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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠉⠉⠉⠉⠓⢦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀ ⠀⢀⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠚⣹⠟⢁⣀⣀⣇⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⢸⡆⠀ ⡴⠁⠀⠀⠀⠀⠈⠑⠢⣄⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠐⠋⠉⠀⠀⠀⠾⠥⢀⣀⣸⠀⠀⠀⠀⠀⠀⡸⠀⠀ ⢳⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢆⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⣠⠃⠀⠀ ⠈⢆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡇⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀ ⠀⢸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⣩⣶⣿⣶⣤⠤⢴⡋⠀⠀⠀⠀⠀ ⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠉⢻⡟⢻⡆⠀⢳⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠰⢚⣥⣶⣶⣶⣦⣄⠀⠀⠀⠸⣿⣦⣠⠾⢷⣿⠇⠀⠀⡇⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠀⣰⠟⠉⠉⠹⣿⠿⢿⡇⠀⠀⠀⠙⢿⣿⠿⠟⠁⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠳⣄⠀⠀⠐⠊⠉⠉⠉⠉⠁⠀⠀⣿⡀⠀⢀⣰⣇⣀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠈⠑⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠛⠛⣿⣿⡟⠀⠀⢶⣿⣿⡇⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠒⠛⠋⠀⠀⠀⡀⢉⣽⠤⠤⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⣠⡊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠊⠁⠈⢢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⡆⠀⠀⠀⠀⠉⠒⢤⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀ ⠀⠀⠀⡼⢸⠁⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀ ⠀⠀⠀⣇⠸⡀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣼⠶⣎⠑⣆ ⠀⠀⠀⢹⡀⠱⣄⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠋⠀⠀⠀⠀⠀⠀⢰⣿⣃⠿⣷⣿ ⠀⠀⠀⠈⢧⠀⢈⠗⠉⠉⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⢀⡏⠙⠿⠿⢯⠏ ⠀⠀⠀⠀⠈⢳⠏⠀⢀⣀⠤⠤⠤⣝⢦⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⣼⠤⠤⣄⡴⠋⠀ ⠀⠀⠀⠀⠀⣾⠀⢠⣾⣅⢴⡶⣾⠎⠻⣧⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⢀⡀⠀⠀⣽⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⡀⠈⢿⠟⢹⣿⡿⠀⠀⡿⠀⣹⣄⠀⠀⠀⠀⠀⠀⠐⢦⠀⢱⠀⠀⠀⠀⠘⣄⡰⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠦⣄⣳⡄⠈⠀⢀⡴⠟⠈⠀⠀⠙⠒⠠⠤⠤⠤⠤⠼⠶⠋⠑⠒⠒⠒⠊⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⣀⡀⠀⠤⠤⠐⠒⠠⠤⣠⠂⠀⠀⠈⠂⠄⡀⠀⠀ ⠀⠀⡠⠃⠀⢈⢢⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⢸⠀⠀ ⡔⠊⠀⠀⠀⠀⠑⢄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠌⠀⠀ ⢣⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠆⠀⠀⠀⠀⠔⠁⠀⠀⠀ ⠀⠑⠠⡀⠀⠀⠀⠀⡘⠉⢳⡄⠀⠀⠀⠀⣼⣿⣤⣼⢢⡀⢀⢾⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢱⣀⠀⣠⢳⣶⣿⢻⠀⠀⠀⠀⠹⣈⣿⡿⢠⠀⠁⠘⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠆⠁⠘⢌⡻⢷⠞⠀⠰⣶⡆⢠⠈⠒⠒⠁⠀⠀⢀⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠈⠰⠓⣻⡇⠀⠀⠀⢀⡀⠄⠊⠀⠀⢀⣀⡀ ⠀⠀⠀⠀⠀⠈⠂⠤⠄⠀⠠⠤⠄⠲⠤⠋⠉⠉⠉⢋⠀⠀⠀⠀⠀⡰⠁⡘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢀⠀⢀⠃⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠨⣺⠀⢠⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡓⠌⡄⠀⣀⡸⢀⡀⢸⠀⠀⠀⠀⠈⡧⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡎⠀⠀⠈⣎⠐⠀⠀⠀⠸⡖⡢⢄⠀⠀⡁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠈⠙⠲⠤⠤⠐⠣⠦⠧⠤⠵⠐⠁⠀⠀⠀

⠀⠀⠀⢠⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡀⠀⠀ ⠀⠀⢰⣿⠿⠏⠉⠛⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠉⣹⣿⣿⡆⠀ ⠀⠀⣴⣿⣧⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠀⠀⠀⠰⠋⣿⡿⣷⡄ ⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠘⠁⢠⡿⠁ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀ ⠀⠀⢀⣿⠷⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀ ⠀⢠⡾⠁⠀⢀⠀⠀⠀⣠⣞⠋⠁⠀⠀⠀⠈⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠁⠀⠀⠀⣈⣉⣳⣄⣀⡀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀ ⠀⣿⠃⢀⣴⣁⣴⠾⠛⠉⠉⠁⠉⠉⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠉⠛⠷⣦⣀⢢⡀⠈⣿⡀⠀ ⠀⣿⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆⣿⡇⠀ ⠀⢹⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠋⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡟⠀⠀ ⢠⣿⡏⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀ ⣸⡟⠀⠀⠀⠀⠀⢠⣶⠟⠁⠀⠀⣰⣾⣟⠉⢹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠉⣿⣷⣄⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⡀⠀⠈⣿⡇⠀ ⣿⡇⠀⢀⠄⠀⣴⡟⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⠻⣆⠀⠀⢹⣦⡀⢹⡇⠀ ⣿⡇⣠⡏⢀⣾⠏⠀⠀⠀⠀⠀⠀⢻⣿⣿⠟⠋⠉⠀⠀⠉⠙⠛⠛⠋⠉⠁⠀⠉⠙⠻⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⣿⣷⣼⡇⠀ ⣿⣿⣿⣁⣾⠃⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣿⣿⠿⠃⠀ ⠈⠉⣿⣿⠃⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⠀⠀⠀ ⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀ ⠀⠀⣿⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢀⠀⢸⣿⠀⠀⠀ ⠀⠀⣿⡀⢸⣷⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠒⠶⠞⠛⠉⠉⠛⠳⠶⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⢸⣧⣸⡟⠀⠀⠀ ⠀⠀⠸⣧⣸⣿⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠁⠀⠀⠀⣾⠿⠿⠃⠀⠀⠀ ⠀⠀⠀⠙⠛⢿⣇⣰⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⡄⠘⣿⡆⠀⠀⣧⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⡼⠀⠀⣼⣿⡇⢠⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⣿⡿⣦⣀⣹⣷⡀⠀⢷⠀⠠⠶⠖⠚⠛⠒⠒⠂⢀⡾⠀⣠⠞⢁⣠⣾⠿⣿⣷⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠈⠙⢻⡏⠉⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠁⠀⠀⣿⡇⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡿⠟⠋⠉⢉⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⣈⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠘⣿⠶⣶⣶⣾⠿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣿⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⣿⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⠹⣦⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡉⠀⠈⠇⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⢈⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢰⡜⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⡄⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⢿⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣀⣼⣷⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⣴⡿⠋⠁⠀⠀⠀⢿⣇⠀⢠⠀⣠⠀⣀⢀⣾⡟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⠾⢶⣦⣼⣾⠏⠀⠀⠀⠀⠀⠀⠀⠻⣶⣾⣷⣿⣷⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⢋⣃⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⢡⠏⠹⡄⠀⠘⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⡞⠀⠀⣧⣀⣠⣬⣧⣤⣀⣀⡀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠋⠙⢳⡄⠀⠀ ⠀⠀⠀⠀⠀⠘⣷⣧⡴⠞⠉⠁⢀⠜⠀⡠⠀⠈⠉⠙⠓⠦⠖⠋⠁⣀⡤⠶⣦⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⢀⡿⠋⠀⠀⠀⡰⠋⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⢴⠋⠁⠀⠀⡏⠀⢸⠇⠀⠀ ⠀⠀⠀⢀⡴⣫⣴⣦⠀⠀⡜⠁⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⢰⠃⠀⡾⠀⠀⠀ ⠀⠀⣴⠟⢸⣿⣿⠏⣠⠞⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠎⠀⣼⠃⠀⠀⠀ ⠀⣼⠃⠀⣸⣿⣯⣬⣁⠀⠀⡇⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀ ⢰⡏⠉⠉⠁⠸⣿⣿⠟⠀⠀⢳⠀⠀⠀⣼⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⢠⡀⠀⣠⠀⠀⠈⡆⠀⠀⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠈⢷⡄⠀⠀⠀⠛⠛⠉⠀⠀⠀⠸⡄⠀⠀⠀⠀⢀⣠⡤⠤⠤⢤⣤⣀⣀⣸⠁⠀⠀⠀⠀⠀ ⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⣤⠴⠞⠋⠁⠀⠀⠀⠀⠀⢈⠉⠙⠓⢦⣄⠀⠀⠀ ⠀⠀⠀⠉⠳⢦⣄⡀⠀⠀⠀⣠⡶⠛⢉⣤⠶⠚⠛⢶⣄⡀⠀⢀⣠⠾⠗⠲⢶⣄⠙⢧⡀⠀ ⠀⠀⠀⠀⢰⡟⠉⢉⠛⠳⣾⠋⠀⢰⠏⠁⠀⠀⠀⠀⠈⢹⣿⣟⠁⠀⠀⠀⠀⠙⢷⠈⢷⠀ ⠀⠀⠀⠀⠈⠳⣦⣧⠀⢰⠇⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⢸⡇⢸⡆ ⠀⠀⠀⠀⠀⠀⠈⠹⡆⣿⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⣸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡋⠀⠀⢀⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⢉⣻⠶⢤⣤⣤⡶⢟⣁⣦⣍⡓⠦⡼⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⢀⠔⠋⢀⣤⡄⢸⣿⢷⡘⣧⣈⣿⢁⡼⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣞⠁⠀⠀⠛⢻⣥⢾⣇⡾⢧⣽⡦⠿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⠬⠿⠞⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢲⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⡏⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡛⣗⠺⢧⣀⠀⠀⠀⠀⠀⠀ ⢺⡉⠛⠿⣍⡑⠲⠤⣄⠀⠀⠀⢀⣠⣧⣴⣧⣀⡀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠳⣄⣙⣏⣹⠀⠀⠀⠀ ⠈⢧⠀⠀⠀⠉⠲⣄⠈⠙⢶⠞⠉⠀⠀⠀⠀⠀⠈⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⡿⠁⠀⠀⠀⠀ ⠀⠈⢧⡀⠀⠀⠀⠈⢷⠀⠀⠀⣴⣶⣦⠀⠀⠀⣰⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠳⣄⠀⠀⢠⠏⠀⠀⠀⠻⠿⠿⠀⠀⠈⠁⣼⣾⣶⠻⣆⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢦⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣯⣠⡏⠀⠀⠀⠀⠀⢸⣭⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⠤⠚⠁⣠⠾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠁⠀⠘⣯⠉⠉⠉⠉⠉⠙⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⡶⣄⣀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⠀⠀⠀⠀⠀⣠ ⠀⠀⠀⢀⡤⢤⡀⠀⠀⡇⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⣙⣒⣒⣶⡾⠟ ⠀⠀⢰⡏⠀⠀⢘⡆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⡇⠀⠈⠁⠀⠀⠀ ⠀⠀⠈⠳⠤⠤⠞⠁⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⢀⡼⠁⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⢠⠇⠀⠀⣠⠾⣅⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠳⢤⣀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢸⢦⠖⠋⠁⠀⠈⢧⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢀⡼⠋⠉⠓⠒⠚⣧⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⢸⡇⠀⠀⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⣄⣀⡴⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠸⢦⣀⡠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠞⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠈⡇⢰⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢞⣻⠛⠉⠉⠉⠉⠉⠉⠛⡛⣻⢶⣤⣿⡾⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡷⠾⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣷⡄⠙⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠰⣿⠏⠀⠀⠀⠀⠀⠀⢠⣾⣷⠀⠀⠀⠈⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⣃⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⡀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⣰⠋⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⠟⠀⢰⡏⣠⣴⠶⠖⠀⠀⢻⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⡟⠁⠀⠀⣿⡏⠀⠹⣆⠀⠀⠀⠀⠉⣿⠛⠛⠋⠁⠀⠀⠀⢤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⡟⠀⠀⠀⠀⢹⣧⠀⠀⠙⠷⣤⣤⣤⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⣠⠟⠛⢦⡀⠀⠀⣠⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣶⡿⠁⠀⠀⠀⠉⠀⣰⠏⠀⠀⠀⠀⠘⣿⡄⠀⠀⢤⣄⡀⠀⠀⠀⠀⠀ ⠻⣆⠀⠀⠀⠀⢀⣠⡿⣧⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠹⣟⠷⣤⡀⠀⠀ ⠀⠉⠛⠿⠿⠟⠛⠉⠀⠈⠛⢶⣤⡀⠻⣏⡉⠉⠋⠉⢀⣴⠋⠀⠀⠀⢀⣠⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⢹⣆⠈⢻⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣯⣿⣦⣌⠛⠓⠒⠚⠋⢀⣤⣯⣶⣾⠛⢿⣯⣨⣇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⣿⠀⠀⢻⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠙⣿⣟⢙⣷⣶⣶⣾⣿⣧⣤⣿⠿⠟⠛⠉⠀⠙⣦⡀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣶⠟⠋⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠳⣦⣠⣴⣶⣦⣤⣴⠟⠀⠀⠀⣰⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠉⠛⢷⣄⣀⡴⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢻⣇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⢻⣆⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠙⣷⡀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠞⠋⠉⠙⠓⠒⠆⠀⠀⠀⠀⠈⢻⣆⡀⢸⡟⠀⠀⠀⡤⠤⠶⠶⠶⠿⢤⣶⡃⠀⠀⠀⠀⠐⠛⠋⠉⠙⠛⠛⠶⢤⡀⠀ ⠀⠀⠀⠀⢰⡏⠀⣠⠞⠀⠀⢠⠄⠀⠀⠀⠀⠀⣾⠏⠛⣿⠃⠀⠀⠀⠀⢠⠀⠀⠀⢤⠀⠈⢻⣆⠀⠀⠀⠰⡄⠀⠀⢳⡄⠀⠀⠈⣿⠀ ⠀⠀⠀⠀⠈⣷⣰⡇⠀⠀⣰⠋⠀⠀⠀⠀⠀⣰⣿⣄⣀⣿⡀⠀⠀⠀⠀⠈⡇⠀⠀⣸⡆⠀⢸⡏⠀⠀⠀⠀⣿⠀⠀⢠⡗⠀⢀⣠⠟⠀ ⠀⠀⠀⠀⠀⠈⠙⠷⣦⣤⣿⣀⣀⣀⣤⣴⠾⠋⠀⠀⠀⠈⠳⢤⣄⣀⡀⣸⠇⠀⣀⣿⣠⡴⠟⠙⠛⠷⠶⠾⠷⠶⠶⠾⠶⠛⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⣤⣴⡶⠿⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠉⠛⢦⡀⣀⡴⠛⠉⠀⠀⠀⠀⠀⠈⠙⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣴⠶⠚⠁⠀⠀⢰⠇⠸⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣆⠀⣠⣶⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⢡⣥⠀⠈⠻⠶⣤⣄⣀⠀⠀⠀ ⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠉⢻⡇⠀⠀ ⢸⣧⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠻⣧⠀⠀⠀⠀⠀⣼⣿⠁⣠⡾⠟⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀ ⠀⠀⠈⠳⣄⠀⢀⣼⣿⡟⢀⡿⠁⡜⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⡾⢋⣽⢿⣆⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠛⢻⡏⠀⢸⡇⠀⣷⣴⣿⠇⠀⠀⠀⠀⠀⠀⢸⠁⣼⠃⢀⣿⠀⠀⣿⠁⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⢿⡀⠻⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⣷⣾⣿⠀⠀⢹⡀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⣤⣀⢳⡶⠊⠙⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣈⢻⣿⠏⠀⣀⣼⣧⠀⢀⡴⠟⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠟⠁⠀⠀⢹⡏⠀⠀⠀⢀⣾⣿⣿⣿⣷⣶⣤⠀⠀⠀⠀⠉⡋⢁⣤⡾⠟⠉⠙⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢣⠀⠀⠀⠀⠀⣷⡀⠀⠀⢸⣯⡀⠀⢀⣹⣿⣿⠀⠀⠀⠀⠀⢹⡿⠟⠒⠒⠒⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣈⡷⠄⠀⠀⠀⠸⣿⣦⣀⠀⠙⠛⠻⠿⠿⠿⠟⠀⠀⠀⠀⣠⣿⠁⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠈⠛⠻⠟⠛⠛⠛⠳⠶⠤⠤⠤⠤⠶⠾⠛⠁⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⠀⠀⠀⠀⠀⢀⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⠿⠛⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢦⣀⣀⣠⣴⡿⠋⠉⠙⠛⠛⠛⠻⠿⣷⣶⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⣹⠋⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠈⡏⠉⠛⢻⣷⣤⣀⣀⣠⣴⡟⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢠⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢀⡇⠀⠀⠘⡟⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⡜⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠏⠀⢸⣿⠀⠀⠀⡇⠀⣙⣿⣷⡄⠀⠀⠀⠀⠀⢀⣾⡿⠀⠀⢀⡜⠁⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⡄⢠⠞⡛⠋⠀⠀⠀⣷⠟⣍⠙⠻⢿⡆⠀⠀⠀⠀⣾⣿⣧⠴⠞⠋⢀⡾⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠷⣿⣰⣁⣸⣆⣀⣤⣯⣠⣿⣄⣤⣶⣦⣤⣤⣤⣤⣶⣤⠤⠶⠶⠚⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠈⠉⠈⠉⠉⠁⠀⠉⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠉⠑⠢⠤⢤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⠤⡴⠚⠉⠉⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠁⠈⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠚⠉⠉⠉⠀⠀⠻⣦⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠚⠉⢁⠀⠀⠀⠀⠀⠀⠀⠠⣬⢷⠀⠀⠀ ⠀⠀⢰⠋⠈⢣⡀⠀⠀⠀⠀⢀⠞⠀⠀⠀⢸⠀⡤⣀⣠⠀⠀⠀⢾⣽⡏⣇⠀⠀ ⠀⠀⠘⡆⠀⠀⠳⡀⠀⠀⠀⢎⠀⠀⠀⠀⡞⠘⢸⣧⡾⠀⠀⠀⠀⢀⣀⠙⢦⡀ ⠀⠀⠀⠙⡄⠀⠀⠙⡄⠀⠀⠈⠳⡄⠀⢠⡇⠀⠀⠉⠀⠀⠀⡴⢒⢁⣾⠀⣠⠇ ⠀⠀⠀⠀⠈⣢⠀⠀⠘⠊⠉⠉⠉⠙⢦⡼⠀⠀⠀⠀⠰⡀⠀⠙⢚⡿⠓⠚⣹⠀ ⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⣀⡤⠞⠁⠀ ⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⡆⠀⠀⠀ ⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀ ⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢾⠀⠀⠀ ⠀⡞⠀⠀⠑⢲⠤⣄⣀⡀⠀⠀⠀⢀⣰⠃⠀⠀⢰⣀⣀⣀⠴⡇⠀⠀⢸⠀⠀⠀ ⢰⠁⠀⠀⢠⠃⠀⠀⢸⠏⠉⠉⠩⡏⢹⠀⠀⠀⢸⠉⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀ ⡆⠀⡀⢠⠙⡄⠀⠀⠸⣄⠐⣆⣣⡸⢸⠀⠀⠀⢸⡀⠀⠀⠀⡇⠀⠀⢘⡓⢤⡀ ⠳⠶⠳⠜⠛⠁⠀⠀⠀⠈⠉⠈⠀⠀⢸⡄⠀⢄⠈⣏⠲⡀⠀⣧⠀⢱⠀⣹⡠⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣼⣄⣼⠚⠃⠀⠈⠙⠉⠉⠁⠀⠀ ⣿⣏⣉⣍⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠛⠙⠓⠦⣄⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⢀⣀⣠⣤⣬⣭⠭⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⢀⣠⣴⡾⠛⠋⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠜⠁⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠖⠒⠒⠒⠋⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣹⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⠶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡷⣦⣹⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠃⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⢸⡇⢀⣤⠆⢀⣠⣤⠀⠀⠀⠀⠀⢸⣷⣶⣿⠇⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡄⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⣿⠁⢸⢃⣾⠏⣩⣿⡆⠀⠀⠀⠀⠀⠉⠉⠁⠀⠻⣷⡄⠀⠀ ⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⢸⡟⠀⠈⢸⣿⣶⣿⠟⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠈⠻⣆⠀ ⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⣸⠇⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⣴⣮⡇⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠙⣧⣀⣀⣠⣤⠤⠤⢽⣧⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣅⢰⡶⣰⣮⡟⠀⣠⣾⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠈⠳⣤⣴⡏⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠉⠉⢩⣽⠋⠛⠛⠋⣼⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣤⣤⡴⠞⠋⠁⠀⠀⣠⣾⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⢹⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀ ⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀ ⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀ ⠀⠀⢸⠇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀ ⠀⠀⡿⠀⠀⠀⠀⠙⠲⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⣀⣠⣿⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀ ⠀⢰⠇⠀⠀⠀⠀⠀⢠⡟⠈⠉⠙⠻⢷⣶⣶⡶⢶⣶⣶⣶⣶⠶⣿⠇⠀⠀⠀⠀⢰⣿⠶⠶⠾⠛⠋⠉⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⡞⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢾⡀⠀⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀ ⢸⠁⠀⠀⠀⠀⠀⢿⣀⠀⠀⠀⠀⠀⣿⠀⠀⠢⣄⠘⢶⠀⢹⡀⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢿⣷⣀⠀⠀⠀ ⣿⠀⠀⢦⠀⠘⣦⠀⢹⡄⠀⠀⠀⠀⠘⣧⣀⣀⣿⣄⣼⠧⠾⠁⣿⠀⠀⠀⠀⠀⠘⣿⣀⠀⠀⠀⠀⠀⣿⡆⠀⢀⡀⠐⠦⣬⡉⠻⣦⠀ ⢻⣦⣤⣿⣦⣤⡿⠓⠛⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠀⠀⠀⠀⣿⡇⠀⠀⢀⠀⠀⢻⡙⠻⣦⡀⠀⠀⢸⡇⠀⠈⢻⡄⠀⢸⡇⠀⣽⠀ ⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠈⣧⠀⠀⢳⡄⢸⣇⠀⠀⠘⢿⣤⣠⣼⣧⣤⡿⠓⠚⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⣠⣿⣦⣀⣼⠟⠛⠁⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⡶⠶⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶ ⣿⣿⣇⣤⣣⣿⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠒⠒⠒⠤⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⢣⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⢞⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⢃⣮⠤⣄⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠒⠤⣀⢠⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⠁⡎⠀⣠⣾⣷⡀⠀⠀⠀⠀⢀⣧⣶⣦⣄⠀⠈⢣⣧⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠞⠁⢸⡁⢠⣿⣼⣿⡇⠀⠀⠀⠀⣸⣟⣿⣿⣿⣿⡄⠀⢻⡣⡀⠀⠀⢧⠀⠀⠀⠀ ⠀⠀⡰⠁⠀⠀⠈⢧⣼⣿⠿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⣿⠀⠀⡇⠱⡄⠀⠈⠳⡀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⢰⣙⣮⣿⡿⢀⠀⠀⠀⠀⠘⣿⠯⠿⠭⠊⡼⠀⠀⢸⠀⢱⠀⠀⠀⠙⢄⠀ ⠀⢸⡄⠀⠀⠀⠀⢘⠁⠀⣀⣾⣟⣻⣳⣶⣦⠀⠈⠙⠲⠴⢮⣀⠀⠀⢸⢀⠏⠀⠀⠀⠀⠈⣆ ⠀⠀⢳⡀⠀⠀⠀⠸⡿⢿⣿⡉⠿⣿⡿⠟⠃⠸⠵⣀⡀⠀⠀⠈⢳⢀⢇⠎⠀⠀⠀⠀⠀⠀⣸ ⠀⠀⠀⠑⢄⣀⠀⠀⠈⢛⡿⢷⡤⢼⡁⠀⠐⢶⣀⣛⡃⠀⢀⣠⠾⠋⢸⠀⠀⠀⠀⠀⠀⢠⠏ ⠀⠀⠀⠀⠀⠈⠉⡳⠒⠋⣠⠊⠀⠀⠉⠉⠉⠉⠀⠀⡏⠉⡁⠈⢦⡀⠈⢣⣀⣀⣀⡠⠖⠉⠀ ⠀⠀⠀⢀⣠⠔⠋⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣀⡁⠀⠀⢹⡉⠉⠉⠉⠀⠀⠀⠀⠀ ⢀⡤⠚⢹⠁⡠⠖⠒⠲⢅⡀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢠⠇⠳⡀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀ ⠘⡇⠀⠈⢿⠁⠀⠀⠀⠀⠙⢆⠀⣠⠚⠉⠀⠀⠈⢳⡏⠀⠀⠙⡄⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀ ⠀⠈⠒⠢⠞⢇⠀⠀⠀⠀⠀⠘⡄⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⢀⣠⠵⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⢀⡧⢧⠀⠀⠀⠀⠀⡼⠀⠀⠀⢠⠧⠔⠒⠉⠀⠀⡌⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠉⠀⠈⢦⣀⣀⣠⣞⣀⣀⣀⣀⡸⠦⠤⢀⣀⣀⣀⣇⣨⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⡇⠈⠐⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⡒⠁⠀⠀⠀⠀⢀⠜⡀⠀⠀⠀⢡⠀⠀⠀⠀ ⠀⠀⠀⡐⡙⢁⢼⡆⠀⠀⢀⣧⣤⣀⠑⣧⠀⠈⡄⠀⠀⠀ ⠀⢠⠊⠀⢣⣼⣿⡿⠀⠀⢸⣿⣿⡿⡆⠘⠡⠀⠐⡄⠀⠀ ⠀⡆⠀⠀⢰⠵⠟⡧⣄⣀⡈⠿⣛⡫⠃⠀⡇⡇⠀⠈⢂⠀ ⠀⠱⡀⠀⠘⣶⣯⠻⢿⠟⠑⢆⡀⠀⠑⡤⡝⠀⠀⠀⢈⠆ ⠀⠀⠈⠒⢠⠤⠫⠋⠑⠀⠙⠒⡖⠒⠪⡁⠃⡀⢀⠠⠊⠀ ⠀⢀⠤⠊⣁⡰⠁⠀⠀⠀⠀⠀⢘⢀⠀⠘⡉⠀⠀⠀⠀⠀ ⠘⡀⠰⡁⠀⠀⠑⡀⡔⠈⠉⠐⡎⠀⢣⠀⠐⢄⠀⠀⠀⠀ ⠀⠀⠉⠑⡀⠀⠀⣠⡇⠀⠀⢀⠃⠀⢸⠠⠔⠊⡱⡀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠁⠘⠠⠄⠂⠀⠀⠓⠒⠀⠤⠧⠃⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠛⠛⠛⠛⠓⢶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢣⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠞⣰⣃⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠙⠛⠦⢤⡀⠀⣤⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠋⢰⠋⠁⠀⣬⣷⡄⠀⠀⠀⠀⠀⠀⠀⢰⣃⣀⣀⡀⠀⠀⠙⢦⡸⡄⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠋⢠⡏⠀⢀⣾⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣄⠀⠀⠻⡽⡄⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⠁⠀⢸⡇⠀⣸⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⢰⣿⣧⣿⣿⣿⣿⣯⣦⠀⠀⢱⡙⣆⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀ ⠀⠀⣴⠃⠀⠀⠀⠀⢿⣀⡿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⡏⣿⡄⠀⠈⣧⠘⢦⠀⠀⠀⠙⣦⠀⠀⠀⠀ ⠀⣸⠃⠀⠀⠀⠀⠀⠀⡽⢻⡙⢦⣾⡟⠀⠀⠀⠀⠀⠀⠘⣿⣽⣻⠿⢿⣫⠞⣱⠇⠀⠀⢹⠀⠘⡆⠀⠀⠀⠈⢳⡀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⢰⡷⠚⠛⠚⠛⣤⣶⣤⣄⣀⣀⡀⠀⠘⢷⣭⡉⠉⢁⡠⠋⠀⠀⠀⢸⠀⢀⡇⠀⠀⠀⠀⠀⠙⡄⠀ ⠀⢿⠀⠀⠀⠀⠀⠀⢸⡀⣀⣀⣤⣸⣿⣦⣭⣭⣿⣿⣿⠂⠀⠀⠈⠉⠙⠛⠲⢤⡀⠀⠀⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠹⡆ ⠀⠈⢧⡀⠀⠀⠀⠀⠈⢿⡧⢿⣽⡀⠙⢿⣿⣿⡿⠟⠁⠰⣯⠇⣀⡀⠀⠀⠀⠀⠙⣦⢀⢏⡞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿ ⠀⠀⠈⠳⣄⠀⠀⠀⠀⠈⠻⠮⣷⣿⣄⣀⡘⡏⠀⠀⠀⣴⡦⠸⡯⠇⠀⠀⠀⠀⣠⣿⠏⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃ ⠀⠀⠀⠀⠈⠛⠶⠤⣄⣀⣀⡴⠋⢁⡽⠋⠙⠷⠤⠤⠤⠥⠗⠓⠒⡶⠤⠤⠖⠻⡍⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⣀⡼⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠁⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢠⡆⠀⠙⠶⣄⡀⢙⣲⣤⣤⣤⠴⠚⠉⠀⠀⠀ ⠀⠀⠀⠀⣠⣴⠖⠉⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⢸⠀⠀⠀⠀⢱⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣠⠴⢻⠏⠀⢀⡠⠤⠤⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠘⣇⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠁⠀⠈⣧⡼⠋⠀⠀⠀⠀⠙⠣⡀⠀⠀⠀⢀⡤⠖⠛⠛⠓⠦⣄⣰⠏⠀⠈⢷⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣄⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⡴⠋⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢻⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠓⠒⠒⠻⣆⠀⠀⠀⠀⠀⠀⠀⢹⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣤⠟⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⢸⣄⣧⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣸⣀⡤⠴⠞⠁⠀⠀⢈⢳⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⢤⣀⣀⣠⠞⠁⠘⣇⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⢸⣅⠀⠀⠀⠀⠀⠀⠀⣿⠀⢿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠤⠤⠤⠾⠥⠤⠤⠤⠤⠤⠒⠋⠛⠓⠒⠦⠤⠤⠤⣿⠤⠟⠀⠀⠀⠀

⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀ ⠀⢐⣯⠉⠙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠹⣿⣄ ⠀⠘⣇⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠈⢠⠃ ⠀⠀⣿⠀⠀⠀⠀⠀⠙⠦⣄⣠⣤⣤⣤⣀⣠⠟⠀⠀⠀⠀⠀⠀⣼⠀ ⠀⢠⠋⠀⠀⣀⠄⠒⠂⠄⠀⠀⠀⠀⠀⠠⠐⠒⣠⣄⣀⠀⠀⠀⣏⠀ ⠀⣧⣴⠖⠋⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣦⣸⠀ ⠀⡿⠁⠀⠀⢀⠤⠂⢉⡁⠀⠀⠀⠀⠀⢀⡁⠐⠠⢄⠀⠀⠀⠈⢿⠀ ⢸⡇⠀⢠⡞⠁⠀⣾⣧⣿⣆⠀⠀⢀⣸⣿⣼⣷⠀⠀⠑⢄⠀⣄⠸⡀ ⢸⣵⢡⠋⠀⠀⢀⡿⠋⠉⠀⣉⣉⣉⠁⠉⠙⠿⠀⠀⠀⠀⠣⣸⣿⠃ ⠀⢹⠏⠀⠀⠀⠉⠀⠀⠀⠘⢿⣿⠿⠃⠀⠀⠀⠀⠂⠀⠀⠀⢹⡇⠀ ⠀⢸⠀⡄⠀⠀⠀⠀⠀⠠⠀⠤⠶⠤⠀⠤⠀⠀⠀⠀⠆⠀⠀⣨⡇⠀ ⠀⠈⠷⣇⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⢀⡼⠛⠁⠀ ⠀⠀⠀⠈⢳⣸⣆⡸⡄⢠⠀⠤⠤⠤⠀⡆⠠⢃⡼⣿⠞⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠀⢩⠉⠀⠂⠀⠀⠀⠀⠀⠀⠘⡄⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡟⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⠶⠲⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣤⣤⡿⠀⠀⠀ ⠀⠀⠀⠀⢠⡞⡇⠀⠀⠑⢄⡐⢄⠀⢀⠊⠀⠀⠀⢸⠀⢹⡆⠀⠀⠀ ⠀⠀⠀⠀⢸⢃⣁⠀⠀⠀⠀⢁⠀⠀⡘⠀⠀⠀⠀⢸⢀⣠⡟⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠻⡄⠀⠀⢀⡼⠟⠛⢇⠀⢀⠀⢠⠧⠾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠓⠓⠓⠋⠀⠀⠀⠈⠓⠛⠚⠋⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠒⠒⠒⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⠒⠦⠈⠓⠢⢄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣠⡶⠋⣿⣟⠆⠀⣀⠔⠀⠀⠀⠘⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠧⠊⢱⠁⣀⡨⠥⠒⠈⡎⠀⠀⠀⠀⡆⠈⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡷⠊⢁⡀⠀⠀⡰⠁⣾⣷⠀⢀⠇⠀⠘⡆ ⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⣧⡀⢹⡿⠆⠀⡇⠀⠈⢁⣴⠏⠀⠀⠀⡕ ⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠐⢌⣦⣀⣀⣜⠤⠔⢺⡅⠇⠀⣠⠖⠋⠀ ⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡄⡜⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠻⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡏⠀⣇⠀⠀⠀⠀⡆⠀⢀⡄⠀⠀⢀⠻⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡆⠀⢸⠀⠀⠀⢰⣃⣀⣈⡄⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀ ⢠⠴⢒⣚⣉⣳⡀⡜⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⢸⣰⣁⠀⠀⠀⠀⠀ ⠘⠂⠀⠐⠃⣇⢹⠁⠀⠀⠀⢧⠀⠀⢠⠃⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠣⣀⠀⠀⣸⠓⠒⣏⠀⠀⠀⡰⠓⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡠⠤⠤⠤⠐⠒⠒⠢⠤⣄⡀⢠⠋⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⠁⠈⠑⢤⡀⠀⠀⣠⠤⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣦⠎⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀ ⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⡀⢉⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀ ⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀ ⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀ ⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠒⢷⡀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀ ⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⢳⡀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣶⣴⣾⡟⢦⣀⠀⣠⢿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠑⣦⠀⠀⠀⠀⣠⣿⣤⣤⣾⣿⡿⣇⠀⠀⠀⠀⠀⠀⠈⢹⠉⠻⣿⣿⣿⠃⣸⠈⠉⠁⠈⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢤⣀⠴⢏⠸⣿⣿⣿⡏⠀⡿⠀⠀⠀⠀⠀⠀⠀⠈⢳⣴⠿⠟⢋⡴⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⢆⡈⠻⠿⢷⡾⠃⠀⠀⢾⣻⣿⡇⠀⢢⠀⠈⠑⠚⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠒⠒⠋⠁⠀⠸⢄⣠⣽⣛⣦⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠉⡴⣿⠆⠀⠀⠀⠀⠀⢀⣀⡠⠔⠋⠀⠀⠀⠀⠀⠀⣀⠠⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣇⠀⣠⠛⠋⠉⠉⠉⠙⢯⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢰⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠉⠉⡽⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⡞⠀⠀⢠⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⠲⣄⠀⡇⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠰⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡴⠋⠁⠀⠈⠙⢦⡻⡇⠀⠀⡞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⣄⠀⡆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠙⢿⣀⡼⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡱⠂⠀⠀⠘⣄⠀⣠⠔⠒⠋⠐⠒⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢰⠁⠀⠀⠀⠀⠈⣟⠁⡔⠁⠀⠀⠀⠀⠀⣸⣶⠒⣲⢄⡀⠀⠀⠀⠈⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣆⣀⣀⣀⣀⠤⢿⣇⣧⠀⠀⠀⠀⠀⢠⡏⡇⢠⡇⠀⠉⠢⡀⢀⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠚⠉⠉⠙⠓⠒⠓⠒⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠒⠀⠐⠒⢆⠀⠀⢀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⣮⡁⠈⠙⠛⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡔⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢠⠄⠀⠀⠀⠑⡄⠀⠀⠀⠀⠼⢖⠎⡁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠸⠀⠀⠀⠀⠀⠐⢄⠀⢀⠔⠒⠂⠣⠕⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠇⠀⠀⠀⠀⠀⠀⠰⡾⠉⠒⣲⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠥⠀⠀⠀⠳⡂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣀⡀⠀⠀⢀⡔⠀⠀⠀⠀⠀⣡⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠁⠒⠊⠀⠀⠀⠀⠢⠀⠼⠐⠂⢄⠀ ⠀⡐⢸⠁⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢆ ⢰⠅⠘⣄⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⢀⡤⠄⠀⢸ ⠘⡁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠐⣲⡎⢱⡁⢀⠀⡸ ⠀⠈⡆⠐⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⢨⠓⠚⠊⠀ ⠀⠀⢇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠄⠀⠀⢀⡠⠪⡠⣀⡠⠃⠀⠀⠀⠀ ⠀⠔⠚⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⡿⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⠀⠀⡎⠁⠀⠀⠀⣀⣀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠃⠀⠀⠰⡀⠀⠀⠀⢆⠀⠀⠀⠀⠀⢤⠒⣂⡩⠋⠛⠛⠭⠉⠁⠶⡂⣤ ⠀⢇⠀⠀⠀⢐⡄⠀⠀⠀⠉⠁⡰⡀⠀⠀⢫⠉⣠⣤⣶⣖⡦⡤⡤⠍⡩⠁ ⠀⠀⠉⠉⠉⠁⠈⠂⠀⠀⠀⠀⠛⠁⠀⠀⠀⠑⠒⠁⠁⠂⠉⠁⠀⠒⠁⠀

