Jobless Emojis & Symbols

⠀⠀⠀⠚⠁⠀⠀⠀⠀⠠⠲⠀⠀⠊⢳⠀⠀⠀⠋⠀⠀⠀⠀⠀⠐⠆⠀⠀⠉⡆⠀⠀⠰⠁⠀⠀⠀⠀⠀⠶⠄⠀⠐
⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⣀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠁⠀⡀⠀⢀⠀⠀⠂
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠈⠄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠐⠆⠀⠀⠉⡂⠀⠀⠘⠁⠀⠀⠀⠀⠀⠒⠄⠀⠈⢙⠀⠀⠀⡋⠀⠀⠀⠀⠀⠐⠳⠀⠀⠉⠃⠀⠀⠐⠋
⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⡀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⢀⠀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⢀⡀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠠⠂⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⡀⠔
⠀⠀⠀⠋⠀⠀⠀⠀⠀⠐⠛⠀⠀⠁⣹⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠃⠀⠀⠉⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠛⠂⠀⠈
⠀⠀⠀⠈⠥⠀⠀⠁⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠤⠀⠈⠀⠀⡀⠀⠀⢀⠈⠀⠀⠀⠀⠡⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣌⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⡀⠀⠀⢠⣀
⢀⠀⠀⠉⠃⠀⠀⢀⠅⠀⠀⠈⡀⡀⠀⠀⠀⡀⠉⠂⠀⠄⢨⠀⢂⠀⠁⢀⠀⠀⠀⢀⠘⠙⠀⠀⠀⡁⠀⠂⠨⢁
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠅
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⡴⢦⠀⠀⠰⠛⠆⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⢠⠶⡄⠀⠀⠞⠳⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⡴⢦⠀⠀⠰⠛
⠂⠀⠄⠀⠂⠄⠠⠀⠠⠄⠀⠀⡀⠀⠀⠀⠀⠠⠒⠀⠠⠀⠐⡠⠀⠄⠀⠤⠀⠀⢀⠀⠀⠀⠀⠀⠔⠂⠀⠄⠀⠀⠄⠠⠀⠠⠄⠀⠀⡀⠀⠀⠀⠀⠠
⠀⠀⠂⠀⠀⠒⠒⢀⠀⠀⠀⠠⠄⠀⠀⠀⠤⠀⠀⠀⠐⠀⠀⠐⠒⠀⡀⠀⠀⠀⠤⠀⠀⠀⠠⠄⠀⠀⠀⠂⠀⠀⠒⠂⢀⠀⠀⠀⠠⠀⠀⠀⠀⠤
⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂
⠀⠀⠀⠀⡴⣦⠀⠀⠐⠛⠆⠀⢀⠀⠸⠉⠀⠀⠀⠀⠀⠀⢠⢶⡄⠀⠀⠚⠳⠀⠀⠀⠀⠏⠁⠀⠀⠀⠀⠀⠀⡴⣦⠀⠀⠐⠛⡆⠀⢀⠀⠸⠉
⠠⠄⠀⠂⠀⠀⠀⠀⠁⠄⠃⠀⠀⠀⠒⠤⠂⠀⠀⠄⠀⠐⠀⠀⠀⠀⠈⠀⠘⠀⠀⠀⠀⠢⠐⠠⠀⠠⠄⠀⠂⠀⠀⠀⠀⠁⠠⠃⠀⠄⠀⠀⠤
⠀⠀⠀⠠⠠⠠⠀⠀⠄⠀⠀⠀⠐⠀⠀⠐⠐⠀⡀⠀⠀⠀⠄⠄⠀⠀⠠⠀⠀⠀⠀⠂⠀⠀⠂⠂⢀⠀⠀⠀⠠⠠⠄⠀⠀⠄⠀⠀⠀⠐⠀⠀⠐⠐
⠀⠀⠀⠀⡀⠀⠀⠀⠀⢒⠈⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⡂⠁⠀⠀⠀⣉⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⢒⠈⠀⠀⠀⢈⡁
⠀⠀⠀⠀⢀⠀⡐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡐
⠀⢀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⡴⢦⠀⠀⠰⠉⠆⠀⡀⠀⠸⠋⠀⠀⠀⠀⠀⠀⢠⠶⡄⠀⠀⠊⠱⠀⡀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⡴⢦⠀⠀⠐⠉
⠃⠀⠂⠀⠠⠄⠒⠀⠠⠄⠐⠒⡀⠀⠀⠀⠀⠐⠓⠀⠐⠀⠀⠄⠐⠂⠀⠤⠀⠒⢀⠀⠀⠀⠀⠠⠈⠂⠀⠂⠀⠠⠆⠒⠀⠠⠄⠐⠂⡀⠀⠀⠀⠀⠐
⠀⠀⠂⠀⠀⠒⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠐⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣀⠀⠀⠀⠀⠄
⠀⢆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⡥⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢄⡃⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⣘⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠂⠀⠂⠀⢄⡃
⠀⠇⠀⠀⠖⢦⠀⠀⠘⠉⡇⢀⡀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠰⠳⡄⠀⠀⠋⢹⠀⡀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠞⢦⠀⠀⠘⠉⠇⢀⠀⠀⠚⠉
⠰⠖⠐⠂⠀⠀⠀⠀⠁⠐⠁⠄⠒⠀⠄⠔⠒⠄⠀⠂⠀⠒⠀⠀⠀⠀⠈⠀⠊⠠⠀⠂⠀⠠⠒⠢⠀⠐⠀⠐⠂⠀⠂⠀⠀⠁⠐⠃⠀⠐⠀⠈⠔⠂⠄
⠀⠂⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⢀⡈⠈⠀⠄⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⣀⠁⠁⠠⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⢀⡈⠈
⠀⡇⠀⠈⣁⠀⠀⠀⠉⢉⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠈⠉⡁⠀⠈⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠉⢉⠀⠀⠁⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠂⠀⢀⣄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣀⡀⠀⠂⠀⢀⣄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣀⣀⠀⡂⠀⢀⣄
⠀⠀⠀⠐⡙⠂⠀⠈⠀⡉⠀⠀⠀⠈⠀⡀⠀⠀⠀⠈⠐⠉⠂⠀⠀⠀⡉⠀⠀⠀⠈⠈⡀⠀⠀⠀⠈⠐⠋⠃⠀⠀⠁⡉⠀⠀⠀⠈⢀
⡀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠈⠁⠀⠁⢉⠌⠁⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠈⠅⠀⠁⢁⡈⠁⢀⠀⠀⠐⠀⠀⠀⢀⠈⠁⠈⠁⠀⠀⢉
⠀⠀⠀⠠⠀⠁⠀⠠⠤⠀⠀⠂⠀⠐⠐⠀⠐⠀⠀⠀⠨⠀⠀⠀⠀⠤⠀⠀⠂⠀⠐⠂⠀⠒⠀⠀⠀⠈⠄⠁⠀⠠⠤⠄⠀⠂⠀⠐⠒
⠀⠀⠀⠀⠂⢀⠄⠀⠐⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠉⠀⠂⠀⠤⠀⠀⠀⢈⠀⠀⠈⠁⠀⠠⠀⠀⠁⠀⠂⠀⡠⠀⠀⠁⢀⠀⠄⠈⠁
⠀⠀⠀⠠⠞⠂⠀⠀⠀⠀⠀⡠⣄⠀⠀⡔⢲⡄⠀⠀⠠⠞⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠐⠲⡄⠀⠀⠀⠞⠂⠁⠀⠀⠀⠀⢠⢄
⠂⠉⠄⠐⠠⠰⠄⠀⠄⠀⠀⠀⠀⠀⠀⠁⠔⠃⠉⠄⠐⠠⠠⠄⠀⠤⠀⠄⡐⠀⠀⠀⠀⠴⠃⠈⠄⠐⠠⠀⠄⠀⠤⠀⠀⡀
⠀⠀⠂⠀⡐⠒⢂⡀⠀⠀⠠⠄⠀⠀⠀⠄⠀⠀⠀⠂⠀⠀⠒⢂⡀⠀⠀⠀⠄⠄⠀⠀⠄⠄⠀⠀⠂⠀⠀⠒⢂⡀⠀⠀⠀⠄⠄
⠁⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠁⠀⢀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢌⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢬⣀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⣀⡐⠀⠀⠀⢬⣁
⠀⠀⠀⠰⠛⠆⠀⢀⠁⣃⠠⠤⠀⡋⠀⠀⠀⠀⠀⠀⠐⠛⠆⠀⢀⠁⣙⠠⠤⠀⠙⠐⠀⠀⠀⠀⠀⠀⠛⠆⠀⢀⠁⢙⠠⠤⠀⢘
⠈⠀⠈⠐⠀⠀⠀⠀⠐⠁⠐⢈⠀⠃⢈⣁⠀⠈⠈⠈⠑⠀⠀⠀⠀⠀⠁⠐⢈⠀⠃⢃⣁⠁⠘⠀⠈⠑⠀⠀⠀⠀⠐⠁⠐⢈⠀⠁⢊
⠀⠀⠀⠉⠀⠀⠀⠌⣠⠀⠀⡄⠀⠠⠀⠀⠐⠀⠀⠀⠉⠀⠀⠀⠈⢁⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠀⠉⠀⠀⠀⠨⢡⡀⠀⠀⠀⠠⠄
⠀⠀⠐⠐⠂⠀⡄⠀⠒⠀⠀⠠⠀⠈⠂⠀⠀⠀⠀⠒⠐⠂⠀⡀⠀⠒⠀⠀⠠⠀⠈⠂⠀⠠⠀⠀⠐⠐⠂⠀⠀⠀⠐⠂⠀⠠⠀⠀⠂
⠀⠀⠀⢠⠖⠈⠀⠀⠀⠁⠀⣠⣄⠀⠀⡠⢦⡈⠀⠀⢠⡖⠈⠀⠀⠀⠀⠀⣠⣄⠀⠀⠠⢦⡈⠀⠀⠀⡔⠈⠁⠀⠀⠀⠀⢠⣄
⢄⠈⠁⢀⢀⠤⡀⠀⡀⠀⠄⠁⠈⠀⢀⠃⡰⠆⠈⠅⠰⢠⠀⠀⠀⡀⠀⠤⠀⠈⠀⠀⠀⡠⠇⡈⠅⢀⢠⠄⠄⠀⠀⠀⠤⡀⠈
⠀⠀⠂⠀⠀⠒⠀⡀⠀⠀⠠⠄⠀⠀⠀⠄⠀⠐⠀⠂⠀⠀⠒⠂⡀⠀⠀⠠⠄⠀⠀⠀⠄⠀⠀⠀⠂⠀⠀⠒⠂⡀⠀⠀⠀⠄
⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢀⠀⡀⠉
⡿⡿⣿⢿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣷⢿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠡⠀⠀⢀⣀⠀⠀⠀⡤⢤⡄⠀⠀⠀⢠⡖⠄⠀⠀⠀⠀⢀⠀⢀⣀⠀⠀⢀⠤⢤⡀⢀⠀⠀⣰⠶⠀⠀⠀⠀⡄⢀⠀⣀⡀⠀⠀⢀⠤⣤⠀⠀⠀⠀⣴⠢
⠀⠈⠈⠀⠩⠈⠁⠀⠀⠀⣨⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠈⠀⠣⠙⠀⠀⠀⠁⣨⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠃⠙⠀⠀⡀⠀⣅⠀⠀⠀⠀⠀⣀
⣄⢀⠀⠀⠂⠀⠀⠀⠈⠈⠁⢀⠉⠁⠀⠂⢁⣉⡁⠀⡀⡀⠀⠀⠂⠀⠀⠀⠀⠈⠁⠀⠉⡀⠀⠁⢉⢈⡁⠀⡀⡀⠀⠐⠀⠀⠀⠀⠁⠈⠁⡌⢩⡀⠀⠈⣁
⠀⠀⠀⠈⣁⠁⠀⠀⠌⣁⡁⠠⠠⠆⠀⠠⠄⠄⠀⠒⠀⠀⠀⠉⡁⠁⠀⠀⢈⣀⡀⠄⠠⠀⠀⠠⠄⠀⠀⠂⠀⠀⠀⢉⡉⠈⠀⠀⢉⣈⡀⠀⠠⠀⠀⠠
⠆⠀⠀⠆⠠⠀⠀⣀⠀⠀⠆⠀⠄⢀⡀⠐⠢⠀⠈⠀⠀⠀⠠⠀⠤⠀⠀⡀⠀⠀⠆⠀⠅⢀⠀⠐⠢⠀⠈⠀⠀⠀⠠⠀⠤⠀⠀⡀⠀⠰⠄⠀⠀⣀⠀⠐⠤
⠐⠀⠂⠁⢀⡄⠐⠁⠀⠀⠘⠠⠃⢀⠀⠀⠀⠀⣠⣀⠁⠀⠀⠁⣠⢄⠐⠁⠀⠀⠀⠤⠂⢀⠀⠀⠀⠀⣨⡀⠀⠘⠈⠀⣠⢄⠚⠁⠀⠀⠠⠰⠂
⡂⠤⠤⠀⣉⠀⠁⠀⠀⠀⠀⠀⠀⠏⠳⠀⠀⢸⠀⢸⠀⠤⠄⠀⡋⢐⠀⠀⠀⠀⠀⠀⠀⠏⠗⠀⠀⠘⠀⣹⠀⠤⠄⠀⡃⠐⠀⠄⠀⠀⠀⠀⠘⡋⠇
⢅⠂⠁⠂⠇⠚⠈⠓⠀⠒⠀⠈⠁⠀⠀⠀⠀⠃⠐⠫⡐⠀⠁⠐⠕⠒⠉⠃⠀⠒⠀⠈⠁⠀⠁⠀⠀⠀⠚⠩⠐⠀⠁⠐⠔⠃⠉⠂⠀⠂⠀⠉⠡⠀⠀⠀⠐
⡈⠀⠉⠀⢀⣈⠉⠁⠤⠀⠀⠀⠐⠒⠂⠀⠀⡒⠂⠀⠁⠀⠁⠀⢀⡈⠉⠠⠄⠀⠀⠀⠒⠐⠂⠀⢀⡒⠐⠀⠉⠈⠁⠀⣀⡉⠉⠠⠄⠀⠀⠀⠒⠒⠂
⠁⠠⠀⠀⠠⢄⠀⠐⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡉⠀⠁⢂⠀⠄⠠⢄⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠈⠉⠀⠀⠄⠀⠁⠤⡀⡀⠂⠀⠀⠀⠀⠀⡁
⠄⠀⠀⡀⠀⠀⠀⠀⠁⠀⠐⠺⠀⠆⠀⣴⣃⠀⠀⠀⠄⠀⡀⠂⠀⠀⠀⠀⠁⢀⠐⠢⠀⠄⠀⣜⡁⠀⠀⠀⠀⠰⠀⠄⠀⠀⠀⠈⠀⢀⠐⠦⠀⠀⠠⣜⡀
⠀⠀⠀⠀⠰⢳⡄⠀⠀⠋⠹⡆⣀⡀⠀⠸⠉⠅⠀⠀⠀⠀⠀⠀⡶⢶⠀⠀⠀⠏⢹⠀⣀⣀⠀⡾⠩⠀⠀⠀⠀⠀⠀⠀⡞⢦⠀⠀⠐⠉⢳⠀⣀⡀⠀⠟⠨
⠠⠠⠀⠒⡈⠀⠀⠀⠈⠱⢾⠃⠄⠰⠀⡘⠤⠖⠤⠀⠠⠀⠐⠒⠘⠀⠀⠀⠈⠠⠞⠂⠄⠄⠀⠇⠴⠲⠤⠀⠤⠀⠐⠂⠈⠀⠀⠀⠏⠤⠞⠠⠀⠀⠀⡣⠴
⠀⠀⠀⠠⠄⠄⠀⠀⠠⠄⠀⠑⠀⠒⠀⠀⠐⠒⠂⣀⠀⠀⠀⠤⠄⠄⠀⠀⠠⠀⠀⠐⠀⠂⠀⠀⠐⠒⠀⡀⠀⠀⠀⠤⠠⠀⠀⠀⠤⠄⠀⠅⠀⠂⠀⠀⠒
⠀⠀⠀⠀⠒⠀⠀⠀⠐⠒⡂⠁⠀⠂⠀⢈⡉⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠒⡂⠁⠘⠀⠀⢈⡉⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠐⠒⠂⠁⠐⠀⠀⣈⠁
⢀⠀⡀⠁⠈⠀⢀⠦⠀⠈⠡⠀⡀⠒⠂⠀⠈⠀⠀⠀⢀⠀⡈⠁⠉⠀⢀⠆⠀⠈⠡⠀⡀⠒⠀⠀⠉⠀⠀⠂⡀⢀⠈⠀⠉⠀⡠⠆⠀⠉⠁⢀⠀⠒⠀⠀⠉
⡀⠀⠀⠀⠴⠓⠈⠀⠀⠀⠀⠀⠀⣤⣆⠀⠀⢠⠚⢦⠀⠀⠀⠀⡾⠓⠈⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⢠⠚⢦⠀⠀⠀⠀⡞⢓⠀⠀⠀⠀⠈⠀⢠⣤⡄
⡆⡈⣍⠀⡅⣠⢤⣄⠀⣀⠀⠠⠄⠁⡈⠀⠀⡘⠀⡼⢀⠉⡁⢀⢇⣤⣤⡄⠀⣀⠀⠠⠄⠁⠉⠀⠀⠐⣀⡾⢀⠉⡁⢀⢆⡄⢤⡀⠀⡀⡀⠤⠌⠀⠁
⠰⠁⠤⠀⠀⠠⠤⠄⠀⡀⠀⠀⣈⣈⠀⠀⠀⣀⡀⠈⠆⠀⠄⠀⠁⠠⠤⠄⠀⠀⠀⡀⣈⢀⠀⠀⠀⣀⢀⠈⠀⠠⠄⠀⠀⠤⠤⠀⠀⠀⠀⢀⣈⣀
⠆⠀⠀⠀⠐⠒⠀⢀⠉⠀⠀⠀⠀⠄⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠐⠒⠀⢀⠁⠀⠁⠀⠀⠄⠀⠀⠀⠠⠤⠀⠀⠀⠀⠄⠒⠂⠀⡈⠁⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠁⠀⠈⣁⠐⣶⣌⡉⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠰⠉⠀⠉⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠰⡿⠁⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⣈⡁⠀⠀⠀⠀⠀⠀⠈⠉⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⣍⡟⠂⠄⣀⠂⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⢈⢙⣂⣲⢻⡈⢁⠶⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⡈⠢⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠠⠦⠤⡰⡟⠀⠋
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠸⢁⡒⢢⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠬⢲
⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⠒⠀⠀⡀⠀⠀⢄⠂⢴⠇⠐⢡⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠐
⠀⠀⠀⠀⠀⠀⠀⡇⡿⠠⡀⠀⠀⠙⢄⡠⢊⠢⢈⠀⢸⠌⠍⡐⠬⠆⠀⠀⠀⠀⠀⡀⠄⠊⠁
⠀⠀⠀⠀⠀⠀⡀⠑⠣⠀⠀⠀⠀⠒⠠⠤⠄⣁⣢⣅⣚⡖⠒⠾⠅⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠃⡀⡀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠜⠐⠀⠀⠀⠀⠀⢨⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⠀⠈⠉⢡⠀⠐
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢠⠆⠠⠄⠤⢤⠤⢆⠔⠀⠀⠀⠈⠑⡄⢀
⠀⠀⠀⠀⠀⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢀⣰⠀⠀⠘⠈⠒⠀⠀⠀⢰⠒⠀⠈⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠓⠒⠆⠀⠀⠀⠀⠋⠘⠓⠀⠈⠑⠀⠀⠀⠀⠀⠚⠒⠁

⠀⠀⠀⠀⢀⡤⠤⠤⠤⠤⠤⠤⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠘⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⠞⠉⠀⠀⠈⠑⢄⠀⢐⢹⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⢀⡴⠚⠉⠁⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠇⠧⣠⣠⡄⠀⠀⢀⣠⣤⡴⢀⡞⠁⠀⠀⣠⣄⡀⠀⠀⢣⡠⢸⠀⠀⠀⡖⢦⡀⠀⠈⡆⠐⡞⠁⠀⠀⢀⣠⠤⠤⣴⠁
⠀⠀⠀⠀⠉⠂⠐⠄⣇⠀⠀⢸⠂⠈⠠⣾⠁⠀⢀⡾⠃⡄⢳⠀⠀⠈⣿⢸⡇⠀⠀⣇⠾⠃⠀⠀⣸⢸⠃⠀⠀⠀⡟⠐⠂
⠀⠀⠀⠀⠀⠀⠀⡇⣗⠀⠀⢸⠀⠀⠂⡇⠀⠀⢸⠀⠀⠸⢸⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⡔⠃⢸⡄⠀⠀⠀⠈⠉⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⡇⣇⠀⠀⢸⡆⢘⠰⡇⠀⠀⢸⠀⠀⠨⢸⠀⠀⠀⣷⢸⡇⠀⠀⠀⠀⠀⠀⠈⢻⣄⠳⣄⣀⣀⣀⡀⠀⠀⠀⠱⡀
⠀⠀⢴⠒⠒⠒⡆⠃⣸⠀⠀⢸⡇⠀⠨⡇⠀⠀⢸⠀⠀⠸⡼⠀⠀⢀⣯⢐⡇⠀⠀⢺⠲⡄⠀⠀⠀⡏⠐⠐⠑⠛⠤⠉⡧⠀⠀⠀⡇
⠀⠰⠸⡀⠀⠀⠑⠗⠃⠀⠀⢸⠃⢠⠀⣇⠀⠀⠈⠳⠤⠾⠃⠀⠀⣸⠰⠠⡇⠀⠀⢸⣰⠞⠀⠀⠀⡇⢰⠒⠒⠒⠒⠋⠀⠀⠀⢠⠃
⠀⠀⢂⠱⣄⠀⠀⠀⠀⠀⢀⠎⢀⠀⢃⠘⢦⡀⠀⠀⠀⠀⠀⢀⡴⠃⢠⢐⡇⠀⠀⠀⠀⠀⠀⣀⠜⢸⢸⠀⠀⠀⠀⠀⢀⣠⠔⠁
⠀⠀⠀⠑⠌⣓⣲⡤⠴⠖⠉⠀⠀⠀⠀⠛⠦⠍⣓⣒⡶⠶⠖⠉⠀⠀⠈⡄⣓⢒⣒⡒⠖⠾⠛⠁⠀⠰⠨⠛⠒⠒⠟⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠀⡀
⠀⠀⠀⠠⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠤⣄⠀⠁⠂⠈⡂⠃
⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠐⠀⠀⢀⡐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠘⡀⠄
⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢀⠀⠀⠀⠀⡀⠀⡏⠀⠀⠀⢰⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⡀⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠂⠀⡏⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢀⠀⠁⠒⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢸⢸⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⢀⡀⠈⠐⠤⡠⠂
⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⢐⢨⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠄⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡀⠀⠘⠀⠀⠀⠨⠀⠀⠰⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠁⠀⠀⠀⠢⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠀⠀⠀⠀⠈⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠙⠻⣿⣿⣿⣿⣿⠿⠛⠛⠻⢿⣿⣿⣿⣿⡿⠟⢁⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣄⡉⠛⠻⠟⠀⠶⠶⠆⠀⠿⠛⠋⣉⣤⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣦⠀⣶⣶⡆⠀⣶⣾⣿⣿⠟⣩⣭⣭⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣠⣴⣿⣿⣿⢃⡾⠁⢀⣴⠟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠈⣷⡴⠋⠁⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠒⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⡔⠒⠒⠒⢦⡀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠑⢤⡀⠀⠀⠀⠀⡠⠤⠤⠤⣄⠀⠀⠀⠀⣀⠴⠋⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠑⠲⠤⢼⠀⡞⠛⢲⢸⡤⠤⠒⠋⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⣸⢸⠀⠀⠀⠀⢀⡤⣴⡼⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠈⠢⠭⠭⠥⠞⠀⠀⠀⢠⢣⠋⣀⢜⣧⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⡼⣺⠕⠉⡰⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠭⠽⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠖⠆⠀⠈⢙⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⠢⠀⠀⠉⠃⠀⠀⠈⠀⠀⠀⠀⠀⠰⠲⠀⠀⠈⡉⠀⠀⠀⠁
⠄⠀⢀⠀⠀⠀⣀⠁⠀⠀⠀⠈⠤⠁⠠⠀⠀⡀⠀⠀⢀⠈⠀⠠⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠐⡂⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀
⠀⠀⠀⣠⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡄⠄⠀⠀⠀⠀⡁⠀⠀⢀⡀⠀⠀⢀⡀⠐⠀⠀⠀⠀⢀
⠀⠀⠀⢁⣀⠀⠀⠀⠀⠈⠑⠀⠀⢀⡅⠀⠀⠈⣀⣀⠀⡀⢀⠀⠙⠀⠀⠀⡬⠀⠀⠈⣀⣀⠀⠀⠀⡀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠌⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄
⠀⠀⠀⣀⡀⠀⢀⢄⠀⠀⠀⣮⠄⠀⠀⠀⠀⢀⡀⠀⠀⠤⡀⠀⠀⢪⠄⠀⠀⠀⠀⠀⣀⠀⠀⡠⣄⠀⠀⢐⡥
⠀⠀⠄⠁⠁⠀⠀⡠⠀⠀⠀⠄⠠⠀⠀⠀⠠⠈⠉⠀⠐⢠⠇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀
⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡴⠀⠀⠀⠀⠀⢠⣄⠀⠀⠴⡄⠀⠀⠰⠂⠁⠀⠀⠀⢀⣤⠀⠀⠴⠄⠀⠀⠠⠖⠀⠀⠀⠀⠀⣤⡀
⠠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠄⠠⠀⠄⠀⠀⠀⠀⠀⠠⠒
⠀⠈⠀⠀⠉⠀⠀⠀⠀⠂⠀⠀⠐⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠐⠀⠀⠀⣂⠀⠀⠁⠀⠄⠉⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⡦⠴⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠒⢋⣀⡀⠤⠴⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⢀⠤⠤⠴⢖⠒⠚⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⢱⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠀⠀⡎⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢰⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⢾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠈⢉⠁⠀⠀⠀⠀⠠⠂⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⡀⠀⠀⠀⠠⠄⠀⠀⠠⠤⣄⡀⠀⠀⢠⠃⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠥⢲⣤⣀⣀⣠⡃⠤⢀⡀
⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⢘⡜⢄⠈⠑⢤⠃⢠⡡⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠠⣬⠰⠶⠴⢀⢣⡠⢚⡽⠂
⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠑⢄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠃⢾⡏⣏⢆⠻⠁⠀⠐
⠀⠀⠀⠀⢽⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠐⠲⠄⠀⠀⠉⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠉⠘⠈⡄⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⡀⠪⣁⣒⢂⣶⠄⠀⠀⢤⠀⠀⡀⠀⠀⣀⠀⠀⢂⠼⠤⠤⠤⠤⠘⡆
⠀⠀⠀⠀⠀⠀⠀⡇⡇⢀⠔⠂⠀⢀⡀⠀⠐⢄⠖⢠⡟⠀⡎⠥⠀⢄⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠃⢧⢅⡀⠀⠀⠀⠱⡀⢀⡞⠠⡀⠂⠀⢳⣈⣀⠢⣈⡆⠀⠀⠀⠀⠀⠀⠀⣠⠐⠙
⠀⠀⠀⠀⠀⠀⢀⠦⢆⠀⠀⠀⠂⠄⢀⣈⠁⠈⠒⠈⡑⠢⢧⡤⠈⢱⠂
⠀⠀⠀⠀⠀⠀⡁⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠈⠛⠓⠈⢳⠎⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠈⠒⠂⠀⠀⠀⣈⠂⠠⣀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡀⠀⢤⢠⢤
⠀⠀⠀⠀⠀⢠⠀⡄⠀⠀⠀⠀⠀⠀⢱⢺⠐⢆⠀⠀⠻⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢃⡘⠀⣀⣀⠀⠀⣄⠀⢀⣀⡀
⠀⠀⠀⠀⠀⡌⢰⠀⠀⠀⠀⠀⠀⠀⢸⢸⠃⠀⠀⠀⠀⠀⠀⠀⢹⠋⠐⡒⠒⠀⠶⣚⢧⠋⠀⠈⢸⢐⠀⠱⡈⠥⢈
⠀⠀⠀⠀⠀⠇⠄⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⠀⠀⠀⢀⣇⣀⣠⢅⡀⠀⠁⠀⠁⠀⠀⠐⠸⡋⢁⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠗⠒⠶⠤⡤⡤⢤⡼⠄⡉⠓⠂⠠⠬⠂⠀⠀⠀⠀⠈⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠂⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠐⠆⠐⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠐⠀⠂⠃⠀⠀⠐

⠀⠀⠀⠀⢠⠤⠤⠤⠤⠤⠤⠤⠤⢄⠀⠀⠀⠀⣀⡤⣀⠀⠀⠀⠀⣀⠀⠤⣤⠄⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⢐⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠔⠉⠀⠀⠀⠉⢢⡀⠀⢹⠀⠀⠀⠀⠀⠈⢢⠀⠀⢠⠖⠋⠁⠀⠀⠀⠀⡅
⠀⠀⠀⠈⡈⠢⠤⢤⠀⠀⢀⡤⠦⠞⢰⠋⠀⠀⡠⠤⣄⠀⠀⢱⡄⢸⠀⠀⢸⠑⡆⠀⠀⢃⢐⡏⠀⠀⢀⡤⠔⠒⠲⠃
⠀⠀⠀⠀⠀⠀⢁⢸⠀⠀⠈⠁⠀⠐⡏⠀⠀⡜⠉⠢⠸⡄⠀⠀⡇⢸⠀⠀⠰⠜⠁⠀⠀⡼⢸⠁⠀⠀⠘⢅⣀⣀
⠀⠀⠀⠀⠀⠀⢰⢸⠀⠀⠀⡀⠀⢰⠁⠀⠀⡇⠀⠀⠀⡇⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠪⣤⠘⡄⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⣀⣀⣀⣀⢸⢸⠀⠀⠘⡇⠀⢸⠀⠀⠀⡇⠀⠀⢰⠁⠀⠀⡇⢸⠀⠀⢀⣄⡀⠀⠀⠈⡧⠈⡲⢐⢖⠦⢄⠀⠀⠀⠇
⠀⠀⢋⠀⠀⠘⣤⡸⠀⠀⠠⠇⢀⠸⡀⠀⠀⢣⡀⢈⡞⠀⠀⢸⠃⢸⠀⠀⠀⡗⣹⠀⠀⠀⡅⢀⡀⠀⠈⠵⠜⠀⠀⠀⡆
⠀⠘⡘⣆⠀⠀⠀⠀⠀⠀⡸⠀⠈⡄⢣⡀⠀⠀⠈⠉⠀⠀⢠⠏⠀⢸⠀⠀⠀⠑⠉⠀⠀⣠⢣⢸⠀⠀⠀⠀⠀⠀⣀⠜
⠀⠀⠐⠌⠓⠤⣄⣀⡤⠚⠁⠀⠀⠈⠦⣝⠲⠤⣤⣠⡤⠖⠁⠀⢀⡨⠤⠤⠤⠤⢤⠶⠚⠁⢠⠸⠦⠤⠤⠶⠶⠚⠁
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢁⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⡀⠀⠀⠁
