⣸ ⡇⠀⢸⣿⣿⣷⠈⣧⠀⠀⠀⠈⠻⣶⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠃⠀⢠⡿⠀⢹⠿⠿⠋⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⡇⢸⣿ ⣇⣀⣼⣿⣿⣿⣴⣿⡆⠀⠀⠀⠀⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⣾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠆⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⢰⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣄⣀⣇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠯⠁⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⢡⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡿⣡⣿⡍⠻⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣰⡾⣿⣿⣿⣿⣶⣶⣦⣤⣴⣶⣾⣿⣿⣿⣿⣿⣯⣾⣿⣿⡆⠀⢹ ⣿⣿⠟⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣄⠀⠀⠀⣀⣲⣿⣯⣠⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡄⢸ ⣿⣧⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢿⡥⣼⢿⠿⡿⡿⢿⣿⣿⣿⣿⣿⣧⣤⣵⣼

⣿⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⢀⠎⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⠀⠀⠀⠀⠀ ⣿⣇⢸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢀⠎⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣟⡆⠀⠀⠀⠀⠀ ⣿⣿⣾⣿⣧⠀⣀⣤⣤⣄⣀⣤⠔⠚⠁⠀⠀⠀⠀⢠⠎⠀⢠⠀⠀⠀⠀⠀⠀⣀⡤⠤⣴⣤⣀⣀⣀⡠⠤⠐⠒⠉⠉⠉⠙⠂⠀⠀⠀⠀ ⠙⣿⣏⣛⣿⣿⣷⣏⣁⠤⠒⠤⢄⡀⠀⠀⠀⠀⡠⠋⠀⠀⢸⠀⠀⠀⠀⡤⠞⠁⠀⠚⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡏⠉⠀⠀⠀⢀⣀⠀⠈⠳⣀⡠⠔⠁⠀⠀⢀⠇⠀⠀⢀⣎⠤⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀ ⢸⣿⣿⣿⣿⠁⢀⣤⡖⢲⢙⡿⠄⠀⡀⢡⠀⠀⠀⠀⣠⠊⠀⣀⡤⠊⠁⠀⠀⢸⠂⠀⣰⠁⢀⠞⠟⠓⡖⠒⠒⡖⠒⢒⡒⠒⠊⠁⢀⡀ ⢸⣿⣿⣿⡟⠪⠥⠐⠓⡏⡉⢀⣀⣀⣿⣄⣧⣤⠤⠒⠓⠚⠉⠉⠀⠀⢀⡠⠀⡜⢀⡴⣣⣾⠏⠀⠀⢀⣈⣲⠀⡇⢀⠎⢉⡷⠀⢠⠋⠉ ⣾⣿⣿⣿⣀⣀⣀⣤⠔⠛⠉⡹⢁⣿⠏⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠴⢋⠴⠯⠴⠯⣞⢻⡏⢠⠀⠶⡌⢣⡀⢀⣧⠎⢀⠞⠀⢀⠂⠄⡰ ⠿⠉⠻⡟⡆⢀⡜⠁⠀⡀⠀⠁⠜⠃⠀⠀⠀⠀⢸⡇⠀⠀⢀⡠⠞⠋⠀⠀⠀⠀⠀⠈⠚⣇⢸⣇⡘⣌⠓⠭⢿⡟⠀⠈⠑⠒⠮⣎⣴⠇ ⠀⠀⢀⠃⡇⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣍⣮⠑⠢⠷⠀⡼⠀⡸⠑⠒⡄⢀⣮⠏⠀ ⢀⡠⢊⠞⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⣠⣠⣖⠛⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠱⡀⠀⢰⠁⣰⠁⠀⡜⠀⡜⠈⠳⠎ ⣉⠔⠁⠀⠀⠀⠀⣀⣀⣀⣀⣈⣵⠒⠉⠁⠀⠹⡄⠘⡄⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠙⠒⢛⠀⡸⠁⡸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⢤⣥⣴⣿⣿⠀⠀⠀⠀⠀⠁⠀⠇⠀⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣶⣶⣾⣿⠃⢰⠃⠀⠀⠀⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠀⡄⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⢀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢀⡧⢤⠏⣀⠔⢊⡠⠒ ⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠁⠀⠀⠀⠀⠀⣠⡿⠃⣠⠞⣁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡖⢾⡿⠖⣫⠴⡶⡘⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣀⡴⠏⠀⣀⣴⢟⣡⣾⣵⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡻⠶⢿⡄⢰⢁⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠓⠒⠒⢺⣿⣿⣿⣿⣿⣿⣿⠀⠙⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢶⣾⡇⠺⠞⠀⠀⢠ ⠓⠷⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⡼⢽⣿⣿⣿⣿⣿⣿⣧⡀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠒⢚⣛⡇⠀⠀⠀⠀ ⠉⣀⣠⡀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣮⣻⡇⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠒⠦⣄⣀⠀⠀⠀⠀⢠⢺⣞⣋⣍⡙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢳⠀⠢⡈⢯⡉⠉⢏⡉⢹⡏⢹⡴⢶⣼⠇⠋⠁⢤⣴⡤⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⠉⠱⡖⠚⢣⠀⠈⠑⠧⣄⡀⠻⠈⢷⡏⠀⠈⢻⠀⣠⡄⠀⡀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠘⢶⠀⠱⡈⠱⣦⣤⣈⡉⠉⠚⣷⠀⢀⣾⡿⢻⣿⣻⣵⣯⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡘⠇⠀⡉⠢⣌⠁⠂⠤⢀⣠⡏⣿⠋⠉⠉⠋⠉⠓⡏⠙⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⣈⣠⢈⠻⠶⠿⣿⣿⡟⠛⠁⠀⠀⠀⠀⣴⣾⣦⡀⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢣⡄⠒⠋⢀⣽⣿⣶⠾⡿⣻⣛⠓⣶⣿⣻⡇⢀⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠚⠉⢡⠟⠁⠀⢇⠑⢚⣁⣤⣿⣡⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⡠⠤⠖⠒⢒⣒⡶⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠤⣴⡇⠀⠀⠀⠈⠳⡏⠉⠉⡇⠙⣄⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀ ⠚⣿⠅⠀⠀⢸⣏⣸⠏⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⢀⠞⡇⠀⢸⠈⠀⠀⠀⠀⠀⠹⡄⠀⠈⠢⡘⣦⡀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀ ⠀⣷⠀⠀⠀⠺⢿⡋⠀⠀⠀⠀⣀⣿⡿⠁⠑⠢⣄⠤⠚⠒⠓⠒⠸⢿⣶⠆⠀⠀⠀⠀⠛⢄⠀⠀⠘⡞⣽⣶⠄⠤⢄⠀⠀⠀⠀⠀⠀ ⠀⣿⣦⡀⠀⠀⠘⢁⣀⣀⣀⣐⣮⣿⠀⠀⣀⠞⠁⠀⣼⠊⠀⠀⠀⠀⠈⠑⢤⣀⠀⠀⠀⠀⣷⡀⠀⣹⣿⣿⠓⢂⡸⢷⡄⠀⠀⠀⠀ ⠀⣽⠛⣥⠖⡚⠉⠁⠀⠀⠀⠀⣸⢧⡶⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠒⠶⡚⠁⠹⣾⡛⣉⣻⣶⣊⣑⣾⡁⣀⠤⠄⠀ ⠀⣧⣾⣷⡀⠃⠀⠀⠀⠀⣠⠊⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣦⠖⢉⣰⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀ ⠀⢿⣿⣿⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⢿⣤⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⣾⡇⠀⠀⠠⣾⢻⠀⠀⠀⠀⠀ ⠀⠘⢿⣿⡀⡄⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠿⣿⡀⠀⠀⢻⢄⣇⠀⠀⠀⠀ ⠀⠀⠀⣿⢿⡇⠀⠀⢸⡏⠀⠀⠀⠀⢀⠀⡇⣶⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠆⠀⠈⠙⠻⣆⠀⠀⠀ ⠀⠀⠀⠁⠀⠙⣄⠀⢸⠃⠀⠀⠀⠀⠀⠙⢧⠙⣷⣄⠀⠘⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡆⢸⣆⡀⠀⠀⠀⠀⠀⠀⠳⣈⠛⢵⣦⣄⣼⠋⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡇⠀ ⠀⠀⠀⠀⣠⣴⡟⢹⢨⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡏⠀⣼⡄⠀⠀⠀⠉⠒⠂⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠟⣿⡇⠀ ⠀⠀⣀⣴⠿⠋⣠⠎⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠲⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠤⣄⣤⣄⣀⣤⡿⠀⠀⢹⡇⠀ ⠤⠤⠤⢤⠖⠋⠁⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣾⣇⠀ ⣀⠀⠀⣍⣠⢤⠤⠤⢤⣈⣏⠁⠀⠀⠀⠀⠀⠀⠀⣸⠉⡇⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⡿⢿⠀ ⠒⠊⠉⠀⠀⠈⠀⠀⠘⣻⡎⠉⠲⢄⠀⠀⠀⠀⣠⠃⠀⠸⡀⠀⠁⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⣇⣼⢇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠷⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢣⠀⠀⢸⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠈ ⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⢸⡆⠀⠀⠋⠈⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠀⠀⠠⣉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣈⣆⠀⠀⠈⠳⣄⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠈⠑⢦⡀⠀⠈⠳⣤⡀⠀⠈⠳⣿⡽⠏⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡴⠋⠙⠛⠓⠿⣄⡙⣿⡲⢤⡄⠀⠀⠀⠀⠀⠈⢳⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣼⠇⠀⠀⠀⠀⢀⣿⣻⠛⠛⠒⠀⠀⠀⠀⠀⠤⣤⡈⢇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣼⣫⠀⠿⡆⠀⠀⠀⣼⣿⣃⡼⣇⡀⠀⠀⠀⠀⠀⠺⣷⣼⣿⠾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡧⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⣏⠓⠶⣄⠀⠀⠀⠈⠻⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣰⣶⠆⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⣸⣦⡀⣶⣦⡸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠒⠉⠈⠁⠀⡴⠋⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡟⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣤⠀⠀⠠⠀⠀⡔⠑⠦⠀⣀⣠⣤⣴⣿⠟⢁⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⣤⣽⣧⣉⣡⣭⢩⣄ ⠀⠀⠀⠁⠀⠀⠀⠀⢸⢀⡴⠚⠓⢻⠿⡟⡟⡏⢠⡏⠀⢸⡿⣿⣤⣤⡀⠀⠀⠀⠀⣀⣠⣀⠘⡄⠀⠀⠱⢤⡤⠘⠦⠆⠶⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⠀⠀⠀⣼⠸⠀⢸⠟⠿⠀⠀⣼⣧⣿⣿⡿⠉⣹⡖⠒⠋⠁⠀⠀⢉⣷⠀⠀⠀⠘⠛⠃⠊⠒⠒⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⣠⠇⠀⢀⣸⣇⠀⠠⣿⡿⢻⣿⢿⡇⠀⣯⠀⠀⠀⠀⢀⣴⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠒⠒⠒⠤⠤⣠⡏⣀⣤⣴⣾⡏⠀⠀⡴⠋⠏⠀⢀⠼⢿⣾⣿⣼⠀⢰⢿⠀⠀⠀⡞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢬⣇⡀⢸⡇⠀⠀⣀⠀⠀⠈⣿⠂⡟⠀⡇⣸⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠒⠿⠿⣿⣤⣾⣿⣶⠁⢸⢁⡏⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠛⠿⣧⣧⣐⡇⠀⠀⠀⢸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⣄⣀⡀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠘⠛⠛⠓⠚⠓⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠘⠀⠀⡰⠀⠀⠀⠸⣄⠈⠀⢄⠒⠒⠒⠂⠈⣀⣠⣞⣽⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡜⠁⠀⠀⠀⠀⠸⡄⢷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢀⣤⠖⣿⢷⣤⡀⠀⠀⠀⢈⣉⣉⣠⠼⠛⠛⠾⣤⣀⠈⣭⠀⠀⢀⣠⡾⠟⠛⠒⢦⣤⣀⠀⠀⢱⠀⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣠⣴⣟⣹⣷⣿⣦⣿⣿⣿⡷⡖⠚⡍⠉⠀⠀⠀⠀⢀⠀⠈⠉⢻⢻⠏⠁⠙⣿⣆⠀⠀⢠⣻⡄⠉⠑⢺⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⡈⣿⡟⣟⣿⣿⣿⢟⠁⠀⠉⢹⠀⣧⠀⢰⣷⠀⠀⢸⣆⠀⢰⠃⢸⠃⠀⠒⢻⣿⡆⠀⠀⠙⣿⣖⡶⠃⠀⢇⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⡇⠘⣤⣾⣿⠿⠃⠈⢠⣄⡀⢸⡀⢹⣄⣿⡼⡇⠀⣸⣿⣷⣸⡠⣼⣲⠉⠉⢹⡇⢣⠀⠀⠀⣻⠟⠀⣠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡜⠫⡉⣧⣠⣿⡟⢧⡤⠔⠒⠛⠛⠛⢺⡷⢼⣿⣿⡁⣷⠀⣿⣿⣹⣿⠿⡟⠹⣤⣀⡼⠀⢸⠄⢀⡔⠁⠀⡴⠁⠀⠀⠀⢀ ⠀⠀⠀⠀⢰⠁⠳⣌⢣⡀⣸⠏⠀⣀⡤⠔⠒⠀⢀⣼⡇⢸⣿⣿⣿⣧⣾⠿⣿⣿⠇⣸⣇⣀⠘⣀⠉⠑⠺⡴⠋⠀⢠⠞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠟⢦⠀⠀⠀⡘⢧⡀⠈⠁⠀⠀⠀⣶⣿⣿⡇⢈⣿⣿⣿⣿⠃⢠⣟⣿⠀⣿⣿⣿⣷⡏⠀⣠⠎⡠⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠋⠀⠀⠱⣄⠀⠀⠢⡈⠦⡀⠀⢀⣸⠟⠋⠁⡇⢈⣿⡟⢹⣮⢷⣿⣿⢛⣴⣿⡀⡈⠙⠒⡖⠁⠈⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈⠓⢌⠻⡁⠠⡖⢺⠋⡇⣼⡟⠀⢸⣿⢿⣿⣶⣾⡧⡟⢳⠙⢦⠞⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠑⢜⢶⠁⢸⠀⢿⣆⣧⠀⣼⡏⠀⢹⣿⣿⠀⡇⠈⡆⡞⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡀⠀⠁⢧⢸⣆⠘⣾⣼⣶⣿⣷⣴⣫⣟⣿⠞⢉⣾⠇⡇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠈⡇⠻⣦⠈⢻⣿⣵⣿⣿⣿⣿⠃⣠⡿⠏⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢳⠀⠙⠷⣾⣟⣿⢿⣿⠛⣧⣴⡿⠁⢀⣾⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢷⣄⡀⢻⠻⣿⡍⢸⣶⠻⠋⢀⣴⣿⠗⢲⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣼⣻⢿⡆⠑⢻⣹⡞⠈⣦⡶⠋⣿⡟⠀⠀⣿⠛⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⠈⠳⢄⡙⠆⢸⣿⡧⠞⣻⡷⢀⠟⠁⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⠀⠀⠹⡆⣾⣽⡃⠀⡏⡇⣸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠑⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⣄⣀⣠⠤⠀⠀⢳⢳⡶⠂⣻⠘⠛⠁⠰⢹⠃⢿⣧⠉⠲⠤⣄⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⢱⣹⣿⣿⣿⣿⣿⠟⢻⡛⢿⣹⣇⢻⣦⢂⠣⣱⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢷⢰⢸⣿⣿⠛⣿⠉⠀⠀⠀⠙⡄⢻⠙⣼⣿⣿⡄⠁⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢠⣿⠀⣸⣿⡇⠀⣿⠀⠈⠓⠲⣶⡿⢾⣷⣿⣿⣿⣿⣦⠹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢰⣿⣷⣻⣿⡞⣦⠐⡄⠀⠀⠀⠀⠀⠀⠻⣿⣯⠙⢦⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠿⣷⣿⠿⢏⡁⠀⠂⢉⡤⣠⡀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠈⠳⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⡾⠁⠀⢿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣄⠀⠀⠀⣠⡾⢫⣿⠀⠀⠀⠀⠀⣉⣛⣻⣿⣿⣿⡿⠋⠀ ⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣥⣿⠁⠁⠀⢸⠿⣆⠀⠀⠀⠀⢿⡿⠿⢿⡿⠀⠀⠉⣁⡴⠟⣿⣤⠴⠖⠋⠉⠉⠉⢯⣥⣤⠞⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⢖⠀⠀⠉⣁⡠⠞⠉⠉⠉⠉⠙⠻⢿⣆⣀⣀⠀⠈⣣⣤⡴⣃⡀⢂⠀⠀⡠⠞⠉⠀⠀⠀⠀⠀⢴⠒⣩⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠺⣉⠁⠀⠀⡈⠉⠐⣂⠤⠴⠦⢝⣉⡉⠹⠟⠀⠠⠄⠈⠉⠩⢭⣙⠒⠤⠤⣀⠀⠀⠀⠀⢀⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠮⣡⠴⠊⠁⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠀⠀⢀⣡⣤⣤⣽⠀⠀⠀⠀⠈⠁⢲⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠹⠦⢶⣽⣶⠂⠀⣠⣾⠧⠖⠊⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⢢⡀⠀⠀⠀⢀⣤⠼⢥⣿⣇⠀⡿⠿⠛⠉⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢹⠀⠀⠀⠀⠈⠙⢻⢯⢻⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⡇⠀⠀⠀⠀⠀⣿⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⣀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⢃⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⡌⢆⠀⠀⠀⠀⠀⣿⣿⣿⡇⡏⠀⠀⠀⠀⠀⡸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢾⠁⠀⠀⠀⠀⣿⡼⣿⠀⣷⠀⠀⠀⠀⣰⣱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠈⢆⠀⠀⠀⠐⣿⡇⢿⢹⣟⠀⠀⠀⠰⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠈⢢⡀⠀⠀⠹⣳⣸⠟⡜⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠠⡲⠊⠁⠀⠀⠀⠀⠀⠀⠈⠰⣄⠈⢊⠒⠤⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠈⠣⠀⠌⠐⠠⡑⠢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠡⠀⢠⠀⡱⢸⡀⠀⠈⠢⠘⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⠔⠉⠢⣡⠀⡄⠰⣇⡞⠢⡄⠀⠑⡘⡹⠀⠀⠀⠀ ⠀⠀⠀⠀⢃⠀⠀⠀⣠⣾⣁⠠⡀⠀⠘⢆⢸⡄⣿⡇⠄⠐⣧⡀⢣⡷⠆⠀⠀⠀ ⠀⠀⠀⠀⠈⠆⠀⡏⠘⠋⣀⣠⣴⣀⠀⠈⢜⠰⠘⠈⢿⠻⡻⢷⠘⣏⡀⠀⠀⠀ ⠀⠀⠀⠢⡀⠈⢃⢣⣧⠞⠟⠉⢀⡹⠆⠀⠈⠀⠹⠀⠀⠋⠉⠒⠳⡙⣿⣦⠀⠀ ⡤⠆⠀⡀⠀⡀⠀⠺⡧⠄⠐⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢣⣀⠈⠑⠠ ⠁⡘⢠⠈⠌⣂⠢⡀⠈⡂⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣢⣽⠀⠀⠘⡄⠑⠄⠀ ⠀⠀⢻⡗⢤⡈⠢⡈⠢⡈⠪⣝⠲⠦⠄⠀⠀⠀⢰⣿⣿⣿⢿⠀⠀⢠⣈⢂⠈⠀ ⠀⠀⢀⠛⠸⢻⣷⣬⢦⢐⡀⠈⢢⠀⠀⠀⠀⠀⠈⠫⡄⢀⣀⡡⠀⣼⣇⠱⣧⠈ ⠀⠘⠐⣀⡠⠛⡀⠀⢀⢃⡳⢀⠰⢣⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢰⣿⡟⢀⠏⠄ ⠀⠆⣸⣵⠁⠀⣿⡻⣿⠃⣀⣀⠱⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠮⠚⠂ ⠀⠀⣿⡌⠀⣠⠟⠙⣇⠀⣓⣻⠀⠈⠂⠈⠙⠒⠶⡶⠶⠚⠛⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠏⠀⢴⡇⢠⢠⠃⠁⡃⢉⣀⡀⠒⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣄⠤⠒⠂⠈⠉⠀⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⠁⡧⠀⠀⠀⠀⠀⠀⠀⠀⠹⡑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠰⣀⡀⠐⠂⠀⠀⠀⠀⠀⢡⢰⠀⠀⡠⢒⠂⢄⠀⠀⠀⠀ ⠫⢁⠀⠀⠀⠀⠀⠠⣤⣭⣴⣤⡈⢆⠀⠀⢠⡚⠀⢸⠠⣿⣷⠂⢣⠀⠀⠀ ⠀⠀⠉⣲⠄⠀⠀⠀⡝⢾⡿⠿⠩⣶⣦⠀⡾⠁⠀⠀⢂⠘⠋⢀⠊⠀⠀⠀ ⠀⠀⠈⢷⡄⢤⡄⠀⠠⠀⢁⡀⣈⡈⠣⣺⠟⡍⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠘⢟⢾⡒⠚⢭⡋⡰⢳⡶⠶⠫⢵⣴⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠑⡞⠉⠉⠈⠒⠂⢿⣇⣽⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠻⣿⣾⣿⡿⠣⠀⢀⡀⠀⠀⠀⢀⣀⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⠃⠀⠀⠀⠀⠀⠈⠙⠅⡀⠀⠀⠀⠄⠁⠂⢀⠈⢵⠀ ⠀⠀⠀⠀⠀⠀⠘⢰⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠬⣦⡐⠃ ⠀⠀⠀⠀⠀⠹⡐⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠃⠙⡷⠀ ⠀⠀⠀⠀⠀⠀⠐⡘⡀⠀⠀⠘⠤⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢀⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠱⠑⢄⠀⠀⠀⠀⠀⠀⠀⣠⡃⠀⠀⠀⠀⠀⡠⢊⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠑⢖⠠⢤⡤⠖⣿⢹⠪⣑⠒⠲⣺⠁⠀⠚⠀⠀ ⠀⠀⠀⠀⡠⠔⠂⠀⡹⡀⠀⠀⠑⢄⡀⡸⡁⢸⠀⠀⠁⠢⢽⠀⠀⠀⠀⠀ ⠀⢀⠄⠊⠀⠀⠠⠂⠀⢣⠀⠀⠀⠀⠈⠀⠈⣼⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠉⠉⢠⡞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣠⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⢠⠀⠀⣸⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⡇⢠⣻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠈⠘⣿⣶⣶⣶⣖⡀ ⠀⠀⠀⠀⢀⡤⣲⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢰⣿⣿⡿⠋⠉⠙ ⠀⠀⠀⣴⣯⣏⣽⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⣼⢿⢻⠀⠀⠀⢀ ⣦⣤⣾⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣿⡊⠀⠀⠀⣠⠞ ⠈⠿⣿⣿⣿⣿⣿⣿⠀⣰⣳⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⣷⡏⢇⠀⠀⠀⠀⣿⡇⠁⠀⣠⠟⠁⠀ ⠀⠀⠙⣿⣿⣿⣿⣿⠀⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣼⣿⣿⡟⠀⠀⠀⢰⣿⣷⣶⠊⡅⠀⠀⠀ ⡀⠀⢀⠈⢻⣿⣿⣿⣆⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⣾⣿⣿⠃⡼⠁⣰⠆⠀ ⠹⣄⠀⢧⠀⢻⣿⣿⣿⣷⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⣿⠃⡰⠁⢀⡏⠀⢀ ⠀⢻⡄⠘⣆⠀⢻⣿⣿⣿⣯⣦⣀⠀⠀⠀⠀⠀⣠⡴⠀⠀⠀⠀⠀⠀⠈⢿⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣸⣿⣿⢠⠃⢀⣾⠁⠀⢈ ⡇⠀⢿⠀⢹⡆⠘⣿⣿⣿⣿⣿⣿⣿⣿⡶⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⣴⣶⣤⣤⣤⡶⠛⠁⢀⣿⣿⣿⣞⡆⢻⣿⠀⠀⠏ ⣷⠀⢨⠃⢠⣧⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⢠⠀⣸⣿⣿⣿⣧⣿⠚⠻⠀⢸⠀ ⡏⠀⡸⠀⡾⠈⢧⣈⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣷⣂⣀⡇⠀ ⢱⡀⢁⡰⠁⠀⠀⢛⡛⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣿⣿⣿⣿⡿⠉⠉⢉⠁⠀

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⡏⠉⠉⠉⠉⠉⣽⣿⣯⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣩⣿⡍⠉⠉⠉⠉⢹ ⡇⠀⠀⠀⠀⣼⡏⢫⠉⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢫⠟⣿⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⢠⣿⠁⠀⢣⠀⠈⢷⡀⠀⠀⠀⠀⠀⢀⡼⠁⢀⠎⠀⢹⡇⠀⠀⠀⢸ ⡏⢉⣶⣦⣼⢸⠀⠀⠀⢣⠀⠀⢳⣄⡒⠒⠲⢤⡼⠁⠀⡎⠀⠀⠀⣧⠀⠀⠀⢸ ⣇⣿⣿⣿⡟⡏⠀⠀⠀⠈⣇⠀⣸⠃⠀⠀⠀⠸⣇⠀⡼⠀⠀⠀⠀⣿⠀⠀⠀⢸ ⣿⣿⣿⣿⣿⡇⠀⠀⣠⠞⣁⣤⣤⣤⣤⣴⣤⣤⣀⡀⠳⣄⠀⠀⠀⣿⠀⠀⠀⢸ ⡏⠉⠙⠻⣼⣧⣠⣾⣿⣿⣿⣿⣿⡿⡋⠀⠈⣿⣿⣿⣿⣶⣵⣤⣠⡇⠀⠀⠀⢸ ⡇⠀⠀⠀⡰⣿⣿⣿⣿⣙⢛⣿⢿⣤⠑⠤⠔⣧⣿⡿⣿⡿⣿⣿⣿⣇⠀⠀⠀⢸ ⡇⠀⠀⡰⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣇⡀⣠⣵⣿⣤⣿⣷⣿⣿⣿⣿⡀⠀⠀⢸ ⡇⠀⠀⣷⣼⠉⣿⡿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣷⡀⠀⢸ ⡇⠀⠀⠘⢌⠻⣿⣇⣄⣉⣁⣉⡛⢟⠛⠛⠛⠻⢛⣛⣟⣉⣩⣿⣿⡿⠋⢨⠆⢸ ⡇⠀⠀⠀⠈⢣⣿⣿⠉⠯⢉⣿⣿⣷⠀⠀⠀⣾⣿⣿⣉⣽⣹⣿⣿⣧⡾⠋⠀⢸ ⡇⠀⠀⢀⠔⠉⢙⠿⣷⠄⣀⡀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠄⢊⣿⡟⠁⠀⠀⠀⢸ ⡇⠀⡰⠁⠀⢠⠃⠀⠈⠒⢤⡇⡹⠯⠁⠠⠭⣉⣫⠁⣧⡂⠁⠀⠻⡄⠀⠀⠀⢸ ⡇⠀⡇⠀⠀⠎⠀⠀⠀⢀⠜⠿⠁⠀⡀⠀⠀⠀⠰⡧⡙⡄⠀⠀⠀⠘⠆⠀⠀⢸ ⡇⠀⢇⠀⠸⠀⣠⢴⡾⠁⠀⠀⠀⠂⠀⡆⠀⡭⢀⡈⠈⠲⢄⣀⠀⠀⠈⡄⠀⢸ ⡇⠀⠈⢆⡶⠋⠀⣸⢁⠀⣀⣨⣥⣜⡺⠔⢰⣥⣴⡀⠀⢀⢨⠇⠉⠑⠢⣵⠀⢸ ⡇⠀⠀⣾⣀⣤⣾⣿⣾⡿⠒⡏⠃⡜⠀⠀⠀⠀⠈⠳⣤⣾⣾⣄⡀⠀⠀⢸⠀⢸ ⡇⠀⠀⠻⣿⣿⣿⣿⡟⠑⠲⡇⠀⠁⠀⠀⠀⠀⠀⠀⣷⠛⠻⣿⣿⣦⣠⡞⠀⢸ ⣇⣀⣀⣀⣈⣙⣛⣋⣀⣀⣀⣱⣀⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣈⣉⣉⣉⣀⣀⣸

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⠒⠛⠣⠄⢈⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡀⠉⠂⠠⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠐⠂⠄⡀⠀⠠⡀⢴⠀⠎⠀⣀⡀⠠⠄⠀⠠⡀⢀⠀⠀⠀ ⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣻⡛⠚⢶⡴⢋⣿⠗⠐⠒⣈⡦⠚⠁⠀⠀⠀ ⢟⠚⠓⡦⣄⣀⠀⠀⣀⡀⠔⠋⠀⡹⠯⠧⢂⢤⢀⢰⣠⢦⠥⢋⠀⠀⠀⠀⠀⠀ ⣾⣭⣟⣳⣶⠝⠁⠀⠀⠀⠀⠀⢰⠁⠀⣀⣎⣎⠀⡠⠐⠁⠀⠀⠑⠤⢀⣀⣠⣴ ⣄⣙⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠉⠉⢉⠝⠁⠀⠀⠀⠀⠀⠀⠀⠁⢸⠥⠄ ⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⡠⠈⡐⠉⠉⡕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀ ⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣿⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠝ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀ ⠋⣁⠜⠢⣀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀ ⠈⠀⠀⢀⣹⠽⠶⠠⠤⡤⠤⣼⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀ ⠄⠐⠉⠁⠀⢀⡠⢔⡩⠔⠋⠀⣭⣿⣧⣤⣀⣀⣀⣀⣠⣤⣶⣿⣿⠄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢽⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢼⣷⡄⠀⠀⢹⡇⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡇⠹⣦⣀⣠⣿⣾⣿⡿⢿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⣸⠟⠙⣿⣿⣟⡃⠀⠵⢿⡿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠀⢸⣾⠿⠀⠀⠙⣿⣿⣷⣄⣸⡿⠇⢉⣹⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠓⢺⣇⣠⠀⣀⣼⣿⠙⠟⠋⠉⠀⢠⢁⡠⢿⡿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⠻⠛⢿⣿⠁⡔⠉⢉⣉⢶⠀⠀⠿⠗⢺⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣀⣀⣘⣿⣼⣗⣾⠿⠴⠊⠁⡤⠄⢀⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠚⠀⠐⠀⠀⠀⢏⠉⠉⠙⣿⡄⠀⠀⠀⠀⣀⣠⠴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢤⣷⣌⣦⣤⣤⣽⣿⣶⣶⠚⠃⠙⠃⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠢⠴⣿⣟⠛⣥⠀⢩⠀⠀⠀⣠⠀⣧⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡿⢳⠀⡀⠄⠒⠈⡀⣦⠿⠷⠷⢦⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⡠⠙⢄⠑⣶⠀⢀⠀⢇⡗⣇⡀⠒⠲⡝⢿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⡤⠢⢄⠀⠀⠴⠋⠀⠀⡰⠉⠀⠀⠀⠁⠺⢧⣀⡨⠱⡖⠃⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⡸⠀⠀⢀⠑⠤⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠘⡀⠘⠂⠀⠦⢄⠀ ⠀⠀⢠⠃⠀⢀⡎⠀⠀⠈⠢⡄⠀⠁⠀⠀⠀⣠⠞⠁⠀⠈⡆⠀⠀⢳⠤⠀⠐⠤⡼⠇ ⠀⠀⡎⠀⠠⣾⣿⡦⣀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡀⠀⠘⡆⠤⠤⠴⠋⠀ ⡠⠚⠀⠀⢰⠋⢇⡸⣿⣆⠀⠀⠈⠑⡀⠀⠀⠀⡴⣿⠙⢻⣿⣇⠀⠀⠱⡀⠀⠀⠀⠀ ⠓⠂⠤⠤⠞⠀⠘⠾⡿⠃⠑⠒⠂⠒⠓⠂⠀⠐⣛⣖⡰⠚⠁⠸⢀⣀⣀⣈⠆⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⡟⠋⠁⠀⠙⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡰⠟⠁⢹⣗⢄⠀⠀⠀⠳⣄⠀⠀⣀⠗⠁⠀⠀⣠⣾⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠈⡿⢦⠑⢆⠀⠀⠀⠉⠉⠀⠀⣠⠔⠊⣡⡟⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢠⠁⠀⢣⠀⠛⠉⠉⠉⠉⠙⠛⢦⣄⡴⢻⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠸⡀⢠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⢸⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠄⠀⠀⠙⠢⣄⣳⠃⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠈⡏⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠞⡏⠀⠸⣏⠓⠒⠇⠀⠀⠀⣰⠁⠀⠉⢦⠀⠀⢀⡴⠋⠳⣿⣿⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠛⢰⠁⠀⠀⣿⣦⡀⠀⠀⠸⠶⣷⢶⣦⠤⢬⡆⠀⣮⠤⠤⢾⣿⣿⡄⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡿⢠⣿⠀⠀⠀⢻⡉⠉⠀⠀⠀⠀⢹⣜⠛⠀⢀⡤⢾⣏⢀⣠⡾⢁⠋⣧⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⢫⡜⣿⡄⠀⠀⠀⠙⢶⣤⣤⣷⣾⠁⠠⣈⠉⠀⠀⠛⠉⠀⠀⣽⣎⢀⣿⡀⠀⠘⡄⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠃⠈⡇⣿⠹⣄⠀⠀⠀⢠⠏⠁⠀⠙⢿⡦⠬⢁⣀⣀⣀⡠⣤⣾⠏⡠⠟⠛⠓⠤⡴⠋⠀⠉⠀⠈⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⠀⡏⠀⣿⠀⠈⠢⡀⠀⢸⠀⠀⠀⠀⠀⠙⠢⣄⣉⠭⠂⣀⣈⣧⠎⠀⠀⠀⠀⠀⣈⣶⡖⡩⠭⠭⢉⣻⡀⠀⠀⠀⠀⠀⠀⠀ ⡏⢸⢁⡆⢹⡄⠀⠀⠈⠑⢺⢳⡀⠀⠀⣄⡀⠀⠀⠑⠤⢤⡀⢀⠎⠀⠀⠀⠀⡤⢊⡤⠚⠻⡀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀ ⣷⠀⠘⢣⠘⣷⡀⠀⠀⠂⢸⠀⠁⠀⠀⣿⡇⠀⠀⠀⠀⠀⠉⡏⠀⠀⢱⣀⠞⡠⠋⠀⠀⠀⠙⢄⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀ ⢻⡆⢢⢿⣆⣿⣤⠒⢦⡀⣼⠀⠀⠀⠀⣿⡄⠀⢠⣾⣷⡆⠸⠀⠀⠀⠘⣿⡞⠁⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⢱⠀⠀⠀⠀⠀⠀ ⠸⣧⠈⢻⣿⣿⣷⡀⠀⠙⣾⠀⠀⠀⢀⡟⣇⡀⠀⠙⠛⠁⡇⠀⠀⠀⠀⠘⠻⣄⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⡆⠀⠀⠀⠀⠀ ⠀⢹⣆⢸⣿⣿⢷⢣⡀⠀⢸⡀⠀⠀⣾⡷⡘⠿⣆⣀⣀⣸⣇⠀⠀⠀⠀⠀⠀⠈⠑⢦⣄⣀⠀⠀⠀⠀⠀⠑⣄⠸⡄⠀⠀⠀⠀ ⠀⠀⢻⣿⠉⢿⣦⡛⢷⡄⠸⠁⢰⡶⢿⡇⠙⢾⡄⠉⠉⢻⠙⠞⠉⢢⣀⠔⠠⠤⠔⠲⣿⡟⢿⡷⢦⣦⠀⠀⠈⢆⢳⠀⠀⠀⠀ ⠀⠀⠀⠻⡇⠀⠉⠻⣽⣝⣿⠀⠀⠀⠀⢣⠀⠀⣱⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠁⣾⠙⢦⣠⠖⡩⠿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡳⣄⠀⠀⢸⠒⠉⢻⣆⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠈⢦⣴⡷⠋⠀⠀⠙⢄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠙⠃⠀⡞⠒⠒⠛⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠋⠀⠀⠀⢀⠞⠈⢷⣄⠀⠀⠀⠀⠉⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢀⠇⠀⠀⠀⠀⡇⠙⠢⣄⣀⣀⣀⣀⡠⢴⣋⡀⣀⣀⠤⠖⠁⠀⠀⠘⡌⠓⠦⠤⡴⠊⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠈⠣⠀⠀⠀⠀⢸⡀⠀⠀⡸⠉⡀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠤⠒⠁⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⡀⠀⢸⡟⠁⠀⢱⡀⠀⣠⠊⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢰⠖⠢⢤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠘⢧⣾⠁⠀⠀⠀⡇⠰⠁⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢠⠔⠫⢤⡀⢀⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡀⢠⡶⠀⠀⢻⡄⠀⠀⢠⡇⠘⢦⡀⠀⠀⠀⠈⠒⢤⡀⠀⢾⡁⠀⠀⠀⣨⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡿⢷⣤⣤⡏⠀⢀⣰⣋⣧⠀⠀⠈⠙⠒⠢⢄⡀⠀⠈⠓⠤⡈⠑⠒⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠑⠚⠉⣸⠁⠀⢸⠖⠒⢺⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣤⣀⣠⡴⠃⠀⢠⢼⣁⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠖⠚⠳⣆⠀⠀⠀⠀⠀⠀⣠⡤⠚⠳⢶⡒⣿⠓⠶⠟⠀⠀⣀⡠⠤⠄⠒⠒⠋⠁⠀⠀⠀⣀⠜⠁⠀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣈⣧⣀⣠⡞⠹⣦⠤⠤⢄⣠⡞⠁⠀⠀⠀⠀⠈⠈⠓⠒⠲⠖⠉⠀⠀⠀⣀⣠⣤⣤⣦⣤⣶⣎⣁⠀⠀⢸⠁⠙⠆⠀⠀⠀ ⠀⠀⠀⠀⠸⣇⠀⠀⠸⣇⠀⠘⣧⣀⣴⣯⣤⣤⣄⣠⠆⠀⠀⠀⠀⢀⠎⠀⣠⣴⠾⠛⠋⠁⠀⠀⠀⠀⠀⠉⠙⢷⣤⣨⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡇⠀⠀⢹⣶⡾⠛⠉⠁⠀⠀⠀⠀⠉⠛⠷⢦⣄⣀⣬⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀ ⣄⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⣴⡟⠛⠿⣦⡀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀ ⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣼⣿⣄⣡⣶⣾⣷⡀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢹⡇⠀⠀⢸⡏⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⢸⡇⠀⠀⢸⡇⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⢀⣿⣧⣤⣤⣼⣿⣀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠀⠈⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⢻⣿⣟⣻⠀⠀⣟⣻⣿⡟⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠉⢹⣿⡿⠿⢼⣿⠿⠿⣆⣸⠿⠿⣿⡧⠿⢿⣿⡏⠉⢀⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣶⣾⡿⢤⣤⣀⣉⣧⠀⠈⠁⠀⣼⣋⣀⣤⡤⢽⣷⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠉⢻⣧⣀⠻⣿⣿⢛⡇⠀⠀⢸⡛⣿⣿⠟⢀⣼⡿⠉⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⣿⡏⠉⠙⠓⠛⠛⠀⠀⠉⠙⠛⠋⠉⢹⣿⠁⢀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⡤⣄⣀⣀⡀⠶⠶⠄⣀⣀⣠⣤⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠉⣳⣤⣼⡿⠛⠛⢻⣧⣤⣞⠙⠛⢧⠀⠀⠀⠀⠀⣀⣠⣤⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠧⢶⠋⠉⠀⠉⠙⢦⡴⠛⠉⠀⠈⠹⡖⠺⢦⣠⣶⡋⣙⡿⠿⠟⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡟⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⣿⠀⠈⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠇⠀⠀⣤⡄⠀⡇⠀⠀⢠⡀⠀⠀⠸⣄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⡇⠀⠀⠀⠀⠀⠀⣹⡀⠀⠀⠀⠀⠀⠀⢈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⢀⠀⠀⠀⣠⠞⠁⠉⠳⡄⠀⠀⠀⠀⠊⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⡇⠀⠀⢸⠀⠀⠀⢰⠇⠀⠀⢸⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠴⠋⠉⠉⠓⠒⠒⠒⠒⠺⠦⠴⠧⢤⣤⣸⡆⠀⠀⢸⢤⣀⣤⠼⠦⠴⠛⠒⠒⠚⠉⠉⠉⠉⠉⠳⣄⠀ ⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⠉⠁⣀⡀⠀⠀⠈⠀⠀⠉⠓⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣡⣾⣿⢿⡷⣄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⡴⢫⣿⡅⠀⣷⠋⠂⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡠⠄⠚⠢⡜⡔⠌⣿⢀⢤⠁⡌⠘⠤⠚⠂⡠⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠒⠁⠀⡀⡀⣰⡇⡸⡼⣿⡄⡼⡄⡏⠂⠰⡈⠂⠇⠀⠁⠢⡀⠀⠀ ⣤⠄⠂⠁⠀⠀⠀⠀⣸⡞⠁⠀⢡⡘⣽⡷⡱⣼⠃⠀⠀⠈⢷⡀⠀⠀⠀⠀⠁⠂ ⠀⠀⠀⠀⠀⢀⡠⠊⢹⠃⠀⠀⢀⢳⣸⣿⣿⢋⢦⠂⠀⠀⣹⠉⠂⢄⠀⠀⠀⠀ ⠀⠀⠀⡠⠖⠁⠀⠀⠀⡇⠀⠀⠀⢣⢹⠈⢹⢎⠀⠀⠀⠀⡏⠀⠀⠀⠉⠢⡀⠀ ⠀⢀⠜⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢃⡇⣎⠎⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠂ ⠊⠀⠀⠀⠀⠀⠀⠀⢠⣷⠀⠀⠀⠀⠈⡇⡟⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀⠀⠀⠀⠘⠉⠁⠀⠀⢀⢀⣀⣹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣐⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡴⠚⠛⠛⡛⠿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⠁⠀⠀⠘⠉⠉⠉⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⣾⠟⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡀⠀⠀⠀⠉⠀⠀⢠⣠⣽⣿⣿ ⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⢠⡿⢸⠻⣆⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⣼⡷⢤⡄⠀⢀⣼⣿⣶⡾⠉⠛⠿⣿ ⠀⠀⠀⣾⣅⠀⠀⠀⠀⠀⣠⢿⠃⡸⠀⠺⣿⣿⡿⣿⣿⣶⣒⣲⣶⣶⣶⣾⣿⠤⣤⣤⣤⣤⣤⣤⣼⣧⣴⣶⣾⣿⡿⠿⣿⡁⠀⠀⢀⣿ ⠀⠀⢠⣏⠈⠳⣄⣀⡴⠚⠁⢸⢀⡇⠀⠀⠈⢻⣧⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠉⠉⠉⣹⠟⠛⣯⣿⣄⡟⠉⠓⠶⠌⠀⠀⠐⢚⣿ ⠀⠀⣼⠁⠀⠁⠀⠀⡀⠀⢰⡇⢸⣷⡄⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⠞⠁⣤⣾⠛⣉⣹⡁⠀⠀⠀⠀⠀⠚⢹⣿⣿ ⠀⡰⠁⠀⠀⠀⠀⠀⢹⠀⠀⠇⢸⣿⣿⣦⡀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⡗⢀⣾⡟⠁⠀⠀⠈⠉⠲⢄⣴⣶⠂⣠⣞⣉⣡ ⣰⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⣷⠈⣿⣿⣿⠟⠓⠒⠒⠒⠿⣿⣿⢛⣿⣿⣿⣿⣿⢋⣿⣰⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣅⡆ ⠈⠙⢦⡀⠀⠀⠀⠀⠀⡇⠀⢻⠀⣻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⠟⢃⠀⢻⡏⢿⡀⠀⠀⣀⡩⢌⡑⠒⠀⠀⠀⠀⠀⠀⠈⠃ ⠀⠀⠀⠑⢤⡀⠀⠀⠔⠀⠀⠈⢀⡣⠤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⣁⠔⠁⠀⠈⠻⠄⢀⡠⠞⠁⠀⠀⠛⠑⣶⣤⣤⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶ ⠀⠀⡀⠀⠀⠀⠈⠳⣄⢀⣃⠤⢊⠭⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠰⠀⠀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠈⠓⢶⣤⣀⠀⠈⠋⠀⠀⠓⠤⠄⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠀⠀⡰⠀⠐⡇⠀⠀⠀⠀⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠈⠺⣌⠉⠲⢄⠀⠀⠀⡒⠒⠒⢚⣽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⡀⠙⠉⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⣐⡞⢦⡀⠠⣈⣉⣉⡹⠋⠀⠀⣠⠴⠀⠀⠀⠀⣠⠤⣤⠤⠒⠊⠁⠀⠙⢤⣀⣀⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠈⠉⠒⠒⠋⠀⡀⠀⠀⣀⣀⠤⠴⠒⠉⠀⠀⢘⡆⠀⠀⠀⠀⠀⠀⠨⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠙⠁⠉⠀⢣⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠤⢄⡙⠫⢛⠠⢊⠠⠄⡀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠀⠀⠀⠀⠀⠀⡀⠀⠀⠺⣦⡀⠑⢄⠑⢌⠐⢝⢄⠀⠀⠀⠀ ⡤⠀⢀⢴⢎⠀⠠⢰⠀⠀⠀⠀⠀⡓⡀⠀⠀⢈⢷⡄⠀⠀⠀⠑⡐⠠⡄⢄⠀⠀ ⠀⠚⠠⡠⠁⢀⠃⡸⠀⠐⢤⣄⣀⡀⣈⣆⣤⠄⠡⢽⡀⠀⠀⠀⢸⣦⡀⠸⡣⠀ ⠀⠀⠳⠀⡰⢸⠀⢧⢇⠀⠀⢡⠸⠠⠤⢤⠝⣬⣢⣌⣣⠀⠀⠀⠀⢿⠀⠁⠀⠱ ⠀⠀⠀⢀⠃⣼⢠⠏⠉⢂⡦⡈⠆⠀⢾⠿⠽⠝⣀⣩⡟⡀⡀⠀⠀⢸⡗⠀⠀⠀ ⠀⠀⠀⢈⢠⡗⢳⡔⣁⡀⢱⠈⣘⠤⠠⣴⡾⠯⠛⠓⠊⡇⠀⠠⠀⠀⣷⡄⠀⠀ ⠀⠀⠀⣼⢸⢠⡷⠿⢙⣉⡜⠊⠋⠐⠈⠉⠁⠀⠀⠀⠀⡇⡆⠀⠀⠀⢷⠒⠀⡀ ⠀⠀⣠⢻⣿⡸⠷⡞⠟⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⠀⠀⠀⠐⠄⠀⠀ ⠀⠀⡭⣎⡷⠃⠚⠀⠀⠀⠀⠀⣀⠠⠄⣀⠀⠀⠀⠀⢸⠂⣻⠀⠀⠀⢸⣆⢠⠁ ⠀⠀⠀⢹⠣⠇⠀⠀⠀⠀⢸⣑⣶⣿⣿⣿⡿⢦⠀⠀⠃⠀⡟⠀⠀⡆⢘⣱⣿⠆ ⠀⠀⢰⠀⡆⠸⡀⠀⠀⠀⢸⣿⣿⡿⠋⢹⠁⢈⢡⠀⠀⠚⡇⡄⢠⠀⣿⣿⠃⠀ ⠀⠀⠘⠀⢠⠀⡔⡄⠀⠀⠈⢿⣿⣇⠀⠘⢄⡈⡏⠓⢦⣼⢣⠀⡌⣸⡟⠉⠁⠀ ⠀⠀⠀⡆⠀⠖⢱⡹⡢⢀⠀⠈⠻⠭⠵⠚⠲⠤⠔⣠⣾⡟⠄⠰⡧⠋⠀⠀⠀⠀ ⠀⠀⢂⠐⣁⠈⢃⢌⢔⢄⢁⠂⠄⡀⠀⠋⢀⣠⣾⣿⠿⡑⢠⠋⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠉⠙⢿⣛⠭⢗⣒⠲⠋⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀⠈⠑⢄⡀⠉⠲⢄⠈⠻⡲⢄⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⡀⠀⠙⢦⡀⠀⠑⢄⠈⠓⢍⠲⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⠀⠁⠀⠀⠀⠱⡄⠀⣁⠀⠑⢄⠀⠀⠀⠀⠀ ⡶⠋⠀⠀⣀⠔⡿⢡⠆⠀⢀⠆⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢣⡀⠀⠀⠀⠈⢦⠹⣿⡄⠀⠀⠀⠀⠀⠀⠘⣄⠈⠑⢴⠀⠳⡄⠀⠀⠀ ⠀⠰⠶⠈⣠⠞⡰⠁⠀⠀⡎⠀⢸⡄⠀⠀⢤⡀⢀⡀⠀⠸⠀⠀⠑⢄⠀⠀⠀⣀⣑⡘⢿⡄⠀⠀⠀⠀⠀⠀⠘⣦⣀⠈⠃⠀⡿⢆⠀⠀ ⠀⠀⠀⢀⠎⡜⠁⠀⠀⢸⠁⠀⡏⢧⠀⠀⠀⠙⢿⡷⢦⡶⠤⠤⠒⠚⠻⣿⠯⣁⠀⠉⠻⣷⠂⠀⠀⠀⠀⠀⠀⢻⣿⠗⠦⡀⠑⢌⢧⠀ ⠀⠀⠀⠎⡼⠀⠀⡰⠀⡌⠀⢰⢃⡿⡄⠀⠀⠀⠀⡇⢠⠗⠀⢤⠤⠤⢤⠼⢧⡤⠷⠦⣄⠙⣇⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠙⠀⠀⠈⢣ ⠀⠀⠀⠀⠁⠀⢠⠇⠀⡇⠀⢸⣸⠠⢼⡄⢠⡀⠀⢱⡘⠀⠀⢀⣤⣶⣿⠶⡿⣻⠟⠛⠿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡸⠀⣰⢷⣰⣾⠃⠀⠀⠙⣜⡗⢄⠀⢧⠀⠀⠘⣻⠛⠒⠒⠚⣁⢠⣠⣴⢿⣋⡇⠀⡄⠀⡀⠀⠀⠈⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠁⠀⣿⡴⢿⣾⣠⠞⠂⠀⠈⢻⡀⠙⠺⢦⡀⡀⠀⣠⣤⣶⠭⢚⣹⢿⡧⠴⠛⡇⠀⠁⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡄⠀⡟⠀⢈⢿⣧⣤⣶⣦⡀⢸⡃⣠⡾⡞⠉⠁⣹⣻⣽⠟⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⢸⠃⣴⣿⣿⡯⠵⠋⢀⣠⡾⠋⠩⠊⠀⠐⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡇⠀⠀⠀⠀⠀⢸⣶⠚⠃⠀⠀⢀ ⠀⠀⠀⠀⠀⢸⣿⣘⡄⢿⡇⢀⣤⣴⣞⣹⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⡄ ⠀⠀⠀⢀⢧⠈⣿⡷⣇⡛⠿⢟⡩⠞⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠿⣷⠀⠀⠀⠀⠀⠀⠸⠦⠀⠀⠀⠁ ⠀⠀⠀⠘⢈⣆⢹⢷⠸⣥⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡜⠀⢿⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⡔⠀ ⠀⠀⠀⠘⠈⢾⣼⡌⢇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⣉⣉⣹⣷⣦⣄⠀⠀⠀⠀⠀⢠⡿⠁⠀⣾⠀⠀⠀⠀⠀⠀⣼⡧⠃⣼⠀⠀ ⠀⠀⠀⠀⡀⠘⡟⢷⠸⡄⠀⠀⠀⠀⠀⠀⠀⣾⣤⢶⣾⣿⣿⣿⣿⣿⣿⣿⡷⣄⠀⠀⠀⠚⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⣏⣠⣾⣿⡶⠀ ⠀⠀⠀⠀⡇⠀⢱⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠿⣿⠋⠀⠞⢣⠀⠀⠀⠀⣀⣼⡇⠀⡀⠀⢸⠀⢰⣿⣿⣿⡟⠁⠀ ⠀⠀⠀⠀⢳⠀⠸⡄⠀⢘⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠁⠀⢰⡏⠀⠀⢇⢈⣆⠀⠀⠀⠀⢸⡇⢰⠀⠀⡎⠀⣸⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⢇⠀⠀⡟⣆⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡀⠀⠀⠀⢧⠀⠀⠹⣿⠛⠷⣦⣀⣀⣾⠃⡆⠀⢰⠁⢠⣿⡿⡹⠋⠁⠀⠀ ⠀⠀⠀⠀⠸⡄⠀⠸⡄⡆⢣⠘⣦⡀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣄⠀⠀⣀⠑⠦⡀⢳⠀⠀⠀⣹⣿⡟⢰⠁⠀⡏⢀⣾⠜⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢧⠀⠀⢱⠸⠸⣧⠹⡝⠢⡀⠀⠀⠀⠀⠙⠯⢄⡠⠭⠔⠚⠳⠦⣄⡴⠂⣠⣾⣿⣿⢃⡆⠀⣼⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⠀⠘⡤⡀⠀⠱⣇⢣⠣⡙⣄⠈⠑⠴⣀⠀⠀⠀⠀⠀⢠⣤⠖⠀⠀⠀⣠⣾⣿⣿⣿⡏⡘⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢦⠀⢱⢱⡀⠀⠻⡌⢧⠘⢎⢦⡀⠀⡈⠉⠲⢤⣀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⠟⡽⠐⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠔⠲⠖⠒⠤⠤⣔⠒⠒⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡔⠉⠁⠀⢀⠔⢀⡠⠀⢠⠀⠘⣧⠀⢢⠀⢣⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⡴⠃⠀⡿⠀⠀⢸⡆⠀⠘⡄⠀⡆⠘⣯⠉⠉⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠃⢀⠔⣠⠞⠀⢀⡼⠁⠀⢠⡿⣷⠀⠀⡇⠀⢹⠀⣿⣧⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⡰⠁⡼⠁⠀⣠⠟⠁⠋⣩⡽⠟⣿⠀⣼⡇⠀⣼⡇⡸⢸⣇⡹⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠰⢁⡞⠀⠠⣶⢣⣤⣶⣞⣿⡇⢠⡏⣼⣿⢁⣼⡿⣾⡇⢸⡟⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⠀⣾⠁⠀⢰⡏⣿⣿⣷⣿⡟⠃⡼⣷⣽⢣⣾⣿⣿⢻⠇⣸⡇⣿⡿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢸⣿⠀⠀⣼⣷⠇⢸⣿⣿⠃⠀⠹⢻⣿⣿⣯⣷⣿⡸⢠⠏⠀⢿⣵⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣾⢿⡀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠏⢸⣷⠋⢀⡗⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣱⣿⢠⣷⣼⣿⢸⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⢰⣿⠇⢀⣼⢰⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⣿⣧⣾⣿⣿⣿⡆⠓⢤⡀⠀⠀⠘⠛⠀⠀⠀⢠⣿⡟⣠⢾⡿⣻⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⢧⣄⠀⠀⢿⡿⣧⣿⣿⡟⣆⠀⠙⠢⣄⣀⣠⣤⣴⣶⣿⣿⣾⣧⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢉⢉⣱⣒⡶⠊⠀⠀⠀⢠⣈⠉⠢⣄⢠⣤⠀⠀⠉⠙⢦⡄⢀⡤⠿⠿⠿⠿⠛⠓⠻⢾⣿⣧⣀⠴⠒⠢⢤⡀⠀⠀⠀⠀⠀⠀ ⢀⣴⠾⢛⣛⣩⣽⠏⠀⠀⠀⠀⣀⣀⠤⠟⠋⠉⠉⠁⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠰⣄⢤⠿⠇⠀⠒⠒⠂⠞⢆⠀⠀⠀⠀⠀ ⢉⡤⣖⡋⢉⢡⡿⠀⠀⠀⠀⡴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢴⣉⠉⠛⠒⠲⠈⢧⠀⠀⠀⠀ ⣫⠞⡟⡵⣽⣿⡇⠰⠒⠒⡟⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⠀⠀⠀⠈⢦⣄⣀⠀ ⠁⣸⢀⣼⣟⡾⠁⠀⠀⢰⠁⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠁⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣄⠀⠀⠀⠘⣿⣶⣭ ⣦⣿⣸⣿⣿⠃⠀⢠⠀⢸⠀⠘⣆⠙⣦⣄⣀⣀⣀⠤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠙⢓⢤⣀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡹⠷⠀⠀⣿⡈⣿ ⠀⠀⠈⠉⠙⠒⠤⠤⢄⣸⡤⠐⠛⠒⠳⠤⠤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⣖⢋⠁⢻⣿⡟⠁⠀⠀⢰⣟⢻⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠰⣤⠀⠀⡿⣿⠀⠈⢿⠃⠀⠀⠀⢸⣿⡀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⡃⠈⢦⡠⠃⠀⠀⠀⠀⣸⡇⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢼⡁⠀⠀⠀⠀⢀⣿⢣⡿⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣲⣄⠀⢀⡞⣁⣾⠼⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢡⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡽⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⠾⣝⠣⣌⡲⣷⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣶⣭⣶⣉⠛⠳⠄⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡛⠿⣿⣿⣶⣶⣤⣄⣀⡈⠑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠤⠚⢰⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠈⠙⠧⣍⠙⠛⢻⠿⠿⣶⣶⣤⣤⣦⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡽⠋⠉⠁⠀⡄⠀⡾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠈⢳⡀⠀⢦⠀⠀⠙⠉⠛⠛⢿⣷⣷⣦⣤⣀⡀⠀⠒⠒⠒⠩⠄⠂⣀⠀⣀⣽⣧⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⡏⠛⢿⣿⣶⣶⣤⣉⡉⠓⠙⠛⡒⠉⢿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢹⡇⠀⡀⢀⠷⣄⣀⣤⠀⠀⠀⡀⠓⢤⣀⣼⠿⠿⠛⣿⡿⠟⠓⠒⠀⠀⠀⠓ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡼⢁⠎⢠⣿⣿⠇⡀⢀⡔⢁⡶⠚⠉⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⣠⠔⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠎⠀⣿⡿⠈⢸⣇⡼⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠈⠀⣼⣿⠃⠀⢸⠏⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⡽⠈⠀⠀⡿⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢸⠁⠀⠀⢰⡇⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢨⠇⠀⠀⠀⡏⠀⠀⠀⡼⠁⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢸⠀⠀⠠⣸⠀⠀⠀⣰⠃⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢀⣿⡇⠀⢠⠇⠀⠀⣼⠇⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⣀⣾⢻⣥⢀⡾⢀⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣃⣀⣠⡾⠋⠀⢸⣿⣾⣧⣸⠻⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣧⣀⣀⣠⣾⣿⣿⡿⠁⠀⠀⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⡄⢈⣉⣙⡛⠛⠿⠶⢤⣤⣴⣺⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢾⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣤⣄⡀⠀⠀⠀⠈⢻⣧⠈⠉⠻⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣿⡟⠻⢷⣦⣄⣀⣴⣿⣧⣀⣀⣬⣿⣿⣿⡷⠢⡄⠀⠀⠀⠀⠀⠀⠀⡿⠿⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢿⣦⡀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⣦⡀⠀⠀⠀⠀⠀⢣⡀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣿⣶⣾⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠙⢆⠀⠀⠀⠀⠀⠱⢤⣾⣿⣿⣿⠏⠉⠉⢉⣽⣿⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣿⡤⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⡆⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠈⠉⠉⠉⠙⠻⣿⠟⢢⡀⠀⠀ ⠀⠀⢰⡁⣿⣿⣿⣿⣧⡀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠱⡀⠀ ⠀⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣧⠀ ⠀⠀⢻⢸⣿⡟⢻⣿⣿⠛⠛⠿⠛⢹⢿⣿⡿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀ ⠀⠀⢸⣿⣿⣿⠾⠁⣿⣦⠀⠀⠀⣇⡸⠏⠀⣿⣿⣿⠿⠢⢄⣀⠀⠀⠀⢀⡀⠤⠀⣤⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⢰⠛⠛⡏⠀ ⠀⠀⠀⢿⣿⣿⡆⠀⠙⠛⠁⠀⣀⠀⠀⢀⣼⣿⠟⡁⠀⠀⠀⠈⠉⠒⠊⠡⠤⠤⢼⣿⣿⣿⣿⣿⣿⠿⠷⣄⣀⣰⣇⣀⡴⠁⠀ ⠀⠀⠀⠈⠻⣿⣿⠀⠂⠤⠤⠤⠤⠖⠊⣿⣿⣿⠑⠌⣳⡆⢠⣤⠴⠊⠁⠉⠉⠉⠒⠢⢍⡻⣿⡟⠁⠀⠀⠈⢿⣿⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠓⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇⠀⠀⠈⢳⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⠃⠀⠀⠀⠀⣼⠯⠤⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢠⠞⠀⡀⢀⡜⠁⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⣀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢴⡿⠀⣮⠀⠀⠀⠀⠀⠀⠈⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡊⢁⠠⠃⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⡀⠀⠀⠈⠑⠢⡄⠀⠀⠀⡼⠉⠉⠉⠓⠒⠉⠘⢦⡀⠀⠀⠀⠀⢀⠔⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡞⢁⣴⣾⣿⣿⣷⣦⣀⡤⢞⡵⠒⠓⢒⣦⡀⠀⠀⠀⠉⢲⡦⠤⠚⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣿⣿⣿⣿⠟⠛⠿⣿⡄⢸⠀⢀⣴⣿⣿⣿⣷⡤⠖⠊⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡇⣴⣶⣆⠘⡷⣈⣰⣿⣿⣿⣿⡿⠟⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣯⠣⣛⣛⣁⣀⡆⠈⠻⢿⣿⣿⠏⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⣥⣴⣾⣿⠀⠀⠀⠉⠛⢦⣄⣀⣌⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡛⠛⠁⠀⠀⠀⠀⠀⠀⠉⢻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠐⠉⠉⠉⢻⣿⣿⣿⣿⣶⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⢄⡀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⡇⠀⣼⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⠉⠓⢤⡚⠉⠉⠉⠛⢏⡀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡏⠀⣧⢰⡏⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢱⠁⠒⣬⣢⢄⠀⠀⠀⠈⠢⡀⢀⣴⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⣿⣿⡁⠀⢸⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠟⠋⠉⢳⡀⠑⢦⡀⠀⠀⠈⢻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢠⣾⣿⣧⣶⣿⣿⣟⣉⡒⣼⠀⠀⠀⣿⣿⡦⠶⠶⠀⠀⠀⠀⠀⠀ ⠀⢨⠃⠀⠀⠀⠀⣇⠀⠀⠿⡖⡄⠀⠀⢻⣿⣿⣿⡆⠀⠀⠀⠀⢠⣿⣿⣿⣥⣿⣋⣹⣿⡋⢙⣻⣆⠀⢰⣾⣿⣷⡈⣷⣤⣤⠀⠀⠀⠀ ⡿⠋⠀⠀⠀⠀⢠⢃⡀⢀⣸⡟⠸⡄⠀⠀⡟⠋⠁⢸⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⢡⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⣠⠯⣄⠙⢾⣿⠇⠀⢹⡀⠀⠸⡀⠀⠀⡇⠀⠀⠀⣏⠙⠛⠿⢿⣿⣯⣽⡟⠻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠦⠤⠤⠟⠁⠀⠀⠙⠷⠮⠧⢤⣞⣀⠄⣀⣇⠀⢀⡷⠔⠒⠂⠛⠿⣶⣶⣶⠈⠉⠃⠀⠀⠛⢛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠁⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠈⠀⢿⣧⣄⣀⣠⠀⣠⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⡀⠀⠉⣦⣙⢦⡉⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠈⣿⡙⠒⢿⠁⠈⠓⠢⠄⠧⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⣸⣆⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⡿⠄⣉⣽⠓⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢤⡷⣼⡟⣽⡞⢻⠖⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⠀⠓⠒⠛⠤⠴⠧⢄⣀⣀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠘⠻⠟⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⣠⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠉⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⠀⠀⢠⠃⠀ ⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⢶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⠁⠀⠀⠀⠀⢀⡴⠋⠀⢱⡼⠀⣠⠎⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣦⡀⠀⠀⢀⠎⠀⠀⢠⠎⣠⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣠⣿⣿⣷⣄⢀⡞⠀⠀⣠⣇⡼⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠿⣿⣿⣿⣿⣿⠉⠉⠐⣏⠀⣰⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⡸⠔⠒⠒⢳⡀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠈⠛⢿⣿⡿⠀⠀⠀⠉⢲⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⣨⡦⠠⠴⠦⠤⠜⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢠⠋⢀⠄⠀⠂⠀⠀⢀⣀⠤⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠐⠿⣟⡫⢂⠝⣆⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠈⠻⡿⢶⣶⣤⣄⣈⡒⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡄⠉⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⢂⠈⠲⡍⠙⠛⠻⠶⢶⣤⣀⡀⠀⢀⡀⠠⡈⠀⠀⢦⡜ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⢠⡀⠁⡀⠀⠀⠈⠙⠟⠻⢶⣶⣬⣁⡀⠛⠈⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⣇⠆⠌⣷⠶⠀⡰⣨⠕⠊⢉⠝⠉⠉⠀⢀⠨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠎⠌⢰⡟⠠⡵⠊⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⡝⠁⠸⠁⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠰⠀⠀⡞⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⠀⠀⠇⠀⡠⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⣾⡇⡼⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣠⣴⣥⠴⠋⢸⣿⣧⠏⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⢿⣿⣿⣯⣽⣿⣿⣿⠓⣒⠻⠿⢧⣀⣬⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠉⠀⠀⠉⠉⠑⠲⢶⣫⣵⣲⣿⡛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸ ⣇⡤⠔⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⣀⣠⠤⠒⠚⠉⠀⢀⣀⢼ ⡏⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣷⡀⠀⠀⠀⠀⠀⠙⢦⣀⠤⠴⠒⠉⢁⣀⣸ ⡿⢗⣲⣦⣤⡀⠀⠈⠻⣧⡀⠀⠀⠀⠀⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠃⠀⡄⠀⠀⠀⠀⠀⠀⢣⡤⠤⠒⠋⣩⣤⣾ ⣇⢴⣿⢹⠻⣿⣿⣦⡀⠈⢷⣄⣦⣶⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡇⡀⡆⢳⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⣾⠁⢸ ⣇⡆⣇⡸⠖⠋⠉⠉⠉⠉⠘⠛⠯⢭⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⡸⢡⡧⡇⠘⠄⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢿⠀⢸ ⣿⢠⠋⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⢀⡴⢡⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣼⠀⢸ ⡿⡆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⢁⠴⠋⠀⣾⡟⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢿⠀⢸ ⡇⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢀⡜⠁⠀⠀⠘⠛⠁⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⣾⣤⣼ ⣗⣾⠀⠀⠀⠀⡅⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢀⡞⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸ ⡇⠸⠀⠀⠀⢸⡇⢀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⣜⣀⣀⢀⡴⢒⡤⠖⠊⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸ ⡇⡀⠀⢸⡄⢸⢷⣌⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⡼⠁⠀⠰⢋⡴⢯⠀⠀⠀⠸⡀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸ ⡇⡇⠀⠀⠀⠸⢸⠀⢉⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢠⣾⣁⡤⠒⠊⠁⢀⡀⠑⠦⡀⠀⢣⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢸ ⡇⠇⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⡼⡏⠀⠈⠲⣄⠀⠀⠙⢆⠀⠈⠑⢬⡦⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸ ⡇⠘⠀⠀⠀⠐⡞⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣼⢷⣤⣤⣤⣬⣷⣤⡄⠀⠃⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣤⣴⠞⠋⣡⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠝⠷⣄⠀⠀⣻⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠶⣶⠖⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠻⠿⣿⠻⣿⣉⢻⣿⣍⣉⣻⣟⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⣠⣴⣻⣿⣿⣿⣿⣿⣿⣿⠟⣿⣏⡟⣤⣾⣿⡟⢿⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⢎⡙⣲⣿⣾⣿⣿⣿⠿⣿⣿⣿⣯⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣟⣱⡿⠿⠛⣉⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⢿⡟⣿⣿⣿⣿⣧⡀⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢫⣴⡿⠛⣳⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠟⠀⢿⣿⣿⣿⣿⣏⠁⡈⠉⠿⢿⣿⣷⡠⡀⠳⡄⠀⠀ ⠀⠀⠀⠀⠈⠁⣠⣿⡟⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⢸⣿⣿⢹⠉⣿⣿⣿⣿⡻⣿⣿⣿⣷⡌⢆⡈⣿⣿⣿⣿⣿⣧⠉⢷⡀⡈⠛⢿⣷⡠⠀⠘⡄⠀ ⠀⠀⠀⠀⠀⣼⣿⣟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⢿⣿⠀⡿⣿⣿⠀⢿⣿⠸⡄⠘⣟⣿⣿⣇⠈⠘⢿⣿⣧⣴⣷⡝⣿⡿⢿⣻⣿⣷⡘⢿⣮⣼⢀⠙⢷⣄⡀⢹⠀ ⢲⣶⣦⣤⣾⣷⣻⣽⣿⣿⣿⣿⣿⣿⣿⢿⠛⣿⣿⣶⣿⣿⣿⠩⣤⣿⡆⠷⢿⣿⠦⢼⣿⠛⠉⠉⢙⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⠇⠘⣧⠐⢷⡀⠿⠿⣤⣽⣿⣿⡀⠀⠉⠙⠲⣤ ⠓⠉⢛⣷⣤⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣟⣍⡽⣿⣿⣷⠀⣿⡇⠀⢘⣣⣠⣴⣿⣶⣾⣿⣿⣿⡿⠿⢿⡟⠋⠉⣿⣿⣿⠀⡀⣹⡆⠈⠱⠡⠀⠀⠈⣹⠻⣿⠷⠶⠶⠶⠶ ⠀⢸⣼⡿⠿⠃⡟⣿⣿⣿⣿⣿⣿⣿⣿⢳⠈⣿⣿⣿⠁⢹⣿⣯⣴⣿⣷⣿⣿⣿⠿⠛⠛⠋⠉⠉⢁⣿⠀⢠⡬⠛⠀⠀⡟⠛⢳⣷⣶⡏⣿⡀⠀⠀⠃⠐⡰⡀⠂⠨⢁⠤⠤⠀⠀ ⠀⠈⣿⡇⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣩⣽⣿⣿⣿⠿⠿⠛⠋⠉⠉⠈⠻⣿⠀⠀⣴⡆⠀⢰⡿⠃⢚⡿⠁⠀⠀⠀⢠⣤⣤⡿⣿⡇⠸⣇⠀⠀⠀⠀⢱⣿⡀⠘⢀⠀⠅⣘⣷ ⠀⢸⢹⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⡇⠀⢠⡀⠀⢰⡾⠇⠀⠀⠀⠙⠀⠀⣿⡇⠀⠸⠏⠀⢀⣀⡀⠀⠀⢀⣾⣿⠃⠀⠸⣧⠀⣻⡄⠀⠀⢠⠀⢻⣿⡄⠙⢿⣞⠛⢉ ⠀⠸⠸⣿⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠿⠃⠀⠈⠁⠀⣀⣴⡇⠀⠐⣦⠀⠀⠀⣿⡇⠀⣐⣀⣠⣾⣿⣷⣶⣿⣿⣿⣿⡀⠀⣾⣿⠀⢹⣷⠀⠀⠀⠀⠫⣿⣷⠀⠀⢹⣷⡈ ⠀⠀⠀⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⣤⡤⠀⠀⠀⠀⠋⠉⣀⣀⣠⣿⣷⣤⣶⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠛⠋⢹⣿⡇⠀⣿⣧⠀⡌⣿⣧⠀⠀⠀⠂⠘⣿⣧⠀⠀⣿⣿ ⠀⠀⠀⠘⣿⡄⣿⢹⣿⣿⣿⣿⣿⣷⡖⠀⢀⣿⣧⣤⣤⣶⣶⣶⠿⠟⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣿⡇⣼⡿⢿⠀⠇⢸⣿⣆⠀⠀⠀⠀⠹⣿⡆⠀⢸⣿ ⠀⠀⠀⠀⠘⢿⣿⡿⣿⣿⡿⣿⠿⢿⣿⣿⣿⡉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣰⡟⢰⢿⣿⣷⠃⣸⣆⣠⢸⣿⣿⡆⠃⠀⠈⡄⠹⣿⡄⠈⣿ ⠀⠀⠀⠀⠀⣰⠛⣿⣿⣿⣿⣿⣆⣺⣿⣿⣇⠙⢢⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⠀⠀⠸⠀⠀⠀⠀⠀⢀⣿⣷⠟⣾⣯⡏⠀⠘⢩⣿⢈⣿⣿⣿⣿⣦⠀⠀⠀⠹⣧⡀⣿ ⠀⠀⠀⣀⡾⠃⠐⣷⣿⣿⣧⠈⢹⣿⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢲⣎⣩⣤⣴⣶⣿⣿⣿⣷⣶⠃⠀⠀⣀⣠⡾⠋⠁⢠⣿⡞⢠⣦⣤⣿⢘⢼⣿⣿⣿⣟⢿⠀⠀⠀⠀⠘⢿⣿ ⣤⡤⠚⠋⡴⠀⣼⡟⢿⣿⣿⣦⣤⣿⣧⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠛⠉⠛⣿⡆⠀⣀⡨⠕⠃⠀⠀⣼⡿⢠⣿⡏⠀⢹⢸⣿⣿⣿⣿⣿⣼⡄⠀⠀⠀⠀⠈⢿ ⠉⠀⠀⢰⡇⣴⡿⠁⢸⣿⣸⣿⢹⣿⣿⣿⣯⣿⣦⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠁⠀⣠⠶⠃⣿⡇⠈⠉⠀⠀⠀⠀⢸⣷⣣⣾⣿⣿⣶⣿⣾⣿⣿⣽⡏⣿⣿⣿⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⣾⢸⣿⠁⠀⠀⣿⡏⡇⠘⣿⣿⣿⣿⣿⣏⠙⠲⠤⠀⠀⠀⠀⠈⣿⣿⣡⠔⠋⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⣼⠉⠉⠉⠉⢹⣿⢋⡿⢻⣿⣿⣷⣼⣿⣿⣧⡀⠀⠀⠀⠀ ⠀⠀⠀⢿⡟⣿⠀⠀⠀⠸⣽⠳⠀⣿⣿⣿⣿⡿⣿⣷⡀⠘⢀⣤⡤⠴⠒⠚⣉⡤⠐⠀⢀⣰⢟⢡⠁⠀⠀⠀⠀⣠⣾⣿⡦⣤⠀⣰⣿⣾⣼⣷⡞⢿⡟⠛⠛⠛⢹⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠘⣇⣇⢆⠀⠀⠀⢻⣧⠀⢿⣿⡟⣿⣆⣸⣿⣿⣗⠋⠀⠀⢀⣶⣾⣋⣀⣤⠴⠿⠵⢄⡠⠀⠀⢀⣠⣾⣿⡟⡿⠀⣿⠀⣿⣿⣿⣿⣿⣿⡀⠹⡀⠉⣆⠰⣿⣿⠆⠀⠀⠀ ⠀⠀⠀⠀⠹⣾⣬⠧⢤⣀⣀⠙⢧⣘⣿⡟⠃⠀⠀⠀⠀⠀⠘⠛⠛⠛⠓⠲⠤⠤⠤⢄⣀⣀⣀⣋⡤⣤⣿⣿⣿⠏⠁⢧⠀⣿⢀⣽⣿⣿⣿⣿⣿⣿⣄⠀⠀⠙⢳⣿⠏⠀⠀⠀⠀ ⠀⠀⣠⠖⠋⠁⠀⠀⠀⢀⣭⢉⣀⣩⡿⠷⠛⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⢤⣀⣀⣀⠀⠀⠀⣀⣠⣤⣿⣿⣿⠋⠀⠀⠸⠀⣿⠀⠉⣿⣿⠿⣿⣿⣿⣿⣷⡂⠀⠀⢹⣦⡀⡇⠀⠀ ⣠⠾⠁⠀⠀⠀⣀⡤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⣀⠀⣿⡆⠀⢸⣿⠀⠹⣿⡻⣿⣿⣿⡀⠃⠀⢛⢿⣇⠀⠀ ⠉⢀⡴⠋⣱⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣶⡶⣄⡀⠀⠉⠉⠛⣫⠍⠁⠀⠀⠀⣰⠃⠀⢻⣿⣦⠀⠘⢦⡀⠈⠳⣽⣿⡿⢧⣷⠀⢸⠀⠻⠄⠀ ⠀⠉⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠛⣻⡿⣙⡲⠿⠿⣭⣙⣉⠁⠀⠀⠀⠀⡼⠁⠀⠀⠀⠙⠿⣿⡶⣾⣷⣦⣤⣸⣿⣿⣿⣻⢆⣼⣤⣀⢀⡄ ⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣈⣩⡽⠟⢉⣭⣿⣶⣦⣤⣉⡛⢦⣄⡀⠚⠁⠀⠀⠀⠀⠀⠀⠈⠙⠲⣼⣿⠛⠮⣽⣿⣧⢀⣽⣿⡿⠿⢿⣄ ⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣠⣤⣴⣶⣾⣿⢧⠤⠴⠾⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⣿⡶⠶⠶⣶⣶⡦⠤⣤⣤⢤⡝⠙⣶⣶⡏⠙⠛⠃⠀⠀⠀⠀⠀⠠ ⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣅⣀⣤⠴⠟⢛⣩⠖⠋⠁⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⣉⠙⠉⢻⠭⡟⠻⣏⢈⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠩⠟⠙⠲⣄⣭⡳⢷⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣠⠀⠀⠀⠀⠀⠀⠘⣗⡄⠳⡙⠧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⠒⠒⠒⠢⠤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡖⡶⣤⠀⠀⠀⣾⡀⣇⠀⢀⡶⠀⠀⠀⠀⠈⠀⠀⢐⣩⠿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠿⠤⢤⣀⠀⠀⠀⠀⠈⠑⢯⡳⣄⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠀⠀⠀⣟⣷⣾⣦⣼⣧⣤⣀⡒⠊⠉⠉⠉⠉⠻⢦⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠹⡈⢿⡽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⡶⡄⠀⠀⣀⡴⠖⠛⠛⠻⣧⠼⠓⠒⠚⠯⣷⣦⣤⡀⠀⢐⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⢦⡀⠀⠀⢀⡇⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠂⣠⠞⠉⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠉⠓⠭⣍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⠂⠙⢦⣤⠞⠀⢣⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢠⠞⣽⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣷⠀⠀⠀⠀⠀⢞⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⢀⠀⢠⠏⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡏⠀⠀⠀⠀⠒⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣇⣀⣀⣴⣯⣼⡏⢰⣤⣝⠷⣜⢦⡀⠒⢦⡀⠀⠀⢠⡀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠒⠉⠉⠙⡿⠀⠀⠀⢀⣴⠾⠟⠳⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠇⢨⣯⣭⠾⠛⠁⠈⠙⠻⠗⣾⣍⠛⠓⠒⠺⡗⠒⠒⠚⠛⠉⣇⠀⠀⠀⠀⠀⠀⢀⣴⠊⣡⠟⠀⠀⠀⢀⡞⢁⣠⠶⠊⠁⠀⠀⠀⣠⣶⡴⠟⠙⠢⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡟⢠⣾⡿⣷⡄⠀⠀⠀⠀⢀⣼⡿⡿⣷⣆⡄⠀⡇⠰⠀⠀⢢⠀⠸⣆⠀⠀⠀⠀⢠⠞⢡⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣾⠟⠉⠀⠀⠀⠀⠈⢧⠀⠀⠀ ⠀⢀⣠⣾⡟⠀⢨⣿⣿⣩⣧⠀⠀⠀⠀⣿⣷⡏⠉⠟⣿⠋⢰⠇⡆⡈⠄⠀⠳⡄⡸⡆⠀⠀⢠⡏⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀ ⠀⠀⣤⡟⠀⠀⠈⠙⣏⣿⣿⢧⣀⠀⢨⡿⣿⡯⢀⣼⠇⠀⣼⡜⠀⡀⡜⣆⠀⠱⣿⢹⣆⠀⡾⣰⢷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⢀⠀⠀⠀⠀⡿⣍⠉⣽⠇⠀⠀⠉⠉⠉⠉⠁⠀⢸⡏⠀⠀⠈⢞⣌⢣⠀⡌⣿⡢⣰⡿⠁⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢋⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⢸⠀⠀⣀⠾⣇⠈⠉⠁⠀⠀⠀⢠⡿⠶⣄⠀⠀⣸⠀⠠⡱⠀⠈⢎⢆⠀⣧⠿⠷⠿⠷⢶⣀⣈⠍⠙⠒⠲⠶⠶⠖⠋⠁⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠻⡼⡄⠀⢘⣆⠈⠳⡮⣷⠤⠖⠋⠉⠁⠀⣼⠀⢀⣿⡆⠀⠑⠀⠄⣆⠀⢀⡟⠦⣄⣀⠠⠴⠖⠉⠉⠙⠲⢦⣀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⣴⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠿⠿⣄⣸⣇⣀⣾⠻⣯⡥⢶⣒⣶⡀⢀⣽⠉⠹⢻⠀⠀⠀⠀⢨⠇⠀⡼⠁⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠈⠳⡄⠀⠀⢸⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣿⣦⠀⠀⠀⠉⠈⡿⠁⠀⠀⠉⠉⠑⣀⣿⣿⣿⣤⣴⠿⢧⡀⠀⣠⠎⣠⣾⡥⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠹⡄⡀⢼⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢷⣄⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⢀⡼⣿⣏⣿⡍⠀⠀⢀⡽⠚⠉⣉⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢁⣸⠖⠛⡿⢄⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⢧⡀⠀⠻⣆⠀⠀⢸⠀⠀⠀⠀⠀⣠⣾⣾⠏⠈⠻⣽⡴⠚⣡⠤⠞⠋⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢚⡟⠀⠀⠐⡇⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠳⣤⡀⠈⠳⣤⡞⠀⠀⠀⣠⣾⣟⡿⠋⠀⠀⣮⠭⣧⠘⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀⡼⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠙⠶⢤⣀⣉⣛⣻⣿⠽⠟⠁⠹⡆⠀⠀⠈⠙⠉⢤⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⣠⠞⠋⠀⠀⠀⢠⠇⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⣣⠞⠁⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣸⠁⠀⠀⠀⠀⠀⠀⣰⠏⡏⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⢀⣯⡋⠀⠀⠀⠀⠀⠀⢠⠗⠋⠉⠉⠉⠉⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢨⠇⠀⠀⠀⠀⠀⠀⢀⡿⣴⠃⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣼⠇⠉⠓⠦⣄⣀⡠⠤⠛⠛⠓⠲⢤⣀⣀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⣸⡄⢸⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠠⡏⠀⠀⠀⠀⠀⠈⠛⠒⠤⠀⠀⠀⠀⠀⠈⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢀⡏⢇⠈⣇⠀⠀⠀⠀⠀⠀⠘⡇⠀⢀⠇⠀⠀⠀⠀⠀⠀⢰⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠒⠋⠙⣓⡾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⣼⠀⠈⠇⠘⢦⡠⠤⠤⢤⣀⡴⢷⡀⣾⠀⠀⠀⠀⠀⠀⠀⡼⠀⠓⣤⡤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣀⣀⠤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠧⣀⠀⠀⠀⠙⢯⣠⠿⣙⣓⣚⣿⠇⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⠉⠙⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠷⢦⡈⠑⡢⣤⣀⣀⣐⣏⣉⣙⣋⡟⠀⠀⠀⠀⠀⠀⠀⢻⡯⡗⢦⣀⠀⠀⠀⠀⠈⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⢠⣿⠿⠟⠉⠉⠉⠍⣷⣶⣄⠀⣀⡀⣀⣀⣀⣀⣀⣀⣾⣻⣍⠙⠲⢿⡁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⣿⠇⢀⢀⣠⣤⣴⢶⢿⣿⣿⣿⣿⣿⣿⣿⡟⠿⢧⣀⠈⠙⠲⢭⣂⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢠⡟⣅⣶⣿⣿⣿⣿⣿⣦⣾⣿⠿⠿⢍⣉⡯⣿⣷⣄⠀⠉⠓⢦⣀⠀⠉⠛⠯ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠉⢹⣿⣿⣯⣿⡿⣻⡿⠋⠉⠀⢀⣘⣿⣿⠿⢿⣯⠙⠲⣄⠀⠈⠑⢦⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠋⠠⣼⣿⣿⠿⣻⣽⡿⢋⠀⠀⠀⠀⠁⠁⠀⠀⠀⠘⣯⠳⣄⠈⠙⠦⣄⣀⡺⠝ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠁⣠⣾⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⠈⠳⣄⠀⠀⠈⠉⠓ ⠀⠀⠀⠀⠀⢠⡼⠛⠛⠉⠉⢀⣿⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠈⠙⠒⠶⠶⠶ ⠀⠀⠀⢀⣴⣿⣧⠀⠀⠀⢀⣿⣿⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀ ⢀⣤⠞⠉⠀⢸⡟⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢨⣿⠀⣼⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⢰⣯⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⢸⣿⣿⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁ ⠀⠀⠀⠀⠀⢸⣿⣇⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀ ⠀⠀⠀⠀⠀⣾⣿⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀ ⠀⠀⠀⠀⠀⣽⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀ ⠀⠀⠀⠀⠈⣻⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠌⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⢔⡮⠒⠒⠒⠂⢌⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⡿⢿⠆⣤⣀⠀⠀⠈⠪⡢⡈⠳⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠃⢠⣤⣸⠿⠓⠛⠦⢔⢄⡈⢟⢞⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⢫⡅⢠⠀⠉⢩⣭⡿⢿⣾⣼⣿⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣷⡄⠀⢣⣌⣤⠀⠀⠈⠀⠈⢹⣿⠇⠠⠤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠙⡈⠐⢕⡅⠀⠀⣀⣔⠆⡜⠇⠀⠀⠔⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠑⠠⣙⡖⠀⠭⢄⡞⠁⠀⣴⠊⠀⠀⣧⠀⠃⠀⠀⠀⢀⠤⠄⠀⠀⠀ ⠀⠀⠀⠀⡐⠈⠀⠈⠤⣤⣤⠠⠀⠈⠁⠀⠀⠀⠘⢧⢸⠀⠀⠠⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠈⢄⡀⠀⠀⠀⠀⠀⠀⣄⠀⠀⡤⢈⡎⡄⢀⠁⠀⣠⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⡄⠀⠈⢻⠀⠀⠀⠀⠘⡄⠘⠫⠧⠶⠻⠠⡈⡎⠀⠀⡄⠡⡀⠀⠀ ⠀⠀⠀⠀⠀⠈⢀⠀⠀⠣⣀⠓⠀⡴⠁⠀⠀⠀⠀⠐⠒⢲⠀⠀⠀⠘⢄⠈⠂⡀ ⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠉⠪⢄⠀⠀⠀⠀⡔⠁⠀⡘⠀⠀⠀⠀⠀⠑⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠱⡆⠀⠚⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣈⣧⡀⠀⠘⡄⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠇⠀ ⠀⠀⠀⡀⠄⠒⠉⠁⠀⠀⠀⠀⠈⠳⣄⠀⠈⢦⡀⠀⠀⠀⢣⠀⠀⠀⢀⠞⠀⠀ ⠀⠀⡌⠀⠀⠀⠀⡄⠀⢀⠀⣀⠀⠤⠉⢳⡄⠈⢌⢢⢀⢠⡤⣡⠔⠺⡧⠬⢶⠀ ⠀⠀⠁⠀⠀⢀⣴⣿⣿⣿⣿⣷⣦⣄⡀⠀⢻⢄⠀⠑⢿⣾⣿⣾⣷⣾⣧⣄⣀⣧ ⠀⠀⠢⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣵⠯⠜⢀⣠⣤⣝⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠂⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣦⠹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠈⠻⣿⣿⣿⣦⡀⠀⠨⣄⡠⣄⡈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠀⠀⠀⠀⠀⠀ ⡄⠀⠈⢻⣿⣿⣿⣦⡀⠀⠙⢦⡉⠓⠤⣀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠿⣷⣦⣄⣙⣷⡈⠻⣿⣦⡀⠀⠙⠲⣄⠈⠙⠦⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠈⠙⠛⠿⣿⣆⠈⠙⠿⣦⣀⠀⠈⠙⠢⣄⡈⠐⢤⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠓⠶⣤⣀⠀⠉⠓⠦⣀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⡼⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⠳⣤⡀⠀⠀⠀⠀⠀⠀⡀⢤⣀⠀⠀⠀⠈⠹⣶⣦⡀⠈⠙⠀⠀⠙⢿⣿⣿⣿⣿⡇⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⠴⠞⠉⠀⠀⣼⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⣿⡄⠀⣹⡷⠶⣤⣀⡀⠀⠈⠙⠲⠄⠀⠀⠀⠀⠈⠙⢷⣦⣄⠀⠀⠀⠀⠹⣿⣿⣿⣷⠘⣧⠀⢀⣀⣀⣠⣤⣤⣄⣀⣀⡀⠉⠀⠀⠀⠀⠀⡼⠛⡇⠀⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀ ⣿⣷⡐⠘⠳⣦⣀⠉⠙⠛⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣄⠀⠀⣈⣿⣿⣯⣴⣾⡟⠉⠁⠀⢀⣤⣴⡶⣠⣬⣉⣙⠓⠲⢤⣀⣼⠁⣸⠁⠘⢁⣄⡤⢴⠖⣶⠏⠀⠀⠀ ⣿⣿⣿⣦⣀⡄⠙⠓⢦⣄⡀⠀⠀⠉⠛⠲⢤⣀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠟⠋⡉⠙⢿⣏⠓⣦⡀⠛⢿⠩⠞⣡⣿⣤⡼⠋⠉⠓⠺⠿⣿⣿⠒⢛⡽⠟⠋⢉⣿⠃⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣧⡀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠀⠈⠛⠶⣄⡀⠀⣴⣿⣿⡿⠋⠀⠀⠀⠙⢦⡈⢿⣿⣿⣿⣦⣸⡀⠀⠋⠿⣫⡀⠀⠀⠀⠀⠀⠀⠉⠓⢾⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠘⠻⢷⣶⡄⠀⠀⠈⠙⣿⣿⡏⣿⠁⠀⠀⠀⠀⠀⠀⢉⣾⣿⣟⠛⢯⣿⣷⡄⠀⢸⡿⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠈ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣀⠀⠀⠈⠛⠶⡄⠀⢠⣿⣏⣠⣿⣦⣶⣶⣶⣶⢲⣶⡿⠿⠿⠿⣿⠿⠿⠉⢻⣦⡈⠓⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⢀⡄⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⡀⢀⣠⣾⣿⣿⣿⡿⠿⠛⢛⣻⣏⣭⠿⣿⣿⠋⣍⠛⠛⢓⡶⠦⢿⣿⣦⡈⢿⡿⠇⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⣴⠏⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⣰⣿⡿⣿⣿⣤⣿⣿⣾⢻⣿⣴⣾⣥⣴⡄⣠⣬⣤⡾⠟⠋⠀⠀⠀⠀⠀⠀⡸⠀⠀⢠⠞⠁⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠋⢀⣀⡤⠀⠸⠃⣾⠀⠀⠺⠏⠈⠟⢡⣿⠟⠉⣸⣿⢟⣿⠻⠿⠋⠛⠆⠀⠀⠀⠀⠀⠀⢰⠃⣠⠖⠋⠀⣠⠂⠀⠀⠀ ⣿⣿⣿⣿⣏⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⠤⢶⡿⠉⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠺⠃⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠿⠋⠀⠀⠀⡴⠁⠀⠀⠀⠀ ⠉⠉⠁⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠈⠉⠭⢭⣛⣛⠲⠶⠤⠤⣄⣀⡀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⢀⠀⢀⡞⡠⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⢤⡄⠈⠉⠓⠲⢤⣀⣉⡓⠲⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠉⠀⣀⠤⠞⠁⢀⡾⠋⠀⠀⠀⠀⠀⠀ ⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠒⠉⠉⠁⠀⠀⠀⠀⠀⠈⠙⠻⣿⣦⡀⠉⠳⣄⠀⠀⠀⠀⣀⠀⣀⡼⠋⠁⡀⠀⠉⡀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠒⠒⠒⠒⠒⠦⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⠇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⢆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⡃⠀⠀⡄⠀⠀⡄⠀⡇⠀⡄⠀⢸⠇⡀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢸⣾⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣼⠁⠀⡼⠁⠸⠘⢠⣸⡁⠰⢡⣧⣿⠁⡇⠀⠀⡇⠀⠀⢠⡀⠀⠀⠀⢸⡿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⣿⢀⠀⣷⠀⡇⠀⣼⣿⠀⠀⣼⣿⣹⣦⣷⡀⠀⡇⠀⠀⢸⡇⠀⠀⠀⢸⡇⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⡇⢼⢸⣿⢸⠃⢀⣯⣿⣀⣴⣿⠏⢸⣷⣿⡀⠀⠀⠀⢀⡾⣿⡙⣦⠀⢸⢣⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⡀⢺⣾⣿⢸⢻⣿⡿⢿⣿⣿⡿⠿⢿⣿⣿⣿⣷⣶⣶⣾⣷⣿⣷⣿⣾⣿⣾⣶⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠿⣿⣿⢺⣿⣿⡇⢰⣿⣿⡇⠀⣤⣼⣿⡄⢸⠇⢸⡇⢸⣿⡇⢠⣌⠉⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠣⠈⣿⣿⣸⣿⣿⠅⢸⣿⣿⡇⠀⣉⣿⣿⡇⠈⢀⠈⠀⣸⣿⡇⢸⡏⠀⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⢤⣿⣿⣿⣿⣿⣀⠈⢹⣿⡇⠀⠛⣿⣿⣧⠀⣸⠀⢠⣿⣿⠃⠸⠇⢀⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢸⣿⣿⣿⡿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣷⣾⣿⣿⣷⣶⣶⣾⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⣾⣿⣿⣿⣿⡀⠀⢸⡖⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⢀⡤⢠⡿⢠⣾⠀⠀⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠛⠛⠻⢿⣿⣿⣷⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⠃⢸⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣇⠀⢹⡶⣄⡀⠀⠰⠾⠃⢀⣤⣾⣿⣿⡏⠀⣾⠤⠤⢤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⣄⣀⠀⠀⠀⢀⠀⠈⢿⣿⡄⢸⣧⠈⠻⠳⢦⣴⣾⣿⣿⠿⠛⣻⡇⢰⠇⠀⠀⠀⠈⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠈⠉⠀⠀⠀⢸⡆⠀⠈⣿⣿⠈⡟⣷⣶⡀⣾⣁⠀⠀⢀⣼⢃⣿⢠⡿⠀⠀⠀⠀⠀⢸⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⢹⣿⣧⣿⢬⣻⣿⡟⠷⣤⣴⠟⠁⢸⣿⣿⠇⣴⡆⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⣿⣿⣿⠀⠉⠛⠦⠀⠟⠁⠀⠀⢸⣿⣿⢸⣿⠃⠀⠀⠀⢸⠃ ⠀⠀⠀⠀⠀⠀⢀⡾⢻⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣷⣴⠄⢸⣏⣿⡄⠀⠀⠀⠀⠀⡄⠀⠀⢸⠉⣿⢸⣿⠀⠀⠀⠀⣾⠀ ⠀⠀⠀⠀⠀⢠⣟⣇⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⣧⠀⠀⢸⣤⣯⠀⠙⢦⡀⠀⠀⡏⠀ ⠀⠀⠀⠀⣠⣿⡟⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⠇⠀⠀⠀⠑⠀⠈⢧⡀⠘⣿⣿⡀⠀⠀⣙⢦⠀⡇⠀ ⠀⠀⠀⢠⠿⡟⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠸⣿⡇⠀⠀⠀⠀⠹⡇⠀ ⠀⠀⢀⡟⠈⠁⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢈⣿⣿⠀⢜⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⣳⡀ ⠀⠀⣾⣇⠀⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⣿⠐⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡚⠁⠀⠀⠀⠀⠀⣹⡇ ⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⠀⠀⠀⢹⡿⠁⠀⠈⢳⠀⠀⠀⢠⠞⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡤⠤⢤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠋⠻⣦⡀⣾⠃⠀⠀⠀⠈⣇⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣏⡀⠀⠀⠈⡷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⡿⠀⣇⠀⠀⠀⠀⠀⠘⠢⣄⡀⠀⠀⠀⠀⣀⡴⠉⠀⠈⠉⠳⢤⡼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣄⣀⣾⠏⠀⠀⠀⣿⠆⠀⠀⠀⣸⡇⠀⠈⠲⣄⣀⠀⠀⠀⠀⠀⠉⠲⢤⡀⠈⠳⣄⡀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣽⠿⢶⣶⣤⣴⡇⠀⠀⣀⣶⣋⣿⡀⠀⠀⠀⠈⠉⠓⠲⢤⣀⠀⠀⠀⠈⠓⢦⣀⠈⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠓⠛⠢⠿⠋⢁⡿⠀⠀⠀⣿⠤⠤⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⢀⡼⠁⠀⠀⢀⡧⠤⠤⢴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠶⠖⣾⣿⡁⠀⢀⣼⡏⠳⠦⣤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠁⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠉⠉⢙⣷⡀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠉⠛⢯⡉⢿⡙⠛⠛⠃⠀⢀⣀⡤⠴⠒⠒⠊⠉⠉⠁⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣹⣧⣄⣀⣴⠋⠙⢷⡄⠤⣤⣄⣀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠈⠈⠙⠛⠒⠲⠖⠋⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣦⣤⣶⣾⣍⡀⠀⠀⠀⢸⠁⠀⠙⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠁⠀⠈⠉⢿⡆⠀⠈⢿⣄⠀⢀⣼⢋⣀⣀⡀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⢀⣠⣴⡶⠿⠛⠋⠉⠀⠀⠀⠀⠈⠉⠙⠻⢷⣦⡀⠈⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢳⡦⠀⠀⠘⣿⡄⣠⣴⣿⠿⠟⠛⠛⠛⠛⠛⠛⠿⣶⣤⣀⠀⠀⠀⠀⠜⢀⣤⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢀⣽⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢶⣤⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⣠⣴⣶⣤⣀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀ ⣶⣤⣀⣀⣀⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢀⣼⡿⣅⡄⠉⠻⣷⡀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣀⡀⠀ ⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢀⣼⣿⣧⣀⣴⣾⣷⣿⣿⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⢀⣀⣠⡦⠀⠀⢲⣾⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣻⣶⣤⣴⣾⡿⠿⠿⠿⠿⠿⠛⠿⠿⢷⣍⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⠉⠁⠀⠀⠀⠀⢠⣤⣤⠀⠀⠀⠈⣙⡊⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠉⢀⣠⣴⣶⠶⠶⠾⣶⠛⠻⢶⣶⣤⣄⣉⠙⠶⣾⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣾⡏⠀⢠⡾⠋⠉⠹⣆⠀⠀⣿⡀⠀⣾⣧⠀⢉⣿⣶⣄⠾⣿⣿⣿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡖ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠁⠀⢈⡟⠀⠀⣿⢷⣄⡀⠀⣿⣷⣾⣿⣿⣿⢿⣿⣷⣿⣿⣿⣿⣷⣌⣉⠛⠷⠿⠿⢷⣶⣶⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢾⣿⢇⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣀⣼⡇⢀⢀⣿⠀⠈⣿⣿⣿⣿⣯⣻⣿⠁⣠⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⣿⡟⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⢛⣿⠇⣸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⢸⣿⡟⠳⣶⣿⣯⠻⠟⣿⠿⣿⣸⣟⣿⣿⠷⠛⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣀⣴⣿⠋⠁⠀⣸⡏⢠⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡇⢸⣿⣄⣀⣴⡿⠃⠀⠶⢶⠶⠶⣁⠉⠈⠁⠀⠀⣀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⣀⣀⣠⣶⢿⣿⠇⠀⠀⠀⡟⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⢸⣿⠀⠉⢻⣧⣴⢶⣶⣶⠀⠚⠉⠀⠀⠀⠀⣰⠁⠀⠀⢀⣿⣿⣿⣽⣾⣿⣿⣿⣿⣶⣿⡿⣿⡿⣿⣵⣿⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡈⡏⣷⣶⣿⣿⡏⢙⡿⠋⠀⠀⠀⠋⠀⠀⠀⠘⢦⣸⣿⣿⣿⣿⣿⡿⠿⠿⣾⣿⣿⡿⢋⣾⠏⣰⠋⣸⠇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⡿⣿⣿⢿⣟⣋⠀⠀⠀⠀⠀⠀⢀⣤⡦⣤⠀⠉⣿⣵⠟⠉⠁⠀⠀⠀⠀⠈⣿⠁⣾⠁⣰⠃⠀⣯⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⢸⣿⣧⢹⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠈⢯⡀⠘⠀⣸⠟⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⡇⠀⣇⠀⠀⠸⣦⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⢳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢳⡀⠀⠀⠀⠙⣿⣾⣿⣿⡿⣿⣦⣄⣠⠖⢀⣄⣀⡀⠙⣀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢿⡄⠹⣦⠀⠀⠙⢷⡄⠀⠀⠀⠀⠙⢦⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢸⣿⣿⣿⣧⣤⣾⣿⣿⣿⣿⢿⣿⣿⣿⣻⣿⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣿⣇⠀⢿⣆⠙⠳⣦⣀⠀⠙⠀⠀⠀⠀⠀⠀⠙⢷⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠋⠳⣿⣿⢿⣻⠿⠟⠁⠀⣤⣶⣾⣿⣷⠶⠾⠿⠟⠛⠿⣿⣿⣿⣷⣄⠀⠙⠻⢶⣦⣤⣄⡀⠀⢀⣀⣤⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢿⡽⠟⠻⣶⡿⠉⠀⠀⠀⠀⠀⠀⣈⡵⠂⣀⣠⣦⣤⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣯⡉⠛⠶⣦⣘⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⣠⠏⠁⠀⠀⠀⠀⠀⣠⣶⣿⡷⣾⡿⠉⢀⣉⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⠾⠋⠙⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⣀⣶⠿⢉⣵⣾⠉⠀⠂⠉⠉⠉⢉⣀⣀⣀⣀⠀⠤⠀⠀⠀⣸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢀⣾⡏⠀⠀⠀⠀⠀⣴⣿⡿⠲⣾⡋⠁⣀⣴⣖⡴⠞⠋⠉⠉⠉⠉⠉⠛⠛⠻⠷⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⣾⣿⣇⠀⠀⠀⠀⣼⡏⢋⣴⠶⠋⣀⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣋⣉⣻⣦⡀⠀⣰⣿⣵⣿⠉⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣤⣴⡶⠶⢾⣋⣉⡉⠛⢛⢿⣿⣶⣿⣿⠟⣡⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠻⣟⡻⢿⣍⠛⠻⢧⣄⡈⢉⣉⡑⠢⢌⣉⠙⢳⣿⣷⣿⣿⣿⣿⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⡀⠈⠳⣦⡉⠳⣄⠀⠈⠙⠷⣄⠉⠀⠠⢉⠳⣿⣌⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣷⡄⠀⠈⠻⡆⠘⢷⡄⠀⠀⠸⣧⢀⣷⠈⣿⡿⣿⣿⡟⠁⠀⠀⠀⠀⢸⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⡇⠀⠀⠀⠁⠀⠈⢻⣆⠀⢀⣼⡇⣿⣴⣏⣿⡿⠋⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣤⠀⠀⠀⠀⠀⠀⠈⣿⣤⣾⣿⣿⣿⣧⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡿⠀⢠⡄⠀⠀⠠⠀⣼⣿⡿⢋⣽⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⢀⣿⠃⠀⠀⣠⣾⣿⣿⣴⡿⠟⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡿⣡⣾⣷⣦⡴⠾⠟⠉⠉⠉⠉⠠⠴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣖⣶⣾⡻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣻⣷⣀⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢻⢡⠋⠳⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⣿⠀⢿⡀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⣿⡄⠀⢷⣄⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠈⡯⠳⣌⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣆⠀⢷⡶⢿⡀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠹⣤⣧⡶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⡄⢨⢏⣠⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⡁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣿⡏⠁⠇⠠⢀⠀⠀⢀⣀

