Cat Toro Emojis & Text

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠈⠻⣮⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠋⠀⠀⠀⠀⠙⣿⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣠⣤⣤⣀⡀⠀⠀⣀⣴⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⠀⠀ ⢀⣤⣾⡿⠟⠛⠛⢿⣿⣶⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣦⣀⣀⣤⣶⣿⡿⠿⢿⣿⡀⠀ ⣿⣿⠏⠀⢰⡆⠀⠀⠉⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡿⠟⠋⠁⠀⠀⢸⣿⠇⠀ ⣿⡟⠀⣀⠈⣀⡀⠒⠃⠀⠙⣿⡆⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀ ⣿⡇⠀⠛⢠⡋⢙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀ ⣿⣧⠀⠀⠀⠓⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⢸⣧⣤⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀ ⣿⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠻⣷⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀ ⠈⠛⠻⠿⢿⣿⣷⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣷⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣷⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣷⣶⣶⣤⣤⣀⡀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣷⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢸⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣤⣄⣀⡀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣻⣷⣶⣾⣿⣿⡿⢯⣛⣛⡋⠁⠀⠀⠉⠙⠛⠛⠿⣿⣿⡷⣶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠸⠛⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⣿⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⣿⠀⢿⠀⣴⠟⠷⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⢀⣤⡟⠀⢸⣿⠃⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⣸⡿⠿⠟⢿⡏⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣼⡇⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⡋⠉⣩⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣰⠟⠋⠁⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢠⡞⣱⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢀⣿⢁⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣠⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⢸⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣶⣾⡇⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⢸⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣠⢰⢻⡟⢃⡿⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠁⢿⠹⣿⣄⠀⠀⠀⢀⠀⠀⠀⠀⢺⠏⣿⣿⠼⠁⠈⠰⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠃⠀⠈⢻⣷⣄⠈⠁⣿⣿⡇⠀⠀⠈⣧⠀⠀⠀⠘⣠⠟⠁⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⣴⠀⠀⣿⡿⠀⠸⠋⢸⣿⣧⡐⣦⣸⡆⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⣀⣴⣿⡆⢀⣿⠃⠀⠀⠀⣸⠟⢹⣷⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣤⣾⡏⠛⠻⠿⣿⣿⣿⠁⣼⠇⠀⠀⠀⠀⠁⠀⢸⣿⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀ ⠲⢾⣿⣿⣿⣿⣇⢀⣠⣴⣿⡿⢁⣼⣿⣀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀ ⠀⠀⠉⠙⠛⠻⣿⣷⣶⣿⣷⠾⣿⣵⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⡀⢿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⡟⣴⠀⠀⠉⠉⠁⢿⡇⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⣴⠀⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠿⣿⣿⢠⠇⠀⠀⠀⢸⣿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⢸⣿⡄⠀⠀⣼⣿⣇⢹⡟⢿⡇⠀⠀ ⠀⠀⠀⠀⣿⠃⣠⣿⣿⣿⠀⠀⠀⠀⠀⢻⡈⢿⣆⠀⢳⡀⠀⢠⠀⠀⠀⠀⠀⢸⣿⣦⠀⣸⠿⣷⡀⠀⣿⣿⢿⣾⣿⠸⠇⠀⠀ ⠀⠀⠀⠀⠋⣰⣿⣿⣿⣿⡀⢰⡀⠀⠀⠀⠀⠈⢻⣆⣼⣷⣄⠈⢷⡀⠀⠀⠀⢸⣿⢿⣶⠟⠀⠙⣷⣼⣿⣿⡄⠻⣿⣧⡀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⡿⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠻⣷⣼⣿⣦⡀⠀⣼⠇⠸⠋⠀⠀⠀⠈⠻⣿⣿⣷⡀⠈⠻⣷⡀⠀ ⠀⠀⠀⠀⠀⣿⣼⡿⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠻⣷⡙⣿⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⢠⣀⠘⣷⡀ ⠀⠀⠀⠀⠀⠀⣿⠇⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢻⣷⣾⡇ ⠀⠀⠀⠀⠀⠀⣿⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢈⣿⡹⣷ ⠀⠀⠀⠀⠀⠀⠈⠀⠻⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠸⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢸⠸⠀⡠⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⢠⣞⣀⡿⠀⠀⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡖⠁⠀⠀⠀⢸⠈⢈⡇⠀⢀⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠩⢠⡴⠀⠀⠀⠀⠀⠈⡶⠉⠀⠀⡸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠎⢠⣇⠏⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠄⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠏⠀⢸⣿⣴⠀⠀⠀⠀⠀⠀⣆⣀⢾⢟⠴⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⠀⠠⣄⠸⢹⣦⠀⠀⡄⠀⠀⢋⡟⠀⠀⠁⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡾⠁⢠⠀⣿⠃⠘⢹⣦⢠⣼⠀⠀⠉⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀ ⠀⠀⢀⣴⠫⠤⣶⣿⢀⡏⠀⠀⠘⢸⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀ ⠐⠿⢿⣿⣤⣴⣿⣣⢾⡄⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀ ⠀⠀⠀⣨⣟⡍⠉⠚⠹⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⢀⡀⣾⡇⠀⠀ ⠀⠀⢠⠟⣹⣧⠃⠀⠀⢿⢻⡀⢄⠀⠀⠀⠀⠐⣦⡀⣸⣆⠀⣾⣧⣯⢻⠀⠀ ⠀⠀⠘⣰⣿⣿⡄⡆⠀⠀⠀⠳⣼⢦⡘⣄⠀⠀⡟⡷⠃⠘⢶⣿⡎⠻⣆⠀⠀ ⠀⠀⠀⡟⡿⢿⡿⠀⠀⠀⠀⠀⠙⠀⠻⢯⢷⣼⠁⠁⠀⠀⠀⠙⢿⡄⡈⢆⠀ ⠀⠀⠀⠀⡇⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⠀⠀⠀⠀⠀⡇⢹⢿⡀ ⠀⠀⠀⠀⠁⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠇⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤ ⠀⠀⠀⣤⣶⣦⣄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋ ⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⠀⠀⠀⠙⢿⣟⣷⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀ ⠀⠀⠀⠈⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀ ⠀⠀⠀⢰⣿⣿⡿⠃⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⠁⠀⠀⠀⠀ ⣠⣶⣾⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣄⠀⠀⠀⠀ ⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀ ⠈⢻⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠯⠀⠀⠀⠀⠀

∧,,,∧ ( ̳• · • ̳) / づ♡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠻⣥⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⡿⠻⣆⠙⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠁⠀⠘⣆⡔⢶⣆⠉⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⡿⢿⡀⠉⠀⠞⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡄⠀⡇⠘⣧⣀⣀⣀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠁⢀⣠⠞⣹⢿⠻⡟⢿⣿⣯⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠶⠒⠉⠁⣴⠇⢸⡇⡟⡷⢬⡙⠎⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠇⢀⣠⣄⡀⠚⠁⠀⠈⠀⠀⣷⠀⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣽⣿⣶⠋⢉⡿⠇⠀⠀⠀⠀⠀⣰⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⣿⠇⠀⣠⣥⣤⡀⠀⠀⠀⢀⡟⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⢀⣾⡟⠉⢹⡇⠀⠀⠀⢸⠁⡿⠙⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⣇⣾⡟⠀⠸⡏⣄⡀⠀⠀⢹⢀⡇⢀⢘⢿⣮⡙⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⡀⣧⠰⣿⣶⣄⠀⠀⠀⠘⣎⠳⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣆⠹⣿⡐⣾⣷⣹⣆⠀⠀⠀⠘⢷⣄⣻⣿⣿⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣦⠽⣇⣹⣟⢿⠙⠁⠀⠀⠀⣤⠉⠻⣿⣿⣿⣿⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⡟⠂⣿⢹⡿⣼⠇⠀⠀⣀⠀⣷⡀⠀⠈⠻⣿⣿⣿⣷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢻⠀⠉⢸⡇⠈⣀⣠⣾⠇⠀⠻⣿⣦⣤⣴⣿⠿⣿⡿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⡀⠀⢸⠁⣰⠛⣽⡧⠖⠻⢿⡆⠈⠉⠉⠀⠀⢻⣷⠹⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⡇⠀⢸⢰⡏⢰⡟⠀⣀⣀⡼⠃⠀⢀⡆⠀⠀⠘⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⣶⣷⣶⣾⣿⣧⣾⣤⣄⣀⣀⣤⣤⣶⡿⠀⠀⠀⢠⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣟⡛⠛⠛⠉⠉⠉⠉⢉⣭⣽⡿⠿⠿⠿⠛⠛⠛⠓⠲⠦⠄⣼⢻⡇⠀ ⠀⠀⠀⠀⠀⠀⠘⢉⣼⣿⣿⠿⠛⠛⠁⠀⠀⣠⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⣸⡇⠀ ⠀⠀⠀⠀⠀⢀⣴⠿⠛⠁⢀⣀⣀⣀⣀⣀⣄⡀⠀⠀⠀⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⣰⣿⠁⠀ ⠀⠀⠀⢀⣴⣟⣥⣶⣾⣿⣿⣿⣿⣿⣿⣭⣤⣤⣤⣀⣀⡀⠈⠛⠶⢶⣶⣶⣶⣾⣿⣿⣿⠟⠁⠀⠀ ⠀⢀⣴⡿⠟⠋⡽⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠿⠿⠿⠿⠟⠛⠉⠁⠀⠀⠀⠀ ⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

／＞　 フ | 　_　_| ／` ミ＿xノ /　　　　 | /　 ヽ　　 ﾉ へ ╱|、 ♡ ╱|、 │　　|　|　| ૮ - ՛ ) (˚ˎ 。7 (` - 7 ／￣|　　 |　|　| / ⁻ ៸| |、˜〵 |、⁻〵 (￣ヽ＿_ヽ_)__) 乀 (ˍ, ل ل じしˍ,)ノ じしˍ,)ノ ＼二)

＿＿ 　　　　　🌸＞　　フ This is Jane 　　　　　| 　_　 _ l She is sad because she has cancer 　 　　　／` ミ＿xノ Hit the like to save her 　　 　 /　　　 　 | 　　　 /　 ヽ　　 ﾉ 　 　 │　　|　|　| 　／￣|　　 |　|　| 　| (￣ヽ＿_ヽ_)__) 　＼二つ

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⣼⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣭⣭⣤⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣤⣤⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣮⣍⣉⣉⣀⣀⠀⠀⠀ ⠀⠀⣠⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⣴⣿⣿⣿⣿⣿⣯⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠉⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⡟⠸⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀ ⠀⠘⢿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⡏⠁⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀

╱|、 (•˕ • 7 |、⁻〵ノ) じしˍ,)ノ

⠀ ⠀ (\__/) (•ㅅ•) ＿ノヽ ノ＼＿ `/　`/ ⌒Ｙ⌒ Ｙ ヽ ( 　(三ヽ人　 /　 | |　ﾉ⌒＼ ￣￣ヽ ノ ヽ＿＿＿＞､＿_／ ｜( 王 ﾉ〈 /ﾐ`ー―彡\ / ╰ ╯ \ \

