Food ascii Emojis & Symbols

⠀⠀⠐⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⡃⣤⢐⣠⡤
⠀⠀⠀⠡⡖⠉⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣰⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠒⠒⠄
⠀⠀⠀⠀⠘⠇⡀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠈⡋⠡⡇⣿⢤⠔⢉⡇⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⢤⠶⠀⣤⣄⠀⠆⠀⠀⠀⢠⠀⢀⠤⢴⡄⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⢃⣀⠗⠢⡀⠀⠀⠀⠀⠀⠁⠆⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀⡠⠚⣀⠔⡄⠂⠀⠀⢄⠓⠪⠁⠀⠀⠀⠘⠄⠠⠤⠀⠶⠄⡀⠑⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠡⡤⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠁⠛⠀⠀⠈⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠳
⠀⠀⠀⠀⡠⠄⠖⠐⠠⢄⠀⠀⠀⠀⠀⠀⠠⣄⡀⡀⠓⠄⠠⠀⡒⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡁⠒⠓⡄
⠀⠀⠀⠈⠀⠀⠨⢄⠀⠀⠑⠀⠀⠀⠀⠀⠀⠈⠲⠤⢤⠐⠶⠒⡄⠀⠀⠀⠀⠀⢠⠆⠀⢀⠀⡀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠈⠉⢉⠆
⠀⠀⠀⢐⠀⠈⠀⢀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢠⠘⠐⠋⠰⠃⠀⠀⠀⠀⠀⢸⠀⠁⠀⠤⠀⠀⢁⣀⡀⡷⠀⠀⠀⠀⠀⠀⠂⠄⠀⠠⠀⡈
⠀⠀⠀⠀⠀⠀⠈⠁⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⢲⠈⠠⠘⠀⠒⠀⠀⠀⠀⠀⠀⠀⡉⠂⣀⠐⠄⡁⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠈⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⢀
⠀⠀⢠⢤⡀⠀⠀⠀⠀⠤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⣬⠓⠃⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠄
⠀⠀⢠⠀⠐⢀⠀⠀⢀⣔⠀⠀⠀⠀⠀⠀⢀⣐⠀⠂⠀⠂⠀⠀⠀⠒⠂⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠆⠤⠤⠀⠀⠠⠤⠼
⠀⠀⢀⠀⠑⡀⢀⠀⢁⢠⡊⠁⠀⠀⠀⠀⠀⠻⡂⢀⠀⠀⠀⡀⠔⡞⠁⠀⠀⠀⠀⠐⠚⠂⠒⠄⠂⠘⢰⠁⠀⠀⠀⠀⠀⠐⡖⠒⠒⠒⠒⠒⠒⢲
⠀⠀⠀⠀⠀⠄⠀⠈⠋⠑⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠐⢟⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠈⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂


⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⡐⠁⠀⢀⢀⠀⠀⠀⠀⠀⠀⢈⠒⠀⠛⠒⠊⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠄⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡅
⠀⠀⠀⠀⠀⠐⢀⠀⢀⢃⠈⠀⠀⠀⠀⠀⠀⠈⣁⠐⠂⠐⠊⠁⡉⠀⠀⠀⠀⠀⠀⠀⢀⠩⠀⠀⠀⠤⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠀⢰⠆
⠀⠀⠀⠀⡌⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠁⣩⢶⡄⡇⠀⠀⠀⠀⠀⠀⠀⠰⢡⡄⠜⣉⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃⠀⠒⠀⠬⡀
⠀⠀⠀⠀⠸⠃⠤⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⣖⢛⣟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⣿⠚⠀⠀⠀⠀⠀⠀⠀⠀⡄⣄⣄⣀⣀⡆⢠
⠀⠀⠀⠰⣁⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢨⣩⡟⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡄⠀⠀⠀⠀⠀⠀⠘⠀⠤⠤⠶⠤⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⢀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈
⠀⠀⠀⠠⠂⠠⠀⠀⠉⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠉⠉⠒⣄
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⣀⡠⠄⢂⡠⢌⢂⠈⠂⠀⠀⠀⠀⠀⢃⠰⠀⠀⠀⠠⢀⠓
⠀⠀⠀⢀⢡⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⢀⣁⠀⠉⠀⠉⠉⠀⢁⠀⢤⠀⠀⠀⠀⠀⠆⠨⡅⣀⣉⣉⣀⣤⠀⡶⠀⠀⠀⠀⠈⠆⠐⠀⠰⠀⠐⠀⡞
⠀⠀⠀⠀⡀⠄⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠮⡭⠀⠐⡒⢊⠙⠉⠁⠥⡴⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠄⠤⠀⡇⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠠⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠒⠒⠂⠀⠀⠉⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠓⠚⠁⠀⠀⠒⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠐
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⢀⣠⡰⠊⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠈⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠈⠈
⠀⠀⠀⠀⠀⠀⡀⢀⡠⠠⠄⠀⠀⢀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠄⠄
⠀⡀⠀⠀⠈⠉⠠⠤⠂⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢠
⠀⢁⠀⡀⠀⠀⡀⠀⠀⠐⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠠⠀⠀⠀⠀⠈⠀⢠⡀⠤⠄⠄
⠀⠈⠀⠂⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠀⡀⠀⠀⠀⠀⣠⡆⠀⠀⠀⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠐⠀⠀⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⢀⢀⠀⠀⠀⢠⠠⠀⠀⠀⡀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⢀⠠⠀⢄
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⠈⠁⠉
⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡁
⠀⠀⠁⠁⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠈⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈
⠀⢀⠈⣠⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⢒⢲⡄⠀⠀⠀⠀⠀⠀⠀⠤⠀⠴
⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⡌⢁⠐⠒⣒⢂⠉⢱⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠔⠀⠠⠠⠁⠐⢀
⠀⠀⠀⠠⠄⠀⠀⠀⡀⠀⠀⠱⠐⠐⠁⠀⠀⠀⠚⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠒⢂⡐⠐⠊⢠
⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⢀⠑⠠⠤⠤⠤⠒⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⣿⣽⣽⣿⣯⣿⣸⣯⣿⣿⣿⣷⣿⣿⣿⣽⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⠿⠟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣤⣿⣻⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⢿⣧⣠⣤⡀⠀⠀⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠸⣿⣿⣿⣿⣷⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣷⣄⡀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣦⡄⠰⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⠿⣿⡿⠿⠿⠿⠏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣦⣤⣀⣿⣿⣽⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⢀⣀⢀⠀⠀⠀⠀⢀⠄⠀⢄
⠀⠀⡖⠿⠊⠉⠉⡇⠀⢀⠄⠁⠀⠀⠀⡢⡀⠀⠀⠀⣀⠀⠀⠀⠈⣥⠀⠀⢲⠀⢰⣴⡄⠀⠀⠖⠲⠂
⠀⠀⢱⠀⠀⠂⠀⢹⡀⢨⠀⠀⠀⠀⠀⠘⡰⠀⡠⠀⠈⢔⡀⠀⠀⢸⠀⠢⡔⠀⠨⠩⠃⠀⠀⡇
⠀⠀⠸⡄⡐⠀⢡⡘⡇⠀⠑⡂⠖⠖⠒⠊⠁⡐⠀⠀⠁⠀⠹⡀⠐⢤⠂⠀⠀⠀⠈⡀⠀⠀⡔⠀⠀⠳
⠀⠀⠀⠫⠀⠈⠐⠀⠁⠀⠀⠗⠒⠒⠒⠆⠀⠁⠉⠉⠉⢋⣉⣁⣀⣐⣂⣐⣂⣀⣀⡁⠀⠀⠁⣀⡀⠈⠁
⠀⠀⠀⢀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠘⡒⣖⡖⠒⠒⢒⣖⢒⠒⠊⠀⠨⠄⠈⠀⠀⠄
⠀⠀⠐⡡⠊⠀⠀⠑⢌⠄⠀⠀⢠⠖⠡⠀⠀⠈⠀⡀⠀⠀⠀⠁⣴⣋⠙⢢⠀⣷⠀⠀⠀⠀⠂⠀⠀⠀⠂
⠀⠀⠀⡌⠈⡇⢦⣶⠆⠀⠀⣀⡊⣀⣃⣀⣀⣀⣀⣠⣀⠀⠀⠀⠻⣟⣸⡟⠀⣿⠀⡐⣄⢠⣀⡄⣀⠀⡆
⠀⠀⠠⡑⡂⠀⠫⠩⢋⠄⠀⠓⠒⠚⠃⠀⠀⠀⠀⠀⠘⠀⠂⠒⠀⠁⠀⠁⠒⠓⠀⠅⠉⠨⠈⠈⠁⠩⠚
⠀⠀⠀⣀⠓⠀⠈⠀⠀⣞⣩⢱⠀⠀⠄⡄⠀⠐⢠⡌⡆⠀⠰⠀⠠⠀⠐⠀⠀⠀⡠⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠈⠁⢰⠈⠉⠉⠀⢰⡀⠐⠸⠘⣀⣔⠇⠀⠘⡏⠉⣿⣿⠀⠀⡩⢛⣋⢋⣙⡙⣙⡛⢫⠆
⠀⠀⢠⠄⠀⠠⡄⠀⠈⠑⠒⠁⠀⠀⠙⠙⠘⠘⠉⠁⠀⠀⠀⣗⠻⢁⣸⠀⠀⡓⠘⠖⠙⡉⠇⠋⠃⠜⡇
⠀⠀⢉⡄⠀⢠⡁⠀⠀⠄⠀⠀⠀⠀⠄⣤⡀⢄⠀⠀⠀⢀⠄⠈⠀⠈⡡⠀⠠⣀
⠀⠀⢋⠀⠀⠠⡐⠀⠀⢀⠈⠉⠉⠉⠉⠍⠭⠉⠉⠉⠉⢰⠀⠀⢀⢄⢲⢀⠀⠀⠠⢈⡱⠄⠀⠄⠀⢦
⠀⠀⠀⠐⣶⠈⠀⠀⠀⠠⠀⠠⢱⠀⠀⠀⡇⠀⠀⠡⠀⠠⠀⠀⢸⣄⣸⠐⠀⠀⡃⡔⠣⡀⠈⠛⠛⢩
⠀⠀⠀⠀⠚⠀⠀⠀⠀⠤⠀⠠⠼⠀⠀⠄⠆⠀⡀⠤⠀⠈⠄⠀⠀⠐⠉⠀⠀⠁⠈⠀⠀⠀⠀⠤⠤⠴
⠀⠀⠀⢀⣀⡀⣀⡤⠴⠒⠀⠀⢀⠤⠀⢀⠤⠐⡞⠀⠀⠀⠀⠀⢠⣤⠤⡄⠢⠕⠀⠀⠀⠀⢀⣤
⠀⠠⠀⠀⠀⠐⠀⢠⠀⠀⠀⡔⠑⢉⠀⠨⣀⡠⠉⠀⠀⠀⠀⢀⣈⣿⣋⡀⠀⠀⠀⠀⠀⡌⢑⣊⠭⢦
⠀⠀⣔⠄⠀⠀⢀⡄⠀⠀⡀⠧⠐⠤⠥⠀⠀⠨⠌⡀⢀⢀⣼⣿⣾⣿⣿⣿⣷⡀⢀⠀⢰⠉⠕⢐⡉⠅
⠀⠀⠁⠀⠓⠈⠀⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠐⠀⠐⠀⠀⠀⠐⠒⠐⠊⠀⠈⠈⠉⠁

⠀⠀⠀⢀⠐⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⡀⠀⠀⢀⠀⠀⠐⡂⠀⠀⠀⠀⠀⠀⢠⡟
⠀⡦⠶⠾⠤⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⡘⠁⠀⠀⢠⣌⠆⠀⠁⠀⠀⠀⠖⠈⠙⠉⠉⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⢠⡈⠀⣀⠁⠀⠀⠀⠀⠈⠂⠀⠈⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢃⠀⠀⠀⠀⠀⠀⠄⠃

⠀⠀⠀⠀⠠
⠀⠀⠀⠈⢀⠀⠀⠀⠀⢰⠉⠁⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⠤⠖⣆⠀⠀⠀⠑⠀⢂⠐⠀⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠸⠄⠀⠀⠀⠀⠈⠄⠀⠠⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠠⠆⠈⣁⣈⡉⠂⠀⠀⠐⣶⡀⢱⣮⠄⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠐⠈⠠⢻⠍⠀⠀⠀⠀⠂⠀⠨⠙⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣊⣄⡤⠄
⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⣸⠀⠀⠀⠀⠀⠀⠠⢀⢀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⡀⠀⠀⠀⢀⡴⠆⠄⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠈⠀⢀⣀⣤⣀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠊⢁⠀⡀⠁⡄
⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠢⢀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠊⠀⠀⠀⠉⠰

⠀⠀⢀⢀⡀
⠀⠀⠸⣿⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡶
⠀⢐⠀⢫⠀⢀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠛⠁⠀⠀⢠⠀⠀⠀⢠⡀
⠀⠸⠀⠸⠀⠸⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠃⠀⠀⠀⠀⠀⣀⠀⠀⠶⠞
⠀⠀⠄⠘⠀⠀⠀⠈⠁⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠦⢤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠤⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣈⣉⡉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣈⡉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠠⠄⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠐⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣁⣉⣙⣈⣁⣉⣈⠀⠀⠀⠀⠀⠁⡉⣉⡉⣉⣉⡉⠉⠉⠀⣘⣉⣉⣉⣉⣉⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠠⠤⠤⠅⢠⠀⠀⠀⠀⠠⡄⠄⠨⠀⠀⠄⠀⠀⠀⠀⠤⠀⠤⠀⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠒⠒⠒⠶⠒⠒⠒⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠐⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⣈⢈⠁⣋⣉⣉⣛⣀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠀⢁⡀⢀⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠠⡄⠡⠨⠥⠍⣭⢭⣍⡩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⢤⢠⠠⠬⠄⠀⠀⠡⠤⣭⢥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠠⠰⠆⠒⠀⠀⠲⠒⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠲⠲⠖⠂⠰⠂⠀⠒⠲⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⡃⣈⢈⠀⠛⣉⢀⡀⡀⢈⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⢀⠀⠀⠀⢀⢘⣉⡀⠀⡘⠂⡀⠛⣉⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡈⢄⡁⠀⠈⣀⣉⣉⣉⣁⡅⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠈⠀⠈⢠⣅⠀⠉⢉⣤⣥⣭⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠦⠶⠴⠆⠤⠴⠤⠦⠄⠶⠴⠤⠤⠴⠀⠀⠤⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠤⠶⠤⠤⠤⠶⠤⠤⠶⠶⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⢚⡃⡛⢛⢚⡃⣓⢛⠚⡃⠀⠀⠈⠀⠂⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⣀⣒⠚⢃⠓⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⡉⡅⣩⣉⣍⣉⡩⠉⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠀⣀⠀⡀⢀⢠⡈⠁⢀⣭⠉⡉⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠰⠄⠤⠤⠤⠤⠆⠀⠠⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠐⠐⠀⠂⠚⠐⠂⠀⢐⠀⠀⠀⠀⠀⠂⠘⠐⠂⠒⠒⠒⠒⠒⠒⠒⠂⠂⠀⠂
⠀⠀⠀⠀⠀⠀⢄⠉⠉⡉⢉⣉⡅⢉⠉⠉⡁⢀⣈⣁⣀⣨⠈⠄⣤⠀⠀⠀⠈⠈⠉⣍⣉⢩⣉⣍⢉⣉⣉⣡⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠤⠤⠠⠄⠀⠀⠀⠄⠀⠀⠀⠠⠤⠀⠤⠤⠤⠤⠤⠤⠤⠤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠐⠀⠒⠐⠀⠂⠐⠀⠀⠂⠂⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡈⢉⡀⢁⠀⢀⡀⡁⣈⢀⣀⡉⢈⣀⡀⢀⡈⠁⠉⣀⠀⡀⡀⢀⠀⠀⠀⠀⠀⠈⢉⣉⣉⣉⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄⠤⠠⠠⠤⠤⠤⠤⠄⠤⠠⠤⠤⠤⠠⠄⠤⠤⠀⠀⠄⠠⠠⠄⠀⠀⠀⠠⠀⠀⠤⠤⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠂⠀⠐⠒⠒⢚⠒⠒⠒⠐⠒⠒⠒⠂⠚⠒⠐⠂⠂⠒⠒⠀⠒⠒⠂⠀⠀⠀⠒⠒⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠈⡉⢉⢉⡉⣉⡉⢈⡉⡁⣉⢉⡀⣉⢉⣉⡁⢈⢀⢈⣉⣉⣉⡁⠀⣈⡉⣉⣉⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠄⠀⠠⠠⠤⠤⠀⠀⠠⠤⠤⠤⠄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠐⠐⠂⠒⠒⠒⠒⠒⠀⠀⠀⠀⠐⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠈⠁⠀⠀⠈⠁⠉⠀⠀⠀⠉


⣿⣾⣿⣶⣾⣷⣾⣿⣶⣿⣶⣾⣷⣾⣶⣷⣾⣷⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣯⣁⣌⣹⣁⣬⣉⣹⣍⣨⣿⣋⣧⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣉⣉⡧⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠇⠀⠀⠀⠀⠀⠀⠀⢀
⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠁
⠛⠛⠛⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⢀⢀⡀⡀⡀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⣀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⢿⣿⡟⠛⠛⠛
⠀⠀⠀⠀⢠⣤⣽⡿⢋⢈⣽⣿⣿⣿⢻⡟⣿⣟⠟⣿⢛⣿⣿⡿⢿⣟⣿⢻⣿⣿⣿⣤⣤⣼⡇⠉⠙⠁
⠀⠀⠀⠀⠀⠹⠿⠿⠿⣿⣿⣿⣿⣿⢻⣻⣿⢻⣿⡟⣿⣿⣿⡟⣿⣿⡟⡟⣿⣿⣿⣿⣿⣿⠧
⠀⠀⠀⠀⠀⠤⣤⣤⠛⣿⣿⣿⣿⣿⣬⣿⣿⣼⣿⣿⣼⣿⣾⣷⣧⣿⣿⣦⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣸⣶⣶⡿⣿⣿⣿⣿⠟⣻⡟⡛⠿⢛⣿⢛⣻⢻⡿⢻⡟⣿⣿⣿⣿⣿⣿⣿⣏⠀⢂
⠀⠀⠀⠀⠀⠈⣹⣿⡟⠰⠿⠿⣿⣿⣳⣊⣇⣵⣇⣐⣷⣙⣻⣸⣡⣌⣇⣛⣿⣿⣿⣿⠛⠉⢁⣤⣴⣷⣤
⠀⠀⠀⠀⠀⠻⣿⣏⠉⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠗⢠⣤⠙⣻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⡰⠿⠿⠿⠁
⣿⣯⡄⠀⠀⠉⠙⣿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣅⠀⠤⠄
⠿⠆⠀⠀⠀⠀⠤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠈⠹⠿⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠐⠲⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣠⣤⣄
⠀⠀⠀⠀⠀⢰⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠺⠂⠀⠀⡀⠀⠀⢀⠀⠀⠀⢰⠇⢹⠈⢣⠀⠀⠀⣴⠈⠀⠀⠀⠀⠀⠀⣰⢫⣞⡳⠄⠀⠀⠀⠀⠀⠀⡀
⠀⠰⠲⠷⠀⢣⣴⢸⠀⠀⣬⣯⣉⡤⠄⠀⠀⠸⣧⠸⠃⠀⡷⠀⠈⡈⣥⡠⢀⠀⠀⢠⢎⡽⣷⡯⠋⠀⠀⠀⠀⠀⢰⡎⢹⡆
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠞⠁⠀⠀⠀⠀⢀⠤⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠀⠀⠈⠑⠉
⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠀⠀⠀⠀⢀⠀⠐⠢⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠘⡁⠀⠀⠀⠀⠀⠀⢀⠀⡠⣤⠀⠀⠀⢀⡐⠶⠙⢀⠆⠀⠈⠙⠻⠿⠋⠁⠀⠀⠁⣠⠈⠀⢤⡀⠀⠀⠸⠿⣿⡿⠓
⠀⠀⠀⠀⢰⠀⠀⠀⠀⡄⠣⠰⠏⠀⠀⠀⠀⠈⠉⠀⠔⠁⠀⠀⠀⠂⠀⠀⠀⢠⡀⢀⡾⠃⠰⠂⠀⠁⠀⠀⠀⠐⠊⠁
⠀⠀⠀⠢⠈⠀⠀⠀⠀⠁⠀⠐⠛⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠐⠚⠛⠛⠃
⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⣄⣄⠀⠀⠀⠀⠒⡶⢀⡀⠀⠀⠀⠀⢀⣀⣈⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠖⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠁⠀⠈⠀⡀⠀⠶⡄⠈⠛⠰⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠤⣄⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⣀⠿⠆
⠀⠀⠀⠀⢺⡷⣶⠀⠀⠓⠀⢀⡀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣦⣴⣶⠆⠀⠀⠀⠁⠠⣦⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠁
⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⢶⠄⠀⠀⠀⠀⡀⢢⠀⣣⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠈⠁⠀⣎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢺⠀⢀⣐⢀⣡⠔⠋⠁⠀⡂⢀⠀⠁⠀⠀⠀⠀⢏⠉⠉⢉⡤⠝
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⠀⠇⠀⠀⠀⠈⠁⠀⠈⠙⠁⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⢠⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢰⠆⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠰⡿⠃⠀⢀⠉⢁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⡇⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⠔⠀⠀⠀⠀⠀⢆⠀⠠⠄⠀⠀⠀⠀⠀⣀⢀⠐⣦
⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠙⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⠧⠟
⠀⠀⠀⠰⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⡈⠀⠀⠀⠀⠀⡀⠀⢰⣾⢛⡛⢿⡄⠀⠀⠀⣠⢄⠀⠀⠀⠀⠖⠆⠀⠰⠚⠆⠀⠀⡰⠀⣘⡄⢀⣀⠀⢀⣴⠶⢦⡆⠘⠂
⠀⠙⠿⠶⠶⠾⠟⠀⠀⠈⠙⠚⠛⠛⠁⠀⠐⣄⣀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠁⢎⡿⠉⣿⣈⠗⠈⠋⠓⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⣶
⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⢴⠆⠀⠀⠀⠘⢻⣟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠻⠄⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠰⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⣀⣴⣃⠀⠀⠀⠀⠀⢠⣀⠀⢀⣹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠤⠈⠀⠈⠄⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⢀⣘⠫⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀
⠀⠀⠠⠆⣀⠴⢇⠀⠀⠔⠠⠄⠉⠅⠀⠀⠠⣆⣿⣧⣌⠁⠀⠀⠀⠀⡄⠐⢳⠀⠀⠀⢀⡀⠈⠉⠁⠀⠀⠀⢴⠔⠶⠰⠖
⠀⠀⠐⠂⠙⠠⠘⠀⠀⠀⣀⣀⡀⠀⠀⠀⠦⠍⠹⠄⠺⠃⠀⠀⢀⣂⠃⣸⠀⠀⠀⠀⠛⢡⣤⠐⠦⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠲⠶⠖
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⠛⡀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠀⠀⠤⠀⢠⡄⠀⠀⠀⠠⣤⣤⠀⢀⠀⠀⠀⠿⠆⠀⢀⡤⢤
⠀⠀⢠⣴⡶⠆⠀⠀⠀⠂⠀⠀⠙⠀⠀⠀⡴⠟⠋⠁⠀⠀⠀⠀⠁⠠⢼⣦⠀⠀⠀⣀⡀⠀⢠⠠⡌⠀⠀⠀⠁⠐⠀⠐⠃⠚⠁
⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠚⠁⠀⠀⠠⠿⠟⠙⠛⠉⠀⠀⠀⠀⠐⢁⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⢿⣿⡿⢿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣤⣤⣿⣦⣾⣤⣼⣦⣴⣿⣵⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠣⠀⠀⠀⠀⡠⠒⠉⠁⠀⠈⠀⠠⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠃⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠂⠁⠀⠁⠀⠁⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠙⢦⣀⠀⣀⣀⡴⠂⠀⠀⠀⠀⢁
⠐⡀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠈⠢⢀⠀⠀⠉⠢⠤⢀⣀⠀⠀⠔⡣⠒⠒⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸
⠄⢀⡠⠊⠁⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸
⠰⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢀⠀⠐⠠⠄⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⢄⡀⠀⡠⠂
⠀⠈⠀⠀⢀⡠⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠔⠁⠀⠀⠈⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠠⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢀⣠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠬⠥⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠦⢠⡴⠶⣦⡀⣠⡶⠶⣤⠀⣶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠂⢿⡀⠀⢸⡇⣿⠀⠀⣸⠇⣿⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠈⠛⠛⠋⠀⠈⠛⠛⠋⠀⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⣾⡄⢠⠞⠓⠀⣦⠆⢠⠞⣓⡂⣾⣳⢠⠞⠓⡆⢶⢰⠆⡷⣄⡆⣾⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠘⠉⠙⠈⠓⠚⠀⠋⠓⠈⠓⠚⠁⠉⠑⠈⠓⠚⠁⠙⠚⠀⠃⠘⠃⠛⠚⠁

⠀⢀⣀⣀⡀
⠑⡈⠶⠆⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠖
⠄⢰⠸⠀⢸⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡠⠂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠚⠁⠀⠀⢄
⠀⠀⡠⠀⠐⢦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠑⠐⠢⠄⣀⠉⠂⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⢀⠀⠀⠀⣀
⠒⠈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡠⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠢⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀⣀⠠⢔⡡⠒⠀⠀⠁⠒⠢⢄⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠇⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠂⠀⠀⣠⠖⠛⠛⠛⠶⣄⠀⠀⡴⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢰⡆⠐⠀⠀⠀⡅⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⢧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡄⠘⡀⠈⠂⠄⣀⠀⠀⢀⡠⠔⠁⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠁⠀⠀⠘⣦⣀⠀⠀⢀⠀⠄⠠⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⢠⣤⠒⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⢠⡟⣴⣧⡀⠀⠀⠀⠀⢀⠒⠄⡀⠀⠀⢰⡵⡄⠀⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠁⠘⣴⡟⠹⠿⠀⠀⢀⣤⣶⣶⣄⠀⠀⠐⠀⠑⢰⣄⠀⠰⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠁⡀⠀⠈⠀⢀⣾⣶⣤⣯⠙⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠜⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⠖⢄⡀⠜⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⢟⠏⣁⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣲⡶⠙⠛⠛⠶⢦⣮⣅⣀⠀⠀⡀⠀⠀⠀⠠⠀⡰⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠰⠶⠻⠀⠀⠀⠠⠃⢀⡴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⣀⣀⣀⠠⠀⠀⠀⠒⠀⢀⠔⠁⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢀⣀⡤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⢐⡈⠢⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠀⠐⠠⠈⢀⢀⣀⡔⠋⣁⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠁⢀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠂

⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡔⠉⠉⠙⢦⠒⠉⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠛⠉⠑⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⣤⡀⠀⡠⠀⠈⠢⣄⣀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⣀⣀⣠⠊⠀⠀⠁⠀⠆⠰⠀⡱⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⠄⠀⠈⠉⠑⠒⠒⠒⠒⠈⠉⠀⠀⠀⠙⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠃⢢⣀⢀⡰⡀⠀⣠⡀⠀⢀⣄⢀⡄⠀⠀⠀⠀⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⢠⠃⠀⠀⠀⠈⠉⠀⠈⠉⠁⠀⠀⠑⢄⠠⠶⣄⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢸⠀⠀⢠⠶⡀⠀⠀⠀⡴⡄⠀⠀⠀⠀⢠⣉⠜⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣅⢀⣸⡀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⣠⡴⡂⠙⠠⢚⠤⡘⠊⠉⠙⠍⠵⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢠⠒⠊⠁
⠀⠀⠀⠀⢸⣏⠒⠁⢮⣑⠌⣉⠎⠹⠰⣉⠶⠘⢋⣼⡀⠀⠀⢀⣀⢤⡔⠯⠐⠚⠁
⠀⠀⠀⠀⠘⠯⣓⠖⣨⣄⣀⠑⠃⣀⣀⣤⠴⢌⡪⠛⡎⢙⡭⡏⠙⡏⠀⠉⠢⡄
⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠋⠥⠭⠭⡖⠒⡎⣇⡰⠀⠹⣁⠀⣈⠉⠀⠀⣢⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⡇⠀⠆⠀⠀⠀⠂⠀⠀⡗⢒⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠃⠀⠘⠀⣀⣀⢧⣈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⣀⣠⣤⡄⣀⣀⣀⣔⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠄⠒⠈⠩⠁⡯⠐⠀⠀⣀⠀⠀⠓⠚⠁⠈⠉⡟⡝⢒⣦⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⢁⠀⡀⠀⠀⠀⠈⠀⠀⠀⠐⠆⠀⠰⡠⡄⢄⡇⠀⠑⠁⠀⠒⠃⠈⣑⠪⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠁⠀⠀⠦⠋⠘⠁⠀⠀⠀⠀⠀⠲⠉⠀⠀⠀⠓⠁⠔⢢⠀⠀⠀⣀⠆⠀⠄⠠⠃⢰⠳⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠋⡠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠑⣳⠀⠀⠀⠐⠃⠑⣄
⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠉⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠉⠤⠀⠀⡔⡄⠘⣼⠆
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠠⡀⠀⠠⣤⠀⠀⠀⠀⢆⡄⠀⠀⠀⠐⠥⠆⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⢠⠉⠀⠀⠉⢋⡱⠀⢰
⠀⠀⠀⠠⡞⠁⢑⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡠⣷⣾⣷⣿⠉⡆⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣹⠀⡠⠀⢰⣶⠢⡀
⠀⠀⠀⢣⣿⣿⣿⠏⠐⣿⣾⠨⣤⡾⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⢀⢀⠀⣀⣴⣤⡸⢿⣠⡿
⠀⠀⠀⠀⠈⣷⣶⣲⣄⣀⣥⣀⢀⡷⠶⢿⣿⡟⠚⣰⠶⣶⡂⢲⣤⣖⠐⡦⠐⣿⠈⣡⣴⡧⢤⣎⢑⠶⠶⢇⢰⣿⣭⠘⢛⣅⠀⠘⢄
⠀⠀⠀⠀⠀⠻⣿⣿⣏⠁⠀⠈⠁⠀⠒⣶⣿⣿⡟⠁⠀⠙⣷⠚⠖⠛⣿⣿⣶⠿⣤⣟⡭⠃⠈⢻⣾⣤⣤⣿⣶⡈⢁⣠⣿⣿⣗⣀⠌
⠀⠀⠀⠀⠈⢱⣦⠈⠉⠉⠛⠛⠛⢛⣉⣩⣭⣿⣤⣀⣀⣠⣿⣷⣶⣾⣿⣿⣿⣭⣉⡉⠛⠤⠄⠚⠛⠉⠉⣹⣿⣿⣿⣿⣿⣿⣦⠃
⠀⠀⠀⠀⠀⣾⣿⡄⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⣿⣿⡃⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡀
⠀⠀⠀⠀⣾⠻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣛⣉⣭⣭⣤⣿⠛⠛⣿⡷⡰⡁
⠀⠀⠀⠀⠹⡏⢘⣿⠙⣦⠈⣭⠭⠍⣡⡤⣤⣶⣾⣿⠗⠠⣭⣌⣉⣉⣉⣉⣉⣽⡽⣾⣿⡛⠉⢹⣿⡿⠠⣿⣿⡿⠃⠀⣿⣛⡙
⠀⠀⠀⠀⠀⢹⣏⣉⡘⠻⣿⠋⢠⣤⡄⠀⠙⠟⠉⢸⣧⣨⣥⠀⠻⣿⠿⣇⠉⣯⠈⠛⢫⡅⢠⡶⠎⡷⠀⠉⠋⠴⣶⣦⣽⣿⡿⠊
⠀⠀⠀⠀⠀⠘⡉⠉⠓⠒⠛⠛⠛⠛⠿⣿⣶⡀⢰⣦⣴⣿⡃⠠⣤⣆⣤⣤⣄⣙⠥⣦⣤⣤⣼⣿⣬⣿⠿⢿⣷⡴⠞⠋⠙⣿⠁
⠀⠀⠀⠀⠀⠀⠱⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠖⠋⠙⠿⠷⠖⠛⠛⠉⠛⠿⠿⠾⠛⠉⠁⠁⠀⠀⠀⠀⠀⠀⢄⣀⣲⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠠⠨⠜⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠐⠒⠒⠒⠂⠂⠀⠀⠄⠤⠤⠀⠄⠀⠒⠂⠒⠒⠂⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢀⠀⠄⢢⡶⠶⠶⠶⠄⠄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡠⠄⠉⠀⠁⠄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠸⠏⠛⣷⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠉⢿⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠄⢈⣻⣷⣄
⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣼⣁⣴⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠈⢓⠶⣦⣄⣀⣀⣀⣀⣀⣀⣠⣀⡀⠀⣀⢀⡀⣉⣀⣀⣀⣄⣤⣤⣴⣾⣿⡿⣿⡟⢉⣩⡆
⠀⠀⠀⠀⠀⠀⣈⣿⣷⣤⣉⣉⣭⣝⣻⣿⡝⠻⠛⢻⣿⢿⣿⣭⣭⣿⠟⣓⣏⣁⣠⣟⠡⠚⠙⠛⢉
⠀⠀⠀⠀⠀⠉⠤⠌⠋⠃⡶⢿⣿⣯⣽⣿⣿⣶⡶⡟⠻⠯⠛⢉⠙⠿⠋⠈⠃⠘⠋⠛⠁⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢹⣏⣷⣦⣤⡴⠗⠉⠀⠭⠄⠛⠃⣀⣀⣠⣤⣄⣠⣤⣤⣴⣶⣶⡶⢶⣿⡏⣿⣩⡟⡓
⠀⠀⠀⠀⠀⠀⣾⣦⡝⣻⣭⡻⣷⣤⡀⠀⣠⣴⣿⣯⣵⣿⣯⣾⢏⣼⠋⣱⡿⣿⢳⣟⣙⣿⣣⣿⢵⡃⢀⠘
⠀⠀⠀⠀⠀⠉⠀⣁⠙⠎⠛⠩⠏⠿⠷⣾⢿⠯⠉⣻⢿⡾⢿⡽⢿⡛⠛⠻⡵⡯⠼⠻⢿⠛⣿⣈⣢⣴⣇
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠐⠂⠐⠢⣤⣶⠦⢶⢾⢿⣷⠤⠾⣬⣥⣴⡤⢶⡶⠶⠿⠒⠒⠷⢶⡟⠉⠉⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⣈⣠⣦⣸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠶⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠶⠶⠴⠴⠶⠟⠓⠒⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣠⠠⠠⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠆⠰⠆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣀⠀⢀⠂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠈⠐⠉⠀⠈⠋⡀
⠀⠀⠐⣧⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠀⠀⠀⠁⠁⠒⠦⠴⢤⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠐⢿⣾⣿⣿⣿⣿⣿⣿⣾⣿⡶⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢰⣤⢬⣉⡅⡉⠽⠉⠿⠯⠶⠷⠳⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠘⠻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠤⠽⠃