⣿⣿⣿⣿⣿⣿⣷⡰⡀⢨⣿⠉⣿⡛⠛⠿⠶⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠠⠖⣴⣿⣦⣶⣦⣀⣀⣠⣤⣵⣶⣤⣿⣴⣀⣽⣸⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⡅⢸⣿⡇⣿⡇⠀⠀⠀⠀⠀⠈⠉⠙⠛⠲⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⠀⢀⣾⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⠁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠈⣿⣯⣗⠒⠦⣤⣀⡀⠀⠀⠀⢠⣶⡀⠀⠀⠀⠈⢷⣾⡿⣿⣿⣛⣛⣛⠘⡎⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢈⠓⢦⣄⠀⠉⠙⠒⠲⣿⣟⣷⣦⡀⠀⠶⣾⣿⡍⣻⣿⣿⣙⠛⠶⠿⢤⣄⣀⣙⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠐⠀⠀⠀⠀⠀⠀⠀⣿⡇⠸⣧⡀⠈⢳⡀⠀⠀⠀⠀⣽⣿⣿⣿⣷⣾⢞⣵⠿⣇⠹⣯⡛⣿⣶⣄⣀⠀⠈⢉⠙⠻⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣅⡀⠀⠀⠀⢠⣿⠁⠀⢹⣷⣤⣼⡇⠀⠀⠈⡀⠈⢻⣿⣿⢟⣡⠞⢁⣾⣿⣷⣿⣿⣷⣼⣏⡛⠿⣶⣤⣙⢦⣀⠻⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡋⡛⢦⣄⡀⢸⣿⡄⠀⠘⣿⠻⠋⡀⠀⠀⠀⠀⠀⠸⣏⣿⡟⢁⣴⣿⣿⣿⣼⡿⠉⣿⣿⣿⣿⣮⡙⢿⡿⠿⣿⣧⢹⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⠶⠾⠛⠛⠻⠿⢿⡿⣿⡟⠉⠁⠀⠀⠀⠀⢀⣸⠿⡏⣠⣾⣿⣿⣟⣿⠿⠇⠀⢥⣿⣿⡟⢸⡟⣮⣿⣄⠈⠻⣿⣿⠉ ⣿⣿⣿⣿⣿⣿⣿⣯⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠰⢦⣍⡻⣆⠢⠀⣿⢩⠀⠀⠀⢀⣴⡿⠬⠿⣤⣿⣿⣿⣼⣯⠉⠀⠀⠀⠀⠀⠀⠀⠉⣳⣶⣭⣇⠘⠀⠀⠙⣿⣧ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠞⠑⠒⠛⠲⣄⣙⢾⣿⣼⡟⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢴⣿⣿⠏⣽⠷⣤⡀⠀⠈⠻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠉⣠⣾⠟⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠙⡛⠻⣦⣄⡀⠀⣀⣴⣿⡟⢋⣼⠟⠀⣸⣿⣄⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣶⣶⣶⣶⣶⣶⡶⠿⠛⠁⠀⠀⠀⠀⢸⣧⣀⠀⠀⠀⠀⣠⡴⠋⠉⠉⠉⠉⠁⠛⠻⢿⣿⣿⣿⠋⣴⣿⠏⠈⣴⡟⣿⣿⣆⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠉⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠗⠙⠛⣻⠶⣾⠏⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⣿⣿⣧⣾⠟⠛⠻⢿⣿⡇⣾⣿⣿⡆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⠀⢀⣠⡤⠖⠛⠉⠁⠀⠀⠀⠉⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠌⠿⣿⣀⠀⠀⠀⠉⠉⠙⠛⠻⠿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣷⣶⣶⣾⣷⠄⠀⠠⣤⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣴⣾⣿⣛⣛⣛⣛⢋⣉⣽⣷⣀⣄⣠⣾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⢠⠖⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣹⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡈⢀⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣀⣠⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠀⢠⡀⠀⠀⠀⠀⢘⡿⢋⣠⣤⣴⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠟⠛⠛⢉⣹⡯⠽⠛⠉⠉⠉⠉⠀⣀⣴⠾⣿⢟⡞⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠈⠳⣤⣤⣤⣴⣿⣿⠿⠟⠛⠛⠛⠛⠛⠛⠿⣿⣷⣤⡀⠀⠀⢸⠟⠉⠀⣀⣤⠶⠛⠉⠀⠤⠖⠛⢁⣀⣤⡶⠟⠋⣠⡾⣫⠟⣸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣆⠀⡼⢀⣴⣾⣿⣤⣂⠀⠀⠹⠶⠶⠛⠛⠉⠁⢀⣤⡾⣫⡾⠋⣐⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⣿⣎⣷⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣿⣿⡿⠋⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣸⢸⢸⢸⡏⠂⠀⣾⠥⡇⠥⡄⣹⠀⠀⢸⣿⡤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⢸⢸⠔⡇⣾⡄⣿⢀⠀⠀⠑⢾⠀⢀⢸⡿⢡⢁⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠈⡼⣇⠇⡿⠯⡟⠂⢴⣶⣶⡷⡄⠸⣸⡇⡏⡾⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢵⢣⢳⣞⣶⣿⢠⡏⠂⠘⠛⢉⢱⠀⣧⡏⡇⡗⣷⡆⠀⠀⠀ ⠀⠀⠀⠀⡈⣸⢣⢆⣫⠛⠋⠀⠀⠀⠀⠀⢸⡆⣼⢁⣇⡇⡇⡁⡇⠀⠀⠀ ⠀⠀⠀⠀⡇⡏⡎⣌⣎⡳⠄⠀⠀⠀⠀⠠⢻⣶⣿⣾⢸⢰⡁⡇⡟⠀⠀⠀ ⠀⠀⠀⠀⠇⣧⣿⣿⣼⣿⣦⣄⡀⠀⢀⢔⠟⣿⣻⡇⢸⡾⣇⠁⡇⠀⠀⠀ ⠀⠀⠀⠀⢀⢸⣿⢹⣿⣿⣿⣿⠈⠉⠀⠁⠀⢷⡟⠃⣾⢳⡟⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⢘⠸⠿⠻⠿⠛⠋⠁⠀⠁⠀⠁⠔⢀⠉⠓⠛⠛⠧⣰⠇⠀⠀⠀ ⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠉⠁⠢⠤⠊⠁⠀⠀⠀⠀⠀⠀⠈⠉⢆⠀⠀ ⠀⠀⠈⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢸⠀⠀ ⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣸⠀⠀ ⠀⡐⠁⡠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀ ⢰⠀⡌⢤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠈⠄ ⢸⠀⠃⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠸⡀⠘ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⢆⠀⠀⠀⠀⠀⠀⠀⠁⠁⢸⠃⢰ ⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⡠⢼⠋⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠒⠁⢠⠂ ⠀⠀⠋⠑⢶⢠⠤⠀⢒⠨⠒⠁⠀⠀⠀⠀⠐⢕⠤⣀⠀⠀⠀⠀⣀⢴⠁⠀ ⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢹⠩⠋⠀⠈⡄⠀