⡿⠛⠻⡉⠉⠛⠻⢷⣠⡀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣀⣀⣀⣉⠙⢿⡆⠀⠀⠀⠀ ⣿⠀⠀⠈⠢⠀⠀⠀⠈⠛⣦⣀⣀⣀⡤⠞⠛⠋⠉⢁⣤⣛⡁⠀⠀⢻⡄⠀⠀⠀ ⣿⠀⠀⠀⠀⢡⣀⠄⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢉⣉⣓⣾⣷⡀⠀⠀ ⢿⡄⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠥⠤⡀⠙⣷⡀⠀ ⠈⣷⡀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢱⠀⠀⠀⠀⠸⣷⠀ ⠀⣸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⢿⡆ ⡆⣿⠁⠀⠀⠀⢀⣠⣶⣯⣍⣽⣋⣉⣉⠀⠀⠀⠀⠀⠀⣠⣥⣤⡶⣶⠟⢻⣿⣇ ⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⡿⣹⠏⠙⣿⣷⣄⣠⣤⣾⣿⣿⡿⢰⠇⠀⣾⣿⡇ ⠹⣯⠈⠉⠉⠛⢻⣿⣿⣿⡿⢡⡟⠀⣰⣿⣿⠛⠛⠋⠹⣿⣿⠃⡿⠀⢸⣿⣿⣇ ⠀⣿⠀⠀⠀⠀⠘⣿⣿⣿⢣⡿⠁⢠⣿⣿⣇⠀⢀⣀⣤⣹⣿⣼⡇⣀⣿⡿⠈⣇ ⣼⠏⠀⡠⠔⠒⠊⠈⠛⠿⣿⣧⣤⣿⠿⢿⡄⠀⠘⣿⠿⠃⠈⠙⠛⠉⠁⠀⠀⢸ ⣷⣤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠔⠛⠒⠂⠀⠀⠀⠀⠀⠀⢀⣽ ⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠉ ⠀⠀⠉⠻⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠟⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⢛⡿⠓⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠄⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠹⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⠾⠛⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠛⠷⣶⣼⣿⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡾⠛⠉⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠉⠙⠛⢶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣧⠀⠀⠀⠀ ⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢿⡇⠀⠀⠀ ⠀⠀⠹⣿⡎⠀⠀⠀⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢻⡆⠀⠀⣆⣿⡇⠀⠀⠀ ⠀⠀⠀⣿⡀⠀⡀⠀⣿⠁⠀⢠⣾⣿⡿⠆⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠆⠀⠀⠀⢈⣿⠀⣄⣾⡿⠁⠀⠀⠀ ⠀⠀⠀⠘⣿⣧⣇⢀⣇⠀⠀⠘⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⠖⠀⠀⠀⢸⣿⣷⠿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠙⠻⣿⣆⡀⠀⠀⠉⠉⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣸⣿⠁⣀⣀⣀⠀⠀⠀⠀ ⠀⢀⣠⡶⠾⠛⠓⠶⣿⡟⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠋⠉⠛⠻⣦⡀⠀ ⢀⣾⠋⠀⠀⠀⠀⠀⠘⣿⣠⣄⡀⠀⠀⠀⠀⠛⠿⠟⠁⠀⠀⠀⠀⠀⡀⡀⠀⣴⣾⡏⠀⠀⠀⠀⠀⠈⣿⡄ ⢸⣯⠀⢠⠀⠀⢀⣄⣠⣿⠿⢿⣷⣤⣦⣀⣤⣤⣤⣤⣀⣀⣀⣼⣆⣼⣷⣿⡾⠿⢿⣧⣀⣦⠀⠀⣤⠀⣸⡧ ⠘⠿⣷⣾⣷⣤⠾⠿⠛⠁⠀⠀⠀⠁⠀⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠛⠻⠷⠾⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣦⣴⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠟⠛⠛⠋⠉⠉⠉⠉⠉⠉⠛⠛⠛⠿⢷⣦⣤⣀⡹⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣶⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⠟⠉⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠉⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣽⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⡏⣤⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⡀⠀⠀⢤⢠⣼⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⠁⠀⠀⠀⠀⣴⡾⠁⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠈⢻⣇⠀⠀⠈⣇⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠀⡀⣀⠀⢠⣿⠃⠀⠀⢀⣾⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡷⠀⠀⠀⠀⠀⢸⣿⠀⢠⣠⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⣷⣇⣽⠀⢈⡏⠀⠀⠀⠸⣿⣿⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⣤⠥⠀⠀⠀⠀⣿⣿⣧⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⠿⣿⣧⣾⣿⡄⠀⠀⠀⠙⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⢸⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡇⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣼⣿⣀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⣠⣶⣾⠿⠛⠛⠻⢷⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠋⠉⠉⠉⠛⢿⣦⡀⠀⠀ ⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠙⣿⡆⢀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⡟⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⠀ ⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣿⣷⣧⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢠⡾⣠⣇⣠⣿⣿⣿⡇⠀⢀⠀⠀⠀⢀⠀⠀⢹⣷⠀ ⣿⣷⡀⠀⣷⠀⠀⠀⣼⣦⣴⣿⠏⠙⠻⠿⣷⡿⠷⣶⣶⡾⠿⠿⠷⢶⣶⣦⣤⣾⣿⣷⣿⣿⠿⠿⠛⠛⠙⠻⣿⣤⣾⣇⠀⢀⣸⣇⣀⣼⣿⠃ ⠘⢿⣿⣾⣿⣷⣴⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠟⠛⠛⠁⠀

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡤⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠇⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀ Sit, Stay,'N Play ⢸⠀⠀⢸⠀⠀⢰⣶⡀⠀⠀⠀⢠⣶⡀⠀⠀⡇⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀ ⠈⢧⣀⢸⡄⠀⠀⠉⠀⠀⠀⠀⠀⠉⠀⠀⢠⡇⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠙⣇⠀⠂⠀⠀⢶⣶⣶⠀⠄⠀⠀⣾⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠞⠓⠤⣤⣀⣀⣠⣤⠴⠚⠉⠑⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⣀⣠⣀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠰⡇⠀⠈⠁⠀⠈⡧⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⢠⠖⡆ ⠀⠀⠀⠀⢸⠀⠀⠑⢦⡀⠀⣠⠞⠁⠀⢸⠀⠀⠀⠀⠀⠀⠈⣷⠞⠋⢠⠇ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠙⡞⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢹⢀⡴⠋⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠀⠀ ⠀⠀⠀⠀⢸⡀⠀⠀⠀⢠⣧⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⠦⠤⠴⠛⠈⠓⠤⠤⠞⠁⠉⠛⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠻⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣤⠶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣠⡾⠋⠁⣀⡀⠀⢻⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡿⠸⠀⠀⠉⠹⣷⣀⢀⣀⣶⣶⠿⠿⠿⠉⠉⠉⠉⠿⣿⠏⠀⢀⠎⠀⢱⠀⠸⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⢴⠒⠢⣀⠀⠙⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠑⢄⣀⡸⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠸⡀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣧⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀ ⠀⠀⠀⠀⢀⡾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀ ⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⢆⠀⠀⠀⢠⠋⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀ ⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣀⡸⠀⠀⠀⠀⠓⠤⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⡀⢀⡠⠄⣴⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣯⠉⠉⠁⠻⣿⠋⠁⠀⠘⣿⣿⡿⠈⠉⠐⠒⠤⣀⠀⠀⠀⠀⠘⣧ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⠻⠿⠟⠀⣤⣠⣼⠟⠷⣶⡶⠗⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀⣿ ⠀⠀⠀⣿⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣬⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⡗ ⠀⠀⠀⢹⣇⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⢦⣾⠁ ⠀⠀⠀⠀⢻⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⢻⡆ ⠀⠀⠀⣀⣦⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠀⠀⠀⠀⢸⡇ ⠀⢀⡾⠋⠉⠀⠈⠻⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⢀⡾⠁ ⢀⡿⠁⠀⠀⠀⠀⠀⢠⣿⠙⢛⡷⠶⠶⠀⠀⠆⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⣼⢃⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠁⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀ ⠀⢿⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀ ⠀⠈⠻⣦⣀⡀⠀⠀⢸⣧⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠛⠿⠟⠛⠻⣦⣀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⠶⠿⣦⣄⠀⠀⠀⠀⢨⣷⠴⠶⠶⠶⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠉⠉⠉⠙⠻⣷⠾⠿⠿⠛⠿⠿⢷⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣶⣦⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠈⠻⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢹⣷ ⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⣤⡄⠀⣿⠀⠀⢸⣿ ⠀⠀⠀⢀⣼⡟⣽⡇⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣤⣀⡀⣀⣤⣾⠟⠀⠀⠀⠘⠛⠀⠀⠀⣀⣀⡀⠿⠇⠀⣿⠀⠀⢸⣿ ⠀⠀⠀⣾⡏⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠻⠿⡟⡀⠀⠀⣿⣤⣴⣾⠟ ⢀⡄⠀⣿⠁⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⠿⠋⠀⢰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⣿⡇⠀⣰⣿⠀⠀⠀⠀ ⢸⣿⣶⣿⣦⠀⢻⣷⡀⠀⠀⠀⣠⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠙⠿⣶⣤⣄⡀⠀⠀⠀⠀⠙⢻⣿⣤⣾⠟⠁⠀⠀⠀⠀ ⢸⣿⠈⠉⠁⠀⠈⢿⣷⣤⣶⡿⠛⠉⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠉⠙⠻⠿⠿⠿⠿⠿⠛⠋⠉⣿⠀⠀⠀⠀⠀⠀ ⠈⢿⣷⣄⠀⠀⠀⣠⣿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠿⣷⣦⣰⣿⠋⠀⠀⠀⠀⠀⣶⣶⣤⣀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⡟⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⡄⢸⣧⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⣠⣿⢻⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡸⣿⡀⠀⠀⠀⠀⠈⣿⠀⠀⠀⣠⣾⣿⡅⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢻⣧⡀⠀⠀⠀⠀⣿⠀⣴⡿⠟⣿⣿⣷⡀⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⣤⣻⣷⣄⠀⠀⠀⣿⡦⣤⣶⣦⣤⣽⣿⠿⠿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣷⣦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣭⣭⣭⣿⡟⠻⣷⣦⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠙⠛⠛⠛⠛⠛⠉⠋⠉⠉⠁⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢦⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⣾⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⢿⣿⣾⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠆⠿⠟⠀⡀⠳⡈⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⣿⣿⣽⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣟⢻⣿⣇⠛⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡜⢠⢄⣀⣀⣿⣄⠈⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣉⣶⣿⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⣿⢿⡛⢴⣶⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⣈⣷⡿⣿⡿⠿⣦⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⣰⡿⢿⣿⣟⢛⣿⠒⠉⢁⠤⢌⠳⡄⠀⠀⠀⠀⠀⠻⢧⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣶⣟⣽⡉⠁⠀⡠⢟⡵⠂⠀⠀⠀⠀⠀⠀⠀⠀⡞⡖⠋⢢⠀⠈⣽⣿⠷⣾⡿⣇⠀⠀⠸⣀⡸⠀⡷⠀⠀⠀⠀⠀⢀⣾⣏⡉⣴⣟⠛⣆⠀⠀⠀⢰⡒⠢⢄⠀⠀ ⠀⠀⠀⢠⣾⣿⣿⠩⣙⢿⠷⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡙⠒⠋⣀⡠⠷⣿⣛⣿⣝⣻⡓⠢⠤⠠⠤⠚⠁⠀⠀⠀⠀⠀⠈⢿⣿⠷⢼⣟⣰⣿⣦⡀⠀⠀⢷⣆⡈⢣⠀ ⠀⠀⡄⣼⣿⣿⠓⠒⠋⢻⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡏⠈⡏⡏⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡆⠀⣇⡽⠿⣝⣿⡄⠀⢸⠘⢧⣸⠀ ⠀⢸⣧⠻⣿⣧⣄⣴⠆⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠤⣿⣷⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣧⠀⣿⠁⠀⠀⠻⣿⡆⢸⣄⠀⣿⠀ ⠀⢸⠸⣠⠋⠈⢻⢻⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣮⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⡿⡄⠀⠀⠀⢱⣽⣼⣿⣼⠃⠀ ⠀⠻⣷⡏⢀⣠⠟⣸⡇⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢀⣧⠿⠦⠄⠀⠈⣧⣶⡟⠁⠀⠀ ⠀⠀⠈⠻⠿⠬⠍⠹⠷⠴⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠉⠉⠉⠈⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠒⣾⣿⣿⡿⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀ ⠀⢀⡴⢢⡀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠘⠯⣒⠲⢴⣸⣻⣚⡿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀⠀⠀⠀⠀⠀⠘⣷⣤⠗⣀⢀⡀ ⢠⢏⣴⢶⡇⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣯⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠞⣿⣿⣿⣤⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢮⣶⣦⠧⣤⣤⣤⣄⡀⢰⠀⠙⢥⡤⠼⠃ ⢌⢸⣿⡸⣧⣴⡠⢤⢀⡤⣸⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⢾⣃⣀⠙⠛⠛⠛⣯⣓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⣇⣿⣙⣿⣭⣿⢻⡿⣏⡸⠉⠹⠛⠃⠀ ⠈⠛⢫⡤⣜⠉⣧⠃⡜⠙⣟⠛⢆⡝⠙⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠸⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⣿⣿⡁⠾⠉⣧⠘⣧⣽⠃⠀⡆⠀⠀⠀ ⠀⠀⠘⡄⠀⣱⡷⣶⢹⠉⠙⣧⣸⠃⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣶⣶⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠈⢻⣶⣿⠗⠛⢻⣷⣾⠁⠀⠀⠀ ⠀⠀⢠⡇⣼⡟⣾⠏⠸⡀⢰⠉⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡙⠋⠙⠋⢳⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡰⡾⣻⠟⢇⠀⣼⠉⡞⠀⠀⠀⠀ ⠀⠀⠈⢇⢣⢳⡹⡄⠀⠃⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⡳⠖⢲⣤⢳⡘⣆⢀⠔⠒⠲⢄⠀⠀⠀⠀⠀⠀⠀⠹⡄⣇⢳⢹⠀⢸⠀⣿⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠚⠃⠓⠛⠀⠳⠾⠷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢣⠀⢸⣽⣇⢳⠹⣧⣠⣶⣤⡈⢣⠀⠀⠀⠀⠀⠀⠀⠱⠼⠂⠳⠿⠈⠦⠿⠴⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⡄⣿⣿⣿⡄⢧⠹⣿⣏⣿⣿⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢻⢸⡁⡇⢣⡉⠳⡈⣇⠹⣿⣿⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠤⣄⠀⠀⣰⡄⠰⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠿⢼⣁⢗⣒⠉⢉⣧⠀⢀⣉⣋⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣞⡴⠛⢬⣧⡞⠉⢻⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⣿⣟⠻⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢣⠷⠤⠈⠀⡇⢰⢿⠻⣟⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣤⣤⣖⠒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟⠟⠉⠀⣈⡗⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡄⢀⣑⣄⠀⠀⢸⣸⠸⡄⢻⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡯⢢⡤⣹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⡁⢈⣻⠀⢀⣼⢷⠴⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣿⣿⠋⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣯⢿⣸⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠈⠒⠒⠚⠋⠁⠈⠣⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⡾⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣹⠃⠀⠀⠉⣶⣒⣲⡶⡀ ⠀⠀⠀⡗⢤⣀⠀⠀⣠⠶⢤⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠇⠀⡘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣠⡴⣿⡇⢰⠁⢱ ⠀⠀⢰⣷⡾⣿⣿⠋⠙⡷⣾⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢤⣄⢀⡟⠀⠑⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡆⢸⡁⠀⠸⠷⡏⢀⡎ ⠀⠀⠀⢻⠳⡌⢏⢣⡀⢀⢸⢘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿⠀⡧⠄⠀⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣇⣸⡛⠂⠀⣰⠟⠋⠀ ⠀⠀⠀⠈⠉⠁⠈⠉⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠘⠓⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

ฅ՞•ﻌ•՞ฅ

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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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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠿⠿⠛⠉⠁⠀⠈⠙⠻⡿⠷⢦⣄⣀⡀⠀⣀⣀⣀⡀⠀ ⠀⣀⣤⣴⠶⠾⠛⠉⠀⣠⡄⣀⠀⠀⠀⠀⠀⠀⢀⡀⢦⡀⠈⠉⠉⠋⠉⠉⠉⢻⡆ ⢸⡏⠀⠀⠀⠀⠀⢀⣰⣿⢼⣿⠇⠀⣤⣤⡄⠀⢿⠷⢈⣿⣦⣀⠀⠀⠀⠀⠀⣸⡇ ⠈⢿⣤⣀⣠⣤⡶⠟⠛⢷⣶⣷⣄⠀⠹⡿⠁⢀⣳⣦⣴⡟⠈⠙⠛⠶⠶⠶⠟⠋⠀ ⠀⠀⠀⠉⠉⠀⠀⢀⣠⣤⣿⣦⠛⠉⠛⠛⠛⠙⠋⣽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡿⣿⣇⣽⡇⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢷⣌⣙⣿⣧⢀⡀⠀⠀⠀⣀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠹⣿⡟⠛⠛⠻⣿⡿⠁⠀⠀⠀⠀⠀⠀ IT'S KINDA WEIRD⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣼⣶⣴⡄⠀⠀⢀⣀⣀⣤⣴⣤⣤⣶⣶⣤⣤⣤⣤⣤⣴⣀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⠋⠁⢀⠉⣡⣶⣿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣴⡿⠿⠅⠀⠀⠀⠀⠐⢿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢋⣦⣴⣶⣶⣿⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣛⣾⠟⠑⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠏⠁⠁⠀⠀⠀⠀⠉⠻⢿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠇⠀⠀⠀⢀⡆⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣴⡶⠟⠋⠁⠀⠀⠀⠀⠀⣠⣿⠇⡆⠀⠀⢀⣾⠾⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀⣿⠇⠄⠀⠀⠀⣿⢹⣰⣍⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⢸⡿⠀⠁⠀⠀⠀⢿⣉⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⡼⣷⡀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣮⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⣷⠀⡤⣄⣀⡀⠀⠉⠉⠁⠀⠀⠀⠀⢈⡆⠀⠠⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣿⢟⣿⠃⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣶⠄⠀⠀⠀⠀⠀⠀ ⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠃⣀⠈⡉⠹⡄⠀⠀⠀⠀⠀⠀⠈⠿⠶⠶⠟⠳⢶⣤⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠳⠾⠟⠃⠀⠀⠀⠀⠘⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢶⣤⡀⠀⠀⠀ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣤⠉⣀⣷⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡖⠒⠒⠒⢶⡤⡀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣤⠀ ⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡇⠸⡏⢷⣸⠇⢹⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷ ⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡏⠈⠻⠿⢶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢶⣾⣿⣥⣴⠟⢆⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⠀⠀⠀⠉⠻⠿⣶⣦⣤⣤⣤⣤⣤⣶⣶⣶⠟⠛⠀⠁⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠷⣶⣤⣤⣤⣤⣄⣀⣀⣀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⣤⣾⠇⠞⠻⣿⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⠿⠉⠈⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠻⠷⠿⢶⣶⣶⠶⢾⣿⣿⠛⠛⠉⠀⠀⠀⠀⠀⠈⢿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠤⢤⡀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⣄⣤⣿⣯⣥⣀⡂⠄⠀⠀⠀⠀⠀⠁⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣀⣼⠇⠀⠀⠀⠀⠀⡆⣿⡇⠀⠀⠀⢀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠞⠛⠉⠉⠉⠛⠛⢿⠦⣄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣤⣀⠀⠀⠀⠀⠀⣀⣠⣴⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⣷⣽⣷⣶⣶⡾⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠉⠒⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⡿⠋⠉⠻⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⢀⣦⣀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⡇⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⣆⣾⡟⠋⠿⠛⢶⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⣧⠀⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⢈⣿⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⢿⡆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⢸⡟⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣦⣬⣤⣤⣶⢄⣀⣴⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣌⣐⠀⠀⠀⠀⠀⣀⣤⡿⢁⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠛⠛⠛⠶⢶⣶⣦⣴⣤⣤⣴⣶⡾⠿⠿⠿⠾⣷⡶⣿⠟⠋⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠤⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣤⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢋⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠉⠓⠦⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡄⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀ ⠀⠀⣠⠞⠁⠀⠀⣀⣠⣏⡀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⡃⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆ ⢀⡞⠁⠀⣠⠶⠛⠉⠉⠉⠙⢦⡸⣿⡿⠀⠀⠀⡄⢀⣀⣀⡶⠀⠀⠀⢀⡄⣀⠀⣢⠟⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃ ⡞⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⢳⢀⣠⠀⠀⠀⠉⠉⠀⠀⣀⠀⠀⠀⢀⣠⡴⠞⠁⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⣀⣤⠞⠁⠀ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠁⠀⢀⣀⣀⡴⠋⢻⡉⠙⠾⡟⢿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠀⠀⠀⠀🦋🩵 ⠘⣦⡀⠀⠀⠀⠀⠀⠀⣀⣤⠞⢉⣹⣯⣍⣿⠉⠟⠀⠀⣸⠳⣄⡀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠒⠒⠒⠒⠚⠋⠁⠀⡴⠋⢀⡀⢠⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⡾⠋⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠉⠋⠻⣄⠀⠀⠀⠀⠀⣀⣠⣴⠞⠋⠳⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⢤⠤⠶⠋⠙⠳⣆⣀⣈⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢰⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⡟⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣟⡿⠭⡉⠻⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆ ⣸⣿⣿⢿⣿⡿⠿⠿⢟⠿⠿⡷⠹⣿⣿⠉⠻⠟⠛⠛⠛⠻⠿⠿⠿⣷⣴⣄⣈⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⣟⣿⣿⣟⣻⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠃⣠⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏ ⢻⣿⣿⣿⡟⠉⠀⢰⣿⣯⣵⣮⣭⣻⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣶⡄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣼⣿⣿⣿⣷⠀⠀⠸⠿⠿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⣿⣭⣽⣿⣿⣿⡆⠙⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⡏⠛⠛⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠻⠰⢿⠛⢿⣿⣿⣿⣿⣿⣿ ⡇⠈⠳⣦⣄⡂⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠛⠛⠊⠛⠋⣹ ⣧⣤⣤⣤⣭⣿⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣦⣀⣠⣿ ⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟ ⢸⣿⣿⣿⡇⠀⠀⠀⠠⡐⢪⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢟⠃⠀⠀⠀⠀⠀⠀⢀⠀⢀⣴⣾⣿⣿⣿⣿⡇ ⣼⣿⣿⣿⣷⠀⠀⠀⡠⢒⡧⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣇⢄⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣷⣤⡿⠟⣩⣾⡿⣗⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣮⣑⢦⢄⠫⡆⠀⠀⣠⣷⣦⢀⣼⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⡿⠻⡙⢾⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡙⠢⡄⢀⢄⣼⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⠏⠀⠃⠀⠈⣟⣿⢻⠀⢰⡿⠉⢹⡟⠉⢻⡿⠛⠻⣿⠿⢻⣿⠃⠘⣿⢹⣿⡿⡄⠈⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇ ⡏⠁⢩⠏⠀⠀⠀⠀⠀⠁⠩⢤⣷⣾⡀⢰⠟⢣⣀⣼⣇⡀⣸⢿⠀⠘⢻⣆⣠⡏⢸⡟⡀⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣦⣼⣇⣠⣌⢉⣇⣀⣿⣥⣾⣿⣿⢳⠈⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⠿⠟⠛⠟⠛⠛⠻⠿⢿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⠏⠿⢁⣿⠉⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⢠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠇⢠⠴⣿⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸

⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣤⡀⣾⣿⣿⠀⣤⣤⡌⠁⠀⠀⠀⠀⠀⣠⠖⢦⡀⡔⠉⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⡇⠘⠛⠁⢸⣿⣿⠃⠀⠀⠀⠘⠆⠂⡇⠀⠀⠈⠃⠀⠀⡴⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣉⣤⣾⣿⣿⡆⠉⣴⣶⣶⠀⠀⠀⠀⠀⠀⠑⠢⡄⣀⠠⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⡀⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠛⠻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣄⣀⣶⣶⣦⣶⣴⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣱⣶⣿⣿⣿⠿⠿⠏⣿⡉⠉⠉⠹⠹⢿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠻⠋⠛⠁⢁⣤⣶⣾⣿⣿⠆⠀⠀⠀⣰⣴⣯⣿⣿⣷⣤⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠟⠁⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⠟⠁⠀⢠⣾⡿⠋⠉⠉⠉⠉⠉⠙⠛⠿⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⢀⣽⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠙⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠗⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣿⣴⣠⣤⣉⡀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⣤⣾⣿⠿⠿⠿⠿⠷⣷⣦⣄⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡅⠀⢽⡿⠏⠀⠀⠀⠀⠀⠀⠀⠉⢿⣧⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢽⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄ ⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣲⣿⡿⠋⠀⠀⣄⣼⣦⠀⠀⡾⡿⢿⣿⣿⣷⠀⠜⣿⣿⣿⣿⣿⣿⣿⣷⣉⣿⣿⣯ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣤⣿⡿⠋⠀⠀⠐⣻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⡟ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠇⠀⠀⠀⠀⣠⣶⣿⡿⣾⡿⠉⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⡿⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠁⠀⠀⠀⠀⢠⣿⡿⠋⠀⢴⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⡿⡿⢿⠟⠃⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⠃⠀⠀⠀⠀⠀ ⡁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡟⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣶⡀⠀⠀⠀⠀⠀⢀⣄⣦⣾⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣼⣿⠏⠁⠀⠀⠀⠀⠀⠀ ⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⣶⣾⣿⣿⣿⣿⠿⠉⠀⢸⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣷⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠋⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣷⣶⣤⣴⣤⣦⣶⣶⣶⣿⢾⣿⠿⡿⠟⠟⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡶⠶⠶⠶⠶⠶⣦⣤⣀⡀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢟⠛⠛⠛⠛⠻⠿⠦⠶⠶⠶⠾⠟⠛⠋⠉⠁⠀⠉⠙⢻⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠛⠉⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿ ⠀⠀⠀⠀⣀⣀⣤⣤⣶⠶⠟⠛⠉⠀⠀⠀⠀⠀⣠⠂⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇ ⠀⢀⣴⡾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢰⣿⣧⠀⠀⠀⡤⠤⠀⠈⢉⡇⠀⠀⠀⠏⢉⡴⣖⡶⢶⣿⡿⢶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⣀⣤⡿⠃⠀ ⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⢀⣀⣠⣛⠁⠀⠀⠀⠷⠴⠚⠒⠚⠁⠀⠀⠀⠀⠘⠹⠝⠚⣻⡿⠁⠀⠀⠈⠉⠙⠛⠛⠛⠟⠻⠟⠛⠛⠉⠀⠀⠀ ⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⢛⣷⣯⢏⡷⡯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢷⣄⣀⠀⠀⠀⠀⣀⣠⣴⣾⢟⣉⣀⣀⣙⢿⣶⣤⣤⣄⣀⣀⣠⣤⡤⠤⠤⠴⠶⠒⠛⠋⠋⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠛⠛⠛⠿⠛⠛⠋⢁⣴⠿⠋⠉⠉⠛⢿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⢀⡄⠀⠀⠹⣦⣤⣀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡀⠀⠀⢠⡿⠛⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠙⠲⠖⠋⠀⠀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠉⣽⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣀⣀⣀⣠⣴⣾⣿⠀⠀⣄⣀⡀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠉⠁⠀⠛⠛⠛⠛⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠙⢿⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠋⠉⠉⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿ ⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⠀⠀⠀⠀⣠⡶⠶⠷⢶⣤⣀⣴⠟⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣴⠾⠋⠀ ⠀⠀⢀⣤⡶⠾⠛⠛⠛⠉⠛⠛⠻⣶⣾⠋⠀⠀⠀⠀⠈⠉⠛⣶⣤⡶⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⡏⠠⡾⠃⠀⠀⠛⠷⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡄⠀ ⣼⠏⠀⠀⠀⣠⣴⠶⠾⠛⠛⠉⠉⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣀⠤⠤⣄⢰⠁⠀⣸⠀ ⠻⣦⣤⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣼⣿⣦⣴⡗⡆⠀⠀⣿⠇⠀⠀⢸⠁⠀⠀⠀⠁⠀⢀⠇⠀ ⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠙⠻⠁⠸⠟⠃⠀⠀⣿⡃⠀⠀⠀⠧⣄⡀⠀⠀⢠⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣠⣴⣶⣾⣿⢶⣦⠀⠙⠛⠷⣦⣄⠀⠀⠀⠉⠆⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⣿⣿⣿⣿⣿⣆⣿⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢶⡄⠀⠀⠉⠛⠋⠁⠀⢀⣾⠂⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣌⠻⣶⣤⣀⣀⣴⣤⣶⣿⣥⣤⣼⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠛⢻⣮⣭⣭⣥⣤⣿⠛⠉⠉⠉⠻⣷⡶⠶⠶⣦⡦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⡶⢶⠶⠶⠶⢿⣇⣰⣆⣴⣤⣽⠃⠀⠁⢹⣿⣼⣷⣼⠷⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠁⠈⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠒⠒⠒⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⢴⠟⢹⡘⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡞⠝⡉⢉⠤⣾⣿⠟⡀⡏⡔⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢱⣀⠀⠀⠀⠀⠀ ⠀⠀⣿⡑⣌⠄⢃⣾⣿⠏⡰⢀⡧⡅⠀⠀⠀⠀⠀⠀⡼⠄⠲⡱⡀⢰⣿⢦⣄⠀⠀ ⠀⠀⠹⣇⢿⡗⣸⣿⡿⡀⠔⠢⡄⡇⠀⠀⠀⠀⠀⡸⠐⣁⠣⠜⢨⢻⣿⣿⡮⣷⣄ ⠀⠀⠀⠸⣿⣧⡿⢰⣿⢩⣧⣶⣥⡃⠀⠀⠀⠀⢀⡟⠐⣠⠢⢕⡈⠾⣿⣿⣇⣼⣿ ⠀⠀⠀⠀⣿⡷⠃⣸⣩⣿⣿⣿⣿⣷⠀⠀⠀⠀⣾⣦⣯⣶⣿⣶⢼⠛⠉⣽⣿⡿⠃ ⠀⠀⠀⠀⠋⠁⠀⣾⢷⢹⣿⣿⡿⠋⠀⠀⠀⠀⣟⡆⣿⣿⣿⣿⣾⠀⠀⢷⡿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣾⠃⠈⠀⠀⠀⠀⠀⠀⠀⠈⢧⢿⣿⡿⠟⠃⠀⠀⠘⠧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡟⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⢀⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⠁⠘⢧⠀⠀⠀⣄⣤⣠⣀⠂⠀⠀⣠⡞⠫⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠘⣷⣔⠀⠘⣻⣟⠋⠀⢀⡼⠋⠀⠀⠘⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⢣⠈⠳⠓⡦⠶⢶⠲⡛⠁⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠜⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀ ⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀ ⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣇⠀⠀ ⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠌⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⡏⠀⠀ ⠀⠀⠀⡆⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⢠⣇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⡞⢸⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⡘⠀⢸⠀⠀⠀⠀⠰⢀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻⠀⠀ ⢰⠁⠀⢸⠀⠀⠀⠀⠀⠁⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠈⡆⠀ ⡏⠀⠀⢸⠰⠀⢀⠀⢐⠀⠼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡅⢠⠀⡀⠀⡆⢀⠀ ⡇⠀⠀⠘⣯⡀⢠⠀⢸⣤⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣸⠀⢱⠀⢹⡜⠀ ⡇⠀⠀⠀⠈⠑⠚⠄⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠼⠖⡎⠀⠀ ⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀ ⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀ ⢀⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀ ⠀⢇⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⣀⣦⣀⢀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀ ⠀⠈⠳⣀⠀⠀⠀⠙⣶⣄⣤⣢⠼⢵⣏⡛⡎⡦⠀⠀⠄⣀⣼⡽⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠢⠄⣀⠈⣿⢳⠈⢢⡀⢹⡝⠁⣁⢂⡠⠞⠋⡴⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⣌⢳⣤⠷⠋⢻⡽⠓⠉⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢸⠁⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⢠⠀⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣞⣼⣰⠞⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⢿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⡅⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣈⣈⠀⡀⣐⡺⠿⠂⠀⠀⠀⠀⠀

