⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⣄⠀⠀⠤⠤⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⡄⠒⠚⠿⡒⠃⠀⠈⠑⢀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣼⠱⠀⠀⠀⢀⡌⠉⠀⠀⠀⡜⠀⠀⠀⠀⠀⢸⣆⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣤⠊⠀⠀⠘⠒⢄⠀⠀⠀⠀⠀⣴⠂⠀⠀⠀⠀⠃⢦⡁⠀⠉⢀⣀⣀⣀⠢⣀⣀⣀⡀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠙⢀⠀⢀⠒⠁⠒⠀⠀⠀⠀⠀⡡⠀⠒⠒⠛⠀⠘⡋⠀⠀⠀⠀⠘⠀⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⠀⠀⢀⡀⠗⠉⡀⢰⣆⣀⣀⣀⣠⠊⠀⠀⢀⣄⠀⠀⠀⠙⠤⡀⠀⠀⠀⠀⣗⠒⠚⠚⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠈⠁⠀⡠⠛⠉⠑⢄⣭⠋⣁⣠⣄⣴⠀⢠⡄⠀⢐⣶⠀⠀⠘⠂⠀⠀⢄⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠶⠖⠘⢶⡰⠴⠆⠦⢴⠎⠀⠀⠀⡀⠀⠀⡀⠀⠀⠑⠉⠓⢘⡃⢠⣘⠘⠂⢀⠀⣼⠂⠀⠀⠑⠂⢴⡦⠊⡖⠶⢴⠲⠶⠶⠶⠖⠶⠶⠶⠲⠖⠆⠶⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠦⡀⠀⠑⢆⡀⢀⣀⠕⠂⠀⣀⣺⠀⠀⢀⡜⠁⠀⢺⣾⣿⠿⠶⢢⣀⢸⡯⠃⢸⣀⣐⡏⡾⣿⠂⠀⠀⠀⠀⠜⠁⠀⡧⠀⢸⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀
⠀⠀⣄⠀⠀⠀⠀⠙⠱⣄⢰⠆⠀⢠⡄⢀⣾⢠⣀⣷⠴⠀⡧⠀⡆⣼⠀⠀⠀⠀⣀⣡⣤⡀⠀⠀⣆⣠⣦⣤⠊⠀⠀⢰⠂⠀⡆⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠃⠀⠀⠀⠀⠀⠀⢈⡛⠀⠀⠈⠓⠊⠛⡍⠙⠛⢀⣠⣹⠒⠳⠚⠀⠀⠀⠀⠛⡘⢉⢷⢢⣮⡀⠀⠙⡁⡀⠀⠀⢘⠀⠀⡛⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⡀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⢀⣾⠀⠀⢸⠄⠁⠉⠀⠀⠀⠀⠀⠀⠀⠸⣟⣿⢼⣾⠿⣿⡠⠊⠉⢁⠀⠀⢸⠀⠀⡇⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠁⣄⠀⠀⠠⠂⠀⠀⠀⠀⢀⡆⠈⠀⠤⣴⣶⠢⡀⠀⠀⠀⠀⢄⣀⣀⡀⠀⠀⠛⢸⣸⡐⡆⠀⠀⣾⠁⠀⠀⡞⠀⠰⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠑⠄⢆⠀⢀⠀⠀⠀⠊⣀⠀⠀⠐⠻⠋⠀⡁⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⠏⡳⠃⠀⠀⠻⠀⠀⠀⣓⠀⢰⠇⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣸⠼⠛⣆⡀⠀⢠⢾⡀⠀⠀⢼⠴⠺⣧⢼⠂⠷⢀⡀⡀⢀⠀⣀⡤⢺⣁⡴⠁⠀⠀⠀⠀⢸⡇⠀⣷⠀⢸⠀⠀⠀⢰⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡁⢠⡄⠶⠟⠀⠀⠙⠂⢄⠀⢄⠀⣼⠉⢰⢫⣹⡇⠁⠀⡜⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⡆⠀⣸⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁⠘⠿⠀⠀⠀⠀⠀⠀⢨⡌⠉⠘⠉⠆⡘⢯⠙⡘⠀⠚⠀⠀⠀⠀⣀⣠⠋⠀⠀⠀⢀⠇⠀⡻⠀⠀⠀⣸⣧⣄⣀⣀?