⠀⠀⠀⠀⠄⠀⠀⠀⢸⢕⣧⣀⣱⣝⢧⣜⣽⢿⣠⣿⣯⢠⣿⣏⠤⠤⡀⠀⠀⠀
⠀⠀⠀⢀⡀⣨⣟⣛⡓⠛⣾⠷⣞⠯⡱⣼⠈⠒⠿⣿⢻⠋⠁⠀⠀⠀⠈⠢⡀⠀
⠀⠀⠄⢭⣾⣴⣶⣛⠫⣽⡎⠻⠌⢃⡐⢷⢀⢰⠇⣸⠅⠀⠼⣿⢿⠿⡅⠀⡇⠀
⠀⠀⠀⢈⡸⠿⣶⣌⠱⡧⠹⠄⢧⠀⢻⡜⠧⢸⢧⣷⠇⠀⠀⠿⠻⠟⠀⠀⡇⠀
⢰⣆⣴⣟⢛⡖⡀⢉⣶⣞⣟⢦⣝⢇⠈⠻⠀⠘⠘⠋⢴⠀⢸⠿⡿⠿⠅⠀⡇⠀
⠀⠹⢿⣞⢿⣗⣪⠩⠒⠉⣉⣶⡬⠅⢀⣀⣼⠂⠀⠈⡍⣶⢤⣀⣀⡀⣠⡜⣀⠀
⠀⣠⣊⣿⣶⣞⣋⢎⣔⣞⣉⣁⢤⡌⢫⣾⡃⣰⡋⢈⠇⡻⠄⢿⣯⣷⣿⣏⠉⠀
⠀⠏⣾⣽⣽⣿⣿⣾⣇⣤⣎⣾⣫⣿⣿⣿⣾⣟⣽⣿⡟⣧⣄⣾⢻⢷⣹⢽⡄⠀
⠀⠀⢹⢟⣿⣿⣾⣿⡟⢿⣷⣷⢟⡿⣻⡟⡟⢪⣿⣿⢿⣿⡷⣵⣾⣿⡿⠀⠀⠀
⠀⠀⢘⣹⣻⣿⣻⣿⢷⣿⣟⣿⡦⣴⡟⢸⣿⡧⢾⣟⣙⣽⣿⡏⣻⣯⡏⠀⠀⠀
⠀⠀⠈⠀⠟⡟⣿⡏⠇⠧⡻⠟⣿⣼⠀⠀⠃⣠⣟⠿⠃⢿⣿⣷⣻⢿⡟⠀⠀⠀
⠀⠀⠀⠀⠐⢫⠟⢿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠚⠀⣷⢿⠈⠁⠈⠀⠀
⠀⠀⠀⠄⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠓⠐⠁⠀⠀⠀⠀⣴⠇⠀⠀⠀⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⢆⡈⠐⢶⣶⣶⣶⠒⠈⡠⢋⣾⠀⠀⠀⠐⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⢠⡀⢷⣄⠀⠀⠀⠀⣠⠞⠀⠜⡏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣠⣴⣾⣿⣿⣄⣷⡌⢯⣓⠒⠒⣾⠟⣰⠀⢰⣿⣶⣄⠀⠀⠀⠀⠀⠀
⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣿⡿⠡⢃⣾⣿⣧⣾⣿⣿⣿⣿⣷⣦⣄⡀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