Headman Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠛⠻⢿⣿⣿⣿⣿⡿⠿⠟⠻⣿⣿⣿⣿⣿⣿⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⠃⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⢰⡿⠿⠛⠿⢿⠆⠀⠀⠀⠀⠀⠰⣿⠿⠟⠻⢿⡆⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢿⡇⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⢸⣿⡿⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠘⣿⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡆⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢤⣄⣈⣉⣁⣀⣤⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠉⠓⠒⠒⠋⠁⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⣠⠤⠚⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣿⢿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣻⣾⣿⣾⣿⣿⣿⢿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣟⠿⠇⠘⠿⢟⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡆⠀⣷⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡀⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⣧⣽⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠿⠻⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣛⢿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠿⣿⣻⣾⣻⣿⣿⠿⣿⡽⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⢀⣼⣿⣿⣿⣯⣹⣿⣿⡧⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠏⠀⣀⣙⡙⢛⡿⡻⣿⣿⡿⣳⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠿⠋⠀⡀⠛⠿⣻⣴⣶⣻⢿⣿⣷⣟⣻⠿⠿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡶⣶⢿⣇⠿⡵⣾⣿⣿⢿⣺⣿⣿⡿⣿⣿⣟⣳⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣯⣿⣿⣿⣽⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢛⣹⣿⣿⣿⣻⣿⣭⣿⣿⣿⣿⣿⣿⣿⢿⣫⢛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣛⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢊⡞⠉⠉⠉⠀⡀⠀⣠⣿⡽⠟⣩⢹⣯⢻⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⣿⠀⠀⢼⣷⣿⣿⣿⣿⡆⠴⠋⠁⠀⣰⣡⣼⣹⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⣶⣼⡇⠠⢤⡈⣿⣿⣿⣿⣿⡏⣄⠀⢀⣼⣽⡿⣣⣿⣿⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣠⣀⣾⣤⡿⢆⡀⢀⡜⠞⣯⢠⡌⠙⠋⠈⠻⠛⠁⠺⢿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⡴⣫⣿⣿⣿⣿⣿⣷⠒⠛⠈⣧⢹⣿⣿⣷⡶⣰⣄⠴⠾⠿⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⢰⠃⠛⣿⣿⣟⣻⣿⣿⠿⢀⠆⠨⢻⡏⣿⣿⣶⠻⣧⡰⠒⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢸⣷⡞⠛⢿⣻⣟⢋⣠⣿⣏⢀⡄⡼⠂⣀⣬⣩⣿⣍⣔⣱⣶⣶⣿⣴⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⢿⣿⠏⣡⣬⡙⢿⣿⣿⣿⡿⠠⠾⠟⠿⠃⠠⠾⣿⣿⡿⣿⣿⡇⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⣦⣿⡀⣏⠋⠉⣀⢱⣿⣉⢁⣶⣤⡄⠀⠀⠀⠐⠙⠿⠿⠿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⠘⢦⠸⢿⡘⣿⣿⣾⣿⣼⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣦⣀⡀⠀⠀⢸⢿⣿⣿⣿⡧⠁⠀⣤⣄⠀⠀⠀⣠⣦⣠⣤⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠫⣙⣿⣾⣄⢤⡏⣉⣻⢿⣿⣄⣈⣿⡇⢀⣴⡟⠛⡿⠋⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠒⠌⢿⣿⣿⣿⢿⡿⣿⣴⠁⡀⡉⣻⢷⣿⡿⡀⢀⠀⣠⣤⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠑⢿⡿⠛⠙⣄⠋⢿⡟⣿⡟⡄⣾⣿⣇⣤⣼⣿⣿⣿⣯⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠄⠢⡉⢰⠀⠀⠏⠙⣷⣞⣿⣿⡧⠁⠰⡉⢿⣟⣿⣿⠑⠘⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣼⡴⠖⢦⣼⣦⣘⠀⠀⡼⠻⣿⣿⣃⠀⠀⠀⣬⠁⠀⠙⠀⠀⠆⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠙⢀⣒⣀⢽⣸⣯⣧⡜⠃⠤⣜⣛⣽⣷⡾⣃⠘⢾⣴⣷⢠⡀⢂⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢴⣤⣁⡀⢠⡞⠉⢻⠉⠀⣀⣤⣡⣿⣿⣯⣭⣿⣿⠏⠈⠙⠾⣷⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣍⣀⠀⢀⣵⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠋⠩⣟⢿⡟⢿⣿⣿⡿⢻⠉⠉⠉⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⡀⠈⢳⣸⡍⢻⣧⡀⣻⠀⠀⡥⠴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢌⡁⣧⢀⡇⢠⣿⣴⡟⠰⠺⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⢿⣇⢡⣿⠃⣿⡄⠁⡘⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣼⠏⠀⡏⢿⡀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡊⠁⠀⢀⠇⠈⠓⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠁⠁⠀⠀⠀⠁⠈⠀⠀⠀⠁⠈⠀⠀⠀⠀⠈⠈⠀⠁⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⣴⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⣦⡀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠁⠀⠙⣿⠿⠻⠟⠹⠟⠁⠀⠀⣸⣷⣶⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⢿⡃
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠋⠀⠈⣧
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣏⡞⡵⠀⠀⠀⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣞⡼⢁⠀⠀⠙⠛⠉⠉⠛⠿⠁⠀⠀⠀⠀⠀⠀⢰⠏⢳⡀⢹⡄
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣰⢋⡄⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⢻⣦⠈⠇⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⢫⠄⠀⠀⠀⠀⠀⠀⣿⣀⡈⣷⠀⠀⠀⢀⣨⡉⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣯⣞⡴⠀⠀⠀⠀⠀⠹⠿⠇⠉⠀⠀⠐⢋⡿⠁⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢡⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣾⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⣠⠞⢶⣾⠴⠿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢛⡛⠛⢿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢐⣦⠀⠀⢸⡇⠀⠀⠀⠀⣰⠞⠁⢴⡄⢹⣖⣛⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠈⢹⣟⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠶⣤⣤⣤⡴⠏⠙⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⠀⠘⢧⡼⢋⠉⢹⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⣉⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⢛⣡⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⣾⡀⣠⡴⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⠖⠀⠀⣰⡟⠀⠀⠀⠀⠀⣼⣧⠹⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠟⠀⠀⠀⠀⣠⣾⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⣀⣰⣋⣁⣀⣀⣀⣴⣶⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣶⠲⣄⡈⠙⠻⢷⣶⣶⡾⠿⣿⡉⠉⣻⣩⣽⣿⣯⣯⣿⣭⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣗⢬⡓⢬⠙⠶⠶⠋⢉⣿⣿⣶⣌⣻⣷⣼⣿⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣕⠪⠂⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣶⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡿⠿⠟⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣽⣿⣿⣿⣿⣿⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠛⠉⠉⠀⠉⠙⠻⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⢠⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⣿⣿⣿⣿⣷⣾⣿⣿⣶⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠈⠉⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠘⠿⢶⣦⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⢀⣠⣤⡤⢀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠛⠃⠀⠉⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣋⣉⣉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠣⣄⠈⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠽⢿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠠⣤⣤⣤⣤⣤⣶⣾⡿⠁⠀⠀⠙⢿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠒⠒⠒⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠚⠛⠛⠛⠛⠒⠶⠶⠚⠛⠛⠛⠛⠓⠶⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡴⠛⠛⠛⠳⣦⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⣠⠟⠀⠀⠀⠀⠀⠈⢷⡀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢀⠀⠀⠀⣶⠀⠀⢀⡾⣿⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠘⡿⣧⠀⠀⢰⣆⠀⠀⢀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⣾⠀⠀⣸⢻⡇⠀⣸⠃⣿⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⡧⢸⡆⠀⢸⢻⡆⠀⢸⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣿⡄⠀⡟⠈⣇⢀⡟⠀⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡇⠀⣷⠀⣿⠀⣷⠀⢸⣿⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠐⡇⠀⠀⠀⣤⠰⡟⢷⢸⡇⠀⢻⣼⠃⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⢸⣶⠇⠀⢻⢀⡟⣿⠀⡆⠀⠀⠀⣿
⠀⠀⠀⠀⢰⡇⠀⠀⠀⣿⣦⡇⠘⣿⠇⠀⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⢸⡿⠀⣿⣼⡇⠀⠀⠀⣿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠹⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⡇⠀⠀⠀⣿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⢀⣀⣀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣏⣀
⢀⡴⠋⠉⠉⠹⣦⡀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡼⠋⠉⠙⢷
⣼⠁⠀⠀⠀⠀⠈⢳⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⠏
⣿⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⢻⡀
⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠈⠻⣦⡀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠉⠛⠛⠋⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠓⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠞⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣙⣛⣲⣶⣶⣶⣶⣶⣶⣞⣛⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠿⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠙⠛⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡄⠀⠀⣀⣤⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⢦⣄⡀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠁⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⣻⠏⠀⠀⢀⡴⠞⠛⠛⠻⣆⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠛⠶⣄⠀⠀⠸⣿⠀⠤⡀
⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠈⠁⠀⠀⢹⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣶⣶⣶⣮⣴⣦⣄⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⣰⣿⡿⠋⠂⠠⠤⠬⠭⠭⠭⠀⠙⢿⣷⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⢰⣿⣿⠁⠀⠀⠀⠠⢤⣤⠤⠀⠀⠀⠘⣿⡆⠀⠀⣰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣄⣀⣀⣀⣀⣤⣤⣤⣀⣀⣠⣼⣿⣧⣴⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⢠⣾⣦⡀⠀⠀⣠⡄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣄⠀⢰⣿⣿⡄⠀⣿⣿⣿⡇⠀⣼⣿⣿⠀⢀⣴⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⡀⢿⣿⣿⣧⢸⣿⣿⣷⠀⣿⣿⣿⡧⢰⣿⣿⣿⢀⣾⣿⣿⡏⣠⣴⣾⡆
⠀⠀⠀⠀⠀⠀⣤⣤⣈⣿⣿⣿⣦⣿⣿⡿⣷⣟⠻⢿⡆⣿⢦⢟⣷⣿⠿⢟⣯⡾⢿⢿⣟⣴⣿⣿⣿⣀⣤⣶
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡝⠻⣧⠀⠘⢿⡄⠀⢻⣿⠀⠈⣿⠃⠀⣸⡟⠀⢀⣾⠟⢻⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠰⣿⣷⣦⣝⣿⣿⡿⡻⣧⡠⠘⢧⠠⠈⣧⢀⠀⣿⠀⢰⡏⠠⢀⡿⢀⢀⡾⢁⢀⡼⣿⢿⣿⣿⣥⣶⣿⣿⠇
⠀⠀⠀⠀⠈⢿⣿⣿⣿⠿⣦⡈⠈⠳⣔⠌⢧⣣⢹⣆⣄⣿⡄⢸⣧⣶⣾⣃⣦⣾⡠⢢⠋⠀⣡⡶⣟⣿⣿⣿⡿⠂
⠀⠀⢿⣿⣷⣶⣽⣷⣄⠑⢌⠙⢦⣱⣼⣿⣿⣿⣿⣿⣿⣿⣷⢾⣿⣿⣿⣿⣿⣿⣿⣷⣢⡞⠉⠄⢉⣴⣾⣷⣾⣿⣿⠟
⠀⠀⠀⠙⢿⣿⣿⣯⠙⠳⢤⣑⣾⣿⣿⣿⣿⣿⣟⣿⡛⣿⠁⢘⡏⣸⣏⣿⣿⣿⣿⣿⣿⣖⣡⠴⠛⠩⣾⣿⣿⠿⠁⡀
⠠⣶⣿⣿⣷⣾⡿⢷⣤⣀⠢⢽⣿⣿⣿⢟⣣⣧⣽⣿⣷⣟⣿⣻⣻⣿⠿⣷⣾⣿⡯⣿⣿⣿⠕⢂⣠⡾⠿⢿⣶⣿⣿⣿⡿
⠀⠀⠙⠻⠿⢿⣧⣀⡀⠬⣿⣿⣿⣿⣿⢿⣻⣿⢻⣯⢹⣿⢸⡿⢸⡏⢹⡟⣻⣽⡿⣟⣯⣿⣿⣷⠖⢀⣠⣿⠿⠿⠛⠋
⣤⣶⣿⣿⣿⣟⡛⠛⢙⣾⣿⣿⣿⣟⣵⠻⣦⢻⣆⣿⣬⡿⣼⠧⠾⠧⢿⣡⡟⣰⠟⣮⡻⣿⣿⣿⣯⠉⠉⠛⣿⣿⣿⣿⣷
⠈⠛⠛⠛⢛⣻⣿⠷⠶⣿⣿⣿⣿⣿⣜⣳⢝⣭⠷⠾⢿⡛⠿⠟⠛⠛⠛⠶⣭⡻⣾⣣⣿⣿⣿⣿⣿⡶⠿⢿⣛⣛⠛⠛⠋
⠀⣠⣾⣿⣿⣯⣤⣤⠾⣿⣿⣿⢋⡙⢻⣿⣿⡶⢶⣦⣴⣿⣿⣿⣷⣶⣾⠿⣿⣿⣿⡿⢉⡹⣿⣿⣿⠶⣤⣤⣾⣿⣿⣷⣄
⠛⠿⠻⢟⣻⠿⣋⣤⣾⣿⣿⣿⡘⠃⣻⡿⠿⠻⢙⣯⡿⣿⠁⠙⣿⢿⣝⡋⠛⠟⢿⣧⡘⢡⣿⣿⣿⣷⣤⣝⡿⣝⡛⠟⠿
⠀⣠⣶⣿⣿⣿⣿⠏⣥⣾⣿⣿⣿⣿⣿⡀⠀⠀⠈⠉⣠⣿⠀⠀⣿⡄⠉⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣮⠹⣿⢿⣿⣿⣷⣄
⠘⠛⠛⢛⣩⣞⣷⣿⢟⣿⢋⣿⣿⡟⢹⣿⣶⣷⠀⢠⡆⡙⠀⠀⠋⢠⡀⠙⣿⣶⣿⣿⣿⣿⢿⡙⢯⡻⣿⣾⣿⣬⡙⠛⠛
⠀⠀⣰⣿⣿⣿⡟⣡⡟⠁⣨⢷⣿⡇⢸⣿⠻⡿⠀⠞⠁⠙⠲⠖⠋⠈⠳⠰⣿⢿⣿⡇⢿⣿⡶⣅⠈⢻⣌⢻⡿⣿⣿⣄
⠀⠰⠿⠛⣱⣿⣿⠏⠀⢰⠃⣼⣿⡇⢸⣿⣀⡇⠀⢀⠤⠴⠤⠤⠦⠤⠀⡄⢹⣸⣿⡇⢸⣿⣧⢘⡆⠀⠙⣿⣿⣮⠛⠻⠆
⠀⠀⠀⣼⣿⠟⠁⠀⠀⣿⢠⣿⣿⣧⣼⣿⣿⣷⣼⣤⣽⠿⠛⠛⠿⣯⣤⣧⣾⣿⣿⣧⣾⣿⣿⢈⣿⠀⠀⠈⠛⢿⣧
⠀⠀⠀⠋⠀⠀⠀⠀⢠⣟⢸⣿⡯⠀⣿⣿⣿⣿⣿⣦⣀⡀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⠀⣿⣿⡄⣿⡄⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣼⣿⡇⢠⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠀⢻⣿⢢⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣧⢹⡿⣿⢿⣍⡛⠛⠋⣿⣿⠿⡏⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣼⣿⠘⣿⠀⣧⠙⢧⡈⠙⠁⢀⡼⠋⣸⠀⣿⣿⣿⣿⣿⣟⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠂⣿⣆⣿⡄⠀⠈⠀⠀⠈⠀⢀⣿⣠⣿⠃⣽⣿⣿⣿⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠇⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠃⠀⣸⣿⡟⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⠀⠹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⢿⣿⡟

⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⣠⠴⢒⣶⣛⡥⠴⠖⠒⠒⠛⠉⠉⠑⠒⠒⠒⣶⣤
⠀⠀⠀⠀⠀⢠⢿⠀⠀⣠⠖⠉⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣖⣉⣉⣀⣀⡀
⠀⠀⠀⠀⠀⡞⠸⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠠⣄
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣆
⠀⢀⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣌⠉⠁
⠙⠹⢭⡉⠓⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⢉⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⢰⠃⠀⠀⠀⡴⡆⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⡇⠀⠀⠀⣸⠀⠹⣄⠀⠀⢸⣧⠀⠀⢠⡷⡄⠀⠀⠀⣦⡀
⠀⠀⡇⠀⠀⠀⡟⠀⠀⠈⠓⠤⣈⣇⠳⣄⠀⡇⠈⠢⣄⠀⠘⣟⠢⣀
⠀⠀⠱⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠈⠙⠲⠬⣦⡈⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠈⡆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠉⢳⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⢹⡀⠀⣿⠀⢠⠔⢒⣒⠲⣄⠀⠀⠀⠀⠀⠀⡴⣋⣉⣈⣉⠳⣄⠀⠀⠀⢸⡄⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⢧⠀⣿⠀⠿⠊⣉⣉⠉⠙⠀⠀⠀⠀⠀⠈⠉⢁⣠⣤⣈⠙⠾⠀⠀⠀⢸⡇⠀⠀⢀⠞
⠀⠀⠀⠀⠈⢇⣿⠀⣰⠋⠁⢿⣙⣦⠀⠀⡀⠀⠀⠀⢰⠃⠀⠘⠤⢿⠀⠀⠀⠀⢸⡇⠀⢠⠏
⠀⠀⠀⡴⠒⠚⡇⠀⠙⢶⣄⣀⡤⠏⢀⠞⠉⡆⠀⠀⠀⠛⠦⠤⠴⠋⠀⠀⠀⠀⢸⣃⡴⢛⡭⣝⢢⡀
⠀⠀⢸⢀⡶⣖⣿⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⣴⣟⡉⠙⠇⣇
⠀⠀⢸⠘⢱⠋⣿⠀⠀⠀⠀⠀⢀⡟⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠛⠁⠙⡄⠀⡏
⠀⠀⠈⢧⡈⢧⣽⠀⠀⠀⠀⠀⡼⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠸⡀⠀⠜⠀⡼⠁
⠀⠀⠀⠀⠙⠢⢼⠀⠀⠀⠀⢀⡇⠀⠀⠀⠈⠁⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢭⣭⠤⠚
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠈⣆⠀⠀⣀⡠⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⣀⡤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠓⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠤⣀⣀⣀⣀⣀⠴⠋⠉
