Tie In Emojis & Text

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⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤ ⠘⣿⣿⣿⣷⣦⣄⣀⠀⢠⠔⠀⢀⡼⠿⠿⢆⠀⠀⠲⣄⠀⣀⣠⣴⣾⣿⣿⣿⠇ ⠀⠈⠉⠉⠛⠛⠻⠿⢿⣿⠀⢀⣾⣷⡀⢀⣾⣷⡀⠀⣿⡿⠿⠿⠛⠛⠉⠉⠁⠀ ⠀⠀⣤⣤⣶⣶⣶⣶⣶⣿⣆⠈⠉⠉⠉⠉⠉⠉⠉⢠⣿⣶⣶⣶⣶⣶⣤⣤⠀⠀ ⠀⠀⠘⣿⡿⠟⠛⠉⣡⣿⣿⣷⣤⠀⢠⣆⠀⣤⣶⣿⣿⣬⡉⠛⠻⠿⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⡿⢋⣿⣿⠛⢠⣿⣿⡄⠛⢿⣿⡘⢿⣿⣦⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠻⠏⠀⣸⣿⡇⢀⠻⣿⣿⠟⣀⠸⣿⣇⠀⠙⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡟⠁⣿⣿⠀⠻⣆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⠉⠙⠓⠀⠘⠏⠀⠘⠟⠉⡻⠋⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡶⠶⢴⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⠛⠓⠶⢶⣤⣄⣀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣄⡀⠀⠀⠀⠈⠉⠛⠟⠛⠉⠉⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢩⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠉⠻⣶⣦⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠃⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢊⣽⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⠯⠀⢰⠏⠀⠀⠀⠀⠀⠀⣠⡴⠿⠛⠋⢙⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠞⠁⠙⠻⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠁⠀⠈⢷⣭⡁⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡟⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣋⣤⣶⣶⣶⣤⡙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⢀⣠⣤⡶⠟⠃⠀⣠⣾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡟⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⣾⣿⡿⢻⣿⣿⣿⣿⣦⡈⠙⢿⠶⢶⣤⣀⣀⣀⣴⣿⣋⣴⣾⣿⣿⣿⡿⣍⠀⠀⣀⣠⠞⠋⠀⠀⠀⠀⠴⠋⠀⠀⠀ ⠀⠀⠀⢠⡿⠈⠀⠀⠀⡸⣆⠀⠀⠀⠀⠀⠀⣠⡾⠋⢠⣿⡿⠋⢀⣿⣿⣿⣿⣿⡻⣷⡀⠀⠀⠀⠀⠈⠉⠉⠉⣩⣿⣿⣿⣿⣿⣿⣷⡈⢿⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⡇⠀⠠⢾⣀⣃⣻⣦⣠⣤⣴⠀⠀⢿⡀⠀⢸⠏⠀⠀⢸⣿⣿⣿⣿⣿⣧⠙⢷⡀⠀⠀⠀⠀⠀⠀⣸⡿⢻⣿⣿⣿⣿⣿⠹⡇⠘⡇⢻⣧⣀⣀⡀⠀⠀⠀⠠⠴⠂⠀⠀ ⠀⠀⢀⣿⢰⣷⡾⠟⠻⣯⣭⣉⠉⢁⡟⠀⠀⢸⡇⠀⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢸⣿⣿⣿⣿⣿⠀⠃⠀⡇⢸⡏⠉⢙⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠇⠸⠈⠻⣆⠀⠀⢠⡟⠛⢾⠃⠀⠀⠈⣷⠀⠀⣄⠀⠀⠘⢿⣿⣿⣿⣿⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⢀⠀⠀⡇⠈⡇⢠⡾⠃⠀⠀⠀⠀⠤⠄⠀⠀ ⠀⢀⡿⠀⠀⠀⠀⠈⠳⣦⠘⠷⣄⡾⠀⠀⠀⠀⢹⣆⡀⠈⢷⣄⠀⠈⠛⠿⠟⣣⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡘⢿⡿⣿⡴⠋⠀⢸⡇⠀⣷⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⡇⠀⠀⠀⠀⠸⡏⠻⣦⣣⣈⠛⠓⠒⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠙⠛⠛⠋⠠⣜⢧⣼⠁⠀⣧⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀ ⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡇⠀⠀⠀⠀⢀⡇⢸⠈⣟⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢠⡇⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀ ⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⣼⠃⣼⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⣸⣯⡀⠹⠞⠁⠀⠀⠀⠀⠀⠀⢰⡶⠶⣶⡶⠶⢶⣶⣶⣶⣶⣶⠀⠀⠀⠀⢀⣤⣾⠋⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⢿⡏⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠸⣿⢻⢿⡷⠈⠁⢿⣿⣿⣿⠇⠀⠀⣀⣶⠟⠁⠹⣷⡀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣿⠀⠀⠀⠈⣛⠳⢦⣤⣀⡀⠀⠀⠹⣯⣛⡟⢀⣹⣀⣿⣿⣡⣤⡶⠟⠋⠀⠀⠀⠀⠘⢷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⡤⠶⠞⣿⠀⣸⡇⠉⠉⠛⠛⠒⠛⠛⠛⠛⣿⠛⠛⣉⣩⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡍⠉⠀⠀⣠⣽⠿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠾⠉⠀⠀⠀⠉⢷⣄⠀⠀⠀⠀⠀⠀⠈⠛⢷⡈⠹⠿⣶⣄⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⠶⠶⠶⠶⠶⠶⠶⠾⣷⡀⠑⠨⣟⣿⣶⣤⡀⠀⠘⣆⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣍⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣸⣷⡧⠤⠤⢀⢀⣿⠁⠀⠀⠙⣆⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠘⣿⠇⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⣰⠟⠘⠁⠀⠀⢠⣿⣷⠀⠀⠀⠀⠸⣦⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⢸⡟⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⢀⡾⠋⠀⠀⠀⠀⠀⣾⠀⢻⡇⠀⠀⡄⠀⠹⣧⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⠾⠛⠉⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⠟⠁⠀⠀⠀⠀⠀⠘⡿⠀⠘⣿⠀⠀⢻⡄⠀⠸⣧⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢹⡇⠀⠀⢳⡀⠀⠹⣇⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⡴ ⣴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣸⡟⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡄⠀⠈⢷⡄⠀⠹⣧⠀⠀⠀⠘⢧⡀⠀⢀⡞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡿⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⣶⡀⠀⠻⢛⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀ ⠀⠀⢠⣾⣿⣿⣿⣿⡦⣼⣯⣵⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⢹⣿⠀⠀⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣦⣀⢀⡘⣿⡇⠀⠀⠀ ⠀⣾⣿⣿⣿⣿⡟⠉⠀⠀⣾⣿⣿⣿⣿⠟⠁⠀⠉⠻⣿⣿⣿⣿⣧⣠⣶⠄ ⢰⣿⣿⣿⡿⠋⠀⠀⠀⢀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠙⠻⣿⣿⣿⡟⠁⠀ ⢸⣿⡿⠋⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠙⢻⡃⠀⠀ ⠀⠁⠀⠀⠀⠀⠀⠀⣾⣿⣿⠿⣿⡿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠙⢿⣿⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣶⣦⣼⣿⣿⣿⣿⣿⣿⡟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣠⣾⣿⣿⣿⣿⣿⣟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣿⡟⣹⡟⣴⢻⣷⠘⠿⣷⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⠐⢋⣴⣋⣯⣽⣷⣦⣤⠤⣾⣿⣿⣿⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⣿⣒⡻⠟⣿⣨⣿⠉⠉⠐⣲⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠙⠛⠻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣷⡤⣢⢹⠉⣣⣠⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣦⣤⣤⣬⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣿⢿⣡⡆⡤⣭⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠛⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣽⣿⣷⣅⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠛⠈⠙⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⠏⠙⠿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⢹⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡿⠃⠀⠀⠀⠈⠙⠋⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡆⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣄⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣧⠸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡆⠙⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⢤⣠⣶⡾⠋⠉⠙⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡷⢤⣤⠖⠛⠉⢙⣏⠻⢷⡦⢾⡉⠉⠑⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠩⡽⠋⡠⠔⠊⠉⠀⢸⣇⠈⠉⠓⠯⠓⠦⣽⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⢚⡟⠀⣠⣞⡵⢊⠄⠀⣠⠴⠒⠉⠉⠉⠉⠀⠒⠢⢄⡈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⡷⢋⣴⡡⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⢉⢝⣵⣷⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣯⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠺⢿⡷⢿⡟⣿⣿⠃⠀⠀⠀⠀⣀⣠⣤⣄⠀⠀⠀⢠⣤⠂⠀⠢⣄⡘⣟⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡟⠰⠻⢰⢹⡇⠀⢀⣤⡶⠿⠓⠚⠛⠋⠀⠀⠀⠀⠉⢉⡭⠭⡭⠉⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣷⣦⡾⠀⣾⣇⠰⠟⢡⣶⣦⣤⣴⣄⡄⠀⠀⠀⠀⠀⢻⣷⣿⣿⣷⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣏⠁⣡⣴⠏⢸⠀⣲⣾⢿⣻⣿⣿⡿⡆⠀⠀⠀⠀⡄⢠⡘⣟⠿⠿⠟⣇⣐⠎⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣀⣀⣀⣼⠿⠿⣿⣸⠀⣇⠈⠓⠘⢯⣉⠩⠏⠁⠀⠀⠀⠀⢧⠀⠈⠉⠀⠀⠀⢿⣧⣤⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠣⡉⠛⢷⠛⠟⠒⢤⣸⣿⡆⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀⢸⡟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠓⠤⣀⠈⠀⠀⣽⣿⡄⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠏⠀⠀⠀⠀⠀⣾⣹⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠑⠦⣴⣿⡿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢰⡏⠁⣆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⠟⠿⣿⣷⣿⣧⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⠉⠁⠀⠀⠀⠀⢠⣿⣧⢆⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣹⠃⢀⣼⡿⠁⣿⡈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣴⣿⣿⣏⢼⡿⣿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣏⣔⡽⣇⠀⠀⠽⢧⢸⣄⢿⣦⢤⣀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢯⡿⢻⣁⡀⣧⡙⡁⠈⠫⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⠋⠀⣿⠀⡶⢼⠘⡆⡿⢸⣿⡀⠈⠉⠙⠒⠒⢲⡶⠞⠁⠀⠈⣷⣿⣿⣷⣽⣷⡜⣦⡀⢱⣄⠑⠦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⡇⠀⢠⣏⠔⠛⠙⠓⠛⠛⢹⡇⠉⠒⠤⢄⡤⠞⠁⠀⠀⠀⣀⣾⠋⣷⣍⣿⣿⡻⠿⣟⢹⣦⣿⣷⡀⢌⠢⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⢀⡴⠋⢸⠀⣠⠚⢹⠁⠀⠀⠀⡠⠞⡽⠁⡰⠃⠈⠙⠛⠛⠂⠘⠚⠿⢿⡛⢿⢿⣆⠈⢷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⣠⣮⠞⣰⠛⡇⢣⣠⢾⠀⣀⠴⠋⢀⠞⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠁⠻⣆⠈⢇⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢠⣾⢿⣿⣾⠃⠀⣸⣤⠴⠞⠋⠁⢀⠔⢁⡄⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠙⣇⠈⠀⢇ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣴⠟⢁⢼⣏⣽⠔⠋⢸⠃⠀⣀⢴⡞⠁⡠⠋⡁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢀⠈⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⢸⠀⣠⡾⠛⡩⢣⠟⠁⣸⣠⠤⢼⠒⠉⣸⠋⢀⠜⢇⢀⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡔⢱⣡⡞⡠⠃⠠⠊⠀⠈⠀⠀⡤⠊⢁⠴⡏⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⢤⣤⣤⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣖⣋⠉⠉⢉⣉⢁⣠⠼⠶⠶⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠀⢀⠩⠉⣃⡴⠞⠋⠁⠀⠀⠀⠀⠀⠈⠑⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢁⠞⠛⠉⢛⠋⣽⠚⠉⢁⣀⣄⡀⠀⠀⠀⠀⠀⠀⠈⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡎⢹⣧⡏⠀⡴⢊⠏⢠⣿⣧⣀⠀⠀⠀⠈⠳⢦⣤⣀⣀⣀⡀⠀⣹⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡾⢸⡇⡈⠁⡏⠀⠈⢹⡏⠪⡙⠲⠤⡀⠀⠈⢻⣌⠉⢉⡽⡾⢉⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠗⣻⠀⠀⠰⢻⠀⢀⡾⠘⢀⣼⣷⣷⠦⡀⠀⢈⣇⡔⢁⡞⠁⣾⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣎⣡⠠⡟⠀⠀⡀⣸⣧⢟⣤⣶⣿⣿⣿⣿⠁⣿⡆⣼⠛⢦⡾⠀⣼⢃⣼⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢳⣾⣽⣾⣿⣗⡀⠀⠁⠃⠈⠟⠋⠀⡿⣿⣿⠦⡀⠱⣴⠃⢸⢛⣄⣳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠷⠞⠛⠉⣿⣿⣹⡟⢻⡄⠀⠀⠀⠀⠀⣰⣇⣭⣿⡄⠹⣦⣹⣤⣯⡞⠁⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣿⣏⠁⢈⣇⡀⠀⠀⠀⠉⠉⢀⣾⠇⡇⢸⣿⣿⣿⠟⠟⠻⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢸⣿⢹⢧⡀⠀⣡⠤⠶⠆⠀⣠⣾⢃⠜⠁⢀⣿⡟⢿⡄⠀⢳⡀⠣⡙⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠛⣻⠟⢁⣴⣽⠿⠋⠁⠉⠳⢄⣐⢃⣠⣴⠵⠛⢁⣠⣶⣿⡾⠦⣬⣧⡀⠀⣧⠀⠈⢸⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡰⠟⠋⠉⠙⠻⣶⠟⠉⠀⠀⠀⠀⠀⣀⣴⠿⠟⣓⡿⠷⠶⣭⣿⣿⣛⡛⠒⠦⣬⣭⠳⣾⣄⣀⣾⠋⢧⠀⠀⠀⠀⠀ ⣀⡤⢴⣄⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡿⣷⠿⠋⣁⠤⠖⠀⠀⠀⠈⠳⣍⠑⠊⣓⣉⣷⣿⣿⠾⣿⣇⠀⠀⠀⠀⠀⠀ ⣥⣀⠈⣿⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠉⣸⡧⣶⠞⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⣾⣹⣇⣍⣙⠳⣦⡏⢹⡷⢤⡀⠀⠀⠀ ⡣⠋⡀⠘⣧⡀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠊⠁⠀⠀⢀⠄⠀⠀⠀⠀⡰⢹⣿⠘⣿⠁⠸⣏⠓⢦⣹⡿⣆⠀⢹⡀⠀⠀ ⣁⢜⡇⠀⠸⣧⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⢐⡟⠀⠀⠀⠀⠸⡁⠈⢿⡅⠘⣧⡄⢹⡄⠀⢻⣄⢻⡆⠘⣷⡀⠀ ⠋⢁⣿⡀⠀⠙⣧⡀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⣠⠴⠊⠀⠀⠀⠀⠀⣤⡇⠀⡿⣧⢀⢿⣿⣤⣿⣂⣈⣿⣦⣿⣄⠸⠙⢦ ⣠⣾⠋⢷⡀⠀⠈⢷⡄⠱⣄⠀⠀⠀⠀⠀⠀⢠⡿⠀⡠⢔⣋⡠⣖⣧⠀⠀⠀⠀⠀⠇⠀⢰⠇⣿⢾⡸⣿⡿⡝⢷⠤⠦⠶⠽⢿⡇⠀⠖ ⣿⠃⠀⠈⢳⡀⠀⠀⠙⢦⡘⢷⣄⠀⠀⠀⣠⣿⣴⣿⣭⣭⣷⣍⣩⠒⢮⡀⠀⠀⠀⠠⢸⡟⣿⠋⢸⡇⣞⢷⡷⢾⡷⠶⣶⣤⠺⡄⣴⠟ ⣧⠀⠀⠀⠀⠻⣦⡀⠀⠈⠳⣆⡙⢷⣄⣴⢋⣥⠞⠋⢀⡀⠀⠀⠈⠙⢦⡪⢣⡀⣸⠀⢸⣿⠃⠀⣸⡇⠹⡈⣿⡌⢧⠀⠀⢈⠀⢿⡇⠀ ⠋⣇⠀⠠⣀⠀⠙⢿⣄⠀⠀⠈⠳⣦⡙⢿⣿⣷⠤⠤⡀⠉⠳⣄⠀⠀⠈⣿⣿⡷⠏⠀⣾⠃⠀⢰⠃⠃⠀⣇⠸⣷⡘⣇⠀⠸⡷⡈⢷⠀ ⡄⢹⡄⠂⠌⢱⣶⡾⠛⢀⣤⣄⠀⠈⠛⣦⣈⠛⢤⡀⠀⠀⠀⠘⢦⠀⢱⠘⣿⡿⣄⠀⣿⠀⢠⠃⠀⠀⠀⢄⣼⣿⣧⠹⡄⠀⢧⡘⠘⣇ ⣋⡴⠃⣤⡄⠘⣿⣆⣀⣸⣿⣻⣷⠒⠋⠙⣿⠟⠲⠿⣳⡄⠀⠀⢘⣗⣡⣷⡿⣷⡘⣶⡟⠀⢁⠔⠁⠀⣠⣮⡾⠀⣿⡦⠿⢶⣄⢳⣧⠹ ⠉⠀⠀⣿⣿⡄⠹⡿⡅⠀⠙⠛⠋⠀⠀⢠⡟⠀⢀⣠⡿⠀⠀⡠⠊⢈⣾⡟⠁⢺⣿⣿⠃⠀⠁⠀⢀⣴⡽⠁⣇⢀⣿⡿⡄⠘⣯⠈⣯⡆ ⠀⠀⠀⣻⠻⣹⡀⢻⣿⣶⣾⡆⠀⠀⣰⡟⠀⠀⣸⡿⠁⠀⠈⣀⣴⢋⣬⣤⣴⠿⡗⠁⡠⠊⠀⣠⣿⠋⠀⠀⢙⣾⠇⢿⣷⠀⢸⣆⡼⣡ ⠀⠀⢠⡿⡀⣸⠃⠀⣿⡿⠋⠀⠀⣰⣟⠀⢠⣶⣿⠀⢀⣴⠞⠋⠉⠉⠛⠉⢀⣸⠷⠊⠀⣠⣾⠛⠁⠀⠀⢀⣾⠏⠀⠘⣿⣧⠀⢿⣰⡟ ⠀⣠⠞⢸⢡⠏⢀⣼⡿⠁⠀⠀⣼⠏⠀⢀⣤⣿⣽⠿⠋⠁⠁⠀⣀⣠⣴⠾⠛⢉⣠⣴⡾⠋⠀⠀⠤⢤⣶⢻⡇⠀⠀⠀⢹⣿⡆⢸⣿⠀ ⡀⠚⠛⠉⡁⢠⣾⡿⠁⠀⢀⣾⡿⠂⢀⣸⣿⡏⢆⠀⠀⠈⡛⢹⢁⣾⣧⣶⡿⠛⠋⠉⠀⠀⣠⣤⡿⠛⣡⢿⡀⢀⣀⡀⣞⠙⣿⡋⢹⡀ ⠀⠀⠀⢀⣉⣿⠈⠀⠀⣢⣾⡙⠀⢄⣼⠏⣀⣿⣿⣒⣶⣶⠶⡟⠛⠉⠉⠀⠀⣀⣠⡴⠷⡛⣁⣠⡴⠛⠁⣠⢟⣽⣿⣻⡟⣖⣾⣿⠚⠓

⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣶⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⣤⣷⣿⣿⣿⣯⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣾⣟⢿⢻⡝⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⠬⢾⣳⠗⢲⣿⣿⣿⡏⠻⠿⢿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣷⣜⢐⡶⣿⣿⣿⣿⣿⣿⣷⣶⡞⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡿⠷⣿⣾⠿⣿⣿⣿⡿⠿⢿⣿⡟⠀⠀⠁⠉⠲⢄⡀⠀⠀⠀⠀ ⠘⠀⠀⠈⠀⠀⠹⣿⣿⣧⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣄⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡖⠊⠉⠁⠀⠀⢀⡤⠔⠉⠁⠀⠈⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠛⠉⠁⠀⠙⡄⢠⠔⠉⠁⠒⢤⡀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⢠⠄⠀⢀⣀⠀⣽⠃⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡿⢡⠆⠀⡰⠁⠀⣰⣟⣿⣧⣴⣿⢻⡄⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡿⢠⡟⠀⡸⠁⠀⡼⠁⠀⠀⠉⠉⠀⠀⠹⡀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⣿⠁⣾⠃⠀⣇⠀⢠⣇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⡀⠀⡄⠘⣼⡷⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣷⣿⡆⠀⣿⣦⡸⡏⠃⠀⠀⠀⠀⠀⠀⠰⣿⢠⠀⠀⡇⠀⢻⣧⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⢻⣶⡿⣿⣻⣧⡀⠀⠀⠀⠀⢀⡀⣀⣧⡈⠀⠀⡇⠆⢸⣿⠃⠀⠀⠀⠀⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡟⡏⠃⣿⣿⣿⠃⠀⠀⠀⠀⠷⢻⠋⣿⣷⣦⣼⡷⣠⣾⡟⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡜⠀⡇⠀⠘⠃⢃⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⢹⣯⢹⠋⠉⣻⣄⠀⠀⠀⢠⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠞⠀⠰⡇⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠘⠓⡸⠀⢠⠏⣋⡉⢙⠒⢺⢖⡦⠤⣀⡀ ⠀⠀⠀⠀⢠⠎⠀⠀⡜⢣⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡸⠀⠈⣀⣻⡦⢤⣀⡠⠤⠟⠃ ⠀⠀⠀⢠⠋⠀⢀⠞⠀⠀⣳⣄⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⡎⠀⢠⣧⣤⡬⠄⠒⠉⣯⠀⠀⠀⠀⠀ ⠀⠀⣠⠃⠀⡰⠃⠀⢀⡔⣻⣏⠳⢄⡀⠀⠀⠀⠀⢀⣀⣤⠔⠚⡿⠀⠀⡼⢀⣟⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⢰⠃⢀⣾⠃⠀⠀⠈⠉⠑⠚⠂⠀⠉⠓⢶⣾⣿⡿⠟⠁⠀⡰⠁⠀⡰⢁⣞⡺⢦⡀⠀⠀⠸⡄⠀⠀⠀⠀ ⢠⠇⢀⢊⠇⠀⠀⠀⢀⠠⠤⠄⣀⠀⠀⣤⣾⠋⠉⠀⠀⠀⡰⠃⢀⣴⠃⠛⠚⠉⠉⠁⠀⠀⠀⢣⠀⠀⠀⠀ ⡞⢀⡎⡜⠀⠀⢠⠊⠀⠀⠀⠀⠀⠉⢹⣿⡇⠀⠀⠀⢀⡜⠁⢠⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀ ⡇⣼⣰⠃⠀⢠⡇⠀⠀⠀⠢⣀⠀⠀⠀⠙⢻⣷⣤⣤⠊⠀⣴⣿⡿⠋⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀ ⣷⡟⡟⠀⠀⢸⡇⠀⢀⡼⠃⠈⠑⢄⠀⠀⠀⢀⠽⣁⠴⠚⠉⠁⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⠠⠈⡆⠀⠀ ⠘⣇⡇⠀⠀⢸⣇⡴⠋⠀⠀⠀⠀⠀⠀⢀⣴⡯⠚⠁⠀⠈⠉⠉⠉⠒⠒⠒⠒⠒⠒⠀⠈⢣⠀⠀⢱⢻⠀⠀ ⠀⢸⠃⠀⠀⢸⠏⠉⠒⠤⡀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢿⡆⠀ ⠀⢸⡆⠀⠀⡇⠀⠀⠀⠀⠈⠳⣄⣠⡿⠁⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⣷⠀ ⠀⠀⣇⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⣽⡏⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠒⠢⣤⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⣿⠀ ⠀⠀⠸⣿⡄⢸⡆⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⡼⠁⠀⠀⠀⢠⣿⠀ ⠀⠀⠀⢻⡘⢄⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⠀⣰⠃⠀⠀⠀⢀⣮⡟⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠖⠒⠒⠚⠒⢢⠤⠤⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢖⣋⣉⣀⠀⠀⠀⠀⠀⢠⡴⠒⠋⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠾⠒⠋⠉⠀⠀⠀⠹⡄⠀⣤⠞⠉⠈⠓⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⢀⠄⠀⠀⠀⠀⠀⢻⠞⠁⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢁⡀⠀⢀⡴⠁⠀⢀⣴⣟⢷⠀⢛⣤⣤⡄⠀⠀⠀⠀⠀⠀⠈⢶⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⣰⡏⠀⢀⡞⠀⠀⢠⡾⠧⠽⣾⣧⣟⡿⠃⢾⣇⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣻⠇⣰⡿⠀⢀⡟⠀⠀⢠⡏⠀⠀⠀⠀⠉⠉⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡏⢀⣧⠃⠀⢸⠇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢰⠀⠀⡆⠀⢣⢸⡙⡄⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⡇⡸⣿⡀⠀⢸⡀⡄⠀⣿⠳⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠄⢸⠀⠀⢃⠀⠸⡏⡇⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣽⣿⣧⠀⢸⣷⡷⣦⣻⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣿⠀⠸⠀⠀⢸⠀⠀⢹⣷⢻⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣟⣿⠟⣿⢟⣷⣦⡀⠀⠀⠀⠀⠀⢀⡠⣄⣀⣻⣠⡇⠀⠀⣿⢸⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡏⢻⠀⣿⣟⣿⡟⠁⠀⠀⠀⠀⠀⣸⠾⣿⠋⣿⣿⣶⣦⣼⣿⣏⢰⣿⣿⠃⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡇⠀⠀⠹⣏⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⣧⣶⣿⣿⡟⠻⣟⠓⡶⠿⠿⢳⡄⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡧⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠻⣿⠇⢸⡟⠛⡇⠀⠀⣼⣿⣦⣀⣀⣀⣀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⡇⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠉⠉⢱⠁⠀⢠⠇⢉⣥⡤⢀⡭⠩⠭⠭⢽⠒⠲⢤⣄ ⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⡼⢹⡄⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⡸⠀⠀⠁⡀⣛⣒⡦⠤⢂⣀⡠⠶⠿⠋ ⠀⠀⠀⠀⠀⣰⠏⠀⠀⢀⡾⠁⠀⠙⣤⡀⠀⠀⠈⠉⠛⠛⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢰⡇⣀⢐⣋⣩⠤⠖⠚⡏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠃⠀⠀⣤⠋⠀⠀⠀⣴⢻⡷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⠇⠀⠀⡾⠉⣿⡏⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠃⠀⢀⣼⠁⠀⠀⢠⣟⣥⠟⢷⡈⠙⢦⣀⠀⠀⠀⢀⣀⣠⣤⣶⡾⠋⠁⢀⠟⠀⠀⣰⠃⢠⠿⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⠀⣠⣻⠁⠀⠀⠀⠀⠀⠈⠉⠛⠃⠀⠀⠈⠉⢹⣿⣿⣿⣿⠟⠋⠀⠀⢠⡞⠀⠀⢠⠟⣰⢟⣛⡟⣆⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀ ⠀⢠⠇⠀⡴⢱⠇⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⣀⣼⣿⠋⠉⠁⠀⠀⠀⢀⡞⠀⠀⢠⡞⠸⠷⠶⠛⠋⠉⠁⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀ ⢀⡾⠀⡸⢁⡏⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠉⠓⠲⢲⣿⡟⠂⠀⠀⠀⠀⠀⣠⠏⠀⢀⣾⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀ ⢸⠁⢰⠇⣼⠁⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣯⣄⠀⠀⠀⠀⡴⠋⠀⢠⡾⣹⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀ ⢸⠀⣿⣰⡏⠀⠀⠀⡟⠀⠀⠀⠀⠘⠦⣄⡀⠀⠀⠀⠈⠙⣿⣷⣶⣴⠞⠁⢀⣴⣿⣿⠿⠉⠈⠓⠦⣄⣀⠀⠀⠀⠀⠀⠐⠀⢀⠈⣧⠀⠀⠀ ⢸⣰⠙⣻⠀⠀⠀⢸⡇⠀⠀⠀⣠⠟⠀⠀⠙⢦⡀⠀⠀⠀⠀⢀⡽⢋⣠⠴⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠳⠤⣀⠀⠀⠀⠘⡆⢹⡀⠀⠀ ⠈⢻⠀⡏⠀⠀⠀⢸⡇⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡴⠛⠁⠀⠒⠒⠒⠒⠒⠤⠤⠤⠤⠤⠤⠤⠤⠀⠙⢣⡀⠀⠀⠸⡄⣇⠀⠀ ⠀⠀⢧⡇⠀⠀⠀⠸⣧⡾⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⢻⣸⡄⠀ ⠀⠀⢸⡇⠀⠀⠀⣠⠋⠀⠀⠈⠛⠦⣄⠀⠀⠀⠀⣼⣷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣟⣇⠀ ⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢸⣾⠀ ⠀⠀⠈⣧⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⡗⠒⠚⠛⠛⠉⠉⠉⠉⠉⠉⠉⠛⠓⠢⠤⣀⡠⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠘⡟⡆ ⠀⠀⠀⢹⡠⣆⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢠⣷⡇ ⠀⠀⠀⠀⢷⡞⣆⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⡸⣿⠃ ⠀⠀⠀⠀⠈⣧⡘⢦⣘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⢀⣼⡃⠀⠀⠀⠀⠀⣠⢳⡟⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣄⣉⠁⠐⠂⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠉⠁⠀⠀⠀⠀⡀⠉⠐⠢⠌⢢⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⣀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⢉⠐⠤⡀⠀⠀⠀ ⡀⠏⢀⠔⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢋⣂⠀⠀ ⠰⡀⠀⠀⠀⠀⠀⡔⢁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡇⠀⠀⠀⢛⡆⠀ ⠀⠡⡀⠀⠀⠀⠺⣄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠈⢆⠀⠀⠈⡇⠀ ⠀⠀⣐⢆⠀⠀⡰⠁⠴⠿⠶⢦⡄⠀⡄⠀⣀⠠⢔⣾⠿⠶⠦⠀⢢⢰⠀⣸⡀ ⠀⠀⠱⡈⠁⢸⠀⠀⣠⢴⣶⣶⣌⠓⠉⠁⠀⠔⣩⣴⣶⡦⣄⠀⠀⠘⠈⠡⠁ ⠀⠀⠀⢱⠆⢸⠀⠸⡁⢸⣿⣿⠇⠱⡀⠀⠀⡔⠁⣿⣿⡷⠈⠇⢰⠀⣆⠃⠀ ⠀⠀⠀⡌⠀⡌⡆⠀⠈⠂⠙⠋⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⡌⢀⡏⠀⠀ ⠀⠀⠀⡀⡔⢀⠋⢄⠀⠀⠀⠀⢤⣤⣀⣑⣁⣠⣤⠆⠀⠀⢀⡜⢀⡼⠀⠀⠀ ⠀⠀⠀⠉⠀⠐⠒⠒⠓⡤⣀⠀⠈⠛⠿⠿⠿⠟⠁⠀⣀⡔⠊⠒⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢘⣒⢒⣊⠏⠀⠐⠒⠒⠂⣞⡋⠐⠓⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⡊⠁⠀⠈⣶⡀⠀⠀⣀⣴⠞⠋⠀⠉⠙⠲⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⣠⢞⠁⠀⠀⠀⡞⡗⡎⣿⣤⠾⠋⡔⡖⡄⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀ ⠀⠀⠚⠁⠀⠀⠀⠀⠓⠃⠱⠙⠋⠓⠊⠛⠁⠃⠃⠀⠘⠂⠀⠐⠒⠛⠂⠀⠀

