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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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⠜⠠⠁⣌⠰⠘⠊⠁⠀⠀⠠⠄⠄⠒⠀⠉⣀⠤⠂⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢴⠞⠁⠀⠄⡁⠂⠐⠀⢀⡆⠳⢡⢆⡛⣤⢋⣊⣁⠂⣉⠻⢾⠿⠳⡜⢦⡹⣙⢿⡋⣡⣾⣿⡿⣞⣿⣽⣇⠉⢀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⢉⣴⣾⠿⣭⢯⣵⡋⣰⣦⠿⣙⠲⢦⣨⣷⠿⣾⣿⣷⣧⠾⣥⣪⢟⣯ ⡌⢂⠩⠀⠐⠀⠂⠁⠀⠄⡀⢀⣄⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⣁⡰⠏⡀⠄⡈⡐⠠⠄⠂⡐⢈⠀⢂⣵⠲⡽⣭⣳⡜⡴⢪⢥⠛⣦⠛⠛⠺⢧⣳⢍⡞⣻⡿⣝⣶⣽⢿⣯⣿⡿⢟⡿⠀⠀⠀⠀⠀⢀⣰⢏⣳⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠀⣰⠏⣼⢯⡟⣳⡏⣶⠟⣩⡵⢯⣬⣙⣇⠻⢧⣟⣿⣹⣏⢛⣿⢞⣹⣯⠧ ⠠⠀⠀⠈⢀⠠⠐⢈⣠⠴⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠐⢬⣘⡡⢉⠡⠐⠠⢁⠠⠁⢀⠂⠌⡀⠿⣶⣛⡶⣹⠖⣭⢓⢮⡹⣔⠲⣍⢳⢦⡹⣎⣾⡋⠻⠿⡼⢾⣿⡿⠋⠘⠁⠀⠀⠀⠀⢀⣤⢟⣡⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠋⢀⠂⢀⣼⣃⡼⠟⠻⡿⢿⣞⣡⣞⣧⡽⣞⣭⣵⡾⢟⡹⣿⣉⣿⡿⣯⣵⣯⣟⣛⣛ ⢦⡀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠖⣴⠋⡄⠀⠄⡀⠄⠡⡔⢀⠂⡁⢂⣤⣦⠙⢦⡈⠐⠄⠂⠌⡉⠛⠳⣏⠶⣩⢖⡱⢎⡳⣌⠳⣮⡵⢋⠡⡙⠳⠖⣋⡾⢋⠁⠀⠀⠀⠀⠀⣠⡴⡛⣥⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⡡⠁⢌⠠⠀⣽⢻⡶⣶⢖⣻⢟⡿⡷⡼⣻⠵⠚⣉⣡⠤⢖⡿⣞⢵⣫⣵⡾⢿⣭⣚⣬⣧⣭ ⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠒⠒⠚⠉⣉⣡⡤⢾⡿⠁⡼⢀⣬⣔⣼⣦⡄⠙⠃⢄⠁⢾⣿⣽⣷⠈⣉⠡⢈⠌⡲⠜⢁⠂⢌⡻⢔⡫⣜⢣⣕⣮⠟⢁⣠⡤⢶⣶⠞⠛⠉⠈⢀⡀⣀⣤⣄⣴⣞⣋⣴⣉⣥⣄⣠⣄⣤⣀⣀⣀⣀⣀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢁⡐⠠⢁⠂⠄⣡⠻⣶⣟⣖⡺⣇⡞⢾⣿⣜⣧⣞⣋⣷⡿⢿⣛⣿⣻⣽⣿⠽⠾⠛⠛⠉⠁⠀⠀ ⠀⠀⠀⠹⣆⣠⠤⠤⠒⠂⠉⠈⡀⠀⠀⠀⣀⣤⠴⠋⢡⠞⣷⣿⡿⣀⠄⣿⣛⠾⣧⣿⡇⡜⡰⠬⠃⠌⡙⠛⡉⣰⣉⠦⡆⢯⡱⣚⢬⡚⣬⢣⢏⣲⡽⠫⢉⡤⢦⣬⣥⣶⣿⣯⠶⠾⠿⠛⠛⠛⠋⠉⠉⠉⠉⠉⠈⠉⠀⠈⠁⠈⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠻⠶⠶⠦⣼⣥⣤⣂⣄⡁⠂⠬⠞⠁⠀⠈⠻⢵⡶⣽⣻⣶⣬⣿⣷⣯⢿⠶⠿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡄⠀⠀⠀⠄⠈⠀⠀⠁⠄⢒⡩⠴⢒⡛⠛⠛⡞⢟⣣⠓⠠⠙⣯⡟⣶⡟⠠⡘⢣⣙⠚⣤⣰⢡⡔⣡⢎⢳⡙⢦⡓⡷⣮⣕⡾⠶⠟⣻⣤⣴⢯⡷⢾⠛⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡙⠛⠲⠶⠦⢤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠔⠲⣉⣍

⠀⠀⠀⣼⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣿⠧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡿⠹⠂⠈⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡟⠂⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣄⣀⣠⣴⣦ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠉⢹⡟⠋ ⢠⡏⢠⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⡷⠶⠶⡶⠦⣤⣄⣀⢀⣴⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⢸⡇⢿⠀⠀⠀⠀⠀⣠⣶⠟⠍⣉⣿⣿⣄⠀⠈⠀⠀⠀⠈⠉⠛⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀ ⠀⣿⡀⠀⠀⠀⢠⣾⣿⡦⣶⣾⣿⡏⢹⣿⣿⣷⡌⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀ ⠀⠘⠛⠷⠶⢶⡿⠉⠙⣿⣿⣿⡿⠃⠸⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢃⡀⣘⣿⣿⡄⢠⠀⢀⠠⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⢀⣰⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣧⣼⠟⠉⠉⠉⠛⢿⣶⡾⠶⠟⠛⠛⠛⠛⠓⢦⣤⡀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢸⡿⠶⠦⠴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⢻⣶⣤⡔⠀⠀⠀⠀⠀⠠⣄⣀⣀⣤⣴⠀⠀⢹⡆⠀⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢷⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⣸⣷⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢷⣔⠈⠁⠀⠠⣤⡄⠀⠀⠀⠈⣛⡛⠋⠀⠀⣰⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⣦⠀⠀⠀⠀⠈⠀⢀⣀⣠⡶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠤⢤⣴⠿⡿⠛⠉⠙⠿⣿⣧⢹⡀⠉⠒⠒⠒⣦⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⢁⣴⡇⠀⠀⠀⠀⠀⠙⠟⠳⡦⢄⣀⡰⠏⠀⢀⣾⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡇⠢⣄⣀⣀⠀⠀⠀⢀⣿⣦⣭⣁⣀⣀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢈⣻⡏⠀⠀⢀⡞⠀⠈⠉⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⠋⠁⠒⢤⡀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠓⢤⣀⣀⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠶⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠋⠁⠀⠀⠀⠀⠈⠈⠈⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⢶⡶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⣧⠀⠀⠀⢀⣀⣤⠤⠐⠂⠈⠁⠉⠉⠉⠙⠛⠛⠻⠷⠶⢦⣼⣯⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣤⣴⢾⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣄⠀⠀⣀⣀⣠⣤⣶⣾⣿⠀⠀⠀⠀⠀⠀ ⠰⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⡿⠿⠛⠋⠀⠀⠀⠀⠀⠀ ⠀⢻⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠶⠟⠻⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠙⢻⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣤⢀⣠⡶⢶⣤⣀⠀⠤⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣤⡀⠀⠀⠀⠀⢰⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢿⡇⠠⣆⣀⡞⠀⠀⠙⠶⠞⠁⣸⣿⣾⡿⠋⠀⠀⠀⠉⠻⢶⣄⡀⣀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢿⣧⡀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠷⢤⣄⣀⠈⢿⣄⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⡀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢘⣿⣿⣷⣄⣸⠃⠀⠀⠀⠀⠀⠐⣀⣶⠟⠁⠀⠀⠀⠀⠈⠙⠛⠶⣯⣿⣿⣦⣠⣀⣦⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⡀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢷⡄⣸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣧⣼⣿⣿⣿⣮⣷⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢤⡀⠀⠀⠸⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⠿⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣀⣀⠀⠀⣀⣤⣾⡿⠃⠄⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣿⣿⠁⣄⠀⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠛⠛⠁⠀⢀⡼⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣏⣽⣆⢿⡧⠀⢹⣿⣿⡀⠀⠀⠀⢀⡸⣷⣤⣀⠀⠀⠀⣀⣤⡾⠏⠀⠀⠀⠀⠀⢰⣖⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣧⣿⡀⠀⠀⠘⣇⢀⣽⣄⠀⠀⠀⠀⠘⠙⠛⠻⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠈⢀⣠⠴⠒⠋⠙⠲⣄⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣆⡉⠰⠀⠀⡿⢸⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠶⠶⠶⠞⣧⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠘⣆⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣿⣆⠀⢠⡧⢸⣿⣿⣿⣿⣦⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠒⢀⣿⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⢀⡼⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⠲⢻⣇⣼⣿⣿⡿⠛⠛⠿⣿⣿⣿⡿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦⠴⠾⠃⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⣴⣾⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢿⣿⠋⠀⠀⠀⠀⠈⠻⣿⣿⣮⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣷⣄⠀⠀⠀⠀⠀⠀⠙⣎⠛⠫⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣿⣿⣿⡿⠿⠛⠙⠛⠿⠿⣿⣿⣿⣿⣿⠃⢸⡟⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠚ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡟⠓⣶⣷⡄⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⣀⣠⡶⠟⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠃⠈⠣⣀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠀⠠⢶⣟⡋⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⢀⡴⠖⠋⠉⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣤⠶⠛⠛⠛⠲⢦⣤⣤⣴⢾⠏⣡⣴⠖⠠⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢀⣀⡤⠴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⣸⡷⠟⠛⠷⠶⣦⣭⣥⣶⡾⠟⠁⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠾⣯⣁⣀⣀⣀⣀⣀⠀⠐⡦⠴⠒⠒⠲⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠞⠉⠉⠀⠀⠀⠀⠀⠀⠈⠓⠒⢄⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⠀⠀ ⢀⡄⠠⠼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀ ⠈⠢⠤⡖⠛⢀⡤⠴⠺⢤⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢱⡀ ⠀⠀⠀⢳⠀⣿⢠⣀⡀⠀⠀⠀⠀⠉⠀⢖⠀⠀⢀⠐⢆⡾⠁ ⠀⠀⠀⠈⢇⢸⡀⠉⠐⡷⠀⠀⠠⣤⡀⠸⡍⠀⠘⢆⡀⢉⡆ ⠀⠀⠀⠀⢎⡝⠑⣤⣀⢯⠃⠀⠀⠀⠀⢠⠃⠀⣀⠜⠉⠉⠀ ⠀⠀⠀⠀⠀⢳⣀⡔⠈⠑⠒⠒⠒⠒⠛⠉⠉⠉⠓⡤⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠗⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⢸⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢳⠦⣟⣲⣄⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠃⠻⣭⡽⠁⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀ ⢰⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇ ⠘⢿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⠛⠋⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣾⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣠⣤⣤⣤⣀⣀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣾⣿⣿⣿⠁⠀⠀⠀ ⠀⠀⠀⠸⣿⣿⣿⣿⢿⣟⣿⣿⣿⣿⣽⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣿⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣻⣿⣯⣿⠿⠽⠿⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣾⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠈⢻⣿⣿⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⢿⣻⣿⠀⣠⣄⠀⠀⠀⣠⣄⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⣿⣾⣿⣿⣿⡄⢿⡿⠀⠀⠀⠹⣿⢃⣿⣿⣿⣿⣿⣿⡿⣷⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣯⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⡖⣶⠠⣴⣿⣿⣿⣿⣟⣿⣷⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⣽⣿⠿⠛⠋⠉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠛⢿⣿⣿⣿⣽⣿⣿⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠟⢡⣆⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠁⠀⠀⠀⠀⣀⣴⡀⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣟⣿⣿⠃⠀⠈⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣟⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡏⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⠀⠀⢸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠰⣏⣹⡆⠀⠀⠀⠀⠈⠉⠉⠀⠀⢀⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣬⣥⡴⠃⠀⠀⠀⠀⠀⠀⢀⣤⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠈⢙⣻⣷⣶⣤⣤⣀⣀⣀⡴⠚⠛⠛⢿⡛⠛⠳⣄⣤⣤⣶⠾⠛⠉⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣰⣸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠈⡧⠀⠀⣹⣿⣿⣿⣶⣶⣼⣇⠄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣤⣄⣀⣈⡉⠁⠀⠀⠈⠉⢉⣽⣿⣿⣿⣿⣿⠷⠀⠀⣠⡼⣧⡄⠀⠉⠙⢿⡿⠿⠟⠋⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠋⠀⠀⢠⡟⠉⢻⣿⡿⠿⠟⠋⠀⠀⢀⣼⠃⠀⠘⣧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⠀⠀⣻⡾⠋⠈⠛⠲⠶⠶⠶⠞⠋⠁⠀⠀⠀⠈⠳⠶⣶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠈⠻⢿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠠⡴⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⢤⣿⡀⠀⠀⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣀⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⠶⠶⠶⠶⠖⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠴⣿⣷⡀⠀⢠⣾⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣷⣿⢷⣿⣷⡀⠀⠀⢀⣤⣤⣌⠙⠧⣀⣸⣏⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡇⠀⠀⢀⣩⡝⠛⠉⠁⠀⠀⠀⠀⠉⠙⠻⣦⣄⠀⣀⣀⣠⣴⣶⣿⣛⣿⣿⣯⣽⣿⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣇⢠⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣟⠛⠛⠿⠷⣿⣿⣿⣷⡿⠟⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡀⢰⣿⠁⠘⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⠋⠙⠋⠁⠀⣸⡏⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢠⣴⢦⡄⢀⣀⠀⠀ ⠈⢿⣤⣀⣀⣀⣰⡟⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠛⡇⠀⠀⠸⣧⠈⠿⠋⣹⡇⠀ ⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⢘⡟⠀⠀⠀⠀⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠇⠀⠀⠀⢿⣦⡀⠀⠙⠷⠶⠟⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠆⠀⠀⠀⠀⠙⠿⠃⠀⠀⠀⣴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣠⣤⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣼⣿⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠾⠿⠿⠿⠿⢿⣧⣀⢽⡍⠻⢶⡄⠀ ⠀⠀⠀⠀⠀⣴⠟⠋⣵⡀⣼⡿⣷⣴⣶⠿⠀⠘⠛⠛⠛⠿⠿⣶⣤⣀⢠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠿⠎⢻⡆ ⠀⠀⠀⠀⢸⣏⠻⠇⠈⠁⠈⣴⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠰⠦⣸⡇ ⠀⠀⠀⠀⠀⢻⣦⡀⠠⣶⡶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⣠⡿⠁ ⠀⠀⠀⠀⠀⣀⣭⣧⣤⣤⣤⣼⣿⣶⣤⣀⣀⣀⠀⢀⣀⣀⣠⣴⣿⣯⣼⣿⣷⣶⣤⣤⣤⣤⣤⣶⣾⣿⣿⣶⣶⣾⣯⣤⡀ ⠀⠀⠀⠀⠈⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠛⠛⠛⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠙⢲⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠘⠁⠀⠀⢸⣧⠹⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠖⠛⠒⠒⠒⠒⠒⠲⠼⢿⣧⠹⣆⠉⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⣤⣀⣈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣄⡈⠹⣶⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠘⢯⡻⢾⣿⣏⠉⠳⢦⡀⠀ ⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⢠⡟⠒⠦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠉⠛⢷⣦⣀⠈⠓ ⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⡼⡄⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠉⠻⣷⣄ ⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢰⠃⡇⠲⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠉ ⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀ ⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠒⠐⠚⠁⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀ ⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠴⠒⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⠢⢤⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣛⣿⣶⣿⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣝⠉⠀⠉⠛⠁⠀⠀⢀⣀⣄⠀⠀⠀⠀⠈⠙⠁⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀ ⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠈⠑⢢⣄⣀⠀⠀⠀⢈⣉⣁⣀⡀⠀⠀⠀⢀⣀⣤⡶⢷⣄⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀ ⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢸⠉⠻⣍⠛⠶⣾⣿⣿⣿⣷⣶⠟⠟⢋⡵⠋⠀⠀⠙⣦⣄⡀⠀⢀⣀⠼⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠦⣄⣀⣀⣀⡴⠋⠀⠀⠀⢸⠀⠀⠈⠓⠦⡾⠉⠛⠉⠀⠙⢦⡴⢟⠀⠀⠀⠀⠀⢻⡇⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⢀⠇⠀⢄⡀⠀⠀⠀⠀⠀⢧⡀⠀⢀⡴⠃⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠤⠴⡎⠀⠀⠀⠈⠩⡉⢱⣄⠀⠀⠈⠉⠉⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣶⣶⣦⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠛⠻⠿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣄⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