Curved arrow Emojis & Symbols

⠀⠀⣀⡀⠀⠀⠀⠀⣀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⣀⣤⣴⣦⣄⡀
⠀⠈⠿⢿⣆⠀⢠⡿⠿⠃⠀⠙⠛⠻⢦⡀⠀⣴⠟⠻⠋⠀⠀⠀⠀⠀⠈⠁⠠⠒⠚⠛⠁⢠⠴⠛⠛⠛⠛⠁⣠⣶⠿⠿⠿⠿⢿⡿⠛⠉
⠀⠀⠀⠀⢻⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠃⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠠⡟⠁
⠀⠀⣀⠀⠈⠀⠁⠀⣀⠀⠀⠀⣠⣀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠓⠄
⠀⠀⠈⠙⣄⠀⢠⠞⠉⠀⠀⠀⠈⠉⠑⡄⠀⠜⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣷⣶⣴⣶⣾⠟⠁⣠⣤⣤⣤⡤⠞⠁⢀⣄⡤⠔⠀⢀
⠀⠀⠐⠄⠀⠀⠀⠠⠂⠀⠀⠀⠰⠦⢄⠀⠀⢀⠤⠆⠀⠀⠀⠈⠙⠿⠟⠛⠋⠉⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⠒⠀⠀⠀⠀⣴⡟⠁⠀⠀⠁
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⣾⠁⠀⠀⠀⡀⠀⠸⣿⠇⠀⠀⢀⣼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠰⠀⠘⠃⠀⠀⢠⡄⠀⠛⠀⠀⠀⢸⡟⠀⠀⠉⠀⠀⠀⢸⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠀⠀⠀⠀⢠⠤⠞⠀⠀⠀⠐⠦⢤⠴⠟⠁
⠀⠀⠀⣀⣤⡀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣤⣄⠀⠀⠀⢀⡀⣀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⣼⠁⠀⢹⡆⠀⠠⡄⠀⠀⢥⠀⠀⢴⠀⠀⢹⡄⠀⢰⡏⠀⠈⣷⠀⠀⡏⠀⠀⠛⠀⠠⠏⠀⠙⠇⠀⢰⡏⠀⠙⡇⠀⠠⡦⠀⠀⣻
⠀⠀⠈⠳⠀⠀⠀⠀⠀⠑⠤⠔⠂⠀⠀⠈⠳⠄⠀⠀⠀⠀⠙⠶⠞⠁⠀⠀⠑⠤⠔⠃⠀⠀⠁⠀⠀⠀⠀⠀⠛⠶⠞⠁⠀⠀⠙⠶⠶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣶⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠋⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉







⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠦⠄⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠿⠿⢿⣷
⠀⠀⠀⠀⠀⢀⣴⠟⠛⡿⠟⠉⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠒⠀⠀⠀⠀⢠⠘⠁
⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢻⣇⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣴⣿⠁⠀⠀⠀⣶⣄⠀⠀⠀⠀⠀⠀⢈⡟⠀⠀⠀⠀⠘⣦⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠱⣄⣀⠀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠗⠂⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠈⠛⠿⣾⣿⣶⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠐⠛⠿⣿⡿⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠉⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠻⡄⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠐⢤⡀⠀⠀⠀⢀⣷⡀⠀⠀⠀⠀⠀⠀⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢠⣰⣿⣁⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⣼⣿⣷⡀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠃⠀⠀⠀⠀⢿⣿⠃⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠁⢻⣧⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⣀⣴⣾⣤⣴⠟⠁
⠀⠀⠀⠀⠀⠀⢿⣷⣶⣶⡶⠋⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠙⠷⣄⣀⣀⡀⠋⠁⠀⠀⠀⠀⠀⠉⠛⠻⠿⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣦⡀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⢋⣉⣥⣤⣤⣤⣤⣤⣤⠄⠀⣠⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⣡⣾⡿⠿⠛⠛⣻⣿⣿⠟⠁⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⣸⣿⠏⠀⠀⣠⣾⣿⣟⣁⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢀⣿⡟⠀⠠⠾⠿⠿⠿⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠃⣾⣿
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣤⣴⣶⣶⣿⣿⠟⢁⣾⣿⠃
⠀⠀⠀⠀⣠⣾⣿⡿⠟⢛⣋⣉⣉⣉⣉⣛⣛⣛⣛⣛⣛⣉⣩⣤⣾⣿⠟⠁
⠀⠀⠀⣼⣿⠟⣡⣶⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠉
⠀⠀⢸⣿⡏⣰⣿⠟⠁
⠀⠀⣿⣿⡇⣿⣿
⠀⠀⢹⣿⡇⢻⣿⡆
⠀⠀⠘⣿⣿⡈⣿⣷⡀
⠀⠀⠀⠹⣿⣧⠘⣿⣷⡀
⠀⠀⠀⠀⢻⣿⣧⠘⣿⣷⡀
⠀⠀⠀⠀⠀⢻⣿⣧⢙⣿⣧
⠀⠀⠀⠀⠀⠀⢻⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠉⠀⠀⠈⠉⠻⢿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠛⠉⠈⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡄
⠀⠀⠀⠀⢠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣀⣴
⠀⠀⠀⢰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣿⣿⣿⣿
⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡇⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⡿
⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢿⣇⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠇
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢷⣶⣶⣶⣶⣶⣾⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠉
⠀⠈⠉⠙⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⢀⣠⠤⠶⠾⠿⠿⠿⣿⣿⣿⣶⣦⣄⡀⢠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠿⠛⠻⠿⢿⣷⣦⣼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣤⣤⣀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⠛⠛⠻⠿⣿⣿⣷⣷
⠀⠀⠈⠓⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⢬⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣬⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡀⠀⠀⠀⠀⣀⣴⣾⠿⠟⠛⠛⠛⠻⠿⢿⣿⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡛⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠈⠛⠲⠾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠻⣿⣿⣷⣶⣶⣶⣾⠟⠁

⠾⣿⣿⣶⣶⣶⣦⣤⣤⣀⣀
⠀⠀⠉⠛⠿⣿⣿⣍⡛⠛⠿⠿⢿⣷⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣤⡀⠀⠀⠉⠙⠛⠿⢿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣤⡀⠀⠀⠀⠀⠈⠉⠻⢿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣍⠉⠉⠉⠉⠉⠉⠹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⣩⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣄⠀⠀⣠⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣾⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⣤⠶⠶⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣬⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀
⠀⠀⣰⠏⠁⠀⠀⠀⠀⣙⣷⣤⡇⠀⠀⠀⣄⠀⠀⠀⠀⠀⠐⢶⣾⣿⡟⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠐⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⣠⣴⠶⣿⣿⣿⡶
⠀⢰⡏⠀⠀⠀⠀⠀⠀⠈⠻⣿⠇⠀⠀⠀⠈⠙⠲⠶⠶⠶⠶⠛⠉⢸⠃⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠉
⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⢿⡄⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠁⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⡀⢹⡇⠀⠀⠀⠀⠀⠀⢷⡄⠀⠀⠀⠀⠐⣫⡿⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⠏
⠀⠀⠀⠀⠀⣀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠹⣾⣷⠋⠀⠀⠀⠀⠀⠀⠙⠳⠦⡤⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⣀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠰⣺⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣧
⠀⠀⠀⢀⣠⠞⠁⠀⠘⠛⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠤⣽⣷⣟⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⡶⠛⠀⠛⠀⠀⠀⠀⠀⢀⣀⣀⣭⡾⠋⠘⠃
⠀⠈⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠠⠤⠶⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣥⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡈⣿⡀⣀⠀⠀⠀⠀⠀⠀⠉⠳⠄⠀⠀⠉⠛⣦⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⣀⠀⠰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢛⣿⠿⠇⠀⠀⠠⣤⣀⣀⣀⣠⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣇⠀⠀⠀⠀⠀⠀⣸⣿⡿⠋
⠀⠀⠀⢱⡄⠀⠀⠀⠀⢠⣶⣿⡇⠀⠀⠀⠰⣶⣾⣏⠉⠁⠉⠙⠳⣄⠀⠀⠀⠀⠀⠈⠃⢹⣇⠀⠀⠀⠀⣸⡏⠘⠁
⠀⠀⠀⠀⠙⠷⣦⣤⣤⡴⠟⠉⠓⠀⠀⠀⠀⡿⠟⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂


⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⣶⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣿⣿⡿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⡿⠟⣋⣉⣉⣤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣫⣭⣶⣾⣿⠿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⢸⣇⣧⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⣾⣿⣿⣦⠀⠀⢠⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⣿⣿⣿⣿⡄⢠⣿⣿⣿⣿⢿⡟⠁⠀⣠⣶⡟
⠀⠀⠀⢻⣿⣿⣿⣧⣿⣿⣿⣿⢷⠿⢀⣴⣿⣿⠟
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠃⢀⣴⣿⣿⣿⠏
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠛⠁
⠀⡀⠀⠀⠀⠀⠘⣿⣿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠿⣿⣿⠃⠀⠀⠀⢀⣤⣾⣿⡿⠿⠛⠉⢻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠈⠛⠀⠀⣠⣾⣿⠿⠛⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣶⣶⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⡿⠿⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⣿⠟⠋⠁
⠀⠀⠀⢀⠎⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⢀⣠⣾⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⢀⣴⣿⠿⠋⠁
⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⢀⣴⡿⠟⠁
⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⣴⡿⠋
⠀⠀⠀⠠⠃⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣼⣿⣷⣤⡀
⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⠿⠛⠋⠁
⠀⠀⠀⢀⠎⠀⠀⠀⢀⣠⠶⠟⠋⠉
⠀⠀⠀⠀⠀⣀⠴⠚⠉
⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠶⠶⠶⠒⠚⠛⠛⠓⢒⣶⡶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢋⠳⠕⣄⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⣻⠞⠉
⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⠀⣼⠋⢧⠀⢀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⡤⣤⣦⣤⣤⣤⣤⣤⣀⣀⣙⣳⣄
⠀⠀⠀⠀⣼⠃⠀⠈⢷⠟⠁⠀⠀⠀⠀⠀⣀⣤⣴⢶⠻⣿⡻⡉⠣⡀⠐⡐⡀⠡⢀⠀⠀⠐⠀⠠⠁⠇⠀⠀⠁⠉⣽⠹⡇
⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠿⢏⣙⠌⠢⣓⣌⣿⠾⠷⠶⠶⠶⠷⠖⠒⠓⠒⠚⠒⠒⠚⠒⠶⠶⠴⠤⠥⡴⠁
⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢠⣶⣟⡛⠭⢵⣲⠴⠓⠉⠁
⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠸⣭⣿⠿⡽⠋⠁
⠀⠘⢦⣄⣀⠀⠀⠀⠀⠀⠀⢷⣬⣉⡃
⠀⠀⠀⠑⠿⣝⣷⣲⣶⢦⡤⣤⣿⡭⣓⡀
⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠺⠶⠷⠮⠶⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠢⡐⠂⠤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠈⢢⠀⠀⠀⠉⠐⠒⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢑⡄⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠄⢖⡶⠀⠀⠀⠀⠀⠠⠊⢀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⢴⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢹⠀⢀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠔⢁⠔⠁
⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⢀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣞⠔⠁
⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁
⠀⠀⠀⢀⠈⠀⠀⢀⡠⠂⠁
⠀⠀⢠⠃⠀⣠⠔⠁
⠀⠠⠁⡠⠊
⢀⠁
⣷⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣶⣶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠁⠈⠉⠛⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠋⠉⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄
⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣀⣴
⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣿⣿⣿⡏
⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⢿⣿⣿⣿⡇⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠛⠇⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⣤⣤⣄⣀⣀⣀⣀⣸⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠤⠶⠶⠚⠛⠋⠉⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣦⣤⣄⡀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣷⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠛⠛⠛⠿⢿⣶⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣤⣄⠀⡀
⠀⠀⠀⠀⡀⠀⠀⣀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢠⡾⠟⠛⠉⠙⠛⢿⣿⣷⣷
⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠐⠿⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠈⣿⣿⣶⣤⡄⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠐⠤⣄⣀⣤⣴⠿⠛⠉⠁⠀⠀⠀⠉⠉⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢹⡿⣿⣷⣤⣀⣀⣀⣠⣴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠙⠛⠿⠿⠛⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡯⣹⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⣤⣤⣤⣤⠀⢠⣤⠀⢀⣤⠖⠂⠀⢀⣤⣤⣤⣤⣤⠀⠀⠀⣀⣀⣀⣤⣤⣄⠀⠀⠀⠀⠐⠲⢄⠀⣠⡴⢦⣤
⢸⡇⠀⢀⣰⡄⠀⣠⡄⠘⠉⣴⠒⠂⠀⠛⠃⠀⡬⠥⢤⣄⢀⣤⣉⠉⠉⠙⠁⢴⡄⢸⡏⠙⠓⢋⣀⣀⣀⣠⣉
⠈⠁⠀⠀⠘⠁⠐⠉⠠⣿⠆⠈⠓⠒⠒⠛⠂⠀⠀⠀⠀⣿⠀⢠⠖⢦⡤⠖⢦⡼⠀⠸⣷⡆⠀⢏⣉⠉⠉⠙⠉
⢠⠎⠁⠀⠔⠊⠒⠲⠶⠟⠀⠀⢀⡜⢀⣀⣁⣤⣤⡄⠈⠟⠀⠀⣀⣀⣀⠀⢀⣒⠀⠀⣬⡤⠶⠖⠒⠒⠀⠀⣀
⠈⠳⢤⣤⣤⣤⣿⣿⠏⠀⣿⠀⠙⠉⠉⣩⣭⣥⡉⠀⣒⣒⡆⠀⣀⠤⣤⠀⢯⣼⣀⣘⡋⠁⡴⠋⢳⠀⠀⣽⠿
⠀⠀⠀⠠⠀⠀⠀⣠⢤⣀⡿⠀⠚⠓⠚⠃⠀⠘⠛⠘⠧⠤⢴⡦⠀⠀⠀⠀⣀⣈⠉⣙⣅⡀⠀⠀⠸⣤⠞⠁⣤
⠀⠴⡷⠖⠒⠒⢦⡀⠀⡌⠀⠶⠤⠤⠞⠃⡴⠟⠿⠃⠀⠶⠖⠂⠀⠓⠦⣤⠉⠁⠀⣿⠄⢈⠉⣴⣀⡀⢀⣤⡿
⠀⣠⠶⣄⠀⠶⠉⠀⡄⠀⠀⢀⣶⠖⠲⣄⠀⠐⠀⠁⠈⠱⢶⡀⢠⣦⡶⠟⢰⠋⢹⡀⠀⣨⠀⠈⣀⠀⠺⢀⣠
⠀⢉⠀⠈⠀⣠⡶⠀⢠⣶⠀⠀⠀⢠⣶⠃⠀⠶⠋⢀⣤⠄⢀⠀⣍⠉⣁⣤⣤⣤⡙⠋⠀⠋⢀⣉⠉⠁⢰⣿⣿
⠘⠻⢃⣈⠚⠉⣠⡶⠋⣠⠔⠁⡤⡄⠀⢼⡇⠀⡞⠁⠀⠀⠒⠦⣄⣀⠙⠋⣁⠈⠙⡛⠛⠉⢉⣋⣀⣴⠿⠋⢀
⠠⡾⠟⠛⠻⠾⠋⠀⣴⠏⠀⢀⠀⠙⠶⠟⣠⠀⢉⣭⣭⣿⠆⠀⠘⠛⣀⣀⣛⣉⠉⠛⠁⠠⢤⡤⠀⠠⣴⠤⠎
⠀⠀⣀⠄⣠⠤⣤⠀⠀⣤⡄⠀⠀⡙⢢⠀⣿⠁⢻⣅⡀⢀⣴⣶⠟⠛⠉⠁⠀⠘⢁⡀⠰⠾⠿⣶⡶⠀⠈⣠⣶
⠀⠈⠋⠉⠀⠾⠵⠖⠋⣉⣀⠒⢂⣀⣈⣀⡿⢀⡀⠉⢁⡈⠉⠀⣀⡼⠿⢀⣀⣠⡾⠃⣰⣶⡞⠉⢰⠶⣄⣼⠏
⠀⡾⠟⠁⡀⠀⡠⡄⣠⠞⠙⠀⠘⠠⢴⠄⠐⠋⢻⡴⠋⢳⣤⠞⢉⡀⣴⠏⢉⣉⣀⡀⢉⣍⣀⣀⠀⠁⠀⠀⢸
⢀⣙⠒⠊⣁⠈⠀⣈⣥⣤⣤⣤⠀⠐⠀⢀⠀⢿⣀⣀⣀⠀⢁⣀⣩⣄⠀⠄⠀⠀⠀⠀⠈⠉⣉⠉⢁⣄⣀⣀⣸

⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠘⢹⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⡀⠀⠀⠀⡻⠁⠀⠀⠀⢱
⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⢀⠔⠊⠁⠀⠀⠉⠓⢄⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠑⠒⠊⠁⠀⠀⠀⠀⠀⣇
⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⢀⠤⢤⣀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢰⠃⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠙⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠘⣆⠀⠀⠀⡎⠀⠙⡆⠀⠀⠀⣠⠞⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⡠⠃⠀⡠⢤⡀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠁
⠀⠀⠀⠈⠓⠤⠤⢧⣔⣊⣀⡤⠔⠋⠀⠀⠀⠀⠀⠀⠈⠓⠤⠤⠔⠊⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠻⠷⢤⣀⣀⣀⣀⡤⠴⠚⠉

⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢀⣤⣾⣿⣶⠄⠀⠀⣰⣿⠋⠉⠈⠙⣧⠀⢤⣾⣿⣷⣦⡄⠀⠀⠀⠀⠀⣠⣴⣿⠀⠀⠀⠀⢀⡀⢙⣿⡆⠀⠀⠀⣠⣴⠶⣿⠷
⠀⠀⢠⣿⡿⠛⠟⠁⠀⠀⣀⣿⣧⠀⠀⠀⠐⠃⠀⠀⠈⠙⠋⢻⣿⠀⠀⠀⠀⢀⣽⣿⠿⠄⠀⠀⢀⣾⣷⣿⡿⠁⠀⢀⡾⠋
⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⠈⢿⠏⠀⠀⠀⠀⠀⠀⠀⠳⣤⣠⣾⠟⠀⠀⠙⠻⠿⠛⠁⠀⠀⠀⠀⠛⠛⠿⠅⠀⠀⠀⠘
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⢦⣀⠀⠀⠀⠀⠀⠀⢠⣾⡿⢿⣿⣆⡄⠀⠀⠀⠀⠀⣴⣾⡇⠀⠻⣿⣷⣶⠿⠿⢻⡇
⠀⠀⠛⠿⣷⣤⣀⣀⡀⠀⠀⠀⣿⠿⠿⠋⠈⠀⠀⠈⠻⢿⣿⣦⡤⠀⠀⢻⡏⠀⠙⠻⡿⠀⠀⠀⣠⣴⣾⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⣸⠂⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⠇⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠰⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠉⠙⢷⣦⡀⠀⠀⠀⣼⠟⠛⠻⠿⣿⠄⠀⠀⢀⣤⣿⣦⡀⠀⠀⠀⢀⣀⣤⣷⣄⠀⠀⠀⣶⣄⠀⠀⠀⠀⠀⢠⣴⣾⣥⣄⡀
⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠟⠉⠀⠀⠀⣾⠿⠟⠛⡿⠟⠁⠀⠘⣿⣿⢁⣤⠤⠄⠀⠀⠙⠿⠙⠛⠻⣧
⠀⠀⠀⠀⠀⠀⠐⣿⡷⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⢀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⠀⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠙⢷⣦⡀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃
⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡿⠋
⠀⠀⠀⠀⠰⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠿⠖⠶⠶⠶⠶⠶⠿⠿⢶⣆⠀⠀⠀⠀⠀⠀⣠⡾⡫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⣠⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⡀⠀⠀⠀⣤⣤⣤⣀⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡀
⠀⠀⠀⠀⣠⣤⣄⠀⠀⣴⣶⣆⢠⣶⠶⠿⠿⠟⠛⣿⡿⠋⠀⠀⠀⠀⠈⠉⢉⣽⡿⠿⠀⠀⣀⣤⣤⣄⣀⣀⣀⣀⣀⣬⣽⣿⡿⠋
⠀⠀⢀⣼⠏⠀⢻⣄⣾⠏⠀⠻⡿⠃⠀⠀⠀⠀⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⠉⠉⠉⠛⠛⠛⠋⠉⢽⡟⠁
⠀⠀⠾⠁⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⣀⣤⡴⠶⠶⠒⠆
⠀⠀⠀⠀⠀⠀⠀⣤⡾⠟⠛⠉⠙⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⣸⣿⡾⢋⣁⠀⠀⠀⠀⠀⠀⠀⣠⣀⣤⣴⣶⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⢀⣾⢏⡀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⢰⣿⣿⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⡀⠀⣀⣀⠀⠉⠙⠿⣶⡀
⠀⠀⠀⠀⢶⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠘⠋⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠛⠛⠉⠛⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠙⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣤⣀⣀⠀⠀⠀⠀⠉⠛⠳⢶⣤⡀⠀⠀⠀⢿⡄⠀⣿⠀⢀⡀⠀⠹⣧⣄⣀⣀⣀⣀⣀⣤⣾⠟⠁
⠀⠀⠀⠀⠴⡶⠶⠶⠾⠿⠿⢿⣿⡿⠋⠀⠀⠀⣠⠴⠶⠶⠶⠞⠁⠀⠀⢿⣼⡇⠀⣿⣠⡿⠃⠀⠀⠈⠉⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠋⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⣹⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⠀⠀⠀⠀⠀⠀⠀⠙⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⢀⠀⠀⣀⣤⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⢀⣾⢿⣦⡀⣼⣿⣦⢀⣼⢿⣆⣰⡿⣷⡄⢉⣿⠟⢻⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⢷⣄⠀⣰⡟⠀⠀⠀⠀⣀⣰⣶⣤⡀
⠀⠀⠀⠀⢠⡾⠁⠀⠙⢿⠟⠀⠻⡿⠋⠀⠻⠟⠁⠘⢿⡿⠁⠀⠙⠁⠀⠀⠀⠀⠀⠀⠿⠈⣿⡄⠉⣰⡟⠀⠀⠀⠀⣾⣛⠉⢹⡿⠁
⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸⣷⣰⡿⠁⠀⠀⠀⠀⢈⣛⣻⣷⣄
⠀⠀⠀⠀⣾⠿⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠷⣦⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⢻⡿⠁⠀⠀⠀⢰⣿⠛⠛⠉⠉⠉⠁
⠀⢰⡀⠀⠈⠳⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣽⣿⣶⣤⡀
⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⢾⣿⣥⣀⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣌⡉⠉⠉
⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠈⢉⣻⡆⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⡶⠿⠿⠿⠗
⠀⠀⠀⠀⠙⢦⣀⠀⠘⣆⠀⠀⠸⡇⠀⠀⠀⣾⣵⡾⠟⠋⠀⠀⠀⠀⠀⠙⠷⣦⣤⣤⣤⣽⣿⣿⡷⠀⠀⠀⠈⠛⠿⢶⡄
⠀⠀⠀⠀⠀⠀⢉⣿⣶⣼⣷⡄⠀⠀⠀⠀⠈⠛⠛⠛⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠿⠋⠀⠀⠀⠀⠒⠒⠚⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠐⠒⠺⠗⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠲⠂⠀⠀⠀⠀⠀⠀⠨⠷

