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⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⢛⣝⢻⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣷⣙⢟⣱⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⠛⠙⢻⣿⣿⣇⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣷⣀⢀⣰⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣺⣿⣿⡿⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⣴⣶⢛⣝⢳⣶⡤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣳⣙⢟⣱⡋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠟⠋⠉⠛⢇⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣠⣀⡀⠀⠀⠀⣀⣠⣀⡀⠀⠀ ⠀⠀⣾⣿⠟⢿⣿⡆⠀⣾⣿⠟⢿⣿⡆⠀ ⠀⠈⣿⣷⣄⣴⣿⡏⠈⣿⣷⣄⣴⣿⡏⠀ ⠀⠀⠈⠛⠻⠛⠋⠀⠀⠈⠛⠻⠛⠋⠀⠀
⠀⠀⠀⠀⣀⣴⣶⣶⣷⣶⣶⣄⡀⠀⠀⠀ ⠀⠀⠀⣸⣿⣿⡟⠉⡌⠙⣿⣿⣿⡀⠀⠀ ⠀⠀⠀⠸⣿⣿⣆⠘⠛⢀⣾⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣿⣿⣾⣿⡿⠃⠀⠀⠀⠀
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⡉⠈⣹⣿⣿⣿⠇⠀⠀ ⠀⠀⠀⠘⢿⣿⣿⣦⣠⣾⣿⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⠿⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣤⣦⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⡿⡻⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣮⣫⣾⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⠿⡿⠿⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⣴⣶⢷⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⠁⠀⡄⠀⢹⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣷⠀⠘⠛⠀⢰⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⢷⣶⣴⣶⠿⠃⠀⠀⠀⠀
⠀⠀⣴⣶⢷⣶⡄⠀⠀⠀⣴⣶⢷⣶⡄⠀ ⠀⠐⣿⣅⢀⣽⡗⠀⠀⠐⣿⣅⢀⣽⡗⠀ ⠀⠀⣽⣿⢿⣿⡅⠀⠀⠀⣽⣿⢿⣿⡅⠀ ⠀⠐⣿⣅⢀⣽⡗⠀⠀⠐⣿⣅⢀⣽⡗⠀
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀ ⠀⠀⠀⣸⣿⣿⣿⢛⣝⢻⣿⣿⣿⡀⠀⠀ ⠀⠀⠀⢻⣿⣿⣷⣙⢟⣱⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⢿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣷⣴⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠁⣤⣦⡄⢹⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⠈⠿⡿⠏⢰⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣶⣴⣶⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣶⣴⣶⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣸⣿⢿⣿⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⠁⣤⣦⡄⢹⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⠈⠿⡿⠏⢰⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣶⣴⣶⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠛⠁⠀⠙⠻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣶⣶⣷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣷⣶⣦⣄⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀ ⠀⠀⢸⣿⣿⣿⡟⢉⣌⠙⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⡟⢉⣌⠙⣿⣿⣿⣿⠀⠀ ⠀⠀⢹⣿⣿⣿⣆⠙⠟⢁⣾⣿⣿⣿⠁⠀⠀⠀⢹⣿⣿⣿⣆⠙⠟⢁⣾⣿⣿⣿⠁⠀ ⠀⠀⠈⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠏⠀⠀ ⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣷⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⠋⠉⡌⠉⠻⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⡃⠒⣾⣿⡖⠂⣻⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣧⡀⠋⠉⠃⣠⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣶⣤⣠⣴⣾⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣏⡉⠉⡉⠉⣉⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡅⠺⡿⠂⣽⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣧⣤⣤⣤⣤⣤⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠿⠛⠛⠙⠛⠻⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣤⣦⡄⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⠀⠀⠀⠈⠿⡿⠏⠀⠀⠀⢰⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣤⣀⣀⢀⣀⣠⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣷⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠿⠻⠿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡏⢠⣶⣷⣦⠈⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠹⣿⣿⡿⠁⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣦⣤⣡⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣷⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣀⣄⣀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⢹⣿⣿⣿⣿⣿⠁⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣦⡀⠙⠛⠟⠛⠁⣠⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⣀⣀⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠟⠛⠛⠋⠉⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣷⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⡄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⢤⣤⣼⣿⣤⣤⠄⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢨⣿⣿⣯⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⠁⠀⠉⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀ ⠀⢀⣿⣿⣿⣿⣿⣿⠟⠛⠙⠛⢿⣿⣿⣿⣿⣿⣇⠀⠀⢀⣿⣿⣿⣿⣿⣿⠟⠛⠙⠛⢿⣿⣿⣿⣿⣿⣇⠀ ⠀⢸⣿⣿⣿⣿⣿⠁⢠⣶⣷⣦⠀⢹⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⠁⢠⣶⣷⣦⠀⢹⣿⣿⣿⣿⣿⠀ ⠀⢹⣿⣿⣿⣿⣷⠀⠹⣿⣿⡿⠁⢰⣿⣿⣿⣿⣿⠁⠀⢹⣿⣿⣿⣿⣷⠀⠹⣿⣿⡿⠁⢰⣿⣿⣿⣿⣿⠁ ⠀⠘⣿⣿⣿⣿⣿⣷⣄⣀⢁⣀⣴⣿⣿⣿⣿⣿⡟⠀⠀⠘⣿⣿⣿⣿⣿⣷⣄⣀⢁⣀⣴⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀ ⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠋⢀⣀⣄⣀⠈⠻⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⢹⣿⣿⣿⣿⣿⠁⢰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣦⡀⠙⠛⠟⠛⠁⣠⣾⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⣯⣶⣦⣤⣶⣮⡿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠙⢿⣿⣿⣿⠟⠁⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⣿⣦⡀⠀⠙⠟⠁⠀⣠⣾⣿⣿⣿⣿⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠟⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢫⣿⣷⣶⣶⣶⣶⣦⣴⣤⣤⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠅⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣻⣿⣿⣿⣿⣿⣿⣿⡿⣽⣗⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⡕⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣟⣿⣿⣿⣿⣿⣿⣿⡽⣟⣾⣕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢽⣻⣽⢾⣻⣿⣿⣿⣿⣿⡿⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣳⡿⣿⣿⣿⢿⣞⣿⡽⣷⢯⡆⢀⢀⢠⣀⢄⣔⣤⣢⣔⣤⣢⣔⣤⣄⢄⡠⡀⡀⢀⢷⣻⣯⣟⣿⢽⡿⣿⣿⣿⣯⣟⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣻⣽⢿⣿⣻⣯⢷⣯⢿⣽⣯⣟⣷⢯⡿⣞⣿⣽⢾⣻⣞⣷⣟⣾⣗⣿⣽⣻⣽⢾⣯⢿⣽⢾⣳⣟⣯⣿⣻⣿⣻⢾⡽⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢽⢾⣻⢳⢻⣾⣻⡽⠟⠝⢚⠻⣻⣿⣿⣯⡷⣟⣯⡿⣞⣷⣟⡾⣗⣿⣞⣯⣿⣿⠻⡋⡛⠻⢯⣟⣷⢯⢗⢿⢞⡿⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣖⡿⣾⢏⠁⠀⠑⠹⣿⣶⣝⣿⣿⣿⣯⡷⣿⢯⣷⢿⡽⣟⣷⣿⣿⠟⠀⠁⠻⣿⣶⣄⢙⢯⣿⢶⣄⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢖⡷⣯⣿⡿⡀⣦⡠⢀⢬⣿⣿⣿⣾⣿⣿⣿⣽⣯⢿⣽⢯⣿⣻⣿⣿⣿⣧⣀⠠⣨⣾⣿⣿⡆⢹⣿⣯⡷⣧⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣯⡿⣯⣿⣿⣆⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣯⡿⣽⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣅⣿⣿⡷⣟⣯⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣽⢾⣻⣽⣿⣿⣿⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣞⣷⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣾⣿⣿⣿⣻⣽⢾⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡫⡿⡽⡺⡹⢻⢹⠻⡻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣷⣿⣞⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡟⡻⡛⡏⡗⡟⡾⣻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢜⢘⢌⠆⡕⡱⠰⡑⡅⡣⡹⠽⣿⣿⣿⣿⡿⣷⣻⢿⣿⣿⣿⢯⣿⣽⣿⣿⣿⣿⡿⡫⡊⡪⡘⢔⢑⢌⠆⡕⡑⢕⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠰⡑⡌⢎⢢⠱⡑⡱⡨⡒⢜⢘⣺⢿⣟⣯⣿⣽⢾⣟⡷⣟⣾⣟⡷⣷⢯⣿⣻⣿⢸⢐⢅⢣⢊⠎⡜⡰⡑⢜⢌⠪⡢⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠕⡱⡘⡌⢆⢣⠱⡨⢢⢊⢎⢦⡷⣿⢽⡷⣷⣻⡯⣿⡽⣟⣷⢯⣿⡽⣟⣾⣻⢾⡮⡢⡣⡑⡌⡪⢢⠱⡘⢔⢅⠣⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠌⠢⠑⡑⠘⠈⠮⢺⢯⣿⣽⣯⣿⣽⢾⣻⡷⣟⣯⣿⣽⢾⣻⣯⢿⣾⣻⣟⡟⠮⠢⠑⠘⠔⠡⠃⠑⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠚⠙⠚⢟⠟⢟⠟⠿⢺⠻⢻⠫⠛⠙⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣶⣶⢿⢿⣿⢿⣿⡿⣾⣶⣤⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢞⢫⢫⣑⣕⣥⡧⣦⢧⣦⢮⣆⣇⣍⢏⢳⠥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣢⣿⣞⣿⣿⣻⣿⣻⣿⢿⡿⣿⢿⣟⣯⣿⣿⡷⣷⣮⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣾⣿⣯⣿⢿⣾⣿⣻⣽⣿⢿⣿⢿⣿⢿⣟⣯⣷⣿⣿⣻⣿⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⡿⣟⣿⣿⣾⡿⣟⣿⣿⣿⣿⣿⢿⡿⣿⣻⣯⣿⣿⣽⡿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣯⣷⣿⢿⣿⢿⣷⣿⣿⢟⠏⢁⠑⠉⠻⣿⣿⡿⣿⣻⣽⣾⣿⣻⣿⣯⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣽⣿⣿⣿⣿⣻⣾⡏⠄⢴⣷⣿⣷⡀⢘⣿⣿⣿⣿⣿⣯⣿⣟⣿⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠛⠙⠝⠙⠚⠙⠛⣿⣇⠀⡻⣿⣿⡿⡁⢠⡿⡏⠋⢋⠋⠫⠋⠛⠹⣿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⣧⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡠⡈⡈⡠⣠⣷⠛⠀⠀⠀⠀⠀⠀⠀⡰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠝⢟⠟⢟⠋⠂⠀⠀⠀⠀⠀⠀⠀⢐⢾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢿⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣾⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣵⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⣨⡿⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠽⡾⣄⢄⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣐⣼⡞⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⡳⣷⣵⡴⣴⣴⣴⣬⢾⢾⠻⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠡⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣺⣷⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣔⣽⣿⣻⣯⣆⡠⡀⡀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣤⣤⣀⠀⠀⠀⠀⠈⣟⣷⣶⣔⣴⣼⢿⣾⢿⣽⣿⣯⣿⣿⣽⣿⣿⣾⣶⡴⣔⣮⣾⣗⠁⠀⠀⠀⠀⣀⢤⣢⣤⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣻⣽⣿⣳⣄⠀⠀⠀⠸⣿⣽⣿⣻⢾⡿⣿⢿⣻⣷⣿⢷⣿⣻⣾⣷⣿⢷⡿⡿⣿⣻⠢⠀⠀⠀⡠⣪⣾⣿⡿⣿⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣻⣾⣿⣟⣯⣿⣿⣕⠀⠀⣰⡽⡳⠑⢠⢁⢊⢙⠿⣿⢿⣾⣿⢿⣻⣯⡷⡏⢃⠅⡊⡈⠪⠂⠀⠀⢰⣽⣿⣿⣽⣿⢿⣿⣯⣿⣕⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣮⣿⣾⡿⣟⣷⣿⡿⣯⣷⣿⢄⢰⣳⢃⢂⢘⣾⣿⣷⡐⡈⡻⣿⣯⣿⣿⢿⣻⢑⠐⡰⣽⣿⣷⡡⢁⠀⠠⡵⣿⣿⡾⣿⣽⣿⢿⣾⡿⣯⡂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣽⣷⣿⣿⡿⣯⣿⣿⣟⣯⡇⣼⣯⡂⠄⡙⣿⣿⣿⢑⠠⣺⣿⣽⣷⣿⣿⢿⡐⠠⢙⢿⣿⣿⢑⢀⢆⢄⢿⣿⣷⣿⡿⣿⣽⣿⣟⣿⡿⡕⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢟⣯⣿⣽⣾⣿⣿⣻⣷⣿⢿⣿⣻⣯⣷⡥⡠⠑⡉⡂⡢⣪⣷⣿⣯⣷⣿⣟⣿⣷⣅⡂⠩⠑⡁⣢⣪⣿⣟⣿⡿⣾⣟⣿⣟⣯⣷⣿⣿⣻⠅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠩⣿⣟⣿⣯⣷⣿⣟⣿⣾⡟⣿⣻⣿⣽⣿⣽⣾⣖⣷⣿⣿⢿⣯⣿⣯⣷⣿⡿⣷⣿⣽⣷⣳⣽⣾⡿⣯⢿⠯⣿⣿⣻⣯⣿⣿⣻⣿⣾⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠩⢻⣯⣿⣯⢿⣻⡯⠗⠁⠀⣫⣿⣽⣾⣿⢷⣿⣟⣿⣾⣿⢿⣷⣿⣻⣷⣿⡿⣯⣷⣿⡿⣟⣿⣟⡏⠄⠀⠑⢟⣿⣻⣽⣾⣿⢷⠫⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⠫⠟⠌⠙⢬⣴⣤⣦⣼⠞⢟⣿⣾⣿⣿⠝⢿⣽⣾⣿⣿⠺⢻⣿⣷⣿⣿⠫⢷⣿⣿⣿⣿⠢⢢⣴⣴⣴⣽⠻⠻⠫⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠣⠀⠨⣻⣿⣿⠇⠀⠨⣻⣿⣿⠇⠂⠁⢿⣿⣿⢃⠁⠈⢿⣿⣿⠣⠀⠑⣻⣿⣿⠪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣻⠣⠀⠀⠀⠐⢟⠇⠀⠀⠀⠐⢟⠇⠀⠀⠀⠨⢻⠇⠀⠀⠀⠈⢿⠣⠀⠀⠀⠐⡻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⢄⣨⢠⡀⡀⡀⢀⠈⢀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⣿⣯⣷⡿⡂⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣲⣾⣿⣿⣧⣢⣤⣤⣤⣀⢄⣀⡀⢀⠀⠀⠀⠀⠀⡀⡤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢾⡷⣿⢾⡷⣟⣿⢦⣲⣶⡽⣟⣷⡿⣽⣿⣿⣻⣽⣾⣷⣿⣿⣿⣷⢿⣽⡿⣯⡿⣷⣟⣶⡶⣴⣵⢿⣟⣯⣷⣿⣽⣟⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣟⣿⣻⣟⣿⣟⣿⣻⡝⠊⠫⠛⡯⣿⣿⣻⣿⣯⣿⡷⣿⣿⣿⣿⣿⣿⣿⢿⠫⠋⠫⠚⠹⡻⣟⣾⣿⣻⣽⣷⢿⡾⣯⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡿⣽⣯⣿⣽⡷⣿⡽⡗⠁⢰⣤⣦⣈⢘⢽⣿⣿⣿⡿⣿⣿⣿⣿⢿⣻⡿⠍⠈⡠⣦⣦⣀⡀⠀⠹⣽⡾⣿⣽⣾⢿⣻⡿⣝⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⢼⣽⢿⡾⣷⢿⠝⠓⠉⠀⠀⠀⣹⣿⣿⣷⣇⢻⣿⣿⣿⣟⣷⡿⣾⣿⣿⠃⠁⠀⠀⢝⣿⣿⣿⣆⠀⠐⢻⣟⣷⡿⣟⣿⣻⣵⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣽⢿⣽⣿⣻⣟⣯⠀⢐⣼⣄⣄⣔⣾⣿⣿⣿⣿⣽⣿⣿⣿⣿⣯⣿⣿⣿⣿⣶⣄⣄⣔⣽⣿⣿⣿⣿⢆⠀⢺⣿⣿⣿⣻⣯⣿⣽⣾⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣽⣿⣽⣾⣯⣿⣿⣎⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡠⣷⣿⣿⣿⣽⡷⣟⣷⣿⣻⠔⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⣾⢷⡿⣾⢷⣟⣿⣿⣧⣂⢻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣑⣴⣿⣿⣿⣿⣿⡾⣟⣿⣻⣾⣻⠕⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠪⡿⣟⣿⣻⣟⣿⣻⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣯⣿⣟⣯⣿⣽⠯⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⡻⣯⣿⣽⣯⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣯⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡾⣷⣟⣯⡷⡫⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢟⣾⡷⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣿⣻⣾⣻⡿⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⣟⣿⢯⣟⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⢽⢾⡷⣿⢾⣯⡿⣟⣿⢿⣻⣟⣿⣷⣿⣿⣽⣿⣾⣟⣿⣟⣿⣿⣯⡿⣿⢿⡿⣿⣻⡿⣾⣟⣯⢿⠚⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣹⣟⣿⢷⡿⣟⣿⣻⣿⣽⢿⡾⣯⡿⣯⣿⣽⣟⣿⣯⣿⢾⣷⢿⣟⣿⣻⣯⣿⣻⣽⣯⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢻⣽⣿⣻⣟⣯⣿⡾⠝⠙⠝⠟⠟⠯⠗⢟⠽⠳⠻⠺⠋⠫⢻⣯⣿⣽⡷⣿⣽⣟⠞⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣄⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣽⣿⣿⣿⣿⣿⣶⣶⣴⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣴⣶⣽⣿⣷⣿⣿⣿⣗⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣻⡾⣿⣿⣿⣿⣿⣿⣿⣽⢮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣺⢷⣿⣿⣿⣿⣿⣿⣿⣟⣞⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣻⢿⣿⣿⣿⣿⣿⣳⢿⡽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣽⣟⣾⢿⣿⣿⣿⣿⣿⢽⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣟⣯⡿⣿⣿⣿⣳⣟⣯⡿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣻⣗⣿⢾⣻⡿⣿⣿⣿⢽⣻⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣯⣷⢿⣻⣯⡷⣿⢽⡷⣟⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡷⣿⢾⣻⣽⣻⣟⣿⣽⣻⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣳⣟⣯⡿⣞⣿⡽⣯⡿⣯⢷⡅⠀⠀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠀⠠⣳⣟⣯⡿⣯⢿⣺⣟⣾⣳⣿⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣽⣽⢾⣻⣯⢷⣟⣯⡿⣽⣟⣾⢼⣼⢾⣞⣷⣻⣞⣷⣻⢾⣮⡮⣞⣾⡽⣷⣻⣯⢿⣻⣞⣯⡷⣿⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢕⣿⣻⣽⣾⢿⢯⣷⣿⣿⣺⣽⢿⡽⣯⡷⣟⣷⣻⡾⣯⢿⣞⡿⣯⡷⣿⣯⣷⢿⢿⣽⡾⣯⣟⣗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣞⣯⣷⠋⠁⠢⣦⣕⢻⣿⣿⣽⣻⢷⣟⣯⣷⢿⡽⣯⡿⣽⣯⣷⣿⡿⠃⢕⢴⣡⠑⢻⣿⢾⣳⡁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣂⢄⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣵⢿⣽⣿⢁⡀⠀⠀⠨⣾⣷⣻⣿⣿⣽⣯⣯⡷⣟⣯⡿⣯⣟⣷⢿⣿⣿⡃⠁⠀⠨⣿⣷⡀⣻⣿⣟⣾⢦⡀⠀⠀⠀⠀⠀⣌⡾⣞⣿⠳⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢮⡿⣽⣟⣿⣯⡄⣿⣶⣬⣾⣿⣿⣿⣿⣿⣷⣟⣾⣻⣯⡷⣿⢷⣻⣽⣿⣿⣿⣿⣦⣦⣿⣿⣿⡅⣼⣿⡿⣞⣿⢽⢄⠀⠀⢠⢕⣯⡿⣯⠓⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣯⣿⣽⢾⣿⣿⢷⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣺⢷⣻⣯⢿⣽⡾⣿⣿⣿⣿⣿⣿⣿⡿⡓⣕⣿⡿⣟⣯⣟⣿⣳⡀⣔⡽⣯⡷⣟⠑⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣻⣞⢗⢍⢇⠕⢜⢘⢌⢆⠫⡛⣿⣿⣿⣿⣿⢷⣻⣞⣯⣿⣻⣾⣻⢷⣻⡿⣿⣿⣿⣿⢟⢝⢱⠨⡢⡱⢸⢘⠕⡝⡾⣷⣳⢯⣿⢽⢏⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢣⠱⡨⠢⣃⢣⠱⡨⡂⢇⠕⡜⡽⣿⡿⣯⢿⡯⣿⣿⣿⣿⣿⣿⣻⣽⢯⡿⣿⢿⡣⡱⡨⠢⡣⡑⢜⢰⠡⡣⠱⡘⣕⠃⠙⢞⣏⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢖⡑⡅⢇⢆⢣⠱⡘⡌⢆⢣⢪⢾⡯⣿⡽⣯⡿⣯⢿⣽⢯⡿⣞⣿⢾⣻⢿⡽⣟⣎⢆⢪⠱⡨⢪⢘⢔⠱⡘⢜⢸⠐⠀⠀⣢⡷⣗⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢚⢮⣖⣕⣌⣎⡬⣪⡮⣾⢽⣯⢿⢷⣟⣯⡿⣽⣟⣾⣟⣟⣯⡿⣽⣻⣽⣟⣯⣟⣷⢵⣵⣸⣰⣱⣨⣪⡮⡞⠑⠀⢀⢜⣾⣻⡯⡯⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠈⡚⡗⣿⣺⢿⡽⣯⣟⣯⣿⣻⣯⡿⣞⣿⣽⢾⣗⣯⣟⣷⣟⣯⡿⣞⣷⣿⢷⣻⣟⡾⣗⣿⣺⡗⡟⠌⡀⡀⢀⢮⡿⣽⡾⡝⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣆⣧⢷⢷⣻⣗⣮⣗⣟⢯⣟⣿⣺⣯⣟⡿⡽⡟⡟⡗⡏⢏⡛⡺⢹⠪⡳⡻⡻⣻⢿⡽⣿⣽⢾⣻⢯⢷⣳⣗⣾⣻⢾⣞⣾⣽⣻⡽⡊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣔⣷⢯⣟⣿⣻⣽⢾⣻⣞⣯⣷⣲⢷⣻⢞⢳⢩⠱⡡⡃⡪⡨⠢⡪⡘⠔⡅⡣⡑⠜⡌⡪⡙⡗⣟⣯⡷⣵⣯⢷⡿⣞⣯⣿⡽⣾⣳⡿⣵⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣟⣾⣻⣽⢾⣻⣾⣻⣯⣯⡷⣟⣾⣟⢝⠌⡆⠥⡱⡐⠕⡌⠜⡌⡢⡊⡪⡂⢎⢌⠪⢢⢑⠬⡘⡌⢷⣟⣿⣺⡿⣽⣟⡷⣯⢿⡽⣷⣟⣯⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢵⢿⡽⣿⢽⣾⣳⣟⣾⣻⣯⢷⣻⢔⡱⡘⡌⢆⠪⡊⡌⢎⠢⡑⡌⢆⠪⡢⢡⠣⡱⡐⢕⢌⢜⢼⣳⣯⡷⣟⣿⣺⢿⡽⣟⣯⡷⣟⠎⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠙⠹⠫⠗⣯⡷⣟⣷⣻⣻⣽⣟⣾⣳⣳⣵⣕⢌⡊⢆⠣⡑⡌⢆⠣⡊⢆⢕⣼⡼⣞⣷⣻⣯⢿⣞⡿⣯⡷⣟⠯⠻⠫⠓⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢳⣟⣯⣷⢿⣽⢾⣽⢾⡯⣿⢾⣞⣧⢮⣢⣣⣱⡸⣨⡪⣜⣼⢽⣳⡿⣯⡷⣿⢾⣻⣽⢯⣷⢿⡯⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠒⣶⢶⣶⣶⣶⣦⣤⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣾⢎⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢙⢿⡿⣿⣿⣿⣿⣿⣿⣿⡯⣗⠄⠀⠀⠀⠀⢀⣀⣀⢤⡤⣤⣤⣤⣤⣤⢤⣀⢄⡀⠀⠀⠀⠀⠀⢰⢷⢿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢿⢿⣿⣿⣿⣿⡿⣷⣟⣷⣅⣄⣖⣮⣟⣷⣻⢾⣻⣽⣟⣾⣳⣷⣻⢿⡽⣯⡿⣽⢷⡵⣤⣠⣫⡿⣯⢿⣻⣿⣿⣿⣿⢿⢝⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣻⣽⣿⣿⣟⣿⣳⢿⣺⣗⣯⡿⣾⣽⢾⣯⢿⣻⣞⣷⣯⡷⣯⡿⣽⣻⣽⢯⣟⣯⣿⣳⣟⣾⣻⣽⣟⡿⣿⣿⡿⣯⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣞⡷⣿⡽⣾⢯⣿⣯⠿⠫⢛⠹⡻⣿⣯⣿⣽⣽⡾⣾⣻⣽⣻⣽⣟⣾⣿⠿⡛⡙⠝⡻⣽⣷⣟⣾⣻⣽⢯⣟⢇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢝⢷⣟⣯⣿⡟⠕⠁⠀⠻⣿⣾⣮⡻⣿⣿⡾⣯⣟⡷⣯⡿⣾⣿⡿⠉⠈⠺⣿⣷⣦⡈⡫⣿⣷⣻⣽⠯⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣿⡽⣿⡿⠐⣤⡀⡀⣔⣿⣿⣿⣿⣽⣿⣿⣟⣾⣻⣽⣿⣿⣿⣦⡠⢀⢬⣿⣿⣿⣿⡄⢹⣿⣽⣾⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢾⢷⡿⣿⣿⢈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣻⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣸⣿⣿⣞⣷⡃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠅⠌⣿⢽⣟⣿⣿⣧⢽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣽⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣸⣾⣿⡷⣟⣾⢕⠠⢂⠐⡀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠂⡂⠌⠌⡨⢈⢺⢯⡿⣽⣿⣿⣿⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣳⣟⡷⣯⢿⣻⣿⣿⣿⣿⣿⣿⣟⣯⣷⣿⣿⡿⣽⢿⡽⡨⢐⠠⢁⢂⠂⠔⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠨⢈⠂⡂⠅⠌⡐⢐⠨⠹⣯⢿⣞⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣾⣿⣾⣿⣿⣻⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⢿⡯⣟⠊⠄⡂⠌⡐⡀⡊⠨⢀⢂⠀⠀⠀⠀ ⠀⠀⠀⠀⠨⢈⢐⢈⢐⠨⠐⡈⠄⠌⠌⠪⣻⡽⣾⣻⣽⣯⢿⣻⢿⡽⣷⣟⡿⣿⣿⣿⣿⣿⣿⡿⣽⣟⣾⣻⣻⣟⣿⡽⣷⣟⡿⡯⡛⠔⡁⠅⢂⠡⢐⠠⠂⠅⡂⡂⠐⠀⠀⠀ ⠀⠀⠀⠀⠈⢐⠠⠂⡂⠂⠅⡂⠡⢁⢊⠐⠄⠝⢽⡻⣾⢾⣻⣯⢿⣯⢷⡿⣽⡯⣿⡽⣯⣟⣷⣟⣿⣺⣽⣽⢷⣻⣞⣯⡷⡟⡝⠅⢊⠐⡐⠨⠐⡈⠄⡂⠅⠡⠐⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢁⠂⠅⡁⡂⠅⡂⢂⠌⠌⠨⢐⠨⠙⢝⢟⡾⣻⣾⡿⣽⣯⣟⣷⣟⣯⡷⣟⣾⢷⣻⣷⣻⢯⢿⠝⠕⠍⡂⢂⠌⡐⠨⢀⠅⡁⡂⠅⠄⠅⠁⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠡⠐⡐⠠⠡⢁⠢⠈⢌⠐⡐⠨⢑⠑⡛⠫⡳⠿⡳⠿⡻⡻⢟⢟⢛⠫⠣⠩⠡⠡⠨⢈⠂⡂⡁⡂⠂⠅⡂⠂⠂⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠠⠈⠌⠐⠈⠄⠅⡂⢂⠌⡐⠄⠅⠂⠅⡂⢂⠡⢐⠐⡈⠌⠨⢐⠁⠅⠂⠡⠐⠀⠂⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣽⣯⢷⡢⠀⠀⢀⢪⠨⣪⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢑⢅⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣀⠀⠀⠀⠀⠘⠕⠟⠍⠀⠀⢀⡊⡢⣣⣿⣟⣿⣿⢾⣿⡾⣿⣾⢿⣾⢏⠇⢕⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣽⣯⢷⡢⠀⠀⠀⠀⠀⠀⠀⠀⠠⡑⢌⢮⣾⣿⣽⣿⣾⣿⣟⣿⣿⣽⣿⠳⡑⡑⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠕⠟⠍⠀⠀⠀⠀⠀⠀⠀⠀⠠⡱⡘⡼⣽⣾⣿⣽⣾⣿⣾⢿⣻⣾⣟⢎⢕⢑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣟⣾⣲⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⡱⡐⣕⣿⡿⣯⣷⣿⣟⣷⣿⣿⣿⡻⡪⢢⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⢽⡾⣳⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡷⣯⢶⡀⠀⠀⠀⠀⠠⡱⡐⣕⣿⣽⣿⡿⣿⣽⣿⣻⣷⣿⢞⠕⢅⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣻⢿⢽⠂⠀⠀⠀⢠⠱⡨⣪⣾⣿⣯⣷⣿⣿⣯⣿⢿⣽⣾⣵⣵⡵⣤⣢⣴⣔⣴⢔⡄⡢⠠⠀⠀⠀⠀⠀⠀⠀⢠⡰⣤⡠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠨⡐⢕⢜⣾⡿⣷⣿⣻⣽⣾⣿⣽⣿⢿⣻⣽⣾⣿⡿⣿⡯⣟⢇⠣⠁⠂⠀⠀⠀⠀⠀⠀⠀⠈⡮⣟⣷⣻⡂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡱⢘⢬⣿⣟⣿⣿⣽⡿⣟⣯⣿⣽⡿⣿⡿⣿⣻⣷⢿⠏⠇⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠫⠻⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠁⠁⠁⠅⠁⠁⠉⠉⠈⠊⣺⢿⡿⣿⢿⡻⡙⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣾⣿⢿⠫⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣸⣽⢿⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣹⠽⡘⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢲⣺⢾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢂⡦⡟⠜⢌⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡫⣿⣻⢞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠢⠪⠗⠟⡑⠩⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣰⣲⣮⣿⡿⣿⣿⢷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣠⣤⡤⣤⣤⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣟⣿⣟⣿⣽⣿⢿⣽⣿⣿⣽⣿⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣾⡽⣯⣷⣟⣾⣻⣽⣾⣻⢷⣯⢿⣽⢶⣤⣀⠀⠀⣠⣾⣾⣿⣻⣯⣿⣟⣯⣿⣿⢿⣷⡿⣷⣿⢿⣽⣿⢦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⡾⣯⠿⠝⡙⢫⠻⣿⣷⣟⣷⣻⣾⣻⣾⣻⣽⣻⣞⣷⣷⣵⢾⣿⢾⣟⣿⣽⣿⣻⣿⣯⣿⡿⣯⣿⣿⣻⣿⢿⣽⣿⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣳⡿⣽⠏⠂⠀⠉⢝⣷⡮⣿⣿⣯⣷⣯⡷⣯⡷⣿⣽⣿⣯⣷⣿⡿⣿⢿⣿⣻⣯⣿⣯⣷⣿⣷⣿⣿⢿⣽⣿⣻⣿⣟⣿⣟⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣞⣷⢿⡿⡈⣦⡀⡀⣤⣿⣿⣿⣿⣿⣿⣺⣯⢿⣽⢷⣻⡷⣟⣯⣿⡿⣿⣿⣻⣿⣯⣿⣽⡿⣷⡿⣷⣿⡿⣿⣽⣿⣽⡿⣯⣿⡊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣯⢿⢾⣻⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣯⡷⣟⣯⡿⣽⡯⣟⣯⣿⣳⣿⣿⣽⡿⣷⣿⣯⣿⢿⣟⣿⡿⣷⣿⣿⣯⣿⣷⣿⣿⡯⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡽⣟⣿⡽⣯⣿⣦⡯⡿⡿⡻⢿⣿⣿⣟⣷⣟⣿⣳⡿⣯⣟⣯⣷⣯⢿⣽⣯⣿⢿⣟⣷⣿⣻⣿⢿⣻⣿⢿⣽⣾⡿⣷⡿⣷⡿⠍⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣟⣯⣷⣟⡿⣞⡿⡝⠨⡐⠨⡐⠌⡷⣟⣾⣗⣯⣷⣟⣷⣟⣷⣻⣾⣻⣽⣯⣿⡿⣿⣻⣟⣿⣽⣿⡿⣿⢿⣟⣿⣟⣿⣿⣻⡩⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢞⣿⣺⣷⣿⣻⡽⢔⠡⡈⡂⡢⡑⣼⣟⣷⣯⡷⣟⣾⣗⡿⣞⣷⣟⣾⣻⣾⣿⣻⣿⢿⣻⣿⣻⣽⣿⢿⣿⢿⣻⣿⣽⣟⣿⡳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣾⣻⢾⣻⠏⡟⢾⢺⢺⢺⢶⢿⣟⣿⣳⡷⣟⣯⡷⣿⢽⣟⢷⡫⠷⡻⣗⡿⣯⡿⣟⣿⣻⣟⣿⣻⣿⣻⣟⡏⠫⠚⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣺⣯⢿⣳⢕⠨⢐⢐⢐⢡⣺⢯⡟⡚⠜⡘⠍⠯⡿⣽⡯⡇⡃⠔⡁⡊⠌⡿⣽⢯⣿⡽⣾⣻⣞⣿⣺⣽⣞⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢯⢿⣻⣽⢾⣔⡦⣧⣗⣯⡿⡨⠂⢅⠂⢅⠅⢯⢿⡽⡔⢄⢑⢐⠨⡐⣽⢽⣯⡷⣟⣯⡷⣟⣷⡻⠕⢂⡠⣤⣢⣔⣤⡢⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣞⣿⣽⢾⣻⣽⢯⣷⣟⡷⣿⣕⣅⡢⣣⣷⣻⣻⣯⢿⣻⡮⣦⢦⢧⣟⣾⣻⣗⣿⣻⣽⣻⡽⡃⠑⡼⣽⢯⡿⣾⣽⢾⣻⣽⣗⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢿⣺⣽⢿⣽⢾⣟⡷⣯⢿⣳⣿⣺⣯⢿⣞⣯⡷⣟⣯⣷⢿⡯⣿⢯⡿⣞⣿⣺⣽⢷⣻⣽⣻⠂⠀⠩⢻⣽⣟⣷⣻⣯⢿⣞⠇⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣦⢶⣺⣞⡿⣯⢿⣻⣽⣗⣶⢶⡤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⢊⠄⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣞⣯⣷⣟⣯⣿⣻⢾⣻⣽⢿⣽⢾⣽⢾⣻⣽⣟⣾⣻⢶⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⠢⡑⠄⡅⠕ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣽⢾⠻⢋⠛⡝⢿⣿⣾⣯⣿⣻⢾⣻⣽⣯⣟⣿⣽⢾⣽⢾⣯⢿⣽⣟⣮⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡸⡐⡡⢂⠕⡐⠅ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣞⡏⠁⠀⠈⢫⣿⣾⣺⣻⣿⣾⣯⢿⣻⡾⣾⣽⢾⣾⣻⣽⣟⣾⣟⣷⣻⣞⣯⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣕⢕⢕⡐⠅⢌⠢⣑ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡯⣿⣟⠄⣵⡀⡀⣔⣽⣿⣿⣿⣿⣿⣯⣿⡽⣯⡷⣟⡿⣞⣿⣺⣽⢾⣳⣯⡷⣟⣷⣟⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣞⢼⢸⢱⢱⢍⢦⢣⢣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡿⣽⣷⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣯⢿⡽⣿⢽⣯⡷⣿⢽⣻⣽⣾⣻⣯⢷⣯⡯⡇⠀⠀⠀⠀⠀⠀⢀⢠⡫⣞⣝⣎⢇⢇⢧⢣⡳⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣟⣯⡿⣿⣷⣽⣻⣿⣿⣿⣿⣿⣿⣿⣽⢾⡯⣟⣯⡿⣯⡷⣟⣟⣿⡽⣷⣻⡾⣽⣻⡾⣯⣃⠀⠀⠀⠀⠀⣔⣵⣷⣻⢺⣪⢮⢯⡺⣕⣗⢽⡺ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣽⣻⣽⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢾⣻⣽⢿⡽⣯⡷⣿⣻⣽⢷⣻⣯⢷⣟⣯⣷⣟⣿⣺⡧⣗⣄⠄⣸⣞⣷⣻⡾⣝⡮⣳⢽⡺⣕⢷⢝⠌ ⠀⠀⠀⠀⠀⠀⠀⢀⡦⣟⣷⢯⣷⣟⡷⣯⡷⣿⢽⣟⣿⣻⣯⡷⣟⣾⣟⣯⢿⣽⣻⣽⢯⣿⢽⣾⣻⣽⡾⣿⢽⣷⣻⡾⣽⣾⣻⣯⡷⣷⣻⣞⣯⡷⣟⣯⣯⣗⣯⣞⣗⣟⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⣗⡿⣯⢿⣽⣗⣯⣿⡽⣯⣟⣯⡿⣞⣷⡯⣟⣯⣷⢿⣽⣿⣽⣿⢾⣻⣽⣯⡷⣟⣷⣟⣯⡿⣞⣷⣟⣿⣺⢷⡯⣿⣽⢾⣯⢷⣿⣻⣽⢾⣽⡾⣾⡽⣗⠅⠀ ⠀⠀⠀⠀⠀⠀⠀⢫⢿⡯⣿⣳⣯⡷⣷⣟⡿⣞⡿⣿⢿⣷⣿⣿⡿⣟⣿⢿⡽⣷⣻⣻⣽⢷⢷⣟⣯⡷⡯⡷⣿⣻⣗⡿⣞⣯⡿⣯⡷⣟⡿⣞⣿⣞⡿⣞⣿⣳⣟⣯⢟⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠽⡯⣷⢯⣿⣳⡿⣽⡑⢌⠝⢝⢗⢿⡺⣟⣯⢿⣽⣻⣽⣽⣻⢾⡻⠯⠯⡓⢍⢊⢮⡿⣾⢽⣻⣯⢿⡽⣷⣟⣿⡽⣟⣷⢯⡿⣯⢿⣞⣿⣺⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠁⠫⡿⣽⣮⢢⢡⢑⢄⢕⠨⡂⢍⢃⠣⡃⡃⡣⢡⢑⢌⢪⠨⡂⢕⢬⡯⣿⣽⠻⢽⢾⣻⣻⢷⣻⣞⡿⣯⢿⡽⣿⢽⣯⡷⣿⢽⠑⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⢷⣻⣽⢷⣯⢷⡷⣗⣮⢆⡢⢑⢐⢌⣦⣗⡷⣯⡷⣿⡽⣯⢿⣽⡳⡁⠁⠈⢟⣽⣯⢿⡯⣯⣿⡽⣿⢽⣻⣽⢷⣻⢯⠃⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢽⡿⣽⡾⣟⣾⣟⣿⢽⣯⢿⣪⡢⣱⢽⣾⣳⡿⣯⣟⣷⣟⡿⣯⡷⣟⠆⠀⠀⠀⠁⠫⣻⡽⣟⣾⢯⣟⣿⡽⣯⠻⠉⠐⠀⠀⠀⠀⠀
Pokémon dot art uses braille Unicode characters to build detailed pixel-style Pokémon — from Pikachu to pokéballs. These multi-line pieces capture the 8-bit pixel art feel of the original games.
💡 Platform tip: Pokémon dot art is hugely popular in gaming and fan communities. The braille pixel pieces evoke the original Game Boy / pixel-art style and look best in Discord code blocks.