⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠙⠶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠓
⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠀
⠀⠀⠛⠤⣠⡀⠀⠀⠉⠑⠳⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⣁⡴⠃
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⠈⠙⢄⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⠤⠤⣤⠤⠀⠀⠀⠀⢀⡤⡖⠉⠀⠖⠞⠁⢀⠀
⠀⠀⠀⠠⠤⣀⡀⠀⠀⠀⠀⢸⡀⠀⠀⠹⣆⠀⢹⡤⡀⠀⢀⣴⢫⣥⢀⠾⠁⠀⠀⠀⢀⣶⠋⠀⣧⢀⠀⣠⠤⠖⠉⠀
⠀⠀⠀⠀⠀⠉⠑⠒⠆⠀⠀⠸⡇⠀⠀⠀⠹⡦⠈⠓⡥⣄⠈⠉⠘⠋⢸⢀⠀⠀⠀⠀⣸⠉⠀⢠⡻⠈⠀⢋⣀⡤⠀⠀
⠀⠀⠀⠀⠀⠤⣀⣀⡀⠀⠀⠀⢳⠀⠀⠀⠀⠉⢧⣄⠓⢚⣪⡤⠀⠀⠀⢳⡄⠀⠀⣴⠃⠀⢀⣾⠁⠀⠘⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⣀⠈⣧⣄⠀⠀⠀⠀⠑⠶⣀⣀⡀⠀⠀⠀⠀⢯⠶⠉⠀⢀⢀⡾⠈⠘⠚⠒⡤⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢤⠒⠊⠉⠁⠀⠈⠱⣄⡄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⡆⣠⣠⠶⢫⣀⠋⠒⣴⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠀⡀⠀⠉⠓⠒⠤⠤⠤⠴⠀⠀⠀⠀⠀⢸⡄⠈⠸⢤⠈⠉⢦⡠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⠀⠀⡴⠋⠀⢠⡆⠀⢀⠀⠀⡗⠀⠀⠀⠀⢠⢯⡙⢧⡄⠀⢷⡦⠀⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⢀⡴⠋⠀⡰⠏⠀⡞⠎⢰⢄⢀⣰⡟⠈⢲⡄⠹⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠘⠁⢀⠞⠀⠀⢸⡯⡟⠹⡦⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⠀⣠⠞⠋⢰⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠀⣼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡀⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⣿⠀⠌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠃⡏⠀⢹⠁⠀⢠⠶⠓⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢹⠀⠀⢧⡀⡀⠀⢀⡼⠂⢀⠀⠀⠀⡴⠛⠉⠉⢦⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣌⢧⣄⣰⠮⣩⠍⠉⠀⣠⠞⠂⠀⠀⢫⣤⣠⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡎⠛⣷⣝⠶⢏⣩⣍⣁⣠⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠙⢻⣦⡈⠿⣍⣍⡉⠀⠀⠀⠀⣀⡠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠉⢫⣄⠈⠳⣈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠹⡆⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