Stimulant Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠈⢷⠒⠒⠒⠀⠀⠀⠇⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⣀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⡆⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⣀⠤⠊⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠄
⠙⠒⠚⠒⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤
⠀⠀⠀⠀⠀⣀⠤⠤⠄⠒⠒⠉⠉⡍⠉⠁⠐⠒⠒⠐⠀⠡⣆⠀⠀⠀⠀⢰⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⣀
⠒⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠀⠿⠀⠀⠀⠀⠈⠐⠀⢳⠀⠀⠀⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⣀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠙⢠⣀⠠⠂⠀⠀⠀⠀⠀⣠⢴⠊⠉⠑⣄⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠶⠚⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢀⠔⠀⠀⠀⢠⠐
⠀⠀⢀⣀⡠⠤⠔⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠊⠀⠀⠀⠂⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢀⠀⠀⠁⠀⠀⠀⠀⠐⡄
⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠤⢀⡀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⡀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣠⠔⠒⠒⢒⣤⡀⠀⠀⠀⠀⠀⣽⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠈⠒⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤
⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⠀⠉⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⢀⡤⠊⡁⠀⠀⠉⠀⠀⠒⡀
⡀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⡠⠼⠇⠤⠀⣀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈
⢈⢦⡀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⡸⠃⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠠⠤⠐⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠁⠀⠑⠀⠀⠀⠑⢄⠀⢀⣠⠴⠊⠀⠀⠀⠀⠠⡀⠀⠀⠀⡠⠒⠒⠒⠒⠀⠄⡀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠐⠒⡂⠉⠁⠀⠀⠀⠈⠰⡄⠀⠀⠀⠀⠀⢸⣀⠠⠄
⠀⠀⠀⢃⠀⠀⠀⠀⠓⡉⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠇⠈⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⢆⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⡌⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠈⠢⢄⣀⡀⠤⠊⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠱⣤⣠⠤⠤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⡀⠤⠀⠄⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠙⠉⠁⠶⠤⣄⢀
⢣⡀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠤⠤⡀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⡨⠀⠀⠈⠐⠠
⠀⠁⠀⠀⠈⠀⠀⠀⣠⠞⠙⠠⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠧⠤⢤⡀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⡰⠊⢀⠁⠀⠀⠐⡄⠀⠀⠀⠊⠀⠀⡷⠐⠒⠀⠤⠤⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠈⠆⠀⠀⠀⠀⠀⠀⠠⠀⣀⠋
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠉⠄⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⡰⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⢤⠄⣀⠀⠀⠀⠀⠤⠄⠀⠀⠀⣀⣀⣀
⠈⠢⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠰⠁⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠆⢀⠁
⠀⠀⠑⣤⡀⠀⢀⡀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⣂⣀⣀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⢰⠀⡅
⠀⡠⠊⠉⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠸⡀⢙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠘⡂⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠤
⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠉⠀⠀⠠⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀
⣆⣀⣀⡀⣀⣀⡀⠈⣀⠀⠀⠀⠀⠐⣏⣀⣀⣀⣀⣀⡀⠀⡀⠀⠀⠀⠀⠀⣼⣄⠒⠈⠁⠀⠀⠀⠀⠀⣀⠐⠉⠀⠀⠀⠉⠉⣻⠀⠀⠀⠀⠀⠀⣀⠊
⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠋⠉⠉⠉⠉⠉⠉⠙⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⢀⣀⣠⡤⠤⠤⢤⣄⣀⡀⠀⠀⠈⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⣄⠀⠀⠈⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⢀⡴⠋⠀⣠⠤⠤⠤⠤⡤⠤⠤⢤⠤⠤⠤⠤⣄⠀⠙⢦⡀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢠⡋⠀⠀⢸⠁⠀⠀⠀⠀⠳⠤⠤⠞⠀⠀⠀⠀⠈⡇⠀⠀⠙⣄⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠈⠑⠲⢼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⣆⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⡼⠀⠀⢰⠒⠦⣄⡀⠀⠀⠈⠑⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⡆⠀⠀⢧
⠀⠀⠀⠀⠀⠀⡇⠀⠀⡾⠀⠀⠀⠉⠓⢦⣄⡀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢷⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠉⠓⠦⣄⡀⠀⠀⠈⠙⠲⢤⣀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢳⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠈⠙⠳⢤⣀⠀⠀⠀⡾⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢳⠀⠀⠸⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣀⣀⡀⠉⠓⠢⣄⡀⠀⠀⠈⠙⠲⠤⠇⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠹⡀⠀⠀⠀⢸⠀⠀⣠⠖⠋⠉⠁⠈⠉⠙⠲⣄⠀⠈⡗⠢⢄⡀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠙⣄⠀⠀⢸⠀⠀⠀⠠⠖⠋⠉⠉⠙⠲⠄⠀⠀⠀⡇⠀⠀⣨⠃⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠈⠳⣄⢸⠀⠀⠀⠀⠀⠐⠉⠉⠂⠀⠀⠀⠀⠀⡇⣠⠞⠁⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠙⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠋⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠈⠉⠉⠓⠒⠒⠚⠉⠉⠁⠀⠀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⣄⣀⣀⣀⣀⣀⣀⣠⠤⠖⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢰⢿⠀⠀⠀⠀⠀⠀⠀⢀⡴⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠟⠃⠀⠀⡟⡋⢸⠀⠀⠀⠀⠀⠀⠀⠉⠓⠼⠆⠀⠀⠀⠀⠀⠀⠀⣤⢤⣀⠀⠀⢀⡶⡴⡿
⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠟⠉⠛⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣠⣄⣀⣀⡀⠀⠀⠈⠓⠛⠀⠀⠸⠷⠾⠁
⠴⣞⠛⢦⠀⠀⢀⣠⠤⠶⠖⠒⠦⢄⡀⠀⡶⠚⠛⠛⠛⡇⠀⠀⡏⠉⠉⠁⠀⢹⡴⠻⠀⠀⠉⠉⠉⠛⠓⠲⠦⠤⣤⣀⣠⡴⠶⠤⠤⢤⣤⣄⣀
⠀⠀⠙⢋⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⢹⢀⡇⠀⠀⠀⠀⠙⠶⠞⠁⠀⠀⠀⠀⠸⣇⠰⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠁
⠀⠀⠀⢺⡄⠀⠀⠀⣠⢦⡀⠀⠀⠀⢨⢜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠲⠦⣄⡠⠟⠀⠀⠀⠀⠀⢰⡇⡸⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⢧⠀⠀⠀⠘⠊⠁⠀⠀⣠⣟⣘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡤⠖⠉⠀⠀⠀⠀⠀⣠⣴⠾⢧⣈⡉⠑⣲⠄⠀⠀⠀⢸
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢋⠃⠀⠀⠀⠀⠀⠰⠿⠭⣤⣄⣀⣬⠟⠋⠁⠀⠀⢀⡤⠞
⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⡤⣄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⡇⠀⠀⠀⠀⠈⠛⠓⢲
⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠙⠋⠀⠀⠀⠀⢸⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣏⠘⠒⠢⠄⠠⢀⡀⠀⠀⠀⠀⢀⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢀⡀⠀⠸⡄⠀⠀⠀⠀⠀⠀⣀⠔⣰⠷⣌⠲⢤⣀⣀⣀⠀⠄⣊⡵⣋⡈⡙⠓⠶⠦⣤⣄⣀⡉⠑⠒⣤⡜⠀⡆⠀⢀⣀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠻⠃⠀⠀⢧⡤⠤⠤⠤⠒⣋⣥⠞⢹⡷⡈⠙⠒⠦⠦⠖⠒⠋⣡⣾⠉⢻⠇⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠧⣤⣭⣭⣭⣄⣀⣀⣤⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠛⠋⠉⠀⠀⠀⠙⠛⠃⠀⢰⣶⠆⠀⠀⠁⡈⠖⠋⠰⡋⣳⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⢀⡴⠒⡆⠀⠀⠀⠀⠀⠀⠀⣻⡍⢿⠂⠀⡞⢳⠀⠰⠿⠛⠀⠀⢸⡖⠁⠀⠀⣠⠠⡧⣮⡇⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁
⠀⠀⠀⠀⠀⠀⠘⠛⣾⠁⠀⠀⠀⠀⠀⠀⢸⡿⢯⡉⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡜⠹⣄⣠⡼⠷⠒⢲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠈⠑⠤⣄⡀⣠⠤⠤⣤⠒⠒⠶⣄⣠⠎⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢀⠝⡡⠀⢄⠀⠑⡄⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡙⠛⠃⠒⠒⠛⠛⠒⠓⠀⠀⣠⣻⠎⣹⠆⣛⣈⠆⠄⠀⣀⢤⠻⢆⠀⠀⠀⠀⠰⢇⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⢀⠜⠓⠢⢧⡭⡴⠏⣩⡌⢀⠚⢁⠸⣀⡸⢧⡀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠙⢾⣴⡿⠛⢯⣀⠬⣀⠼⠁⡞⢣⠀⠀⠀⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠗⠀⠀⢠⠃⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠻⢄⣞⠒⡺⢀⡜⠀⠀⠀⠀⠀⠙⠓⠢⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⠸⡄⠀⠀⠀⢀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣀⠀⠀⠀⠀⠀⠈⠓⠲⠖⠋⠀⠀⠀⠀⢀⣀⣴⠾⠛⡓⢦⠀⠀⠀⠀⠀⠀⠀⠰⡊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣲⠆⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠛⠣⣼⠲⣇⢻⢲⡇⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠈⠦⢟⡲⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡁⣀⣀⡠⠤⣤⠀⠀⠀⢀⣼⡀⠀⠀⠀⢀⣠⠷⠋⠉⠒⠢⢄⡀⠀⠘⡏⠉⠉⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⡰⠁⠀⡠⠖⠁⠀⠓⠶⠶⠚⠋⠀⠀⠀⣀⠀⠀⠀⠈⠑⠠⣘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢁⡤⠊⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣧⠝⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⢀⣴⠊⠘⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⣠⡶⠚⠛⠉⠙⠓⢶⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢫⢤⠀⢀⣤⢟⠉⠀⢀⠤⠤⣒⡄⢀⠉⡀⠀⢀⠀⠙⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣀⣠⡟⠀⠈⡡⠂⠈⠓⢛⡈⠈⢀⣀⣀⣀⢀⣀⣁⣉⣱⠛⠟⠂⠰⡭⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⢹⡯⢟⡩⠝⠊⠉⠉⠑⠄⡎⠉⠉⠹⣀⠏⠀⠀⠈⡟⢀⠀⠀⠈⠉⠉⠒⢲⠞⠋⠐⠛⠒⢲⣄
⠀⠀⠀⠀⠀⠀⢠⡏⠀⢪⠀⠀⢠⡄⠀⠀⡸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡟⠒⢢⡥⠂⠀⠀⢀⡿⠄⠀⠀⠀⠀⠨⠙⢷⡀
⠀⠀⠀⠀⠀⠀⣼⠀⠀⠊⡆⠀⠀⠀⠀⠘⠓⢧⠀⠀⠀⠀⠀⠀⠀⠀⣷⠊⠁⠀⠀⠠⢖⣋⣉⣲⠆⠁⠀⣀⠴⠀⠈⣷
⠀⠀⠀⠀⠀⣀⡿⠀⢸⠀⠸⡀⠀⢰⡆⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣸⢃⡀⠀⠀⠀⠀⠀⢀⠉⠁⠀⠀⠈⠉⠓⠀⠀⣹
⠀⠀⠀⢠⡞⠁⠀⡠⠚⢀⠀⢣⠀⠀⠀⠀⠀⣸⢇⡠⠀⠀⠀⣀⡴⣛⡒⠦⠤⣀⣀⠀⢠⡄⢀⠀⠀⠀⠀⠀⡄⠓⢄⠛⢦⡀
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠀⠘⠶⣂⡨⠥⠚⠙⢧⠍⢉⣉⠉⠱⠻⡹⠃⢄⠀⠀⠈⠉⠁⠓⠒⠒⠒⠒⠚⢉⣅⠀⠀⠃⠀⠹⣆
⠀⠀⠀⣿⠀⠀⢰⠀⠀⠀⠀⣠⣲⠄⠀⠀⠀⠀⣶⣲⠀⢽⠀⠒⠓⠀⢰⠊⠀⣠⠸⢽⠀⠀⠀⠀⠀⠹⠂⠀⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠸⡆⠀⠈⢄⠀⠀⠀⠀⠋⠀⠀⠀⠀⠈⡉⠂⢀⠈⢀⣀⣀⠤⢄⢀⡜⠈⠂⠈⠁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡿
⠀⠀⠀⠀⠹⣦⠀⠈⠰⠀⠀⠀⠀⡀⢀⠀⠀⠀⢣⠀⠀⣈⢃⢀⡀⠀⠀⠹⣄⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⢠⠒⠁⢀⡼⠃
⠀⠀⠀⠀⠰⡇⠀⠀⠁⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⢀⠼⠫⣜⡡⣂⠀⠰⢈⣈⢦⠀⠀⠉⠀⠒⠂⡰⠀⠀⠀⠀⠈⠀⠀⣯
⠀⠀⠀⠀⠀⢷⡀⠀⠈⠀⡀⠀⠀⠀⠀⠠⡄⠀⠠⠁⠀⠀⠀⣷⠏⠙⣄⢢⠀⠌⡀⠀⠀⠀⡤⡊⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⡐⠆⠈⠀⠀⢃⠀⠀⣀⠜⠁⠀⠀⠀⠙⠒⠂⠀⠀⠀⠀⢀⡀⡥⠛⠂⠀⠁⠀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⣦⠉⠐⠀⠠⡀⠀⠈⠉⠁⠀⣀⠤⢖⣛⠡⢠⠀⠀⠀⠀⠘⢤⠖⠁⠀⣠⠶⠚⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡠⠊⠀⠀⠀⠀⠀⠊⠀⠀⠀⢰⣴⡋⠀⠀⢀⠀⠀⠀⠁⣤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠘⠃⠀⠀⡝⠀⡠⠶⣧⣄⣤⠶⠿⢚⠉⠑⠂⠈⣗⠒⠚⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠉⣹⠓⢦⡄⠀⠀⢰⠀⠈⠀⠠⡄⠀⠀⠀⠀⠸⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣭⣥⡼⠃⠀⠀⠀⠀⠀⠘⠂⠃

⠀⠀⠀⠀⠀⣞⠛⠛⣷
⠀⠀⠀⠀⠀⢿⣤⠞⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣴⢷⣄⠀⠀⠀⠀⢀⣴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⠀⠀⠀⠀⢰⡟⠻⣦⡀⠀⠀⢀⣀⡾⠃⠀⠘⢷⣄⣀⣴⠟⠁⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣄⠀⠀⢀⣿⠀⠉⠻⢶⡄⢀⣿⠀⠀⠀⠙⢶⣴⠞⣻⠁⠀⢀⡤⠞⠁⠹⡁⠀⠀⠘⣇⠀⠀⠀⣀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣾⠁⠈⠻⢦⣼⡏⠀⠀⠀⠀⠙⠻⠃⠀⠀⣠⢤⡀⠈⠛⠉⣴⠚⠁⠀⠀⠀⠀⠹⡄⠀⠀⠻⠶⠾⠛⠋⠉⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠛⠲⢦⣤⣠⡟⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣀⡠⠴⠺⡏⠄⠀⠀⢀⠀⠀⠀⡸⢀⡀⠀⠀⠀⠀⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⣀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠹⡌⠒⣊⣨⠁⠀⠰⠗⠉⢣⡀⠀⠀⠀⠀⢿⣧⣤⣀
⠀⠀⣤⣤⣤⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠀⢰⡋⠁⠀⠀⣀⡀⠀⠀⠀⣰⠏⠉⣹⡇⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⣠⠞⠉⠺⣌⠒⣚⣩⣤⠃⠀⠀⠰⠿⠚⠋⠃⠐⡀⠀⠀⠀⡠⢔⡟⢁⣤⡄⠀⣴⡟⠁
⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⢱⡄⠀⠀⠀⢾⡀⠀⠀⠀⠈⢻⡁⢀⡎⠀⠀⠀⠀⠀⠀⠀⠘⡀⠠⣀⠔⣋⠴⠋⣀⠀⠈⠀⠀⠈⠛⠳⣦⣀
⢀⣠⡴⠟⠋⠀⠀⠀⠀⠀⠀⣠⢤⠀⠀⠱⠏⣠⠔⠳⣄⡼⠃⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⣀⠤⢐⡿⣤⠴⠋⠀⠀⠈⠻⠇⠀⠀⠀⠀⣀⣠⡼⠟⠃
⠻⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠗⠀⠀⠀⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣀⠄⠂⢀⣠⠤⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣏⠁
⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⢮⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠴⠖⠛⠉⠀⠀⠀⠰⡖⣳⡀⢠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⢱⠙⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡴⠾⡆⣤⢢⠀⠀⢠⣜⢉⡟⠁⠀⢇⠀⠀⢠⣤⣤⣤⣤⣤⣸⣷⡀
⠀⠀⣰⡟⠁⠠⢦⡤⣄⢠⡏⠀⠀⣴⢦⠀⠀⠘⠋⠉⠉⠂⡀⠀⠀⠀⠀⠀⢀⡜⠡⠟⠲⠃⠈⢺⠀⠀⢸⠈⠉⠀⠀⠀⠸⡀⣀⠼⠋⠁⡍⠀⠈⠉
⠀⠀⠛⠳⠶⠶⢿⣦⠉⢸⣀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠙⣧⣀⣀⡩⠔⢋⣀⠀⠠⡾⠃⠀⠀⠀⣀⣸⡀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢠⢁⡀⠤⢰⠆
⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠈⠓⢤⡀⠀⠀⠀⠺⠷⠀⠀⠀⡀⡸⢶⣢⡤⠀⠙⠻⣶⡀⠀⠀⢀⣼⢉⠀⠉⠙⣳⠶⢤⣄⡀⠀⠀⠀⠀⠉⠁⠀⡐⠁
⠀⠀⠀⠀⠀⠀⣸⡇⠀⢀⣀⣠⠀⠉⠲⣄⠀⠀⠀⠀⢀⡔⣰⠃⠀⠀⠶⣝⣳⣶⠶⣥⣀⣰⠁⠀⣀⡙⠄⢀⠅⡱⠰⠂⡏⢢⠀⠀⠀⠀⠀⣜
⠀⠀⠀⠀⠀⠀⠻⠟⠛⠋⢹⡟⠀⠀⣀⣴⠿⣦⣀⡴⣋⠜⠁⣿⢷⣄⡀⢿⡛⠋⠀⠉⠉⢉⡖⡶⠹⡒⣤⣠⣀⡐⢲⡔⣉⡼⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣴⠾⠋⠷⠄⢹⣿⠉⢁⣄⠠⣿⠀⠈⠛⠿⠛⠢⣄⠀⠀⣸⢓⡭⠞⣠⣽⠇⠉⠉⠉⠉⠉⣀⡀⠀⠀⠀⠀⠀⢀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⣿⡄⣧⢾⣼⡟⠀⠀⠀⠀⢀⠔⠚⠁⠀⡏⠀⠀⠀⠀⢹⠀⠀⠀⠀⣴⢯⡲⠜⣆⠀⠀⠀⠘⠧⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠸⣧⠀⠀⢸⡇⠀⣀⠤⠊⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⣼⠀⠀⠀⡼⠋⠮⣙⣞⣧⠠⠤⠐⠒⠒⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠓⠶⣿⠀⠀⣿⠇⠀⠑⠂⠠⠀⣀⣀⡀⠀⠘⣄⠀⠀⣠⠇⠀⠀⣸⠁⠀⠀⠀⡾⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢠⣤⣄⡀⢀⣿⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠉⠉⠀⠀⠀⠀⢇⠀⠀⠀⣰⠁⠀⠀⠑⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠉⠉⠛⠛⠛⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⣀⢠⡄⠀⠀⠀⠀⠀⢀⠗⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠉⠁⠀⠀⡇⠀⢀⡴⡆⠀⡜⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠉⠀⢇⢠⠁⠀⢰⣠⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠘⠆
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣠⣶⠿⠛⠋⠉⠙⠛⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠋⠉⠙⠛⠿⣶⣄
⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⢸⡿⠀⠀⠀⠀⢰⣶⠶⢶⣦⣀⣈⣿⣆⣀⠀⠀⣀⣰⣿⣁⣀⣴⡶⠶⣶⡄⠀⠀⠀⠀⢿⡇
⠀⠀⠀⢸⣇⠀⣿⡆⠀⢸⣿⣤⣴⡿⠛⠛⣿⡟⠛⢿⡿⠛⢻⣿⠛⢿⣿⣤⣤⣿⠇⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠘⣿⣄⠘⢿⣦⣀⣈⠉⠉⠀⠀⣰⡿⠀⣰⡾⢷⣆⠀⢿⣆⠈⢿⣯⣍⣁⠀⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠈⢿⣦⣄⡉⠛⠛⠀⢀⣠⣾⠟⠁⠀⣿⡇⢸⣿⠀⠈⠻⣷⣄⡈⠙⠛⠁⢀⣠⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠛⠋⢁⣴⡶⠿⠿⠿⠿⠿⠿⣶⣦⡈⠙⠛⠿⠿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⣠⣴⣦⣄⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢿⣧⣼⡿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠶⠾⠿⣷⣦⠀⠀⠀⠉⠉⠀⠀⠀⣶⡾⠿⠷⠶⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⢸⣿⠀⠀⣠⣶⣶⣄⠀⠀⣿⡇⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡟⠀⠀⠀⢸⣿⠀⠀⢿⣧⣼⡿⠀⠀⣿⡇⠀⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣷⠀⠀⠀⣸⣿⠀⠀⠀⠈⠁⠀⠀⠀⣿⡇⠀⠀⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⣿⡟⠋⠀⠀⣰⡾⢷⣆⠀⠀⠛⢻⣿⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠻⣷⣾⠟⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣄⣀⣀⣀⣀⣠⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⡀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⣀⠀⢀⢀⡀⢀⢀⡀⡀
⠀⠀⠀⠈⡴⡬⠊⡑⡯⠷⠀⡀⠀⠀⢀⣀⡀⡀⠀⢪⠭⢆⡰⠭⡕⠀⠀⢀⣇⠀⢏⡶⡼⠀⢂⣋⠓⣔⢃⣩⠂
⠀⠀⠀⢠⣙⣂⡀⣴⠀⢀⠀⠋⣍⢩⢭⡉⡭⠇⠀⠄⠀⢸⡇⠀⠢⠀⢀⠀⠇⢀⠀⣝⠀⠀⢠⠬⠿⡬⠿⢥
⠀⠀⠀⢸⣤⣤⣅⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣤⡜⢣⣤⡾⠀⢈⠐⡐⣈⠈⠊⠊⠀⠚⠓⠞⠙⠲⠚⠂
⠀⠀⠀⠀⢀⣠⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡤⣄⠀⠀⢀⠤⢄⠀⠀⠤⢄
⠀⠀⠀⢠⠋⠀⠴⠠⠙⣆⠀⡔⠐⠀⡤⠐⠐⠄⠀⠺⠦⢸⡇⠼⠇⠀⠸⢌⢩⣷⡻⢇⠘⠀⠴⠓⠾⠶⢷⠺⠄
⠀⠀⠀⢸⡀⠠⢉⠀⠀⡞⠀⠃⢈⡁⠎⣈⢀⠄⠀⠀⢈⣿⣿⡁⠀⠀⠀⠠⠢⢘⢸⢢⠀⠀⠀⠀⢺⡇⠠
⠀⠀⠀⠀⠉⠢⠤⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠤⠄⠀⠀⠀⠈⠋⠰⠼⠋⠀⠀⠈⠁⠛⠒⠃⠉

