⠀⠀⠀ ⠀ ⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⣩⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀ ⠀ ⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀ ⠀ ⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⠀⢸⣟⣻⣿⡿⠿⠛⠛⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀ ⠀ ⠀⠀⠀ ⠀⠀⢠⣼⣿⠏⡠⠞⠋⠁⠀⠀⢀⣴⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⠻⢿⣿⣯⡙⠻⣿⣿⣆⠀⠀⠀⠀
⠀⠀⠀⠀ ⠀ ⠀⠀⠀ ⠀⠀⣾⡿⠁⠂⠀⠀⠀⠀⢀⢂⣴⣿⣿⣿⣿⣿⡿⢟⣩⠵⢶⣿⡏⢴⣮⣝⠻⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⠙⠿⣷⣌⠻⣿⣧⠀⠀⠀
⠀⠀⠀ ⠀ ⠀⠀⠀ ⡆⠀⢸⣿⠃⠁⠀⠀⠀⠀⠀⣧⠹⢿⣿⣿⣿⡟⣫⠖⠉⠀⠀⠀⡟⠁⠀⠉⠻⣷⣌⠻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠐⠈⠻⣷⡌⢿⣧⠀⢰
⠀⠀⠀ ⠀ ⠀⠀⠀ ⡇⠀⢻⣿⢸⠀⠀⠀⠀⠀⠀⠙⠳⢶⣤⣭⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡸⣿⣿⡿⠿⠿⡿⠀⠀⠀⠀⠀⠹⣿⣾⣿⣧⣸
⠀⠀⠀ ⠀ ⠀⠀⠀ ⣇⠀⢸⣏⣸⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠷⠶⠶⠖⠚⠋⠁⠀⢀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀ ⠀ ⠀⠀⠀ ⣿⣠⡄⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠂⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿
⠀⠀⠀ ⠀ ⠀⠀⠀ ⣿⣿⣇⠹⣿⣯⣴⣶⣶⣖⣀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣠⣿⣾⣿⣿⣿⣿
⠀⠀⠀ ⠀ ⠀⠀⠀ ⣟⢿⣿⢀⠻⣿⣿⣿⣿⣿⣿⣿⣷⣮⢢⣀⠀⠀⠀⠀⠀⠀⢰⠨⠸⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣠⣀⢏⣿⣿⣿⣿⣿⣿
⠀⠀⠀ ⠀ ⠀⠀⠀ ⠈⠛⢬⣛⠀⡙⢿⣿⣿⣿⡿⠿⠿⠛⢋⠀⠢⢀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀ ⠀ ⠀⠀⠀ ⣀⠀⠀⠈⠳⢦⣈⠩⢐⡠⢤⡀⠠⠄⠀⠀⢉⠀⢧⡆⠀⠀⠸⠀⠀⢀⡀⢀⡠⠔⠆⢀⡀⠉⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀ ⠀ ⠀⠀⠀ ⠈⠀⠀⠈⠀⠀⠈⠛⠦⡙⢿⣶⣮⣭⠳⠄⠌⣦⠈⠙⠄⢆⠀⠀⠀⠤⠾⠟⠢⠀⠀⠀⠈⠀⠈⠉⣁⣀⣬⣽⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀
⠀⠀⠀ ⠀ ⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢮⡻⣿⣿⠗⠂⠁⠘⢂⠀⡀⠃⠀⢀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⡀⠀⠀⠀
⠀⠀⠀ ⠀ ⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢀⠠⢀⠃⢸⢠⠃⢠⠀⠈⠀⢆⢀⠀⠀⢹⣏⢻⣿⣿⡟⢻⠍⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀ ⠀ ⠀⠀⠀ ⠁⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢀⠀⠆⠈⠀⠀⠀⠀⡘⢸⠀⠆⠀⠀⠀⠀⠀⡑⢀⠀⠛⠷⢬⣭⣃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙
⠀⠀⠀ ⠀ ⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡂⠂⠇⠀⠀⠀⠀⠀⠃⢧⣀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀ ⠀ ⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀ ⠀ ⠀⠀⠀ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢁⠆⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⢠⠒⠋⠁
⠀⠀⠀ ⠀ ⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄⣀⠠⠤⠤⠄⠀⠐⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠴⡈⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀ ⠀ ⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡠⢈⠂⠌⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀ ⠀ ⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠪⠀⢕⠄⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀ ⠀ ⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