⠀⠤⠤⢠⠒⡒⠉⠉⡇⠀⡄⠀⠀⢰⡄⠀⠀⡱⣃⠠⡀⠀⠱⡀⢣⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠃⠀⢠⣷⠀⡇⡀⠀⠘⣿⠀⠀⠸⣿⠀⡷⠀⠘⣧⠀⢃⠀⠀⢠⠀ ⠀⠀⠀⡾⡀⠀⠀⢸⠈⢆⢹⡇⠀⠀⣣⡷⠖⠂⢟⣄⠋⠷⢲⠟⡆⠈⡆⠀⠀⠤ ⠀⠀⢀⠻⣧⡇⠀⢸⠒⠸⣾⡹⠔⠒⠛⢠⡰⣞⣨⣯⣤⣀⠈⡎⠑⠀⢰⠀⠀⠀ ⠀⠀⣟⠋⠉⠳⠂⠙⡆⠀⢳⡉⠉⠉⠉⣯⡾⠟⡹⠀⠀⠉⡷⠇⡀⠀⠀⣇⠀⠀ ⠔⢲⣾⣅⣴⠾⡿⣿⣿⠆⠐⠁⠀⠀⠀⠋⠈⣉⣤⡤⠤⢔⢅⢀⡇⠸⠀⢹⡄⠀ ⠀⣸⡟⢿⡇⠀⣈⣒⣂⢀⠴⡀⠀⠀⠀⣠⡿⢫⠎⢔⠔⣽⣫⠞⢳⡆⠀⢸⢱⡀ ⠀⠃⣧⠈⢃⣏⣝⢔⡧⠒⠀⠀⠀⠀⠈⠁⠀⠀⠐⢁⠝⠉⠧⠀⡰⢠⠀⠈⠀⣷ ⠀⢸⣾⣧⢐⢫⠊⠟⠀⠀⠀⢀⣀⠠⠄⣀⠀⠀⡠⠁⠀⠀⣀⡴⠑⡿⠀⠀⠀⠼ ⢇⠘⣿⡏⠲⠅⠈⠀⠠⣄⣔⣥⣶⣾⣿⣶⣿⣿⠃⠀⠀⠉⠀⠀⠀⡇⠀⠀⠀⠀ ⢸⠢⡘⢿⡄⠀⣸⠀⠀⠈⣿⡟⠛⣿⠟⠉⢹⠏⠀⠀⠀⠀⠀⢀⣼⣿⡇⢠⠀⢀ ⡽⠀⣸⣷⣾⣶⡒⠁⠀⠀⢘⠁⠀⡏⠀⠀⣾⠀⠀⠀⠀⢀⣠⣿⣿⣏⡳⣸⢄⠈ ⠑⠚⠿⣿⣯⣿⢈⣷⣄⡀⠰⠀⠠⠇⠀⡠⠓⠃⠀⣀⣴⣿⣿⣽⣿⣿⢧⣿⣜⠦ ⠀⠀⠀⠈⠙⠷⡾⣿⣿⣿⣶⣇⠀⢠⠎⠀⢀⡤⣚⣻⠿⠟⠛⠉⠉⠁⣾⡗⠙⢆ ⠀⠀⠀⠀⠀⠀⠈⠢⡈⠉⠉⠉⠹⠉⡶⠾⠓⠉⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣴⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⣿⣿⣿⡿⣩⣿⣿⣧⡀⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⣠⣾⠟⣿⣿⡁⠀⠃⢿⣧⢻⠱⡄⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⣼⠟⢁⢰⣿⣿⡇⠄⠀⣼⠟⠈⡄⢹⡀⠀⠹⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠚⠙⠲⣴⠇⣴⢃⠞⣿⣿⢀⣠⣤⡇⠀⢧⠀⠀⢣⡖⠋⠉⠑⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⡆⠀⠀⠀⢀⣷⢰⠃⣷⠰⣿⣿⡈⠉⢉⡇⠀⣿⠆⠀⠀⡇⠀⠢⣄⣘⡆⠀⠉⠲⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡠⠔⠋⠀⠀⠀⠀⢳⡀⢤⣠⣿⡿⠘⣆⢻⢆⢻⣼⣯⢀⡿⣹⢀⡏⠀⠃⠀⠸⣦⣄⠀⠝⠁⠀⠀⠀⠀⠑⠦⣄⡀⠀⠀ ⣀⣀⡤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⣽⡿⠏⠑⠈⠀⠹⡄⠘⣮⢿⣿⠏⣰⢃⣾⡇⠀⠀⠀⠀⠀⠙⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠵⠢ ⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣿⢧⠁⠀⠀⠀⠀⢻⣦⠙⣿⣿⣦⢧⣿⡿⠁⠀⡰⠀⠀⠀⠀⢼⡿⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁⠀⢻⡌⠀⠀⠀⠀⠐⣄⢹⣦⣿⣽⣿⣿⡿⢡⠃⡎⠀⠀⠀⠀⠀⣼⠇⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠘⣧⠈⣿⡅⠉⣿⣧⠏⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀ ⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠘⣦⠹⡇⠀⣿⠁⡴⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀⠀ ⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠘⣇⡇⢀⣿⡼⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄ ⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⣿⠁⠀⠀⠀⠀⠀⠀⠃⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣷⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠛⠋⠛⠁⠀⠀⠀⠀⠀⠀⢀⡀⠈⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣶⣶⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣶⣶⣾⣶⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⣀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣴⣯⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⢴⣨⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣽⢿⣿⡏⣾⣿⠏⢿⡘⢿⣆⠀⠀⢹⣿⡟⢉⢉⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⠟⣿⡁⠘⣿⡇⣻⢻⣷⠆⠀⢘⣿⡄⠀⠀⠙⠷⢼⣄⠈⠙⡗⠢⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡆⣿⣧⣀⣿⣿⡏⠀⠀⠀⠀⠘⢻⡇⠀⠀⠀⠀⠀⢉⠔⠲⢇⠀⠈⠒⣀⠤⠾⠿⠷⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡇⣷⣼⣿⣿⣿⢿⣧⡀⠀⠀⢀⣠⣴⡇⠀⣠⣴⢶⣮⣁⠀⠀⠀⣩⠖⠉⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣷⣿⣿⣿⡙⠿⣮⣯⠳⣄⠀⠀⠀⠀⡇⣰⠏⠀⠀⠀⠈⠑⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⢻⣼⣿⣷⣟⠛⠛⠓⠀⠀⠀⢀⣞⣿⢿⠘⣆⡀⠠⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢀⡄ ⠀⠀⠀⢿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠹⣿⢅⡎⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢸⠁ ⠀⠀⢀⠜⠁⣿⣿⣿⣿⣦⠄⠀⠀⠀⣈⣶⠇⠀⠀⣠⠴⠊⠉⠀⠀⠀⠉⠓⠤⡀⠀⠀⠀⠀⡠⠞⢉⡿⠀⠀⠀⠀⠀⡎⠀ ⠀⠀⠀⠀⢀⠟⠉⣡⣼⣿⣠⡤⠖⠋⠀⠀⡀⠉⠉⠀⢀⣤⣆⣠⠀⠀⠀⠀⠀⠈⢏⠉⠘⠛⠢⠴⣊⡀⠀⠀⠀⠀⢰⡇⠀ ⠀⠀⠀⡠⣀⡴⠞⠛⠉⠁⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠇⠒⠢⠄⡀⠀⠈⠒⠤⣀⠀⢸⡇⠀ ⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡇⠀ ⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⢧⠤⠬⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠃⠀ ⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠸⡄⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠐⠻⣄⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⢫⠁⠒⠚⠓⠦⠤⢄⣀⣠⡤⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠑⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠉⠁⠀⠀⠀⠀⠀⠉⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⢁⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣢⠋⠀⠀⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣿⠀⠀⢀⣎⡇⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣦⡀⢾⣿⡄⡔⡇⠀⠀⠀⡀⢸⠀⠀⠀⢈⣦⣌⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣶⡇⡀⠀⢸⣷⢸⣇⣇⠀⣸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⡯⣿⣿⣷⣶⣾⡇⢸⣿⣿⣿⣿⠹⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡟⣧⣿⣿⣿⣿⣿⣿⣿⡟⢠⢻⣿⣿⣿⣧⠇⢸⣿⡏⣿⡿⠄⣿⢻⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣽⠙⠛⠃⣀⣤⠤⡀⠀⠀⠀⠀⠈⠁⠙⠓⠲⡿⣸⣾⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣟⡇⠨⣿⣿⣿⣿⠰⣞⠛⠉⠉⠳⠄⠀⠀⠀⠀⢠⣐⣢⣄⠀⠈⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣄⣿⣿⣿⣿⠀⠘⢦⣠⠏⠀⠀⠀⠀⠀⠀⡉⠀⡰⠉⠓⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⢻⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⡩⠓⢶⣦⣄⡳⠚⠁⠀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠈⠉⠀⠠⠉⠉⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⣼⣿⣿⣿⣿⣿⡏⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢿⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠇⣏⢹⣿⣿⣿⣿⣿⠀⠙⣷⣄⠀⠀⠀⠀⠀⢀⣄⠴⠾⠏⠥⣏⣿⡇⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠏⡸⢸⣸⠿⠛⠉⣿⣿⡄⠀⠈⠻⣷⣶⣤⡤⠒⢻⠁⠀⠀⠀⢀⠴⣿⠃⠉⠑⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠟⠺⠓⣉⡁⠀⠀⠀⢹⣿⠘⡄⠀⠀⠈⠙⠛⡇⠀⠀⠀⢀⣠⠔⠁⠀⣿⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀ ⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠑⠲⢄⣈⣿⡄⠈⢦⡀⠀⠀⠀⠀⢀⠗⠊⠉⠀⠀⠀⣸⠃⠀⠀⠀⣸⢿⠀⠀⠀⠀⠀⠀ ⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠒⠒⠓⠄⠀⠀⠀⠉⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⢀⣿⠸⡆⠀⠀⠀⠀⠀ ⠸⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣼⣿⡁⡇⠀⠀⠀⠀⠀ ⠀⡟⠿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⢈⡃⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣣⣷⠀⠀⠀⠀⠀ ⠀⢹⡐⡚⣛⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠈⠐⠤⠀⠀⠀⠀⠀⠀⠀⠹⢧⡗⠑⡄⠀⠀⠀ ⠀⠈⣧⠘⣌⡷⡙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠀⠀⠀⠀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣷⠀⠀⠀ ⠀⠀⢹⣢⠈⢦⠻⣷⢝⣧⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⢇⠀⠀ ⠀⠀⠀⢧⠳⡀⠳⡸⣷⣿⠀⠀⠀⠀⠀⠀⡴⠁⠉⠉⠑⠒⢄⡰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠈⣆⠀ ⠀⠀⠀⠘⡄⠛⢄⢽⣽⠇⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠙⢞⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⡀ ⠀⠀⠀⠀⢳⣠⠊⠁⡾⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⢌⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠈⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠘⡄⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠈⣞⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁ ⠀⠀⠀⠀⠀⠀⢹⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡬⠓⠒⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⢣⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠑⠒⠤⣀⣀⠤⠔⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠱⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⣀⠴⠊⠀⣀⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠑⠦⣄⡀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⢀⣀⠤⠒⠛⠒⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⣀⡠⣤⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⣀⡠⠴⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⣿⣿⣿⡤⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾ ⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⣷⣝⢻⡶⣽⣿⣿⣿⣿⣿⣿⡿⣤⣿ ⣿⣿⣿⣿⣿⡵⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠹⣌⠙⢿⣿⣿⣿⣿⣿⡾⢿⣿⣿⣿⣮⡻⣿⣿⣿⣿⣿⣇⢹⣿ ⣿⣿⠿⠿⢿⢿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⠟⠉⢀⡀⢸⣇⠹⣧⠀⠙⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢻⣿⣿ ⣵⠐⠀⠀⠚⠘⢿⡄⢻⡶⠛⠃⠶⠈⠉⢩⣿⣵⣿⠿⠋⣰⣾⠏⣴⣾⣿⣆⠹⣧⣰⡈⢻⣿⣿⣿⠀⣿⣿⣿⠋⠁⠙⢿⣿⣿⣿⣾⣿⣿ ⣝⣶⡀⠀⠀⠀⠈⢿⡀⢻⣦⠄⠀⠀⢠⡟⣭⣿⠃⠀⣼⣿⢫⣾⡿⠁⢿⡿⣆⠙⣧⣧⠀⠻⣖⣿⡇⢹⣿⠏⠀⠀⠀⠀⢹⣿⣯⣿⣿⣿ ⠈⢿⡿⣄⠀⠀⠀⠈⢻⡴⢻⡆⠀⢠⣟⣠⣿⡏⢀⣼⣿⣷⣿⠟⠀⠀⠈⣿⣿⣧⣿⡿⣇⠀⢿⣿⣿⣘⣿⢀⣠⣤⣔⣦⣤⣿⣿⣿⣿⣿ ⠀⠀⠙⢿⡷⠾⠛⠻⠿⣿⣶⣿⣦⣿⣾⣿⡿⠀⣼⣿⣿⣿⡏⠓⠋⠉⠉⠉⠋⢻⣿⣿⣿⡀⠘⣿⣿⣿⣿⣿⣿⣄⣤⣘⣻⣿⣿⣿⣿⣿ ⠀⠀⠀⡟⠀⠀⠀⠀⢠⡃⠈⢿⣿⣿⣿⣿⠁⢰⣿⣿⢿⡟⠁⠠⣴⣶⣶⣶⢶⣶⢽⣿⣾⡇⠀⢿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠙⣿⣧⢻⣏ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⢳⡀⠈⣿⣿⣿⣯⣾⣿⣿⣿⣾⡅⠀⠀⠨⠿⠛⠛⠚⠁⢰⣿⣿⣧⡄⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣇⢿ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣹⣶⣿⣿⣿⣿⡇⣿⣿⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⠁⣼⣿⣿⣿⡇⠀⠀⣀⣀⣀⠀⠸⣿⣿⡌ ⠀⠀⠀⠹⡄⠀⣠⣶⢟⠋⣻⣿⣿⣿⢿⣿⡇⣿⡏⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣽⣸⣿⡟⢀⣿⢹⣿⣿⣧⣾⣿⢭⣿⣭⢿⣶⣿⣿⣷ ⠀⠀⠀⠀⠹⣼⣯⣛⣡⠖⠋⠉⠈⠻⡘⣿⠇⣿⡇⠀⠀⢀⣠⣄⣀⠀⣀⡖⠒⣾⡽⣿⣿⠁⣼⣿⣼⣿⣿⣿⣿⡧⠟⠛⠛⠛⠻⣿⣿⣿ ⠀⠀⠀⠀⠀⠸⣿⠟⠁⠀⠀⠀⠀⠀⢙⣿⣼⣿⣿⣦⡀⣸⢧⣍⣙⣿⠟⠳⠦⢜⣟⣿⡏⢠⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠘⣿⣿ ⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⢀⣴⡞⢻⡿⢿⣿⣿⣿⣿⣧⡸⠓⠷⠛⠃⠀⠀⠀⠋⣸⣿⢡⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠳⣄⢠⣯⣯⠞⠋⠀⣸⡿⠁⠉⠻⣿⣿⣦⡀⠀⠀⢀⡀⠀⠘⣿⣿⣾⣿⣿⡿⠿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠇⠀⠀⠀⣿⣅⠀⠀⠘⠿⢿⣿⣿⣶⣶⣶⣿⠁⢰⣿⣿⣿⣿⠏⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⣿⠸⠀⠀⠀⠀⠐⠯⣉⠉⠉⠙⠏⠀⢠⢿⣿⣿⠏⣒⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡀⠀⠈⠛⠻⠁⠀⠀⠀⠀⠈⠉⠒⢄⠀⠠⠚⠉⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣻⠇⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⣾⡧⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⣸⣿⢠⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⢰⣿⡟⣾⣿ ⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⣿⣿ ⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡘⣿⠀⣿⣿ ⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⡄⣿⣿ ⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿ ⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿ ⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣿⣿ ⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢠⣾⠀⣿⣿ ⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣉⣴⣿⢃⠀⣿⣿ ⠀⠀⠀⠀⠀⠈⠳⠦⣀⡀⠀⣀⣀⡀⠤⢆⣀⡤⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⠄⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣾⣿⣿⡿⣠⠀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⡏⠁⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⣿⣛⣿⣿⣿⣿⣿⣧⠻⠀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣬⠀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⢑⠀⣿⣿ ⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⢻⡇⠐⠀⣿⣿

