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⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠿⠟⠿⠻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⠻⠛⠛⠛⠟⠻⠛⡻⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠛⠉⢀⠠⠖⠚⠒⠒⠀⠙⣿⣿⡿⢁⣾⣿⣫⡴⠞⠛⠛⠛⠓⠀⠀⡀⠀⠀⠙⠛⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀⣐⣤⣴⡤⠤⠤⠤⢤⡐⠬⣿⢷⠀⠐⢹⡿⠛⠛⣛⣛⣓⣛⡓⣶⣄⠀⣦⠈⠂⠎⢻⣧⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⠿⠵⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣳⡵⠀⠂⢴⣿⣿⣷⡿⠿⣿⣿⠿⣿⣿⣿⣿⣿⡉⣄⣀⣼⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡿⠻⢻⣷⣾⣿⣿⣿⡟⠉⣰⣿⣷⡌⠻⣿⣿⣿⣿⠀⠀⠀⣿⣿⠏⠀⣼⣿⣿⣷⡈⢹⣿⣿⣿⣿⣿⣿⡟⠿⢿⣷⣄⠀⠀ ⡇⢀⣶⠋⣥⢶⣿⣈⣽⣿⣿⣿⣿⣇⠀⢿⣿⣿⡟⢀⣿⣿⣿⣿⠀⠀⠸⣿⣿⣦⠀⠻⣿⣿⣿⢃⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⡙⣷⡀ ⣷⣾⠁⡼⢡⣿⠛⣡⣭⣙⠿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄⠛⣷⠀⢳⢘⣷ ⣿⣿⠀⠇⢸⣏⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢿⣿⣿⡿⠟⠛⠛⠀⠀⠈⠛⠛⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡀⢸⢰⣿ ⣿⢿⣧⠘⣾⣿⡄⢻⣿⣿⣿⢻⣿⣿⣿⣧⣄⡀⠈⠿⣷⣾⣷⣶⣤⣭⣂⣼⠿⣷⣬⡟⣁⣠⣴⣿⣿⣿⡟⣿⣿⣿⣿⡿⠉⣰⠂⣾⣾⡿ ⡇⠀⠿⣷⡈⠻⣷⡈⣿⣿⣿⣦⠘⡷⠈⢻⠛⠿⣿⣶⣦⣬⣄⣈⣉⣠⣿⣦⣤⣴⣿⣿⣿⠿⠟⡟⠻⠙⢠⣼⣿⣿⣿⠁⣼⠃⣼⣿⠟⠁ ⠃⠀⠀⠙⢿⣦⠹⠏⢻⣿⣿⣿⣧⣿⣧⣰⠀⡀⠛⠃⠊⠹⡟⠋⠛⣿⠿⠛⠛⡏⠉⠋⡇⠀⣀⠇⢰⣇⣶⣿⣿⣿⡿⢠⠎⣸⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⣿⣆⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣤⣸⠀⡇⢠⠀⣼⣠⣀⠀⡇⠀⡀⣄⣰⣿⣧⣾⣿⣿⣿⣿⣿⠃⡞⣰⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣟⣻⣿⣿⣿⡟⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⢹⣿⣿⣿⣿⣷⡟⠁⠀⠀⠀⠀ ⠀⠀⠐⠀⠀⠀⠈⠹⢿⡙⠻⣿⡇⢀⠇⣥⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠀⠀⣀⣸⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣆⠙⣿⣿⣆⣉⠁⠀⢋⠋⠀⡋⢹⡟⠉⢻⠋⠉⡏⠏⠀⢨⡀⠀⠀⡐⣾⣿⣿⣿⣿⢿⡧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⢸⡇⠙⠳⣌⠻⣿⣿⣆⠐⣼⣆⢠⠀⢻⣄⠀⢸⡂⠀⠂⡄⠀⢸⣷⣼⣶⣿⣿⠟⣻⣯⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡦⠀⠀⠀⢸⣧⠀⠀⠙⣷⣌⠛⢿⣿⣿⣿⣄⣠⣿⣄⡂⣸⣇⣀⢰⣿⣧⣾⣿⣿⠿⢋⣱⣾⣿⣇⠀⢸⡇⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⣸⣿⠁⠀⠀⠘⢨⣿⠀⣀⠻⣿⣿⣿⣦⣌⣙⠛⠿⠿⢿⣿⢿⣿⣿⡿⠿⠿⠿⠟⣿⣷⣶⣿⣿⣿⠋⠅⠀⠀⣇⠈⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⠇⠀⠀⠀⣠⡟⣣⣠⣍⣳⣾⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣠⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣂⠀⠀⢙⣧⡐ ⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠿⠟⠿⠻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⠻⠛⠛⠛⠟⠻⠛⡻⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠛⠉⢀⠠⠖⠚⠒⠒⠀⠙⣿⣿⡿⢁⣾⣿⣫⡴⠞⠛⠛⠛⠓⠀⠀⡀⠀⠀⠙⠛⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀⣐⣤⣴⡤⠤⠤⠤⢤⡐⠬⣿⢷⠀⠐⢹⡿⠛⠛⣛⣛⣓⣛⡓⣶⣄⠀⣦⠈⠂⠎⢻⣧⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⠿⠵⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣳⡵⠀⠂⢴⣿⣿⣷⡿⠿⣿⣿⠿⣿⣿⣿⣿⣿⡉⣄⣀⣼⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡿⠻⢻⣷⣾⣿⣿⣿⡟⠉⣰⣿⣷⡌⠻⣿⣿⣿⣿⠀⠀⠀⣿⣿⠏⠀⣼⣿⣿⣷⡈⢹⣿⣿⣿⣿⣿⣿⡟⠿⢿⣷⣄⠀⠀ ⡇⢀⣶⠋⣥⢶⣿⣈⣽⣿⣿⣿⣿⣇⠀⢿⣿⣿⡟⢀⣿⣿⣿⣿⠀⠀⠸⣿⣿⣦⠀⠻⣿⣿⣿⢃⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⡙⣷⡀ ⣷⣾⠁⡼⢡⣿⠛⣡⣭⣙⠿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄⠛⣷⠀⢳⢘⣷ ⣿⣿⠀⠇⢸⣏⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢿⣿⣿⡿⠟⠛⠛⠀⠀⠈⠛⠛⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡀⢸⢰⣿ ⣿⢿⣧⠘⣾⣿⡄⢻⣿⣿⣿⢻⣿⣿⣿⣧⣄⡀⠈⠿⣷⣾⣷⣶⣤⣭⣂⣼⠿⣷⣬⡟⣁⣠⣴⣿⣿⣿⡟⣿⣿⣿⣿⡿⠉⣰⠂⣾⣾⡿ ⡇⠀⠿⣷⡈⠻⣷⡈⣿⣿⣿⣦⠘⡷⠈⢻⠛⠿⣿⣶⣦⣬⣄⣈⣉⣠⣿⣦⣤⣴⣿⣿⣿⠿⠟⡟⠻⠙⢠⣼⣿⣿⣿⠁⣼⠃⣼⣿⠟⠁ ⠃⠀⠀⠙⢿⣦⠹⠏⢻⣿⣿⣿⣧⣿⣧⣰⠀⡀⠛⠃⠊⠹⡟⠋⠛⣿⠿⠛⠛⡏⠉⠋⡇⠀⣀⠇⢰⣇⣶⣿⣿⣿⡿⢠⠎⣸⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⣿⣆⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣤⣸⠀⡇⢠⠀⣼⣠⣀⠀⡇⠀⡀⣄⣰⣿⣧⣾⣿⣿⣿⣿⣿⠃⡞⣰⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣟⣻⣿⣿⣿⡟⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⢹⣿⣿⣿⣿⣷⡟⠁⠀⠀⠀⠀ ⠀⠀⠐⠀⠀⠀⠈⠹⢿⡙⠻⣿⡇⢀⠇⣥⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠀⠀⣀⣸⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣆⠙⣿⣿⣆⣉⠁⠀⢋⠋⠀⡋⢹⡟⠉⢻⠋⠉⡏⠏⠀⢨⡀⠀⠀⡐⣾⣿⣿⣿⣿⢿⡧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⢸⡇⠙⠳⣌⠻⣿⣿⣆⠐⣼⣆⢠⠀⢻⣄⠀⢸⡂⠀⠂⡄⠀⢸⣷⣼⣶⣿⣿⠟⣻⣯⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡦⠀⠀⠀⢸⣧⠀⠀⠙⣷⣌⠛⢿⣿⣿⣿⣄⣠⣿⣄⡂⣸⣇⣀⢰⣿⣧⣾⣿⣿⠿⢋⣱⣾⣿⣇⠀⢸⡇⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⣸⣿⠁⠀⠀⠘⢨⣿⠀⣀⠻⣿⣿⣿⣦⣌⣙⠛⠿⠿⢿⣿⢿⣿⣿⡿⠿⠿⠿⠟⣿⣷⣶⣿⣿⣿⠋⠅⠀⠀⣇⠈⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⠇⠀⠀⠀⣠⡟⣣⣠⣍⣳⣾⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣠⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣂⠀⠀⢙⣧⡐⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠿⠟⠿⠻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⠻⠛⠛⠛⠟⠻⠛⡻⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠛⠉⢀⠠⠖⠚⠒⠒⠀⠙⣿⣿⡿⢁⣾⣿⣫⡴⠞⠛⠛⠛⠓⠀⠀⡀⠀⠀⠙⠛⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀⣐⣤⣴⡤⠤⠤⠤⢤⡐⠬⣿⢷⠀⠐⢹⡿⠛⠛⣛⣛⣓⣛⡓⣶⣄⠀⣦⠈⠂⠎⢻⣧⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⠿⠵⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣳⡵⠀⠂⢴⣿⣿⣷⡿⠿⣿⣿⠿⣿⣿⣿⣿⣿⡉⣄⣀⣼⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡿⠻⢻⣷⣾⣿⣿⣿⡟⠉⣰⣿⣷⡌⠻⣿⣿⣿⣿⠀⠀⠀⣿⣿⠏⠀⣼⣿⣿⣷⡈⢹⣿⣿⣿⣿⣿⣿⡟⠿⢿⣷⣄⠀⠀ ⡇⢀⣶⠋⣥⢶⣿⣈⣽⣿⣿⣿⣿⣇⠀⢿⣿⣿⡟⢀⣿⣿⣿⣿⠀⠀⠸⣿⣿⣦⠀⠻⣿⣿⣿⢃⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⡙⣷⡀ ⣷⣾⠁⡼⢡⣿⠛⣡⣭⣙⠿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄⠛⣷⠀⢳⢘⣷ ⣿⣿⠀⠇⢸⣏⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢿⣿⣿⡿⠟⠛⠛⠀⠀⠈⠛⠛⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡀⢸⢰⣿ ⣿⢿⣧⠘⣾⣿⡄⢻⣿⣿⣿⢻⣿⣿⣿⣧⣄⡀⠈⠿⣷⣾⣷⣶⣤⣭⣂⣼⠿⣷⣬⡟⣁⣠⣴⣿⣿⣿⡟⣿⣿⣿⣿⡿⠉⣰⠂⣾⣾⡿ ⡇⠀⠿⣷⡈⠻⣷⡈⣿⣿⣿⣦⠘⡷⠈⢻⠛⠿⣿⣶⣦⣬⣄⣈⣉⣠⣿⣦⣤⣴⣿⣿⣿⠿⠟⡟⠻⠙⢠⣼⣿⣿⣿⠁⣼⠃⣼⣿⠟⠁ ⠃⠀⠀⠙⢿⣦⠹⠏⢻⣿⣿⣿⣧⣿⣧⣰⠀⡀⠛⠃⠊⠹⡟⠋⠛⣿⠿⠛⠛⡏⠉⠋⡇⠀⣀⠇⢰⣇⣶⣿⣿⣿⡿⢠⠎⣸⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⣿⣆⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣤⣸⠀⡇⢠⠀⣼⣠⣀⠀⡇⠀⡀⣄⣰⣿⣧⣾⣿⣿⣿⣿⣿⠃⡞⣰⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣟⣻⣿⣿⣿⡟⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⢹⣿⣿⣿⣿⣷⡟⠁⠀⠀⠀⠀ ⠀⠀⠐⠀⠀⠀⠈⠹⢿⡙⠻⣿⡇⢀⠇⣥⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠀⠀⣀⣸⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣆⠙⣿⣿⣆⣉⠁⠀⢋⠋⠀⡋⢹⡟⠉⢻⠋⠉⡏⠏⠀⢨⡀⠀⠀⡐⣾⣿⣿⣿⣿⢿⡧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⢸⡇⠙⠳⣌⠻⣿⣿⣆⠐⣼⣆⢠⠀⢻⣄⠀⢸⡂⠀⠂⡄⠀⢸⣷⣼⣶⣿⣿⠟⣻⣯⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡦⠀⠀⠀⢸⣧⠀⠀⠙⣷⣌⠛⢿⣿⣿⣿⣄⣠⣿⣄⡂⣸⣇⣀⢰⣿⣧⣾⣿⣿⠿⢋⣱⣾⣿⣇⠀⢸⡇⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⣸⣿⠁⠀⠀⠘⢨⣿⠀⣀⠻⣿⣿⣿⣦⣌⣙⠛⠿⠿⢿⣿⢿⣿⣿⡿⠿⠿⠿⠟⣿⣷⣶⣿⣿⣿⠋⠅⠀⠀⣇⠈⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⠇⠀⠀⠀⣠⡟⣣⣠⣍⣳⣾⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣠⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣂⠀⠀⢙⣧⡐ ⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠿⠟⠿⠻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⠻⠛⠛⠛⠟⠻⠛⡻⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠛⠉⢀⠠⠖⠚⠒⠒⠀⠙⣿⣿⡿⢁⣾⣿⣫⡴⠞⠛⠛⠛⠓⠀⠀⡀⠀⠀⠙⠛⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀⣐⣤⣴⡤⠤⠤⠤⢤⡐⠬⣿⢷⠀⠐⢹⡿⠛⠛⣛⣛⣓⣛⡓⣶⣄⠀⣦⠈⠂⠎⢻⣧⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⠿⠵⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣳⡵⠀⠂⢴⣿⣿⣷⡿⠿⣿⣿⠿⣿⣿⣿⣿⣿⡉⣄⣀⣼⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡿⠻⢻⣷⣾⣿⣿⣿⡟⠉⣰⣿⣷⡌⠻⣿⣿⣿⣿⠀⠀⠀⣿⣿⠏⠀⣼⣿⣿⣷⡈⢹⣿⣿⣿⣿⣿⣿⡟⠿⢿⣷⣄⠀⠀ ⡇⢀⣶⠋⣥⢶⣿⣈⣽⣿⣿⣿⣿⣇⠀⢿⣿⣿⡟⢀⣿⣿⣿⣿⠀⠀⠸⣿⣿⣦⠀⠻⣿⣿⣿⢃⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⡙⣷⡀ ⣷⣾⠁⡼⢡⣿⠛⣡⣭⣙⠿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄⠛⣷⠀⢳⢘⣷ ⣿⣿⠀⠇⢸⣏⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢿⣿⣿⡿⠟⠛⠛⠀⠀⠈⠛⠛⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡀⢸⢰⣿ ⣿⢿⣧⠘⣾⣿⡄⢻⣿⣿⣿⢻⣿⣿⣿⣧⣄⡀⠈⠿⣷⣾⣷⣶⣤⣭⣂⣼⠿⣷⣬⡟⣁⣠⣴⣿⣿⣿⡟⣿⣿⣿⣿⡿⠉⣰⠂⣾⣾⡿ ⡇⠀⠿⣷⡈⠻⣷⡈⣿⣿⣿⣦⠘⡷⠈⢻⠛⠿⣿⣶⣦⣬⣄⣈⣉⣠⣿⣦⣤⣴⣿⣿⣿⠿⠟⡟⠻⠙⢠⣼⣿⣿⣿⠁⣼⠃⣼⣿⠟⠁ ⠃⠀⠀⠙⢿⣦⠹⠏⢻⣿⣿⣿⣧⣿⣧⣰⠀⡀⠛⠃⠊⠹⡟⠋⠛⣿⠿⠛⠛⡏⠉⠋⡇⠀⣀⠇⢰⣇⣶⣿⣿⣿⡿⢠⠎⣸⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⣿⣆⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣤⣸⠀⡇⢠⠀⣼⣠⣀⠀⡇⠀⡀⣄⣰⣿⣧⣾⣿⣿⣿⣿⣿⠃⡞⣰⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣟⣻⣿⣿⣿⡟⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⢹⣿⣿⣿⣿⣷⡟⠁⠀⠀⠀⠀ ⠀⠀⠐⠀⠀⠀⠈⠹⢿⡙⠻⣿⡇⢀⠇⣥⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠀⠀⣀⣸⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣆⠙⣿⣿⣆⣉⠁⠀⢋⠋⠀⡋⢹⡟⠉⢻⠋⠉⡏⠏⠀⢨⡀⠀⠀⡐⣾⣿⣿⣿⣿⢿⡧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⢸⡇⠙⠳⣌⠻⣿⣿⣆⠐⣼⣆⢠⠀⢻⣄⠀⢸⡂⠀⠂⡄⠀⢸⣷⣼⣶⣿⣿⠟⣻⣯⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡦⠀⠀⠀⢸⣧⠀⠀⠙⣷⣌⠛⢿⣿⣿⣿⣄⣠⣿⣄⡂⣸⣇⣀⢰⣿⣧⣾⣿⣿⠿⢋⣱⣾⣿⣇⠀⢸⡇⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⣸⣿⠁⠀⠀⠘⢨⣿⠀⣀⠻⣿⣿⣿⣦⣌⣙⠛⠿⠿⢿⣿⢿⣿⣿⡿⠿⠿⠿⠟⣿⣷⣶⣿⣿⣿⠋⠅⠀⠀⣇⠈⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⠇⠀⠀⠀⣠⡟⣣⣠⣍⣳⣾⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣠⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣂⠀⠀⢙⣧⡐⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠿⠟⠿⠻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⠻⠛⠛⠛⠟⠻⠛⡻⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠛⠉⢀⠠⠖⠚⠒⠒⠀⠙⣿⣿⡿⢁⣾⣿⣫⡴⠞⠛⠛⠛⠓⠀⠀⡀⠀⠀⠙⠛⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀⣐⣤⣴⡤⠤⠤⠤⢤⡐⠬⣿⢷⠀⠐⢹⡿⠛⠛⣛⣛⣓⣛⡓⣶⣄⠀⣦⠈⠂⠎⢻⣧⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⠿⠵⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣳⡵⠀⠂⢴⣿⣿⣷⡿⠿⣿⣿⠿⣿⣿⣿⣿⣿⡉⣄⣀⣼⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡿⠻⢻⣷⣾⣿⣿⣿⡟⠉⣰⣿⣷⡌⠻⣿⣿⣿⣿⠀⠀⠀⣿⣿⠏⠀⣼⣿⣿⣷⡈⢹⣿⣿⣿⣿⣿⣿⡟⠿⢿⣷⣄⠀⠀ ⡇⢀⣶⠋⣥⢶⣿⣈⣽⣿⣿⣿⣿⣇⠀⢿⣿⣿⡟⢀⣿⣿⣿⣿⠀⠀⠸⣿⣿⣦⠀⠻⣿⣿⣿⢃⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⡙⣷⡀ ⣷⣾⠁⡼⢡⣿⠛⣡⣭⣙⠿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄⠛⣷⠀⢳⢘⣷ ⣿⣿⠀⠇⢸⣏⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢿⣿⣿⡿⠟⠛⠛⠀⠀⠈⠛⠛⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡀⢸⢰⣿ ⣿⢿⣧⠘⣾⣿⡄⢻⣿⣿⣿⢻⣿⣿⣿⣧⣄⡀⠈⠿⣷⣾⣷⣶⣤⣭⣂⣼⠿⣷⣬⡟⣁⣠⣴⣿⣿⣿⡟⣿⣿⣿⣿⡿⠉⣰⠂⣾⣾⡿ ⡇⠀⠿⣷⡈⠻⣷⡈⣿⣿⣿⣦⠘⡷⠈⢻⠛⠿⣿⣶⣦⣬⣄⣈⣉⣠⣿⣦⣤⣴⣿⣿⣿⠿⠟⡟⠻⠙⢠⣼⣿⣿⣿⠁⣼⠃⣼⣿⠟⠁ ⠃⠀⠀⠙⢿⣦⠹⠏⢻⣿⣿⣿⣧⣿⣧⣰⠀⡀⠛⠃⠊⠹⡟⠋⠛⣿⠿⠛⠛⡏⠉⠋⡇⠀⣀⠇⢰⣇⣶⣿⣿⣿⡿⢠⠎⣸⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⣿⣆⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣤⣸⠀⡇⢠⠀⣼⣠⣀⠀⡇⠀⡀⣄⣰⣿⣧⣾⣿⣿⣿⣿⣿⠃⡞⣰⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣟⣻⣿⣿⣿⡟⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⢹⣿⣿⣿⣿⣷⡟⠁⠀⠀⠀⠀ ⠀⠀⠐⠀⠀⠀⠈⠹⢿⡙⠻⣿⡇⢀⠇⣥⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠀⠀⣀⣸⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣆⠙⣿⣿⣆⣉⠁⠀⢋⠋⠀⡋⢹⡟⠉⢻⠋⠉⡏⠏⠀⢨⡀⠀⠀⡐⣾⣿⣿⣿⣿⢿⡧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⢸⡇⠙⠳⣌⠻⣿⣿⣆⠐⣼⣆⢠⠀⢻⣄⠀⢸⡂⠀⠂⡄⠀⢸⣷⣼⣶⣿⣿⠟⣻⣯⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡦⠀⠀⠀⢸⣧⠀⠀⠙⣷⣌⠛⢿⣿⣿⣿⣄⣠⣿⣄⡂⣸⣇⣀⢰⣿⣧⣾⣿⣿⠿⢋⣱⣾⣿⣇⠀⢸⡇⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⣸⣿⠁⠀⠀⠘⢨⣿⠀⣀⠻⣿⣿⣿⣦⣌⣙⠛⠿⠿⢿⣿⢿⣿⣿⡿⠿⠿⠿⠟⣿⣷⣶⣿⣿⣿⠋⠅⠀⠀⣇⠈⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⠇⠀⠀⠀⣠⡟⣣⣠⣍⣳⣾⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣠⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣂⠀⠀⢙⣧⡐ ⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠿⠟⠿⠻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⠻⠛⠛⠛⠟⠻⠛⡻⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠛⠉⢀⠠⠖⠚⠒⠒⠀⠙⣿⣿⡿⢁⣾⣿⣫⡴⠞⠛⠛⠛⠓⠀⠀⡀⠀⠀⠙⠛⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀⣐⣤⣴⡤⠤⠤⠤⢤⡐⠬⣿⢷⠀⠐⢹⡿⠛⠛⣛⣛⣓⣛⡓⣶⣄⠀⣦⠈⠂⠎⢻⣧⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⠿⠵⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣳⡵⠀⠂⢴⣿⣿⣷⡿⠿⣿⣿⠿⣿⣿⣿⣿⣿⡉⣄⣀⣼⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡿⠻⢻⣷⣾⣿⣿⣿⡟⠉⣰⣿⣷⡌⠻⣿⣿⣿⣿⠀⠀⠀⣿⣿⠏⠀⣼⣿⣿⣷⡈⢹⣿⣿⣿⣿⣿⣿⡟⠿⢿⣷⣄⠀⠀ ⡇⢀⣶⠋⣥⢶⣿⣈⣽⣿⣿⣿⣿⣇⠀⢿⣿⣿⡟⢀⣿⣿⣿⣿⠀⠀⠸⣿⣿⣦⠀⠻⣿⣿⣿⢃⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⡙⣷⡀ ⣷⣾⠁⡼⢡⣿⠛⣡⣭⣙⠿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄⠛⣷⠀⢳⢘⣷ ⣿⣿⠀⠇⢸⣏⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢿⣿⣿⡿⠟⠛⠛⠀⠀⠈⠛⠛⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡀⢸⢰⣿ ⣿⢿⣧⠘⣾⣿⡄⢻⣿⣿⣿⢻⣿⣿⣿⣧⣄⡀⠈⠿⣷⣾⣷⣶⣤⣭⣂⣼⠿⣷⣬⡟⣁⣠⣴⣿⣿⣿⡟⣿⣿⣿⣿⡿⠉⣰⠂⣾⣾⡿ ⡇⠀⠿⣷⡈⠻⣷⡈⣿⣿⣿⣦⠘⡷⠈⢻⠛⠿⣿⣶⣦⣬⣄⣈⣉⣠⣿⣦⣤⣴⣿⣿⣿⠿⠟⡟⠻⠙⢠⣼⣿⣿⣿⠁⣼⠃⣼⣿⠟⠁ ⠃⠀⠀⠙⢿⣦⠹⠏⢻⣿⣿⣿⣧⣿⣧⣰⠀⡀⠛⠃⠊⠹⡟⠋⠛⣿⠿⠛⠛⡏⠉⠋⡇⠀⣀⠇⢰⣇⣶⣿⣿⣿⡿⢠⠎⣸⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⣿⣆⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣤⣸⠀⡇⢠⠀⣼⣠⣀⠀⡇⠀⡀⣄⣰⣿⣧⣾⣿⣿⣿⣿⣿⠃⡞⣰⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣟⣻⣿⣿⣿⡟⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⢹⣿⣿⣿⣿⣷⡟⠁⠀⠀⠀⠀ ⠀⠀⠐⠀⠀⠀⠈⠹⢿⡙⠻⣿⡇⢀⠇⣥⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠀⠀⣀⣸⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣆⠙⣿⣿⣆⣉⠁⠀⢋⠋⠀⡋⢹⡟⠉⢻⠋⠉⡏⠏⠀⢨⡀⠀⠀⡐⣾⣿⣿⣿⣿⢿⡧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⢸⡇⠙⠳⣌⠻⣿⣿⣆⠐⣼⣆⢠⠀⢻⣄⠀⢸⡂⠀⠂⡄⠀⢸⣷⣼⣶⣿⣿⠟⣻⣯⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡦⠀⠀⠀⢸⣧⠀⠀⠙⣷⣌⠛⢿⣿⣿⣿⣄⣠⣿⣄⡂⣸⣇⣀⢰⣿⣧⣾⣿⣿⠿⢋⣱⣾⣿⣇⠀⢸⡇⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⣸⣿⠁⠀⠀⠘⢨⣿⠀⣀⠻⣿⣿⣿⣦⣌⣙⠛⠿⠿⢿⣿⢿⣿⣿⡿⠿⠿⠿⠟⣿⣷⣶⣿⣿⣿⠋⠅⠀⠀⣇⠈⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⠇⠀⠀⠀⣠⡟⣣⣠⣍⣳⣾⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣠⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣂⠀⠀⢙⣧⡐⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠿⠟⠿⠻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⠻⠛⠛⠛⠟⠻⠛⡻⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠛⠉⢀⠠⠖⠚⠒⠒⠀⠙⣿⣿⡿⢁⣾⣿⣫⡴⠞⠛⠛⠛⠓⠀⠀⡀⠀⠀⠙⠛⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀⣐⣤⣴⡤⠤⠤⠤⢤⡐⠬⣿⢷⠀⠐⢹⡿⠛⠛⣛⣛⣓⣛⡓⣶⣄⠀⣦⠈⠂⠎⢻⣧⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⠿⠵⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣳⡵⠀⠂⢴⣿⣿⣷⡿⠿⣿⣿⠿⣿⣿⣿⣿⣿⡉⣄⣀⣼⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡿⠻⢻⣷⣾⣿⣿⣿⡟⠉⣰⣿⣷⡌⠻⣿⣿⣿⣿⠀⠀⠀⣿⣿⠏⠀⣼⣿⣿⣷⡈⢹⣿⣿⣿⣿⣿⣿⡟⠿⢿⣷⣄⠀⠀ ⡇⢀⣶⠋⣥⢶⣿⣈⣽⣿⣿⣿⣿⣇⠀⢿⣿⣿⡟⢀⣿⣿⣿⣿⠀⠀⠸⣿⣿⣦⠀⠻⣿⣿⣿⢃⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⡙⣷⡀ ⣷⣾⠁⡼⢡⣿⠛⣡⣭⣙⠿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄⠛⣷⠀⢳⢘⣷ ⣿⣿⠀⠇⢸⣏⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢿⣿⣿⡿⠟⠛⠛⠀⠀⠈⠛⠛⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡀⢸⢰⣿ ⣿⢿⣧⠘⣾⣿⡄⢻⣿⣿⣿⢻⣿⣿⣿⣧⣄⡀⠈⠿⣷⣾⣷⣶⣤⣭⣂⣼⠿⣷⣬⡟⣁⣠⣴⣿⣿⣿⡟⣿⣿⣿⣿⡿⠉⣰⠂⣾⣾⡿ ⡇⠀⠿⣷⡈⠻⣷⡈⣿⣿⣿⣦⠘⡷⠈⢻⠛⠿⣿⣶⣦⣬⣄⣈⣉⣠⣿⣦⣤⣴⣿⣿⣿⠿⠟⡟⠻⠙⢠⣼⣿⣿⣿⠁⣼⠃⣼⣿⠟⠁ ⠃⠀⠀⠙⢿⣦⠹⠏⢻⣿⣿⣿⣧⣿⣧⣰⠀⡀⠛⠃⠊⠹⡟⠋⠛⣿⠿⠛⠛⡏⠉⠋⡇⠀⣀⠇⢰⣇⣶⣿⣿⣿⡿⢠⠎⣸⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⣿⣆⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣤⣸⠀⡇⢠⠀⣼⣠⣀⠀⡇⠀⡀⣄⣰⣿⣧⣾⣿⣿⣿⣿⣿⠃⡞⣰⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣟⣻⣿⣿⣿⡟⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⢹⣿⣿⣿⣿⣷⡟⠁⠀⠀⠀⠀ ⠀⠀⠐⠀⠀⠀⠈⠹⢿⡙⠻⣿⡇⢀⠇⣥⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠀⠀⣀⣸⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣆⠙⣿⣿⣆⣉⠁⠀⢋⠋⠀⡋⢹⡟⠉⢻⠋⠉⡏⠏⠀⢨⡀⠀⠀⡐⣾⣿⣿⣿⣿⢿⡧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⢸⡇⠙⠳⣌⠻⣿⣿⣆⠐⣼⣆⢠⠀⢻⣄⠀⢸⡂⠀⠂⡄⠀⢸⣷⣼⣶⣿⣿⠟⣻⣯⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡦⠀⠀⠀⢸⣧⠀⠀⠙⣷⣌⠛⢿⣿⣿⣿⣄⣠⣿⣄⡂⣸⣇⣀⢰⣿⣧⣾⣿⣿⠿⢋⣱⣾⣿⣇⠀⢸⡇⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⣸⣿⠁⠀⠀⠘⢨⣿⠀⣀⠻⣿⣿⣿⣦⣌⣙⠛⠿⠿⢿⣿⢿⣿⣿⡿⠿⠿⠿⠟⣿⣷⣶⣿⣿⣿⠋⠅⠀⠀⣇⠈⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⠇⠀⠀⠀⣠⡟⣣⣠⣍⣳⣾⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣠⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣂⠀⠀⢙⣧⡐ ⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠿⠟⠿⠻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⠻⠛⠛⠛⠟⠻⠛⡻⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠛⠉⢀⠠⠖⠚⠒⠒⠀⠙⣿⣿⡿⢁⣾⣿⣫⡴⠞⠛⠛⠛⠓⠀⠀⡀⠀⠀⠙⠛⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀⣐⣤⣴⡤⠤⠤⠤⢤⡐⠬⣿⢷⠀⠐⢹⡿⠛⠛⣛⣛⣓⣛⡓⣶⣄⠀⣦⠈⠂⠎⢻⣧⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⠿⠵⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣳⡵⠀⠂⢴⣿⣿⣷⡿⠿⣿⣿⠿⣿⣿⣿⣿⣿⡉⣄⣀⣼⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡿⠻⢻⣷⣾⣿⣿⣿⡟⠉⣰⣿⣷⡌⠻⣿⣿⣿⣿⠀⠀⠀⣿⣿⠏⠀⣼⣿⣿⣷⡈⢹⣿⣿⣿⣿⣿⣿⡟⠿⢿⣷⣄⠀⠀ ⡇⢀⣶⠋⣥⢶⣿⣈⣽⣿⣿⣿⣿⣇⠀⢿⣿⣿⡟⢀⣿⣿⣿⣿⠀⠀⠸⣿⣿⣦⠀⠻⣿⣿⣿⢃⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⡙⣷⡀ ⣷⣾⠁⡼⢡⣿⠛⣡⣭⣙⠿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄⠛⣷⠀⢳⢘⣷ ⣿⣿⠀⠇⢸⣏⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢿⣿⣿⡿⠟⠛⠛⠀⠀⠈⠛⠛⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡀⢸⢰⣿ ⣿⢿⣧⠘⣾⣿⡄⢻⣿⣿⣿⢻⣿⣿⣿⣧⣄⡀⠈⠿⣷⣾⣷⣶⣤⣭⣂⣼⠿⣷⣬⡟⣁⣠⣴⣿⣿⣿⡟⣿⣿⣿⣿⡿⠉⣰⠂⣾⣾⡿ ⡇⠀⠿⣷⡈⠻⣷⡈⣿⣿⣿⣦⠘⡷⠈⢻⠛⠿⣿⣶⣦⣬⣄⣈⣉⣠⣿⣦⣤⣴⣿⣿⣿⠿⠟⡟⠻⠙⢠⣼⣿⣿⣿⠁⣼⠃⣼⣿⠟⠁ ⠃⠀⠀⠙⢿⣦⠹⠏⢻⣿⣿⣿⣧⣿⣧⣰⠀⡀⠛⠃⠊⠹⡟⠋⠛⣿⠿⠛⠛⡏⠉⠋⡇⠀⣀⠇⢰⣇⣶⣿⣿⣿⡿⢠⠎⣸⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⣿⣆⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣤⣸⠀⡇⢠⠀⣼⣠⣀⠀⡇⠀⡀⣄⣰⣿⣧⣾⣿⣿⣿⣿⣿⠃⡞⣰⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣟⣻⣿⣿⣿⡟⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⢹⣿⣿⣿⣿⣷⡟⠁⠀⠀⠀⠀ ⠀⠀⠐⠀⠀⠀⠈⠹⢿⡙⠻⣿⡇⢀⠇⣥⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠀⠀⣀⣸⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣆⠙⣿⣿⣆⣉⠁⠀⢋⠋⠀⡋⢹⡟⠉⢻⠋⠉⡏⠏⠀⢨⡀⠀⠀⡐⣾⣿⣿⣿⣿⢿⡧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⢸⡇⠙⠳⣌⠻⣿⣿⣆⠐⣼⣆⢠⠀⢻⣄⠀⢸⡂⠀⠂⡄⠀⢸⣷⣼⣶⣿⣿⠟⣻⣯⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡦⠀⠀⠀⢸⣧⠀⠀⠙⣷⣌⠛⢿⣿⣿⣿⣄⣠⣿⣄⡂⣸⣇⣀⢰⣿⣧⣾⣿⣿⠿⢋⣱⣾⣿⣇⠀⢸⡇⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⣸⣿⠁⠀⠀⠘⢨⣿⠀⣀⠻⣿⣿⣿⣦⣌⣙⠛⠿⠿⢿⣿⢿⣿⣿⡿⠿⠿⠿⠟⣿⣷⣶⣿⣿⣿⠋⠅⠀⠀⣇⠈⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⠇⠀⠀⠀⣠⡟⣣⣠⣍⣳⣾⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣠⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣂⠀⠀⢙⣧⡐⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠿⠟⠿⠻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⠻⠛⠛⠛⠟⠻⠛⡻⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠛⠉⢀⠠⠖⠚⠒⠒⠀⠙⣿⣿⡿⢁⣾⣿⣫⡴⠞⠛⠛⠛⠓⠀⠀⡀⠀⠀⠙⠛⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀⣐⣤⣴⡤⠤⠤⠤⢤⡐⠬⣿⢷⠀⠐⢹⡿⠛⠛⣛⣛⣓⣛⡓⣶⣄⠀⣦⠈⠂⠎⢻⣧⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⠿⠵⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣳⡵⠀⠂⢴⣿⣿⣷⡿⠿⣿⣿⠿⣿⣿⣿⣿⣿⡉⣄⣀⣼⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡿⠻⢻⣷⣾⣿⣿⣿⡟⠉⣰⣿⣷⡌⠻⣿⣿⣿⣿⠀⠀⠀⣿⣿⠏⠀⣼⣿⣿⣷⡈⢹⣿⣿⣿⣿⣿⣿⡟⠿⢿⣷⣄⠀⠀ ⡇⢀⣶⠋⣥⢶⣿⣈⣽⣿⣿⣿⣿⣇⠀⢿⣿⣿⡟⢀⣿⣿⣿⣿⠀⠀⠸⣿⣿⣦⠀⠻⣿⣿⣿⢃⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⡙⣷⡀ ⣷⣾⠁⡼⢡⣿⠛⣡⣭⣙⠿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄⠛⣷⠀⢳⢘⣷ ⣿⣿⠀⠇⢸⣏⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢿⣿⣿⡿⠟⠛⠛⠀⠀⠈⠛⠛⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡀⢸⢰⣿ ⣿⢿⣧⠘⣾⣿⡄⢻⣿⣿⣿⢻⣿⣿⣿⣧⣄⡀⠈⠿⣷⣾⣷⣶⣤⣭⣂⣼⠿⣷⣬⡟⣁⣠⣴⣿⣿⣿⡟⣿⣿⣿⣿⡿⠉⣰⠂⣾⣾⡿ ⡇⠀⠿⣷⡈⠻⣷⡈⣿⣿⣿⣦⠘⡷⠈⢻⠛⠿⣿⣶⣦⣬⣄⣈⣉⣠⣿⣦⣤⣴⣿⣿⣿⠿⠟⡟⠻⠙⢠⣼⣿⣿⣿⠁⣼⠃⣼⣿⠟⠁ ⠃⠀⠀⠙⢿⣦⠹⠏⢻⣿⣿⣿⣧⣿⣧⣰⠀⡀⠛⠃⠊⠹⡟⠋⠛⣿⠿⠛⠛⡏⠉⠋⡇⠀⣀⠇⢰⣇⣶⣿⣿⣿⡿⢠⠎⣸⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⣿⣆⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣤⣸⠀⡇⢠⠀⣼⣠⣀⠀⡇⠀⡀⣄⣰⣿⣧⣾⣿⣿⣿⣿⣿⠃⡞⣰⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣟⣻⣿⣿⣿⡟⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⢹⣿⣿⣿⣿⣷⡟⠁⠀⠀⠀⠀ ⠀⠀⠐⠀⠀⠀⠈⠹⢿⡙⠻⣿⡇⢀⠇⣥⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠀⠀⣀⣸⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣆⠙⣿⣿⣆⣉⠁⠀⢋⠋⠀⡋⢹⡟⠉⢻⠋⠉⡏⠏⠀⢨⡀⠀⠀⡐⣾⣿⣿⣿⣿⢿⡧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⢸⡇⠙⠳⣌⠻⣿⣿⣆⠐⣼⣆⢠⠀⢻⣄⠀⢸⡂⠀⠂⡄⠀⢸⣷⣼⣶⣿⣿⠟⣻⣯⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡦⠀⠀⠀⢸⣧⠀⠀⠙⣷⣌⠛⢿⣿⣿⣿⣄⣠⣿⣄⡂⣸⣇⣀⢰⣿⣧⣾⣿⣿⠿⢋⣱⣾⣿⣇⠀⢸⡇⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⣸⣿⠁⠀⠀⠘⢨⣿⠀⣀⠻⣿⣿⣿⣦⣌⣙⠛⠿⠿⢿⣿⢿⣿⣿⡿⠿⠿⠿⠟⣿⣷⣶⣿⣿⣿⠋⠅⠀⠀⣇⠈⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⠇⠀⠀⠀⣠⡟⣣⣠⣍⣳⣾⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣠⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣂⠀⠀⢙⣧⡐ ⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠿⠟⠿⠻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⠻⠛⠛⠛⠟⠻⠛⡻⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠛⠉⢀⠠⠖⠚⠒⠒⠀⠙⣿⣿⡿⢁⣾⣿⣫⡴⠞⠛⠛⠛⠓⠀⠀⡀⠀⠀⠙⠛⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀⣐⣤⣴⡤⠤⠤⠤⢤⡐⠬⣿⢷⠀⠐⢹⡿⠛⠛⣛⣛⣓⣛⡓⣶⣄⠀⣦⠈⠂⠎⢻⣧⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⠿⠵⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣳⡵⠀⠂⢴⣿⣿⣷⡿⠿⣿⣿⠿⣿⣿⣿⣿⣿⡉⣄⣀⣼⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡿⠻⢻⣷⣾⣿⣿⣿⡟⠉⣰⣿⣷⡌⠻⣿⣿⣿⣿⠀⠀⠀⣿⣿⠏⠀⣼⣿⣿⣷⡈⢹⣿⣿⣿⣿⣿⣿⡟⠿⢿⣷⣄⠀⠀ ⡇⢀⣶⠋⣥⢶⣿⣈⣽⣿⣿⣿⣿⣇⠀⢿⣿⣿⡟⢀⣿⣿⣿⣿⠀⠀⠸⣿⣿⣦⠀⠻⣿⣿⣿⢃⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⡙⣷⡀ ⣷⣾⠁⡼⢡⣿⠛⣡⣭⣙⠿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄⠛⣷⠀⢳⢘⣷ ⣿⣿⠀⠇⢸⣏⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢿⣿⣿⡿⠟⠛⠛⠀⠀⠈⠛⠛⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡀⢸⢰⣿ ⣿⢿⣧⠘⣾⣿⡄⢻⣿⣿⣿⢻⣿⣿⣿⣧⣄⡀⠈⠿⣷⣾⣷⣶⣤⣭⣂⣼⠿⣷⣬⡟⣁⣠⣴⣿⣿⣿⡟⣿⣿⣿⣿⡿⠉⣰⠂⣾⣾⡿ ⡇⠀⠿⣷⡈⠻⣷⡈⣿⣿⣿⣦⠘⡷⠈⢻⠛⠿⣿⣶⣦⣬⣄⣈⣉⣠⣿⣦⣤⣴⣿⣿⣿⠿⠟⡟⠻⠙⢠⣼⣿⣿⣿⠁⣼⠃⣼⣿⠟⠁ ⠃⠀⠀⠙⢿⣦⠹⠏⢻⣿⣿⣿⣧⣿⣧⣰⠀⡀⠛⠃⠊⠹⡟⠋⠛⣿⠿⠛⠛⡏⠉⠋⡇⠀⣀⠇⢰⣇⣶⣿⣿⣿⡿⢠⠎⣸⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⣿⣆⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣤⣸⠀⡇⢠⠀⣼⣠⣀⠀⡇⠀⡀⣄⣰⣿⣧⣾⣿⣿⣿⣿⣿⠃⡞⣰⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣟⣻⣿⣿⣿⡟⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⢹⣿⣿⣿⣿⣷⡟⠁⠀⠀⠀⠀ ⠀⠀⠐⠀⠀⠀⠈⠹⢿⡙⠻⣿⡇⢀⠇⣥⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠀⠀⣀⣸⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣆⠙⣿⣿⣆⣉⠁⠀⢋⠋⠀⡋⢹⡟⠉⢻⠋⠉⡏⠏⠀⢨⡀⠀⠀⡐⣾⣿⣿⣿⣿⢿⡧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⢸⡇⠙⠳⣌⠻⣿⣿⣆⠐⣼⣆⢠⠀⢻⣄⠀⢸⡂⠀⠂⡄⠀⢸⣷⣼⣶⣿⣿⠟⣻⣯⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡦⠀⠀⠀⢸⣧⠀⠀⠙⣷⣌⠛⢿⣿⣿⣿⣄⣠⣿⣄⡂⣸⣇⣀⢰⣿⣧⣾⣿⣿⠿⢋⣱⣾⣿⣇⠀⢸⡇⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⣸⣿⠁⠀⠀⠘⢨⣿⠀⣀⠻⣿⣿⣿⣦⣌⣙⠛⠿⠿⢿⣿⢿⣿⣿⡿⠿⠿⠿⠟⣿⣷⣶⣿⣿⣿⠋⠅⠀⠀⣇⠈⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⠇⠀⠀⠀⣠⡟⣣⣠⣍⣳⣾⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣠⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣂⠀⠀⢙⣧⡐⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠿⠟⠿⠻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⠻⠛⠛⠛⠟⠻⠛⡻⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠛⠉⢀⠠⠖⠚⠒⠒⠀⠙⣿⣿⡿⢁⣾⣿⣫⡴⠞⠛⠛⠛⠓⠀⠀⡀⠀⠀⠙⠛⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀⣐⣤⣴⡤⠤⠤⠤⢤⡐⠬⣿⢷⠀⠐⢹⡿⠛⠛⣛⣛⣓⣛⡓⣶⣄⠀⣦⠈⠂⠎⢻⣧⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⠿⠵⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣳⡵⠀⠂⢴⣿⣿⣷⡿⠿⣿⣿⠿⣿⣿⣿⣿⣿⡉⣄⣀⣼⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡿⠻⢻⣷⣾⣿⣿⣿⡟⠉⣰⣿⣷⡌⠻⣿⣿⣿⣿⠀⠀⠀⣿⣿⠏⠀⣼⣿⣿⣷⡈⢹⣿⣿⣿⣿⣿⣿⡟⠿⢿⣷⣄⠀⠀ ⡇⢀⣶⠋⣥⢶⣿⣈⣽⣿⣿⣿⣿⣇⠀⢿⣿⣿⡟⢀⣿⣿⣿⣿⠀⠀⠸⣿⣿⣦⠀⠻⣿⣿⣿⢃⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⡙⣷⡀ ⣷⣾⠁⡼⢡⣿⠛⣡⣭⣙⠿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄⠛⣷⠀⢳⢘⣷ ⣿⣿⠀⠇⢸⣏⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢿⣿⣿⡿⠟⠛⠛⠀⠀⠈⠛⠛⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡀⢸⢰⣿ ⣿⢿⣧⠘⣾⣿⡄⢻⣿⣿⣿⢻⣿⣿⣿⣧⣄⡀⠈⠿⣷⣾⣷⣶⣤⣭⣂⣼⠿⣷⣬⡟⣁⣠⣴⣿⣿⣿⡟⣿⣿⣿⣿⡿⠉⣰⠂⣾⣾⡿ ⡇⠀⠿⣷⡈⠻⣷⡈⣿⣿⣿⣦⠘⡷⠈⢻⠛⠿⣿⣶⣦⣬⣄⣈⣉⣠⣿⣦⣤⣴⣿⣿⣿⠿⠟⡟⠻⠙⢠⣼⣿⣿⣿⠁⣼⠃⣼⣿⠟⠁ ⠃⠀⠀⠙⢿⣦⠹⠏⢻⣿⣿⣿⣧⣿⣧⣰⠀⡀⠛⠃⠊⠹⡟⠋⠛⣿⠿⠛⠛⡏⠉⠋⡇⠀⣀⠇⢰⣇⣶⣿⣿⣿⡿⢠⠎⣸⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⣿⣆⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣤⣸⠀⡇⢠⠀⣼⣠⣀⠀⡇⠀⡀⣄⣰⣿⣧⣾⣿⣿⣿⣿⣿⠃⡞⣰⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣟⣻⣿⣿⣿⡟⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⢹⣿⣿⣿⣿⣷⡟⠁⠀⠀⠀⠀ ⠀⠀⠐⠀⠀⠀⠈⠹⢿⡙⠻⣿⡇⢀⠇⣥⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠀⠀⣀⣸⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣆⠙⣿⣿⣆⣉⠁⠀⢋⠋⠀⡋⢹⡟⠉⢻⠋⠉⡏⠏⠀⢨⡀⠀⠀⡐⣾⣿⣿⣿⣿⢿⡧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⢸⡇⠙⠳⣌⠻⣿⣿⣆⠐⣼⣆⢠⠀⢻⣄⠀⢸⡂⠀⠂⡄⠀⢸⣷⣼⣶⣿⣿⠟⣻⣯⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡦⠀⠀⠀⢸⣧⠀⠀⠙⣷⣌⠛⢿⣿⣿⣿⣄⣠⣿⣄⡂⣸⣇⣀⢰⣿⣧⣾⣿⣿⠿⢋⣱⣾⣿⣇⠀⢸⡇⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⣸⣿⠁⠀⠀⠘⢨⣿⠀⣀⠻⣿⣿⣿⣦⣌⣙⠛⠿⠿⢿⣿⢿⣿⣿⡿⠿⠿⠿⠟⣿⣷⣶⣿⣿⣿⠋⠅⠀⠀⣇⠈⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⠇⠀⠀⠀⣠⡟⣣⣠⣍⣳⣾⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣠⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣂⠀⠀⢙⣧⡐ ⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠿⠟⠿⠻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⠻⠛⠛⠛⠟⠻⠛⡻⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠛⠉⢀⠠⠖⠚⠒⠒⠀⠙⣿⣿⡿⢁⣾⣿⣫⡴⠞⠛⠛⠛⠓⠀⠀⡀⠀⠀⠙⠛⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀⣐⣤⣴⡤⠤⠤⠤⢤⡐⠬⣿⢷⠀⠐⢹⡿⠛⠛⣛⣛⣓⣛⡓⣶⣄⠀⣦⠈⠂⠎⢻⣧⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⠿⠵⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣳⡵⠀⠂⢴⣿⣿⣷⡿⠿⣿⣿⠿⣿⣿⣿⣿⣿⡉⣄⣀⣼⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡿⠻⢻⣷⣾⣿⣿⣿⡟⠉⣰⣿⣷⡌⠻⣿⣿⣿⣿⠀⠀⠀⣿⣿⠏⠀⣼⣿⣿⣷⡈⢹⣿⣿⣿⣿⣿⣿⡟⠿⢿⣷⣄⠀⠀ ⡇⢀⣶⠋⣥⢶⣿⣈⣽⣿⣿⣿⣿⣇⠀⢿⣿⣿⡟⢀⣿⣿⣿⣿⠀⠀⠸⣿⣿⣦⠀⠻⣿⣿⣿⢃⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⡙⣷⡀ ⣷⣾⠁⡼⢡⣿⠛⣡⣭⣙⠿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄⠛⣷⠀⢳⢘⣷ ⣿⣿⠀⠇⢸⣏⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢿⣿⣿⡿⠟⠛⠛⠀⠀⠈⠛⠛⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡀⢸⢰⣿ ⣿⢿⣧⠘⣾⣿⡄⢻⣿⣿⣿⢻⣿⣿⣿⣧⣄⡀⠈⠿⣷⣾⣷⣶⣤⣭⣂⣼⠿⣷⣬⡟⣁⣠⣴⣿⣿⣿⡟⣿⣿⣿⣿⡿⠉⣰⠂⣾⣾⡿ ⡇⠀⠿⣷⡈⠻⣷⡈⣿⣿⣿⣦⠘⡷⠈⢻⠛⠿⣿⣶⣦⣬⣄⣈⣉⣠⣿⣦⣤⣴⣿⣿⣿⠿⠟⡟⠻⠙⢠⣼⣿⣿⣿⠁⣼⠃⣼⣿⠟⠁ ⠃⠀⠀⠙⢿⣦⠹⠏⢻⣿⣿⣿⣧⣿⣧⣰⠀⡀⠛⠃⠊⠹⡟⠋⠛⣿⠿⠛⠛⡏⠉⠋⡇⠀⣀⠇⢰⣇⣶⣿⣿⣿⡿⢠⠎⣸⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⣿⣆⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣤⣸⠀⡇⢠⠀⣼⣠⣀⠀⡇⠀⡀⣄⣰⣿⣧⣾⣿⣿⣿⣿⣿⠃⡞⣰⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣟⣻⣿⣿⣿⡟⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⢹⣿⣿⣿⣿⣷⡟⠁⠀⠀⠀⠀ ⠀⠀⠐⠀⠀⠀⠈⠹⢿⡙⠻⣿⡇⢀⠇⣥⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠀⠀⣀⣸⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣆⠙⣿⣿⣆⣉⠁⠀⢋⠋⠀⡋⢹⡟⠉⢻⠋⠉⡏⠏⠀⢨⡀⠀⠀⡐⣾⣿⣿⣿⣿⢿⡧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⢸⡇⠙⠳⣌⠻⣿⣿⣆⠐⣼⣆⢠⠀⢻⣄⠀⢸⡂⠀⠂⡄⠀⢸⣷⣼⣶⣿⣿⠟⣻⣯⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡦⠀⠀⠀⢸⣧⠀⠀⠙⣷⣌⠛⢿⣿⣿⣿⣄⣠⣿⣄⡂⣸⣇⣀⢰⣿⣧⣾⣿⣿⠿⢋⣱⣾⣿⣇⠀⢸⡇⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⣸⣿⠁⠀⠀⠘⢨⣿⠀⣀⠻⣿⣿⣿⣦⣌⣙⠛⠿⠿⢿⣿⢿⣿⣿⡿⠿⠿⠿⠟⣿⣷⣶⣿⣿⣿⠋⠅⠀⠀⣇⠈⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⠇⠀⠀⠀⣠⡟⣣⣠⣍⣳⣾⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣠⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣂⠀⠀⢙⣧⡐⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠿⠟⠿⠻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⠻⠛⠛⠛⠟⠻⠛⡻⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠛⠉⢀⠠⠖⠚⠒⠒⠀⠙⣿⣿⡿⢁⣾⣿⣫⡴⠞⠛⠛⠛⠓⠀⠀⡀⠀⠀⠙⠛⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀⣐⣤⣴⡤⠤⠤⠤⢤⡐⠬⣿⢷⠀⠐⢹⡿⠛⠛⣛⣛⣓⣛⡓⣶⣄⠀⣦⠈⠂⠎⢻⣧⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⠿⠵⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣳⡵⠀⠂⢴⣿⣿⣷⡿⠿⣿⣿⠿⣿⣿⣿⣿⣿⡉⣄⣀⣼⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡿⠻⢻⣷⣾⣿⣿⣿⡟⠉⣰⣿⣷⡌⠻⣿⣿⣿⣿⠀⠀⠀⣿⣿⠏⠀⣼⣿⣿⣷⡈⢹⣿⣿⣿⣿⣿⣿⡟⠿⢿⣷⣄⠀⠀ ⡇⢀⣶⠋⣥⢶⣿⣈⣽⣿⣿⣿⣿⣇⠀⢿⣿⣿⡟⢀⣿⣿⣿⣿⠀⠀⠸⣿⣿⣦⠀⠻⣿⣿⣿⢃⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⡙⣷⡀ ⣷⣾⠁⡼⢡⣿⠛⣡⣭⣙⠿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄⠛⣷⠀⢳⢘⣷ ⣿⣿⠀⠇⢸⣏⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢿⣿⣿⡿⠟⠛⠛⠀⠀⠈⠛⠛⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡀⢸⢰⣿ ⣿⢿⣧⠘⣾⣿⡄⢻⣿⣿⣿⢻⣿⣿⣿⣧⣄⡀⠈⠿⣷⣾⣷⣶⣤⣭⣂⣼⠿⣷⣬⡟⣁⣠⣴⣿⣿⣿⡟⣿⣿⣿⣿⡿⠉⣰⠂⣾⣾⡿ ⡇⠀⠿⣷⡈⠻⣷⡈⣿⣿⣿⣦⠘⡷⠈⢻⠛⠿⣿⣶⣦⣬⣄⣈⣉⣠⣿⣦⣤⣴⣿⣿⣿⠿⠟⡟⠻⠙⢠⣼⣿⣿⣿⠁⣼⠃⣼⣿⠟⠁ ⠃⠀⠀⠙⢿⣦⠹⠏⢻⣿⣿⣿⣧⣿⣧⣰⠀⡀⠛⠃⠊⠹⡟⠋⠛⣿⠿⠛⠛⡏⠉⠋⡇⠀⣀⠇⢰⣇⣶⣿⣿⣿⡿⢠⠎⣸⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⣿⣆⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣤⣸⠀⡇⢠⠀⣼⣠⣀⠀⡇⠀⡀⣄⣰⣿⣧⣾⣿⣿⣿⣿⣿⠃⡞⣰⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣟⣻⣿⣿⣿⡟⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⢹⣿⣿⣿⣿⣷⡟⠁⠀⠀⠀⠀ ⠀⠀⠐⠀⠀⠀⠈⠹⢿⡙⠻⣿⡇⢀⠇⣥⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠀⠀⣀⣸⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣆⠙⣿⣿⣆⣉⠁⠀⢋⠋⠀⡋⢹⡟⠉⢻⠋⠉⡏⠏⠀⢨⡀⠀⠀⡐⣾⣿⣿⣿⣿⢿⡧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⢸⡇⠙⠳⣌⠻⣿⣿⣆⠐⣼⣆⢠⠀⢻⣄⠀⢸⡂⠀⠂⡄⠀⢸⣷⣼⣶⣿⣿⠟⣻⣯⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡦⠀⠀⠀⢸⣧⠀⠀⠙⣷⣌⠛⢿⣿⣿⣿⣄⣠⣿⣄⡂⣸⣇⣀⢰⣿⣧⣾⣿⣿⠿⢋⣱⣾⣿⣇⠀⢸⡇⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⣸⣿⠁⠀⠀⠘⢨⣿⠀⣀⠻⣿⣿⣿⣦⣌⣙⠛⠿⠿⢿⣿⢿⣿⣿⡿⠿⠿⠿⠟⣿⣷⣶⣿⣿⣿⠋⠅⠀⠀⣇⠈⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⠇⠀⠀⠀⣠⡟⣣⣠⣍⣳⣾⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣠⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣂⠀⠀⢙⣧⡐ ⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠿⠟⠿⠻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⠻⠛⠛⠛⠟⠻⠛⡻⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠛⠉⢀⠠⠖⠚⠒⠒⠀⠙⣿⣿⡿⢁⣾⣿⣫⡴⠞⠛⠛⠛⠓⠀⠀⡀⠀⠀⠙⠛⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀⣐⣤⣴⡤⠤⠤⠤⢤⡐⠬⣿⢷⠀⠐⢹⡿⠛⠛⣛⣛⣓⣛⡓⣶⣄⠀⣦⠈⠂⠎⢻⣧⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⠿⠵⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣳⡵⠀⠂⢴⣿⣿⣷⡿⠿⣿⣿⠿⣿⣿⣿⣿⣿⡉⣄⣀⣼⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡿⠻⢻⣷⣾⣿⣿⣿⡟⠉⣰⣿⣷⡌⠻⣿⣿⣿⣿⠀⠀⠀⣿⣿⠏⠀⣼⣿⣿⣷⡈⢹⣿⣿⣿⣿⣿⣿⡟⠿⢿⣷⣄⠀⠀ ⡇⢀⣶⠋⣥⢶⣿⣈⣽⣿⣿⣿⣿⣇⠀⢿⣿⣿⡟⢀⣿⣿⣿⣿⠀⠀⠸⣿⣿⣦⠀⠻⣿⣿⣿⢃⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⡙⣷⡀ ⣷⣾⠁⡼⢡⣿⠛⣡⣭⣙⠿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄⠛⣷⠀⢳⢘⣷ ⣿⣿⠀⠇⢸⣏⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢿⣿⣿⡿⠟⠛⠛⠀⠀⠈⠛⠛⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡀⢸⢰⣿ ⣿⢿⣧⠘⣾⣿⡄⢻⣿⣿⣿⢻⣿⣿⣿⣧⣄⡀⠈⠿⣷⣾⣷⣶⣤⣭⣂⣼⠿⣷⣬⡟⣁⣠⣴⣿⣿⣿⡟⣿⣿⣿⣿⡿⠉⣰⠂⣾⣾⡿ ⡇⠀⠿⣷⡈⠻⣷⡈⣿⣿⣿⣦⠘⡷⠈⢻⠛⠿⣿⣶⣦⣬⣄⣈⣉⣠⣿⣦⣤⣴⣿⣿⣿⠿⠟⡟⠻⠙⢠⣼⣿⣿⣿⠁⣼⠃⣼⣿⠟⠁ ⠃⠀⠀⠙⢿⣦⠹⠏⢻⣿⣿⣿⣧⣿⣧⣰⠀⡀⠛⠃⠊⠹⡟⠋⠛⣿⠿⠛⠛⡏⠉⠋⡇⠀⣀⠇⢰⣇⣶⣿⣿⣿⡿⢠⠎⣸⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⣿⣆⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣤⣸⠀⡇⢠⠀⣼⣠⣀⠀⡇⠀⡀⣄⣰⣿⣧⣾⣿⣿⣿⣿⣿⠃⡞⣰⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣟⣻⣿⣿⣿⡟⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⢹⣿⣿⣿⣿⣷⡟⠁⠀⠀⠀⠀ ⠀⠀⠐⠀⠀⠀⠈⠹⢿⡙⠻⣿⡇⢀⠇⣥⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠀⠀⣀⣸⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣆⠙⣿⣿⣆⣉⠁⠀⢋⠋⠀⡋⢹⡟⠉⢻⠋⠉⡏⠏⠀⢨⡀⠀⠀⡐⣾⣿⣿⣿⣿⢿⡧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⢸⡇⠙⠳⣌⠻⣿⣿⣆⠐⣼⣆⢠⠀⢻⣄⠀⢸⡂⠀⠂⡄⠀⢸⣷⣼⣶⣿⣿⠟⣻⣯⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡦⠀⠀⠀⢸⣧⠀⠀⠙⣷⣌⠛⢿⣿⣿⣿⣄⣠⣿⣄⡂⣸⣇⣀⢰⣿⣧⣾⣿⣿⠿⢋⣱⣾⣿⣇⠀⢸⡇⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⣸⣿⠁⠀⠀⠘⢨⣿⠀⣀⠻⣿⣿⣿⣦⣌⣙⠛⠿⠿⢿⣿⢿⣿⣿⡿⠿⠿⠿⠟⣿⣷⣶⣿⣿⣿⠋⠅⠀⠀⣇⠈⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⠇⠀⠀⠀⣠⡟⣣⣠⣍⣳⣾⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣠⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣂⠀⠀⢙⣧⡐⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠿⠟⠿⠻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⠻⠛⠛⠛⠟⠻⠛⡻⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠛⠉⢀⠠⠖⠚⠒⠒⠀⠙⣿⣿⡿⢁⣾⣿⣫⡴⠞⠛⠛⠛⠓⠀⠀⡀⠀⠀⠙⠛⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀⣐⣤⣴⡤⠤⠤⠤⢤⡐⠬⣿⢷⠀⠐⢹⡿⠛⠛⣛⣛⣓⣛⡓⣶⣄⠀⣦⠈⠂⠎⢻⣧⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⠿⠵⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣳⡵⠀⠂⢴⣿⣿⣷⡿⠿⣿⣿⠿⣿⣿⣿⣿⣿⡉⣄⣀⣼⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡿⠻⢻⣷⣾⣿⣿⣿⡟⠉⣰⣿⣷⡌⠻⣿⣿⣿⣿⠀⠀⠀⣿⣿⠏⠀⣼⣿⣿⣷⡈⢹⣿⣿⣿⣿⣿⣿⡟⠿⢿⣷⣄⠀⠀ ⡇⢀⣶⠋⣥⢶⣿⣈⣽⣿⣿⣿⣿⣇⠀⢿⣿⣿⡟⢀⣿⣿⣿⣿⠀⠀⠸⣿⣿⣦⠀⠻⣿⣿⣿⢃⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⡙⣷⡀ ⣷⣾⠁⡼⢡⣿⠛⣡⣭⣙⠿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄⠛⣷⠀⢳⢘⣷ ⣿⣿⠀⠇⢸⣏⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢿⣿⣿⡿⠟⠛⠛⠀⠀⠈⠛⠛⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡀⢸⢰⣿ ⣿⢿⣧⠘⣾⣿⡄⢻⣿⣿⣿⢻⣿⣿⣿⣧⣄⡀⠈⠿⣷⣾⣷⣶⣤⣭⣂⣼⠿⣷⣬⡟⣁⣠⣴⣿⣿⣿⡟⣿⣿⣿⣿⡿⠉⣰⠂⣾⣾⡿ ⡇⠀⠿⣷⡈⠻⣷⡈⣿⣿⣿⣦⠘⡷⠈⢻⠛⠿⣿⣶⣦⣬⣄⣈⣉⣠⣿⣦⣤⣴⣿⣿⣿⠿⠟⡟⠻⠙⢠⣼⣿⣿⣿⠁⣼⠃⣼⣿⠟⠁ ⠃⠀⠀⠙⢿⣦⠹⠏⢻⣿⣿⣿⣧⣿⣧⣰⠀⡀⠛⠃⠊⠹⡟⠋⠛⣿⠿⠛⠛⡏⠉⠋⡇⠀⣀⠇⢰⣇⣶⣿⣿⣿⡿⢠⠎⣸⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⣿⣆⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣤⣸⠀⡇⢠⠀⣼⣠⣀⠀⡇⠀⡀⣄⣰⣿⣧⣾⣿⣿⣿⣿⣿⠃⡞⣰⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣟⣻⣿⣿⣿⡟⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⢹⣿⣿⣿⣿⣷⡟⠁⠀⠀⠀⠀ ⠀⠀⠐⠀⠀⠀⠈⠹⢿⡙⠻⣿⡇⢀⠇⣥⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠀⠀⣀⣸⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣆⠙⣿⣿⣆⣉⠁⠀⢋⠋⠀⡋⢹⡟⠉⢻⠋⠉⡏⠏⠀⢨⡀⠀⠀⡐⣾⣿⣿⣿⣿⢿⡧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⢸⡇⠙⠳⣌⠻⣿⣿⣆⠐⣼⣆⢠⠀⢻⣄⠀⢸⡂⠀⠂⡄⠀⢸⣷⣼⣶⣿⣿⠟⣻⣯⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡦⠀⠀⠀⢸⣧⠀⠀⠙⣷⣌⠛⢿⣿⣿⣿⣄⣠⣿⣄⡂⣸⣇⣀⢰⣿⣧⣾⣿⣿⠿⢋⣱⣾⣿⣇⠀⢸⡇⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⣸⣿⠁⠀⠀⠘⢨⣿⠀⣀⠻⣿⣿⣿⣦⣌⣙⠛⠿⠿⢿⣿⢿⣿⣿⡿⠿⠿⠿⠟⣿⣷⣶⣿⣿⣿⠋⠅⠀⠀⣇⠈⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⠇⠀⠀⠀⣠⡟⣣⣠⣍⣳⣾⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣠⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣂⠀⠀⢙⣧⡐ ⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠿⠟⠿⠻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⠻⠛⠛⠛⠟⠻⠛⡻⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠛⠉⢀⠠⠖⠚⠒⠒⠀⠙⣿⣿⡿⢁⣾⣿⣫⡴⠞⠛⠛⠛⠓⠀⠀⡀⠀⠀⠙⠛⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀⣐⣤⣴⡤⠤⠤⠤⢤⡐⠬⣿⢷⠀⠐⢹⡿⠛⠛⣛⣛⣓⣛⡓⣶⣄⠀⣦⠈⠂⠎⢻⣧⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⠿⠵⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣳⡵⠀⠂⢴⣿⣿⣷⡿⠿⣿⣿⠿⣿⣿⣿⣿⣿⡉⣄⣀⣼⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡿⠻⢻⣷⣾⣿⣿⣿⡟⠉⣰⣿⣷⡌⠻⣿⣿⣿⣿⠀⠀⠀⣿⣿⠏⠀⣼⣿⣿⣷⡈⢹⣿⣿⣿⣿⣿⣿⡟⠿⢿⣷⣄⠀⠀ ⡇⢀⣶⠋⣥⢶⣿⣈⣽⣿⣿⣿⣿⣇⠀⢿⣿⣿⡟⢀⣿⣿⣿⣿⠀⠀⠸⣿⣿⣦⠀⠻⣿⣿⣿⢃⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⡙⣷⡀ ⣷⣾⠁⡼⢡⣿⠛⣡⣭⣙⠿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄⠛⣷⠀⢳⢘⣷ ⣿⣿⠀⠇⢸⣏⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢿⣿⣿⡿⠟⠛⠛⠀⠀⠈⠛⠛⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡀⢸⢰⣿ ⣿⢿⣧⠘⣾⣿⡄⢻⣿⣿⣿⢻⣿⣿⣿⣧⣄⡀⠈⠿⣷⣾⣷⣶⣤⣭⣂⣼⠿⣷⣬⡟⣁⣠⣴⣿⣿⣿⡟⣿⣿⣿⣿⡿⠉⣰⠂⣾⣾⡿ ⡇⠀⠿⣷⡈⠻⣷⡈⣿⣿⣿⣦⠘⡷⠈⢻⠛⠿⣿⣶⣦⣬⣄⣈⣉⣠⣿⣦⣤⣴⣿⣿⣿⠿⠟⡟⠻⠙⢠⣼⣿⣿⣿⠁⣼⠃⣼⣿⠟⠁ ⠃⠀⠀⠙⢿⣦⠹⠏⢻⣿⣿⣿⣧⣿⣧⣰⠀⡀⠛⠃⠊⠹⡟⠋⠛⣿⠿⠛⠛⡏⠉⠋⡇⠀⣀⠇⢰⣇⣶⣿⣿⣿⡿⢠⠎⣸⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⣿⣆⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣤⣸⠀⡇⢠⠀⣼⣠⣀⠀⡇⠀⡀⣄⣰⣿⣧⣾⣿⣿⣿⣿⣿⠃⡞⣰⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣟⣻⣿⣿⣿⡟⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⢹⣿⣿⣿⣿⣷⡟⠁⠀⠀⠀⠀ ⠀⠀⠐⠀⠀⠀⠈⠹⢿⡙⠻⣿⡇⢀⠇⣥⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠀⠀⣀⣸⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣆⠙⣿⣿⣆⣉⠁⠀⢋⠋⠀⡋⢹⡟⠉⢻⠋⠉⡏⠏⠀⢨⡀⠀⠀⡐⣾⣿⣿⣿⣿⢿⡧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⢸⡇⠙⠳⣌⠻⣿⣿⣆⠐⣼⣆⢠⠀⢻⣄⠀⢸⡂⠀⠂⡄⠀⢸⣷⣼⣶⣿⣿⠟⣻⣯⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡦⠀⠀⠀⢸⣧⠀⠀⠙⣷⣌⠛⢿⣿⣿⣿⣄⣠⣿⣄⡂⣸⣇⣀⢰⣿⣧⣾⣿⣿⠿⢋⣱⣾⣿⣇⠀⢸⡇⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⣸⣿⠁⠀⠀⠘⢨⣿⠀⣀⠻⣿⣿⣿⣦⣌⣙⠛⠿⠿⢿⣿⢿⣿⣿⡿⠿⠿⠿⠟⣿⣷⣶⣿⣿⣿⠋⠅⠀⠀⣇⠈⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⠇⠀⠀⠀⣠⡟⣣⣠⣍⣳⣾⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣠⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣂⠀⠀⢙⣧⡐⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠿⠟⠿⠻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⠻⠛⠛⠛⠟⠻⠛⡻⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠛⠉⢀⠠⠖⠚⠒⠒⠀⠙⣿⣿⡿⢁⣾⣿⣫⡴⠞⠛⠛⠛⠓⠀⠀⡀⠀⠀⠙⠛⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀⣐⣤⣴⡤⠤⠤⠤⢤⡐⠬⣿⢷⠀⠐⢹⡿⠛⠛⣛⣛⣓⣛⡓⣶⣄⠀⣦⠈⠂⠎⢻⣧⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⠿⠵⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣳⡵⠀⠂⢴⣿⣿⣷⡿⠿⣿⣿⠿⣿⣿⣿⣿⣿⡉⣄⣀⣼⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡿⠻⢻⣷⣾⣿⣿⣿⡟⠉⣰⣿⣷⡌⠻⣿⣿⣿⣿⠀⠀⠀⣿⣿⠏⠀⣼⣿⣿⣷⡈⢹⣿⣿⣿⣿⣿⣿⡟⠿⢿⣷⣄⠀⠀ ⡇⢀⣶⠋⣥⢶⣿⣈⣽⣿⣿⣿⣿⣇⠀⢿⣿⣿⡟⢀⣿⣿⣿⣿⠀⠀⠸⣿⣿⣦⠀⠻⣿⣿⣿⢃⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⡙⣷⡀ ⣷⣾⠁⡼⢡⣿⠛⣡⣭⣙⠿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄⠛⣷⠀⢳⢘⣷ ⣿⣿⠀⠇⢸⣏⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢿⣿⣿⡿⠟⠛⠛⠀⠀⠈⠛⠛⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡀⢸⢰⣿ ⣿⢿⣧⠘⣾⣿⡄⢻⣿⣿⣿⢻⣿⣿⣿⣧⣄⡀⠈⠿⣷⣾⣷⣶⣤⣭⣂⣼⠿⣷⣬⡟⣁⣠⣴⣿⣿⣿⡟⣿⣿⣿⣿⡿⠉⣰⠂⣾⣾⡿ ⡇⠀⠿⣷⡈⠻⣷⡈⣿⣿⣿⣦⠘⡷⠈⢻⠛⠿⣿⣶⣦⣬⣄⣈⣉⣠⣿⣦⣤⣴⣿⣿⣿⠿⠟⡟⠻⠙⢠⣼⣿⣿⣿⠁⣼⠃⣼⣿⠟⠁ ⠃⠀⠀⠙⢿⣦⠹⠏⢻⣿⣿⣿⣧⣿⣧⣰⠀⡀⠛⠃⠊⠹⡟⠋⠛⣿⠿⠛⠛⡏⠉⠋⡇⠀⣀⠇⢰⣇⣶⣿⣿⣿⡿⢠⠎⣸⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⣿⣆⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣤⣸⠀⡇⢠⠀⣼⣠⣀⠀⡇⠀⡀⣄⣰⣿⣧⣾⣿⣿⣿⣿⣿⠃⡞⣰⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣟⣻⣿⣿⣿⡟⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⢹⣿⣿⣿⣿⣷⡟⠁⠀⠀⠀⠀ ⠀⠀⠐⠀⠀⠀⠈⠹⢿⡙⠻⣿⡇⢀⠇⣥⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠀⠀⣀⣸⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣆⠙⣿⣿⣆⣉⠁⠀⢋⠋⠀⡋⢹⡟⠉⢻⠋⠉⡏⠏⠀⢨⡀⠀⠀⡐⣾⣿⣿⣿⣿⢿⡧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⢸⡇⠙⠳⣌⠻⣿⣿⣆⠐⣼⣆⢠⠀⢻⣄⠀⢸⡂⠀⠂⡄⠀⢸⣷⣼⣶⣿⣿⠟⣻⣯⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡦⠀⠀⠀⢸⣧⠀⠀⠙⣷⣌⠛⢿⣿⣿⣿⣄⣠⣿⣄⡂⣸⣇⣀⢰⣿⣧⣾⣿⣿⠿⢋⣱⣾⣿⣇⠀⢸⡇⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⣸⣿⠁⠀⠀⠘⢨⣿⠀⣀⠻⣿⣿⣿⣦⣌⣙⠛⠿⠿⢿⣿⢿⣿⣿⡿⠿⠿⠿⠟⣿⣷⣶⣿⣿⣿⠋⠅⠀⠀⣇⠈⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⠇⠀⠀⠀⣠⡟⣣⣠⣍⣳⣾⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣠⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣂⠀⠀⢙⣧⡐ ⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠿⠟⠿⠻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⠻⠛⠛⠛⠟⠻⠛⡻⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠛⠉⢀⠠⠖⠚⠒⠒⠀⠙⣿⣿⡿⢁⣾⣿⣫⡴⠞⠛⠛⠛⠓⠀⠀⡀⠀⠀⠙⠛⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀⣐⣤⣴⡤⠤⠤⠤⢤⡐⠬⣿⢷⠀⠐⢹⡿⠛⠛⣛⣛⣓⣛⡓⣶⣄⠀⣦⠈⠂⠎⢻⣧⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⠿⠵⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣳⡵⠀⠂⢴⣿⣿⣷⡿⠿⣿⣿⠿⣿⣿⣿⣿⣿⡉⣄⣀⣼⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡿⠻⢻⣷⣾⣿⣿⣿⡟⠉⣰⣿⣷⡌⠻⣿⣿⣿⣿⠀⠀⠀⣿⣿⠏⠀⣼⣿⣿⣷⡈⢹⣿⣿⣿⣿⣿⣿⡟⠿⢿⣷⣄⠀⠀ ⡇⢀⣶⠋⣥⢶⣿⣈⣽⣿⣿⣿⣿⣇⠀⢿⣿⣿⡟⢀⣿⣿⣿⣿⠀⠀⠸⣿⣿⣦⠀⠻⣿⣿⣿⢃⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⡙⣷⡀ ⣷⣾⠁⡼⢡⣿⠛⣡⣭⣙⠿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄⠛⣷⠀⢳⢘⣷ ⣿⣿⠀⠇⢸⣏⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢿⣿⣿⡿⠟⠛⠛⠀⠀⠈⠛⠛⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡀⢸⢰⣿ ⣿⢿⣧⠘⣾⣿⡄⢻⣿⣿⣿⢻⣿⣿⣿⣧⣄⡀⠈⠿⣷⣾⣷⣶⣤⣭⣂⣼⠿⣷⣬⡟⣁⣠⣴⣿⣿⣿⡟⣿⣿⣿⣿⡿⠉⣰⠂⣾⣾⡿ ⡇⠀⠿⣷⡈⠻⣷⡈⣿⣿⣿⣦⠘⡷⠈⢻⠛⠿⣿⣶⣦⣬⣄⣈⣉⣠⣿⣦⣤⣴⣿⣿⣿⠿⠟⡟⠻⠙⢠⣼⣿⣿⣿⠁⣼⠃⣼⣿⠟⠁ ⠃⠀⠀⠙⢿⣦⠹⠏⢻⣿⣿⣿⣧⣿⣧⣰⠀⡀⠛⠃⠊⠹⡟⠋⠛⣿⠿⠛⠛⡏⠉⠋⡇⠀⣀⠇⢰⣇⣶⣿⣿⣿⡿⢠⠎⣸⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⣿⣆⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣤⣸⠀⡇⢠⠀⣼⣠⣀⠀⡇⠀⡀⣄⣰⣿⣧⣾⣿⣿⣿⣿⣿⠃⡞⣰⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣟⣻⣿⣿⣿⡟⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⢹⣿⣿⣿⣿⣷⡟⠁⠀⠀⠀⠀ ⠀⠀⠐⠀⠀⠀⠈⠹⢿⡙⠻⣿⡇⢀⠇⣥⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠀⠀⣀⣸⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣆⠙⣿⣿⣆⣉⠁⠀⢋⠋⠀⡋⢹⡟⠉⢻⠋⠉⡏⠏⠀⢨⡀⠀⠀⡐⣾⣿⣿⣿⣿⢿⡧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⢸⡇⠙⠳⣌⠻⣿⣿⣆⠐⣼⣆⢠⠀⢻⣄⠀⢸⡂⠀⠂⡄⠀⢸⣷⣼⣶⣿⣿⠟⣻⣯⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡦⠀⠀⠀⢸⣧⠀⠀⠙⣷⣌⠛⢿⣿⣿⣿⣄⣠⣿⣄⡂⣸⣇⣀⢰⣿⣧⣾⣿⣿⠿⢋⣱⣾⣿⣇⠀⢸⡇⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⣸⣿⠁⠀⠀⠘⢨⣿⠀⣀⠻⣿⣿⣿⣦⣌⣙⠛⠿⠿⢿⣿⢿⣿⣿⡿⠿⠿⠿⠟⣿⣷⣶⣿⣿⣿⠋⠅⠀⠀⣇⠈⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⠇⠀⠀⠀⣠⡟⣣⣠⣍⣳⣾⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣠⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣂⠀⠀⢙⣧⡐⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠿⠟⠿⠻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⠻⠛⠛⠛⠟⠻⠛⡻⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠛⠉⢀⠠⠖⠚⠒⠒⠀⠙⣿⣿⡿⢁⣾⣿⣫⡴⠞⠛⠛⠛⠓⠀⠀⡀⠀⠀⠙⠛⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀⣐⣤⣴⡤⠤⠤⠤⢤⡐⠬⣿⢷⠀⠐⢹⡿⠛⠛⣛⣛⣓⣛⡓⣶⣄⠀⣦⠈⠂⠎⢻⣧⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⠿⠵⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣳⡵⠀⠂⢴⣿⣿⣷⡿⠿⣿⣿⠿⣿⣿⣿⣿⣿⡉⣄⣀⣼⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡿⠻⢻⣷⣾⣿⣿⣿⡟⠉⣰⣿⣷⡌⠻⣿⣿⣿⣿⠀⠀⠀⣿⣿⠏⠀⣼⣿⣿⣷⡈⢹⣿⣿⣿⣿⣿⣿⡟⠿⢿⣷⣄⠀⠀ ⡇⢀⣶⠋⣥⢶⣿⣈⣽⣿⣿⣿⣿⣇⠀⢿⣿⣿⡟⢀⣿⣿⣿⣿⠀⠀⠸⣿⣿⣦⠀⠻⣿⣿⣿⢃⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⡙⣷⡀ ⣷⣾⠁⡼⢡⣿⠛⣡⣭⣙⠿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄⠛⣷⠀⢳⢘⣷ ⣿⣿⠀⠇⢸⣏⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢿⣿⣿⡿⠟⠛⠛⠀⠀⠈⠛⠛⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡀⢸⢰⣿ ⣿⢿⣧⠘⣾⣿⡄⢻⣿⣿⣿⢻⣿⣿⣿⣧⣄⡀⠈⠿⣷⣾⣷⣶⣤⣭⣂⣼⠿⣷⣬⡟⣁⣠⣴⣿⣿⣿⡟⣿⣿⣿⣿⡿⠉⣰⠂⣾⣾⡿ ⡇⠀⠿⣷⡈⠻⣷⡈⣿⣿⣿⣦⠘⡷⠈⢻⠛⠿⣿⣶⣦⣬⣄⣈⣉⣠⣿⣦⣤⣴⣿⣿⣿⠿⠟⡟⠻⠙⢠⣼⣿⣿⣿⠁⣼⠃⣼⣿⠟⠁ ⠃⠀⠀⠙⢿⣦⠹⠏⢻⣿⣿⣿⣧⣿⣧⣰⠀⡀⠛⠃⠊⠹⡟⠋⠛⣿⠿⠛⠛⡏⠉⠋⡇⠀⣀⠇⢰⣇⣶⣿⣿⣿⡿⢠⠎⣸⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⣿⣆⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣤⣸⠀⡇⢠⠀⣼⣠⣀⠀⡇⠀⡀⣄⣰⣿⣧⣾⣿⣿⣿⣿⣿⠃⡞⣰⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣟⣻⣿⣿⣿⡟⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⢹⣿⣿⣿⣿⣷⡟⠁⠀⠀⠀⠀ ⠀⠀⠐⠀⠀⠀⠈⠹⢿⡙⠻⣿⡇⢀⠇⣥⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠀⠀⣀⣸⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣆⠙⣿⣿⣆⣉⠁⠀⢋⠋⠀⡋⢹⡟⠉⢻⠋⠉⡏⠏⠀⢨⡀⠀⠀⡐⣾⣿⣿⣿⣿⢿⡧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⢸⡇⠙⠳⣌⠻⣿⣿⣆⠐⣼⣆⢠⠀⢻⣄⠀⢸⡂⠀⠂⡄⠀⢸⣷⣼⣶⣿⣿⠟⣻⣯⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡦⠀⠀⠀⢸⣧⠀⠀⠙⣷⣌⠛⢿⣿⣿⣿⣄⣠⣿⣄⡂⣸⣇⣀⢰⣿⣧⣾⣿⣿⠿⢋⣱⣾⣿⣇⠀⢸⡇⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⣸⣿⠁⠀⠀⠘⢨⣿⠀⣀⠻⣿⣿⣿⣦⣌⣙⠛⠿⠿⢿⣿⢿⣿⣿⡿⠿⠿⠿⠟⣿⣷⣶⣿⣿⣿⠋⠅⠀⠀⣇⠈⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⠇⠀⠀⠀⣠⡟⣣⣠⣍⣳⣾⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣠⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣂⠀⠀⢙⣧⡐ ⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠿⠟⠿⠻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⠻⠛⠛⠛⠟⠻⠛⡻⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠛⠉⢀⠠⠖⠚⠒⠒⠀⠙⣿⣿⡿⢁⣾⣿⣫⡴⠞⠛⠛⠛⠓⠀⠀⡀⠀⠀⠙⠛⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀⣐⣤⣴⡤⠤⠤⠤⢤⡐⠬⣿⢷⠀⠐⢹⡿⠛⠛⣛⣛⣓⣛⡓⣶⣄⠀⣦⠈⠂⠎⢻⣧⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⠿⠵⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣳⡵⠀⠂⢴⣿⣿⣷⡿⠿⣿⣿⠿⣿⣿⣿⣿⣿⡉⣄⣀⣼⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡿⠻⢻⣷⣾⣿⣿⣿⡟⠉⣰⣿⣷⡌⠻⣿⣿⣿⣿⠀⠀⠀⣿⣿⠏⠀⣼⣿⣿⣷⡈⢹⣿⣿⣿⣿⣿⣿⡟⠿⢿⣷⣄⠀⠀ ⡇⢀⣶⠋⣥⢶⣿⣈⣽⣿⣿⣿⣿⣇⠀⢿⣿⣿⡟⢀⣿⣿⣿⣿⠀⠀⠸⣿⣿⣦⠀⠻⣿⣿⣿⢃⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⡙⣷⡀ ⣷⣾⠁⡼⢡⣿⠛⣡⣭⣙⠿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄⠛⣷⠀⢳⢘⣷ ⣿⣿⠀⠇⢸⣏⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢿⣿⣿⡿⠟⠛⠛⠀⠀⠈⠛⠛⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡀⢸⢰⣿ ⣿⢿⣧⠘⣾⣿⡄⢻⣿⣿⣿⢻⣿⣿⣿⣧⣄⡀⠈⠿⣷⣾⣷⣶⣤⣭⣂⣼⠿⣷⣬⡟⣁⣠⣴⣿⣿⣿⡟⣿⣿⣿⣿⡿⠉⣰⠂⣾⣾⡿ ⡇⠀⠿⣷⡈⠻⣷⡈⣿⣿⣿⣦⠘⡷⠈⢻⠛⠿⣿⣶⣦⣬⣄⣈⣉⣠⣿⣦⣤⣴⣿⣿⣿⠿⠟⡟⠻⠙⢠⣼⣿⣿⣿⠁⣼⠃⣼⣿⠟⠁ ⠃⠀⠀⠙⢿⣦⠹⠏⢻⣿⣿⣿⣧⣿⣧⣰⠀⡀⠛⠃⠊⠹⡟⠋⠛⣿⠿⠛⠛⡏⠉⠋⡇⠀⣀⠇⢰⣇⣶⣿⣿⣿⡿⢠⠎⣸⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⣿⣆⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣤⣸⠀⡇⢠⠀⣼⣠⣀⠀⡇⠀⡀⣄⣰⣿⣧⣾⣿⣿⣿⣿⣿⠃⡞⣰⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣟⣻⣿⣿⣿⡟⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⢹⣿⣿⣿⣿⣷⡟⠁⠀⠀⠀⠀ ⠀⠀⠐⠀⠀⠀⠈⠹⢿⡙⠻⣿⡇⢀⠇⣥⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠀⠀⣀⣸⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣆⠙⣿⣿⣆⣉⠁⠀⢋⠋⠀⡋⢹⡟⠉⢻⠋⠉⡏⠏⠀⢨⡀⠀⠀⡐⣾⣿⣿⣿⣿⢿⡧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⢸⡇⠙⠳⣌⠻⣿⣿⣆⠐⣼⣆⢠⠀⢻⣄⠀⢸⡂⠀⠂⡄⠀⢸⣷⣼⣶⣿⣿⠟⣻⣯⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡦⠀⠀⠀⢸⣧⠀⠀⠙⣷⣌⠛⢿⣿⣿⣿⣄⣠⣿⣄⡂⣸⣇⣀⢰⣿⣧⣾⣿⣿⠿⢋⣱⣾⣿⣇⠀⢸⡇⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⣸⣿⠁⠀⠀⠘⢨⣿⠀⣀⠻⣿⣿⣿⣦⣌⣙⠛⠿⠿⢿⣿⢿⣿⣿⡿⠿⠿⠿⠟⣿⣷⣶⣿⣿⣿⠋⠅⠀⠀⣇⠈⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⠇⠀⠀⠀⣠⡟⣣⣠⣍⣳⣾⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣠⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣂⠀⠀⢙⣧⡐⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠿⠟⠿⠻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⠻⠛⠛⠛⠟⠻⠛⡻⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠛⠉⢀⠠⠖⠚⠒⠒⠀⠙⣿⣿⡿⢁⣾⣿⣫⡴⠞⠛⠛⠛⠓⠀⠀⡀⠀⠀⠙⠛⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀⣐⣤⣴⡤⠤⠤⠤⢤⡐⠬⣿⢷⠀⠐⢹⡿⠛⠛⣛⣛⣓⣛⡓⣶⣄⠀⣦⠈⠂⠎⢻⣧⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⠿⠵⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣳⡵⠀⠂⢴⣿⣿⣷⡿⠿⣿⣿⠿⣿⣿⣿⣿⣿⡉⣄⣀⣼⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡿⠻⢻⣷⣾⣿⣿⣿⡟⠉⣰⣿⣷⡌⠻⣿⣿⣿⣿⠀⠀⠀⣿⣿⠏⠀⣼⣿⣿⣷⡈⢹⣿⣿⣿⣿⣿⣿⡟⠿⢿⣷⣄⠀⠀ ⡇⢀⣶⠋⣥⢶⣿⣈⣽⣿⣿⣿⣿⣇⠀⢿⣿⣿⡟⢀⣿⣿⣿⣿⠀⠀⠸⣿⣿⣦⠀⠻⣿⣿⣿⢃⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⡙⣷⡀ ⣷⣾⠁⡼⢡⣿⠛⣡⣭⣙⠿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄⠛⣷⠀⢳⢘⣷ ⣿⣿⠀⠇⢸⣏⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢿⣿⣿⡿⠟⠛⠛⠀⠀⠈⠛⠛⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡀⢸⢰⣿ ⣿⢿⣧⠘⣾⣿⡄⢻⣿⣿⣿⢻⣿⣿⣿⣧⣄⡀⠈⠿⣷⣾⣷⣶⣤⣭⣂⣼⠿⣷⣬⡟⣁⣠⣴⣿⣿⣿⡟⣿⣿⣿⣿⡿⠉⣰⠂⣾⣾⡿ ⡇⠀⠿⣷⡈⠻⣷⡈⣿⣿⣿⣦⠘⡷⠈⢻⠛⠿⣿⣶⣦⣬⣄⣈⣉⣠⣿⣦⣤⣴⣿⣿⣿⠿⠟⡟⠻⠙⢠⣼⣿⣿⣿⠁⣼⠃⣼⣿⠟⠁ ⠃⠀⠀⠙⢿⣦⠹⠏⢻⣿⣿⣿⣧⣿⣧⣰⠀⡀⠛⠃⠊⠹⡟⠋⠛⣿⠿⠛⠛⡏⠉⠋⡇⠀⣀⠇⢰⣇⣶⣿⣿⣿⡿⢠⠎⣸⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⣿⣆⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣤⣸⠀⡇⢠⠀⣼⣠⣀⠀⡇⠀⡀⣄⣰⣿⣧⣾⣿⣿⣿⣿⣿⠃⡞⣰⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣟⣻⣿⣿⣿⡟⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⢹⣿⣿⣿⣿⣷⡟⠁⠀⠀⠀⠀ ⠀⠀⠐⠀⠀⠀⠈⠹⢿⡙⠻⣿⡇⢀⠇⣥⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠀⠀⣀⣸⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣆⠙⣿⣿⣆⣉⠁⠀⢋⠋⠀⡋⢹⡟⠉⢻⠋⠉⡏⠏⠀⢨⡀⠀⠀⡐⣾⣿⣿⣿⣿⢿⡧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⢸⡇⠙⠳⣌⠻⣿⣿⣆⠐⣼⣆⢠⠀⢻⣄⠀⢸⡂⠀⠂⡄⠀⢸⣷⣼⣶⣿⣿⠟⣻⣯⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡦⠀⠀⠀⢸⣧⠀⠀⠙⣷⣌⠛⢿⣿⣿⣿⣄⣠⣿⣄⡂⣸⣇⣀⢰⣿⣧⣾⣿⣿⠿⢋⣱⣾⣿⣇⠀⢸⡇⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⣸⣿⠁⠀⠀⠘⢨⣿⠀⣀⠻⣿⣿⣿⣦⣌⣙⠛⠿⠿⢿⣿⢿⣿⣿⡿⠿⠿⠿⠟⣿⣷⣶⣿⣿⣿⠋⠅⠀⠀⣇⠈⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⠇⠀⠀⠀⣠⡟⣣⣠⣍⣳⣾⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣠⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣂⠀⠀⢙⣧⡐ ⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠿⠟⠿⠻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⠻⠛⠛⠛⠟⠻⠛⡻⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠛⠉⢀⠠⠖⠚⠒⠒⠀⠙⣿⣿⡿⢁⣾⣿⣫⡴⠞⠛⠛⠛⠓⠀⠀⡀⠀⠀⠙⠛⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀⣐⣤⣴⡤⠤⠤⠤⢤⡐⠬⣿⢷⠀⠐⢹⡿⠛⠛⣛⣛⣓⣛⡓⣶⣄⠀⣦⠈⠂⠎⢻⣧⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⠿⠵⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣳⡵⠀⠂⢴⣿⣿⣷⡿⠿⣿⣿⠿⣿⣿⣿⣿⣿⡉⣄⣀⣼⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡿⠻⢻⣷⣾⣿⣿⣿⡟⠉⣰⣿⣷⡌⠻⣿⣿⣿⣿⠀⠀⠀⣿⣿⠏⠀⣼⣿⣿⣷⡈⢹⣿⣿⣿⣿⣿⣿⡟⠿⢿⣷⣄⠀⠀ ⡇⢀⣶⠋⣥⢶⣿⣈⣽⣿⣿⣿⣿⣇⠀⢿⣿⣿⡟⢀⣿⣿⣿⣿⠀⠀⠸⣿⣿⣦⠀⠻⣿⣿⣿⢃⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⡙⣷⡀ ⣷⣾⠁⡼⢡⣿⠛⣡⣭⣙⠿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄⠛⣷⠀⢳⢘⣷ ⣿⣿⠀⠇⢸⣏⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢿⣿⣿⡿⠟⠛⠛⠀⠀⠈⠛⠛⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⡀⢸⢰⣿ ⣿⢿⣧⠘⣾⣿⡄⢻⣿⣿⣿⢻⣿⣿⣿⣧⣄⡀⠈⠿⣷⣾⣷⣶⣤⣭⣂⣼⠿⣷⣬⡟⣁⣠⣴⣿⣿⣿⡟⣿⣿⣿⣿⡿⠉⣰⠂⣾⣾⡿ ⡇⠀⠿⣷⡈⠻⣷⡈⣿⣿⣿⣦⠘⡷⠈⢻⠛⠿⣿⣶⣦⣬⣄⣈⣉⣠⣿⣦⣤⣴⣿⣿⣿⠿⠟⡟⠻⠙⢠⣼⣿⣿⣿⠁⣼⠃⣼⣿⠟⠁ ⠃⠀⠀⠙⢿⣦⠹⠏⢻⣿⣿⣿⣧⣿⣧⣰⠀⡀⠛⠃⠊⠹⡟⠋⠛⣿⠿⠛⠛⡏⠉⠋⡇⠀⣀⠇⢰⣇⣶⣿⣿⣿⡿⢠⠎⣸⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⣿⣆⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣤⣸⠀⡇⢠⠀⣼⣠⣀⠀⡇⠀⡀⣄⣰⣿⣧⣾⣿⣿⣿⣿⣿⠃⡞⣰⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣟⣻⣿⣿⣿⡟⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⢹⣿⣿⣿⣿⣷⡟⠁⠀⠀⠀⠀ ⠀⠀⠐⠀⠀⠀⠈⠹⢿⡙⠻⣿⡇⢀⠇⣥⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠀⠀⣀⣸⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣆⠙⣿⣿⣆⣉⠁⠀⢋⠋⠀⡋⢹⡟⠉⢻⠋⠉⡏⠏⠀⢨⡀⠀⠀⡐⣾⣿⣿⣿⣿⢿⡧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⢸⡇⠙⠳⣌⠻⣿⣿⣆⠐⣼⣆⢠⠀⢻⣄⠀⢸⡂⠀⠂⡄⠀⢸⣷⣼⣶⣿⣿⠟⣻⣯⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡦⠀⠀⠀⢸⣧⠀⠀⠙⣷⣌⠛⢿⣿⣿⣿⣄⣠⣿⣄⡂⣸⣇⣀⢰⣿⣧⣾⣿⣿⠿⢋⣱⣾⣿⣇⠀⢸⡇⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⣸⣿⠁⠀⠀⠘⢨⣿⠀⣀⠻⣿⣿⣿⣦⣌⣙⠛⠿⠿⢿⣿⢿⣿⣿⡿⠿⠿⠿⠟⣿⣷⣶⣿⣿⣿⠋⠅⠀⠀⣇⠈⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⠇⠀⠀⠀⣠⡟⣣⣠⣍⣳⣾⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣠⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣂⠀⠀⢙⣧⡐
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My SUSSY POWERS ARE AWAKENING ?? Part 1. I just did my daily jackoff ☺️ to my impostor body pillow, ? but when I came, ? I started floating, ? and think I got teleported into the skeld. ? I swear for a second I felt the imposter's strong hands grip my asscheeks.? ? ? I immediately was transported back to earth, ? and I instantly got on all fours on my bed naked, ? as you would, and started screaming in my best efforts to summon the imposter ? “IM READY FUCK ME FUCK ME FUCK ME FUCK ME PLEASE DADDY IMPOSTER” I was so close to feeling the imposters sweet cock fuck the shit out of me ? but then my NAZI RACIST mother came in and beat the shit out of me. ???☹️ She then said I was going to a magical place called the “mental asylum” ? I’m not too sure where that dimension is located but it sounds EPIC ?
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⢿⣿⣿⣿⣭⠹⠛⠛⠛⢿⣿⣿⣿⣿⡿⣿⠷⠶⠿⢻⣿⣛⣦⣙⠻⣿ ⣿⣿⢿⣿⠏⠀⠀⡀⠀⠈⣿⢛⣽⣜⠯⣽⠀⠀⠀⠀⠙⢿⣷⣻⡀⢿ ⠐⠛⢿⣾⣖⣤⡀⠀⢀⡰⠿⢷⣶⣿⡇⠻⣖⣒⣒⣶⣿⣿⡟⢙⣶⣮ ⣤⠀⠀⠛⠻⠗⠿⠿⣯⡆⣿⣛⣿⡿⠿⠮⡶⠼⠟⠙⠊⠁⠀⠸⢣⣿ ⣿⣷⡀⠀⠀⠀⠀⠠⠭⣍⡉⢩⣥⡤⠥⣤⡶⣒⠀⠀⠀⠀⠀⢰⣿⣿ ⣿⣿⡽⡄⠀⠀⠀⢿⣿⣆⣿⣧⢡⣾⣿⡇⣾⣿⡇⠀⠀⠀⠀⣿⡇⠃ ⣿⣿⣷⣻⣆⢄⠀⠈⠉⠉⠛⠛⠘⠛⠛⠛⠙⠛⠁⠀⠀⠀⠀⣿⡇⢸ ⢞⣿⣿⣷⣝⣷⣝⠦⡀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠛⣿⠈ ⣦⡑⠛⣟⢿⡿⣿⣷⣝⢧⡀⠀⠀⣶⣸⡇⣿⢸⣧⠀⠀⠀⠀⢸⡿⡆ ⣿⣿⣷⣮⣭⣍⡛⠻⢿⣷⠿⣶⣶⣬⣬⣁⣉⣀⣀⣁⡤⢴⣺⣾⣽⡇
beans
hey vsauce michael here
beans
like shart subscribe
oooooooooooooooooooooooogh
this site doesnt even check emails for verification lmao
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭
butthongminhatalkpen5
Bút Thông Minh ATalk Pen 5 Dịch Chuẩn Xác, Giá Tốt butthongminhatalkpen5_mpdvn Atalk Pen 5 là bút dịch thuật thông minh thế hệ mới, cho phép dịch OFFLINE tiếng Việt và nhiều ngôn ngữ khác mà không cần kết nối Internet. Sản phẩm tích hợp công nghệ AI tiên tiến, hỗ trợ dịch giọng nói 2 chiều, quét – scan văn bản, trích xuất nội dung sang máy tính/điện thoại, dịch ghi âm và dịch hình ảnh qua camera hiện đại. Với độ chính xác lên đến 98% và tốc độ phản hồi chỉ 0,5 giây, Atalk Pen 5 trở thành trợ thủ đắc lực cho học tập, công việc và du lịch. Bút hỗ trợ kết nối Wi-Fi, Bluetooth, thẻ nhớ ngoài, đáp ứng nhu cầu dịch thuật mọi lúc, mọi nơi, ngay cả khi không có mạng. https://www.akaqa.com/question/q19192576364-But-thong-minh-atalk-pen-5
coachingmarketing
Coaching Marketing dong hanh xay dung chien luoc tiep thi ben vung coachingmarketing_stm Nhieu doanh nghiep gap kho khan trong marketing do thieu chien luoc tong the, xac dinh sai doi tuong va khong do luong hieu qua. Coaching marketing mang den giai phap huan luyen chuyen sau, giup toi uu tiep can khach hang va nang cao hieu suat. SIEU TOC MARKETING voi chuyen gia Vo Tuan Hai truc tiep coaching, ap dung mo hinh Ma Tran Bao Vay doc quyen de xay dung lo trinh ca nhan hoa. Doanh nghiep se tiet kiem thoi gian thu sai, hieu ro khach hang va co chien luoc dai han. Day la nen tang giup he thong hoa quy trinh va but pha doanh thu ben vung. [http://ofbiz.116.s1.nabble.com/Coaching-Marketing-td4911246.html](http://ofbiz.116.s1.nabble.com/Coaching-Marketing-td4911246.html)
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