You Like Kissing Boys Dont You Emojis & Text

Copy & Paste You Like Kissing Boys Dont You Emojis & Symbols ⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣀⠀⠀⠀⠀⠀⢹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠀ ⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣧⡀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣄⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀ ⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣄⠂⠀⠀⠈⢿⣿⣧⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠀⠀⠀⠀⠀ ⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣆⣀⣠⣼⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀ ⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠛⠻⠻⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀ ⠈⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀ ⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣷⣶⣶⣴⣴⣶⣿⣾⣿⣷⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀ ⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠂⠀⠀⠀⠀ ⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣯⠀⠀⠀⠀⠀ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣷⠀⠀⠀⠀⠀ ⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡷⠀⠀⠀⠀⠀ ⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⣿⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠾⠁⠀⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣴⣀⣴⣶⣶⣾⣿⣿⣷⣾⣿⣿⣿⣶⣷⣷⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣶⣶⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠈⠉⠈⠙⣿⣿⣍⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⠉⠉⢨⣿⣿⠋⠉⠉⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⢿⣿⣦⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣤⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢇⣤⠀⠀⠀⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⡆⠀⠀⠀⠀⢀⠀⣰⣾⣿⣿⣋⣁⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀ ⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⣠⠀⠀⠀⠀⠀⠈⢻⣿⣷⣶⣄⡀⠀⠀⠐⣿⣿⠏⠈⠃⠀⠀⠀⠐⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠐⢹⣿⣷⠂⠀⠀⢨⣿⣷⣾⣿⣿⣿⠿⣿⣷⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦⣽⣿⣿⣯⣿⠿⠰⠀⣿⣿⠄⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠄⠀⠀⠀⠀⠀⠺⣿⣿⠄⠀⠀⠈⠛⠋⠉⠉⠉⠀⠁⠈⠀⢀⣼⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⣿⣧⠉⠉⠉⠉⠛⠉⠛⠙⣻⡿⠿⠤⢰⠌⣿⡏⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢯⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠟⠁⠀⠀⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣄⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠸⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⡄⠀⠀⠀⠀⢯⣿⣿⣽⡇⠀⠠⠀⠀⠀⠀⠀⠀⣤⣾⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣦⡀⢠⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠿⠻⠿⠛⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣯⡉⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣷⣿⣀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣏⠉⠉⢈⣿⡆⠀⠀⠀⠀⢠⣿⣿⠿⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⠋⠛⣰⣾⣶⣿⣿⣿⠋⠀⢘⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⣶⣿⣿⠏⣡⣶⣿⣿⠋⠀⠀⠀⠀⠻⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠠⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡴⠒⠒⠒⠒⠒⠶⠦⠄⢹⣄⠀⠀⠑⠄⣀⡠⠤⠴⠒⠒⠒⠀⠀ ⢇⠀⠀⠀⠀⠀⠀⠐⠋⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀ ⠈⢆⠀⠀⠀⠀⡤⠤⣄⠀⠀⠀⠀⡤⠤⢄⠀⠀⠀⠀⠀⣠⠃⠀ ⠀⡀⠑⢄⡀⡜⠀⡜⠉⡆⠀⠀⠀⡎⠙⡄⠳⡀⢀⣀⣜⠁⠀⠀ ⠀⠹⣍⠑⠀⡇⠀⢣⣰⠁⠀⠀⠀⠱⣠⠃⠀⡇⠁⣠⠞⠀⠀⠀ ⠀⠀⠀⡇⠔⣦⠀⠀⠀⠈⣉⣀⡀⠀⠀⠰⠶⠖⠘⢧⠀⠀⠀⠀ ⠀⠀⠰⠤⠐⠤⣀⡀⠀⠈⠑⣄⡁⠀⡀⣀⠴⠒⠀⠒⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢯⡉⠁⠀⠀⠀⠀⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣞⡄⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀
⠀⢸⠂⠀⠀⠀⠘⣧⠀⠀⣟⠛⠲⢤⡀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢹⡀ ⠀⡿⠀⠀⠀⠀⠀⠈⢷⡀⢻⡀⠀⠀⠙⢦⣰⠏⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⢀⣻⠞⠛⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠛⠓⠒⠓⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀ ⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⢀⡟⠀ ⠀⠘⣇⠀⠘⣿⠋⢹⠛⣿⡇⠀⠀⠀⠀⣿⣿⡇⠀⢳⠉⠀⣠⡾⠁⠀ ⣦⣤⣽⣆⢀⡇⠀⢸⡇⣾⡇⠀⠀⠀⠀⣿⣿⡷⠀⢸⡇⠐⠛⠛⣿⠀ ⠹⣦⠀⠀⠸⡇⠀⠸⣿⡿⠁⢀⡀⠀⠀⠿⠿⠃⠀⢸⠇⠀⢀⡾⠁⠀ ⠀⠈⡿⢠⢶⣡⡄⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣴⣧⠆⠀⢻⡄⠀⠀ ⠀⢸⠃⠀⠘⠉⠀⠀⠀⠠⣄⡴⠲⠶⠴⠃⠀⠀⠀⠉⡀⠀⠀⢻⡄⠀ ⠀⠘⠒⠒⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠞⠛⠒⠛⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⠸⣟⠓⠒⠂⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⢿⡄⠀⠀⠀⠀⣠⡶⠛⠉⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠈⢿⡀⠀⣠⡾⠋⠀⢀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠘⣧⡾⠋⠀⢀⣴⢿⡆⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡥⠀⢀⣀⣤⣤⣀⣴⠏⠀⠀⣰⠟⠁⢸⡇⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢻⡷⠞⠋⠉⣼⢻⡟⠁⠀⢀⡾⠃⠀⠀⣼⣇⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣀⠈⠁⠀⠀⠀⣰⠟⠀⠀⣴⠟⠀⠀⠀⠀⠈⢉⣿⠃⢸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⡀⠀⠉⠻⣦⡀⠀⡾⠋⠀⢀⡾⠃⠀⠀⠀⢀⣀⣤⣞⣁⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣦⡀⠀⠈⠻⣆⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠉⢉⣽⠟⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠙⣧⡀⢸⡄⠀⠀⠀⠀⠐⠶⢾⣿⠀⢀⡟⠀⠀⢀⣠⣄⠀⠀⠀⠀ ⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢈⣷⣬⡷⠶⠖⠒⣻⣿⡟⠋⠁⢀⣾⡷⠖⠛⠋⠉⢹⠀⠀⠀⠀ ⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡁⠀⠀⢀⣤⠞⢋⡿⠀⠀⢴⣟⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⣚⣸⣿⣿⣿⣿⠟⢉⣤⣤⣤⣌⠛⢶⡶⠋⠀⢀⡾⢧⣄⣀⣀⣉⣿⡶⠄⠀⠀⠀⣾⠀⠀⠀⠀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣰⣿⣿⣿⣿⣿⣷⡈⣷⠀⢠⡾⠁⠀⠙⠿⣯⡉⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀ ⠀⠹⣿⣿⣿⠛⢉⠙⢿⣿⣿⢻⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⠃⣿⣴⠛⢿⡛⠛⠛⠛⠋⠁⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀ ⠀⠀⠙⢛⣰⣾⣿⣿⡄⢁⣶⣿⣿⣿⣿⣿⣌⡻⠿⣿⡿⠿⢃⣼⣿⠷⠖⠚⠋⠀⠀⠀⣀⣀⡀⠀⠀⢿⣅⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡿⠿⠷⠶⠶⠞⠛⠛⠋⠀⠀⠀⠀⣠⣶⠿⠛⠛⠛⠿⢶⣤⡙⢷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⣉⣉⣁⣀⣤⡤⠶⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⣤⣶⣿⣿⣶⣦⣉⠻⣦⡙⢧⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣾⣿⣿⣿⣿⣿⣿⣿⣧⡈⢿⡄⠹⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢿⡄⠘⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠹⣦⣸⣷⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⣷⡟⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠸⡟⣿⣆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣤⣀⣠⡾⠋⠀⠀⣀⣤⡶⢿⣿⢿⣧⡈⠻⣿⣿⣿⣿⣿⣿⣿⠃⣸⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⣀⣠⠶⠋⠁⣉⣁⣤⡴⠶⠛⠋⠁⠀⠈⢿⠀⠙⢿⣦⣈⠛⠿⠿⠿⠛⢁⣴⡿⢹⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣿⠛⠛⠛⠋⢻⣅⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⠛⠿⢷⣶⣶⡾⠟⢻⠃⢸⠃⠀
╱|、 (˚ˎ 。7 |、˜〵 じしˍ,)ノ
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢰⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⢹⠰⡀⠀⠀⡃⠑⢾⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⡀⠀⡆⠇⠀⠛⣄⠀⣇⣰⡿⣧⣤⣤⣬⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⠀⠸⠐⣧⣈⢸⣄⢈⣷⣿⣿⢃⣿⣫⣴⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⡄⠐⡁⠈⢆⠈⠉⠻⣿⡿⡛⠉⣀⣤⣤⣤⣭⣿⡓⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠀⠐⡆⠈⢳⣶⣶⢯⠊⣠⣾⣿⣿⣿⣿⡍⠉⠳⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢆⠀⠑⠀⡀⠙⡿⠁⣾⣿⣿⣿⣿⠝⠒⠢⢄⠀⠀⠑⢤⡀⠀⠀⠀ ⠀⠀⠀⠐⣤⣈⣦⣀⣀⠀⢀⡧⢤⣿⣿⣿⣿⣀⠄⠀⠀⠀⣣⣷⣦⡀⠈⠢⡀⠀ ⠀⠀⠀⠀⢣⡈⠙⢣⡀⢨⠃⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣶⣶⣿⡆ ⠀⠀⢀⣐⣶⣛⠯⠖⠳⢼⠀⠀⠀⠀⡜⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠹⣁⠀⠀⣈⣩⠥⠀⠳⣦⠀⠀⣳⡿⢿⣿⣿⣿⣮⡻⢿⣿⣿⣿⣿⡫⣺⠀ ⠀⠀⠀⢈⣻⢛⡳⠤⠤⡾⣟⣒⠛⠯⡽⣍⠐⢌⡉⠙⠛⠛⠳⠬⠟⠋⠐⢊⠍⠀ ⠀⠀⡠⢐⡗⢁⡾⠋⣉⣬⠖⠒⠲⡤⠌⣂⠥⢀⡈⢣⡈⠀⠀⠀⠐⠪⢽⣋⠒⢄ ⡠⠊⠀⠛⠲⣿⡃⠜⡯⣴⢺⡛⠲⣵⢄⡀⠨⠁⠒⠒⠈⠀⠀⠀⠀⣀⣀⣉⡹⠂ ⠀⠀⠀⠀⠀⠘⡿⠀⢀⢿⢸⡇⠀⠀⠑⠪⡍⠒⠂⠀⠀⠀⠀⣠⠤⠐⠒⢾⡿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠓⠊⢉⠃⠀⠀⠀⠀ ⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⢄⠀⡀⠄⡪⠊⠀⠀⠀⠀⡘⣠⠀⠀⠀⠀ ⣿⣿⣷⣶⣎⠥⣔⣀⡠⠤⠄⠠⠃⠠⠑⠍⣠⣋⠀⠀⠀⠀⠀⢠⡏⠽⡀⠘⠀⠀ ⣿⣿⣿⣿⡿⠀⠟⣄⠤⠍⠒⠂⠉⠁⠈⠀⠀⠘⠑⢄⠀⠀⠐⢁⡇⡄⢡⠀⠀⠀ ⠛⠛⠋⠉⠀⠀⠀⠸⡑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⣼⠇⣆⣸⢤⣤⠜ ⢶⣶⣶⠖⠀⢀⣔⡈⠁⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣄⠺⡖⡾⠁⠀ ⡋⠉⠀⠀⠠⡄⣋⠀⠠⠤⢀⠀⡶⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢼⢚⡻⠀⠠ ⢣⠀⠀⠀⠀⠁⡇⢀⡤⣧⣌⡄⢹⢿⠕⠀⡐⠈⣡⠇⠀⠀⠀⠀⠀⡿⡥⠃⠀⠀ ⢢⠡⡀⠀⠀⠀⡇⡿⢰⣿⣿⠀⠘⠀⠀⠀⠓⠚⣁⣠⣴⣶⠀⠀⠈⠚⠡⠄⣀⠀ ⠀⠣⡰⣉⠐⠀⢱⣇⠸⠫⢸⠄⠀⠀⠀⠘⠛⠋⠉⠉⠉⠀⠠⡰⠀⠀⣔⣀⠤⠊ ⠀⠀⠈⠂⡽⡥⠝⠟⠂⠑⠉⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⠵⢒⢖⣹⠈⠀ ⠀⠀⠀⠀⢑⡝⣢⠤⢀⠀⠀⠀⠀⠀⠤⠴⠀⠀⠀⠀⢀⡠⠾⠵⠓⠊⢋⣤⠃⠀⠀ ⠀⠀⡠⢊⠅⠂⠈⠁⠀⠈⠁⠒⠤⠤⠤⡄⠐⡶⠽⠃⠀⠀⠀⠀⠀⠛⠉⠁⠒⠠ ⠀⠀⠐⡙⢅⠐⣂⡀⠀⠀⠀⠀⠀⠻⡒⠊⡭⠉⠒⠈⠁⠒⠠⠄⠀⠀⠀⠀⢴⠒ ⠀⠀⠀⠈⢀⣑⠢⠄⠈⠀⠀⠠⠤⢀⣽⣶⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡠⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⡘⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⢘⡷⣝⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⡀⠀⠀⠀⠀⢀⡏⠀⢠⡟⠁⠙⣆⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡈⠛⠶⢤⣀⠀⣼⠁⠀⡞⠀⠀⠀⠸⡆⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣷⣄⡀⠀⠈⠉⡟⠀⣼⠁⠀⠀⠀⠀⢿⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠉⠀⠈⠙⠳⠄⠀⡇⠀⡏⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢻⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣧⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢀⣤⠄⠀⠀⠀⠀⠈⣧⠹⣦⡀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣠⡾⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠛⠶⢄⣀⠀⠻⣄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡶⠚⣩⠿⠿⣹⠷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣸⢀⣠⢾⣿⠇⠀⠀⠀⠀⠀⡄⠀⠀⡾⠀⠀⠀⠀⠀⠈⠙⠛⠛⠃⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠁⠀⠀⠰⣏⢀⣴⢏⣤⣹⣦⠀ ⠛⠛⠛⠛⠛⠛⠉⠉⠛⠋⢠⡏⠘⣆⠀⠀⠀⠀⠀⣧⢀⡼⠁⢀⣄⡀⠀⠀⠀⠀⠀⢀⡶⢧⠀⠀⢀⣾⣷⠆⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠁⠀⠀⠀⠀⣠⡤⣍⣹⡿⠋⠀⣻⣾⠀ ⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠙⢷⣄⡀⠀⠀⢸⡟⠁⢰⠏⠉⣿⠀⠀⠀⠀⠀⠘⢤⡾⠒⣫⣉⣏⢙⡇⠀⠀⣀⣠⡴⠒⠉⠀⠀⠀⠀⠀⠀⠀⢸⡋⠀⠉⢻⢹⡶⠾⣯⣿⠀ ⡀⠀⠉⠙⠓⠶⣤⣀⡀⠀⡇⠀⠀⠀⠀⠈⣽⠒⢦⣾⠁⠀⠘⢶⡼⠃⣤⣶⡿⠛⠀⠀⣴⡷⠛⠉⣉⣹⣿⣗⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡆⢀⣼⣿⣁⣴⡿⠃⠀ ⣷⡀⠀⠀⠀⠀⠀⠀⠉⠙⣇⠀⠀⠀⠀⠀⢳⣔⣆⣽⠇⠀⠀⠀⢰⣿⣿⠏⠀⢀⣠⠞⠁⠀⠀⠘⠛⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⢈⣽⠟⠀⠀⠀ ⢳⡻⣄⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢀⣀⣄⣀⠀⠀⠀⢀⣀⣀⣉⣅⡤⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀ ⠀⠻⣮⡛⠦⣄⡀⠀⠀⠀⢠⣿⡀⠀⠾⠿⠿⣿⣿⡇⠀⣾⡯⠼⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠛⢦⣌⡉⠓⠲⠤⠼⣿⣭⣄⠀⠀⠀⢈⣽⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⡿⠋⠁⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠉⠀⠀⠀⣀⣠⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⢀⡴⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣇⣰⠖⠒⠀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠹⣧⠴⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢹⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠳⣤⣤⣀⣠⣤⡤⠖⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠦⠶⠒⠲⠦⢤⠤⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠖⠛⣫⠿⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣯⠴⢶⣟⠳⣄⠀⠈⠳⣦⡀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣼⣄⠀⣿⢦⠿⠀⠀⠀⠀⠙⢆⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣇⣙⣿⡟⠛⢳⡆⠀⠀⠀⠀⠈⠓⣞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⢶⡀⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⣤⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⡿⢀⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠛⠋⠉⠉⠉⠉⠙⠒⠦⣄⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠘⣿⠶⣄⡀⠀⠀⠀⣰⠏⠀⢸⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⢀⣀⡤⠤⣄⣀⣀⠀⣀⡈⠙⠶⣄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠈⠳⣄⡉⠓⠦⣄⣇⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠪⣝⡛⠛⢦⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡀⠀⠉⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⢳⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀ ⠳⡀⠀⠀⠀⠀⠈⢧⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣦⣄⣀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠰⡼⠀⠀⠀⠀⠀⠀⠀⠀ ⠦⣝⢦⡀⠀⠀⠀⠈⣷⣄⠈⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠟⠋⠉⠁⠀⠀⠀⠙⢷⣤⣄⡘⢧⠀⠀⠐⣆⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠸⡇⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⢦⡀⠉⠛⠒⠀⠀⠀⢻⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣰⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⠙⢮⣇⠀⠀⢹⣄⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢻⡀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣦⣄⡀⠀⠀⠀⠀⠹⣄⠈⠳⢦⠀⠀⠀⠀⠘⠁⠀⣀⣤⣶⣶⣶⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⡸⠙⢦⡀⠀⠀⢷⡀⠀⠀⠀⠀⠀⢳⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠳⢭⣗⣲⠀⠀⠀⠘⢧⣀⠀⣀⣀⣀⠀⠀⣠⣾⣿⡿⠿⠛⠛⠿⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣇⣠⠇⠀⠀⠙⠦⣀⠈⠳⡄⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢦⡀⠀⣀⡼⠷⣬⣙⣀⣀⣠⠴⠛⠉⠉⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⣸⡏⠻⣿⡿⡄⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠈⠙⠒⠿⢦⡀⠀⠀⠀⠀⠈⠧⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⣽⠛⢁⣠⣀⡈⢻⡽⠋⠀⣀⡤⠀⠀⠀⢤⡷⣿⡏⢸⠀⠀⠀⠀⠀⡟⠁⠙⠢⣿⡷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢠⡍⠲⢤⣀⠀⠀⠀⠈⢑⣶⠆⠀⠀⠀⠀ ⢼⠁⢠⠟⠀⠀⢩⠏⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⢻⡇⠸⡄⠀⠀⠀⠀⠳⣄⣠⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣷⣴⡿⠁⠀⢦⡈⢻⡍⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⣾⠀⢸⣄⡀⠀⣇⣰⠋⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠿⣆⣙⣦⣄⣀⣀⡠⠞⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⠛⠉⠙⠿⠯⠼⠀⠀⠀⠙⢦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⠀⠘⣄⠉⠛⢻⠃⠀⠀⢀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠦⠤⣀⡀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⣀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢳⣄⠈⠓⠒⡇⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠓⠢⠤⣇⣠⠎⠀⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠲⠦⢤⣤⣤⡤⠞⠙⢧⠀⡄⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢺⡏⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⢳⣄⣰⠶⣄⠀⠀⡇⢠⢶⡾⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠾⣇⣀⣏⡿⠋⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢣⣸⡇⠀⢰⠏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⢀⣀⡤⡴⠧⢤⣀⣀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠔⠚⠛⠚⢿⡇⠀⣼⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⣧⠔⣲⠒⠛⠓⠛⠳⠤⣀⡀⠉⠓⠢⢤⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⠊⣡⠤⠤⠤⢤⠀⢳⠀⡇⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠙⢷⡶⢤⣤⣤⡤⠶⠚⢉⣻⣽⡿⠯⠤⣤⣄⡀⠀⠀⠈⠙⠲⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀ ⣰⠷⠋⠀⠀⠀⠀⠀⢀⣈⣷⣇⠀⠀⠀⢀⡏⣠⠶⠚⠉⠓⠲⢤⡀⠀⢀⡼⢳⡀⠀⠀⠙⢷⣠⠟⢷⠀⠸⣍⣨⡟⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠋⠀⠀⠀⠀⢀⡤⠞⠉⠁⠈⠹⣆⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⡭⠷⠊⠁⢈⡇⠀⠀⠀⠀⠉⠳⠦⣇⣀⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀ ⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⡀⠀⠈⠧⣀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠳⣿⠛⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀ ⠀⠀⠀⠀⣿⠀⣠⠴⠒⡶⠃⠀⠀⠀⠈⠙⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠈⠑⠲⢤⣀⡀⠀⠀⠀⢀⣸⣷⠒⠛⠀⠀⠀⠀⠉⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠀⠀⠀⣿⡾⠁⢀⡾⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠚⢉⣥⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⡠⠀⠉⠁⠀⣼⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠤⠶⠖⠉⡽⠀⠀⠈⠙⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠇⠀⠀⠀⠀⢻⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⣀⣀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠈⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⡆⠀⠀⠀⠀⠀⠙⢦⡀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⢿⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⡿⣽⣻⡽⢯⡿⣽⣫⡟⣽⣫⢟⣽⢫⡟⣽⢫⡟⣭⡻⣭⢻⡭⢯⡽⣭⢯⡽⣭⠻⣜⡣⢟⣜⡣⢟⡜⣣⢛⡜⣣⢛⡜⣣⢏⡼⣡⢏⡼⣡⢏⡼⣡⢏⡼⡱ ⣿⣷⣻⣟⣾⣳⢿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡷⣯⡽⣯⢷⣏⡷⣽⣣⢯⣟⢮⣯⢽⣚⡷⣹⢧⣻⡜⣧⣛⢧⡻⣜⢮⡳⣭⢻⡔⣏⡳⢎⡝⢮⠼⣱⢫⠼⣱⢫⡜⡱⢎⠶⡱⢎⠶⡱⢎⠶⡱⢎⠶⣙ ⣿⢿⣽⡾⣷⣟⣯⢿⡾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⣞⣯⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣽⣻⢾⣽⣻⢾⣽⢾⣯⢷⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⢯⣟⡷⢯⣟⡷⣻⣵⡻⣾⣱⢷⣫⠷⣞⢯⡞⣧⢟⡼⣏⢷⣣⢟⡵⣫⢞⡽⣎⢷⡹⣞⢣⡞⣱⢭⡛⡼⣙⡞⣥⣋⢗⣣⠳⣜⡹⢎⡳⣙⢎⡳⣙⢎⡳⣙⢮⡹⣒ ⣿⣯⣷⢿⣳⣯⣟⣯⡿⣽⢯⣿⢾⣽⣻⢾⣽⣻⣞⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢯⣷⣟⡿⣞⡿⣞⣯⡿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣾⣽⣿⣾⣿⣿⣾⣿⣷⣿⣷⣯⣟⣾⣭⢿⡹⣾⣹⢮⣏⢷⣫⢞⡵⣫⢷⡹⣎⢷⡹⣎⠷⡭⢮⡕⣏⠶⣹⢱⢣⠞⡴⣩⠞⡴⣋⠶⣙⢮⡱⣍⢮⡱⣍⢮⡱⡍⢶⣑⢣ ⣿⡾⣽⡿⣽⡾⣽⣳⡿⣯⣟⣾⣻⢾⣽⣻⣞⡷⣯⢿⡽⣯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣟⣾⣽⣻⡽⣟⣯⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣛⡾⣼⢣⡟⣮⢳⡝⣮⢳⡝⣮⠳⣭⢛⡼⢣⢞⡬⡳⣍⢎⢧⡛⡴⢣⡛⡴⣍⢞⡱⢎⡵⣊⠶⡱⢎⡖⣱⡙⢦⡍⡖ ⣿⣻⣽⣟⡷⣟⣯⡷⣟⡷⣯⢷⣻⣟⣾⣳⢯⡿⣽⢯⣟⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⣟⣯⡷⣯⣷⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣫⢞⡵⣏⢾⡱⢯⡞⡵⣛⢦⣛⡼⣍⠾⣰⠳⡜⣎⠶⡹⣜⢣⡝⡲⣍⢮⡱⢫⠴⣩⠞⣡⠳⡜⡥⣚⢥⡚⡜ ⣿⣽⣳⣯⣟⣯⡷⣟⣯⢿⡽⣯⢷⣻⢾⡽⣯⢿⣽⣻⢾⣽⣻⢯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣞⣯⢿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡽⢮⡝⣧⡛⣵⡩⢖⣣⠞⣬⠳⣥⢛⡼⣌⢳⡱⢎⢧⡚⡵⣊⠶⣉⢧⢛⡤⣛⠴⣋⠼⡱⡜⣆⢧⡙ ⣿⢾⣽⡾⣽⣳⣟⣯⣟⣯⢿⡽⣯⣟⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻⡞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣯⣟⣯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⢟⠶⣙⢦⡛⡵⢪⡝⢦⡛⡴⣋⠶⣩⢖⡹⢎⠶⡹⠴⣩⠞⡱⢎⡣⠞⡴⢋⡼⣡⠣⡵⣈⠦⣙ ⣿⢯⣷⣟⣯⡷⣯⣷⣻⣞⣯⣟⣷⣻⣞⡿⣾⣽⣻⢾⡽⣻⡞⣷⡻⢷⣛⣾⣳⣟⣾⣳⣯⡿⣽⢯⡿⣽⣳⣟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⢻⡽⢺⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢯⡹⣆⠻⣜⢣⠞⣥⢛⡴⣩⢞⡱⢎⡵⢋⡞⣱⢋⠶⣉⠷⡩⢞⡱⣘⠣⢖⡡⢓⡴⣉⠖⣡ ⣿⣻⢷⣻⡾⣽⢷⣯⢷⣻⢾⡽⣞⡷⣯⣟⣷⣳⢯⣟⢾⣳⢟⣳⣟⣯⣟⣾⣳⡽⣞⡷⣯⢿⡽⣯⣟⣷⣻⣞⣿⣿⣿⡟⢥⠲⡝⣾⣟⣿⣿⣻⣿⣟⣿⣯⢿⣞⣷⣻⣽⣚⠷⣘⢧⡚⡕⢦⢫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⢣⡭⢳⢬⢣⡛⡴⣋⠶⡱⢎⡵⢋⡜⣣⠞⡥⢫⡜⡱⢎⡱⢎⠴⢣⡙⢦⡙⢦⠱⣌⠚⡤ ⣿⣽⣻⢷⣻⢯⣟⡾⣯⣟⣯⢿⣽⣻⢷⣻⢮⣽⣳⢯⣻⣭⡟⣷⣞⣳⣞⡷⣯⢿⡽⣽⣏⣯⣟⣷⣻⣞⣷⣻⣿⣿⠫⠄⣉⣳⣽⣼⣿⣿⣿⢿⣟⣿⢯⣟⡿⣞⣷⡳⢞⡜⢢⠏⡖⡩⢞⡥⣛⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⢞⡱⢎⢧⡙⢶⡩⢞⡱⣋⠶⣩⠞⣡⠞⣱⠣⡜⡱⢊⠖⡩⢎⡱⡘⠦⡑⢎⡱⢌⡓⡔ ⣿⢾⣽⣻⣯⢿⣽⣻⢷⣻⣞⣯⢷⡯⣟⣞⡿⣼⢏⣯⢷⣳⣻⣳⣞⢷⣫⣟⡷⣯⣟⢷⣻⢮⡽⣞⣷⡻⣞⣿⣿⠁⠳⢾⣧⣽⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⡝⣮⢞⡳⣎⠳⡵⢊⡴⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢮⠳⣍⠶⣙⢦⡙⣎⠵⣊⠗⡱⢎⡱⣊⠥⡓⣬⢱⡉⢎⡱⢊⠴⣡⠣⣙⠢⡑⠦⡱⢌ ⣿⢯⣟⡷⣯⣟⣾⡽⣯⢷⣻⣞⣯⣽⣻⣼⣛⣾⣛⡾⣏⡷⣏⡷⣞⣯⢷⢯⡽⣶⢯⣛⣧⢿⡽⣳⢾⣽⣻⣿⠃⢉⡷⣿⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡿⣯⢟⡞⣞⡳⣜⣫⡑⠳⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢌⡳⢬⢳⡩⢖⡹⡸⡜⡡⢏⡕⢎⡱⣉⠖⡱⢢⠱⡘⠦⡑⣍⠲⢄⠳⣄⢣⡙⢆⡱⢊ ⣿⣯⢿⡽⣷⣻⣞⡿⣽⢯⣷⣻⢮⢷⣳⣳⠿⣜⣯⢷⣏⡿⣽⣹⢯⣞⣯⢯⣟⡾⣽⣛⣾⣫⡽⢯⣷⣫⣿⡟⢠⣯⣄⢿⣿⣿⣿⡧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡱⢦⡝⢳⡒⠦⡄⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡱⣋⠶⣙⢎⡵⢱⠱⣙⠲⡘⢎⡱⢌⢎⡑⢣⠱⣡⢣⡑⠦⡙⣌⢃⢆⠣⡜⠢⣅⠣ ⣿⣞⣿⡽⣷⢯⡿⣽⣻⣟⡶⣯⢟⣯⣗⡯⣿⠽⣞⣯⢾⣝⡧⣟⡧⢿⣜⡯⢾⡽⣞⡽⣶⢏⣿⣛⡶⣯⣿⠇⠿⢱⣿⢸⣿⣿⣡⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⠧⡝⢲⠱⣌⡠⢘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠳⣍⢞⡱⢎⠴⣋⢜⣢⡙⡱⢣⠜⡌⠦⣙⢂⠳⡐⠦⣑⢣⠱⡌⠎⡜⢢⡑⢣⠆⢣ ⣿⡾⣽⣻⡽⣯⣟⣷⣻⠾⣝⣳⣟⣞⡾⣽⢞⡿⣽⣺⣝⣮⡽⣞⡽⣏⡾⣝⣯⠾⣽⣹⢞⣟⣮⢿⣱⢯⣿⠀⣐⡊⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣜⢣⠷⢤⡡⠉⠆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡵⣊⢮⡱⢍⡲⢩⡒⢤⢣⡑⢣⠚⢬⡑⢢⢍⠲⣉⠖⡡⢎⠱⡘⡜⣠⠣⣘⢂⢎⡡ ⣿⡽⣷⢯⣟⣷⣻⢾⣽⣻⡽⣳⢾⣝⡾⣭⢿⣹⢧⢷⢾⣱⡟⡾⣵⢏⣷⢻⡼⣻⡵⢯⣾⣹⢮⣯⣻⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣭⡞⢣⢏⣬⡱⡌⢒⡠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢲⠍⣦⠱⡎⡜⣡⠚⡔⢢⡙⢢⡙⢦⡘⢥⢊⠵⡨⠜⡐⢎⠱⡐⢆⡡⢒⡡⢊⠴⡐ ⣿⣳⣟⡾⣽⢯⣟⡾⣽⣫⢷⣻⣞⣽⣳⣛⣞⢯⣞⠾⣼⢏⣷⡳⡽⣞⡽⣞⢧⡿⣱⠾⣭⡟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⢞⡩⣇⠣⠌⡑⢺⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⡑⢎⡴⢩⡒⢥⠣⣍⠲⣑⠪⡑⢎⡱⢨⠱⡌⢚⠤⢃⠲⡑⡌⢆⠓⡌⢃⠎⡱⠘⡄⢣ ⣿⡽⣞⡿⣽⣻⢾⣽⣳⢯⣟⡵⣞⣧⢷⡻⣼⢏⣾⢻⡽⣺⢧⢿⣹⢾⣹⡞⣯⠾⣝⡯⣗⢿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣖⣿⢯⢀⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡶⡷⣎⠷⣤⢓⡒⣩⢒⣿⣿⣿⣿⡟⡹⠋⢴⣆⡘⣿⣷⣏⢲⡘⢥⡙⢆⠳⣨⠱⠌⡥⣙⠢⣅⠣⢃⠍⡆⠣⠍⠦⡑⠌⡌⠱⡈⠆⡜⢠⠃⡜⢠ ⣿⡽⣯⣟⡷⣯⣟⡾⣵⣻⠾⣽⣻⡼⣳⢏⣷⢻⢮⣏⡷⣏⢿⡺⣽⣚⣧⢟⣧⢿⣹⢾⣹⢾⣹⢟⡿⢥⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⠚⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣭⡛⠿⡵⣉⠞⣩⠳⢦⡀⢎⣽⣿⣿⣿⣇⢠⣅⠮⠿⢿⠿⣿⣗⠦⣙⢢⡙⣌⠳⣄⠫⡜⡰⢡⠣⡔⢩⢊⠜⡰⢩⠘⡰⢁⠞⡄⢣⠑⡌⠔⡡⢊⠔⡡ ⣿⣽⣳⣯⣟⡷⣯⣟⣳⣽⢻⣳⣭⠷⣏⣟⡮⣟⡽⢮⣗⢯⡯⢷⡳⣏⣾⢫⣞⣳⢯⢾⣹⡞⣽⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣇⡋⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢮⡓⢦⡙⣷⡳⣬⣦⢥⡛⣤⡙⣦⣿⣿⣿⣿⣏⣿⢸⣿⣿⣿⣿⣾⣿⡜⣌⠣⣜⠰⢣⢌⡱⢢⢙⣂⠳⢌⡡⠎⢆⡑⢢⠡⡑⢊⠴⡈⢆⠱⣈⠒⡡⠎⡰⢁ ⣿⣞⣷⣻⢾⣽⣳⢯⣷⢫⣯⢷⣚⣯⡽⣞⡵⣯⢽⡻⣼⣛⠾⣯⢽⡳⣽⢻⡼⣽⡺⣏⡷⣽⢣⣟⡞⣿⣾⣥⣿⣿⣿⣯⣿⡳⢷⡈⡑⠌⢠⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣶⣍⢏⡞⣴⣙⣦⡹⢆⣿⣴⣽⣾⣿⣿⣿⣿⠐⡻⢷⢩⣿⣿⣿⣿⣿⡗⣨⠱⣌⠹⣂⠎⡔⢣⢌⠢⢃⠆⢢⠍⢢⠘⡄⢣⠘⣐⠢⡑⢌⠢⡁⢎⠰⡁⢆⠡ ⣿⢾⣳⣯⢿⡾⣽⣻⣼⣻⢞⣽⣹⢶⣻⢼⣻⢼⣳⡻⣵⣫⢟⡮⣗⣻⡼⣳⡽⣖⣻⡝⣾⡱⣟⢮⣽⡟⢻⣿⣿⣿⣟⣿⣯⢳⣦⣷⣶⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣆⢳⣎⠿⣖⣾⣿⣾⣿⣿⣿⣿⣿⡀⣟⢈⣦⣹⣿⣿⢿⣿⠓⡤⢓⣌⢣⠱⡊⢜⡂⢎⡱⢊⡜⢄⠚⡄⢣⠘⡄⢃⠆⡱⢈⠆⡱⢈⠆⡱⢈⠄⡃ ⣿⢯⣟⡾⣯⣟⡷⣯⢶⣏⣟⡮⣗⣻⡼⣏⡾⡽⢶⡻⣵⢫⣾⡹⣞⡵⣫⢷⣹⢞⡵⣻⢖⣻⡝⣾⣿⠁⠰⠟⣿⣯⢸⣿⣯⡧⣴⣠⣴⣶⣦⣄⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣮⣷⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⠃⢿⣿⠟⣽⣿⣿⠣⡙⡔⢣⠜⣢⠣⢍⠢⡙⢄⢢⠡⡘⢄⠣⡘⢄⠣⡘⢄⠊⡄⠣⡐⢄⠃⡔⢠⠃⡌⡐ ⣿⢯⡿⣽⣻⢾⡽⢯⡷⣞⢧⣟⣭⠷⣝⡾⣱⠿⣭⢗⣯⢳⡞⣵⡻⣼⣛⢮⡗⣯⡝⣧⡟⣧⢻⡞⣿⠀⠀⣦⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣛⣷⠿⣫⣾⢃⠧⡱⡘⢥⠚⣄⠳⣈⠱⡈⢆⠢⡑⢌⠢⡑⢌⠢⡑⠰⡈⢆⠡⢃⠌⡂⠜⡠⢂⠅⢢⠁ ⣿⢯⣿⣳⣟⣯⣟⣯⠷⣏⡿⡼⣞⢯⣻⠼⣏⣟⢮⣻⡜⣯⢞⣳⡽⣣⢯⣳⢻⡼⣽⢲⡟⣼⡳⣏⢿⣆⠀⢿⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢟⣿⢅⠺⡰⢡⡙⠤⢋⠤⠓⡄⢣⠘⡄⢣⠘⡄⢣⠘⠤⡑⢨⠑⠌⡄⢃⠢⡘⠄⡃⠔⣁⠊⡄⢃ ⣿⣻⣞⡷⣿⢮⡽⣞⣿⡹⣞⡽⣞⢯⣳⢻⡝⣮⢟⡶⣻⡝⣞⣧⢻⡵⣫⣗⢯⣳⡭⢷⣫⢷⡹⣎⡯⢿⣆⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⢻⡯⢌⢣⡑⢧⠘⡥⢋⠌⡓⢌⠢⡑⢌⠢⡑⢌⠢⢉⠆⢡⠂⡜⡐⢌⠂⡅⠢⡑⠌⢒⡀⠣⠌⡄ ⣿⣳⢯⡿⣽⣏⡿⣽⣲⢟⡽⣞⣭⢷⣫⢟⡼⣏⡾⣳⢧⣛⢷⡺⣝⡾⡵⣞⢯⡖⣯⡳⣝⡮⢷⡹⣞⣻⣿⡄⣿⣿⣿⡟⢛⣫⣿⣿⣿⣿⣿⣿⠟⣿⠛⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣹⡟⣌⠲⣡⠊⡕⢢⠡⢚⠰⡈⠖⡡⢊⠔⠡⢂⠱⡈⢌⠂⡅⢒⡈⢄⠣⡐⢡⠂⢍⠂⡌⢡⠒⠠ ⣿⡽⣯⣟⡷⣯⢷⣳⡽⢾⣹⡞⡽⣎⡷⣫⡽⣞⡵⣛⣮⢟⣮⢽⣣⢟⣵⢫⡾⣹⢖⣯⢳⡝⣧⢻⡜⣷⣿⣿⣿⣿⣿⣴⣿⡿⡏⢻⣿⣟⣤⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⢚⡯⣐⠣⢆⠹⣠⢃⠣⢌⠢⡑⠌⠴⢁⢊⠱⡈⢆⠘⡠⢃⡘⢄⡘⢄⠢⢑⢂⠩⢄⠊⡔⠡⠌⡡ ⣿⣽⣳⣯⣟⣷⣛⣶⢻⡝⣧⡻⣝⢾⣱⣏⢷⣹⢞⡽⣎⢿⡜⣧⣛⠾⣜⢯⣳⣛⠾⣜⢧⡻⣜⢧⡻⣜⣿⣿⣿⣿⣿⣿⡟⠳⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⡐⢫⢄⠫⡜⢠⢃⠌⡒⢌⠢⢑⠊⡄⠣⢌⠰⡐⡈⢆⠡⢂⠔⡂⠔⡈⢆⠡⢊⠰⡈⠒⢄⠣⡘⠠ ⣿⣞⣷⣻⣞⡾⣝⡾⢯⣽⢺⡵⣏⡟⣶⡹⣞⡽⣚⡷⣹⢮⡻⣵⢫⡟⡽⣎⠷⣭⣛⢮⡳⣝⢮⡳⣝⡞⡶⣿⣿⣿⣿⡿⠈⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠬⣙⠆⢳⠘⠤⣉⠆⡱⢈⢆⠡⢊⠰⡁⢆⠡⢂⠱⣀⠣⠌⢒⡈⢆⠡⢂⠱⡈⠤⢡⠉⡂⢆⠡⡁ ⣿⢾⣽⣳⢯⣟⡽⣞⡿⣜⣳⡽⣺⡝⣶⢫⢷⡹⣝⠾⣭⣳⢻⣜⡳⣽⢳⣭⣛⢶⣭⢳⡝⣮⢳⡝⣮⣝⡳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡈⠴⣈⢏⠰⣉⠒⡡⢊⠔⡡⢈⠆⡡⢒⠈⡔⡈⢆⠡⡐⢂⡑⠢⡐⢂⠅⡊⠔⡠⢃⠢⡑⠨⠄⡃⠔ ⣿⣻⢾⣽⣳⢾⣹⣳⢽⡺⣵⢫⢷⡹⣞⡽⢮⣽⣚⢯⣳⢭⣳⢭⣳⢭⣳⢮⡝⡾⣜⢧⡻⣜⢧⡻⢶⣭⢳⢧⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡐⢈⠲⢡⢎⡱⢄⡩⢐⠡⢊⠄⣃⠰⢁⠢⡑⠰⡈⢄⠃⡔⣁⠢⡑⢄⠃⡌⠰⣁⠒⡄⢃⠌⡑⢌⠰⢁ ⣿⣽⣻⢾⡽⣞⣧⢟⣞⣳⡭⣟⢮⢷⡹⣞⣳⢮⡝⣾⣱⢻⡜⣧⣛⢮⡳⣏⢾⣱⢏⡾⣱⢏⡾⣹⢳⣎⡟⡾⣴⢛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠭⡀⢡⠌⡡⢂⡅⢺⡔⡨⢔⡡⢊⡅⢒⠠⡑⣈⠒⡈⢅⠒⣈⠒⡐⢄⠒⡨⠐⡌⠰⣁⢂⠒⡈⢆⡘⠰⢈⠢⢁ ⣿⢾⡽⣯⢷⣻⢮⣛⣮⢳⣝⣮⣛⢮⢷⡹⣎⢷⣹⠶⣭⣳⣛⠶⣭⡳⣝⡞⣧⣛⢮⣳⡝⣮⢳⣝⡳⢮⣝⡳⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡁⠞⡌⠐⡤⠂⠤⢡⠘⣐⠣⣏⡐⠆⡔⣡⠈⡆⡑⠰⣀⠃⡜⢠⢊⡐⢌⠰⣈⠂⡅⢃⠌⡡⢐⢂⠱⢈⠆⢌⠡⢊⠄⠡ ⡿⣯⣟⡷⢯⢷⣫⠷⣭⢷⣚⢶⡹⢮⡳⣝⢮⣳⢭⣛⢶⣣⢏⡟⡶⣝⢮⣝⠶⣭⡳⢧⣻⣜⡳⢮⣝⡳⢮⣽⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣍⡳⢍⢦⣹⡰⢬⠑⡠⠨⠰⢀⣋⠄⠳⣼⡄⣙⠰⢠⡘⠤⣁⠣⡐⢌⡐⢢⠐⡰⢈⠢⠄⡃⠔⣈⠢⠑⡂⢌⠢⡁⢎⠠⠃⡄⢊⠐ ⣿⢷⣯⣟⢯⢷⣫⣟⢮⣳⡝⣮⣛⢧⣛⢮⡳⣝⡮⣝⣮⢳⣏⣞⡳⣝⠾⣜⡻⢶⣹⢳⡳⢮⣝⡳⢮⣝⡳⣞⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣭⢻⣌⠳⣭⢖⣦⠳⣌⢌⠡⢁⠒⢡⠈⢎⠡⠜⣷⡈⠜⣠⠘⡰⢀⢣⠘⡄⠒⡄⢣⠐⡡⢂⠱⢈⠒⡠⢁⠣⢘⠠⢂⠅⢊⠐⠡⠐⠂⠌ ⣿⣻⢶⢯⣛⡾⡵⣞⢯⢶⡹⣖⢯⡞⣭⣳⢻⣜⡳⣝⢮⡳⣞⡼⣳⢭⣛⣮⡝⣧⢏⡷⣹⢳⢮⣝⡳⣎⠷⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣽⣳⢮⡳⣎⡳⡼⡞⡴⢫⡜⠌⢦⠉⠈⠄⡐⠂⡜⢨⢽⣿⡔⢂⠱⣀⠃⢆⠱⣈⠱⡈⢆⠱⣀⠣⡘⢄⠣⡐⢡⠊⡄⠣⢌⠘⡀⢊⠡⠌⠡⢈ ⣟⡷⢯⣟⡽⣺⣝⢾⡹⣎⢷⡹⢮⣝⠶⣭⡳⢮⣝⢮⡳⣝⢮⡳⣝⢮⣳⢮⣝⢮⡻⡼⣭⣛⠾⣜⡳⣭⣛⠶⣭⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣟⡳⢞⡥⢯⡽⣭⢳⢧⡹⢜⣣⡙⢾⡀⠎⠡⠀⢄⠡⡀⠣⢎⢿⣿⣧⣖⡠⢉⠆⡒⠤⡑⡈⢆⠱⣀⠣⡘⢄⠣⡘⢄⠣⡘⠰⡈⠆⡁⠢⠐⡈⢂⠁ ⣯⣟⣟⣮⡽⣳⢞⣯⢳⡝⣮⢽⡳⣎⡟⡶⣝⢯⡞⣧⣛⢮⢷⡹⣞⢧⣛⠾⣜⢧⡻⣵⢣⣏⠿⣜⡳⢧⣏⠿⣜⡧⣏⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢾⡸⣹⡍⣞⣱⠞⣥⢻⢦⡙⣦⠧⡙⢦⡑⢎⠡⡀⠆⠰⢀⢣⠘⡼⣷⣏⡿⣿⣶⣾⣤⣵⣠⡑⣈⠒⠤⢑⠰⡈⢆⠱⡈⢆⠡⢃⠜⡠⠑⣂⠑⡠⠁⠌ ⣷⣻⡼⢶⣻⢵⣫⢞⣧⢻⡜⣧⢻⡼⣹⢳⡝⣮⡝⡶⣭⣛⢮⣳⡝⣮⣝⡻⣜⢧⡻⣜⡳⣞⡽⢮⣝⡳⣎⠿⣜⡳⣝⠾⣭⣛⠿⡿⢿⠿⣿⢿⣿⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣞⡧⢷⡩⡜⠶⣥⢯⡙⣧⣾⠵⣣⠝⣌⠣⡜⢢⠡⡁⠂⠅⣂⠢⠘⢤⢫⡝⣻⣷⣻⢞⣽⣻⣟⣿⡿⣿⣶⣮⣴⣡⣈⠆⡑⠌⢢⠁⢎⡐⠡⡀⠎⢠⢁⠂ ⣷⣳⢻⣏⣞⢧⣛⡾⣜⢧⡻⣜⣧⢻⡵⣫⢾⡱⣏⢷⣣⢟⣮⢳⡝⡶⣭⢳⡝⣮⢳⣭⢳⡝⣞⡳⢮⡝⣾⡹⢧⡻⣜⡻⢶⡍⡷⣍⣛⠮⡵⢎⣽⠀⠀⠀⠀⢮⣿⣿⣿⣿⣿⣿⡿⡞⣥⢳⡉⢳⡜⣦⢿⡻⣌⠷⣢⠝⣠⠒⡌⢠⠃⡔⢁⠂⠴⢈⡑⢎⡳⢼⢯⡷⣯⣟⣮⢷⣻⣾⣟⡿⣽⣿⣻⣿⣿⣿⣷⣾⣤⣉⡤⠘⢠⠁⡌⠂⡄⢂ ⡷⢯⣛⣞⢮⡻⣜⡳⣝⢮⢷⡹⣎⢷⡹⢧⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⢷⡺⣝⠾⣱⢏⡳⣝⢶⣹⢳⡝⣧⣛⢧⠞⡵⢎⢧⡛⣜⢣⢾⡃⠀⠀⠀⠠⣼⣿⣿⣿⣿⣟⣷⡻⣬⢓⣌⠶⣹⣯⣗⣳⣭⠳⡆⣍⠲⠠⠄⠃⡜⠐⡌⡀⢂⠬⠑⡎⡵⢋⡞⣹⢳⣻⣾⣿⢿⣟⣾⣟⣷⣿⣿⣽⣷⡿⣯⣿⣿⣿⣿⣿⣦⣴⣀⠡⠐⠂ ⣟⢯⡽⣎⣯⢳⡭⣗⢯⡞⣧⢻⡜⣯⣝⡳⢮⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⠷⣭⢻⡥⣏⢷⡹⣎⢷⣫⢞⡵⣭⠺⡭⣝⢮⢣⡝⣬⠓⡾⡇⠀⠀⠀⠐⢼⣽⣿⣿⣿⣿⣷⣿⠶⣏⢬⣛⣷⣻⣞⡷⣊⠷⣉⠦⣁⠣⣘⠐⡈⠱⣀⠖⠡⠀⡝⡘⡔⠫⡔⢣⡞⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣾⢿⣟⣷⡿⣯⣿⣿⢿⣿⣿⣿⣾⣤ ⣯⣛⢾⡱⣏⢷⡹⣎⢷⡹⣎⢷⣛⠶⣭⣛⠷⣎⢯⡳⡽⣎⢷⣫⢞⣧⢻⡵⣫⠷⣭⢻⡜⣧⢳⡝⣎⢷⡹⣎⢷⣋⠾⣜⢫⡵⣚⡬⢳⡜⢦⡛⡴⣧⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣯⡿⣜⡶⣹⣾⢯⣟⣳⡽⢎⡕⢢⠰⣁⠣⡜⢀⠡⡘⢠⠁⢆⠐⡤⢩⠓⣬⢓⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣻⣿⣿ ⡷⣭⡗⣯⠽⣎⢷⣫⢞⡵⣫⡞⣭⣛⠶⣭⢻⡼⣣⢟⡵⣫⢞⡵⣫⢞⣧⢻⡵⣻⡜⣧⢻⣜⡳⢞⡭⡞⣵⢫⡞⣭⢻⢬⡳⣜⡱⢺⡱⢎⢧⡙⡖⣿⠀⠐⠄⢀⠀⠀⠉⣿⣿⣿⣿⣿⣟⡷⣏⣷⣿⣿⢿⣻⡝⢮⡜⣡⠓⠬⣑⠜⣨⠂⡁⢃⡚⢤⡈⢠⢃⡝⢦⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣽⣿ ⣟⡵⣻⣜⡻⣜⢧⣛⢮⡳⢧⡻⣵⢫⡟⡼⢧⡻⣵⢫⡞⣵⢫⡞⣵⢫⡞⣧⣛⢶⡹⣎⢷⣪⠽⣹⢼⣙⢮⣳⢹⡜⣣⢳⣙⠦⣝⢣⡝⢎⢶⣭⡿⠛⠀⠀⠀⢹⠆⣄⣀⠿⣿⣿⣿⣿⣯⣿⡽⣾⣿⣯⡿⣧⣛⢧⡚⡥⢊⠶⣩⢎⡡⢚⠄⢃⠜⡢⣄⠣⡘⣬⢣⠿⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣯⢞⡵⣎⡷⣹⢎⣯⢳⡽⣳⡝⣮⢳⡽⣹⢧⡻⣜⢧⡻⣜⢧⣻⡜⣧⣛⢶⡹⣎⢷⡹⢶⣩⢏⠷⡮⣝⡞⣬⡓⣞⣱⢫⡜⣹⢬⣳⡾⠟⠋⠁⠀⢀⠀⠀⠀⢸⡅⣦⢉⡉⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣖⡻⢦⡛⣌⢏⡾⡵⢪⡕⢯⣌⢣⣌⡱⢎⡧⣙⣤⢏⡿⣵⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣫⢞⡵⣫⢗⡯⣞⢧⡻⣵⢻⡜⣧⢻⡵⣫⢷⡹⣎⢷⡹⣎⢷⡹⢶⡹⣎⢷⡹⢎⡗⣯⣜⢫⢷⡹⡖⣽⠲⣝⡼⢲⣍⣾⠟⠋⡁⢀⠀⠀⠀⢰⣿⠀⠀⠀⠈⡇⠸⣧⣌⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣋⢷⡙⣞⣮⡽⣽⢳⣚⠷⣜⡲⣬⡳⢯⣶⢻⣼⣻⣞⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣫⢞⡵⣫⢞⡽⣎⠷⣭⢳⡝⣮⢷⡹⢧⣏⢷⡹⣎⢷⡹⢮⡝⣧⢳⡝⡮⡝⣏⡞⢶⢎⡿⢬⡳⣝⠮⣝⣲⣽⠟⠋⠀⠠⠀⢀⡀⢀⡈⢷⣾⣿⠀⠀⢠⠀⢻⡄⢽⣷⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡍⣎⢿⣼⣳⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⣱⣏⣞⡳⣝⢮⣳⢭⡟⣼⢫⡞⣵⢫⣝⡳⣎⢷⡹⣞⢧⣛⢧⢻⡜⣳⠞⡵⣋⢶⡹⣚⢮⡜⢧⣛⡼⣹⣶⠟⢡⣀⠈⢒⠠⣇⢢⣽⣦⣿⣿⣿⣿⠃⠀⠈⢣⠀⢳⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡼⣣⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⢯⣟⡳⡽⣎⢷⣛⣾⣳⣿⣿⣿⣿⣿⣿⣿ ⣳⢯⡽⣹⢧⡻⣜⢯⡞⣵⢫⡞⣵⢫⡞⣽⢣⡟⡼⢧⡻⣜⡻⣜⢮⣓⢏⡖⢧⠻⣜⡣⢟⣬⢓⡮⢫⣵⡿⠋⠀⠈⢻⣤⣚⡤⢿⡞⣿⣻⣿⣿⣿⠏⠀⠀⠀⠈⡆⠸⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡵⣿⣿⣿⣧⣻⣾⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⡿⣟⣿⣯⣿⣟⡿⣿⣻⣿⣽⣟⣷⣿⢾⣟⡾⣽⣳⢧⣻⣼⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⢯⡞⣵⢏⡾⣱⢯⡞⡽⣎⢷⡹⣎⢷⡹⣎⢷⡹⣝⢧⡟⣼⡱⢏⡶⢭⡺⣜⢫⣝⡲⢭⣓⢮⡹⣼⡟⠃⠀⠀⠀⣐⡠⠞⣿⡽⢎⡽⣶⢿⣾⢏⡆⠀⠀⠀⠀⠀⠑⠀⣧⠀⢺⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣝⡮⣝⡾⣿⣳⣿⣟⣿⣿⣽⣷⣿⣿⣿⣿⣷⣿⣿⣿⣯⣿⣾⣟⣷⣿⣻⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣣⡟⣼⢣⡟⣼⢳⡝⣮⢳⡝⣮⢳⡝⣾⡱⣏⠾⣜⢧⡝⡞⣜⡣⢗⣎⠳⣎⣵⣫⣼⣶⠟⣉⣠⠀⠀⠀⢀⡿⣷⢍⣙⣧⣿⣾⣿⣫⣝⣾⣤⣄⣲⣤⣹⣦⠲⠤⣄⠀⠈⢿⣿⣿⣿⣿⣿⠃⢤⣿⣿⡿⢫⣙⢮⣳⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⢯ ⣞⡳⣝⢾⡱⣏⣞⢧⡻⣜⢧⡻⣜⢧⡟⣼⢣⡝⣮⣛⡼⢎⣞⡹⡲⣍⣷⡾⠟⢋⢉⣥⣶⣾⣿⣿⣿⣿⠿⡩⢞⣷⠟⠉⡐⢎⠛⡍⢯⡽⣻⣿⡻⢿⣿⣿⣿⣿⣷⣦⣜⣦⡀⠹⣿⣿⣿⣿⠏⢀⣿⡿⠉⢁⠣⣞⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣟⣿⣟⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠾⣝⢯ ⣯⣝⢾⣣⢟⡼⣎⡷⣹⢎⣯⢳⡝⣮⡝⣮⢳⡝⢶⡹⣜⣫⣖⣽⠿⢋⡡⢴⠶⣞⡾⣞⣷⣿⣾⣿⣿⣟⡶⣡⣿⠋⠀⠀⢁⠢⠕⡚⢡⢎⡱⠭⣽⠿⣟⢿⡻⣝⣮⣿⣿⣿⣷⡧⣿⣿⣿⡋⢥⣿⡏⣠⣄⣠⣔⣫⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣟⡿⣿⣾⣿⣿⡿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣯⢿⡽⣞ ⡷⢮⣳⡝⣮⢳⡝⣾⡱⣏⡞⣧⣛⢶⣽⣮⡷⠿⢛⠛⡫⢍⠋⡅⣎⢱⡙⣎⠿⣜⣻⡽⣿⣾⣿⣿⣿⣿⣿⣿⠏⢀⢠⡐⣠⠉⠒⠬⡁⢎⡰⢿⣬⡻⣜⣯⢷⣻⣿⣿⣿⣿⣿⣷⣉⡟⢦⡑⣮⢯⣴⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣻⡾⣿⣟⣯⡿⣿⣿⣯⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣯⡿⣽⢯ ⣽⢳⢧⡻⣜⢧⡻⢶⣹⢮⣽⡶⠿⠛⠉⠀⠐⠤⠣⡘⠐⢊⠒⡌⢂⠧⣜⡎⣷⣹⡾⣽⣷⡿⣿⣿⣿⣿⠿⣡⠲⣌⢶⡹⢿⣆⣙⣲⠱⣮⢙⠶⣣⢿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢷⣯⣟⣷⣿⣳⣯⢿⡽⣷⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⡷⣟⣯⣿ ⣳⢯⡞⣵⣫⢞⣽⣳⠟⠋⠁⠀⠀⠀⠀⠐⠠⠂⢀⠈⠄⢡⠘⡰⣍⡞⣴⢯⡷⣯⣟⣿⡾⣟⡿⡹⣍⢆⡳⢣⡽⣘⣮⡟⣽⣿⣿⢣⠷⣌⣯⣛⣷⣻⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣯⢷⡿⣜⢯⢾⣭⢿⡿⣿⡿⣿⣾⢿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣻⣿⣾ ⣟⢮⣽⢺⣵⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠢⡜⢢⡝⢲⣟⡾⣽⣯⣿⣿⣻⡽⣛⢥⢳⡱⢎⢎⣝⢣⡻⣵⣳⡿⣟⣿⣞⣯⢿⣝⡶⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣟⡾⣞⡯⣝⢿⣫⡗⣾⣯⣿⡽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣷⣿ ⣻⢞⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠔⣠⠒⣭⠳⡜⣧⣿⣟⣷⣯⢷⣫⢇⡧⣙⢎⢣⠳⡞⡼⣌⢷⣻⢽⣯⢿⡽⣯⣟⡞⡿⣮⣽⢳⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⢦⡈⢿⣞⣿⣿⣿⣿⣷⡿⣿⣟⡾⣽⣟⡾⣽⢣⡟⣽⣺⢷⣻⢽⣳⣯⣿⢿⣻⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢬⡸⣔⢫⢖⣻⣾⣿⠿⣝⡾⣡⠧⣍⠞⣰⠙⢎⡲⢥⣛⣼⣻⡼⢯⡟⣞⢯⣿⣱⢿⡜⣷⡝⣾⢻⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢳⣄⡆⣹⣜⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣳⢏⡷⣭⢗⣯⣛⣷⢻⣾⢯⣿⣻⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢆⡞⠶⣱⣮⣾⣿⣿⢿⡽⣛⡮⢱⡡⣚⡜⡸⢣⢛⣤⡝⣫⣼⠶⡽⢾⡹⡞⡭⢞⠶⢭⢞⡹⣞⡽⣮⢿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⣻⣽⢻⡼⣾⢿⣿⣿⢿⣻⣿⣿⣾⣳⢯⡻⣼⢛⡾⢧⣻⣼⣻⣾⢿⣽⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⡌⣞⣬⣿⣿⣿⣿⣿⣯⣿⡟⢧⠘⡅⣶⢩⠞⣱⢛⣼⢲⡝⣣⢟⡽⢞⡹⢻⡱⣛⢮⣙⣧⢫⡷⣭⢷⣯⣟⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣻⣿⣯⣿⣿⣿⣿⣿⣟⣮⢷⡏⣯⢳⣭⢻⡼⣟⣧⣿⣹⣽⣻⣯⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⡜⣰⣿⣿⣿⣻⣽⣯⢿⣿⣯⠳⡜⢠⢛⡘⢤⡃⣞⡥⢏⡞⡶⣙⢮⣟⡼⡳⣍⣳⣫⡝⣮⣝⣮⣻⡽⢯⣿⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡷⢧⣿⣿⣿⣿⢯⣟⡾⣽⢻⡯⣟⣳⡛⢾⣳⣽⡽⣞⡿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⡼⣼⣿⣻⣷⢿⣽⣿⣽⣿⣿⣦⠃⡄⠙⠦⠸⠀⡗⡌⢲⡛⣜⠶⣙⡞⣼⣱⢯⣝⣣⢿⣝⣯⣟⣾⣳⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣼⣿⣋⢿⡟⣞⣻⣞⡷⣹⢏⡷⣫⢷⣹⣛⣷⣻⣽⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⡉⣥⢻⣽⣷⢿⣷⣯⣿⣿⣿⣿⣿⣿⠂⠄⠡⠒⠐⠈⠳⢐⡚⡡⢜⡭⢻⡴⣛⢶⣭⡞⣧⣟⣯⢿⣭⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⠙⣇⣿⢫⡝⣭⣓⣮⠷⣳⢾⣱⢟⣯⣟⣯⣷⣻⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣟⡷⣯⣿⣿ ⠀⠀⣀⣄⣠⠌⢦⡱⣯⣿⣻⣾⡿⣯⣿⣿⣿⣿⣿⣿⡏⠙⠀⠀⠀⡰⣃⡤⢋⣜⣍⣫⣜⣣⣷⣻⣟⣶⡿⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡉⠁⡫⢜⠣⢯⣜⣦⠳⣬⠷⣽⣚⣷⣞⣳⣾⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣹⣿⣽⣯⣿
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶⢶⣄⠀⠀ ⠀⠀⣿⢩⣛⣿⣯⣽⣒⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⣛⣩⡤⠤⣦⡀⢻⡆⠀ ⠀⠀⣇⣼⠋⠀⠀⠀⠀⠉⠛⠦⣌⡙⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠟⠋⠉⠀⠀⠀⠈⣧⢸⣷⠀ ⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣽⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⣻⠀ ⠀⢸⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣄⣀⣠⣤⣤⣤⣤⣀⣀⣀⣸⣽⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹⠇ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠒⠚⠛⠒⠒⠒⠛⠻⠿⣿⣭⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⠀ ⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡟⠀ ⠀⠀⣹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢾⠇⠀ ⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣾⠀⠀ ⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣽⠋⠀⠀ ⠀⠀⢰⡇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢉⣁⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡋⠀⠀⠀ ⠀⠀⡞⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡟⠉⠉⢳⡀⠀⠀⠀⠀⠀⢀⠴⠒⢿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⠀ ⠀⢸⢳⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠻⣿⡿⢧⣤⣤⣾⣷⡀⠀⠀⠀⠀⣿⣀⣀⡼⠿⣿⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀ ⠀⡞⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢿⣷⣾⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣷⣴⣿⡟⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡾⡆⠀ ⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠙⠛⠛⢛⣹⣿⠇⠀⠀⠀⠘⣿⡿⠿⠿⠛⠉⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀ ⢠⢇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡤⠤⠐⣚⣽⠿⠋⠀⠀⠀⠀⠀⠹⣿⣦⣀⠀⢀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀ ⢸⠈⣇⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⣠⣴⣶⡆⠀⠀⣿⣿⠀ ⢸⡇⠹⣄⠀⠈⠙⢿⣿⡲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣾⣿⡿⠿⠇⠀⠀⡇⣿⡇ ⠘⢷⣄⠙⣦⡀⠀⠀⠙⠻⣷⣮⣽⣓⣶⣤⣀⣀⣀⠀⣄⣠⣦⠀⣠⠄⠀⠀⠀⠀⢀⣀⣠⠤⠶⠒⢉⣤⣾⡿⠃⠀⠀⠀⢀⡼⢁⣿⠃ ⠀⠀⠙⢿⣿⣿⣷⢤⣀⠀⠈⠙⠻⢯⣿⣛⠿⠿⣯⣭⣼⣍⣊⣙⣉⠒⠲⠶⠟⢛⣻⣁⣤⣤⣶⣿⡿⠟⠉⠀⠀⠀⢀⣴⢟⣤⡿⠃⠀ ⠀⠀⠀⠀⠈⠛⠿⣦⣌⡙⠲⢤⣄⣀⡬⣽⣿⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⢡⣿⣟⠉⠁⠀⠀⢀⣠⣴⢞⣫⡷⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⢶⣭⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣓⣚⣛⣿⠽⠞⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀ ⠀⢾⣻⠶⢆⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢾⡫⠥⢄⢳⠀ ⢠⣼⠀⠀⠀⠀⠑⠪⢝⣢⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠋⠁⠀⠀⠘⣼⡇ ⢸⠹⠀⠀⠀⠀⠀⠀⠀⠉⢻⣦⡤⣤⡤⢤⣤⣠⣽⡟⠁⠀⠀⠀⠀⠀⠀⠘⡇ ⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⢠⢀⠇ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣺⠀ ⠀⢸⡇⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀ ⠀⢇⠃⠀⠀⠀⠀⠀⣀⣥⠤⠤⠀⠀⠀⠀⢈⢡⣤⣄⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⢸⡞⠀⠀⠀⠀⠀⡼⢹⡟⣦⣴⣧⠀⠀⢀⣧⣤⢻⣿⢣⠀⠀⠀⠀⠀⢸⢧⠀ ⡄⡇⠀⠀⠀⠀⠀⡇⠈⠻⠿⢟⣿⠀⠀⢸⡿⠿⠿⠋⣸⠀⠀⠀⠀⠀⠀⣿⡀ ⣷⠀⠀⠀⠀⠀⠀⠙⢶⣶⡬⠟⠁⠀⠀⠀⠻⠦⢤⠴⠃⠀⠀⠀⢀⡀⠀⢸⡇ ⡇⢇⠀⠚⢷⡠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣺⠿⠿⠀⡏⡇ ⠙⢮⣷⣄⡀⠙⠷⣿⡷⣶⣦⣔⡜⠦⠆⢀⣤⠤⠖⣂⣩⣴⠾⠁⠀⢀⣜⡽⠃ ⠀⠀⠙⠺⢬⣑⡢⢤⣭⡗⠀⠉⠉⠉⠉⠉⠉⠉⢩⣿⣉⣀⣀⣤⣾⠽⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠊⠉⠀⠀⠀⠀⠀
⠀⠀⠀⣠⠖⠲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠖⢢⡀⠀⠀⠀⠀ ⠀⠀⣴⠋⢠⡆⢹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇⢰⡀⠹⣦⠀⠀⠀ ⠀⣼⡏⠀⠸⡇⠸⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠁⢸⠃⠀⢹⣧⠀⠀ ⢰⣿⡇⠀⠀⠁⠀⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⠀⠌⠀⠀⢸⣿⡄⠀ ⢸⣿⣿⣦⡀⠠⠀⢻⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⣴⣿⣿⡇⠀ ⠈⠿⣿⣿⣿⣤⣤⣤⡍⢩⣭⡍⠉⢩⣭⠓⢠⣤⣤⣤⣄⡀⠀⠀⣭⣭⣭⣍⡛⢿⢻⣯⠀⠀⢠⣿⣿⣿⠟⠀⠀ ⠀⠈⠙⢻⣿⡟⠛⠛⠃⢸⣿⡇⠀⢸⣿⠀⢸⣿⡟⠛⢻⣷⠀⠀⣿⡟⠛⢻⣿⡄⠈⣿⣇⠀⣿⡿⠛⠋⠀⠀⠀ ⠀⠀⠠⢸⣿⡃⠀⠀⠀⢸⣿⡇⠀⢸⣿⠀⢸⣿⡇⠀⢸⣿⠀⠀⣿⡇⠀⢸⣿⡇⠀⠸⣿⣼⣿⠁⠄⠀⠀⠀⠀ ⠐⠂⠀⢸⣿⡿⠿⠇⠀⢸⣿⡇⠀⢸⣿⠀⢸⣿⣷⣶⣿⠟⠀⠀⣿⣷⣶⣾⡟⠀⠀⠀⢻⣿⠇⠀⠀⠒⠂⠀⠀ ⢀⠔⠁⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⢸⣿⠀⢸⣿⡇⠘⣿⡇⠀⠀⣿⡏⠈⣿⣧⠀⠀⠀⢸⣿⠀⠀⠉⠢⡀⠀⠀ ⠀⠀⠀⢸⣿⠇⠀⠀⠀⠈⢿⣷⣤⣾⡿⠀⢸⣿⡇⠀⢻⣿⡀⠀⣿⡇⠀⢸⣿⡄⠀⠀⢸⣿⣿⣾⣤⢄⠀⠀⠀ ⠀⠀⠀⠈⠉⠀⣀⡀⢀⡀⠀⠉⠉⠉⠀⠀⠈⠉⠁⠀⠈⠉⠁⠀⠉⠁⠀⠀⠉⠁⠀⠀⠈⠉⢻⣿⣿⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⠀⠀ ⠀⠀⢀⣴⣶⡿⠿⣏⡹⠿⢿⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀ ⠀⠀⢸⣿⣿⢃⣾⣿⣿⣧⡸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀ ⠀⠀⠀⣩⣷⣿⣿⣿⣿⣿⣿⣮⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄ ⠀⠀⠀⢿⣿⣿⣿⢿⡿⣿⣿⣿⡿⠀⠀⢀⣾⣷⣼⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠛⣋⣀⡀⠀⠈⠙⠛⠁⣠⣤⣸⣿⡿⢹⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇ ⠀⠀⢀⣴⣿⣿⣿⣿⣷⣄⠀⠀⢀⣿⣿⡇⣩⣾⣷⣮⠰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠛⣻⣵⣿⣿⣿⣿⣷⣝⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡟⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⠿⠿⠋⠉⠉⠙⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠃⠀ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀ ⠀⠐⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀ ⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡇⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠖⠚⣩⠏ ⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢔⣺⡯⠝⠚⠉⠀⢀⡜⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡤⠖⢛⣩⠵⠚⠉⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⣀⣴⡿⠟⠋⢁⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⣠⢴⡒⢀⣾⣋⣤⠤⠀⠀⠀⣠⣾⠿⠋⢀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡇⡇⠀⠀⢠⠀⠀⠀⠀⠀⠈⣧⠀⠀⣠⡴⠞⠁⠙⢿⠾⠿⡏⠀⠉⠭⣿⣛⠯⣄⢀⡴⠋⣀⣤⢤⣤⡶⠖⠛⠋⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡟⢹⡀⠀⢸⡀⠀⡇⠀⠀⠀⢹⣟⡟⠁⠀⠀⠀⣸⠟⠀⠀⠀⠀⠀⣀⣶⢬⣟⠺⣿⣾⡿⠒⣚⠋⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⡇⠸⡇⠀⠈⢧⣼⡁⠀⣴⡶⢋⡿⠀⠀⠀⠀⢀⡏⠀⠀⢠⣾⡴⠛⠁⠀⠀⠈⠳⣌⠙⠟⣶⣄⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⡀⢻⣤⠀⠘⠃⣩⠟⠁⢀⡾⠁⠀⠀⠀⠀⣼⠇⠀⢀⣼⣟⠓⢦⣄⠀⠀⠀⠀⠈⢷⡀⠈⠛⣷⡄⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣷⠌⢧⠀⠀⣰⠏⠀⠀⣾⠁⠀⠀⠀⠀⣰⠿⡄⠀⠘⠀⣿⠀⠀⠈⠛⢦⡀⠀⠀⠈⢳⠀⠀⠹⣿⣻⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⢟⣩⣿⡆⠘⢧⣴⠇⠀⠀⢰⠇⠀⠀⠀⠀⣰⠃⠀⣷⠀⠀⠀⣗⠀⠀⠀⠀⠀⠹⣄⠀⠀⠈⣷⠀⠀⢿⣧⢻⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣞⣵⡿⠋⠀⠹⣤⣯⡟⠀⠀⠀⣾⠀⠀⠀⠀⣰⠋⠀⠀⢹⠀⠀⠀⡧⠀⣴⣴⣿⣿⣿⣿⣿⣿⣯⡼⡄⠀⠸⣽⠈⡜⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⢏⡟⠀⠀⠀⣀⡞⢸⠃⠀⠀⠀⣿⠀⠀⠀⢀⠏⠀⠀⣀⣸⡄⠀⢰⠃⣸⣿⣽⣿⡿⢿⣙⢿⣿⠿⢿⣷⣇⣀⣿⣇⣷⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⢃⡾⠁⠀⢠⡏⢸⠃⠸⠀⠀⠀⠀⣿⢀⣀⣀⣾⠶⠖⠋⠉⢹⡇⠀⣸⠔⡿⡿⣿⣿⣿⣤⣹⠀⢹⠀⢨⣿⡟⣿⡙⠂⣉⣹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣏⢸⠇⠀⢠⡟⢰⣿⠶⣶⠶⠶⠶⢺⣿⣽⣽⣿⣿⣿⣶⣤⣀⢸⠀⠀⡿⠀⠻⣷⠿⣿⣿⡟⢸⠀⠈⣇⣸⣽⣷⣿⣷⣞⡉⢹⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠿⢸⠀⢀⣿⡇⠈⢹⠂⢸⡄⢀⣀⣴⣿⣿⠛⣾⣿⣿⣏⣹⣏⣻⠀⢠⠃⠀⠀⠈⠳⠤⣥⠴⠛⠀⠀⣿⣿⣿⣿⠟⠯⣍⠻⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠀⣸⢻⡇⠀⠸⡆⢈⢧⢘⣿⣿⣿⣿⠀⣿⣿⣿⣿⡿⣻⣿⠀⣾⣀⣀⠤⠤⠀⠀⠀⠀⠀⠀⠀⣿⠇⣹⡟⠀⠀⠈⢧⣙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢸⠀⡇⢸⡇⠀⠀⢳⣼⡘⣟⠛⠻⢿⢿⠀⠈⡇⠉⢉⠥⠛⡿⢲⡟⠉⠱⠶⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡿⠁⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡄⡇⠈⣇⠀⠀⢈⣿⣿⠿⣆⠀⠈⣧⣧⠀⣧⠀⠀⠀⠀⡇⡾⠀⠀⠀⣴⣹⢦⠀⠀⠀⠀⠀⢠⣿⠀⠋⠘⣿⣶⡄⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠤⠄⠀⢳⣣⠀⢸⡄⠀⡞⣃⣽⣇⠹⣄⠀⠘⣎⢦⢸⡀⠀⠀⢸⢣⠇⠀⠀⣾⡿⠛⢙⡇⠀⠀⠀⣠⣾⠟⡶⣄⣠⡏⡿⠹⣤⡇⠀⠠⠤⠤⠤⠤⠤⠤⠤⠄⢀⠀ ⢸⠀⠀⠀⠘⣿⣇⠀⢣⢸⡿⣻⠏⠈⠳⣌⢷⡀⠙⣎⢷⣷⠀⠀⣼⡿⠀⠀⠀⣏⡠⠴⠋⠀⢀⡴⢛⡿⡿⠆⣶⣾⡿⣰⠃⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢸⠀⠀⠀⠀⠈⠻⣄⠈⢫⡳⣽⡆⠀⠀⣼⣿⠿⢦⡘⢦⣙⣷⣀⣿⣃⣀⣀⣀⣀⣀⣀⣠⠶⣿⣿⣟⣼⠃⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄ ⠸⠀⠀⠀⠀⠀⠀⠈⠃⠈⢳⣷⡳⣄⢰⠻⣿⠀⠀⣹⣶⣿⣿⣿⣟⠙⣿⠉⠉⠉⠉⠉⠀⠀⣿⡏⠀⠃⢠⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡉⠛⠂⠻⣆⣾⠻⣿⡀⠀⣽⠉⠉⣿⡆⠀⠀⠀⠀⠀⠀⢿⣀⢀⣴⣿⠟⠛⠿⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣤⠟⢻⣿⡛⠛⠒⢥⣤⣤⣿⠃⠀⠀⠀⠀⠀⠀⠘⣏⡿⠛⠁⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⢭⡅⠀⠈⠙⠦⢤⣤⣶⡝⠀⠀⠀⠀⠀⢀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠚⠯⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡘⠁⠀⠀⠀⠀⠀⢀⣠⣤⠴⠒⠛⣁⡠⠄⠒⠋⠀⠀⠀⠀⢶⠀⠀⢠⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣁⡤⠿⠾⠒⠒⠛⢛⣭⠕⠒⠚⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠈⣆⠈⢾⡀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⠀⠀⠀⣠⠯⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠹⣄⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣨⠏⢠⠃⢀⣀⣠⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣬⣇⣀⢻⡀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⣴⣲⣴⠚⢹⡇ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⣠⠞⠿⣿⠉⠉⣿⠉⠹⡄⠀⢻⠀⠀⠀⠀⠀⠀⣾⠁⠀⣿⠀⠀⣿⠉⢹⣷⣄⠘⢧⠀⠀⠀⠀⠀⢀⣴⠟⠫⡽⠂⢸⡇ ⢸⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣤⣯⣤⣴⣇⠀⠀⢻⡀⠀⢸⡄⠀⣧⢀⣿⣤⣤⣤⣤⣤⣤⣿⡀⢸⡇⠀⣰⠃⠀⣼⠏⢈⣧⣼⣧⣤⣤⣤⣤⣭⣤⡤⢤⣤⣤⣼⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠴⠷⢤⣼⠙⠾⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⠾⠳⣾⠹⠦⠾⠿⠶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⠀⢀⣀⡀⠀⡀⠀⢀⠀⢀⣀⣀⣀⡤⠀⢀⣀⠀⠀⠀⠀⣀⠀⠀⠀⢠⣤⡄⠀⢀⣀⢀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⢀⣀⣠⣄⣀⣀⣀⡀⠀⠀ ⠀⠀⠀⠈⢷⣶⣧⣼⢿⣧⣼⣯⣀⡞⣇⢻⣿⠉⠛⠁⣾⣯⣿⣷⠀⠀⢀⣿⣆⠀⠀⠀⠻⠛⣿⣩⡭⣽⡃⠀⡟⣿⣋⣹⡷⡟⢉⣻⠹⣄⡾⠛⠻⠏⣩⣰⠽⠇⠀⠀ ⠀⠀⠀⠀⠸⡿⠼⠏⠸⡇⠰⠧⡾⠿⠿⠿⣿⠀⠀⠀⢶⣧⠾⠋⠀⠀⡿⠷⠿⠦⠀⠀⠀⠀⣿⠀⠀⠸⠷⠾⠧⠿⠿⠯⠀⠿⠿⠥⠠⠟⠁⠀⠀⠀⠿⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣻⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠁⠀⠀⡠⠢⡄⠈⢣⠀⢠⡀⠀⢀⣤⡖⢀⡴⠋⣠⣚⣉⣦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡞⠀⠀⢠⠎⠀⠀⣳⠀⠀⢧⢸⢹⡴⢋⣟⡠⠾⠒⠋⠉⢁⠼⡏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⡁⠀⢠⠏⠀⠀⠀⢸⡆⠀⠘⡞⠘⠁⠞⠉⠀⢀⣀⠴⠚⠓⠒⠳⠾⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡿⡃⠀⢸⠀⠀⠀⠀⠈⡇⠀⠀⣿⡆⠀⢶⢄⢀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⣄⣱⠀⠀⠹⣷⡀⠈⢟⣆⠙⠒⠒⠒⠒⠊⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡄⠀⠀⢸⡀⠀⠀⢀⣾⠙⠷⣀⡤⣾⣷⣄⠘⢿⡀⠀⣀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣷⠀⠀⠀⢧⠀⠀⣾⡉⢠⣾⣿⡭⢥⡀⢳⠉⠛⠋⢲⡮⣭⣶⣖⣀⣀⣀⣱⠶⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣆⠀⠀⠈⢣⣀⡏⠀⡾⢹⢫⣿⡤⠙⡌⡆⠀⠀⢸⣷⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣆⠀⠀⠀⣹⣷⣨⡇⢠⣾⣿⣿⠀⡇⡇⠀⠀⢀⣿⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢧⡶⣖⠛⠀⠉⠓⠚⠚⠿⢯⣼⣀⣽⠔⠊⠉⠀⠀⠀⢈⣙⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⢽⠋⠀⠀⠀⠀⠀⡀⣀⠀⠈⠉⠈⠳⠤⣀⣀⣤⠚⠉⠀⢀⡏⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⡽⠁⠀⠀⠀⠀⠈⠉⠙⢷⣄⠀⠀⠀⠀⠀⠀⠙⠦⣍⡤⠋⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠋⢹⣁⢀⠀⠀⠀⠀⠀⠀⠳⡑⠦⣀⡀⠀⠀⠀⢀⣴⡷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⠟⢷⣂⣀⣀⣀⣀⠀⠙⢄⣌⡉⠑⠒⠊⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⢿⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⣉⡻⠾⢶⣫⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⡖⠋⠁⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⢻⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⢲⡺⠎⣧⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⣀⠀⠀⠀⠈⢰⡠⠋⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠭⠭⠭⠵⠖⠚⠁⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⢀⣀⣀⣀⣠⣄⣀⣀⣄⣀⣀⣀⡀⣀⣀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠈⠉⠉⠉⢉⢈⠋⠉⠉⠉⠉⡋⠉⠉⠉⢉⠁
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣠⠴⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠈⢳⡄⠀⢀⡴⠛⣡⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⢦⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠞⠁⠀⠀⣧⠾⠋⠀⣰⣿⣿⣿⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⠁⠙⠻⢿⣧⠈⢷⡟⠛⢋⣩⣽⠿⠟⠛⢛⣛⣽⠇⠀⠀⠀⣸⣧⣤⡤⠴⠿⠟⠛⠋⠉⠉⢉⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⠸⣆⢀⣿⠞⠋⠁⢀⣤⠶⠛⠉⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⡷⠶⠂⢀⡽⠋⠀⢀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⢿⣿⣿⠏⠀⠀⣴⠟⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⢷⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠾⠯⠳⠶⣶⡶⠆⠀⠀⠀⠀⠀ ⠀⣼⠃⢹⣿⣿⣾⣿⣾⠃⠀⠀⢀⡾⢡⠖⠉⠉⠉⠉⠓⢬⣧⡀⣟⢦⣄⠀⠀⠀⠀⢀⡀⠀⡀⠀⣀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀ ⢠⡏⠀⢸⣿⣿⣿⣿⠁⠀⠀⢀⡾⠱⠕⠒⣉⣉⡉⠉⠉⠑⠻⠳⠿⠀⠈⢹⣷⣶⣤⣬⣿⣞⡟⢻⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠃⣀⡀⣧⠀⢹⡇⠀⠀⠀⣸⠃⠀⣠⡾⠋⠉⠙⢷⣄⠀⠀⠀⠀⠀⢠⡟⠀⠀⢙⣷⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡀⠸⣿⠻⠆⢸⡇⠀⠀⠀⡟⠀⣰⡟⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⣼⠁⠀⠀⢘⣿⠀⣾⠁⢸⠁⠀⠀⠀⠀⠀⢠⣿⡇⢀⡀ ⠘⣧⠀⠈⠻⠶⢼⡇⠀⠀⢸⡇⠀⣿⡄⠀⠀⠀⠀⢨⣿⢿⠀⠀⠀⠀⢿⠀⠀⠀⣿⣿⠀⡟⢀⡿⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⡇ ⠀⠈⢷⣦⡀⠀⣏⣇⠀⠀⢸⣇⠀⠀⠹⢦⣀⠀⠀⢸⣿⡾⠂⠀⠀⠀⠸⢦⣠⡠⠟⠋⠀⡿⣸⣇⣀⣀⠀⠀⠀⠀⠹⣿⡿⠋⠀ ⠀⠀⠀⠙⣿⡳⣽⡸⣀⣾⠾⠋⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⣀⣷⠏⠀⠈⢙⣻⣶⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⣾⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⠶⣦⢹⡇⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣋⣀⣀⣀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠛⢿⣿⣶⡿⠋⠈⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠛⣳⣄⠐⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠿⠥⢤⣀⠀⠀⠀⠀⠀⠀⣈⠲⣄⡀⠀⣀⣤⠞⠳⠤⢤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣄⡀⠀⠀⠀⠀⠙⠲⢦⣭⡭⠤⠤⠶⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⠆⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠖⠋⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣠⠶⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠒⡶⠂⠀⠀⠈⠉⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣠⣞⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢺⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠬⢽⣆⡉⠛⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⢤⠤⠤⠤⠶⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠢⡀⠀⢀⣴⠢⠢⠀⢂⡆⠀⠀ ⢇⠐⢌⠑⠢⢄⡑⢄⠀⠀⠀⠀⠀⠀⠀⢣⠈⣲⠁⢡⠃⡆⠐⣾⣷⠀⠀ ⠉⡄⠈⠢⣀⠄⠊⡁⠓⠀⠀⠀⠀⠀⠀⠀⡜⡇⢰⡋⠀⡗⡰⠁⡄⡇⠀ ⠀⠐⡀⠈⢒⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⡔⢰⠀⢰⢇⡄⠇⢸⠀ ⠀⠆⠱⣀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠈⠢⢄⠁⣼⠀⡇⠀⠀⡄ ⠀⠰⡠⠃⠀⠀⠀⢤⠀⠀⠀⡠⣢⠔⢁⣠⣤⣄⣀⠀⠑⡿⠄⡇⠀⠀⡇ ⠀⠐⢧⡄⣁⡠⠄⣤⡴⠒⠋⠉⠀⡼⣭⣴⣦⣤⣭⣆⠀⣘⡀⠣⡀⠀⡗ ⠀⠀⢋⠁⢠⠹⣴⣻⢿⠀⠀⠀⠰⡹⠋⢺⠻⡿⡫⠃⠀⠀⠀⠉⢙⡲⠁ ⠀⠀⠸⣆⠸⡀⠉⠛⠯⢀⠀⠀⠈⡷⠲⠌⠑⠈⠀⠀⠀⠀⠀⣠⡯⢤⠀ ⠀⠀⠀⢸⣎⠵⢊⣴⣵⡇⠀⡠⠊⠀⠀⢀⡔⠂⠁⠀⠀⠀⢀⠞⢠⠇⠀ ⠀⠀⢤⠘⢆⠰⣿⣿⣿⡿⠞⠀⠀⠀⠀⡺⠀⠀⠀⡀⣀⠔⢋⡖⠓⠖⠀ ⠀⠀⠀⠳⡈⢄⠈⣛⡉⠀⠀⢀⡠⣀⠜⡀⠄⢂⠡⠊⠀⢴⠋⣠⠞⠀⠀ ⠀⠀⠀⠙⣅⠈⠻⣽⡫⠟⠂⢀⡨⠒⠁⠀⠈⠀⠀⠀⠀⠚⢒⣕⡠⠋⠀ ⠀⠀⠠⡌⣾⠀⠀⠈⢲⠖⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⣭⠖⠀ ⠀⠀⠠⢷⢀⠕⡀⢠⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀
⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠈⣩⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡻⠉⠀⠀⠀ ⠂⠀⠀⠀⠘⢦⠀⠀⠀⠀⣾⣿⣿⡆⡀⢸⣷⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠐⠁⢠⡀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⣊⡞⠁⠀⠀⢀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣴⠟⠁⢀⣾ ⠀⠀⠀⠀⠀⠒⠀⠀⠀⠈⣿⣿⣿⠟⠋⠀⠀⢀⣴⣿⣿⡿⠁⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⠈⠛⢿⣿⣿⡿⡻⠙⠁⠀⠠⣾⠇⠁⣴⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⢲⣤⣈⣻⠟⠃⠀⠀⢀⣴⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣆⠀⠀⠀⠀⠎⠣⡀⠀⠀⠀⣐⣿⣇⣴⣾⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⢀⡬⠟⠒⠒⠦⢄⡀⠀⠀⣩⣷⠾⢶⡀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡆⠀⠀⠀⠀⠘⢾⣦⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⢀⡜⢁⣤⡤⠄⠀⠀⠀⠈⠣⣼⡟⠁⠀⠘⡇⠀⠀⠀⠀⠀⢀⡴⠛⠛⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠉⢭⣴⣿⣿⠟⠠⠀⠀⠀ ⠀⠀⠀⠀⠘⣳⠟⠁⠀⠀⠀⠀⠀⠈⠀⣿⠁⠀⢀⣀⡇⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⢹⣿⡄⠀⠀⠠⠄⠀⠀⠢⠤⢄⣈⣳⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡇⠀⢀⡄⠀⠐⠀⠀⢠⠀⠹⣆⠐⣷⣿⠁⠀⠀⠀⠀⢸⣰⣦⡀⠀⠀⢠⡿⠁⠀⣠⠆⠀⠀⠀⠀⢆⠀⠙⢦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠧⣾⣋⣀⣀⡀⠀⠠⣦⣶⣄⡈⠉⢹⠋⠉⠉⠙⡒⠢⢼⣿⣧⠃⣀⡴⠟⠁⢀⡜⠁⠀⠀⠀⠀⠀⠀⠹⣦⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣦⣄⡀⠉⠁⢉⣧⠖⠁⠀⠀⠀⠀⠀⠀⣠⠆⠉⠉⢁⣐⣡⠞⣿⣼⠀⠀⠀⠀⠈⢢⡄⠀⢱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣶⣿⡟⠀⠀⠉⣳⠞⣉⣤⣤⣤⣤⡀⠀⠀⣀⣴⡇⠀⣠⡾⠋⠀⠀⠀⢈⠥⣚⣻⣶⡶⠤⠤⠽⠶⠼⠆⠀⠀⠀⠀⠀ ⣄⣀⣀⣀⠀⠀⢈⡿⠞⠁⠀⠀⠀⣇⢸⣿⣿⣿⣿⣿⣿⣧⠈⠉⢻⡇⢸⢏⣠⠖⠀⣠⡶⠛⠉⠉⠙⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣾⣿⣅⢠⠏⠀⠀⠀⠀⠀⠀⠈⢳⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⣴⠗⠋⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣶⣦⡄⠀⠀⣠⡄⠀⠁⠀⠉⠛⠯⠿⠶⠤⠤⠒⠋⠁⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⡙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⠏⢷⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣟⡏⠀⢸⡇⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣼⠁⠀⠨⣧⠀⠈⢻⣴⣞⡛⠛⠛⠛⠛⠲⠦⣤⡀⢀⡾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡏⡿⠀⠀⠀⣹⣤⠴⠶⡛⡟⠉⠛⠲⢤⠀⠀⠀⠀⠙⢾⡃⢹⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⢞⣽⠟⠁⠈⢷⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⡇⡇⠀⠠⣾⣿⣷⡾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠹⣦⡀⠀⠀⢀⣠⠴⢏⣹⠟⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⣿⣧⣤⡤⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⡀⢈⣿⠾⠛⠋⠁⠀⡾⠃⠀⠀⠀⠀⠀⠀⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⠛⠧⣤⣄⣀⣀⣀⣀⣠⠤⠒⠀⠀⠀⠀⠀⠀⠀⣠⠀⠈⡇⠈⠁⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠈⠿⣇⠀⠀⡹⢀⡿⠋⠀⠀⠀⠀⠀⢀⣠⠄⠀⢀⣴⠃⠀⣸⡇⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⡀⠀⠘⠆⠀⣿⠿⠒⠒⠒⠒⠲⠶⣏⣉⣀⡠⠶⣿⣯⣠⠞⠻⣆⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⢀⡟⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠳⣄⡀⢀⣸⡇⠀⣴⠖⣦⣠⠀⠀⠈⠉⣾⣦⣽⣿⣯⣀⣀⠀⠈⢧⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⣠⡟⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣻⡦⠾⠋⠀⢸⡏⢀⣾⣿⠀⠀⠀⠀⠈⠉⣻⣿⣿⡛⠛⠛⠓⢾⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⣴⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣽⣯⡆⠀⠀⠀⢸⡇⠘⣻⣿⠀⠀⠀⠀⠀⣠⠏⢽⡟⣿⣆⡀⠀⠀⠻⡄⠀⠀⠀⠀⢀⣠⠴⠋⠒⠋⢉⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⡟⡄⠀⠀⠀⠀⠹⣤⡽⠇⠀⠀⠀⠀⢰⠇⠀⠸⣟⣿⡟⣿⠄⠀⠀⢷⠀⠀⠀⠈⠉⠁⠀⠀⠀⣶⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⡇⠀⣠⣄⣤⣔⣛⣀⡀⠀⠀⠀⠀⢺⣄⠀⠀⢉⣿⠷⠟⠂⠀⠙⢻⣷⡀⠀⠀⡀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⣇⢸⡃⢯⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠄⣿⣄⣠⣀⢉⣛⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣞⡇⠀⠳⣄⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣻⣿⠉⠙⠉⣹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠲⣄⠈⢻⡊⠉⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⣠⡶⠻⠃⣤⣶⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣷⠦⡷⢤⣄⣀⡀⢀⣠⡴⣿⠀⠀⢀⣠⠴⠚⠁⢤⣶⡖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢳⠀⠀⠀⠈⠁⢀⡞⢀⣠⠞⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡳⢄⣀⣠⠴⣻⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢟⡷⣶⢶⢴⢸⣾⣵⡦⡆⣯⣇⡔⢹⣹⡷⠷⣶⣶⡴⠀⢆⠦⡴⣀⠆
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⡏⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠘⣯⣼⣿⠟⣿⣿⠟⠁⣸⠁⠒⠠⢀⡀⠀⠠⠈⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡧⠖⠒⠒⠁⠉⠁⠀⠀⢻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⠀⣴⡇⠀⢰⠀⠀⠀⢀⠀⡜⠀⠀⠹⡏⢁⣴⠛⠁⠀⢠⠇⠀⠀⠀⠀⠀⠜⠁⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⢹⣒⣒⠶⠶⢦⡤⠝⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⠞⢠⡁⠀⢷⠀⠀⢀⠎⠸⠀⠀⠀⢀⣴⠋⠁⠀⠀⢀⠏⠈⠉⠀⠀⢀⣀⠀⠤⠐⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠸⡇⠀⠈⠆⢀⠇⠀⠁⠀⣼⢠⡞⡁⠀⠀⠀⢀⠏⠀⠀⠀⠚⠛⠂⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⠀⠀⢀⣀⣀⣀⣀⠠⠄⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⡄⠀⠈⠚⠂⠀⠀⣴⣿⡎⠀⠀⠀⠀⠀⡞⠀⠀⠐⠒⠐⠀⠀⠀⠀⠈⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⢀⠀⠀⠤⠄⠒⠂⠨⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠢⢤⣀⡀⢳⢀⣀⣠⠤⠤⠤⠤⠬⡇⠒⠈⠉⠀⠀⠀⠀⠀⠀⢀⠀⠘⣆⢀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠤⠂⠈⠙⠁⡀⠄⢂⠐⡀⠆⠐⣻⠀⠀⢀⡀⠄⠐⠂⠉⢀⣀⣀⣠⣼⣦⣤⣂⠐⠐⡈⠐⢂⠁⠒⠠⢁⠂⠌⢉⠑⢦⠀⣠⠤⠴⠾⢲⠶⠶⠤⠤⢤⣀⣀⠒⠀⠤⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⠤⣌⣌⣠⠁⡐⠈⠄⢂⠐⡈⠄⣹⡖⠀⣀⣠⣦⣶⣿⣿⣭⣽⣶⣷⣽⣶⣬⣭⡳⣥⠀⠡⠀⠌⠠⢁⠂⠌⡀⠂⠌⢀⣾⣥⣶⣶⣿⣿⢿⡿⣿⣿⣿⣿⣮⣽⣿⣶⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠌⠐⡀⢂⠐⠠⢈⣷⣿⣿⣿⣟⡿⣽⣻⣿⣟⡷⣯⣟⣿⣿⣟⣿⣿⠇⠠⢁⠈⡐⠠⠈⠄⠠⢁⠂⣼⣿⣯⣷⣻⣿⣽⢯⣟⣷⣿⣟⣾⣽⣻⣟⡿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣌⡐⢀⠂⡈⠐⡀⠻⣿⣿⣿⣾⣿⣿⣽⣯⣿⣟⣷⣿⣾⣿⣿⣿⡿⠀⡁⠂⡐⠠⠁⠌⠠⠁⠂⠄⡈⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣷⣿⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠃⠐⠤⠀⠙⠛⠿⠿⣿⣿⣿⣿⠿⠿⠟⠛⢋⠉⡀⠄⢂⠐⠠⠐⠠⠁⠌⠠⠁⠌⠠⠐⡀⠈⠉⠛⠛⠟⠻⠟⠟⠻⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠐⠒⠂⠂⠂⠑⠀⠃⠈⠀⠃⠈⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀
/>  フ << goofy |  _ _| /` ミ_xノ /     | silly funky /  ヽ   ノ へ ╱|、 ♡ ╱|、happy │  | | | ૮ - ՛ ) (˚ˎ 。7 (` - 7 / ̄|   | | | / ⁻ ៸| |、˜〵 |、⁻〵 ( ̄ヽ__ヽ_)__) 乀 (ˍ, ل ل じしˍ,)ノ じしˍ,)ノ \二) Cat Family
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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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⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠐⠶⣿⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣇⡀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⡿⠟⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣆⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
႔ ႔ ᠸᵕ ᵕ 𐅠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠞⠛⠲⣦⣤⠤⠤⢴⠏⣦⣈⣷⣚⠉⠻⡄⠀⠀ ⠀⠀⠀⣿⣀⠀⠈⠁⠀⠀⠀⢾⡀⢻⡿⠉⠉⣷⡞⠻⣦⠀ ⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⣤⣴⠿⠿⣠⡟⠀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡶⢻⡄⠀ ⠠⠤⡧⠤⠄⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠋⢹⡏⠁ ⠀⢀⣿⡤⠄⠘⠿⠁⠀⠠⣞⣻⠄⠀⠀⠻⠏⢀⡈⣽⠛⠃ ⠀⠀⢈⡷⣶⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠛⠂⠀ ⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠒⠒⠒⠚⠛⠛⠉⠁⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⡶⠁⣠⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣴⣿⠿⠋⣁⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣿⡿⠟⠋⠉⠀⣀⣀⣀⣨⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣴⠂ ⠈⠉⠁⠀⠀⣀⣴⣾⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠛⠻⠿⠿⠿⠿⠿⠿⠟⠋⠁⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⡿⠁⠀⢀⣀⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⡿⠁⢀⣴⣿⠋⠉⠉⠉⠉⠛⣿⣿⣶⣤⣤⣤⣤⣶⠖⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⡇⢀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⡇⠈⢿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣷⡀⠀⠉⠉⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣋⣠⡤⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢄⣸⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠙⠳⠤⣀⡉⠒⠤⣀⠀⣀⣠⠤⠖⠋⣷⣶⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠟⠢⣀⠀⠀⠈⠉⠲⠞⠉⠀⠀⠀⠀⠘⣁⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡄⠰⣞⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣦⡙⢻⠃⠀⠀⠀⠀⠀⠀⣀⣀⣀⡸⣿⠟⣆⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠻⢿⡇⠈⠻⡄⠀⠀⠀⠀⠀⠚⠛⠛⠻⢿⡦⠀⠀⠿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣾⣟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠤⢤⣴⣦⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣆⣀⠀⠀⣠⢶⠀⠀⠀⠀⠘⠷⠾⠖⢋⡥⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠈⠀⡿⠙⠚⠓⡏⠀⢀⡄⠀⢀⡤⠔⠚⠁⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢶⣒⠒⠊⠉⠉⠀⠀⠀⠉⠉⠓⠒⠋⠁⠀⠀⣸⣅⢴⣟⣀⣠⡟⠀⠀⠀⠀⠀⠀⠀ ⣟⠳⡖⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣏⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⠹⡆⠈⠢⠀⠈⠑⠲⢤⣀⠀⠀⠀⣘⣇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠤⣴⠀⠀⠀⠀⠀⠀ ⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⢯⡽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣒⠾⠃⠀⠀⠀⠀⠀⠀ ⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⢤⣳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠀⠀⠀⠀⠀⠀⠀⢠⠗⠢⡤⢄⡀⠈⢧⠀⠀⠀⠀⢸⠷⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⢕⣂⠀⠀⠀⠀⢀⣠⣼⠝⢹⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢳⠈⠛⢷⡟⠀⠀⠀⠀⠸⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⣼⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠸⡀⠀⠈⢧⠀⠀⠀⠀⠀⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⢀⡼⠉⢧⠀⠀⠀⢠⠇⠀⠀⠈⢇⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣰⠋⠀⠀⣸⠀⠀⠀⡞⠀⠀⠀⠀⠈⣆⠀⠀⠀⢹⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⠇⠀⠀⠀⢹⡀⠀⠈⣇⠀⠀⠀⠀⠀⠘⡄⠀⠀⠘⣎⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢸⠀⠀⠀⠀⠀⢳⡀⠀⠹⡄⠀⠀⠀⠀⠀⢹⡀⠀⠀⢳⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⣀⣬⡇⠀⠀⠀⠀⠈⠷⣴⣤⣿⠀⠀⠀⠀⠀⠀⠳⣤⣀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣤⣼⣬⣭⣦⣤⣤⣀⣀⢶⣶⣦⡤⡤⣤⠀⣴⣶⣤⣤⣤⢴⣤⣤⣤⣶⢤⣤⣤⣤⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠁⠉⠉⠉⢉⠉⠉⠉⠁⠈⠉⠉⠉⠈⠉⠉⠉⠀⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⢀⣠⣴⢛⣉⣁⣀⣀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣶⣶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⢿⣶⣾⡿⣻⣿⢟⣫⠽⠿⠟⠓⠒⠶⢤⣤⣄⣀⣤⣤⣄⣀⣤⣾⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢾⣿⠛⢿⣦⣀⣹⡿⠒⠶⠖⠒⠚⣿⣿⣿⣿⣿⣿⣿⣴⡟⠡⣶⣶⣶⣦⣬⣭⣅⣤⣶⡿⠋⠁⠀⠀⠈⢻⣿⣿⠋⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⠀⠈⣿⣿⡏⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣍⣉⠍⠙⢻⣯⣥⣤⣤⠀⠀⢀⣴⣾⣿⣃⠀⢀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣷⢶⠽⠋⠁⠀⠀⢀⣴⣿⣿⣿⡟⣻⣿⣿⣿⢿⣿⡏⣁⠉⠉⠙⠿⢿⣏⠛⠻⢷⣄⡀⠤⠀⠁⢀⡴⠛⠫⢄⣼⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⢠⣾⡿⢯⣼⢟⣿⣿⣿⣿⠇⣾⡎⣿⣿⣷⣴⣦⡀⠀⠙⢷⣄⠀⣀⣛⢦⣀⠀⡏⠉⣀⣠⡾⢻⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣷⣿⣶⡀⢐⣿⠟⣠⣿⣿⡿⣽⣿⡿⣿⡆⢻⠀⢾⡟⢷⣝⢾⡝⠷⣤⡰⣿⣷⣍⠛⢿⡿⣦⣵⠸⡏⠁⢠⠞⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠨⣷⣾⣿⣾⣻⠎⡿⢠⡏⢰⣻⣿⡇⣿⡇⢸⡆⠘⣷⡀⠙⣷⡙⢧⡈⠻⣮⠳⣟⠃⠀⠙⢮⢻⣾⠷⣶⡒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣼⡿⣁⡞⠀⡾⢰⢏⠏⣿⢰⠋⡃⠘⣇⠀⢹⢷⣄⠀⠙⢧⡝⣦⡀⠳⣌⢧⡀⠀⠸⣧⡻⣆⢸⡏⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠤⠖⠉⢸⣟⣾⢻⡇⠀⢡⣯⠟⣼⢻⠸⡆⢣⡀⠙⠀⢸⣷⠙⢷⡤⡀⠹⣶⣝⢶⣌⣾⡷⡄⠀⢿⣷⡽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⡼⠁⢸⡇⠀⣿⣟⡼⡁⢸⣷⣿⠀⠳⣄⠀⠈⣿⣆⠀⣙⣿⣅⠈⠿⣿⣾⣿⣷⠻⡀⠀⢿⣿⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠴⠋⣿⡇⠀⠸⡇⠰⢹⣿⣧⣤⣀⣿⡈⣧⠀⠈⠳⣄⢻⢹⡆⢨⣵⡿⢛⣻⣿⣿⣿⣿⠀⢱⠀⠘⢹⣿⣿⢬⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡟⢧⠀⠀⢷⡀⢾⠟⠛⢿⣷⣿⣿⠿⣷⣄⠀⠀⠘⡇⠹⣬⣷⣿⣿⣿⡟⠁⣸⢿⠀⡾⠀⠀⣸⣿⣿⡄⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⣧⠘⣧⠀⠈⢧⡘⡿⣦⡀⠻⢿⣿⡿⠿⠌⠻⢦⡀⢻⡄⠙⠿⠟⢛⣛⣡⡴⠋⢸⣴⠃⢠⢠⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢦⠈⢧⡀⠈⢳⡕⠈⠛⠲⠤⢤⣤⠀⢀⣀⠀⠉⣿⣧⡄⢈⣩⠭⠍⠁⠀⢀⣾⡿⠀⣠⣿⣿⣿⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢸⠛⢦⠀⢹⣶⡀⣀⣠⣄⡈⠁⣍⣻⣷⣦⣾⡉⠰⢁⣠⠴⠋⠀⢒⢿⣷⣷⣾⣿⣿⣿⣿⠀⠀⠉⠓⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣿⣦⣻⡿⠁⠀⠀⠈⠓⠼⣏⣁⣀⣸⡆⠀⠛⠁⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢹⣿⣿⣿⣆⢀⡀⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀⠀⠈⠓⣦⣼⣿⣿⣿⣤⣾⣷⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⣧⣿⣿⣿⣿⣄⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣠⡿⣻⣿⣿⣿⣿⣿⣿⣿⣮⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⢹⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠈⠀⣀⡤⠞⡯⢀⣿⣹⡾⠻⢿⣿⣿⡁⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⣹⡏⠀⡙⢿⣿⣿⠉⢻⠹⡗⠦⣤⣀⡤⠶⠞⠉⠀⢸⡇⠘⢻⡏⣧⠀⠈⠻⣿⣇⢸⡟⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣠⣤⣴⣾⠏⢯⠀⢠⣿⣷⠀⠙⠻⣿⣿⡇⢸⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⢸⡇⣿⠀⠀⠀⠉⢻⣿⠃⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣾⠿⣿⣿⡏⠹⣦⠘⣧⡈⠻⣿⣧⠀⠀⠻⢻⣷⣸⡇⠀⠹⡄⠀⠀⠀⠀⠀⠈⠁⣠⠤⡺⠁⡿⠀⠀⠀⣠⣼⠋⠀⣀⣿⡿⣧⡆⠀⠀⠀⠀⠀⠀⠀ ⢴⣿⣿⠟⢉⣿⣿⣿⠦⣌⡷⣾⣷⡀⠙⠻⣷⣄⠀⠙⢿⣿⢿⠀⠀⠀⠀⢠⠀⣀⡴⠞⠉⠀⣠⠇⡸⠃⢀⣴⠞⠉⠀⣀⣴⣿⠟⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣠⢸⣿⣿⣿⠀⢈⠙⠛⠿⣷⣄⠀⠈⠛⠿⣦⣜⠿⣿⣇⠈⠙⠓⠚⠋⠁⠀⠀⠀⣰⣁⣼⡷⠞⢋⣀⣤⣶⠿⠛⢁⣠⡴⠾⠛⣻⣦⣀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⡀⠀⠀⠈⠛⢷⣦⣤⡄⣨⡙⢷⣽⣿⣇⠀⠀⠀⠀⢒⣶⣴⢿⠟⠋⢀⣠⣶⣿⣛⣯⣥⣶⣾⠟⠉⠀⠀⠀⣼⠿⣿⣷⣦⣄⠀⠀ ⠀⠈⠙⠻⣿⣿⣿⣿⣷⣀⡃⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣾⣿⣿⣿⣦⣤⢶⣛⣛⣁⣁⣠⣴⣶⣿⣿⠿⠛⠉⠉⣠⡾⠋⠀⠀⠀⠀⣼⣿⣴⣾⣿⣿⣿⣷⡄ ⠀⠀⠀⠀⠀⠉⠛⠿⣿⣽⣛⠿⢶⣤⣄⡀⠀⠀⠀⠀⡍⠐⠪⢹⠿⠿⢿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢶⣴⣭⡙⠳⠶⠦⡄⠀⠀⠀⠈⠁⠶⠆⠠⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷⣦⣤⣄⡀⠀⠀⠀⠉⠁⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⣤⡾⠿⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠛⠛⠲⢶⣤⣤⣤⣶⣶⠶⠒⠂⠒⠚⠋⠉⠙⠛⠛⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡄⠀⠀⠀⠀⠀⠀⣠⠖⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠘⢟⢆⠀⢠⣦⡀⠀⠘⠹⠀⠀⠀⠀⣠⠞⠉⢷⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢕⠮⣦⢢⣸⡀⠙⢦⡀⠀⠀⠀⠀⡴⠋⠀⠀⢸⡇⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⣄⣑⠀⠁⠉⢧⡀⠀⠙⠢⣄⣀⡞⠁⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡖⠉⠀⠀⠀⠀⠀⠀⠉⠑⠒⠢⠿⠦⣀⠀⠈⠛⠶⣤⣀⣀⠀⣸⠃⠀⡆⠀⠀⠀⣀⣀⣀⣠⢤⣴⠖⠛⢳⡄⠀ ⠀⠀⠀⠀⢮⠀⣀⣤⡴⠖⠛⠉⠉⠀⡀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠈⠩⣟⡛⠛⠚⠛⠋⢉⡽⠋⠁⢀⡴⠛⠁⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⠉⢠⠏⠀⠀⠀⠀⡴⠋⢹⡶⠞⠉⠁⠀⠉⠙⢦⡀⠀⠠⣖⠋⠉⠀⠀⣀⡴⠋⠀⢀⣴⠿⠓⢲⡆⠀⠀⣸⠃⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣸⠁⠀⣸⢃⣠⣴⡶⠚⣻⡿⠀⢹⡄⠀⠙⠶⠶⠖⠚⠉⠀⢀⡴⠟⠁⢀⣠⠞⢀⣀⢠⡏⠀⠀ ⠀⠰⣒⠤⣀⠀⠘⣇⠀⠀⠀⣯⠀⢀⣇⡾⠁⣿⡿⠛⣉⠚⠛⠋⢷⡤⠴⠾⢶⣄⣀⡤⠞⠫⠤⠶⢾⡏⠁⣴⣿⣏⢻⠀⠀⠀ ⠀⠀⢀⡉⠲⢍⡂⠘⠳⢤⡼⠙⣦⡼⢹⢃⣴⡏⠀⢤⣍⠙⠓⠂⠀⠀⠀⢀⣾⠉⠀⡀⠀⠀⠀⢀⣠⠇⠀⣹⡌⣻⠟⠀⠀⠀ ⠀⠀⢐⡴⠂⠀⠀⠀⠀⢠⡇⠀⣿⠀⣾⣿⣯⡤⣤⣄⠈⠓⠀⠀⠀⠀⣠⣿⠭⠧⠤⡉⢻⡋⠉⠉⢀⣠⣾⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⣠⠼⣀⡴⠛⠀⠈⢛⡿⠣⣼⣿⣧⠀⠀⠀⠀⠈⠉⠉⠛⡆⠀⡻⠿⠤⠴⠚⠋⣉⡤⠖⠋⠁⠀⠀⠀⠀ ⠀⠀⣀⣀⣤⡤⣒⣯⣵⣟⡁⠀⠀⠀⣠⠟⢷⣶⣿⣍⣿⠀⠀⠀⠀⠀⢀⣠⠞⠁⣠⠇⠀⠀⠀⠴⠞⠛⠚⠓⢦⡀⠀⠀⠀⠀ ⠀⢰⠋⣡⣿⠏⢁⡤⠀⠈⢹⡄⣠⣞⣁⣀⣤⣿⢋⣽⡟⠀⠀⠀⠀⠀⢙⡇⣠⠴⠥⠤⠤⣄⡀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀ ⢀⣼⣶⡟⠁⠘⠑⠃⠀⠀⣸⢿⣥⠭⠏⠀⢸⢷⠚⣿⠁⠀⠀⠀⣠⠖⠋⠀⠀⣀⣀⣀⣀⡀⠉⢳⡖⠚⠉⠉⠉⠀⠀⠀⠀⠀ ⠾⠥⠞⠧⣄⠀⠀⠀⣠⢾⡥⠤⠽⠆⠀⠀⡼⣾⣶⠃⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠯⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⠋⠉⠉⠁⠀⠀⣀⣠⣶⢧⣴⠃⠀⠀⠀⣰⣃⡠⠤⠒⠒⠒⠲⡶⠶⠤⢤⣤⡤⠿⠋⡉⠛⠲⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠴⠒⢀⡀⠀⠀⠳⡈⣹⠟⠁⠀⠀⢀⣠⡿⣿⣃⣤⣄⣀⡀⠀⢳⡴⠚⠩⠀⠀⠀⠀⠀⠀⣴⡟⠁⠙⠳⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠁⠀⠀⠀⣿⣁⣀⣀⣠⡴⠛⢹⣤⡿⠋⠀⠀⠉⠛⠷⢮⣿⣄⡀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣁⣀⣀⣴⣋⣀⣀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣦⣶⣾⣏⣠⣤⡶⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣶⠿⠛⠻⢿⣯⡙⠛⠿⣿⣿⡻⠶⢦⣤⣀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠈⠙⢷⣄⠀⠙⠻⣦⣄⠈⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠈⠙⢷⣤⡀⠀⠈⠙⠳⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀ ⢾⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣴⣶⣿⣿⣿⣿⡇ ⠈⢿⣿⣿⣿⡛⠛⠈⠳⣄⠂⠀⠀⠀⠀⠀⣠⠞⠉⠛⢻⣿⣿⣿⡟⠀ ⠀⠸⣿⣿⣿⠥⠀⠀⠀⠈⢢⠀⠀⠀⠀⡜⠁⠀⠀⠀⢸⣿⣿⣿⠁⠀ ⠀⠀⣿⣿⣯⠭⠤⠀⠀⠀⠀⠃⣰⡄⠌⠀⠀⠀⠀⠨⢭⣿⣿⣿⠀⠀ ⠀⠀⠹⢿⣿⣈⣀⣀⠀⠀⠠⢴⣿⣿⡦⠀⠀⠀⣀⣈⣱⣿⠿⠃⠀⠀ ⠀⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⠘⣻⣿⣶⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⢂⠀⠀⠀⠀⠘⢸⡇⠆⠀⠀⠀⢀⠰⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣷⣿⣆⡀⠀⠀⠁⠈⠀⠠⠀⠀⢀⣶⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣷⣴⡜⠀⠀⠀⠀⣦⣤⣾⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡿⠛⠿⠿⠛⠁⠀⠀⠀⠀⠘⠿⠿⠿⠿⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣤⠟⡇⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣼⣿⡃⠀⠀⢀⡾⡃⠀⣿⠀⠀⠀⠀⢠⡼⠋⢸⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⠟⠋⠁⣰⡟⣠⡇⠀⢻⡀⠀⢀⣴⠏⢀⡀⠘⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠟⣶⣿⡇⠠⠸⣧⣠⠟⠁⢀⣾⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠐⣧⡀⠀⠀⠀⣸⠏⢾⠿⣿⡇⠀⠀⠙⠃⠀⢠⣾⣿⡇⠀⣿⡆⠀⠀⢀⣀⠀⠀ ⠀⠀⠙⢦⣀⡾⢿⣶⣮⣅⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠅⠀⢹⣇⣠⠶⠛⠛⠀⠀ ⠀⢠⣄⣀⣹⡇⠘⣿⣿⣿⠿⠆⠀⠒⢻⣾⣶⣶⣤⡀⠀⣠⣼⡟⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣸⣧⠀⠀⠀⠀⠰⡆⠀⠀⠈⠿⣿⡿⡟⠻⠞⢯⣼⣇⣀⠀⠀⠀⠀⠀ ⠀⠠⡾⠛⠁⠘⠷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠉⠛⠶⣤⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣿⣶⣶⣶⣶⣶⣶⠶⠛⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠙⠛⠛⠛⢻⣇⠀⠀⠀⠀⠉⠳⣦⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡆⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⡇⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢸⠇⠀⠀⠀⣷⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⠴⠞⠛⠛⡆⠀⠀⠀⢸⣆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣋⢀⣀⣠⣴⣾⠇⠀⠀⣰⠟⠙⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⢁⡴⠋⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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/) /) ~ ┏━━━━━━━━━━━━━━━━━┓ ( •-• ) ~ ♡ You are amazing ♡ /づづ ~ ┗━━━━━━━━━━━━━━━━━┛
⠀⠀⠀⠀⠀⠀⡠⠄⠂⠀⠈⠉⠁⠀⠐⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣽⠖⠋⡍⢳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡏⣰⠿⡔⢠⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣼⣷⠃⠀⣿⢀⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣀⠀⠀⠀⣿⣿⠁⠀⠀⠀⣿⣷⣶⣰⣿⣿⠀⢰⡇⣾⠁⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠬⠓⠲⣶⣿⢿⠤⠖⠒⠚⣹⠿⢿⠁⢀⣿⣇⣼⡷⠃⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡰⠊⠀⠀⣠⡔⠛⣿⣿⠂⠀⢀⣾⣿⣾⣯⣷⡌⠻⢿⡿⠃⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠁⠀⠀⢰⡏⢀⣶⠛⠛⠲⠄⠸⣟⣿⣿⠟⠉⠁⠀⠈⡇⠀⠀⣀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡀⠀⠀⠹⢷⣠⡟⣦⠶⠗⠀⠀⣠⡀⠀⠀⠀⠑⢦⣸⠁⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠳⡀⠀⠀⠈⠳⡗⠛⠤⣀⠤⠊⠁⠀⠀⠀⢀⡤⠚⠁⠀⠈⠑⠒⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡔⠛⠀⠀⠀⠀⠘⠢⢤⡤⠤⠒⠒⠒⢚⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠣⡤⠚⠉⠉⠉⠒⢄⡀⡇⠀⠀⠀⠀⢼⡅⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡞⠀⠀⠀⠀⠀⠀⠀⠛⠳⢄⡀⠀⠀⠀⠳⡊⠁⠀⠉⠢⡀⠀⠀⠀⣀⣀⣰⣁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠈⠉⠶⠴⠒⠒⠿⠦⢄⣀⡬⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⠀⠀⠀⠀⠀⠀ ⠈⢇⠀⢄⠀⠀⠀⣀⠴⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡙⠢⢄⠀⠀⠀ ⠀⠘⢆⠀⢀⡴⠋⠀⠀⠀⠀⣠⠴⠚⡉⠏⠙⠲⣤⡀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠙⠦⣤⠷⣦⠀ ⠀⠀⠘⡶⠋⠀⠀⠀⠀⠀⡴⠋⢠⡞⣿⠓⣄⡀⠆⠘⢦⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠐⠸⢷⣿⠃ ⠀⠀⣸⠁⠀⠀⠀⠀⠀⢸⠁⢀⢹⣇⢿⣇⣹⠆⠰⢀⠸⡇⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠈⠀⢆⡏⠀ ⠀⢠⡗⠀⠀⠀⠀⠀⠀⢾⡀⠂⠈⡙⠛⠞⠉⡀⠂⠄⣼⠇⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣥⠾⡏⠀ ⠀⢸⡀⡆⠀⠀⠀⠀⠀⠈⢷⣼⣄⡀⠂⠄⡁⣀⣦⡿⠋⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀ ⠀⠘⣧⠱⡄⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀ ⠀⠀⠘⢧⡈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⠀ ⠀⠀⠀⠀⠑⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠔⠊⠉⠒⠒⠤⠤⠤⠤⠤⠤⠤⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠒⠚⠘⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⠀⠀ ⠀⠀⣠⣤⣤⣄⣀⣾⣿⠟⠛⠻⢿⣷⠀ ⢰⣿⡿⠛⠙⠻⣿⣿⠁⠀⠀⠀⣶⢿⡇ ⢿⣿⣇⠀⠀⠀⠈⠏⠀⠀⠀ text here ⠀⠻⣿⣷⣦⣤⣀⠀⠀⠀⠀⣾⡿⠃⠀ ⠀⠀⠀⠀⠉⠉⠻⣿⣄⣴⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣄⡀⠀⠀⠀ ⠀⠀⣤⡶⢶⣖⡶⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡿⠛⠉⢉⠉⠙⣿⡄⠀⠀ ⠀⠀⣿⢰⣌⣭⡽⠷⠶⢮⣭⣛⣲⢶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣻⡵⢞⣋⣥⠶⠶⠒⠿⣧⡀⢸⣿⡀⠀ ⠀⠀⡏⣾⡟⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣌⡙⠻⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⣿⣫⣷⠞⠋⠉⠀⠀⠀⠀⠀⠘⣧⠀⡟⡇⠀ ⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣌⡛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣿⣿⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⡇⢿⠀ ⠀⣿⡟⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢩⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣧⢸⠀ ⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⡿⣷⣶⠶⠶⠒⠒⠒⠲⠶⢶⣦⣤⣤⣴⣷⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾⠀ ⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠚⠛⠋⠉⠉⠉⠉⠉⠉⠑⠒⠛⠿⢿⣥⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢀⡿⠀ ⠀⠸⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀ ⠀⠀⢻⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⣿⠁⠀ ⠀⠀⢺⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢩⡇⠀⠀ ⠀⠀⠈⠻⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣣⣿⡇⠀⠀ ⠀⠀⠀⢰⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣼⠟⠁⠀⠀ ⠀⠀⠀⣿⢁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀ ⠀⠀⣸⠇⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⠶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀ ⠀⢠⡟⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⡿⠁⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠉⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⣆⠀⠀⠀ ⠀⣸⢳⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⢼⣿⣿⠿⣦⣄⣠⣾⣿⣧⠀⠀⠀⠀⠀⠀⣸⣇⣀⣀⣴⡿⢿⣿⣿⡏⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⢿⡀⠀⠀ ⠀⡏⢼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠸⣿⣷⣤⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣄⣴⣿⣿⠇⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡞⣧⠀⠀ ⢰⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠙⠿⣿⣿⣿⣿⠟⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣿⡄⠀ ⢸⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠁⠀⠀⠀⠀⠀⢻⣿⣍⠙⠛⠉⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀ ⣸⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⣿⣗⣒⠒⢚⣋⣡⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣦⣀⠀⢀⣤⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀ ⣿⠘⣇⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣤⠀⠀⠀⣼⢻⣿⠀ ⣿⠀⢻⡄⠀⠀⠰⠿⢿⣿⡶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢟⣿⣿⣿⣿⠀⠀⠀⣿⢸⣿⠀ ⣿⡄⠀⢻⣄⠀⠀⠀⠈⠻⣿⣶⣍⡙⠳⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⣡⣴⣿⠟⠉⠉⠀⠀⠀⢠⡟⣸⣿⠂ ⠙⢿⣦⡀⣹⣶⣄⡀⠀⠀⠈⠙⠿⣿⣷⣶⣬⣝⣛⣶⡤⣤⣤⣀⣀⣰⣄⣾⣷⣄⣀⣾⠀⠀⠀⠀⠀⣀⣀⣠⡤⠴⠞⠛⠋⢁⣠⣴⣾⣿⠟⠁⠀⠀⠀⠀⠀⣠⠟⢡⣿⡟⠀ ⠀⠀⠙⢿⣮⣟⠿⣟⠶⣤⣀⠀⠀⠈⠙⠻⢶⣬⣝⣛⠿⠿⢿⣶⣤⣬⣥⣄⣃⣉⣉⡀⠚⠻⠿⠿⠛⠛⣛⣛⣀⣤⣤⣶⣾⣿⣿⠟⠋⠁⠀⠀⠀⠀⢀⣤⡾⢏⣴⡿⠛⠀⠀ ⠀⠀⠀⠀⠈⠛⠷⣮⣗⣈⠙⠛⢦⣄⣀⠀⠀⢈⣍⣛⣿⡆⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢉⣽⠿⠿⠛⠉⠀⠀⠀⠀⠀⣀⣤⡾⢟⣫⣴⠿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣶⣦⣬⣉⣙⠳⠿⣭⣽⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣻⣥⣤⣄⣤⣤⣤⡶⠿⣛⣭⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣶⣶⣶⠶⠶⠞⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⣆⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣼⣿⡗⠀⠀⠀⠀ ⠀⠀⠀⣠⠟⠀⠘⠷⠶⠶⠶⠾⠉⢳⡄⠀⠀⠀⠀⠀⣧⣿⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⣤⣤⣤⣿⢿⣄⠀⠀⠀⠀ ⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠙⣷⡴⠶⣦ ⠀⠀⢱⡀⠀⠉⠉⠀⠀⠀⠀⠛⠃⠀⢠⡟⠂⠀⠀⢀⣀⣠⣤⠿⠞⠛⠋ ⣠⠾⠋⠙⣶⣤⣤⣤⣤⣤⣀⣠⣤⣾⣿⠴⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀ ⠛⠒⠛⠉⠉⠀⠀⠀⣴⠟⣣⡴⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⣶⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⢀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣟⣋⣼⣽⣾⣽⣦⡀⠀⠀⠀ ⢀⣼⣿⣷⣾⡽⡄⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣿⡿⢿⣟⣽⣾⣿⣿⣦⠀⠀ ⣸⣿⣿⣾⣿⣿⣮⣤⣤⣤⣤⡀⠀⠀⠻⣿⡯⠽⠿⠛⠛⠉⠉⢿⣿⣿⣿⣿⣷⡀ ⣿⣿⢻⣿⣿⣿⣛⡿⠿⠟⠛⠁⣀⣠⣤⣤⣶⣶⣶⣶⣷⣶⠀⠀⠻⣿⣿⣿⣿⣇ ⢻⣿⡆⢿⣿⣿⣿⣿⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⣠⣶⣿⣿⣿⣿⡟ ⠈⠛⠃⠈⢿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠋⠁⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠊⡇⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⡴⠋⠁⠀⠀⡇⠀⠘⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣺⡟⢠⣏⡀⠀⠀⠀⠀⡇⠀⢠⡇⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡭⠓⡪⡅⠮⠦⣌⠉⠒⠤⣀⠗⠀⡽⠁⠀⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⠎⢀⡼⠁⡼⣤⣀⠙⢕⢦⡀⠈⠙⠮⣄⠀⠀⢸⢧⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢯⠏⢠⠎⡀⣇⠇⣻⡭⢞⣧⣵⡝⢖⠶⡠⣬⢭⡿⣈⢵⣿⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⡎⢠⠃⢠⢹⡟⠘⠹⡷⣹⣾⠛⠛⣎⡽⠊⣉⡽⠏⠒⠂⠀⠘⠫⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠁⢳⡇⡌⠀⡆⣸⡤⠀⡎⣇⣳⠃⣠⢞⠼⣾⠉⢸⠁⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢳⡀⠀⠀⠀⠘⣴⡇⠀⡇⡿⣿⣦⣶⣯⠋⠀⢁⡅⠀⣽⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⠀⠣⡄⠀⠀⠀⠹⡇⠀⢣⢱⣿⡎⡏⠣⣀⣴⠋⠀⠀⢁⡆⣰⠀⠀⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠓⣌⣧⠀⠀⠀⠀⢻⠀⣾⢻⡋⢳⡈⠒⠮⢅⣁⠀⢀⠞⢹⠏⠀⠀⠀⠉⠁⠉⠢⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣅⠀⠀⠀⢸⡰⢽⡀⢀⢎⠏⠀⠀⠀⠀⠉⢁⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡗⢤⣀⠀⡇⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠈⢡⠀⠀⢸⠃⠀⢠⠃⣬⠀⠀⠀⢀⣀⠔⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣧⠀⠈⢹⠁⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠓⢦⣳⡀⠁⠀⠀⠎⠀⠃⠀⠀⠀⠘⣿⠇⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠇⠀⠀⠀⠀⠀⡸⠱⣿⡷⠷⠴⠶⢧⠿⡶⠶⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⣠⠖⡪⠿⢋⣭⢶⡄⠀⡜⡇⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⡟⠀⡸⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠒⠒⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢁⠞⠁⣴⣿⣅⠀⣟⡢⣅⠹⣄⠀⢠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⠇⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡞⢀⡾⠫⠒⠚⠷⡄⠈⠛⢗⣮⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡜⠀⠀⠀⢀⡼⠁⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⢸⢃⠂⠀⠀⠀⢈⠢⡀⠀⠙⠿⣦⡀⠀⠀⠀⠀⢀⣀⡀⠀⢀⠇⡰⠁⠀⠀⢠⡟⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⣇⠘⣄⠀⠀⠀⠀⢓⡝⢄⠀⠀⠙⢟⢷⡀⠠⠖⢒⣊⣈⣓⣾⡜⠃⠠⠤⢄⡞⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⢀⡠⠒⠈⠉⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡂⠈⢆⠀⠀⠀⠈⣁⢌⢆⠀⠀⠀⠳⡙⣏⠉⠉⠁⠀⣰⠃⠀⠀⠀⠀⡃⢇⠀⣀⠔⠁⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠘⡄⠀⠀⠀⠇⠈⢮⢆⠀⣄⠀⠱⡘⡆⠀⢀⣴⠇⡠⣀⠀⠀⠀⢱⠸⣝⢧⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠇⠀⠀⠀⢸⠀⠀⢫⡆⢣⠱⡀⢡⠹⡄⠙⠒⠊⠀⠀⢇⠀⢠⠀⢇⠷⢝⢧⡀⣀⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣰⠀⠀⠀⠈⡄⠀⠀⢟⠈⢆⠑⡌⡆⢻⠀⠀⠀⠀⠀⠀⣧⠈⣷⡈⢞⡌⢺⢻⢭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡟⠁⠀⡏⡀⠀⠀⠀⢇⠀⠀⠈⡆⠘⡄⠐⠸⠈⡇⠀⠀⠀⠀⢀⡇⢇⢸⣧⣾⣿⣧⣈⡆⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⢳⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⠀⢁⠀⡇⢠⠀⡇⡇⠀⠀⠀⠀⣸⢀⢾⣾⣿⣿⣿⣿⣿⠁⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠴⠊⠀⠀⠀⠀⠀⠈⢧⠀⠸⣰⠀⠀⠀⠀⡆⠀⠀⢸⠀⢠⠸⠀⡇⡇⠀⠀⠀⠀⢁⡎⢸⣿⣿⣿⣿⣿⢿⡀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⠵⠶⠂⠤⢤⡤⠤⠀⠀⠈⢣⠀⡏⡄⠀⠀⠀⢃⠀⠀⢸⠀⢸⡇⠀⡇⡇⠀⠀⡰⠃⡞⣼⣆⢟⡿⡿⢽⠟⠒⠓⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⣾⠋⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⢳⡇⠱⣀⠀⠀⠈⠢⢄⠆⠀⠘⠀⢰⢱⣡⡴⠋⠀⣨⡾⠟⢉⠸⠚⢸⡎⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡠⣄⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⡤⠂⠀⣧⡀⠀⡤⠒⠬⣫⡲⣬⡧⠀⢀⠎⡌⢹⣦⣔⣊⡝⠡⠔⠉⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⢸⠇⠀⢠⣧⠘⠑⠺⠧⡀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡤⠴⠚⢹⢣⢸⠀⠀⠀⠀⠙⢿⠛⢀⢸⣴⠁⡴⠋⠀⡸⠁⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⡈⠀⠀⠀⠀⠈⠒ ⠀⠸⡇⠀⣀⡤⠤⢤⣄⡀⠀⠀⠀⡿⠀⠀⠀⣸⣌⡠⣠⠶⠀⠀⠀⢸⡇⡗⠁⣿⠎⠀⠀⠀⡇⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀ ⠀⠀⢳⡞⠁⠀⠀⠀⠈⠈⢦⠀⡼⠁⢠⣴⡿⠛⠁⠀⠀⠀⠀⠸⣦⣹⣷⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠠⢚⣂⠀⠀⠀⠀⠀ ⠀⠀⢈⠀⣴⠂⠀⠀⠀⠀⣸⠋⠀⣴⢋⡞⠀⠀⠀⠀⠐⣂⠀⠀⠈⠳⣽⠇⢠⡷⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠈⠑⠤⡀⠀⠀ ⠀⠀⣸⠘⠁⠀⠀⠈⠉⠑⠳⣄⣸⠃⣼⠁⠀⠀⠀⠀⠀⠈⠣⡀⠀⠸⣎⠁⡸⢢⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒ ⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠉⠀⡄⠀⠀⠀⠀⠀⠀⢣⠀⠀⠉⡔⠁⡸⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡇⠀⠀⠀⠱⣀⠀⠀⠀⠀⢀⠎⠀⠀⢸⠤⠖⠁⠀⢀⡇⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠈⠀⠀⠀⠀⡰⠓⠤⣀⣀⣀⢤⠮⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⢀⡴⠥⢀⠀⣩⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣀⣀⣀⡀⢀⣤⢞⡄⠀⣀⣴⠋⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢉⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⠉⠉⠁⠉⠉⠀⠈⣧⠾⠋⠁⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡛⡛⠻⠷⢤⣤⠄⣀⣀⣀⣰⢇⡀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠤⢤⣈⠉⠉⠉⠉⠈⠙⠳⡦⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⡿⡜⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⠁⢣⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣧⠃⠀⢸⡄⠘⢦⣴⡖⠒⠒⠲⠶⢤⣀⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⢳⡀⠀⠀⠀⠀⠀⠀ ⢸⢹⠀⠀⣨⣷⢒⣺⣹⠉⠉⠒⠄⠀⠀⠈⢻⠀⢧⡀⠀⠀⠀⠀⢀⡤⣪⠗⠉⠀⢧⣧⠀⠀⠀⠀⠀⠀ ⣿⣼⠀⢘⣻⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠹⣆⣠⠤⠖⢋⡴⠃⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⣸⣽⠿⢇⣀⠀⠀⠀⢀⣀⠄⠀⠀⠀⠀⠀⢀⠀⢲⠘⠋⠀⠀⠀⡼⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⡟⠑⢧⠀⢨⣏⡿⠋⠁⠀⠀⣀⡠⠄⠀⣠⠏⢀⡟⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⢳⡀⠈⠃⢸⠛⢉⣉⠉⠙⠛⠧⢤⡔⣺⣿⠴⠊⠳⡄⠀⠀⡼⠁⠀⠀⠀⠀⠀⣠⢣⠏⠀⠀⠀⠀⠀⠀ ⠀⠹⣆⣰⠏⠀⡞⢉⣿⠆⠀⠀⠘⠿⢿⣿⡷⠶⢤⣸⡄⠀⠀⠀⠀⠀⠀⠀⡴⢃⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⡇⠀⠀⠀⡇⢘⣿⠀⠀⠀⠀⣰⠋⣽⣷⣄⠀⠀⢳⠀⠀⠀⠀⣀⡴⠊⠓⢋⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣄⠀⠀⠀⠙⣤⠟⠀⠀⠀⢠⠃⠀⢯⣛⢽⡇⠀⣈⣆⠀⠀⠈⠁⠀⠀⣰⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⡏⢠⢶⠾⠿⠶⠦⣄⡀⠀⠘⠦⠤⠤⠞⠉⠉⠀⠈⢻⠇⠀⠰⢤⣠⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⡼⡀⠣⡀⠀⠀⣀⡿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⣿⠓⠻⠒⣾⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠓⢄⠈⢲⠚⠉⠀⠀⠀⠀⣰⠏⠀⠀⠀⣀⠔⠟⠠⣶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⡺⠳⠦⠤⠄⠴⢾⠇⠀⣠⣖⣋⣁⣦⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢱⡣⡀⠀⢀⡴⣣⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⠯⠭⠭⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡶⣦⡶⣲⣶⣴⢶⣷⣂⠎⣻⡶⢶⣶⡶⡠⡠⡠⡒
⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣀⠀⠀⠀ ⠀⣿⣁⢈⠉⠉⣉⣉⡧⠀⠀⣼⠋⠁⠀⠘⠢⡾⠋⠉⠉⢳⠀ ⠐⠛⢻⣯⠀⢠⠋⠉⠀⠀⢸⣷⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇ ⠀⠀⢸⡿⠀⢸⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀ ⢴⣯⣉⣁⣀⡈⠒⠒⡀⠀⠀⠈⠻⣧⡀⠀⠀⠀⢀⡠⠊⠀⠀ ⠈⠉⠉⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠉⠢⡠⠒⠁⠀⠀⠀⠀ ⢰⣖⠒⡀⠀⢠⣴⠒⡂⢀⣀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠙⣦⠈⢄⡾⠃⡜⣴⠟⢉⢥⡈⢢⢶⣯⢀⠁⠀⢰⡯⠉⡇ ⠀⠀⠈⢿⡬⢁⠌⢠⡿⠁⠆⠈⡇⢸⣿⣇⢸⠀⠀⢸⡇⠀⡇ ⠀⠀⠀⢸⡯⢻⠀⢸⡇⠀⡀⢸⠇⢸⣿⠃⢈⠀⠀⣿⡀⠀⡇ ⠀⠀⠀⣾⠁⠘⠀⢸⣧⠀⠈⠁⢀⠎⣿⠀⢺⠀⣰⡿⠀⢠⠁ ⠀⠀⠀⠛⠒⠃⠀⠈⠛⠳⠶⠖⠋⠀⢿⣄⡀⠉⠁⠀⡠⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀
⠀⠀⠀⠀⣾⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠉⠻⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠟⠋⢻⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠇⠀⠀⠀⠻⣿⣧⣤⣄⣀⣤⣤⣾⡟⠉⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡄⠀⢀⣠⣴⠟⠋⠉⠀⠀⠈⠙⠻⠿⣷⣀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢐⣦⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣾⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⢾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⣰⣾⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡇⡀⠀⠀⣀⣿⣻⡗⠀⠰⣛⣍⠀⠀⠘⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡇⠀⢰⢧⡻⢎⠿⠆⠼⣏⠻⣣⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⢡⠀⢠⣶⠖⠃⠐⠂⠀⠈⠉⢉⠀⢀⡄⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡠⠒⠛⠻⣮⠈⣿⣦⡀⠰⡷⡇⠀⢀⣽⣂⣿⣇⣿⣇⠀⣀⡤⠤⢀⠀⠀ ⠀⠀⣞⠀⠀⠀⡀⣼⣿⣿⣿⠛⡳⠦⠖⠀⡘⣿⣿⠃⢻⣿⣿⠊⠁⠀⠀⠀⠈⢂ ⠀⢸⡟⢀⠀⢸⡇⣿⢿⣿⠟⠑⠑⢄⠀⠀⡾⠟⡏⠀⢸⠀⠃⠀⣰⡖⠀⠀⢀⢸ ⣰⠀⠃⢸⠆⢼⣷⠙⠀⡀⠀⠀⠀⠘⠓⠎⠆⠀⠈⢲⣤⡄⠀⢰⡿⢃⣴⣶⣼⡏ ⣿⠀⠀⠈⠀⠈⠀⠀⡾⣅⣀⡀⢀⠀⠀⢸⡄⣠⡾⠛⠉⣿⣦⡿⠇⠀⠉⠉⠁⠀ ⣿⣄⠀⠀⢀⡷⠀⠸⡇⠀⠈⠉⠉⠉⠀⠈⠀⠀⠀⠀⠀⣼⠙⠃⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣦⣼⡅⠀⠀⣷⣦⡀⠀⠀⢀⣠⣶⣶⣤⣀⣤⣾⠇⠀
⠀⠀⠀⠀⠀⠀⢠⠖⠒⠲⢤⣀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⣀⣠⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣃⣀⣀⣀⣀⣈⡷⠦⠐⠒⠚⠻⡝⢲⣶⠞⡏⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠃⢴⠃⢀⡴⠚⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡤⠷⠿⠀⠀⠀⡴⠚⠲⡄⢰⠋⠉⠳⣄⠀⠀⠀⠀⢹⠀⠀⢠⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢧⠀⠀⠀⠀⠀⣷⡀⢀⡇⠘⢧⣀⢀⡿⠀⠀⠀⠀⠈⡇⢀⡞⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢧⠀⠀⣴⡾⢿⠻⢿⡄⠀⠀⡿⠿⡷⠲⣤⡀⠀⠀⠻⠊⠀⢀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠏⠀⠀⠈⠀⠘⣧⠘⣧⡀⠀⠀⠀⢹⡀⣨⣿⠀⠀⠀⣦⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠙⠒⢲⠄⠀⠀⠈⠉⠉⢠⣀⠀⠀⠈⠉⠉⠁⠀⠀⣀⣼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠿⠴⣆⠀⠀⢀⣀⣨⣿⣧⣀⣀⣠⣤⣀⣀⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠫⣿⠁⠛⠋⠁⠀⠀⢀⡤⣿⣤⡉⠛⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡏⠀⠀⠀⠀⢀⣠⣿⣿⡿⡶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣉⠳⣄⠀⣀⠴⠋⠁⠸⣯⣁⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡽⠆⠀⠈⠚⠁⠀⠀⠀⠀⣻⠋⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠔⠃⠀⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡤⠞⠁⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠋⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡼⠁⠀⠀⠀⠀⡸⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⡴⠋⠉⢻⠇⠀⠀⠀⠀⠀⠙⢦⣀⣀⣀⡤⠆⠸⡄⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⣠⢧⣀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⣷⡤⠶⠒⠒⠲⢤⡀⠀⠀ ⠘⣇⠀⣭⢉⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠳⣄⠀⣄⠀⢀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠙⣆⠀ ⠀⠀⠉⠉⠉⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢸⠟⡿⠤⣾⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆ ⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇ ⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡞⢿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀ ⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠸⣇⠏⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠓⠦⢤⣤⣤⣤⡴⠛⠤⣴⣤⣤⠤⠶⠚⠉⠙⠒⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⡾⠋⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠙⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣾⠟⢠⡄⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⢠⡄⠻⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⠏⢀⣿⠁⢸⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡇⠈⣿⡀⠹⣿⡀⠀⠀⠀⠀⠀ ⠀⢸⣿⠀⠸⡏⠀⠀⢻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡟⠀⠀⢹⠇⠀⣿⡇⠀⠀⠀⠀⠀ ⠀⣾⣇⠀⠀⠁⠀⠀⢰⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡆⠀⠀⠈⠀⠀⣽⣷⠀⠀⠀⠀⠀ ⢠⣿⣿⣄⠀⠄⠀⠀⠒⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠒⠀⠀⠠⠀⣠⣿⣿⡄⠀⠀⠀⠀ ⠘⣻⣿⣿⣷⣶⣶⣶⠈⣶⡆⠉⢱⣶⡍⠀⣶⣶⣶⣦⡄⠀⠀⣷⣶⣶⣮⣝⠃⢶⣦⠀⠀⣾⣿⣿⣟⠁⠀⠀⠀⠀ ⠀⠈⠙⣿⡏⠉⠉⠁⠀⣿⡇⠀⢸⣿⡇⠀⣿⡏⠉⢹⣿⠀⠀⣿⡏⠉⢹⣿⠀⠘⣿⣇⢰⣿⠋⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣧⣀⣀⠀⠀⣿⡇⠀⢸⣿⡇⠀⣿⡇⠀⣸⣿⠀⠀⣿⡇⠀⣸⣿⠀⠀⢹⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡟⠛⠛⠀⠀⣿⡇⠀⢸⣿⡇⠀⣿⡿⢿⣿⡇⠀⠀⣿⡿⢿⣿⡏⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⣇⠀⢸⣿⠇⠀⣿⡇⠀⣿⣧⠀⠀⣿⡇⠀⣿⣧⠀⠀⠀⣿⣿⣴⣆⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠿⠇⠀⠀⠀⠀⠙⠿⣿⡿⠟⠀⠀⠿⠇⠀⠸⠿⠄⠀⠿⠇⠀⠸⠿⠄⠀⠀⠿⢿⣿⣿⣿⣿⡂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣯⣠⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⣰⣰⣿⣿⢿⣿⣿⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠾⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⠛⣫⣦⣟⠋⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠻⠿⣣⣾⣿⣿⣿⣦⣻⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣆⢀⣆⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢿⣿⠿⠛⠛⠙⢿⣿⠟⠀⢠⢰⣿⣿⢻⣿⣷⢠⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣤⣾⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣞⠿⣟⣜⡿⢟⣾⣷⡀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢇⣼⣿⣿⣿⣄⢿⣿⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠻⠿⠻⣿⣿⡿⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠙⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⡰⢂⢀⢄⠀⠚⠀⠀⢠⠚⢣⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⢈⣈⠓⠘⠄⠑⠦⡀⡰⠁⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠌⠁⣀⡠⠤⠈⠁⠘⠒⠀⠈⠓⠢⢤⣼⣀⡧⠤⡤⠄⢐⠖⠊⢱⠀ ⠀⠀⠀⠁⠹⠁⠀⢠⠂⣦⠒⠉⣉⡒⡄⠀⡞⠃⢀⡠⠊⢀⠴⠓⡆⠀⡸⠀ ⠀⢤⢀⠀⢠⠀⠀⡆⢠⣣⢺⡯⠞⠥⠜⣄⠨⢭⢁⡠⢖⠡⣴⢊⣴⡲⠃⠀ ⠀⠀⢁⠚⠀⠑⠚⢱⠊⣧⠞⠀⠪⠍⠁⠀⢀⠾⡁⢤⡀⠤⠘⣠⣧⠟⠀⠀ ⠀⠀⠁⠀⢀⡠⣃⠜⠀⢙⡟⣼⣧⠀⠀⠀⠋⢓⠀⡗⠧⠐⢊⢭⠛⠁⠀⠀ ⠀⡰⢒⡎⢛⠙⠢⢀⡔⢋⣹⢟⡾⠀⠀⠀⢲⢁⠔⠀⣀⠈⠁⠀⢙⡆⠀⠀ ⢠⢿⡏⠈⠈⠀⡰⠻⡚⠀⣟⣩⠇⠀⢀⠎⠁⠀⠤⠤⠤⣽⠉⠉⠁⠀⠀⠀ ⠀⠀⠀⠁⠒⠁⠃⠀⡤⣴⣯⠋⠀⢀⣣⠄⠐⠒⢂⠀⣠⠤⠗⠕⠒⣤⣄⠀ ⠀⠀⠀⠀⠈⡠⠂⠀⢈⡔⠁⣀⠴⢎⡽⠚⠒⠢⢜⣏⠀⠀⠀⢀⡾⠁⠀⠑ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠮⣤⣤⣄⣀⠀⠈⠙⠒⠾⠧⠖⠊⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠉⠳⣄⠙⠲⣌⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠈⠳⡀⠈⠙⢦⡀⠈⠁⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣺⣿⠿⣷⣦⡀⣄⠀⠀⠀⠀⢀⣤⣶⣿⣿⣷⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⢽⢿⣿⣷⡀⠀⢰⣿⠋⠁⠀⠈⠙⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠈⣧⠹⣿⡇⠀⣿⡇⠀⠀⠀⠀⢦⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢸⣿⠀⣿⡇⣸⣿⡄⠀⠀⠀⠀⠀⢣⠈⣿⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣹⣇⠀⠀⠀⠀⣸⡏⠀⣿⡇⣸⡿⠀⠀⠀⠀⠀⠀⣸⠀⢻⣿⠀⠀⢀⡖⣀⣤⣶⣶⡂⠀⠀⠀ ⠀⠀⣀⣀⣀⣄⡀⠀⠀⢸⣿⠉⠀⠀⠀⣴⣿⣤⢄⣿⡇⣿⡇⠀⠀⠀⠀⠀⣴⣿⣁⣼⣿⡀⢠⣿⣿⡿⠛⠙⢿⣷⣀⠀⠀ ⢀⣾⣿⣿⣿⣿⣿⣶⣄⠘⣿⡆⠀⠀⠀⢠⣾⢻⣾⣿⠁⢻⣷⠀⠀⠀⠀⠀⢉⡽⠙⣿⣿⡇⣿⡟⠛⠀⠀⢆⠀⢿⣿⡀⠀ ⣿⣿⠋⠀⠀⠲⢌⡛⢿⣧⡘⣿⣦⣄⣀⣿⣧⣾⣿⠃⠀⠹⣿⣗⡀⠀⢸⣶⡟⣠⣾⠏⢸⣿⡿⠀⠀⠀⠀⠘⣆⡈⣿⡇⠀ ⣿⡟⠀⠀⠀⠀⠹⣿⠄⢻⣿⡌⠛⠿⢿⣿⡿⠃⠀⠀⠀⠀⠈⠛⠿⣷⣾⣷⣾⠟⠁⠀⢸⡇⠁⠀⠀⠀⠀⢠⠏⡇⢻⡇⠀ ⢻⣷⠀⠀⠀⠀⠀⠹⡆⢸⣿⡷⠀⠀⠈⠋⢀⣠⣴⣶⣶⣤⡄⠀⠀⠀⠈⠉⠁⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⢠⡇⣿⡇⠀ ⣎⣿⣧⡀⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀⣠⣾⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠈⣿⣇⠀⠀⠀⠀⣀⣼⠃⣿⣷⠃ ⢿⣿⣟⡛⠂⠀⠀⠀⣿⠃⣿⡇⠀⢰⣿⣿⠋⠀⠀⠀⠀⠉⠉⠉⠉⠛⠉⠉⠛⢿⣿⣆⠀⠹⣿⣆⠀⠀⢀⣿⠏⢠⣿⠇⠀ ⠀⠻⣿⣦⣀⠀⠀⢀⣿⣴⣿⡇⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⣿⣿⡄⠀⢻⣿⣀⣠⣾⢃⣴⣿⠏⠀⠀ ⠀⠰⣿⣿⣧⣀⢀⣾⡿⠛⠟⢀⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⢸⣿⣿⡄⠸⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀ ⠀⠀⠈⠙⠿⢿⣿⣿⠁⢀⣤⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠀⠀⠈⠻⣿⣧⡀⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣷⣦⣄⠀⠘⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠙⠃⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⠛⢻⡇⠀⠀⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣴⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⣀⣤⡴⠂⠀⣠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠉⠻⣿⣿⣦⣀⣠⣤⣶⣾⣿⠿⠋⠁⢸⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⣄⠀⠀ ⠀⠀⠀⣴⣾⣿⣿⣶⡄ ⠀⠀⠀⣼⣿⣿⣿⣿⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⠀ ⠀⠀⣽⣿⣿⣿⣿⡿⠀ ⠀⠀⣽⣿⣿⣿⣿⡇⠀ ⠀⠀⣿⣿⣿⣿⣿⠁⠀ ⠀⠀⣼⣿⣿⣿⠇⠀⠀ ⢀⣤⣿⣿⣿⣿⣦⡀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⢿⣿⣿⣿⣿⣿⣿⡿⠀ ⠈⢿⣿⣿⣿⡟⠁⠀⠀ ⠀⣾⣿⣿⣿⡇⠀⠀⠀

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