⠀⠀⠀⢀⡀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⣀⡴⢾⣻⣹⣼⡿⣿⣟⣿⢶⣤⡀⠀⠀⠀⠀⠀⣀⠰⢒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣾⣿⣿⣿⢹⣿⣷⢺⣿⣿⡿⣿⡿⣿⣦⠀⠀⠀⠀⣽⣷⣻⣿⡿⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⣿⣿⣻⣽⡞⣿⢿⡏⣿⣿⣿⠇⠼⣧⠈⢿⣧⠀⠀⠀⠀⡿⡹⡉⡀⠤⢌⡓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡿⣯⢾⡏⡇⠀⢻⡿⡇⢹⣿⣿⣷⣦⠈⠀⢙⢿⣇⠀⠀⠀⠙⠷⡷⣽⡄⠀⠈⠳⣝⠦⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⣧⠈⣧⢧⠀⢸⣷⣿⣾⠇⠙⠉⠁⠀⠀⠻⢿⣿⠀⠀⠀⠀⠀⠀⠈⠛⠋⣀⣤⡾⠀⠈⠓⢄⡀⠀⣀⣤⣟⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡇⣿⡀⣿⣟⣇⣾⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⢿⠄⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠙⠢⣄⠀⣠⠵⠚⠛⠋⠁⠁⠉⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣧⢸⣷⣾⣿⣿⣿⣏⢻⣿⣧⠀⠀⠀⠀⢠⢤⣶⣿⠀⠀⣠⡶⠭⠿⢷⢤⡀⠀⠀⠀⢀⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⣾⡟⣿⣿⡌⠻⠿⣦⣿⡜⢷⣄⠀⠀⠀⠀⠀⢼⠀⣴⣏⠀⠀⠀⠀⠀⠉⠲⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡿⣷⢸⡿⣿⣴⡶⠾⣝⣿⣄⡈⠃⠀⠀⠀⣠⣾⣿⣟⡘⣆⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠘⠀⢹⣞⣷⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣺⠋⡜⠀⢸⠒⠂⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⣿⡿⣟⢿⡿⣿⣦⡀⠀⠀⠀⠀⠀⠘⢿⡗⢴⠃⠀⠠⠃⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⣄⡀⠀⠀⠀⠀⠀⠀⣸⠀ ⠀⠀⠀⢀⡟⠁⢹⡿⣿⣿⣻⣿⣦⡀⠀⠀⠀⠀⢈⣳⣞⠆⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠉⠙⠦⣄⠀⠀⠀⠀⠀⠀⢀⡴⠋⠈⡿⠁⠀⠀⠀⠀⠀⠀⡏⠀ ⠀⠀⠀⠉⠀⠀⢰⠿⠻⠃⢉⣏⡇⢀⡀⣤⡤⠖⠋⠀⠀⠐⠒⠒⠋⠁⠀⢀⣀⡄⢀⠀⠀⠀⠀⠀⠀⠈⠳⡖⠒⠲⠴⠭⢅⣀⣲⠝⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠋⣀⣴⣾⣟⠿⠏⠛⠉⠁⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⣴⣿⣿⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⣀⠀⠀⠈⠀⠛⠢⣄⡀⠀⠀⠀⠀⡞⡇⠀ ⠀⠀⠀⢠⢖⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⣿⣯⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠈⠉⠓⠲⠤⢀⠀⠀⠉⠲⢤⣄⠀⣇⡇⠀ ⠀⠀⠀⡰⢻⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠁⠀ ⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⣀⣀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀ ⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠉⠚⢦⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠻⡉⠒⠶⠚⠛⠦⣤⣀⣀⡀⠀⢀⣀⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠓⠶⠶⠶⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⡀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠁⣾⠏⠸⡄⠀⠀⠀⠀⠀⡆⢰⢦⡀⠀⠀⠈⢷⣄⠀⠀⠀⠈⠲⣄⢆⠀⠀⣄⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⠋⢸⡼⠃⠀⠀⡇⠀⠀⠀⠀⢰⣿⣼⠿⠾⣶⣄⡀⠀⢻⣷⣄⠑⠦⣀⠈⠺⣷⢤⡀⠳⣽⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡜⠁⢰⠟⠃⢠⡎⠀⣷⠀⠀⠀⣐⡟⢨⣿⣶⣿⣿⣿⡿⣦⡀⠹⣿⣦⠀⠈⢻⡦⢬⣦⡙⠢⡈⠻⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠁⢠⠃⢀⡶⢹⣿⠀⣿⣗⠀⠀⡼⠁⠹⠋⠻⣽⣧⠟⠀⠘⡟⣦⣿⢸⣧⠀⠘⣧⣼⢪⡻⣄⠈⠳⣜⢿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢠⠏⢀⣾⠁⠈⠹⣧⡏⢹⣧⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡟⣻⣯⠀⢧⠀⣿⡇⠀⠑⢌⠳⣄⠈⠑⢿⣜⢿⡶⣄⠀ ⠀⠀⠀⠀⢀⣷⡏⢠⠿⢈⣷⠀⢰⣌⣿⡿⡟⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢁⣿⢈⣿⡘⣧⣿⣧⠀⠀⠈⠣⡈⠳⣦⡀⠙⢷⡉⢻⡁ ⠀⢀⡴⢃⣾⡟⢠⣏⣀⡞⢻⡄⠈⢿⣿⢻⠾⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠈⠢⡈⠻⣤⡀⠙⢦⡉ ⠖⡏⠀⢸⠛⢗⠻⡃⠙⢦⢠⣿⣦⠀⠻⣷⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠈⠢⡈⠻⣦⡈⠻ ⠀⡇⢀⣸⡀⠘⡄⢹⣆⠘⣿⣿⣻⣿⣦⣿⣏⣹⣶⣄⣀⣀⣀⠀⣀⠴⠋⠀⠀⠀⠀⢸⣿⠙⢿⣿⣿⣿⣿⠿⠷⠦⠤⣀⠀⠈⠂⠈⠻⡆ ⢠⠁⠈⠛⢳⣀⣇⣸⣿⣂⠷⠋⣀⣴⠯⠾⠿⠿⠻⣿⣿⢿⣿⠿⠁⠀⠀⠀⠀⠀⠀⣸⣁⣲⣤⠻⠛⠉⠀⠀⠀⠀⠀⠀⢳⢄⠀⠀⠀⠙ ⢾⠀⠀⠀⠈⠿⡿⠟⠉⠀⢀⣾⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠑⠦⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢣⠀⠀⠀ ⣼⡄⠀⠀⠀⠐⠁⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠤⢄⡀⠀⠀⠘⣆⠀⠀ ⠁⣿⡀⠀⠀⠀⠀⠀⣠⣾⣉⣷⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢶⣾⣟⠹⡦ ⣼⣯⠋⠓⠒⠒⢒⠋⣹⣟⡉⣹⣶⣶⣶⣤⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿ ⣈⣿⠀⠀⠃⠀⢸⡴⣁⣀⣽⠛⠛⠻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟ ⣩⣏⢀⣀⣤⠴⢯⣀⣸⣿⡏⣀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣄⣼⠋⠙⣧⣤⣾⣿⠟⢿⣽⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠉⠉⢻⣿⢛⡋⠁⢸⠀⠸⡏⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠯⡑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠈⠀⠀⠀⠀⠘⡀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⢹⡈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⡼⠀⠀⠈⠙⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⣿ ⠀⣄⡄⠀⠀⠀⠀⠀⠸⡀⠀⠸⣷⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣠⢾⠥⢤⣀⣤⣄⣀⣈⠙⡻⠶⠖⠒⠒⠒⢲⡟⠉⠲⣤⡀⡿

⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⡛⠫⢽⣖⠒⠲⢤⠾⠁⢀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⣠⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢦⣄⡀⠀⠉⠓⢦⡈⠉⠑⠲⣤⡀⠉⠓⠲⣤⣀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣶⡄⠀⠀⠈⠲⣄⠀⠀⠙⠦⣀⠉⠳⣍⢓⢦⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠹⣟⢮⡳⡀⠀⠀⠈⠳⡄⠀⠀⠘⢧⡀⠈⠛⠳⡈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⣾⠟⠁⠐⠁⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇⠀⠀⠀⠀⠀⠀⠈⠻⣽⣿⣄⠀⠀⠀⠘⠂⠀⠀⠀⠙⢦⠀⠀⢘⠂⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀ ⣠⣴⠆⠀⠀⠀⢀⣠⢾⠟⢁⠄⠀⠀⢠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠘⢆⠀⠀⠀⠀⠀⠀⢢⡘⢮⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠈⠓⣄⢰⠀⠱⣄⠀⠀⠀⠀⠀ ⠛⠁⠀⢀⣠⠴⠋⣰⠏⡴⠃⠀⠀⢰⠋⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢧⠀⠀⠀⠀⠀⠀⠹⣄⠳⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠈⠻⣇⠀⠙⣦⡀⠀⠀⠀ ⠀⠈⠻⠯⠤⠤⡞⢁⡞⠁⠀⠀⠀⡏⠀⠀⣿⡄⠀⠀⠀⢶⣀⠀⣆⡀⠀⢀⠃⠐⠒⠀⠳⡄⠀⡀⢀⣀⣀⣈⣳⡘⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣦⣀⠀⠈⠀⠀⡇⢳⡄⠀⠀ ⠀⠀⠀⠀⠀⡼⢡⡞⠀⠀⠀⠀⣸⠁⠀⢰⡇⣇⠀⠀⠀⠠⠙⠿⣮⡷⢤⣼⠤⠤⠤⠤⠖⠛⢿⣻⡻⣄⡀⠀⠀⠉⢿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⠟⠦⣄⠀⠳⣄⠻⣄⠀ ⠀⠀⠀⠀⡸⢁⡎⠀⠀⠀⡤⠀⡟⠀⠀⣸⠁⣼⡆⠀⠀⠀⠀⠀⢸⡀⠀⣟⣀⡀⠀⠀⠀⣀⣀⣙⣷⣀⡙⣦⣄⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠘⢆⠀⠈⠃⠹⣄ ⠀⠀⠀⠠⠃⡾⠀⠀⠀⣸⠁⠀⡇⠀⠀⡏⢸⠃⢹⡀⠀⠀⠀⠀⠈⣇⢰⠏⠀⠈⡹⠋⠉⢉⣿⢉⣉⣽⣯⣭⣭⣭⣶⣤⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⡆⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢸⡇⠀⠀⣧⡿⠐⠲⢷⡀⢳⡄⠀⠀⢹⡜⠀⠀⠀⠀⣖⣿⣿⡿⢟⣻⢏⡽⠉⠉⠉⠛⣿⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⢷⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢠⣾⢷⠀⣧⡟⠁⠀⠀⠀⠱⡄⡟⢦⡀⠀⢷⡀⠀⠀⠸⢋⡟⠳⠶⠶⠒⠋⢀⣀⡠⣴⣴⣿⡋⣹⠀⠀⣤⠀⢰⠀⠀⠀⠀⢸⣼⡏⠉⠂⠀⠀⠀⠀⠀ ⠀⠒⠂⠀⠀⠀⠀⢰⠁⠀⢸⡇⣨⡟⣧⡇⢀⣴⣂⡀⠀⠙⢾⡀⠘⠲⢌⣧⠀⠀⠀⠈⠀⠀⣀⣠⢴⣺⡭⢖⣿⡿⢇⣀⡽⢿⠀⠀⢻⠀⠈⡄⠀⠀⠀⠈⡟⣧⠀⠀⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣾⡿⠁⠹⣜⣶⠋⠁⢀⡄⠀⠀⠘⡿⡀⠀⣠⢝⣹⣤⠒⡤⣶⠯⠟⢿⣯⡥⠖⠛⠉⠛⠉⠉⠀⠘⡆⠀⢸⠀⠀⡇⠀⠀⠀⠀⢃⡿⢷⡄⠀⠀⠀⡀⠀ ⠀⠀⠁⠀⠀⠀⠀⢸⡆⠀⣿⠁⠀⣠⢛⣾⣶⡶⡿⣿⣥⡀⠀⡧⣁⣼⡷⣫⠆⠀⢀⡴⣯⣝⣻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠿⠋⠀⠀⠢⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡾⡇⢠⡟⢀⣾⣷⢿⣟⣣⠶⠚⠁⠀⣠⣼⠟⠉⠡⠞⠁⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⢸⡾⠋⠁⠀⢱⡀⢀ ⠀⠀⠀⠀⠀⠀⠀⡧⣷⠘⡇⢘⣾⡏⠀⠀⢀⡠⣤⠞⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣻⠀⠀⠀⠀⠀⠀⠀⢸⢸⠃⠀⠀⠀⠀⢳⠀ ⠀⠀⢸⠀⠀⣤⠀⢿⣿⣧⢳⠀⣿⣧⣤⣺⠽⣛⡥⠾⠋⠋⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⠀⡼⣿⠀⠀⠀⠀⠀⠀⠀⠸⠸⣆⠀⠀⠀⠀⠈⠇ ⠀⠀⠈⠀⢰⡘⡇⠈⣿⣯⠻⣤⠉⠛⢛⡥⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣸⠃⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡟⠓⠄⠀⠀⢠⠀ ⠀⠀⠀⠀⢸⢣⢱⡀⢻⣹⡆⣿⣠⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⢠⠎⠀ ⠀⠀⠀⠀⠸⠀⢣⣷⡸⡇⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠖⠋⠉⢙⣲⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡞⠀⠀⣿⡇⠀⠀⠀⠀⠀⡄⠀⢸⣿⣠⠆⢠⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣷⣽⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣛⢛⣉⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⣿⡇⠀⠀⠀⠀⢠⠀⠀⢸⠟⠁⣰⣿⣇⡠⡀ ⠀⠀⠀⠀⠀⣆⠀⠈⡇⠙⠆⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⣝⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⢧⡀⠀⠀⠀⠁⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⢸⠀⠀⣯⣠⣾⣿⣿⣿⠞⠀ ⠀⠀⠀⠀⠄⣿⠀⠀⢻⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⢋⠀⢰⠛⢳⡀⠀⠀⠀⠀⢀⣀⣼⣿⠀⢀⠀⠀⠀⡟⠀⢐⣿⣿⣿⣿⡿⠁⠀⠀ ⠀⠈⠠⠀⠀⢸⡀⠀⢸⡇⠀⠀⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⢰⠗⠁⠀⢸⡄⠀⣧⠀⠀⠀⠀⠀⠉⢸⣾⠀⡾⠀⠀⢸⠇⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡇⠀⠀⢣⠀⠀⠸⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢹⡄⠀⠀⠠⣿⣶⣿⠳⣄⠀⠀⠀⠀⣼⡟⢠⠃⠀⠀⡟⠀⢠⣿⣿⡿⢿⡠⠖⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⡀⢀⠀⡇⠹⣄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠳⣄⠀⠀⠘⣿⠉⠉⠛⠿⣶⢤⣴⣷⠁⣸⠀⠀⢠⠃⠀⡞⢿⡿⠡⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢇⠘⡀⢹⡄⢹⣦⡀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⢷⣄⠀⠀⢠⡀⠉⠙⢦⡀⠹⡄⠀⠀⠀⢠⣿⣿⡟⢠⠇⠀⢀⣿⠀⢰⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡆⡀⠀⠘⡆⢷⠈⣿⡈⢷⠙⢦⡀⠀⠀⠀⠀⠀⠈⠻⢿⣉⠉⠉⣙⣒⡶⠬⢧⣶⣄⠁⢀⡇⠀⢀⣴⣿⣿⣿⠃⡼⠀⠀⣼⣿⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢧⢁⠀⠀⠸⡌⡆⢹⡱⡌⢧⡀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢀⣠⠄⠈⠈⠉⠉⢁⣴⣿⣿⣿⣿⡇⢰⠃⠀⣴⣣⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⡀⠀⠘⡎⢣⠀⠀⠹⣽⡀⢇⠘⢆⠻⡄⠀⠀⠉⠳⣄⣀⠀⠀⠀⠀⠀⠘⠿⠏⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⡿⢠⠎⠀⣸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠱⡄⠀⢹⡌⣆⠀⠀⠣⢷⡘⣧⠈⠳⡘⢦⣀⡈⢦⡀⠈⠛⠲⣤⣀⠀⠀⠀⡀⢀⣀⣠⣶⣿⣿⣿⣿⣿⠛⡹⢃⠎⠀⣴⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠉⠉⠀⣴⠏⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⢳⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠘⡇⢠⣿⣇⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠁⠘⢿⣷⣶⣶⣴⡦⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⢴⣲⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢀⣿⣿⣿⣿⡿⠛⠛⢷ ⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢸⣿⣿⡿⠋⠀⠀⠀⠁ ⠀⠀⠀⢠⣾⣽⣿⣧⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣾⠿⡏⠇⠀⠀⠀⠀⢀ ⣷⣤⣴⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⣿⡷⠀⠀⠀⠀⠀⣠⠟ ⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢠⣾⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢲⣤⡖⣦⠀⠀⠀⠀⠀⢰⣿⡏⠁⠀⠀⢀⣴⠟⠁⠀ ⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡄⢠⣿⣲⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⣿⣿⣷⣼⠀⠀⠀⠀⠀⣸⣿⣧⡀⢀⡴⠟⠁⠀⠀⠀ ⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇⠈⢿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⢀⡆⠀⠀⠀⠀ ⠀⠀⠀⣀⠀⠹⣿⣿⣿⣿⣷⡀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⣸⣿⣿⣿⠏⢠⡏⠀⢠⡾⠀⠀ ⠹⣆⠀⠘⣧⠀⠸⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏⠀⡞⠀⠀⣿⠁⠀⠀ ⠀⢻⡆⠀⢹⡄⠀⠹⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠐⠒⠒⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢋⣿⣿⡏⠀⡼⠁⠀⣸⡇⠀⠀⠰ ⡀⠀⢿⡄⠀⢿⡄⠀⢹⣿⣿⣿⣿⣿⣿⣗⣦⣄⣀⠀⠀⠀⣀⣤⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⣼⣿⣿⣿⠀⡃⠀⣼⣿⠀⠀⢀⢳ ⣇⠀⠈⣗⠀⠈⣿⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣶⣶⣶⣦⣤⣤⣴⣾⠛⠁⠀⢠⣿⣿⣿⣿⣆⣧⠚⢹⣿⠀⠀⠠⠋ ⣿⠀⠀⢸⠆⠀⣹⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋⠁⠀⠀⡀⠀⣺⣿⣿⣿⣿⣯⣽⡦⠾⢿⠀⠀⡆⠀ ⣿⠀⠀⡼⠀⢠⡟⢻⡀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⣿⣿⣿⣿⣿⣿⣿⣷⡀⡌⠀⢠⠉⠀ ⢻⠀⠀⠁⠀⣼⠁⠀⠹⡦⣼⣿⣿⣿⣿⣿⣿⣿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣶⣾⠀⠀ ⠘⣇⠀⢀⡼⠃⠀⠀⠀⣛⣋⠙⣿⣿⣿⣿⣿⣿⣿⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠻⣿⣿⣿⣿⣿⣿⣿⠏⠁⠈⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⢉⠉⠀⠁⠀⠀⠀⠀⢉⣉⣃⣈⣹⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣯⠿⠛⠛⠓⠶⣭⡀⠀⠀⠀⠀⠀⢀⣴⠛⠉⠀⠀⠀⡈⠙⠻⣿⣿⣿ ⣿⣿⡿⠋⡠⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠰⢹⠄⡘⢿⢻ ⢫⢟⠀⠁⠀⠀⣠⠤⠐⠠⢄⠀⣸⠀⠀⠀⢀⣷⣀⠔⡨⠭⠥⡢⠉⡏⠉⠈⠺⡇ ⣼⠁⠀⠀⠀⡼⠁⡴⢉⣦⡴⢞⠉⠓⠀⠀⠈⠀⢮⣛⠲⠦⣄⣸⢀⠤⠀⠀⢠⡇ ⠸⣆⠀⠀⣀⣧⠶⠛⠉⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠶⢻⣀ ⣰⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾ ⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠛⠋⠉⠁⠉⠚⠃⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟

⠀⠀⠀⢰⣦⡉⠉⣄⠑⢷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡘⢿⡄⣼⣓⣞⣅⣉⣐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢱⢆⡚⣡⣿⣿⣿⣿⣿⡉⠉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣣⣼⣧⠫⣳⣿⣿⠿⠿⢿⣇⠀⠀⠠⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀ ⠀⠀⠀⠀⡸⣿⣿⠿⢋⡀⠁⠛⣼⣶⣶⣿⣮⠀⢀⣶⣿⡦⡀⠀⠀⠀⠘⡀⠀⠀ ⠀⠀⠀⠀⠁⢹⣿⣴⡻⠃⠀⠀⢈⢼⣿⠿⢿⡀⢸⠟⠛⢣⣼⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣻⡿⣦⡤⠀⠐⠧⡠⢋⠀⠀⡁⠸⣀⣠⣀⣿⢷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⡏⠀⠀⠀⢀⢤⡎⠀⢀⠃⠀⠹⠿⠟⢸⠀⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠙⢦⠎⠁⠠⣀⣴⣏⣀⠜⠀⠀⡌⠀⠐⠜⠀⠀⢈⣞⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠰⠀⠘⡄⠀⣠⣿⣿⣿⠁⠀⠀⡐⠀⠀⠀⠀⠀⠀⢸⠛⡇⠀⠀⠀⠀⠀ ⠀⠆⠀⠀⢁⠀⢸⠙⠿⣿⡟⠛⠒⡈⠝⠁⠉⠀⠀⠀⠀⠤⠦⠔⠠⠤⠄⠀⠀⠀ ⠀⠈⠀⠀⠀⠄⠘⠤⠔⠺⣤⠲⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠈⡆⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢈⡄⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠐⠢⠄⣀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⣸⣿ ⠀⠀⠀⠀⡀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠆⠈⣑⠦⠖⠊⠉⠓⠤⣀⠀⠀⣰⣿⣿ ⡀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⢈⣶⣿⣿⣿ ⣷⣤⡀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠉⠀⢹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀ ⠀⠀⠀⠃⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣤⣼⠀⠀⠈⣦⣤⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀ ⠀⠀⠀⠀⠚⢿⠿⠿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣍⣹⠀⠀⢠⣉⣩⣿⣿⠁⢻⣿⣿⣿⣿⣿⣿⠿⠿⡿⢧⠀ ⣤⠀⢠⡄⠀⣼⣀⠀⠀⠈⣿⣿⣿⣿⣤⣜⠿⠿⠿⠿⡆⠀⡼⠿⠿⠿⢿⣀⣬⣿⣟⣿⣿⠀⠀⠀⢀⡇⠀⣇ ⠉⠀⠉⡇⢠⣿⣿⣷⣦⣤⣿⠏⠀⠀⠀⠈⠙⢦⠀⠀⠘⡴⠁⠀⢀⡴⠋⠁⠀⠀⠀⠙⣿⣤⣴⣾⣿⣿⠈⠛ ⠀⠀⠀⠇⠈⣿⠉⠙⠻⢿⣿⣤⣀⣀⡀⠀⠀⠀⢳⠀⠀⠀⠀⠀⡞⠀⠀⠀⢀⣀⣀⣠⣿⣿⠿⠛⠉⢹⠀⠀ ⠀⠀⢰⠀⠀⣿⠀⠀⠀⠈⢿⣷⣄⠘⠿⣿⣿⡶⢶⡇⠀⠀⠀⣸⡷⠶⣿⣿⠿⠋⣀⣼⣿⠋⠀⠀⠀⡾⣳⠀ ⠁⠀⠈⢄⠀⠉⢧⣄⠀⠀⢸⣿⡇⠉⠑⠒⠓⠒⠊⠳⠀⠀⠀⠛⠙⠒⠒⠒⠊⠉⢹⣿⡟⠀⠀⣀⣴⡏⠁⠀ ⠀⠀⠀⠀⠑⢄⠘⢿⣿⣷⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣶⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⢄⠀⠉⢙⣻⠿⠯⠉⠱⣶⣤⠤⣴⠟⠓⠋⢣⡤⠴⣶⡖⠉⣸⠿⢿⣫⠟⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⢠⡇⠀⠀⠀⠀⠀⠈⡽⠁⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣶⡄⣄⠀⠀⠀⢸⣶⠒⠒⠲⠖⣿⠁⠀⠀⢀⡆⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣤⣿⢉⣹⠤⠤⠀⠘⠿⢤⣄⣤⡶⠿⠀⠤⠤⢼⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⠟⠉⠀⠀⠀⠀⠀⠀⢀⠝⠁⠀⠀⠀⠀⠀⠀⠈⠑⢄⣸⣀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣥⣤⣤⣈⠙⡲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠄⠀⠀⠀⠀⣀⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⡉⠻⣿⣷⣶⣶⣍⡉⠑⠢⣀⠀⠀ ⠚⠁⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⣻⣿⣿⣶⣼⣿⣿⣿⣿⣿⣶⣄⠈⠳⣄ ⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠙⠯⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣧⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣀⣄⣀⣤⣤⠀⠀⠀⠀⢨⣝⡛⠻⠿⢿⣿⣿⣿⡏⠁⠀⣹⣿⣿⣿⣿⣿⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⣼⡿⠟⠋⠉⠉⠈⠁⠀⢆⠀⠀⠀⠈⠛⠶⢄⡀⠉⠉⠻⡇⢀⣾⣿⣿⣿⣿⣿⣿⡿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠫⠔⠋⠁⣀⣀⡀⠀⠀⠀⠀⠀⠈⣢⡀⠀⠀⠀⣀⡀⠈⠑⠒⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄⠀⠀⣀⣀⣈⡁⡀⠀⠏⠀⣀⣀⠀⠀⠀⠃⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⢀⣠⣤⣴⣾⣧⣴⡃⠉⠉⠍⠉⠙⠛⠃⣴⣿⠟⠛⢻⣿⢾⣧⣔⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢐⣪⣶⡿⠟⠛⢋⣟⠉⠙⠀⠀⠀⠀⠀⠀⣤⡝⠚⠿⠶⠿⢥⣤⠾⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡄⠀⣲⡿⠛⠙⣳⣶⣞⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠦⠤⣶⣤⣀⡈⠀⠀⠀⢿⣿⣿⡟⢻⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⠛⠛⣲⠿⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿ ⠀⠀⣉⢿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣊⣁⣈⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⠿⣿⣿⣿⣿ ⠀⠀⠀⠈⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣇⣀⠀⠈⠻⣿⣿ ⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢻⠃⠙⠛⢿⠻⣿⡇⠀⠀⠀⠀⠀⠀⢰⠃⠉⠉⠉⠉⠙⢿ ⠀⠀⠀⠀⠀⠈⣿⣁⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⢠⣿⣟⡏⡄⠀⠀⠀⠃⠹⣷⠀⠀⠀⠀⠀⢀⡟⠲⠦⠤⠤⠤⠤⣀ ⠀⠀⠀⠀⠀⠀⠸⣿⡁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠸⡙⠈⠓⠙⠄⠀⠀⠀⠀⡙⠀⠀⠀⠀⢈⡟⠀⠀⠀⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⡀⠀⠘⢇⡀⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠙⢦⡀⡀⠀⠀⠀⢀⡴⠁⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡄⢄⠀⠉⠒⠮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠱⡈⠑⢦⠀⡏⠀⠀⠂⢀⡴⠁⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠸⣏⠈⠳⣄⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⠀⠀⢣⠀⠀⢛⡇⠀⢀⡴⠋⣠⠊⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣤⡏⣇⠀⢻⣆⠀⠘⣦⡀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⠉⠑⡚⢲⠒⢶⡖⠒⠋⠀⠊⠁⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⣇⢸⠀⠈⠻⡇⠀⠈⠻⢄⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣄⣀⣘⠃⠀⠀⠿⣿⣿⣷⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠁⢸⠘⡆⠰⡀⢹⠀⠀⠀⠀⠳⠤⠤⢄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣶⢐⣿⣿⣿⣷⣖⠉⢙⡀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠀⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡖⡁⠀⠀⡀⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⢠⡎⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣿⣄⣾⣥⠎⠀⢀⣸⣀⠀⣤⣼⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣽⣿⣿⣿⣷⣦⣼⠁⣿⣶⡿⣿⢿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠘⡟⠻⠛⠐⠿⠿⣃⡟⣘⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠉⣿⣿⡇⡔⠛⡓⠀⠀⠀⡠⢤⡀⢹⡟⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣷⣿⣿⡇⠈⠊⠀⠤⣤⣀⠦⠂⢀⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⢻⣿⣿⣿⣄⠀⠀⠀⠈⠀⠈⠁⢀⣾⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡸⣟⣿⣿⣿⡌⠲⣄⠀⠀⠀⣀⠤⠞⢿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣡⠼⠛⠉⢻⡧⠀⠙⠷⢶⠈⠁⠀⡠⠐⡏⠀⢡⡀⠀⠀⠀ ⠀⡰⠊⠁⠀⠀⠐⠠⠼⣇⠱⠀⠀⠈⡠⠒⠈⠀⢰⠃⠀⢸⡇⠀⠀⠀ ⠰⣇⠀⠀⠀⠀⠀⠀⠀⠹⠈⠉⠀⠀⠀⠀⠀⠀⠁⠀⢀⣾⢸⠀⠀⠀ ⠀⡟⣷⣦⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠨⠀⠀⠀⠀⠀⠈⢿⣿⢄⠀⠀ ⠀⢸⠰⡪⣻⣆⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢀⠀⠀⠀⠀⠀⠙⢤⡄⠀ ⠀⠀⡇⡐⡙⣾⡆⠀⠀⠀⡠⠮⠤⡀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠑⡀ ⠀⠀⠸⠘⣈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠑⡧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠡ ⠀⠀⠀⢻⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠈⡄⢃⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⢆⣀⠀⠀⠀⠀⠀⠀⠀⠌ ⠀⠀⠀⠀⠘⡈⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠑⠀⠄⡀⠄⠂⠀ ⠀⠀⠀⠀⠀⠡⠈⠢⣀⠀⠀⠀⠀⡀⠔⠁⠀⢀⠤⠆⠡⠔⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢣⠀⠀⠉⠀⠀⢈⡀⠤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠒⠀⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⠀⠀⠀⢀⡤⠒⣁⣀⢀⣤⠤⠞⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠈⢉⡡⠞⠉⠀⠉⠙⠒⠢⢄⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⡠⠚⠉⢉⣭⠽⠯⢖⡲⢶⣤⣄⠀⠀⠈⢧⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⣼⣥⣤⡾⠇⠀⢀⣠⡤⠨⠶⡅⠻⡷⡀⠀⠘⡆⠀⠀⠀⠀⠈⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠋⠀⠀⠀⠀⢰⠋⣴⢯⢀⣤⣶⣯⢹⣶⠀⡀⡚⠢⡽⣧⠀⠀⠹⣄⡤⠖⠒⠈⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⠃⠀⠀⠀⠀⢀⡟⠀⢸⣿⢸⡯⢷⣿⡼⣿⣸⢠⡏⠑⢿⣛⠳⣦⠜⠁⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⠃⠀⢀⣀⣀⣀⡞⠀⡶⡞⠋⠛⠃⠀⠀⠀⡿⢿⠀⢳⡀⠀⠉⠻⣁⠀⠀⠀⠀⢀⡜⡉⠉⠉⠉⠉⠉⠉⠓⠒⢤⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠉⠓⠦⣧⡿⣄⣀⣤⣤⣄⣀⣱⠀⣇⡌⢟⢦⡀⠀⠀⠙⠢⢄⣠⢋⣀⣸⡄⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀ ⠉⠛⢆⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠉⠉⠙⠚⢹⣷⠈⢫⡛⢦⡀⠀⠀⠀⠈⠑⠶⢴⣧⡀⠀⣀⣠⠴⠊⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠟⠁⣷⡄⠱⣄⠈⠓⠤⣀⡀⠀⠀⠀⠀⠉⠛⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠾⢿⡇⢸⡗⠽⢦⣤⣀⠉⠓⠒⠤⠤⣀⣀⡀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⠀⠀⠀⡸⢛⡄⠀⠀⠀⠀⠀⠀⠈⢷⡤⠖⢋⣠⡿⡇⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠈⢉⣭⣣⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢮⣴⣶⣚⡡⠋⢻⢦⡀⠀⠀⠀⠀⠀⠀⠉⠉⢉⡼⠃⠀⠀⠀⠀⠀⠀⠀⠈⢳⡒⢲⡒⢺⢾⣛⡢⢤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⣴⢚⢀⠟⠁⠀⢸⡄⠑⢦⣀⠀⠀⠀⠀⣀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣇⢘⣿⠇⠈⢢⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠁⣮⠏⠀⠀⠀⡇⢱⡄⠀⠈⢀⢤⣀⡰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣷⠾⠓⠚⠛⠛⠒⠲⠤⣀⠀⠀ ⠀⠀⠀⠀⣿⢸⢿⠀⠀⠀⠀⠘⣼⠷⠀⠀⠀⠁⠈⣏⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲ ⠀⠀⠀⠀⠈⠻⠼⣄⠀⠀⢀⡜⠁⠀⠀⠀⢀⣀⡠⠹⠾⢤⣀⡀⢀⠀⠀⠀⡀⢠⠃⢀⡎⠀⢘⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢶⢤⠟⠀⢀⡠⠖⠊⠉⠀⠀⠀⠀⠀⠀⠉⠓⢭⡙⠪⣡⠏⢢⢈⣂⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠏⣸⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢏⣁⡠⢶⢛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢴⣷⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠄⢨⠁⡀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⢁⣈⡆⠀⠀⠀⠀⠀⠀⠀⢴⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢹⠉⢳⡀⠀⠀⠀⠀⠀⠀⢸⢱⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⣸⣶⣸⢷⡐⠰⠀⠀⠀⠀⡸⢸⣳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⠀⠙⠤⠀⡿⡋⢧⢟⠻⢤⣀⠀⢀⡠⣣⠟⠁⠙⠢⠀⠀⠀⠀ ⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⣀⠀⣸⠃⠁⣼⢰⣕⢒⡛⣏⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⣰⠇⠀⠀⢹⠿⢸⠈⠀⠹⡷⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢝⣩⣡⠾⠹⠀⠀⢈⢿⣽⡮⡇⠀⢀⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣏⡀⠀⠀⢸⢻⣿⣿⣏⣧⡿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢳⡄⡆⢨⢲⡇⢸⠛⠛⠦⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣯⣿⡍⠙⢸⡎⠀⠀⣀⣿⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠃⢸⣼⠷⠚⠋⠀⠀⠉⠢⣄⠙⠳⣄⠀⠀⠀⠀ ⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣈⠙⠦⣄⡀ ⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡄⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⠀⢸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣿⠀⠈⣇⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⢀⣿⣀⣀⣿⣀⡙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡯⢽⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢠⡄⢄⣢⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣯⡇⢘⣬⣿⣿⣿⡿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠙⢻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠏⣼⣷⡆⢸⣶⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡆⠀⠀⣠⣶⡾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡯⢴⣿⠿⠿⠾⢿⣿⣿⣿⣇⢸⣿⣿⡏⠁⠀⢰⠀⣴⣤⠞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠙⣶⣶⣾⡷⡀⠀⢀⣶⣭⣥⣤⡭⠿⣿⣧⣤⣴⣾⠹⠉⡏⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠒⠒⠢⡞⠉⠉⠙⠻⣤⣈⣛⣛⣡⡇⠀⢸⣌⠻⠿⠟⠁⣀⣿⡏⠉⢁⡠⠤⠗⠓⠒⠒⠒⠤⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⡀⢸⢷⣄⡀⠀⢀⠄⠀⢄⠉⠉⠉⣉⠽⠋⠑⢞⠁⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠄ ⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠒⠓⠁⠀⠋⠋⡹⠓⠤⠤⠒⠉⢢⢠⠋⠀⠀⠀⢸⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀ ⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠐⡏⢄⠰⡄⢣⠞⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⡄ ⠀⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⡠⠀⣤⠀⢤⡾⠄⠀⠉⠉⠁⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⣿⣿⣗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⣿⣿⣿⣿⠛⢛⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣠⣿⣿⣿⣻⣿⣿⣧⠀⠛⢿⣿⣧⡁⣀⢀⡠⠤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣏⣿⢳⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠯⣉⣤⣼⣿⣿⠿⠉⡀⠀⣠⠖⠛⠟⠻⣭⣀⠀⠀⠈⡆⠀⣀⣤⡀⠀⠀⠀⠀⠀⢀⣿⣧⡿⠋⠙⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⣿⣿⣿⣶⣤⣽⠟⠁⠀⠀⠀⠀⡵⠈⠑⠒⠲⣧⣞⠁⠀⠉⠳⢦⡀⠀⡠⠊⢹⠛⣇⡴⢦⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⣻⣿⣿⠋⠀⠈⠁⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⡜⢸⠀⠀⠀⠀⠀⠉⠚⢥⡀⠘⡆⢸⠃⠈⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢰⠁⠀⢧⠀⠀⠀⠀⠀⠀⠀⠉⢻⠇⠀⠀⢰⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠺⣯⡿⠁⠀⠀⠀⢀⣆⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠙⠲⠤⢤⣤⣽⣶⣄⠈⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⠋⠉⠉⠒⠒⠶⠭⣉⡉⠙⠛⣶⠶⠿⢶⣶⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠈⡿⢷⣧⠈⢢⣀⠀⢀⡞⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣇⠀⠀⠀⢀⣴⣄⠀⡠⡿⢿⢦⣍⣒⠀⠘⢻⡄⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⠋⠀⠀⢨⣿⠋⠀⠀⠘⠦⣀⠀⠀⠀⠀⠀⠀ ⠀⠙⠛⠛⠛⠋⠀⠉⠙⢇⠘⢾⠙⡍⣿⠆⠀⠈⢇⡀⠸⡀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⢀⠞⠫⣀⡀⠀⠀⢀⠀⠉⠳⣦⣄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣼⠳⠟⠋⠀⠀⠀⠈⢇⠀⠁⠀⠀⠀⠀⠀⠀⢠⡏⠉⠉⠛⠧⣄⠀⠀⠈⠑⣤⡀⠙⠒⣄⣷⣏⣿⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⣀⠴⠛⢧⡀⠀⠀⠀⠈⠳⡄⠀⠀⠈⠻⠷⢦⣸⣧⠾⠏⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣯⠉⠁⠀⠀⠈⡇⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠙⠦⠤⠤⣼⠇⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠲⠤⠤⠤⠖⠉⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢆⡀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠖⠶⠶⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⣀⢤⣤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠈⢢⡑⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠊⣠⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠱⡤⣀⠈⠑⠢⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⡀⠀⠀⠀⠀⠈⢣⡀⠀⢡⠀⠑⠢⣄⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⡀⠀⠀⠘⡄⠀⠀⢀⠀⠀⠱⡄⠀⡄⠀⠀⠀⠑⢄⠀⠉⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⠢⣀⠀⠘⡄⠀⠘⡆⠀⢢⠘⡀⣷⣄⠀⠀⠀⠈⠳⡄⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢀⠔⠋⠳⣄⠘⡄⠀⢰⠀⠀⢧⢡⢸⠮⢷⣄⠀⠀⠀⠈⢆⠀⢏⠻⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠈⠣⣰⡀⠀⣇⠀⠈⣿⣮⡆⠀⠈⢏⢳⡀⠀⠈⢧⢸⣶⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⣠⡞⡏⠀⣀⣀⠀⠀⠀⠀⠘⢧⠀⣹⢆⠀⢿⣿⡇⢠⠒⠀⢳⣷⡄⠀⢹⡌⡿⢶⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⡤⠊⠹⢻⠗⠉⠀⠀⠉⣀⠀⠀⠀⠈⢇⢹⠈⣆⢸⡏⠧⣧⣶⣶⣦⣿⣿⡄⠀⣷⡷⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⠐⡇⠀⡇⠘⢀⣤⣤⣶⣾⣧⣤⣀⠀⠀⠈⣿⠀⠘⡄⠁⠀⣟⣟⠙⢫⡙⠿⢿⡀⢸⣇⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠣⡀⠀⠀⠘⡆⠀⣇⣸⣠⣾⣿⡿⠛⠉⠁⠈⢉⣧⠀⠀⠀⠈⠀⠀⢹⡆⠀⠈⠙⠏⠉⠛⠢⠜⢧⡜⠙⢿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⢆⠸⣿⡿⠉⠀⠀⢄⣀⡤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠈⠿⢿⣇⠀⠀⠀ ⣤⣴⡄⠀⠀⡀⠀⡀⡀⠀⠀⠀⠳⡿⠤⠤⠖⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠑⠢⢄ ⢟⠀⢡⠀⠀⠘⢆⠑⡜⢤⡀⠀⠀⠈⠲⣄⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠤⢠⡄⠀⠀⠀⠘⡉⠙⠢⡀⠀⠀⠀ ⠈⠀⡄⣆⢲⡀⠈⠢⣌⣆⠙⢦⡀⠀⠠⡈⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣥⣶⣿⡅⠀⠀⠀⠀⣷⡀⠀⠙⢆⠀⠀ ⠀⠀⠀⠸⣸⡟⢦⡀⠀⠉⠣⡀⠉⠢⡀⠈⠲⣄⡚⠿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⡆⠑⠄⠀⠈⠆⠀ ⠀⠀⠀⠀⠹⣿⡀⢻⢷⣄⡀⠙⢆⠀⠈⢆⠀⠀⠙⣦⡀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⣿⣿⡿⠿⠿⠛⠻⣄⠀⠀⠀⢠⣷⠤⣄⢣⡀⠀⣆ ⠀⠀⠀⠀⢀⠟⠳⢼⡞⣿⣿⣷⣤⣷⣄⠠⣣⡀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣀⠀⠀⠀⠀⠈⣢⠀⠀⣼⣿⢆⠈⣷⣷⡄⠇ ⠀⠀⢠⠀⢇⠀⠀⠀⢳⢹⠛⠉⠉⠀⠹⡆⠱⣧⠀⠀⠀⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⢿⠿⡿⠁⠀⣰⣿⣿⣾⠀⢸⣿⠃⠀ ⠀⠀⠀⠀⠈⣦⣀⡤⠊⠘⣄⠀⠀⢀⣀⣹⣀⠽⠧⢄⡀⢣⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⣿⣿⣿⠇⠀⡼⠃⡜⠀ ⠀⠀⠇⠀⣼⢣⣼⠀⠀⠈⣿⡿⢿⣿⣿⡿⠁⠀⠀⠀⠹⣼⡆⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡤⢞⣡⡾⠴⠂ ⠀⠀⠀⣰⣿⢸⡇⠀⠀⠀⣿⣷⣬⣻⡏⠀⠀⡶⢤⣤⡄⠸⠿⡀⡇⠠⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣰⣿⠿⠿⠛⠋⠉⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⡰⠀⠀⠀⣸⡿⠛⠘⣿⡀⠀⠀⡏⠉⢯⠁⠀⠀⠙⡇⠀⠀⠉⠙⠛⠿⣿⣿⣿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡿⠁⠀⢀⣾⠏⠀⠀⠀⠸⠟⠢⣄⡇⠿⠷⠂⠀⠀⢀⣇⠀⣀⣀⣀⠠⠄⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡘⠁⠀⢠⢻⣿⠀⠀⡆⢓⡎⠀⢀⣀⠅⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⠉⠀⠀⠀⠀⠀⠀⠉⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠤⠤⠤⠤⠄⠒⠁⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠑⠤⠀⠀⠠⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠒⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠈⠃⠀⢀⢃⠀⠀⠀⠀⠀⠀⢀⣔⠁⣰⢹⠡⡘⡀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀ ⠀⢀⠄⠁⡜⠀⠀⠀⠀⠀⡔⠁⠀⡜⠙⠉⡖⡌⢿⣂⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀ ⠉⠀⠀⢀⠗⠒⢄⠀⠀⠜⠀⡠⠊⢀⣅⣀⡑⢇⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⢶⠊⠣⠀⢀⢘⠇⠀⣜⠈⢀⠀⠘⡴⢥⡾⠈⡗⠀⢇⠀⠀⠀⠀⡆⠀⠀⠀⠀ ⠀⠀⠹⠀⠀⢠⡊⠀⠀⠨⣆⠈⢆⢘⣾⣟⣃⠀⠑⠄⠸⡀⠀⠀⢠⠀⠀⠀⠀⠀ ⠀⠀⡠⠤⠊⠀⠈⠂⢀⠀⠘⢄⡀⠉⡛⠳⡖⠐⠠⢀⢀⡧⡒⠒⠇⡀⠀⠀⠀⠀ ⡠⠊⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⠀⠀⠘⢠⣙⠀⠒⠂⠁⡅⠀⠈⠀⠈⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠔⠈⠈⢂⠀⠀⠀⠈⢂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⡀⠀⠑⢄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⢾⡭⠈⠀⠀⠀⠀⠈⡶⠫⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀ ⠉⠉⢁⣒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀ ⠀⠀⢸⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀

