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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠉⢹⣯⠉⠉⠛⠲⢤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠀⣣⠤⠒⠒⣺⣿⡒⠒⠢⢤⡃⠉⠳⣄⠀⠀⠀⠀ ⢀⡀⠀⣠⠋⠀⡰⠊⠀⠀⢀⣼⠏⠈⢿⣄⠀⠀⠈⠲⡀⠈⢧⡀⠀⣀ ⠀⠈⢳⠧⢤⣞⠀⠀⠀⢀⣾⠏⠀⠀⠈⢿⣆⠀⠀⠀⢘⣦⠤⢷⠋⠀ ⠀⠀⡾⠤⡼⠈⠛⢦⣤⣾⡏⣠⠶⠲⢦⡈⣿⣦⣤⠞⠋⢹⡤⠼⡇⠀ ⠀⠀⡇⠀⠆⠀⠀⢾⣿⣿⢸⡁⣾⣿⠆⣻⢸⣿⢾⠄⠀⠀⠆⠀⡇⠀ ⠀⠀⣧⠐⢲⠀⣠⡼⠟⣿⡆⠳⢬⣥⠴⢃⣿⡟⠻⣤⡀⢸⠒⢠⡇⠀ ⠀⢀⣸⡤⠞⢏⠁⠀⠀⠘⢿⡄⠀⠀⠀⣼⠟⠀⠀⠀⢙⠟⠦⣼⣀⠀ ⠐⠉⠀⠹⡄⠈⠣⡀⠀⠀⠈⢿⣄⢀⣾⠏⠀⠀⠀⡠⠋⢀⡼⠁⠈⠑ ⠀⠀⠀⠀⠙⢦⣀⠈⡗⠢⠤⢈⣻⣿⣃⠠⠤⠲⡍⢀⣠⠞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⣀⡀⢸⣏⠀⣀⣀⡤⠞⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣾⡿⠿⠿⠿⣿⣿⠿⠿⠿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠿⠛⠋⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⢿⡄⠀⠀⠀⠀⠀⠀⣀⣀⣠⣿⣿⣄⣀⣀⠀⠀⠀⠀⠀⠀⢀⡾⠛⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠁⠀⠀⠀⢻⣄⣤⠶⠶⠛⠛⠋⠉⣹⣿⣿⣯⠉⠙⠛⠛⠶⠦⣤⣠⡿⠁⠀⠀⠈⠻⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⣠⡴⠟⠉⠁⠀⠀⠀⠀⢀⣾⣿⡿⢿⣿⣧⡀⠀⠀⠀⠀⠀⠙⠻⢦⣄⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡿⠉⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠀⠀⠻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀ ⠙⠳⣦⣄⠀⢀⣼⡟⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠋⠀⠀⠀⠀⠙⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⢻⣷⠀⠀⣠⣴⠾⠋ ⠀⠀⠈⠙⠿⣾⣿⣄⣀⡀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⢀⣀⣠⣿⣷⠿⠋⠁⠀⠀ ⠀⠀⠀⠀⢰⡿⠉⠉⠛⢻⣿⣶⣤⣀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡟⠛⠉⠉⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣇⠀⠀⠀⣿⠁⠈⠛⢿⣷⣦⣀⡀⢀⣾⣿⣿⡇⠀⢀⣤⣤⣶⣶⣦⣤⡀⠀⠸⣿⣿⣷⡀⠀⣀⣴⣾⡿⠛⠁⠈⣿⠀⠀⠀⣸⣿⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠉⠛⠛⢻⡟⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡏⠀⣴⡿⠛⠉⢀⡀⠉⠛⢿⣆⡀⢻⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢹⡟⠛⠛⠉⣿⡇⠀⠀⠀ ⠀⠀⠀⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣼⠋⣽⣿⣿⣿⠃⢸⡟⠀⢠⣾⣿⣿⣷⡄⠈⢿⣇⠈⣿⣿⣿⣯⠹⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⢹⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⣿⡀⢿⣿⣿⣿⡀⢸⣇⠀⠸⣿⣿⣿⣿⠇⠀⣸⡟⠀⣿⣿⣿⣿⢠⣿⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⢸⣿⠀⠀⣀⣸⣇⠀⠀⠀⠀⠀⣸⣿⣾⣿⣿⣿⡇⠈⢿⣧⡀⠈⠛⠋⠁⢀⣴⡿⠃⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣇⣀⠀⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⠸⣿⡞⠉⠉⠉⣿⠀⠀⢀⣤⣾⡿⠟⠋⠙⣿⣿⣿⡄⠈⠙⠿⣿⣶⣶⣿⠿⠋⠀⢠⣿⣿⣿⠋⠉⠻⢿⣷⣦⣀⠀⠀⣿⠉⠉⠉⢻⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⢸⣧⠀⠀⢀⣹⣷⣾⠿⠛⠁⠀⠀⠀⠀⠘⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠋⠀⠀⠀⠀⠈⠛⠿⣷⣶⣏⡀⠀⠀⣾⡟⠀⠀⠀⠀ ⠀⠀⠀⢀⣬⣿⣿⠿⠟⠛⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠙⠻⠿⣿⣿⣥⡀⠀⠀⠀ ⢀⣠⡴⠟⠉⠘⢿⣆⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀⠀⠀⠀⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⣰⣿⠁⠙⠻⢷⣄⡀ ⠋⠁⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣄⠀⠀⢠⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠁⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠈⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠈⠳⣦⣄⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⣴⣿⣿⠏⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⣹⠟⠶⣤⣤⣀⣀⡀⠈⢿⣿⣿⡿⠁⢀⣀⣀⣤⣤⠶⠻⣯⠀⠀⠀⠀⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣤⡀⣴⠏⠀⠀⠀⠉⠉⠉⠛⠛⠻⣿⣿⠟⠛⠛⠉⠉⠉⠀⠀⠀⠹⣧⢀⣤⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⢿⣶⣶⣦⣤⣤⣤⣿⣿⣤⣤⣤⣴⣶⣶⡿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣿⡟⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠠⠤⠄⠤⠤⠶⠤⠤⠤⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠁⠀⠀⠀⣀⡤⣤⣀⣠⠤⠦⠦⠶⠶⠶⠦⠤⠤⠤⣖⣦⣄⡀⠀⠀⠛⢯⡳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⠗⠉⠀⠀⣠⣶⡿⡟⡍⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢹⢻⣷⠄⠀⠀⢫⣮⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣼⠿⢿⡶⠀⠀⠘⠳⣧⣇⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢼⡾⠛⠀⠀⠀⠀⣫⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢀⣿⡃⠀⠀⠀⠀⠀⠉⠓⠿⢯⣭⠛⠒⠒⠒⠚⠛⠉⠉⠉⠉⠙⠋⠁⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡟⢙⡿⠁⠈⠙⠲⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⢀⠞⠀⠀⠀⠀⠀⢸⢹⠟⠉⠉⠉⠛⠛⠛⠓⠒⠒⠛⠛⠛⠋⠉⠉⠉⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⢠⠏⠀⠀⠀⠀⠀⠀⣿⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⣿⡿⢟⣒⢦⠤⣶⣄⣀⣀⣐⣀⣀⣠⡤⠴⢶⣶⣿⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣰⢃⣀⠀⠀⠀⠀⠀⠀⠀⣿⢹⣆⠈⠙⠓⠒⠶⠶⠶⠶⠶⠾⠾⠿⠛⠻⠟⢻⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠁⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡀⠀⠀ ⠀⠀⠀⠀⢀⡼⠁⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⠶⠒⠛⠛⠛⢭⡍⠿⡏⠳⡄⠀ ⠀⠀⠀⢀⡞⠁⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣦⢀⡀⢀⡀⠀⠀⠀⠀⠀⢹⣆ ⠀⠀⢠⡞⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠻⠷⠚⠓⠒⠒⠒⠛⠉⠉⠉ ⠀⢠⣿⠃⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⠇⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⠀⠀⠀⠈⠙⠒⠲⠤⣤⣤⣤⣤⣤⣤⠤⠤⠖⠒⠋⢉⢄⣶⠾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣽⠀⠀⠀⣤⣗⣷⣄⠀⢠⣤⣾⠏⠋⠀⠀⠀⠀⢀⡤⢾⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⢷⣪⣿⠏⠀⠀⠉⣹⠒⣦⢤⣤⠴⠚⠉⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⠞⠀⠀⠀⠀⢀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣰⣢⠤⣤⣦⢠⢤⣶⢤⣤⠄⡀⡤⡤⠀⠠⡤⠤⡄⣶⡖⣴⣰⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣦⠤⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⠿⠿⠿⠿⠿⠿⠿⠿⢿⣷⣶⣶⣤⣄⣀⠀⠀⠉⠹⠀⠀⠀⠀⢸⣄⣀⠄⠀⠀⠀⠀⢹⣄⠀⣀ ⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣶⣄⡀⠀⠀⠀⠊⠙⢿⠀⠀⠀⠀⠠⠶⠿⣿⠋⠁ ⠀⠀⠀⣀⣴⡿⠟⠉⠀⠀⠀⠀⢀⣀⣤⡤⠶⠶⠚⠛⠛⠛⠛⢛⠛⠳⠶⣤⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠈⠃⠀⠀⡀⠀⠀⠀⠘⠇⠀ ⠀⢀⣾⡿⠋⠀⠀⠀⠀⣠⡴⠞⠋⠉⢀⣠⡤⠶⢒⣛⣩⠭⠭⠽⠿⣿⣿⡿⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⠀⠀⠀⠀⠀ ⢠⣿⠋⡄⢀⠀⠀⣴⠟⠁⠀⣀⠴⢚⣩⠴⠒⠉⠉⢀⣠⣤⠶⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⠀⠀ ⣿⡏⢰⠃⣯⡇⣼⠇⠀⢀⡞⢡⠴⠋⠀⠀⣀⣤⠾⠛⠁⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⠿⠋⠀⠀⠀⠀⢠⡟⢻⡟⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠘⣇⢿⡷⠘⢷⣄⡞⣰⠃⢀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠟⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⣠⡟⣰⡟⠀⡀⠀⠀⠀⠀⠀⠀ ⠸⣿⡄⠈⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠟⠋⠀⡰⢻⣇⠀⠀⠀⠀⠀⠀⠀⣰⠏⣰⠏⠀⠀⣧⣀⡀⠀⠀⠀⠀ ⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠟⠋⠀⢀⡤⠞⣠⠟⣿⡀⠀⠀⠀⠀⠀⣰⠏⣰⠏⠀⠐⠚⠻⡏⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⠿⣷⣦⣤⣄⣀⣀⣀⣀⣤⣤⣶⡿⠟⠉⠀⣀⣠⠴⠚⣉⡤⠚⣡⠀⢹⣇⠀⠀⠀⠀⣴⠋⣼⠏⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠛⣿⡿⠿⠿⠿⠭⠥⠖⠒⠒⢉⣡⡤⠴⠚⢁⡤⠞⣡⠖⠀⢿⡆⠀⠀⣼⠃⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠉⠉⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠈⠖⢋⣡⠞⡁⠘⢿⣄⡼⢃⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣋⡠⠞⢁⠄⢘⡿⢁⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡤⠖⣁⢶⡾⢁⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⢡⡾⢡⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⣿⡟⣠⠟⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠶⠶⠶⠶⠶⠶⠞⠛⠛⠉⠁⣰⣏⣰⠟⠀⠀⠠⠴⢿⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣒⡒⢲⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⠣⣄⠒⠛⠒⠒⠠⢤⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠬⣾⠀⠸⠁⢀⣀⠸⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢀⡠⠌⠀⡖⠁⠀⢑⠞⠃⠀ ⠀⠀⠀⠀⠀⣀⠠⠤⠄⠠⠤⡄⣤⢊⢝⠡⢊⠠⠴⠊⠛⠳⠾⠆⠀⠀ ⠀⠀⢀⠔⢈⡀⢀⠀⠀⠀⠀⠀⠈⠙⢳⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠂⠀⠀⠀⢐⣀⣀⠀⠀⠀⠀⠀⠑⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣧⠀⠀⢠⣾⣿⣷⡆⠀⢀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠿⠿⠀⠀⢺⣿⣿⣿⠇⠀⠀⠤⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠁⠆⠶⠣⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠡⡀⠀⠀⠀⠀⠐⠀⢠⡀⠀⠀⠀⠀⣁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠶⢄⡀⠀⣠⠄⠠⠀⡁⠀⠀⢀⡤⠋⡑⠀⠤⠤⠤⠐⢁⠃⠀⠀ ⠀⢀⢐⣄⡉⠿⡅⢀⣀⢘⠣⠴⠂⠛⠣⠆⣑⡤⠄⣀⡂⠕⠊⠀⠀⠀ ⠀⠐⠥⢜⡫⣿⠾⢦⣴⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠦⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⢇⣂⡤⠒⠒⠓⢚⡶⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢠⠆⠘⠤⣤⠶⠚⠊⠒⠑⠛⠓⠲⠦⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠈⠪⢬⢶⠁⠑⢲⠖⠛⠉⠉⠓⠒⣒⠶⠽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠩⢢⢧⣸⠠⢄⠘⡢⠤⠤⣀⣀⡠⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢀⠘⡸⣀⡆⠠⢑⡼⠚⠉⠒⠒⠳⢬⡭⠷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⣤⠗⢉⠏⡀⠐⡘⢤⣀⣀⡀⠀⢀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢤⠴⠴⠦⠤⠤⢄⣀⣠⡔⠉⡠⠊⢀⠴⠃⢑⡚⠥⠗⠒⠒⠚⠙⠭⠗⣳⡄⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⡘⢰⠀⠀⡀⠀⠀⠘⠪⠍⠻⢿⣶⣊⢡⡦⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠞⡉⣐⢆⠤⢡⠰⠃⢀⠐⡀⠄⡁⢀⠀⠀⡀⢀⠈⠻⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡴⠉⠀⠉⠀⡀⠀⡀⠔⡨⠒⠒⠄⠂⠠⢀⠂⠁⢀⠀⠈⠆⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣦⠀⠈⠄⢁⠠⠐⢀⣧⣷⣶⣢⡐⠈⠠⢀⠂⠌⠀⡀⠌⠀⡀⠌⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⡇⠠⠈⢀⠀⢠⣿⣿⣿⣿⣧⣇⠠⠁⡀⢂⠈⠄⢀⠀⠂⢀⠀⡸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⢿⠐⣈⠒⢄⣿⣿⣿⣿⣿⣿⡜⢀⡐⢨⡘⢄⠐⡀⠠⠁⡀⠀⢰⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠻⠟⠜⠀⡀⠉⢆⣿⣿⣿⣿⣿⡿⠋⠀⠉⠀⠁⠂⠒⠘⠀⠠⠀⢁⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢧⠃⠈⠄⣶⠀⣵⣌⡄⣀⡀⠀⢀⠀⡀⠐⠈⠠⠈⠐⠀⠂⠈⠀⠐⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡄⢁⠠⠉⠀⠌⢀⠀⠑⢌⢆⠀⠄⡀⠁⡈⠔⠂⠥⠊⠐⠁⠨⡐⢢⢱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢱⡀⠄⢈⠐⠈⡀⠌⠠⢈⠼⠀⡀⠄⡜⠔⠈⠠⢀⠂⠁⠌⢀⠘⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢙⣔⠀⡈⠐⡀⠂⣁⠖⠁⢀⠀⡀⢓⠤⠈⠐⡀⠄⠡⠈⠀⣼⠟⢧⣀⠀⠀⠀⠀⠀⠀⠀⣀⠶⣲⠀⠀⠀ ⠀⠀⢸⠹⢷⣤⠐⠠⢌⣨⠖⠛⠉⠳⠀⡘⠆⠁⢂⠠⠐⢀⣬⡾⢏⠀⣄⠈⠙⠒⠒⠒⠒⠚⢉⠁⢄⡧⠀⠀⠀ ⠀⠀⠀⠣⣀⠙⠻⢷⣽⠃⢠⠀⠀⠄⠀⡏⣄⣈⣄⡴⠚⠿⠯⣐⠤⠊⢧⣘⠐⡄⠢⠐⣁⠎⢉⣬⠞⠀⠀⠀⠀ ⠀⢰⢲⡽⢿⣷⣦⣀⣨⢧⡀⠂⠫⢢⠀⠏⠉⠉⠀⠀⠀⠀⠀⠈⠙⠓⠺⠤⠤⠬⠥⠵⠒⠚⠉⠀⠀⠀⠀⠀⠀ ⠀⠘⠯⠤⣖⡚⣉⣱⢗⡯⢿⣷⣦⣙⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠏⠠⣔⠎⢉⣡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠤⠤⠤⣤⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠚⢏⣂⡤⠖⠒⠒⠒⡶⠚⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠎⠘⠦⣤⠖⠚⠉⠉⠉⠛⠛⠒⠦⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠪⢄⢶⡅⠑⢢⡴⠒⠂⠒⠒⠒⢲⡶⠽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠨⢢⢿⣸⠀⠤⠈⡢⠤⠤⣀⣀⡀⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠘⣸⣠⡏⠀⢁⡴⠚⠉⠑⠚⠚⢮⡭⠷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣁⣠⠔⢋⠟⡀⢀⠘⢇⣀⣀⡀⠀⢀⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠤⠤⠤⣄⣀⣠⡔⠋⡠⠊⣁⠴⠫⢑⣒⠤⠵⠒⠺⠟⠻⠽⢟⣷⡄⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠘⢸⠀⠀⠀⠀⠀⠈⠢⠍⠻⢿⣷⣊⢁⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠖⠁⣀⢂⡀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡴⠃⠉⠉⠀⠀⠀⠀⡄⡀⠐⠂⠄⠀⠀⠀⠀⠀⠀⠀⠈⠆⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣧⠀⠀⠀⠀⠀⠀⢀⣧⣷⣶⡶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⢿⠀⠀⠐⢄⣾⣿⣿⣿⣿⣿⡼⠀⠀⣀⠘⠄⠀⠀⠀⠀⠀⠀⢸⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠛⢻⠞⠀⠀⠉⢢⢿⣿⣿⣿⣿⡿⠋⠉⠁⠀⠁⠒⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢷⠀⠊⠀⣦⠀⣴⣜⡘⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡄⠀⠀⠉⠀⠈⠀⠈⠑⢝⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢢⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠈⢸⠀⠀⠀⡄⠄⠀⠀⠀⠀⠀⠀⠀⠈⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢙⣔⠀⠀⠀⠀⠀⢀⠔⠃⠀⠀⠀⢃⡆⠀⠀⠀⠀⠀⠀⠀⣸⠿⢧⡀⠀⠀⠀⠀⠀⠀⠀⣀⠶⣦⠀⠀⠀ ⠀⠀⢸⠋⠳⣄⡀⠀⠀⣸⠴⠒⠃⠲⠀⡜⠎⠀⠀⠀⠀⢀⣠⠞⢁⠀⡄⠉⠑⠒⠒⠒⠒⠒⢋⠁⢀⡇⠀⠀⠀ ⠀⠀⠀⢳⡀⠀⠙⣲⢽⠋⠀⠀⠀⠀⠀⡇⡆⣀⣀⡤⠖⠿⠭⣐⠤⡈⢣⣈⡀⡀⠀⠀⢀⠔⢉⣤⠎⠀⠀⠀⠀ ⠀⢠⢚⡿⠿⣷⣤⣀⢉⢧⡀⠀⠪⢢⠀⠏⠉⠉⠀⠀⠀⠀⠀⠈⠙⠓⠚⠦⠤⠬⠥⠴⠒⠊⠁⠀⠀⠀⠀⠀⠀ ⠀⠘⢏⢤⣴⡛⢋⣽⢟⡾⢿⠷⣤⣜⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠁⠘⠏⢠⣴⠚⢍⣡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣒⠒⢒⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡐⠫⡴⠒⢓⣒⣒⠲⢄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡓⠩⣾⢀⠸⡥⢀⣀⡔⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢈⡡⡞⠈⡎⠁⠉⢁⡟⠂⠀ ⠀⠀⠀⠀⠀⣀⡤⠤⠄⠠⠤⣄⣤⣊⢘⡡⢒⡐⠧⠚⠛⠓⠾⠄⠀⠀ ⠀⠀⢀⠴⢋⡀⠄⠇⠀⡀⢀⠈⠀⠙⢷⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⡋⠀⠀⢀⠰⣈⣐⠁⠠⠐⠀⠀⠂⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣧⠐⠈⢠⣿⣿⣷⡅⠂⡁⠌⠀⡐⠀⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⠿⠿⢀⠹⢺⣿⣿⣿⠕⠆⠘⠤⠆⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡀⢁⠆⠲⠱⢠⡀⠀⠀⡀⢠⢀⠠⢀⢈⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠱⡀⠂⡁⠄⠠⣁⠀⢢⡔⠀⠠⠐⢀⢨⠕⠀⠀⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠻⣆⡀⠌⣸⠄⠢⠠⡁⠄⠁⢂⣰⠏⠑⡂⠤⠤⠤⠒⣉⡃⠀⠀ ⠀⢀⢝⣬⡙⠿⡅⣀⣄⠘⠧⠴⠚⠙⠣⠮⣐⡴⠂⣘⡠⠝⠁⠀⠀⠀ ⠀⠸⠅⢜⡫⣾⠺⢦⣴⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠊⠓⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣷⣽⣯⡤⠦⠀⠀⣿⣏⢾⡱⢧⣿⣿⡵⣫⠞⣭⣿⣿⣷⢭⣎⢷⣿⣿⢲⠭⣯⣿⡏⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠛⠉⠀⠀⠀⠀⠀⣿⣏⢶⣹⣻⡿⠙⢿⣧⣟⣶⣿⣯⣿⣷⣞⢮⣿⣟⢯⣾⣿⢿⡿⣷⣶⣄⢰⣿⡿⣟⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣮⣷⠟⠁⠀⠀⠈⣽⣿⠯⣝⡺⣝⣫⢾⡵⣮⣟⡼⣙⢮⡵⢳⣫⣿⣿⣿⡵⣣⣿⣿⣷⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢸⣿⢧⣛⡼⣱⢧⣽⣿⡿⣭⣿⣾⣝⡶⣩⣷⣵⣿⠛⣿⡷⣱⢿⣿⡿⣝⢺⡜⣵⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣾⣾⣷⣿⣿⢯⡳⢵⣻⡏⠛⣿⣿⡿⣿⢿⡶⣿⣿⣧⢻⣏⠷⣎⡷⣮⣿⣿⣤⡀⠀⣴⣿⣿⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢹⣿⢧⣛⣧⣿⡇⢸⣿⢣⡝⡶⣭⣚⣽⣿⣟⢧⡺⣽⣶⣿⣻⣿⡟⢿⣷⣼⡿⢭⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠁⣠⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⣽⣽⡿⠁⠸⣿⣎⣳⣥⣯⣿⣿⠿⣹⣾⣥⢏⡿⢿⣿⣿⣓⠾⣿⣿⢣⣞⣿⣿⣄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⣴⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠙⠛⠛⠛⢻⡿⣍⢯⣳⣿⣿⣎⢷⢫⣿⣿⣯⡹⣽⣟⢿⣿⡟⣟⣿⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣴⠛⠀⠀⣼⠃⠀⠀⢀⡞⠁⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢻⡜⣮⣽⡿⠙⢿⣿⣧⣿⣿⣿⣿⡜⢯⡞⣥⢿⣼⣿⡿⠁ 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⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠈⠻⠦⠀⠀⠉⠀⠀⠘⡇⢠⡞⠁⠀⢀⡞⠀⠀⠀⠀⣸⠁⠀⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⣠⡶⠒⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠤⠶⠾⣧⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⡴⠋⠀⠀⢀⡞⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⣷⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣀⣾⠁⠀⠀⠀⢹⣧⠶⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡾⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠸⣧⡞⠉⠉⠻⠆⠀⠀⠀⠈⠁⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡿⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⣠⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⠢⡾⠗⠶⣦⠀⠀⠀⠀⠀ ⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠈⢿⣄⠘⠁⠀⣼⠗⠲⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠈⠿⣤⣀⠀⠀⢿⡁⠉⣳⣤⡀⠀⠀⠀⢀⣀⣸⡇⠀⠀⠀⠀ ⠘⣦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠙⠗⠀⠙⠁⢠⣤⠾⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠉⠙⣦⠀⠀⠈⠉⠉⠙⢳⡄⠀⠀ ⠀⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠋⠀⠀⠀⠀⢀⣀⣸⡇⠀⠀ ⠀⠀⣿⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠙⠲⣿⡁⠀⣠⡖⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠉⠉⢷⡀⠀ ⠀⠀⠈⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢧⡤⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢀⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢶⡄⠀⣼⠀⠀⠀⠀⠠⣴⣤⡾⠁⠀ ⠀⠀⠀⠀⠀⢿⣀⣀⣴⠀⠀⠀⢠⣶⠖⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⢠⡄⠀⢀⡀⠀⠀⠀⣾⠀⠀⢀⡄⠀⠀⠀⢰⣆⣀⣰⠟⠀⠀⠀⠀⠈⠉⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠈⢣⣄⣀⣸⣿⠾⠋⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠶⠖⠻⢧⡾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠶⠛⠷⠖⠋⠁⠀⠀⠀⠿⣦⣤⠾⢷⣄⣀⡤⠟⠉⠉⠁⠀⠀⠀⠘⠛⣷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⡀⠈⠉⠁⣠⡀⠀⠀⠀⠘⣶⣤⣤⣴⠿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣄⠀⠀⠀⣶⣄⣀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⣿⠁⠀⠀⠀⣿⣄⡀⠀⢀⡷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠖⠒⠋⣿⠀⠀⠀⠀⢠⡗⠀⣠⣶⠂⠀⠀⠀⣤⡀⠀⠀⠀⢠⡆⠀⠀⠀⣿⣄⣀⣀⡿⣦⣤⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠟⠳⠦⠼⠛⠳⣤⣤⡴⠋⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠚⠋⠉⠛⢻⣁⠀⠀⠀⢰⣿⠀⠀⠀⢀⡿⠷⠤⠤⣞⣉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠉⠓⠒⠒⠋⠁⠀⠀⠀⠈⠉⠛⠲⠶⠶⠶⠖⠒⠶⢦⣤⣀⣀⣀⣤⠶⠖⠶⠦⣤⣤⣤⠴⠞⠛⠉⠛⠛⠓⠒⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠁⢀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠌⠀⠀⠈⠉⠉⠙⣿⠁⠀⣿⠀⡇⠸⡄⠳⠈⠁⠀⠀⢲⣿⣛⣏⠉⣶⠀⠀⠈⢳⡀⠀⣠⠈⢦⠀⠀⠀⠙⡄⢷⠀⡀⠀⠀⠂⠈⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀ ⠀⠀⠄⠀⠀⠁⢀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠁⠀⠈⠀⠀⠘⢿⡄⢸⡟⠀⣩⣤⣷⣀⠀⠀⠀⠀⠘⣿⣿⣿⡷⠏⣀⣶⣤⡄⢻⣴⠇⠀⠀⢧⠀⣀⠀⠀⠈⣧⠀⠀⠠⠈⠐⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⡈⠀⠄⠀⠀⠀ ⠀⠌⠠⠐⠀⠁⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠄⠀⠀⠀⠀⠄⠘⣧⠸⣇⠀⢿⣷⣦⡉⣷⠀⣀⣤⡀⠉⠉⠁⠀⢰⣿⣿⣿⢏⡼⠿⡆⠀⠀⠈⢧⠘⣆⠀⠀⠹⡆⠀⠀⠀⠄⠈⠠⠀⠁⠄⠀⠀⠀⠐⠀⠀⠌⢀⠀⠀⠀ ⢀⠂⠄⠂⠀⠈⢀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠈⠀⢹⣧⠹⡄⠈⠛⠿⠛⠉⠀⠻⠟⠁⠀⣴⠀⠀⢹⡿⣏⣿⣏⣀⣠⠻⣆⠀⠀⠈⠃⠹⣆⠈⣆⢻⡄⠀⠀⡀⠄⠁⠀⢂⠀⠀⠀⢀⠠⠈⢀⠐⠀⠀⡀⠄ ⢀⠂⠰⠀⠌⠐⠠⠀⡀⠀⠀⠠⠀⠂⠁⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠹⣧⠙⣦⣸⠷⣝⣦⠀⠀⠓⠖⠛⠁⠀⣀⡬⣿⠋⠀⢈⡽⠋⢻⠟⠶⢤⣄⡀⠀⢹⡄⠘⣦⢷⡀⠀⠄⠀⢂⠀⢂⠠⠁⠀⢀⠀⠀⠠⠈⠄⠠⢀⠂ ⠀⠌⠠⠁⠌⠐⡀⠁⠀⠀⠄⡐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠘⣧⠀⠙⢻⣷⣦⣤⣤⣤⣤⣶⠾⠿⠿⠞⢋⣠⡴⢋⣤⣴⠿⢦⣄⣤⣬⣽⣿⣷⣷⡀⠸⡆⠻⣤⠀⠄⠀⠌⡀⢀⣠⣀⣤⣤⢶⣠⡅⢂⠁⠂⠀ ⠈⠄⠡⠈⠀⠐⡀⠁⡐⠀⠂⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⢷⡘⢦⡙⣆⠀⠰⣤⡟⠛⠲⠶⣦⡀⢉⣀⣠⠿⣿⣿⣆⠀⠀⠀⠀⠀⢈⡿⣬⣷⠀⠹⣆⠈⠳⣤⣂⠐⢠⡟⠛⠉⠉⠀⠉⢰⣧⡀⠈⠀⢀ ⠀⠌⠠⠀⢂⠁⢀⠐⠀⠌⠐⡈⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣤⢶⡄⠀⠀⠀⠐⠀⠀⠀⠌⢻⣌⢳⡌⢧⣰⠟⠓⠦⣄⣠⣾⡷⣟⣿⣿⣿⣿⣿⣿⣟⣟⡷⡶⢿⣻⣡⣿⣯⢳⡀⠘⢦⡀⠀⠉⠛⠋⠀⢠⢔⡶⠦⣤⠀⢠⠇⢒⠦⢤ ⠀⠂⠄⠡⢀⠈⠀⠀⠌⢀⠂⠄⡁⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⡙⢃⡾⣿⣶⣤⣤⣌⣠⣐⣀⣬⠀⢻⣆⣿⠞⠁⠀⢀⣼⣿⣿⣿⣿⢻⣧⠿⠛⠉⠋⠛⣿⠿⢯⣿⡿⠷⢟⣾⡙⢷⡹⣄⠀⠙⢢⣀⠀⠀⠀⠀⠈⠀⢊⣩⡿⠀⠀⠁⠀⠊ ⠀⡁⠂⠐⠠⠀⠀⡐⠀⠂⠌⠠⠐⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⣿⢋⣵⡞⣷⣾⠿⠦⠙⠛⠙⠛⣯⡻⠶⠛⠉⠀⠀⢀⣤⢾⣿⣷⢿⣽⣿⠿⠃⡀⠀⠀⠀⠀⠀⠀⢰⡾⣝⣿⣿⣿⢷⡀⠻⣌⠓⢦⣀⠈⠁⠀⠀⠀⠀⠀⢠⡯⠗⠀⠀⠩⣷⠤ ⠀⠄⠁⠈⠀⠀⠄⢀⠠⠁⠌⠠⠁⠌⠀⠀⠄⠂⠀⠠⠀⢀⣄⠀⠐⠀⡁⢈⠀⡀⠂⠀⠀⠀⠄⠐⠀⠠⣾⠳⣿⣿⢿⣟⠟⢻⡿⠗⠀⣠⡶⠞⠛⣿⠏⡙⣶⡤⠶⠲⠞⠋⠀⣿⣿⣟⣶⣶⢿⣷⠀⠙⢳⡖⠒⠋⢉⣴⣾⢷⣏⣿⡉⠻⣞⣷⠀⠈⠂⠀⠉⠛⠆⠀⠀⠀⠀⢛⡏⣄⣠⣀⣰⡟⠉⠀ ⠀⠁⠂⢈⠀⠌⠐⡀⠂⠌⠠⠁⠌⡐⠠⠁⠠⠀⢀⠠⢀⣼⣿⠀⢀⠂⢀⠂⠄⠠⢀⠈⡀⠄⢀⠂⢁⣶⡿⢦⣭⣙⣷⣛⣷⣿⡷⠆⣰⣟⡉⠀⠀⠙⢻⣷⠋⠹⣦⣸⠀⠀⣿⣥⣿⢻⣿⣝⣶⣧⣶⠲⢧⣽⠶⣶⣚⡻⣿⢻⣿⠟⣹⣾⡟⢷⡀⠀⢀⡀⠀⠀⠀⠀⢀⡀⠶⡾⢷⣞⠁⠀⠉⢠⣴⣾ ⠀⡁⠈⠄⠂⠌⠐⠠⢁⠠⠁⠌⠠⠀⠄⠂⠁⠐⢀⠸⠿⠛⠛⢀⠠⠐⠀⠂⠄⡁⢀⠂⠄⢈⠠⣀⣼⣿⡷⣚⣧⠿⣿⣿⢿⣿⣷⠶⣿⣥⣤⣆⣀⣴⠏⣥⠤⣤⡘⣿⡿⣶⠋⠀⠉⠋⣷⢈⣿⣟⣿⣟⣻⣹⡟⢹⡿⣟⠛⣾⡿⡾⣹⠏⠀⠈⢷⠾⠉⣿⡙⢦⣸⣏⣿⡇⢀⣶⣸⠿⠷⣼⠟⠉⠀⠉ ⠀⠄⡁⠂⠌⠠⢁⠂⠄⢂⠁⠂⠄⡁⢂⠐⠈⠄⡀⠂⠄⢂⠈⠠⢀⠂⠌⠐⠠⠐⠠⢈⠐⢀⣾⣏⣿⣿⢧⣿⣟⡛⢁⣾⣸⣍⠙⢀⠟⢷⣿⣿⣯⣿⣛⣟⣛⣛⠟⣻⣿⡜⢧⡀⠠⣔⠷⠿⣀⡟⠁⠙⢿⣩⡽⣏⢸⡇⠀⠛⠒⠛⠋⢀⣠⢶⡏⢀⣼⣿⠛⠋⠉⠉⠩⠟⠋⠉⠁⠀⠀⠀⠀⢀⠐⡀ ⠈⠄⠰⠁⢌⠐⠠⢈⠐⠠⢈⠄⠂⠄⡀⠂⠌⠀⠄⠡⠈⠄⡈⠐⠠⠐⡈⠄⠡⢈⠐⡀⠂⣼⣟⣩⢤⣿⣿⡟⢉⣭⢤⣤⣿⣯⣴⠀⢳⡾⣯⡿⢻⣶⣶⠾⠯⣽⣟⣛⢷⣿⣌⣹⠶⣬⣳⠶⣭⣅⡀⠀⠀⢸⣷⠋⠛⢁⣀⡀⢀⣤⠞⠛⠿⡿⠷⠋⠀⠀⠀⡀⠐⡀⠐⠠⠀⠀⠠⠀⠀⠂⠀⠂⠄⠠ ⠠⠈⠃⠌⠠⠈⠄⠡⡈⡐⠌⡐⢈⠐⠠⢁⠂⠁⠌⠠⢁⠂⠤⢁⠂⠡⠀⠌⠐⡀⠂⠄⠡⠙⣿⣧⢾⣿⣯⡟⣿⣿⣤⡷⠾⡟⢙⣷⣾⣷⠶⣔⣿⠀⠉⠛⠶⣄⡈⢉⡛⢾⣝⠁⠀⠀⠈⠙⠳⠦⢭⣭⣭⣭⣭⣭⣭⡽⠿⠛⠉⠀⠀⠀⠀⠀⠀⡀⠄⠐⠀⢀⠐⠠⠁⠀⠁⠠⠀⢀⠠⠀⠡⠐⡈⠁ ⠠⢁⣌⣠⢅⡌⠠⢁⡐⢀⠒⡀⠂⠌⡐⠠⢈⠐⡈⠐⠠⡈⢐⠠⠈⠄⡁⠈⠄⢀⠡⢈⠐⠠⢈⠉⣾⡷⢼⣳⡟⠓⣦⣹⠶⢢⠸⢏⣉⣹⠟⢻⠏⠀⠀⠀⠀⠈⠙⠲⣬⡁⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⣠⣌⢀⣁⠈⠠⠀⠁⡀⠀⠈⠄⣡⠤⢵ ⡢⠞⢂⠁⠈⠸⠧⡄⡐⢂⠐⠌⡁⠂⠄⡁⢂⠐⠠⢁⢂⠰⢀⠂⠡⠀⠄⠁⢂⠠⠀⢂⠈⡐⠠⠀⠿⡶⢻⡏⢷⡞⠓⣿⡖⠋⢳⣤⣹⡏⠐⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠙⠶⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠌⡀⢐⣀⣿⠹⢿⢿⣧⡀⠄⡁⢀⠂⠡⠘⢲⠖⣀ ⣤⣶⣏⢀⡟⠛⠙⡁⡐⣀⢊⠐⠠⢁⠂⠰⠀⠌⡐⠠⢂⠐⠠⠌⡀⠡⢈⠐⠠⢀⠡⠀⢂⠠⠁⡈⠄⡀⢈⠻⠾⠃⢀⠀⣀⣤⠟⠉⢀⠀⡀⠁⠠⠀⠀⠀⠀⣠⣤⣾⣦⣤⣀⡀⠀⠀⡀⠠⠀⠂⠀⠄⠘⢁⠀⠀⣤⣄⣀⣤⣴⡿⠙⠻⣇⠀⠌⠀⠀⢿⣥⣠⣶⢰⣶⣿⠁⠀⠐⡀⠌⠠⢁⠓⠒⢉ ⣋⠿⡏⠉⡀⠄⠡⢐⡰⠠⠈⠄⡡⠂⠌⠠⣡⣦⣤⡵⠞⣿⣤⣦⠀⢁⠂⠠⢁⠀⢂⠐⣠⣴⡄⡐⠀⠄⠂⠄⣠⣴⠾⠛⠉⠀⠀⢀⠂⠠⠐⠈⠀⠀⠀⠀⢰⣿⣤⣏⣳⠾⣿⠁⠀⠂⠀⠄⠐⠀⡌⠠⢈⢀⣤⠞⣣⠽⡋⠴⡟⡿⠚⠛⠋⢀⠂⠌⠐⣺⣧⣿⢻⡟⠁⣀⡀⢈⠐⠠⢈⠐⠠⠈⠔⡀ ⢮⡑⢀⡇⠠⡩⢰⠢⣘⢃⠌⡐⠠⠁⣌⡘⣷⣤⡬⣤⠊⣡⣤⣿⠀⠂⠌⡐⢠⣬⢶⣿⣯⡾⠛⣿⣄⣬⠶⢛⠉⡀⠀⢀⠀⠂⢈⠀⢂⠡⠀⠂⠁⠀⠀⠀⠀⠀⠀⠈⠡⠾⠋⡀⠌⠐⠀⡈⠄⠂⣧⣐⣠⠶⠉⠿⠷⠒⠙⣻⠃⠠⠐⠠⢈⠀⠄⠂⠄⠿⢯⣿⣸⣇⣶⣿⠿⠂⢀⠁⡂⠌⠠⢉⠐⡀ ⣦⠆⡒⠭⠔⣐⡬⢀⣉⢯⣴⣠⣥⣶⣴⠇⠿⠷⠾⠹⣦⣤⡿⠏⢀⠁⢂⠄⠻⣿⠞⢹⡆⠉⠻⣯⠁⡀⠂⠄⢂⠐⠡⢀⠂⠁⠂⡀⠂⠄⡁⠂⠄⠈⠀⠀⢀⠀⠀⠀⠄⢀⠒⠀⠄⣈⡐⣀⣌⠐⢸⣿⣻⠀⠀⠀⠄⠀⡀⠋⠀⠐⡀⢁⣦⣤⣌⣠⣈⠀⠀⠈⣿⠟⠉⢀⠠⢀⠂⡐⠠⠌⡐⢀⠂⠄ ⠮⢀⣽⣫⢓⡠⢳⣎⢿⣢⡽⢛⡿⢓⣇⠃⡐⠤⢂⠡⢀⠡⠐⡀⠂⠌⠠⠐⠰⢿⠶⠞⠛⡒⠒⠟⢠⠀⡑⢈⠄⡈⠐⠠⢀⠁⠂⠐⢈⣠⣼⠟⠒⣷⡀⠐⠀⠀⠂⠠⠰⣧⡾⠦⣾⣭⣟⢙⠛⡶⢿⣿⢻⡄⠂⠁⡀⠂⠠⢐⡴⠶⠶⢿⠇⡸⠟⣉⣽⠗⠠⠑⡉⠠⠐⡀⢂⠀⢂⠄⢁⠂⡰⢤⠈⠄ ⣞⣻⣿⣿⡟⠹⣮⣿⣾⣏⣴⡞⢤⡟⢀⢖⡨⢐⠀⠂⠄⢂⠡⢀⠡⢈⠐⡈⠀⠄⡠⢀⠡⢀⠡⠈⠄⠂⠌⣁⠂⢄⠁⠂⠄⠂⠁⡀⠂⠛⢳⣧⡷⢾⣧⠀⠀⠀⠌⢀⢸⣿⣄⣀⠞⠓⣻⡾⠿⠗⢻⣧⠘⣷⠀⠀⠄⡐⠠⠈⠳⣶⡶⠞⣤⠘⣿⡉⡭⢽⡆⠐⠠⢁⠂⡐⠠⠈⠄⢲⣍⠉⠃⠚⠉⣟ ⢻⠋⠉⠙⢷⡀⣿⠷⠋⢙⡿⠛⡼⢠⣫⠏⣐⠊⣌⠐⡈⠢⠈⠄⠂⢄⡂⠐⣋⢐⠠⠂⠔⡀⢂⠡⠘⣖⠺⠹⣎⢽⡅⢈⠐⡀⠄⠐⠠⠐⡀⣸⡏⣋⣟⣷⢤⡁⠀⢂⣈⣿⣅⣤⣴⠏⢀⡏⠛⡛⠋⠉⠀⠸⣇⠀⠂⠠⢀⠁⠄⠿⡴⠞⣿⠦⢾⣶⣷⣬⡀⢁⠒⠠⠐⠠⠡⠚⡀⠦⠔⠚⣅⠇⠒⠊ ⣾⠿⠖⠂⠀⠙⠁⠤⠴⢯⣴⢯⡑⡤⠉⣶⣶⡙⠦⠐⣌⣆⢏⠚⠠⡜⢧⡓⢀⡂⣦⡁⢂⠐⠢⣘⡸⣭⠄⡐⣞⣾⠁⠄⠂⡴⢌⣤⠁⠠⣠⣿⣏⣹⠋⠀⠀⠀⢬⠄⢡⣤⣤⡍⣟⣛⠋⣄⠐⡀⢂⡅⠈⢤⢹⣄⠈⠄⡀⠂⠄⣢⡇⣤⣿⣱⣿⣿⡟⠉⡐⠠⠈⠄⣁⠂⡁⠆⡐⡄⢂⠐⣀⡂⠌⣠

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

⠀⣶⣶⠄⢀⣤⣤⣤⣶⣤⣤⣤⣤⣦⣤⣨⣭⣭⣭⣤⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⢉⣉⠉⠀⠀⠈⠁⠀⠈⠈⠁⠀⠀⠁⠉⠉⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣁⣤⣀⣤⣈⣠⣀⢈⣿⠟⢁⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣦⠀⢸⡀⠉⠀⣨⡿⠋⠛⢙⣿⡆⠉⢠⣄⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢟⣿⣥⡄⠀⠀⠀⣖⠀⠀⠀⢀⠐⣀⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡄⠸⠟⣿⣿⣿⢿⣿⣿⣿⣿⣷⣶⣼⣿⢛⣿⠟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⣾⡟⠳⣾⣿⣿⣆⣠⣴⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⣍⠁⣸⡿⠛⠛⢿⡟⠿⠟⢻⠟⢻⡿⠟⠙⠿⠀⠀⢀⡆⠀⠀ ⢸⣿⣷⠀⢸⣟⠩⠄⣿⠋⠛⠋⢻⣍⢻⣿⣙⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⡿⠟⣁⣀⣼⣧⣾⣟⠁⠀⠉⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⣿⠀⣽⡇⠙⠁⢀⠙⢶⡤⠀⠒⠀⣰⠈⣷⠘⠿⣀⠀⠀⣈⡃⠀⠀ ⢸⣿⡇⠀⠈⠻⣶⠞⠛⢿⣿⠿⠟⠿⠟⠻⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣼⠁⢸⠿⠛⢁⣾⡿⣿⣿⣿⣿⣾⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣿⠀⣿⠻⠶⣦⡾⢷⣤⣿⣤⣤⣼⣧⣤⣴⡾⠶⢿⣦⣤⣿⡇⠀⠀ ⠈⣿⡿⠀⠀⠀⠹⣧⣀⣴⡿⠠⣦⣴⣶⣶⣿⣡⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⠛⢙⣻⣤⣠⣴⣾⣿⢷⣿⣀⣻⣧⡙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣤⣤⣤⣤⣀⣤⣴⣇⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⡿⠁⠀⠀ ⠀⣿⡇⠀⠀⠀⣤⠙⣿⠋⠀⠀⣿⡏⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠟⠋⠙⠻⣇⠸⣿⡄⠹⣿⣏⣩⣤⣄⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣋⣍⠉⢉⣙⡟⠉⠉⠀⠈⠛⠙⠛⠛⠋⠉⠀⠀⠀⠀ ⠀⢿⠗⠀⠀⣀⣨⣶⣿⠿⠾⣷⣾⣷⣦⣶⣿⠿⢿⣷⣦⣀⣀⠀⢀⣠⣴⣶⠾⠿⢿⣿⣄⣀⡀⠀⠀⠀⣤⣶⡶⠿⠿⠿⠾⠷⠿⠿⣷⣿⣿⣶⢾⡿⠛⣹⣿⣿⠷⢾⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⣿⡿⠟⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⠀⢠⣾⡿⠟⢁⣀⣤⣤⣤⣈⠉⠋⢁⣀⣄⣠⣀⣀⠉⢻⣿⡿⠋⢁⣠⣤⣤⣤⣀⡉⠛⢿⣶⠀⣿⡟⠁⣠⣤⣤⣤⣤⣤⣤⣤⡀⢹⣿⡄⠀⣠⣾⡿⠋⢀⣴⡄⠙⣿⣧⣤⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠃⢈⣠⣶⣄⠈⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣽⣶⣿⠏⢀⣴⠟⣋⣡⣤⣈⠻⣧⠀⠸⣿⡍⢉⡿⢿⠇⠘⠋⢀⣾⠟⢉⣥⢤⣌⡙⢿⣆⠈⢻⣷⣿⡄⠀⢿⣅⠀⢀⠙⢧⣌⢻⣧⠀⠹⠿⠿⠿⠿⠀⣼⡟⢡⡇⠀⣿⡿⠃⠀⠛⠿⣶⣶⣶⡾⠿⠿⠿⠿⠷⠶⣶⣤⡿⠏⠀⣶⡟⢋⣿⠃⠀⠿⠟⠛⠿⠿⢷⣶⣄⣀⣀⣀⠀⡀⠀ ⠸⢿⡟⠁⢀⣿⢃⣸⠏⠀⠀⠙⠛⠛⠀⠀⢸⡇⢸⡇⠀⠀⠀⢠⣿⢇⣶⡟⠀⠀⡈⢿⡆⢻⣇⠀⢹⣿⣿⡄⠀⣿⠀⣿⡀⢀⣉⣉⠋⢀⣠⣶⠶⢶⣦⡄⠙⢛⣠⣴⡄⠁⣠⣴⣶⢶⣤⡀⠉⢁⣤⣶⡦⣶⢶⣤⡀⠙⠉⣀⣤⣾⡏⠖⢹⣿⠀⢀⣴⣶⠶⠶⣦⡀⠙⣿⣿⣿⣿⣿⣿⡇ ⠀⣿⡇⠀⣾⡏⣿⡟⠀⢀⣤⣤⣤⣤⣤⠀⢸⡇⢸⡇⠀⠀⠀⢿⣇⢸⡏⠀⠀⠀⠓⠈⣷⢸⣿⠀⢸⣿⣿⡇⠀⣿⡇⣈⣿⣿⣋⣻⣥⣿⡉⢉⣤⣤⣿⡁⢾⡛⢹⡟⢀⣾⠏⠀⠘⢶⣈⣿⡀⣿⣇⣀⡶⠻⣦⢻⡷⠀⣾⣿⣿⠟⢷⣦⢸⣿⠀⣾⡏⢠⣌⠛⢿⠇⢀⣿⡟⠋⠙⠛⠋⠁ ⠀⢿⣿⠀⢿⣧⠸⣿⡀⠸⢿⣧⡈⣿⡿⠀⢸⡇⢸⡇⠀⠀⣀⠘⣿⡸⣿⣄⠀⠀⠀⣼⡏⢸⡟⠀⣸⣿⣿⡇⠀⣿⠷⣿⠀⠈⠉⠛⡇⢸⡿⣿⡇⠀⠈⠁⠘⣷⢸⡇⠸⣿⡀⢀⣶⠶⠟⠋⠀⢈⡏⣿⡀⠀⣿⢼⣇⠀⣿⠻⣧⠀⠀⣿⢿⣿⠀⠘⡿⠶⣭⡛⢿⣦⠈⢻⣷⡀⠀⠀⠀⠀ ⠀⢾⣿⣆⠈⢻⣧⡙⠻⢶⣤⡿⢃⣿⠃⢠⣿⡃⠈⣷⡴⠛⢻⣇⠙⣷⣌⠻⢷⣤⠾⠋⣰⡿⠁⣴⣿⣿⠏⢠⣾⣟⠀⢻⣷⣄⠀⠀⢀⣾⡃⠙⢿⣤⠀⠀⣴⡿⠀⢿⡀⢿⣧⣄⠁⠀⢐⣿⠂⣼⡇⠸⣧⣀⣿⡈⢻⣆⢻⣦⡙⢷⣾⡋⠀⢻⡄⢺⡛⢶⣬⣿⣸⡟⠀⣸⣿⡃⠀⠀⠀⠀ ⠀⠀⠿⣿⣶⡀⠈⠛⠷⠶⠶⠶⠟⠋⡀⠘⠛⠛⠟⠒⠒⠳⠟⠁⣀⡀⠙⠻⠶⠶⠶⠛⠋⣠⣼⣿⠋⣿⣆⠈⠛⠛⠛⠛⠛⠛⣦⣀⠈⠛⠿⠿⠿⠟⠀⡀⠙⠛⠛⠛⠓⣀⠙⠛⠿⠟⠛⢁⠀⠛⠛⠛⠋⠉⠛⠛⠛⠛⠀⠙⠻⠛⠛⠛⠛⠛⠛⠈⠛⠛⠛⠛⠛⣁⣴⣿⡿⠃⠀⠀⠀⠀ ⠀⠻⡆⠈⠻⢿⣿⣶⣤⣤⣤⣤⣶⡿⣿⣶⣤⣤⣤⣤⣤⣤⣶⣾⡿⠿⢷⣦⣤⣤⣴⣾⣿⠿⠛⠁⠀⠈⠻⢷⣦⣤⣤⣶⣶⡾⠿⢿⣷⣤⣤⣤⣤⣶⡿⢿⣶⣦⣶⣶⣶⣿⣿⣶⣤⣴⣶⣿⣷⣶⣤⣴⣶⣶⣶⣶⣶⣾⣿⣷⣶⣴⣶⣶⣶⣶⣾⣿⣷⣦⣴⣶⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀ ⠸⣧⡀⠀⠀⠀⠁⠈⠁⣴⠎⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⢀⣠⠄⠀⢀⣀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠁⠈⠁⣤⣴⠿⠉⠉⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠋⣿⣿⠋⠉⠁⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣬⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠋⠁⠀⠀⠉⠁⢀⣀⡀⠘⢷⣤⠄⡀⠀⠀⠀⢀⣴⠶⢷⣤⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣽⣿⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠒⣤⣹⣦⡀⣰⡿⢿⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠁⠀⠀⣿⠙⣷⣽⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠛⠉⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠉⠉⠛⠿⠿⣾⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠡⣴⣷⡾⠋⠀⠀⠙⠻⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣦⠀⠀⠀⠀⠀⠀⣀⣠⣴⡿⠋⠁⠀⠀⢀⣴⣿⣤⠶⠿⠟⠋⠉⠀⠀⠀⠀⠀⠈⠉⠛⠲⢶⣤⣀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣛⡅⠀⢀⡿⢸⡷⠀⠀⠀⠀⠀⢀⣉⣛⠻⣿⣿⣄⣠⣤⣤⣀⢀⣀⣀⣀⠀⠀⠀⠀ ⢠⡈⠋⠀⠀⠀⠀⣰⣿⣿⡿⠋⠀⠀⣀⣾⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⠀⠀⠀⠹⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⣰⣿⡿⠟⠋⠀⣰⡿⠃⢸⣿⢶⣤⣾⠷⡾⠛⠛⡙⣷⡄⠉⠛⠿⠏⠈⠉⠛⠉⠉⠻⣿⣦⠀⠀ ⠸⠗⠀⠀⠀⢠⣿⣿⡿⠋⠀⠀⣠⣾⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⡀⠀⠀⠈⠫⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠃⣠⠾⠋⠀⠀⣀⣤⡾⠋⠀⠀⠀⣽⠠⣿⣷⡄⠘⣿⣇⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠀⠀ ⠀⣴⠀⢀⠀⣿⠟⠉⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⢿⣹⡟⢶⣤⣾⢿⣿⣷⣄⣠⣶⠟⠁⠄⠀⢀⣤⣴⠾⠛⢉⣽⡀⠀⠀⠤⢀⣿⢀⣻⠟⠓⠛⢧⣽⡿⠁⠀⠀⢀⣀⣀⣠⣤⣴⡶⢿⣍⡀⠀⠀⠀ ⠀⣷⠀⠄⠸⢫⡄⠀⠀⣴⡿⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠈⢿⣤⠞⠁⠉⠛⢷⡿⢿⢿⡍⠀⢀⣠⣶⡿⠿⢤⡤⢶⡿⠉⣿⣦⣈⠀⢘⣷⣜⠛⣛⣿⣛⡤⠭⢤⣤⣀⣤⣼⠿⢛⣩⡿⠛⠃⣠⣿⢃⡄⠀⠀ ⠐⠛⢀⠀⠀⠘⠁⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠈⣿⠆⢀⡀⢰⡿⠀⠀⢿⣄⣰⣿⣯⣥⣤⡶⠶⠶⢾⡿⢦⣼⣿⠿⣧⣼⡇⢹⣾⡟⢩⣿⣇⠴⠟⠋⣡⣴⣷⡾⠛⠉⠀⣠⡾⢟⣵⡿⠃⢀⠀ ⠀⠿⠈⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠹⠿⢿⣟⣿⠃⠀⢠⣿⡿⣇⠋⠀⠀⠀⠀⠀⠀⢈⣷⣟⣋⣻⣧⣻⣿⣷⡘⠻⠿⢿⣏⡀⣶⣶⣿⣟⣉⣉⣤⠴⠶⣛⣡⣴⠟⠋⢀⣼⡟⠀ ⢸⡷⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠈⣠⣿⣛⣡⣤⠀⣾⣿⣷⣶⣶⣄⡀⠀⠀⠀⣴⣿⣯⣙⡻⠟⠉⣿⣿⣧⣿⣷⣶⣦⣈⣁⣈⣙⣣⣍⣉⣥⣶⣾⠛⠛⠋⠀⢀⣠⣿⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢰⣯⠈⠉⢉⣹⣤⣼⠟⠹⢶⣿⣿⡿⠀⠀⠀⠻⠿⣿⠟⠁⠀⠀⣼⠟⠈⢳⣤⡈⠉⠉⠙⢫⣍⠉⠉⠉⠁⠀⡀⠀⣠⣴⣾⣿⠟⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠻⠷⣶⠞⢉⣈⠙⠆⠀⠀⠀⣀⡀⠶⠛⠂⣠⡀⠀⠀⠀⠀⣠⣙⣦⡴⠋⠈⢻⡆⢠⡄⠀⠘⢷⣄⣠⣴⣾⣿⣿⣿⣿⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠀⠘⠃⢶⣶⠿⠋⠁⠀⠀⣀⡴⠛⠉⠉⡀⠀⠀⢀⠻⣾⠟⠻⠆⣼⣿⣿⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⠀⠀⠀⠀⠀⠰⠀⢀⠀⠙⠻⠶⣤⣤⣠⡥⢤⣄⣠⡴⢿⡋⠀⠀⠀⠀⠙⣦⣀⣾⢷⣷⣶⣶⣾⡿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⢀⡄⣴⣿⣻⣾⣛⠲⣦⣄⡀⢈⡁⠀⠀⠀⠈⠉⣁⣀⣻⣠⣴⣖⣿⣿⣿⣿⠿⠿⠻⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢈⡀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠈⣠⣴⠿⠿⠿⠛⠾⣯⡝⢿⠿⣿⣶⣿⣶⣾⣿⣿⠿⠛⠛⠛⢛⡉⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⡃⢀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⣠⣾⣿⡁⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠁⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣧⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⢀⣿⣿⡿⠃⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⢠⠀⠀⠀⠀⠀⣠⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣿⣦⡄⠀⠀⠃⢹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⣼⣿⠟⠁⢰⡁⠀⣠⣴⠟⠛⠛⠀⠀⠀⣀⣠⡶⠆⢠⣴⣶⣄⠀⢠⣶⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