⠀⠀⠀⠀⠀⢰⠠⠀⠀⠀⠀⠀⠤⠤⢶⠦⠀⠀⠀⠳⠤⠤⠤⢼⡦⠀⠀⠀⠤⠤⠤⠤⢾⠆⠀⠀⠀⠤⠤⠤⠤⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣦⠤⠀⠀⠀⠠⠤⠤⠤⠤⡦⠀⠀⠀⠤⠤⠤⠤⢼⡦⠀⠀⠀⠤⠤⠤⠤⢴⡄⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⢀⣀⣀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⣀⣀⣠⣀⣠⡄⠀⠀⠀⠀⠀⣀⣀⣦⡀
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢀⣀⣀⣀⣀⣄⡀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣦⡀
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠜⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠈⠀⠉⠟⠀⠀⠀⠈⠉⠉⠉⠙⠛⠀⠀⠀⠉⠉⠉⠙⠁⠀⠀⠀⠀⠛⠛⠉⠹⠛⠁⠀⠀⠀⠉⠉⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠐⠒⠛⠂⠀⠀⠰⠚⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠒⠒⡺⠃⠀⠀⠀⠒⠒⠒⠒⠛

⠀⠐⠒⠒⠒⢾⠖⠀⠀⠀⠐⠒⠒⠒⣿⠶⠀⠀⠀⠐⠒⠒⠒⢚⠗⠀⠀⠀⠀⠀⠐⠒⠾⠆⠀⠀⠀⠒⠒⠒⠺⠷

⠀⠀⠀⠀⠀⢰⡦⠀⠀⠀⠠⠤⠤⠤⡂⠤⠀⠀⠀⠤⠤⠤⠤⠤⡦⠀⠀⠀⠤⠤⠤⠤⣽⠆⠀⠀⠠⠤⠤⠤⢴⡦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⡽⠁
⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⣾⣠⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡀
⠀⠀⠺⢭⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡿
⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠻⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣽⣄

⠀⠀⠀⠀⠀⣀⣤⣶⡗⠀⠀⢠⣄⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⡄⠀⠀⠀⢀⣾⡆⠀⠀⠀⠀⣀⣴⡆⠀⠀⠀⢢
⠀⠀⠀⠀⢈⣽⢻⡿⠀⠀⢀⣿⣿⢦⠀⠀⡼⣿⢿⣄⠀⠀⠀⡇⠀⠀⠀⡼⣿⣿⡀⠀⠀⢺⡟⣿⠃⠀⠀⠀⠸⡇
⠀⠀⠀⢠⡟⠁⠀⠁⠀⠀⠘⢩⣿⠀⠀⠈⠀⣿⡀⠁⠀⠀⠀⣧⠀⠀⠈⠁⣿⠈⠁⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠸⣇⠀⠀⠸⣦⣿⡴⠀⠀⠀⣿⠀⠀⠀⠸⣧⣞⣻⠆⠀⠀⠀⢰⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠘⠚⠉⠀⠀⠀⠀⠀⠀⠀⠙⠷⠀⠀⢹⣿⠃⠀⠀⠀⢹⡇⠀⠀⠀⠹⡏⠁⠀⠀⠀⢿⣾⣷⠆
⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠙⠄⠀⠀⠀⠺⠟⠁
⠀⠀⠀⠀⠀⣴⣿⣿⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣀⣴⣿⠃⠀⠀⣠⠆⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠚⢡⡟⠹⠇⠀⠀⢠⡟⠀⠀⠀⠀⣈⣽⠟⣿⠀⢀⡾⠁⠀⠀⠀⠀⣰⣿⡇⠀⢰⠀⢀⣾⠛⢉⡧
⠀⠀⠀⠀⢠⡿⠁⠀⠀⢰⣠⡿⠁⠀⠀⠀⣾⠋⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠚⣱⡟⠿⠀⠈⠳⣼⣧⠶⠟⠁
⠀⠀⠀⢠⡟⠁⠀⠀⠀⢸⣿⠟⠋⠀⠀⠀⣿⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠊⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠈⠓⠶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣜⣧⡀
⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⣈⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠂
⠀⠀⠀⠀⡤⢾⣿⡟⠀⠀⠀⠀⠀⠈⠁⠀⣸⡆⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠤⠒⠒⠛⠓⠶⢶⣤⣀
⠀⠀⠀⠀⣴⠟⠈⠁⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠒⣻⡿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⡀⣦
⠀⠀⢀⡾⠁⢠⠴⢦⠀⠀⠀⠀⣠⢀⣼⠟⠀⠀⠀⣼⡟⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣲⣶⣶⠶⠀⠀⢀⣙⣿⣿⡆
⠀⠀⠸⡇⠀⠈⣠⡿⠀⠀⢀⣼⣿⣿⡷⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠁⠟⠁⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⢈⡉⠉⠀⠀⠀⠀⠀⠘⣇⠀⠀⢀⠄⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡇⠀⠀⢐⠀⠀⠀⠀⠙⠶⠖⠁⠀⠀⠁⣀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢤⣶⣶⡟
⠀⠀⠀⣴⠛⣷⡀⠀⣠⡿⠙⠁⠀⠀⠘⢆⡀⠀⠀⠀⠀⠀⠠⠤⣶⣿⡟⠀⠀⡠⠒⠉⠉⢻⡇⠀⠀⣠⡴⠛⠟
⠀⠀⡼⠃⠀⣿⣇⣴⠟⠀⠀⠀⠀⠀⠀⠈⠙⠶⢦⣤⣤⣤⣶⠾⠛⠿⠀⠀⠈⠀⠀⠀⠀⠈⠻⠶⠛⠁
⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠥⠀⠀⠉⠠⠔⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣠⡄⣀⡐⣲⢦⣔⢭⣟⡣⠯⠅⣀⣠⡔⣚⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢐⢂⠀⠐⠛⠙⠛⠋⠉⠉⠉⠉⠁⠉⠉⠈⠀⠀⠀⠈⠋⠹⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣢⡋⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣀⠀⠀⠀⠳⣤⡀⠀⠀⠀⠀⠪⢇⣀
⠀⠀⠀⡐⠀⠀⠀⠈⠻⢦⣄⣀⣀⠀⡀⠘⠀⠀⠀⢀⡝⠀⠀⠀⠈⠻⣆⣀⢸⡁⣆⢄⠀⠉⠓⠀⠒⠠⠄⡀
⠀⠀⠀⠈⢦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣠⢴⡿⠃⠀⠀⠀⠀⠀⠈⠛⠿⠀⠉⠛⢿⡲⣄⠀⠀⠀⠀⠀⠁⠢⡀
⠀⠀⠀⠀⠀⠙⠻⠏⣰⣟⣧⣤⣁⠩⢵⠛⢊⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⡀⠀⠀⠀⠉⠻⣷⡢⡀⠀⠀⣶⣖⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⢠⠒⠠⠠⠊⠀⠈⠳⣄⠀⠀⠀⠀⠈⠑⢽⣦⡀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠀⠀⠀⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⢀⢞⡃⠀⠀⠀⠀⠀⠀⠹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⣀⠀⠀⡰⡒⣄⡀⠀⡰⠁⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢤⢠⣀⠀⢀⡜⡄⠿⡖⠅⡼⠉⠺⢯⡡⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠚⠁⠉⠛⠋⠋⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⡀
⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⣠⡄⢐⣵⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠋⢁⢤⣄⣀⠀⣀⣀⡀
⠀⠀⠀⠀⣀⠔⠁⠀⣴⠏⠙⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⠌⠀⠀⠆⠀⠉⠁⠀⢃⠈⠙⠻⡷⠶⢶⣦⣤
⠀⠀⢀⠜⠁⠀⢠⣾⠏⠀⠀⠘⠋⠀⠀⢀⠤⢶⡫⠭⠹⠛⠛⠋⠁⠀⠀⡠⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⠰⢾⣽⣍
⠀⡰⠁⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⢠⣚⡠⠊⠁⠀⢀⡀⠠⠤⠀⠠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠐⡀⣠⣄⠀⠈⠻⡝⡄
⠀⢧⣀⣀⢀⢳⡿⠀⠀⠀⠀⠀⡴⣻⠋⠀⠀⢠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠂⠀⠀⣗⠇
⠀⠀⠙⠛⠿⠿⠇⠀⠀⠀⠀⠀⠘⠻⣶⣤⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⡀⠀⢀⣠⠆⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠈⠉⠉⠉⠛⠀⠀⠉⠉⠉⠟⠀⠐⠛⠛⠺⠃⠀⠐⠒⠒⢺⠗⠀⠐⠒⠒⡿⠂⠀⠀⠒⠒⠶⠀⠀⠀⠖⠲⠗⠀⠀⠐⠒⠒⠿⠂

⠀⢠⣤⣤⣶⡄⠀⢠⣤⣤⣴⣦⠀⢠⣤⣤⣦⡄⠀⠐⣶⣤⣴⡄⠀⢰⣶⣾⣦⡄⠀⢰⣶⣶⣦⡄⠀⢰⣶⣶⣶⡄⠀⢰⣶⣶⣶⣦
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠈⠉⠁⠉⠀⠀⠈⠉⠙⠁⠀⠀⠈⠉⠙⠁⠀⠀⠈⠉⠉⠉⠀⠀⠈⠉⠉⠉⠁
⠀⠀⣀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠟⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⢠⡀⠀⠀⠀⡀⣀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⡀⣀
⠀⢀⠕⢕⠗⠀⠀⠀⠿⠿⠃⠀⠀⠀⢀⡽⠂⠀⠀⠀⣨⢯⡿⠂⠀⠀⡽⣪⢯⠗⠀⠀⠀⣨⠗⠀⠀⠀⠀⣸⡿⠂⠀⠀⢀⡽⣪⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⢀⣄⣤⣦⡀⠀⢰⣤⢰⣄⠀⠀⢰⣶⣤⡀⠀⠀⠀⢲⣤⣄⠀⠀⢠⣶⣄⠀⠀⠀⢠⣤⣿⣤⠀⠀⠀⢀⣤⣴⣦⠀⠀⣀⣈⠙⣷
⠀⠀⠀⠈⠋⠀⠀⠘⠁⠘⠁⠀⠀⠘⠋⠁⠀⠀⠀⠀⠛⠉⠀⠀⠀⠈⠛⠁⠀⠀⠀⠈⠩⠟⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠙⠛⠛⠁
⠀⠀⠤⠀⢄⠀⠀⠀⠤⡀⢄⠀⠀⢀⣤⣤⡄⠀⠀⠀⠤⡀⠄⠀⠀⠀⠄⠀⢄⠀⠀⠀⠤⡀⢄⠀⠀⠀⣠⣄⠀⠀⠀⠀⠠⠶⣦⡄
⠀⠘⣀⠘⡡⠀⠀⠘⣛⠟⡀⠀⠀⠘⣷⣼⠟⠀⠀⠀⢀⠚⡈⠀⠀⠘⣀⠛⡰⠀⠀⠀⣀⠜⡠⠀⠀⠘⢧⡜⠃⠀⠀⠈⣷⣆⣉⡛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠳⡀⠹⣆⠘⢷⡈⢻⣆⠹⣷⡘⢿⣎⢻⣷⡽⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠙⣄⠈⢧⡈⠻⣄⠹⣧⡘⢿⣌⢻⣷⡹⣿⣞⢿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠈⢦⠀⠳⡄⠙⣦⠘⢷⡌⢻⣦⠹⣿⡜⢿⣯⣻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢠⠎⢀⡼⠁⣰⠟⢠⡾⢃⣼⠟⣰⡿⣣⣿⢟⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⡰⠃⢠⠞⢀⡼⠃⣰⠟⣡⣾⢋⣾⡟⣵⣿⣫⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⡜⠁⣰⠋⢠⡞⢁⣼⠏⣴⡿⢡⣿⢏⣾⡿⣵⣿⣿⣿⣿⣿⣿⠟