⠀⠀⠀⠀⠀⠀⣶⣶⢠⣶⣠⣶⢠⣖⡦⠀⠰⢶⡶⢠⣶⣶⠀⣴⣆⠠⡆⢰⣄⣴⢰⡆⣴⣄⣶⢠⡶⠶
⠀⠀⠀⠀⠀⠀⠿⠭⠜⠏⠿⠻⠰⠯⠟⠀⠀⠸⠇⠸⠏⠻⠴⠟⠻⠞⠇⠸⠙⠿⠸⠇⠿⠙⠿⠘⠧⠿⠃

⠀⠀⠀⢠⢲⡄⠀⠀⡄⢂⠀⡀⠀⡀⠀⡀⠀⡀⠀⠀⠂⠀⠀⠂⠀⠀⠀⢀⣦⢶⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⡀
⠀⠀⠀⠀⢸⡅⠀⠀⡯⢠⠀⡥⢴⣏⢂⡳⠤⡅⠀⢀⠀⣠⠀⠀⠀⠀⠀⠈⠀⠀⡿⡀⠀⠀⡷⢴⣂⠀⣐⣧⡆
⠀⠀⠀⠠⠀⢙⠶⡞⠁⡐⠀⠡⠴⠋⣋⠽⠤⠃⠀⠀⠉⠳⠋⢱⡆⠀⠀⢨⠀⢼⢲⠚⠀⠀⠷⠐⠘⠚⠛⠂⠆
⠀⠀⠀⠀⠈⠈⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠐⠂⠚⠂⠚
⠀⠀⠀⠀⢎⣉⣉⣵⠀⠀⠀⠀⢐⣛⢻⣛⠀⠀⠀⠤⠠⡄⢀⠄⠠⠀⠐⢚⣯⡿⣽⡿⠕⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠮⡄⢈⠻⢀⡀⠀⠀⠠⣮⢩⣰⡆⠀⠀⢔⡢⠃⠙⢴⡲⠀⢸⡆⣰⡟⡠⡿⢰⠀⠁⠁⣞⠟⡃⠉
⠀⠀⠀⠀⢠⠢⠔⣤⣠⠇⠀⠀⡒⣚⢹⡒⡂⠀⠀⠈⠁⠢⠀⠠⠁⠀⢈⢃⡺⣧⢭⣩⢼⠀⠁⠀⠘⠖⠁⠂
⠀⠀⠀⠀⠉⠁⠈⠉⠁⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⣀⣴⠶⠛⠛⠋⠛⠛⢶⣤⣠⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢫⣁⠀⠀⣀⣿⠋⠁⠀⢀⡠⣤⠶⣄⡀⠉⠉⠀⠀⠀⠈⠹⣦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠳⢫⠔⢈⡯⠼⠓⠒⠆⠁⠀⠀⠉⠃⠈⠑⠚⠓⢤⠾⡷⠄⠀⣍⣉⠳⣄
⠀⠀⠀⠀⠠⣼⠓⣶⠖⣚⡣⠤⠖⠶⢅⠀⡴⠒⠒⠲⡄⢀⡞⠋⠉⠙⣦⠋⠉⠙⠓⠒⠲⠤⠤⣀⣈⡦⠤⠼⠷⣀⣀⡀
⠀⠀⠀⠀⢠⡞⠉⡵⠋⠁⠀⠀⠀⠀⠀⢣⡇⠀⠀⠀⠙⠊⠀⠀⠀⠀⣿⣀⡒⠠⢤⡀⠀⠀⠀⢸⢃⠀⠀⠀⠀⠀⠀⢷⣤
⠀⠀⠀⠀⡿⠀⠀⣱⠀⠀⠘⠽⠂⠀⣠⡎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡩⠟⠁⠀⠀⢀⣠⢾⡘⠂⢤⡀⠀⠀⢰⠀⠙⣷⡀
⠀⠀⠀⢸⡇⠀⠐⠁⢧⠀⠀⠀⠀⠀⠁⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠐⠫⠤⣤⣬⠟⠉⠀⢀⡤⠚⠀⠀⢸⡇
⠀⠀⣀⡼⠇⠀⢴⠀⠘⡆⠀⠀⠷⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⣼⠣⣀⡀⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠈⢹⢀⠀⢈⡟
⢠⡿⠋⠀⢀⡔⠊⢀⠀⢱⠀⠀⠀⠀⠀⡠⣸⢮⡂⠄⡀⠀⠀⣀⡼⣋⡓⠲⠤⢤⣀⣀⠒⣤⡌⢀⠀⠀⠀⠀⠀⠀⣸⠘⠢⡈⠳⣦⡀
⣿⠁⠀⠀⡈⠀⠀⠉⠀⠈⢧⣒⣒⣈⠥⠚⠹⣧⡍⠙⣒⠙⠉⠱⢮⣹⠇⣀⠀⠀⠀⠈⠉⠁⠓⠒⠓⠒⠀⠤⠞⠋⣁⠀⠀⠙⡄⠈⢻
⣿⠀⠀⠀⡇⠀⠀⠀⠀⢀⡤⡄⠀⠀⠀⠀⠀⢶⢠⠄⢹⢧⠀⠴⠆⠁⢀⡴⠁⠀⡀⣾⣳⠀⠀⠀⠀⠀⠘⣷⠂⠀⠉⠀⠀⠀⢰
⢹⡄⠀⠀⢣⠀⠀⠀⠀⠘⠲⠁⠀⠀⠀⠀⢸⠻⢍⠀⠀⠃⠀⠀⠀⠀⠈⠀⢀⠜⠡⠠⠟⠒⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⢻⡄⠀⠈⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠈⠑⢠⠖⠉⠚⠉⠙⢢⡎⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠁⠀⣰
⠀⠀⣿⠂⠀⠀⡎⠀⠀⠀⠀⠰⡒⠂⠀⠒⠒⠸⠀⠀⣰⡇⣣⢐⡒⠀⠀⠀⡹⢆⠀⠀⠀⢼⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡾⠋
⠀⠀⣿⠀⠀⠀⠇⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠠⠊⠑⠲⢖⠊⣵⣄⠈⠠⠣⠜⣣⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⡄⠀⢸⡇
⠀⠀⠘⣧⡀⠀⠀⠢⢀⡀⠀⠀⠀⠀⢑⠄⠀⢰⠁⠀⠀⠀⢈⡿⠃⠈⠲⣉⠆⠴⢁⠀⠀⠀⠀⠴⠁⢀⣀⡀⠀⠀⡀⠔⠀⠀⢸⡇
⠀⠀⠀⠈⠻⢦⣀⡀⠀⠀⠈⢉⠗⠈⠀⠀⠀⠸⡀⠀⢀⡴⠋⠀⠀⠀⠀⣈⠙⠓⠁⠀⠀⠀⠀⣀⡤⢠⠜⠋⠉⠉⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⢷⡈⠉⠒⠤⢀⡀⠀⠈⠉⠉⠀⠀⣠⠤⢖⢛⡝⣍⡄⠀⠀⠀⠀⠘⠤⡴⠋⠀⠀⣰⠶⠚⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⡀⠊⠀⠀⠀⠀⠀⢠⠊⠀⠀⠈⠢⣗⠖⠁⠀⠀⠀⠀⠀⠀⠀⠢⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠁⠀⠐⢲⠂⠀⣠⣼⣄⠀⣀⣤⣾⡵⠟⠒⠠⢀⠘⡦⠤⠴⠶⠿⠋
⠀⠀⠀⠀⠀⠀⢀⡴⠒⠶⣤⣄⡀⠀⠀⠀⢠⢃⠀⠊⠀⢉⠉⠉⠉⠁⠀⢰⡢⠄⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠘⣷⠀⠾⠇⠈⣿⠆⠀⠀⠙⠁⠀⠠⣄⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠙⠷⠛⠛⠛⠁
⠀⠀⢀⣀⣀⣀⡀
⠀⠀⢿⡉⠉⢉⣿
⠀⠀⠸⣧⣾⠋⠉
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡸⢻⡿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠷⣂⡀⠀⠀⠀⠈⠀⢙⡿⣷⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢟⠁⠀⠀⠀⠀⠳⢌⣛⣋⣤⡄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠘⠁⠀⠀⠆⠰⠒⠉⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣟⣳⠀⠐⠀⣴⠀⠀⠀⠉⠀⠀⠰⠀⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠵⠠⠀⠐⠀⠄⠉⠀⠀⠀⠒⢠⣶⠀⠀⢰⡹⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠩⠰⢞⡀⡀⢠⠄⣴⡟⢂⠀⠀⠀⠑⠰⠀⠶⠍⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣠⣴⣧⣹⣀⣠⣄⣂⣥⠒⠤⠀⢚⠻⠂⠀⠀⠀⠃⠈⢫⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡯⡀⠀⠉⠈⠛⢻⣿⣿⣿⣿⣿⣿⡦⢸⣧⠀⠘⠃⡀⢀⡀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⢀⡠⢦⣤⡔⠚⠣⡙⢆⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣧⣽⡧⠀⢀⡀
⠀⠀⢀⡴⠋⠀⠀⠙⢿⣄⠀⠈⢦⡑⢄⠀⠀⠀⠀⠠⠾⣿⣿⣿⣯⣤⠻⠈⢁⠀⠀⠐
⠀⢠⠋⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠙⢦⡑⢄⠀⠀⠀⠐⠻⣿⣿⣿⣿⡳⢂
⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠙⢦⡢⡀⠀⠀⢶⣿⣿⣿⣿⠟
⠀⢸⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠈⠻⣮⡶⠚⠋⢡⣿⣿⣇⣟⠠⠄
⠀⠸⣄⠈⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀⣹⣦⠀⢀⣈⠿⠀⠀⣸⣿⡟⠁
⠀⠀⠘⢷⣄⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⠛⠋⠉⠀⢀⣤⡾⠟⠁
⠀⠀⠀⠀⠉⠳⢦⣄⣀⡀⠀⠀⠀⢀⣀⣀⣤⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠉⠁
⣿⡿⠻⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠞⠛⠛⠛⠛⠛⠛⠳⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⣀⣤⣤⣴⣶⠶⣶⣤⣤⣀⠀⠉⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠀⣠⡶⠟⠉⠁⠀⠀⣿⠀⣿⠀⠈⠉⠻⢶⣄⠀⠉⢳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⣠⡀⠈⠻⣦⡀⠀⠀⢀⣿⠻⣿⡀⠀⠀⠀⠀⠉⢳⣄⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⣼⠏⠻⣦⡀⠈⠻⣦⣴⠟⠁⠀⠈⠻⣦⡀⠀⠀⠀⠀⠹⣧⠀⠘⣷
⠀⠀⠀⠀⠀⠀⣸⠇⠀⣼⠇⠀⠀⠈⠻⣦⡀⣾⠁⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠸⣧⠀⠸⣇
⠀⠀⠀⠀⠀⠀⣿⠀⢠⡿⠀⠀⠀⠀⠀⠈⠻⣿⣄⣠⡾⠛⢷⣄⣠⣿⠀⠀⠀⠀⠀⠀⢿⡀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠷⠶⠿⠉⠉⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⣿⠀⠰⠶⠶⠶⠆⠀⣿⡀⠀⠀⠀⠀⠀⣾⠁⠀⣿
⠀⠀⠀⠀⠀⠀⢹⡆⠀⢻⡆⢠⣤⣤⣤⣤⡄⣿⣤⣤⣤⣤⣤⣤⣴⣿⠻⣦⡀⠀⠀⢰⡟⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⢻⣼⣇⠀⠀⣿⠀⣿⠀⢠⣤⣤⣤⡄⠈⣿⡀⠈⠻⣦⣰⡟⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠙⣿⣀⣀⣿⠀⣿⠀⠠⡄⢠⣤⠄⠀⣿⠻⣦⡀⠈⠋⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⠉⠙⠿⣯⣀⣿⠀⠀⠀⠀⠀⠀⠀⣿⣴⠾⠋⠀⣀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⠀⠉⠻⠷⠶⠶⠶⠶⠶⠾⠋⠀⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⢦⣤⣤⣤⣤⣤⣤⡴⠶⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠋⠉⠉⠀⠀⠀⠀⠉⠉⠙⠒⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⢀⣀⡤⠤⠶⠖⠲⠶⠤⢤⣀⡀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢹⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡄⠙⢢⡀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣠⠋⠳⣄⢸⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡇⠀⠀⠙⣄⠀⠀⢳
⠀⠀⠀⠀⠀⠀⡼⠀⠀⢰⠃⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡇⠀⠀⠀⠘⡆⠀⠀⢧
⠀⠀⠀⠀⠀⢀⡇⠀⠀⡏⠀⠀⠀⠀⢸⠀⠀⠀⢀⡤⠞⠉⢢⠀⢰⠁⠙⡄⠀⡇⠀⠀⠀⠀⢹⠀⠀⢸⡀
⠀⠀⠀⠀⠀⢸⠀⠀⢸⠇⠀⠀⠀⠀⢸⠀⠀⡞⠁⠘⣦⠴⠋⠀⢸⡀⢀⠇⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⠀⠓⠶⠊⠁⣀⣀⣀⠀⠙⠉⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠈⡇⠀⠀⣇⠀⠀⠀⠀⢸⠀⢀⣀⣀⣠⠎⠀⢀⡴⠳⣄⣀⠀⠀⡇⠀⠀⠀⠀⣸⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⢳⠀⠀⠸⡄⠀⠀⠀⢸⠀⢸⠀⠀⢸⣆⡴⠋⠀⣰⠃⠈⡆⠀⣧⡀⠀⠀⢠⠃⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠙⣄⠀⠀⢸⠀⠘⠒⠒⠚⠈⠓⠒⠚⠙⠒⠊⠀⠀⡇⠙⢦⣠⠋⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠈⠣⣀⠘⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⣇⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠈⠉⠓⠒⠶⠦⠶⠶⠒⠚⠉⠁⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⣄⣀⣀⠀⠀⠀⠀⣀⣀⣠⠤⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣶⣤⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠛⢿⣿⠿⣿⣿⣿⣥⡄⠀⠀⠀⠀⠀⠀⣠⣤⣤⣠⣿⣿⣿⠿⣿⡟⠛⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⣿⡏⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣿⣿⣿⠀⢹⣿⠀⠹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠘⣿⡿⠁⣠⣄⣀⣀⠀⠻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⡿⠃⢀⣀⣠⣤⠀⢹⣿⠃
⠀⠀⠀⠀⠀⠀⠘⠃⠀⣿⣿⣿⣿⡇⢀⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⠀⣿⣿⣿⣿⣇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⢻⣿⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣶⣶⣶⣶⣾⠿⠛⠉

⠀⠀⢠⡀⠀⠀⠀⣀⠀⢠⣶⠀⠀⠀⢤⡀⢠⡆⣀⡤⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠐⠂⠀⡰⠀⠀⠀⢹⠀⠀⡆⠀⢷⣿⢁⠟⠡⠎⠠⣄⡀⠀⠀⠀⠀⠀⢤⠀⢀⡤
⠀⠀⠀⠺⠛⠀⠱⠄⠫⠋⡠⠀⠈⡇⢀⠀⠁⠀⠀⠀⠀⠀⣽⡇⠀⣤⠆⠤⡦⠤⠁⠈⣤⠤⠀⠀⠒⠛⠛⠁
⠀⠀⠀⠀⢈⣰⠇⢠⣤⣀⠓⠀⠀⠃⠀⠁⠤⠀⠀⠀⢀⠘⢻⠟⢸⣿⡁⠀⢶⣄⠠⠼⢛⣉⡀⠀⠀⣀⠀⠀⠀⣦⡞⠠⡀
⠀⠀⠀⠀⠊⠁⠛⣿⠿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠆⢋⣴⣿⠿⠁⠀⣼⠟⠲⠐⣋⣁⡀⠀⠁⠈⠙⠻⢶⣿⠘⢿
⠀⠀⠼⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠃⠉⠁⠀⠀⠀⢠⡿⠛⠊⡈⠉⣀⣀⡀⠀⠐⠀⠀⠀⣀⣤⣀
⠀⠀⠀⡈⠀⡠⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡔⠀⠈⠁⠀⣠⡄⠀⠛⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠏⠳⠆
⠀⠀⠀⠁⠀⠘⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠘⣿⢆
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢠⠂⠂⠀⠀⠀⠀⠀⠛⢷⣦⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣦⢰⣿⣷⣶⠀⠀⡀⠤⠀⠀⠀⠂⠀⢠⡈⣀⠀⢀⠀⠀⠀⠀⠀⠈⢻
⠀⠀⠀⠀⠀⠅⡄⠀⠀⠀⠀⠀⠀⠈⠹⡇⢿⡿⠃⠀⠀⠑⢂⠀⠀⢠⡀⠐⢻⠈⠀⢀⠀⠀⠀⠀⢀⠜⠱⢾⠿⠷⠀⡀
⠀⠀⢠⣆⠀⠀⠀⣃⠒⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⢤⡜⡶⠀⠀⢳⡀⠙⠆⠠⠾⠖⠀⠂⠀⠀⠀⠀⢸⠀⠀⠘⠃
⠀⠀⠈⠋⣴⡆⠀⠉⠇⠀⠀⠀⠀⣀⠔⠀⢠⡆⠀⠐⠃⣀⠘⠃⡀⢀⠀⠑⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸
⠀⠀⢀⠀⣿⣅⡂⣘⠀⠑⠀⠀⢀⠁⠀⠀⠚⡇⠀⠀⠀⠘⠷⢀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀
⠀⠀⠀⠘⢉⣠⣿⣟⠁⣤⠀⠀⠠⠀⠀⠀⠀⠑⠀⠀⠀⠈⠓⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⢸
⠀⠀⠀⠐⠛⠉⠻⠍⠛⠓⠀⠀⠐⠀⠀⠀⠲⠖⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣶⠀⠀⠀⠀⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠀⠀⠗⠚⠀⠀⢀⣀⣀⠁⣀⣀⣀⠀⠻⠆⠀⠯⠏
⠀⠀⠀⠀⠀⠀⠋⢵⡤⠒⠊⠉⠉⠢⠸⠉⠁⠹⠠⠃⠀⠀⢿⠁⠀⠀⠉⠉⠁⢲⠖⠋⠀⠒⠒⠢
⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠰⠆⠀⣠⢣⠀⠀⠀⠀⠀⠀⠀⢸⢁⡲⠞⠁⠀⢀⣼⠠⠀⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠉⠙⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠒⠫⢤⠼⠃⠀⢠⣔⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠘⠀⠀⠀⡆⠀⠀⠀⠀⠀⣰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠀⢰⡀⠀⠀⣀⠴⣍⠢⠄⠤⠄⣺⡕⡆⠉⠉⠐⠂⠔⠻⣀⣀⣀⣀⡠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠈⠉⠀⠀⢬⢥⠘⣇⠀⡤⠍⢀⡝⠀⠀⣴⡆⠀⠀⠀⠀⢶⠄⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠀⠀⠀⠀⡛⠉⠀⠈⠀⠀⣀⣀⠀⡰⠹⠄⠛⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢐⠀⠀⡑⠃⢀⠁⠀⠙⣄⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠚⠩⣌⢐⡄⠀⠈⢈⢆⠀⠀⠁⠀⠐⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⢠⠀⠀⠀⢈⠞⠉⠲⣰⠀⠈⠀⠀⠀⠰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⠄⣀⠔⠋⠀⠀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠆⠀⠀⠀⠀⡠⠒⠉⠓⣀⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠁⠀⢤⠀⠀⠠⡀⠀⣀⠼⠛⠀⠄⠀⠒⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠐⠁⢀⠈⠉⠀⠀⢰⠆⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣀⣀⣀⣿⣿⣿⣀⣀⣀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠉⠉⠉⣿⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠃⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⡀⠀⠀⠀⠈⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠈⠲

⠀⠀⢀⣀⡀⢀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡀⠀⠀⠀⠀⣀⡀⠀⣀⣀
⠀⠀⣿⣯⣬⣉⣉⣥⣾⠗⠚⠛⠀⠀⠀⠀⠀⠰⠄⠀⠀⢻⡏⢉⠀⢼⣇⣦⠀⣿⡅⢻⠁⣺⠏⢍⠈⣯⣔⠢
⠀⠀⠛⠛⠛⠛⣛⣋⣡⡄⠀⠀⠀⠀⠀⠀⠐⣦⡄⠀⠀⠈⣿⡶⢀⣼⣧⣦⡀⢸⡇⠞⡀⢻⣾⡟⠂⢬⣝⣿⡀
⠀⠀⠀⠀⠀⣻⣷⡿⠿⠷⠶⠒⠐⠒⠒⡐⠀⠉⠀⣤⡆⠀⠛⠉⠀⠈⠁⠈⢩⠀⠉⠋⠁⠀⠉⠋⠀⠈⠛⠋⠁
⠀⠀⠦⠃⠀⠀⠀⠀⡀⢄⡀⡀⠀⠘⠿⠃⠀⠀⠀⠈⠀⠀⠀⠀⡀⡀⠀⠨⠀⠀⠀⠀⣰⣎⠑⠠⢾⡿
⠀⠀⠂⠉⠀⠑⠀⠉⠉⠁⠀⠀⠀⠀⢰⣻⣿⣿⣻⣿⣿⣧⡁⣈⣑⣖⡀⠀⢠⣴⡄⠀⢉⣀⠶⠴⠊⠀⡄⠒⠠⠇
⠀⠀⠀⠀⣼⠄⠀⠀⠀⠉⠉⠁⠉⠉⠈⠛⠛⠛⠛⠿⠿⠷⠦⡯⠝⠋⠀⠀⠺⠞⠀⠀⢰⠯⠇⣠⣤⣄⠈⡅⠀⡀
⠀⠀⣶⡀⣿⠀⣠⡆⠀⠀⠀⠀⢒⣈⡉⠀⠀⠀⠀⠀⠀⢀⣀⣈⣀⡀⢀⠀⣄⠀⠀⠀⠀⢀⣠⣈⠉⠉⠉⠀⢀⡰⠠⠤
⠀⢠⣽⣷⣿⣾⣿⣶⠏⠀⠀⠀⠉⠠⠂⠀⠀⠀⢀⡴⠋⠉⠀⠉⢙⣃⣘⠷⣌⣙⠀⠀⣾⣿⣿⡿⠀⠀⣾⡓⠊
⠀⠀⣙⣿⣿⣿⣿⣭⡄⠀⠀⠀⣤⣾⠻⣼⡄⢀⡎⠀⢠⠤⣤⢤⣿⣿⣻⣷⡍⠋⠀⠀⠀⠋⠁⠀⠀⠀⠀⠑⢄
⠀⠀⠉⠉⠉⠙⠃⠀⠀⠀⠀⠀⠙⢿⣦⣉⣛⡿⠁⠀⠀⠀⣿⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠺⣧⠀⠀⠀⠀⠀⢠⠂⠒
⠀⠀⠀⠀⡄⠀⢀⣶⣄⣀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⣿⣿⠈⠟⠟⠟⢋⣠⡾⠋⠀⠀⠀⠀⢱⠤⠄⣴⣶⢃
⠀⠀⠀⠀⠀⠀⡘⣿⣽⢉⣼⠟⠆⠀⠀⣼⠉⠢⠀⠀⠀⣿⡿⠀⠀⣠⠀⠀⠉⠑⠀⠐⠈⠀⡀⠁⠀⠀⠈⠉⠹⣆
⠀⢠⣬⡀⡀⠈⣛⢻⡿⣿⠁⢀⠀⠀⣨⡍⡆⢠⠦⡀⠀⠿⠃⠀⠀⠀⠄⡀⠠⠀⡀⠀⠀⠀⢳⡀⠀⠀⠀⡀⢀⠜⠉⠉
⠀⠘⠿⠷⠖⠀⢹⣟⠀⠈⠻⡿⠃⠀⢹⣶⡷⢏⡇⠀⠀⠀⠀⠀⠀⠆⠆⠉⠠⠘⠁⠀⠀⠀⢾⡗⠐⠶⢾⣷⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠾⠿⠿⠿⠛⠛⠘⠓⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠘⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠛⠛⠛⠛⠻⠿⠿⣿⣿⣿⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠈⠻⣿⣶⣄⠀⠀⢀⣀⣀⣠⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠈⠙⠻⣿⣿⣟⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⠀⠀⠀⠀⠙⠻⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣦⣄⠀⠀⠀⠀⠙⠻⢿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠟⠛⠻⣿⣶⣦⣄⠀⠀⠀⠀⠀⠈⠛⢿⣿⣶⣤⣀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣷⣶⣤⣤⣄⣀⣀⣀⣠⣿⣿⠃
⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠁⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣄⡀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠈⠉⠙⠛⠿⠿⠿⠿⠿⠿⣿⠏
⠀⠀⠀⠀⢀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣷⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⣿⡿⠿⠿⠶⠶⠾⠛⠋
⠀⠀⠀⠀⢸⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣦⣄⠀⠀⠀⠀⢀⣼⣿⣿⡇
⠀⠀⠀⠀⢸⣿⡏⠻⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣶⣤⣴⣿⠟⢸⣿⡇
⠀⠀⠀⠀⠀⢿⣿⣄⡀⠉⠛⠿⢿⣿⣷⣶⣶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣽⣿⡿⠋⠁⢀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠻⢿⣷⣦⣀⠀⠀⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉⠁⠀⢀⣴⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠟⠛⠛⠋⠉
⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠖⠒⠛⠛⠛⠛⠛⠛⠛⠒⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⠲⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⢿
⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠫⣉⠀⠸⣄⠀⠀⠀⠈⠈⠉⠉⠉⠉⠉⠉⠁⠀⣀⠟
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⠳⡄⢸⠉⠛⠒⠒⠶⠤⠴⠤⠶⠶⠖⠚⠛⠃⣠⡤⠤⠤⢤⣄⡀
⠀⠀⠀⠀⣜⣀⣤⣀⡀⠀⠀⠀⠀⠹⣼⡇⠢⠤⢤⣄⣀⣀⣀⡀⠀⠀⠀⢰⣿⠧⠤⠤⠤⠤⠴⢿
⠀⠀⡴⡿⠋⠉⠙⢦⡹⣄⠀⠀⠀⠀⢹⡇⠀⠀⠀⡠⠤⡄⠀⣿⠀⠀⠀⢸⡿⠶⠤⠤⠤⠴⠶⣏⣀
⠀⡼⢰⡇⠀⠀⢀⣈⣧⠘⡆⠀⠀⠀⠀⡇⠀⠀⠀⠷⢮⡤⠀⣿⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠈⡏⠉⠓⠦⢤⣀
⠀⣧⢸⡇⠀⢾⣉⣈⢿⠀⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠉⠀⢸⠀⠀⠀⣿⠤⣀⣀⠀⠀⢀⣀⡤⣇⠀⠀⠀⠀⠈⣹⠦⡄
⠀⢹⡀⢧⠔⠋⢩⠿⣼⢀⡏⠀⠀⠀⠀⣧⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡿⠀⠀⠉⠉⠉⠉⠀⠀⡷⠀⡀⠀⠀⡞⢁⡀⣿⡀
⠀⠀⠳⣜⡦⣴⣋⣴⣣⠞⠀⠀⠀⠀⠀⢿⠈⠙⠒⠲⠶⠶⠖⠋⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠁⡄⣸⠀⡏⠀⢀⣽⡆
⠀⠀⠀⠈⠉⠉⠉⠉⠳⢤⣀⣀⣀⣀⡤⠾⠦⣄⣀⠀⠀⠀⠀⠀⠀⣀⡤⣿⡀⠀⠀⠀⠀⠀⠀⢀⡏⠛⠲⢧⣿⣤⠽⠳⠾⠋⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠤⠒⠛⠉⢹⡄⠉⠉⠀⠀⠀⠀⠀⣉⣉⣉⡙⠛⠋⠉⠀⠀⠈⠳⣭⣓⣒⣒⣒⡪⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤
⡞⠋⠉⡟⠛⠓⢦⡴⠒⠋⠀⠀⠀⢀⣀⣀⡀⡾⣒⣂⣉⣹⡆⠀⣀⣀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡖⠉⠉⠉⠹⠉⠓⢦⡀
⠉⠒⠲⠦⠤⠤⠼⠁⠀⠀⠀⢠⡎⠁⡸⠁⢉⡷⠦⠭⠭⣾⠖⠫⡁⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣤⣼⡤⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣙⣛⣛⣭⠇⠀⠀⡼⠁⠀⠀⣸⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠯⢭⣭⣭⣭⣍⣉⣉⣉⣉⣉⣭⣭⣿⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣟⠙⠳⠦⢤⣤⣄⣀⣀⣀⣀⣉⣁⣀⣠⣤⡤⠾⠛⢳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⢻⡶⢶⣶⣦⣤⣤⣭⣭⣭⣥⣤⣤⣴⣶⡶⢿⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣼⣧⣸⣇⣸⣇⣸⣇⣸⣇⣸⣇⣸⣇⣼⣧⣾⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢾⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⠆⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠘⠻⠿⠿⠿⠿⠿⠿⠗⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠰⠷⢶⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣴⣶⠿⣿⡇⠀⠀⠀⠀⢀⣴⠟⡽⠊⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⣶⣦⣤⣄⡀⠀⠀⢸⣿⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⣿⣇⠀⠀⠀⣰⡿⠛⠳⣄⣠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⣸⠒⠲⠍⣿⠀⠀⢸⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⠄⠀⣿⡀⠀⣠⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣿⣶⣦⣶⠟⠀⠀⠀⠙⠿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⡿⠟⠋⠀⠀⠈⠻⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⢿⡟⠛⠻⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠈⠉⢹⡇⠀⣀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⠿⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠶⠶⠶⠶⠦⠤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠚⠋⢿⡄⠉⠉⠋⠛⠓⠒⠒⠒⡖⠒⠒⠛⠋⠉⣼
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠈⠳⣄⠈⢳⠶⢤⣤⣄⣀⣀⣀⣀⣃⣀⣥⣤⠴⡞⠁⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠈⢷⣸⡄⣀⡀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⣷⣞⠉⠉⠉⠉⣙⣷
⠀⠀⠀⠀⠀⣀⣴⠷⠛⢿⡓⢦⠀⠀⠀⠀⠈⢿⡇⠀⠉⠉⢙⣛⠛⠛⣷⠀⠀⠀⢀⣿⣈⣉⣉⣉⣉⣉⡼
⠀⠀⠀⠀⣰⢫⠇⠀⠀⠀⠹⡌⢷⡀⠀⠀⠀⠘⡇⠀⠀⠀⣯⡬⢃⠀⣿⠀⠀⠀⢰⠏⠀⠉⠉⠉⠉⠀⠙⡖⠶⢤⣀
⠀⠀⠀⠀⡇⢸⠀⠀⡠⠖⠲⣿⠈⣇⠀⠀⠀⠀⡇⠀⠀⠀⠉⠽⠫⠀⢻⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠉⠓⠦⣄
⠀⠀⠀⠀⣇⠸⡆⢀⡵⠶⣞⢹⠀⡟⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠉⠒⠶⠶⠶⠶⠖⠋⣿⠀⠀⠀⠀⢠⠞⠉⢳
⠀⠀⠀⠀⠸⣆⢿⡁⣠⠟⢉⡟⣸⠃⠀⠀⠀⠀⣿⠲⢤⣀⣀⣀⣀⣀⣼⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡖⠀⢀⡎⢠⠂⠛⢢⡄
⠀⠀⠀⠀⠀⠈⠳⠯⠿⠶⠿⡚⠁⠀⠀⠀⠀⠀⣻⡀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣇⡇⢸⠀⢻⣄⣰⣷⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠬⣟⠲⠶⠶⠖⠛⠉⠉⠓⠦⢤⣤⣤⣤⡤⠤⠖⠋⠹⣶⠤⣀⣀⣀⣀⣀⣴⠏⠀⠈⠙⠛⠓⠋⠀⠉⠁⠀⠈⠙⠲⠦⣄⡀
⠀⠀⠀⣠⣤⣤⣤⣴⣋⠀⢘⣀⡼⠁⠀⠀⠀⠀⠀⠀⣠⣒⣲⠶⢦⡀⠀⠀⠀⠀⠀⠈⠛⠲⠾⠶⠷⠚⠉⠀⠀⢀⣤⠤⠤⢤⡤⣀⡀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⢧⣀⣀⠃⠀⠈⢻⠉⠁⠀⠀⠀⡠⠴⢶⠶⢤⣟⠲⠤⠤⢞⢇⣠⠶⠲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⡇⠀⠉⡧
⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉⠀⠀⠀⠀⢸⠆⣀⣎⣀⡴⡏⠉⠛⢋⠟⠋⠉⢆⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠓⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠦⠶⠚⠁⠀⠀⣯⠀⠀⣀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡏⣩⡛⣉⣝⣙⣯⣏⣿⣫⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠋⠁⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠁⠀⠀⠀⠀⢈⣭⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣶⣶⠹⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣷⠀⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⡀⡠⣾⣿⣿⣿⣿⠀⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡈⠛⢿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⣀⠙⢿⣿⣿⡟⣿⡽⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⡽⣿⣟⢿⣿⣿⡇⢸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣝⢿⣿⣿⣿⣿⣿⣷⣄⠙⢛⣬⠻⣿⣮⣝⣃⡸⠿⣿⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⣭⣿⣿⣿⣭⣽⣾⠿⠋⠀⠀⠉⠙⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠖⠒⠒⠲⠦⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢿⠒⠦⠤⠤⡤⡤⡤⢤⠤⠴⢾
⠀⠀⠀⠀⠀⢀⠔⠋⠁⠙⢦⡘⡶⠤⠤⢤⣀⣄⣤⣤⠤⢴⢋⣀⣀⣀⡀
⠀⠀⠀⠀⢀⣯⣤⣄⠀⠀⠀⠱⣟⠐⠤⠤⠤⠤⣄⠀⠀⢸⡿⠤⠤⠤⢽⡆
⠀⠀⠀⡜⡏⠀⠈⢣⢳⡀⠀⠀⢻⠀⠀⢰⡵⡀⣿⠀⠀⡸⠋⠙⠛⠋⠙⡶⠤⣀⡀
⠀⠀⢸⡀⡇⠠⣊⡹⡇⡇⠀⠀⢸⠀⠀⠀⠊⠁⢸⠀⠀⡧⢀⣀⣀⣀⣀⢼⠀⠀⠉⢑⠦⡀
⠀⠀⠀⢧⢳⢈⡼⢳⢣⠇⠀⠀⢸⠦⣄⣀⣀⣀⣸⠀⠀⡇⠀⠀⠉⠁⠀⢸⢠⠀⢠⢃⠄⠧⡀
⠀⠀⠀⠀⠙⠛⠛⠻⣅⣀⠀⣀⣨⢦⣀⠀⠉⠁⠀⠀⣀⣇⠀⠀⠀⠀⠀⡽⠾⢤⣼⣸⠦⠾⠳⢤⣀
⠀⠀⢀⣀⣀⣠⠒⢋⣹⠈⠉⠁⠀⠀⣈⢭⣭⡙⠉⠉⠀⠙⠿⠷⠶⠶⠟⠃⠀⣀⣀⣀⣀⡀⠀⠀⠈⠉⠒
⠀⠀⠧⢄⣅⣈⣹⠉⠀⠀⡠⠐⡖⠲⣟⣒⣖⣧⣤⠒⣦⠀⠀⠀⠀⠀⠀⠀⠘⢇⡀⢀⣆⣈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣒⣓⡾⠃⠀⡜⠁⢀⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠉

⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⡶⣦⡄⠀⠀⠀⠀⠀⢀⡤⠤⠦⠴⠶⠶⠦⣄
⠀⠀⠀⠀⠀⠀⢸⣉⣉⣀⣉⣉⡇⠀⠀⠀⠀⠀⢸⣃⣀⣀⣀⣀⣀⢀⣻⠀⠀⠀⠔⠉⠉⠉⠑⠒⢄
⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⢼⡁⠀⠀⠀⠀⢀⡴⠃⠈⠀⠀⠀⠀⠈⠳⢄⠀⠸⡣⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⡇⠀⠀⠀⠀⠀⡀⠒⡂⡐⠈⡇⠀⠉⠒⠦⠤⠤⠒⠋
⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⡇⠆⡬⠀⠙⠒⠐⠀⠀⡀⡀⡇⠀⡴⠒⠒⠛⠛⠻⣿⣿⣿⣶⣆
⠀⠀⠀⢸⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡇⠀⡇⠄⡋⠀⣀⣾⣆⡀⠀⡘⠀⡇⠸⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿
⠀⠀⠀⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡇⠠⠃⠀⠉⢿⠏⠁⠀⠅⠂⡇⠀⠉⠛⠒⠒⠒⠛⠛⠛⠛⠉
⠀⠀⠀⣼⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡇⠀⡇⠁⠙⠤⠤⡠⠤⡠⠔⠁⠂⡇⠀⡔⠋⠉⠉⠉⠉⠉⠉⠉⠒⡄
⠀⠀⠀⣾⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡇⠀⡇⠁⠈⠓⠖⢂⡈⠡⡃⠂⠀⡇⠘⡅⠀⠀⠀⠐⠀⠀⠀⠀⢀⡇
⠀⠀⠀⣻⠀⠀⠀⠀⢶⣿⠶⠀⠀⠀⠀⡇⠀⠈⠑⠒⠒⠒⠒⠒⠒⠒⠒⠊⠁⠀⠈⠉⠛⠓⠒⠒⠒⠒⠋⠉
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣤⠤⠲⠤⠠⠴⠲⡤⠤⠶⠒⠖⠲⠖⠒⢲⠲⠶⠒⠒⡶⠦⡀
⠀⠀⠀⣿⣶⢶⣦⣶⣦⣤⣤⣶⣶⣶⣖⡇⠀⠀⢀⡞⢡⣀⠀⠛⣄⡀⠈⠃⢥⡄⠀⠉⢠⣤⠀⠈⠀⢦⠀⠀⠁⡼
⠀⠀⠀⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣟⡇⠀⢀⠎⠀⠀⡀⡀⠀⠀⡀⠀⠀⠀⡄⢀⠀⠀⣠⠀⠠⠀⠀⣀⠀⡰⠁
⠀⠀⠀⢻⡻⣽⣿⣿⣿⣿⣿⣿⣿⣿⢟⠇⢠⠋⢠⣤⠀⠋⢤⠄⠈⠁⢢⡆⠀⠀⠰⠖⠈⠈⠀⠲⡖⠈⠈⣰⠃
⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠒⠒⠛⠉⠀⠘⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠶⠶⠦⠴⠶⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣤⣤⣤⣴⠶⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠺⠿⡿⠛⢻⣿⡟⢉⣡⠔⢀⣀⣤⣀⠀⢀⣤⠄⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠠⣴⡿⠤⣤⣬⣿⡛⠛⠛⢶⣶⣿⣅⠀⠀⣴⣿⠁⣠⣴⣿⣿⢀⣾⠏⢠⣿⢏⣴⣿⠟⠛⣏⢀⣾⣿⠀⣼⡏
⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⣨⣿⠛⣿⣦⢀⣾⡟⠩⣿⡷⢸⣿⠃⣴⡿⡫⠿⠃⣾⠏⠀⣾⠏⣾⣿⠋⠀⣰⠟⣼⢿⣿⣰⡟
⠀⠀⠀⠀⠀⢀⡾⣿⡏⠀⣰⡿⠁⣠⡿⢫⣿⠏⣠⣾⠟⢡⡿⢁⣾⠟⠀⣀⠀⣼⠟⠀⣼⠏⢠⣿⣇⣀⣼⡟⣸⡏⠀⣿⣿⠃
⠀⠀⢀⣀⣠⣿⣷⣿⠗⣴⣟⣥⠾⠋⣰⣿⣧⡾⠋⠁⢠⡿⢁⣾⢏⣠⠞⠀⣼⠏⠀⣸⠏⠀⠀⠻⠿⠟⠉⢠⠏⠀⠀⠹⠁
⠀⠀⠉⣸⠏⠀⢸⢇⣼⡿⠛⢁⣠⣴⠿⠛⠁⠀⠀⢠⠞⠁⠸⠿⠟⠁⠀⡰⠏⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⡜⠁⠀⠠⠟⡽⠁⠀⠀⠋⡹⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣷⣶⣶⣶⠶⠶⠖⠚⠀⠀⠀⠀⢠⣾⡏
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⠴⠿⣿⡿⠟⠛⣿⣿⠋⠁⢀⣴⣿⣿⡆⠀⢠⣶⡗⢠⣿⣿⠁
⠀⠀⠀⠀⠀⣠⢠⡶⠒⠀⠀⠀⣴⠃⠉⠛⠉⣛⣿⡿⠉⢉⣿⣿⢇⣾⣿⠃⠀⣼⣿⠃⢀⣴⣿⠟⣹⣿⠃⢠⣿⡟⠀⣼⡿⠃
⠀⠀⠀⠀⣰⠃⠘⣧⠀⢀⣀⣾⡿⠀⠀⠀⢠⣿⣿⣃⣴⣿⠟⠋⣼⣿⠃⠀⣸⡿⠁⣠⣿⡟⠁⠐⢋⢤⣴⣿⣿⣷⣿⣿⠓
⠀⠀⠀⢠⠃⠰⠒⠋⠀⠀⠋⠐⠃⠀⠀⣠⣾⣿⣿⣿⣏⡁⠀⢠⣿⠃⠀⣰⣿⠇⢠⣿⡟⠀⠀⣀⡴⢢⣿⠏⠉⣹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⠏⠈⣹⣿⣿⢠⣿⠃⠀⢰⡿⠁⢠⣿⣿⣀⣤⣾⠏⠀⣾⡏⠀⢰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⣴⣿⡿⠛⢁⣿⠋⠀⢠⡿⠁⠀⠘⢿⣿⡿⠛⠁⠀⣸⠏⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⡿⠟⠛⠋⠁⠀⢀⡞⠁⠀⢠⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⠀⠀⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣶⣶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⠿⠿⠛⣛⣛⣛⣛⠛⠿⢿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⢛⣩⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣉⠻⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⢋⣴⣿⣿⠟⢋⣩⣤⣴⣶⣶⣤⣬⣉⡛⠿⣿⣷⣦⡙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠏⣴⣿⣿⣋⣤⣾⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣷⣌⣻⣿⣿⣄⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⣾⣿⣿⣿⣿⣿⠟⣋⣤⣶⣾⣿⣿⣷⣶⣬⡙⢿⣿⣿⣿⣿⣿⣆⢹⣿⣿⡄
⠀⠀⠀⠀⠀⣸⣿⣿⡏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣉⣭⣍⣙⠻⣿⣿⣾⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⡀
⠀⠀⠀⠀⢀⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣾⣿⡿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣧
⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⠟⣠⡌⢿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⣸⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢁⣼⣿⣿⣦⠉⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿
⠀⠀⢀⣴⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⠟⣡⣿⣿⣿⣿⣿⣷⡌⢿⣿⣿⣿⣿⣿⣿⣿⢡⣿⣿⣿⣿
⠀⣰⣿⣿⣿⣿⣿⣿⣿⣧⠹⣿⣿⣿⣿⡿⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣆⠹⣿⣿⣿⣿⡿⢃⣾⣿⣿⣿⣿
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⢿⣿⣿⣥⣬⣭⢹⣿⣿⣿⣿⣿⣿⠋⣭⣤⣼⣿⣿⠟⣡⣿⣿⣿⣿⣿⡏
⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠻⢿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡀⣿⣿⡿⢛⣡⣾⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣬⣉⢸⣿⣿⣿⣿⣿⣿⠀⣉⣥⣶⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢸⣿⣿⣿⣿⣿⣿⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⢸⣿⣿⣿⣿⣿⣿⠄⣿⢸⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣥⣿⢸⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⢠⡖⣶⢰⣖⡂⣶⢲⡄⡴⠒⢢⣖⡒⢰⠒⡦⢲⡖⢲⡆⣴⠒⣦⢰⣦⢰⡆
⣀⣀⠀⣀⠀⢀⢀⣏⣉⣸⣯⣅⣿⢹⣆⢷⣤⣘⣯⣅⣸⣋⡁⢸⣇⣘⣇⢻⣤⡟⣸⡏⣿⡇⢀⠀⣀⡀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠀⠈⠙⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢤⣬⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠴⠋⠉⠀⣰⠿⠿⢿⡿⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠔⢁⣤⣶⣶⢌⠻⢷⣊⠈⠙⠧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⢠⢣⠀⡀⢀⡠⢂⣉⣤⣾⠻⣿⣿⣿⣿⣿⣿⣦⡝⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⣇⣾⣿⣵⢋⠴⠋⠈⢿⡟⠆⠸⣿⣿⣿⣿⣿⣿⡛⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣏⡈⣱⠊⠀⣀⠀⢈⡇⠀⠀⢹⣿⣿⣿⣿⣿⡇⠏⢹⡀
⠀⠀⠀⢀⣠⡴⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣋⠘⠛⠁⠙⠛⠛⠛⠀⣤⣾⣿⣿⣿⣿⣯⠇⢸⣽⠃
⠀⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣟⣶⠶⠆⠀⠂⠀⠀⠉⠻⣿⣿⣟⣿⡏⠀⣾⡏
⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⢻⣿⣄⣀⣀⡀⢀⣀⠀⠀⠀⠙⣿⣿⣿⡶⠁
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡔⠀⠀⠀⠀⠀⠀⠀⠻⢦⡽⡿⠋⠉⠁⠀⠀⠀⢀⠀⠀⠙⣷⠟⠁
⢈⠻⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠈⡀⡺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠀⠀⠀⠀⠀⠀⢀⡀
⠈⠻⣦⣬⡉⠛⠛⠛⠛⠛⠛⠛⢉⠉⡤⠀⣾⠀⠈⠀⠀⠀⠀⠀⠀⠸⣤⢀⠀⡀⠀⠀⠀⠀⢶⠀⠀⠀⠈⣧⣄⡠⠒⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⣷⠄
⠀⠀⠈⠙⠲⠼⠄⠀⢀⣃⠈⠈⠄⠐⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠁⠀⠀⠀⠀⣸⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠈⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢄⣠⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣄⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠦⣤⣤⡄⠀⠀⡀⠀⠀⠀⠙⢦⣤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠏⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢀⠀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣚⠉⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢞⣫⠵⠊⠁⠀⠀⠀⠀⢈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢛⠥⢖⡩⠔⢀⠀⠀⢀⣠⢴⡺⠟⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⢀⡤⠖⠋⠀⠀⣁⡴⣚⠽⠊⠁⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡤⢞⡫⠀⢀⡤⠞⠉⠀⠀⣀⣴⡾⠕⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⢀⡠⢞⡩⠖⢋⠤⠚⢉⠤⢊⣠⣴⡾⠛⠁⠀⠀⠀⢀⠀⠀⠀⢠⡞⠋⠉⢳⡄⠈⢧⡀
⠀⠀⠀⡞⠉⠐⠉⠀⠀⠀⠀⠀⣠⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢸⣇⣀⣠⡼⡷⠀⠀⠹⣦⡀
⠀⠀⠀⠙⢦⡀⠀⠀⠀⣠⣴⡿⠛⠁⠀⠀⠀⠀⣀⡤⠤⣄⣀⣤⣤⣀⡤⢶⠿⣿⠷⠊⠁⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠙⣦⡴⡪⠟⠁⠀⠀⠀⠀⠀⠀⡞⠢⠤⢤⣌⣿⠀⠀⣾⠀⢸⠀⢸⡏⠙⣢⠤⠤⣄⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⣀⣷⣄⣀⣠⡴⣿⣤⠖⢿⣦⣼⣦⡞⢡⡎⠉⠲⣤⡾⡆⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⡼⡏⠣⡈⠙⣦⢰⡇⢿⡴⠋⣷⠀⠘⣬⠿⠿⢾⣋⣩⠴⡧⠶⠶⣄⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⢷⠳⣄⡙⢆⡿⠈⣧⣈⣳⣤⠟⠀⣾⠓⠲⢖⣰⢿⠀⢸⡄⠀⠀⣸⡇⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠈⠳⠮⠽⠟⢡⠾⡀⠉⢍⢱⣴⡟⠻⣿⣭⣭⠵⠋⠀⠘⠮⣭⣭⡽⠃⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠈⢧⣉⠓⢶⣿⡘⢿⢦⡈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢀⣽⡉⠁⠀⢸⡆⠑⠿⠞⠃⠀⢀⠤⠶⢤⡀⠀⠀⠀⠀⢀⣴⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠈⢧⣙⡲⢶⡿⠁⠀⠀⠀⠀⢠⣇⠀⠀⣨⡇⠀⠀⠀⢐⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠈⠉⠉⠀⣠⠴⡶⢤⡀⠈⠻⢿⡭⠟⠁⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⢰⡇⠀⡇⢀⣿⠀⠀⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠸⣿⣶⣷⣻⠏⠀⣠⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠉⠉⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⣠⣶⣿⣿⣿⣝⢷⣄
⠀⠀⠀⣴⢿⣿⣿⣿⣿⣿⣧⠹⣷
⢀⠀⣰⣿⣿⣿⢿⣿⣿⣿⣿⡄⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡳⣦⡀
⠙⠒⢤⣬⣭⡅⢀⢈⣿⣿⣿⡇⢸⡿⠉⢢⢤⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣠⣯⣿⣿⣿⣿⣷⡘⣷
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⡇⠀⠇⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠿⠷⢾⠇⠙⡿⠛⢻⣿⣿⡇⣿⣆⡀
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⢏⣼⡟⠑⠀⠰⡀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠈⢷⠀⢹⣶⣾⣿⣿⣇⣿⠛⠛
⠀⠀⠀⠈⠻⢿⣿⣿⣛⣵⡿⠋⠀⠀⡆⠀⠱⡄⠀⠀⠀⣼⣿⡿⢋⡙⢇⠀⠀⠀⢸⠆⠀⣿⣿⣿⢟⣾⠏
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢹⡄⠀⠹⣄⠀⠀⣿⠛⠀⠈⠀⢸⠀⠀⠀⣎⡀⠀⡿⠿⠷⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠱⣄⡙⠂⢀⣀⠀⢸⣄⡤⠋⠀⠁⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⣠⣀⠉⠑⠢⣌⠙⠻⢦⡀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠙⠉⠂⠀⠀⢹⣧⡀⠀⢳⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠠⢄⣸⣿⣿⣷⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⣼⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣠⣼⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⠛⠋⠷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠉⠁⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⡤⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣰⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⣠⣿⡇⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡆⢢⡄⣀⣀⠀⢠⠋⠙⠊⠉⠁⠐⡇⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣦⣻⡀⠀⠈⠓⠁⠀⠀⠀⢀⡠⠚⢏⣁⣩⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⣿⣾⣁⣀⣉⣳⣤⣀⠀⠀⣠⣴⣋⣀⣀⣼⣿⣿⣷⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠁⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢗⣻⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢵⢟⣩⢿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣿⠏⣿⣳⣿⣿⣯⣞⣯⣿⢿⡿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠜⠁⠙⠙⠉⣾⠋⡩⣻⣟⢕⠿⣻⢻⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠺⠿⣷⠿⣻⣷⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢊⣠⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣫⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣻⣿⣿⣠⡔⠁⠀⠀⠀⠀⠀⠀⣠⣾⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢿⣿⣻⣿⣾⣿⣟⠕⠀⠀⠀⠀⢀⠀⡺⣫⣽⢟⢽⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⢛⣿⠟⠁⠀⠀⠀⠀⠁⠀⠈⢫⣴⣷⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢇⣬⢠⡔⠀⠀⠀⠀⠀⠀⢀⣤⠚⠁⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣧⣾⣿⣿⣻⣷⠛⠔⠀⠀⠀⠠⢛⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⠿⢿⣿⡿⠃⠀⠀⠀⠀⠺⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣡⣴⡷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢀⡤⠞⠙⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣩⣿⠿⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠛⡧
⠀⠀⣠⠴⠚⢉⣤⡴⠁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣟⠁⠀⠀⠜⠁
⠀⠀⢿⠀⠿⠟⠉⣀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣴⡻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠈⢑⢀⣴⡁
⠀⠀⠈⠳⠦⠖⠋⣁⣀⡤⠴⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣦⠹⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢀⢘⡵⣿⣤⣴⠇
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠒⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢦⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠉⠀⠈⠛⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⢲
⠀⠀⠀⢻⣷⡀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⡀⠤⠒⡠⢄⡀
⠀⠀⠀⢠⣿⠇⠀⣀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣥⣤⣤⣤⣤⣥⣬⠽
⠀⠀⠀⢸⠸⠠⢚⠕⠋⣠⡴⠚⠉⠢⠀⠀⠀⠀⠀⠀⢸⣷⠂⠐⣸⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣭⣭⠽⠛⠛⠛⠛⢓⡄
⠀⠀⠀⠈⠲⠀⣡⠴⠋⠁⢀⡤⠂⠀⠀⠀⠀⠀⠀⠀⢸⢹⠀⠀⡇⣿⠦⠄⣿⠀⠀⠀⠀⠀⠀⠀⢸⡍⠉⠉⠉⠛⠛⠛⠛⢻
⠀⠀⠀⠀⠀⢾⡙⣧⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠓⠚⠁⠘⢦⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠤⠤⠤⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠄⠀⠀⠠⠤⠧


⠀⠀⠀⠐⣏⣽⡷⠄⣀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⢻⣼⣿⡾⡿⣿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣱⣃⣀⣐⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣴⠾⢛⣁
⠀⠀⠀⠀⣸⣙⣟⠛⣽⣷⣶⡟⠂⠀⠀⠀⠀⠀⠀⠀⣴⠶⡄⠊⠹⠍⠉⠯⢹⠋⠁⠀⠀⠀⠀⢀⡴⠋⡀⠈⠛⠛⠊⢡⣄⠑
⠀⠀⠀⠀⠉⢿⠙⢿⣟⡀⢀⢹⠀⠀⠀⠀⠀⠀⢀⡾⣟⠻⣿⢢⣟⣠⣤⣷⣸⠀⢀⠀⠀⠀⠀⡾⠀⠾⣤⡖⢠⣤⠘⢇⡙⠗
⠀⠀⠀⠀⠀⠸⡄⠿⠥⣔⣊⣀⣀⠀⠀⠀⠀⠀⢸⡗⣿⠗⣇⢸⠿⣭⣨⠾⣽⠀⢸⠀⠀⠀⠀⣧⠀⠀⢉⡴⠒⠒⠲⣌⠉
⠀⠀⠀⠀⠀⠀⢹⣿⣯⠭⠿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠉⠉⠉⠀⠉⠉⠉⠀⠀⠀⠀⠈⠲⠖⠋⠀⠀⠀⠀⠈⠑⠢⠖

⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⣄
⠀⠀⠀⠀⢰⣿⠭⠵⠖⠲⣌⡷⣄
⠀⠀⠀⠀⢸⢫⠄⠀⠚⠛⢻⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⣿⠀⠞⠂⣉⣉⠙⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠉⢁⣀⣀⣀⣠⡴⠊
⠀⠀⠀⠀⡇⠀⠀⠐⠻⣭⡼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⡇⢰⡂⠀⠀⣿⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⣀
⠀⠀⠀⠀⢷⡈⠙⢛⣯⡵⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠰⣫⠿⠭⠋⠁
⠀⠀⠀⠀⠈⣇⢀⠀⠈⠘⣆⠻⡄⠀⠀⠀⠀⢀⣤⠶⠛⠉⠉⠙⠛⠾⣷⡶⣄⠀⢤⡀
⠀⠀⠀⠀⠀⣿⠀⢷⡀⠀⠈⠃⠹⣦⡀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢷⡀⠹⣦⡀
⠀⠀⠀⠀⠀⣿⠀⠈⢧⠀⠀⠀⠀⠈⠻⣦⡿⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡈⠻⣦⣀
⠀⠀⠀⠀⠀⣿⠀⠀⠘⡇⠀⠀⠀⠀⠀⠈⠻⣶⣀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠉⠳⣄⠉⠛⠛⠒⠒⠒
⠀⠀⠀⠀⠀⢻⡰⡀⠘⣽⢦⠀⠀⠀⠀⠀⠀⢹⡍⢷⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⡇⣸⠀⠛
⠀⠀⠀⠀⠀⠘⣧⠫⠀⣿⠙⠿⠟⠂⠀⠀⠀⢨⣷⢾⠠⢤⣤⣤⣤⠞⠋⣠⣴⠄⠀⣧⡏
⠀⠀⠀⠀⠀⠀⠸⣆⠀⠹⣆⡀⠀⠀⠀⠠⠴⠚⠸⡇⠀⠀⠀⠀⣀⢄⡰⡝⠁⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠨⡉⠛⠛⠒⠒⠀⠀⠘⢁⡼⠀⠀⠀⠀⠑⠒⠺⠀⢀⣼⠋⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠘⢦⣀⣀⣀⠀⠔⠋⠉⠀⠀⠀⠀⠀⢀⣀⣤⡴⠟⠁⠀⠈⠙⠷⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣬⣉⢁⣠⡴⠶⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⢸⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⢰⣿⣿⠁⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⣿⡟⠀⠀⠀⠀⢀⣾⣿⡶
⠀⠀⠀⠀⣿⣿⣿⣿⠋⠀⠀⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⣼⣿⠁
⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠈⠉⠉⣿⡿⠃⠀⠀⠀⠀⠘⠛⣿⣿⠟⠀⠀⠀⠀⠀⠸⢿⣿⠋
⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⠀⡿⠃
⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⢀⣼⡿⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⣴⡿
⠀⠀⠀⠀⢠⣾⣿⡇⠀⠀⠀⠀⠀⢀⣼⣿⣿⣀⡀⠀⠀⠀⢰⣿⣿⡗⠀⠀⠀⠀⢀⣾⣿⣇⣀⣀
⠀⠀⠀⠀⠛⢿⣿⣷⣦⠀⠀⠀⠀⠘⣻⣿⣿⣟⡀⠀⠀⠀⢀⣿⣿⡀⠀⠀⠀⣠⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠘⢻⣿⣿⠟⠁⠀⠀⠀⠈⢹⡟⠁⠀⠀⠀⠉⠁⣸⣿⡟⠁
⠀⠀⠀⠀⠀⣾⠟⠀⠀⠀⠀⠀⠀⠀⣸⡿⠋⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⣿⠏
⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠸⠃

⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⣰⣾⠿⢛⣫⣭⡗⠀⠀⠀⠀⠀⢦⡀⢸⡇⢀⡴⠀⠀⠀⠀⠀⠀⢀⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠇
⠀⠀⠀⠀⢹⣶⣿⠿⠛⠋⠁⠀⠀⠀⠀⢀⣈⢿⣼⣧⡟⣁⡀⠀⠀⠀⠀⠀⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣺⢿⠟⠁
⠀⠀⠀⣠⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠩⠽⠟⠻⠯⠅⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⢨⣬⡇⠀⠀⠀⠀⠀⣠⠟⠷⠁
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠉⠁⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⢀⣰⣿⣶⣇⠀⠀⠀⠀⠀⠀⠀⣴⡄⠙⠉⠬⠦⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣠⣤⠘⠛⠓⠒⠒⠒⠂
⠀⠀⢀⣴⠋⠙⢿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡙⣾⡷⠊⡄⠀⠀⠀⠀⠀⢿⣿⣴⣶⡀
⠀⠀⠘⢿⣷⣄⡠⠋⠀⠀⠀⠀⠀⠀⠀⣶⣦⣴⠆⢰⣿⣿⡆⠀⠀⠀⠀⠀⢈⣓⣦⢴⣚⡋⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠈⠋⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣁⠤⠷⠄⠀⠀⠀⠀⠀⠀⠀⠸⣧⣬⣤⡼⠀⠀⠀⠀⠀⠀⢰⠂
⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣂⠘⣿⣶⠒⠛⠆⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢹⠀⠀⠀⠀⠀⠀⣀⣡⣤
⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠘⣏⡷⢁⠼⠀⠀⠀⠀⠀⠀⢸⠀⠃⢀⣸⠀⠀⠀⠀⠀⠀⠈⢻⣯⣠⣤⡶⠒⠋⠁
⠀⠀⠐⠚⠛⠓⠚⠓⠂⠀⠀⠀⠀⠀⠀⠀⠱⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠧⠤⠾⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠶⠤⠤⠤⠤⢴⡂⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢁⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⢀⡴⠻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⣀⣠⡄
⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡀⠀⣨⠟⡕⡰⢄⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣤⡄⠀⠀⠀⠀⠀⠀⢨⣴⣶⠿⠛⠉⠁
⠀⠀⠸⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠛⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⡀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣽⣿⣿⣿⣦⡀⢀⣾⣿⣿⣿⣿⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣟⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣶⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣻⣿⣯⣵⣶⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣽⣿⣿⣷⣝⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣾⢿⣿⣿⣿⣿⣿⢻⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡷⠶⢟⣼⣿⣿⣭⣭⣭⡾⢿⣾⣻⣶⣿⣽⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢏⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⡇⣿⣿⣿⣯⣿⢧⣿⣿⣻⣿⣿⣿⡿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⣻⣵⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣟⢿⣿⣻⢿⣾⣽⣿⣿⢋⣾⣿⡿⣿⣿⣿⣿⣴⢿⣛⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣎⣿⣿⣿⣶⣯⣿⡷⣾⢯⣿⣿⣿⡎⣿⣇⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣯⡻⣿⣷⢿⣧⣟⣻⣿⡿⣯⣾⣷⣽⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣞⢿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣽⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣯⣽⣟⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡟⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠙⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣤⣶⠀⠀⠿⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣛⢉⣿⣿⣀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣫⣿⣟⡽⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⠞⠁⣨⣮⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⡔⣯⣾⢟⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣫⠞⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠻⣯⡺⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⡙⢅⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢦⡴⠋⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡛⢋⣴⣦⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠘⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣿⣿⣆⠀⠀⠀⠀⠈⠛⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠉⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢋⣿⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⢿⡁⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠈⣿⠀⠀⠀⠀⢀⣿⡇⠹⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢸⡏⠹⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⡤⠞⠁⠀⠀⢀⣴⡿⠟⠀⠀⠘⣿⣿⣧⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⣄⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⣿⠁⢀⠜⠀⢀⣤⣤⣾⡟⠉⠀⠀⠀⠀⠀⠈⣿⣿⣷⡀⠀⠀⢠⠞⠋⠀⠀⠀⠀⠀⠀⠘⣷⣄⡀
⠀⠀⠀⣠⣤⣤⣤⣴⣶⡾⠟⠋⠁⠀⢸⡟⠀⠁⠀⠚⠁⠀⠀⢸⣧⠀⠀⠀⠀⠀⢀⣾⣿⡿⣿⣧⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⣇⣀⣀⡀
⠀⠀⢰⠟⠀⠀⠀⣠⡟⠁⠀⠀⠀⠠⣿⠁⠀⠀⠀⠀⠀⣠⣴⡿⠋⠀⠀⠀⠀⢠⣾⣿⡟⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂⠈⠁⠈⢳
⠀⠀⡻⠀⠀⠀⣾⠁⠀⠀⠀⠀⣠⡤⡼⣷⣴⣶⡶⠿⠛⠋⠁⠀⠀⠀⠀⠀⣠⣿⣿⠏⠀⠀⠀⢻⣷⣴⣶⣶⠶⠶⠶⣦⣀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠃
⡠⠞⠁⠀⠀⠀⢻⠀⠀⠀⢀⠞⠁⢀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣿⣿⠃⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠈⠛⣷⠀⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠘⠀⠀⠎⠀⠀⢀⣀⣠⣤⡶⠶⠟⣿⡟⠋⠉⠙⣿⣿⣆⠀⠀⠀⠀⠙⠷⠶⣤⡀⠀⠀⠀⠀⢈⡿
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⣴⠏⠀⠀⢠⣿⠀⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠘⢿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠈⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠈⣿⣿⣿⣷⣦⣄⣀⣀⣀⣀⣤⣤⠤⠤⢄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢹⣿⣇⠈⠉⠛⠿⢿⣧⣄⠀⠀⠓⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⠀⠀⠀⠀⠀⠀⣰⠚⠁⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠉⠀⠀⠀⠀⠀⢀⡸⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⣇⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠀⠀⠀⠀⠀⠈⠿⢶⣶⣤⣤⣤⣄⣀⣤⣤⠾
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠉⠉⢠⡞⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⠀⢻⣆⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠟⣫⣿⣿⠟⠀⠀⣿⡆⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠋⠁⣠⣾⣿⣿⠁⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣾⣿⠟⠁⢻⣇⠀⠀⠀⠈⠻⣆⣠⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡼⠁⠀⠀⣴⣿⠟⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠉⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠘⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣀⣸⣿⠇⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠻⣆⠀⠀⠀⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠙⠦⣀⠀⠀⠀⠀⠻⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⠞⢻⣿⠀⠀⠀⠀⠀⢽⠀⠀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢻⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠷⠴⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢊⠡⠂⣉⠁⠐⢢⣬⣑⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢁⠔⡁⠚⠁⠈⠙⠲⢯⣄⣨⣷⡦⣙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⢁⢔⡵⠊⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢥⣌⢷⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⢔⡴⠋⢀⡴⠊⡉⢉⠉⠁⠲⢤⡀⠀⠀⠀⠈⢛⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢃⡔⡡⠊⢀⠔⠁⠀⠘⠉⠇⣴⠄⠀⠀⠃⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢠⢊⠔⠀⢀⠎⠀⠀⠀⣰⣄⠂⡀⠀⠀⢀⠇⢀⣴⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⡰⠡⠊⠀⠀⢸⠀⠀⣶⣄⢀⠈⠘⠃⢀⠔⢁⣴⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢁⡔⡐⠁⢀⣀⠠⠔⠀⢀⡀⣈⣙⣁⠤⠐⢁⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢠⢍⡌⠀⠀⠈⠉⠀⠈⠉⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡱⢁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠰⠁⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠃⠓⠒⠀⠠⠤⣄⠀⢀⣀⣀⡀⠀⣴⣿⠃⠀⠀⠀⢀⡤⠞⠉⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣠⠀⠀⠀⠀⡞⠁⢙⠃⠀⡍⢭⢻⡟⠁⠀⠀⠀⡠⠁⠀⠀⠀⠀⠈⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⠤⠤⠥⠤⠥⠤⠴⠌⠦⠋⠀⠀⠀⠀⠀⢡⡀⠀⣀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠛⠃⠀⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⢈⣀⠀⠱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠂⠀⠀⠀⠀⠻⡈⢂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠉⠀⠀⡇⠈⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⠀⠀⣠⠃⠠⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠁⠀⡐⠀⠰⠃⠂⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠓⠤⠠⠒⠈⠀⠀⠀⠀⠀⡰⠛⠒⠂⠀⢰⡅⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠠⠐⣋⡀⣤⡚⠁⠠⠭⠁⠀⡿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠂⡈⠭⠉⠀⠠⠄⡒⠂⠈⠀⢠⣙⠀⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠐⢂⡡⡐⢾⠀⠐⠢⠄⠉⠀⢠⠋⠈⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⢀⠰⣌⠢⡑⠙⠆⢻⡀⠐⣈⠡⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠺⡆⠁⢀⡤⠖⠒⠛⠉⠇⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠠⡑⠈⢠⠎⠀⠀⠀⠀⠀⠸⠀⠀⠄⠀⡀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣔⠂⠀⠠⠑⠀⠀⠎⢀⠀⡀⠀⠀⠀⠀⢃⠀⠈⠤⢐⠀⢣⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⠤⠠⠊⠠⢊⠔⠁⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⢣⡀⠠⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠊⠤⢂⡀⢤
⠀⠀⠀⠀⣠⣤⠴⠒⣖⣲⣲⣲⣒⣦⣠⣄⣄⣀⣀⣐⣂⣒⣒⣒⠀⠀⠠⠄⠀⠀⠀⠄⠀⠀⠉⠐⠀⣠⣄
⠀⠀⠀⠸⣵⡿⠻⠋⠛⠉⠍⢍⠍⠌⠡⢉⠊⠌⠈⠁⢠⠀⠉⠉⠉⠙⠓⢤⠟⠀⠛⠰⠶⠶⠶⠦⠒⠁⠌⠑⠀⠁⠢⡴⠂⠐
⠀⠀⠀⠀⠈⠙⠓⠳⠶⠤⠬⠈⣈⣠⣀⣆⣈⣰⣠⣠⣄⠼⠦⠼⠖⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠪⢒⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠊⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠁⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⠀⠀⠐⠒⠶⣶⣄⡀⠀⠀⠀⠀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⢽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠉⠻⢷⡂⠤⠒⠋⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⢼⡇
⢀⡄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣃⢸⣦⡀⠀⠀⠀⠀⢀⡠⠛⠲⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⡈
⡟⠁⠀⠀⠘⡄⠀⠠⠄⠀⠀⠀⠀⣻⠀⠈⠳⡀⠀⢠⠔⠁⠀⠀⠀⠀⠙⢄⢀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠁
⢹⡄⠁⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢳⣤⣶⣷⣦⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠁
⠀⢹⡄⢰⣄⢤⣼⡄⠀⠀⠀⠀⠀⣸⣽⡄⠀⣀⢀⠆⡶⣄⡀⢐⡤⠀⣀⣀⣨⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠃⠀⠀⠀⠀⠀⣰⠄
⠀⠀⢻⣿⣷⡈⢿⣿⡆⠀⠀⠀⣠⡿⠻⠃⠚⠉⠉⠈⠐⠋⠻⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⠟⢋⣡⣤⣶⠄⠀⢀⣠⡴⠞⠋
⠀⠀⠀⢿⣿⣷⡈⢻⣿⡄⠈⠈⠍⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠉⠉⠣⠛⡄⠀⠀⠀⠀⠀⠘⣧⣴⣾⣿⣿⣿⡿⠷⠛⠉
⠀⠀⠀⠈⢿⣿⣷⣼⠛⡇⢀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢼⠇⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⢸⡉⠀⠀⠀⠠⡙⣶⣤⡀⠀⠀⠀⣀⣀⡀⣠⡴⠔⠋⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⡀⢢⣼⠿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⣿⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣠⡀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡱⠂⠈⠛⢿⣿⣤⣌⠻⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠀⠈⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠚⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢆⠀⠙⠻⣿⣧⣄⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠁⠀⠀⠀⣸⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠀⢀⢂⢀
⠀⠀⠀⠀⢺⢆⡀⠀⠀⠀⠀⣀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⠀⠈
⠀⠀⠀⠀⠀⠢⣍⣿⣷⣏⣍⣇⡴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣆⠈⠁⠀⠀⠀⣠⣴⡄⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢳⣿⠞⣻⣦⣡⣄⡙⠿⣷⣇⠢⣌⠛⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠨⢻⠞⣏⠻⡟⠛⠿⢦⡀⠙⢆⠹⢿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠻⠁⢰⠃⠀⠸⠀⠈⠁⠠⢀⠉⠀⠘⠇⠈
⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⢸⣀⡀⠀⠀⠀⢂⠀⣈⡄
⠀⠀⠀⠀⢨⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠩⠋⠀⠀⣸⠃⠁⠼⠀⠀⠈⠁⠘⠇
⠀⠀⠀⠀⠉⢈⣉⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠄⠀⣿⡀⢀⡄⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢀⠀⠀⠀⠓⠀⠨⣄⠀⠀⠀⡤⠀⠀⠐
⠀⠀⠀⠈⠛⠿⠾⠛⠀⠀⠀⠀⠀⠀⠉⠛⠛⠒⠂⠀⠀⠀⠀⠀⠐⠙⠁⠁⠀⠀⠀⡄⠀⠀⠉⠑⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠂⡰⠀⢰⠀⠖⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁⠃⢈⡉⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣴⠚⠙⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠛⠛⠉⠙⢛⠞⠁⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⢀⠀⢉⠂⠁⠀⣀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⡠⠋⢀⡇⠄⠁⠀⡀⠀⠀⠀⠤⠀⢹⡆
⠀⠀⠀⢀⡴⠛⠙⢷⣠⠟⣀⣤⣤⡄⠐⠚⣹⣄⣀⠙⡲⣤⡼⠀⣐⣀⠄⡠⠖⠋⢳⡄
⠀⠀⢠⠞⠀⠀⠀⠈⣿⡞⣻⣿⠿⠃⠀⠀⠀⠸⣿⠁⠜⠋⠁⢠⡏⠀⠀⢠⠀⠀⠀⡿⠛⠙⠳⣄
⠀⡴⠋⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⡀⠁⠀⢠⣸⡋⢀⠀⣰⠊⢻⣟⠀⠀⠛⠿⢧⡜⠁⠀⠀⠀⠹⣦
⣾⢁⠐⠂⠉⠀⠁⡟⠀⠈⢹⣿⢻⡇⠀⡔⠀⠉⠑⢛⡧⠁⠀⢸⣿⣤⡀⠀⡠⠈⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠻⠶⠴⠶⣶⠀⣟⢧⣄⡀⠟⡛⢟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠣⠎⢀⣀⡀⠀⡀⢀⡀⠀⠀⠀⢻
⠀⠀⠀⢀⡿⢀⠨⢉⣟⡀⠃⠀⡈⠀⠀⠀⠀⠂⠐⠠⡀⠀⢠⣴⣶⣶⣄⣢⣃⠀⢠⡤⠀⣄⠁⠐⠀⣠⢸
⠀⠀⢀⡞⠁⢀⡀⣘⠉⠸⠀⠟⠸⠃⡤⢡⠀⡄⣀⢸⣿⣿⠛⠷⠾⠏⡸⠛⠒⠛⠉⠀⠐⠉⠡⣤⠶⠖⠋
⠀⠀⠸⣥⣶⣤⣆⡚⣛⣉⣿⠁⢺⣶⣧⣴⣤⣤⣯⣽⣿⠏⠀⠀⠀⢸⣯⠁⠀⣠⡌⠀⡀⠂⠄⡙⣷
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⡿⠘⢀⡼⢋⠿⠋⣿⠟⠛⠉⢰⠀⠀⣦⢸⡷⣦⡉⠈⠙⢋⣸⠷⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢠⠋⢰⠃⠀⢰⠃⠀⢀⠁⠘⠀⠀⠁⣾⠃⠀⠉⠛⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡇⠁⣷⡄⠄⡞⠀⠀⠊⠁⠀⣀⣴⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⡏⠀⠀⡇⠀⠀⣄⡠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢨⣀⠀⡇⠀⠀⣧⡴⠆⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣼⠉⠃⣿⠛⡛⡇⠀⣀⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣸⠀⠀⠈⠁⠀⢠⡇⠀⠀⢠⠘
⣶⣶⢶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⠛⠛⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⡁⠀⠀⠀⠀⠀⠀⠀⡙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠈⠙⣷⠶⢦⣤⠴⢶⡟⠁⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⢸⡇⠀⢸⡇⠀⢀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⢿⡀⠀⢻⣄⡀⢀⣠⡾⠃⠀⣼⠃⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⣤⢶⣶⣦⡍⠳⣆⠀⠀⠀⠈⠻⣦⣀⠉⠉⠉⠉⢀⣠⠾⠃⠀⠀⠀⣴⠞⠉⠀⠀⠀⠀⠈⠙⢷⡄
⠀⠀⠀⠀⠀⢰⡏⠀⠀⣼⢳⡏⠙⣧⢻⡄⠘⣧⠀⠀⠀⠀⠀⠉⠛⢻⡟⠛⠋⠁⠀⠀⠀⠀⣼⠃⠀⣀⣤⡴⢶⣤⣄⡀⠀⢹⡆
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⢻⡆⢀⣾⠃⠀⢹⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢰⡏⢰⡞⢹⡏⣾⢻⡎⣿⠙⣷⡄⣿
⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠘⠋⣴⠟⠁⠀⠀⣼⠛⠶⢦⣄⣀⠀⢀⣸⣧⡀⠀⢀⣠⣤⠶⠞⣷⠈⠙⠾⣷⣝⣛⣵⡿⠟⠁⢠⡟
⠀⠀⠀⠀⠀⠈⢷⣄⠀⢾⡀⣠⡏⠀⠀⢀⣼⠋⠀⠀⠀⠈⠉⠛⣿⠁⠈⢻⡟⠋⠁⠀⠀⠀⠙⣧⡀⠀⠀⠈⠁⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠳⢮⣭⣭⣤⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⣠⡿⠷⠶⠿⣄⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣤⣤⣤⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀⠀⢀⣴⠋⠀⠀⠀⠀⠙⢷⣄⠀⣀⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠋⠁⢀⡶⠀⠀⠙⠳⣟⠁⠀⠀⠀⠀⠀⠀⠀⣹⠟⠋⣡⡴⣶⣦⣌⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢀⡾⠁⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⣿⣿⣉⣿⣿⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠈⠉⠁⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢰⡏⠀⣀⣀⠋⢻⡆⠀⢀⣿⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣿⢠⣤⡄⣿⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣌⠛⠛⠋⠙⠓⠛⠁⣀⡾⠃⠀⠀⠀⠀⠀⠀⠘⢷⣀⠀⡿⠲⠶⠖⢿⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣤⣤⡴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢦⣤⣤⣤⡴⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⠄⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⡶⠒⠛⠛⠙⠉⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢫⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢣⠏
⠀⠀⠀⢠⡇⡰⣊⠩⢀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⢀⡟
⠀⠀⠀⢸⡇⠁⠁⠀⠙⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢸⡇⠀⢀⣀⣀⡀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠘⠒⠒⠲⢦⡄
⠀⠀⠀⢸⠁⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠘⠛⠛⠉⠉⣹⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠉⣹⠇⠀⠀⠀⡜⠀⣀⣀⡀⠀⠀⠀⣴⠋
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⠛⢉⡟⠀⠀⠀⠀⣼⠃⠀⠀⢀⡀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣯⣤⣄⠀⠀⠀⢲⡏⠀⠀⠀⠀⠉⠉⢉⡽⠃⢀⢀⡼⠁
⠀⠀⠀⣿⣀⣠⣤⠀⠀⠀⢀⡞⠀⠀⠀⠀⢠⣏⣴⡶⠟⢋⡏⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⣢⡟
⠀⠀⠀⠀⠀⠀⡿⠀⠀⢀⡾⠁⠀⠀⠀⠀⠘⠋⠁⠀⠀⢸⡇⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣾⣁⣀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠟⢛⡿
⠀⠀⠀⠀⠀⠰⡇⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⢠⠏⠀⠀⠀⠀⠿⠛⠒⡖⠀⢠⡟
⠀⠀⠀⠀⠀⢸⡧⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⡤⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⢸⡇⣰⠟
⠀⠀⠀⠀⠀⢸⡇⢡⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠋
⠀⠀⠀⠀⠀⢸⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡞⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠃
⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡶⢶⡶⠶⠶⣦⠀⠀⠀⠀⠀⠀⠐⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠠⡇⢷⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⡴⠶⠖⠒⡒⣲⠆
⠀⠀⠀⠀⠀⢰⣶⠛⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⠀⢀⡇⠈⢣⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⡶⠛⠁⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⢣⠀⠀⠀⠀⠀⡾⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⢠⡶⠞⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⡞⠉⠀⠀⢀⢂⡴⠛⠀⠀⠀⠀⠀⡇⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣰⢏⠀⠀⠀⠀⢠⣿⣃⣀⣀⡀
⠀⠀⠀⠀⣿⡄⠀⠀⠀⣠⣭⠇⠀⠀⠀⠘⣇⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠐⠉⠉⠉⣩⠞⠁
⠀⠀⠀⠀⠸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣧⣤⡄⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠠⣞⠃⠀⠀⣈⣷⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠓⢲⠀⠀⠀⠀⠀⣸⠀⢀⡀⠀⢠⠞⠀⠀⠀⢰⡯⠶⠖⠚⣿⠀⠀⠁⣴⠋
⠀⠀⠀⠀⠹⣆⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡜⡀⢸⠀⠀⠀⠀⠀⠙⠋⢹⡟⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠹⣆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢸⡄⠀⠀⠀⠀⠀⢀⡟⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠹⣆⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⡇⠀⠀⠀⠀⠀⢸⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠄⣤⠶⣄⢠⡴⢦⡀⣤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠁⠷⣤⠟⠸⣦⡼⠃⢯⡴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⡀⠀⣀⣀⠀⣀⣀⠀⣀⡀⣀⣀⣀⣀⡀⠀⣀⡀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⢸⡏⣹⠆⣯⢉⡇⢸⡇⢸⡉⠉⠈⣿⠁⢸⡇⣾⡉⣹⢸⡟⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠉⠉⠀⠉⠉⠀⠉⠁⠈⠉⠉⠀⠉⠀⠉⠁⠈⠉⠉⠈⠁⠈⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢾⢹⢶⡀⠀⣠⢾⢹⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⢸⢸⢸⢹⢸⢹⢸⢸⢸⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⢿⣀⠀⠈⢸⢸⠈⠀⠀⣸⡟⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⣠⠴⠃⠳⣄⠈⠧⠀⣸⠸⡄⠀⠞⢁⡤⠃⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠀⠀⠙⢮⠁⠀⠀⡤⣾⣓⣒⣒⣷⣤⣟⣒⣒⣚⡆⠀⠀⠀⠈⠑⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣼⣄⣰⣾⠛⠙⠋⠉⠙⠃⠀⠋⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⢹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠴⠚⠉⠉⠉⢁⣠⠤⠤⣄⡀⠀⠀⠀⠀⠀⣠⡀⠀⢀⡤⣄⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⡴⡫⢒⡭⣝⠲⣝⣆⠀⠀⠀⠀⠑⢡⠖⠚⠓⠚⠒⢮⠀⠴⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢸⢹⢷⣃⠔⡡⢺⢸⢸⠀⠀⠀⢀⣼⣉⣉⣉⣉⡉⠉⠉⢙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⣎⢧⡱⠮⠤⣊⢞⡼⠀⠀⠀⢸⢹⣁⣠⢤⣀⣠⠤⣈⣻⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠩⠡⠠⠈⠓⠯⣭⡭⣵⠋⠀⠀⠀⠀⢸⢸⡇⠀⡀⠠⠀⢂⠀⢹⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣄⣀⣁⣁⣁⣁⣁⣀⣁⣀⣀⡼⠃⠀⠀⠀⠀⢸⣾⡇⡀⠀⠀⠐⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣓⣒⣒⣲⣴⢰⣖⣆⣶⣒⣚⣷⡀⠀⠀⠀⣠⢺⡯⡗⠒⠒⠒⠒⠒⠒⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠷⠶⠶⠶⠶⠿⠶⠶⠶⠶⠶⠷⡜⢦⣀⡞⠁⢸⡇⣗⣒⣒⣒⣒⣒⣒⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠃⠀⠉⠀⠀⠀⠳⠼⠾⠿⠿⠿⠿⠿⠵⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠶⠒⠛⠛⠉⠉⠙⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⢀⣼⠃
⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘
⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⣀⣀⠀⠀⠀⢀⠔⠋
⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⡏⠀⢈⡱⡄⠀⣯⠀⣰⠋⠀⡄
⠀⠀⣿⠀⠀⠀⠀⠀⣀⠞⡡⠖⠂⠂⠀⢣⡀⠀⠳⣷⡀⠘⠿⣥⡤⠞⠁
⠀⠀⡇⠀⠀⠀⢀⡼⠃⢸⡁⢀⡜⠁⢀⠀⠁⠀⠀⠉⢃⠀⠀⠀⠀⠀⡠⠖⠲⢦⡀
⠀⠀⢹⠀⠀⣴⠋⠀⠀⠀⠻⢯⣤⠴⠋⣠⠄⢦⣀⡠⠎⠀⠀⠀⠀⠛⠀⠀⡀⢨⠇
⠀⠀⠈⣦⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⣠⠆⠀⠀⠀⢀⣞⣀⠀⢀⣴⣫⠖⠋
⠀⠀⣰⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⡄
⠀⣰⠇
⠀⡏
⢸
⣾
⣿
⢿
⢸⡆
⠀⢿⡀
⠀⠘⣧
⠀⠀⠘⢷⡀
⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣶⣾⣦⣾⣿⣿⣿⣿⣽⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⠉⠋⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠡⠄⠈⠄⠀⠀⠀⠀⠀⠀⠀⡾⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠌⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠈⡀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠉⠈⠉⠟⠀⠀⠀⠀⠈⠀⡀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠉⠀⠀⠀⠀⠀⠀⣠⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⢀⣤⣤⠀⡆⠀⢀⠔⠀⠀⠀⠀⠔⣠⣤⣄⢠⠀⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣿⡑⠛⠀⢀⣤⣾⣦⣠⣶⣦⡀⠀⠙⢂⣿⡆⠄⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠀⠀⠀⠀⠀⠙⠻⠶⢿⠟⠋⠉⢈⡁⠉⠙⠻⡿⢶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⠀⠂⠄⠜⠣⠀⠄⠊⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣈⡄⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠘⠛⠛⠛⠢⠀⠀⠀⠀⠀⠀⠀⡀⠘⠛⠛⠛⡄⠀⠀⠀⡀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣀⣀⣀⣀⣀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠛⠛⠛⠛⠛⠛⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠸⠉⠉⢹⠀⠯⠉⠉⠽⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠠⡀⠀⡈⠀⠰⠀⠀⡄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣷⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣠⣄⣠⣄⣀⣀⣥⣀⣇⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⣿⣿⠉⠉⠉⢹⣿⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣠⣿⣿⠀⠀⠀⢿⣿⣄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠸⠟⠋⠁⠀⠀⠀⠈⠙⠻⠷⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⡀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⣦⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠈⠻⣿⣦⡀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠈⣿⣿⣆⡀⠀⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠻⣿⣦⣠⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠈⠙⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣦⡀⠀⠀⠀⠙⢿⣿⡋⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠋⠀⠀⠘⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠻⣿⣦⡀⠀⠀⠀⠉⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣦⡀⠀⠀⠀⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠙⢿⣦⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⢿⣦⡀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠃⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⣠⣾⡟⠋⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⢠⣾⠿⠁⠀⠀⠀⠀⠀⠀⣹⣿⣷⣄⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⣠⣾⠟⠁⠙⢿⣷⣤⣾⠟⠁
⠀⠀⠀⠀⠀⣠⣿⣿⣦⡀⣠⣾⠟⠁⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⣠⣾⠟⠁⠀⠙⠿⠟⠁
⠀⣠⣾⠟⠁
⣾⡟⠁
⣿⣿⡿⠻⠟⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⢦⣶⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣰⡯⠙⠛⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣸⣿⣿⣿⣏⣤⣿⣆⠀⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣏⢷⡿⠏⠲⣤⠙⣆⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⢺⠿⠛⣿⣿⣿⣿⣿⡷⠀⠀⠀⠈⠃⢹⠂⠄⢠⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣄⠀⠀⣀⣴⠶⠋⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠸⢿⢸⠀⣼⣿⡟⠁⠙⠿⢆⣄
⠀⠀⠀⠀⠀⢰⣿⣿⠛⢿⣿⠻⣿⠋⠀⠀⠀⠀⠠⠿⠿⢿⣟⣛⣂⣠⣤⡤⠤⠴⣾⢸⡆⢻⣿⡇⠘⠟⣿⡟⠋
⠀⠀⠀⡄⠀⢸⣿⡇⢰⣂⢥⣼⠷⠶⠒⠒⠚⢛⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⣧⣷⡜⣿⣿⣦⣴⣿⠇
⠀⠀⠀⢣⢠⠸⣿⣿⣄⣴⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠣⣧⣙⢿⣿⣿⡿⠃⠀⠀⠀⠀⠐⢿⣿⣿⡿⣟⠛⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢠⠘⠁⣿⠇⢻⡄⠘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣸⡏⠀⠀⣇⡰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢹⣷⠀⠀⠈⠃⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⢄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣇⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣭⣾⣿⣇⠀⢛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠉⠉⠁⠀⠓⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠐⠫⠊
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡤⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⠀⠀⠀⠚⠋
⠀⠀⠀⠀⠀⠀⠀⣰⡟⢀⣀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠆⠀⠀⠀⠀⣰⣿⣿⡶⠛⠀⠀⢀⡄⣀
⠀⠀⠀⠀⠀⠀⠼⢿⣿⡿⠋⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⢈⡽⠟⠁⠀⠀⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠠⠎
⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⢀⠐⡁⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠁⠌⠁⠀⠀⠀⠀⠀⠐⠁⢠⢌⠁⠀⠀⠀⠀⠀⠀⠐⠐⠒⠀⠀⠀⠀⠀⢃⠔⠃
⠀⠀⠀⠀⢀⢀⡘⠂⡰⠀⠀⠀⠀⠈⠀⡪⠐⠁⠀⠀⠀⠀⠈⣱⠃⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⢀⠔⠁⠈⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⢴⡩⠇⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠚⠋
⠀⠀⠀⠀⠀⠠⣸⣁⣀⡀⠀⠀⠀⡠⠋⢠⣎⠁⠀⠀⠀⣠⠊⢘⡂⠖⠀⠀⠀⠀⢠⠎⣠⠄
⠀⠀⠀⠀⠰⢓⢖⡴⠋⠀⠀⠀⠈⣩⡿⠒⠁⠀⠀⠀⠀⣩⠏⠋⠀⠀⠀⠀⠀⠀⡠⠂⠁
⠀⠀⠀⠀⣰⠟⠉⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠰⠎
⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⠶⠤⠤⠤⠤⡴⣶⣶⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣤⣤⢤⡄⣤⣥⣾⢿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⣮⣭⣵⣿⣭⣍⣩⠼⣯⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣋⠉⠀⠐⠃⠉⠀⠀⠘⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠣⠄⠁⠀⣤⣀⠀⠈⠐⣮⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠈⠁⠀⠈⠉⠀⠁⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⠟⠛⢳⡖⢂⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡔⠀⠀⠀⣸⢿⢈⡽⠓⠶⣤⡴⠆⢀⣐⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠰⠷⣴⣉⡠⠈⠸⠊⠁⢀⠔⠁⠀⣀⣽⣯⣽⡷⣷⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⢳⣤⣉⣁⠓⢤⣰⣶⠃⠀⠀⠚⠿⣿⡿⣉⣃⡈⠑⡀⠀⠀⠀⢀⣠⣴⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠿⠍⠉⣙⠁⠰⣶⣿⢰⠀⠛⠁⣀⠘⢿⣿⣭⣿⣿⡟⠛⣤⡀⠜⡿⣾⣇⠀⠀⢀
⠀⠀⠀⠀⢠⣶⣾⣿⣯⡖⠶⠓⠒⢒⣼⠿⢿⣥⣠⣮⢹⣶⣆⠀⣩⡗⠐⠀⣸⣿⡿⣷⡿⢅⡥⠂⣠⢞⣿⡆
⠀⠀⠀⠀⠈⢲⣭⣭⣭⣭⣭⣭⣥⣤⣴⡖⠁⠀⠉⠻⡞⢿⡙⣧⠍⠉⠐⢀⣈⣽⠛⣡⠛⠿⣧⣽⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠙⠿⠟⠛⡛⡛⠩⠍⠙⠀⠀⠀⠀⠀⠘⠂⢛⢿⣄⡰⢶⣆⣍⡠⠊⠁⣡⢞⣽⢿⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠰⠛⠠⣼⠀⡘⠑⠛⠉⠐⡛⠛⢹⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠀⢀⡄⡙⠒⠇⣀⣰⡛⠋⠁⣰⣷⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⣀⡠⢾⠿⣋⡄⣶⣾⣿⠧⣼⡟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⡔⠛⠛⢡⡾⠿⠿⠚⣿⣶⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠏⠁⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣬⣍⣈⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣎⠁
⠀⠀⠀⠀⠀⡇⠀⠀⣀⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀
⠀⠀⠀⠀⠐⠛⠛⠋⠉⠉⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣤⣶⡶⠾⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⣀⣀⣀⡄⠀⠀⠀⣀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠋⠉⠉⢀⡇⠀⠀⠈⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣿
⠀⡀⠀⣠⡶⢻⡄⠀⠀⢀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠙⣦⠄⠀⠀⠀⠀⠀⠘⣿⠙⠛⠳⠿
⠀⠱⠞⠁⠀⠈⢷⣀⣴⠟⠉⣷⠀⠀⣠⠔⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠁⠀⠀⢠⣤⣄⣀⡀⣿
⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠘⣧⠞⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡇
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⣷⣆⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠃⡩⠤⠀⠌⠁⠀⠀⠀⠀⡤⠶⢶⣖⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⢀⣅⡛⠾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠄⠀⠀⠀⠀⢀⣶⣶⢄⠀⢠⣶⣷⣦⣴⢶⣿⣦⠀⠀⠈⠁⠠⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⢃⡀⠁⠀⠀⢀⣀⣾⣽⣿⠿⠃⢿⣿⣯⠿⠛⠿⣿⡵⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⠂⠺⠀⠀⠀⢰⣿⣿⣻⢇⣤⣀⡀⣰⣾⣿⣿⣗⠀⠀⢰⣿⣿⣿⡆⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡠⠁⢀⣤⡠⣄⠻⠿⣩⣾⣿⡿⢿⣿⣿⢿⠻⢿⣷⢶⣷⣜⡳⠿⣿⣳⣦⡄⠀⠇⠙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣿⡟⠀⠀⣸⣯⣿⡕⠆⠉⠀⠈⠀⠘⠿⡻⢿⣿⡿⠀⢻⣿⡻⠃⠀⠈⢤⢩⡿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡄⣾⣾⣟⠋⠉⡀⠀⠄⢀⠁⠠⠀⠈⠁⣨⣿⣅⡀⣠⣭⣀⠀⠀⠀⠘⠀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣴⠆⡀⠀⠀⢺⣿⣷⣿⢾⣿⢿⣯⠁⠀⠄⠀⠒⠤⠀⠂⠀⠀⣻⣷⣿⣷⣿⢿⣿⡧⠀⠀⠈⠰⠟
⠀⠀⠀⠀⠀⠀⣰⣿⠀⡄⠀⠀⠀⠙⣛⠋⠈⢙⣿⡋⠀⡐⠀⠂⢀⠆⠐⠀⠀⣀⣠⣽⡿⣿⠘⣿⣿⡁
⠀⠀⠀⠀⠀⠀⢿⣾⣃⠓⡀⠀⢠⣮⣿⣧⠀⣾⣿⣷⣮⣶⡄⠀⠀⠀⣀⠰⢜⣿⣻⡏⠀⠀⣼⣿⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⢰⠀⠘⠻⢯⣿⣶⢮⡹⢿⠷⢿⣷⣦⣷⣿⣿⣷⣾⣿⡿⢏⣶⣦⠙⠊⠛⠁⢀⠊⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠸⣿⣿⣿⠇⠀⠀⣽⣿⢿⡿⠏⠈⠙⠛⢱⣯⣿⣿⠇⠀⠀⠀⡦⠠⡾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢞⣿⣶⣤⣶⣻⣾⣷⢠⣶⣿⣟⡿⠋⠁⠀⠀⢀⠈⢡⣟⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠂⣀⠀⠀⠀⠻⣿⠷⠛⠻⢿⠿⠋⠀⠑⠿⠿⠁⠀⠀⠀⠀⠐⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⣬⢑⠁⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠽⠷⠶⠚⠀⠀⠀⠀⢀⡐⠀⠒⣚⢠⣤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠹⢿⣽⡿⠋

⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠷⠾⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠆
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠹⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⢿⣿⣿⣦⡀⠀⠀⠀⠀⣴⣿⣿⣦⠀⠀⠀⠀⢀⣠⣿⣿⡿⠏⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⣀⡀⢸⣿⣿⣿⣿⠀⠀⢀⣴⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣶⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠁⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠈⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠘⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⢿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣤⣴⣤⣄⡀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣦⣾⡿⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠞⠿⠿⠟⢿⡿⣦⣠⣶⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣷⡄
⠀⠀⠸⣋⠈⢉⠀⣿⣿⡏⢀⠀⠀⣻⢿⣿⣿⠀⠀⠀⠀⠀⠀⢖⠂⠐⠦⢸⣿⣿⣿⢿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣴⣶⣶⣬⡋⠁⠘⣿⢿⣿⡧
⠀⠀⠀⠎⠂⠘⠄⣠⠜⠁⠸⠃⠐⡁⢼⡿⠃⠀⠀⠀⠀⠀⠀⡏⠓⠈⠃⠘⣩⠏⠀⠠⡀⠙⣹⣿⣿⡇⠀⠀⠀⢰⡿⣿⢿⣿⣿⣿⡶⠠⠉⠸⡿⠃
⠀⠀⠀⠐⠀⡴⠛⢅⠀⠀⣀⣠⡰⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠎⠁⠀⢈⡀⢀⣂⣽⠛⠋⠀⠀⠀⠀⠈⢃⡉⢀⡁⢻⢿⡄⢀⢬⠀⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠈⣑⠂⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢱⠒⠉⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠈⣱⠐⠈⢀⣀⠀⠀⠀⠀⠁
⠀⠀⠀⢈⠃⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠻⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣳⣧⡚⠁⠀⠁
⠀⠀⢀⡤⠆⠠⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⡎⠀⠈⠀⡀
⠀⠀⠀⠜⠁⡴⡈⠧⠀⠀⠀⠀⢠⠢⡀⢀⡀⠁⠄⠀⠀⠀⢸⣿⣿⣿⡋⠣⠀⠀⠐⠈⡤⢤⠤⣀⠈⠠⠀⠀⠀⠀⠋⠇⣴⠚⠏⠀⠀⠀⢠⠢⡄⢀⡀⠁
⠀⣀⣔⣦⢠⠤⠄⠀⠀⠀⠀⣀⣸⠶⣆⣠⣀⠀⠀⠀⠀⣀⣼⣿⣿⠧⠤⠀⠀⠀⠀⢀⣌⠔⣄⣀⡀⠀⠀⠀⠀⠀⣼⡷⢧⠄⡀⠀⠀⢀⣈⠶⢆⣸⣀
⠀⠉⠙⠂⠉⠀⠀⠁⠀⠀⠂⠀⠉⠘⠃⠙⠋⠛⠀⠀⠀⠉⠙⠋⠉⠁⠀⠈⠀⠀⠀⠀⠉⠙⠉⠛⠁⠃⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠉⠈⠛⠘⠋⠙⠃
⠀⠀⠀⢀⣴⣶⣶⣶⣤⡀⢀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣶⣦⣄⢀⣤⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀
⠀⠀⢠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣻⣝⠛⠋⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣆
⠀⠀⣿⢠⠈⢹⡛⣿⣿⣿⠙⠋⠻⡿⣿⣿⣿⠀⠀⠀⠀⠘⠇⡀⠀⣉⢈⣿⣿⡿⣦⠄⡸⠋⣿⣿⠃⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣿⠻⠟⢿⡿⣿⣿⣿
⠀⠀⠙⡈⠁⠈⣴⣿⣿⠟⠅⠲⢀⢰⣿⣿⠟⠀⠀⠀⠀⠀⠐⠓⠀⠩⠈⠛⠋⠀⠉⠀⡰⠈⢟⠁⠀⠀⠀⠀⠀⢸⡏⠸⡏⠈⢻⣿⣆⠀⠄⠠⣾⠿⠟
⠀⠀⠀⠀⡰⠎⠙⣢⣀⢀⣶⣤⡖⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣵⣤⣀⣠⣶⡤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠆⠰⢆⠈⡹⠃⠀⠸⠄⠛⢀
⠀⠀⠀⠀⡇⠀⠀⣤⣭⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣯⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣄⡄⠺⠿⠃⡀
⠀⠀⠀⢀⡁⠀⠀⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡛⠛⠂
⠀⠀⠀⠁⠀⠀⠠⡁⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⠩⠋⡉⢹⡃⠀⠀⠀⠂⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠴⣿⣿⣿⣧⠀⠀⠀⠄⠀⠀⠀⠀⠄
⠀⠀⠀⢤⡠⢳⠀⠁⠀⠀⠀⠘⠉⡋⢹⠂⠀⠀⠀⠀⠀⠀⠀⣸⢸⢒⠀⠁⠀⠀⠀⠀⡍⢀⢰⠀⠀⠀⠀⠀⠀⠀⣰⡦⢹⠀⠁⠀⠀⠀⠘⠉⡋⢱⠂
⠀⠀⠰⡜⠾⠛⠀⠄⠀⠀⠀⠲⢌⡽⢶⡶⢤⠀⠀⠀⠀⠀⠾⡿⠽⠚⠀⠄⠀⢀⠐⠶⢯⡭⢾⡦⣤⠀⠀⠀⠀⠘⠻⠟⠙⠀⠄⠀⠀⠀⠲⣮⣽⢾⡶⢤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠣⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⢂
⠀⠀⢀⠤⠒⠒⢒⡂⠒⠤⡀⠀⠀⡠⠄⠒⢒⣖⠒⠂⢄⡀⠀⢀⡠⠔⠓⠒⡒⠓⠠⢄⠀⠀⣈⠄⠚⠛⢩⡛⠓⠠⡁
⠀⠀⠑⠠⢄⣈⢛⣁⡠⠄⠊⠀⠈⠓⠤⢀⡙⢛⣀⠠⠔⠁⠀⠈⡢⠄⣀⡛⢋⡀⠤⡞⠁⠀⠑⠦⢄⣈⣛⣁⡠⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠀⠈⢣⠀⡞⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⣀⣠⠤⢴⠖⠒⣶⠒⠶⠤⣤⡀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⡏⢠⡾⡩⠠⠀⢸⡇⠀⢸⢀⢀⢠⢠⡹⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠁⠀⠈⠱⣜⢦⣙⠳⠧⠧⢤⡇⠀⢸⠴⢖⣒⡭⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠈⠳⣌⠉⠙⠛⢻⠃⠀⢸⠉⢉⡤⠖⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣠⠶⠒⠚⡏⠉⡷⠒⠲⢤⡈⢳⠀⠀⡼⠀⠀⣾⠴⠋⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣙⠦⣤⣀⡇⠀⣷⣀⣠⠴⢃⡜⠀⢰⠃⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣈⠉⠓⠒⡇⠀⢸⠒⠒⠚⠉⠀⢠⠏⠀⠀⡼⢞⣋⣉⡋⠁⢻⠓⠒⢦⠀⢸
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠈⠑⢦⡀⢹⠀⠘⡇⠀⠀⠀⢀⡎⠀⠀⣰⠓⠢⠬⢭⡇⠀⣸⣋⣩⠭⠔⠃
⠀⠀⠀⠀⠀⡞⠁⣀⣀⡠⢤⣤⣄⣀⠹⡈⡇⠀⢹⡀⠀⠀⡼⠀⠀⢠⠇⠀⠀⠀⣸⠁⠀⡇
⠀⠀⠀⠀⠀⠣⣘⡳⠦⡇⠠⡶⣒⣫⠜⠁⠸⡄⠀⢳⡀⢠⠇⠀⠀⡼⠀⠀⠀⢠⠃⣀⠴⠓⠓⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⢣⠀⢏⠀⠀⠀⠀⠀⢳⡀⠀⢳⡼⠀⠀⢀⡇⠀⠀⣰⢃⠎⣀⣀⣀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠈⢦⠀⠀⠀⠀⠀⢧⠀⠀⢣⠀⠀⢸⠀⢀⠞⠁⠀⢢⣗⢲⠏⢨⢫⡶⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠈⠳⣄⠀⠀⠀⠘⡆⠀⠀⢧⠀⢸⡴⠃⠀⠀⡴⠃⢀⠞⠀⡞⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠈⢢⡀⠀⠀⢹⠀⠀⠘⡆⢸⡀⠀⢠⠞⠀⡰⠋⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠙⣆⠀⠈⡇⠀⠀⢱⠀⣇⣰⠃⣠⠞⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠈⢦⠀⡇⠀⠀⢸⠀⠸⡇⣴⠃⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⢘⡆⡇⠀⠀⡸⠀⢠⢷⡇⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠀⠙⠒⠚⠉⠋⠁⠀⠙⠚⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠶⠶⠶⠶⠶⠶⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢶⡶⠶⠶⠲⠶⠶⢶⡶⠛⠀⢀⣤⠀⠀⠀⠀⣤⡞⠛⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠾⠇⠀⠶⠶⠶⠶⠾⠷⢶⣄⣾⠙⣧⠀⠀⣼⠋⠙⢦⡀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠸⡆⠀⢹⡄⠀⠀⠙⠆⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⡟⠀⣤⠀⢿⠀⠀⠙⠦⣤⣤⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⣉⡉⠉⠉⠉⠉⠁⢸⡇⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢿⡙⠛⠳⠦⣤⡀⢸⡇⠀⣿⠀⢸⡇⣀⣤⠶⠞⠛⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠙⢿⣇⠀⣿⠀⣼⡟⠋⣠⣤⡀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠉⠀⠛⠀⠉⠀⣴⠋⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⠄⠀⣤⠀⠀⣼⠃⠀⡇⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⢠⡏⢀⡾⠁⠀⠀⡇⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠛⠛⠃⣸⠃⠀⢀⣴⠟⢀⡾⠁⠀⠀⠀⡁⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⣀⣀⣀⣀⣀⢀⣿⣤⠶⠛⠁⠀⣿⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠣⠘⠀⠀⠂⠀⠀⠀⠀⠐⠁⠀⠐⠂⠐