⠀⣠⠀⠐⠤⠴⢂⣿⣿⡿⠋⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠻⣿⣄⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⠿⣿⣿⣷⣌⣉⠁⠀⠀⢀⣤⣾⠟⠋⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠉⠙⠻⢿⣷⣶⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⢹⣯⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⠄⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⣸⣿⠟⠛⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⣤⣤⣴⡾⠋⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⡌⣷⠈⣿⣿⡇⠀⠀⠀⢠⣤⡀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣿⣷⡈⠀⢸⣅⣹⣄⠀⠀⠀⠙⠛⠻⠾⠛⠋⠁⠀⠀⠀⠀⠀⠉⠁⢀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠠⡀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣧⣀⠂⢰⡛⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠶⠾⣿⡆⠀⢀⠖⠁⠀⠀⠀⠀⠀⣧⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠿⢄⣼⣟⣿⣿⣿⠿⣷⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⡿⠁⢠⠃⠀⠀⠀⠀⠀⣄⣼⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⠏⠀⠀⠀⠉⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣬⣆⠀⠀⠀⠀⠀⠹⡝⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠟⠛⠉⠙⠛⠻⠿⢿⣿⣇⣸⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣬⠟⢧⡀⠀⠀⠀⠀⡼⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⡄⠒⠊⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣀⣠⠴⠚⠉⣽⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣶⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⠟⠻⢿ ⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⠴⠒⠋⠃⠀⠀⠀⠀⠀⢀⡠⠒⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⣿⠟⠋⠉⠉⠙⠛⠛⠛⠋⠁⠀⠀⠀ ⠀⠀⠈⠉⠉⠙⠛⠒⠶⠤⣶⣞⣁⣀⠀⠀⠀⠀⡠⠤⠀⠤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠒⣆ ⢰⠟⠉⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣸ ⢸⣴⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⣷⠶⠶⠃ ⠀⠉⠛⢿⡟⠛⠿⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠉⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠈⠙⠻⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡾⠛⠋⠁⠀⠀⠀⠀⢠⣿⠀⠀⠀ ⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⣀⣠⣤⣤⡤⠴⠶⠶⠶⠦⢤⣤⣤⣄⣀⡀⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⣀⣠⣴⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⢷⣶⣤⣄⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟⠛⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⢈⣿⣿⣿⣿⡇⠀⢹⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣾⣿⣿⣿⣿⣿⣦⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠦⣤⣀⡈⠙⠻⣿⠛⡟⣿⡟⠋⠁⣀⣠⡴⠶⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠋⠀⠀⠀⠀⠉⠛⠻⢶⣬⣀⣁⣹⣵⠾⠛⠋⠁⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠙⢷⡄⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⣰⡟⠁⠸⣮⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣽⠇⠈⢻⡆⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⢠⣿⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠈⢿⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⢸⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⢸⣷⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⢠⡶⠲⣦⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⢀⣿⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠳⠶⠛⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠤⡤⠴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡿⠿⠶⣶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣶⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠻⠿⠿⠷⠶⠶⠶⠾⠿⠟⠛⠛⠛⠉⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⡍⠙⣷⠾⢥⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣀⣀⣀⣈⣳⣴⠛⠻⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⡴⠟⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⣠⡤⠚⠉⠓⢦⣄⡀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⢻⣤⣴⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠈⠉⠲⢤⣠⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠆⠀⠀⠀⠀⠠⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡇⠀⢀⣠⣤⠄⠐⠀⠀⠈⠉⠉⠉⠛⠛⠲⠶⠿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡷⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⡄⠀⠀⠀⠀⠀⣀⣠⡇⠀⠀⠀⠀ ⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣶⣶⣾⣿⠿⠟⠃⠀⠀⠀⠀ ⠀⢷⣄⣀⣀⣀⣀⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠒⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠛⠛⠛⠛⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⡀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⠀⡠⠀⠰⠤⠴⢀⣿⣿⡖⠋⠉⠙⠲⣄⡀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠻⣷⣀⠀⠀⡾⠀⠀⠀⠀⠀⠀⣀⡴⠚⠲⠤⣄⡈⢷⣌⣉⠀⠀⠀⢀⣴⣾⠟⠉⠀⠀⠀⠀⠀⠀⠙⠺⣄⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣷⣼⠃⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠉⠛⠻⢿⣷⣶⣾⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣷⣄⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⢸⡆⠀⠀⠀⠀⠀ ⠀⠀⢻⣯⣿⣿⣿⣿⣦⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡧⠄⠀⠈⣿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⣸⣿⠟⠛⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⣤⣤⣴⡿⠋⠀⡀⠀⠀⣹⡿⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⡰⣦⠈⣿⣿⡇⠀⠀⠀⢠⣄⡀⠀⠀⠀⣀⣴⠟⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⠎⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠈⢻⣿⣧⠉⠀⢸⡁⣱⣄⠀⠀⠀⠙⠛⠻⠖⠛⠋⠁⠀⠀⠀⠀⠀⠉⠁⣀⠀⠀⠀⠀⢀⠤⠔⠒⠒⢤⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣤⣀⠀⢸⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡒⠒⠛⢹⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⡷⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠿⢤⣾⢻⣿⣿⡿⠿⣷⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠈⢷⣄⣠⡿⠀⢰⠁⠀⠀⠀⠀⠀⣠⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠋⠀⠀⠀⠙⢿⣷⣝⣷⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⣦⠀⠀⠀⠀⠀⠻⡙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿⠛⠋⠉⠙⠛⠻⠿⣿⣿⣁⣻⡀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠊ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢷⣼⠟⢧⠀⠀⠀⠀⢀⡞⠀⠀⠀⣠⣤⠶⠋⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⡤⠒⠋⠀⠀⠀⠀⠈⠙⢲⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣠⠔⠋⠉⡹⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣴⣛⣉⣉⣓⠶⢶⡶⠛⣩⡴⠒⠲⢤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠉⠇⠀⠀⠀⠀⠀⢀⡤⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⠟⠉⠉⠉⠙⠛⠚⠛⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠁⠒⠲⠤⢶⣞⣁⣀⢀⣀⠀⠀⠤⠤⠤⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣶⣦⣤⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡈⠙⠛⠻⢿⣿⣿⣿⣷⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⣉⠙⠛⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⢠⣿⡟⠙⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠿⢿⣿⣿⣦⣤⣿⡟⠀⢸⣿⣿⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⣀⣸⣿⠋⠉⣿⣿⠿⣷⣿⣿⣿⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠛⢿⣿⣿⣦⣴⣿⡃⠀⣸⣿⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⣅⣀⣾⡟⠁⢸⣿⡿⠻⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⠟⠛⣿⣿⣿⣶⣾⣿⣀⣀⣿⣿⣿⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⡟⠀⢠⣿⠏⠀⣹⣿⠟⠻⣿⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⣀⣀⣼⣿⣿⣿⣁⣀⣿⣟⣀⣠⣿⣏⣀⣰⣿⣿⣿⣃⣀⣀⣀⣀⠀ ⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃

｡ﾟﾟ･｡･ﾟﾟ｡ ﾟ。𝓒𝐮𝐬𝐭𝐨𝐦𝐢𝐳𝐞 𝐲𝐨𝐮𝐫 𝐩𝐫𝐨𝐟𝐢𝐥𝐞 　ﾟ･｡･⸜(｡˃ ᵕ ˂ )⸝♡✩₊˚.⋆☾⋆⁺₊✧๋࣭ ⭑⚝

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠞⠛⠛⠛⠛⡟⣛⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠛⠓⠦⣤⡀⠀⠀⢀⡴⠚⠉⠁⠈⠉⠛⢿⣛⡶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠙⢷⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡶⣿⠟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠸⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠏⣼⠏⢸⡇⠀⠀⠀⠀⠀⠀⢠⣶⣶⡄⣇⠀⣶⣷⡆⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠇⣼⡿⠀⠈⣧⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃⡞⢆⠙⠛⠁⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀ ⠀⢠⡏⢰⣿⡀⠀⢸⡿⠣⡀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠈⠓⢤⣀⡀⠀⢀⣠⠴⠋⠀⠹⣆⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀ ⠀⡾⠀⣿⣿⣇⠀⣹⠃⠀⠈⠑⠲⠤⠤⠔⠒⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣀⣀⣀⠀⢻⡀⡀⠀⢿⡀⠀⠀⠀⠀⠀ ⢰⡇⢸⣿⣿⣿⠀⣿⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⡆⢸⣷⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⢸⡇⢸⣿⣿⣿⡆⣿⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡴⢃⣾⡟⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⢸⡇⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠔⠋⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⢸⡇⠸⣿⡿⠀⡐⠹⠟⢷⣄⡀⢀⣀⣀⣀⣀⣀⣤⣴⣒⣒⣒⣒⣒⣒⣶⠚⠋⠉⠛⢧⣤⡄⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠘⣇⠀⣿⡄⠦⠃⠀⠀⣾⡿⠋⠁⠀⠀⢈⣿⣟⠉⠉⠉⠁⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠙⣿⠀⠀⢸⠁⠀⠀⠀⠀⠀ ⠀⢻⡀⢹⡗⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⣹⣿⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⢠⣿⠀⢠⡟⠀⠀⠀⠀⠀⠀ ⠀⠈⢇⠈⣷⣀⠀⠀⠈⠿⣦⡀⠀⠀⠀⢘⣿⣟⣳⣦⣤⣀⣀⣀⣀⣤⣷⣄⣀⣀⣠⣴⣿⣀⣠⣾⣃⣀⠀⡀⠀⠀⠀ ⠀⠀⠸⠗⠛⠛⠛⠉⠉⠉⠉⠉⠓⠒⠒⠋⠁⠀⠈⢀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⠀⠀⠈⠉⠉⠉⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣯⣉⣀⣴⣿⡿⠭⠿⠛⠛⠰⢿⡖⠛⠉⣉⣿⣷⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠷⢶⣶⣶⣶⣶⣾⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀

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

⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀

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

૮₍ ´ ꒳ `₎ა

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀

⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠐⢢ ⣞⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⣄⣀⡼ ⠈⠓⢶⡟⠷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⣿⠀⠀ ⠀⠀⢸⡇⠀⠀⠈⠙⠳⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⢠⡇⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀ ⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣤⣤⠴⠶⠶⠶⠶⠶⠶⢤⣤⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀ ⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⢸⠃⠀⠀⠀ ⠀⠀⠀⠀⢸⣇⡀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣤⠶⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠛⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢻⣿⣿⣿⡟⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣾⣿⣿⣿⣷⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠓⠲⢤⣌⡙⠿⠻⢻⣏⣡⡤⠶⠚⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣴⡏⠁⠀⠀⠀⠀⠀⠀⠉⠛⠒⠛⠋⠁⠀⠀⠀⠀⠀⠈⡻⣦⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⡟⠀⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠇⠈⢷⡀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⡾⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠘⡇⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⣧⠀⠀⠘⠿⠿⠟⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠘⠿⠿⠟⠀⠀⢀⡇⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠻⠤⠞⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠈⠒⠲⠒⠁⠀⠀⠀⠀⠀⠀⢀⣠⣾⠷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠛⠓⠶⠦⠤⣤⣤⣤⣄⣀⣠⣤⣤⠤⠶⠶⠛⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⢳⡴⢮⣥⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣙⣦⡴⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠚⠁⠀⠀⠀⠀⠀⠘⣆⠀⠀⢀⡠⠖⠋⠉⠲⢤⣀⠀⢀⡞⠀⠀⠀⠀⠀⠈⠳⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢶⡞⠉⠀⠀⠀⠀⠀⠀⠈⢱⠾⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢦⣤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⣏⣈⢈⡬⠋⠉⠁⠉⠉⠊⠉⠉⠉⠛⢦⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁ ⠀⠀⣠⠎⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀ ⠞⢁⡠⣞⠀⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠊⠁⠀⠀⠀⠀ ⠓⢼⠧⣏⠉⡡⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀ ⠔⢀⠀⣜⡩⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀ ⠂⠈⣀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠈⠙⢄ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⠒⠀⠐⠂⠁⠁⠂⠤⠄⠀⠀⠀⠀⠀⠃⢄⠀⠀⢀⡜ ⠀⠀⠀⠀⠀⡲⣠⣁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡌⠢⡀⠀⠀⠀⣸⠏⠉⠁⠀ ⠀⠀⠀⣠⠔⣽⣿⣿⡆⠀⠀⠀⠀⡀⠀⠀⠸⣿⣿⡇⠀⢣⠀⠀⣴⠁⠀⠀⠀⠀ ⠀⠀⠀⡸⠀⠙⢿⠿⠃⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⢀⠔⣠⠎⠁⠀⠀⠀⠀⠀ ⡟⠦⡀⠒⠄⡒⠭⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠚⠐⠺⣀⠤⡄⠀⠀⠀⠀⠀ ⡄⠀⢈⠕⠈⠁⠁⠐⠒⠀⠀⠀⠀⠒⠂⠈⢁⡀⠤⠐⠊⠁⠀⠀⡇⠀⠀⠀⠀⠀ ⠁⠀⡌⠀⠀⠊⠉⠑⠐⠒⠤⣀⣀⠤⡂⠉⠀⠀⠀⠀⠀⠀⢀⠔⡂⠀⠀⠀⠀⠀ ⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇⢉⣢⠵⠀⠀⠀⠀⢀⠠⢲⠁⠀⠈⡆⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠉⠉⠉⠛⢶⣄⣀⣀⣀⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣀⣀⠀⣠⣶⣿⣿⣿⣶⣟⠉⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠈⠛⢯⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⣿⡿⣯⣷⣻⣽⣿⣷⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣯⣟⣷⢯⣟⣾⣳⣿⣧⣤⣄⡀⠙⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢾⣽⣾⣿⣿⣿⣿⡿⣿⣻⢿⣿⣿⣿⣿⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣾⣽⣿⣿⣿⣯⣟⡷⣿⢯⣟⣿⣿⣯⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠁⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⣾⡽⣿⣿⣿⣾⣽⣻⣽⣯⢿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⣾⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣯⣿⢳⣿⣿⣿⣾⣿⣾⣽⣿⣿⣿⡟⣿⡇⠀⠀ ⠀⠀⠀⠀⣼⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠁⠀⠉⠛⠻⣿⣿⣻⣽⣿⡟⠀⠀⠀ ⠀⠀⠀⢸⡏⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⠲⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⢿⡋⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀ ⣀⣀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⢀⣀⣀ ⠉⠉⢹⡟⠛⠓⠶⠦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠞⣿⠛⠉⠉⠉ ⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⢈⣉⠛⠓⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢻⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣀⣤⠆⠀⠀⠀⠀⡧⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡄⠀⠈⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣾⣿⣿⡇⠀⠀⠶⠛⢻⠟⠲⠶⠆⠀ ⠀⠀⠀⠸⣇⠀⠀⠀⠀⣀⣀⣤⡼⢿⣷⡀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠇⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣻⣦⠶⠞⠛⠉⠉⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠰⢶⣾⣥⣄⡀⠀⠀⠀ ⠀⠠⠶⠛⠉⠹⣦⠀⠀⠀⠀⠀⠀⠀⣠⡿⢿⣿⣦⡀⠀⠀⠀⠙⢿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣶⠛⠻⣶⠀⠀⠀⠀⠀⠀⠀⠀⣤⠿⠛⠋⠛⠛⢷⣄⠀ ⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⢀⣠⠞⠋⠀⠈⠻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀⠀⣀⣴⣾⠃⠀⠀⠀⠀⠀⠀⠹⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣴⠟⠁⠀⠀⠀⠀⠀⠙⢿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣴⣶⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠙⠳⢦⣄⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠈⠙⠲⢦⣤⣄⣀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣾⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢰⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠊⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣯⠳⣍⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢆⡻⡜⢮⢼⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⢾⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⢧⡹⢎⡵⣙⡎⡞⡽⢿⣶⣄⣀⣀⣀⣤⠾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣤⣄⣀⡀⠀⠀⠀⢺⣿⢱⢫⡜⣭⢋⡟⣭⢛⡭⢫⡕⢮⡱⢭⡲⣙⢮⡜⡵⢪⡝⣜⣻⡿⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠈⠉⠙⠛⠻⠶⣾⣿⢬⠳⣜⠲⣭⢚⡴⢫⡜⡳⣜⡣⡝⢶⣩⢓⡮⢼⡱⢫⡜⣮⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣟⡧⣜⡻⣄⠿⡸⢇⡼⢣⡜⣣⢻⢤⣃⡟⣸⢇⡻⢇⡼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⣌⡳⣜⢣⢏⡽⣘⢧⡹⢲⢭⡒⢧⣚⠵⣪⠵⣋⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣾⣟⡱⢎⡵⢎⡝⣎⠶⣍⠶⣍⡳⢎⣝⢣⡎⢷⣡⢟⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⢀⣼⡿⢎⡵⢪⡕⣫⡜⣳⢚⣬⢓⡎⡗⢮⣱⢫⡜⣣⢞⣱⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠶⢾⣿⡛⡵⢫⣜⢣⢞⡱⢎⡵⣋⠶⣩⢞⡹⢎⣖⣣⣽⣾⣿⣿⣿⡿⠟⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡵⣋⠷⣌⢏⠮⣕⡫⢖⡹⢎⡵⣎⣷⣿⣾⢿⣿⠿⠟⠛⠉⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡵⢫⡜⢮⣙⠦⣝⢣⡝⢮⡙⠿⣭⣳⣿⠀⠻⣦⣤⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣾⣧⣮⣽⣬⣷⣾⣧⣿⠿⠟⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠉⠉⠉⠁⠁⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠶⠶⠶⠶⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠂⠀⠀⠐⠂⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠈⠀⠀⠀⠀⠀⠀⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⣀⣀⣀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡱⠴⠒⠉⠀⠀⠀⠀⠀⠉⠉⠑⠢⢄⡀⠀⠀⠀⣀⡇⠀⠀ ⢠⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠲⡿⠛⠛⠁⠀⠀ ⠀⠛⠛⠛⢻⠏⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠙⢦⡀⣀⣀⠀⠀⠀⠑⡄⠀⠀⠀⠀ ⠰⣆⠀⢠⠋⠀⠀⠀⣀⠤⢄⡘⢆⠒⠁⠈⣨⡾⠋⠀⠀⠉⠢⣄⠀⢹⡀⠀⠀⠀ ⠀⢾⣿⣎⡀⠀⡠⠊⠀⠀⠀⠈⠉⠛⠶⠿⠋⠀⠀⠀⠀⠀⠀⠈⢣⠀⡇⠀⠀⠀ ⠀⢸⣽⣿⣷⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠄⠀⢳⡇⠀⠀⠀ ⠀⡼⡇⡌⢿⡇⠀⠀⣀⠀⠀⢀⡰⠀⠀⢀⡀⠀⠈⠓⠒⠋⢁⠀⠀⡼⠁⠀⠀⠀ ⠀⠙⡗⠀⢸⣼⣆⠀⠈⠉⠋⠉⠀⠀⢀⣀⡠⡄⠀⡀⠔⠊⠁⢂⡐⠁⠀⠀⠀⠀ ⠀⠀⠘⠧⢼⣿⡿⠷⢶⣦⣄⠀⠀⠀⠈⠦⠤⠃⡌⠀⠀⠀⣠⣮⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⠀⠀⠀⠹⣿⣷⠤⠄⠠⠤⢶⣶⡻⡆⠀⠀⠘⡀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠐⠚⠡⢀⣀⠠⠁⠀⠰⢖⡉⠀⠀ ⠀⠀⠀⠀⠀⠘⠄⠠⠒⣹⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢖⡒⣲⣤⣚⡡⠂⠤ ⠀⠀⠀⠀⠤⠄⣤⣊⠁⡈⢀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠈⠁⠀⠀⠀

⣿⣿⣿⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡆⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⠛⠛⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡖⢄⠀⠐⠷⢹⣿⣿⣿⠿⣿⣿⣿⣿⣿⣅⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡀⠀⠀⣐⣿⣿⡟⠁⠀⠀⠉⠻⢿⣿⣿⡆⠀⠀ ⠿⢿⣿⣿⣿⣿⡿⠋⠛⠻⢿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣠⣎⡀⠀⠀⠙⣿⣷⠀⠀ ⠀⣾⣿⣿⣿⠏⠀⣀⠀⠀⠀⠀⠉⠛⠛⠋⠀⠀⠠⣾⣿⣿⣧⠀⠀⠀⠸⣿⠀⠀ ⠀⣿⣿⣿⠏⠀⠀⣼⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠀⠀⠀⠀⡿⠀⠀ ⠀⢹⣿⣿⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⡠⡄⠀⠀⠀⠀⠉⠀⠀⠀⠀⢰⠃⠀⠀ ⠀⠀⢿⣿⡀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠉⠁⣀⣀⡀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀ ⠀⠀⠀⠻⣧⠀⢀⡀⠤⠐⠀⠀⠂⣀⠴⣾⣧⡿⣵⣏⢻⡄⠀⢀⠔⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢈⠇⠁⢀⠤⠄⠀⠀⠀⢸⢻⢿⢻⢻⣿⡟⡝⣧⣶⣿⣿⣿⡿⠿⠛⠋ ⠤⢤⡖⢐⡎⠀⠀⠈⠉⢁⣀⣀⣠⠿⠝⠛⠃⠉⠉⠀⠀⢀⠠⠯⡉⠢⡤⠦⠤⢤ ⠀⢈⠈⠉⢧⠀⠀⠀⠀⠀⡈⣼⡇⠀⠀⠀⢀⣤⣄⠀⢠⠁⠀⠀⠀⠀⠈⡄⣤⣾ ⡀⣀⡀⠀⢈⢑⡢⢄⣀⡰⠒⡏⢱⠀⠀⠀⣼⠁⠉⠳⣼⠀⠀⠀⠀⠀⡰⠁⢈⣻

⠀⢀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⢤ ⠀⠏⠀⠀⠀⠈⠳⡄⠀⠀⡠⠚⠁⠀⠀⠀⠘⡄ ⢸⠀⠀⠀⠤⣤⣤⡆⠀⠈⣱⣤⣴⡄⠀⠀⠀⡇ ⠘⡀⠀⠀⠀⠀⢈⣷⠤⠴⢺⣀⠀⠀⠀⠀⢀⡇ ⠀⠡⣀⣀⣤⠶⠻⡏⠀⠀⢸⡟⠙⣶⡤⠤⠼ ⠀⠀⢠⡾⠉⠀⢠⡆⠀⠀⢸⠃⠀⠈⢻⣆ ⠀⠀⣿⣠⢶⣄⠀⡇⠀⠀⠘⠃⣀⡤⢌⣈⡀⠀ ⠀⠀⠀⠀⠀⠙⠼⠀⠀⠀⠀⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠙⢷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣇⠀⢀⣴⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⡏⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠃⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠉⠀⠀⠀⢸⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢾⠉⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠙⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣀⣤⠶⠚⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⠳⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀ ⠀⠀⠀⢠⣴⣾⣷⣶⣄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⢀⣀⡿⠀⠀⠀⠀⠀ ⢠⣶⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠈⣿⣿⣿⣇⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡋⠉⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡀⠀⠀⠘⠒⠶⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠴⣿⣿⣿⣿⡷⠟⠃⣠⢦⣀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀ ⠈⠛⠿⠿⠿⠿⠟⠛⠃⠀⢀⣴⣿⣶⣶⣦⣤⣀⡀⠀⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⠲⠦⣄⣀⡀⠻⠇⠻⠛⢃⣤⠞⠋⠀⠉⠓⢦⣀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠿⢿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠉⠓⠶⠦⠶⠋⠁⠀⠀⠀⠀⢀⡞⡘⢶⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠛⢿⣷⣦⡀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡁⠀⢻⡄⠀⢰⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠈⠙⠻⠆⢸⠁⠀⢀⣶⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⡇⠀⣸⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸⠟⠉⠙⠻⣷⡀⠀⠀⠀⠀⢰⣟⣻⡆⠀⠙⠿⢿⣟⣁⣀⠀⡇⢀⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⡄⠀⠀⠀⢀⣀⣀⣀⠀⠁⠀⢀⣀⠀⠀⠉⢁⡀⠀⠀⠀⣾⣿⣿⡿⣰⢁⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠻⡄⠀⢰⣿⣿⣿⣿⠁⠀⠀⠘