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡄⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠄⠀⠀⢤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢄⠀⠁⡀⢠
⠀⠀⠀⠐⢪⣷⣻⠯⡑⠀⠳⠟⣓⡃⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠈⠹⠧⠃⡁⠤⠚⡤
⠀⠀⠀⠀⢸⡋⠚⠧⢵⠒⢲⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡜⣒⠙⠉⣀⢐⠸⡆⣀⡚⡀
⠀⠀⠀⠀⠀⣷⠋⠠⢈⣵⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⡟⠻⡶⢄⠻⣯⠑⣾⡟⢘⡟⣾
⠀⠀⠀⠀⠀⠘⣆⠀⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⢛⢯⠟⣾⣠⣿⣯⣽⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠁⠚⠾⠉⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠶⠒⠒⠂⠀⠒⠒⠲⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠁⠀⠀⠀⠀⢐⠀⠀⠀⠐⠂⠀⠀⠀⠈⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠁⠀⠢⠀⠀⠀⡠⠄⣄⠀⠀⠀⢀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡆⠴⠂⠀⠀⠀⠀⠀⠀⠀⠣⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠁⠀⠀⠋⠀⠈⠓⡂⠀⠀⠁⠀⡀⠀⠁⠀⠀⠈⠂⠀⢀⡄⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠂⠀⠘⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣾⣷⣶⣤⣤⣖⡒⠒⠒⠛⠛⠉⠙⠋⠛⠓⠒⠒⠶⠤⣤⣤⣀⣀⣀⣀⣀⣠⠞⠳⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠻⡟⠁⠀⠀⠀⠈⠍⠙⠒⠢⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣷⡀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⡇⠀⣤⣄⠀⢀⣤⣤⡄⠀⠁⠂⠬⡉⠲⢤⠴⠒⠂⠉⠉⠡⠄⠀⠀⠐⠒⣩⣥⢳⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠘⠢⣝⣋⠀⠸⠿⠿⠃⠀⠀⠠⣤⣤⠁⠒⠀⠁⣾⡇⠀⠀⢿⣿⠀⠀⠠⠿⣃⢾⠛⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠖⡟⢇⠀⠀⠉⡉⠉⠉⠐⠒⠒⡖⠒⠒⠒⠒⠒⠒⠒⠒⢒⠒⠒⠒⠚⠋⠉⢩⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠘⢦⡀⣸⠙⡆⠀⣤⢤⡀⠀⠀⠀⠘⡆⢀⡀⠀⠀⠘⣆⣴⠋⠙⠳⣤⡞⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠁⠀⢳⣀⣸⠆⠘⢦⣀⣀⣀⠟⠉⠹⣄⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣕⣤⣀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⢀⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠭⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⢀⡀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠤⠄⡀⠀⠀⠀⢀⡀⠀⠀⠀⡀⣠⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢠⠄
⠀⠘⠀⠀⠀⠀⠀⠈⢄⠀⠰⠁⢀⠀⠉⠆⠀⠀⠌⠠⠊⠠⠀⠟⠊⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠈⠀⠡⣈⢀⡄⠐⠰⣲
⠀⠀⠐⠀⠐⠀⠀⢉⠣⠀⠀⠣⡀⠈⠀⠈⠆⠈⢠⠴⡀⠊⠀⠀⠀⠂⠀⠠⠀⠄⠀⠁⠀⠀⡠⠁⠀⠒⠄⠀⠉⠉⠀⢐
⠀⢀⠀⣋⡀⠀⠀⠀⠈⣀⢀⢀⠈⠒⠈⠄⢀⡴⠀⡯⢚⠁⠀⠀⢠⠐⠂⡐⠠⢀⢀⠀⢀⠜⠀⢣⢄⣀⡀⠀⠀⠀⠤
⠀⠘⠀⠀⡆⠀⡠⠊⡁⠀⠃⠂⢌⡑⢄⠀⠸⠋⠀⢸⡵⠀⠀⢸⠃⠀⢀⡅⡀⠘⠄⠐⠁⢀⠀⠠⣀⡀⠀⡀⠠
⠀⢠⠖⢦⠀⢄⣠⠒⡂⢜⣊⠼⠓⢊⠁⢠⠒⠒⠤⡀⠃⠀⠀⠀⠁⠨⠉⠁⠀⠀⠀⠀⠠⠂⢤⠀⠠⠀⠀⠁⠀⠈
⠀⠀⡆⣈⢂⠀⠀⠀⠀⠒⠒⠒⠈⠁⠀⡌⠀⠀⢰⠀⠰⢠⠀⠀⠂⠆⠀⢀⣴⣶⢻⣟⣳⡆⠀⡀⠀⢀⠀⢀⡰⠉⡘
⠀⠀⡄⠂⢠⠀⠀⠀⢖⠒⠀⠠⠀⢲⠆⠑⠀⠲⠈⠀⠀⠁⠃⠀⠀⠀⠀⢀⢀⠽⠉⠉⠉⠉⠀⠀⡀⠐⠀⠀⠉⠉
⠀⠀⠈⠉⠁⠔⢄⠀⡄⠉⠀⠒⠀⠁⢀⠀⣴⡢⡄⠀⠠⠀⠀⠀⢀⠖⡆⠀⠀⠀⠀⠍⠀⠁⠀⡀⠃⠀⠀⡔⠉⢆⠁⢠
⠀⠦⠀⠀⠈⠀⠀⠀⠀⢀⠀⢈⠈⠡⠏⠓⢉⠠⠣⢶⠠⢅⢤⡤⠀⠀⠀⡀⠈⣁⠀⠈⠈⠀⠂⠀⠀⠀⠨⠀⡠⠊⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠐⠀⠀⠂⠈⢀⣐⣃⡠⠤⠗⢉⠀⠀⠀⠀⠰⠀⠀⡀⠼⢑⠀⠉⡂⠲⢀⠑⢀⡱
⠀⠀⠐⠀⠘⢀⠀⠀⠀⠀⠀⠤⠀⠀⠘⠀⠈⠉⣤⠀⠀⢘⠭⠁⣀⠀⠐⣁⠀⠀⠀⠁⠀⠀⠀⠀⠀⢈⠀⠀⠀⠎
⠀⠐⠂⠀⠀⡠⠄⠀⠀⠊⢟⠀⠀⢠⠶⠛⠉⠐⢹⣶⠄⠈⡠⠀⠀⠀⠀⠈⠀⢠⠄⠀⠀⠀⠀⠀⠀⣡⠀⠀⠘⠀⠂⠄
⠀⠰⠠⠍⢀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⢈⠠⠒⠀⠀⠀⠀⠉⠉⠉⠈⠐⠡⠄⢀⣀⠀⠂
⠀⢠⠀⠀⡀⠄⠈⡆⡕⠀⠈⠀⠐⠀⠀⠠⠒⠃⠀⠀⠀⢰⠀⠀⠀⠌⠀⠀⠄⠠⠏⠀⡀⠀⢀⠠⠀⠀⠙⠇
⠀⠀⠀⡀⢀⡄⠀⢡⠁⢀⡀⠌⠀⡄⠂⠂⠀⠀⠀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡰⠒⠀⠀⠒⢅⡀⢀⠰
⠀⠠⠐⠊⠸⠈⠆⠈⢀⠡⠀⠀⠦⠠⢖⠀⠀⠀⠈⠁⠀⠈⠀⠐⠀⡄⠀⢠⠂⠉⠀⠀⠀⠈⠀⢀⠜⡀⠀⠀⢻⠧⠂⠁
⠀⠀⠠⠨⠄⠀⠂⠀⠀⠒⠈⠀⠀⠀⠀⠄⠀⠀⠀⠠⠒⠃⠀⠀⣀⠀⢌⢀⠢⠤⠬⠔⡀⠤⠔⢊⠈⠃⡀⠈
⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠈⠠⠂⠀⣀⡀⡔⠒⠒⡆⠀⢢⠀⠐⠀⠀⠁⠀⠈⠀⠠⡈⡀⢄⠀⠠⠀⠈⠀⠀⠀⠀⠐⠁
⠀⢀⡀⠐⠀⠀⠀⠀⠂⠄⠁⠀⠀⠘⠄⠂⢘⣀⣸⠀⠀⡀⠀⠐⠄⢤⠆⠀⠀⠈⠚⠁⠡⠊⠈⠠⠁⠀⠤⠀⠐⠀⠒⢤
⠀⠀⣠⡶⢀⡶⠀⢀⠀⠃⡀⠂⠈⠠⠀⠀⡀⠄⠠⣀⠀⠀⠘⠀⢀⠀⠀⠀⠃⠀⠠⣀⣠⣤⠄⠀⠀⠀⢄⠀⠀⠀⠀⠔
⠀⢸⣆⠅⠊⠀⡀⠁⠀⡂⠀⠀⡀⢊⠀⠌⡠⠊⢉⡉⠠⠀⠈⠠⠊⠀⠀⠀⠁⠀⢀⠜⠈⠡⡀⠀⠀⠀⡈⠀⠈⠁⠁⢠
⠀⠀⠁⠂⠀⠀⠃⠀⠀⠈⠀⠉⠀⠈⠀⠋⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠘⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠈⠀⠀⠦⠀⠀⢘⣺⣄⡠⢀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⠄⣠⡁⠀⠄⠐
⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⠀⠋⠀⠀⠐⠀⠀⠀⠀⠀⢀⠘⠛⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⢀⠀⠀⡆⠀⠠⠘⢥⠽⠀⠀⠀⡀
⠀⡀⠀⠐⠀⢠⠀⠒⠈⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠠⠄⠀⠀⠀⠀⢀⡠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠄⠀⠀⠀⠰⣷⢄⠀⠀⠂⠀⠁⠀⢠⡇
⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣊⢄⠀⠀⠀⠐⢜⢃⡀⢀⣀⣐⣤⡤⢊
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠑⠈⠉⣓⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠈⠀⠀⠀⠈⠆⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⢀
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰⠄⠀⠀⢀⡀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⡀⢊⠀⠀⠀⠀⡊
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠈⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢈⡠⠀⠀⠀⠉⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠁⠀⠀⠀⠀⠀⠐⠊⠀⠀⠐⡀⠀⠀⡰⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠠⡀⠀⠀⠀⠀⠀⠀⠐⠃⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⡉⢉⡒⡄⠀⠀⠀⠐⠠⠀⠀⠀⠀⣄⡠⠉
⠀⠀⠀⠀⠀⠤⢤⢤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠠⡄⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠺⠀⠀⠈⢶⠀⠀⠈⢱⠂⠐⠒⠒⠋⠁⠄⠀⡇
⠀⠀⠀⠀⠀⢠⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠢⣄⡀⠐⢆⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠈⠃⠀⠘⠀⠀⡠⡧⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠈⠉⠘⣆⡀⠀⢀⠀⠲⡄⠀⠐⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⠄⠼⠀⠀⠀⠀⠀⠀⠀⢌⠢⣄⠐⠀⢀⡴⠤⢛⢽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⠛⠐⠒⠂⠈⡼⠀⠀⠀⠀⡀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⣀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⣠⠀⠑⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣠⠞⠁
⠀⠃⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠛⠫⠄⠀⠀⠁⠀⠐⠤⢀⣀⣀⡠⠴⠋⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠘⠀⠀⠘⠋⠀⠠⠀⠐⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⣰⠀⠀⠀⠀⣠⠄
⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠛⠉⠉⠉⠰⠊⠙⢟⠟⠛⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⠛⢋⠈⣀⠀⡰⠀⠀⠀⠐⠀⢐⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠃⠀⠻⠀⠀⠈⠀⡄⠀⠀⠀⠀⢀⠀⢉⣙⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠶⠀⢠⡀⢀⡄⠘⢃⡉⠐⠙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣤⣤⣼⣥⣤⣭⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠭⢽⣿⣿⡿⠟⢛⣻⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⢿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠒⠛⠉⠉⣉⣉⠭⠭⠶⠿⠃⠀⣚⣩⡽⢟⣋⠉⡐⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣄⣴⣶⣶⣿⠿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣌⣶⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠿⣇⣀⣠⣤⣦⣼⣧⣽⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠦⢄⣉⣛⣾⣿⣿⢿⠉⠉⣛⣿⠿⣿⣯⠭⠽⠿⣿⡂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⡿⣾⠄⠴⠤⠴⠷⠦⠉⠚⠹⠶⠖⠢⢼⣲⣶⣶⣾⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣘⣁⣴⣿⣿⣿⣿⣿⣫⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⠶⠶⠶⠶⠾⠿⠶⠶⠶⠶⠶⠦⠤⢤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠿⠗⠛⣩⠍⠀⠀⠀⠚⠉⠀⠀⡄⠀⠠⠤⠀⠀⢦⠄⠀⠀⠠⡀⠈⠉⠙⠛⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⣋⡁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⣤⠀⠀⠐⠦⠀⠀⠾⠙⠳⢦⣄
⠀⠀⠀⠀⠀⣴⡶⠛⠁⠀⠈⠊⠀⠀⣤⠄⠀⠀⠔⠂⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⡀⠀⠀⢤⡀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠰⠦⠙⢳⡀
⠀⠀⠀⠀⣴⢋⠤⠀⠀⠀⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⠔⠀⠀⠀⠀⠶⠙⣦⡀
⠀⠀⢀⣾⢣⠈⠁⠀⠀⠈⠀⠀⠘⠁⠀⠀⢀⠔⢄⠀⠀⡀⠀⡀⠀⠠⠢⠀⣀⠠⠂⠈⠂⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⢀⡀⠀⠈⢷
⠀⠀⢸⡧⡃⣄⠄⠀⠀⠀⠀⠀⢀⠠⡀⠠⠋⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠠⢄⡀⠀⢀⠀⠀⠀⠁⠀⠀⠘⡇
⠀⠀⢸⢇⣾⣆⢀⡤⢤⡄⠀⠀⢀⣴⢠⢀⣦⣇⣧⣦⣼⣼⣼⣿⣼⣾⣶⣾⣶⣶⣴⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⣿⣿⢿⠿⢣⣰⣿⣿⣢⣼⣾⣾⣿⣿⣿⠿⠿⠛⠛⠛⢋⡉⠉⣉⣉⣉⣉⠉⠉⠉⠉⣩⣿⣽⣛⠛⠛⢳⣶⠶⠶⢦⣤⣤⣤⣤⣤⣀⣀⣤⠏
⠀⠀⠘⣿⣿⣷⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⢀⣤⠶⠛⠛⠓⠲⠋⠙⠛⠉⠉⠈⠉⠙⠛⠲⠞⠁⠀⠀⠉⠉⠙⠉⠉⡓⠛⠶⣄⡀⣀⣈⣉⡉⢉⣉⠳⣄
⠀⠀⠀⢈⡽⠿⣟⣛⣭⣥⣤⣤⣤⣄⣀⡴⠋⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠻⠏⠉⠙⠲⢿⢻⡞⠛
⠀⠲⠛⠋⣶⣿⠿⠁⠀⣔⠀⠀⢀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⢀⡤⠀⠀⣿
⠀⠀⠀⠀⣿⣀⣬⣀⠀⠀⠀⠀⠙⠀⠀⣠⣾⣛⣛⣛⣯⣤⣤⣤⣤⣤⣤⣤⠀⢀⡀⠀⠀⢀⣀⢀⣶⣾⣶⣶⣶⣦⡄⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠈⠻⣿⣿⣷⠀⣴⢦⠾⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠹⣷⣿⣿⡄⢰⣿⣿⣿⣁⣀⡀⠀⠈⣻⣧⠀⣴⣦⡾⠛⠟⠻⠷⣶⣾⠋
⠀⠀⠀⠀⠀⠘⣿⣻⣿⣠⠃⠀⣀⣀⣀⣀⣠⣤⣤⡤⠤⠴⠶⠶⠶⠒⠚⠛⠛⠛⠿⠿⠞⠛⠋⠀⠀⠈⠉⠉⠙⠛⠛⠒⠷⠦⠤⠤⣄⣀⣀⣠⣟
⠀⠀⠀⣠⣴⠿⢿⡿⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄
⠀⠀⣼⣿⣿⣿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢠⠴⠀⠀⠀⠀⠀⢀⣠⣴⠶⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⠿⣦⣠⣶⣤⠀⠀⠀⠀⢠⣼⣧⡀
⠀⢨⡟⢉⠉⠳⣶⠖⠉⠈⠙⠛⢻⣶⣤⡀⠀⠀⠀⠸⣇⡄⠀⠀⠀⠀⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠾⣇⠀⢰⢦⡍⠈⠙⣷
⠀⠈⣷⣦⣤⣼⣷⠆⠀⢠⡀⠀⠀⠈⠙⠻⣷⣄⡀⠀⠉⠀⠀⢀⣠⣼⠏⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠟⠀⢀⡀⢠⡇
⠀⠀⠈⢻⣿⣮⣤⣅⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣿⣿⣶⡄⢀⣾⠋⠀⠀⠀⣈⣳⣄⣀⣀⣤⣤⣤⣤⣄⣀⣀⣀⣉⣀⣀⡀⢀⢀⣀⣰⣦⣀⣀⣀⣀⣴⠟
⠀⠀⠀⣿⣿⣿⡛⠙⢹⡿⣿⣯⠟⠋⠻⣿⠽⠿⣿⣿⣿⣿⣾⡟⠛⣿⡟⠛⠉⢉⠉⠉⢹⡏⠁⣽⠋⠉⢻⠟⢿⣍⣛⣻⠟⠛⣿⠛⠻⠻⣩⡿⣯⣿⠇
⠀⠀⠀⠛⢹⣿⣿⣤⠏⠀⠈⠀⠀⠀⠀⢻⣄⣠⠋⠉⠛⠛⠋⠀⠀⢸⡇⠀⢰⠋⢷⡴⠋⠀⠀⣻⣦⣤⠏⠀⠀⠉⠉⠁⠀⠀⣿⡆⠀⢀⡟⠀⠉⣿
⠀⠀⠀⠀⢸⣿⣽⣥⠤⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠞⠃⠀⠀⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣧⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠳⠶⠶⠤⠤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠶⠶⠖⠒⠛⠋⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⢿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠛⠛⠛⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠦⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠠⣶⡄⠀⠀⣧⠶⠛⠛⠉⠉⠉⠙⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⢀⣀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⣠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⣀⣀⣀⣀⣀⣠⣴⡾⠛⡅⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠘⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⢿⢻⠛⡟⢻⢻⠛⠙⢹⡇⢀⣷⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⡶⡟⣿⢷⣤⡾⣿⠀⡇⢸⠘⡀⡇⢸⣈⣀⣠⣤⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⣴⢿⠉⡏⢻⡇⣧⢸⢸⡈⡇⢸⣀⣷⡾⠟⠛⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⢀⣠⡴⠶⠶⠶⠶⠾⠿⠟⠛⠁⠀⠀⠀⠘⠃⠀⠀⢠⣴⣿⣾⡄⢇⢸⣧⣼⣼⣤⣇⣧⡾⠛⠁
⠀⠀⢠⡶⠋⠁⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢳⢸⣿⣧⣼⣼⣿⠁⠈⠙⠛⠋
⠀⢰⡟⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠙⢿⡜⢿⡏⠀⠈⠉
⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⣠⢾⣷⠟⠋
⠀⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⣼⣷⢸⣿
⠀⢸⣷⢹⠛⡿⢿⡿⡷⢶⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣼⡿
⠀⠀⠻⣿⣄⣧⠘⡇⡇⢸⢼⣧⠀⠀⠀⠻⠇⠀⠀⠀⠀⢀⣾⣿⠋
⠀⠀⠀⠈⠙⠛⠿⠿⠿⠾⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠻⡿⣶⣤⣤⣀⣤⣴⡿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⡇⠀⡏⢹⠉⢻⠈⡇⢣⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣦⣷⣬⣦⣼⣤⡷⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠒⠂⠉⡆⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⠀⠀⣀⡠⠠⢦⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⡎⠁⠀⠈⠄⠀⡅⠀⠀⠈⡀⢀⠎⠓⠠⢄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢂⠰⡀⠀⠀⠘⡀⢃⠀⠀⠀⠃⡈⠀⠀⠀⡜⢠⠃⠈⠑⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⢠⠔⠋⢡⠀⠀⠀⢣⢸⠀⠀⠀⢸⠀⠀⠀⢠⠧⣇⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⢆⠀⠈⡆⠀⠀⠀⣎⠀⠀⠀⡌⠀⠀⠀⡆⠀⢀⠇⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠈⡄⠀⢡⠀⠀⠀⢹⠀⠀⠠⠁⠀⠀⢠⠀⠀⡘⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠰⠀⠀⡄⠀⠀⢸⠀⠀⢸⠀⠀⠀⠨⠀⠠⠁⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠑⢄⡆⠀⡇⠀⠀⠸⠀⠀⡈⠀⠀⠀⡄⠀⣸⠔⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠍⠒⠢⢄⣀⣆⣀⣀⣇⣀⢀⡤⠗⠚⠇⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⢸⠀⠀⠘⡀⠀⠀⠈⠀⠀⢠⠀⠀⠸⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡆⠀⠀⡇⠀⠀⣀⠀⠀⠸⠀⠀⡅⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢂⠠⠒⠉⠉⠁⠀⠈⠈⠉⠒⢤⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠘⡦⢀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⡇⠀⠈⠁⠉⡆⠉⠉⡇⠀⢀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢇⡀⡄⠀⠀⡇⠀⠀⡇⢀⡸⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠁⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣿⣛⠲⣄
⠀⠀⠀⠀⡴⢋⠩⢉⠍⡉⠍⠙⢦⠀⠀⠀⠀⠀⣠⣖⣛⣛⣛⣳⡀⠀⠀⠀⠀⠀⢀⡇⠘⡇⠀⠀⠀⠀⠀⢠⠖⣫⡥⢾⢳⣗⣯⣙⣮⡇
⠀⠀⠀⢸⡧⠬⠤⠤⠤⠥⠤⠤⢼⡇⠀⠀⠀⠀⢧⡤⠤⠤⠤⢤⡟⠀⠀⠀⠀⠀⣼⣉⠉⢻⡀⠀⠀⠀⢠⠏⡾⡥⣌⢸⢸⠿⣚⣭⢶⡀
⠀⠀⠀⢸⡗⠚⠒⣖⣛⣲⠒⠓⢺⠅⠀⠀⠀⠀⠸⡇⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣏⢈⡇⢸⡇⠀⠀⠀⢸⠸⡇⢓⡛⠾⠖⣫⣅⢸⢸⡇
⠀⠀⠀⠀⢿⣙⣯⡉⠉⢉⣽⣋⡿⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢹⠉⠀⢸⠀⠀⠀⠀⠘⣇⠳⣜⠿⢊⣤⣙⣡⢏⡼
⠀⠀⠀⠀⠀⠉⠉⠙⠶⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⣰⡇⠀⠀⠀⠀⠀⠀⣟⠀⠀⢸⡄⠀⠀⠀⠀⠈⠳⢬⣛⣛⣚⣋⡵⠚
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⣠⣖⢳⡏⣿⢓⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠻⣟⢦⡀
⠀⠀⠀⢸⠷⠾⢦⣷⣯⠼⠶⢻⠂⠀⠀⠀⠀⠀⣠⣤⣭⣼⣤⣤⠀⠀⠀⠀⠀⢀⡴⠋⡁⠂⠐⢈⠙⠦⡄⠀⠀⠀⠀⢀⡞⡁⢈⠀⡉⢺⡇
⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢸⠋⣳⠀⠀⠀⠘⢶⠒⢶⠖⠒⣶⠒⡶⠃⠀⠀⠀⠀⣸⡀⠄⠠⢀⡠⠏
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣀⣀⣻⣀⣀⣀⣀⣿⣛⣁⠀⠀⠀⠀⠘⡇⢸⡆⢀⡏⢰⠇⠀⠀⢀⣠⡴⣋⡽⠶⠚⠋
⠀⠀⠀⠀⠸⠤⠤⠤⠤⠤⠼⠁⠀⠀⠀⠀⠻⣄⣀⣀⣀⣀⣀⣀⣠⠽⠁⠀⠀⠀⠀⠹⢤⣧⣼⡧⠟⠀⠀⠀⠈⠳⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⣙⣦⡀
⠀⠀⠀⠀⠀⢀⣀⡤⠞⢧⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠙⢦⠀⠀⠀⢠⣯⣤⣬⣷⣬⣷⡀
⠀⠀⠀⠀⣰⠯⠤⠤⠤⠬⢿⡀⠀⠀⠀⢰⠏⠁⠀⠟⠁⠀⠿⠁⠀⠉⢧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠓⠺⡆⠀⠀⠈⢷⠛⢓⣺⠷⡾⠁
⠀⠀⠀⠀⣷⠶⣤⠴⢤⡴⢶⡏⠀⠀⠀⣞⣶⡒⣲⣒⣒⣖⢒⣖⣒⣲⣺⡆⠀⠀⠀⠀⢀⣴⠋⠉⠳⢤⣠⠇⠀⠀⠀⠸⡖⢋⣥⢶⠇
⠀⠀⠀⠀⢹⡀⢸⠀⢸⠁⣸⠃⠀⠀⠀⢿⠲⠭⣽⠮⠥⣬⠭⢾⡭⠵⣻⠇⠀⠀⣀⣴⡏⠉⠳⡄⠀⠀⡽⠀⠀⠀⠀⠀⢻⣉⡤⡞
⠀⠀⠀⠀⠈⣧⣸⣆⣸⣀⡏⠀⠀⠀⠀⠈⠉⠙⠛⠒⠒⠒⠒⠚⠛⠉⠉⠀⠀⠈⠳⢤⣽⣄⣀⡽⠶⠚⠁⠀⠀⠀⠀⠀⠈⣇⣸⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⢶⣤⣄⠀⠀⠀⠀⢀⣤⡀⠀⢀⣤⡀⠀⠀⠀⠀⢠⡤⠤⣤⠀⣰⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢺⠶⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠛⢧⡼⣷⣦⢷⡄⠀⠀⣠⠏⢠⠙⢶⠏⢠⠙⢦⠀⠀⠀⠈⣿⠉⡏⠘⣷⠶⡿⠀⠀⠀⠀⠀⠀⢀⡴⣳⢛⡞⠁⠙⣦
⠀⠀⠀⠀⢀⡴⠋⠀⠀⣸⠦⢾⣹⠏⠀⠀⠀⡇⠀⡼⠃⢸⡇⡼⠃⢸⡇⠀⠀⠀⡿⠀⣧⡞⠃⠀⠛⡆⠀⠀⢀⣠⢖⣫⣞⡵⠋⠀⠀⢠⡟
⠀⠀⠀⣰⠋⠀⠀⢀⡴⠋⣠⠞⠁⠀⠀⠀⠀⠻⣄⠓⢀⡼⡄⠓⢀⡾⠀⠀⠀⣾⠁⠀⠈⡇⠀⠀⠀⡇⠀⠀⢸⡖⣻⠖⠋⠀⠀⢀⡴⠋
⠀⠀⠀⠘⢦⣀⡴⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠘⠶⠋⠀⠘⠶⠋⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠙⢧⡀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠙⠷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠶⠳⠶⠒⠶⠃⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠾⠋⠉⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣢⡉⠙⠓⣲⡶⠶⢦⠤⡦⣤⡤⡤⢤⢤⡤⡶⠶⠶⠶⠲⠛⠛⣉⠁⠀⢀⣤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠩⠿⠻⠋⠿⢦⣀⠀⢀⣠⣶⠿⠶⣤⡀⠀⣠⠞⠶⢤⣠⡾⠉⠹⡶⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⣀⠼⠛⠻⣥⣀⣀⣀⣠⣽⣻⢿⣀⣀⣀⣀⣀⣀⣤⠟⠻⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⣝⣒⡒⠖⠚⠁⠀⠀⠀⠈⠉⠛⠛⠉⠉⠀⠀⠈⠉⠉⠁⠀⠀⣀⣠⠼⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣉⣒⡶⢿⣭⠭⠭⠭⠭⣭⣉⣉⣙⣛⣻⣛⣛⣛⣛⣛⣉⣉⠭⠭⠥⠴⠖⠒⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠈⠳⠤⠴⠚⠋⠛⠦⣄⠀⠀⠈⠁⢀⣤⣄⢀⡴⠒⠦⣤⠴⢻⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣀⣀⣀⣀⣀⣀⡀⠀⠈⠙⠓⠒⠒⠋⢀⣈⣉⣁⣀⣀⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⠛⠛⣿⡇⠀⠀⠀⣠⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡀⠀⠀⠈⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⣿⡟⠛⠛⠛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⠿⠟⠛⣿⣧⠀⣀⣠⣿⣧⠀⠀⠀⢹⣿⣶⣶⣶⣿⣷⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⣾⣿⠿⠟⠛⢻⣿⡀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠿⠿⠿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣼⣿⡄⠀⠀⢸⣿⡄⠀⠀⠈⣿⣇⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⠛⠉⢿⣧⠀⠀⠀⣿⣧⠀⠀⠀⢹⣿⠀⠀⢸⣿⠀⠀⠀⣸⣿⣀⣀⣀⣼⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠸⣿⡄⠀⢀⣸⣿⣤⡀⠀⣼⣿⣷⣶⡿⣿⣷⠀⢸⣿⡟⠛⠻⠿⢿⣿⡆⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⣿⣿⡿⠿⠛⠛⣿⡇⠀⢿⣿⠀⠀⠀⢸⣿⠀⢸⣿⡇⠀⠀⠀⢸⣿⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⢻⣿⠀⠀⠀⠀⢹⣿⡀⢸⣿⡀⠀⠀⠸⣿⡇⢸⣿⡇⠀⠀⠀⢸⣿⣀⣀⣸⣿⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠘⣿⡇⠀⠀⠀⠈⣿⣇⠘⣿⡇⠀⠀⠀⣿⡇⢸⣿⡇⠀⠀⠀⢸⣿⡿⠛⠛⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣷⣴⣶⣿⣿⠀⠀⠀⠀⢹⣿⠀⣿⡇⠀⠀⠀⣿⣿⢸⣿⡇⠀⠀⣠⣿⠟⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡏⠉⠉⠁⠙⢿⣷⣄⠀⠀⠘⣿⡇⢿⣿⠀⠀⠀⢸⣿⠘⣿⣇⣠⣾⡿⠋⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠙⠻⣿⣶⣤⣿⣿⣸⣿⠀⠀⠀⣸⣿⣶⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⠿⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣾⣿⣶⣶⣾⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⣤⣴⣶⣾⣿⣿⡿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄
⠀⠐⡆⢀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⡀⢠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠑⠒⠰⠀⠄⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠊⠁⠉⠱⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠠⠤⠀⠀⠐⠀⠀⠀⠀⠀⠄⠐⠢⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠄⢀⠀⠆
⠀⢀⠀⠀⠀⠀⠀⠀⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⢂⠘⠢⠊⠠⠀⠀⠁⠲⢆⡶⠜⠛⠁⠀⠀⠀⠀⠀⠀⠒⠀⢨⠀⡀⠂⠀⠀⢀⡀
⠀⠨⣀⠀⣀⠀⠠⠄⠒⠀⠀⠀⠀⣀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠃⠀⢒⡤⠈⠁⠀⡀⡀⠀⠀⠀⠀⠀⢀⡘⠡⣏⠟⠉⣢⠀⠃⠁⠈⠊
⠀⠀⢉⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠁⠀⢀⠈⠁⢂⠘⠀⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠉⠀⠀⡄
⠀⠀⠈⠁⠀⠀⠀⠀⡘⠡⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠶⠊⠃⠄⠀⠁⠀⠀⠀⠀⠐⠀⠁⠀⠀⠄⠀⠀⠀⠀⠅
⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠈⢀⣀⣀⣤⣤⣤⣀⣀⣀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⡠⠚⠁⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢒⠀⠀⡊⢀⠀⠀⠀⣰⣾⣿⣿⣏⣉⣉⣙⣿⣿⣿⣿⣦⠀⠀⠀⠁⠀⢄⠀⠡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠃⠐⠀⠀⠀⠀⠀⠀⠂
⠀⠈⠅⠀⠀⠀⠠⠀⢰⣿⢩⠛⡏⣯⢩⣿⡩⠍⠛⠙⠉⢿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠈⢠⠀⢠⣠⡤⠠⣄⠀⠠⠤
⠀⠀⢂⢰⠀⠀⠀⠀⠈⣿⢰⣀⠷⢹⢸⣿⢰⡀⠀⠄⠘⣸⠇⠀⠀⠀⠀⠁⠀⠀⡀⠘⠀⠀⠠⠀⠀⠀⠀⠁⠀⢂⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⡀⠀⠀⠔⢀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣷⣿⠾⠟⠋⠀⡄⠀⠀⠈⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠄⠀⢀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡇⢠⠠⠰⠄⠘⠀⠀⠀⠀⡆⠀⠀⠈⠀⠀⠀⠀⠄⡢⠂⠉⠁⠂⠀⠀⠐⠐⠄⠀⠀⠁⠉⠉⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠄⡀⠀⠀⡐⠀⠀⠀⠐⠢⠀⠀⠄⠀⠀⡀⠀⠀⠑⠞⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠁⠀⠀⠀⠈⠄
⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠃⠀⠀⠃⠠⣀⢀⠼⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠠⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠐⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⢀⠀⠠⠤⢀⢀⠀⠀⠀⠀⠐⢀⡀⢀⠀⠀⠈⠁⠀⠀⠀⠐⠀⠀⠅⠀⠀⠀⢠
⠀⠉⠀⠔⠀⠂⠈⠈⠠⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⡄⠀⠀⠀⠁⠀⠈⠑⢧⠋⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠂⠀⠀⠰⡀⠀⠀⢀⠄⠀⡀⠀⠀⠀⠀⢀⠀⡈⠁⢀⢁⢄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠘⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠈⡄⠐⠈⠀⠀⠀⠁⠠⠀⠑⠢⠄⠐⠀⠀⢠⢰⠚⢣⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⣀⡀⠀⠐⠃⠀⠊⠡
⠀⣀⠀⢂⠠⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠀⠀⠐⠀⢀⠀⠉⠑⠰⠼⠓⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⠀⠢⢀⠐⠀⠀⠁⠄⠀⠁⠀⠀⠖
⠀⠀⠀⠈⠀⠀⠤⠄⠐⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠉⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢤⡤⠤⠄⢀⣀⠀⡸⠀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠣⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠀⠀⠉⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠂⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠈⡉⠉⠉⠁⠀⠀⠒⠂⠐⠈⠉⠉⠁⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠢⠤⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠔⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠃⠘⠉⠭⠽⠟⠛⠛⠛⠋⠈⠉⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠚⠛⠻⠛⠛⠓⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣠⠤⣄
⠀⠀⠀⠀⠀⢀⡴⢚⠁⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠈⠙⢦⡀⠀⢀⣠⡤⠖⠛⣉⠥⠄⠠⠜⠻⣦⡀
⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣞⠉⠀⠀⠀⠁⠀⠔⠊⠉⠴⠊⠩⡝⢳⣄⡀
⠠⢶⠤⣰⣇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⢣⡺⡤⣿⣌⠙⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣿⣠⢼⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⡲⠤⣄⣀
⡠⢀⠙⠺⠻⣷⣶⡤⠤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⣩⡾⡃⣀⣚⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣠⣤⣽⣦⣀⠤⢶⢺
⠀⠐⠣⡅⣙⢄⣋⣭⣛⣓⣶⠶⢶⣤⡤⣤⡴⠶⠶⠶⠶⠚⡟⠛⠶⠿⢱⣚⡏⠩⠈⠓⢄⡀⠀⠀⠀⠀⣀⣤⣤⣶⡶⢿⢿⠿⠿⠟⠛⠉⠉⢀⣀⣼⠿
⠀⠀⣾⣷⡔⠀⢨⠃⠂⠘⠑⠷⢶⣧⣲⡖⠃⢂⡵⠷⠒⠛⣓⣲⡒⠄⡽⣿⡀⠀⠀⠀⠀⠙⠢⣀⣴⡟⠛⢿⡟⠀⣠⣲⣷⣲⠶⢶⣒⠚⠿⢍⡳⢤⣤
⠀⠀⡟⠬⡙⠗⠦⣤⣀⠀⠀⣀⣀⠀⠀⣙⡉⠀⢀⠭⠒⣈⠡⠖⠴⠼⢂⣿⡁⢠⢠⡔⠀⠀⢠⣾⡇⠘⡳⡖⠀⡴⣱⡁⢸⡌⠉⢳⢦⣍⡒⠤⣉⣲⠖
⠀⢀⠛⣦⡘⠀⢀⡈⠉⠛⠖⠀⣀⣀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⢀⣠⠎⢱⠙⢦⡸⢃⠄⠀⣾⣿⡇⠀⣷⡉⢙⡴⣝⢧⡀⣷⠀⠈⣶⣄⣹⣲⣇⡰
⠀⠐⡀⠈⠀⠩⠴⠿⠧⠤⠤⢤⣁⣉⣥⣌⡱⣶⡴⠭⢄⣒⣂⠭⠔⠋⠀⡸⠀⠀⠙⢼⠃⢠⡟⣿⣿⠀⠸⣿⡋⠵⢾⣭⣏⣻⡖⠐⡧⣄⣈⣉⣏⣹
⠀⠀⠑⢄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠙⢮⡇⠈⢻⠇⠀⢳⡉⠲⣤⣄⠤⣞⠛⢟⠿⣓⠊
⠀⠀⠀⠀⠈⠉⠒⠛⠛⠉⠁⠲⠶⠶⠶⠦⠤⠤⠄⠀⠐⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠈⢿⠭⡛⡘⣤⡉⢉⠇⠈⠑⢤⣙⡚⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⣈⣆⠱⣸⣌⣄⠉⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⠲⡆⢀⣠⢄⣾⠉⠉⠉⡏⠉⠉⢹⡟⠛⢳⡤⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠒⢦⢻⠀⠀⢡⢸⠀⠀⢿⠀⠀⢀⡧⠀⢤⠼⠧⣠⠼⠤⡄⠀⡇⣠⠎⠉⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢘⣾⣧⡀⠀⢿⡇⠀⠸⠓⢹⣤⡄⣀⠀⠀⠀⡏⠀⠀⢀⡞⠛⠟⠀⡴⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢸⠀⠀⢡⡴⠚⢳⡄⠀⠀⠀⡇⠀⠘⢀⠀⠀⣧⠀⠀⢘⠁⠀⠀⢀⠃⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⡶⠋⢷⣇⠈⠀⠀⢸⠃⠀⠘⣧⠶⠴⡀⡇⠀⠀⠘⠀⠀⢻⠀⠀⢸⠀⠀⠀⠘⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠘⡛⠛⡆⢀⡼⢤⠀⠀⡇⠀⠀⠗⠳⡆⢰⠀⡆⠀⢸⠀⠀⢸⠀⠀⡆⡏⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⣇⠀⠠⢸⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢸⠀⡇⠀⢸⡆⠀⢸⠀⠀⣧⠃⢠⣛⡚⠿⣷
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣱⣀⣹⣀⠸⠐⠀⠀⠀⢰⡇⠀⢨⠀⠀⣀⣼⠤⠧⠤⠼⠧⠰⠾⠲⠶⡟⠒⠉⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⢻⠉⠉⠉⠉⠁⢸⠀⣶⠀⠀⠀⢸⡇⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠈⡆⢹⠀⠀⡆⢸⠃⠀⢸⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠘⠾⣀⠀⡇⢸⡄⠀⢸⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠓⠦⣀⠀⠀⠀⠀⠈⠉⠛⠚⠓⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠞⢡⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠁⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡴⠃⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠉⠢⢄⡀⠠⠦⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢘⠃⢠⠎⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠤⣀⠀⠀⠀⠀⠀⠀⠈⠂⠇⠀⠀⠈⠑⠢⠤⣀⠀⠀⠀⠀⠀⠀⢸⠠⠂⠀⡹⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠈⠑⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⡀⠀⣸⠀⠀⠐⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠁⠢⢄⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠇⠀⡀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠈⠒⢤⣘⡄⠈⠉⠒⠢⢄⣀⠀⠀⠀⠀⢀⠀⡴⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⣸⡌⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠦⠤⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢀⣀⣼⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢉⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢉⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣃⢸⡀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠓⡏⠀⠀⠀⠀⢀⡠⢄⢴⠊⠉⢱⡀⡏⠉⠀⣁⢀⠖⠤⣄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠰⡁⠀⠈⢎⡆⠀⠀⢣⠡⠀⠀⢠⡌⠀⠀⡰⡰⠁⠉⢢
⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣼⠀⣧⣤⣤⣤⣀⣱⡀⢺⠁⠘⡀⠀⠀⣾⠀⠀⢸⠁⠀⢠⠛⠳⡄⢀⠎
⠀⠀⠀⢰⡉⢖⠉⠉⠀⠀⠀⠘⠤⠃⠀⠀⠀⠉⢁⡣⢉⣇⠀⢇⠀⠀⢹⠀⠀⡍⠀⠀⠸⠀⡸⠀⡎
⠀⠀⠀⢸⠪⠭⢉⣛⣒⣛⠛⠚⠶⠚⠛⣛⣚⣛⡉⠭⠑⡟⡀⢸⠀⠀⢸⠀⠀⠇⠀⠀⡇⠀⠇⣼
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⠧⣀⡇⠀⠸⠀⢸⠀⠀⠀⣃⡴⠊⠸
⠀⠀⠀⠀⡇⠀⠀⠀⣼⢷⡀⠀⠀⠀⢠⡾⣦⠀⠀⠀⢸⡀⠀⠈⠉⠒⠓⠒⠚⠒⠒⠉⠁⠀⠀⡇
⠀⠀⠀⠀⢡⠀⠀⠈⠁⠀⢁⣴⣶⣦⡉⠀⠈⠁⠀⠀⡏⡇⠀⠞⠋⠳⠀⠀⠀⠀⠞⠉⠳⠀⢰
⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠘⣿⡟⣻⠁⠀⠀⠀⠀⢠⠄⢻⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠛⠁⢀⣀⠀⣀⠀⢼⢀⣸⡀⠀⠀⠀⠀⠻⡿⠀⠀⠀⠀⠀⡇⠀⠀⣀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⡴⠋⠒⡝⡤⠖⢀⣉⣛⠫⠽⠿⣓⠒⠶⣶⣶⣶⣶⣤⣬⡿⣍⡓⠛⣉⣐⡶⣚⠭⠭⠓⢄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡃⠀⢀⡴⠛⢒⡒⢛⡒⠢⠤⠤⠒⢬⠲⣦⣄⣢⣶⠖⠥⠦⠶⠶⠛⠛⠛⠚⠲⢄⠀⠀⢸
⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠉⢲⠋⠀⠀⠰⠃⠈⠁⠺⡄⠘⣀⠘⢣⡄⠰⠂⣰⠂⡤⢸⡇⣨⡃⠘⠁⠀⠀⠀⠱⡖⠁
⠀⠀⠀⠀⠀⠀⢣⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⠀⠀⠀⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠉⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠆⠤⠤⠤⢀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⡀⠤⠤⠄⠒⠒⠊⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠁⠀⠀⠀⠀⠀⠀⡠⠆⠤⡀⠀⠀⠀⠀⠀⣀⢤⡤⢠⣆⣠⠤⡄
⠀⠀⠀⠀⠀⡔⠋⠀⠄⠀⠀⠀⠉⢢⠀⠀⠀⠀⠀⠀⣠⣖⣛⣒⣲⣀⡀⠀⠀⠀⣔⡉⢉⣎⣑⡄⠀⠀⠀⠀⣨⠞⢀⡎⠲⣁⡞⢻⣉⠆
⠀⠀⠀⠀⢸⡤⠤⠤⠤⢤⠤⢤⠤⢤⡇⠀⠀⠀⠀⠨⣅⣀⣀⣀⡀⣠⠇⠀⠀⠀⢳⣾⣛⡳⠶⡇⠀⠀⠀⠀⠹⡓⠾⠽⠤⠿⠚⠉⢩⠃
⠀⠀⠀⠀⠀⣿⣉⣩⣭⣭⠽⢭⣙⣲⠎⠀⠀⠀⠀⠀⢡⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⢟⣉⠷⡾⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠘⢤⣀⣀⣙⣇⢛⡧⠇⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⣍⣴⠃⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠤⠤⠞⠀⠀⠀⠀⠀⠀⠀⠸⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠒⠒⠒⠚
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣀
⠀⠀⠀⠀⠀⡠⠊⡡⢤⠤⠤⣌⣱⣠⠖⢆⠀⠀⠀⠀⣠⠊⠉⠈⠙⢦⠀⠀⠀⡔⠱⠆⢠⡍⠰⠗⠄⠀⠀⠀⠀⣀⠤⢄⡀⠀⢀⣀⢀
⠀⠀⠀⠀⡜⢰⠛⣲⣁⢀⠴⣿⠿⠃⢱⠸⠀⠀⠀⠀⡇⠀⡀⠁⡁⢈⠆⠀⠀⢳⠲⡖⠦⡲⠖⠲⠇⠀⠀⢐⢉⡿⠿⣶⠾⡽⢷⣶⢾⡛⡂
⠀⠀⠀⠀⢇⢸⠈⠔⠁⠉⢁⡞⢻⠾⠍⠉⠀⠀⠀⠀⠃⡀⠀⠀⠄⡜⠀⠀⠀⠀⡇⢱⠀⡃⡸⢸⠀⠀⠀⠀⢻⠀⠂⠀⠉⠀⠉⠀⡁⢹⠁
⠀⠀⠀⠀⠘⣌⠻⣅⣠⣱⣀⡰⠃⡼⠀⠀⠀⠀⠀⠀⠀⠑⢴⠒⡼⠁⠀⠀⠀⠀⠑⠠⢄⠵⠒⠃⠀⠀⠀⠀⠘⠦⣈⣀⣀⣀⣀⡠⠔⠃
⠀⠀⠀⠀⠀⠈⠑⠢⠤⠭⠤⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠺⡭⣭⠎⢿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂⢰⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣞⣋⣹⠀⠀⠀⠀⠀⢀⡀⠀⢀⡰⢄
⠀⠀⠀⠀⠀⢠⣾⠥⣄⡴⢮⡱⢄⠀⠀⠀⠀⠀⠀⡴⠶⠶⠷⠾⠷⠖⣦⢤⠀⠀⠀⢀⡼⢀⠟⠁⠈⠦⢤⠀⠀⢠⠧⡌⠛⢧⡀⡆⠙⢦
⠀⠀⠀⠀⢀⡏⡰⠋⠀⠉⠑⠂⠺⡓⡆⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⣰⡿⠵⠃⠀⠀⢩⠀⠘⡄⠀⠀⠀⢸⠀⠀⡇⠀⡟⠀⠀⢃⢱⠀⠀⡇
⠀⠀⠀⠀⢸⡴⠃⠀⠀⡀⠀⡀⠂⠙⡗⠀⠀⠀⠰⣚⠓⠒⠈⢉⣉⣉⣉⠏⠀⠀⠀⢺⠀⠀⡇⠀⠀⠀⠈⡇⠀⠑⠤⢝⡂⣠⢧⣈⡴⠊
⠀⠀⠀⠀⠸⡤⠤⠤⠄⠒⠒⠒⠒⠒⠃⠀⠀⠀⠀⠈⠉⠉⢀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠒⠒⢧⠠⠤⠄⠀⠁⠀⠀⠀⠀⠙⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡊⠉
⠀⠀⠀⠀⠀⠀⢀⡠⠤⡔⠒⢤⣀⡀⠀⠀⠀⠀⠀⠀⣿⡿⡇⠀⠀⠀⠀⠀⠀⢰⠒⠟⣻⣓⡆
⠀⠀⠀⠀⠀⡔⠉⠀⠀⠘⣄⠘⡄⠈⢢⠀⠀⠀⠀⠀⡟⡇⣣⠀⠀⠀⠀⠀⠀⢘⢁⠿⡵⠉⢹⠀⠀⠀⠀⡴⠒⢤⠔⠒⢲⠔⠲⡤⢲⢦
⠀⠀⠀⠀⡰⠻⣄⠀⠀⠀⢈⡏⠉⠓⠋⠀⠀⠀⠀⢜⣉⣉⠈⠑⡆⠀⠀⠀⠀⢸⠀⡜⠀⣀⢸⠀⠀⠀⢀⣇⣀⣁⠤⠤⣁⡠⠤⢤⠤⣴⡄
⠀⠀⠀⠀⡟⠦⣈⡱⠦⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢈⠆⡜⠀⠀⠀⠀⠀⠘⡞⠠⠀⠀⠀⡇⠀⠀⢮⣵⣒⡬⣉⡡⢔⣂⠭⠭⡭⢧⠜
⠀⠀⠀⠀⠸⡀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠉⠀⢇⠀⠀⠀⠀⠀⠀⡃⠀⠰⠀⠄⢱⠀⠀⠀⠲⠤⠒⠒⠒⠒⠒⠊⠉⠉⠉
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣄⣠⡨⠇⠀⠀⠀⠀⠀⠧⠤⠒⠒⠒⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠤⢀⡀
⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣄
⠀⠀⠀⠀⢃⣑⡒⢂⡀⠀⠀⠀⠀⠀⠀⣐⣊⣡⡞⠀⠀⠀⠀⢳⡾⠶⣦⢀⠀⠀⠀⠀⠀⣀⠴⠂⣳⡶⠁
⠀⠀⠀⠀⣜⠛⠿⠿⢿⠷⠾⣿⡾⠿⠿⠿⠛⠋⡱⠀⠀⠀⠀⢜⡛⠷⠾⠿⡿⠶⣤⡶⠿⠿⠿⠛⠛⢩⠆
⠀⠀⠀⠀⠸⡑⠒⠓⠒⠲⠤⠴⠦⠤⠚⠓⠊⣩⠇⠀⠀⠀⠀⠘⣝⠒⠓⠒⠒⠤⠤⠦⠤⠒⠛⠚⢉⠏
⠀⠀⠀⠀⠀⠈⠑⠒⠲⠤⠤⠤⠤⠤⠖⠒⠊⠁⠀⠀⠀⠀⠀⠀⠈⠑⠒⠲⠤⠤⠤⠤⠤⠖⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⠄⠒⠒⠠⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢
⠀⠀⠀⠀⠀⠀⡠⠒⠉⠁⠀⠀⠀⠀⠈⠑⠢⡀⠀⠀⠀⠀⠀⢀⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⡀
⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠳⣖⠟⠴⢄⣐⠒⠒⠒⢒⣂⠶⠊⣰⣶⠃
⠀⠀⠀⠀⢮⣵⡦⣤⠄⠀⠀⠀⠀⠀⠠⡤⠄⢮⣭⠂⠀⠀⠀⢰⣉⠛⠛⠻⠿⠿⠶⠶⠿⠿⠛⠛⢛⣁⠇
⠀⠀⠀⠀⡸⠷⣤⣼⣿⣶⣦⣀⣤⣶⣷⣷⠶⠿⢓⡄⠀⠀⠀⣔⡻⠿⣿⣷⣶⣶⣴⣶⣦⣾⣿⣿⠿⢛⡄
⠀⠀⠀⠀⠸⣷⣤⣶⣤⣤⣀⣀⣄⣀⣴⣶⣴⣶⡎⠀⠀⠀⠀⠸⣤⣤⣁⣀⡠⣈⠉⢉⣠⣔⣠⣬⣤⣾
⠀⠀⠀⠀⠸⡀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠋⠉⢁⠇⠀⠀⠀⠀⠀⢇⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⢁⡜
⠀⠀⠀⠀⠀⠈⠑⠒⠤⠤⠤⠤⠤⠤⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠁⠒⠢⠤⠤⠤⠤⠤⠤⠔⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⡄⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⠀⠀⢠⡒⠌⠦⠀⠀⠠⠂⠄⠀⠀⢠⡰⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠇⠂⣝⣠⠀⠀⠀⠀⠠⠄⠈⠀⠈⠁⢆⠀⠀⠀⠃⡀
⠀⠀⠀⠀⠀⠀⢄⡀⠒⠀⠀⠀⡀⠀⠀⠐⠊⠉⠀⡄⠠⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠨⢀⠁
⠀⠀⠀⠀⠀⠀⡀⢐⠀⠀⠠⠀⡀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⡓⠀⠀⢔
⠀⠀⠀⠀⠀⠀⢉⠂⠀⠀⠁⠀⢘⠀⠀⠈⠁⠁⠀⠀⠀⡄⠐⠒⠂⠀⠀⡀⢀⠆⠄⠀⠀⠁⠀⠀⠉⠄⠠⠈
⠀⠀⠠⠀⠐⠄⢆⠀⠀⠑⠀⠀⠈⠀⠀⠀⠈⡉⠀⠰⠀⢀⡁⠀⡰⠀⠀⠀⠰⠀⠀⠠⠀⠀⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠘⠦⠀⠀⠀⠀⠀⠴⠄⠀⠄⠁⡠⠌⠀⠂⢠
⠀⠀⢀⠠⠀⠀⠍⠀⡀⠀⢠⠀⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠀⡠⠄⠀⠀⠈⠰⠂⡄⠀⠀⢀⠀⠀⠠⠄
⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠁⠀⠀⠀⠀⠀⠒⠘⠄⠀⠀⠂⠂⠠⠴⠋⠰
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠂⠀⠄⠁⠀⠈⠁⠰⠀⠀⠀⠀⠐⠈⠐⠀⡀⠈⠀⠀⠐⠂⠐⠀⠀⠁⢬⠀⢀⡀⠀⢂
⠠⠄⠁⠀⠀⠀⠤⠐⠄⠀⠀⠀⠉⠀⠀⠀⠀⡂⠁⠀⠀⠀⠈⠉⠀⠀⠁⠀⠐⠃⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈
⠀⢀⠠⠄⠀⢀⠒⠁⠀⠀⠀⠒⠀⢀⠀⠀⠂⠘⠂⠀⠀⠀⠀⠀⠀⠴⠒⠢⠒⠀⠠⠐⢀⡄⠀⢈⡲⠀⠀⠐⠒⢁
⠀⠀⠀⠀⠴⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠈⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠐⠁⡄⠀⠀⠎⠀⠀⠂⠄⠀⠀⠃⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡁⠈⢄⠀⡀⢀⡀⠐⠦⠆⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠐⠂⢠⠌⠀⠀⠀⡀⠀⠄⠰⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠰⢁⠔⠂⢰⠀⠂⠀⠀⠀⠀⠀⠀⠒⠒⢖⢂⠀⠀⢀⠀⠀⠐⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠉⠈⠉⠀⢀⠀⢀⡤⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⠀⠀⠀⠀⠀⠀⠀⠒⠀⠫⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠂


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠁⠂⠈⠁⠀⠂⠐⢄⠀⠀⠀⠒⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠤⠶⠶⠦⠤⣤⣄⣀⡀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠉⠴⠀⢀⠀⠒⠀⣀⠀⠶⠀⠈⡙⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡁⠀⠘⠀⠀⠒⠀⠀⠠⠀⠀⠀⠀⠀⠒⠀⠀⠀⠄⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠞⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣶⣶⠬⢭⣙⣓⠒⠒⠶⠶⠶⠦⠤⠤⠤⠤⠴⠶⠶⠖⢒⣛⠭⠵⢒⡶⣶⣶⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣌⣙⡒⠒⣛⣉⣳⣶⣤⣀⠀⢀⡀⢀⡀⢀⣠⣶⣏⣉⣉⣉⣩⣥⣾⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠛⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣦⣍⣡⣶⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠍⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣆⠈⠀⢀⡀⠀⠀⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣀⣀⠠⡤⢀⣤⣄⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣀⣚⣤⣴⣦⣤⣀⣤⣾⣿⣿⣿⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠓⠲⠶⠶⠶⠶⠶⠶⠖⠒⠚⠛⠛⠉⠉



⣿⣿⢛⢿⠛⡟⣿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣄⠀⠀⠀⣠⢤⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⣆⠈⢡⠀⢀⣀⡀⠀⢰⢎⠁⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠖⠉⢣⡀⢀⠳⠊⡃⢠⠀⢀⠳⢚⠀⠀⢱⠀⠲⠀⠸⠁⢰⠀⣸⠀⠆⠀⡘⢨⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠻⣤⠠⠀⡇⠉⣻⢍⣾⣼⢠⣲⣾⡆⢀⣧⣰⢀⣼⡀⣻⠀⢠⣀⠇⡆⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣴⣿⢿⣄⠿⣷⣿⢸⠏⡽⣇⡉⢸⡗⣻⣤⣿⠞⠠⡾⣿⠠⡦⢺⠀⡇⢸⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢭⢳⠈⢿⢸⣾⡿⢀⢎⣏⢸⠀⡇⠉⡿⢃⡔⣱⡇⢻⠀⠀⡇⣿⠀⡇⢸⢰⠅⡘⡫⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠆⢣⢸⢸⡏⡇⡜⡦⠈⢸⠀⡇⡆⢀⠎⣼⠁⡇⣤⡀⠀⣿⣉⣾⡇⠘⣾⢎⠜⡐⣀⢾⣩⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠘⡌⣿⠘⣼⣿⢹⢃⡄⡌⠀⡇⣆⠎⣜⢹⢰⠟⣤⡷⢸⡇⡃⢸⡇⡠⢣⢋⣮⠟⡵⢁⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠹⡘⡆⣿⡏⡞⠏⠃⠃⠀⢳⡏⢀⢹⡐⡎⢠⢫⠃⢸⡇⡇⢸⡟⢡⢣⣯⢋⣞⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡛⠓⠛⠛⠛⠛⠛⠓⠿⠶⠿⠷⠷⠶⠾⠶⠾⠶⠤⢼⣧⣧⣸⣁⣡⡷⠗⠛⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⡖⠂⣿⡄⠀⢸⠁⢎⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢷⠃⢹⡇⢰⢸⠃⠈⢧⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠘⠀⠂⠘⠚⠘⠧⠐⠋⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣥⣤⣤⣄⣠⣤⣤⣤⣄⣀⣀⣤⣀⣀⣀⣀⣸⣥⠶⠋




⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣟⡉⡻⠿⠿⠿⠿⠻⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤⣤⠆⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣾⣿⣟⣉⣟⣿⣹⠟⠟⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣂⠀⠀⡾⣀⣺⡍⢻⠐⠛⢻⣴⣟⢳⡽⠧⡀⠀⣤⣄⡄
⠀⠀⠀⠀⠀⠀⠠⢦⣑⠿⢩⠀⢠⢸⡟⠸⣿⠭⢷⠒⣉⡸⠛⣛⡏⣟⢏⠀⢱⢜⢡⣾⢦
⠀⠀⠀⠀⠀⠀⠶⠧⠝⠒⠊⠀⠘⣑⣭⣩⡿⠶⠞⠚⠛⠶⠿⣿⣿⣿⡇⠀⠘⠚⠛⠾⠷⡂
⠀⠀⠀⠀⠀⠀⢀⣀⢀⠠⢄⡠⣀⠀⠉⠁⡀⡤⢄⣰⠠⠤⡄⡀⠉⠀⣀⠠⢤⢒⠠⠤⣀
⠀⠀⠀⠀⣠⡪⣵⡆⣾⣷⡗⡥⠎⠀⠴⣬⣷⣯⢦⣿⣿⣶⡿⢉⣦⡀⠀⢞⡺⣽⡟⣹⡾⣇⡢
⠀⠀⠀⣼⣵⣶⣶⣟⣿⣿⣿⠇⠀⣄⣾⠿⠿⠿⡿⣆⣀⣴⢏⢏⡙⣸⡄⠐⣯⣯⢽⣛⣷⠛⢲⡙
⠀⠀⠠⡿⣾⣧⣬⢿⣾⡻⠴⠀⠰⣻⡽⠿⠿⢿⣷⣶⡭⢾⡿⡻⠉⣦⣧⠀⢸⣥⣤⣽⣛⠾⣟⢣⡅
⠀⠀⠈⣌⢵⢞⣲⣿⠏⠙⣷⠀⠰⡹⢏⣿⢻⣾⡷⢬⣋⣿⣇⠵⣸⡿⠐⠀⠨⠽⢻⡝⢣⣿⣡⢧⡆
⠀⠀⠀⠫⡛⣿⡿⢝⠿⢿⢟⣃⠀⠗⠮⡿⣿⠟⣵⠶⢾⣥⣿⣽⢉⣺⠁⢠⠜⣛⣿⠇⠸⣿⢶⣻
⠀⠀⠀⠀⠙⢜⡤⢞⣿⣿⣇⣨⢆⠀⠐⢽⣉⢏⢿⣀⣼⠫⣳⣿⠟⠁⣠⡤⡟⡻⡚⢒⢶⣎⠅
⠀⠀⠀⠀⠀⢀⠉⠀⠂⠈⠁⠁⠁⢀⣀⡀⠉⠘⠓⠸⠂⠀⠉⠀⢀⡀⠀⠀⠃⠛⠛⠚⠋
⠀⠀⠀⠀⠀⠸⡀⣶⢢⣴⢤⠀⠀⢿⡋⣍⣱⠐⣲⢤⣦⣔⡖⣿⣺⡭⢳⠀⢀⠶⢦⣐⢊⣻
⠀⠀⠀⠀⠀⠐⣿⣫⣟⠳⡾⠀⠨⡬⣞⣶⠿⣿⢻⣧⣿⠛⣿⣧⣪⡨⡄⠀⠘⠲⣾⢤⡞⠘
⠀⠀⠀⠀⠀⠀⠀⠣⠜⡢⢞⡆⠀⢓⢻⢟⣓⣹⣟⢛⣿⡼⡋⢀⣼⠅⠁⢠⡿⣮⢝⣺⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠟⠀⠀⠋⠽⢿⡻⡻⢾⡟⡟⢻⠛⠅⠀⠀⠋⠉⠛⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠹⠑⠐⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠀⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⢂⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⢀⡜⠹⠋⠟⡆⠀⠀⢠⣉⣀⣀⠀⠀⠀⢀⣀⣀⣀⢁⠀⠀⠀⠀⠀⣠⣴⠟⠉⠀⠀⠄⠀⠀⠉⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⣢⡈⢂⠀⠀⢀⠃⠀⠠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠅⠀⠀⠀⡴⠟⠁⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⣀⡴⠊⠀⢁⠐⢎⡠⠚⠀⢀⠈⡇⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣅⠀⠀⠀⠀⠠⠀⠀⡄⠀⠀⡀⠐⠀⡸
⠀⡠⢔⣂⠍⠁⢀⡤⠆⠈⡔⠀⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⣧⠀⠁⠀⠄⠀⠀⣀⡀⠀⡄⠀⠀⠀⠀⢼⠿⣶⣶⠤⣀⣤⢀⣀⣀⢠⡤⣔⠚⡄
⠘⠐⣈⡄⠖⡀⠩⡀⢀⠀⡃⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⢻⡤⠤⠤⠤⠤⠒⠁⠀⢀⠁⠀⠀⠀⠀⣾⢦⠥⢌⣾⠛⠛⠀⠀⣢⡀⠀⠨⠼⣧⠄
⡸⠋⠀⠰⠈⠁⠀⠀⠀⠊⠀⠀⠀⠈⠀⡰⠁⠀⠀⠀⠀⠀⢸⠀⢀⣀⡤⠄⠀⠤⠖⠩⠀⠀⠀⠀⣀⠧⢈⠉⠣⠜⠓⠨⠭⣽⣚⡤⠎⠔⡨⠟
⢫⣄⠀⢀⠠⣀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠈⡁⠈⠀⠀⠀⠀⢀⠀⡇⠀⠀⠀⠘⠠⣄⠄⡀⢈⣁⡀⡠⠞⠡⠤⠄⠂⠀⠀⢠⠐
⠀⠁⠒⠒⠑⠢⠭⣉⣉⡀⠤⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣂⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠀⠈⠒⠳⠭⠤⣄⡀⣀⡀⣀⠀⠤⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢀
⠀⠀⠀⣀⠜⠁⠀⠀⡀⠢⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣗⡈⠉⠀⠀⣞⣽⣷⡻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠀⠀⠀⠗⠀⡄
⢀⠔⢪⡀⠀⠀⠆⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡑⠦⠌⠭⠉⠉⠩⠍⠄⠀⠉⡀⠀⠀⠀⠀⠀⠀⢠⠆⠁⢀⠄⠀⠀⢀⠠⠗
⠘⠀⠗⡹⢄⠀⠀⠀⠀⢀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠊⠀⠠⠄⡌
⠀⠀⠀⠀⠈⡆⠀⣴⠃⠉⠀⠁⠠⣀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡀⠄⠂⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠢⠀⠂⠀⢀⠀⠀⢀⠄
⠸⡦⡀⠀⢠⣧⠞⠁⠈⠲⢄⡀⠀⠠⡑⠄⡀⠀⠀⠀⠀⡟⠉⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⢀⡈⠇⣀⠂⠆
⠀⠘⡊⢗⢍⠡⠀⠀⠀⠀⠀⠈⠢⣄⠔⢀⣼⠀⠀⠀⠀⣻⡀⠀⠀⠠⠐⠊⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠡⢔⠉⡰
⠀⠀⠑⢀⠙⠫⡂⠀⠀⠀⠀⠠⠀⡠⣔⡝⠁⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠤⢉⠃
⠀⠀⠀⠀⠁⠠⡀⠀⠀⡂⠤⢐⠬⠊⠜⠀⠀⠀⠀⠀⠀⠸⡓⠀⠀⠀⡀⠄⠂⠁⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡁⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠉⠀⠉⠀⠀⠀⣠⠤⠀⠀⠐⠠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠐⠒⠤⡄⠴⡴⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠞⠣⠒⠗⠒⠀⠀⠀⢄⢠⠤⠄⠤⣤⠲⠈⠀⡠⠶⠈⠑⠀⠤⣥⡔⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣁⣂⣀⠁⠀⠈⠀⠀⠀⠀⠀⢂⠤⣎⣁⠠⠄
⠀⠣⠀⠐⠠⠄⠀⠀⠀⠤⠀⠀⠀⢠⠞⠀⠀⠀⢎⡀⠀⠀⠀⠀⠀⠀⠁⢀⡠⠐⠁⠀⢠⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠤⠄⠊⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠓⠦⢀⡀⠀⡠⠖⡩⠄⠀⠀⠀⢸⡄⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠐⠈⠀⠈⠀⠀⠄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⠭⠔⠉⠀⠀⠀⠀⠀⠘⡇⡞⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠠⠄⢠⡄⠀⠒⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⢀⡀⠀⠀⠀⠄⠠⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⠀⠀⠈⠀⢠⠘⣠⠀⠅⠤⠀⠃
⠀⠀⠀⠒⠂⠀⠀⠀⠀⠠⢀⡌⠀⠈⠀⠸⠁⠐⠀⠀⢀⠁⠉⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠠⠴⠄⠊⠀⢀⠘⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠠⠃⠀⡜⠚⠀⠁⠂⠀⠀⢄⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠄⠀⣴⠄⢀⡀⠙⠂⡀⢀⡀⠀⠀⠐⠧⡄⠣⡀⠀⠀⠀⠀⠀⠛⡠⠄⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⡀⠀⠰⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠄⢠⣄⣀⠀⠀⠀⢀⠀⠐⠠⠤⠀⠉⠈⠒⠈⠁⠀⠀⠀⠀⠀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠈⠠⢌⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠄⠀⠀⡐⠁⠀⠀⠀⠁⠀⠀⠀⢰⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠠⠄⠈⠀⢀⠀⠒⠂⠉
⠀⠀⠀⠀⠀⢆⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢸⠀⣀⠔⠉
⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠨⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢀⠀⡀
⠰⢦⡀⠴⠄⠦⠔⠃⠀⠀⣀⠤⢠⡄⡶⠠⢄⠀⡆⠀⠀⠀⡀⠀⡝⠤⢀⡀⢠⡄⢤⣤⠀⣀⡠⠄⠀⡢⠄⠠⠄⠀⠀⣀⠤⠀⢨⣅⡰
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠐⢠⠀⡥⠀⣶⠀⠀⠀⠀⠀⠀⠀⠁⢀⢈⣛⡀⠀⢠⠀⠀⠘⠡⡤⠀⠁⠀⠕⠀⢀⡀⣤⠀⠀⠂⠁⠁
⠀⠀⠀⠀⠀⠀⠠⠄⠆⠀⠀⠐⠈⠀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⢩⠁⠀⣠⡀⠑⠓⠐⠆⠀⠀⠀⠀⠈⠉⠀⠉⠀⠂
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥⠀⣀⣀⣈⡀⠴⠗⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠤⠀⠀⠀⠠⠀⠀⠃
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⢬⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠁⠀⠈⠁⠉⠀⠦⠤⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠷⠀⠀⠐⡶⠀⡀⠀⠀⣀⡀⠀⠁⠀⠄⠀⠺⢷⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠔⠀⠀⠠⠤⠀⡀⠠
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠌⠓⠀⠀⠁⠀⠒⠀⠀⠀⠑⠠⠌⠂⠉⠐⠂⠉⠀⠀⠀⠀⠔⠀⠑⠒⠂⢀⣁⡀⠀⠈⠁⡠⠀⠀⠀⠄
⠀⣤⣄⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠊⠆⠀⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⡀⠀⠀⠀⢈⠄⠠⠐
⡇⠀⠀⠁⢄⠘⠦⣄⢠⡄⠔⠀⠘⣰⠀⠀⠀⣀⣦⠄⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠡⠀⠀⣤⠀⠀⠀⢠⠁⠀⢠⡏⠀⠀⠀⠀⠀⡘⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠄⡀⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣥⡀⠘⢇⣀⠀⣀⠀⠔⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⢋⡤⠀⠀⠀⠀⠐⢀⠁⠀⠀⠠⠒⠈⠉⠉⠁⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠀⠀⠀⠇⠀⠀⠀⠀⢀⠄⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠤⡀⠀⢀⠀⠀⠀⡀⠀⡇⠀⠀⠀⠀⣦⠀⠀⠀⢰⠀⠀⠃⢄⣀⡀⢀⣀⡰⠞⠀⡈⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠀⠊⠔⣈⠉⠋⣀⠲⠀⠀⡄
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⣊⠤⠖⠶⠤⡑⠀⠀⠡⠀⠀⠀⠀⠄⠀⠀⡐⠀⠀⣀⡀⣀⣀⠈⠁⠈⠣⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠊⠀⠀⠁⠀⠀⠀⠀⠀⠑⠀⠀⠀⠐⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⡧⠼⣀⠀⠀⠀⠀⠀⠆⠀⠴⠀⠀⢀⠤
⠀⠀⠀⠀⠓⠈⠜⢉⠲⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⣰⠁⠀⠀⠀⠀⢠⠈⠁⠜⠂⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⢶⠀⠃⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣀⣠⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⣈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠴⠶⠒⠒⢒⠚⠛⡉⠉⠉⠁⠀⠘⡋⠓⠒⠦⠤⣄⠠
⠀⠀⠀⠀⠀⢀⣠⡤⠒⢫⡍⠀⠀⡠⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⢈⡀⠀⠘⢁⠦⠂⠀⢀⠢⣄
⠀⠀⠀⢀⡴⣫⠟⠁⡀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⢀⠈⠀⠀⠂⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠉⠉⢪⡑⣆
⠀⠀⢠⢎⠀⡆⠁⠀⠁⠀⠐⠀⠀⠰⠆⠀⠀⠀⠀⠀⠘⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠠⠆⡀⠀⠀⠴⠀⠘⣿⡜⣇
⠀⢠⢯⡟⠃⡀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠂⠠⠀⠐⠀⠀⠀⠒⢀⡄⠀⠈⣹⣇⢿
⠀⣼⢺⡁⡈⠁⠈⠊⢀⠀⠀⠔⠀⠀⠁⠀⠀⢀⠀⠀⣄⠀⠀⠁⠀⠘⠀⠀⠀⡄⠉⠐⠁⠠⠀⢀⠄⢲⣿⣿⡏⣼
⠀⠸⡜⠿⣫⡄⠀⢀⠀⢀⠀⠀⠀⠀⠐⠄⠀⠈⢀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⠀⣄⢀⠐⣠⣒⡤⠾⢛⣋⣥⣾⣅
⠀⣠⣾⣷⣶⢶⣤⣔⠂⠊⠀⠀⠃⠀⠀⠀⢀⠀⠀⡀⠀⡈⠀⠀⠀⠤⠦⠀⠀⣒⣂⣩⣤⣴⣶⣶⣿⣿⣿⣿⡿⡀⢚
⡞⠁⣺⣿⣾⣮⣉⣟⣿⣻⣿⣿⣿⣷⣶⣶⣶⣶⣤⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⠿⠍⠀⠁⢨
⢣⠀⠈⠙⡉⠙⠛⠏⠭⠻⠿⠿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠶⣷⣿⣟⣻⣿⣿⣿⡿⠿⠿⠟⠛⠛⠋⣡⣤⠤⢴⡞⠉
⠀⠙⢲⢏⣹⣄⣀⠀⠀⢀⣠⠶⣲⣖⠬⣩⡥⢤⡉⠉⢁⣰⠟⠛⠛⠋⠋⠉⠉⠉⠿⠷⢄⣤⣴⣚⣩⣵⣶⣾⠋⡆
⠀⠀⠸⡸⣿⣻⢿⡿⢿⢿⣤⠞⠛⠿⢻⠾⠿⣶⣉⠛⣉⣀⣠⡤⣤⣀⣰⣶⣦⣤⣴⠶⠛⠋⠉⠓⠁⡉⠀⠈⡰⠃
⠀⠀⠀⣙⣶⣤⣀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠸⠈⠛⠉⠉⠉⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⣀⣨⣵⣶⣿⡷⠑⡄
⠀⠀⢰⠀⣿⣿⣿⢿⣷⣶⣦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣠⣤⣤⣤⣴⣶⣿⣿⣿⣿⣯⣿⣾⣿⠿⠁⢀⠇
⠀⠀⠈⣣⣌⣓⠟⣓⡛⠻⢭⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣵⠟⣉⣀⣀⣠⡴⢋
⠀⠀⠀⢏⠈⠽⠷⠤⣭⣽⣦⣈⠉⠀⠈⠙⠻⣿⡿⠟⠛⠋⣉⡭⠭⣭⣉⣉⠉⣉⣡⠴⠿⢋⠭⠵⠾⠟⣛⣋⣡⡞
⠀⠀⠀⣸⠹⠗⠤⠤⢤⣄⡀⢈⡳⠦⠤⡈⣁⣠⣐⠺⠟⠂⠀⠒⠠⢤⣤⣬⣭⣭⣤⣤⣶⢯⣤⣴⠟⠚⠉⠛⢹⠇
⠀⠀⢰⣿⣆⡀⠀⠀⠈⠈⠁⠀⠑⠶⠶⠒⠻⠟⠛⠛⡳⠊⠉⠛⠳⠄⣈⣉⠤⠞⠛⠋⠀⠀⢀⠀⠀⠀⣀⡴⠋
⠀⠀⠘⠛⢻⣷⣤⣄⣀⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣀⣮⠵⠖⠋⠁
⠀⠀⠀⠀⠀⠉⠉⠛⠛⠟⠻⠿⠷⢶⣤⣤⣤⣤⣤⣀⣀⣐⣀⣠⣤⣤⣤⡤⠴⠖⠛⠋⠉⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣾⣿⣿⣿⣾⣷⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⡀⠀⠠⠅⠀⠀⡠⠂⠈⠢⡈⠁⠠⠄⠄⠀⠂⠀⢀⠴⠀⠐⠛⠻⠀⠸⠇⠄⠄⢄⠀⠀⠊⠅⠀⠀⡠⠊⠉⠠⢀⠇⠘⡄⢀⠀⠀⠀⢀⠴⠀⠐⠛⠳⠁⠸⠔⠠
⠀⠀⠈⠀⠐⠀⠂⠁⠀⠀⢀⠜⠀⠀⠖⠀⠨⠀⠠⡀⠀⠀⡠⠊⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠂⠑⠄⠀⢀⠘⠀⠀⠖⠂⠀⠀⠀⠀⠀⠀⠠⠊⠀⡀
⠺⠂⠳⣀⠀⠈⠈⠒⠚⠀⠁⠀⠀⠀⠠⠀⠠⠃⠀⠈⠠⠈⠀⡔⠓⡜⢂⠀⣾⠃⠺⢆⠽⣠⠀⠈⠈⠒⠚⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠔⠂⠔⢂⠀⣺
⠀⠘⠂⠁⠀⠀⡠⠐⠀⠁⠐⠠⠀⠀⠀⠀⠈⠀⠀⠀⡀⢀⠈⠲⢪⡖⡛⠀⢙⠒⠂⠛⠛⠏⠀⠀⠠⠐⠀⠀⠐⠢⠀⠀⠀⠀⠌⠀⠀⠀⢀⠀⠈⠶⢢⠔⡛⠀⢛
⠀⠀⠀⠀⠀⠀⡶⠤⣂⢴⡤⢴⡆⠀⡏⠀⠄⢩⠂⠀⠀⠆⠐⠈⡧⢾⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⡶⠄⣂⢠⡆⢶⡆⠀⡍⠀⠈⢩⠂⢰⠀⠀⠀⠈⡳⢮⠃⠀⠈
⠀⠀⠉⠀⠀⠀⠉⠉⠷⠘⣣⠍⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠆⠀⠐⠂⣀⢀⡀⠁⠀⠀⠉⠀⠀⠀⠉⠉⠳⡜⣫⠝⠁⠀⢠⠀⠀⡀⠀⠀⠑⠀⠆⠀⠐⠂⢀⢀⡀
⠀⢀⠊⠀⠈⢢⠀⠀⠀⠈⠁⠀⠀⠀⠸⠄⠀⠄⠀⠀⢀⣲⠦⠀⠀⡁⠀⠀⡀⣥⠀⠠⠈⠀⠈⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⣀⣶⠦⡀⠰⡉⠀⢀⡀
⠀⢨⠀⠀⡠⠂⢀⢀⣑⠄⢀⣴⠤⠂⠀⠀⠀⣦⣡⡾⠟⠁⠀⡀⠀⠀⠂⠀⠀⡀⠀⢀⡀⠀⡀⠂⠀⢂⡐⠄⢀⡕⠴⠠⠀⠀⠀⣤⣱⡾⠟⠋⠀⠀⠀⠁
⡄⢢⠘⠈⠀⠀⢈⠠⡔⠲⠵⠷⣄⠒⠀⠀⠈⢜⠁⠀⠀⠠⠊⠀⠀⠀⠒⠐⠀⠀⠄⠡⠚⠈⠀⠀⠄⠀⡴⠲⠾⠶⣄⠂⠀⠀⠀⢎⠀⠀⠀⠠⠊⠀⠀⠈⠂
⢀⡁⠀⣀⠀⠀⠈⢐⠂⠠⠄⢂⠄⢀⠀⢠⣂⠀⠀⠀⠀⠀⠘⠀⠇⡈⣄⠀⠀⠀⢀⡀⠀⣀⠀⠀⠐⢐⠂⠠⠄⢂⠄⠀⠀⣘⣀⢀⠀⠀⠀⠀⠸⠁⠇⡘⡀
⠀⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⡯⠇⠀⠀⢀⠀⡰⠂⠺⠀⠀⠠⠀⠌⠢⠰⠁⠄⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⣠⡿⠇⠀⠀⢀⠀⡯⠒⠲⡀
⠀⠃⢀⠀⠀⠀⣠⠄⠒⠀⠲⠀⠐⠂⠁⠂⠈⠁⠐⠀⠀⠀⠁⠀⠀⠀⠀⢸⠀⢀⠀⠀⢀⠀⠃⠀⢠⢄⡒⣀⢶⣄⠐⠂⠑⠐⠈⠁⠐
⠀⠂⠁⠐⠊⠀⠃⠀⠀⠀⠀⠀⠆⠀⠀⡀⠀⠀⡀⡀⡀⠀⠄⢀⡀⠀⠀⢀⠀⠀⠀⠒⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⠀⡀⠀⠄⠀⡄
⠀⠀⠀⠀⠀⠀⡆⣀⠠⠀⠒⣀⠁⠀⠦⢷⠀⠘⡉⠁⡙⠀⠀⠀⠉⠀⠀⠉⠀⣀⠀⠀⠀⠀⠀⠀⣂⣀⠠⠀⠒⡀⠁⠀⢨⠷⠄⠘⠃⠉⠛⠀⠀⠀⠉⠀⠀⠉
⠉⠀⠉⢉⡄⠀⠀⠀⠀⢀⠨⠀⠁⢀⣀⡀⠄⠀⠠⠀⠀⡀⠴⣀⢦⠀⢀⡁⠉⠀⠉⠀⠋⢉⡆⠀⠀⠀⠀⠀⡤⠀⡃⠀⢌⡄⣄⠀⠃⠀⠂⠠⠴⣐⢦⠀⢀⡀⠉
⢉⣑⠈⢛⠄⠀⠀⡠⠊⠈⠐⡈⠃⠀⠖⠀⢀⠂⠀⣀⠖⠐⠒⠋⠺⠀⠰⡃⣀⣄⢢⣄⠨⢋⠖⠀⠀⡀⠊⠈⠀⢀⠃⠐⡔⠀⠀⠀⠀⠀⠔⠐⠒⠉⡳⠁⠘⡏⣑
⠀⠀⠀⠀⠀⠀⠪⠀⠀⠀⢀⠘⠀⠀⠔⠀⠰⠀⠨⡀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢋⠐⠀⠀⢀⠜⠀⠀⠆⠂⢀⠀⠈⡀⠀⠀⡠⠈
⠿⣆⡵⣠⠀⠀⠈⠃⠈⠃⠀⠀⠀⠀⠂⠀⠀⠃⠀⠈⠂⠊⠀⡐⡁⣜⢂⠀⣷⢃⡿⢂⠵⣠⠀⠀⠈⠁⠈⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠈⠂⠂⢀⡜⡁⣄⢂⠀⣾
⠒⠛⠈⠁⠀⠀⡀⠂⠁⠀⠁⠢⠀⠀⢀⣀⣃⣀⠀⠀⠤⠀⡀⠒⠢⢔⡚⠁⠙⠐⠓⠛⠋⠇⠀⠀⠀⠀⠉⠉⠁⠢⠀⠀⢀⣀⣂⣀⠀⠀⠤⠄⡈⠖⠢⢔⡺⠀⢋
⠀⠀⢀⠀⠀⠀⡷⢒⣒⢒⡒⢶⡇⠐⡅⠀⠀⢨⠂⢀⠀⠆⠀⠈⡗⠺⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⣶⢒⣂⢒⡒⢶⡆⠐⠍⠀⠀⢨⠂⢰⠀⠀⢐⠈⡷⢮⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠐⠌⠶⡜⣣⠍⠀⠀⢀⠀⠀⠈⠀⠀⠁⠒⠒⠀⠐⢂⠀⠀⢀⠀⠀⠀⠀⣀⡀⠀⠙⠌⠷⠜⣯⠈⠁⠀⠀⠀⠀⡀⠀⠀⠁⠒⠂⠀⠐⠂⠀⠀⢀
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠁⠀⠀⠀⠰⠀⠀⠆⠀⠀⣐⣶⠶⡄⢠⣁⡀⣀⡀⡤⠀⠠⠀⠀⠀⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⣶⠶⡀⠰⣁⠀⣀⣀
⠀⢠⠀⠀⡀⠂⢀⢀⡠⠄⠠⡔⠴⠂⠀⠀⠀⣤⣦⡿⠟⠁⠀⠈⠀⠀⠂⠀⠀⡀⠀⢠⠀⠀⡠⠂⠀⢀⡈⠄⠨⡔⢤⠢⠀⠀⢠⣔⣤⡿⠟⠁⠀⠄⠀⠁
⡔⢢⠊⠀⠀⠀⠀⠀⠌⠒⣋⠶⡴⠒⠀⠀⠈⢊⠀⠀⢀⠄⠊⢀⡀⢈⠁⠂⠉⠀⣔⠠⠈⠁⠀⠀⠁⠀⡌⠒⣟⠧⢴⠒⠀⠀⠀⢎⠀⠀⠀⠠⠊⣀⡀⢈⠁⠂⠉
⢀⡁⠀⣀⠀⠀⠈⠜⠂⠰⠄⢀⠄⠀⠀⢠⡇⠀⠉⠁⠀⠀⠘⠒⠃⡌⣄⠀⠀⠀⢀⡁⠀⣀⠀⠀⠀⠈⠊⠡⠤⢈⠄⠀⠀⢘⡄⠀⠉⠉⠀⠀⠘⠒⠂⡬⣄
⠁⠈⠂⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣨⠯⠇⠀⠀⢀⠀⡸⠂⠸⠀⠀⠠⠁⡀⠃⠰⠀⠀⠀⠀⠈⠀⠀⠀⠀⠨⡀⠀⠀⣨⡿⠅⠀⠀⢠⠀⡯⠂⠒
⠀⠁⠀⠀⠀⠄⣠⢀⡔⠭⣳⠄⠘⠄⣉⣀⢈⡁⠜⠀⠀⠀⠁⠀⠀⠀⠀⢘⠀⠀⠀⠀⢀⠀⠃⠄⣠⢆⡔⢭⣳⢄⠘⠆⣉⣀⣈⡁⠜⠀⠀⠀⠁
⠀⠂⠀⠐⠀⠀⠁⠂⠀⠀⠀⠐⠇⠀⠀⡀⠂⠀⣀⣀⡀⠀⠄⢠⡀⠀⠀⢰⠀⠀⠀⠂⠀⠑⠀⠀⠡⠀⠀⠀⠀⠈⡆⠀⠀⠠⠂⠀⣀⣀⣀⠀⢀⢠⡀
⠀⣀⠀⠀⠀⠀⣎⠀⠄⠀⠀⢈⠀⠀⠲⢿⠀⠘⠅⠀⠜⠀⠀⠀⠀⠀⠀⢀⠀⡀⡀⣀⠀⠀⠀⠀⣂⠀⠄⠐⠀⣀⠀⠀⢰⡷⠀⠸⠁⠀⠘⠀⠀⠀⠀⠀⠈⢀
⣁⣀⣉⣈⡀⠀⠀⠀⠀⠀⡈⣀⣁⢀⣀⣀⣄⠀⠠⠠⠀⣀⡒⣑⢢⡀⢀⣀⣁⣀⣉⣀⣃⣀⡂⠀⠀⠀⠀⢀⡤⣀⣃⢀⣌⣄⣀⠀⠃⠀⠂⣀⠐⣑⣦⡀⢀⣀⣁
⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢈⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡀⠀⠀⠀⡔⠁⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⠀⢠⠊⠀⢀⠎⢀⡀⠤⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡰⠁⣀⠤⠛⠉⣀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠘⡠⠊⠁⢀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢇⠀⣆⠤⠒⠒⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡟⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⣰⣫⢄⠀⠀⣢⠡⠀⣀⡠⠒⠈⠉⠐⠢⡄⠀⠀⠀⠀⠀⢀⣀⣰⠁⠔⠊⢙⠢⡊
⠀⠀⠀⠀⡴⠊⠀⠀⠈⠉⠉⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠘⠀⠀⢀⠔⠊⠀⠀⠀⠑⠺⡌⠂⠁⡈⠖⠒⠒⠠⣀
⠀⠀⠀⢸⠀⠀⠀⡆⠈⡇⡇⢀⣤⠀⠀⠀⢸⠀⠀⠀⠀⢀⠁⡰⠁⠀⠐⢦⣄⠀⠀⠀⢰⠔⠊⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠈⡆⠀⠀⡁⠀⣧⡗⢡⠂⠀⠀⠀⢸⠀⠀⠀⠀⢸⠎⠀⠀⠀⠀⠀⠈⠑⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⢲⢼⡀⠀⡇⢀⠏⢀⠃⠀⠀⠀⠀⢸⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⢣⠑⢄⠀⡎⠀⣼⠀⠀⠀⠀⠀⢸⠀⠀⡐⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⢣⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⢃⠈⢶⠀⠀⠀⡆⠄⠀⠀⠀⢸⠀⡜⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⡄⡰⠁⠀⠣⡀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⣀
⠀⠀⠀⠀⠀⠘⠀⠈⡆⠀⠀⠰⢀⠀⠀⠀⢨⠜⠲⢄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠼⠄⠒⠀⠐⠚⠢⢌⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄
⠀⠀⠀⠀⣀⠠⢇⡠⢦⡠⢄⡀⠏⠀⠀⢀⠎⠀⠀⠀⠀⢀⣀⠤⠔⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠑⢄
⠀⠀⠔⠋⠀⠀⠈⠀⠈⠀⠀⠈⠙⢄⠀⠎⠀⢠⠴⠶⠭⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠬⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠱
⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧
⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠨⣵⡄⠀⠀⠀⠀⠀⠔⠈⠐⠄⠀⠀⠀⠀⠀⡆⠀⠀⢱⠀⠀⢸⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⢆⣀⣀⠆⠀⠀⠀⠀⠀⠈⠂⠒⠁⠀⠀⢸⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠘⢄⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠁⢀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠹⣦⡀
⠀⠀⠉⠢⢍⡂⠄⠀⠀⠀⣀⡤⠂⠁⠀⠀⢀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⡂⠀⠀⠀⢸⢄⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠈⠲⢄⡴⠊⠀⢇⠀⢀⡠⠒⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠂⠒⠄⠀⠀⠀⠈⠊⠁⠀⠀⠀⢸⠀⠑⠢⢀⠀⠀⠀⠉⠓⢀⡤⠒⠁
⣶⣶⡶⠶⣶⣶⣶⣾⣶⣶⣶⣾⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⠔⠂⠈⠉⠀⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣴⠶⣋⢛⢦⡀
⠀⡃⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠃⠘⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠸⠪⠝⣃⡥⢚⡡⠖⠛⢇
⠀⡉⠀⡀⠉⠉⠀⠀⣀⣉⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠘⢈⡀⢈⣉⡩⠤⠒⠉⠀⠀⠀⡜
⠘⠒⠢⠂⠄⠐⠐⠤⠠⢶⠂⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊
⠀⠍⣉⣀⣐⠒⢒⣒⣒⡾⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠂⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠐⠀⠐⠀⠀⢨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⡠⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡔⢪⠔⠒⡶⡄
⠀⠀⠀⠀⡔⠒⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⠐⢉⡉⠀⠁⢑⣻⡇
⠀⠀⠀⢀⠗⢐⠢⡀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡙⠃⠀⠁⡥⠜⠉⠤⠌⢣
⠀⠀⢀⠞⠐⠀⠇⠈⠆⠈⢇⠀⠀⠀⠀⠀⠀⠐⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠒⠒⠒⠒⠒⠒⢺⢁⡤
⠀⢀⠞⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠠⠀⠀⠀⠀⠀⠄⠐⠐
⢀⠚⠁⢪⣹⡠⠮⠒⠛⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠆⠀⠀⠀⣸
⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠈⠒⠋
⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⣠⠴⠊⠽⢣⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⢄⡀
⢀⣴⣋⣀⣀⠀⠠⢥⠤⠤⠤⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢐⡀⠥⠭⠤⢐⠙⢦⡀
⠈⡤⠤⠄⠤⣀⡠⠔⠢⠤⠴⡇⠀⠀⠀⠀⠀⠀⡠⠔⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠖⠁⠀⠀⠀⠀⠀⠈⢺⡇
⠀⠧⠀⢀⣀⣀⣀⣀⣀⣀⠠⠇⠀⠀⠀⠀⠐⣊⣀⣀⠀⠠⠀⠀⠀⠀⠤⢝⠢⠀⠀⠀⠀⠀⠈⠁⠀⠠⠤⠤⠤⠤⠤⠄⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠉⠀⠐
⠀⠀⠀⠀⢀⠆⡐⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣯⡀
⠀⣠⠀⢀⣀⡀⠐⢒⡒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⡄
⠀⠘⡉⠁⠀⠒⠒⠂⠀⣻⠯⣱⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⢀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⢀⡀⠱⣤⢀⣀⣀⡀⣴⢉⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠒⠒⠁⠀⡠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠈⠉⠀⠀⠀⢁⠆⢀
⠘⠠⣤⣤⡤⠤⠤⠤⠤⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄⠂⡀⠈⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⠀⠠⠈⠰⠋
⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠈⠉⠉⠀⠀⠁⠀⠒⠂⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠃⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣀⣀⣀⣠⡶⠾⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣉⣀⣀⣀⣠⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠛⠉⠉⠝⢻⡇⠀⠀⠀⠀⠀⠀⣄⣀⡀⠀⠀⠙⠛⢶⣄⠀⠀⠈⠑⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠰⡇⠀⠀⠠⠙⠿⠷⢶⣄⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⡼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣤⠶⠃⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠷⠛⠉⠀⠀⠀⠀⠀⠀⠈⠛⠾⠶⠶⣶⣶⡶⠶⠶⠟⠛⠉⠉⠀⠀⠀⠀⢀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠉⠁⠀⠁⢰⣿
⠀⠀⠀⠀⠀⠀⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠏⠀⠀⠀⠀⠀⠤⡦
⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣖⣤⣤⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠒⠦⠀⠀⠀⡄⠀⠀⢀⡎⠀⠁⢀⡖⠀⠀⠀⠀⢸⠃
⠀⠀⢸⣶⣤⡀⠀⠀⠀⠀⠀⠉⠛⠒⠳⠶⢢⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠄⠀⠉⠀⠀⠀⣀⡤⠖⠉⠀⢀⣤⢸⡂⠀⠀⡘⠋⠀⠀⠀⠐⣿
⠀⢀⠉⠉⠛⠛⠽⠆⣶⣶⠀⢸⡗⠒⠛⡿⠟⠁⠀⠀⠀⢀⣀⣀⠈⠉⠑⠂⠀⠀⠀⢀⣀⠦⠚⠉⠀⠀⠀⠀⢰⠃⠉⠀⡻⢣⡞⠁⠀⠀⠀⠀⠜⠁
⠀⠈⠻⢿⣶⣤⡄⢀⣀⠀⠀⣾⠂⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠈⠉⠀⠀⣀⡠⠴⠂⠉⠀⠀⠀⠀⠀⠀⠀⢀⣸⡀⠀⠀⢁⡌⠁⠀⠀⠀⢶⣾
⠀⠀⠀⠀⠀⠉⠁⠉⠛⠛⠀⠁⠀⠀⠀⠀⠒⠲⠀⠀⠀⠀⢀⠠⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠛⣇⡄⣴⠉⠀⠀⠀⠀⢠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⣀⣤⡤⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢀⣿⣤⠍⠀⠀⢀⣠⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣀⠄⠂⠈⠀⠉⠉⠓⠶⠤⣀⠀⠀⠀⠀⠀⠀⡾⣿⡁⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣦⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠀⠀⠛⠒⠒⠚⠛⠋
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠠⡄⡀⠀⠀⠀⠸⣿⣿⣿⢷⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠤⠦⡀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠉⠛⠿⣿⣮⣭⡙⠳⢦⣤⠔⠒⠀⠀⢠⣼⠃⠀⠀⠀⠀⠀⠠⡶⠋⠉⠋⠉⠓⣆
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠀⠀⠀⠀⠀⠀⠉⠙⠟⢿⣷⣀⣠⡦⠔⠋⠉⠀⠀⠀⠀⠠⠎⠈⠐⢦⣄⣀⣀⠀⠀⣸⠷⣦⡀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠰⠛⠙⢸⡟⢛⣏⠀⠀⠘⡇
⠀⠀⠀⠑⣤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠁⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡄⣠⠀⠀⠀⠀⠈⡿⠁⠀⠀⢰⠇
⠀⠀⠀⠀⠈⠙⠿⠿⢿⣏⣀⣚⢛⡿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣤⣀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⢻⡄⠀⠀⠀⡀⠑⢤⣴⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠲⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠋⠉⠉⠉⠉⠙⠛⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠟⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠻⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣄⠀⢀⡴⠞⠲⣄⡀⢀⣴⠖⠲⣦⡀⢀⣠⠖⠳⢦⡀⠀⣠⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⠙⠉⠀⠀⠀⠈⠙⠉⠁⠀⠀⠈⠉⠋⠁⠀⠀⠀⠉⠋⠁⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠉⠉⠉⢩⣍⣉⠉⠉⠉⠉⢩⣍⣉⠉⠉⠉⠉⠉⢉⣩⠉⠉⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠉⠙⠓⠶⠶⠒⠛⠋⠙⠓⠶⢤⠴⠋⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠖⢒⣺⠿⠟⠒⠒⠲⠶⣤⣤⠤⠶⣒⣺⡿⠿⠟⠛⠛⠛⠓⠲⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⣩⠟⠉⢀⡤⠞⠉⠀⠀⢀⣠⠴⠚⠉⣁⡤⠖⠋⠁⠀⠀⠀⢀⣤⠴⠚⠋⢉⣉⣉⣭⣭⣙⣶⣤⣀
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠸⣥⡴⠚⠉⠀⠀⠀⠀⠰⢯⡤⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠸⠭⠴⠖⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄
⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⢀⣧⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⡤⠤⣤⡤⢤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⢀⡴⢻⡼⣟⠲⣦⡤⠤⠶⣶⡖⣒⡿⣻⣿⣛⣛⣉⣀⣤⣾⣥⣿⣿⣿⣥⣿⡿⠟⠲⢬⣅⣀⡤⠥⠚⠉⢯⡻⣿⣯⣽⣷⣶⠲⣶⡶⠶⢖⣒⡝⢹⢢
⠀⢸⡀⠀⠙⢮⣉⣁⣀⣠⠴⣟⣛⣓⡮⠕⠋⢈⣉⣁⣤⠤⠤⠬⠭⠭⢭⡽⠶⢦⠤⠤⣤⠤⠤⠤⠤⣤⣤⣄⣉⣓⠻⠽⠿⠽⠟⠋⠙⠒⠶⠶⠖⡫⠎
⠀⢠⣽⣶⠶⠒⣲⣿⡓⠒⠒⠒⠒⠒⢾⣯⠟⢉⡴⠦⣀⣀⣀⣀⠀⣰⠋⣹⢀⣉⣛⣛⠋⠀⠀⠀⢰⠟⡆⠀⠰⡿⠉⠉⠛⠿⠷⠖⠒⢲⡖⠚⡭⢤⡤
⡴⠛⣋⠭⢶⠚⠃⠀⠙⠋⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠁⠀⠉⠉⠀⠀⠉⠉⠛⠓⠚⠋⠈⠛⠛⠉⠉⠉⠉⠉⠉⠉⠙⢳⠶⢭⣉⡵⠋
⠓⠋⠁⠀⠈⠢⣄⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣄⣀⣀⣀⣀⠀⠀⠀⣀⣠⠴⠋⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⢀⡶⠛⠛⠛⠻⡷⠖⠛⠛⠛⣶⡴⠶⢶⡄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠁⠸⡆⠀⡶⠚⠛⢶⡇⠀⠀⠀⠀⣇⠀⠀⠀⠀⣻⠀⠀⠀⣿⠋⠉⠛⠳⡦⠀⠀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⣶⠟⠛⢳⡄⢷⠀⠀⠀⢹⡀⣧⠀⠀⠸⣿⠀⠀⠀⠀⡿⠖⠒⣶⠦⠾⢶⣤⡶⠿⠶⠦⠀⠀⡇⠀⡼⠋⠀⢸⡇
⠀⠀⠀⠀⠀⢿⠀⠀⠀⢻⣼⣇⠀⠀⠀⢷⣿⠀⠀⠀⡿⠶⠒⣆⠐⡄⠀⠀⢹⠀⠀⠘⣻⠀⠀⠀⢨⢠⠶⠿⢿⡇⠀⢀⣼⠁
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠞⠛⠉⠹⡄⠀⣈⣿⣄⠀⠀⡇⠀⠀⢻⠉⠉⠉⣷⠘⠀⠀⠀⣿⠀⠀⠀⠘⢸⠀⠀⠀⠁⠀⡿⠉⠛⢶⡄
⠀⠀⠀⠀⢀⣀⢻⡀⢨⠃⠀⠀⠀⣇⡟⠉⠉⢹⡇⠀⡇⠀⠀⢸⠀⠀⠀⡇⠀⡄⠀⠀⣿⠀⠀⠀⠀⣜⠀⠀⠀⠀⢰⡇⠀⠀⣸⠃
⠀⠀⢠⡾⠋⠹⣎⣧⢸⠀⠀⠀⠀⣿⠁⠀⠀⢸⣇⡴⠦⠴⡄⢸⡄⠀⠀⡇⠘⡇⠀⠀⢸⡄⠀⠀⠀⣿⠀⠀⠀⠀⢰⠀⠀⢠⡇
⠀⠀⠘⣇⠀⠀⢿⣿⣼⣦⠀⠀⠀⣿⠀⠀⠀⢸⣿⠀⠀⠀⣇⣸⣧⡄⠀⡇⠀⡇⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⢀⠀⡟⠀⠀⣾
⠀⠀⠀⢻⡀⠀⢸⡆⠀⠈⡇⠀⡖⠛⠻⠀⠀⢸⡏⠀⠀⠀⡏⠀⢀⡇⠀⡇⠀⣇⠀⠀⠸⡇⠀⠀⠀⣿⠀⠀⢸⢰⡇⠀⢰⣇⣀⣀⣀
⠀⠀⠀⠘⣇⠀⠀⣧⠀⠀⢁⠀⡇⠀⠀⡀⠀⢸⡇⠀⠀⠀⠁⠀⢀⠀⠀⡇⠀⣿⠀⠀⠀⣷⠀⠀⠀⣿⠀⠀⢸⣼⠀⠀⣞⣉⣩⠝⠛
⠀⠀⠀⠀⢹⡄⠀⢹⡄⠀⢸⠀⡇⠀⠀⡇⠀⢸⡇⠀⠀⢸⠀⠀⠘⠀⠀⡇⢀⣹⣀⣀⣀⣿⣀⣠⣤⣧⣤⣤⣼⡧⠶⠚⠉⠁⠀⠀⢀
⣤⠶⠶⠶⠾⠗⠒⠚⠓⡆⠈⡄⡇⠀⠀⡇⠀⢸⡇⠀⠀⢸⠀⠀⠀⡗⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢷⡇⠀⠀⡇⠀⢸⡇⠀⠀⢸⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⡜
⠈⣧⠀⠀⠀⠄⠀⠀⠀⢹⠀⢸⡇⠀⠀⡇⠀⢸⡇⠀⠀⢸⡇⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⡇
⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⢳⣈⡇⠀⠀⣧⠀⢸⡅⠀⠀⢸⡇⣠⠏⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣄⣿⡀⢸⡇⢀⣀⡼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡞⣿
⠀⠀⣿⠉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⢀⡴⠋⠀⡿
⠀⠀⢻⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠞⠀⠀⣠⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠑⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢰⣇⠀⠀⡴⢻⡇
⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠸⡟⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡸⠁⢀⡾⠁⢸⠇
⠀⠀⠀⣿⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣿⠀⠀⠀⠈⠉⠓⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡜⠀⠀⢈⡇⠀⣸
⠀⠀⠀⢸⡆⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⣀⠀⠀⠀⠀⠀⣂⠈⠀⠀⢠⠟⠀⠀⣿
⠀⠀⠀⠘⣇⠀⠀⠀⠀⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⡏⠀⠀⠀⠁⠀⠀⢠⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠁⠀⢠⠂⠀⠀⠀⢸⠃
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣀⠀⢻⠈⠉⠛⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢠⠏⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⠇⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⣀⠀⠀⠀⠀⡆⢠⠋⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⣷⠁⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢀⣤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠳⠶⠶⠶⢤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣾⠾⠋
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣀⣁⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⠥⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠤⢴⠀⡦⠤⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠂⡀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢀⠰⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠨⠉⠉⠁⠒⣒⣒⣒⠒⠀⠉⠉⠁⠀⠂⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠀⠀⢀⡼⢷⡀⠀⠀⠀⢀⡼⢷⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⢁⣴⣶⣦⡈⠁⠈⠁⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠀⠙⠀⠐⠈⠉⠁⠀⠤⠀⠀⠀⠀⠀⠘⣿⡟⢻⠃⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢄⠁⠀⠁⣀⠀⠀⠡⠀⠀⠀⢀⡌⠀⠀⡈⠀⠁⠀⠄⠈⠓⠃⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠉⠂⠀⠀⢢⠀⠀⠘⠁⠀⢠⠒⢠⠀⢀⠠⠐⠀⠠⠀⠂⠀⠀⠀⠈⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠘⠀⠀⢸⡆⠀⠀⠀⠀⠆⠀⠀⢀⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⢠⣶⡄⠀⠀⢠⣶⡄⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠘⠄⣀⠀⠀⠀⠀⠀⠀⢀⡀⠜⠀⠁⠀⠀⠀⠀⠈⠛⢡⣶⣶⡌⠛⠁⠀⠀⠀⠀⠀⠘⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣈⠉⠀⠈⠁⢁⣀⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠉⠃⢀⡀⠀⠋⠈⠉⠀⣐⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠂⠁⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠄⠀⠀⠀⠀⠄⠱⠄⠀⠀⠀⠀⠀⠠⣤⠒⠉⠉⠉⠁⠀⠀⣀⠀⠄⢺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⢀⠃⠀⠀⠑⠚⠉⠁⠀⠀⠉⠀⠙⠀⠘⠋⠁⠀⠀⠀⢰⡆⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠈⠉⠁⠨⠍⠁⠉⠉⠉⠉⠉⡉⠉⢉⠉⠉⠉⠉⠉⠻⠄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠈⠐⠀⠀⠂⠀⠉⠉⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠒⠂⠈⠁⠀⠀⠀⠀⠀⠁⠀⠒⠒⠒⠂⠀⠒⠒⠒⠒⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⣀⣀⡀⢼⢸⠄⢀⣀⣀
⠀⡠⠔⠒⠒⠛⠤⣀⠤⠚⠚⠒⠤⡀⣠⠝⠒⠒⠢⢄⡀
⡜⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠑⡄
⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡠⠗⠊⠉⠉⠒⢤⡀
⢡⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡠⢔⣾⣦⠀⠀⢀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣄
⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣇⠔⠁⠀⢟⡫⠜⠀⠀⠈⠁⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣼⠖⠢
⠀⡆⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡿⡄⠀⠀⠀⢠⡄⠀⢀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⡗⢢⣴⠃⠀⡰
⠀⠇⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠦⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⡟⠀⡼⠁⣹⠎
⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡏⢢⠀⠀⠀⣄⠀⠀⠘⠀⠀⠀⣀⠤⢒⣍⠉⠑⢦⠀⣴⠋⠀⠞⠠⡎⣨⣇
⠀⠀⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡇⠀⢱⢄⠀⠀⢀⣠⡦⠔⠒⠉⠀⠀⠀⢻⣄⠀⠀⢻⠁⠀⠀⠤⢖⣛⣅⠤⠃
⠀⠀⢇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⠧⢤⡟⠒⠋⠉⠁⠀⢻⡄⠀⠀⠀⣦⠀⠀⠛⠀⠀⢸⠓⠒⠛⠛⠉⠁
⠀⠀⠈⠢⢄⣀⣀⡱⢄⣀⣀⡰⠋⠀⠀⠀⠁⠀⠀⢠⡀⠀⠈⠛⠀⠀⠀⠹⣧⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢄⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⡀⠤⠤⠤⠍⠒⠒⠉
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣤⡤⠶⠶⠶⠛⠛⢻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⠴⠶⠶⠶⠶⠶⠞⠛⠛⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣹⠇
⠀⠀⠀⠀⢀⣤⡴⠶⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣠⡞⠁
⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣴⠾⡋
⠀⠀⢸⠟⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⢀⣴⣿⣴⣿⣁⣤⢶⣆
⠀⠀⣿⠀⠀⠀⠈⠉⠛⠛⠶⠶⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⣠⢾⣿⣡⣾⡿⠋⠀⠰⣿
⠀⠀⠙⠷⠶⢶⣴⣦⣤⣄⣀⠀⠀⠀⠈⠉⠛⠛⠶⠶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⡾⢃⡼⢿⡿⠋⠀⠀⣠⣼⣇
⠀⠀⠀⢀⣀⣀⡻⠶⠾⣿⣉⣹⡷⢦⣤⣤⣤⣀⡀⠀⠀⠀⠉⠉⠛⠳⠶⢦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⣾⣯⡴⢋⡵⠋⠀⢀⣴⣾⠋⢀⣿
⠀⠀⢠⣾⣯⣉⣉⣛⣒⠿⢿⣥⣤⣀⣘⣧⡀⠉⠙⢛⡲⠶⣤⣤⣀⣀⠀⠀⠀⠈⠉⠙⠓⠶⢦⣤⣤⡴⠋⢀⣴⣾⣵⢟⡵⠋⠀⣀⣴⣿⠟⢁⣤⠞⢻⡇
⠀⠀⣿⠀⠀⠉⠉⠉⠉⠛⠓⠶⠶⣭⣭⣍⣉⣛⡿⢿⣿⣦⣀⣀⣉⡉⠛⠳⠶⣤⣤⣀⣀⠀⠀⠀⢻⠄⣠⣿⡿⢛⡵⠋⠀⣠⡞⢉⣀⣤⠾⢿⡷⠚⠻⡧
⠀⠀⣿⣟⠳⠶⠶⢦⣄⣀⣀⣀⡀⠀⠀⠀⠉⠉⠛⠛⠳⠾⠯⣭⣍⣙⣦⠀⠀⠀⠀⠉⠉⣿⠷⢦⣼⣿⠿⣻⡴⠋⢀⣤⣾⠏⣿⣋⣭⠟⠛⠛⠁⠀⣰⡗
⠀⠸⣧⠙⠳⠶⣤⣤⣈⣉⣉⣉⣽⡿⠿⠟⠛⣶⡶⣤⣀⣀⣀⠀⠉⠉⠙⢷⣄⣀⣀⣴⣾⣙⣛⣛⣩⡴⠟⠉⠀⢠⣿⡿⠋⣴⠋⠙⣷⠀⠀⠀⣠⡴⠋
⠀⠀⣿⠻⣦⣤⣤⣀⣈⣉⣉⣀⣀⣤⣤⠶⠟⠻⣆⠈⠻⢧⣍⠻⠟⠳⣦⣄⣉⡉⠉⠀⠈⠉⠉⠉⠁⠀⠀⣠⠾⠋⣁⣤⣾⣥⠶⠟⠋⢀⣤⠞⠋
⠀⠀⢻⡆⠀⠀⠀⠈⠙⢿⣍⡉⠁⠀⠀⠀⠀⠀⠈⠳⣤⡀⠉⠛⠶⣦⣤⣀⣉⣙⠛⢛⣛⣶⣤⣤⣀⣠⣾⡷⠶⠛⢁⣿⠁⠀⠀⢀⣴⠟⠁
⠀⠀⠘⢷⣄⡀⠀⠀⠀⠀⠈⠙⠳⠶⠶⠶⠶⠶⠶⠶⠾⠿⢦⣤⣤⣄⣀⣈⠉⠉⠉⠉⢉⣁⣤⡼⠟⠁⠀⠀⢀⣴⠞⠁⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠉⠙⠳⠶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣍⣉⣙⣛⣛⡛⠛⠉⠁⠀⠀⠀⠀⢀⣾⠁⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠳⣤⣀⣀⣀⣤⡾⠃⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠷⠶⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠉⠁⢀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠳⠶⠶⠶⢦⣄⣨⣧⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉








⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣉⣙⣋⣛⣉⣛⣉⣀⣉⣙⣿⣋⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣯⣤⣭⣭⣭⣭⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽

⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠀⣤⡄⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠀⡤⡄
⠀⠀⠀⠈⠳⠄⣀⡀⣀⡴⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠁⠀⠀⠀⠀⠈⠳⠄⣀⡀⣀⡴⠂⠀⠀⠀⠀⠀⠈⠈⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠸⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⡿⠇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⢽⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⢿⠟
⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡆
⠻⠋⠀⠀⠀⠀⢀⡠⠐⢊⣱⡀⠀⠀⠀⠀⣀⡾⠤⣄⠀⠀⠻⠋⠀⠀⠀⠀⠀⣠⠖⠈⣱⡀⠀⠀⠀⢀⣠⡾⠤⣄
⠀⠀⠀⠀⠀⢀⡛⠀⠤⠊⠉⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢀⠠⠂⠉⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠾

⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠀⣤⡄⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠀⡤⡄
⠀⠀⠀⠈⠳⠄⣀⡀⣀⡴⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠀⠀⠀⠀⠈⠳⠄⣀⡀⣀⡤⠂⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠸⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⡿⠇⠀⠀⠘⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣤⣄
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟
⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡆
⠻⠋⠀⠀⠀⠀⠀⡠⠴⣚⣵⡀⠀⠀⠀⢀⣠⡾⠤⣄⠀⠀⠳⠏⠀⠀⠀⠀⠀⣠⠔⢘⣱⡀⠀⠀⠀⢀⣠⡾⠤⣄
⠀⠀⠀⠀⠀⢀⠛⡁⠐⠂⠉⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠁⠤⠊⠉⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣠⠴⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡸⠁⡀⠙⣆⣀⢸⠁⢄⠀⢸⡠⠔⠒⢄⡀⠀⠀⢀⡤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢀⠈⢱⣰⠁⠠⠁⡜⢉⠀⠙⡆⠀⠀⢸⡇⠀⠤⡴⠗⠒⢤⡏⠀⡀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠃⠀⠀⢀⠇⠀⠁⢀⠃⠘⠀⢸⡇⠀⠀⡇⠐⠆⢀⡇⠀⣠⢤⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠉⡉⢦⢸⠀⢠⠀⢸⣀⡤⣄⣾⠖⠚⠳⣼⠓⢶⡀⢸⣀⣤⣀⠇⠀⠀⢸⡇⠏⠠⡤⠈⣇⠔⠒⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠉⠂⠈⢿⠀⢨⠀⢸⠁⣀⠀⡟⠀⠐⠀⡼⢀⠀⡅⡎⠠⡀⠈⡇⠀⠀⢸⡧⠦⣄⡃⠀⣿⠀⠱⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠈⢇⠸⠀⡆⠀⡀⣸⠃⢀⠀⢰⠁⠐⠀⣿⠃⠀⠀⢰⣅⡤⣄⡜⠀⡄⠈⡇⢀⠇⢀⠁⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠄⠈⣷⢰⠁⠀⢡⣏⡴⠋⠑⢿⠀⡄⠀⡿⠀⠰⠀⡼⠀⠤⠈⡗⢀⠁⢰⡇⡜⠀⠄⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠤⠼⢤⣬⣮⣀⣈⣾⢸⠁⠢⠀⠘⢠⠖⠚⠳⢤⣃⡤⠷⡀⡆⢀⡇⠂⢀⡏⡸⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢤⣀⣀⣀⡀⠹⡇⢸⠀⢨⠀⢈⢸⠀⠑⠁⢸⠃⢄⡀⢹⠀⢸⣁⣀⣼⣰⡃⢀⠂⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠹⣼⠀⠀⠀⡯⡘⠀⠀⠀⡟⠀⠀⠀⡎⠀⡼⠁⣀⣀⣉⠉⠉⠉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡀⠈⠲⣄⠀⠗⡇⠀⠀⢰⠁⠀⠁⢰⡥⠊⠀⠀⠀⠈⠉⠉⠉⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠙⠛⠷⠤⠤⠾⠴⠖⠚⠉⢀⡄⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣀⣀⣀⣀⣀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⣠⣎⣉⣳⡀⠀⠀⠀⠀⡤⡤⠒⡶⣠⠒⡦⡀
⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠉⢆⠀⠀⠀⠀⢠⠮⠭⠭⠭⠽⠄⠀⠀⠀⣸⠥⠄⠬⠦⠨⣆⠀⠀⠀⣜⠁⣼⡙⣧⢎⢫⣾
⠀⠀⠀⢠⡗⡒⡒⢖⠠⣒⡲⣶⠾⡀⠀⠀⠀⠘⡎⠉⠉⠉⢹⠁⠀⠀⠀⠙⣟⢻⡭⡛⢹⠁⠀⠀⠀⢹⠙⠓⠓⠚⠚⢉⡇
⠀⠀⠀⠀⢹⠒⠾⡉⣘⢿⠓⠞⡟⠀⠀⠀⠀⠀⢣⠀⠀⠀⡌⠀⠀⠀⠀⠀⠘⡟⢤⣺⠃⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠉⠁⠘⠳⣰⠞⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠸⡁⡝⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠄⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢀⡤⢒⣂⡉⣐⠲⡄⣠⢤⠀⠀⠀⠀⠀⣀⠤⢤⠒⠢⡄⠤⡀⠀⠀⢀⡠⠔⠒⠒⠠⢄⠀⠀⠀⠀⠀⢀⠤⠒⠢⢄
⠀⠀⠀⢠⢋⠖⠧⠎⢀⡠⡫⠞⠹⡆⠇⠀⠀⢠⠞⠁⠀⠀⠣⡀⢣⣀⣈⠆⠀⣎⣀⣀⣀⣀⣀⣠⡕⠀⠀⠀⢠⠋⠀⠀⠀⠀⢣
⠀⠀⠀⢸⠈⠆⠏⠋⠻⠒⡿⢭⢅⠙⠂⠀⠀⡜⠣⡀⠀⠀⢀⡝⠁⠀⠀⠀⠀⠈⡄⢠⠈⡄⠰⢠⠁⠀⠀⠀⠸⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⢆⠳⢖⢐⢢⣀⡰⢋⡞⠀⠀⠀⠀⡗⢄⣈⡶⠒⠁⠀⠀⠀⠀⠀⠀⠀⢡⣘⠀⢃⣃⠎⠀⠀⠀⠀⡼⢑⣤⠴⠊
⠀⠀⠀⠀⠀⠑⠢⠤⠭⠤⠒⠋⠀⠀⠀⠀⠀⢇⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠸⢭⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠠⠄⠀⠀⠀⠀⠀⠀⠀⣔⣒⣢⢠⡆⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⣴⢖⣂⠴⡒⣒⣄⠀⠀⠀⠀⠀⡤⠤⠤⠧⠧⠤⣄⣀⡀⠀⠀⠀⢸⠀⣇⠾⠼⠄⠀⠀⠀⢀⡔⡢⣄⡠⢚⠦⡀
⠀⠀⠀⠀⡎⡡⠒⠉⠒⠒⠒⢝⢦⠀⠀⠀⠀⢧⠀⠀⠀⠀⢀⣯⣗⠅⠀⠀⠀⡸⠀⡧⠋⠈⠣⡄⠀⢠⠊⠀⢱⠈⢳⠸⡄⠈⠆
⠀⠀⠀⢸⡴⠁⠀⠀⠀⠀⠀⠈⢿⠂⠀⠠⡆⠀⠷⠤⠄⠖⠋⠃⡲⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⢸⠀⠸⡀⢀⠇⠀⢸⠀⡇⠀⡄
⠀⠀⠀⠸⠤⠤⠤⠀⠒⠀⠀⠤⠊⠀⠀⠀⠈⠑⠒⠒⠒⠒⠂⠉⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⢸⠀⠀⠑⢤⣃⠴⠛⢄⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠣⠤⠤⠄⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣄⡀⠀⠀⠀⠀⠠⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣀
⠀⠀⠀⠀⠀⠀⣀⠀⣞⣵⣵⠗⠺⡄⠀⠀⠀⢠⠃⠘⡀⠀⠀⠀⠀⠀⠀⣠⠊⠱⢼⢌⢷⠀⠀⠀⣠⣀⡠⠤⣄⡀⢀⣀⣀⡀
⠀⠀⠀⢰⣊⠭⣔⡺⣽⠝⠁⠀⠀⡇⠀⠀⠀⡞⣚⠓⠙⡆⠀⠀⠀⠀⣴⠥⠔⠚⠉⢉⡏⠀⠀⢸⠀⠘⠀⣀⠈⠀⠀⠋⠀⢹
⠀⠀⠀⢎⣪⠛⠊⠉⠀⠀⠀⣠⠎⠀⠀⠀⠀⠹⠀⡇⢰⠃⠀⠀⡠⠊⠀⠀⠀⠀⡠⠋⠀⠀⠀⣞⡋⢛⡓⠒⡞⠉⣖⡛⢳⣋⡢
⠀⠀⠀⠈⠡⡀⠀⢀⣀⠤⠊⠁⠀⠀⠀⠀⠀⠸⠋⠁⠸⡄⠀⠀⠣⢄⡀⠀⠀⡔⠁⠀⠀⠀⠀⠘⠬⠅⠈⠫⠬⠍⠤⠬⠥⠜
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⡄⠠⠃⠀⠀⠀⠀⠈⠢⠞
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠏⠉⠙⠃⠐⠀⠀⠂⠀⢀⠉⠉⢉⠓⡲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡚⠉⠀⠂⠀⠀⠀⠐⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⢒⡫⣚⠄⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢏⢏⠉⠑⢒⡲⡤⠤⠤⢤⣄⣄⣀⣀⣀⣀⣀⠤⣤⣤⠤⢤⣶⣒⣪⣭⣋⠡⠭⠍⠓⠉⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠪⢷⣮⣭⣥⣤⣽⣿⠶⠿⠟⢻⡙⠳⠤⠤⠤⠤⠷⢄⣀⣉⣀⣁⣀⣀⣠⡤⠤⠴⠒⠚⠉⣇
⠀⠀⠀⠀⠀⠀⣀⠀⢳⠚⠉⠉⠉⠉⠓⠺⢖⡢⢄⡀⠀⠀⠈⠙⠒⠒⠒⠒⠚⠉⠉⠉⢀⣄⣐⣂⣐⣒⣒⣒⣒⣂⣀⣸
⠀⠀⠀⠀⠀⠀⡏⠉⠺⣄⠀⠀⠀⠀⠀⠀⠀⠉⠢⣍⠢⡀⠀⠀⠀⣀⠠⣀⡤⠔⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢥
⠀⠀⠀⠀⠀⠀⣹⠄⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡘⢄⡠⢊⡵⠊⠁⠀⠀⠀⠐⠊⢀⣉⣁⠔⠒⠲⠤⣀⡠⠇⠈⡇
⠀⠀⠀⠀⠀⠰⠧⠤⢤⡀⠈⠳⠤⢶⣤⣤⣤⣀⡀⠀⣀⠳⢤⠔⠋⠀⢀⣀⡤⢄⡀⣠⠞⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡧⢤⡀⠀⠀⠀⠀⠀⢀⣉⠉⠉⠉⠉⠉⠙⢋⣉⡴⠢⣄⣩⣀⣀⢀⣠⠖⠒⠤⢤⠤⠤⠤⢤⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠓⠤⠖⠒⠦⠔⠋⠀⠉⠙⠒⠒⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠴⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣿⣿⠟⣰⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡰⠿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣽⣿⡟⠛⠛⡁⣴⣶⠋⣀⣀⣈⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⣼⣿⡏⣉⡔⠀⣾⣿⣿⣷⣷⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣴⡟⢺⠟⠟⡀⢀⣧⣌⢡⣼⢟⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡗⠈⢸⠃⠀⢀⣼⣿⣿⠿⢿⣿⣿⣿⣿⡿⣿⣿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣾⣁⠖⠠⣶⠶⣾⣿⡿⠋⣴⣇⠻⣿⣥⣤⣶⡀⠁⣀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠴⣿⣷⣷⠦⠀⢡⣦⡺⣿⡇⣸⣿⣿⣿⣾⣿⣿⠏⢁⡀⠀⠘⠃⠀⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠁⠀⠈⠙⣶⣄⢀⡀⣀⠀⢀⠠⠏⠂⠀⣶⣦⣽⣿⠉⠙⠛⠛⠿⠿⠿⠿⢷⡋⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠂⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⢀⢼⣿⣯⣾⣥⡶⠟⠛⠀⠈⢳⣿⣿⣿⣿⡿⢾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣼⣾⣿⡿⠉⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣶⡄⠀⣀
⠀⠀⠀⠀⠀⢀⡀⠀⢼⣿⣿⣷⣤⣶⣶⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣻⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣄⡀
⠀⠀⠀⠀⠐⠁⠀⠁⠀⠈⠛⢿⣿⣿⣿⣟⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠛⠻⢿⣿⣿⣿⣿⣿⡿⠇
⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠂

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠁⠀⠁⠀⠀⢀⠠⠤⠀⠀⠀⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⢀⠤⡀⢤⠰⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠦⠤⠐⠀⠈⠀⠠⠀⡀⣤⠀⠤⢤⡌⠛⠂⠀⠤⠆⠉⠉⠁⠠⠤⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠂⠀⠀⠀⠀⠀⣀⣡⡒⠦⠤
⠀⠂⠀⠀⠢⠄⠀⠀⠀⠄⠀⠀⠀⡀⠞⠀⠀⠀⠆⠀⠀⠀⠈⠀⠀⠀⠀⢀⡠⠘⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁
⠀⠀⠀⠐⠀⠀⠀⢀⣀⠀⠠⠄⠊⠁⠀⠀⠀⠀⠀⠁⠒⠦⢀⡀⢀⡤⢊⠡⠀⠀⠀⠀⢠⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠔⠈⠀⠀⠀⠂⠄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠠⠥⠖⠁⠀⠀⠀⠀⠀⠸⡄⠃⠀⠄⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⡤⠄⠤⠀⢤⠄⠀⢂⠀⡰
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠉⠀⠀⠀⡆⠀⠀⠄⠂⢀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠐⠄⠃⡤⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠌⠀⢀⠀⠘⠀⠐⠄⠀⠀⠁⠀⠁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠑
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⡀⠀⠀⠀⠀⠀⠀⡐⠁⢠⡕⠁⠀⠀⠀⠀⢠⡄⠀⠀⠀⠇
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⣀⠂⢀⠀⠙⠂⠀⡀⠀⠀⠀⠑⢧⠘⠀⠀⠀⠀⠀⠀⠐⢁⠤⠀⠀⠘⠀⠠⢀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠄⣀⠀⠈⠀⠀⠀⠀⠢⠤⠀⠈⠀⠂⠈⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠐⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠
⠀⠀⠀⠈⠠⢌⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠁⠀⡄⠀⠊⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠦⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⢀⠀⣀⢀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠘⠲⡀⠶⠄⠦⠐⠃⠀⠀⡀⠀⢠⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢀⠁⠤⠄⠀⠀⠀⠤⠄⠀⢀⡀⠀⢀⠠⠐⠠⠀⠀⠀⠠⠄⠀⠀⢀⠂
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⣁⡀⠠⠄⠄⠀⠈⠠⠄⠈⠀⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠀⠀⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⠀⠠⢤⠄⠙⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⠀⠀⠠⠤⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠀⠀⠀⠀⠀⣀⠀⠀⠀⢰⠀⠀⠨⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠈⠉⠉⠀⠦⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠐⠖⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠛⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠄⠀⠀⠀⠀⠀⠐⠢⠀⠀⠀⠐⠈⠁⠀⠂⠀⠀⠀⠀⠐⠒⠈⣀⣁⠀⠀⠀⡁⠀⠀⠀⠀⠃
⢀⠤⢄⡀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠂⢀⠀⠀⢀⠀⠀⠐⠢⠀⠀⠀⠀⠀⡄
⡇⠀⠀⠈⢂⠘⠢⠄⠀⠠⠒⠀⠈⡠⠀⠀⢀⡄⠆⠆⠀⠙⣂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠰⠀⠂⠀⠀⠀⠀⠁⠂
⠀⢀⠀⠀⠀⠱⡀⠀⠄⠒⠀⠀⢰⠁⠀⢰⠑⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⢂⠈⠀⠀⠀⠀⣀⡀⢀⣀⠀⠀⠀⠊
⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣀⠀⢆⣀⣀⡀⠀⠂⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠥⠄⠀⠀⠀⠀⡀⠀⠀⠀⠄⠐⠈⠉⠉⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠁⢀⠀⠀⠀⠠⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠓⢠⠄⠀⠀⣤⠚⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠐⠢⠄⡈⠣⡙⠃⠀⠘
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠔⠒⣉⡐⠒⠤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⣠⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⣤
⠀⠂⠀⠀⠀⡀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⡀⠁⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠶⠾⡄⠀⠁⠀⢂⠐⠃⠐⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉
⠀⠀⠀⠀⠑⠀⠈⣉⠲⠀⠀⠀⠀⠀⠀⢀⡉⠀⠭⠭⣝⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠲⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣑⣤⣤⡤⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠶⡄⠀⢸⠋⢻⠀⢰⠖⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⣿⠀⣾⠀⣿⣀⣸⠀⣿⣤⣤⡄⢠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⣷⠀⢸⠛⠛⡆⣿⠉⠙⣧⣿⡀⠀⣇⣸⠀⣸⠧⣄⠀⠀⣰⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢾⡀⢸⡆⢸⡆⠀⡿⢿⠀⢸⡇⠉⣿⢸⡏⢹⣇⡇⢠⡏⡞⠚⣧⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⣇⠈⣇⠸⡇⠀⡇⢸⡆⢸⣅⡀⡟⢸⠀⣼⢙⡇⣼⠻⡇⢠⠏⢠⠟⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢻⠀⢻⠀⣇⠀⡇⢸⡇⣸⢸⡇⡇⣿⢠⡇⣸⢡⡇⢰⢣⡏⣠⢯⠾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣘⣇⠸⡇⢿⠀⣇⢸⡇⡿⢸⢱⡇⣯⣼⢀⡏⣸⢁⡏⡾⣰⣿⢋⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠙⠛⠓⠻⠾⢧⡇⣿⢸⢸⠇⣏⣸⢃⡇⣼⣼⢡⡿⢡⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠈⠛⢧⣼⣾⡼⠏⠉⠛⠳⠿⢧⣿⣵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠈⠉⠛⠓⠲⠶⠤⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠛⠲⠶⢤⣄⣀⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠓⠒⠒⠒⠒⠒⠒⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠲⠶⠶⠤⣤⣤⣴⠏





⠀⠀⡀⠀⠀⢀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣿⣿⠿⠻⡿⠛⠿⢿⡿⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣤⠃⠘⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⣴⠃⠐⠀⢠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠑⠀⠝⢱⠀⠼⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠍⠱⠀⠼⢉⡀
⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⡀⠀⠀⠀⠀⡴⠋⡏⡩⠦⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠉⠀⠐⠀⠀⠀⡴⠫⡎
⠙⢣⡴⠀⠀⠔⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠆⠅⠜⢃⡶⠀⠀⠔⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠄
⠀⠀⠀⠀⠀⠐⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠰⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠰⠤⠒
⡄⠀⢀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠀⠀⠐⢷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠐⢷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠖⡼⣿⡆⢊⠀⠀⠀⠌⠄⢉⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣬⣖⣾⣻⡆⠊⠀⠀⠀⠌⠆⢙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠁⠀⣰⠀⠀⠀⠀⠶⢋⠘⠃⢦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡤⠀⠀⠀⠀⠶⠛⠘⠇⢦⡴⠂
⠀⠀⢀⣀⠀⠀⠈⠀⠀⠃⠀⠀⠨⣁⠀⡤⠈⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⣀⠀⠀⠈⠀⠀⠃⠀⠀⠈⣀⠂⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢉⠀⠁⠀⠀⠀⠀⠀⠀⠚⠀⠈⠀⠀⡠⠦⡴⠐⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⡁⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡠⠢⡤⠀⠀⠀⠀⠆
⠀⠀⠈⠛⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠒⠖⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠒⠆⠀⠀⠉⠛⠃
⠀⠀⠀⠀⢀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂
⠀⠀⠀⢀⠉⡰⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⡰⠉⠆
⠀⠀⠀⠀⡶⠃⠘⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⡶⠃⠠⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠜⠹⠀⠼⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠱⠀⠍⠹⠀⠨⢡⡀
⠦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠐⠀⠀⠀⣴⠁⡏⠩⡦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠉⠀⠐⠀⠀⠀⡰⠉⡏
⠙⡃⡶⠀⠀⠔⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⠔⠁⠜⠃⡴⠀⠀⠔⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆
⠀⠀⠀⠀⠀⠐⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠐⡤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠒
⡀⠀⢀⠀⠀⠀⠀⠀⢀⠀⢀⣀⠀⠀⠐⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⢀⠀⢀⣀⠀⠀⠐⠷⠆
⣗⠺⣻⡆⢂⠀⠀⠀⠌⠂⢉⠿⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡷⣊⣖⢾⣹⡖⠊⠀⠀⠀⠈⠂⢉⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠁⠀⣤⠀⠀⠀⠀⠖⢋⠘⠃⢦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡴⠀⠀⠀⠀⠷⢛⠘⠃⢢⠴
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠃⠀⠀⠈⣁⠐⠤⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⣀⠀⠀⠈⠀⠀⠃⠀⠀⠈⣁⠂⠤⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢉⠀⠁⠀⠀⠀⠀⠀⠀⠚⠀⠉⠀⠀⡰⠦⠶⡀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠁⠀⠀⠀⠀⠀⠀⠚⠀⠉⠀⠀⡤⠲⡴⠐⠀⠀⠀⠂
⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠒⠆⠈⠀⠉⠛⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠆⠀⠀⠉⠛⠃⠀⠀⢀
⠀⠀⠀⠀⢀⠀⡠⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠅⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠈⠉⠰⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠉⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠃⠀⠊⠀⠀⠈⠀⠐⠀⠓⠀⠀⠀⠂⠐⠀⠀⠀⠐⠈⠒⠒⠀⠁⠁⠘⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠊⠉⠉⠀⠀⠀⠈⠉⠉⠐⠒⠀⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⡠⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠈⢉⡀
⠀⠀⠀⠀⣠⠾⣅⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣰⠒⢰⠖⠋⠀⣠⢾⠃
⠀⠀⠀⢰⣇⠀⠙⣌⠳⣦⡀⠀⣀⢴⡾⢉⠛⠲⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⢶⠗⠒⡷⠒⣳⠿⣷⡟
⠀⠀⠀⠀⠛⠷⢶⣬⣵⢦⣭⣟⡋⠀⠤⣤⣷⡀⠘⡏⠓⠒⠒⠲⣤⣤⣠⠞⣹⠃⠀⡀⠁⢀⡴⠣⡎⢉⡴⣘⡅
⠀⠀⠀⠀⠀⠀⢮⠑⠻⡫⢭⡛⠒⣦⢾⡶⠆⣴⣤⡟⠤⠀⠰⣟⣋⡉⣉⡿⠥⠠⠴⠛⣫⣟⣒⢒⣛⠭⠎⠀⢸⡀
⠀⠀⠀⠀⠀⠀⣸⣷⣄⡈⠑⠒⠒⠒⠛⠥⠆⣺⣷⣕⠦⢲⡀⢲⠌⡻⠥⠤⢦⣶⣒⠝⠀⠀⠀⠀⠀⠀⣀⣴⠿⢿⡄
⠀⠀⠀⢀⢴⡞⢷⡹⡿⣿⣗⣦⣄⣀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠐⠒⠀⠀⠀⠀⢀⣀⠠⠤⢒⣾⠿⢤⣀⣼⠷
⠀⠀⠀⣯⡈⢧⣴⠑⡌⠐⠉⠙⠿⢤⡙⢿⣶⣒⣒⣤⣤⣤⡤⠤⠤⠒⢒⣒⣻⠋⠭⢿⡿⢶⡴⠯⠑⠉⠀⣀⣬⠟
⠀⠀⠀⠈⠉⢿⡹⣄⣈⢒⣒⢒⣤⣀⠈⠙⠦⣍⠛⠋⠉⠀⢹⠭⢤⠦⠛⠉⠉⠉⠁⠁⠁⠀⣀⣠⣴⣖⠚⣡⡞
⠀⠀⠀⠀⠀⠀⢷⣀⣩⠞⠉⠉⠻⣙⠒⠶⣅⡢⢍⣒⣤⣰⢏⣀⡵⠋⢉⠉⣑⡷⠳⢦⡖⠉⠡⠋⠀⠈⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠐⠙⠷⣄⡀⠀⢀⡾⠞⠋⠉⠉⠉⠉⠁⠒⠛⠈⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⠂⠀⠤⠄⠤⠀⠀⠀⠀⠀⠄⠤⠄⠀⠒⠂⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠉⠉⠙⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠄⠀⠀⠈⠑⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠄⠀⠰⠀⠀⠀⠉⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠀⠀⢠⠄⠁⠀⡄⠈⡝⠢⣄⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⣀⣠⠤⠤⠶⡿
⠀⠀⠀⠀⣠⠞⡁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠔⠒⠊⠉⠉⠀⡀⠀⢎⠜⠁
⠀⠀⢀⠞⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠖⠒⠋⠉⠁⠀⠀⠀⠀⠄⠀⣊⣠⠴⠗⠚⠻⣄
⠀⠀⣧⣂⡀⠰⢀⣀⣁⣠⠤⠤⠖⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠒⠚⠋⢁⣀⡴⠚⢻⠉⠁
⠀⠀⣧⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⢶⠶⢶⣾⡯⠏⠙⠉⠉⠉⠉⠉⠉⢀⣠⠴⣪⡟
⠀⠀⠓⡶⢬⠤⣄⣀⣀⣀⣠⣤⣴⣒⠋⠉⠅⠈⠂⣀⠞⠀⠠⠀⠀⠀⠀⢀⣀⡤⠴⠒⣋⡡⠴⠚⠁⢣
⠀⠀⠀⡹⢌⣀⡀⠀⠀⠀⠀⠀⡀⠈⣉⣉⣉⣉⣉⣡⠤⠤⠤⣖⣒⣚⠭⠥⠔⠒⠊⠉⠁⠀⠀⠸⢀⠜
⠀⠀⠘⢧⠤⠤⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠴⠚⠁
⠀⠀⠀⢼⢰⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⠖⠊⠉
⠀⠀⠀⠈⠒⠲⠷⠤⠤⠶⠶⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠉⠉⠉⠉⠉⠁

