⢸⣿⣿⠀⣰⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿
⠘⣿⣿⠀⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠂⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿
⠀⡿⣿⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿
⠀⡇⠸⡆⠀⠀⢸⠀⠀⠀⠀⠀⣰⡿⠁⣀⡠⠤⣀⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿
⠀⡇⠀⢻⠀⠀⢸⣄⠀⠀⠀⠸⠟⠐⢻⣶⢾⡏⡹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿
⢠⡇⠀⠈⣇⠀⠀⠛⠷⣦⡀⠀⠀⠀⠈⠞⠷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢸⠀⠀⠀⠸⡄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⢳⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠈⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⡄⠀⠀⠀⠀⢹⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠣⠀⠀⠀⠀⠘⡆⢘⠀⠀⠀⠀⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠱⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⣀⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⣠⣪⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⠀⣀⣠⠞⢏⠉⠙⢢⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⡭⢖⣲⠬⠷⢤⣀⣙⣢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣀⣿⡁⠀⠀⢾⠀⠘⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣝⣦⡀⠈⢣⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠖⣚⣞⠀⢉⡏⠉⠉⠙⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁⠀⢀⡤⣺⠵⠚⡆⠈⢆⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠀⠀⠀⣠⠞⡵⢋⡤⠖⣉⢽⠤⡬⢷⣤⣤⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⣠⠊⣠⢞⡴⣁⡤⢴⠵⠊⣠⠃⣸⠁⢸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⢀⣼⣕⡯⠓⠉⣰⠁⢀⡸⢦⡚⠁⡼⠁⠀⡞⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⣠⠾⠊⠁⢀⡤⠖⠁⠀⡎⠀⠀⠉⠑⣳⢤⣤⣧⡤
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⡴⠃⢀⡤⠚⠁⠀⠀⢀⡼⠁⠀⣠⠖⠉⢀⠞⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⠊⠀⡴⠋⠀⠀⠀⣀⠞⠁⠀⠀⣰⠁⠀⠀⡸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡴⠁⢀⠞⠀⠀⠀⠀⡴⠁⠀⠀⢀⠜⠁⠀⢀⠔⠁⠀⠀⠀⠀