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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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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠒⠈⢉⠉⠉⠉⢒⠢⢤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠈⠀⠀⠠⡀⢣⠸⣈⠑⠢⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄⠈⢄⡄⡩⠂⠀⠈⠳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⡄⣖⠊⢪⢶⢤⡵⣀⣀⣄⡀⠀⠱⡀ ⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⣃⡽⢄⡠⠞⢃⢤⠸⣗⢠⣽⡆⠀⢱ ⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠐⠂⠤⠤⠔⢡⣀⠀⠀⢏⠒⠛⠁⠀⠘ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣛⡓⠒⠦⢆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣀⣹⣤⣤⠂⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⣧⣴⣧⣱⠂⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡸⣿⣿⡿⣟⡽⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⣨⠦⣄⠀⠀⠀⠀⠀⠀⡠⠠⠦⠨⣀⡐⢁⡁⠀⠀⡠⠊⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⠰⣄⠀⠙⠢⢤⣀⣠⠊⠀⠋⠀⠀⠀⠈⣀⡥⠔⠊⠀⠀⠀ ⠀⠀⠀⢀⠴⠊⠀⠀⠀⠈⢢⡀⠀⠀⠀⠉⠉⠉⢹⣗⠀⠀⠉⠁⠀⠀⠀⢄⢠⢀ ⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⡰⠃⠀⣑⢼⣼⡴⡂⢀⡠⠊⠉⠁ ⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠖⠒⡞⠉⠉⠁⠀⠀⠑⠬⠓⠁⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡶⣤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣼⣿⣿⣿⣿⠟⢀⣼⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡙⠶⢤⣿⣿⣿⡟⢁⣴⣾⡿⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠈⠙⠻⢶⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣽⡷⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⢐⡢⡴⠬⢴⡖⣲⣖⣀⠀⠀⠀⢹⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⢹⠍⢀⠈⣏⠉⢩⣿⡏⠀⠀⠈⡇⠀⠀ ⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⡆⠈⠻⠶⣏⢀⣧⡀⡹⢾⣾⡿⡆⠀⠀⠀⠃⠀⠀ ⠸⣀⣀⣘⠀⠀⠀⠀⠀⠀⢟⣤⣤⣖⣻⣿⣿⣿⣿⣷⣶⠶⡧⣄⠈⣆⠇⠀⠀ ⠀⠙⣶⡋⠀⠀⠀⠀⠀⠀⠘⢍⠊⠉⠀⠙⡿⠿⠁⠉⠁⠀⡧⠊⡠⠊⠀⠀⠀ ⠀⠀⢻⠛⠲⣄⠀⠀⠀⠀⠀⠀⢱⣄⡀⠀⠃⠀⠀⠀⢀⣀⡇⠊⠀⠀⠀⠀⠀ ⠀⠀⠚⠀⠀⠘⢦⡀⠀⢀⡤⢴⣏⣯⠙⢳⣒⠒⡖⢛⡟⢡⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠚⠉⢀⢟⡑⠠⢳⠋⠹⢻⠓⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡁⠁⢸⡇⡖⠁⠀⡇⢳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢓⠣⢾⠞⠤⢴⣶⣧⢄⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⠋⠁⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠒⠛⠛⠉⠙⠓⠒⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⣦⠀⠉⠛⠦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⠘⡇⠀⢆⣤⠈⠛⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢦⣄⣦⡈⠳⣿⣠⠟⠁⠀⠀⠀⠻⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⣴⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⡗⢿⡻⣿⣶⠿⢿⣤⣴⣷⣤⡀⠀⠹⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⣷⣬⣧⣾⣴⠿⠂⢀⡀⣻⣿⢻⣿⣿⠀⠀⢹⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣭⣭⠟⠀⠀⠀⠃⠸⣟⣺⠟⠋⠀⠀⠈⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠲⡄⠀⠹⣍⠉⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠓⠲⣄⠀⠀⡿⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⢰⠄⠠⠦⠀⠀⠀⣈⣠⣴⡤⢾⣙⡋⠁⠀⠀⠀⠀⠀⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠚⢹⣏⡞⠛⠒⣾⣿⠀⠀⠀⠀⠀⢠⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢠⣿⡉⠀⠀⢠⣧⡟⠀⠀⠀⠀⢠⡞⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣸⢤⣝⠲⠤⠞⢹⡇⠀⠀⢀⡴⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⡄⠈⠓⠦⣄⡀⠀⠀⣠⠞⠁⠘⠃⠀⠈⠉⠛⠛⢉⣧⡤⠞⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠴⠛⠁⠀⠀⠙⢦⡀⠀⠀⠉⠙⠛⠛⠲⠶⠤⢤⡤⠶⠶⠒⠛⠉⠁⠀⠀⠀⠀⣀⠀⠀ ⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣰⠟⢧⣄⢠⡄⣄⢀⠀⠀⠀⠸⣦⡿⠾⠀ ⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⢀⣀⣾⣡⠤⠤⠟⠻⣿⢿⣾⣆⣀⡴⠞⠁⠀⠀⠀ ⢠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⢉⡟⠁⠀⠀⠀⠀⠀⠈⠻⠞⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠋⠻⣿⣿⡿⢿⣿⣽⣿⣷⣦⡄⠀⠀ ⠀⠀⣰⠋⠀⠀⠀⠈⠻⢿⡽⣒⣿⣭⠿⢿⣇⣀⠀ ⠀⣰⣳⡀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠭⠍⣿⠀⠀ ⠀⢿⣽⣷⠄⠠⠤⡀⢠⠤⠤⠤⠤⠀⠀⠀⠘⣇⠀ ⠀⠘⣿⡇⠠⢶⡶⠶⢦⡿⠉⠨⣧⡶⠦⡤⢀⡽⠂ ⢠⡖⢿⠀⠬⣾⣷⠤⢾⡅⢸⡀⢿⣤⠶⡇⢈⡧⠀ ⢸⡡⡙⡦⡀⠈⠓⠂⠀⣤⣼⣧⣬⠟⢉⢔⡞⣹⠀ ⠈⢳⡀⢹⠈⠳⢶⣶⣾⣭⡽⢾⣿⣿⠏⡘⢰⠇⠀ ⠀⠀⠙⠚⡇⠀⠀⠉⠛⣭⠾⡟⠋⠁⠀⡟⠋⠀⠀ ⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⠦⣀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠒⠛⠉⠀⠀⠀⠀