⠀⠀⠀⡀⠀⠀⠁⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢵
⠀⠀⠀⠀⡀⠀⠁⠀⠐⠀⡙⠀⠀⠀⠀⠐⠶⠒⠘⠺⠿⣄⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡴⠂
⠀⠀⠈⠀⠂⠀⠦⠀⠂⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⣤⢠⠈⣁⢀⡀⣈⢉⡀⢀⡀⠀⠀⠀⠙⠒⠂
⠀⠀⠀⠀⠀⠦⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⡇⠀⠈⠛⠴⣦⣰⣀⣤⡀⠧⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠁⠀⢠⡄⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣦⣷⣄⡀⣴⣿⣿⡟⠀⠀⠀⠀⠀⠄⠤⢀⠀⠀⡇⠀⠀⠀⠐⠐⠀⠠⡀
⠀⠀⠀⠀⠀⡀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⢀⡀⠀⢀⠇⠀⢠⠁⠀⣀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠰⠀⠀⠘⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠁⢠⣴⠃⠀⠀⠘⢄⣀⢀⣠⣠⣷⠎
⠀⠀⠀⠀⢀⠀⠀⢠⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠹⣶⣶⣾⡽⢁⡖⠀⠀⠀⠀⠀⣨⠇⠀⠀⠀⠀⠙⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⠥⠖⠋⠀⠀⠀⠀⠀⢸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⡇⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠐⠀⡎⠀⠀⠀⢦⣀⣢⣀⣴⠷⠃⠀⠀⣑⣎⠦⠭⠾⣷⣄⠀⠀⠀⣎⠀⠀⠈⠻⣄⣀⣀⣀⣰⣦⡾⠃
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⢹⡄⠀⠀⢹⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠄⠃⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠐⠤⣤⣤⣼⡷⠟⠋⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣠⡀⣤⠶⡀⠀⠀⠆
⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣮⡉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣄⠀⠀⠃⠀⠀⠀⠀⠀⠉⠁⠘⠀⠇
⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣟⠋⠀⠀⠳⢦⣄⣀⣀⣀⣀⣀⣤⣤⣴⠿⠃
⠀⠀⠀⠀⠀⠀⠈⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠤⠤⠄⠄⠀⡐⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠰⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠤⠐⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⢄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠉⠉⠙⠓⠒⠒⠀⠁⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠉⠛⠉⠙⠒⠲⢤⡀⠀⠀⠀⢀⣸⠤⠔⢢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⠖⠋⠁⠀⠠⠖⠡⠟⡷⣄⡀
⠀⠀⠀⠀⠀⠐⡒⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠰⡄⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄
⠀⠀⠀⠀⠀⡈⠹⠿⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⢟⣹⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⣉⣲⣄⣀⢤⠄
⠀⠀⠀⠀⠀⠀⢁⣮⠆⢽⡍⢿⣖⢶⠶⢶⠒⣒⣚⣹⠉⠞⣳⡽⠉⠈⠢⣀⠀⣀⣤⣴⡶⢛⣟⢛⡛⣉⣁⣤⠞⠃
⠀⠀⠀⠀⠀⠀⠸⢛⠦⢄⣀⠀⠈⠉⠙⡓⠀⣉⠀⠘⠋⡥⢎⡟⢠⢀⠀⠀⣽⠉⢤⡏⠀⡎⢻⠛⢯⣄⡈⢙⣭⠗
⠀⠀⠀⠀⠀⠀⠘⠦⢀⣠⡌⠛⠁⠤⢄⢠⣈⣁⡀⠀⡀⣠⠎⠁⠣⣌⠄⢸⣿⡄⢸⣬⣖⡽⠄⣇⢀⠦⠽⢾⡜
⠀⠀⠀⠀⠀⠀⠐⢄⢀⠈⠉⠁⠈⠀⠈⠁⠉⠉⠉⠁⠈⢀⠄⠁⠀⠈⠢⣥⠙⣧⠈⣟⠬⣉⣁⡟⢴⣟⠓⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠀⠐⠒⠒⠒⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢂⠙⡓⡁⢶⠨⠇⠈⠂⠭⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠱⠘⠏⠇

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢼⣶⣿⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢳⠁⣀⡀⡱⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢹⡧⣟⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⣷⠋⠀⣀⣀⣀⣀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⡚⢛⡛⠻⠟⠛⢓⠔⢻⠀⢸⣿⣿⠿⢟⢃⣤⣾⣿⣿⣿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠰⣇⠎⡠⡀⢃⡄⠀⠈⠀⠈⣃⠈⠅⠀⠀⠠⡏⠁⠀⠀⣤⣴⣶⡶⠷⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠂⠀⡀⠐⢻⠀⠏⠦⠬⠤⠿⠧⠶⠉⠁⣦⡏⠦⠤⠦⣠⣤⣥⣤⣄⠐⣨⠒⠠⠦⢠⠁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⠑⠀⣠⣶⣿⣿⣿⣷⣦⠀⠀⢀⣀⣀⡷⣧⣀⠔⡿⠚⣿⢄⠀⠊⡗⠐⠒⠀⠠⣼⠐⣅⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣿⣿⠀⣠⣵⣿⣿⣿⣷⡜⣿⣴⣾⣿⣿⣿⣿⢩⠏⢰⠁⠀⠈⣿⡂⣤⢣⠶⠿⠄⠀⣿⣏⢉⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⡛⠛⠉⠻⢿⣿⣿⡿⣿⠀⠀⠁⢸⣿⣿⠿⠘⢄⣿⡀⠀⠀⣼⣇⣏⣨⠃⠒⠒⢰⡿⠕⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⢤⣀⣀⠀⠘⠒⠒⠒⠛⠛⠀⠀⠀⠀⠈⠉⠉⠉⢉⣀⣈⠩⠴⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣺⣿⣿⡏⢻⠿⣶⣶⡖⣶⣖⣶⡾⢿⢻⣿⣷⣿⣶⣶⠶⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⡟⢹⠀⠈⠉⢓⢺⡀⠀⢹⣯⣿⣿⣃⡒⠠⢸⡇⠀⠉⠙⢏⣾⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡠⠚⠓⢺⡒⠦⠠⠾⠎⠉⠁⠈⠀⣌⡇⠀⠉⣉⣉⣑⠒⠠⠸⠟⠛⠿⠋⢩⣉⣉⣭⣽⡇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠇⠀⠉⢘⠛⢛⣀⠀⠀⠄⢀⣀⡈⠓⢛⡿⣿⣿⣿⣿⠛⢷⣶⠛⠻⠿⣿⠿⠟⢻⣷⣾⠧⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠠⡀⠀⠀⢨⡾⠥⣀⣀⠀⠀⢀⣀⣨⡆⣸⣼⣿⣿⣿⣿⣷⠈⣿⡃⠀⠀⠠⠀⣀⣇⣀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠭⢍⣛⣉⠓⠤⢀⣀⠈⢉⣁⣀⡽⠿⠛⢿⣿⣿⣿⣿⣿⣾⣋⡈⣁⣂⡿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠒⠒⠲⠶⠶⠶⣦⣤⠦⠤⠉⠑⠒⠒⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠭⠽⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢀⡾⠵⠥⠤⠴⢲⡎⢳⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡛⠿⣤⣤⣤⣤⣤⣀⠢⠭⢛⣩⣿⣷⣦⣄⣀⡀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠂⠀⠐⠒⠒⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⣌⡷⢆⠁⠄⣸⣽⢿⡏⠙⠉⠙⠂⠠⠄⠅⠆
⠀⠀⠀⠘⣠⣀⣠⣀⣀⣀⣬⣅⡩⠕⣖⠲⢦⠤⣤⠄⣤⡞
⠀⠀⠀⠀⣽⢟⣦⣤⣤⣶⣴⣮⣶⣶⣾⡼⡇⠊⠉⡦⣿⡧⠀⠀⠀⢠⠛⠘⠒⠠⣄⠄⢠⠀⡄⢠⢀⡀⣠⡀⢤⠄⠠⠖⠃
⠀⠀⠀⠀⠙⠓⠷⠶⠶⣾⣾⣭⣬⡶⢯⣿⠿⠟⠛⠛⠙⠁⠀⠀⠀⠀⠈⣁⠾⠇⢠⠠⢀⣠⠀⠠⠘⠃⣤⡀⣠⠤⠿
⠀⠀⠀⢀⢤⣄⣀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠪⠄⠤⠀⠶⠀⠀⠀⠀⢉⣉⠀⠀⠀⠀⠀⠀⠈⠐⠛⠛⠉⠙⠑⠒⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠏⠉⠉⠁⠲⠞⡄⠁⠃⠄⠀⠀⠀⠀⠀⠀⠘⠿⣿⣯⣿⣶⣤⣤⣶⣿⣟⣿⣻⣝⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠐⠄⢄⠀⠀⠀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⢻⡉⠙⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠉⣓⠢⢤⣀⣀⣀⡴⢁⣤⡀⠳⣄⠀⠀⠀⠀⢳⡀⠀⠀⣶⢬⡙⠲⣄⡀⠀⠀⠀⡰⠋⠀⠀⢸⠀⠀⠀⢀⡤⠚
⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠈⠐⠢⢀⠀⠠⠚⠉⠙⠣⡈⠳⣄⡀⠀⢀⣷⠀⠀⡿⠀⠙⣆⠢⣙⠦⣄⠜⠀⣠⢆⡴⢁⣀⡤⠞⠉⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠡⡀⠀⢀⣀⠀⠠⢙⠢⡀⢀⣀⡤⢌⣀⠄⠉⠛⠛⢹⡆⠰⣅⢦⠀⠘⡆⠈⢻⡎⠀⣴⢃⣞⣉⠉⠀⠀⠀⠀⢰⠁⠀⢀⡠⠖⢊⡅
⠀⠀⠀⠀⠐⢧⡁⠒⠲⢬⣇⣳⡀⣏⠀⠙⠢⣄⠙⢮⣿⣇⢀⠀⠈⠻⣆⣤⠤⠴⠓⠒⠚⢚⠓⠒⠋⢉⣉⣉⣉⡀⠉⠉⠦⢀⡆⠀⠀⣰⡸⠄⠊⠁⡠⠀⠎
⠀⠀⠀⠀⠀⠀⠻⡄⢣⣀⡈⠙⠳⣌⡳⡕⢄⠈⢦⢑⣽⠿⠷⡕⢤⡀⠘⢦⣤⠤⠦⡔⠉⠉⢱⣒⣊⣭⠭⢿⡏⡤⠴⠊⠁⡼⣡⡤⢚⢁⣠⡤⠚⣉⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠢⣍⠒⠤⣄⡈⠻⡎⢇⠀⢫⡐⠦⠶⣚⢧⣙⣆⣀⣹⡛⢹⠁⢠⢅⠿⣹⣤⠼⠖⠚⠛⠓⠂⡄⣰⡷⢋⡴⣛⢯⡴⡆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⢳⣦⠽⠷⣿⡜⣆⠀⠻⠋⠉⠉⠉⣉⣁⣈⠉⢉⠉⠒⣲⠾⠛⠉⢀⣤⠶⢋⣁⡴⢋⡼⢋⢔⣥⡾⠑⢈⠉⣉⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⡄⢀⢢⡄⠉⠛⢦⢄⣀⣉⣭⣭⡿⠷⣯⣥⣖⡿⠞⠁⢀⣠⣖⡵⠒⠋⠛⠓⠾⢯⣴⣣⠞⢁⡴⢂⣵⣺⣏⣇⣀
⠀⠀⠀⠀⠀⣀⠤⠤⠤⠒⠒⠓⠚⠒⠠⠷⢤⡐⠤⡀⠑⢤⠽⠒⠒⢂⡀⠼⠒⢉⣠⡤⢔⡭⢾⣽⣒⡂⠄⣤⣤⠤⠀⠈⠉⡿⢋⠴⠥⠤⠤⣤⠀⠈⠉⣙⠶
⠀⠀⠀⠀⠹⡠⣬⡒⠤⠀⢀⣀⡤⠽⣿⡿⠟⠛⠢⣌⠷⣤⣑⡾⢛⡡⠴⠒⣀⣩⣤⡖⢻⡴⠯⠤⠽⢽⣏⣲⡶⠲⠶⡶⢒⣷⣭⣗⡈⠙⠶⡶⡤⠒⠉⠁
⠀⠀⠀⠀⠀⠑⠤⠄⠒⢩⢟⣼⠴⠋⢁⣀⠴⣿⠿⢷⡟⢸⠋⠐⢉⣠⡖⠉⠜⣻⡸⡷⠀⢿⠶⠴⠤⣤⣄⣀⠉⠉⠛⠳⢯⣌⡙⠓⢍⠑⠢⠈⠓⢦
⠀⠀⠀⠀⠀⠀⠀⢀⡴⣃⠺⠁⢀⣀⣫⠔⣉⣤⣤⣀⣿⡘⠀⣔⣿⡀⠑⢮⠞⣩⢷⣳⡄⠈⢯⠛⢉⠿⠓⢯⣉⠐⠓⣢⠀⠨⠉⠛⢆⠈⣦⣉⠛⠀⠳⢄
⠀⠀⠀⠀⠀⢀⠔⡡⠊⠀⠀⠀⠀⣀⣠⣎⣁⣒⡒⠶⠤⠤⣭⡽⠻⣿⠀⠈⢿⡗⠚⣳⡙⢄⠀⠙⢁⣠⠖⢉⣼⠳⢔⠮⠥⣄⣁⣀⣀⣱⡏⡼⠙⠓⠒⠒⠃
⠀⠀⠀⠀⡠⠋⠈⠀⠀⠀⠈⠉⠁⠋⠉⠽⢿⡿⠟⠉⣉⣽⠏⠀⠰⢻⡌⡄⠈⢯⡉⠋⡛⢄⠂⠀⡰⢋⣴⢿⣀⠑⠢⢷⠒⠲⠒⠶⠠⠤⠷⠷⠤⣀⣀
⠀⠀⠀⡐⠁⠀⠀⠀⠀⢀⣀⣀⣀⡰⠖⠋⢁⡴⠲⢟⣻⠃⠠⠄⣠⡻⠓⣈⠂⣈⠑⢶⢦⣐⠛⣣⠾⢥⣤⣙⣯⣕⠢⡀⠙⠶⣒⣒⡯⠭⠤⢤⣄⣀⠀⠈⠁⡀
⠀⠀⡐⠀⣀⣤⠴⠚⠛⠉⠉⠩⠯⠤⣄⣚⣁⣤⡾⢯⣽⣲⢦⣋⠟⠁⡰⢫⠷⢬⡤⠚⠓⠪⢽⣓⠤⡀⠈⢹⣤⣈⠳⣌⠢⡀⠉⠫⣍⠉⠻⢲⡖⠀⠉⠀⠉
⠀⠠⡷⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠻⢶⣆⣍⣿⠋⣠⠞⣰⠃⠤⠤⠤⠤⠴⢖⣻⣭⠷⣮⠴⠚⢿⣿⣿⡾⣷⣤⢥⣤⡬⠷⠄⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠁⡰⡃⣰⣛⣋⣓⡞⠚⠚⡛⢃⣒⣀⣢⣤⡷⠾⠟⠛⠉⠉⠲⢍⡓⢤⡑⠂⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠐⡹⣡⠃⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠪⢥⣀⡀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠑⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠓
⣄⣀⣄⣀⣀⣠⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⠄⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠒⠀⠂⠂⠀⠀⠘⠀⠀⠀⠁⠀⠘⠀⠀⠀⠠⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠖⠦⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⠋⠀⠀⠰
⠀⠀⠀⠀⠀⣀⠄⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠙⠀⠀⠈⠁⠀⠀⠄⠀⠀⢀⠀⠠⡀⠀⠀⠀⠀⠠⣰⡄
⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚
⠀⠀⠀⠀⠀⠈⠃⠀⠐⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠂
⠀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠈⠀⠂⠀⠀⠀⠀⡀⠈⠀⠀⡕⢈⠀⠀⠀⠀⠀⡲⠤⣤⡀⢀⣀⠀⠀⠀⢀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠔⠀⠀⠀⠀⠉⢀⡂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠑⠀⠈
⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢜⢣⠑⣄⠀⠀⠀⠀⠀⠀⠀⣀⣈⣿⣟⣃⣠⠤⠄⣤⢤⣤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢂⠀⠠⢀⣀⠀⠀⢰⠆⠀⢸⡀⠀⠀⠘⠂⣀⣠⣆⠀⠀⠀⢉⡀⠈⡩⠋⣡⠖⣀⡼⠛⠁⠀⠾⠛⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠻⢶⣄⢆⣤⠀⠀⠀⠀⠀⢀⡄⣦⠠⠐⠲⠂⠀⠀⢈⣠⠀⢀⣺⠡⢞⣭⡴⠖⠀⣏⠀⠀⠀⣼⡃⠈⣐
⠀⠀⠀⠀⠀⠀⣤⣠⠔⢉⠋⠂⢴⢾⣾⣧⠈⠋⠃⡀⢸⡇⠀⢸⢈⡁⢀⠈⠆⡸⠦⢠⡾⠛⠉⠁⠀⠀⠀⠙⠁⠀⣠⣿⣆⡴⠋⡙⠇⠀⠩⠄
⠀⠀⠀⠀⠀⣴⡾⠧⠀⡼⠷⠀⠀⡄⠻⣿⠄⠀⢠⡇⠀⠀⠀⡺⠈⠁⠁⠂⠤⣅⠀⠀⠁⠀⠀⠀⠀⠀⠀⡠⠇⠐⢛⡛⠛⠛⠺⢤⡉⠁⠴⠀⠀⠠
⠀⠀⠀⠠⣤⡹⢟⣀⡀⠀⠠⣆⠻⣇⠀⠙⢠⠀⠸⡇⠀⡆⠠⢵⡀⠀⡀⠀⡀⢀⠀⠀⣳⠄⠀⢀⣀⡀⡼⠐⠊⢐⠀⢠⠡⠄⠘⠀⠜⢆⢸⡷⠂⣰
⠀⠀⢠⠀⠽⠇⠉⣉⠝⠃⢲⡏⠘⢆⡇⠀⢠⣇⠀⣇⣀⣇⣿⣼⣄⡀⠃⢠⠇⢨⠄⢨⡴⣄⠈⠛⠣⠟⠮⠀⠈⠁⠀⠨⠀⠈⠔⠃⠀⡾⠈⡿⠘⠣⢤⣁
⠀⠀⠇⠀⠀⠀⠀⣿⠄⠀⠘⠱⣴⠆⠀⠀⠀⠀⢠⠜⠋⠁⠀⠈⠑⠚⠒⣤⠐⣈⡁⠀⢠⡋⠙⢁⠀⠐⠶⣣⠀⠀⠀⠀⠀⠀⠀⠀⠰⢓⡞⠁⠀⠀⠀⠈⠃
⠀⠀⣤⡀⠀⠀⠐⠃⠀⢤⡦⠀⠑⣶⠆⡆⠊⡄⣀⠀⢀⣤⡀⢲⠄⠀⠘⢴⠆⠈⠁⠐⡀⢐⠁⢄⠀⣠⡤⠙⠃⢀⣀⣀⣀⣠⡴⠋⠀⠉⠛⠦⠄⠀⠀⣶
⠀⠰⡿⠁⠀⠀⠀⠀⠀⠀⠉⠀⠙⠃⢤⡟⠀⢴⡄⡀⠄⢹⠁⠚⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠞⠀⡄⠀⠀⠀⠀⠙⣿⠿⢭⠁⢀⡤⠀⢸⠄⢠⠀⠰⠛⠂
⠀⠀⡁⠀⠀⠙⠗⠀⢠⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠈⣫⣄⡦⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠰⢿⡀⠀⢀⠀⠠⡔⣆⠈⡇⠀⠀⠀⢰⠀⠀⢀⠟⢠
⠀⢠⡟⠀⡀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠛⡁⠀⠁⠀⡸⣏⣀⣨⣷⣦⣹⣿⠆⠀⠀⠀⠀⠀⠀⠀⣾⡄
⠀⠸⠁⠐⣿⢠⣸⠃⣺⠇⠀⠀⠀⠀⢀⣰⠷⠄⠠⣀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠄⠀⠉⠀⡈⠀⢻⡷⢿⠈⣦⡡⢉⣿⣶⣤⣄⣀⠀⠀⠀⠨⢁⡀
⠀⠀⣀⣀⣈⣩⣇⣀⡟⠀⠀⠀⠀⠿⠋⠁⢀⡀⠑⢾⣿⠄⠀⠀⠀⢀⡀⠀⠰⠺⣆⢀⠀⠰⠂⠀⠏⠀⣿⠟⠻⡖⡿⠚⠎⠏⠉⠙⠛⠿⢿⣷⡶⠒⢎⣀
⠀⠈⡹⠟⠈⠛⠒⠿⣧⠀⠀⣀⡴⢠⡀⠀⠀⠉⠀⠰⣮⠄⠀⠤⣀⣠⡀⠀⠐⠛⢈⣃⠤⠦⣉⢹⠶⠶⢢⣄⡀⠀⠀⠀⠀⠀⢻⣶⣤⣄⣀⠀⡀⠀⣜⡉
⠀⠀⠀⠀⠀⠀⡰⠆⠀⠀⠀⠈⡇⠈⠙⣀⡊⠀⣤⠀⠀⠀⠀⠀⠈⣿⡋⢋⢉⣄⠈⣁⣀⠀⠁⢤⠘⠀⣁⡌⠻⢦⡀⠀⠀⠀⣼⣿⣿⣿⣿⣽⡷⢾⡬
⠀⠀⠀⠀⠀⢰⡇⠾⢠⣄⡠⣾⡇⢀⠀⣹⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⡗⢨⡉⠒⣀⠀⠄⠘⠓⢶⠀⢁⡰⠠⢀⠸⣇⣠⡴⠊⠉⠙⢿⡏⠙⠢⣽⠓⠧⠀⡀
⠀⠀⢍⠒⠀⠈⠀⠀⠘⠉⠳⡴⢷⠘⡃⠈⠃⠈⠁⠀⠀⠀⠀⢦⣄⣼⡀⠛⠠⠤⢈⡃⠤⠙⣂⠂⣘⡃⢠⣴⠶⢋⠈⠻⣄⡀⠀⠀⠀⣥⣀⠠⠘⣤⡖⠙⠃
⠀⠀⣰⡄⠀⢀⡀⣠⡼⠅⠴⠟⢊⡀⠁⢐⡄⠀⠀⠻⠀⠀⡀⠀⠡⠙⠻⠦⡀⠀⠈⠉⠘⠒⠒⠂⠛⠉⠉⠀⡠⠞⢣⣤⣈⠫⠄⠀⠚⠛⠿⣷⣿⠀⠀⠀⢠
⠀⠀⠸⣿⣾⢏⠘⢁⣠⠀⠀⢀⠞⠃⠀⠙⠀⢀⡀⠐⣠⠄⠐⠲⢃⢠⡆⢱⠈⢳⣤⠄⠀⠀⠀⠀⣀⠀⠀⢀⣠⣶⠦⠋⠉⠀⠀⠀⠀⠀⢸⡟⠁⠁⠀⡄
⠀⠀⠀⢹⡏⠀⠀⠘⢇⠀⢘⣿⡀⠸⣷⡀⠀⠺⠧⠘⣧⠀⣈⠐⣮⠀⠁⢸⠇⢈⠁⠀⢀⠀⠀⠈⠁⠔⠃⠀⠛⠡⠤⣠⣤⠐⠀⡰⠶⣶⠏
⠀⠀⠀⠜⠀⠀⠀⠀⠈⠁⠀⠠⠿⠿⠿⠟⡠⢀⡀⠀⠀⠀⠈⠁⢁⣤⠈⢁⠀⠚⣦⠀⠀⠀⠀⠀⣰⢀⡄⠀⠠⠀⠀⠀⠉⠶⠛⠁⠀⠈⢦⣄⡴⠂
⠀⠀⠀⠀⠀⠛⣄⣀⡄⠀⡴⠀⠀⠀⢌⠂⠀⠀⠙⠤⢭⡷⠿⠇⡄⠐⠀⢈⡄⡠⠘⢷⣤⣤⣤⠊⠙⡏⡍⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠀⠨⡿⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⢨⡁⠀⠀⠀⠇⠀⣠⠀⠀⢐⠋⣀⠄⢀⡴⢀⢠⠄⢀⡆⣠⠆⠛⠉⠙⢀⠄⡓⠦⣄⠀⠀⠀⠀⠀⡴⠏⠁
⠀⠀⠀⠀⠀⠢⣤⡄⠀⢤⡈⡆⠀⠀⠀⡠⠄⠀⡀⠀⠀⢏⠀⠈⢤⡈⠀⠀⠈⠉⢹⠲⠇⠀⠈⡟⠀⠁⠀⠈⠳⣶⡴⠖⠛⠀⠀⠀⢀⣀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⡉⠉⠉⢉⠁⠀⠠⢄⡐⡒⠉⠂⠀⠿⠁⠀⠀⠀⠀⢸⠣⡀⡠⠊⠤⢶⠀⠐⠄⠀⣠⠙⠳⣶⡖⠁⠀⠘⠉⠔⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣏⠀⠀⠀⡸⠃⠉⠲⠞⢀⠂⠀⠀⠀⠀⠀⠸⡄⠻⠆⣸⠒⠾⠶⠿⠇⠀⠀⠠⠂⠁⠉⠁⠁⠢⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⡩⢣⠀⣤⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠓⣀⢦⠠⠤⡏⠇⠰⠰⡅⢈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠐⢆⡰⢌⡄⠹⡤⠿⠲⠁⣎⡹⠆⠡⠀⢂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⣄⢀⡸⠒⠎⠘⡀⡠⠞⢢⠀⠨⠁⠈⡀⢂⠈⠎⠖⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠘⢹⠇⣤⠋⢄⠀⠑⢻⠲⠉⢇⠀⠁⠡⠐⠀⣃⣸⠞⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠶⣶⠀⠀⠀⠀⠀⣀⡇⠀⠈⢆⠈⡆⠀⠈⠓⠋⢇⢃⠘⡆⠀⠀⣣⡶⠟⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⣰⠃⠀⠀⠀⠀⢸⡗⠶⠦⢤⣬⣤⣽⣄⣦⣤⣥⣸⣬⣤⡴⣶⠞⠉⠀⠀⠀⠀⠀⡇
⠀⠀⣠⡤⠔⠒⠂⠀⣈⡧⡤⠓⠒⠤⢤⡀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣠⣤⣤⣤⣤⣧⣤⣀⣀
⠀⣼⣏⠀⠀⠀⣠⣾⡿⠀⠀⠀⠀⠀⣀⢟⡆⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠛⠉⠉⠁⢀⠀⠀⠉⠉⠉⠛⠻⢷⣦⣤⡀
⠀⡷⠬⣍⣛⣒⠚⠛⠒⠒⠒⣒⣚⡉⠥⠚⡇⠀⢸⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⢉⡁⡄⠀⠀⠠⠀⠂⠀⠉⠊⠁⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣄
⠀⡏⠀⠀⠈⠉⠉⠉⠉⠉⠁⠁⠀⠀⠈⠀⡇⠀⠸⡆⠀⠀⣀⣴⠾⠋⠁⡠⢰⠄⠉⠀⠂⢂⣠⠤⠖⠒⡈⠁⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠈⢿⣷
⢠⡇⠀⠀⠀⠀⠀⠠⠀⠀⠄⢀⡀⠀⠀⢀⡇⠀⠀⣇⣠⡾⠋⠁⠀⠀⢀⣈⣀⣤⠤⣤⠴⠿⠤⠤⣤⣉⣀⠀⢴⡴⠀⠉⠉⠠⡠⠆⠀⠀⠀⠈⣿
⢸⡇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡇⢀⣴⠟⠁⠀⢀⠀⠐⠊⠉⠁⣠⠔⠋⠀⠀⡄⠀⣀⠀⠈⠉⠛⠲⣄⠀⣆⠜⠀⠀⠀⠀⠀⠀⣸⣿
⢸⡇⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⡀⢸⣷⠟⠁⠀⠀⠺⠈⢀⡠⠂⣤⠞⠁⠀⢀⡀⠉⠀⠠⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣼⡿⠃
⢸⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠄⡆⠀⣠⠞⠁⠐⠁⠐⠒⠁⢠⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⢻⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⣰⡟⠀⠀⠀⠀⠀⠀⠋⠀⡴⠃⠀⠀⠸⠥⠛⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠋⢀⣤⡞
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠛⠉⣀⣤⠞⠋⣠⡇
⢸⡇⠀⠀⠁⠀⠀⠀⠀⡜⠀⠀⢨⣿⣦⣄⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡿⠿⠛⠉⣀⣤⠶⠛⠉⢀⣤⠞⠉⡷⢤⡀
⣿⡇⠀⠀⠀⠀⠀⢠⠎⢀⡀⠔⠉⠳⣍⡛⠿⢿⣶⣶⣴⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⡿⠿⠟⠛⢉⣁⣤⠴⠞⠋⠉⠀⣀⣤⠾⠋⠁⣀⡼⠃⠀⣿
⣿⠇⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠸⣇⠙⠓⠦⢤⣈⣉⡉⠉⠉⠉⠉⠉⢉⣉⣁⣠⣤⠴⠖⠚⠋⠁⠀⢀⣠⣤⠶⠛⠉⠀⣀⣴⠞⠋⠀⠀⢠⣿
⣿⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⢦⣄⣀⠀⠉⠉⠉⠛⠛⠛⠛⠉⠉⠉⠀⠀⢀⣀⣤⡴⠶⠛⠋⠉⢀⣀⣤⠶⠛⠉⠀⠀⠀⢀⣴⡿⠁
⣿⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢦⣌⠉⠙⠛⠓⠒⠲⠶⠶⠶⠖⠒⠛⠛⠋⠉⠁⢀⣀⣤⡴⠶⠛⠋⠁⠀⠀⠀⠀⠀⢀⣤⡿⠋
⣿⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠉⠓⠲⠶⠤⢤⣤⣤⣤⣤⠤⠴⠶⠶⠞⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋
⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠁
⠘⣿⣦⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡾⢛⣻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⠿⠛⠁
⠀⢿⣝⡛⠻⠷⠶⠿⠿⠟⢛⣋⣩⡴⠖⠛⠁⠀⠉⠛⠷⠶⣤⣤⣤⣄⣀⣀⣀⣠⣤⣤⣤⣴⠶⠶⠟⠛⠋⠁
⣤⣤⣬⣭⣿⣿⣷⣾⣿⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣉⣭⣏⣼⣉⣯⣩⣿⣹⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠒⠀⠋⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡠⠒⠉⠁⠒⠀⢇⠀⠀⠀⠁⠀⢀⠠⠔⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠐⠂⠄⢀⠀⡐⠈⠀⠀⡇⠀⢁⠀⠁⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⡄⠂⠙⡇⠀⠀⠀⠁⠀⢸⠀⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⡄
⠀⢀⠠⡄⠀⠤⠀⡀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢠⠤⢚⠀⠑⠀⠤⡀⠀⠀⢠⠀⠀⣀⡄⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢐⠀⠐⠀⠄
⠀⠁⠀⠁⠀⠀⠀⠀⢠⠄⠀⠀⠀⣤⠀⡄⠀⠀⠀⠀⢸⠀⠀⠈⠀⠆⠁⠀⠀⠀⠠⠘⠣⠀⡀⠠⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠀⡖⠈
⠀⠃⠀⠀⠀⠀⠀⠘⠃⠀⠀⢤⠊⠀⠀⠇⢠⢀⡀⠀⣈⠀⠀⠀⠀⠀⠀⡇⠀⠀⢈⠀⠀⢸⠀⠀⠀⠀⣀⢀⠀⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠘⠀⠀⠀⠸⠀⠀⠀⠀⡀⠀⢡⠘⠑⢠⠠⠄⠐⠚⠂⠀⢰⠀⣠⠅⠠⠤⠴⡄⠀⢸⠀⠀⠀⠈⠁⠀⠀⠀⠉⠰⠀⠀⠀⢸
⡄⣠⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃⠀⠄⠀⠒⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠐⠒⠺⡀⠀⠀⢸⠀⡠
⢀⠀⠁⠐⠆⣀⠀⠀⣇⠀⠤⠀⡀⠀⠀⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠒⠘⠆⢠⠘⠁
⠈⠀⠀⠀⠀⢘⠁⣀⠉⠀⠂⠄⡀⠙⠂⠃⠀⠸⠀⠀⠀⡠⠄⠀⡄⠐⠀⢀⠀⠀⠀⠀⠁⢘⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⠀⠀⠀⢠⠃
⠀⠃⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠂⡀⠀⠰⠀⠊⠄⡀⠠⠐⠈⠁⠀⠘⠀⠀⠀⢀⠀⡸⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠄⠀⠀⡠⠁⠀⠄
⠀⠰⠀⠀⠀⠀⠀⠀⠈⠢⡀⢠⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⡘⠃⠤⠀⠀⢁⠳⡄⠀⠀⠈⠀⢀⠀⠀⠈⠀⠀⠀⠁
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⢀⡀⠁⠀⡀⠀⡄⠀⠀⠀⠀⠀⢰⠀⠃⠀⠀⠀⠁⠀⠀⠀⠘⠀⠀⠂⠀⠀⠆⠀⣈⠄⠁
⠀⠀⢁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠
⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⡅⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⠀⠇⠀⢸⡀⠜⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠃⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠼⢀⡀⠀⠀⡄⠀⠀⠀⢘⠀⠀⠀⠠⠓⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠐⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠸
⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠈⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠈⠉⠀⠀⠈⠉⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠘⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⠀⣀⡀⢀⣀⠀⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣤⣀⣒⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠊⠓⠁⠀⠘⠃⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠸⠀⠀⠘⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠠⠀⢀⠀⠀⡄⠘⠔⠀⠀⡠⠒⠐⠂⠄⠀⣀⠀⠀⠀⡀⠀⠠⢒⠄⠀⠀⠀⠀⠀⠚
⠀⠄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠇⠀⡄⠀⠀⠀⠰⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠑⠀⠂⠂⠀⡀⠀⠀⠠
⠀⠁⠀⠀⣠⢂⢶⡀⠀⠀⠀⠀⠀⠀⠈⠐⠔⠀⠁⠀⠀⠄⠈⢀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠈
⠀⠀⠀⠀⠅⠬⠋⠀⠀⠀⠀⠄⢀⡀⠠⡀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠁⡂
⠀⠀⢀⡄⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠚⠀⠂⠀⢠⠉⡄⠠⠀⠀⠀⠀⠂⠁⠠⠀⠐⣢⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠠⢴⠰⡄⢀⡐⠀⠀⠈⠀⠀⠀⠀⠀⡀⢤⡶⠄⠘⢊⣁⠠
⠀⠀⠀⠂⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠁⠉⠀⠀⡀⠤⢀⠀⠀⣼⡟⠁⠀⠀⠀⠈⠀⠠⡴⢡⢿⡄⠈⠂
⠀⠀⠀⠀⠐⠀⠧⠰⢺⠀⠀⢀⡀⠀⠐⠀⠀⠀⡊⠀⠀⠀⢁⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠒⠒⠁⠀⠀⣀
⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⣮⣹⣲⣲⠀⠀⠱⢄⣀⡠⠜⠀⠀⠄⠃⠀⣯⣩⡣⢭⠀⠀⠀⡀⠄
⠀⠢⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣿⡨⠟⠀⠀⠄⠀⠀⠀⣀⠰⢆⠠⡀⠠⠀⠀⠀⠀⠀⠀⠀⢨⠁⢀⠀⢀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣇⠊⠀⠀⠀⠀⠀⡀⠀⠃⠀⠈⠀⠃⠀⠀⡄⡐⡠⠀⠀⢁⠈⠀⡌
⠀⠀⠠⠀⠀⢰⠃⠀⠀⠀⠀⠀⠉⠀⠀⠐⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡆⠀⠄⠐⠀⠘⠒⠓⡇
⠀⡄⠀⠐⠤⠤⢴⠂⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⢀
⡐⢀⡂⠀⢠⣀⣼⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠒⠀⠐⠂⠂⠀⢬⡣⣁⣸⠀⠀⠐⠀⡂⠀⠀⠐⠂⠀⣘
⣿⡫⠁⠀⠀⢉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⡻⣥⡆⠀⠀⠅⠀⠀⠀⠀⠀⠀⠄⠸
⠎⠋⢀⣴⠿⠝⠛⠁⠀⠀⢀⠀⠀⢀⣾⣦⡄⠀⠀⢨⢀⠠⠶⠀⠀⠉⠊⠀⣀⣀
⣄⠀⠀⠉⠀⠀⠀⠀⠀⠐⠀⡂⠀⣾⣿⡿⠟⠁⠀⠈⠠⠄⠊⠀⠀⠀⠰⠎⢲⡻⠄⠀⠀⠠⠠⠀⠀⠠
⠄⠀⠀⠆⠀⠀⠀⠀⣏⡀⠐⡆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⢄⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠐⠂⠀⠀⠀⠀⠤⠀⠀⠀⠉⠀⠨⠁⠸⠆⠀⠀⠀⠰⠂⠠⠀⠀⠡⠀⠄⠀⠀⠀⠔⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⣀⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠔
⠀⠀⠀⠀⢰⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⢸⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡆
⠀⠀⣠⠔⠃⣉⠸⠉⢧⣦⠀⢲⡀⠀⠀⠀⣠⡄⠰⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡷⣄
⠀⠀⠁⠘⠛⠉⠁⠀⠙⠻⠤⠤⣽⣤⣤⣶⡛⠫⢤⣄⡀⠀⠀⠀⣀⣀⠀⠠⠤⠴⠤⣤⢠⣤⠿⢴⣆⠃⠐⠀⢀
⠀⠀⠀⠀⠀⣙⠓⣻⡶⢦⡤⠤⣈⣧⠀⠀⠈⠑⠀⠀⠀⠀⠀⠐⠚⠃⠀⢀⡠⠤⠄⠒⠈⠀⠀⠁⠀⠀⠀⠄⠈
⠀⠀⠀⠀⠠⣶⣦⡤⠘⠦⣉⠓⠤⢄⣠⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣿⠓⠒⣂⣲⡤⠤⢀⡀⠈⠁
⠀⠀⠀⠀⠀⠘⢿⢀⣦⣠⠘⣩⡿⠟⠚⡻⢤⠀⠀⠀⠀⣠⡊⠁⠈⡉⠙⠛⠉⠉⠉⠀⠉⠉⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠺⠥⠀⠄⠀⠀⠐⠂⠀⠑⠄⢠⣊⠁⠀⠀⠀⠙⢤⠀⠁⠀⣇⡤⠄⠞⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠦⣄⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⢦⣀
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠠⣀⡀⠀⣄⣀⣠⠈⠐⢄⠀⠀⠀⡀⠀⠀⠀⢀⢀⠀⠀⠀⡀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠘⠛⠂⣠⢈⠀⣠⡔⣮⠉⢳⣤⣭⠠⠀⠀⠘⠁⡁⡀⠄⠀⢠⡿⠀⠀⠠⢼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠁⠀⠀⠀⠠⠟⠓⠠⣀⣉⡤⠔⢈⡭⣬⣈⣻⡆⢀⡀⠁⠀⠀⠀⢷
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠐⢲⣿⣿⠿⠃⠀⠀⠃⠀⠀⠀⠀⠀⠉⠁⢀⡜⠀⠁⠀⠀⠐⡒⠉⠀⠐⠈
⠀⠀⠀⠀⠀⠙⢀⣠⣥⣤⣬⣉⣡⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣮⣤⣤⣄⣀⠀⠉⢀⡶⣿⠟⠹⣿⠿⠆
⠀⠀⠀⠀⠀⠈⠀⠙⠩⠼⠿⢿⣿⣟⠛⣿⣿⣧⣀⣤⣾⠿⣛⣛⣿⣿⢩⣽⣿⣿⣽⣦⣭⡴⠟⢓⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠀⠀⢀⣀⣀⣴⡾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠂⠈⠉⠁⠉⠉⠉⠉




