Mouthwatering Emojis & Symbols

⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⢤⣦⣄⣀⠀⠀⠀⠀⠀⠠⠂⣠⠄⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⣀⣤⣄
⠀⠀⠀⠘⢿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢠⣾⣿⣿⣾⠁⠀⠀⠀⠀⢰⣿⣧⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠘⠟⠛⠛⠳⠂⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢘⣛⣿⣿⣿⠄⠀⠀⠀⠠⣿⣿⣷⠀⠀⠀⠀⠀⢀⣾⣿⠏⠁⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠐⣾⣾⣿⣽⡇
⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⢻⣿⠇⠀⠀⠀⠀⢠⠿⠋⠁⠀⠀⠀⠀⠀⠈⠀⠈⠉⠁⠀⠀⠀⠀⠉⠛⠛⠛⠁

⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⡴⣣⣄⠀⠀⠀⠀⠀⣤⣶⣶⣤⠀⠀⠀⠀⠀⠘⠀⠀⣠⠀⠀⠀⠀⣿⣿⣿⣿⡆
⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠹⣿⠏⠀⠀⠀⠀⠘⠛⠿⠿⠛⠃⠀⠀⠀⠹⣿⣿⣿⠏⠀⠀⠀⠀⠿⣿⣿⣿⡇
⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⢠⣶⠿⢷⣦⠀⠀⠀⠀⡆⣠⣤⣄⡶⠀⠀⠀⠀⢀⣴⣿⣦⡀⠀⠀⠀⠀⠀⣠⣮⣄⠀⠀⠀⠀⢀⣀⣴⣋
⠀⠀⠻⣟⣀⣨⣻⠁⠀⠀⠀⡟⣿⣿⡿⡇⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠖⠔⠓⣶⣶⠄⠀⠀⠀⠘⣿⢻⡇
⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠃⠀⠁⠀⠃⠀⠀⠀⠘⠛⠉⠉⠀⠀⠀⠀⠀⠈⠒⠊⠙⠁⠀⠀⠀⠀⠀⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡀⠀⠀⠀⠀⠀⠠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀
⠀⠀⣠⣻⣿⣶⠴⠄⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⢰⣿⣿⣿⣿⡆⠀⠀⠀⢠⣾⣿⣿⣦⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠃⠀⠀⠀⠈⠻⠿⠿⠟⠁⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠙⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⠿⠿⠿⠋⠁⠀⠀⠀⠙⠿⠿⠿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⠁⠀⠀⣠⣾⣿⡷⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠈⣿⣿⣧⡀
⠀⠀⠀⠀⢀⣀⣤⣀⣀⠀⣀⣾⣿⣿⡋⠀⣀⣰⣿⣿⠟⠁⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠙⢻⣿⣿⣄
⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⢹⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣠⣴⣾⣶⠀⠀⣠⣾⣿⣿⠃
⠀⠀⢸⣿⣿⣿⣿⡟⠀⠈⣿⣿⣿⣿⡏⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⢾⣿⣿⠿⠛⠉⠀⠀⣿⣿⡟⠁
⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠀⠀⠀⠀⠀⢠⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣷⣀⣀⣿⣿⣿⣿⣇⣀⣠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⡟
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣤⣶⣿⣿⣿⣿⣿⠿⠋
⠀⠀⣿⣿⣿⣿⣿⡿⠉⠉⣿⣿⣿⣿⡏⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠉⠉
⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣧⠀⢀⣿⣿⣿⣿⣇⠀⢠⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠈⠉⠛⠉⠁⠀⠉⠉⠋⠉⠁⠀⠉⠙⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠈⠉⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠊⠀⠀⠈⠐⠄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠐⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⡀⠂⠂⠀⠀⢄⠼⠂⠀⠀⢄⡀⠀⠂⠀⠁⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠘⠄⣀⠀⢠⡀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠈⠂⠠⠄⠀⠑⢄⣀⣀⢀⠄⠊⠉⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⢂⢄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠤⠒⠉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠃⠀⠡⠀⠠⠒⠢⡀⢀⡩⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠂⠀⠀⠀⠀⠀⠀⣀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡏⠀⠀⠀⠁⠉⡆⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢣⠀⡠⠁⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠠⠂⠀⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⡴⠂⠀⠀⠃⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⡂⠄⡀
⢠⠊⢄⠀⠰⠀⣀⡀⠀⢀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⠤⠀⣀⠄⠈
⠀⠁⠢⣍⠁⠀⠀⠀⠀⠁⠀⠀⠠⠌⢁⣐⠒⠂⠀⠀⠤⠊⠀⠀⠀⠀⠀⠀⠈⢦⠤⠤⠀⠒⠒⣈⣁⡄⠀⠀⠀⠀⡠⠐⠊
⠀⠀⠀⠀⠑⠒⠒⡆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢄⡀⠤⠄⠀⠠⠎⠀⠀⠈⠁⠀⠀⠀⠤⠠⠔⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⡀⠈⠁⠒⠀⠀⠀⠀⠀⠀⠨⠄⠤⠤⠀⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⡠⠂⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠠⠤⠀⠤⠒⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠉⠉


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣴⣦⣷⣶⣴⣧⣴⣯⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣄⠙⢿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⡈⠻⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠙⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢻⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⣷⣦⣼⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠉⠛⠿⣷⣿⣿⣿⣿⣿⣿⣧⣴⣾⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣶⣤⣀⣀⣀⣀⣤⣶⡿⠟⠋⠉⠀⠀⠉⠙⠻⢿⣶⣤⣀⣀⣀⣀⣤⣶⡿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠠⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠘⡄⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢸⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠒⠒⠒⠠⠄⠀⠐⠁⠀⠀⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡸⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠻⠃⠀⢰⠀⠀⠀⢀⠀⢠⠖⠛⠓⠂⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⢀⠂⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⡠⢠⠀⠘⠄⣠⠊⡀⠈⠄⡠⠂⠀⠀⠀⠀⠀⠀⠀⣰⠞
⠀⠀⠀⠀⠀⠀⠘⠋⢳⠀⠀⠀⠀⠀⠢⣆⣡⡔⠉⢒⠰⡖⠫⠀⡀⠀⢀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠠⡀⠢⠁⠥⠓⠒⠒⠆⠰⠂⣶⠃⠀⢀⠠⠊⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠢⠀⡀⠀⠀⠐⡄⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠸⡀⠈⠢⣰⡠⠺⡀⠀⡇⠀⣟⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠐⠶⠣⡀⠀⠙⡀⠀⡇⠀⡇⢠⠏⠀⠙⢆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⡧⠀⡇⢈⠃⡎⣸⠀⢰⠈⡄⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠐⢒⡶⡇⠸⠀⠀⠟⢠⢆⡼⠁⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡍⢄⢠⣀⣁⡀⡀⠱⠴⠓⠉⠀⠀⠀⢤⡀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢽⣀⠀⠀⠀⠀⠀⠀⠀⢰⡤⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠝⠲⠤⡀⠀⠀⠀⢨⢀⠔⠂⠀⢀⡀⠨⣤⣤⣤⡤⠤⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⡀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⡘⡆⠀⠀⢀⠈⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠘⠀⠀⠀⢢⡀⠉⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠓⠈⠀⠀⢀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠐⠚⠋⠉

⡿⢿⠿⠿⠿⡻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣮⠋⠉⣿⠑⢶⣤⣾⠉⠀⠀⢀⡄⠤⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡛⢀⣤⢀⡀⠀⢠⠇⢈⡿⣴⣄⣶⡷⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢣⡁⠀⠉⠛⠁⠠⠆⠀⣿⣿⡿⢿⣃⡇⠀⢀⣀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠗⠠⠤⠋⣴⠀⠀⠰⠦⠀⠹⠟⠳⣯⡙⢭⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠑⢋⣄⠘⠃⠀⠠⠦⠀⠶⣠⡄⠲⢃⣹⣷⣶⣦⠿⠶⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⢀⣀⣀⣀⣀⡜⠃⣤⡜⠉⠶⠀⣤⠀⡤⠀⠶⠀⠀⠀⠈⣽⣿⡼⡏
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⢒⣶⣿⣷⣿⢛⢿⣿⣿⣟⣻⣿⣿⣿⣿⠿⣿⡿⣿⡟⠙⢁⣠⣠⠄⢠⣤⠀⠀⠀⠠⡦⠀⠻⣤⡀⢈⣿⣷⡛⠦
⠀⠀⠀⠀⣰⣾⣿⣿⣭⣿⣿⣿⠗⠋⣻⠿⣯⡍⣿⣽⡃⣿⣥⣾⣿⣿⠿⣏⣿⣇⣫⡷⢸⡶⠒⣈⠁⠱⠆⠀⢁⠀⠙⠃⡈⠐⠶⠀⠉⢀⣼⣤⣿⣿⣦⡀⠀⡀
⠀⠀⠆⠈⠛⠿⣿⣾⡟⢋⣿⣿⠞⣛⢣⣬⣿⡿⣿⣷⠤⣛⡟⢀⡋⢿⣿⣿⠯⣭⣽⣾⣛⣿⣯⣿⣥⣤⣀⣛⢀⡤⢀⣹⣇⠠⠞⢛⣀⣠⣴⣿⣿⡿⠿⠃⠀⠆
⠀⠀⢀⣽⣀⠄⠀⠉⠉⠉⠻⠛⢶⣿⣾⡧⢿⣱⠾⠣⣦⡿⢛⣫⣽⣤⢍⡙⢺⣿⣛⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣭⣤⣶⣤⣿⣿⠿⠟⠛⠉⢀⣠⡘⡄
⠀⠀⢸⣿⢿⣷⣶⣴⣯⣤⠶⣆⡀⡀⢉⠁⠈⠐⠁⠚⠛⠓⠺⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠲⠛⠟⠛⠛⠛⠚⠉⠉⠉⠁⠉⠀⢀⣠⣤⣶⡗⢲⣾⣿⢿⣷
⠀⠀⢸⣿⣿⡿⣿⣷⣾⣿⣾⣿⣿⣿⢶⣶⣴⣯⣤⣴⣧⣠⡴⣶⡴⣶⣶⣶⣴⣤⣶⠆⠀⠀⠐⣀⣀⣀⡀⣀⡠⣤⡴⠠⣞⢂⡲⠯⠁⠉⢿⡷⣮⣽⣿⣲⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⡉⠙⢿⠟⠻⠿⠾⠛⢯⡿⠿⠿⢿⣷⣾⣿⢿⡿⣯⡝⢋⣹⡌⣾⢋⡙⠴⢏⠱⠻⣿⡓⣿⢿⡇⠶⢫⡴⠊⣿⠶⠛⢡⡿⢡⡟⢻⣿
⠀⡆⢸⣿⣟⠿⣥⣿⣿⡃⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠠⣷⣾⣿⡟⣻⣿⣿⡿⠿⢷⡖⠛⢿⡟⠶⠀⢶⣓⢾⡟⠤⢓⠖⣴⡇⠟⠰⠯⠘⠁⢀⣱⠘⠃⠿⣿
⠀⡇⣸⣿⣻⣿⣿⢻⣟⡿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣯⣿⠎⣹⣯⣹⣧⣤⣀⡐⢏⣄⢸⡟⣦⢚⡱⢦⣏⣰⡿⠟⠷⠍⠴⠶⠞⢓⠀⠀⠀⣯⣀⣿⢿⣿
⠀⠀⣿⣿⣟⣵⣿⣟⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣌⡛⢡⣞⢋⣽⣿⣯⣼⣷⣾⠁⣿⢿⣴⣀⣤⢿⣍⢰⣶⢐⡋⣴⡾⠒⣟⠀⠀⠀⣟⢫⡿⠺⣿⡆
⠀⠀⣿⣿⣿⣿⣻⣟⣙⠋⠀⠀⠀⠀⠻⠆⠀⠂⠸⠗⠀⣿⣤⣿⣿⣩⣤⣬⣶⠆⢀⠛⠣⣿⢿⡿⠾⠿⢿⡻⠧⠜⣁⣉⡷⠘⢧⣠⡆⠀⠀⢀⡿⢰⣿⣿⣿⡇
⠀⠀⠉⠻⢿⣿⣿⣿⣿⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣫⠙⠿⣽⣏⣽⣿⢁⡀⠐⢹⣇⣠⠰⣃⡀⢹⡇⢰⡞⢶⣿⡇⢔⣢⣜⣿⠀⠀⠀⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠈⠙⠻⢿⣀⠀⠀⠀⣾⡄⠀⠀⠠⠶⠄⢙⣿⡿⣷⣿⢉⣟⣭⣁⣩⣴⣦⡿⠽⢿⣿⡣⠞⣁⡷⢻⣧⣉⣷⡟⣺⢿⣏⣱⠀⡀⠀⠛⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⠀⠀⠀⠀⠀⠀⢰⣟⣧⣿⣿⣿⣿⣿⣿⣧⣸⣿⣷⣿⣩⣷⣾⣘⣿⣄⣫⣦⣯⡿⠷⠚⠚⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠁
⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠰
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠃
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⢸⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠇
⠀⢿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠏
⠀⠈⠻⣿⣿⡿⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡶⠖⡋⠟⣡⠞⠁
⠀⠀⠀⠘⠻⣷⣄⠉⠙⠳⣾⣋⣹⢟⡻⣦⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⣀⠤⢤⡴⠒⡒⠋⠉⠈⠊⠀⣀⠴⠊⠁
⠀⠀⠀⠀⠀⠈⠛⢿⣶⣄⣀⠀⠉⠀⠲⠈⠀⣄⡉⢀⡉⠉⠉⠛⢉⠞⠚⠋⢻⡟⢻⠛⠛⠓⠂⠛⠀⠁⢠⠉⠁⡀⠦⡀⠀⠀⠀⣠⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢷⣶⣤⣤⡀⠈⠉⠀⠙⠁⠘⠂⠁⠐⠂⠀⠌⠡⠴⠁⠐⠂⠀⠀⠀⠀⠀⡀⢀⣀⡤⠤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠾⠶⠶⠶⣶⣦⣤⣤⣤⣤⣠⣤⣠⣤⣀⡶⠶⠶⠖⠛⠛⠋⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠠⠦⠀⡰⠊⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢀⡀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠒⠢⢎⠀⠀⠀⠀⠀⠉⠄⠀⣀⠀⠀⠀⠀⢠⠀⡀⡔⠁⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⢠⠚⠉⠁⠈⠉⠑⡴⠛⠉⠉⠁⠒⢤⠀⠀⠀⠀⠀⠉⢢⠀⠀⡀⠤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⣁⠈⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠣⣀⡀⠀⢣⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢀⠜⠉⡀⠀⠀⠀⠀⠀⡠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⠤⠤⠘⠦⡀⠀⠀⠀⡠⠔⠉⠒⠒⠒⠉⠁⠀⠀⠈⠢⠀⣀⠠⠀⠁⢀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠢⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠒⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⡔⠉⠱⡀⠈⢁⡰⢀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠀⠀⠀⠒⠒⠒⠒⠈⠉⠁⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⠊⠀⠀⠀⠈⠉⠁⠀⠀⠓⠒⠊⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠦⠤⠊⠑⠤⠠⣄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡸⡂⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠢⠤⠊⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⢀⠔⠒⠒⢒⠃⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠢⣤⠤⢀⡀
⢀⡤⣊⠀⠀⠰⠁⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⢀⡀⠉⠒⡌⠓
⠘⠄⣉⠒⠤⠈⠒⠊⠑⠒⠒⠉⢉⡒⠒⠤⠄⣀⣀⣀⢀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⣀⣀⡠⠤⠒⠋⠁⠀⠈⠉⠁⠉⣀⠴
⠀⠀⠀⠑⠤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠉⠁⠒⠢⠤⠤⠄⠈⠉⠩⣤⣄⠀⠀⠀⠀⠀⠀⠀⡋⠉⠉⠡⠤⠤⠤⠔⠒⠉⠀⠀⡀⠀⠐⣅
⠀⠀⠀⠀⠀⠀⠁⠨⡃⠘⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠠⠤⣀⠀⠈⠢⠔⠂⠉⠐⠒⠊⠁⠀⠀⠀⠀⠀⠀⠐⠒⠒⢒⣉⣀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣤⢀⠀⠈⢉⣒⡂⠀⠀⠀⠀⠀⠸⠴⠖⠒⢛⣉⣉⣛⣉⣒⣒⣋⣁⣀⣀⣀⣀⡀⣤⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠠⠤⠤⠴⠊



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠄⣄⠀⠀⠀⡀⡀⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣤⠔⠓⢆⡀⢐⣦⣠⠼⠷⡖⠀⠀⢀⠠⡾⠀⣤⣤⣤⣭⣥⣀⣀⡀⠀⠀⠘⠿⠃
⠶⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡶⠶⢶⣮⣷⢶⡚⠙⢯⣀⣈⣶⣤⠀⠀⠀⠀⠀⢱⠀⢒⣒⣒⣿⣿⣿⠿⠇
⠀⠈⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢻⣧⠟⢾⡉⠉⢳⣄⡈⠀⠀⠠⠄⠀⠀⠀⢴⠚⠛⠩⠉
⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠺⠗⠀⠀⠀⠀⠀⣿⠶⠖⠛⠛⠩⡈⠀⠐⡀⠀⠀⠀⠀⠀⢸⣆⠀⠀⣶⢆⣶⠁⢀⣀⠄
⠀⠀⠀⠀⢿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠰⠷⠀⠀⠰⡦⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⣠⣧⠀⠀⠀⠀⠀⢸⣿⡆⢰⣿⢸⠇⣴⣿⣿⣿⣦⢠⡀
⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⡀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡭⠋⠀⠀⠀⠀⠀⢸⣿⡇⠀⢿⣾⡄⢿⣿⣿⣿⡿⢰⡿
⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣾⢿⣁⠀⠀⠙⠿⢦⣽⡿⣿⡁⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⠀⠀⠀⠈⠓⠛⠋⠁⠀⠀⠀⠀⠀⠀⢁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠄⠀⠀⠀⠀⢸⣧⠀⠀⣀⣠⣤⣤⣤⣤⣤⡶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠟⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠿⠛⢷⣦⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠿⠛⠻⠷⢶⣤⡀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⢹⡇⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⣿⠁⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⣀⣠⡾⠃⠀⠀⠀⣰⡟⠀⢀⣀⣀⠀⠀⠀⢀⣀⣀⠀⠘⣷⡀⠀⠀⠀⠻⣦⣀⣀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠀⠀⠀⠀⠀⣿⠁⠠⣿⣉⣻⡇⠀⠀⣿⣋⣹⡧⠀⢹⡇⠀⠀⠀⠀⠈⠙⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢻⣦⠀⠀⣿⡄⠀⠙⠻⠛⠁⠀⠀⠙⠻⠛⠁⠀⣼⡇⠀⢀⣾⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠸⣷⡀⠀⠀⣤⡀⠀⠀⣠⡄⠀⠀⣰⡿⠀⠀⠀⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⡀⠈⠛⠛⠛⠋⠀⣠⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⣿⠓⠀⠉⠛⠿⠶⠶⠶⠾⠟⠋⠀⠐⢻⡿⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠿⠀⠀⠀⣤⣀⠀⠀⠀⢀⣤⡄⠀⠀⠸⠇⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⢀⣤⣤⣤⣤⣤⣬⣽⣷⣦⣶⣿⣭⣤⣤⣤⣤⣤⣄⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢸⣿⣦⣼⠿⣧⣤⡿⢿⣤⣼⠿⣧⣤⡿⢿⣤⣾⣿⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⣿⡿⠷⠶⠾⠿⠶⠶⠿⠷⠶⠾⠿⠶⠶⠿⣿⡟⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡇⠀⠀⢀⣴⡾⢻⣷⠟⠻⣶⣄⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡇⣠⡾⠟⠁⠀⢘⣿⣀⠀⠀⠙⠿⣦⡀⣿⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣿⠿⠋⠀⠀⣀⣴⠟⠋⠛⢷⣄⡀⠀⠈⠻⢿⣇⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠺⠛⠁⠀⢀⣤⡾⠛⠁⠀⠀⠀⠀⠙⠻⣦⣄⠀⠀⠙⠻⠂⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⣴⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢷⣤⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣾⣷⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣿⣶⣶⣶⠆