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⢛⢻⠛⡟⣻⠟⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠻⣦⡀
⠀⠈⠻⣦⡀
⠀⠀⠀⠈⠻⣦⣤⡀
⠀⠀⠀⠀⠀⠻⣄⠙⠷⣄⡀⣠⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠘⢧⡀⣨⠟⢁⣽⠟⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣨⠟⠁⣴⠟⠁⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠙⣷⠟⠁⠀⠀⢀⡀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣟⢁⡴⠀⢀⡴⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⡴⠋⣀⠀⠀⣀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣾⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣅⣠⠖⢀⣴⠗⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣴⠟⢁⡄⠀⢀⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣏⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠙⢦⡴⠋⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⡾⠃⠀⠀⠀⠀⠀⢀⡴⠋⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⢀⡴⠋⣠⠞⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡴⠋⣠⠞⠁⠀⠀⠈⠻⣦⢀⣤⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠞⠻⣦⡀⠀⠀⠀⢀⣼⠟⣡⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠞⠁⠀⠀⠈⠻⣦⡀⣴⠟⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⣡⡾⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣷⣞⣋⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⠉⠉⠉⠉⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠒⢤⡀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⢀⣿⠀⠈⣷⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⡄⠘⠿⠋⠀⢠⡿⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⢦⣄⣠⣴⠟⠁⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣰⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⡀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⠋⢿⡄⠈⠻⣿⣦⡀⠀⠀⢀⣠⣤⢤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣶⣿⣿⣿⠿⠛⠉⢿⣿⠀⠈⠛⠀⠀⠀⠙⢿⣶⣜⠉⠀⠀⠀⠀⠈⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣆⠀⠀⢠⠀⢀⣴⣶⣿⡟⠉⠛⠳⡄⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡏⠀⠀⠀⢱⣾⣿⣿⣿⣿⠀⢀⣄⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⢹⣿⣿⣿⠈⠉⠀⠀⠁⢀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⠀⠀⠉⣯⣈⡅⡀⠀⠀⠠⠆⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡍⠉⣀⣤⠀⠀⠉⢤⣷⣶⡶⠶⠀⢀⣠⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠸⣿⠀⠀⢸⡆⢹⣿⡿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⣿⠀⠀⠀⠃⠸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⢀⠁⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⢀⠔⠀⠀⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠿⣷⣦⣤⠴⠖⠁⠀⠀⠀⠁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣀⣀⣀⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣶⣿⠟⠋⠉⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⠀⠀⠐⠢⣄⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠟⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠂⠀⠀⠀⠀⢈⣷⣄⠀⠀⠀⠀⣸⣿⠋⠁⠀⠀⠀⢀⣠⣴⡿⠁⠀⠀⡠⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⣠⣿⣷⣦⣤⣶⣶⣿⣿⣿⣿⡇⠀⠀⢰⢣⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢀⠀⠀⠀⢀⣼⣿⣿⠃⣀⣠⣴⡿⠿⠿⠟⠛⠛⠋⠉⠀⢸⣿⡇⠀⠀⠉⠆
⣠⣴⣦⡤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠊⠀⢠⣿⣾⣿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠸
⣿⣿⣿⠀⣤⣀⣀⠀⠈⠑⣦⣤⡤⢾⡇⢀⡅⠀⣰⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠇
⢹⣿⣿⣷⠟⠛⠿⣷⣤⣤⡇⠀⠀⠈⢻⣏⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠃⠀⠺⠇
⢻⣿⣿⡇⠀⠀⠀⠀⠙⢿⡇⣀⠀⠀⠀⠙⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣠⡄
⠘⠿⢿⣷⠄⠀⠀⠀⠀⠀⠻⠼⠗⠢⠴⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣦⣄⣀⣀⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣴⣶⠂⠀⠀⠀⠀⠀⠀⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣃⣤⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⢸⣿⣥⣤⠄⠀⠀⠀⠀⢸⣿⣿⣶⣾⠂
⠀⠀⠀⠀⠀⠼⢋⣿⣿⣿⢃⣠⡄⠀⠀⠀⠀⠀⢠⣿⠇⢀⣠⡔⠀⠀⠀⠀⣰⣿⣿⣶⡗⠀⠀⠀⠀⠛⢛⣿⡟⠀⠀⠀⠀⠀⠟⢻⣿⣿⠏
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⣾⣿⣾⣿⡟⠀⠀⠀⠀⠰⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⣾⣿⡟
⠀⠀⠀⠀⠀⣼⠟⣽⣿⣿⠏⠀⠀⠀⠀⠀⢀⣾⠿⢛⣿⡟⠀⠀⠀⠀⠀⠀⣸⣿⣿⣡⣤⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⢰⣿⡿
⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠁⠀⠀⠀⢀⣾⣯⣤⠆⠀⠀⠀⠀⠀⣿⣿⣷⡾⠁
⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡿⠁⠀⠀⠀⠀⠘⠛⣹⠏⠀⠀⠀⠀⠀⣸⣿⣿⡟⠁
⠀⠀⠀⠀⠀⣸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠉⣼⡟
⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣰⠂⠀⠀⠀⠀⢀⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣤⡤
⠀⠀⠀⠀⠀⢠⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⢀⣿⣿⣯⣤⣤⣶⡶⠂⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣤⡄⠀⠀⠀⠀⠀⢠⣿⣿⣿⣶⠆⠀⠀⠀⠀⣸⣿⣿⣿⣏⣀⡀
⠀⠀⠀⠀⠸⠿⠟⢿⣿⣿⠟⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠃⠀⠀⠀⠿⠿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⠠⠿⢿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⠃⠀⠀⠀⠀⠀⢰⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢰⣿⣿⡟
⠀⠀⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠁⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁
⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁
⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁
⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠀⠀⠀⠈⠁⠁⠀⠀⠀⠁⠁⠀⠀⠀⠁⠀⠀⠀⠂⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣿⣷⣄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣴⢋⡴⣫⡼⠛⠋⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠙⢿⣯⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣀⡿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢞⡥⠤⣤⠄⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⢰⡏⣠⠞⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣭⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣟⣷⣝⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠶⠶⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡴⠞⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣭⡅⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⢸⡇⣒⡂⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠶⠶⠶⣦⠀⠀⠀⠀⣸⠀⣧⠀⠀⠀⠀⢸⡇⠭⠥⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣼⠀⠀⠀⠀⡟⠀⢹⡀⠀⠀⠀⢸⡇⣛⡃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠉⠉⠳⡄⠀⠀⠐⣇⠀⢸⠇⠀⠀⠀⢸⡇⠶⠆⠀⢸⡇
⠀⠀⠀⠀⠀⢠⡏⠈⣧⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣤⣤⣤⣤⡄⣿⠀⠀⣴⠋⠀⠈⢷⠀⠀⠀⢸⡇⠉⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠈⠳⠴⠃⡞⢹⠄⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⡇⣿⠀⠀⣿⠀⣾⠛⢻⠀⠀⣠⡼⣧⣤⣤⣤⣼⣧⣤
⠀⠀⠀⠀⣰⠻⡄⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⡇⣿⠀⠀⣿⠀⣿⠀⢸⠀⠀⠙⠛⠻⡟⣿⢻⡟⠛⠋
⠀⠀⠀⠀⠳⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⡇⣿⠀⠀⣿⠀⢿⠀⢸⠀⠀⠀⠀⢰⡇⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣤⣤⣤⣤⠇⣿⠀⠀⣿⠀⠘⠒⢾⠀⠀⠀⠀⣸⣇⣿⣸⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠶⠶⠶⠞⠃⠀⠀⠙⠶⠶⠶⠋⠀⠀⠀⠘⠷⠿⠿⠿⠾⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠠⣤⣀⡀⠀⢀⠀⢀⣼⢶⡚⠳⠀⢀⣀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠾⢶⣦⣽⠀⠈⠉⠙⠁⠂⠉⠁⢰⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠠⠐⢢⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠰⠀⠀⣸⢳⡖⠀⠀⠉⠠⠤⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠃⠀⠀⠀⠀⣠⠞⣁⠀⠀⠀⠀⠀⢠⠃⠀⠀⡿⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⣀⡤⠚⠁⠉⠙⠛⠁⠀⠀⢀⡎⠀⢠⠴⠃⠀⠉⠓⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⢠⡀⠓⠋⠟⠀⠀⠠⣀⠄⠀⠀⣸⠃⠀⠀⠀⠰⠋⠘
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡀⠀⠠⢟⡧⣀⣀⣀⠰⡄⠀⠀⠀⠀⠒⣼⠶⠴⠚⠈⣳⢄⡀⡄⣀⡠⠂
⠀⠀⠀⠀⠀⠀⠨⠃⠀⠀⠀⠀⡿⠇⠀⠀⠱⣈⣹⠋⠈⠙⠄⢰⣶⣄⣀⣅⠀⣀⣠⣴⣧⠀⠀⠈⠁
⠀⠀⠀⠠⠄⠀⠀⠀⠀⢀⠀⠀⠐⠤⣄⢶⡾⠛⠛⠀⠀⠀⠈⣟⠉⠉⢹⣛⣛⣯⡅⠀⢢⠁⣠⠄
⠀⠀⠀⠀⠀⣅⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣌⢻⣋⠙⠻⠿⢿⡄⠂⠈⠚⠁⠀⠀⡀
⠀⠀⠀⠤⠤⠂⠀⠀⠀⡀⠐⢢⣄⠀⣀⠀⠀⠀⠹⣀⠀⢠⠞⣿⢽⣯⣷⡄⠀⠀⢉⡄⠀⢠⣄⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠹⠀⠈⠀⠒⠒⢂⠀⠉⠁⠈⠀⠀⠀⡳⠳⠾⠛⠋⠀⠉⠀⠈⠀⠀⠈⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠁⠀⠀⠀⠀⠀⢀⡴⠀⡠⣇⠀⠀⠁⠀⠀⡄⠀⠀⠀⠀⠀⢀⠄⠀⠀⢠⡔⠊⠀⠀⡀
⠀⠀⢀⠠⠂⠀⠀⠀⠹⠿⠄⠀⠀⠀⠀⠀⠀⠜⠀⠀⡁⠁⠀⠀⠀⣠⡴⠀⠀⠀⠐⠂⠀⠀⠀⠀⠐⠁⠀⠠⡀
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠔⠉⠀⢠⣀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⢿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣠⡷⠾⠛⢹⡄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⢇⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⣄⣀⣄⣀⣠⡀⡀⢀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣰⡴⠼⠞⣛⠉⠹⣿⣍⣩⣍⣻⢏⡉⠉⠓⠛⠳⠦⣎⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠴⠚⠉⠀⠀⠀⠀⠈⠀⠀⠠⡿⠿⣿⣁⡀⠁⠀⠀⠀⠀⠀⠀⠉⠲⢤⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢠⢀⡅⠁⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⣬⣿⣿⣿⣆⡄⠀⠀⠀⠀⡇⠀⠀⠂⠀⠀⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠻⣿⠀⠀⠀⠀⠀⠀⠀⠺⡷⢸⣆⠀⣚⣿⣿⣿⣿⣟⠀⠀⣥⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣸⢷⣞⡿⣿⣿⢹⣿⣿⣷⡴⢧⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣐⡺⠯⢥⣚⡿⢿⡏⠘⣟⡿⢟⣿⠷⣚⣅⠀⠀⠀⠀⣀⡠⡔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡚⠳⠦⢥⣌⣓⠶⢭⣓⠂⠐⢿⣚⡭⢖⣋⡭⠶⣒⣒⣒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣬⣙⣓⣒⣶⣬⣭⣙⣒⣯⣽⡁⠀⣻⣭⣵⣚⣫⣭⡖⡚⢫⣭⣥⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢶⣂⣉⣉⡉⠿⠶⢶⣊⣉⠷⢶⣇⠀⢀⣨⡷⠶⢏⣉⣲⠶⠿⣉⣁⣲⠶⠶⠦
⠀⠀⠀⠀⠀⠀⣠⣤⣤⠔⠛⠛⠛⣻⣥⣤⣤⠚⠛⢻⣤⣼⠁⠀⠀⠀⣡⣤⣼⠛⠛⢠⣤⣼⡟⠛⠓⢤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠚⠛⢛⣯⣤⣤⣤⠜⠛⠛⢛⣧⣤⣤⠛⠛⢻⡷⠂⠐⠾⣿⠛⠛⢧⣤⣤⡟⠛⠛⢠⣤⣤⣿⡛⠛⠛⠂
⠀⠀⣠⣤⣤⣤⡄⠛⠛⠛⠛⣻⣤⣤⣤⡜⠛⠛⢻⣤⣤⣜⠀⠀⠀⠀⠘⣤⣤⣼⠟⠛⠛⣤⣤⣤⣽⠛⠛⠛⠠⣤⣤⣤⣤⣄
⢀⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣦⡀⠀⠀⣰⣿⣿⣿⡇⠀⠀⠘⣿⣿⣿⣷⡀⠀⠀⠘⢿⣿⣿⣿⣿⣦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠴⠄⠲⠂⠐⠒⠀⠶⠆⢤⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠶⠓⠈⠁⠀⠀⠀⡀⢀⣀⠀⣀⠀⠀⠀⠀⠈⠙⠰⢦⡀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠉⠀⠀⢀⣤⠄⠖⠃⠉⠉⠈⠉⠀⠉⠁⠘⠓⠠⢤⡀⠀⠀⠀⢀⡴⠋⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠀⢀⠠⠞⠀⠀⠀⢀⣀⣤⣤⠤⠤⠤⣤⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢠⡏⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⠀⢀⡐⠋⠀⠀⣠⡴⠞⠋⠁⠀⠀⠀⠀⢀⣀⣄⣀⠀⣠⡴⠛⠻⣯⠀⠰⠄⠘⠷⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠀⠀⣠⠛⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀⣴⠋⢻⡄⠉⠻⣅⠀⢀⡼⠃⠀⠀⠈⠷⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⣀⠋⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⢀⡴⣏⠙⣦⠀⠙⢦⡀⠈⠳⣞⠁⠀⠀⠀⠀⠀⢳⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⢐⠃⠀⢠⡟⠀⠀⠀⠀⠀⠀⢀⣴⠛⣇⠘⢧⡈⠻⢦⠀⠙⢦⣄⢸⡆⠀⠈⢷⡀⠀⠀⢶⠀⠀⠸⠆
⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠟⠀⠀⡾⠀⠀⠀⠀⠀⢀⡴⣏⠙⣦⠈⠳⣄⠙⠓⠀⠀⠀⠀⣨⡟⠁⠀⠀⠈⣇⠀⠀⠠⡆⠀⠀⣷
⠀⠀⠀⠀⠀⠀⢨⠁⠀⠸⠇⠀⠐⠃⠀⠀⠀⢀⡴⠻⣆⠙⢦⡈⠳⢦⠈⠁⠀⠀⠀⠀⠾⠃⠀⠀⠀⠀⠀⢻⠀⠀⠀⣥⠀⠀⢰
⠀⠀⠀⠀⠀⠀⢘⠀⠀⢰⡆⠀⠀⠀⣤⢀⡴⢿⠀⠀⠙⢧⣄⠙⠆⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣙⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠸⠀⠀⢠⡄⠀⠀⠀⠈⢿⡀⠈⢷⡀⠰⣦⡉⠀⠀⠀⠀⣠⠞⢁⣠⠶⠚⠋⠉⠛⠓⢦⣄⠈⠀⠀⠀⠟⠀⠀⣈
⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠁⠀⠀⠀⠀⢈⣷⡄⠀⠙⢦⣌⠳⣄⠀⣠⠞⠁⣠⠟⠁⣠⠖⠛⠛⠛⠶⣄⠈⢳⡀⠀⠀⠃⠀⠀⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⡿⢦⣄⠀⠉⠳⣾⠞⠁⠀⢠⡏⠀⡾⠁⠀⠀⠀⠀⠀⠘⣇⠀⢷⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡛⢷⡴⠋⢠⡾⠋⣠⠞⠉⠛⠶⣾⠁⠀⠀⠀⢸⡇⠀⣧⣠⠤⢤⣠⡤⢤⣀⡟⠀⢸⠀⠀⠀⠠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⢦⣈⣠⠞⠁⢀⡀⠀⠀⠈⠃⠀⠀⠀⠘⣧⠀⢸⣛⡒⢋⣬⠓⢞⣹⠇⢀⡿⠀⠀⠠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⢳⡄⠀⠈⠙⠲⢤⣄⣀⣀⠀⠀⠀⠘⢧⡀⠉⠻⠦⣤⠼⠋⠉⣠⠞⠁⠀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⣀⡀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠙⠳⠶⢤⣤⠤⠶⠛⠁⠀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠀⠓⠆⢤⣤⢀⣀⡀⣀⣀⢀⡤⠀⠀⠀⠀⠀⠀⣀⡄⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳⢀⣄⡀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⣀⡀⠶⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠃⠰⠶⠠⠶⠄⠶⠖⠐⠛⠈⠉

⠀⠀⠀⣠⠴⠖⠒⠂⣠⣄⠀⠀⠀⠀⢀⡤⠶⠒⠒⠲⢤⡀⠀⠀⠀⢀⣠⠤⢤⡤⡤⢄⡀⠀⠀⠀⠀⣠⠴⠒⢒⡲⠦⣄⠀⠀⠀⠀⠀⢀⠤⠆⣶⠦⣄
⠀⠀⢰⣁⡤⠴⠚⠉⠁⢀⡇⠀⠀⢠⡗⠒⠒⠒⠒⠒⢒⣿⠀⠀⠀⣿⡀⠀⠘⡐⠀⠀⢹⡆⠀⠀⠀⡷⣦⣝⣃⣀⣠⡴⡇⠀⠀⠀⠠⣟⠓⢲⡟⠒⣨⡇
⠀⠀⠘⢝⡓⠲⠶⠖⢚⡻⠁⠀⠀⠘⢏⡓⠒⠒⠒⠚⣉⠜⠀⠀⠀⠳⢌⣙⣛⣓⣒⡨⠝⠀⠀⠀⠀⠳⣄⣀⣀⣀⠤⠔⠃⠀⠀⠀⠀⠳⠅⠛⠻⠿⠋
⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⣀⣀⡀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⢀⢜⢧⠀⠀⠀⠀⠀⠀⡠⢆⠀⠲⡄⠀⠀⠀⠀⠀⡴⡡⠒⠒⠪⠣⠀⠀⠀⠀⠀⠀⢠⢮⡀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⠕⠁⢸⠇⠀⠀⠀⠀⢸⡀⡨⢶⠁⢸⠀⠀⠀⠀⠀⡗⡀⠀⠀⢀⢆⠂⠀⠀⠀⠀⠀⡇⠀⠙⠦⣄⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡊⠁⢀⣠⠎⠀⠀⠀⠀⠀⠀⠙⠤⠤⠗⠁⠀⠀⠀⠀⠀⠙⠾⣦⣐⡭⠊⠀⠀⠀⠀⠀⠀⠙⢤⣀⣀⡼⠋
⠀⠀⠀⠀⠀⠀⣀⡠⠄⡀⠈⠉⠉⠀⠀⠀⠀⠀⣀⠤⢄⡀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⢤⡀
⠀⠀⠀⢀⣴⣊⠁⠀⠀⢈⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⢀⢿⠀⠀⠀⢀⡠⠒⠉⠀⠈⠃⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⣠⡚⠁⠀⠀⢀⠇
⠀⢀⡔⠁⠀⠈⢳⢀⡴⠋⠀⠀⠀⣠⠊⠙⢵⣄⢀⠴⣫⠞⠀⠀⣰⣟⡳⣦⠀⠀⡠⠂⠀⠀⢠⠞⠁⠀⠀⠀⣠⢞⠕⠁⠀⠀⠀⣠⠊⠀⠑⢤⡀⡠⠊
⠀⢸⠀⠀⢀⣠⠞⠋⠀⠀⠀⢀⡜⠁⠀⢀⡠⢟⡵⠊⠁⠀⠀⣜⣿⣺⣽⣽⡧⠚⠁⠀⠀⢠⣇⡀⣀⡀⢔⡫⠚⠁⠀⠀⠀⠀⢰⡃⠀⠀⢀⠔⠋
⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠸⢦⣤⠖⠉⠊⠁⠀⠀⠀⠀⠀⠙⠾⠷⠛⠉⠀⠀⠀⠀⠀⠀⠓⠁⠑⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⢀⡤⣔⣒⣒⠢⣄
⠀⠀⠀⡠⠴⠤⠶⠤⠶⠦⣄⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠂⣎⠀⠀⠀⢱⠈⡇⠀⠀⠀⠀⢠⢶⣒⡉⠉⣏⢉⣀⢶⡄
⠀⠀⠀⠳⠤⠄⣀⣀⣠⠶⠞⠀⠀⠀⠀⢯⠲⠤⣤⣤⠤⢶⠃⠀⠀⠀⠀⠘⡧⠬⣭⣃⡭⠥⢊⠇⠀⠀⠀⠀⠘⠦⠤⠤⠥⢤⣤⣤⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠐⠚⠁⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠒⠐⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠿⠟⠛⣿⣿⣿⡯⠉⠉⢙⢛⠻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⡿⡩⡰⢠⢠⠀⢻⣿⣿⣿⢌⢎⢢⡱⡝⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣄⠈⢻⣷⣔⣁⠇⡆⠾⢸⣿⣿⣿⣘⣈⣢⣵⣾⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⠙⠛⠻⠿⠿⣿⣿⣿⣿⠛⠛⠉⣉⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⣿⣿⣿⡿⢀⣴⣾⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⢍⠀⠀⠠⣿⣿⣿⠀⠀⢈⢉⢻⣿⠀⠀⠀⣸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣂⣂⡂⣿⣿⣿⢡⢃⣁⣣⣾⠟⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠈⠉⠛⠛⣿⣿⣿⡟⠛⠛⠉⠁⠀⠀⢀⣾⣿⣿⣿⣯⡂⠄⠆⣸⣿⣿⡇⡀⣨⠉⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣄⡀⠀⠀⢹⣿⣿⣇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠙⠻⠿⣶⣾⣿⣿⣷⣶⣶⡾⠿⠋
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠘⣿⣿⣿⡄⠀⠀⠀⠀⣸⣿⣿⣿⡿⠁⠀⠀⠀⢀⣿⣿⣿⠁
⠀⠀⠀⠀⠀⣿⡛⡉⠀⣾⣿⡇⠀⠠⣨⡿⠀⠀⢹⣿⣿⣷⡀⠀⠀⢠⣿⣿⣿⣿⠇⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠈⠛⠓⠶⢿⣿⣿⠛⠛⠉⠀⠀⠀⠀⢿⣿⣿⣷⡀⠀⣼⣿⣿⣿⡿⠀⠀⠀⠀⣼⣿⣿⣿⢁⣤⣶⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣀⣿⣿⣿⣿⡇⠀⠀⢀⣾⣿⣿⣿⢣⣿⠿⠿⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣴⣿⣿⣿⣿⠃⠀⠻⢦⣤⣼⣿⡟⠀⢉⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⣼⣿⣿⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣦⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣠⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣠⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣦⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢠⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢰⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠇⠘⣿⣿⣿⡿⢿⣿⡿⠏⠀⠀⢸⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠛⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⣼⠥⠀⠀⠀⠈⠑⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣿⠾⠃⠀⠀⠀⠀⠀⢀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣀⣴⣶⣶⡶⠶⢶⢶⡏⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠀⠀⣼⢸⡇⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡼⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣸⠃⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠺⠛⠛⠛⠻⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢠⠇⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣠⣴⠶⠿⠛⠷⠶⣦⣀⡏⠈⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠉⢷⡀⠀⠀⠀⠀⢰⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠴⠞⠛⢧⣄⣀⠀⠀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⢀⡴⠞⠛⠒⠒⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠺⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣶⣤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢨⢿⣿⣿⣷⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⢸⢄⠀⠀⠀⠀⠈⠛⣻⣿⣿⠃⠀⣠⣤⣀⠀⠀⠀⣀⢣
⠀⠀⠀⠀⠀⠸⡘⢿⣷⣷⣀⣶⣾⣿⡿⠋⢰⣿⣿⣿⡿⠛⡳⣾⣿⡇
⠀⠀⠀⠀⠀⠀⢻⣧⡙⡻⣿⣿⣿⡿⠃⠀⢯⡻⠟⠛⠁⠀⣱⡮⠟⠰⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠳⣗⣎⠹⣋⣉⠀⠀⠀⠀⠀⠀⠀⢀⢰⣿⠇⣀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣷⡈⠿⢿⣭⣻⣶⣤⠀⠀⠁⠁⠀⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⣿⠀⠸⠿⢸⡟⠉⠄⠤⠀⠄⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣯⢟⡿⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠴⢿⡆⠀⢺⣌⢛⠁⠀⠀⠀⠀⠁⡅⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣟⣾⡞⣫⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣬⣿⣷⣤⣤⣁⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣟⣿⣧⣿⡻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⣧⡘⢻⣿⣿⣿⡏⢶⡦⣤⣀⣀⣀⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⢫⡧⢼⠁
⠀⠀⠀⠀⠀⣀⣤⣾⣿⣶⣿⡌⠻⠿⠿⣿⣄⠀⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣿⢲⠃
⠀⠀⡠⢶⣿⣿⣿⣿⣿⡿⣿⣷⡀⠀⢰⣿⣿⡧⠘⣿⣿⣿⣖⡲⣄⠀⠀⠀⠀⠀⠀⠀⢠⣷⣄⠙⠳⣄
⠀⠀⠀⠛⠻⢿⣿⣿⣿⡇⣿⣿⣷⡀⠉⠊⣿⣷⡄⢻⣿⣿⣿⣿⣎⢧⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣦⣄⠀⠂
⠀⠀⠀⠀⢀⣺⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣿⣿⣿⣼⣿⡿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣼⣿⣿⣿⣿⢿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣜⣿⠿⣿⣷⡄⢻⣿⣿⣿⣟⣿⣿⣿⣿⣿⡏⢇⠀⠀⣸⣿⣿⣿⣿⣿⣄⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⢟⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠟⠻⡿⠟⠛⠋⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠿⠿⠿⠃⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⢷⠝⠏⠁⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⢛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠶⠶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣛⣭⣶⠾⠿⠿⢶⣾⣽⡻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢫⣾⣟⣭⣶⡿⠿⠿⢷⣶⣝⣿⣮⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢣⣿⣿⣿⣯⣵⡿⢿⠿⣷⣮⣿⣿⣿⣧⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⡏⣾⡟⢿⣎⣿⣿⣿⣿⣿⡞⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣧⢫⣾⣮⡣⣿⣿⣿⣿⣿⢳⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣏⢿⣿⣿⡿⣵⣿⣿⣿⣷⡝⣿⣿⣿⢏⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣧⡻⢿⣶⡌⣿⣿⣿⣿⣴⣾⡿⣫⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣭⡁⣿⣿⣿⣿⣩⣵⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣏⡇⣿⣿⣿⣿⣟⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡇⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠿⠛⢿⣿⣿⣿⣿⣿⣷⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⣀⡀⣀⢀⡀⣀⢀⣀⡀⣀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠹⠧⠟⠟⠧⠸⠄⠟⠁⠇⠟⠧⠗⠟⠇


