⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣶⣶⣦⣤⣤⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠘⠇⠙⠛⠛⠛⢻⠋⠁
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⠀⢀⡉⠙⠛⠻⢶⣦⠀⠀⢠⡶⠟⠋⢁⢸⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⢸⢯⣉⠙⣲⢤⣬⠀⣄⢨⡠⠖⣦⣚⣿⠀⠀
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠉⠛⠒⠟⠀⠸⡜⠟⠚⠉⠁⠙⡆⠀
⠀⠀⠀⠀⠀⠀⡟⠓⢦⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⢃⠀
⠀⠀⠀⠀⠀⠀⠹⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠎⠀⠀⠀⠀⢸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⡇⠀⠀⠒⠉⠉⢉⡩⠏⠀⠀⠀⢠⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⠎⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠓⠂⠒⠁⠀⢀⡴⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠇⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⢸⠀⠀⠀⠀⢀⣶⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠘⣆⠈⠓⢤⣄⣠⠞⠀⢱⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⢦⣠⠎⢹⢀⡙⣄⡞⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⢘⠘⠃⠈⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠰⡀⠀⢧⠀⠀⠀⠀⠀
⠀⠀⣼⠁⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣇⠀⠸⡇⠀⠀⠀⠀
⠀⢠⠃⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢸⢰⡦⠀⠀⠀⠀⡎⠀⠀⣹⠀⠀⠀⠀
⠀⠈⢻⠲⠤⢄⣀⣀⡎⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡗⠒⢹⡇⠀⠀⠀⠀
⠀⠀⢰⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠘⡆⠀⠀⠀⠀
⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀
⠀⠀⠸⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⡀⠀⠀⠀⢣⠀⠀⡇⠀⠀⠀⠀
⠀⠀⢠⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠁⠀⠀⠀⠘⡄⠀⡇⠀⠀⠀⠀
⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢣⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⠀⠀⠀⢀⠀⢸⠀⡇⠀⠀⠀⠀
⠀⠀⠀⡆⠀⠀⢸⣀⢐⣄⡀⠀⠀⠀⠀⠀⢻⣿⣁⣀⣠⢮⣴⠃⠀⢁⠀⠀⠀⠀
⠀⠀⢀⠄⠀⠀⢸⠈⠁⠀⢹⠉⡖⠒⡖⠊⠁⠀⠀⡇⢾⢸⣟⠀⠀⢹⡀⠀⠀⠀
⠀⢠⠏⠀⠀⠀⢸⠓⠒⠦⢼⠀⠧⠤⣇⣀⣀⣀⡠⠗⠛⠈⢸⠀⠀⢸⠁⠀⠀⠀
⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⣼⠃⠀⠀⠀
⢰⠋⢠⠇⢠⠇⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢋⡴⠃⠀⠀⠀⠀
⠘⠒⣧⣴⠧⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠰⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣀⣠⠟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣳⠤⢤⣀⣀⣀⣀⣀⠤⣴⠋⠉⠉⠉⠉⠀⠈⠾⣦⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠈⠉⠛⠳⢶⣤⠀
⠀⠀⠀⠀⠀⣿⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⣄⠀⠀⢀⡀⣀⡠⣿⠀
⠀⠀⠀⠀⠀⠙⠓⠒⠚⠙⠶⡤⠤⠄⠤⠀⠀⠤⠄⠤⠔⠗⠀⠀⠀⠀⠀⠀⠀⠀