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

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⢀⣀⣀⠀⠀⣀⣀⣠⡤⠤⠤⠤⣄⣀⡀⠀⠀⠀⠀⠈⠱⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⣠⢾⡏⠁⠈⠹⢻⡅⠂⠀⠀⠀⠀⠈⠙⠒⠫⠿⠻⠭⡿⣶⣄⠀⠹⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⡼⢻⠋⠀⢀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⣰⠻⡄⠀⠀⠻⣼⣾⣧⡀⠈⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣠⠟⣵⠏⠀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢷⠀⠀⠀⠈⢷⡕⠙⢦⡀⠈⠛⢦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⢀⣠⠞⣡⠞⠁⠀⠀⣿⣿⠁⠀⠀⠀⣠⣤⣤⣄⡀⠀⢸⡇⠀⢸⡇⠀⣀⣀⡀⣿⡦⠸⢿⣶⣄⠀⠳⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣠⣶⠟⠁⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢠⣿⣿⣿⣿⣯⠻⡆⣾⠇⠀⠈⣿⣾⣿⣿⡟⣿⣿⡆⠀⠈⢼⡇⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣿⣿⣧⣽⠀⢹⣿⠀⠀⠀⢹⣿⣿⣷⣿⢸⡿⠃⠀⢀⣿⡇⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠛⢿⣿⣿⣿⡟⣀⡟⠁⠀⠀⠀⠈⠻⣿⣿⣧⣿⠃⠀⠀⢸⡟⠀⣠⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣤⣤⠽⠿⠓⠛⠉⠀⠀⣀⣤⣴⣶⣶⣶⣯⣽⣯⠀⠀⢀⡿⠁⢠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠙⢿⣿⣄⠀⠀⠀⠀⠀⠀⢸⣿⣷⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⣿⡇⢠⡞⠁⢠⠎⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢹⣿⣄⠀⠀⠀⠀⠀⣼⣿⡿⣇⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⡿⠟⠋⢀⣿⣵⠏⠀⣰⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠹⣿⡄⠀⠀⠀⣰⣿⠋⠛⠿⣎⠻⣷⢤⡀⠀⠀⠀⠀⢀⣀⡤⠞⠻⣄⢀⣾⠟⠁⢀⡜⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠹⣿⣦⣤⣴⡿⠃⠀⠀⠀⢈⡳⣭⣓⢯⣦⣤⡴⠚⠋⠉⢀⣠⣴⣻⡿⠋⠀⣠⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠉⢛⡿⠋⠀⠀⠀⠀⠀⣼⠃⠀⠉⠉⠉⠉⠉⠉⠉⢹⡏⠈⠉⠁⢀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⣰⡟⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⣴⣿⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⣤⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢀⣴⠟⣹⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⢀⡄⠀⢸⣿⡄⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⣴⡟⠁⠐⠟⣹⡟⠀⠀⠀⠀⠀⠀⠀⢀⡿⢸⡇⡆⠀⠀⠀⢀⣴⣿⠇⠀⢸⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⡾⡇⠀⠀⠀⠀⣹⠃⠀⠀⠀⠀⠀⢀⣰⠟⠁⢸⠁⠁⠀⠀⢶⡿⢿⠟⠀⢠⠞⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢀⡟⢁⡀⠀⠀⠀⢘⡟⠀⠀⢀⣠⠤⠖⠋⠁⠀⠀⣯⠤⠤⠶⣿⠋⢀⠏⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣾⣥⠾⠓⠛⠲⠾⣿⣇⠀⣴⠛⠁⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⣿⠀⠘⠀⠀⠀⠀⠀⣼⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡤⠋⠀⢸⠟⠁⠀⠀⠀⠀⠘⢾⣿⡾⣇⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⢀⡴⠛⡆⠀⠀⠀⠀⠀⢠⡇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠶⠊⠁⢀⣠⣴⡏⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⢹⡆⠀⠀⠀⠀⢠⡏⠀⠀⢀⡾⠁⠀⣇⠀⠀⠀⠀⠀⢸⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡴⠋⠀⣀⣤⣶⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠇⠀⠀⠀⠀⡿⠀⠀⢠⡾⠀⠀⠀⣿⠀⠂⠀⠀⠀⢸⡄⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢀⣤⣿⣿⣿⣿⠿⠿⠟⢻⡀⠀⢠⣤⣤⡀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢸⡁⠀⣠⠟⠀⠀⣀⣴⣻⡀⠀⠀⠀⠀⠐⠳⣄⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣇⠀⢸⡏⠀⠀⡄⠀⢀⡿⢚⠉⠉⠉⠉⢲⡀⠰⣿⠃⠀⠀⠀⠀⠈⠉⡻⣥⠀⠚⠉⠁⠀⠸⣖⣄⡀⠀⢠⠀⠀⣌⡇⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⡀⠈⠛⠒⠿⠂⢀⢇⠀⢸⣄⣏⠀⣸⠃⠀⠀⢁⣿⠟⣦⡀⠀⠀⠘⡆⢀⣷⠟⠒⠒⠒⠦⠤⠖⠛⠓⠻⠤⠼⠧⠞⠛⠁⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠳⠦⣄⣠⠴⠃⠘⣄⡀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣼⠟⠉⠙⠻⠶⣤⣤⣤⣤⡤⠤⢤⣄⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠁⠀⠉⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡾⠉⠙⣧⣀⠀⠀⠀⠀⠀⢀⡴⠁⢀⢤⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠃⠀⠀⢸⠛⠛⠛⠛⠛⠛⣿⡁⠐⢸⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⢀⡿⠧⢤⣄⣀⠀⠀⡘⣷⣤⡉⠀⠀⠛⠢⠴⠀⠀⢰⡳⠀⠀⠀⠀⠈⠙⠷⢤⣄⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⡏⠀⠀⣼⠃⣆⠀⠈⠉⠻⡟⠉⠉⢻⣿⡷⠦⣄⣀⠀⠀⠀⣔⠒⠢⢰⡆⠀⠀⠀⠀⠀⠀⠉⠙⢷⡆⠀ ⠀⠀⢀⣴⡧⢄⣰⠇⠀⢻⠀⠀⠀⠀⠙⢦⡀⢈⡏⠀⡠⠂⠈⠉⢳⡶⠖⠴⣶⡟⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢠⣿⠁⠀⣧⢹⠀⠀⣾⠀⠀⠀⠀⠀⠀⠙⠾⣧⣘⠧⠖⠂⠀⠘⡁⠠⢤⠈⡟⠀⠈⠛⠷⣦⣤⣀⣀⣀⣴⠿⢷ ⣴⠟⠹⣄⣰⣋⡞⢳⡀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠤⠴⡽⠶⠯⣴⣿⣀⠀⠀⠀⠀⣈⣽⠟⠋⠀⠀⣾ ⣯⠀⣠⣾⠙⡇⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣴⡾⠋⠀⠀⠀⠀⢰⡏ ⠙⠉⠉⢹⣆⢻⡀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠸⡉⣍⠙⠓⠒⠲⠤⢤⣄⣀⡀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⣼⠀ ⠀⠀⠀⠀⠙⠿⣧⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢷⡸⡆⠀⠀⠀⠀⠀⠀⠈⠹⡄⠀⠀⠀⠀⢰⡟⠛⠓⠲⠶⣴⡇⠀ ⠀⠀⠀⠀⠀⠀⠘⢷⣄⣠⡿⠙⠛⠛⠒⠶⠶⠾⣷⡹⡄⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠙⢦⡀⠀⠀⠘⢷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡹⣄⠀⠀⠀⠀⠀⠀⠀⠘⣿⠛⠛⠻⠶⠾⠻⣦⣄⠀⠘⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣜⢦⡀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠉⠻⠶⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣙⠦⣄⣀⠀⠀⠀⠀⠘⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣮⣭⣍⣛⣒⣒⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢛⣛⣋⣉⣁⣈⣉⣉⣛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢉⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⣁⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⠋⢀⣤⣶⡿⠛⢋⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣷⣄⡙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡟⠀⠐⢋⣿⣿⢁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⣷⣿⣿⣿⣶⣤⡈⠙⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡟⠀⣴⣿⣿⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢦⡀⠻⣿⣿⣿⣿⣿ ⣿⣿⣿⡟⢀⣾⣿⣿⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣷⣄⠀⢀⣭⣿⣿⣿⣿ ⣿⣿⣿⠁⣼⣿⣿⠋⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⢿⣿⣿⣿⣿ ⣿⣿⠃⣸⣿⣿⠋⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠘⣿⣿⣿⣿ ⣿⠇⢰⣿⣿⠏⠀⣸⣿⣿⡿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⣿⣿⣿ ⡟⢀⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⠀⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⡉⠉⠙⠻⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢿⣿⣿ ⠇⢸⠟⣿⣿⠀⢰⣿⣿⣿⣀⠂⠀⠀⢠⢛⣫⣭⣭⣭⣭⣍⡛⠻⢿⣿⡅⠘⠋⠀⠀⠀⢹⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿ ⡄⠀⠀⣿⣿⠀⠘⣿⣿⣿⣿⡷⢂⣴⣿⣿⡿⠋⠉⠙⠛⣿⣿⣿⣶⣍⠃⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⠃⢸⣿⣿ ⣿⣿⠀⠿⣿⠀⠀⢿⣿⣿⢏⣴⣿⣿⣿⣿⣧⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⣌⢲⣶⣾⣿⣿⣿⣿⢠⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⣄⣸⣿⣿ ⣿⣿⣆⡀⠸⣇⠀⠈⢿⣿⢸⣿⣿⣿⣟⠛⠿⠟⠀⠺⠿⣿⠿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⠀⠀⠸⣿⣿⣿⣿⣿⣿⠟⠃⢰⣿⣿⣿⣿ ⣿⣿⣿⣷⣤⣈⣉⣀⣀⠉⠢⠽⣿⣿⣿⣷⣶⣾⣿⣶⣤⣤⣴⣿⣿⣿⣿⣿⠇⣼⣿⣿⣿⣿⣿⡄⠷⠀⠙⣿⣿⡿⠿⠏⠀⢀⣾⡿⢿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢉⣾⣿⣿⣿⠿⠛⠋⠁⣠⡤⠄⠀⠉⠁⠈⣠⣴⣿⣿⡇⣀⠙⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⡔⢶⣦⣤⣀⣈⣉⡉⠉⠉⠛⠋⠉⠁⠉⢉⣉⣀⣤⣤⠶⠞⣉⣤⣶⣾⣿⣿⣷⣄⠙⢿⣿⠏⢀⣿⠀⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⡈⢀⣴⣿⣿⣿⣿⣷⣮⣭⣙⡛⢻⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⢁⣴⣿⡟⠀⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡞⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠈⣿⣿⡄⠀⣾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠿⠋⣠⣾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣯⣹⠀⢿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⠀⣴⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡦⡀⠻⣿⣿⣿⣿⣿⡇⠹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠹⠋⢠⣿⣿⣿⣿⣿⣿⡏⠀⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣷⣦⠀⡀⠉⠛⠿⣿⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⡀⢸⡟⢻⣿⡄⠻⡇⠀⣶⡤⠀⡼⢿⡿⣿⣿⣿⣿⣿⡿⠀⠀⢀⡿⢿⣿⠿⣿⡛⣁⠀⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠁⠻⠇⠿⠿⠗⠀⠁⢸⣿⡁⢸⠀⣿⠀⣿⣿⣿⣿⣿⠃⠀⠀⠘⠇⠿⠿⠀⠟⠃⠋⣠⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣤⣤⣬⣄⣈⣉⣡⣤⣤⣴⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⣤⡤⠤⠤⣤⢾⣋⡳⣤⣀⣀⣠⡤⠴⠶⠲⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⠽⣳⣿⠍⠀⠀⠀⠒⣌⣧⣿⣽⠟⠀⠈⠀⠀⠀⠀⠀⠈⡇ ⠀⠀⠀⠀⣀⣠⢶⢿⢿⣽⣾⣿⠀⢀⠀⠐⡠⠼⣿⣰⠘⣧⣀⣀⠀⠀⣀⣀⣤⠾⠁ ⢠⣶⠛⠉⠉⠀⠈⢹⢸⡛⣟⣿⠃⡘⢷⣻⡇⠀⠙⢚⣸⡟⠈⠉⠉⠉⠉⠉⠀⠀⠀ ⠸⣏⠀⠤⠄⠀⣠⣴⠟⢷⣌⣉⣁⣽⣴⣿⢶⣶⢾⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠒⠒⠛⠙⠁⠀⢀⡀⣸⣿⣮⣿⠁⢸⡻⣮⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⣿⣿⣭⠿⠿⢀⠈⢉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣶⠤⠬⠤⢶⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⢀⡀⠀⢀⣠⣤⣤⣧⣻⣿⡿⣓⣶⣤⠖⠉⠉⠓⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠫⡿⠟⠋⠛⠛⠋⡩⠛⠛⠿⢿⣿⣿⣤⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠀⢴⡄⠀⠀⠉⠁⠒⠉⠈⠀⠀⠀⠀⠀⠀⠀⠙⠻⣯⠿⠿⢾⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠁⠀⠀⢀⡾⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣤⡴⠞⠛⠉⠀⠀⠀⠀⠀⢠⡿⠁⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠤⣍⠉⠉⠀⣤⣀⣤⡀⢀⠀⠀⠀⠶⠷⣦⠀⠀⠈⣧⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀ ⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⣷⡀⠀⠙⠀⠀⢀⣬⣿⣿⡿⣿⡁⠀⠀⠀⡀⠀⠠⢤⠀⣿⡀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀ ⠸⣆⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠂⠊⠛⠶⢦⣴⠾⣿⡚⠷⣼⣿⠟⣹⣦⣀⠀⠑⠀⠀⢀⣴⠟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣆⠀ ⠀⠙⠻⠶⠤⠴⠾⠛⠋⠀⠀⠀⠀⠀⠀⢀⣾⢁⣴⣟⠻⢦⡤⠼⢿⡏⠉⠻⣷⢶⣟⠛⣏⣁⡀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠛⠻⢟⣛⣛⣶⣾⢿⣄⠀⠘⠋⢿⡟⠋⠉⠛⢶⣌⠻⢦⣀⠀⠀⠀⠀⠀⢀⣴⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢠⣀⡀⠀⢉⣄⡀⠀⠈⠀⠀⠀⠘⣷⠀⢠⡄⠀⢹⡆⠀⠉⠛⠛⠲⠒⠚⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠾⠏⢻⣤⡟⠉⢻⣆⠀⠀⠀⠀⠀⣿⠛⠛⠁⠀⣼⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⢸⣿⠀⠀⠀⢹⡀⠀⠀⢀⣴⠿⢦⣤⣴⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠟⠻⠷⠶⠶⠿⠷⠾⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⢁⣀⡈⢁⢤⡤⡀⠑⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢏⡝⡴⡧⢪⡱⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠃⡷⠉⡺⡳⠁⠸⣸⠀⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⠒⠠⠔⢉⣀⡉⠢⠀⠀⢀⣀⣤⣴⣶⣾⢅⠳⢌⣸⣷⣥⠣⢌⣱⣿⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠸⡃⢡⠇⠓⠀⠠⢰⡹⠀⢟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣀⢮⠵⡢⡰⡛⠙⣡⠈⣣⣶⣿⣿⣿⣿⣿⣿⠌⣶⣿⠽⣗⣻⠿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡣⣀⠳⡀⢈⠀⠀⡧⡠⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠈⡼⡀⢈⠋⠀⠄⢹⠀⣿⣿⣿⣿⣿⣿⣿⣿⢼⣡⣛⣿⢟⡻⢽⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣵⡥⠦⠔⢁⠀⠶⡁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠇⠘⢢⠀⢠⣄⢢⠃⢴⣿⣿⣿⣿⣿⣿⣿⣿⢖⣳⣬⣟⣼⡱⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠣⠅⢀⣇⣴⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠠⠤⡀⠛⠛⠀⠄⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⠌⠒⣀⡾⠧⣈⣀⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣳⣿⣿⣿⣿⣿⣽⣿⣿⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠃⡉⠑⢄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣷⣿⣾⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠐⠌⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡔⣒⡰⠏⢉⠰⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⠛⢃⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⣠⢊⢅⡽⠎⢣⠀⡴⢃⠀⠙⢿⣿⣿⣿⣿⣿⣳⢯⣿⡿⣽⢯⡷⣿⣿⣻⣏⣿⣿⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣾⣽⣿⡿⠿⠋⢀⢤⡀⠛⠄ ⡎⢼⣨⡁⠶⢡⡓⣧⡀⠂⡏⠀⡶⡄⠱⡀⢸⣿⣿⣿⣿⣷⣿⣿⢼⣿⣯⣿⣽⣿⣿⣽⣿⠸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⢤⡳⢁⠋⡄⠘ ⡇⡾⡀⠙⠶⣦⢡⠜⢿⣦⠘⠩⢀⢹⠀⣇⣾⣿⣿⣿⣿⡿⠏⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⠃⢀⠂⠅⠠ ⠱⡘⢕⠄⢊⠇⢻⣶⢶⡿⢃⢁⡪⠞⡀⢰⣿⣿⣿⣿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣇⣪⣭⣵⣬⣽⣿⠿⠚⢽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣄⢰⡀⢀⠃⢰ ⠀⠘⢢⠹⡀⢘⢪⢻⣿⣿⣴⠃⢀⠤⣌⣿⣿⣿⣿⣟⠀⢠⣀⣀⣐⣂⠹⣿⣿⣿⣿⣿⣿⣿⣏⠁⣼⣿⢿⣿⡿⢶⡤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢢⠀⠉⠈⢁⡠⠃ ⠀⠀⠀⢑⠬⢉⡼⣀⣠⡟⢠⠫⢇⢹⣾⣿⣿⣿⣿⣿⣄⠙⠻⠟⠛⠋⠁⠈⠻⣿⣿⣿⣿⣛⠛⠁⣿⣆⣄⣿⡇⠘⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢪⠀⠣⠁⢸⠃⠀ ⠀⠀⡰⢁⣴⣯⡿⠋⢍⡤⠒⢒⠦⡈⠛⣿⣿⣟⣿⣿⠋⠁⠀⠀⠀⠀⠈⠄⠀⠈⠙⠛⠛⠿⠛⠂⠉⠈⠚⠛⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⠒⠁⠀⠀ ⠀⠀⠧⠸⣻⣿⠡⢬⠇⢫⡲⡀⢳⡘⣍⡘⢋⣾⣿⣿⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⢤⣀⠀ ⠀⠀⠈⡇⢿⣿⣷⣾⣿⡔⡡⡗⠘⢣⢇⣘⡼⡅⢿⣿⣦⡀⠀⠀⠀⠀⠀⢻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡀⣹⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠿⣿⣿⡿⣿⣻⠗⠊⠀ ⠀⠀⠀⢡⡘⢿⣽⢾⣽⣧⠰⣉⢍⠓⡜⢌⣋⠗⠀⠻⡄⠽⠦⣠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⢘⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⠆⢩⣿⣾⣟⠿⣽⣧⣽⣿⣆⢼⣢⣿⡠⢔⡲⠦⣿⣿⣶⣦⣤⣤⣄⣀⣀⣀⣠⣤⣤⣤⣶⣞⠋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣦⡝⢩⡍⢠⣽⡞⣷⣽⣾⣤⢣⣿⡞⠉⣴⣾⡍⡟⢻⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣎⠆⣶⢖⡤⣎⢃⠹⢳⠟⣛⠛⠛⢉⣠⢾⠉⠧⡸⡑⢎⡭⢿⣿⢛⡟⠛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⠌⢫⢄⠌⠙⠀⢀⢿⠄⢀⠈⡏⠀⠀⣾⣦⣂⡉⢎⡚⣴⡧⣠⣭⠑⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢹⣄⠑⢤⢐⠈⠀⡉⡌⢀⣼⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠉⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢧⡈⠦⠝⠲⠘⢀⡿⠖⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢀⣴⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⠓⠊⠉⠀⠀⠀⠀⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⠿⠟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠉⠉⠉⠉⠁⠀⠉⠛⠿⠿⣿⠿⠿⠟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇ ⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿ ⠐⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇ ⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠟⠛⠉⠁⠀⠀⠈⣽⡻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀ ⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢿⣿⣦⣤⣶⣶⣶⣶⣶⣦⣤⣤⣀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣶⣶⣾⣿⠟⠁⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠿⠟⠉⠀⠀⠀⠀⠀⣶⣦⠼⣿⠷⣼⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠀⠀ ⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠃⠾⠛⠛⠉⠉⠉⠉⠉⠉⠛⢛⣿⣿⣷⣤⣾⣿⠿⠛⠋⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⡛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠋⠀⠀⠀ ⠀⠀⠘⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⣿⣿⡿⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡧⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣳⣿⣿⣶⣤⣤⣤⣤⣴⣾⣿⣿⠟⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⢿⣿⣶⣤⣤⣀⣀⣀⣠⣤⣤⣶⣾⣿⠿⠛⠁⠀⢹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢃⣀⣤⣴⣶⣿⣿⣿⣶⣤⣤⣤⣄⣀⣀⣀⣀⣤⣭⣿⣿⣿⠟⠉⠙⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠈⢉⣹⣿⡿⣿⣿⣯⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡿⠿⠟⠛⠋⠁⠀⠉⠙⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣶⣶⣶⣶⣾⣿⠿⠋⠀⠀⠙⠻⢿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠤⠤⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀ ⢠⠞⠁⠀⣀⣠⣤⠤⠤⠤⠤⢤⣤⠤⠤⠤⠤⣤⣀⣀⡀⠀⠀⠀⠑⢤⠀⠀⠀⠀ ⣣⠔⠚⠻⣄⣡⣞⣄⣠⣆⠀⢼⣼⣄⣀⣀⣠⣆⠜⡘⡻⠟⠙⣲⠦⣈⢳⡀⠀⠀ ⡇⠒⢲⡤⡜⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠤⣖⠬⠓⠂⠉⣿⠇⠀⠀ ⠙⠲⠦⠬⣧⡀⠀⠀⠀⠀⠀⣠⣿⣿⣷⡄⠀⠀⠀⠀⠀⣞⠀⢀⣲⠖⠋⠀⠀⠀ ⠀⠀⠀⠀⠘⣟⢢⠃⠀⠀⠀⠉⠙⠻⠛⠁⠀⠀⠀⢀⡜⠒⢋⡝⠁⢀⣀⣤⠂⠀ ⠀⠀⠀⠀⠀⡇⠷⠆⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⣠⠮⠤⠟⠉⠀⢰⠱⡾⣧⠀⠀ ⠀⠀⠀⠀⠀⠹⢄⣀⣀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⢠⣤⡀⣼⢾⠀⠀⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠒⡏⠀⡡⠣⢖⣯⠶⢄⣀⣿⡾⠋⢸⢀⡶⠿⠲⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣹⠃⣀⣤⠞⠋⠀⠉⠢⣿⣿⡄⠀⣿⠏⠀⠀⠐⢣ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢱⢡⡾⠋⠀⠀⢀⡐⣦⣀⠈⠻⣇⢸⢁⣤⡙⡆⠈⡏ ⠀⠀⠀⠀⠀⠀⣠⠎⢁⠔⡳⡟⠀⠐⠒⠒⠋⠀⠠⡯⠙⢧⡈⠻⣮⠯⣥⠧⠞⠁ ⠀⠀⠀⣀⠴⠋⠀⢶⠋⢸⡝⠀⠀⠀⠀⠀⠀⠀⠀⣸⢦⠀⠙⡆⠘⠦⢄⡀⠀⠀ ⠀⠀⣸⠅⢀⡤⢺⢸⠀⢸⡃⠤⠀⠀⠀⠀⣀⡤⢚⣋⣿⢄⡀⢇⡀⠀⠀⣝⡶⠀ ⠀⠀⢿⠀⡏⠀⠘⠞⠀⢸⡵⣦⠤⠤⠖⣿⠥⠞⠉⠀⢸⠖⠁⠀⠙⠢⣑⠶⣽⢂ ⠀⠀⠸⠤⠃⠀⠀⠀⠀⠀⠉⢳⠂⠈⡽⠁⠀⠀⠀⢀⡼⠒⠓⢤⠀⠀⠀⠙⠚⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡎⠀⠀⠀⠀⢠⠎⣠⠀⠀⠈⢳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡶⠗⠋⣱⠄⠀⠀⠀⣧⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠒⠦⣤⣷⠂⢀⡸⠁⠀⡼⠁⠀⠀⠀⠈⢺⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠋⢀⣀⡀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠙⠢⠤⠤⣄⡤⠼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⢦⣄⣉⣑⠢⠄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠃⠀⠀⠀⠀🇹🕯️

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣤⢾⠛⠳⠦⠞⣁⣰⣠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⣈⣷⣖⣠⠶⢯⣿⣿⣿⠇⠀⢀⣴⠒⡒⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⢲⠴⣤⡀⠀⠀⠀⠀⣠⣤⡤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⣿⣿⣡⣤⣤⣿⣿⡟⠀⠀⡿⠁⠀⠃⠀⠀⠀⠉⠛⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠁⣀⠴⠏⢠⢸⣧⠀⠀⠀⣼⡇⣀⣇⡈⠳⠤⠴⠲⢶⣄⠀ ⠀⠀⠀⠈⠙⠿⣿⣿⣿⡿⠋⠀⠀⠠⣧⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⠋⠁⠀⡈⢳⣶⣶⣿⣿⣿⡍⣀⠀⢘⠀⣸⣿⠀⠀⠀⢹⣷⡀⠉⠛⠒⠒⢲⣶⣾⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠠⣿⡷⠁⣴⡿⠿⣤⣤⣶⣬⣹⣧⣄⣈⣻⣿⣿⣉⣀⠀⣠⣶⠿⢷⣿⣿⣿⣿⠀⠀⠀⠀⢿⣿⣞⠁⠐⣻⢿⣿⣿⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣤⣤⣶⠾⠟⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⢷⣤⣶⡿⠿⠿⠇⢀⠀⠀⠀⠀⠻⣿⣷⣿⣿⠿⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⠊⠉⠁⠀⣀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠓⣄⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⢀⣤⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢀⡴⢣⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣠⡞⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⠁⣠⣟⢸⡇⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⢀⠀⣼⢠⡆⢠⠆⣰⢇⡀⠀⢀⣤⣤⡀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠀⣰⡟⣾⡿⠀⠀⠀⠀⠀⢠⣾⣯⣿⣧⠀⢠⡟⣾⢣⡿⢠⡟⢰⡏⣸⠇⠀⣾⣧⣿⣷⠀⠀⢆⠀⠀⣻⡄⠀⢠⡀⠈⠳⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠐⠋⠀⢀⣴⡟⡔⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⡿⠃⠀⠛⢰⢁⡞⡀⠛⢰⠏⣰⠏⠀⠀⠘⠿⣿⠿⠀⠀⠘⠀⠀⢙⣷⠀⠀⠃⠀⠀⠀⠙⢦⡀⠀⠀ ⠀⠀⠀⠀⠀⣴⣯⠍⠀⣿⡟⣇⢀⣴⠞⠋⣉⣓⠶⢤⣄⠀⠀⠀⢸⣾⠋⣁⣤⣁⠙⣻⡆⠀⠀⠀⣀⠀⠘⣉⣉⣹⣿⣶⣜⣿⠀⡀⠀⠀⠀⠀⠀⠀⠙⣆⠀ ⠀⠀⠀⠀⠀⠟⠈⢀⣼⠿⠀⢻⣟⢿⣿⣿⣿⣿⣿⣾⣿⢆⢄⠀⢀⣉⣉⢉⢀⠉⣉⣉⡠⠀⠀⠸⣿⣴⣾⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆ ⡇⠀⠀⠀⠀⠀⠠⠟⠁⠀⠀⠀⠻⣧⣈⣙⣿⣿⠿⢿⣭⣿⣌⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣷⣧⣬⡿⠿⠿⢿⣿⣷⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿ ⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣨⡿⠋⠁⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣯⣬⣽⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏ ⠀⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣇⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠀ ⠀⠀⠈⠛⠷⢤⣄⣀⣀⣠⡤⠶⠛⢻⣦⣄⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⠀⠀⠀⠀⠒⢒⣢⣾⠟⠳⠦⠤⠤⠤⠤⠶⠛⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣤⣄⣤⣤⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣤⣤⣤⣤⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⡇⠀⢀⡇⠀⢀⣉⠂⢴⣦⡤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣽⠃⠀⠀⢰⠀⠀⢸⠇⠀⠀⠀⠉⢰⢁⡌⠉⠂⠛⠋⠷⢦⣆⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀ ⣿⣻⡽⣯⢿⡽⣞⣷⣻⡽⣯⣿⠀⠀⠀⡞⠀⠀⢸⠀⠀⠀⠀⠀⠘⠂⠁⠀⠀⠀⠀⠀⠀⠀⠁⠉⠏⠀⠀⠀⢠⡤⣀⠀⠀⠀⠀⠀⠀⠀ ⣟⡳⠿⡽⢯⠿⠿⠺⠵⠻⢿⡇⠀⠀⡄⠇⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠛⠳⠶⡢⣄⣀⡀ ⠀⠄⢂⠐⠠⠀⠄⡐⠀⢂⢨⡇⠀⠀⣸⠂⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛ ⠐⡈⠄⡈⠄⡁⢂⠐⠈⠀⡾⠄⠐⣡⣴⣶⣛⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢐⢨⣕⣥⣀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⢁⢂⠐⣀⠒⠠⣈⠐⠡⡇⠀⣴⣿⣿⣿⣿⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠸⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢄⠣⢌⠒⡠⠌⢡⠠⢘⢰⡅⠀⣾⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⢃⠌⢢⠡⡘⠄⢢⠁⢾⠀⠀⢈⡝⠂⠀⠀⠀⠀⠀⣀⣠⣀⣄⠤⡤⠴⣤⡤⣀⠄⠀⠀⠀⠀⠀⠙⢻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢢⡉⢬⡁⢦⡑⢌⠢⡉⠞⠔⢂⠓⠀⠀⠀⠀⣀⣤⣾⣷⣧⢿⣞⣯⣟⡿⣿⣿⣯⣧⣀⠄⠀⠀⠀⠀⠈⠙⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢢⢍⡒⡘⡤⣘⢢⡑⢬⡫⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⡽⣿⣮⢷⣯⡟⣿⢫⡿⣟⣿⣻⣶⣄⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢣⢎⡴⢃⠖⣡⣦⣚⠁⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣻⣷⣯⣿⣶⣿⣯⣷⣿⣽⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣾⣶⣫⣾⣿⡿⠑⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣯⣽⣿⡇⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡟⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠠⠤⠠⠤ ⣿⣿⣿⣿⣿⠄⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠇⠰⢖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠐⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢄⠂⠸⣀⠀⣀⣀⣀ ⣿⣿⣿⣿⣶⢩⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⣳⡁⢿⣿⣿⣿⣿⣿ ⣿⣯⣿⣷⣿⣷⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢏⡵⢼⣾⣿⣿⣿⡿⣿ ⣿⣿⣿⣟⣿⣷⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣗⢮⣝⣾⣿⣽⡿⣿⣯⣿ ⣿⣿⣿⣾⣷⣟⣿⣾⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡿⣿⡿⣽⣿⢿⣯⣿ ⣿⣿⣿⣾⣿⣟⣿⣽⣿⣿⢏⡛⢟⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣟⣻⣭⣿⣾⣿⣿⡿⣟⡿⣿⣻⣿ ⢿⣷⣿⣿⡿⣿⣿⣾⣾⣿⠂⠈⡌⢜⢠⣱⡞⣼⣳⢯⣟⣿⣟⣿⣻⣟⡿⣻⣽⢫⡟⢧⠋⠔⠈⠀⠀⣿⣿⣿⣾⣿⣦⣿⣯⣿⡿⣿⣷⢿

⣿⣿⣿⣿⣿⣿⣿⣿⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⡿⣿⣽⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣾⣿⡿⢿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣿⣿⣧⣾⣻⣿⣭⣝⡹⣾⣿⣿⣿⣯⣙⣟⣿⡿⣿⢻⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣧⣟⣿⣿⣋⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣵⣾⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣾⣿⡿⣿⣿⣿⠿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣽⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⣿⣛⣽⣿⣻⣷⣿⣿⣿⣧⣹⣾⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣟⣺⣾⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣽⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣤⣄⡤⠀⠀⠀⠀⠀⠠⣼⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⣿⣿⣿ ⠟⢟⡿⣯⣿⣿⣿⣿⡿⣿⠿⣿⡿⡟⣿⣿⣿⡏⠀⢰⠊⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣴⣶⣴⣾⣏⠿⠿⠉⠙⡏⠀⠁⣙⠽⠚⠻⣿⡇⢀⢏⠄⠀⠠⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠻⣥⣖⢄⣲⣀⠪⠳⡉⠀⢠⣾⢀⣤⣌⣿⠀⣸⠂⠀⠀⠀⡁⠐⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡇⢂⣿⣿⣿⣿⣿⡿⣿⡟⣻⣿⣿⣿⣿ ⠁⢐⠋⠋⠁⠉⠈⠓⠀⠏⠳⠋⢺⠩⠞⢁⣟⣶⠁⠀⠀⠀⠸⢡⡄⢿⣷⡄⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⣿⠿⣭⣿⣾⣾⣯⢿⣿⣤⠽⢫⡽ ⠐⡂⠂⠀⢀⢤⣨⠵⣿⣦⡖⢚⡿⢋⣉⠟⣿⠃⠀⠀⠀⠀⠀⠏⠀⢸⣽⡇⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢰⣿⢾⡰⣅⡆⠘⣿⣿⣿⣏⡟⡓⡑⡎⠂⠠⣿⠵⠀ ⠠⣇⣀⠰⢞⢫⣅⠠⠋⢶⣧⣤⣶⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢄⠀⣀⠀⣠⣐⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣸⣹⠆⣹⠇⠀⠀⠹⣿⣿⣿⡯⡍⡿⣧⣭⢷⣧⡐⠉ ⠚⢿⡟⡐⠙⢏⠉⣅⣢⣻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣨⠅⣶⣇⢸⣟⣿⣮⣟⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣴⣇⢾⡼⠋⠀⠈⠀⣾⣿⣛⣹⣷⣞⣽⡘⢔⠩⢿⡇⠱ ⠁⢿⠿⣃⡐⠺⢆⣭⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠊⢹⡷⢫⠿⠿⠛⣉⣿⣿⣿⠉⡉⣉⡟⠀⠙⠟⠻⠧⢰⣾⣿⣿⣾⡷⠄⠀⠀⠰⣿⣵⠿⡭⣵⡟⡿⣷⣎⣷⣿⣇⢼ ⠕⣿⠀⣸⣧⣶⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠁⠀⠀⠀⠀⠛⠿⠹⡻⠀⠻⢿⠁⠀⠀⠀⠀⠀⠀⠘⢫⢿⣯⠀⠢⣄⣢⣿⣿⣿⣭⣿⣷⣿⣯⣧⣾⣿⣮⣬⢄ ⠀⢀⣾⣻⣿⣽⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢂⢲⣿⣿⣿⣝⡿⡿⣏⣩⣿⣠⣞⣿⣿⣿⣿⣿ ⠍⣽⣿⣿⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⢿⣥⣿⣿⣿⣿⣭⣷⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠂⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣻⣿⣟⣵⣿⣟⠛⣩⣽⣿⣿⣿ ⢻⣿⡿⠁⠀⠀⠀⠀⣠⣤⣤⣵⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄⠀⠀⠀⠀⠀⠈⣿⡛⢛⠛⠛⣶⣿⡟⣷⣾⣤⣶⠾⠏⢹ ⠾⡿⠁⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢔⣦⠄⠀⠀⠀⠀⢠⣜⣦⣹⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⢟⡳⣿⡶⡿⣿⣿⣾⢛⣹⣧⣼⠿ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣮⣿⣷⢤⡀⠀⢰⣔⣮⣿⣿⣣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⣿⣯⣿⣯⣹⣿⣿⣿⣻ ⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡠⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⣾⣟⣜⣿⣿⣿⣿⣿⣟⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⢿⣶⣞ ⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣾⣿⣿⣿⣿⣿⣿⣿⣿⠱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⣟⣿⣿⡟⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢆⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿ ⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣻⣿⣿⣿⣿⣿⣦⣽⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣄⢔⠂⠀⡀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⣿⣿⣿⡏⠿⣿⣿⣴⠉⢆⡾⢀⢑⡘⡀⡀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡂⠀⠀⠀⠀⠀⠀⠀⢘⠀⣡⣿⣿⣿⣿⢻⣿⣟⣿⣿⣽⣟⣘⣧⣧⣮⣳⣷⣿⣇⣙⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣭⣭⣟⣿⣿⣻⣿⣿⣿⣿⣿⢃⡿⣹⣯⡻⣮⣿⣿⣿⣿⣿⡟⠹⣿⣿⣿ ⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡩⣦⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⣀⢿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡀⢹⣿⣿ ⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡈⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣟⣻⡿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣇⠀⣀⠀⢀⡤⢁⣴⡃⣾⢳⢿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣽⣷⣾⣯⣿⣿⣿⣿⠿⣿⡟⣫⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣿⣿⣿⣿⢿⡟⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣡⣽⣿⣿⣿⣿⣿⣿⣿⣾⣽⠿⣺⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣿⣿⣽⣿⣿⢿⣿⣿⣿⣿⣿⢟⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⣭⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀ ⠀⢀⡶⢛⡳⢄⡀⣀⡤⢖⣓⣿⣿⣿⣯⣿⣿⣿⣻⣿⣶⣦⣤⣠⡊⡌⣿⣦⣀⠀ ⣴⣿⡏⣏⣜⡸⣟⣽⣾⣿⣿⣿⣽⣿⣿⣶⣾⣿⣿⣿⣿⣾⣿⣻⣿⡆⢿⣿⣿⣶ ⣿⢿⡜⢴⣿⡿⠛⠋⠀⠀⠈⠿⠿⣿⣷⣾⣿⣫⡿⠋⠁⠀⠉⠛⢿⣧⣎⢻⣿⡿ ⠁⠣⢬⠋⠀⢠⣴⣾⣶⡄⠀⢹⡟⣂⢿⣿⣿⣬⠁⠀⢠⣶⣶⣶⣄⠀⠁⠨⠗⠁ ⠀⠀⣿⡀⠀⣿⣿⣍⣿⡿⠀⠠⠈⠁⠀⠀⠈⠙⠀⠀⢿⣿⣩⣿⣿⠀⢀⡇⠀⠀ ⠀⢸⣿⣷⠀⠈⠛⠛⠋⣁⡀⠀⠀⠀⠀⠀⠈⠀⠀⢠⡈⠛⠿⠟⠋⢠⣾⡽⡄⠀ ⠀⣼⣿⣿⣀⢄⣤⣴⣶⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣤⡀⠀⠀⣸⣿⣧⡇⠀ ⠀⢹⡿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣤⠻⣿⣿⠍⠀ ⣶⡆⣴⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢻⣿⣏⡼⠏⡀⠀ ⣿⠇⠻⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⣿⣿⢶⢁⡟⣶ ⣿⢦⠀⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⢯⠃⣼⣝⣞ ⣿⣇⢦⡀⠻⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡺⢋⣁⠞⣥⣿⣿ ⣿⣿⣮⡥⠈⢿⣿⣿⣿⢤⡀⠀⢀⢀⡤⣄⡀⢀⠀⣠⠴⠏⣠⢧⢚⣩⣾⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⢤⣠⢀⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠛⠯⣃⡤⣮⣼⣭⣷⣧⣠⣦⣥⣷⣶⣿⡳⣄⠀⠀⠀⢀⣤⠶⣋⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣿⣷⡿⠷⢿⠟⠻⢿⣿⣿⣾⣿⣾⣻⣿⣦⣵⣤⣾⣿⣶⣶⡾⣟⣿⣯⢣⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⡿⠋⠁⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣷⡻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣎⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⡿⣿⣿⣿⢿⢻⣻⣿⢿⣻⡜⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡧⣾⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡟⢿⣿⣿⣿⣷⣹⣽⣾⡟⣏⣯⣿⣿⣿⣷⢱⠀⠀ ⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡜⠑⢿⣿⣿⣥⣶⣶⣶⣦⣠⡄⠀⢠⡀⣠⣤⣤⣤⣤⣄⡉⢿⣿⣿⣿⣟⡏⣶⣿⣻⡾⡾⡻⣿⡾⣧⢧⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡎⣠⢲⣼⣿⠉⠀⣀⣈⡉⠉⠙⠇⠁⠸⡟⠛⠉⠋⠉⠉⠙⠿⣞⣿⣿⣿⣿⣻⣿⣟⣯⣧⣷⣻⣿⣿⣻⡌⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⡏⢸⣟⡏⣰⣿⣷⣶⣿⣦⠂⠀⠀⠀⢏⣴⣾⣿⡿⣶⣦⡀⠉⢻⣿⣿⣏⡟⣯⣿⢿⣽⡞⣟⣿⣟⣯⢿⡘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⣁⣠⣤⣦⣤⣴⣀⡀⠀⠻⣴⢿⠃⠁⠒⠾⠿⠛⠁⠀⠀⠀⠀⠀⠻⢯⡭⠭⠭⠭⠛⠀⠈⣿⣿⣻⣷⣻⣼⣿⣷⣿⣿⢶⢿⣽⡞⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢿⡿⠋⠉⠉⠉⠙⢿⣿⣿⣷⣤⡨⡞⠀⠀⠀⠀⠀⡴⠓⠀⠀⠀⠀⠱⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡗⣿⡿⣿⣿⣿⡿⡟⡿⢏⣧⢻⡸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⢿⣾⣿⡇⠀⠀⠀⢀⣼⠗⠷⢆⣀⣤⢦⣤⠟⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣻⣷⣻⣾⣏⣷⣿⡸⠘⡼⡎⡷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣭⠟⣁⢤⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠠⡾⠃⠀⠀⠀⢍⠓⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣏⡾⡎⣿⡟⣿⢿⣹⣟⣧⢇⣥⢻⡸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠘⠿⡶⣶⣿⢽⣷⣒⣒⣦⣄⣀⠀⠀⠀⠀⠀⢰⣿⣷⡟⣿⣵⣽⣽⢿⠿⡽⣎⢧⠛⡜⡎⡧ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⣓⣒⡯⣭⣂⣀⣸⠀⠀⠀⠀⣤⡀⠦⣀⠈⣿⣿⣿⣿⣧⠀⠀⠀⠈⠻⢟⣮⠀⢦⡤⠔⠊⠙⠣⠀⠀⠀⢀⣾⠥⢚⣿⣿⣿⣏⣉⠛⢷⣷⣽⡈⡆⢡⠼⡸ ⣀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠙⠻⢲⠟⣡⢖⣼⣥⣎⡀⠈⠀⠙⣿⣿⣿⣿⣿⣿⡷⣄⢢⠀⠀⠀⠉⠁⠛⠀⠀⠀⠀⢀⣠⡴⠟⠉⠀⣴⣿⣿⣿⣿⣿⣿⣧⡀⠈⠳⢯⣹⠈⡞⣣ ⢽⣿⣦⣄⡀⠀⠎⡀⠀⠀⠀⢐⢶⡚⠞⠁⣹⣇⠙⢿⣿⣭⣲⣶⣿⣿⣿⣿⣿⣿⡝⢻⣱⣧⡀⠀⠀⠀⠀⠀⠀⢀⣴⡿⡋⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡑⣠⠝⣳⠟⡞⠻ ⠀⠉⠛⢿⣿⡶⢠⢣⣴⣦⠴⠋⢿⣦⣄⣮⡌⢹⡆⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⡯⢹⣿⣿⠏⠛⢤⣄⣀⣀⣠⡴⢿⠟⠞⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⢯⣿⠗⠋⠁⠀⠻⣦⡀⢀ ⠀⠀⠀⠀⣼⠃⠀⣿⠟⠁⠀⠀⢀⠹⠛⠻⠿⠞⠇⠀⠀⠀⠀⣸⣿⣿⣿⣿⡛⣧⣿⣷⣝⢾⡙⢅⡔⠊⢉⢉⡼⠃⠀⠀⣄⠀⢀⣄⣹⣿⣿⣿⣧⣿⣼⡿⡃⡄⣂⠌⣆⠀⠀⠉⠉ ⠲⢄⣀⢰⢻⡀⢸⠿⠑⣿⣿⣾⣿⣶⣦⠀⠀⠀⢀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠢⢤⡴⠞⠉⢅⣠⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⡿⡯⣪⡮⠞⠛⠩⠁⡀⠀⠀⠄ ⠀⠰⠖⣫⣿⣇⠎⢮⡷⣷⣦⣨⠟⠻⢿⢟⣦⣤⡿⠂⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠂⣘⡥⠶⡞⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⢻⣩⠋⠂⡀⠀⠀⠉⠛⠿⣷⣿⣿⣿⣟⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣯⣿⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⠟⡕⣼⣷⡀⠀⠃⣶⣦⣾⣤⣀⣌⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀ ⡤⢞⣷⣿⣿⣷⣄⣀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⣟⢽⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⢹⣿⣿⣿⣯⣁⣭⣿⣇⣹⣿⢯⣿⣿⣿⣯⢾⣿⣿⣿⣿⣿⡏⢻⣿⣿⡿⣞⡿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣽⣿⣛⣿⢿⣆⠀⠀⠀⠀⠀⠐⠀⠀⠀

