⠀⠀⠀⠀⠀⠀⢀⣾⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢧⡀
⠀⠀⠀⠀⠀⢀⣾⠃⢘⣷⣀⣀⣤⣤⣤⣄⣀⢸⡏⠈⢷⡀
⠀⠀⠀⠀⠀⣼⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣷
⠀⠀⠀⠀⢰⣿⣿⣿⣿⠁⠸⠗⢹⣿⡟⠰⠷⠈⢻⣿⣿⣿⡇
⠀⠀⢐⣒⣺⣿⣿⣿⣿⣀⠀⣀⣼⠛⢷⣄⠀⢀⣼⣿⣿⣿⣿⣉⡁
⠀⠀⠀⠤⢺⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠢

⠀⠀⠀⠀⠀⠀⠀⢸⡟⣄⠂⢄⣀⣀⣄⣠⣾⣯⡀⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢛⡩⣖⠿⡴⠟⡕⢦⣕⠠⣗⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡰⣣⡾⢡⠾⡁⠀⡽⡈⡜⢷⡜⠧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⢱⣿⢀⠸⡆⢳⣧⣱⡇⢠⠘⣏⡌⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢹⣞⣿⡚⢖⠷⢠⣾⣯⣷⠘⡀⢡⣦⢹⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢻⡿⠛⠂⠀⠀⠙⠋⠀⠀⡇⢸⣿⢸⣧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣼⠀⠀⢡⣤⠄⠀⠀⢸⠀⣸⠙⡆⢸⠀⠀⠌⡁
⠀⠀⠀⠀⠀⠀⠀⢘⡄⣑⢤⣀⢀⣠⢖⢇⡟⣠⢏⢳⠀⣾⢀⠌⡰⠀
⠀⠀⠀⠀⠀⠀⠀⡞⢀⢡⢏⣼⡧⠒⢎⡎⠤⠫⡮⡎⠀⡿⠋⠔⠁⠀
⠀⠀⠀⠀⠀⢀⠜⣴⢺⣿⣾⠷⣽⢋⠊⡔⢩⡖⢺⠧⣀⠀⣮⠑⡀⠀
⢀⠀⠀⣀⠔⢁⣶⣿⡿⣿⣥⡞⣡⡇⡜⡇⣿⠀⡇⠈⠚⠷⠇⡠⢉⠆
⠒⠂⢉⡠⣴⣾⣿⣋⣴⣗⣭⣼⢿⡇⠱⡿⢿⡤⣧⣉⣉⣵⣾⠷