⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠀⠀⠀⣠⣴⣶⣤⣀⣶⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣯⣯⣯⣷⣿⣯⣯⣯⣯⣏⣯⣯⣯⣯⣯⣿⣿⣯⣏⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣧⣯⣯⣯⣿⣿⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣿⣯⣯⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣯⣯⣏⣿⣿⣿⣿⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣿⣯⣯⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣯⣿⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⢋⣀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣄⣄⢄⢤⢠⢠⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⢫⢃⢇⣇⣇⣇⣦⢀⣠⢴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣏⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⢋⢃⢇⣇⣇⣇⣇⣮⢞⢫⢇⣧⣦⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣦⣮⣯⣶⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣏⢃⢇⣇⣇⣇⣇⣦⣾⣇⣇⣇⣇⣇⣇⣇⣇⣇⣇⣇⣧⣄⣠⣤⣴⢲⠏⠛⣿⠿⣦⣆⣪⣇⣣⣢⡿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢾⣯⣭⡋⢥⣤⣤⣤⣤⣤⣀⠉⢙⠉⠉⠁⠉⠀⠀⢀⢉⢉⠛⢉⢄⣎⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢂⣇⢂⣮⣦⢹⣿⣿⣇⠃⠀⢋⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⢳⣀⣿⣤⣄⣿⣿⣧⣆⠀⠀⠀⠀⢂⢠⣄⣀⣀⣤⣔⢆⠀⠘⣦⢋⣿⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢯⣎⣫⣄⢿⢋⢃⣦⣇⣄⠀⢀⢀⣀⣀⣀⢘⣦⣦⣤⣀⣤⣯⣄⣿⠀⠈⢋⣶⣤⣖⢏⢫⣿⣶⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣇⢊⣇⣧⣧⣧⣯⣧⣿⣿⣯⡏⢉⣍⠋⠉⠁⢉⢍⠋⣾⣿⠳⣄⠀⠈⠁⣦⠀⠀⢸⢂⣆⢈⣷⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠙⢇⢿⣇⣯⣯⣯⣯⣯⣿⣷⣀⣖⢤⣀⠀⠀⠈⢉⣝⣇⣿⠀⠀⢳⠀⠀⢻⠀⠀⣎⢞⢻⢀⢂⢻⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣉⡀⠀⠀⠈⢫⢉⢿⣧⣯⣯⣯⣯⣿⣷⣆⠉⠲⣤⣀⣀⣠⠔⢫⣿⠋⢉⠛⠋⠋⣦⢦⣀⣸⣦⢋⢀⢂⢪⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠛⠛⠛⠛⠻⣶⣄⠀⠈⢫⢀⢉⢛⢿⣯⣿⣿⣿⣧⣤⣾⣯⣯⣧⣤⣾⣿⠀⢈⣄⣤⣦⣾⠀⠀⣰⠀⢸⢂⢂⣰⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠈⠙⢯⠇⠁⠉⠛⣿⣿⣿⣿⣯⣯⣯⣯⣯⣿⣌⢧⣦⣤⠞⠉⠀⠀⠙⣀⠀⢋⣦⢿⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠑⢣⠃⠀⠀⠉⠙⢻⠛⠛⠉⠁⠈⣿⠷⣤⣀⢇⣇⣧⣢⣤⣄⣦⣇⣠⠛⢹⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢈⣦⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⣯⣷⠀⠀⠀⠀⠈⡟⣿⢁⣁⠁⠉⠁⠁⠉⠉⠀⢀⣤⣿⡇
⠀⠀⠀⠀⠀⣴⢏⠀⠀⠀⣆⣤⣄⣀⢀⢀⠀⢀⠀⠀⠀⠀⠀⢇⠀⠀⣖⠀⠈⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀⢀⣤⠉⣿⠃⢣⣇⣦⣦⣦⣦⣾⣿⣯⡿⢻⠁
⠀⠀⠀⠀⢰⠁⠈⠉⠉⠙⢻⣶⣦⣀⢀⣽⠛⠁⠀⠀⠀⠀⠀⢸⣀⣀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣠⠋⠀⢀⣯⢀⠀⠈⣷⣄⠈⠉⠋⠋⠋⠉⠉⣀⣶⡟⠀
⠀⠀⠀⢠⣾⠀⠀⠃⠉⢀⣠⣦⣦⢙⣿⣬⣧⠀⠀⠀⠀⠀⠀⣾⠀⠀⣀⠉⢫⣯⣯⣯⣧⠋⢠⢋⠊⣾⠙⢲⣼⣆⣂⣇⣧⢫⣦⠀⣇⣆⣆⣆⣮⣯⣠⠟⠀⠀
⠀⠀⠀⣿⢂⣤⠁⢠⣮⢂⠇⠋⣴⠋⠉⠉⠙⣧⠀⠀⠀⣠⣮⣦⣤⣤⣤⣦⣀⠀⠚⣶⠆⢀⣀⣤⣾⠁⠀⠀⠀⠈⠉⠛⢿⣦⣬⣿⣤⠀⠀⢠⢮⠟⠉⠀⠀⠀
⠀⠀⠀⢻⣄⠀⣴⣮⠀⠁⠀⣎⠀⠀⠀⠀⠈⠉⠉⢛⠻⣯⣇⣯⣯⣯⣯⣏⣯⣷⠓⣰⠊⢿⣯⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⢰⣿⣯⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⣧⣯⣯⣧⣧⣧⣶⣿⣧⣯⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⢻⣧⠃⢀⣯⠓⠀⠀⠀⠀⠀⠀⠀⠀⠰⣮⣢⣿⣧⣯⣯⣯⣇⣇⣯⣇⣯⣯⣯⣯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠓⢾⢦⣧⣦⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣏⣏⣟⣿⣏⣣⣏⣯⣯⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⢂⢪⣇⣧⣦⣦⣦⣦⣦⣶⣯⣯⣯⣯⣯⣏⣷⣿⣯⣿⣧⣿⠋⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⢀⢂⢂⢂⢂⢂⢠⡏⣾⣇⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣯⣗⠀⠙⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