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠈⠙⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢨⠀⠀⠠⠀⠀⠀⡀⠂⠀⠀⠀⠀⢘⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⡀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠠⣀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⡀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⡀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⡿⣿⣿⡿⢿⡿⣿⢿⣿
⠀⠀⠀⠀⢾⣷⠀⠀⠀⠀⠀⠰⣿⣧⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⡷⣿⢈⢸⢸⡇⣿⣜⢷⡝⣿
⠀⠀⠀⠐⠚⠓⠂⠀⠀⠀⢠⣾⣿⣿⣿⣾⣯⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⣿⣿⢟⡻⡞⣷⣿⠖⣷⢾⡗⢿⠚⣿
⠀⠘⠐⠐⠃⠘⠀⠃⠂⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⣿⢸⡿⡇⣿⣿⠰⢸⣼⡇⡈⡀⣿
⠀⠀⠀⢰⡶⢰⡆⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⣿⣿⣷⣶⣷⣶⣷⣿⣾⣾⣷⣷⣷⣿
⠀⠀⠀⢸⡇⢸⣇⠀⠀⠀⠀⢸⣿⣿⠿⡟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠈⠁⠈⠉⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⢴⣶⠄⠀⠀⠀⢤⡿⠿⢷⡄
⠀⠀⠀⠀⣠⣄⠀⠀⣠⣄⣀⡀⠀⠀⠀⣀⣿⣏⡀⠀⠀⠀⠀⠀⣠⣾⢷⡶⠖⠚⠃⢿⣇⣛⣼⡏
⠀⠀⢠⣤⣿⣿⡄⠀⢿⡿⣿⡏⠀⠀⢰⢿⣿⣿⣿⡀⠀⠀⠀⠀⡟⠻⣸⡇⠀⠀⠀⠀⠉⠋⠉
⠀⠀⣿⣿⣿⣿⣿⡦⠤⠤⠀⠀⠀⠀⠛⠀⣹⣿⣷⣷⠀⠀⠀⠀⠃⣴⣿⡇⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⣀⠁
⠀⠀⠙⠛⣿⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢿⣿⠇⠀⠀⠀⠀⣿⣿⡇⠀⠀⢿⠟⠀⠘⢿⠇⠀⠸⣿⠇
⠀⠀⠀⠒⠛⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠘⠛⠀⠀⠀⠀⠀⠛⠙⠃⢠⣿⣿⣿⣷⣿⣿⣿⣶⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠁⠁
⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⢸⣶⣶⣶⣶⣶⡆
⠀⠀⠀⣰⣿⡆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⢿⡿⠀⠐⢿⠗⠀⠸⣿⠇⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⣸⣿⣿⣿⣀⠀⠀⠸⡿⠃⠀⠀⠀⠀⠀⣾⣷⠀⢠⣿⣷⠀⢠⣿⡧⠀⢰⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠈⣿⣿⡇⠩⠀⠴⠿⠿⠿⠆⠀⠀⠀⠘⣿⣿⣶⡼⣿⣿⣶⡸⣿⣿⣦⡸⣿⣷⣦⡀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⢸⣿⠋⠀⢸⡟⠋⠀⢸⡟⠉⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⣸⡏⠀⠀⣼⡇⠀⠀⣼⠇⠀⠀⣸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠒⠒⠢⣀⣦⠦⠒⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⡌⠀⠀⣀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠰⡄⠀⣀⠈⢻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡘⢆⠀⠀⠀⠇⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢀⠽⣼⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢸⠀⠀⠀⠀⠀⠨⠂⢀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣠⠔⠲⠀⠀⠀⠀⠁⠐⠋⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣦⣠⡀⠀⠘⠦⣀⣀⣀⠤⠤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢹⠐⡄⠀⠀⠀⠀⠀⣠⠴⡆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⠀⠘⡄⢀⡠⢖⣉⠤⠎⠁⠄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⡄⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣠⠜⠙⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠗⠐⠉⡀⠀⠀⡆⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠙⡀⠄⠁⠜⠀⢀⣠⢶⠚⠒⠦⡀⠮⣨⡀⠀⠀⡠⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠈⠁⡄⢀⠀⠁⠞⣭⣾⠒⠒⠚⡗⠈⠀⡯⠗⠊⠑⠢⠔⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠹⠈⠄⠀⢡⢹⡼⣗⠂⠘⡏⠰⠎⠆⠀⠀⣀⠀⠀⠀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠁⠀⠀⠈⠀⢏⠓⠋⡊⠁⠈⣀⠤⠐⣋⠀⠒⠁⠀⠀⠀⠀⢐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⡀⠀⠀⠆⠀⠀⠸⠄⢐⢹⡁⠀⠴⠂⠈⠀⠀⠀⡀⠀⠤⠴⠂⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠀⠀⡂⠀⠀⠇⢃⠈⠉⡏⠉⠉⠉⠉⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡇⠀⠅⢀⢀⠀⢀⢸⣀⣘⠌⡗⢰⡁⠀⠀⠀⠀⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠥⠔⠶⠶⠐⠒⠒⠂⠃⠈⠐⠋⢸⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠙⠒⢲⠾⠄⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣒⣈⣉⣙⣛⣒⣲⣤⣤⣀⣸⠀⠄⠀⠀⠠⠤⢀⣒⡪⣽⠤⠤⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠑⠒⠛⠒⠂⠀⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠐⠂⠀⠀⠐⠀⠐⠐⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠂⠃⠀⠀⠀⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣨⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⣿⠟⠛⠛⣛⠛⣛⣛⡛⠛⠛⠛⠉⠉⢩⣿⣯⣍⠉⠉⣻⣶⣶⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿
⠛⠋⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡋⡀⢠⣾⠟⠻⠛⢷⣤⢤⣤⣤⠶⠂⠉⣿⣿⣿⣿⣿⣿⣿⠻⡿⣿⡿⣿⣿⣷⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣺⣿⣿⣛⣶⣿⣄⣿⣿⡞⣿⣿⣿⣿⣤⣿⣿⣿⣿⡟⢠⣿⣭⠻⣿⣀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢭⡿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡛⠿⠗⠀⠀⠠⠿⠿⠿⠿⣿⣿⣿⣷⣾⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣺⣷⣼⣷⣾⣿⣤⣤⣤⣤⣤⣾⣿⣿⣿⣧⡆⢿⣿⣿⣿⣿⣷⣶⣯⣦⠀⠀⠀⠀⠀⠀⠿⣿⣮⣿⣷⡙⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿
⣀⣀⣚⣟⣛⠛⠻⠿⠛⠛⠛⠻⠛⠛⢻⣿⣿⣿⣿⣧⡘⣿⢿⣿⣿⣿⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣭⣤⣡⣄⣹⡟⠛⠛⠘⠛⠙⢻⣿⣿⣧⣞⣛⣿⣿⣿⣟⣛⣛⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⠿⣿⠿⢿⣿⣿⣿⣿
⡟⡛⠈⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣻⡿⠿⢷⣦⣄⠀⠀⠀⢀⣀⣠⠤⠚⣉⠵⠾⣻⣶⣿⣿⣿⣿⣿
⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠂⠙⠛⠛⢶⣷⣤⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿
⣿⣷⣾⣿⣿⣿⣿⣿⣯⣥⣬⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⢀⡀⢸⣿⡿⣷⡦⠠⣀⠀⠀⠀⠀⠀⠤⠄⠀⠚⠻⣿⣿⣿⣿
⣿⠿⠉⠉⠉⠙⠻⠿⠷⠿⠋⠉⢁⣺⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⣧⠋⣩⣅⣿⣿⣿⣿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠿⠿⠿
⣾⣿⣶⣦⣀⣀⡀⠈⠁⠀⠀⠀⠉⠉⣿⣿⣿⣿⣿⡎⣿⣿⣿⡿⣿⣟⠛⢛⣤⣤⣤⣘⡿⠿⠏⢀
⣿⣿⣿⣯⣉⣉⣉⣀⣀⣀⣀⣉⣀⢀⣿⣿⣿⣿⣿⣇⠘⠋⠤⠀⢿⣿⡦⣨⡙⣿⣿⣿⣿⠀⠀⠈⠓⠀⠀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠒⠒
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣷⣿⣇⣻⣿⣿⣿⡀⢠⡟⠃⠀⠀⠉⠉⠉⠉⠐⠶⠶⠤⠤⠤⠴⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⢉⣭⣯⡉⣿⣶⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣬⣿⣿⣛⣛⠛⢿⣿⣿⣿⣿⣿⣿⣿⠷⠼⣷⣿⣆
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡈⣉⣩⣏⣿⡿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣓⣶⣿⣿⣿⣷⣀⣀⣀⣀⡀
⣿⣿⣿⣥⡼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⣤⡄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⣿⣿⣏⠀⠀⠀⠉⠉⠉⠉⠛⠛⠒⠲⠶⠶
⣿⣿⣷⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣸⣷⣄⣀⣀⣂⣤⣤⣄⣤⣄⣠⣤⣄⣀⣀⣠⣄⣦⣻⣿⣿⣌⠑⠒⠢⣤⣤⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣶⣿⣿⣿⡀⠀⢘⡷⡏⠀⠀⢺⣿⣿⠛⣿⠇⣠⣾⠏⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢻⣯⠿⣿⣯⢟⡵⣫⡇⠀⢨⢅⡇⠀⠀⣤⢟⠴⠀⢀⣴⡶⢛⢲⡏
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣦⣽⣿⣯⣾⣿⡇⠀⢸⣀⣡⠀⢀⡕⡴⢛⣠⢸⣿⠧⠚⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣇⣿⣿⡿⡇⠀⣿⡏⢻⡀⠸⠖⣡⠑⣰⠸⣟⣘⣥⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡏⣽⣾⣿⣿⠇⠀⣿⣤⣜⡃⢸⣷⠃⠚⡡⢰⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢀⣿⡿⣫⠖⠀⢸⠏⠘⢽⡇⠈⠯⣀⣼⠿⢘⡟⣽⠿⡏
⠀⠀⠀⠀⠀⠀⠀⣸⣽⣿⠘⣻⣿⡿⠀⠀⣟⠂⠀⠈⢳⠈⢦⣿⣟⣶⣾⣷⡿⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢰⣿⣿⠂⠀⠀⠈⢷⣄⣀⡼⠂⢸⡟⣿⠉⢻⢿⣿⠩⢤
⠀⠀⠀⠀⠀⠀⣸⡟⣱⡇⢸⣿⡿⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠙⣎⠇⠈⢸⣿⡀⠦
⠀⠀⠀⠀⠀⢠⣿⣿⣿⢣⣿⣿⠛⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀⣉⢉⣡⠀⠐⢿⣷⣞⡀
⠀⠀⠀⠀⢀⡌⠛⣻⡟⣼⣿⣇⣴⣾⡟⣟⣿⣏⣉⣉⡹⣿⠿⠟⢸⣿⣿⡢⠙⣿⣿⠿⣄
⠀⠀⠀⠔⢉⠀⣸⣿⣾⣿⣿⠇⢀⡟⣛⡹⣿⣿⣿⣿⡿⣹⣿⢳⣿⢿⣾⣷⣬⡿⣶⣶⡀⠙⢢
⠀⠀⡴⠀⠘⠋⠉⢁⣿⣻⣫⣶⣯⡼⠝⣛⠿⢿⣿⠞⠜⠿⠿⣿⢟⣿⣿⣿⡏⠁⠀⠀⠩⢶⡀
⠀⠀⠀⣀⣴⣾⣜⣿⣿⣯⣿⣿⢯⣞⣿⣿⣿⠊⢿⣿⣷⣶⡜⠁⠾⣿⣿⣿⣿⣦⡤⠤⡶⢀⠈⠂
⠀⠀⠀⠙⠋⠀⣾⢸⣿⣿⣿⠿⢟⡛⡽⣿⣷⡆⣾⣷⣹⡾⣷⢫⢖⡴⣹⡿⣿⣿⡏⠓⠉⠉⠟⠁
⠀⠀⠀⠀⠀⠀⢰⣾⣿⢯⣿⣿⣏⣼⡾⣻⡿⢸⠇⢹⣿⣧⣿⣯⡞⣵⣿⣫⢻⡟⠃
⠀⠀⠀⠀⠀⠀⠈⠛⢁⣿⣿⣿⣿⡟⣕⢿⣿⣿⡄⠀⣿⣏⢸⣿⡿⣵⣿⢧⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⣿⣟⣾⣳⣵⣿⡿⣿⠆⣿⣿⡜⣫⣾⢻⣿⡟⣳
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣹⣿⣿⣿⣿⡿⣿⣿⣿⣾⠈⣿⢿⣏⣿⣿⣿⣿⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⡿⣿⠿⣯⡿⣿⣟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⣽⣷⣿⣿⣿⣿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣩⡁⣸⢰⣿⢯⣓⡦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⢸⡑⣻⣣⡿⠃⠀⠀⡴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡞⣡⠶⠯⠿⠟⠁⠀⠀⠀⢸⣹⠁⠀⠀⠀⣠⣤⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠳⣿⠋⠁⠀⠀⠀⠀⠀⣀⣀⣀⣈⣥⣤⣤⣤⣞⣽⣿⣿⡿⣿⣟⠿⢯⣍⡓⠂
