Sleep Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⢔⠒⠲⡄⠤⠤⠤⠤⠤⠤⠤⠤⠐⠒⠒⠀⠉⠉⠉⠉⠉⠉⠁⠒⠒⠒⠠⠤⠤⠤⠤⠤⠤⠤⠄⡔⠒⢒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⢱⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠒⠒⠒⠒⠒⠒⡖⠒⠒⠒⡖⠲⠒⠒⠂⠐⠂⠒⠀⠐⢺⠁⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⡀⠀⢰⠀⠃⠀⠀⠀⠘⠀⡇⠀⠀⠀⡇⠀⡇⠀⠀⢰⠀⠃⠀⠀⠀⢰⠀⡄⠀⠀⡈⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⡇⠀⠈⡀⢰⠀⠀⠀⠀⠀⢁⠀⠀⠀⡇⠀⡇⠀⠀⠘⠀⠀⠀⠀⠀⡄⠀⠃⠀⠀⡇⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⡇⠀⠀⡇⢸⠀⠀⠀⠀⡇⠸⠀⠀⠀⠁⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠧⠤⠔⠃⠚⠒⠒⠒⠒⠓⠚⠒⠒⠒⠒⠒⠚⠒⠒⠚⠚⠒⠒⠒⠒⠓⠚⠒⠒⠒⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠐⠒⠂⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠒⠒⠠⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⢀⠎⣀⠤⠤⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠠⠤⢤⡈⢇
⠀⠀⠀⠀⠀⢸⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠐⠒⠒⠒⠖⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⡒⠒⠒⠒⢲⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠳⠤⠤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⠞⠀⠉⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡟⠁⠀⠀⣴⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠁⠀⢀⣾⣿⣿⡿⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⣼⣿⣿⠋⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⢠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠁⠘⠟⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⡈
⠀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⡷⠆⠀⠤⠀⠠⠂⠀⠀⠀⠀⡰⠒⠆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⡇⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠠⠃⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠰⢻⠃⠀⠘
⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠈⠙⠧⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⢸⠀⠀⢀⠄
⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡠⠃
⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠄⢠⠑⠤⢀⠌
⣿⣿⣿⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣥⣀⠀⠀⠀⠄
⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⠀⠀⠀⠀⠁⠂⠀⠀⠄⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣠⣿⣿⣿⠋
⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⡿⠁
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⡟
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡄⠀⠀⠀⢠⠀⠀⢰⠀⠀⠀⣾⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣿⣿⣿⡄⠀⠀⠀⠆⠀⠈⡀⠀⠀⢼⣷⠀⠀⢀⣠⣤⣤⣤⣤⣄⣀⠀⠀⣽⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⣠⠿⠃⠿⠿⠿⠿⣆⠀⠀⠰⡀⠀⠁⠀⠀⣾⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⢀⠈⠀⢀⣼⣿⣿⡇⣿⣿⣿⣿⣿⣧⡀⠀⠱⡀⠠⠂⢀⣭⣭⣏⣉⣉⣙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠄⠁⠀⣰⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⣦⡤⠊⠀⣴⣿⡉⠀⠙⢿⣿⣿⡿⠀⠀⠀⠙⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠀⠘⠀⠀⠀⢀⣠⠚⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢸⡟⠠⠂⢸⡿⠃⢤⡄⠀⠀⠹⢿⣷⡄⠀⠀⠀⠈⠻⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⢰⣏⣉⠀⣩⣭⣭⣭⣭⡁⣩⣭⣭⣭⣭⣭⡸⠀⠀⡈⠀⠀⠠⠄⠀⠀⢰⡀⡘⠉⠀⠀⠀⠀⠀⢠⣾⣿⣿
⠀⠀⠀⠀⠀⡆⠀⣀⣀⣀⣀⣿⣿⡇⣿⣿⠿⠿⠿⠃⠛⣻⠿⠿⣿⣿⡇⠀⢀⠀⠀⠤⠀⠀⠀⠐⠀⢐⠃⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠐⠃⠉⠁⠀⠀⠀⠉⠉⠙⠓⠢⢄⡀⠀⠀⠀⠉⢬⠀⠘⢁⡿⠙⠁⢆⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠀⠀⠀⠉⠳⡄⠀⠀⠀⠚⠀⠘⢇⣠⣤⣈⣦⣤⠀⠊⢀⠞⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⢻⠵⠶⠷⣖⣛⠃⠚⠁⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠙⢃⠀⣀⣉⡙⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠉⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣋⠄⠀⠀⠀⠀⠀⠑⡅⠐⠴⠀⠀⠉⠙⠝⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠛⢥⢀⣀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⢀⣀⡀⠠⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠠⠆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣶⣄⣀⣶⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⡇⠀⠲⣤⣀⣤⠴⠂⠐⠦⣤⣠⣤⠖⠀⢸⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠹⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡟⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣧⠀⠀⠀⠀⠀⣀⡷⠀⠀⠀⠀⠀⣼⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⣩⡄⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠉⠁⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠛⠛⠛⠛⠛⠛⠛⢻⠀⠉⠀⠀⠉⠀⡟⠛⠛⠛⠛⠛⠛⠛⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠹⠀⠀⠀⠀⠀⠀⠍⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢀⡀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠠⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⠈⠀⠀⠀⠉⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⢀⡀⡀
⠀⠀⠀⣀⠀⠄⠐⠀⠀⠀⡀⠀⠀⢀⠛⠁⢂⠀⠀⠀⠤⠜⠉⠀⠀⠀⠈⠀⠀⠂⠀⠉⠄⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠲⠞
⡔⠈⠁⢱⠀⠀⢲⠂⠀⠀⠁⡄⢘⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡀⠀⠀⣌⡀⠀⠀⣄⠀⠠
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⡈⠁⠐⠄⣀⣀⣠⢴⠢⢄⠀⠀⠃⠀⠀⠀⠀⠀⢨⠁⠈⠉⠃⠀⠆⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠈⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢼⠀⠘⠁⠐⠀⠀⠈⠛⠁⠠⠖⠀⢀⠀⠀⠠⠀⠀⢀⠀⠘⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠃⠈⠀⠆⠀⠀⠀⠀⠀⠁⠀⠒⠢⡀⠀⢄⠀⢀⠠⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⢀⠈⠁
⠀⠀⠀⡤⠯⠤⠤⠤⠄⣀⣀⣀⣀⠀⠀⠀⠀⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄
⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠘⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡓⠀⠂⠀⠂⠀⠀⠆⠀⠀⠃⠐⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠘
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠄⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠁⠰⠀⠀⢀⡀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢹⣿⣿⣿⣿⣿⠿⣿⠿⢻⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⡏⠚⠀⠀⠀⠙⣿⣿⣿⣿⣆⠀⠀⡻⠿⠿⠿⣿⣿⣿⣿⣦⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠙⢿⣿⣿⢿⣿⡟⠁⠀⠀⠀⠀⠈⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠆⠁⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⡘⠟⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢀⠄⡄⠀⢀⠄⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠚⠂⠑⠛⠘⠀⠃⠀⠃⠂⠃⠋⠞⠁⠐⠃⠀⠋⠘⠁⠐⠑⠃⠀⠂⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠋⠉⢁⡾⠁⣀⣒⣲⠆⠀⡱⠯⠀⠀⠐⠀⠈⠀⣈⡀
⠀⠀⠀⠀⠀⡄⠒⢤⠀⠀⠀⣀⣀⡤⠴⠒⣲⠟⠉⠉⢡⣿⣥⠄⠀⠈⠉⠉⠙⠒⠒⠠⠎⠀⢨⠆
⠀⠀⠀⠀⠀⠣⡀⠀⠓⠒⠉⠁⠀⠀⣠⣞⣡⣤⠤⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠌⢢⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⡜⠀⠀⢈⠔⢀⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⢧⠀⠀⢀⠠⠀⢀⠊⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠸⡀⠀⠈⠄⠀⠁⠠⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠱⡀⠀⠈⢀⠔⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠘⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡶⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠒⠢⣀⢀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡠⠋⠈⠉⠓⠒⠒⠶⠶⠖⠒⠒⠒⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣤⡀⠀⣴⣾⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣧⣴⣾⣿⣿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠈⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⢈⣿⣿⡿⠛⠁⣠⡄⠀⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⡾⠀⣸⣿⣿⣦⣤⣾⣿⡇⠀⢻⣿⣿⣿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⠟⠁⣠⣼⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠻⣿⡿⠀⠘⠛⢉⣠⣼⣿⣿⣿⣧⠀⠈⠁⣠⣾⣿⣿⣿⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣶⡟⢀⣼⣿⣷⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣄⣠⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⣀⣉⣉⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠟⠀⠉⠛⠿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣆⠀⠀⠉⠛⠛⠋⠁⠀⠈⠻⠿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⣠⣶⣦⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⣾⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠈⠓⠒⠂⠠⠤⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠉⠉⠓⠲⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⣠⣶⣿⣿⣧⣽⣿⢿⣦⣠⣄⡀⠀⠀⠀⠀⠀⠀⠉⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢠⣶⢤⣤⣾⣿⣿⡯⠛⠁⠀⠀⠈⢉⣙⡛⣿⡌⠉⠤⠤⠤⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⡔⠁⠀⣼⣿⣿⣿⡿⡏⠀⠀⠀⠢⣄⠀⠀⠀⠻⣿⢿⣇⣀⠤⠔⠂
⠀⠀⢀⠤⠖⠲⣶⣦⣶⣉⠀⠀⠈⠳⣼⣿⣿⣿⣿⢿⠛⠃⠀⠀⠙⠄⠈⠀⠀⠀⢀⡿⠛⠉
⠀⠀⠀⣴⣂⡤⠈⠙⠿⣿⡷⣤⡀⠀⢸⡙⠿⠟⠛⢫⠀⠀⠀⠀⠀⠀⠐⣅⠉⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠙⢿⣷⣶⡀⠉⠻⣿⠿⣦⡌⡇⠀⠄⠀⠘⢆⠀⠀⢿⡦⠘⢀⣈⠐⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠠⣤⣀⡀⠉⠻⣿⣮⡀⠈⠛⢾⣿⣅⠀⠇⠀⠀⣈⣧⡄⠠⠴⠊⠵⠁⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠈⠻⢷⣧⢀⠀⠉⠻⣾⡤⠀⠉⠙⠳⢄⡐⠿⠟⠉⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠻⠷⣄⣀⠀⠀⠉⠑⠲⣤⣤⡀⠉⠒⠦⣴⠚⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣁⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠤⣂⡀⠀⠀⠹⣿⣾⣆⠤⠀⠻⣦⣀⠉⠓⠦⣄⠀⠀⠀⢀⣴⡷⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠯⠤⠀⠈⠻⢿⣦⠐⠂⠘⢿⣦⡀⠀⠀⠁⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⠓