⠀⢚⠟⢁⣴⡏⠀⠀⠀⡼⠁⢀⢞⣿⠀⡼⠀⢳⠀⠀⠀⠀⢰⡘⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡞⢆⠀⠀⠀⠀⠀⠈⠐⠠⠀⠀⠀⠀ ⡔⢁⡔⢩⠛⠀⠀⠀⢰⠃⢀⣎⡾⢿⠀⡇⠀⠀⡇⢡⠀⠀⠈⣇⠈⢷⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠹⡈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⡟⢀⠇⠀⠀⠀⣀⡌⠀⣼⠞⠀⠘⡄⠁⠀⠀⠸⡀⣇⠀⠀⢿⡄⠀⠻⣄⠀⠀⠀⠘⣄⠀⠀⠀⠀⢱⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡞⠀⡸⠀⠀⠀⠀⠈⡟⢶⣯⣀⠀⠀⢡⡀⠀⠀⠀⢣⠸⡄⠀⠸⡷⡀⠀⠈⢆⠀⠀⠀⠸⣧⡀⠀⠀⠀⢷⢄⠘⠢⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠇⠀⠀⢀⠀⠀⡇⡸⠓⢌⠑⢦⡸⡇⠀⠀⠀⠀⢧⢱⡀⠀⢿⣧⠀⠀⠀⠳⡀⠀⠀⠹⣿⡄⠀⠀⠈⠈⢦⠀⠈⠢⡀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⢸⡀⠸⣧⣿⣶⣞⠷⣄⢻⣿⠀⠀⠀⠀⠘⡏⣷⠀⠸⡿⣷⡀⠀⠀⠙⡄⠀⠀⠹⣏⢢⠀⠀⠀⠀⠳⣄⡀⠈⠑⠢⢄⣁⣀ ⡇⠀⠀⠀⠀⠸⣇⠀⣿⢸⡿⠉⢻⣮⣿⣿⠓⠀⠀⠀⠀⢡⢸⢦⠀⢱⠹⣿⣄⠀⠀⠘⣆⠀⠀⠘⢆⠑⢀⠀⠀⠀⠙⣿⡳⢦⡤⠤⠤⠖ ⡇⠀⠀⠀⠀⠀⡟⢆⢹⣸⠃⠀⢸⣽⣿⣿⣷⠀⠀⠀⠀⢸⡎⠈⠳⡈⡆⠹⡌⠳⡀⠀⠈⢦⠀⠀⠈⢦⠈⢦⠀⠀⠀⠘⡍⠲⢬⣲⡀⠰ ⢧⠀⠀⠀⠀⠀⣷⠈⢮⣿⡆⠀⠘⢻⣿⣿⣿⡆⠀⠀⠀⣸⠁⠀⠀⠘⢾⡀⠘⣆⠘⠄⠳⡀⠣⠀⢆⠈⢂⠈⢷⡀⠀⠀⠹⡄⠀⠈⢿⣦ ⠈⠀⠀⠀⠀⡄⣹⡇⠘⡿⣷⠀⢸⡈⣹⣿⣿⠛⠀⠀⠠⠃⠀⠀⢀⣤⣤⣷⡾⠼⠷⠚⠲⡛⣦⣣⣘⣆⠀⠀⠈⣧⡌⢂⠀⠹⣄⠀⠈⠣ ⠀⠀⠀⠀⣰⡳⡹⠹⡄⢇⠈⢦⡘⠳⢬⣽⡽⣻⠀⠀⠀⠀⠀⠺⠛⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⡟⢿⡻⣗⠶⡀⠘⣾⣄⠣⡀⢻⣦⡀⠀ ⠀⠀⠀⢠⣿⢣⠇⠀⣿⣼⡀⠀⠀⠉⠓⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠠⣖⠋⠀⣀⣀⣀⡀⠀⠈⢷⠀⠱⣿⣆⢣⠀⠸⣿⢦⡱⡄⢻⡿⠦ ⠀⢠⢠⡿⣟⣼⢀⠶⡇⠻⣧⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠻⠯⢭⣻⣇⡀⢹⡿⢆⣆⠀⢻⠈⡷⣜⣆⢻⣄ ⠀⡼⠋⠀⣿⢏⡜⠀⡇⠀⠙⢦⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠄⢸⠇⣨⢿⡆⠈⣷⣧⣬⡿⢷⣌ ⠋⠀⠀⢠⡯⢻⠃⠀⢿⡀⠀⠀⠉⠛⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠴⢤⠏⣰⡟⠈⢿⠀⢻⣿⠟⠁⠘⢦ ⠦⣤⡔⠉⠇⣿⠀⠀⢸⣷⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⡴⡹⠁⠀⣾⣇⢸⠛⠲⠤⠔⠚ ⠀⠀⠈⢱⠒⢧⣄⠀⢸⠘⢷⡀⠀⠈⠓⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⡰⠁⣠⣾⢿⣿⢺⣆⣀⡠⠔⠚ ⣀⣀⠀⠀⠀⠀⢸⣓⠲⢤⣸⠻⣄⠀⠀⠈⠑⢶⣤⡤⢀⣤⠤⢄⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠁⣿⠞⠁⡰⣱⣿⣿⢿⣾⣿⡁⠀⠀⠀ ⡄⠀⠙⠲⢦⣀⣀⣀⣉⣿⡇⠀⠈⢦⠀⠀⠀⠀⡀⠉⠉⠛⠒⠻⠿⠟⠊⠁⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⡜⣰⣿⣿⡇⠀⠉⠀⢣⡀⠀⠠ ⠳⡀⠀⠀⢸⣾⠀⠀⣿⡿⠁⠀⠀⠀⢣⠀⠀⠀⠉⠒⠢⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢻⡏⠀⡜⢀⣿⡟⠁⢻⣄⠀⠀⠀⢻⣦⡀ ⠀⠱⡄⠀⢸⣿⡤⠤⠯⣄⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠒⠉⠀⢠⣾⠃⠸⣱⡿⠛⣧⣿⣎⢯⠳⡦⡀⠸⣧⠉ ⠀⠀⣸⡶⠋⠁⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠙⢦⣄⣀⣀⣀⣤⣤⣶⣾⣿⠟⠉⠀⠀⠀⢠⢏⣿⢀⡼⠁⠀⠀⢿⡟⣿⠢⣷⣦⢬⣕⣻⣦ ⡀⡴⠟⠀⠀⠀⢀⣠⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠛⠉⠁⠀⠀⠀⠀⢀⡎⠘⢿⡼⠁⠀⠀⠀⠘⡇⠈⠦⠀⠉⠉⠀⠀⠈ ⡹⠁⠀⣀⡤⠖⠉⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⢦⡀⠀⣀⣀⣀⣀⠀ ⣀⡤⠊⠁⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠈⠀⠀⢀⣀⣠⠤⣶⣿⡭⠽⠶⠒⠒⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣷⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠒⠛⠛⠛⠒⠄⠀⠀⠈⠉⠙⠛⠿⣿⣾⣍⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⣭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣦⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⣽⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⡁⢸⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⠋⣠⠆⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣾⠙⢢⣄⡀⠀⠀⠀⠀⠘⡏⣼⠀⣾⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⣟⣴⡟⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⢰⣿⢠⣿⣿⡿⠟⠛⠓⠦⣀⡀⠀⢹⡿⠆⣸⡄⠀⠀⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠟⣿⠃⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠋⣀⣠⣤⣄⡀⠈⠻⣷⡂⢻⣤⣿⠃⠀⠀⠀⠀⠙⢿⣶⣤⣀⣀⣠⣄⡀⠀⠀ ⠋⢠⡿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⢡⣾⣿⣿⣿⣿⡇⠀⠀⢸⣷⡄⠻⣷⡀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁⢸⡇⠀⠀ ⠀⢸⡇⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣠⣿⠿⠋⠀⣿⠈⢿⣿⣿⠿⠁⠀⠀⢸⡇⠈⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀ ⠀⢸⠇⠀⠀⠀⡏⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠃⠀⠨⠛⠁⠀⠀⠀⠀⢸⡆⠀⣸⣷⣦⣤⣤⣀⣀⢀⣀⣀⠤⠖⠛⠉⠀⠀⠀⠀ ⠀⢸⠀⠀⢀⣼⡇⠀⢀⣶⣶⣶⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣄⣿⡀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠞⣹⡇⠀⢸⣿⣿⠛⢿⣿⣿⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠻⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠋⢠⡿⠁⣠⣿⠻⣿⡒⠀⠉⠀⠘⠓⠀⣀⣀⣀⡀⠀⠀⠀⢠⣿⣦⣶⣶⠒⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⢠⡿⠗⠋⠁⢹⡀⢸⣷⣀⠀⠀⠀⠀⢘⣅⣀⠀⠀⠀⢀⣴⣿⣆⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢸⡏⠙⠿⢿⡖⢦⡤⠋⠋⢳⣤⣾⣿⣿⣿⣿⠟⠁⠀⠀⠉⠉⠛⢲⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣆⠀⠀⠀⣹⠊⠀⠀⠛⢷⣿⣿⠿⣿⠏⠀⠀⠀⠀⠀⠀⢠⢶⣿⠟⠛⢿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣰⠇⠀⠀⠀⠀⢀⣿⣯⡞⠁⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣿⠀⠀⠀⣠⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠘⢷⣶⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⡄⠀⠘⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⣷⡀⠀⢀⣼⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⠀⠈⠛⢦⣤⣾⡿⠇⠀⠀⠀⢻⡄ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢸⣧⣠⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⢀⣶⠟⠁⠀⠀⠀⠀⣠⠾⠁ ⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠈⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⣴⠟⠁⠀⠀⠀⢀⣴⠟⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠒⠒⠊⠳⠶⢤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡖⢒⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠁⠀⠐⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⡴⠀⠀⠈⠻⣿⣦⡀⠀⠀ ⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠂⠀⠀⢊⡄⠁⠀⠀⠀⠈⢻⣿⡄⠀ ⠀⠀⡜⠃⠀⠀⠀⠀⠀⠀⠀⠊⣠⠀⢀⢀⡰⠋⠸⡄⠀⠀⠀⠀⠀⢹⣷⡀ ⠀⣸⢀⠀⡖⠁⢀⣀⣤⣤⠶⠚⣝⡠⠕⠋⠀⠀⠀⢻⠄⠀⠀⠀⢀⠈⣿⣇ ⢸⠋⢸⣾⢲⣶⣿⡍⠀⠀⠀⠌⠂⠈⠀⠀⠀⣀⣀⡀⢣⡄⠀⢀⠆⠀⣿⣿ ⠈⢆⡼⠃⠻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡿⠀⢣⠀⡬⠤⠛⠛⢻ ⣠⠞⠝⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠉⠁⢀⡇⢠⠃⠀⠀⣠⠊ ⢷⡈⡀⠀⠀⠀⠀⠙⠦⠞⠳⢤⣤⣤⠴⠃⠀⠀⠀⠀⣼⠃⢸⠀⢀⣴⡇⠀ ⠈⠳⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡎⡀⢸⣾⣿⣿⡇⠀ ⠀⠀⠈⢻⠷⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⢼⠀⠁⣴⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠱⠎⠀⠀⣉⣽⣁⣀⡀⣰⣉⠉⠉⠁⠀⠀⣄⣾⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⡾⢿⡄⠀⣀⣤⠴⣛⢟⣦⡀⠀⠀⠁⠹⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⡸⢹⠁⠘⣟⡿⠋⠀⠀⠀⣾⡕⠛⡄⠀⠀⠀⠹⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⡇⡟⠀⠀⠉⠀⠀⠀⠀⠀⡏⠀⠀⠸⠀⠀⠀⠀⠘⠏⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠲⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠉⠉⠛⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠒⠋⠉⠉⠉⠉⠉⠙⠒⠒⠦⢤⣀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠀⠀⠀⠉⠒⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⣄⠀⠀⠀⠀⠀⠀ ⠀⣠⡤⠴⠒⠉⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠘⢵⢄⠀⠀⠀⠀ ⣀⣨⠆⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⢋⢳⡀⠀⠀ ⢻⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠈⢯⣷⠀⠀ ⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣿⡄⠀⠀⠀⠀⠀⠸⣾⡇⠀ ⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⢾⣁⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠋⡴⠃⠙⣄⠀⠀⠀⠀⠀⢹⣇⠀ ⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⡸⠋⠒⢢⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣟⣁⠀⠀⠈⢣⡀⠀⠀⠀⠈⣿⠀ ⠀⠀⠀⣀⡙⢦⡀⠀⠀⠀⡴⠁⠀⠰⠟⠛⠻⠿⢿⣶⡒⠒⠒⢲⠀⠀⢀⣀⡤⠴⢒⣯⣿⡿⠿⠿⠿⠦⠀⠀⢳⠀⢰⠀⠀⣸⣄ ⠀⠀⠀⢹⡉⠑⠻⡆⠀⡞⠀⠀⠀⠀⠀⣀⣤⣤⣄⡈⠛⠷⣤⠟⠚⠉⠁⠀⢀⣴⠟⠋⣁⣀⣀⣀⠀⠀⠀⠀⠈⡇⢸⠭⠟⠋⡽ ⠀⠀⠀⠀⢳⡀⠀⡇⠀⡇⠀⠀⠀⣴⠞⢻⣿⣿⣿⣿⠷⣄⠈⠁⠀⠀⠀⠀⠉⢀⣴⢿⣿⣿⣿⣟⠻⣆⠀⠀⠀⡇⠈⡆⠀⡼⠁ ⠀⠀⠀⠀⠀⢳⣼⠀⠀⣇⠀⠀⢼⠁⠀⢸⣿⣿⣿⣿⠀⠙⢧⠀⠀⠀⠀⠀⢠⠟⠁⢸⣿⣿⣿⣿⠀⠈⣳⠀⢀⡇⠀⡇⢰⠁⠀ ⠀⠀⠀⠀⠀⢸⠃⠀⢠⣿⠀⠀⠀⠱⢄⠈⢿⣿⣿⠟⠀⠀⠀⠃⠀⠀⠀⠀⠋⠀⠀⠸⣿⣿⣿⠏⠀⠀⠁⠀⢸⠁⠀⣷⡏⠀⠀ ⠀⠀⠀⠀⢠⠇⠀⠀⣸⢬⣇⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢀⡏⠀⢘⡟⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⣰⠃⢠⠟⣆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠘⠦⠖⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢀⣾⠃⠀⠀⠀ ⠀⠀⠀⠀⠸⣀⡜⠁⢀⠎⠀⠈⢦⡀⠀⠀⠀⠀⠀⠈⢿⣿⣽⣶⣶⣶⣶⣶⣮⣽⣿⠋⠀⠀⠀⠀⠀⣠⠎⠀⢠⣾⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠀⠀⠈⠓⠒⠒⠒⠛⠲⣤⡀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⢀⡤⠾⠧⠴⠒⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡃⠉⠙⣲⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠴⠚⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣩⡭⢭⣤⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣉⡉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠉⠉⠉⠛⠲⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠔⠃⠀⠀⢀⣀⡀⠻⣿⣄⠀⠀⠀⣀⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⡀⠀⠀⠀⠀⠀⠀⡿⢻⡿⣇⠹⣿⣦⣴⣾⠟⠋⢰⠶⣾⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠋⠀⠊⠀⠀⠀⠀⠀⣶⢀⡇⠸⡇⢸⣶⡟⣿⣉⣡⠖⣶⡿⢀⡟⠀⡇⠀⠀⠀⣤⠀⠀⠀⠀⢀⣀⣹⣷⣄⠀⠀⠀ ⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠃⠀⠉⠀⠉⠉⠉⠉⠉⠈⠉⠁⠈⠁⠀⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠈⣹⣷⣀⣴⠀⢠⣤⣶⡦⠀⠀⠀⠀⠀⠀ ⠢⣀⠀⠀⠀⠀⠀⢄⠀⠈⣆⣠⣼⣿⣿⣿⣿⣿⣦⣼⣏⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⣶⣄⡀⠀⣨⣷⡿⠟⠋⠉⠉⠉⠉⠛⠿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⡿⠋⠀⠀⠀⠀⢠⡄⠀⠀⠀⠈⠙⣿⣿⣏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⣠⣿⣿⣆⠀⠀⠀⠀⠈⣿⣿⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⠒⢺⣿⠁⠀⠀⠀⠀⡰⠿⠿⠿⠿⢆⠀⠀⠀⠀⠸⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⣿⠀⠀⠀⠀⣴⣷⡀⠀⠀⢀⣼⣦⠀⠀⠀⠀⣿⣿⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⣹⣿⠀⠀⠀⣼⣿⣿⣷⡀⢀⣾⣿⣿⣧⡀⠀⢠⣿⡧⠤⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⢿⣆⠀⠈⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠁⠀⣼⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠚⢻⣿⣿⣦⣄⡀⠀⠀⠀⠀⢀⣠⣶⣿⡋⠀⠈⠙⠻⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢙⣿⠿⢿⣿⣿⣿⣿⣿⠛⠙⡁⠀⠁⠀⠀⠀⠀⠀⠉⠂⠄ ⠀⠀⠀⠀⠀⠰⣶⡾⠿⠀⠸⠋⠻⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠒⠈⠉⡕⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⣿⡀⣸⡀⢀⣀⠀⣇⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⡛⠰⠁⠳⣤⠧⠼⢥⡜⠈⡌⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠃⢈⠶⠗⠈⢀⡠⠀⣀⠁⠺⠶⣉⠈⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⢉⡜⠀⠀⠀⠮⠵⠮⠵⠀⠀⠀⢸⡉⣹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⡓⠦⣄⣷⣍⡇⠠⠤⣀⠀⠀⠀⠀⣀⡤⠄⢈⣏⡾⣀⡤⠖⡻⠀⠀⠀ ⠀⠀⠀⠀⢱⡭⠶⡩⡗⣷⠾⢦⣬⣉⠂⠀⢋⣥⡴⠶⣾⡟⠯⠒⢯⡌⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⢶⣼⣻⠈⠓⠄⠻⠉⠀⠀⠀⠿⠡⠘⠉⣇⣆⡼⣟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⢗⠾⡟⢑⣆⠀⠀⠀⠀⠀⠃⠀⠀⠀⢒⣰⡏⢹⠹⡒⠇⡀⠀⠀⠀ ⠀⠀⢀⢞⣷⡯⡠⣻⢂⢸⣦⡀⠀⠠⠤⠠⠄⠀⢀⣴⣯⠨⢺⢤⡼⡴⣑⠄⠀⠀ ⠠⣿⣃⢋⣿⡼⢤⣳⢢⢈⣿⣿⢦⣀⡈⠁⣀⡴⢻⣿⡁⠑⢾⣦⢇⢵⣝⡜⣶⠄ ⠸⠙⠣⢹⡱⢧⢿⡷⠨⢀⡿⢿⣄⠙⢿⡿⠏⣠⣼⠿⡁⠣⢼⣿⣤⢆⣧⢻⠃⢃ ⠘⠚⠁⢹⠳⡼⣎⡣⡄⢙⠀⠀⠉⢣⡀⢀⡴⠋⠁⠀⡎⢠⢴⢱⢧⡞⣿⠈⠓⠊ ⠀⠀⠀⠈⢿⠳⡼⣷⡴⢹⡦⢤⣀⠀⠘⠏⠀⢀⣤⢴⡎⢢⣾⢷⠜⢿⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⢲⠚⢼⣵⣩⣟⣦⣙⢟⣦⣤⣺⣏⣤⣿⡭⣪⡿⠞⡖⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠒⢰⡟⠻⣶⣿⣿⣾⣟⣾⣿⣷⠟⠻⡆⠒⠊⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣃⡴⠁⢸⡻⢿⣿⢿⡇⠈⠢⣸⡃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠻⠟⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠ ⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃ ⠀⠈⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀ ⠀⠀⠀⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣧⣽⣿⣯⣾⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠘⢿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠉⠋⠀⣿⣿⡟⠈⠙⠉⠙⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⡄⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠙⣦⣄⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⡀⠀⠀⠀⠀⢀⣸⠏⣤⢻⡇⠀⢀⠀⠀⠀⢀⣀⣠⣤⣴⣾⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣷⣦⣄⡀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣟⠉⠙⢿⣿⣿⣿⠟⠛⠉⣙⣼⣿⣦⡁⠉⠙⠻⣿⣿⣿⡿⠋⠉⣻⣿⣿⡿⠟⠛⠁⠀⠀⠀⠀⢀⣠⣴⣾⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠉⠙⠓⠂⢀⣿⡟⠁⠀⠀⢀⣿⡉⠉⢉⣧⡀⠀⠀⠈⠻⣿⡄⠐⠚⠋⠉⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣷⣶⣶⡶⠶⣾⣿⣿⠀⠀⠀⢠⣾⣿⣿⣤⣿⣿⣷⡀⠀⠀⠀⣿⣿⣷⠶⢶⣶⣶⣶⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠓⠂⢀⣿⣿⣦⣀⣠⣴⡶⠖⢀⣦⠀⠲⢶⣦⣄⣀⣠⣿⣿⣀⠐⠚⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣟⠉⢻⣿⣿⣿⣿⢀⣴⣿⣿⣷⣦⠄⣻⣿⣿⣿⡟⠉⣛⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣤⣴⣶⣶⣿⣿⠿⠿⠛⠋⢁⣠⣟⠛⠛⠀⠉⢰⠏⣿⣿⣿⠻⡄⠉⠀⠙⢛⣻⣆⡈⠙⠛⠿⠿⣿⣿⣷⣶⣦⣤⣤⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠿⠛⠉⠀⠀⠀⣠⠆⣾⣿⣿⡿⣧⢸⣄⠀⠀⠀⠉⠛⠿⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠴⠃⢼⣿⡇⠹⠰⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⣿⡀⠀⢰⡄⡿⣰⠂⠀⣀⣿⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⡼⠏⠀⠈⣿⣠⣿⠀⠀⠻⢧⠈⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⣿⣿⣿⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣠⡔⢒⡢⠶⡯⣍⣙⠦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠜⢫⢖⠅⠂⠈⣱⣈⡘⠑⠢⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣾⣴⢗⢕⠄⠂⠁⠀⠀⠀⠈⠐⢌⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⣩⣵⣷⡟⠁⠀⠀⠀⠀⠀⠀⢀⢀⠀⢿⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠱⡣⣹⠀⣠⠶⠉⠛⠃⠀⠀⢃⡤⣬⡙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⠛⣡⠟⠈⣴⣿⣿⣷⡅⠀⠀⡀⡹⠿⡿⠇⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠤⣄⢰⢛⢻⢅⢣⠉⠘⠉⠋⠀⠀⠀⢃⠈⠁⠀⢸⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠢⢀⠀⢹⣮⢹⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⠀⣘⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣩⠿⣽⣼⡀⠀⠀⠀⠀⠄⠀⠀⠒⠀⣰⣇⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣨⢁⣼⠋⢻⠹⢢⡀⠀⠀⠀⠀⠀⠀⣴⣿⠗⢛⠟⠦⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠋⢸⢠⣴⢣⣇⣷⡉⠐⠒⣂⠔⠊⠈⣶⢿⣼⣮⣦⡐⣕⠠⡀⠀⠀⠀ ⠀⠀⠀⠉⠀⠖⠁⠀⠀⡠⢣⢀⠅⡎⠀⢀⠠⠞⡸⠓⠿⠯⠡⠿⡿⠶⣎⢢⡀⠀ ⠀⠀⠀⠀⡌⠀⠀⣠⣾⡢⠉⣐⣔⡧⠐⡡⠊⡜⠀⠀⠀⠀⠀⠀⠈⠢⡈⢦⢃⠀ ⠀⠀⠀⠀⠃⢀⣴⡩⣟⠧⠊⡏⡀⣤⠊⠔⡁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⡈⠈⠈ ⠀⠀⠀⠀⡠⣍⢔⠌⠀⠂⠈⢃⠔⡡⠊⢣⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀

⡣⠀⡐⡁⠀⠘⠀⠀⡀⠁⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⠄⡲⠋⠔⠁⠌⠀⡀ ⢣⣏⠎⠀⡌⢱⣾⡄⠐⡀⠀⠙⢕⠢⢀⡀⠀⠀⠑⠢⢤⣌⣁⣒⣂⢠⡺⠞⣱⠁ ⣾⢣⠆⠀⡇⡎⠈⢳⠘⡘⡢⣀⠀⠑⣤⣶⢿⡷⡒⠢⠤⢤⣭⣬⠟⢻⠭⠻⢄⠀ ⡇⢸⠀⠀⢧⡟⠳⢄⢡⢫⠪⣄⡩⠚⠃⢬⣵⣦⣽⣖⣂⠤⠶⡖⢈⠄⠲⢀⠞⠀ ⢳⠸⠀⡆⢸⡇⡿⣦⡱⠫⣆⠈⠓⠤⣾⣿⠱⡀⢹⠆⢡⠀⠀⢳⠹⠀⡠⣮⣶⡶ ⡾⣧⠃⢧⠀⢿⡁⡾⣧⠀⠈⠣⡀⠀⠻⡛⣠⡃⠘⡀⣸⡆⠈⡼⣡⣜⠦⠖⠋⠀ ⠷⠋⠳⡘⣷⣌⢖⠰⠽⠁⠄⠀⠈⠀⠀⠀⠀⠐⠋⠉⡽⡇⠀⢸⣏⣈⣓⡶⠊⠀ ⠀⠆⠀⠈⠻⡌⡏⠓⠀⢮⠀⠀⠀⠀⣀⠤⠐⠃⠀⠐⠁⡇⢰⣼⣳⠊⠁⠀⠀⠐ ⡈⠀⠀⠀⢠⡃⠘⣄⠀⠀⢆⠒⠈⠁⠀⢀⣀⣸⠀⢀⠎⠇⡼⠑⢲⠊⠁⠀⠀⡇ ⠁⠀⠀⠀⠈⡇⢸⠀⠑⠢⣀⠣⣀⠒⠐⠁⠀⣈⠔⠁⢠⠎⢗⢠⠺⣇⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠘⣼⡇⠀⠀⠀⠁⠪⣦⣀⣠⣶⠋⠀⠀⠘⠀⠈⢼⠀⠎⠑⠢⢄⡸ ⠀⠀⠀⠀⠀⣀⡞⡞⢉⠏⣽⣿⣶⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⢸⢰⠀⠀⠀⠠⠂ ⠀⠀⢀⠴⠊⢰⡽⢁⠎⣼⣿⣿⣿⣿⡿⠀⢠⠀⠀⠀⠀⠀⢠⠂⡜⠀⠀⢰⠁⠀ ⠀⢠⠃⠀⢀⠟⠀⣾⢸⠀⠈⠙⠛⠋⠁⠠⠥⠄⠀⠀⠀⡠⢃⡜⠀⠀⠀⠀⠀⠀ ⠀⡆⠀⢀⠎⠀⠀⠈⠳⠬⢁⢢⠀⠀⠀⠀⠀⠠⠤⢔⠞⡴⠋⠀⠀⠀⠀⠀⡇⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠈⠁⠀⠀⠀⠀⠀⠈⠉⠀⠢⠄⣀⠀⠀⠀⠀⠀⠀ ⠀⢀⡀⠀⠀⠀⣠⣖⡁⠤⠐⠒⠀⠐⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀ ⠀⠀⠹⢍⠩⢉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡶⠤⠤⠄⣁⠀⠀⠑⡄⠀⠀ ⠀⠀⠀⡰⣳⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠑⢄⠀⠘⡄⠀ ⠀⠀⣰⠗⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡀⠀⠀⠀⠀⠈⢣⠀⢰⠀ ⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⣜⠈⢂⠀⠀⠀⠀⠈⡇⠈⡀ ⠀⠀⠀⠀⠀⠸⠿⠶⠦⣤⣀⠀⠀⠀⠀⠀⠀⢠⠎⣀⣷⡶⠟⢛⠂⠀⠀⠇⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⠔⢁⠪⠁⡀⠈⠢⡀⠡⡀⠀⡖⠊⠁ ⢳⠒⢤⠤⡀⡀⠀⠀⣀⣀⣀⡔⢀⡠⣖⠡⠂⠁⠀⢀⣀⣀⡀⠈⠢⣈⠰⣇⠀⠀ ⠀⠑⣄⡏⣀⣀⣠⡟⠭⠉⠉⠉⠙⠀⠀⠀⠀⠀⠊⠉⠉⠉⠙⠳⠂⡜⠁⠩⠔⠁ ⠀⠀⠹⢄⠐⡌⢸⠀⠀⠀⢀⣀⢀⣀⣀⣁⣀⠀⠀⠀⠀⠀⠀⠀⡸⢠⠃⡀⠀⠀ ⠀⠀⠀⠀⡹⠁⠈⡧⡀⡀⠈⢿⡵⠒⠒⠒⠲⠶⣶⣿⠏⠀⢀⣴⣇⠈⢀⠇⠀⠀ ⠀⠀⠀⢰⠁⠀⡸⠁⢹⣶⣄⡀⠑⠤⢀⣀⠀⠤⠚⢁⣴⡖⡉⡞⢹⢀⠎⠀⠀⠀ ⠀⠀⠀⠈⣆⡜⠁⠀⣠⡇⠀⠉⢱⡂⠒⠒⠒⢲⡞⠉⠉⠙⣿⡀⠐⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⠀⠁⡇⠀⠀⠀⠣⠂⠠⢤⠋⠀⠀⠀⠀⣠⢾⠆⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄ ⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀ ⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣮⣿⣿⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠀⠀ ⠀⠀⠀⠈⠻⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⣿⣿⠀⠉⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠰⣄⠀⠀⠀⠈⠙⠿⣿⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣸⢏⠻⡇⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⡿⠋⠁⠀⠀⠀⣠⠆⠀⠀ ⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⠈⠙⠻⠿⣿⣿⠉⠛⣿⣿⡿⠛⠉⣹⣾⣧⡁⠉⠛⢿⣿⣿⠛⠉⣿⣿⡿⠟⠋⠁⠀⠀⢀⣠⣴⠾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠿⣷⣶⣤⣄⣀⡀⠀⠈⠉⣀⣼⠏⠀⠀⢠⣿⡀⢀⣷⡀⠀⠀⠹⣧⣀⠉⠁⠀⢀⣀⣠⣤⣶⣾⠿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⢿⣿⡉⢻⣿⡀⠀⢀⣛⡛⢛⠛⢛⣓⡀⠀⢀⣿⡟⠉⣻⡿⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡞⠻⣿⣿⣿⠋⣠⣾⣷⣄⠙⣿⣿⣿⠟⢻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⡶⠾⠿⠿⠛⠋⣁⣼⡛⠋⠈⠀⢛⣿⣿⡻⠀⠁⠙⢛⣷⣈⠙⠛⠿⠿⠷⢶⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠚⠛⠁⠀⠀⣠⡆⡿⣿⣿⢷⢰⣄⠀⠀⠈⠙⠓⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡟⠋⢀⢻⡟⠈⠈⢻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢉⡿⠀⠘⡇⣸⠀⠀⢯⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⣿⣿⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⣿⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣀⡄⢀⣄⠀⢀⣤⠤⠒⠈⠀⠀⠀⠀⠀⠀⠀⣤⠄⢀⣤⠀⢠⣄⠀⠀⠠⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠙⠋⠁ ⣿⣿⣿⣿⣿⣿⠟⠈⠀⠀⠉⣀⣤⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⢀⣠⡥⠴⢬⣍⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⡿⠋⠀⠀⠀ ⣿⣿⣿⣿⣿⢧⠀⠾⠀⠒⠛⠃⠐⣛⣤⣤⣾⢴⠖⠿⠯⢭⣽⡉⢿⡻⡍⠑⠲⢄⠘⢿⣏⠉⢷⡀⠀⠀⠀⠀⠀⠀⠙⢿⡉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣸⠀⠀ ⣿⣿⣿⠟⠁⠀⠀⣴⠀⣀⣶⣶⠟⢋⣉⣉⡉⠿⠧⠤⠤⠤⠤⠽⠦⠷⠷⣉⣓⠺⠿⠦⠭⣀⡀⢻⢷⡒⠶⣄⠄⠀⠀⢾⣷⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠀⠀⠁⠀⠀ ⡿⠟⠁⠀⣀⣀⣠⣴⣾⣿⠵⠟⠋⠉⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠤⣀⠀⠈⠙⠓⢤⣄⠘⣧⣀⣴⢟⣿⠀⣠⡄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠐⠀⠀⠀⠀⠀ ⣶⠿⣿⣿⣿⣿⣿⣿⠏⠁⠀⡩⠒⠶⢤⣀⠀⠈⠙⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⢈⣱⠿⠋⠀⣼⣇⡀⢈⣁⠀⢉⣿⣿⣿⣿⣿⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠋⠀⠀⠉⣿⣿⣿⡇⠀⠀⡜⠁⢹⣦⣄⣀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠦⠤⠤⠤⣀⣠⣤⣤⣓⠒⢋⡉⣀⣠⠴⡾⣅⠀⠉⠻⣏⡀⠉⠉⢻⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⣿⣿⣻⠀⠀⡸⠁⡄⢸⠀⠈⠙⠳⠶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣈⣭⡭⠭⢿⡋⠉⣇⠀⠘⡜⣦⣄⠀⠈⠻⣾⠃⠀⢿⡟⠻⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⣿⡟⡇⠀⣰⠃⢠⠁⡏⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⠬⣍⣉⣉⣉⣉⣉⣉⣓⣲⣄⣏⠲⣄⠈⠳⣬⣆⠀⢳⠘⡜⢿⡦⣄⠈⢷⡀⠚⢻⡔⠛⠀⠙⠓⠦⣄⠀⠀⠀⠀ ⣷⠀⠀⠀⣿⣇⡇⢠⠏⠀⢸⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⢀⣴⠧⠀⠀⣤⣼⣾⠿⣿⡇⠉⠚⢦⡀⠀⠹⡄⠘⣄⠇⠀⢿⡼⣷⡄⢷⡦⠀⢷⡶⠀⠰⠆⠀⢈⢷⡀⠀⠀ ⣿⡄⠀⠀⣿⣿⡆⡞⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠒⠟⠁⠀⣠⣿⣿⣋⠁⢀⡿⠀⠀⠀⠈⢷⡀⠀⢣⠀⣿⠀⠀⢸⢻⣻⣿⣾⡧⠀⢸⣧⠀⢠⡄⠀⢠⠄⣇⠀⠀ ⣿⣿⠀⠀⣿⣿⢷⡇⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⢏⢸⣷⠟⠁⠀⠀⠀⠀⠀⢳⡀⢸⡄⣿⡆⠀⢸⣸⠙⣿⠇⣷⣄⢀⣹⣆⣀⡀⠀⠀⡀⣻⠀⠀ ⣿⣿⣧⠀⣿⡏⡎⡇⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⢸⡇⣼⢹⠀⢸⡏⠀⠋⢠⣿⣿⣿⣯⡙⣯⠁⠀⠀⠀⣿⠀⠀ ⣿⣿⣿⠀⣿⢹⠃⢡⠀⠀⠀⠀⢱⠀⠀⢹⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⣷⣿⣧⣧⡇⠙⢦⣀⢾⣿⡿⠉⣿⣿⣿⣟⠀⠐⠃⣼⠀⠀ ⣿⣿⣿⠁⣿⢸⠀⢸⠀⠀⠀⠀⡸⡄⠀⢸⡇⡟⠒⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡿⡏⠸⡌⠳⣄⠀⠉⠓⣒⣺⡾⠛⣛⠿⣿⣧⠀⠄⣿⠀⠀ ⣿⣿⣿⠀⢻⡿⡀⢸⡄⠀⠀⢀⣇⢹⡀⢸⣳⠃⠀⣀⠤⠄⠉⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢀⡞⢰⠁⢻⠀⢳⣸⣏⠹⡍⠉⠙⣄⠉⠻⢻⡟⢹⣿⣷⢰⣿⠀⠀ ⣿⣿⣿⠄⢸⣿⡀⠈⡇⠀⠀⢸⣿⣆⠳⡜⠙⣰⣯⣴⣶⣯⣉⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡠⠋⠀⢸⡇⠀⢣⠉⠓⢯⠙⢦⠈⢆⠀⠈⢷⣼⠟⣠⣾⣿⡀⠀ ⣿⠟⢻⠀⠈⣿⢳⠀⢹⠀⠀⣸⣿⣾⢆⠙⢶⣿⣿⡡⢿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⠊⠉⠉⠁⠀⠀⣼⢻⡄⠈⢳⡀⠚⠓⢼⡯⡙⠣⡀⣸⠋⣴⠋⠁⠻⣧⡀ ⠀⠀⣸⠀⠀⡏⠈⣧⡘⡆⠀⢹⣿⣿⣿⣦⣿⠿⢿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠐⠀⣀⣠⠖⣫⣿⡿⠁⠉⢳⠀⠀⠀⠀⢠⠇⠀⢇⠠⣀⠱⣤⡔⠊⠉⠙⣦⣏⢸⣿⣇⣼⠆⠀⠉⠹ ⠀⠀⣿⠀⢀⡇⠀⣿⣷⣱⠀⠸⣷⡹⣿⣿⣷⡀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣵⡾⠟⠋⠈⠀⠀⠘⡆⠀⠀⠀⣼⠂⠀⢸⡀⠘⣷⠴⣬⣉⣉⡴⠋⠈⢧⣉⣵⠏⡄⠀⠒⢸ ⠀⠀⣿⠀⢸⡇⠀⢻⣿⣿⣦⣄⠸⡗⠤⣙⣛⡻⠒⠦⣊⡉⠉⠉⣉⣲⣤⣀⠀⠀⠋⠻⣄⠀⠀⠀⠀⠀⠸⣱⠃⠀⢠⣿⠀⠀⢸⣧⡀⠈⠓⠦⠬⣙⣿⡦⣼⣾⠏⠀⢀⠀⠀⣠⠃ ⠀⠀⣿⠀⢸⣷⡀⠸⣷⣿⣍⠘⣆⠙⢦⡤⠖⠯⣍⣀⣤⢽⡓⠋⠉⣠⠀⠈⢳⢄⡀⠀⠈⠳⢤⣀⣀⣀⣸⠃⠀⠀⣸⣿⣷⠀⡜⢸⣟⡶⠤⣦⣄⠈⡇⠙⢮⣿⡟⠀⠀⢑⡼⢧⡀ ⠀⠀⡟⠂⠀⢹⡿⠦⣽⣛⣿⢄⣼⡄⠀⠙⢦⣀⠈⢿⠀⠈⠁⠀⠀⠁⠀⠀⠀⠈⠳⣄⣀⣀⣀⡀⠀⠀⠁⠀⠀⣰⣿⣿⣿⣿⠃⠈⢿⣿⣿⡿⣻⣆⡟⢶⣏⡴⠧⠀⣰⠞⠁⠘⢻ ⠠⠄⡇⠄⠀⠠⢷⣄⣸⣿⣿⣸⣿⠻⠦⢤⣤⣜⣾⣿⣀⣰⣇⣀⣀⡛⠀⠀⠈⠀⠀⠈⠻⣟⠻⣯⡉⠻⢿⣿⣿⣿⣿⡿⢋⠘⠀⠀⠘⣿⣿⠙⢛⠉⢹⣯⣟⣀⣤⣶⣿⣔⠀⠴⢼ ⠀⠀⡇⠐⢶⢀⠀⠹⣿⣿⣿⣿⡿⠑⣦⣄⣀⡀⠘⣯⠉⢩⣭⠉⠻⣿⣶⣄⡰⠀⠀⠀⠀⠈⠳⢶⡏⠙⠺⢿⣿⣉⣁⣤⠛⣦⡄⠀⢀⡼⠓⣦⣾⣖⣋⡼⠛⠋⢋⡼⠁⡏⠀⢀⣼ ⡀⠀⡏⠉⠘⢿⣷⣶⣛⣩⣿⡏⠀⠀⣿⡿⠛⣿⣴⣃⠀⢀⣀⠀⠀⣈⢻⡿⣷⢦⣄⡀⠀⠀⠀⢠⡟⠦⣤⡠⠀⠈⠿⠿⢿⠿⣧⣼⣿⣵⣭⣴⣿⣋⣁⣐⠂⠀⠗⠀⢈⣇⡀⢈⡏ ⠀⠀⡇⠒⠀⠐⠚⠉⠙⠃⣸⠿⡄⢋⡿⠁⠀⣺⡟⠉⠀⠀⠉⠀⠀⠉⠀⢻⣽⣆⠉⢛⢦⣀⠀⠀⡀⠀⢀⣀⠀⢨⡐⠲⣦⣤⣀⣠⣾⠋⣿⣦⣿⣿⡉⠩⠟⠻⢶⡦⠴⠆⢳⣾⠀ ⠀⠀⢱⣦⠀⢰⣶⠀⢰⡆⣇⠀⠗⣸⡟⠀⠛⠉⠀⠛⠃⠀⠛⠀⠀⠙⠁⠈⢿⡹⣆⠀⠀⠙⡳⣤⣁⠀⠈⠉⠀⠀⠁⠀⢀⠈⢙⣿⡅⣴⡿⠉⠀⠙⢿⣷⣦⣄⢠⠟⢴⡀⢸⣿⣆

⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃ ⠀⠈⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠴⠿⢻⡟⠿⠦⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠁⠀ ⠀⠀⠀⠙⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠋⠀⠀⠀ ⠀⠈⠢⣀⠀⠉⠛⠿⣿⡶⢶⣤⡤⠤⣭⡏⠠⢤⣤⡴⢶⣿⠿⠛⠉⠀⣀⡔⠁⠀ ⠀⠀⠀⠉⠻⠶⣦⣤⣄⣉⣤⡏⠀⣠⣧⣼⡄⠀⢹⣤⣉⣠⣤⣴⠶⠟⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢉⣡⡼⢷⣶⡞⣠⣌⢳⣶⣾⢧⣌⡉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠒⠒⠛⠋⣉⡴⠏⠁⡀⣽⣯⢀⠈⠩⢦⣉⠙⠛⠒⠒⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⢙⡋⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⠁⢸⡇⠈⢂⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢸⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⣠⣴⣶⠭⠍⠙⠛⣓⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣊⠉⠀⠀⣠⣤⠽⠿⠻⡷⢶⣶⣤⡀⢠⡿⡛⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣫⣅⡾⠟⠉⢀⣀⠤⠤⢿⣌⠑⡺⣭⣙⠷⣄⡀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠋⠁⠴⡿⠋⣠⠴⠋⠁⠀⠀⠀⢈⣯⢀⠀⠀⠈⠙⠢⠍⠓⠦⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⡟⠀⠀⣠⠞⣡⠞⢁⡤⠀⢀⣠⠤⠞⠛⠛⠛⠙⠛⠓⠒⠶⢤⣀⠀⠙⣿⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣵⣿⣷⣴⣾⣻⠞⣡⡖⢉⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣄⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣿⢞⡿⠱⢃⣶⣯⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣾⣽⠏⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⡞⢁⣜⣡⣾⣿⣷⣿⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⢿⣾⠾⣿⠟⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣠⡤⠤⠠⠤⢤⣀⠈⢟⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⣴⡿⢠⠏⣿⠁⠀⠀⠀⣀⣤⣶⣏⡭⠶⠶⠾⠇⠀⠀⠀⠀⠙⠟⠒⠒⠒⠒⠚⠓⠺⣼⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠁⡄⠞⢸⢿⠀⠀⣴⡾⠛⠋⣉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡎⣩⣭⣭⣄⡀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣟⣼⡇⠀⡿⡼⡆⠞⠁⠠⣾⣿⣶⣶⣶⣿⣤⠆⠀⠀⠀⠀⠀⠀⠀⢻⢻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡇⠡⢸⣧⣼⢿⠁⡇⠀⢶⣿⡿⣟⣻⣿⣿⡿⣿⡆⠀⠀⠀⠀⠀⢠⠀⣼⠈⢿⠿⠿⣝⡿⠹⡗⢛⡻⠉⢉⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⣾⣿⡟⠰⡇⢸⡀⠙⠻⡀⢻⡟⠛⠛⢻⡞⠼⠀⠀⠀⠀⠀⢸⡇⠈⠙⠒⠛⠀⠀⠀⠀⣿⣍⢀⣀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⠒⢶⣶⣖⣲⣿⣭⣉⡉⠉⣿⢸⣇⠘⣧⠀⠀⠀⠀⠙⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠲⣄⠈⠙⠆⠀⢇⠈⠙⢦⣿⡆⡿⣤⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣆⠀⠀⠀⠀⠀⠀⠀⣧⣇⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠦⣄⡀⠈⠁⠂⠀⣿⣷⢣⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠙⠺⠋⠀⠀⠀⠀⠀⠀⠀⡟⣹⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⣼⣿⣿⣾⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠋⡄⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡿⣿⢇⣿⣤⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⠤⠤⠤⠖⠂⠀⠀⠀⣰⣟⡇⡀⣷⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⢏⣾⣧⢟⡟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣤⣿⣿⣰⢣⣯⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠋⣱⠋⠀⣠⢯⣿⠋⢸⣿⠀⢹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣼⣿⣿⣿⢣⢾⡿⣟⣜⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⡟⢀⢜⡵⡏⠀⠀⠀⡇⣇⠈⣇⡈⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣝⣿⣿⡟⠁⠀⢳⡈⢮⠳⠙⢮⡳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣵⡿⠋⠀⣷⠀⣇⠈⣇⢸⡆⢳⢣⢹⣿⡈⠛⠒⠦⠤⣄⣀⣀⣀⣀⣀⣠⠞⠁⠀⢹⣇⣠⣷⣣⣧⢸⣷⣌⠳⡀⠀⠙⣆⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡟⠁⠀⢀⣿⠀⢿⢘⣿⠀⢻⣼⣏⣰⡿⣷⡀⠀⠀⠀⠀⠀⠈⣉⡭⠟⠁⠀⠀⠀⢀⣿⣟⢻⣻⣞⣾⣿⣟⣦⣿⣦⡀⠸⣷⡀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⡃⠀⠀⣸⣋⡔⠛⠉⠉⠉⠛⠛⠉⢩⣧⠈⠉⠓⠢⢤⣀⡴⠚⠉⠀⠀⠀⠀⠀⣰⣾⠁⢸⣷⣍⢿⣽⣗⠻⠽⣿⠈⣿⣦⣽⣿⣦⠀⣄⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⡷⠋⠀⠀⠀⠀⠀⠀⢀⣴⠋⢸⡄⠀⢀⡴⠒⡏⠀⠀⠀⠀⠀⢀⡰⠋⡽⠁⢀⡟⠀⠉⠛⠷⠿⠷⠦⠨⠷⣽⣿⣛⡛⢿⡻⣏⢆⠀⠻⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⣠⠞⣡⢀⣼⣷⠐⡏⠀⢀⡇⠀⠀⠀⣠⠖⠋⢀⡞⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠱⣌⢿⣧⠀⠹⡗⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢀⣜⡷⡟⣠⡾⠁⠸⡄⠑⠴⠋⣇⣠⠴⠚⠁⢀⡤⠋⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠻⣧⡀⢹⡀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢀⣴⣿⠿⡾⣽⣻⠁⠀⢠⣷⣶⠶⠛⠋⠁⠀⢀⡤⠊⢀⣴⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠹⣇⠀⡇⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⣠⣾⠏⢁⣼⡿⢋⣧⡤⠚⠁⢸⠀⠀⠀⢀⣤⡶⠋⠀⡰⠋⡸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⡄⠘⠀⠀⠀⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣴⣷⠷⢶⠎⣾⠷⠋⢹⠀⠀⠀⢸⣠⠶⠚⣯⡾⠁⢀⣼⠁⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢱⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⢿⠟⠀⡰⢃⡞⠀⠀⣠⠞⠲⠛⠉⢹⠀⢀⡴⠋⠀⣠⠞⠘⢆⢠⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⠰⢁⣏⡴⡞⢁⠞⢀⠴⠋⠀⠀⠀⠀⠀⢸⡶⠋⢀⡠⠞⣇⠀⠀⢸⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠠⠛⠛⣿⣿⡄⠀⠀⢠⣤⠀⠀⠀⢀⡀⣀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣦⣤⣼⣿⠇⠀⢰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢀⣽⣿⡏⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⢀⣿⣦⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⣾⣿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⣄⡀⠀⠀⣠⣾⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠲⠶⢶⣦⣤⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣧⣤⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⣿⣿⣇⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣸⣿⣿⡿⠟⠿⠷⠶⠤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣇⠀⠀⠀⠠⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠧⠼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠄⠀⠀⢠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠟⠁⠀⠈⠙⠻⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⠿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⠿⠿⢿⠉⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⡿⠋⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⣴⣿⣿⣧⡄⠀⢠⣼⡿⠛⢿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⠛⠛⠋⠀⠀⠘⠿⠁⠀⠀⠙⣿⣿⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣠⡔⠒⠀⠉⡩⠐⠀⠐⠂⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠔⠉⠁⠀⠈⡴⠁⠀⠑⢄⠀⠀⠀⠑⡄⠀⠀⠀ ⠀⠀⠀⢠⡞⡕⢠⠂⡠⠿⣧⡾⢢⠀⠀⠀⢂⠀⠀⠀⢸⡀⠀⠀ ⠀⠀⠀⡟⣸⠁⡇⢠⠁⠀⠀⠀⠀⡇⠄⢀⢈⡦⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⠹⢿⣀⣷⣜⠁⠀⠀⠀⠐⠇⠆⢸⡈⣧⡄⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⢀⠟⢹⣿⡇⠀⠀⠰⠖⣷⣤⣼⣡⡿⠀⠀⠀⠇⠀⠀ ⠀⠀⠀⢀⠎⡀⠀⢁⠄⠀⠀⠀⢿⡿⠉⠗⠁⠹⠦⠄⢰⣀⠀⠀ ⠀⠀⢀⠂⢀⠲⠀⠀⢀⣀⣀⠀⠀⠀⠀⡘⢀⠃⡉⠺⣬⠨⠄⠃ ⠀⢠⠃⡠⠁⠀⢳⢄⠀⠀⠀⠀⢀⡀⢴⠃⡘⢺⠈⠀⢸⠀⠀⠀ ⢀⠃⣴⠁⠀⠉⠑⠃⠈⢐⡾⠟⠋⢀⠂⢠⣱⣿⠢⠀⠈⡀⠀⠀ ⡌⡌⠆⠀⠔⠈⠉⠐⠲⣿⠁⠀⢠⠂⣰⣷⠀⠀⠀⠀⠀⢡⠀⠀ ⣱⡜⠀⣸⠀⢀⠂⢄⠀⠉⠳⡶⢁⠼⠟⠉⠒⠠⢀⠀⠀⠈⡄⠀ ⢹⡇⠀⢿⡔⠀⠀⠀⠁⣠⡮⠊⠀⠒⠒⠒⠒⠒⠂⠑⡄⠐⣤⠀ ⠀⡇⠀⡎⠀⠁⠢⡀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡄ ⠀⢇⡀⢇⠀⠀⠀⠈⡏⠈⠉⠉⠉⠉⠉⠒⠄⠀⠀⢠⠃⠀⢈⡇ ⠀⠘⡗⣸⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⠇⠀⢀⠆⠀⠀⣘⠇

⠀⠀⠀⣠⡴⣅⠘⠦⣠⣄⡑⢢⣄⠀⣧⡴⠋⡠⣂⡤⠖⠚⠉⣀⡀⢀⣼⣧⠄⢋⡤⡶⡇⣀⣴⣾⠀⠐⢁⣔⠁⠀⢀⠆⢰⡆⢀⠏⠄⠀ ⠀⠀⢠⣿⣣⡈⠻⣶⣠⣤⣀⣀⣀⡽⡟⠙⢯⣾⠅⠔⣶⡮⠍⢀⡴⠋⢠⢸⡏⡡⠞⠁⢹⡵⠋⣾⡤⢚⡷⢻⢀⣴⣏⢠⡳⣡⠎⠀⠀⠀ ⠀⢀⢿⣯⣈⣙⣓⣂⠠⠐⡖⠫⣽⡧⣁⡠⠂⢹⡆⣠⣃⡤⠶⣽⡄⠐⡾⠊⡟⠁⢀⡶⣾⠀⣰⢻⡔⠋⣠⣾⡿⢋⣹⣟⢵⠟⣆⠀⠀⢳ ⠀⠈⡟⠀⠈⢸⡈⠙⠲⡤⠼⢦⡈⢷⡙⡄⠀⣼⢡⣿⠕⠋⠉⢿⣿⢰⠁⣸⠁⢀⡞⣰⠃⣴⢣⡏⢀⢜⣳⡏⣠⡿⠃⢃⠈⡇⠸⡄⠀⠈ ⣦⡀⡟⢲⡒⢼⣿⡄⡘⣡⣀⣈⣙⡲⣕⢝⣠⣿⣻⠁⠀⠀⠀⢸⣾⣇⠜⠙⢦⣾⠔⠁⢼⡿⠛⠠⠿⠛⢹⠼⡟⠁⠀⢸⠀⣇⠀⢣⠀⠀ ⠳⡴⡹⣄⠱⣜⡘⢿⣷⣷⣳⠀⠀⠙⢮⠙⢿⠓⡇⠀⠀⠀⠀⠠⠻⡏⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⡇⢸⡆⡘⡄⠀ ⠀⢵⣝⢾⡷⢄⠙⣪⡟⢮⣿⣆⠀⠀⠀⢣⠘⡄⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠤⣼⡈⡆⠀⠀⡇⢸⣾⢱⠇⢀ ⠀⠈⠳⠽⢿⣾⣽⡟⠓⠀⠁⠈⠃⠀⠀⠈⢧⣧⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣴⡾⠟⠛⠉⠀⠀⠀⠸⡇⠁⠀⠀⡇⢸⢁⣸⠴⠋ ⠀⠀⠀⠀⢸⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⠤⢴⣲⡽⠟⠋⢁⣀⣠⠴⠒⢂⣀⣠⣤⣿⠀⠀⠀⠇⢾⠋⢁⠠⠒ ⠀⠀⠀⠀⠸⣏⣼⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⣁⡴⠟⣉⡤⢶⢒⣯⣽⣶⣶⣾⡿⢿⣿⡿⠻⡇⠀⠀⠃⢸⣴⠋⠄⠀ ⠀⢠⣄⣀⠀⢿⣧⣏⠉⠙⣻⡻⠭⣭⣭⣉⣢⡀⠀⠀⠀⠀⠛⠋⠁⠀⠈⢷⣶⣿⡿⠿⣿⣿⠉⡷⠀⢠⣿⡟⢀⡇⠀⠀⠀⢸⠀⠳⠀⠀ ⠀⠈⣧⠸⢭⣿⣿⣿⣶⣭⣿⣭⣿⣭⣿⣟⣛⣤⢀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡟⠁⠹⣤⣉⣁⡤⣃⢤⠿⠿⠂⢸⡇⠀⠀⠀⢸⡀⠀⡣⣣ ⠀⠀⠈⢣⡀⠈⣿⣿⣿⣿⡿⠟⠛⠿⣏⠛⣿⡿⣯⢢⡀⠀⠀⠀⠀⠀⠘⠿⣇⣠⠴⠶⠖⠛⠉⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢸⡧⢞⣱⡏ ⠀⠀⠀⠀⠹⣴⡿⣳⠻⣞⣷⣄⠀⠀⠙⢦⣬⣤⣻⠇⢳⡄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢸⢽⡿⣧⢃ ⠀⠀⠀⠀⠀⠙⣼⡏⡆⢻⡀⠉⠛⠒⠛⠛⠛⠈⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⣿⣿⣿⣖ ⠀⠀⠀⠀⠀⠀⠈⣧⠙⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⣿⣿⢻⣷⢿ ⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡏⡏⢧⢹⢿ ⠀⠀⠀⠀⠀⠀⢺⣿⡇⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠀⠀⣷⠀⣾⡌⠈ ⠀⠀⠀⠀⠀⠀⠈⠹⢻⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⡀⠀⢀⣿⠀⠈⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡄⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⡼⠤⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⡇⠀⢸⣿⠀⢀⢺⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡇⠀⠀⢸⡿⣄⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠁⢸⠁⠀⣾⣿⠀⢸⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⡇⡇⠀⣸⣿⠈⠳⣄⠀⠀⠀⠀⠀⠀⢤⣀⣀⠤⠴⠖⠉⠀⠀⠀⠀⠀⢀⡴⠋⢹⢋⣹⣉⣿⡟⣿⠀⢸⣼⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣯⢉⣉⣉⣉⣧⡟⠀⢠⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣿⠟⣛⡩⠽⡇⡏⠀⣸⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⡟⠣⡀⠑⣼⣿⠀⣰⠃⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⣿⠞⠹⠀⢸⣧⠇⠀⡿⠘⠀ ⠀⠀⠀⠀⠀⠀⢀⣇⣁⣀⣈⣲⣿⠇⣰⡏⠀⠀⠀⠀⠀⠀⠉⠲⣤⣀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⣯⣝⡒⠪⢍⣿⡀⡘⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣠⢄⣀⣀⣸⡟⢰⢿⠁⠀⠀⠀⠀⡀⠀⠀⠀⣸⠏⠙⠋⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢀⡽⠓⠤⡇⣷⡿⠀⡄⠀ ⠀⠀⠀⠀⣀⣼⣟⢮⡑⢦⣠⣿⢀⡏⡎⠀⠀⠀⠀⢠⠃⠀⠀⠀⡏⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢭⣉⣁⡒⣧⠘⢷⡄⠁⠀ ⢀⣠⣴⣾⣿⣟⣥⣴⠟⢆⣝⡇⡞⢰⠃⠀⠀⠀⠀⡸⠀⠀⠀⠸⠀⢀⡠⢾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂⠐⠛⣋⣹⡀⠀⠻⣄⠀ ⠿⠋⠉⢸⢿⣏⣉⠒⠢⡼⠛⠳⠷⣾⣤⣄⣀⣤⣤⣧⣤⣲⡶⠗⠚⠉⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⡲⠟⠋⣩⡇⠀⠀⠈⢢ ⠀⠀⠀⠘⡞⠒⠤⣉⣶⠇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢏⠀⣠⡞⠥⣸⡄⠀⠀⠀ ⠀⠀⠀⢸⠗⠒⠒⢚⡿⠀⠀⠀⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠸⡎⠀⢹⣄⡤⢷⠀⠀⠀ ⠀⠀⠀⡟⢐⡪⠭⢿⠃⠀⠀⠀⠀⠀⠀⠉⠑⠲⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⢻⣞⠉⣠⡴⠞⣧⡀⠀ ⠀⠀⢸⠋⢁⣀⣤⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⢻⡎⠜⢡⠎⠀⢱⣄ ⠀⠀⣿⠾⠕⠒⢴⠗⠭⣗⡦⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠗⠒⠒⠒⠒⠒⠒⠹⣔⠁⡠⠊⢡⠼ ⠀⠀⣏⠙⠢⣄⢸⠀⢀⣠⣜⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡊⠀⠀ ⠀⠀⡗⠛⠲⣀⣵⡼⠟⠚⣷⣲⠖⢲⣤⡀⠀⠀⠀⠀⠀⠀⢀⢄⡠⠤⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢾⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⡤⠤⠤⠤⠤⠤⢤⡠⣀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡇⣴⣶⣾⡉⣠⣤⣄⣀⡠⣖⣟⢿⣺⣿⠓⢦⠃⢇⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠃⣧⢻⢹⣝⣯⠎⠉⠙⡾⣿⡴⢹⡿⠛⠳⡀⢾⢷⣺⡶⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣸⣯⠀⠻⠘⢷⠳⣄⡰⣱⣯⠕⣋⣤⣀⠀⢹⡸⢦⠟⢡⣼⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣽⠃⢠⠤⣄⠀⣳⣌⡴⠋⠀⠈⢁⣀⡀⠀⠀⢳⠘⣷⢚⠥⡼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣽⣼⣀⣀⢤⡒⠋⠁⠈⠀⠀⠀⡴⢿⣿⣿⠙⠂⠈⡇⣷⠷⣼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⢿⣽⠰⠛⣿⣷⣦⠀⠀⠀⠞⠀⢹⣿⣿⡷⠁⠀⡇⣻⠴⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣿⡄⠠⣻⣿⠗⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢰⠁⣟⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⢻⣄⠀⠀⠀⠀⢤⡤⠤⠀⠀⠀⠀⠀⣴⠿⣦⠈⡟⠀⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠎⠸⠤⡍⡷⣤⣀⡀⠀⠀⠀⠀⠀⣠⣴⠛⠁⠀⡼⣸⠁⠀⡜⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠤⣖⣺⠉⠀⠀⠀⢰⣷⠃⠀⣨⣽⢟⣛⠿⣍⣀⣽⣍⠯⡳⣄⠗⠁⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢜⡿⠟⠉⠀⠀⠀⠀⠀⠀⠁⣀⠜⢻⣁⣼⠁⠀⠈⣇⠀⣸⢝⡏⠙⠲⢄⣀⣀⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣼⡾⣉⣙⣦⣤⡞⠉⢛⡧⣮⣞⣀⣠⡔⠋⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠯⣗⣻⠁⠀⠀⠀⠈⠉⡇⠘⣿⡏⠀⠈⣷⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⣰⠏⠻⣄⡀⢀⣀⡤⠖⠋⡟⢏⡇⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢸⠀⠀⠀⠉⠉⠀⠀⠀⠀⣧⢘⣾⣤⠴⠊⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⠎⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣾⠁⢷⡀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠉⠉⠓⠒⠒⠒⢒⡟⠁⠀⢀⠔⢡⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢣⡀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢤⣒⡒⠉⠙⠋⢀⡠⠖⠉⠀⡼⡿⣦⡤⠤⢤⡀⠀⠀⣾⠋⠉⢻⠀⠀⠀⠳⣄⠀⠈⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡸⠉⠒⢂⡿⠉⠀⠀⠀⠀⢳⢁⣿⡞⠒⣄⠘⣿⠉⠉⡆⠀⢈⡇⠀⠀⠀⠈⠢⡀⠀⠣⣀⣀⣀⣠⡄ ⠀⠀⢀⣾⢶⢲⡲⢿⣧⠀⠀⠀⠀⠀⡟⢾⣾⣦⣀⡼⢀⣿⣄⣀⡿⠉⣿⠀⠀⠀⠀⠀⠀⠈⠲⡤⢤⡬⢷⡏⠀ ⠀⠀⠀⠀⠸⠿⠇⠀⠈⠀⠀⠀⠀⣼⠁⢠⣏⠛⠳⢶⠿⢇⢹⡇⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⣇⣤⡶⡶⡼⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣸⡟⠈⠁⠘⠀⠤⣾⠇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢰⠟⡷⢣⡇⠘⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣿⠙⠢⡼⢄⡆⠉⣿⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⢸⠇⣠⠞⣉⠢⡀⢰⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⡆⠀⢀⣯⣪⣅⣤⣥⠤⣝⣿⡏⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠟⢀⡞⠀⠀⡸⡏⠁⢠⢰⠃⠀⠙⣿⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⠋⢠⡎⠀⠀⢠⡋⠊⠀⢀⠐⡠⡤⣤⣿⠀⠀⣀⣴⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⣰⠏⠀⠀⠀⢻⣀⠀⠂⢓⢀⣈⣵⡿⠃⠀⡾⠋⣹⠾⠫⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⣃⣀⣰⠋⠀⠀⠀⠀⠀⠙⢖⣰⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠛⠒⠓⠒⠒⠒⠒⠤⠬⠧⠤⠤⠤⠤⠤⠒⠒⠒⠒⠒⠚⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠄⠀⠀⠀⠀⠤⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡤⠤⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⢂⠭⠷⠎⢤⠄⣁⠐⠊⠦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⢿⡣⢧⢞⠒⢄⡁⠪⠵⠦⡢⡐⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⡧⣿⠐⠁⠀⠓⢔⡈⣱⡬⡇⠋⡟⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣇⡇⣲⡤⡀⠠⢤⣤⡭⢱⢌⠢⡜⣙⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⡇⠛⠛⠃⠀⠘⠹⠟⠀⠀⡏⣛⡝⠱⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⢂⡎⣧⠀⠀⢀⡀⠀⠀⠀⢸⠀⣏⠃⡇⡄⠃⠀⠀⠀ ⠀⠀⠀⠀⢿⡇⣇⠽⡣⡐⠂⠢⠄⠀⢀⢾⠐⣏⢜⡗⣠⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⢾⣶⣽⣿⡦⠤⠔⠊⢰⣿⣼⣷⡙⠉⠀⠀⠀⠀⠀ ⠀⠀⣠⡴⢿⣟⡳⣕⡄⠸⡨⠁⠀⠈⣁⡜⠻⢿⣭⣷⣦⠀⠀⠀⠀ ⢀⣿⠀⠀⠈⠻⣷⡘⣇⢀⣼⠿⠓⠛⠛⠒⠛⠛⠛⠓⠚⡇⠀⠀⠀ ⢸⠈⠀⠀⠀⠀⢙⡿⢻⠋⣀⠤⠤⠤⠤⢄⣀⡤⠤⠤⠴⣼⡀⠀⠀ ⢸⠀⠀⠀⣠⡾⢋⠏⣿⠓⠒⠒⠚⠛⠉⠉⠀⠀⠀⠀⠀⠘⢿⡄⠀ ⢸⢀⡴⡫⠋⠀⠗⠁⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠬⠿⢤ ⠸⠯⠊⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠁⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣦⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀ ⠸⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⡏ ⠀⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⠁ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⢀⣴⡟⠀⠀⠀⠀⢠⣟⠛⠛⠛⠛⠛⠛⣣⡀⠀⠀⠀⠀⠹⣷⡀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀ ⠀⠀⠉⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣰⣿⣿⣦⠀⠀⠀⠀⣰⣿⣿⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠛⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⣿⣿⡀⠀⠀⣴⣿⣿⣿⣿⣷⡀⠀⣼⣿⣿⣿⣿⣦⠀⠀⠀⣿⣿⡿⠿⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣶⣿⣿⡇⠀⠼⠿⠿⠿⠿⠿⠿⠷⠾⠿⠿⠿⠿⠿⠿⠷⠀⢰⣿⣿⣷⣦⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢁⣹⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⡀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⠿⠟⠛⠉⠁⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢀⣾⣿⣆⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠉⠛⠻⠿⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡿⠋⣸⣿⣿⣿⣿⡿⠃⢀⣾⣿⣿⣿⡄⠀⠿⣿⣿⣿⣿⣯⠈⢿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⠋⠀⢠⣿⣿⣿⡏⠀⠀⢀⣼⣿⣿⣿⣿⣷⡀⠀⠀⠘⣿⣿⣿⡆⠀⠙⢿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⠟⠁⠀⠀⣾⣿⣿⣿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⢿⣿⣿⣿⡀⠀⠀⠙⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⣸⣿⣿⣿⡇⠀⢠⣤⡀⠉⢻⣿⣿⣿⠋⠀⣠⣄⠀⠘⣿⣿⣿⣧⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠀⢠⣿⣿⠃⠀⢸⣿⣿⣿⠀⠈⢿⣿⣇⠀⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⢸⣿⣿⣿⠂⠀⠈⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡿⠿⠿⠿⣿⣿⡆⠀⠀⠈⢿⣿⠃⠀⠀⠰⣿⣿⠿⠿⠿⢿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢧⡀⠀⠀⠘⠉⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠈⠛⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⢣⡀⠀⠀⡰⠁⠀⠀⠈⠻⠁⠀⠀⠀⠀⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢴⡾⠋⢠⠎⠀⣰⠁⠀⠀⠀ ⣤⠁⢀⡜⢁⡔⠀⢠⣄⠀⢀⡄⠀⠰⡀⠀⠀⠉⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠻⠭⣡⣤⠔⠋⠀⠀⠁⠀⣠⠃⣀⣠⣴⠂ ⠻⣀⣏⡴⠋⠀⠀⡏⠀⣿⣾⣿⠀⠀⠳⡀⠀⠀⠀⠙⢎⡓⠦⣀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣤⣄⣀⠀⠈⠙⠒⠲⠦⠤⠴⢿⡽⠛⣠⠏⠀ ⢰⣿⡟⢁⡄⠀⠀⡇⢀⠟⠟⢻⣇⠀⢆⠹⣦⡀⠀⠀⠀⠙⢦⡀⠈⡑⣲⣶⣤⣤⣀⣀⠀⠀⠈⠉⠛⠻⠭⢿⣛⣛⣾⡿⠥⢶⡞⠋⠀⠀ ⣟⡿⢠⡞⠀⠀⠀⡇⢸⡆⡀⠀⠻⡆⠘⣆⠹⡝⠦⣄⠀⠀⠀⣘⣶⣏⡷⠶⣛⣷⣍⠉⠙⠛⠶⠶⢖⣒⣴⣶⠖⠀⣲⡶⠾⠯⠷⢤⠀⠀ ⡟⠀⢸⠇⠀⠀⠀⣷⢸⡿⢽⣦⡀⠙⡄⢻⠣⡘⢆⠀⠉⢲⡾⠿⣉⣀⠙⠶⣤⣍⣙⣶⠤⠤⣄⣀⣀⣤⣤⡶⠒⠋⣁⡤⣴⠂⠀⣼⠀⠀ ⣧⠀⢸⠀⠐⡆⠀⣿⣼⠀⣀⡈⠛⢦⡰⡈⣧⠈⠻⣧⣴⠋⠀⠀⣠⣬⣽⡿⠛⠻⣿⣿⠗⢲⡖⠚⠉⠀⢿⡀⣴⡊⠁⠀⠃⢀⡾⠁⠀⠀ ⢻⣇⠸⡀⠀⡇⠀⢻⢿⡆⣿⢿⣦⡀⢳⠙⣜⣆⠀⠈⠙⠲⢤⣾⣿⣹⣿⠹⡄⠀⠈⣿⠆⠀⡇⠀⠀⠀⠘⡟⢠⠇⠀⠀⣴⣯⣉⣉⣭⣿ ⡄⣿⡄⢣⠀⣿⠀⠈⣾⣿⡏⢈⣻⣿⡄⠀⠈⠻⣦⡀⠀⠀⠀⣿⣿⣿⣿⠀⣻⠀⠀⡟⠀⠀⣷⢀⠀⠀⡄⢳⠞⠀⢀⣞⣀⣈⣭⡭⠋⠀ ⢻⢻⣿⡌⠇⢸⣧⠀⠘⣿⣇⠘⡏⢿⣷⡀⠀⠀⠈⠳⢄⠀⠀⠀⢸⣌⣁⣠⣃⠄⠀⣀⠄⣀⣿⡎⠀⠀⢱⣼⣤⠶⣯⠴⠖⠋⠁⠀⠀⠀ ⡇⡼⣟⢿⣆⠀⣿⣷⡄⠘⡟⠆⣱⣈⣹⠇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠁⠀⠴⠾⠓⠛⠉⣿⡇⠀⠀⠀⣿⡟⠛⠒⠿⠶⠖⣶⠞⠀⠀ ⠉⠁⡟⠀⠈⠳⣼⣿⡿⢷⣼⣦⡀⠉⠁⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣸⠏⡇⠀⠀⡀⣿⡇⠀⠀⣶⡶⠛⠁⠀⠀⠀ ⠀⢠⠃⠀⠀⠀⠈⠻⣧⠈⣏⠉⠓⠒⠀⢾⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠛⡄⠀⠀⠐⠁⠀⡇⠀⢠⣧⢿⡗⣞⠋⠁⠀⠀⠀⠀⠀⠐ ⠀⠌⠀⠀⠀⠀⠀⠀⣿⠀⠘⣄⠀⠀⠀⠀⢙⡀⠀⣀⡠⠤⠒⠊⠉⠀⠀⠀⠀⣇⠀⠀⠀⢀⣴⡇⠀⣸⡿⣉⣛⣛⣲⠶⠀⠀⠀⠀⢣⠀ ⡀⠀⠀⠀⠀⠀⠀⢀⣏⠀⠀⣸⢦⡀⠀⠀⠈⢫⡉⠀⠀⠀⠀⠀⠀⢀⣠⠤⣄⣸⠀⠀⣠⠞⠁⡇⣰⣿⠁⠀⢨⣿⠀⠀⠀⠀⠀⠀⢸⠀ ⠇⠀⠀⠀⠀⠀⠀⡼⢹⠀⠀⣿⠀⠙⠳⣄⡀⠀⠱⡀⠀⢀⡴⠒⠶⠋⠀⠀⠀⡇⢀⡾⠋⠀⢰⡷⢫⡷⠖⢲⣼⣿⡆⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢰⣿⡀⠀⠀⠀⠙⠲⣄⡘⢦⡋⠀⠀⠀⠀⠀⠀⣰⣷⠋⠀⠀⠀⢸⠃⠘⢹⡀⢸⠈⢽⢿⣄⠀⠀⠀⠀⠀⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⣿⡇⠀⠀⠀⠀⠀⠀⠉⠲⢷⣦⣀⠀⣀⣤⣾⡿⠁⠀⠀⠀⠀⠘⠀⠀⠀⢳⣼⠀⢸⠀⠈⠑⠢⢤⣀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⣽⡦⠤⢤⡤⠤⣴⣦⣀⣤⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⣼⠀⠀⠀⠀⠀⠈⢩⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡏⢹⣏⠀⣰⠏⢀⣾⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡿⠀⠀⠀⠀⠀⡠⠃⠀ ⠀⠀⠀⠀⠀⠀⣴⠞⠉⢸⣣⡿⠀⣰⠏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢠⠇⠀⠀⠀⠀⣴⠁⠀⠀ ⠀⠀⠀⢀⡴⠋⠁⠀⢀⣾⡟⠀⢰⡟⢠⡟⠻⢿⣿⣿⣿⣿⣿⢿⠇⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⢠⡞⠀⠀⠀⠀⠀⢿⠀⠀⠀ ⠀⠀⢠⠏⠀⠀⠀⠀⣼⠋⠀⠀⣿⠁⣞⠀⠀⠀⠀⠉⠙⠻⠋⠀⠀⠀⣾⡤⠤⠐⠂⠀⠀⠀⠀⢀⡞⢁⣴⡟⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀ ⠀⠀⡞⠀⠀⠀⠀⡰⠁⠀⠀⠀⠻⣦⡉⠓⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀ ⠀⢰⠃⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⣀⣳⠀⠀⠀⠀⠀⠀⠀⠠⠤⠖⠒⠒⢩⡟⢁⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠈⠢⣀⣤⢴⡶⣖⡿⠟⢏⣉⣹⠛⠽⢳⡶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⢠⠏⣠⡮⠊⠁⠀⠀⢸⣿⢿⠀⠀⠀⠉⠺⢿⣆⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⣀⢀⢖⡟⡼⠋⢀⠀⠀⢀⣴⠾⠿⠿⠶⡄⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢸ ⠀⠀⠀⠱⣼⠏⢀⡄⠀⢀⠔⡱⠁⠀⠀⠀⠀⠈⠊⠐⢄⠀⠀⠀⢱⡄⡀⠀⠀⢸ ⠀⠀⠀⢈⡿⣄⠘⡇⢰⢛⣿⣷⣶⡄⠀⠀⢠⣿⣿⣿⡋⡗⢸⢁⡿⠁⠀⠐⠀⢹ ⠀⠀⠀⣼⢁⣿⡦⣱⣸⡏⠸⣿⣾⢻⡄⠀⠘⢿⣿⠃⢹⣧⡷⠻⠧⣄⣀⠀⠀⢸ ⢈⣴⠞⠋⠡⠔⢢⢈⢯⠣⠀⠉⠁⠀⢧⡄⠀⠈⠉⠀⠞⡽⠣⡇⠐⠒⠭⣙⣲⢸ ⢀⠈⠙⣲⡦⣄⣘⡌⢦⣆⠀⠀⣀⣀⣤⣤⣀⡀⠀⠀⣼⡶⢡⣃⣤⡶⠚⠋⠄⣸ ⠀⠀⠀⠀⢳⠘⣿⣿⣾⡆⢢⠀⠘⣟⠛⠛⢻⠃⠀⡠⢃⣷⡿⣿⠿⠁⠀⠀⠀⢸ ⠀⠀⣠⣤⣼⣇⠸⣿⣿⣾⡢⣕⡤⣈⠉⠉⢁⣠⣊⡔⣹⣿⢳⠇⠒⠒⠀⠀⠉⢹ ⠀⠀⣿⣿⣿⣿⡀⢿⣿⣿⣷⣿⡌⠀⠉⠉⠁⢹⣿⣿⣷⣽⡏⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⣿⢹⣿⣿⡧⠼⠿⣿⣿⣿⣷⣦⣄⡀⣠⣾⣿⣿⣿⡿⢿⣦⡀⠀⠀⠀⠀⢸ ⠀⣀⣿⡞⠋⠁⢀⣠⣴⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣈⠉⠓⢦⠀⠀⢸ ⠚⠉⢀⡈⢲⣾⣿⣿⣿⣿⡟⠙⠛⠛⠛⣻⣫⡶⢻⢿⣿⣿⣿⣿⣷⣦⠎⠙⠦⣼ ⡆⠀⠑⢄⣤⣿⣿⣿⣿⣿⠁⠀⠀⣠⣾⣷⣜⢷⠟⣼⠏⢻⣿⣿⣿⡯⠀⠀⠀⢸ ⡌⠄⠀⠈⢿⣿⣿⣿⣿⡇⢀⣴⣾⣿⣿⣿⣿⣷⡾⠃⠀⠘⣿⣯⠟⠀⠀⠀⢠⢾ ⡿⡌⢂⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣀⣀⣀⣿⣯⠀⠀⠀⣰⠋⣾ ⢻⡜⣆⠣⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⣛⣛⡛⢿⣿⣿⣿⣿⣿⡟⠠⢊⡼⢁⣼⠃ ⠀⠹⣮⣧⠡⠀⠀⠙⣿⣿⣿⣿⣿⡇⣿⣉⣁⢸⣿⣿⣿⣿⣿⡀⢠⡎⣠⡾⠁⠀ ⠀⠀⠈⠻⣦⡑⠐⠂⢸⣿⣿⣿⣿⣧⣍⣉⣁⣼⣿⣿⣿⣿⣿⡇⣠⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣦⣴⠟⠛⠛⠉⠉⠛⠻⠿⠿⠿⠏⠛⠛⢛⣿⠿⠋⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⢿⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠛⣛⣉⡛⠛⠲⢬⣉⡛⢿⡉⢳⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣍⡉⢁⡤⠔⠋⣁⠀⠀⠀⠀⠀⠀⠲⣤⠀⠹⣷⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢛⡠⠖⠉⠀⠀⠀⠀⠀⠉⠑⠢⣈⢿⣿⣎⣿⠏⠙⣻⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⡌⣿⣆⠀⠀⢠⣤⣾⣁⠖⠁⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⢚⢿⣿⠾⠿⢤⡀⠺⢷⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⢡⣿⣿⣀⣀⣤⣾⠟⠉⠀⠀⠀⠀⣠⠖⠉⠁⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠈⠳⣄⠈⢛⠿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⠷⣤⣸⠟⠉⠉⢻⣿⣶⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠄⠀⠀⠈⠫⢷⣾⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⠇⢀⣾⡏⠀⠲⣶⣿⣿⡇⠀⢀⣴⣾⣵⠎⣴⠀⠀⠀⠀⠀⠀⣠⣟⠆⠀⠀⠀⠈⢳⣆⠈⢦⠀⢻⠀⠀⣠⠀⠀⠀⠀⠀ ⠀⡼⠻⣶⣿⣿⣏⠙⠳⣾⣍⡽⢃⡾⠋⠉⣴⣯⣾⠃⠀⠀⠀⠀⢀⡼⠁⣿⠀⠀⢰⠀⠀⠀⢻⡆⣄⠧⣾⣶⣾⣿⡀⠀⠀⠀⠀ ⠀⢧⠀⢹⡟⠻⢟⠓⠀⢹⡿⢷⣿⣀⣴⣾⣿⡇⡞⠀⠀⠀⣠⣶⣁⣀⡀⠿⣆⠀⣼⡇⠀⠀⢸⡷⢬⠘⣿⡏⠀⠈⠙⢦⡀⠀⠀ ⠀⠈⣿⣶⣥⠴⠚⠱⡀⡼⠈⠙⢻⣿⣿⢿⣦⣀⣧⡎⢀⣾⣯⣍⣉⢽⠛⠿⣾⣧⣻⣷⣄⢀⣶⣧⣤⣿⡫⠀⠀⢀⣶⡖⠿⡆⠀ ⢰⣟⣿⣿⠀⢸⢢⠠⠟⠁⠀⠀⠀⣽⢿⡿⠿⣿⢿⣧⠎⠈⢹⣿⣿⠻⣦⡀⠘⡇⠉⣿⣿⣿⠿⠛⠉⢀⡽⠂⠀⠈⣿⡿⠋⠀⠀ ⢰⣿⠟⠁⠀⠘⠺⠇⠀⠀⠀⠀⢰⠇⢸⠀⠀⠃⠚⠁⠀⠀⢄⠛⠛⠈⠁⠀⠀⡇⠀⣿⣿⣋⣲⣶⡞⠯⣤⣤⡤⠶⠟⠀⠀⠀⠀ ⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⠟⣦⣬⠽⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢙⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢷⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣧⠀⢸⣿⣮⣟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣇⢸⣛⣛⣆⠀⠀⠀⣀⡠⠴⠒⢋⠝⠀⣿⡏⣸⣻⣿⠿⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⢿⣾⣿⡿⣿⣿⡿⣏⠀⠀⠠⠔⠁⠀⢸⢉⣷⡟⠿⣏⣿⡇⠉⠉⠙⠛⠶⠶⣤⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⢸⣿⣿⣿⣿⡟⠀⢸⠀⠀⠀⠀⠀⢀⠇⠘⠋⠁⠀⡟⢀⠃⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⣀⡴⢋⡟⠀⡀⠀⢸⣿⡏⢹⣿⣧⢄⣈⣀⠀⠀⠀⢠⡞⠀⣀⠀⠀⢀⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⢠⣶⣎⠁⠀⠈⠀⠀⡇⠀⠈⢿⡇⢘⣿⡟⠲⣤⣍⣃⣀⣰⣛⣉⠁⠀⠀⠀⣸⠁⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃ ⠀⠀⠀⠀⠀⠙⢆⠁⠀⠀⠀⠀⢁⡇⠀⠸⡇⠀⣿⣧⣦⣌⠉⠀⠓⠒⠀⠤⠍⠉⠉⣉⡏⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⣸⠁⠀⠀⣿⠀⠉⠸⣇⠉⢳⡀⢀⡴⠖⠶⠒⠒⠋⠉⠀⠐⠃⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⡏⠀⠀⠀⠸⣷⢾⣆⣹⣧⣤⠳⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠚⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⡀⠀⢻⣆⡿⢿⡁⣹⠀⠋⠈⠉⢒⡶⡀⠀⠀⠀⠠⠤⣤⠤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠇⢼⣿⣿⡄⢀⢀⣀⣶⣰⠘⠾⠥⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠶⠒⠶⠦⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠉⠉⠙⠒⠶⣤⡤⠤⠴⢶⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⠞⠀⠀⠀⠀⠀⠀⣠⣴⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⡆⠀⠀⠀⠀⠈⠉⣻⡗⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠃⢠⠎⠀⠀⠀⠀⠀⡴⠞⠛⢉⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢿⣦⣄⠀⠀⠀⣰⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡞⠁⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣀⣈⡙⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠁⠀⠀⣙⣶⠀⠀⣰⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡞⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⣠⢾⣷⣿⢿⣿⣿⣷⣌⠛⢷⣤⣄⣀⣀⣀⣰⣿⣫⣴⣦⣴⣾⡛⠉⢀⣠⠞⠋⠀⠀⡠⠆⠀⠀ ⠀⠀⢠⡟⠀⠀⠀⢻⡀⠀⠀⠀⠀⣠⠞⢁⣾⠟⠁⣼⣿⣿⣿⡿⣧⠀⠀⠀⠉⠉⠉⢉⣿⣿⣿⣿⣿⣯⠹⡆⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⢃⣀⣺⣤⣤⠿⠶⢶⡇⠀⢻⠀⠸⠃⠀⢠⣿⣿⣿⣿⡇⠘⠂⠀⠀⠀⠀⠀⡿⠉⣿⣿⣿⣿⠹⠀⡇⢹⠷⢤⣄⠀⠀⠀⠊⠀⠀ ⠀⠀⡟⠸⠻⣅⠀⠉⣳⠶⣼⠀⠀⠘⡆⠀⢀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⡇⢸⡀⣰⠏⠀⠀⠀⣀⠀⠀ ⠀⢸⠃⠀⠀⠈⠳⣄⠻⢤⡎⠀⠀⠀⢷⣀⠘⢦⣀⠈⠛⠛⣫⠜⠁⠀⠀⠀⠀⠀⠀⠀⢦⣘⢿⣿⡵⠃⠀⡇⢸⡷⠃⠀⠀⠀⢀⠀⠀⠀ ⠀⡾⠀⠀⠀⠀⠀⠙⢦⣠⡇⠀⠀⠀⢸⠉⠳⣷⣌⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠉⠉⠁⠐⠞⢲⠇⢸⡇⠀⠀⠀⠀⠈⠁⠀⠀ ⢠⠇⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⣼⢸⢷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣸⠃⠀⠀⠀⠘⠀⠀⠀⠀ ⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⣰⣇⠘⠞⠁⠀⠀⠀⠀⢠⣤⣤⣤⢤⣤⣤⣤⣤⡄⠀⠀⠀⣠⣶⠋⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠉⠻⠦⣄⡀⠀⠀⠀⠈⣿⣻⣿⡀⡈⢿⣿⡟⠀⣀⡴⠟⠁⠘⢷⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣀⣀⡤⣆⠉⡟⠒⠦⠤⠼⠿⠿⢴⣷⠾⠿⢾⠟⠉⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠉⠀⣠⡿⠾⣇⠀⠀⠀⠀⠀⠀⢀⣿⣶⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠈⢳⣄⠀⠀⠀⠀⠈⠙⣦⠙⡛⢦⣄⡀⠀⠀⢠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣯⡀⠀⠀⠀⠀⠀⠀⠙⣏⠉⠉⠉⠉⠉⠙⣧⣀⢘⠋⠛⡷⠀⠈⢧⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣿⠏⠙⢦⡀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢀⡾⠛⠁⠀⢀⣾⡇⠀⠀⠈⢧⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠀⢠⡟⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠹⣄⣠⠞⠀⠀⠀⠀⣼⠁⢿⠀⠀⡄⠈⢷⡀⠀⠹⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⠤⠚⠋⠁⠀⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣿⠀⠘⣇⠀⠹⡄⠈⢷⡀⠀⠘⣆⠀⠀⠀⠀⢀ ⡴⠒⠉⠀⠀⠀⠀⠀⠀⡤⣸⠃⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢻⡄⠀⢻⡄⠈⢷⡄⠀⠈⢧⡀⠀⡠⠃

⠁⡰⠊⠁⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣶⡿⠚⠁⠀⢀⣧⣼⣿⣴⣶⡶⢋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠊⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠙⠛⠛⠛⠛⠛⣋⣽⠿⠋⠁⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠖⠋⠁⠀⠀⠀⢴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠋⢀⣀⣤⡤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⢀⡀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡧⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠒⢀⣀⡤⠶⠷⠤⠤⢤⣴⣾⣋⡤⠞⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⡀⠀⠀⠀⠀⠐⢦⣤⣄⣉⠒⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠁⠀⣀⣤⠤⠶⠛⠛⠉⠁⣠⣾⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠳⣄⠀⠀⠀⠀⢹⣯⡉⠉⠉⠑⠒⠿⠷⠦⣄⡀⠀⠀⠀⠀⠀⠀⣄⠈⢯⠉⠀⠀⠀⠀⠀⣀⣴⢞⣟⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣇⠀⠀⠀⠀⠹⣿⣶⣶⣥⣄⣶⣤⣀⡀⠙⢷⢦⡀⠀⠳⣄⠘⢇⠈⢣⠀⣀⣠⣶⠾⣫⣷⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢻⣻⣿⣿⠉⠉⠛⠛⠻⢷⣦⣹⣾⢦⡀⠘⣆⠈⣷⣌⢿⣞⡯⠔⢛⣭⠞⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀ ⠀⠀⢀⡆⠀⣷⠄⠀⠀⠀⠈⢧⠳⡽⡆⠀⠀⢀⡴⢚⡿⠛⢾⣿⣵⡀⠹⡆⠘⡞⣾⣧⣤⣶⠯⠗⠚⠉⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⢸⡀⢰⡀⠀⠀⠘⡆⢹⣿⡀⢠⠏⣠⢻⣦⣤⣬⡿⣯⠻⡄⢳⠀⢹⢿⣏⠉⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀ ⠀⢀⡟⠀⠀⢸⠇⠀⢷⡀⠀⠀⠹⡀⠻⣷⣏⡼⠃⡞⢀⣿⣿⡀⠈⠀⠹⣼⡄⢈⣿⢼⠀⠀⠀⠀⠀⠀⣰⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀ ⠀⣼⠃⠀⡀⢸⠀⡄⠘⣷⡀⠀⠀⢧⢀⣿⣟⠀⠸⠀⣼⣿⣷⣿⣆⠀⠀⢹⡇⢸⢻⡜⠆⠀⠀⠀⠀⣸⠃⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣆⠀⠀⠀ ⣼⠃⠀⠀⡇⢘⡴⠁⠀⢹⣷⡀⠀⢘⣿⠻⣿⡀⠀⢸⣿⠻⣇⣻⢿⣿⢦⣨⣿⡸⠀⡇⠀⠀⠀⠀⠀⠉⠀⠀⠘⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀ ⡟⠀⠀⠀⡇⢸⡇⠀⠀⢸⣿⣷⡀⡾⠹⠀⣷⢧⠀⢸⡟⠀⠈⠁⢼⣭⣭⣽⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣤⡀⠀⠀⠀⠀⠀⢿⣆⠀ ⠇⠀⠀⠀⡇⣾⣇⠀⠀⢸⢱⣷⢿⡅⠀⢣⣿⣞⣇⣼⣷⣶⠶⠖⠒⠋⠉⠀⡞⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣅⠀⠀⠀⠀⠈⠏⢦ ⠀⠀⠀⢸⠃⣿⣿⠀⠀⢸⠘⣿⡀⢻⡄⠈⢿⡘⢿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠸⡌ ⠀⠀⠀⣿⢴⠛⣿⡇⠀⢸⠀⢻⡇⠀⣿⡀⠈⡇⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⢠⠏⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣳ ⡀⠀⢠⢻⢸⡀⢹⣷⠀⠸⡄⢸⣿⠀⣿⢻⡎⢷⣤⣀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⣰⣧⠖⠋⠈⠙⢦⣄⠀⣠⣄⡀⢀⣠⣤⠀⢠⣤⡀⠀⠉ ⠻⢤⣜⢸⡇⠻⡄⢹⣇⠀⡇⠀⢿⢢⠘⣷⡽⣞⡗⠻⢵⣶⣭⣷⣄⣀⡀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡤⠞⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠳⣍⣛⣿⢟⣾⣯⣤⣬⣿⡞⣊⣥ ⠀⠀⠉⠻⢷⣄⠳⡄⢻⣆⢱⠀⠈⢿⣆⢹⡿⣾⣿⡄⠠⠤⢤⣤⣴⡖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⢳⠟⠓⣽⣧⢸⣿⠊⠉⠢ ⠀⠀⠀⠀⠀⠉⠳⢿⣦⢻⣾⣇⠀⠸⣿⡄⢻⡾⣿⣷⡀⠀⠀⠉⠉⠻⠿⢭⣉⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠼⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠽⣿⣆⠀⠙⣿⡄⢳⡀⠉⠻⣷⢤⣀⣀⠀⠀⠀⠀⢀⣉⡭⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⢜⣿⣄⣓⠤⠀⠈⠐⠒⠻⠟⠳⠶⣾⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡿⠃⠀⠀⠀⠀⣠⠴⠋⣹⣿⣷⡶⠦⣶⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣽⡖⣦⣤⣤⣄⣀⣀⡀⠀⠭⣽⡒⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢡⡿⠁⠀⠀⣠⡴⠟⣑⣶⣾⣿⣿⣿⣿⣿⣿⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣤⣄⣀⣀⣉⣉⡀⠀⠈⠙⠾⣿⣦⡀⠀⠀⠀⠀⢀⣠⠖⠉⠀⠀⣿⡇⡀⣠⠾⢋⣰⣾⡿⠿⢿⡿⠟⣉⣉⠙⠻⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣈⠉⠛⠿⣯⣟⠲⠶⠤⣹⣿⠳⣤⣤⠞⠉⠀⠀⠀⠀⠀⠀⠙⠿⣧⡶⠛⠁⠀⢀⡴⢋⣠⣾⠟⠉⠁⠚⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⢄⣀⡈⠻⢟⠛⠛⠛⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡤⠞⣋⣴⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⡄⠀⠀⠀⠀⠀⠀⢸⡇⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡛⠛⠛⠦⣿⡖⠒⠒⠒⠛⠛⠛⠛⠛⠉⠉⠛⠛⠛⠒⠒⠚⠛⠒⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⢦⡀⠀⠀⠀⠀⠈⡇⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠛⢶⣤⣀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠛⢏⠛⢆⡀⠀⠀⠀⢻⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠻⣮⣍⡓⠲⠶⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡨⢧⡀⠙⢦⠀⠀⢸⡀⠀⠈⡇⠀⠀⠀⠀⠀⣰⠇⡇⢀⡤⢖⡿⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣤⣉⡛⠷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠩⠛⢀⡼⠫⡀⠀⠱⣄⠀⣇⠀⠀⡇⠀⢠⡔⣀⡼⣁⡼⠛⢁⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠟⠿⢶⣬⣛⡛⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠒⠂⠐⢒⠂⠤⠄⣀⡀⢀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠚⠁⠀⠀⠀⠀⠀⠀⠉⠂⢄⠀⠈⠀⡰⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠘⢦⣀⠀⠀⠀ ⠀⠀⠀⢀⡴⢡⠃⠀⠀⣀⡴⢾⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣄⠀⠀⢈⡝⠀⠀ ⠀⠀⢀⠎⢠⠃⠀⠀⠀⠀⡠⣋⣝⡻⣄⠀⠀⠀⠀⢀⡾⠋⢁⣙⠇⢀⡞⠀⠀⠀ ⠀⢀⠇⠀⢢⠀⠀⠀⡠⢪⡿⢻⣿⣿⣦⠙⠐⠒⠒⣿⣾⣿⣗⠄⡖⠁⠀⠀⠁⠀ ⠀⡸⣤⠗⠶⣓⡚⠀⡇⠈⠀⢾⣿⣿⠈⠀⠀⠀⠘⠹⣿⣿⠙⠀⠟⢒⠄⠀⠈⠀ ⠀⠇⠀⠑⢄⠣⡇⠀⢰⣄⡢⣈⣛⡫⠂⠀⠀⠀⠀⠠⣻⡯⢂⠈⢸⠋⠀⠀⡉⠀ ⠸⠀⠀⠀⠈⠱⡀⠀⢸⠸⡍⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢁⠇⡼⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠙⢤⡯⣕⠁⠀⠀⢰⣶⡖⢶⣶⡖⠀⣠⠴⣅⢠⠃⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠈⣃⠤⣍⣲⠂⠤⠿⠯⡧⢟⡲⠉⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠑⢄⠀⠀⠀⠻⡛⣤⣀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⣾⠧⡀⠀⠀⠀⠣⡀⠀⠉⣵⠌⠉⡝⠀⠱⡀⢣⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡠⠎⠁⡎⠀⠘⢦⠀⠀⠀⠑⣄⠞⠀⠀⣸⢹⠀⠄⠱⡀⠱⡀⠀⠀⠀ ⡠⠔⠈⠁⠀⢀⡸⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢇⠘⡄⠱⡀⠘⠄⠀⡐

⣿⣿⣿⠛⠀⣀⠤⠒⠀⠀⠀⣀⣐⢀⡀⠂⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⠇⠁ ⣿⠟⠃⠠⣩⡤⣒⠛⠯⠭⠷⠭⠎⡵⠽⢈⡦⠤⡀⠈⡇⠹⣿⣿⣿⣿⣿⠃⠐⠀ ⡵⢶⣶⡿⠋⢇⠤⠀⠂⠤⢀⡀⠀⠀⠁⠢⠀⣉⠾⢊⠇⣀⢘⢿⣿⣟⠋⠀⠀⠀ ⠀⠀⣿⠃⡌⢰⠁⠒⠤⠄⣀⠀⠀⠉⢩⡭⣄⠖⡨⠙⢢⣈⠲⡀⣻⠣⢄⡀⠀⠀ ⡇⠀⣿⠐⠀⠘⠀⠀⠀⠀⠔⢈⠏⢉⡽⢻⠏⠳⡈⠃⠻⠘⣵⣜⡈⠆⠀⠈⢢⠀ ⣿⡀⣿⡇⠀⢂⠀⠀⠀⠀⠀⠀⢰⣿⠝⠋⠀⠀⠐⢸⢰⡀⡏⠏⣧⣼⡄⠀⢸⠀ ⣿⡇⣿⠀⠀⢸⠀⠋⠤⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡃⡎⡳⡐⠸⢿⡽⢿⣄⢱⠀ ⣿⡇⣿⢰⠀⢰⡡⡟⣔⣦⣸⠂⠀⠀⠀⠀⠀⠀⣑⠝⢰⠰⡫⠆⠕⡈⢣⣟⣼⡀ ⠋⡇⡏⢆⡄⢺⣷⡼⠿⠝⠁⠀⠀⠀⡠⣰⠞⠣⠀⠀⡌⠃⠐⠭⡙⣨⡺⣮⠄⠑ ⠀⡇⡇⢸⣧⠜⡪⢟⡒⠕⣒⠢⠄⡀⠻⡁⠀⠀⠄⢠⡇⠸⣈⠋⠔⢧⢼⠈⡀⡜ ⠀⠇⠹⡪⣿⣸⣌⠢⣝⠍⠀⠀⠀⠈⠦⣬⡍⣈⣀⣾⡿⠃⢳⡾⠧⣶⠝⢀⠎⢐ ⠀⠁⢄⡹⢿⡟⢰⣤⣸⠉⠉⠛⣶⣀⠀⠘⢺⡘⠛⢭⣶⣆⣰⣑⡶⠝⠉⠍⡅⢸ ⠀⡀⠀⠉⣹⠡⣽⠨⠋⠀⠄⠀⠘⣧⠙⠢⣀⠀⠀⠁⠒⢶⣏⡷⠻⣍⡙⡆⡙⣆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣰⣶⣊⣥⣀⣤⣖⣿⡗⢰⢱⢰⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣼⠙⠗⠿⡀⣼⣗⢜⡁⠑⡼⡻⣃⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢣⡏⠐⢂⡬⠢⠊⠀⣡⣤⢀⢱⢱⡟⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⢿⠹⢳⣦⠀⠀⠎⣸⣿⠆⢸⢸⠽⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⢧⠘⠋⠀⣀⡀⠀⠀⢀⣼⡘⡄⢃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠔⠋⠲⡵⠦⣄⣀⣀⠀⡴⣉⠀⡷⠁⢸⠀⠀⠀⠀ ⠀⠀⠀⡶⠗⠈⠀⠀⠘⣁⠔⣏⡏⠉⣎⢹⠳⠛⠄⣀⡎⠀⠀⠀⠀ ⠀⠀⠸⠀⠀⠀⠀⠀⠀⡸⡿⠖⠛⠚⢠⠻⣿⠒⢮⡴⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡰⢧⠋⠢⡀⠤⠚⢹⢿⠀⣈⡀⠀⠀⠀⠀⠀ ⢀⡴⠁⠀⠀⠀⢠⠞⠁⣼⠀⠀⠀⠀⠀⠸⡞⢫⠀⢣⠀⠀⠀⠀⠀ ⠀⠀⢀⡩⠭⠝⠁⡠⠊⣾⣀⣀⠀⠀⢠⠼⡇⠀⢢⠀⠱⡀⠀⠀⠀ ⠀⠀⢀⣋⠀⡔⠁⠀⠀⣇⣷⠒⡌⡆⠙⣀⡴⠀⠀⠑⢄⠑⠤⣤⡄ ⠀⠀⠉⠽⠏⠑⠀⠀⡸⢈⡟⠧⠵⢻⡎⠁⢧⠀⠀⠀⠀⢉⣩⣭⡆ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⢸⢇⣠⠀⢸⠃⠀⢸⠀⠀⠀⠀⠋⠛⠃⠉ ⠀⠀⠀⠀⠀⠀⡰⠁⠀⣎⠐⠁⢅⣸⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡜⡱⠀⢸⠛⠉⠛⠑⡿⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠎⡰⠁⢠⠋⠁⠀⠰⣲⡇⣠⢴⡠⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⠥⡜⡁⠀⠀⠑⠶⠞⠋⠁⠀⠀⠀⢀⣸⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠐⣺⠟⠉⢀⣾⠃⠀⠀⠀⠀⡾⠃⠀⢠⠞⣾⠁⢀⡇⠀⢹⡀⠀⠀⠀⠀⠀⣸⠈⣖⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡞⣆⠀⠀⠀⠀⠀⠀⠈⠈⠐⠂⣀⠀⠀⠀⠀⢄ ⢀⡾⠁⣠⠞⡟⡏⠀⠀⠀⠀⢰⠃⠀⢀⣏⣼⢿⠀⢸⡇⠀⠀⣷⠀⣇⠀⠀⠀⢸⣦⠈⢾⣆⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢳⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠂⠀⠄ ⠋⣠⡾⠃⡸⠀⠁⠀⠀⠀⢠⡏⠀⢀⠞⡼⠋⢻⡇⢸⡇⠀⠀⠘⡆⠹⡀⠀⠀⠘⡾⡀⠀⢿⣦⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠈⣧⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀ ⠞⡝⠁⢀⡇⠀⠀⠀⠠⢄⣸⠃⠀⡼⡼⠁⠀⠈⣇⠈⠀⠀⠀⠀⢱⠀⢧⠀⠀⠀⢿⢧⠀⠀⠙⢧⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠸⡆⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡼⠁⠀⡾⠀⠀⠀⠀⠀⠀⢹⠿⣲⣿⡁⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⢧⠘⣇⠀⠀⠈⣞⣆⠀⠀⠀⠳⡀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⢹⠲⡀⠈⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⢠⠇⠀⠀⠀⠀⠀⠀⡼⠀⣹⢷⣍⠳⣤⡀⠈⣿⡆⠀⠀⠀⠀⠈⣆⠘⡄⠀⠀⢻⡽⡄⠀⠀⠀⠹⣄⠀⠀⠀⠀⢿⣗⣄⠀⠀⠀⠀⢧⠙⣄⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠀⠈⠀⠀⠀⠀⣼⠀⠀⡇⢠⣇⣀⡙⢦⡀⠙⢧⣹⡇⠀⠀⠀⠀⠀⢹⡆⣵⡀⠀⠸⣿⣱⡄⠀⠀⠀⠘⣦⠀⠀⠀⠀⢿⣎⢦⠀⠀⠀⠈⠀⠉⢦⠀⠀⠈⠳⢤⡀⠀⠀⢢⡀⠀ ⡀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣿⡼⣿⣾⣭⣙⠻⣦⡘⣿⣷⠀⠀⠀⠀⠀⠀⢻⠸⣷⠀⠀⢻⣱⣿⣆⠀⠀⠀⠈⢳⡀⠀⠀⠈⢟⡎⠳⡀⠀⠀⠀⠀⠈⢳⣦⣀⠀⠀⠉⠓⠦⢤⣬⣤ ⡇⠀⠀⠀⠀⠀⠀⢸⣇⠀⢹⡇⣿⣿⠋⠛⣿⣮⣻⣽⣯⠳⠀⠀⠀⠀⠀⠘⡄⡟⢦⠀⠈⡇⠻⣿⢧⡀⠀⠀⠀⢳⡄⠀⠀⠘⠘⣆⠙⢆⠀⠀⠀⠀⠀⢻⣟⠷⠦⣤⡤⠤⠤⠤⠖ ⡇⠀⠀⠀⠀⠀⠀⢸⡿⣆⠸⡇⣿⡏⠀⠀⣿⢹⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣧⡇⠈⠧⡀⢹⠀⠻⣇⠻⣄⠀⠀⠀⠹⡄⠀⠀⠀⠘⣆⠈⢳⡀⠀⠀⠀⠀⢹⡛⠦⣌⡙⢦⡀⠀⢢ ⣧⠀⠀⠀⠀⠀⠀⢸⡇⠘⣄⢿⣿⡁⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⠃⠀⠀⠹⣌⢇⠀⠹⣆⠈⢦⡀⠠⡀⠹⣆⠀⢀⠀⠘⣆⠀⢱⣄⠀⠀⠀⠀⢳⡀⠈⠙⠶⣷⣄⠈ ⢻⠀⠀⠀⠀⠀⠀⠀⣿⡄⠘⣎⣿⡇⠀⠀⡏⢹⣿⣿⣿⣿⣇⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠈⢿⡄⠀⠘⣆⠀⠱⡀⠱⣄⠘⢦⠈⢧⠀⠘⡄⠀⢻⢦⠀⣄⠀⠀⢳⡀⠀⠀⠘⣟⠧ ⠀⠇⠀⠀⠀⠀⢠⡆⢹⣧⠀⢸⠿⣿⣄⠀⣿⠈⢉⣿⡟⣿⡿⠀⠀⠀⢀⡞⠀⠀⠀⠀⣀⢤⣠⣿⣖⣯⡼⠷⠶⠿⢶⠛⣷⡬⢧⡘⣦⠀⠈⠀⠀⢳⣤⠈⢧⠀⠈⢷⡄⠀⠀⠘⢦ ⠀⢀⠀⠀⠀⠀⡞⡸⢹⠟⡆⠸⡆⠙⢧⡀⠻⣷⣘⣉⣳⣻⢿⠀⠀⠀⠀⠀⠀⠀⣴⡾⠟⠛⠛⠛⠻⠒⠒⠒⠒⠒⠒⢷⡾⣿⢾⣯⢿⣦⣤⣠⠀⠈⢯⣧⡀⢳⡀⠈⢿⣄⡀⠀⠀ ⠀⠀⡄⠀⠀⣼⣹⢃⡎⠀⣿⡄⣷⠀⠀⠙⠲⢤⣍⣙⠛⢉⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠄⠀⠀⠀⠀⠀⠀⠙⣞⡄⠙⢦⢹⣆⠉⣧⠀⠈⣾⣷⡄⠱⡄⠘⣿⣷⣄⠀ ⠀⠀⠁⠀⢰⣿⡇⣼⠁⠀⢻⢻⡜⡆⠀⠀⠀⠀⠀⣨⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢏⣀⣀⣀⣤⣤⣤⣤⣀⣀⣀⠈⢷⠀⠈⢻⣿⣆⠘⡆⠀⢹⣷⠙⣦⠹⣆⠙⣿⡛⠛ ⠀⠀⡆⢠⡿⣿⣸⣷⢀⡞⡞⠈⢻⣵⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠋⠛⠛⠻⠾⠦⢬⣉⢿⣇⠀⠈⣿⡿⣦⢱⡀⠀⢿⡄⢹⠷⣜⣦⡙⣿⡀ ⠀⢰⣧⠏⠀⡏⣷⠃⡼⠁⣷⠀⠀⠹⣧⡀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡍⠀⢻⠃⠈⣿⣳⠀⠘⡇⣸⠀⠈⣮⢿⣌⠙ ⣠⠞⠁⠀⠀⣿⢃⣾⠇⠀⢿⡆⠀⠀⠈⠳⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⢠⠿⢀⣾⠏⢻⡇⠀⢹⣿⣿⣿⡇⠈⢯⠓ ⠁⠀⠀⠀⣰⣿⢫⣿⠀⠀⠸⣷⡀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⢲⡏⢀⣞⡟⠀⠈⣿⡀⢸⣿⡿⠋⠀⠀⠈⢧ ⠦⣄⣠⠞⠁⠟⢸⡏⠀⠀⠀⡿⣷⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣠⠏⡼⠀⠀⢠⣿⣇⢸⡏⠛⠲⠶⠶⠒⠉ ⠀⠀⠈⠙⢲⡦⣼⡁⠀⠀⠀⡇⠝⣷⡀⠀⠀⠙⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⣾⠃⡼⠁⠀⣠⣾⣸⢻⡸⣷⠀⠀⠀⣀⡤⠾ ⠀⠀⠀⠀⠘⠁⠀⠙⢳⣤⣀⡃⠀⢘⢷⣄⠀⠀⠀⠈⠳⢭⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⣽⢃⡜⠁⢀⡞⣽⣇⢧⣿⣇⣿⢺⠞⠋⠀⠀⠀ ⠤⠤⣤⣀⠀⠀⠀⠀⠸⠦⣌⣙⣲⣾⠀⠹⣦⠀⠀⠀⠀⠀⠻⠭⣝⣒⡢⠭⠍⢒⣒⣦⡄⡀⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⠏⠀⢠⠏⣰⣽⣟⡎⠸⣽⡧⢿⡀⠀⠀⠀⠀ ⡆⠀⠀⠉⠳⢦⣤⣤⣀⣀⣀⣩⣿⡜⠀⠀⠈⢦⡀⠀⠀⠀⠀⣀⠀⠈⠉⠉⠑⠒⠛⠛⠛⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⣰⠃⣜⣿⢯⣾⠀⠀⡌⠀⠀⢳⡀⠀⠀⠠ ⢳⡀⠀⠀⠀⠸⣤⣿⠀⠀⢸⣧⣿⠃⠀⠀⠀⠈⢳⡀⠀⠀⠀⠈⠳⠦⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⣿⡇⠀⣰⠇⢸⣾⣿⠏⠉⣧⡀⠀⠀⠀⠈⢿⣳⣄⠀ ⠀⢱⡀⠀⠀⠀⣿⣿⠀⠀⢸⠽⠋⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⢰⣿⠀⢠⠏⣰⢏⡾⡏⣰⣄⢹⡿⣦⣀⠀⠀⢈⢏⠛⠦ ⠀⠀⠹⣄⠀⣀⣿⠿⠚⠋⠙⠛⠲⣄⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡾⠛⠁⠀⠀⠀⣴⣿⡏⠀⢚⡴⠓⠋⠀⣷⣿⣟⣆⠹⣌⠻⠓⢤⣈⢾⣧⠀ ⠀⠀⢀⣿⡟⠉⠀⠀⠀⠀⠀⠀⠈⢘⣇⠀⠀⠀⠀⠀⠀⠘⢷⣤⣄⣀⣤⣤⣤⣤⣶⣶⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣰⠃⣿⡇⣤⡾⠁⠀⠀⠀⢿⣿⢻⡏⠳⣜⣿⡲⢶⣬⣍⣛⣧ ⠂⢀⣞⡟⠀⠀⠀⠀⠀⠀⣠⣤⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⢀⡏⠀⢻⣇⡿⠁⠀⠀⠀⠀⠈⣿⠀⠹⣆⠀⠉⠙⠒⠂⠈⠉⠉ ⢷⠟⠀⠀⠀⠀⢀⣠⠶⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡿⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠘⣦⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠾⠀⠀⣠⡴⠚⠋⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⠀⠀⠀⠨⡿⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⣦⣠⡤⠤⠴⠲⠶⠤⡀ ⣀⡤⢞⠁⠀⠀⠀⠀⠀⠀⢙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⣞⣿⣯⡤⠶⡓⠚⠛⠛⠓⠀⠀

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