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

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