Naughty face Emojis & Symbols

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠙⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣄⠀⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠻⢿⣿⣿⠇⢸⣿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣄⠀⠉⠁⠀⠀⠉⠛⠻⢿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠙⠿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠟⠁⠀⠀⠀⢀⣬⣄⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠈⢻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣤⣤⣤⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠻⣿⣿⠟⣹⣿⡿⠋⠉⠹⣿⣟⠛⢿⣿⣿⠛⣿⣿⠿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠘⣿⣿⣦⣤⣴⣾⣿⡿⠁⠀⠀⠀⢻⣿⣄⡀⠉⣀⣴⣿⡏⠀⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠈⣙⢿⡿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⠿⠋⠀⠀⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠁⠘⢠⣤⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⣰⣶⡄⣀⣐⣠⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣶⣾⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣯⡹⠿⠋⠉⠉⠉⠉⠻⠏⠀⠀⠀⠀⠘⢿⢃⣴⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⡿⢿⣿⠿⠿⠿⠛⠉⠹


⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣷⣶⣤⣄⣀
⠀⠀⠀⠀⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣾⣿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠙⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣤⣆⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⡟⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⣿⣄⣽⣿⣿⠟⠻⠿⢿⣿⡿⢿⣿⠟⣿⣿⡏⠉⠉⠁⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠻⣧⣿⣿⠟⠀⠀⠀⢠⡿⠀⠀⢿⣹⣿⣿⠇⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣾⢿⡄⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠻⣆⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣼
⠀⢀⣴⣿⡟⠉⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠈⠛⠶⣤⣤⣤⣤⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⣼⠇
⢠⡞⠁⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⠶⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠋⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⢹⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠈⣿⡈⠛⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⢿⠛⠻⠷⢶⣦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣶⠶⠟⠛⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⢸⡆⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⣿⠋⠉⠉⠉⠉⣽⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⣧⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠒⠿⢶⡤⠤⣤⣤⣧⣀⣀⣀⣀⣀⣿⣀⣀⣤⣤⣤⠧⣤⠶⠶⠒⠛⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⢸⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣤⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢻⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣤⣇⣀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣘⣇⣠⣤⣴⡶⠿⠟⠛⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠉⠛⠲⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠚⠋⠉⠉⠉⠓⠒⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⡇⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⣀⠤⠚⠁⠀⠀⢱⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⢠⠏⢉⣡⣄⠀⠀⠀⠀⠀⠀⣤⣤⣤⣀⠀⠳⡆⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⢀⠎⠾⠿⠟⠋⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠃⠀⢰⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣀⣀⣀⣠⠋⠀⣠⣴⣶⡦⣄⠀⢠⡀⠀⠀⡠⢴⣶⣶⢄⠀⠈⣇⡠⠄⠠⡀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠎⠀⢀⣀⣇⠀⠰⢅⣿⣿⣣⠞⠀⠀⡇⠀⠈⠣⢼⣿⣯⠤⠃⠀⢸⣤⡒⠀⡸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢧⡀⠀⠚⢹⠀⠀⠀⠀⠁⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣀⡠⠔⠁⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠑⠒⠚⡇⠀⠀⠀⠀⠀⠀⠀⠙⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠰⣦⣤⣤⣶⣿⠇⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠙⢿⣋⣉⠟⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⣀⡀⠀⠀⠀⠀⠉⠒⠢⡤⠤⠤⠒⢲⠚⠉⠀⠀⠀⠀⢀⣀⡠⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⠒⠒⠢⠤⠤⡇⠀⠀⠀⢸⡤⠴⠖⠒⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡇⠀⠀⠀⠀⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣯⡀⢸⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣹⣿⣿⣿⣿⣿⣿⣿⡏⠉⣹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣇⠀⣸⣿⣿⣿⣿⣾⣿⣿⣿⠿⠛⢿⣿⣿⣿⣶⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣦⡄
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⢿⣿⣿
⠀⠀⠀⠀⢸⣿⡿⠙⡟⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⢸⢸⣿⣿⠃
⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠻⣿⣿⣤⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣿⣿⠟⠀⠀⠐⢸⣿⣿
⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⢀⣤⡄⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⣴⣦⠀⠀⠸⣿⣿⠀⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣧⠀⠀⣸⣿⡏⠀⠀⠀⠀⠀⠻⣿⣷⣤⣾⣿⡟⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠻⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠃⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣷⠀⠀⢀⣴⣄⠀⢀⣴⣦⡀⢠⣿⣿⡆⠀⠀⠀⠀⣈⣉⣹⣿⡟⠉⠉⠃
⠀⠀⠀⠀⠙⣿⠛⢹⣿⣿⣭⡁⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠘⢿⣿⣿⣿⣷⣶⣤⣄
⠀⠀⠀⠀⢀⣧⣴⣾⣿⣿⣿⠃⠀⠀⠀⠀⠉⠉⠉⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠛⠻⡿⠟
⠀⠀⠀⠀⠻⢿⠟⠋⠙⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⢻⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⠿⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⢿⠿⠿⠛⠛⠉⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⡤⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⠚⠋⠉⠙⠳⣄⠀⠀⠀⣠⣤⣴⡶⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⣠⣤⡀⠀⠈⢧⠀⠸⠟⠋⠁⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣦⣾⣿⣿⡆⠀⢸⡆⠀⠀⠔⣠⣶⣫⠥⠶⠶⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠱⢿⣿⠟⠁⠀⣼⠀⠀⠠⠾⠛⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⣾⣿⠛⠻⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿⣷⠲⠦⠤⠴⠖⠋⠉⠀⠀⠀⠀⢀⣀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣀⣀⣀⣀⣀⣀⣠⣤⣶⣾⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⣿⣿⡿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⠿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠉⠀⠀⠀⠈⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠶⠶⠶⣦⣄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠀⠈⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠣⢤⡀⠀⠀⠈⠻⣿⡿⠉⠀⠀⠀⢠⠀⢠⠀⠀⠀⠈⠻⣿⡿⠉⠀⠀⠀⣠⠤⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠸⣄⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⣠⡤⠴⠚⠉⠀⠀⠀⠀⠀⠉⠐⠂⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠫⠽⢿⣿⢋⡿⣻⣿⠱⡼⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⣿⡄⡆⡀⠀⣿⠟⠑⠂⠠⢸⡏⠱⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣼⠛⢀⢁⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣵⣯⣶⣤⣴⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡿⠟⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣠⣊⣠⣴⠶⠶⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢏⣴⣾⣿⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣾⣿⢋⡾⣉⡼⠷⠒⠒⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣱⢟⡿⢡⣿⡼⢋⡶⠚⠉⠉⠳⣌⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢸⡏⣿⡃⠀⠈⠀⠋⢀⣤⢤⣄⡀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠙⣾⢀⠏⠀⠀⠠⠜⠚⠓⢤⠠⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠃⡈⠀⠀⠀⠀⠀⠘⠙⣻⡄⢧⠐⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢽⣿⢍⣉⠁⠂⠀⠀⠀⠀⠀⠀⢉⡷⢸⡓⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⣽⣯⢶⡶⣶⣦⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡽⠁⠀⣼⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢋⣽⡕⣽⣊⠀⢁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠟⠀⠁⠀⣤⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢧⠙⣰⠊⠉⠉⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣋⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⣰⠞⠉⠛⠻⢦⢀⠀⠀⠈⠆⠀⠀⠆⠀⠀⠀⣠⠛⠃⠀⠙⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡍⠀⠀⠈⡀⠀⠀⠀⠀⢹⣆⡀⠀⠀⠀⠀⠀⠀⣰⡞⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⡋⠀⠀⠠⢵⣄⠀⠀⠀⠀⣿⢥⣀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠄⣀⠤⠀⠀⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⣷⠀⠀⠀⠀⠏⠀⠶⣄⠀⠸⣜⡏⠀⠀⠀⣀⡘⠀⠀⣠⡦⠒⠸⠁⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠐⢈⢹⣧⡀⠀⠀⠀⣃⠀⠀⢈⡙⢦⠈⢷⣃⠀⢱⠿⢁⣴⢋⡁⠀⠀⡸⠀⠀⠀⠀⢠⡇⢀
⠀⠀⠀⠀⠀⠀⢀⣑⣶⡝⣼⠳⢀⠀⡄⠩⣆⠀⢸⣆⣆⠀⡌⠋⠀⠈⢠⠋⣷⣸⡇⠀⣰⠋⠀⠐⠀⠀⡹⣷⣧⡀
⠀⠀⠀⣠⣤⠶⠿⢿⡟⠅⠀⠿⣽⡀⢋⠀⠈⠱⢄⣙⠁⢀⡇⠀⠀⠀⢰⡀⠘⢋⣠⠞⠁⠀⠀⠀⠀⠀⡌⠛⢿⡿⣻⣄⡀
⠀⠀⣸⣯⡝⡆⠘⢉⡟⠑⠊⠀⠀⠀⠀⠀⠀⠀⢀⡭⠟⠛⢀⣤⡤⠤⠈⠻⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠑⢹⡆
⠀⣾⢏⡻⠟⡷⠖⠂⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠫⢭⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠂⠀⠀⠈⠲⣽⡇
⢰⣡⣾⣏⠉⣠⠔⠖⡶⠒⠛⠁⢰⣆⠀⠀⠀⢀⡶⢶⣀⣀⠀⠀⠀⢀⣀⠀⣀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠉⠓⢦⣁⡀⠀⠀⠈⢳
⠰⣯⡿⡾⢡⠇⠀⢸⠀⠀⠀⣠⣄⣿⢠⡤⣤⣨⣷⡄⠈⣭⢀⡀⢠⡬⣭⣠⣿⡶⢆⣤⢤⡀⢻⣇⣀⣴⠂⠀⠀⡟⢏⠣⡀⠀⠸
⠐⣯⢠⣿⣏⡗⠀⠀⠀⠀⠘⢧⡼⠿⠻⣯⣩⠄⠹⣧⠀⣿⢸⡷⣾⠀⣿⠁⢸⡇⠘⢿⣩⡅⢸⡏⣿⠏⠀⠀⠀⡇⠈⠀⠀⠐⢦
⠀⢸⣤⣟⣧⢸⡀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠈⠁⠀⠀⢠⣤⠈⣡⡄⠀⠀⠀⠀⠸⠏⣠⣤⠀⢠⠃⠀⠀⠀⠀⣾
⠀⠀⠛⢳⣺⣏⠁⠀⠱⡀⠀⣰⠀⢰⣿⣷⠀⢠⣿⠀⢰⣷⠀⣤⣶⡄⠸⣿⠀⣿⣷⣿⣿⣿⣿⣿⣆⣿⠃⢀⠎⠀⠀⠀⠠⢰⠋
⠀⠀⠀⠀⠙⢷⣵⣄⡀⠙⢄⣿⡇⣸⠇⣿⡇⢸⣿⠀⢸⣿⢸⣿⠋⠁⠀⣿⠀⣿⠛⠛⣿⣿⠉⠈⢿⡏⣠⠎⠀⠄⢶⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠘⢾⣷⣄⢀⣿⣷⡿⢰⡿⣿⡘⣿⠀⢸⡏⣾⡇⣴⣾⡆⣿⡿⣿⠀⠀⢹⣿⠀⠀⢸⡟⠁⡴⢋⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⢻⠇⢸⣷⣿⣇⢿⣤⣾⠃⢹⣧⠙⣿⠀⣿⠀⣿⠀⠀⢸⡏⠀⠀⢸⣿⣠⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠘⠀⠿⠋⠙⠛⠀⠉⠁⠀⠀⢻⣷⣿⡇⢸⠀⠋⠀⠀⢸⡇⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣤⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣦⣤⣙⣷⣾⣿⣿⣴⣿⣵⠾⣂⣀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠶⠶⠿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⣻⣿⣿⡿⠟⠛⠉⠉⠉⠉⠀⠀⠉⠉⠉⠙⠛⠿⣿⣿⣿⠷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢻⡿⠋⠀⠀⠀⠀⠴⠛⠛⠆⠀⢀⣀⠀⠀⠐⠛⠛⠆⠀⠀⠀⠀⠈⢻⡟⢻⣧
⠀⠀⠀⠀⠀⣀⣠⣦⠀⠈⠳⣾⠁⢰⣾⣿⣶⡀⠀⡴⣆⠀⠀⠉⠉⠁⠀⠀⣰⢦⠀⠀⠀⠀⣠⣀⠀⢿⡼⠃⠀⠀⣴⣄⣀
⠀⠀⠀⢠⣼⡏⢻⡌⣷⢶⡄⣿⠀⠘⣿⣿⣿⡇⠈⠀⠈⠳⣦⣤⣤⣤⢴⠞⠁⠀⠀⠀⢠⣾⣿⣿⠀⣸⡇⢠⡶⣾⢡⡟⢹⣧⡄
⠀⠀⠀⡼⢦⡙⢀⣴⣄⡞⠁⠹⣆⠀⠈⠋⠛⠃⠀⠀⠀⠀⢳⣄⣿⣠⡞⠀⠀⠀⠀⠀⠈⠈⠙⠁⢠⡟⠀⠈⢳⣠⣦⡀⢋⡴⢧
⠀⠀⠀⠙⠲⢦⡈⢻⠇⠻⣆⠀⠙⠷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾⠋⠀⠀⣰⠟⠸⡟⢁⡴⠖⠋
⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠈⢳⣤⣀⣀⠉⠙⠛⢲⣶⣶⣶⠶⠶⠶⠶⠶⠶⣶⣶⣶⡚⠛⠉⠁⢀⣀⣤⡞⠁⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣠⣿⣻⡏⠛⠻⠿⢿⣿⠛⠉⣿⡀⠀⠀⠀⠀⢀⣿⠉⠙⣿⡿⠿⠟⠛⢹⣿⣿⣄⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡻⠋⠀⠀⠀⠀⢀⣿⠠⡦⣿⣷⣶⣶⣶⣶⣾⣿⢴⠄⣿⡀⠀⠀⠀⠀⠙⢟⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⣠⡾⠻⣷⣴⡿⠃⠀⠀⣴⣤⡈⢿⣦⣾⠟⢷⣄⣀⣀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠶⠟⠋⠀⠀⠀⠀⠀⠀⣀⠀⠈⠻⢿⢦⡀⠀⢠⣿⠉⠉⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⣠⡶⠿⠛⠛⠻⣷⡄⠀⣠⣴⠾⠛⢻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⣿⡆⠀⢠⡞⠉⠀⠀⣾⣷⣄⠈⣿⡼⠋⠀⠀⢠⣿⣿⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⡇⠀⠈⠀⠀⠀⠀⠈⠻⠿⠁⡿⠀⠀⠀⠀⠘⠟⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠉⠁⠀⠀⠀⠀⠀⣶⠀⠀⠀⢠⣷⠿⠿⣷⣴⠀⠀⠀⢀⣿⡾⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⣀⣀⣀⣀⣿⠀⠀⢰⠟⢡⣶⠀⣿⣿⡀⠀⢀⡾⠁⣀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⢿⡄⠀⠈⢀⡟⠁⣰⡏⢹⡇⠀⠈⢠⣾⡏⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⣀⣴⠟⠀⠈⢿⣄⠐⠛⢋⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀⠙⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢀⣴⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠶⠶⣦⣤⣀⡀⢸⣟⣰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣁⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠿⠛⠛⠛⠉⠉⠉⠙⠛⠛⠿⢷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠿⠛⠉⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣤⠀⠀⢀⣠⣤⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠉⠀⠀⠀⠀⠞⠁⠀⠈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣾⡿⠟⠛⠉⠉⠉⠙
⠀⠀⣠⣶⡿⢶⣦⣄⠀⢀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⣀⣀⣀⡀
⠀⣼⡿⠋⠀⠀⠈⢻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢾⣧⠀⠀⢾⡇⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠿⠿⠟⠛⠃
⣸⣿⠁⠰⠿⠿⣶⣾⣿⠋⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠺⠏⠀⠀⠘⠁⠀⠀⠀⢈⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⠀⠀⠀⠀⠀⣀
⣿⣿⣀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠸⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠿⣿⣿⣿⠿⠟
⠛⠿⠿⠿⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⢦⣤⣤⣴⣶⣶⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟
⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠁⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋
⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣶⠶⠿⠛⠋⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣀⣀⣠⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠟⠉⠀⠀⢀⡀⠉⠉⠛⠿⣿⣿⠿⠋⠉⠁⡀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡏⠀⠀⢰⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⣰⣿⢿⣿⣿⣷⡄⠀⠀⢻⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⢿⣇⠛⠟⣡⣿⡇⠀⠀⠀⠀⣿⣿⡘⠛⢋⣿⠇⠀⠀⠘⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⠀⠀⠀⠙⠻⠿⠟⠋⠀⠀⠀⠀⠀⠈⠛⠟⠿⠟⠋⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡀⠀⠀⢀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⠀⢸⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣧⠀⠀⣿⠋⠉⠛⠓⠶⠤⠀⠤⠠⠤⠴⠖⠚⠋⠉⢹⡇⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡄⠀⢹⣷⡀⠳⣶⣶⣤⣤⣤⣤⣤⣴⣶⡶⠃⣠⣿⠁⠀⣸⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣄⠀⠙⢿⣦⡀⠙⠻⠿⠿⠿⠿⠟⠋⣠⣼⠟⠁⠀⣼⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣦⡀⠀⠙⠛⠷⢦⣤⣤⣤⣤⠶⠾⠛⠁⠀⢀⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⣉⡉⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠻⣿⡿⣿⡿⠛⠋⠙⠻⠿⣿⡿⣿⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣿⠁⠻⠀⠀⠀⠀⠀⠀⠻⠁⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣿⣿⣿⣿⣿⣷⣾⣷⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣽⢟⣿⠿⢻⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣾⣿⣿⣿⣿⣿⣿⣟⣿⣿⣽⣿⡿⠿⠚⠉⠒⠋⢁⠎⡌⠡⠹⣿⣽⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢯⣿⣿⣿⣿⣿⣽⣾⣿⠋⠉⠀⠀⠀⠀⠀⢀⠔⠁⡰⠁⠀⢇⠙⠉⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠰⣿⢹⣿⡿⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢾⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣸⣟⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣌⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠐⣾⣿⡗⠄⠀⠀⠀⠀⠀⠀⠀⠠⢶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⣀⣀⠀⣀⡀⣀⣀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣯⣩⣛⣩⣽⣿⡿⠁⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠈⠻⠿⣿⣿⡿⠿⠛⠁⢀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁
⣿⣿⢛⢿⢛⠟⣿⢟⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⠟⠋⣠⣶⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠁⢠⣾⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⡀⠈⠻⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡟⠁⠀⢀⣿⣿⣿⠃⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣦⠀⠈⢿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠏⠀⠀⠀⠘⣿⣿⣿⡀⠀⢀⣠⣶⣿⣿⣿⠇⠀⠀⢸⣿⣦⠀⠀⠀⠈⢿⣿⡇⠀⠈⢻⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡏⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢸⣿⣿⣷⣤⣀⣠⣾⣿⡇⠀⠀⠈⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⣿⣿⣿⠀⠀⠀⠀⣸⣿⣿⠿⢿⣿⡿⠿⠋⠀⠀⠀⠀⠸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣄⠀⣠⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠙⠻⠿⣿⣶⣦⣤⣀⣀⡀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⣀⣀⣤⣤⣶⣾⡿⠿⠛⠉⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣿⣿⠛⢿⣿⣷⣶⣦⡀⠀⠀⠀⠀⢠⣴⣾⠿⣿⣿⠛⣹⣿⠇⠀⠀⠀⠀⢸⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠘⢿⣷⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⠿⠋⠀⠀⠀⠀⢀⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣆⠀⠀⠀⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⡗⠀⠀⢀⣾⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⣄⠀⠈⠻⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⠟⠁⢀⣤⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣦⣄⠈⠙⠿⣿⣿⣿⣯⣍⣉⣉⣉⣩⣽⣿⣿⡿⠛⠁⣠⣴⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣶⣤⣈⡉⠛⠻⠿⠿⠿⠿⠿⠛⢋⣹⣤⣶⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠛⠛⠛⠛⠛⠋⠉⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠶⠒⠚⠛⠉⠉⠉⢹⠀⠀⣸⠀⠀⠀⠈⠉⠉⠙⠛⠒⠲⠦⢤⣤⣀⣀
⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡟⠀⠀⠻⠤⢤⡤⣤⣤⡤⠤⠤⠤⠤⠤⣤⠤⠤⠤⠤⠇
⠀⠀⠀⠀⠀⠘⠓⠚⠛⠋⠉⢻⠉⠉⠉⠉⠉⠙⠋⠀⣼⠀⢀⡄⠀⠀⠀⠘⣇⠈⠉⠀⠀⠀⠀⠀⢠⠇
⠀⣾⠻⢤⡁⠀⠀⠀⠀⠀⠀⠈⠳⣀⠀⠀⠀⠀⢀⡴⠃⠀⢸⠁⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⣠⠔⠃⠀⠀⠀⠀⠀⠀⠐⢒⣲⠖⣢
⠀⢫⢣⡀⢨⠗⠢⣄⣀⠀⠀⠀⠀⠈⠉⠓⠒⠋⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⠤⢶⠋⠁⢸⣴⡟
⠀⠀⠁⠱⣏⡀⠀⢀⡏⠙⠒⠦⢤⣀⣀⡀⠀⠀⠀⠀⠀⣰⠚⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢤⠖⠊⡏⠀⠀⢸⣤⣴⠋⠚
⠀⠀⠀⠀⠘⢯⡒⢾⡀⠀⠀⠀⢸⠇⠈⠉⢹⠗⠒⣶⠶⠞⡆⠀⡰⠾⠶⠖⢲⠒⠚⠛⠉⢹⡅⠀⡼⠀⠀⡇⠀⣀⣼⠞⠁
⠀⠀⠀⠀⠀⠀⠑⢄⠙⠲⢤⣀⣸⠀⠀⢀⡏⠀⢰⡇⠀⠀⠘⠚⠁⠀⠀⠀⢸⠀⠀⠀⠀⢸⣧⣴⣧⣤⢤⡟⢉⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠈⢹⠉⠓⠾⣅⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⡤⠴⠖⢻⠁⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣟⠀⠀⠀⣿⠉⠉⠉⠑⠒⠒⠒⠒⠒⠒⡶⠛⢿⠀⠀⠀⣸⠀⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢸⠀⠀⣀⡿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢀⣼⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠦⢤⣤⡤⠤⠟⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠖⠒⠒⠂⠒⠒⠒⠢⠤⣀⠀⠀⠀⠀⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⡀⠀⡏⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣁⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣸⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣧⠴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⣀⡤⠔⠒⢃⡿⣋⡤⠒⠋⠉⠀⠀⠀⠀⠈⠉⠑⠢⣄⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢀⡴⠊⢁⠀⠀⣠⡿⠚⠁⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⢀⡽⠋⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠞⣹⠃⣴⠟⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⢷⡀⠀⡜⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡴⠁⠀⡟⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣠⠞⠲⢄⠀⠀⠀⠀⣠⠒⢦⡀⢳
⠀⠀⠀⠀⠀⠀⠀⠚⣉⠥⠤⠄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠸⡀⠀⠀⠀⠺⣄⠀⠀⢷⣠⣄⠀⡇⠀⠈⡇⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢡⠖⠒⠲⣄⠀⢸⡇⠀⣠⠴⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠈⢳⠀⡇⠀⠀⠀⠀⠈⠣⠀⡾⠁⠀⡿⠇⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠘⡆⠀⡇⣸⠁⠀⠀⠀⠓⣰⠚⠑⢢⠀⠀⠀⢁⣀⣤⣤⣤⣤⣼⡀⠱⡀⢠⠔⡶⠒⠲⠆⠷⣀⡴⠃⠀⠀⡼⠁
⠀⢀⠀⠀⢀⣠⣄⣠⠖⠘⠳⡄⠀⡱⠊⠻⣼⡶⠟⠛⠓⠀⠹⠄⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠉⠛⠁⠀⢙⡏⠸⣇⣀⣀⡀⢰⡆⠀⠀⣀⡜⠁
⡀⢸⠀⣴⠋⠀⠀⡇⠀⠀⡆⠀⠀⠸⠂⣼⠃⠀⠀⢀⣤⠤⠶⠤⢄⣀⠀⠀⠀⠀⠀⠰⣻⠟⠳⠆⠀⠀⠈⠁⠀⣨⠋⢠⠃⠀⠁⠀⢸⠁
⢃⠀⣄⠘⣄⡠⠒⠻⣄⣀⠞⠀⣇⠀⠀⣇⠀⠀⢰⠁⠀⠀⢀⡴⠊⠉⠉⠑⠒⡶⠒⠒⠁⠀⠀⠀⠀⠀⢠⠟⠉⠀⡰⠃⠀⠀⠀⠀⡸
⠈⢦⡘⢦⡀⠀⠀⠀⠘⠣⣤⣤⠌⠁⠀⠘⣆⠀⠈⠳⣄⣀⠀⠀⠀⣀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⢀⡠⠋⠀⣠⠞⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠈⠙⠶⢄⣀⣉⠉⠉⠉⠉⠁⠀⣀⠀⠀⠀⣀⣠⠤⠶⣫⣤⡶⠞⠁⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠉⠉⠉⠉⠉⠙⠄⠠⠴⠁⠀⠀⠀⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣄⡀⣧⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣄⢀⣀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣣⣀⡀⠤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡈⠛⠲⠤⢄⣀⡤⠤⠴⠚⠉⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⢶⡶⠖⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡶⢤⣄⡀⠀⠀⢀⡙⣇⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡇⠈⠑⢢⣼⠁⣿⡠⢴⠒⠒⠙⣏⡵⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠋⠉⠳⣄⠀⢸⠋⠀⠈⠃⢻⠀⠀⣠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠆⠴⢤⡾⠓⠲⠄⣼⣠⣯⣳⠀⠀⣀⣼⠞⠋⠉⢉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡁⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⢐⣾⠁⠀⠸⣄⠛⢒⡩⠟⠛⠛⠛⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣙⠲⢤⣤⣀⣀⣀⣀⣼⣡⡤⢒⣩⠎⠀⠀⠀⣿⣄⣎⠀⠀⠀⠀⠀⠀⠀⢈⡷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠦⠤⠤⠭⠤⠤⠔⠚⠉⠀⠀⠀⠀⠀⠘⢮⡙⠓⠤⢤⣀⣠⡤⠔⠋⢀⡜
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣑⣒⣤⣤⣤⣤⣄⣒⣉⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠻⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣶⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⠀⣀⣀⣤⣤⣬⣭⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠃⣠⣴⣾⣿⠿⠛⢿⣿⠛⠿⢿⣿⣶⣄⠀⠀⠀⢀⣴⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣼⣿⠟⠉⠀⠀⠀⢸⡇⠀⠀⠀⠈⠻⣿⣷⣄⠀⠻⠿⠟⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⢁⣀⣀⡀⠀⠀⠈⠁⣠⣴⣶⣾⡦⠈⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣿⠿⢿⣿⣶⡄⠀⢰⣿⡿⠋⠉⠀⠀⠀⣿⣿⡆
