⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠖⠛⠛⠛⠓⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⡤⠤⠤⠤⣤⠶⣶⣿⠭⠖⠒⠚⠉⠉⠉⢳⡆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡙⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠚⠋⠉⠉⠀⢀⣀⣤⡤⠤⠤⠤⠿⣬⢿⡈⠳⣄⠀⠀⠀⠀⠀⡿⠁⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠚⠉⠁⠀⢀⣠⡤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠈⠙⠦⣄⣀⡼⠁⣰⠏⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠉⢀⣼⠏⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⠞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⢀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠖⠋⠁⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢚⠥⢬⢓⠦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠀⠀⠀⠀⠀⢀⡒⠀⣉⠠⣐⠈⠀⠀⠀⠀⠑⢬⡃⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠰⣶⣄⠀⠀⠠⠖⠉⡈⠈⠩⢍⣁⠀⠀⠀⠀⠀⠀⠁⠮⡳⣄⠀⠀⠀⠀⠀⠱⡌⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣼⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⠀⠀⠻⣆⠀⠀⠀⢀⡟⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⢢⡄⠀⠀⠀⠀⠀⡀⠐⠢⠁⡒⢄⠀⠀⠀⠀⠀⠈⠮⢦⡀⣀⡴⠇⠀⢻⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣸⠃⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⢹⡄⠀⠀⢸⠃⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠇⠈⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠉⠢⢝⠢⣀⠀⠀⠀⠀⣹⡿⠋⠀⠀⠀⡼⢸⢀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢠⡏⠀⠀⠈⢥⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢷⠀⠀⡿⠀⠀⠀⡸⠃⠀⣼⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣂⣀⠀⠐⠀⠱⠤⢴⣀⡆⠀⠀⠙⠲⣕⡲⢤⣾⣋⠀⠀⢀⢠⣾⡵⠟⢣⣉⣥⢳ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⣼⠁⠀⠀⢤⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⢶⣤⡀⠳⡄⠀⠀⠀⣀⣀⣀⢸⠁⢀⡼⢡⣄⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠿⠒⠮⢍⣬⡿⠛⣁⢤⣀⠀⠈⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢠⡏⠀⢤⣄⠘⠆⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢁⡾⣆⠙⣶⡥⠶⢻⡉⠉⠉⡏⠉⠙⠚⢧⣄⠙⣷⢮⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣠⣴⣿⣅⠀⠀⠸⣄⠊⣝⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⣼⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⢻⢀⣼⠟⠉⠀⠀⠈⢳⡄⠀⡇⠀⠀⠀⠀⠈⠙⢿⣄⣠⣤⠤⠶⠖⠒⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠶⠤⣤⣀⡀⠀⠀⠀⠀⠙⢂⡼⠋⢸⡧⣬⡇⠀⠀⠈⠙⠘⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⣀⣠⣤⠤⠶⠶⠒⠒⠛⠛⠛⠛⠛⠛⠒⠒⠲⠶⠦⠤⣄⡼⢋⡇⠀⠀⠀⠀⠀⠸⡿⣦⡇⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⢀⡀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⣼⠀⠀⠀⠀⠀⠀⠀⣇⠈⣿⢦⣤⣶⣶⣶⣶⣄⣤⠞⢉⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⡀⠀⠀⠀⣠⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⣞⠁⠀⢰⠗⠒⠲⠦⣤⣀⠀⠀⣹⠀⢸⣼⣿⣿⣿⣿⣿⣿⡴⠚⠁⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠁⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⣇⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠈⠙⠒⠶⠤⡄⣀⣀⣀⣙⣁⣠⠏⠀⠈⠿⠿⠿⣿⠿⠟⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠁⠘⠙⠈⠀⠀⡇⣬⡧⢸⠋⡼⢂⠙⠀⠀⠀⠀⡀⣀⣤⠤⠶⠒⠓⠛⠛⠛⠛⠛⠛⠛⠛⠒⠖⠶⠤⣤⣠⣄⢿⠙⠈⠀⠀⠀⠀⡇⠀⡄⢳⠈⠀⠀⠉⠟⣼⢀⢻⡷⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⣄⢦⠙⠈⠀⠀⠀⣼⠀⠀⠃⣸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡄⣝⠊⣄⠸⠀⠀⣅⣿⣴⣠⠀⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢮⣷⠙⣄⢧⠚⠙⠉⡏⠉⠉⡉⢻⠶⡥⣶⠙⣆⡾⢁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠹⠀⠀⠀⠆⠘⣄⢤⠀⡏⢠⠀⠀⡟⢀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠈⠀⣀⢤⣁⠛⡿⣬⢍⠮⠒⠿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⣄⢡⡼⢀⠁⢸⣀⣀⣀⠀⠀⠀⡄⠳⡀⣤⢶⡖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠹⠀⠀⠀⢤⠀⠀⠁⣼⠀⠀⠃⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⢳⣥⣉⢣⠟⡵⣾⢠⢀⠀⠀⣋⣾⢤⡲⣕⠲⠙⠀⠀⡆⣀⢴⠤⠱⠀⠐⠀⣀⣂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠛⣼⠀⠃⡸⠀⠀⠀⡿⠀⠀⢷⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢻⠀⢥⠈⠀⠀⡏⢠⠀⠀⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⢀⢸⡼⠀⠀⠀⠋⡿⣹⠀⠀⠀⠀⣀⠢⢝⠢⠉⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠈⠇⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣴⠀⠀⠀⠃⢸⠀⠀⡄⢹⠀⠀⡄⢷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠃⣸⠀⠀⡏⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢻⠀⠇⡴⣀⡀⢦⠮⠈⠀⠀⠀⠀⠀⢄⡒⠁⠢⠐⡀⠀⠀⠀⠀⠀⡄⢢⠀⠔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡼⢀⠀⠀⠀⠀⡟⢀⠀⠀⠀⣆⠻⠀⠀⠀⣄⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠃⣼⠀⠀⠏⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣆⡌⠱⠀⠀⠀⠀⠀⣄⡳⠮⠁⠀⠀⠀⠀⠀⠀⣁⢍⠩⠈⡈⠉⠖⠠⠀⠀⣄⣶⠰⠀⠀⠀⠀⠀⠀⠂⡴⢀⠀⠀⠀⠀⠀⡏⢰⠀⠀⠀⠀⠀⣆⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣰⠀⠀⠏⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⡃⢬⠑⠀⠀⠀⠀⠈⣐⠠⣉⠀⡒⢀⠀⠀⠀⠀⠀⠤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡴⢀⠀⠃⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠦⢓⢬⠥⢚⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣰⠀⠀⠀⠀⠀⠀⠁⠋⠖⠒⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠾⣤⢀⠀⠉⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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