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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠤⠤⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠊⠉⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⢩⡴⢷⣄⣭⣭⣭⢉⣩⣿⡻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣁⣿⣴⣿⣿⣧⣴⠿⣟⣉⣽⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⣿⣁⣼⣿⠋⣹⣿⡶⠟⣿⠇⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⣿⣷⡿⢿⣏⣿⣷⣶⠟⣰⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣾⠟⣿⣴⠞⣿⣋⣠⡿⣰⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⠙⠓⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣅⣼⢿⡟⢉⣿⣴⠿⢿⡇⣴⡿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣄⣰⣻⣆⢀⠀⠀⣀⣾⠙⢲⣄⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠈⠙⠛⠉⢷⣶⣿⣿⠟⠀⠀⠀ ⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣻⣿⣿⠟⣿⣿⣶⣼⣿⣿⣤⢟⣣⡝⢦⡀⠀⠀⠀⠀⠈⢿⣶⣤⣤⣤⡾⠟⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣼⢿⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠿⠋⠀⣸⣿⣿⣿⡏⣫⣿⡛⠃⠀⠀⠙⢆⠀⠀⠀⠀⢰⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⣧⠙⠳⠦⣄⣀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠖⠋⠁⠀⠀⠀⠘⣿⣿⠟⢿⣷⡟⢿⣷⣄⡀⠀⠀⠈⠧⣄⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⠓⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⠿⣿⠟⠻⡟⠛⠛⢿⣬⡛⢦⣄⡀⠀⠈⠳⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢳⡒⠒⠲⠶⠦⠤⣤⣄⣀⡀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⢻⣦⣈⡙⢶⣶⣦⡿⠉⠳⢬⡉⠓⠶⠾⢿⣷⣄⣀⣤⣴⣶⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣙⣦⣀⢀⣀⣀⣀⡀⠉⠉⠙⠲⢦⣴⣋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠻⣤⡤⠴⠒⠒⠒⣲⡶⣛⡶⠒⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠙⢧⣀⠀⠀⠉⠉⠉⠉⢒⡾⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠋⢉⡉⠉⢙⡶⠶⠦⣬⣭⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠤⠴⠒⠛⠻⣍⡉⠉⠉⠉⢹⠋⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠀⣹⠯⣅⣠⡖⠋⠁⢸⡌⠉⠓⠢⢤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡞⠀⠀⢠⡇⢰⠃⠀⠙⠳⢤⣀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠿⠛⠉⠀⠉⠓⠦⣼⡇⠀⠀⠀⠀⠈⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⢸⠁⡞⠀⠀⠀⠀⠀⠉⠛⠺⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣴⢻⠏⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⢶⣶⣶⠶⠶⠖⠒⠋⢉⡁⡴⢳⠏⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⣻⢡⡇⠀⢀⡤⠴⣏⣉⡉⠙⢮⡀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⢀⡏⢸⠀⠀⣸⡇⢀⢹⠀⠉⠓⣤⡇⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡤⠤⠤⠤⣄⣀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢷⠘⣇⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢸⡇⢿⠀⢠⡿⣿⣟⣏⠙⢢⣤⠏⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠳⢦⡀⢀⡈⠹⢦⡀⠀⢸⡇⠀⠀⠀⠀⠀⠈⢧⡘⢦⡀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢿⡘⣶⡏⠀⠈⠉⠙⢷⣤⠏⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠶⣽⠀⠈⠻⣄⠀⣧⠀⠀⠀⠀⠀⠀⠈⠳⣄⠛⢦⣀⡼⠁⠀⠀⠀⠀⠀⠀⣀⣠⣽⠋⠀⠀⠀⠀⠠⡼⠃⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢧⡀⠀⠘⢦⣸⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣬⣍⣛⣒⣒⣒⣚⣫⣭⠥⠟⢳⡀⠀⠀⠀⢀⣤⠇⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⣨⡟⠶⣦⣤⡼⠃⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢈⣧⡀⠀⢀⣤⠞⠋⠉⠉⠻⣧⠀⣀⣀⣴⢦⠀⠀⠀⠀⠀⠻⣿⣷⡟⠁⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢲⠟⢹⣷⡀⣾⠁⠀⠀⠀⠀⠀⣸⣾⣿⠋⠈⣸⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⣼⣿⣧⠿⠶⣴⣶⣶⡶⠶⠋⢹⠃⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⢀⣀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠉⠉⠉⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣦⣶⣦⣄⣀⠀⠀⣾⠹⡄⠀⡤⣀⠀⢰⣞⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣶⠇⠀⠱⣀⠹⣿⣷⣃⣹⣿⣿⣷⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠙⠻⣿⣿⣿⣏⣀⣠⣾⣿⣿⣿⣿⣿⠋⠀⣤⠈⡿⢡⡄⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⢁⣴⣇⡀⠀⣠⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣟⡻⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠘⠻⠿⢿⣿⣿⣿⣿⣿⣿⡆⠉⠛⢶⣄⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⢨⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡷⣄⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠅⠀⠀⠀⠀⠤⠤⢖⣃⠀⠀⢀⠇⠉⢧⠀⠀⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠘⣇⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⣿⣿⣿⣿⣿⠇⠀⠀⢠⠀⢎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡶⠀ ⣼⣿⣿⣿⣿⣿⡿⠿⠻⢿⣿⣟⣉⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠘⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀ ⢸⣿⣿⣿⣟⠛⠓⣠⠀⣄⠙⢿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣤ ⢸⣿⣿⣿⣿⣶⣾⣁⣰⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⣀⣸⠛⠛ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠉⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠐⢦⠀⢄⠀⠀⠀⠓⠄⣰⣯⡄⠀ ⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣀⣤⣼⣿⣿⣷⡀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢇⠀⠀⣀⣰⠟⠀⠁⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠐⠁⠀⣠⠀⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⢤⠀⠀⢀⠀⢀⣴⡿⢿⠀⠀⠀⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠙⢻⣷⣴⣀⠁⠀⡀⠀⠂⠀⡇⠀⠀⠇⠀⠀⡘⡀⣰⣨⣶⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣤⣿⣿⣿⣿⣿⣶⠓⠦⠤⣤⠁⠇⢦⡤⠒⢲⣿⠟⠙⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠿⠿⠿⠿⠟⠛⠛⠿⢆⠀⡰⠇⣀⡀⠀⠙⠦⣈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡴⠁⠀⠀⠈⠑⢦⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢰⠤⣱⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⢿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠹⠴⠃⠀⠀⠀⢀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣟⠒⠒⠤⠤⠤⠤⠤⠤⠤⢴⣴⣶⣶⡖⠒⠂⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⡿⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠿⠿⣒⠂⢴⡲⣄⠀⠀⡤⠶⠿⠟⠛⠋⠉⠑⠤⡉⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠄⣀⣀⣀⠀⠀⠈⢙⣆⡨⠾⠀⠀⠑⠒⠒⠒⠲⠦⠤⠤⠔⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⣤⣣⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⢠⢲⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⣀⠀⠀⠀⠀⣰⡿⠉⠈⠉⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⢀⡀⠀⠀⠀⠘⣷⠀⠀⠀⠀⢜⣞⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌⠳⣄⡄⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠙⠻⢷⣦⣄⢹⣧⢀⣀⠀⢀⡠⠭⣵⢗⢆⣀⡠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡘⢿⣦⣿⣷⣴⣾⣷⣶⠀⠀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣈⣙⣿⣿⢳⣮⣷⣭⠤⢴⣾⣞⡋⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⡀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⠙⣯⣙⡛⠿⠽⣿⣭⣿⡍⠙⠒⠛⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⢲⣮⣉⠉⠉⠉⠀⣀⣤⢞⡽⣻⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣻⣿⡿⠁⠀⢀⣀⡀⠀ ⠀⠀⠀⡜⡹⣮⢷⣄⣿⣿⣿⣿⢿⠿⣿⡿⠛⡻⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⣶⡆⠀⢷⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⠿⢷⣿⣾⢿⣿⠀⣠⣾⠟⠻⣷⠀ ⠀⠀⠀⣿⡇⠀⠙⢿⣎⢿⣿⣿⣿⣷⣿⣿⡷⠃⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠟⠳⠽⠁⠀⣾⠆⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⠁⠀⠀⡿⡇ ⠀⠀⢰⡿⢿⣱⠀⠀⣿⣆⠉⠛⠻⠿⠛⠋⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠘⢜⢤⡤⠤⡴⡶⣤⣿⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢻⡄⢰⡲⣷⣇ ⠀⠀⠀⠙⠛⠚⠀⠀⣿⣧⡷⢤⣀⠀⠀⢀⣠⣔⠚⢳⡄⠉⠓⠒⠠⠤⠤⣤⠶⠾⠿⣶⡿⠾⠼⣟⣿⣿⣤⣾⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⠚⣷⠀⠣⠗⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⡰⠊⠉⣹⣧⡾⠟⠒⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣹⣿⣿⣿⣿⢋⣀⣿⡇⠀⠀⠀⠀⣀⠀⠀⢀⣠⢟⣉⢙⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠧⢄⣀⣟⣏⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠁⣿⣓⠈⣿⢺⢟⣿⡇⠀⠀⠀⢸⣿⣶⠾⣍⠐⢦⠈⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠺⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣠⣤⠚⠓⢤⢹⣿⡎⠉⠁⠀⠀⠀⠀⠈⠻⣿⣴⣌⣇⣠⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⡁⠀⠉⢆⣠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠏⠙⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⣶⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀
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