⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠶⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿
⠀⠀⣀⣶⣤⣤⠿⠶⠿⠿⠿⣿⣿⣿⣉⣿⣿
⠿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣤⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⠿⣛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠿⠀⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⠀⠀⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠀⠀⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿
⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿
⠀⠀⣀⣶⣤⣤⠿⠶⠿⠿⠿⣿⣿⣿⣉⣿⣿
⠿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣤⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⠿⣛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠿⠀⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⠀⠀⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠀⠀⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿
⠀⠀⣀
⠀⠿⣿⣿⣀
⠀⠉⣿⣿⣀
⠀⠀⠛⣿⣭⣀⣀⣤
⠀⠀⣿⣿⣿⣿⣿⠛⠿⣶⣀
⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣉⣶
⠀⠀⠉⣿⣿⣿⣿⣀⠀⠀⣿⠉
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⣿⣿⣿⠿⠉⣿⣿⣿⣿
⠀⣿⣿⠿⠀⠀⣿⣿⣿⣿
⣶⣿⣿⠀⠀⠀⠀⣿⣿⣿
⠛⣿⣿⣀⠀⠀⠀⣿⣿⣿⣿⣶⣀
⠀⣿⣿⠉⠀⠀⠀⠉⠉⠉⠛⠛⠿⣿⣶
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⣀⣶⣿⠛
⠀⠿⣿⣿⣀
⠀⠉⣿⣿⣀
⠀⠀⠛⣿⣭⣀⣀⣤
⠀⠀⣿⣿⣿⣿⣿⠛⠿⣶⣀
⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣉⣶
⠀⠀⠉⣿⣿⣿⣿⣀⠀⠀⣿⠉
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⣿⣿⣿⠿⠉⣿⣿⣿⣿
⠀⣿⣿⠿⠀⠀⣿⣿⣿⣿
⣶⣿⣿⠀⠀⠀⠀⣿⣿⣿
⠛⣿⣿⣀⠀⠀⠀⣿⣿⣿⣿⣶⣀
⠀⣿⣿⠉⠀⠀⠀⠉⠉⠉⠛⠛⠿⣿⣶
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⣀⣶⣿⠛
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣶⣿⣿⣿⣶⣶⣤⣶⣶⠶⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣤⣿⠿⣿⣿⣿⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⣿⣤⣤⣀⣤⠿⠉⠀⠉⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠉⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠛⠿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⠛⠉⠀⠀⠀⠛⠿⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣶⣿⣿⣿⣶⣶⣤⣶⣶⠶⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣤⣿⠿⣿⣿⣿⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⣿⣤⣤⣀⣤⠿⠉⠀⠉⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠉⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠛⠿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⠛⠉⠀⠀⠀⠛⠿⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣤⣶⣶
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣀⣀
⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿
⣤⣶⣀⠿⠶⣿⣿⣿⠿⣿⣿⣿⣿
⠉⠿⣿⣿⠿⠛⠉⠀⣿⣿⣿⣿⣿
⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣤
⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣿⣿⣿⠿⠉⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⠿⠉⠀⠀⠀⠀⠿⣿⣿⠛
⠀⠀⠀⠀⠛⣿⣿⣀⠀⠀⠀⠀⠀⣿⣿⣀
⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠿⣿⣿
⠀⠀⠀⠀⠀⠉⣿⣿⠀⠀⠀⠀⠀⠀⠉⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣿
⠀⠀⠀⠀⠀⠀⣀⣿⣿
⠀⠀⠀⠀⠤⣿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣀⣀
⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿
⣤⣶⣀⠿⠶⣿⣿⣿⠿⣿⣿⣿⣿
⠉⠿⣿⣿⠿⠛⠉⠀⣿⣿⣿⣿⣿
⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣤
⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣿⣿⣿⠿⠉⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⠿⠉⠀⠀⠀⠀⠿⣿⣿⠛
⠀⠀⠀⠀⠛⣿⣿⣀⠀⠀⠀⠀⠀⣿⣿⣀
⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠿⣿⣿
⠀⠀⠀⠀⠀⠉⣿⣿⠀⠀⠀⠀⠀⠀⠉⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣿
⠀⠀⠀⠀⠀⠀⣀⣿⣿
⠀⠀⠀⠀⠤⣿⠿⠿⠿