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠈⠀⡀⠈⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠰⠀⠚⠍⠉⢙⠉⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠀⠄⠀⠀⠀⠈⢧⡀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠋⠛⠛⠳⢶⣾⣷⢊⡅⠈⠀⠈⠈⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠐⠀⠀⠀⠀⠀⠀⠀⠙⠁⠁⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡙⠀⠀⠀⠀⠀⠀⠀⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⡠⠂⡡⢊⡀⠀⡀⠀⠀⡀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠃⡀⠰⠿⠃⡄⢿⠆⠀⠽⠄⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠀⠀⠀⠀⠓⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⡡⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⠶⠶⠶⠺⢿⣿⣷⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⡏⠀⠄⠀⠀⠀⣿⣿⠟⠉⠈⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⢖⣘⣯⣽⣯⡻⣷⡀⠀⢸⣶⣶⣿⠄⠀⡀⢸⣿⡿⣿⣿⣲⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⣶⠞⢛⣉⣸⣿⣌⡻⣮⡗⠀⠂⣸⣟⡅⠘⠀⠀⠼⣇⢻⣿⣿⣭⣛⡾⣏⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣸⢷⠞⠛⠉⣡⣹⡷⣎⠿⠀⠀⣆⠙⢷⠀⠀⢰⣧⠹⣾⣿⣤⣍⡽⢷⡜⣧⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢠⡏⡿⢶⡾⡟⠻⣿⣷⣉⢿⡇⢘⠻⣿⢦⡆⢀⣮⢻⣷⣛⣷⣯⣸⣷⠙⣷⣙⣧⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢁⡟⣸⢃⡿⣿⣷⣾⣿⣿⣿⣎⢿⣾⣦⡈⠻⣧⣼⡙⣧⣼⣿⣶⣤⣿⣻⣷⡾⣧⡼⡞⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣡⣏⡾⢠⣿⣿⣿⣿⣿⣿⣿⣎⢿⠻⢿⣦⣼⣯⢿⣽⣿⣿⣿⣿⠋⠙⠁⢫⣼⣗⢷⢾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⢣⡏⣽⠓⣾⡉⣿⣿⣿⣿⣿⣿⣿⣮⣷⣄⣹⣿⣿⣾⣿⣿⣿⣟⢁⣀⣀⣈⣼⣿⣿⡻⡾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢋⡟⢩⡟⢲⣿⣽⣿⡿⠛⠉⡑⢺⠦⣬⣉⣏⠙⡟⠿⣿⣦⣈⣉⠛⠛⡷⠶⢧⠤⢬⣿⣽⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⠋⣿⢉⣻⣇⣸⣋⠀⠀⠀⡟⢻⠶⣾⣬⣍⡙⡛⠒⠶⢼⣍⡙⠷⠲⣦⣤⣠⣀⣀⣇⣀⣤⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡟⢸⣏⣠⣿⣿⣿⣻⠿⢭⣿⡛⡿⢶⣦⣄⣍⠉⠛⠳⡷⣴⣌⣙⠓⠶⣤⣄⣈⣁⢈⣉⣀⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⣾⡇⢈⣿⣿⠷⣭⣹⠷⢤⣏⠉⠟⠳⡿⢿⣿⣶⡶⠤⣬⣉⣛⠻⢶⣦⣀⣉⠉⠉⢉⣩⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⣿⠂⠁⢿⣟⠷⣤⡟⠳⢦⣍⡙⠗⢲⠆⢠⣍⣉⡋⢸⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣥⣀⠀⣿⣄⢈⣛⣶⣦⣬⣽⣷⡾⡖⠞⢿⠿⠿⠛⠛⠉⢙⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡿⡿⠷⠾⠶⠶⠧⣼⣭⣇⡀⠀⢸⣴⣶⠶⠿⠛⠛⠉⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠟⠛⠛⠲⠿⠶⠶⢾⠀⠀⠀⠸⣇⣤⢄⣴⡶⠾⠟⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠈⠁⠀⠀⠀⠀⠈⠈⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⠿⣿⠁⣶⡎⢻⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣄⡀⣾⠉⢿⡄⠲⢤⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣝⣺⣕⡦⠴⠛⠻⣿⣶⣦⡝⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠮⢽⠯⢟⣫⣤⣔⠊⠙⠛⢦⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⣽⡞⠀⢾⣷⠄⣸⠿⣟⡠⣤⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠂⢩⣿⡥⠌⣿⣇⣀⡤⣿⡻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣖⣠⣤⣖⣮⣟⣳⣽⣳⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⠀⢈⡹⠿⡛⠯⢟⠮⠿⡷⠽
⣿⣿⣿⣿⣿⣿⣿⡿⢁⣤⣾⣿⠞⢠⣤⠤⠘⠳⣾⣧⣄⡹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⡾⠟⠋⠉⣭⡿⢛⣻⣿⣍⠉⠙⠻⣧
⣿⣿⣿⣿⣿⣿⣿⠃⠛⢿⣿⣿⣄⠐⠿⠟⠀⣠⣿⣿⠟⠃⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣥⡀⠀⠈⢿⣯⣕⣤⣿⠟⠀⠀⣠⣼⡆
⣿⣿⣿⣿⣿⣿⣿⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣲⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⢚⣿⣟⣛⠛⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠞⣋⣭⠤⢶⡺⠉⢠⣤⠈⠳⣌⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣛⡩⠔⠚⠉⠀⠀⠀⣈⣇⠀⠈⣽⡄⠀⢿⠜⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⣋⠕⠊⠁⣀⠀⠄⠀⠀⢀⠀⠈⠘⣧⣦⣄⡐⠼⠋⡀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⡥⠔⠉⠀⣀⠀⠀⠉⠀⠢⡄⠁⠰⠀⠄⠀⠀⠉⠁⠀⠀⠀⢃⡀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⢉⠰⠂⠁⠀⠀⠀⠀⢠⠀⠰⣠⠀⠎⠸⡀⠊⡀⠈⠀⠀⠀⠀⠀⠀⠀⣘⣧⠘⣧
⠀⠀⢀⣀⣀⣀⣀⣀⣤⠤⠶⠖⠛⡩⠄⠒⠈⠀⠀⠠⠐⠀⢀⠀⠀⠀⡇⠂⠀⢣⠐⡀⢣⠈⠘⡄⢀⠀⠀⠀⠀⠀⣠⠽⢿⡄⠹⣆
⠀⠀⢸⡇⢡⡥⠼⠒⠶⠦⣄⡈⠁⠀⢀⠀⠀⠀⢀⠀⢀⡁⠘⡘⡆⠄⠹⠘⡀⠈⣇⢡⠘⠶⠃⢉⡡⠀⠀⠀⠀⠀⡇⢸⣦⠹⡆⢹⡄
⠀⠀⠀⣷⠀⡇⠀⠲⣶⡆⠘⡇⠠⠀⠠⠀⠀⡄⠰⡀⣋⡀⠀⡇⢡⡌⠄⢃⣉⠕⠘⠋⢠⣀⣠⣌⠀⣀⣀⠤⠔⢒⣙⣲⣴⣞⣁⣈⣧⡀
⠀⠀⠀⠘⣇⠙⢄⠀⠼⠧⣠⣷⠂⠀⠘⡄⠠⠃⠐⣷⠀⠄⢀⡇⠀⠘⠶⠀⠀⠤⣀⠤⠛⢉⡠⢈⣈⣥⣴⠶⠿⣻⣛⣛⠛⠛⣯⠉⠁
⠀⠀⠀⢀⣘⣦⠀⠙⠒⠚⠟⠉⠀⠀⠀⢳⠀⠶⡀⢹⣇⢉⡠⠷⠊⠀⢀⡠⠔⠉⣀⠤⣊⣥⠶⠿⠿⠁⢲⣲⠟⢉⣭⡉⠳⡄⢹
⠀⠀⣠⢺⡇⢹⡎⠠⢱⠄⠀⠀⠀⠀⠀⠀⣇⡀⠱⠖⠁⠀⠀⢀⡠⠒⠁⡀⢔⣪⣷⡟⠫⠀⠀⠀⠀⠀⣈⡁⠀⢘⣻⡀⠀⣿⢸⡀
⢀⡔⠻⢸⡇⢨⢿⡀⠀⢾⡄⣀⣀⡀⠈⠀⠈⠠⠀⠀⢰⠦⠂⠁⠠⢐⣯⡶⠛⡡⠀⠐⠂⡤⠀⠀⠖⠄⠐⢷⣄⡀⡉⣄⡴⠋⠘⡇
⣾⢐⠀⠈⣧⠸⣌⣧⠀⡼⠉⠠⣤⠙⣦⠀⠀⠀⠀⣀⠓⢀⣰⣴⢾⠋⠀⢃⠰⠐⢲⠐⠊⢱⠀⣰⠃⠁⠀⠈⠙⠉⠉⠁⠀⢇⠀⣧
⢻⠘⡇⠀⢹⡀⠈⠛⣶⠀⠳⣄⠙⢂⡾⢠⠀⣂⣭⣶⠞⠋⠁⣼⠘⠂⡄⢸⠀⠀⢸⡆⡀⢸⠀⡴⡄⢰⠀⠀⠀⠀⠀⠀⠀⣿⡀⢿
⢸⠀⡇⠀⠘⣇⠀⢘⡜⠶⠶⠶⠿⠿⠖⡟⠛⣏⠈⣷⠘⣁⣀⡇⠀⠃⠐⢸⠀⠂⡀⡇⠃⠸⠆⢃⣃⠈⠀⢀⣀⠀⠀⠀⢒⣿⡇⢺⡇
⢸⠀⢹⠀⠀⣿⠀⠀⣶⠀⠀⠀⠀⠆⠀⡧⡤⢸⢠⠟⠠⠤⠼⠧⠆⠈⠓⠈⠉⠉⠁⠙⢉⡴⠋⠁⠀⠀⠀⠀⠀⠉⠒⢎⣭⠙⢧⠘⡇
⢸⠀⢸⠀⡀⣿⡀⢀⡝⢉⣉⠑⣄⠀⠀⠀⠀⠀⠀⣄⣠⣀⣄⠀⡀⠠⠤⠤⠤⠤⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡬⠭⠥⣝⣰⠷
⢸⡀⠀⡀⠁⢸⣇⠈⣇⠀⢿⠀⣿⠀⠀⠀⢀⣀⠫⠉⠁⠀⠀⠀⠤⠤⠤⠤⢤⡄⢰⠁⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠸⡇⢣⠃⠸⠀⣷⣀⣈⣱⣰⣾⣥⣯⣤⠤⠴⠶⠶⠶⠶⠖⠚⠛⠛⠛⠛⠛⠉⠃⡆⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⣧⠘⠈⠀⡶⠭⠭⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠸⡄⣣⠿⢥⣄⡤⠤⠤⠶⠖⠒⠂⠀⠉⠉⠉⠉⠀⢀⣒⣒⣒⣀⣀⣀⣈⣥⠥⠽⣦⠀⠀⠀⢸⠁⠀⠀⠇⡄⠀⠀⠴⠀⠀⠘⠂⠘⠀⠄⠀⠸
⠀⠀⠱⠏⠠⠤⠤⠴⠒⠒⠒⠒⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⢸⠀⠄⠘⠀⡇⠀⣐⠀⠀⡀⠀⢰⠀⠀⡂⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⡆⠀⠁⠈⠈⠁⠙⠀⠉⠈⠉⠈⠀⠁⠙⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣶⣶⣶⣶⣶⣯⣥⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⡀⠀⣀⠀⠀⣀⣀⣀⣀⡤⣤⣠⢤⣄⣀⣀⣠⣤⣤⣤⠀⡔⡖⣿⣱⣽⢠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⡼⠿⠘⠁⠀⠓⠈⠐⢛⠛⣫⠏⡇⢟⡕⠙⠟⠛⠉⠉⠉⠉⠉⠁⠉⠩⠤⠀⠉⣼⣯⣿⠅
⠀⠀⠀⠀⠀⠀⢀⢔⡕⠁⠀⢀⢤⡠⡀⠀⠀⡰⣡⣾⡟⡼⢱⢿⡇⠀⡆⠀⠀⢠⣠⣤⣤⡄⠀⠀⠀⠀⡇⢩⣏⣿⡄
⠀⠀⠀⠀⠀⡠⡣⠋⠀⠂⠀⠀⠂⠑⠁⠀⠀⣿⣿⣧⢊⡆⣿⣿⡇⢠⠃⠀⠀⠊⠛⠛⠛⠀⠀⢀⠀⡜⡀⣾⣿⣷⠃
⠀⠀⠀⠀⡔⣵⣅⣤⣤⢠⢂⡀⡴⠴⢂⣀⣀⣰⡿⢃⢪⡇⣿⣫⣄⣁⣀⣀⠃⣀⡀⢃⣐⣛⣫⠭⡜⣸⡞⣼⣿⠃
⠀⠀⠀⢬⣬⣭⣿⠿⣶⠶⣶⣮⣭⣥⣭⣍⣙⣻⣣⣇⣬⣇⣿⣭⣿⣿⣿⣿⣿⣿⣿⣯⡭⠼⠶⠶⡾⣻⣿⣿⠁
⠀⠀⠀⢸⢻⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣗⣒⣶⠿⣿⣄⣀⣈⣭⣙⣶⣖⣶⣿⣿⠇
⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠛⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠿⠿⢯⣿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠉⠙⠻⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠈⠻⣿⣦⣀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⢀⣤⣄⣀⣀⡴⢦⣀⣠⣿⡿⠛⠉⠛⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⣠⠞⠁⠈⠉⢁⣠⣶⡿⠟⠉⠀⠀⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⢀⡾⠁⠀⠀⣠⣴⣿⠟⠉⢀⣠⠶⣤⣀⣀⣠⡄⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⢀⡴⠋⠀⣀⣴⣿⠟⠋⢀⣠⠶⠋⠁⠀⠀⠉⠉⠁⠹⣦⠀⠘⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⣀⣴⣾⠿⠋⠀⢠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⣤⣤⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠄⠀⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⢀⣤⣾⡿⠛⠁⣀⠀⠀⢻⣦⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢋⣠⣶⡿⠛⠁⢀⣴⠞⠉⠀⠀⣼⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⡿⠟⠉⢀⣤⠞⠋⠀⠀⠀⠀⠀⠹⣿⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⢀⣠⣶⡿⠟⠁
⠀⠀⠀⠀⢠⣾⣿⣿⠟⠉⠀⠀⠸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⢀⣠⠶⠋⠁⣠⣴⡿⠟⠉
⠀⠀⠀⣰⣿⠋⢸⣿⡀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣶⣤⣾⡟⠀⠀⠀⠛⠁⣠⣴⣿⠟⠋
⠀⠀⠀⢿⣧⡀⠀⠹⣿⣄⠀⠠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠻⠀⠀⣀⣴⣾⠟⠋
⠀⠀⠀⠈⠻⢿⣦⣄⠘⢿⣧⡀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠀⢀⣴⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠙⢿⣷⣌⠻⣷⣄⠀⠻⣄⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⢀⣤⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⠀⠙⠛⠉⠙⠳⣦⠞⠋⢀⣠⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⡀⠀⠀⠀⠀⢀⣠⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣆⣀⣠⣴⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣶⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠉⠁⠀⠀⠀⠀⠀⠉⠉⢛⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣀⣀⡀⠀⠀⢸⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣶⠿⠛⠛⠉⠉⠉⠉⠉⠙⠛⠿⣷⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⣤⣤⣤⣄⣀⣤⣤⣴⠶⠛⠋⣀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⣁⣠⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣤⣾⠿⠟⠛⠻⠿⣶⣤⡐⢶⣶⣶⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⡉⠙⠛⠻⠿⠿⠿⠏⣰⡿⢋⣤⣶⡿⠿⢿⣶⣄⠙⢿⡆⠹⠿⠿⠟⠛⠋⢁⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣶⣶⣤⡄⢸⡿⢡⣾⣿⡏⢰⣶⣦⣽⣿⣷⡀⣴⡄⢠⣤⣶⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⡇⣿⡇⢸⣿⣿⣷⣬⣈⡙⢿⣿⣿⡇⠘⠃⢸⣿⡿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⢸⣷⣶⣦⣤⣤⣤⣄⢸⣷⡈⢿⣿⣏⠻⠿⠟⣸⣿⡿⢁⣿⠇⣀⣀⣤⣤⣶⣾⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⠻⣷⣌⠛⠿⣷⣤⣾⠿⠋⣠⣾⠏⣼⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣧⡌⠛⠿⣶⣦⣤⣴⣶⠿⠛⠡⠾⠿⠿⠿⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣶⣿⣿⣿⠿⠿⢿⣷⣶⣦⣤⣀⣠⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠛⠋⢉⣁⣀⣀⣀⡉⠻⢿⣿⣿⣦⡀⠈⠙⣿⣿⣿⣿⣷⡙⣿⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠋⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣷⣤⡹⣿⣿⣷⡄⠀⠈⢻⣆⠻⣿⣇⠘⠃⠀⢀⠀⠹⣅⠁⠁⠀⠻⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⣴⣿⡿⠟⠁⣠⣴⠿⠟⠛⠋⠉⠉⠉⠛⠻⢿⣿⣿⣷⣌⢿⣿⣷⡀⠀⠀⢿⡀⠙⣿⡄⠀⠀⢸⡆⠀⣿⡆⠱⣆⠀⠈⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠚⠉⠀⢀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠙⢿⣿⣿⣾⣿⣿⣧⠀⠀⢸⡇⠀⠹⣧⠀⠀⣸⡇⠀⣿⣷⠀⢻⡆⠀⢸⣿⣿⣿⣿⣿⣄
⡀⠀⠀⠀⠀⢸⣧⣶⣶⠶⠂⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠈⢿⣿⣿⣿⣿⣿⠀⢸⣄⡇⠀⠀⣿⡇⠀⣿⠃⣰⣿⡿⠀⢸⣷⠀⠀⣿⣿⣿⡇⢻⣿⢆
⡟⢢⡀⠀⠀⢸⠟⣋⡀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠘⣿⣿⣿⢿⣿⡆⢸⣿⠀⠀⠀⣿⣇⣸⡟⣰⣿⣿⠇⠀⣼⡏⠀⢰⣿⣿⣿⡇⢸⣇⣘
⣿⣆⠙⠢⠤⠶⠞⠋⣀⣴⣿⣿⣿⣿⣿⢿⣿⣷⣤⡉⠙⢿⣿⣿⣿⡄⢹⣿⣿⠘⣿⠀⢸⣿⠀⠀⢰⣿⣿⣿⣾⣿⡿⠃⠀⣸⡿⠁⢀⣾⣿⣿⠿⠓⣛⠛⠿⠷⣄
⢸⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣧⣤⣈⡉⠛⢿⣤⠀⠙⢿⣿⣷⠈⣿⡟⠀⠟⠀⣿⣿⠀⢠⣿⣿⣿⣿⡿⠋⠀⢀⣼⠟⠁⢠⣾⡿⠋⠁⠀⡀⠈⠙⠻⣶⣾
⠀⢻⡿⠿⠿⠿⠿⢿⣿⣿⡿⠿⠿⠤⠄⠈⠉⠛⠻⠶⠌⠷⠄⣀⣹⣿⡀⡿⠁⠀⠀⣸⣿⣿⣴⣿⣿⣿⠟⣉⣀⣠⡶⠿⠧⠄⢶⠻⣿⡇⠀⠀⠀⠈⠻⢶⣤⡀⠹
⠀⢘⠛⠛⠛⠷⠶⣶⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠻⣿⣦⡀⠀⠀⠀⠀⠙⢿⣷
⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⡈⠻⣿⣶⣦⣤⣄⣀⡈⠻
⠀⣿⣿⣿⡿⠿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣤⡀⠉⠛⠿⣿⣿⣿⣿
⠀⢹⣡⣤⣴⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣶⣤⡀⠈⠙⢿⡇
⠀⠈⣥⣴⣶⣿⡟⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡝⢿⣿⣿⣍⠙⠛⢷⣄⠀⠂
⠀⠀⠿⠟⢋⣽⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⠀⣀⠀⢀⠀⠈⢿⣄⠙⣿⣿⣷⣄⠀⠉⢳⠆
⠀⠀⢶⣿⣿⢿⠀⠀⠀⡌⠀⣴⣿⣿⣿⣷⣶⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⢷⡄⠀⠀⠈⣿⣦⠈⢿⡝⢿⣧⡀⠸⠃
⠀⠀⠸⠋⠀⡀⠀⠀⠀⠁⠸⠛⠉⠉⠛⠛⠛⠻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠛⠛⠛⠋⠉⠀⠈⠉⠃⠀⠁⠀⠀⠀⣿⣿⣷⡀⠻⣆⠙⢿⠇
⣠⠞⠒⠻⢄⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠀⠄⢀⠉⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⣀⣀⣀⣤⡤⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠹⣿⣿⣤⠬⢷⡞
⣇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⠠⠝⠟⣋⠛⠛⠷⡇⠸⣿⣿⠀⠀⠀⠀⠀⠀⢠⠎⠀⠠⠞⠋⠙⣩⡉⠛⠛⠄⠀⠀⠀⠀⠀⠀⠀⠘⣦⡈⢻⡏⠀⠀⢹
⣿⣦⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣉⣤⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠘⢆⡀⠀⠀⠀⠰⢤⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣰⡶⢤⡄
⢹⣿⠻⣦⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣴⢻⣷⠀⡇
⠸⣿⠀⠈⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡿⢇⠸⡇⢸⡇
⠀⢿⡄⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⡆⣷⠘⡇
⠀⠸⣷⠀⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣁⣠⡇⡏⢠⠁
⠀⠀⢿⡆⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⣾⠛⠉⣠⠏⢸
⠀⠀⠘⡃⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⢠⡿⠐⠋⠁⣰⠋
⠀⠀⠀⠻⣄⠀⣸⡟⣷⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠁⠀⠐⠄⠶⡄⠀⢠⠶⠂⠀⠾⠃⠀⠀⠈⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠠⠶⠊⠁
⠀⠀⠀⠀⠈⠉⠉⣷⠘⠇⠀⠀⠀⠀⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣞⠛⠛⠛⠛⠛⠛⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⣻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⢠⠀⠀⠀⠀⢸⠀⠈⢿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⡟⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠘⣇⠀⠀⠀⠈⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠸⣧⠀⠀⠀⠂⠀⠀⠀⠙⢏⣁⠀⠀⠀⠀⠀⠀⠀⠉⢉⠿⠟⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡹⣦⠀⠀⠀⠀⠀⠀⠒⢶⣤⣤⣤⣤⣤⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣇⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⢀⡾⠃⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣁⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⢦⣤⣤⣤⣀⣀⣀⣀⣠⣤⣤⡴⠶⠚⠋⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⡏⠀⠉⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⣿⣙⠒⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⣿⣉⣤⣴⣿⣿⣿⠿⣿⣿⣿⣯⣻⣿⠛⠛⣼⣟⣻⣿⣿⡟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠓⢲⣿⡿⣿⣧⣴⣶⣿⣶⢟⠿⢶⣴⣿⣧⣴⣶⣯⣽⣿⣅⣈⣧⣿⣼⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠟⢻⣿⢃⣼⣿⣬⣥⣿⠟⣻⣷⡏⠹⣿⡘⢋⣾⣿⡏⠻⡿⢻⣿⣛⣧⢹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⠐⢿⣿⣿⣯⠥⠿⠿⠟⠛⠞⠛⠓⠒⠒⠚⠛⠛⠿⠯⠿⢾⣿⣟⣋⠛⣿⠋⣿⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⡆⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣧⣼⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡛⢦⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣁⣤⣀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢿⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠛⡟⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠁⠀⠇⢀⣠⣶⣾⠿⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣶⣦⡄⠀⠀⣷⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⡏⠀⠀⠐⠋⠉⠁⡀⠀⠀⠈⠉⠛⠿⠃⠀⠀⠀⢀⣾⣿⠿⠟⠛⠋⠉⠉⠛⠆⠀⣿⣿⣀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⣿⣿⠃⠀⠀⠀⠀⠀⠡⠲⢊⠛⠒⠄⠀⢆⠀⠀⠀⠀⢸⣿⢡⠴⠶⡒⠮⢄⠀⠀⠀⠀⣿⡟⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⣦⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠀⠀⠠⠊⠀⠀⠀⠀⢸⣧⠀⠀⠰⠶⠀⠀⠀⠀⠀⠀⠹⡇⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡏⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠋⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣦⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⡘⠳⣟⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡈⠑⢻⠀⠑⠄⠀⠀⠀⠀⠀⠀⢀⡤⢪⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⡆⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠀⠉⠀⠉⠀⠀⠀⠁⠀⠀⠈⠙⠲⠄⠀⠀⠀⠜⣹⠢⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠉⠉⣉⠁⠈⠀⠉⠉⠉⠁⢈⠉⠉⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡈⠉⠉⠉⠀⠀⠀⠀⡀⠂⠀⠀⠀⢀⡎⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠶⠶⠶⠶⢾⣿⡁⠀⠀⠀⢀⡞⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠶⠶⠶⠶⠶⠚⠛⠉⠁

