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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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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣷⣤⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡇⠀⠀⠀⠀ ⢀⠀⣿⣿⣿⣿⣿⠋⠀⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣷⡆⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⠇⠀⠀⣛⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⡀⣿⣿⣿⣿⠄⠀⠀⠀ ⠀⠘⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀ ⠀⠀⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀ ⠀⢸⣿⣿⢿⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀ ⠀⠸⣿⣿⡘⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣟⣿⣿⠏⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠙⠛⠁⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡐⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢿⡗⠻⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣾⢁⠀⣿⣿⣏⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⡄⠀⣻⣿⡏⣿⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡇⠀⠘⠻⣗⣿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠐⣿⠈⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⢻⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣯⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠏⠀⠈⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣧⠀⢰⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠟⠀⠘⠿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡷⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠀⠈⠀⠀⠁⠈⠀⠁⠈⠀⠉⠀⠁⠈⠀⠁⠀⠈⠀⠀⠀⠀⠀⠁⠀⠁⠈⠀⠁⠈⠀⠀⠈⠀⠈⠀⠀⠀⠈⠀⠁⠉ ⡁⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⡆⢀⣄⠀⡤⢄⢠⢠⡀⡄⢠⠤⢀⡤⠄⠀⢠⠀⢠⠤⠄⢠⡄⢠⠤⡄⠀⠤⡤⢠⠀⢠⢠⠤⠄⠠⡄⣤⢠⠀⣤⠠⡄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠜⡇⡼⠸⡄⡟⢏⢸⢸⠱⡇⢸⣁⡀⣉⡶⠀⢸⣀⢸⣘⣀⡟⢳⢸⣀⡜⠀⢸⡇⢸⠁⢺⢸⣉⡀⠀⢷⠙⡜⢰⠛⣇⢸⠁⠀⠀⠀⠈⠀⠀⠀⠀⠈ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣑⣄⠀⣠⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣾⣷⣦⣽⣿⣿⣿⣿⣿⣿⣏⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣯⡉⢀⣼⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠉⠻⢽⣥⣴⣴⣤⣄⣴⠂⠒⠂⢀⣀⣀⣰ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠂⠀⡀⢀⠀⠄⢀⠠⠀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠈⠲⢭⣄⣽⣇⣈⣄⣁⠊⠍⡉⢼ ⣃⠀⢀⠀⠀⡀⢀⡐⢀⠁⡀⢀⠀⡀⣀⠀⡀⢀⡀⣀⠀⡀⢀⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⢿⣿⣿⣿⣶⣤⣼⡏⠉⠛⢦⣤⢮⣴⣤⢽ ⢧⠘⡀⢊⠰⢀⠃⡐⣂⠒⠠⢂⠰⠐⢂⠒⡐⢀⠒⡠⠒⠄⡁⠒⠠⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢠⠀⡂⠄⢛⣿⣿⣿⡟⠿⣶⣧⣜⣭⣿⡍⣯⣽ ⣧⣄⡴⣠⣂⣥⣊⣔⣤⣊⣥⣨⣄⣣⣄⣎⣤⣃⣦⣡⣍⣤⣡⣉⣆⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣟⣿⣛⣿⣥⣦⣴⣴⣮⣾⣿⣟⣾⣶⣶⣶⣿⣿⣿⣾⣷⣶⣾

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Just a reminder to keep veterans and activity duty soldiers out of y'alls anti-military performative activism bullshit, thanks. Also, go Free Palestine yourself and do something worthwhile to actually help if you care so much. Yapping on an emoji website ain't it.🪖

ᡕᠵデ气亠ζ͜͡𝕲𝖍𝖔𝖘𝖙

✮BRRCKS✮

⚔️🔫⚔⚔⚔⚔⚔

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cadets commandosᡕᠵデ气亠

🔫🥝🦑🎖🩶📁🖤

⚪, V,

˚⋆｡°₊ ✮˖⁺‧₊˚🪖୨🦈୧🎖️˚₊‧⁺˖✮ ˚｡⋆

☠️

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▄︻デ⚡๖ۣۜ✞☬⎝⎝✧GͥOͣDͫ✧⎠⎠✞༒✞☠︎ཧᜰ꙰ꦿ➢꧁༒☬★彡❄️💤📿⋆ǂ⌕ꉂǂᯅ⌗ 34⋈⋆ꉂ✧;⌗ ୨୧ǂ﹅ 𓂅⋆ ꉂ⌕⌯୨୧⌯⋆𓍼ǂଘᯅ46;ᯅ ୨୧ꗃǂ⊹⌯﹅𓍼ଘꉂ5ᯅ;ǂ⌯﹅ꗃ⌗⌕୨୧✧﹅𐂯 ⌯ǂ⋈﹆⌕;﹅ଘ⌗ǂ ✦ᯅ୨୧ꗃ﹅⌯ ✦ ✦⋈⌕⌗୨୧ᯅꗃ;⌕⋈⌯୨୧ᨒ⊹୨୧45;ଘꮺ ᯅ୨୧ꗃ﹅⌗✧𓂅ᨒ⌕⋈ꉂ﹅𓂅ഒ⋆𓂅𝓝𝑇𝑇ℒ;𝓖𝓥ℐ 𝓒𝓚ℐŹ𝓧𝓝𝓚ℛℱ𝓥ℋ𝓒ℬ 📿💤❄️彡★☬༒꧂༒☠︎✞༒✞⎝⎝✧GͥOͣDͫ✧⎠⎠☬✞༻࿌𖣘⚡══━一

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🪖🐍⚓️🐻🥀 ⚔️⚡️🎖️🤙🏻🛡️

⠀⠀⢀⡴⣦⣴⢶⣤⢶⣤⡶⣦⣶⣦⣴⢶⣤⣶⣤⡶⣦⡀⠀⠀ ⠀⠀⣾⠁⠸⠏⠘⠿⠀⠿⠁⠻⠃⠸⠏⠘⠿⠀⠿⠁⠘⣧⠀⠀ ⠀⢸⡇⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⢿⡄⠀ ⠀⣾⠀⠀⠀⠀⠛⠋⣉⠛⠋⠀⠀⠛⣉⣉⠛⠃⠀⠀⠀⢸⣇⠀ ⢠⡟⠀⠀⠀⢠⡾⠋⠉⠛⢦⡀⣰⠟⠉⠉⢳⡄⠀⠀⠀⠀⣿⠀ ⢸⡇⠀⠀⠀⣾⠀⠠⣿⠀⠘⣧⡏⠀⢺⡇⠀⣿⠀⠀⠀⠀⢿⡀ ⣼⠃⠀⠀⠀⢻⡀⠐⡿⠀⣰⡏⣷⡀⢻⠇⢀⡿⠀⠀⠀⠀⢸⡇ ⣿⠀⠀⢀⣀⣄⠛⠶⠤⠶⠋⠀⠈⠛⠶⠶⠛⢁⣀⢄⠀⠀⢸⡇ ⢹⡄⠀⡳⣜⢢⡇⠀⢲⣦⣀⣀⣀⣠⣶⠆⠠⢳⡌⣏⡇⠀⣸⡇ ⠸⣇⠀⠀⠁⠋⠁⠀⠀⠉⠙⠛⠛⠉⠁⠀⠀⠁⠘⠊⠀⠀⣿⠀ ⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀ ⠀⠀⠙⠻⢶⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡶⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀ by addinoir linktr.ee/addinoirr

