⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⡸⠀⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⠀⠠⠤⠐⠈⠀⣴⣿⢯⣟⣿⣻⢿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠠⠄⠒⠻⣿⣽⣻⣞⣷⣻⣟⡾⣽⣻⣽⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣞⣷⣻⣞⡷⣯⣟⣯⢿⣷⢿⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⡿⣞⣷⣻⣞⣿⣳⢯⣟⡿⣾⣻⡽⣯⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠚⠛⠓⠛⠛⠻⠾⠷⠿⢾⣽⣯⢿⣽⣳⡿⣽⢷⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⣿⣽⣯⡟⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠉⠛⠿⣷⣯⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠒⠉⠉⠁⠈⠁⠈⠉⠉⠉⠉⠒⠒⠢⠦⢥⣀⣀⠀⠀⠀⠀⠈⠙⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡑⠲⠤⣀⡀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⣠⣶⠀⠀⠀⠀⠀⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀⠙⠲⣄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⣉⣠⡤⠴⢦⣤⣀⠉⠋⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠈⣆⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢾⡖⠚⢻⣍⠡⢉⣷⡀⠊⣷⠌⣷⡀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⡾⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠾⠯⣿⣴⣼⣷⡨⣴⡯⢰⠦⣾⠥⢖⣾⢟⡾⠁⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠉⣿⣟⠛⠛⠛⠺⠾⠟⠋⠀⠀⠀⠀⣀⡀⠀⠻⠿⠃⠀⠀⠀⠀⢠⠃⠀⠀⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣵⡀⠈⠛⢡⣀⡀⠀⠀⢀⡀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢀⣴⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡽⣷⣄⠀⠙⠛⠁⠀⠀⢿⠿⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⠴⠊⠁⠀⢀⣠⠶⡛⢴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⣽⠋⠈⣿⣶⢶⣤⡤⢤⣀⣀⣀⣀⣀⣀⣀⣠⣔⣤⣤⣤⢤⣶⣶⣿⢿⣿⢡⡙⢬⣿⣄⠀⠀⠀⢀⡄⠀⠀⣧⠀⠀⢠⡆⠀
⠸⢷⣤⣀⠈⣷⡀⠀⠀⠀⠀⠀⠀⣿⣷⣻⡏⠀⠀⢻⣾⢯⣟⣷⠀⠀⠉⠀⠹⣿⢿⣻⢿⣧⠈⠀⠀⣈⣿⡷⣯⢿⣿⡆⡍⢆⣻⣿⠆⠀⠀⢼⣿⡀⣼⣿⣠⣶⠋⠀⠀
⢠⣀⣈⣛⣿⣿⣷⠀⠀⠀⠀⣠⠎⠀⠙⠿⣀⠀⠀⠈⣿⣯⢿⣽⣧⠀⠀⠀⠀⢻⣿⡽⣯⣿⣤⣖⡛⣍⢺⣿⣻⣟⣾⣷⣜⣦⡷⠻⣀⠀⠀⠈⣯⡿⣇⢻⣿⣷⠾⠛⠀
⠈⠙⢛⣿⣿⠿⢾⣗⡶⣤⠜⠁⠀⠀⠀⠀⠈⠛⠲⢤⣿⣯⢿⣞⣿⠀⠀⠀⠀⣹⣿⣽⣳⣿⡆⠈⢉⣉⣩⣿⣷⡿⠾⢛⣻⠏⠀⠀⠘⢦⣀⣴⣿⡶⠟⠛⠉⠀⠀⠀⠀
⠀⠈⠉⠁⠀⠀⠀⠉⢻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠛⠛⠿⠶⠶⣶⣶⣿⣷⣯⡷⠿⠷⣿⠿⣛⠛⣩⠁⠆⣱⣸⠃⠀⠀⠀⢠⣾⢻⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⢿⣻⢿⡿⣿⠇⠀⠀⠀⠀⠘⠛⠋⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣷⣻⢯⣟⣯⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣯⣿⣽⡾⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⡿⣿⣟⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣯⣟⡷⣯⣟⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡛⠙⣿⣿⣽⣿⣇⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣟⣸⣿⡿⣦⣿⠻⣟⠛⠇⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⠖⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠹⡏⣽⡇⠀⠻⠀⢈⠄⠀⠀⠀⠀⠀⠀⢀⡟⠉⠉⠓⠤⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡠⠔⠉⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠰⢄⠀⠈⠒⢤⡀⠀
⠀⠀⠀⠀⢠⣇⣀⣀⣠⣀⣈⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠊⠁⠀⠀⠀⠀⠀⣀⣀⣠⡼⠥⠤⠤⠤⠤⠤⠤⠴⠶⠤⠾⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠒⠦⠤⠤⠤⠤⠤⣄⣀⣀⣀⣀⣀⣠⡠⠤⠤⠤⠤⠤⠤⠖⠒⠒⠒⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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