⣶⣶⣶⣶⣶⡷⢾⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣿⣶⣿⢷⡾⢷⠾⠶⢶⣶⡷⠶⠶⠾⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠃⠒⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⠟⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⣀⣀⣀⣾⣿⣁⡀⠀⠀⠙⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⣾⣶⡿⠿⠛⠛⠛⠛⠛⠛⠉⠙⠉⠉⠉⡆⠀⠀⠀⠈⠛⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠙⠻⣟⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢀⠀⢀⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠉⢩⣍⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⡀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣰⣿⣏⣹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠻⣿⣯⣿⣿⡄⠤⠀⠀⣀⡤⠤⣄⠀⠠⠤⠤⠄⣾⣿⣿⣿⠛⠿⠦⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠈⠛⣿⣿⡅⠀⣶⣦⠀⠀⠀⣠⣴⣾⣷⣦⡀⣿⡟⠙⢯⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠛⠒⣿⣿⠧⣼⣿⣧⣤⣤⣾⣿⣯⣍⣩⣿⣿⣿⣷⠄⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⠇⠈⢿⣿⣿⣿⠿⠁⠉⣉⣽⣿⠏⢽⣿⡀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⣀⣀⣀⣉⣉⣡⣤⣤⣀⠈⣛⣁⣀⣿⣿⡄⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⣿⠉⠁⠀⠀⠀⢸⣇⠀⠉⠛⢤⣀⠀⣹⢹⣧⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⢸⣿⡀⠀⣰⠞⠶⣀⢿⣄⠀⠀⠀⠈⠉⠻⢀⣽⣇⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⠴⠶⢾⣿⠇⠀⣿⣦⠀⠈⠃⠙⣷⣦⣀⠀⠀⠀⠀⠙⣿⡀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠈⣿⣄⠀⠀⠈⠆⠘⠏⠳⢤⣀⣀⡄⠘⣷⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⢷⣤⣤⣤⣿⣶⠀⠀⠀⠐⢶⣿⣾⣿⣻⣿⣦⠈⠇⠀⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠁⠙⢏⡀⠠⣧⡀⠀⠀⠀⠙⢿⣿⣿⡙⢧⣄⠈⠀⡀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠁⠺⣿⣿⣷⣄⠀⠀⠀⠈⠛⠷⣄⣽⣧⠀⢠⣤⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠗⢀⡀⢀⠈⠉⠛⢿⣷⡄⠐⠀⠀⠀⠀⠋⠀⠀⣸⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢠⣾⣿⣧⣄⠀⠀⠀⠉⠑⠲⣆⡀⠀⠀⠀⣶⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⣾⠿⣷⠻⣿⢿⡄⠀⠀⠀⠀⢻⣅⣀⣴⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡆⠀⠀⠀⠀⠁⠀⢀⢤⡀⠀⠀⢠⢜⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⢲⣾⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⣀⣀⣀⣤⣶⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠛⠿⢿⣿⡿⠿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠠⠴⢬⣭⠷⢶⣿⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠛⠳⢦⣶⣦⣀⠂⠠⠍⢸⣿⣿⣿⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠉⠙⠓⠚⠂⠿⠿⠿⣿⡿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣀⣄⣀⣀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⣛⡿⢿⣿⣿⣿⣿⣿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⠿⠛⢛⠹⠁⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠛⠛⠓⠶⠴⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣞⠥⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡠⠂⠀⠀⣠⠀⣠⣾⢀⣴⣡⠞⠉⢧⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⣀⣤⣾⠴⢾⡁⠺⠛⢉⣤⠤⢤⡈⢿⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡛⠙⠿⠒⠒⠒⠃⠀⠀⠘⠒⠒⠒⠚⢸⡋⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⣴⣿⡆⠀⡟⠀⠀⢀⣴⣦⠀⠘⡇⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⠛⠁⣸⠃⠀⠀⠈⠿⠋⠀⠀⣷⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⠀⢀⣠⡤⠤⠿⣶⣤⣤⣤⣄⡀⠀⢸⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⠖⠹⢀⡶⡟⠛⠛⠛⠛⢻⣦⠙⠗⠾⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠸⢧⡙⠦⣤⣀⡤⣎⠾⠀⠀⢠⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⡀⡄⢀⠉⠓⠒⠚⠋⠁⢀⠀⣆⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢓⣼⣤⣤⣧⣤⡴⠤⣾⣖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠖⢺⠏⠸⡀⠀⠇⠀⠀⠀⡿⠈⣟⠒⠶⠤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⡀⠀⠀⠀⢸⠀⠀⠳⡄⠀⠀⠀⣰⠃⠀⣽⠀⠀⠀⢠⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠘⣄⠀⠀⢸⣄⡤⡄⠘⢦⣠⠞⠁⡤⣤⠏⠀⠀⠀⠃⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⣤⣇⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⡄⠐⠶⠒⠒⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠲⢤⣀⡀⢠⠀⠉⠉⠉⠉⠉⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⡤⠖⢙⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛⠶⠤⣭⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣭⡤⠶⠺⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣀⣿⡤⠄⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠈⠉⠛⠓⠶⠶⣶⣶⣶⠶⠶⣤⣿⣤⣤⣴⣶⣚⣋⣉⡀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠋⠉⠉⠀⠀⠀⠉⢙⡻⣟⠀⠀⠀⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⢀⣲⢽⣾⣷⡖⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣽⢿⡕⣃⢹⢰⣿⠷⠲⣦⣄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣜⣿⣅⠀⢿⣟⠀⢶⡏⣸⢛⡿⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠌⣻⣶⠋⠉⢛⣾⡷⣷⠋⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⠁⢳⣦⡘⠦⢸⣇⣼⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⢋⣤⣠⣾⣟⠛⢿⣿⠉⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣴⣶⡤⣤⣞⡃⠀⠀⠀⠙⣿⡧⠾⡛⠛⠛⠚⠛⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⣻⣿⣿⣿⣿⣿⡇⢿⣿⡃⠀⠀⢀⣼⠟⠳⣶⣿⣶⣤⣤⣴⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣿⣿⣿⣿⣿⡇⢿⡋⢡⣄⡀⣀⠏⠀⣧⣉⣰⣀⣀⣀⣀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⠈⠉⣿⡃⢀⣾⢿⣿⡛⢻⠉⠛⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣵⣿⣿⣿⣿⣿⣿⣿⣇⢸⣇⣀⣴⣿⠂⠀⣼⡿⠈⣷⠈⢲⣶⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⢿⣿⣵⠃⠀⢰⣿⠃⠀⠉⠄⢡⢻⣿⡿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿⡿⢃⠎⠀⡼⠂⠀⠀⠀⠀⠈⢆⢻⡍⢌⢷⣀⠀⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⣻⣿⣿⣿⡿⢡⠏⠀⣼⣤⡶⢾⡷⠶⣤⣄⠈⠊⢿⡌⢣⡻⣷⣄⠠⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠛⢰⠋⠀⣴⣿⣿⡀⢸⡇⠀⠈⢻⠀⠀⠈⢻⡄⠀⢹⣾⣷⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⣿⠃⠀⠀⠀⠀⠻⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠈⠃⠀⠀⢻⡿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣯⣹⡇⢀⣤⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⡌⢿⣕⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣥⣿⠀⣞⠇⡐⠀⠀⠀⠀⠀⠀⢹⣿⢿⣿⣿⣷⢀⠀⡄⠀⠀⠈⣿⣿⢞⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⢸⣿⣿⡃⠀⢠⠀⣄⠀⠀⠸⣿⠀⢻⣿⡟⠈⢀⣡⢀⠁⢠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⣾⣿⣿⣧⠀⣞⡀⢿⣷⣤⣠⣿⣤⡿⠋⠀⠀⢿⡟⢸⣼⣈⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⢠⣿⡇⠀⠀⠀⠉⠛⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠀⣿⣿⢳⣼⣇⢠⢰⢠⣰⢠⣧⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣧⣹⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠐⢃⡠⠄⠄⢦⣄⠩⢂⠀⠀⠀⠀⠀⢀⣐⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠒⣦⠈⠆⠀⠦⢀⣶⣿⣿⣿⠿⠿⠿⢿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠱⠀⠀⠸⠏⢻⠀⠠⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢢⡀⠀⠀⠀⠀⠀⢄⠀⠀⢁⡀⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠁⠈⠢⠤⠀⠀⠠⠠⠦⢤⣤⣀⠤⠦⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠠⢄⠀⣻⣣⠄⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠤⠀⢀⠀⠀⠈⢀⡿⠁⠄⠀⠀⡄⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⣰⠉⠃⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠁⣇⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⢀⠀⠄⢰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠉⠁⠉⠰⠎⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠰⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢠⠀⡆⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠇⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣶⡶⠇⢷⣶⣶⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠉⠙⠋⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠈⠉⠙⠛⠛⠛⠛⠻⠛⠛⠛⠋⠉⢹⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣰⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⡄⠀⠈⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⢠⣤⣤⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⢻⣿⣿⣿
⠀⠀⠀⠀⠀⢀⡾⣿⠀⠀⠀⠘⠿⠟⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠃⠀⠀⠀⠀⠀⠛⠉⠻⡄
⠀⠀⠀⠀⠀⠘⣇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⣰⠒⠲⠤⠤⠤⠴⠖⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⢻⣷⣶⣦⣤⣤⣶⣶⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⡇⠈⢙⣟⠁⢠⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⣸⣇⠀⣼⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⠀⠀⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠘⠻⠟⠋

⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢠⢟⣋⢛⠛⠉⠀⠀⠀⠀⠔⠒⠒⠒⠂⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⣇⢿⠿⣺⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠘⢪⣭⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⣀⡤⠏⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠃⠀⠀⠀⠀⠀⢰⣶⣦⠤⢤⣤⣀⣀⣠⡤⠤⠴⣲⣶⠆⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⠟⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠙⠿⣿⠟⠛⠻⠛⠻⣿⠿⠃⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠋⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⣀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠒⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠋⠑⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡯⣀⠀⠀⠀⠀⠀⠀⡼⠷⠷⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠘⢷⣦⡀⣧⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⣿⣿⣿⣾⣿⣇⠘⣤⣀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠴⣻⢿⢿⠿⡟⡏⠁⠉⠛⠛⠛⠛⠻⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⢸⣯⡟⡼⠈⡀⠐⠂⠀⢰⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⡀⠠⠤⠐⠈⠀⠀⠀⠀⠀⠀⢘⡟⠠⠁⢸⣧⣀⡰⠼⠟⠓⠓⠓⠛⠃
⠀⠀⠀⣠⣦⣾⣷⣿⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠓⠀⠀⢀⡉⠉⠀⠀⣸⠀⠀⠀⠀⣠
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⡆⠀⠀⠀⠀⠀⠀⢀⣰⠟⠀⠀⢀⣤⣿⣷⣤⣥⠶⠛⠛⠛⠛⠛⢣
⠀⠀⠸⠿⠁⠋⠛⡉⣿⢹⠀⢸⠛⠁⠀⠀⢠⣴⣿⠏⠀⠀⠀⢼⣿⢹⡥⡍⠀⠀⣹⣀⣀⣀⣀⣄⡇
⠀⠀⣤⠀⣦⣄⣦⣷⣿⢸⠀⠈⣿⡿⣷⣚⣻⣿⡏⠀⠀⠀⠀⠘⢿⣾⣇⣿⠷⠾⠟⠛⠛⠛⠛⠛⢇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⢹⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢹⡿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠈
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⢸⠀⠈⣟⠀⠀⢸⠇⠀⠀⠀⠀⠀⣤⣤⢸⡇⢹⠉⣿⡆⠀⠀⠀⠀⢀
⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡆⣇⡀⠘⠀⠀⢸⣳⣄⠀⠀⠀⠀⠘⢿⣾⣧⣼⣶⣿⠃⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠘⡿⣿⣿⣿⣿⣿⣿⣿⣼⡇⠀⠀⠀⣀⣿⣿⣷⣦⡄⠀⠀⠀⠹⠏⠻⠉⠀⠀⠀⠀⠀⠀⠀⣀⡴⠂
⠀⠀⠀⠁⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣶⣶⣤⣤⣤⣄⣀⣀⣀⡀⢀⣀⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠙⠉⠉⠁


⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣳⣫⡍⠀⠀⣠⣿⣿⣿⣷⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣻⣿⣿⡿⣻⣿⣿⣿⡦⢚⣩⣴⣖⡛⢿⣿⣿⣯⣹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣋⣾⣿⣛⣽⣿⣿⣿⡿⢋⣴⣿⣿⣭⡙⣿⣷⣿⢻⣿⣤⣙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠞⢯⣏⢹⣿⣿⣿⣿⢟⣴⣿⠿⠿⠿⠿⠛⠋⠉⠁⠀⠹⣝⣻⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡵⡡⣻⠟⠾⢿⣿⡿⠷⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣥⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣫⢏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⣾⣿⡀⠀⢀⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠐⢿⣿⣿⡷⠿⢿⣦⡄⢸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡧⢀⡾⠋⠉⠉⠙⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠁⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠭⢅⠀⠀⠀⠀⣿⣿⠆⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣌⢿⣯⠀⠀⠀⢰⡏⠀⠉⢂⠀⠀⠀⠀⠀⢰⠀⢿⣀⣀⡤⠃⠀⠀⠀⣿⣏⣿⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠘⣯⣿⠆⠀⠀⠀⠙⠓⠂⠀⠀⠘⠀⠀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⣿⢿⣹⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⡎⡰⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣹⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡱⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢣⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠤⠀⠀⠴⠚⠀⠒⠤⠶⠆⠀⠀⣆⡸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⣸⡄⠀⠃⠀⢰⢊⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠈⠀⠸⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⢹⠟⠁⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠈⠁⠒⠠⠤⠤⠐⠒⠁⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⢶⣶⠶⠶⠶⠂⠀⠀⡀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣔⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠒⠓⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣿⣿⣿⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠉⠉⠉⠁⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢿⠀⢒⠆⠀⠐⠂⠀⡿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠠⠤⠔⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⡠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠉⠉⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡁⠀⠀⠀⠀⢀⠗⠦⡤⣀⣀
⠫⢉⡁⠒⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠊⠉⡇⠀⢫⠉⣷⣶⠉⡹⠀⠀⡇⠈⡇⠉⠑⠢⢄
