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⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢧⠀⠀⣠⡶⠖⠒⠚⠋⠁⠀⠀⠀⠈⠙⠛⠒⠒⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⣷⣿⣋⠀⠀⠀⠀⠀⠀⠿⢯⣉⡉⠙⠓⢦⣄⠀⠀⠀⠉⠛⠶⠦⠤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠸⡀⠈⠛⠶⠤⠤⠶⠤⣄⡀⠈⠉⠉⠓⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡇⢀⣠⢤⡀⠀⠀⠀⠀⠉⠓⠶⢤⣤⣤⣤⣾⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⢰⣶⣶⣤⡀⠀⠈⠙⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣧⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢮⣭⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡁⠀⠀⠀⠀⠀⠉⠙⠛⠒⠒⠲⢤⡀⠀⠀⠀
⠀⠀⣿⡀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠲⣦⣀⠀⠀⠘⠿⣯⣉⠓⠲⠤⣀⠀⠘⠿⣭⣷⣦⡀⠀⠀⠀⠀
⠀⠤⢧⣝⣒⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠶⠶⢦⣌⡙⠓⠒⠚⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣘⡏⠑⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣤⣤⣤⣀⠀⢀⣠⡤⠔⠒⠚⠉
⠉⠉⠉⠙⠳⢦⣄⠀⠀⣙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠼⠛⠉⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠈⠛⣶⡯⠏⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⡵⠋⠁⠀⠀⠀⠀⠀⣠⡾⠋⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠁⠻⣆⠀⠀⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡽⠋⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⠀⢠
⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢼⡿⠙⣄⣀⣀⣀⠤⣴⢶⠚⠉⠉⠉⢹⣿⡏⠉⠉⠙⣓⣲⡶⢮⣀⠀⠀⠀⠀⢀⣤⡾⠿⠛⠛⠛⠉⠉
⡽⠋⠑⠦⢄⣀⣀⠀⠀⠀⣀⣸⠆⠀⢀⣈⡉⠀⠀⠀⣻⣾⠧⠶⠒⠶⠚⠛⠲⠶⣤⣤⣹⣾⠃⠀⠈⠓⡖⠚⠻⡏⠀⠀⠀⠀⠀⠀⠀⠀
⠓⣦⡤⠤⠤⣀⣉⢩⠿⡍⠁⠀⠀⠀⣿⡿⠇⠀⣰⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠷⡄⠰⣏⡽⠃⠀⣹⣀⣀⣀⣀⣤⣤⠖⠚
⣼⠁⠀⠀⠀⠀⠈⠉⠛⠓⠒⠿⠟⢛⡻⣄⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣴⠋⠉⠁⠉⠉⠛⠲⢿⣽⡀⠀
⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠨⡷⣄⣤⢿⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠋⠀⠀⣴⠷⣤⣄⣀⡀⠀⠀⠀⠀⠀⠉⠛
⠀⠀⠉⠓⠒⠦⠤⠴⠒⠒⠉⠁⠀⠀⠀⠀⠈⠈⠟⢯⡀⠈⠉⠒⠢⠤⣤⠤⠤⠴⠒⠋⠹⣍⣇⣠⠞⠁⠀⠈⠙⢦⣉⣿⠗⠒⠒⠶⠤⠤
⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⣀⣸⣽⣃⣀⣀⣀⣤⡴⠚⠉⠹⡟⢢⣄⡀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⢸⠋⢱⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⢹⣿⣿⣿⠓⣦⣄⣀⠙⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⠇⢠⡏⠀⠀⠈⣳⢄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢹⣦⡀⠀⢻⡿⠃⣴⠟⠀⠉⠉⠛⠀⠀⠀⠀
⠀⠀⠀⠀⠑⠦⣀⣀⣀⣀⠀⠈⠉⠒⠤⣤⠃⠀⠑⠄⠀⠀⠀⠀⣠⠞⠁⠀⠙⠀⠀⠀⣠⡾⠁⠙⠲⠾⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⡞⠀⠀⣰⠟⠀⢀⣿⡿⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠔⠋⠀⠀⢰⣏⡤⠖⠉⠛⣇⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜
⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜
⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜
⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜
⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛
⬛🟨🟨🟨🟨🟨🟨🟨⬛⬛⬛⬛⬛🟨🟨🟨🟨🟨🟨🟨⬛⬛⬛⬛🟨🟨🟨⬛
⬛🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬛⬛🟨🟨🟨🟨⬛⬜⬜⬜⬜⬛🟨🟨⬛
⬛🟨🟨🟨🟨🟨⬛⬜⬜⬛⬛⬜⬜⬜⬜⬛🟨🟨⬛⬛⬛⬛⬜⬜⬜⬛🟨⬛