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⣿⣿⣿⣿⡀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢳⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾ ⣿⣿⣿⣿⣿⡻⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⠿⣧⣭⣝⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢷⣿ ⣿⣿⣿⣿⣿⣿⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢏⣿⣿⣮⡿⣍⠻⣶⣽⣿⣿⣿⣿⣿⣿⣿⡸⣸⣿ ⣿⣿⣿⣿⣿⣿⣷⡡⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⣀⠙⣷⡀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣸⢻⣿⣿⣿⣿⣷⣜⠻⢿⣿⣿⣿⣿⣿⡏⢃⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡏⠉⠁⢀⡀⠀⣿⡆⠈⢿⣄⠀⠈⢿⣿⣿⣿⣿⣿⡏⠸⣿⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⢣⣸⣿⣿ ⣯⠅⠄⠀⠀⠤⠆⠿⣷⡄⠹⣿⣤⠶⡶⢀⣴⠘⠛⠛⣻⣿⣫⣾⣿⣿⠟⢁⣤⣶⡿⢁⣴⣿⣿⣆⠘⣿⣆⢠⡀⠻⣿⣿⣿⣿⣧⠀⣿⣿⣿⣿⠟⠋⠙⠻⣿⣿⣿⣿⣿⣾⣿⣿⣿ ⢿⣦⡀⠀⠀⠀⠀⠀⠘⢷⡄⠹⣷⡀⠀⠎⠀⠀⠀⢰⣿⠛⣽⣿⠏⠀⢀⣾⣿⠟⣴⣿⡿⠻⣿⣿⣆⠘⢿⣏⢿⠀⠙⣿⡟⢻⣿⡆⢹⣿⣿⡟⠀⠀⠀⠀⠈⢻⣿⣿⡿⣿⣿⣿⣿ ⢷⣽⢷⡀⠀⠀⠀⠀⠀⠸⣷⡄⠹⣿⡋⠀⠀⠀⢰⡿⠡⣾⣿⠏⠀⢀⣾⣿⢏⣼⣿⠟⠁⠀⢻⡯⣿⣆⠘⣿⣾⣧⠀⠘⣷⣽⣿⣧⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿ ⠀⠹⣿⣻⣦⡀⠀⠀⠀⠀⠈⣿⡼⠙⣷⡀⠀⣰⡟⣁⣼⣿⡟⠀⣠⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⣻⣟⣿⣷⣿⣿⣻⣦⠀⢹⣿⣿⣿⣆⣿⣧⢀⣤⣖⣶⣮⣷⣶⣾⣿⣿⣿⣿⣿⣿ ⠀⠀⠈⠻⢿⣿⠶⠾⠛⠻⢿⣿⣿⣴⣝⣿⣀⣿⣽⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⠟⠓⠛⠛⠉⠉⠉⠹⠟⢿⣿⣿⣿⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣆⣠⣤⣘⣛⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⢀⡈⠈⠙⣿⣿⣿⣿⣿⣿⣿⠃⢀⣿⣿⣿⡿⣻⠟⠀⠀⢀⣀⣤⣤⣤⣤⣄⣜⣻⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠈⠉⠙⠻⣿⣿⠹⣿⡟ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⢿⣿⣿⣿⣿⡟⣠⣼⣿⣿⣿⡇⡏⠀⠀⠀⠙⠿⣿⣿⣿⣋⣿⠏⠉⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⢹⣷ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⢨⣿⣿⣾⣿⢻⡿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⢠⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⢻ ⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⣀⣽⣶⣾⣿⣿⣿⣿⢸⡇⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣿⣿⣿⠇⢠⣿⣿⣿⣿⣿⠀⠀⠀⢀⣠⣄⣀⡀⠀⠘⣿⣿⣿⡄ ⠀⠀⠀⠀⠹⣄⠀⠀⢀⣤⣾⠿⠟⠽⣿⣿⣿⣿⣿⣿⣼⠁⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣱⠧⣿⣿⡿⠀⢸⣿⢹⣿⣿⣿⣧⣴⡿⣟⣻⣿⣻⣛⣷⣤⣿⣿⣿⣧ ⠀⠀⠀⠀⠀⠻⡄⣰⣿⣯⠕⢊⣠⠾⠿⠋⠻⣟⠉⣿⣸⠀⣿⣿⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣠⠤⣤⣴⣿⣾⣿⣿⠃⢠⣿⣿⢸⣿⣿⣿⣿⣿⣟⣩⣿⣻⠶⠶⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠙⣿⣿⣧⡶⠋⠁⠀⠀⠀⠀⠈⢳⣼⣿⢀⣿⣿⡆⠀⠀⠀⣶⠞⣿⣦⣤⣤⣶⣧⠀⠘⣿⣿⣿⣿⡿⠀⣼⣿⣶⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠉⠻⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣀⣽⣿⣾⣿⣿⣿⣶⡄⢠⣿⢷⣦⣄⣿⡟⠋⠙⠛⠒⢫⡿⣿⣿⠇⣰⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⣠⠾⠟⢿⣿⡿⣿⣿⣿⣿⣿⣿⣷⡌⠟⠻⠶⠾⠛⠀⠀⠀⠀⠰⠋⣰⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⢀⣾⣻⣯⡴⠟⠉⠀⣿⣿⠏⠉⠻⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣾⣿⣿⠋⠀⠀⠀⢸⣿⠋⠀⠀⠀⢤⣿⣿⣿⣿⣷⣄⣀⣀⣐⣶⣤⡀⢸⣿⣿⣷⣿⣿⣿⠟⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟⠀⠀⠀⠀⢸⡟⢧⠀⠀⠀⠀⠙⠙⢿⣿⣿⣿⣿⡧⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⠏⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠈⢸⣧⠸⡀⠀⠀⠀⠀⠈⠙⠦⣉⡉⠁⠀⠉⠟⠀⠀⢰⢻⣿⣿⣿⠇⢂⡵⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣄⠀⠀⠀⠙⠳⠿⠃⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⣀⠀⠀⠠⠞⠉⠹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠛⠿⣷⣤⡄⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⣰⣿⠻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢠⣿⡟⢠⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠾⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⣿⣿⠇⣸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣆⠀⣾⣿⡿⢰⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⣿⠁⣼⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡌⢿⣿⠀⢸⣿⣿ ⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠈⣿⡀⢸⣿⣿ ⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢸⣿⣿ ⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿ ⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢻⣿⣿ ⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿ ⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸⣿⣿ ⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢠⣿⠀⢸⣿⣿ ⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⢁⣰⣿⡏⠀⢸⣿⣿ ⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡏⠴⠀⢸⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠦⣤⣄⣀⠤⠤⠤⠤⠐⣚⣤⣤⠴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣴⣾⣿⣿⣿⣿⣿⡇⣾⠀⢸⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⣿⠁⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⢸⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠀⢸⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠀⢸⣿⣿ ⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠟⠀⠀⢸⣿⣿ ⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠛⣿⠀⠀⠀⢸⣿⣿

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⠀⠀⠀⢸⠀⠀⠀⢠⣾⡇⢠⡏⠀⢠⡟⢠⠇⢠⡾⣣⡾⠀⡴⠃⣰⠂⣴⣿⠟⠁⣠⡶⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠉⢿⣿⣷⡄⠀⣤⡀⠀ ⠀⠀⠀⠸⠀⢰⡞⠋⠘⡇⢸⡇⣰⠟⢀⠏⢠⣾⣵⠟⢀⠞⢁⣼⠇⣠⠟⠁⣠⠞⠋⣀⣀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣠⣾⡿⠛⠻⣿⣿⣮⣿⣿⣷⡀⠹⣷⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⣷⡈⠻⠋⣠⡿⠀⣿⣽⠏⣠⠏⢠⣾⡏⠀⠉⣤⠞⠁⣰⣾⣿⣿⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠰⠟⠋⠻⣿⣦⠀⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⣿⡇ ⠀⠀⠀⠀⡀⠸⡇⠀⠀⠈⠛⠶⠾⠛⣷⠀⠛⢁⣼⠋⣴⠿⣿⠀⣠⠞⢁⣴⢟⣁⣼⡿⠟⢁⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⠘⢿⠆⠀⠀⢀⣿⣿⣿⣿⣿⣿⢠⣿⠁ ⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠛⠛⠛⠁⠀⠹⣿⠁⠐⠛⠋⢉⣁⣠⠤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⣿⣿⠉⠁⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣴⣾⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⣀⣤⠶⠛⢋⣉⣤⣾⡿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⣠⣤⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠈⠀⠀⣠⡾⢋⣡⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⣠⣶⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⢀⣰⣿⣿⣾⣿⡿⠟⠛⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣧⡀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⡿⣛⠁⠀⠀⠀⠀⠀⠀⠀⠐⣦⡀⠐⠶⣄⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣰⣾⡇⣠⣾⣿⣿⣿⣿⡷⠛⠛⠛⠳⣄⠀⠀⠀⠀⢀⣀⡈⠙⠢⡀⠈⠃⠀⠸⣿⡉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠏⠀⢠⡿⣡⣿⣿⣿⣿⣿⣿⣻⣷⣶⣦⣿⣷⡜⠁⠀⢀⣾⣇⠀⠐⠆⠀⠙⠲⠤⠀⠀⢿⠙⢷⣼⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⣠⢿⡟⠉⠉⣼⣷⣿⣟⡟⣻⣿⣿⣿⣿⠏⢉⣿⣿⣿⠃⠀⠀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⢸⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣥⣿⣡⣾⣿⣿⡿⠛⠀⠀⠈⠀⠀⠀⠀⠈⠓⠀⠀⣤⡀⠀⠀⠀⣿⣿⣏⠸⣿⣿⣿⣿⣿⠏⠉⠻⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣞⡿⠋⣀⣴⣶⣶⣀⡀⠀⠀⠀⠀⢠⡄⠀⠈⠁⠀⠀⠀⣿⣿⣿⡆⣿⣿⢿⣿⣿⠀⠀⠀⠈⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠙⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠞⢻⣿⣿⠟⠋⠉⠀⣾⣯⣽⣷⡝⣦⠀⢀⠀⠀⣰⣿⣿⣿⣿⡿⠃⣾⣿⣿⡇⠀⠀⢀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡴⠏⢀⣸⣶⣾⣿⠿⣿⣿⡿⠁⢘⡷⠀⢀⣼⣿⣿⣿⣿⡟⠁⣰⣿⣿⣿⡇⠀⢀⣾⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢷⣰⠟⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡿⢛⣻⣿⣶⣻⣿⣷⣶⣾⠀⣠⣾⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣇⣤⣾⣿⣿⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⡟⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⠟⠛⣿⣿⣿⡿⠛⣁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⣿⣆⣰⡿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠈⠻⣿⣿⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⣿⣹⣿⣿⣦⣀⣼⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠔⣿⣿⣿⣿⣿⣿⣿⣯⠁⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣀⣿⣿⠉⠙⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣿⣥⣼⣿⣾⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⠟⠙⢿⣿⡇⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⢰⣿⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣾⡿⠟⠁⠀⠀⣸⡿⠁⠀⠀⠀⣠⣠⣿⠟⠁⠀⢰⣿⠟⠁⠀ ⠀⠀⠀⠤⠴⠶⠤⠤⠶⠴⠶⠒⠒⠋⣉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣭⣤⡤⠶⠖⢚⡟⠀⠀⢀⣴⣿⡾⠟⠉⠀⠀⣠⡟⠁⠦⠤⠔ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠉⠀⠀⠁⠐⠊⢀⣤⡶⣿⡟⠋⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀ ⠂⠀⠉⠛⠳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣡⣾⣿⣿⡿⠋⢀⣼⠟⢹⡇⠀⠀⠀⠀⠀⠀⠀⠐⣉⣡⠾⠁⠀⠀⠀⠀⢀⣾⣿⣿⣄⡀⠀⠀⠀ ⠀⠀⠀⠐⢒⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⡿⣿⣿⣶⠾⠟⠁⠀⣾⠁⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⠀⠀⠀⠀⠀⣠⠏⠀⢿⣟⠿⢿⡀⠀⠀ ⣤⢤⡤⠦⠄⠀⠈⢛⣛⠶⣦⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣼⣧⣀⠈⢳⡄⠉⣻⡷⠤⣄⣀⣀⣤⠞⠁⠀⠀⠀⠀⢀⣠⣾⡏⣸⠃⠀⠀⠀⠀⣠⠞⠁⠀⠀⣨⢿⡀⣼⢣⡦⠀ ⠶⠚⠛⣶⣄⠀⠀⠀⠙⠳⠶⣦⣭⣽⣿⣿⣯⣉⣡⣤⡶⠚⠹⣿⣿⡟⠒⠋⠀⢰⢿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠋⣱⡏⣸⡇⡀⠀⠀⣠⣾⣏⣀⡀⣼⣿⠃⢸⡽⢡⢋⡴⡄ ⠒⠀⣧⣿⣿⣷⣤⣤⣤⣤⣤⣶⣿⡿⠻⣿⣀⠈⠛⠛⠲⠦⣶⣷⢻⣿⠀⠀⢠⠎⠸⠁⠀⠀⣤⡶⠒⠒⠚⠛⠉⠀⠀⠀⣿⡿⢟⣋⣉⠻⣿⣿⣿⡝⢩⢣⢣⢇⡄⡿⢣⣫⠟⠼⣣ ⠀⢰⠟⣿⣿⣿⣿⣿⣿⣿⣇⠀⠙⢷⣄⠀⠉⠙⠲⠶⠶⠞⠳⠏⢸⡟⠀⠀⠀⢠⡇⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⣻⡀⢸⣿⠟⡾⣷⣿⣟⡇⣾⡿⡿⣼⠋⣱⣧⠿⣠⠞⠁ ⠀⢻⠀⣿⣿⣷⣯⣛⣿⡟⠻⢷⣤⣀⣈⠛⢦⡖⠁⣄⠀⠀⠀⠀⣼⠇⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡈⢯⣼⡁⣿⣿⣿⣿⣿⣽⣱⢻⣰⣯⡯⠚⠁⠀⠀ ⠀⠈⢷⣼⣿⣿⣿⣿⣿⣿⣄⣾⣿⡄⠀⠀⠀⠙⢳⡿⢤⣤⠤⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡘⣿⡟⢾⡿⠃⠀⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠒⠒⠒⠚⠁⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣻⣧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣥⣴⡀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠸⡆⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⠉⠳⢦⣲⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠳⡄⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡁⠀⠀⠀⠀⠀⠀⠛⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠚⠿⢉⣿⣿⣿⣿⣿⣿⠀⠘⡇⠀⠀⠀⠀⠀⠀⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀ ⠛⠷⠶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀ ⣠⣴⡿⠶⠛⠛⠛⠒⠶⠶⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀ ⠃⠀⠀⠀⠀⠐⠚⠛⠁⠀⠀⠀⠀⠙⠛⠛⠷⢶⠤⣤⣄⣀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⢀⣀⣀⣴⡖⠚⠛⠋⠛⠒⠶⠦⢤⣀⣀⣠⠶⣿⠿⣝⡷⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀ ⠀⠀⣾⠛⠋⡉⠉⠛⢲⡀⠀⢠⡴⠚⠛⠳⡄⢨⡏⠀⣿⢀⡞⢁⣾⣟⡛⢿⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⠙⡇⠀⠀ ⠀⠀⢹⠀⢰⡟⠛⢶⡀⢻⠾⠋⣠⡔⢳⠀⣿⡞⢀⡾⣡⡞⢁⡾⠋⠈⡟⡴⢾⣧⡼⠿⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠒⠀⠀⠀⠀⣇⠀⠀

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⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠉⠉⠀⠣⠈⠍⠉⢁⢃⣤⠃⠉⢀⠹⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⢤⠰⢿⡄⠀⢸⡇⢻⡆⠂⠛⠁⣘⣆⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⢿⣿⣿⣿⣿⠀⠸⣧⠈⣿⡌⠸⣷⠈⣿⣀⠸⣦⢸⣿⡆⠀⠀⠀⠀ ⠀⠀⣸⣿⣧⣿⡿⣿⢿⣿⣿⣿⠁⡀⠘⣿⣿⣿⣿⣿⣿⣿⣯⣾⢏⣾⣿⠁⢿⣿⣦⠂⣿⣧⢿⣷⡄⣿⣇⢿⣿⢶⣿⡟⣿⣧⠀⠀⠀⠀ ⠀⠀⠉⣿⣿⣿⡇⠘⢯⣿⣿⡟⠳⣿⠤⣿⣿⣿⣿⡿⠋⠘⠙⠃⣹⣿⣿⢒⣚⣿⣿⣧⢿⣿⣿⣿⠿⠻⣿⣼⣿⣸⣿⣇⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⢹⣿⣿⠇⠀⠰⣿⠻⡀⠀⠈⠉⢹⣿⣿⠇⠀⠀⠀⠀⠀⣸⣿⣿⡘⠁⠹⢿⣟⣿⣿⣿⣿⠀⠉⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⠀⣠⠶⠛⠉⠉⠉⠑⢦⡘⣿⡏⠀⠀⠀⠀⣠⡞⢡⡼⠛⠧⡀⡀⠈⠿⣎⣿⠀⠙⡗⣠⢾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀ ⠀⠀⠀⠈⡿⠹⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⢀⣠⡞⠃⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠘⣿⣿⣿⣿⡿⣸⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⠚⠋⠳⣄⠀⠀⠸⣄⣀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠃⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠑⢆⡀⠀⠙⠦⣄⢹⡀⠀⠀⠀⠀⢀⡤⠖⠁⠀⠀⠀⠀⢸⡿⠹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⡀⠈⠙⠿⣤⣤⣒⣮⣿⡄⠀⢀⠀⠀⠀⠀⣠⠋⢹⣒⡆⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠴⠶⠿⠿⠿⠿⠥⠤⠤⠤⠤⠤⠤⠞⠁⠀⠀⠈⠙⢦⡄⠀⠃⠀ ⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣾⣧⣀⠀⠀ ⣸⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀ ⣿⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⣄⣀⣤⣤⣴⠒⠒⠉⣩⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⢹⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢈⣼⣿⣿⣿⣿⣇⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠠⠷⠒⠂⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢈⡋⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣏⡎⣧⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻ ⣿⣿⣷⣿⣼⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⢸⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿ ⡿⣵⣾⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⣿⠟⠁⠀ ⣿⣹⡿⣻⢉⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣷⠀⠀ ⣧⢿⠠⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀ ⣿⢠⡞⠂⠀⠀⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣼⠿⢟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣄⠈⠉⠉⣽⣻⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀ ⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⢿⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣆⣈⠳⢄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣾⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣝⢯⣻⣿⣿⣿⣿⣿⣿⡏⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣿⣿⣿⣿⣿⡇⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀ ⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⡷⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀ ⠒⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⠃⠀⠀⠀⣠⣷⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⠒⠢⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⠀⠀⢀⡴⢋⣠⠤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣶⡮⠚⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣶⣦⣤⣤⣀⠤⠔⠒⠒⠒⠒⠒⠠⠤⠄⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠹⡄⠀⠀⠀⢀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣞⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡴⣶⣿⣇⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⣿⣿⣿⠿⢟⠛⠛⠿⠿⢯⣝⣛⠻⢿⣛⡛⠋⠉⠁⠙⣯⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⢿⣿⣿⣿⢳⣶⣦⣤⣀⡀⠉⢍⡙⠛⠿⠷⣶⣤⠀⠈⠹⣧⠀⠀⣄⠀⣀⡤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣌⡁⠀⠀⠀⠻⢽⣲⣼⣿⣷⣄⠈⠻⣅⡀⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠚⠉⠀⠀⠀⠀⠀⢀⣾⢿⣿⡏⠉⠉⣿⡿⠿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠙⢷⡮⠙⢿⣷⣤⣨⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢾⣿⣵⠀⠀⠙⣧⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣦⣀⠈⠻⣦⠠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣿⣿⣿⡏⢻⣿⣶⡀⠀⢿⣷⣄⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣷⣄⣹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢾⡁⠀⣿⣿⣿⣷⡀⠙⢿⣷⣦⣘⡟⢿⣿⣶⣤⣤⣄⣀⣼⡿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠴⠞⠉⠀⠈⣇⠀⣿⢻⣿⡿⣿⡀⠀⠁⠻⣿⣷⣤⣉⣛⣿⣿⣿⠿⢛⣃⡉⠹⣿⡟⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⠒⠉⠁⠀⠀⠀⠀⠀⣸⡆⢻⣼⣿⡇⠙⣷⣤⡀⠀⠈⠙⠿⢿⣯⡍⣙⡓⠐⠻⠿⠿⣿⣿⡀⠀⠀⠀⢀⣴⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣻⠃⠀⠹⣿⢱⡄⠀⠙⠿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⢀⣤⡤⠴⣷⡀⢀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡤⠛⠉⣿⠀⠀⠀⣿⠀⠙⢦⣀⠀⠀⠰⠄⠀⠀⠀⠒⠦⣄⣀⢁⡏⠀⠒⠂⠘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⢀⡟⠀⠀⣴⢃⡇⠀⠀⠿⠑⠦⣄⡀⠀⠀⠀⠓⠒⢶⠾⢻⡷⢾⣶⣶⣦⣾⣧⡀⠀⠀⠀⠀⢀⣀⣠⣴⣶⣶⡿⠉⠀⠀⠀⠀ ⠀⠀⣠⡶⠋⠀⠀⠀⠀⢀⡞⠀⠀⢰⡧⠞⣅⠀⠀⠀⠀⠀⠀⠀⣼⠃⠰⠶⠤⠤⡤⡿⠄⠀⠨⡍⢹⣿⣿⣿⠷⠿⠟⠛⠛⠉⠉⠀⣴⢟⠁⠀⠀⠀⠀⠀ ⠀⠘⠉⠀⠀⠀⠀⠀⢠⡎⠀⠀⢀⡾⠁⠀⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢀⣠⠤⠖⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⣼⠀⠀⠀⠀⢀⡆ ⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⢠⡀⡼⠁⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠀⢀⣼⠃⠀⠀⠀⠀⡼⠀ ⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⢸⢰⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⣸⠁⠀ ⠀⠀⣀⠀⠋⠁⠀⠀⠀⠀⣾⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣀⠀⠛⠟⣦⡳⣄⠀⠀⢀⣾⣿⣿⣿⣿⠛⠻⢿⣿⣟⣽⣿⣿⣿⣿⣿⠿⣡⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣄⣄⡈⣻⣾⣷⣄⣹⣿⣿⣿⣿⠃⣦⡀⠀⠀⠉⠛⠛⣿⣿⠟⠁⣾⣿⣿⢿⣿⣾⠁⣼⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⢤⣀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⠏⠀⠘⢛⣻⣧⡀⠀⠀⠈⠈⠳⢿⡁⣼⠃⢾⣿⣿⣤⣿⣿⣿⣿⢫⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠦⠤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣤⣄⠀⠙⠳⣄⣿⣿⣿⣿⣿⣿⣿⢋⣾⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠾⠯⠙⢛⣋⣭⣤⠀⠀⠈⠻⢿⣿⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⢿⣿⣅⡀⠀⠈⠀⠹⢿⣿⣿⡿⢣⣿⣿⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⢂⣠⣴⡾⠟⠋⣁⣠⢴⣾⣛⣵⣿⠟⠀⠀⠀⠀⠀⠀⠻⡆⠀⠀⢰⡞⠀⠀⠀⠀⠀⠀⠑⠊⠉⠙⠀⠀⢠⣾⣿⢟⣵⡟⠋⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢤⡭⣶⡛⢍⣩⢾⣯⡿⠛⠉⠀⣴⠋⠀⠀⠀⠀⠀⠀⢻⣆⣻⣜⠿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣫⣾⣫⠄⣰⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣯⡏⡄⡏⣿⣷⡿⣧⣾⠋⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⣍⣛⠲⢤⡀⠀⠀⠀⠀⢀⣠⡾⣻⣿⣿⣿⣟⣁⣡⣾⣿⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢻⣿⣿⣿⣴⣿⣿⣿⣿⣿⠏⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣬⣩⣍⣹⣶⣤⣤⣶⣚⣛⣁⡾⣻⣿⣿⣿⣿⣿⣿⣿⡛⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣴⣿⣿⣿⣿⣿⣟⠻⣿⣿⣿⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠋⠉⠉⠁⠀⠀⠀⠀⠈⠉⠙⠒⢿⣿⣿⣿⣿⣿⣯⣛⣿⡿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢡⣾⣿⡿⢋⡿⣿⠻⣿⣦⡘⣿⠸⣇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⣿⣿⣝⣛⣿⢿ ⠀⠀⠀⠀⠀⢀⣰⣶⣯⣴⣿⡿⠋⢀⡞⢰⡇⢸⣿⣿⣷⡸⣦⢻⣆⠀⠀⠀⠀⠒⣆⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿ ⠀⠀⠀⠀⢠⡾⣹⢯⣾⡿⢋⡅⠀⣸⠁⣼⠁⣸⠛⡛⣿⣿⣿⣦⢻⡄⠀⠀⡀⠀⠈⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡟⣴⢫⣿⠏⠀⣾⠀⣴⡏⡄⣿⠀⡿⢡⡗⢸⣇⠙⢿⣄⣷⡔⠀⢸⣄⠀⠀⣤⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣧⠀⠀⢸⣿⣿⡿⠃⣾⡿⣿⣿⠱⣷⠏⣰⠇⠉⡄⠈⢿⡆⠈⠻⣿⣿⣆⠀⠻⣦⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⡀⢀⣿⣿⣿⡇⣴⣏⠙⣿⠇⣸⢟⣼⠏⠀⠰⠇⣼⠈⠉⠀⠀⠈⠻⣿⣦⡀⢻⣇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣇⣿⣿⢹⣿⡷⣝⢳⢾⣯⣰⢏⣾⠋⠀⠀⢀⣴⠏⠀⠀⠀⠀⡀⠀⠈⢿⣿⣾⣾⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢻⣿⣿⣎⣧⢿⡙⢦⣶⣘⣋⣾⣡⡤⠖⢛⣛⣁⣉⣠⣤⣤⣤⣬⣱⣀⣾⣿⠟⠉⠉⠉⠛⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠿⣏⢻⡿⡟⠿⣶⣭⣬⣽⣿⣛⢉⣉⣉⣉⣉⣈⣀⣁⣀⣈⠙⣿⣛⣿⠇⠀⠀⠀⠀⠰⣄⠈⢯⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢧⣝⠲⠼⣗⢲⠧⠤⠶⠾⠟⠛⠛⠉⠁⠈⠉⠉⠉⡉⠉⠁⣴⢿⣧⠀⠀⠀⠀⠀⠘⢠⠞⠁⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠻⢶⣬⣾⣷⠶⠶⠤⠤⠤⠤⠤⠬⠿⠿⠿⠶⠿⠾⠿⠿⣟⣿⣷⣄⡀⠀⢀⣼⡍⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣢⠆⢸⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣖⡋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢁⣀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠻⣻⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣾⡿⠳⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⡏⠁⠀⠀⠑⢦⣬⡙⠓⢦⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠳⣄⣀⠀⠐⡌⠻⣹⠦⣄⠹⢿⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡾⠀⠀⡿⢀⡞⠙⠲⢮⡁⠀⠑⣌⠻⣶⡂⢀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⠃⠀⣾⠁⡾⠀⠀⣠⠖⠛⠳⢄⠻⢧⣬⣙⠿⠷⠶⠶⣤⣀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡇⠀⢸⡇⢰⠇⠀⢸⠇⢠⠚⠙⢦⣀⠀⠻⣯⠹⠗⠒⠒⠶⣬⣅⠀⢠⣿⣿⣷⣶⡦⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⢤⣐⣢ ⢸⣷⠀⢸⠇⢸⠀⠀⢸⠀⢸⡆⢀⠀⠈⠱⡄⠹⣧⢀⠀⢀⡼⢹⡇⠀⣾⣿⣿⣿⣿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣚⠙⢿ ⣿⡏⠀⠸⡄⠠⠀⠀⢸⡄⠸⣆⠈⢷⣄⠀⠙⢆⠘⢿⣦⠘⡇⣾⠁⢸⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣽⢿⣿ ⣿⡇⠀⢸⠃⢠⠀⠀⠘⣇⠀⢻⡄⠀⠛⢦⡀⠈⠓⢦⡈⠙⠻⠋⠀⣿⣿⣿⣿⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿ ⢳⣿⠀⠈⡇⢸⡄⠀⠀⠸⡆⠈⣷⠀⠀⠊⢿⣦⣀⡀⣽⠀⠀⠀⣸⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿ ⠘⡟⢾⠀⢳⠈⢧⠀⠀⠀⢷⠀⠸⡆⠄⠰⢾⣿⣿⣿⠿⠃⠀⢰⣿⡼⠛⢻⣿⣿⣿⣿⣶⣶⣦⣀⣠⣤⣤⣤⣄⣀⣀⣿⣾⣿⣿⣿ ⠀⢹⡼⡀⠈⢦⡈⠳⣄⠀⢸⡀⢰⠃⠀⠰⣞⣿⡏⠀⠎⠀⣤⣿⠏⠀⠀⠀⢹⡟⢿⠛⠛⢿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠳⣿⣄⠀⠉⠂⠀⠀⣸⡇⢸⠀⠀⢀⣼⡏⣰⡇⠀⢰⣿⠏⠀⠀⠀⠀⢸⡇⣼⠃⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉ ⠀⠀⠀⠙⢿⡷⣄⣀⣀⡴⣋⠠⡈⠀⠀⢀⣾⠟⠛⠁⢀⣿⡏⠀⠀⠀⠀⠀⡾⢠⠏⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁⠀⠹⠿⡿⠿⠉⠀⠀⠀⣸⡿⠀⠀⠀⠀⢀⡾⣱⠋⠀⣤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠘⠀⠁⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢠⣬⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢩⣝⢶⡳⡖⢲⠖⡖⠞⢭⠽⡏⢩⠉⣭⡦⠔⡲⢆⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠛⢳⣿⡷⠛⠓⠓⠚⠒⠚⠓⠒⠒⠋⠂⠒⠒⣒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⢀⠴⠗⠀⠀⠀⣸⣀⣤⣾⣧⣤⣶⡿⠟⣩⣷⣶⣭⣳⣄⠁⢀⣼⣛⠛⠒⠀⢸⣿⣧⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠏⠀⠀⢀⣤⣾⣿⣿⣿⣿⠿⠟⠛⠛⣋⣉⣉⠉⠉⢙⣿⣷⡟⠋⠛⠷⠄⠄⢈⣿⣿⣿⡟⠻⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡜⠀⣠⣾⣿⠟⠋⠉⠁⠀⠐⠀⠀⠉⢉⣀⡀⠀⠀⣹⣿⣿⡛⠛⠦⢤⣀⠀⠀⠀⠀⠉⠛⢿⡀⠘⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢃⣼⣿⢟⡟⠀⢀⣴⠾⠓⠒⠀⠉⠉⠉⠁⠀⠐⠚⠛⠛⠛⠛⠛⠻⠶⠮⠟⠷⠦⢤⣀⣀⡐⠻⢶⣬⡆⠀⠀⠀⠀⠀ ⠀⠀⢀⠏⣼⣿⠎⢀⣴⡟⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠛⠿⣄⠀⠀⠀⠀ ⠀⠀⢼⠀⣿⡇⠠⢺⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣄⡀ ⠀⠀⠀⠀⣿⣷⢁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣷ ⠀⠀⢸⠀⢿⠹⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⠀⠀⡸⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⠀⠀⡇⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟ ⠀⠀⡇⠀⠀⠀⠸⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃ ⠀⠀⠃⠀⠀⠀⠀⢻⣷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣤⣤⣤⣤⣤⡤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⣤⣤⣾⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⢰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢹⡿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡞⢠⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⡇⠀⠀⠀ ⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢼⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠉⠓⠦⣤⣄⡀⠀⡇⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠉⠻⣼⠁⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣷⣄⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢝⢿⣷⣄⠀⠀⠀⠀⠈⠦⣀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣈⠳⢿⣿⣷⡄⠀⠀⠀⠀⠈⣲⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣻⠋⠀⣾⡷⢿⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⣻⡄⣀⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠟⠋⠉⠉⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⣤⣤⠼⠗⠚⠒⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠒⠦⢄⡀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⢀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⢼⣿⠁⠀⠀⠀⢾⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⣄⡀⠘⢦⡀⠀⠀⠀⣸⣿⠦⠤⠤⠤⣌⡀⠀⠀⠀⠸⣿⡿⠻⠛⠋⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠔⠛⠓⢤⣱⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠙⢧⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠉⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣼⡀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣄⠀⢻⣆⢀⡠⠄⠀⠀⠀ ⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣾⣿⣧⡀⠀⠀⠀⠀ ⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣦⣄⣀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠉⠉⠀ ⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣶⠤⢄⣀⣀⣀⣀⣀⠠⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣷⡙⠳⠶⣤⣤⣤⠤⠄⠠⠒⠉⠀⠘⢆⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣶⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠈⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣧⢰⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⣇⠘⡞⣿⣌⣧⣹⣷⠸⣇⠀⢧⣹⡄⠈⢿⢳⠈⠻⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⣿⡌⢆⠀⠘⡆⠹⣿⣇⠉⡟⣿⡟⢻⣹⣏⣿⣷⠒⠚⢿⡧⠀⠹⣿⡆⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣆⡄⠱⠹⣿⡜⣆⠀⢹⡄⢻⡟⠀⠰⠹⠛⠉⢁⣴⣿⣿⣿⣿⣿⣿⣶⣶⣿⣧⣸⡯⠋⣹⣿⣿⣿⣿⣿⣷⡄ ⣿⣿⣿⣿⣿⠛⠁⠸⣷⣼⣿⣷⣀⠀⠀⢻⣌⡦⠜⠛⠊⠁⠀⠀⠀⠀⠀⣩⠏⠉⠀⢀⣈⣉⠉⠙⠛⢿⣿⣿⣧⣄⣿⣿⣿⣿⣿⣿⣿⣾ ⣿⣿⣿⡟⠁⠀⠀⠀⠹⣽⣷⡘⢿⣦⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⢼⣷⣾⡿⣿⣻⣦⡀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿ ⣿⣿⣿⡇⠀⠀⠀⢠⣼⣷⡈⠳⡄⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⠉⠀⢈⣿⣿⡇⠀⠀⢹⣇⢻⣿⣿⣿⣿⣿⣿⣮⣿ ⣿⣏⠈⢻⡄⢀⣷⣋⠔⢒⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡤⠤⣞⣉⣉⣠⣤⣄⢚⡏⠲⢿⣿⣿⣿⣿⣎⢿⣿ ⣷⢻⡆⠀⣹⣿⠟⣡⣶⣿⣶⣾⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠉⠉⠉⢹⠛⠓⠠⠭⠭⠽⠶⠴⢿⣿⣿⣿⣿⣿⣝ ⡜⣧⠱⣾⠏⣠⣾⣿⡿⠋⢁⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢿⣷⣶⣦⣤⣤⣤⣤⣬⡿⢿⣿⣿⣿ ⣿⡌⢧⡈⣴⣿⣿⢋⣶⣶⣿⠿⣟⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣿⣟⣿⣟⣉⣀⣠⣤⣾⠿⣿ ⣿⠿⣄⣹⣿⡿⢁⡾⣿⠟⠿⠀⣸⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⣿⣿⣿⠏⠋⣻⣶ ⣾⠟⠋⣿⣿⠇⠈⣿⣷⣄⣀⡴⣻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⢁⣴⣿⣿⣿ ⣿⡤⢺⣿⣿⠀⠀⠹⣿⡿⣏⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⢚⣷⣶⣄⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣿⣿⣿⣿⣿ ⣇⢳⣾⣿⡿⣦⠀⠀⢠⡟⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⣠⣴⣿⣍⣻⣿⣆⠀⠀⠀⠀⠀⠀⠈⡟⢿⡿⣿⡭⠭⢤ ⣿⣿⣿⣷⣄⠀⠀⣄⡻⠤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠴⢲⣾⠿⠟⠉⠀⠀⠈⠙⡿⠀⠀⠀⠀⠀⠀⡸⠀⠈⢷⠀⢀⣦⠞ ⣿⣿⣿⣿⡙⠛⠒⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣡⠞⠉⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⣰⣥⣤⣤⣼⣛⣽⠋⠀ ⠻⣿⣿⣿⣿⣶⣄⠀⠀⢀⡾⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠏⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⣀⡈⠙⢿⣽⣿⣿⣷⠶⠿⣷⣿⠇⠀⠀⢠⣾⢿⣷⠀⠀⠀⠀⠈⠓⠢⠤⠤⣀⣀⣀⠠⠋⠀⠀⠀⠀⠀⠀⣰⠏⠉⠉⠙⠻⢿⠃⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡏⠀⠀⣠⣾⠧⣀⣀⡴⠛⠉⠚⣿⣛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡄⠀⠀⠀⠀⢀⠞⢹⠗⣄⡀⠀⣀⠜⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣷⡿⠻⠿⣷⣾⠛⠀⠀⣠⡾⠙⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣣⠔⣹⠾⢿⡿⢯⣁⠀⠀⠀⠀⠀ ⣿⡿⠟⢿⣿⣿⣿⣿⠁⠀⣠⣾⣿⣤⣤⡼⣿⠁⠀⣸⠓⣶⣶⡤⠀⢀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣾⣿⣿⣿⠏⢀⣼⢸⠉⢫⢣⠀⠀⠀⠀ ⠏⠀⠀⠘⣿⣿⣿⣿⣆⣰⣿⣿⣿⣿⠟⣸⣿⡀⣀⡟⢠⣿⣽⣇⢀⣀⣀⣀⣀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣣⡶⡿⠒⠉⠀⢘⡀⡆⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⡟⠵⡚⠀⢈⢻⡿⠋⣴⣿⣿⣿⠿⠓⠚⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠓⠷⠖⠛⠛⠛⠓⠁⠀⠀⠀

