⡀⡂⡀⡂⡀⡂⡀⡂⡂⡂⡂⡂⡂⡂⡂⡂⡢⡂⡢⡂⡢⡂⡢⡂⡢⡂⡢⡂⡢⡂⣢⣂⣢⡂⣂⣂⡢⡂⡢⡂⡢⡂⡢⡂⡢⡂⡢⡂⡂⡂⡂⡂⡂⡂⡀⡂⡀⡂⡀⡂
⡀⡂⡀⡂⡀⡂⡂⡂⡂⡂⡂⡂⡢⡂⡢⡂⡢⡂⡢⡂⣢⡢⡦⡂⡢⠒⠲⡂⡊⠉⠄⠄⠄⠄⠄⠊⡂⠋⡒⡂⡢⡦⣢⡂⡢⡂⡢⡂⡂⡂⡂⡂⡂⡂⡂⡂⡀⡂⡀⡂
⡀⡂⡀⡂⡂⡂⡂⡂⡢⡂⡂⡂⡢⡂⡢⡂⡢⡂⡢⠊⡂⠄⠄⠂⠂⠂⠄⠄⠄⡀⡠⡀⡠⡀⡀⡀⡀⡀⡀⠂⡀⡂⡢⣻⡢⡂⡢⡂⡢⡂⡢⡂⡂⡂⡂⡂⡂⡂⡀⡂
⡀⡂⡂⡂⡂⡂⡢⡂⡢⡂⡢⡂⡢⡂⡢⡂⡢⡒⡂⠂⡀⠂⠄⠄⠄⠄⠄⠄⠄⠂⡀⡊⡢⡊⡪⡺⣪⣺⣾⣾⣶⣾⣮⣮⣳⡪⡢⡂⡢⡂⡢⡂⡢⡂⡂⡂⡂⡂⡂⡂
⡀⡂⡂⡂⡢⡂⡢⡂⡢⡂⡢⡂⡢⡂⡢⡂⡺⠂⠄⠂⡀⠄⠄⠄⠄⠄⠄⠄⠄⠄⡀⠂⡀⡂⡢⡪⣪⣺⣾⣻⣾⣿⣿⣿⣿⣾⡢⡊⡢⡂⡢⡂⡢⡂⡢⡂⡂⡂⡂⡂
⡂⡂⡂⡂⡢⡂⡢⡂⡢⡂⡢⡂⡢⡊⡢⣪⡂⠂⡀⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⡀⡂⡠⡂⡢⡪⣪⣺⣾⣻⣾⣿⣿⣿⣿⣿⣯⡪⡢⡊⡢⡂⡢⡂⡢⡂⡢⡂⡂⡂
⡂⡂⡢⡂⡢⡂⡢⡂⡢⡂⡢⡂⡢⡊⡢⡊⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⡀⠄⠄⠂⠄⠊⠊⠊⡪⡺⣺⣻⣾⣿⣿⣿⣿⣿⣿⡪⡢⡊⡢⡂⡢⡂⡢⡂⡢⡂⡢⡂
⡢⡂⡢⡂⡢⡂⡢⡂⡢⡂⡢⡊⡢⡊⡢⠃⠄⠄⡀⠄⠄⠄⠄⠄⡀⠄⡀⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠊⡪⡺⣺⡻⡿⡿⣿⣯⡢⡊⡢⡊⡢⡂⡢⡂⡢⡂⡢⡂
⡂⡂⡢⡂⡢⡂⡢⡂⡢⡂⡢⡊⡢⡎⠄⠄⠄⠄⠄⠄⠄⠄⡠⡂⡂⡂⡠⡢⣢⡂⡀⠂⡒⡂⡢⡀⠄⠄⠄⠄⣲⣾⡮⡂⡂⡂⡂⡪⡦⡊⡢⡊⡢⡂⡢⡂⡢⡂⡢⡂
⡢⡂⡢⡂⡢⡂⡢⡊⡢⡊⡢⡊⣺⠄⠄⠄⠄⠄⠄⠄⠄⡪⡪⡂⡀⡂⡢⡊⡪⡪⣢⣢⣢⡊⣠⡂⡀⠄⠄⠄⡪⣻⡦⡺⣢⣪⣢⣊⡧⡪⡢⡊⡢⡂⡢⡂⡢⡂⡢⡂
⡢⡂⡢⡂⡢⡂⡢⡊⡢⡊⡢⡊⣺⠄⠄⠄⠄⠄⠄⠄⠄⡪⡂⠄⡀⠂⡀⠂⡀⡊⡪⡺⣺⣻⡪⡊⡀⠄⡀⠄⡨⣺⣿⣺⣪⣺⣺⣾⣧⡪⡢⡊⡢⡊⡢⡂⡢⡂⡢⡂
⡢⡂⡢⡂⡢⡊⡢⡊⡢⡊⡢⡊⡺⠄⠄⠄⠄⠄⡀⠄⡠⡊⡂⠄⠄⠄⡀⠂⡀⡂⡢⡪⡪⡊⡢⠂⡀⡀⡀⡂⡪⣺⣿⣿⣿⣿⣿⣿⣿⡮⡢⡪⡢⡊⡢⡂⡢⡂⡢⡂
⡢⡂⡢⡂⡢⡊⡢⡊⡢⡊⡢⡊⣺⣂⡀⠄⠄⡀⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⡀⡀⡀⡂⡢⡊⠄⠄⠄⠂⡀⠂⡂⡺⣿⣿⣿⣿⣿⣿⣿⡯⡢⡊⡢⡊⡢⡊⡢⡂⡢⡂
⡢⡂⡢⡂⡢⡊⡢⡊⡢⡊⡢⡊⣺⡺⡢⡢⡌⠄⠄⠄⠄⠄⠄⠄⠄⠄⡀⡂⠄⠂⠂⠂⠂⠄⡀⠄⡀⠄⠄⠄⠄⠈⡪⡻⣿⣿⣾⣿⣿⡫⡢⡊⡢⡊⡢⡊⡢⡂⡢⡂
⡢⡂⡢⡂⡢⡊⡢⡊⡢⡊⡢⣢⡯⠂⢀⠊⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⡀⠄⡀⠄⠄⠄⡀⠄⡀⡂⡀⡊⡺⣺⣾⣿⣿⣿⡫⡪⡢⡊⡢⡊⡢⡊⡢⡂⡢⡂
⡢⡂⡢⡂⡢⡊⡢⡊⡢⡊⡢⣾⡂⢀⠂⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⡀⠄⡀⡀⠂⠂⠂⡢⡢⣮⣾⣺⡺⣿⡫⡢⡊⡢⡊⡢⡊⡢⡊⡢⡂⡢⡂
⡢⡂⡢⡂⡢⡊⡢⡊⡢⡊⣢⡿⡂⠆⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⡈⡊⡂⡺⡾⣲⣶⣶⣮⡎⣺⣯⡯⡪⡢⡊⡢⡊⡢⡊⡢⡊⡢⡂⡢⡂
⡢⡂⡢⡂⡢⡊⡢⡊⡢⡊⣺⡋⢰⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠂⡂⡊⡪⡪⣫⣺⣿⣦⣾⡺⡪⡊⡢⡊⡢⡊⡢⡊⡢⡂⡢⡂⡢⡂
⡢⡂⡢⡂⡢⡊⡢⡊⡢⣪⡯⡂⠈⡀⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠂⠂⠊⡪⡺⣺⣿⡯⡎⡢⡊⡢⡊⡢⡊⡢⡊⡢⡂⡢⡂⡢⡂
⡢⡂⡢⡂⡢⡊⡢⡊⡢⣾⡂⠄⠄⡊⡀⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⡀⠄⡀⡀⡀⡀⡈⣺⣪⡋⡢⡊⡢⡊⡢⡊⡢⡂⡢⡂⡢⡂⡢⡂
⡢⡂⡢⡂⡢⡊⡢⡊⣢⡿⡂⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠂⡀⡂⡢⡪⣢⡪⣪⡮⡢⡊⡢⡊⡢⡊⡢⡊⡢⡂⡢⡂⡢⡂
⡂⡂⡢⡂⡢⡂⡢⡊⣺⡋⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⡀⠂⡀⡊⡪⡺⣪⡏⡢⡊⡢⡊⡢⡊⡢⡂⡢⡂⡢⡂⡢⡂
⡂⡂⡢⡂⡢⡂⡢⡂⡯⠂⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⡀⠄⡀⠂⡀⡂⡢⡪⣺⡊⡢⡊⡢⡊⡢⡊⡢⡂⡢⡂⡢⡂⡢⡂
⡂⡂⡢⡂⡢⡂⡢⡺⡂⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⡀⠂⡀⠄⡀⠂⡢⡪⣺⡊⡢⡊⡢⡊⡢⡊⡢⡂⡢⡂⡢⡂⡂⡂
⡂⡂⡢⡂⡢⡂⡲⠃⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⡀⡊⣺⡊⡢⡊⡢⡊⡢⡂⡢⡂⡢⡂⡢⡂⡂⡂
⡂⡂⡂⣂⡦⡲⡃⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⡀⡀⡀⡀⡀⠄⠄⠄⠄⠄⡀⢂⡮⡪⡢⡊⡢⡂⡢⡂⡢⡂⡢⡂⡂⡂⡂⡂
⡠⡒⡋⡂⡲⠂⡀⠄⠄⠄⠄⠄⡀⠄⠄⠄⠄⠄⠄⠄⠄⠄⡀⠄⠄⠄⠄⠄⠄⠄⡀⡂⡢⡪⡪⡊⣢⣺⣾⣾⣢⣺⣾⣿⣿⣪⡢⡪⡢⡂⡢⡂⡢⡂⡢⡂⡂⡂⡀⡂
⡂⡂⡢⡊⡂⠄⠄⠄⠄⠄⠄⠄⡀⠄⠄⠄⠄⠄⠄⠄⠄⠄⡀⠄⠄⠄⠄⠄⠄⠄⡀⡂⡢⡪⡂⡂⣪⣺⣾⣿⣮⡺⣿⣿⣿⣿⣿⣾⣦⣪⡢⡂⡢⡂⡢⡂⡂⡂⡀⡂
⡀⡂⡀⠂⡀⠄⡀⠄⡀⡀⡀⠂⡀⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⡂⡀⠄⠄⠄⠄⠄⡀⡂⡢⡊⡢⡪⣪⣺⣿⣿⣾⣺⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣂⡢⡂⡂⡂⡂⡂
⡂⠂⡀⠂⡀⡂⡀⡂⡀⡂⡀⠂⡀⠄⠄⠄⠄⠄⡀⠄⠄⠄⠄⠂⡀⡂⡀⠄⡀⡂⡢⡊⡂⡂⡢⡪⡪⡺⣾⣿⣾⣺⣪⡺⣻⣻⣾⣿⣿⣿⣿⣿⣿⣻⣿⣶⣦⡂⡂⡂