⬛🟨🟨🟨🟨⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬛🟨🟨⬛⬛⬜⬛⬛⬜⬜⬜⬛⬛
⬛🟨🟨🟨⬛⬛⬛⬛⬛⬜⬜⬛⬛⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬛⬛
⬛🟨🟨🟨⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬛⬛
⬛🟨🟨🟨⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬛⬛
⬛🟨🟨🟨⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬛⬛
⬛🟨🟨🟨⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬛⬛
⬛🟨🟨🟨⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬛⬛
⬛🟨🟨🟨⬛⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬛⬛⬜⬛⬛⬛⬜⬜⬜⬜⬛⬛
⬛🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛
⬜⬛🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨⬛⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜
⬜⬛🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨⬛⬜⬜⬜⬜⬜⬛🟨⬛⬜
⬜⬜⬛🟨🟨🟨🟨🟨⬛⬛⬛⬛⬛⬛🟨🟨🟨🟨🟨⬛⬛⬛⬛⬛🟨🟨⬛⬜
⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜
⬜⬜⬜⬜⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⢀⣀⡀⢄⣀⣀⣀⠀⠠⠀⠒⠀⠈⠉⠛⠩⡉⢂⠑⡄⠀⠐⠒⠂⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⢢⠀⠀⠀⢀⠄⢊⠜⠋⠉⠁⠀⠀⠀⠀⠀⡠⠒⠉⠀⡠⠃⠑⠺⢄⠀⠀⠀⠀⠉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠑⣄⠈⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⢀⠀⠀⠘⠰⣆⠀⠀⠀⢢⠀⠀⠀⠂⠤⢄⡀⠈⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣸⠊⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⠊⡰⠃⠀⠀⡆⠀⣏⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠈⠁⠣⣔⡈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⢁⠀⠀⠀⠀⠀⢀⠄⢀⠞⠀⢆⡜⠁⠀⠀⢰⠅⡀⠹⡇⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠚⠦⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡡⢋⡔⠁⠀⠀⠀⡰⢀⠎⠠⡝⠀⢸⡜⠀⠀⠀⢀⢃⢡⢣⠀⢣⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢐⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠮⡎⡝⠀⠀⠀⢀⡞⠁⡞⢠⡝⠀⠀⣿⠃⠀⠀⠀⡜⡌⡜⡼⣆⠈⢣⠀⠀⠀⠀⠈⠀⣀⣀⠀⠀⠀⠠⠄⠂⢁⠔⠋⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠊⠁⡜⡌⠀⠀⠀⢒⠞⢲⠸⢧⣿⠁⠀⢀⡟⠀⢀⠆⢠⠡⡰⡇⡘⢿⣦⡀⠣⡀⠀⠀⠀⡆⢢⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡙⠀⢠⠁⠀⡌⡄⣎⡗⡡⡌⠀⠀⡼⠇⠀⡜⠀⡬⢤⠧⣇⢱⠀⠑⠱⢄⡈⠢⢄⠀⠇⢢⢣⠀⠀⡠⡪⢲⡆⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⢠⡇⠀⡜⡠⠐⢹⡌⠀⡇⠀⢰⢸⠀⢀⠇⡷⡆⠸⠀⡇⢩⠂⢄⠀⠀⠈⠁⠀⠀⠁⡎⡆⡤⢊⠔⠀⠀⣇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢣⠀⣞⠁⢰⣯⣤⣤⡘⢅⠀⡇⠀⡄⡀⠀⢸⢠⢃⢀⡇⠀⣠⢨⠀⡇⠁⡆⠀⠀⠀⠀⠀⣇⠏⡗⠁⠀⠀⠀⢹⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⢞⢰⢸⠀⡘⢈⣶⣶⣾⣵⠀⢳⡇⡇⡇⠀⢸⡎⣌⠸⠥⡀⠉⡄⠀⡇⠀⠀⠀⠀⠀⠀⠚⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⡏⢸⠀⡀⣇⢸⠉⢻⡽⢟⠁⠘⢷⢻⡅⠀⣺⣿⣭⣭⣿⣰⢤⣱⠀⠃⢀⡀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢰⡏⠀⣇⡿⡦⣃⡘⣁⠎⠀⠀⠈⢻⠱⡀⠘⠛⠿⣟⣻⣿⡷⡝⣷⠀⣸⠀⠀⢸⢀⢲⠀⡆⢰⠀⠀⡇⠀⢠⡇⠀⡸⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣀⡏⣇⢞⢼⠉⠑⠈⠀⠀⠀⠀⠉⠻⢄⣆⠸⣻⠟⠁⠹⠅⣸⢀⡋⠀⠀⡎⡸⡈⠰⠀⡛⠀⢠⠇⢀⢳⠁⢰⢁⢼⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⢠⠎⠉⠐⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⢹⠊⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣘⠢⢤⣠⡔⣎⠀⡇⡌⠃⠀⡸⢠⢣⡇⢆⢠⠁⢠⢻⠀⣌⣸⠀⢃⠎⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