⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣯⣯⣯⣯⣯⣯⣯⣯⣇⣯⣯⣯⣯⣯⣯⣯⣯⣯⣇⣯⣯⣯⣯⣯⣯⣯⣯⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⣯⣯⣯⣯⣯⣯⣯⣷⣿⣿⣿⣧⣇⣯⣯⣧⣿⣿⣿⣿⣇⣯⣇⣯⣯⣯⣯⣯⣏⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣯⣯⣯⣯⣯⣯⣯⣧⣿⠋⠉⠉⠀⠀⠀⠀⠀⠀⣀⠀⢈⠀⣯⣯⣿⣯⣯⣯⣯⣯⣯⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣯⣯⣯⣯⣯⣯⣯⣿⣿⠀⠀⠀⠀⢀⠆⢉⣉⣙⠀⠀⠀⢀⢻⣯⣿⣇⣯⣯⣯⣯⣯⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣯⣯⣯⣯⣯⣯⣷⣯⣿⣯⠴⠖⠒⢣⠋⡋⠫⠟⢹⠋⠉⢋⢻⣧⡇⣇⣯⣯⣯⣯⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣯⣯⣯⣯⣯⣯⣿⣇⣿⡇⠀⠀⠀⠁⠉⠁⠁⠉⠀⠀⠀⠀⢀⢸⣿⠁⣇⣿⣇⣯⣯⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣯⣯⣯⣯⣯⣯⣿⣷⣿⡃⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⢀⢸⣿⢀⣯⣿⣇⣯⣯⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣯⣯⣯⣯⣯⣯⣿⣿⣏⣷⣿⣿⣿⢿⠿⠿⠿⠿⠿⠿⢿⢿⢿⣯⣿⣇⣿⣇⣯⣯⣇⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣯⣯⣯⣯⣯⣯⣯⣿⣧⣯⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⢔⢞⣿⠉⠁⣯⣿⣇⣯⣯⣇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣯⣯⣯⣯⣇⣯⣿⣥⣈⣇⠀⠊⢢⠀⠀⠀⠀⠀⢂⢀⠊⣈⣿⣤⣦⣿⣯⣇⣯⣿⣧⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣯⣯⣯⣯⣿⣯⣿⠁⠀⢹⠀⠁⠀⣻⠀⠀⠀⠘⠺⠀⠀⠀⠀⠀⠈⣿⠀⣯⣯⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣯⣯⣯⣿⣇⣿⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⢀⠀⠑⠀⠀⠀⠀⠀⡏⢠⣯⣯⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⣯⣯⣿⡇⣿⡗⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⢸⣯⣧⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣫⣇⣯⣯⣿⡗⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣯⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡏⣇⣯⣿⡗⠀⢻⢀⠀⠀⠀⠀⠀⠈⢣⢢⢏⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢿⣯⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣧⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠁⠈⣇⣿⡏⣄⠀⠀⠀⠀⢸⠇⠉⠉⠁⠁⠉⠒⣾⡏⠀⢠⣢⣯⣿⣿⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣯⣿⣿⣯⣿⣦⣿⣯⣯⣿⢛⠉⢹⣿⡗⢳⢂⡀⠀⢸⠀⠀⠂⠂⠂⠂⠈⣿ ⢀⣠⣺⣿⣇⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣤⣶⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣿⣯⣿⣆⠀⢿⡗⠀⢂⠀⢲⢸⠀⠀⠀⠀⠀⠀⣾⡟⢀⢔⢋⢀⢀⢉⣯⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣆⠘⣏⣵⢪⢀⢀⢊⢆⢀⠀⠀⠀⣾⣯⢎⢀⢀⢀⡎⢀⠈⣿⠉⠻⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣯⣯⣿⣿⣯⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣯⣿⣯⣆⠀⠈⠀⠀⣎⢀⢀⢀⢀⠀⢆⢊⠀⢀⢀⢀⢀⠊⢨⠊⠐⢯⡯⠀⠀⣿⣯⣷⣀⠀⠀⠀⠀⠀
⠀⠀⢸⣯⣯⣯⣿⣿⣿⣿⣯⣯⣿⣯⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣯⣯⡌⠐⣄⢠⠈⢤⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠂⠀⢎⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣿⣶⣤⣀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣯⣯⣿⣿⣯⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⡀⠈⠊⢆⡀⠈⠘⠊⠪⠊⠊⠈⢰⡞⠀⢰⠂⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣯⣯
⠀⠀⢸⣿⣿⣯⣿⣿⣿⣿⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣶⣄⠀⠀⠐⠠⠀⠠⣎⢑⣄⠗⠀⠀⢇⢠⣠⠤⠒⠈⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣶⣤⠀⠀⠀⢆⢀⠊⡀⠀⠀⠉⠀⠀⢀⣠⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠷⢶⣦⠀⠀⠀⢰⡆⠀⡀⠀⠀ ⠀⣦⠀⠀⠀ ⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡦⠀ ⢠⣶⢀⢀⠀⠀⣀⣀⣀⣄⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣶⠶⠛⢷⣄⠈⠉⣿⠁⢀⢀⠀⠀⢀⣿⠈⠋⠉⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠉⠀⠀⣴⢟⣤⣀⣿⠁⢠⣤⣤⣤⣿⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⠐⠟⠉⠀⠈⣿ ⠀⢀⣿⢀⣴⠖⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⣿⠀⠀⠀⠀⠀⣠⣿⠿⠂⠀ ⠀ ⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠛⠛⠉⠁⠀⠀⠉⠀⠉⠋⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀ ⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