⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠋⠉⠈⠉⠉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠
⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠
⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⣿⣿⣿⣿⣿⡏⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠
⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⣿⣿⣿⣿⣿⢏⣴⣿⣷⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠
⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⣿⣿⣿⣿⣟⣾⣿⡟⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⢢⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠
⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⣿⣿⣿⣿⣿⣿⣿⣟⠀⡴⠄⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠
⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⣿⣿⣿⣿⣿⠟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢴⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠
⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⣿⣿⣿⣁⡀⠀⠀⢰⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡄⠀⣴⣶⣿⡄⣿⣿⣿⣿⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠
⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⣿⣿⣿⡋⠀⠀⠀⠎⢸⣿⡆⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠗⢘⣿⣟⠛⠿⣼⣿⣿⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠
⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⣿⣿⣿⠋⢀⡌⢰⣿⡿⢿⡀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣧⢀⣼⣿⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠
⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⣿⣿⣷⢻⠄⠘⠛⠋⠛⠃⠀⠀⠀⠀⠀⢿⣧⠈⠉⠙⠛⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠
⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⣿⣿⣧⠀⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⢀⢃⠀⠀⢸⣿⣿⣿⣿⣿⣿⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠
⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⣿⣿⣿⡿⠀⠴⢗⣠⣤⣴⡶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠀⣿⣿⣿⣿⣿⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠
⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⣿⣿⣿⣿⡀⢠⣾⣿⠏⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⣿⣿⣿⣿⣿⣿⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠
⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⣿⣿⣿⣿⣧⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠
⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⣿⣿⣿⣿⣿⣿⡄⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠
⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠
⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠
⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⣿⣿⣿⣿⣿⣦⣄⣀⣀⣀⣀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠
⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠
⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠙⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠
⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠁⠀⠀⠹⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠
⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠
⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⣿⣿⣿⣿⣿⠿⠛⠉⠉⠁⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⢀⠈⣿⣿⡿⠉⠛⠛⠛⠉⠉⠀⠉⢻⣿⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠
⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⣿⣿⡿⠋⠁⠀⠀⢀⣀⣠⡴⣸⣿⣇⡄⠀⠀⠀⠀⢀⡿⠄⠙⠛⠀⣀⣠⣤⣤⠄⠀⠀⠀⠀⠀⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠⠠