⠀⠀⠀⠀⠀⠀⢀⡠⠔⠀⠀⣐⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⣠⣿⣿⠧⠶⠆⠀⠠⠤⢀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⠚⠁⠀⠀⠀⡶⡞⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠔⠀⠀⠀⠀⣠⠊⣀⣤⡙⠟⡴⠛⠉⠉⠉⠉⠛⣶⠶⣤⣀⠀⠀⠈⠂⣽⣦⣀⣴⣾⠀⠀⠀⠀⠀
⠀⠀⠀⠌⠀⠀⡆⠀⢠⡷⢾⠃⠀⠱⠼⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠹⡿⢶⣄⠀⣹⣿⣿⣿⠏⠀⠀⠀⠀⠀
⠀⠀⠘⠀⠀⢸⠀⠀⡏⠀⡜⠀⠀⢢⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠁⠀⠉⢳⠹⠿⣿⣇⠀⠀⠀⠀⠀⠀
⠀⢠⠃⠀⠀⢸⠀⣠⡇⠀⢁⠀⡀⡜⠀⠀⡆⠀⠇⠀⠁⠀⠀⠀⠀⠀⡄⠀⠀⢸⣤⣾⣿⣿⠀⠀⠀⠀⠀⠀
⠀⣼⢠⣰⡀⠈⢀⣿⡇⢸⣗⣶⠞⠓⣿⢺⡗⢲⠀⠀⠀⡇⠀⠀⠀⠀⢁⠀⠀⡄⢸⠙⠛⢻⡄⠀⠀⠀⠀⠀
⣶⡇⢸⣿⣇⡆⢸⡏⠀⣾⡟⠁⠀⢸⣿⣸⡇⢸⢸⠀⠀⡇⠀⠀⡆⠀⣘⡀⠀⡇⣾⠀⠀⠀⣿⡄⠀⠀⠀⠀
⣿⢁⣼⡿⠉⢃⢸⡇⠐⣿⠷⢶⣶⣾⣶⣿⠰⣸⣾⢀⠀⡇⠀⣸⡇⢀⢣⠏⡿⢣⣇⡆⠀⢸⣿⡿⠄⠀⠀⠀
⡇⣿⣿⠃⠀⣾⢸⠃⠀⣏⠓⠿⠾⢿⣯⠋⠁⠃⠹⣼⣾⢀⣰⣿⣥⣷⣿⡶⢃⡟⢿⠇⠀⢸⢿⣷⠀⢂⠀⠀
⣿⡟⠻⠀⠀⢸⠈⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠹⠻⣿⣿⣿⡷⣼⣀⣸⠀⠀⣿⠀⣿⣷⡀⢂⠀
⡇⡇⠐⢣⡀⢺⡀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢿⣃⣈⡿⣿⠁⢠⡏⡀⢇⠩⡳⡀⢳
⠃⡃⠀⠀⣿⣾⡆⠀⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⢸⠃⠀⢈⠀⠱⡙⢄
⠀⠀⢸⡆⢸⣿⡇⡀⣿⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⣿⠀⢸⠀⢀⠈⣧⠀⠘⣾
⠀⣧⢸⡇⠸⢿⡇⠃⣿⣷⠀⠀⠀⠀⣼⣇⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⠀⣾⣀⢸⠀⢹⡄⠀⠘
⠀⣿⠘⡇⠀⢺⡇⣀⣿⡿⠀⠀⠀⠈⢉⠀⠀⠙⠛⠓⣄⠀⠀⠀⠀⠀⣠⡾⠛⣻⡇⢀⣯⢟⡸⣧⠀⢟⡄⠀
⠀⡟⢠⡇⠠⣿⡇⣇⢃⡇⣇⠀⠀⠀⠐⠀⠀⡀⠀⢀⠜⢆⠀⠀⢠⣼⠋⡇⠀⡟⣇⢸⣟⣿⡇⣷⣧⢪⡄⡀
⠀⡇⡇⡇⠀⣼⡇⢱⢸⢃⡏⠻⢦⡀⠀⠀⠀⠀⠈⠀⠀⠀⠦⠀⠀⠙⣶⣿⣶⣷⣿⡀⣿⠿⣿⠻⠿⢿⣞⣽
⣼⣸⣇⣇⣀⣿⣇⣸⣘⣿⡇⠀⠀⠈⣀⣤⣒⠒⢒⣤⣄⣀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⡀⠈⢆⡀⠀⠙⢿