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣶⠏⠀⠀⣠⡤⠶⠚⠛⠉⠉⠠⠚⠉⠿⡦⠀⠀⢉⣭⠭⢟⡓⠶⢿⣷⣤⣉⠑⠂
⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⠃⣀⡴⠛⠁⠀⠀⠀⠀⣤⠶⠖⠒⠒⠒⠒⠀⠀⠀⠀⠀⠘⢻⠀⠀⠈⠙⠻⢿⣦⣄
⠀⠀⣰⣿⣿⣿⣿⣿⡿⠁⣴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠙⠻⣷⡀
⠀⠘⢿⢿⣿⣿⣿⡿⠁⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠈⢻⠟⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠶⠛⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⣠⠴⠚⣋⣭⣟⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣳⠦⠈⠙⠚⠁⠀⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠲⠦⣄⡀
⠀⠀⠀⠀⠀⢀⡴⠋⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣽⣂⡀
⠀⠀⠀⠀⠀⠘⠚⠉⡽⠁⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠒⠙⣆⠀⢻⠉⠳⠬⣷⠲⢤⣀⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣈⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣸⠀⠀⠀⠀⠠⢔⣀⡉⠙⠒⠤⠤⣘⣯⡉⠙⢲⠒⠦⠬⣷⣦⡀⠈⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡟⠀⠀⠀⢀⡞⠉⠈⠉⠓⢄⠀⠀⠀⣀⣰⣤⠈⢧
⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⡏⡼⠁⠀⠀⠀⢸⠃⠀⠀⠀⠀⠈⢷⣰⠋⠀⠀⠈⡆⠈⢧⣀⡀
⠀⠀⠀⠀⡞⢉⣀⣉⠑⢾⡼⠁⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣷⠀⠳⠆⠺⡄
⠀⠀⠀⠀⢇⠀⠈⠳⠻⠄⠁⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⣠⣀⣸⢠⢴⣄⠀⢀⡇⠀⠘⢯⡍⡣
⠀⠀⠀⠀⠀⠑⠲⠤⠴⢶⡀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⣳⣿⠋⠻⠿⠯⠤⠚⣠⠖⠒⡄⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⠒⠲⠖⠛⠁⠀⠀⠀⠀⠀⠀⠁⢀⡴⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⢀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠄⠀⠉⠓⠦⢤⣀⡀⠀⠀⠀⡠⢀⡴⠒⣒⡧⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡸⢀⠆⠀⠀⠀⢸⠉⣉⣹⠭⠼⠧⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⢱⠓⢺⠀⠀⠀⠀⢸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢖⡓⠄⠛⠀⡞⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡯⠤⠤⠴⠃⠀⠀⠀⢀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢲⡖⠒⠒⠒⢻⢹⡉⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠼⢾⠷⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⣀⣀⣠⣤⢾⠒⠲⣍⣹⡆⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣢⠤⠤⠾⠷⢓⣚⡪⠽⠛⠉⠀⠀⠀⢀⣠⣤⣤⣤⠄⠍⠉⠉⠉⠛⠛⠳⠶⠶⠦⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠶⠿⠯⠭⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠟⠻⠎⠙⠁⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠐⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠠⠐⠀⠁⠀⠀⠀⠈⠉⠒⠦⢀⣠⠞⠀⠀⠀⠀⠀⠒⠈⢷⣄⠀⠀⠀⠀⠀⢼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⠀⠳⢤⣀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⢀⣀⣠⡤⠄⠚⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠀⠀⠀⠈⣇⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠈⢉⡥⠤⠄⠤⣀⠀⠀⠀⠀⠀⠀⢀⣀⠤⣀⡀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡤⡇⠀⠀⠀⠀⠀⢰⠋⠀⣠⣴⡆⠈⢳⠀⠀⠀⠀⡴⢉⣤⣤⠀⠈⢢⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⣿⣿⣿⡶⢸⡇⠀⠀⢰⠀⣿⣿⣷⣶⠀⠀⡇⠀⠀⠀⠀⡟⢷
⠀⠀⠀⠀⠀⠀⠀⠹⣆⣧⠀⠀⠀⠀⠀⠘⠲⠤⢌⢛⠋⣁⠜⠀⠀⠀⠀⠣⠙⠛⣛⢋⢀⡼⠁⠀⠀⠀⢀⡇⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛
⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⢀⣄⡀
⠀⠀⠀⠀⠈⢧⡈⠙⠦⣄⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⡤⠖⠋⣠⠟
⠀⣠⠤⠤⠶⠶⠞⠓⠀⠈⠙⣆⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠙⠂⠀⠀⠀⠀⣠⢞⡟⠉⠀⡀⠛⠷⠶⠤⢤⢤⡀
⣾⣃⣈⠭⠅⠀⠀⠈⠉⠙⡆⣜⠀⠀⠉⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠊⠁⢘⡇⡔⠉⠉⠀⠀⠀⢭⣭⣁⣙
⢯⠁⣀⣀⣀⣀⣀⣠⣤⠴⠃⢹⡀⠀⠀⠀⠀⡽⠓⣶⢤⣤⣄⣀⣀⣀⣤⣤⡴⠶⣏⠁⠀⠀⠀⣸⠃⠳⢤⣤⣄⣀⣀⣀⣀⡀⢨
⠈⠉⠉⠀⠀⠀⠀⠀⠸⡄⠀⠀⢳⣀⣀⣠⠞⠁⠀⣿⢢⡀⠴⣿⣿⡷⢄⡌⣿⠀⠙⢦⣄⣀⣠⠏⠀⠀⣼⠁⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠈⠉⠀⠀⣠⠞⣯⠀⠀⠀⢨⣽⡀⠀⠀⢸⣦⡀⠀⠀⠉⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠄⠤⠖⠚⠁⠀⡃⠀⠀⠀⠈⠛⣇⠀⠀⠈⡇⠉⠓⠦⠤⠤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⣿⣿⣿⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⣿⡿⠃⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠉⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣾⠒⢲⡆⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⢰⠀⢸⠃⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⢀⡴⠋⠀⠘⢧⡀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⢯⡀⠀⠀⠀⠀⡹⠂⠀⠀⣽
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⣦⣤⣤⣷⣄⣀⣠⣾⣥⣤⣤⣴⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⣸⡿⠃⠀⠀⠀⠀⠀⠀⢸⡏⠀⠉⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⢀⣙⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⢀⣴⣶⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⢾⠏⠉⢻⣷⡄
⠀⠀⠀⠀⣿⡁⠀⠙⣿⠇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⣿⡇
⠀⠀⠀⠀⠙⠋⠀⢼⡏⠀⠀⠀⠀⠀⠀⠀⠀⢻⠑⠦⣄⠀⠀⠈⢯⠳⢄⡀⠀⢀⡀⠀⠀⠀⠀⣀⡛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⣴⣶⠀⠀⠀⠠⣤⣤⣤⠼⠀⠀⠀⠉⠒⠒⠋⠀⠀⠙⠦⠼⠏⠲⣄⠀⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣈⣢⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⢀⡤⠤⢤⣀⠀⠀⠀⠉⠁⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢀⡏⠀⠀⠀⠈⢳⡀⢠⠒⠒⢢⡀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢠⡇⠀⠀⢸⡀⠀⠀⠀⠀⣸⡇⢻⠉⠀⠀⡇⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣥⣬⡓⠋⠀⠀⠀⠈⢇⠀⠀⠀⠀⣹⠁⠈⠳⠤⠞⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⠖⣆⠀⠀⠀⠀⠈⠣⣄⣀⡴⠃⠀⠀⠀⠐⢦⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠒⠐⠋⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠦⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⠀⠈⠙⠒⣦⢤⣄⣀⣁⣤⠴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠦⡴⠃⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⠺⠟⠀⢰⠁⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠭⠀⣀⣯⣀⡀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⠁⠀⢨⡭⠉⣹⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⠉⠙⡟⢒⣶⣶⡾⠖⢺⠟⠛⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠭⠭⠭⠟⠋⠉⠑⠛⠭⠿⠯⠝⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⡀⠀⠀⣠⠄⠀⣀⠤⣦⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⡠⠀⢼⣤⣾⢟⡦⠄⠤⠜⠻⢷⠛⣷⣶⣄⠀⢲⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠲⡯⠐⡚⠛⣻⢖⠈⠁⠂⠒⠦⠐⣎⡁⠾⡖⢩⠲⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠓⠶⢗⠀⠠⡎⠉⠀⢀⣀⣤⣄⣀⠀⠁⠠⠓⣷⣀⡹⠶⢒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠏⠀⣑⠀⢀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣆⠀⠀⠋⡰⠂⠀⣀⣁⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⢄⡶⣿⣼⠃⠀⠀⠸⠿⠿⠟⠀⠀⢹⣿⣿⠀⠸⣀⠄⠸⡄⠈⠉⡗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣞⡿⣃⡀⠀⢤⠀⠀⠤⢀⡔⠀⣠⣿⣿⡟⠀⠐⠋⢓⠸⣀⣀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⡅⠀⣦⠀⡰⠋⠠⡟⠍⢀⣾⣿⣿⠟⠀⠀⡀⢠⡎⠈⢉⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⢁⣀⡭⣦⣳⠸⣏⠀⠀⣾⣿⣿⠋⠀⠀⠰⠛⢻⠷⡄⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣿⠂⠀⠻⣼⣋⣀⠀⠉⠉⢉⠤⣠⡒⠒⢢⠁⠹⡑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠟⡄⠊⣱⣿⣿⡁⠀⣿⣿⣿⠀⠈⣕⣦⠬⠀⠀⠈⠉⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠡⢀⡧⢰⡟⣷⡿⢷⠀⠉⠉⢉⣠⢼⡥⢤⠵⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠷⠞⠛⠀⠤⠉⠌⢉⡀⠀⠀⠰⠄⠀⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣾⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠋⠉⠛⠛⠛⠛⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠤⠄⠀⡤⠤⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠿⠂⠀⠀⠷⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣠⣴⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢲⢰⠃⡖⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢵⣏⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⡀⣤⣶⣦⡄⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⡟⠋⠉⠻⡿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣤⣾⡿⠋⢿⣿⣿⠏⠻⣿⣦⣄⠀⠀⠀⠀⣿⣿⣿⣿⠟⠋⢀⣴⣄⠀⠀⢀⣦⡀⠈⠻⣿⣿⣿