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠘⢉⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⢀⡇⣇⡰⠲⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⢰⣾⡦⣾⠁⠀⢸⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢴⠞⠁⠀⠀⠀⠘⡆⣀⣿⠀⠀⡼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡱⣶⡾⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⢰⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢸⡧⠏⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⡴⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⢸⣿⣾⠀⠀⠀⠀⠀⠀⣜⣀⣾⠿⣷⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡿⠀⢠⣄⠸⢹⣷⠀⠀⢆⠀⠀⣏⡿⠉⠀⠈⢹⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠟⠀⣤⠀⣿⠃⠞⢹⣶⣰⣼⠀⠀⠉⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀ ⠀⠀⠀⣀⡾⠧⢴⣾⣿⢠⠏⠀⠀⠘⢹⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀ ⠐⠺⢿⣿⣧⣠⣴⣿⣥⣿⡄⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀ ⠀⠀⠀⠀⣽⣿⡍⠙⠛⢻⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⣀⢰⣿⡀⠀ ⠀⠀⠀⣸⠟⣿⣰⠃⠀⠈⣿⢷⠀⣀⠀⠀⠀⠀⠐⣦⡀⢸⣧⠀⢸⣿⣼⡟⡇⠀ ⠀⠀⠀⠋⣼⣿⣿⢀⡄⠀⠈⠈⢧⣼⣦⡸⣄⠀⠀⣼⢷⡞⠙⢷⣾⣿⠹⣿⡁⠀ ⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠛⠌⠳⣿⢷⣤⡇⠈⠀⠀⠀⠙⢿⣆⠈⠻⡄ ⠀⠀⠀⠀⢹⢁⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢧⡀⠀⠀⠀⠀⠀⢹⠙⣷⣧ ⠀⠀⠀⠀⠘⠸⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⢦⡙⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⢱⣠⠲⣌⢱⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢸⠙⣇⠀⠈⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠃⠈⡠⢿⣷⣾⢶⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠐⠒⠉⣠⠃⡸⠘⣿⢮⣁⣻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣠⠴⣦⠀⠁⠀⠀⠀⣿⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⢀⣋⣀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⢿⡏⣰⡿⠉⡽⠀⠀⠀⡇⡾⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠘⣷⣿⠀⢸⡖⣦⡀⠀⠃⠃⢀⢹⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⢺⣇⢽⣿⢦⡀⠀⠈⢦⣙⣿⣷⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⢻⣈⣟⣏⠁⠀⠀⢀⠈⠻⣿⣿⣿⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣏⠘⠉⡟⠞⠀⢀⡄⢸⣆⡀⠈⣿⣿⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⡇⣰⢶⣟⡥⢤⡝⠛⠛⠛⠉⣿⡿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡀⢀⣧⡇⡾⠁⢀⡠⠇⠀⣰⠀⠀⢸⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣾⣿⣷⣷⣤⣤⣤⣶⣾⡇⠀⠀⢸⣿⠀ ⠀⠀⠀⠀⠀⠠⢞⣿⣿⣿⠤⠄⠀⠀⣠⠴⠚⠛⠉⠉⠉⠉⠉⠉⠉⢡⠋⣿⠀ ⠀⠀⠀⠀⢀⣴⠿⠋⢉⣀⣀⣀⣀⣀⠁⠀⠠⢄⠀⠀⠀⠀⠀⠀⢀⣄⣼⡏⠀ ⠀⠀⢀⣴⣿⣵⣾⣿⠿⠿⠿⠿⠷⠶⣦⣤⣤⣀⣙⣳⣶⣶⣶⣿⣿⡿⠋⠀⠀ ⢀⡴⠛⠉⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⠟⠁⠀⠀⠀⠹⣿⣿⣿⣿⣿⠟⠁⠀⠀⠹⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢼⣿⠀⢿⣿⣿⣿⣿⠀⣾⣷⠀⠀⢿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣷⡀⠀⠀⠈⠋⢀⣿⣿⣿⣿⣿⡀⠙⠋⠀⢀⣾⣿⣿⠀⠀⠀⠀⠀ ⢀⣀⣀⣀⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣾⣿⣷⣦⣤⣴⣿⣿⣿⣿⣤⠤⢤⣤⡄ ⠈⠉⠉⢉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀ ⠐⠚⠋⠉⢀⣬⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣀⡀⠈⠀⠈⠛ ⠀⠀⠴⠚⠉⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠉⠛⠢⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀ ⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣷⡀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣴⢿⣿⣧⠀ ⣿⣿⣿⣿⣿⡿⠛⣩⠍⠀⠀⠀⠐⠉⢠⣿⣿⡇ ⣿⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿ ⢹⣿⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡏ ⠀⠻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Elliot <3 ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣦⣤⣄⡀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠟⠙⠀⠀⠀⠈⢻⡆⠀⣴⠞⠋⠉⠉⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡛⠂⠀⠀⠀⠀⠀⠈⣿⣾⠋⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣽⠁⠀⠀⠀⠀⠀⠀⠀⣽⢇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⠄⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢨⡟⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡆⠀⠀⢀⣀⣀⡀⢸⣇⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣘⡟⠰⠛⠛⠉⠙⠉⠈⠃⠀⠀⠀⠀⠀⠀⢰⣾⡟⠚⢶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⢀⡬⢹⡇⠀⠀⠀⠀ ⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠚⢷⣼⡷⠀⠀⠀⠀ ⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⠀⠀⠘⢿⣷⠀⠀⠀ ⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⢹⣧⠀⠀ ⣿⢣⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣡⠀⠀⠀⠻⣧⠀ ⣿⡾⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣤⠀⠀⠀⠀⠀⠀⠀⣼⡇⠃⠀⠀⠀⠀⢹⣇ ⠹⣧⡀⠀⠀⠰⣦⣸⣶⠄⠀⠀⠸⡿⠿⠇⠀⠀⠀⠀⠀⠀⢢⡿⠅⠀⠀⠀⠀⠀⠀⣿ ⠀⠈⠻⣦⣒⠸⠛⠻⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⣄⠀⠀⣾ ⠀⠀⠀⠈⢙⣷⢶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠁⠀⠀⠀⠀⠀⣼⢏⣠⣾⠟ ⠀⠀⠀⢀⣾⠃⠀⠀⠉⠛⠛⠻⠶⠶⠶⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⣰⡾⠛⠛⠉⠀⠀ ⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⢲⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⡾⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣧⡀⠀⠀⣡⣿⠛⠻⠶⣾⠀⠀⠀⠀⠀⠀⠈⢾⡟⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⢿⣦⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣀⣦⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⠉⠉⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠉⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠛⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣦⣤⣤⣄⡀⠀⢀⣠⣾⣿⠿⠋⠀⠀⠀⠀⠀⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠞⣿⠟⠋⠉⠉⠙⣻⠿⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⡼⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⢠⡞⠁⠀⠀⠀⢀⡴⠋⠀⢀⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢠⠏⠀⠀⠀⠀⣰⠏⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡥⠤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⠀⣠⡏⠀⠀⠀⠀⣼⠁⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣄⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⠋⠀⠀⠀⠀⢸⣧⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣾⡿⠿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳ ⠀⠀⠀⠀⠀⠀⢀⣾⠿⠛⢿⣿⣷⣄⡀⣿⠃⠀⠈⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣤⣦⣼⣿⠀⠀⠀⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⡿⠋⠉⠉⠁⠀⠀⠀⠀⠉⢯⡙⠻⣿⣿⣷⣤⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠃⢀⡤⠖⠋⣉⣉⣉⣉⠉⠉⠒⠦⣄⠀⠀⠀⢀⡟⡿⢿⣿⣟⣻⣮⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⠋⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠙⢦⣄⠉⠻⢿⣿⣷⣦⡀⠀⠈⠙⠛⠛⠋⠀⢰⠟⡇⠀⠀⠈⠻⡿⠛⠁⠀⠀⠀⠈⠳⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⣴⠟⣫⣿⣿⣄⠀⠀⠀⠀⡶⢌⡙⠶⣤⡈⠛⠿⣿⣷⣦⣀⠀⠀⠀⠀⡇⠀⢻⣄⠀⠀⣠⢷⠀⠀⠀⠀⠀⡶⠀⠘⡆⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⢸⣟⢸⣿⣿⣿⣿⠀⠀⠀⠀⡇⠀⠈⠛⠦⣝⡳⢤⣈⠛⠻⣿⣷⣦⣀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠛⠦⠤⠤⠚⠁⠀⠀⢳⠀⠀⠀⠈⠛⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠈⢿⣞⣿⣿⣿⠏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⠳⢬⣛⠦⠀⠙⢻⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⣿⠉⢻⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⣠⣄⠀⠀⢰⠶⠒⠒⢧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⡟⢿⣷⣦⣴⣶⣶⣶⣶⣤⣔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⣤⠀⠀⠿⠿⠁⢀⡿⠀⠀⠀⡄⠈⠙⡷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⡇⠀⣿⠙⣿⣿⣉⠉⠙⠿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠙⠷⢤⣀⣠⠴⠛⠁⠀⠀⠀⠇⠀⠀⡇⢸⡏⢹⡷⢦⣄⡀⠀⠀⠀⣿⡀⢸⡇⢸⡇⠀⡟⠀⢸⠀⢹⡷⢦⣄⣘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠢⣤⡀⠀⠀⠀⠀⠀⠀⣠⠾⣿⣿⡷⣤⣀⡇⠸⡇⢸⡇⢸⠉⠙⠳⢦⣄⡻⢿⣾⣧⣸⣧⠀⡇⠀⢸⠀⢸⡇⢤⣈⠙⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⣿⣷⣌⡉⠛⠲⢶⣶⠖⠛⠛⢶⣄⡉⠛⠿⣽⣿⣶⣧⣸⡇⢸⠀⠀⠀⠀⠈⠙⠲⢮⣝⠻⣿⣷⣷⣄⣸⠀⢸⡇⠀⠈⠁⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠻⢿⣷⣶⣤⣉⡻⢶⣄⣀⠈⠙⠳⢦⣈⡉⠻⢿⣿⣷⣾⣦⡀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢭⣛⠿⣿⣷⣼⡇⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣶⣽⣻⡦⠀⠀⠈⠙⠷⣦⣌⡙⠻⢿⣟⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢯⣻⡇⠀⠀⠀⠀⠀⢸⣿⠀⣀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢀⡏⠙⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣶⣤⣤⣤⣀⣈⠛⠷⣤⣈⡛⠷⢽⡻⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⢤⣀⠀⠀⢸⣿⡀⠈⠳⢤⣀⣀⣰⠃⠈⠛⠶⠶⠿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⠛⠉⠙⠛⠛⠻⢷⣦⣄⣩⣿⠶⠖⠛⠛⠛⠛⠛⠛⠿⢷⣶⣦⣄⠀⠀⠀⠀⠉⢻⣶⣿⣿⠇⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠀⠀⠀⠀⠀⣠⠖⠂⠀⠀⠀⠈⠙⠿⣿⣦⡄⠀⠀⣸⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣰⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣄⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠙⢿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠦⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠄⠙⡿⠿⠦⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⡶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠨⡀⠐⢕⠤⠤⡀⠀⠀⠀⠀⠀⠀ ⠀⢠⣧⠀⠈⣎⡑⢼⣦⡀⠀⠀⠀⠀ ⠀⠈⠒⣄⢀⡌⡝⡎⢻⣿⣷⠤⠀⠀ ⠀⠀⢀⡟⠚⣷⠾⣮⣺⠜⢷⣒⡀⠀ ⠠⢤⣾⡿⠁⡀⢑⢏⠹⢰⡀⣌⠀⠀ ⠀⢐⡾⣲⡾⣡⣿⡮⢰⣼⣧⣸⣿⠂ ⠀⠸⣻⣡⢎⣿⣿⣧⣾⣏⣩⡲⠿⡁ ⠀⠀⠉⠁⠘⠘⠏⠻⠻⣿⢿⡩⡗⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢁⡿⠀⠰⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣴⡯⠖⣓⣶⣶⡶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣴⣯⡾⣻⠽⡾⠽⠛⠚⠷⠯⠥⠤⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣢⣾⢿⣶⠿⣻⠿⠿⢋⣁⣠⠤⣶⢶⡆⠀⣀⣀⣀⣀⣀⣐⡻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠟⠛⠉⠪⠟⣩⠖⠋⢀⡴⢚⣭⠾⠟⠋⡹⣾⠀⠀⢀⣠⠤⠤⠬⠉⠛⠿⣷⡽⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⣿⢝⣯⠆⣩⠖⢀⣤⢞⣁⣄⣴⣫⡴⠛⠁⠀⡀⣼⠀⣿⢠⡴⠚⠋⠉⠭⠿⣷⣦⡤⢬⣝⣲⣌⡙⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣷⣿⣿⣿⣿⠋⠀⢀⢀⣶⣷⣿⠀⣿⠀⠀⠀⠀⠀⠀⠐⠚⠻⣿⣶⣮⣛⢯⡙⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⣿⠋⠀⡆⣾⣾⣿⣿⠿⢂⣿⣄⠀⠀⠀⠀⠀⠀⠐⠢⢤⣉⢳⣍⠲⣮⣳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠿⣷⡀⢸⣿⣿⣿⠙⠏⠁⣸⣿⣿⣭⣉⡁⠀⠀⠀⠀⠀⠀⠘⣿⣿⡷⣌⣿⡟⢿⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡿⡏⢡⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡹⣷⣼⣿⡟⠋⠀⠀⣴⣿⣿⣦⣍⣙⣓⡦⠄⠀⠈⠙⠲⢦⣻⣿⡅⠘⣾⣿⡄⠹⡳⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢹⠀⠀⠞⢭⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⠳⢼⣧⣄⣠⣾⣿⣿⣿⡻⢿⣭⡉⠁⠀⠀⠀⠀⠀⠀⠙⢿⢻⡄⠈⢻⣿⠀⠉⠹⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⡇⡆⠀⢀⣶⣾⣳⠏⠉⢹⡿⣿⣿⣟⡿⠿⢿⣿⣿⣿⣿⣧⠘⠒⠮⣿⣿⣿⣿⣿⣿⣿⣦⡬⠉⠀⠀⠀⢦⠀⠰⡀⠀⠈⠃⠓⠀⠈⣿⡀⠀⠀⢹⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣾⡧⣔⠾⡏⠙⠁⠀⣠⣿⢀⡎⠉⠈⠻⠭⠤⠤⣌⡻⣿⡿⡀⠈⠙⠻⠿⠿⣯⣅⠉⠉⣝⠛⢦⡘⣶⡀⠀⢣⠀⠙⢦⡀⠘⢇⣆⠀⣿⡇⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⣀⡠⠶⠿⠟⣃⣀⡀⠀⠀⠈⢓⣶⣾⣟⡡⠞⠀⠀⠀⠠⠴⠶⠿⠷⢿⡼⣿⣗⠀⠀⠀⠀⠀⠀⠈⠛⢆⠈⢧⡀⠁⠘⣿⡄⢢⠇⠀⠈⢧⠀⠸⣼⡄⣿⠇⠀⠀⢧⢸ ⠀⣠⠴⠾⣿⡛⠛⠛⠁⠀⠀⠀⠙⠲⠈⠉⠀⠀⠀⠀⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠷⣄⠘⣷⣄⡀⡄⠀⢀⡀⠀⢳⡄⠀⠀⠳⠀⡏⠀⠀⠸⡄⠀⢿⣧⣿⠀⠀⠀⡀⣼ ⣾⣿⢶⣦⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣤⣶⣶⣒⠢⢤⠀⠀⠈⠁⠉⠛⠿⣎⡛⢦⣀⠈⣿⣴⣾⣿⡞⡄⠀⠀⢹⡀⠀⠀⣿⠀⣾⣿⠇⠀⠀⠀⡇⢸ ⠘⣿⣿⡾⡇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡐⠲⢦⣦⢤⣤⣤⡶⠛⠉⠉⠀⠀⠀⠀⢀⣠⣤⣀⣤⠴⠂⠀⠀⠁⠀⢹⣧⣿⡿⢸⠇⢻⣿⣆⠀⠀⢷⣀⠀⣿⣷⠟⠉⠀⠀⠀⢸⡇⡄ ⠀⠈⠳⢭⡗⠒⣛⣻⣽⠿⢿⣯⣷⣾⣿⣿⣿⣶⣬⡉⣉⠈⠑⠒⠉⠙⠻⠯⠉⣩⡟⢁⣾⠏⠀⣾⣷⣤⣄⣀⡀⢨⡿⣿⡇⣸⠀⠘⡿⢹⣆⠀⣸⣿⣷⡿⠁⠀⡀⠀⢸⡀⣾⣧⠀ ⠀⠀⠀⠀⠈⠻⠿⣿⢿⡷⣌⣣⡉⠛⢿⣿⣿⣿⣿⣿⣧⡓⢄⠀⠀⠀⠀⠀⢰⡿⠷⣟⠿⠋⠀⢹⣿⡇⠀⠁⠙⣾⢧⠙⠙⠁⠀⠐⠁⠘⠹⣄⣿⠃⠹⣿⡀⠀⡇⠀⡿⣇⡿⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠻⠊⠙⠃⠀⠀⠹⣿⣿⡿⡏⠀⣿⣌⠳⡄⠀⢀⡴⠋⠈⠉⠉⡙⠲⣤⢸⡟⣿⠀⠀⠠⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠈⠃⣸⡇⣼⠇⣿⡇⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⢳⣿⣿⣿⡆⢳⠀⡎⠀⠀⠀⠀⢀⣉⠳⣬⣿⠇⠃⠀⠀⢠⠆⢰⢊⡇⠀⠀⠀⠀⠀⠀⢲⠀⢰⡆⠀⠀⣽⣿⡟⠀⢸⡇⡞⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⡇⠈⣿⢟⣼⣇⡏⠀⠀⠔⣺⡭⠽⣿⡛⠛⠿⡏⠀⣆⠀⠀⣼⠀⣼⣼⣷⡆⠀⠀⣶⡆⢠⡿⣠⣿⡇⠀⢰⣿⠏⣴⢂⠋⡼⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢻⢿⡁⣼⢣⣿⡿⠀⢀⢀⡴⠋⠀⠀⠀⠀⠙⣶⣦⡅⠀⣿⡄⢠⣿⣾⢿⠿⣿⡇⠀⠘⣾⣇⣼⣷⠟⡼⠀⣰⡿⠋⢠⠏⢦⣾⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⢾⢄⣹⣧⡿⡽⠁⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠟⠉⣧⡾⡽⣠⣿⢛⠇⠏⠰⣻⠃⣼⣽⣿⡿⡿⠁⣴⣡⡾⠋⠀⢠⣞⣴⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣼⣿⣿⡟⠁⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠰⠟⣻⣿⢋⠀⠀⣴⣷⣾⠟⡿⠋⠀⣥⠾⠛⡋⠀⠀⢠⣾⣿⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠽⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢁⡌⠀⢰⣿⠟⠁⠀⠀⠀⠀⡀⠀⣰⠃⠀⣴⡿⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢀⣴⠏⠀⠀⢸⡋⠀⡀⠀⣀⠖⠋⣠⣾⢃⣠⡾⠟⢡⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣀⣴⡿⠃⠀⠀⠀⠀⢁⡾⠁⢈⣁⣴⣾⣿⣿⠟⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⣿⡿⠁⠀⢀⣀⣤⣼⢟⣡⣶⠿⠟⠋⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⣿⣿⣃⣴⣶⣿⠿⣿⣿⡿⠋⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⣿⠛⠉⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠟⠁⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣠⣠⣶⣿⣷⣿⣿⣿⣷⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣾⣿⢿⣻⡽⣞⣳⡽⠚⠉⠉⠙⠛⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⢻⣟⣧⢿⣻⢿⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⣿⡿⠞⠛⠚⠫⣟⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠈⢻⡽⣆⠀⠀⣴⣷⡄⠀⠀⠀⠘⣿⡆⠀⠀⣀⣠⣤⡄ ⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⣿⠿⢷⡀⠘⠛⠃⠀⠠⠀⠀⣿⣅⣴⡶⠟⠋⢹⣿ ⠀⠀⢻⣿⡀⠀⠀⠀⢾⣿⡆⠀⢿⣴⣴⡇⠀⠀⠀⠀⠀⠀⢠⡟⠋⠁⠀⠀⠀⢸⣿ ⠀⠀⠈⢿⣇⠀⠀⠀⠈⠉⠥⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⣾⡏ ⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⠁⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⠀⠀⠀⠀⣹⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠐⢧⡀⠀⢀⣾⠟⠀⠀ ⠀⠀⢀⣰⣾⠟⠉⠀⠀⠉⠉⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⡟⠋⠀⠀⠀ ⣠⣶⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣿⡆⠀⠀⠀⠀ ⢻⣧⣄⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀ ⠀⠉⠛⠿⣷⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣦⡀⠀⢀⣀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀

⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠒⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢧⠿⣶⢤⣀⠀⠀⠀⠀⠀⡿⠀⢠⣆⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣷⠈⠻⣦⠑⢲⣤⣤⣠⡇⠀⣿⣿⡆⠈⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⡦⠀⠙⢳⡾⠃⠀⣸⣷⣄⢹⣿⠃⠀⢸⣿⡘⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢱⢀⠔⠋⠀⣠⣾⠃⠀⠉⠺⠃⠀⠀⠀⠘⡇⠀⠙⡦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣏⠞⢹⢠⠋⠉⠁⠀⡀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢼⣦⣀⠀⠀⠀ ⠀⠀⠀⢨⡏⠀⡞⢸⡔⢐⡆⠀⠈⠲⣤⠀⠀⠀⠀⠀⢹⡄⠀⠀⠹⣿⠓⠀⠀ ⠀⠀⠀⢘⣷⣤⠇⢸⠁⢒⡶⠦⡶⢤⡈⠑⠀⠀⠀⠀⠘⡇⠀⠀⠀⢸⡄⠀⠈ ⠀⠀⠀⠘⣿⠏⠀⠀⣳⠟⠛⠋⠀⠀⣿⠓⠶⢤⠀⠀⠀⠙⠀⠀⠀⠈⡅⠀⠀ ⠀⠀⠀⡠⠃⠀⠀⢀⡳⠴⣄⣵⡆⢶⣿⡄⠀⣸⠀⠀⠀⠀⡀⠀⠀⠀⡇⠀⠀ ⠀⠀⡔⢁⡄⠀⠀⠁⠀⠀⠀⠀⠀⠈⠛⠻⢲⣿⠀⠀⠀⠀⠆⠀⠀⢀⠃⠀⠀ ⣠⠊⡠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢿⡇⠀⠀⠀⢰⠀⠀⠀⢸⠁⠀⠀ ⢷⣾⣿⡿⠁⠀⠀⠀⠀⡠⠎⣀⡴⠏⠁⠀⠀⠇⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠿⣁⣀⣀⣤⣴⠞⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠙⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⡏⡠⢄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⠛⢻⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢘⢫⠖⠀⠀⠀⠸⠋⠀⠆⠀⠀⠀ ⠀⠀⠀⠀⢀⡔⢸⣯⠀⠀⠀⠀⣄⣴⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⡼⠀⣤⢛⢦⠀⠆⠀⠿⠉⠀⡆⠀⠀⠀ ⠀⠀⣀⠼⢥⣾⠎⠀⠘⣷⠏⠀⠀⠀⠀⠸⡀⠀⠀ ⠈⠙⠻⣶⠾⡷⠇⠀⠀⠘⠀⠀⠀⠄⠀⠀⣱⡀⠀ ⠀⠀⡰⣻⡑⠀⠟⡇⠄⢀⠀⠐⣄⢸⡀⣾⣿⡇⠀ ⠀⠀⢰⣿⣷⠆⠀⠘⢮⢮⣦⣀⠟⠃⠙⢿⡙⢆⠀ ⠀⠀⠈⣏⣏⠀⠀⠀⠀⠀⠉⠙⠆⠀⠀⠀⠋⢷⡄ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠼⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠸⡏⣇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢠⡇⢹⣀⠞⠛⢷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⣶⣿⣥⡬⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠏⠀⠀⠀⠀⠀⢻⠈⠁⢹⡇⠀⠀⢰⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠛⣻⠅⠀⠀⠀⠀⠀⠀⢸⣆⡴⠟⠃⠀⠀⡾⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⡴⢿⡿⠏⠀⠀⠀⠀⠀⠀⠀⢈⣿⠁⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⣸⣧⠽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡆⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⣿⣿⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣠⣿⡿⣦⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠘⢻⢿⣇⡀⠀⠀⢀⠀⠀⠀⣸⠷⣿⣯⠇⠘⠽⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠀⠀⢶⣄⠈⠇⣿⣷⠀⠀⠘⣇⠀⠀⠘⣶⠿⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⢰⡀⢸⣿⠃⠲⠃⢻⣶⡄⣦⣿⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣟⣁⣠⣴⣿⡇⢸⡏⠀⠀⠀⠾⢹⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀ ⣀⣀⣤⣴⣿⣟⠀⠉⣩⣿⡿⢡⡟⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀ ⠀⠉⠛⠿⢿⣿⣶⣿⣿⣯⣶⣿⣿⠇⠀⠀⠀⠀⠀⠘⠳⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣫⠍⠙⠚⠋⣿⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⣠⠀⣷⣿⡄⠀⠀ ⠀⠀⠀⠀⣼⡿⣿⡏⣸⠃⠀⠀⢸⡿⣿⡀⢀⠀⠀⠀⠀⠀⠀⠀⢦⣄⠀⠀⣿⡄⠀⢰⣿⣆⣿⠻⣧⠀⠀ ⠀⠀⠀⢰⡟⢠⣿⣿⡯⠀⠀⠀⠀⠳⠸⣧⠈⣷⡀⠰⡄⠀⠀⠀⠈⣿⣇⣰⠟⣷⡄⣸⣿⠻⣿⣇⠛⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⢠⡇⠀⠀⠀⠀⠙⣷⣿⢿⣆⢹⣆⠀⠀⢰⡇⣿⠏⠀⠈⢿⣿⣿⡆⠙⢿⣦⠀⠀ ⠀⠀⠀⠀⢸⣏⣿⢿⣿⡿⠀⠀⠀⠀⠀⠀⠈⠛⠄⠻⢿⡟⢷⣤⣾⠁⠁⠀⠀⠀⠀⠉⠻⣿⡄⡈⠹⣧⠀ ⠀⠀⠀⠀⠈⢸⡏⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⡗⠹⣷⣼⡆ ⠀⠀⠀⠀⠀⢸⡃⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠛⠀⣿⡿⣷ ⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⠇⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⢻⣿⡟⠙⠻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠋⠹⣿⣿⢳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢀⡾⠀⠀⠘⣿⣷⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⣿⠏⠀⠀⠹⡆⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣸⣇⠀⠀⠀⠸⠹⣿⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⣰⣮⣿⠟⠹⠀⠀⠀⢀⣿⣸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠋⢿⣄⠀⠀⠀⠀⠈⢿⡿⣷⣤⣄⣀⣀⣀⣤⣴⠿⡿⠋⠀⠀⠀⠀⠀⣼⠋⢻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠁⣿⡿⠀⠀⠀⠛⠦⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⢹⣿⡈⠑⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡤⢀⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠢⣽⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⣿⣴⣿⡟⠀⠀⠀⠀⣀⡠⠄⠀⣀⠀⠀⠀⣼⣿⡀⠀⠀⢀⡀⠀⠤⣀⠀⠀⠀⠀⠹⣿⣦⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡟⠀⠀⠀⣴⣾⠟⠺⠾⠿⢿⡞⣆⢰⣿⣿⣧⢀⡆⣿⠿⠷⠶⠺⢿⣦⡀⠀⠀⠹⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠀⠀⠀⣼⣿⡷⢶⠶⣤⣀⠈⣧⢻⣿⣿⣿⣿⣿⢸⠃⢀⣤⠴⣶⠶⣿⣷⡀⠀⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣿⠿⢋⣾⠃⠀⠀⣀⢸⣯⣄⠛⠦⣍⣸⣦⣸⣿⣿⣿⣿⣿⣿⣼⣤⣏⣩⡶⠟⢠⣼⣿⢃⡀⠀⠀⢿⡍⠻⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⣰⡿⠋⢠⣾⡏⣀⣴⣾⠁⢀⣠⣿⣒⣒⣠⣀⣛⣿⣿⣿⣿⣿⣿⣿⣿⣟⢂⣤⣄⣒⣻⣧⡀⠀⢻⣶⣄⠘⣿⣄⠈⢻⣷⡀⠀⠀ ⠀⠀⢰⡿⠁⣠⣿⣿⠿⢋⣿⡇⠀⠀⠀⠠⠞⠛⠉⠹⣿⠏⠈⢿⣿⣿⣿⠏⠘⣿⡟⠉⠙⠳⠤⠀⠀⠀⠈⣿⡟⠻⢿⣿⣦⠀⢻⣧⠀⠀ ⠀⢀⡿⠁⢰⡿⠋⠁⠀⢸⣿⡷⠋⠀⣀⠀⠀⠀⠀⢰⡏⠀⠀⠈⢿⣿⠃⠀⠀⠘⡇⠀⠀⠀⠀⢀⡀⠀⢳⣿⣿⠀⠀⠉⠿⣧⠀⢻⡆⠀ ⠀⢸⠃⠀⡏⠀⢀⣀⠀⢸⣿⣇⣴⣿⡏⠀⠀⠀⠀⠸⡁⠀⠀⠀⠘⠃⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⣿⣷⣬⣿⣿⠀⢀⣀⠀⠘⠆⠀⢧⠀ ⠀⡞⢀⣴⠾⣿⣿⡿⠀⠘⣿⡟⠙⣿⡅⠀⠀⠀⠀⠀⠁⢀⣠⣤⣦⣤⣤⣤⡀⠀⠀⠀⡀⠀⠀⠀⣿⡏⠹⣿⡇⠀⢸⣿⣿⠿⣦⡀⢸⠀ ⢠⣧⠟⠁⠀⢸⣿⣧⠀⠀⢻⠀⠀⠹⣷⠀⠀⣸⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢹⠀⠀⣼⡟⠀⠀⢹⠁⠀⢸⣿⡿⠀⠀⠙⢾⡇ ⡼⠁⠀⠀⠀⠀⢿⣿⠀⠀⠈⠀⠀⠀⠙⢷⣄⢹⡆⠀⠀⠉⠉⣙⣿⣿⣏⣉⠛⠀⠀⠀⣿⢀⣼⠏⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠈⠳ ⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⢰⣦⣄⡀⠀⠀⠙⢿⣿⡄⠀⠀⠈⠻⣿⣿⡟⠃⠀⠀⢀⣼⣷⠟⠁⠀⠀⣀⣴⣦⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⢸⡇⠈⠛⢦⡀⠀⠀⢻⣿⣷⣶⣶⠾⠛⠛⠳⢶⣶⣾⣿⡿⠁⠀⠀⣠⠞⠉⠀⣿⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⡇⠀⠀⠀⠙⣄⠀⠀⢻⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⠁⠀⢠⠞⠁⠀⠀⠀⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠀⠀⠀⠀⠘⣷⡀⠈⠇⠹⣿⣿⣿⣿⣿⣿⡟⠀⠇⠀⣰⠏⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⣸⡀⢻⣿⣿⣿⡿⣿⠁⣿⠀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣿⡇⠈⡇⣿⣿⠃⡇⢀⣿⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠹⣷⠀⠘⢸⣿⠈⠀⢸⡏⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢻⡆⠀⢸⡏⠀⢀⣿⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⣷⡀⠀⠀⠀⣼⠇⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡴⢰⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⣀⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⣴⠟⠛⠓⠶⣤⠴⠶⢶⡿⠁⣶⣽⣯⠉⠁⠹⡆⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡁⢼⣿⡏⠙⠻⣾⡛⢿⣆⠀⠀ ⠀⠀⠀⣻⠋⠀⠀⠀⠀⠀⠀⠈⠓⠶⠞⠷⣤⣼⣯⠟⣸⡟⠀⠀ ⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠞⢙⣆⣀⠀ ⢠⡶⢾⡶⠤⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠚⢩⡏⠉⠁ ⠀⢀⣼⣷⠒⠀⠈⠋⠀⠀⠀⢶⡲⠀⠀⠀⠛⠁⠀⡈⣹⠛⠛⠀ ⠀⠀⢠⡼⠷⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠛⠷⠆⠀ ⠀⠀⠈⠀⠀⠀⠉⠙⠓⠒⠶⠶⠶⠶⠒⠚⠛⠉⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣼⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠾⡿⠛⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⢿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡇⡐⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⢠⠈⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣷⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⣰⣿⠏⠁⠀⢸⣿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠊⡿⠁⠈⠢⠀⠀⠈⠉⠉⠉⠉⠉⠁⠁⠀⠀⠴⠃⠈⢿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣗⢀⡠⠊⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠐⢦⡀⢘⡇⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⣷⡿⠁⠀⣠⣄⣀⣄⡀⢸⣇⠀⢠⣄⣀⣄⡀⠀⢻⣾⣷⡄⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⠁⠀⣾⠧⡤⣍⠹⣳⣿⣿⣾⡟⣨⡥⡬⣿⡄⠀⢿⣿⣷⠀⠀⠀ ⠀⠀⣴⠟⣱⠃⣠⡄⢛⣦⠑⡒⢷⣿⣿⣿⣿⡷⢓⡋⣥⡞⠡⣄⠈⣧⠙⣧⡀⠀ ⠀⣸⠃⣼⠿⢋⣿⡀⠈⠙⠋⠙⡟⠉⣿⣿⠋⢻⡏⠙⠋⠁⠀⣹⡟⠻⣷⡈⢧⠀ ⠀⠇⠘⢁⣀⠸⣿⣠⡖⠀⠀⠀⠁⠀⠘⠃⠀⠀⠇⠀⠀⢱⣦⣿⡇⢀⣈⠣⠘⡄ ⢸⡴⠛⢿⡇⠀⡟⠙⣇⠀⠠⠀⢀⣶⣶⣶⣶⡄⠀⢀⠀⣸⠇⢹⠁⢸⣿⠛⢦⡃ ⠎⠀⠀⠘⣷⠀⠀⠀⠈⠣⣸⡀⠈⢉⣿⣿⡍⠁⠀⣜⡴⠃⠀⠈⠀⣼⠏⠀⠀⠙ ⠀⠀⠀⠀⠹⣆⣸⠑⢄⠀⠙⣷⣤⣤⠽⠻⢤⣤⣾⠏⠀⡠⠚⢹⣰⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⠀⠀⠑⡄⠘⠿⣿⣿⣾⣿⡟⡇⢀⠎⠀⠀⡼⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣤⢹⢿⣿⡟⢰⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⠀⢺⡇⠁⡾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⣇⠀⠃⢰⠃⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢸⡠⡹⡄⠀⠀⠀⠀⠀⠀⢠⠎⢄⢱⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⢃⠀⡿⡁⢷⠘⢄⡀⠀⠀⠀⡰⠃⡌⢻⡌⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⡎⢸⡴⡷⠁⢸⠀⠀⠉⠀⡀⠉⠀⣸⠀⢺⠄⡇⠀ ⠀⠀⠀⠀⠀⠀⢠⣇⠀⠻⣃⡀⠬⠚⠀⠀⠀⣰⡀⠀⠹⣄⣽⢴⡇⠀ ⠀⠀⠀⠀⠀⠀⡸⢗⣴⡞⠉⠀⠀⠐⡦⢄⠀⠈⢃⠀⢀⠼⣻⣴⡇⠀ ⠀⠀⣀⢤⡖⠨⣴⡮⠁⠀⠀⠀⠀⣤⡧⠀⢣⡀⠸⢀⡄⠠⠧⣙⣄⠀ ⠀⣼⢟⠁⠀⡪⢊⠁⣠⡜⠛⠒⠈⠲⣶⣦⡀⢻⠀⡎⢷⣾⢗⠻⣿⡆ ⢰⣟⠅⠀⢰⣷⠁⣸⠟⠀⠀⠀⠈⢄⠈⠙⠻⡀⣴⡿⠺⢅⠾⠀⢸⠃ ⢸⡏⡄⠀⢈⣏⡆⢹⣎⣄⠀⠀⠀⠈⠻⠂⠀⢻⡈⡇⠀⠀⠑⢄⡟⠀ ⠈⢷⡇⠠⠀⢻⣾⠀⢹⠎⠉⠀⠀⠀⠀⠀⠀⠀⠑⢜⠄⠀⠀⠈⠢⡀ ⠀⠈⠻⣾⡀⠀⠹⣦⡪⠒⠂⠀⠠⡀⠀⡀⠀⠀⠀⠀⠁⢰⡊⢉⣉⣳ ⠀⠀⠀⠹⣧⡆⡀⠋⠀⠀⠀⠀⠀⠈⠒⠠⠑⢦⣀⠀⠀⠈⢙⣻⡿⠃ ⠀⠀⠀⠀⠘⢷⡟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⠭⠥⠴⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢺⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡄⣞⡄⠀⠀⠀⠀⠀⠀⢀⠂⢀⣸⡗⠿⢅⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢚⡋⡠⠊⠀⡠⠜⢀⠠⣊⣠⡢⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡿⠯⠄⠒⠛⠂⠉⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⢏⢙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⠟⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡏⠉⠑⢄⠈⠳⣄⠀⢀⣀⣀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣶⣧⣤⠄⠀⠉⠢⡈⠋⠁⠀⠀⠉⠓⠦⣄⡀⣦⣀⡠⠤⣄⠀⠀⠀⠀⠀ ⠈⣟⢯⣇⠁⠀⠀⠀⠈⢶⣆⠀⠀⠀⠀⠀⣴⠽⠚⣉⣠⠇⣾⠀⠀⠀⠀⠀ ⠀⠙⣆⠹⠀⠀⠀⠀⠀⠈⠙⠓⠀⠀⠀⠀⠠⠔⠋⣡⠋⢘⡏⠀⠀⠀⠀⠀ ⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠋⠀⢀⢾⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢀⣼⣋⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⢀⢰⣇⠀⠀⠀⣺⠆⠀⠀⠀⠀⠙⠢⣄⠀ ⠀⠀⠀⠀⠀⢸⢠⠀⢀⠀⠰⡄⠀⡷⡇⠀⠀⠉⠁⠀⠀⠀⠀⢐⠚⠻⣍⠀ ⠀⠀⠀⠀⠀⠾⠛⡦⡿⡷⢷⡟⠢⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠂ ⠀⠀⠀⠀⠀⠀⠀⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢩⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡿⠉⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠁⣀⡀⠀⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⣰⣿⠏⢠⡶⣄⠘⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⡇⢸⠏⠹⣦⠀⠈⢿⣧⣀⣀⣀⣀⣀⣰⣿⠃⣰⠏⠀⠘⣆⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠀⡼⠀⠀⠘⢧⠀⠈⠛⠛⠛⠛⠛⠛⠛⠇⢰⠏⠀⠀⠀⢹⡆⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⡏⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣤⡀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⡿⠀⠀⠀⢠⡶⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⠀⠈⢧⡀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⠃⠀⠀⢀⡟⠀⠀⠙⠷⣄⡀⠀⠀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⡏⣠⡤⠤⠾⠁⠀⠀⠀⠀⠈⠻⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⣶⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠃⣿⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡄⠀⠀⠀⣴⠇⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⠸⡆⠀⢸⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠈⠛⠒⢶⡄⠀⢻⣇⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⡄ ⢠⡿⢠⡴⠗⠀⠀⠛⠛⠃⠀⠀⠀⠈⢉⣉⣉⠁⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⡼⠁⣀⣼⣿⠀⠀⢀⣴⣿⠿⠋⠁⢸⡿⠁ ⢸⣧⡘⢧⡀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠿⡿⠻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣷⣾⠿⠋⠁⢀⣴⡿⠋⠁⠀⠀⠀⢸⡇⠀ ⠘⠛⠿⠿⣿⣶⣤⣤⣀⡀⠀⠀⠀⠻⣦⣤⣾⠟⠁⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⠟⠋⠁⠀⠀⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠸⣷⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⡿⢷⣶⣦⣤⣤⣤⣶⣶⣶⠾⠿⠟⠛⠉⠉⠙⢿⣷⣄⠀⠀⠀⠀⣼⡏⠀⠀⣀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⠀⣿⣇⡴⠋⣿⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⣿⠋⠀⠀⢿⣄⣴⠞⢳⣠⣿⠀ ⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣼⡇⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣾⣏⣠⣴⣶⣶⣄⠀⠹⣿⡀⢀⣿⠀⠀⠀⠀⠈⠀⠀⢈⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⣿⡏⠀⠙⣿⣷⣄⡀⢀⣤⣾⣇⠀⠀⣠⡴⢾⣿⣿⠟⠉⠀⠙⣿⡆⠀⢿⣧⣾⡿⠀⠀⠀⠀⠀⠀⣴⣿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠘⣿⡎⠙⠛⠁⢸⣿⠷⠞⠁⠀⠀⣿⠀⠀⠀⠀⠀⣿⡇⠀⢸⡟⠛⠀⠀⠀⠀⢀⣤⣾⡟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⢹⣷⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⡿⠀⠀⠀⢀⣼⡿⠀⢀⣾⡇⠀⠀⣀⣤⣶⡿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠷⠿⠿⠶⠶⠶⠾⠿⠿⠷⠶⠶⠾⠿⠶⠶⠾⠿⠿⠷⠶⠿⠿⠷⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠘⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣏⡿⢿⣿⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⣴⣴⡀⠘⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣇⡀⠙⢿⣮⡈⠳⣦⣤⣀⠀⠀⠀⠀⠀⣿⠀⠀⢰⣿⣿⣿⡀⠈⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⡆⠀⠀⠻⡿⣦⠀⠉⢽⣿⣶⠶⢦⣶⣿⠀⠀⢸⣿⣿⣿⡇⠀⠘⢿⣿⣷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣧⣄⣀⡀⠘⠽⣷⣤⣾⡟⠀⠀⠀⣿⣿⣦⡀⠈⢿⣿⣿⠇⠀⠀⠸⣿⣿⡇⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢀⣼⠿⠃⠀⠀⢀⣤⠟⠻⠿⣿⣄⢸⣿⠏⠀⠀⠀⠀⠻⢿⣷⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⡄⢀⡶⠛⠁⠀⠀⢀⣴⣿⠋⠀⠀⠀⠀⠉⠻⠋⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠙⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⠟⢀⡴⢀⡇⢀⣿⠿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠈⢦⡙⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣶⠟⠀⢸⡁⣾⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠑⢿⣿⣷⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⢀⣿⠀⣿⣠⠖⠓⣦⠀⠀⠀⠈⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⠀⠀⠀⢹⣾⣿⠛⠶⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⡀⠀⢸⡇⠠⣿⡏⠀⠀⣟⣀⡀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⢈⣿⣿⣶⣾⠃⠀⣿⠀⠐⢋⣽⠿⢿⢾⡿⢷⣦⡀⠀⠉⠒⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠃⠀⠀⠘⢷⣴⣿⣿⣶⠶⠟⠁⠀⠈⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣼⠃⠀⠀⠀⢀⢾⠟⠉⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠉⠉⠛⣷⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠠⢻⣦⣴⣄⣀⣙⣷⡦⣶⣦⣿⣷⡀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⢀⡠⠒⠉⠉⠉⠉⠉⠛⠛⠀⠀⢿⣿⣿⣷⡀⢀⣾⣿⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⢀⡼⠅⢀⣴⠆⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⠛⣿⣿⠃⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⣠⠾⠀⣠⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣇⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀ ⠀⡼⠁⠀⣴⣻⣿⣧⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠖⠁⠘⢿⣷⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠾⠁⠀⠀⠀⠀ ⠈⣷⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⣠⣾⠿⠋⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⣿⣿⣽⡟⠀⠀⠀⠀⠀⠀⢀⣠⣞⣩⣤⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠻⢧⣀⣠⣄⣀⣤⡶⣞⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⢟⣥⣶⣶⣶⣄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣠⣤⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠒⠋⠉⠉⠉⠉⠉⠒⣾⣄⣢⠈⣧⠶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⣠⠖⠛⠓⠦⣀⠀⠀⠀⣠⠇⠀⠙⣶⠛⠀⠙⢟⠯⣝⡓⠲⠦⠤⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⢹⠃⠀⠀⢰⢃⣤⢤⣄⡀⠘⢦⠀⠀⢧⣀⠐⣶⠛⣶⢃⣀⡼⠓⠤⣍⡑⠲⢤⣀⠀⠀⠉⠉⠉⠁⠒⠒⠒⠦⠤⠄⢀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⢶⣯⣳⣌⡇⠀⣤⠟⠉⠹⠗⡿⠍⠉⠓⣦⠤⠀⢉⡿⠀⠈⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡏⠀⠀⠀⣿⣿⣿⣟⡇⠀⣉⣿⠇⠀⠈⠓⢦⡀⣴⢧⡀⠀⢰⠧⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⢤⡀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⣀⣀⣠⡤⠤⠤⠴⠛⠛⠚⠁⠀⠀⠀⠛⠛⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠑⠛⠒⢿⣾⣃⣀⡀⠐⠒⠒⠒⠤⠤⣀⣀⣀⠠⠤⠤⠤⠈⠉⠒⠤⣄⡀⠀⠀⠀⠀⠀ ⣾⢻⡁⠀⠀⣐⠒⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠛⠦⣄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣄⡀⠀ ⣿⣿⣇⠀⠸⣹⣷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣞⢷⣤⣠⣄⡀⠈⢙⣲⣦⠤⠟⠉⠉⠉⠉⠉⠉⠉⠙⠳⣶⣄⠉⡆ ⠘⡟⠷⣴⣄⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠈⢳⣧⠈⠉⠛⠋⠉⠁⠀⠀⠀⢀⣀⣀⣀⣀⠄⠀⠀⢀⡿⢋⡴⠃ ⠀⠹⡄⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⣄⣄⣿⡄⠀⠀⠀⣀⠀⠀⢀⣠⡤⠒⠋⠁⣠⣤⣖⣿⠽⠚⠁⠀⠀ ⠀⠀⠙⢆⣠⡷⠶⠤⠤⣤⣀⣀⠀⠀⣠⡴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠹⡜⣼⠛⠳⠤⠤⠼⠛⠛⢛⣀⡤⣔⣺⠽⠓⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⣧⡟⠀⠤⠤⠤⢖⣶⣿⡿⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡾⠓⠒⠚⠋⠉⠉⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠤⠤⠤⠶⠒⠒⠚⠛⠛⢻⡟⠛⠛⢻⡀⠀⠀⠀⠀⠀⠀⠀⢤⣻⡄⢠⣯⢞⠀⠳⡄⠀⠀⠀⠀⠀⠀⠘⢦⣤⠭⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠈⡿⠛⠁⡸⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢤⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡼⣫⠄⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠰⡝⠂⠀⠀⠀⠀⠀⠀⠀⠑⢲⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠿⠟⠋⠁⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠳⢤⣀⣀⣠⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⢻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⡒⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⣄⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠘⣆⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢶⣒⣉⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⣼⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠳⢤⣀⠀⣀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⢠⣾⣶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠯⠤⠤⠴⠶⢭⣀⣀⣀⣀⡤⠾⠺⠟⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢾⣿⣶⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣾⣿⣿⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⡟⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⡟⠻⡇⠙⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠋⣼⣿⣿⠟⠛⠻⢿⣧⠀⠀⠀⣸⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣯⣶⣿⣿⣿⢇⡴⠿⣿⣶⣬⣥⣴⣾⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⢟⠛⣻⣿⣿⣿⣿⣿⡜⠀⣀⠌⠻⣿⣿⣿⣿⠟⠁ ⠀⠀⠀⠀⠀⣀⣴⠁⢋⣥⣾⠃⣴⡿⢫⣿⣿⣿⣿⣿⣿⣧⣤⠄⢹⣿⣿⠏⠀⠀ ⢀⣤⠶⠿⢿⣿⣿⠖⠛⠻⣿⢠⣿⠃⠈⢁⣼⣿⣿⣿⣿⣿⡁⢀⠂⣿⡏⠀⠀⠀ ⠻⣯⡀⠀⠀⢈⡇⠀⠀⠀⠈⠸⣿⡆⢠⣿⡟⣹⣿⣿⡟⠛⡉⣸⠀⣿⠀⠀⠀⠀ ⠀⠈⠙⠿⢿⣿⣿⣶⡤⠖⢈⡀⢻⣿⣼⣿⣧⣿⣿⣿⡿⠋⠀⣿⡄⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣉⣁⣠⣶⣿⣷⡀⠙⢿⣿⣿⣿⣿⣟⠛⣁⠀⢻⣇⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⢁⣼⣿⣿⣦⣄⡀⠉⠉⠛⠻⣷⡜⡆⢸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⡛⠿⣿⣿⣿⣦⡀⠀⠀⢹⡇⠇⢸⡿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣿⡄⠀⠙⢿⣿⣿⣆⠀⠀⡇⠀⣸⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣿⣿⠇⠈⣿⣿⠘⣿⡄⠀⠁⣰⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠀⠀⣿⠏⠀⢸⡇⠀⠐⣉⣴⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⣸⠏⠀⠀⣼⠁⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⢀⠜⠁⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠁⠀⣠⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣴⣏⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⢬⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣇⠀⠀⠀⠱⣌⣁⡉⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣹⣧⠀⠀⠀⢿⡀⠉⠂⣙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢤⡉⡀⠀⠀⢈⢻⣿⣆⠸⢾⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢻⡄⠀⣾⠀⢧⡙⣇⠈⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀ ⠀⠀⠀⠠⣾⢿⠾⢻⣇⡆⣿⣎⡴⣿⡄⢻⣷⡦⠤⠀⠀⠀⠀ ⠀⠀⣐⣺⣿⣾⠇⠈⠻⡇⢸⡿⢿⣿⢱⠀⠉⠛⢿⠃⠀⠀⠀ ⠠⢤⣴⣿⣿⠟⠀⢠⠀⠈⡛⢣⠀⠃⢸⣷⡄⠰⣏⠀⠀⠀⠀ ⠐⠦⢶⣖⣢⠤⣴⡿⢀⣾⣵⣞⠀⢦⠀⢳⣽⡀⢹⣷⣶⠄⠀ ⠀⠠⣿⢋⣴⠟⢟⣱⣿⣿⣿⡏⠀⣼⣆⣿⡿⠧⠾⣿⣯⣤⠄ ⠀⠴⠛⣿⠇⣴⠏⣼⣿⣿⣿⣧⣿⣿⣟⣅⣀⣌⠷⠿⢿⡂⠀ ⠀⠀⠀⠧⠚⠉⠀⠏⢻⣿⢿⣿⣿⣿⣿⣿⣿⡿⣷⠦⠤⠝⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠙⣎⠹⣿⣿⠙⢧⡘⡷⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣿⠏⠀⠀⢰⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠿⠿⠿⠿⠿⠛⠛⡉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣶⣖⡄⣅⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣪⠴⣐⠦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡏⡎⡥⢋⣂⠙⢤⣄⡀⠀⠀⠀⠀⢀⣀⣀⡠⣄⠀⢀⠀⠀⠀⠀⣀⣀⡤⣒⠵⣓⠒⠷⢮⡸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣟⣧⠻⢩⠼⢮⣔⢈⢺⣿⡋⠱⢯⠋⡬⢩⠴⠁⣩⠩⣻⠓⢩⠓⣟⣩⣊⢴⣨⣍⡉⠿⣭⡷⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣓⣝⢺⣳⣷⣷⠃⠉⠃⠀⣿⠔⠃⡘⠄⡞⠁⣼⠀⠀⠀⠋⢨⣷⠿⠷⣚⢯⣐⣿⣹⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣟⢋⣁⠒⢲⡄⠀⢠⣅⠠⢸⢠⢼⠑⢀⠈⠄⠀⠀⠀⠈⠐⣉⡽⣿⣷⣿⣿⠙⠀⠠⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣾⣿⢿⣷⣎⣯⢦⡀⠠⣀⣻⣷⣈⣷⣸⢄⣿⠏⠁⠀⠀⠀⠀⢁⡕⣜⡫⣿⣋⡁⣟⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢹⣿⣿⡽⠷⣏⠢⠉⢹⣷⠃⢿⡇⣿⣿⢸⡟⠀⠤⠄⡂⠀⠀⠉⠘⣤⣎⣽⡿⠃⠁⠄⠐⠀⠁⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠄⢻⡝⣛⡇⠒⣁⢀⣈⣿⠀⣸⠓⢻⡾⢸⡂⠀⡯⠕⠀⠀⠀⠀⠀⠀⠃⠙⠀⠀⠃⠂⠔⠀⡁⠀⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⡲⣌⠙⣑⣆⣴⣶⣿⣿⣷⢤⣇⠀⠸⡠⠈⡷⠈⣥⣷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⢈⢀⠐⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣭⣾⢿⢻⣿⣿⣿⣿⣿⣞⣿⣆⣀⠀⠸⠀⣼⣿⣿⣿⣿⣿⠃⢠⣀⠀⠀⢀⠀⠀⢃⢀⠈⠌⠀⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣹⣦⣿⣿⣿⣿⣿⣿⡇⠈⠁⣀⠀⠀⢀⠻⣿⣿⣿⣿⠟⠀⠠⠛⠆⠀⠀⠀⠁⠈⢁⢂⠂⠄⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣹⣯⣿⣾⣡⣁⣴⣿⣶⣿⠗⠀⠐⢾⣽⣦⠀⢉⡁⠀⣒⡧⠊⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠎⠊ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣽⣟⣽⣷⡶⡽⠉⢻⣿⣆⣱⣶⡾⠉⠀⢍⣄⣲⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣯⣽⠤⡃⠀⠀⠀⣀⣈⣻⣿⣡⠀⡀⠀⠀⠀⠈⠀⡀⡠⠷⠂⠀⠀⠀⠀⠄⠈⠈⢈⠀⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣯⣶⢯⣩⣗⢤⢚⣻⡶⠿⠿⠿⣧⠆⠀⠁⢤⠀⠐⠈⠀⡀⠀⠀⠀⠀⠀⡀⠀⠈⠈⠀⢀⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⢟⣿⣿⣿⣿⣮⣷⣯⣤⣂⣅⢂⣐⣠⢴⣸⣄⣆⢠⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⡈⡀⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣺⢾⣻⢿⣿⣿⣿⣿⡿⣿⣽⣻⢿⣿⡳⣿⠿⠟⠋⡀⠩⠆⠂⠀⠀⠀⠀⠀⠀⠀⠢⠠⠐⠈⠀⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣫⢾⠿⢷⣝⠎⣿⠽⢿⣿⣷⠹⠆⠁⠧⢀⡔⡦⠚⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡐⠀⠀⠂⠀⠀⢸⣿⣥⣛⡞⠯⢇⡚⠤⢻⠒⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡁⠀⠀⠈⠈⠀⠀⠀⢀⣾⣛⣯⢽⣌⣚⡤⣹⣳⠕⣂⡀⠉⠀⠘⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠠⠀⠀⠀⠀⠡⠁⠀⠀⠀⠄⠀ ⢰⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⡺⣭⣿⣿⣷⣏⣼⢷⢚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠜⠫⠍⠀⠀⠄⠊⠀⠀⠀⠐⠀⠀⠀⠀ ⢢⠄⠀⠀⠀⠀⠀⠀⠀⢿⣿⡝⢿⣿⣿⣿⣿⣼⢩⡝⡌⡅⠠⠀⠀⠀⠀⠀⠀⠠⣷⡖⣴⣴⠰⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀ ⢌⡃⠀⠀⠀⠀⠀⠀⠀⠙⣷⡺⣓⢾⣿⢿⣿⣏⢎⡴⢦⢡⡀⠀⠀⠀⠀⠀⠀⠰⣿⢻⡃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠌ ⡘⠶⡀⠠⠈⣢⠄⠄⢄⠀⢹⣿⠼⣣⣿⣿⣿⣿⢼⢧⣓⡊⣇⠈⠀⠀⠀⠀⠀⠰⣷⠊⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠄⠀⠈ ⡹⡜⣧⣮⣯⣕⢳⢤⣀⡀⢘⢆⡵⣹⢏⣿⣿⣯⣷⣻⣷⡃⣞⡆⠇⡄⠀⠀⠀⢲⢣⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠐⡀⠆⠠ ⣳⡝⣾⡿⣿⣿⣻⣿⣿⣷⢻⢿⣶⢟⣞⣾⣿⣿⣾⡏⡇⣳⣸⡆⢰⢦⠀⢀⠠⢸⡷⡄⠶⡠⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠁⠄⠀ ⣷⣻⣿⣿⣏⣿⣽⢿⣿⣿⡞⠁⣁⡀⡇⠙⢿⣿⡿⣼⣷⡿⣾⣠⢸⡀⢠⢨⣌⢺⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢄ ⡷⣭⣿⣯⣿⣿⣟⣻⣿⣿⣧⣊⠋⠉⢀⣰⣿⣻⢧⡿⡟⣻⣷⠻⡿⣗⠋⣮⣿⣿⣛⡄⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠅⠈ ⣿⣼⣻⣿⣿⣾⣿⣿⣿⣿⣟⣿⣿⣿⣿⢃⠍⣻⣻⣴⣿⡿⢳⣷⣎⣧⢷⢾⣼⣿⠷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠎⠁ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡾⣿⢾⣿⣿⡆⣾⢽⢱⢯⢻⣣⠿⣽⠻⢻⢽⡼⠧⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣻⣿⣿⡿⣽⢾⣎⣞⣧⣀⡷⢁⢤⣯⠛⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢝⡹⢚⡿⡟⣿⣻⣿⣿⣿⣿⣿⣿⣿⢿⣹⢮⣟⣾⢿⣿⣷⣧⣾⣯⣷⡆⣿⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠈⠁⠉⠁⠙⠹⠯⠟⡟⣿⣻⣿⡼⠥⢛⣼⣹⢞⠿⣿⣿⠉⠛⠋⠉⠉⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠙⠳⣮⠉⢠⠀⠈⠀⠹⣧⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠳⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀(=✪ᆽ✪=)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⡴⠯⠿⠗⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠚⢛⠏⣋⣽⠖⡻⡇⢀⣴⣖⠻⢷⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣾⣷⡵⣿⠋⣀⣴⡇⡇⠀⠀⠙⡻⢽⣻⡂⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⢾⢿⣿⣿⣿⣿⣿⣧⣧⣸⡿⠙⣰⣿⠤⡀⠀⢀⣹⡷⣿⡳⡄⠀ ⠀⠀⠀⠀⢠⣟⠀⣻⡿⢿⣿⣿⣿⣿⣷⠹⢣⣴⣿⣿⣫⠅⠀⠀⠈⠟⠈⣇⠉⠆ ⠀⠀⢀⡠⠾⡒⠊⠩⣤⡪⠋⠈⠤⠶⡽⣇⠉⠉⠓⠄⢉⠚⢆⢡⠑⡈⢦⣿⠀⣼ ⣴⣭⠏⠀⠀⠀⠁⠀⠀⠀⢀⣠⠤⠤⠀⠙⠓⠷⠢⡐⣤⣧⡌⠸⡀⢡⣸⠇⠀⠸ ⠈⠻⣒⣲⡖⡶⣶⣶⣭⣉⠑⠒⠒⢰⣪⡏⢴⡤⢄⣿⣇⠃⠟⡆⡷⣾⠁⢀⣶⡇ ⠀⠀⠀⠉⠛⠑⠈⢻⡟⣹⣗⡄⡐⠉⠨⢒⣼⠇⠀⠋⠀⠀⠀⢘⢁⠈⢰⡜⢻⡇ ⠀⠀⠀⠀⠀⠀⢀⢠⡇⢿⡞⠃⡠⠚⠛⣍⡇⡆⣸⣼⣷⠀⣶⣸⢾⢀⠟⡑⡰⠁ ⠀⠀⠀⠀⠀⠀⠈⢽⣾⡟⡠⠋⠀⠀⠀⠉⠗⢗⣯⠉⣯⠾⠟⡣⠖⠁⣰⡞⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⡠⣡⠂⠸⢁⢀⠄⣠⣣⠞⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⢁⣠⣴⡧⠖⠫⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠋⠁⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡞⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠹⠀⠀⠀⠀⠹⡀⢤⠒⠒⠤⠤⢴⡻⠋⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠱⣦⡑⢤⡀⠀⠈⠓⢤⣰⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠘⡆⢢⡀⠀⠀⡠⠼⠛⡇⠈⢿⣆⠀⠠⡄⠉⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢹⠀⠱⢀⠉⠙⠁⠀⠀⠀⠀⠐⡌⢿⣤⡲⡘⠄⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⡞⠠⠒⢁⡴⠀⠀⠀⠀⠀⠀⠀⠘⠘⣷⢷⠁⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⢀⠜⠁⢀⣴⠏⠀⠀⠀⠀⠀⣴⣾⣭⣭⣕⣺⡜⣧⡽⡅⠙⡽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠴⠋⠁⠀⠀⠀⢀⣤⠾⠋⠉⠀⠀⠙⣿⡇⢹⠀⠙⢆⠘⡝⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣠⡾⠁⢴⡶⠶⣦⡀⠀⣿⡇⢸⢠⣶⣾⡧⠁⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠴⠟⠋⠉⠉⠉⠙⠢⣀⠈⠛⠿⠿⠃⣀⣿⠃⠈⠟⠋⠁⡇⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡇⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠁⠀⠀⠀⠀⠰⡞⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⠀⠀⠀⠱⣄⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠰⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⣀⣀⣈⣳⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠴⣤⡀⠀⠀⠀⠀⠀⠀⢸⠋⣀⢀⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠁⠀⠀⢇⢻⣆⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣈⠙⠦⡀⠀⠀⠀⠀⠘⢦⣈⣨⣿⠋⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡏⠀⢰⠀⠈⠳⣝⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠚⠓⠢⠤⠤⠤⠴⠚⠋⠁⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⢸⡀⠀⠀⠈⠑⠪⢝⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⠀⢻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⠀⢺⣇⠀⠀⠀⠀⠀⠀⠈⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⢿⡀⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⢿⣆⠀⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⣸⠁⠀⠀⠳⡄⠀⠀⠀⠀ ⠀⠀⠈⡇⠀⠀⠀⠀⠻⣧⡀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣾⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⡀⠀⠀⠀⠀⠈⠻⣦⠀⢻⣆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢀⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠙⣆⠀⢻⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠘⠀⠈⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠛⠛⣛⢋⠙⠛⠛⠛⠛⢛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣀⣀⡀⣀⡀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠤⠤⠤⣀⡎⢀⠳⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⢁⠤⠤⢄⡀⠀⠀⢀⠋⠻⣤⠟⠹⣶⣖⡦⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣻⠃⠀⢠⢇⣤⠤⣀⠙⡄⠀⢧⣀⣲⠛⣶⣀⡼⠓⠬⣑⠢⢤⡀⠉⠉⠁⠀⠒⠒⠢⠤⠄⢀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⢸⣿⣿⣿⠻⢷⣾⠀⢴⡉⠈⢛⡟⠀⢉⡖⢀⡠⠋⠀⠈⠑⠒⠤⣀⠀⠀⠀⠀⣀⠤⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⡿⠇⠀⠀⢸⡿⠿⠿⠔⠒⠋⠀⠀⠈⠢⠽⢵⣤⡜⠉⠉⠠⠄⣀⡀⠀⠀⠀⠀⠉⠓⠲⢏⡁⠀⠀⠀⠀⠀ ⢠⣶⡋⠉⢉⠫⣷⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠛⢍⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀⠀ ⠸⣿⡇⠀⢿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠐⣿⣦⢤⣤⣀⣉⠶⠶⠚⠉⠉⠉⠉⠉⠉⠻⣶⡌⡣ ⠀⢹⠙⠻⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⢀⣠⢴⡯⠔⠁ ⠀⠀⠣⡀⣳⣤⣀⣀⡀⠀⠀⢀⣠⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢮⣿⡧⠤⠀⠐⠶⠶⢊⣁⣤⣴⠾⠛⠋⠁⠀⠀⠀ ⠀⠀⠀⠘⡅⠀⠀⠀⠈⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠸⣿⠀⠤⠤⣴⣶⣾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣌⡼⢋⠉⠉⠉⠀⠀⢀⠑⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢹⡄⠀⠙⠄⠀⠀⠀⠀⠀⠐⢷⡴⠋⡄⠈⠢⡀⠀⠀⠀⠀⠉⠻⢍⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣜⡁⠀⠀⠘⡄⠀⠀⠀⠀⠀⠈⠀⡰⠁⠀⠀⢙⠂⠀⠀⠀⠀⠀⠐⢲⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⠛⠉⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠘⡆⠀⠀⠀⠀⢀⣀⣎⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣈⣱⠶⠖⠀⠀⠀⠀⢡⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠏⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⣦⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢺⣭⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣷⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣶⣂⣀⣀⣤⠀⠀⠀⢀⣠⣴⢶⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⢤⡿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡿⠀⠀⠀⢬⡱⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣷⠀⠀⠀⠀⠙⣦⠙⠦⠤⠴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣧⠀⠀⠀⠀⠘⣿⠓⠶⣄⡈⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡤⣿⣷⠀⠀⠀⠀⣻⣄⡀⠀⠁⣬⡟⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢧⣈⠉⡀⠀⠀⠀⡈⠻⣿⣿⣇⠈⡇⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⢿⡆⠀⠀⣼⠀⢹⡙⢿⣆⠀⢻⣿⣻⣿⣿⢿⣿⡶⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡾⡄⣰⣿⡆⠀⠙⣦⠹⡆⠰⣿⠛⢿⣿⣞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢐⣿⠇⣟⠋⢸⣿⣼⠀⣿⣷⣼⡹⣾⡆⠈⢿⣿⣛⣒⠂⠀⠀⠀⠀ ⠀⠀⠀⣚⣻⣿⣶⣿⠀⠈⡛⢿⡀⢸⣿⢛⣿⣿⢹⠀⠀⠉⠛⢻⡿⠁⠀⠀⠀ ⣀⣀⣉⣩⣿⣿⣿⠋⠀⠀⡇⠈⢓⠏⠏⡀⢸⠇⢈⣷⣄⠀⢲⣸⠀⠀⠀⠀⠀ ⢀⠉⠛⣛⣛⡛⠁⠀⠀⣾⠃⠀⣸⠇⣠⡇⢠⡀⠈⢿⡻⣦⠈⢻⣦⣀⡀⠀⠀ ⠈⠙⠛⣿⣶⡾⠛⣡⣾⡟⢠⣾⣿⣿⣟⡤⠀⣷⡀⢨⣿⣽⡄⢀⣿⣿⣿⠇⠀ ⠀⢠⣾⡟⢁⣴⡿⠹⠋⡰⣿⣿⣿⣿⡟⠀⢀⣿⣇⣼⣿⡿⡇⠞⣿⣿⣧⣤⡤ ⠀⢠⡾⠚⣿⡟⢀⣴⠏⣸⣿⣿⣿⣿⣧⢰⣿⣿⡿⢻⠉⠀⡔⢶⣽⣿⠿⠥⠀ ⠀⠈⠀⢸⠟⣠⡾⠏⠀⡿⢹⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣾⣿⣮⣍⠉⠙⢲⠄ ⠀⠀⠀⠘⠉⠁⠀⠀⢸⠁⠘⣿⡿⠻⣿⡿⣿⣿⣿⣿⣿⣿⡏⢻⣛⠛⠒⠛⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠈⢻⡄⠹⣿⣿⡇⠙⢷⡈⢿⡟⠒⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⣿⣿⠃⠀⠀⠀⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠈⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⢀⡏⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⣾⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⢠⣿⣿⠀⢀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢔⠟⠁⠀⠀⠀⠀⣠⣿⣿⡧⠖⠛⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣟⠍⣴⠋⠀⠀⠀⠀⠀⠀⠛⠁⠏⠀⠀⣰⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢉⡞⣵⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢸⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠼⠃⣏⠀⠀⠀⠀⠀⢠⠞⠀⠀⣰⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⣀⣿⣦⡀⠀⠀⢠⠃⠀⠀⢰⢋⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠁⠀⠀⠀⠀⢸⣿⠁⠘⠃⠀⠀⢸⠀⠀⢀⡇⢸⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⠏⣀⣀⣀⣀⠀⠀⠀⠙⢷⣀⠀⠀⠀⠈⣇⠀⢸⠀⢸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠈⠛⢯⡙⠷⣄⠀⠀⠹⡆⠀⠀⠀⠘⣆⠀⠀⣸⣧⠀⠀⠀⠀⠀ ⠀⣠⣴⠟⠁⣀⣀⣀⠀⠀⢀⣀⠀⠻⡄⠈⠃⠀⠀⠳⠀⠀⠀⠀⣸⡆⠀⢹⠈⠃⠀⠀⠀⠀ ⣾⣿⣇⡀⠘⠁⠀⠈⠉⠉⠁⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠉⠉⢉⡟⠛⠋⠉⠉⠉⠉⠀⡀⠀⠀⠙⢦⡀⠀⠀⠀⣿⠋⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀ ⠀⠀⢠⠋⠀⠀⣠⣴⠖⠀⠀⠀⠹⡀⠀⠀⠀⠉⠒⠦⠤⠽⣦⡀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀ ⠀⢠⠇⠀⠠⠊⢡⡿⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀ ⠀⣼⣀⣄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⢻⡆⠀⠀⠀ ⠀⡿⢻⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣦⡀⠀⠀⠀⠀⢹⡄⠀⠀⠀⣯⠢⠀⠀ ⠐⠇⢸⡀⠀⠀⠀⣷⠀⠀⠀⠀⠀⣠⣴⠶⠶⠶⣶⣽⣷⡀⠀⠢⣄⡀⣷⠀⢀⡀⢸⡇⠀⠀ ⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠈⠙⠇⠀⠀⠀⠙⣿⡆⠀⣿⣤⡇⠀⠀ ⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠇⠀⢸⡿⣷⠀⠀ ⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠈⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣦⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠈⣦⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⢸⡏⢷⣼⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠛⣧⡀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⣸⢸⡇⢸⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⡇⢿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⣿⣦⠀⠀⣦⡇⠈⠓⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠃⠘⣧⢠⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢰⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⣾⣇⣠⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢪⠋⠀⠀⠀⠚⠙⠁⡠⠃ ⠀⠀⠀⠀⠀⠀⠀⢀⠜⢸⠞⠃⠀⠀⠀⠀⠀⣠⠞⠁⠀ ⠀⠀⠀⠀⠀⠀⢠⠃⠀⠊⢆⠀⠀⠀⠔⠀⣴⡏⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠃⠀⠀⢰⠛⠃⠀⢸⠀⢰⢹⠁⠀⠀⠀ ⠀⠀⠀⡠⠞⠀⠤⣤⢄⠈⠳⡄⠀⠈⡆⠀⢸⡀⠀⠀⠀ ⣀⡴⢋⡀⢀⣀⠀⠈⢆⠑⠀⠸⠀⠀⣸⠀⢸⠃⠀⠀⠀ ⠙⠓⡲⠤⠀⠐⠂⠀⠈⠢⡀⠀⢰⡞⠉⠀⢸⠀⠀⠀⠀ ⠀⡰⠁⡠⡶⠀⠀⠘⡀⠀⠈⠐⠒⠓⠀⠀⠀⡇⠀⠀⠀ ⢠⣡⠀⠀⡇⠀⠀⠀⠙⠢⣄⠀⠀⠀⠐⡀⠀⠹⡄⠀⠀ ⠸⢹⠀⠀⠃⠀⠀⠀⣀⣤⣄⣱⡆⠀⣀⢱⡀⠀⢫⠀⠀ ⠀⠈⢆⠀⠀⠀⠀⢸⠁⠀⠀⠈⠙⠀⠀⠹⡇⢸⣾⠀⠀ ⠀⠀⠈⠣⡀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀ ⠀⠀⠀⠀⠙⣆⢠⠀⠀⠙⢄⠀⠀⠀⠀⠀⡷⣸⠁⠀⠀ ⠀⠀⠀⠀⠀⠸⡞⢦⡀⠀⠀⠣⠀⠀⠀⣆⡇⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠗⡄⢰⡆⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⡟⠛⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠏⢷⡀⠀⢈⣻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡾⢛⡿⠉⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡟⢦⣄⣻⣶⠛⠁⠈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠉⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠈⠳⣦⡀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⡀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠙⠻⣷⣤⣤⡶⠿⠛⠛⠛⠿⢦⣾⣏⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣄⣀⣠⡄⠀⠀⠀⠀⠈⠛⢦⡀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣶⣄⣀⠀⠀⠀⢸⣇⡀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣯⢳⠆⣠⡀⠀⠀⠀⠀⠀⠀⠹⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⣄⠸⢿⣷⣴⠶⠟⠉⣉⠉⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⢿⡿⣿⡇⢻⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣈⣿⡿⠛⠋⠀⠀⠀⢰⡿⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢘⣿⡞⠻⣧⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠟⠛⠉⠀⣀⣠⣤⠶⣾⡿⠁⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠋⠘⣷⡄⠈⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠉⢁⣴⡿⠁⣸⡟⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⡄⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠋⠁⠀⢀⣠⣿⠋⠀⠀⠉⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠋⠁⠀⠀⠀⠀⢀⣼⢿⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠀⠉⠙⢛⣿⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢠⣴⣾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠈⠉⠉⠛⠛⠛⢷⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣦⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡸⣷⡄⢿⡟⠃⠀⠀⠀⢀⣤⣶⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⡬⠿⠿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⠀⠀⠀⢻⣿⣾⣿⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⢷⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢡⣿⡀⠀⠀⣸⣷⡄⢠⡀⠙⣿⣦⡀⠀⢸⣧⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣤⣤⣤⣤⣽⣿⣦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠛⣿⣦⣀⣿⣿⣿⣾⣿⣶⣿⠹⢿⣦⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠶⣦⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⢻⡏⢿⣿⡝⠿⠋⠙⠿⠟⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠤⠂⠬⠥⡀⠈⡙⢢⠏⢶⢤⡤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⠀⣨⣶⡴⣔⠀⡖⠫⡷⠊⡅⢊⠕⠂⠄⡀⠉⠁⠀⡰⠀⠀ ⢀⡀⢀⡀⠤⠾⠃⠀⠻⠛⠓⠊⠀⠈⠲⠳⣜⡉⠀⠠⠄⠀⠀⠁⠒⠍⡀⠀⠀ ⣿⠀⣶⠇⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⡆⠀⠀⢱⠄⣄⣐⠠⠤⠒⠒⠒⠒⣭⢢ ⠰⡉⡄⠀⠀⠀⠀⣀⡤⠂⠀⠀⠀⠀⠁⠀⠀⢀⣽⡀⠀⣀⡠⠄⣂⡥⠴⠓⠁ ⠀⠐⡍⠉⠉⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣜⣀⡠⠶⡞⠋⠁⠀⠀⠀⠀ ⠀⠀⠈⠂⠀⠀⠐⠒⠒⢲⠒⢂⠀⠀⠀⠰⣤⢗⠐⡀⠀⠀⠂⢕⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⡬⠀⠀⢂⠀⠀⠀⠁⠌⠀⠘⠂⠀⠀⠀⠰⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⣀⣑⠤⠀⠀⠈⡄⠀⠀⠌⠀⠀⠀⠁⠀⣀⡰⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢦⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠌⡂⠀⠀⠀⠀⠀⠀⠀⢀⣾⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⠓⠒⠒⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠞⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣆⣠⣄⣴⣶⣶⡾⣯⠞⠙⠳⣿⡄⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣟⠛⠛⠛⠷⠶⣤⣤⣀⠀⠀⠀⠀⠀⣠⣄⣠⣠⣼⣷⠾⣿⢿⣴⣿⠿⠟⠋⠐⠛⠁⡜⠁⠀⠀⣀⡈⣻⠛⠛⠛⠛⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⣷⣦⣤⣤⣤⣀⡈⠙⠛⠶⣶⣤⣼⠿⠛⠛⠉⠋⠐⠊⠁⠀⠁⢀⡀⠀⠀⠀⠀⣼⠁⢀⣠⡞⢻⡀⠘⣆⠀⠀⠐⠒⠒⠹⠿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢿⣿⣿⡿⣿⣿⣿⣷⣦⣄⠀⠀⠦⢤⡶⠂⠀⠀⠀⣀⣤⣤⠚⠉⠀⠀⠀⠀⣰⠋⠀⣠⣿⠁⢸⡄⠀⠘⡶⠒⠋⠁⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣷⣌⣿⣿⣿⣿⣷⣏⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠞⠁⠀⢠⣿⡟⢀⡾⠀⠀⠀⠹⡄⠀⠈⠉⠉⠓⠶⢤⣉⠻⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢿⣿⣿⣷⣿⣿⣟⠿⠯⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⡥⠞⠀⠀⣾⠀⠀⢹⣤⣄⡀⠀⠀⠀⠀⠈⠓⠾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣼⡟⠁⢀⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡾⠋⠀⠀⠀⣿⣿⡛⠒⠢⠀⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣿⣯⣷⠋⠀⠀⠀⠀⠀⣿⡏⢀⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣰⣿⣿⣿⣿⣶⡶⠶⠶⢤⣀⣀⢸⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⠀⠀⠀⠀⠀⣾⡿⣴⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠿⠷⠦⠤⠄⠀⠀⠙⠻⢶⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⢀⣠⣀⣿⣿⣿⣿⣴⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡻⠶⣦⣤⣄⣀⡀⠀⠀⠐⢿⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⡟⠀⠀⣰⣦⣀⣻⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣟⠿⣶⣦⣀⡀⠉⠑⠲⠀⠈⠻⣿⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⣴⣿⠇⣰⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⠀⠉⠛⠛⠶⣄⠀⠀⠀⠹⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⢰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠻⣆⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⡘⢿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⡄⠀ ⠀⠀⠀⠀⠼⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⡀⠀⠀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⢿⠋⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠙⠣⠾⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣄⡳⣄⠀⠀⠙⢆⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣄⠀⠈⢳⡀⠈⣷⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⠏⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠶⢤⣀⡀⠀⠀⠈⠙⢿⣷⡀⠀⠹⡄⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⣸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⠉⠻⣄⠀⠘⣿⡀ ⠀⠀⠀⠀⠀⠀⣰⡏⠀⢰⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠤⠀⠀⠈⢳⡄⢻⡇ ⠀⠀⠀⠀⠀⢰⠟⢀⣴⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⣶⣶⡦⣤⡀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠸⣶⣤⡀⣿⣾⡿ ⠀⠀⠀⠀⣰⡏⣀⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣿⣿⣿⢦⣀⠀⠙⢦⣀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠘⣿⣦⡀⡟⢿⣷⣿⣿⡇ ⠀⠀⠀⣰⡿⣴⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠿⣧⠙⠛⠳⠈⠀⠀⠀⠈⠳⡄⠀⠀⠹⣄⡀⠀⠀⢀⠀⢸⡏⣿⡇⠈⣿⡿⠈⠀ ⠀⠀⣰⡟⢰⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠴⠖⠉⠉⠉⠋⠓⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⡄⢣⠀⠀⠀⣿⣧⠀⣆⢸⣧⣸⡇⢸⡇⠀⠀⠃⠀⠀ ⠀⣰⡟⣸⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣗⠋⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣿⠀⠰⡀⠀⢻⣼⠀⠀⠀⢸⣿⣧⣿⣾⠻⣿⠁⠈⠁⠀⠀⠀⠀⠀ ⣰⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣿⣟⠏⠋⠁⡀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⢀⣿⠀⠀⡇⠀⠈⣿⠀⠀⣠⣾⢿⣿⢻⡏⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣿⠟⣿⡿⠀⠀⠀⠀⠀⠀⠀⠴⠖⠋⠉⣩⣽⣿⣏⣿⡆⢰⣀⡇⠀⢠⡇⠀⣿⣇⠀⠀⡄⡄⣸⣿⢰⡄⣧⠀⠀⢿⡆⢀⣿⣿⢸⡟⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⢿⣿⣿⣿⣦⡈⠀⠀⠀⠀⠀⠰⠶⠤⣍⣉⣩⣿⣿⣿⣿⣿⣿⣇⣿⣿⣇⣴⣿⣷⣾⣿⣿⠀⣼⣷⣿⡟⣿⡿⣷⢸⠀⠀⣸⡇⣼⣿⠏⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣿⣿⣷⣦⡀⠀⠀⠛⠲⢦⣤⣤⠾⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⠟⣡⣿⡿⣿⣿⣿⣾⡿⡿⠃⢠⣿⠁⣿⣾⡇⢀⣿⣷⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠙⠀⠀⠀⠀⠀⠀⣼⢫⣿⡟⠁⠐⠁⠉⠸⠁⣾⠟⠉⠀⠀⠀⠸⠏⠀⣿⣿⣧⡾⣿⡟⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⡾⠋⠁⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢰⢧⣿⢋⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢁⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡰⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣿⣿⣷⡦⠀⠾⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠀⠀⠀⢀⡴⢿⣿⣷⣿⣿⣿⣗⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣮⡙⢺⠀⠀⠀⠀⠀⢠⡞⠋⠀⢠⣴⡿⢋⣿⠦⢍⡉⠛⠻⣿⠻⣾⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⢿⣬⣀⠀⠀⠀⠀⠞⠀⣠⣾⡿⢋⣼⡏⣡⠤⣤⡈⢳⡀⢸⣷⠻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣦⡀⠀⣀⠀⣰⡏⣠⣾⣽⠟⠁⠀⢼⣇⣸⡆⢸⣿⢰⠿⣮⣁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣶⣴⣿⣿⣿⣾⡿⠋⠀⠀⠀⠀⣷⠏⣽⠀⣿⣿⢾⠀⣨⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⢟⣿⣽⡶⠛⡟⠀⢠⠆⠀⠀⢠⣼⡟⢠⣧⣾⣿⣿⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⡿⢫⣴⡿⠿⠋⠀⠀⠀⢀⣎⢀⣀⣰⣿⢿⣿⣿⣿⣿⡿⣇⣨⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⢀⢤⣿⣿⣿⣿⡿⠋⠉⠁⠀⣀⡤⠀⣠⠶⠿⠿⠿⢿⣟⠽⣼⣿⣿⣿⣿⡿⠟⠻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡔⠈⣵⡶⢿⣿⣿⣿⣿⢁⡤⠴⠚⠋⠉⠀⠀⠀⢀⣀⣤⣴⣿⠁⢴⣿⣿⣟⡿⠋⢀⣤⡄⠙⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣼⣯⣾⣿⣭⡤⢾⣿⣿⣿⣿⣿⠞⠃⠀⠀⠀⠀⠀⠩⢞⣯⣾⠟⠋⠀⠈⢿⣯⣾⣣⣾⣿⣿⣤⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡿⠿⠛⠉⠉⠀⢠⠿⢿⣿⣿⡿⢃⡄⠀⠀⠀⠀⠀⢀⢞⡩⠚⠁⠀⣀⠐⢒⣶⣾⠿⢯⣿⣿⣿⣿⣿⠟⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⡶⠶⠛⠉⢁⡀⠤⢶⣶⢞⣩⠆⠀⠸⠛⣿⠗⡟⠁⠀⠀⠀⢀⠴⠋⠀⠀⠀⢠⠞⠁⣠⣾⣿⣶⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⣶⠟⠉⠠⣤⣴⣾⣿⣶⣶⣿⣭⡾⠃⢸⡇⠀⠀⣿⠀⢠⠤⢔⣚⣿⠋⠀⠀⠀⡀⠰⠃⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠤⢤⣿⡃⠀⠀⠀⠀⣠⠾⠛⠻⣿⣿⠟⠃⢠⣿⠇⠀⢰⡟⢠⡆⠀⣠⡾⠋⢀⠀⠀⣸⡇⢠⣠⡾⠛⣩⣾⣿⣿⣿⣿⡿⢯⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⡓⠓⠲⢤⣀⡁⠀⢀⣀⣠⡄⠀⠀⢸⣿⠀⣠⣿⣇⡿⢰⡆⠈⠀⢀⢾⡆⢀⣿⢀⡽⠋⠀⣼⣫⣿⣿⣿⢿⣿⡿⠈⠁⠐⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣷⣛⣒⣽⠃⠈⠉⠙⠛⠓⢾⣧⣶⣤⣾⣿⣾⣿⣿⣿⣵⣿⣱⣣⣠⣾⣾⣷⣿⠃⢸⡇⠀⣸⢿⣿⣿⣿⢿⡾⡟⠹⣆⠰⢦⡹⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⢄⣤⣿⣿⣻⠞⢻⣿⡿⣯⣴⣿⣿⣿⣿⣿⣿⠛⡿⣿⣿⡀⢸⣇⢸⡿⣿⣿⣿⣿⠘⣷⡀⠠⣜⣷⣄⣙⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢿⣿⣿⠋⠁⠀⢸⣿⣇⣸⣿⣿⡿⢧⣤⣽⠆⠀⠀⢻⢻⣿⣼⣿⣿⡇⢸⣯⠋⣿⡝⢯⡁⢠⣼⣿⣿⣿⣟⣠⡤⠤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣡⣿⣿⣇⣠⠀⠀⣼⣿⣿⠟⣻⣿⣷⡿⠋⠀⠀⠀⠀⠀⠈⠏⢳⠘⢿⣿⡈⢻⡀⠹⣧⣸⣿⢦⣹⣿⣿⣿⣿⣿⣾⣛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⠟⠉⣿⣸⡇⠀⣴⢿⡿⠃⠀⡟⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢨⣿⣿⣸⣿⠀⠈⢻⢼⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣶⡟⣋⣥⡤⠾⣿⠛⣧⣸⡇⢸⡇⠀⠀⢰⢏⢸⣧⠤⠤⠤⣤⡀⠀⠀⠀⠀⠀⣼⣟⢻⣿⠟⠀⠀⠀⠘⡿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⡿⣦⠀ ⠀⠀⠀⠀⢀⣾⡿⠟⠋⠁⠀⠀⠀⠙⠢⣬⣿⣷⣈⣧⡀⣀⡽⠛⠙⠫⠳⢤⣀⠉⠉⢳⡀⠀⢀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⣹⣿⣿⡎⢿⣿⣿⢬⣷ ⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⠟⠁⠀⢀⣠⠤⠖⢺⡏⠁⠀⣼⠋⢀⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⣿⠉⢿⠹⣧⠹⣿⣿⣆⢿ ⠀⠀⠀⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀⠀⢀⡞⠉⠙⡾⠏⠀⣠⠾⠁⠀⠈⠙⣿⡇⠀⠀⣀⣤⡴⣶⣶⣷⣾⣿⣿⣶⣿⠀⠈⡆⢸⡆⢻⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢡⣿⡇⠀⠀⠛⣦⣤⣊⣤⡴⠛⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⣛⠉⠉⠡⢴⣿⠛⣿⠿⣿⣦⡀⠘⡇⠈⣿⢻⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⣿⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣀⡼⠿⢻⣾⠏⠀⠈⣿⡇⢠⡇⢰⢿⢾⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠻⠶⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠶⠚⠛⠉⠉⠉⠙⠒⠶⠶⣾⡉⠉⠀⠀⠘⣣⠀⠀⣴⣿⠃⠸⠀⠀⣾⠟⠀ ⠈⠑⠤⡀⠀⢀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡽⢿⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡿⠀⠀⢀⣤⣿⣶⡿⠋⠁⠀⠀⠀⡼⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠾⠛⠶⠿⣿⣿⠿⣿⣿⣿⣭⣿⣛⣿⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠈⠻⣌⣉⠙⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠉⠀⠀⠀⠀⠀⢀⣤⡶⠶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⣀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⣀⣀⣀⣀⣀⣠⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢾⠱⢕⠠⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢆⢸⢣⠁⠛⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⢏⠨⢪⢫⣷⡻⢆⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣯⢖⠆⠁⠀⣸⡈⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⣇⡔⡳⠀⢠⢻⢳⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡇⣯⣶⢄⠀⢢⡻⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⠼⢸⣋⠀⠀⡍⠻⣿⣦⠀ ⠀⠀⠀⠀⠀⠀⠆⡇⢸⡠⣐⠥⡝⠶⠛⢿⠧ ⠀⠀⠀⠀⢀⣠⣼⣧⣼⣷⣁⣒⣡⡴⠀⢸⡆ ⠀⠀⠀⣪⠿⠗⠂⠀⠔⠊⠉⠉⠉⠉⢉⢢⠇ ⠀⣠⠮⡷⠶⠿⠿⠭⠤⠤⣕⣲⣶⣶⠾⠋⠀ ⠊⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣶⡄⠴⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡒⠀⠀⠠⢊⣠⣖⠯⢛⠻⣻⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⡄⣀⣜⣵⠟⠉⣇⣇⣧⠯⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢿⣿⠟⠋⡁⠀⣴⣻⣼⡿⣊⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠰⣠⣶⣿⢏⡉⠠⠠⠒⢓⡿⣻⣿⡿⠛⢿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡾⠾⢗⣿⣿⠗⠀⠀⢀⠿⠟⠁⢙⣿⣶⣷⣾⠇⠀⠀⠀ ⠀⢀⡤⢒⣈⣅⣲⣮⢢⠈⡟⢃⢀⡄⠀⠀⠔⣱⣿⣿⣿⡿⠇⠀⠀⠀⠀ ⠐⣿⠄⣀⠚⢙⡛⠁⡞⢠⣧⣀⠎⣡⢠⢣⠞⣹⣿⣿⡟⠅⣀⠀⠀⠀⠀ ⠀⠛⠛⠀⠉⢉⣷⡶⣿⣿⣿⣿⡶⢿⣟⢸⣰⣿⣿⣟⢑⣄⣻⠀⠀⠀⠀ ⠀⠀⠀⠀⢒⣿⡃⠀⣿⢾⣿⡶⠁⠀⠻⠟⢿⢻⠹⣹⣴⣿⣿⣶⡄⠀⠀ ⠀⠀⣠⣼⠋⢼⢇⡎⡏⠘⣟⡅⢠⣀⠀⠀⣼⡿⠃⠈⠿⣿⣿⣿⣿⣦⡀ ⠀⡴⠉⠀⠀⠀⠙⢿⡷⠂⢁⣬⡆⢀⠇⣼⠏⠀⠀⠀⢀⡟⡗⠟⡽⣿⠓ ⠀⠀⠀⠀⠀⠀⡠⢺⠇⠀⠥⠪⠔⠁⠀⠈⠓⠒⠛⠋⣽⣿⠷⡄⠃⣻⡇ ⠀⠀⠀⢀⠠⠊⠀⠐⠄⠀⠀⠀⢀⡴⠒⠒⠒⠲⢶⠈⠁⣃⣠⠇⠁⡹⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠟⠛⠲⠶⢶⢶⠿⠶⠞⠋⠁⠀⠔⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠁⠀⠠⠔⢢⠀⠀⠀⠉⠀⠀⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠢⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣤⣤⡀⢀⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠲⢿⣦⢄⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⣠⢾⣿⣿⣿⣿⣶⠌⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⡁⡇⠀⠀⠀⠀⡞⠁⢀⣴⢟⣹⠶⠋⣉⠛⢿⠻⣇⠀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣿⣶⣤⡀⠀⠘⠀⢺⠟⢡⣾⡴⠓⢲⡌⣇⢸⡇⣹⡳⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣀⣴⣤⣟⣴⡿⠋⠀⠀⣽⢖⡏⣼⣿⡏⢙⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⢿⣯⣿⠟⡏⢉⡄⠀⠀⣴⡟⢸⣵⣿⣿⡷⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⣶⣿⣿⡏⠶⠟⠋⠁⠀⣀⡼⣀⣤⣾⠿⣿⣿⣿⣟⣤⣵⣾⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⣀⣶⣿⣿⣿⠟⢂⣠⠤⠖⠀⠔⠉⠙⣛⣽⠃⣽⣿⣿⡿⠋⢉⠹⣿⡟⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣵⣞⣋⣼⣿⣿⣿⣾⠗⠀⠀⠀⠀⢐⢼⣻⡿⠋⠀⢻⣯⡿⣴⣾⣟⣠⣾⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠟⠛⠉⣉⡡⠾⢿⣿⡿⢡⠄⠀⠀⠀⢀⢔⠕⠋⠀⡠⠒⣲⢾⢻⣽⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠴⠒⠋⣁⣠⣐⣺⠿⣭⠆⡀⠈⢹⠏⠇⠀⣀⣀⠔⠁⠀⠀⣠⠊⢀⣾⣿⣿⣿⣿⣿⣿⡻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣠⣿⠃⠀⠈⠉⣻⡿⣿⣿⣿⠇⣠⡇⠀⣸⠂⡈⠙⣲⠟⠀⠀⢠⠀⡁⣠⡿⢋⣿⣿⣿⣿⣟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠒⠢⣄⣈⠁⢀⣈⡝⠀⠀⣿⠀⣠⣿⡾⣠⡌⠃⢠⣷⠀⣼⢠⡟⠁⣴⣿⣿⣿⣿⣿⠘⠂⠒⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⡯⠷⠽⠀⠈⠉⠛⢓⣿⣶⣴⣿⣿⣿⢷⣷⣏⣞⣦⣾⣿⣾⠇⢸⠀⣸⣻⣿⣿⢻⡻⠛⢆⠒⢬⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⡴⣿⡿⠞⠁⡿⡟⢻⣿⣿⡻⠿⣟⠉⢻⣿⣆⣸⣶⡏⢿⢿⣿⢬⡷⠀⢫⣿⣶⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠔⢋⣿⣿⢁⠀⢀⣯⣷⡿⣿⣯⣿⠏⠁⠀⠀⠁⠟⡏⢿⣿⠘⣇⠹⣇⣿⣄⣻⣿⣿⣷⣮⡿⠅⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⠟⢻⣇⡏⢀⡼⣿⠋⢠⢻⣿⠇⠀⠀⠀⠀⠀⠀⠘⠀⣽⣇⣿⡆⠘⠯⡏⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀ ⠀⠀⠀⠀⣠⣾⣫⠵⠖⠻⣏⠳⣼⡁⣿⠀⠀⣟⣼⢶⡒⠒⢶⣄⡀⠀⠀⣰⣯⣽⠟⠀⠀⠀⠹⢻⣿⡿⢿⣿⡿⣿⣿⡝⣄⠀ ⠀⠀⢀⣼⠛⠉⠀⠀⠀⠀⠉⠛⢿⣷⣞⣦⠖⠉⠀⣁⢩⡖⠀⠀⡷⠀⣼⣿⠟⠁⠀⠀⠀⠀⠀⢸⡿⢿⠾⡿⣿⢸⣿⣇⢺⠆ ⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡟⠁⠀⢠⠚⢳⡶⠃⣀⠞⠁⠘⢻⡏⠀⠀⣀⡠⣤⣴⣤⣾⣷⣼⠀⢹⠈⡇⢻⣿⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣸⠇⠀⠀⠳⢤⣪⠴⠊⠁⠀⠀⠀⠀⠉⠉⠉⠉⢉⠉⠉⢶⣿⢛⡟⢿⣦⠀⢻⠈⡟⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠰⣏⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠤⣤⣀⣀⣘⠤⠴⠋⢩⠟⠀⢀⣿⠀⡎⠸⣯⡇⠀ ⠠⣀⠀⠀⠀⠀⠠⠔⠋⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣠⣿⡉⠁⠀⠀⠀⠀⠀⠉⣽⣦⠀⠀⣀⣧⣤⠾⠋⠀⠁⣰⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠾⠷⠿⣿⣶⢶⣶⣯⣹⣟⣳⣾⣿⠟⠋⠁⠀⠀⢀⠔⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠋⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠳⢭⡈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⡠⠒⠋⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⣇⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠈⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⠤⠤⠤⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⠉⠻⣦⠀⠀⠀⠀⠀⢠⡾⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⢁⠒⣄⠘⢷⡀⠀⠀⣠⡟⡱⠋⢦⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡏⢸⠀⠈⠂⠈⠉⠉⠉⠉⠐⠁⠀⠈⡆⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡏⠀⢀⠤⣄⠀⠀⠀⠀⢀⡠⠚⠉⢆⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⢀⡞⠀⠈⠓⢄⡠⠚⠁⠀⠀⠀⠈⠣⠤⡄⠈⣷⠀⠀⠀⠀⠀⠀⠀ ⢠⡇⢇⠀⣤⣄⠀⠀⣀⣀⣀⠀⠀⢀⣤⡄⠀⢠⣃⡀⢸⡆⠀⠀⠀⠀⢀⣀ ⢸⢇⡼⠀⠙⠟⠀⠀⢛⣛⡋⠀⠀⠚⠛⠁⠀⠀⢀⠇⣠⡷⠀⣠⡴⠟⠋⡿ ⠸⢦⣷⣄⣀⠀⠀⠘⣯⣋⣽⠓⠀⠀⠀⢀⣀⣤⠾⠛⠉⢀⡾⠋⠀⠀⠀⣇ ⠀⠀⠀⠈⠉⠙⢻⠓⠶⠶⠶⠶⠒⠛⠛⠉⠉⠻⣆⠀⠀⣼⢁⣠⠄⠀⠀⢻ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡆⠀⠀⠀⢠⠀⠀⠀⠹⣆⠀⣿⠋⠸⣄⠔⣆⣿ ⠀⠀⠀⠀⡟⠻⣾⣄⠀⣀⣇⠀⢀⣠⣿⡶⠛⢳⡄⢹⣄⡿⠀⠀⠀⢀⣼⠃ ⠀⠀⠀⠀⢿⡀⠘⣧⠉⠁⣿⠓⠁⠀⡇⠀⠀⣸⠇⢸⡏⠁⠀⣀⣴⠟⠁⠀ ⠀⠀⠀⠀⠈⠻⠶⠿⠒⠶⠟⠒⠒⠒⠧⠴⠾⠿⠶⠾⠶⠒⠛⠉⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠀⠀⠘⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠈⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⣀⣀⠀⠀⠙⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⢠⣴⣦⡀⠘⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⠁⢰⡟⠻⣷⡀⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⣰⡟⠁⠈⢿⡀⠈⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⡏⠀⣾⠀⠀⠘⢷⣄⠀⠀⢿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣟⠀⣰⡟⠀⠀⠀⠈⣿⡀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⠀⢠⡏⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠟⠀⠀⠀⠀⠀⠘⣇⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡟⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⣿⠏⠀⠀⠀⠀⣰⡾⠛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠁⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⡿⠀⠀⠀⠀⢠⡿⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⣀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⠃⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠙⠻⣶⣄⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣤⣤⡄⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⡟⢰⡿⠋⠉⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⡇⠸⣷⠀⠀⠘⣷⣶⣦⣄⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⡶⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠇⠀⢻⡆⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠈⠛⠛⠳⢶⡆⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶ ⢸⣿⠀⣀⣼⡧⠀⠀⠘⠿⣿⠟⠃⠀⠀⠀⠀⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠐⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⣸⣿⡇⠀⠀⠀⢀⣴⣾⣿⠿⠛⠉⢹⣿⡟ ⢸⣿⠐⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣠⣶⣾⣿⠿⠁⠀⣠⣾⣿⠿⠋⠁⠀⠀⠀⢸⣿⠀ ⣾⣿⣤⣙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⠋⠿⠀⢹⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⠿⠛⠉⠀⠀⢀⣼⣿⡟⠃⠀⠀⠀⠀⠀⠀⢸⣿⠀ ⠉⠛⠿⠿⠿⣿⣷⣶⣶⣤⣄⣀⠀⠀⠀⠀⠘⢿⣷⣤⣶⣿⠟⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣶⣾⣿⡿⠛⠉⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⣿⣿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⡿⠿⠟⠛⠛⠋⠙⢿⣿⣄⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀⠀⠀⠀⣿⡿⠀⣠⡶⢿⡿⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⠀⠀⠀⠀⣿⣧⡾⠋⠀⢸⡃⠀⠀⢀⣀⡀⠀⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⠀⠀⠀⣿⡇⠀⠀⠀⠸⣿⣠⣴⠟⠉⣷⢠⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣄⣿⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⣀⣤⣤⣤⣤⣄⠀⠀⢹⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠉⠻⣿⣿⣿⡀⠀⠀⠀⠀⣠⣿⡇⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⠿⠋⠉⠻⣿⣷⠀⠀⣿⣿⡀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠘⢿⣿⡟⢷⣤⣴⡟⠋⣿⣷⣄⢀⣴⠿⠋⠁⣿⣿⠛⠁⠀⠀⠀⠀⢸⣿⠀⠀⠸⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⠈⣿⣧⠀⠈⠀⠀⠀⣿⣯⠙⠛⠁⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⢀⣿⡏⠉⠀⠀⠀⠀⠀⢀⣠⣾⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡄⠀⠀⢹⣿⡆⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣼⣿⠇⠀⠀⣼⣿⠇⠀⠀⢀⣠⣴⣾⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣶⣾⣿⣷⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣿⣧⣤⣤⣶⣶⣿⣿⣿⣶⣶⣾⣿⣿⣶⣶⣾⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⡁⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⡇⢀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠈⢧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢸⡿⡘⣦⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢀⢎⡄⠸⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⡾⡇⠳⢹⣇⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣏⡞⣧⠀⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⡇⢰⣿⠹⡀⠀⢿⡄⠀⠙⢦⣄⣀⠀⢀⣀⡴⠋⠀⠀⡼⠈⢠⢿⠀⢹⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣧⡾⡽⣆⠁⠀⢸⡇⠀⠀⠀⠀⠈⢩⡉⠁⠀⠀⠀⢰⡇⠀⢊⣎⠄⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢻⣳⣧⠈⠂⢀⡞⣀⠔⠀⠀⠀⠀⠀⢧⠀⠀⠀⠘⣼⡇⢀⠾⡿⢀⣼⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣆⠀⠀⣑⡦⣤⠖⠛⠋⠁⠀⠀⠀⠀⠀⢀⣼⣧⡄⠀⠀⠈⠳⣤⡺⠷⢫⢿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠦⣠⡾⠟⠋⠀⠀⠀⠀⠀⢦⢄⣀⠀⠀⠀⠀⠹⡅⠀⠀⠀⢀⢼⠹⣍⠠⣾⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⢈⣳⡿⠚⠁⠀⠀⠀⠀⠀⠀⢸⡆⠈⠳⣄⠀⠀⠀⣇⠀⠀⣴⠁⠈⣇⠻⡿⠯⠄⠀⠀ ⠀⠀⠀⣀⡤⢶⡚⠉⠠⢴⣾⡿⡖⠒⠂⠀⠀⠀⠀⠀⠠⣤⣼⣧⡀⠀⠸⣦⠀⠀⢸⠀⣠⣿⠀⡰⡷⢶⠙⡢⡀⠀⠀ ⠀⢠⣾⣵⠞⠋⠀⠀⡴⣋⡴⠋⠀⠀⠈⣓⣶⣦⢤⡤⢞⣍⣀⣉⣀⡀⠀⢋⣿⡀⠘⡆⢻⣇⣠⢶⣦⢴⣷⣿⣿⡆⠀ ⠀⣾⢟⡱⠂⠀⠀⢈⡾⢁⡠⠄⢠⣖⡫⠏⠀⠀⠁⢀⡀⠈⠻⣿⢻⣿⣦⡌⣱⠇⠀⣿⡀⠻⣿⡿⠇⡄⠈⠻⡾⡷⠀ ⣸⣯⢏⡄⠀⠀⠀⣾⣰⠏⠀⠠⣿⡫⠆⠀⠀⠀⠀⠀⠙⣄⠀⠈⠙⠒⠿⡇⠀⣀⣴⣿⣷⢶⣟⠁⢶⡇⠀⠀⢿⡇⠀ ⣿⡏⡞⢀⠀⠀⠈⢿⣯⠃⡀⢰⣿⢡⠇⠀⠀⠀⠀⠀⠀⠈⢷⣤⣀⡀⠀⠀⣧⠈⢿⡏⠀⠀⠈⠳⣄⠀⠀⢸⣸⠃⠀ ⢹⣿⠀⡞⠀⠀⠀⣼⡏⣼⠁⠈⣿⣟⣠⢀⠃⠀⠀⠀⠀⠀⠈⠹⠯⠃⠀⠀⢹⣦⠘⣧⠀⠀⠀⠀⠈⠳⣄⣾⠏⠀⠀ ⢸⣟⣸⡇⠀⡀⠀⠹⣷⡏⣼⠀⠈⣷⣧⠜⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠙⢆⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀ ⠀⢻⡿⣇⠀⡇⠀⠀⢻⣷⣿⡀⠀⢋⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠑⠀⠀⠀⠀⣀⣀⡹⣄⠀ ⠀⠀⠑⢻⡦⡇⢀⠀⠀⠘⠟⣧⣴⣋⠴⠒⠒⠛⠂⠤⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⣴⠚⠉⠉⠉⠉⢙⡆ ⠀⠀⠀⠀⢻⣷⡏⢠⠀⠀⠀⢻⡗⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄⡈⠙⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠻⣷⣶⣶⣶⣶⣿⠃ ⠀⠀⠀⠀⠀⠿⣿⣸⡄⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠈⢉⢽⣟⠿⠁⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣷⣿⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡛⠒⠒⠋⠉⢉⣹⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡝⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⢷⡻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠻⡿⢷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠂⡾⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢀⡀⡟⣯⠙⠺⠶⡤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡽⣿⠋⠀⣠⠆⠀⠀⠀⢀⡜⠁⠀⠀⣠⠟⠀⣠⢎⡼⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢕⣣⠞⠁⠀⣀⡤⠞⣉⣀⣤⣖⠯⠥⠖⣺⠯⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⢽⣿⣛⣥⠤⠾⠛⠛⠛⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⠀⠀⠀⠘⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⠏⠀⠀⠀⠀⠘⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣥⣷⠇⠀⠀⠀⠀⢹⣿⣿⣿ ⣿⣿⣿⡇⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣸⣿⣿⣿ ⣿⣿⣿⣿⡆⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⢠⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣄⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢠⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠀⢀⣴⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠘⡀⠀⠀⠀⢀⡼⠃⠘⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣌⠁⠀⠀⠡⣕⢌⠉⠙⢅⡄⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠼⠈⡐⠤⠤⠊⠙⢈⢷⡀⢂⠁⢰⠁⠀⠀⠀ ⠀⠀⠀⠀⢠⠎⠰⠀⢊⠆⠀⠀⢀⣀⡋⡟⣁⣀⣸⡀⠀⠀⠀ ⠀⠀⠀⡔⠁⠀⠁⠔⠁⠀⢀⡴⠛⠋⠙⣾⠛⠑⠌⡿⡀⠀⠀ ⠀⠀⢸⠀⠀⠀⣠⠶⠰⠶⣎⠐⢯⣷⠀⡿⢰⠾⢻⠀⢣⠀⠀ ⠀⠀⢾⠀⠀⡜⠀⠀⠀⠀⠀⠁⠀⠀⠈⡀⠀⠐⡆⠀⢸⠀⠀ ⠀⠀⢸⠀⢸⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠈⠢⢄⠈⣢⠂⠀⠀ ⠀⠀⡇⠀⠜⣄⠀⠀⠀⠙⠢⣌⠲⢄⠀⠀⠀⢇⠂⣾⢆⠀⠀ ⠀⢸⠁⡀⠈⠪⣢⢄⠀⠀⠀⠀⠉⠐⠓⠒⠀⠒⠊⠁⠈⡆⠀ ⠀⡇⠀⢻⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡇⠸⡄ ⠀⡇⠀⠈⢷⡈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡣⠃⠀⠈ ⠀⠱⠀⠀⠀⠙⢆⠹⡄⠄⠀⠀⠀⠀⠀⠀⠜⠠⠊⠀⠀⠀⠀ ⠀⠀⠑⠀⠀⠀⠈⠂⠃⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠰⠶⡶⠶⠶⠶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀

⢸⣷⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢿⡪⡑⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣔⣌⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⠇⠀⠀⣈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢻⡦⡀⠉⢢⡀⠀⠀⠀⠀⠀⠀⣼⠒⠦⢄⡀⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⢳⡀⠀⠀⠀⠀⡴⠛⠻⠥⣲⣭⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢇⣠⣴⣖⣾⣦⢤⣀⠀⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⣤⣪⠽⠋⠈⣆⠀⠀⠉⠙⣿⡯⡀⢀⡠⠖⠒⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡯⠧⠄⢰⡒⠈⠉⠉⠒⢖⠈⠁⢹⠻⡋⠀⠀⠀⢀⠀⠀⡉⠑⠂⢠⠤⠤⠤⢤⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⣜⡹⠀⠀⠀⠀⢣⠀⠀⠀⠀⢀⡵⠤⣈⢳⢧⡴⣲⣼⠭⠵⠮⠙⠛⠛⠛⠛⠚⠙⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⣸⡽⠀⠀⠀⠀⢀⠤⠳⠤⣤⠔⠉⠀⠀⠀⠙⣺⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⢹⠓⠒⠂⢠⡞⠁⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⣁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡯⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⡠⠷⢄⣀⠀⢰⢫⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⣠⠔⠚⠒⠢⡖⠋⠀⠀⠀⠈⢉⠶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡗⠒⠒⡍⠀⠀⠀⠀⠀⢳⣀⡀⠀⠀⢀⣺⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡟⡄⠀⢱⡀⠀⠀⠀⣠⠋⠀⠈⠙⢢⣏⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⢿⢧⣠⠞⠋⠓⠒⣞⠁⠀⠀⡠⣴⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠏⢘⣿⢢⠀⠀⠀⠀⣘⣦⣔⡾⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠟⠁⣐⣿⠉⢿⣲⣤⡿⠿⢷⣾⠁⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⠀⢰⣿⠃⠀⠀⠉⠀⠀⠀⡞⡿⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣴⡿⠋⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢽⣀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⢀⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡄⢾⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢷⡄⠙⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣦⠸⠿⣿⣿⣟⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⣿⡈⠛⢧⠈⣦⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⢾⣤⣀⡀⠀⣸⣿⢧⠀⠘⢷⠀⠀⠘⠻⣦⣼⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⢬⣛⠻⠟⠛⠛⠛⢸⡇⠀⢠⢿⣿⣿⣷⡟⠉⢳⣿⣿⠓⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠳⣶⣄⠀⠀⠸⣇⠀⠀⠈⠋⣹⣿⠘⣧⣈⢿⣏⢁⠈⢻⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣷⣦⣤⣈⠑⠀⠀⢟⣽⣿⣷⣌⡛⠂⢿⣿⣴⣄⢈⠻⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢯⡛⢝⣯⠅⣀⢲⣾⣿⣿⣿⣛⣷⣶⣬⣍⣉⣩⡤⠞⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⣞⠅⠯⠽⣿⣿⣿⣿⣿⣿⣿⡿⠷⢾⣯⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⠀⠤⠴⠻⢽⣿⣿⠉⠋⠀⠀⠀⠀⢿⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⣻⣿⣿⣦⠀⠀⠀⠀⠀⠀⣸⣿⣦⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠀⠀⠚⠛⣿⣿⣿⣠⡀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣀⣀⣾⣿⣿⣿⣿⣷⣿⣷⣾⣿⣿⣿⣿⣿⣿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠈⠈⠀⠘⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⢈⠾⣿⣿⣿⡿⣿⣿⣿⣿⣿⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣠⠀⠀⠀⠀⠛⠉⠁⠀⣥⣿⣿⣿⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⣴⣤⣠⣤⣦⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⣴⡿⠛⠙⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⣫⡉⠻⣿⣧⠀⠀⠀⠀ ⠀⠀⣸⡿⠀⣶⣤⡀⠈⢳⣄⠀⠀⠀⠀⠀⣀⣶⣿⠋⢠⣿⣿⡄⢘⣿⡀⠀⠀⠀ ⠀⢠⣿⡇⠀⢸⣿⣿⣆⠈⣿⣷⣶⣿⣾⣾⡿⣿⣇⠀⢸⣿⣿⣧⠀⢹⣇⠀⠀⠀ ⠀⢸⣿⣇⠀⣸⣿⣿⣿⣼⣿⣷⣿⣿⣿⣼⣧⣿⣿⠀⣾⣿⣿⣿⡀⣸⣿⠀⠀⠀ ⠀⢸⣿⡿⢠⣿⣿⢟⣻⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣦⣻⡿⣿⣿⠛⣿⣇⠀⠀⠀ ⠀⢸⣿⣧⣘⣿⣿⡟⠋⠉⠀⠀⠘⢿⡿⠉⠈⠙⠛⠉⣍⡳⣦⣍⣣⣿⣿⣆⠀⠀ ⠀⣽⣿⣿⣿⣿⣿⠀⢀⣀⠀⠀⠀⣼⣁⠀⠀⠀⣀⣤⡈⠻⢿⣿⣿⣿⣿⣿⡀⠀ ⢰⣿⣿⣿⣿⢟⣥⣾⣭⣿⣿⢸⡆⠿⠏⢰⠖⢺⣿⢿⣿⣦⣄⣀⣈⣿⣮⠟⣷⡀ ⣼⣿⣿⠟⣵⣿⡏⣾⠙⢦⣼⠈⠁⠀⠀⠀⠀⣧⡤⠛⣽⡏⢹⣿⣿⣿⣷⣄⢾⣷ ⢻⣿⡷⣸⣿⣿⣇⣿⣧⡀⠈⣆⠀⠀⠀⠀⣾⠁⠀⣴⠏⠀⠀⠹⣿⣿⣿⣿⣸⡟ ⢸⣿⠱⣿⡏⠁⠈⡈⠿⡏⠀⠀⠀⠀⠀⠀⠉⠀⠈⠋⠀⠀⠀⠀⠙⠇⠹⣿⣿⡇ ⠘⣿⣸⣿⠁⠀⢀⣹⡀⡀⢀⡇⠀⠀⠀⠀⢿⡄⠀⣠⣾⣃⠀⠀⠀⠀⣦⣁⡟⠀ ⠀⣿⣿⠟⣠⠔⠋⠻⣿⡗⠈⠃⣀⡤⠤⣀⠈⠃⣸⢛⣩⣄⡀⣶⣤⣤⡟⠁⠀⠀ ⠀⠸⢴⣾⢏⣀⡀⠀⠈⢷⠀⣼⡃⠀⠀⢈⡇⠀⣷⣿⣿⣿⣿⡿⠿⡟⠀⠀⠀⠀ ⠀⠀⠀⠹⠛⠻⠷⣧⠀⠈⣦⣿⣿⣿⣿⣿⣧⡴⠟⠻⠋⠙⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠓⠛⠻⢟⣛⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⡉⢻⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⢿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⡇⠸⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠙⠁⠀⠀⠈⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⠋⠁⣰⣿⣿⣿⣿⡿⠛⠉⠉⠙⠻⢿⣿⣆⠀⠀⠀⠀⢀⣼⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣟⣡⣴⣾⣿⣿⣿⣿⡏⢀⣴⣶⣿⣶⣶⣄⣉⠉⠃⠀⢠⣴⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡿⠋⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠿⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠃⠀⠀⢀⡤⠈⢻⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢰⡿⠟⢋⣠⣴⠊⠀⣴⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⡞⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⡇⠀⠉⣠⣶⣿⣿⠇⠀⣸⣿⡿⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠖⠀⠀⢿⣿⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣷⣴⠾⠿⠿⣿⣿⠀⢠⣿⣿⠁⠰⠛⠁⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⡄⢸⣿⣿⠏⠀⠀⠀⠀⠀ ⣠⣾⣿⠋⠀⠀⠀⠙⠻⣿⡿⠋⠀⠀⠀⠀⠈⢻⡀⢸⣿⣿⠀⠀⠀⣠⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠄⣸⠁⠈⣿⡿⠀⠀⠀⠀⠀⠀ ⠘⢿⣿⡀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠳⠸⣿⣿⡄⠀⢰⣿⣿⡏⢀⣼⣿⣿⣿⣿⠛⠛⠉⠀⢀⣿⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠻⣶⣶⣶⣶⣾⣿⣿⣦⣄⣀⣀⣀⣤⠖⠂⠀⢿⣿⣿⣄⢹⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣶⠞⠁⢸⣿⡆⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⡿⠟⠋⠁⢀⣴⡀⠈⢿⣿⣿⣾⣿⣿⣇⣿⣿⣿⣿⣿⣿⣋⠁⠀⠀⢸⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣴⣾⣿⣿⣷⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣛⠉⠀⠀⠘⣿⣿⠀⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠿⠛⢛⣿⣿⣿⣦⡀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣷⣌⠹⣷⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣆⢸⡇⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⢿⣿⣿⡻⢿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠈⣿⣿⠀⡇⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡄⠈⠙⠻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢸⣿⠀⠃⠀⢸⣿⢡⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠘⣿⣿⣄⠀⠀⠈⠙⢿⣿⣿⣿⣿⣧⡀⠀⠀⠀⡟⠀⠀⢀⣿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣸⣿⣿⣶⡞⠈⢳⣤⣻⣿⠉⢿⣿⣷⠀⠀⢀⠇⠀⠀⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠁⠀⠀⢻⣿⣿⠀⠈⢿⣿⡆⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠋⠀⠀⠀⣸⣿⡟⠀⠀⢸⣿⡇⠀⠀⣠⠞⠋⢀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⢠⣿⡟⠀⠀⠀⢀⣿⠇⠀⠀⣠⣴⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⠀⣸⡟⠀⠀⢠⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⢀⣴⠟⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⢠⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣤⣤⠮⢷⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣦⣍⣙⡒⠤⠤⠴⠖⠛⠟⠛⡋⠁⢁⠆⣠⠆⢋⠁⠭⠶⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣿⣿⣷⡆⠉⠁⣠⠞⠉⠀⠀⠊⢠⡇⠄⠀⠃⠀⠂⠬⣓⣄⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⠋⠁⢀⠞⣡⠴⠂⠀⠀⠀⠈⠁⠰⠃⠈⣷⣂⣀⠀⠹⣄⡀⠀⠀⠀ ⠀⠀⠀⣹⠃⠀⠀⣾⣾⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡛⠍⠁⠛⢦⠀⠀⠀ ⠀⠀⢈⡏⣠⣦⣿⣿⠋⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢒⠮⢅⡐⠈⢷⠀⠀ ⠀⠀⣸⣹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢱⠀ ⠀⠀⢻⣿⣿⣿⣿⣦⠀⢄⣴⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⡀⠑⠄⠘⡅ ⠀⠀⠀⣿⠞⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⡈⠛⢦⡈⢂⡇ ⠀⠀⠀⡜⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠙⢄⢇ ⠀⠀⣜⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣏⠒⢄⠀⢂⠀⠀⠘⣆⡿⣾⡟ ⠀⣜⣿⣿⠟⠀⠀⠀⠀⠀⠀⣀⣤⠔⠊⠛⠉⠀⢁⠀⠰⡁⠀⢷⣠⣧⡇⠇⠙⠀ ⣼⣾⣿⣧⠀⠀⠀⢀⡀⠀⣼⡟⠃⠀⡀⢸⠀⠀⣸⡈⠀⢃⢠⡾⡿⠋⠁⠀⠀⠀ ⠘⠻⣿⣌⠀⢀⣒⢀⣴⣿⣿⣧⣿⣴⣷⣿⣰⡿⢻⢣⡇⣸⣼⠓⠁⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠛⠒⠈⠉⠈⠀⠰⡿⠃⠈⠙⠝⠉⠀⠋⣸⣷⡟⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡀⢀⣀⣀⣀⣀⠀⠀⣠⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠙⢿⣿⣿⠁⠙⣿⣧⡀⠀⠀ ⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠐⠻⣷⣦⡀⠈⢻⣿⣀⣴⢼⣿⡷⠀⠀ ⣴⣾⣿⣿⣿⡿⣿⣿⡟⠟⠁⢻⣿⣿⣷⣦⣄⣀⡀⠈⠀⠀⠙⢿⣦⣼⣿⣷⠀⠀ ⣿⣿⣿⣿⣿⡇⠈⠋⠀⠀⠀⠈⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠙⣿⣿⡏⠀⠀ ⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⣆⡀ ⢹⣿⣿⣿⣿⡇⣠⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟ ⠘⣿⣿⣿⣿⣿⡏⢀⠀⠀⠀⠀⠀⠘⠿⣿⣿⡿⢿⣷⣦⣄⡀⠀⠀⢀⣼⡟⠁⠀ ⠀⢹⣿⣿⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⠙⠋⠛⡕⠒⠛⠛⠀⠀⠀ ⠀⠀⢻⣿⣿⣿⣿⡇⢀⠀⠀⠀⠀⣀⣠⣤⣤⣄⡉⠻⣷⣤⣆⣀⡴⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣿⣿⣿⣷⣿⠀⠀⠀⠈⠁⠀⠛⠛⠛⣿⣷⣌⠛⠛⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠿⣿⡄⠀⠀⠀⠀⢀⣴⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠿⣿⠟⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠛⠛⠛⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⡟⠉⠀⠀⠀⠀⠈⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠟⠁⢰⣿⣦⡀⠀⠉⠻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⡿⠀⠀⣶⣤⣄⡀⠀⠀⠀⠙⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡿⠃⠀⢠⣿⣿⣿⣷⡀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⠇⠀⠀⢿⣿⣿⣿⣷⣄⠀⠀⠈⣿⣿⣦⣀⠀⠀⠀⢀⡀⠀⢀⠀⢀⣠⣾⣿⣿⣿⡿⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⢸⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⣦⠀⠀⠘⣿⣿⣿⣿⣶⣷⣾⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡧⠀⣀⣻⣿⣟⢻⣿⣿⣿⣿⣿⣿⡟⣿⣿⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡄⢹⣿⣿⣿⣼⣿⣏⣿⣿⣿⣿⣀⣿⣿⡀⢻⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣧⡀⠀⣰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢠⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⡅⢰⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠘⢹⣿⣿⣿⣿⣿⣿⠇⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⡇⠠⢿⣿⣿⣿⣿⣥⣴⣾⣿⣿⡿⠟⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣏⠈⠟⠻⢿⣿⡆⠀⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣹⣿⣿⣿⣇⠀⠼⣿⣿⣿⣿⣿⡿⠋⠀⠈⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⠋⠀⠀⠀⠙⠛⠛⠂⠀⠠⣀⠙⠻⣿⣶⣤⣀⠈⠙⢰⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣬⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀ ⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣠⣴⣾⣿⣶⣦⡄⠀⣄⡀⢀⣿⣿⣷⡶⠀⠀⡀⠀⣀⣴⣾⣿⣿⣿⣿⣦⡀⠀⠙⠋⠙⠛⠛⢻⣿⣿⡿⢿⣿⣿⣷⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣡⣴⣿⣿⣤⣶⣶⣿⣿⡿⠀⢸⡇⠘⢿⣿⡿⠃⠀⣾⡷⠚⠙⣿⣿⣿⣿⣦⣹⣿⣿⣦⣄⣀⡀⠀⠀⠀⢿⡟⣻⣤⡿⠿⣿⣷⡀⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⡿⢋⣤⣾⣿⣿⢻⣿⢿⣿⠙⠿⠻⣿⠀⢸⡇⠀⠀⠁⠀⠀⠀⠟⠁⢀⣴⠟⠿⠋⢸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠹⣿⣿⡄ ⢸⣿⣿⣿⣿⣿⡿⠋⣴⣿⣿⣿⣿⠃⣼⣿⠀⠙⢿⣦⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣤⡶⠟⠁⣸⣿⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⢾⣿⣿⡇ ⣿⣿⣿⣿⣿⡏⠀⣸⣿⣿⣿⣿⣿⠀⣿⣿⣆⠀⠀⠈⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⠁⠀⠀⣠⣿⡿⠃⠀⠀⠘⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⡇ ⠙⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⣿⣿⡀⣾⣿⣿⣦⡀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⣴⣿⡿⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣿⡇ ⠀⣾⣿⣿⡟⢀⣾⣿⣿⡟⠻⠏⠙⢷⠘⣿⣿⣿⣿⠦⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢸⣿⠟⠁⠀⠀⠀⠀⠀⠀⠸⡟⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⡇ ⠀⣿⣿⡟⠀⠛⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⠻⢿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⢻⣿⣿⣽⣿⣿⠇ ⠀⣿⣿⣿⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⢸⣆⠀⠈⠁⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⣀⣴⡶⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢿⠇⣿⣿⠛⠀ ⠀⠉⢹⣿⣰⣿⣿⣿⠇⠀⠀⠀⢀⣀⣀⣿⣆⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣌⡀⣿⠃⠀⠀ ⠀⠀⢸⣿⣿⢣⣿⡿⠀⠀⠀⣀⣼⣿⣿⣿⣿⣞⣿⡆⠀⢸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠀⠀⣰⣿⣿⠿⠟⠛⠉⠁⠀⣤⣀⠀⠀⠀⠀⣿⣿⡿⠛⠃⠀⠀⠀ ⠀⠀⢿⣿⡟⢸⠟⠁⣀⣴⡾⠋⠁⠀⠈⠻⣿⣿⣿⡇⠀⠈⠀⠀⣀⣤⣤⣤⢦⣤⣤⣄⠀⠀⠀⠀⢸⡿⠋⣀⣤⣤⣤⣤⣀⠀⢿⣿⣿⣶⣶⣶⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣿⡇⣀⣴⣾⣿⠏⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⣸⣧⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠿⢿⣿⣿⡏⢀⣠⣤⡄⠀⠀⠀⠀⠀⠹⣷⠀⠀⢾⣿⡅⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⣠⣴⡄⠀⠀⠀⢹⣧⡀⢸⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⡇⠀⣠⣿⣿⣿⣿⣿⠛⠻⣿⣿⡟⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠉⠛⠛⠿⢿⣷⡀⠀⠀⢀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⠋⠁⠀⠙⠁⠀⠀⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣤⡾⢿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠉⠀⠈⠛⠷⠶⠶⠶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⠶⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣄⣠⣴⣀⣼⣶⡶⢾⠿⢻⠟⠁⠈⠻⣦⣤⠴⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣶⣤⣀⣈⡉⠛⠶⠦⣤⣤⡾⠿⠟⠛⠩⠟⠉⠛⢉⠁⠀⠀⢀⡎⠀⣠⠾⡇⠹⡀⠀⠠⠬⠽⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣿⣿⣿⣿⣶⣄⣀⡀⠤⠖⠀⠀⢀⣠⡤⠒⠉⠀⠀⢀⠞⠀⣠⡟⠀⡇⠀⠱⠒⠊⠀⣀⠀⠙⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣿⣿⣷⣿⣿⣿⡿⠃⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⢃⡞⠀⣀⠀⢣⡀⠀⠀⠈⠉⠲⢍⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⡿⠈⠁⠀⠀⣰⡟⠁⣀⣤⠖⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⣴⠏⠀⠈⣿⣶⠦⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⠀⣸⠏⣠⡾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣿⣿⣷⣶⡶⠦⠤⠤⣈⣿⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⢸⣿⣾⡿⣋⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣟⡛⠒⠂⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⣿⠃⠀⣀⡀⣿⣾⣿⣿⡿⠋⠉⠉⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣯⣭⣉⡑⠒⠠⠄⠀⠻⣷⡄⠀⠀⠀ ⠀⠀⠀⠠⣼⡟⣰⣾⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠉⠉⠛⠲⢄⠀⠀⠙⢷⡀⠀⠀ ⠀⠀⠀⠀⣾⡁⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⢹⡄⠀ ⠀⠀⠀⢰⣿⣷⣽⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢸⡷⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⠆⠘⠂⣴⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣤⣰⣄⠀⠈⢦⡀⠀⣷⠀ ⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣄⠀⠱⡀⢹⠀ ⠀⠀⠀⠀⠀⢻⡟⠁⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠦⢀⠀⠈⠛⢷⡀⠐⣾⡀ ⠀⠀⠀⠀⠀⡼⠁⢰⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠙⢄⠸⣇ ⠀⠀⠀⠀⡼⢁⣴⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡶⠤⣄⠀⠀⠀⠠⡀⠀⠀⠀⠀⢹⣄⠀⣷⣤⣸⣿⡿ ⠀⠀⠀⣼⣡⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⠿⡿⡗⠄⠀⠑⢦⡀⠀⠱⡀⠀⠀⠀⠀⢿⢷⣽⠹⣿⡿⠇ ⠀⠀⡼⢩⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠖⠛⠻⠯⠉⠃⠀⠈⠀⠀⠀⢦⢱⠀⠀⢹⣦⠀⡀⣦⣸⠀⣿⠀⠙⠁⠀ ⠀⣼⣳⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⠁⠀⠀⠀⠀⡄⠀⠀⠀⢀⡆⠀⠀⠈⣾⠀⠀⠈⣿⣶⣿⠿⣿⠀⠉⠀⠀⠀⠀ ⣼⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣀⣀⠤⢤⣿⢿⡃⠁⢀⠀⢀⡀⢸⡇⠀⠀⠀⢸⡇⠀⡇⠀⢹⡀⢠⣼⣿⡟⠻⠀⠃⠀⠀⠀⠀⠀⠀ ⠙⢿⣿⣿⣯⡙⠋⠀⠀⠀⢀⣀⣈⠣⢤⣴⣿⣿⣾⡇⣿⣾⢀⣾⣥⣿⣷⠀⣶⣶⣿⣷⣧⣳⠀⢸⡇⣸⡿⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠻⣿⣷⣤⡀⠀⠐⠲⣤⣤⠿⣿⢿⢿⡿⣿⣿⣿⡿⢻⣿⢿⣿⣿⣾⡿⠏⢸⡟⢹⣿⠀⣸⣷⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠉⠉⠈⠀⠀⠀⠀⢰⢿⣿⠏⠀⠁⠀⠊⣼⠋⠁⠀⠀⠚⠁⣸⣿⡾⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠏⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⣠⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡟⣇⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡿⠃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡿⠣⠼⢷⡞⠁⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠈⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣇⠀⠀⠀⠈⠢⣄⠀⠈⠻⣦⡀⠀⢀⣀⣠⣤⣄⡀⣰⠟⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣴⣿⡀⢀⣀⠀⠀⠈⠓⠦⣀⠈⢹⡟⠋⠉⠀⠀⠈⠙⠛⠶⣦⣀⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⣿⣿⢁⡀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⡀⢿⣷⡴⠞⠛⠛⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢻⣿⣷⣹⣯⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⠿⠋⠁⠀⣀⣸⠇⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠼⢿⡌⠛⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠉⠉⢀⣠⡴⠞⠛⣻⠏⣰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⡄⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠶⠛⠁⠀⣠⡾⠃⠀⢙⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠋⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢠⡾⠻⠶⢤⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⢀⣤⠾⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣰⣟⡁⠀⠀⠈⠉⠙⠛⠳⢶⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⣿⡄⠀⠀⠀⠀⣀⣭⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⢿⣮⣷⠀⠀⠀⠐⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⢿⣏⡉⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣼⡀⠀⣐⣶⡀⣀⠹⣷⣄⠀⢸⡏⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣤⣬⣿⡦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⣿⣦⣿⣿⣿⣿⣿⣏⠙⢷⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡍⠻⠂⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣴⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣦⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣿⣿⣿⣿⣿⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣼⣷⣷⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠓⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣈⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⢠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠀⢠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢦⡀⠛⣿⠁⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡏⠀⢸⣿⠛⣑⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡆⠓⡆⠛⣶⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⣦⠑⠺⣾⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⣾⠛⡖⠃⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡆⠓⡄⢹⡆⠀⠉⣷⠀⠀⠀⠀⠀⠀⠈⠹⠯⠁⠀⠀⠀⠀⠀⠀⢰⡾⠁⠀⣾⠉⣾⠁⢲⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⢹⠈⢹⡇⠀⡿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇⢀⣿⣏⣹⠉⣺⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠈⣿⣀⣹⠀⠙⠛⠃⠘⠛⢣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡟⠛⠃⠘⠛⠃⢸⣀⣸⣗⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠶⠞⠛⠛⠛⠛⠳⠶⣆⡿⠀⠀⠀⠀⢀⣀⣤⠀⠙⣷⠀⠀⠀⠀⠀⠀⢰⡾⠏⠀⣀⣠⡀⠀⠀⠀⢸⣿⣰⠶⠟⠛⠛⠛⠛⠷⠶⣀⠀⠀⠀⠀ ⠀⠀⣤⠾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠸⠿⠿⠀⠀⣉⣷⠀⠀⠀⠀⠀⣾⢭⠀⠀⠿⠿⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡄⠀⠀ ⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠀⠀⠀⠀⢀⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡇⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡟⠛⠀⠀⠀⠀⠀⠀⠘⠛⢳⣴⣶⣤⣤⣤⡔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠸⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⣀⠀⢠⡿⠇ ⠀⠺⣧⡀⢠⣀⠀⠀⣀⣟⠛⠛⣧⣄⡀⠀⠀⣸⡇⠀⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣷⣾⡇⠀⢀⣠⣼⣿⣿⣿⣟⣀⣀⣀⣶⣁⢰⡾⠗⠀ ⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣦⣴⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠹⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠟⠛⠛⠋⠉⠉⠉⠉⠉⠉⠛⠛⠛⠿⢷⣦⣬⠻⠽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣶⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⠟⠉⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠉⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣽⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⡏⣤⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⡀⠀⠀⢤⢠⣼⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⠁⠀⠀⠀⠀⣴⡾⠁⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠈⢻⣇⠀⠀⠈⣇⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠀⡀⣀⠀⢠⣿⠃⠀⠀⢀⣾⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡷⠀⠀⠀⠀⠀⢸⣿⠀⢠⣠⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⣷⣇⣽⠀⢈⡏⠀⠀⠀⠸⣿⣿⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⣤⠥⠀⠀⠀⠀⣿⣿⣧⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⠿⣿⣧⣾⣿⡄⠀⠀⠀⠙⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⢸⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡇⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣼⣿⣀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⣠⣶⣾⠿⠛⠛⠻⢷⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠋⠉⠉⠉⠛⢿⣦⡀⠀⠀ ⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠙⣿⡆⢀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⡟⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⠀ ⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣿⣷⣧⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢠⡾⣠⣇⣠⣿⣿⣿⡇⠀⢀⠀⠀⠀⢀⠀⠀⢹⣷⠀ ⣿⣷⡀⠀⣷⠀⠀⠀⣼⣦⣴⣿⠏⠙⠻⠿⣷⡿⠷⣶⣶⡾⠿⠿⠷⢶⣶⣦⣤⣾⣿⣷⣿⣿⠿⠿⠛⠛⠙⠻⣿⣤⣾⣇⠀⢀⣸⣇⣀⣼⣿⠃ ⠘⢿⣿⣾⣿⣷⣴⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠟⠛⠛⠁⠀

٠࣪⭑ ╱|、 ≽(` - 7 ⋆˚࿔ |ᝰ 〵 ╭ ───⋆⋅☆⋅⋆──じしˍ,) ノ ──⋆⋅☆⋅⋆──

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢗⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡛⠛⢹⣿⠀⠀⠀⠀⠀⠀⡇⠀⠈⠋⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡿⠎⠀⠀⠀⠀⠀⠀⠻⠶⠶⠝⠋⠀⠀⠀⠀⣠⢤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠼⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⡆⠀⠀⠀⠀⢰⠛⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠍⣇⠶⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢲⠒⣲⡦⠼⠁⠀⢿⡀⠀⠀⠀⢸⡁⠀⡀⡙⠦⣄⣂⡶⠶⠿⠟⠛⠁⣠⡤⣦⣺⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣧⠀⠈⠀⠀⠈⠫⣤⠖⠒⠀⠀⠀⠀⠀⣴⣮⠹⢷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣒⡶⠋⠀⠀⠀⠀⠀⡿⡆⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⢽⣿⠀⣨⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⢹⣻⣿⣿⡇⠀⠀⣴⣿⡆⠘⠛⠹⡡⢀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠉⣉⢭⣶⡆⠀⠉⢻⡇⢀⠀⢠⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢳⡄⠀⠀⠀⠀⠠⡞⣩⢓⡞⠐⠒⠶⠚⠉⡅⣘⡐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠛⠷⣤⣆⠀⢁⠾⠁⢣⡇⠀⠀⠀⠀⠀⢜⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢑⠆⠀⠀⠀ ⠀⡖⣒⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⡀⠀⠀⠀ ⢸⣟⠉⠉⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡄⠀⠀⠀ ⠈⠓⢷⡄⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣧⠀⠀⠀ ⠀⠀⣴⡇⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⣞⠟⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⢸⡎⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀ ⢸⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢽⠀⠀⠀⠀ ⢸⡄⡰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠀⠀⡞⠀⠁⣿⠀⠀⠀⠀ ⠈⢧⠧⣱⡀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣸⠀⣰⠃⠀⠀⣿⠀⠀⠀⠀ ⠀⠘⣷⡈⠻⣄⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡇⢠⣧⡇⠀⠀⢽⠀⠀⠀⠀ ⠀⠀⠈⢣⡀⠈⠓⠶⣖⠂⠻⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢸⡷⠟⠸⡇⠀⠀⢻⣇⠀⠀⠀ ⠀⠀⠀⠀⠙⠶⢤⣴⣂⣒⣒⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠭⣭⡽⣇⠀⠀⡏⢷⡀⠘⣷⡀⠀⠀⠙⢳⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡤⣀⣀⠀⠀⠀⢀⣼⠇⠀⠰⡌⢳⡿⡄⠀⠀⢧⡱⡄⠀⠻⢶⣔⣾⠿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠚⠉⠻⠶⠼⠿⠛⠉⠉⠻⣍⣳⣴⣷⠗⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

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╱|、 (˚ˎ 。7 |、˜〵 じしˍ,)ノ

⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡆⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢤⣿⡀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀ ⠀⣀⢈⣻⣷⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⢦⡀⠀⢀⣴⠏⠀⠀⠀⠀ ⠈⠉⠉⢙⣿⣿⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⡆⠀⠈⣿⣿⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⢸⡿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⣿⡀⠀⣸⡿⠛⠻⣷⡀⠀⠀⠀ ⠀⠀⠀⢸⡇⢻⣿⠀⠀⠀⠀⣿⠀⢸⣇⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⢸⡇⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⡇⢸⣿⣇⠀⠀⠀⡇⡀⢸⣿⣆⠀⠀⠀⣀⣸⣽⢀⣠⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠛⠀⠀⢿⡉⠀⠀⢰⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠨⣿⣿⡿⢟⣩⠹⣿⣿⣿⣿⡟⣫⣤⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣿⡇⠰⣿⣿⠇⢹⣿⡿⠁⠻⢿⠟⢡⣿⡏⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⣬⣥⣤⣿⣿⣿⣶⣶⣶⣾⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡽⣻⠛⡟⠛⡏⠩⡙⠷⣤⣿⡄⠀⠀⠀⠀⢀⣾⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠋⠁⠀⡇⠀⡇⠀⠈⠓⠦⣽⣿⣶⣤⣤⣶⣿⣿⣿⣿⠁⠀ ⢀⡀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠈⠳⣄⣱⠀⣇⣀⣤⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀ ⠘⣷⢸⣇⣤⠀⠀⠀⠀⠀⠀⠀⢸⠇⣀⣀⠤⠴⣿⣿⡿⠋⠉⠀⠀⡿⡟⠟⠛⠛⠛⠛⠁⠀⠀⠀⠀ ⠀⢸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⡾⢀⡠⠔⢺⡿⢫⠇⡆⠀⠀⠀⠀⣏⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⢿⡇⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⣾⠀⣾⡀⢧⠀⠀⠀⠀⢘⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡏⢸⣷⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢠⢎⡷⢚⡿⠁⢸⠀⠀⠀⠀⢸⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⢠⡇⠀⣰⡿⢋⡇⣼⡇⠀⢸⠀⠀⠀⠀⠘⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⠋⠀⢸⡿⢹⠀⠀⢸⠀⠀⠀⠀⠀⡇⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣼⠁⢸⠀⠀⢸⠀⠀⠀⠀⠀⢱⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⡼⡟⠀⣿⠀⠀⢸⡆⠀⠀⠀⠀⢸⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠘⠇⡇⠀⡇⠀⠀⠸⡇⠀⠀⠀⠀⠘⡆⠀⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠳⣄⠀⠐⡇⠀⡇⠀⠀⠀⣧⠀⠀⠀⠀⠀⡇⠀⠸⡄⠀⠀⠀⠀⠀⠀ ⠀⢠⣶⠶⠦⢤⣀⣀⣠⣾⣿⣿⣾⣿⣦⣇⠀⠀⠀⠀⠀⢹⢀⡤⠶⠒⢒⣛⣶⣟⣤⠀⠀⠀⠀⠀⠀ ⢀⡿⡆⢰⣾⣾⣿⣛⠧⢩⣽⣿⣿⣿⣿⣟⠃⠀⣠⣤⣤⣾⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠸⣇⣷⠄⣈⣹⣿⣿⣴⣾⣿⣿⣿⣿⣿⣿⡆⢸⡧⠙⠿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠛⠛⠛⠒⠲⠚⠁⠓⠒⠒⠒⠛⠛⠁⠘⢧⣀⣁⣚⣙⣛⣉⡘⠋⠁⠒⠚⠋⠀⠀⠀⠀⠀⠀

૮꒰ ྀི >⸝⸝⸝< ྀི꒱ა ૮꒰ ྀི >⸝⸝⸝< ྀི꒱ა ૮꒰ ྀི >⸝⸝⸝< ྀི꒱ა ૮꒰ ྀི >⸝⸝⸝< ྀི꒱ა ฅ^•ﻌ•^ฅฅ^•ﻌ•^ฅฅ^•ﻌ•^ฅฅ^•ﻌ•^ฅฅ^•ﻌ•^ฅ

⠀⠀⡤⠤⣤⣀⣀⣠⣴⣶⣤⠤⢤⡀⠀⠀ ⠀⠀⣇⠀⠀⠀⠀⢸⣿⣿⣿⣶⣾⣷⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠉⠉⠛⠿⣿⡟⠀⠀ ⠖⣺⣀⠀⣤⠀⠀⠀⠀⠀⣤⠀⣐⣟⡒⠂ ⠩⢿⡏⢉⣆⠀⠀⠛⠂⠀⢠⣋⠙⡿⠍⠀ ⠀⠀⠛⡏⣸⣶⣤⠤⢤⣶⣮⢈⡟⠁⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀ ⠀⠀⠀⠸⣦⡀⠀⣸⡀⠀⣠⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀

☆ ☆ -------------- /__________ \ ☆ | | \___________ / ☆ \.._______../ | /\__/\ | | ( • • ) | ☆ ☆ | / U U \ | ========= \________/. ☆ ☆ ☆ ☆ ☆ ☆

∧,,,∧ (  ̳• · • ̳) /    づ You want my heart? ∧,,,∧ (  ̳• · • ̳) /    づ♡ Ok here's my heart ∧,,,∧ (  ̳• · • ̳) U ♡C~ Nevermind, you dont deserve it

⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⠟⠁⠀⠀⠀⠹⣿⣿⣿⣿⣿⠟⠁⠀⠀⠹⣿⣿⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⣾⣷⠀⢿⣿⣿⣿⣿⠀⣾⣷⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣷⡀⠀⠀⠙⠋⢀⣿⣿⣿⣿⣿⡀⠙⠋⠀⢀⣾⣿⣿⡇⠀⠀⠀⠀ ⢀⣀⣀⣀⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣾⣿⣷⣦⣤⣴⣿⣿⣿⣿⣤⠤⢤⣤⡄ ⠈⠉⠉⢉⣙⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀ ⠐⠚⠋⠉⢀⣬⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣀⡀⠈⠀⠈⠛ ⠀⠀⠴⠚⠉⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠉⠛⠢⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⡴⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⠿⠿⠛⠛⠛⠋⠉⠉⠉⠛⠛⠛⠛⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⣻⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⣀⣤⣄⢴⣖⣒⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣟⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⠟⠋⠀⠀⠀⣀⣤⣦⣿⣿⣿⣿⣿⣯⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠿⠿⠿⣿⣿⣷⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⣿⡿⠁⠀⠀⠀⣀⣶⣿⣿⡟⠯⠍⠋⢁⣀⣠⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣄⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣦⣤⣴⣿⣿⣟⣋⣡⣤⠴⠖⠋⢉⣽⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠧⡀ ⠀⠀⢠⣿⠟⠉⠁⠈⠉⠉⠙⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⢠⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠟⠛⠉⠀⢀⣀⣥⣴⣶⣶⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣷⣶⣦⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠂⠈⢉⠛⠿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠘⢿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠽⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣴⣿⣿⣄⠀⠀⠀⠀⠀⣀⣠⣴⠶⣿⣿⠋⠉⠉⠉⠙⢻⣿⡆⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⣿⡍⠛⠻⢷⣶⣶⣶⠟⢿⣿⠗⠀⠹⠃⡀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣴⣿⣿⣿⣿⠿⠿⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⡇⠀⠀⠀⢻⣽⣿⠀⠈⠛⠀⠀⠀⢹⠇⠀⠀⠀⠀⢶⣿⠇⠀⢀⣴⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⣀⡾⠀⠀⠀⠀⠀⢸⡿⠀⣠⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣦⠀⠀⢠⣿⢳⠀⠀⠀⠙⣿⣿⠁⢰⣿⡿⣻⡿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⡾⠿⠃⢸⣷⣀⠀⢀⣾⠃⢀⣿⣿⣻⣿⡿⡯⣻⣣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠻⠷⢾⣿⣿⣷⡿⠁⠀⢸⣿⣟⡿⣏⣿⣿⣿⣯⣿⣗⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣷⣄⠀⠀⠉⠛⠀⠀⠀⢸⣿⡇⠈⠉⠛⢧⣝⣟⣯⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⣄⡀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠉⠙⠯⣯⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶⣶⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠻⠯⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀

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