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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠙⢻⣿⣿⡇⠀⠀⠀⠀⠀⠁⠉⠀⠈⠉⠉⠉⠉⠈⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣀⠀⣙⣿⣀⣀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠛⠛⠿⠟⠛⠉⠙⠛⠻⣷⠿⠾⠷⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠤⠤⡴⠠⢀⡀⠀⡀⠀⣤⣤⡀⠠⣧⣈⣧⣀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣠⣿⠀⠿⠟⠃⠀⠒⠻⠟⠋⠀⢻⡏⠀⠈⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢀⣀⣀⠀⠀⠀⠀⢬⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣄⠀⢸⣿⣿⣻⣄⣠⠶⣻⠟⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣘⣿⣿⠀⠀⠻⠿⠟⢉⡐⠚⠁⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛ ⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⠉⠻⠿⠿⠿⣷⣿⠿⠛⠿⠀⠀⢀⠀⢀⡀⣇⠀⠀⠀⢀⡀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⡈⣠⣞⣠⣧⠀⠀⠀⠀⢳⠀⢀⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣀⣠⣀⣤⣄⠀⠀⢀⡝⠉⠀⠀⠀⠀⠀⠀⠀⠸⣦⣞⡇⠀⠀⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠙⣿⣿⣉⣹⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢿⡇⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⠀⢮⣙⣙⠓⠶⣦⣄⠀⠀⣠⣀⣀⡴⠋⠘⡆⢻⣄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠂⠀⠀⠉⠙⢦⡙⠛⠻⠷⠋⠙⠉⠀⠀⠀⠻⣌⠻⢷⣄⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⡄⠉⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⡀⠠⠀⠀⠀⠀⠀⡀⢀⠀⠜⠂⠈⠀⠘⠒⠀⠀⠀⣤⠀⠐⡂⠐⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣠⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀ ⠀⠀⠀⠀⣀⡤⣤⠶⠛⠉⠉⠀⠀⠉⠉⠛⠲⣤⣤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢧⠀⠀⠀⠀ ⠀⠀⡼⢁⡆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢰⡈⢧⠀⠀⠀ ⢀⡞⠁⣸⠁⠀⢠⠬⠓⠀⣀⠀⠀⢀⠀⠛⠥⣄⠀⠀⡇⠈⢳⡀⠀ ⡞⠀⠀⠹⣆⢰⣒⠆⠀⠀⠓⠊⠙⠚⠁⠀⠸⠭⠇⣰⠇⠀⠀⢻⠀ ⣇⠀⠀⠀⠈⣹⠶⠦⠤⠤⣤⣤⣤⡤⠤⠤⠴⠶⣏⠁⠀⠀⠀⣸⠁ ⠈⠓⠲⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⠚⠁⠀

┌ ˏ ヘ レ - ՛ ❭ ~ ♡ˎˊ˗ / ⁻ ៸| ㄟ( ৲ ل ل ┚

⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠛⣿⣿⣆⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠘⣿⣿⠒⠒⠒⠂⠤⣾⣿⠏⠀⡇⠀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠨⠄⠠⠙⠁⠀⠀⠀⠀⠘⢿⠏⠀⠀⠃⢀⢿⡇⠀⠀⠀⠀⠀ ⠀⠰⠁⠀⠀⣾⣤⠀⠀⠀⣠⣠⡄⠐⠀⢈⠉⠪⡠⠁⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⣙⠟⠁⠀⠐⠿⠟⠀⠀⠀⠀⡄⠀⠐⠄⠀⠀⠀⠀⠀ ⠀⢁⠀⠀⠀⠉⠀⢀⣄⠀⠀⠋⠀⠀⠀⠀⠇⠀⠀⠈⣆⠀⠀⠀⠀ ⠀⠈⣄⠀⠀⠀⠀⠠⠜⠀⠀⠀⠀⠀⠀⡜⡇⠀⠀⠀⠘⣆⠀⠀⢀ ⠀⡔⢃⠑⠤⡀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠠⠁⠀⠀⢀⣴⣿⣷⡤⠊ ⢸⣧⡀⠀⢤⣐⠉⣉⡀⠀⢊⣁⣀⡠⠐⠁⢴⣿⣿⣿⣿⡿⠋⠀⠀ ⠈⠛⠛⠛⠛⠳⡀⢿⠁⢀⣼⣿⣆⣀⣀⣠⣼⣿⡿⠟⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠈⠉⠻⠿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢴⣶⣦⡷⣶⣶⢶⣴⣶⢖⣶⣶⢶⣶⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠎⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠁⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠁⠀⠀⡀⣀⣀⣠⡤⡄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⣁⣤⡖⠗⠋⠛⠃⠃⠙⠋⠋⠁⠘⠉⡋⠍⡓⢄⠀⠀⠀⡃⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢨⣷⡟⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢄⣂⠀⠀⠘⠽⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠈⢧⣀⣀⣀⣀⠀⠀⡇⡟⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠉⠉⠉⠡⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠉⠉⣯⡃⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣄⡀⠀⠀⠀⠀⠀⠀⠈⢄⡈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⡠⠤⡄⠀⠀⠀⠀⠀⠀⡗⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠦⡀⡇⠀⠈⠉⠉⠉⠉⠑⠲⢄⡀⡗⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠖⠉⠉⠉⠟⠁⠁⠉⠁⠀⠀⠀⠀⠀⠰⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢧⠀⠀⠀ ⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠦⠤⠤⠤⠤⠤⠤⣀⣀⡀⣀⡐⣲⠦⠖⠤⢴⡀⡠⡀⡠ ⠀⠀⠀⠀⠑⢗⢄⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠚⠉⠑⠒⠒⠓⠒⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢾⣷⣾⠉⠛⠻⢿⣿⡿⢿⣿⣿⣿⣿⣯⣠⣶⣴⣶⣶⣤⣤⣿⣷⣦⣤⣀⠀⠀ ⠀⠀⢠⣦⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⢿⣿⣶⣆⣢⣼⡿⠶⠚⠛⠛⠛⠻⠿⠿⣿⣮⣽⣿⠷⣿⣿⣿⣿⣿⣿⣿⡦ ⢀⣦⣈⡛⠋⠈⣽⣿⣿⣿⣿⣿⣿⡿⠉⠉⠙⣻⣿⣿⣿⣿⣿⣿⢿⣯⠿⠛⠋⠀⠀⡀⠤⣤⣀⣀⡀⠑⣫⣙⠿⣷⣮⣿⣿⣿⣿⣿⣿⡏ ⠘⣿⣿⣿⣿⠿⣓⣿⠛⠛⠛⠋⠉⠀⠀⣴⠞⠁⠀⠀⠈⠉⢁⡴⠋⠁⠀⢠⣠⣤⠿⠁⠀⢀⣿⣿⣿⣿⠈⠻⣷⣌⠻⣿⣿⣷⣿⣟⣿⣇ ⠀⠀⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⡴⠋⢉⣤⡴⠉⠀⢠⢼⣿⣿⣏⣁⡀⠀⢠⣿⣿⣿⣿⣿⣷⣆⢈⠻⣧⡘⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⢩⣠⡴⠋⠀⠀⠞⣿⣷⠇⠰⣾⣿⣿⣿⣿⣿⣿⣆⣾⣿⣿⣿⣿⣿⣿⣿⣯⡀⢻⡅⠘⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢸⡏⠀⠀⠠⠀⢰⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢶⣿⡄⢿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢀⡤⢶⡿⠃⠀⠀⠀⣼⠀⣠⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⠧⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠖⠋⣠⡞⠁⠀⠀⠀⣠⣧⠰⠁⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⢻⣿⣿⣿⣿⣿⣿⣿⣹⣦⡈⢻⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢠⣶⡟⠀⠀⠀⣷⠿⠛⣿⣆⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠁⠀⣀⡀⠀⠀⠻⣿⣿⣿⣿⣿⣾⣷⣾⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣾⣿⠈⠀⣼⠞⠁⠀⠀⣸⣿⣿⡄⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⠃⣴⣿⣿⣿⣿⣧⠀⠀⠈⠙⣿⣿⣿⡿⣾⡟⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠁⣷⢄⡼⠃⠀⠀⠀⠀⠐⣿⣿⣇⣠⠠⠞⢻⣿⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⠀⠀⢠⣼⣿⣿⣿⣓⣼⠇⠸⣝⣿⣿⣿ ⠀⠀⠀⠀⠀⢿⣾⡃⠀⠀⠀⠀⠀⠈⣿⠿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⠿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⠿⣯⣽⠏⠀⠀⠀⠑⢙⡟ ⠀⠀⠀⠀⠀⣸⣿⣷⠀⠀⠀⠀⠂⢰⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣽⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⣟⢻⣿⣆⠀⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⡿⢫⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⡟⣏⢘⠛⣿⣶⡀⢀⢀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣿⣿⣿⣿⠟⢃⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡾⠃⠂⣿⠀⠀⢹⣿⣿⣾⣿⣖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣾⠋⢁⣤⡟⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠋⠀⠀⠀⢹⣦⠀⠀⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠋⠛⣠⣴⣿⠷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠤⠸⣿⣷⠤⡀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣥⣤⣶⡿⠟⠉⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣤⣴⣾⣷⠼⠟⢿⣞⣳⠄⠴⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢋⣽⣥⢀⣠⣤⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠟⠋⠀⡀⠨⣿⣷⣖⣦⠈⡉⠛⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⢟⣓⢛⡿⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡇⠀⠀⠀⠀⠀⣿⣿⣷⢱⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⢆⡀⠀⣀⣠⠤⠤⠄⠤⠤⣄⣀⡠⠂⠀⢸⠀⠀⠀⠀⠀⣿⣿⣿⣜⣷⣏⡏⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⢑⠞⠁⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠁⠢⡀⠀⠀⠀⣿⣻⣿⣟⡿⡿⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀⠀⠀⢱⠀⠀⠀⠟⠿⠯⠿⠟⠙⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢆⠀⠸⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⠈⠃⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⡇⠂⠀⠀⠀⡹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠒⠁⠀⠀⠀⠀⠀⠀⠀⠺⠕⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⢻⠀⠀⠀⠀⡜⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡌⠈⣆⠀⠈⠛⢠⠠⠤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢆⣬⡀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⡗⠀⠀⢉⡉⠉⠀⠀⣀⠇⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠀⢐⠀⢀⠞⠏⠀⢳⡠⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠃⠀⠀⠀⠀⠈⠋⡉⠉⠀⠀⠀⠀⠀⠀⡕⠒⠂⠒⢖⡤⠤⡯⠧⠊⠀⣐⢢⡾⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⡇⠀⠀⠀⠰⠈⡄⠀⠀⠀⠀⢰⠑⠄⣀⣇⡬⣋⣀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣖⣖⠠⣘⡐⠑⢄⣈⣎⡖⠁⠀⣀⡤⠓⢋⡡⡊⢅⡒⢉⠋⠀⠀⠀⠀⠀⠀⡘⠠⠀⠀⠀⠀⠀ ⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠒⠒⠤⠒⠊⠙⠊⠉⠁⠀⠒⠁⢁⠔⠋⡠⠂⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⠐⠈⠀⠀⠀⠈⠀⠀⠀⣀⠀⠀⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠅⠁⠀⠀⠀⠀⠀⢀⠀⠀⠒⡀⠀⠈⠀⠀⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⣀⠀⢀⣀⠀⠀⠀⡀⡤⠔⠒⡒⠏⠑⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠉⠉⠉⠉⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⣿⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣸⠿⠿⠿⢿⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡜⠛⠀⡇⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⠛⠛⠛⠀⠀⠀⠀⠛⠛⢣⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠏⢇⣀⣀⡏⢾⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⠛⡌⢱⡈⠔⡰⢈⠞⣛⠻⢷⣦⣶⠀⣰⣶⣴⣦⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⣿⢍⠡⢎⠰⡥⢜⠬⡐⡡⢊⢄⠃⡎⠍⠭⣷⡯⠽⠉⣿⣇⣀⣀⣀⣀⣀⣀⣀⣸⣿⠉⠀⠀⠀⠀⢀⢀⣀⣿⣿⣷⣀⠀⠀⠀⠉⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⣿⠚⢲⢸⣵⣧⡜⠤⡑⡰⢉⠢⡑⢌⢊⡱⢄⠂⠀⠀⣿⡟⣛⢛⠻⣛⠛⡟⣛⢻⣿⡄⠤⠠⢤⣤⣼⣾⢟⡳⣜⠺⣟⣤⡄⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢈⣿⠀⠸⠸⢩⡿⡟⠰⣁⠖⡡⠣⢘⠢⣁⠲⣈⠓⣒⣼⡿⠷⡐⢊⠔⢢⠉⠴⣀⢋⡹⣿⢿⡿⣿⠯⠹⡍⢮⠱⢎⠳⣎⡿⣇⣀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⠃⠒⡌⢱⠠⠎⣴⣤⣮⡇⠴⡁⠦⡑⢼⣿⡇⢆⡑⢊⠜⡠⢍⠒⡌⠢⡔⢩⠒⡹⠘⣄⠣⡘⢄⠣⢌⠓⣌⠳⣍⢶⣤⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⣷⡆⠀⠀⢸⣿⣿⠴⡥⢮⢹⣿⡏⢆⠱⢂⣿⣿⢫⡕⢢⠘⡌⢢⠑⡌⠒⡌⠱⡈⢆⡑⢢⢉⡄⢣⠘⡄⠣⢌⠒⡌⢩⢜⡺⡝⣷⣶⣾⢿⠿⣖⢀⡀⡀⠀⠀ ⠀⠀⠀⠀⠀⣠⣤⠟⡿⣧⣤⣤⡜⡞⠛⠀⠀⠘⠒⠒⠚⠒⠓⣮⣿⢻⠙⢢⢁⠎⡰⢁⠎⡰⢉⠔⢣⠑⢢⠘⠤⠒⡌⢢⠑⡌⠱⣈⠒⡌⢅⠪⢱⠭⣿⡇⠀⠀⠀⠘⠛⠛⣣⡄⠀ ⣀⣰⣶⣶⣶⣏⣍⣒⣧⣿⣿⣛⣿⣷⣶⣶⣆⣀⣀⣀⣀⣰⣶⢯⢣⡓⠬⣁⡎⡔⡡⢎⡰⢡⠎⡘⢤⢉⡆⢍⠒⡡⠜⡠⢃⠬⡑⢄⠣⡘⠤⢩⠸⣍⣿⣿⣶⣶⣀⣀⣀⠀⠈⢹⣾ ⣿⣧⣼⣶⣶⣼⣾⠿⠿⠟⠼⡿⢿⡟⣼⠃⠟⠻⠛⠟⠻⠛⠘⡧⢃⡜⣰⠇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠷⢈⡒⢡⠊⡔⢡⠊⡔⢡⠊⢵⡸⡜⣿⡇⠈⠀⠛⠛⠻⣤⣥⣼⣿ ⣿⡏⠉⠉⠭⢭⣙⣤⣃⣎⣱⣩⣷⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣾⡅⢎⠰⡁⢎⠰⣁⠚⣬⢳⣍⣿⣷⢲⠀⠀⠀⠀⠉⠉⢹⣿ ⠛⢧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡜⠛⠛⣧⣤⣤⣤⣤⣤⣤⠛⠛⢻⣤⠀⢸⢣⠵⣌⢦⢣⣍⠻⣔⣻⣿⣯⣶⣭⣿⣤⡄⠀⠀⡀⢸⣿ ⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣷⣶⣶⣶⣶⣶⣶⣶⡏⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⣶⣾⣿⣚⣜⣎⣳⣼⣿⣾⡿⠉⠉⠉⠉⠉⠉⢹⣶⣶⣶⡞⠙

⠀⠀⠀⢿⣿⣿⣿⣻⣝⢮⣱⡅⠉⠀⠀⠀⠀⠀⠉⠛⠟⠉⠒⠀⠀⠀⠀⠀⠀⠀ ⠈⠄⠀⠘⣿⣿⣿⣿⣾⣷⢟⣠⡄⠀⠀⠀⠀⠀⠀⡀⠸⡔⠀⠀⠁⠀⠀⠀⠀⠀ ⠌⣠⢀⣀⣽⣿⣿⣿⣿⢋⣾⣿⡇⠁⠀⠀⠀⢸⣿⣷⡄⣧⠰⣄⠀⠁⠀⠀⠀⠀ ⠀⠀⠈⠉⠛⠿⣿⣹⡟⠀⡞⠈⢀⡄⠀⠀⠀⠀⠋⠉⠃⠄⢐⣿⠀⡰⡠⢆⡳⣌ ⠀⠀⠀⠀⠀⠀⠈⢯⠑⣦⢀⠒⣿⣿⣷⣯⣹⡆⠀⠀⠀⠀⠈⠁⣴⡯⣛⢬⠳⡌ ⠀⠀⠀⠠⠤⢐⠒⣈⢻⡿⠃⠀⠙⣿⣿⡿⠋⠀⠀⠀⠠⢠⣆⡾⠃⠁⠓⠊⠑⠀ ⡐⢆⠃⠇⢓⡈⣄⠢⠄⣘⠔⢀⡤⠼⠿⢄⡀⠀⠀⣨⠇⣎⣹⡐⠢⡐⠀⠀⠀⠀ ⡙⢤⠓⡬⢊⠔⢢⠓⡸⠷⣀⣴⣠⣀⡀⣀⡈⡡⣴⢡⠐⠨⢢⠑⡡⢂⠂⠀⠀⠀ ⣉⠚⡌⣆⡡⣆⢧⠔⠁⣷⣿⣿⠋⢹⣿⣿⣿⡶⠿⠙⠀⢘⡐⢣⠒⡈⠄⠀⠀⠀ ⡾⣹⣹⣶⢿⣾⡿⠀⢰⣿⡏⡉⠸⣶⣿⣿⣿⣿⡆⣿⡇⠀⠀⠇⠷⢀⠀⣀⠀⠀ ⣽⣳⣿⣾⣿⣿⠁⠀⢸⡟⡇⠻⢶⣌⣿⣿⣿⣿⣿⠀⠀⢰⠃⠘⡲⣈⣠⠐⡀⠀ ⣿⣿⣿⣿⣿⣷⣮⣤⣷⣿⣾⠷⠾⢿⡏⣿⣿⣿⣷⣆⣾⠋⢐⠀⣿⡱⣄⠮⣐⡡ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣭⣄⣨⣁⣸⣿⣿⣦⣿⡗⣙⠄⠐⣯⣷⣩⢞⣥⢲ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⡍⠻⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⡔⠛⠯⠽⣞⣮⢳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠻⣿⡿⠍⠁⠀⠀⠀⢀⣟⡱⣊⠖⡌⠜⠣ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⡋⠀⠀⠀⠀⢀⣴⡿⣜⡳⣭⠟⣬⢃⠍ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢀⠀⣀⣤⣿⣿⡿⣝⣳⢫⣝⢮⡍⡞ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢂⠀⠀⠹⣿⡿⢽⣾⡽⣛⢯⣟⠬⠗⡩⢧ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢡⠀⢂⠀⠁⣠⣿⣿⡿⢶⢻⡽⣾⢺⠹⡙⠜⢆

｡ﾟ☼ spread the word about palestine! check the facts! Upvote it and repost! ☼｡ﾟ---> From the sky to the group Isr@el is going down! From the river to the sea palestine will be free! ⩇⩇:⩇⩇ <--- doomsday will come at random, so support whats right before it happens. ١٥٧٤❤️🇵🇸 فِلَـٓسَـٓــِٰٓطٓـيَنَُ 𓂆🍉

⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⠷⡞⠛⢳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⣷⠾⣻⢷⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣷⠑⡆⢳⡆⠀⣿⠀⠀⠀⠀⠀⢭⢓⠿⠇⠀⠀⠀⠀⠀⣿⠀⢰⡟⠐⢃⡞⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢅⡹⡈⠿⡀⢹⡇⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⢹⠉⣀⠏⡽⢁⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠐⡜⠣⠬⠙⠦⢄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⠛⠶⡟⠐⠃⣞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣤⠛⠛⠛⠛⣤⣍⡏⠁⠀⠀⣀⣀⠈⢻⡄⠀⠀⠀⠀⢠⠟⠁⣀⣄⠀⠀⠈⣿⣩⣤⠛⠛⠛⠻⣤⣀⠀⠀⠀ ⠀⣠⡔⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠙⠛⠀⢨⣿⠀⠀⠀⠀⣞⡇⠀⠛⠃⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠹⢧⣀⠀ ⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡟⠀⠀⠀⠀⢣⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⣀⠀⣼⠇ ⠀⠻⢆⣴⣤⣤⣤⣯⣭⣵⣦⣤⣤⣼⣄⡸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣾⣧⣤⣴⣾⣿⣿⣿⣤⣤⣼⣤⡼⠛⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀

⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⣠⠴⣖⡶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣞⣯⣿⣽⣝⣓⡶⣫⡶⠛⠉⠙⣦⢹⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣸⡇⠀⢀⣬⣿⠛⢻⡷⢶⡄⠀⢹⣦⣵⣶⣶⣭⣝⡲⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⢹⡇⠀⠻⢧⣽⣷⣿⣧⣭⣥⣀⢸⣿⣿⣿⣿⣿⣿⣿⣌⢧⠀⠀⠀⠀⠀ ⠀⠀⠸⡜⣧⢠⡾⢋⣽⡟⠉⠻⣶⣈⠙⣿⣿⠋⠀⠈⢿⣿⣿⣿⢸⣆⠀⠀⠀⠀ ⠀⣠⡴⣿⣽⣿⣤⣾⣿⣧⣀⢀⣨⣿⣿⣿⣿⣄⡀⣀⣼⣿⣿⣿⣾⣿⣕⠢⡄⠀ ⣿⢯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⢦ ⡟⣿⣿⣿⡟⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠈⣿⣿⣿⣿⠘ ⣇⣿⣿⣿⣿⣤⣀⣤⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣤⣀⣴⣿⣿⣿⣿⢠ ⠙⢌⠻⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟⡣⠟ ⠀⠀⠙⢮⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡏⡵⠊⠀⠀ ⠀⠀⠀⠘⡾⣿⣿⣿⣿⣿⣧⣄⣀⣠⣤⣤⣄⣀⣠⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠳⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠮⣟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⠥⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠒⠫⠽⠭⢯⠒⡒⡒⡊⠉⠀⠀⠀⠀⠀⠀⠀⠀

·ᴥ·

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠛⢋⣽⣿⡟⢷⣥⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣶⣶⣾⣿⣟⠄⠀⣺⣿⣿⡋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡅⣼⣷⣤⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠘⣿⠟⢻⣷⢮⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠰⣿⣿⡿⣯⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣠⡿⠄⠀⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⠋⠀⣿⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢸⣿⣿⣯⣿⢿⣿⣿⣿⣿⣯⠒⠀⠀⣿⠁⠀⠀⢸⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⠏⠀⠀⢸⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠘⣿⣿⡫⠇⢸⠿⣿⣿⡿⠁⠀⢠⣾⢯⠲⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠀⠀⠀⠘⣿⡦⢀⠡⣾⢿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠘⣿⣥⢖⡉⢪⢏⠓⠀⢀⣬⣿⡏⠀⢀⢀⣰⣴⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠈⣶⣹⣯⣢⡐⠈⣢⣻⢿⣯⡌⢲⣠⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠘⢿⣝⣴⢁⣀⣆⡀⣽⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢹⡗⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣁⢀⣿⣷⣷⠞⠁⡠⢈⣉⢙⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣸⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡷⠋⠀⣾⡇⠀⠀⠈⢿⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣳⣇⣉⣙⣾⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡟⠀⠀⠀⡇⠀⠀⠀⠀⠘⣿⣿⣿⣿⡟⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⠏⠃⠀⠀⠀⡇⠀⠀⠀⠀⠐⠛⣿⣿⣿⣯⠹⡟⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣾⣿⣿⠃⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠄⢹⣹⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠛⢀⣀⣿⣿⣇⣀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣀⣀⢧⢻⣿⡷⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⡿⣛⣽⣿⣿⣿⣍⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢰⢟⣿⣿⣭⣝⡻⣿⣿⡇⠱⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠣⣴⣿⡏⣼⣿⣿⣿⣿⣿⣿⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡄⣿⣷⡄⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⡏⢰⣿⡟⢱⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠘⢙⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣹⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣧⣸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⢿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⡎⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠦⣿⣿⠀⢸⣿⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡿⠟⢿⣿⣿⣿⣿⣿⠃⠀⣸⣟⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⠘⣿⠀⠀⢻⣄⣼⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢧⣄⣼⣿⣿⣿⣿⡿⠂⣰⣿⢻⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠛⠛⠿⠟⠛⠋⣀⣠⠶⣲⣶⣶⡶⢶⣶⣶⣦⣤⣈⠻⠿⣿⣿⣿⡿⠄⠀⠀⠁⢸⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⡂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡿⢫⣿⣿⣿⣧⣶⣶⣦⣿⣿⣷⡞⣛⣶⡄⠀⠀⠀⠀⠀⠀⠀⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣴⣿⡆⠀⠀⠀⠀⠀⠀⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⣿⠀⠀⠀⠀⠀⢠⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡿⠟⠛⠛⠙⠻⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠂⠚⠛⠃⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⣠⣮⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⡆⠘⠙⠛⠶⠶⠤⠤⠶⠾⠛⠉⢰⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⠟⣟⣿⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⢻⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⡿⠟⠋⠀⠀⢸⡟⠀⠀⠉⠓⠠⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠈⠛⢿⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣻⠷⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢀⣠⣎⣀⣼⣷⣄⣀⠀⠀⠀⣀⣀⣒⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⣀⣀⣀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣄⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⣴⡀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⣿⣦⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⢾⣿⡇⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⢰⠋⠙⡆⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠞⠁⠈⠃⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀ ⠀⠀⠀⠒⠒⠒⡗⠢⠤⢀⠀⢀⣠⣤⣤⣀⠀⠀⢠⠀⠀⠙⢛⠋⠀⠀⢠⠀⠀⣤⣶⣶⣦⡀⠀⠀⠉⢹⠉⠉⠉⠉⠁ ⠀⠀⠀⣀⣀⣠⣧⣤⣄⣀⠀⣾⣿⣿⣿⣿⡆⠀⢸⡀⠀⠀⡾⣄⠀⢀⡜⠀⢸⣿⣿⣿⣿⣷⠀⠐⠒⣺⠒⠒⠒⠒⠄ ⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⠀⢻⣿⣿⣿⣿⠇⠀⠀⠑⠒⠊⠀⠈⠉⠉⠀⠀⠘⠿⣿⣿⡿⠃⠀⠉⢰⠗⠲⠦⢤⣀⠀ ⠀⠀⠀⠒⠚⠉⠉⢣⡀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⢿⡿⢿⠿⠿⣿⠛⣻⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠘⠒⠖⠳⠒⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢠⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⡀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣼⣷⠀⠀⠙⠒⠚⠛⠛⠛⠛⠛⠓⠒⠒⠦⠚⠀⢀⣴⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡠⠤⢴⡷⠤⢤⡤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⢾⣅⠙⢦⡀⠙⢦⡀⠙⢦⡈⠻⣕⢦⡀⠀⠀⠀⠀⠀⠀⣠⠴⢶⡋⠙⠫⣍⠙⢯⡉⠙⢯⡲⣄⠀⠀⠀⠀ ⠀⠀⠀⢸⡄⠙⢷⡀⠙⢦⡀⠙⢦⡀⠙⢦⡘⢧⣷⠚⠉⠉⠛⠒⣾⠉⠳⡄⠙⢦⡀⠈⠳⣄⠉⠢⣄⠙⢾⡄⠀⠀⠀ ⠀⠀⠀⠸⡝⢧⡀⠙⢦⡀⠙⢦⡀⠙⢦⡀⠙⢦⡝⠀⣠⣤⣤⠀⢹⠳⣄⠙⢦⡀⠉⠳⣄⠈⠑⢄⠈⠳⣼⠁⠀⠀⠀ ⠁⠒⠒⠦⠽⣄⠙⢦⡀⠙⢦⡀⠙⢷⣄⠙⣦⠞⠁⠀⠈⢻⠋⠀⠀⢣⡈⠳⣄⠙⢦⡀⠈⠳⣄⠀⠙⣶⣃⣀⣀⣀⣄ ⣀⣀⣀⣀⣀⣀⣻⡶⣿⣦⣤⣿⣦⣤⠿⠟⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠻⢦⣜⣷⣄⣻⣦⣀⣸⣷⠟⠃⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⢹⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉⠩⢼⠒⠒⠲⠤⠤⠤⠀ ⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢶⢿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⠝⢿⣿⣿⡿⠹⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣷⣬⡙⢿⣿⣿⣿⢻⣧⠀⠀⠀⠀⣼⣷⡀⠙⠟⢁⣼⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣦⣽⠻⣷⣾⣿⣠⣤⣤⣼⣿⣿⣿⣆⣠⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⠿⠿⠿⣿⡿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢼⣿⠀⢿⣿⣯⣿⣿⠀⣾⣷⠀⠀⢷⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣷⡀⠀⠀⠈⠋⢀⡿⢿⣿⣿⣿⡀⠙⠋⠀⢀⣾⣿⣿⠀⠀⠀⠀⠀⠀ ⢀⣀⣀⣀⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⠀⠀⠀⣈⣿⣷⣦⣤⣴⣿⣿⣿⣿⣤⠤⢤⣤⡄⠀ ⠈⠉⠉⢉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀⠀ ⠐⠚⠋⠉⢀⣬⡿⢿⣿⣿⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⣥⣀⡀⠈⠀⠈⠛⠀ ⠀⠀⠴⠚⠉⠀⠀⠀⠉⠛⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⡿⠛⠋⣁⣤⣄⣀⡉⠛⠢⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⡧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢰⡯⠋⠀⠈⢻⣿⣷⣎⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⠃⠀⠀⠀⢸⣿⣟⣿⣻⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢀⣧⣿⣿⣿⢿⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⢞⣿⣿⣟⢟⠇⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡤⣣⣿⣿⣿⣯⠃⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣛⡿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠛⠋⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⣤⠖⠛⠉⠉⠉⠉⠉⠙⠒⠦⣿⣏⣀⠀⠀⠀⠁ ⠀⠀⣠⠞⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⡄⠀⠀ ⠀⢰⣯⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⠀⠀ ⠀⠈⣇⢀⢠⠇⠀⣶⡶⠄⠀⠀⠀⢠⣶⡶⠀⠀⣸⣀⣼⠟⠀⠀ ⠀⠀⠙⠛⠾⡆⠀⠙⠛⠃⠀⠀⠀⠀⠙⠋⠀⠀⣹⠟⠁⠀⠀⠀ ⢀⡴⠚⠉⠛⢿⠀⠀⠀⠀⢿⣿⠆⠀⠀⠀⠀⢀⣿⠋⠉⠉⢳⡄ ⢾⡀⡄⠀⣄⡼⠻⢧⠤⣤⠤⠤⣤⣠⣦⣾⠶⠞⢿⣤⡄⣠⣀⡷ ⠈⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ Cute dog

