⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⢀⣀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢋⣭⡍⣿⣿⣿⣿⣿⣿⠀
⠀⢀⣴⣶⣶⣝⢷⡝⢿⣿⣿⣿⠿⠛⠉⠀⠀⣰⣿⣿⢣⣿⣿⣿⣿⣿⣿⡇
⢀⣾⣿⣿⣿⣿⣧⠻⡌⠿⠋⠁⠀⠀⠀⠀⢰⣿⣿⡏⣸⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠇⢻⣿⣿⣿⣿⣿⣿⡟
⠙⢹⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡿⠟⠁
⠀⠀⠉⠁⠀⠀

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

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

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

⠀⠀⣀
⠀⠿⣿⣿⣀
⠀⠉⣿⣿⣀
⠀⠀⠛⣿⣭⣀⣀⣤
⠀⠀⣿⣿⣿⣿⣿⠛⠿⣶⣀
⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣉⣶
⠀⠀⠉⣿⣿⣿⣿⣀⠀⠀⣿⠉
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⣿⣿⣿⠿⠉⣿⣿⣿⣿
⠀⣿⣿⠿⠀⠀⣿⣿⣿⣿
⣶⣿⣿⠀⠀⠀⠀⣿⣿⣿
⠛⣿⣿⣀⠀⠀⠀⣿⣿⣿⣿⣶⣀
⠀⣿⣿⠉⠀⠀⠀⠉⠉⠉⠛⠛⠿⣿⣶
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⣀⣶⣿⠛

⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣶⣿⣿⣿⣶⣶⣤⣶⣶⠶⠛⠉⠉
⠀⠀⠀⠀⠀⠀⣤⣿⠿⣿⣿⣿⣿⣿⠀⠀⠉
⠛⣿⣤⣤⣀⣤⠿⠉⠀⠉⣿⣿⣿⣿
⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠉⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣛⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠛⠿⣿⣿⣿⣶⣤⠀
⠀⠀⠀⠀⠀⠀⠀⣿⠛⠉⠀⠀⠀⠛⠿⣿⣿⣶⣀⠀
⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⠀⠀
⠀⠀⠀⠀⠀⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⠿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠀