⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣤⣴⣶⠶⣶⣶⣴⣴⣖⡦⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣳⠻⣴⣢⣀⠀⣿⣟⣳⡟⣿⣯⢲⣞⣮⡟⠃⣀⣤⣶⠾⣻⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡌⠙⣗⢿⣾⣶⣾⣷⣿⣟⣼⣷⣶⣿⠿⡿⠋⣡⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣬⣆⠛⠉⠉⠉⠉⠉⠉⠉⢉⢩⡼⡤⣖⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⠟⡇⢀⣾⢸⠀⠀⢸⡇⠀⢸⠀⣷⡈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⣼⠇⣸⠿⣾⠀⠀⢸⣷⠆⠀⠀⢹⡗⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⣀⣀⣠⣴⣶
⣿⣛⠧⠶⠿⠛⠛⠶⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⢇⣿⣸⣇⠗⠒⠚⠹⣷⡦⡧⠾⡿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠁⠀⠉⣉⣉⣽⡾⠋
⠈⠙⠿⠶⣶⣦⡀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠈⢁⣙⠂⠀⠀⠀⣊⣀⠁⠀⣳⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣾⠛⠋⠉⠁⠀⠀
⠀⠀⠀⠀⠀⢹⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⣽⠘⠚⠛⠛⠀⠀⠀⠀⠛⠛⠛⢃⣷⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢰⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣷⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣿⣧⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⣼⡟⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⢸⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⣿⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡜⠻⣄⠀⠀⠀⠤⠤⠖⠀⢀⡴⠟⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⡄⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠐⡌⢓⣦⣀⠀⠁⣀⢴⡫⠜⡄⢘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⢹⡇⠀⠀⠀⠀⣰⡾⠿⠿⠥⠶⠶⠶⠮⢿⣤⣜⣤⣿⠀⠉⠉⠀⡼⠹⣇⣌⣨⣟⣤⣤⣴⠦⢶⡤⡀⠀⠀⠀⠀⣿⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠈⣿⣀⣀⣴⣾⣿⡁⠀⠀⠀⠀⠀⢀⡾⡻⠋⠀⣠⠋⠀⢀⡤⠊⠀⣰⣾⠏⠁⠀⠀⠀⠀⠀⠀⣹⣟⡦⣀⣀⣸⡿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠉⠉⠉⠉⢧⣿⣧⠀⠀⠀⠀⠀⣼⡝⠁⠀⢠⠷⢖⠖⠉⠀⠀⡜⡿⡏⠀⠀⠀⠀⠰⡀⠀⣴⣿⣻⠉⠉⠉⠉⠁⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⣀⢰⢻⣹⠀⠀⠀⢀⣼⣏⣠⣶⣶⣿⣶⣷⣦⣤⣀⠞⡽⢣⣟⠀⠀⠀⠀⠀⠁⠀⣿⣯⢣⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠾⠿⣶⢤⣾⡿⣯⣿⣿⣿⣿⡿⣫⣛⣷⣾⠷⠟⡹⣆⠽⣄⠀⠦⣤⣤⣀⣀⣬⣿⠾⠿⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⡿⣿⣿⣛⢿⣵⠟⡽⢁⠎⡰⢁⠌⡛⣼⣷⣶⣿⢏⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣽⡿⣹⣿⡧⢏⡾⡇⢠⣃⠌⡒⠄⢣⠘⡔⢠⢻⡏⢸⣟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