⠀⠀⠈⠉⢐⡤⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⢠⠃⠀⠈⡄⢹⡏⢀⠇⠀⠀⡇⠀⢱⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⢣⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢸⠀⠀⠀⠸⢄⣀⡀⢱⣼⣷⡸⠀⣀⣀⠅⠀⠸⡄⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠑⣄⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⠁⠈⣿⣿⠇⠀⢣⠀⠀⠀⠀⢃⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠈⢦⡠⠊⠁⠀⠀⠀⠀⢀⡤⢺⠀⠀⠀⠀⠀⠈⢢⡀⢸⡿⠀⡠⠊⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠳⡀⠀⠀⢀⡤⠚⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠙⠦⠧⠎⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⣱⡠⠖⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠞⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢃
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠀⠀⠚⠀⠀⣠⠞⠁⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⡰⠞⠛⠋⠛⠛⢶⣄⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⣰⠎⠳⣆⠀⠀⠀⣠⠞⠙⣧⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡟⠀⠀⠈⠳⣤⠞⠁⠀⠀⢸⡇⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⢻⣤⣤⣤⣤⣤⣾⠁⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣗⠲⠶⠤⢬⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⡁⠸⣏⣉⣛⣛⣺⡇⠀⢛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢁⡜⠁⠀⠻⣍⣉⣉⡽⠁⠀⢯⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢸⠀⠀⢠⡄⠈⠉⠉⠀⠀⠀⠈⣇⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠳⢤⣜⡧⠤⣤⣤⣀⡀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠉⢧⡀⠈⠓⢺⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠻⢤⡀⠀⠀⠀⢠⠇⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⡇⠀⢀⡴⠋⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣀⡀⠀⠙⠚⢉⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⠉⠉⠉⠉⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠙⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⣠⣾⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣷⣦⡀⠀⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⣀⣀⣀⣀⣀⣀⡈⠁⠀⠀⠀⠀⠀⠀⠀⢉⣀⣀⣀⣄⣀⣀⡀⠀⢻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠻⢿⣿⣿⣶⠟⠁⢈⣿⣿⣿⣿⣏⠙⠲⣶⣦⣤⣶⡶⠋⣩⣾⣿⣿⠧⠉⠈⠙⣶⣾⡿⠗⣈⢱
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢑⢦⡈⢟⢻⠀⠀⢠⣴⣾⣿⣿⣿⠀⢀⡿⠋⠉⢻⡇⠸⣿⣿⣿⣿⣶⠀⠀⠀⣾⢹⣠⠾⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢑⢸⠸⡄⠀⠘⣿⣿⣿⣿⠇⠀⢸⠃⠀⠀⠀⢧⠀⠻⣿⣿⣿⡿⠀⠀⠀⡇⣸⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠈⠀⡆⠳⣄⣀⣠⣀⠀⠀⣀⡴⠃⠀⠀⠀⠀⠈⠣⣀⡀⠀⠀⣀⣀⣀⠼⠀⣇⠀⢀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠊⡇⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠩⠁⠀⠀⢠⠁⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠸⣦⣀⣀⣀⣀⣀⣀⣀⡼⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠙⠿⣟⣉⣉⣙⡿⠋⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⣀⣀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⣠⡮⡃⠿⠃⠀⣴⡄⠀⠀⠀⠀⠀⠉⠑⠒⠦⢤⣀⡀⠀⠀⠀⠀⢐⠾⠟⠷⠾⠿⢦⡀⢠⠦⣤⠄⡀⢀⡀⠐⠀⠀⠀⠐⠶⠀⠁
⠀⠀⠀⠀⠀⢰⣿⡿⠋⠀⠀⣘⡛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⣠⠤⢤⡀⢠⡐⠟⣀⡀⠃⠀⠢⠹⠶⠋⡈⢿⣀⠗
⠀⠀⠀⡠⠋⠀⠙⢠⣄⠀⠐⠿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡕⢀⠀⠈⡀⠀⢀⠀⠰⠂⡀⣀⡈⠈⠁⣀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⡐⠀⠀⠈⣿⠃⠀⠀⠿⠃⠀⠓⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠙⡆⢸⠀⢸⡇⠸⣍⡉⠀⠂⡏⠁⠙⡆⡮⠤⠽⠸⣍⡉⠸⣅⡉
⠀⢤⣈⠠⠃⠀⠀⠀⡀⣠⣤⠄⠀⠀⠖⠀⠀⠀⠈⡉⠛⠓⠲⠤⡄⠀⠀⠀⣇⣀⣀⠆⢸⣀⣠⣇⢠⣀⡸⢸⠀⡇⠀⢰⡏⢧⣀⡰⠠⣄⡸⠠⣄⡸
⠀⠀⠈⠙⠈⢀⠉⠀⢸⣿⣏⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⡠⢠⣤⣤⣤⣤⡤⠤⢤
⠀⠈⠒⠃⠀⠈⣀⢹⣿⣯⠉⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⡇⠺⣿⠿⣿⡟⠡⠶
⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣯⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡆⣴⣿⣽⣿⠙⣉⣤⣠⠀⠀⣧⣤⣤⣤⣤⣼⣦⣤⣤
⠀⠀⠀⠠⠀⠀⠂⢀⠀⣄⠀⠀⠀⠀⠀⣀⠀⠄⠀⠠⠄⠀⠀⢄⠀⠀⣿⣯⣿⣽⣯⣿⡇⠻⣿⣿⠟⣼⣻⡞⣞⣿⠀⠙⠛⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⢀⠓⠒⢶⠎⠀⢿⢌⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢱⠀⠿⠿⠿⠿⠿⠿⠛⠃⠀⣀⣀⠘⣾⣭⡵⠏
⠀⠀⡐⠁⠀⠀⠈⠇⠀⢾⠀⠁⠀⠀⢀⣠⠤⠒⠒⠲⡄⠀⢸⠀⡌⠀⠀⠀⠀⠒⠂⠀⠀⢀⣴⣿⡿⠀⠀⠀⠀⢀
⠀⠠⡁⠀⠀⠀⠀⢹⠀⠘⡀⠤⠶⠶⢶⠶⠶⢦⣤⣠⣿⣁⣿⡖⢃⠀⠀⠀⠀⢀⠁⠀⠀⣼⣿⡾⠆⠀⠀⠀⠀⠘⢛⠛⠃⠀⠀⠀⠀⠠
⠀⠀⠈⠂⠄⠤⠐⠊⠀⠀⡇⠀⠀⡞⠃⠀⢄⡀⠀⠉⠉⠀⠈⣧⣰⢄⠀⠀⠀⠀⠀⠀⠘⠟⠛⠀⠀⠜⠦⠀⠀⠠⠍⠁⠀⠀⠀⠀⡀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⢠⣧⠀⠀⠺⠂⠀⠀⠰⠆⠀⢸⢧⡈⠂⣄⡀⠈⠁⠀⠀⠈⠀⠘⠀⠂⠀⠀⠅⠀⠀⠀⣀⣴⣤⣤⣤⣤⠀⠠⣴⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡁⠰⠙⠂⠀⠀⠀⠀⡆⠀⠀⠀⣼⠀⡝⡹⠁⠀⠑⠤⡀⠀⠀⠀⠢⠀⠀⠀⢠⠀⢀⠀⡄⠈⠉⠉⠉⢉⡛⠂⠰⠶⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣶⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡏⠀⠑⡷⠋⠁⠀⠀⠰⠀⠀⠀⠄⠀⠀⣼⠈⠀⢸⢰⡇⣿⠀⠀⠀⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠓⢦⣰⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⠃⠇⠀⠀⠘⢻⣿⡉
⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⢹⠣⡀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⣀⣧⣄⣀⣸⠀⠀⢀⣀⣀⡀⠀⠀⠐⠶⠶⠶⠶⠲⡀⠀⠀⣿⣇
⠀⠀⠀⣀⢠⢀⠀⠀⠀⠀⠀⠀⣸⡆⠉⠲⢤⡤⢤⡴⠋⢀⢦⡀⠀⡠⢠⣧⣤⣄⣀⣀⡀⣔⡵⠒⠚⠪⠣⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢻⣿⣾⣷
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡠⠊⠸⣇⠀⠀⠀⠀⠀⡓⠄⢘⢷⠄⢝⡅⣼⣿⣿⣿⣿⣿⠋⢸⠁⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠈⠁⠀⠀⢘⠛⠙⣿⡆
⠀⠀⠀⠨⠀⠀⢀⣀⣤⡞⠁⠀⠀⠈⠓⠦⣤⣠⠔⠁⢰⣌⡑⠀⠚⠀⣿⣿⣿⣿⣿⣿⠀⠳⢄⡀⢀⣨⡜⠀⠀⠀⠀⢀⣀⠤⠴⢦⡀⠀⠀⠀⢹⣿⡀
⠀⠀⠀⢀⣴⣾⣿⣿⣿⠃⠀⢀⣠⠴⠺⣿⣿⣿⡟⢦⣌⣿⣿⣶⡄⢸⣿⣿⣿⣿⣿⡇⠀⠀⢀⠀⠙⡄⢳⡀⠀⠀⠘⠧⠔⠒⠈⠀⠈⠈⠀⠀⠈⣿⣧
⠀⠀⣴⣿⣿⣿⣿⣿⣿⣶⣿⣏⠀⠀⠀⠘⣿⣿⠀⢸⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⠃⠀⠀⠒⠀⠀⢡⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠸⠿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢣⠹⡧⠀⠂⠀⠀⠀⠀⠀⠀⢀⣠
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠈⡀⠠⠔⠒⠈⠁⠈
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠉⠁⠀⠀⠀⠂⢄⡀
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣶⣶⣶⣿⠿⠿⣿⣿⠁⠀⠀⠉⠙⠻⢿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣾⡿⠿⠿⠟⠛⠛⠋⠉⠉⢀⣀⠀⠀⠀⢸⣿⣆⣀⣀⡴⠲⢤⣀⠀⠉⠛⠿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠉⠉⠁⢀⣀⣀⣤⡤⠤⠶⠖⠚⠛⠋⠉⠙⢦⣀⡀⠀⣿⣟⠉⠁⠀⠀⠀⠈⠙⠓⠦⣄⣀⠉⠙⠻⢿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⢀⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⡀⠀⠉⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⢲⠋⠀⠀⠀⠀⠀⢠⡞⠛⢷⠀⠀⠀⠀⠀⠀⢸⡄⠸⣿⡆⠀⠀⠀⢠⡞⠉⢳⡄⠀⠀⠀⠀⠸⣇⠀⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠸⡆⠀⠀⠀⠀⠀⠘⠧⡤⠞⠀⠀⠀⠀⠀⠀⠘⡇⠀⣿⣇⠀⠀⠀⠈⠳⠤⠞⠁⠀⠀⠀⠀⠀⢹⡇⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢸⣿⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣷⠀⢻⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣦⣄⡀⠀⠀⢸⡄⠘⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⢀⡞⠀⣸⣿⣧⣀
⠀⠀⠀⢀⣠⣶⡿⠟⠉⢹⣿⡀⠸⡇⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣦⠀⠈⡇⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⡾⠁⣰⣿⠋⠙⠿⣷⣦⣀
⠀⣠⣶⡿⠟⠉⠀⠀⠀⠈⣿⡇⠀⣧⠀⠀⣾⣿⡿⠋⣿⣿⠁⢀⣀⠈⢿⣿⣇⠀⢿⠀⢹⣿⠋⣀⡀⠙⣿⣿⡇⠀⠀⣼⠁⢠⣿⠏⠀⠀⠀⠈⠙⠿⣷⣦⡀
⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⢹⠀⢸⣿⡿⠁⠰⢟⡋⠀⣭⣭⠀⢰⣿⣿⠀⢸⡄⠘⣿⣷⣭⡃⠀⣿⣿⡇⠀⣸⠃⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿
⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⢸⣿⡀⠸⡇⠈⣿⣿⣆⠈⠉⠁⢠⣿⣇⣠⣾⣿⡟⠀⠈⣇⠀⣿⣿⣀⣠⣾⣾⡿⠀⣰⠃⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿
⣿⡏⠙⠻⢿⣶⣄⡀⠀⠀⠈⣿⡇⠀⣧⠀⠘⢿⣿⣷⣶⣾⣿⣿⣿⣿⣿⠟⠀⠀⠀⢻⠀⢸⣿⣿⣿⡿⠋⠀⣰⠏⢀⣾⡟⠀⠀⠀⠀⠀⣀⣴⣾⠿⠛⠉⣿
⣿⡇⠀⠀⠀⠉⠻⢿⣶⣄⡀⢻⣿⠀⢹⡀⠀⠀⠉⠻⠿⢿⣿⠿⠿⠛⠁⠀⠀⠀⠀⢸⡆⠘⣿⡏⠁⠀⠀⢠⠏⠀⣾⡿⠁⠀⠀⣀⣴⣾⠿⠋⠁⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⡄⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣿⣷⠀⠀⢠⡏⠀⣼⡿⠁⣀⣴⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡇⠀⣷⠀⠀⠀⠀⠀⠀⢠⡴⠲⣤⠀⠀⠀⠀⠀⠀⢻⠀⢸⣿⡀⢀⡞⠀⣼⣿⣷⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⢸⡀⠀⠀⠀⠀⠀⠸⣄⣀⡼⠀⠀⠀⠀⠀⠀⣸⡆⠈⣿⣇⡾⠀⣰⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢿⣿⠁⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠙⠛⢦⡀⣀⣀⣠⣤⠤⠴⠶⠒⠚⠛⠉⠁⠀⢀⣀⣾⡿⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠈⠉⠉⢀⣀⣀⣠⣤⣤⣴⣶⣶⣾⣿⣿⡿⠛⠋⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣶⣶⣶⣿⠿⠿⠿⠛⠛⠛⠉⠙⠿⠟⠉⠙⠻⢿⣷⣶⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿
⠀⠙⢿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⠟⠁

⠀⠀⠀⠀⠀⣀⣤⠀⣴⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⣤⣄⡀
⠀⠀⠀⢀⡘⣿⡙⠷⠟⢸⣧⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡾⠋⠀⠀⠀⠀⠉⠻⣆
⠀⠀⠀⣿⣙⠛⢡⡶⠶⣦⠉⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⣨⡾⠛⠛⠛⢷⣄⠀⠀⢹⣆⡀
⠀⠀⠀⣩⡽⠇⠸⣧⣤⠿⢀⣙⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⡇⠀⠀⢰⡏⠀⠀⠀⠀⠀⢹⡆⠀⠀⠈⠻⣆
⠀⠀⠀⠹⡷⠞⣷⢀⣴⣄⢻⣍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠁⠀⠀⠸⣧⠀⢤⣴⡄⠀⣼⠃⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠘⠻⠾⠃⠹⠛⠁⣶⠶⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⣿⢰⡞⠁⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠻⣦⣀⣿⠀⢀⣿⣠⡾⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⢰⡾⠷⠿⠾⣷⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠈⠉⠁⠀⠀⠉⠋⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣭⡛⢿⡄⠀⠀⠀⠘⠿⣾⠿⡷⠟⠀⣼⠛⠛⠉
⠀⠀⠀⠀⠀⢠⣤⣤⣴⠟⠀⢠⡾⠛⠛⢶⡄⠈⢿⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠀⣨⡗⠈⠻⢶⣤⡴⣦⣀⡀⠀⢀⣠⡾⠃
⠀⠀⠀⠀⠀⢸⣇⣀⣀⡀⠀⢿⡄⠀⠀⢸⡇⠀⢀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣦⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠉⣩⡷⠀⠈⠛⠶⠾⠋⠀⠀⣿⡉⠉⠉⠀⠀⣀⣀⣀⣀⡀⠀⠻⠶⠟
⠀⠀⠀⠀⠀⠀⠀⢾⣏⠀⣠⡶⣤⠀⠀⣴⢦⣄⠈⣻⡦⣠⡶⠛⠉⠉⠉⠉⠛⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⣿⠀⢀⣿⠀⠙⠿⠋⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠰⠟⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣄⣠⣤⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⢠⡞⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣬⣥⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⣀⣤⠀⠀⠀⣠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠃⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⣄
⠀⠀⠀⠀⠀⢠⣄⢀⡤⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⢸⡇⠀⣀⣀⡀⣠⣤⡀⠀⠀⠀⣴⠶⠾⠋
⠀⠀⠀⠀⠀⢀⡭⢨⣄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⢸⡏⠉⠿⠋⢀⣿⠆⠀⠛
⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⣨⡿⠃⠀⠀⠘⣧⣀⡼⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠻⣦⡀⠀⠀⠀⠀⠉⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣷⠄⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠈⠻⣦⡀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⣧⣤⣤⣤⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣤⣤⣄⣼⡇⠀⠀⠀⠈⠻⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣧⠈⠙⢿⣿⣿⣿⠋⢠⡀
⠴⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⣸⣏⠀⠀⠈⣿⣦⣤⣀
⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⣿⣏⠀⠀⠀⢹⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣾⣿⣦⡀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡇⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣶⣿⣿⣿⣿⣷⣄⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠟⠋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡿⠟⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⢠⣶⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣷⣦⡀⠀⢹⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠬⢿⣿⣿⠇⠀⠀⠀⣲⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣇⠂⠀⠀⠀⠀⣿⠿⠒⡐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⢄⠙⢿⠀⠀⠀⠀⣉⣩⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠇⡴⠊⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠱⡈⡄⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⠏⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠇⠀⠀⠀⠈⡛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠃⠀⠀⠀⠀⡈⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⠔⢣⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢲⠀⠀⠀⠀⠏⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⢶⠒⠒⠒⠒⠒⠒⠒⡶⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠄⠐⠒⠉⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⣀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠤⠒⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⣿⡛⢿⣧⡍⠙⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣿⡟⢉⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⢻⣿⡟⠻⠿⢀⣿⡟⠻⣿⣿⣿⡿⢦⣀
⠀⠀⠀⠀⠀⠀⣠⣾⡿⣧⣀⣽⣿⣿⣿⣯⠁⣌⣙⣿⣇⣠⣿⣿⣧⣈⣉⣿⡿⠃⢀⣀⣟⠛⢿⣿⠛⠋⠹⡄⢰⡉⢦⡀
⠀⠀⠀⠀⠀⣰⣿⣿⣧⣤⣩⣿⣿⠛⢻⣿⠿⢿⡿⢿⣿⣏⣴⣙⣛⣿⣿⣿⠛⣿⡿⢻⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⠻⣿⣦
⠀⠀⠀⠀⣼⣿⣿⡿⠛⠋⠉⣿⢏⣤⣾⣿⣶⣶⣤⣿⡿⢋⣹⣿⣿⠀⠸⠿⡇⢋⣀⣛⣻⣿⡅⠹⣿⠏⣹⣿⣉⣹⣦⢹⣿⣷⡀
⠀⠀⠀⣸⣿⣿⣿⠀⠺⣿⣿⣿⣿⣯⣤⣿⣿⡯⠽⠿⠷⠾⠿⠷⠶⠶⠶⠶⠷⠿⠿⠿⣿⣭⣿⣶⣿⣿⡟⠛⠛⢿⡟⠛⢻⣿⣷⡀
⠀⠀⢀⣿⣿⣿⡁⣀⠀⣾⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠶⠾⣿⡆⢹⣿⠈⣧
⠀⠀⢸⣿⣿⣿⣿⣿⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠺⣿⣿⣿⡄
⠀⠀⣾⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣴⡿⢿⣿⡇
⠀⠀⣿⣿⣿⣿⠿⢿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡛⢷⣄⣹⡇
⠀⠀⣿⣿⡟⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣶⣿⠿⡇
⠀⠀⣿⣿⣿⣾⣿⣷⡾⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢹⡄⣿⣸⡇
⠀⠀⣿⣿⡏⠀⠉⣽⠁⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⣿⠛⢿⡇
⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⡇⠀⢀⣤⣶⣾⣿⣿⣿⣿⣶⣤⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣀⣤⣴⣶⣦⣤⠀⡄⠀⢻⣶⣾
⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⣇⠶⠟⠛⠋⠉⠀⠀⠈⠉⠛⠿⢿⣿⣿⠃⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠿⠿⠛⠛⠻⢷⣌⠀⢸⣿⣿
⢀⡴⠊⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⡠⠔⣒⣀⣀⣀⠀⠀⢠⠈⠁⠀⠀⠀⠀⠀⣼⣿⡿⢋⠉⣀⢀⠤⢀⡀⠀⠀⠀⠉⠀⢸⣿⣿⠶⠒⠲
⡜⠀⠀⠸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠔⠛⡋⣤⠉⠉⠛⠂⠀⢳⠀⠀⠀⠀⠀⠀⣿⣿⠀⠷⠛⡛⣩⠛⡓⠆⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⢀
⡧⢸⣦⡀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠞⠀⠀⠀⡠⠎⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠰⠤⠖⠄⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⣠⣿
⡇⢸⡏⢳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠞⠙⣿
⡿⢸⣇⡌⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢰⡟
⡇⢸⢿⡁⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⣾⠃