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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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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢈⣩⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣴⣶⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⣤⠶⠚⠛⠉⠉⠉⠉⠛⠓⠶⣤⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣀⣀⣠⣤⠤⠶⠚⠋⠉⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠳⢦⣄⣀⣀⣀⣠⣤⣤⣀⡀⠀ ⢠⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠈⢷⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠙⣦ ⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⣿⡿⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⠈⢷⣀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠹⣶⣟⣙⣲⠀⠀⠀⠀⣓⡯⣽⣚⡀⠀⠀⢰⣟⢋⣻⡾⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟ ⠀⠀⠉⠛⠲⠶⠶⠶⠚⡏⢹⡃⠀⠀⠈⠻⠿⢥⣤⣀⣤⣮⡻⠷⣾⠿⣻⣄⣠⣤⡼⠟⠋⠀⠀⠀⣶⢹⡟⠓⠶⠶⠶⠶⠖⠛⠉⠀ ⠀⠀⠀⠀⢀⣤⠶⠒⠒⢧⡈⠳⢦⣄⣀⠀⠀⠀⡾⠙⠳⣌⣛⠛⠒⠚⣻⡿⠘⣏⣙⢧⣀⣠⡴⠞⠁⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡟⠁⣠⠖⠛⡶⠇⠀⠀⠈⠉⠛⠛⠺⠷⠷⠦⢟⣙⡛⢙⣛⡽⣤⠿⠛⠛⠋⠉⡤⠄⠔⠐⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⢠⡏⠀⠀⣷⡔⠂⠀⠢⠤⣀⠀⠀⠀⣀⡀⣀⣀⢭⣉⣀⡀⣀⡀⢀⡀⠀⠀⣆⠀⠀⠀⡸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣇⠈⣧⠀⠀⢻⡱⠀⡀⣴⣶⣹⣾⣿⡟⠿⡷⠿⠿⠸⠿⠿⢟⠿⠟⠿⢿⣿⢾⣯⡿⠀⠊⢰⡇⠀⠀⠀⠀⠀⣴⣶⣄⡀ ⠀⠀⠀⠀⠙⢦⡈⠳⣤⡘⣇⠈⠐⠋⠉⠁⠀⠀⠀⠀⠀⠹⠄⠀⠠⠀⠘⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⡾⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠙⣷⣬⣙⠻⣆⡀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠔⢢⠀⢀⡼⠛⠲⣤⡀⠀⠀⠀⠈⠉⠉⠀ ⠀⠀⢀⠀⠀⣠⠞⠁⣴⢉⣽⣮⣷⡀⠀⢅⡀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⢅⡀⠀⠀⠀⡊⣠⠞⠁⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⣾⣿⣷⢸⡁⠀⠀⠙⣶⣿⣿⣿⣿⣶⣶⡉⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⣈⣤⠞⠁⠀⢀⣀⣀⣤⣤⣸⡇⠀⠀⠀⠀⠀ ⠀⠉⠛⠋⢸⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠤⣤⣤⣤⣤⣤⣤⡤⠴⠖⠛⣉⣤⠴⠒⠋⠉⠁⠀⣀⣀⣬⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣦⣄⡀⠉⠛⠻⠿⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⣁⣀⡤⠤⠖⢒⣛⡭⣽⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠾⣷⣲⡤⣄⣀⣀⣭⠭⠵⠶⠒⠒⠒⠲⢒⣫⠭⠶⣒⡋⣉⣁⠤⢄⣀⣩⡥⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢾⢱⡀⠀⠀⠀⠀⠀⣠⣷⠯⠭⠿⠿⠟⠒⠒⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣓⣶⣶⣒⣺⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀ ⣿⣿⣷⠀⠀⢐⠆⠆⠴⢶⡀⠀⠀⣾⣿⣿⠂ ⠙⠿⠿⣧⠞⠉⠀⠀⠀⠀⠈⠑⢼⠿⠟⠉⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀ ⠀⠀⢠⠀⠀⢴⡆⠠⠀⢶⠄⠀⠀⢇⠀⠀⠀ ⠀⠀⠸⣀⢀⡴⢠⡀⠀⠀⠂⠀⣀⠜⠀⠀⠀ ⠀⠀⠀⠀⠏⠀⠜⠁⠀⠀⠀⠁⠈⢑⠄⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡆⠉⠀⠀⠀ ⠀⠀⠀⠘⢄⡀⣀⣀⣀⣀⠀⢀⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠀⠀⠀⠀⠀

⠈⠛⠛⠉⠉⠉⠍⠽⠿⢿⣷⣬⣓⣿⣯⢿⣿⣿⠃⡇⠀⠀⠠⣾⣿⣿⣿⡖⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⣀⣧⣿⣛⣻⣟⣿⣾⡿⢻⣿⡿⣧⣤⣼⣿⣿⣿⣿⣽⣧⣤ ⠀⠊⠁⣉⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⢸⡷⠈⠙⠻⣿⠿⠿⢿ ⠀⣰⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣷⣿⠀⠀⠀⠀ ⢨⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠌⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢟⣻⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣻⣿⣿⡼⠉⣶⣬⣭⣦⣌⠙⡀⠀⠀⠀⠀⠀⠀⠀ ⣻⣿⣿⣿⣿⣿⣿⠼⣟⣫⣤⡈⢻⠿⠿⢶⣿⣿⣿⣿⣿⡅⡀⠀⠀⠀⠀⠀⠀⠀ ⡽⢽⡟⠻⣿⣿⢡⣾⣿⣿⣿⣿⣮⣶⣧⠬⠨⠿⠿⣽⡿⠃⠀⠀⠀⢀⠀⠀⠀⠀ ⢕⣄⡀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠈⠄⠀⢨⠙⣞⠻⠿⠟⠁⡠⠀⠀⠀⠀⠀⠈⠂⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠀⠀⣋⠀⢿⡄⠀⠀⢀⣇⣀⢀⣰⣤⣤⠞⠁⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠈⠙⠂⠀⢘⡊⠻⢿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠀⠈⠂⠀⠀⠀⠀⠉⠁⠀⢃⣠⡠⣔⠁⣁⣦⠀⢰⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠀⠀⠀⠄⠀⠂⠀⠠⠀⠰⣿⣿⠿⡿⠿⣡⡎⠀⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠐⢢⣀⠀⠀⢀⠈⣛⣮⣬⡽⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡆⢨⠀⠉⠒⠤⠒⢬⠓⢋⠖⢚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⠛⣸⡤⡀⠀⠀⠀⡄⡆⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⠇⠘⣿⡏⠀⠈⠁⠀⠀⢸⡧⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣷⡿⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⡈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣇⣳⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠈⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠄⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⡤⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠼⠀⡣⡀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠠⠊⠀⠉⠰⠀⠀⠀⢸⠇⠀⢠⠘⠁⠘⢢⡀⠀⠀⠀⠀⠀⠐⠒⢄⠀⣠⠼⠃⠀⡰⠊⠉⠀⢉⡉⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡆⠀⠀⠀⠀⠃⠀⠀⣼⠀⠀⠈⠙⠆⡰⠉⠁⢀⣤⢤⡄⠀⠀⠀⠈⠤⠁⠀⠀⣜⡁⡐⠁⠀⠀⠈⢂⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⡇⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢀⣠⠬⠵⠒⠒⣾⠖⣶⡧⣄⣀⠀⠀⠀⠀⠀⠀⣼⠀⠱⠀⠀⠀⠀⢀⠀⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣴⡯⣖⠺⣍⢻⡙⢯⡹⢜⣓⡒⠮⣍⡳⢤⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠠⠀⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣮⣳⢌⡇⡞⢥⡚⡼⢤⢋⡳⢦⣙⠳⣿⡀⣰⠇⠀⠀⠀⠀⠀⡠⠁⢠⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠉⡄⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⠾⠷⢼⣵⠮⠧⣷⣦⣭⠿⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⣊⠁⠀⠋⣒⡄⠀⠀⠘⠲⣄⣰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⢤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢱⢀⠏⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡠⢎⠰⢆⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠠⡤⠤⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠁⠀⠸⢅⡈⢀⣈⡵⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠶⠶⢤⡀⢠⠏⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⣶⡄⠀⠀⠀⠀⢠⣤⣀⡀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢱⡰⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢐⠁⠂⠀⠀⠙⠏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣴⡾⣧⣀⣸⡆⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢠⢄⠀⠀ ⠀⠀⠀⠀⠘⣆⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣠⠖⠛⠓⣆⢠⠔⠃⠈⠢⠄ ⠀⠀⢀⡀⠀⠙⣦⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⣾⠀⠉⢊⢰⠋⠁ ⠀⣠⠆⠸⣄⠀⠈⠳⡼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠊⣴⠋⠀⠀⠀⠁⠀⠀ ⠘⠃⠄⢰⠄⠃⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠊⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⢸⡁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⠅⣀⠼⠁⠳⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⣾⠀⠐⠲⠀⡴⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢇⡀⣀⢀⡀⣀⢀⡀⣀⢀⡀⣀⢀⡀⣀⠀⣀⢀⡀⢀⡀⣀⠀⣀⢀⡀⢀⡀⣀⠀⣀⢈⠀⡀⢀⡀⡇⠀⠀⠀⠑⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⢻⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠏⢡⡽⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠇⣤⡼⠓⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⣤⡾⠃⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣯⡉⠷⠾⠿⣆⣠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⠡⠀⣿⡇⠀⠀⠈⢹⣶⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⢵⡶⣇⣠⡍⢉⠉⠉⠉⠉⠹⠶⠶⢶⠶⣶⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠁⠀⣶⡏⠁⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢱⠏⠉⠽⠶⣾⣖⣳⣞⢲⢒⠲⣡⠚⢬⢹⣽⡶⠶⡶⢶⠶⣶⣶⣶⡏⠁⠀⣤⡿⠇⢀⣀⣀⠀⠸⢿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢳⡆⠀⠀⠈⠉⠉⢻⣿⣾⣱⣦⢙⢢⡽⠛⠀⠀⠀⢀⠀⠐⠈⢿⡇⠀⠀⣿⣷⣶⣾⣻⡿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠷⣄⡀⠀⠀⠀⠀⠀⠈⣛⣹⡾⠁⠀⠀⠀⠀⠈⠀⠀⠂⢀⠀⠀⠀⠠⠐⠀⠱⢜⢳⣄⡀⠀⢸⡷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢳⣆⡀⠀⠀⠰⣾⣉⠋⠁⠀⠀⠄⠂⠁⢀⠈⠀⠄⠂⠀⠄⠐⠀⠠⠀⠄⠸⢲⣟⠉⢀⣠⣟⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⡄⢐⣰⣼⠛⠀⠀⠄⠀⡀⠠⠀⠀⠠⠀⢀⠠⠀⠀⠄⠂⠀⠄⠠⠐⠸⢷⣄⢸⣿⣴⢛⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜⢛⢻⣿⠀⠀⠁⠀⢂⠀⠄⠀⠁⡀⠄⠀⡀⠄⠂⢀⠠⠀⠀⠄⠀⠘⢻⣟⠛⢀⣤⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣿⣤⢠⣦⣶⣤⢁⠀⠀⠂⢀⠐⠀⢀⠂⠀⠀⠐⠀⠠⠀⠁⡀⠈⡀⣠⠀⠀⠈⠛⢻⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⡞⠛⠏⠀⠀⢸⣯⠘⢿⣤⣿⣿⠀⡁⠄⠂⠀⠐⠀⣀⣮⣴⣶⡄⠁⠠⠀⠀⣀⡅⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡼⠋⠁⠀⠀⠀⠀⠈⠙⠢⠘⢿⣩⣿⡁⠀⢀⠀⠈⠀⣴⠟⢏⣽⣏⣽⡗⠀⡀⢁⡏⠀⠀⠀⠐⠻⠛⠧⣄⠀⠀⠀⠀ ⠀⠀⣠⡞⠀⠀⣠⡄⠀⠀⠀⠀⠀⠐⠀⠀⠉⠁⢠⠀⠀⠂⡅⠈⠿⠛⠿⠻⠋⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣤⠀⠀ ⠀⠀⢿⣅⡾⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠧⠼⠁⠀⠀⠀⠀⠀⠧⡄⠀⠀⠠⢀⡤⠥⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⠀ ⠀⠀⠈⠉⣱⠏⢁⡰⠶⢇⣀⣀⠀⠀⢀⣠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⠉⣾ ⠀⠀⠀⠀⠸⠷⠏⠁⠀⠈⠉⢱⣆⢰⣾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠘⢿⣉⠶⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣾⠉⠀⣠⣶⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣶⠆⠀⠀⠀⠀⠀⢀⣰⠾⠉⠉⠙⠶⢶⣰⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠠⣿⣿⣿⣿⠀⠀⠀⠀⠄⣀⣶⠟⠁⠀⠀⠀⠀⠀⢰⣞⠋⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢶⣶⢶⣿⣉⠀⠀⠀⣀⣁⡶⣏⡷⠶⠶⠶⠶⠶⠶⠶⢆⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠛⢹⣶⣶⣶⣋⠙⣷⡛⠁⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣤⣤⣤⣤⣤⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡴⠶⢆⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣳⡄⠀⢠⡗⠀⠀⠀⠀⠀ ⡰⠒⠶⠖⣉⣉⠉⠉⢉⣩⣅⠲⠖⢲⣆ ⠑⠦⠤⢾⣧⡋⠠⠤⠄⢿⣸⠦⠤⠴⠿ ⠀⠀⠀⡰⣿⡏⡿⠿⡏⢹⠁⠀⠀⠀⠀ ⠀⠀⠀⠱⠽⢧⠤⠤⢤⡸⠀smol

SEARCH “DWEADFUL” FOR MORE 🦋 ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠁⠐⠀⠀⠀⠀⠂⠀⠢⡀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠻⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣴⢻⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⣰⢟⠁⠂⠀⠀⠈⡎⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⣤⠴⠚⠁⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠆⠀⠀⠀⠀⠀⣹⣨⠷⠶⠚⠛⠉⠉⠉⠙⠛⠒⠶⠶⠒⠒⠲⠶⢶⣤⣀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⣠⡶⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠈⢳⡀⠀⣠⠴⠛⠃⠀⠀⠀⠀⠀⢠⡟⠄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⣤⢀⣴⠞⠋⠀⠀⢠⡾⠃⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣇⣴⠃⠀⠀⠀⠀⠀⠀⠀⣠⡾⠗⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣄⠀⠀⠀⣰⠋⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡼⠃⣀⡀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠁⣠⠶⠒⠲⣄⠀⠀⠀⠀⠀⠀⠂⠁⠀⣨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢧⣌⢳⡀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡋⣷⠆⠀⠀⠀⠀⣀⣤⡴⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠈⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡴⠋⠉⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣍⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⡇⠀⠀⢀⣤⢞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠸⣄⣀⣀⣠⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢭⡄⢒⡴⠒⠲⢤⡲⢤⣀⣠⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣻⠇⠀⣹⠟⠀⠀⠀⠀⠉⠳⣤⠉⡛⠿⣿⣿⣿⣿⡷⠀⠀⣀⣀⣀⣀⣀⣄⣀⡀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣷⣶⣤⡀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣻⠃⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠈⠙⢿⣋⡥⠖⠋⢡⣶⣶⣶⣶⣥⣬⡉⠓⠶⣄⢀⠀⣾⣿⣿⢿⠟⠛⣻⠏⠉⠉⠉⠉⠉⠉⠉⠉⠙⢯⡙⠲⠦⣄⡰⠃⠙⢧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡿⠃⠀⢠⡿⣤⡀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⠻⣿⣿⣿⣿⠟⠀⠀⢀⣨⠵⠚⠉⠁⠀⢄⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠙⠦⣀⠙⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡾⠁⠀⠀⢸⠃⠀⠉⠓⠲⠶⠶⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠉⡟⠉⠄⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠐⠀⠢⠔⠂⠀⠀⠀⠀⠀⠀⣸⠴⢦⡀⠀⠀⠈⢧⣹⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣀⡴⣧⡀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡼⠁⠀⣸⠁⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⠀⠀⠀⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢈⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠒⠒⠚⠋⠉⡼⠁⠀⢠⡏⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⡀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⢸⠁⠀⠀⠀⠀⣠⣼⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⣠⠏⠀⠀⢀⣠⢞⣽⠇⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⣰⢋⠤⠴⠚⢉⣴⠾⠉⠈⢻⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠹⡿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⣰⣃⣀⣠⣤⣾⠋⠁⠀⢀⣤⠏⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠙⠮⣿⣍⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⢰⣏⣉⡽⠖⠋⠁⠀⣠⡶⠋⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠘⡏⠳⣤⡀⠉⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡠⠤⠶⠖⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⡞⠁⢀⡼⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇⠀⠈⠙⢶⣤⡀⠈⠙⠲⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⢈⡡⠴⠒⠊⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠖⠋⢀⣤⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠰⢫⡆⠀⠀⠀⢸⠇⠉⠛⠲⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣀⣀⣤⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠋⠁⠀⠀⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⡟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠛⣧⠀⠀⠀⠀⣠⠾⢷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⣿⠂⠀⣰⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠴⣶⠋⠉⠀⠀⠀⠀⠸⣷⡀⠀⠀⠘⣦⠞⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣼⡇⠀⢰⠃⠀⠀⠀⠙⠲⠀⢄⠁⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠋⠀⠀⠀⠀⠀⣤ ⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⢹⡇⠀⡏⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠞⠁⠀⠀⠀⠀⠀⢰⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⢀⣤⠶⢚⡏⠉⠉⠉ ⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢰⡏⠘⡇⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠪⣄⠀⠀⣼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠠⠄⠠⣄⣀⠀⠈⢿⡍⠀⣀⠞⠁⠀⠀⠀ ⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⣾⢸⠀⢿⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⢀⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢌⣿⡌⠉⠉⠛⠒⣦⢤ ⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣼⡏⠈⢳⡸⡆⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⣸⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠈⠓ ⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢿⡇⠁⠀⢳⣻⣿⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣰⡿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡲⢦⣀⠀⠀ ⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢸⠀⠀⠀⠀⠻⣛⣆⠠⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⣴⣻⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠉⢷⣄ SEARCH “DWEADFUL” FOR MORE 🦋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠹⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⠾⠛⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠛⠷⣶⣼⣿⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡾⠛⠉⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠉⠙⠛⢶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣧⠀⠀⠀⠀ ⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢿⡇⠀⠀⠀ ⠀⠀⠹⣿⡎⠀⠀⠀⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢻⡆⠀⠀⣆⣿⡇⠀⠀⠀ ⠀⠀⠀⣿⡀⠀⡀⠀⣿⠁⠀⢠⣾⣿⡿⠆⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠆⠀⠀⠀⢈⣿⠀⣄⣾⡿⠁⠀⠀⠀ ⠀⠀⠀⠘⣿⣧⣇⢀⣇⠀⠀⠘⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⠖⠀⠀⠀⢸⣿⣷⠿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠙⠻⣿⣆⡀⠀⠀⠉⠉⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣸⣿⠁⣀⣀⣀⠀⠀⠀⠀ ⠀⢀⣠⡶⠾⠛⠓⠶⣿⡟⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠋⠉⠛⠻⣦⡀⠀ ⢀⣾⠋⠀⠀⠀⠀⠀⠘⣿⣠⣄⡀⠀⠀⠀⠀⠛⠿⠟⠁⠀⠀⠀⠀⠀⡀⡀⠀⣴⣾⡏⠀⠀⠀⠀⠀⠈⣿⡄ ⢸⣯⠀⢠⠀⠀⢀⣄⣠⣿⠿⢿⣷⣤⣦⣀⣤⣤⣤⣤⣀⣀⣀⣼⣆⣼⣷⣿⡾⠿⢿⣧⣀⣦⠀⠀⣤⠀⣸⡧ ⠘⠿⣷⣾⣷⣤⠾⠿⠛⠁⠀⠀⠀⠁⠀⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠛⠻⠷⠾⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⣀⡤⠖⡓⢎⡋⠇ ⠀⢠⡗⠬⣉⠗⠦⣄⠀⠀⠀⣿⣯⡆⠀⠀⣀⡴⢋⠵⢨⠱⣉⠦⣙⠇ ⠀⠰⣍⠲⣁⢎⡱⢌⡓⢦⣰⣟⣗⣣⢠⡼⢃⡌⣣⠮⡓⣇⠲⡘⢬⡇ ⠀⠈⣆⠓⣼⠯⡟⣷⣜⢢⣙⣿⣿⡿⣣⠖⣵⢚⠥⡓⣍⢮⢡⠓⡼⠀ ⠀⠀⣧⢙⡰⣟⢼⡽⢎⢣⡑⠻⡿⠳⣄⡫⠜⣙⠾⣱⢌⡇⢦⡹⠁⠀ ⠀⠀⠺⣄⠣⣼⢫⢴⠁⣾⣿⡕⣌⣳⣿⣿⣆⠈⢲⣹⢮⣜⠎⠁⠀⠀ ⠀⠀⠀⣽⣾⠥⣿⣆⠐⣿⣿⣿⠤⣿⣿⣿⣿⠀⢺⡿⢎⣱⠀⠀⠀⠀ ⠀⠀⢰⣿⣧⢃⠟⣣⠈⣿⣿⡟⡰⠻⣿⣿⢃⣠⢋⡜⢢⠜⡇⠀⠀⠀ ⠀⠀⢸⣿⣷⢈⠞⣈⠓⡎⣍⢒⡿⢳⡐⢆⠣⢆⠣⠜⣢⢙⠇⠀⠀⠀ ⠀⠀⠘⣿⣿⣎⠜⡤⢫⣶⣾⣶⣿⣶⣾⣾⡇⢪⢅⠫⣄⠟⠀⠀⠀⠀ ⠀⠀⠀⢹⣿⣿⣞⡤⢋⠽⡿⣿⣿⣿⣿⠫⢌⠥⣊⢖⠍⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣿⠟⠳⣬⣵⣬⣷⣼⣤⣯⣼⣶⠙⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠀⣰⠿⠿⣿⢿⡿⣟⠿⡿⠟⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡄⠀⠀⠀⣼⠡⢎⡑⢆⠣⡔⣌⠲⣁⠏⠼⡄⠀⠀⠀⠀⠀⠀ ⠠⣼⠓⡆⠀⠀⡼⢃⡜⢢⠩⠜⣢⢑⢢⠱⢌⢪⠱⣹⠀⠀⠀⠀⠀⠀ ⢸⡇⡍⢳⡀⡼⢃⠣⣌⠣⢍⡚⢤⢊⠦⡙⡌⢆⡓⡔⣣⠀⠀⠀⠀⠀ ⡾⡱⢌⠣⡜⣡⠋⠖⡤⢋⡒⠜⡤⢃⡚⢔⡉⠖⢬⠰⡡⢇⠀⠀⠀⠀ ⠸⣇⡎⡑⠦⡡⢎⡱⢌⡱⢌⠓⡬⡑⠜⣢⢉⠞⠤⢣⡑⢫⡄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⠁⠀⠈⢌⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠣⢌⠰⠠⢁⠠⢀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠁⣿⠰⡈⠆⡑⠂⠄⠀⡿⢄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⢰⡯⡑⣌⣂⠁⠀⠠⢰⡯⡾⣀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡜⡁⠠⠀⠀⣾⡗⣹⣛⢯⡿⣷⡤⣾⡵⠢⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡃⢐⠀⠀⢀⣿⣏⣿⣯⣗⢾⡽⣾⢿⣹⠠⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⠘⠄⠁⠐⢰⣿⣞⡯⠟⢏⢷⡖⢈⠗⣾⡇⠉⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣄⠛⠠⠃⠠⣼⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣿⠃⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⢣⠎⡁⢀⣴⣿⣿⢿⣽⣿⣽⣾⡿⣟⣿⢿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠟⠦⠘⣰⣿⣿⣿⣻⣿⣿⣾⢿⣽⣿⢿⣻⣿⣻⣾⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣾⣿⢿⣾⣿⣟⣿⣽⣷⡿⣿⡆⠀⠀⠂⠀⠀⠀⠀⠀ ⢀⣴⠃⡄⠀⠀⠀⠀⣿⣿⣿⣿⠿⠁⠉⠘⠛⠛⠚⠻⢯⣿⡾⠟⠛⢳⠀⠀⠀⢄⠀⠀⠀⠀ ⣿⣣⢏⡰⢀⠀⡀⣸⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠈⠙⠄⠀⠀⢰⡀⢦⣩⠞⠀⠀⠀⠀ ⠈⢳⣏⢖⡡⢦⣑⣾⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢀⣾⡆⢐⣾⡆⠀⢸⣞⣧⠃⠀⠀⠀⠀⠀ ⠀⠀⠙⢪⣽⠷⣏⢿⣿⣿⣿⣿⣿⣿⣦⣓⠢⠀⠘⠿⠃⠘⠟⠃⣰⡾⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢘⢮⣓⢎⡖⢉⢻⣿⣿⣿⣿⣿⣿⠃⡐⠀⠀⠀⡀⠀⣆⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⡯⢾⡱⢎⠄⢸⣿⣿⣿⣿⣿⡇⠾⣵⣮⢶⣻⣷⡾⢛⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⢥⡓⣎⠱⢈⣿⡿⠀⠈⠒⠯⡫⠍⠋⠁⢀⣷⠀⠈⢛⠻⣿⣿⡿⢟⡍⢲⠱⡄ ⠀⠀⠀⠀⠸⡶⣙⢆⣳⣿⣿⣃⠀⠀⠀⡐⠀⠀⣀⣴⣾⡿⣷⠀⠀⠄⠀⠙⢿⣦⠘⣥⣣⣇ ⠀⠀⠀⠀⠀⢳⣻⣼⣿⣻⢿⣿⣿⣶⣤⣷⡀⠘⢛⢀⡳⢝⢿⣇⠀⠈⠀⠀⠀⠹⠿⠚⠋⠁ ⠀⠀⠀⠀⠀⠘⡟⣦⢋⠿⠿⣿⣿⣿⣿⣿⣻⣦⣄⠈⠘⠊⣾⣽⣆⠀⠈⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣯⡹⣎⠵⡀⠉⣿⡾⢳⣿⡿⣯⡛⣶⣤⡀⠹⣿⡆⠀⠀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢳⣷⣿⣜⠴⢁⢸⣟⣧⡿⣯⣉⠙⡿⣟⡿⠀⣌⣿⡂⠀⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠂⡄⡟⣿⣽⣿⣿⡟⠚⠁⠀⣤⡇⣿⣧⠀⠀⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⢞⡸⡑⠹⣿⣾⣿⠁⢠⣴⡿⡟⡤⢿⣿⣧⠀⠀⠡⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣋⢿⡿⠿⠟⢹⣆⠥⠒⡀⠹⣿⣿⣦⣄⠉⠙⠌⠋⠉⢿⣿⣧⠀⠀⡅⠀⠀ ⠀⠀⠀⠀⠀⣾⣎⠶⣡⢋⠴⣹⠙⣞⢧⡑⡠⠜⣯⣟⣿⣿⡶⣲⣶⣤⣴⣿⣿⣆⢀⠆⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⢧⣏⠶⣹⠀⠈⠳⣭⣒⡱⡘⢿⣿⣿⣿⣿⣿⡿⠙⢿⠯⠔⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⠛⠞⠻⠛⠀⠀⠀⠈⠳⣧⣱⣃⠜⢿⢿⣿⠳⡅⢃⢼⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠀⠈⠙⠻⠝⠋⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠾⢟⠩⡐⢌⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⡟⢋⡱⢌⠃⡎⡱⠘⢦⠱⡌⡘⠻⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠾⠛⢭⢂⠳⢌⠣⡔⢊⡱⡐⣡⢋⠤⠓⣌⠲⠅⡒⢤⣙⡻⢖⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣎⠍⣂⠎⡕⢪⠱⢌⡱⢄⡓⠔⣊⢌⠣⢌⢒⣼⣾⠿⢿⠿⣿⣦⠣⢍⡹⠻⢶⠶⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣚⠌⡑⢎⠲⢌⡒⢌⡓⢬⡘⢜⡨⠹⢿⣯⣿⣮⣿⣿⡟⡘⠦⡱⣉⠦⡑⢤⠢⢍⡩⢛⠛⣹⡿⠂⠀⠀⠀⠀⣴⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡿⣽⣻⣷⣭⣊⡑⢎⡘⢆⡜⢢⠜⢢⠱⣉⠦⡩⢭⡙⡍⡡⢎⡱⢌⡑⢆⠲⣉⠦⣑⠪⢔⡡⢾⣿⣇⣠⣤⣤⣤⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣳⢯⣿⣿⣿⣿⣦⣝⡢⢘⢦⣉⠦⡱⡘⢦⡑⢦⠱⣌⠱⣊⠔⡣⠜⣌⠓⡤⠓⡤⠳⢌⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⢟⣾⣿⣿⣿⣿⣿⣿⣷⣦⣬⣘⠱⠑⢢⠜⣂⠳⢨⠱⡌⢎⡱⣉⠦⣙⠰⡩⢔⣩⣾⣿⣿⣿⣿⣿⣿⣿⡟⣿⣡⣭⠛⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣿⣯⣟⢾⣽⣿⣿⣿⣟⣾⣽⣟⡿⣿⣿⣾⣦⣜⣀⡃⠅⠣⠜⢢⠑⢦⡘⢩⢒⠱⢢⣾⣿⣿⣟⣾⣻⣿⣿⣿⣧⣄⠛⠻⠐⣻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⢿⠻⣟⠿⣻⢟⡿⢿⡿⣿⣿⣿⢿⡷⣯⣟⣾⣿⣿⣿⢯⣟⣯⡿⣽⣳⣯⢿⣽⣻⡿⣿⣿⣷⣮⣤⣍⣆⣘⡡⠎⣼⣿⣿⣿⣿⣿⣷⣿⡼⣯⢟⣻⢿⣿⣷⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⣴⣾⢿⣻⡽⣞⣿⢿⡿⣿⢷⡿⣾⢿⡾⣷⣾⢷⢯⣻⡵⣾⣟⣿⣿⣿⣻⣞⡿⣽⢯⡷⣯⢿⣾⣷⣿⣿⣿⣿⣿⣟⡿⣿⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⡟⣾⣝⣯⢿⣹⡟⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⢀⣴⣿⣿⢿⡿⣟⣿⣺⣯⣷⢿⣯⢿⣯⣿⣽⢾⣽⣯⢯⣽⣳⣽⣫⢿⣵⣻⣷⡾⠿⢻⣿⡷⣭⣻⡽⢯⡿⣽⣿⢿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣯⢿⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⢿⣳⢾⣹⣞⢷⣻⡳⣟⣿⡄⠀⠀⠀⠀⠀ ⢸⣿⢯⣟⣯⢷⣿⣷⣿⡿⣞⣿⣾⢿⣿⡿⣿⣿⣶⣿⣿⣶⣿⣶⣿⣿⠛⠉⠉⠀⠀⠀⠙⠻⣵⣣⢟⡯⣽⣿⣯⣟⢾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣯⣿⢾⡽⣯⣟⣿⢷⣯⣟⢾⡽⡽⣾⣿⠀⠀⠀⠀⠀ ⠸⣿⣿⣿⣽⣾⢿⡿⣿⣿⠟⠙⠻⣿⣯⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⣵⣏⣿⣷⣯⣻⠾⣽⣻⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡷⣿⣽⢯⣟⣷⣻⣿⣯⣞⡾⣟⡾⣽⣳⣿⢿⣷⣦⣄⠀ ⠀⠈⠛⠛⠻⣯⣟⣿⣽⡷⠀⠀⠀⠀⠙⠻⢷⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿⣻⣟⣧⢿⡹⣾⣽⣻⣿⣿⣿⣿⣞⣿⠉⠙⠻⣿⣞⣿⣻⣾⣿⣻⣿⣿⣿⣷⣯⢷⢯⡽⣾⣿⣟⣻⢮⣽⣿⡆ ⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣽⣻⣽⣻⣶⡹⡷⣯⢿⣿⣿⡿⠁⠀⠀⠀⠈⠉⠛⠳⢿⣿⣿⣿⣿⢿⣯⢟⣭⢿⣽⣿⣳⢯⣿⣻⣽⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣯⣷⣯⢷⣯⠽⣯⣟⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⡿⠾⠿⠞⠛⠉⠙⠿⣿⣾⡷⠟⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣟⣿⣾⢿⣦⡛⣿⣻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣿⣿⣿⣿⣿⣿⣿⣟⣿⣦⡛⣷⣿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣽⢿⣿⣿⣿⣿⣻⣿⣿⣿⣾⣽⣟⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣟⣿⣟⣿⣿⣷⣽⣿⣿⣻⡽⣞⣿⣿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣻⣟⣿⣿⣿⡿⣟⣯⣽⢻⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣿⣾⣿⣳⢟⡽⣞⣞⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣳⢯⣻⡽⣽⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣳⢯⡿⣵⣻⡷⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣻⣾⣷⢯⡿⢷⣹⢷⣻⢿⣻⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣿⣟⣷⡿⣿⣿⣯⣿⣯⣯⣟⣞⣿⡷⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⡻⣽⣿⣿⣿⣏⠀⠉⠛⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣯⣿⢿⢿⣿⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠾⠿⠛⠻⠿⠶⢦⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⢠⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡉⠙⠻⢶⣤⣠⣤⣤⣿⣿⡿⠛⠛⠛⠻⠶⣶⡶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠻⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⡈⠙⠛⠉⠻⣦⡀⣴⣿⡯⠉⢀⣯⣤⡄⠀⠰⠶⠶⠄⠀⠁⡀⠈⠙⠻⠶⢤⣤⣤⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠺⠶⠛⠋⠁⠀⠀⠀⠀⠘⣿⣿⠛⠶⠟⢸⣅⣀⣿⡆⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠈⠉⠻⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠈⠀⢀⣠⣴⣾⡇⠀⠀⠀⠀⠀⠀⢠⡾⠲⢿⣇⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⢀⣿⠙ ⠀⠀⠀⠀⠀⢀⣀⣠⡴⠟⠋⠀⠀⠀⠀⠀⡄⣀⣤⠶⠞⠛⠀⠀⠀⠉⢻⡿⢶⡖⠋⠉⠘⠷⣤⣤⠿⣤⣀⢠⡶⠟⠛⠷⠂⠀⠀⠐⣦⣠⣴⠟⠉⠙⠻⠶⠶⠶⠴⠶⠟⠁⠀ ⠀⢀⣴⠶⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⢀⣸⣯⠿⢦⣤⡀⠀⠀⠀⠀⠀⢠⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⢶⣤⡄⠀⠀⠀⠀⠈⢻⣶⠾⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢁⣠⣤⣤⣧⡀⢀⣀⠠⠟⢰⣾⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠁⠀⠈⠁⠀⠀⠈⠙⢿⣻⣷⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠿⣦⣤⣤⣤⣤⣤⣴⠶⠟⠋⢹⣰⣄⠀⠀⠀⠀⠀⠀⠘⢣⡟⠙⠳⣦⣀⠀⠀⠀⠀⢰⡄⣀⣠⣴⠾⠋⠛⠛⠛⠶⠶⠶⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠈⠷⣍⣙⣓⣒⣛⣉⣹⠶⠋⠀⠀⠀⠈⠙⣧⡀⠀⠀⣼⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠟⠋⠀⠀‌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠁⠉⠈⠁⠁⠂⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠂⠒⠂⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠈⡂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠑⡄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢑⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠘⡄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⡃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢇⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡅⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡸⠤⠥⠦⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⠅⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡄⠀⣤⣄⠀⠀⢾⡰⠇⢀⣀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⡆⠀ ⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⢸⠘⠾⢱⠀⠓⠋⠀⡈⠀⠀⠇⠘⠿⠇⠀⠀⣠⡊⠀⠧⢤⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠔⠊⠋⠓⢄⠀⡆⠊⠉⢇⠀⠀⠄⠂⠁⠀⠹⡄⡠⠂⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⢇⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⡎⠁⠀⠀⠀⡗⠁⠀⠀⠀⠀⡔⠁⠃⠀⠀⠀⠀⡠⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⡒⠖⠂⠂⠂⠂⠉⢗⠖⠒⠒⠂⠃⠂⠒⠒⠒⠓⠒⠒⢲⡂⣁⡀⠀⠀⠀⠀⢀⠆⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡝⠀⠀⠈⠉⠑⢦⣔⣁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡇⠀⠀⠀⠀⠀⠀⠐⠀⠑⢦⡀⠀ ⠀⠀⠀⠀⠀⠠⠛⠄⠄⣀⢀⢀⢀⢀⡠⠄⠔⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠣⠄⡀⡀⠀⠀⢀⢀⣀⠤⠒⢣⠀ ⠀⠀⠀⠀⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠤⠤⠄⠤⠠⠠⠄⠒⠐⠒⠚⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠈⡆ ⠀⠀⠔⠈⠁⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠤⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡸⠀ ⢰⠁⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠉⠁⠉⠉⠁⠑⠠⠤⠤⠔⠁⠀ ⠈⣆⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠑⠒⠤⠤⠤⠖⠊⠉⠉⠉⠐⠂⠒⠂⠂⠒⠒⠊⠉⠉⠉⠁⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠁⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠁⠉⠈⠒⠤⣆⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⡐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⠤⡀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣄⠀⢀⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⡿⣽⣞⡿⣧⣾⣿⣽⢾⣳⣟⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣯⢿⣽⡾⣟⡿⣿⡷⣯⣿⣻⢾⣳⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣶⣦⣄⣿⣯⢿⣳⣿⣻⡽⢿⣿⡽⣞⣿⣻⣻⣠⣶⣦⣄⠀⠀ ⠀⣾⡿⣯⢿⣽⣿⠿⣯⣟⣾⣿⡿⡘⢯⣿⣟⣷⣿⣿⡿⣯⣷⢿⣧⠀ ⢸⣿⢿⡽⣿⢾⣽⣇⠚⠉⣹⣷⣶⣶⣶⣍⠻⠟⣿⣿⡽⣷⢯⣟⡟⡄ ⠘⣿⣯⢿⣯⢿⡾⡽⠀⣴⣿⣟⣷⣻⡾⣯⣆⠀⣿⣷⢿⣯⢿⣯⢿⠁ ⠀⠹⢾⡿⣽⢯⣿⢣⣼⣿⣻⢾⡽⣷⣟⣯⢿⣧⣌⢿⣻⡾⣟⣾⠏⠀ ⠀⠀⠀⠉⠛⣿⣷⣿⣟⣷⣻⣯⢿⡷⣯⣟⡿⣾⢾⣶⣯⠹⠉⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣻⡾⣽⡾⣯⣟⣯⣿⣽⢾⡿⣽⣻⣽⣻⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⡷⣟⣯⢿⣳⣿⣽⣾⣽⣯⣟⡿⣽⣳⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀

⢀. ⡤⠖⠒⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠒⠲⢤⡀⠀ ⢀⡟⢠⡖⠋⠙⢳⣤⠽⠖⠛⠉⠉⠉⠉⠙⠓⠾⣤⡖⠋⠙⠲⡄⠹⡄ ⢸⡀⣿⠀🎀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉🎀⠀⣹⠀⡇ ⠈⢧⣘⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣏⡴⠃ ⠀⠀. ⡽⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⢹🐻🐻. ݁₊ ⊹ . ݁˖ . ݁

⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣞⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⠳⢮⣙⠲⣤⣠⠤⠴⠖⠒⠒⠶⠴⢞⣡⢾⡍⠈⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⠀⣸⣯⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣗⠀⣿⠇⠀⠀⠀⠀ ⠀⢠⠤⠒⢤⡀⠘⣿⣄⡜⠉⠀⢀⢀⡀⠀⠀⠀⠀⠀⡄⠠⡀⠀⠈⠳⡿⠀⠀⠀⠀⠀ ⠀⡇⠰⣶⠂⣱⠀⢸⡏⠀⠀⠰⠅⠤⠇⠀⠀⠀⠀⠀⠓⠒⠚⠀⠀⠀⢻⡄⠀⠀⠀⠀ ⠀⠙⠦⠤⠶⠷⠀⣼⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣠⠴⣤⡀⠀⠀⠀⢧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⡀⣾⣿⣉⣷⣀⣤⣤⣤⢤⣿⣤⣿⡿⢄⣒⣒⠾⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣿⠭⠒⠨⢝⠾⠿⠋⢡⠈⣻⡋⣠⠈⠙⠉⡔⠁⠀⠀⠙⡝⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⡸⠀⠀⠀⠈⢻⣻⣿⡇⠀⠀⠀⠙⠢⠤⠄⠊⢠⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣄⠉⠉⠉⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡷⠒⠒⠒⠂⠀⠀⠐⠒⠺⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠴⠒⠛⠓⠲⣄⠀⠀⣰⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡼⠁⡴⠊⠉⠈⠑⢮⡧⣴⠃⠀⠀⠙⠦⡀⠀⠀⠀⠀⢀⠏⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⢸⠀⠀⠠⡞⣦⣰⣿⠃⠀⢀⣀⡄⠀⠈⢦⠀⠀⠀⡸⠀⢿⢤⣀⣤⣀⠀⠀⠀⠀ ⠈⡇⢸⡀⠀⠀⠙⢦⣤⡇⠀⠀⠉⢨⡟⠒⢦⡀⢱⠀⠀⡇⠀⢸⢰⢏⢰⡜⡆⠀⠀⠀ ⠀⠹⣄⠙⠢⠤⠤⠔⢺⡀⠀⠀⠀⣸⠰⢻⠄⡇⠘⡆⢸⡀⢀⣸⣿⢠⠒⣆⡇⠀⠀⠀ ⠀⠀⠈⡓⠦⠤⠤⠤⠤⢧⡀⠀⠀⢸⢰⢉⣇⡟⠉⢻⣸⡏⠀⠀⢳⣈⣺⡼⠡⠤⣀⠀ ⠀⠀⠘⠤⢄⣀⡀⠀⠀⠀⠙⠒⠦⠼⢤⡭⠾⣄⣶⣰⡿⠙⠦⠧⠟⠁⠀⠀⣀⠠⠤⠃ ⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠺⠭⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠥⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⠤⢤⣶⠮⣭⣧⣤⣄⣒⣠⣀⣠⣔⣶⣄⣤⣬⣶⣿⠾⠷⠛⠛⠻⠟⠿⠛⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⢿⣿⠟⠁⠀⢀⣾⠏⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢽⠊⠁⠀⢀⣀⣀⣄⣤⣤⣦⣤⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠉⢦⣀⡠⣾⡅⣴⣏⢿⣿⣽⣻⣿⣿⣿⣯⠍⠇⠈⢿⣧⢇⠀⠀⣴⣿⣶⣾⣿⠛⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢸⣡⣾⣿⠏⠑⠻⠿⠿⠿⡫⣾⡿⠋⠁⠀⠀⠀⠈⢻⣿⡡⡄⣼⣿⣿⢿⣷⣶⣽⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠘⣿⡿⢯⣖⣂⣴⣢⣤⡼⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⣻⣷⣿⣿⣿⣯⢉⠉⠉⠉⠉⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⡟⠜⠀⠀⠀⠀⡴⢋⢀⣀⣔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠛⠟⢿⣿⢿⣷⣶⡶⠾⠷ ⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⣀⣠⠇⠂⠀⠀⠀⠀⡇⠀⠀⠀⣠⠾⠀⣴⣿⣿⣿⣿⣶⣶⣶⣶⣤⣀⣀⡀⠀⠀⠀⠐⠼⣽⣭⣭⣽⣿⡇⠀ ⣶⠙⠘⠩⢱⢲⠙⠈⠀⠉⠨⣸⣇⠀⠀⠀⠀⠐⡷⡀⠐⠈⠁⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠂⠂⠙⣿⣷⣿⠿⢿⡀ ⡇⠀⠀⠂⠀⠺⡇⠀⠀⠀⠀⠀⣵⠀⠀⠀⠀⠀⡇⡸⠂⠀⢀⠀⠜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢐⠿⣿⣿⡂⠁ ⡇⠠⢀⢄⡀⡀⢵⢔⢀⢀⠠⢠⢾⡰⠀⠀⠀⠀⣻⡇⠀⠀⠘⡎⣀⢀⠹⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡇⠀ ⠃⢨⡁⠀⠀⢆⢀⣀⠀⠀⠀⠀⠀⠈⠉⠒⠢⡀⣺⠀⠀⠠⠀⢀⠛⡞⡐⠛⠝⠿⠿⠿⠿⢿⣷⠄⣤⠀⠀⠀⠀⠀⠑⢲⣦⣿⣿⣿⠇⠀ ⠀⠈⠱⠤⣀⣁⣑⣐⠔⢄⠈⢁⢢⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠦⠄⠰⣾⣿⣧⠀⠀⠀⡁⠀⠀⢰⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⡟⠀⠀ ⠀⠀⠀⠀⠊⠊⠟⠛⠛⣻⣷⣇⠣⠁⠀⠀⠀⠀⠀⠠⡃⠀⠀⠀⠁⠀⠉⠛⠿⠷⣶⣾⣷⣶⣾⠿⠛⠁⠀⠀⠈⠿⠿⠟⠛⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ฅ՞•ﻌ•՞ฅ

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⡀⢀⡀⠄⡀⠂⡂⢐⢤⠀⠀⠀⠀⠀⠀⢀⠐⠒⠄⡀⠀⠀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠉⠉⠁⠉⠈⠂⠂⠒⠤⠤⡀ ⠀⠂⠀⠈⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢔⠅⡛⠛⠀⠀⠀⡂⢀⡞⠁⠀⠀⠀⠉⣉⣒⣦⣄⡠⠔⠊⠉⠉⠁⠉⠀⠀⠀⠀⠉⠑⠒⢄⡀⠠⠔⠒⠂⠂⠂⠄⣄⠀⠀⠈ ⠁⠀⠐⠂⠀⠀⡀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⡀⠐⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠄⢸⠀⠀⠀⢰⠋⠉⠀⠀⢀⡏⠑⠀⠀⠀⠀⢀⡤⡶⠦⢤⣀⡀⠀⠀⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⣇⠀⠀ ⠀⠀⡁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠄⠊⠁⠀⠁⠓⠂⠀⠀⠀⢐⠁⠀⠀⠀⠀⠄⠀⠀⢧⡀⠀⠈⣇⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⡏⠀⡇⠀⠀⠀⡽⠀⠀⢠⠋⡷⠳⣻⠉⠢⡀⠀⠀⠀⢅⠀ ⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⢀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠉⠦⣌⡳⣀⠀⡇⠀⠀⠀⠀⠀⠀⠣⣌⣿⣶⣆⠔⠁⠀⠀⡏⢸⠁⠀⡿⠀⠀⠈⢧⠀⠀⠸⡀ ⠀⠀⡄⣦⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠋⠀⡁⠂⠁⠈⠈⠁⠀⠁⠬⠗⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⡧⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠒⠦⣤⣧⣬⠭⠏⢡⣀⣀⡀⠀⡇⠀⣠⠇ ⠀⠠⠀⢍⠀⢀⡄⠢⡆⠁⠀⠀⠀⠁⠀⠨⠀⠈⠀⠈⠀⠀⠁⠂⢀⠠⡅⠃⡀⣠⠀⠂⡀⠀⠀⡀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠳⢄⣀⣀⣀⣀⡴⠋⠀⠉⠁⠀⢘⠀⠀⠉⠉⠉⠉⠁⠀ ⠈⠠⠀⠢⠀⠀⠄⠀⠀⠁⠀⠂⠄⠠⠀⡈⢄⠀⠠⠀⠀⡖⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⡠⠀⠀⠀⣇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢢⣀⣀⣀⠄⡼⠀⠀⠀⠀⣶⡖⠂⠀ ⠂⠂⠀⠂⠀⠈⠁⠁⠁⠈⠀⠂⠀⠀⠂⠀⠀⠊⠀⠃⠃⠀⡀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠐⠀⡀⠐⠂⠑⠉⠀⠠⢤⣿⣻⣷⣵⡤⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⡤⠎⠁⠀⠀⠤⠄⡄⠚⠃⠀ ⠀⠂⠠⠂⠀⠀⠀⢠⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠙⠛⠿⣿⣷⣧⣷⣌⠉⠉⠉⠉⠉⠉⠀⠀⠦⠆⠆⠢⠈⠅⠀⡀⠀⠀ ⠀⡁⠄⠁⠀⠀⠀⡏⠀⣧⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⣀⣀⡀⣀⣀⣀⣀⠀⡀⣀⡀⣀⡀⣀⢀⡀⣀⣀⣀⣀⣤⠇⠀⠀⠀⠀⡂⠉⠙⡿⢾⣷⢦⣤⣤⣤⣄⠀⠀⠀⠀⠒⠲⠠⠂⠆⡁⠀⠀ ⠀⠄⠤⠁⠀⠀⠀⡇⠀⡅⢣⣀⡔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⡀⠀⠀⠈⠀⠁⠀⠀⠀⠘⠀⠀⢠⠇⢸⢀⡟⠁⠙⣽⠁⡇⠀⠀⠀⠀⠒⠂⠂⠲⠁⣀⠀ ⠨⠀⢪⠀⠀⠀⠀⡇⠀⡂⠘⠃⠀⡀⠄⠈⠀⠀⠀⡀⢀⠠⠀⠠⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⡏⠀⠈⣾⢄⡀⣀⡟⢠⠃⠀⠀⠀⠀⠀⠀⠀⢀⢀⠜⠀ ⢪⠀⣱⠀⠀⠀⠀⡇⠀⢑⠀⠠⠆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠘⠓⠫⠥⠤⠎⠀⠀⠀⠀⣀⣄⢂⡈⡀⣀⣀⠀ ⠀⢮⡿⣄⡀⡀⠀⠈⠣⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⠀⠀⡇⠀⠐⠀⠂⠂⠂⠠⠠⠀⠤⠀⠤⠠⠄⠤⠄⠤⠤⠒⠊⠀ ⠀⠀⠀⠀⠀⠁⠁⠓⠥⠵⡀⡇⡀⠀⠀⠀⠀⠄⢁⡖⠚⠒⠒⠦⡥⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠔⡖⠛⠉⠁⡇⠀⠀⠀⠁⠀⡞⠁⢀⢀⢀⢀⠀⡀⠀⡀⠀⡀⠀⡀⠀⢀⠀⢀⠀⡀⡀⣀⡤ ⠤⠖⠒⠒⠉⠁⠉⠁⠁⠉⠀⡇⠀⠀⠀⢀⠌⠀⡞⠀⣀⠂⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠈⡇⠀⠀⠀⠁⢰⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠃⠀⣰⠃⠀⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠁⣇⡤⠄⠈⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⡠⠧⣄⣀⣀⡤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠣⣄⣀⣀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠄⠠⠀⠠⠀⠠⠀⠄⠀⠄⠀⠄⠀⠄⠀⠄⠀⠄⠀⠠⠀⠠⠀⠀⠄⠀⠄⠄⠀⠄⠄⠐⠀⠂⠂⠀⠂⠂⠠⠠⠀⠤⠠⢀⡀ ⠀⠁⠈⠁⠁⠁⠈⠀⠈⠀⠀⠈⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠄⠂⠀⠢⠀⠀⠂⠀⡀⠠⠀⠀⡀⠀⢀⠀⠀⠐⠀⠀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠄⢄⠠⡀⠀⠄⠀⠠⠄⠀⠀⠀⠄⠀⠀⠀⠠⠆⠀⠀⢀⠀⠀⠀⠀⠄⡀⠂⠀⠀⠀⠄⠀⡀⠀⠀⠄⠄⠀⠀⠠⠀⠀⠁⢀⠀⠀⠂⠁⠀⠄⣀⡀⡉⣂⣄⣀⠀ ⠀⠀⠀⠀⡒⠉⠂⡂⠀⠀⠒⠑⠀⠀⠐⠀⠀⡀⠀⠀⡃⠀⠀⠀⠠⠀⠐⠀⣄⡀⠠⠀⡀⠴⠁⠀⠔⡀⠀⠄⢄⠀⡀⠤⠀⠀⠄⠀⠀⡄⠈⠄⠄⠀⠀⠄⠀⠀⠂⠐⡀⠀⣀⠀⣇⠀⠀⠈⠒⠛ ⢂⠀⠀⢀⠅⠁⠄⠀⡕⣄⠀⢁⠈⠀⠠⢀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⢁⠁⠀⠀⠀⡀⠀⡀⠀⣰⠇⢀⠨⠀⠀⠀⠀⠀ ⠀⠀⠀⠄⠀⠀⡀⠄⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠈⡀⠀⠀⠀⢀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢢⠀⠀⠀⠀⠀ ⠀⡀⠐⠄⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⢀⠈⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠆⡀⠀⠀⠀⠀⠀⠀⠈⢐⠀⠀⠈⠁⠀⠀⠈⠁⠄⠐⠀⠘⠀⣇⡄⠀⠄⠀ ⠁⠀⠠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠁⠂⠀⠁⠀⠈⠀⠂⠀⠈⡀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠁⠄⠄⠀⡀⡤⢀⠀⢇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠃⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠡⡄⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠌⠀⠂⠂⠐⠂⠁⠀⠀⡀⣀⠀⠁⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⡀⠀⣀⠀⠀⠀⠠⠔⠀⢀⠂⡀⠀⠀⠉⢀⠁⠀⠀⣁⠉⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡂⠄⠄⠂⠀⠆⢔⠂⠀⠈⠄⡀⠀⠀⡀⠁⡄⠈⠃⠀⠀⠈⠄⠂⠄⠀⠁⠁⠁⠀⠀⠀⠂⠀⠀⠀⠀⠡⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠈⡠⠑⠀⠐⠀⠀⠃⠀⠀⠀⠀⠠⡀⠀⣀⠀⠀⠀ ⠀⠀⠁⠒⠀⠂⠁⠀⠀⠀⠀⢀⡄⣐⠀⠀⠀⠄⠄⠁⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠂⠀⠀⠉⠒⠈⡀⠀⠀⡁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀ ⠀⠀⠠⣿⢻⣷⠶⠒⠒⠒⠚⢿⡏⣿⠀⠀ ⡴⣒⢆⢻⡞⢁⢤⡄⠀⠀⣖⡄⠙⢟⠀⠀ ⠙⠛⠓⡸⠀⢠⡥⡀⠀⡀⣴⣦⣀⣸⡄⠀ ⠀⠀⢀⡶⠛⢹⠛⠫⣽⣷⠙⠻⡋⢉⣷⠀ ⠀⠀⠈⢯⡐⠉⠀⠀⠙⠋⠀⠀⠀⣠⠞⠀ ⠀⠀⣀⠀⠉⢒⡆⠀⠀⠀⠒⡖⠉⠀⠀⠀ ⡰⡩⠒⡺⣧⠞⠉⠢⡀⠀⠀⢿⠀⠀⠀⠀ ⡇⡄⠘⢿⡟⠀⢒⢧⣌⣆⢰⢸⣷⣶⣆⠀ ⠘⡮⠍⠉⢧⡀⢸⣟⣿⠿⣼⢚⣇⣿⠏⣀ ⠀⠑⠒⠂⠀⠉⠉⠚⠓⠛⠋⠉⠉⠐⠒⠊

⊹₊꒷︵︵︵୭﹒୨🍰୧﹒୧︵︵︵₊˚⊹ ୨💌៸៸₊ ♡⌟ name: (ur name/nickname) ୨🍓៸៸₊ ♡⌟ prns: (ur prns) ˚ ̟ ︶︶ ୨🍰୧ ︶︶︶︶ ⠀⠀⣠⣤⣤⣄⣀⣾⣿⠟⠛⠻⢿⣷⠀ ⢰⣿⡿⠛⠙⠻⣿⣿⠁⠀⠀⠀⢸⣿⡇ ⢿⣿⣇⠀⠀⠀⠈⠏⠀⠀⠀⠀⣼⣿⠀ ⠀⠻⣿⣷⣮⣤⣀⠀ ⠀⣾⡿⠃ (person's name here) search sarrowchan for more!

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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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⡿⣽⢯⣻⢽⣫⠿⣝⣯⢿⡽⣯⢻⡽⣏⣿⡹⢯⣿⣹⢯⣻⣝⢯⡟⣽⢯⣻⡽⣏⡿⣽⢯⡿⣽⢯⡿⣽⣫⣟⡽⢯⣻⣝⢯⣿⣹⢯⣻⣽⣫⢿⣽⣻⢟⣿⡻⣟⣿⢻⣟⡿⣻⢿⣹ ⡿⣭⢷⣏⡟⣉⠻⢽⣮⣯⡽⣞⣿⢋⡭⢹⣿⣽⠶⢛⡛⢛⠛⢾⣽⡷⠟⣓⠿⢾⣽⣳⢯⣻⡭⣷⢻⣵⡳⠟⠾⠛⠳⣾⣛⡾⣽⣫⢷⣳⢯⡟⡾⣝⣻⢾⣝⣟⡾⣻⢾⣝⣯⣟⣳ ⣿⣹⢾⡁⢴⡌⢙⡰⢋⡽⣿⢫⣭⣤⣯⣬⡍⢻⠎⠉⣽⢉⠉⢾⣿⣰⣿⣝⡛⣷⢻⡯⠟⢓⡛⡓⠛⣮⡇⣺⠁⢾⠡⣿⢯⣽⢳⣯⣟⡾⣯⣽⣻⣭⣟⣮⢿⡼⣽⣳⢯⣞⡾⣽⣳ ⡷⣯⣻⡽⡖⣀⣭⠶⢋⣼⣿⣦⡆⣼⠇⣶⣶⣿⣮⠛⣯⠉⠋⢽⣧⢻⣜⣿⣧⣿⣸⣷⣭⣭⣭⣭⣥⣿⢡⡟⡀⣻⣀⣭⢹⣞⡿⣺⢷⣛⡷⢯⣳⡟⣾⣹⢯⡟⡷⢯⣟⡾⣽⣯⢷ ⣟⡷⣳⣏⣧⣭⣴⣶⡿⣟⢧⣟⣦⣭⣾⣿⣛⣮⢟⣷⣝⣛⣿⣾⣿⣶⣭⣿⣯⣵⣿⡟⣯⢿⣝⣯⣻⡽⣦⣴⣿⣭⣭⣿⣾⣟⣳⢯⡿⣭⣟⣯⢷⣻⡵⣯⢷⣻⣽⣻⢾⡽⣶⣻⢞ ⣯⣽⣳⣛⡞⢓⠈⡽⣽⣹⣉⣙⣩⣹⣽⡟⣽⣯⣟⡾⣽⣻⡽⣛⣮⢷⣯⣻⣝⣯⢷⣻⡽⣻⢮⣷⣻⣼⣻⡽⣏⡿⣽⣫⢷⣞⣯⣟⣷⣛⡾⣽⣫⢷⣻⣽⡳⣟⡾⣵⢯⡷⣯⣟⢾ ⡷⣞⡷⣏⡿⢩⣄⣴⡻⢸⣿⠘⡟⣼⡟⣠⡭⢹⣾⡟⡙⣷⣿⣹⢯⣟⡞⣷⢯⣞⣯⢷⣻⡽⣛⣶⡻⣞⣳⡟⣽⣻⡵⣯⣟⡾⣵⣞⣳⢯⣟⡷⢯⣟⡷⣽⣻⣝⣿⣺⢯⣷⣛⡾⢯ ⣟⡾⣽⣫⢷⡶⣬⢷⣳⢷⣶⣾⢿⡿⣷⢿⣿⣶⣾⣷⡶⣿⣳⣽⣾⣷⣿⣽⣾⡽⣮⣷⣯⣾⣽⣾⣷⣯⣷⣿⣧⣷⣻⣵⢾⣹⣳⢯⣟⣻⢮⣟⡿⣞⣽⣳⣟⡾⣳⣽⣻⢶⡯⣟⣯ ⣯⣽⣳⢯⡷⢻⣭⢷⢻⡮⣷⢻⣞⡷⢯⡻⣶⣻⣼⣷⣿⠟⠛⠉⠉⠉⣉⣭⡿⠿⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠿⠿⣿⣿⣾⣭⣏⡿⣞⣽⣻⣞⡷⣽⣞⡷⣏⡿⣾⢽⣻⡼ ⣷⣏⣷⣏⡿⣾⡾⣶⣏⣿⣹⠿⣾⣹⣏⣿⣿⣿⠿⠁⠀⠀⠆⠀⠀⠾⠉⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠈⠉⠿⢿⣿⣿⣶⣏⣾⣹⢷⣾⣹⡏⣿⣉⣿⣱⢿ ⡷⣞⣶⣛⣾⣳⣽⣳⢟⡶⣯⣿⣷⣿⡾⠟⠋⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠂⠈⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠉⠙⠻⣿⣾⣧⣟⣳⢯⣻⢷⣻⢾⡽⣞ ⡿⡽⣞⡽⣾⣱⢷⣯⣿⣿⠿⠟⠋⠁⠠⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⢀⠀⠀⠄⠂⠀⠀⠄⠂⠁⢀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣯⣯⢽⣫⢟⡽ ⣟⣷⣯⣿⣶⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⡆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠁⠀⠂⠀⠐⠀⡀⠀⠙⢯⡉⠛⢿⣿⣽⡾⣽ ⠛⠛⠛⠋⠉⠁⠀⢀⠀⠂⠁⠀⠀⢀⠀⠈⢤⣩⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠄⠂⠀⠐⠀⠀⠀⠄⢂⠄⠙⠀⠀⢈⢻⣿⣾ ⠀⠐⠀⠀⠂⠀⠈⢀⠀⠄⠀⠀⠀⠀⢀⣄⣾⡿⡥⠀⠀⠀⣀⣠⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⡀⠀⢀⠀⠀⡀⠀⠀⠂⠀⢀⠀⠈⠀⠀⠀⠀⢀⡃⡂⠀⠀⠀⠀⠀⠘⣿ ⡀⠀⡀⢀⠐⠀⠀⠀⡀⠀⠐⠀⠐⢀⣎⣿⡟⡏⠀⠁⠰⣾⣿⣿⣿⣧⠀⢀⠀⠠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠄⠀⠸ ⠄⠀⠀⠀⠠⠀⠈⢀⠀⠠⠀⠀⠌⢻⣹⡟⡈⢞⢀⠀⣷⣿⣿⣿⣿⡟⠀⠠⠀⠀⠄⠀⠁⠀⡀⠈⠀⠀⠁⠀⠈⠀⠀⠁⢀⠀⠀⠁⠈⠀⠁⠈⠀⠀⠀⠀⠀⠈⣿⣄⠀⠁⠀⠀⠀ ⠀⠀⠀⠂⠐⠀⠀⡀⠀⠀⡀⠀⠀⣼⣿⣷⣇⠀⢀⣀⢻⣿⣿⣿⠟⠁⠠⠐⠀⠀⠄⠀⠀⠀⠀⡀⠀⠂⠀⠀⣀⠂⠐⠀⡀⠀⢀⠀⣀⣤⣶⣤⡀⠈⢀⠀⠀⠀⠻⢻⡆⠀⠐⠀⠀ ⠂⠈⠀⠄⠁⠀⠀⠀⡀⠀⠀⠄⠀⣹⣿⣿⡹⡟⣿⡹⢿⣎⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⢠⣴⣦⣅⡓⠀⠄⢘⣼⣿⣿⣿⣿⠀⠀⡀⠀⠄⠀⢾⣿⡀⠀⠀⠀ ⠀⠀⠀⢀⠂⠀⠀⠀⠀⣀⣤⣴⣾⡿⣿⣿⣷⣽⣦⣽⠿⠃⠀⠀⠀⡀⠀⢀⠀⠀⠸⣿⣦⣴⣾⣄⡂⠀⣠⣿⣿⣿⣿⣟⣿⣦⠀⠘⣿⣿⣿⣿⣿⡄⠀⠀⠀⡀⠀⠀⣿⡇⠀⠀⠀ ⠀⠐⠠⠀⢀⣀⣠⣴⣷⣿⣟⢿⡽⣾⣝⣿⣿⣶⣄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠻⠛⢻⣿⡿⢿⡿⡟⣿⠻⠿⡿⢿⣿⣿⡿⠋⠀⡑⠀⠁⠀⠀⠀⣿⣇⣀⣀⡀ ⣤⣶⣶⣿⣿⣿⢿⢿⡽⣾⡽⣫⣽⣳⢯⢾⣽⢻⣿⣷⣦⣄⡀⠐⠈⠀⠀⠀⠐⠀⠈⠀⠀⠈⠀⠀⠀⣰⣿⣿⣿⢶⣱⡙⢦⣛⡟⡼⣍⢳⣻⢷⣄⠀⣀⠀⢁⣤⣾⡿⠟⠛⠉⠁⠀ ⣿⢻⣯⣛⡾⣽⣞⣯⢷⣏⡷⣟⡾⣭⣟⣾⣭⣷⣯⣽⣿⣿⣿⣿⣶⣦⣴⣦⣤⣀⣀⣀⣠⣤⣤⣤⣼⣿⣿⣿⣿⡷⣷⢩⢇⡳⢎⡷⣊⠷⣭⢛⣿⣟⣻⣿⣿⠋⠡⠀⠀⠀⠀⠀⠀ ⣯⣟⡾⣽⣻⡵⣾⡽⣾⣽⡻⣝⣾⣽⣾⠿⠛⠉⠉⠁⠈⠉⠛⠻⣾⣟⣻⣿⢋⠀⠟⠻⢉⠉⠉⡙⠙⠛⠿⣿⣿⣻⢼⣿⣾⣱⢫⠼⣱⣏⠶⣩⢾⣿⣿⣧⣿⡇⠀⠀⠀⠀⠄⠀⠀ ⣷⣫⣟⢾⣳⢯⣷⢻⣵⣳⢯⣿⣿⠟⠁⠀⠀⡀⠀⠀⠀⠀⠀⢰⢺⣿⡿⠅⠐⠀⠠⠀⠀⠠⠁⠀⠀⢀⣰⣽⣿⠟⡿⣿⣿⣿⣬⣷⣿⣿⣾⢱⣚⣽⣿⣷⡟⠁⠀⠀⠀⠀⠀⠀⠀ ⣷⣛⡾⣏⣿⢳⣞⣿⡺⣽⣿⣿⠃⣃⠀⡄⣾⠅⠀⠆⠀⠄⠴⣸⣿⠿⠂⠀⠀⠀⡐⢀⣤⣀⣲⣤⣶⣿⣿⣿⣯⢏⣵⣿⣿⠋⠉⠙⠿⣿⣙⢦⣽⣿⡋⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡽⣽⡻⣞⣟⣾⣣⢿⣽⣿⣇⢱⠀⠀⣧⣿⡆⢀⣄⠀⣀⣿⣿⡛⠂⠀⠀⠀⠀⠄⠀⣴⣿⣿⣿⣿⣿⣿⣼⣿⣿⡟⣿⣿⡄⠀⠀⠀⠈⣿⣾⣿⢿⣧⡀⠀⠀⢀⠀⠁⠀⠀⠀⠀ ⣿⡽⢾⣽⣻⣞⣧⣟⣧⢿⣿⡇⢊⠀⠀⠙⢿⣿⣿⡿⢿⣿⣿⠃⠀⠄⠀⠠⠀⢀⠀⠀⠻⣷⣿⡏⣟⣿⣿⣿⣯⣿⣿⣼⣿⣿⣤⣀⣀⣴⣿⣿⣿⣾⡽⣿⣦⣅⣀⠀⠀⠀⠀⠀⠀ ⣿⣹⢿⣶⢿⡾⣾⣹⣎⡿⣿⣿⡰⠀⠀⠀⣾⣿⡉⠁⠉⠈⣿⣶⡆⠀⠀⠀⠀⠀⡀⢀⣸⣿⡿⢱⣿⣾⣿⣿⢷⠹⣿⣏⡾⠿⣿⠿⢿⣿⡿⠏⠹⢿⣿⢷⠿⣿⣿⣿⣿⣾⣿⣿⣿ ⣿⡽⣾⢽⣫⣟⣷⡻⢾⣵⢻⣿⣷⣓⠄⠀⢯⣿⠂⠀⠀⠘⠹⣿⠃⠀⠀⠈⠀⠀⠀⢮⣿⢯⣽⢳⣿⣿⣿⢇⢯⡹⢭⣻⣽⡭⣿⡇⡾⠋⠀⠀⠀⢸⣿⣯⣟⢷⡾⣝⣯⣟⣻⣟⣻ ⣿⣳⢯⣟⣳⢿⣼⢻⣟⢾⣳⢯⢿⣿⣷⣦⣴⣿⣇⣦⠀⠀⢀⠀⠀⠀⡄⠈⠀⡀⢰⣿⣯⢋⣾⣷⡜⣯⢛⡼⢲⣙⢾⡿⠻⠷⠿⠃⠀⠀⠈⠀⠀⣸⣿⣿⢞⣯⣻⡽⣞⡽⣧⣟⣳ ⣿⣭⣟⡾⣽⣛⣾⣻⣞⣯⣟⣾⢻⡼⣏⣿⢻⣿⣿⡍⠀⠈⠀⠀⠀⠀⣿⡇⠀⠀⠈⢿⣧⡿⠋⠙⠻⠷⣿⡜⢧⢺⣿⠁⠀⠀⠀⠀⠀⠁⠂⠀⢀⣹⣿⣯⢟⣾⡳⣿⢽⣻⣳⡽⣳ ⣿⣞⢾⣽⣳⣟⣞⢷⣻⢮⡿⣼⣛⡷⣿⢾⣿⢿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣷⣶⣾⣶⣤⣥⣤⣶⣆⣒⣂⣻⣿⣭⣿⣃⣤⣦⣤⣷⣶⣆⣠⣐⣀⣶⣿⣿⢯⣟⡾⣽⢯⣟⡷⢯⣻⡵ ⣿⣞⡿⡾⣵⣻⣞⣯⣟⣯⣟⡷⣯⣟⣾⣻⣞⣿⣺⣝⢿⣻⢿⡟⣿⣻⢿⣻⢿⣟⡿⢿⣟⡿⣻⢿⢿⡿⢿⢿⡿⣿⣿⢿⡿⡿⢿⡿⢿⡿⣿⡿⣿⢿⣻⣟⡾⣽⣳⣟⡾⣽⢯⣗⣻ ⣷⣻⢾⣽⣳⣟⣮⢷⣛⡶⣯⢷⣻⢮⣷⣻⡼⣞⣷⣫⢷⣯⠿⣽⣳⢯⡿⣽⡻⡾⣽⣻⢾⡽⣯⣟⡾⣽⢯⣟⡷⣯⣞⡷⢯⣟⣯⢟⡿⣞⡷⣽⡽⣞⡷⣽⣽⢳⣯⢾⡽⢯⡾⣽⣳ ⡿⣽⣻⣞⣳⣟⡞⣯⠿⣽⢯⣟⣽⣻⣞⣷⣻⡽⣾⣽⣻⣞⣿⣳⢯⣟⡷⣯⢿⣽⣳⢯⣟⡽⣶⢯⣟⣾⣻⢾⣽⣳⢯⣟⣟⣮⢷⣻⡽⣾⣽⣳⣻⡽⣽⣳⢯⣟⡾⣏⡿⣏⣿⣳⡽ ⣟⣳⣟⡾⡇⡛⠛⠹⣿⡭⣟⣾⣳⢷⣻⢞⣷⣻⢷⣳⣟⡾⢾⣽⣛⡾⣽⢯⡷⣏⣿⣛⡾⣽⢯⣟⡾⣳⢯⣟⡾⣽⣻⢾⡽⣞⣯⢷⣻⣗⡿⣞⣷⣻⣳⢯⣟⡾⣽⢏⡿⣽⢶⣯⡽ ⣯⢷⣯⣟⡷⢾⡷⣾⣳⣽⢻⡾⣝⣯⡽⣛⣮⡽⣻⡼⡽⣞⡟⣶⣏⢿⡵⣯⢷⣻⣼⢫⣽⣳⡻⢮⣟⡽⣏⡾⣽⣣⢿⣹⠾⣝⡾⣫⢷⢾⣹⢷⣚⡷⣽⣛⣮⠿⣝⣯⠿⣭⣟⡾⣽ (˶˃ ᵕ ˂˶)