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠤⠶⠒⠲⠦⠤⣀⡀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⣴⠉⢳⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⡀⠀⠈⠑⠢⠤⣤⣀⣀⡼⢶⣁⣀⠀⠀⠓⠿⣼⣁⣀⡤⠞⠉⠀⠀⠀⡠⠚⠉
⠀⠀⠀⠾⡖⠒⠲⢤⡀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠲⠤⡀⠀⠀⠀⢀⡤⠔⠒⠒⠒⠢⣴⡄⠀⠀⠀⠸⣀
⠀⠀⠘⠒⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠁⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠐⠛
⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠈⢢⣀⣀⣀
⠀⠀⡄⠀⠀⠀⠈⠛⠀⠀⠀⠀⠈⠓⠤⣄⣠⣦⠄⠀⠀⠀⠀⢀⣀⣀⣠⡀⠀⠀⠀⢠⠊⠉⣧⠀⠀⠉⠑⠦⡀
⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠤⢄⡀⠀⠀⠀⠀⠁⠀⠀⢀⠔⠋⠁⠀⠀⠙⠁⠀⠀⠀⠘⠦⠴⠃⠀⠀⠀⠀⠀⢈⣦⡄
⠀⠀⠀⠑⠤⣄⣀⣤⡀⠀⢴⢋⡏⠉⠑⠦⡀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢰⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠁
⠀⠀⢀⠀⠀⠀⠀⠁⠠⣄⠈⠉⠀⠀⠀⠀⢹⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡔⠁⠁⠀⠀⠀⣀⣤⣄⡀⠀⢠⠋⣀⣄
⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣼⠄⠀⠀⢧⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⡸⠫⣤⡤⠃
⠀⠀⠸⡄⠀⠀⠀⠀⢰⣞⠀⠀⣴⣄⠀⠀⠀⠀⠀⠀⠘⢆⡀⠀⠀⠀⠁⠀⠀⠀⣶⠇⠀⠀⣤⡄⠀⢰⠁
⠀⠀⠀⠙⢦⣀⣤⡀⠈⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⡀⠀⠀⠉⠳⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠋⠁⠀⢰⣶⠄⠀⠘⢦⡀⠀⠀⠈⢧⣖⠆⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢀⡜⠀⠀⠸⡄
⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠑⠀⠀⠀⠘⠦⢤⢶⠄⠀⠀⢀⠇⠀⠀⠀⠒⠋⠀⠀⠀⠀⠙⠦⣠⡀
⠀⠀⢸⡩⠛⡆⠀⠀⠀⣀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠉⠁
⠀⠀⠀⠀⢠⣿⡀⠀⠈⠁⠀⠀⠀⠀⠀⣀⣶⠆⠀⠠⣤⠄⠀⠀⠀⠀⠀⠀⠱⣄⣀⠀⠀⢼⠷⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠋⠀⢀⡠⠴⠿⠂⠀⢀⠞⠁⠈⠀⢠⠎⠉⠀⠀⠀⠱⡄⠀⠀⠀⠀⠟⠃⠀⢸⡀⠀⠀⠀⡴⢺⣄
⠀⠀⠀⠀⠀⠀⣴⡋⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠈⠲⢄⡀⢀⡀⠀⠀⠀⢇⠀⠀⠀⠙⠋⠈⡆
⠀⠀⠀⠀⠠⠞⢇⣹⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠓⢄⣀⠀⠀⠀⠀⠀⠀⠈⠹⠛⠀⠀⠀⠈⠳⣄⠀⠀⠀⠘⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⢀⣿⣿⡿⠂⠀⠀⠀⣀⣤⣶⣾⣿⣷⡤⠀⠀⠀⢀⣤⣶⣶⣶⣦⣄⡀
⠀⠀⢻⣿⣿⠀⠀⠀⠀⣴⣿⠟⠻⠁⠀⠀⢀⣼⣿⠟⠉⠙⠋⠁⠀⠀⠀⣴⣿⠟⠉⠉⠉⠙⢿⣿⣦⡄
⠀⠀⣿⡿⠈⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠘⠿⣿⡇

⠀⠀⠀⠀⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⠀⠀⠰
⠀⠀⠀⠀⡠⠃⠀⠀⡠⠐⠀⠀⠐⢄⡀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⡇⠈⠒⠀⠐⠁⠀⠀⠀⢁
⠀⠀⡠⠊⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠘⠀⠀⠀⠔⠢⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⡅⠀⠀⠠⠤⢄⠀⠀⠀⢀⠀⠀⠀⡅⠀⠀⠀⠀⡰⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠘⠤⠀⢥⡠⠊⣀⠤⠒⠁⠀⠀⠀⠐⠤⠀⠠⠐⠁⠀⠅⠉⠁⠀⠀⠠⡤⣀⠀⠀⣀⠀⠔⠊

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





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠈⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⠀⠀⠀⠀⠀⠀⠀⠃⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢀⣾⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠘⢿⡿⠋⣸⣿⣿⡇⠙⢿⡿⠇⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⣾⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⡄⠀⠀⠀⠀⣠⣾⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⢿⣿⣿⣧⡈⠛⠋⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⠋⣿⣿⣿⠙⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠁⠀⠀⠀⠀⠀⠉⠀⠀⣿⣿⣿⣦⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟

⠀⠀⠀⣀⣀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⡀
⠀⠀⠀⢸⣯⣿⣽⣏⣿⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⡷⠆⠐⠀⠈⠀⠦
⠀⠀⠐⠋⠛⠛⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⡠⡤⠤⡄⢠⡀
⠀⠀⠰⡭⠡⠤⠈⠤⢩⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠠⡇⠀⠀⠀⠀⠀⠐
⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠈

⠀⠀⠀⠲⣶⣶⣶⣦⣦⣄
⠀⠀⠐⠀⣨⣭⣭⣭⣭⣭⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠂⠠⠀⠂
⠀⠀⠀⠚⠋⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⣤⢤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠠⠀⣀
⠀⠀⠘⣟⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢨⠂⠀⠀⠄⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠐⢒⡀⠀⠦⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡂⠀⠠⠄⣀
⠀⠀⠘⠛⢛⣛⣓⣛⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠗⠀⠀⠀⠄⠀⠛
⠀⠀⠈⠉⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⢀⢠⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢳⠔⠀⠀⠤⣀
⠀⠀⠙⠷⠾⠷⠾⠶⠷⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠀⣰⠆⠀⠀⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡄⠈⠉⠛⠿⢿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠈⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣷⡄⠀⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠿⠛⠛⢻⣿⣷⣰⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠟⠋⠀⠀⠀⠀⠈⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿
⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟
⠀⠀⠀⠀⠀⢻⣿⣿⣶⣤⣄⡀⠀⠀⠀⢠⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣶⣤⣀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠈⢿⡄⠀⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⣼⣷⣴⠶⠟⠋⠁
⠀⠀⠀⠀⠀⢀⡀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣤⣀⣀⣀⣀⣸⣧⠸⠋⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠉⠉⠙⠛⠉⠹⣆⢀⡾⠃⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠘⠷⠶⠶⠞⠻⣧⡀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⣤⣤⣤⣌⠻⣞⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⡀⠀⠀⠀⠀⠀⣀⣤⠾⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣿⣿⣿⣿⣿⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠄⢰⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⢀⡀⠀⠀⠀⠀⠔⠈⠈⠐⡈⠉⠐⠆⠀⠀⠀⢀⠠⡀⠀⢀⠀⢄⠀⠀⣀
⠀⠀⠀⠀⠀⠂⠀⠀⠘⠀⠀⠀⠂⠀⠀⠐⠉⠐⠂⠈⠁⠀⠀⠀⠈⠀⠀⠐⠤⠁⠀⠀⠀⠀⠀⠐⠁⠀⠁⠀⠁⠀⠀⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⡀⠀⠀⠀⠀⡀⠁⠠⠂⠀⢀⡀⠀⠀⠀⡀⠀⢀⡄⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠡⡀⠀⠀⢂⡀⠄⠀⠀⡀⠀⠀⠀⠠⠁⠀⡠⠊⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠐⢄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠶⠀⠀⠀⠀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⢀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠀⠀⠀⠐⠀⠀⠐⠁⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀
⠀⠀⠠⠊⠀⠀⠀⠀⠀⠁⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠐⠈⠀⠀⠑⠄
⠀⠀⠀⢀⠀⠂⠐⢄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠄
⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠠⡄⠀⠁⠂⠀⠤⠄⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠠⠀⠤⠐⠁⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢰⡦⣀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠈⠉⡩⢦⡀⠀⠀⠀⠀⠁⠙⢆⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⢜⠀⠀⠀⠀⠈⠋⠢⡀⠀⠀⠈⠈⠑⠤⣀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠑⢪⣼⠄⠀⠀⠀⠀⠎⡞⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⢄⠃⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠐⠚⣡⠆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠠⠜⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⣄⡀⠀⠀⠀⠀⠀⠀⢰⣦⣀⠀⠀⠀⠀⠀⠀⠀⣦⡀
⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠆⠀⠀⠶⠶⣿⣿⡷⠆⠀⠀⣿⣿⣿⣿⣿⡷⠀⠀⠠⠶⢾⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠋⠉⠀⠀⠀⠀⠀⠀⠸⠟⠉⠀⠀⠀⠀⠀⠀⠀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣤⡤⣤⣤⢤⡤⣼⣦⡀⠀⠀⢶⣶⣾⣿⣦⠀⠀⢀⡀⠀⠐⢤⣄⡀⠀⠀⣀⣀⣀⣀⣸⣦⣄⡀
⠀⠀⣿⣟⣿⣿⣸⣟⣟⣿⡿⠂⠀⣨⣿⣿⣿⣿⠇⠀⢸⠿⠃⠀⣀⡽⠿⠓⠀⠿⠿⠿⠿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠋⠙⠹⠿⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⡀
⣿⣟⣉⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠙⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠁⠀⠀⠀⠀⠙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣋⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣈⣻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁


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

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠰⡄⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⠫⠀⠀⠈⠀⠁⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠐⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠂⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⠀⠀⠀⠁
⠀⠀⠀⠀⣀⠀⠀⠀⠙⠒⠒⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⢀⡀⠀⠀⢀⣀⠀⠀⢀⡄⡤⣄⣠⡀⠀⢠⡀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⢀⠠⠶⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠴⠃⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡄⠀⠢⠀⠀⠰
⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠊⠉⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠂⠁


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⢀⠌⠡⡀
⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠐⢄
⠀⠀⢀⡠⠂⠁⠐⠂⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠐⠀⠁⠢⣀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠴⠡⡀⠀⠀⢀⠈⠆
⠀⠐⠅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠕⠀⠀⠀⠄⠘⠀⠀⠀⠓⢠⠄⠀⠀⠀⠀⠀⡆⠀⠀⢸
⠀⠀⠀⠈⠒⢄⢐⠂⠀⠀⠀⠀⠀⠁⠀⠀⠁⠐⠀⠀⠀⠐⢒⢀⠔⠊⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⢸



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣦⡀
⠀⠀⠀⢀⣠⣾⣿⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣸⣷⣦⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣷⡄
⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⠀⠀⠀⣀⣸⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠈⠛⢿⣿⣿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠿⠿⠿⠿⠿⠿⢿⣿⣿⠟⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄
⠀⠀⠀⠀⢀⡴⠾⣿⠟⠋⠀⠀⠀⢀⣶⠟⠉⠉⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠘⣷⣦⠄⠀⠀⠀⠠⠊⠉⠀⠉⠉
⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠋⢻⡆⠀⠀⠀⡆
⠀⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣟⠀⠀⠀⣷⡄⠀⠀⠀⠀⢸⠇⠀⠀⠀⠹⣤⣀⣤⣀
⠀⠀⠀⠀⠀⠙⠶⣶⣶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠁⠀⠀⠀⠈⠛⠶⠤⠄⠔⠃⠀⠀⠀⠀⠀⠀⠉⠿⠛⠋