⠀⠀⡞⡟⠳⣄⠀⣀⡀
⠀⢰⢻⣌⣖⠋⠻⣄⣹⠶⣄
⠀⠘⣟⢸⡉⣳⡀⠈⠳⣄⠈⠳⣄
⠀⢰⠻⡄⠉⠉⢳⡀⠀⠀⠙⢆⠈⠙⢦⣀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣿⠛⢦⠀⠈⠲⣄⠀⠀⣱⣦⡀⣙⢷⣄⢀⣠⠞⡭⣷
⠀⢀⣴⣇⠒⠚⢇⠀⠀⠈⢧⡀⠈⡠⢷⡄⠋⠙⣯⡟⠀⠳⢿⡀
⠀⢸⠁⠙⡄⠀⠈⢆⠀⡠⣢⡙⣦⠀⠀⢻⡄⠀⠘⣧⡀⠀⠸⡇
⠀⡆⠀⢀⠿⣄⠀⠈⠣⡀⠀⠘⠉⣧⠀⠀⠙⣆⠀⠈⠳⣤⡀⠙⣆
⢰⠇⠀⢹⠀⢹⡆⠀⡴⡟⢦⠀⠀⠘⣧⠀⠀⠘⢦⠀⠀⠈⠻⣄⠙⣆
⣼⠀⠀⢸⡀⠉⢻⡄⠀⠀⠞⢦⡀⠀⠘⢷⡀⠀⠀⠑⠀⠀⠀⠈⠓⠮⠳⣄
⡇⠀⠀⠜⢧⡀⠈⣧⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠹⡄⠀⠀⠀⠱⣄⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠙⣆⠀⠀⠀⣹⠁⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠈⢦⠀⠀⠁⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠸⡆⠀⠀⠀⠀⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⣧⠈⣧
⠀⠀⠀⠀⢳⡀⠀⠀⠔⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠸⡄⢸⡄
⠀⠀⠀⠀⠀⢹⡗⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣳⡈⢧⣀⠀⠀⣀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢄⣨⠷⠋⠁⠀⠀⠈⠛⢳⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⡸⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠙⠳⠦
⠀⠀⠀⠀⠀⠀⡈⠀⠙⣆⠀⠀⠀⠁⠀⣸⣿⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠰⠀⠀⠀⢸⣇⠀⠀⠀⢀⠼⠁⣠⣿⣿⠳⣄⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⢸⠀⠀⢀⡏⠈⠓⠦⠀⠀⠒⠾⢡⠞⠁⢀⠈⠻⢦⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⢸⠀⠀⠸⣧⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⣸⠀⠀⡞⡽⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠨⢸⣄⣇⣿⣆⣀⣤⠤⠞⠁⠀⠀⠁⠀⡏⢀⡾⠁⡇⠀⣄⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠳⡉⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣧⠀⠙⣦⣀⣀⣠⠤⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠒⢲⠒⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⣀⣼⠷⠒⠊⠉⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⣀⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦
⠀⠀⠀⠀⠀⠀⠀⣆⢀⠀⠁⢠⡐⣦
⠀⠀⠀⠀⠀⠀⢾⠡⠘⣧⡀⠈⠿⣎⠉⢢⡀
⠀⠀⠀⠀⠀⠀⢈⡔⠆⠁⠱⡀⠀⠈⠳⣄⠙⠲⣄
⠀⠀⠀⠀⠀⡀⣸⡿⢒⣄⠀⢻⣆⠀⠀⠈⠷⡀⠘⢷⡄
⠀⠀⠀⠀⠀⢀⣿⡇⠄⠹⣆⠀⠙⣧⣀⠖⢀⠙⢦⡀⠻⠆
⠀⠀⠀⠀⠰⠃⢰⣇⠀⠀⢻⡄⠀⠘⣿⢦⡀⠀⣀⢵⡠⠸⢶⡀⠠⡄⡄⣠⡁
⠀⠀⠀⢀⠀⢀⣿⣿⡄⠀⠀⢳⡀⢀⠀⠈⣿⠀⠘⠈⢧⡀⠘⠿⣾⢸⠀⠈⠁
⠀⠀⠀⠂⠀⣸⣿⣻⣧⠀⠀⠀⠣⡄⡴⠀⢸⣇⠀⠀⠘⢷⡀⠀⢿⣼⡄
⠀⠀⢰⠀⠈⣿⡟⢿⣿⣧⠀⠀⠈⢠⡄⠀⠈⢿⡆⠀⠀⠘⣷⠀⠀⠈⢻⣄⡂
⠀⠀⠈⠀⠀⣿⡇⢻⣾⣿⡇⠀⠀⠠⣿⡄⠀⠈⢻⣄⠀⠀⠈⠁⠀⠡⡀⠙⣷⣄
⠀⠀⢠⣀⠀⣌⢻⣄⣹⢿⡇⠀⠀⠀⢘⣷⠀⠀⠀⠛⠀⠀⠀⠈⠂⠀⠀⠀⠪⠛⢧⡀
⠀⠀⠀⠁⡀⠈⡆⢿⠹⣬⣿⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠁⠀⠘⣾⣿⣷⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⠀⠸⣦
⠀⠀⠀⠀⠀⠀⠀⠁⢾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣿⡇
⠀⠀⠀⠀⠀⢇⠀⠀⠀⣻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇
⠀⠀⠀⠀⠀⠘⣤⡀⠀⠘⠻⣿⣿⣆⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠈⣿⣿⣿⣆⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡙⠃
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢸⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⢾⢿⣿⣿⡜⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣾⣿⣄
⠀⠀⠀⠀⠀⠀⠠⠀⢸⣦⠀⢺⡆⠘⣿⣿⣿⣮⡳⣄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣈⠛⢻⡦⠀⠀⠀⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠠⠁⣠⢿⣿⡃⠈⢶⣄⠀⢸⣿⡿⠟⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⢶⣶⣄
⠀⠀⠀⠀⢀⠁⣰⣿⣾⡿⠃⠰⢀⠉⣥⣾⣿⣤⣮⡶⢻⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡿⠏⠁
⠀⠀⠀⠀⡌⢰⡿⣯⢸⡷⠀⠚⠛⠷⠀⠙⠻⣿⣿⡗⡸⢋⠛⠻⢿⣦⡀⢀⠔⠀⠀⠀⣧⣀⣀⠀⠀⠀⠀⠀⠸⠟
⠀⠀⠀⠀⠃⣿⠄⢁⠘⡇⠘⠃⠀⠀⣠⢇⣠⠟⡩⠀⣤⡟⠀⠀⢈⠛⠟⠁⠀⠀⠀⠀⠈⠉⠉⢳
⠀⠀⠀⠀⠣⡙⠠⣿⠿⠿⠶⠖⠒⣻⠿⠋⣀⠞⠁⠈⢉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠙⠄⣀⣄⣀⣀⡀⠀⠀⠀⠈⠁⠀⠀⠀⠘⠀⠀⠀⠀⡆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡿⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢈⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠊⠉⠻⠃
⣶⣶⡿⠶⡶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢉⣽⠷⠀⣀⡤⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣷⢸⡇⣂⠀⠙⣧⣶⣾⡷⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠠⠈⠙⢿⡟⠇⠀⠻⡇⣄⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣧⠰⣤⣄⠻⣷⠀⠀⠘⢜⣃⠁⠈⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⠿⣆⣀⠉⠀⠘⢷⡀⠀⠀⠹⣆⠀⠀⠘⢦⠀⠀⠀⠀⣀⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠻⡇⢀⠀⢹⣧⡀⠀⠀⢿⣦⠀⠀⠈⠳⣧⠀⠈⢳⣀⣰⢟⢉⣽⠟⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠈⢶⡇⠸⣄⠀⠀⠈⢿⣄⠀⠀⠀⠘⣧⠀⠀⠈⢿⣄⣾⠇⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢠⣿⣧⠀⠀⠀⠸⣧⠀⠀⠈⠻⣧⠀⢀⠀⠘⣧⣤⡆⠈⢿⣿⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢻⡿⣿⣧⡀⢀⠀⢹⣆⠀⠀⠀⠘⣿⠀⠀⠀⠈⢯⠄⠀⠀⠹⣿⠋⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢀⣵⣿⠾⣷⡸⣇⠀⠻⣄⠀⠀⠀⠘⣷⣄⠀⠀⠀⢻⣄⡀⠀⠘⣧⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⣿⣷⣿⣧⢣⡀⠀⢺⡖⡁⠀⠀⠘⢿⣦⡀⠀⠀⠙⠃⠀⠤⠹⣷⣀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⢰⣆⣽⡟⠛⢿⣆⢤⣰⡀⠹⣿⣣⠀⠀⠀⠻⠇⠀⢀⠀⠀⠀⠀⠀⠘⣯⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⢋⣻⣿⣿⣿⣿⡎⠹⠁⠀⠘⣷⡄⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣽⣿⣿⣿⣿⣿⡄⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢠⣼⣽⣿⠟⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⠉⠀⠀⠀⡠⢠⣿⣷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⡠⠀⠓⠏⣿⣿⡆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⡣⡚⠁⠀⠀⠀⠿⢻⣷⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇⣤⠀⠀⠀⠈⢹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠐⣨⣭⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⢧⡀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⡀⠈⢥⣶⣬⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡈⠻⣿⢿⢿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣄⠀⠰⠶⢦⣿⣿⣷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢌⣶⠃⠸⣿⣿⡿⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠈⣧⠻⣿⣿⣿⡕⣶⣄⠀⠀⠀⠀⠈⢄⠁⢂⣠⠞⡡⢀⠾⠿⠋⠁⢸⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⡄⠀⠀⠘⠀⢹⣿⣿⣿⣮⢻⣦⡠⣄⣄⠑⣈⡴⠛⠁⠀⠀⠀⠀⠀⠀⢀⡆⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣱⣾⢿⡧⠀⠀⢠⣤⠟⢻⣽⣿⣿⣷⣹⣷⣽⡿⠟⠉⠀⠀⠀⠀⠀⠀⢀⡔⠀⠘⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢧⡻⠿⢿⣶⣶⡶⠟⠁⡠⣾⣿⡟⠉⣽⡿⠟⢋⠤⠀⠀⠀⢀⡤⠀⠀⠀⠞⠀⠀⠰⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣄⡀⢠⣡⡾⠋⢀⣠⠎⢪⣿⢁⠋⠀⠀⠀⠀⢀⢀⣠⡄⢟⡁⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢖⡀⢸⣿⣷⠞⠋⠀⠀⡉⢤⣣⣿⣷⠘⢦⣤⣶⠿⣿⡉⠉⢁⣬⡧⠴⠦⠚⠫⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣮⡝⠋⠉⠀⠀⠀⡈⠀⠀⠈⠛⢻⣿⠀⠂⠀⠀⠒⠀⣠⠶⠋⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣠⡤⠀⠀⠀⠁⠀⠀⠀⠀⠀⠹⠿⠀⠶⠀⠀⠀⠉⠳⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠻⠙⠻⠟⠉⡟⠛⣛⠻⢙⣿⠟⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⢠⣤⣴⣶⣶⣶⣦⣄⣀⣀⣀⠠⠤⢄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⡴⠊⣇⠑⢄
⠀⠀⢀⠤⠒⢉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢆⠀⠀⠀⢠⠔⠉⠀⠀⠀⠀⠀⠀⠀⢣⢂⣀⣁
⠀⠎⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⡄⣀⢈⣄⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢗⠀⠀⠀⠠⠤⠤⠀⠀⢀
⢰⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡆⠀⠩⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠖⡀⠀⠠
⢸⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠁⠀⢀⠔⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠕⢈⡴⢨
⠀⡄⠀⠀⢹⣿⣿⣿⣿⣿⡈⠁⠀⠀⠀⠀⠀⠀⠀⢨⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⣠⣶⠟⠃⠂
⠀⠘⡄⠀⠀⠙⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡘⢄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢊⣴⣾⠟⠁
⠀⠀⠈⠢⡄⠀⠀⠹⣿⣿⣿⣆⠀⠀⠈⠀⠀⠀⠀⡠⠃⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣠⣾⡿⠊
⠀⠀⠀⠀⠸⠒⠠⠀⠀⠉⢩⠍⠋⠖⡀⣶⡒⠒⡘⠁⠐⠀⠶⣓⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠁
⠀⠀⠀⠀⠀⠀⢰⠀⢠⠄⡄⠀⠀⠀⡜⠀⠀⠩⠄⠀⢀⠀⠀⠀⠀⠉⠉⢀⠒⠄⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⢰⠀⢸⣴⡾⡄⠀⠀⠹⣶⣦⢤⣤⣀⣀⡀⠀⠀⠀⠀⠆⢁⡠⡆⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠻⡀⠀⠔⠛⢿⣿⣿⣿⣿⣿⣿⣿⡖⠒⢶⣻⣿⠿⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⣈⠩⠀⠉⠉⠛⠛⠿⠿⡇⠀⡟⠋⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⢠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣶⣧⣼⣶⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⡿⣿⠿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣾⣷⣾⣷⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣏⣿⣿⣿⣿⣹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⣿⣿⡇⢸⣿⣯⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢱⣿⣿⡇⢸⣿⣿⡎⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣟⣿⣿⣿⡇⢸⣿⣿⣷⣻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠇⠸⣿⣿⣿⣧⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆⢰⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠈⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠈⠢⠠⡁⠀⠀⠀⡠⠀⠒⠲⠶⢦⡄⠠⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠑⠄⠀⡈⠀⠀⠀⠀⠀⠈⠙⠱⡄⠀⠀⠀⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠁⢈⠀⠄⣄⠠⠀⡐⠀⠀⡀⠈⡀⠃⠐⠠⡀⠀⢐⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⠀⠁⠴⢡⡄⣀⢠⡄⠲⠀⠀⠀⠀⠀⠄⡀⣀⣴⠇⢀⠀⠀⠉⠁⠐⠓⠄⡀⠀⠀⠀⠈⠀⢄
⠀⠀⠀⠃⠀⠘⢺⠟⠋⠙⠙⠿⡗⠃⠀⠀⠀⠀⠀⠀⠉⠁⢆⡭⠌⠀⠂⠀⠀⠀⠀⠀⠒⠀⠈⠀⠀⠀⠂
⠀⠀⠂⠀⠀⠀⣎⠀⠀⠴⠀⠀⢹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠛⢎⡀⣀⠀⣀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠿⠓⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⣀⠠⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠀⣀⠳⣄⡈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠘⢦⠀⠉⠲⣤⡀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⡀⠙⢦⡀⠀⠉⠒⢄⠀⠈⠲⢄⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡗⠀⠙⢄⠀⠙⠲⣄⠀⠀⠳⣄⠀⠀⠑⢦⡀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⣦⠀⠈⠲⡀⠀⠘⢷⡀⠀⠘⠳⡀⠀⠀⢳⣄⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⣿⢷⡀⠀⠘⢆⠀⠀⠻⣄⡀⠀⠈⠀⡀⠀⠙⠲⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣷⣄⠀⠀⠳⡄⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⢈⠑⢾⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠉⠻⣆⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢡⡀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢪⢣⡀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣀⠈⢷⡀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠀⠁⠙⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠌⠑⠸⣷⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⠈⠙⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢳⡀⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⢸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⡘⢧⡀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠀⠋⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣍⠛⠿⢿⣿⠏⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⢸⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣶⠆⣱⠏⢁⣼⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠃⠈⢿⠏⢹⡶⣤⡀⠀⠀⠀⠀⠀⠀⠛⢁⣴⠇⢠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⣤⣄⣀⠀⠉⠀⠸⠉⠳⣦⣀⡠⠊⠀⣠⡾⠁⢠⡿⠋⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠻⡀⠙⠦⣤⡀⠀⢀⣴⣿⠋⢀⣠⣾⣿⠇⠀⣸⠃⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⡆⠈⠉⠀⠈⠑⢰⣿⠟⣡⣾⣿⠏⠁⢀⣠⡶⠋⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢧⠹⣄⡀⠀⣀⣀⣸⠏⣼⢇⣿⣯⣴⣾⠟⠋⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡎⠷⠠⠁⠀⠀⢡⣏⣼⣏⣼⣿⣿⣿⣷⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⣿⣿⣿⣿⡿⠟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠾⠛⠛⠉




