⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣴⡶⠶⠚⠛⠛⣲⣿⣉⣀⣈⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⡾⠋⠁⢿⡀⠀⠰⡆⠉⠉⠉⣉⡉⠉⠙⢷⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢤⡶⠛⠋⠀⠀⠀⠈⣻⡶⠿⠛⠃⠀⠀⠿⠙⢲⣲⡆⣿⠀⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⢻⣄⠀⠀⠀⠀⣴⠏⠀⠀⠀⢀⡀⠀⠀⠀⠀⠉⢻⡿⣤⣁⡈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⡽⠷⠶⠶⣾⠃⠀⠀⣆⣴⠟⠁⠀⠀⠀⠀⣴⡼⢤⡌⠉⠻⠿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣭⣀⠀⠀⠀⠛⠓⡿⠿⣿⡹⢶⡶⠢⠀⠀⠀⣿⠁⠀⠇⠀⠀⢀⡾⣟⠻⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⠛⠓⡆⠀⠀⠻⣦⣿⣿⡟⠁⠀⠀⠀⢀⣿⠀⠲⠤⣤⣤⣞⣁⣛⣆⣀⣀⣀⣉⠛⠓⠦⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⣼⠿⢿⣿⡶⣦⠀⠲⣾⡟⠀⢠⡾⠁⣸⠏⠉⠉⠉⢿⣍⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⠾⠋⠀⠀⣠⣾⠋⠀⢸⡟⣧⣸⣄⣠⣿⣀⡀⠈⠀⢰⡏⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠙⠛⢛⣿⠟⠁⠀⠀⢸⠁⠘⣿⡟⣿⠇⠈⠙⢻⣗⡋⠀⠀⠰⣦⣄⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣶⠟⠁⠀⠀⠀⠀⠈⠀⠀⠘⠟⠏⠀⠀⣠⠀⠈⠙⠷⡀⠀⠈⠛⠇⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⣅⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡄⠀⠀⠀⢉⣼⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⠀⠘⢷⠄⠀⠀⠀⠀⠀⢠⣅⡀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠋⢹⠇⠀⠀⠀⠈⠀⢹⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⢦⠘⢁⣀⣀⣀⢿⣀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠤⠤⠤⠿⠶⢶⣶⣤⣤⣤⠀⣀⣤⣤⡶⠶⣶⠟⠛⠿⢯⣍⠻⢯⣛⡶⢶⣶⣶⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠉⠀⠀⢰⡏⠀⠸⠶⠈⠙⢷⣄⠉⠛⠶⣮⣉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣯⣀⣀⣀⣀⣀⣀⣤⠾⠛⠀⠀⠀⡾⠀⢹⣦⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⢤⡀⠀⠀⠀⠈⠉⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⠐⠦⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢛⠶⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⠀⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⢀⣴⠞⢹⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠈⠛⠛⠲⠶⠶⠶⠒⠛⢻⡷⢶⣤⣤⣤⡤⠶⠛⢋⣤⢴⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠶⢦⣤⡀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠉⢻⡟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡶⠶⠚⠋⠁⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣤⣤⣄⣤⣤⣤⣴⣋⡀⠀⠀⢀⣀⣀⣤⣤⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