Army🪖🪖

dragon war 2007🐉🐍🐲🀄🇰🇷⚔👑🥷🏻🥷🏴‍☠️

▶︎ •၊၊||၊|။|||| |⚔️

ִ ࣪𖤐⚔️ ⚔️

🎖️

🔪⚔️🔫🔥🚁💣

╾━╤デ╦︻,( -_•)╦̵̵̿╤─🌎,🌎,⚔️,㊗,🏛,📃

BARRET 🪂⚔️

🫡( -_•)╦̵̵̿╤─🫡

⣲⣿⣾⣷⣿⣾⣿⣿⣽⣷⣿⣾⣷⣿⣾⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡟⢿⢻⡿⢻⣿⢛⡻⣿⡟⢿⣿⡟⣛⣻⢻⡿⣻⣛⣻⡟⣛⢿⣿⢟⣛⡟⣿⡟⣿⠟⣿⡟⢿⢻⡿⣛⣻⡟⣛⣿⢛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢱⡸⣼⢃⣃⢿⢸⡱⣿⡇⣏⢻⡇⣿⣿⡆⢧⡗⣽⣿⠆⣍⢾⣯⢻⡿⡇⣽⡅⡏⣜⡸⡿⣎⢿⡏⢿⠽⡇⣿⣿⢶⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣧⣼⣿⣿⣼⣿⣿⣼⣧⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⢩⣿⣿⣿⣿⣿⣿⠯⠿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⡟⠉⠀⠀⠀⠉⠟⠁⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡏⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⡇⠞⢿⣿⣿⡟⠀⠀⠀⢆⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢁⠹⣀⠉⠿⣿⣶⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⠃⡜⠀⠁⠋⡜⡰⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⢁⠖⠀⠂⠂⠰⢌⡱⠂⠠⢣⡑⠤⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⡁⢎⠤⣀⠀⡌⢆⠤⡀⠬⡑⡄⡈⠒⢀⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠴⣒⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣷⡌⣀⡳⠘⡌⠆⡘⠴⣑⡘⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠄⠀⠔⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣧⣇⢿⣷⣶⣭⠀⠤⠑⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⢠⠀⠈⠁⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣽⣿⣿⣿⣿⣿⡿⢉⠡⢉⣿⣿⣿⣿⣿⣿⣿⢿⠷⡾⡄⠏⠉⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠰⢤⣈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢺⣿⣿⣿⣿⡿⡟⢀⠐⡸⢛⠫⡙⠩⡁⢣⢈⠆⡡⠔⡌⢒⡐⢂⠆⢄⠀⠀⠀⠀⠀⠀⠸⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣬⣙⠲⠤⣉⠛⠿⢿⣿⣿⣿⣿⣿⣿ ⠈⠉⠌⠁⠂⠐⠈⠀⡁⠐⠠⠒⠀⠃⠡⠃⠌⠂⠡⠃⠘⠠⠁⠊⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡿⢿⣿⣿⣿⣦⣈⠉⠀⣤⣉⡙⠿⢿⣿⠟

Army 🇮🇳

\ _ / __ _\_(0)_/___ +----=====\\( + )//=====----+ * o @ o *

\ _ / __ _\_(0)_/___ +----=====\\( + )//=====----+ * o @ o *

🗡️✈️

🫡

💥🕵🕴👞

Hello(˶ᵔ ᵕ ᵔ˶)( ˶ˆᗜˆ˵ )(´｡•᎑•`)っ(´｡•᎑•`)っ(っ ᐛ )っ🍔🍟 *ੈ✩‧₊˚ *ੈ✩‧₊˚ 😎🎈👌😎Tamam 🫡💝💐🌍💕👋🏻👍ദ്ദി(˵ •̀ ᴗ - ˵ ) ✧ε(´｡•᎑•`)っ 💕🖖🏻👇👐🎟🎀ദ്ദി(˵ •̀ ᴗ - ˵ ) ✧🚀🤧ε(´｡•᎑•`)っ 💕ε(´｡•᎑•`)っ 💕👀(╥﹏╥)😎✍🌐🚚

⚔️✧˖°.🐎༄｡°

⚓🌊🐟🇹🇷☪

💂

⚔️

😈😈😈😈😈😈😈😈⌖

☠︎︎⛨☭⚔︎⛊⛑⍟

╾━╤デ╦︻

☭🇷🇺 ☭🇷🇺🪖

Army 🪖

╾━╤デ╦︻ (▀̿ĺ̯▀̿ ̿)

