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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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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠾⠛⠛⠋⠉⠛⠛⠷⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⣴⣶⡆⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠛⠟⠃⠀⠀⠀⠀⠘⠻⠛⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀ ⠀⠀⠀⢸⣿⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠘⣿⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠙⢷⣦⣀⡀⠀⣀⣠⡾⠋⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠉⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣄⣀⣀⣀⣀⣠⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⣀⣀⡀⠀⠀⢀⡀⠀⣀ ⠘⠘⡛⠚⠛⣻⡟⣻⠛⣟⢻⠓⠐⠓⠒⠛⠁⠀⠘⠖⡓⢟⡛⠛⠻⠛⠻⠃⠧⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠤⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣤⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢋⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠉⠓⠦⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡄⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀ ⠀⠀⣠⠞⠁⠀⠀⣀⣠⣏⡀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⡃⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆ ⢀⡞⠁⠀⣠⠶⠛⠉⠉⠉⠙⢦⡸⣿⡿⠀⠀⠀⡄⢀⣀⣀⡶⠀⠀⠀⢀⡄⣀⠀⣢⠟⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃ ⡞⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⢳⢀⣠⠀⠀⠀⠉⠉⠀⠀⣀⠀⠀⠀⢀⣠⡴⠞⠁⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⣀⣤⠞⠁⠀ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠁⠀⢀⣀⣀⡴⠋⢻⡉⠙⠾⡟⢿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠀⠀⠀⠀ ⠘⣦⡀⠀⠀⠀⠀⠀⠀⣀⣤⠞⢉⣹⣯⣍⣿⠉⠟⠀⠀⣸⠳⣄⡀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠒⠒⠒⠒⠚⠋⠁⠀⡴⠋⢀⡀⢠⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⡾⠋⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠉⠋⠻⣄⠀⠀⠀⠀⠀⣀⣠⣴⠞⠋⠳⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⢤⠤⠶⠋⠙⠳⣆⣀⣈⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣷⣶⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠁⣰⣿⣿⣿⡿⠿⠻⠿⣿⣿⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠏⠀⣴⣿⣿⣿⠉⠀⠀⠀⠀⠀⠈⢻⣿⣿⣇⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣼⣿⣿⡏⠀⢠⣿⣿⣿⠇⠀⠀⠀ ⠀⠈⣿⣿⣿⡀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⡀⠀⠀⠀ ⠀⣿⣿⣿⡇⠀⠀ ⠀⠀⢰⣿⣿⡿⣿⣿⣿⡇⠀⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⠁⠀⠀ ⠀⠀⣿⣿⣿⠁⣿⣿⣿⡇⠀⠀⠻⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⢰⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⢸⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⢉⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣇⠀⣿⣿⣿⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⢸⣿⣿⣿⣷⣦⠀⠀⠀ ⠀⠀⢻⣿⣿⣶⣿⣿⣿⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⡀⠀⠉⠉⠻⣿⣿⡇⠀⠀ ⠀⠀⠀⠛⠿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠈⠹⣿⣿⣇⣀⠀⣠⣾⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣦⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣼⡏⠙⣷⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣇⣈⢁⣀⣘⣶⣿⣴⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠙⢯⣽⣸⣿⣏⣿⡟⠁⠀⠈⠻⣆⣀⣀⣀⣀⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢻⡟⢿⠛⠿⠀⠀⠀⠀⠀⠈⠉⣉⣁⡀⠸⣿⣿⣿⠋⢻⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣀⣀⠀⣸⠇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣄⠀⠀⢰⣋⣉⣁⣀⠀⠀⠉⠀⠀⠈⠛⠛⠋⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⢉⣉⣹⡟⠀⠀⠸⣿⡆⠀⢠⣽⣿⠄⠀⠻⠟⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠚⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢀⣤⣄⠀ ⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣠⣾⠛⢿⣿⠇ ⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢻⣿⣦⡾⠋⠀ ⠀⠀⠀⠀⠀⢛⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠶⠞⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⣴⠋⠉⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⣴⡶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣤⠾⠃⠀⠀⠀⣿⣁⡾⠷⠶⠤⢤⣤⣤⣻⣿⣋⣁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠂⣠⡴⠋⠉⠉⠛⣦⠀⠀⠀⠀⠀⠀ ⣼⠋⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⣀⣠⡄⠀⠀⠀⠀⠉⠉⠉⠉⠛⠻⣟⠛⠛⠿⠿⣿⣟⣛⡻⠖⠛⠁⠀⠀⠀⠀⣀⣼⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⣦⣐⡆⠀⠀⠀⠉⠉⠀⠀⠀⠀⢶⣀⣤⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠉⠙⠛⠶⢦⣶⣶⡞⠛⠉⢹⠀⠀⠀⠀⠀⠀ ⠙⢶⣄⣀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⠀⣀⡀⠀⠀⠉⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⣀⣤⣠⡴⢶⠀⠉⠙⠛⠶⠾⡤⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⣀⣤⠶⠛⠁⠀⠀⠀⢀⣴⠞⠉⠀⠈⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠳⠦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⠤⠤⠤⠶⠋⠁⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠳⣄⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣹⣆⣹⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣴⠞⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⣈⣒⣤⣤⠤⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⠀⠀⡔⣿⣿⣿⣿⣿⣿⣿⣦⣄⠈⠑⠒⠀⠂⠀⠀⠀⠀⠈⠒⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡅⠹⡄⢀⢤⡼⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠴⣶⠲⠀⠀⠀⢀⡤⡄⠀⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠑⠒⠒⠓⠃⠘⢾⣿⣾⡇⠀⠀⠉⠁⠈⠉⢻⣿⡇⠠⠄⠤⣀⠀⠀⠀⠻⢅⣀⣈⣒⠀⠀⠀⠀⠀⠀⠀⠲⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢠⠴⠦⠦⢦⣘⢻⣿⣷⣦⣤⠠⣄⣀⡀⢸⣿⣧⡀⠀⠸⣻⡇⠀⠠⣦⡀⠉⠙⢤⣀⣀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⡠⠒⡇⠂⢲⠒⠒⣼⣮⣿⠉⠉⠙⠀⠻⠛⠛⢺⡏⠬⡭⣵⣀⠈⠁⠀⠀⡿⣟⣆⠀⠀⠀⠀⠣⣄⡀⠀⠢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠞⣀⠢⠀⠀⠀⠀⢑⡤⠄⠠⠬⢏⣉⣹⣿⡗⠀⠀⡿⡒⠀⠀⠀⢿⡗⠒⠒⢺⠊⡵⠀⠀⠀⡿⣭⠏⡄⠀⠁⢀⠀⠀⠓⢤⡀⠈⡆⠀⡀⠀ ⠀⠀⠄⠀⠀⢹⠀⠀⠀⠀⢀⡰⠛⠷⡀⠀⠀⠀⢗⠒⠒⠒⠚⠂⠤⠼⢤⣧⡈⠙⠯⠽⠲⠀⡖⠻⠀⢀⣉⣹⣉⣧⠀⠀⠀⠉⣵⢆⠑⢆⠀⢀⡨⠆⣀⣀⠀⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠈⠁⠢⢄⠏⠀⠒⠒⡇⠀⠀⠴⡈⠑⣎⣀⣁⣀⡴⠊⢁⡟⠷⢄⡀⠀⠤⢣⣤⡐⠒⠒⠦⢼⠖⠋⡀⠀⠀⣶⣟⣊⣢⡈⠒⣁⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠀⠀⠀⠀⠇⠀⠀⢀⡨⠆⠈⠉⠒⠚⢠⣤⢿⣇⠀⠀⠀⠀⢀⠞⣿⣿⣟⣤⣖⣊⠠⠞⠃⠀⠀⢻⠤⡧⠤⢣⣊⠁⠁⡀⠉⣀⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠀⠈⣏⣹⠤⣆⡤⠀⠀⠀⠀⠀⠈⢀⡔⣫⠭⢹⣿⢯⡿⣾⣿⣤⡄⣀⠴⠋⢠⣿⣿⣿⣷⣦⣭⣭⣖⣺⣶⣤⡄⠒⠓⢺⠈⠠⣀⢠⠟⠀⠋⠁⠀⠒⠂⠀⠀ ⠀⠀⠀⢰⠀⠀⠠⡈⣬⢵⠟⣘⠲⠶⠀⠀⠀⣴⠟⣉⣴⣾⣿⣿⣸⢷⢸⠁⠹⡟⠃⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⡿⣈⠲⣤⠏⡴⠦⡀⡖⠒⠲⠄⠀⠀ ⠀⠀⠀⠠⠤⠂⠊⠁⠈⠉⣎⣈⠵⢄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣇⣟⣓⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢠⠑⠇⠏⢴⡱⠒⣇⠘⢄⠀⠀⠀⠀ ⠀⠂⠀⣠⠂⠀⠀⠀⠀⠸⡀⢰⡀⢸⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣒⡺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠧⠀⠀⠀⠉⠑⠛⠀⢧⠀⠀⠀⠀ ⢀⠤⠾⠷⣀⣀⠇⡴⣆⠀⠳⡀⠀⢹⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣀⡿⠶⠭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢀⠀⣟⠯⢦⡀⠈⠓⢤⡀⠀ ⡎⠓⠒⠂⠤⡞⢠⠓⠺⡀⠀⢧⠀⡘⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣍⡯⠭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠈⣆⠳⢬⠒⠚⠒⡄⠀⠀⠀ ⠘⠢⡀⠒⢒⠁⡎⢀⡰⠃⠤⡈⡤⢿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢭⣿⣟⣓⣿⣿⣿⣿⣿⣏⠩⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣘⠈⠀⢇⣩⣉⣹⠂⠀⠀ ⢀⠐⢍⠁⠘⢰⢉⡽⢀⡀⢍⢳⠸⡷⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣒⣾⣿⣿⣿⣿⣿⠷⡀⠂⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⢉⢀⣖⠁⠀⡆⠀ ⠈⠱⠀⠀⠀⠛⠉⡴⠛⠘⠢⡉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠭⢽⣿⣿⣿⣿⣿⣿⣭⣤⡄⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀⠔⢋⡤⡄⠐⠂ ⠀⠀⠀⠀⠀⡠⠚⠀⠀⠩⡍⠓⣄⠀⠀⠀⢸⣿⣿⣿⣿⠿⠿⠛⣛⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⡧⠀⠈⢢⠀ ⠀⠀⢰⠀⠀⢏⠉⠉⠉⠀⠉⠱⡼⠀⠀⠀⠰⣿⣿⣯⣤⡎⠭⠤⠜⣿⣿⣿⣓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢥⠀⠰⣿⣄⣀⠀⠀⠀ ⠀⠀⠸⠀⠀⡀⠉⡀⠀⠀⡰⠉⠀⠀⠀⠀⠀⠸⣿⣿⣿⡃⠒⣒⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡇⠀⠉⠉⠡⠄⠀⠀⠠⠜⠀⠀⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⢙⣄⠉⠢⠊⢀⡖⢆⠀⠀⠀⠐⠢⡌⠛⢿⣷⣤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⠀⠈⢳⠀⠔⠉⠀⣸⠀⠀⠀⠀⠀⠙⢢⠀⠌⣽⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣀⠌⠀⢠⢿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠑⠢⠄⣀⠉⠓⠦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀ ⠀⠂⠤⣀⠈⠑⠂⠤⣀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡡⠀⠀⠀ ⠂⢄⣀⠀⠉⠒⠤⣀⠀⠉⠒⠤⣀⠈⠑⠢⢄⡀⠀⣀⠤⠒⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⣀⠀⠉⠒⠤⢀⠀⠈⠑⠢⢀⡀⠉⠒⠤⣀⢨⠟⠛⠒⠦⢄⣀⠀⠈⠑⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠉⠒⠤⣀⠀⠉⠒⠠⢄⡀⠈⠑⠢⣄⣀⡉⠀⢀⣠⣄⡀⠈⠉⠒⠦⢄⣀⠀⠉⠓⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠉⠒⠤⣀⠀⠉⠒⠢⢄⠀⠈⠑⠢⢼⠉⢻⠣⠀⢸⠀⠀⡉⠑⠲⠤⣀⠀⠈⠉⠒⠢⣄⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠑⠢⢄⡀⠉⠑⠢⢄⡀⠈⠑⠢⢄⣸⠀⢸⣷⠀⢸⠀⠸⠟⠀⠀⠀⢠⡿⣷⣶⢤⡀⠀⢳⠀⠀⢱⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠑⠢⢄⣀⠈⠑⠢⠄⡀⠈⢧⡀⢻⠀⢸⣄⠀⠀⢀⣀⡀⠀⠘⡇⠈⠳⣿⠀⠀⡇⠀⢸⡤⠋⠀⡇⠀⠀⠀⠀⡠⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⡀⠈⠉⠒⠿⣿⠀⢸⠁⠀⠀⠘⠚⠁⣤⣄⣣⠀⠀⠘⠒⠚⠓⠒⠚⠁⠀⠀⣷⠀⠀⠀⢠⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠤⣀⢸⠀⠘⣄⠀⠿⠇⠀⢀⡉⢹⠃⠀⠀⣠⣄⠀⠀⠀⠀⠀⣠⣄⠸⡆⠀⣠⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⡴⠈⡟⠢⢄⣀⠙⠃⢸⣀⠠⢄⠻⠋⠀⠀⣤⡄⠀⠛⢛⠅⢿⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⠿⠤⣀⠈⠙⠒⠼⣷⣄⠜⠀⢠⠀⠀⣸⠀⠀⡤⠘⣦⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠒⠦⣄⡀⠉⠒⢤⣌⣉⣉⣉⣉⣻⣥⠒⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡎⠀⣴⡇⢀⣼⡂⠈⢣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠴⠋⠉⠉⠀⠈⠓⠊⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⢦⣤⣤⣄⣀⣀⣴⠿⠋⠉⠉⢙⡿⠋⠉⠁⠀⠀⠀⠀⠉⠉⠉⢉⣉⣉⠉⠉⠙⠛⠒⠒⠲⠶⠦⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⠏⠀⠀⡴⠚⠓⠒⠤⣄⣀⣀⡴⠋⠀⠈⠙⠲⢤⣀⡠⠖⡛⠒⡆⠀⠀⠙⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣤⡾⠋⠀⠀⡾⢀⡤⠼⢱⣳⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⢾⡵⠀⢣⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡉⠛⠛⠛⠉⠉⢁⣠⡶⠶⢶⡇⠸⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢺⡿⠀⠀⠀⢻⠒⡦⢤⣀⠀⠀⢉⣶⣀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣶⣤⣤⣴⡾⠛⠉⠀⠀⣸⠀⠀⣹⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢻⠒⠬⣙⠻⢭⡉⠉⠉⠉⠉⠉⠓⠢⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⢻⠀⢠⠃⠀⠀⠀⠀⠀⣿⣹⠄⠀⠀⠀⠀⢀⣀⠀⠀⣇⠘⡆⠀⣬⡳⠀⠙⠀⠀⠀⠀⠀⠀⠀⠈⢏⢉⣉⣉ ⣤⣄⣀⣀⣀⣴⡾⠋⠀⠀⢸⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠘⠞⠀⠀⢹⡄⠹⡊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡴⣠⠎ ⠉⠉⠉⠉⠉⠁⠀⢀⣤⢶⣼⠀⠀⢨⣧⡀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⢳⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠤⠊ ⣤⣤⣤⣤⣤⣤⡾⠛⠁⠀⠸⡇⠀⢸⠉⠁⠀⠀⠀⣰⣶⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠈⡇⠀⠀⠀⠀⣀⣸⣦⡀⠀⠀⠀⠀⣀⣸⣇⠀⠀ ⣩⠿⣭⠉⠉⠁⠀⢀⣴⠶⢶⣷⢠⡘⢧⢀⠀⠀⠀⠉⠉⠀⠀⢀⣀⠀⠀⠘⠓⠃⠀⠀⢧⠀⠀⠀⠀⢿⣿⡿⠀⠀⣀⡀⠀⠙⠛⢻⠀⠀ ⢇⠀⠈⠻⢶⣶⣾⣟⡡⠴⠊⢉⣿⠇⢸⣼⣃⡤⢤⣀⠀⠀⠀⣙⡋⠀⠀⢀⡞⠀⠀⠀⡼⣦⡀⠀⠀⠀⠀⠀⠀⡀⢙⣡⠀⠀⣠⠞⠀⠀ ⠈⠢⣄⠀⠀⠀⠀⠀⣀⣤⣶⣹⣿⠀⠀⠀⢸⣇⣀⠈⠙⠚⠋⠉⠉⠓⠒⣻⠁⠀⠀⢸⡷⠉⢻⠦⣄⡀⠀⠀⠀⠉⢉⣉⡤⠞⠁⠀⠀⠀ ⠀⠀⣀⣭⣭⣭⣭⣉⣰⡟⠉⠻⣿⡀⠀⠀⡟⠀⠈⠉⠉⠉⠉⠒⠒⠒⠒⣻⠀⠀⠀⣿⡀⠀⢸⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠾⠟⠋⠁⠀⠀⠈⠉⠉⠀⠀⠀⠈⠙⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣤⣤⡟⠷⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⡀⣀⠤⠒⠊⠉⠀⠙⠒⢤⣴⣲⡀⠀⠀⠀ ⠀⣇⠉⢀⣀⠀⠀⠀⠀⠀⠤⠸⠀⠃⠇⠀⠀⠀ ⠀⡜⠰⢻⠣⡇⠗⠈⣋⣁⠤⣴⣒⣶⠤⡄⠀⠀ ⢼⡠⠤⠴⣾⠿⢟⠛⡏⠉⢯⠀⢳⣀⣦⣸⣦⡀ ⠀⠀⠀⠘⣌⢦⢬⣷⣺⠶⠾⠟⠛⢛⣉⣉⡤⠇ ⠀⠀⠀⠀⠈⠾⠭⠤⠤⠤⠐⠒⠉⠁⠀⠀⠀⠀
⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢋⣩⣉⢻ ⣿⣿⣿⠀⣿⣶⣕⣈⠹⠿⠿⠿⠿⠟⠛⣛⢋⣰⠣⣿⣿⠀⣿ ⣿⣿⣿⡀⣿⣿⣿⣧⢻⣿⣶⣷⣿⣿⣿⣿⣿⣿⠿⠶⡝⠀⣿ ⣿⣿⣿⣷⠘⣿⣿⣿⢏⣿⣿⣋⣀⣈⣻⣿⣿⣷⣤⣤⣿⡐⢿ ⣿⣿⣿⣿⣆⢩⣝⣫⣾⣿⣿⣿⣿⡟⠿⠿⠦⠀⠸⠿⣻⣿⡄⢻ ⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⠇⣼ ⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣰ ⣿⣿⣿⣿⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿ ⣿⣿⣿⣿⣿⠏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿ ⣿⣿⣿⣿⠟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿ ⣿⣿⣿⠋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿ ⣿⣿⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠤⠤⠤⠤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠋⢀⣠⣤⣤⣤⣤⣄⣀⡀⠉⠉⠛⠷⣆⠀⠀⠀⠀⠀⠀ ⠀⢠⠿⡄⠀⠀⡜⠀⡞⢁⡴⢦⠀⠀⠈⠉⠙⠛⠶⣦⠀⠘⡆⠀⠀⠀⣀⣀ ⠀⡼⠀⣇⣀⣀⣇⣄⣇⡼⠁⠘⡆⠀⠀⠀⠀⠀⠀⠘⡆⠀⠁⠀⠀⣼⠋⢹ ⠀⡇⠘⠋⠉⠉⠀⠉⠉⠛⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣠⡾⠁⠀⣸ ⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⡇⠀⣈⠉⠀⣀⡴⠃ ⡞⠘⠃⢰⣶⣶⠀⠀⠀⠰⠆⠀⣸⡀⠀⠀⠀⠀⢀⡼⠁⢠⠟⠛⠛⠉⠀⠀ ⠹⣦⡀⠀⠀⠀⠀⠀⠀⢀⣠⡼⣫⣿⡛⠶⠶⢚⣫⣥⣤⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠙⢳⡶⠒⣶⣿⣯⣭⡼⠁⣠⣇⣀⣀⣼⣧⡀⢹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⡵⠞⠋⠀⢀⣟⣠⠞⠉⠀⠘⣇⠹⡈⠻⣦⣳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠻⠇⠀⠈⠛⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠟⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⠛⠻⠿⠿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⢸⠃⠀⢰⡿⠋⠉⣭⣭⠉⠉⠉⠉⠉⠛⠛⠿⢷⣶⣶⣤⣀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⡏⢻⡄⠀⠀⠀⠀⣿⠀⠀⡿⠀⢀⣾⠏⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⡀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣠⣤⣤⠀ ⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⣟⠀⠀⡇⠀⣾⠃⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⡇⠀⠀⠀⢀⣾⠟⠉⠹⡇ ⠀⢠⡏⠀⣸⣷⣶⣶⡾⠿⠿⠿⢷⣿⣾⣏⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⢀⣾⠏⠀⠀⠀⡇ ⠀⢰⡇⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣧⣀⣤⡿⠃⠀⠀⠀⣰⡇ ⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡟⠛⠋⠀⠀⠀⢀⣴⡟⠀ ⣸⠇⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣸⣧⣀⢀⣀⣠⣴⡿⠛⠀⠀ ⡟⠀⠙⠃⠀⢰⣾⣦⣰⡆⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⢠⡿⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀ ⣷⡀⠀⠀⠀⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠈⠁⠀⠀⣼⡿⢷⣶⣤⣤⣀⣀⣀⣠⣤⣾⠿⠃⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⢏⣶⣶⣯⡍⠉⠛⠛⠛⠉⣩⣥⣶⣶⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠛⠿⠿⣿⣶⣶⣶⣶⣶⣶⣶⡿⠿⠟⠉⢀⣾⠃⠀⢈⡇⠀⠀⠀⠀⠈⢿⣍⠀⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⣸⣿⡿⠷⠶⢶⣶⡿⠁⢀⣤⣿⣷⣶⣶⣶⣶⢶⡿⢿⣦⡀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣏⣤⣶⡿⠟⠋⠀⠀⠀⣼⠟⢀⣴⡿⠋⠀⠀⠀⠈⢿⡄⠀⣧⠀⠙⢿⣦⡈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠛⠛⠋⠁⠀⠀⠀⠀⠀⠸⢿⡾⠟⠋⠀⠀⠀⠀⠀⠀⠘⢿⣦⣹⡆⠀⠀⠙⢿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣛⠁⠀⠀⠀⠀⣙⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣅⣁⢈⣭⣿⣷⣾⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣖⣦⣤⣲⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⡿⠟⠋⠉⠻⡟⢟⡽⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⢞⢝⣍⢿⣹⡿⠳⣛⣋⣓⣩⣲⡤⡀⠀⠀⠀⠀⠀⣰⡿⣣⠟⠁⠀⠀⠀⠀⠀⠘⢑⡻⣟⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⣿⣽⡿⣿⣟⡁⠀⠀⠀⠉⠉⢻⣟⠋⠝⢓⢤⣠⡴⣶⡿⣟⣭⣓⠖⠢⣤⣀⣀⣀⣬⡶⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣹⣫⢿⡇⣃⠴⡀⣀⡠⠤⠶⠒⣺⠿⣟⢸⣯⣃⣳⡾⡲⠷⣮⣥⣼⣮⣤⣥⣾⣿⣿⣻⡿⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⠣⣿⣿⣶⣾⣿⣷⣶⡂⢩⡭⢊⣽⣿⡿⠿⠿⢿⣦⣴⣙⠈⠙⠏⠉⠋⠉⠀⠩⠀⠂⠀⢀⣤⢤⣤⣤⣂⣅⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠉⠙⠟⡟⢛⠋⡵⣻⣿⠏⠀⠀⠀⠘⢿⢯⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣀⠖⣫⠵⢏⣽⣿⣿⡧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣩⢅⡏⠀⠀⠀⠀⠀⠈⠫⣳⠄⢹⡆⠀⠀⠀⠀⣢⣴⣿⣿⣿⠟⠁⠈⢿⢿⡿⠄⠀ ⠀⠀⣰⣾⣏⣩⣉⠰⣄⠀⠀⠀⠀⣠⢖⣴⢟⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣾⣿⡀⠀⢠⣾⣿⣿⡿⠟⠁⠀⠀⠀⣸⣾⠣⠂⢀ ⠀⣰⡇⠈⠙⠤⣽⣿⣹⣷⣤⣈⣴⣩⡤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⡫⠁⠀⠀⠀⣀⣴⣾⡿⠃⠁⠀⠘ ⢰⣿⣹⡄⠀⠀⠀⠉⠛⠻⠿⠛⠋⠉⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡀⣤⡶⠁⢼⣿⠃⠀⠀⠀⠀ ⢹⡇⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⡆⠡⣬⣧⣀⡜⠁⠀⠀⠀⠀⠀ ⠀⠱⡄⢂⠣⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⠃⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠢⢀⣙⠿⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⡄⠀⠀⠀⣀⣀⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠈⠑⠊⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢿⣿⣿⡶⡤⣕⡤⠀⠂⠀ ⠀⢀⠀⣤⠔⠆⢶⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠄⠀⠀ ⠁⣠⡎⠀⣀⣠⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠀ ⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀ ⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⋆౨ৎ˚⟡˖ ࣪⋆୨୧⋆⋆ ˚。⋆୨♡୧⋆ ˚。⋆