⠀⠀⠀⠻⠿⣿⣷⣶⣤⣭⣥⣴⣶⣿⡿⠿⠃⠀⠀⠀⣿⣿⣿⣧⣀⡀⠈⠉⠛⠓⠚⠛⠋⠁⠀⣀⣼⣿⣿
⠀⠀⠀⠀⠀⡀⢉⣿⣿⣿⣿⣿⣏⠁⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡼⠉⠉⠀⠀⢸⠀⠀⠈⠉⠹⡄⠀⠀⠀⠀⣿⣿⣿⣿⡏⣴⣶⣿⣿⣿⣾⣿⣿⣿⣷⡹⣿⣿⣿
⠀⠀⠀⣼⣧⣤⣒⣒⣒⣼⣔⣒⣒⣢⣤⣿⡄⠀⠀⠀⣿⣿⣿⡟⠸⠿⠿⠭⠭⠟⠹⠭⠭⠿⠿⡇⢹⣿⣿
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠶⠞⠉⠉⠉⠉⠛⠛⠒⠶⠶⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⣄⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠂⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⣿⣦⠀⠀⠀⠀⠀⠹⠿⠿⠛⠻⠻⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⣠⡤⠴⠶⠶⠦⠤⠤⠄⣀⣀⣀⡀⠀⠀⠀⢉⣠⠾⠁⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠉⠁⠙⣦⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⠀⠀⠒⣿⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⠴⣞⣽⣃⣶⠀⠀⠀⠀⠰⣟⣛⣻⣿⣿⡑⡄⠀⠀⠀⣿⣉⠀⢊⠁⣿⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠊⠉⠉⠉⠈⠀⠙⡄⠀⠀⠉⠉⠀⠀⠉⠉⠁⠀⠀⠀⣿⣀⠄⠉⣰⣇⡀⠀⠀⠀⢰⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣀⠠⣤⣤⣄⠀⢸⠀⠀⠀⡀⠀⣤⣤⡀⠀⠀⠀⠀⠈⢷⡀⣸⠋⠈⢳⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠂⠀⠀⠀⠈⠉⠉⠀⡌⠀⠀⠀⠑⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⣧⠃⡴⠀⢘⠀⠀⠀⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣠⡀⢈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠐⠀⡟⠀⠀⣠⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⠃⠀⠀⢿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠶⠋⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠠⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⢰⡿⠶⠶⠀⠀⠀⠒⠒⠻⢧⡀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠸⠤⠔⠒⠒⠒⠒⠂⢐⠂⠘⠁⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⢰⠲⣄⠀⠀⠀⠀⠀⠈⢶⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⣠⣤⣤⣤⡬⣷⡌⠳⣄⠀⠀⠀⠀⠀⠈⠓⠶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡼⠁⢀⠀⡀
⠀⠀⣾⠿⠶⠾⠀⠀⠀⠴⢤⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢻⣾⠛⢛⠛⢿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣀⡙⠁⠉⠿⠽⣟⣷⡀
⠀⠀⠳⠤⠤⢤⣤⣀⣀⣀⣠⠷⢻⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠏⣠⣎⠁⠀⢀⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣧⣘⠁⠀⠀⠀⢀⣁⣀⣈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡅⠀⢀⡽⣄⠀⠀⠀⠀⢀⡴⢿⠀⠃⠘⢻⣿⡿⠆⠴⠋⠀⠀⠉⡿⢦⠀⠀⠀⠀⠀⠀⣠⠋⠀⠉⠳⠚⠛⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡁⠀⠈⠳⣄⠀⣠⠞⠁⢹⠀⡀⢠⣾⣿⡇⠔⠀⠀⠀⠀⣸⠃⠈⢳⡄⠀⠀⠀⠴⠉⠑⢢⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⢹⠋⠀⠀⢰⢀⠀⢸⣿⣿⠃⠀⠀⠀⠀⣰⢦⡀⠀⠀⠙⢦⡞⠁⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⣾⠀⣀⡴⢻⡆⠄⢸⣿⠃⠀⠀⠀⠀⢰⠏⠀⠙⢦⡀⠀⢸⡀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠴⠚⠉⠀⠘⡇⠀⢠⠁⡠⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⠦⣌⣁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢠⠀⠀⠀⠀⠀⠄⡇⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠈⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡁⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢠⡅⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣾⠻⣄⣀⣀⣀⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠁⠲⡍⠉⠉⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢳⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠈⡆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣧⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢈⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢸⡄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡆⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡦⠄⠘⣷⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢤⣀⠀⣷⣶⠶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠚⠛⠁⠀⣀⡈⣻⠋⠠⠀⢹⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡠⡏⣀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⣀⣀⠀⠀⣀⣀⣠⠤⠴⠼⠮⣍⠒⠃⠋⠁⠚⠐⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠒⠼⠦⠬⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣛⠂
⠀⠀⠀⠀⠀⠀⠶⣶⠦⠴⠞⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⣀⣤⣤⣤⣤⣀⠈⠙⣆
⠀⠀⠀⠀⣠⠤⠒⠚⠉⠉⠉⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣀⡘⢾⡜⣡⠖⠋⠁⠀⠀⠀⠀⠈⠳⡄⠀⠑⢄
⠀⠀⠀⠙⠓⠒⣦⠖⠁⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⠀⠙⢾⡟⠁⢀⣄⣀⡀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢳⡀
⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣙⠳⣤⠀⠀⠀⠀⡇⠀⠀⢻⠁
⠀⠀⠀⢠⣣⢴⠆⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠀⠀⠉⠳⣎⠁⠀⠀⠀⣿⠀⠀⢸⡄
⠀⠀⠀⠋⠁⢸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⣿⠀⠀⠘⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⣿⣄⣀⡀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠞⡋⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⢍⡁⢀⡇
⠀⠀⠀⠀⠀⢸⠈⠩⠭⣷⠀⠒⢶⠶⠶⠾⠟⠛⠋⠉⠀⠘⠿⠂⠀⠘⠗⠀⠀⠀⠀⠀⢠⡿⠀⢠⡇⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠈⡇⠀⠀⢹⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⣾⠀⠀⠀⡾
⠀⠀⠀⠀⢀⣀⣸⡄⠀⠈⡆⠀⠀⠈⠛⢦⣤⣀⣀⣤⣤⡶⠂⠀⠀⣀⠀⠀⠀⠴⢾⡯⠀⠀⠀⣇⠀⣀⠴⠗⢒⢶⡄
⠀⠀⠀⣴⠋⠉⢀⠈⠓⠊⠁⠀⠀⠀⠀⠀⠀⠠⠴⠿⠋⠀⠀⠀⠘⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣴⢾⡉⠀⢹⡄
⠀⠀⠀⣇⠀⠞⢩⡿⣆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⡚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢻⠇⠀⢸⡇
⠀⠀⠀⠹⣄⠀⠘⠀⠹⠀⣧⠀⠀⠀⠀⢀⣤⣖⡋⠉⠉⠉⠉⠀⠀⠈⠉⠉⢙⣶⣄⠀⠀⠀⠀⢀⣷⣄⠀⠉⠀⣀⡾⠁
⠀⠀⠀⠀⠈⠳⠦⣤⡤⠞⠹⡆⠀⠀⠀⣾⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣶⣶⣿⣿⣿⣇⠀⠀⠀⣼⠃⠈⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠙⢟⣿⠿⠿⠭⢌⣙⣉⣩⠿⠿⠟⠻⣿⣿⠏⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠉⠒⠦⠤⠤⣄⣀⣠⣤⣤⠤⠖⠋⠁⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠋⠉⠁
⣿⣿⣿⣿⣻⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣻⣿⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⠒⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠘⠉⠉⠳⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠃⠀⣀⠜⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⡬⠂⠀⠀⠀⠀⠀⠀⠀⡃⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⠀⠉⠁⠒⠒⡆⠀⠀⠀⠀⠀⡝⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⡨⠀⠀⠀⠀⢀⣤⣄⡅⠀⠀⠀⠀⠀⠑⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠹⠀⠀⠀⢀⠨⣀⠨⡄⠀⠀⠀⠀⠀⡀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠢⡀⠀⠀⠀⢀⣀⢀⡞⠉⡗⠀⠀⡁⠀⠀⠀⠀⠸⡶⠅⢪
⠀⠀⠀⠀⠀⠀⠀⢠⠀⡄⠠⠉⠐⠐⠶⣚⠁⠀⠀⠀⠈⠉⠉⠀⠈⠛⢻⣻⠃⠀⠀⠀⠀⠀⣫⣁⡯⣀
⠀⠀⠀⠀⠀⠀⠀⠅⡠⡍⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠣⠄⠀⠠⠔⣊⢙⣯⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢰⠒⠲⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠂⠉⠘⣼⣻⠀⠀⣷⠘
⠀⠀⠀⠀⠀⠀⠀⡘⠶⣤⡞⢉⡱⠈⠉⣽⡄⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠜⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠘⢄⢠⠄⠀⠈⠓⠒⠦⠏⠢⡜⠗⠊⠙⡀⠀⡔⠐⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⣀⣀⣀⠀⠁
⠀⠀⠀⠀⠀⡄⠀⠚⠈⠉⠀⠀⢁⠀⢠⠐⠉⠀⠀⠀⠀⠈⢱⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⢉⠉⠉⣤⣹
