⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠎⠚⠒⠚⠋⠶⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡓⣕⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠀⡆⣀⣴⣶⠿⠿⠿⠿⣶⣦⣄⣞⣯⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣳⠀⢨⣿⢟⣉⣀⣀⣀⣀⣀⣀⣈⠿⢿⠸⠋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⣿⡏⣽⡋⣶⢳⡆⠒⣦⡆⢤⠤⢤⡧⣧⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⢣⡏⣧⣿⠘⣧⠀⡟⡽⣼⣆⢸⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⠜⠛⠛⣛⣛⣻⡟⠛⠋⣿⣟⢸⡿⣟⣁⣿⡘⠀⠸⣧⠃⣇⣹⣿⣮⣿⣧⡏⠙⣿⢻⢛⣋⣛⠛⠛⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⡾⠉⠀⠀⠀⠀⠨⠟⠉⠀⠀⠀⣿⣿⡆⣿⠁⠙⠛⠃⠀⠀⠘⠈⠸⠿⠛⢹⣿⢻⡇⠀⠈⠉⠻⣏⠀⠀⠈⠛⠟⡟⣷⡀⠀⠀⠀
⠀⠀⣟⢇⢤⣄⣀⣠⣤⣿⠀⠀⠀⠀⠀⣿⣧⣇⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣻⣿⣼⡇⠀⠀⠀⠀⠘⣤⣤⣄⣀⡤⠅⣸⢷⡶⡀⠀
⣀⣸⣿⣿⣗⣿⡟⠋⠁⠀⠀⠀⠀⠀⢀⣿⣿⣿⢸⣧⣄⡀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠉⢹⣿⢗⣵⣾⢸⣟⣧⠀
⢇⣿⡟⠙⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣇⢻⣿⣿⣉⡒⡀⣖⣾⣿⣿⣿⣿⣿⣟⠇⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⠿⢹⢸⡸⣿⡆
⠘⡟⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⣤⣺⠿⠿⠿⢿⣿⣾⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡿⠷⠤⡀⠀⠀⠀⠀⠃⠀⣟⠁⠀⢸⣾⣧⣿⣧
⠀⠀⠀⠀⢀⠜⡀⣤⠆⢴⡊⠫⢹⠀⠀⠀⠀⠀⣿⣿⣹⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⡉⠞⢓⠤⠤⡀⣟⢏⠉⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢰⠞⠈⠁⠀⠈⠐⢀⡄⠀⠀⠀⢀⣿⣿⣷⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠏⠀⠀⠀⣌⠇⠊⠁⠀⠈⠹⢨⡌⠉⠉⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⠀⢌⡜⡀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣰⣝⠄⠀⣀⠀⠀⠀⠀⠑⠀⠀⢨⠻⠿⠋
⠀⠀⠀⠀⠀⠀⠒⠀⠑⠂⣢⣬⢶⣵⡵⡀⠀⠀⣺⢟⡟⠙⢿⣿⣿⣿⣿⠋⢮⢿⠧⠀⠀⢠⣷⡗⠚⠑⠒⠒⠛⠒⠒⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣵⡄⠀⣯⠞⠀⠀⢸⡿⠻⠋⢹⣇⠈⢫⡅⠀⡰⣿⠳⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