⠀⠀⠀⠀⣀⠠⠤⢀⡀⠀⢀⠠⠤⠴⠆⢄
⠀⢀⡰⠃⠀⠀⠀⠀⠀⡵⢏⠀⠀⠀⠀⠀⠰⡀
⠀⣘⠀⠀⠀⠀⠀⠀⣰⠁⠈⡄⠀⠀⠀⠀⠀⠳
⠀⢭⠀⠀⠀⠀⠀⠀⠙⣄⣀⠞⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖
⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⣶⣶⣿⠀
⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢻⣇
⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⢿⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠈⠒⣄⡀⠀⡠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠛⠛⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⠐⠉
⠤⠄⠴⠐⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠐⠒⠰⠄⠤⠄⠤⠄⠴⠐⠒⠘⠉

⠀⠀⠀⠀⣀⠠⠤⢀⡀⠀⢀⠠⠤⠴⠆⢄
⠀⢀⡰⠃⠀⠀⠀⠀⠀⡵⢏⠀⠀⠀⠀⠀⠰⡀
⠀⣘⠀⠀⠀⠀⠀⠀⣰⠁⠈⡄⠀⠀⠀⠀⠀⠳
⠀⢭⠀⠀⠀⠀⠀⠀⠙⣄⣀⠞⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖
⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⣶⣶⣿⠀
⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢻⣇
⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⢿⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠈⠒⣄⡀⠀⡠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠛⠛⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⠐⠉
⠤⠄⠴⠐⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠐⠒⠰⠄⠤⠄⠤⠄⠴⠐⠒⠘⠉

⠀⠀⠀⠀⣀⠠⠤⢀⡀⠀⢀⠠⠤⠴⠆⢄
⠀⢀⡰⠃⠀⠀⠀⠀⠀⡵⢏⠀⠀⠀⠀⠀⠰⡀
⠀⣘⠀⠀⠀⠀⠀⠀⣰⠁⠈⡄⠀⠀⠀⠀⠀⠳
⠀⢭⠀⠀⠀⠀⠀⠀⠙⣄⣀⠞⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖
⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⣶⣶⣿⠀
⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢻⣇
⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⢿⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠈⠒⣄⡀⠀⡠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠛⠛⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⠐⠉
⠤⠄⠴⠐⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠐⠒⠰⠄⠤⠄⠤⠄⠴⠐⠒⠘⠉

⠀⠀⠀⠀⣀⠠⠤⢀⡀⠀⢀⠠⠤⠴⠆⢄
⠀⢀⡰⠃⠀⠀⠀⠀⠀⡵⢏⠀⠀⠀⠀⠀⠰⡀
⠀⣘⠀⠀⠀⠀⠀⠀⣰⠁⠈⡄⠀⠀⠀⠀⠀⠳
⠀⢭⠀⠀⠀⠀⠀⠀⠙⣄⣀⠞⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖
⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⣶⣶⣿⠀
⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢻⣇
⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⢿⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠈⠒⣄⡀⠀⡠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠛⠛⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⠐⠉
⠤⠄⠴⠐⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠐⠒⠰⠄⠤⠄⠤⠄⠴⠐⠒⠘⠉

⠀⠀⠀⠀⣀⠠⠤⢀⡀⠀⢀⠠⠤⠴⠆⢄
⠀⢀⡰⠃⠀⠀⠀⠀⠀⡵⢏⠀⠀⠀⠀⠀⠰⡀
⠀⣘⠀⠀⠀⠀⠀⠀⣰⠁⠈⡄⠀⠀⠀⠀⠀⠳
⠀⢭⠀⠀⠀⠀⠀⠀⠙⣄⣀⠞⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖
⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⣶⣶⣿⠀
⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢻⣇
⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⢿⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠈⠒⣄⡀⠀⡠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠛⠛⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⠐⠉
⠤⠄⠴⠐⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠐⠒⠰⠄⠤⠄⠤⠄⠴⠐⠒⠘⠉

⠀⠀⠀⠀⣀⠠⠤⢀⡀⠀⢀⠠⠤⠴⠆⢄
⠀⢀⡰⠃⠀⠀⠀⠀⠀⡵⢏⠀⠀⠀⠀⠀⠰⡀
⠀⣘⠀⠀⠀⠀⠀⠀⣰⠁⠈⡄⠀⠀⠀⠀⠀⠳
⠀⢭⠀⠀⠀⠀⠀⠀⠙⣄⣀⠞⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖
⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⣶⣶⣿⠀
⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢻⣇
⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⢿⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠈⠒⣄⡀⠀⡠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠛⠛⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⠐⠉
⠤⠄⠴⠐⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠐⠒⠰⠄⠤⠄⠤⠄⠴⠐⠒⠘⠉