⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⠿⠿⠿⢶⣦⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⣀⣀⣀⣈⣻⣷⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⣾⣟⠛⠋⠉⠉⠙⠛⢷⣄⠀
⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⢀⣀⢹⡆
⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣶⣶⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⠿⠿⠛⢻⡇⡇
⠀⠀⠀⠀⠀⢀⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢀⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡇⠀⣿⠀
⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢸⡟⠀
⠀⠀⠀⠀⣿⠃⠀⠀⢰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀
⠀⠀⠀⣸⡟⠀⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀
⠀⠀⢠⣿⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀
⠀⢀⣾⠃⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀
⠀⣸⡟⠀⠀⠀⠀⠪⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀
⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠀⠀⠀
⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀
⣿⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡆⠀⣰⡿⠀⠀⠀⠀⠀⠀
⣿⡆⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠁⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀
⢸⣧⢈⡅⠀⠀⠀⠀⠀⠀⠀⠶⠶⠋⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀
⠈⢻⣦⠓⠂⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠙⠿⠶⣶⣤⣤⣶⡶⠿⠛⠉⠀