⣏⠉⢉⡽⠋⠀⠀⠀⠀⠀⠁⢀⣼⣷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠹⣄⠀⠉⠛⠛⠁⠀⠀⠀⠀⠙⠷⠋⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡼⠛⠒⠺⠷⠦⣄⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣤⡤⠴⠖⠛⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⢻⣧⣄⣀⣀⣀⣀⠀⠀⠀⠀⠈⠉⠉⣉⠉⠁⠀⠀⠀⢰⠶⢤⣄⡀⠈⣳⠖⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠶⠚⠁⠀⠀⠀⠉⠙⣧⡀⠀⠀⢀⣠⠖⠋⠛⠶⣄⡀⠀⣸⡀⠀⠀⠉⠉⠳⣄⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠙⣶⠋⠀⠀⠀⠀⠀⠈⢙⡟⠉⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⠋⠀⠀⠀⢀⣠⠟⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠁⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀ ⠀⠀⣠⡟⠁⣀⣤⠴⠾⡟⠁⠀⠀⠀⠀⢿⠉⢹⣿⣿⡋⠙⣿⠀⠀⠀⠀⠓⠂⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀ ⡴⠚⠻⡶⠛⠉⠀⠀⢸⡇⠀⣠⠾⠷⣤⣈⠻⢿⣿⣿⣷⠖⠃⢀⣠⠤⠤⣄⡀⠀⠈⢧⣀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀ ⠱⢤⠴⠃⠀⠀⠀⠀⠸⣧⢰⠿⣆⠀⠀⠈⠛⠶⢯⠿⠿⢞⠋⠁⠀⠀⠀⠀⠙⢷⡄⠀⠈⠙⠓⢦⣤⣀⡀⠀⠀⢹⣆⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⢻⣿⣿⡧⠀⠀⠀⠀⠀⠙⢳⣦⣤⣀⣀⣀⠀⠀⠙⡆⠀⠀⢀⡾⠁⠈⠉⠙⠻⡇⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠛⠟⠃⠀⠀⣀⡀⠀⠀⠈⢿⣿⣿⣿⠋⠀⠀⠀⡗⠀⣠⡾⠁⠀⠀⠀⠀⠀⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⡀⠀⢀⡛⠛⠁⠀⠀⠀⠉⠉⠁⠀⠀⣠⣾⣥⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢙⣿⣏⣁⣉⠛⠓⠾⠧⢤⣤⣤⣤⣤⣤⠤⠴⠶⠛⠛⠉⠈⠳⣦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⡇⠀⠀⣀⣠⠴⢦⣄⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠱⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢧⠖⠋⠁⠀⠀⠀⠈⠛⠦⣄⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠉⠲⣄⡀⠀⠀⠀⢀⡠⠤⠤⢤⡾⠁⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⢙⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠲⢤⡴⠋⠀⠀⠀⠀⠳⣀⠤⠤⢄⡀⠀⠀⢀⣼⠤⠤⠤⠿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠙⡄⠤⠾⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⠀⠀⠀⢰⡄⠦⣷⣀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⣄⠓⣨⠟⠉⠀⠈⠦⣀⣀⣀⡠⠞⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠹⣦⡇⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣼⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⠳⡀⠀⠀⠀⠀⢀⡜⠉⠙⠒⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡍⠲⢄⡀⠀ ⠀⠀⠀⠀⠀⢀⠞⠀⠀⠉⠓⠒⠒⠊⠉⠀⠀⢀⣠⠤⠴⠒⠒⠒⠂⠒⠒⠒⠒⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢆⠀⠉⡷ ⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀ ⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⣠⠞⠉⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀ ⠀⠀⠀⢸⠃⠀⠀⠀⠀⣠⠞⠁⢀⣴⡿⠋⠛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠷⣶⣄⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠉⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⡴⠃⠀⣴⣿⣿⡀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⢸⣿⣷⣄⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠀⠀⠀⣸⠁⠀⣸⣿⡿⠘⣿⣄⣀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⣴⣿⡿⠹⣿⣆⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⢠⡇⠀⠀⣿⣯⣄⢀⣬⣿⠟⠙⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⣿⣥⡄⢀⣭⣿⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⡀⠀⠈⡇⠀⠀⠙⢿⣿⣾⣿⣿⣶⣶⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⣿⣿⣿⣾⡿⠏⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡀⠀⢧⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⠀⠀⢳⡀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡴⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣦⡈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣠⣞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣌⣳⣄⠀⢀⠤⠒⠈⠉⠐⠢⢄⡀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠒⠒⠤⡀⠀⠀⠀⣠⣞⡥⠚⢡⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⢠⠞⣱⠤⠀⠬⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⢠⠚⠁⠀⠀⠀⠀⠀⠀⠘⣤⡴⠞⠋⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠔⠃⠀⠀⠀⣶⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢧⠀⠀⣿⡇⠀⢸⠃⠀⠀⠀⠀⠀ ⠀⠀⣤⣀⠀⢠⠋⠀⠀⠀⠀⢰⣣⠾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣼⡆⠀⠟⠀⠀⢸⠂⠀⠀⠀⠀⠀ ⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⣶⠟⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠀⠀⠀⠀⢰⢦⣤⠄⠀⠀⠀⠀⠀⣄⠀⠀⢰⣄⠀⠀⠀⡀⣤⣀⠀⠀⠀ ⠀⠀⠀⣀⠀⠀⠀⠀⠘⢷⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣩⢺⣿⣿⣻⢹⡛⣟⣿⠇⢘⣟⢻⣿⣾⣿⣿⢽⢰⣿⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣡⡏⠁⣀⠄⢀⣀⣤⡤⢀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠷⠊⡼⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣡⢔⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑ ⠀⠀⠀⠀⠀⠀⢀⣠⡚⠍⡂⡽⠫⡕⣰⣄⠅⢸⣷⣶⣶⠶⡆⠀⠀⡠⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⢂⠜⣱⢊⠔⡳⢱⣿⡿⠃⠀⠘⢿⠟⠛⠈⠉⠙⢃⢳⡀⠃⠀⠀ ⠀⠀⠀⢀⠎⡰⢑⢎⡁⠕⠊⢀⠞⣞⣿⣦⣀⡶⠂⠀⠀⠀⣀⡀⣤⡜⠁⠀⠀⠀ ⢀⠆⠒⢅⡿⡻⠡⠘⠀⠀⠀⢸⠀⠈⠛⠟⠉⠀⠀⠀⣰⣿⣿⠁⢟⣿⣿⣆⠀⠀ ⡪⢁⠔⡿⡀⠁⠀⠀⠀⠀⠀⠀⠹⣿⡀⣄⣶⣴⣰⣀⣿⡟⠀⠀⣼⣿⠁⠀⠀⢀ ⡵⢋⣌⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠋⠁⠂⠒⠁⠙⠋⠀⠔⢁⣿⡏⢳⠛⠋⠁ ⣰⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠀⠀⠀⠀⢀⣀⣠⡼⠶⠛⢻⠦⠥⠀⣀⠀ ⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠚⠉⠉⢙⢯⣀⠔⠂⣯⣁⠒⠈⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⢀⡀⠀⣴⡤⣾⣷⠎⠁⠚⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣔⣖⡒⠒⠤⢂⠯⠢⡈⠑⣼⠗⠛⡫⠭⠓⢖⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠙⠣⢹⢢⣀⠙⣖⠠⠬⣛⢱⠒⢁⢘⣛⠴⠶⠦⢉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⠟⠉⠁⠈⠉⠻⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠊⠉⠉⠲⢦⠀ ⠀⠀⢤⣀⠇⢸⠁⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠈⣧ ⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⣸⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⣿⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠓⠀⠒⠶⠶⢤⣤⣤⣤⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇ ⠀⠀⣿⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⣀⣀⣀⣀⣀⣠⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠄ ⠀⠀⣿⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⢠⠶⣄⣿⠉⠉⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀ ⠀⠀⡟⠀⠀⠀⠀⠀⠹⣆⠀⣀⠀⢹⡉⠁⢀⡈⠛⢲⠄⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀ ⡴⠚⠁⠀⠀⠀⠀⠀⠀⠈⣷⠋⠑⠚⠓⢹⠛⠃⢰⡁⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀ ⠱⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢸⣉⠇⠈⠛⣿⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠙⡆⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⠀⠀⣰⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⢹⡀⠀⠀ ⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡇⠓⠊⠉⠓⠃⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀ ⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡤⠒⠋⠉⠀⠀⠀⠀⠀⠈⠉⠑⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠙⠦⡀⠀⠀⠀⢀⡞⠁⠀⠀ ⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⠀⢠⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡄⠀⠀⠘⡆⠀⢀⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⣱⡠⠚⠉⠉⠙⢢⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢺⣭⣀⠀⠀⠲⢶⣀⣀⣀⣀⠀⠈⠙⠛⠁⢀⣠⠴⢻⡇⠀⠀⠀⢀⡼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠸⢍⣉⣒⣢⡼⠿⠿⢿⣿⠷⠴⠒⠒⢯⣡⠤⠖⢯⠀⠀⠀⡞⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣄⣀⣀⣠⠼⡀⠘⠓⠒⢞⣻⡿⠙⣶⠤⠀⢨⠇⠀⠀⡾⢖⠲⣞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠟⠙⢣⡀⠱⡀⠀⠀⠀⡸⠒⠋⢁⣀⣀⠀⠀⣠⠞⠀⢸⢀⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠱⡀⠈⠉⠉⠉⠱⢄⣠⠎⠀⠈⢶⠊⠁⠀⠀⡾⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⡇⠀⠀⠀⠀⣄⠀⢸⡀⠀⠀⢸⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠖⠓⠒⠶⠖⠒⠋⠳⢤⣇⠀⠀⣼⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠒⠒⠲⢶⣤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠦⣤⣄⠀⠀⠀ ⠀⠀⠀⠠⠄⣀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠙⢿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠉⠀⠀⠀⠀⠀⠉⢻⣄⠀ ⠀⠀⠀⣧⡤⠏⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀ ⠀⠀⠀⣿⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃ ⠀⠀⠀⣿⢀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀ ⠀⠀⠀⣿⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣿⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡉⠉⠀⠉⠛⠛⠿⠷⠶⣶⡶⣶⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠁ ⠀⠀⠀⣿⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⢀⣀⣀⣀⣀⣀⣀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡤⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⢿⡷⠒⠛⠋⠉⠉⠉⠉⠉⢉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀ ⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠈⣦⣤⣤⠞⠁⠹⣜⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀ ⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⣠⣀⠀⢸⡇⠀⣀⣠⣄⠈⠉⣽⠃⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⠀⠀⠀ ⣴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡿⠈⠛⠿⠗⠋⢹⠛⠛⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⡟⠁⠀⠀⠀⠀ ⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⠃⠀⣰⠒⣦⠀⠸⢴⣶⢦⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⢻⡄⠀⠀⠀⠀⠀ ⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⠀⠀⠙⠖⠋⠀⠀⣠⠽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢿⡀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⠀⠀⣀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀ ⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠶⠋⠉⠙⠻⠁⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣠⠤⠖⠛⠋⠉⠀⠀⠀⠈⠉⠙⠛⠒⠦⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀ ⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⡯⠀⠀⠀⠀ ⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢰⠏⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀ ⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⢰⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡀⠀⠀⠀⠘⣆⠀⡀⢠⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⢀⣴⠿⠚⠛⠒⠶⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣝⠿⠟⠃⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠻⢿⣿⡿⠇⠀⠀⠀⣠⣿⡟⠁⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⢶⣤⣀⠀⠀⠉⠻⣧⣤⣤⣴⡦⣤⠀⠀⠀⠀⠀⣀⣤⠴⠚⠋⣨⠇⠀⠀⠀⠀⣀⣴⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠾⣥⣈⣙⣒⣒⣶⠿⠿⠿⢿⣿⡿⠷⠖⠒⠚⠋⣯⣤⣤⠴⠚⢿⠀⠀⠀⠀⣿⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⣸⡄⠀⠸⠯⠤⢶⡞⣿⣿⡟⠶⣤⣀⡀⠀⢈⡷⠀⠀⠀⣼⣶⠦⢤⡴⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢙⣳⣶⢶⡞⠁⢻⡀⠀⠀⠀⠀⠉⠺⣍⣠⠴⠋⠀⠉⠉⠉⠁⠀⠀⡼⠃⢸⡆⠀⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠙⣆⠀⠹⣄⣀⣀⣀⣠⣾⠃⠀⠀⣠⠴⠦⣄⠀⢀⡠⠊⠀⠀⢸⣇⣼⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⣆⠀⠀⠉⠉⠉⠀⠘⠦⣀⣰⠁⠀⠀⠘⡗⠉⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⡀⠀⠀⢿⠀⠀⠀⠀⢹⠀⠀⠀⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⣀⣀⣼⣀⣀⣀⣀⣀⣠⠿⢦⡀⢸⡄⠀⠀⠀⣸⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀⠀⠉⠳⠷⣄⣀⣰⠷⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⠶⠯⠭⣀⠀⢀⠔⠊⠉⠛⢗⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡾⡟⠁⠀⠀⠀⠈⢷⠃⠀⠀⠀⠀⠀⢣⢼⣆⠀⠀⠀⠀⠀ ⠀⠀⡸⡾⠹⡁⠀⠀⠀⢠⣶⢸⢠⣶⡄⠀⠀⠀⢸⡇⠘⣆⠀⠀⠀⠀ ⠀⡰⢹⠃⢠⡧⡀⠀⠀⠀⠉⠌⠡⢄⠀⠀⢀⡠⠛⡆⠀⢸⡀⠀⠀⠀ ⢀⠇⣿⡇⢸⠀⠈⠐⠒⠒⠈⠀⠀⠀⠀⠉⠀⠤⠄⢸⡀⢀⡇⠀⠀⠀ ⢸⠀⣿⣧⢹⠀⠀⠘⠄⠀⠀⠀⠀⢀⡀⠀⠀⠀⡰⣼⠇⠀⡇⠀⠀⠀ ⢸⠀⣿⡟⢻⣧⡀⠀⠀⠀⠀⢈⣀⣁⣀⣀⣀⠤⢴⣇⠀⠀⡇⠀⠀⠀ ⠘⡄⢯⠜⠀⢰⡟⠊⠉⢹⣟⠋⠉⠉⠉⢩⠗⠀⠀⠙⡇⠀⡇⠀⠀⠀ ⠀⢡⢸⠀⠀⢺⡄⠀⠀⠠⡿⣄⣀⣀⣀⣀⣇⠀⢀⣴⣃⣸⠁⠀⠀⠀ ⠀⠐⠚⠛⠉⠉⠉⠑⠒⠊⠉⣉⡠⠤⣤⡤⢤⡭⣭⣭⣍⣉⡉⠉⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠺⢮⣭⣭⣥⣽⡦⠖⠚⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⡟⠀⠀⠀⠀⠀⣾⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⣼⡟⣿⣿⡶⢶⣶⣦⡄⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⢰⡿⣿⣿⣿⠿⣿⣩⡿⠁⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⣤⣤⣤⣤⣀⢀⣿⡏⠀⠀⠀⠀⢠⡟⣺⡿⣅⣀⣠⡴⠛⣧⡶⠶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠻⣄⠙⠻⠿⣿⣿⡇⠀⠀⠀⢀⡿⢠⡟⠀⠀⠈⠀⠀⡼⠋⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀ ⠀⠀⠀⠈⠛⠒⢲⣿⣿⠀⠀⠀⢀⣾⣥⡾⠀⠀⠀⠀⠀⡼⠁⣰⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡏⣿⠀⠀⢀⡾⢡⡾⠁⠀⠀⠀⠀⣸⠃⢀⣿⠀⠀⠈⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣹⠀⢀⡟⢁⡞⠁⠀⠀⠀⢀⣼⡏⠀⣼⢹⠀⠀⠀⢿⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡧⣿⢠⣿⣤⡟⠀⠀⠀⠀⣠⡟⢹⠃⢠⡏⠈⠆⠀⢀⣸⣧⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⣹⠿⣦⡟⠀⠀⠀⣠⢾⣥⣻⣿⣠⠾⠓⠛⠉⠉⠉⠉⠉⠉⠉⠛⠻⢿⣿⣿⡿⡋⠀⠀⠙⢿⣿⣿⣿⡇⠐⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠋⢀⡟⠀⠀⣠⣾⡁⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⡄⡀⠀⠸⠿⢿⠛⠃⠿⠷⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠃⢀⡾⠀⣠⣞⡋⣨⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⡀⠆⠀⣼⠶⢶⣄⠀⠀⠀ ⠀⠀⠀⠀⢀⡾⠁⣄⣾⣵⠞⠁⢈⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⡆⠀⠉⠀⠈⠿⠀⠀⠀ ⠀⠀⠀⢀⡾⢁⣠⡼⠏⣁⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡞⣠⡞⠋⠀⢠⣼⢯⡟⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⡟⠁⠀⠀⣠⠞⠁⡞⠀⠀⠀⠀⠀⠀⢠⣿⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠀ ⠀⣼⠋⠀⠀⣠⠞⠁⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⣿⣴⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀ ⣼⢡⡓⣦⠞⠁⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀ ⠃⠀⣹⠃⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⢰⠇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣀⠤⠴⠖⠒⠛⠛⠛⠓⠒⠒⠒⠲⠴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⣴⠏⠀⠀⠀⠀⠀⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣀⣀⣤⢿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⠶⣤⣤⡴⠃⠀⠀⠀⠀⠀⠀⢠⠿⠋⠙⢛⣇⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢏⣇⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⣿⣷⠤⣭⣍⣀⣀⣀⣠⣤⠤⣤⠤⠖⠚⢉⡹⢦⡀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢻⡀⠀⠀⠀⠀⠀⠀⢰⠇⢸⠃⠈⠳⠦⣄⣐⣿⠀⠀⠀⠀⢻⣤⠴⠚⠁⠀⠀⢹⡶⢦⣶⠾⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⡹⣄⠀⠀⠀⠀⣰⠟⠀⣾⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠛⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢸⠤⣄⣀⡤⠴⠻⡄⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⣠⠋⠀⠀⡇⡇⠀⠀⠈⠲⠤⠤⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡗⠒⠊⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⡇⢷⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⣸⠀⠈⢧⡀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠤⠤⠶⠃⠀⠀⠀⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢠⣾⣟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣽⣿⠆ ⠈⠛⠿⡗⠲⠦⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠚⣿⠏⠁⠀ ⠀⠀⠀⢻⠀⠀⠀⠀⠈⠉⠛⠒⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⠋⠉⠁⠀⠀⠀⠀⡟⠀⠀⠀ ⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀ ⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠖⠚⠋⠉⠉⠉⠉⠙⠒⠶⢧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠙⠳⢤⡀⠀⠀⠈⠳⣄⠠⠀⢀⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⣾⣿⠆⠀⢰⣿⣎⣷⠀⠀⠀⠀⠙⣦⣠⣾⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⠤⢤⣤⡤⠀⠀⠀⠀⠀⠀⣀⠤⠾⢿⣿⣿⣏⢠⠀⡌⣻⣿⡿⠶⠲⣦⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠉⠙⠻⠿⠿⠛⠁⠀⠀⠀⣈⠳⣄⠀⢸⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣴⠋⠀⢲⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡔⠻⡆⠘⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⡼⠁⠀⠈⢻⣿⣿⣿⡇⠀⠀⠀⡰⠀⠐⡠⠀⠀⣿⣿⣿⡇⠀⢻⣶⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⠀⢰⡇⠀⠀⠀⠸⣿⣿⡿⠃⠀⠀⠊⠀⠀⣤⣤⠀⠀⠘⠛⠛⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠠⠤⠤⢤⡄⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣈⣽⣷⣤⣀⣀⠠⠤⠧⣄⠀⠀⠀⠀⠀⣀⠤⢼⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡼⠋⣩⠋⠐⠋⠀⠀⠀⠀⠈⡆⠀⠀⠀⠰⠁⠀⠀⠈⠙⣿⣶⠒⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠘⡄⠀⠀⠀⠀⢸⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⢀⡠⣞⣁⣀⣀⣀⣀⣀⣈⣲⣤⠀⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⢤⡄⠀⠀⢹⠃⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠛⢿⣶⡄⠀⢀⣀⣤⣤⣦⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠈⠙⠻⢿⣶⣶⣶⣶⣶⣶⣶⣿⠟⠀⠀⠀⠀⠹⣿⡿⠟⠋⠉⠁⠈⢻⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡧⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣾⡏⠀⠀⢠⣾⢶⣶⣽⣷⣄⡀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣧⣾⠟⠉⠉⠙⢿⣿⠿⠿⠿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⣀⣠⣼⣿⠀⠀⠀⠀⣸⣿⣦⡀⠀⠈⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠻⣷⣤⣤⣶⣿⣧⣿⠃⠀⣰⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣀⠀⠀⣀⣴⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛⠉⢸⣿⠀⠀⠀⠀ ⢀⣠⣤⣤⣼⣿⣤⣄⠀⠀⠀⡶⠟⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡄⠀⠀⠀⠀⢀⣀⣿⣄⣀⠀⠀ ⠀⠉⠉⠉⢹⣿⣩⣿⠿⠿⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣤⡀⠀⠀⠀⠀⠀⠿⡿⠃⠀⠀⠀⠘⠛⠛⣿⠋⠉⠙⠃ ⠀⠀⠀⣤⣼⣿⣿⡇⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠘⠿⣤⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣀⠀⠀⠀ ⠀⠀⣾⡏⠀⠈⠙⢧⠀⠀⠀⢿⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠙⠛⠓⠀ ⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣯⡀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⢀⣴⠿⠿⠗⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⠋⠉⠛⠷⠄⠀⠀ ⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢿⣇⠀⢀⣠⡄⢘⣿⣶⣶⣤⣤⣤⣤⣀⣤⣤⣤⣤⣶⣶⡿⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠈⠛⠛⠛⠋⠁⣼⡟⠈⠻⣿⣿⣿⣿⡿⠛⠛⢿⣿⣿⣿⣡⣾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⣀⣀⣀⣀⣴⣾⣿⡁⠀⠀⠀⡉⣉⠁⠀⠀⣠⣾⠟⠉⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠀⠹⣿⣶⣤⣤⣷⣿⣧⣴⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢦⣭⡽⣯⣡⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠤⠤⠤⠤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀ ⠒⠒⠲⠤⠄⣀⠀⠀⠀⣠⠞⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠖⠒⠒⠒⠈⠉⠉⠉⠉⠑⠒⠒⠲⠤⠤⣴⣤⣀⣀⡀⠀⠀⠀⠀⠀⠙⣯⡉⠉⠉ ⠀⠀⠀⠀⠀⠀⢠⡿⠉⠀⠀⣀⡤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠘⠃⠀⠀ ⠀⠀⠀⠀⠀⢀⡟⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣰⡶ ⠀⠀⠀⠀⠀⢸⣡⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄ ⠀⠀⠀⠀⠀⠀⠻⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠛⠿⣿⣿⣿ ⠀⠀⠀⠀⣀⣠⣤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠀⠀⠀⠀⢀⣀⣀⠤⢄⣀⠀⠀⠀⠀⠀⡥⠀⠀⠀⠀⠀⠉ ⢀⣤⣶⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⡤⠖⠊⠉⠀⠀⠀⠀⠀⠉⠲⣄⠀⢀⡇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠉⠉⠉⠉⠉⠙⠒⠒ ⣿⣿⣿⣿⣿⣿⣿⠿⠋⠱⡀⠀⠀⠀⢀⡴⠀⣠⣶⣶⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⢳⡀⠀⢠⠟⠀⠘⣿⠟⠁⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⠛⠁⠀⠀⠀⠀⢀⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠖⢉⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠀⠀⡠⠚⠁⡠⠊⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠓⠤⠄⠀⣀⠠⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⡦⣄⠈⠀⢀⡞⠁⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢀⡒⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⢸⡄⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡷⠒⠐⠒⢲⠞⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡀⠀⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡄⣠⠞⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠳⣄⡀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁⣀⡴⠋⠁⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠁⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⣰⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣤⣴⣶⣾⣿⣿⣿⣿⣿⡿⠁⠀⠈⠻⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣴⢟⣶⡿⢿⣿⣿⣿⣿⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠙⣿⡏⠀⠀⠘⣯⡉⠉⠹⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣾⣯⠟⠀⢰⣿⠀⠀ ⠀⠀⠀⠀⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣤⣿⡃⠀⠀ ⠀⠀⠀⠈⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠀ ⠀⠀⠀⠀⣤⠴⣿⣿⣿⣿⣿⣿⣌⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⣨⣿⣿⣿⣿⣿⡿⠤⡤⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⢻⣿⣿⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠞⠛⠙⢿⣿⣷⠀⠀⠀⠀⠀⠈⠉⠛⠟⠛⠉⠁⠀⠀⠀⠀⠀⣾⣿⠿⠋⠛⠒⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣷⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⢻⣿⠛⠛⢛⡿⠛⢛⠛⢿⡛⠋⠙⢿⡟⠻⢷⣦⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⠁⠀⢰⡿⠁⠀⠾⠿⡿⢶⣿⣶⡿⠿⠶⠀⠈⢷⡀⠀⠙⣿⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣦⣿⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠸⣧⣴⣿⣿⣿⢿⣧⠀⠀ ⠀⠀⠀⢀⣿⣿⣟⠿⣿⣿⣿⣿⣉⣉⣟⣉⣉⣹⣋⣉⣹⣏⣉⣉⣏⣉⣹⣿⣿⣿⣿⢟⣿⣿⣧⠀ ⠀⠀⠀⣸⣿⣿⣿⣿⣶⣿⣹⡿⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⢿⡟⣦⣶⣿⣿⣿⣿⡆ ⠀⠀⠀⣿⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⡀⠀⠙⢻⣿⠟⠉⠀⢀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⢿⡇ ⠀⠀⠀⠉⠀⡿⠁⠀⢻⡿⢿⣧⣤⣴⣿⣷⣦⣤⣴⣿⣤⣤⣴⣾⣷⣤⣤⣼⡿⣿⡏⢻⡏⣿⠘⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠈⡃⠀⠁⠋⠀⠀

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