⣿⣿⣿⣿⣿⡿⢻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⡿⠿⣿⣿⣿⠿⢿⠿⠿⢿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠶⠀⢈⣽⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣁⠀⠚⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⣷⡄⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⢸⣧⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡾⠋⢀⣴⡆⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡟⠻⣿⣿⣯⠉⠀⠀⠈⠉⠁⠀⣿⣇
⠀⠀⠀⠀⠀⠀⡀⣠⣶⣟⠋⠻⣿⣿⣆⠈⠻⣿⡇⠀⠀⠀⠀⠀⠀⠈⠛⣷⣄
⣶⡿⠛⠛⠛⠛⠛⠛⠻⢿⣷⡄⠈⢻⣿⠀⠀⠈⠁⠀⠀⠀⠀⣤⠀⠀⣴⣿⣿⣆
⠙⣷⣄⠐⢿⡇⠀⠀⠀⠀⠙⠿⠀⠀⠁⠀⠀⠀⠀⠰⢦⡴⠾⠋⠀⠈⠉⣡⣼⣿⡄
⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⣿⣷⣶⣦⣤⡀
⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠙⢻⣄⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⣿⣿⣷⣄
⠀⠀⠀⢸⡇⠀⠀⠰⣦⣤⡾⠋⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠉⠀⠘⠋⢁⣾⣿⣆
⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣧⡀⠀⠀⠀⠀⠚⠛⣩⣿⡄
⠀⠀⠀⠀⠘⣿⣿⡿⠛⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣏⠈⠙⢷⠀⠀⠀⠀⠀⠘⠻⢿⡇
⠀⠀⠀⠀⠀⠈⠻⣷⣶⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⡍⠈⠙⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣸⡏⢹⠿⠳⠶⠶⠶⠶⠶⢶⣾⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣷⣤⣤⣤⣀⣠⣆⣠⣆⣸⣿⣇⣰⣷⣀⣴⣦⣄⣤⣶⣀⣀⣀⣀⣀⣤⣴⣶⣶⣾⣿⣿⠏⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠋⠛⠋⠛⠋⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠋⠙⠉⠉⠉⠁⠀⠀⠉⢿⣦⣤⣾⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠿⠟⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⣀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣀⣠⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⣤⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣤⣄⡀
⠀⡀⠄⠀⠤⠤⠤⠤⠤⠤⠀⠀⠀⣀⣀⣀⣒⣒⣒⣒⣒⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠴⠚⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣽⣿⣿⠿⠋⠁⠀⠀⠈⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠃⠀⠀⠀⠀⠀⡀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⠀⠁⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⠋⠈⠙
⠀⣤⠄⠤⠤⠄⠀⠀⠐⠐⠒⠒⠒⠒⠒⠒⢺⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠹⠿⠋⠀⠀⠀⠀⢐⡞⠀⠀⠀⠀⠀⠀⠧⠆⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠒⢄⠀⠘⣼⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠒⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢹⡄⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢣⡀⠀⢣⠀⠀⠀⠀⠀⠀⠀⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢳⠀⢇⠀⠀⠀⢡
⠀⠀⢳⡀⠀⡆⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡘⡄⠀⡄⠀⡆
⠀⠀⠈⡇⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠉⠉⠁⠀⠀⠀⠚⢤⣸⠀⠀⠠
⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠐⠚⠳⠄⣀
⠀⠀⠀⠀⡇⠀⠸⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠓⠒⠒⠒⠊⠉⢀⣀⠠⠤⠒⠉⠀⢀⣀⠠⠤⠔⠒⠃⠉⠉⠉⠉⠉⠉⠙⠂⠤⢀⡀
⠀⠀⠀⢰⠥⢤⣔⣧⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣀⠤⠒⠊⠉⠀⣀⡠⠄⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤
⠀⠀⠀⢠⠂⠁⠀⠘⠀⠀⠀⠀⢀⠄⣀⠴⠊⠁⠀⢀⡠⠔⠊⠉
⠀⠀⠀⠘⠀⢰⠁⠀⣀⠤⠒⢉⠴⠊⠁⢀⡠⠔⠊⠁
⠀⠀⠀⢀⠀⡆⠀⡸⠁⢀⠔⠁⠀⢀⠔⠉
⠀⠀⠀⠈⠀⡇⠀⡇⢀⠇⠀⠀⡰⠃
⠀⠀⠀⠉⠀⠇⢀⠀⡌⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣴⣄⣀⣀⣤⣤⣤⣄⣀⣀⣀⠒⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⡃⡴⠈⠡⠀⠁⠄⠘⢉⣓⣲⣾⣿⣿⣿⣿⣿⣿⣿⣍⣙⡛⠛⠶⢶⣭⣖
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠘⠀⡁⠀⠃⠠⠀⠀⠀⢈⠬⢭⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠯⢭⣍⣛⡲⠦⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠄⠀⠐⢀⠀⠊⢀⠡⠘⠶⣾⣿⣆⠂⠉⠉⠁⢸⣿⣿⣏⣙⠛⠲⠶⢭⣍⡇
⠀⠀⠀⠀⠉⠀⠀⠀⠘⡀⠀⠃⢀⠀⠈⠀⡀⠆⡘⢛⠛⢿⠟⠀⢀⠀⠀⠀⠁⠀⠈⠙⠛⠻⢗⠲⠶⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠣⠥⣴⣀⣤⣀⣁⡄⡄⡀⢁⠠⠄⣼⠀⠀⠉⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢩⡽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠁⠀⠈⠀⣿⣧⡀⢀⠀⡄⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠋

⠀⠀⠀⠒⠒⠒⠒⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠
⠀⠀⠘⠛⠛⠻⠿⢶⣤⣌⡑⠂⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⢶⣶⣶⣤⡭⠃⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠉⣀⣠⣤⡄
⠀⠀⢰⣶⣶⣤⣄⣀⡠⠉⠙⠳⠶⣤⣍⣉⣍⣉⣉⡄⠀⠀⠀⠠⡤⠤⠄⠀⠀⠀⢀⡀⠀⠠⠶⣬⣽⣭⣭⣤⡶⠿⠛⠉⠁⢀
⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⢿⣷⣶⣤⣬⣉⣉⣉⣋⣩⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠙⠿⢷⣦⣄⣀⣀⣀⣀⣀⣤⣤⡶⠾⠛⠋
⠀⠀⠀⠀⠀⠂⠤⠄⠀⣀⠀⠀⠈⠉⠉⠛⠉⠉⠍⠁⠐⠀⠀⠀⠐⠂⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠠⠄

⠀⠀⢀⣶⣿⣦⡀
⠀⠀⢸⡇⣆⢈⣿⣴⣶⣶⣦⡀
⠀⠀⢸⣷⣾⣭⣈⠻⣧⣧⣉⡿⣶⣄
⠀⠀⠸⡿⢿⣈⣻⣷⣌⠙⠷⣄⡈⠛⢷⣄
⠀⠀⣾⡻⣄⢻⠧⠹⣿⣇⠁⠊⠻⢶⣌⡻⣷⣦⣀⠀⠀⠀⣠⣤⣶⣶⡄
⠀⢠⣿⣿⡿⢿⣷⠀⠙⢿⣄⠀⠀⣠⣿⣷⡄⠉⠻⣧⣀⣸⣿⢧⠛⣿⠁
⠀⢸⣏⣽⡇⢸⢻⣇⠀⠀⠙⢷⣤⡙⢿⡍⢿⣄⠀⠹⣿⣿⣿⢸⣄⣿
⠀⢸⡿⠀⣿⡌⠛⢿⣄⠀⠀⣼⣿⣿⣆⠹⣮⢿⣦⣄⠈⢻⡟⠀⢨⣿⡇
⠀⣸⠇⠀⢈⣷⡀⠸⢿⣿⣧⡀⠛⢿⣻⡆⠈⠃⠙⣎⡆⢠⡻⣄⠀⠻⣷⡄
⢠⣿⠠⣴⣿⣿⣧⢀⣘⣿⣿⡻⡄⠀⠈⣿⣄⠀⠀⠸⠄⠀⠙⠊⠳⣴⡜⢿⣶⣄
⣼⡏⠀⠀⢿⣿⣿⣷⣫⡛⠋⠑⣿⠄⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠈⣹⠀⠙⣿⣷⡀
⣿⠀⣰⠀⢸⣧⢿⣿⡏⠃⠀⠀⠘⣿⡂⢀⠀⠻⣿⣦⠀⠀⠀⠀⠀⠀⠈⠃⠰⡌⣿⣷
⠘⣆⠈⠰⠛⠻⣯⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⣿
⠀⠘⣆⢀⠀⠀⡼⣷⢿⣿⠲⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣿
⠀⠀⠸⣆⠄⠀⠃⡿⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢛⣴⠆⡄⠀⠀⠀⠀⠀⠀⠁⢿⡀
⠀⠀⠀⢻⣎⠀⢘⠟⠁⢻⣇⢀⠀⠀⠀⠀⠀⠰⣀⡄⠀⣿⣤⣿⡀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠘⣿⡄⠈⠀⢴⠀⣿⣞⣇⠀⠀⠀⠀⠀⢿⣿⡀⢡⠜⣿⠇⢠⣤⡄⠀⠀⠀⡄⢿⡄
⠀⠀⠀⠀⢻⣷⠀⠀⢘⣡⠿⣿⣿⣦⠀⠀⠀⠀⠈⠻⣡⠻⣤⢶⣦⣶⡉⣻⡆⠀⠀⣿⢸⣧
⠀⠀⠀⠀⠀⢻⣧⢀⢭⠷⠀⠈⢻⣷⠀⠀⠀⢀⡀⠀⠹⠃⠰⣾⣿⣿⣿⣿⡿⠀⠀⢹⣮⡻⣦⡀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢻⡜⡆⠀⠀⠀⠀⠹⣆⠠⠀⠛⠟⠀⠀⠀⠀⠉⠉⠙⠉⠉⠀⠀⠀⢀⡿⣣⣿⣿⠿⠟⡛⠻⠍⠙⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⢀⡀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣾⠟⡫⠔⠀⠀⠀⠀⡀⢀⣾⠿⠋⠥⠉⠻⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣼⢳⣄⠀⠀⠈⠁⠀⢈⠻⣷⣄⢠⣦⡄⠀⠀⠂⠀⠁⠀⢀⣴⣿⠟⠡⠊⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠠⣭⣛⠳⣤
⠀⠀⠀⠀⠀⠀⢀⡏⠀⢻⣆⢠⠈⢡⣄⣀⡉⠂⠉⠓⣿⣿⣶⣤⣀⣀⡀⣰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣩⡿⠇⠈
⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⣿⠀⠀⠀⠛⠟⠃⢘⣂⡴⢿⣿⣿⣿⣝⣋⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⣿⠇⠀⢸⣿⠀⠀⠒⠚⠿⠛⢛⠩⢄⣼⠟⣉⡉⠻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⣀⡼⠋
⠀⠀⠀⠀⠀⠀⣿⢀⡅⠸⣷⠀⠀⠀⢀⡀⢀⣤⡾⠋⠁⠈⠀⠀⡀⢸⣿⡇⠀⠀⠀⠀⠀⠂⠀⠀⢰⣿⠇⠀⠀⠀⠀⢀⠾⠋
⠀⠀⠀⠀⠀⠀⣿⣆⠉⠀⢿⣷⣭⣾⣭⡾⠋⠁⠀⠀⠀⠀⢀⡴⣣⣿⣿⡇⠀⠀⠀⠀⣶⣶⠀⣠⣾⡿⠀⠀⢀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠚⠛⠛⢩⠵⢋⣤⠀⠀⠀⠀⡴⣫⠞⠁⢸⣿⣷⣅⣀⣀⣀⣬⣶⣾⠿⠛⠁⣠⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⢤⣶⡄⠉⣄⠀⢀⡼⠞⠁⠀⠀⢀⣿⡿⠿⠛⠛⠉⠁⠀⠀⠀⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⣾⡏⡀⠀⠀⠀⠀⢀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣇⠀⢀⡴⢚⡡⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣉⣡⡴⠖⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣙⣋⣛⣹⣟⣩⣉⣻⣛⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣽⣿⣿⣿⣯⣭⣽⣯⣭⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠑⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠃⠀⠀⠀⠀⢀⣀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠆⠂⠒⠀⠀⠀⠀⠀⠉⢂⠀⠀⠀⠀⡀⠀⠉⠉⠀⠀⢀⠴⠊⠉⠀⠀⠀⠈⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢂⠀⠀⠚⠂⣀⣀⣀⣀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸⠀⠒⠢⣄⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢲⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⢀⡼⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⢀⠄⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⢂⠀⠆⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄
⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⠁⠀⠠⠂⠁⠈⢰⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠒⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠙⠢⢅⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠜⢀
⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠤⠤⠤⠤⠤⠤⠀⠒⠀⠀⠀⠀⠈⠓⠤⠤⠄⠀⣀⣀⡀⠠⠤⠤⠬⠦⠤⣤⣤⣄⣀⣈⣉⣀⣀⣀⣠⣤⠤⠤⠤⠖⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠑⢄⠀⠀⠀⢀⠐⠓⠂⠀⢀⠤⠒⠉⠉⠑⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠠⡀⠂⠀⠐⠀⡀⢀⣀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢂⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠐⢔⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠀⠀⠀⠀⠹⢀
⠀⠀⠀⠀⠀⠁⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⠤⠀⠀⠠⠤⠤⠄⠧⠤⠤⠤⠤⠄⠥⠤⠤⠤⠤⠤⠐⠒⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⢄
⠀⠀⠀⠀⠀⠀⣀⡠⠤⣲⣶⣾⣿⣿⣿⣿⣿⣿⣦⣤⠤⠤⠔⠒⠓⠲⡄⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠤⠤⠔⠁⢀⡧⠀⠑⢄
⠀⠀⠀⣠⠔⠋⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⠀⠀⢹⡀⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⠓⣄⣀⣱
⠀⡰⠋⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣯⠁⠀⠀⢣⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠙⢽⠂⠀⠤⠤⠤⢀⣀⣀⣀⣀⣀⣀
⠀⠇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠉⠳⠟⢬⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⠤⠤⠤⠤⠤⡤⠀⢀⠄⢉
⢸⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠙⠻⠀⠀⠈⠡⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠠⠊⣀⡔⠁
⠘⡀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠄⠀⠀⠀⠀⠀⠀⢠⠊⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⢁⡤⡞⠁⠇
⠀⢃⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣠⡴⣿⠟⠛⠚
⠀⠈⢆⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢈⠢⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢊⣴⣾⡿⠚⠁
⠀⠀⠀⠳⣄⠀⠀⠀⠈⢿⣿⣿⣿⣧⡀⠀⠀⠘⠒⠂⠀⠀⠀⠀⢀⠎⠈⠀⠙⡄⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣠⣖⢿⡿⠋
⠀⠀⠀⠀⠀⢡⣀⠀⠀⠀⠙⠻⠿⠿⡷⠤⣀⡀⠀⠀⣀⣀⣀⣤⡊⣀⡀⠀⣀⡇⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠟⠁
⠀⠀⠀⠀⠀⠸⠉⠉⠉⠒⠒⠒⠒⡶⠁⠁⠸⡡⢈⠿⠥⣀⡰⠃⠀⠀⠀⠘⠛⠥⠤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠐⠒⠆⠠⡇⠀⠀⠀⢠⠉⠁⠐⠂⠀⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠕⢢⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⢸⣤⣦⢧⡀⠀⠀⠈⢷⡶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠐⠂⢠⠂⠁⣀⣼⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⡜⠙⠛⠿⣷⠀⠀⠀⡸⣽⣟⣿⣾⣿⣿⣿⣿⣶⣶⠦⣤⠤⢨⣤⣞⣿⣾⡄⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠁⠀⢤⣸⠳⠿⢿⣿⣟⣿⣿⣿⣟⣿⠀⢀⣟⡿⠟⠁⠱⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠤⠤⠤⠐⠃⠀⠀⠀⠀⠉⠉⠙⠋⢿⠀⠸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠃

⠀⠀⠎⠿⣦⡀
⠀⢀⡀⠐⠛⠃⢠⡄⢶⣦
⠀⠸⡷⠰⣦⡄⠀⠿⣤⡉⠈⢳⣄
⠀⠀⠁⠐⠘⢧⡀⢀⠀⠹⣶⣄⠈⠳⣦⡀
⠀⠐⠀⣄⠀⠈⠓⡀⠁⠀⠘⣿⣿⣄⠀⠻⢶⣄⠀⠀⠀⠀⠀⠀⣀
⠀⡇⣼⡏⢠⣶⣄⠙⢦⡢⡀⠈⠻⣿⣷⣦⡀⠹⣷⣄⠀⠀⠠⠊⢹⡇
⠀⠀⣿⡇⠀⢩⣽⣷⠀⠹⣟⢦⡀⠈⢻⣿⡷⡄⠸⣿⣆⢸⡇⠀⠘⣄
⠀⢸⠁⢀⡀⠘⢿⡽⣷⣄⢈⣷⣝⢶⡀⠹⣿⣆⠀⠉⢿⣿⡗⡗⢄⣻⡄
⠀⠇⠀⣾⣿⡄⠈⢿⣜⢿⡁⠀⢙⣿⣧⠀⠘⢿⣦⡀⠀⠿⠇⠹⡈⠹⣷⡀
⢸⠀⢰⣿⢿⣷⡀⠈⠹⣿⣿⣆⠀⠈⢻⣧⠀⠈⣿⣿⣦⠀⠀⠠⣵⣄⠙⢷⡀
⡇⠀⠈⣿⠘⠿⣷⡀⠀⠘⢻⣞⣿⣄⠈⢿⡆⠀⠘⠉⢦⣄⠀⠀⣿⣿⣕⢾⣿⣄
⡇⠀⠀⣿⠃⠈⣿⣷⡀⠀⠈⢻⡞⢿⡄⠀⠁⠀⠀⠀⠀⠙⠗⢀⠘⣧⠙⣷⠈⠛⢷⡄
⠀⠀⢀⣿⣇⠀⠸⣿⣧⠀⠀⠈⣿⣎⠟⠀⠀⠀⠀⠀⠀⢀⡀⢸⣇⠈⢳⣟⠀⠀⢰⣍
⠐⡄⠀⠀⠻⣧⠀⢻⣿⡆⠀⠀⠸⣿⡆⠀⠀⢀⠀⠀⠀⢸⣷⡀⢿⠀⠀⢹⡜⣆⠈⣿⣆
⠀⠘⢇⠀⠀⠘⣷⣼⣿⣿⡀⠀⠀⣿⡃⠀⠀⢸⣦⣤⡀⠈⢿⣿⡄⠀⢀⡀⠠⣿⣆⢹⣿⡄
⠀⠀⠈⢧⠀⠀⠘⣱⣿⣿⣇⠀⠀⢸⣿⣦⣆⠈⢻⣿⣿⣆⠸⣿⣿⡀⢸⣧⠀⠹⣿⣿⣿⡇
⠀⠀⠀⠈⣷⠀⠀⠀⠹⣿⣿⠀⠀⠈⠉⠻⣿⠃⠀⢻⣿⣿⣦⠹⣿⣷⡌⢿⣷⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠹⡄⠀⠀⠀⠙⣿⣇⠀⠀⠀⠀⠉⠀⠀⠈⢿⣿⣿⡇⠙⣿⡛⠀⠻⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠙⣄⠀⠀⠈⠙⣿⣆⠀⠀⠀⠀⢾⣷⣦⣀⠻⣿⡇⠀⣾⣇⠀⠀⢻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⢿⣷⡄⠀⠀⠀⠉⠙⢻⣧⡈⠀⠀⠿⠛⢃⡀⢸⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠈⣿⣿⣆⢠⣄⠀⠀⠈⠛⠃⠀⠀⢀⣴⣿⡇⠀⠈⠙⠻⠿⣿⣿⣷⠆⣴⣿⣿⣿⣿⣿⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠐⣿⣿⣿⣷⡛⢿⣖⠀⠀⠀⠀⠀⠉⠙⠛⣧⣄⡀⡀⢸⣶⣤⠄⠀⢾⣿⣿⣿⣿⣿⣿⣿⠟⣋⣙⡻⢦⣀
⠀⠀⠀⠀⠀⠀⠀⣰⣯⣄⣀⠀⠀⠹⢿⣿⣿⣿⣦⣝⢿⣦⣀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⠋⠁⠀⠀⢾⣿⣿⣿⣿⣿⡿⢡⣾⣿⣿⠿⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣸⡟⣿⣿⣿⣷⣀⠀⠉⠹⣿⣿⣿⣿⣷⣌⡛⢿⣶⣶⣿⣛⠀⠀⠀⠀⠁⢀⠀⠀⠀⢨⣿⣿⣿⣿⠟⣱⣿⠟⠉⠀⢀⣴⠶⠃
⠀⠀⠀⠀⠀⠀⡟⠈⢿⣿⣿⠻⣷⠂⠀⣤⣿⠿⠋⢋⣵⣿⡿⣶⣮⠻⣿⣿⣤⡀⠀⠀⠀⠘⠓⠶⠶⣄⢙⣿⣿⢃⣴⣿⠃⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⡇⢀⣿⣿⣿⠀⠈⠓⠀⠀⠠⠴⣾⣿⡿⠏⣰⣿⣿⣷⣮⡛⡿⠃⠀⠀⠀⠀⠀⠀⠀⢻⡌⠀⢡⣿⠟⠁⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠆⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⡿⠋⠀⣰⣿⣿⣿⣿⣿⠃⡀⠀⠀⢠⣆⠀⠀⠀⠀⠈⢷⠀⣾⠇⠀⠀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢊⣠⡖⠀⢩⣿⣿⣿⣿⠟⢸⡇⠀⠀⣿⣿⣦⡔⢀⡀⠀⠈⢠⣿⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⡘⠻⠿⠿⣿⣟⣛⣤⣴⣾⣿⠏⢀⣴⣿⣿⣿⣿⠏⠀⢸⡇⠀⠀⠻⣿⣿⣿⣿⢖⣠⡀⣸⡇⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣴⣿⣿⣿⣿⣿⣿⡿⠃⠀⠈⢡⣿⡿⠟⠁⠀⠀⠈⢷⣤⣤⣼⠶⠍⠉⠁⠉⠀⢀⣿⣵⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣭⣀⣀⣠⠄⠀⠀⡴⠟⠋⠀⠀⠀⠀⠀⣠⣸⣯⣵⡖⠂⠀⠀⠀⠀⢀⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢿⣿⣿⣥⠤⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠒⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣤⣤⠤⠔⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣦⣄⢀⡀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣓⡦⡀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣠⡴⠖⠚⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠻⠁⣠⡶⠉⠀⠙⠳⣝⡆⠀⠀⣠⡴⠋⠉⠙⠋
⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⡟⠀⠀⣦⠀⠀⠀⠉⠲⣴⠋⠀⠀⠀⡼⠁
⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠈⠁⠀⠚⠁⠀⠀⠀⠀⠀⠘⣾⡄⠀⢸⠁⠀⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣟⠛⠃⢀⣴⠀⠲⠦⣀⠀⠀⠀⠀⣸⠀⠀⢹⣷⡀⠘⣇⠀⠳⣌⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣿⠃⣀⡼⠀⠈⠓⠀⠀⣠⠏⠞⠀⢀⡇⠱⡄⠈⠳⢦⡙⢦⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢯⡀⢀⣀⣀⡀⠔⠁⠀⠀⢀⡼⣧⠀⠙⣆⠀⠀⠙⠲⣝⣦⡙⠦⣄⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢿⣝⣒⣾⠋⠉⠛⠲⢾⣉⡁⠈⠳⢄⡈⠳⢤⡄⠀⢀⣹⣿⣷⣄⣙⣦⣤⠽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣥⣒⣒⣒⣒⣀⠀⠀⠀⠀⠈⠉⠙⠓⠚⠷⠶⠶⢄⠁⠉⢙⡛⠒⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣄⣀⠀⠀⢀⣀⣀⣀⠹⣎⢻⡄⠈⠙⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉⠉⠉⠉⠙⠇⠹⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠟⠛⠛⠋⢉⠉⠉⠉⠉⠉⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠛⠉⠀⠢⠠⠀⠀⠀⠀⢄⠨⣀⠔⠀⠠⠔⠠⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣄⢀⡾⠁⠀⠀⠈⠑⠈⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠰⠀⠄⠀⠀⣴⣿⣿⣿⡿⠻⣿⣿⣿⡌⠁⢀⠠⢀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣣⣀⡀⠈⠀⠁⠀⢸⣿⡿⠿⠋⠀⠀⠈⠹⡿⠆⠀⠐⠠⠐⠀⠀⠀⠠⠐⠠⢿
⢀⣀⣠⡤⠴⠶⠖⠒⠊⠋⠉⠉⠉⠉⠉⢋⢙⢧⡀⠀⠀⠘⣥⣀⠀⠚⡉⠅⠀⠀⠀⠀⠀⠔⠒⠋⡁⠀⠀⠀⠐⠀⢸
⠈⠉⠀⠀⣀⣀⠀⠀⠀⣀⣤⣴⣶⣶⣲⣶⣠⡀⢻⣦⠠⠌⢸⡆⠡⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠅⢈⡠⠴⣚⣛⣿⣿⣿⣟
⠀⠂⠁⡂⠀⠀⠉⣠⣾⣿⣿⣿⣯⣽⣿⣛⣯⣿⡆⢻⡇⠁⠈⠑⡀⠠⡆⠀⠀⢀⠀⠀⣀⣭⢖⣫⣵⣾⢿⣿⣿⠏⠻⣿⣿
⠀⠁⣁⣁⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⢻⡇⠘⣇⠀⠀⡀⠈⠢⣤⡤⠊⢁⣤⢞⣿⣾⠿⢿⣿⣃⢂⣽⣿⣦⣾⣿⣿
⠒⠉⠉⠉⢉⣴⣿⣿⣿⣿⣿⠟⠋⢀⠀⢀⠤⣿⡇⠀⣿⠀⠅⡀⠅⣠⢞⣥⢞⣫⣾⡿⢿⣿⣀⣰⣿⡿⠟⠛⠉⠉⠁
⠀⡒⠁⣼⣿⣿⣿⣿⣿⣿⣇⠀⠈⠁⠀⠸⢸⡿⠀⡀⣿⠀⣀⢴⣪⠷⣫⣴⡿⢿⣿⣁⣸⣿⣿⠟⠉
⠀⠀⠁⣿⣿⣿⠿⢿⣿⣿⡝⠦⠀⠠⠤⢠⣿⡇⠨⠀⢇⣸⢷⣫⣵⣿⣿⣿⣃⠀⣿⣿⡿⠋⠁
⠀⣀⣤⣤⣶⣶⣶⣶⣤⣬⣥⡔⠦⠤⠤⢿⣿⣿⣴⣾⣿⣿⣿⣿⡟⠀⣹⣿⣿⣿⠟⠁
⠀⣿⡿⠙⣻⣿⡟⢙⣿⣿⠛⢻⣿⡿⠛⢿⣿⠟⠛⣿⣏⠀⣸⣿⣿⣶⣿⠿⠋
⠀⣿⣿⠶⠿⠿⠟⠻⠿⠿⠶⢿⣿⣷⣴⣿⣿⣦⣼⣿⣿⣿⣿⠿⠛⠉
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⢂⣶⣶⣶⣦⠀⢰⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠈⠛⣻⣿⣿⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠛⠚⠛⠛⠛⠀⠘⠛⠛⠛⠛⠛⡃
⠀⠀⠀⠐⠀⠀⢸⠀⠀⣾⣾⣿⣿⣿⣿⣿⠀⢸⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡟⠀⢀⠀⠀⠀⠁⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠛⠛⠛⠋⠀⠘⠛⠛⠛⠛⠉⠉⠀⠸⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⢰⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣰⣾⣿⣿⠿⠟⠟⣻⣦⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⣀⠀⠆⡀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣶⣶⣖⣀⣀⠿⠿⢶⡐⢠⣄⠔⢘⣁⣀⣼⣿⣿⣿⠃⠀⠀⠀⠁⠋⣿⡀⠀⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⢂⣴⡎⠁⠀⣿⣿⣿⢀⣀⣸⣿⣿⣈⣢⣼⣋⢱⣿⣿⠿⠿⠀⠀⠀⠀⢀⠀⠞⠁⠀⠀⠀⠀⢀⡔⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⣤⣤⠤⠖⣻⡿⢻⣶⣶⣿⠁⠀⢸⣿⣿⡇⠀⢸⣿⣿⡉⣿⣿⣉⣉⡃⠢⡀⠀⠠⠄⠁⠀⠄⠀⠀⠀⣠⠰⠏⠀⣾⣿⡇
⠀⠀⠀⠀⡠⠚⢹⣷⣶⠉⠉⣿⣿⣿⣃⣠⡼⠛⠛⢻⣶⣶⡞⠛⠋⣿⣿⣿⠁⠀⢹⣷⠈⣿⣿⣷⠀⠘⠶⢀⠀⠀⠀⠀⠀⡀⢦⡈⠃⠀⠀⣿⣿⡇
⠀⠀⠀⣴⣷⣶⠋⠉⣿⣿⡟⠉⠁⢸⣿⣿⡇⠀⠀⣸⣿⡿⣇⣀⣀⠿⠿⠿⣧⣤⡼⠛⢶⡏⠉⠉⠃⠀⠀⠀⠀⢤⠤⠶⠮⠧⠥⠀⠐⠂⠀⣿⣿⡇
⠀⢠⣶⠞⠛⣷⣶⡴⠛⠛⣷⣶⣶⡏⠉⠉⣿⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⠀⣿⢿⣿⣆⡘⣧⠴⠶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠰⠛⢻⣤⣴⠛⠛⣧⣤⣴⠛⠛⠻⣦⣤⣤⠿⠟⠛⣷⣶⣶⡏⠉⢹⣿⣿⣿⡧⠀⠀⠀⠈⣷⣶⣦⣾⡇⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⣀⢀⣿⣿⡇
⣥⣤⠿⠿⣧⣀⣠⠿⠿⢿⣀⣀⣠⠟⠛⠛⣤⣤⣤⡟⠛⠛⣧⣤⣼⡛⠛⠛⣧⡀⠀⠀⣠⡇⠀⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⢸⣿⣿⡇
⠛⠛⠀⠀⣿⣿⡟⠀⠀⠘⠛⠛⠛⠂⠀⠀⠛⠙⠋⠃⠀⠀⠉⠉⠙⠃⠀⡀⠀⠉⠛⠉⢉⠉⠀⠈⠁⠉⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠸⣿⣿⡇
⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠊⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⡀⠀⠀⠀⡚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⣀⠈⠑⡤⢌⠁⠀⠀⠀⠀⣀⠤⠔⠒⠶⣶⠦⡤⠠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠄⠀⠀⠐⠧⡀⠀⠀⡜⠀⠀⠀⠀⠀⠀⡘⠛⢕⣢⠀⠀⠉⠀⠀⠀⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⠐⢲⠀⠈⠁⠀⠀⠀⠀⡈⠀⠀⠀⠘⡤⢸⠤⣀⠀⠀⠀⠀⢠⠁⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠈⠑⠢
⠀⠀⠀⠀⠀⠀⡠⠔⢊⠅⠒⠀⠀⠒⠢⠉⠁⠒⠤⢌⡀⡄⠈⠀⠀⠃⠀⣳⠀⠀⠀⣉⠢⣀⡀⢸⡀⠀⠀⠀⠀⠀⠈⠒⢄
⠀⠀⠀⠀⡠⠊⠀⡰⢋⣰⠄⣠⡀⢴⢈⠙⠄⠀⠀⠀⠀⠁⠂⠤⢀⣠⣶⠟⠀⣰⠁⠀⠀⠀⠀⠈⠉⠓⠤⡀⠀⠀⠀⠀⠀⠁⢢
⠀⠀⠀⢰⠁⠀⠀⠳⣻⠟⠏⠙⢉⠻⢿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢩⡤⠄⠉⠒⠠⠀⠠⠤⠀⠀⠘⠓⠈⠉⠁⠀⠀⠀⢡
⠀⠀⠰⠁⠠⠤⠤⣴⠋⠀⠐⢄⠆⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠰⢯⢊⠅⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔
⠀⠀⠀⠀⠒⠒⠒⢺⣅⠀⠀⠈⠀⠀⠀⣸⠗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠒⠛⠉⠀⠛⠠⡀⠀⠀⠈⠉⠀⠀⠉⠁⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡄⢀⠀⣠⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠉⠉⠉⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⢀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡦⠀⣀⠳⢄⡈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⠀⠙⣦⠀⠉⠲⣤⡀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣦⢀⡀⠙⢦⡀⠀⠙⠓⢆⠀⠈⠲⢄⠀⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇⠀⠙⣄⠀⠙⠲⣄⠀⠀⠳⣄⠀⠀⠑⢦⡀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⣦⠀⠈⠶⡀⠀⠘⣷⡀⠀⠈⠳⡀⠀⠀⢳⣄⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣿⢷⡀⠀⠙⢆⠀⠈⠻⣤⡀⠀⠉⠠⡀⠀⠙⠲⣀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢿⡄⣿⣄⠀⠀⠱⡄⠀⠈⠻⡆⠀⠀⠅⠀⠀⠀⢈⠑⢺⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣇⠉⠻⣆⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢣⡀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⢫⠷⡀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠈⢷⡀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠙⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠄⠀⢈⠑⠸⣷⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠉⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢲⡈⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⡈⢷⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡄⠀⠊⠘⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣍⠛⠿⢿⣿⠋⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢸⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠛⣷⠆⣰⠏⢁⣼⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠉⠈⣿⠏⢹⡶⣤⡀⠀⠀⠀⠀⠀⡀⠛⢁⣼⠃⣠⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⣤⣤⣀⠀⠈⠀⠘⠉⠳⣦⣀⣠⠊⠀⣠⡾⠁⢠⣿⠟⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⡀⠙⠶⣤⡀⠀⢀⣴⣿⠋⢀⣤⣾⣿⠇⠀⣸⠃⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⡆⠈⠉⠀⠈⠙⢰⣿⡟⣡⢾⣿⠟⠁⢀⣠⡶⠋⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢧⠹⣄⡀⠀⣀⡀⣸⠏⣼⢃⣿⣯⣴⣾⠿⠋⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⠷⠠⠁⠀⠀⢠⣏⣼⣧⣼⣿⣿⣿⣷⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⣾⣿⣿⣿⡿⠟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠠⠾⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⠄⢀⠀⠀⢀⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⢀⠀⠤⠀⠈⠖⠠⠀⠀⠀⠀⢀⠄⠒⠛⠛⠻⢒⣒⣂⠀⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⡀⠀⠀⠠⠂⢀⠀⠈⠣⡀⠀⠰⠁⠀⠀⠀⠀⠀⠐⠉⠓⠵⡄⠀⠀⠀⠀⠀⠒⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠀⠈⠉⠄⣀⠀⠀⢀⠀⠀⠤⠄⠀⠀⠘⡂⠞⠒⠤⡀⠀⠀⠀⡇⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡠⠒⢁⣔⠉⠀⠀⠀⢉⣆⡀⠈⠁⠒⠤⢆⠀⠀⠀⠀⢀⡇⠀⢀⠄⠈⠒⠠⠤⢧⣀⠀⠀⠀⠀⠀⠈⠢⢀
⠀⠀⠀⢀⠊⠀⢠⣉⣴⣿⣴⣶⣼⣷⣤⣡⠀⠀⠀⠀⠀⠉⠑⠰⠾⣟⣁⠠⠇⠤⣀⠀⠀⠀⠀⠀⠑⠢⣀⢀⡀⠄⠀⠀⠑⡀
⠀⠀⢀⠌⠀⠀⠀⢡⡟⠉⠀⢠⠀⠉⣷⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠖⡫⠄⠀⠈⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⡀⠀⢐⣯⠀⠀⠈⠎⠀⠀⠈⣗⢀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠉⢣⣄⢡⡤⠄⢤⡐⠒⠂⠀⠤⠤⠤⠤⠤⠄⠐⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣝⠿⠦⠶⠼⢟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⢀⠠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠈


⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣦⣶⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢆⠀⠀⠀⠀⠀⠀⡀⠀⠈⣿⣿⣿⣿⣿⣷⣾⣶⣶⣿⣷⡆⣤⣴⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⡌⠐⠀⠀⠀⠀⠀⣿⣄⡀⠘⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡇⣯⣸⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⣿⠅⠋⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣵⡏⣽⣿⣟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⢴⢀⡀⠀⢨⡰⡄⠀⠀⣿⢠⡀⠀⠘⣿⣿⣿⣯⣿⣿⣿⣿⣿⠣⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢹⡇⡈⢌⠃⠀⠀⠙⣧⠀⠀⣿⡸⣿⢠⣄⠸⣿⣿⣿⣿⣿⣿⣿⣿⠠⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⢸⡇⣡⠈⡓⠀⢲⡄⠹⡄⢀⣼⢳⣷⡆⡋⣤⠨⠉⣛⣻⣛⡿⠉⠹⠃⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠁⠁⠀⣼⢅⢸⣧⡳⡀⢻⠆⠛⠃⢸⣰⣌⣽⡇⠻⢼⡟⢀⡀⢰⣸⣉⢉⠀⠘⠛⠊⠲⠶⣾⢤
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢸⣿⣿⡟⠃⠀⠀⠀⠀⠀⠻⣿⠆⠀⢸⠀⠸⡇⠘⢻⣿⣿⡶
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣟⠋⣡⣽⣷⣶⣶⣦⣀⠀⠀⠈⠸⡀⡅⢠⠀⠀⠇⠀⢠⠛⣹⠁⠀⠠
⠀⠀⠀⠂⠀⠀⠀⠇⡙⠁⣰⣾⡿⠿⢿⣼⣿⠟⣿⣦⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⡅⠀⢨⠰
⠀⠀⠀⠀⠀⢀⠂⠀⠸⢭⣿⡿⠀⠀⠀⠈⠁⠂⠾⣿⡄⠀⠀⠀⠀⠀⠓⠄⢀⡸⠁⣤
⠀⠀⠀⡀⡠⠀⠀⠀⠀⠀⠉⠡⡀⠘⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⡤⠀⠂⠀⠀⠙⡀⡈
⠀⠀⠀⠈⠧⢤⣀⡠⠀⠀⠀⠀⢔⣴⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠠⠀⠀⠈⠉⠀⠀⠀⠠⠾⠈⣷⣤⠁⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄
⠀⢀⠜⠂⢈⠇⠐⡀⠀⠀⢀⠙⢖⠀⠈⢉⠀⠀⠀⠘⠒⠀⠀⠀⠀⢀⠀⡁⠀⠁⠀⠠
⠀⠀⠀⠁⠘⠀⠀⡇⠀⠀⠸⡇⠄⠆⠀⠨⠀⠀⠀⠀⠀⠀⡀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠃⠐⠀⠀⠂⠀⠀⠆⠀⢀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠀⠀⡀⠀⠀⠰⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⠀⠀⢠⠆⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠶⢲⡆⠀⠘⠛⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣠⣤⣀⣤⠴⠦⣄⡀⠀⠀⠀⠀⠀⢁⣴⠋⡀⠀⣴⣏⣤⡄⠀⣴⣋⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠙⠏⠁⠚⠉⠀⠀⠀⢸⡇⣀⡀⠀⠀⠀⠛⠛⠋⠁⠀⠉⠉⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⣠⠶⠶⣄⠀⠀⠀⠀⣴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⣷
⠀⠀⠀⠀⠀⣿⠀⠀⠘⣧⣀⡀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠙⢳⡄⠀⠀⣠⡤⠴⠶⠶⢦
⠀⠀⠀⠀⠀⣽⠆⠀⠀⠈⢮⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⡶⢿⣤⣤⣤⡄⠀⠀⠀⠘⢿⣦⣼⠃⠀⠀⠀⠀⢘⡷⠶⠤⣤⣀
⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⢸⡷⠶⠶⠞⠋⠁⢀⠀⠤⣄⡀⠈⠙⢦⡤⠀⠀⠀⣼⠃⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠈⢷⣶⠒⠒⠦⢤⣀
⠀⢀⣠⣾⣅⠀⠀⠀⠀⠀⠀⠀⢀⣙⣷⣄⣾⠁⢠⠶⢦⣄⠀⢀⣀⣠⡾⠁⠀⠀⠀⢻⡄⢀⣴⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠸⡏⠳⡄⠀⠀⠈⠉⠓⠦⣄
⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡇⠀⣿⠀⠀⣹⡦⠈⠉⠁⠀⠀⢢⡶⠃⠘⣷⡾⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠹⡄⠀⠀⠀⠀⠀⠈
⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠛⠶⠚⢿⠃⠀⠀⣰⠀⠀⢸⡇⠀⢰⡿⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢷
⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠘⠦⠤⠟⠁⠀⠀⣸⠇⢀⡾⠁⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠸⡆
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⣷⠀⠀⠀⢀⣀⡠⠋⠀⣾⠃⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠁
⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⡉⠂⠛⠋⠉⠀⠀⣸⠏⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠋⡳⣶⣶⣤⣤⣴⡿⠀⠀⠀⠀⠀⢀⡍
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣫⣴⠾⠛⣃⠀⠉⠙⠛⣿⠃⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⣠⡶⠟⣉⠀⢀⠀⠀⣿⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠛⢷⣿⣋⣴⠿⣫⣾⡿⠛⢾⡇⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠦⣤⣄⣀⣀⣀⣈⣿⣿⡿⠿⠛⠁⠀⠀⢸⡇⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣏⢯⠀⢭⠽
⠀⠀⠀⠀⢀⡀⣀⣀⡀⠀⠠⣸⠃⠀⠤⠀⠴
⠀⠀⠀⠀⠙⣄⠤⢤⠤⠬⠀⠀⠀⠄⡀⣰⠀⠖⠈⠩⡑⢄
⠀⠀⠀⠀⠀⠈⠣⡀⠀⠢⢐⠒⠂⠀⠡⠂⠀⠀⠀⠀⠘⣆⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⢹⠱⡄⠘⡆⢹⡀⠉⠀⠀⠘⠆⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⡆⠘⢶⡁⠘⢏⠉⠉⠉⠉⣉⣉⣀⣀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⠀⣠⠎⠳⣦⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠚⠁⠀⢠⠁⠀⠀⠀⠀⠉⠉⠉⠑⠒⠲⠤⡄⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣀⢤⠄⡸⠤⠤⠤⠤⠄⠀⠠⡀⠀⠠⠃⢠⠇⠀⢐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠊⠀⠀⠀⠀⠤⠴⠒⢀⠔⠀⢠⡈⠒⡀⢀⣞⣀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⠦⠤⠤⠤⠴⠄⢰⠀⠀⡞⠀⠀⠀⢳⡀⠈⠡⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠐⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠇⠀⠀⠀⠀⠹⡄⠀⠙⢆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⠀⠀⠀⠀⠀⠙⢆⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⠀⠈⠂⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⣀⠲⡄⣈⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠒⢲⠚⡁⠀⢰⣌⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣰⡄⠙⠳⠶⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠐⠀⡠⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⠁⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⡀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠰⠦⠀⠀⠐⠒⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⢣⣀⣠⠤⠤⢤⣆⠀⠀⠀⢀⣶⠏⣿⣶⣶⣶⣦⠀⣀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⡀⠀⠀⠀⠀⠀⢹⠄⠀⠀⠘⣿⣆⢽⡟⣿⡷⣹⠻⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠙⠛⠒⠀⠀⠉⠀⠀⠀⠀⠀⠘⣿⣙⣧⣿⣰⠇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠟⠋⠛
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⡿⠁⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢠⠀⠀⠀⠈⠂⠔
⠀⠀⠀⠀⠀⢀⣀⠤⣤⣿⢀⣀⡠⠴⠟⢛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⠼⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠙⠉⠀⠀⠛⠋⠈⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙


⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣶⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣸⣠⠂⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠿⠶⠦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢤⠤⢤⣀⣀⠈⠉⠙⠓⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡀⣠⠤⠤⠄⠀⠉⠙⠒⠦⢄⡀⠈⠉⠛⢶⠶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠒⠶⢋⡉⠀⡌⠐⠁⠀⠀⠀⠈⠑⠢⠄⠀⠀⠉⠒⠤⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠛⠛⠡⠄⣀⠀⠀⠈⠉⠢⢄⡀⠀⠀⢠⠂⡠⠂⠀⠒⠀⡀⠀⠀⠂⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠀⠀⠈⠉⠒⠲⠤⢤⣤⠶⠄⠂⠉⠑⠢⢄⠀⡇
⠀⠀⠀⠀⣀⣀⣤⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠦⡀⠀⠄⠀⡆⡇
⠀⠀⢰⠿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣒⢄⠀⠀⠁⠀⠀⢀⠃⡇
⠀⠀⢸⡖⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⡄⠀⠀⠀⠀⢸⠀⡇
⠀⠀⢸⡈⡓⠢⠄⡁⠒⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠖⠊⡽⢠⡇
⠀⠀⢸⡇⢨⡐⠀⠀⠁⠂⠄⣈⠑⠲⠤⣀⡤⣖⠀⣀⠠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⣞⠁⣸⡇
⠀⠀⠸⡇⠢⣌⡑⠤⣀⠐⠠⠀⠉⠒⠤⣈⠁⠸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡦⠶⠟⠀⠉⠛⠋
⠀⠀⠀⢿⣤⠏⠙⠳⣤⣉⠒⠤⣀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣉⠑⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⡇⢰⠀⠀⠀⢀⣠⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡶⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠃

⠀⣴⠟⠳⣄⠀⠀⣀
⣠⡏⠳⣤⠞⠳⣾⡏⢙⣶⣄⡀
⣿⢹⣤⡶⣤⡀⢈⡻⣟⠁⣤⣏⣷⣦⣄⡀
⢿⣿⠛⡄⣶⡿⣬⠻⠈⠛⢮⣅⡉⠉⠉⢽⣦⣄⠀⠀⠀⠀⠀⠀⠀⣀
⡞⠛⣧⠀⢉⣿⣼⢳⡄⠀⠀⢬⣿⡶⣤⡀⢹⣯⢳⡀⠀⠀⢀⣶⢿⡟⣿
⣷⠀⣸⣿⠟⡻⣿⢦⡙⢦⣀⡀⠈⢡⡾⠻⣄⠛⠿⢻⣦⡀⢼⠁⠀⢃⢻⡀
⢻⢠⣾⡟⠢⠿⡛⢧⡀⠀⠙⢿⣆⠘⣻⣣⣼⢧⡀⠈⢿⠷⣼⡆⣶⣈⢿⣇
⢸⣼⠏⢻⠀⢠⣿⣾⢳⡀⠘⢦⠙⢦⡈⠉⠹⠃⠻⣦⡀⠀⠈⢧⣽⣯⣳⣾⣧
⠀⢿⠀⢻⣧⠈⠘⠛⣧⠻⣄⠀⣴⢆⣽⣦⠀⠀⠀⢈⣿⣆⠀⠀⠙⢿⣯⡉⠹⣇
⢀⡏⠀⣿⣿⣧⠀⠀⠘⣧⡘⢦⡙⠀⠙⣏⢷⡀⠀⠀⠻⠿⣧⠀⠀⡀⠙⣿⣶⣬⡳⢦⡀
⢸⡇⠀⢿⡏⢸⣧⡀⠀⠹⣿⣌⠳⣄⠀⠁⠘⣷⡀⠀⠀⠀⢈⣄⠀⠘⠄⠈⠻⣍⠛⢦⣷⡀
⢸⡇⠀⢾⣿⡨⣿⣿⡄⠈⠿⠻⣦⠹⣷⡀⠀⠙⠿⢦⠀⠀⠹⠛⠆⢤⠀⠀⢷⡹⣧⡀⠉⣳⣄
⠀⣷⠀⣺⣿⡇⠉⢻⣿⡄⠀⠀⠘⠁⠙⣷⠀⠀⠀⠘⢶⡀⠀⠀⠀⠈⢷⡄⠘⢧⣿⡇⠀⠙⢿⣆
⠀⢹⠀⢹⡿⣷⡀⠸⣿⣷⠀⠀⠀⠀⣦⠈⠃⢠⡀⠀⠀⠃⠀⠀⠀⣦⠈⣷⠀⠀⠙⠃⠀⠀⠸⣿⡄
⠀⠈⣧⠀⠙⢾⣿⡄⢻⣿⣆⠀⠀⠀⢻⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⣿⠀⡀⢠⠀⠀⠀⠰⣤⡀⣻⡇
⠀⠀⠘⣧⠀⠀⠙⣿⣾⣿⡛⣆⠀⠀⠈⠁⠀⠀⠀⠀⠀⠸⣦⡀⠀⠛⠀⢿⠈⢧⣀⡀⠐⢾⣿⣿⣷
⠀⠀⠀⠘⢷⡀⢠⡟⣹⣿⣿⡜⣦⠀⠀⠀⠀⢸⣷⡄⠀⠀⠹⠀⠀⠀⠀⠸⡇⠈⢿⣇⠀⠘⣿⡉⢿⡆
⠀⠀⠀⠀⠈⢿⡁⠀⠀⠑⠻⣿⣿⣧⠀⠀⠀⠈⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣜⡌⢻⣷⣦⠘⢧⡘⣿⡄
⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⣺⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣜⡆⠹⣿⣷⡈⢛⡘⢿⡄⠀⠀⢀⣀⣤⣴⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠠⠞⠋⠹⠿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡴⢿⣿⢿⣿⣿⣶⣿⣶⠟⠋⠁⠴⠋⠀⢀⠈⢙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠁⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣄⠀⠀⠀⠈⠈⠻⣿⡿⠁⠀⢀⡴⣠⢞⣴⢟⡴⢋⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⢨⣾⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠊⠀⠈⢩⣶⣤⣤⣤⣤⡖⠛⠁⠀⠰⠋⡴⢡⣿⢣⣾⢵⣿⡿⢃⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢐⣿⣿⣿⣿⡿⣿⣆⠀⠀⢀⠀⢀⡄⠀⠀⠀⠋⠀⠈⣿⠋⠀⠀⠀⠀⠀⠀⠀⡻⣣⡿⠋⠜⠛⢡⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣻⣦⡀⠐⢉⣉⠉⠉⠈⢸⢿⣿⣷⣶⣭⣘⡛⠛⠀⠀⠀⠀⠀⢰⠇⠀⢀⣄⡀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⣴⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⡿⣿⣿⣦⠈⠉⠀⠀⢀⣼⠟⠛⢏⣼⠿⣿⠋⠻⣦⣄⢀⣀⣰⠋⠀⠀⠘⢿⣿⣦⡀⠀⢈⡞⢠⡖⠀⠀⢰⡏⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢻⣿⢹⣿⠷⢦⡄⠒⠋⢁⣀⣴⣿⣯⡾⢃⣾⣣⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⡟⣽⡷⠀⠾⢠⣿⣽⡆⠀⢻⢡⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⣿⢸⡏⠀⠀⠘⠃⠀⢨⣿⣿⠟⠋⢠⢟⣿⣿⣿⡟⢩⡇⢠⣠⠀⠀⠀⠀⢸⡈⠇⠀⠀⣾⣷⣿⡇⢈⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⣿⣾⣇⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⢈⣾⣿⣿⡟⠀⡞⠣⣏⣿⣠⠶⣄⡀⠘⠃⠀⠀⢰⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⡀⡀⢠⡞⠀⠀⠀⠀⣠⣾⣿⣿⡟⠀⣆⣿⣯⡿⠛⠁⠀⠀⠉⠳⠦⣤⣤⣼⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠻⣿⣿⣿⣿⡿⠟⠋⠀⠀⢀⡀⠀⣾⢟⣿⠟⣷⣷⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠉⠟⠁⢀⣀⣤⡶⣾⡿⡂⢈⣵⠟⣣⣾⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⣴⠾⣿⣿⣿⣿⣿⣿⣶⠿⠿⠛⠋⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣀⣀⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠲⣤⢎⣀⠄⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣀⠔⠀⢀⢥⣴⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡠⠂⠀⡠⠊⠀⢠⡃⢀⢊⡷⡁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠲⡄⢂⠀⠠⠊⠀⠀⡜⠀⠀⡴⠁⠀⢁⣾⠧⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢉⠀⡽⠁⠀⣠⠞⠀⠀⠐⠀⠀⣴⡀⡀⣷⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠞⠁⠀⢰⠇⠀⣠⠊⠀⢀⠔⠀⠉⢀⡏⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⡾⠃⠀⠀⢠⠋⠀⢰⠁⠀⢀⡜⠀⠀⠀⣮⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢀⠞⠀⠀⠀⠠⠁⠀⢠⠃⠀⢠⠎⠀⠀⠀⣰⢛⡶⠆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠴⠋⠀⠀⠀⠀⠁⠀⣠⠃⠀⠀⠃⠀⠀⠀⡰⠃⢸⡇⠀⠀⢡⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠳⠄⢠⠷⢄⠀⢸⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠰⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣴⠋⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⡇⠀⢀⠇⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⡼⠁⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⡏⠉⠳⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⣸⡃⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠄⢀⠔⠁⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⣰⠏⠙⠢⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢫⣁⠠⡌⠉⠲⡁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⡠⠤⠴⠖⠻⢤⡰⣿⡍⠓⡀⠀⠀⠈⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠁⠈⠓⠢⢴⣶⣾⠃⠑⢽⣦⡀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⣀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⣴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠙⢟⢦⡀⠀⠀⠀⠀⣼⡿⣿⣾⡿⢫⣷⠻⣿⣧⣤⣀⣀⣀⠀⢀⣴⡋⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠈⠈⣷⡶⠚⠀⠀⠀⠀⢸⣯⡞⠁⠹⣷⣮⡙⠻⣯⡉⠙⠚⠃⠈⡗⣧⡀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⣯⢀⣈⡆⢿⣧⠙⠄⠈⠻⣦⣀⣬⡾⢁⣿⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠘⣆⠀⠀⢻⠶⠶⠤⣀⠀⢀⣼⠈⣿⣾⣧⠸⣿⡀⠀⠀⠀⠈⠻⣿⣷⣿⣿⢃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣌⢿⣿⠶⠄⡙⠿⣿⣀⡽⠿⣿⣆⠙⢧⡀⠰⣄⠢⣤⣀⣈⣀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡃⠀⠀⠀⠀⠀⠈⢳⡀⡆⠈⠧⣄⣀⡀⠈⠉⢋⡵⠋⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠳⢤⣀⡀⠀⠠⠤⠾⠁⠁⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⠓⠶⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⢨⠀⠀⠉⡅⠀⠀⠁⢤⠤⠤⠤⠤⠤⣤⠠⠀⠀⠀⠀⠀⢀⡀⠅⠀⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡄⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸⠀⠀⠀⠂⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⠐⠀⠀⠀⠰⠸
⠀⠀⠀⠸⠀⠀⢈⠀⠀⠤⡀⠆⠀⢸⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡄⡄
⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⡀⠀⠠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣓⡂
⠀⠀⠀⠀⠈⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠉⡇⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⠀⢰⠀⠀⠀⠀⠀⠀⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣇⣀⡀⠀⠀⠀⡀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠆⠸
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠠⠖⢠⠜⠉⠣⠀⠀⠉⠓⢤⠤⠥⢆⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡠⠊⢉⣰⠎⡀⠔⠉⠀⠀⠀⡀⠀⠈⠉⠐⢱⡆⡈⠉⠷⠒⠒⠛⠘⠤⠤⠄⠀⠄
⠀⠀⠀⠀⠀⣧⠔⠁⠀⡌⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇⠀⠑⡼⠁⢉⠁⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠺⠃⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⡌⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠃⠀⠀⣰⠠⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠑⢄⡀⢀⣀⣀⣀⠀⠀⠠⠊⠀⠀⠀⠀⠸⣇⠘⣖⣲⠆⠁⠈⢂
⠀⢀⠀⠀⠀⠀⣿⠄⠀⠤⠂⢁⡁⡀⢀⢀⡀⠀⢉⠐⠖⡀⠒⠐⣃⣤⡈⠉⠉⠀⠊⠉⠉⣨⣀⣀⣀⣀⣀⣀⡀
⠀⠈⠀⠀⠀⠀⡏⠤⡎⠀⣀⠿⢣⠄⠀⠀⠄⣉⠞⠵⡀⢘⠀⠀⠉⠘⠁⠉⠉⠉⠋⠉⢻⣿⣉⣉⠉⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠰⠄⠲⠚⠚⢁⠄⠊⠐⠄⠂⢀⠀⠁⠀⠉⣛⡛⢛⠂⠻⣃⠀⠂⠂⠀⣶⣼⢇⡀⡈⣧⠀⠀⠀⡇
⠀⠀⠀⠀⢀⠃⠀⠄⠀⢀⠥⢠⠀⠈⠁⠉⠂⠁⢤⠤⢄⠁⠈⠡⠃⠀⠩⡉⠉⠉⡉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠁
⠀⠀⠀⠀⡞⠄⠡⠔⠂⠇⢀⠌⠈⠓⠒⠐⠒⠂⠈⢄⢀⠃⠐⠀⠀⠄⠈⠡⠀⠐⠠⢤⠔⠈⠀⠀⠀⢠
⠀⠀⢠⠘⠀⠀⠀⠀⠀⠉⠉⠈⠉⠀⠀⠀⠃⠀⠀⠈⠉⠀⠉⠉⠉⠁⠀⠀⠓⠀⠃⠀⠀⠀⠈⠀⠀⠀⠂
⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠂⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠤⠤⠬⠥⠍⠉⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠀⠀⠀⠀⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⣨⡴⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠐⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⡠⢀⠀⢰⢁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡾⢣⠇⠀⣏⣿⡟⠃⠀⢀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠈⡄
⠀⠀⠈⠀⠀⠀⢠⢯⠗⠀⠀⠉⠨⠑⠓⠐⠀⠀⠀⠀⣀⡀⠀⢀⠀⣇⡀
⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠂⠈⠩⠀⠀⢀⣈⠉⢑⣈⡀⠈⠀⠀⠀⡀⠄⠀⣀⡀⠀⠀⠀⢀⠠⢄⡀⠀⠀⣀⣀⠀⣀⣀⡀⣀
⠀⠀⠃⠀⠀⠀⠁⠀⢀⠀⠔⣠⠈⠀⠀⢀⠁⣴⠛⠠⡖⢒⠒⣻⣻⢾⡑⡢⠠⠒⠉⠉⠈⠁⠀⠙⠋⣭⡙⠲⢾⡗⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⡀⠠⠋⠘⣅⠴⠀⠙⠋⠀⠉⠻⠚⠾⠠⢣⠀⠀⠀⠀⠀⠀⠈⠀⡘⣇⠀⠀⠁
⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⣦⠀⠀⣠⠃⠐⠀⢊⠁⠀⠰⠁⣰⠀⠀⠀⠀⠀⡌⠀⠀⡀⠀⠀⠀⠀⠀⠀⢹⡄⠂⢸⣜⡆
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢻⠀⠄⢹⢠⣼⣷⣾⠋⠀⠀⠁⠀⢀⠀⡀⠀⠀⢹⠄⣠⡉⢦⠴⠷⠂⠀⠀⠀⢡⡟⢨⣝⡇⢠
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⢧⡀⢳⠌⡿⢿⠍⠀⡄⠈⡀⠀⠋⢸⠛⠀⢀⣾⠂⠀⣐⠟⠋⠙⠢⠀⠀⠀⢈⡇⡟⣿⣿⡖⠀⠈
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠑⢼⠟⠳⠾⠗⠤⣅⡚⠀⠀⠀⢀⠤⠀⠚⠛⠶⠋⠀⠀⠀⠀⠀⠀⣶⡀⡼⡿⢱⡯⡿⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⠂⠀⠤⠒⠀⠀⠀⠀⠉⠉⠓⠚⠳⠾⢤⡀⠀⠀⠀⠀⠀⠀⣀⣠⡴⢿⢿⠿⢣⠄⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣄⠀⠀⠀⠀⠀⠀⠀⠈⣴⠶⠿⣟⣉⣿⠟⣽⣁⡄⠀⢀⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣆⠿⠓⠤⣄⡀⠀⠀⣀⣤⠏⠀⠀⢀⡾⠃⢸⡟⠄⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⠁⠀⠀⠀⠀⠀⠉⠉⠁⠀⢀⡀⠠⠜⠁⢀⡮⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⡀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣾⠀⠀⢺⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠋⠁⠀⠀⠘⠀⠀⠸⠊

⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⢠⠄⠐⠂⠠⢀
⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠑⢄⠀⢀⠄⠀⠠⠀⠄⡀⠀⠀⠀⢀⡀⠠⠤⠤⠀⢀
⠀⠀⠀⠀⡠⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⠀⠀⠀⣀⠀⠀⠑⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⠌⠁⠐⢄
⠀⠀⠀⠐⠁⠀⠀⠀⠀⠠⠁⠃⠀⢐⠀⠀⠀⠀⠉⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⡌⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠁⠀⠀⠀⠀⠠⣀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⡀
⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠐⠁⣀⠠⢄⡀⢢⡀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠀⠤⠤⠤⠴⠦⠄⠀⠀⠀⠀⠀⠀⠇
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⡀
⠀⠀⠀⠀⢐⠀⢰⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣧
⠀⠀⠀⠀⠾⣇⡸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠚⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⣶⠂⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⢀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢠⡾⢁⣀⣀⣋⣹⣟⣀⣀⡞⠓⠂⠀⠀⠁⠀⠈⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⡠⠒⠢⣄⠀⠀⠀⠀⢀⣀⣠⠤⠶⢒⣾⠟⠉⠉⠁⣠⣟⣡⣤⠀⠀⠀⠉⠉⠉⠑⠒⠲⠤⠴⠁⠀⢸⠆
⠀⠀⠀⠀⠀⠀⢣⡀⠀⠘⡤⠴⠒⠋⠉⠁⠀⠀⣰⠟⠁⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢠⣄⠀⠀⠀⠀⠘⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢀⠃⡨⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢨⠊⠀⡔⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⢀⠊⠀⡠⠋⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠘⡃⠀⠔⠁⢀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠐⡎⠀⡰⠁⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠠⡎⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⠀⠡⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⠂⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠒⠋⢦⣀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⣠⠏⠈⠙⠓⠲⠶⠤⠤⠤⠤⠤⠤⠤⠴⠒⠒⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⠁

⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⣿⣿⣿⣄⣿⣿⣿⣿⠃⠹⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣠⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠉⠁⢹⣿⣿⣄⣸⣿⣿⣿⣿⣿⡿⠟⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⢸⣿⣿⣿⣿⠛⠋⠙⣿⡿⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠸⠿⠃⠛⠛⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠖⠊⠉⠀⣷⠀⠀⠀⠀⠀⠀⠀⡼⠲⣄⣠⠴⠚
⠀⠀⠀⠀⡇⣀⣠⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⣀⡠⠴⠚⠁
⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠉⠉⠉⠉⠉⠙⠓⠲⠤⣄
⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠒⠊⠉⠉⣓⠦⠖⠚⠉⠉⠓⠒⣦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⢴⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠻⣄
⠀⠀⠀⠀⣀⡤⠴⠚⠉⠀⠀⠀⢀⣀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⡤⢤⣀⡠⣄⡠⠖⠚⠉⠉⢽⣋⣀⣠⢾⡇⠀⠈⢧⡀
⠓⠶⢞⣉⠁⠀⣀⠤⠖⠚⠉⠉⠉⠀⠉⠉⠓⠲⢤⡀⢀⣀⣀⡀⠀⢰⡃⢾⠀⠀⠋⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⣧
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢤⡀⠉⠉⠉⠉⠛⢷⡀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⠀⠘⣷⡀⠀⠀⡏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢳⠀⢠⠷⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⢳⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡞⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠸⡇⠀⠈⢳⠙⣄⠀⠀⠸⠀⠀⠀⣠⢏⡟⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⡇⠀⠀⠘⠊⠁⠀⠀⠀⣀⠤⠚⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢸⠲⢄⡀⠀⠀⢠⠶⣾⠗⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠳⢄⡈⠙⠋⢙⣎⣀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠈⠑⠲⠾⡷⠚⠉⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢸⠆⠀⠀⠀⠀⡠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⢠⠧⠤⠴⠋⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠒⠒⠉⠑⠒⠒⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣀⣠⣤⣤⣤⡀⠒⠂⠉⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠒⢨⣾⣿⣿⣿⣿⣿⣿⣦⡠⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠀⠀⠀⢸⡏⠛⠫⠙⠻⠟⣻⣿⣿⣄⡠⠄⠀⠈⠢⡀
⠀⠀⠀⢀⡠⠐⠉⠀⠀⠀⠀⠀⠀⠈⠓⢀⡀⠂⠀⠀⣿⣿⣿⣿⣿⣦⡀⠀⠀⠑⡄
⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠰⣅⣒⣠⣤⣹⣿⡏⠀⠀⠀⠙⠢⡀⣀⣈⣂⣀⠀⡀
⠀⠀⠀⠀⢣⠀⠀⠀⠀⢀⢠⣄⣤⠀⠀⠂⢻⣿⣿⣿⠹⣿⠀⠀⠀⢀⠗⠈⠁⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠡⡀⠀⠀⠸⣿⠋⠉⠑⡄⡀⠀⠙⠻⣯⠆⢨⢀⠠⠒⠁⠀⠀⠀⢀⡀⠀⠒⠒⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⠐⠢⡊⠀⠀⠈⠁⠂⣼⠷⠊⠁⠀⠀⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⢈⡢⠄⠀⠈⠁⠀⠀⠀⠀⢀⡠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠵⠄⠊⠁⠀⠀⠀⠀⣀⠠⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣄⠀⠀⠀⠀⠀⢠⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣼⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠉⠉⠉⠉⠉⠉⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⠟⠛⠛⠋⠉⠉⠉⠉⠉⠉⠻⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢸⣿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⣿⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠘⣿⡄⠀⠀⠻⣿⣦⣄⣀⣀⣀⣠⣴⡿⠇⠀⠀⠸⢿⣦⣄⣀⣀⣀⣠⣴⣿⠟⠀⠀⢠⣿⡇⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢹⣇⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⣸⡿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣤⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠻⣿⡿⠃⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣄⣀⣀⣀⣀⣤⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠾⣉⡑⠒⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⣠⣄⣈⡉⠒⠦⢤⣉⡓⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠉⠑⠢⣄⠀⠉⠑⠲⠤⢭⣙⠒⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠒⠉⠙⠪⢷⣢⣄⣀⠀⠀⢀⣴⡾⠛⠉⠉⠉⠑⠲⢤⡀⠉⠐⠢⢤⡬⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢶⣚⠻⣄⡀⠀⠀⠀⠀⢀⡤⠭⢷⡤⣀⣘⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠮⢵⣲⣤⠴⠥⢖⣋⠭⠖⠊⠙⡇⢸⡇
⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⠷⢾⠉⠀⠀⢀⣠⠴⠃⢸⡇
⠀⠀⠀⢰⡇⠈⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⣸⡤⠔⠊⠉⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢱⠤⣀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠚⠉⠀⠀⣀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⢠⠀⠀⠉⠓⠦⣄⡀⠀⠈⠉⠒⠦⣄⡀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠚⠉
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠉⠓⠲⡶⠒⠋⠁⠀⠀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉
⠀⠀⠀⠀⠘⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠄⡀⠀⡇⠀⢀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠑⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⠀⡇⠀⠀⢀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠧⠔⠊⠁

⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠖⠒⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠒⠒⠶⠤⢤⡞⠁⢠⣄⠀⡶⣄⠀⠈⠑⣤⠶⠒⠒⠒⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢀⣶⡯⠀⣠⠟⠊⠉⠃⠈⠙⠒⢦⡈⣷⡀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣀⡴⠊⠉⠀⣧⡞⠑⠦⠖⠀⠀⠐⠦⠔⠀⡇⣸⠈⠑⢆⣀⡀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⡇⠀⠈⢳⢹⡇⠀⠀⠀⢤⡤⠄⠀⠀⠀⡿⢙⡏⠀⢸⡇⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠙⢦⡀⠈⠓⠳⣀⡀⠀⠀⠀⠀⠀⢀⡰⠗⠋⠀⢀⡜⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢦⣀⡀⠀⠀⠙⢦⡀⠀⠀⢹⡻⠃⠀⢿⡏⠉⠀⠀⢀⡴⠋⢀⣀⣀⡤⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠉⠙⠓⠒⠲⠿⡦⠀⠀⠈⠉⠉⠉⠀⠀⠀⡖⠋⠉⠉⠉⠁⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⢀⣠⣤⠤⢦⠀⠀⢀⡜⣡⢴⣒⣚⣫⣩⣭⣩⣍⣙⣒⣤⣱⡀⠀⠀⡴⠲⣄⣄⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⡖⢯⠳⠼⡀⢸⠀⠀⢘⡾⠉⠁⠀⠀⢸⣾⠻⣾⠀⠀⠈⠉⠳⡗⠀⠀⣿⠀⠟⢜⡹⣦⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⢏⠂⠀⠀⠀⢸⡀⢀⠞⠀⠀⠀⠀⠀⠉⢸⢸⡏⠀⠀⠀⠀⠀⠙⣄⢠⠏⠀⠀⠀⠘⡹⠃⠀⠀⠙⣄
⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⣷⠋⠀⠀⠀⠀⠀⠀⠀⢸⣼⠃⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠘⢳⡀⠀⠀⠀⠀⢀⡴⠋⠈⠳⣄⠀⠀⠀⠀⢀⠞⠃⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢧⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠱⣄⠀⠀⣾⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⣠⣞⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠻⣄⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠉⠙⠒⠲⠦⠤⠤⣤⣀⣀⣈⣙⣒⣋⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⣙⣒⣋⣁⣀⣠⣤⡤⠤⠤⠴⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠉⠉⠉⠉⠉

⠀⢰⡃⠠⠀⢀
⢀⡈⠙⠂⢀⡀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⣄
⠀⠀⣠⣞⣿⣿⣻⣄⠀⠀⠀⠀⠀⢨⢹⢣⡿⣿⣷⣹⢻⠀⠀⠀⠀⠀⠀⣿⣤⣦⣄⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣼⣽⡅⠀⠀⢀⣭⣷⡄
⠀⠈⢹⣿⡟⢻⣿⡏⠁⠀⠀⠀⠀⢸⣿⣿⣆⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣶⣷⣟⣻⣿⣿⣿⣗⡀⠀⠀⠀⠀⢀⡤⠝⣿⣷⡛⠛⣻⣿⠟⠤⣀
⠀⠀⠸⠿⠃⠘⠿⠇⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠾⠀⠀⠀⠀⠀⠀⠿⠋⠉⠉⠉⠉⠉⠉⠻⠇⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠸⠿⠋

⠀⠀⠀⣰⠂
⠀⠀⠀⠀⠀⠋
⠀⠀⠀⣠⣤⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⢿⣿⡿⠀⠀⠀⠀⠀⠀⢰⣿⡛⠉⢛⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠙⠁⠀⠀⣀⡀
⠀⢀⣴⣶⣿⣶⣦⡀⠀⠀⠀⠀⠸⠙⠻⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠏⠻⢷⣶⣇⡀⢓⣢⣄⠀⠀⠀⠀⠀⠀⠀⢁⣀⣀⣀⣀⣀⣀
⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⠻⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠛⠚⠉⠉⠁⠀⠀⠀⠠⠖⠛⠉⠉⠉⠉⠉⠉⠉⠙⠛⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⣴⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣰⣦⣄
⠀⢹⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⠾⠋⣿⣿⡏⠙⢷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢳⣀⣄⣰⠃
⠀⠈⣭⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢸⡇⠀⢻⣿⠃
⠀⢠⣤⣧⡄⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡶⠊⠀⠈⠲⣾⣿⣿⡆⠀⠀⠀⠀⢸⣇⣀⣸⣿⣶⣄⣀⣀⣀
⠀⠸⠿⠿⢃⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⡿⠀⠀⠀⠀⠀⠀⠘⠿⠿⠋⠀⠀⠀⠀⠀⠈⠿⣿⠇⠀⠀⠀⠀⠸⡟⠛⠋⢹⢿⠏⠉⠙⠿
⠀⠀⠀⠀⠙⠁


⣴⣶⣦⠀⠀⠀⣶⣆⡀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⢂⣀⣀⠶⣶
⠁⢻⣿⣇⣀⣼⣿⣿⠇⠀⠀⠀⠀⠀⣿⣿⣿⠟⠛⢿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⢩⠉⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⣁⣾⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡼⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡟⠛⢛⠛⠛⣛⣛⡛⣿
⠀⠀⠙⠿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣩⣿⢤⢤⣼⠇⠀⠀⠀⠀⠹⣦⣋⠀⢀⣠⡿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠄⠤⠄⣿
⠀⠀⠀⠀⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⢉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠾⠙⠛⠋⠹⠆⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠛⠛⠻⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⡰⠶⠖⠒⠒⠲⠤⠤⢀⡀⠀⡠⣄
⠀⠀⢀⣀⢀⠠⣂⠕⠈⣁⠀⠀⠀⠀⠔⠐⠀⠀⣀⣈⣍⣻⣐
⠀⠀⢀⠈⠹⣪⠀⢀⣤⠡⠤⠱⠐⠒⠚⢾⣙⡉⠁⠀⠀⠀⠀⠀⠑⢄
⠀⠀⢸⢸⢿⢁⠒⠉⡀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡦⠀⠀⠀⢀⣀⣀⡀⣧⡀⡀⣀
⠀⠀⠀⠸⠃⠀⠀⠡⡈⠀⠀⠀⠠⠔⠒⠒⠀⠀⠉⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⠄⣀
⠀⠀⣤⠠⡀⠀⠀⠁⠀⡩⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⢄⡀
⠀⠀⢘⢈⡙⠳⢤⢀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⡂⠤⣀
⠀⠀⠈⠸⠿⢶⣄⠉⠫⢔⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠉⠙⢶⣄⠈⠐⠥⣂⢄⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⢠⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⣤⠀⠀⠊⠔⡂⢀⠀⠀⠀⠀⠀⠀⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡄⠀⢜⣈⡑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⣀⠀⠑⠨⢂⠄⡀⠀⠀⠅⠀⠀⢀⢀⣀⢠⠠⠤⢒⢐⣒⡏⠬⠭⢖⠶⡒⣋⣩⣭⣿⠄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⡀⠉⠒⢅⣀⣠⠉⠭⡽⠖⡲⠂⡋⣝⣑⣔⡤⠴⠴⠐⠿⠭⠭⠭⠁⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⣄⠀⡇⢁⣠⡼⠴⠴⢞⢛⡓⠩⠁⠉⠉⠉⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠬⠾⠛⠓⠉⠂

⠀⠀⠀⠀⠀⢀⣀⢠⣤⣴⣶⣶⣶⣦⣄⣀⣀⣀⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠔⢉⡈⠢⡀
⠀⠀⣀⠔⠊⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠈⡆⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠈⣞⣄⣈⡀
⠀⡎⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⢷⣀⡀⢸⣄⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡃⠀⠒⠀⠀⠤⠄⠀⠀⣤
⢰⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⡄⠀⠹⡉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⡐⢂⠀⢀⠔
⠸⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠁⠀⠠⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠂⣠⠂⠅
⠀⠆⠀⠀⠹⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢁⣴⡻⠛⠒
⠀⠘⢄⠀⠀⠙⠻⣿⣿⣿⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⡦⡔⢄⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⢀⠄⢂⣡⢾⠿⠋
⠀⠀⠈⠐⠄⠀⠀⠙⢿⣿⣿⣆⡀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⡇⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⣧⣴⡿⠞⠁
⠀⠀⠀⠀⠘⠒⠐⠠⠤⠤⢤⠁⠋⢖⠐⠶⣘⢉⠝⠉⠁⠐⠾⠂⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋
⠀⠀⠀⠀⠀⠀⢸⠀⠲⠀⠆⠀⠀⠀⡊⠀⠐⠀⠠⠄⠀⠀⠀⠀⠀⠀⠈⡉⠒⠄⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⢠⠀⣼⣶⣿⡄⠀⠀⢹⣷⣶⣦⣤⣤⣀⣀⡀⠀⠀⠐⠊⣠⣴⡇⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠉⠻⡄⠀⠈⠛⣿⣻⣿⣿⣿⣿⣿⣿⡇⠘⣿⣷⠯⢣⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣠⠌⠑⠀⠈⠉⠙⠛⠛⠿⡇⠀⠏⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈

⠀⠀⠀⢠⠎⠙⢦
⠀⠀⠀⠘⡄⠀⠴⠣⣤⠆⢄⡀
⠀⠀⠀⠰⠩⠿⡄⠀⠹⣄⠚⠙⢦⣀
⠀⠀⣠⣷⡈⠤⠛⣦⠀⠘⢷⡀⠀⠈⠳⣄
⠀⠀⢳⠘⡧⣀⠀⠘⢷⡀⠀⠙⢦⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⢸⠀⣧⣘⣆⠀⠈⢳⡄⠀⠀⠙⢦⡀⠀⣈⢳⣄⠀⠀⠀⠀⡰⠋⡝⠃
⠀⢀⡾⠺⡎⠉⠹⣆⠀⠀⠹⣄⠀⠠⣎⢳⡄⠑⠃⠙⢷⣤⠞⠛⠃⠀⠙⡇
⠀⢸⠁⠀⢣⠀⠀⢻⡄⠀⠀⠘⢧⡀⠉⠀⠻⣄⠀⠀⠀⢻⣄⢸⠀⠀⣀⣧
⢀⡾⢦⡀⡾⣆⠀⠀⢻⣄⠐⢯⡺⢧⡀⠀⠀⢹⣦⠀⠀⠀⢻⣿⠀⠀⠻⡏
⢈⠃⠘⣧⠇⠸⣧⠀⢀⡹⣦⠀⠀⠀⢷⡀⠀⠀⠻⣷⡀⠀⠈⣿⡄⠀⠀⣿
⠸⠀⠀⣿⠀⡀⠙⣧⠀⠹⠘⣇⠀⠀⠈⢷⣄⠀⠀⠈⠁⠀⠀⠘⣿⣄⠀⠹⣇
⡇⠀⢰⣿⡀⠳⠀⢹⡄⠀⠀⢸⣦⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠹⡆
⢳⡀⠘⠁⢻⡄⣧⠈⣧⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢻
⠀⢳⡀⠀⠀⢳⡘⣧⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢳⡀⠀⠀⠷⠚⠁⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠈⣷⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⢈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀
⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠈⣹⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡽⠿⠿⠿⠿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠁⣼⣿⣿⣶⣤⣀⣀⣀⣀⣠⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠉⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣤⣴⡶⠿⣷⣄
⠀⠀⠀⠀⠀⣠⣿⣷⡀⠀⠀⠀⠀⠁⠸⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⡿⠋⠀⠀⠘⢿⣷⣦⡀
⠀⠀⠀⢀⣼⠋⠀⠙⣿⣷⣦⠀⠀⠀⠀⠛⠛⠋⠉⠉⢻⣷⡄⠀⠀⢀⣴⣿⣿⠏⠀⠀⠀⠀⠀⠀⠐⣫⣼⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠉⠻⣿
⠀⠀⢠⡾⠁⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣆⣠⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣬⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⢰⡟⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⢀⣠⣴⡞⢁⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠉
⠀⣿⠃⠀⠀⠀⠀⢻⣿⣿⣷⣶⣶⣿⣿⡿⠋⠀⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠏⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⢠⣿⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠛⣉⣤⡆⢰⡿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⢀⣴⣾⠟⠁
⢸⡟⠀⠀⠀⣀⣀⣀⣀⣤⣤⣶⣶⣿⡟⠉⠀⠀⠀⠋⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠀⠀⠀⠀⣴⣿⡿⠋
⢸⡇⣰⣦⣄⣻⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⣠⣾⣿⠟⠁
⣿⣷⡈⠻⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⠀⣠⣾⣿⡿⠃
⠹⣿⣿⣦⣀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣯⣴⣿⣿⠿⠋
⠀⠀⠙⢿⣿⣿⠦⠄⠀⠀⣠⣶⣾⣶⣾⣿⣦⡼⠟⠉⠀⠙⢿⣇⡀⠴⢶⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⠙⠿⣶⣶⣶⣶⣿⣿⣿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠋⠉