⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠁⠉⠀⠉⠈⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣠⣄⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⠀⢀⢀⠀⠀⠀⠀⢄⢤⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⢘⠳⠄⠀⠀⠀⢀⢁⠂⠄⠀⠀⢀⣠⠞⣡⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⢠⣁⢱⠠⡆⠀⡼⠢⠞⡆⠂⠰⣻⣿⣿⡎⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣽⣿⣿⡷
⢷⣶⣾⣷⣤⣠⣴⣄⣄⣠⣤⣾⠀⠀⢀⡠⡄⡠⣄⢺⣾⣾⣿⡶⣠⣶⣲⡯⡂⠃⠂⡨⠅⠀⢠⢄⢠⢄⠀⠀⠀⣿⣿⣿⣿⢿⣯⡇
⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠆⠈⠀⣷⡾⡢⡉⡻⢉⣭⠔⠊⢞⡿⣮⣠⣾⠈⢀⢴⢵⡾⠀⠁⠱⠀⠀⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠻⣿⣯⣿⣿⣟⣿⣿⣽⣿⠀⠀⠀⠀⠀⣿⡿⠕⠚⠩⡄⠀⡁⡀⠀⣫⣯⠭⢠⠈⠓⢪⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⣿⡁
⠀⠀⠀⠘⢿⣿⡿⣿⣿⡿⣿⣿⠀⠀⠀⠀⢎⢸⣿⢯⣔⠵⡩⣍⡅⣭⢡⡍⢭⣨⢁⡮⢖⠷⣿⡇⣱⠀⠀⠀⠀⣿⣿⣿⣿⣻⠉⠀
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⡟⠀⡟⡧⠲⢵⡰⠞⠿⠟⠯⠟⠰⠱⢖⡮⠞⢜⢿⠀⢿⠀⠀⠀⠀⣿⣿⣿⢿⣿⡗⠀
⠀⠀⠀⠀⠀⠹⢿⣿⣷⣿⣿⣿⠀⠀⠀⢀⠇⢰⢋⡸⢟⠉⣿⡿⣟⣛⢛⣛⡿⣿⣿⠉⡻⠏⡘⡄⢸⡀⠀⠀⠀⣿⣿⣿⣿⣿⡕⠀
⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣽⣿⠀⠀⠀⠈⠃⡇⣖⢧⠀⠀⢻⣿⣿⣿⢸⣿⣿⣿⡏⠐⠀⠼⡴⢸⠘⠁⠀⠀⠀⣿⣿⣿⣟⣿⣷⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⡄⠀⠀⠀⠴⠕⢃⠀⠂⡠⠈⢿⣿⣿⢸⣿⣿⡟⠁⢄⠐⠀⡙⠸⠆⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡀⡤⠐⠜⡤⣄⣤⣾⣿⣻⢿⣾⣿⣯⣾⣧⠤⣀⠈⡂⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡿⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⣷⣾⡁⢥⠼⡯⡿⢅⠂⣤⡌⢨⡿⣿⣬⠙⢲⣶⣼⡃⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠙⠛⠛⠓⠒⠒⠓⠓⠚⠚⠛⠓⠚⠓⠒⠒⠒⠛⠛⠛⠉⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠂⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠢⠤⠀⠤⠤⠤⠄⢄⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