⠀⠀⠀⠀⢀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡶⢦⣄
⠀⠀⠀⠀⠈⠙⠻⠟⠻⢦⡀⠀⠀⠀⠀⢀⡴⠒⠒⢀⡀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣰⡏⠀⠀⠀⠀⠹⣆⠀⠀⣼⣷⡀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠈⣿⡟⠀⠀⠀⠀⢰⣿⠀⠀⠉⢿⡀⠀⠀⠀⢀⡟⠀⠀⠀⢀⣠⣴⣦⣴⠞⠁
⠀⠀⠀⠀⠘⠻⠿⠟⠋⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠛⠦⠤⠀⠁⠀⠀⠀⠀⠈⠉⠙⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡀
⠀⢀⠀⢠⠤⢄⣀⣠⠞⠳⣄⠀⢀⣨⣷⣄⠀⠀⣤⣶⣤⣤⣴⠞⠋⠙⣦⣠⠞⠻⡄⠀⠀⠀⠲⢤⡀
⠀⢸⠀⠀⠀⠀⠈⠀⠀⢀⠈⠛⠋⠱⠟⠁⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠈⠉⠀⣀⠑⠀⠀⢀⣀⡀⣹
⠀⢸⡄⢀⣤⡀⠀⠀⣜⠁⠀⠀⠀⠀⠀⢠⣴⣾⣃⡀⠀⠀⠀⠀⢀⡴⠒⣶⡏⠉⢳⡄⠀⢿⣭⡽⢿⡄
⠀⠀⠙⣿⡴⠇⡀⠀⠘⢆⠀⠐⣆⠀⠀⠀⠙⠃⠈⠉⠳⢦⡀⠀⢸⡀⠀⠻⠃⠀⢸⠇⠀⣀⣤⣄⣠⡇
⠀⠀⠀⠘⠳⠤⢿⡿⠁⠈⣇⠀⠈⠳⢦⣀⠀⣄⠀⠀⠀⠀⠹⣦⠈⠳⣄⠀⠠⠿⣯⡀⠐⢿⣭⠿⠻⣆
⠀⠀⢀⡴⠂⠀⠘⠁⢀⡴⠃⠀⠀⠀⠀⠉⢛⣿⣷⣄⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⡿
⠀⠀⢾⣀⣀⠀⠀⠀⢺⡅⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣀⡀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⣼⣿⣿⡁
⠀⠀⣾⠳⠾⠀⠀⠀⠀⣻⣆⣴⠆⠀⠐⣄⠀⣠⣄⠀⢠⡞⠁⠙⠦⣄⣠⡴⠛⠇⠀⠀⠀⠀⠛⠉⠉
⠀⠀⠙⠦⣤⣀⣀⡀⠀⠹⡿⠃⠀⠀⠀⠈⠙⣗⠋⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠛⠓⠶⣄
⠀⠀⠀⠀⠀⠀⠉⠙⢷⡀⠀⠀⠠⢴⣿⠀⠀⠈⠉⠉⠀⠀⠱⡄⠀⣄⠀⠀⠐⠁⠀⢀⠔⠀⠀⠘⣧⢀⡤
⠀⠀⠀⣀⣀⣀⣀⣠⡼⠃⠀⠀⢠⡾⠙⠇⠀⠀⠀⢀⡀⠀⠀⠘⡾⠹⡆⠀⠀⠀⢠⣿⠛⢳⡄⢰⣿⡟⠁
⠀⢠⡟⠉⠉⠉⠉⠁⠀⠀⢀⣴⠟⠀⣠⠄⠀⠘⣩⣿⡇⠀⣀⡀⠀⠀⢿⣀⡇⠀⣿⠈⠛⠋⠀⠀⠉
⠀⠘⣧⡀⠀⠀⠀⣀⣤⠶⠋⠁⠀⠀⢧⣤⡀⢠⡟⠘⠃⣠⠟⠟⠀⠀⢺⣿⠃⠀⠙⢦⣄⣤⠶⠛⠳⣄
⠀⠀⠈⠉⠛⠛⠋⢉⣠⡤⠀⢀⡀⠀⠘⠋⠀⢸⡇⠀⠀⠃⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢰⠞⢳⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠇⠀⠀⣧⣠⣤⡀⠀⠈⢷⡀⠀⠀⠀⡞⠉⠹⡄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⣹
⠀⠀⠀⠀⣰⠛⢶⠟⠀⠀⠀⠀⠈⠁⠘⣧⣶⠀⠈⠻⢶⣤⣀⣳⣤⡼⠃⠀⠀⠀⠀⣠⣴⣂⣀⣀⡴⠋
⠀⠀⠀⠼⠁⠀⢀⣀⣀⣼⢿⡆⢠⣄⡀⠛⢿⠀⠀⠠⣀⠈⠉⠉⠉⠉⠛⠒⠒⠒⠀⠹⣯⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠀⠈⠛⠦⡄⠀⠀⠀⠀⠈⠛⠲⢶⣷⠆⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣟⣛⣟⣛⣻⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠣⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠘⢄
⠀⠀⠀⢀⠤⠊⠁⠦⠀⠀⠀⠀⠀⠠⡀⠀⢀⠄⠀⠤⠄⠄⠀⠼⠈⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣁⡀⠀⠀⠀⣈⢢
⠀⠠⢖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣲⠄⠀⠀⢀⠀⠄⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠑⠢⡀⠀⠤⠤⠤⠤⠤⠤⠤⠃⠀⠘⠤⠤⠤⠤⠤⠤⢤⠀⢀⠄⠊⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡄
⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣆
⠀⠀⠀⣠⣴⣿⣿⣷⣶⣶⣶⣶⣶⣶⡄⠀⢠⣶⣤⣦⣤⣴⣶⣾⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠼⠿⣿⣿⣿⣿⠿⠷
⠀⠐⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠂⠀⠀⢤⣤⣿⣿⣿⣿⣦⡤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠈⠛⢿⣿⡟⠛⠛⠛⠛⠛⠛⠁⠀⠘⠛⠛⠛⠛⠛⠛⢻⣿⡿⠛⠁⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣽⣷⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⠤⣤⣴⣶⣤⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠻⠿⢆
⠀⠀⠀⠀⠀⢀⣾⠋⠀⢀⣿⣿⣿⡇⠀⢀⣀⡤⠴⠖⠛⠛⠉⠉⠉⠉⠀⠠⠀⠀⠀⠡⠠⢰⣿⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠙⢦
⠀⠀⠀⢀⣴⡟⠁⠀⠀⣸⣿⣭⡿⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣺⣯⠀⠀⠀⢰⣶⣦⡀⠀⢀⠔⠁⠀⠀⠀⣠⣾⡿⠟
⠀⠀⣰⡿⠋⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢀⠀⠀⢸⠈⠱⣽⠖⠁⠀⠀⠀⢠⣾⠟⠁
⢠⣾⣯⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⠚⠛⠛⠛⠛⠛⠛⠛⠿⠿⠷⠶⠶⢶⣶⣶⣲⣶⣶⣦⣤⣿⡿⢿⠁⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁
⠉⠙⠻⢿⣦⣄⠀⠀⠀⠈⢿⣯⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠙⠛⠒⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢀⣜⣱⠁
⠀⠀⠀⠀⠈⠉⠛⢶⣤⡀⠘⣷⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠶⠶⠤⣤⣤⣈⣙⣿⠗
⠀⠀⠀⢀⣀⣤⣤⣤⣀⡙⠳⢾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⢠⠞⠋⠁⠀⠀⠀⠉⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣿⠲⠤⣀⡀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢽⡆⠀⠀⠈⠉⠒⠢⠤⣄⣀⣀
⠀⢻⠀⢀⣤⢶⡲⣶⣦⣄⠀⠀⠀⠻⣗⡒⢒⣺⠟⠀⠀⠀⠀⢀⣤⣤⣄⣀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠏
⠀⢸⣴⣿⣿⣮⡷⠟⠉⠉⠓⣄⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⣰⢋⢈⣳⣤⣭⣷⣄⠀⠀⠀⠙⢷⣤⣄⣀⣤⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠈⠙⠛⠿⠋⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢽⡿⠉⠀⠀⠀⠈⢳⡀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⢀⣰⢟⣴⡟⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢻⣆⠀⢀⡴⠋
⠀⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠶⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢀⡴⠋⠈⠳⢿⡴⠋
⠀⠸⣟⠽⡭⠉⠛⠛⠛⠶⠶⠶⠶⢶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠋⠁
⠀⠀⠹⣆⠁⠐⠀⠀⠀⠀⠀⠀⢠⣾⡙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⡀
⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠻⢾⣿⣿⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠛⠙⡟⢻⣶⡦
⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠲⠶⠶⠤⠤⠤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠤⠴⠶⠖⠚⠛⠉⠁⠀⠀⠀⠀⣿⣈⣿⡇
⠀⠀⠀⠀⠀⠘⣆⠀⣠⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡒⣿⡇
⠀⠀⠀⠀⠀⠛⠚⠿⣿⣿⣿⡟⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠙⠻⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠷⣶⣶⣤⣤⣄⣀⣀⣀⣀⡀⣀⣀⣀⣀⣠⣤⣤⣴⣶⠿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠭⠆⠀⠀⠀⠀⢀⣹⠆
⠀⠀⠐⠊⠉⠉⠉⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⣄⠀⠀⢰⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠤⠼⢦⣀⠀⠀⠀⠀⠀⠀⢰⣋⠉⠉⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⢀⡤⣀⢐⣇⣩⡾
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡇⠙⢦⡀⠀⠀⠀⠘⢮⣷⠃⠀⠀⠀⠑⣼⡞⠀⠀⠀⣧⣏⠤⣏⡇
⠀⠀⠀⠀⠀⠀⠀⠑⠲⠒⠋⠀⠀⠀⠙⢦⣆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠁⠀⠈⠀⣀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣅⡒⠒⠒⠒⠊⠁
⠀⠀⢀⣀⣀⠤⢤⣀⠀⠀⢀⣀⣀⣢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣳⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠠⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣊⡠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⠤⢭⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣒⣀⣀⣀⡀
⠀⠀⣠⠖⠋⠉⢹⡉⣳⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠀⠀⠀⠉⡧
⠀⠀⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⣒⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⠀⣠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠟⠓⠋⠁
⠀⠀⠀⠀⠀⠀⠘⠥⠴⠃⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡶⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠒⢚⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡦⢤⡀⠀⠀⠀⡸⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡬⠇⠀⠀⠀⠀⠈⡹⠹⠇⠀⠀⣴⣆⠀⠀⡰⡷⡄⠀⠀⠘⠳⣄⠀⠀⠀⠀⠙⠼⣟
⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢀⣠⣄⣸⠁⠀⠀⠀⠘⠁⡏⠃⠀⠁⠳⣍⠀⠀⠀⠀⠈⠲⢤⣠⣖⠆⠀⠈⠑⠂
⠀⠀⢰⠋⠉⠉⠁⠀⠀⠀⠀⠀⢠⠋⠀⠀⡏⢳⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠺⡦⢄⠀⠈⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡽⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⢗⠲⢄⠙⠢⠷⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠉⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⠑⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠒⠒⢦⡀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⣀⡤⠖⠒⠋⠉⠉⠉⠉⠓⠲⠤⣄⣀⠀⠲⢤⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⣿⢷⢦⡄⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠙⢦⣀⡀⣀⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⠘⢦⡀⠀⠀⠀⢀⣰⠃⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉

⠀⠀⠀⠀⠀⣠⣖⣒⠒⠒⠤⣀
⠀⠀⠀⢠⣞⡿⡏⠉⣻⡄⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠽⡫⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⢦⠀⠀⡠⠀⠀⡠⠒
⠀⠀⠀⢹⣏⠀⠹⡜⠉⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠲⠤⣀⠤⢄⣰⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣩⣻⣯⣤⢥⣄⡠⠔
⠀⠀⢀⡇⢣⠙⠲⡝⠟⡇⠀⡰⠃⠀⠀⠀⠀⢀⠔⠒⠊⠓⡷⡄⠀⢸⠉⢳⣰⠉⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢩⣿⣷⡿⣿⣿⣤
⠀⠀⠘⡇⠀⠑⠒⠋⣀⣷⠋⢀⡀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠣⠝⠀⠘⢆⣸⠙⡄⠀⢱⡀⠀⠀⠀⠀⠀⠀⢀⠄⠊⢻⠻⣿⣏⣙⡫⢤⠃
⠀⠀⠀⠈⠓⠒⠒⠉⠁⠈⠲⠤⠍⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠜⠁⠀⠀⠀⠀⢀⣀⠄⠀⠀⠀⠀⠉⠛⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉


⠀⠀⠀⠀⡠⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠶⠤⣦⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⣐⣢⡀
⠀⠀⠀⠊⢰⢰⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢠⡄⡄⠈⠃⠀⠀⠀⠀⢀⡞⠀⠀⠈⠉⠛⡇⠀⠀⠀⠀⠀⠠⡼⢀⠀⠸⣀⣀⠜⡆
⠀⠀⠀⠀⠈⢆⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡇⠀⢣⠀⠀⠀⡠⠁⢀⣨⡶
⠀⠀⠀⠀⠀⠀⠳⣝⠢⣀⡀⠀⠀⠀⠀⠀⠀⠀⠸⠃⡇⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⠜⠀⠀⠰⠁⢀⠊⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠬⠭⠍⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠢⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠀⠀⠀⠐⠒⠒⠀⢐⣋⣹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠒⠈⠁⢀⣠⡤⡤⠶⠔⠂⠐⠂⠀⠉⠁⠀⠸⡄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⢠⡠⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠐⠟⢄⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠂⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡤⡎⢀⢂⢄⣬⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠘⣤⡀⠀⠀⠀⢈⡝⠃⡠⠎⠀⢌⢘⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠹⡆⠀⠀⢠⡛⠠⢞⡀⠈⢈⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⢄⡘⠀⢠⠶⠦⣍⠐⠾⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩
⠀⠀⠀⠀⠀⠀⠈⠀⣰⠃⠐⡱⡿⠋⠓⠦⣌⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⣰⠁⢁⢼⡿⠁⠀⠀⠀⠈⠙⠳⢤⣑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣺
⠀⠀⠀⠀⠀⠀⢠⠉⠢⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣌⡐⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⢀⠛⢢⢐⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣍⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⢀⠷⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢄⡁⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⡌⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣌⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⡉⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠘⠀⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣌⣐⡶⢔⠀⠈⠭⠷⢽⣧⡀
⠀⠀⠀⠀⠀⠨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠈⡝⠭⠦⣭⡙⢻⣿⣿⡣⢠⣀
⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢤⡰⢨⣑⣝⣿⣿⠚⠛⠉
⠀⠀⠀⠀⠆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⣄⠀⢉⣯⠿⠛
⠀⠀⠀⠀⡆⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡠⡔⠶⠒⠛⠉⠚⠇
⠀⠀⠀⠀⠇⠨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠦⠞⠓⠚⠉⠁⠀⠀⠈⠀⠈
⠀⠀⠀⠀⢠⠀⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⠤⠶⠚⠛⠋⠈⠁
⠀⠀⠀⠀⠈⡆⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⢴⠲⠍⠙⠓⠊⠉⠁
⠀⠀⠀⠀⢀⡤⡼⣇⣠⣤⡴⠶⠞⠛⠋⠉⠉
⠀⠀⠀⠀⡸⢢⡟⠉⠁⠀⠐
⠀⣀⠔⣊⡴⠋
⠀⠀⠉⠁⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢀⠀⡠⠀⡀⢀⠀⡀⢀⠀⡀⠀⠀⢀⠀⡀⠀⠀⠠⢀⠄⡠⢀⠄⡀⢀⠀⡀⢀⢀⠀⡀⢀⠀⠀⢀
⠀⠐⠀⠄⠀⠀⣈⠅⠀⠅⠢⠄⠠⠀⠨⠂⠡⠂⠁⠊⠐⠀⠀⠁⠊⠐⠀⠂⠡⠊⠒⠀⠀⠐⠁⠊⠐⠁⠊⠐⠁⠘⠓⠁⠊⠔⠡⠊⠑⠑⠨⠂⠁⠀⠊⠔⠀⠨⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀
⠀⠀⠀⠀⠏⣭⣬⣭⣥⣤⣤⣤⣬⣭⣭⣭⣭⣤⣼⣿⣶⣅⡂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣶⣶⣶⣤⣤⣤⣤⣀⣀⣈⣻⣿⣦⣄⡀
⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⣇⡻⠿⠟⠻⠿⠿⠿⠿⠿⠿⠿⢟⢿⢻⣿⡿⢛⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⣻⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⡀
⠀⠀⠀⠀⠈⠳⣄⠓⣄⠑⢄⠙⢦⡘⢦⡈⠢⡈⠣⡀⠳⣄⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣤⣤⣤⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⣈⠇⢈⠷⢀⡵⢀⡵⠀⡹⠂⣨⠆⣨⠆⢈⠗⢀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠂
⠀⠀⠀⠀⠠⠞⠁⠔⠁⠔⠋⠴⠋⠤⠊⠠⠊⠡⠞⠡⠞⠁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⢛⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉


⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀⣀⠀⣀⡀⢀⢀⣰⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄
⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⣿⠀⣿⡇⣾⢸⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠶⡲⢖⡶⢒⠖⡲⢒⠖⡲⢒⠖⡣⠀⠙⠢⣀
⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⣿⠀⣿⡇⣿⢸⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⢊⠔⡩⠞⡡⢊⠔⡡⢊⠔⡡⢊⡅⠀⠀⠀⢈⠷
⠀⠀⠀⠀⠀⠸⡿⠀⣿⠇⢿⠀⢿⡇⢿⠸⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠥⠮⠴⠯⠶⠥⠮⠴⠥⠮⠴⠥⡄⠀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢀⣀⢀⡀⣠⢀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⡀⣠⠔⠢⣄⠀⠀⠀⠀⠀⢀⣀⣴⠂⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⢀⠴⠂
⠀⠀⠀⠘⠓⠀⠀⠈⠀⠀⣤⣀⡰⠃⠸⣈⡣⠀⠀⠀⠇⠑⠴⠋⠣⠤⠖⠉⠃⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠥⢄⣀⡹

⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡔⠉⠁⠀⣄⡀⠀⠀⢀⡠⢤⡀⢰⠁⠸⠞⢀⣀⠔⠉⠀⠀⠙⢦⡀
⠀⠀⠀⠘⠟⠒⠒⠁⠀⠀⠀⠀⠈⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠲⡄⣀⡀⠀⠀⠤⢄⡀⢀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⣠⠤⣀⡸⡶⠀⠀⠀⠀⢑⡤⠧⠚⠇⠀⠀⠀⠀⡝⢧⠀⠘⠁⠀⠘⠦⣄⣀⡠⠤⠚⠇
⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⢠⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⡀⠀⢐⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⢀⣌⠸⢠⠊⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠀⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⢰⠁⠈⠂⠁⠀⠀⠀⠀⠀⣀⡴⢻⠁⢱⠀⠀⠀⠐⠥⢜⣄⣀⠀⢀⡰⠆⠀⠀⠀⠀⣎⠁
⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠀⠀⠀⠀⠀⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂

⠀⠀⠀⠀⣄⡀⠀⠀⠀⣀⣤⡦⣤⡀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⣠⣾⣿⡿⠃⠀⢰⡟⠁⠀⢀⠇⠐⠻⢿⢿⣦⠀⠀⠀⠀⣾⣿⠀⠀⠀⣠⣠⣿⡇⠀⢀⡴⠛⠛⠋
⠀⠀⡟⠁⠈⠀⠀⠀⢻⡟⠀⠀⠀⠀⠀⢠⣀⣠⡿⠀⠐⠶⠾⠟⠁⠀⠀⠰⠿⢿⠉⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⠀⣀⣀
⠀⢸⣷⣆⠀⠀⠀⠀⠀⣠⣤⣾⠿⠀⠘⣦⣤⣀⠀⠀⢠⣿⠛⣿⣷⠆⠀⠀⢀⣰⣿⡇⠀⠹⠛⠛⠛⢹⠇
⠀⠀⠈⠛⠛⠒⠂⠀⠀⢹⠉⠁⠀⠀⠀⠀⠹⢿⡟⠀⠈⢿⡀⠀⠉⠀⠀⣼⠟⠋⠁⠀⠀⠀⠀⠀⠀⠏
⠀⠀⣀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠋
⠀⠀⠀⠉⢳⣦⠀⠀⣸⠋⠙⠛⠿⠂⠀⣠⣶⣷⠄⠀⠀⣠⣤⣼⣶⡄⠀⣴⣦⡀⠀⠀⠀⢶⣿⣶⣤⡀
⠀⠀⠀⠀⠀⣿⣇⠀⡏⠀⠀⠀⠀⠀⠰⣟⠀⠀⠀⠀⢸⠋⠉⠘⠁⠀⠀⢹⣿⡶⠋⠁⠀⠀⠉⠀⠈⢻
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⢀⣼⣷⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⣠⠟⠁⣿⣿⡏⠀⠀⠀⣀⣀⣤⠤⠤⠴⠶⠖⠒⠒⠒⠛⢻⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠉⠢⡀
⠀⠀⠀⣠⡾⠁⠀⢸⣿⣿⡧⠔⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢀⣀⣀⠀⠀⡠⠋⠀⠀⢀⣴⡾
⠀⢀⡼⠋⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⢸⠉⠻⠷⠊⠀⠀⢀⣴⠟⠁
⡴⣿⣅⠀⠀⠀⠀⢠⣶⣿⡋⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠷⠶⠶⣶⣶⣶⠿⠛⠁⠀⢸⠁⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠉⠛⠶⣄⡀⠀⢷⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣼⣀⣀⣀⠀⠰⢶⣧
⠀⠀⠀⣀⣀⣀⣉⠓⢮⣿⠟⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠋
⠀⡴⠋⠉⠀⠀⠉⠙⢦⡀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠈⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⢀⡴⣗⠢⠄⣀
⠰⡇⠀⠀⣀⣀⡀⠀⠀⠙⢦⣀⡀⣀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⢧⣾⠆⠀⠀⠈⠉⠒⠢⢤⣄
⠀⣇⣴⣿⣿⣽⠿⠷⢄⠀⠈⠓⠾⠚⠁⠀⠀⢀⡖⠻⣟⣲⣄⠀⠀⠙⢦⣀⡀⠀⣀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠉⠻⠿⠋⠁⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢀⡞⢾⡞⠉⠁⠉⠑⡄⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⣀⠀⠀⣠⣞⣷⠟⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⣠⣞⢧⠀⡠⠊
⠘⣷⣶⡤⢤⣤⣄⣀⣀⣀⣀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⠤⠚⠁⠈⠛⠋
⠀⠘⣎⠋⠄⠀⠀⠀⠉⠉⣹⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠘⣆⠀⠀⠀⠀⠀⠘⠿⣷⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠽⠛⡟⢲⣦⠄
⠀⠀⠀⠘⣆⠀⠀⢀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠒⠒⠒⠶⠶⠶⠶⠖⠒⠒⠒⠒⠛⠉⠉⠁⠀⠀⠀⢿⢸⣿
⠀⠀⠀⠀⢌⣦⣴⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⣿⡄
⠀⠀⠀⠀⠀⠀⠉⠙⠋⠀⠈⠛⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⢶⣦⣤⣤⣄⣀⣀⣀⣀⣀⣠⣤⣤⣴⠶⠟⠛⠉

⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⢀⣤⣤⣼⣦⡀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⣀⣤⣤⣄⡀⠀⣀⣤⣤⣄⡀⠀⣀⣤⣴⣦⡀
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠻⠿⠛⠉⠉⠉⠙⠻⠿⠛⠉⠉⠙⠁⠀⠀⠀⠻⠿⠛⠉⠉⠙⠻⠿⠛⠉⠉⠙⠻⠿⠛⠉⠉⠙⠻⠿⠛⠉⠉⠋
⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⡀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀⠀⠀⠀⣀⣠⣤⣤⣤⣦⡀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠻⠿⠟⠛⠉⠉⠉⠉⠉⠛⠛⠿⠿⠛⠛⠉⠉⠉⠉⠉⠛⠻⠿⠿⠛⠋⠉⠉⠉⠉⠙⠛⠿⠿⠟⠛⠋⠉⠉⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⢸⣿⣿⣿⣿⣿⠀⠀⢀⣤⣾⣿⣿⣷⣤⡀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣷⣤⡀
⢀⣸⣿⣿⣿⣿⣿⣄⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠂⠀⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓
⠀⠈⠛⢿⣿⠿⠋⠁⠀⠀⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠙⠻⢿⣿⣿⠿⠋⠁⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⡀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠀⠀⠀⠠⢾⣿⣿⡷⠄⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡆
⠀⠀⠙⢿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠠⠾⠿⠿⠿⠿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣷⣀⠀⠀⠀⠐⢶⣿⣿⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠋⠀⠀⠀⠀⠀⠙⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⠾⠿⠿⠿⠿⠿⠿⠿⢶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣶⣤⣀
⠀⠀⠀⠀⠀⢀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣻⣷⣤⡀
⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠟⠛⠛⠛⠛⣿⡿⢷⣦⣤⡀
⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠈⠙⠻⢷⣤⡀
⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠙⢿⣦⡀
⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣀⠀⠀⠀⢀⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣄⠀⠘⣿⡄⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣼⣿⣿

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠒
⠀⠀⠀⠀⠁⠀⠀⢀⠀⠤⠤⢤⠀⠀⠀⠀⠀⠀⡠⠂⠉⢁⠄⠂⠀⠀⠀⠀⠈⠁⡠⠊⠀⠀⠀⠀⢀⠓
⠀⠐⣀⠀⠠⠐⠈⠀⡀⢠⠀⠀⢀⠠⠆⠀⡠⠊⢀⠠⠔⢅⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⢡⠇⡀⠄
⠀⠀⠉⠀⢀⠄⠊⠁⠀⠈⠀⠐⠁⠀⠀⠐⠀⠠⠁⢰⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠄⠂⢁⠄⠐⠀⠀⠉
⠀⠠⠠⠐⠁⢀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠁⠠⠁⠀⠈⠤⠔⡀⠄⠚⠀⢀⣀⡀⠀⠀⠊⠀⢀⠔⠃
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠈⠀⡠⠀⠀⠀⠙
⠀⠀⠀⠊⠀⠀⠀⡀⠀⠀⡴⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⡐⠈⠀⠋⡆
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⢈⠀⠀⢀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠉⠀⢀⠛⢀⠄
⠀⠀⠀⡠⠐⠀⢁⠠⠀⠐⠂⠀⠀⠐⠲⠀⢀⠄⠂⠀⠈⠁⡠⠃⠀⠀⠢⡀⠀⠀⠀⠀⠀⡀⠐⠁⢀⠂
⠀⠀⠊⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⢀⣀⡀⠀⠀⠄⠀⠀⠀⠀⣠⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⢀⠀⠀⠉⠐⠄⠀⠀⠀⡥
⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⢀⠜⠂⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⡀⠔⠈⠀⡰⠆⠀⠰
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠀⠐⠀⠄⠠⠄⠐⠈⣀⠀⠀⠀⠑⠄⠀⠠⠚
⠀⠀⠀⠀⠠⡇⠀⠀⢠⡅⠀⠀⢀⠠⠃⠀⠀⠄⠀⠀⣀⠁⠂⠄⠀⠀⠠⠀⠂⠉⠀⠀⠀⠠⠀⠀⠰⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣶⣶⣦⣤⣀⡀⣸⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁






⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣀⠤⡤⠄⢀⠤⠀⠀⠀⠀⢀⠤⠒⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⡀⠀⢀⡤⠀⠀⢀⡄⠀⠀⠀⢀⠀⢀⣀⣀⣀⣄
⠀⠈⠀⣀⣤⡄⠀⠀⠀⠠⠴⠖⠀⠈⠀⢀⡰⠾⠀⠀⠀⠀⠚⠁⠀⠀⠀⡠⠊⢤⠔⠉⡠⠒⠄⠈⠀⠀⢻⠀⢸⠀⠀⠀⠀⢈⡉
⠀⠂⠁⠀⠀⢠⡄⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠄⠚⠋⠀⠀⠘⠀⠀⠀⠀⠊⠀⠀⠀⢀⠀⠀⢸⠀⢸⠀⠉⠉⠉⢩⣁
⠀⠀⠠⠀⠂⠁⣀⣀⡀⠀⡔⠉⠀⢁⠄⠂⡉⠥⠰⠆⠀⠐⠒⠟⠁⣀⠤⠛⠁⠀⢀⡴⠺⠋⠀⠹⢀⡄⢸⠀⢸⠀⠈⠉⠉⠙⠋
⠀⠀⣀⡠⠴⠚⠙⠁⠀⠀⠀⠀⠀⠁⠰⠁⠀⠀⢀⣴⠶⠂⠀⠐⠊⢁⠀⢀⠤⠊⠁⠀⠀⠀⣀⠀⢀⠁⣠⡀⠹⠃⠀⠀⠀⠀⠁
⠀⠞⠃⠀⢀⡠⠴⠖⠀⣀⠴⠖⢀⣠⠀⠀⠀⠊⠁⠀⠠⠔⠛⠃⠀⠀⠈⠀⠀⢀⡠⠾⠋⠀⠹⠀⢸⠀⢸⠁⠀⠀⠀⠀⠀⠀⠁
⠀⢀⠔⠊⣀⡠⠤⠒⠉⠀⠐⠊⠁⠁⡀⠤⠒⠟⠁⠀⠀⣠⠄⠀⠀⠀⠠⠔⠊⠁⢠⣤⣤⠀⢸⠀⢸⠀⢸⠀⠀⣠⣀⣀⣀⡉
⠀⢀⡀⠀⢀⠀⠀⠀⢀⣤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠴⠒⠛⠉⠛⠁⠀⠈⠀⠀⣀⣤⣀⣀⣀⣀⣀⣀⣉
⠀⠉⠉⠁⠀⢀⠔⠊⠁⠀⠀⠀⠐⠙⠁⠀⠀⠀⠐⠈⠉⠀⠐⠀⠁⠀⠀⠀⡀⠀⢀⡴⠀⢀⠀⠀⠀⢉⡭⠥⠤⠤⠤⠤⣴⣤⣀
⠀⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡤⠊⠀⣠⠎⢀⠀⢀⣠⣤⠤⠤⠤⠤⠤⠤⣄⡀
⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠀⠀⠉⠀⠀⠀⠄⠀⠀⢀⣠⣤⠴⠚⠉⢀⣤⠞⠁⠀⢸⠇⠀⢀⡠⠤⠤⠤⠤⠤⠤⣤⣄
⠀⠈⠁⠀⠀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣰⣤⡀⠈⠀⠁⠀⠀⠀⠉⠉⠀⣀⡀⠈⠉⠁⠀⠀⢀⡾⠀⢀⣠⣦⠔⠒⠒⠒⠒⠒⠂
⠀⠉⠉⠉⠉⠛⠉⠁⠀⠐⠉⠁⢀⣀⣈⣁⡀⠀⠀⠂⠐⠀⠒⠒⠒⠉⠉⣀⣀⠤⠴⠟⠀⠘⠁⠀⠈⠀⠠⠤⠶⠦⠀⠉⠉⠲⡄
⠀⠶⠶⠒⠶⠶⠿⠗⠀⠀⠀⠉⠀⠀⠈⢩⣀⠀⠐⠒⠀⠀⠀⠒⠒⠈⠉⠁⡀⠀⠀⠀⢀⡀⠒⠿⠒⠒⠒⠒⠀⠀⠈⠛⠁⠀⠻
⠀⣠⣤⣶⠤⠔⠒⠀⠀⠔⠒⠈⠉⠉⠉⢙⣉⣀⣤⣀⡀⢀⣀⣤⠐⠒⠒⠒⠿⠀⠈⠛⠙⠋⠀⡤⠄⠐⠦⠄⠨⠟⠀⡸⠆⠀⠷
⠀⠉⠉⠉⣠⣤⣤⣤⠀⠀⠀⠉⠉⠁⠀⢀⣀⠀⠉⠁⠀⠀⠀⠁⠀⣀⠀⠀⠀⠀⠀⠀⠒⠂⣠⣀⠀⠐⠦⣄⠀⠰⢤⡀⠀⢤⡀
⠀⠚⠋⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠘⠛⠛⠛⠋⠉⠙⠟⠛⠀⠀⠛⠋⠉⠉⠉⠙⠋⠀⠐⠋⠁⠀⠘⠉⠀⠐⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⣀⡤⠖⠛⠋⠉⠉⠛⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠻⠃⠀⠀⠀⠀⣠⠞⠙⡄⠀⠀⡠⠚⠙⣦⠀⢠⢋⡇
⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⡇⠀⢠⠃⠀⠀⡟⠀⠀⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢽⣦⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠁⠀⢸⠀⠀⢰⠇⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡀⠀⡸⠀⠀⠈⢧⣠⠜
⠀⠀⠀⠀⠀⢀⣤⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⠚⠁
⠀⠀⠀⠀⠀⡴⠚⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠻⢧⡀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡯⣄
⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⢄⠀⠀⠀⠠⠺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠈⠢⣀⣠⠜⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠈⠛⠻⡄⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠲⢄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢣⠀⠀⠸⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾
⠀⠀⠀⠀⠀⠀⠋⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⡀⢀⡏⠀⠀⠀⠀⠀⣼⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣀⡠⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠂⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠶⣾⣿⠶⠤
⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⠀⠀⠀⣤⠞⠉⠁⠀⠀⠀⠁
⠀⠀⠈⠓⠲⠦⠤⢤⡀⠀⠀⠀⠀⠀⠀⠐⢆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠶⠋⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⣠⠶⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⡠⠦⡄
⠀⠀⠀⠳⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⡀⠀⠀⠀⠀⣀⡠⢶⡶⠃⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢸⠀⠀⠹⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠉⡦⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⡁
⠀⠀⠀⠀⠀⣀⡤⠖⠁⠀⠀⠀⠀⠚⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠇⠀⢀⠰⠁
⠀⠀⠀⠠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⢠⠴⠒⠲⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠉⠑⠓⠒⢢⠀⠀⠀⠀⠀⠀⠀⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⢳⡄⠀⠀⡏⠀⠀⠀⠈⢓⣉⣲⡤⠀⠀⠀⠀⠀⢸⣾⡠
⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⠦⠶⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⠋

⣿⣿⡿⠿⣿⡿⢿⢿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣾⣴⣿⣷⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠐⠒⠶⢶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠗⠳⣿⣶⠒⠀⠀⠒⠲⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠀⠛⠛⠿⠿⠿⠟⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀
⠀⠈⠛⠲⠶⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠿⠿⠿⠿⠟⠛⠁⠈⠳⠟⠁⠈⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀
⠀⠠⢄⣠⡦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣾⣿⣿⣟⠁⠀⠀⠠⢤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢴⣿⣿⣿⣿⡋
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠈⠃⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠠⢤⣴⠄⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⢶⣿⣿⣿⣿⣿⠀⠀⠄⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣚⠁⠈⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠒⠻⠝⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⡂⡐⠀⠀⠠⠆⠀⠂⠸⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⢗⣟⣿⡓⠂

