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

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

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

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