⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⣰⡿⠁⠀⢀⣠⠂⢀⣀⡤⠴⠶⠶⠶⢦⣄⡀⠀⠈⠙⠻⣿⣧⣀⠀⢀⣰⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⡿⠀⠀⠰⠋⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⣈⣙⣽⣿⣿⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢱⠀⢃⣄⣶⡷⠃⠀⣬⣶⣦⣤⢀⠢⠀🍁⠐⡄⢠⠹⣷⠀⠀⠀⠛⣿⣿⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⣾⣿⣿⣿⣤⡄⠀⠹⠟⠋⠁⣠⣮⡂⠀⡀⠘⣆⢻⢮⣷⡀⠻⣶⡬⣿⡂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⢨⣿⣿⣿⡟⠛⠀⢀⢀⣠⣴⢶⣤⣄⠈⡄⢰⠀⢿⡌⢃⠙⠷⢶⣼⣷⣤⠇⠀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠘⢿⣿⣿⡿⣰⣰⡿⣫⣵⣷⢿⣿⣿⣿⠇⠀⡿⢀⡯⠀⠀⠀⣀⡠⠖⠛⣻⠟⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⡋⡻⣯⢿⣛⣭⡪⢀ ▪️⠠⣭⣹⣻⠇⠀⠀⠁⢰⢵⣄⠀⢻⡀⠀⣴⠞⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡂⢕ ▪️⣿⣿⣿⣾⡀⠁⢀⣿⢿⠏⠀⢀⡠⢀⣷⢽⣽⡾⠀⠘⠦⠸⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡁⠬⣖⢿⣿⣿⣿⣯⣯⣿⣾⣡⣴⣾⣿⣣⡷⡯⣧⡷⠃⠀⡐⠀⠁⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⣗⡏⡀⠀⠀⢉⡹⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⠿⢿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣟⡚⢽⠜⣄⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣝⣹⣿⣿⣿⣿⣿⢿⣫⣿⣳⡪⠈⠂⠵⠋⠀⠡⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⡿⡟⣋⣡⡾⢯⣛⠮⢵⣾⣾⠅⠀⠀⠀⠈⢄⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠩⣸⢵⠞⠚⠉⠀⠀⠺⠏⠓⠁⠀⠀⠀⠀⠀⠈⠑⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⢂⢀⡨⠀⠀⢜⡽⡅⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣹⣿⣿⣿⠃⠀⠀⣅⡁⠁⠀⣼⣿⣿⣿⣶⣤⣄⣀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢠⣿⣿⡿⠇⠀⠀⠸⣿⡃⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⠻⣿⣿⣿⣿⣿⣿⣿