⣿⢿⠿⡿⡿⢟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣛⣛⣟⣿⣟⣛⣻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣤⢠⢀⡄⣀⢠⣤⡀⣤⡄⢠⡤⠀⣤⣄⠀⠀⢠⣤⢠⢤⡀⣤⠤⢀⡤⣤⢠⡄⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡀⡏⢸⢼⡇⣿⢸⣤⠇⣧⡿⢸⠶⠀⡇⢸⠀⠀⣿⠈⢸⣼⠃⣿⠆⢸⣧⣼⢸⡿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠻⠃⢸⠘⠇⠿⠸⡇⠀⠯⠀⠸⠤⠄⣧⠞⠀⠀⢻⡴⠸⠘⠆⠿⠤⠸⠇⠸⠸⠇⠸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠆⠀⡆⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⡇⠀⠇⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡇⠀⠘⡀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⡻⠀⠀⠀⠁⠀⢰⠀⠀⢰⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠥⢀⡔⠁⠀⢀⠌⠀⠀⠀⠀⠀⢸⠀⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡥⠚⠁⠀⢀⠠⠋⠀⠀⠀⠠⠀⢀⠌⢠⠃⠌⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⢀⠔⠁⠀⠀⠄⡀⠔⠁⡠⠂⡴⠃⢠⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠉⠉⠑⠀⠀⠀⢀⠠⠔⠊⣀⠄⠊⣠⠀⠀⠀⢠⠀⢰⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⢀⠂⠀⠈⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠠⠊⠀⢀⠠⠐⣈⣉⣀⡠⠤⠔⠊⠁⠀⠀⠀⡀⠔⠁⠀⡠⠀⢀⣼⡅⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⡥⠚⠉⠀⠀⠀⠀⠀⠀⢀⠠⠐⠂⠉⠀⢀⡠⠊⡠⠞⠁⢸⡇⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠉⠀⠀⠠⠒⠀⠒⠒⠒⠀⠉⠀⠀⠀⠠⠔⠊⡁⠀⠈⠀⠀⠀⡸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠀⠄⠐⢒⡀⠀⡈⢉⣉⠥⠄⠒⠒⠒⠀⠁⠀⢀⠔⠀⢀⡴⠁⠀⠀⠀⣾⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠘⠃⢀⣠⠔⠚⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣠⠴⠋⠀⠀⠀⢀⡜⠁⢇⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠈⠉⠀⠀⠀⠀⠀⠉⠀⠒⠒⠒⠈⠀⠀⢀⠤⠚⠉⠉⠉⠀⠀⠀⠀⠀⠀⠖⢹⠀⠀⡸⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠒⠀⡀⠀⢠⠞⠉⠉⠓⠒⠢⠤⠤⠤⠔⠂⠁⠒⠁⠀⠀⢀⠀⠀⠁⠀⠀⠀⣠⠃⠀⣠⠃⢀⠂⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠐⠈⢙⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠊⠁⠀⠀⢀⠤⠊⠀⠀⠀⠀⣀⡤⠚⠁⢀⠔⠁⡐⠁⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⣀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠒⠁⢀⣠⠴⠒⠋⠉⠀⠀⣠⠆⠀⠀⠈⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆⠀⠀⠀⡠⠒⠉⠉⠉⠉⠁⠀⢀⣠⠔⠋⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⣠⡤⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣔⣋⡠⠴⢾⡉⠙⠂⠀⠛⠉⠀⠀⠀⠀⣠⣴⣒⣋⣉⠴⠚⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⢤⣄⣀⣀⣀⣤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠒⠒⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⢀⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠏⣻⠇⠀⢀⠃⠀⠀⠀⠀⣰⣿⣿⠟⠛⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⡠⠄⠒⠙⠠⠤⠐⠁⠀⠀⠀⠀⠀⢿⣿⣯⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⠁⠘⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠐⠒⣸⣿⣯⣐⠒⠂⢰⠦⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠘⢿⣿⣷⣦⣤⣀⠔⠊⠁⠀⠀⠀⠀⣸⣿⣿⡿⠁⠀⢀⠆⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⡟⠀⠀⠀⠈⢛⠿⣿⣿⣿⣶⣄⠀⠀⠀⠀⣿⣿⠏⠀⠀⡠⠃⠀⠀⢠⣶⣄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠠⠾⠋⠀⠀⠀⠀⡠⠁⠀⠈⠙⢿⣿⣿⣷⡀⠀⠀⠙⠿⠄⠄⠊⠀⠀⠀⠀⢺⡟⠁⢀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⠀⠀⠀⠀⠀⣠⣶⣦⡀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠉⠐⠢⢄⣴⣿⣿⣷⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢀⡤⠖⢐⣾⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⣇⣀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠁⠀⠀⠀⠀⠑⢄⡀⠀⠀⢀⣠⣿⠟⢡⣿⠁⠀⣾⣿⣿⡟⠀⠈⠁⠂⠤⣀⠀⠀⠀⠀⠀⠀⡙
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⢰⣿⣿⡿⠁⠑⠢⢤⣤⡾⠆⠀⠈⠉⠉⠉⠉⠀⠀⠘⠛⠀⣸⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⣈⠁⠀⠒⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⢦⠀⠀⠀⣿⣿⣿⠁⠀⢠⣶⣶⠀⠀⠙⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⢀⣴⣾⡿⠷⣆⠀⠀⣾⣇⠀⠀⢠⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⠀⠀⡆⠀⠙⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⢠⣿⡟⠁⠀⠀⣰⣶⣤⡹⣿⣦⣠⠃⠀⠀⠀⣿⣿⠁⠀⠀⡆⠻⣿⣀⡠⠀⠀⠀⢘⣿⣷⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⢸⣿⠀⠀⢀⣴⣿⣿⠿⠃⠙⣿⣿⣦⣄⠀⠀⢻⣿⠀⠀⠀⠃⠀⠈⠉⠀⠀⡠⠒⠁⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢀⠃⠈⠉⠁⣼⣿⠟⠁⠀⢀⠌⠀⠛⢿⣿⣷⣄⠈⢿⣇⠀⠘⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⢀⠂⠀⠀⠀⢰⣿⠃⠀⣀⠔⠁⠀⠀⠀⠈⠻⣿⣿⣷⡀⠙⠒⠁⠀⠀⡠⠃⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠐⠁⠀⠀⠀⠀⠈⠃⠄⠊⠀⢀⠤⢤⣄⡀⠀⠀⠘⣿⣿⣿⡄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢹⣿⡄⠀⠀⢹⣿⣿⣧⠀⠀⠀⢁⠀⠀⠀⠀⠀⣠⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠈⠋⠉⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠁⠂⠀⠐⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⣀⣀⣀⣠⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⢀⠠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠀⡀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⡀⠀⢀⡀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠢⢤⠀⢠⡠⠀⠀⣠⢀⡲⠶⠔⡉⢅⠉⠀⠀⢭⡉⠐⠦⡀⠀⠀⠀⠀⠨⠤⢉⡀⠄⠠
⠀⠀⠀⠀⠀⠠⠔⠀⠐⠀⠼⡋⠉⢹⠈⠑⠐⣀⠤⣶⣧⠴⠄⠊⢠⡦⢆⡷⠀⠽⠀⠀⡔⣩⣉⢀⡀⠴⣾⠇⣐⠀⠀⠀⠀⠤⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢄⠙⠟⠛⣆⣉⡔⣀⡠⣔⣎⠰⠤⠚⠁⠀⠀⠀⡂⠉⣁⠉⣠⣤⣀⠅⠉⣠⠒⠷⠦⠊⡶⠀⠒⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠘⢆⠤⣄⡀⢌⡨⢵⠀⠌⢰⡀⢠⠰⠞⠁⠠⢁⣄⡘⠿⠈⡃⣠⠈⡛⢲⣋⡴⢣⠇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠐⠈⠔⠂⡀⠰⣄⣈⠐⠀⡤⠃⠤⣈⣧⡀⠧⠭⠀⣀⣤⠃⠀⠉⠉⢉⠔⠁⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⠀⠀⠢⢄⡄⠀⠐⠃⠀⠎⠙⠛⠛⣛⠉⡑⣲⠐⢀⣣⠀⠀⠀⡀⡄⡀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⠀⠀⠐⢠⡠⠖⠀⠴⠆⣤⣤⣠⣤⠅⡥⢨⠟⠀⠀⠀⡆⣆⡗⢡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣄⠒⠒⠂⡠⢀⣐⡐⠲⠔⠒⠚⢖⠦⠚⠃⠀⠀⠀⠃⠓⠋⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⢀⠀⠀⠀⠀⠀⠈⠒⠀⠄⠀⠀⠀⠀⠀⠐⡀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠍⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⡀⠀⠀⠀⠀⠈⣀⠤⠈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠐⢉⠁⠀⠀⠀⠈⡒⠰⢂⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠁⠀⠀⠂⠄⢀⠀⠀⠀⡀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⣠⠖⢲⠔⠊⢹⠀⠀⠀⠀⠐⠉⠁
⠀⠀⠀⢀⣀⢀⡜⠁⡰⠃⠀⠀⢸⠀⣠⠀⡰⠊⠉⠲⣄
⣴⡖⠤⠋⠈⠋⠀⠰⡁⠀⠀⠀⣸⡤⠄⠠⢇⡀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡀
⠀⠓⠊⠉⡆⢀⡠⠤⣈⢧⠀⢼⡡⠤⠄⠒⢶⣸⢶⡖⣒⡇⠀⣀⣀⠤⠤⠤⠔⠲⠤⢄⡀⠀⠀⠀⠀⢾⡵⠒⣷⣄⣤⣄⣀⡀
⠀⠀⠀⠀⠉⠁⠀⣀⣈⣯⣷⠀⠉⠓⠒⠚⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡆⠸⡅
⠀⠀⠀⠀⠀⢀⣸⡁⠠⠶⠮⠁⠀⠀⢀⡀⠀⠀⠀⠲⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⡔⠛⢤⠀⠀⡟⠲⡁
⠀⠀⠀⠀⠀⠈⢧⢈⣲⠶⠒⢢⠀⠈⠙⡧⣄⠀⠀⠀⠀⠉⠂⠄⢀⡀⠀⠄⠀⢀⣀⡴⠋⠀⠀⠀⠀⠀⠀⢱⠸⠊⠀⠀⠈⡯⣉⣱
⠀⠀⠀⠀⠀⢀⠜⠉⠀⠀⢀⡜⢣⠀⠀⠹⡜⢳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢯⠤⢤⣤⣀⠠⠄⣶⠤⠒⠁⣀⠷⠖⠒⠚⠁
⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠑⢤⣣⣀⡀⠈⠃⠀⠙⠂⠀⠀⣀⣀⣀⣀⡤⢄⣈⢻⠉⠓⠤⢀⠀⡇⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⡝⠀⠙⠢⠤⣄⣈⣉⠉⠉⠉⠁⠀⠀⡆⠀⠀⠉⠳⠝⠂⠀⠃⠉⠛⣢⣄⡀⠀⢀⣀⢠⣤⠤⠒⠉⢉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠐⠒⠂⠃⠀⠀⠀⠀⠀⠀⢀⣠⠒⠉⠀⠤⠋⠁⠀⡠⠊⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠥⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠒⠌⡒⢄⠄⠀⢀⡞⠁⠀⣀⠄⣠⣞⠾⠶⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⡛⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⢀⡤⠞⠛⠂⠤⢾⣴⠊⢉⣼⡶⠋⠁⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⢦⣕⡢⢄⡀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠉⠑⠻⣁⠀⣀⡠⠤⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡇⠀⠉⠓⠮⣕⣢⢄⣠⢎⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⡼⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢰⠃⠀⠀⢀⣀⠜⣹⠙⠓⠦⠭⣕⣢⣤⣄⣀⣀⣠⡯⠛⠉⡷⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠸⠤⠖⣊⠭⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢩⢹⠀⠀⠀⡰⠁⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠦⠒⣹⠁⠀⠀⣘⠤⠢⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠁⠻⠔⣒⡺⠅⢴⣉⠦⢶⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣶⣶⡿⠇⠀⠓⠆⠀⠀⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣯⢟⡿⣿⣭⣭⣶⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋⠁⠀⠈⠉⢛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠢⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠀⠀⠀⢀⠀⣀⣀⣾⠈⢠⡟⠚⢈⣏⣿⣿⣿⣿⣿⣿⣦⣴⣤⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣶⣤⣶⣾⣿⣿⣿⣿⣿⣷⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣯⣤⡤⠤⣧⣀⡀⠀⣉⣀⣀⣈⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣴⣶⣶⣤⣤⣀⣭⣤⣤⣶⣾⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⠉⠛⠋⠋⠉⠉⠉⠉⠛⠛⠛⠿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢿⣿⣿⡇⢠⡀⠀⠀⠀⠀⠀⠀⡉⠒⠀⠒⠈⠁⠀⠈⠉⠙⠛⢿⣿⠿⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠻⣿⣇⣿⣷⠀⠀⠀⠀⠀⡈⠁⠛⠦⣀⣤⣤⣤⣀⠀⠀⠀⣸⠃⣀⣤⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⢿⣜⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⢻⣿⣶⣾⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠻⣷⣤⡀⠀⠀⠀⢀⡲⣦⣄⠀⠏⢸⣶⣾⡿⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣷⣿⣿⣝⣿⣷⣾⡿⢟⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠋⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠤⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⡤⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢀⠀⠔⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠉⠃⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢀⡄⡨⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣦⡌⠀⠸⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠚⠈⠀⠈⠂⠐⠂⠈⠑⠀⠀⠂⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣐⣻⠿⠟⠓⠁⢻⡁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢰⠊⠀⠀⠀⡀⠀⠀⣀⣀⠘⠉⢑⠠⠠⠄⣄⣀⣰⡂⠉⠁⠀⠀⠀⠁⠈⠀⠀⢀⡀⠀⣄⣤⣦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢱⣶⣷⣶⣷⡎⠸⢦⣶⣾⣷⣶⣷⣶⣷⣤⣿⣯⣭⣄⡨⣉⠀⢂⡰⢦⠒⣊⣥⣾⣾⣿⣿⣿⣃⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⣿⣿⣿⣄⡼⠿⠛⠉⠉⠉⠉⠛⠿⣿⣿⣿⣿⣧⣿⣤⣸⣶⣿⠿⠿⠛⠋⠉⠀⠀⢀⡄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠉⠉⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠌⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⡠⠀⠀⠘⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠦⡄⠀⠀⣀⠄⠀⠖⠒⢀⡉⠙⠤⠤⠥⣱⠀⠀⣀⠈⠐⠒⣒⠂⠀⣀⣊⠈⢧⡈⢢⣽⣷⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢀⣀⡤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠚⠀⠀⠀⠂⠀⠀⠀⠀⠈⠄⢀⡬⠩⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠁⢰⠁⢠⡄⣀⡤⠂⠒⠀⠤⢄⠀⠀⠀⠀⠈⠃⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⣸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠥⠔⠋⠁⠀⠀⠀⠀⠀⢀⠱⠢⢀⠀⠀⠀⠀⠈⢢⠄⠀⠀⠀⢀⡠⠜⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠒⡀⠱⠒⠤⠤⠤⠤⠄⠒⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠐⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⢤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠁⠀⢰⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⡉⠐⠒⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠦⣙⣤⠀⠀⠀⠀⠀⠀⠀⢮⠟⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠶⠶⣦⣫⡶⠋⠀⠀⠀⠀⠈⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠿⣷⣋⡦⠀⠀⠈⢻⢲⣄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⡲⠆⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠸⡾⠀⠑⣄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡔⠁⠀⢀⠄⣢⡆⠀⠀⠀⠀⠀⠀⠘⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣻⡦⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡀⠀⠀⠀⠀⠀⠀⢀⡈⢧⠀⠀⠀⡇
⠀⠀⠀⢀⠊⢠⠃⠰⣷⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣾⡇⠀⠀⠀⢠⣿⡟⠀⢳⠀⠀⡇
⠀⠀⠀⠊⠀⠁⠀⠀⠀⢠⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠋⠀⠀⠀⠀⠘⠛⢁⠀⠀⡇⠀⡇
⠀⠀⠶⢀⡵⠀⠀⠀⠀⢨⣼⠁⠀⠀⠀⠀⠀⠀⢀⣠⣖⣮⣽⣦⣤⣴⣦⣤⣇⣤⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⢄⡀⠸⡄⡇
⠀⢘⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⠛⠷⠟⠀⢻⡇
⠀⢨⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠿⣿⣿⠟⠛⠉⠉⠉⠉⠉⠉⠙⠻⣅⣀⠤⢊⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⠁⠀⠀⠀⠰⠀⣠⡇⣸⡃
⠀⣈⡀⠠⠀⠀⠀⣸⡿⢳⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠒⠈⠙⠲⠤⠤⠤⡤⠤⠤⠔⠒⠚⡉⠑⠊⠁⠀⠀⠀⠀⠀⠀⠀⣶⣤⣾⣿⡷⠀⢀⡴⠏⢀⣼⣿⢠⠟⡇
⠀⡍⡄⠰⣴⣆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠐⠀⠀⠉⠀⠀⠀⠀⠂⠀⢀⣀⠀⠀⠀⠀⠀⠈⠉⠉⢀⡤⠖⠋⢀⣤⣿⣿⢿⣿⢘⡇
⠀⠳⡙⡄⠈⢿⣷⣤⡀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⠤⣄⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢀⣠⣒⠋⠀⢀⣠⣴⣿⣿⣟⣵⣿⡇⢨⡇
⠀⠀⢹⣿⣷⣦⡙⢿⣿⣷⣤⣘⢮⣭⡹⠳⠂⠀⢀⢾⣷⠀⠀⠀⠀⠀⠀⠸⠶⠾⠿⠋⠀⠀⠀⠀⠀⠿⠏⠀⠀⠀⠚⠀⢀⣴⣦⣴⣿⣿⣿⡅⣴⣿⣿⣿⠇⠰⡇
⠀⠀⠈⡄⠙⠿⣿⣜⠿⠿⠀⠙⢻⢞⡂⢀⡀⠀⠻⠞⣡⣶⡦⠀⠀⠀⠀⠀⠄⠀⣀⠠⠤⠤⠀⠀⠀⠀⠀⣀⣀⣠⣤⢰⣿⣿⣿⣿⡿⠟⠃⣼⣿⣿⣿⠏⠀⢸⡇
⠀⠀⠀⠱⡀⠀⠈⠿⢿⣶⣦⡀⠈⠛⢿⡿⣷⠿⠷⣾⣿⣯⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⣛⣯⣤⣴⣾⣿⣿⣿⠋⠀⠀⢸⡇
⠀⠀⠀⠀⠙⢦⡀⠀⠀⠛⠿⣿⣦⣤⣤⣤⣤⣀⣀⡀⠈⠛⢿⣿⣿⣿⣿⣿⠿⠟⠻⠛⢛⣿⣋⣽⣷⣶⣬⣟⣛⣉⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠈⠉⠉⠛⠟⠿⢿⣿⣿⣦⣄⡀⠉⠛⠛⢉⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢦⣴⠀⠀⠀⠀⠉⠈⠛⠿⣿⣷⣦⣤⣶⣿⠿⡿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⣤⣤⣀⠀⠀⠑⠛⠛⢿⣯⣶⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠾⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠤⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏

⠀⠀⡇⠘⣦⠈⡇⠀⠀⣿⠀⢀⡄⡇⠀⣶⠛⣿⠀⠀⢸⠀⠛⢣⣿⠣⡆⢸⠀⠀⡶⣾⡏⢻⡇⣼⠃⣸⡏⠀⠠⡗⠀⠀⠀⣿⡾⠈⢿
⠀⠠⣇⠀⢘⢧⢻⠛⠛⣟⢛⡛⠛⣟⠛⣛⣛⡿⢛⢛⢻⠟⠛⠛⡇⢸⠀⠸⠀⠀⡇⢸⠀⣼⢱⢏⠀⣿⡗⠒⠺⡿⠒⠒⢲⡗⠒⠒⣾
⠀⠀⣿⣀⣾⢾⢿⡇⠀⣿⠙⠃⠀⠁⠀⢀⠀⠀⠀⠀⠈⠓⢆⠀⡇⢸⡀⠀⢰⡄⠇⢸⠀⣿⡿⢸⠀⣏⣇⣰⠷⡇⠀⠀⠀⡇⠸⡿⢹
⠀⠀⣿⠻⠃⢸⣈⣃⣀⣿⣠⠃⢀⣈⡓⠀⠀⠀⠀⠀⡄⢀⢈⣆⡇⢸⣅⣤⠟⢿⡇⢘⠀⣿⠁⢸⡆⡇⡏⣛⣀⣇⣴⣶⣾⣷⣶⣦⣼
⠀⠀⣿⠀⢀⢸⢤⠀⠀⣿⢸⠽⠛⣓⠛⠀⠀⠀⠀⠀⠀⠉⢸⠁⡆⢸⠉⢟⣀⡾⠃⢸⠀⠁⣠⣼⡷⠆⣧⡀⠀⣿⡏⠛⠿⠛⠙⣿⣿
⠀⠀⣿⣿⣿⣿⡄⢁⡀⣿⠀⢄⠠⠇⠐⢚⣳⠦⠄⠀⢀⣀⣼⣦⡇⠈⠀⠈⠻⠃⠀⢘⠀⡀⠛⠛⠂⠀⡇⠘⠀⠻⣧⡀⠀⣀⠈⣿⢿
⠀⠀⣿⣿⣿⡿⢀⢂⢉⣿⡄⠆⠀⠀⠀⠈⠉⠁⠀⠀⠛⢲⣛⣻⣿⢀⣤⣶⣶⣶⣿⣿⣿⣿⣿⣶⣤⡀⠧⠀⠠⠀⠈⡆⠠⠀⠀⣉⢸
⠀⠀⣿⢗⡓⣦⠒⡼⢘⣿⡾⠂⠀⠀⠀⠀⠀⠀⠀⢠⠀⣼⣿⡿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠄⠀⠄⠈⢫⠀⣀⠔⢹⣿
⠀⠀⣿⠀⠀⠉⠛⠷⣾⡟⠁⠀⢀⠀⠀⠀⠀⣀⣀⠀⣰⡋⠄⣼⣿⠿⡟⣵⣿⣿⣿⣿⢾⣯⣽⣭⡻⣿⣿⡄⢠⠄⠸⢾⣩⣄⠀⣾⣿
⡀⣀⣟⣀⣤⣤⣶⣿⣿⡀⠀⢢⠘⣷⣄⠀⠀⠀⠁⡼⡅⠀⢸⣿⣿⣾⣿⣿⡟⠛⠋⠁⠀⠙⢿⣿⣿⣿⣿⣇⡀⡴⣆⠟⣸⡇⢸⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠑⠾⣿⣿⡿⠟⣯⡐⢃⠀⢸⣿⡟⡿⠋⠁⠀⠠⠤⣄⡀⠀⠀⠈⠉⣿⣿⠇⠀⠉⡹⢲⠟⢷⣾⣿⣿
⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣤⣥⣄⠀⣿⣿⣦⢨⣈⠿⣷⡅⠀⠀⠀⠦⢥⡀⢁⠀⣠⠴⢶⡟⢁⠀⠀⡼⢡⡇⠀⠈⢻⣿⣿
⣎⠂⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⡴⠋⢹⣿⠙⠧⣿⣿⣿⠿⠟⢳⠏⡆⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⢳⡇⠈⠀⡼⠁⠸⡇⠀⠀⠀⠹⣿
⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢀⣾⡿⠖⠒⣩⣽⣟⣦⡀⠀⠛⡄⠻⣄⠀⠀⠠⣤⣴⠃⡄⢸⠀⢿⡄⡼⠁⠀⠀⠙⠐⣄⠀⠀⠘
⣎⠛⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⡜⠉⠀⠀⠉⠀⢀⣀⣉⡛⠀⠀⠘⠱⢹⣶⣤⣀⣀⠏⠀⠀⠀⠀⠘⡟⡅⠀⠀⠀⢠⣴⣿⣷⣄⡀
⡙⠳⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡎⠀⣠⠊⠀⠀⠀⠐⠀⢈⣿⠿⣶⣄⡀⠈⠘⠙⠹⡟⠀⠀⠀⠀⠁⠀⠙⡘⡄⠀⠀⢠⣿⣿⣿⣿⣿
⣿⡷⢠⣿⣿⣿⣿⣿⣿⣿⣿⣟⢀⡔⠁⠀⠀⠀⠀⢀⡀⢸⣯⣿⢬⣿⣿⣿⡗⣶⡾⠁⠀⠀⠀⠀⠀⠀⠀⢑⡞⠀⣠⣿⣿⣿⣿⣿⣿
⣿⣦⣸⣿⠿⠿⣿⣟⣿⣿⡟⠀⣼⠀⠀⠀⢀⡴⠊⣷⡞⣻⣿⣿⣾⡿⣾⣿⣷⣾⣷⢶⢺⣵⡦⣄⣠⣴⣾⠁⣠⠄⢿⣿⣿⣿⣿⣿⣿
⣵⣿⣷⣶⣴⣿⣿⣿⣿⣿⡇⠀⢻⣤⡖⠉⠁⠀⢰⣿⣿⣏⣿⣽⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠉⠉⠉⢆⠀⠀⠈⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠞⠋⠉⠀⠐⢁⠀⠀⠉⠙⠛⠷⢶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣤⣀⡀⣀⣤⡶⠞⠛⠉⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠿⠿⠿⠿⠿⢿⣿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠐⠀⢡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣍⣁⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠐⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣔
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⠟⠋⠀⠁⠀⠂⠀⠀⠁⠀⠀⢀⠀⠉⠛⢿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⣿⣿⣿⠟⠁⠀⣜⠐⢶⣶⡄⠀⠀⠰⠿⠛⠀⠇⠀⠀⠀⠈⠛⢿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣤⡀⠀⠰⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠇⠀⠄⢻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠈⣷⣉⠛⣛⣿⣿⠿⠱⠿⣿⣍⣉⣤⣴⣶⣶⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⠠⠄⢻⣿⣿⡟⠀⠀⠀⠀⠘⣿⣿⣿⠏⢻⣿⣿⣿⣿⡧⠀⠈⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠈⢿⠿⠷⠀⠀⠀⠀⠐⠛⠛⠿⠀⠘⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠃⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠠⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠉⠻⢦⣀⣴⠶⠛⠛⠛⠻⢿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⡾⠃⠀⣀⣠⣤⣤⣬⣿⣧⣤⣄⣀⠀⠀⠀⠈⠛⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠉⠙⣋⣵⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠛⠷⣤⣀⠀⠈⢿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣼⣇⢀⣴⠞⠋⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣸⣏⡙⠻⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⣠⡞⠉⠀⣽⠟⠁⠀⠀⠘⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣏⠙⢻⡎⠙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⣰⠏⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣷⡦⠀⠀⠀⠀⢠⣴⣦⡄⠀⠀⠙⣧⡘⢷⣤⣄⡹⣿⣿⣿⣆
⠀⠀⠀⢠⡿⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⢷⡀⠀⠉⢻⡎⢿⣿⣿⣧⡀
⠀⠀⠀⢸⡇⢠⡿⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⢀⣼⠃⠈⢿⣿⣿⣷
⠀⠀⠀⠈⣷⣾⠁⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠈⣷⡟⠉⠻⣆⠈⣿⣿⣿⣧
⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠃⠀⠀⠀⠀⠸⣧⠀⠀⢹⡆⢸⣿⣿⣿⡄
⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⣼⠃⢸⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠘⠷⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣷⣾⣃⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⠀⠈
⠀⠀⠀⠀⠀⠈⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⡘⠀⣰⠂⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⡇⡠⠉⣀⠄⠤
⠀⠈⠀⠀⠐⠀⠀⠀⢄⠀⠀⠢⠀⠠⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠠⢵⡆⡄⣏⣤⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⣄⠀⠀⠀⢈⡙⠾⣄⠀⠀⠀⠀⠌⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠈⠀⠨⠉⠀⠉⠀⢐⣀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⡀⠀⠀⠈⠂⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠄⣀⠀⠀⡀⠂⠀⠀⠆⢠⠀⠩⠑⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡤⠉⠙⠒⠺⢦⣁⣢⡀⢾⠀⢠⠐⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠖⠋⠁⠘⠂⠈⣃⠈⠠⠀⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠒⠀⠀⠀⣀⠤⢤⣄⣢⢄⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠉⠉⠀⠒⠠⠀⠐⠂⠀⠀⠙⠒⢛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⡀⠙⠋⠉⠑⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⣠⢰⢠⠀⣀⠄⡄⢠⠄⡆⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠉⠘⠘⠐⠙⠐⠁⠘⡘⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⠿⠿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⡿⠿⠿⣿⣿⣶⣶⣤⣀
⠀⠀⠀⢀⣴⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣷⣄⠀⠀⣠⣾⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣦⡀
⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷⣾⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆
⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠘⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃
⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣾⡿⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⠀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⢠⣿⣧⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣌⣿⣿⡿⣀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢰⣶⠿⣸⣿⣿⣯⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⢌⣱⡞⢿⠛⠟⢻⣿⡟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠁⠀⠐⡚⠛⣋⠩⣴⡗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠂⠀⠀⠀⠛⢷⣶⣴⣾⠖⢠⣼⢹⡇⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠐⢴⠃⢌⣭⡾⠷⢺⣛⣱⡿⠈⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⡕⠊⠉⠀⠀⢘⣠⡞⢁⣀⣤⡾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠉⠉⠙⠲⠖⠒⠉⠙⠛⠿⠛⠉⢶⣶⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠆⠐⠐⠄⢠⠀⢀⡀⠀⡀⠀⡠⣦⡔⢾⢙⣧⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⣠⠀⣆⢔⣀⣀⡆⠀⡇⣰⡆⠹⠳⡿⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⢇⢻⡀⣄⠙⣿⣀⡿⢁⡗⣾⢦⣷⣼⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⢼⡾⡏⣭⠓⢿⣀⣧⣾⡧⣼⣾⣿⣿⣿⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣧⣷⢻⣧⣼⡍⣿⣸⣏⣿⣹⣿⣿⡗⣥⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⢼⣧⣹⣟⣿⣻⣿⣿⣿⣿⡿⠽⣋⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⡗⠻⢭⠄⠊⠀⠈