⠀⠀⠀⠀⠀⣀⣀⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡀
⠀⠀⣠⣶⠿⠟⠛⣿⠿⠓⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⢿⣿⠟⠂
⠀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠘⠋⠉⠉⠀⠀⠀⠀⠀⣾⣿⠟⠛⠉⠹⠟⠁⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⠈
⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⢀⣤⣶⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⣿⡿⠋⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣦⡄
⠀⢀⣼⠿⠛⢉⡿⠟⠋⠁⠀⠀⠀⠀⠀⢀⡿⠋⠁⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠋⠀⠀⠀⠀⠀⢰⡿⠛⠉⠩⠟⠋⠁
⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠸⡇⠀⠀⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⠄⠂⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠁⡂⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠃⠠⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⢀⠄⠀⠀⠀⠀⣠⡤⢀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⣖⠒⠒⣇⠀⢀⠂⠀⠀⠀⡠⢊⠔⠁⠐⠚⠃⠀⠄⠐⠀⡹⠄
⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⢂⠋⠀⠀⠀⡠⠁⠀⠀⣠⢎⠔⠁⠀⠂⠀⠀⠀⠀⠀⠀⢠⠹
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⠆⠀⠀⠀⡐⠀⠀⢀⠔⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡆
⠀⠀⠀⠀⠀⠀⠀⢀⠆⠌⠀⠀⠀⠄⠀⠀⡠⢂⠜⠀⠀⠀⠐⠁⠀⠀⠀⣀⠤⠄⣀⢥
⠀⠀⠀⠀⠀⠀⠀⡖⡜⠀⠀⠀⠄⠀⠀⡐⡡⠁⠀⠀⠠⠊⠀⠀⡀⠔⣈⠔⠊⠂⢬⡇
⠀⠀⠀⠀⠀⠀⢰⡑⠀⠀⠀⠀⠀⠀⢌⠌⠀⠀⢀⠄⠀⢀⠔⣈⠔⠊⠀⠀⠠
⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⢠⠪⠂⠀⠀⡠⢀⡠⢊⠄⠊⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢀⡲⠁⠀⢀⠈⣤⡪⠊⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠪⠊
⠀⠀⠀⠀⠀⠸⠀⠀⠀⢀⢠⠟⠀⠀⢠⣠⠞⠉⠀⡀⠄⠂⠁⠀⣀⣀⠤⠤⠄⢰⠆⠀⡠⣊⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠏⠀⠀⠰⠛⠁⢀⣔⣠⠤⣒⠂⠭⠑⠒⠒⠈⠉⠉⠣⣸⣎⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠐⠋⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⠀⠀⠄⠀⠀⠀⠀⣦⠄⠀⠀⠀⠀⠀⠀⠤⠤⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠤⠤⠄⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⣳⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠉⠉⠉⠁⠹⠅⠁⠀⠀⠀⠀⠀⠉⠉⠙⠟⠋⠀⠀⠀⠈⠉⠉⠉⠉⠉⠟⠁⠀⠀⠀⠉⠉⠉⠉⠉⠻⠋⠀⠀⠀⠈⠉⠉⠉⠉⢽⠋

⠀⠀⠄⠀⠠⠠⣦⣤⠄⠀⠀⠀⠠⠤⠤⠤⠤⢼⡦⠀⠀⠀⠠⡤⠤⠤⠤⡬⣷⡄⠀⠀⠀⠤⠤⠤⠤⠤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠘⡆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠁⠈⠉⡼⠃⠀⠀⠀⠘⠙⠛⠛⠹⠛⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠟⠁⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠈⠉⠙⠻⠛

⠀⠀⣤⣤⣤⣤⣄⣶⡄⠀⠀⠀⢠⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢘⣦
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠓⠓⠒⠓⠚⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠘⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟

⠀⠀⣀⣀⣀⢀⣀⣶⡄⠀⠀⠀⢀⣀⢠⣀⣤⣤⣤⠀⠀⠀⢠⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⢤⣤⡤⣤⣴⣦⣄⠀⠀⠀⣤⣤⣤⣤⣤⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠒⠒⠻⠃⠀⠀⠀⠴⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠐⠒⠛⣻⠇⠀⠀⠀⠘⠓⠛⠓⠒⠺⠓

⠀⠀⣀⣀⣀⣀⣰⣤⠀⠀⠀⠀⢀⣀⣀⣀⣐⣦⣄⠀⠀⠀⢀⣀⣀⣀⣀⣀⣦⡀⠀⠀⠀⠀⡀⡀⣀⣀⣤⡄⠀⠀⠀⢀⣀⣀⣀⣀⣶⣄
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠸⠟⠂⠀⠀⠀⠐⠒⠒⠒⠺⠥⠒⠀⠀⠀⠐⠒⠒⠒⠒⠒⠿⠂⠀⠀⠀⠒⠒⠒⠒⠒⣿⠇⠀⠀⠀⠐⠒⠒⠒⠒⠿⠓

⠀⠀⣿⣶⣄⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⣐⣦⣤⡀⠀⠀⣀⡤⠶⠒⠛⠛⠶⢦⣄⣄
⠀⠀⠙⠙⢷⣤⣤⣤⡴⠚⠁⠀⠀⠀⠸⣄⠀⠀⠉⠙⠛⠋⠿⠋⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡆⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⣠⡶⠶⠶⠦
⠀⠀⠀⠀⠀⣠⣴⠦⠀⠀⢉⡟⡇⠀⠀⠀⠙⢷⣄⠀⣀⠀⠀⠀⠀⢩⠟⠃⠀⠀⣼⠃
⠀⠀⠀⢠⣾⠛⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠙⢻⣾⣷⣄⠀⠀⢸⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢸⣿⡥⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠘⣧⠀⠀⠀⠻⣷⣤⣀⣀⣠⡿⢿⠁
⠀⠀⠀⠋⠀⣠⣄⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠈⠉⠛⠛⠉
⠀⠀⠀⠀⢰⢿⣿⢆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠰⣶⣶⣖⣀⣀⣀⣀⣴⠆⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠘⠊⠙⠛⠛⠛⠉⠀⠀⢀⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⡿⠋⠀⢀⣤⣴⣆⣀⣤⡴⠞⠁⠀⠀⠀⣼⠇⠁
⠀⠀⠴⣶⣶⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⡖⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠈⠻⠉⠙⠛⠻⠷⢶⣶⣤⡄⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠸⠟
⠀⠀⠸⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡷⠄
⠀⠀⠀⠛⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠋⠙⠛⢷⣤⣧⠀⠀⠀⠻⣷⣤⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠉⠛⠷⠶⠶⠶⠚⠋⠀⠀⣸⠁⠀⠀⠀⠉⠛⠿⢿⠀⠀⠀⠀⠀⠉⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣾⣿⠃
⠀⠀⠀⢀⣤⡶⠟⠛⠋⠉⠙⣻⣿⣧⠀⠈⠻⢶⣤⣤⣤⠴⠂⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⠿⠛⠹⠃
⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠙⢦⡀
⣤⡤⠤⠤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⡄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢫⣴⢘
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡋⡔⢷⢇⣳
⠻⣿⡿⡻⡻⢛⢛⣛⡿⡻⠛⢟⠟⡻⣻⢛⠛⡛⠛⢓⠷⣒⠒⠖⡲⣲⢖⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠕⠁⡀⢈⠞⠁
⠀⠈⠻⣞⢔⠅⠙⡁⠊⢂⠔⡡⠊⢈⠄⡡⠈⠀⠀⡁⠈⡁⠀⠨⢚⠕⡡⣾⠁⠀⠀⠀⠀⠀⠀⣠⡞⠁⠆⠀⢀⡼⠋
⠀⠀⠀⠙⠾⠞⠾⠶⠷⠮⠾⠾⠵⠧⠤⠴⠤⠮⣬⣀⣀⣠⣌⣀⣀⣊⡐⣿⠀⠀⠀⠀⠀⢀⡴⠏⠀⢂⠀⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠀⠀⠀⢀⡴⢋⠄⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢀⣴⠋⡰⠁⠄⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣴⠿⠐⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡴⠋

⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠀⠤⠤⠄⡄
⠀⠀⠀⠀⠀⡀⠿⠀⠀⠀⠀⠀⠀⠰⠟⡀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠈⠋⣭⠉⠉⠉⠉⠉⠉⢩⣍⠟⠁⠀⠀⠀⢀⣴⣿⣿⣿⣿⠋⠙⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⣧⣀
⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⣀⠰⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⢀⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⠻⣿⠏⠀⠀⠀⠀⠀⢀⣀⣤⡄⠀⠀⠀⠤⠈⠛⠁
⠀⠀⠀⢀⡀⡀⣀⡀⡀⠔⠑⠠⢄⠀⠀⠀⠀⠀⠀⠀⠙⠗⠀⠀⢀⡄⠀⢀⣴⠟⠉⠉
⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢀⣨⡧
⠀⠀⠀⠀⠂⠐⠐⠐⠐⢂⠀⠄⠈⠀⠀⠀⢲⠀⠀⠀⠀⢠⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠐⠄⠦⠐⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣠⠀⠀⠀⢠⣤⣤⠀⠀⠀⠀⠀⠀⠈⢗⠊⢶⢄⠀⠀⠀⠀⡄⠀⠀⣠⣾⣿⣤⣤⣤⣤⣤⣤
⠀⠀⠀⢾⣿⡧⠀⣴⣿⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠑⡢⡠⠪⠂⠀⠘⢿⣿⣿⣼⣯⣿⣿⣹⣿
⠀⠀⠀⠘⣿⣆⠀⣿⢁⣤⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠒⠁⠀⠀⠀⠈⢻⡿⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠈⠉⠃⠈⠈⠁⠀⠈⠛⠛⠃⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⠛⠒⢦⡀
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠈⠀⠐⢄⠀⠀⠀⠀⠀⠀⠄⣠⣾⣶⡄⠠⠀⠀⠀⠀⠀⢠⡞⠁⢀⣴⣷⣄⠀⠙⣆
⠀⠀⠀⡇⢀⣀⣀⣀⣀⡀⠀⣠⣾⡧⠀⠀⠀⠀⠀⣾⣿⠛⠻⣿⣦⠀⠀⠀⠀⠀⣼⠀⠀⠚⣿⣿⡟⠂⠀⢹
⠀⠀⠀⠈⠻⠛⠛⠛⢛⣛⣺⡿⢋⣠⣿⡄⠀⠀⠀⠛⠁⠀⠀⠈⠻⠀⠀⠀⠀⠀⠸⡄⠀⠀⣿⣿⡇⠀⢀⡟
⠀⠀⠀⠀⠀⠹⠿⠿⠿⠛⠛⠷⣿⠟⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣉⣉⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⢠⣾⠋⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⢠⣾⡅⠀⠘⣷⡄⠀⠈⢻⣆⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣴⣿⡿⠃⠀⢨⣿⠻⣦⣤⣾⠏⠀⢠⣾⠋⠀⠀⡀⠀⠀⡀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣼⠟⠀⠀⣠⣾⠃⠀⠈⠉⠀⠀⢰⡟⠁⠀⢀⣾⡇⠀⠀⣿⣆⠀⠀⠙⣷⠀⠀⠀⠀⠀⣴⡿⠉⠉⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠰⣿⡁⠀⠀⠀⠀⠀⠀⠘⢿⣦⣴⡿⢻⡇⠀⠀⢿⣿⣷⣤⣾⠟⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠘⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠻⣧⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⠄⠀⢘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡆⠀⠀⣻⡇⠀⠀⢀⣾⠏⠀⠀⣠⡯⠀⠀⣻⣄⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⢠⣿⠁⠀⠀⠈⢿⣄⣠⣾⢿⣇⠀⠀⣾⡿⣧⣄⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠉⠉⠁⠘⣷⡀⠀⠘⢷⣌⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⢼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡿⠂⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠗⠀⠀⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⢠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⠿⠋