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

about me

hello! again, my name is pyrus. i use he/him pronouns and am 20 something years old. i am a student studying english and philosophy and hope to become a high school english teacher once i graduate.

im a big fan of ocs!! this will be a landing page for all things about me, my art, my characters, and my interests. speaking of interests, some of my main ones are undertale, homestuck, and danganronpa. i am cringe but i am free.

i'm pretty chill when it comes to "dni criteria" and such like that. just dont be a weirdo i suppose? i am very pro-media, pro-piracy and pro- people do whatever they want. i'm also pro- closing the tab if i dont like it and encourage you to do the same!

fun facts

  • my classpect is a knight of mind
  • i am an infp, 4w5
  • i am a cat person !!
  • i am transmasc aroace (in the mlm flavor)
  • one might call me a fudanshi but the word fujoshi is more pleasing to my ears

favorite things

shows games books

hobbies

find me elsewhere

kin list

i'm very lowkey about kinning these guys are just similar to me in silly ways :3

kinassigned pokemon