yall who tf is Alexandra and why are you all beefing over her 😟

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⡀⠀⠀⠀⠀⠀⣼⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣻⣧⠀⠀⠀⠀⢠⣿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⣿⡆⠀⠀⠀⣼⣿⠀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢸⣧⠀⠀⢠⣿⣿⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠘⣿⣤⠀⢸⣿⣿⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⢿⡇⠀⢸⣿⣿⠀⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⢸⡇⠀⢿⣿⣿⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⢸⡇⠀⢸⣿⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⡇⠀⠀⣿⡿⢸⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣼⡗⠄⠀⣿⣇⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣇⣰⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⡟⢻⣿⣿⣿⠞⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠂⠀⠀⢀⡥⣧⣟⠻⣿⣟⣾⡷⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡀⠀⠀⠘⢺⣾⣿⣖⣗⣿⠁⠠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠆⠀⠀⢀⡻⣭⠿⢋⡁⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡇⠀⠀⠀⠀⣙⠳⠾⠋⣠⡀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠈⠛⠶⠞⠋⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣄⠀⠀ ⠀⠀⠀⠀⣿⣫⣭⢤⠭⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢿⡍⣿⣦⠀ ⠀⠀⠀⢠⡿⡇⢹⡆⠀⠙⠻⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠛⠛⠉⠁⠦⢋⣿⡆ ⠀⠀⠀⢼⡇⠃⠀⠀⠀⢰⡷⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⣻⠀⠀⠀⠈⣷⠃ ⠀⠀⠀⠘⣷⡀⠀⢠⣀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⣴⠟⣴⣿⠏⠀ ⠀⠀⠀⠀⠈⣷⣤⣆⡙⣧⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣷⠾⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⣿⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣅⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⣯⣍⡛⢷⡄⠀⠀⠀⠀⠀ ⠀⠀⢀⡤⠤⠤⣤⣤⣤⣬⣿⣿⣿⣷⣄⡀⠀⣀⣀⣀⣀⡠⠤⠤⠤⠔⠒⠒⠉⠁⠀⠀⠈⣿⣰⠟⠀⠀⠀⠀⠀ ⢀⣴⠏⠛⠛⣃⣀⡙⢿⣿⣿⣿⣿⣿⣿⣿⣟⡗⠈⠉⠉⠙⠛⠛⠛⠛⠳⠤⠤⠤⠤⠤⠞⠋⠀⠀⠀⠀⠀⠀⠀ ⠸⣧⡀⢀⡾⠃⠀⠀⠀⢉⣟⡻⠟⠋⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠚⠳⠦⠶⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⡀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⣟⣧⠀⠀⠀⠀⠀⠀⣼⣿⠀⣿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⢹⣿⢷⡀⠀⠀⠀⠀⣿⡟⠀⢻⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠀⢹⣞⢻⣆⠀⠀⠀⣿⣇⠀⠘⡇⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⡇⠀⠙⢾⡟⢧⡀⠀⢿⣿⠀⠀⣷⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣆⠀⠈⢳⣴⣹⡄⠘⣿⡄⠀⣿⠀⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣳⣀⠀⠹⣶⣿⣆⢻⣿⠀⣿⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢻⣷⣄⠘⣯⠹⣬⣿⣦⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣾⣷⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⡿⢿⣷⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠀⢸⣿⠀⢷⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢸⣿⣿⡅⢸⣿⣾⢿⣛⣻⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣧⣿⣿⣿⣷⣿⣿⠿⠿⠓⠒⠚⠛⢷⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⢶⣶⣿⣽⣿⠿⢯⢽⡥⣿⣏⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠴⠞⡹⢿⣟⠉⠀⠀⠙⢦⣁⣼⠁⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠳⢤⣄⣀⠀⠉⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⣀⣀⣀⣤⣤⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡼⠿⣷⣄⠀⠀⠈⣿⡍⠉⠉⠉⠉⠂⠀⢈⡁⠁⠀⢿⡇⠀ ⠀⠀⠀⣀⣀⣠⠴⠶⠋⣸⣠⣆⡉⣹⣦⠀⠀⣁⠉⢳⡄⠀⠀⢀⣀⣹⣯⣽⣷⣿⡇⠀ ⣠⡶⠻⠍⠛⠓⠛⠶⠶⠮⢭⣿⡽⢾⢾⣧⠀⠈⢧⠀⢿⡶⠒⠋⠉⢹⡅⢽⣿⡿⠁⠀ ⢿⡇⢠⠀⠁⠐⠂⠀⢀⣉⣼⣏⣰⢾⣿⣿⣆⠀⠀⠀⠈⢧⠀⠀⢀⣾⣿⣿⡟⠁⠀⠀ ⠀⠙⠓⠒⠶⠞⠒⠛⠛⠛⠛⢻⠃⠀⠃⢷⠙⣦⠀⠀⠀⠈⠻⣦⣯⡤⣤⣼⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠻⡄⠀⠀⠀⠀⢺⠛⠦⣤⡄⠀⠈⢷⡇⠇⢸⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠛⢀⣀⣀⣀⡈⣷⡦⠾⠃⠀⠀⠘⣿⣄⡼⢹⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢶⣿⣿⣉⣀⣶⠋⠀⠀⠀⠀⠀⠀⣸⢷⣁⣾⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣇⢹⡟⠙⣇⠀⠀⠀⠀⠀⢠⣿⢸⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⣿⣼⠇⠀⠙⣆⠀⠀⠀⢠⡾⢁⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠮⡿⠀⣦⣀⢙⣷⣤⣴⣿⣾⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠠⣶⡾⣴⣿⠿⣌⣽⣿⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢉⣿⣿⡾⠆⢨⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢤⡾⣿⠉⠉⠀⢸⣯⢳⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠜⡂⢚⣿⠁⠀⠀⢰⡏⠸⡏⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣍⣠⠵⣾⣇⠀⠠⣴⡟⠀⢸⢣⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠂⢰⢤⡿⣄⣐⠚⣸⠘⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⢻⡏⠁⠀⢸⡿⠀⠀⠙⠛⠃⢠⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣿⠁⠀⠀⢸⡷⣾⣁⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣼⣿⠄⠀⠀⠈⡀⠀⠈⣹⠿⠖⠛⠒⠶⢤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡈⠳⣄⡀⠀⣁⡴⠛⠁⠀⠀⠀⠀⢠⡀⠹⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠉⠋⠉⠀⠀⠀⠐⢦⠀⠀⠀⢱⡀⢹⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣀⡀⠀⠀⠀⠈⣇⠀⠀⢨⣿⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⣀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡷⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢚⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡞⢁⡠⢿⡿⠁⠀⠀⠀⢀⡀⠀ ⠀⠀⠀⠀⠀⣰⣇⣰⠞⣰⠟⠀⠀⣀⣤⣶⣿⠃⠀ ⠀⠀⠀⠀⠀⡟⢻⣣⣾⡥⠶⣾⡿⢟⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⢳⣾⣿⣯⣶⣭⠵⠖⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⠛⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣿⣿⣽⣦⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠉⡿⠋⢻⣿⡿⢿⣻⡿⢿⣶⣦⠄⠀⠀⠀⠀ ⠀⠀⠚⠻⣍⡀⠀⠀⠘⠲⢃⡠⠚⠁⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⢙⣶⡄⢧⢤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠯⣿⡎⠳⣌⣑⣢⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣐⠺⣷⡴⢋⣽⣿⣷⣿⠀⠀ ⠀⠀⠀⠀⣀⡀⠀⣏⡿⣷⠛⣷⢾⠟⠛⠉⠀⠀⠀ ⠀⠀⠀⢰⣿⣿⣶⣿⣳⡟⠚⠋⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣏⣿⣿⠟⢿⡟⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⠛⣿⡀⢸⡁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⢻⡇⠘⡗⠒⣟⠋⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠁⣀⣧⠀⠸⡇⠸⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡆⠀⢸⡀⢰⢇⢐⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢳⠀⠀⣧⠏⢸⣿⣠⡴⠒⠒⠲⡄ ⠀⢀⣀⣀⣀⣀⣨⣆⠀⠸⣆⣈⣷⠟⠁⢠⠀⣳⡇ ⣴⠋⡠⠀⠉⠻⣅⠈⢠⣤⡿⠤⢄⣀⣀⠼⠞⠋⠀ ⠙⣞⠀⢠⠀⠀⠈⠉⢉⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠒⠚⠢⠤⠤⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠋⠉⠈⠉⠉⠉⠉⠉⠉⠙⢹⣧⠀⠀⠀⢣⡀⠀⠀⠹⡆⠀⠀⠀⠀⢻⡗⠊⠻⣿⠏⠀⠀⠀⠐⡞⠀⠀⣰⠃⠀⢀⣾⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⡉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣆⠀⠀⠈⢷⠀⠀⠀⢹⡀⠀⠀⠀⠘⡇⠀⢰⣿⠀⠀⠀⠀⢠⠃⠀⣰⠇⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠐⠀⠀⠀⠒⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⢧⡀⠀⠈⣷⠀⠀⠀⠀⣿⠀⣿⡏⠀⠀⠀⠀⣿⠀⣰⠃⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠳⡀⠀⠸⡆⠀⠀⠀⣿⠇⣻⡇⠀⠀⠀⢐⣇⡼⠁⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠹⣆⠀⢿⠀⠀⠀⣿⣶⣿⡇⠀⠀⣀⣸⡟⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠈⢳⣼⠀⠀⠀⣿⣿⣿⡷⣶⡿⠛⠹⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠒⠒⠒⠒⠻⠿⢧⠀⠀⠀⢹⠀⠀⠴⠻⠛⡡⠞⣋⣈⡽⠶⠶⣶⣏⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢳⡄⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⣅⠉⠛⠋⠉⠉⠙⡟⡿⢶⣄⠀⠀⠀⣰⢾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⣹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⢳⡀⠀⠀⠀⠀⡇⡇⠀⢻⡀⠀⠀⡟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠙⡄⠀⠀⠀⢳⡀⠀⠀⠀⠇⡇⠀⣿⡇⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⡆⠀⠀⠀⠀⠁⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⡇⢸⡇⠀⠀⣿⢸⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠈⠳⣄⣀⠀⠀⠀⠈⣧⠀⠀⠀⡇⣾⠁⠀⠀⣿⣾⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⡶⠋⠀⠀⣸⠃⠈⠉⠛⠒⢦⣬⣇⠀⠀⣷⡏⠀⠀⢰⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⣧⠘⣦⢘⡿⠀⠀⠀⢸⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠇⠀⠀⢘⣀⣤⣤⣤⣤⣤⣤⣤⣤⣽⡀⠀⣿⠤⣤⣤⣤⡤⠤⢽⠀⠘⣿⣧⠀⠀⠠⣾⢸⢀⣀⣀⣠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢒⣠⣯⠤⠤⣤⣬⣷⣄⣀⠈⠙⠛⠛⠃⢀⡞⢀⣀⣙⣦⣈⠉⠉⢀⣴⣿⡤⠴⢚⣻⠶⣶⡞⡿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡋⣁⣀⣀⣀⠀⠀⠈⠉⠙⠻⠭⣲⡦⣾⣿⡯⠽⠶⠶⠿⠯⣩⡽⢛⣉⠤⠖⠋⠉⢀⣀⣀⣙⣇⡿⠀⠀⠴⠦⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⣒⣢⠴⢯⣛⠊⠛⠦⣄⡀⢀⡴⠓⡺⣯⢤⡒⠛⠋⠉⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⠂⠀⠀⠀⠀⣤⣄⠀⣴⡇⣼⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠿⠥⠤⠒⠺⡗⢦⣀⡀⠀⢻⠉⢀⣠⣴⡟⠋⠙⢦⡛⠛⠛⠓⠒⠒⠤⣶⣷⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣾⣿⣀⣤⠤⠒⠒⠉⠙⠊⠀⠀⠀⠀⠐⢦⡀⣱⠀⠈⠉⠉⣿⠉⠉⠁⢸⣡⠀⠀⠀⠙⠀⠀⠀⠀⠀⢠⣿⣏⠀⠀⠈⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠀⠀⠀⠀⡏⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡄⠀⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⠃⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣦⣾⣶⣴⣶⣶⣿⣿⣿⣿⣷⣾⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣄⣀⣈⣀⣀⣠⠇⠀⠀⠀⠀⠀⠀⣠⣴⠟⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠶⢦⣤⡤⠤⠤⠤⠤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣭⣵⣴⣌⣿⣧⣄⣤⣄⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⡀⠈⡿⠑⠒⢶⡒⠤⠤⠤⠤⠤⢲⣶⠒⠚⣏⠁⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢀⠔⠋⠉⠉⠙⠳⣄⠀⠈⢳⡀⠀⠀⠀⢀⡞⡟⠀⠀⠘⡆⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀⠀⠈⠛⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⡴⠃⠀⠀⠀⠀⠀⠀⠹⣟⢦⡈⣇⠀⠀⠀⠉⢰⠃⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣙⣾⡦⠤⠤⠤⠿⠶⠖⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⣿⣟⣁⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⣠⣤⣴⣶⣶⣶⣶⣶⣦⣤⣄⣀⣀⣀⣀⣠⣤⣤⣤⣤⣄⣀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠿⠟⠛⢿⣿⣿⣿⣿⣿⠟⠉⢿⠉⠉⠉⠉⠙⢛⡟⠛⣿⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⢊⢧⡀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢸⣿⣿⣿⠟⠁⠀⠀⠘⡎⠀⠀⠀⣀⡞⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⠔⠊⠉⠐⠂⠠⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠇⠀⢠⡤⢤⢤⣀⡀⠀⠈⠉⠐⠐⠢⠤⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠣⡀⠀⠑⢧⡘⢤⢋⠵⡒⠦⡤⢄⣀⣀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠀⠉⠀⠒⠒⠄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢂⠀⠈⠳⡌⢎⠴⡉⢖⡡⢋⠴⢡⢋⡝⡱⢒⠖⡲⢒⠖⡲⢒⠖⣒⡒⣒⢒⠲⠴⠤⢤⠤⣄⡀⠀⠈⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⡄⠀⠘⢮⡒⡙⢶⣥⣍⣎⣆⠣⡔⣡⠋⡬⣑⠩⢬⠱⢩⡘⢤⠱⢌⡊⢥⠋⡜⢢⠓⡤⢋⡝⡢⣄⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠢⡀⠀⠈⠫⣆⡌⡻⢾⣹⡟⣽⡭⢿⣹⡽⣻⢯⣟⢿⡻⢯⡷⣞⡾⣤⣯⣌⣱⢊⡔⠣⣌⡑⠦⡱⢄⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠈⠑⠵⣢⢍⡛⠾⣽⣫⢷⣹⢧⡟⣮⢯⣽⢻⡼⣝⣳⣏⡾⣭⣛⣯⢾⣵⡰⢌⠥⢃⠭⣣⡀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠈⠙⠚⠵⠦⣩⣋⡛⡞⠻⠷⢯⠾⡭⠷⢯⣷⣾⣵⣯⣷⣞⣳⡾⣝⡷⣬⣃⠚⣄⠳⡄⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠤⣧⣼⠧⣘⢠⣠⣄⣤⣠⣘⡄⣛⡛⠿⢧⣟⣟⢠⢛⢻⡀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠚⠉⠀⠀⣀⡤⢴⠒⣎⢫⠱⢌⠲⢡⠒⡴⣈⠦⢡⢋⡝⣫⢞⡵⣊⠬⣙⠳⣎⢆⢳⡀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡔⠁⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠁⠀⠀⣀⡠⢴⠲⣙⠢⢍⢆⡹⢠⠎⣑⢪⢡⣣⣩⣔⣢⣍⣆⡣⢔⢢⢃⢻⣦⢱⢌⠣⡜⢨⢒⢳⡀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢇⠀⠈⠻⣍⠏⡕⠲⠦⢤⢤⡒⢖⠪⣍⠣⡜⢂⠳⣠⢋⣆⣮⣴⡷⣞⠿⣏⣿⣹⣳⣽⡶⠿⣚⢛⠻⠷⡾⢯⡽⣋⢌⣳⠼⢧⡊⠖⣳⡀⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠑⢀⠀⠀⠙⠮⣱⡉⢖⢢⡉⣬⡵⣤⣷⣼⣳⢷⡻⣟⡽⣣⢿⡼⣫⣟⣽⢶⣛⡩⠴⠦⠓⠒⠛⠚⠓⠚⣥⢷⣌⡾⢡⡙⢼⣡⢋⠴⡙⡲⣄⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠢⠄⠀⠀⠙⠺⠴⣘⣢⠙⣛⠺⠶⢯⠷⠿⠵⠿⡭⣷⡻⠯⠛⠉⠁⠀⠀⢀⣀⣀⡤⠀⠀⣠⢞⡍⡞⢬⡶⢷⡘⢼⢂⢎⡒⠥⣑⢪⠳⡀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠀⠤⣀⠀⠀⠉⠙⠒⠛⠮⠦⠷⠼⠓⠛⠉⠁⠀⢀⡠⠄⠐⠊⠉⠀⠀⠜⠀⢀⣔⠳⠌⡴⣩⠏⢦⢹⡜⢢⡉⢦⡘⣑⠢⠥⡩⠽⡄⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠠⠠⠀⣀⣀⣀⣀⠠⠤⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⡈⠀⢀⡞⣌⡷⢩⢴⢣⡙⣂⠻⡘⢤⠓⢢⠜⣄⢫⣔⠡⣃⢷⠀⠀⠉⠂⢤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⡼⢱⢸⢇⠣⣾⡥⠶⠓⣯⠵⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠉⠑⠢⣀⠀⠈⠠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⣯⠖⡻⢌⢣⣿⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢷⡀⠀⠱⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠁⠀⣼⣟⡠⡵⢮⣖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠈⠀⢠⣶⢷⡶⠑⡈⠁⠀⠀⣀⡠⠤⠐⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣸⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⡠⠒⢹⢯⠏⠀⣜⡠⠔⠊⣉⡠⠤⠔⠒⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠃⠀⣰⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡎⠀⠀⠘⠃⠠⢪⡣⠔⠂⠉⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠠⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠐⠒⠒⣈⣹⠽⠙⢣⣠⣤⣀⡂⠀⠁⢧⠐⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢔⡎⠀⢀⠔⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⣀⠤⠐⠊⠉⢀⢴⠒⠉⢼⠀⠀⠀⠈⠉⠀⠊⠓⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡚⣌⠒⡇⠀⢰⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠉⠀⠀⠀⢠⠊⠁⡄⡆⠀⠈⢣⡄⠒⢠⣤⣤⣤⣤⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⡎⠓⣴⠑⢢⡍⣷⠀⠀⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠉⠀⠀⠉⠘⣠⠆⠈⠀⡠⠋⠂⠂⠉⠀⠀⠀⠀⠀⠉⠑⠒⠛⠽⣭⣳⣽⣇⠀⠀⢀⠀⠀⠀⠀⠀⣀⠴⣪⣅⡓⢬⢑⢢⡑⠎⡴⣘⡄⠀⠱⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣷⣾⡄⠀⠐⠀⠀⣾⡆⠀⠀⢀⣴⡶⠿⠿⠷⣶⣄⠀⠀⠀⠀⠀⢸⣿⢿⣆⠀⠸⡀⠀⣀⠔⠋⠀⠀⠀⠀⠉⠒⠭⡆⡜⡱⡐⠦⡹⡄⠀⠐⢄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⡟⢿⣆⠀⠀⠀⣿⡇⠀⢰⣿⠋⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠸⡻⢿⡿⠀⠀⢣⠞⠁⠀⡀⠀⠁⠁⠀⠢⠀⠀⠈⠳⢕⠬⣑⡑⣚⢆⠀⠀⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⡇⠈⢻⣦⠀⠀⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⡸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠙⢴⡘⠤⣫⠃⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⡇⠀⠀⠹⣷⡀⣿⡇⠀⢿⣧⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⡀⠀⠈⠉⠉⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠈⠳⡣⠋⠀⡠⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⡇⠀⠀⠀⠙⣷⣿⡇⠀⠈⢿⣦⣀⠀⠀⢀⣠⡿⠃⠀⢠⠒⠉⠀⠈⠐⠐⠀⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⢠⠔⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠛⠃⠀⢸⢄⠀⠈⠛⠃⠀⠀⠀⠉⠛⠛⠛⠛⠋⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠤⠤⠔⠉⠈⠒⠤⠤⠤⠄⠁⠑⠢⠤⠀⠤⠤⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠞⣿⣿⠿⠛⢋⣍⣙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠋⠰⠏⣡⡶⠛⡏⠉⠙⣷⣌⣻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠈⠋⣠⣼⠃⠀⠀⠙⢿⣄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢤⣤⣶⣾⣿⣷⣄⠀⠀⠀⠀⣿⣷⣦⣄⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⡿⠀⠀⠀⠀⡼⢿⣿⣿⡟⢻⣿⣆⠀⠀⠀⣿⣿⣻⣿⣧⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢠⡇⠀⠀⠀⣸⠃⢸⣿⣿⣿⣿⣿⣿⡆⠀⠘⣿⣿⣿⣿⣿⣇⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣸⠇⠀⠀⢠⣏⠀⠈⢿⣿⣿⣿⡿⠟⣇⠀⣤⣿⠻⠿⠿⠟⢹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⢠⣿⣤⠤⠞⣫⠟⠀⠀⠀⠉⠉⢁⣠⣴⣿⣿⣿⣿⣧⣀⣀⣀⣀⣙⡿⢧⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⢀⣀⡤⣶⠶⠒⣛⣿⣿⠿⠿⠭⢽⡿⠼⣿⠻⡷⠤⢤⣉⡃⠀⠑⠦⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢠⣾⣷⠏⣠⠴⠒⠊⠉⠁⢀⣠⠿⢒⡿⠋⠀⢹⠀⠀⠀⠀⡇⠀⡏⠀⢹⡀⠀⠀⠉⠙⠒⠤⣄⡙⠢⡀⠀ ⠀⠀⢀⡼⠃⠀⠀⠀⣠⣴⡿⠋⠁⠐⠁⠀⠀⣠⠴⠚⠉⠀⢠⠎⠀⠀⢀⣨⣇⠀⠀⢸⠁⣰⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡆ ⠀⢀⡞⠀⣀⣤⠶⣻⣿⠋⠀⠀⠀⢀⡠⠖⠋⠀⠀⠀⠀⠀⠉⠀⠀⠚⠉⠀⠈⠓⠒⠟⠋⠁⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀ ⠀⣼⡶⠟⠉⠀⠀⢩⣷⡄⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣠⡾⢥⣄⣀⣀⣀⣀⣀⣤⣴⠞⠉⠀⠀ ⢸⡏⠀⠀⠀⠀⠀⠸⣿⣷⣯⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠙⠳⣄⠀⠀⠀⠀⠀⠀⣸⠋⠂⠀⠀⠀⠙⡇⠀⠀⠈⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⣠⡾⠋⠹⠟⠛⢦⡤⠤⠶⠒⠚⠉⠁⠀⠀⠀⠀⠀⣴⣾⣶⣦⣤⣤⣀⣤⣿⣿⣦⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣧⣈⡉⠻⠛⠛⠛⠛⠛⠿⣦⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣧⠀⠀⠛⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣇⠹⣿⣿⣷⣦⣤⣤⣤⣤⣤⣿⣇⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠻⢷⣦⣭⣟⣻⣿⠿⠿⢿⣿⣿⣿⠁⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢷⠆⠀⠀⠀⠀⠀⠀⠿⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣤⡀⠈⠉⠙⠛⠛⠛⠛⠛⢻⡇⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⡁⠉⠛⠻⢶⣦⣤⣤⣥⣤⣶⡿⢷⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⠷⢶⣶⠶⠶⠿⢛⣛⣯⡥⠾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠉⠉⠙⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⡄⠀⠀⠀⢠⣾⡃⠀⠀⠀⠀⠀⠀ ⠀⢸⣷⡀⠀⠀⡞⠡⡇⠀⠀⠀⠀⠀⠀ ⠀⢸⡙⢷⣄⠰⡇⢸⢱⠀⠀⠀⠀⠀⠀ ⠀⠈⢷⡈⢪⣆⢳⠀⣌⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢦⣹⣿⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣿⠟⡟⢆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣿⣿⣼⡿⠿⠷⡄⠀⠀⠀⠀ ⠀⠜⢿⠛⠙⣋⠇⠀⢀⠔⠁⠀⠀⠀⠀ ⠀⠀⠀⢉⡴⢦⡀⢸⢖⠒⠒⢒⣂⣲⠀ ⡔⠖⠛⠓⢽⢶⣷⡄⠂⢧⠒⢸⣹⡟⠀ ⠙⠒⠒⠒⢛⡏⠙⠓⣄⡈⠲⣯⢽⠀⠀ ⠀⠀⠀⠀⠸⣀⡤⢀⡗⠋⠀⢹⣌⡇⠀ ⠀⠀⠀⠀⠀⢸⣏⡏⢃⠀⢀⣜⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⡹⢠⣄⡷⣻⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠁⢠⡟⠃⣸⡅⠀⠀⠀ ⠀⠀⠀⠀⠀⠳⠨⡼⠀⡴⢀⣶⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⢲⠁⢸⡉⠒⢡⠀⠀⠀ ⠀⠀⠀⠀⠀⠧⣷⡀⠨⢉⠖⠚⠀⢄⠀ ⠀⠀⠀⠀⠀⠀⠐⠨⡈⠁⠀⠆⠈⣮⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⢺⡷⣓⣢⣖⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠁⠚⣹⠂⠸⢗⠛⠦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠁⠀⢰⣶⣿⣷⡄⠀⠈⣷⣦⡜⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠁⡇⠀⢀⠆⣿⣿⣾⣿⡄⠸⣿⣿⣿⣸⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠴⠋⠀⢰⣃⡠⣼⠄⠈⠛⠛⣉⣧⣾⣏⠉⠁⢻⢷⡀⠀⠀⠀⠀ ⠀⠀⢀⠔⠁⠀⣠⣶⠟⢀⡀⠤⠔⣖⣪⠽⡟⠊⢹⠛⡟⢗⠂⠭⣈⠒⠤⡀⠀ ⠀⡠⠋⠀⣀⣴⠟⠁⠋⢀⡠⠒⠈⡕⠁⢀⣧⠀⢸⢠⠃⠈⠀⠀⠀⠈⠁⠚⡆ ⣰⡡⠖⠋⣿⠁⢀⠤⠊⠁⠀⠀⠀⠀⠈⠀⠀⠉⠉⠀⣠⣔⠂⠀⠀⢀⣀⠼⠁ ⡇⠀⠀⠀⡻⣶⣅⠀⠀⢀⡀⠤⠐⠊⠙⣍⡀⠀⠀⢰⣁⠀⠈⢹⠀⠈⠀⠀⠀ ⡇⠀⣠⠞⠁⠈⠀⡏⠁⠀⠀⠀⠀⠀⣸⣏⣛⠟⠿⠿⠿⢇⠀⠈⠀⠀⠀⠀⠀ ⢣⠀⠁⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢀⣿⣜⡻⣷⣶⣶⣶⣿⡄⢸⠀⠀⠀⠀⠀ ⠘⡆⠀⠀⠀⠐⢯⠀⠀⠀⠀⠀⠀⢨⣷⢬⣉⠉⠛⠒⠛⣻⢀⠇⠀⠀⠀⠀⠀ ⠀⠘⣄⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢾⣷⠦⣬⠭⠿⣿⣿⠽⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠣⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢞⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢋⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⣋⠤⣠⠞⣱⡿⠃⠀⠀⠀⠀⠀⣠⣤⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⠂⢐⡾⠃⣼⠟⠁⠀⠀⢀⣀⡤⣾⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⣼⢭⣿⠟⣠⡾⢃⣠⣤⣶⣾⣿⣿⣿⡿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⢽⠀⣏⣼⣿⠟⢉⣠⠿⠛⣉⣴⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣯⣴⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠛⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⣿⡛⣇⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣤⣤⣤⣶⣶⣟⣻⢿⣯⣿⣿⣿⣿⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣏⣁⣀⡿⠾⠟⠻⡧⢿⡟⠻⠯⣿⣖⣒⡆⠀⠀⠀⠀ ⠀⠀⠒⠛⢿⣅⠀⠀⠀⠀⠙⠷⠾⠁⣀⡴⠋⠀⠈⠉⠛⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠛⠒⠶⣤⣀⢰⣟⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡞⢿⣆⠻⣍⠓⢦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠳⣿⡄⠘⢿⡤⣬⣽⡶⢤⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⠓⢾⣷⣠⠾⣉⣿⣿⣷⣞⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢻⣟⣦⠿⢿⣤⣿⠴⠿⠟⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⣷⢦⣄⠈⣿⢸⡹⣟⣐⣾⠏⣸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⢿⠋⣻⣵⣿⣬⡿⠉⠉⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣏⣼⡴⡿⠛⢾⣿⠁⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⡽⣯⡇⠀⠸⡇⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠦⢼⣿⠀⢸⣇⣀⣠⣤⣞⢷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⠐⠀⣻⠉⠈⣧⡈⠸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⣸⡀⠀⠸⡆⠀⢿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠈⣇⠀⢠⡿⠀⢻⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠑⢻⢀⡾⠘⡷⡞⠀⢀⣀⣀⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠘⣿⠀⠈⣿⠧⣼⠟⠃⠁⢠⣈⢷ ⠀⠀⣀⣀⣀⣀⣀⣀⣼⣧⠀⠀⢻⣆⣐⣹⣾⠏⠀⠐⣤⠀⣹⣿ ⣠⡞⢉⡀⠀⠙⠻⣟⠂⠊⠃⣀⣸⣿⣍⣉⠁⠀⠀⢠⣿⡾⠟⠁ ⢻⣴⠟⠁⠀⡀⠀⠈⠻⠶⠶⠛⢱⠇⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀ ⠀⢹⣀⠀⢸⠀⠀⠀⠀⠀⢀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠉⠛⠛⠓⠦⠤⠖⠛⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠉⠉⠉⠉⠉⠉⠉⠉⢷⡄⠀⠘⡄⠀⠈⢧⠀⠀⠀⢹⡗⠘⣿⠃⠀⠀⠀⡇⠀⣰⠃⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠘⣆⠀⠈⡆⠀⠀⠈⡇⢠⣿⠀⠀⠀⢰⠀⡰⠃⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⢆⠀⢸⡄⠀⠀⣷⠸⡏⠀⠀⠀⣎⡜⠁⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠈⢣⡀⡇⠀⠀⣿⣾⡇⢀⣀⣠⡏⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣀⣀⣨⣧⡀⠀⠙⢿⠀⢀⣿⡿⣻⣿⣋⣀⣁⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⣸⠀⠀⠀⠀⠁⠈⠉⠻⢼⡛⠲⠖⠒⠒⣶⡶⣄⠀⠀⠀⣠⡖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠞⠁⠀⠀⠀⠀⠀⢀⣠⡀⠀⠘⢆⠀⠀⠀⣆⡇⠈⡇⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⢸⡁⠃⠀⠀⠘⣆⠀⠀⠋⡇⢸⠇⠀⣾⡇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢀⡄⠳⣄⠀⠀⠀⠘⡄⠀⠀⡇⡟⠀⠀⣟⡇⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢀⣠⠤⠤⡤⠤⢴⠊⠀⠀⡏⠉⠁⠒⠢⡼⡄⠀⣿⠃⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡰⠀⠀⠞⠀⠀⠀⠀⠀⠈⢣⠀⢰⡀⠀⠀⠀⠀⣇⠹⣤⡏⠀⠀⣸⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⣰⣃⣀⣀⣶⣋⠉⠻⠿⠿⠋⣹⠀⠘⣏⡙⠛⠋⣉⣟⣀⡼⣿⣤⣤⡿⡿⠒⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣋⣁⣀⣀⡀⣉⡙⠛⠿⢶⣦⣾⣿⠭⠛⠻⠿⣭⢟⣋⠥⠒⢉⢁⣀⠉⢧⠧⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠀⠀⠀⠀⢠⢏⠀⠀⠀⠀⠀⠀⠀⢈⣩⡶⣒⣫⣅⠈⠑⠤⡤⠊⠙⣻⠶⢄⡉⣀⣀⣀⣀⠀⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣶⣤⣤⣼⣿⣶⣿⣼⡀⢀⣀⠤⠔⠲⠚⠉⠉⠁⣄⠘⡍⠑⠒⠠⠇⠒⠊⣿⡀⠀⠱⠄⠀⠀⠀⢈⣿⠋⠑⠒⠒⠤⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡇⠀⠀⢸⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⣾⣿⣧⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⣛⡛⢛⡛⢛⢛⣛⣿⣿⣛⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠘⠀⠀⡎⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠚⠀⠀⠀⣀⢤⣶⣿⣵⣿⣿⣿⣿⣿⣿⣿⣟⣏⣉⢻⣟⣉⡉⠉ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⢀⣈⢉⠖⠒⢤⠤⠤⠤⠤⠤⣴⠒⢺⡁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⡠⠊⠁⠈⠙⢢⣄⠈⢧⠀⠀⠀⡜⡍⠀⠀⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠈⠻⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠥⠞⠀⠀⠀⠀⠀⠀⠻⡑⢬⣆⣀⣀⣰⣁⣠⠾⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⠟⠁⡀⠀⠀⠀⠀⠀⠀⠙ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠹⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⢲⠃⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⢳⣀⣠⣤⣶⣶⣿⣿⣶⣶⣦⣤⣤⣤⣤⣤⣴⣦⣤⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠁⠀⠠⡀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⠿⠿⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠀⠀⠀⠳⡀⠀⠀⠀⠀⢵⡀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠈⣿⣿⡿⠋⠀⠀⡇⠀⠀⢀⡜⠁⠈⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣧⠀⠀⠀⠀⠀⢰⡿⢻⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⣿⣦⠀⠀⠀⠀⡏⡇⢸⡘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠘⣯⢷⡄⠀⠀⡇⡀⠀⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⡄⠈⠻⡛⢦⠀⢷⡇⠀⢳⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⣄⠀⠙⣗⣣⡘⣷⡀⢸⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣄⡈⢿⢳⣹⣧⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠿⣾⣾⣿⣿⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⠛⣿⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡜⣿⣿⡃⣤⣿⣦⠿⣾⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣾⣧⣿⡿⣷⣿⠿⠾⠛⠒⠛⣖⠂⠀⠀⠀⠀⠀ ⠀⠀⣠⢽⣿⡿⠟⠛⣗⠇⢻⠆⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠧⣄⡀⠈⠓⠋⠀⠀⣠⠔⠋⠀⠀⠀⠀⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡩⠿⢷⡄⠀⠈⡿⣍⠉⠉⠙⠉⢉⣉⢉⢹⡆ ⠀⣀⡤⣴⣒⣊⣁⡾⢾⣠⣼⣆⠀⢤⡈⢳⣀⣀⠤⢾⡗⣿⣽⠇ ⣾⠇⡁⠄⠤⠈⠉⠭⣿⢋⣽⣿⣇⠀⠑⠈⣏⠀⠀⢸⣧⣿⠟⠀ ⠈⠓⠓⠶⠐⠒⠒⠛⢛⡏⠘⠸⠟⢦⠀⠀⠈⠲⣼⢭⡬⣹⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⢣⠀⠀⠀⠸⡉⢒⡆⠀⠘⣯⠃⡿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣴⡶⠒⣦⠟⠉⠀⠀⠀⢸⣗⢃⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢾⡋⣿⠙⡆⠀⠀⠀⠀⣼⢸⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⢷⡏⠀⠸⣄⠀⢀⣼⣧⡞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⠁⣼⡂⣺⣿⠻⣿⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢈⣿⣷⠆⢹⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣀⢰⣞⡏⠀⠁⡼⣏⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡤⣑⣠⡞⠀⠀⡼⠁⣽⡸⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣼⠏⠠⡼⣅⣀⢃⡇⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣽⠀⠀⢰⢃⡀⠈⠉⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⣇⠀⠀⠸⠙⠲⢤⣄⠼⢁⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡙⢆⡀⠈⣠⠖⠉⠀⠀⠀⢄⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡉⠉⠁⠀⠀⠐⣄⠀⠈⣇⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠤⠤⠼⠤⠤⠞⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⡀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⢤⡟⠀⠀⠀ ⠀⠀⠀⠀⡠⢊⢕⡟⠀⠀⣠⠀ ⠀⠀⠀⢰⠷⣡⡫⣤⠶⣾⠏⠀ ⠀⠀⠀⠈⣾⣿⡞⠒⠉⠀⠀⠀ ⠀⣀⣀⣸⣿⣧⣿⣀⠀⠀⠀⠀ ⠀⠀⠼⡂⠉⠹⠼⡉⠟⠂⠀⠀ ⠀⠀⠀⠀⢉⣵⣜⢖⢄⡀⠀⠀ ⠀⠀⠀⠀⠀⣗⣻⡌⣿⣿⡷⠀ ⠀⠀⢀⣶⣬⣮⠧⠞⡅⠀⠀⠀ ⠀⠀⢸⣿⠋⡟⠀⢠⠁⠀⠀⠀ ⠀⠀⠀⠘⡇⠳⠲⡊⡄⠀⠀⠀ ⠀⠀⠀⠀⡆⢸⠀⢇⡅⠀⠀⠀ ⠀⠀⠀⠀⢰⠀⢟⠸⣣⠂⠩⣢ ⢠⣊⠍⠙⢏⣃⢼⠩⠅⠠⠗⠃ ⠀⠁⠬⠄⠀⠔⠁⠀⠀⠀⠀⠀

⠉⠉⠈⠀⠉⢣⠀⢂⠀⢃⠀⠈⡅⣽⠀⠀⠆⡰⢁⡞⠀⠀⠀⠀⠀⠁⠠⠤⠀⠄ ⠀⠀⠀⠀⠀⠀⢣⠀⠣⠈⡄⠀⡇⡇⠀⢰⠔⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⣀⣱⡀⠑⠅⢀⣿⢧⣖⣚⢠⠊⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠄⠀⠀⠀⠉⠑⢯⠛⠉⠰⠲⡀⢠⡖⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠀⠀⠠⠁⠀⠀⠀⠀⠏⠂⠀⢣⠀⠈⢰⠃⣼⠁⠀⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⣀⣀⣀⠔⠈⠖⠠⠤⣆⠀⡜⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠀⡜⠀⡂⠀⣀⣀⢡⠰⠤⣤⠤⡇⢺⡁⢠⣏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡤⠊⠉⠉⠉⣒⠶⣴⢷⠒⠛⣶⡚⢉⠃⠉⠹⡇⠠⠀⠀⠀⠀⠀⠀ ⣦⣀⣠⣦⣾⡆⢀⠀⠤⠄⠒⢓⢛⠢⠌⠮⠌⡏⠐⠀⠐⠒⣾⠠⠤⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⢹⠀⠰⠀⠘⠁⠀⠀⢀⣴⣿⡆⠐⠀⠀⠀⠀⠀ ⣿⣾⣾⣿⣿⣿⣿⣷⡦⠄⣀⠀⠀⠒⠒⠒⠃⣀⠠⢴⣯⣿⣿⣿⣿⣟⣩⣲⣒⡒ ⣿⣿⣿⣿⣿⣿⣿⠋⠀⠒⠸⣈⠩⠉⠉⢝⠁⢃⣠⣾⣿⣿⣿⣿⣿⡿⠟⠋⠛⢿ ⣿⣿⣿⣿⣿⡿⠓⠊⠀⠀⠀⠘⠵⠧⠄⠈⠐⠛⠛⠛⠛⠛⠻⠿⠁⡄⠀⠀⠀⠈ ⣿⣿⣿⠿⠛⠀⠀⠈⡄⠀⠀⠀⠘⣀⣤⣴⣶⣶⣤⣤⣤⣤⣤⣤⡴⠀⠀⠀⠀⠀ ⣿⣿⣿⠀⠈⡄⠀⠀⠠⡀⠀⠀⠀⡙⠋⢹⣿⡿⠉⠏⠉⢉⠋⠛⠁⠀⠀⠀⠀⠀

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