⠲⠤⠤⠤⠴⠋⠉⣹⠋⢉⣉⠉⠉⠉⢉⠭⣉⠁⠂⢐⣒⠂⠤⣄⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⣀⡴⠋⢩⢁⡀⢧⠀⠉⠐⠒⠁⠀⠀⠁⠒⢱⠄⠅⠀⢸⠀⠀⠀⠀⠀⠀ ⣤⣀⣀⣤⠖⠋⡋⠘⡄⠀⠀⠀⠀⠀⠘⠋⠀⢠⠹⠔⡠⣤⠗⠚⠀⠠⢄⡀⠀⠀ ⠀⠉⠉⢀⡤⠚⡇⢰⠁⠀⠀⠸⠕⠀⠀⠀⡄⠈⡆⢃⠨⠂⠑⠀⠀⠀⠀⠈⠀⢉ ⠙⠛⠛⠉⢀⡤⡇⠀⣵⡀⠀⠀⠀⠐⠀⠀⠀⠀⠘⡌⠀⠀⠀⠀⠀⠀⠀⠀⡬⠔ ⣶⡶⠶⠚⢉⣀⣸⢀⢇⠀⠀⠸⠗⠀⠀⠀⠐⠆⠀⢃⠀⠀⢶⡿⠀⠀⠀⠰⠇⠀ ⢇⠈⠓⠾⠙⠂⡡⡿⠀⠿⡖⠢⢄⠠⠭⣀⣠⠀⠀⣜⢄⠀⠀⠀⠠⠼⠆⡠⠆⠀ ⢀⣁⣶⣶⣂⡽⠛⢦⡀⣸⠉⠐⠒⠒⠀⠀⢺⠀⢸⡇⢀⠉⠑⠒⠒⠂⠉⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢔⣒⠂⣀⣀⣤⣄⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⢠⣟⡼⣷⠼⣆⣼⢇⣿⣄⠱⣄ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⣆⠙⠢⠐⠉⠉⣴⣾⣽⢟⡰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⠀⠤⢴⣿⠿⢋⣴⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡙⠻⣿⣶⣦⣭⣉⠁⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⠉⠉⠉⠉⠇⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣘⣦⣀⠀⠀⣀⡴⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢻⣿⣿⣿⣿⠻⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣿⠉⠻⣇⠘⠓⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢶⣾⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠻⢿⣿⣿⠿⠛⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠈⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⠘⠁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⠀⠀⡇⠀⠀⠀⠀ ⣀⣀⣀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠄⠀⠀⠸⢰⡏⠉⠳⣄⠰⠀⠀⢰⣷⠶⠛⣧⠀ ⢻⡀⠈⠙⠲⡄⣿⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⠀⠀⠀⠈⠓⠒⠒⠛⠁⠀⠀⣿⠀ ⠀⠻⣄⠀⠀⠙⣿⠀⠀⠀⠈⠁⠀⢠⠄⣰⠟⠀⢀⡔⢠⠀⠀⠀⠀⣠⠠⡄⠘⢧ ⠀⠀⠈⠛⢦⣀⣿⠀⠀⢠⡆⠀⠀⠈⠀⣯⠀⠀⠈⠛⠛⠀⠠⢦⠄⠙⠛⠃⠀⢸ ⠀⠀⠀⠀⠀⠉⣿⠀⠀⠀⢠⠀⠀⢠⠀⠹⣆⠀⠀⠀⠢⢤⠠⠞⠤⡠⠄⠀⢀⡾ ⠀⠀⠀⠀⠀⢀⡿⠦⢤⣤⣤⣤⣤⣤⣤⣤⡼⣷⠶⠤⢤⣤⣤⡤⢤⡤⠶⠖⠋⠀ ⠀⠀⠀⠀⠀⠸⣤⡴⠋⠸⣇⣠⠼⠁⠀⠀⠀⠹⣄⣠⠞⠀⢾⡀⣠⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠛⠂⠀⠀⢰⠇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣰⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⣀⣀⡀⠀⠀ ⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⢰⡇⠀⣿⠁⠀⠉⠻⣦⡀⠠⠟⠀⠀⠀⠀⣿⣧⣶⠿⠛⠙⣿⠀⠀ ⣿⡋⠉⠙⠛⠷⣦⣄⠀⠀⣿⡇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⠻⣦⣀⣀⣀⣀⣰⣿⠟⠁⠀⠀⠀⣿⠀⠀ ⠸⣷⡀⠀⠀⠀⠈⠛⣷⡄⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣿⡀⠀ ⠀⠘⢿⣆⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠐⠟⠀⠀⠀⠀⡀⠀⢀⣴⡿⠃⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠙⣷⡄ ⠀⠀⠀⠙⢷⣤⡀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠇⠀⣼⡏⠀⠀⠀⠀⣾⣅⣀⣿⠀⠀⠀⠀⠀⠀⠀⣾⣅⢈⣷⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠙⠿⣦⣀⠀⢸⡇⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠘⠻⠿⠟⠀⠀⠠⣖⢒⡶⠀⠙⠿⠿⠟⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣾⡇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢈⣏⠀⠀⠀⠀⡀⠀⠀⠀⢀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⢰⡆⠀⠀⢻⣧⡀⠀⠀⠀⠀⠈⠻⠶⣤⡴⠟⠙⠶⣤⡤⠞⠁⠀⠀⢀⣾⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣧⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣿⣶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⠿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠉⠉⠛⣿⠛⢻⠿⠿⠿⠿⣿⡿⠿⠛⠛⠛⠛⠛⣿⠛⠉⠙⠛⣿⠛⠛⣿⠟⠛⠛⢻⡏⠉⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣀⣤⡾⠃⠀⣿⣀⣀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣀⣴⠟⠀⠀⣿⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠙⠷⠶⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣀⣀⣠⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠛⠋⠉⠉⠛⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣀⡤⣤⢤⡤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⣀⣤⣶⠿⠛⠋⠁⠁⠀⠀⠀⠉⠛⣯⣳⡀⠀⠀⠀⠀⠀⠀⢠⡿⠃ ⠀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⠀⠀⠀⠀⠀⣠⡿⠃⠀ ⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⢹⡆⠀⠀⢸⣿⠀⠀⠀⠀⢠⡿⠁⠀⠀ ⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⢀⣮⠏⠀⠀⠀⠀⠘⣷⡀⠀⠀ ⠀⠙⠿⣶⣤⣀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀ ⠀⠀⠀⠀⠉⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣄⣀⣀⣤⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠈⠉⠉⠙⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ 𐙚 -`♡´-˙✧˖°📷 ༘ ⋆。˚˙✧˖°📷 ༘ ⋆。˚˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆˚‧。⋆🌻⋆。‧˚⛷🧚‍♀️🛖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⠶⠶⠾⠋⠀⠘⠿⠶⣦⣄⡀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣶⣤⣄⣀⣀⣤⡶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣼⣿⡭⢍⢿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡄⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠈⢿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣇⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠺⠗⠂⠛⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢈⣿⢦⠀⣴⢿⣯⢷⠸⣧⢀⣶⡄⠀⠘⢷⠟⠛⠛⠁⠀⠀⢀⣀⣠⣤⣤⣶⡟⢀⣀⡀⠀⠀⠀⠀⠀ ⠀⢀⡾⠃⠀⠒⠏⠨⣿⠶⢓⣿⠀⠉⠁⠀⣀⣀⣤⣴⡶⠶⣾⣛⣻⣽⣿⣶⡾⢾⣟⠛⠛⢿⡀⠀⠀⠀⠀ ⢀⣿⠁⠀⠀⠀⢀⣀⣒⣴⣾⣷⣶⣶⣿⣿⣯⣿⠿⠾⠛⠛⣿⡋⠉⠀⢿⡄⠀⠀⢻⣆⠀⠈⢿⣦⡀⠀⠀ ⠹⣿⡴⠶⠟⠛⠛⠋⢉⣿⡿⠿⠛⠻⣯⠁⠀⠻⣦⡀⠀⠀⠙⣷⡀⠀⠀⢻⣆⣀⣤⣿⠶⢶⣿⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⢾⡏⢻⣆⠀⠀⠙⢷⣄⣀⣨⣷⣤⣤⡶⢾⣿⣻⣿⣿⣿⣿⡿⠾⠛⠛⠛⠉⠀⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠹⣷⠟⣛⣻⣯⣭⣿⠾⠿⠿⠛⠛⠋⠉⠁⠀⢀⣀⣠⣤⣤⣶⠶⠶⠿⠻⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⣿⡟⠉⠉⠀⠀⣀⢀⣀⣀⣀⣤⣤⡴⠶⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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