⠃⢸⡈⠛⠾⡏⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⢰⡿
⠘⣆⠙⠳⠄⣷⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⢸⠃
⠀⠈⠓⠤⠤⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠙⢦⡀⠤⠄⠀⠀⠀⢀⡆⠠⠂⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⢠⠿⣏⠀⣠⠟
⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠀⠀⠀⠀⠂⣸⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠒⢚⠃⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⡐⠒⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⣄⠉⠓⠶⠦⠤⠤⡤⠤⠄⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⠁⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠛⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠎⠀⠀⠀⠀⠀⢠⡏⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣏⠀⠀⠀⠀⠀⢠⡟⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠑⢆⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢠⡟⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠳⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⢦⣤⣤⣤⣤⣤⣤⣤⡴⠶⠖⠛⠉⠁
⣿⣿⣿⠿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣤⣤⣤⡀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠠⡀⠀⠀⢤⡀⠀⠂⢦⠀⠀⠚⠀⠀⠀⠀⢹⡆⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡀⠀⠀⠄
⠀⠀⠀⠈⠢⠀⠀⠈⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⢸⡇⠀⠒⠰⠻⡧⢀⠀⠰⠖⠓⠀⢠⣀⠁⠈⠀⠘⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠒⠄⠀⠈⠁⢈⠴⠚⠁⠀⠀⣀⠁⠀⡄
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠰⠁⠀⠀⠀⠉⠠⠐⠊⢀⠄⠈⠩⠵⠂⢀⣄⠄
⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⣸⠂⠀⠀⠀⢸⣶⣆⠀⢆⠀⠀⠈⠀⠉⢁⣀⡤⠀⠒⢉⠜⡠⢀⠃⠐⠂
⠀⠐⠀⠀⡀⠀⠀⣿⠀⠀⠀⠀⠀⢙⠀⠀⠀⠀⢸⣿⡏⠀⠀⠁⠀⠀⠀⠀⠠⡶⠿⠷⠗⠚⢊⣴⣧⡀
⠀⠀⠀⠀⡁⠀⠀⡁⢘⠀⠀⠀⠀⣿⠀⠀⠀⠀⢺⣿⡇⠐⠀⠀⠀⢠⡆⠀⠀⠈⠓⠶⠠⠶⠻⠀⠙⠛⣠⠄
⠀⠀⠀⠀⡄⠀⠀⠁⢈⠀⠀⠀⠀⠸⠀⠀⣀⠀⠼⠛⠛⠀⠀⠀⠀⢻⡃⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠹⣿⣄⣀
⠀⠀⠀⠀⡀⠀⣀⠆⠀⢀⠤⠀⠄⠉⠉⠀⠀⠀⠀⠀⠒⠀⠀⠀⣀⢸⡇⢈⢀⡤⠐⠂⠀⠀⠁⠀⠈⢘⣿⠟⠋
⠀⠂⠄⠲⠀⠀⠀⠀⠐⠭⠿⠿⡖⢂⡀⠀⠀⠀⢠⣄⡀⠅⠀⠀⢨⣿⡏⢠⡠⠧⠖⠀⠀⠰⠏⡀⠀⠼⠿⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠄⠩⢈⣀⣋⣉⣁⡄⡀⠀⠀⠈⣿⠧⠴⠓⣺⣉⠲⣄⠉⢳⠀⠀⠀⠤⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠟⣻⣥⢬⣴⣿⣽⣷⠂⠀⠀⢘⣿⣿⣅⠀⠀⠀⣨⠟⢀⣀⣤⡴⠤⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠃⠡⠖⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⣅⠀⡀⠀⣰⠍⠩⠃


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⣠⣴⣶⡿⠿⠿⢿⣶⣦⣄⠀⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠟⠉⠀⣀⡀⢀⠀⠀⠉⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⢰⡶⣛⣛⢿⣥⡀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⢰⣿⠁⠀⠀⢿⡗⣿⣿⢇⣿⡅⠀⠀⠀⠈⣿⡆⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠀⠀⢸⣿⠀⠀⢀⣜⣟⣶⡶⢿⢽⠞⣓⢷⡄⠀⣿⡇⠀⠀⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠠⡏⣶⢝⡇⣠⣤⣹⣮⣋⡼⠃⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠙⠖⠛⠙⢿⣻⠇⠈⠁⠀⣰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡷⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⢾⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⣶⣶⣶⣶⣿⠇⠀⠀⠀⠀⠀⠀⠙⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣿⣶⣶⣶⣶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢽⣿⣿⣿⣿⡯⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡆⠈⠙⠿⣿⣿⠿⠋⠁⢰⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⢠⣴⣶⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⣴⣦⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣶⣦⡄
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣹⣏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢰⣿⣿⡆⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣼⣿⣿⣧⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢦⠀⠀⢀⣠⣀⠀⠀⠀⢠⣤⡤
⠀⠀⠀⠀⠀⣴⣶⠶⠀⠀⠀⠀⠠⣤⠄⠀⠀⣞⠋⢻⠀⠀⠀⠘⠅
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠻⠀⠛⠀⠀⢴⣶⠀⢰⣦
⠀⠀⢀⣶⠟⠉⠁⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠈⣾⣿⠀⠘⣿
⠀⠀⠀⠁⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠀⠀⠿⠟⠓⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠀⠀⠆
⠀⠀⠀⠀⢰⣶⣶⣶⣆⠀⠀⢸⣿⣿⣿⣧
⠀⠀⠀⠀⣿⣿⠋⢿⣿⠀⠀⠸⣿⣿⣿⣿
⠀⠀⠀⢰⣿⠇⠀⠘⣿⡇⠀⠀⣿⣿⣿⣿
⠀⠀⠀⣾⠏⠀⠀⠀⢹⣇⠀⠀⢿⣿⣿⣿
⠀⠀⢠⡟⠀⠀⠀⠀⠈⣿⠀⠀⢸⣿⢹⣿
⠀⠀⠲⠤⠀⠀⠀⠀⠀⠰⠤⣠⠾⠏⣸⡿⠀⠀⠀⠀⠀⢶⡄⠀⠀⠘⠻⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⡤⠠⣤⣤⣤⡤⡤⢤⢤⣤⡤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣦⣄⣀⠀⢀⣠⣶⣶⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠠⣾⠀⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣦⡀⠙⠀⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⡴⣛⣭⣭⣮⣭⣭⡓⢦⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⣀⠉⠻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣴⢫⣾⣿⡿⠛⠈⠻⣿⣿⣦⡹⡎⢻⣿⡿⠿⣿⣿⠿⣿⣟⣯⣵⣿⣿⣿⠁⠙⣿⠀⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢰⡇⣿⣿⣿⡅⠺⢸⣧⣼⣿⣿⣷⢹⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣧⣀⠈⠀⠉⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⡿⣷⢠⡉⢻⣿⣿⣿⢸⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠈⢷⡹⣿⣿⣧⣈⠈⣁⣼⣿⣿⢣⡟⣴⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠳⣬⡻⠿⣿⣾⡿⠿⣛⡵⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠚⠛⠉⠀⠀⠉⠛⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠛⠛⠛⠻⠿⠿⢿⣿⣷⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣶⣿⣿⡿⢆⣴⠃⠀⣀⡀⠀⠀⠚⠛⠉⠉⢛⣻⣿⣿⣿⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⣿⣿⣿⣭⠉⢿⣿⣟⡅⣴⢛⡵⠂⠀⠀⠙⠻⣷⣦⡀⢉⠉⣩⣥⣼⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣁⠀⠈⠛⠿⠿⣦⠀⢿⡿⣼⠁⣫⡶⠒⢀⣤⠀⠀⠛⣿⣿⣿⠷⠀⣛⠛⢫⣥⣦⣌⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠟⠠⣤⣴⣶⣦⡀⠀⢁⡏⣼⡟⣴⣿⣿⣷⠀⣠⡤⠶⠒⣚⡛⣋⣡⠄⡤⠤⣤⣴⣎⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠿⠋⣀⢀⣶⢾⣝⡻⠉⠙⠂⠈⠙⠛⠛⣫⢿⣿⠟⡼⠡⣶⣋⡉⠙⠻⣿⣿⣶⡀⠀⠀⠻⣿⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠐⣷⣤⡍⠉⠙⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁⣾⠃⠈⠐⠻⠿⢿⠿⠀⠀⠉⣭⣭⣥⣶⠀⠹⣮⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⣻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⣾⣿⠃⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⣿⡿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⣉⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠿⣧⣘⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⡖⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠃⠀⠀⠀⠀⠀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣵⡟⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⣿⣿⡆⠀⠀⢠⣶⡿⠟⠛⠿⠿⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣶⣤⣄⠀⠀⠀⠘⣿⣧⢼⣇
⠀⠀⠀⠀⠀⠀⠀⣼⢯⡀⠘⢿⣧⠀⠀⠋⠀⠀⢀⣤⠤⠤⣀⠈⠉⠀⠀⠀⠀⠀⠀⡴⠀⠛⢛⣛⣉⠉⠉⠉⠛⠷⣄⠀⢸⡟⠀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⢹⡄⡿⣦⠈⠟⠀⢀⣀⠀⢚⣭⢶⣶⠶⣶⠦⡀⠀⠀⢆⠀⢀⡾⡡⠊⣛⣭⣭⣭⣿⣷⠀⠀⠀⠀⠀⠘⠁⣾⢁⣾
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠃⣽⠂⠀⠀⢀⣁⡀⠉⠁⠈⠉⠉⣉⣀⠀⠀⠞⢸⠀⢸⡧⡇⠀⠉⠘⠓⠛⠶⠉⠳⠔⢋⣁⡀⠀⣰⣏⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⣿⠀⠀⠀⠉⠁⠀⠀⠀⠉⠛⠋⠉⠁⠀⠀⠀⢸⠀⠘⣇⠙⢦⠈⠙⠓⠒⠂⠀⠀⠀⠀⠀⠀⠘⢻⠏⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠘⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠉⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⠆⠀⠁⠀⠀⠁⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣼⣇⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⢻⡤⢦⡄⠀⢀⣤⡀⡿⠘⢶⣤⣀⠀⠀⠀⠀⠀⠞⣿⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢻⡆⠀⣀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠘⠶⠟⠁⠀⠀⠀⠀⠈⠙⣷⠀⠀⠀⠀⢸⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠘⣧⠀⠘⠀⢠⣀⣀⣀⣤⣤⣤⣤⣤⣤⣄⣀⣀⣠⡄⠀⠉⠀⢠⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⢿⠀⠀⠀⠀⠈⠉⠻⢦⣤⣀⣀⣀⣠⣤⡖⠛⠁⠀⠀⠀⢀⡟⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠈⠧⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣼⠃⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⠶⠶⠄⠀⠀⠀⠀⠀⣼⠏⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣤⣤⣤⣤⣤⣴⡶⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣷⣦⣤⣀⣀⣀⣀⣤⣴⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⣾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣍⡛⠛⠛⠛⠋⣡⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⢠⡟⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣥⣤⣴⣶⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢸⣿⡿⠀⠀⠀⠛⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣿⣾⣿⣷⣶⣠⣾⡇⢀⣠⣤⣤⣽⣿⣿⣿⣿⣿⣟⠻⠿⢿⣿⣿⣿⣭⣉⣉⣉⣽⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⠿⠿⠟⠛⠁⠀⠀⠀⠉⠉⠉⠉⠙⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠉⠉⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣶⣤⣤⣄⡘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢀⣴⣾⣶⣄⠀⢸⣿⡿⠿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡷⠀⠀⠀⠀⠙⠿⠿⢿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣷⣄⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣻⡿⠁⠀⠀⠈⢿⠇⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠋⠁⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣶⣞⣀⡀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠻⣦⣿⣿⠇⠀⠀⠹⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠛⠿⣿⣿⣿⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⣤⣤⡀⠈⠻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠘⠃⣬⣿⣆⠀⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠘⣿⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣸⣿⣦⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣄⠘⠃⠀⠀⣰⣆⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⠃⠀⠀⠈⠉⠛⠛⠛⠛⠟⠛⠛⠉⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢶⣶⡾⠟⣿⣦⠀⠀⠀⠀⠀⠀⠈⠁⠙⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣶⣶⣦⣤⣶⣶⣾⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠭⠴⠛⠉⠉⡩⢲⠎⢩⡏⢐⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣟⣉⣀⡀⠀⠀⠀⠀⢛⠈⣢⣉⣴⣟⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠺⠑⠒⠀⠈⠉⠒⠚⠳⠦⣀⡀⣠⣾⣿⣫⣷⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡼⢟⠒⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⡿⠧⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⣒⠭⠒⠁⠀⠈⢄⡀⠀⠐⠭⠩⢛⣶⡦⣄⢀⢆⢆⣿⣿⣿⡿⠏⣏⣠⣷⣿
⠀⠀⠀⠀⠀⠀⣀⠠⠔⣊⣥⢖⠙⠓⡀⠀⠀⠀⠀⠀⠉⠒⠒⠚⢈⡡⣪⣾⣿⠀⢫⣾⣿⡿⠟⢁⣶⢿⣿⢻⢫⡇
⠀⠀⠀⠀⠀⢀⣿⢴⣢⣉⡁⢦⣀⠑⠒⡀⠀⠀⠀⠀⠀⢀⡠⣒⢵⣾⣾⣿⣿⠁⣿⣿⡟⠟⠚⠻⣿⣕⡕⣵⠋
⠀⠀⠀⠀⠀⠀⡏⠑⢶⡬⣉⡓⠶⣭⣕⣲⠊⣩⡽⠟⡩⢵⣺⣵⣿⣿⣿⣿⣯⣖⠛⠈⠀⠀⣀⡄⣿⣮⣾⠋⠱⠶⢤⣀
⠀⠀⠀⠀⠀⠠⡏⠀⠀⠙⡑⠪⢝⣒⢿⣾⣽⣓⣞⣿⣾⢿⣿⣿⣿⠿⠿⠏⠓⠒⣦⣤⣄⢦⡛⣄⣿⡿⣙⣑⣦⠀⠩⠃⣩⡕⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⢭⣛⡲⠬⣅⡂⠉⢘⠛⣿⣶⣿⣧⣟⠛⠈⠤⠤⠔⡪⣻⣯⡟⢺⠁⣹⠟⠋⠉⡀⠺⢕⡶⢄⣠⣶⣷⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣋⠳⠦⢌⣙⡋⣼⡿⠟⠋⠬⠍⠀⠀⠀⢀⢞⣵⢿⣿⡏⢃⡽⠓⠀⢀⠔⠁⠀⠀⠈⣉⡚⠻⢿⠷⢇⣀
⠀⠀⠀⠀⠀⠀⢀⣠⠖⢉⠴⠉⢰⡁⠒⠂⢬⣙⣋⠉⠁⠀⠀⣀⣀⣀⢔⣕⣟⡷⣿⣿⣦⠯⠄⠀⠒⠁⠀⠀⠀⠀⠤⠀⠀⠀⡜⠀⢄⢨⠉⣱⡆
⠀⠀⠀⠀⠀⠀⢐⡯⠬⠥⠉⣀⣀⡒⠊⠭⠭⠶⣢⡤⠤⠊⢁⠖⣃⢴⡿⡯⣾⣾⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠐⠂⣸⢄⣠⠴⢊⠥⢻⠄
⠀⠀⠀⠀⠀⠀⠀⣿⠤⢂⣐⡒⠒⠀⠭⠭⠤⠐⢀⣀⣀⡨⡭⠍⠐⣫⣺⣿⣿⣏⣀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⠠⠔⡚⠭⢒⡩⣴⣫⣵⣞⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠸⢅⣒⣒⣒⡰⠯⠭⠭⠥⠔⢛⣒⣐⡤⠭⡍⡭⣿⣿⠿⡟⠙⠿⣿⢤⣘⠓⢬⠑⠲⣔⡢⠭⣐⣻⣵⣶⣿⢿⣿⠿⠛⡋⢬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⢕⠬⡛⢌⡙⠩⢋⢟⡹⡋⢞⠑⡋⠛⠝⡒⢛⢷⣕⡢⠀⠀⠀⠹⢦⢽⣒⣺⣽⣕⣛⣭⣶⣿⡯⠟⢛⠩⢔⣊⣥⠔⠟
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠉⠢⢤⣄⡀⢀⣁⣈⣀⡁⠈⣈⣰⣥⡿⣻⣄⠀⠀⠀⠈⠃⢰⣿⣿⠿⢟⢚⣉⣥⡒⠥⢒⠮⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠀⠨⣛⢥⡀⠴⠚⣋⣽⢿⣿⣿⡿⣿⣟⠝⠒⢄⡀⠀⠐⣗⣖⣯⣽⠿⠙⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⣀⠀⠀⠀⠸⡩⡉⠹⢿⣻⣷⣟⣯⡿⠟⠊⠀⠀⠀⠀⠈⠁⠊⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠄⡀⠈⡆⢐⣿⡿⠷⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⢐⠀⠂⠐⡠⠂⠔⡠⠂⡀⠀⠄⡠⢀⠀⠀⠀⠠⢀⠄⠀⠀⡠⢂⠐⠀⠀⠠⢀⠄⠀⢀⠔⡠⡠⢀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠊⠔⠥⢂⠔⢈⢔⡠⢊⠔⢊⠔⡠⢂⠑⡨⠐⠡⢊⠐⡡⢂⠀⡠⡠⢊⠄⠁⢒⡑⡠⢂⡔⢃⠔⡡⢪⠊⠔⠑⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁⠘⠁⠊⠁⠊⠐⠁⠊⠐⠡⠂⡠⢊⠔⠡⠪⠊⠀⠁⠊⠀⠋⠀⠁⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠈⠁⠙⠛⠛⠛⠛⠛⠛⠛⠋




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⠛⣿⠿⠿⠻⡿⢯⡽⠛⢿⠿⠻⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣛⣛⣛⣛⣛⣻⣿⣿⣛⣛⣛⡛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠛⠛⠲⠶⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⠀⣀⠀⢁⠂⡁⠢⡈⢢⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠠⢤⣅⣂⣍⣢⣑⠌⠤⠅⠀⡇⢀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠌⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢀⡊⠀⢀⠀⢀⠀⠀⠀⠀⠀⣀⡀⠀⢓⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⡏⠉⠻⠿⠍⡶⢲⠚⠿⠿⠏⠙⣿⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⠀⠣⠀⣀⣀⡐⠁⠀⠣⢀⣀⣀⠠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠐⠐⠒⠢⠦⠀⠔⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡏⢢⡀⠀⠀⠈⠉⠉⠀⠀⢀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠃⠀⢳⡀⠑⢤⣀⡀⠀⢀⣀⡴⢋⣿⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠴⠒⠋⡽⠈⡇⠀⠀⠱⣄⠀⠈⠉⠋⠉⠀⣠⠎⣼⠀⠙⢶⠦⢄⣀⡀
⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠁⠀⠀⠀⠀⡼⠁⠀⢣⠀⠀⠀⠈⠳⣄⠀⠀⣠⠞⠁⠀⡇⠀⠀⠈⢇⠀⠀⠉⠙⠒⠦⢤⡀
⠀⠀⠀⠀⡼⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠄⠀⠘⡆⠀⢀⣠⢴⡾⠟⠿⢷⠦⣀⠀⡇⠀⠀⠠⡞⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⢰⠇⠀⠈⡀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⠀⠙⣞⠁⠀⠀⢱⡀⠀⡎⠀⠈⢳⡇⠀⠀⠀⠙⡦⠀⠀⠀⠀⠀⠀⡄⢹
⠀⠀⠀⡼⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢸⠀⠀⠀⢠⠗⡞⡅⠀⠀⢸⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠇⢸⡆
⠀⠀⢀⡇⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠈⡇⠀⢀⡏⠘⠃⢹⠀⠀⣼⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢳⠀⣸⠀⠀⠀⠈⡇⠀⡇⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣧
⠀⠀⠉⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⠀⠋⠀⠀⠀⠀⠳⠀⠃⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠿⠿⠿⠟⠻⠿⠿⠿⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠋⢁⣀⣤⠤⠶⠶⠶⠶⠤⣤⣀⡈⠙⠻⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⡀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠈⢿⣧
⠀⠀⠀⠀⠀⠀⢰⣿⠁⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠿⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠹⡆⠈⣿⡆
⠀⠀⠀⠀⠀⠀⣿⡇⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣿⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⣿
⠀⠀⠀⠀⠀⠀⣿⡆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣿
⠀⠀⠀⠀⠀⠀⣿⡇⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠸⣿⡀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣶⣶⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⣰⠇⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠈⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠁⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣄⡈⠉⠛⠒⠶⠶⠶⠶⠒⠛⠉⢁⣠⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣶⣶⣦⣤⣤⣶⣶⣶⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⠞⠿⣿⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠘⣷⣿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡏⠀⠀⣤⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣡⣀⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠁⣠⠤⣤⣤⣄⡀⠀⠀⠲⡶⠿⠋⠉⠉⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⣿⠐⠁⠠⣤⠭⠅⠀⠀⠀⣎⢰⣷⠲⠀⠀⠘⣏⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠈⠁⠀⠀⠀⠀⣟⠃⠀⠀⠀⠀⢀⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢀⣀⠀⠀⢋⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⡁⠀⠀⠴⠂⠈⠈⠀⠚⢁⣀⣬⠁⠀⢸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠓⢦⡈⠁⠈⢁⡸⠋⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠀⠀⠀⠈⣩⣭⣤⠀⠀⢠⣰⡿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⢠
⠀⠀⠀⠀⠀⢀⡄⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠝⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⢠⣶⠸
⠀⠀⠀⠀⠀⠀⠀⣠⠠⠀⠀⠠⣦⠸⠃⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣶⣾⠀⠀⣸⠇⠐⠈⠿⣦
⠀⠀⠀⠀⠀⢀⣨⡛⠀⠀⣠⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣶⣶⠀⠻⠿⠀⢠⣤⣦⠀⠀⠀⠀⠀⠹⠏⢍⡁⢀⡴⠋⢀⠐
⠀⠀⠀⠀⠀⣿⢻⡇⠀⠀⠀⣤⠀⠘⠁⠀⠀⠀⠀⠀⠀⣼⢿⡿⠀⠀⠀⠀⢸⡟⣿⠀⠀⠀⠀⠀⠀⠀⠠⠶⠋⠁⢸⣿⣿⣿⢻⡀
⠀⠀⠀⠀⠀⡿⠈⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⡾⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣀⣀⣷⣿⣿⣿⣿⣿⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠙⠛⠉⠛⠋



⣿⣿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⢸⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠘⡇⠀⠀⠘⠀⠀⠀⡟⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⣀⡴⠖⠛⠛⠛⠓⠶⣄⡀⠠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⡀⠀⣠⠞⠁⣀⡀⣰⡖⣶⡀⣀⡀⠙⢦⡀⠀⣀⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⠏⠀⠸⣏⠙⣩⠤⢬⡙⢉⡿⠀⠈⢷⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⣤⡀⣿⠀⢰⠞⠃⡞⠁⠀⠀⠙⡆⠓⢦⠀⢸⡇⣠⣤⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠘⠳⣆⠳⡀⠀⠀⡰⢃⡶⠋⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠘⣧⠀⠸⣧⡴⢬⠉⢩⡴⣤⡿⠀⢠⡟⠰⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣈⢳⡀⠀⠀⠘⠓⠛⠀⠀⠀⣴⢋⡀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢹⡄⠀⠀⠀⠀⠀⠀⣼⠁⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣛⣛⣛⣛⣛⣛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤⠤⠤⠤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣛⣙⣛⣋⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣾⡈⠙⠿⣿⡿⠃⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣧⠀⠀⢸⡦⠀⢻⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢼⣿⡄⠀⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⣿⣧⠀⢸⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⡆⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣷⠀⢹⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⣿⣿⡆⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣷⣸⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠙⢿⣿⡿⠀⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣯⣤⣤⣴⣦⣤⣤⣤⣤⣽⣴⣶⣾⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠁⠀⠸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡄⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠛⠛⠛⠿⠿⠿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⡿⠗

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⢀⡾⢛⠉⢛⣿⡿⠛⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⢀⣶⢟⠋⢛⣿⡿⠛⢻⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⢸⠱⣷⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⠱⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⡄⠀⠛⠛⠋⠉⠀⠈⠉⠉⣿⡷⠻⣿⣇⠀⠀⠀⠀⡤⠀⠛⠛⠋⠉⠀⠈⠉⠉⣿⡷⠻⢿⣇
⠀⠀⠀⠀⢸⠃⣠⣀⠀⠀⢀⣀⣀⡀⠀⠿⣿⣆⣸⡿⠀⠀⠀⢰⠃⣠⣀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡆⣸⣿
⠀⠀⠀⠀⠸⡀⣡⡉⠀⠀⠛⣩⣍⠉⠀⠀⣾⡿⢿⠇⠀⠀⠀⠸⡄⣡⣍⠀⠀⠚⠛⠋⠑⠀⠀⣼⡿⢿⡇
⠀⠀⠀⠀⠀⠀⠘⠋⣠⠀⠀⠹⠏⠈⠁⠀⠡⡎⢈⠇⠀⠀⠀⠀⡁⠘⠋⢰⠀⠈⠉⠉⠈⠀⠀⠩⡎⢀⠇
⠀⠀⠀⠀⠸⡆⠀⠰⡁⠠⠀⠀⠀⠀⠀⠀⠀⣡⠊⠀⠀⠀⠀⠐⡇⠀⠰⡅⠀⠀⠀⢀⠀⠀⠀⠀⣡⠎
⠀⠀⠀⠀⠀⢳⠀⠠⠤⠤⠤⠐⠛⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⢳⡀⠲⣖⣒⣲⠖⠃⠁⠀⡴⠉⠁
⠀⠀⠀⠀⠀⠀⠳⡀⠀⠉⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠈⠭⠁⠀⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠙⠲⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠖⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣿⣿⢻⡟⣿⣿⢻⡟⣿⣿⢻⡟⣿⢻⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣿⣿⣼⣧⣿⣿⣼⣧⣿⣿⣼⣧⣿⣼⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⢻⡟⡟⣿⢹⡟⡟⣿⢻⡟⡟⣿⢻⡟
⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣀⣷⣿⣾⣷⣷⣿⣾⣷⣷⣿⣾⣷⣷⣿⣾⠷
⠀⠀⢸⢹⡏⣿⢹⢹⡏⣿⣽⡿⢟⣛⣭⣭⣭⣭⣛⡻⢶⣼⣏⡏⣿⢹⡏⡏⣿⢹⡏⣿⣿⢹⡏⣿⣿⢹⡇
⠀⣀⣸⣾⣷⣿⣾⣾⣿⢟⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡻⣿⣿⣾⣷⣿⣿⣾⣷⣿⣿⣾⣷⣿⣿⣾⣅
⠀⣿⢹⣿⡏⣿⢹⡿⣡⣿⣿⣿⣿⠿⠛⠀⠀⠛⠻⢿⣿⣿⣷⡌⢿⣿⢹⡿⡏⣿⢸⣿⡏⣿⢹⡏⡏⣿⢸
⠀⠙⣿⣿⣿⣿⣿⢱⣿⣿⣿⣿⡏⠀⠀⢰⣦⣤⣄⣾⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛
⠀⠀⣿⣸⢸⣿⡏⣾⣿⣿⣿⣿⣷⣄⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣧⢹⡇⣿⣸⢸⡇⣿⣸⢸⡇⣿⢸
⣤⣤⢿⣿⣿⣿⣇⢿⣿⣿⣿⣿⡿⢿⣿⣶⣦⠀⠀⠘⣿⣿⣿⣿⡏⣼⣿⣿⣿⣿⢿⣿⣿⣿⢿⡿⣿⣤
⣇⣿⣸⣇⣇⣿⣿⡜⣿⣿⣿⣿⣅⡀⠀⠉⠁⠀⣀⣼⣿⣿⣿⣿⢣⣿⣸⣇⣇⣿⣸⣇⣇⣿⣸⣇⣿⣿
⠉⡿⣿⢿⣿⡿⣿⢷⡜⢿⣿⣿⣿⣿⣿⣀⣀⣿⣿⣿⣿⣿⡿⣣⣿⣿⢿⡿⣿⣿⢿⡿⣿⢿⢿⡿⡏⠉
⠀⣇⣿⣸⣿⣇⣿⣸⣿⣦⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⣫⣾⣟⣿⣿⣸⣇⣿⣿⣸⣇⣿⣼⣸⣇⡇
⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⠶⣮⣭⣭⣭⣭⣵⠶⠟⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠐⢣⡄⠀⠀⠴⢴⡄
⠀⠀⡔⠛⠳⡄⠀⠂⠀⠐⢄⠀⠀⠀⠈⠁⠰⠀⠀⠧⠀⠦⠀⠀⠀⡗⠀⠈⠁⢀⡂⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠂⠀⠀⡇⠀⠀⠀⠐⠀⢹⡦⠀⢀⢠⠀⠀⠀⠠⠀⡀⠀⠀⠀⡇⠀⠀⠀⠸⠇⠽⠀⢀⣀⣀
⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠢⠘⣆⠀⢀⣐⠂⠀⠀⠀⠺⠟⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠦
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⢀⠄⡉⠉⠁⠀⠀⠀⢀⣀⠀⠀⣠⣶
⠀⠀⠀⢀⢠⠀⠀⠀⠄⠁⠠⠄⠀⠀⠀⢩⡄⠋⠁⠀⠀⠀⠀⠨⠀⠀⠀⢸⣿⡆⠀⠀⠀⢰⣤⣄⣠
⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠈⠀⠀⠘⠋⠀⠀⠀⠀⠻⠿⠿⠿⠷⣶⣶⠆
⠀⠀⠀⠊⡍⠙⠀⠉⢢⠉⡗⠉⢉⠖⢩⠑⡀⢉⠉⠇⠀⣀⠆⠀⡐⠆⠐⠈⠇⠐⢢⡔⡆⢂⠆⠰⡴⢆⢂⡐⡄
⠀⠀⠀⠀⡁⠰⠄⠀⡌⠁⡇⠀⠀⠰⢀⢴⠁⠈⡒⠆⠀⡄⠂⠀⢡⠂⠀⢑⠂⠀⣤⠁⡇⠘⡦⠸⡅⢸⠆⢠⠁
⠀⠀⠀⠀⠑⠒⠄⠀⠇⠀⠇⠀⠔⠀⠸⠀⠆⠀⠁⠆⠀⠇⠀⠠⠧⠇⠠⠈⠙⠠⠜⠠⠇⠀⠙⠃⠀⠂⠐⠛⠂
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠺⡉⠋⠒⢦⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢶⡶⠵⠛⠋⠁⠀⠀⢰⣄⣂⣍⢠⣤⡄⠀⠀⠄⠀⠀⠀⠀⢱⠀⠀⣾⠀⠘⠀⠀⠀⠀⠀⡴⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠁⠂⠀⠠⠴⠋⣀⠠⠝⠀⠀⠀⡤⡄⡛⡆⡇⢸
⠀⠀⠀⣀⣄⣤⣤⣄⠀⠀⠀⠀⠠⢖⡉⣱⠙⠓⢀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⢀⣀⣇⣆⣧⠁⠸⠄⠄
⠀⠀⠀⢻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣸⠁⡠⠀⢀⡆⠀⢰⠇⡅⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠘⢯⣽⣾⣿⣿⠄⠀⠀⢀⠈⠻⢼⠃⠀⠸⠁⠀⣸⠁⠄⠀⠀⠀⠀⢆⡀⡰⠄⠀⠀⠐⡁⢈⠆
⠀⠀⠀⠀⠀⠙⠧⠿⠟⠂⠃⠀⠀⠁⠀⠀⠀⠈⠀⠀⡎⢴⣦⠑⠀⠀⠀⠀⠒⠀⠀⠃⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢲⣷⡀⠀⠀⠀⠰⢄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠸⢟⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⣠⡄⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⣄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢠⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠀⡴⣦⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠼⢄⣠⡆⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠀⠀⠀⡧⠈⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⡇⠀⠀⠀⠀⠏⠀⢿⣿⠃⠀⠀⣶⡄⠃⢺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠸⠏⠛⠋⠀⠀⠀⠀⠀⠀⠚⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡴⠟⠛⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠸⠀⠀⠀⠀⡰⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡄⠀⠀⠀⠈⠿⠾⠋⠀⠀⠀⣤⠊⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣶⠄⣀⣀⣀⣶⠤⠔⠋⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⠈⠉⠉⠀⠀⠀⠀⣀⠀⠐⠶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠙⠛⣶⣶⡞⡀⠀⠀⢠⡞⢠⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣤⠾⣄⢨⡟⠋⠳⣴⠆⠀⢰⡏⠘⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⠇⠀⢩⠛⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠈⠀⢸⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⢸⠇⠀⣾⠀⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⣿⠀⠀⣤⡄⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡸⠀⠀⣿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⢹⠆⠀⠙⢻⣇
⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⡆⠀⠀⠀⢏⡀⠀⠀⣿⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣴⠟⠀⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⣴⠏⠀⢀⠇⠀⠀⠀⠀⢣⠀⠀⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⠋⠀⠀⠀⢠⣤⡄⠙⢿⣦⡀
⠀⠀⠀⠀⢀⣾⠏⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠙⢿⣦⣀
⠀⠀⢀⣴⠟⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠈⠀⠀⠀⠀⠈⣦⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⢿⣆⠀⠀⠙⠻⣷⣦⣀
⣀⣴⠟⠁⠀⣤⣴⣞⢀⡟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢆⠀⠀⠀⠀⣰⡿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠙⣷⣄⠀⣀⠀⠈⠉⢱
⠟⣁⡀⠀⠀⠈⠉⠛⠛⠿⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠓⢤⣄⡾⠋⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⢻⣿⣿⠟⠀⠀⠈
⠀⠙⠳⣦⡀⠀⠀⠀⢀⠰⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠠⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⣠⡶⠿⠋⠀⠀⠀⣀⣀
⠀⠀⠀⠈⠻⣦⡀⢀⡞⠀⢱⡄⠀⠀⠀⠀⢀⡏⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠀⠀⣀⣤⡶⠟⠉⠁
⠀⠀⠀⠀⠀⠈⢻⣾⠀⠀⠸⠏⠀⠀⠀⠀⣾⡇⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠠⠤⣤⡟⠉⢿⡄⣀⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠈⠿⠋⠁
⠀⠀⠀⠀⠀⠤⠀⠙⠇⠀⠀⠀⣴⡄⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠈⠲⠶⣄⣠⣤⡀⠀⠰⠋⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠑⠄⠀⠀⢶⣄⠹⣛⠿⠆
⠀⠀⠀⠀⢠⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠻⠿⢶⡆⠀⠀⠀⠉⠁⠉
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣛⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⡤⢼⣇⡀⠀⠀⠀⠀⠀⠚⠋⠀⣀⣀⣠⣤⣴⣶⣾⣿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⢀⡻⠛⠉⠛⠋⠛⠉⠁⣀⠀⠀⢈⣧⠀⠙⠻⠶⠶⠶⠶⢶⣶⡿⠟⠛⠛⠋⠉⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⢀⡔⠋⠀⠀⠀⣠⣤⡴⠞⠈⠻⠗⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⢤⣤⣀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⣠⣄⣁⡠⠤⠶⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣄⡀
⣤⣤⣤⣬⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⡿⠿⠻⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⡂⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠐⢀⣠⡄⠀⢀⠤⣤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣼⣿⣦⣄⣀⣼⢠⠁⣠⠛⠒⠪⣕⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠸⣿⣿⣇⣿⣿⣿⣿⣿⣿⠀⠀⡆⠀⠀⢸⠹⡌⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢀⠐⣾⣿⣿⡯⠿⣿⣿⣿⣿⡟⠀⢤⠃⠀⠀⠚⢴⠃⠀⡿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⢰⣿⣿⣿⠀⠀⣿⣿⣿⣿⣧⠤⠼⠧⠀⠀⠀⢸⠀⠈⠹⡾⣆
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠳⠧⣀⣸⣿⣿⣿⠀⠀⣯⣿⡿⠛⡇⠀⠀⠀⠔⠚⠋⠉⠓⢄⠀⢷⢸⣇
⠀⠀⠀⠀⠀⠀⠀⣼⣷⣦⠄⠠⠬⣍⣛⡟⠀⠀⣿⣿⡇⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠘⢹⡄
⠀⠀⠀⠀⠀⠀⢀⣿⡿⠁⠀⠁⠙⠊⡌⠣⡀⢀⣿⣿⡇⢸⡷⠖⠒⠒⠮⠀⠀⡀⢀⡦⠴⠃⣰⠞⢳
⠀⠀⠀⠀⠀⠀⢸⣯⢁⠎⠀⠐⠄⠀⠀⠀⢘⡞⠛⢻⡇⢸⡇⠀⠀⠀⠀⠀⢀⡍⠉⠁⠀⠀⠻⠀⢸⡆
⠀⠀⠀⠀⠀⠀⢸⣿⠌⠙⢀⠔⠈⠀⠀⠀⠘⣷⠀⠈⡇⢸⡇⠀⠀⠀⢰⡴⠊⠀⠀⠴⠒⠢⡄⠀⢼⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢄⠤⠐⠀⠀⠀⠹⡄⠀⠃⢸⣷⠶⠶⠶⣏⠀⠀⠀⠀⢀⠀⠀⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠸⣽⠀⠀⠀⠀⣤⣤⡇⢀⠄⠀⠁⠀⠀⢸⡇⠀⠀⢀⠈⠙⠒⠒⠒⠋⠀⣶⠋⣸⣸⠃
⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⣷⣷⡇⠈⠒⠀⢈⠀⠀⢸⡇⠀⠀⣸⠷⠤⠤⠾⠦⠤⠤⠻⣦⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠧⣍⡇⠀⠄⠀⢸⣴⣷⣼⡇⠀⣰⠏⠀⢰⣄⣠⠖⠒⢦⡀⢘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢝⣦⢬⡑⣴⠁⣠⠂⢀⡏⢻⣿⣿⣧⠾⠯⡤⠔⠋⠈⣷⠀⠀⢀⣷⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⡙⣧⡰⢋⣴⣾⣷⣿⣿⣿⡇⠀⠀⢤⣄⣴⠾⠋⢀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⡿⣿⣿⣿⣿⠏⡷⠶⠛⡋⠉⢀⣆⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠋⠀⠘⠦⠶⠿⠖⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠁

⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⡀⠀⡤⣄⠀⠀⠀⢠⠤⠤⣤⣤
⠀⠀⠀⠀⠀⠢⣝⣅⠀⣀⠀⠀⠀⢀⣾⠇⠘⣿⡆⠀⠀⠀⠠⠶⡿⠶⠶⠀⠀⠀⠀⠑⣷⢌⠫⠛⠀⠀⠀⢸⠀⠉⣕⣻
⠀⠀⠀⠀⠀⣠⣿⣽⣾⣯⠀⠀⠀⠀⠻⣄⣀⡼⠃⠀⠀⠀⢸⣶⣯⣷⣾⠀⠀⠀⠀⢰⢿⠘⠃⠀⠀⠀⠀⠈⠉⠙⠺⢿⡃
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠁⠉⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠾⠸⡟⠓⠓⠀⠀⠀⠀⠀⠤⡧⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⠀⠀⡾⠷⠀⡯⠀⠀⠀⠀⢸⡅⠹⠆
⠀⠀⠀⠀⠀⣸⡇⠙⡔⣦⠀⠀⠀⠀⠀⠸⠇⠙⠀⠀⠀⠀⠈⠉⠹⠮⣧⠄⠀⠀⠀⢀⣾⠇⢴⡆⠀⠀⠀⠈⣳⡏⣷⣶
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠈⠋⠀⠀⠀⠀⠀⠀⠈⠋⠁

⠀⠀⠀⠀⠀⠐⠆⠰⠰⠆⠀⠀⠀⢠⠶⡾⠶⡆⠀⠀⠀⠀⠀⣤⠆⣶⢻⠆⠀⠀⠀⢂⡀⢰⣝⢷⠀⠀⠀⢠⣤⠒⢰⣹⡆
⠀⠀⠀⠀⠀⣤⣁⣹⣌⣡⠀⠀⠀⢸⡯⣯⢭⡧⡀⠀⠀⠀⢘⣿⡆⣈⡭⠀⠀⠀⠀⣌⣡⣮⡙⢉⠀⠀⠀⠙⣅⢇⣻⣘
⠀⠀⠀⠀⠀⠈⠙⠟⠛⠁⠀⠀⠀⠘⠚⠛⠛⠧⠏⠀⠀⠀⠙⠛⠙⠋⠁⠀⠀⠀⠀⠀⠉⢩⠐⠘⠀⠀⠀⠀⠈⠙⠿⠟⠃

⠀⠀⠀⠀⠀⣠⢤⡄⢀⣠⡀⠀⠀⢀⡤⡄⢠⡴⠀⠀⠀⠀⠀⠀⢴⠄⠀⠀⠀⠀⠀⢴⠀⣄⡀⡄⠀⠀⠀⠀⠀⠀⢠⣤⡄
