⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⠟⠉⠉⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⡿⢆⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣼⡏⠀⠀⠙⢿⣿⣁⣀⣀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢹⣧⠀⠀⢀⣀⠙⢿⠛⣿⣿⠛⢻⡿⠛⠻⣾⡟⢻⣷⡾⢿⣷⠀⠀⠀
⠀⠀⠀⢻⣦⡀⠈⢻⣷⡄⠀⣿⣿⠀⢸⠀⢀⡀⠈⡇⢸⣿⡇⢸⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⣷⡄⠀⠻⣿⠀⢻⡿⠀⢸⠀⣿⡿⠀⡇⢸⣿⡇⠈⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢘⣿⠄⠀⢹⣆⡀⣀⠀⢸⣄⠈⠀⣸⣇⠀⠉⡀⠀⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣾⠏⠀⢀⣿⣿⣿⠿⠀⣼⡟⠻⠿⠛⠻⠷⠾⠷⠶⠟⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⠋⠀⢀⣾⠏⣿⡇⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣇⣀⣰⡿⠃⠀⠘⠛⠛⠋⠀⠀⠀⠀
⠀⠀⠀⢸⣇⣀⣰⡿⠃⠀⠘⠛⠛⠋⠀

⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⠟⠉⠉⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⡿⢆⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣼⡏⠀⠀⠙⢿⣿⣁⣀⣀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢹⣧⠀⠀⢀⣀⠙⢿⠛⣿⣿⠛⢻⡿⠛⠻⣾⡟⢻⣷⡾⢿⣷⠀⠀⠀
⠀⠀⠀⢻⣦⡀⠈⢻⣷⡄⠀⣿⣿⠀⢸⠀⢀⡀⠈⡇⢸⣿⡇⢸⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⣷⡄⠀⠻⣿⠀⢻⡿⠀⢸⠀⣿⡿⠀⡇⢸⣿⡇⠈⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢘⣿⠄⠀⢹⣆⡀⣀⠀⢸⣄⠈⠀⣸⣇⠀⠉⡀⠀⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣾⠏⠀⢀⣿⣿⣿⠿⠀⣼⡟⠻⠿⠛⠻⠷⠾⠷⠶⠟⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⠋⠀⢀⣾⠏⣿⡇⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣇⣀⣰⡿⠃⠀⠘⠛⠛⠋⠀⠀⠀⠀
⠀⠀⠀⢸⣇⣀⣰⡿⠃⠀⠘⠛⠛⠋⠀

⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⠟⠉⠉⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⡿⢆⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣼⡏⠀⠀⠙⢿⣿⣁⣀⣀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢹⣧⠀⠀⢀⣀⠙⢿⠛⣿⣿⠛⢻⡿⠛⠻⣾⡟⢻⣷⡾⢿⣷⠀⠀⠀
⠀⠀⠀⢻⣦⡀⠈⢻⣷⡄⠀⣿⣿⠀⢸⠀⢀⡀⠈⡇⢸⣿⡇⢸⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⣷⡄⠀⠻⣿⠀⢻⡿⠀⢸⠀⣿⡿⠀⡇⢸⣿⡇⠈⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢘⣿⠄⠀⢹⣆⡀⣀⠀⢸⣄⠈⠀⣸⣇⠀⠉⡀⠀⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣾⠏⠀⢀⣿⣿⣿⠿⠀⣼⡟⠻⠿⠛⠻⠷⠾⠷⠶⠟⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⠋⠀⢀⣾⠏⣿⡇⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣇⣀⣰⡿⠃⠀⠘⠛⠛⠋⠀⠀⠀⠀
⠀⠀⠀⢸⣇⣀⣰⡿⠃⠀⠘⠛⠛⠋⠀

⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⠟⠉⠉⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⡿⢆⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣼⡏⠀⠀⠙⢿⣿⣁⣀⣀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢹⣧⠀⠀⢀⣀⠙⢿⠛⣿⣿⠛⢻⡿⠛⠻⣾⡟⢻⣷⡾⢿⣷⠀⠀⠀
⠀⠀⠀⢻⣦⡀⠈⢻⣷⡄⠀⣿⣿⠀⢸⠀⢀⡀⠈⡇⢸⣿⡇⢸⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⣷⡄⠀⠻⣿⠀⢻⡿⠀⢸⠀⣿⡿⠀⡇⢸⣿⡇⠈⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢘⣿⠄⠀⢹⣆⡀⣀⠀⢸⣄⠈⠀⣸⣇⠀⠉⡀⠀⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣾⠏⠀⢀⣿⣿⣿⠿⠀⣼⡟⠻⠿⠛⠻⠷⠾⠷⠶⠟⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⠋⠀⢀⣾⠏⣿⡇⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣇⣀⣰⡿⠃⠀⠘⠛⠛⠋⠀⠀⠀⠀
⠀⠀⠀⢸⣇⣀⣰⡿⠃⠀⠘⠛⠛⠋⠀

⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⠟⠉⠉⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⡿⢆⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣼⡏⠀⠀⠙⢿⣿⣁⣀⣀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢹⣧⠀⠀⢀⣀⠙⢿⠛⣿⣿⠛⢻⡿⠛⠻⣾⡟⢻⣷⡾⢿⣷⠀⠀⠀
⠀⠀⠀⢻⣦⡀⠈⢻⣷⡄⠀⣿⣿⠀⢸⠀⢀⡀⠈⡇⢸⣿⡇⢸⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⣷⡄⠀⠻⣿⠀⢻⡿⠀⢸⠀⣿⡿⠀⡇⢸⣿⡇⠈⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢘⣿⠄⠀⢹⣆⡀⣀⠀⢸⣄⠈⠀⣸⣇⠀⠉⡀⠀⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣾⠏⠀⢀⣿⣿⣿⠿⠀⣼⡟⠻⠿⠛⠻⠷⠾⠷⠶⠟⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⠋⠀⢀⣾⠏⣿⡇⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣇⣀⣰⡿⠃⠀⠘⠛⠛⠋⠀⠀⠀⠀
⠀⠀⠀⢸⣇⣀⣰⡿⠃⠀⠘⠛⠛⠋⠀

⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⠟⠉⠉⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⡿⢆⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣼⡏⠀⠀⠙⢿⣿⣁⣀⣀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢹⣧⠀⠀⢀⣀⠙⢿⠛⣿⣿⠛⢻⡿⠛⠻⣾⡟⢻⣷⡾⢿⣷⠀⠀⠀
⠀⠀⠀⢻⣦⡀⠈⢻⣷⡄⠀⣿⣿⠀⢸⠀⢀⡀⠈⡇⢸⣿⡇⢸⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⣷⡄⠀⠻⣿⠀⢻⡿⠀⢸⠀⣿⡿⠀⡇⢸⣿⡇⠈⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢘⣿⠄⠀⢹⣆⡀⣀⠀⢸⣄⠈⠀⣸⣇⠀⠉⡀⠀⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣾⠏⠀⢀⣿⣿⣿⠿⠀⣼⡟⠻⠿⠛⠻⠷⠾⠷⠶⠟⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⠋⠀⢀⣾⠏⣿⡇⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣇⣀⣰⡿⠃⠀⠘⠛⠛⠋⠀⠀⠀⠀
⠀⠀⠀⢸⣇⣀⣰⡿⠃⠀⠘⠛⠛⠋⠀