⚔️✊

/̸͆̅̿̎͞ ̎̅̿ ̄̿ ͆ ̚ ̎/̸͆̅̿̎͞ ̎̅̿ ̄̿ ͆ ̚

⌖☠︎︎⚚=★=

☤𓃮⛿

grenade💣

୧⍤⃝🚩जय श्री राम👨‍✈️Army 🇮🇳

🤠,⚔️

🪖🎖️✨🪖🎖️

⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⠃⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣦⣼⣿⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⠿⠦⠤⠤⠴ ⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡟⢋⣽⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣩⣵⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠿⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⡠⠔⠉⠁⠀⠀⠈⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢐⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡀⢇⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠿⠢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠘⡆⠀⠀⠀⠀⢀⣠⡟⢋⠁⠀⢘⣯⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣼⡇⠀⢸⢀⣠⣴⣾⣿⡟⠳⣄⠱⡀⠀⢓⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠇⠀⠀⠈⢩⢼⣿⡏⠉⠻⣷⣾⣷⠼⠒⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⣶⠀⠀⢠⠃⠀⠉⠛⠶⣤⣈⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⣿⣿⠀⣠⠯⣄⠀⠀⠀⠀⠀⠉⠛⣏⠈⠲⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠿⠯⢍⣐⠢⢟⢦⡀⠀⠀⠀⢀⣿⣧⡀⠈⣿⣷⣄⠀⠀⠀ ⣀⣴⣟⡁⠀⠀⢀⡼⠙⢦⡱⡝⠳⣄⠀⢸⡇⠘⢷⣤⣿⣿⣿⣆⠀⠀ ⠉⠀⠀⠈⠙⠲⣿⠁⠀⠀⠱⡌⢆⠈⠳⣼⠁⠀⠀⠙⠟⠛⠻⢿⣆⠀ ⠀⠀⠀⠀⠀⠀⡙⣆⠀⠀⠀⠙⣌⢣⣄⣉⡀⠀⠀⠀⠀⠀⠀⠀⠹⣆ ⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⡼⠛⠦⠛⣁⠬⢧⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠠⢒⡹⠆⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⣠⠴⠛⠉⠁⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠁⠀⠀⣠⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡋⠘⢧⠀⠀⠀⠀⣩⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣺⣿⡆⣿⡇⠀⠀⠘⣧⠀⠀⠀⣠⣴⣶⣿⣿⣿⡿⢷⣄⠀⠳⡄⠀⠀⠁⠾⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⣿⣿⠿⠋⠀⠀⢀⣿⣤⡶⣿⣿⣿⣿⣿⣿⣯⣄⡀⠙⢷⡀⠙⢦⠀⢀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠉⢁⣤⣿⣿⣿⡏⠁⠀⠻⣿⣿⣿⣿⣿⣦⡴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣸⣿⣇⡀⠀⠀⠀⠀⢠⡿⠀⠙⠻⢿⣷⣤⡀⠀⠈⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠉⠛⠿⣷⣦⣤⣌⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣿⣿⣿⡇⠀⠀⢀⣾⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⠁⠉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣇⣤⣶⣛⣉⡙⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠈⠙⢷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⡿⠿⣿⣤⣌⣉⠙⠓⢾⣟⢿⣦⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⡀⠀⠀⢸⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⣾⠟⠉⠀⠀⠀⠀⠈⢩⣿⢶⣄⠙⢷⡌⠻⣶⣄⠀⠀⠀⠀⣸⣿⠉⠻⣿⣆⠀⣸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⢠⣶⣿⣿⣦⣤⣀⡀⠀⠀⢀⣴⡿⠁⠀⠙⢷⡄⠹⣆⠈⠻⣷⣄⠀⠀⣿⡏⠀⠀⠈⠻⣷⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⠘⠁⠀⠀⠀⠀⠈⠉⠓⢶⣿⣿⡇⠀⠀⠀⠀⠹⣦⡈⢷⡀⠀⠙⢷⣤⣿⠃⠀⠀⠀⠀⠈⢿⠟⠛⠛⠿⣿⣿⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⠀⠀⠀⠀⠘⣷⡈⠻⣄⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡙⣿⡄⠀⠀⠀⠀⠀⠈⣿⡄⠙⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣄⠀⠀⠀⠀⣰⣿⣿⣄⣸⡷⠞⠋⠉⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠀⠀⠀⣰⠟⠁⠀⠉⠉⠀⠠⠖⠋⠉⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⡤⠖⠋⣉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠔⠉⣠⠀⠀⠈⠛⢲⣟⠃⠢⡀⠀⠀⠀⠀⠀ ⠀⢀⣠⠞⠀⠼⠋⠁⣠⣤⣤⣤⠈⣷⣭⡆⠈⡄⠀⠀⠀⠀ ⢀⠺⠃⣀⣤⣖⣶⣿⣿⣿⣿⣿⣦⣘⣽⣣⣴⣿⠀⠀⠀⠀ ⡘⠃⣼⣯⣻⣿⠀⠀⠀⠀⠀⠈⠀⢈⣿⢹⣯⠧⠀⠀⠀⠀ ⠣⠠⠕⣿⠏⠿⠂⠠⣄⡀⢀⣠⠄⠐⠿⣸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠟⢠⣿⣿⣶⣬⡟⢿⣥⣶⣿⣷⡄⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⡆⢿⣿⣿⡟⣇⢸⢿⣿⣿⡟⠰⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣷⣤⣖⠉⡻⣿⣿⢟⠉⣻⣤⡾⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣧⠛⠧⠏⠛⠷⢚⣼⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⢀⣀⣤⣧⣿⣿⡿⣾⢶⢿⣿⠿⠽⠄⢀⣀⢀⣀⢀⡄ ⠀⢸⣶⡿⢿⢿⡿⣿⡷⣶⠶⢾⣭⢿⡒⢒⣒⠒⠬⠑⠈⠀ ⠀⠀⠁⠀⠀⠀⠱⡄⢍⠻⠈⠩⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠂⠒⠲⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠤⠴⠤⠤⠤⠴⠤⠤⠤⠀⠆⠶⠶⠶⠤⠶⠴⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠉⠙⠷⣶⣬⣭⣗⣶⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣀⣠⡤⠂⠀⠀⠀⠀⠀⠀⠈⢿⠯⢄⣀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣶⠋⠀⢀⡸⠟⠋⠀⠀⣀⣠⣤⣤⣀⣤⠀⠘⣷⣦⣈⣱⡀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⡼⠁⠀⠀⠀⣀⣀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣅⠀⠹⣟⢯⣽⠇⠀⣸⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣳⠋⠀⢀⣴⣾⣟⣯⡿⠿⠿⠿⠿⠿⠿⠿⢿⣟⣿⣷⣦⣼⣷⣯⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⡯⠇⠀⣴⣿⢟⡟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⢽⣿⡟⢻⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀ ⢸⠃⢀⣺⠟⣽⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡇⣾⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀ ⠈⠧⠤⠴⠊⣿⢿⡏⣼⠿⠛⠂⠀⢶⣤⡀⠀⠀⢀⣤⡶⠀⠐⠻⠿⣇⢿⡏⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡾⢡⢴⣶⣶⣶⣤⣄⠙⢻⣿⣿⣟⠁⣀⣴⣶⣿⣶⡄⠘⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣇⠈⢿⢿⣿⣿⣿⣿⣿⣿⠃⠸⣿⣿⣿⣿⣿⣿⣿⡿⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⡇⠈⣾⣿⣿⣿⣿⡟⢫⣀⣐⣟⣿⣿⣿⣿⣿⣼⠁⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢺⣿⣧⡄⠈⢉⡙⠻⢿⣷⣯⣿⣷⣿⣿⡿⠟⣏⡫⠡⣀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠿⣷⣶⣿⢅⣀⠀⡞⣼⣿⣿⣇⠣⠀⠀⠸⣿⣶⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⠻⠿⣧⣻⠏⠛⢛⣿⠦⠏⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢻⣿⣦⣤⣤⣀⣄⣀⣀⣤⣤⣴⣿⡟⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡤⠤⣀⣠⣤⣾⣧⣿⣿⣿⣿⡿⣿⢿⡿⡿⢿⣿⣯⠿⠷⠼⠣⠤⠤⣀⣀⠀⢀⣠⡄⠠⣤⠄ ⠀⠀⢸⣷⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣼⣦⣶⣾⣟⣓⣶⡶⠶⠦⠤⠤⠤⠴⠶⢊⣁⠴⠊⠁⠀ ⠀⠀⠀⢿⣿⠟⠋⠛⠛⠛⢿⡛⠛⢿⣟⣻⣿⡋⣉⣭⡟⠛⢉⡿⠂⠒⠒⠒⠒⠂⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠠⠈⠉⠿⠉⢉⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⢀⣇⣸⣈⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠛⠟⠛⠛⠛⠛⠛⠟⠻⠛⠒⠛⠟⠛⠃⠀⠘⠸⠋⠟⠛⠛⠺⠿⠻⠛⠓⠛⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠀⠀⠙⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠘⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⠀⠀⣰⣧⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⢀⣼⡿⢻⣷⡄⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⣴⣿⠏⠀⠀⠙⢿⣦⡀⠀⠀⠙⢿⣷⣄⠀⠀⠀ ⢀⣤⣾⡿⠋⠀⠀⠀⣠⣾⠟⠁⠀⠀⡀⠀⠀⠻⣿⣦⡀⠀⠀⠙⢿⣿⣦⡀ ⢸⣿⠉⠀⠀⢀⣠⣾⠟⠁⠀⠀⣠⣾⣿⣄⠀⠀⠈⠻⣿⣦⡀⠀⠀⠈⣿⣿ ⢸⣿⠀⣀⣴⡿⠟⠁⠀⠀⣠⣾⣿⠟⠙⢿⣷⣄⠀⠀⠈⠙⢿⣦⣄⠀⣿⣿ ⢸⣿⣾⠿⠋⠀⠀⢀⣠⣾⣿⠟⠁⠀⠀⠀⠙⢿⣷⣦⡀⠀⠀⠙⠻⣷⣿⣿ ⢸⣿⠁⠀⠀⣀⣴⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⣄⠀⠀⠀⣿⣿ ⢸⣿⣀⣴⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣦⣄⣿⣿ ⢸⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿ ⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣷⡶⠶⠶⠶⠦⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣠⣾⣿⣿⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣧⣤⣤⣤⣤⣤⣤⣤⣶ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⡿⠿⠛⠋⣩⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠓⠚⣿⣿⣿⠀⠀⢠⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠿⠛⠋⣀⣶⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣤⣶⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⢀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠶⠛⠛⠛⠛⠛⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⢠⡤⠤⡄⠈⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⡤⠀⠀⠀⠘⣇⣠⠇⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠃⠀⣠⡞⠒⠒⠒⠒⠒⠒⢒⠒⣶⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢷⡎⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠿⠦⣀⠀⠀⣀⡴⠿⢧⣤⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣤⡶⠾⠛⢉⣇⠸⡄⢠⠞⢹⢯⠓⣄⠀⡼⢁⡏⠙⠻⠶⣦⣄⡀⠀ ⠀⣾⠋⠹⡤⠖⠊⠉⠀⠀⠹⡞⢣⡏⠈⣧⠛⡞⠁⠀⠉⠙⠲⠤⡼⠉⢻⡆ ⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡼⠁⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠸⣧ ⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⠶⠷⠶⠾⠶⠾⠀⠀⠀⠀⣿ ⣿⣀⣀⣠⣀⣀⣀⣀⣀⣀⣠⣠⣠⣀⣇⣀⣀⣠⣤⣤⣤⣀⣀⣀⣀⣀⣀⣿ ⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⠷⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⠿⠶⠶⣶⣶⢿⣶⢶⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠙⢮⢎⢌⢾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠌⣼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣞⣏⣘⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠟⠁⢀⣤⡾⠛⡟⠛⠛⠛⠛⠛⠛⢏⠏⡙⡏⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡾⠃⣠⡶⠟⠁⠀⢸⠇⠀⠀⠀⠀⠀⠀⠈⡞⡰⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡼⠋⣠⡾⠋⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢀⡴⡔⠠⢻⡀⠀⠀⠀⠀⠀⠀ ⡴⠋⢀⡾⠋⠀⠀⠀⠀⠀⠞⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠻⡆⠀⠀⠀⠀⠀ ⡇⠀⡼⠁⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⠀⠀ ⡇⠀⡇⠀⠀⠀⠀⢀⣠⡟⣧⣄⣠⣤⣄⣀⣀⡀⣀⣠⣤⡤⡶⢫⠻⣦⡀⠀⠀⠀ ⡇⠀⡇⠀⠀⢠⣴⡿⠿⠺⢼⡱⢹⢏⡬⠼⠭⠭⢯⣜⡸⡵⡷⠋⠉⠙⠻⢷⣄⠀ ⠇⠀⡇⠀⢀⡟⠁⠀⠀⠀⠀⢱⡞⠁⠀⠀⠀⠀⠀⠈⠳⣿⠀⠀⠀⠀⠀⠀⠹⡆ ⠀⢠⠇⠀⢸⣅⡀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣠⣷ ⡿⠋⠀⠀⣿⠈⠻⢶⣤⣄⣀⣸⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣠⣤⣶⡾⡿⡹⢸ ⠀⠀⠀⠀⣿⠀⠀⠀⠈⢫⢛⢿⠛⠛⠛⠛⠛⠿⢟⡟⡟⠿⡏⠉⠁⠉⠳⡡⡠⢻ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢫⢾⠀⠀⠀⠀⠀⠀⠀⠈⡞⡜⡇⠀⠀⠀⠀⠘⣡⢻ ⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⣦⢾⠀⠀⠀⠀⠀⠀⠀⠀⡼⠌⡇⠀⠀⠀⠀⢀⣣⣾ ⠀⠀⠀⠀⠘⣿⢦⣤⣤⡾⠣⢾⠀⠀⠀⠀⠀⠀⠀⣰⠏⠜⡇⠀⠀⣀⣴⣻⣗⡏ ⠀⠀⠀⠀⠀⢿⡀⠉⠛⠻⠷⣾⣶⣤⣤⣤⣤⣴⣾⣽⣾⣶⡷⠾⢿⠟⡟⡹⣿⠁ ⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠉⢎⡴⣰⡇⠀⠀⢯⢌⣼⡏⠀ ⠀⠀⠀⠀⠀⠀⠹⣗⠶⡖⣞⢼⡆⠀⠀⠀⠀⠀⠀⣸⠎⣼⠁⠀⠀⣦⢪⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣷⣴⣎⡸⡇⠀⠀⠀⢀⣠⡼⠃⠎⣼⠀⣠⣾⣷⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡙⠛⢿⠷⠶⠹⠿⠷⠷⠾⢾⡿⠛⠛⣽⡟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣘⣧⠀⠀⠀⠀⠀⢀⣾⢁⣠⣾⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⢤⣤⣤⡴⣾⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀ ⣶⣶⢶⢶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶ ⣿⣿⣧⣽⣿⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠶⠒⠒⠒⠒⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠀⠀⠀⠈⠉⠉⠽⠿⣲⣶⢬⣉⣛⣓⣶⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⣀⡴⠂⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣞⡋⠉⠁⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠿⠁⠀⢀⡶⣷⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡉⠛⠶⢄⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⢞⡿⠃⠀⠀⠠⠴⠋⠁⠀⠀⠀⢠⣤⣴⣾⣿⣧⣤⣖⣒⠀⠈⣿⣻⢷⣤⣼⡆⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣞⣧⠞⠁⠀⠀⠀⠀⠀⣀⡀⢀⣴⣾⣽⣿⣾⣿⣿⣿⣿⣿⣭⣄⡀⠙⣿⡳⣯⣷⡇⠀⠀⣸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⠏⡾⠃⠀⠀⣠⣴⣶⡿⢋⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣦⣤⣈⣽⣶⣎⣠⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡟⡼⠁⠀⣠⣾⣿⠿⣯⢾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⡍⠛⠛⠻⣷⣯⡭⣿⣛⡻⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠇⠇⠀⣴⣿⡿⣣⣾⡁⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⣿⣿⡇⢈⣿⣿⣷⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⣟⠀⢀⣨⠿⢋⣼⣿⣿⣧⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣦⣀⣤⡴⠋⣿⢸⣿⡇⣸⣿⡿⠓⠂⠀⢶⣦⣀⠀⠀⠀⠀⠀⣠⣴⠶⠀⠐⠻⣿⣿⣇⢻⣿⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣼⡿⢀⣙⣀⡦⣤⣤⣀⠀⠈⠻⣿⣶⣶⣶⣿⠟⠁⠀⣀⣤⣶⢶⣄⣉⠀⢿⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡿⠁⣹⣰⣿⣿⣿⣷⣿⣿⣦⣤⢼⡿⠿⣿⣧⣤⣴⣿⣿⣾⣿⣿⣿⡤⣍⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣄⠁⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢻⡟⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡆⠈⢷⣿⣿⣿⣿⣿⣿⠟⢹⣀⣀⣐⣟⣻⣿⣿⣿⣿⣿⣧⡾⠀⣰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⡿⡿⣃⠀⣉⡛⠛⠻⢿⡿⣞⣵⡞⣻⣿⣜⣿⣮⡻⢿⡭⡟⢛⣛⣁⠀⣉⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢷⣷⢭⣭⣈⣥⡶⠖⠀⠈⠛⣽⢻⣿⣿⣿⡘⣏⠋⠃⠀⠺⢶⣄⣩⣭⡵⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⡛⠲⣔⡆⢸⡃⣾⣿⢹⣿⣧⢘⡂⢰⣠⠖⢿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠙⠽⢾⣧⣹⡟⠈⠛⣋⣿⡷⠶⠃⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠹⡿⣿⣤⣀⣬⣀⡈⢁⠀⡀⠀⣀⣀⢠⣴⣿⣿⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣏⣀⣿⣿⢿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⡿⡟⣿⣾⣀⣹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀ ⠀⠀⠀⡾⠋⠓⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣽⣸⡈⡽⠉⣿⠙⡏⢩⣇⣧⡗⠉⠉⠉⠉⠈⠉⠓⠒⠒⠒⠒⠒⢒⣲⠖⠊⢹⠟⠋ ⠀⠀⠀⣧⣶⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⣿⣶⣿⠿⠿⢉⣙⣛⣛⣛⠻⠷⠶⠶⠶⠶⠾⠟⠋⣉⣠⠴⠋⠁⠀⠀ ⠀⠀⠀⢹⣿⣿⠟⠛⠛⠛⠛⠛⢻⣿⠛⡿⢻⣟⣟⢻⣿⣟⠉⡍⣽⣽⡟⢿⠉⣹⡟⠓⠒⠒⠒⠒⠒⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠘⡈⠋⠛⢿⡟⠚⠛⠉⠈⠃⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠙⠰⠆⣴⠀⡴⢰⠀⠃⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠧⣄⣠⣽⢤⣧⣄⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡀⢀⣀⣀⣀⣀⡀⠀⠀⣤⢠⣤⣤⣀⡄⣠⠠⣄⣀⣠⣤⣠⣠⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠂⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠚⠛⠛⠛⠋⠋⠀⠀⠚⠒⠋⠚⠋⠋⠙⠓⠛⠛⠛⠋⠛⠛⠋⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠕⠊⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⡀⠀⠀⡜⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⢣⠀⠀⠀⣠⣀⠀⠀⠀ ⠀⠀⣱⠠⣧⠀⡸⢸⣿⣠⠀⠀⣀⡀⢀⣀⠀⠀⠀⠀⣆⢧⠀⣴⡃⠈⡦⠤⡄ ⡎⢉⣁⣤⣈⡳⢡⣿⣿⣧⣦⡠⠟⡁⢀⢜⡀⠁⠀⣠⠿⠈⢾⠋⢀⡀⠀⣰⠁ ⠉⠉⠁⠀⠉⢇⠛⣏⣷⣦⣭⣙⣛⣒⣒⣂⣀⣦⣽⣲⣻⠻⣸⠚⠛⠳⠚⠁⠀ ⠀⠀⠀⠀⠀⠈⢢⠿⢘⣿⣿⣿⣷⢳⡺⣾⣿⣿⣿⡏⠮⡔⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣄⣠⢬⡭⠁⢣⠛⠳⠋⠋⣭⢩⣄⣠⠇⠀⠀⠀⠀⠀⠀⠀ ⢠⠊⠉⠱⠔⠒⡋⢕⢼⠟⣰⠠⢀⢀⠀⠤⠒⡸⣾⣌⡓⠤⣀⣀⣠⣄⣀⠀⠀ ⠘⠂⢴⡆⠀⢎⡞⢡⡊⠀⠻⣶⠬⢤⠤⢰⡻⠒⠈⢫⠻⣆⠈⠑⠀⠀⡼⠁⠀ ⠀⠀⠰⣁⣈⡼⠁⠀⠉⢳⡄⠀⢉⣬⣬⠅⢀⣠⠞⠉⠀⠹⣀⢺⠋⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠋⠉⠙⠳⠾⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠄⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠒⠒⠒⠒⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⢀⡵⣄⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⢹⡤⣸⠁⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣀⠤⠤⣀⡀⠀⠀⣀⠠⠤⢀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢾⣿⡯⢤⣀⣀⢹⠏⣿⣁⣀⣠⢤⣿⣿⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⠁⠀⣷⣿⡋⠀⠈⣿⣿⠃⠀⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣈⣧⡀⠀⠀⣰⠀⠀⠀⢹⡀⠀⠀⣸⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠖⣺⣍⣽⣵⣾⠏⢟⠛⠉⠈⠓⣤⡔⠋⠈⠑⢛⠟⣿⣤⣹⢍⣷⡒⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⡖⢹⣣⠘⣿⣧⠿⠿⠛⢻⠸⡄⠈⠳⠤⠤⠔⠉⠓⠤⠤⠴⠊⠀⡇⢹⠛⠲⠿⢄⣿⡇⢠⣿⠓⢢⡄⠀⠀⠀ ⠀⠀⢠⣾⡉⠑⠔⠛⠉⠁⠀⠀⠀⠀⢸⠀⠑⠤⢄⣀⣀⣀⣀⣀⣀⣀⣀⡤⠞⠁⢸⠀⠀⠀⠀⠀⠉⠙⠃⠖⠁⣹⣆⠀⠀ ⠀⠀⣸⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡤⢤⠀⠈⢟⠳⣄⡔⢹⠏⠀⢠⠤⣄⡏⠀⠀⠀⠀⠀⠀⠀⣀⡤⠊⠀⢸⠀⠀ ⠀⠀⡇⠀⠀⠀⠈⢇⠀⠀⣤⠤⠤⠤⠤⠤⣤⣼⠀⠀⠈⣞⠀⢸⠏⠀⠀⢨⣾⠽⠯⠿⠿⠿⢯⡇⠀⢠⠏⠀⠀⠀⠘⡇⠀ ⠀⠀⡇⠀⠀⠀⠀⠈⢦⠀⠧⣀⠀⠀⠀⣀⠼⠉⠉⠒⠦⢼⣆⣎⠤⠖⠊⠁⠸⢄⡀⠀⠀⢀⡠⠇⢠⠏⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠁⠀⠀⠀⠀⠀⢸⡷⣄⠀⠉⠉⠉⠀⠀⠀⠀⠀⢀⣀⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⢀⠴⣟⡀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⣆⠀⠀⠀⠀⠀⣸⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢸⡃⠀⠀⠀⠀⢀⡇⠀ ⠀⣰⠋⠉⠉⠉⠉⠉⠉⠳⡄⠈⢧⡀⠀⠀⠀⠀⠀⠀⠰⣶⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢀⡴⠋⠉⠉⠉⠉⠉⠉⢳⡀ ⢀⡇⠀⠀⠀⠀⠀⠀⠀⢡⣸⠆⠀⠉⣹⠷⢶⣶⣶⣤⣤⡤⢼⣤⣤⣤⣤⣶⣶⠶⢿⡉⠁⠀⣎⣠⠂⠀⠀⠀⠀⠀⠀⠀⡇ ⠈⡇⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠧⡀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠀⠀⠀⠀⢀⡴⠇⠀⠀⢸⢿⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⢱⣄⢀⠀⠀⢠⡀⠀⢀⡞⠀⠀⠀⠀⡇⠀⠀⠀⠀⠐⢢⠦⢴⠒⠀⠀⠀⠀⢈⡇⠀⠀⠀⠘⣆⠀⠀⡀⠀⠀⢀⣀⣼⠃ ⠀⠀⠈⠉⠓⠤⠔⠛⠊⠉⠀⠀⠀⠀⠀⠙⢄⣀⠀⢀⣀⠜⠀⠘⢄⡀⠀⢀⣀⠜⠀⠀⠀⠀⠀⠈⠉⠚⠓⠠⠴⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣷⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠋⠙⠛⠃⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⠿⠷⢒⡶⠖⠒⠛⠛⠛⠉⠉⢙⣶⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡻⠿⠃⠀⠀⢿⣇⣀⣀⣀⣠⠤⠤⠤⢬⡟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⣷⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠻⣤⠀⠀⠀⠈⠛⠒⠒⠶⠶⣶⣶⡶⢾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡷⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢃⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣟⡙⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠻⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡍⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⣀⣴⢶⣳⡀⠀⠀ ⠀⠀⠀⠀⢀⡠⠤⠤⢤⣄⣀⣀⡀⣀⣀⡠⠴⠺⣿⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠈⢸⣿⣿⡀⠀ ⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢨⡏⠀⠀⠀⠀⠀⠿⠿⢶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⢿⣗⡇⠀ ⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠈⣟⡇⠀ ⢰⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⡀⠀⠀⠀⠀⣸⠉⠀⠀⠀⠀⣀⣠⣷⣿⣆ ⡏⠉⠛⠷⣦⣤⣀⣀⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣄⣤⣤⣤⣿⠶⣶⡶⠿⠿⠛⠛⠋⠁⢸ ⣷⣾⢿⡆⠀⠀⣩⡉⠙⠛⠛⠻⠿⠿⠿⠶⠶⠶⠶⣶⣦⣴⣶⣶⠶⠶⡿⡿⠿⠻⣻⡙⠉⠁⠁⢠⣄⠀⠀⠀⢰⣷⡀⠀⠀⢸ ⠈⠁⠸⠦⣀⣸⡿⠿⢳⡆⠀⠀⢠⣞⣷⡆⠀⠀⢠⣤⣦⠀⠀⠀⢰⢶⣿⣷⠒⠋⠉⢹⡀⠀⠀⣾⣿⡀⠀⢀⣸⡟⢧⣀⠴⠞ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⠤⠤⠾⠛⠁⢷⣀⣀⣸⠟⠛⡆⠀⠀⣸⡾⠋⠀⠀⠀⠀⠈⠧⠤⠶⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠹⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠀⠀⠹⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠀⠀⠀⠀⠙⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠀⠀⠀⠀⠀⣠⣧⠀⠀⠀⠀⠀⠙⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠃⠀⠀⠀⠀⢀⣴⣿⣿⣷⡄⠀⠀⠀⠀⠈⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠋⠀⠀⠀⠀⠀⣠⣾⣿⡿⠻⣿⣿⣦⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠁⠀⠀⠀⠀⢀⣴⣿⣿⠏⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁⠀⠀⠀⠀⠀⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⠀⠀ ⢠⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⣰⣧⡀⠀⠀⠀⠀⠈⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣦ ⢸⣿⣿⠋⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣄⠀⠀⠀⠀⠀⠙⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠈⢻⣿⣿ ⢸⣿⣿⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣄⠀⠀⠀⠀⢸⣿⣿ ⢸⣿⣿⠀⠀⣠⣶⣿⣿⠟⠉⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⠟⠁⠀⠙⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣤⡀⠀⢸⣿⣿ ⢸⣿⣿⣴⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣶⣾⣿⣿ ⢸⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿ ⢸⣿⣿⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⢹⣿⣿ ⢸⣿⣿⠀⠀⠀⣠⣴⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣄⡀⠀⠀⢸⣿⣿ ⢸⣿⣿⣠⣴⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣶⣄⣸⣿⣿ ⢸⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿ ⢸⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿ ⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛

⠀⣀⣤⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⠶⠞⠛⠛⠳⠶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣽⣿⣿⠏⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⠛⣿⠁⠀⠀⠀⠀⠀⣠⡾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⢸⡇⠀⠀⠀⠀⢠⣿⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠿⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⡀⣿⡀⠀⠀⠀⣾⢁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢭⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⣸⡿⠛⢿⡆⠀⠀⣿⢸⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢓⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⢿⡇⠀⠘⣿⠀⢨⣿⣀⣤⣶⠶⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠶⣶⣤⡚⢿⣿⡄⠀⠀⠀⠀ ⠀⠀⢸⡿⠃⠀⢹⣇⠈⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣿⠁⠀⠀⠀⠀ ⠀⠀⠘⣿⡀⠀⠘⢿⡄⠈⢻⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣿⠀⠀⠸⣷⡀⠘⡏⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡟⠀⠀⢻⣧⠀⢷⡸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣟⣉⠀⢉⣿⣇⠈⢷⣘⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣆⣠⣾⣿⣀⣴⠿⣿⣉⠉⠛⠿⠶⠶⠶⠾⠛⠋⢁⣠⠞⠁⠈⠙⢿⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⣿⣀⣽⡿⠟⠙⣷⣄⠉⠛⠷⣶⣶⣤⣤⣤⣴⠞⠛⠁⠀⠀⠀⠀⠀⠬⣻⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⠀⣾⡦⠀⠙⢦⣄⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢭⣿⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⢻⣿⣦⡀⠠⣴⣦⡄⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡆⠀ ⠀⠀⠀⠀⠀⢰⣿⡽⠀⠙⢿⣿⣄⠙⠿⣿⣷⠀⠙⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⢒⢻⣷⠀ ⠀⠀⠀⠀⠀⣾⣏⠆⠀⠀⢸⡿⣿⣷⣄⠀⠀⣠⣤⣄⠈⠹⣷⣄⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠨⣽⣿⠀ ⠀⠀⠀⠀⢸⣿⣟⠀⠀⠀⣸⠀⠈⠛⢿⣷⣄⠙⢿⣿⣷⠦⠀⠙⢿⣦⡀⠀⠀⠀⠀⠻⡆⠀⠀⠐⠺⣿⠀ ⠀⠀⠀⠀⢸⣿⠿⠄⠀⠀⣿⠀⠀⠀⠀⠙⣿⣷⣄⡉⠁⠀⠀⣀⣀⡈⠻⢷⣤⡀⠀⢶⣿⡄⠀⢀⣙⣿⠀ ⠀⠀⠀⠀⢸⣿⣟⡂⠀⠀⣿⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠛⢿⣿⣿⣦⣄⠉⠻⢷⣶⣾⣷⠀⠐⠺⣿⠀ ⠀⠀⠀⠀⢸⣿⣷⡄⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣤⣍⣛⣋⣁⣀⣀⣀⣉⣻⣿⣦⣄⣸⣿⡄ ⠀⠀⠀⠀⠀⠉⠉⠓⠒⠒⠛⠛⠒⠛⠋⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡀⣀⣀⣀⣀⡀⣀⣀⣀⢀⣀⣀⢀⡀⠀⠀⡀⢀⢀⣀⡀⠀⠀⠤⠀⠀⢠⠠⡄⣠⠠⠤⣀⣀⢄⢠⠀⡄ ⠀⠂⠃⠛⠛⠓⠃⠓⠚⠘⠈⠚⢚⠓⠊⠃⠈⠂⠃⠛⠃⠃⠀⠀⠒⠀⠂⠒⠐⠊⠉⠁⡁⠛⠑⠉⠙⠐⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣴⣤⣤⡄⠀⠀⠀⠀⠀⣀⣤⡴⠶⠛⠛⠉⠉⠛⠻⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠸⡿⢿⠏⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⢷⠸⡇⠀⠀⠀⣰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣷⡀⠀⠀⠀⠀ ⠀⠘⣆⣷⡀⠀⠀⡟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⠀⠀⠀ ⠀⢰⡏⠉⢻⡀⢠⡇⢁⣀⣤⣤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣤⣄⣀⣽⣿⡆⠀⠀⠀ ⠀⠈⣷⠂⠘⣧⠘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⡇⠀⠀⠀ ⠀⠀⢻⡄⠀⢻⡆⠈⡟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀ ⠀⠀⠈⣯⡄⠈⣿⡀⢹⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⡖⠀⠘⣷⠈⢧⣻⣦⣀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣷⡁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣇⣤⣿⣇⣴⡿⣏⡉⠛⠲⠶⠶⠞⠛⢉⡠⠊⠀⠙⢷⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠉⢿⣦⡿⢋⡉⠳⣄⠉⠛⠿⣶⣶⣶⠞⠉⠀⠀⠀⠀⠀⠸⢷⣄⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣧⡘⠋⣀⡈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣇⠀ ⠀⠀⠀⠀⣸⡿⠈⠻⣿⣄⠻⠿⣦⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠸⣿⠀ ⠀⠀⠀⢀⣿⡇⠀⠀⡿⢿⣷⣄⠀⣴⣦⣀⠙⢷⣄⠀⠀⠀⠀⠸⣆⠀⠀⠸⣿⡆ ⠀⠀⠀⢸⣿⡅⠀⠀⡇⠀⠈⠻⣷⣌⠛⠛⠃⠀⠈⠳⢦⣀⠀⠀⣹⡄⠀⠈⢿⡇ ⠀⠀⠀⢸⣿⡆⠀⢸⡇⠀⠀⠀⠈⠻⣿⣦⡀⠲⣿⣷⣄⡙⠳⣶⣭⣿⠀⠸⢿⡇ ⠀⠀⠀⠸⣿⣆⠀⠀⣇⠀⣀⣀⣀⣀⣈⣻⣿⣶⣬⣝⣋⣥⣤⣤⣽⣿⣧⣤⣿⡇ ⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀ ⠀⠀⠚⠚⠛⠻⠛⠒⠃⠛⠚⠓⠀⠐⠐⠛⠀⠀⠀⠀⠂⠇⠀⠓⠀⠛⠛⠁⠂⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⡿⠿⠟⠛⠛⠛⠉⠉⠛⠿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠛⠛⢻⡇⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⣿⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠟⠁⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⢀⣼⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣄⣠⣴⠟⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⠚⠚⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⠟⠋⠻⢷⣤⣀⠀⠀⢀⣠⣴⠟⠛⠻⢿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⠿⠛⠻⣏⠀⠹⣇⠀⠀⣀⣽⠟⢻⣿⡛⢿⣄⠀⠀⠀⣼⠏⠈⣿⠛⠻⢿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣤⣶⣿⣿⠟⠋⠁⠀⣀⣠⣴⠿⠂⠀⢹⣆⢠⣿⡁⢀⡿⠙⣧⠀⢙⣷⠀⣼⠏⠀⠸⢧⣤⣀⠀⠀⠉⠙⠻⣿⣷⣦⣄⠀⠀ ⠀⠀⣸⣿⠋⠀⠹⣧⣤⠶⠟⠋⠉⠀⠀⠀⠀⠀⢻⣿⠙⢷⣾⠃⠀⢹⣦⡾⠻⣿⠏⠀⠀⠀⠀⠈⠙⠛⠶⣦⣄⣼⠃⠀⢹⣿⡄⠀ ⠀⠀⣿⡟⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢻⣆⠀⣴⠟⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣿⣧⠀ ⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠃⠀⠀⣤⣀⣠⣀⣀⣀⣀⣀⣀⣀⣄⠀⠀⠀⠀⠀⠀⢿⣿⠀ ⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣤⣬⣿⣤⣤⣼⣿⣤⣬⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀ ⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆ ⢀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⡇ ⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢛⡉⠉⠀⠀⠀⠉⠉⠛⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡤⠤⣤⡀⠀⠀⠀⡾⢁⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠘⣷⡀⠀⠀⠀⢀⣶⠶⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡆⢀⣸⡇⠀⠀⢸⠃⣼⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⣧⠀⠀⣠⡾⠁⠀⠸⡧⣤⣠⣄ ⢀⣠⠤⠶⠿⠃⠀⠙⢿⣄⣠⡟⢠⣿⣿⣿⡜⣆⠀⠀⢸⣿⡶⠖⠒⠒⠻⡇⠀⡀⠀⠀⠀⠀⣿⡇⢹⣆⣠⣿⡷⠀⠀⠀⠙⠀⠀⣿ ⢸⣇⠀⢀⣠⣤⣴⣤⣀⣹⠏⣠⣿⣿⣿⣿⣿⣾⣦⡀⢌⠻⣀⠀⠀⣠⠜⣡⠊⠀⠀⠀⣠⣾⡿⠗⠀⠹⣿⠋⠀⢀⣀⠀⠀⢀⣼⠇ ⠀⠛⠷⠟⠋⠉⠉⠉⠻⣿⠀⠾⣿⠓⡶⣬⣉⡙⠛⠿⠷⠷⠦⠉⣉⠤⠞⠀⠀⠤⠐⣚⣩⣴⢾⡿⢿⡄⣻⡶⠾⠿⣷⣀⣤⠞⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢻⣤⡇⣿⣿⣿⣿⣶⣶⠶⣶⠶⠶⡶⢲⣶⣶⣿⣿⣿⣷⣱⢸⡇⠊⣠⡿⠀⠀⠀⠀⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⡟⠀⣻⣿⣿⣿⣿⣿⣿⡿⣷⡻⣿⣿⣿⣿⣿⣿⣿⣿⠈⢿⣥⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠉⠛⠛⠛⠛⠙⡟⣰⣿⣷⠘⡿⢿⡿⠿⠿⠟⠋⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢈⣷⣦⡶⣾⠻⡿⠑⠦⠀⠠⠋⠈⠉⢧⠀⠀⠠⢺⡏⣹⣷⣶⡤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡴⠋⠉⠙⠓⣤⡤⠶⠾⠛⣋⠥⣺⣿⡷⡅⠦⢀⡀⠀⠀⠀⠀⢀⣀⡤⠲⡎⣇⣿⣤⡉⠛⢦⣄⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⣀⡀⠉⠀⠀⢀⡤⢊⣵⠞⢡⡞⠉⢸⣧⢈⠁⠹⠁⢹⠁⢹⠁⣡⣰⢻⠉⠙⣿⠿⣦⡀⠈⠙⠷⣖⠛⠛⠛⠛⠷⣦⠀⠀ ⠀⠀⠙⠓⠾⣿⡆⠀⠀⠎⣸⠟⠁⢰⡏⠀⠀⠘⠻⣏⡷⠤⡤⢤⠤⢴⠒⣏⠿⠋⠃⠀⠈⣷⠈⢻⣇⡀⠀⠀⠉⠀⠀⢀⡼⠋⠀⠀ ⠀⠀⠀⠀⠀⣼⠁⠠⠚⢠⡿⠀⠀⠈⠛⠲⣤⣀⠀⠀⠙⠒⠣⠸⠂⠛⠚⠀⠀⠀⢀⣴⠿⠋⠀⠀⢻⠉⠀⢴⣶⠗⠶⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣦⣤⡴⠟⠁⠀⠀⠀⠀⠀⠸⣿⡇⠀⣀⣤⣶⣶⣾⣯⡁⠀⣠⣶⠟⠀⠀⠀⠀⠀⠈⠷⣤⣨⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠋⠀⠀⠈⠛⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠒⠒⠒⠶⠆⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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