⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⢠⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⢀⠀⠀⠀⣰⡇⠀⡆⡄⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀
⠀⠀⠀⢸⢸⡆⠀⢴⢷⡧⣼⣇⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣇⠀⢹⠀⢧⠀⣧⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠀⠀⠀⠀⠀
⠀⠀⠀⢸⠉⢻⣦⣾⣶⣾⣌⠛⣌⢸⠀⠀⠀⠀⡐⠀⠀⠀⣠⢿⢸⠀⠀⠀⠀⠀
⡀⠀⠀⢸⢰⡿⢻⣼⣿⣦⢱⠁⠉⠸⠀⡀⢠⡞⠁⠀⢀⡜⠉⣾⣾⢀⣴⠀⠀⠀
⠀⠉⠉⢸⡀⠇⡟⣿⣿⢏⠏⠃⢰⠷⢻⠗⠋⢀⡠⡲⢟⡚⠲⠻⢑⢟⣿⠀⡄⠀
⠀⠀⠀⠘⠁⠀⠸⠦⠄⠊⠀⠀⠀⠈⠉⠛⠋⠉⣷⣟⣿⣛⢻⢫⣁⣾⢇⣼⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢿⣿⣿⢠⠡⡟⠵⡏⡘⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠸⡘⢛⡡⠃⣠⢧⡾⠐⠕⡱⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠈⠀⠀⢈⡴⣩⣴⡤⡞⡻⠓
⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⡝⠀⡧⠁⠀
⠀⠀⠀⢸⣧⡀⠀⠀⠀⠩⣐⠂⠤⢀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⠧⠚⠁⠀⠀
⠀⠀⠀⣸⣿⡷⣄⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⢀⢴⢃⠠⠊⢹⠀⢠⡆⠀⠀
⠀⡠⠊⢸⣿⡇⠈⢢⡀⠀⠀⠀⠀⣀⡀⡤⠔⡖⠈⠁⡸⡘⠀⠀⡄⠀⢸⠁⠀⠀
⠁⠀⠀⢸⣿⡇⠀⠀⠹⠶⠿⠟⠋⢁⠜⠣⡀⡇⠀⠀⣿⠁⠀⢠⠀⠀⠿⠀⠀⠀
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠈⠲⡀⠀⡟⠀⠀⡌⠀⠀⡆⠀⠀⠀
⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⣀⡴⠃⠀⠀⠀⠀⠀⠙⣾⡇⠀⠀⠁⠀⢸⠁⠀⠀⡀