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣇⠀⠀⠈⠙⠛⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⠀⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠃⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣾⣿⣦⣤⣤⣤⣄⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡀⠀⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣾⣿⣿⣿⡿⢩⣿⣿⣿⣿⣿⣿⡀⣿⣿⡇⠀⠘⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡟⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⢡⣾⣿⣿⣿⣿⣿⣿⣇⣿⣿⡇⠀⠀⠙⢿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⢠⣶⣶⣸⣿⣿⣿⣷⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠃⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⢿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣰⣶⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠈⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⣿⣿⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡏⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢩⣥⡄⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠇⣸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠏⠙⠃⠀⣰⣿⣿⣿⣟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡅⠿⠇⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⢀⣠⣾⣿⣿⣿⣿⢿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢉⣁⣀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⢛⣯⣭⡙⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣍⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⢸⣿⣿⡏⠙⢿⣿⣿⣿⣿⡀⢀⣤⣤⠀⠀⣠⣤⣄⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⢠⣤⣤⡀⠀⣤⣤⡀⠀⣸⣿⣿⣿⡿⠋⢸⣿⣿⣧⣾⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣇⠀⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇⢸⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⣉⠉⠉⠉⢹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⡿⠿⠟⠿⠿⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⢿⡿⠿⠿⣿⣿⣿⠿⠿⠛⠛⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠿⠀⠀⠿⠿⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⣠⡶⠛⠋⠉⠉⠉⠉⠙⠻⠿⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠿⠛⠛⠋⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⢴⣾⣿⣶⣦⠀⠀⠀⠈⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⠀⠀⠀⢠⣴⣿⣾⣶⣄⡀⠀⠀⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠙⢿⣿⣿⣷⠀⠀⠀⠸⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⣰⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠻⣿⣿⡆⠀⠀⢠⣿ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠙⠟⠁⠀⠀⣼⠇ ⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⡟⠀⠀⢠⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⡇⠙⣆⠀⠀⢀⣴⠏⠀ ⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠻⠿⡟⠀⠀⢠⣿⣇⠀⠈⠁⠈⠉⠋⢙⣿⡏⠉⠛⠉⠉⠉⠉⠉⢹⣧⠘⣿⣧⣀⣀⣽⣤⣾⣦⣴⠛⠁⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⣰⠁⠀⠀⣾⣿⣿⣿⣶⣶⣤⣤⣤⣾⢻⣷⣶⣦⣤⣄⣀⣤⣤⣾⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀ ⠀⠀⠀⣰⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⢠⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀ ⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠙⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⡙⣿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣀⣀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠛⢁⡼⢟⡽⠟⠁⠀⣾⣿⣿⣷⠀⢹⣿⣿⣿⠿⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠈⠀⠀⠀⢸⣷⣼⣿⣿⡇⢸⣿⣿⣿⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣷⣶⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠈⣿⣿⣿⡀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠈⠛⠿⠿⠃⠀⠸⣿⣿⣧⠀⠀⠀⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧⡀⠀⠀ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⣀⠴⢧⣀⡴⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠳⢤⣀ ⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⢱⠀⠀ ⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⡿⢸⠀⠀ ⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣉⣛⠛⠛⠗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⢃⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣖⡒⢶⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⢈⡽⠛⠙⠋⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⢿⣿⡿⠟⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠲⣦⡀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠈⠻⣦⡀⠀⠈⢿⣿⣿⣿⣿⣼⣿⣇⣿⣼⣿⣿⣇⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⡄⢠⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠐⣄⠹⣇⠀⠀⢹⣿⣿⣿⣿⣿⣿⣧⢿⣿⣿⣿⣷⠀⡆⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢿⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⡇⡇⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣧⡇⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⣰⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⣆⡰⠃⠀⠀⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⡤⠞⠁⠀⠀⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢦⡀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢀⡠⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠀⠙⡒⠤⣠⠤⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⢄⢀⡤⠖⠋⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠖⠋⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⣑⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢀⡖⠉⠀⠀⣀⡀⠀⠀⠀⠺⠛⢿⡋⠉⠉⠐⠲⠤⣀⡀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣀⡀⠀⠀⣟⠀⠀⠀⣸⠿⠇⢀⣶⣆⣇⠀⠘⡇⠀⠀⠀⠀⠀⠀⠉⠓⣄⠀⠀⠸⡅⠀⢀⣠⠴⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠲⣌⠓⠒⠚⡏⠀⠀⠈⠛⢻⣿⣦⣤⣧⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠈⠉⠉⠀⠈⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡒⢒⡒⠒⠋⠁⠀⠀⠀⣿⣤⣄⣶⡶⢾⡿⠉⠀⠀⠀⡤⠤⠤⣦⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢌⣀⠀⠀⠀⠀⠀⠳⠬⠼⠟⠀⢰⠃⠀⣀⠀⠀⡇⠀⠀⢸⡄⠀⠀⠀⣸⡀⠀⠀⠀⠀⢀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⣄⣀⡀⠀⠀⠀⠸⣆⢤⣿⣿⣿⡷⠤⠤⠤⠷⣿⡷⠶⠾⠥⠤⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠁⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

thorny ppl please get out of here, kids who are like 9 years old are on here looking for combos and can see what's posted. it's gross please let them stay kids, there are other websites for that. thanks :3

Hi my name is Carmen Winstead. I'm 17 years old. I am very similar to you. Did I mention to you that I'm dead? A few years ago a group of girls pushed me down a sewer hole to try and embarrass me. When I didn't come back up the police came.The girl said that I had fell and everyone believed them. The police found my body in the sewer. I had a broken neck and my face was torn off. Send this message to 15 people after you listened the whole message if you value your life. A boy called David received this message. He just left and deleted it. When he was in the shower he heard laughing. My laughter. He got really scared and rushed to his phone to repost this message but he was too late. The next morning his mom entered his bedroom and all she found was a message written in his blood saying 'You will never have him back'. No one has found his body yet because he is with me. A girl called Charlotte received this message and she immediately sent it to 25 people, 10 more than required. I still watch over every second of her life to make sure that she is safe and to keep her and everyone close to her out of danger. Send this to 15 people in the next five minutes if you don't want your fate to be the same as David's. Your time starts now.the story is true you can research it on Google.

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

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

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

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

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⠶⠶⠶⠶⠦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠾⠟⣿⣿⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣤⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠉⠀⠀⠸⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣀⠈⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⢀⡿⠁⠀⠀⣰⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠐⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡇⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠉⠁⠉⠈⠉⠀⠀⠀⠀⠀⠀⣠⢤⣀⠀⠀⠀⠀⠀⠉⠿⠿⠁⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⠀⠀⠀ ⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠤⠠⠐⢀⡀⠀⠀⠀⠀⠀⠋⠁⠉⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⢁⠀⠀⣼⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀ ⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠻⢶⣤⣴⡾⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣤⠀⠜⣀⣴⠟⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀ ⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⣿⠃⠀⠀⢸⡟⠳⠶⠶⠶⢦⣶⣴⣶⣴⣶⣶⣿⠉⠀⠹⣷⣿⣿⣥⣄⡀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢿⣆⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠀⢀⣿⠟⠉⠉⠉⠛⣷⡄⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇ ⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠃⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠿⣷⡀⠀⠀⣀⠀⠈⣿⡄⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⣀⣼⠏⠀ ⠀⠀⠉⠛⠷⠶⠶⠶⠶⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣤⣴⠏⠀⠀⣽⡇⠀⠀⠀⠈⠛⠿⠶⠶⠶⠶⠿⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡾⠋⠀⠁⠀⠀⠀⠀⠀⢀⣾⠛⠉⠙⠓⠀⠀⢀⣴⠟⠛⠿⠾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠐⢶⣶⣶⣶⣶⣾⣿⡀⠀⠀⢶⡶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⣠⡿⠁⠀⠀⠀⠀⢹⣇⡀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠤⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣤⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢋⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠉⠓⠦⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡄⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀ ⠀⠀⣠⠞⠁⠀⠀⣀⣠⣏⡀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⡃⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆ ⢀⡞⠁⠀⣠⠶⠛⠉⠉⠉⠙⢦⡸⣿⡿⠀⠀⠀⡄⢀⣀⣀⡶⠀⠀⠀⢀⡄⣀⠀⣢⠟⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃ ⡞⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⢳⢀⣠⠀⠀⠀⠉⠉⠀⠀⣀⠀⠀⠀⢀⣠⡴⠞⠁⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⣀⣤⠞⠁⠀ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠁⠀⢀⣀⣀⡴⠋⢻⡉⠙⠾⡟⢿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠀⠀⠀⠀ ⠘⣦⡀⠀⠀⠀⠀⠀⠀⣀⣤⠞⢉⣹⣯⣍⣿⠉⠟⠀⠀⣸⠳⣄⡀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠒⠒⠒⠒⠚⠋⠁⠀⡴⠋⢀⡀⢠⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⡾⠋⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠉⠋⠻⣄⠀⠀⠀⠀⠀⣀⣠⣴⠞⠋⠳⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⢤⠤⠶⠋⠙⠳⣆⣀⣈⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣤⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠈⠙⣿⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⢸⣿⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⢸⣿⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣿⠃⠀⠀⠀⠀⠀⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣀⡀⣀⣼⡿⠃⠀⠀⠀⠀⠀⣼⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠉⠁⠀⠀⠀⠀⠈⠉⠛⢿⣯⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⣠⣴⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⣀⣤⣾⠟⠉⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⠋⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡝⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠛⣶⡀⠀⢈⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⡿⢡⣶⠀⠀⢀⡴⢶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⢈⠥⠔⠊⢸⡗⠀⠀⠀⠀⠀⠀ ⢀⢀⣿⠃⢸⡟⠀⠀⠸⠇⠈⠉⠀⢠⡴⣀⣤⣤⣼⡿⠀⠀⠀⠢⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀ ⢐⣾⠋⠀⠸⣿⡀⠂⠉⠐⢢⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⡀⣀⣤⣼⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⢹⡟⠀⠀⠀⠙⢿⣤⣀⣐⣁⠀⢀⣀⣀⣠⣤⣤⣴⣶⠾⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣧⠀⠀⠀⠀⠀⠈⢩⣿⠛⠛⠛⠛⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢻⣦⣀⣀⣀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠤⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣤⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢋⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠉⠓⠦⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡄⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀ ⠀⠀⣠⠞⠁⠀⠀⣀⣠⣏⡀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⡃⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆ ⢀⡞⠁⠀⣠⠶⠛⠉⠉⠉⠙⢦⡸⣿⡿⠀⠀⠀⡄⢀⣀⣀⡶⠀⠀⠀⢀⡄⣀⠀⣢⠟⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃ ⡞⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⢳⢀⣠⠀⠀⠀⠉⠉⠀⠀⣀⠀⠀⠀⢀⣠⡴⠞⠁⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⣀⣤⠞⠁⠀ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠁⠀⢀⣀⣀⡴⠋⢻⡉⠙⠾⡟⢿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠀⠀⠀⠀ ⠘⣦⡀⠀⠀⠀⠀⠀⠀⣀⣤⠞⢉⣹⣯⣍⣿⠉⠟⠀⠀⣸⠳⣄⡀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠒⠒⠒⠒⠚⠋⠁⠀⡴⠋⢀⡀⢠⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⡾⠋⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠉⠋⠻⣄⠀⠀⠀⠀⠀⣀⣠⣴⠞⠋⠳⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⢤⠤⠶⠋⠙⠳⣆⣀⣈⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⠶⠶⠖⠛⠶⠲⠶⠶⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋⠘⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠙⠂⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⢀⠀⠀⠀⢸⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣇⠀⠀⠀⠀⡄⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⢠⠏⠀⠀⠀⢻⣿⡿⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢤⡀⠀⠀⠀⢿⣿⠟⠀⠀⠀⠀⠸⡄⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⢠⡟⢀⠤⠄⠢⠤⢄⠀⠀⠀⠀⠀⠹⠷⠶⠛⠓⠶⠾⠃⠀⠀⠀⠀⢀⠤⠒⠒⠒⠤⡀⢿⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⢸⡇⢀⡀⠀⠀⠀⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣀⠀⠀⣀⠀⢺⡇⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠸⣷⡀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢶⣄⠀⠀⠀⠀⠀⣀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⢿⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⠁⠀⠙⣷⣤⣴⠶⠟⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣦⡀⠀⠀⠀ ⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣴⡾⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠀⠀⠀⠘⠏⢿⡄⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⠀ ⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⣼⡏⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠈⣿⡀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆ ⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⢠⡿⠷⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇ ⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠋⠀⢰⡏⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡟⠀ ⠀⠀⠙⠻⢶⣦⣤⣤⣤⣤⣴⠶⠟⢿⡇⠀⠀⠸⣧⣄⣀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠈⠛⠷⣦⣤⣤⣤⣤⣴⠶⠟⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠉⠉⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⣤⣤⡤⢾⣇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢨⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⣴⠟⠛⠒⠶⠶⠶⠤⠶⠶⠶⠖⠚⠻⢷⣤⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠶⠶⠶⠶⢦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣟⣿⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠁⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⣴⠶⠞⠋⠁⠀⠀⠀⢰⣿⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢴⣤⣾⢿⣆⠀⠀⠈⠙⠳⢶⣤⣀⠀⠀ ⢀⣾⠏⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠝⠋⠉⠀⠀⣦⣤⣴⠆⠀⡀⠙⢺⣷⣄⠀⠀⠀⠀⠀⠀⠙⣷⡀ ⢹⣏⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⣿⣀⡀⠀⠈⠀⠀⠀⠀⠈⠀⣀⣀⣈⣦⡾⠛⠻⣦⣀⠀⠀⠀⠀⣀⡿⠃ ⠈⠻⢧⣤⣤⣤⣤⣴⠾⠛⠁⠀⣠⣼⣿⠿⣿⡿⠻⠿⠿⢿⣿⡿⣿⣿⡟⠉⠀⠀⠀⠀⠙⠛⠲⡶⠟⠋⠀⠀ ⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⢰⣿⠁⢸⣄⡿⠁⠀⠀⢠⣴⣭⣻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡄⠈⢹⣇⠀⠀⠀⠀⢹⡿⠻⣿⠟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⠿⠿⢦⣤⣄⣀⣼⣷⣴⣿⣾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀(˶˃ ᵕ ˂˶)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣀⣀⠙⡆⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⠀⠀⠀⠀⣿⣿⣿ ⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⣿⣿⣿ ⠀⠀⠉⠉⠉⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣟⢋⢿⣿⣿⣿⣿⣿⣷⣍⣿⣿⣿ ⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢫⣻⣿⣿⣆⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠛⠉⠉⣽⣿⣿⣿⣿⣿⡟⠿⠿⠿⠿⠿⠿⠛⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣌⡂⠐⠀⣂⣆⣼⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠟⡟⡛⣿⣿⣿⣿⣿⣿⡿⢿⠛⠛⠿⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠁⣀⠤⣐⢾⠁⠈⢎⠙⢿⡿⠟⡡⠁⠀⠱⡤⡀⠀⠀⠉⣿⣿⣿ ⠀⠀⠀⠀⠀⢠⠾⡀⠁⠀⠛⡺⡯⠀⠑⣹⡟⢰⠁⠙⡯⡀⠁⠈⢑⠤⡀⣿⣿⣿ ⠀⠀⠀⠀⢀⠃⠀⠈⢢⠀⠀⠙⠦⣄⠀⠈⢿⠃⠀⠀⡨⠋⢀⠔⠁⠀⢡⣿⣿⣿ ⠀⠀⠀⠀⡎⠀⠀⠀⠀⡆⠀⠀⠀⠈⠙⠲⡌⢀⡠⠊⠀⠀⡎⠀⠀⠀⠈⣿⣿⣿ ⣤⣤⣤⣴⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣴⣴⣯⣤⣤⣤⣤⣧⣤⣤⣤⣤⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ made by @frizzylovesobjectshows on tiktok!!!

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠶⠶⠶⠶⢦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣟⣿⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠁⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⣴⠶⠞⠋⠁⠀⠀⠀⢰⣿⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢴⣤⣾⢿⣆⠀⠀⠈⠙⠳⢶⣤⣀⠀⠀ ⢀⣾⠏⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠝⠋⠉⠀⠀⣦⣤⣴⠆⠀⡀⠙⢺⣷⣄⠀⠀⠀⠀⠀⠀⠙⣷⡀ ⢹⣏⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⣿⣀⡀⠀⠈⠀⠀⠀⠀⠈⠀⣀⣀⣈⣦⡾⠛⠻⣦⣀⠀⠀⠀⠀⣀⡿⠃ ⠈⠻⢧⣤⣤⣤⣤⣴⠾⠛⠁⠀⣠⣼⣿⠿⣿⡿⠻⠿⠿⢿⣿⡿⣿⣿⡟⠉⠀⠀⠀⠀⠙⠛⠲⡶⠟⠋⠀⠀ ⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⢰⣿⠁⢸⣄⡿⠁⠀⠀⢠⣴⣭⣻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡄⠈⢹⣇⠀⠀⠀⠀⢹⡿⠻⣿⠟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⠿⠿⢦⣤⣄⣀⣼⣷⣴⣿⣾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

There are literally so many things I am thankful for! You guys are 4 sure at the top of my list! Thanks 4 for being my friend even when the other girls aren't. I am presently watching the parade. 😝🥳😂😆😁😄SO MUCH FUN!!!!!!!!!!! TeTeHehE. I miss you guys tons. I hope u guys r having a great thanksgiving! I will see u on MOONDAYYYY! I love you 1%❤ I love you 2%🧡 I love you 3%💛 I love you 4%💚 I love you 5%💙 I love you 6%💜 I love you 7%💗 I love you 8%❤ I love you 9%🧡 I love you 10%💛 I love you 11%💚 I love you 12%💙 I love you 13%💜 I love you 14%💗 I love you 15%❤ I love you 16%🧡 I love you 17%💛 I love you 18%💚 I love you 19%💙 I love you 20%💜 I love you 21%💗 I love you 22%❤ I love you 23%🧡 I love you 24%💛 I love you 25%💚 I love you 26%💙 I love you 27%💜 I love you 28%💗 I love you 29%❤ I love you 30%🧡 I love you 31%💛 I love you 32%💚 I love you 33%💙 I love you 34%💜 I love you 35%💗 I love you 36%❤ I love you 37%🧡 I love you 38%💛 I love you 39%💚 I love you 40%💙 I love you 41%💜 I love you 42%💗 I love you 43%❤ I love you 44%🧡 I love you 45%💛 I love you 46%💚 I love you 47%💙 I love you 48%💜 I love you 49%💗 I love you 50%❤ I love you 51%🧡 I love you 52%💛 I love you 53%💚 I love you 54%💙 I love you 55%💜 I love you 56%💗 I love you 57%❤ I love you 58%🧡 I love you 59%💛 I love you 60%💚 I love you 61%💙 I love you 62%💜 I love you 63%💗 I love you 64%❤ I love you 65%🧡 I love you 66%💛 I love you 67%💚 I love you 68%💙 I love you 69%💜 I love you 69%💗 I love you 70%❤ I love you 71%🧡 I love you 72%💛 I love you 73%💚 I love you 74%💙 I love you 75%💜 I love you 76%💗 I love you 77%❤ I love you 78%🧡 I love you 79%💛 I love you 80%💚 I love you 81%💙 I love you 82%💜 I love you 83%💗 I love you 84%❤ I love you 85%🧡 I love you 86%💛 I love you 87%💚 I love you 88%💙 I love you 89%💜 I love you 90%💗 I love you 91%❤ I love you 92%🧡 I love you 93%💛 I love you 94%💚 I love you 95%💙 I love you 96%💜 I love you 97%💗 I love you 98%❤ I love you 99%🧡 I LOVE YOU 100%💖 I love you 101%❤ I love you 102%🧡 I love you 103%💛 I love you 104%💚 I love you 105%💙 I love you 106%💜 I love you 107%💗 I love you 108%❤ I love you 109%🧡 I love you 110%💛 I love you 111%💚 I love you 112%💙 I love you 113%💜 I love you 114%💗 I love you 115%❤ I love you 116%🧡 I love you 117%💛 I love you 118%💚 I love you 119%💙 I love you 120%💜 I love you 121%💗 I love you 122%❤ I love you 123%🧡 I love you 124%💛 I love you 125%💚 I love you 126%💙 I love you 127%💜 I love you 128%💗 I love you 129%❤ I love you 130%🧡 I love you 131%💛 I love you 132%💚 I love you 133%💙 I love you 134%💜 I love you 135%💗 I love you 136%❤ I love you 37%🧡 I love you 138%💛 I love you 139%💚 I love you 140%💙 I love you 141%💜 I love you 142%💗 I love you 143%❤ I love you 144%🧡 I love you 145%💛 I love you 146%💚 I love you 147%💙 I love you 148%💜 I love you 149%💗 I love you 150%❤ I love you 151%🧡 I love you 152%💛 I love you 153%💚 I love you 154%💙 I love you 155%💜 I love you 156%💗 I love you 157%❤ I love you 158%🧡 I love you 159%💛 I love you 160%💚 I love you 161%💙 I love you 162%💜 I love you 163%💗 I love you 164%❤ I love you 165%🧡 I love you 166%💛 I love you 167%💚 I love you 168%💙 I love you 169%💜 I love you 169%💗 I love you 170%❤ I love you 171%🧡 I love you 172%💛 I love you 173%💚 I love you 174%💙 I love you 175%💜 I love you 176%💗 I love you 177%❤ I love you 178%🧡 I love you 179%💛 I love you 180%💚 I love you 181%💙 I love you 182%💜 I love you 183%💗 I love you 184%❤ I love you 185%🧡 I love you 186%💛 I love you 187%💚 I love you 188%💙 I love you 189%💜 I love you 190%💗 I love you 191%❤ I love you 192%🧡 I love you 193%💛 I love you 194%💚 I love you 195%💙 I love you 196%💜 I love you 197%💗 I love you 198%❤ I love you 199%🧡 I LOVE YOU 200%💖 THIS TAKES WAYYYYYYY TO LONG, LOVE U GUYSSSSSSS! ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⠟⠁⠀⠀⠀⠹⣿⣿⣿⣿⣿⠟⠁⠀⠀⠹⣿⣿⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢼⣿⠀⢿⣿⣿⣿⣿⠀⣾⣷⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣷⡀⠀⠀⠈⠋⢀⣿⣿⣿⣿⣿⡀⠙⠋⠀⢀⣾⣿⣿⡇⠀⠀⠀⠀ ⢀⣀⣀⣀⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣾⣿⣷⣦⣤⣴⣿⣿⣿⣿⣤⠤⢤⣤⡄ ⠈⠉⠉⢉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀ ⠐⠚⠋⠉⢀⣬⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣀⡀⠈⠀⠈⠛ ⠀⠀⠴⠚⠉⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠉⠛⠢⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⠟⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣇⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣟⣃⡤⠤⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣴⡶⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⠟⠁⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡆⠀⢿⣿⠁⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠯⠀⢠⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⠀⣿⡏⠀⠀⠀⢠⡀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⠀⠀⠘⡆⠀⣰⣿⣿⣿⣿⣿⣿⣿⣜⣷⣿⠁⠀⠀⠀⢸⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⠀⠀⠘⣿⢠⣿⣿⣿⣿⣿⣿⣟⠿⢿⠛⠁⠓⠆⠀⠀⣼⠁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡄⠀⠀⣾⣾⣷⣿⣿⣿⠿⢿⣿⣶⣾⣶⣶⣾⣷⣶⣶⣿⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⢹⣇⣾⣿⢿⡟⠀⠸⣿⡄⢹⡁⠀⠀⠀⠀⠈⢹⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⣿⡟⠉⠘⣇⠀⠀⠉⠙⠺⡇⠀⠀⠀⠀⡓⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣷⠀⠀⣼⡿⠧⠒⠒⠛⠛⠒⣶⢤⣄⣳⡀⣀⣀⡤⠥⠤⠬⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⣿⣿⡿⠑⠀⠀⠀⠀⠀⠈⠙⠓⠢⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⢋⣷⠊⠀⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣯⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀ ⢠⡴⢻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣗⡇⠀⠀⠀⠀⠀⠀⠀ ⠈⣷⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⣿⣿⣿⡟⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡷⠖⠒⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢁⣢⣿⡿⡿⣇⠈⠙⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡞⠀⠀⠀⣀⣀⡀⠀⠀ ⢠⠞⠀⠀⠀⠀⠀⠹⣶⢤⡀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠈⡇⢀⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢀⡴⠊⠁⠀⠈⢦⡀ ⡞⠀⠀⠀⠀⠀⠀⠀⠙⠳⣽⣷⡀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢷⣶⡿⠀⠀⠀⠀⠀⠀⢧ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⢦⡀⠀⢠⢿⠀⠀⠀⠀⠀⢧⠈⠀⠀⠀⠀⣀⡤⠤⠤⠤⣴⣻⣳⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾ ⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣏⡇⢹⡀⣸⡏⠀⠀⠀⠀⠀⠘⡆⠀⠀⣰⠋⠁⠀⠀⠀⢰⣳⣧⡇⠀⡆⠀⠀⠀⠰⠀⠀⢀⡟ ⠘⣆⠀⠀⠀⠀⠀⠀⣄⢧⣾⣿⣿⠁⠀⢷⡿⠀⠀⠀⠀⠀⠀⠀⢱⠀⡴⠃⠀⠀⠀⠀⠀⣾⣿⢧⣧⠀⡇⢰⠀⠀⡀⠀⠀⣼⠃ ⠀⠸⡄⠀⠀⠀⠀⠀⠈⣿⣿⡽⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⢸⠁⠀⠀⠀⠀⠀⠀⠻⣿⣮⣿⣷⡇⠀⡄⠀⠀⠀⣔⡏⠀ ⠀⢰⠻⡄⠀⠀⠀⠀⠀⢹⣏⡄⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠸⡌⠒⠀⠀⠀⠀⠀⠀⠀⢘⣻⣿⡟⠁⡀⠀⠀⠀⠀⠙⡇⠀ ⠀⡼⠰⢿⠀⠀⠀⠀⠀⠈⠛⣶⣦⣀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢤⣀⣠⠤⠴⠚⠉⠀⡼⠁⠀⠁⠀⠀⠀⠀⠀⢹⠀ ⠀⡇⠀⠈⠀⠀⡀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢠⠀⠀⠀⢸⠀ ⠀⢧⠀⠀⠀⠀⠹⢤⡀⠀⠀⠀⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢲⠇⠀⠀⠀⠀⠀⠞⠀⠀⠀⣸⠀ ⠀⠈⠳⠤⣀⣀⣀⣀⡤⠤⠤⠤⠵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠯⢤⣀⣀⣀⡤⠤⠤⠤⠤⠴⠏⠀

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Place it down my throat Tongue tickle yo' dick but not telling a joke Peddle in this pussy that's how you rock a boat It get live in this pussy, I'm not talking Periscope In the sheets I am a bully Give more head than a hoodie Every time you make me cum it look just like vanilla pudding Sit on yo face all day until you say, "Bae, it hurt me" Then I turn around and give the dick more kisses than Hershey's Yo' dick brick-hard like a medal (uh) I got three holes for it like a pretzel (mhm) Tight as a virgin boy don't get nervous (tight) I'm here to serve you customer service (right) I save dick by giving it CPR (I save dick by giving it CPR, yes) Put my mouth on it like CPR (Let's make porn and watch it on VCR) I think we should fuck up in every zip code It would make my pussy wetter than a fishbowl Pussy a kitty cat, I pet it like a pet I fuck doggy style so much I need to go to the vet Hotbox? More like a scorching pussy Open this coochie up like a fortune cookie Yo' banana in my mouth watch my tongue go ape Yo' dick getting more blows than a birthday cake When I'm near it, no, I don't fear it Licking on that penis like a letter when I seal it Today way wetter than my past slob And if you unemployed, I can give you a ass job Pussy already wet don't need no lube ointment Dick twisting in my stomach like food poisoning That's how you know when you hit the spot I'll make your pants unzip more than Ziploc Yo' dick brick-hard like a medal (uh) I got three holes for it like a pretzel (mhm) Tight as a virgin boy don't get nervous (tight) I'm here to serve you customer service (right) I save dick by giving it CPR (I save dick by giving it CPR, yes) Put my mouth on it like CPR (Let's make porn and watch it on VCR) Anything goes when you up in my hole Dirty panties from the sex, yeah, I got me some loads Listen, I'm the most explicit Long stick inside my river but we not going fishing Know what to do every time you have a horrible day I'll eat that sausage all day like it's Memorial Day I'm talking BBQ sauce and mustard on it And the mayonnaise comes when you bust right on it Name anything freaky and you know I'm 'bout that shit Only time I'm not on the dick is when I'm 'bout to shit Pubic hairs all in my mouth, not again So when I suck yo' dick now, I use bobby pins Who need a gym when you got dick to work you out? I want my face to lose weight so stroke my mouth And any time my pussy wanna be hairy like Harry Potter Becky with the good hair is what you could call her Let's get it A little faster A little more Right there Give it to me now (Uh, uh, uh, uh, uh, uh) (Uh, uh, uh, uh, uh, uh, uh, uh) ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⸜(｡˃ ᵕ ˂ )⸝♡⸜(｡˃ ᵕ ˂ )⸝♡⸜(｡˃ ᵕ ˂ )⸝♡⸜(｡˃ ᵕ ˂ )⸝♡⸜(｡˃ ᵕ ˂ )⸝♡⸜(｡˃ ᵕ ˂ )⸝♡⸜(｡˃ ᵕ ˂ )⸝♡૮꒰ ˶• ༝ •˶꒱ა ♡₊˚⊹ ᰔ⋅˚₊‧ ୨୧ ‧₊˚ ⋅(˶ᵔ ᵕ ᵔ˶)(˶ᵔ ᵕ ᵔ˶)ʚɞ 𐙚 🪼⋆.ೃ࿔*:･🪼⋆.ೃ࿔*:･⋅˚₊‧ ୨୧ ‧₊˚ ⋅🪼⋆.ೃ࿔*:･ദ്ദി ˉ͈̀꒳ˉ͈́ )✧≽^•⩊•^≼ྀི☆⋆｡𖦹°‧★✩°｡⋆⸜ 🎧✮⋆｡‧˚ʚ🍓ɞ˚‧｡⋆✩°｡⋆⸜ 🎧✮𓍯𓂃‧₊˚🖇️✩ ₊˚🎧⊹♡‧₊˚🖇️✩ ₊˚🎧⊹♡୭ 🧷 ✧ ˚. ᵎᵎ 🎀✮ ⋆ ˚｡𖦹 ⋆｡°✩𓏲 ๋࣭  ࣪ ˖𓏲 ๋࣭  ࣪ ˖૮₍ ˶ᵔ ᵕ ᵔ˶ ₎აﮩ٨ـﮩﮩ٨ـ♡ﮩ٨ـﮩﮩ٨ـﮩ٨ـﮩﮩ٨ـ♡ﮩ٨ـﮩﮩ٨ـ༘⋆✿𓇢𓆸ε(´｡•᎑•`)っ 💕ε(´｡•᎑•`)っ 💕(˵ •̀ ᴗ - ˵ ) ✧(˵ •̀ ᴗ - ˵ ) ✧

✧ ⢠⣤⣤⣀ ⠀⠀⠀⠀⠀⠀ ⣀⣤⣤⡄ ⢸⣿⣿⣿⣿⣦⣄⣀⣠⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⊹ ⣸⣿⣿⣿⣿⣿⡽⣿⣯⣿⣿⣿⣿⣿⣇ ⢻⣿⣿⣿⠿⣻⣵⡟⣮⣟⠿⣿⣿⣿⡟ ⠀⠀⠀⠀⣼⣿⡿ ⠀⢿⣿⣷⡀ ⊹⠀⣠⣾⣿⣿⠃ ⠀⠈⢿⣿⣿⣦⡀ ⠀⠈⠉⠹⡿⠁⠀⠀⠀⠀⠈⢻⡇⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ₊˚⊹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠄⠀⠀⢤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⣀⠖⠒⢚⠒⡆ ⡋⣭⠋⠉⠉⠛⠖⢦⡀⠀⠉⠈⠂⠤⡀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⡐⡗⠁⣴⣟⠆⠀⢰⡇⠀ ⠇⣏⣡⠀⠫⣍⣒⢤⡈⠳⣋⣀⣁⣻⡗⠁⠀⡜⠀⢀⡈⠑⣆⠀⣼⢁⣮⠞⠃⠀⠀⢀⠏⠀⠀ ⠀⠈⠚⠿⣆⢀⠀⠉⠋⠐⠛⠂⠀⠁⠋⠉⠛⡋⠁⠀⠋⠏⠙⠿⠋⡥⠄⡄⡴⠶⠚⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠹⠂⡆⠆⡇⡇⢘⡄⢘⠑⠀⡄⡁⠈⡗⠚⠧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡽⡊⢠⠃⡅⡇⡀⠀⡗⢨⠀⠘⠅⡆⠀⠲⠀⠀⣰⡄⠉⠇⠰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣻⡇⢸⢶⡟⡄⢧⠀⠓⠊⠧⠈⠆⣷⠴⠊⠓⡿⡴⡢⠒⠲⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢾⡟⠀⠙⠃⠀⠁⠀⠀⠀⠀⠀⠀⠛⠀⠀⢰⢳⣱⠁⠳⡤⠆⠸⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⡏⠀⠀⠚⠓⢀⡋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠳⢄⡖⠲⣄⣀⣠⠞⠀⠀⡎⣫⠏⠀⡟⠒⠒⠚⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡟⠢⠤⣀⣀⣀⣀⢤⣤⣤⣔⣂⣀⢿⢡⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⣿⠭⠿⡿⢿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢾⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⣏⢙⠁⠁⠙⣑⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⡇⡴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡄⠀⠀⡄⢲⢀⣤⠀⡇⣀⡀⣀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠉⠉⣿⠀⠀⡏⠀⠏⠀⢸⠀⠏⠀⡅⠘⠒⠚⡃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠑⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠦⠤⠤⣀⣀⣀⣀⣀⡤⠔⠋⠀⠀⠀⠀⠀⠀⠀

ATTENTION PORN/SMUT ETC HATERS!!!! SPAM HATE TO .lemon, .blueberry, .cherry, .pinetree, and .lavender!!!! DONT STOP UNTILL THEY STOP!!!!! - lvy