⠀⠀⠀⠀⣠⣤⣤⣦⣤⠀⠀⢸⣿⡇⠈⠁⣀⣀⠉⠿⠀⠀⠀⠹⠁⢀⣾⣿⣿⣆⢸⣿⣿
⠀⠀⠀⠀⠙⠛⠛⢿⠟⠂⠀⢸⣿⡇⢀⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠐⣿⣿⠀⠀⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣇⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⢸⣿⣿⠃⠀⠿⢿⠿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠻⣿⣿⣷⣦⣤⣤⣤⣴⣾⣿⣿⡀⢠⣿⣿⠃⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⣿⣿⡟⠛⠻⠿⠿⠟⠋⠹⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⣠⣿⣿⡿⠻⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠉⠀⠀⢻⡏⢹⣿⣿⣿⣿⣶⣶⣾⣿⣿⠿⠛⠁⢀⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠈⢻⠉⠀⠀⠀⠀⢸⡇⠈⢡⣾⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠘⢿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠘⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠉⠿⠏⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣤⣀⠀⣼⠳⣄⠀⠀⣀⣠⠶⠛⠉⠀⠸⣇
⠀⠀⠀⠀⣀⠔⠋⠁⠀⠀⠀⠉⠉⠙⠒⠒⠒⠛⠓⠦⡀⠀⠀⠀⢀⡾⠁⠀⠀⠈⠉⠁⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⢦⡀
⠀⡴⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⣠⠎⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠈⣷⠀⠀⠀⢳
⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡞⠁⠀⠀⠀⠃⠀⠈⠉⠉⠁⠸⣆⠀⠀⢠⠞⠉⠙⢷⡀⠀⠙⠷⢦⣄
⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠸⣄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠙⠷⡄⠀⠀⢸⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠁⠀⠀⠀⠈⠉⠙⠛⣆⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⠀⠀⠀⠀⠀⠸⡇
⠀⠈⠓⠒⠚⠉⠓⠦⣤⣤⠤⠖⠲⠶⠖⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠓⠦⠤⠤⡤⠴⠒⠀⠀⠀⠘⢧⣄⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠴⠚⠉⠛⠲⠤⣄⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⠀⠀⠀⣠⣤⡤⠜⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠙⠚⠀⢀⠞⠑⠓⡆⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠓⠚⠀⠀⠀⠀⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠉⠳⠦⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠇⠀⢀⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠚⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠙⠳⣄⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⡰⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⣀⣤⠾⠋⠁⠀⠀⠀⠀⣀⠄⣷⠀⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠙⠀⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠀⠀⠀⠀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢀⠼⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⡿⠿⠿⠛⠛⠛⠛⠛⠻⠿⠿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄
⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆
⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇
⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆
⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⣿⣿⠃⠀⠀⠀⠠⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⢻⣿⡇
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣠⣴⣾⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⢿⣿⡆⠀⠀⠀⠈⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⣾⣿⠇
⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿
⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠀⠈⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⡀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏
⠀⠀⠀⠀⠀⠀⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣤⣤⣤⣤⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⡿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⢹⣏⣛⣛⣛⣫⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠛⠛⠓⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⣀⡤⠖⠛⠋⠉⠉⠉⠉⠙⠛⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢀⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⣀⣀⣄⣀⣀⡙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⢀⣀
⢀⡴⠋⠉⠀⠀⠀⠀⠉⠙⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡞⠉⢹⣆
⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢳
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏
⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣀
⠀⠀⠉⠓⠲⠶⣦⠶⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠸⠀⠀⠀⠀⠀⠀⢹⢆⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⡄⠑⢤⡀⠀⠀⠀⣀⠜⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠓⠤⣤⡤⢴⠚⠉⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠉⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠄⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⡠⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘⢄⣀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢀⡖⠚⡞⠛⢻⠋⠒⡄⠀⠉⠒⠀⠚⠁⠀⡴⠒⡟⠛⣓⠒⠲⡄⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠸⡀⠀⠑⠒⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠉⠒⠁⠀⠀⡇⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠳⠶⠶⠶⠶⠶⠖⠁⠀⠀⠀⠀⠀⠀⠀⠳⠶⠶⠤⠤⠤⠞⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠋⠁⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⢁⠄⠉⡆⠀⠀⠀⠀⠀⠀⣞
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠓⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠁⣠⠇⠀⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢤⡤⠶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⡷⠤⠤⠤⠤⠤⣽⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠘⠧⣀⠤⢦⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⡃
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠉⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⠀⠀⠀⠀⠉⠓⠦⠤⣄⣀⣀⣀⣀⡠⠤⠖⢺⠁⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠤⣄⣠⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠙⠶⠦⠤⠴⠶⠳⣤⣀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⣧⠾⠳⣄⡀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⡏⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠉⠓⠒⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠃⠀⠀⠀⠀⠀⠀⠻⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⢦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⢶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠶⠟⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠿⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠛⠛⠛⠻⠷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣛⡉⠀⠀⠀⠀⠀⠈⠉⣓⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠿⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢤⠴




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠉⠉⠉⠉⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠴⠲⠄⠀⠀⠠⠖⠦⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠠⡪⢵⠄⠀⠀⠠⡮⢕⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠘⣇⠉⠉⣸⠃⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⠀⠀⠀⣀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠉
⠀⠀⣠⠔⠊⠁⠉⠉⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠉⠉⠉⠒⠦⡀⠀⠀⠀⠀⠀⠀⢀⡤⡒⠉⠈⠉⠉⠑⡢⣄
⢀⠞⠁⢰⣖⠀⠀⠀⢐⣶⠀⠙⢄⠀⠀⠀⠀⡔⠁⢀⣤⡀⠀⠀⢀⣤⡀⠈⢢⠀⠀⠀⠀⡠⠋⠀⣨⡂⠀⠀⠀⣪⡀⠈⠳
⡌⠀⠀⠙⠙⠀⠀⠀⠙⠛⠀⠀⠘⡀⠀⠀⢸⠀⠀⠘⠛⠃⠀⠀⠘⠛⠃⠀⠀⡇⠀⠀⢀⠃⠀⠀⠋⠊⠀⠀⠀⠻⠋
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠀⠀⠀⠀⢠⠔⠒⢦
⢱⡀⠀⠀⠀⣰⣋⣲⡀⠀⠀⠀⡸⠁⠀⠀⠘⡄⠀⠀⠀⣀⠔⠊⠉⠢⡀⠀⢀⠃⠀⠀⠈⢇⠀⠀⠀⠸⣀⣀⣠
⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠘⢆⡀⠀⠀⠀⠀⠀⠀⢀⡰⠃⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⡠⠎
⠀⠀⠀⠙⠒⠤⠤⠤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠤⠤⠔⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠤⠤⠒⠉

⠀⠀⢀⡤⠒⠂⠉⠀⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠈⠁⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⢀⡤⢒⡍⠉⠉⠉⣕⠢⢄
⢀⡔⠁⢈⣑⠀⠀⠀⢚⡉⠀⠑⡄⠀⠀⠀⠀⡰⠋⢀⣔⠁⠀⠀⠈⣢⡀⠙⢆⠀⠀⠀⠀⡰⠋⠀⣫⡄⠀⠀⠀⣤⡃⠀⠳
⡜⠀⠀⠻⠼⠀⠀⠀⠻⠼⠀⠀⠸⡀⠀⠀⢰⠁⠀⠘⠧⠃⠀⠀⠸⠦⠃⠀⠈⡆⠀⠀⢠⠃⠀⠀⠓⠊⠀⠀⠀⠓⠋
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⢸
⢡⠀⠀⠀⠀⡔⠒⠒⡄⠀⠀⠀⢰⠁⠀⠀⠸⡀⠀⠀⠒⠂⠂⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⢇⠀⠀⣏⡱⠀⠀⠀⠀⠀⠀⢀
⠀⠣⡀⠀⠀⠈⠉⠉⠀⠀⠀⡴⠃⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⣀⣀⣈⣓⣤⣀⣀⣀⣠⣒⣉⣀⣀⣀⣀⣀⣀⣀⣀⣑⣢⣄⣀⣀⣠⣔⣊⣀⣀⣀⣀⣀⣀⣀⣀⣈⣑⣒⣀⣀⣐⣒⣉⣀⣀
⣿⣿⠋⢛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⡰⠀⠀⠀⠒⠶⠤⠄⡁⠁⠤⠤⠶⠒⠂⠀⠀⠀⠀⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⡧⠀⠀⠀⠠⠤⠄⢰⠀⠀⠀⣤⣤⠤⠀⠀⠀⠀⠀⠐⢻
⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⢀⠀⠐⠰⠿⠛⠛⠉⠉⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⡜⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠇⡎
⠀⠀⠀⠀⠀⠀⠀⠅⢀⣴⠶⠚⠀⠀⠀⠈⢀⣀⡤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠄⡀⠀⠘⠄⠀⠀⠀⢀⠈⠀⠄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠖⠁⠀⠀⠀⠆⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠔⠀⠙⡄⠀⠘⡀⠀⠀⢀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⢀⠎⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠇⢠⠔⠊⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠄⠇⠀⠀⢧⠀⠀⠸⠐⣵⣶⣶⣮⠁⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡇⠀⠀⠴⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠃⢠⠁⠀⠀⠸⢧⠀⠀⠀⡬⠭⠭⠤⠀⠀⠀⢠⠊⢰
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠁⠉⠀⢀⡀⢀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠔⠁⣀⠠⠤⠤⢇⠑⢄⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠈⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⡠⠊⡠⣔⣶⣦⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⠊⠁⠀⠀⠀⠀⠈⠀⠀⠉⠒⠀⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢡⣾⣿⠿⠛⠉⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠆⠀⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠒⠁⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⢠⡄⠀⣀⠜⠒⡤⠤⠄⠤⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠂⠈⠉⠉⠁⠀⠀⠀⠀⠉⠁⠒⠠⣀
⠀⠀⠀⠀⢠⢃⠀⢸⠁⠀⢸⢇⠀⠛⠈⠉⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⣠⠁⢸⠀⠘⡧⡀⠘⠌⡀⠰⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⢀⠔⠉⠈⢂⠈⢳⡀⠘⡕⡀⠘⠜⢄⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠁⠀⠀⠀⠀⠑⣀⢻⢄⠘⡜⢄⢘⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠢⠌⠀⠁


⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⢀⣈⣀⣠⣾⣿⣿⣷⡆⠀⠀⠀⠀⣠⣶⣾⣿⣿⣷⠄⠀⠀⣴⣿⣿⣿⣶⣦⡀⠀⠀⢰⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣷⡄⠀⠀⢠
⠀⠀⠒⠀⠀⣼⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣯⠀⠀⢠⣿⣿⣿⣿⣿⣿⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⢿⣿⡇⢿⣿⣿⣿⣿⣿⡇⠀⠀⠈⢿⣿⣿⣿⣿⣿⣦⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⢿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠹⣿⣿⠟⠛⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⠉⠉⠀⠀⠀⠀⠸⢿⣿⣿⡿⠛⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠻⠿⠋⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⣠⣴⣤⣤⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⠀⠀⠀⠀⢠⣶⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⢿⡟⠁
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠹⣿⣿⣿⣿⣿⠃⢠⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠛⠀⠀⠀⠀⠲⣾⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣄⠀⠈⠙⠿⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣧⠀⢀⣤⣤⣤⣤⣄⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⠟⢰⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⣾⣿⣿⣿⣿⣿⣆⠀⢿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⡿⠋⠀⠸⣿⣿⣿⣿⣿⣿⣇⠀⠀⢠⣿⣿⣿⣿⣿⣿⡟⠀⠸⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢹⡿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠘⠋⠉⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⠀⠀⢹⣿⣿⣿⣿⣿⡿⠁⠀⠀⠈⠻⠏⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠘⠻⣿⣿⡟⠙⠁⠀⠀⠈⠉⢻⡿⠟⠁⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣦⣴⣦⣄⠀⠀⣸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣠⣤⣄⡈⠛⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣯⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣴⣿⣿⣿⣿⣿⡄⠀⠀⠀⣠⣾⣿⣿⣿⣿⣆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠈⠉⣿⣿⣿⣿⣿⠃⠀⢀⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡀⠀⠀⢾⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠙⠛⢿⣿⠟⠁⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⠧⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⢿⣿⡇⠀⢀⣤⣤⣤⣄⡀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠉⠁⠀⠀⠀⠀⠙⠋⢻⡿⠟⠋⠁⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣷⣦⢸⠟⠀⢀⣿⣿⣿⣿⣿⣿⠆⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⠀⠀⠀⠀⠀⣤⣤⣶⣦⣄⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠄⠀⠀⣸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸⣿⣿⣿⣿⡿⠿⠀⠀⠀⢻⣿⣿⣿⣿⠀⠄⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⠁⠀⠀⢠⣿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠿⠿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⠻⣿⠋⠉⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢁⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉⠉⠉⠛⠛⠿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣛⣭⣤⣤⡄⠀⠀⠀⠀⣀⣤⣤⣤⣌⠻⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠃⠘⠛⠛⠛⣛⠁⠀⠀⠀⠈⠛⡛⠛⠛⠛⠀⠈⠛⠛⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣏⠀⠀⠀⠙⠳⠞⠃⠀⠀⠀⠀⠀⠈⠻⣦⠾⠃⠀⠀⢠⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⢀⣀⠀⠀⢸⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣇⠀⠀⣿⣦⡀⠀⠀⠀⣹⡷⠀⠀⠀⣿⣿⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢿⣿⡇⠀⠀⠀⠉⠀⠀⠀⠀⣿⡟⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠐⠛⠛⠛⠃⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⢠⡤⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⣠⣤⣤⣶⣶⣶⣿⡿⣿⢓⠻⣛⢲⣦⣄⣀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⢨⡐⢬⠀⠀⢾⠀⢨⠘⡇⠃⠘⢀⠁⠆⠹⢀⠈⡇⠆⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠇⠆⠄⠸⣘⡠⠀⠀⠻⠀⠫⠀⠇⠠⣆⣸⢄⣁⠴⡈⡠⠇⠁⠌⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢀⣀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⣠⣿⣿⡄⢀⡀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⢠⣾⣿⣿⠋⣘⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⢠⣿⡿⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀
⠀⣼⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⢰⣿⡇⣰⠋⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣼⣿⡆⢿⡄⠀⠀⠀⠀⠀⠀⠀⢈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡿⠃⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⣿⠃⠹⣿⣷⡖⠒⠒⠠⠄⡀⠈⣇⠀⠀⣀⣀⣀⣤⣶⣶⣶⣶⣶⣶⣿⣿⣿⠟⠉⠉⠀⠀⠀⠀⠀⠈
⣿⣷⠆⠀⠹⣿⢧⠀⠈⠏⢠⣿⣿⡋⠁⠀⢹⣿⣿⣿⣿⣿⣿⠟⢋⣁⠈⠁⣿
⢹⣿⣿⡏⠀⣿⣷⣭⣦⣴⣿⣿⠃⠁⠀⠀⣼⣿⣻⣿⣿⡟⠁⠀⠀⠖⠀⠀⣿⠀⣀⣠⡴⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⢸⣿⣿⣧⣀⠀⠑⠺⠿⣽⣿⣿⠀⠀⠀⠘⠛⠋⠁⠒⢿⣧⡤⠀⠀⠀⢀⢰⣵⣼⠟⠁⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠈⢿⣿⣻⣿⣷⣄⠀⠀⠀⣿⣿⠇⠀⠀⠀⢀⠋⢻⣶⣦⣈⠛⠓⠶⠤⠤⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠈⣿⣿⣿⣿⣿⣆⢀⣾⠛⢿⣄⠀⠀⢠⡟⢁⣸⣛⣋⣛⡛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠻⣿⣹⣿⣿⣿⣿⢇⡴⠶⣿⠀⢀⡿⠟⠋⢉⠉⠀⠉⠳⣄⠘⢦⠀⠀⠀⠀⢀⣀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠹⣯⠋⣿⣿⣿⡜⣇⠀⢿⣶⣾⡁⠀⠀⠈⠻⠀⠀⠀⠹⡆⠈⡇⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠃
⠀⠀⠀⠀⠘⢷⣅⣿⣿⣧⠘⣆⠀⠈⠻⡅⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⡀⡙⢿⡿⢿⣄⠘⢧⢀⡀⢰⢀⠀⡀⣀⢀⡄⣀⠀⠈⠆⢀⠀⡿⠀⠀⡀⡀⢀⠀⢀⠀⡀⡀⠀⠀⠀⣴⢟⢁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⠀⢀⡠⠘⠀⠀⠀⠀⠂⡅⠀⠀⠀⠀⠀⠀⢘⠀⠆⠂⠀⠀⠁⠘⠀⠀⠐⠂⠀⡇⣨⠀⠉⢸
⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠈⠻⢷⡌⠁⣼⡇⠀⠀⠈⠀⠀⠈⠐⠛⢦⠈⠄⠁⠀⠀⠁⠀⠀⠀⠀⠀⣀⡴⠟⠉⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣥⣀⣀⠀⠀⠈⢁⠀⢀⠘⠈⡑⠈⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠳⠶⠶⠶⢤⣤⣤⣤⣤⣤⠶⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇

⠀⠀⣠⡾⠟⠁
⢀⣼⠋
⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⢀⡶⣤⡀⠀⢠⡟⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡟⠹⣆⠀⣿⡆⠀⣿⢦⡀⠀⣾⢷⣄⠀⢠⡟⠛⢦⡾⠁⠈⠛⠶⠟⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⣄⣿⢻⣴⡏⠈⠻⣤⣿⠀⠙⢷⡾⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠛⠃⠀⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠉⠉⠻⢦⣄⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⣠⡴⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⣹⣦⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠉⠙⠳⣦⡀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿⣆⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⣾⠁⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⣿⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⣿⠀⢀⣾⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⣿⠀⢸⡟⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠻⣦⣀⡀⠀⠀⢀⣰⠏⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⣿⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⢷⣄⡀⠀⠀⢀⣀⣤⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⣀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢀⡀⠘⣟⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⣿
⠀⠀⠀⠀⠀⠀⢸⣧⠀⠹⡆⠀⠉⠛⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠈⠁⠀⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠈⣿⢧⡀⢻⡄⠀⠀⠀⠀⠉⠉⠛⠳⠦⣤⣤⣀⣀⠀⠀⠀⣀⣀⣤⣤⡴⠶⠛⠋⠁⠀⠄⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠈⢻⣄⢦⠀⠈⠆⠀⠂⣤⠠⡐⡀⢶⣄⠉⠉⠛⠛⠛⠉⠉⠀⠀⠀⢀⠛⠀⢀⡀⠀⢠⢀⡿⠁⢠⣿
⠀⠀⠀⢴⡀⠀⠀⠸⡇⠀⠉⡄⠀⠀⠀⢿⣆⠈⠀⠁⠀⠀⢨⢛⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠠⠰⠆⠀⠀⠂⣼⣃⡔⠋⣿
⠀⠀⠀⢸⣿⡄⠀⠀⢻⡄⠀⠁⠶⠈⠮⠀⢿⡀⠀⠀⠀⢂⠀⠀⠈⠃⠊⠁⠐⠀⠀⢀⡀⣀⠴⠀⢰⠀⣀⠃⠿⠋⠀⢰⡇
⠀⠀⠀⠀⣿⠹⣆⠀⠀⠹⠆⠃⠀⠀⠐⠀⢸⡇⠀⠀⠀⠀⠀⠰⠦⢤⡤⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⠀⠀⠂⠀⠀⠀⢸⠇
⠀⠀⠀⠀⢹⡆⠘⢧⡀⠀⠀⠄⠀⠀⢀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠈⢿⡀⠈⠛⢶⡄⡖⢶⠆⡌⠀⠀⡏⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠜⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢉⠄⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⡀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠜⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠈⠃⠀⠒⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠂⠑⠈⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈

⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠋⠉⠉⠛⠻⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠿⠿⠶⣄
⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠰⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣶⣖
⠀⠀⠀⠀⠀⠀⢐⣒⣿⣿⣿⣿⣿⡿⢿⢿⠿⠻⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⠶⠒⠲⠄⠀⠀⢠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢔⣾⡟⣻⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠈⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣧⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⣿⣿⣿⣿⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠻⠽⠷⠿⠿⠿⠛⠛⠁
⡀

⠀⢠⡄⠀⢠⣤⣤⣄⣀⣀⠠⣦⣀⠀⠀⢀⡀⢰⡄⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⢦
⠀⣾⠁⠀⣾⣿⣿⡟⣿⣿⣷⢿⡟⠿⣶⠄⣿⣦⣉⠀⠀⢀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⣼
⠀⣇⠀⢸⣿⣿⣿⡏⣈⠛⢉⣼⣧⣴⣾⣿⣿⣿⣿⡆⣦⣼⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⣼⣿
⠀⣿⣷⣾⣿⣌⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⢹⣿⠀⠀⠁⢠⣾⣧⡀⠀⠀⢀⣰⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢹⠀⢸⣿⡇⣠⣆⣾⣿⣿⣷⣦⣶⣿⣿⣿⣿⡇
⠀⢻⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⠃⢀⣠⣶⣾⣿⡇⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⡇
⠀⠸⣿⡋⣿⣿⣿⣿⣿⣿⡿⣿⠿⠀⠃⣶⠟⠛⠿⠟⠛⣿⣧⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⢿⣘⣿⣿⣿⢿⡝⠻⡕⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⢀⣾⣿⣿⣿⣿⣿
⠀⠀⠈⣿⣿⣿⣿⣧⣰⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠇
⠀⠀⠀⠀⠀⢿⠿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠟⣾
⠀⠀⠀⠀⠀⠈⣾⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡟⢸⠃⢸⠋⢠⠗⡻⡶⠤⠀⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⡀⠀⠺⡟⣿⢹⣿⣿⢻⠋⡀⠀⠀⠀⠀⠏⢸⡿⠀⢀⠘⠃
⠀⠀⠀⠀⠀⠀⢷⢹⡟⢧⠻⡌⠿⣿⣿⣿⣿⣇⠀⠀⠁⠛⠈⠀⠀⠀⠈⠁⠀⠠⢤⡼⠤⢦⡆⢀⡾⠁⠀⣀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠘⠈⡇⠀⠀⠀⢰⣿⣿⣿⣿⣯⣉⣷⡄⢀⣤⣤⢀⣤⡄⣤⣤⡀⠀⠀⠀⠀⠈⢣⡄⠀⢰⠁⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣶⣿⣗⣶⣞⣻⣦⢠⡟⠃⠀⠀⠀⠁⠀⠀⢦⠀⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⣿⣯⠋⠉⠈⠉⠉⠈⠛⠟⠈⠉⣡⣬⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢁⡤⠊⠁⠀⠀⠀⠀⢀⣰⡇⠀⡠⠞⠁⣦⡀⠀⠸⠆⠀⡠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠋⠀⠀⠀⠀⠀⠀⣠⡟⣾⣥⣈⣠⣤⣬⣽⣿⣿⣿⣿⡟⠀⠀⣠⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⣿⢛⠇⠿⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠟⠀⠈⠙⠲