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣿⣟⣛⣛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣀⣀⡤⠤⠤⠤⠤⠤⣄⣀⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⢁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⣄⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣨⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠄⠄⠀⠀⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⢀⠖⠉⡉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⡴⠶⠶⠶⠶⠶⠶⣦⣤⣤⣤⣀⡀⠀⠀⠀⠀⢡⠖⠛⢛⢲⣞⠒⢇⠁⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣴⡾⠛⠛⠋⠉⠉⠓⢦⠤⠤⣤⠶⠤⣤⠤⠖⢉⣨⠽⠛⣿⣆⠀⠀⠇⢴⠊⢱⠛⠉⠁⠀⢓⠩⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠀⠀⠀⢀⣀⣈⣷⢖⣚⡷⢀⡔⠒⠛⠉⠀⢀⣴⡿⠋⠀⠀⠀⠘⠑⠎⡳⠖⢟⡠⠳⡄
⠀⠀⠀⠀⣠⣶⠿⠷⠈⠙⢷⣦⣀⡏⠉⠉⠁⠀⠀⠛⠉⠳⣄⣀⣤⡶⠛⢁⠀⣀⠤⠤⢤⡀⠀⠀⠁⢴⠈⢱⡆⣿⠐
⠀⠀⠀⠀⠛⣿⣄⠀⠀⠁⠀⡀⠉⠛⠷⠶⠶⢤⠶⠶⠶⠛⠋⢉⣀⣤⠖⠃⠰⢑⡄⠆⣤⢹⣄⡤⠦⠉⠙⠈⠡⠃
⠀⠀⠀⠀⠐⠈⠛⢷⣤⡀⣎⠉⠉⠀⠀⠀⠠⠀⠠⣄⢀⣠⣴⠿⠋⠁⠈⠀⠀⣈⠃⣄⠿⣸⠃⣠⠰⢤⡘⡇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⢦⣤⣤⣤⣤⠴⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⢹⠟⠉⢿⢦⡀⠗⣤⡺⢡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⠀⠀⠀⠀⠠⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⣴⣻⡌⡇⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠉⠂⠚⢉⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒


⣿⣿⣿⣻⣛⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣛⣿⣿⣟⣟⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠏⠐⠂⠒⢄⡀⠀⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⢢⡀⢀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⣀⡀⠂⢀⠀⠈⣄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠄⠀⢀⠀⠀⡫⠵⠀⢤⡔⠌⠀⠀⢱⣦⡈⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⢼⠡⢠⡶⠋⠀⢀⣀⠀⡀⠀⠁⠀⠀⠀⣸⠃⣝⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢄⠑⠃⠈⠃⠠⠄⣠⡖⢀⡴⣻⠟⠂⠀⣀⣀⣼⣿⠎⣩⠇⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠆⠀⠈⠁⡤⠛⠀⢘⣇⣴⣀⣤⣾⣿⣿⣿⠃⠀⡟⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠘⠹⠿⢿⠿⠟⠛⠉⠀⠀⠀⣇⣀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡠⠀⠀⢀⠰⡀⠀⠀⠀⠀⠀⠀⡏⠀⢢⠈⠉⡇⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⡠⠴⠄⡁⠀⠀⢀⠀⠀⠀⡠⠀⢸⠀⢆⠸⠀⠈⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣂⣤⠖⠁⠀⠀⠀⠁⠀⠀⠶⠀⠊⠀⠈⠢⡁⠈⠂⠀⠀⠸⠀⢄
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⣘⠁⠀⠀⠀⠠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⣀⣀⠀⢀⠀⢀⢱⣀⣀⣀⠀⠁⡀⠁
⠀⠀⠀⠀⠀⠀⣠⠃⢃⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⢀⡀⠀⠀⠀⢔⠛⣻⣿⠋⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⡴⠁⠀⢸⠀⠀⠀⡐⠸⠀⠀⢀⡝⢶⣄⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢒⣒⠒⠒⠒⠀⠀⠀⠀⠒⡒⠞⠋⠉
⠀⠀⠀⠀⡜⠀⠀⠀⠸⠀⠀⡐⠀⡀⡧⠀⠀⠑⣄⠙⠿⣦⣄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢹⠃⡉⠛⡋⠉⢩⡍⠀⠡
⠀⠀⠀⠰⠁⠀⠀⠀⠀⡆⠰⠁⠀⡇⠱⣄⠐⢄⣀⠁⠀⠈⠛⢿⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⢒⠃⠠⢾⡇⠀⠀⢣
⠀⠀⠀⡧⠀⠀⠀⠀⠀⠱⠃⠀⠸⠁⠀⣨⠗⠸⠁⢀⡀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢦⣀⠠⡄⠀⠀⠀⠄
⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⡠⠖⣿⠐⢉⡤⠛⣧⠀⠀⠙⠳⣦⡀⠀⠉⠒⢄⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠘
⠀⠀⣜⣀⡀⠤⠤⢴⠖⠉⠀⠘⠁⡠⠋⠀⠰⠁⠀⠸⡀⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⢤⢚⠀⠀⠀⢀⠆
⠀⠀⠀⠀⡇⠀⠀⠈⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠒⠁⠈⠁⠀⠈
⠀⠀⠀⠀⠈⠒⠦⠠⠤⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣶⣿⣿⠿⠛⠛⠛⠛⠿⣿⣿⣷⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⠀⠀⠀⠀⢀⣴⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⠟⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⢀⣠⣼⣿⣿⣥⣀⠀⠀⣀⣤⣤⣼⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡀
⠀⠀⠀⠀⢠⣾⣿⣿⠿⠿⠿⣿⣿⣷⣿⣿⠿⠿⠿⢿⣿⣷⣾⣿⡿⠿⠿⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⢠⣿⣿⠏⠀⠀⠀⠀⠀⠙⠿⠟⠁⠀⠀⠀⠀⠙⠿⠿⠁⠀⠀⠀⠀⠈⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⢸⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠃
⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣷⡆⠀⠀⠀⢀⣤⣾⣿⡿⠃
⠀⠀⠀⠀⢹⣿⣿⣦⠀⠀⠀⢀⣴⣦⠀⠀⠀⠀⠀⠀⠀⢠⣶⣆⠀⠀⠀⢠⣾⣿⣿⠃⠀⠀⠀⠀⠀⣴⣾⣿⣿⠿⠛⠉⠀⠀⠀⠀⢸⣿⣿⠋
⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠙⣿⣿⣦⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏
⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠘⢿⡿⠀⠀⠀⠀⠀⠀⠀⠸⢿⠟⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟
⠀⠀⠀⠈⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣴⣾⣿⡿⠋
⠀⠀⠀⠀⣴⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣄⣀⣀⣀⣀⣠⣴⣾⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⢀⣴⣦⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⢹⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢀⣿⣿⠇
⠀⠀⠀⠘⣿⣿⣦⡀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢀⣾⣿⡿
⠀⠀⠀⠀⣸⣿⣿⡿⠀⠀⠀⠘⢿⡿⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠀⠀⠀⠰⣿⣿⣿⡀
⠀⠀⠀⢰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷
⠀⠀⠀⢼⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⣸⣿⣿⠁
⠀⠀⠀⠀⠹⣿⣿⣶⣤⣤⣤⣶⣿⣿⣿⣷⣦⣤⣤⣴⣿⣿⣿⣿⣦⣤⣤⣴⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠟⠋⠁⠙⠛⠿⠿⠿⠿⠛⠁⠈⠛⠿⠿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣴⠖⢲⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢸⣿⡇⠀⠀⣿⡄⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢙⠆⠈⣿⣿⠀⠀⣿⠁⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⣿⣿⠀⠀⢸⡇⠀⣿⣿⠀⢸⡇⠀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢹⣿⡄⠀⢸⡇⠀⢻⣿⣆⣾⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡠⠈⣿⣿⡄⠈⡇⠀⢸⣟⣿⡇⢀⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠘⠸⣿⣷⡴⠷⠆⣸⣿⣏⠀⠘⠟⠉⠃⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⡀⠀⠀⠘⣧⡀⠸⠿⠃⠀⠀⠀⠈⠁⠀⣀⡆⢠⣤⣀⡀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠿⣿⣷⣿⡀⠀⢀⡿⠈⠀⠀⠀⢀⣤⣾⣮⣿⡷⣿⠿⠊⣿⠿⣿⣦⣄⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⡇⢹⣿⣿⡇⢀⡞⠁⠀⢀⣤⣶⣿⠟⣿⣿⢉⡄⠨⣅⣈⣀⣐⡉⢻⣿⣄⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⢸⣿⣿⣷⡟⠀⠀⠀⠠⣿⣿⡛⣾⣿⣿⣿⣿⣷⢻⣿⣿⣿⣷⣷⣉⣻⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡇⢘⣿⣿⡟⢀⠀⠀⠀⣠⣿⠇⣜⣶⣿⣿⣛⣿⠟⠠⠿⠿⠟⠛⠛⠛⠛⠓⠾⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⢨⣿⣿⢱⡇⠀⠀⢠⣿⠏⠱⣿⡿⢿⣿⡟⠃⠀⠀⠀⠀⠀⣠⣤⣤⣤⡤⢀⡀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡀⠘⢻⡟⣾⠀⠀⠀⣾⡿⣦⣼⣿⠀⣾⡟⠀⢀⠐⣂⣷⡞⠇⠉⢉⣩⣟⡳⠆⠙⢃⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⠀⠙⠛⠾⣷⡯⠀⠀⣾⣿⣿⣿⣿⣿⡻⣿⠇⠀⢈⣰⣿⣟⠋⣀⣤⣿⣷⣾⣿⣿⣷⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢃⠰⠋⠀⠀⠀⠀⢸⣿⡀⣠⣿⣿⣿⣿⣿⡏⣾⡿⠀⢠⣞⣿⣿⡟⣠⣿⣿⣏⢻⣿⣿⣛⣻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣀⠿⠂⠀⠀⠀⠀⠀⣼⣿⣿⣾⣿⣿⣶⣿⣿⢱⡿⠆⠀⢸⣿⣿⡋⠀⣿⡿⠉⢻⡿⠛⣩⣿⡛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣤⣽⣿⣤⣴⣾⣦⣤⣼⣿⣿⣿⣿⣿⣿⠏⢩⣶⣟⠉⠀⢀⣽⣿⣿⣿⠀⣿⣿⣤⡟⠃⣼⣿⣭⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢰⣿⣿⣿⡿⣿⠁⠋⢹⣿⣿⣿⣿⡿⠛⠁⠐⠈⠉⠁⠰⢦⣿⣿⣿⣿⣿⡗⣿⣿⠛⢷⣦⠙⣿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⣼⣿⡿⠋⠀⠈⠎⣠⡞⣿⣿⠏⣠⡄⠀⣠⣄⣀⣤⣠⣤⣤⣬⣍⢙⠛⠿⠛⢿⣿⣦⡈⠛⠂⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣿⣿⠃⠠⠀⢲⣄⣽⣿⣿⠏⣸⣿⣦⡀⠳⠛⣿⡿⠿⣿⣯⣻⣟⣭⣷⣿⣧⠈⣿⣿⣿⣾⠛⠿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⢠⣿⣿⣿⡶⢤⣬⣿⣿⢟⢁⣴⣁⢈⠙⠛⠀⠀⠁⢣⣾⣷⠿⢟⠿⣹⣿⢻⡙⠣⣙⢿⡿⠛⠻⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠰⡙⠟⣻⣶⣮⣽⡿⢏⠀⢠⠟⣉⠀⢀⠀⠀⢄⠀⠄⠀⠛⠀⠈⣶⠜⠀⢻⣿⡀⠈⠀⣀⡤⢒⣈⡉⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢸⣿⣿⣿⠿⠋⠀⠀⠀⡌⠋⣀⣴⣦⣶⣦⣾⣃⣴⠋⠒⣀⠀⡁⢀⠀⡸⣿⠓⢠⡞⣻⣿⣿⣿⣿⣧⡀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣾⣿⠋⠡⠀⠀⢀⣠⣾⣇⣼⡿⣿⡹⢻⣿⣿⣿⣇⡙⢷⠁⡆⠛⠀⠰⠟⣿⣠⣿⠀⣿⣿⢿⣿⣿⣿⣦⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⡄⠀⠀⠀⢸⡟⢡⡦⠙⣵⣌⠰⣜⣿⣟⣹⣾⣳⠄⠳⡀⢶⠋⠀⢰⡟⠛⠃⣰⡇⠈⣿⣿⣿⣿⣿⠄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠗⠀⡝⠀⠀⠻⡄⠉⢠⣶⡙⢻⣧⣼⣿⣾⢦⣾⣳⡾⠋⠑⣆⡵⠊⣀⣰⠟⣱⢿⣴⣛⣻⣿⣿⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⢰⡏⠀⠀⠹⠀⢴⢸⣿⣧⠘⡏⢬⣹⡔⠂⡸⢍⢰⠆⠚⣉⣤⡿⣿⠁⢰⡟⢻⣿⣛⢋⣷⣾⣿⣏⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⢸⣿⡄⠀⠘⣀⣆⣸⣿⣿⣿⠋⠂⡘⢏⡠⠁⣸⠇⠔⠊⠙⢧⠙⠁⣶⠎⢁⠞⢹⣧⡝⣳⢾⣿⡏⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡾⣿⣿⣷⡄⢿⡟⣿⣿⣿⣿⡀⠂⠀⠂⠠⠀⠡⣶⠄⠀⢠⣾⠀⣾⢋⣴⡟⢠⠟⣻⠰⣍⡾⣩⠃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡌⢿⣿⣞⠳⣝⠻⡿⢹⠿⡇⠠⠒⢀⣠⣏⡐⢀⡠⠲⡄⠁⣼⢃⡽⠁⣼⡿⢠⡿⠓⡈⠻⠈⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣮⣿⢯⣷⠜⣁⣄⣀⠀⡧⠀⣤⣟⣥⣿⣿⢟⠁⣴⠀⢐⣃⣜⣱⣾⢛⣿⡟⢁⡖⠀⢂⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣻⣿⢼⣯⡧⣀⣿⣌⢿⡿⢿⣿⡶⠂⡀⢀⡀⢏⣹⣟⠿⣧⣴⠟⢳⣬⠃⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡙⢿⣷⣧⣼⣿⣿⠛⠻⠋⠀⠀⢀⠎⠁⢰⡏⢠⡾⢿⡅⣨⠳⣄⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣭⠓⣏⢉⡱⣟⢀⢠⡔⣰⣁⣌⡁⢲⣤⡉⢱⣿⣬⠟⢶⠆⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣡⣬⡵⠏⢰⠋⣀⡞⠓⠾⣟⣁⣿⣠⣷⢾⠉⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣈⣷⠶⣻⣿⣿⠇⣿⡿⢁⣅⢹⢃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣍⣿⣧⣠⡽⣧⡾⠿⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣷⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡛⠘⢏⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠡⠀⠈⠙⠢⢤⣀⠰⠜⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⢱⣄⠀⠀⠀⠙⣷⣾⠇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠄⠀⣠⡆⢀⠤⠀⣐⣈⡀⠐⢿⡇⠀⠀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠰⠖⠉⠒⠓⠳⢰⠋⠉⣩⡶⠛⠁⠙⢦⠀⠀⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⠃⠀⠀⠀⠀⢨⣷⣾⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⠤⠞⠃⠀⣼⠀⠀⠀⠀⠀⡸⠃⢸⡥⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠞⢃⣀⣀⣤⠶⠛⠁⠀⣠⣵⢀⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⣴⠖⠲⠤⠔⠒⠒⠒⠐⠂⣀⡤⠖⠛⠉⠉⠁⠀⢀⣀⣠⣤⣿⣷⣟⡻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠉⠢⣄⡀⠀⠀⠀⣠⣴⠟⠁⠀⠀⢀⣀⣤⣴⣾⡿⢟⡭⠏⠹⡋⣋⢱⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠈⠙⠛⠛⠛⠻⠻⠟⠗⠖⠻⠟⠻⠋⠉⠁⢀⠈⢰⣞⣴⣷⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠹⡦⣤⣄⣠⡄⠀⣀⠀⣀⢀⣀⣀⣁⣘⢠⣂⣠⣤⣼⣾⢿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢣⢹⡄⢹⡟⠈⢿⠛⣿⠛⢻⡟⢻⠟⢻⡟⢻⡏⢩⣇⣸⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⡎⣧⠀⣿⠀⢸⡀⢿⠀⣸⡁⢸⠃⢼⠀⢺⠇⢺⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢠⣸⡆⢿⠂⠸⡇⢸⢢⣼⡇⢸⠂⣿⡀⣿⢓⣿⣿⣿⢿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠸⣿⣇⢺⣧⠀⣷⢾⡧⣿⣧⣿⢲⣿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣷⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣾⣿⡸⣿⣿⡧⣿⡎⣿⣾⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣧⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣿⣿⣿⣧⣿⣿⣷⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣶⠧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣾⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⢟⡛⠓⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠿⠟⠻⠛⠛⠙⠉⠉⠉⠁



⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⠶⠶⠶⢶⣶⡶⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠛⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠛⠉⠁⠀⠀⠹⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⡤⣤⣄⣄⠀⢠⠀⣀⡼⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣤⣄⣀⡀⡀⢀⢠⢀⣼⢧
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠉⠉⠛⠋⠉⠀⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠈⠉⠙⠛⠚⠛⠋⠀⠚⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠟⠛⠛⠓⠶⠶⠴⠤⣤⣦⣦⡤⠼⢳⡄⠀⠀⠀⠀⠀⠀⠀⢀⡿⠷⠷⢶⣴⣴⣴⣠⣀⣆⣄⣶⣼⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⢸⣸⣠⢀⢀⡃⣀⡰⠈⠉⠉⠩⠅⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⢸⠯⠍⠉⠉⠛⠛⠛⠳⠶⡖⣴⣴⣤⣴⠏⠀⠀⠀⠀⠀⠀⠀⢸⣯⡝⠛⠛⠛⠿⠿⠿⢿⣷⣶⣶⣶⣶⠏
⠀⠀⠀⠀⠀⠀⠀⢼⣁⠀⢀⡀⠀⠀⠀⠀⠸⣅⣸⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⣾⠍⠀⢀⣀⠀⠀⠀⠀⢸⣇⣿⠀⡉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⢻⣉⡽⢿⡚⠳⢿⡵⣦⣤⣄⣒⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠛⠛⠻⠿⠿⠿⣶⣶⣯⣁⣀⣯⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⢙⣄⡤⠷⡖⠛⠻⣅⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠁⠀⢀⠤⠄⠀⠢⠈⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠉⢉⣧⡤⠞⢾⠉⣙⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠉⢀⠀⠐⠔⠀⢛⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠻⡉⢀⣳⣤⠴⠷⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠈⢀⡀⠀⢤⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡖⠛⢯⠁⣘⣦⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠒⠀⠁⠀⣐⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡖⠚⠻⣅⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠢⠀⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣈⣦⣴⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠐⢀⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⣤⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣄⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⠏⣂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⠯⣴⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣯⠋⠻⢿⡿⣿⠇
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣁⣔⢀⠓⠈⣤⣀⡀
⠀⠀⠀⠀⠀⣤⣿⣿⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣬⣰⣴⣿⣿⣿⣦⡀
⠀⠀⠀⠀⢐⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣹⣿⣿⣿⣅⠀⠁⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠤⠼⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣀⠦⡈⡀⣿⡗⢰⣼⡀⢰⣦⣶⣶⡀⢉⣡⡀
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠻⢳⣿⣿⣿⠿⡇⠐⢻⢟⡛⠁⠹⣿⣁⡀
⠀⠀⠀⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠿⣿⡇⠐⠃⠘⣻⣿⣿⣿⣿⡟⢡⣽⠁⢀⡘⠀⠀⢀⢧⠀⠚⠂⠀⠰⡎⠃⢀⣤⣀⣀⣠⡄
⠀⡀⢀⢀⣸⣿⣿⣿⣿⣟⣿⣿⣿⣿⣟⣳⠁⡐⠛⠀⠀⠀⢾⣿⣿⣿⣿⡏⢀⣸⣿⣄⡉⠄⢸⡆⡈⢰⡀⢿⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠀⠈⢳⡀⠀⠀⠹⣿⣿⣿⠁⢸⣿⣿⣿⣿⣶⣿⣿⣵⣿⠀⠈⡄⢀⣀⣵⣞⣸⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢈⣀⠀⠀⠘⢷⣤⠀⠐⠿⢿⠋⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⠀⠇⠸⢻⣿⡖⡘⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣇⠀⠀⠰⣏⢀⣤⣀⡘⢢⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣤⣄⡆⢹⣿⡟⠀⣿⣿⣿⣿⣾
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠐⠂⠀⡼⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢭⠃⠀⠀⠀⠀⢱⣐⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠃⠀⠀⠀⠀⠀⠽⠿⠿⠿⠛⠋⠉⠠⠞⠋⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⡞
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⣲⠆⠀⠀⢀⡀⠀⠀⠀⠀⠙⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⠉
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣠⡄⠴⠞⠀⠀⠀⡰⠏⠀⠀⠀⠀⣦⠐⢯⣤⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣥⣄⠀⠀⠀⠀⠛⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶
⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⡍⠙⠻⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⢟⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⣿⠟⠟⢋⠉⠉⠀⠀⠀⠻⣄⠀⠉⠉⠉⠉⣏⣙⣇⠀⠂⠀⠀⠀⠀⠀⠀⢺⣯⢻⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⣀⠠⠄⠀⠉⠻⣀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣷⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠶⠀⠀⠈⠛⠛⠓⠢⠄⢀⡴⠟⠋⠉


⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⡃⠠⠃⠰⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣬⡿⣷⣶⡌⠁⠀⠀⣠⣶⣶⣾⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠿⣿⣧⣿⠃⠀⠀⣰⣿⣿⣋⡛⢻⠿⠛⠉⣻⣿⣧⣶⡾⠆⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠈⣿⣾⠁⠀⠀⢰⣿⣿⠏⠉⠈⠁⠀⢠⣾⣿⣿⣿⠟⠱⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣿⣏⢀⠀⢠⣿⣿⢿⢀⠀⠀⠀⢀⣾⡟⠋⠉⠀⠀⠐⣻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⢀⣸⠿⢿⣿⡴⢻⣿⣿⣾⠘⠁⠀⠀⣸⣇⠀⠀⠀⣠⠞⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠁⠀⠀⢸⣿⣾⣿⣿⣟⠅⠀⠀⠀⣿⣣⣴⣾⣿⠟⠂⠐⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⢇⠀⡀⢼⡻⣿⡟⠁⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⣀⣠⡟⠁⠹⣿⣿⣿⣷⣧⣚⠡⠞⢿⣤⣄⡀⢀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢰⣽⡿⠁⠀⠀⠐⠋⢿⠉⠀⠁⠀⠂⠀⢙⠻⠟⠳⠾⠷⠛⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⢀⣼⣿⡁⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣬⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠁⠀⠀⠆⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡍⠀⠀⠀⠀⠂⠐⢒⡄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠾⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡀⠀⠀⠀⠀⠴⠊⠀⠆⠀⠀⢀⠄⠀⠀⠀⠈⠀⠀⠀⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⢰⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡗⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣾⣿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣎⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⢠⠀⠠⠃⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⣶⣞⠿⠟⣠⡧⢀⣷⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣮⣟⣦⣼⣧⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠢⠤⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠈⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢰⣤⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⣿⡏⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠛⠉⢲⠇⣼⢸⠿⡂⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⡩⢷⡰⠀⠂⢐⣿⢸⡆⠘⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⣼⠁⠀⡹⠁⠀⢾⣿⠈⡆⠀⠠⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢐⢺⡇⠀⠀⡇⠀⠀⠘⣿⠀⢿⣄⠀⠊⠉⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⠄⠐⣄⠀⠳⣄⠀⠙⠹⣧⡈⢿⣼⣄⣀⡼⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⢠⣶⠶⢈⡉⠒⠺⣟⣶⣶⠶⢷⣆⡈⠃⠒⠒⠺⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠘⠿⣼⠁⠀⠀⢀⢀⡀⠈⠉⠛⠁⠠⠤⢀⡀⠀⠀⠒⠊⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢘⢧⣄⠈⠢⠤⡔⠋⠀⠙⠲⢄⡀⠀⠀⠀⠀⠉⠲⣏⣿⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠉⠻⢦⣄⠀⠀⠀⠀⠀⠀⢀⠉⠙⠲⠤⢤⣤⣀⣈⢙⡛⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⢀⣀⣀⠙⠓⠾⣦⣠⡆⡀⠈⢉⠑⡒⠂⠢⠤⠈⠉⢉⣡⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⠛⣿⡦⠤⣤⣭⣭⣿⣷⣦⣤⣤⣤⡴⠶⠞⣮⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢹⡇⠀⡇⠀⣿⠀⣾⠉⢹⠇⠀⡿⠀⢸⡇⣼⠱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⣿⠀⢁⠀⣿⠀⣿⠀⢸⠀⢸⡇⢀⣿⢠⡏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢹⡇⠘⠀⢹⠀⡿⠀⡼⠀⣼⡅⣸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠈⢧⠀⠀⢸⠀⣷⢠⣧⣰⣿⢡⣿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣻⡆⠓⢺⣶⡿⢸⡟⣿⣿⣿⡿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠘⠋⠓⠚⠚⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠒⠂⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠘⠃⢀⡀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠁⠀⢀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠋⠀⠀⡀⠈⠁⠀⠡
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠘⠂⠀⣤⡀⠈⠁⠀⢀⣀⠀⡗⢄
⠀⠀⠀⠀⠀⢠⠎⠀⠑⠄⣀⣀⣀⣀⡀⠀⠄⣀⡀⣉⠰⣡⢀⠦⡀
⠀⠀⠀⠀⠰⠁⢄⠐⠃⠀⠀⠀⠒⠀⠀⠠⠤⠀⠀⠀⢀⠤⢊⣀⠈⢆
⠀⠀⠀⠀⡆⠀⢀⠉⠒⠀⠤⠀⠀⠀⠀⠤⠄⠀⠒⠈⠀⢀⠀⠀⠀⢸
⠀⠀⠀⠀⠘⣄⠈⠁⠀⠀⠋⠀⠀⠀⠐⠒⠀⠀⠘⠁⠀⠉⢁⡀⡴⠁
⠀⠀⠀⠀⠀⠸⠈⠉⠀⠀⠉⠉⠀⠉⠉⠀⠉⠁⠀⠉⠁⠉⠀⢀⠃
⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠩⠶⠦⠀⠀⠀⠀⠤⠶⠭⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠢⠴⠃⠀⠀⣀⢄⢶⠋⢉⠔⠖⢄⣀⡀⠤⠐⠈⠉⢡
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⡤⠠⠤⠄⠀⢀⠔⢠⢂⡆⢀⠊⠘⠀⠱⠱⡤⠄⠒⠁⠀⠉⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⣀⣀⠧⠀⠀⠀⠤⡜⠀⠂⢻⠃⣬⡀⠿⠆⠀⠀⡇⠠⠤⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡀⢄⢰⠀⠸⠈⣻⠏⢀⠀⡜⡰⠁⠒⠠⢄⣀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⠀⠈⢀⡠⠘⢢⡀⠀⠄⠰⡀⠈⣎⠔⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠒⠁⠀⠀⠀⠈⠑⠚⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠐⠀⠈⠀⠀⠀⢀⡀⠀⠀⠀⠀⡰⡆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣢⡒⢷⡀⠀⠀⠀⠀⡐⠱⣍⠀⠄⡑⢇⣳⣀⠠⢊⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡊⠉⢲⣀⣀⠹⠁⠑⣄⠴⢾⡽⣿⣣⢟⡠⢡⢄⡏⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠱⠘⠃⠀⣤⣋⢌⣛⢻⣷⣟⠋⢠⠁⡼⡀⠘⡄⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠉⢁⠀⡁⢳⡄⢠⣴⠾⡴⡮⢤⣹⣷⣿⠚⣕⡁⢻⣧⡴⠀⣉⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡄⠁⠀⡡⠉⠠⡜⢁⠰⣦⡀⣋⣿⣼⣄⠑⢾⣟⣾⣫⣭⡽⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠛⡔⠧⠀⠀⡠⠿⣲⣦⣹⣃⣼⠋⣻⣸⣟⢖⠻⣟⢻⣿⣦⡁⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⠀⠀⡀⠤⡄⠞⠡⠩⣝⠛⠯⡼⡹⢃⣽⡉⠿⣾⠿⡶⠖⢚⠉⠉⡨⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠐⠒⠶⢄⠧⠰⣴⣤⠐⡟⢗⣼⠏⢷⡀⠛⢻⣒⠶⠲⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠛⣵⡛⡧⡠⢉⡔⠋⢸⠀⣾⠄⢰⡋⠁⠀⠀⠢⣵⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠠⠀⠀⠠⠜⠿⠆⠰⠯⣱⣤⡼⣶⡅⢩⢸⠗⡠⠐⢈⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠈⢻⣠⠿⣷⣿⠈⣟⡭⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⠹⠟⣄⣽⣷⠾⠇⣿⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⢄⠈⣄⣀⠅⡃⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣜⣤⠾⣧⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠘⠗⢾⣰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡻⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠂⠁⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⣼⡇⠀⠀⠀⣤
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣄⡀⢀⠀⣿⠃⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣟⠋⠙⢿⡄⠀⠀⠸⠃
⠀⠀⠀⠀⠀⢴⣾⣣⣂⠀⠀⡀⠀⠀⣀⣴⣿⣿⡟⠁⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣧⠀⠀⣿⣿⠟⠉⠀⠀⣀⣄⣠⡏⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣠⣤⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣏⠀⠀⠀⠁⠀⢀⣴⣾⣫⣽⡿⠖⠀⠀⠀⠀⣴⣶⠟⠋⠁⠀⠁⢦⣤⣶⡿⠛⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⣰⣿⣿⣿⣿⣏⡴⠀⠀⠀⢠⣾⣿⠁⠀⠀⠀⣷⠿⣟⠿⠋⠀⠀⠀⠀⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⠆⠀⠀⢰⣿⣿⣿⣿⣿⡏⠸⠂⠀⠀⢸⣿⣿⠀⠀⠀⠼⣽⠞⠁⠀⠀⠀⡄⠀⠀⠉
⠀⠀⠀⠀⠀⢀⣀⣤⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⣾⣿⡿⣄⠀⠀⠀⠀⠀⠀⠀⢀⡾⣇
⢀⡠⢐⠒⣿⣽⣿⣿⣿⣿⣿⣿⡏⠐⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⢀⠀⣾⣿⣷⡴⠀⠀⠄⠀⠀⠀⠀⢸⣿⣿⡃
⣞⣿⡋⠽⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⢸⣿⣿⣿⣿⣏⡂⠀⠀⡎⠃⣘⣿⣿⣿⣎⡥⢀⡀⠀⠀⠀⢼⣿⣿⣿⣦⣀
⢹⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣻⣷⡄⠸⣿⣿⣿⣿⣿⣿⠳⣄⣤⣾⣿⣿⣿⣿⣿⣿⠉⡆⠀⠀⠐⢸⣿⣿⣿⣿⠿⠛⠋
⠀⠙⠛⠛⠉⠀⠀⠀⣼⣿⣿⣿⣿⠬⢽⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡾⠁⠀⠀⠀⠈⣿⣿⣿⣿⣷⡄
⠀⠀⣠⣤⡴⣶⣶⣾⣿⣿⣿⣿⣿⡇⡀⠈⢡⡀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⣿⡃⠀⠀⡀⠀⠸⣿⣿⣇⡙⢷⣿⣷⣠
⠀⠀⢰⣯⢵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣵⣾⣿⣇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⠟⣡⠶⠒⠉⢄⠀⠀⠈⠀⢿⣿⣿⣤⠌⢿⡄
⠀⠀⠸⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣫⣿⣿⡷⠋⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⢀⢾⠻⢷⣦⣼⣀⡴⣄⠀⠀⠀⣿⣿⣷⡄⠈⣧
⠀⠀⢠⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⢟⣿⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⡟⠿⣇⠀⢤⡰⠉⢿⢿⣿⡚⠳⢄⣴⠋⢿⣿⣧⡰⡏
⠀⠀⢘⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣻⣝⣷⣮⣷⣿⣿⣿⡿⢻⣿⣿⣿⢣⡀⣈⠲⢄⠴⢃⢰⢧⣿⣷⣿⣶⠋⠀⠀⢹⡛⣿⠁
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠟⢁⣾⣿⡿⢣⡈⠙⢿⣷⣬⣤⠀⣪⣷⣿⣿⣿⣧⠄⢐⠀⠀⢧⠘
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⡏⠀⣼⣿⣿⣿⠋⣢⢐⣶⣿⣿⣿⣮⠙⠦⣿⣧⣼⣯⠀⢀⠐⣜⠢⡄
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⣯⣠⡈⢿⣿⣿⢿⣉⣷⢾⡟⣷⣼⢿⣷⣿⣾⣟⡿⠏⠀⢰⠄⠈
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⣿⣿⣿⣿⣿⢳⡌⠻⣿⣧⣴⣿⣿⣿⣿⡿⢫⢼⣿⣿⣿⣿⡆⠀⠋⠀⠀⢀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣇⣽⡧⣾⣏⡿⢉⣿⣴⣦⣻⣿⣿⣿⠛⠉⠹⠀⢈⣿⣿⣿⣿⠀⠐⣄⠀⠀⠃⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠁⣾⣯⡿⣿⣿⣿⠟⠉⠀⠐⡈⣿⣧⣿⡿⠀⡉⠸⣷⡄⣶⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⣟⠀⣿⣿⡟⣼⡿⠿⡄⠀⢠⣄⣀⣛⣿⣿⡇⠸⠁⠀⢻⡛⣹⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣶⣯⣸⣿⣿⣦⣀⣈⡐⢂⠈⠙⠻⣿⣯⡄⣷⢀⠀⢾⣇⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣻⣿⣗⣢⠌⢹⣿⣿⣿⢹⢾⡖⠈⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣟⣿⡟⢤⢿⣿⣿⣇⠿⠾⣅⡦⡿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣯⣴⠿⣽⣿⠀⣶⢾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡛⣰⣿⠉⣆⠺⢻⡿⡣⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⣍⡿⣿⢧⣶⣼⣿⢏⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⡿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⠈⠉⣹⣋⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡟⣀⠔⠊⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠙⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢒⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⢐⣀⣩⣤⠤⠄⣤⣀⣀⠀⠠⡄⠤⢤⣀⡙⢅⠢⣀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣀⡤⠖⠋⢩⠏⠁⠀⠀⠀⠀⠀⠈⠉⠒⢼⡳⡄⠈⠉⠓⠧⠀⢠⡄⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢨⠁⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⢸⡄⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠃⠀⠈⠂⠀⠀⠀⠀⠈⠀⠀⠙⡆⠀⠀⠀⠀⠀⢸⠋⢀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠴⡇⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠙⠦⡤⠖⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⣄⡀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠈⠑⠲⠦⠴⠖⠋⡁⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⠄⣤⣠⡤⡤⠼⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠒⡈⠃⠛⢐⠒⠂⠀⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⡀⠀⠀⠻⣄⡔⠁⠀⠀⠀⡄⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣤⣀⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⣇⣀⡴⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⡔⠀⢨⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⢧⡀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡉⠂⢀⠠⠒⠈⠁⡴⠃⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠊⢁⡠⠤⠗
⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠹⡀⡄⠤⠴⠒⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢊⣡⢄
⢁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣎⡵⠊
⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠶⠤⠤⠤⠤⠶⠶⠒⢻⡉
⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣢⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠉⠙⠒⠐⠒⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⣠⣤⠤⠼⢰⣤⣤⡤⣤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⠀⠀⣸⠀⢸⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠈⠁⠀⠀⠘⠢⠚⠡⠀⠀⡘⠀⠙⠋⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣅⣀⠀⠀⣀⣀⣀⣤⠴⠖⠒⠃⠀⠑⠦⣤⣀⡀⠀⠀⠀⠈⢢

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⣿⣿⣿⣿⡿⠿⠋⠁


⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⢸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠁
⠀⠀⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠏
⠀⠀⠈⠻⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⠋
⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠉⠛⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠁⠀⠙⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⢹⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⢠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠬⡗⣿⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⢿⣾⡿⠾⠼⣶⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣴⣦⡀⠀⠀⠐⢆⡀⠁⣀⡐⣹⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⢯⡓⣿⡄⠀⠀⠀⠀⠈⠊⢥⣿⡏⡉⠀⠙⣿⣧⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢠⢾⣿⣷⣠⣏⢠⣀⡀⡀⠀⢀⣿⠿⣿⣷⠋⠙⢷⣿⣿⣿⡟⢿⡄⠀⠀⠀⠀⠀⠀⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⡖⠘⠛⠋⢸⡟⢤⣹⠀⠻⠈⠀⠘⠛⢿⠀⠀⣿⡏⠋⠱⢿⡄⣿⡄⠀⠀⠀⠀⠀⢆⠸⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠓⠀⠀⡀⢰⠖⠻⠿⠚⠏⢈⡈⣿⡤⠀⠀⡀⠀⠸⠁⠀⠀⢀⣭⣤⣬⣽⣿
⠀⢀⣀⣴⡶⢚⣁⠀⠄⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠂⠒⠤⠠⡠⠐⠁⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⠉⠉⠉⠉
⢀⡩⠤⣞⠟⡉⠀⠄⠀⢢⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢠⠠⢦⡀⠻⠁⢀⡀⢠⠔⠀⠀⠀⠀⠴⠀⠀⠀⠈⠀⠀⣠⣼⣿⢤⣤⣤⣴
⠨⡁⠀⡷⠰⡅⠀⡨⠄⣠⡆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢻⠄⡘⠢⡿⠃⠀⠀⠀⠀⠀⣀⡐⡀⢀⠀⠆⠀⠀⢸⡇
⠀⢳⣰⢵⡀⠨⠁⠺⣿⠄⠀⠀⠀⠀⠈⠃⠀⠤⡆⢠⠀⡾⠠⠴⠄⠑⢤⠎⠀⠀⠀⠀⡀⡴⢚⡾⢿⠗⠶⡌⠀⠀⠀⡾
⢀⣹⡋⠛⠓⠂⣀⣴⢻⣇⡀⠀⠀⣤⠈⠛⠠⠏⠻⠈⠋⠀⠣⠀⡴⠂⢸⡀⠀⠀⠀⠹⠇⣠⠟⠁⠁⠀⠀⣨⣵⠙⣺⡓⠦⢴⡷⣴⡦
⠠⣟⡷⢈⠓⠖⠛⠛⠷⠼⠃⠀⠉⠁⢠⣎⠐⠀⠸⣼⡄⠀⠀⠀⠀⠀⠀⠧⠤⠶⠤⠤⠬⠴⠾⠆⠀⠠⠞⢿⣿⠂⠙⠓⠒⠈⠁






⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠆⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠤⢄⣀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡍⠁⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠠⠤⡀⠀⠀⠀⠑⢤⠀⠀⠀⠀⠄⡇⠀⠀⠀⠀⠀⢸⠁⢀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠈⠓⠄⡀⠀⢧⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠸⢀⡈⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡷⠟⠃⠀⠰⠟⠛⠛⠦⡈⠐⣄⠃⠀⠀⠂⠠⠆⠀⠀⠀⠀⠀⠞⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠽⠀⠀⠻⠥⠀⠀⠀⠀⢹⡆⠀⠀⠀⡨⢄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠀⠀⢀⠁⠄⠀⢀⠀⢰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⡀⠀⠀⢠⠀⣀⣀⣤⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⡄⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢊⠄⢁⠀⠀⠸⠀⠀⠐⠿⢿⣛⣛⢻⡷⠖⠀⠀⠀⢸⣷⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⡀⠀⠀⣠⠜⠁⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⡠⠚⠀⢨⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡴⢦⣤⡤⠔⠊⠀⠀⡠⠋⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠐⣾⡇⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠈⠙⠲⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠐⢊⠁⡘⠃⠀⠉⠿⠦⣤⣀⣀⢐⣐⠧⠀⢀⡴⠊⣴⠁⠀⠀⢉⢑⠖⠦⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠠⢋⡜⠁⠀⠀⣠⠀⠀⠀⠀⠀⠉⣉⠉⠉⠆⠁⣸⠏⠀⡆⢰⠃⠏⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠐⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⠀⣦⡿⠀⠈⢀⡟⣀⣔⢀⡀⠀⢰⡀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⣸⣿⢣⡇⢠⢾⠇⣿⠟⠀⠀⢠⣤⠑⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠰⠙⣧⣿⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢡⠏⠞⢸⣠⠇⡜⠸⢻⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇
⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠙⠀⢸⠁⠀⠀⢸⡟⠀⠃⠀⢿⠀⣠⠄⢠⣤⠀⠈⠢⠀⠠⠂⠈⣁
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠃⠐⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⣸⠃⠀⠀⠀⠈⠣⡄⢰⡿⠋⡁⠀⣤⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢰⢸⠇⡀⠳⡄⠘⠧⡀⠀⠀⡈
⠀⢀⡆⠀⠀⠀⠀⠀⠀⢰⠀⠘⡷⠸⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⢀⡄⠀⡇⠀⠀⠘⠀⣰⠀⠀⠀⠀⢠⠂⠀⠁⠷⠄⢁⡀⡀
⠀⡇⠠⠀⠀⠀⠀⢀⠔⠠⠁⡤⠃⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⡇⠀⠀⠀⢐⡅
⠀⢱⠐⠀⠀⠀⡰⠃⠀⡴⢠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢼⡇⠀⠀⠀⠘
⠀⠀⢣⣄⠀⠈⠀⣠⡌⠔⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠁
⠀⠀⠀⠐⠢⠔⠊⠁⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠰⠆⠀⠃⠀⠀⠀⠈⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⠀⠀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⢖⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⠀⠀⢀⣠⣤⣉⡛⠛⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠛⠉⠹⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠷⠦⠤⠾⠋⢹⡆⠀⠀⢀⣠⠶⢻⡟⠀⠈⠉⢉⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠲⠦⣄⣹⡎⠙⠶⣤⣀⣤⣤⣴⠶⣾⠁⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⠉⠁⠀⣾⠁⠀⠀⣠⡟⠁⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⣀⣀⣠⣿⠾⠛⠀⠀⠀⠀⠀⢸⠻⡇⠀⠀⠀⢸⡇⠀⠀⣰⠏⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⣇⠉⠛⠛⠋⠉⠉⠀⣿⠀⠀⠀⠀⠀⠀⢀⡿⠀⣷⠀⠀⠀⣾⣀⣤⠾⠁⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⣸⠷⠶⢿⡶⠚⢻⡏⠉⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢸⡇⢻⣄⠀⠀⠀⣠⡏⠀⠀⢸⡇⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢸⡇⠀⠙⣶⡀⠀⠟⠀⠀⠀⢨⣧⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⢹⣇⣠⣀⣀⣀⣀⣀⣀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⢀⣀⣀⣤⣤⣿⠀⠀⠀⠀⠈⢷⣤⣀⣀⣀⣀⣠⣤⣤⠤⠶⠋⠀⠀⢸⡇⠀⠀⠉⠉⠉⢹⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢶⡟⠛⠋⠉⠉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠉⠉⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⣠⠄⣸⠏⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⡀
⠀⠀⠀⠀⠀⠉⠐⢿⣤⡀⠀⠀⠀⠀⠀⣸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠇⠀⠀⠀⣿⡀⠀⠀⠀⢀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠃⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠙⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠙⠿⠆⠀⠰⠿⠟⠁

⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠙⠛⠛⠁⠀⢀⠀⠀⠀⠀⠘⠑⠛⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠘⠙⠛
⠀⡀⣀⢂⠀⠀⠀⠁⠀⠀⠀⠀⢠⣠⠄⢙⡇⠀⠀⠀⠐⣦⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢂⠀⠀⠈⠁⠀⠀⠀⠀⢠⣀⠄⢙⡇⠀⠀⠀⠐⣶
⠀⠱⠂⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢚⠈⢡⡄⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢚⠈⢡⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠈⠓⠇⠀⠀⠀⠻⠲⡰⠦⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠓⠇⠀⠀⠀⠻⠲⡰⠶⠀⠀⠀⠀⠀⡀
⣀⠀⠀⠀⠀⠀⠙⠶⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠃⠢⠤⠴⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠙⠶⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠦⠤⠴
⠉⠀⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠂⠈⠁⠀⢀⡀⠠⠀⠀⠀⠉⠀⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠐⠂⠈⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠂⠀⠀⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⢤⠤⠤⣄⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠈⠁⡁⠀⠀⠀⠀⠀⠀⢐⠀⠀⡀⠀⢀⢤⠤⠤⣄
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠂⠋⠁⠀⡋⢠⠂⠂⠀⠆⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠉⠁⠀⡋⢠⠒⠂⠀⠆
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣀⠀⠀⠀⠀⢣⡀⠀⢁⡰⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣀⠀⠀⠀⠀⢣⡀⠀⢁⡠⠃
⡆⠀⠀⢰⠁⡞⠛⡆⢀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⢠⢚⠶⢀⡆⠀⠀⢰⠁⡞⠛⡆⢀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⢰⠾⠶
⠀⠀⠀⠸⣦⣀⢀⣡⠟⠀⠀⠀⠀⠀⠀⢀⣶⡄⠀⠀⠀⠠⠀⠐⠀⠈⠁⠀⢸⠁⠀⠀⠸⣦⣀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠠⠀⠂⠀⠈⠁
⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠰⣶⡆⠀⠀⠘⣿⣧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠘⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠰⣶⡆⠀⠀⠀⣿⣧⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣠⡄⠀⠀⠉⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣠⡄⠀⠀⠙⠁⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠉⠁⠀⠐⠀⠀⠸⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢠⠤⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠀⠀⠘⢿⣿⡿⠇⠀⠀⠀⠀⠀⠀⣤⢤⣼⠁
⠀⠀⠀⡀⠀⠈⠱⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠡⠆⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⢀⣀
⠀⢂⡒⡐⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣡⠰⠇⠀⠀⠀⡀⠟⠀⠀⠀⠀⠀⠀⠀⠀⢂⡒⡐⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣡⡰⠆⠀⠀⠀⠀⠟
⠀⠀⠀⠑⠀⠀⠀⠠⣄⡄⠀⠀⠀⡯⣑⠀⣘⠃⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠀⠀⠀⢀⣄⡄⠀⠀⠀⣯⣁⠀⣘⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠐⢦⣀⡀⠁⠀⠀⠀⠈⠈⠘⠁⠀⠀⠤⡄⠀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⡀⠁⠀⠀⠀⠈⠈⠊⠉⠀⠀⠤⡄⠀⠃⢀
⠶⠀⠄⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⢀⠄⠀⠀⠃⡀⠠⠍⠉⠁⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠉⠓⠃⠀⠀⠀⠀⢀⠄⠀⠀⠀⡀⠠⠉⠉⠁
⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈
⡀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⣀⠤⠆⠀⡴⠉⣉⡉⠃⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸⣀⠤⠇⠀⡴⠉⢉⡉⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠀⠀⡅⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠄⠀⡅
⡆⠀⠀⢀⠄⣠⣤⡀⠀⠀⠀⠀⠠⢶⡽⠒⠀⠀⠀⠀⠘⠀⠤⠰⠊⠀⣠⣀⠀⠂⠀⠀⢀⠄⣠⣤⡀⠀⠀⠀⠀⠠⠶⠽⠖⠀⠀⠀⠀⠈⠀⠤⠰⠊⠀⣠⣀
⠃⠀⠀⢸⡀⠃⠀⠃⣴⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⣀⠀⠸⡄⠉⢰⠇⠀⠀⢸⡀⠃⠀⢃⣴⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⡀⠀⠸⡔⠉
⠀⠀⠀⠈⠻⠶⠴⠞⠁⠀⢀⣀⡀⠀⠀⢰⣿⡇⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠻⠶⠴⠞⠁⠀⢀⣀⡀⠀⠀⠀⣿⡇⠀⠀⠀⠨⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⢿⠟
⠀⠀⠀⠤⠄⠀⢀⣀⠀⢸⣶⣶⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠂⠀⠀⠀⠀⠠⠄⠀⠀⡀⠀⢰⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⣩⠔⠚⠓⠢⣍⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⢋⡥⠒⠉⢀⣠⣼⣦⣄⡀⠉⠲⢌⡙⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠦⣈⠳⢤⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⠴⢋⡠⠜⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠑⠢⣌⡙⠿⣿⣿⣿⡿⠟⢉⠤⠒⠉⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⠀⠀⠉⠒⠤⣉⣡⠔⠊⠁⠀⣀⣀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⣿⣿⣧⣠⣄⡀⠀⢸⠀⠀⠀⢠⠿⢄⡀⠙⠲⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⣿⣿⣿⣿⣿⣿⡄⢸⠀⠀⠀⠀⠳⢄⡈⠑⡶⠊⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⣿⣿⣿⣿⣿⠃⢸⠀⠀⠀⠀⠀⣀⣘⠀⢁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⢿⡿⣿⣶⣿⠿⣶⣄⡀⠀⠀⠀⠀⡇⠀⠀⠈⠻⣿⠟⠁⠀⢸⠀⠀⠀⢠⠛⢅⣉⠀⢸⠀⣿
⠀⠀⠀⠀⠀⣀⣴⣾⣿⣛⣻⣿⡿⢟⣿⣻⢿⣿⣟⣿⡿⣷⣤⣀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠓⢄⡉⠀⠸⠀⣿⣶⣤⣄⡀
⠀⠀⠀⢰⣿⡿⣷⣾⣯⣿⣿⣯⡺⠿⠿⠿⢿⣪⣿⣿⣾⣟⣿⣿⢿⡆⠀⠉⠓⠦⣄⡀⠀⠀⢸⠀⠀⠀⢀⣠⣴⣿⣷⣿⣾⣿⣿⠿⠋⠁
⠀⠀⠀⢸⣿⣿⣷⣭⣻⢿⣭⣿⢿⣷⣾⣶⢿⣿⣭⣿⠿⣻⣽⣾⣿⣷⠀⠀⠀⠀⠀⠙⠳⢤⣸⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⢸⡏⠻⣿⣿⣿⣷⣯⣛⠿⣿⣟⣻⡿⢟⣫⣷⣿⣿⡿⠿⠋⣿⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⡿⠟⠋⠁⠈⠁
⠀⠀⠀⠘⠳⣄⡀⠉⠙⠻⢿⣿⣿⣾⡍⣽⣾⣿⡿⠛⠁⠀⠀⣀⣤⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠉⠓⢦⣀⠀⠙⠻⢿⣧⡿⠟⠁⠀⢀⣠⣴⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⢸⠀⣀⣤⣾⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠃⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠠⠇⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⣀⠉⠈⠦⠄⠃⢥⡤⠀⠄⠐⢀⡜⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣢⠀⡁⠖⣀⠰⢍⡳⠀⠀⣀⣀⡀⠠⠤⠒⠃⠀⠀⢾⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⣠⣾⣛⣫⠍⠐⠁⠀⠉⠉⠀⠀⠀⠀⠀⠖⣦⣿⠁⠘⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠞⠛⠋⠉⠉⠉⣀⣦⠴⣶⡾⡋⢻⣤⢤⣤⣿⣟⣿⣽⣦⣄⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠛⡟⠛⡃⢀⡠⣤⣿⣉⠉⢋⠁⣐⠛⠈⢁⠈⢿⣟⣩⡜⣟⣥⣶⡻⣻⣷
⠀⠀⠀⠀⠀⢠⠗⠋⢓⡆⠲⠛⠿⠧⠜⠉⠉⡠⠆⠈⠁⢀⡴⠇⠤⣀⠙⠛⢿⠷⠿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠙⠓⠛⠳⠄⠁⠀⠂⠒⢂⡽⢣⠴⠀⠀⠈⠑⠠⠄⠻⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠉⠒⢦⣀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡤⢄⠐⠀⡀⠈⣆⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⠖⠀⢀⡆⠀⠐⠒⠂⠰⠦⠂⠀⠀⢸⡶⣌⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢺⣀⠐⣯⠂⠾⠋⠀⡀⠲⣀⣤⠀⠀⠀⠀⢀⣼⢡⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠢⠈⠀⠈⢄⠉⢰⡞⠀⡾⢛⠛⠁⢀⣤⣤⣾⡿⠃⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠰⠉⠀⠀⣷⣾⣶⣶⣿⣿⡿⠟⠁⠀⡇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠁⠀⠀⠀⠀⡦⠒⡂⢶⢤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢀⠊⠢⡀⠀⠀⠀⠀⠀⠡⠀⢓⢈⠈⡆⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⢀⠀⣀⠔⠉⠁⠂⠀⠀⠑⣀⡀⠰⠋⠢⡘⠀⠣⠁⠀⠀⡌⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠖⠘⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⡂⠀⠀⠀⠀⠅⠀⠢⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⠚⡁⠀⠀⠀⢰⡆⠀⠀⠀⠀⠁⠘⡆⠀⠀⠀⠀⠀⠀⠀⡠⣴⣶⡶⠧⠶⠓⠒⠒⠛⠒⠒⠷⠴⠂⠀⠀⣀
⠀⠀⠀⠀⠀⡠⠃⠀⡇⠀⠀⠀⠜⡄⠀⠀⡲⣤⡀⠀⠺⡄⠀⠈⠀⠀⠀⠀⠁⠒⠻⢧⡤⠤⠠⠀⠀⠀⠀⠀⠀⠀⠤⣤⠶⠞⠃
⠀⠀⠀⠀⡰⠁⠀⠀⢡⠀⠀⡄⠀⢱⠀⠀⠙⣈⠻⣶⣄⡉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡷⡒⢲⠶⠒⠒⡒⠂⠢
⠀⠀⠀⡰⠁⠀⠀⠀⢸⠀⡐⠀⢰⠸⡄⠀⢄⠈⠓⠀⠙⠻⣿⣄⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢱⠈⠢⠌⠀⣰⡇⠀⠀⢁
⠀⠀⠀⡇⠀⠀⠀⠀⠘⠴⠁⠀⠞⠀⠈⡲⢈⠏⢀⠀⠀⠀⠈⢃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢢⡀⠈⡁⠀⠀⠈
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡠⢶⡖⠒⣋⡵⢲⠀⠀⠙⢶⣄⠀⠈⠓⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁⠀⠀⠀⠀⠐
⠀⢀⡜⣀⣀⣀⠤⣤⠒⠉⠀⠞⢁⡔⠁⠀⡎⠀⠸⡄⠀⠈⠻⢦⣀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠠⡄⠀⠀⠈⢠⡐⠂⠀⠀⠀⡀
⠀⠀⠀⠈⡁⠀⠀⠉⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠊⠈⠑⠒
⠀⠀⠀⠀⠑⠲⠄⠤⠤⠚⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠏⣰⣿⣿⣿⣿⠟⠉⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣾⣿⠻⡆⠘⢿⣿⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣼⣿⣿⣿⡿⠋⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⣺⢱⣿⠿⠁⠀⠁⠀⠀⠻⣿
⣿⣿⣿⣿⣿⡟⣿⣿⣿⡟⢸⣿⣿⣿⣿⣇⣾⣿⣿⣿⠟⢁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⡀⣠⣴⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠹
⣿⣿⣿⣿⣿⢠⣿⣿⣿⠁⣼⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠞⣿⣿⣿⣿⣿⠁
⣿⣿⣿⡿⣿⣎⣿⣿⣿⣾⣿⡟⣸⣿⣿⣿⣿⠃⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⡟⠻⡟⠀⠀⠀⠀⠀⡀⣤⡀⠠
⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠃⢀⣴⠏⠀⠀⠠⠂⠀⢀⣤⣠⣴⠞⣽⣿⣿⡏⠀⣴⡇⠀⠀⠀⠀⠀⡇⢹⡇
⣿⣿⣿⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇⢠⡿⠃⠀⠀⠀⣠⣴⣾⣿⣿⣿⣣⣾⣿⣿⣿⠀⣼⣿⣧⣤⠀⠀⠀⠀⠁⢸⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣷⡿⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⡆⡀⠀⠀⠀⢸⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⡿⣧⠃⠀⠀⠀⠸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣷⣼⣿⣿⣿⡿⢨⣿⢿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣧⠟⠀⠀⠀⡀⠀⠁
⣿⣿⣿⣿⣿⣿⣻⣿⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣯⣾⣿⣿⣿⣿⡟⠁⢸⡞⣿⣿⣿⣿⣧⠀⠀⢠⣇
⣿⣿⣟⣿⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠸⠿⣿⠟⠀⣿⣿⣿⡿⣿⠛⣿⣧⡄⠀⢇⠈⠻⢿⡇⠀⠀⠀⠘⣿
⣿⣿⣿⣿⣿⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⡟⠀⣠⢿⣿⣿⣿⣿⠀⠈⠻⣷⡀⠘⠆⠀⢸⣷⡀⠘⠀⠀⢻⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠇⠀⡇⠈⣿⣿⣿⢹⡆⠀⠀⠹⣧⠀⠀⠀⢸⣿⣷⡤⠀⠀⠈⣿
⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠋⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠃⠀⠸⣾⣿⣯⠇⠀⠀⠀⠙⡆⠀⠀⠀⢿⣿⣧⣇⠀⠀⢹⡆
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢰⣿⠃⠀⠀⠀⣰⣶⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣾⠀⠀⠀⠀⢰⡄⠀⠀⠈⢻⡿⣿⡀⠀⢼⠁
⣿⣿⣿⣿⣿⣿⣿⣟⣁⡀⠟⠁⠀⠀⠀⣴⣿⣿⡄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇⠀⠀⠀⠀⠳⠀⠀⠀⠘⣇⣿⣧⠀⢸⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣀⣀⣾⣿⡟⢸⣷⠀⠀⠀⠀⡀⠀⠀⢿⣿⣿⣿⣷⣀⠀⣀⣤⣴⣄⣀⣤⣴⣿⣿⠀⠸⡇⠀⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠁⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣧⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⠀⠀⢀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⣿⡗⠀⠀⣿⠟⠿⠛⠛⠻⠿⠿⠛⠛⠛⠉⠁⠀⢸⣿⡟⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠋⠀⠀⣸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠹⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⢠⣿⣿⣿⣿
⣿⣿⣿⣿⠸⠛⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣴⣟⠋⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢠⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡄⠀⢹⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠙⠻⢦⣀⣀⣀⣀⣴⣿⣿⡧⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡷⣰⡌⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠉⠻⣿⡟⠛⠛⠉⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⡟⣿⣿⣿⡿⣟⡿⠛
⣿⣿⣿⣿⣷⡜⣷⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡚⢿⣿⣿⣶⣶⣾⣿⣶⣶⣶⣶⠂⣠⣤⣾⣿⣿⣿⣿⣿⠇⠿⣿⠿⠚⠉
⣿⣿⣿⣿⣿⣿⣞⢷⡌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣽⣾⡖
⣿⣿⣿⣿⣿⣿⣿⣯⠻⣆⠈⠛⠿⣿⡿⣿⣿⣿⣿⣿⣷⣦⣀⣀⣀⣉⣉⣭⣿⣿⣿⣿⣿⠿⠟⠫⠐⠋⠁⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣆⠙⣷⣦⡀⠀⠉⠲⠬⣝⣛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠉⠉⠉⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⢁⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⡀⠀⠀⠀⠀⠀⠀⢿⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣤⠀⠀⠀⠀⠀⠀⠀⢬⣡⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣄⠀⠀⠀⠀⠀⢠⣾⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⠀⣻⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠘⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠿⡄⠀⠀⣀⠀⠀⠀⠀⣲⠀⠀⠀⠀⢰⣷⠂⠀⠀⠀⠀⣿⣴⠂
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠘⣷⡆⠀⠀⠙⠀⠀⡀⠀⠛⠁⠀⠀⠀⣺⣟⠄⠀⠀⠀⢠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠂⣙⠂⠀⠀⢼⠁⠀⣤⠀⢺⠃⠀⠀⠀⠿⠁⡀⠀⠀⠀⠘⠿⣁⠄
⠀⠀⠀⠀⠀⠀⠀⢠⣺⣀⠐⠢⠿⠓⠀⠀⢿⠄⠀⢤⠀⣿⠃⠀⠀⠠⣤⣠⡆⠀⠀⠀⢀⣶⡄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⣤⣤⠄⠔⢠⢼⡄⠘⠇⢉⣠⠄⠀⠀⢻⡿⠇⠀⠀⠐⣿⣇⠀⠀⢿⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣤⠀⢩⣇⠀⠙⡿⣩⠆⢱⣿⡴⠀⠀⠱⣤⣿⠀⠀⠀⠀⢻⡞⠀⢠⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣛⣤⡞⢯⡆⠀⠀⣽⠂⢪⣽⣧⠈⠀⠢⣬⡉⠂⠀⠀⢀⣀⠸⢟⣄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢷⠀⣾⠃⠀⠀⠫⡜⠻⠛⢷⠀⠀⠀⠹⣿⠀⠀⢀⡀⠟⠀⠀⣿⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⣷⠉⣶⠀⢿⠆⠻⠦⢙⡟⠀⠀⢳⣤⣈⠃⠀⠘⣵⣏⠀⢀⣿⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⣠⠿⠇⠀⠁⣠⣶⣛⠁⢀⠀⣰⣿⡏⠀⠀⠀⢛⣧⡀⢸⡷⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣃⡾⠁⣿⠆⠸⡇⠘⣧⣾⣿⣇⣻⡇⠀⢿⣄⠴⠀⢼⡋⠐⡏⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢋⡀⢈⠀⠳⡆⢁⡌⢻⣩⣟⢀⣹⡇⠤⣼⠋⣤⣈⢈⡡⠤⣘⢯⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣷⣾⡃⠂⣩⣾⠀⡌⠱⣿⠗⢹⡏⠁⢿⣦⢆⣡⣬⣦⡐⢾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢜⣷⠄⠶⣁⡖⠀⠛⣴⡶⣿⠀⢁⣸⣇⡿⠘⠛⠛⣷⣾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⡤⢹⡿⠀⠀⢠⡀⢈⠀⠘⡁⠈⣿⣦⠶⠀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⡘⣿⢳⣄⠀⢙⠋⠀⢸⣻⡟⢪⣤⠴⢀⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⣿⣯⠀⣾⡿⠄⠘⣿⣃⢹⡅⠲⠿⠗⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡿⢋⡀⠀⠟⣴⣿⣧⣍⠠⠿⠀⣰⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣷⡀⠛⣽⠋⠈⣤⡀⠆⠈⢿⣿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡌⢷⠀⣀⣾⡀⠛⣶⠀⠱⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣰⡄⢻⡿⡇⢸⠟⣿⢲⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⢻⡏⢹⣷⣀⠀⢀⣿⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢰⣿⣯⣿⣡⢿⣨⡅⢀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⢿⣿⠃⣶⣿⡅⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⢻⣾⣿⣷⡈⣿⠁⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸⣷⣼⣯⣿⣿⣌⠳⣀⠀⠀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣬⣥⣼⣆⣻⡕⠒⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣾⠿⣿⡗⢈⢿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⢳⡾⣿⣷⡌⠀⣿⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢣⣏⡟⣡⠀⠈⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠇⣼⠘⠃⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⣟⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠀⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠶⠤⠤⣄⡀⠀⢰⡃⠡⠀⠀⠀⠀⠐⠀⠀⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠺⠋⠐⠑⠁⠈⠁⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⡄⠀⠀⢀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠄⠀⠀⠒⢀⠀⠀⢸⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⠓
⠀⠀⠀⠀⠀⠀⠀⠐⠚⡄⠀⠈⢀⠆⠀⠀⠀⠅⠂⠀⠦⡀⠀⠀⠠⠐⠀⠀⡀⠴⠳⣱⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠞⣁⠀⠈⠁⠀⣠⠆⠀⠀⠀⡀⠐⣒⠖⢲⢫⠀⠀⠀⢀⡱⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⠀⠈⠃⠉⡀⠙⠐⠒⠒⠉⠀⠀⠀⠀⢸⢸⠀⠀⠀⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡥⠤⠤⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠤⢃⡀
⠀⠀⠀⠀⠀⠰⠂⠐⠎⠁⠀⠀⢸⣀⣠⢀⠅⠀⠀⠀⠀⠀⠉⠛⡛⠐⠒⠔⠁⠀⢀⡄
⠀⠀⠀⠀⠀⠡⡀⠀⢀⠜⠀⠀⠀⡄⠀⠀⣄⡀⠀⠀⠀⠀⢀⣀⡇⢸⡀⠀⠀⠀⢂⠖⠉⠒⠒⡄
⠀⠀⠀⠀⠀⠀⠘⠁⢠⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⡀⢠⡦⠂⠀⠊
⠀⠀⠀⠀⠨⠀⠀⠀⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠃⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⢾⣄
⠀⠀⠀⠀⠀⠀⠀⣰⢻⠻⡐⠀⠀⠀⢠⡟⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠰⣟⣲⠿⣋⣩⡝
⠀⠀⠀⠀⠀⠀⠀⠉⣥⣀⣤⡀⣤⣤⣠⠁⠀⣠⡮⣭⡁⠀⠘⡆⠀⢸⣿⣿⣫⣭⣽⡿⣻⡆
⠀⠀⡠⠒⠚⠓⠶⣄⠉⣿⣏⠉⣉⣿⠟⢠⠞⠉⠀⣠⠼⠶⠴⢧⡀⠐⣿⣷⣶⣶⣶⣿⣉⠀⠀⣸⢷⣤⡀
⠀⢸⡁⠀⠀⠀⠀⣽⡆⢻⣿⠿⣿⣿⠀⣮⠁⠀⣴⠃⠀⠀⠀⠀⠨⡀⢻⣞⣽⣟⣩⣿⠇⠀⢸⡼⣊⡿⢽⣄
⠀⠀⠇⠀⠀⠀⠖⢾⡀⢸⣿⡟⣿⡟⠀⠀⡏⣶⠻⡄⠀⠀⠀⠀⢸⡇⠀⣿⣯⣭⣿⡏⠀⢲⡟⣓⢻⡆⣽⣷⡆
⠀⠀⢰⣠⢀⣶⣤⡞⠁⠈⣷⡟⣿⠇⠀⠈⠳⣿⣤⢈⣖⠒⢘⣿⡿⠀⠀⢸⣟⠟⣿⡇⠀⠙⣷⣷⣦⣭⣽⣶⠃
⠀⠀⠘⣭⢻⣽⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠋⠀⠀⠀⠘⣯⡿⣿⠀⠀⠀⢻⣿⡿⣷⠺⡟
⠀⠀⠀⢆⣹⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣉⡏⠀⠀⠀⠀⠀⢿⠿⣿⠀⠀⠀⠸⣾⡷⢿⢿⠇
⠀⠀⠀⢸⠷⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢻⣶⢛⠃⠀⠀⠀⠀⠀⢸⣶⡏⠀⠀⠀⠀⢹⣿⢾⡟
⠀⠀⠀⠀⢂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣬⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⢤⣀⠀⠀⡔⠋⠱⠤⢶⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢠⠒⣄⠀⠀⢀⠚⠠⠂⢀⠤⣄⠓⠛⢢⡑⢄⣆⠀⡀⡱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠑⣄⠀⡴⢶⠲⡒⠒⡖⡚⢲⠲⣆⣠⠙⠚⡗
⠀⠱⡤⡑⠼⠟⢍⡑⣄⡀⠘⠂⠊⠀⢤⡠⣵⠋⠁⢌⣀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢠⣍⣘⢃⠀⢣⢸⠀⢰⢀⠀⡇⣿⣁⠀⠘⢆
⢀⠞⠀⠀⠀⠀⣠⠞⠳⠥⠀⠀⠀⢇⣠⠇⢸⡧⣵⠀⢠⠒⡾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠀⢀⡀⢹⣤⠂⢸⢀⠀⢸⡄⢠⢇⡿⢹⣱⠒⠋
⢇⠀⢀⡴⢾⡉⠙⠢⣄⣔⡇⠈⡂⢀⠤⣤⠋⠧⣈⣁⡜⠀⠀⠀⠀⢀⡀⠤⡤⠤⠤⢤⣤⣤⣀⡀⠀⠈⠓⢻⠃⣧⠜⠋⠈⠒⠞⠚⠒⠛⠛⠉⠉⠀⠀⠉
⠀⠉⠉⠀⠀⠑⠤⠴⠛⠾⣌⣉⣠⡧⠞⠁⠀⠀⠀⠀⠀⠀⠀⢠⡎⠑⠠⠀⣌⡶⡷⠷⢶⡀⠤⣍⣣⠀⠀⠘⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠉⡒⠲⠤⠤⡶⠤⠤⠼⠖⠚⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢁⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠉⠉⠙⠲⢄⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢸⠀⠀⠀⡇⠀⠀⢀⡄⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠉⠒⡩⠤⢕⢤
⠀⠀⠀⠀⠀⡰⠲⡋⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠈⠐⠚⠠⠤⠤⠧⠤⠤⠚⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢡⠀⡠⢀⠑⠤⠚⠀⣣
⠀⠀⠀⠀⠀⣧⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠒⠁⠀⠢⠴⠃⢀⣀⠸⣄⡆
⠀⠀⠀⠀⠀⢏⠳⣄⠈⠓⠤⣀⡀⠀⠀⢀⣰⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠐⠒⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠠⡄⠀⠐⢄⠸⣄⡨⠃⡠⠁
⠀⠀⠀⠀⠀⠘⢦⠀⠑⠢⠤⣀⣉⡉⢉⢉⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⠀⠀⠀⣀⡴⠂⠈⠉⠑⠢⠤⣀⠀⠀⠈⠣⣆⠀⠁⡁⠄⣀⣰⠻⠥⣀
⠀⠀⠀⠀⠀⠀⠀⢹⠦⣀⡀⠀⠈⣉⡡⠟⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠂⠁⠀⠒⠀⠤⣠⠀⠈⠁⠀⠀⠀⠀⣀⠄⠊⠉⡄⠀⠀⠀⠀⠈⠈⡑⢟⡉⢠⠻⡖⠊
⠀⠀⠀⠀⠀⠀⠀⡼⠀⡰⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣎⣁⡘⠊⢇⡀⠀⠀⠀⠂⠀⠀⠀⠉⠓⢂⠔⠊⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠉⠁⠈⠙⡀⠸⡄
⠀⠀⠀⠀⠀⠀⣰⠃⡰⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠁⠀⠀⠈⠉⢀⠿⣓⣦⣀⠀⠀⢀⣤⣀⠂⠀⢸⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠱⡀
⠀⠀⠀⠀⠀⣰⠃⣰⠃⠀⠀⠀⠀⠀⠀⠀⣞⡋⠤⡀⠀⠀⠀⠀⠀⠔⠅⠈⠀⠀⠀⢉⡹⠓⡄⠉⡆⠀⣸⠗⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠱⣄⢑
⠀⠀⠀⠀⢰⠃⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠲⢬⠑⠒⠒⢮⠒⠉⠓⢦⠒⠒⠲⣤⠐⠀⢠⠀⡾⠊⠀⠀⠀⠀⠀⣠⠔⠛⠉⡡⢈⠩⠛⢦⡀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠘⠲⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⣆⠠⣀⣔⠠⠤⢄⣍⣀⠀⣀⣸⠀⡠⠞⠉⠁⠀⠀⠀⠀⢠⠞⠁⠀⠀⢀⣀⣀⡀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⢏⠠⡀⢀⡴⢋⢀⢔⢹⡏⠩⢑⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠑⠚⡟⠀⠰⡉⢁⣼⢅⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠤⣼⠗⠀⠈⠲⡀⠀⠀⠀⠀⠀⠀⠈⢷⡤⢀⣷⣀⠴⡻⠉⠈⠎⣆⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔⠚⠉⠙⠢⡈⢆⠀⠈⣷⡖⠀⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣄⣙⣺⣤⡤⠴⡟⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⠐⠚⠉⠁⢄⠙⢆⠀⠀⠀⢹⠈⣄⡴⠙⠛⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘⢆
⠀⠀⠀⠀⡀⠠⣀⡀⠀⠀⠔⠉⢍⡉⠲⣌⠢⠀⠀⠀⠑⠘⣀⣠⠤⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠳⡄
⠀⠀⠀⠐⡀⠀⠸⡈⠑⠚⠒⢀⡀⠱⠀⠈⢆⣷⣠⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠘⢆
⠀⠀⠀⠀⡝⠉⠀⡨⠛⢳⠔⠣⠤⠤⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠘
⠀⠀⠀⠀⢇⠀⣸⠽⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠐⠲⣌⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠘⠇⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡀⠀⠀⠀⠀⠀⢀⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⠀⠀⠀⠀⠀⠀⠀⠤⣍⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⡀⠀⢀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⡃⢻⡋⣿⣖⢒⣾⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢿⣩⠿⣧⡼⠻⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣞⢙⣶⡋⣳⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠻⣤⠿⢷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⡉⣷⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣹⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⢿⠀⡥⠁⠀⠀⠀⠀⠀⠀⠀⢹⡣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣼⣸⠃⠀⠀⠀⠀⠘⠀⠀⡀⡀⡑⠀⠀⠀⠀⠀⠀⢀⣀⣰⣶⣶⣶⣶⣶⣤⣶⣶⡴⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⠈⢿⠁⠀⠊⠀⠀⠀⠀⠀⠀⠉⡷⠁⠈⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⡱⣼⠀⠀⠀⠀⠀⠀⠀⠀⢠⡘⠁⠀⠀⠐⠀⠀⡀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⡞⠀⠀⠀⠀⠀⠀⠀⠈⢹⣣⠞⠂⠊⠀⠀⠀⠀⠈⠉⠀⠺⠿⠿⠿⠿⠿⠿⠛⢛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⡀⢀⠀⢀⠋⠱⡇⢠⠄⡀⠂⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠳⣘⠶⢴⡷⣶⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠁⠐⡌⢡⠀⢀⣹⡇⠰⠁⡈⠀⢀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⢠⡆⠂
⠀⠀⠀⠀⠀⠀⠑⢈⣀⠇⠀⡀⢀⠀⢰⡇⠀⢀⠀⡀⢠⢧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⡆⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣦⡈⠄⢸⠀⣠⢎⠜⠠⡾⡈⠀⢠⠇⠀⠀⠒⠀⠀⠀⡀⠀⠀⠀⢰⡼⠀⣀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠀⠐⠄⠘⠀⠀⢫⠏⠒⢼⣠⣴⠋⠀⢸⠃⢀⠄⡱⠂⠀⠀⠐⠀⣤⠀⠸⠀⠀⠀⠀⣟⠉⢀⠀⠀⠄⠀⠰⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠑⠷⣄⢄⠀⠄⠀⢸⠕⠁⠀⠀⣼⣴⣠⠜⠁⠀⠀⠀⠀⠈⠘⠧⣼⡀⠀⡀⢤⣼⡰⠊⠋⠀⠀⠀⠀⡟⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⠀⠈⠀⡙⠀⠀⠀⠀⠷⠋⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡄⢈⣼⡅⡴⠀⠀⠂⠀⢰⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠠⣯⡠⣄⠀⣠⣐⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⡀⠙⠏⢹⡜⠀⠀⠀⢠⠀⠀⠠⠇⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠄⠀⢱⡀⡏⠉⢳⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣄⢸⠀⣄⣠⠂⣰⡧⣀⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡇⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡖⠘⠁⡰⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡎⠀⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⡏⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡀⢘⡠⠛⠳⢦⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠋⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠉⠁⠀⠀⠀⠙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⢠⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣀
⠀⠀⠀⠀⠀⠀⡏⡇⠈⠙⣒⠤⢄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⡇⠑⠖⠋⠉⡷⠀⠀⠉⣉⡒⠲⠤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⡇⠀⣀⠀⠀⠣⣤⠴⠋⠀⠱⣀⡠⠔⠒⢦⠉⠉⠙⣒⣶⠦⠤⠤⣄⣑⣄
⠀⠀⠀⠀⠀⠀⢧⠈⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠑⠒⠉⠀⠀⠙⠒⠶⠤⠖⠛⡇
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢤⣀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⢤⣀⡀⠀⠀⠀⠀⢾⠆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⢤⣀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⣠⣤⣼⣿⣿⣿⠶⠀⠀⠀⠐⠁⠐⡄⠀⠀⠀⡠⠤⠶⢶⣦⣀⡀⠀⠀⠀⠶⡄⠀⠀⠀⠀⠠⠞⠀⠠⠞⠁⠀⠴⠋⠀⠄
⠀⠀⠀⠉⠉⠋⡁⠰⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠄⠀⢾⣼⣿⡇⠀⠀⠀⠀⣿⠀⠀⢰⣦⣤⣴⣦⣀⣰⣤⣀⣠⣤⣄⣒⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⠃⠀⠀⠰⠀⡿⠀⠀⠘⠛⠈⠡⠜⠆⠛⠰⠼⠧⠴⠦⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠇⠀⠀⡆⠀⠀⠀⠀⠀⠀⠸⠟⠛⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠇⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⠀⠀⢀⡀⠀⣠⡆⢀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠄⢀⠀⠀⠀⠈⠁⠀⠀⢀⣴⡿⠛⠛⠻⠛⠢⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣽⣶⣿⣿⠻⠿⠇⠀⠉⠉⠀⠁
⠀⠀⢀⠐⠄⠀⠀⠀⠀⠂⢈⠄⠀⠀⠀⢀⣽⠏⠁⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠁⠀⠀⠀⡄⠀⡀⠀⠘
⠀⠀⣄⠀⠁⠒⠠⠁⠀⠖⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠷⠀⠀⠀⠀⠇⠀⠀⢰⠘⡆
⠀⠀⠓⠺⢿⣈⡢⠞⠁⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⢀⡀⠀⠀⠔⠀⠀⠀⠀⠂⠀⠀⣠⠁⢀⠘⠞⢣⡄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⡷⠈⠀⠀⣤⣶⠆⠀⠀⠀⠀⠀⠀⡅⠀⢠⡇⡇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣟⣻⣿⣿⣟⣩⠁⠀⠀⠈⢂⠀⠀⠸⣿⣏⠰⡇⠀⠀⠀⠀⠀⢁⠀⠀⡇⡇⢸
⠀⠀⠀⠀⠀⡀⠀⠓⠂⠀⠀⠀⢀⡆⠀⠀⠀⠀⠿⠉⠉⠉⢙⠉⠹⠀⠀⠠⠀⠀⢻⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠇⡁⣹
⠀⠀⠀⠀⠈⢡⡆⢈⠜⢧⠠⠤⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⣄⣠⣄⠀⢀⠀⠀⣦⠀⠀⢆⠃⣿
⠀⠀⠀⠀⠀⠉⡤⠋⠀⠈⡆⠒⡀⠀⠀⠀⠀⢀⣠⠄⡐⢻⠷⠢⠀⠀⠀⠀⠀⠀⣸⠀⠀⡟⠛⠋⠉⠻⠀⠈⠙⠂⠀⠀⠀⢸⡃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢰⣮⣿⣷⣽⣭⣦⣴⣿⡤⠀⠆⠀⣠⠋⠀⠀⠷⠂⠀⠀⠀⠀⢀⡀⠀⠀⣀⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣐⠶⢿⣯⣝⡳⣆⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠰⠃⠀⠚⠀⠀⠘⠆⠀⠀⠀⠄⠀⣹⠀⢀⡳⢶⣶⡼⢷
⠀⠀⠀⠀⣀⠀⠀⠛⢷⣦⠋⠟⠁⠛⠁⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡜⠀⣴⠏⠀⠀⠉⠀⠋⠑⠚
⠀⠀⡆⠀⢹⡟⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠤⠀⠀⠀⠀⠀⢀⣤⢴⡶⠀⠀⠀⠀⠜⠀⣼⠇⠀⠀⠀⢀⡀
⠀⠀⡇⠀⠈⡱⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠜⠋⠀⠀⠀⠀⠀⠤⣴⠏⠀⠀⠀⠠⢸⢃⠐
⠀⢀⡇⠀⠀⡷⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠈⠀⠀⠄⠀⠀⠀⢀⡴⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⣀⣤⡀⡀⠀⠀⠀⡘⠘⠀⣇⡁⡐
⠀⠸⡇⠀⢀⡘⠂⡁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠁⠁⠈⢹⡷⠁
⠀⠀⡇⠀⢠⠟⠀⠀⠀⠀⣄⡀⣔⡾⢤⠗⣤⢠⣆⠤⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣶⡄⠄⠆⢂⢐⡐⡀⠀⠀⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⣾⡾⠂⠀⠀⢃⣀⠐⣛⣂⢛⡚⣘⣋⢳⠞⠋⠂⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠸⡟⠒⠐⠂⠂⠃⠐⠀⠀⠀⠀⠀⠀⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢤⠀⠀⠠⠠⠤⠤⠄⠤⠤⠠⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠖⠂⠈⠌⡁⠀⠰⠀⠀⠐⠋⠉⠈⠀⠀⡤⣀⣄⡀⢔⡂⠚⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠠⠀⠋⠀⠀⠀⢄⠀⠘⠛⠀⢀⠀⣐⡷⠘⠋⠀⠀⠄⣈⣄⡈⠉⠁⠀⡀⠀⠀⢠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠈⠀⠲⠀⠀⠀⠀⠀⠈⠀⠀⢀⣤⠀⡀⠌⣈⢡⢶⠅⠘⠟⠛⠁⠘⢶⠂⠑⠉⠀⠖
⠀⠀⠀⠀⣴⡄⠀⠀⠈⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢰⠈⢋⣁⣀⣰⣚⡉⠛⠁⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠠⠀⠁⠀⠁⠀⠐⠾⢃⡁⠒⠃⠀⢄⠀⠀⠀⠀⠀⠊⠁⠀⠈⠁⠀⠀⠀⢉⠀⢀⣀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠁⠠⠁⠐⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠈⠁⠀⠀⠈⠀⠠⢄⠄⠀⠐⠁⢈
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢅⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡏⠉⠉⠛⠛⠲⠶⠶⠶⣶⣤⣤⣤⣤⣤⠄⠀⠰⠀⠦⠀⠐⠶⢶⣶⣶⠒⠒⠲⣶⣶⣶⢶⣶⣶⣶⣶⣴⣤⣦⡴⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠤⠤⡁⣀⠀⣈⣩⣨⡶⠿⠛⠛⠉⠏⠀⠀⠠⠀⠀⠀⢚⠁⢘⣄⣄⣀⢠⣌⡇⢀⣀⢠⣿⣍⡉⠉⠉⠉⠈⠉⠉⠉⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠉⢛⠙⠀⠀⠁⠐⣤⣤⣄⠀⠆⠐⠙⢄⣩⡤⢯⡟⢢⠉⣉⣉⣉⣿⣿⣓⠒⠒⠤⠤⠤⠤⠄⠔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠡⣴⡧⡖⠀⠂⠃⠀⡀⠀⠰⠚⢿⣿⣿⡷⠊⠀⡀⠀⣤⣬⣏⣆⣩⣈⣁⡀⠈⠉⠉⠉⠁⠉⠀⠉⠁⠉⠉⠁
⠀⠀⠀⠀⠈⠀⢁⠉⠀⠀⠠⣴⣿⣈⠁⠐⠊⠥⢷⢳⡞⢛⣻⣿⣿⣿⣧⣾⣇⣀⣼⣆⣭⣏⣛⣛⣻⡿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⡀⠀⠈⠁⠀⠠⢟⣳⣌⣹⡿⠏⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠛⠛⠋⠀⠉⠉⠉⠀⠀⣀⠵⢿⠫⠹⣟⣿⢿⠶⠒⠂⠀⠐⢉⠃
⠀⠐⠿⠏⠰⡀⠀⠢⣈⡇⢫⣫⠀⠀⠁⢀⠀⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⢺⡄⠀⠃⠀⣞⠿⡉⠀⠀⠀⠀⢀⠀⠈⠠⡀
⠀⠀⠀⠀⠀⠉⠁⠀⠻⢣⠍⠏⠐⠀⢀⣰⣶⠿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠏⠡⡶⠅⠐⠀⠄⠱⢂⡀⡀⠀⠐⠀⠀⠀⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⢁⣀⡅⠀⣯⢹⠻⡟⢦⡀⠀⠀⠀⠀⡠⠎⠁⠀⠉⣒⣀⣀⡀⠲⡆⠀⢨⠶⠤⠟⢀⣘⣚⡳⠆
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠈⠛⠿⠷⠜⠁⠀⠀⠆⠑⢄⠀⠀⠀⢴⠄⠑⠋⠀⠀⠀⠨⣉⠀⠀⠀⠀⠀⠀⠀⠀⢉⠙⠂⠀⠀⠠⠁
⠀⠀⠀⠀⠄⠀⠀⣰⠠⠄⠀⠀⠀⠀⠀⠀⠀⢀⢔⣤⣶⣶⣶⣶⠲⠴⠖⠒⢲⢶⣦⣤⣠⡄⠤⠐⠠⡆⠀⠀⠀⠀⠀⠀⠀⠊⠀⢀⠐⠈
⠀⠀⠀⠀⠀⠈⠒⠼⢤⣀⡀⣀⣀⡠⣄⠀⠀⣀⠉⢚⣛⣓⠛⠒⠒⠒⠂⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⠀⣰⢀⣀⡀⠤⠔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠒⠒⠛⠁⠁⠒⠒⠂⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡤⠒⣈⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠏⢸⠀⠀⢱⢄⠀⠀⠘⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡂⠀⡟⠀⢸⠀⠀⠈⠚⠝⡲⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⣆⣇⣂⡇⠀⠸⠁⠀⠉⠑⠄⠘⡌⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⣇⣆⣲⣿⡿⠉⠀⠀⠀⠀⠀⡀⢠⠀⠀⡇⢸⣶⠀⢀⠀⢀⠀⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣶⡶⠒⡟⣷⣿⡟⠀⠀⣀⠤⠀⠀⠀⡠⠋⠀⠜⠀⡿⣒⣾⠒⢀⣰⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⣿⣷⣶⣿⣿⡇⣠⠞⠁⣀⣠⠔⠊⠁⠐⠋⠐⠚⡇⢻⣿⣶⣸⠘⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠛⣿⣧⣄⣿⡉⠉⠉⠉⠁⠀⠀⠀⣠⠀⠀⠀⠀⡰⠁⢀⣿⣿⣿⣺⡛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡧⢄⣿⣟⣀⣀⣠⣤⡴⠖⣋⠠⠀⠀⣠⠞⠁⢠⢿⠹⣾⣾⠻⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠍⠟⢿⡁⠀⠀⠀⠉⠀⠀⠀⠀⢀⣠⠞⠁⢀⡴⠃⣸⠀⣹⠻⢿⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⣥⣿⣃⠀⠀⠀⠀⢀⣀⠤⠖⠋⣀⣤⠖⠋⢀⡴⠋⢀⣿⣦⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⡌⠉⠙⠛⠛⠻⠶⠶⠒⠚⠋⠉⣀⡤⠖⠋⠀⢀⡞⠀⡏⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⢽⣇⠀⣀⠀⠀⢀⣀⣀⡤⠖⠋⠉⡁⠀⠀⢀⡠⠋⢀⡼⠁⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⣿⠻⢭⣝⣲⠶⠖⠒⠚⠈⣀⣠⣄⣒⡯⠶⠚⠁⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢻⡄⠀⠀⠉⠉⠉⠉⠙⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣓⠶⠤⠤⠤⠤⠤⠔⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠉⠁⡀⠒⠂⡀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠂⣀⠐⢀⡀⠐⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠐⠀⣀⠐⢂⣀⠐⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠚⢁⣀⠒⢂⣀⠉⢲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣁⠤⠒⢂⠤⡉⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣁⣉⣉⣀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣿⣿⣿⣿⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⠿⢿⠿⢿⣿⠿⠿⡿⠿⠿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠒⠤⠀⠰⠶⠴⢿⠛⠋⠙⠂⠋⠀⠀⠀⠀⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠈⠣⠆⠀⠀⠀⠀⠠⢀⣰⠒⠛⠃⠀⠀⠀⠔⠒⠀⠚⠀⣠⣄⣬⠀⠀⢂⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣹⠇⠀⠀⠚⣿⠁⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠛⠆⢿⣷⠀⠀⢀⡀⠜⠳⢄⣀⡴⠖⠲⣄⠀⠀⠐⠚⠀⠀⠀⠀⠀⠀⠠⠏⢠⣦⡄⠀⠀⠈⠀⠻⠿⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⣻⣍⣁⠀⠀⠀⠀⢀⣰⡆⠠⠆⠀⠀⠀⣤⣀⡀⠈⠉⠉⠠⣴⠐⠀⠠⣤⡤⠖⠒⠚⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⣠⠀⠀⠀⠀⢀⠀⠉⠈⢡⠉⠀⠀⠀⠀⠈⠁⣾⠤⠀⢠⡖⠛⠉⠛⠀⣁⣀⠀⠀⠁⠈⣷⣶⡏⠀⠀⠀⠀⠀⠙⡷
⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢻⣶⣾⠋⠀⠀⠀⠠⣾⡥⠄⣤⠈⡴⢄⠀⠀⠀⠈⢃⡹⠂⢀⡸⠇⢀⠀⠚⢿⣿⠛⠀⢀⡸⠛⢀⣠⣴⣿⠐⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠋⣸⣆⠀⠀⠀⣤⠃⠘⣷⡘⠧⠀⠀⢦⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠲⣦⡟⠁⠀⠈⠁⣭⣤⣌⣀⠀⠀⠚⡂
⠀⠄⠀⠀⠃⠀⠀⠀⠀⠀⢀⣄⣈⣉⠇⠠⠾⡇⢠⡄⠘⠁⡈⠃⠀⠐⠊⠁⠀⠀⠀⠀⢹⣦⠀⠀⠀⠀⠘⠛⠀⠀⠻⣄⠀⠀⠀⠀⠈⣹⣙⠉⠀⠐⡀⠉⠲⠶
⡀⣀⣰⣆⠀⠀⠀⠀⠁⠈⠿⢧⣄⠀⠀⠀⠀⠀⠀⣻⢾⡇⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠘⠉⠘⢻⠀⠀⠀⠀⠀⢳⣤⡄⣸⣷⠶⠖⠂⠈⠛⢀⣾⣿⣦⠀⠀⢀⡀
⠀⠀⠙⠟⠀⢀⠀⠀⠈⠀⠀⠀⣹⡄⠀⠀⠀⠀⢀⠣⠈⠁⠘⠲⣄⠙⣿⣶⠶⠖⠲⡇⠀⠀⠀⠈⣇⠀⠀⠀⠀⣾⠃⠀⠈⢙⠀⠀⠀⠀⢢⡈⠻⠛⠁⠀⠀⣼⡇
⠀⠀⠀⢦⣤⠾⣳⠴⢀⡀⠀⠀⠉⠁⠂⠐⠆⠀⠀⠐⠀⠀⣀⣼⣿⡄⠀⠀⠀⠀⠀⢰⡿⠰⢀⣠⣄⡄⠂⠐⠂⠛⢃⣉⠀⠈⠁⡟⠀⠀⣤⡄⠸⠻⠇⢠⡔⠉
⠀⠀⠀⠸⡇⠀⠀⠀⠘⠁⠀⡀⠀⠰⠓⠀⠀⣀⢠⠀⢤⣠⡈⢉⣿⣥⡀⠀⡀⠐⣦⠈⠀⠀⠀⢹⣿⣤⡀⠀⠀⢰⣦⠙⢶⡌⠀⠀⠒⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣇⠀⠀⠂⠀⠄⣀⣽⠿⠇⠀⢰⣾⡟⢣⠀⠀⠉⠛⢀⣄⡙⠟⠈⢀⣸⣿⡇⠀⣠⣀⣠⣷⣄⢡⡀⣤⡈⠛⠃⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠉⠛⢇⣸⠀⠀⠀⠀⠸⣿⣇⠀⠀⢿⣿⡄⠀⠀⠉⠹⠾⠿⠛⡛⠛⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢼⠣⢀⣠⣿⣄⡀⠘⠀⠀⠀⠈⡃⢀⠶⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠋⠙⣻⡀⢀⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠅⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠄⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠔⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣃⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠂⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⡀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠄⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⢄⡁⠀⡉⠠⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢬⣗⠀⠀⠀⠀⣙⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣤⣿⠀⠀⣀⡴⠞⠋⠁