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢖⡨⠌⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⢭⣎⣶⣸⣄⢬⣠⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠰⢯⣿⣾⢞⣻⣿⣿⡴⣯⢲⣄⣀⢀⠠⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣺⣿⣟⣿⣾⢻⣿⣜⣿⣿⣿⣲⣸⣿⢣⠁⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠽⡿⣿⣿⡿⣿⣿⡿⣿⣿⡽⢾⣼⣟⣫⠳⡣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣰⢿⡿⠿⡿⣿⣿⢷⣿⣿⣿⣷⣿⣿⣿⣷⢿⡿⣽⡳⠁⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡐⠁⠀⠀⠰⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠝⠻⣻⣟⣿⡻⣿⣟⣿⣯⣯⣿⣿⣿⣾⣿⡽⠀⢚⣨⡂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠈⠀⠈⠑⠿⠫⢻⢳⣭⣛⣞⠛⠛⠛⠃⠀⠀⢠⡟⡐⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠎⠀⠀⠌⠒⢿⡥⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠢⠹⠿⠋⠁⠈⠓⠀⠀⠀⠀⠀⢸⡯⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠌⠀⠀⠀⢀⡗⢾⣧⠀⠀⠀⠀⠀⢸⡷⠄⠀⠀⣴⣤⡄⠀⠠⠀⠀⠓⠀⠀⠀⠀⠀⠀⢀⢀⣴⣴⡀⠀⠀⣠⡄⠀⠀⠀⠀⣽⣳⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣌⢺⣿⡆⠀⠀⠀⠀⢼⡁⡀⠀⢸⣿⣿⣿⠀⢀⠀⠀⠀⣠⢄⠀⠀⠀⠀⠀⣰⣿⣿⡏⠀⠀⠚⢉⠀⠀⠀⢘⣿⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠔⠛⣵⡋⣿⣧⠄⠀⠀⠀⠘⡋⠁⠀⠀⠉⠛⠁⠀⠀⠀⠠⠺⡀⠀⡹⠀⠀⠀⠀⠈⠛⠋⡀⠀⠐⢴⢃⠈⢀⢤⣿⣿⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠄⠀⠀⠀⠀⠴⢫⡶⢋⣿⣧⣀⠀⠀⠀⢱⠲⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠁⠀⠀⠐⠀⠀⠀⠀⠀⠈⣷⡶⠶⠋⢠⢌⣾⣿⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠀⠀⠀⠀⠀⠄⣼⣔⢿⣽⣿⠙⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⢠⣀⣤⣞⢱⣦⣧⡾⠋⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢂⢿⡔⢋⣿⣿⠄⠀⡹⠏⠳⡒⠴⡴⠀⠉⠀⠀⠀⠀⠣⠉⠊⠡⠁⠘⠁⠭⠋⠛⢉⣿⣿⡞⠏⠋⠭⣽⣿⣾⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⢨⠤⢝⣼⣿⡴⠉⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⠀⠀⢂⠀⡀⠀⠀⠀⢠⡀⣿⠟⠕⠀⠈⢸⣽⣟⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠀⢋⡴⢋⣾⣿⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠀⠀⠀⠀⠀⠈⠚⠿⢃⡌⠀⠀⠨⠩⣝⢿⣯⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠆⠀⠀⠀⠀⠀⠀⢉⡶⣫⣿⢟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣀⠦⡒⠐⠋⠀⠀⠀⠀⠀⠀⠀⠈⠦⣄⡈⣠⣡⠎⢸⢧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠡⠀⠀⠀⠀⠀⠀⡼⢞⣵⡟⠀⠡⡄⠠⠠⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠃⠉⠁⠀⠀⣣⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⢀⠀⠀⠀⠀⠔⠀⣟⣽⣿⠃⠀⠀⠈⢨⠀⠀⡄⢮⡰⢀⡀⠀⠀⠀⠀⣸⡆⠀⠀⠐⠀⢠⣲⡄⢸⢱⠂⠁⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⡄⠀⠀⠘⢆⣎⣿⣿⠋⠀⠀⠀⠀⣌⡀⠈⠟⢂⡀⠟⠿⠁⠀⠀⠐⢾⣇⣠⠂⠀⢠⠨⣉⡀⠄⡢⡤⠀⠀⢔⡀⠀⠀⠀⠀⠀⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠠⠄⠼⠿⠻⠋⠀⠀⠀⠀⠀⠀⠘⠥⢀⠠⡟⢫⢆⠀⠠⠂⠀⠀⢹⣿⡅⣆⠀⢡⣿⣿⣻⠇⠈⠁⠂⠀⢀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡠⠀⠠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠛⠋⢀⢰⠶⡤⠴⢸⣿⠿⣧⡦⣀⣥⢋⠉⠠⠴⠣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⡿⣟⣿⣻⣟⣿⣻⣟⢿⣽⣻⢽⢯⡟⡿⣽⢯⣟⠿⣽⣻⡽⢯⣟⣯⣟⢯⣟⡿⣽⣻⣽⢻⣯⡟⡿⣽⢯⣻⡝⣯⢽⣩⢏⢮⡱⢎⢲⡑⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣫⢿⣹⣝⡺⡔⢢⠀⡀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⡾⣟⣯⢿⣻⣞⣷⣻⣞⡷⢯⣻⠶⣏⢿⡺⣽⣹⡞⣽⣚⡟⣧⢷⣛⡿⡼⢶⣫⣟⡾⣽⣳⢯⣞⡿⣶⣻⣽⣳⢯⣷⣹⢧⡻⣜⣚⢦⡙⢮⡱⢬⡙⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣻⡜⣧⡙⢆⡡⢀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⡿⣯⣟⣿⣽⣻⢷⣻⣞⡷⣯⣻⢏⣷⢿⣿⣾⣷⣿⢯⣽⣝⡛⠾⣧⣟⡼⢳⡝⣯⢳⡞⣽⠾⣵⣻⢾⣽⣳⡟⣾⡽⣳⢧⡟⣧⢻⡼⣩⠶⣙⢦⠳⡌⢞⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⢻⡴⣩⠦⡑⠂⡌⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣟⣿⣽⣟⣾⣳⢿⣯⢷⣯⣟⣷⣯⢿⣭⡟⢯⣽⢃⢆⢺⣴⣊⠙⢦⡀⠈⠙⠧⣞⢌⡳⣹⢧⣛⠷⣯⣻⢶⣯⢟⣷⣻⡽⢯⡽⣝⣧⢻⣥⢻⡜⣎⢧⡙⣎⢆⣿⣿⣿⣾⣿⣟⣿⣿⣿⣿⣿⣿⢿⣻⣾⢯⣿⡱⣏⠼⣁⠒⡈⢄⠂⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣾⣟⣷⣟⡿⣾⣽⣷⣻⣟⣾⣻⣾⣿⢿⣸⣿⢫⢼⣷⡏⣷⡾⠟⠏⠃⠀⠀⠑⢆⠀⠀⠈⠳⣔⠱⢮⡝⣯⢳⣏⡿⣞⡿⣞⣷⣻⢯⣟⢷⣭⣳⢎⡷⣚⡼⢢⡝⡜⢮⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⣮⠷⣭⢻⡔⣫⠔⣊⠔⡁ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⣟⣷⣿⣻⣾⣟⣿⢾⣳⡿⣞⣷⣿⣿⣟⢣⣾⡏⢆⣿⢼⡇⠋⡁⠀⢸⠠⠰⡀⡀⠀⢢⠀⠀⢂⠈⠳⣜⠺⣵⡛⣞⡽⣯⢿⡽⣾⣽⣻⣞⡿⢶⣫⢟⡼⣣⡝⣧⡝⡞⣥⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣳⣛⡾⣵⢫⡖⣍⠲ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⡾⣟⣾⣟⡷⣿⢯⣿⣻⣽⣿⣿⣿⣿⢏⣾⣿⢘⡞⡽⢸⢣⠀⠇⠀⠀⡆⡇⣷⡈⠀⠀⢣⠀⠀⢠⠘⢿⣧⠳⣝⣎⡳⣏⡿⣽⣳⢯⡷⣯⣟⣯⢯⣟⢾⣱⣛⢶⡹⣝⢮⡳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣯⢷⣻⡜⣯ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⡿⣯⣷⢿⣟⣿⢾⣿⣻⡿⣽⣿⣿⣿⣿⣿⡿⢎⣿⡟⢸⢡⣷⠈⣇⠣⣀⡃⠀⣧⢧⡛⠻⣦⡀⠄⢇⠀⠀⢆⠈⢿⣧⢻⣎⣷⢺⣽⣳⣟⣯⣟⣷⣻⣞⡿⣞⣯⣳⢏⡷⣝⢮⡳⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣽⣏⣯⣗⣿⣳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣯⣷⢿⣻⣽⡿⣯⢿⣻⣽⣷⣿⣿⣿⣿⣿⣿⣿⡿⡞⣿⡇⡘⣾⢱⠀⣿⣤⠞⠑⢲⣿⣿⣇⠀⠈⠳⣜⣿⡀⠀⠈⡆⠈⢾⡧⢿⡜⣟⣾⣳⣟⡾⣽⣞⡷⣯⢿⡽⣞⡷⣯⡟⣾⣭⢷⣛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣽⣾⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⢿⣽⡾⣟⣿⣳⣿⣻⡿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣳⡛⡿⡇⢹⠇⢈⣾⠻⣿⡄⢠⢾⣿⡾⡏⠈⠉⠉⠙⢿⡇⠀⢠⠸⠰⡀⢻⡞⣽⢯⣞⡷⣯⣟⣯⢿⣽⢯⣿⡽⣯⣟⣷⣻⠷⣞⣯⣳⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣟⣿⣳⡿⣿⣽⢯⣷⡿⣽⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣥⢃⣧⣧⡞⠊⠁⠻⣧⠿⣘⣏⣾⠿⠽⣷⣿⠿⢿⡻⣾⣷⡇⢸⡌⡇⢱⡄⣙⢧⣿⣾⣟⣷⣻⢾⣻⣽⢿⣾⣻⣷⣻⢾⣽⣻⡽⣶⢯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⣷⣟⣷⣯⡷⣿⣽⣟⣾⢿⣯⢿⣟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⣼⢁⣤⣶⡿⠟⠒⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⠆⢨⣿⢹⡀⣷⣌⢻⡝⣻⢼⣳⢯⡿⣽⡾⣟⣷⣿⣳⡿⣟⣾⢷⣻⣽⣻⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣻⣟⣾⣟⣾⣽⣟⣾⣯⢿⣻⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⣧⠘⢿⠯⠤⠉⠀⠀⠀⠀⠀⣲⠀⠀⠀⠀⠀⠀⠀⠎⣿⡂⠐⣿⠀⣧⢸⡞⣆⢻⡜⣧⣻⢯⣟⡷⣿⣻⣽⣾⢿⣽⡿⣯⣿⢯⣷⢿⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢷⣿⢯⣷⢿⣽⡾⣯⣷⢿⣻⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣽⣿⢯⣷⡀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢠⣣⠀⢀⣿⢠⡏⣿⡗⣽⢸⣟⡶⣯⣟⣾⣽⣟⣯⣿⣯⣿⣟⣿⣿⣽⡿⣯⣿⢾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣻⣿⢯⣿⢯⣿⣞⣿⣳⡿⣟⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡟⠛⡆⠈⠻⣷⡭⡂⠀⠀⠀⠀⣤⣶⠶⠿⢿⡆⠀⢸⢀⣾⡇⠀⣸⠀⣸⣷⠸⣿⣾⣿⣯⣷⣿⢾⣽⣾⣟⣿⣷⣿⣻⣿⣿⣾⣟⣿⡿⣯⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢿⣽⡿⣯⣿⢷⣯⣿⡽⣟⣿⣯⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣻⠇⣸⡁⠀⣹⡄⠠⡙⢷⡌⠑⠀⠀⠀⠛⠁⠒⠂⠉⠁⠀⠐⣡⡿⠀⢀⡇⢀⡏⣼⢸⣿⣿⣿⣯⣿⣿⣞⣿⣷⡿⣿⣾⣿⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣻⣽⡿⣽⣯⣷⣟⣿⣟⣿⡾⣟⣾⣿⣿⣯⣿⣾⣿⣿⣿⣽⢠⡟⣇⢳⡘⣿⡄⠑⠌⢻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣧⠀⣼⣿⢸⣧⢇⣿⣼⣻⣧⢻⡿⣿⣿⣿⡿⣽⣿⣷⣿⣿⣽⣿⣷⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣽⣿⢯⣿⣟⣷⡿⣾⣻⣾⢯⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡼⣏⣷⣹⣆⢻⣽⣿⢦⠀⠂⢹⣿⣿⣿⠒⡤⣄⣀⡤⠊⣡⢿⣿⡇⢀⣧⣿⣎⣿⣸⡿⣼⣿⣧⡟⣯⢻⣱⣿⣻⣟⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣠⣤⡜⠀⢈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠏⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠰⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡆⢤⡄⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠘⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢁⣀⠀⠀⠀⠀⡀⢈⠻⣿⣿⣿⢿⡿⣿⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢳⣦⣤⣠⠜⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠙⠒⢤⣤⣄⣀⣀⣀⣀⣤⡶⠇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠉⠀⢀⣈⡉⠰⠄⣈⣀⣠⡈⠻⣞⣯⢿⣽⣻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣉⠉⣡⡾⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠋⠉⠀⠀⠀⣀⣀⠀⠔⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⡾⢯⡷⣳⢯ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣥⢶⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠋⠀⣼⠀⠀⠀⠼⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠚⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⢾⠱⡏ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠶⢦⣤⣤⣶⠞⢤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣺⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡘⢧⡸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠣⢞⣿⠤⢹⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡍⢲⠱ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡑⠌⠾⣧⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡅⢂ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠓⡌⠱⡹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⢝⠒⢂⣀⣠⣤⣤⣶⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠄⡡ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡄⢃⠌⡑⢄⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠻⢿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢈⡐⠄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠇⡌⠌⣳⠈⡜⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠴⣤⢳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠣⠌⢂⢍⠒⢬⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠑⡌⠢⢌⡘⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣛⠿⣟⢻⡿⣿⣿⠰⣈⠑⢢⡐⣿⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣟⡾⣽⣳⢯⣟⣿⣿⠿⠿⠷⠳⢦⣈⡛⠬⠆⡙⢌⢻⠰⢠⠉⢆⣸⣿⠁⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⣿ ⣿⣿⣿⣿⣿⣿⡿⣿⡽⡾⣝⠾⣜⡳⢭⡳⢫⠞⡽⣛⡿⣳⢶⣤⣀⠈⢁⠢⠑⡌⠢⢽⡎⠤⡉⢆⣾⡿⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⡳⢟⡽ ⣿⣿⣿⣿⣟⣯⡟⣷⣹⢳⣭⢻⣬⢳⢫⢵⢫⡽⣱⢫⣜⡷⠿⠻⠿⠿⠦⢁⠃⡄⠣⡘⠷⢂⡱⣪⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⡰⢉⡒⠄ ⣿⣿⣟⣷⢻⡼⣽⢲⣏⠷⣎⠷⣜⣣⠟⣎⢷⡺⣵⣫⣟⡿⣶⣶⣤⣤⣤⣀⣦⣰⣵⣼⣷⣷⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⢢⠁⢆⠡ ⣿⡳⣞⡾⣹⢞⡵⣫⢞⡽⢎⡟⣬⡓⣿⡸⢧⣛⣶⣻⣼⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢈⠆⡑⠈⠄ ⣷⢻⡵⣫⢗⡯⣞⡵⣫⢞⡽⢺⣱⢛⣶⣹⣧⣟⡶⠯⠿⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠐⠚⠒⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠡⡈⠔⡈⠡⠀ ⡽⣣⢟⡵⣫⢞⣬⡷⠽⠚⠛⠋⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢀⠌⠐⡀⠡⠀ ⡻⣵⢫⣞⠵⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⢤⣀⠀⠀⠀⠀⢰⣠⠀⠀⠀⠀⢸⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢂⠈⠄⠠⠐⠀ ⣟⠼⡳⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠀⠀⠀⢿⡆⢠⠀⠀⢸⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡀⠈⠀⡀⠂⠀ ⢮⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠸⡿⢆⠀⠀⠘⣀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀⠈⠀⠀⠀⠀ ⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡙⣄⠀⠀⣿⣮⣆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⡀⢻⣿⣿⣄⣰⣿⡆⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣟⣿⣿⠍⠰⡀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡞⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⣽⠙⣿⡄⡀⡱⡄⢠⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠳⡍⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢯⡒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄⠀⠀⢀⠄⠀⠀⠈⠀⠀⢀⠿⡇⢹⣧⡀⠌⠈⠙⢢⣡⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢱⢊⠴⡙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⡜⠀⠃⢸⣿⣷⣧⣆⣀⣀⡈⠓⣤⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⡍⠰⢈⠂⡙⢮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠿⣦⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢂⠀⠀⠀⠀⠀⢀⡰⠯⠇⢀⣾⠻⠛⠛⠉⠉⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢂⠄⡁⢂⠐⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⢀⣀⡤⠔⠋⢀⡠⠶⠋⠀⠀⠀⠀⠀⣀⠤⠴⠋⠌⠙⠩⢛⠿⣻⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⠂⠈⠀⠂⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣾⣭⣤⢤⣴⣶⠉⠒⠈⢉⡠⠞⠉⠉⠉⠀⠀⠀⠀⠀⠀⠁⠀⠂⠙⣻⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⡀⠈⡀⠄⡁⠄⣁⠢⣔⡹⣆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠉⠈⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠐⣀⠒⣤⢫⣞⣷⣯⣷⣿⣷⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢋⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠄⡒⢬⣻⣞⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡻⠍⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢀⠂⠀⢀⠀⠄⠀⠀⠀⢀⠀⠀ ⠀⢂⢹⣚⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠿⣝⠣⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡿⠃⠞⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠈⠀⠀⠀⠀ ⠀⢊⢶⣹⡾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣏⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠄⠂⠠ she wants some juicy cock in her😘🥵⠀🍑𓂸🍑𓂸( • )( • )ԅ(‾⌣‾ԅ)🥵🔥☄️❤️‍🔥👩‍🚒👅{(ᶅ͒)}( ๏ 人 ๏ )( ๏ 人 ๏ )🤍🎀🧸🌷🍭𓀿𓀐🤍🎀🧸🌷🍭𓀿𓀐𓀿𓀐𓀐𓂸📹( ๏ 人 ๏ )( ๏ 人 ๏ )( ๏ 人 ๏ )👅{(ᶅ͒)}👅{(ᶅ͒)}🤭😴😪🥱💤🛌🏼😴😪🥱💤🛌🏼♱🍒💋🫀♱♱🍒💋🫀♱🌬𓂸🍆+🍑+🥛=👶🍆+🍑+🥛=👶ﮩ٨ـﮩﮩ٨ـ♡ﮩ٨ـﮩﮩ٨ـﮩ٨ـﮩﮩ٨ـ♡ﮩ٨ـﮩﮩ٨ـεつ▄█▀█●εつ▄█▀█●εつ▄█▀█●

⠀⢀⣀⣴⠟⣩⣾⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠟⢛⢻⣿⠃⢰⣿⠋⢛⠛⠛⠻⠷⢶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⢋⡁⠢⠐⠌⣀⠚⣿⣦⣽⡏⠐⠂⡌⢡⠊⡐⠠⡀⠌⡙⠻⢶⣄⡀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠿⠷⢶⣤⡿⠋⢄⠢⠑⠂⠤⣁⠩⠐⡄⢂⠤⢉⠙⠿⢃⠡⠐⠂⡔⠡⢡⠐⠂⣤⣵⡿⠛⢿⣦⣀⣼⠟⡉⢁⡈⢉⠻⣶⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡾⢋⠡⢀⢂⣴⡿⢋⠠⠘⡀⠆⣉⠘⡠⠄⢂⠱⢈⡐⠂⠆⢌⠐⣠⣦⣥⣥⣄⠃⠤⠈⣶⡿⠃⠀⠀⠸⣿⢿⣇⠐⠠⣁⠐⡂⡐⠠⠙⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⠋⡐⠄⢂⢡⣾⣏⡐⠠⠡⢁⠆⣁⠂⠥⠐⠌⢂⠒⠤⠠⢉⠌⡐⠂⣿⡇⠀⠉⠛⢿⣦⣽⣟⣠⡤⠀⠀⠀⣿⡘⣿⡎⠡⢀⢃⠰⢁⠂⡅⠈⢿⣦⠀⠀⠀ ⠀⠀⠀⠀⣠⡿⢁⠂⠜⡈⢤⣿⣿⡟⠡⡈⢅⠢⠐⡠⢊⠐⡉⢰⣤⠈⡔⠡⣈⠂⠜⠠⠸⣷⡀⠀⠠⢶⣿⣏⣿⣿⡦⠀⠀⠀⠹⣷⡘⣿⡄⡁⢂⢂⠡⠊⢄⠡⢂⠹⣧⠀⠀ ⠀⠀⠀⢠⡿⢁⢂⠩⢐⢠⣿⢧⣿⠃⠡⠐⠂⠌⡡⠐⠡⡈⠔⣼⡟⡐⢠⠡⡐⠌⢂⠁⢂⢹⣧⠀⠀⠚⢩⣿⢿⣧⣄⠀⠀⠀⠀⠸⣷⢹⣷⠠⠁⠆⢂⠩⠐⣂⠂⡐⢻⡇⠀ ⠀⠀⠀⣿⠇⠠⠄⢃⠄⣼⡟⣸⡿⢀⠣⢸⣤⢃⠠⠛⡀⢃⢘⣿⢃⠠⠃⢄⠠⠛⡀⣿⣇⣸⣧⠀⠀⠀⣼⣿⡼⣿⠻⣧⣤⣄⣀⣠⣿⠀⣿⡇⠸⢘⠠⠘⢃⠠⠘⡀⢻⣧⠀ ⠀⠀⢀⣿⠈⢂⠅⢊⠰⣿⠇⣿⡇⠂⡔⣸⡿⢀⠂⣡⣴⡦⢸⣿⢀⢊⡁⠆⡘⠠⠑⣿⣿⠻⣿⣀⣠⣾⠏⣿⡇⠻⣧⣀⣠⣿⠟⢉⠁⡂⢽⣧⢁⠊⡄⠑⡈⠔⡁⠒⡀⣿⡄ ⠀⠀⢸⡗⡈⠆⡈⠆⣸⣿⠁⣿⢃⠡⢀⣿⡟⣰⣾⠟⠋⠄⣾⣇⠂⡰⠀⠜⡀⢃⢉⣿⣿⡄⠙⢻⣟⣀⣤⣿⠃⠄⡙⠟⢻⣿⢀⠂⡌⢐⢺⣿⠀⡜⠠⢁⠂⠥⣈⠡⡐⢹⡇ ⠀⠀⣾⡇⠰⢈⡐⠂⣼⣿⢰⣿⠠⠘⡀⣿⡗⠈⠄⡈⠌⣼⣿⡇⡂⠄⢩⠐⡈⠔⡈⣿⠹⣧⢬⣼⠛⡉⠉⣿⡆⠌⡐⣈⠘⣿⡂⠌⡐⠂⢼⣿⠐⡠⢁⢂⠡⠒⡀⠆⡐⢹⣧ ⠀⠀⣿⢀⠃⠆⡐⢁⢾⣿⣾⣿⢀⠃⡄⣿⡟⣿⡔⢀⣾⡟⢘⣿⣷⠈⠄⡂⠡⠂⠌⣿⠀⢙⣿⣿⣧⣀⡡⢿⡇⢂⠡⠄⢂⣿⣧⣦⣐⠉⣼⡿⢀⠡⢂⠂⠔⠡⡘⠠⠌⡘⣿ ⠀⢠⣿⢀⠣⠘⡀⠎⣸⣿⣿⣿⠀⠆⠄⣿⣇⣼⣿⡿⠿⠿⣿⣿⣿⣇⣦⣴⣥⣮⣴⣿⡿⠟⣛⣿⣿⣿⣿⣿⣿⠠⠌⡘⠠⢹⡇⠉⠻⣧⣿⢿⡆⠠⠃⠌⡐⠡⢂⠅⠒⡀⣿ ⠀⢸⣿⠀⠆⡱⠠⡁⠸⡿⢹⣿⢈⡐⠂⣿⣿⠟⠁⣠⣶⣿⣿⣿⣿⡉⠉⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠐⢨⠐⡁⢺⣷⠀⠀⣿⡄⠸⣯⢀⠩⡐⢈⠤⠁⡌⠐⡁⣿ ⠀⢸⡏⠰⡈⠤⠑⡠⢁⡐⣿⣿⠠⢀⠃⣾⡇⠀⣼⣿⣿⣿⢿⣻⣿⣷⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣷⣿⣻⣿⣿⡈⠔⡈⠤⢹⣿⠀⠀⣿⠇⠀⣿⡀⠆⣁⠢⢀⠃⡌⠰⢀⣿ ⠀⢸⡇⠱⠐⢂⡑⠤⠁⡄⢿⣿⠠⡁⠆⣿⡇⠀⣿⣿⣿⣽⣿⢿⣻⣿⡇⠀⠀⠀⠀⠀⠸⣿⣷⣿⣯⣿⢿⣽⣿⡆⠌⡐⠢⢀⣿⠀⣰⡟⠀⠀⣿⡇⡐⢄⠂⡁⠆⡘⢠⠁⢿ ⠀⢸⡇⠱⢈⢂⠐⡂⠥⠐⡘⣿⡇⠐⡠⢿⡇⠀⠘⢿⣿⣿⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠹⢿⣷⣿⣿⣿⠟⣿⡇⢠⠡⠑⡠⣿⡾⠋⠀⠀⠀⢸⡇⠰⢈⡐⠐⡨⠐⠤⢈⢸ ⠀⢸⡇⠱⢈⠄⠂⡅⠢⢁⠔⣿⡇⠡⢀⢿⣧⡀⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢈⣀⡄⠀⣿⡇⢂⠡⠊⠄⣿⡄⠀⠀⠀⠀⢸⡧⠘⢄⠂⡡⠐⣉⠐⠂⢼ ⠀⢼⡇⠱⢈⠄⠃⡄⢃⠌⡀⣿⣧⠁⡂⢼⡏⠻⢶⣀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⢰⣏⣁⣿⣤⣿⡇⢌⢂⠩⠐⣿⠆⠀⠀⠀⠀⢸⣿⢈⠰⠈⡄⢑⠠⢈⠅⢺ ⠀⢺⡇⠱⢈⠄⢃⠰⢈⡐⠠⣿⣿⠠⠐⢸⣿⠀⠀⠉⠛⠶⣤⣄⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣤⣬⣿⢿⠿⠋⣹⡇⠢⠌⡐⠡⣿⡆⠀⠀⠀⠀⢸⣿⠠⢈⠅⡰⠈⡔⢈⠰⢸ ⠀⣹⡇⠱⡈⠰⠈⡄⠃⠤⢁⣿⣿⡆⠡⢈⣿⣀⣴⣶⠶⣶⡀⠈⠉⠉⠙⠛⠛⣿⡛⠋⠉⣿⠁⠀⠀⠀⠀⠀⣸⡇⡑⢂⠡⢂⣿⡇⠀⠀⠀⠀⠈⣿⢀⠃⡔⠠⡁⠆⢨⠐⣸ ⠀⣿⡇⡑⢠⠑⠂⡌⡘⠄⠌⣿⢹⡇⡐⠠⢿⣏⣽⣿⡄⠙⣿⠀⠀⠀⣀⣠⣤⣿⣄⠀⢠⣿⠶⢶⣄⡀⠀⠀⢼⡇⠰⢁⠂⣄⣿⡇⠀⠀⠀⠀⠀⣿⢀⠣⠠⡁⠔⡨⠀⠆⢸ ⠀⣿⡇⠠⠃⢌⠰⢐⠰⢈⠰⣿⢸⣟⠠⢁⢺⣿⠋⢈⣿⣄⣿⠀⣠⡾⠋⠹⣧⣼⠟⢻⣟⢙⣷⠟⠉⠻⣦⠀⣿⡇⠡⢂⣼⣿⣿⡃⠀⠀⠀⠀⠀⣿⠀⢆⡑⠠⢘⠠⠡⢈⢼ ⠀⣿⠃⢡⠉⡄⠊⡔⠂⡌⢠⣿⣾⣿⠐⠀⠂⣿⣷⡟⠋⣿⠃⣴⡟⠀⠀⠀⠙⢻⣷⣾⡟⠛⠁⠀⠀⠀⠙⣷⣿⡇⢡⣾⡟⢹⣿⠃⠀⠀⠀⠀⠀⣿⠈⡄⢢⠁⠂⡆⠁⠂⢸ ⠀⣿⢀⠃⡌⠰⢁⡐⣰⣾⠟⠋⠀⢿⣦⣷⣄⡘⣿⣄⣠⠾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠹⣿⡷⠟⠋⠀⢸⡿⠀⠀⠀⠀⠀⠀⣿⠡⢘⠠⠌⢂⠄⠩⣀⢹ ⠀⣿⢀⠣⢀⠣⢀⣼⡟⠁⠀⠀⠀⠘⠿⣿⣿⣿⣾⣿⣿⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠙⣧⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⣿⡇⠂⠥⢈⠰⢈⡐⠠⠘ ⢀⣿⠀⠎⠄⡊⢰⣿⠀⠀⠀⠀⠀⠀⠀⢻⡍⠙⢿⡉⢉⣿⠷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⣴⣦⣼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⡘⠤⢁⠂⠆⠠⢃⠁ ⢸⣿⠈⠜⢠⠁⣾⠋⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣀⠻⢾⠃⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠁⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠰⡈⠄⠊⠄⠃⡄⠃ ⢸⡇⠌⢂⠡⢢⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠁⠜⡠⢉⠐⡡⠠⢁ ⣸⡇⡘⠄⠃⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢀⣤⣤⣀⡀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⢸⣿⢀⠊⠔⠠⠡⢠⠁⢂ ⣿⠃⠰⡈⢁⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠟⠁⠀⠉⠻⠷⠄⠈⢿⡄⠀⠀⠀⠀⠀⠀⣿⡠⠘⠄⢃⠰⠁⢌⠠ ⣿⠈⠡⠐⢂⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣣⣴⡶⢶⣦⣤⣀⡀⠀⠈⢿⡄⠀⠀⠀⠀⠀⢻⡇⠌⡘⠀⠆⡉⠄⢂ദ്ദി ˉ͈̀꒳ˉ͈́ )✧( ꩜ ᯅ ꩜;) ( ꩜ ᯅ ꩜;) ⋆˚🐾˖°( ꩜ ᯅ ꩜;) ໒꒰ྀིっ˕ -｡꒱ྀི১

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣰⣿⣿⡻⠟⠋⠉⠉⣻⠟⠉⠉⠉⠛⢯⡛⢿⣿⣷⣤⣀⠀⠀⠀⠀⠀ ⠀⣠⣴⠾⠛⢋⣿⠟⠋⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠈⠂⣹⣿⡈⠙⠻⢶⣄⡀⠀ ⣸⠏⠀⠀⠀⣾⣋⣀⣀⡀⠀⠀⠀⢸⠁⠀⠀⢀⣀⣀⣀⡀⠀⠈⠻⣧⠀⠀⠀⠉⠻⣦ ⢿⡀⠀⣿⣿⠟⣫⣽⣿⣿⣿⣿⣶⣶⣶⡶⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿ ⠸⣧⠀⠈⣿⢸⣿⣿⣿⣿⣿⣿⣿⠁⢹⡇⣼⣿⣿⣿⣿⣿⣿⣿⠁⣼⡇⠀⠀⠀⣼⠇ ⠀⠹⣷⡀⢹⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠏⠀⣿⡇⠀⣠⡾⠋⠀ ⠀⠀⠈⢿⣿⢿⡿⠿⠿⣿⠟⠉⠀⠀⠀⠀⠙⠛⢿⡿⠿⠛⠉⠀⠀⡿⣷⣾⠏⠀⠀⠀ ⠀⠀⠀⠈⠋⠘⣷⠀⢀⡿⢰⣾⣟⣛⣿⣿⣷⡄⠀⢻⣆⠀⠀⠀⢰⡇⠘⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣧⣼⠃⠈⣧⣼⣿⣇⣈⣿⠃⠀⠀⣿⣀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠈⠙⢿⡛⠉⠁⠀⠀⣠⡿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⢶⣶⣾⣿⣶⣤⣤⣶⢿⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡼⠁⠉⠏⠁⠈⢹⣠⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⣸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣤⣤⡾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢶⣾⣶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⢀⠀⠀⡀⠀ ⠀⠈⠘⠛⠚⠛⠻⠛⠓⠃⠟⠻⠓⠐⠒⠒⠛⠁⠀⠀⠠⠇⠗⠟⠛⠚⠛⠒⠁⠐⠟⠀ I JUST LOST MY DAWWGGG

⢸⣿⡽⣾⣿⡿⢎⢾⢷⡛⢝⣆⣿⡀⣿⡺⣿⣿⣿⣿⣿⣿⢃⡱⡂⠠⠰⡀⢀⡐⠒⠢⡂⡀⢀⠂⡀⡀⡀⡀⡀⡀⡀⢀⡀⡀⠠⠠⡐⠐⢐⢕⠿⠛⠿⠿⠟⠝⠋⠇ ⢈⣯⣣⣺⣝⣫⣪⣒⣊⣍⣫⣏⣿⡄⣿⣸⣿⣿⣿⣿⣿⡟⠆⢂⠂⡀⡀⠄⡀⡀⡁⠂⠄⡀⡀⡀⠠⠁⡀⡀⡀⡀⡀⡀⣠⣄⣉⣈⣨⠖⠂⠨⠐⠄⠠⡠⡀⡌⡐⡁ ⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠂⠬⠕⠫⢕⢂⢊⠂⡀⡀⡀⡀⠄⠐⠁⠂⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢀⣥⣴⣮⠼⠴⠴⠦⠴⠶⠶⠶⠶⠶⠷⠧⠇ ⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠓⠐⠈⠂⡀⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀ ⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀ ⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠄⡀⢀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀ ⡀⡀⡀⡀⡀⡀⡀⡀⡀⢀⢐⠄⠠⠁⠁⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢂⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀ ⡀⡀⡀⡀⡀⡀⡀⢀⠢⠢⠄⠁⠐⠁⡀⠐⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡦⠂⠠⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀ ⡀⡀⡀⡀⡀⡀⠔⢒⢑⡂⡂⡂⠄⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣷⠤⠠⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀ ⡀⡀⡀⡀⡀⢔⡑⢑⠌⡁⠈⠂⠂⡀⠠⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣟⢜⡈⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀ ⡀⡀⡀⡀⡼⡢⠌⡘⠐⠈⠠⠄⠡⢁⠁⠠⠁⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣷⣕⡪⠡⠂⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀ ⡀⡀⡀⢰⡪⠱⠢⢌⡠⡐⠢⠐⠐⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣼⢻⣕⠸⠆⢐⠄⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀ ⡀⡀⡀⠕⠨⠸⠪⢕⠜⢅⠠⡂⢈⠈⡀⡀⢀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⢸⣗⡪⣊⢈⠈⠠⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀ ⡀⡀⡰⠆⢐⡘⠅⠌⢂⠌⠂⡁⠐⡂⡀⢀⠂⠐⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⠘⣷⡜⠭⡌⠅⠠⠐⠐⢀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀ ⡀⡀⡪⡕⢇⡔⠆⢐⡁⢐⢂⢁⠈⠁⠁⠐⠄⠈⠄⢁⡀⡀⡀⡀⡀⡀⡀⣼⣿⡇⢻⣞⡓⣱⣒⢐⡊⠐⠁⠄⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀ ⡀⡀⢇⡜⡣⢒⡐⢑⣘⠅⢅⠠⠄⠁⡈⢂⠅⠂⡈⠂⠠⠐⠄⠠⡐⢂⣰⠇⣇⡀⡅⢿⣕⣪⡳⢎⡜⠆⢐⢑⠂⠂⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀ ⡀⡀⡢⢕⡣⢆⡨⢜⡑⠄⢔⠅⠠⠐⠅⢈⠅⠐⠡⠊⠨⠢⢂⠆⠌⢠⣿⢀⠃⣆⢇⡊⣿⣾⡮⠽⠣⡢⢆⠨⡀⠐⢂⠂⢀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀ ⡀⡀⢱⡪⡱⢪⡑⢓⡑⢢⡱⡂⢐⣂⢌⢨⠂⠐⢂⠈⢁⠄⢈⡁⢀⣿⣯⣿⡀⣏⠈⠂⢸⣿⢽⡕⣸⢇⡲⠣⢅⢐⡐⡁⠄⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀ ⢀⡀⡪⠱⢎⢱⢆⡸⢕⡥⡰⠎⠔⠡⡰⡊⢂⠄⡁⠄⠠⢈⠈⡀⣾⣿⡽⡇⣿⣿⢸⠡⣾⣿⡝⡍⢸⡇⢜⡣⢕⡱⠌⠊⠔⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠐⡀⡀⡀⡀ ⢀⡀⢧⢢⢲⡎⢪⢕⡎⡜⡹⠣⠜⠬⠕⡨⠠⠂⠨⠐⠐⠔⠄⡀⢳⡇⠻⣯⠟⠻⣯⠾⠈⣿⡗⢱⡜⡃⢸⡇⡘⢱⢪⡂⡀⠨⢀⢂⠐⠠⡀⡀⡀⠄⡀⠨⡀⡀⡀⡀ ⡀⡀⠸⢕⢪⡣⢜⡸⢇⡱⡲⡢⢰⢕⡌⠌⠄⠆⡐⢂⠨⡂⠈⠐⣹⡀⡀⡀⡀⡀⡀⡀⡀⠸⡦⢎⢱⡖⢊⡸⢇⣘⣑⣂⡡⠅⠠⠠⡀⠠⠁⡀⠄⡀⠐⠂⡀⡀⡀⡀ ⠐⠡⡀⢝⢏⣇⣓⣸⣇⡸⢇⡣⢎⡡⡌⡒⢅⢄⠨⢅⢄⢨⠔⢂⠇⡀⡀⡀⡀⡀⡀⡀⡀⡀⢿⣝⣹⣇⡸⢣⡕⢪⡕⡃⡰⡢⢌⡢⡑⠡⡁⡀⡀⡀⠈⡀⡀⡀⡀⡀ ⠠⠅⡀⢯⠽⢳⡝⢺⣕⣺⢧⡜⢸⢕⡱⠬⡇⡑⡑⠌⡐⠡⢌⠏⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢻⡝⡝⢹⣓⡎⢣⡕⢇⡸⢣⢜⢆⠌⢐⠅⠁⠐⠠⣈⡀⡀⡀⡀⡀ ⠠⠈⡀⢸⣣⣵⣧⣽⣼⣯⣜⣇⣰⣖⣱⣪⣦⣖⣪⣢⣢⡆⠊⡀⡀⡀⡀⡀⡀⡀⡀⢀⡀⡀⡀⡀⠻⣯⣮⣞⣧⣺⣯⣖⣲⣆⣌⣔⣔⡰⢌⢌⠌⢁⠎⡀⡀⡀⡀⡀

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