⠀⠀⠀⠀⠀⡠⠤⠴⠶⠤⠶⠦⠦⠶⢖⣻⠽⠛⠩⡹⠿⢿⠿⣶⣔⡶⠤⠤⠤⠤⠄⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿ ⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣻⣿⣒⡬⠳⠛⣁⣴⢾⠿⣿⣿⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣼⢡⢏⡞⢿⣄⡾⠻⣅⢰⣆⠐⢮⣿⣷⡈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿ ⠰⣄⡆⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣟⣥⠖⠛⢦⣤⡽⣟⣿⡆⠸⣿⣿⣿⣤⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⣼⠳⣄⠀⠀⠴⠖⠊⠉⢹⣯⣷⣻⢩⢸⣴⣶⣽⡿⡇⠸⣹⣿⣼⣿⣿⣿⣿⣿⣟⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠛⠀⠈⠓⢤⡀⢀⣀⣀⣘⣿⣿⣿⣎⠀⠘⢛⠟⠁⢻⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿ ⢠⠀⠀⠀⠀⠀⠙⠻⣍⡉⠻⢁⣿⣿⡾⠃⠀⠀⠀⠀⠈⢿⡟⠉⠉⠉⠉⠙⠻⣿⣿⣿⣷⣌⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠀⠀⠀⠀⠀⠀⠀⠀⡹⠲⣼⣉⢿⣿⢦⣀⣤⠤⠀⠀⣾⠒⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⡇⠀⠀⠀⠀⠀⠀⣀⣶⣪⣾⠃⣿⢻⣿⣷⣭⣀⢀⣠⢾⣿⡄⠀⠀⠀⢀⣴⣾⠟⠛⣻⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⢀⣀⢰⠐⣤⠖⢩⡼⢃⠔⠀⣼⢿⣿⣿⣿⣿⣿⣿⡟⠃⡀⠀⢀⣮⠋⢤⣴⢿⣿⣿⣿⣿⣿⣿⣿⣍⡛⠛⠻⢿⣖⣦⣄⠀⠀⠀⠀ ⡴⢚⣽⠉⢴⠇⠘⣧⠞⢰⠏⣤⣾⣿⣮⣻⣿⣿⠟⢹⡏⠀⠀⠘⢦⣸⣧⣠⣿⣇⡀⠻⣿⣿⣿⣿⡿⣿⣿⣿⣦⣴⡦⠈⣉⠉⠁⢀⣈⠠ ⡴⢻⡂⠈⡈⠀⠀⣻⣠⠴⠚⠋⠉⣉⠉⠀⠀⠀⠀⣿⡄⠀⠀⠀⠘⠟⣿⣿⣿⣿⣿⣷⣾⣿⠟⣥⣾⣿⣿⣿⣷⣖⢍⡀⠂⠀⠀⠀⠀⠀ ⠀⢘⣗⠀⠘⣄⡴⠋⣀⡠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠸⣿⣦⡀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠙⠂⢠⡀⡀ ⣤⡤⠞⢧⣴⣿⠇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢯⣀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⣼⡇⢀ ⠋⣠⣔⡽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠉⠀⡎⣿⣿ ⣼⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⣘⡿⢀⡞⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠈⠀⠀⣿⣿⣿ ⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠈⠉⠁⠀⢸⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⡀⠀⢀⣾⣿⣿⣿ ⠋⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢟⠀⠀⠀⠀⠀⠀⠰⠤⠤⣄⣠⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⠿⢿⣿⡿ ⠀⢻⣧⣀⠀⠀⠀⠀⠀⠀⣀⡠⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⠀⠀⠈⠉ ⠀⠈⢿⣿⣄⣀⣠⣀⣼⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⠈⠙⠛⠿⠿⠿⣿⣿⣿⣿⣿⢿⣧⣹⣿⡄⠀⠀⠀ ⠀⠀⠀⠙⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣳⡆⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣎⠻⣷⣿⣿⡄⠀⠀ ⠀⠀⠀⣠⣿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣿⣿⣿⣿⠀⠀ ⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⡄ ⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⡜⣿⣆ ⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣒⢶⣤⣤⣾⣿⣇⣬⠅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡸⣿ ⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⢛⡷⢸⢸⡀⠀⠯⡭⣍⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢻ ⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣺⣿⢷⡞⣿⠃⢸⠈⠀⣼⠀⠱⣿⡀⠉⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣾⠷⢋⣽⣡⡿⠘⢁⠀⢸⠀⢸⣿⡄⠀⣻⣷⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡥⠛⠁⢠⣾⣇⣿⠃⣠⠏⡀⠈⢰⡟⠀⢷⠀⣿⣿⡆⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼ ⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡵⠋⠀⠀⢰⣿⣿⣿⣿⣴⠃⠀⡇⢠⢻⡇⠀⠸⢸⣿⣿⣷⠈⠳⡝⣄⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿ ⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⡟⠡⠤⠖⠚⠿⣿⣿⣿⣿⡏⠀⢰⠇⢸⣾⡇⠀⢠⣾⣭⣿⣿⣧⠀⠹⣞⢧⡀⣠⣤⣾⣿⣿⣿⣿⣿ ⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠐⠣⠞⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⡇⠀⣾⢠⢇⣿⠀⢰⣿⡏⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⣶⣤⣂⡀⣀⣀⡀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣇⣼⠇⣾⣸⣿⢀⣅⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣨⣫⣽⣿⣾⣧⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⡿⠏⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠈⢙⣿⣿⣿⣿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿

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⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⡸⠀⠀⠀⣴⡴⢸⢻⡿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠱⡜⠀⡃⡜⠀⣼⠏⡶⡏⢸⣧⣿⣿⣿⣿⣿⣷⣿⢿⣿⣷⣹⣿⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠵⣿⢠⢷⠃⣞⢇⢶⢁⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⢸⢰⣾⣼⣇⣾⣧⣿⣿⣿⣿⣿⢟⣹⣡⣿⣿⣿⣣⡟⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⣾⡿⣿⣧⣼⣿⡿⠛⠹⣿⣟⣛⣻⣿⣿⠟⣻⠁⡇⠀⠀⡠⠖⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⣿⣿⣀⡇⠳⠛⠁⠀⠀⠀⠀⠈⠉⠉⠉⠀⣠⠇⣀⡤⠔⠋⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⠉⣿⣿⡻⡷⠤⣄⡀⠀⣀⣀⣀⡤⠄⢀⣼⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠳⢶⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣴⣿⣜⢷⣷⡀⣀⡭⣖⣤⣄⣀⡠⠔⠿⣿⣷⣬⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡤⠀⢬⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡁⣾⣵⡿⠿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⣿⡷⠦⠤⠤⢤⣤⡤⠒⠋⠁⠀⢀⣾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡴⠘⣿⡿⠋⠀⠀⠀⠀⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠀⠀⠀⠀⠀⠉⠳⢤⠄⠀⢩⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⢀⣾⡟⠀⠀⠀⠀⠀⠀⣀⠀⠑⢄⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣔⠛⣀⣠⣤⣄⠀ ⠀⠀⠀⠀⠀⠀⣼⢛⣵⠃⠁⢀⠀⡄⠀⣸⠋⠙⠢⣬⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣡⣿⠏⢸⣧ ⠀⠀⠀⠀⠀⡼⣡⠞⠈⢠⡀⢨⠀⡇⠀⣧⠀⠀⠀⠈⠃⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⠟⣶⣿⡿ ⣤⠄⠀⡀⡸⡿⠃⠀⢸⠈⡷⣼⣄⢸⠀⢹⠀⠀⢀⣠⠴⠒⠋⠉⠉⣻⠉⠉⠉⠓⠲⢤⣀⠀⠀⠀⠀⠀⣀⡠⠿⠛⠻⣷⣦⣿⡿⠁ ⠋⠀⠀⢰⡟⠳⣤⡀⠈⢦⠃⠘⠈⠓⠿⣺⠖⠚⠉⢀⣀⠤⠖⠛⠉⠹⠉⠉⠉⠉⠙⠒⢬⣑⢦⡀⠴⠊⠁⠀⠀⠀⠀⠈⢿⣿⠁⠀ ⡀⠀⠀⣸⠳⣀⣠⣿⠿⠋⠉⠉⠉⠙⠒⡻⢤⣒⠋⠁⠀⠀⠀⢐⠲⠤⣀⠀⠀⠀⠀⠀⠀⠈⠛⣷⡖⠢⣄⠀⠀⠀⠀⠀⢨⠀⠀⠀ ⠀⠀⣠⣿⠞⠉⠈⠁⠀⠀⠀⣀⡤⠖⠒⠋⠉⠉⠉⠑⠦⣄⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⣿⠀⢠⠂⠆⠰⢸⠀⠀⠀ ⠀⢠⡟⢀⡀⠀⣀⡤⢀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣖⣒⠂⠀⠀⠀⠀⠀⠀⠀⣠⠤⠊⠀⣿⡋⢠⠇⢰⠁⡆⢸⡴⠀⠀ ⢰⡞⠀⡞⣠⠞⣡⠴⠃⠀⠀⠀⠀⠀⣀⣴⠾⠗⠒⠒⠒⠦⢤⣸⠁⠙⢦⣀⠀⠀⠀⣴⠋⠁⠀⠀⣰⠋⣧⢎⣠⡧⡴⠃⠀⢸⡀⠀ ⢿⠀⢸⣷⣣⠞⠁⠀⠀⠀⢀⣠⡴⣾⣿⠁⢀⣀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠈⠀⢀⡰⠃⠀⠀⠀⡼⠃⢀⡟⠉⠀⢀⣃⣤⠾⢻⡇⠀ ⣿⠀⠸⣿⠃⠀⠀⣠⣴⣾⡿⠉⣰⣿⠿⣄⣾⣿⣦⠘⣧⣤⣄⠀⠙⢿⣦⡀⠀⠀⠹⣆⠀⢀⡾⠳⠒⣶⡗⠊⠉⠉⠁⠀⠀⠰⡇⠀ ⡁⠀⣼⠁⣀⣤⢾⡋⢀⡾⠁⢠⣿⠏⠀⠨⡻⣿⣎⠳⢿⣿⡻⣿⡄⠈⢻⡿⣄⠀⠀⠈⢦⡞⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⢿⠀⣿⡞⡋⢀⣿⠀⣾⠃⠀⣼⠏⠀⠀⣀⣬⠆⠈⠙⠛⠓⠛⠋⣿⣦⠀⢻⡽⣆⠀⠀⣦⡇⠀⠠⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠘⣼⡿⣦⡟⣼⡇⣸⣿⡆⢀⣿⠀⠐⠛⢋⣁⠀⠀⠀⠀⣒⣲⣤⣬⣿⡄⠀⢻⡜⣆⠀⣼⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀ ⠖⢻⣧⣻⣇⣿⡇⣿⣿⡇⠸⣿⢀⣠⣤⣴⠼⡄⠀⠀⣾⠛⠋⢀⡿⣿⣧⠀⠈⣷⣼⣾⡏⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠂⠛⠛⠛⠿⢿⣧⣿⣿⡇⢠⣿⠋⠀⠉⣀⣠⠃⠀⢀⣈⠙⠉⠁⠀⢻⣿⡇⠀⢸⣿⣿⢻⡘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⢿⣿⡇⠀⣿⠉⠛⠁⠀⠀⠀⠀⣀⣡⣄⠀⠀⠀⢸⣿⡇⠀⠘⣿⣿⣾⡏⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀ ⠀⠀⠀⠀⠀⡀⠀⣯⣿⡇⠀⢹⣦⠀⠀⠀⠀⢠⣾⢷⣶⣿⠀⠀⢀⣾⣿⠀⠀⢸⡇⠸⠈⠳⣿⣄⠀⠀⢀⣀⡀⠀⢀⣰⠏⠀⠀⠀ ⣧⣀⣀⣀⣀⣵⠴⢿⣿⣧⠀⢻⣿⣆⡀⠀⠀⢸⣷⡀⠀⠈⢀⡴⠋⢀⡇⠀⢀⣸⡇⠀⠀⠀⠈⠛⢷⣦⣤⣤⣩⣿⠟⠛⠂⠀⠀⠀ ⢆⠉⠻⡉⠉⣿⡄⠀⣿⣿⣇⠈⢷⡎⠙⠒⠦⠤⣝⣿⣤⣀⣾⣁⡴⡋⠀⣴⠟⣻⣝⡲⠤⣄⠀⠀⠀⠉⠻⣯⣉⠓⠲⢤⡀⠀⠀⠀ ⠈⠣⠀⠙⠀⢹⠻⡄⠹⣿⣽⣆⠘⣿⠳⣄⣀⣀⠀⠀⣤⣘⠻⢿⡿⢣⣞⣡⠖⠋⢀⠉⢗⠢⢕⣤⣀⣀⣀⡀⠙⣝⠒⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣇⠙⢆⠈⠛⠿⣷⠮⣷⣄⡀⠉⠉⠉⠉⠉⠛⢶⣖⢿⡼⠁⣠⠖⠁⡠⠈⠢⡀⠙⠖⠋⠉⠉⠉⠺⢦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⠘⠀⠈⢧⡀⠀⠈⠳⣄⡀⠀⠓⢤⡀⠀⠀⠀⠐⠪⣝⣷⡎⢀⡤⠊⠀⡤⠀⠀⠀⠀⢀⣀⣀⠀⠀⢈⢷⠄⠀⠀⠀

⡠⠔⠲⠈⠀⢰⡎⠀⢃⠃⠇⠀⣿⠀⢠⣀⣼⣣⡻⠊⠁⠀⠀⠀⢘⡀⠀⠀⠀⠀ ⡠⢠⡇⠠⢠⡟⠀⠀⠈⠀⠰⣸⢳⠀⠀⣇⡷⣷⠃⠀⠀⠀⡠⣺⠟⠈⠣⠄⠀⢀ ⠁⡼⠀⠀⡞⠀⠀⠀⠀⠀⠀⠙⠸⠀⠀⣻⠾⠃⠀⢀⠄⢊⠜⠁⠀⠀⠀⢀⠆⠈ ⠀⣷⡆⣴⠠⠤⠤⠤⢤⣄⣀⣀⠀⠡⡰⢣⠡⠐⠈⡠⠔⠁⢀⣀⠠⠔⠊⠁⠀⠸ ⢀⡀⣧⢸⠀⠀⠀⠀⠀⠙⠈⠁⠀⠀⠁⠁⠀⣴⡋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀ ⡇⢹⣷⣿⣶⣷⣤⣂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣳⡶⣤⣀⠀⠀⠀⠀⠀⢘ ⡇⠸⣈⡏⠙⣿⣿⢻⣷⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠈⠛⢦⡀⠀⠀⠸ ⣿⣄⢗⠘⢄⠱⠯⢟⡿⠁⠀⠀⠀⠀⠀⠀⠀⣠⠴⠥⡄⣀⡀⠀⠀⠀⠈⠢⠀⢀ ⣿⡏⠹⠶⠖⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠾⣿⣿⡿⣿⣷⣦⣤⡀⡀⡠⠚ ⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣷⡯⢹⠟⠛⣿⠦⠤⡔ ⢀⣄⡀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢉⡥⠐⠊⠀⢀⠞⢠ ⠜⡁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⣣⣴⣿ ⠀⡏⠀⡔⡉⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡍⣸⣿⠿ ⠀⠱⡴⠋⠀⠀⠍⠒⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⡴⠿⠿⢿ ⢀⠊⠀⢀⠤⠊⠀⡼⠿⣿⠁⢀⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡔⠁⠀⠀⠀⠀ ⠈⣄⠜⠁⢀⠠⣪⠊⠀⣜⣑⣤⣯⠃⠀⠀⠀⠀⡠⠔⡒⠖⠛⡍⠀⠀⠀⠀⠀⠀ ⠠⠁⢀⠔⠁⢀⣼⠀⢳⡧⡀⠈⡎⣂⣀⣠⣤⡞⣰⠟⢀⣀⣴⠀⠀⠀⠀⠀⠀⠀ ⠀⠒⢂⣩⡊⢽⠀⢑⠤⠇⠹⡭⡿⠽⢿⠿⣿⡄⣶⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀

⢀⡴⠻⣿⡻⡉⣴⣏⣀⣴⣿⠿⠿⢓⠟⣿⣿⢟⢿⣿⠁⡀⡄⢰⠀⢳⡆⢒⡀⠀ ⣿⠏⢑⣮⢕⣜⣏⡴⣫⡟⠀⢀⣰⡏⣼⠟⡼⠋⠘⠏⠰⡀⡇⣇⠃⠘⣷⠈⣄⢀ ⣟⣴⡿⢩⣿⣿⡿⢿⡟⢀⣴⣿⣟⠜⠿⣶⣄⡀⠀⢧⢰⠁⠀⡏⡄⢀⠃⣧⢨⢢ ⣿⣟⡴⠛⡿⠃⠀⣞⣴⣿⡿⣻⠋⠀⠀⠀⠉⠻⣶⣍⡈⡆⠀⣿⡀⢸⡀⢺⣮⡆ ⣿⡟⢁⣼⣅⣀⣼⡿⠻⠋⡴⠁⠀⠀⠀⠈⠉⠐⢸⠙⢣⣿⡄⢿⣧⠘⣷⣸⣿⣿ ⣿⣿⡉⠉⢻⡟⠿⣦⡀⠈⠀⠀⠀⠀⡐⣒⡀⠤⠄⠂⠈⡏⢻⣾⠻⡆⣿⣿⣿⣿ ⢸⡇⢁⠂⠒⠹⠿⠉⠀⠀⠀⠀⠀⠀⠛⠻⣟⠿⠿⣷⣶⣼⠀⠹⣶⣿⣿⠟⠛⢿ ⠋⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⠟⡛⠋⠀⢙⣷⣄⡿⢻⢿⠂⠀⢸ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠀⢉⠉⠊⡧⢃⠏⢅⡤⢸ ⠀⠰⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠠⡱⠉⠜⢊⣤⡿ ⢄⠀⢡⡀⠀⠀⠈⣿⣿⠓⡐⠂⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⢀⣔⡀⣤⣾⣿⢿⠂ ⠁⠓⢤⠈⢄⠀⠀⠏⢹⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠔⠉⠀⡸⠉⣿⠟⠁⢸ ⠀⠀⠀⠡⡰⠱⣬⠘⠢⡙⡦⠒⠹⢖⠋⠀⢀⠠⠔⠊⡀⠀⠀⠆⢤⠾⠁⠀⠀⣨ ⠀⠀⠀⠀⡇⠀⠸⣦⡀⡇⢤⢤⣤⣶⡂⠋⠀⠀⠀⠀⠐⠄⣠⡼⡬⢔⢄⢀⠔⠁ ⠀⠀⠀⠠⢃⠀⠀⣧⢳⠀⠘⡞⢺⢨⣍⣒⣀⠄⠀⢠⡶⠛⠓⠂⠂⠀⠀⡿⢇⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢩⠎⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⣴⡋⢠⠏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠾⠋⢁⠀⡀⠁⠑⢎⣀⣀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⡎⢀⠷⣄⠀⠀⠀⢀⡉⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣠⠏⠀⠀⢀⡜⠀⡸⠀⢹⣉⡵⢶⠦⣭⣢⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⡒⠊⢉⢩⠋⠀⠀⢠⠎⠀⡴⠓⢒⣿⣽⣒⠏⠀⠈⢹⡆⠀⠘⣆⠀⠀⠀⣀⢤⡴⠶⠏⠉⠀⣀⣀⣀⣀⣀⠈⠙⠓⠒⠤⣀⠀ ⠀⠀⠈⠻⣦⡀⠀⡎⠀⠀⢠⠇⣠⠻⡆⠀⠀⠛⠛⠉⠀⠀⠀⢸⠁⠀⠀⢸⡤⡖⠫⢊⣠⣴⣶⠾⠿⠛⠋⠉⠉⠉⠑⠛⠿⠷⣶⣄⣀⠃ ⠀⠀⠀⠀⠀⠙⠺⢇⠀⠀⡞⣾⣧⣿⡿⠆⢀⣠⡀⠀⢀⡀⠀⡸⡄⠀⢀⣸⠟⠛⠚⠯⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻ ⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⣿⠀⡇⠀⠀⢀⡛⠋⣀⣴⡿⢻⢀⠇⠘⣶⡉⢀⡀⠀⠀⠀⠹⣆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣜⠄⠹⢄⣀⣀⣀⣉⠉⠻⣄⣸⡼⠿⠉⠝⠊⠙⠢⡀⢠⡖⠒⢿⣆⡴⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠤⣀⠀⣠⠞⢉⡽⠉⠀⠀⠀⠀⠀⠀⠀⠘⡾⣹⣀⢤⡟⠀⡇⢻⣆⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢼⠊⡤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢷⠏⠉⣛⠀⡇⠈⠒⠛⢤⣀⠀⠈⠉⠙⠒⠤⣀⡴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠗⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣼⠇⠀⢹⡠⠷⣆⠀⠀⠀⣿⣄⡀⠠⠔⢀⡴⠏⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⣀⣀⠴⠚⠁⢸⡄⠀⠀⠈⣟⠪⢍⢣⠀⠀⠋⢹⠁⢀⡴⠋⠀⠀⠀ ⠉⠒⠤⣀⠀⠀⠀⠀⠀⢴⠋⠀⠀⠀⠀⠀⠀⠠⢡⠀⠀⠠⠒⠒⠉⠁⠀⠀⠀⠀⡏⡇⠀⠀⠀⠈⢆⠀⠳⣶⡒⡒⢂⡧⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠲⣀⠀⠀⢹⠁⠀⠀⠀⠀⠀⡰⠃⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢳⠀⠀⠀⢀⣼⣧⣀⡉⠏⣠⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠣⡀⠀⠀⠀⢸⠁⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣒⣇⣀⠴⣻⣿⣿⡇⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡘⠲⠤⢤⡇⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢄⡀⠀⠀⠈⠙⠿⡷⠛⢡⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣦⡀⠀⢣⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠘⢦⣿⡾⠉⠙⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠈⣢⡀⢳⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠿⣍⡀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢄⡤⠖⠋⠉⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡾⣻⠋⠀⠀⠉⠲⢤⡙⠀⠀⠀⠈⠳⣄⠀⠀ ⠀⠀⠀⠀⣠⠞⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠱⣄⣀⣀⣀⣀⣀⣤⢤⣴⠶⣺⡿⠟⢡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣅⠁⢀⠀⠀⠱⣄ ⠀⠀⢀⡼⠋⠀⠀⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡄⠉⠉⠉⢁⡰⣶⡿⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢔⠀⠀⠀⠛ ⠀⢠⠞⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣔⠀⠀ ⢰⠋⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣄⠀⢀⠟⣳⣀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀ ⡏⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⣿⢠⣯⠋⠁⠉⢛⠶⣔⢄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳ ⣟⣄⠠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⢿⢱⠀⠀⠀⠘⡄⠈⢫⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⡠ ⠈⢻⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠸⠀⠀⠀⠀⠸⡄⠀⢷⠀⠀⠀⠀⠀⠀⠀⢠⠤⣀⠀⠙⠄⠀⠀⠀⢘⠁ ⣄⠀⠙⢦⡀⠀⠀⣀⡤⠔⠚⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⡇⠀⠀⠀⠀⢳⠀⠸⡀⠀⠀⠀⠀⠀⡤⢼⠀⠀⠑⢄⡀⣢⠀⠀⠀⠃ ⠀⠉⠒⢤⣽⠢⡴⠁⠀⠀⣠⠎⠀⢀⠤⢤⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠈⡆⠀⡇⠀⠀⢠⡀⢠⠈⠈⢧⡀⠀⠀⠉⠁⠀⢀⣴⠶ ⠀⠀⠀⠀⠈⠙⠻⣄⣀⡜⠁⡠⠞⠁⠀⣸⣠⡄⠀⠀⠀⠀⠈⡄⢸⣀⡤⠖⠒⠒⠶⢤⣱⣀⡀⢸⠈⠻⡀⠂⠀⠙⠃⠀⢀⡠⠖⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠬⣀⠀⢀⡴⠁⠀⢱⢀⡀⠀⠀⠀⣷⠊⠁⠀⠀⠀⠀⠀⠀⠙⡄⠉⠉⠳⠤⢙⣂⣀⣠⠴⠊⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢍⡀⠀⠀⡸⠉⣇⣀⠤⠴⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠒⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢞⣠⠖⠀⣀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠑⠛⠀⠀⢀⡞⠁⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