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢠⠖⠛⠀⠈⢄⡤⠶⡄⢀⣀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡄⠀⡟⠋
⠀⠀⠀⠎⠉⢒⣁⠀⠀⣠⣬⡓⠈⢁⠀⠈⢡⠐⠁⢺⠀⣥⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠇⠀⡅
⠀⠀⠀⠣⠤⠏⠉⠀⠘⣇⡀⣹⣤⠼⠀⠀⠈⢄⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣘⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠀⠀⠀⠒⠒⠒⠂⠐⠚⠛⠛⠓⠂⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠤⠤⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠋⠀⢀⡠⠐⠈⠉⠁⠀⠉⠉⠛⠢⣀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⢻⣁⣠⣔⣉⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢠⠶⠛⠉⠉⠀⠀⠀⠈⠉⠉⠓⠦⣀⠀⠀⠀⢸⠄⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⣼⡄⢠⡀⣾⣦⣿⡘⢧⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⣃⡀⠴⢋⣧⠞⢳⡟⠀⠈⢳⠘⡆⠀⠀⠀⠀⢀⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢀⡇⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠞⠀⠀⠀⠠⣦⣤⣀⡈⠁⠀⠀⠀⠀⠀⠈⡇⢹⠀⠀⠀⠀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢸⡇⠀⠀⠀⠘⠛⣛⣛⣉⡉⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠃⠀⠀⠀⣷⢸⡆⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⡴⠋⠀⠀⠀⠀⡴⠋⠁⣀⣀⡉⠳⡄⠀⠀⠀⠀⢀⠔⠊⡉⠉⠓⢦⡀⠀⠀⠀⣿⣸⠇
⠀⠀⠀⠀⠀⠀⠀⣾⠁⣿⠀⠀⠀⠀⠀⢸⠁⠀⣼⣿⣿⣤⡄⢹⠀⠀⠀⠀⡏⣴⣿⣿⣀⡀⠀⢳⠀⠀⠀⠀⢹⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠹⣄⣿⠀⠀⠀⠀⠀⠘⣀⠀⠘⠿⣿⠿⠁⣘⠀⠀⠀⠀⣇⠻⣿⣿⡿⠃⠀⡸⠀⠀⠀⠀⢸⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡄⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠶⠞⠁⠀⠀⠀⠀⠘⠦⠤⠶⠶⠒⠚⠁⠀⠀⠀⢀⡿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⢠⠴⢄⡀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠘⢦⣀⠙⠲⣄⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠒⠒⠲⠦⣄⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣀⡤⠖⠋⣙⡆
⢀⣤⣀⣒⣒⠂⠒⠉⢁⣀⠀⠘⣆⠈⠱⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⢀⡔⠉⠁⠀⠴⣮⣉⣀
⣾⣩⡭⠭⠤⠀⠀⠀⠈⠉⢹⡄⡟⠀⠀⠀⠙⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠖⠋⠁⠀⠀⠀⢸⢄⡶⠛⠛⠀⠀⠀⠩⠭⣽⣶⡄
⢻⣀⣀⣀⣀⣀⣀⣀⣠⡤⠾⠁⢿⠀⠀⠀⠀⠀⣠⠏⡿⠙⠛⢶⣖⠒⠒⣒⡿⠉⠹⡎⣧⠀⠀⠀⠀⢀⡟⠘⣧⣀⠀⠀⠀⠀⠘⠓⠶⢬⣿
⠈⠉⠉⠀⠀⠀⠀⠀⠀⣧⠀⠀⠘⣆⠀⠀⣀⡴⠃⢀⡇⠀⠀⠀⠈⣉⣉⡉⠀⠀⠀⢷⠈⠳⣄⣀⣠⠞⠀⠀⢀⡟⠉⠛⠓⠒⠶⢤⣄⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⠙⠋⠁⠀⠀⣼⠃⠀⠀⠀⠈⠛⢻⣿⡆⠀⠀⢸⡆⠀⠀⠉⠁⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⣤⠴⠋⢹⠀⠀⠀⠀⢿⣿⣿⣿⠃⠀⠀⠀⣿⠲⠤⣤⣤⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠤⠤⠤⠤⠶⠶⠶⠶⠶⠒⠒⠒⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠰⣶⠂⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠛⠐⠒⠂⠂⠀⣻⠒⠲⠖⠦⠴⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣀⣀⡀⠀⣿⣀⣀⣀⣀⣀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠼⣯⡉⠉⠉⠉⠙⣧⡽⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢻⠀⠀⠀⣾⠁⠀⠀⠙⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠒⠤⠤⠀⠀⠬⢧
⠀⠀⠀⠀⠀⠀⣤⡄⣀⣀⡀⢀⣤⡤⠦⣄⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢾⣍⣹⡆⠀⠘⢆⡀
⠀⠀⠀⠀⠀⠀⢧⡦⠀⠀⠉⠉⠉⡗⠀⠾⢦⠀⠀⠀⢠⡔⠋⠁⠀⠉⠐⠂⠀⠒⠐⣂⠀⠀⠈⢓⠆
⠀⠀⠀⠀⠀⠀⠈⠻⣯⣿⣶⣒⣚⡡⠚⢦⠀⢳⡀⠀⠈⠑⣤⣠⠔⡇⠀⠀⣏⣉⢹⣹⡷⢤⣶⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠈⢦⠀⠹⠤⠄⢼⣉⣩⣥⣭⠙⠒⣚⡿⢉⡉⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣀⣀⣀⣹⣷⣶⡦⠽⢊⣯⢄⡿⠀⠀⠀⠀⠘⡏⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣉⡉⡠⠞⡏⢿⠉⡇⠀⢀⡖⠦⢠⡇⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠃⠉⠀⠀⢸⠈⢳⡇⠀⢸⣅⣠⠞⠀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣸⠃⠀⣼⠀⠀⠀⣊⠥⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣤⣄⡀⣱⣿⡧⠶⢯⡀⠐⠯⠅⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⠀⠙⠮⣿⣿⡿⠋⠀⣀⠀⠈⠳⣤⣐⠂⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢪⣩⣷⡄⠀⠀⢀⡾⠗⠦⣤⣤⡼⠋⠀⢀⣤⣄⠀⣀⣠⣿⣿⣷⡀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⢴⣦⢭⠕⠀⠀⠀⢻⣀⣀⣀⠁⣤⣴⣞⠉⠉⠉⢻⣿⣿⣿⣿⣿⣷⠀⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠈⠑⠶⠶⠟⠻⠿⣿⣿⡿⠿⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠈⠉⠉⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⣀⠄⠒⠒⠒⠒⠚⡗⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠈⣄⣀⣀⡀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⡀⠤⠤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⣀⠤⠒⠉⠉⠹⡀⠀⠈⠑⣄⣎⡠⠤⢄⣀⣀⣠⡤⣖⠉⠉⡇⠀⠀⠀⠀⠀⠀⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡧⠊⠁⠀⠀⠀⠀⠀⠙⠢⢤⡶⡿⠛⠈⠉⠀⡠⠊⠁⠉⠉⠳⢤⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⢀⠜⡇⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⢀⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡏⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⢹⠱⡀
⠀⠀⠀⠀⠀⢀⡎⠀⢰⠀⠀⠀⠀⠀⢀⣾⠋⠀⢠⠎⠀⠀⠀⠀⠘⢄⠀⠀⠀⢀⠼⠁⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘
⠀⠀⠀⠀⠀⡘⠀⠀⠀⢣⠀⠀⠀⢀⡿⠁⠀⣠⠧⠴⠒⠒⠒⠒⠢⣄⠉⠒⠊⢁⣸⠴⠆⠦⣖⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠣⡀⠀⢸⢃⣴⠟⠁⠀⠀⠀⢀⠔⠉⠁⢸⠉⢢⡔⢩⠃⠀⠀⠀⡼⢢⢀⠤⠒⠉⠉⠑⢾⡀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠢⣾⠉⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⡸⢀⠏⣳⠃⣀⠤⠒⠢⡆⡼⠁⠀⠀⠀⠀⠀⡇⠙⡄
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠏⠑⠢⢄⣀⠀⠀⢸⠀⠀⠀⢠⢃⣸⢖⡷⠊⠀⠀⠀⣸⣿⡿⠀⠤⢄⠀⠀⢠⠃⠀⢰
⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⡌⡄⠀⠀⠀⠀⠉⠁⠚⡖⠒⢲⠋⣡⠼⣡⠃⠀⠀⠀⡰⠋⡿⢆⠀⠀⠀⡇⢀⡇⠀⠀⠰
⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠃⢡⠀⠀⠀⠀⠀⠀⠀⠈⡲⣁⠞⠁⢠⢇⠀⠀⡠⡾⢁⢼⠃⠈⠳⢄⠀⠇⡜⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢰⠀⠀⢢⠀⠀⠀⠀⠀⣠⠎⡰⠋⠁⡲⠃⠜⢖⠈⠀⡧⠋⠸⠀⠀⠀⠀⢹⠟⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠸⠀⠀⠀⠱⣄⠀⡠⠚⠁⡐⠁⢀⠔⠁⠀⠀⢀⡱⢞⡇⠀⡇⠀⠀⢀⣠⠏⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⡀⡆⢀⣀⠤⠚⠛⢄⡀⣰⡡⠔⠁⠀⢀⡠⠖⠉⠀⠀⠟⠲⠂⠒⠒⠉⡸⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣭⠤⠄⠒⠒⠃⠉⠉⡛⠐⠒⠒⠉⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠁⠀⠈⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠈⠢⡀⢀⠆⠀⠀⠀⢀⡠⠊
⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⢈⠟⠒⠒⠒⠊⠁
⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢀⠎
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⣈⣢⣀⡠⠤⠒⠁⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠄⣀⣀⣀⡠⠔⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⢠⣶⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⡏⣶⢹⠰⢹⢹⣿⠰⣯⡰⣿⡱⣽⣿
⠀⠀⠀⠀⢀⣙⣟⣁⠀⠀⠀⠀⠀⢀⣈⣻⣋⡿⣟⣾⡷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⣧⣋⣾⣘⣼⣘⣻⣘⣯⣛⣼⣝⣼⣿
⠀⠀⡀⢀⡀⡀⢀⣀⢀⠀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⢸⣿⣿⢩⣌⣻⢹⣿⣿⠇⢹⣿⢹⡇⢹⠏⢹⣿
⠀⠈⠁⠘⠘⠃⠘⠀⠐⠀⠉⠀⠀⡏⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⢸⡿⢻⢸⣿⣿⢘⡂⣿⢸⠂⡌⣠⢸⣿
⠀⠀⠀⠀⢰⣶⢰⣶⠀⠀⠀⠀⠀⠁⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⢸⣿⣿⣶⣴⣿⣶⣶⣷⣾⣷⣿⣾⣶⣷⣿⣾⣿
⠀⠀⠀⠀⢸⡿⠘⣿⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⢿⠇⠀⢿⠇⠀⠀⠀⠀⠀⠿⠟⠿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠤⠠⠤⠠⠀⠀⠤⠄⠄⠤⠠⠤⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠤⠀⠀⢀⣀⣄⣀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡷⠀⠀⠀⠀⢰⣾⠟⣛⢻⣶⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⣠⣄⣀⡀⠀⠀⠀⠀⠀⣈⣻⣏⡀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣶⠶⠶⠛⠋⢸⣿⣌⣛⣰⣿⠃⠀⠀⠀⢸
⠀⠀⠀⢀⣀⣿⣿⣇⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⡿⡆⠀⠀⠀⠀⠀⢰⡿⢿⠀⣿⠀⠀⠀⠀⠀⠘⠛⠟⠛⠁⠀⡀⣀⠀⢸
⠀⠀⠀⣿⣿⣿⣿⣿⣆⡀⠐⠉⠉⠙⠀⠀⠀⢰⡇⠙⢿⣿⣷⣽⡄⠀⠀⠀⠀⢸⡇⢀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠸
⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠛⠛⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣤⣦⡀⠀⢀⣴⣤⠀⠀⢠⣤⣄
⠀⠀⠀⠉⠉⣿⠉⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢻⣿⡿⠃⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢀⣻⣟⡁⠀⢈⣻⣟⡀⠀⣘⣿⣋
⠀⠀⠀⠐⠒⠛⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠘⠛⠃⠀⠀⠀⠀⠀⠀⠛⠉⠛⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠋⠛⠘⠛⠛⠛⠛⠛⠛⠛⠘⠃
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠘⢀⣀⡀⠀⠀⢄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⣠⣤⡄⠀⠀⣤⣤⡀⠀⢀⣤⣤⠀⠀⠋⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⢀⣼⣿⣟⠀⠀⠀⠀⠀⣀⣈⠀⠀⠀⠀⠀⠀⠀⢀⣘⠿⠋⠀⢀⣹⠿⠃⠀⣀⡻⠟⠁⠀⣈⡻⠟⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣇⡀⠀⠀⠘⢿⠿⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⢠⣿⣿⡆⠀⢰⣿⣿⠀⠀⣸⣿⣷⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢹⣿⣿⣿⠉⣁⠀⣰⣿⡟⣿⣷⣄⡀⠀⠀⠀⠸⣿⣿⣧⣦⢸⣿⣿⣷⣆⢸⣿⣿⣴⣄⢿⣿⣿⣴⡄⠀⠀⣇⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠟⠃⢙⣿⡿⠟⠁⢹⣿⡿⠛⠈⢻⣿⠿⠋⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠂⠀⠀⢸⣿⠀⠀⠀⢸⡷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠸⠿⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⢸⡿⠀⠀⠀⣾⡏⠀⠀⠀⣿⠇⠀⢀⣀⣄⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠂⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡠⠀⠐⠀⢀⠐⢀⠀⠒⠈⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄
⠀⠀⢇⠒⠠⠓⠀⠀⠐⠁⠉⠀⠀⠀⢂⡀⠈⠀⠐⠦⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡤⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⢶
⠀⠀⠀⠀⠀⡀⠀⢘⠀⠀⠀⠀⠀⠀⠊⠀⠁⠀⡀⠀⡌⢀⠀⠀⠀⠀⠂⢀⠠⠴⠀⠀⠀⠀⠀⠐⢠⠄⠀⠖⠀⠒⠀⠀⡀⠀⠱⣂
⠀⠀⠀⠀⠀⠀⠅⠈⢀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠁⠀⠀⠀⠄⠑⠁⠀⠀⠀⠀⠀⠀⢐⠀⠤⠀⡀⠠⠐⠉⠂⠈⠑⠀⠄⠀⠀⠀⠉
⠀⠀⠀⠀⠈⠀⠀⠂⠸⠄⠐⠀⠀⠀⠀⠂⡀⠄⠐⡀⠀⠀⠚⢁⠄⡘⠀⠀⠀⠂⠀⠈⠁⣄⠈⠐⢄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⣀⠐⢀⠂⠌⠐⠀⠉⢡⠀⡄⠀⠠⠉⢩⠀⠉⠉⠁⠀⠉⠀⠈⠁⠀⠈⠀⠀⠀⠀⢀⠀⡄⠀⠀⢸⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⣀⠠⠲⠐⠈⠁⠄⢀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⠀⠈⠀⠀⠀⠠⠠⢠⡶⡦⣦⢴⣤⡔⠁⠐⠂⠁⠠⠀⠀⠀⠐⠀⠀⢁
⠀⠀⠀⠀⠀⡀⠀⠀⠁⠤⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⡿⠷⠆⢳⣗⣮⠀⣙⣣⡀⠀⢈⠐⢀⡠⡡
⠀⠀⠀⠀⠐⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠉⠉⠁⠀⠐⠰⢦⢯⠈⢐⢚⠉⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢥⡄⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠊⣽⠂⠀⠀⠀⠀⠀⠀⠀⠘⢘⠀⠀⠀⠀⢀⡠⠐⠠
⠀⠀⠀⠀⠀⠀⠁⠂⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⣄⠀⠀⢀⡄⠀⠀⠈⠉⠀⠁⠈⠉⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡆⠈⠁⠈⠁⠠⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣿⢧⡀⠀⠀⠀⢰⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣧⢿⣶⣤⣤⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣱⣿⣻⣿⣷⠩⣽⡟⢩⣿⡇⠀⠀⢠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡻⣿⣽⠯⠶⣟⣿⣿⣿⡇⠀⠀⢸⣿⣿⣷⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠻⠶⠟⠀⠀⠀⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⢀⣀⣤⠾⢿⣄⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠖⠒⠛⠉⠉⠀⠀⣀⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣦⣀⣤⣤⡶⠾⠛⢋⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⢀⣤⣶⣿⠿⠟⠛⠛⠛⣻⣿⠟⠛⠛⢛⣿⣿⣿⠿⠿⢿⣷⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠋⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⢸⣿⣿⡎⢻⣇⠀⠀⠀⠈⠉⠛⠻⠿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠉⠉⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣀⠀⠀⠀⢀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⠿⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⡀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⢿⣷⣶⣶⣤⣤⣤⣄⣀⣀⣀⣀⣀⣤⣤⣤⣶⣾⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⣹⡇⠀⠀⠀⠀⢰⣿⡇⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠙⠛⠛⠀⠀⠀⠀⠀⢸⣿⠀⠺⣿⣽⣻⣷⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⠦⠀⠀⠀⠀⠀⠀⢸⣿⠀⠰⢾⣯⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠀⠀⠀⢰⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢹⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡆⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠟⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡿⢿⣿⣷⣄⡀⠀⠀⠀⠈⠻⣧⡀
⠀⠀⠀⢀⣠⣴⡾⠟⢉⣿⡇⠀⠀⠀⠀⣰⠏⠀⢸⡟⡀⠀⣼⢿⡄⠀⠀⠀⡿⣧⠀⠀⣼⡇⠘⣿⣇⠙⢿⣦⣄⣀⠀⠀⢹⣷
⢀⣴⡾⠟⠋⠁⠀⠀⣸⣿⠀⠀⠀⠀⢠⡏⠀⠀⢸⡇⠳⣴⡇⠈⢿⣄⠀⣼⠇⢸⣂⡴⢉⡇⠀⢹⣿⡄⠀⠈⠙⠻⢿⣶⣾⠟
⠛⠿⣶⣤⣀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣾⡀⠀⠀⢸⡇⠀⠙⠁⠀⠀⣹⣿⣇⠀⠈⠋⠀⢸⡇⠠⢴⣿⣧
⠀⠀⠀⠉⠻⣷⡄⢸⣿⠁⠀⠀⠀⠹⣧⠀⠀⠀⠀⡇⠀⠀⠀⠀⣼⠏⠀⠙⣦⠀⠀⠀⢸⡇⠀⢰⢿⣿⡀
⠀⢀⡀⡀⠀⣼⡏⣼⡟⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⣿⠀⠀⠀⣼⠏⠀⠀⠀⠘⣷⡀⠀⢸⡇⢠⠟⠈⣿⡇
⠀⣼⣿⣿⣿⠏⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⣿⠀⠀⣸⡟⠀⠀⠀⠀⠀⠘⣷⠀⢸⣷⠏⠀⠀⢻⣿
⠀⠀⠉⠉⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⢿⣦⣤⣀⣀⣀⣠⣴⠿⠃⢸⠃⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠸⠿⣿⣶⣶⣶⣤⣤⣤⣤⣄⣀⣀⣸⣆⣀⣀⣀⣉⠙⠛⠛⢉⣀⣀⣀⣿⣀⣀⣀⣀⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⢻⣿⠟⠻⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⠿⠿⠟⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡶⠶⢤⣤⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣤⡶⠶⢶⠶⠶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⡆⠀⠀⢀⣀⠙⣷⡀⠀⠀⠀⠀⠀⠀⣴⠟⢉⣁⡀⠀⠀⠆⠀⢀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠷⠾⠛⠋⣿⣄⣼⡷⠀⠀⠀⠀⠀⠘⢷⣤⣾⠏⠛⠛⠛⠛⠛⠛⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣀⣀⣀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⡱⠄⠀⢰⢣⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⣎⠉⠉⣠⠊⠀⠀⢰⡏⠙⠻⠶⠀⠀⠀⢀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⣠⢯⠴⢦⡼⠀⠀⠀⢸⣧⠀⠀⢠⠤⠀⠘⢿⣷⠀⠀⠀⡼
⠀⠀⠉⠒⠤⣀⠀⠀⠸⣆⠈⠁⠈⡱⢂⠇⠀⠀⠀⠀⠙⣾⢀⡉⠲⣄⠀⢰⠇⠀⢐⡍⡳
⠀⠀⠀⠀⠀⠀⠉⠒⠤⣈⠓⠤⠺⡄⠈⢳⡀⠀⠀⠀⠀⠈⢢⣈⠒⠊⠀⠐⠀⠲⠌⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣹⡄⠀⠙⠦⣀⣀⠤⡖⠁⢽⡿⠀⠀⠰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢦⡀⠀⠀⠀⢸⠀⢀⣾⠇⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⢁⡀⣑⣯⡒⠒⠒⡇⢀⣾⣿⠀⠀⢳⡀⠀⠘⣆⢀⠠⢄⣰⡖⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡠⠒⠁⠀⠀⠙⠻⣦⡜⠀⢸⣿⣿⠀⠀⠀⢳⡀⠀⠸⣼⣶⠀⠈⠑⠢⢄⡉⠓⠦⡄
⠀⠀⠀⠀⠀⠀⢀⠔⠁⡠⠊⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠸⣿⣿⠆⠀⠀⢠⣧⠀⠀⢹⡝⢄⡀⠀⠀⠀⠈⠑⠢⢷⡀
⠀⠀⢀⠀⠀⠀⠀⡠⠊⠀⠀⢀⡠⠂⠈⢢⡀⠀⠀⠀⠈⠃⠈⠃⠀⠀⢀⡎⠘⣇⠀⠀⢳⠀⠈⠑⠢⢄⡀⠀⠀⠀⢈⠑⣄
⠀⠐⣇⡠⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠸⡄⠀⠘⡇⠀⠀⠀⠘⠼⠛⠲⢤⣸⡇⢸
⠀⠀⠘⢦⡀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⣀⠀⢀⡠⠎⠀⠀⠀⢀⠗⠀⠀⠛⠦⠄⣀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠺⣀⣀⠓⣦⣀⠀⠈⢳⠢⢄⡀⠀⠀⡇⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠇⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣴⣆⢀⠠⠀⠑⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡉⠋⣹⢭⣿⣤⣦⠴⣦⡤⠬⢧⣄⣠⠄⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢠⠊⠀⠼⣦⣶⣿⣋⣿⣾⠭⠶⣿⣹⠲⢊⠛⠩⣹⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠻⠌⠄⢰⠿⠟⢢⣶⣿⣿⣷⣽⣿⢷⣿⣿⡿⢷⣿⠛⣤⣤⡘⣿⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣰⣾⣿⣉⢉⣽⣿⣿⣾⣚⣾⡿⣷⣶⣍⣯⠉⣼⣿⣯⡰⣤⡂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⣸⡥⣾⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠹⠭⣛⡛⢿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢃⠛⠀⣿⣥⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⢿⣶⠛⡟⣍⢻⡐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡇⢴⣿⣿⣿⠟⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢶⣿⣤⠇⣙⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠁⠶⠀⠳⡌⢧⡹⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣿⣿⣁⡨⡝⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠈⢁⠀⠃⢈⣷⡘⠳⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠤⢧⡿⣍⡴⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⢐⡊⠙⣿⣇⣲⣮⡿⣿⣿⣿⣿⣻⣯⣿⠟⠉⣱⣸⠿⠘⠉⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⢷⣄⡈⣹⠟⠓⠂⠻⠿⠟⠛⠻⠛⣧⢚⣥⡿⠉⠐⡀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠛⢭⡋⠑⠒⢻⣥⢤⡤⠉⠀⠀⣨⠿⡨⠧⠤⣤⣥⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠾⠀⡾⢯⠋⠛⠯⠀⠬⠁⠆⠀⡛⠀⠀⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡀⠀⢀⠓⠀⠀⠀⠄⠛⠳⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⠆⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢀⠤⠤⠤⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⠁⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠖⠊⠁⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠧⣀⡀⣀⡀⡀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸⠀⠘⠞⣻⡟⢭⠋⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠸⣤⣄⢀⡛⡁⠀⢸⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠉⡃⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀
⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠄⣀⣀⠀⠠⠖⠀⠀⠘⠦⣀⣀⣀⣀⠀⠀⠠⠤⠤⠄⠠⠀⠀⠀⢀⣀⡀⠀⠀⠠⠤⠤


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣀⣀⣀⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠿⠂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⣀⣀⣀⡠⠶⠦⠀⠀⢀⣀⡀⠀⠀⠀⠀⠉⠉⠰⠶⠆⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠠⣾⡟⠉⠛⠙⠛⢧⣄⠀⠀⠀⠉⠙⠛⢶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠤⣤⣤⡤⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡾⠛⠃⠀⠉⠁⠀⠀⠀⠀⠀⠘⢷⣤⡀⠀⠀⠀⣀⣀⠽⣷⣤⣤⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠟⢠⣄
⠠⣾⣿⠛⠶⠶⠀⠒⠀⠀⣀⣉⣀⡀⠀⣠⠀⠀⠀⠀⠀⠀⠰⠆⠈⠙⢿⡀⠀⠀⠀⠀⠀⠈⠛⣏⠀⠀⠀⠺⠷⣀⠀⠀⣀⡀⠰⠂⠀⠀⠀⠀⠁⠰⠆
⠀⠈⠉⠀⠀⠀⠠⠄⠀⠈⠙⠛⠉⠁⢰⡿⢷⠦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠛⣦⠀⠀⠀⠀⠀⠀⠙⣀⡀⠀⠀⠀⠿⣿⡆⠉⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠛⢦⣄⠀⠀⠀⠀⠀⠀⠈⣶⣄⣠⣤⣤⠀⠘⢿⠟⠙⠁⠀⠀⠀⣼⡆
⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⢠⣴⠃⠀⠀⠀⠈⠃⠀⠀⠉⢷⣤⣀⠐⠛⠓⠂⠈⠙⢧⡀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⢣⣄⠀⠀⠀⠀⠀⠀⢾⡏⠀⠀⠀⣰⡶⠶⠖⠀⣶⠟⠻⣿⣷⠶⢄⣀⠀⠀⠈⠹⢶⡀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠈⠉⠁⠀⠀⠉⠁⠀⠈⣳⡤⠈⠉⠛⠁⠀⠀⣤⠀⠀⠀⠘⢃⣀⠈⠻⣷⣤⠠⣤⡴⠿⣶⣤⣀⣹⡿⠂⠄⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠛⣧⠀⠸⠀⠀⠀⠀⣿⠀⠀⠀⠀⣼⡿⠃⠀⠉⠁⠀⠀⠀⠀⣀⠛⠛⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣽⡇⠀⠀⠀⠀⠀⢿⣄⠀⠐⠀⠈⠁⠀⠀⢀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢉⣹⠶⠶⠖⠂⠀⠀⣠⡄⠐⠒⠖⠊⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠀⠉⢿⠀⠀⠀⠀⠀⠀⠹⣿⣆⣀⡀⢀⣶⡆⠈⠀⠀⠆⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠁⠀⢶⣄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⡀⠀⠀⠀⢶⡄⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⣿⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢣⡄
⠀⢀⣴⠀⠀⠚⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠿⠿⠲⠂⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⢀⣀⣀⡠⠶⠶⠶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢷⣦⠄⠠⠾⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣦⣤⣤⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡄⠀⠀⠀⠀⢀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⢀⣴⣦⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠃⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠙⠛⠛⠃⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠶⠾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠂⣀⣤⣀⡀⠀⠀⢀⣀⣀⡀⠘⠛⠃⠺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢻⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⢄⣀⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠰⠦⢀⠀⠀⠀⠀⠘⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣤⡄⠀⠀⠈⠃⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢧⣀⠈⠋⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠾⣿⣄⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠀⠀⢀⠀⠀⠐
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣀⣠⣤⣄⣠⣤⣀⣤⣤⣄⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣤⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⣷⣦⡄⠀⠀⠀⠀⠀⠘⢡⣿⠆⠀⢀⣀⣀⡤⠄⠀⠀⠀⠀⢀⣻⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠀⢀⣿⣿⣀⣠⠤⠆⠀⣀⡤⠶⠚⠋⠉⣀⣤⠤⠶⠒⠛⠉⠉⠉⠙⠋⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠋⢁⣀⠤⠒⠉⣀⣀⣤⣶⣚⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣩⣭⡠⠖⢋⣠⣴⣾⣿⣿⣿⣿⣿⣿⡟⣰⣾⣶⣦⡀⠀⠀⠀⠀⠠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠋⢀⡠⠟⠛⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠸⣿⣿⣿⣿⣿⣦⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢀⡴⠋⢀⣤⣾⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⣀⣀⠀⠹⣏⡙⢿⣿⣿⡄⢋⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⠞⠉⢸⣿⡿⠟⣿⣿⡟⠁⠀⣀⣉⡙⠛⣩⡤⠂⠀⠉⠁⠀⣿⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢃⡠⠚⣁⣀⠀⠘⣿⡅⢠⣿⠏⠀⠀⠉⢁⣈⠉⠛⠁⢀⣴⣶⡄⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠞⠀⠘⢛⣿⡷⠀⢻⡇⠘⠿⠀⠀⣴⣾⠿⠻⣿⠀⢰⠟⠋⠹⠇⠀⢸⣏⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢧⣀⠀⠀⢨⣥⠀⠀⠘⣷⠀⠀⠀⠸⠋⠁⠀⠀⠁⢠⡀⠀⢀⡀⠀⠀⢸⣿⣭⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠙⠀⠀⠀⣠⠶⠦⣿⡄⠀⠀⠀⠀⢠⣶⡆⠀⠀⢷⠀⠻⡿⠀⠀⣾⣿⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣤⡀⠀⢰⣿⠀⠛⢻⣷⠀⠀⠀⠀⠀⠙⢡⠆⠀⠸⣇⠐⢦⡀⠀⣿⣿⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⣿⣇⠀⠀⠀⠀⠴⠋⠀⣀⠀⢻⡀⠀⠁⠀⢸⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣀⣹⡟⠀⠀⠀⠀⠀⠀⠀⢻⡟⠋⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀⣁⣤⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠺⢿⡟⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠠⠿⠶⣦⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣼⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⣀⣀⣴⡧⠾⠋⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣶⣦⣤⣍⣩⣤⣤⣤⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠛⠻⠿⠟⠛⠻⠿⠿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⣂⣀⡛⠉⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠁⠀⠈⢀⠰⢲⣌⡉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠃⠀⠰⠉⠉⠉⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⡀⠀⡰⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠓⡤⡇⠀⠀⣐⠉⣠⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢴⡿⠀⢠⠊⠁⢈⡇⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢉⡁⠀⠀⠈⠂⠴⠋⠉⠈⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠠⠑⠄⡀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⡠⠁⠀⠀⠈⠐⠄⡀⠀⠀⠀⢈⡀
⠀⠀⢠⡖⠒⠂⠀⠈⠉⠁⠸⡩⡳⠦⣀⢀⠂⠠⠒⠂⠀⡰⠁⠀⠀⠀⢀⠔⠂⠉⢓⣂⣰⠺⣈⢁⡶⣀⣀
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢫⠙⢄⠀⠏⠀⠀⠉⠃⡰⠁⠀⠀⠀⣠⡃⠄⠀⡽⡨⠥⡭⡠⡿⠀⡟⣵⠁
⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢠⠓⢄⠙⠄⡀⠀⠀⣠⠁⠀⠀⠀⢀⣵⣤⡠⠏⠴⢽⠉⣏⡽⠁⠀⠘⣥⡀
⠀⠀⠀⠈⠓⢚⢹⠉⠉⠉⡽⠃⠀⠀⠳⡀⠈⣢⣰⢉⡄⢸⠃⠀⢠⣔⠝⠀⣠⡄⠀⣀⣉⠑⠒⠒⠦⢼⡆⠀⠀⠥⠴
⠀⠀⠀⠀⠀⠸⠸⠀⡠⠎⠁⠀⡀⠀⠠⡐⠎⣸⡇⠰⢣⠤⢀⣠⠟⠁⠀⠈⠀⠁⠀⠛⠁⠘⡉⠴⠊⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⡼⢄⠀⠀⠀⠑⡀⣠⠚⢄⡘⠀⢰⡌⣐⠂⣸⠄⠀⠀⠀⠀⠀⢀⡠⠐⠉
⠀⠀⠀⠀⠀⡠⠲⢄⠀⠈⠀⠂⠤⠌⣀⣈⣐⣌⡐⢸⡶⠠⢽⡂⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠁⠂⢄⡀⠀⠀⠀⠈⠉⠉⢉⠟⠀⠀⠈⠈⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⡜⡹⠁⠀⠒⠠⠌⢑⣤⣀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠤⠒⠒⢒⠒⠒⠢
⠀⠀⠀⠀⠘⢠⠁⠀⠀⠀⠀⠀⢸⢸⡝⠑⠀⠀⠁⠒⠢⢤⡤⢄⡀⢀⣀⣈⡖⡠⠐⠢⢐⠐⠂⡄⢧⠒⡀
⠀⠀⠀⠀⡇⡈⠀⠀⠀⠀⠀⠀⢸⠘⠀⠀⠀⠀⠀⠀⠀⡘⠀⢠⠀⠀⠀⠌⠬⠁⠀⠀⢰⠴⡀⠘⠈⠁⠃
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢘⠀⠦⢤⣄⣀⣀⢀⣀⣟⠻⠏⠁⠀⢢⠀⠀⠀⠀⠀⠰⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠉⠘⠓⠠⠌⠄⠆