⢸⣆⠀⠀⠀⠀⢸⠃⠀⠀⢰⠉⠑⠤⠃⠀⡇⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢲⣿⡟⣾⣾⡦⠱⣸⣿⠘⠀⣰⡡⠁⠸⣇⢀⠇⠀⠎⡌⣼⡪⢷⠸⠃⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠙⠲⠤⠄⠀⠎⠀⠀⠀⠈⢆⢄⠀⠀⢠⠃⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠈⠉⡝⠚⠿⠃⠆⡝⡝⡆⡴⠟⢁⠂⢀⢋⣬⢀⢊⡜⡼⠋⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⣣⡘⡀⠀⡎⢀⡧⠂⡏⡰⢱⠊⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠤⠐⠂⠈⠋⡏⢱⢠⣿⡇⣬⣀⠀⢷⠁⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡉⠀⠀⡇⠀⠀⠀⠉⠀⠉⠉⠉⠉⠉⠁⣠⡔⠛⢆⠰⡼⣣⠀⠀⠀⠀⠀⠀⡠⠊⠀⡇⣿⣾⠛⠳⠇⠶⣭⣺⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠴⠿⡷⡀⠘⡄⢻⡿⠆⠀⠀⡠⠔⠁⠀⠀⣀⣿⣽⠟⠠⠠⠐⠂⠙⠋⣁⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠱⡹⡄⢱⠈⣿⠘⡆⠁⠀⠀⣠⡖⠟⠋⣉⠠⠄⡀⠒⠂⠀⠋⠁⠩⣃⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢵⣿⡄⡇⢹⠘⠀⢀⣴⠟⢉⠤⡚⠭⠐⠈⠀⣀⠀⠠⠤⠀⠐⠂⠉⠉⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠸⡀⠀⠀⣸⣿⣿⣤⢸⠀⡴⠋⣠⡾⢛⠭⠔⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠀⠀⠐⠒⠤⢄⡀⠀⠀⠐⡀⡵⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⡇⠀⠀⠀⠀⠀⠀⠀⢻⡇⠉⢻⣰⠊⣠⠾⠓⠉⠀⢀⡀⠀⣀⣤⣀⡀⠀⠀⠀⠀⠒⠂⠤⠤⢐⣣⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠸⣿⠡⠀⠀⠉⠉⠉⠉⠉⢩⣿⢼⡟⣅⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠠⠀⠀⠀⠉⢢⡀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢀⠁⠀⡄⣿⠀⠀⠀⠀⠀⠀⠀⢠⡿⣹⠀⢰⠸⡀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡰⠁⠀⠀⠀⣀⠔⠊⠁⠈⠉⠒⠠⠔⠊⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡇⠀⠀⠀⢸⠀⠀⣧⠁⠀⠀⠀⠀⠀⠀⢀⢧⠃⣿⠀⠈⡀⡇⠀⠀⠀⢀⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡜⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡇⠀⠀⠀⠘⠀⠀⣋⡇⠀⠀⠀⠀⠀⠀⡸⡜⠀⢻⠀⠀⡇⢣⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠘⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠒⠒⠒⠒⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠁⠀⠀⠀⡀⠀⢰⡿⡇⠀⠀⠀⠀⠀⠀⡇⡇⢰⢸⣰⠀⢱⢸⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡇⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⢸⣷⠁⠀⠀⠀⠀⠀⢠⢻⠀⡘⢸⣷⣀⠼⣼⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢐⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⡇⠀⠸⣯⠀⠀⠀⠀⠀⠀⠸⡾⠿⣿⡟⢽⠁⠊⢡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠤⠤⠼⠀⠀⠀⢸⠠⠤⠤⠤⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡼⡇⢸⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠆⠀⠀⠀⡆⠀⠀⠀⢇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡜⠀⠀⠀⠀⠸⡀⠀⠀⠀⠣⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣞⡘⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⢈⠓⢄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠜⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⡠⠊⡜⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠠⡀⠑⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠇⠀⠀⣸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⢀⠜⠀⠀⠀⠀⠀⠀⡠⠊⠀⡰⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⡄⠸⠀⢠⢀⠂⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡠⠃⠀⠀⠀⠀⠀⡠⠊⠀⠀⡰⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠄⠀⢣⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠄⠀⠀⠘⠈⠄⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⣄⠜⠀⠀⠀⠀⠀⡠⠊⠀⡠⢀⡌⠀⡠⢠⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠈⠄⠀⠀⢇⠈⢆⠰⡀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⢀⠠⠀⢁⠔⡙⠀⠌⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⡄⠀⠈⠀⠀⠘⡄⠀⢂⢣⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠂⠁⠀⡠⠂⠰⠁⠌⠀⠀⠀⠀⡼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢡⠀⠀⠀⠀⠀⢇⠣⠀⠊⠆⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⢀⠃⡜⠀⠀⠀⠇⢜⠠⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⡄⠀⠀⠀⢸⠘⡀⠡⡀⠨⡄⠀⡘⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⡌⠰⠁⠀⠀⢠⠌⡜⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠆⠀⢃⠀⠀⠀⠘⡄⢃⢀⠘⢄⠈⢲⠁⠀⠀⠀⠀⠄⠊⠀⠠⠐⠈⠀⡸⢠⠁⠀⠀⡠⠊⠰⠀⠀⠀⠀⡗⡄⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠄⠈⡄⠀⠀⡀⣇⠘⡀⠑⢄⠑⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⢃⠂⠀⠀⠔⠁⡰⠁⠀⠀⠀⠀⡇⠘⡄⠀⠀⠀⢀⠔⠁⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠄⠘⡀⠀⠀⡇⢀⠰⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⡠⠊⢀⠔⠁⠀⠀⠀⠀⠀⡇⠀⠘⠄⢀⠔⠁⠀⠀⠀⢈⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢂⠀⠀⠀⢸⡄⢂⢁⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠊⠀⠐⠁⠀⠀⠀⠀⠀⠀⢀⠀⠠⠠⡈⠅⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⢸⢁⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠑⡈⠄⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠺⣏⠳⣄⠀⠀⠀⠀⠀⠀⣘⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⠜⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠁⠀⠀⡇⠉⠺⣛⢦⠤⠤⢶⣟⣽⡙⡵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠪⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠁⠈⡟⣻⡿⠑⢼⢞⢢⡀⠀⠀⠀⠀⠀⠀⠀⢁⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢧⡂⠄⢀⠀⢀⣼⢰⠋⠀⠀⠀⠑⠍⣚⡷⠶⢲⡶⠶⠶⢿⡛⣿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⢪⠋⠀⠀⢠⣖⣢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢓⠢⠤⠤⣬⢞⢆⠀⠀⠀⠀⠀⠀⠈⠁⠀⠛⠒⠀⣡⣾⠘⣦⣕⠤⡀⠀⠀⠀⣶⡆⠀⣶⡦⠀⠀⠀⠠⢐⣤⢶⢾⢿⡔⠁⠀⠀⣰⡟⠀⠀⠈⠁⠘⠲⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠀⢰⢰⢡⠂⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⡱⢡⠊⠁⠀⠁⡈⢆⠀⢀⣀⡀⠀⠉⠀⠀⠀⣀⡴⠛⢹⠀⠀⠸⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠈⠑⢏⠡⠶⠤⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣸⠈⣼⢁⠂⠄⢀⠙⢢⣀⣀⣀⣀⣀⠀⠀⠠⠤⣧⠇⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠻⢆⠴⠛⠁⠀⠀⡏⠀⢠⠃⢒⡮⠋⠁⠙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣿⣰⠂⠄⠎⣠⡏⣰⣟⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡰⠁⢀⠊⠀⠀⠀⠀⢘⡌⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⡜⣼⣿⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡪⠁⡴⠃⡀⣀⢄⡐⠠⠅⠒⠒⠂⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠳⣠⠄⡀⠀⠀⠀⣀⠀⡀⠀⠐⠒⠊⢉⣉⣻⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠊⢁⠩⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠪⠤⡤⠥⠔⠒⠒⠒⠒⠈⠁⠀⠀⣼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⢤⡤⢶⠒⣰⣨⣧⡧⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠐⣦⡷⢟⣫⢷⡝⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡠⠄⠂⠀⠀⢀⡠⠜⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⢁⣀⣀⡀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢀⣀⣀⡀⠀⠀⠀⢀⣈⡰⠤⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
🧷🖤🕷🗡⛓🗝
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██╔══██║██║╚██╔╝██║██║░░██║██║░░╚██╗██║░░░██║░╚═══██╗
██║░░██║██║░╚═╝░██║╚█████╔╝╚██████╔╝╚██████╔╝██████╔╝
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⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣰⡾⠛⠀⣄⠀⠈⠹⣧⣄⣤⣴⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢀⣾⣿⣏⣀⠀⠁⠀⢺⡄⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⣿⠿⠋⠀⠀⠀⠀⢼⣿⣾⡿⠿⣌⣿⣿⣿⢷⣿⣀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠈⢻⡅⠀⣀⣀⣀⣀⡀⠀⣿⣿⣷⠀⣽⣿⣿⣿⣿⣯⣿⣦⣰⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢻⣿⣿⣿⡿⠟⠁⣠⣾⣿⡏⠀⠻⠛⣿⣯⣸⣿⣿⣿⠛⢤⣀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢈⣿⣿⣿⣷⣄⣴⣿⣿⣿⣿⡆⠀⠀⠘⠿⢿⣿⣿⣫⠀⠀⠈⠙⢦⣄⠀⠀⠀⣿
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣧⠀⢀⣀⣾⣿⣿⣽⣷⣾⡀⠀⠀⠙⠳⣄⡀⣿
⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡆⣸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠐⢶⣤⠈⠻⣿
⠀⠀⠀⠀⠀⢿⣦⣹⣿⣿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣾⠿⠀⢠⣿
⠀⠀⢠⡆⣠⣼⣿⠿⠋⢤⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣶⣿⣿
⠀⣴⣿⠟⠋⠉⢀⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡿⢀⣀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢻⣧⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠙⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠙⠛⠻⠟⠋⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠻⠛⠛⠛⠛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠛⠛⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣶⣶⣤⣤⣤⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢻⣿⣇⣌⣿⢿⣿⣹⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷⣿⡿⣿⣿⣿⣷⡀⣿⡄⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣻⣿⡿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣯⣾⣿⣿⡇⠈⠛⠻⢿⣿⣷⣿⡏⢻⣿⣿⣿⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣤⣶⠟⣩⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⣏⢀⣍⠹⣿⣿⣿⠀⠀⣿
⠀⠀⠀⠀⠀⣠⡾⢟⣴⢿⣿⣿⣿⣿⡟⠛⠿⢶⣾⣿⡿⢿⣿⣿⣿⣿⣧⢨⣿⣏⠀⠀⣿
⠀⠀⠀⠀⣴⠏⣤⣾⠛⣿⡿⠿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣦⣿
⠀⠀⢀⣾⠃⣠⣿⢃⣄⣋⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⣛⣡⣿⣿⣿⣿⣿⣿
⠀⢀⡾⠁⠀⣿⣿⠸⢻⣿⢤⡦⡟⣿⡇⠀⢀⡶⠀⠀⣽⢉⣟⣩⡴⠻⣿⠛⠋⣿⣿⣾⣿
⠀⠘⠁⠀⠀⢸⣿⡇⢸⡏⠘⠷⠶⣿⣇⢰⣿⣇⠀⢸⣿⣄⢉⡈⢡⣀⢻⣷⣼⣿⠻⢿⣿
⠀⠀⣰⢀⣦⣿⣿⡇⣾⠇⠀⠀⢠⣿⣟⠉⠀⠙⠷⢸⡟⠻⣿⡷⠄⡁⣴⣿⢿⣿⣌⣹⣿
⠘⢶⣼⣿⣿⣿⣿⠁⠋⠀⠀⢰⣿⣿⡻⣆⠀⠀⠀⢸⣿⣾⣿⣿⣶⣿⣿⣿⡇⠸⣿⣿⣿
⠘⢿⣿⣿⣿⣿⠏⠀⠷⠖⠀⠘⣿⣿⣷⠙⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡁⢀⣿⢙⣿