⣏⣈⣯⣏⣟⣯⣿⣹⣽⣽⣋⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢀⠔⠋⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡰⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠁⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⠁⠀⠀⠁⠢⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠶⠲⠤⣀⠸⣄⣀⣀⣀⣀⣀⡀⠤⡏⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠈⠂⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⢄⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠠⠀⣀⣑⣅⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠻⡀⠀⠀⠀⠀⠀⢠⠏⠀⢀⣠⠴⠒⠋⣉⠝⢓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣤⣠⠤⠖⠁⠀⢠⠏⠀⢀⠄⢊⠤⠊⠀⢠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠫⢍⡉⠈⠉⠒⢄⡀⠀⠀⠀⠀⢸⠤⠎⣀⣐⡁⠀⠄⢊⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠁⠂⠌⡑⠢⢄⡀⠙⢆⠀⠀⠀⠀⠑⠒⠶⠶⠶⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠐⠠⠀⢀⡀⢁⣢⡬⠑⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠒⠒⠒⠂⠈⠁⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⠉⠀⢀⠈⠉⢻⠀⠀⠀⣿⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠈⠀⠉⠉⠀⢹⠀⠀⠀⣏⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠛⠃⠀⠀⠀⠰⣧⠀⠀⠀⡇⠀⠀⠀⠈⠁⠁⠸⠀⠀⠀⣏
⠀⠀⠀⢸⠀⠀⣠⡀⠀⠀⡇⢠⣧⢜⣿⣁⠀⠀⠀⠀⠸⡄⠀⠀⡇⠀⠉⠉⠁⣶⡄⣿⠀⠀⠀⣧
⠀⠀⠀⠸⠀⠀⡩⡰⢦⡀⢠⡈⠁⠀⢩⡉⠀⠀⠀⠀⢰⡇⠀⠀⣇⣤⣈⡃⠢⣤⡄⢿⠀⠀⠀⡇
⠀⠀⠀⢰⠀⠀⠀⠶⠯⠉⣾⣻⣷⣶⡿⠀⠀⠀⠀⣀⠀⠃⠀⠀⣿⣿⣿⣿⢷⠟⠐⣘⠀⠀⠀⡿⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠁⠀⠒⣰⣿⣿⣿⣿⠇⠐⠂⠀⣼⣇⠀⢺⡇⢠⠿⡿⠿⠛⠓⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⢺⣿⣧⠐⠀⠀⠀⠀⢸⡄⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⣀⡠⠤
⠀⠀⠈⠒⠲⠤⢾⣛⡛⠓⠀⠀⣿⣿⠀⠀⠀⠀⠀⡈⡧⣿⣏⡀⠀⠆⠀⢀⣀⡠⠤⠶⠒⠊⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠻⠭⢍⣀⣀⠀⠀⠀⣀⣉⣩⠯⠿⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠈⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠉⣡
⠀⠀⠀⠀⠀⠀⢰⡿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢀⠛
⠀⠀⠀⠀⠀⠀⢾⡇⣷⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊
⠀⠀⠀⠒⢤⣀⠼⠧⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠴⠂⠀⠀⣀⣠⣴⣦⣁⡀⠀⠐⠒⠂
⠀⠀⠀⠀⠀⠉⠛⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⠿⠿⠋⠉

⠀⠀⠀⠀⠀⠐⠀⠀⣰⣶⢖⡴⣶⡖⠒⡶⢒⡲⣶⣦⣀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣰⣶⣦⣶⠖⣶⢶⣶
⠀⠉⢠⡜⢢⣦⡀⣀⣀⣠⣪⣾⡿⡀⠀⠀⠀⠁⢸⣿⣿⠀⣤⠞⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢠⣂⢴⣽⣿⢿⣿⠿⣱⣿⣯⣿
⠠⡤⣾⣋⡾⣿⢾⡼⣼⣷⣡⡟⠀⠀⠀⣽⣶⣶⣾⣿⡧⢐⣿⡒⡅⠀⠀⠀⠀⢰⣿⣿⣿⠷⠀⠀⢠⣿⣃⠂⢨⡟⡱⣿⣲⣇⣿⣿⣿
⠨⠅⢻⣿⡵⢷⢏⣙⣿⡉⠛⢛⠃⠀⠀⢻⣯⣿⣿⣿⣦⣼⠛⠋⠁⠀⠀⠀⠄⠈⠉⠁⠀⠀⠀⣾⣿⣿⣿⣿⡔⣿⣙⡿⢯⣿⣿⣿⠟
⠐⠀⢶⡈⣴⡿⢀⣿⣈⡉⠁⠉⠀⢀⣴⠿⢿⣿⣿⢿⡿⢿⢀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡸⣭⣿⡾⣻⡿⣅⣿⣿⠝⠛⠋
⠀⠁⢈⠉⠿⣁⣼⣿⣿⣷⣷⡄⢸⢸⠷⣶⢸⣿⣿⣿⣿⣾⡆⣁⠀⠀⠀⠀⣸⡐⠳⠀⠈⠀⣿⣿⡿⣽⣕⣹⡏⠀⠀⠀⡀
⠀⠀⠘⠃⠈⠉⢿⣿⣿⣿⡷⠁⠘⢸⡄⣿⠀⠛⢿⣿⣿⣿⣿⣿⣶⣤⣴⠀⠈⢉⠀⠐⣀⣿⣿⣿⣿⣷⢉⣉⡠⡄⠰
⠀⠀⠀⠀⠀⠀⢰⡿⠟⠻⠇⠀⠀⢸⣿⠇⠆⣠⣾⡋⢡⠀⢈⡉⣻⠄⠀⣤⡤⡜⣳⣾⣿⣿⣿⣿⢿⣟⢧⣿⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡟⢲⣾⣴⣿⣿⣿⡳⣰⠟⣰⣿⣿⣿⣯⣭⣿⣷⣿⣶⣿⣝⡏
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠂⠀⠀⠈⠀⠛⢻⣏⡍⢤⣴⠾⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠁
⠀⠀⠀⠀⠀⡧⡀⠀⠀⢀⣀⡋⠈⠈⢳⣬⠂⠀⠀⠀⠀⢠⣾⣿⡿⣾⠿⣉⣽⣿⣿⡿⠛⣟⠛⠟⠉⣩⠟⠁⡀⠀⠀⢀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⠏⠀⣰⣿⣟⠡⠄⡀⣤⣀⣤⠼⠿⣻⡛⠿⠋⠉⠁⠈⣨⣿⡄⠁⠀⠐⣛⣥⡶⠊⠁⠀⢰⣮⣀⠂⠃
⠀⠀⠀⠀⠀⢥⣿⣿⣶⣿⣷⣶⣾⣿⣷⣶⢓⡿⠋⠘⠀⢰⡞⢩⡅⠴⠄⠀⠐⠶⠋⣿⣶⠀⠀⠀⠁⠀⠠⠀⢀⣠⣾⣿⣿⣽⣿⠄
⢀⠐⠀⠀⣤⣾⣿⣿⠿⠿⠟⣛⣻⠟⣿⢣⢞⡿⡰⢀⠈⣰⡪⠼⢿⠻⠷⡆⣰⣾⣿⡟⠋⢠⣀⣀⣻⣶⣤⣴⣿⣻⣿⣟⣿⣿⡇
⠀⠀⠀⠠⠦⠉⠉⡙⠻⣷⣿⣿⣿⠀⠈⣥⣶⣶⡃⠁⠀⠀⠂⠀⠀⠻⠂⠁⠙⢿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠇
⠀⠀⠀⠀⠀⠀⢀⡈⠀⠂⡉⢻⣿⡄⢲⡾⢿⡾⠛⠀⠀⣴⣄⠘⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣦⣤⡀⠢⢤⠀⠚⠋⢠⣴⣬⣍⡀⠀⠀⣽⡆⠁⠂⠠⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠸⠿⠟⠋⠁⣿⣿⡟⢐⣿⣿⣻⣷⣷⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⣿⢿⠿⠛⠉
⠀⠀⠀⠀⠀⠙⠋⠀⠈⠁⡌⠅⠈⠻⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⢄⡴⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣤⡶⢿⣭⣿⣽⡿⢶⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⡓⠀⢼⣿⠿⠿⠿⠟⠛⢶⣿⣻⡿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠶⢀⠇⠃⠀⠀⠛⠀⠀⠀⣀⣀⠀⠻⣯⣿⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢛⢿⡄⠚⠙⢶⠤⠐⡿⠟⢿⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠍⠀⠀⠀⠀⠀⢐⣀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣘⣃⠀⠀⠀⠀⣻⣦⣿⠁
⠀⠀⠀⠀⡄⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⣀⣤⠞⣿⢇⡽⣿⣦
⠀⠀⠀⡈⠀⠀⠀⢠⡇⠀⠀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⡀⠀⠙⣾⠿⠋⠀⠀⠸⣼⣛⣯⡟
⠀⠀⠀⡧⠀⠀⠐⠀⠉⠉⠉⠉⠉⠉⠉⠛⠻⣝⣟⠁⠈⢹⣷⣾⣿⣄⠀⠀⠀⠀⠙⣿⢯
⠀⠀⠀⣧⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢹⡆⠀⠈⠻⠿⠉⠛⢦⠀⠀⢀⡴⠃⣰⠷⣄
⠀⠀⠀⠀⠉⠙⠲⠤⣄⣀⣀⠀⠀⠀⢠⣴⣾⡟⡼⠁⠀⠀⠠⣤⠴⢻⡞⣷⣞⣉⡀⢰⡇⠀⠈⠙⠲⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢻⣷⣶⣿⣿⣦⡆⣸⠇⠀⠀⠀⠀⠘⢻⡿⠁⠀⠳⣸⠁⡠⠂⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠻⠛⠿⢾⠏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠠⣿⡀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠇⠀⠘⠟⠒⠒⣤⠶⣦⣶⣶⣿⣷⢔⠤⣄⣄⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⡄⠀⢚⠃⠀⠀⠀⠀⠀⠐⠟⣿⢛⣻⣿⣿⣯⣗⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠙⠄⢻⡅⠀⠀⠀⠀⠉⠉⣼⢣⣏⣭⣵⣾⣯⣟⠭⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠠⡄⠸⡘⡇⠀⠀⠀⠀⠀⢸⣧⠜⠋⠁⠀⠀⠀⠙⢷⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⡈⠣⠐⢧⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⣀⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠉⢂⣀⡨⠤⠖⠋⠁⠀⠀⠀⠀⢀⣠⡴⠖⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠁⠀⠀⠀⣀⠀⠤⠤⠖⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁⠀⠀⠀⣠⠆⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤
⠀⠀⠀⠀⠀⢠⣤⣾⠛⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣶⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⢛⣷⣤⡄
⠀⠀⠀⠀⠀⢸⡇⢸⠀⣿⢸⡇⠀⠀⢠⣤⣤⣤⣤⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠻⣮⠙⠷⣤⠀⠀⠀⠀⢀⣤⣤⣤⣤⡄⠀⠀⢸⡇⣿⢸⡇⢸⡇
⠀⠀⠀⠀⢸⣿⡇⢸⠀⣿⢸⣷⣶⣶⣾⣇⡀⢀⣼⣷⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣿⣶⣶⣶⣶⣾⣧⡀⢀⣸⣷⣶⣶⣾⡇⣿⢸⡇⢸⣿⡇
⠀⠀⠀⠀⠀⢹⡇⢸⠀⣿⢸⡇⠀⠀⠀⠉⢻⣏⠙⢧⡀⠀⠀⠀⢹⣣⡟⠳⠶⣤⣤⣤⣤⣤⠀⣿⠀⠀⠀⢠⡾⠉⣹⡟⠁⠀⠀⠀⢸⡇⣿⢸⡇⢸⡏
⠀⠀⠀⠀⠀⠸⠷⣾⣀⣿⢸⡇⠀⠀⠀⠀⠀⢹⣄⠈⢻⣄⠀⠀⢹⣿⡃⠲⠶⠀⠀⠾⠆⢸⡆⣿⠀⠀⣰⠟⠀⣰⠏⠀⠀⠀⠀⠀⢸⡇⣿⣨⡷⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⠾⠇⠀⠀⠀⠀⠀⠀⠻⣆⠀⠹⣦⣄⠘⢿⣇⠀⢀⣀⣀⠀⢀⣾⣿⠃⣠⡼⠋⠀⣰⠏⠀⠀⠀⠀⠀⠀⠸⠷⠿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠙⠳⣌⠙⢦⣀⣉⣉⣠⠾⢋⣵⠞⠉⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠘⢷⣴⣟⠉⠉⣿⣤⡾⠁⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⣠⡟⠁⠙⠛⠛⠋⠈⢷⣄⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢀⣤⡄⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⢹⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠉⠉⠉⠉⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣤⣤⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢸⡇⢹⡆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢦⣾⠀⠈⣷⠴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⣿⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢰⡏⠀⠀⢻⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⢸⡇⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣤⣼⠁⠀⠀⠘⣧⣤⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠁

⠀⢀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⡟⣉⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠻⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡷⠀⠀⠀⠙⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡄⠀⣠⣿⣿⣿⣿⣿⣥⠀⠀⠀⠀⠈⢿⣿⣿⣿⣆
⠀⠀⠀⠀⢸⡿⠿⠿⠿⠿⠿⣿⠀⣿⠿⠿⠿⠿⠿⣿⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣤
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠄⢸⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⡅
⠀⠀⠀⠀⢸⣷⣶⣶⣶⣶⣶⣿⠀⣿⣶⣶⣶⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⢻⣿⣆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⣀
⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⡿⠟⠀⠻⢿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠔⠂⢌⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣠⢤⠖⠒⢦⢤⡀⠀⠀⠀⠀⠱⣁⠨⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡤⠐⢊⠁⠀⠀⠉⢢⠀⠀⠈⠻⣿⠟⢻⠛⢻⡿⠋
⠀⠀⠀⠠⢎⡇⡇⢤⣿⠆⡅⣏⠦⠀⠀⠀⠐⡭⠀⢀⠃⠀⠀⢀⠆⠀⠀⠈⡄⠀⠀⠀⠀⢈⠝⣁⠄⠀⠀⠀⢸⠀⠀⠀⠀⠈⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠉⠚⠦⠤⠞⠚⠁⠀⠀⠀⠀⠈⠂⢁⠎⠀⠀⠀⠊⡀⠀⠀⠀⡈⡆⠀⠀⠰⡡⠜⠑⠪⣴⢀⠔⠁⠀⠀⠀⠀⠀⠢⠈⠠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁⠀⠀⠀⠀⠑⠙⠢⠴⢚⠑⠁⠀⠀⠁⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣖⠂⠀⠀⢒⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣭⣭⣭⣭⣭⣍⣭⣩⣩⣩⣍⣉⣉⣉⣉⡉⣋⢩⣎⢉⣻⢾⣭⣭⣩⣭⣩⣭⣭⣍⣭⣭⣍⣉⣉⣉⣉⡉⣙⣉⣋⣙⣋⣛⣉⣉⣉⣛⣋⣛⣉⣛⣙⣋⣙
⣾⡋⢡⣤⡎⠉⣑⠀⣷⢙⡋⠉⠛⣦⡤⠖⣽⠶⠲⢯⡁⠀⠹⡏⣥⠽⠇⣬⠻⡿⠁⣿⢠⡿⠛⠛⠉⡛⢙⡛⠛⠛⠛⣛⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⡯⢿⠢⢈⣡⣽⠶⠒⢾⣥⣍⠠⢾⠈⢰⢳⣅⠪⠀⡇⠸⢦⠇⡿⠀⠀⢸⠀⢹⠈⣿⢁⣷⠒⣛⠉⠀⠀⠙⢶⣶⣶⣿⣿⣿⡿⢻⠟⢿⣿⣿⣿⣿⣿
⠻⣦⣄⡵⣏⣿⡇⢤⣿⠆⡿⣏⡷⣤⢮⣏⢱⡏⠀⢁⠃⡼⡲⢲⡇⠀⠀⠈⣄⢸⠀⠛⠄⣩⡿⣩⠄⠀⠀⠀⢸⠇⣀⡔⠱⢸⠀⢸⠀⢸⠁⡯⣥⡤⢬
⣀⣻⡿⣆⢌⠙⠿⠦⠤⠾⠟⣉⡠⣶⣾⠀⣜⠂⢁⠎⢰⠉⢰⠏⡀⠀⠀⠀⡈⡇⠠⠚⣰⣩⠔⠓⢾⣵⢀⡴⢫⡄⠙⢳⠰⡘⢧⣈⡠⠞⠰⠐⢹⣇⣾
⣿⣿⣈⡈⠁⢑⣿⣨⣬⣽⣿⠑⠛⣾⣇⣠⣛⠒⢁⢀⡿⠦⢮⠓⣙⠦⠤⢊⠑⠁⢈⢜⡋⠺⠆⣹⣦⠬⢩⡌⠛⣾⣶⠿⠅⢘⣓⣰⢤⡛⢜⣶⣸⢿⣿
⢶⠛⠛⠛⢻⠛⡿⢩⠉⣹⣿⣿⣿⣿⣿⣿⣯⣿⣵⣾⣿⣦⣸⣊⣭⣼⣣⣬⣵⣾⣶⣿⣬⣧⣶⣿⣥⣶⣮⣤⣶⣿⣯⣴⣯⣤⣾⣷⣰⣵⣮⣷⣿⣾⣼
⠿⣥⣤⠄⣠⠄⠌⢸⣾⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