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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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⠀⠀⠀⠀⠀⠀⡸⠗⠎⠁⠉⠀⠀⠈⢡⠀⠀⠀⠀⠀⠀⠆⣱⣀⠀⠀⠀⠀⠀ ⠀⣠⠃⠀⠀⡰⢰⡜⠀⠀⠀⠀⠸⡄⢸⠀⠀⠀⠀⠀⠀⠋⠈⡀⠁⠀⠀⠀⠀ ⠀⢧⠀⠀⡐⠁⣞⡠⢄⣒⠆⢀⢣⠀⢨⠀⠀⠀⠀⠰⡸⠀⠀⡇⠀⡇⠀⠀⠀ ⠀⢀⢂⠎⣠⣾⣿⣿⡛⠻⣷⡊⡌⡠⢼⡆⠀⠀⡠⢎⣴⣮⣶⡁⡰⡇⠀⠀⠀ ⠀⠀⡅⣨⣿⣿⢿⣿⠿⠉⠙⠒⠉⠀⠘⠀⠀⢰⡡⣺⣿⣷⠤⣿⢰⠑⠀⠀⠀ ⠀⠀⢩⠉⢿⢿⠛⢉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡯⢻⡆⢀⠇⡎⠀⠀⠀⠀ ⠀⠀⠀⢃⠀⠙⠢⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠜⡁⠈⠀⡇⠀⠀⠀⠀ ⠠⠠⠤⠬⠢⠄⠀⠀⠠⠤⠤⠤⢤⠤⠤⠤⢤⣤⣄⡤⠤⠤⢤⣤⣥⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⠿⠿⢿⣿⣷⣴⠄⠀⠀⠀⠀⣠⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⣤⣾⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠂⠐⠒⢒⣀⢖⣿⣶⣿⠿ ⠀⠀⠀⠀⠀⠀⠶⡦⢤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⢟⣡⡴⢿⣿⣿⣿⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠉⠻⣿⠟⢿⣿⣿⣿⠭⠁⢸⣿⣿⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢌⣿⣹⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠤⠤⣭⡖⠛⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣤⣤⣤⣶⣤⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠟⠛⠛⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣶⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠋⠀⠀⢸⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠋⠉⠁ ⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣤⣄⣀⣀⣀⣀⣤⣶⣿⣿⣿⡀⠀⠀ ⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⠉⠀⠀⠉⠉⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠸⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⣿⣿⣿⡿⠛⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠞⠉⠀⠀⠀⠀⠉⠳⡶⠚⠛⠉⠉⠉⠉⠉⠉⠙⠛⠶⠤⣄⣀⡤⠴⠶⠶⠶⠶⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⢀⡠⠶⠒⠒⠲⢦⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⢀⣀⣀⣤⣤⣤⣀⡀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣠⠊⠀⠀⣀⡀⠀⠈⣇⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣭⡀⠀⠀⠀⠀⠀⠉⢣⡈⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢰⠃⠀⠀⠀⣹⠏⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣿⠛⠂⠀⠀⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⣠⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠘⣇⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣄⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⡤⠖⠒⠒⠒⠒⠺⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡟⠇⠀⠀⢀⣀⣀⣀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⣿⣩⣿⣿⡆⠀⠀⠀⢿⠄⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢠⣄⠈⢭⡉⠃⣤⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠸⣧⡀⣀⣤⣈⡛⢒⣾⣿⡁⠀⣀⡾⠁⠀⠀⠀⠀⣠⠾⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⠙⠶⢤⣀⣀⡀⣰⠞⣉⢭⡿⠛⠉⠁⠀⠀⠉⠻⣿⣫⣽⣿⡏⠀⢀⣀⡤⠖⠋⠁⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠈⠉⢹⡏⢻⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣼⠇⠀⠀⠀⣠⡀⠀⠀⣠⣶⡆⠀⠀⢻⣦⡤⢤⡄⠀⢠⡄⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣻⡟⢹⣿⣟⣛⣧⠀⠀⢨⣗⣀⡰⣛⣧⡾⠃⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⣧⠀⠀⠀⠀⢿⠀⣼⣿⣽⣷⠼⠗⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠙⢷⡀⠀⠀⠈⠓⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣴⣋⣉⣙⡓⢒⡞⢑⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⢧⣿⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⣀⣠⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⣀⡀⠀⠀⢀⢀⣀⣴⢿⣯⠉⠉⣉⣤⠼⠗⠒⠛⠒⠲⠤⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣿⠉⡿⠚⠿⠋⢉⡵⢶⣽⡇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⢦⣄⡀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⣼⣿⣿⡆⠀⠀⣾⠃⡼⣿⠃⠀⠀⠀⠀⠀⣠⣤⢤⣄⡀⠀⠀⢹⡆ ⠀⠀⠀⣀⡤⠴⠒⠒⠳⠤⢤⣀⠉⠛⠛⠒⠒⠒⠚⠛⠲⠤⢤⣀⣀⣀⣀⣴⣿⡾⠷⣿⠀⠙⢦⣀⣙⣿⡽⠃⠀⠀⠀⢀⡴⠋⠀⠀⠀⠈⢿⠀⠀⠈⡇ ⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⣁⣀⡀⢘⡇⠀⠀⠈⠉⠉⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⢸⡆⠀⢸⡇ ⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⣾⠁⢠⡇⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢀⡾⠀⢀⡾⠀ ⣿⠀⠀⢠⡞⠛⠉⠉⠉⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠻⢶⣻⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⡾⠁⠀ ⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠙⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡶⠖⠋⠁⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠿⣀⣀⣀⣀⡤⠞⠁⠀⣴⠏⠀⠀⠀ ⢻⣄⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⣀⡴⠚⠁⠀⠀⠀⠀ ⠀⠙⣦⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⣀⣀⣀⣠⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠳⢄⡀⠀⠉⠑⠶⠤⣄⣠⠤⠞⠁⠀⠀⠀⠀⣀⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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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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