⠀⠀⠀⠀⠀⢀⣠⣤⡤⣤⣄⣀⣤⢤⡤⢶⣤⣀⣀⣀⣤⠤⠤⡶⢤⣤⣄⣀⣠⣤⣴⠶⠦⣤⣀
⠀⠀⠀⢀⡴⠋⠀⠀⠳⠤⣤⣤⠤⠞⠀⠘⢆⡀⠀⣀⣀⡤⠞⠁⠘⢦⣀⡀⣀⣠⠜⠀⡤⡀⠈⠳⣄
⠀⠀⠀⣼⠁⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠈⠀⠀⠀⠈⠉⠉⢀⣀⣀⣀⣀⣀⣀⣹
⠀⠀⣴⠛⠤⠤⠤⠤⠤⠴⠶⠶⠶⠶⢲⠲⠒⠒⠒⢒⡒⠒⠛⣉⣭⣍⡉⢉⣭⣍⣉⣉⣉⣀⣠⣤⣉⡗
⠀⠀⠈⣛⣿⣙⣲⣒⣉⣶⣖⣟⣶⣖⣉⣉⣓⣶⣫⣭⢯⣉⣭⡤⠤⠤⠽⠧⠤⠤⠤⠤⠤⠧⠤⠖⡟⣶
⠀⠀⠀⣏⠓⠒⠊⠓⠤⠴⠒⠲⠒⠊⠓⠒⠒⠛⠒⠒⠛⠉⠉⠈⠙⠋⠙⠋⠉⠙⠋⠉⠑⠒⠊⠉⢀⡏
⠀⠀⠀⠙⢦⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠞
⠀⠀⠀⠀⠀⠉⠙⠛⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⢀⠖⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⣰⠲⡄⠀⠀⠀⠀⠀⠀⠀⢀⣞⡅⠀⠀⠀⠀⠀⠀⠀⡴⠂⠒⢦
⠀⠀⠀⠀⠀⠀⢮⣀⣄⣄⡼⠀⠀⠀⠀⠀⠀⡰⠣⠭⢽⡀⠀⠀⠀⠀⢀⡴⠋⠉⠉⠦⡀⠀⠀⠀⠀⢀⠷⠔⠒⢺⡄
⠀⠀⠀⠀⠀⠀⠈⢟⠢⡱⠁⠀⠀⠀⠀⠀⠀⣗⢒⠒⢒⡇⠀⠀⠀⠀⠪⣀⢤⣀⡠⣀⡼⠀⠀⠀⠀⠸⡀⠀⠀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠈⣷⠃⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⢸⠁⠀⠀⠀⠀⠀⠸⣴⣤⣦⠇⠀⠀⠀⠀⠀⠀⠈⢹⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠀⠀⠀⢠⢾⣱⠦⡀⠀⠀⠀⠀⠀⠀⢀⡖
⠀⠀⠀⠀⠀⢀⡤⠒⠒⠒⠢⡀⠀⠀⠀⠀⢀⡠⠚⣧⣼⣦⠀⠀⠀⠀⠀⡰⠁⠉⠉⡖⠁⠀⠀⠀⠀⠀⡴⠷⠞⢄
⠀⠀⠀⠀⢰⣫⢤⣀⠤⣄⡠⢌⣲⠀⠀⠀⣏⣩⣭⣤⣤⣤⡇⠀⠀⠀⠀⠳⡒⠒⢲⠞⠀⠀⠀⠀⢀⣠⣏⣙⣉⣹⣄⡀
⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠊⠀⠀⠀⠀⠯⠭⠭⠭⠤⠴⠃⠀⠀⠀⠀⠀⢹⢻⠏⠀⠀⠀⠀⠀⠈⠑⠒⣢⣖⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠽⠦⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⠤⠶⠭⡉⠑⣄⠀⠀⠀⠀⢰⠣⢢⢔⢮⢣⠀⠀⠀⠀⠀⡔⠉⠀⠈⠱⡄⠀⠀⠀⠀⢸⣿⣿⡿⣿⡇
⠀⠀⠀⠀⠀⡏⡞⡉⠳⡈⡆⢸⠀⠀⠀⠀⠸⡰⣐⣾⣮⡾⠀⠀⠀⠀⢰⠳⡖⢶⢲⡖⣷⠀⠀⠀⠀⢸⣿⣿⡛⢻⡇
⠀⠀⠀⠀⠀⠱⣱⢌⣒⣁⠷⠊⠀⠀⠀⠀⠀⠉⢲⣿⠃⠀⠀⠀⠀⠀⠈⣇⣧⢸⢸⢧⡏⠀⠀⠀⠀⢸⠋⠛⠻⠿⣯
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡔⠋⠀⢙⠲⡀⠀⠀⠀⠀⠀⠀⢀⣠⡓⢤⠀⠀⠀⠀⠀⠀⡞⡁⡙⡆⠀⠀⠀⠀⠀⠀⣀⣄⣤⣀
⠀⠀⠀⠀⠀⡜⠡⠆⠀⠈⠀⢳⠀⠀⠀⠀⠀⡴⡏⢣⠈⡞⠁⠀⠀⠀⠀⡖⠚⠈⠘⠒⡆⠀⠀⠀⣰⡎⢱⡀⢀⠎⢑⡆
⠀⠀⠀⠀⠀⢸⣀⠀⠀⠙⢀⠎⠀⠀⠀⠐⣮⠣⣸⡤⠋⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⢏⠀⠀⠀⠀⠙⢌⡏⠙⠋⢹⣡⠃
⠀⠀⠀⠀⠀⠀⠈⠙⣾⠉⠁⠀⠀⠀⠀⠀⠈⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠯⠤⠋⠳⠬⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢿⠏⢉⠀⡈⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡄⠀⠂⠀⠀⡍
⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⢇⠳⣀⢦⡤⡎⠑⠒⠲⢤⡀
⠀⠀⠀⠀⠀⣠⢋⡀⠀⠀⠈⠦⢎⣹⠒⠁⠀⠀⠀⣀⣨⣦⣤⣀
⠀⠀⠀⠀⠀⡇⠀⠈⠂⠀⠀⠀⣸⠙⡄⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠸⠀⠀⠀⢸⠀⣷⠀⠀⣿⣿⣿⠿⣋⣌⠻⡏⢹⣧⣀⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⡆⠀⠀⢸⠀⢸⠀⢠⢋⠋⡾⣪⠞⡩⡇⠀⠈⢁⠛⣍⠉⠓⠒⢦
⠀⠀⠀⠀⢰⡧⠖⠒⢤⡇⠀⠀⢸⠀⢸⠀⢸⢸⠀⠀⠀⢜⡾⠃⣠⠃⡸⠀⠟⠤⣷⣯⣿⠗⢄
⠀⠀⠀⠀⠸⠤⠒⠒⠢⣵⢀⣀⣸⠀⢸⣤⡼⡍⠀⡴⠒⠉⠈⡏⣉⣦⠁⣤⡄⠀⠀⠈⠋⠀⠀⠳⡀
⠀⠀⠀⠀⠀⣴⠀⠀⢸⠈⠀⠐⠺⣄⢸⠃⣷⡇⠀⡇⠀⠀⠀⠘⠏⢻⢶⠏⠀⠀⠀⠀⢀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⡟⠀⠀⠸⠀⠀⠀⠀⠈⠁⠀⣿⠀⠀⡇⠀⡀⠀⠀⠀⡜⠉⡆⠀⠠⠄⠀⠈⡄⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⡇⡇⠀⡇⠀⠀⠀⢠⠀⠀⠀⣿⠀⠀⢳⠀⣱⡀⠀⢰⠇⠀⣧⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢱
⠀⠀⢀⣀⣰⡇⡃⢀⡁⠀⠀⠀⡄⠀⠀⠀⡏⠀⠀⢸⢠⠇⠙⡄⡼⠀⢀⣿⡄⠀⠀⠀⠀⠀⣴⠒⣛⡓⠺⡆
⠀⠀⠀⣈⣭⠋⢀⠈⡟⠛⠓⠒⠓⠒⠲⠶⣇⠀⠀⢸⢻⣀⣀⣸⢃⡤⠾⢌⣁⣀⣠⠤⠴⠒⠋⠉⠉⠉⢣⢹
⠀⠀⠰⠿⠓⠊⢩⡔⠁⠀⠀⠀⠀⠀⠀⠀⠘⣄⣠⣯⠏⢠⠞⠁⢼⣿⡆⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⡤⠾⠯⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠓⠒⠒⠋⠙⠂⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⠉⠅⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⣿⠿⠋⠀⠀⠀⢀⠀⠒⠀⠠⡀
⠀⠀⠀⠀⠀⠀⢠⣴⣿⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠲⣄⢀⠀⢀⣾⣿⡿⠏⠈⠀⠀⢀⡠⠄⠈⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣰⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣧⣿⣿⡗⠀⠀⢀⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⢀⣿⣿⣿⣿⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠿⠛⢁⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣆⢠
⠀⠀⠀⠀⢸⣿⣿⣿⣏⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠿⠛⠛⣿⣿⡿
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⣀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠀⠀⠀⠀⠀⠰⠞⠁
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠾⠝⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠘⣮⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡞⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠒⠒⠣⡀
⠀⠀⠀⠀⠘⢿⠹⡌⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⡔
⠀⠀⠀⠀⠀⠘⡅⠁⠄⠀⠀⠀⠀⠀⠀⣀⣠⣴⠞⠛⠋⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠙⠢⢤⣭⣤⣤⣶⣶⣿⣿⠉⠀⠀⠀⠀⣀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣷⣠⡢⠄⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠻⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠞⠟⠋⣿⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⣶⣾⡧⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠛⠋⠁⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⣇⠀⠀⠀⠀⢀⣠⣶⣿⣟⠉⠀⠀⠀⠀⠀⣠⣾⠟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢞⣻⠂⠀⠲⣿⣿⣿⣿⣅⡀⠀⣀⣠⣶⣾⢿⠁⠠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣷⡾⠛⠻⡛⢁⣀⣧⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡀
⠀⠀⠀⠐⠦⢳⡋⠀⠀⠀⠂⠀⢠⠁⠀⠀⢆⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠁
⠀⠀⠀⠀⠀⠀⡁⠀⠈⠈⠲⠡⠏⠀⠀⣀⡎⢀⠄⠨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢉⡁⠀⠀⠀⡘⠀⢐⢤⠁⠋⠘⢨⡅⢱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠰⣤⣘⠅⢰⡞⢃⠃⠉⠰⣿⠊⠳⡏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇
⠀⠀⠀⠀⠀⠀⠤⠀⠋⢛⣸⠐⠀⡁⣻⢜⠘⡋⣠⢆⠎⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣆⠄⠄
⠀⠀⠀⠀⠀⠀⠀⢀⢧⡏⢩⠄⠈⠁⡯⠈⢸⡏⣭⠜⢱⣫⡴⠀⠀⠀⠀⠀⠀⠀⢠⡄⠈⠃⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠰⠸⣇⠃⠀⢠⡄⠀⣖⢳⡀⣼⡇⡾⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣾⣧⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠄⠌⢲⢸⡎⢰⡦⠛⠛⠙⠋⣰⠤⠒⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢤⠀⠀⣠⢼⡖⢋⡔⢙⡐⠁⠀⠀⠀⠀⠀⢀⣤⡶⢀⠀⠀⠀⠀⣆⡃⠀⡀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣤⣾⣾⡿⢾⣤⣿⡁⠀⠀⠀⠀⠀⢰⠟⠋⠀⠈⠀⠀⠀⠀⣈⣳⠿⠡⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢺⠛⣙⣴⣿⠸⢻⡵⠂⠀⠀⠀⠀⢸⡲⠆⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⢠⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣹⣸⣿⡀⠛⠀⠀⡀⠀⠈⡅⢸⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣾⠃⠀⠀⠀⠀⢀⡴⠗⢺⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁
⠀⠀⠀⠄⠀⡆⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡴⠋⠀⠠⣼⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄⣠⡖⠁⢀⣀⡀
⠀⠀⠀⠀⠀⣷⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠋
⠀⠀⠀⠀⠘⣻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⠀⠀⣠
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠁⠀⠔⠂⠀⠀⠋⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢻⣌⣀⠾⠁
⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⡄⠀⠀⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠈⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢀⣀⣀⢨⡤⣀⣀⣖⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⠀⠀⡀⠀⠀⠀⠳⠇⠀⠈⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠘⠋⠋⠈⢀⠲⠘⠚⠁⠈⠙⠃⠀⢠⠈⠀⣤⣤⠀⠓⠦⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⠤⣤⠄⠤⡤⠤⠰⠦⠄⠀⢀⢀⣤⠀⠙⢀⢷⠀⠰⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠙⢱⠀⠀⠈⠀⠄⠀⢀⠀⠀⠸⠀⠀⠀⠀⢉⢠⠄⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠯⠉⠉⠉⠉⠋⠉⡋⠁⠀⢀⠀⠲⠟⠀⠸⠆⠰⠄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣼⣤⣀⣀⡀⣀⣀⣩⡀⠀⠘⠓⠒⠂⠚⠁⠀⠀⠀⠄⠊⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠁⡀⢀⠀⠀⠀⠀⠀⢀⣠⡀⠠⡜⠋⠀⠠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠴⠶⠤⠤⠤⠮⠧⠤⢒⠄⠀⢈⠉⠀⣀⡉⠈⡧⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠞⠀⡀⡀⠀⠠⠖⠀⠀⠀⡐⠬⠀⠈⠉⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⠐⠂⠉⠁⠀⠀⠐⠒⠊⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁





⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣛⣿⣿⣟⣻⣛⣻

⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⣠⠖⠋⠉⠁⠉⠉⠒⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠉⠀⠀⠉⠙⠶⣄
⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠋⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡋⠀⠀⠀⠀⠀⠀⠀⣠⠅⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠈⠙⠒⠦⠤⢤⣤⡤⠴⠋⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⣀⣀⡠⠤⠔⠁⠀⠀⠀⠀⣀⣀⣀⠀⣠⠞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠋⠉⠙⣦⠀⠀⠀⠀⠀⠀⢀⣀⠛⠛⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠉⢷⡈⠉⠙⢄⣀⡀⠀⣀⣀⣠⠤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠈⠉⠀⡴⠋⠉⠙⣆⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢀⣼⠃⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⣒⡚⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⢀⣿⡀⠀⠀⠀⠀⢀⣠⣬⣙⣛⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠋⠁⠙⣷⣤⡀⠀⠀⠀⠀⠀⣸⠃⠙⠲⠶⠛⠉⣷⣀⣀⣤⠖⢫⡏⠀⠀⢉⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠈⠙⠲⢾⣄⠙⠓⠒⠒⠛⠛⣿⣠⡄⠀⠀⠀⠀⣿⡏⠁⠀⠀⣾⠀⠀⣠⠏⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠓⠶⠶⠖⠒⠛⣿⠁⠀⠀⠀⠀⢰⡇⣷⠀⠀⢰⠇⣀⡴⠋⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⣾⠶⢾⡶⠶⣾⠋⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢸⡏⢷⡀⠀⠀⣼⠃⠀⢸⡇⠀⡏⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⢸⡇⠀⠙⠆⠀⠃⠀⠀⠀⣇⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣇⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⢀⣀⣠⣿⠀⠀⠀⠘⣧⣀⣀⣀⣀⣀⣀⣠⡤⠟⠀⠙⡟⠙⠛⠛⠛⢻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⡶⠛⠋⠉⢹⠁⠀⠀⠀⠀⠀⠀⠉⢹⡏⠉⠉⢹⡇⠀⠀⠀⢀⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⣼⠋⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠈⣻⡆⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠆⠀⠀⠀⠀⢿⣤⡀⠀⠀⠀⠀⠀⠀⠰⠟⠃⠀⠀⠸⢷⡄⠀⣠⣶⠟⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⣤⣤⣄⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣽⣾⣿⣿⣿⣿⡇⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⣿⣿⣿⣿⣞⢦⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⡟⣭⡿⣿⣿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⢸⣿⡇⣿⡇⣿⢱⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⢿⠇⣿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢞⡇⠀⠀⣿⠇
⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇
⣿⣿⣿⣦⡀
⣿⣟⠀⣸⣿⣦⡀
⣿⣿⣿⣿⣿⣿⣿⣦⡀
⣿⣶⣷⣿⣿⣿⣿⣿⣿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣙⣻⣛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⣸⣤⡾⠻⠶⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⢀⣴⣏⡾⠁⠀⡀⠀⠀⠈⠙⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⢦⣤⠶⠛⠉⠘⠷⣤⣤⡤⠖⠋⣡⣏⣀⡀⠀⠙⢦⡀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⣤⡀⠙⢦⣄⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⢾⡏⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠙⢷⣄⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠛⠻⣾⣧⣀⣀⣀⣠⣶⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠙⣧⠀⠀⠀⠀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠈⣿⠀⠀⠀⠙⣦⡉⠉⢩⡿⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⣿⡀⠀⠀⠀⣼⣇⣰⡟⠁⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢸⡇⠀⠀⣼⠋⣿⣏⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢋⣾⣧⣤⠤⠤⠴⠶⢶⣶⡶⠶⠶⢼⡇
⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⣧⡾⠉⢿⣆⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⣠⡿⠁⠀⠀⠀⢀⣠⡶⠛⠁
⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣾⡟⠀⠀⠀⠻⣆⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⣾⣿⠟⠀⠀⠀⣠⡶⠛⠁
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⢹⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠛⠁⠀⣠⡴⠛⠁
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣠⣄⣠⡾⠋⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢻⣄
⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣟⣩⠟⢿⣄⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⣀⣴⢟⣡⡾⠟⠁⠀⠀⠹⣷⡄⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠘⣧⠀⠀⢀⣠⣾⣯⡶⠛⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠙⣷⣴⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠈⠻⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⣶⣶⡄⠉⠀⠀⠀⠀⠀⣠⣤⣬⣿⡀⠀⠀⠀⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⣀⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠓



⠀⠀⣀⡀⠀⠀⢀⠀⠀⡀
⣿⡟⣉⣻⠿⠿⠿⠿⠿⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣠⣤⣤⣤⣶⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣻⣾⠿⠏⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣾⣛⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠋⠁⠀⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⡛⠿⣦⣌⣉⣉⣉⡉⣻⠉⠉⠉⠉⠉⠁⠀⠀⠀⣉⣈⣀⣀⣠⡤⠤⠖⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣀⡍⠉⠉⠉⠉⠉⠀⠀⠉⠀⠀⠉⠉⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣦⣀⡀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⣿⠁⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢷⣶⠿⠶⢷⢶⣶⠶⠾⣿⠿⠋⠉⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣅⣀⠀⠈⠉⠀⠀⠁⠠⠴⠀⠈⠀⠰⠒⠀⠀⠳⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣠⡤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣾⣦⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠤⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣏⢻⡛⠭⠽⠋⠿⠿⣷⣦⣀⢀⡀⠀⣀⠀⢀⣀⣠⣤⡶⠖⠛⠛⠛⠉⠉⠁⡀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⡶⣦⠄⣀⡀⠈⠉⠉⠙⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣤⣤⣀⣀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣴⣶⣾⡿⠛⠛⠋⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⡿⢿⡟⠅⠁⠀⠀⠀⠀⠀⠀⣠⡔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣿⣿⣿⣿⣿⣭⣟⠉⠉⠙⠙⠀⠀⠀⠀⠀⠛⠋⠉⠉⠀⠀⠀⣁⣤⣄⣤⣤⠶⠛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣛⡳⠦⢙⠻⢿⣿⣿⣿⣿⣾⣾⣶⣶⣶⣶⣦⣶⣶⣶⣾⣷⣾⣿⣿⠿⠛⠋⠡⠀⠐⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⣈⡙⠛⠲⠶⠍⢉⡛⠛⠛⠛⠉⠉⠋⠙⠛⠛⠛⠛⠛⠋⠀⠐⠊⠁⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⣀⣤⡴⠶⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠋⠁⠀⠀⠀⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣈⠣⣰⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⢀⣄⠀⠀⢱⡀⠠⠋⡀⢹⠛⢢
⠀⠀⠀⠀⠀⠸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢄⢱⠀⠃⠀⢳⠀⠂⠁⠀⠸⢀⠈⡘⡜⠐⠀⢀⣀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⢠⠿⡇⠀⢠⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⢢⣆⠀⢠⠈⢷⠃⡎⣠⢆⠌⢰⡇⠀⠀⡶⠃⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⡏⢀⠂⢡⣳⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠯⣇⠀⢡⠘⣴⠷⢁⡜⠥⢼⠁⠎⠀⡆⣴⠀⣠⠖⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡜⡀⠀⠀⠀⢸⠀⠈⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠁⠀⠈⢢⡀⣶⠛⢦⠜⢣⡕⠚⡄⡀⠘⣡⠇⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠸⡆⠘⡆⡿⢀⡆⢠⡿⠃⠀⣀⡤⠖⠊⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⠶⡛⡇⢐⠈⠒⢸⠀⡀⠜⠁⡄⢀⠀⡀⢺⠁
⠀⠀⣤⠠⠤⠤⠄⣀⣀⠘⣆⣿⣤⠃⣿⣠⡇⢸⠅⢀⠞⠁⠀⠀⠀⠐⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠱⡀⢀⣰⡇⡞⡟⢀⠜⣠⠏⠐⢀⡜
⠀⠀⠈⠓⠦⣤⣀⡀⠀⣉⢪⣉⠣⣀⢺⣿⣥⠂⢠⣏⢀⡀⠔⢃⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠈⣾⢿⡏⠀⣷⣥⣶⠿⠒⠒⠉
⠀⠀⠀⠀⠀⠀⢈⠝⠛⠉⢁⣈⣈⣻⣧⡽⠟⠁⣸⣞⣉⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢍⠹⣿⠁⣰⠿⠋
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢴⣶⠞⢿⡀⡀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⢻⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠈⠀⠀⠀⢳⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠟⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣋⡥⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⢲⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠛⠁⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠶⠶⠾⣇⢀⣀⣤⣤⡿⠓⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⢀⡶⠛⠛⠳⢦⡀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠛⠛⢶
⢸⠁⠀⠀⠀⠀⣙⣃⠀⢀⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠹⡀
⢸⠀⠀⢀⡴⠋⠁⠀⠉⠃⠀⠀⠀⠱⡀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢣⡤⠒⠠⣀⠀⠀⠀⠀⡠⠞⠙⡆⠀⠀⢀
⠈⣇⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⠀⠀⠀⠘⠆⠀⢠⠞⠀⠀⠀⠇⠀⣠⡟
⣠⠟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠞⢠⣧
⢇⠀⢈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠈⢻⠆⠈⠉⠐⠒⠤⠤⣀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⠖⠊⠉⠀⢴⠞
⠀⢸⡆⢠⠒⠂⠤⠄⣀⣀⣿⠀⠀⣼⠁⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠉⠉⠉⣷⠀⢰⣏⡠⠤⠔⠲⡄⢸
⠀⠈⡇⠘⡀⠀⠀⠀⠀⠀⠉⠲⠖⠋⠀⠒⠲⠶⠖⠒⠖⠒⠒⠒⠖⠒⠒⠛⠛⠉⣿⠀⣼⠁⠀⠀⠀⢰⠁⢸
⠀⠀⢿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⣸⠀⡏
⠀⠀⠸⡆⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⡏⢰⠃
⠀⠀⠀⢻⡀⢷⠀⠀⣠⠔⠛⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠹⠆⠀⠀⠀⣼⢁⡟
⠀⠀⠀⠈⢷⡈⢧⠀⠘⣄⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⢀⢰⠇⠀⠀⣰⢃⡾⠁
⠀⠀⠀⠀⠈⢷⡈⢳⡀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣰⢃⡾⠁
⠀⠀⠀⠀⠀⠀⠻⣆⠙⣄⠀⠀⠀⠀⠀⠀⠀⢠⠉⠉⠉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢣⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠳⣄⠀⠀⠀⠀⠀⠈⠳⠤⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣬⡑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢞⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣌⡑⠢⢤⣀⡀⠀⠀⠀⠀⢀⣀⡤⢖⣩⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣷⠀⠀⠉⠉⠉⠉⠉⠁⠠⣶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⣴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠛⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣍⣒⣠⡤⠦⢤⣤⠤⠤⢤⡤⠤⠤⠤⠶⢶⣒⣫⡽⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡿⠁⠉⠉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠉⠉⠉⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⡿⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⣀⣀⣀⣀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⣠⠖⠋⢉⡇⠀⠀⠀⠀⢀⡾⠁⠀⠀⡏⠉⠉⠁⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⡴⠋⠁⠀⢀⡾⠁⠀⠀⠀⣰⠏⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⣰⠏⠀⠀⢀⣴⠋⠀⠀⠀⣠⡞⠁⠀⠀⣀⣀⣀⣀⠀⢀⣠⣀⣀⡀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⡼⠁⠀⢀⡴⠛⠁⠀⠀⢀⡴⠋⠀⠀⠀⠀⣿⠉⠉⠉⠀⢸⡀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠧⠴⠞⠉⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠘⠃⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⢠⡤⠤⠤⠄⠀⠀⠀⣟⠛⠛⠋⠀⠀⠀⡾
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⢀⣀⣀⣀⡀⠀⠈⠃⠀⠀⢰⠶⠶⠶⠀⠀⠀⠀⢀⣼⣥⣤⣤⣀⡀
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠈⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠳⣤⣤⠤⠶⠚⠉⠁⠀⢠⡤⠤⠤⠄⠀⠘⠃⠀⠀⠀⣾⠛⠛⠓⠀⠈⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡽⠂
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⣤⣄⣀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢾⡉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠈⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⡀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣀⣤⠖⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠲⠦⢤⣤⣬⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠶⠶⠶⠶⠶⠖⠛⠉⠁⠀⠀⢿⠀⠀⠀⠀⣀⣀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⣿⠙⠷⣄⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⢠⡇⠀⠀⠈⠙⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣤⠤⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠡⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⠂⠀⠀⠂⠠⠀⠀⠀⠀⠈⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠸⣆⡀⢀⣀⣀⣐⣒⣒⣂⣀⣀⣠⣠⣤⣤⣤⣀⡄⡀⢠⣤⠤⠤⠤⠤⠐⠒⠉
⠀⠀⠀⠀⠠⠔⢶⠀⠀⠀⠈⠙⢲⣤⢀⣀⣀⣤⣤⠶⠛⠉⠉⠁⠀⣀⣴⡀⠀⠀⠀⠀⠐⠉⠈⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢠⣤⠤⠶⢍⡉⠁⠀⠉⠉⠀⠀⢀⣀⣤⣤⣖⣋⣁⡀⡁⠂⢐⠀⣋⡀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⡎⢭⠀⠀⠒⠬⠍⠉⠓⠒⠒⠊⢉⡀⠤⠛⠉⠉⠩⠉⠉⠻⠄⠀⡠⠂⠀⠹⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠲⠀⠀⢀⣠⣴⠶⡋⠉⠉⠉⢀⠀⢀⠀⠀⠀⢀⣀⣀⠰⠀⢠⠀⠀⢀⡀⠄⠁⢀⣀⣀
⠀⠀⠀⠀⠀⢱⠀⠀⠀⢀⠴⢋⠉⠙⠂⠈⠛⠛⠒⠀⠀⠘⠁⠤⠄⠈⠀⠀⠂⠀⠐⠶⠚⠉⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠔⠛⠇⠀⠀⢠⠶⠶⣿⡆⠀⠀⠀⢀⠴⠖⠶⠄⠀⢀⠞⠳⠄⠀⠟⡟⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠑⢾⠀⠀⠀⠐⠤⠐⠁⠀⠀⠈⠃⠐⠂⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉


⢀⣀⡀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⡏⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣰⠂⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢠⡏⠀⠀⠀⠀⠀⠻⣦⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣻⡇⢸⡇⠀⡀⠀⠀⠀⠀⠈⠙⠛⠛⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠛⠛⠛⠛⠻⠇⠈⠀⣸⠃⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠴⠚⠉⢀⣠⠴⠖⠚⢻⡆⠀⢈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠠⠴⠚⠋⣀⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣷⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣴⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠉⢀⠀⠀⠀⠀⠀⠀⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⡾⢷⠄⠀⠀⠀⠀⠀⠈⠙⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠉⢀⣀⣤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⣀⣀⣀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠠⠞⠋⠁⠀⠀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⣦⣤⣤⣤⣤⣤⡶⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⣀⣀⡀⠀⠀⠀⠀⠀⡟⠀⡰⠀⠀⢻⡇⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⣦⡀⠀⠀⠁⢠⡇⠀⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣼⠀⢰⠁⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⡀⠀⠻⣤⠏⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⡾⠃


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠈⠑⠢⡄⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣠⠃⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣀⡀⣀⡀⠀⠀⡠⠒⠂⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⢀⠎⡄⠩⣑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⡠⠋⠀⠀⠀⠈⢠⠔⠢⠤⣈⠀⠀⢀⣀⣀⠼⠀⠀⠀⠀⠀⠀⠸⢠⠀⠀⠈⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠢⠘⢰⠁⠀⠀⠀⠀⠀⠰⠀⠀⡠⠂⡠⠊⠀⠀⢠⠀⠀⠑⠆⠀⠀⠀⡆⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠀⣠⠔⠒⠒⠚⢦⠀⠀⠀⠀⠀⠀⢀⣼⢀⡜⠀⠀⠀⠀⡇⣠⠀⠀⠸⠇⠀⠘⣱⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠖⡠⠚⠁⢀⣀⣠⠎⠀⠀⠀⠀⠀⢀⡇⠀⠀⠠⢀⠜⠁⠀⠈⠀⠀⠀⣀⠀⣶⠁⠀⠀⣸⠋⠀⠀⢣
⠀⠀⠀⠀⢀⠖⢁⠔⠉⠀⠀⡜⡩⠋⠀⢄⣀⣠⠤⠤⠐⠁⢀⡓⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⡏⠀⠀⢠⡏⠀⠀⠀⣿⢈⡀⢨⠀⠘
⠀⠀⠀⠀⡆⠀⣼⣦⡤⠚⡁⠐⠁⠀⠀⠀⠀⠀⣀⣠⣗⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠧⠄⠀⡾⠁⡀⣠⢲⡿⠈⠄⠀⠂
⠈⠀⡄⠀⠐⠀⠻⠽⠐⠠⠄⠀⠀⢁⣈⣩⣽⣛⡋⠍⠁⠀⠀⣓⣂⠀⠀⠀⠒⠈⠈⠉⢡⠀⠀⠀⠀⠀⣰⠃⡼⢋⡵⠏
⠀⠀⠄⠀⣀⣀⡀⠀⠀⣀⡀⠄⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡤⢂⡀⠀⣠⠔⠰⠤⢼⡤⠤⠲⢖⣪⣥⣾⣿⣋⣀⣀⣀⣀
⠀⠀⠀⢀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠖⠫⠊⠀⠀⣀⣠⡀⡼⠀⠀⠀⢐⠀⠀⠘⠋⠉⠉⠉⠙⠛⠿⣟⡲⢤⣀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡥⠤⠴⠛⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⣀⠠⢄⡽⢄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠉⠊⠑⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠚⠋⣁⡠⠶⠖⠳⣄⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠒⠊⠉⠀⠀⠀⠀⠀⠣⣄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡆⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠁⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢡⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡀⠀⠄⠉⠀⠀⠈⠳⡖⠒⢦⣄⣀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀⠀⠀⠀⣠⠞⠋⠙⠳⣄⣧⣴⠤⢤⣀⠀⠀⠀⡇⠀⠀⣨⣅⡀⠀⠙⢧
⠀⠀⠀⠀⠀⠀⠀⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡗⠀⠀⣸⢁⣀⣤⠤⠤⠤⣄⠀⠀⠀⠈⠉⠛⠳⣇⡴⠛⠁⠀⠙⢦⣤⣬⣇
⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠠⣿⣤⡀⣠⠟⠋⠁⠀⠀⠀⠀⠈⠳⣤⣤⠴⠶⣏⢉⡽⠛⠋⠉⠉⠛⠳⢦⡀⠸⡇
⠀⠀⠀⢀⡴⠛⠉⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠙⣷⠒⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣴⠇
⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠳⣤⣀⡀⠀⠀⢠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄
⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣤⡾⢧⣄⣀⣀⣀⣀⣀⣈⣹⣆⣀⣏⣀⣀⣀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘
⠀⣠⠞⠉⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣙⣦⣤⣴⠚⢉⠉⢻⡄
⠰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⠇⠀⠀⠀⢰
⣠⠟⠀⠀⠀⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠰⣾⡁⢠⡄⠀⠀⢀⣤⠀⠀⠀⢠⣄⠀⠀⠀⢀⣤⠀⠀⢠⣿⠀⠀⠀⠀⣼
⣏⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠈⢷⢾⡇⠀⠀⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⠀⠀⢸⣿⣆⠀⠀⠀⢹
⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢸⡇⠀⠀⢸⡿⠀⠀⠀⢸⡇⠀⠀⠀⠈⣿⠀⠀⢸⡷⠈⢳⡄⠀⠘
⠀⠈⢹⡶⠶⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠁⢺⡇⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢸⣿⠀⢸⡇
⠀⠀⢸⡇⠀⠀⠀⣠⢶⡄⠀⠀⠀⠀⠀⠀⠀⠐⠤⠤⠄⠀⠀⢠⡆⢹⡇⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⢸⣿
⠀⠀⠀⠳⣄⣠⠾⠁⠀⠹⣶⠶⠶⠓⢦⣀⣤⣄⠀⠀⣠⣤⡶⠋⣧⢸⡇⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⡜⢸⠀⢠
⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠢⡀⢀⡠⠌⠃⢾⠀⣾⠋⣼⠁⠀⣿⠘⣧⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⡇⢸⣤⠞
⠀⠀⠀⠀⠸⡇⠀⠀⢢⡀⠀⠒⠉⠃⠄⠀⢠⡟⢠⡇⣼⠃⠀⠀⢸⡆⢻⡀⠈⣷⠀⠀⠘⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⣼⠃⢸⠁⣿⠁
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠐⢂⣀⡀⠠⠈⠉⣹⠃⢸⣷⠏⠀⠀⠀⠈⣷⠘⣧⠀⢻⡀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⢠⡇⠀⢀⡟⢠⡏⢸⡟
⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠉⠢⠀⠀⣰⠏⢀⣼⡏⠀⠀⠀⠀⠀⠸⣇⠸⣇⠈⢣⠀⠀⠸⡆⠀⠀⢸⠇⠀⠀⠀⡈⠁⠀⡘⢀⡾⢠⡿⠁
⠀⠀⠀⠀⠀⢸⡇⠀⠐⢤⡀⠀⠶⠈⠉⠙⠓⢛⡿⠀⠀⠀⠀⠀⠀⠀⠹⣆⠹⣦⠈⢣⠀⠀⠙⡀⠀⠀⠀⠀⠀⠰⠁⠀⡜⢁⡾⢡⡿⠁
⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠑⠠⡀⡀⠄⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡘⢷⡄⠑⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠊⣠⠏⣠⡿⠁
⠀⠀⠀⠀⠀⠀⣿⠀⠘⠢⠀⠈⠉⠁⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⣀⡴⠞⢁⣴⠏
⠀⠀⠀⠀⠀⠀⢸⡆⠐⢀⠘⠓⠂⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣈⠉⠓⠒⠶⠖⠚⠛⢉⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠸⡇⠀⡀⠑⠶⠆⠈⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⠶⠶⠶⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠐⠦⠤⠀⢁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠢⢤⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⢧⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢤⣀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⢠⠀⠀⢀⡀⠀⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁⠀⠀⣴⠋⠀⠀⠈⢧⠀⠀⠀⠀⠙⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⣀⠀⠀⠚⠁⠀⠀⠀⠀⠈⠣⠀⠀⠀⢀⣀⣤⠟
⣀⣀⣀⣀⣀⣀⣀⣀⣘⣷⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣙⣛⣳⣦⣤⣶⣤⣤⣶⣶⣶⣚⣛⣉⣉⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠓⢄⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⣀⠄⠀⠀⠍⠄⠠⣝⠅⠀⠀⣦⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠷⠀⠀⢡⡀
⠀⠀⠀⠀⠀⠠⠀⢀⡐⡁⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢠⡏⣼⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢂⣄⠀⠀⠀⠀⠀⠀⢀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠆⠀⠀⠋⡋⠉⣠⣤⣴⣿⠃⠸⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡄⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⢿⣷⣾⣿⠿⠟⠃⠀⢸⢇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇⠀⠀⠀⠀⡔⠁⠀⠢⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠋⠀⠀⢠⠄⠀⠐⡂⡘⠀⠘⠧⠤⠤⣀⣰⡀⢀⠄⣠⠀⠀⡀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢀⠴⠃⠀⠀⣠⢆⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢺⡀⠀⠜⠁⠀⠐⠀⠀⠀⠀⠰⠀⠁⣰⠇⠘⢰⠁⠀⠀⠀⠀⠙⠂⠠⢶⣎⡁⠀⣤⡶⠿⠿⠉
⠀⠀⠀⠀⠀⢀⠀⠀⢀⣿⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄⣠⡏⡄⠀⠀⠀⢰⣿⣦⣡⣾⢿⡇⠀⣸⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣿⠀⠀⠀⠤⠀⠀⠀⠀⢠⠀⠰⠃⠉⣷⠁⠙⠁⠀⠀⠀⣿⢏⣿⣿⡿⠀⠙⠔⢁
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡇⠀⠀⠸⢇⠀⠈⣿⣿⣿⣿⣧⢀⡄
⠀⠀⠀⠀⠀⢀⠔⠟⠁⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠠⠁⠀⠹⣿⡷⠿⠿⠞
⠀⠑⠄⣀⣤⣶⣊⡤⠖⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠒⠀⠀⠀⠀⡜⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠠⠄⠀⠀⠀⠀⡀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⡀⠀⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⣊⡘⡁⠀⠀⠀⢹⣧⠀⠀⠀⠉⠀⠀⣼⡿⠀⠀⠀⠀⣠⡾⠛⠾⢿⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠛⠻⢷⣤⣠⡁⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣠⡾⠋⡠⠞⠚⠛⢿⣿⠟⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⡀⠀⠀⠀⢸⣿⠀⠀⣴⠟⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡟⣳⣦⠀⠀⣸⡏⠀⣰⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⣸⣿⣕⠀⠀⣿⣷⣤⠛⠉⠀⠀⠀⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠇⢀⣿⣿⣿⣤⣾⡿⠃⠀⠀⠀⠀⠀⣄⣀⢀⣿⣦⡀⠀⠀⠀⠀⠀⣠⣾⢟⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⣿⣟⠀⠀⠸⣿⣼⣿⠿⠉⠀⠀⢀⣴⣤⣶⣿⣿⣿⡟⣿⣿⣿⣦⣴⣶⡶⠿⠿⠛⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣠⣾⣿⣿⡿⠃⠀⠀⢠⣾⣿⣧⣤⣤⡿⡯⠼⠟⠛⠉⠀⠀⠀⠀⠀⠀⢀⣿⣇⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⣿⡿⠀⠀⠀⢰⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡃⠀⠀⠀⢾⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣾⠿⠟⠛⢻⠿⣿⣿⣏⣉⡙⣿⣿⠇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣏⡠⢿⣿⣿⡅⠀⠀⢿⣿⣿⣿⠟⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢟⣾⠿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢾⣿⣿⣿⣀⣀⣿⣿⠟⡟⠀⠀⠀⠀⢀⡿⠀⠀⠀⣀⡀⠀⠀⢸⣧⠀⠀⢉⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣽⣿⡿⢷⣾⣿⣿⣿⣿⣿⠏⠁⣾⡵⠦⠤⠀⢀⣾⠃⢀⣠⣴⡟⠻⢷⡀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠿⣧⣾⠛⠉⠉⠹⣿⣻⢋⣿⡟⠁⠀⠀⠀⣾⣿⣾⣿⣯⠋⠀⠀⠀⢹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣯⣿⣿⢿⣿⠁⠀⠀⠀⠀⠈⠉⢻⣿⡀⢤⠀⠀⠀⣿⣿⣿⡟⢠⡄⠀⠀⠀⠀⢿⡇⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⢟⣼⣿⠄⠀⠀⠀⠀⠀⠀⣼⠁⠙⢾⠢⠤⠀⠸⣿⣿⣇⠸⣃⠀⠀⢀⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢻⡏⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣷⣾⣶⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⡟⣾⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠈⠛⠿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢷⡀⠀⠀⠈⠉⠉⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢹⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠘⠂⣤⡴⠶⢾⣿⠀⠀⢻⡆⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⡀⠀⡤⠞⠁⠀⢀⣿⡏⠀⠀⠀⢹⡄⠀⠀⠀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠸⡇⠀⠀⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⣼⠟⢹⡄⠀⠀⠀⠀⠈⠀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢀⣼⠏⠀⠀⠗⠀⠀⠀⢀⣠⣶⣿⡟⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣦⠀⣀⣾⠏⠀⠀⠀⠀⠀⠀⢠⣞⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⣫⠿⣗⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⡾⠟⠊⠁⠀⠀⠀⠑⠽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣋⡽⠖⠒⠒⠺⠿⠿⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠒⠶⣦⣄⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⣀⣠⡤⠤⣤⠤⠖⠋⠉⢹⡀⠀⠀⢸⡈⠳⡄⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⢠⡾⠁⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⢸⣧⣀⣻⣄⣀⣀⣹⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⣰⣯⣧⣤⣤⣤⣆⣿⣷⣤⣤⠤⠾⠓⠚⠛⠋⡩⠟⠛⢋⡥⠐⠉⠀⢨⣷⢦⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣀⡤⠾⠶⡖⠖⠛⠉⠉⠩⠛⠉⠁⠀⠤⠂⠁⠀⠀⠀⠀⠀⠀⠈⠀⣀⠔⠋⠀⠀⠀⠀⢫⣠⡀⣠⣠⣼
⢀⣤⠤⠶⠖⠛⠟⠁⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠄⠤⣒⠉⠀⢀⣀⣴⣨⣶⣀⣠⣤⣶⣦⣴⣿⠟⠉⠉⠉
⢿⣤⣤⣤⣶⣿⣼⣷⣲⣶⣿⣿⣛⣻⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠾⢿⣖⣿⠿⠉⠉⡽
⠀⠀⠤⠠⠀⠠⠤⠀⠻⣭⠩⠉⠉⠻⣄⢸⡍⠉⢻⠿⠿⢿⢿⣿⣿⠿⠙⠻⡯⠄⠀⣾⣤⠼⠉⠤⠠⠀⣴⢡⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠙⠲⢤⣼⣀⣀⣀⣀⣻⣀⣀⣀⣀⣷⠴⠖⠋⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡖⠛⠛⠛⠒⠒⠒⠂⡐⠓⡄⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢀⡇⠀⠀⠀⠀⠀⠀⢀⡣⠀⠃⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠒⠉⠉⠄⠉⠑⢄
⠀⠀⠀⠀⢠⠖⠉⠀⣀⠠⠂⠁⠀⠄⠐⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠂
⠀⠀⠀⠀⠇⠀⠈⠀⠈⠀⠀⠂⠀⡀⠀⠰⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣬⡀
⠀⠀⠀⠀⢇⠈⢁⠀⠉⠀⠋⡀⠀⠀⠀⠀⠀⡠⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⡎⠐⠾⠓⢹
⠀⠀⠀⠀⠈⡆⠀⠀⠀⣀⠀⠁⢠⠋⠉⢆⠀⠰⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠠⠀⠀⡧⣀⣀⣀⠜⢦⡀
⠀⠀⠀⠀⠀⠸⡌⠀⣾⠉⠙⠒⠋⠀⠀⠈⠂⠐⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠐⠀⡁⠐⠀⠬⠀⠈⠀⠠⠙⡄
⠀⠀⠀⠀⠀⠀⢣⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠈⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠹⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢀⡠⡶⡻⠃⣿⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠖⣩⠊⡴⠁⠀⣇⠑⠤⣆⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⡰⠁⢰⠁⠀⠀⠈⢦⡀⠀⠉⠳⣽⢦⡔⢢⢀⣤⡀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⣀⣠⡎⠀⠀⠇⠀⢸⠀⠀⠀⠀⠀⠹⡄⠀⠀⠈⣦⣹⠃⢸⠤⠻⢖⠚⠉⡦⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠔⠒⡏⠀⢸⣇⠀⠀⡇⠀⠈⢆⠀⠀⠀⠀⠀⡇⠀⠀⣠⠣⣈⠒⢛⣦⣀⠠⢵⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢄⣱⢄⣾⠀⠑⠒⠚⠢⠄⣈⠷⠤⠠⡤⠚⠉⠉⠉⠀⠏⠉⠣⡀⠀⠑⢦⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠓⠂⠉⢸⡁⠒⠪⠕⣤⠊⠉⠢⠔⠉⠑⠤⠊⠉⠲⠊⠙⢦⠖⠻⢶⣀⣉⠯⠽⠥⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⠏⠀⡏⠒⢶⠐⠸⡆⠀⠐⡄⠀⠀⡆⠀⠀⡛⠀⠀⣇⡤⠚⡉⠀⠠⠀⠀⠂⠀⠠⠉⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠰⠀⠘⡄⠀⢣⠀⠀⠇⠀⠀⡇⠀⠀⡇⠀⡼⠃⠀⠂⠀⠀⣠⢄⠴⠛⢤⣀⠀⢁⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢣⠀⢱⣀⡈⡆⠀⢸⠀⠀⠁⠀⢰⠁⡜⠀⠈⡁⠉⢔⡲⠗⠂⠉⠉⠐⢦⠇⠄⠐⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠲⣧⠄⠠⢔⠂⠘⠿⠁⠀⠈⢷⡀⠀⡆⠀⠀⠀⡸⢠⠅⠈⠀⠀⠂⡈⠣⢄⣀⣀⡀⠤⠊⡀⠀⢠⠲⢄⡨
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠀⠀⠘⡂⠀⠀⠀⠀⠀⢸⠥⠄⠁⠀⠀⠤⠅⠤⠵⡞⠦⠚⢢⠀⠀⠀⠁⠄⠐⢀⠁⢀⠤⠃⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⡸⣁⠀⠀⠀⢀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⠀⠓⠒⠉⠑⠤⠔⠉⠁⠉⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠶⠶⠖⠊⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⣀⣀⣀⣀⡀⠤⠔⠊⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣟⠿⠋⠉⠉⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠉⠙⠛⠿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠋⠁⠀⠀⠀⠐⣿⣏⠀⠀⠀⠽⠿⠁⠀⠀⢠⣴⡀⠀⠀⠙⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠀⢀⣶⣦⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠈⠺⣻⣷⡄⠀⣀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⠀⠀⠀⠘⠀⢀⣠⣶⠾⠟⠛⠉⠛⠛⠙⠛⠛⠷⣶⣄⡀⠀⠀⠀⢀⣀⣤⣼⣿⣿⠿⠟⠛⢻⣷
⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⠀⣶⡧⠄⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣻⣿⣶⡾⠿⠟⠛⠋⠉⢀⡀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠁⠀⣰⡿⠋⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⠿⠿⠛⠋⠉⢀⠀⣠⣴⣦⡐⣿⡛⠃⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⣸⡟⢁⣀⣠⣤⣴⣶⠿⠿⠛⠛⠉⠁⢀⣀⣤⡄⣶⡀⢹⡇⢿⡇⠹⠃⢹⣧⡶⠄⠀⠀⠀⠀⢿⣇
⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⣀⣠⣤⣴⣿⡿⠿⠛⠋⠉⢁⢀⣀⠀⠀⣶⠟⣷⡌⣿⡁⣀⢻⣿⣎⣿⡘⣿⠀⣠⡌⣿⣀⣀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⠀⣀⣀⣼⣿⣷⡾⠿⠛⠛⠉⠁⣀⣠⣄⠀⣶⡀⢻⡇⢿⡆⠀⢻⣇⢬⣧⢹⣿⠛⠈⣿⡘⢿⣧⠹⣧⣼⡇⠘⠛⠛⠀⢀⣀⣠⣤⣿⣷
⠀⢾⣿⠟⠛⠉⠁⠀⣀⡀⣤⡀⢸⣇⢻⡏⠹⣧⢹⣧⠈⣿⡘⣷⠀⠘⣿⡄⢻⡆⢿⣤⣶⠸⠇⠈⠛⠀⢀⣀⣠⣤⣶⣶⣿⣿⡟⠋⠉⠁
⠀⠘⣿⡄⠀⠀⠀⠀⢹⣧⢻⣿⣌⣿⡘⣿⠀⢿⡆⣿⡄⢻⡇⢻⣧⣶⠘⠿⠟⠋⠈⠁⣀⣠⣤⣴⣶⣿⠿⠛⠋⠉⠁⠀⣼⣿⡇
⠀⠀⢹⣷⠀⠀⠀⠀⠀⢿⡎⢿⡙⣿⣇⢹⣧⣼⡷⠘⠻⠟⠃⠀⠉⣀⣀⣤⣴⣶⡿⠿⠛⠛⠉⠁⣽⡟⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠈⣿⡇⠀⠀⠀⠀⠘⣷⠸⡧⠈⠛⠈⠉⠉⣀⣀⣤⣴⣶⡾⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⢠⣾⠟⠀⢀⠀⠀⠀⠀⣼⣿⠇
⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠉⣀⣀⣤⣤⣶⣾⢿⣿⣟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠟⠁⠀⠐⢾⠿⠀⢀⣼⣿⡏
⠀⠀⠀⠀⣿⣧⣤⣤⣶⣾⣿⡟⠛⠉⠉⠀⠀⠀⠈⠛⠿⣦⣦⣤⣀⣀⣀⣠⣤⣴⣶⠾⠛⠁⠀⡀⠀⠀⠀⠀⢠⣾⣿⠏
⠀⠀⠀⠀⠘⠛⠋⠉⠀⠘⢿⣿⣦⡀⠀⠀⠀⠀⠀⣄⡀⠀⠈⠉⠉⠛⠋⠉⠉⠁⠀⠀⠀⠀⢻⢿⠁⠀⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣮⣦⣄⡀⠀⠉⠟⠇⠀⠀⢀⣦⣖⠀⠀⠀⣱⣿⠄⠀⠀⠀⢀⣠⣶⣽⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣯⣰⣤⣀⡀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⢀⣀⣄⣰⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣾⣿⣶⣶⣶⣤⣤⣶⣶⣾⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠉⠉⠉⠁


⡿⢿⠿⢿⠿⡿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣿⣿⡿⣿⣿⢿⣿