⠀⠀⠀⠠⠀⢠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⠿⠿⠸⠿⠏⠀⠀⠤⠘⠿⠿⠿⠿⠿⠃⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠉⠉⠉⠛⠷⣦⣄⣀⣀⣀⣤⠾⠋⠉⠀⠀⠀⠀⠀⠀⠉⠙⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⢀⣀⣀⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣶⣦⣄⡀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣰⣿⣿⣿⡿⠿⠿⣿⣿⣷⣶⣶⣶⣶⣶⣿⢿⡿⠛⠉⢹⡏⠉⢿⢿⣿⣿⣿⣦⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⡿⣿⡿⢹⠀⠀⠀⢸⠀⠉⠉⠙⡟⠉⠉⠀⠀⡇⠀⠀⢸⠁⠀⡎⠀⢹⣿⣿⣿⡆⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⣿⠻⣸⠦⣀⣀⡼⣄⠀⠀⢀⡇⠀⠀⠀⣠⠧⠤⠤⡏⢀⡼⣁⣀⡼⢻⣿⡇⠃⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈⠉⠉⠉⠁⠀⠀⠀⠉⠉⠠⠤⢝⡒⠚⣿⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⣀⣴⣿⣿⣿⣿⣷⡮⠀⢹⣿⣇⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣴⣏⣴⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢿⣿⡄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⢿⣿⡄⠀⠀⠀⢀⣴⠾⢛⣫⣭⠍⣩⡽⠟⢋⣉⣥⣄⣉⠙⠻⣿⣿⡇⢸⠘⣿⣿⣶⣤⣾⣿
⠀⠀⠤⠄⠀⠤⠂⠐⠀⠴⢿⣿⣿⣿⡆⠀⢰⡾⢧⡾⠿⠿⡷⠟⢣⣴⣶⣿⣿⣿⣿⣿⣷⣶⡤⠻⣷⣾⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣠⡟⠰⠋⠀⢀⡾⠁⣰⣿⠿⠛⠋⠉⠙⠻⢿⣿⣿⣿⠆⣨⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠁⠀⠀⠀⡾⠁⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠿⢁⣾⣿⣿⠿⠟⠛⠻⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃⠀⠀⠀⣸⠃⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁⠀⠀⠀⠀⠈⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⢠⡏⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠃⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠃⠀⠀⠀⠀⠀⢀⣼⠋
⠀⣤⠶⠶⠶⢦⣤⣤⣤⡴⠞⠋⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠇⠀⠀⠀⠀⠀⣠⡾⠃
⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠋⠀⠀⠀⢀⣠⡾⠋
⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠃⠀⣀⣤⡶⠟⠉
⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣯⣴⠶⠛⠋⠁
⠀⠀⠀⠈⠻⢶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠋⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠠⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠠⡀
⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠
⠀⠀⠀⡀⠄⠊
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠟⠉⠉⠛⠲⢶⣦⣤⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⡲⢤⣀⣠⣴⠛⠛⠛⠋⠀⠴⣤⣴⣶⡶⠤⠤⣴⣶⣶⣶⣤⠆
⠀⠀⠀⠀⠀⣀⣤⣴⣶⡦⠄⢀⠀⢉⠁⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⣀⣀⡠⠿⠿⠿⡿⠁
⠀⠀⢀⣀⡠⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁
⠀⠀⠉⠀⠀⠀⠀⢀⣀⣤⣴⠶⣾⣿⣿⣶⠲⠤⢤⣀⡀
⠀⠀⠀⠐⠛⠻⠟⠛⠙⠻⠿⢄⣀⡈⣽⢿⣶⣤⣄⣤⣈⣀⣷⣶⡂⠂⣶⣋⣱⣶⣶⣤⣤⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠉⣹⣿⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠄⠌⠙⠛⠛⠢⠄⣤⣿⠛⠛⢻⠀⠀⢠⣿⣿⣿⣄⣀⣀⡀
⠀⠀⡀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠉⠒⡒⠚⠒⠛⠉⣩⠅
⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠁⠀⡠⠞⠀⠀⠠⠔⠋⠁⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠀⠀⣀⡠⠊⠀⠀⢀⠌⠀⠀⠀⠠⠚⠁⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣴⠞⠀⠀⠀⠀⠁⠀⠀⣠⠔⠁⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⢀⣀⣀⢀⡠⠤⠀⠀⠠⡤⠊⠀⠀⠀⠀⠀⠀⢀⠴⠛⠁⠀⠀⠁⠀⠀⠀⠁⠀⠈⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠐⣢⠄⠁⠖⠄⠀⢀⣀
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠆⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠒⠲⠤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⣠⠤⠤⠶⠲⠦⢄⣀⡤⠴⢒⣒⣒⡒⢤⣝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣠⠖⠛⢶⣊⠭⠽⠧⢬⣏⢹⣎⠭⠽⠒⠚⢃⣛⣩⣧⠟⠦⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠈⠷⠶⠤⠀⡧⣤⣤⡤⠬⠽⠛⠢⠤⠤⠤⠤⠴⠒⠛⠁⣶⠂⣧
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠸⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠙⠲⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠞⠋⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠿⡤⢶⠼⡇⠀⣼⡥⣤⠶⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢀⡠⣄⡀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠘⠂⠀⠒⠉⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠗⠦⢤⣀⡀⠀⠀⠀⠀⢀⣀⣠⠴⠊⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠢⢤⣶⣖⡢⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠔⠈⠉⠐⡄⠀⠀⠀⠀⠀⣴⠁⠀⠈⠀⡀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠠⣴⠖⠓⠒⠀⠨⠀⠀⠀⠀⠰⠁⢂⠀⠉⠛⢾⠔⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⡀⣴⣦⡔⡰⠀⠀⠀⠀⠀⢄⢱⣿⣤⢠⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠸⠐⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠄⠀⠠⠈⠀⠀⠀⠀⢀⡀⠞⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠉⠀⠀⠉⠙⢄⡀⠁⠤⣀⣀⣤⠤⠤⠶⣒⡒⠚⠋⠉⠁⠀⡱
⠀⠀⠀⠀⠀⠀⠀⡔⠉⠁⠀⠀⡀⠀⠀⠠⠀⠀⢑⣋⣭⡥⠶⠒⠊⢉⣁⡤⠤⠒⣒⠩⠔⠊
⠀⠀⠀⠀⠀⠀⠀⡇⠠⡄⠀⠀⠀⠀⠀⠀⡅⠀⢨⣥⠤⠴⠒⣚⡉⠭⠔⠒⠈⠁
⠀⠀⠀⠀⠀⡠⢒⡡⠚⠡⡀⠀⢀⣧⣤⣴⣿⡾⠟⠂⠈⠉
⠀⠀⠀⠀⠰⡁⢀⣀⡠⠭⠿⠿⠟⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠒⠒⠒⠒⠒⠒⠲⠦⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠄⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠒⠀⠀⠀⠒⠒⠂⠀⠀⠤⠒⠈⠁⠈⠐⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠒⠂⠈⠉⠉⠑⢂⡀⠒⠈⠉⠉⠁⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠔⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢓⠊⠉⠉⠉⠉⠉⠂⣽
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠿⢿⣿⣉⣓⠆⠀⠀⠀⠀⠀⠀⠀⣶⣭⡍⠍⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠐⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⠉⠉⠙⠲⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠀⠀⠀⠀⠀⠀⢈⡆⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⡴⠒⠉⠉⢧⣀⠀⠠⠤⠀⢀⣀⡞⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠘⠠⢎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠁⠈⠳⣄⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠢⠤⠤⣄⣀⡀⠀⠀⠀⠀⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⡀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠀⠀⠉⠙⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃
⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢀⡴⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⢶⠶⠒⠋⠁
⠀⠀⠀⠀⠀⠀⢀⣀⣴⡋⠀⠀⠀⠀⣀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠘⢦⣄⣀⣀⣀⣀⣀⣀⡀
⢀⣀⣀⡤⠖⠛⠉⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⢀⠔⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢋⣥⣤⣤⣤⣍⡛⠲⠦⠤⠶⠞⢛⣩⣭⣤⣤⣄⡙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣴⣿⣿⠿⠻⢿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢁⣴⣿⠟⠋⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠈⠛⢿⣿⣦⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⠙⢧⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠙⢦⡀
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⣀⠀⠀⠀⠀⠀⠀⣠⣤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠋⠉⠓⣦⣤⣠⣤⠞⠉⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣋⣡⡿⠶⠤⣤⣤⣬⣭⠴⠷⢬⣭⣴⣤⣤⣤⠤⠿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⢠⠞⠁⠀⣀⣴⣾⡿⣿⡿⠞⠫⣙⣷⠿⠛⠉⣉⠙⣛⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠲⢤⣄⣀⠀⠀⢀⠀⠀⠀⠹