⠀⠀⠀⠀⠀⠛⢺⢅⢰⣿⠇⠀⠀⠀⠟⢁⣾⣹⡄⠀⠀⠀⠤⣤⡿⣧⡤⠄⠀⠀⠀⣼⠖⣤⣿⠁⠀⠀⠀⢀⢟⣟⠐⠛⠂
⠀⠀⠀⠀⠀⠠⡞⠁⠀⠀⠀⠀⠀⠰⡦⢶⣿⡽⠃⠀⠀⠀⠀⠈⢧⡟⠀⠀⠀⠀⠀⠻⡽⠊⠹⡆⠀⠀⠀⣿⠃⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠈⠙⠻⠿⠿⣿⣿⣿⠿⠿⠟⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠀⠀⢀⣤⣤⣤⣤⠀⠀⠀⠀⠀⣤⣤⣤⣤⣄⠀⠀⠀⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢀⠤⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢅
⠀⠀⠀⠀⠀⠀⠀⠂⠀⢾⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠇⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⣄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠣⡀⢸⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⢀⠃⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠈⠑⢌⠉⠉⠉⢉⠠⠊⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⢀⡀⠤⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⡤⠒⣀⠐⠂⠤⢤⡤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠈⣀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡄⢰⣦⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠳⠦⠀⠀⠀⠀⢄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⢰⠀⠘⣄⠀⢀⡱⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠘⠠⣀⠀⠉⠁⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠬⠁⠴⠂⢨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⢀⣘⣀⣀
⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢉⠓⢒⡶⡒⢺⠉⠀⠀⠀⠑⠤⡀
⠀⡀⠀⠀⠀⢠⡀⢀⡀⠀⠀⠀⠀⠀⠀⣀⠤⠂⢁⠎⢀⠎⢸⠈⣶⠉⡆⠈⠠⠀⠀⠀⠀⠈⠓⢄⡀
⠀⠀⠐⣩⠀⠈⠀⠀⡏⠑⠒⠒⠶⠒⠉⠀⠀⢀⡜⢐⠉⠀⠸⢀⡟⠀⡆⡰⠁⠀⠀⠀⡀⠀⠀⠀⠉⠒⢤⡀
⠀⠂⠀⢠⠆⣤⣀⠰⡇⠀⠀⠀⠀⠀⠀⣀⡴⢻⠅⠀⢂⠀⠀⢠⠁⢀⡰⠃⠀⠀⠀⠀⠍⠒⢄⡀⠀⠀⠀⠈⠁⠂⠄⣀
⠀⠀⠂⠠⠔⠀⠀⠀⠉⠉⠀⠀⠀⠒⠈⠁⠀⣌⠀⠀⠈⡄⠇⡌⠀⣸⠁⠀⠀⠀⠀⠀⢰⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠉⡶⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢸⣄⠃⣧⠏⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠉⠓⠢⢄⣀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠙⠤⢿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠂⠄⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢸⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠘⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣀⡀⢀⣰⠀⢸⠀⢀⣀⣀⠀⠀⠀⡀⢀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠍⠉⠁⠀⠈⠉⠉⠉⠉⠉⠉⠁⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠓⠂⠠⢤⣤⣴⠦⠤⠤⠤⠐⣒⡶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠒⠒⠂⠉⠱⠮⠤⠤⠔⠒⠚⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠶⠛⠉⠉⠉⠉⠉⠓⠒⠲⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⣠⠴⠚⠛⠉⠉⠉⠛⠓⠲⠶⠦⢤⣤⣤⣤⠴⣎⠁⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⠞⠁⠀⢀⡀⠀⠀⠀⠀⣠⢶⣄⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣀⡴⢏⠗⠀⠀⠀⠀⠈⠻⢮⣿⡶⢦⠄⠀⠀⢸⡗⠀⠠⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠛⠁⢛⣁⣀⡀⢢⠀⠀⠀⠀⠀⢈⣁⠀⠀⠀⠀⢸⠃⡀⠚⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠊⠀⢴⣦⡟⠀⡁⠀⠀⠹⠀⢠⣤⡑⡄⠀⠀⠈⢻⡅⢱⠟⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠖⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠃⠀⠀⠀⠀⢷⡋⡀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⣠⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⢀⠄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⢰⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⡠⠄⠂⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠨⠍⠉⢉⣁⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠁
⠀⠀⠀⠀⠀⠀⢠⡖⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⢶⡶⠶⠲⠾⣏⠉
⠀⠀⠀⠀⠀⠀⢀⣹⠶⢀⣀⡈⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡏⣠⣆⠀⠀⣹⣤⣀
⠀⠀⠀⢀⣴⣞⡋⠀⠀⠀⠀⣹⡜⠳⡄⠀⠀⠀⠀⠀⢀⣾⡃⠀⠐⠛⣿⡿⠢⠞⠁⠀⠈⣹⡆
⠀⠀⠀⠸⠖⠋⠁⡀⠤⠐⠋⢡⠀⠀⠘⠆⡀⠀⠀⢠⠏⢸⡇⠤⠀⣾⠻⣥⠀⠀⠀⠀⡼⠁⢷
⠀⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⠀⠉⢧⡀⠀⠙⠳⣴⠃⠀⠘⡿⠀⢨⣧⡿⠁⠀⠠⠀⣰⠃⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⣹⠀⣀⠞⣷⠀⠈⡿⠁⠀⠀⠀⢀⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣥⠞⠁⠀⢹⠀⠐⠀⠀⠀⠀⠀⢸⠙⣦⠔⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠘⠃⠀⠀⠀⠀⣹⠀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠇⠀⠀⠀⠀⢿⠀⢳⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡀⠀⠀⠀⠀⢘⠀⢸⡀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⣸⠳⣄⣀⣀⣀⣼⠆⡏⠀⠀⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠛⢻⣍⠉⠁⢹⣠⡟⠛⠒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⡟⣆⠀⠈⡟⠧⣤⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣧⠸⡄⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢿⠀⢷⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢸⠀⠀⡄⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⢷⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡀⢸⡀⠀⠸⣆⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣅⡀⠈⣇⠀⠀⣧⣴⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠶⠚⠋⠀⣀⡉⣿⠁⠀⣠⠏⠁⠀⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢀⣈⢁⠈⡀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠎⠘⠓⠆⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣶
⠀⠀⠀⢰⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉
⠀⠀⠀⠘⣷⣾⢻⢘⡢⡾⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡄⡄⣄⢤⠔⠂⡤⠰⡄
⠀⠀⠀⠀⠘⠃⠈⠈⠁⠁⡜⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣷⣦⣴⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣻⣮⢻⣽⡟⣟⣸⣿⣟⣽⣧⣻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠙⠛⠛⠛⠻⠛⠋⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡼⢡
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠊⢐⡞⠀⡀
⠀⢸⡒⡆⢰⣄⠰⡔⡇⢙⢵⢴⡆⢠⡆⠀⠀⠀⠀⠀⠀⠸⣷⡿⠑⠂⠀⠀⠀⠀⠀⠀⠀⣄⡄⡄⡀⣠⢤⡀⡄⠲⢀⣤⣰⡀
⠀⠈⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠝⢓⠀⠄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠉⠃⠉⠉⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣰⢶⠐⡠⢲⠂⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠉⠁⠁⠈⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⢻⣿⣛⣛⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠙⠛⢿⡿⠿⠿⠛⢫⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⡒⠲⣄⠀⢠⣤⣤⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢿⠀⠉⠁⠹⠀⠒⠒⠀⡄⣽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⠀⢠⠘⠃⠐⢀⠀⢠⡇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠈⣥⠐⢀⠔⡡⡛⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⡿⡉⠿⣦⣀⡀⢀⣸⣌⢰⣡⣆⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣾⣿⠿⢟⠿⣿⠁⡆⠐⢌⠉⠉⢱⡏⠓⠋⠙⠁⢠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⢛⠉⠉⠙⠁⠀⢀⡎⠀⠏⠈⡇⠀⢀⣷⣄⠙⣿⡄⠸⠀⠀⠟⠛⠻⠷⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣍⠀⠈⡇⠀⠀⠀⠀⡜⠀⠀⠀⠀⢷⢠⠋⣿⡟⠂⢸⣿⣄⠀⠀⡈⠧⡀⠀⠀⠈⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢸⠗⠀⢳⠀⠀⠤⠌⠢⢤⣄⠀⠀⢸⠁⣾⣿⣿⡆⣼⣿⣿⠔⠉⡴⠁⠱⡀⠀⡜⠀⣸
⠀⠀⠀⠀⠀⠀⢀⣼⠏⠑⠈⠙⢦⣸⡀⢸⡆⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣿⣿⡖⠀⠚⢇⡀⠀⠘⢦⣠⡾⣿
⠀⠀⠀⠀⠀⢰⣯⠀⠁⢒⣠⠤⢤⣿⣧⠈⢿⡄⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠏⢻⣿⣿⡄⠀⠈⡆⠄⠀⠀⠹⡔⠛⠆
⠀⠀⠀⠀⠀⣾⡇⠣⢄⡀⠉⠙⠎⣻⡏⠀⠀⣿⡄⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⢳⣄⢤⡀
⠀⠀⠀⢀⠼⣋⣤⣶⠶⢮⣍⢵⣾⣿⡇⠀⢸⡟⠹⡀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠹⣿⣿⣦⡀⠀⠀⠀⠀⠰⡌⢳⢱⡀
⠀⠀⢰⣷⣿⡖⠋⠿⢲⣄⠀⣼⣿⡻⠇⠀⣼⠃⠀⢱⡀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢹⣿⢻⡙⢦⠀⠀⠀⠀⢣⠀⣸⢣
⠀⠀⢹⠟⡕⠁⠀⣀⡀⠈⠻⢿⣿⡿⢖⢤⣿⠀⠀⠀⢳⡀⠀⠀⠀⢹⡿⠀⠀⠀⠀⢀⣾⣿⠞⢻⣆⡀⠀⠀⠀⠀⢢⢏⡞
⣶⣶⣾⡔⠀⣠⠞⠁⢀⡠⢂⣴⠋⢤⡀⠱⢴⠗⣤⣶⣤⣷⣶⣶⣶⣼⣷⣤⣶⣶⣶⣾⣿⣿⣷⣦⣿⡿⢦⣄⠀⠀⣠⡾⠶⠶⠤⠶⠶⠶⠶⠶⠶
⠀⠀⠀⠻⣿⣧⣤⣄⣧⢰⠋⣿⠐⢦⡄⠀⠄⡑⢿⣿⡿⠿⠟⠛⠛⠛⠋⠉⠉⠉⠉⠉⠙⠢⣤⣀⠉⠙⠛⠛⠓⠛⠉
⠀⠀⠀⠀⠀⠀⠉⠙⣻⣧⠕⠻⢎⠲⡀⠁⢲⠤⠝⠇⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠦⣄⡀
⠀⠀⠀⠀⠀⠰⣯⡉⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⣀⠀⠀⠀⠀⢀⣀⠠⣄⠀⣀⡤⠤⠶⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣱⠦⠴⠚⠒⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⡀⠀⢀⣀⡤⡴⠶⠒⠂⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⢸
⠀⠀⠄⣡⠆⠐⢄⠠⠀⠀⠀⠀⠄⡥⠂⣄⣀⡀⠀⠀⠠⢀⡴⠶⢦⡅⠄⠀⠀⠀⠠⢀⢔⠀⡢⡀⠄⠀⠀⠀⠰⢉⠞⠒⣷⣈⠂⠀⢸
⠀⠀⠐⡃⠀⠀⢀⠀⠂⠀⠀⠐⠀⡀⠀⢈⣿⠁⠀⠀⠂⢸⡁⠀⢀⡂⠐⠀⠀⠀⠂⢀⢆⡋⡠⡀⠐⠀⠀⠰⣈⢀⠀⠀⠀⡇⣁⠆⢸
⠀⠀⠀⠑⣀⣠⠃⠀⠀⠀⠀⠀⠀⠱⣀⠟⠉⠁⠀⠀⠀⠀⢩⣙⡙⠁⠀⠀⠀⠀⠀⠀⢃⣿⡘⠀⠀⠀⠀⠀⢠⡀⢂⣀⡜⣀⡆⠀⢸
⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⢸
⣿⣿⠟⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠠⢄⣀⠀⠀⢀⣀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⣓⠄⠰⡱⠙⠦⠠⢀⣩⠤⢀⠝⡦
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠈⠁⠀⠀⠉⠛⠒⠀⠒⠛⠋⠉⠁
⠀⠀⠀⣀⠤⣆⡒⠺⡺⢻⡅⡀⠲⣦⠴⠀⠀⠁⢐⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣤⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠆⠰⢤⣀⡀⠀⢀
⠀⠠⠎⠘⠒⠛⠒⠬⠠⣈⠽⠛⠚⠁⠀⠀⠀⠀⠀⠈⢡⠄⠀⠀⠀⠀⢀⠖⠀⠀⠠⠂⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠠⠔⢠⠞⠂⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⡴⠿⣥⠭⡅⠂⠀⢀⢄⠞⠁⠀⠀⢀⠀⡂⠤⣀⠠⡀⢀⣼⠇⠒⠒⠀⣲⣤⣤⢀⣀⣠⡷⢶⠔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢘⠲⡀⠀⢀⠄⠠⠂⠁⠀⠀⠀⠐⠃⢈⡠⠤⢍⡿⢀⠾⢇⡀⠀⠀⠈⢚⣈⣡⠁⡠⢄⡀⠹⣌⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠙⠒⠒⣩⠔⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠉⠁⠀⠀⠀⠢⠀⠀⠀⠉⠀⠀⡀⠞⠩⠝⡟⡳⠁⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠰⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢆⢀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⠀⠸⠀⠀⠀⠀⠀⠊⠀⠈⡷
⠀⠀⠀⠀⠀⠀⠢⢧⣀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠲⠥⠠⠄⠀⠀⠀⠐⠒⠦⠒⠂⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠧⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠕⣒⠀⠀⢰⠽⠒⠰⡦⠤⣔⢃⢷⣮⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠖⠒⠒⠒⢀⣢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢝⠚⠉⠁⠊⠀⠑⠫⣢⡰⠂
⠀⠀⠀⠀⠀⠀⣀⠀⡀⣀⣀⡠⣄⠀⠺⠄⢲⣆⣀⠨⣟⠐⠯⠕⠶⠤⠤⢤⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢥⣀⠐⣀⠀⠀⠈⠑
⠀⠀⠀⠠⡊⠁⠀⠏⠃⠁⢠⣄⡜⢢⠀⠈⠀⠀⠀⠈⠁⠛⠬⠤⠤⣥⡤⠤⠍⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⠀⠉⠀⠉⠐
⠀⠀⠀⢠⡁⠂⢅⠱⠒⠂⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⡖⠚⠒⠲⠄⡀⠄
⠀⠀⠀⠈⢏⡑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠐⠯⠷⡷⢄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠀⠉⠊⠸⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠆⢁⣠⠬⡈⠦
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⠄⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⢩⠱⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢇⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⣠⡃⠀⠐⡘⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠄⠐⠆⠠⠔⠀⠤⠓⠒⠈⠈⠀⠉⡉⡙⠒⠶⢤⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠤⠄⢺⠀⠀⠀⠀⠀⢀⢀⡐⠛⠛⠉⠀⠀⠖⠒⠤⠤⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠒⠁⠀⢢⠀⠀⠀⠀⠀⠐⠒⢋⠤⣄⠀⢦⣴⠪⢕⣺⣓⠪⢶⡶⢄⡠⣀⠈⣁⣍⣤⡒⠈⠁⠁
⠀⠀⠀⢠⠀⠀⢀⣬⠤⠤⡁⠒⠒⠀⠒⠘⡂⠀⠂⢻⣉⢀⡀⠀⠀⢀⠀⠐⠂⠀⠀⠀⠉⣀⡠⠄⢂⣀⡇⠰⠂
⠀⠀⠀⠀⠈⠉⢍⡀⡈⣉⣅⠀⠀⠀⢒⣸⠷⠤⠬⣟⡁⢭⠅⠉⠉⠛⠛⠻⠷⠆⣀⠩⠭⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠁⠉⠉⠉⠀⠀⠀⠀⣅⠀⠀⠐⠂⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠁⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⣿⡔⣫⡤⠒⠐⠆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠉⠀⠀⢄⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢀⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⠜⠁⡀⠃⠀⠀⢘⣠⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⣿⠀⣿⣥⣦⡀⣎⠛⠀⢀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠙⡀⠙⠋⠁⠀⠀⠀⢀⣀⣨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢄⡎⠀⠀⡆⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠋⠀⠀⠐⠀⣀⠆⠀⠀⢰⡄⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⡆⠀⢀⠀⢸⠇⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠁⣁⠀⠀⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣅⠀⠀⠀⠀⠀⠀⣀⡴⠋⠘⡄⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⢀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠉⠁⠀⠀⠀⣘⣄⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠈⠄⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⡴⠁⠀⡜⠧⢤⡤⢤⠏⠉⠁⠐
⠀⠀⠀⠀⠒⡄⠀⠁⢀⣀⠤⠤⠤⠀⠀⠐⠒⠂⠈⠉⠀⠀⠀⡰⠀⠀⠒⢰⡤⠀⠠⣄⠐⢀⠀⠀⠀⠡
⣄⠉⠀⢈⡛⠘⠄⠀⢀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢴⠃⠀⠀⡄⠸⠀⡾⠀⠋
⠠⡁⠀⣈⡅⠀⠀⣠⠏⠸⡧⠆⠤⣤⠤⠐⠶⠂⠉⠁⠀⠀⡈⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡆
⠀⠁⠀⠬⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠇⠀⠀⣠⠃⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⢸⠀⠀⠀⡏⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢸⠀⠀⠰⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠂⡤⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡆⠀⠀⠃⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡇⠀⢰⠀⠀⠀⠀⣀⠄⠚⠒⠒⠚⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣠⡤⠤⠤⠤⠦⠤⠴⠤⠤⣔⢊⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⡡⣿⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡌⠀⣀⣀⡀⣘⢒⣉⠓⣋⡁⠉⠖⠉⠽⡈⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠚⠠⠄⠀⠀⠢⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠡⠤⠤⠤⠤⠤⣴⠖⠂⠁⠈⠃⠀⠀⠀⣀⡴⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣶⣶⣶⣶⣶⣶⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⠁⠉⢉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣀⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣀⣀⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡀⠀⠀⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠇⠰⠟⠛⠛⠛⠛⠛⠿⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠿⠛⠛⠛⠛⠛⠗⠀⢿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⣀⣀
⠀⠀⠀⠀⠀⣰⠚⠻⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠚⣉⡉⡇
⠀⠀⠀⠀⠀⡇⠈⣳⣄⠙⢿⠁⠀⠀⠀⠀⣀⣤⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⢶⣤⣄⠀⠀⠀⠀⠀⣸⣠⠾⠥⠀⡇
⠀⠀⠀⠀⠀⢣⠀⠀⠈⢳⡸⡄⠀⠀⠰⠾⠋⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠀⠀⠙⠳⠆⠀⠀⠀⢿⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠘⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⡰⡇⠀⠀⠀⠀⠿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⢸⠓⠤⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠻⣍⠉⠉⠉⠉⠉⠉⣉⠿⠁⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⠶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣤⣤⠴⠚⠉


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⢁⣈⣉⣉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢰⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢣⡔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⠛⠛⠛⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⠁⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡀⣰⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⢅⠁⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠰⣾⠄⠈⣠⡞⠖⠠⠄⢀⡀⠀⠀⠀⠀⢀⡀⢠⠁⠀⠀⣆⠈⠁⠀⠀⡠⠂⠁⠀⠀⠀⡐
⠀⠀⠀⡞⠢⣴⠀⠀⠀⠀⠀⠀⠰⠁⠀⢠⠃⣸⣼⣏⣠⠁⠀⡀⢀⠋⠀⢣⡀⠄⠂⠈⠀⡌⠷⢠⡔⠋⠘⡁⠀⠈⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠑⣀⠀⣆⠀⠀⠀⠀⠀⠆⠀⠃⢈⠰⡄⠏⣸⠃⡤⠚⠁⡌⠀⠀⠋⠀⠀⡆⠀⢀⠃⠀⠶⠾⢿⠀⢡⠀⢠⠀⠀⢀⠄⠁
⠀⠀⠀⠀⠈⢻⠉⠙⢦⡀⠀⠸⠀⠀⡅⠈⢴⡷⠀⠟⢀⠄⠀⠀⡇⠀⠘⠀⠀⠀⡀⠀⠈⢆⠀⠘⣠⠸⠇⠎⠀⢻⡠⠖⠁
⠀⠀⠀⠀⠀⠈⢢⡀⠀⠑⢠⠆⠀⠀⠄⠀⠈⣷⡘⠀⠃⠀⠀⠀⠰⣀⠃⠀⠀⢀⠃⠀⠀⠀⠗⠀⢻⠀⠀⢸⠠⠞
⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⢀⡖⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠟⠀⠀⢀⠋⠀⠀⠀⠈⠐⠄⡀⠁⢄⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⡠⠚⡁⠀⠀⢸⠀⢀⢀⠀⠀⠀⣸⠀⠀⠀⢾⠀⠀⠐⢦⠀⠀⠀⠈⠐⠺⢇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⡀⠀⠀⢸⠔⠁⠈⠓⢤⠐⡇⠀⠀⡰⠚⠁⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡠⠋⠀⠀⠀⡐⠉⠀⠃⠀⠀⠇⠀⠀⠀⠀⠀⠈⠌⠡⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠦⡀⢀⠔⠚⢻⡤⢾⠀⠀⣰⠆⠐⠀⠀⠀⠀⠀⠈⢠⠙⢄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡘⢿⢀⡀⠂⠀⠈⠀⢀⡉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠉⠀⢠⡀⠀⠁⠢⢠⠆⠀⢸⠃⠀⠀⢀⡀⣀⣀⠀⡀⢀⡀⠀⠀⣀⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⢈⡀⢀⣾⠀⠀⠀⠀⡏⠉⠉⠉⡉⠉⠉⢉⡉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠘⠋⢙⠀⡆⠀⠀⠀⢃⠀⠀⠔⠁⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢸⡇⠀⢠⠰⡞⢠⡇⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⡇⠀⠸⠆⠁⠘⡇⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⢸⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡆⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠰⠂⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⠉⠀⢆⣀⣀⣤⠀⠀⠀⠀⠃⠀⢀⡎⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⡿⠟⠛⠛⠀⠀⣸⣿⣿⡿⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⡿⠁⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⠿⠿⠿⠿⠻⠿⣯⠻⠿⢿⠿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣛⣛⣛⣛⣟⣻⣿⣟⣛⣛⣛⣛⣛⣻

⠀⠀⠀⠀⠀⠀⠀⣶⠖⠶⠖⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠲⣶
⠀⠀⠀⠀⠀⣤⠴⢿⠶⠶⠶⠶⠖⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠓⠛⠚⣿⠶⠶⣦
⠀⠀⠀⠀⠀⣿⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠂⠀⣿
⠀⠀⠀⠀⠀⢸⣆⣘⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣧⣤⣴⠏
⠀⠀⠀⠀⠀⠀⣩⡿⠹⢧⣭⣥⣭⣤⣤⣤⣤⣤⣤⣤⡤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠋⡘⠧⣄⡀
⠀⠀⠀⣠⡶⢋⡵⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢮⣄⡈⠙⢶⡄
⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣌⠛⣦⡀⠹⣆
⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠲⠶⠶⠶⠴⣯⣴⣤⣭⡛⠶⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠈⠳⣌⣷⠀⢹
⣼⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢁⡞⠙⠒⠒⠲⠶⣄⢀⡟⠉⠓⣦⠀⣩⣿⣤⣀⣀⣤⣤⠀⠀⠀⢈⣤⣤
⣿⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⣏⡴⠚⢉⡙⢦⢠⠇⣼⠃⢀⠞⢁⡼⠷⠤⠤⣄⠀⢰⡏⠀⠀⠀⠈⠳⠞
⣿⠀⠀⠀⢀⡾⠻⣦⣀⣀⣼⣧⣮⣼⣼⣧⣏⣿⣼⣿⣼⣧⣴⣧⣴⣯⣤⣤⣤⣴⣧⣠⣟⣀⣀⣀⣤⠞⢷⡀
⣿⠀⠀⠀⠀⠙⣦⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣥⣴⡟⠁
⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⣼⠛⠺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⡟⠳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⢀⡟⢠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⢸⡇⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⣿⠀⣼⠁⠘⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠉⠛⣳⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⢀
⣿⠀⣠⡾⢋⣴⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣷⣝⠳⣼
⣿⠐⠻⢦⣿⣄⣠⠾⠿⣗⣶⡶⢶⡶⠶⠶⠶⣶⢶⠶⢶⣶⠶⢶⡶⠶⠶⠶⠶⠶⠶⢶⣶⠶⢶⣿⣄⣉⡿⣰⢿
⢻⠀⠀⠀⠀⠉⠙⢛⣶⣦⣍⣀⡾⠁⣀⣀⢰⡗⢒⣉⣭⣤⣶⣾⠃⣶⣾⣿⣛⡿⣷⣀⣈⣷⣄⠙⠿⢋⡾⠃⢸
⢸⠀⠀⠀⠀⠀⢰⣿⠁⢰⠾⢹⣿⡿⢛⠛⠻⣟⠛⠛⣿⣿⣿⣿⡶⢿⣼⣷⣞⣶⣛⣽⣇⢈⣿⡷⡴⠋⠀⠀⣿
⢸⡇⠀⠀⠀⠀⢸⣿⢮⣿⡏⣭⣛⢧⡘⡧⢠⣿⣽⣿⣿⣿⣯⣿⣭⣿⣯⣿⠿⣯⣅⣠⣿⣯⠿⠃⠀⠀⠀⠀⣿
⠘⣧⠀⠀⠀⠀⠀⠉⠛⠻⣽⣶⣬⣼⠷⠖⠋⠀⠀⢸⣿⣟⣿⣻⣻⣿⣿⣿⣶⣶⣿⠿⠋⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠘⢷⣄⠀⠙⠒⠚⠛⠻⠾⠿⠿⠿⠶⠶⠶⠶⠶⠾⠿⠿⠯⠯⠭⠴⠴⠶⠿⠿⠶⠶⠶⠶⠒⠚⠋⠀⢀⣼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠤⠴⠶⠤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠞⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢀⣠⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⣤⣀⠀⠈⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠈⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠑⢜⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢀⠎⢀⡤⠖⠋⠉⠉⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠉⠓⠦⡀⠘⡄⠈⠌⣷
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠈⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠘⢦⠘⠀⠈⠸⣇
⠀⠀⠀⠀⢠⣤⣿⠀⠀⠀⠀⡏⠀⠀⣠⣾⠋⠙⠆⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⣼⠀⠀⢀⣴⠋⠙⠗⠀⠀⠀⠘⡆⠀⠀⠀⣻⣤⣄
⠀⠀⠀⢠⡏⠙⡎⠇⠀⠀⠀⡇⠀⢠⣿⣿⣶⣾⣦⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⣾⣿⣶⣶⣶⡀⠀⠀⠀⡇⠀⠀⢰⢃⠎⢹⡇
⠀⠀⠀⠸⡇⠀⠁⠀⠀⠀⠀⢳⡀⠈⢿⣿⣿⣿⡟⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠸⡄⠀⠛⣿⣿⣿⣿⠀⠀⠀⣰⠃⠀⠀⠘⠘⠀⢸⡇
⠀⠀⠀⠀⢿⡀⡀⠀⠀⠀⠀⠀⠳⣄⠀⠁⠈⠛⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠙⠁⠀⢀⡴⠃⠀⠀⠀⠀⢀⡀⣼⠃
⠀⠀⠀⠀⠈⢷⣅⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠊⠁⠀⠀⠀⠀⢀⠀⢨⡽⠃
⠀⠀⠀⠀⠀⠀⢿⠀⡇⠀⠀⠀⠀⢉⡗⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠐⡍⠁⠀⠀⠀⠈⡄⣾⠁
⠀⠀⠀⠀⠀⠀⠸⣇⡇⠀⠀⠀⠀⠘⢹⣷⣦⡤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⣴⣶⣿⠹⠀⠀⠀⠀⢰⣧⡏
⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠈⣿⣿⣇⣀⢸⠉⠉⠉⢻⠛⠛⠛⠛⢻⡋⠉⠉⢹⢀⣀⣿⣿⡏⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣶⣶⣿⣷⣦⣤⣶⣾⣷⣶⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠻⢿⡟⡟⠻⠿⢿⠿⠿⠿⠿⢿⠿⠿⠛⠟⣻⠟⠁⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠙⠳⠤⣀⣘⡀⠀⠀⠀⢸⣀⣠⠴⠛⠁⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠓⠒⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠶⠿⠿⠿⠿⠷⠶⢶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢀⣤⠀⠀⠀⣿⠉⠉⠉⣿⠀⠀⢀⣤⡀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⢀⣴⠟⠙⢿⡶⠿⠛⠀⠀⠀⠛⠿⣶⡿⠋⠻⣦⡀⠀⠀⠀⠀⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣠⣼⠟⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⢀⣴⠿⠛⠛⠛⠿⣦⡀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⣾⡟⠛⠛⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠛⠛⢻⡇⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠙⠛⠻⣷⡀⠀⠀⢻⣦⡀⠀⠀⠀⢀⣴⠟⠀⠀⢀⣿⠛⠛⠃⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡷⠀⠀⠀⠉⠛⠷⠶⠿⠛⠁⠀⠀⠀⢾⣇⡀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⡀⠀⣀⣄⡀⠀⠀⠀⠀⠀⢀⣠⡀⠀⢀⣽⠗⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⠟⠙⠛⣷⠀⠀⠀⣿⠛⠉⠻⣶⠟⠁⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠐⠿⢷⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣶⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟
⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁
⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠘⠛⠿⠶⢶⣶⣶⠶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠀⠒⠀⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠅⠒⠉⠀⠀⠀⠢⢤⣙⡖⡴⠖⠒⠒⠒⠀⠀⠀⠀⠀⠐⠒⠒⢒⠛⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠂⠀⠀⠀⠀⠀⠀⢸⡄⠠⡇⡏⠈⠉⠉⠉⠀⠀⠀⠀⠉⠉⠁⡀⠨⡇⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠔⠲⠀⠀⢿⠉⣷⣠⣯⠀⠈⠀⠀⠀⠀⠀⠐⠂⠐⠚⡇⠀⠃⠰⡍⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠁⠀⠀⠀⠀⠀⠀⣾⣿⢿⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⡇⠀⠀⠀⠁⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⠀⠀⡀⠀⠀⣿⡏⡀⣧⡄⠀⠀⠀⠀⠀⠰⠚⠀⠀⠈⠁⠀⠐⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢀⣄⡀⠠⠀⠀⡀⠙⠃⣇⡿⡀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣇⠘⠋⠁⠀⠀⠀⠀⢀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⣉⠀⠀⠀⠀⠀⠴⠤⡏⢸⢃⣀⢀⠀⠀⠈⠉⠉⠀⠀⠉⠀⠀⠸⠖⠄⠀⠈⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⡀⠀⠴⠒⢒⣲⣦⣤⡆⣸⢈⣁⣀⣀⣀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⣀⡇⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⢐⣦⣤⡴⣶⣶⣿⣽⢠⡏⣬⣿⣶⣆⡀⠀⠉⠀⠀⠀⠀⠐⠒⢒⣒⣶⠓⣟⣰⠀⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⡿⢾⣿⠤⣴⣨⣌⣙⣛⣳⢾⣯⣅⣀⠀⠀⠐⠂⠀⠀⠀⠀⠈⣣⠭⠽⡤⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⠶⢷⠾⣽⣹⣻⡧⠄⠀⣠⣀⠈⠉⠙⢛⡛⠻⣶⡶⣦⣤⣤⣀⣉⣉⠉⠀⠒⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠲⠤⢤⣌⣉⣁⠑⠒⠦⢥⣄⢂⠨⣛⣛⠿⢿⣿⣗⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠒⠺⠟⠚⠓⠶⠾⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡡⢖⠶⢒⠦⢄⡈⠉⢹⡯⣍⣉⣁⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢸⡁⢘⢰⠑⢉⡭⣟⣦⡀⠉⠪⡙⠫⠍⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣆⠢⣑⢦⣀⠠⡘⢼⣿⠞⣉⣦⣔⠌⠒⢤⣀⣀⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣿⣿⣶⡵⠚⠛⠓⠊⠿⠾⠏⠁⠈⠛⠲⣤⣤⣭⡭⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠑⢶⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡟⠀⣠⣴⣶⣶⣶⠖⠀⠀⠀⠲⣶⣶⣶⣦⡄⢘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣿⡇⠀⠉⢠⠄⠀⠀⠀⠀⠀⠀⡴⠀⠀⢠⡀⠉⢸⣆⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢇⢠⢿⠃⠀⠀⠀⠀⠂⠀⡰⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡟⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⢸⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣧⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠘⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠇⠀⠀⠀⢀⠤⠊⠀⠁⠀⠈⠀⠑⠦⡀⠀⠀⢸⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠿⠿⠿⣷⣦⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠁⠠⡄⠠⡬⣿⠃⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⠈⠁⠀⠁⣽⠆⠀⠀⠀⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠂⠀⠀⠀⠀⠓⠀⠀⠀⠀⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣄⡀⣠⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⢠⣦⡄
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣼⠛⠿⠟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢹⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡼⠃
⠀⠀⠀⠀⢀⣠⣴⣶⠁⣁⠈⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣀⣡⣶⣄⡀
⠀⠀⠀⠀⣿⣿⣿⣿⡋⠛⢹⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⢠⣿⣿⣿⣿⣷⡀
⠀⠀⠀⢀⣿⣿⣿⣿⣷⠀⣾⣿⣿⣿⣿⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⢱⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣶⣾⣿⣿⠿⠛⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⠹⣿⣿⡄
⠀⠀⠀⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇
⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢀⣿⣿
⠀⠀⠀⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠇
⠀⠀⠀⢉⡇⠈⠉⠉⠉⠉⠉⠉⠉⠇⢸⠉⠀⠀⠀⠀⠀⠀⢀⠉⠉⠙⠛⠉⠉⠁⢠⠟⠟
⠀⠀⠀⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣰⢧⣀⡒⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠘⠒⠒⠒⠋⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢃⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⡀⠀⠘⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠠⠁⠀⠀⠀⠀⠀⠠⡀⠀⠀⠁
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠐⠀⠀⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢀
⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⢀⠀⡀⢀⠀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠈⡄
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⣷⣤⣶⠖⢲⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠘⣿⡵⠶⠋⣽⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡇⠀⠀⢀⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢸⣟⣠⣇⣠⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⢸⣯⣭⣤⣶⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠶⠶⠦⠤⠤⢤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣛⣓⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠒⣰⠖⠶⠖⡒⠲⠶⣦⡄⡶⠖⠀⠖⠰⠶⡄⢰⠏⣿
⠀⠀⠀⠀⠀⠀⢰⣿⠻⠿⠿⠿⠿⠶⣶⣤⣤⣄⡀⠀⠀⢠⡾⣱⣷⡈⠿⠀⠀⣠⢄⣄⢀⢠⠃⡅⠀⠀⠀⠐⣤⢤⠆⣰⣿
⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⢀⡀⠈⠉⠙⠿⣦⣤⡟⠑⣿⣟⡆⠀⠀⠘⣇⣿⣿⡀⢀⡴⠃⠀⢀⣠⣶⢏⡞⣰⣿⡇
⠀⠀⠀⠀⠀⢀⣿⠛⠂⠀⠀⠀⠀⠀⠙⠢⣌⠲⣄⠈⠙⠷⣶⣶⣭⣌⡓⠀⠀⠚⠺⠿⠿⠿⠶⠼⢦⡴⡿⠄⠞⣰⣿⣿⡧
⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⢜⣷⣬⣳⣦⡀⡀⠈⠉⠛⠻⣷⣶⣶⢶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⣿⣿⡇
⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⢀⣤⣄⠙⠎⠛⠉⠉⠉⠩⠬⢦⡀⠀⠀⠈⠛⢿⣿⣭⣭⣭⣽⣿⣟⣛⣛⣛⣛⣻⣿⣿⡇
⠀⠀⠀⢠⣿⡟⠀⡆⠀⠀⠀⠀⠀⠙⣿⣷⣦⣴⣾⣿⣿⣿⠗⠀⠁⠀⠀⠀⠀⠀⠻⣿⣿⣟⣳⣖⣲⣶⣶⣿⣾⣿⣿⣿⡇
⠀⠀⠀⣾⣿⠁⣄⢻⢸⠠⢠⡀⡀⠀⠈⣿⣿⣿⣷⣤⡉⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣛⣓⣶⣟⣿⣿⣿⡇
⠀⠀⢰⣿⠇⢠⣿⣿⣾⣷⣌⣷⣿⡀⠀⣿⣷⣀⣩⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⢀⠀⣠⡿⠿⠿⠿⠶⠶⠶⠶⠿⢿⣿⣥
⠀⠀⣾⣿⡀⢾⣿⢏⡉⢩⣽⡻⣿⣿⠇⠈⠛⠿⠿⠟⠿⣿⣿⣍⠉⣿⣿⡇⠀⢠⣾⠟⣫⣾⣛⠿⠷⣶⣶⣲⣶⣶⠖⠠⣿
⠀⠀⢹⣿⡇⢼⣿⠈⣛⠒⠒⣃⣼⣿⡷⣁⠄⠀⢀⣴⣶⣬⣿⣿⣿⡿⠃⣠⣼⠟⣡⣶⣯⣭⣀⣀⡀⢈⣤⣼⠏⠀⢄⣠⣿
⠀⠀⣀⣿⣷⣾⣿⣓⠭⣭⣍⡭⣿⣿⣿⣷⣫⠵⠀⠛⠛⠛⠛⢿⣿⣿⡾⠋⣡⡾⣿⣛⢓⣈⣿⣿⣿⡿⢋⠤⣪⡴⠋⢡⣿
⢰⣞⡉⠉⢙⣻⣿⡝⠻⢒⣠⣬⣿⣿⣿⣯⡴⣞⣥⣶⡶⢂⣠⣾⠟⢉⣴⡿⠁⠛⠻⢿⣿⣭⣿⣟⣡⢖⣡⡞⠁⡠⠞⠁⣿
⣿⠯⣝⡶⣾⣼⣿⣍⣓⣒⢶⣚⣿⣿⡟⣛⢿⠿⣿⣿⣿⡟⢋⣤⣶⣿⣭⣷⣤⣤⣶⣾⣿⣿⡿⣫⡴⡫⠊⢀⡤⠂⠀⣘⡯
⣿⣖⠶⠖⠒⢚⣿⠧⢈⣉⣉⣭⣿⣟⢰⠋⠀⣰⢸⣿⣿⣿⠤⠤⠤⠤⠴⠶⠶⠶⠖⠒⢶⣿⢞⣵⠋⣠⠖⠉⢀⣠⠞⠋
⣿⣇⠪⠭⣉⠩⣿⡛⠓⠦⠭⠴⣿⡿⢦⣍⣉⡥⢾⣿⣿⣿⣍⣉⠉⠉⠉⣉⣉⣉⣉⣉⣹⣷⢟⣡⠚⢑⢅⡴⠛⠁
⣿⣧⣍⣒⣒⠚⣿⣛⣛⠛⠒⠛⣻⣷⣝⣒⣐⣚⣿⣿⣿⣿⡖⠒⠒⠒⠒⠒⠒⣒⣒⣒⣾⣿⣿⣭⣖⡵⠋
⠙⠷⣤⣭⣤⡴⢿⣍⣛⣉⣛⣉⣽⣷⣬⣭⣭⣷⠾⠟⠁⢸⣿⣿⣟⣛⣛⣛⣛⣋⣩⣝⣛⣿⣿⡿⠋
⣤⣤⣤⣤⣤⣤⣤⣬⣽⣿⣿⣯⣥⣤⣬⣭⣭⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣽⣤⣭⣿⣵⣯⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