⣿⣿⠛⠄⠄⠄⠄⠄⠄⠄⠄⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠃⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢻⣿⣿⣿⡿⠋⠉⠉⠁⠉⠉⠉⠙⠻⢿⣿
⣿⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣿⣿⠉⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠹
⣿⡄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣿⠃⠄⠄⠠⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄
⣿⡇⢀⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠘⠟⠄⠄⠄⠄⠄⠄⠄⠐⠄⠄⠄⠄⠄⠄
⣿⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠁⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣠
⠃⠄⠄⠄⠄⠄⠄⠇⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢠⣿
⡄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢀⣄⡄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠨⢿
⡹⠂⠄⠄⠄⠄⠄⠄⠄⣸⣶⣦⣤⣾⣿⣧⣀⣀⣀⣀⠄⠄⠄⠄⠄⠄⠄⠔⣱⣿
⡧⣆⠄⠄⠄⠄⠄⠄⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⠄⠄⠄⣠⣮⣾⣿⣿

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

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

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

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

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