⣯⠀⣠⡾⡉⣤⣴⡿⢋⣠⣴⣿⡏⣥⣴⢞⠋⢿⢿⡷⣭⣮⣷⣄⢀⡀⣀⣀⣠⣤⣤⢴⠖⢶⣶⣶⠚⠿⣿⠾⠿⣿⣿⣧⡤⠴⠖⡄⡀
⠹⣤⣿⢆⡾⢁⡞⣀⡼⠃⣰⣣⣲⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⣰
⠀⣼⡟⣼⠁⣾⢰⣼⠁⢠⣯⢣⡏⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⣿⠁⣿⢶⡇⣿⡇⠀⢸⣿⢸⠛⠻⠿⢿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣶⣾⣷⣶⣦⡀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠸⣆⢘⢾⡇⣿⣧⡀⢸⢼⣸⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠉⠙⠂⠀⠀⠀⢀⡴⠋
⠀⠀⠙⢮⣝⣷⠀⢿⣛⡿⣏⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠈⠙⢧⡈⠳⣄⣹⣜⠟⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠈⠳⢮⣖⣻⣝⣷⣄⠉⠛⢛⣛⣻⣶⣶⠶⠶⠶⠤⠤⠶⠶⠶⠶⠖⠒⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠓⠒⠚⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠈⠙⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠴⠚⠛⠛⠲⠄⠀⠀⠀⠀⢠⠴⠶⠶⠶⠦⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⠀⠀⡂⠉⠉⠉⣶⠀⠀⠀⠀⡔⠀⠀⠀⢶⡄⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⠀⠈⠛⠒⠂⠂⠀⠀⠀⠀⠘⠓⠒⠒⠛⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢻⡿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠄⢤⣄⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⣶⣤⠀⠀⠀⠀⠀⡠⠀⠀⠀⢠⠈⠀⠀⠀⠀⠐⠢⡄⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠓⠠⢀⡈⠀⠘⢀⡀⠤⠂⡃⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣉⣁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⡇⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⣿⡆⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⣿⡇⠀⠀⠀⠘⢿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡟⠁⠰⣿⡷⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣧
⠀⠀⣰⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣴⣶⡄⠀⠀⣸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣈⣉⣀⣤⣾⣿⣿⣿⣿⣷⣤⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⣀⣀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠶⠶⠶⢶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣖⣚⣉⣉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠉⠉⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡤⣄⡀⠀⠀⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠛⠉⠀⠀⠹⢦⠀⠈⣘⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠀⠀⠀⠀⠀⠀⠈⠳⣄⠘⣆⣻
⠀⠀⠀⠀⠀⠀⣇⡼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢀⡄⠒⢻⣿⣶⣦⡘⢦⠈⢻⣇
⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢀⣠⠖⠋⠉⠉⠙⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢀⣾⣷⣤⣾⣿⣿⣿⣿⡌⣇⠀⢹⣆
⠀⠀⠀⢀⢠⣿⡇⠀⠀⠀⣰⠋⠀⠀⠀⢠⣤⣤⣄⡀⢿⡓⣦⠀⠀⠀⠀⠀⠈⢳⡀⠀⢨⣀⣸⣿⣿⣿⣿⣿⣿⡇⠈⡇⠀⢿⣧⡀
⠀⠀⠀⢸⠈⣻⠃⠀⠀⢠⡏⠀⠀⣾⣤⣤⣿⣿⣿⣿⣎⠉⡾⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⢻⣿⣿⣿⣿⣿⣿⡿⠀⣠⠇⠀⠘⡆⣧
⠀⠀⠀⢸⢠⠇⠀⠀⠀⠸⣦⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢭⣿⣛⣟⣛⣉⣠⠴⠋⠀⠀⠀⢹⡌⣇
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢹⠀⠀⠹⢿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣹
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠈⠉⢉⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠤⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⢋⠉⢁⣠⣴⣦⡀⣀⡴⠻⠼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⢸⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⢁⡼⠳⠴⠛⠳⠋⠀⠁⠈⠉⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠸⡎⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⢀⣠⡤⣤⣤⡴⠒⠒⠒⠶⡄⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢹⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡤⠞⠟⠃⠀⠀⠈⠃⠀⠀⠀⠀⢻⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠈⢧⡹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢴⣟⢳⣤⢤⣤⡖⢛⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⢻⠀⢳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠈⠑⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⠛⠛⠛⠛⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣴⣦⣤⣤⣦⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡷⢠⣿⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠻⣿⣿⣿⣿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠲⠶⠖⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢠⣬⣛⣫⣥⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣤⣴⣦⣿⣷⣄⣀⣠⣼⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠿⠛⠛⠦⠈⠿⠿⠿⠏⣠⠎⠛⠻⠿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢸⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⣀⣀⣴⣶⣶⣄⠀⠀⠀⢀⣤⣴⣦⣤⡄⠀⢀⣤⣶⣦⣤⡀⠀⠀⣠⣾⣿⣿⣿⠀⠀⠀⣤⣶⣶⣶⣤⠀⠀⢀
⠀⠐⠀⠀⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⣾⣿⣿⣿⣿⡀⠀⢸⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⢿⣿⠸⣿⣿⣿⣿⡇⠀⠀⠙⣿⣿⣿⣿⡷⠀⢸⣿⣿⣿⣿⠇⠀⠀⠈⣿⣿⣿⣿⡏⠀⠀⠹⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⢸⣿⠀⠈⠻⠿⠉⠀⠀⠀⠀⠻⣿⣿⣿⡷⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠉⠻⣿⠋⠁⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⣠⣤⣤⣤⣤⣤⡄⠈⠁⠀⠀⠀⠘⣿⣿⡟⠀⠀⠀⢀⣴⣶⣶⣦⣄⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄
⠀⠀⠀⠀⠘⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⣿⠅⠀⠀⢀⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⢿⠋⠁
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⢹⣿⣿⣿⣿⡧⠀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠀⠀⠀⣀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⢠⣶⣶⣶⣶⣄⠈⠛⢿⡟⠛⠃⢸⣿⣿⣿⣿⣦⡀⠀⢀⣀⡀⠀⠀⠙⠿⠿⠁⠀⠀⠀⠀⣹⣿⣿⣿⣿⣧
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⣾⣿⣿⣿⣿⡀⠀⠀⣴⣶⣶⣶⣶⡄⠸⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠸⠿⣿⣿⡿⠁⠈⣿⣿⣿⣿⣿⣧⠀⢀⣿⣿⣿⣿⣿⡏⠀⠿⣿⣿⢿⡧
⠀⠀⠀⠀⠀⠛⠛⠿⠟⠁⠀⠀⠀⣠⣤⣤⣤⡀⠉⠀⠀⠀⠀⢘⣿⣿⣿⣿⡇⠀⠘⣿⣿⣿⡿⠟⠁⠀⠀⠙⠃⠀⠀⠀⠆
⠀⠀⠀⠀⠀⣠⣤⣤⣀⣀⡀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⢠⣴⣶⣦⣤⡀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣻⣿⡆⢸⣿⣿⣿⣿⣿⣿⠀⠀⣴⣿⣿⣿⣦⠀⠀⠀⣠⣾⣿⣿⣦⡀⠀⠀⢼⣿⣿⣿⣿⣷
⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣇⠀⠉⠻⠿⢿⣿⠋⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⢻⣿⣿⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⠏⠀⠀⢀
⠀⠀⠀⠀⠈⠙⠿⠋⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⠹⣿⢿⣿⣿⠿⠀⠀⠘⠛⢿⣿⠟⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⣠⣤⣤⣤⡈⣿⠃⢀⣾⣿⣿⣶⣦⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⣀⣈⣁
⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠁⠀⢸⣿⣿⣿⣿⣏⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⣷⠀⠀⢸⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢻⣿⣿⣿⣿⡷⠀⠀⢸⣿⣿⣿⠿⠇⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⢼⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠐⢿⣿⣿⢿⠇⠀⠀⠘⠛⠿⠟⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠘⠛⣿⡿⠛⠁⠀⠀⠘⠛⢻⡿⠃
⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠤