⠀⠀⢸⡿⢦⣄⠀⢀⣠⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣷⠀⠉⠛⠛⠉⢰⡇⠀⠀⠘⣷⣦⣾⡇⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣰⠿⠀⠀⠀⠀⠀⢿⡁⠀⢀⣴⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀
⣴⣿⣁⡀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⢿⠃⠀⢀⣤⡀⠀⠀⠀⠀
⠀⠈⠉⠛⣿⡀⠀⣰⠟⠛⠛⠛⠛⠀⠀⠀⠀⣠⡾⢻⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠈⣷⣼⠏⠀⠀⠀⢻⣟⠻⠿⢶⡾⠋⠀⢸⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠃⠀⣴⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠻⢶⣤⣀⠀
⠀⠀⠀⠀⠀⠘⢷⣾⣿⣤⣄⠀⢈⣿⠀⠀⠀⠀⠀⠀⠀⢀⣉⣿⠿
⠀⠀⠀⠀⠀⢀⣾⠿⣿⡏⠉⢠⣾⠃⠀⠀⠀⠀⠀⢀⣾⠛⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⣿⡷⠿⠟⠛⢿⣦⡀⢸⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢿⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠀⠀⠀⠀⠀
. ˚ . ⋆. . ˚ * ˚ . . ˚
⠀⠀⢸⡿⢦⣄⠀⢀⣠⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣷⠀⠉⠛⠛⠉⢰⡇⠀⠀⠘⣷⣦⣾⡇⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣰⠿⠀⠀⠀⠀⠀⢿⡁⠀⢀⣴⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀
⣴⣿⣁⡀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⢿⠃⠀⢀⣤⡀⠀⠀⠀⠀
⠀⠈⠉⠛⣿⡀⠀⣰⠟⠛⠛⠛⠛⠀⠀⠀⠀⣠⡾⢻⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠈⣷⣼⠏⠀⠀⠀⢻⣟⠻⠿⢶⡾⠋⠀⢸⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠃⠀⣴⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠻⢶⣤⣀⠀
⠀⠀⠀⠀⠀⠘⢷⣾⣿⣤⣄⠀⢈⣿⠀⠀⠀⠀⠀⠀⠀⢀⣉⣿⠿
⠀⠀⠀⠀⠀⢀⣾⠿⣿⡏⠉⢠⣾⠃⠀⠀⠀⠀⠀⢀⣾⠛⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⣿⡷⠿⠟⠛⢿⣦⡀⢸⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢿⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠀⠀⠀⠀⠀
⠀⠀⢸⡿⢦⣄⠀⢀⣠⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣷⠀⠉⠛⠛⠉⢰⡇⠀⠀⠘⣷⣦⣾⡇⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣰⠿⠀⠀⠀⠀⠀⢿⡁⠀⢀⣴⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀
⣴⣿⣁⡀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⢿⠃⠀⢀⣤⡀⠀⠀⠀⠀
⠀⠈⠉⠛⣿⡀⠀⣰⠟⠛⠛⠛⠛⠀⠀⠀⠀⣠⡾⢻⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠈⣷⣼⠏⠀⠀⠀⢻⣟⠻⠿⢶⡾⠋⠀⢸⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠃⠀⣴⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠻⢶⣤⣀⠀
⠀⠀⠀⠀⠀⠘⢷⣾⣿⣤⣄⠀⢈⣿⠀⠀⠀⠀⠀⠀⠀⢀⣉⣿⠿
⠀⠀⠀⠀⠀⢀⣾⠿⣿⡏⠉⢠⣾⠃⠀⠀⠀⠀⠀⢀⣾⠛⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⣿⡷⠿⠟⠛⢿⣦⡀⢸⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢿⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠀⠀⠀⠀⠀
⠀⠀⢸⡿⢦⣄⠀⢀⣠⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣷⠀⠉⠛⠛⠉⢰⡇⠀⠀⠘⣷⣦⣾⡇⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣰⠿⠀⠀⠀⠀⠀⢿⡁⠀⢀⣴⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀
⣴⣿⣁⡀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⢿⠃⠀⢀⣤⡀⠀⠀⠀⠀
⠀⠈⠉⠛⣿⡀⠀⣰⠟⠛⠛⠛⠛⠀⠀⠀⠀⣠⡾⢻⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠈⣷⣼⠏⠀⠀⠀⢻⣟⠻⠿⢶⡾⠋⠀⢸⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠃⠀⣴⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠻⢶⣤⣀⠀
⠀⠀⠀⠀⠀⠘⢷⣾⣿⣤⣄⠀⢈⣿⠀⠀⠀⠀⠀⠀⠀⢀⣉⣿⠿
⠀⠀⠀⠀⠀⢀⣾⠿⣿⡏⠉⢠⣾⠃⠀⠀⠀⠀⠀⢀⣾⠛⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⣿⡷⠿⠟⠛⢿⣦⡀⢸⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢿⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠀⠀⠀⠀⠀