⣶⠀⠻⠻⣿⣆⠀⠀⠀⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⣼⣿⣧⣠⣴⣿⢻⣿⣭⡁⢀⣴⣶⣾⠓⠾⠟⢁⡔⠺⣷⣤⡀⣬⡿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⣿⣿⣦⡄⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠀⠀⠀⢀⣾⣿⠿⢀⡉⢸⡿⠞⠁⠈⣹⣿⣍⣉⣉⣀⣨⣴⣾⠛⢷⣶⠿⠃⠽⣧⡀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⠃⠀⠀⠀⠙⢿⣿⣿⡀⠀⠀⠀⠙⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⠟⠋⠀⠀⠀⠀⣴⣿⣿⠛⢀⣿⣥⣿⣇⠀⠰⠂⣿⣯⣉⡉⠉⠉⣉⣹⠟⣷⣾⣿⣟⢀⠀⠘⣷⡀⠀⢘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣦⣄⠀⠀⠀⠀⠙⢿⣿⣦⣄⡀⠀⠀⠈⠙⠛⠶⢦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠛⠉⠀⠀⠀⠀⢀⣤⣾⠋⣼⡇⣠⣾⠋⣿⠉⠉⢳⡀⢀⣴⠀⠙⣷⠀⠀⠉⠙⢿⡉⠈⠉⠻⣧⡀⠀⢻⣷⡀⠀⢻⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⣹⡏⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠉⠙⠛⡟⣛⡉⠉⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⠡⣾⠏⣵⢿⡅⢠⠉⢀⠀⠀⢳⠘⣿⣿⡦⠉⣠⣶⣶⠀⣸⠇⠀⠀⠀⠘⣿⣷⢰⣿⡇⠀⠀⠻⣏⠻⣦⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄ ⢰⣶⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⢷⣶⣄⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣾⣿⣿⡿⢫⣽⣐⣿⡿⠏⠈⣷⡎⠀⠈⠳⣄⠠⠀⠈⠉⢡⣶⣾⠿⠟⠘⠛⠂⠀⠀⠀⠀⢸⣿⡞⣻⣷⣤⣾⠿⠻⠤⢤⡉⠻⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⣶⣤⣀⣶⣤⣤⣤⣶⣶⣶⣶⣾⣿⣿⣏⣡⣾⡟⠛⠀⠀⠙⣿⣿⡇⠀⠀⠸⣷⢀⡄⢀⣾⣷⣄⠀⠀⠀⠈⠁⠀⣶⠀⠀⠀⠀⠀⠀⠀⣸⣿⣾⠏⣩⣿⠿⣦⣀⡀⠀⠻⢶⡄⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠋⠹⠛⠉⠉⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣿⣿⣷⣄⠀⠀⠹⣦⡻⠆⠉⠉⠹⣷⣄⡘⠃⠀⠀⠀⠀⠓⠀⠀⠀⣀⣼⡿⢻⣿⣿⡛⠁⠀⠀⠙⢿⣆⠀⠀⢻⡄⠈⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢹⣿⣿⡄⠀⠀⠈⠻⣦⣄⡀⠀⠈⠙⠳⠾⢲⣤⣤⣤⣴⡶⠶⠿⢋⣩⣴⡿⠁⣹⣿⣆⠀⠀⠀⠈⢿⣦⢸⡿⠃⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠹⠿⠿⠀⠀⠀⠀⠀⠉⠻⠶⢦⣤⣀⣀⣼⣿⣿⣾⡿⠶⣶⠾⠛⠉⠁⠀⠐⢿⣌⠁⠙⠶⠤⢀⣼⣿⣾⡇⠀⠀⠈⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡦⠀⠧⠀⠀⠀⠀⠀⠲⠀⠈⠉⣹⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣨⣿⣧⠀⠀⠀⠸⣿⡝⣿⡄⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣤⣦⣤⡀⠛⠋⠁⠐⠶⠀⠀⣀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⢹⣷⢀⡄⠀⠘⣿⡌⠻⣶⣶⣶⠟⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣯⣙⣿⣥⣤⣤⣤⣤⠄⠀⠀⣦⠘⣷⣤⣶⡀⣀⠀⠀⢀⣴⡟⠀⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢿⣷⣾⢷⡀⢠⣿⠁⣼⣷⣈⣿⠀⣿⡇⠠⢀⣀⠀⠀⡀⠀⠀⠀⠀ ⠀⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢸⡟⠁⢿⣥⣤⡀⠀⠀⣠⣤⣤⣤⡿⠿⣿⣥⡀⠉⠉⠁⠀⠿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⣿⣟⠻⢿⣟⣼⣟⣴⡿⢃⣤⡼⣿⣆⢸⣯⣴⣾⢿⣦⠀⠀⠀ ⠀⢻⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠀⠀⠀⠉⠉⠛⠛⠛⢛⣩⣮⣙⣃⣀⣘⣉⣟⠛⠷⣶⣶⣶⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠆⠀⠀⠀⠀⣿⣿⠀⠀⠈⠉⠛⠉⠀⠀⠈⠙⠉⠿⠷⢿⣿⣿⣶⣿⠀⠀⠀ ⢰⣿⣷⣦⡄⠀⠀⠀⠀⣀⣀⠀⠀⣠⣾⣧⣶⠟⣽⠿⠦⣤⣤⣶⡄⣀⢀⣀⠀⠀⠀⣀⡀⢀⠀⣀⣴⡿⠃⠀⠀⠀⠀⣀⣤⣴⡾⠟⣫⠉⠉⠉⠉⠉⠉⠙⠿⣶⢿⣄⡀⢻⡄⠀⠀⠀⠀⢶⣌⢳⣤⣶⠟⠛⠿⣷⡄⢠⣥⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠻⣿⢿⣿⡄⠀⠀ ⢸⣿⣿⡉⠀⣴⣿⣿⠿⠋⠉⠀⠀⠀⣀⣀⣤⠤⠤⠤⠤⠬⠤⠽⣶⣟⡛⠛⠛⠿⠶⠾⣿⣟⣛⣿⠿⣟⠃⠀⣠⣴⠟⠋⠉⠁⠀⠈⠻⠄⠀⠀⠀⠀⠀⠐⣷⡙⢷⡈⢻⣾⣇⣹⣦⣄⣀⣼⡿⣿⣯⠀⠀⢀⡀⣿⣿⣶⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⣠⡀⠀⣤⡈⠛⢿⡇⠀⠀ ⡜⠛⢻⣿⠿⣟⣉⣤⣠⣤⣤⣴⣤⣾⣿⣫⣥⣤⣤⣤⡤⢤⣤⣄⣀⣉⠉⠙⠳⠶⣤⡀⣠⠟⠉⠉⣀⣀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣬⣷⣄⣽⡀⠐⢿⣿⣿⣟⣿⡏⠀⠘⢿⣄⠀⢸⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣬⠉⠉⠁⠘⢻⣦⠀⠀⠀⠀⠀ ⠰⣴⡿⢋⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠱⠶⠶⢶⣤⣽⠋⣠⣶⡿⠟⠛⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠶⠟⠁⠀⢀⣽⠛⠳⣤⡀⠻⣿⣿⣿⡇⠀⠀⠀⠙⠆⣼⡏⠉⠙⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⣤⣤⣤⣤⡘⢿⡄⠀⠀⠀⠀ ⢠⣿⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣥⡶⠀⣶⡀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⢀⣶⣿⠾⠻⠿⢿⣶⣄⠙⣿⣄⠈⠻⣿⡿⣶⣄⠀⣠⣾⠟⠁⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠉⠉⠉⠉⠻⣿⡅⠀⠀⠀⠀ ⢈⣿⡀⠀⠙⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡏⠀⠀⠈⣷⡀⠻⠄⠀⠀⠀⠀⠀⠀⣴⠟⠁⣠⡿⠛⠁⠀⠀⠀⠀⠈⢻⣧⠈⢿⣆⡀⠈⢻⣦⠉⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠻⢶⣤⣶⡿⠿⠶⢶⣦⣤⡀⠀⠀⠈⣷⡄⠀⠀⠀ ⢸⣿⣷⡀⠀⠀⠉⠙⠛⢿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹⣏⣴⡶⢶⣦⣿⡇⠲⣶⡶⠶⡆⠀⠀⠀⠟⠀⣼⡿⠁⠀⣀⣀⣀⠀⠀⠀⠈⣿⡆⠘⠋⠙⠒⠛⢻⡇⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡈⠉⠙⢷⣆⠀⠀⠈⠙⢿⣶⣤⣴⣿⠇⠀⠀⠀ ⠀⠙⣿⣿⣦⣀⠀⠀⠀⠀⠀⠈⠉⠻⠿⠶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣶⡆⢿⠙⣧⠀⠀⠀⠀⠄⠀⠀⠀⠀⢰⣿⠁⣴⣿⠟⠋⠻⢷⣆⠀⠀⢩⣿⢀⠀⠀⠀⠀⢸⣷⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠠⣬⠛⣷⣤⣴⡶⠞⣫⣭⠉⠳⠞⠁⠀⠀ ⠀⢐⠈⠙⠛⢿⣷⣶⣤⣀⣄⡀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⣶⠶⠶⣶⣤⣤⣼⡇⣿⣟⣿⣿⣿⣿⡇⣹⣷⡤⠶⠶⢶⣦⣄⡀⠀⠿⢁⣼⣿⣤⣤⡀⠀⠀⢿⡆⠀⣼⡇⣼⠀⠀⠀⢀⣸⣿⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⣴⣾⣟⠉⣴⠾⠛⠛⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣶⣶⣤⣄⡀⣠⣀⡀⠀⠀⠀⠀⠲⠀⠰⣌⠉⢿⣧⣿⣿⣿⣿⣿⣟⣴⡟⠁⠀⠀⠀⠀⠈⠙⢿⣧⠀⣿⣿⣻⣿⣿⣿⣆⠀⢨⡿⢠⣿⣆⣿⣄⣠⣤⣾⠿⣿⠀⢰⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⣴⣿⠟⠃⠈⠉⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠿⠛⠿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠈⢿⣯⠿⢿⡿⢛⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠻⣿⣿⣿⣿⣿⡿⢠⣿⢁⣾⣯⣿⡟⠙⠋⠁⠀⣾⠏⠁⣾⡿⡃⠀⠀⠀⠀⠀⣠⣴⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⣿⣦⣠⣄⠀⠀⠀⠈⠻⣷⣶⣶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⢻⣿⣿⣿⡿⣡⡾⣣⣾⠏⣽⡿⠁⠀⠀⠀⣸⡟⠀⣤⣿⡇⠁⠀⠀⠰⣿⣟⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀ ⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣦⡄⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣾⣿⡿⠿⢿⣇⣟⣠⣾⠏⠀⠀⠀⠀⣠⡿⠃⢠⣿⠇⠀⠀⠀⠀⠀⠈⠙⠛⡉⠿⠺⠿⠷⣶⣤⣤⣤⣤⣤⣶⣾⣿⣿⠿⠻⣯⡍⠉⠉⠉ ⠀⢰⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢹⣿⣶⠀⠀⠙⣷⡀⠀⢸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠾⠿⠟⠋⠀⠀⠀⢠⡾⢣⣾⠃⣰⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠓⢠⣈⣧⣶⣼⠿⠛⠿⣿⡟⠁⠐⠦⠀⠀⠀⠀⠀ ⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣆⠀⠀⠙⣷⣄⡀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣤⣤⡔⢋⣴⠟⢁⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⢷⣄⠀⠀⢸⠋⠀⠉⠻⢷⣄⠀⠈⠻⣤⡄⠀⠀⠀⠀⠀⠀ ⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄⠀⠈⠉⠛⢿⡛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⢁⣴⣆⣴⣿⣡⡾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠙⠻⣷⣾⡆⠀⠀⠀⠈⠻⣧⡀⠀⠸⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢸⡇⠀⠀⠀⠀⠀⠳⣌⡿⠳⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣶⡟⢫⠉⠁⠘⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠈⢿⣿⡂⠀⠀⠀⠀⠙⣷⣀⠀⠈⢿⡄⠀⠀⠀⠀ ⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣿⠀⠀⠀⠀⠷⢀⠿⠷⠄⠀⠉⠙⠿⢾⣶⠶⠟⠻⣶⣶⣾⠿⠋⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠘⠆⠘⢿⡀⢀⣿⠇⠀⠀⠀⠀ ⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡾⠁⠀⠀⠀⠀⠀⣼⠗⠀⠀⠀⠈⢳⣶⠟⠁⠀⠀⠀⠈⣻⣷⣾⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢰⣟⢱⣾⠏⠀⠀⠀⠀⠀ ⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣶⣦⣤⣤⣄⣀⠀⣀⡀⠀⠠⠿⠁⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⢘⣿⠃⠀⠀⠀⠀⢀⣼⡿⠁⠙⠻⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣓⣤⣶⡿⠛⢿⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⡜⢛⣿⠏⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠀⠀⠀⠀⢀⠀⣀⣤⣶⣶⡾⠿⠛⠋⠉⣉⣉⣉⣉⣉⣉⡉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⢠⣾⣏⠀⠀⠀⢠⡞⣸⣿⣿⡇⠀⠀⠀⠈⢿⣿⠟⠻⠿⠶⠶⠶⢾⣶⣶⡿⠶⠟⠛⠛⠉⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠸⠇⡀⠀⠀⣸⣧⣽⠏⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⡶⠀⢀⣤⣿⡿⠟⣋⣿⣾⠛⠛⠛⠿⢿⣿⡉⣠⣤⡿⠛⡛⠛⠛⠳⠄⠠⠄⠀⠀⠀⢠⣴⠏⠀⠀⠀⠀⠀⣰⣿⢩⣿⠀⠀⠀⢸⡇⢹⣿⣿⣇⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⣘⣿⠀⠀⠀⠀⠀⠀⠀⠳⣦⣸⠟⠀⠀⠀⠀⠀⢠⣶⠀⠁⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⣿⣿⣦⣼⣿⠟⣋⣠⣾⠿⠋⠉⢀⣀⣀⣴⠾⠛⠁⠀⢀⣤⣼⠛⢷⣤⠶⢶⣆⠀⠀⠀⣠⡾⢋⠀⠀⠀⣠⣴⡾⠋⠁⠘⢿⡆⠀⠀⠀⢻⡌⢻⡟⠿⠇⠀⠀⠀⠀⠈⣿⣦⣤⣤⣤⡾⠟⠁⠀⠀⠀⠂⠀⠄⠀⠀⢨⡿⠂⠀⠀⠀⠀⠀⣼⠋⠀⠀⢀⡾⠇⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀ ⠘⣿⣿⣿⣿⠋⢸⣿⡉⠡⠀⣠⣶⠿⠛⠉⠁⠀⠀⠀⠀⠘⠛⢡⡄⢀⣠⣀⣼⣷⠀⣴⠟⠋⠀⣀⣤⣾⡿⠛⠁⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠁⢸⣷⡄⠀⠀⠀⠂⠀⠀⣿⠁⠉⠉⠁⠀⠀⡀⠀⡄⠀⠀⠀⣘⠶⣤⣼⠃⠀⠀⠀⠀⠀⠀⣿⠀⣀⠀⠸⠷⣤⣄⣀⠀⠀⣠⡾⣿⡇⠀⠀ ⠠⣿⣿⣿⡇⠀⠀⠙⠛⠓⠻⠿⣧⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠘⠿⠏⠉⣩⠉⠁⣀⣀⣠⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⢶⡈⣿⡆⠀⠀⠀⠀⠀⠻⣃⡀⠀⣀⣀⣠⡾⠛⠀⠀⠀⢀⣠⣾⣿⡆⠁⠀⠀⠀⠈⢧⣼⠏⠀⠀⠀⠀⠀⠀⢾⡏⠀⠉⠁⠀⠀⢀⠈⠻⣷⡞⠛⣱⣿⠃⠀⠀ ⢰⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠷⠶⠶⠶⠶⠶⠶⠶⠶⠿⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠈⠳⠘⠳⠀⠀⠀⠀⠀⠈⣿⣟⠿⠛⠛⠋⠀⠀⠀⣠⣶⣿⣿⡟⣿⠃⠀⠀⠀⠀⠀⢨⡏⠀⠀⠀⠀⠀⠀⠀⠾⠷⢶⣤⡀⠀⠀⠀⠀⠀⣿⡇⣼⣿⠁⠀⠀⠀ ⢸⣿⣿⡿⠉⢻⣿⣶⣴⣶⣄⣀⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣾⣷⡀⡄⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡿⠀⠀⠀⢀⣴⣶⣿⣿⡿⠛⠈⣿⡏⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⣀⣤⡾⢋⣴⣿⡿⠀⠀⠀⠀ ⢸⣿⣿⡆⠀⠀⡀⠾⢟⣿⡿⣛⠿⠛⠛⠻⢿⣷⣶⣶⣶⣶⣶⣶⣶⡶⠶⠾⠿⠿⢿⣿⠿⠿⠛⠛⠛⣿⣷⡄⠀⠘⣿⣆⡀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⢀⣤⣾⣿⣿⡿⠟⠁⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠙⠀⢘⣫⣾⣿⠁⠀⠀⠀⠀ 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