Shuba Duck Emojis & Text

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⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⠛⠁⢰⣧⡈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣇⣼⡀⠻⠟⠁⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⣹⠙⣧⡀⠀⠀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⡴⠋⠀⣀⣴⣿⡷⠴⠞⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢾⣁⣀⡤⠾⠛⠁⣸⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠁⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⠁⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⢿⣶⠶⠿⠟⠿⠿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠈⠙⠛⠿⠶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⣠⣤⣤⣤⣤⣤⣀⠀⠉⠙⠳⢦⣄⡀⣀⣤⣀⣀⡄⠀ ⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠉⠻⢶⣀⠀⠀⠈⠉⢁⠈⠏⣿⣁⠀ ⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣀⡴⠁⠀⠀⢙⣿⡾ ⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⣀⣠⡾⠟⠃ ⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡔⢊⣵⠞⠋⠁⠀⠀⠀ ⠀⠀⠀⠙⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠳⠶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣴⠊⣁⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⡷⢶⡶⠶⠤⠔⢺⠃⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢰⡇⠀⡇⠀⠀⠀⢸⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣤⣭⠿⠟⣃⣾⠋⠀⠀⢠⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠙⠛⢋⣿⣙⣶⣾⡿⢷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠻⠧⠶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⠛⠚⠛⠻⠟⠛⠓⠟⠻⠓⠐⠚⠒⠛⠁⠀⠀⠸⠓⠇⠞⠛⠚⠙⠲⠀⠐⠞⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⠿⠷⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⢀⣀⡀⠙⣷⡀⠀⠀⠀ ⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠘⠿⠃⠀⢸⣿⣿⣿⣿ ⠀⣠⡿⠛⢷⣦⡀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠟ ⢰⡿⠁⠀⠀⠙⢿⣦⣤⣤⣼⣿⣄⠀⠀⠀⠀⠀⢴⡟⠛⠋⠁⠀ ⣿⠇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀ ⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀ ⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀ ⠀⠹⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠉⠙⠛⠿⠶⣶⣶⣶⣶⣶⠶⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠉⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⡿⠿⠟⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣶⣾⣿⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⣷⣦⣤⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⣿⣿⣿⣿⡿⠀⠀⠀⠀ ⠀⠀⠈⢿⣿⣿⣯⡙⠛⠿⠿⠿⣿⠿⠿⠿⠛⠋⣁⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠿⣿⣿⣷⣶⣶⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⢿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣤⣤⣤⣤⣤⣴⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⠛⠛⠉⠉⠉⠉⠉⠉⠙⠛⠻⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⣠⣴⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⢀⣴⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⣼⣿⠋⠉⢹⣿⣿⣿⣿⣿⡄⠀⠀⣾⣿⢁⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⣿⣿⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠙⢿⣷⣤⣀⣹⣿⣿⣿⠟⠀⠀⠀⠈⠛⠛⠛⠛⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠁⠀⢀⣠⣴⣶⣶⣶⣶⣶⣾⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠛⠉⣉⠉⠉⣽⣏⠛⠿⣿⣿⣶⣤⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠁⠀⠀⠺⣿⠇⠈⠻⠛⠀⠀⠀⠈⠙⠛⠿⣿⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⣿⣿⣶⣦⣤⣤⣤⣤⣤⣶⣶⣾⣿⡿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⡿⠛⠉⠉⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⡿⠟⠋⠉⠙⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣧⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣤⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⣷⣄⠀⠀⣸⣿⠿⣿⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠋⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣿⣦⣠⣿⡟⠀⠈⠉⠛⢻⣿⡿⠿⠿⢿⢿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠁⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⣿⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⣿⣷⣶⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠆⠀⠀⠛⠿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⠉⠻⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠚⠉⠉⠉⠙⢯⣢⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢺⠊⠀⠀⣀⠀⠀⠀⠀⢱⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣮⠃⠀⠀⠘⠛⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⢀⣼⠒⣺⣻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠛⠃⠀⠀⠀⠀⠀⠀⢞⠁⠈⠉⡿⡿⡄⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⡴⠊⠁⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⡀⣹⣖⠀⠀⠀⠀ ⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣧⠀⠀⠀ ⠀⠀⣎⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀ ⣠⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠈⠳⡅ ⢳⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠈⢞⣁⣀⣀⡀⢀⡀⣀⡀⠓⠉⠒⠦⡀⠀⢱ ⡾⠀⠀⠀⠀⠀⠀⠀⢰⠛⠉⠀⠀⠀⢰⠛⠛⠛⠁⠈⠙⠛⠛⡇⠀⠀⠀⠈⠛⡄ ⢻⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣀⡀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⣀⣀⣠⠃ ⢸⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠁⢠ ⠸⡽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡼ ⠀⠙⠹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡞⠀ ⠀⠀⠀⠀⠙⢲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣿⣿⣶⡦⠶⠶⣾⠏⠉⠉⠉⠉⠉⠉⢉⢿⣿⣷⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠁⡸⠷⣶⣴⣶⣦⡀⠀⠀⢀⣤⣤⣴⣵⡿⢞⠿⡶⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⠤⠿⠧⠶⠶⠤⢧⠃⠀⠀⠙⠾⢟⣛⣁⣒⣻⣅⣙⡾⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠉⠙⠲⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡞⠁⣀⣀⣀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⡀⠘⡆⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⠉⠉⠉⣹⡆⠀⠀⣿⣿⣿⣿⡇⠀⢀⣀⡿⠀⢹⠀⠀ ⠀⢀⣀⣠⡬⠿⠿⠟⠓⠚⠛⠉⠉⠉⠙⢲⡈⠉⠉⠉⠉⠉⠉⠀⠀⠀⢸⡆⠀ ⣞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⠉⠓⠶⠶⣶⠶⠶⠶⠖⠒⠒⠒⠒⠒⢦⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⠈⠓⠒⠶⠶⠶⠶⠶⡶⠶⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣩⣭⣶⣶⣮⣭⡙⠿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠿⣋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⡃⠄⠹⡿⣿⣿⣿⣿⠟⠛⣿⣿⣿⣿⣷⡌⢿⣿⣿ ⣿⣿⣿⣿⣿⠐⣠⡶⣶⣲⡎⢻⣿⣤⣴⣾⣿⣿⣿⣿⣿⠸⣿⣿ ⣿⠟⣋⡥⡶⣞⡯⣟⣾⣺⢽⡧⣥⣭⣉⢻⣿⣿⣿⣿⣿⣆⢻⣿ ⡃⣾⢯⢿⢽⣫⡯⣷⣳⢯⡯⠯⠷⠻⠞⣼⣿⣿⣿⣿⣿⣿⡌⣿ ⣦⣍⡙⠫⠛⠕⣋⡓⠭⣡⢶⠗⣡⣶⡝⣿⣿⣿⣿⣿⣿⣿⣧⢹ ⣿⣿⣿⣿⣿⣿⣘⣛⣋⣡⣵⣾⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠛⠛⠛⠛⠛⠷⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⠃⠀⣀⣀⣀⣀⡀⠀⠀⢀⣭⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡿⠁⠀⣼⡏⢉⣿⣿⣿⡆⠀⣾⢡⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠃⠀⠀⠸⣷⣄⣻⣿⡿⠁⠀⠙⠛⠛⢻⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠉⠉⢀⣴⡾⠿⠿⢿⡿⢷⣤⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⢰⣿⠉⠀⠺⠇⠘⠃⠀⠉⠙⠛⢷⣄⠀ ⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠘⠿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠂ ⠀⠀⠀⠀⠀⣹⣧⡀⠀⠀⠀⠀⠀⠀⠀⢉⣹⡿⠷⢶⢶⡶⠶⠛⠛⠁⠀ ⠀⠀⢠⣶⠟⠋⠙⠛⠀⠀⠀⠀⠀⠀⠈⢿⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⢸⡟⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠘⣧⠀⠀⠀⠀⠀⠀⠀ ⢸⣷⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢹⡇⠀⠀⠀⠀⠀⠀ ⠀⢿⡄⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⣄⠀⠀⣰⣿⡀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣧⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣧⣀⡿⠉⠛⢷⣶⠶⠤⢦⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠟⠃⠀⠀⢸⡇⠀⠀⢸⣇⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⡶⠀⠘⠻⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣿⣇⣿⣼⣷⣼⣼⣯⣇⣀⣸⡏⠙⡿⠶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⢠⣿⢻⣻⣟⣸⣿⣿⣿⣿⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣧⡄⠠⠄⠀⢸⣿⣿⣿⣷⠶⣤⣤⡄⠀⡾⠻⣖⣸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣶⣿⠇⠘⣿⠀⠁⣿⡇⠀⠀⠠⠀⠀⠀⣿⡟⡛⠛⠀⢿⣿⡇⠀⠁⣶⡎⠹⣿⣿⣿⣿⣿⣿⣯⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⢿⣿⣧⣼⣇⡂⠈⠀⣿⡟⠃⠀⢰⣇⣀⣀⡀⣿⣇⣿⣄⠀⣸⣿⡇⠀⠀⠛⢆⣺⣿⣿⠿⠛⠉⠉⠉⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠉⠉⢽⣿⣶⣿⠏⡙⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⢤⣿⣿⠃⠀⣠⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⢤ ⣠⣀⣀⠀⠀⠀⠀⠈⢉⠓⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢐⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡧⡴⢾ ⠟⠉⠉⠛⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣤⣿⠅⠀⠀⠀⠀⢀⣠⡴⠒⠋⠉⠁⠀⠀⠀⠀⠉⠙⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣶⣾ ⣿⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡆⠀⣩⡿⠛⠛⠉⠁⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢀⣴⡿⣿⣿⣦⡀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠅⠀⠀⠀⠀⠀⠀⠄⢸⡯⣰⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣩⣤⡄⣄⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠂⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⢸⣀⠀⠀⠀⠀⠀⠀⣹⡿⢳⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣷⣶⣦⣄⣀⣀⠀⠀⢀⣠⣾ ⢺⣿⡄⠀⠀⠀⣰⣾⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿ ⣸⣿⣷⣦⣥⣤⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿ ⡏⠉⠉⠉⠛⠛⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣟⠻⢿⣷⣶⣶⣶⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣶⡶⠾⠟⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⡹⣎⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣿⣇⣂⣿⣒⣾⣗⣒⡟⢉⣿⣚⢷⡏⣯⣈⠇⡏⣶⢿⣯⣈⠿⣿⣒⣿⠹⣌⢏⣯⡓⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢀⣾⠿⠿⠽⠷⠾⠿⠾⠿⠷⠶⠶⠿⠿⠿⠷⠿⠿⠿⠶⠿⠶⠾⢿⠾⠷⠿⠶⠾⠷⠿⠾⠷⠶⠿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠼⠿⠿⠿⠿⠿⣿⢿⣿⣿⣿ ⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠀⠸⠷⣶⡶⠶⣶⠀⠀⣶⣾⣷⣤⣶⢶⣦⠀⢰⣶⠶⣦⣄⣶⡆⠀⣶⣦⣤⡶⢶⣤⣰⣶⢀⣶⠞⠁⣶⢤⣴⠶⣦⡀⢰⣶⠀⢰⣿⠀⢰⣿⣆⠀⣶⡶⢶⣤⣶⡶⣶⣜⣷⣄ ⠀⠀⠀⠀⠀⣿⡗⠀⣿⡷⠶⣿⣿⣿⣟⡻⢷⣦⣀⣾⣿⠀⢸⣿⣿⡇⠀⣿⣿⣿⠀⢀⣉⣸⣿⣿⣅⠀⠀⣿⣿⣻⢷⣦⣄⢸⣿⠶⢾⣿⣠⣿⣿⣿⣸⣿⣷⠾⠟⣿⣷⠾⠏⠘⢿ ⠀⠀⠀⠀⠀⠿⠇⠀⠿⠀⠀⠿⠇⠿⠟⠿⠶⠟⠁⠸⠿⠾⠟⠃⠙⠿⠾⠟⠈⠻⠷⠾⠛⠹⠿⠘⠿⠦⠀⠿⠏⠻⠶⠿⠃⠸⠿⠀⠸⠿⠿⠏⠉⠹⠿⠿⠇⠀⠀⠿⠇⠀⠀⠀⢿ ⠀⠀⣀⠀⢀⣀⣤⣄⣠⣀⣀⣀⣀⠀⠀⣀⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⢀⡀⠀⢀⠀⠀⠀⡀⣄⡀⠀⠀⠀⡀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈ ⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⢟⢿⡿⣿⢿⣿⣿⣟⢿⠿⡿⡿⣻⣿⡛⣿⣟⣿⣿⣿⣻⢿⣿⣿⣿⢿⠿⡿⢿⡿⣿⣿⣿⣿⡿⣿⣿⣟⣿⣿⢿⣛⡿⣟⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛ ⠀⢸⣿⣾⣿⣿⣿⣿⣿⣛⣽⣜⣷⣷⣯⣾⣟⣷⣙⣿⣷⣭⣇⣺⣿⣿⣿⣛⣿⣟⣿⣻⣾⣿⣶⣾⣾⣶⣱⣼⣷⣶⣿⣜⣿⣗⣿⣷⣟⣷⣛⣼⣿⣗⣛⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⡿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⡿⠋⠁⢠⣷⣇⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⠁⣶⠀⢸⣿⡿⠋⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠿⡾⢻⡆⠀⠈⠁⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠟⠤⠗⠈⣿⣤⠀⠀⢀⣸⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⠞⠁⠀⢀⣠⣶⣽⣿⣶⠾⠛⠁⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠋⠀⢀⣠⣶⡿⠞⠁⣸⡇⠀⠀⠀⠀⠀⣿⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠛⠛⠉⠁⠀⠀⠀⢀⣿⠃⠁⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠸⣿⣴⣶⣿⡿⠿⢿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⠶⠶⠶⠶⣶⣦⣤⣄⠀⠀⠈⠙⠛⠷⣦⣀⣠⣤⣶⣄⣠⣴⡄⠀⠀ ⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣦⡀⠀⠀⠀⠀⠉⠁⣀⠈⡏⢹⣟⠀⠀⠀ ⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⡀⠀⠀⣠⡞⠁⠀⠀⠸⠿⣭⣼⠇ ⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠖⠛⠀⠀⠀⠀⠀⣾⣿⣯⠀ ⠀⠀⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣤⡶⠿⠛⠉⠀⠀ ⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⠟⢉⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠉⣁⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⣀⣤⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠷⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠘⣛⡶⢾⣭⣤⣴⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠛⢿⠿⠿⠶⠖⠋⢹⠁⢸⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢸⣏⠀⢸⡀⠀⠀⠀⠀⢸⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣏⠉⣛⣻⣶⣿⡧⣰⡷⠷⠀⠀⠀⢠⡿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⢿⣏⣅⣤⣶⢿⣧⣀⣀⣀⣠⣾⣃⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⣾⣃⣤⣼⠿⡿⢛⣻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠻⠿⠦⡴⠶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡀⣄⢀⢀⣀⣄⣀⣀⣀⣠⣀⣀⣀⣀⡀⠀⣀⣀⢀⣀⡀⠀⠀⢤⢀⡀⢀⠀⡄⣀⠀⡄⣤⠠⠄⠀⠠⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠂⠋⡛⠛⡓⢃⠻⠛⠘⡛⠛⢛⠛⠛⠓⠘⠚⠓⠛⠃⠃⠀⠀⠒⠚⠚⠚⠚⠚⠓⠋⠃⠚⠛⠂⠐⠘⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⢀⡴⠖⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⣹⠖⠋⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⢹⠏⠀⠀⠀⠘⠁⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⢠⠏⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠉⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⣤⣄⣀⠀⠀⢠⡇⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡇⠀⠀⠳⣄⡀⠉⠑⠚⠳⠤⣇⡀⠀⠀⠀⠀⢀⣶⣶⡀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⡀⠀⠀⠻⣍⠓⠲⠤⣄⣀⡀⠙⢦⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⣷⣀⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⢀⣤⣄⣠⣤⡄⠀⠀ ⠀⠘⣧⠀⠀⠀⠈⠓⠤⣄⣀⣀⣉⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⣠⠞⢩⡾⠛⢁⣴⠿⣷⠀ ⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠉⠀⣠⠞⢁⣴⢿⡄ ⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⢁⡼⠁ ⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢈⡷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⡾⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠠⡴⠛⣻⣠⠴⣄⣀⡴⠚⠙⣧⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠴⠛⠀⣰⠟⠁⠀⠀⢠⡏⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣏⠉⠉⠉⠉⠉⠉⠉⣿⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠾⠀⣿⠀⠀⠀⠀⠀⠀⠀⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠽⣿⣿⠀⣀⣤⠟⠀⠀⠀⠀⠀⢀⣀⡗⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠛⠉⠉⠀⠀⠀⠀⠀⣐⣶⣟⣁⠀⢀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣀⠐⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⢡⢸⡧⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠎⠝⣄⢀⡀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣒⣁⡴⠚⡏⠉⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠀⠀⣰⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠋⠀⠀⠈⣧⠴⠶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠃⠀⠀⠀⠀⠈⠢⠀⠀⠀⠈⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀ ⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠑⢦⡀⠈⢉⡉⢻⡇⡀ ⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠊⠀⣀⡾⠁ ⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢆⡵⠋⠁⠀⠀ ⠀⠀⠀⠉⠳⠤⣄⣀⡀⠀⠀⠀⠀⣀⡔⣃⡤⠚⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠟⡖⠒⠊⣇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣯⣵⢞⣳⠒⠀⣰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠼⢼⣛⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠤⠴⠤⠤⠤⠴⠠⠤⠄⠀⠢⠴⠤⠤⠠⠄⠴⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣇⣀⣿⣿⣷⣶⣶⣶⣶⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠿⠿⠿⠛⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀ ⠀⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⣿⣿⣟⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡤⠊⢉⠖⠉⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠋⠌⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠃⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⡎⠀⡠⠒⠈⠉⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⢰⡒⠠⠤⢄⡜⠀⠀⠀⣠⣀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡄⠀⠩⣁⠒⠤⠌⢱⠀⠀⠙⠋⠀⠀⠀⠀⠸⠤⠤⠤⠤⣀⠀⢀⡠⣦⠴⣆⡀ ⠀⠹⡄⠀⠀⠉⢦⠀⠁⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠙⠁⠚⢡⠞⡱⠇ ⠀⠀⠘⢆⠀⠀⠈⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡰⠁ ⠀⠀⠀⠀⠙⠦⢀⡜⠀⠉⠀⠀⠀⠀⠀⡄⠀⠔⢹⠤⢢⠤⠊⢱⠀⠀⠀⡎⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁⠀⠁⠀⢀⠇⠀⠀⢠⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⢀⠴⠃⠀⠀⢠⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠉⠒⠒⠈⠁⠀⠀⢀⡴⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⣀⡀⠀⠀⠀⠀⣀⣀⠠⠔⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⠉⠁⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢽⣿⡀⠤⠃⠀⢀⡀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠐⡛⠗⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠂⠙⠒⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠻⣽⠇⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣠⣤⠶⠛⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠞⠋⠗⠀⠀⢀⣀⣽⣷⣤⣄⣤⠆⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠓⠒⠒⠚⠉⠉⠁⠀⠀⢀⡴⠃⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣰⠏⠀⠀⢀⣤⠴⠖⠚⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠓⠶⠶⠦⢤⣤⣤⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⣰⠋⡠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣶⠋⠀⠀⠀⠀⣀⠀ ⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⢰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⢛⣩⠏⠀ ⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⣻⣯⣥⣤⠖ ⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⣲⠖⠋⠁⠀⣠⣿⡶ ⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠒⠤⣤⣤⣤⠶⠟⠁⠀⠀⠀⠀⣡⡾⢈ ⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡀⠀⠀⠙⣦⣤⣀⣀⣠⡼⠗⠲⠤⠤⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠠⢾⡯⣴⡾ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀ ⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠖⠚⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⢀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢙⡿⠗⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠟⠛⠋⠉⠙⠛⠻⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠘⣿⣿⣆⣀⣀⣀⣀⣀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢀⣾⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟ ⠀⠀⣠⣿⣿⠟⠀⠉⠛⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠟⠀ ⠀⣰⣿⣿⠋⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠘⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠿⠿⠋⠁⠀⠀ ⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣄⣀⣀⣀⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⠿⠿⢿⣿⣿⡿⠿⠿⠿⠿⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⡤⠠⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⡨⠀⠀⠀⠈⢆⠈⠁⠪⡒⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡐⠁⠈⠀⢀⡆⡀⠀⠈⡘⡦⢀⡁⠈⣧⡀⠀⠀⠀ ⠀⠀⠀⡜⠀⠀⡠⠔⠁⠡⠁⠀⢀⣢⠇⠀⠑⡄⢾⣷⡀⠀⠀ ⠀⠀⢰⡀⢠⢠⢁⣀⡀⠀⠉⠒⠛⡍⠀⢲⡶⢹⣮⠻⡇⠀⠀ ⠀⠀⡸⢇⠿⠃⠀⠛⠁⠀⠦⢉⠀⠈⠵⠂⠀⠐⠟⣧⡇⠀⠀ ⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡑⡀⠀ ⢀⠁⠀⠀⣠⣂⢀⡀⠄⠒⢹⠄⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀ ⠈⡆⠀⠰⠁⡏⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡆ ⠀⠐⠤⠧⠤⠉⠒⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⠤⠃ ⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀ ⠀⠀⠀⠀⠑⠠⢀⣀⡀⠀⠀⠀⠀⠀⠀⡠⠤⡔⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠒⠊⠉⠉⠉⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀
⣿⣷⡀⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢿⣿⠈⠀⠈⣿⣿⣹⣿⣿⣿ ⣿⣿⣷⡈⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠂⠸⠯⣉⡀⠀⣿⢻⣿⣿⣿⣿ ⣿⣿⣿⣷⡘⠏⠀⣸⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣿⡌⠁⠉⢻⣿ ⡿⠋⠙⢻⣇⣰⣦⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⣷⣿⣶⣿⣿ ⠀⠀⠀⠈⢿⣿⣿⣿⣿⣕⡞⠀⠙⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠀⠀⢸⣀⣛⣿⣿ ⠀⠀⢀⡀⠀⠙⢦⠙⣿⡟⠟⠈⠹⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠈⣿⣿⣿⣿ ⠀⢀⣼⣷⣶⡶⠴⠚⠁⠰⠟⠁⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⢿⣹⣿⣿ ⣿⣾⠟⡩⠃⣀⠀⠀⠀⢀⣀⣀⣀⣠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣸⣿⣿⣿ ⣿⣿⣦⣷⣶⣶⣶⣿⣿⣿⣿⠿⠛⠉⣠⠇⠀⠀⠀⡠⠀⠀⠀⠀⡠⢸⣿⡿⣿⣿ ⣿⣿⣿⣿⣿⠛⠹⠉⠀⠈⣀⣤⣾⣿⣧⣄⣀⠠⠊⠀⠀⠀⠀⠠⠃⢼⡟⠀⢸⣿ ⠈⠙⣿⡏⢨⣒⡥⢴⣾⣿⣿⣿⣿⡿⢻⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⠀⠀⠈ ⠀⠀⠉⠉⠉⣡⣀⣸⣿⣿⣿⣿⣿⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣫⣾⣷⡄⠀ ⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣤ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⡜⣿⣿⣿⣿ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣄⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠷⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⢹⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣷⣶⠶⠛⠛⠛⠛⠳⢶⣦⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣯⠉⠉⠉⠉⠉⠛⣷⠀⠀⢿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣠⣿⣀⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣀⣀⣤⣴⠟⠀⠀⠸⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿⣿⠶⠶⠶⠿⠛⠛⠛⠛⠛⠛⢷⣦⡀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⢀⣠⣴⠶⠾⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀ ⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀ ⠈⢿⣦⣄⣀⣀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣄⣀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀ ⠀⠀⠈⠉⠛⠛⠛⢻⣟⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⠷⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⢶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢏⠑⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣶⢸⠆⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠣⢠⡞⠺⡧⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠸⡀⠈⠧⣀⠈⡤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡒⠉⠀⠀⠀⠀⣀⣀⣈⣉⣑⡺⢄⠈⠢⠋⠁⠀⠑⢄ ⢀⣀⠈⠙⠻⢒⡶⠟⣪⡥⢤⣤⡤⠤⠤⣀⠀⠀⠀⠀⠒⠨⢍⠊⢔⠒⠀⠀⠀⢸ ⣤⣭⣵⠞⠫⠭⢍⠑⠢⠄⣉⠁⠊⠉⠁⠀⠈⠀⠀⠀⠀⠀⢈⡆⠀⡀⠀⠀⠀⡜ ⠐⠶⠭⣭⡭⠥⢸⡄⠀⠀⠀⠉⠐⠢⠤⣀⣀⠀⠀⣀⣀⠠⠊⠀⠀⢱⠒⡖⠉⠀ ⠀⠈⠣⠤⠐⠒⠉⠙⠦⣤⣀⣄⠀⠀⠀⠀⠀⢨⡅⠀⠀⠀⠀⠀⣠⡦⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⠀⢀⡀⠾⣬⣦⣤⠤⠖⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠸⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢇⢗⣲⣦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⠤⣖⣏⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣽⣈⣽⣼⣱⣦⣾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣾⡿⠿⠛⠋⠉⠉⠉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣤⣄⠀⠀⠀⣀⣾⡟⢻⣿⠟⢿⠟⡿⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠃⠀⠀⠸⣯⣿⣟⣏⣿⡗⢘⣹⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣇⣾⣿⢟⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⠟⠶⠽⢿⣿⣿⣟⣯⣶⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣅⡀⠀⠀⠤⠿⢾⣿⣿⣿⣿⣿ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠛⠛⢿⣷⢦⣄⡀⠈⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡷⡎⢻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣏⠙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣟⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⣴⣿⣿⣿⣿⣿⣿ ⣿⣿⣷⣿⣭⣿⣕⣏⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⣠⣿⣣⣿⣿⣿⣿⣿⣿⣿ ⡿⢿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⣼⣿⣾⣿⣿⣿⣿⣿⣿⣽⣿ ⣷⡾⣿⣿⣿⠿⣋⡁⠀⠀⣠⣴⣿⣿⣦⣤⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⣰⣟⣡⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠶⢛⡿⠂⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣶⣬⣉⣉⣀⣀⣀⣀⣐⣉⣠⣴⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡅⠀⠀⠀⣀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠁⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡇⡝⠿⣄⠁⠹⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⠇⠀⢰⣬⢛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢋⠉⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢇⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⣿⡆⢸⠆⢀⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣇⠀⠉⠃⡜⡄⣰⠁⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠘⠦⢰⣾⠉⠁⠹⣦⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠈⣿⣄⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠒⠒⠲⠶⠶⠦⣤⣄⣀⠀⠈⢧⡀⠀⠘⡟⠳⣤⣀⣼⠓⠲⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⢷⣄⠀⠈⠦⠼⠃⠀⠀⠀⠀⠙⢦⡀ ⠀⠀⠀⠀⢠⣤⣀⣀⣀⡀⠀⣠⠶⢟⡡⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠋⠉⠉⠉⠙⠓⠒⠦⢍⣳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⢷ ⠀⠀⠀⠀⠀⠀⠉⠻⢭⣙⠛⠯⠽⣛⣒⠦⠤⢤⣖⣒⠒⠒⠲⠦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠲⣤⠈⠙⢦⡈⠁⠀⠀⠀⠀⠀⠀⢸ ⠈⠉⠛⠻⣿⣭⣉⣉⡁⠉⠛⠓⠦⣄⡀⠉⠉⠒⠒⠨⠍⠙⠒⠒⠀⠀⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾ ⠶⠿⢉⣯⣍⣉⣁⣉⣙⠛⠒⡤⠀⠀⠉⠓⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠐⡄⠀⠀⠀⠀⢀⡼⠃ ⠀⢰⣖⡛⠋⠉⠉⢉⣉⣀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⢱⠤⠖⢲⠞⠋⠀⠀ ⠀⠀⠀⣤⠽⠛⠋⠉⠁⢀⣠⠾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠦⠤⠤⠴⠖⠒⠊⠉⠀⠀⠀⠀⠀⠀⡸⢀⣴⠋⠀⠀⠀⠀ ⠀⠀⠀⠙⠶⠖⠒⠒⠚⠉⠁⠀⠈⠻⢶⣤⣄⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣵⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠻⣄⡀⠀⠀⠀⠀⠀⠀⢀⡼⠘⢆⣀⠀⠀⠀⢀⣀⣤⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢶⠲⡆⠀⣤⠔⠚⠿⠷⠶⠾⠿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣧⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠘⡆⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣵⠀⢯⡛⢿⣯⣥⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢶⡅⠀⠠⢟⣛⣛⣲⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠶⠦⣼⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣾⡷⣿⣧⣼⠙⠛⣷⣦⣄⣀⢰⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣟⣇⠃⡼⠇⢀⣀⣽⣍⢘⣿⠀⢇⣿⡿⠟⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⡧⠈⠉⠉⠉⠉⢙⡫⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠖⠒⠀⠄⠁⠀⠀⣀⣐⣲⠏⠀⢀⡠⠔⠒⠐⠓⠢⣄⠀⠀⠀⠀⠀⠀⠀⠈⢻⠭ ⡇⠀⠀⠀⠀⠀⣡⡋⠀⠀⢀⠔⠁⠀⠀⢀⡀⠀⠀⠈⢳⣶⡆⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠄⣆⣾⣿⣿⣦⡤⠁⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⣿⣅⣄⠀⠀⠀⠀⠀⠀ ⣂⠀⠀⢈⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠙⠻⠶⢤⣄⣀⣀⣰ ⡿⢦⣴⣿⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣏⣀⣀⠀⠀⣀⣠⣿⣿⣿⣿ ⠦⠐⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠽⡻⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢿⣿⣿⣿⣿⣿ ⠀⣠⣴⢶⣶⣶⡶⣶⣶⢶⢶⣶⢶⣶⣶⢶⢶⡄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿ ⢀⠛⠛⠛⠛⠛⠚⠛⠛⠛⠓⠚⠓⠓⠓⠚⠚⠃⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛ ⠀⠐⣲⢲⣄⣶⣶⣖⡆⡖⢲⣖⢰⣶⠲⢶⡴⠂⣶⣶⡆⣦⣰⢠⣦⣰⣲⣶⣶⢶ ⠀⠀⠙⠈⠀⠋⠋⠛⠁⠛⠋⠙⠊⠉⠊⠙⠘⠂⠋⠑⠁⠃⠘⠋⠉⠛⠀⠛⠀⠘ ⠠⣿⣿⣿⣿⣿⣟⣿⣻⣟⣿⣯⣯⣿⣯⣿⣿⣟⣿⣿⣿⣽⣿⣿⣽⡟⠉⠉⠉⠉
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣻⣿⣿⣿⢻⣿⣿⣿⡟⣿⣿⡟⣽⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣿⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣯⣿⣿⣿⣾⣿⣯⣿⣧⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⡿⣿⢻⢋⠏⠿⢹⠏⡇⣈⣽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⣾⣿⣯⢛⢿⣿⣿⣿⣷⣽⣿⣿⣧⣿⣿⠿⠿⠿⠿⠿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⡗⣶⣿⡷⢺⣷⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣶⣾⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣯⢿⣿⣿⣿⣹⣿ ⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢸⣿⣥⡿⣻⣾⢹⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⣿⣷⣦⠀⠀⠀⢠⣤⣼⣿⣏⣹⣿⢛⠋⣿⡃⣶⢚⠸ ⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠁⠀⠀⠀⠛⣇⣾⣿⣩⣇⣵⣿⡟⣩⣥⣿⣿⣿ ⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣻⣾⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣃⣥⣾⣿⡿⣛ ⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣋⡻⣿⣿⣿⣿⣿⣿⠟⣫⣵⣾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣼⣿⣿⠻⠀⠉⠉⠉⠿⣿⠛⣭⣶⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⣿⣶⣄⣀⡀⠀⠠⠶⠛⢛⣿⣿⣿⣿⣿⣿⣿ ⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠟⠿⠿⣿⣟⠶⣄⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿ ⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣌⠛⢷⣶⣾⣿⣿⣿⣿⣿⣿ ⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⠳⠈⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡁⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⣷⣽⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿ ⣿⣯⣷⢾⣿⣿⣿⣿⠿⢿⣷⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣃⣼⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢿⣿⢷⣿⣣⣩⣟⣁⣗⣻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠏⠀⠀⢀⡾⣿⢬⣿⣿⣿⣿⣿⣿⣿⡿⣿ ⣿⢸⣿⡷⣿⣿⣺⣿⣿⣿⣿⣿⣿⠿⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠐⠀⣴⣿⣃⣾⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿ ⣧⡈⢻⣿⣹⡿⣿⣿⣿⠿⠛⠉⠀⠁⠀⢈⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠇⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡗⢯⣾⣿⡿⠿⠋⠤⠄⠀⠀⢀⣠⣾⣿⣿⣿⣿⣷⣦⣔⡒⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠐⠂⠀⢀⣴⣯⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⠟⢋⡿⠟⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣿⣦⣤⣀⣈⣉⣀⣀⣀⣀⡀⠋⣁⣠⣤⣞⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⠀⠀⠊⠀⠀⢐⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠛⢿⣿⡟⠫⠅⡿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⠐⢷⠉⠻⣦⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⠄⠀⢐⠶⣎⣹⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠒⠒⠲⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠸⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣠⣴⢿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣾⣟⠛⠉⠀⠀⠈⠻⣿⡄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣏⠀⠘⠉⠀⣀⣠⣤⣴⠶⠿⠟⠓⠶⢶⡾⠃⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣰⠞⠁⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⣀⣠⣤⠶⠶⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠻⠿⠶⠶⣶⣤⣤⣄⣤⣤⡶⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⢀⣠⠴⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣉⣩⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢯⣄⣀⢀⣀⣠⣤⣴⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣡⣴⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣻⣯⣁⣠⣼⠇ ⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⣤⡴⠶⠛⠉⠁⠀⣴⣣⣴ ⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⣠⣾⠏⠀⠀⠀⠀⠀⠞⢫⡿⠨ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⡀⠀⠀⠀⠀⠀⠐⢆⡀⠀⠀⠀⠀⠀⠀⢦⣀⠀⠀⠀⠀⠀⠉⢓⣲⡶⠲⠛⠛⠉⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⣨ ⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⣀⠀⠀⠀⠀⣙⣲⣤⣤⣤⣤⣤⡶⠟⠛⠒⠶⠶⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢿⡯⠴⣺⡟ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠋⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⠾⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⡶⠶⠶⠖⠚⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣭⣇⣤⣄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⣑⡽⠛⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡏ ⣀⡀⢀⣠⣤⣤⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣀⣤⣶⣿⣿⣿⡟⠀ ⠉⠙⠛⠻⠿⢿⣿⣦⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⢀⣴⣾⣿⣿⣿⣿⣿⣿⠏⠁⠀ ⠀⠀⠀⠀⠀⠀⢻⣟⣧⣀⣸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⠁⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡠⠔⠈⠉⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠔⠹⣄⠈⠃⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣪⠥⠶⠊⢺⡄⠀⠀⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⡠⠃⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢄⡠⡄⠀⠀ ⠀⠀⠀⠀⢀⠞⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⡀⡸⠀⠃⡸⠆⠀ ⠀⠀⠀⠀⢿⠀⠀⠀⠀⠈⠉⠂⡐⠒⠈⠉⠀⠀⠀⠀⡠⠊⡹⢛⠇⠀⠐⣡⠃⠀ ⠀⠀⠀⣸⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⡰⠉⣐⣺⡤⠊⠀⠀⢚⡗⠀⠀ ⠀⠀⠀⡇⢆⠀⠀⠀⠀⡇⠄⠀⠀⠀⢀⡠⠒⠈⡠⢀⡀⠴⠁⠀⠀⣤⠋⠀⠀⠀ ⠀⠀⠀⠡⠀⢠⡀⠀⠀⠱⢈⡂⠀⠄⡤⠊⣈⠡⠒⢀⠺⠁⠀⢠⠂⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⠠⠡⢀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⢀⣠⠔⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⡇⡖⠠⢤⡤⠤⠤⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⡠⠃⠀⡄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⡥⠒⠉⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠒⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣎⠁⠀⣀⣀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⢿⡀⠀⠘⠛⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠤⠚⠉⣀⣠⠔⣻⡆⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣤⡶⠿⠛⠋⠉⠉⢹⢷⠆⠀⠀⠀⠠⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⡀⠀⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠙⣶⠁⢻⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⡀⣠⠏⠀⠈⠀⢠⡷⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢄⣀⣀⣀⠤⠴⠒⠚⠉⠉⠉⠀⠀⠀⠀⠀⢀⡴⠛⢛⣿⣿⡯⠀⠀⢀⡴⠋⣠⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⡠⠋⠀⣰⠃⠀⠀⠀⡠⢾⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠖⢚⣷⡤⠞⠁⠀⠀⠀⠔⠒⣻⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⢡⡀⠀⠀⠀⠀⠀⠀⠀⡰⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠋⢀⠀⠈⠉⢉⣹⠇⠀⠀⠀⠀⠀⢤⡞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⠈⠣⡀⠀⠀⠀⠀⠀⠀⡇⠈⣦⠀⠀⠀⠀⠀⣀⡠⠔⡋⣀⣀⣀⡴⠃⠠⠤⠒⣻⠃⠀⠀⠀⠀⢀⡶⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠈⠓⠄⠀⠀⡀⢀⡠⠞⠁⠀⠉⣠⠖⠥⠤⠔⡾⠁⠀⠀⠀⢠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣄⠀⠸⢦⠀⠀⠀⠀⠀⠈⠙⠒⠤⠤⠤⠬⠽⠤⠤⠼⠿⠭⠤⠤⠤⠖⠋⠀⠀⢀⠸⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠬⠷⢄⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠤⠤⣄⣽⠲⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠠⠇⠀⠈⢩⠏⡿⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⢀⡼⠀⠀⠀⡼⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠤⠤⠔⠒⠊⢀⣠⠴⠒⠁⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡁⠀⣀⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶ ⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠚⠉⠉⠉⠙⢯⣢⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢺⠊⠀⠀⣀⠀⠀⠀⠀⢱⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣮⠃⠀⠀⠘⠛⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⢀⣼⠒⣺⣻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠛⠃⠀⠀⠀⠀⠀⠀⢞⠁⠈⠁⠹⡿⡄⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⡴⠊⠁⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⡀⢹⣖⠀⠀⠀⠀ ⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢾⣧⠀⠀⠀ ⠀⠀⣎⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀ ⣠⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠈⠳⡅ ⢳⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠈⢞⣁⣀⣀⡀⢀⡀⣀⡀⠓⠉⠒⠦⡀⠀⢱ ⡾⠀⠀⠀⠀⠀⠀⠀⢰⠛⠉⠀⠀⠀⢰⠛⠛⠛⠁⠈⠙⠛⠛⡇⠀⠀⠀⠈⠛⡄ ⢻⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣀⡀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⣀⣀⣠⠃
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⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠐⠒⠒⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⡖⣚⢢⠀⠀ ⠐⡟⡴⠅⡆⠀⢰⠁⠀⠀⠰⠀⠶⠶⠆⠒⠀⠘⠆⠀⠓⠉⠚⠀⠀ ⠀⠐⠁⠚⠁⣀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠒⠒⡀⠀⠀⠀ ⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀ ⠀⠀⠀⢼⡀⢀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠞⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡊⢩⡅⢄ ⠀⠀⠀⠀⠀⠀⢳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⠀⠣⠠⠤⠂ ⠀⠀⠀⠀⠀⠀⠀⠘⠛⠟⠈⠉⠉⠉⠉⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣷⣿⣿⣦⣠⡏⠙⠿⠿⢿⣷⣦⣄⠀⠀⠀⠀⣼⣿⣿⣧⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠉⣿⠛⢻⣿⠛⠂⠃⠀⠸⣿⣿⡿⠻⣿⡆⠐⢏⡛⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣟⣿⡄⠘⠀⣾⠿⠀⢠⡀⠀⠰⣿⣰⡄⠀⣿⡇⠀⠸⢇⣸⣿⣿⠿⠛⠛⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠈⠉⠩⣿⣾⡿⠈⠛⠛⠋⠛⠛⠿⠿⠿⠼⡿⠇⣀⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠿⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠖⣲ ⡶⠲⠶⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠒⢒⣾⠃⠀⠀⠀⠀⣀⡤⠔⠚⠛⠙⠛⠓⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣭⣭ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢈⡶⠞⠛⠋⠉⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠀⠀⠀⠀⠀⢠⡆⣠⣾⣿⣿⣿⣦⣀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠆⠀⠀⠀⠀⠀⠈⣿⠿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢡⡀⠀⠀⠀⠀⣽⡟⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠈⠙⠻⠿⢷⣶⣤⣄⣀⣀⣀⣠⣼ ⢻⣧⡀⠀⢠⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿ ⡟⠛⠿⠿⢿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢷⣦⢤⣤⣤⣀⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿ ⣷⡤⠴⠖⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢝⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣿⣿⣿⡭⣿⣿⣿⠽⢏⣹⣿⣿⣿⣯⡿⡻⠟⣿⣝⢻⠿⢿⢋⠹⡿⠽⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡸⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛ ⠀⠁⢠⣤⣤⣤⣤⠀⢠⣤⣤⣠⣤⣄⠀⣤⣤⣄⣠⡄⠀⣤⣀⣤⣤⣀⣄⢀⣤⠄⣤⣀⣤⣄⠀⣤⠀⢠⡄⢀⣤⠀⢠⣤⣄⣠⣤⣤⣤⣄ ⠀⠀⠀⢠⣿⠀⣿⠶⢾⣿⣿⣿⢷⣭⡰⣿⠀⣹⣿⣇⢀⣿⣿⡁⢈⣹⣿⣿⡁⠀⣿⣿⡷⣯⡀⣿⡶⢾⣇⣾⣿⣷⣾⡷⠿⢿⡷⠿⠋⢿ ⠀⠀⠀⠈⠛⠀⠛⠀⠘⠉⠛⠙⠛⠋⠀⠛⠛⠋⠀⠙⠛⠁⠈⠛⠋⠉⠋⠈⠓⠀⠙⠉⠛⠋⠀⠛⠀⠘⠛⠋⠀⠙⠛⠃⠀⠘⠃⠀⠀⠸ ⠀⢰⣤⣴⣶⣶⣶⣶⣶⣶⣤⣴⣦⣴⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣴⣶⣤⣤⣴⣤⣴⣶⣶⣤⣤⣤⣤⡤⠤⠤⠤⠤⠤⠶ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣽⣟⣿⣷⣿⣻⣿⣿⣿⣿⣿⣿⣷⣭⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣟⡟⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⡶⠒⠒⠶⠦⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠚⠉⠁⠀⠀⠉⠻⣦⡀⠀⠠⠤⢬⣉⡛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⢁⡤⠀⠀⠀⠀⠀⠀⠀⠐⢬⣧⠀⠀⠀⠀⠈⠙⣶⡈⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⡄⠀⠀⠀⡀⢹⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠊⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⣿⠀⢿⢦⣄⠀⠀⠀⠀⠀⠈⣼⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢀⡼⢻⡇⢣⠀⠀⠀⠀⠀⣼⠀⠘⡇⠈⠛⠳⢦⡀⠀⠐⠘⣿⣻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠁⢠⠃⠀⠀⠀⡀⢀⡴⠋⠀⠼⡇⠘⣆⠀⠀⠀⠀⣿⠄⢰⡇⠀⠀⠀⠈⢻⡄⠀⢲⣜⣷⢿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠀⠀⠋⠀⠀⠀⣴⠛⠉⠀⠀⠀⠀⠹⣄⠀⠀⠀⣀⠀⣿⣼⣾⠃⠀⠀⠀⠀⠀⢻⡆⠘⣿⣾⣿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠃⠀⠀⠀⡀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣿⣹⣿⠟⠁⠀⢀⣀⣀⣤⡤⠽⢿⣷⡈⢻⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⢠⠀⢀⢰⡇⢸⠃⢀⣀⣀⣴⡤⠦⠀⠀⠀⠀⠀⠀⠉⠁⠓⣆⠀⠀⠀⠀⣿⣿⡿⠀⣻⣿⣷⣆⠙⢿⣿⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⢸⠀⢸⣿⢳⣿⠀⠀⠀⣿⣿⡟⠀⠀⠀⢀⣤⠴⠒⠚⠛⠛⠛⠛⠦⣄⠀⠘⠙⠀⠀⠉⣠⣿⣿⡆⢸⣿⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⣟⣧⡏⠿⠀⠋⠀⠀⠀⠈⠉⠀⠀⠀⠀⠿⣧⣀⣀⣀⣀⣀⣀⣤⡤⠞⠉⠒⠒⠓⠒⠒⠻⠋⠈⣇⣼⠇⠀⠀⠀⠀ ⠀⠀⢠⡟⠀⠈⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⢶⡀⠀⠀⠀ ⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⠀⢻⡄⠀⠀ ⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢻⡀⠀ ⣼⠁⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⣀⣤⠴⠚⠉⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢷⠀ ⣿⠀⠀⠀⠀⠀⠀⣰⠯⠤⣤⣤⡤⠴⠒⠛⠉⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⡇ ⣿⡀⠀⠀⠀⠀⢰⠃⠀⡞⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿ ⠘⣧⠀⠀⠀⢠⠟⠀⠀⣧⣧⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿ ⠀⠘⣄⠀⠀⡼⠀⠀⠀⠈⠛⣳⡤⠤⠤⠤⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣄⠀⠀⣿ ⠀⠀⠸⠦⢾⡓⠒⠖⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠙⠦⠼⠏ ⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢤⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⠒⠓⠲⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⣤⠿⢧⣤⣤⠽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠈⠉⠀⠀⠉⠳⣄⠀⠀⠦⢭⣓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢁⠔⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠈⠳⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠞⠁⠐⠁⠀⠀⠀⣠⠀⠀⠀⠀⠀⢳⠸⣦⣀⠀⠀⠀⠀⢘⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⢀⡔⢹⠀⡄⠀⠀⠀⢸⠀⢻⠈⠛⠲⣄⠀⠀⢻⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⠁⠰⠁⠀⢀⣤⠔⠋⠀⠸⣄⠑⠀⠀⠀⣸⣀⡿⠀⠀⠀⠘⣦⠈⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⢠⠇⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠘⠦⣀⢀⣆⣿⡿⠁⠀⣀⣀⣀⣺⣷⡜⢿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⣼⢠⠀⣠⣇⡜⠀⣠⣤⣤⠄⠀⠀⠀⠀⠉⠉⢙⣄⠀⠀⠉⣿⡿⠀⣿⣷⣆⠛⣿⠂⠀⠀⠀ ⠀⠀⠀⢹⣿⢠⢿⠻⡇⠀⠀⠿⠟⠁⠀⢀⣴⠚⠉⠉⠉⠉⠉⢲⣄⣈⣀⣀⣠⡾⢿⡆⣿⠀⠀⠀⠀ ⠀⠀⣰⠋⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⢀⣿⣯⡀⠀⠀⠀ ⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡏⠱⡄⠀⠀ ⢰⠃⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⢀⡠⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢱⡀⠀ ⣼⠀⠀⠀⠀⢀⣜⣁⣀⣀⣠⠤⠖⠊⠁⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢧⠀ ⢻⠀⠀⠀⠀⡜⠀⣼⡏⠁⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡀ ⠈⣇⠀⠀⢸⠁⠀⢻⣇⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⡇ ⠀⠈⢆⣠⡧⠀⠠⠤⠜⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠳⣄⡼⠀ ⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⠔⠢⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠾⢍⣈⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⣠⠒⠈⠉⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠃⣠⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⡠⣏⡀⠑⠁⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢔⠙⣁⣀⠤⠷⠤⡴⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠀⠀⢀⠎⠀⣀⡤⠤⠒⠒⠒⠒⠒⠒⠲⠦⠤⠤⣠⡄⠀⠀⠀ ⠀⠀⠀⢀⠞⠁⠀⠀⠀⡮⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠾⠀⣀⢤⠄ ⠀⠀⢀⠎⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢐⡲⠭⡔ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣀⡨⠏⠁⠀⢚⠏ ⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⣨⠶⠤⠤⠛⠒⠒⠒⠉⠀⠀⠀⠀⠐⢋⠞ ⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠔⠊⠁⠀ ⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠒⠤⠄⣀⣀⣀⣀⣀⣀⡀⠤⠄⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢳⠦⠘⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣶⠀⠈⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⣻⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣾⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⢀⣀⣠⡿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠉⠁⠀⠈⠻⣿⣿⣿⣿⣿ ⣿⣿⠈⠙⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠸⣿⣿⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⢀⣿⣿⣿⣿ ⣿⣿⣷⡀⠀⠀⠐⢦⣤⣀⣀⣀⠀⣀⣀⣀⣤⣴⠾⠋⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⣿⣿⣿⣷⣤⣀⠀⠀⠈⠉⠉⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠉⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣉⡥⠶⢶⣿⣿⣿⣿⣷⣆⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⢡⡞⠁⠀⠀⠤⠈⠿⠿⠿⠿⣿⠀⢻⣦⡈⠻⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡇⠘⡁⠀⢀⣀⣀⣀⣈⣁⣐⡒⠢⢤⡈⠛⢿⡄⠻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠉⠐⠄⡈⢀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠇⢠⣿⣿⣿⣿⡿⢿⣿⣿⣿⠁⢈⣿⡄⠀⢀⣀⠸⣿⣿⣿⣿ ⣿⣿⣿⣿⡿⠟⣡⣶⣶⣬⣭⣥⣴⠀⣾⣿⣿⣿⣶⣾⣿⣧⠀⣼⣿⣷⣌⡻⢿⣿ ⣿⣿⠟⣋⣴⣾⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣷⠄⢻ ⡏⠰⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢂⣭⣿⣿⣿⣿⣿⠇⠘⠛⠛⢉⣉⣠⣴⣾ ⣿⣷⣦⣬⣍⣉⣉⣛⣛⣉⠉⣤⣶⣾⣿⣿⣿⣿⣿⣿⡿⢰⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠉⠙⠿⠟⠛⠻⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠚⠂⠰⣶⣴⡀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⠛⠛⠉⠉⠉⠉⠉⠛⢷⣦⣀⠀⠀⣿⡄⠀⠀⡀⠀⠤⠃⠀⣾⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣄⠈⠻⣦⣀⠀⠀⣠⣴⡾⠋⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⣠⠤⣄⠀⢸⡷⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⢰⣶⠀⠘⠷⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠛⠉⠙⠻⢷⣦⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀ ⠀⠀⢀⣠⣴⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀ ⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠏⠀⠀ ⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣉⠀⠀⠀⠀ ⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀ ⠀⠙⠷⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀ ⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⡀⢀⠤⠒⠒⠢⣄⠀⢀⣠⣶⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⢶⣤⣤⣤⢴⣯⣥⣤⣤⣴⡿⢿⣤⣦⣴⠶⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀ "search 'sleepy pudding' in 'search for emojis' for more !>_<"⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⣀⣠⣤⣤⠤⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⡤⠤⠖⠛⠛⠛⠻⢡⣉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠒⠀⠀⣇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⠰⣿⣥⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⢶⡶⠾⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⠤⠤ ⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠀⠀⠀⠀ ⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠈⢷⡄⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡄⠀⠀⠀⠀⠀ ⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣸⠦⢿⣆⣶⣶⠾⢧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⢀⡿⣦⣤⣶⠀⠀⠀⢰⣶⡄⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⢠⣾⡻⠛⠉⠉⣉⣻⣷⢿⠁⠐⠛⠻⠷⣤⡀⠀⠉⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣠⡴⠟⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⣿⠟⠀⠀⠀⠀⠿⣾⡤⠶⠶⢶⣷⣦⣤⠿⠋⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢀⣼⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣭⡳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⢀⣴⠟⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡎⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠑⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣴⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡽⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⢁⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢠⣤⡴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣠⣤⣤⣤⣤⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠉⠀⠀⣠⠟⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣟⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣅⡀⠀⠀⣸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢯⣗⣦⡀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠏⠛⢿⣾⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣶⢤⣀⣀⣴⠟⠁⣠⣾⣯⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣉⣀⣠⡿⠟⠁⢀⡿⠉⠛⠛⠶⠦⠤⣤⣤⣤⣤⣤⡤⠴⠶⠶⠶⠶⠚⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⣧⣿⣍⠉⠉⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠤⠤⠀⠀⠀⠈⠉⠈⠙⢷⡶⠶⠶⢶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣔⢄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⢉⣵⣿⠿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣻⣿⣆⠀⠀⠀⣀⡠⠂⠀⠀⠠⣤⣴⠟⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢘⣭⣾⣿⣿⡟⠲⢤⣀⣀⣼⡏⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠃⠀⠀⠈⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠲⣍⢩⣤⣤⣀⣀⣾⠇⢠⠐⢤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⢈⣷⣮⣝⡛⠟⠉⠀⠈⢃⢈⣯⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⣴⠟⠋⠁⠀⠙⣦⣄⣀⣠⣼⣧⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠏⠀⣤⣾⠏⠀⠀⠀⠀⠀⠀⠻⠛⠿⢶⡆⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣣⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣰⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠦⡻⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⢶⣤⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣴⣚⡝⠀⠀⠀ ⠘⡄⠕⡽⣄⢸⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠊⠉⠉⠑⠒⠒⠉⠁⠀⠀⢹⠴⠒⢒⠆ ⠀⡵⢈⣿⠞⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣜⣠⠒⠁⠀ ⢰⣡⠞⠧⣄⠀⠀⠀⠈⠓⠤⢄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⢶⣤⣀⣀⡨⠜⠋⢀⠦⡄⠀ ⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⢢⣄⡤⠚⠁⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢗⡖⡋⠀⠘⡀ ⠀⠀⠀⠀⠀⠀⠈⡝⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁ ⠀⠀⠀⠀⠀⠀⢀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀ ⠀⠀⠀⠀⠀⠀⠘⡀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⢸⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠱⡈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠘⠦⠄⠀⠀⣀⡀⠀⠀⢀⡔⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠉⢁⣀⣐⠤⡀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⣀⣀⡀⠈⠉⠀⠁⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠁⠀⠀⠑⠬⣑⠀⢈⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⡏⠁⠀⠈⠓⢄⡀⠀⣀⡼⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠞⢸⠀⠀⠀⠀⢀⡬⢫⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠇⠀⠀⠀⠀⢀⡼⡫⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠮⠭⡄⠀⠠⢸⠀⢀⡠⠚⠉⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⣋⠉⠁⠀⠆⠀⢀⡤⠒⠉⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠵⠊⠉⠺⠂⠈⠉⠹⠴⠛⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠴⠚⠳⠄⠀⠈⠉⢧⡴⠓⠼⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡌⢹⡀⠀⠀⠀⠀⢀⡀⠤⠐⠒⠒⠂⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠄⣏⣗⡀⠀⢠⠔⠁⠀⠀⠀⠀⠀⠀⠐⠠⡈⠢⡀⠀⠀⠀⠀⠀⠀ ⢸⠀⣇⣸⣇⢀⠇⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⡀⠀⠀⠀⠀⠀ ⠈⡄⢣⣚⢿⠾⠀⠀⢀⣤⠀⠀⣀⣀⠀⠾⠆⠀⠘⠄⢡⠀⠀⠀⠀⠀ ⠀⢡⠈⣾⢭⣛⡄⠀⠀⠉⠀⠾⡿⠾⠃⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀ ⠀⠀⢓⣘⢮⡥⢹⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢃⠀⠀⠀⠀ ⠀⠀⠀⠮⡬⢮⠥⠷⡌⠠⡀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠈⠀⢂⠀⠀⠀ ⠀⠀⠀⠀⢩⢷⣖⣟⡿⣵⢠⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⠊⢱ ⠀⠀⠀⠀⢸⠀⣿⡘⣷⣻⡡⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⡀⡸ ⠀⠀⠀⠤⡀⢹⢹⡞⡴⢫⣽⡙⠒⠒⠲⠒⠒⠈⠐⠈⠓⡄⢀⢀⡧⠃ ⠀⠀⠀⠈⠀⠘⡆⢻⣷⢳⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠘⠘⡎⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢬⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣬⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠾⣿⣟⡶⡶⣶⠖⠒⢲⣶⡾⣛⡿⣼⠎⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈⠉⠁⠈⠀⠀⠀⠀⠀⠀
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣩⣭⣶⣶⣮⣭⡙⠿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠿⣋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⡃⠄⠹⡿⣿⣿⣿⣿⠟⠛⣿⣿⣿⣿⣷⡌⢿⣿⣿ ⣿⣿⣿⣿⣿⠐⣠⡶⣶⣲⡎⢻⣿⣤⣴⣾⣿⣿⣿⣿⣿⠸⣿⣿ ⣿⠟⣋⡥⡶⣞⡯⣟⣾⣺⢽⡧⣥⣭⣉⢻⣿⣿⣿⣿⣿⣆⢻⣿ ⡃⣾⢯⢿⢽⣫⡯⣷⣳⢯⡯⠯⠷⠻⠞⣼⣿⣿⣿⣿⣿⣿⡌⣿ ⣦⣍⡙⠫⠛⠕⣋⡓⠭⣡⢶⠗⣡⣶⡝⣿⣿⣿⣿⣿⣿⣿⣧⢹ ⣿⣿⣿⣿⣿⣿⣘⣛⣋⣡⣵⣾⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⡿⠟⢻⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠟⠛⠉⢱⣾⣶⣿⡿⠛⠿⢿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠙⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣄⠀⠀⠀⢀⣀⣀⠈⢿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⠀⠀⢀⣤⣶⣄⠀⠀⠀⠀⣾⡿⣉⣽⣿⡇⠀⠀⣾⣿⣿⡇⠘⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⠃⠀⠀⢠⡶⠂⠸⣿⣿⣿⠂⠀⠀⠈⣿⣿⣿⣿⣿⠁⠀⠀⠈⠛⠫⠁⠀⣿⣿⠀⠀⠀⠀⠀ ⠀⢀⣤⣶⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⣩⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠀⠀⠀⠀⠸⣧⠀⠀⣿⣿⣿⣷⣦⣄⠀ ⠀⣿⣿⠋⠀⠈⠉⠛⢿⣿⣶⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠄⢿⣿⡇⠈⠹⣿⡆ ⢸⣿⣧⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⢠⣿⡇ ⢹⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣿⠟⠀ ⢸⣿⡿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠈⣿⣇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀ ⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀ ⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀ ⠀⠀⠘⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣶⣶⣦⣤⣤⣤⣴⣶⣶⣶⣿⠿⠿⠛⠻⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠟⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⡤⠴⠒⠒⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡏⣤⡄⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡏⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⡗⢲⣠⠞⠉⠉⠓⠢⡀⠀⠀⠘⡄⠀⢠⠞⠉⠉⠉⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⢀⡋⢠⡄⠀⠀⠀ ⢸⠀⡞⠁⠀⠀⠀⠀⠀⠈⡂⠀⠀⠀⠩⠃⠀⠀⠀⢠⢤⠀⠈⢷⠀⠀⠀⠀⠀⠠⠗⣨⠊⠀⡅⢂⣃ ⣯⠏⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⡇⠀⠀⠀⠀⠇⠀⡇⠀⠀⠈⣇⠀⠀⠀⣸⡿⡯⠑⡬⣳⢹⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⢃⠀⠀⠀⠀⢀⡴⠧⠤⢄⠀⠘⣆⠀⡾⡗⡕⠁⢠⠜⣿⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣟⣯⡱⣵⣋⣂⡿⠳⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⠒⢄⠀⠀⠀⠀⣀⠞⠀⠀⡰⠉⠛⢷⡯⠯⠂⡄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠑⠒⠒⠉⠀⠀⠀⡠⠃⠀⠀⠀⠀⠁⠀⠈⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⠒⠒⠒⠒⠺⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣻⢆⠀⠀⢠⣞⣿⡉⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠕⠚⠋⠈⠃⠘⠃⠋⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠒⠦⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⣤⡄⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⢡⠉⠉⠉⠉⠉⠑⠒⠒⡶⡄⠀⠀⠀⢸⠁⠀⠘⠃⠀⠀⢀⠀⠀⠇⠀⠀⠀ ⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠯⠽⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⡏⠀⠒⠦⣄ ⡖⠒⢺⠀⠀⣴⢲⡖⠒⠒⠒⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⡃⠀⠈⠀⠀⢀⡇ ⡇⠀⢸⠀⠀⣏⠛⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢹⠒⠚⠛⠋⠉ ⠓⠒⢸⠀⠀⣇⠀⠀⠉⠲⢄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠸⠤⣤⠇⠀⠀⠀⠀⠀⠉⠲⠤⣄⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⣩⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠓⠒⠒⠒⠚⠁⡇⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢳⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠰⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠇⠀
⠱⡈⢆⠡⢂⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠ ⠱⣈⠦⢑⠂⡌⠰⠈⡔⠰⠈⡔⢠⢁⠒⠰⡈⠔⠰⡈⠔⡠⢁⠒⠰⡈⠔⠰⡈⠔⡠⢁⠒⠰⡈⠔⠰⡈⠔⡠⢁⠒⠰⡈⠔⠰⡈⠔⡐⠢⠌⡐⠂⢆⠡⢂⠒⠤⢁⠒⠰⡈⠔⠰⡈⠔⡐⠢⠌⡐⠂⢆⠡⢂⠒⠤⢁⠒⠰⡈⠤⢁⠆⠒⠤⢁⠒⠤⠁⢆⠡⢂⠒⠤⢁⠒⠤⠁⢆⠡⢂⠒⠤⢁⠒⠤⠁⢆⠡⠂⢆⠡⢂⠌⡐⠂⢆⠡⠂⢆⠡⢂⠌⡐⠂⢆⠡⠂⢆⠡⢂⠌⡐ ⡱⢠⠊⡄⢡⠐⡡⠡⠄⢃⠌⠰⡀⠆⢌⠡⡐⠌⠡⢄⠡⡐⠡⡈⠅⡰⢈⠡⠄⡡⠄⠃⡌⠡⡐⠌⠡⢄⠡⠄⠃⡌⠡⡐⠌⢡⠐⠌⡠⠡⢘⠠⠉⡄⠢⢁⠌⡰⠈⢌⠡⠐⠌⡡⠐⠌⡠⠡⢘⠠⠉⡄⠢⢁⠌⡰⠈⢌⠡⠐⢂⠡⣈⠒⡈⠔⠨⠄⡩⠀⢆⠡⠌⠰⡈⠰⢈⠡⠂⡌⠰⢈⠰⢈⠰⢈⠡⠂⡌⠌⡄⠢⢁⠌⠤⠉⡄⠢⢉⠄⠢⡁⠌⠤⠉⡄⠢⢉⠄⠢⡁⢌⠐ ⡑⢢⠑⡨⠄⢃⠤⠑⡈⠆⢨⠁⡔⢈⠢⢐⠰⢈⠡⢂⠂⢅⠂⠥⠘⡀⠆⢡⠂⡡⠌⢡⠐⡡⠐⠌⣁⠢⠌⡈⠥⠐⡡⠐⠌⡂⢌⢂⠡⡘⢀⠎⠡⡐⣁⠊⡐⠤⠉⡄⢊⠁⠎⢠⠑⡨⠐⡁⠆⣁⠣⢀⠃⡌⠰⢀⠍⡠⢊⠁⠎⡐⢠⠂⢡⠊⡁⠆⡁⠎⢠⠂⡉⠔⠠⢃⠌⠰⢁⠢⠑⡈⠔⡈⠔⡈⠔⠡⡐⠂⡔⢁⠊⡰⢈⠡⡐⠡⢂⠌⢡⠐⡉⠄⣃⠰⢁⠢⠌⢡⠐⡨⠐ ⢍⠢⡑⠰⣈⠢⠄⢃⠰⠉⢄⠒⡈⠔⣈⠂⢌⠂⡡⢂⠉⡄⢊⠰⢁⡘⡀⢃⠰⠁⡌⢂⠂⠅⡊⠔⢠⠂⡑⡈⢄⢃⡐⢉⠰⠈⡄⢂⠡⡐⠡⡈⢒⠠⡐⢨⠐⠂⡅⠒⡈⢌⠂⡅⢂⠡⢘⠠⡘⢀⠢⢁⠊⢄⡑⠨⢐⠰⢀⠩⠐⢌⠠⢊⡐⠤⠑⡠⠑⡈⠆⡘⠠⢉⠒⡈⠄⡃⢂⠅⠊⠔⡈⢄⠃⢌⠘⡠⢁⠎⡐⠨⡐⢁⢂⠡⡐⠡⢂⠜⡀⠆⢡⠘⡀⠆⢌⠰⢈⠂⠆⠡⠌ ⢎⠱⡈⠥⣀⠒⣈⢂⠡⠊⢄⠊⡐⠌⡠⠘⡠⠘⡀⠆⣁⠢⢁⠢⢁⠰⠈⡄⠃⡌⢐⠂⡉⠔⡈⢌⡐⠤⢁⠌⡄⢂⠌⠄⢃⠡⡐⡁⢢⠁⡡⢂⠡⢂⡁⠆⠌⡡⠐⡡⠌⡐⡈⠔⡈⠔⡁⢢⠘⠠⣁⠊⢌⠠⢂⡑⡈⠔⡈⢂⡉⢄⠢⢁⡐⢂⠱⢀⢃⠰⢁⠢⠑⡈⠤⠑⡈⠔⠡⡈⡑⠌⠰⠈⡌⡐⠌⡐⢂⠰⢈⠡⡐⠡⡈⠔⠠⢃⠂⠆⡘⢈⠔⢂⠡⠌⢂⠢⢁⠜⡈⢡⠂ ⢎⠰⣁⠒⢄⡘⢀⠢⢁⠩⡀⠎⢠⠑⡠⢃⠐⡡⠘⡀⠆⡰⠁⡌⢂⠡⡁⠆⡑⡈⠤⠑⡈⠤⢁⠂⡔⠠⢃⡐⡈⢄⠊⠌⡄⢃⡐⠌⡄⡘⡀⠆⢡⠂⠔⡈⠆⢡⠘⡀⠆⠡⠌⡐⠌⡰⠈⠤⡈⠅⠤⠘⡠⠘⡠⢐⡈⠔⡁⢢⠈⡄⠢⣁⠰⢈⠰⠈⡄⠢⢁⠢⢑⡈⠄⡃⢌⠘⡠⠡⠐⡌⠡⢡⠐⠄⡃⠌⠤⢁⢊⡐⠄⢃⠤⢉⠰⠁⡌⢂⠡⠌⡰⢈⠰⢈⢂⠡⢊⠐⡈⢄⠂ ⣊⠱⡀⠎⢄⠢⢁⠢⢁⠆⢡⠘⡀⠆⣁⠂⠥⠐⡡⠌⠰⢠⢁⠒⡈⠔⡠⠑⡠⢁⠆⡑⠨⠄⢃⠌⢄⠱⠠⡐⠌⡠⢊⠰⠐⢂⡐⠢⢠⠁⡔⣈⠂⢌⢂⠡⡘⡀⠆⠡⠌⡁⠆⡡⠘⢠⠑⢂⠌⡰⢁⠊⢄⡑⠄⢢⠐⢌⠠⡁⠆⡘⢠⠐⡄⠃⡌⠒⡠⢑⡈⠔⠂⡄⠃⡌⠄⡊⢄⠡⣁⠢⠑⡠⢊⠐⡌⠄⡃⠌⡄⠰⢈⠢⠐⡌⢠⠃⢄⠃⡌⠰⢐⠠⢃⠰⢈⡐⢂⠡⠌⡐⡈ ⢆⠱⣈⠒⡈⠔⢂⠡⢂⠌⡐⢂⠡⠌⡠⢘⡀⠣⢐⠨⢁⠢⡐⠌⡐⢌⠠⡑⠐⡂⠔⣈⠡⡘⠠⠌⢂⠔⠡⡐⠌⡐⠤⠁⠎⡐⢠⠑⡠⢊⠐⡠⠘⡀⠆⢡⠐⢨⠐⡡⢊⠐⠌⡄⡑⠂⡌⢂⠌⡐⠤⠉⠤⠐⡌⡐⠌⡄⢂⠅⡂⢅⠂⢆⠰⢁⠰⠁⡔⢂⠰⢈⠡⡐⢡⠐⠌⡰⢀⠃⢄⠢⠑⡠⢂⠡⡐⠌⡐⢂⠌⡰⢁⠢⢁⠒⡠⢘⢀⠒⡈⠔⡨⠐⢂⠡⢂⠄⠃⡌⡐⠡⠐ ⠎⡔⢢⠁⡜⠠⠃⢌⠰⠈⡄⠃⡄⠃⠔⢂⠰⢁⠊⢄⠃⡰⠐⡨⠐⢂⠡⡐⠡⠌⡰⢀⠒⢠⠃⡘⠤⢈⠒⢠⢁⠒⠤⠉⠤⠑⡠⢂⠁⠆⡡⢐⠡⠌⢂⠥⠘⡀⠆⣁⢂⠩⠐⡄⠢⠑⡐⠨⡐⢐⢂⠩⠄⢃⠰⠐⢂⠌⠄⡒⢈⠄⢊⠄⢒⡈⢄⠃⡐⢂⠡⠌⢂⠔⠡⣈⠒⢠⠂⡉⢄⠢⠑⠤⡈⠔⡐⠌⡰⢈⠰⠐⡠⢁⠎⡐⠤⠡⢈⠂⠜⡀⠆⡑⠨⠄⠃⡌⠒⡐⣈⠡⠊ ⢣⠘⠤⣁⠢⢑⡈⢂⠆⡑⠠⢃⡐⠉⡔⠨⡐⠌⡰⢈⠰⢀⠃⠔⣁⠊⠔⡠⢃⠒⢠⠂⡉⢄⠢⢁⠒⡈⢄⠃⡄⢊⠤⠉⡄⠃⡔⠈⡌⠒⢠⠁⡒⢈⠆⠄⡃⢌⠰⠀⠆⢌⠡⠄⢃⠡⠌⢡⠐⠌⡠⠒⣈⠂⢅⠊⡄⠊⠔⡈⠔⣈⠢⠌⢂⠰⠈⠤⠑⡈⠔⡈⠆⣈⠒⢠⠘⡀⠆⢡⠂⠆⣉⠰⠐⡨⠐⢂⡁⠆⠢⢑⠐⠢⡐⢐⠂⡅⠊⢌⠰⠠⢑⢈⠡⠌⡡⠐⡡⠐⠄⢢⠁ ⣃⠚⡰⢀⠅⠢⠄⢃⠰⢈⠁⠆⠰⢁⠢⢁⠔⢂⡁⠆⣁⠊⢌⠰⠀⠎⡐⠰⢀⠎⢠⠂⢅⠢⠘⢠⠡⠌⢂⠒⢠⢁⠂⢅⠂⠥⢀⠣⢠⠉⢄⠢⠁⠆⣈⠒⡈⢄⠢⠉⡔⢈⠰⢈⠂⡅⠊⡄⢊⡐⢁⠒⡠⠘⡠⠘⢠⠉⠔⠨⡐⠄⠒⣈⠂⠅⡊⠔⠡⠘⡐⠤⠑⡠⠘⡀⠆⢡⠘⡠⠘⡀⠆⢂⠱⢀⢃⠢⠐⠌⡁⠆⡡⢁⠆⠡⠒⢠⠉⡄⠢⠑⡈⢄⠒⡈⠤⠑⡠⢉⠂⡅⡈ ⢆⢩⠐⡡⠌⢡⠘⢠⠂⠅⡊⠌⡁⠆⡘⡀⠎⢠⠐⠌⡠⠘⡠⠘⡈⠔⠡⡁⠆⡘⢠⠘⡀⠆⡉⢄⠒⡈⠆⡘⣀⠢⠉⡄⠊⠤⢁⠒⡀⠎⡐⢂⠩⢐⠠⠒⡈⢄⠢⠡⡐⡈⠔⡈⠔⡀⢃⠤⢁⠰⠈⠤⠑⡠⠑⡈⠆⡘⢈⠡⡐⠌⢡⠐⡈⠆⠡⠌⣁⠃⠔⢂⡑⠠⠃⢌⠘⡠⢂⡁⠆⡑⡈⠆⠌⢂⠢⠌⡁⠎⡐⠌⡐⢂⠌⡁⠎⡐⠂⡔⢁⠃⢌⠰⠈⠤⠑⡈⠔⢂⠡⡐⠄ ⠎⣄⠣⡐⠌⡂⠜⢠⠘⡠⠁⠎⢠⠑⡠⠡⢘⡀⠎⡐⡁⠆⢡⠘⢠⢉⠰⠠⢑⠠⣁⠢⢁⠆⢡⠂⠜⡀⠆⠡⠄⢢⠁⣂⠉⠔⡈⣴⣼⣿⣿⣶⣤⣃⡄⢃⡐⢂⠢⠑⠄⠒⢌⡐⢂⠡⢂⠌⠂⡌⠡⢂⠑⡠⠑⡈⠤⠑⡈⠔⡠⠉⡄⠢⠡⠌⣁⠒⢠⠘⡈⢄⠂⠥⠉⡄⢊⠐⠄⠒⡈⠔⡐⠌⡘⠠⠒⢠⠑⡠⠡⢘⠀⠎⡐⡈⠔⠡⠘⡠⠌⣈⢂⠂⠍⡐⢡⠘⡐⠨⡐⠰⢈ ⠣⡄⢣⠐⡡⠌⢂⠡⢂⠡⡘⢈⠔⢂⡁⠆⡡⠐⢂⠡⡐⠌⢂⡘⠄⣂⠡⠊⢄⠡⠄⣂⠡⠌⢂⠌⠒⡈⠌⡡⠘⣀⠒⢠⠘⣀⠲⣿⣿⣯⣯⣝⣻⠿⣿⣷⣶⣶⣷⣾⣾⣷⣶⣶⣬⣴⣈⣌⠡⡐⠡⠌⢂⡁⠆⡁⠆⡑⡈⠔⣀⠣⠐⡡⢁⠒⡠⠘⡀⠆⢡⠂⡉⢄⠃⡄⠃⡌⠌⡡⠘⡠⠘⡠⠡⣁⠩⠄⣂⠡⢘⠠⢉⠰⢀⠅⢊⠡⠑⡠⠒⣀⠢⢉⡐⠁⠆⢂⠡⢑⡀⠣⡀ ⢣⠘⡄⠣⠐⡌⢂⠡⠌⡐⠄⡃⠌⠤⠐⡌⣀⠣⠌⡐⠤⠉⡄⠢⠌⡀⠆⡉⢄⢊⠰⠀⠆⡑⢨⢀⠃⡌⡐⢁⠒⡠⠘⣀⠒⣀⠂⡙⢿⣿⣿⣿⣿⣿⣦⣭⡍⢯⣭⡹⢭⡹⣍⣛⡻⢻⠿⡿⣿⣷⣶⣌⡤⠈⠔⡡⢈⠔⡀⢃⠄⠢⢑⠠⡁⠆⢡⠡⠘⡈⢄⠢⢁⠢⠌⣀⢃⠰⢈⠤⠑⡠⢑⠠⠡⠄⢒⡈⢄⡘⠠⣁⠊⠰⡈⢄⠃⡌⢡⠐⡡⠄⢢⠁⠤⢉⠌⢂⠡⢂⠰⢁⡐ ⢣⠘⡄⠃⡅⠒⠈⡔⠈⡔⠈⡔⠈⠂⣥⠐⢠⠂⡜⠀⡆⠑⢠⠑⠂⢡⠘⠀⡆⠂⡌⢡⠘⢠⠁⢢⡌⠐⡄⠃⡌⡄⠑⠀⡆⢠⢢⣵⣿⣿⣿⣿⢻⣾⡟⣯⣿⣿⣽⣿⡟⣿⡟⣿⣽⣿⣿⣿⣷⣯⣽⣿⣿⣷⡆⣤⠁⢢⠘⢠⠈⢡⠂⢡⠐⡌⠂⡔⢡⡌⠐⡄⠃⡄⠃⡄⠂⢡⠂⠂⠑⡄⠊⡄⠃⠘⡄⠐⠂⡄⠃⣤⠈⡅⢰⠈⢰⠐⢠⢡⠐⡌⡄⠊⡔⠈⡄⠃⡌⡄⠃⢰⠀ ⣊⠱⡈⠆⢡⠂⡑⠄⢃⠰⢁⢂⠩⡐⢠⠘⡠⠌⢄⡑⠠⡑⡈⠔⣈⢂⠡⢊⠐⡌⢠⠃⠌⡄⠣⢀⠆⢡⠐⠡⡐⠄⢃⡁⢆⣼⣾⣿⣿⣿⣿⣯⣿⣷⣿⣻⣽⡷⣟⣷⡿⣯⣿⡽⣟⣷⢿⣾⡽⣿⣻⢿⣾⣿⣿⣶⡅⡈⢆⡈⢌⡐⠌⢂⠡⡐⠌⡐⠄⣂⠑⡠⠑⡈⠤⠑⣈⠢⠌⡈⢅⠰⠈⡔⢈⠡⡐⡁⠎⡐⠌⡠⠘⢠⠁⡜⠀⢆⠡⠌⡐⠄⡡⢂⠡⡘⢐⡈⠤⢁⠜⠠⠌ ⢆⡱⢈⠜⢠⠡⠌⡘⢠⢁⠊⢄⠂⢅⢂⠡⡐⠌⡠⢐⠡⠄⡡⠌⡀⠆⢡⠂⡡⢐⠂⢌⠒⢠⠑⠂⡌⢂⠌⠡⡐⠨⠄⣴⣿⣿⢫⣼⣿⣿⣿⣿⣿⣟⣷⢿⣳⡿⣿⣽⣻⣽⡾⣟⣿⡽⣿⣞⣿⣽⣟⣯⣷⢿⣻⣿⣿⣧⠠⠌⡠⠐⠌⢂⠡⠄⢃⠌⡰⠀⠎⢠⠑⡈⢄⠃⡄⠒⡈⠔⡈⢄⠃⡄⠃⠤⡁⠔⢂⠡⢂⠡⠑⡂⠡⢄⠩⡀⠆⡡⠌⢂⡁⠆⢡⠐⡡⠐⢂⠡⠌⠒⡈ ⢆⠢⢅⠊⡄⢒⡈⠔⠂⠤⠉⡄⢊⠤⠈⡔⠠⡑⢠⠁⢆⡘⢀⠆⢡⠘⡀⠆⡁⠆⡘⢠⠘⡠⠌⢡⠐⡈⠄⠃⠤⢑⣾⣿⠟⣦⣿⣿⣻⣽⣯⣷⢿⡾⣯⣿⣻⣽⣟⣾⣟⣷⣿⣻⣽⢿⣳⣿⣻⣞⣯⣿⢾⣟⣯⣿⣿⣿⣷⡠⠁⠜⡈⠤⢁⠊⡔⠐⡄⠃⡜⠀⢆⠡⢂⠌⠄⡃⢌⠰⢈⠄⢊⠄⡩⠐⠄⡃⠌⡄⠃⡌⢂⠡⡁⠆⢂⠡⢂⠡⡘⢠⠐⠌⡂⠔⠡⡘⢠⢁⠊⡡⠐ ⢎⡘⢄⠃⡌⠤⢐⠨⢁⠎⡐⡐⠢⠄⢃⠄⢃⠄⠃⡌⠤⢐⠨⢐⠂⡡⢂⠑⡨⠐⡁⠆⢂⠡⡘⡀⠆⠡⠌⡁⢆⣿⣿⢫⣾⣿⣟⣷⢿⣳⡿⣾⣟⣿⡽⣷⡿⣽⣾⣿⣾⣿⣾⣻⣽⡿⣯⣷⣟⣯⣿⢾⣟⣯⣿⣽⣿⣿⣿⣷⠁⡒⢈⠔⡈⠔⠠⠃⡄⠃⠤⢉⠄⢢⠡⢈⠒⡈⢄⠒⡈⠔⠨⡐⠄⢃⡘⠠⢡⠐⡡⠐⡌⠰⠠⡑⠨⠄⢃⠰⠠⠡⠌⠒⡈⠔⠡⡐⡁⠢⢡⠐⠡ ⡒⢌⠢⣁⠒⢨⠐⠌⡄⠒⢠⠁⠆⡑⠨⡐⠌⡠⢃⠐⠢⠌⢂⠌⡐⣁⠢⠡⡐⣁⠒⡈⠆⢡⠐⠤⠑⡈⠔⡐⣾⣿⣏⣿⠟⣿⣿⡽⣿⢯⣿⢷⣻⣽⢿⣽⣿⣿⣿⢿⣿⣿⣿⣿⣿⣽⣟⣾⢯⣿⢾⣟⣯⣿⣞⣿⣿⣿⣿⣿⣖⠠⢁⠢⠌⠰⠁⡅⢂⠩⡐⠌⡐⢂⠔⡁⠢⢁⠆⡘⠠⡉⠔⡐⠌⢂⠰⠁⠆⢂⠡⠒⢠⠡⢁⠆⢡⠊⠄⡃⢌⠡⠘⡄⡑⠨⡁⠔⡠⢃⠰⢈⠡ ⡱⢈⡒⠄⡑⢂⠌⢢⠐⡉⢄⢊⡐⠡⢁⠆⡘⢀⠆⡉⠔⡈⠆⢨⠐⢠⠂⡑⢠⠐⠤⠡⢘⠠⠌⣀⠃⡐⢂⢼⣿⡷⣾⣿⣼⣿⣿⣟⣯⣿⢯⣿⢿⣽⣟⣿⣿⣿⡸⢆⣸⣿⣿⣿⣿⣿⣯⣿⣻⣽⣟⣯⣿⣞⣯⣿⣿⣿⣿⣿⣿⠐⢂⠡⠘⢠⠃⠰⡈⠔⡐⢨⠐⢨⠐⣈⠡⢂⠂⢅⠢⢁⠒⡈⢌⠂⡡⢊⠘⡠⢁⠎⠄⢢⠁⡌⠂⡌⠒⡈⢄⠊⢡⠐⠄⢃⠔⠨⢐⠠⣁⠊⠄ ⡱⢌⠰⡁⠜⣀⠊⢄⠢⢁⠂⠆⢠⠃⢂⠂⢅⠊⡐⠌⡰⠠⢉⠄⢊⠄⠢⠑⡠⠊⢄⠃⢢⠘⢠⠐⡈⠔⡈⣿⣿⣹⣿⣿⣿⣿⣿⣾⣯⣿⣿⣯⣿⣾⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣳⣿⣻⣾⣽⣿⣿⣿⣿⣿⣿⣿⡰⢈⠰⠉⠄⡌⢡⠐⠌⡐⢂⠡⢂⠒⢠⠂⠅⢊⠄⠢⣁⠊⠰⡀⠃⠔⢂⠡⠒⠠⢌⠘⣀⠒⠠⢃⡐⠡⠌⡐⠌⢂⠌⡘⡀⠎⡐⡁⠆⡐⠌⢂ ⡒⢌⠒⢌⠰⢀⠎⢠⠂⠅⢊⠌⡐⠌⢂⡉⢄⠊⡐⢂⡁⠆⢡⠘⣀⠊⠡⡑⠠⡑⢂⡘⠠⢘⠀⠆⡁⠆⢩⣿⣧⣿⣿⡟⠻⢿⣿⢿⢟⣛⢏⡙⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⢯⣿⣞⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⠓⡀⠎⡐⠡⡐⢂⡘⠄⡑⡈⢄⠃⠌⣂⠘⡈⠔⣈⠡⠄⢊⠡⡐⢉⠰⠈⡔⢁⢃⠰⠈⠤⡈⡑⢠⠂⡑⢂⠡⡘⢠⠊⡐⠤⠑⡐⠤⠑⡐⠌⢂ ⡱⢨⠘⡄⢊⠤⠘⢠⠘⡈⠔⣈⠰⢈⠂⠔⡈⠤⠑⡠⠒⣈⠂⢒⠠⠉⡔⠠⢃⠐⠂⡄⢃⠂⣉⠰⠐⣈⣴⣿⣿⢟⣿⢞⣿⣍⠌⡌⢢⠐⢢⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣾⣻⣟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⢁⠢⢁⠆⡁⠆⠰⢈⠔⡈⢄⠊⠔⡠⠡⢘⡀⠆⡐⡉⠤⢁⠢⢁⢊⠡⡐⠨⡀⠎⡁⠆⢡⠐⡁⢂⠡⠌⡐⠤⢁⠂⢅⠂⡱⠐⢂⡑⢈⠔⠂ ⣑⠢⡑⠰⡈⠤⠉⡄⠢⠡⢌⡀⠆⣁⠊⠤⠑⡠⠃⠤⠑⡠⠘⡠⢂⠱⢀⠃⠤⢉⡐⠤⣈⣰⣤⣶⣿⡿⠟⡛⠣⢌⡘⢄⠻⠌⡒⢌⠢⡉⢆⠹⢦⡴⣽⣚⠿⣿⣿⣯⣟⣯⣿⣳⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠌⡄⢡⠂⠔⡈⠌⡁⠆⢂⠌⡐⠌⠒⡠⠑⢂⠰⢈⡐⠤⠑⢂⠡⠊⢄⢂⠡⣁⠒⢠⠡⢘⠠⡘⢠⢁⠊⠤⢁⠒⡈⠌⢂⡘⠠⠑⠂⡌⠄⣊⠐ ⢆⠱⡈⠅⢒⡈⢡⠐⡡⢁⠂⡔⢈⠤⠘⣀⠣⢀⠣⠘⡠⢁⠆⡁⠆⠌⡐⠨⠐⢢⣴⣿⡿⡿⡟⠭⡁⢆⠱⣈⠑⢢⠘⡄⢣⠘⡰⢈⠆⡱⢈⣾⣿⣼⣣⣛⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⢈⠂⠤⡁⠌⢂⠡⡘⢠⠘⢄⡘⠠⢌⠡⡐⠡⠊⡄⢡⠐⢂⡉⠤⠑⡨⠄⣂⠡⠄⢊⠄⢢⠁⡒⢠⢁⠢⢘⠠⣁⠊⢄⠩⠄⡰⢁⡉⠆⠰⢁⠄⢊ ⢎⠰⡁⠎⡐⠤⢁⠒⡠⠡⠌⡐⢨⠠⢑⡀⠆⢡⠂⡑⡐⠢⠄⡑⡈⠒⣈⠡⠌⣿⣿⡹⢎⡱⢈⠆⡱⢈⠒⠤⡉⢆⠱⡈⢆⠱⣀⠣⡘⢤⣛⣿⣿⢿⣻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⠂⡡⠌⡐⡐⢈⠂⠥⠐⡡⢈⠤⠐⣁⠂⠆⠡⠌⡡⠄⠃⢌⢂⡐⢂⠱⢀⠒⡀⠆⡉⢄⠊⠤⠘⢠⠁⡂⠆⡁⢆⠐⡌⡐⢂⠡⡐⢂⠰⢈⠡⠂⠜⡀ ⢎⠰⡁⠎⠰⡈⠔⡈⠤⠑⡠⠑⡠⢂⠡⡐⠌⢂⠔⠡⡐⢁⠆⢡⠐⡡⠄⢂⠂⠛⣿⣷⣮⣁⠧⠜⡠⢃⠜⡠⠑⡌⢢⠑⡌⠒⢤⡱⣎⣷⣿⣿⢫⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⠀⠆⡈⠔⡠⢁⠰⢁⢊⠰⠁⡔⢂⠢⢁⠆⡘⡈⢡⠒⠠⠌⡡⢂⠂⡔⠨⡐⠌⠤⠑⡠⢁⠆⡘⠄⡩⠄⢢⠁⠆⢡⠂⢌⡐⠤⢁⠒⡠⢁⠆⠡⠌⡁⠎⡐ ⢎⠰⡁⠎⢡⠐⠌⡐⢂⠱⢀⠃⠔⢂⠡⡐⠌⢂⠌⠒⡠⠡⠌⢂⠔⡐⠌⣂⠡⠡⣀⠛⠿⣿⣿⣿⣶⣣⣞⣴⢣⡼⣤⢧⡞⣵⣫⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢃⠰⢀⠊⢄⠡⠒⠠⠌⡐⠌⢠⠂⡑⢠⠂⢡⠂⠒⡠⢁⠆⠌⢡⠂⡁⠆⠡⠄⢃⠰⢈⢂⠱⠐⠂⡔⢈⠔⡐⠌⡄⠊⢌⡐⠌⠤⠐⢂⠌⠒⢠⠡⢈⠆⡑⡐⠢⠐ ⢎⠰⡁⢎⡐⠌⠂⠥⢈⠢⠌⣈⠒⡈⠔⡠⢉⠄⢊⠔⡁⢒⠈⠆⢂⠌⡰⢀⡑⠢⠄⠌⡐⠠⢉⢉⠛⠻⠿⠿⠿⣿⣿⣿⡿⠿⠿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⡯⠩⠐⢡⠈⢂⠆⠡⢂⠢⢁⠃⠔⠨⡐⣁⠢⢁⠢⠘⠠⠌⢡⠐⠂⡌⠌⡐⠤⠑⡈⠅⢊⠄⢃⠢⠌⢠⠃⢡⠂⢌⠰⠐⢂⠔⡉⠤⠐⠌⢂⠩⠄⢊⡘⢀⠆⠡⢂⠔⠠⢃⠡ ⢎⠰⡁⢆⠰⢈⡑⢈⠢⠐⡌⡀⠆⠡⠒⡐⢨⢀⠃⡰⠈⡄⢃⡘⠄⡘⢀⠆⠠⢃⠘⡠⢁⠃⢂⠆⠌⣁⠢⠌⡐⢠⢀⠂⡐⡈⠔⡈⠔⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢛⠩⠍⡐⢨⣰⣤⣷⣿⣶⣿⣷⣾⣷⣾⣶⣶⣭⣦⣵⣤⣤⣆⣁⡢⢉⠒⣈⠂⢌⠡⡐⠌⡐⢂⠑⡨⠐⠡⣈⠂⠔⡈⠆⡘⢠⠘⢠⠂⠩⠄⠒⡐⠌⡘⡈⢄⠃⡘⢠⠐⠡⡈⠆⢡⠈⠆⣁⠂ ⣊⠱⡈⢄⠊⡄⠂⡅⠢⠑⡀⠆⡉⠔⠡⠌⢄⠂⡅⠂⠥⠐⡂⠰⢈⠰⠁⡌⢂⠅⢂⡁⠆⡉⠤⢈⠒⡀⠒⡈⠤⢁⠂⠜⠠⠌⡐⠰⠈⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡐⠐⡂⣔⣦⣿⡿⠟⠋⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠛⠿⠿⠿⣿⣷⣾⣶⣤⣦⣡⡈⠄⠃⡄⡉⠔⠠⠌⢂⠁⠆⡁⠆⡘⠠⠌⣁⠊⢡⠐⠌⡐⠰⠈⠤⠑⠂⡌⢡⠐⠌⡂⠜⡐⠠⠌ ⢆⠱⡈⠆⡡⢂⠑⡠⢁⠃⡌⡐⠡⡘⠠⠃⢌⠰⠠⢉⠄⢃⠌⠡⠌⢂⠅⠒⡈⠄⢃⠰⢈⡐⠄⢃⠰⢈⠡⡐⢂⠌⡰⢈⠒⠄⡡⢂⠉⣼⣿⠿⢿⣿⣿⣿⣿⡿⠿⣿⣟⠡⣀⣳⣾⡿⠛⠁⠀⣀⠤⠒⠀⠉⠉⠉⠈⠁⠀⡀⢂⠂⠀⠐⠀⠤⠤⢀⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣈⡂⢡⠊⠌⡐⠡⡘⠠⡑⡈⠤⠘⡀⠎⡐⠡⣁⠩⠄⣉⠒⡈⢄⠊⡐⡁⢒⢈⠡⢂ ⢎⠰⡁⢆⠡⢂⠡⢂⠡⠌⡐⠄⢃⠰⢁⡉⢄⠢⠑⡈⢌⠰⢈⠡⡘⠠⠌⡡⠘⡈⢄⠃⡰⠀⢎⡀⢃⠌⡰⢀⠃⡰⠀⠆⠌⢂⡁⢂⢌⣿⣿⣹⢂⠖⡰⢆⠲⢌⣱⣿⣿⣶⣿⠟⠁⢀⡤⠒⠁⠀⢀⠀⠐⠀⠄⠠⠀⠂⠁⢾⡉⢯⡙⠳⠖⠶⠤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠠⡈⠔⠡⢡⠐⡡⠐⣁⠢⠑⡈⠤⠑⡐⠄⢢⠡⠐⠤⢁⠢⢁⠂⠥⡈⢄⠊⠄ ⣊⠱⡈⠆⡘⢠⢁⢊⡐⠌⡐⠌⣂⠡⠂⡔⠈⡄⢃⠌⢄⠢⢁⠢⢁⠅⠢⢁⠆⢡⠂⠜⠠⡁⠆⡠⢃⠰⠐⡈⠤⢁⠊⢌⠂⡡⠐⣈⢸⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣯⢉⣀⠴⠊⠁⠀⠀⠀⠂⠠⠀⠁⠂⠄⠐⡀⠂⠐⠈⠹⢦⣘⠡⣏⢸⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢉⠰⢈⠰⠁⡄⠃⡌⡐⠤⢁⠜⡀⠢⢑⡈⢄⠃⡌⠰⢁⢂⠩⡐⠌⡠⠃⢌⠰⠐⡈⢌⡐ ⢆⠱⡈⠆⡑⠄⣂⠢⠐⡌⢠⠃⢄⠢⠑⣀⠣⠐⡌⢐⠂⢌⠂⡡⠂⡌⠡⢂⠌⢂⠌⣂⠑⡰⢈⡐⠄⢊⠡⠌⡰⢈⠂⠆⡘⢠⠡⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⡀⠄⠈⠐⠀⠁⢼⡛⡹⢲⠦⣄⣈⠀⠄⠀⠀⢈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣴⣈⠄⠃⡌⠰⠐⡰⠈⡄⠒⣈⠡⢂⠰⢈⠰⢀⠃⡌⠄⡒⠠⡑⢠⠑⡈⢄⠃⡌⠤⠐ ⢎⠰⡁⠎⡠⢑⡀⠆⢡⠒⠠⠌⢂⠔⣁⠢⢐⠡⡐⠌⡨⠄⢊⠄⡑⠠⢃⠢⠘⡠⠒⢠⠘⡀⠆⠰⡈⢂⠅⢒⠠⠂⡅⢊⠐⡄⢂⠡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⡀⠁⢀⠐⠀⡈⠀⠈⠈⢳⣑⢢⠱⣈⠍⣛⠲⣮⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎⡐⢨⠐⠡⠄⢃⠄⢃⠄⢢⠁⡒⡈⠔⠨⡐⠰⢈⡐⠡⡐⢂⠌⡐⢂⠌⠰⡀⢃ ⢎⠰⡁⠎⡐⢄⠢⢘⠠⡘⠄⢃⠌⠰⠀⠆⢡⠒⡐⠌⡐⠌⢂⠌⡐⢡⠂⠆⡑⢠⠑⢂⠂⠥⢈⠅⡰⠁⡌⠂⠆⡑⢠⠊⡐⠰⢈⡐⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠄⠀⣿⠛⠶⣄⠀⠁⢀⠀⠘⢦⣷⣨⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⢄⠡⠂⡌⢁⠎⢠⠊⡐⠌⡐⢂⠡⡐⢉⠰⢀⢃⠢⢐⠡⡐⠌⡐⠌⡄⢊⠡⢐⠂ ⢎⠰⡁⢎⠐⡂⠢⢁⠒⠄⢊⠔⡈⢡⠊⡘⣀⠒⡐⠌⡐⠌⢂⠌⡐⢂⠌⠒⡈⢄⠊⡄⠩⡐⠌⡐⠤⠑⡠⠉⡔⢈⠄⠢⠑⡨⢀⠤⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠂⠀⠄⠸⣯⠰⡍⠷⢦⣄⢀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠛⠛⢋⠉⢄⠂⡡⢂⠢⠑⣀⠊⡐⢂⠡⠌⢂⠡⢂⠡⡐⡁⢢⠁⡂⠆⠡⠒⡐⠌⡐⠢⠐⠌⡄⠃⠌ ⢎⠰⡁⠆⡑⢠⠃⠌⢂⠩⣀⠒⡈⠔⡠⠡⢐⠰⢈⡐⠡⢘⡀⠎⡐⢨⢀⠃⢌⠰⠈⠤⠑⡠⢊⠐⡄⢃⠰⢁⠰⢈⠰⢁⠡⢂⡁⠢⠌⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⠀⠀⠀⠂⠀⠘⣿⣷⣽⣦⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⠐⠤⢁⠃⢂⡉⠄⣂⢁⠢⠐⡡⢀⠆⠡⠌⢂⠜⠠⡁⠆⢡⠐⠌⢄⠢⠡⠌⡑⢂⠡⢂⡑⠈⡅⠊⢄⠩⠐ ⣊⠱⡈⠆⡑⠄⢊⡘⠠⢡⠀⠆⢡⠒⢠⠑⣈⠐⡂⢄⠃⡂⠔⢂⠡⢂⢂⡉⢄⠢⠉⡄⠃⠔⢂⠡⡐⠌⡰⠈⡄⢃⠢⠌⡐⢡⠠⡁⠆⡘⣿⣿⣿⣿⣿⣿⣿⠏⡀⠠⠐⠀⠁⠠⠈⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡛⢅⢢⠙⡛⢛⠻⠿⠿⠿⣿⣿⣿⠛⣀⠂⢌⠐⢂⠉⡄⡐⢂⠄⠢⡐⠡⠄⠃⢌⠂⡱⠈⡄⢃⠰⢈⠂⠜⡈⢄⠢⠑⢂⠌⠄⡃⠰⢀⢃⠰⠉⡄⢊⡐ ⢆⠱⣈⠒⠌⡘⢠⠐⠡⢂⠉⡌⡐⢨⠐⡈⠤⠘⡀⠆⡡⠘⡐⠨⠄⠃⡄⢂⠢⠌⢡⠐⣉⠰⢈⠰⠠⠑⡠⠑⡠⢊⠐⠌⡐⢂⡁⠒⡄⠡⠘⣿⣿⣿⣿⣿⠏⠀⠀⢀⠀⠄⠂⠁⠐⡀⠂⠀⢀⠀⠉⠙⣛⣻⠛⠭⡑⢢⢑⢊⠤⢃⠥⢋⠴⣙⣬⣿⣿⠛⡁⢂⠤⢈⠂⠌⢂⠌⡐⠤⢁⠊⢡⠐⣁⠊⢡⠂⡡⠄⢃⠰⠈⡄⢃⡘⠄⡘⡀⠆⡉⢄⠊⠤⢁⠱⠈⡄⠢⢑⠠⢡⠀ ⢎⠰⢂⠅⡊⠤⢁⠌⡡⠌⢂⠔⡈⢄⠢⢁⠆⡑⢨⠐⠤⠑⣈⠡⠌⠡⠄⢃⠰⢈⠂⡌⠄⠢⣁⠢⢁⠃⡔⠡⡐⢂⡉⠤⢁⠆⡈⢅⠢⠑⢂⠄⠛⣿⣿⣤⡈⠐⠀⡀⠀⣀⣰⠞⠖⠶⡰⢌⠖⡲⢚⢫⠑⢢⣉⠒⣡⠃⡌⢎⡰⡉⢆⣣⣾⣿⠟⡋⠄⢂⠔⡁⢂⠂⣉⠰⢈⠰⠈⡔⢈⠌⡰⠈⠤⠘⡀⠆⢡⠘⡠⢁⢃⡐⢂⠰⢈⠄⡡⠘⡠⠌⢂⠅⠊⡄⢃⠄⡃⢌⡐⠂⠌ ⣊⠱⣈⠒⡈⠔⣈⠰⠠⡘⣀⠒⡈⢄⠢⢁⠢⠌⡐⠨⠄⢃⠄⢢⠉⡰⠉⢄⠊⠤⢁⠢⠌⢡⠀⢆⠡⠌⡠⢡⠐⢂⠰⢈⠄⠢⢁⠢⠌⡑⢌⠠⠃⠄⡙⠻⣿⣿⣵⣦⡤⢋⠥⢚⣼⣧⣶⣬⣎⣱⡉⢆⡙⢢⢄⢋⠤⢓⣘⣢⣵⣿⣿⠿⢋⢁⠒⢠⠘⣀⠢⠐⡁⢒⠀⢆⠡⠂⡅⠢⠌⡐⠄⡃⢌⠡⢘⡀⢃⠤⢁⠂⠆⡰⠈⡔⢈⠰⢀⠃⡔⢈⠢⢈⠥⠐⣈⠰⠈⠤⢠⢉⡐ ⢆⠱⡀⠎⡐⠡⠄⢢⠡⠐⢄⠢⢁⠆⡘⢠⠂⠅⡌⢡⠘⡀⠎⡀⠆⢡⠘⡀⠎⣀⠣⠐⠌⡂⢡⠂⡌⡐⢁⠢⠘⡠⢁⠊⢄⠃⡌⡐⢂⠌⡠⠃⠜⡐⢠⠡⢀⠍⠛⢻⢿⣿⣿⣾⣿⢯⠙⢻⠻⠿⢿⢿⣿⣷⣾⣮⣾⣿⣿⢿⣿⣿⠰⠐⡈⠤⠘⡀⠆⡀⠆⡑⡈⠤⠉⡄⠢⢑⠠⡁⠆⢡⠘⡀⠆⡘⠠⠄⢃⠰⠈⡌⠰⢠⠁⠆⠌⣂⠡⠌⡐⢂⠡⢂⢂⠱⠀⢆⠉⡔⠂⠤⠐ ⢎⠰⡁⠎⡐⢡⠊⢄⠢⠉⡄⠒⣈⠰⠈⠤⠘⡠⠒⢠⢁⠒⠤⠑⡈⠆⠰⢁⠒⢠⠂⢩⠐⠌⡐⠰⠐⡈⠔⢂⠱⠠⣁⠊⢄⠊⡐⠰⢈⠰⠠⠑⡈⠤⠁⢆⠡⠌⢂⡁⠦⣾⣿⡟⣋⡯⡘⡄⢣⡘⣄⠫⢌⠦⠹⡟⠿⡛⢆⣼⣿⠿⢀⠡⠒⢠⠁⠒⡠⢁⠒⠄⡡⠂⢅⠢⠑⢂⠡⡐⠌⡂⠔⠡⡘⠠⡑⡈⠆⠌⡡⢐⠡⠂⠜⡈⠔⢠⠂⢅⠢⠡⢘⡀⠆⠌⡡⠂⡌⠤⠑⡈⠆ ⢎⠰⡁⠎⡐⠡⡈⠔⡠⠃⢄⠃⡄⠢⢉⠄⢃⠤⠑⢂⠰⢈⢂⠱⠐⡨⠁⢆⠘⡄⡘⠄⡘⠤⠑⡈⠅⠌⠒⡈⠤⠑⡠⠘⡀⠎⣀⠃⠌⡄⢃⠡⠌⡐⠉⡄⠒⠨⠄⡰⢀⡙⠻⢿⣷⡐⢣⣘⣤⣩⣤⣧⣾⣶⣷⣾⣷⣾⣿⡿⠛⠠⠌⣀⠣⠄⢊⠡⡐⠌⠢⢘⠠⠑⠂⡔⠉⡄⠢⢁⠆⢡⠘⡐⠤⠑⡠⠒⡈⠔⡁⢂⠆⡉⠔⡈⠔⠡⣈⠂⡔⠡⢂⠰⢈⠂⠅⢒⠠⢂⡑⠨⠐ ⢎⠰⡁⢎⠐⣁⠒⡈⠤⠑⡈⠔⠠⠃⢌⠰⠈⡄⠣⢈⠆⠌⡄⠢⠑⡠⠃⢌⠰⠐⡐⠌⡐⢂⡑⢈⠌⠌⡁⠆⡁⠎⢠⠑⡐⢂⠄⠊⡔⠐⡈⠔⣂⠡⣁⢂⠩⡐⠢⠐⠤⢀⠃⠻⣿⣿⡿⠿⡟⢟⣻⣿⣿⡻⠝⣿⣯⠬⢁⢂⠡⡁⠒⡀⠆⡘⠠⠡⡐⣈⠡⢂⠡⢊⠡⠄⢃⠰⠁⠆⡘⡀⠆⡁⠆⡑⢠⠑⡈⠔⡈⠔⡐⢨⠐⠌⢂⠥⠐⢂⠄⢃⠌⡰⠈⢌⡘⠠⡁⠆⠰⢁⠡ ⡜⢠⠃⡄⢃⠄⠄⡃⢄⠣⠘⡘⠃⡜⠠⠄⢣⢀⠣⠄⡘⠄⡠⢃⠣⢀⠣⠘⡀⠇⡘⠠⠃⡄⠘⡄⡘⠄⡃⠸⠠⢘⠠⣀⠃⡄⡘⢃⠀⢇⣘⣠⣀⣄⣠⢄⢧⡠⢧⠧⣜⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⡃⢄⠛⢻⣿⡤⣤⣀⣤⣘⣃⣘⠠⠃⠇⠤⢀⡀⢄⠃⢄⠃⠤⠘⠄⡃⠜⡠⢃⠠⡘⠠⡘⠠⠃⢄⠃⡸⠀⡜⠠⠄⡘⠸⢀⠄⠛⡀⠜⡀⠜⡀⠣⠄⡀⠇⡠⢘⠃⠜⡀ ⡜⢠⠃⡌⢂⠌⠒⡈⢄⠢⠑⡈⠔⡠⢃⠘⡀⠆⠒⡈⠔⡈⠔⡠⢁⠊⢄⠃⢌⠰⢈⡁⢒⠈⡔⠐⡰⢈⡐⠡⣁⠢⠁⣄⡶⠶⣖⢫⢏⡽⡰⢥⠲⡜⢆⡏⣖⠹⣌⣷⣿⣿⡻⣭⢏⡭⢮⡝⣷⣚⢶⡳⡼⢶⣫⢼⣿⡷⢣⡝⢢⠭⡭⣍⡛⡟⠶⠾⣤⡐⠢⢈⠆⡘⢠⠉⠔⡈⠔⡐⢠⠁⠆⡑⠠⢃⠡⠂⠜⠠⠡⠄⢃⠌⡐⠡⢂⠌⢡⠘⢠⠁⡒⢈⠡⢂⠡⢂⡁⠆⡘⡐⠄ ⡜⢢⠑⡄⠃⡌⠂⢅⠢⠘⡠⠑⢂⡁⠢⠡⢘⢀⠃⢌⠰⠈⡔⠠⠃⢌⠂⠜⡀⠆⢡⠐⠌⢂⠔⡁⠆⢂⠄⢃⠄⢢⠡⡈⠻⠷⢬⣗⣪⢖⡙⣎⢳⡙⡎⢶⣉⠷⡌⡽⢿⠿⣿⠿⣿⢿⡿⣿⠿⣿⠿⣿⢿⡿⣿⢿⠿⣋⠧⣜⢣⡛⢴⢣⡹⣜⡭⠷⠛⡃⠔⡁⠢⢘⠠⢘⠠⡁⠆⢡⠂⡡⠊⠄⢃⠂⡅⢊⡘⠄⢃⡘⠤⠘⢠⠑⢂⡘⠄⢊⡐⢂⠡⢊⠐⠌⡐⠂⡔⠨⢐⠰⢈ ⡜⢠⠃⡄⠣⢐⠉⡄⠢⢑⡀⢃⠢⠐⡡⠑⡈⢄⢊⠐⡂⠱⢀⠃⠜⣀⠊⠔⡈⢌⠂⠜⣈⠐⡂⢌⠰⠁⡌⢂⠌⠄⣂⠡⠑⢂⠆⠤⢉⡉⢩⠉⡃⠛⠚⠓⡚⠶⠻⠶⠯⠾⠴⢋⠦⠓⠜⢢⠛⠤⠛⠴⠣⠞⢒⠛⠚⡑⠛⢊⢋⠉⡍⠂⠥⢀⠒⢠⠃⠌⡐⡈⠅⣂⠡⢂⠡⡐⠌⢂⠔⠡⢘⢈⠂⠥⠐⢂⠰⢈⠂⠔⢂⡉⠄⡊⢄⠢⠘⡠⠐⠌⡐⢂⡉⠤⢁⠱⢀⢃⠢⠌⠠ ⡜⢠⠃⡔⠡⢊⠐⡄⢃⠂⠌⠤⢁⢃⠰⠁⡌⠄⡊⢄⠡⠑⡈⢌⠂⠔⣈⢂⠡⢂⡘⠄⢂⠡⠌⡠⢂⡑⠄⢊⡐⠌⡀⠆⡉⠤⢈⠔⠂⠤⢁⠢⠁⠥⢉⢂⡁⠆⡑⢂⠒⡐⢈⠂⡔⢉⠘⡀⠎⡐⢉⢂⡑⢈⢂⠉⡔⠈⡌⡐⠨⡐⠤⠉⡄⠃⢌⠂⢌⠂⡡⠐⡡⢀⠆⠡⠒⣈⠰⠁⡌⢂⠡⢂⠉⠤⢉⠄⠃⡌⠌⡘⢠⠐⣁⠒⢠⠊⢡⠐⡉⠤⠑⡠⠒⡈⠔⣈⠂⠔⢂⡉⠔ ⣌⢡⠊⡄⢃⠌⢂⠔⡈⢌⠘⠄⡊⠄⢢⠑⢠⠊⡐⡈⢄⠃⡌⠰⢈⠒⡀⠆⢡⠂⠰⡈⢂⠅⠢⢁⠆⠰⢈⠂⡔⢈⠔⡈⠔⢂⠡⠌⡘⠠⣁⠢⢉⡐⠢⢀⠒⠰⠐⢂⠒⡈⠤⠡⢐⡈⠔⡐⢂⠡⢂⠂⡔⠈⡄⠊⢄⠡⡐⠄⢃⠰⢀⠃⠤⠉⡄⠊⠤⠘⢠⠑⡠⠡⣈⠑⡰⠀⠆⡑⠠⠃⠌⡄⠩⡐⡈⢄⢃⠰⢈⠰⢁⠢⢐⠨⠄⢊⠄⠢⢁⠆⡑⢠⠑⡈⠔⡀⠎⡈⢄⠒⡈ ⢆⢢⠑⡰⢈⠄⡃⠰⢈⠄⡊⠔⠡⡘⢠⠘⡀⠆⠡⠌⢄⠊⢄⡑⢂⠡⢂⡉⠤⡈⢅⠰⠁⡌⢡⠂⡘⠄⠃⡌⡐⠨⡐⠨⠄⢃⠄⡃⠌⢡⠀⠆⡡⢀⠃⡌⢂⠱⢈⠂⠆⡁⠆⡑⢠⠂⠜⠠⠌⡐⢂⠡⠄⢃⠤⠉⡄⠒⡠⢉⠄⡊⢄⠩⣀⢃⠰⠉⠤⢉⠄⢢⠁⡒⢠⠘⠠⡑⡈⠔⠡⡑⢨⠠⢑⠠⣁⠢⠌⢠⠃⡐⢂⠡⢂⠡⡘⠠⠌⡁⠆⢂⠜⡀⠆⢡⠘⡀⢆⠡⢂⡘⠠ ⠎⣄⠣⡐⣁⠢⠌⡁⠆⢌⡐⠌⢡⠐⢂⠡⡘⢀⠣⠌⢂⠌⢂⠰⠈⡔⢂⠰⠠⣁⠢⠌⠒⡠⠂⠜⠠⠌⡡⢐⡈⢡⠐⡡⠘⡠⠒⡈⢌⡐⠌⢂⡁⠆⡡⠐⡌⠰⢈⠰⠁⡌⡐⣁⠢⠌⡘⢠⠑⡈⠤⢁⠊⡄⠢⢑⡀⠣⠐⡌⡐⠰⢈⡐⠄⠢⠌⡘⠄⢊⡐⢂⠡⡐⠡⡈⢅⠰⠈⡔⠡⢄⠡⢂⠌⡐⠄⢢⠘⡀⠆⠡⠌⢂⠡⠒⣀⠣⠌⡐⠌⡂⠔⡈⠔⡁⢢⢁⠢⠘⡠⠐⠡ ⠣⡄⢣⠐⠄⡒⠤⠑⠨⢄⠰⢈⠂⡌⢂⠡⡐⡁⠆⡘⠤⠘⡠⢁⠎⡐⠄⢃⠔⠠⠒⣈⠡⡐⢉⠄⢃⠢⠁⢆⠠⣁⠒⢠⠑⡠⠑⡈⠤⠐⠌⡂⠔⢂⠡⠒⢠⠑⡨⠄⢃⠰⠐⡠⠒⡈⠤⢁⠢⢁⠆⠡⠊⢄⠱⢀⠢⢁⢃⡐⢈⠡⠂⡔⠈⡅⠢⢁⠜⠠⡐⠌⡰⢀⠃⡔⠈⡄⠃⠤⡁⠆⡘⢠⠘⡀⠎⢄⠢⠡⠌⢡⠘⡠⢁⠒⢠⠒⢠⠁⢆⠡⢘⠀⠎⢠⢁⠂⠆⡑⢠⢉⡐ ⢣⠘⠤⡉⠒⢄⠢⠉⡔⢂⠢⠡⠌⡐⠌⡰⠐⡠⠑⡠⢂⠱⠀⢆⠂⡌⠰⡈⢄⠣⠘⣀⠒⢠⠡⠌⢂⠆⡉⢄⠒⢠⠘⡀⠆⢡⠘⢠⠂⠍⡰⢀⠣⢈⠔⠡⢂⠜⠠⢘⠠⡁⠎⢠⠑⠰⢈⠂⠜⢠⠈⢅⠊⢄⠢⢁⠆⠡⠂⡄⢃⠢⠑⡠⠃⠤⠑⡈⢄⠃⡔⠈⡔⠠⠃⢄⠃⡰⢉⡐⠤⠑⡈⢄⠢⠡⢘⠀⢆⠡⢊⡐⠤⢁⠢⠉⠤⠘⡀⠎⢠⠘⢠⠉⡰⢁⠢⠘⡐⠌⢄⠢⠐ ⡃⢎⠱⡀⢍⠠⢂⠱⠀⠆⢂⠱⠠⣁⠒⠄⡱⢀⠃⠤⡁⠢⢉⠄⠒⡈⠔⡐⢂⠢⠑⡠⢘⢀⠒⡈⠆⡠⢁⠆⡘⢠⠂⠥⠘⡠⠘⡠⠘⡐⡐⢂⠡⠂⠜⣀⠃⠌⣂⠡⠒⡐⠌⢂⠌⡁⠆⣉⠐⡂⡉⢄⠊⢄⠢⠡⡈⠆⡑⡐⢂⠡⠊⢄⠑⡂⠱⠈⡄⠒⡠⠃⢄⠃⠜⡀⠎⡐⠤⠐⢂⠥⠘⡀⠆⡑⡈⢌⡐⢂⠡⠐⡂⢌⡐⠉⡄⢃⠌⡰⠁⡌⢂⠂⢅⠂⠆⡑⠰⢈⠂⡔⠡ ⡱⢈⠆⡡⠌⢂⠡⢂⠩⠐⡁⠆⠡⠄⢊⠰⠐⢂⡉⠰⢀⠣⠌⠰⢁⡘⠐⡨⠐⢂⠱⠐⡈⢄⢊⠐⡂⡁⠆⢂⠡⢂⡘⠠⢃⡐⠡⢂⠑⡐⠨⠄⢃⡘⡐⠠⢊⠰⠀⠆⡑⠰⢈⠂⡌⠰⢈⠄⡘⢠⠘⡀⠎⢠⠂⡑⠰⢈⡐⠄⢃⠰⠉⡄⢊⠐⡡⢁⠢⠑⡠⠑⢂⡘⠐⡨⠐⡐⢂⠩⢀⠆⡑⠠⠃⠤⢁⠢⢐⠨⡐⠡⠒⣀⠢⠑⡐⠨⠐⡄⠱⢀⠊⢌⡐⠌⠒⣈⠁⠆⡡⠄⡡ ⡱⢈⠆⡡⢘⠠⣁⠊⢄⠃⠌⡌⢁⠎⣀⠃⠜⠠⡐⡁⠎⡐⡈⢅⠂⢌⠂⢅⡘⠄⢊⡐⠡⠂⢌⠂⡡⠐⡡⠊⢄⠡⠄⢃⠰⢀⠃⡌⢂⠡⡁⠎⢠⠐⣈⠡⢂⠡⢉⠰⢈⡁⠆⡡⠐⣁⠊⡐⠌⢄⠢⢁⠜⡀⠆⢡⠁⢆⠰⢈⠂⡅⢊⠐⠌⢂⠔⡁⠢⢑⠠⢉⠄⠢⠑⡠⠃⠌⡄⠃⡌⡐⡈⠅⢊⠄⢃⠰⢁⠢⠐⡡⢁⠢⠐⡡⠌⢡⢁⠢⠑⡈⠌⠤⢐⡈⠥⠐⣈⠒⢠⠘⡀ ⡱⢈⠆⡡⠌⡐⠄⡘⡀⠎⡐⡈⢄⠒⢠⠘⣈⠡⡐⠤⠑⡠⢁⠢⠘⡀⠎⢠⠐⠌⡂⢄⠃⡉⢄⠊⢄⠱⢀⠱⢈⠰⢈⢂⠡⢊⠐⠤⢁⢂⠡⡘⠠⣁⠢⠐⡡⢈⢂⠡⠂⡔⢈⠤⠑⡠⠘⡀⠎⡀⢆⠁⢆⠨⠘⡀⠎⢠⠂⡡⠌⡐⡈⢌⠘⣀⠒⡈⢡⠂⡡⠊⢄⠃⡡⢂⠑⡌⢀⢃⠰⢀⠅⢊⠰⢈⢂⠡⢂⡁⢃⠤⢁⠢⠑⡠⢘⡀⠆⠌⡡⠘⡈⠔⢂⡐⢂⠱⠀⡜⠀⢆⠡ ⡱⢈⠆⡡⢘⠠⡑⢠⠁⠆⠡⠌⡐⠌⢂⠒⣀⠒⢄⠢⠑⡠⠁⢆⡑⠨⡐⠡⡈⠆⣁⠢⠘⡠⠌⠒⣈⠰⢈⠰⠈⡄⠃⡄⠃⠤⢉⠰⠈⠤⢁⠂⠥⡀⠆⡑⢠⢁⠢⢁⠅⠢⠌⣀⠃⠔⠡⠌⡐⣁⠂⡉⠤⢈⠅⠢⠑⢂⠡⡐⢂⠡⠌⡐⠌⡀⢆⠁⠆⢂⠅⡘⢠⠘⡀⠆⡡⠄⠃⡌⠰⠈⡄⠃⡄⠃⠤⢁⠆⢨⠐⡰⢈⠰⢁⢂⠡⡐⡈⠆⡁⠆⡁⠎⢠⠐⠌⡠⠃⠤⠉⡄⢂ ⡱⢈⠆⡑⢂⠡⠄⠃⡌⠌⡁⠆⢡⠘⡠⢁⠂⡌⢄⠢⠑⡠⢉⠤⢀⠃⡄⢃⠤⠡⡐⠄⣃⠰⢈⠡⠄⢢⠡⡈⢅⠰⢁⠰⢉⠰⠈⠤⢉⠰⠈⡌⠰⠠⢑⡈⢄⠢⠌⢂⠌⣁⠒⢠⠘⡈⠔⣁⠢⠄⡑⡈⢄⠃⢌⢂⡉⠤⢁⠒⡈⠔⡈⠔⢨⠐⢂⡉⢄⠃⡌⠤⢁⠢⢁⠒⠄⡌⢡⠐⡡⢁⠢⡁⠜⡈⠔⣈⠐⡂⢡⠐⢂⠡⠌⡠⢂⠡⡐⠌⠤⠑⡈⠔⠡⡈⠆⢡⠘⣀⠃⠔⢂ ⠵⡈⢦⠑⡨⠐⠌⢡⠐⠌⢄⠩⢀⠆⣁⠢⠡⠐⠂⡌⠡⡐⢁⠢⠌⠰⠐⡈⠤⠁⡔⠈⡄⠢⢁⠢⠉⠄⠒⢠⠊⡐⠌⠰⠈⠤⢉⠰⠈⡄⠃⡄⢃⠡⢂⠐⠢⠐⠌⢂⠌⢠⠘⡀⠆⠡⠌⣀⠒⡈⠔⡈⠄⢊⠄⠂⡔⠨⢐⡈⠄⠃⠌⠌⡐⠌⡐⠄⢊⠐⠄⠢⢁⠢⢁⠊⠔⡈⠄⢒⠠⢁⠒⡈⠔⡈⠔⠠⠡⠘⢠⠘⠠⡁⠆⣁⠢⠁⡔⠨⠐⡡⠘⡈⠔⠡⠘⣀⠒⢠⠘⡈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⢻⠍⠀⠀⡰⣉⠟⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⡊⠙⠋⠣⠜⠃⠀⠀⠀⠣⠟⢡⠎⢷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣅⠀⡖⠤⡀⠀⠀⠀⠀⠀⠀⢠⠐⢊⠴⣉⠳⢶⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣯⠜⡡⣱⠄⠀⠰⡐⡌⢰⡁⠆⠊⠒⣂⣹⣼⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠘⠿⣴⣯⡶⣭⢶⣱⣬⢣⣜⣰⣉⣥⡶⠿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠈⠉⡿⠛⢛⣿⡟⠋⠉⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⢦⣄⣤⣀⣀⡀⠀⠀⠀⠀⠀⢠⠅⠈⢞⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⣾⣼⡻⡽⣍⢏⡝⢳⡄⠀⠀⠀⣸⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠎⠁⠙⠸⠘⣈⠃⣳⠀⠀⢠⡇⠀⠀⠀⢀⣷⠀⠀⡀⠀⠀⢀⠀⠀ ⠀⢰⣷⣶⣯⠀⣠⡆⠀⣟⣆⡣⣝⠀⠀⢼⡃⠀⠀⠀⠀⢹⡄⠐⠀⠐⠀⢂⠀⠀ ⢸⠻⡿⡜⢸⣖⠈⢀⠠⣋⣬⠽⣧⠀⢀⣸⡇⠀⠀⠀⢠⡐⣧⢤⡄⣀⠐⠀⠀⠀ ⢸⣼⣿⣻⣛⣿⠀⠀⣼⡟⠛⠛⠀⠀⣀⠘⣇⢘⠀⠀⡀⡇⣧⢇⢸⠟⠀⠀⠀⠀ ⠀⢉⠻⣟⣉⣁⣀⡥⡟⠀⢀⢀⠀⢸⣀⢹⠸⣆⡆⠀⣤⣗⡫⢌⡈⠑⠀⠀⠀⠀ ⠀⠀⠸⣃⣩⠏⠓⠖⠋⠰⠈⠀⠀⠀⠈⠉⠪⠄⠨⠪⠭⠠⠝⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠒⠂⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠖⠛⠛⠉⠉⠛⠓⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣾⣿⣷⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣾⣿⣿⣿⣿⣿⣿⡍⠛⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠹⡆⠀⠀⢀⣤⣦⡀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⣿⣯⣭⡛⠻⢿⣿⣿⣇⠀⠀⠀⢹⡄⠀⢺⣿⣿⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠷⢮⣯⡶⠛⠙⠿⣿⣆⠀⠀⠀⠻⣖⠶⡉⠁⠀⠀⠀⠀⠀⢠⡿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠙⠻⣷⣦⣤⣀⠙⣦⡈⠙⢦⣀⠀⠀⢠⠟⠁⢸⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣼⠷⢦⡀⠀⠀⠀⠀⠉⠉⠉⠛⠃⠀⠠⠈⢑⣶⠏⠀⠀⠀⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⢠⣶⡿⣫⠖⠀⠑⠒⠦⠤⠤⠤⣤⣀⣀⣠⣤⠤⠖⠚⠁⠀⠀⠀⠀⠈⠷⣤⠀⠀⠀ ⠀⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀ ⠀⠀⣼⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀ ⠀⠀⣿⣿⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄ ⠀⠀⣿⢸⠀⠀⠀⠈⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃ ⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀ ⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠂⠀⠀⠀⠀⠀⢀⣠⡴⠋⠀⠀ ⠀⠀⠀⠀⠀⠘⠷⣴⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠞⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⠷⠶⠶⣶⣶⣶⡶⠶⠖⠚⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠉⠀⠀⠀⠀⠀⠀⠈⠉⠻⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢾⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢦⣴⣄⡀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠞⠚⠉⠉⠁⠀⠀⠀⠀⠉⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠙⠿⣄⠀⠀⠀⠀⠀⣠⣤⣤⠶⢶⡀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⡤⣄⠀⠀⠀⠀⠀⠀⣶⠿⠁⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⢸⣗⠆⣮⣽⢂⣟⠀⠀⠀⠀ ⣀⡾⣻⢍⣧⡙⢎⡷⠀⠀⠀⠀⣼⠟⡁⠂⠁⠘⠀⢀⣤⡀⠀⣤⣦⣴⣴⣤⠀⣴⣔⡀⠀⠀⢿⡄⠀⠀⠀⢹⣚⣎⣹⣌⣾⠃⠀⠀⠀ ⠀⢷⢯⡞⢿⣉⢮⣻⠀⠀⠀⠀⣿⡇⠎⠀⠌⠀⠡⠘⠏⠁⠈⠛⠛⠚⠛⠉⠀⠘⠉⠁⠀⠀⠘⣯⠀⠀⠀⠀⠉⠉⠁⠈⠀⠀⠀⠀⠀ ⠀⠘⠷⢭⡶⠾⠖⠋⠀⠀⠀⠀⣿⡇⠀⢂⠠⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠋⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠾⠛⠉⠐⠂⠹⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢴⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡿⠇⠀⠀⢀⠀⠀⠀⢀⠀⠄⠂⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⠠⠐⢀⣠⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⢁⠰⠀⠌⠠⠀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠠⠐⠀⠁⠀⠀⠠⠈⣴⢀⣶⡟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣏⣞⣠⣁⣬⣦⠝⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢁⠸⣟⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠛⠟⡛⣯⠁⠆⠡⢀⠠⠀⠠⠐⠈⠀⡀⠄⠀⡀⠀⠐⠀⠐⠀⠀⡀⠐⠀⢀⠀⠂⡔⣿⡄⠀⡶⠛⠲⠋⠉⢹⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡉⠄⠃⠄⡐⢂⠠⢀⠀⠠⢀⠐⠠⢀⠡⢈⠐⠠⠁⢂⠀⡐⠈⠄⡌⢒⣸⡏⠁⢈⣧⡀⠀⣾⡶⠀⠙⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣍⠲⡐⢄⢃⠰⢠⠉⣆⠡⠒⡄⢂⠔⢢⠘⡠⢌⠰⢠⠐⣈⠒⣌⣲⡿⠉⠀⠀⢼⡁⠀⢈⠁⠀⣼⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣌⠦⢌⠢⢅⠓⠤⡙⣘⠰⡉⡜⢂⢣⢑⡊⢜⠡⣊⣴⣭⠾⠋⠀⠀⠀⠀⠈⠓⠲⠚⠓⠛⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣻⣾⠾⠷⠷⠞⠛⠛⠛⠋⠛⠛⠛⠛⠿⣿⣏⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠙⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⠀⠀⠘⣿⣿⣷⣶⣶⣶⣶⣶⣶⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠟⠀⠀⠀⢹⣿⣿⣿⣯⣏⠉⢹⣿⣿ ⠀⠀⠀⠀⠀⣰⣾⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡛⢀⣾⣿⡿ ⠀⠀⠀⢀⣾⣿⣿⠿⢿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢻⣿⣿⣿⣿⡿⠁ ⠀⠀⢠⣿⣿⡿⠃⠀⠀⠈⠻⢿⣿⣿⣦⡀⠀⠀⠀⠀⠈⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣴⣿⣿⣿⠟⠁⠀ ⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣤⣤⣤⣤⣤⣼⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠿⠛⠛⠛⠉⠀⠀⠀⠀ ⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠿⠿⠿⠿⠿⠿⢿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠻⢿⣿⣿⣷⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣬⣽⠏⠙⣿⣿⡟⣋⣭⡝⠻⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢘⣭⣿⣄⠺⣿⡿⣾⠿⠿⠇⣰⢹⠀⠀⠀⠀⠀ ⠀⠀⢠⣴⣶⣶⣬⣝⠻⢿⠾⣿⣇⣴⣿⣿⣦⢛⣾⠀⠀⠀⠀⠀ ⠀⠀⠹⠿⠛⣛⠛⠿⣿⣐⡳⢊⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⣤⣬⣭⣵⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⣛⣩⣭⣵⡖⣤⠲⣶⣦⣭⣭⣛⠿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⣿⡿⣫⣾⣿⣷⣦⣙⠻⣿⣿⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⠿⢟⣩⣾⣿⣿⣿⣿⣿⣿⣷⣌⠻⣿⣿⣷⡄⠀⠀ ⠀⠀⢰⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⡄⠀ ⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠁⠀
⣿⡿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿ ⣿⠀where are the grapes >:(⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡀⢀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠁⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⡦⣠⣰⡆⡄⣶⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠠⠛⠓⠚⠚⠆⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣖⢶⣶⣶⣶⡖⠢⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣸⣿⣿⣿⣇⠡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣥⣄⣈⣉⣽⣩⣠⣄⣌⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣩⣭⣶⣶⣮⣭⡙⠿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠿⣋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⡃⠄⠹⡿⣿⣿⣿⣿⠟⠛⣿⣿⣿⣿⣷⡌⢿⣿⣿ ⣿⣿⣿⣿⣿⠐⣠⡶⣶⣲⡎⢻⣿⣤⣴⣾⣿⣿⣿⣿⣿⠸⣿⣿ ⣿⠟⣋⡥⡶⣞⡯⣟⣾⣺⢽⡧⣥⣭⣉⢻⣿⣿⣿⣿⣿⣆⢻⣿ ⡃⣾⢯⢿⢽⣫⡯⣷⣳⢯⡯⠯⠷⠻⠞⣼⣿⣿⣿⣿⣿⣿⡌⣿ ⣦⣍⡙⠫⠛⠕⣋⡓⠭⣡⢶⠗⣡⣶⡝⣿⣿⣿⣿⣿⣿⣿⣧⢹ ⣿⣿⣿⣿⣿⣿⣘⣛⣋⣡⣵⣾⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢸🦢🦢🦢🦢🦢🦢🦢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠈⠉⠛⢻⣶⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⢰⣿⠂⠀⢀⣤⣼⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⣠⣶⠿⡛⡜⢿⣷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⢀⣾⡿⠿⠿⣷⣼⣢⢻⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠘⠻⣿⣤⣿⡃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠈⠻⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⣶⢶⣦⣤⣀⣀⣀⣄⣠⣤⣤⣤⣤⣤⣴⡾⢿⡄⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⠏⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⡀⢀⣀⣤⠾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣻⢿⠉⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣽⣻⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣻⢷⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣯⣿⢾⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⡽⣟⡿⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⡽⣯⠇⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢀⡀⠀⠀⣀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣶⣶⣿⡟⠉⠛⠛⣶⠛⠛⢻⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⢩⡙⣿⣄⠀⠀⠀⠀⠀⠀⣾⣏⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⢢⠱⡩⢿⣆⠀⠀⠀⠀⢸⣿⢄⠫⡹⠟⠿⣻⣷⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣋⠬⢥⢣⡑⢎⣿⣦⠀⠀⠀⠀⠻⣯⣶⣡⢋⠖⡡⣾⣾⠗⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣯⣴⣿⣶⡣⣼⣦⣙⣿⡆⠀⠀⠀⠀⠈⠛⠿⣾⣼⣷⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠘⠿⠟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣯⣿⣷⣿⣻⣾⣟⣷⣿⣻⣾⣟⣷⣿⣷⣿⣻⣾⣿⣾⣟⣷⣿⣷⣿⣻⣾⣿⣾⣟⣷⣿⣷⣿⣻⣾⣟⣷⣿⣷⣿⣻⣾⣿⣾⣟⣷⣿ ⣿⣿⣽⣿⣽⣾⣿⣯⣿⡿⣽⣿⣯⣿⢿⣾⣿⣾⢿⣟⣾⣯⣿⢿⣾⣿⣾⢿⣟⣾⣯⣿⢿⣾⣿⣾⢿⣯⣿⢿⣾⣿⣾⢿⣟⣾⣯⣿⣿⣽ ⣿⣯⣿⣾⣿⣽⣾⡿⣷⣿⡿⣷⣿⣻⣿⢿⣾⡿⣿⣻⣿⣽⡿⣿⣻⣾⡿⣿⣿⣿⣽⡿⣿⣿⣾⢿⣿⣻⣿⢿⣻⣾⡿⣿⣻⣿⣽⣷⣿⣻ ⣿⣿⣽⣷⣿⣯⣿⢿⣿⣽⣿⢿⣽⣿⣻⣿⣯⣿⡿⣿⣽⡿⣿⣟⣿⣿⣽⣿⠷⢿⢿⣿⣿⣷⣿⣿⣻⣿⣽⣿⢿⣻⣽⣿⣿⣽⣿⣾⣟⣿ ⣿⣯⣿⣾⣿⣽⡿⣿⣯⣿⣾⣿⡿⣽⣿⣷⣿⣻⣽⣿⣻⣿⣿⣿⠟⡉⠄⠠⢈⠀⢂⠀⡉⠛⢿⣿⣿⣽⣿⣾⣿⢿⡿⣷⣿⣻⣾⣟⣿⣿ ⣿⣿⣽⣷⡿⣯⣿⣿⣽⣷⡿⣷⣿⡿⣷⣿⢯⣿⣿⣽⡿⣷⣿⣷⣾⣥⣌⠐⢠⠈⢀⢂⢳⢌⣂⠹⢿⣿⣷⣿⣻⣿⢿⣿⣽⣿⣯⣿⢿⣾ ⣿⣿⣯⣿⢿⣿⣻⣽⣿⣾⣿⣟⣿⡿⣟⣿⣿⢿⣾⣿⣿⣿⡿⣯⣿⢿⣿⣷⠂⡈⢤⣾⣿⣿⣌⠂⠌⣻⣿⣽⣿⣻⣿⣟⣿⣾⣟⣿⡿⣿ ⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⣟⣛⢻⣻⣿⣿⣟⣷⡿⣿⣽⡿⣯⣿⣷⢀⠉⣿⠿⡿⠏⢀⠂⠰⣿⣛⢻⣛⣛⣛⣛⣛⣛⣛⣛⠻ ⡱⢎⠶⡱⢎⠶⡱⢎⠶⡱⢎⠶⣡⡛⣴⣭⣿⣿⣟⣷⡿⣯⣿⣟⣷⡿⣿⣽⣿⣷⠀⠄⢂⠠⠐⠠⢈⠐⣽⣎⡳⡜⢦⠳⡜⢦⠳⡜⣬⢛ ⣍⢏⡞⣱⢋⣞⡱⣋⢞⡱⣋⢞⣱⣿⣿⣿⣻⣽⣾⣿⣽⣿⣳⡿⣯⣿⣟⣾⣽⣿⣯⠐⠠⠐⠈⠄⠂⡄⣹⣧⢳⡙⣎⢳⡙⣎⠷⣙⢦⢫ ⡜⢮⡜⣥⢫⢖⣷⠿⢮⣵⣍⢮⡹⡹⣍⢯⡹⣍⠯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠡⠈⠄⠃⠤⢹⡧⢧⡹⣌⢧⡹⣌⡳⣍⢎⢧ ⡹⢦⣙⢦⣋⠞⡽⣳⠶⡾⢟⢦⢳⡱⢎⠶⡱⢎⣳⣿⣿⣿⣿⣽⣿⣽⣿⣽⣿⣿⠟⡉⢂⠡⠈⠄⡁⠎⣼⣏⢧⠳⣜⢲⡱⢣⠳⡜⣎⢮ ⢣⡏⣜⢦⡙⢮⣷⠷⠟⠻⢻⣮⢣⡝⣎⢳⣙⢮⣿⣿⣿⢿⣾⣿⣾⣿⣿⠿⢋⠁⡐⢀⠂⠄⡁⢂⠐⠄⣺⡧⢞⡱⢎⢧⡙⢧⢫⠵⣚⢦ ⠳⡜⣎⠶⣩⢏⡛⣟⢻⣛⣿⣭⡳⠼⣌⡳⢬⣿⣿⣿⣿⣿⣿⣿⠿⣫⢿⡆⢀⠂⡐⠠⢈⠐⡀⠂⠌⡠⢽⡗⣫⠼⣩⠖⣭⢣⢏⡞⡱⢎ ⣛⠼⣌⣳⠱⣎⣵⣾⣋⣭⡶⢾⣋⠷⣎⠵⣳⢚⡿⢿⠿⣟⡹⢆⡻⣔⢫⣿⠀⡐⠠⢁⠂⡐⠠⢁⠂⠡⢸⣯⢱⣋⠶⣙⢦⣋⠞⡼⣱⢋ ⣮⣷⣼⣦⣿⣴⣮⣽⣽⣧⣽⠟⣹⣷⣮⣷⣵⣯⣼⣧⣿⣴⣽⣮⣵⣮⣧⣿⡇⠠⢁⠂⡐⠠⢁⠂⠌⠡⢈⣿⣶⣭⣾⣵⣮⣼⣽⣶⣥⣯ ⣿⣿⡿⣿⡿⣿⣿⢿⣿⣿⣵⣾⣿⣿⡿⣿⣿⢿⣿⢿⡿⣿⡿⣿⣿⢿⣿⣿⡇⠰⢀⠂⠄⡁⠂⠌⠠⠁⠌⣿⣿⡿⣿⢿⣿⡿⣿⡿⣿⣿ ⣿⣯⣿⣟⣿⣿⣽⣿⢯⣿⣟⣿⣻⠏⣰⣿⣿⢿⣯⣿⢿⣟⣿⣿⣾⢿⣻⣾⣏⠐⠠⢈⠐⠠⠁⠌⠠⠁⠌⣿⣿⣟⣿⡿⣷⣿⣟⣿⣿⣽ ⣿⣿⣽⣿⣻⣾⡿⣽⣿⢿⣾⢿⣿⣾⣿⣿⢿⣟⣿⣻⣿⢿⣻⣾⢿⣿⡿⣽⣿⠠⢁⠂⠌⠠⠁⠌⠠⢁⠂⠼⣿⣿⣯⣿⢿⣷⡿⣿⣾⢿ ⣿⣯⣿⣾⣿⣻⣽⣿⣟⣿⣿⣻⣯⣿⣯⣿⢿⣻⣿⣻⣽⣿⢿⣻⣿⣯⣿⢿⡏⢐⠠⠈⠄⠡⠈⠄⡁⠂⠌⠰⢿⣿⣷⡿⣿⣯⣿⣿⣽⣿ ⣿⣿⣽⣷⡿⣿⣻⣽⣾⣿⣽⣿⣽⣷⡿⣯⣿⣿⣻⣿⣯⣿⡿⣿⣯⣿⣽⣿⡏⢀⠂⠡⠈⠄⡁⠂⠄⡁⢊⠐⢚⣿⣷⡿⣿⣽⣷⡿⣯⣿ ⣿⣯⣿⣾⣿⢿⣟⣿⡿⣾⣿⣾⢿⣽⣿⣟⣯⣷⣿⣷⣿⣯⣿⣿⣽⣷⡿⣿⡇⠠⠈⠄⡁⠂⠄⡁⢂⠐⠠⡈⠄⣿⣿⣟⣿⣽⣾⣿⣟⣿ ⣿⣿⣽⣷⡿⣿⣻⣯⣿⡿⣷⣿⡿⣿⣾⢿⣻⣯⣷⣿⣷⣿⣻⣾⣿⣳⣿⣿⡇⠠⢁⠂⠄⡁⢂⠐⠠⢈⠐⡐⠠⢀⣿⣿⣯⣿⣟⣾⣿⣻ ⣿⣯⣿⣾⣿⢿⣟⣿⣽⡿⣟⣷⣿⣟⣿⡿⣟⣿⣽⣷⣿⣽⡿⣷⣿⣻⣷⣿⡃⠐⠠⢈⠐⡀⠂⠌⡐⢀⠂⠌⡐⠠⢹⣿⣿⣳⣿⡿⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣷⣛⣻⣿⣿⣭⣭⣽⣿⣿⣿⣛⡳⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣟⣿⡾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣽⡻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣞⠻⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣍⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⡧⠒⡌⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⣿⡿⢇⠱⣘⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡟⣾⣿⣿⡇⡜⢢⡑⢦⡐⠂⡌⡐⢄⢂⠰⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⣿⣿⡿⠶⣈⢱⠸⣆⡈⢱⣀⠱⡈⢆⣁⠉⠶⡈⢰⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠹⡾⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣧⣿⣿⡏⠱⣠⣣⣷⣼⣾⣥⣆⡳⣉⠶⣌⡛⢶⡉⢆⣲⣠⣥⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠙⢾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⣦⣿⣿⢃⣿⡿⠟⡉⠉⠈⠙⠛⠿⣷⣷⣢⡙⢦⡙⢆⣿⣿⣿⣿⣿⣿⣧⠀⡀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠡⣌⢳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⣿⢿⣿⣿⣿⠋⡔⠁⠀⠀⠀⠀⠀⠀⠀⠉⠿⣷⡢⢍⠚⣿⣿⣿⣿⣿⣿⢳⠐⡄⠡⣀⠂⢄⣿⠁⠀⠀⠀⠀⠈⠉⠙⢧⡀⠀⠀⠀⠀⠀ ⣰⢻⡗⡛⠛⢋⣉⡀⠁⠚⠶⣥⣆⡀⠀⠀⠀⠀⠀⠀⠹⣷⡌⠒⡈⠛⡿⠿⡟⡡⢆⡹⢄⡓⢄⠊⣼⡏⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⣆⠀⠀⠀⠀ ⣿⢸⣟⣷⣫⣿⡿⠿⣷⣤⣀⠈⠙⠻⠇⠄⠀⠀⠀⠀⢀⠹⣿⡤⢁⠣⡘⠱⢨⠑⢎⡔⠣⠌⣀⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡽⣇⠀⠀⠀ ⠹⣿⣏⣹⣯⠿⣡⡴⣭⣛⠿⣿⣦⣄⢀⣮⣐⠤⣘⠼⣌⣳⣽⣿⣦⡁⠌⡑⠢⢉⠆⡌⠑⣠⣺⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡜⣧⡀⠀ ⠀⠘⠿⣿⣭⣼⣱⣮⣵⣭⣟⣼⣫⠿⣿⣿⣿⣿⣩⢟⡻⣏⢯⣟⣿⡿⠂⠄⠡⢈⠐⡈⣖⣷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡎⣷⡀ ⠀⠀⠀⣨⣿⣿⣿⡻⠍⠀⠉⠉⠛⠻⢷⣾⣽⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⣁⣮⣼⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡇ ⠀⠀⢸⣏⣾⡏⡹⢃⠌⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠷⠶⢶⣶⣶⠾⠷⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧ ⠀⢀⣿⣹⣟⣠⠱⣁⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⡏ ⠀⢸⣇⡿⢈⡖⢡⠢⣍⠢⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⣾⠇ ⠀⣿⢸⡇⢘⡜⡄⠳⣄⠳⣄⢁⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⢻⡟⠀ ⠀⣿⢸⡗⢘⠣⡜⠳⣌⠳⡌⢆⡡⢐⠠⢀⠀⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⣿⠁⠀ ⠀⣿⢸⣟⠠⠓⢌⠳⣌⠳⣍⢲⡑⢎⡰⢈⡔⡁⢆⠰⢠⠁⡌⡐⢠⠐⢠⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣹⠇⠀⠀ ⠀⣿⢸⡏⠀⠸⠀⠷⡈⢇⠸⢆⠹⡸⢶⢇⡸⢱⠎⣱⢈⢱⢰⢁⡆⢉⡀⢇⠸⢀⡀⠆⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢱⡏⠀⠀⠀ ⠀⢻⣼⣯⠀⠀⢁⠒⡩⢘⡌⢪⠱⣉⠖⣪⠱⣉⠞⣡⢋⠖⡍⠶⣘⠧⡜⢦⠓⢦⠑⡌⠄⠁⠂⠁⠀⠀⢀⠠⠐⡈⠤⡁⠈⣴⣿⣷⠟⠁⠀⠀⠀ ⠀⠀⢻⣿⢷⡀⠀⠂⠁⠒⡌⢡⠚⡄⢋⠔⠣⢌⠳⢰⡉⢎⡙⢲⡉⢎⡙⢎⡹⢄⠣⠐⠈⠀⢀⠠⠐⣀⢂⠦⡑⣌⠒⢀⣼⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⢮⣿⣦⡀⠀⠁⠈⠢⢑⡘⠌⡌⠱⡈⢆⠡⡘⠤⠙⡠⠓⡌⠱⢊⠔⡈⠄⢁⠐⡠⢂⠦⡑⠦⣉⠖⡱⠈⡴⢟⣿⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢧⣜⡛⢦⣀⠀⠀⠐⠈⠰⠁⠒⡈⠒⠤⠑⠌⡑⠢⢌⠱⡈⠆⡐⢨⠰⠌⠒⠡⢊⠑⠢⠐⠈⢰⣼⣶⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣬⣁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢁⠊⠄⠑⠠⠑⠀⠂⠈⠄⠁⣂⣨⣤⣤⣶⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢭⣝⣛⠳⠶⢶⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⢀⣀⣤⣤⡶⣛⣭⣵⡿⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⡈⠉⢛⡛⠷⠶⢶⣦⣭⣭⣝⡻⠟⠷⠛⢫⣭⡷⠟⢛⡋⢁⣈⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠉⠉⠉⠉⠉⠛⠻⢿⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠁⠀⠀⢠⣤⣄⠀⠀⠀⠀⠙⣿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⠀⠘⠻⠋⠀⠀⠀⠀⠀⢸⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣿⣄⠀⢠⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠈⠻⣿⣶⠶⣶⣤⣤⣜⣿⣦⡈⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣭⣛⣿⣿⣷⣼⣿ ⠀⠀⠀⠀⠀⣰⣶⣾⠿⠿⢿⣷⣶⣄⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⢛⣿⣿ ⠀⠀⠀⠀⠀⢹⣿⣆⠀⠀⠀⠈⠻⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏ ⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀ ⠀⠀⠀⢀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀ ⠀⠀⠀⣼⣿⠃⠹⣿⣷⣄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀ ⠀⠀⠀⣿⡿⠀⠀⠈⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀ ⠀⠀⢸⣿⣧⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠀⠀ ⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀ ⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀ ⠀⠀⠀⢻⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇ ⠀⠀⠀⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿ ⠀⠀⠀⣤⣸⣿⣿⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃ ⠀⠀⠘⣿⡿⠿⣿⣿⣿⣷⡶⢶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀ ⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠉⠀⠀ ⠀⠀⣼⣿⠇⠀⣴⣄⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⠁⠀⠀⠀⠀ ⢀⣼⣿⠋⠀⠀⠘⣿⣧⠀⠀⠀⢸⣿⣧⣄⣀⠀⠀⠀⢀⣀⣤⣶⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀ ⢾⣯⣁⠀⠀⠀⠀⠈⢿⡄⠀⠀⣸⡿⠉⠙⠛⠛⠛⠛⢻⣿⡏⢹⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⢿⣷⣦⣤⣀⡀⠀⠀⠀⣠⣿⣷⣶⣶⣶⣶⣶⣦⣤⣿⣿⡜⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⡿⣷⣶⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣁⡸⠟⠈⣩⣿⣿⣿⠶⠀⠀ ⠀⠀⠀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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kcid ru kcys ot tnaw I ⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠇⣿⣿⠹⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⣁⣋⣟⣿⣿⣿⣿⣴⢀⠀⠀⠀⡿⣿⣿⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠇⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠇⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣦⣿⣿⣿⣿⠻⠿⠻⠀⠀⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⠟⣿⢻⣮⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣾⣠⣦⣿⡝⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣦⣶⣶⣠⠀⠀⢿⣝⣩⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠛⠿⠿⠻⠙⡄⣿⣿⣿⣿⢿⠿⠘⠀⠀⠀⠀ ⠀⠀⡅⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⠸⣷⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀ ⠀⠀⡨⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⢠⡇⣿⣿⣿⣿⣿⣧⣿⣿⠙⠀ ⠀⠇⢀⠀⠀⠀⠀⠀⣀⣤⣤⣠⢀⠀⡄⣿⣿⣿⣿⣿⠉⣿⣿⣾⢠ ⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣾⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣼⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣩⣉⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣿⣿⢿⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣶⣿⣿⣾⣴⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⠯⠟⠛⠓⠋⠿⢖⣆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣟⣷⣻⠀⠀⣠⣤⡀⠀⠀⠈⠺⡽⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣠⣤⣴⣾⣻⣞⡷⣿⡠⠰⢿⣿⠃⠀⠀⠀⠀⠈⢻⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣻⣽⣳⣯⢷⣟⡿⣽⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠙⠓⠛⠳⠯⠿⢯⣟⡿⣧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⠛⢷⢦⠀⠀⠀⠀⠀⢸⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⢸⣯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣼⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⠃⠀⠀⠀⢂⣟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠎⠀⠀⠀⢀⢸⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠎⠀⠀⠀⠀⠠⢸⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠎⠀⠀⠀⠀⠀⠀⠈⣷⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠎⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⢷⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⡎⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠓⠚⠁⠉⠈⠁⠉⠚⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣻⠀⠀⠀⠀⠀⠀⠀⣀⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣇⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠴⣦⢤⣀⡀⢀⣀⣀⣀⣠⣤⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣾⠀⠀⠀⠀⠀⢸⣯⡇⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠐⠀⡀⠂⢀⠐⠀⢀⠀⠀⠀⠀⠉⠚⠓⠙⠮⠽⣎⠷⣜⡞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡾⣇⠀⠀⠀⠀⢸⡷⡇⠀⠀⠀⠀⠀⠂⠁⠀⠄⠐⠀⠁⢀⠐⠀⠠⠈⠀⢀⠂⠠⠀⠀⠀⠀⠀⢀⣼⢎⣿⠎⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡽⣆⠀⠀⠀⠀⢿⣱⡀⠀⠀⠀⠁⠠⠈⠀⠀⠂⠈⠀⡀⠀⠂⠀⠄⠁⠀⡀⠄⠐⠈⠀⣀⣴⢟⡵⣫⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡽⣦⠀⠀⠀⠈⢳⡻⣄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠂⠀⠀⠄⠀⠀⠠⠐⠚⡿⡼⢭⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣳⡀⠀⠀⠀⠙⢗⡻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⣀⣤⢾⣫⢗⡻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣟⣦⡀⠀⠀⠀⠈⠓⢮⡽⣳⢦⣤⣤⣀⣀⣀⣀⣀⣀⣁⣤⢤⡶⡻⣝⢮⣓⢧⡾⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣛⣦⡀⠀⠀⠀⠀⠈⠑⠫⢞⡶⣹⢮⡝⢯⡻⢭⡳⣎⢷⡹⡵⢫⡞⣭⡞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⢻⣦⡄⠀⠀⠀⠀⠀⠀⠈⣷⢣⡟⢣⡟⣧⢻⡜⣧⣯⡝⣧⢻⡎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⡵⣛⢶⢦⣤⣤⣤⣤⢶⣛⢮⣝⣫⢶⡹⣎⣗⡳⣎⢷⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣝⢮⡳⣎⢷⣙⢮⡳⣝⣺⢲⡭⢶⡹⢞⣲⡽⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⣷⡹⢮⡝⣮⡗⠋⠉⠉⠉⠑⠋⠹⣯⢿⡽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣳⡟⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢯⣟⡷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡷⣳⣻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣛⣮⡽⣯⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⣴⢾⣯⣽⣳⢯⣧⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣻⣞⡽⣾⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣽⣳⣻⣭⣷⣞⡷⣯⣿⠾⠀⠀⠀⠀⠀⠀⠛⠋⠓⠛⢒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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