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⠐⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⡀⠀⠀⢀⠀⠀⠐⡂⠀⠀⠀⠀⠀⠀⢠⡟
⠀⡦⠶⠾⠤⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⡘⠁⠀⠀⢠⣌⠆⠀⠁⠀⠀⠀⠖⠈⠙⠉⠉⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⢠⡈⠀⣀⠁⠀⠀⠀⠀⠈⠂⠀⠈⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢃⠀⠀⠀⠀⠀⠀⠄⠃

⠀⠀⠀⠀⠠
⠀⠀⠀⠈⢀⠀⠀⠀⠀⢰⠉⠁⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⠤⠖⣆⠀⠀⠀⠑⠀⢂⠐⠀⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠸⠄⠀⠀⠀⠀⠈⠄⠀⠠⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠠⠆⠈⣁⣈⡉⠂⠀⠀⠐⣶⡀⢱⣮⠄⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠐⠈⠠⢻⠍⠀⠀⠀⠀⠂⠀⠨⠙⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣊⣄⡤⠄
⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⣸⠀⠀⠀⠀⠀⠀⠠⢀⢀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⡀⠀⠀⠀⢀⡴⠆⠄⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠈⠀⢀⣀⣤⣀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠊⢁⠀⡀⠁⡄
⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠢⢀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠊⠀⠀⠀⠉⠰

⠀⠀⢀⢀⡀
⠀⠀⠸⣿⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡶
⠀⢐⠀⢫⠀⢀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠛⠁⠀⠀⢠⠀⠀⠀⢠⡀
⠀⠸⠀⠸⠀⠸⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠃⠀⠀⠀⠀⠀⣀⠀⠀⠶⠞
⠀⠀⠄⠘⠀⠀⠀⠈⠁⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠦⢤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠑⠃⠐⠀⠀⠀⣀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠒⠀⠀⣀⠀⠂⢀⡀⠘⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠠⡠⠀⠀⠉⠀⠀⠀⠀⠂⠀⠀⠀⠠⠄⠀⠀⢀⠀⠈⠁⢀⠀⠀⡙
⠀⠀⠀⠀⠀⠀⠸⠀⠀⡤⠀⠀⠀⡀⡀⠀⠈⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁
⠀⠀⠀⠀⠀⠠⢆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡆⣡⢤⠤⡀⡒⢀⠐⠀⠒⠀⠀⠶⠦⠴⠶⠒⢀⠀⠒⠂⣄⡀⠘⠐⠐⡀⠀⡰⠆⠁
⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⢈⠉⠉⠉⠚⠒⠀⡓⠛⠈⠙⠃⠁⠈⠀⠘⠃⠃⠈⠉⠉⠉⠉⠁⠈⠀⠂
⠀⠀⠀⠀⠀⠀⢍⠣⠲⡀⢄⢤⠠⡀⣞⢁⠀⠀⡘⣀⣀⡀⠠⢃⡀⠀⣀⣉⡀⠀⠀⠡⠀⠀⠐⠋⢉
⠀⠀⠀⠀⠀⠀⣀⡑⠒⠬⠦⡓⣕⣜⢮⣂⣀⣀⠀⢀⣀⡀⡀⡀⣀⣀⣀⠀⣀⡀⣀⢀⢀⣠⡤⠤⢨⠄
⠀⠀⠀⠀⢀⣈⡉⠄⠀⠀⠀⠒⠂⠠⠀⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠄⠠⡤⠤⠖⠚⠁⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣄⠰⠁⠘⠀⢀⠴⡀⠈⡠⢖⡤⠀⢀⢺⠁⢰⢢⡀⠈⢰⠢⡀⠀⠁⠀⠜⣠⡀
⠀⠀⠀⠀⠀⠀⠀⢯⡀⠠⠍⠀⢤⡚⠊⠐⠒⠃⠁⠀⠀⠾⠈⠀⠀⠀⠈⣆⠂⠉⠛⠀⠁⠤⠀⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠀⠀⠠⠀⠈⠀⠀⠤⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠉⠀⣈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠐⠆⢀⡀⠀⠀⠆⠀⡀⠈⠀⣀⠀⠄⠠⠄⠀⠠⠀⠀⢠⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠀⠀⠀⠤⣀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠰⠅⠀⠀⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠘⠀⠇⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⡄⠀⠘⠂⢄⠀⠔⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⣀⣀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢀⣘⣆⠀⠀⣠⠤⠤⠤⠄⣀⠀⠁⠈⠀⠐⠒⠀⠀⠁⠀⠀⠀⠀⠸⠂⠀⠀⡇
⠀⠀⠀⠀⠰⠉⠀⠀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⣀⠀⠤⠤⠀⣀⡴⠁⠀⢀⠠⠁
⠀⠀⠀⠀⠀⢂⠀⡸⠁⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠱⡤⠊⠉⠄⠀⠀⠀⠀⠀⠁⠲⡈⠁
⠀⠀⠀⠀⠀⡔⠙⠃⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠱⡀
⠀⠀⠀⠀⠈⠣⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠂⠀⠀⠀⢠⠒⡦⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣱⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠀⡇
⠀⠀⠀⠀⠀⡆⢂⠈⢀⠌⢢⡀⠀⠀⠀⠀⠀⡸⡆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠁
⠀⠀⠀⠀⢸⢂⠀⠀⠅⠀⠘⡋⠐⢒⡒⣈⠁⠀⠘⢄⠀⠀⠀⠂⠀⠀⠈⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⢈⡇⠀⡊⠀⠀⠉⠉⠑⡄⠑⠤⣄⢀⠀⢀⣀⠤⠐⠉
⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⢩⠔⠒⠃⠤⠐⠂⡀⠀⠸⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢃⠀⠀⠀⡄⠀⠀⠀⠀⠀⢰⠲⡀⢠⠊⠉⠉⠉⠒⠶⠆⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠈⠁⠛⠀⠀⠠⠀⠁⠀⡔⠁⢀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠁⡀⠈⠢⡀
⠀⠀⠀⠀⠀⡠⠶⠀⠀⠄⠀⡀⠚⠀⢠⠀⠃⠀⠀⡩⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠈⢂
⠀⠀⠀⠀⢀⠀⠀⡈⠀⠀⠘⢃⠀⠀⠈⢄⣀⡠⠤⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠐⠀⠈⠀⠘⢄⢀⡸⢆⡀⠜⠁⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⣁⠤⢖⠁⠠⢀⠠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣠⣤⣤⡤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⡏⠓⠒⠯⠝⢻⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠆⠀⠀⠹⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⢉⡐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣾⣿⣥⣤⡀⡥⠀⠀⠀⠀⠀⠀⣐⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢰⠞⡃⠠⡠⢹⣦⣾⣟⣽⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣞⣻⣿⣿⣻⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣯⠙⢋⡿⠣⣮⣉⣙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣿⣿⣿⣏⡉⠙⠁⠀⠀⠒⠦⠈⠉⠉⠉⠿⣿⣿⣿⣿⡟⣶⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠛⠻⠛⠲⠶⠶⣄⣲⣀⡀⡒⠒⠺⠽⠛⠛⢋⣼⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣛⣉⣤⣶⣶⣮⠙⠉⠉⠉⠉⠉⠉⢉⣭⣶⣶⣤⣀⣾⣿⣿⠏⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡿⣭⣙⡻⣿⣿⣿⣷⡄⠀⠀⢀⣴⣿⢿⡟⣛⣹⣿⣿⣿⣿⢾⣾⡏⠎⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⠆⣈⡴⣋⠿⡝⢁⣙⠳⢶⡟⡇⠈⠀⢽⠋⡛⠞⢻⠁⢀⣰⡗⣵⠐⣯⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣷⡔⢡⠗⡂⣨⣍⠳⢮⠀⣀⣚⠋⠘⠀⠀⠀⢡⣴⣿⣉⣸⡏⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣏⡟⠳⠓⠜⠉⠉⠐⠚⠛⠿⢆⠍⣀⣎⣹⠷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠓⠒⠒⠶⠤⠤⠤⠄⠒⠂⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠛⠛⠉⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⣾⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡘⠂⠠⠂
⠀⠀⠀⠀⠀⠀⠀⡶⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢀⠀⠀⣀⢨⠌⠀⠀⠠
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⢻⣿⣿⣟⠀⠀⠀⠀⠂⠰⠆⠠⢤⣁⡄⠀⡰⠀⡓⢢⠀⠦⡀⡀⠠⡦⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⢟⡸⠥⠉⠘⣶⣧⡀⠀⠀⠰⠀⢹⠄⠙⠳⣲⣼⠦⠁⠀⠹⡆⠈⡗⠀⢐⣴⠥⠶⡀⢰⠁
⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠈⠀⠀⠀⠀⠿⢭⡿⣂⠈⢦⡀⡤⢤⣀⠀⠈⠂⠐⠰⢤⣆⣂⣌⣳⣶⠫⣤⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣀⣌⠿⠛⠓⠂⠤⠤⣤⡂⠀⠀⠀⠛⠶⡄⣷⣼⣏⣷⡴⠀⠀⠀⠀⠀⠘⢿⡛⢿⠿⠄⡀⠻⣦⡀⠀⠀⠂
⠀⠀⣄⢔⠋⣁⠀⠠⢐⣢⠿⠃⣀⠄⠋⢳⢞⡠⠒⠀⠜⠻⢿⡉⠉⠺⣿⣆⡀⠀⠀⣀⣸⡧⣾⣦⠀⠛⠁⠦⣽⣶
⠀⠀⠛⢧⣤⠖⠀⡸⠏⢀⢀⠚⠁⢀⡀⢀⠠⠐⠞⠁⠠⣾⣾⠛⠢⢄⠈⠻⣻⢿⡏⠉⠉⠉⣯⢉⣰⣇⠀⣀⠈⣯
⠀⠀⠀⠀⠀⢠⡊⠠⠀⣠⡖⠊⠉⠁⠀⠀⠀⡠⠤⣴⡉⢻⡦⣀⠀⠀⠀⠂⠀⠀⢇⠀⠀⠀⠉⠀⠈⢉⠿⣴⣉⠃⣄⡀
⠀⠀⠀⠀⠀⠀⠓⠐⠛⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢾⣿⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠄⠈⠙⠋⠁⠾⢦
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣾⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠊⠉⠁⣠⠈⠀⠈⣡⠀⠉⢉⠑⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⣡⠀⠀⠀⠈⢁⠀⠁⠀⣄⠀⠀⠦⠀⠉⠀⠀⠀⣀⠈⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠴⠀⠀⠋⢀⡀⠀⠀⣀⡀⠀⠀⡤⠀⠀⠀⠀⠀⠖⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠐⠆⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⢀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠒⢦
⠀⠀⠻⣍⠉⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡴⠁
⠀⠀⠀⠈⠳⣄⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠈⠱⣄
⠀⠀⠀⠀⠀⡸⠓⢄⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠈⢆
⠀⠀⠀⠀⡰⠁⠀⠀⠑⢄⡈⠑⠢⠤⢄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠤⠶⠯⠤⠤⠤⠤⢤⡤⢄⣘
⠀⠀⠀⠀⠘⢦⣀⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣉⣉⡍⠭⠟⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠁
⠀⠀⠀⣤⠄⢺⡀⠈⠉⠐⠂⠀⠙⠢⡀⠀⠀⠀⣀⡠⠤⠔⠒⠉⠉⡹⡁⠲⢄⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⠤⠄⠒⠊⠉⠀⢠⠦⣀
⠀⠀⠀⠈⠉⠲⠋⢲⠂⠀⠀⠐⠐⠂⠙⠒⠛⠋⠁⠒⠒⠐⠀⠂⠉⠀⠉⠒⠒⠛⠒⠒⠒⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⡃⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠣⣀⠈⠦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠤⣫⠁⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠟⠒⠂⠀⠀⠒⠀⠤⣤⠤⠀⠒⠒⠒⠂⠀⠀⠀⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠠⠤⠒⠚⡷⠒⠒⠀⠒⠒⠢⠇
⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣀⠀⠀⠀⠀⠀⠀⢀⣀⠭⠶⠤⠤⠔⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠤⠤⠄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠤⠤⠴⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁



⡿⠉⢙⡟⡿⠻⠿⠟⠿⡛⠿⠻⠿⠿⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⡿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣀⠀⠀⠡⡀⠀⢳⣄⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣉⠒⠫⠵⣒⣬⣦⣄⣙⣳⣄⣤⣶⠾⠛⠉⠀⣀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡤⠤⠤⠤⢤⣼⣷⣤⣤⣤⠾⢟⣻⡿⠟⠋⠉⠀⣀⣤⣖⣊⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣖⣯⠭⠔⠒⠒⠒⠒⠒⣺⣿⣿⣿⠟⠛⠛⠉⠉⠉⠁⢀⣀⣤⣴⡒⠋⠚⠛⠛⠙⠛⠛⠫⢭⣗⣲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⠥⠴⠾⠟⠒⠒⠒⠛⣛⣫⣿⡿⣇⣔⣀⣠⡤⠴⠚⢿⢿⣿⣿⡿⠽⢛⡓⢲⠶⠤⠤⣤⣤⣀⣙⣋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡳⠞⠛⠿⣿⡠⠽⠛⠉⠀⢀⣤⣶⣮⣍⣀⠀⠈⠛⠳⠤⣄⣀⣉⠉⠉⠉⠙⣦⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⠤⠒⠋⠁⠀⢀⣠⣶⡛⠛⠛⠶⠦⠬⠭⣿⣶⣤⣀⠀⠀⠈⠻⢭⡉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⡟⠁⢀⣀⠤⠐⠾⣻⢏⡼⠋⠓⠲⠤⣤⣀⣀⣒⣒⣉⣻⣽⣳⢄⡀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡾⠶⠚⠉⠀⢀⠎⡰⠁⣾⡡⢒⡩⡟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡲⣄⣤⠼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠻⠭⠟⣒⣒⡲⠦⠤⠤⠠⢤⣤⠎⡰⡁⣼⠟⠋⠁⢀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠤⣀⣐⠀⠀⠀⠀⠈⠉⠉⠉⢉⡟⢠⠃⢰⡯⠶⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠒⠒⠒⠒⠒⢸⠁⡜⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⡇⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠶⠋

⠀⠀⠀⠀⠀⠠⣒⣺⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠁⠘⡦⠀⠦⣤⣔⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡆⠛⠫⣿⢹⣼⣿⠅⠀⠀⠀⠀⠀⡓⠀⠘⢦⣀⡄⢫⠙⠒⠶⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⣐⣀⣦⣤⣈⣡⢿⣬⡀⠀⠀⠀⠀⠃⢐⠛⠘⣿⠋⠙⣳⣤⣿⡥⠐⠚⡆⠀⠀⠀⢤⣀⣀⠔⢞⠀⠁⠀⢙⡆
⠀⠀⠀⠀⠀⠩⡀⠁⠀⠁⡡⠄⠀⠁⠀⠀⠀⠈⠓⠤⢆⣴⣛⠶⠖⠃⠉⠀⠀⠀⠀⡇⠀⠀⢠⢲⠊⡁⠐⠀⣠⡀⢢⣼⡷⣀
⠀⠀⠀⠀⢺⡀⣀⡍⣠⣄⣁⣽⡀⠁⠀⠀⠸⠤⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⣨⣛⡁⠀⠈⠋⠀⢁⣈⣤⡴⠿⠂
⠀⠀⠀⠀⠀⣏⠉⠁⠉⠀⠉⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠾⠋⠀⠀⠀⢠⠀⠀⠉⠉⠁⠀⠈⠀⠀⢀⡆
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⠁
⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⣣⣤⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠉⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢰⠀⠀⢐⠂⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⣶⣄⣀⣀⣀⣀⣤⣼
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢛⣛⡛⠻⢟⣛⠕
⠀⠀⠀⠀⠀⠀⠀⣥⠀⠁⠀⠀⠀⠀⠀⢀⠆⠀⠀⢀⠀⠀⢠⠀⠀⠀⡀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠢⣌⢣⣀⢸⡀⢠⣴⠁⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⢙⠀⠀⠉⠉⠁⠉⠉⠙⠧⣀⡠⠊⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⢀⡀⠀⠤⠒⠂⠐⠀⠠⠤⢄⠀⠈⠢⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠲⢒⢶⣧⠀⠀⠀⡀
⠀⠀⠀⠠⠀⠀⠀⠠⡄⠀⢀⡄⢠⡄⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠄⣥⣮⣽⣿⠿⢀⠞⠋⠔⠡
⠀⠀⠀⡆⠠⠀⠚⠄⣸⣦⣾⢤⠖⢀⠆⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠂⠀⣄⡈⠛⠛⠋⠉⢉⡉⠙⣁⣔⣀⣀⣀⡀
⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠀⠉⠙⠋⠁⠉⠉
⠀⠀⠀⠂⠉⠢⠖⠐⠂⠄⠒⠀⠤⣄⠏⡴⠀⠀⠀⠐⠒⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣀⣀⠀⢀⣠⡄
⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⢀⠀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣀⠀⠀⠀⠈⠛⠿⠛⠺⠽⠿⠿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠂⠒⠐⠃⠐⠒⠒⠂⠐⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠴⠖⠒⠛⠋⠉⠛⠟⠏⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⠛⠉⠁⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠄⢠⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠈⠀⢀⠀⠐⠀⠠⠀⠀⠀⣀⣀⣀⣀⠀⠀⠁⣰⠃⠀⢉⣳
⠀⠀⠀⠀⠀⠀⢠⠖⢿⣯⣰⣀⣦⠤⠤⠤⠴⠖⠒⠒⠚⠉⠉⠉⠁⠀⠀⢀⣀⣰⠃⠀⠐⢿⣅
⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⢀⣀⣀⣠⡤⠤⠤⠴⠖⠒⠒⠒⠛⠋⠉⠉⠉⠉⠉⠋⢀⣤⣤⣤⡿
⠀⠀⠀⠀⢀⡴⠞⠉⠋⠉⠉⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⡖⠲⠦⠀⠒⠒⢾⢦⢷⠀⢹⡆
⠀⠀⠀⠀⠸⠷⣾⠇⢀⣴⡚⢧⠀⡠⠊⠙⡄⣠⠞⠱⠶⠉⠓⠊⣃⣐⣤⣖⡠⠗⣦⠠⠋⠀⡼
⠀⠀⠀⠀⠀⠀⠿⠞⢁⣷⠤⠬⣭⣴⣂⣀⣈⣓⣒⣈⣭⠭⠭⠟⠓⢋⣉⣡⠤⠚⣷⡜⠀⡼⠁
⠀⠀⠀⠀⠀⠀⢀⡴⠚⠓⠶⠤⠤⠤⠤⢤⣤⣴⠶⠒⠒⣒⣿⣯⣉⣉⣀⣀⣀⣠⢾⠄⣼⠃
⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⠀⠀⣀⣤⡶⣛⢁⠙⡛⣛⣛⣉⣁⣀⣀⣩⣭⣽⣫⠴⠋⣰⠃
⠀⠀⠀⠀⠀⠘⠳⢶⣶⠖⡛⠿⠯⠤⠭⠭⠭⠭⠭⠭⠭⠭⠴⠶⠖⠚⠋⠉⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⢼⣇⢄⠀⠐⠀⠐⠐⣀⣀⣀⣀⣀⣀⣤⣤⣤⣴⠶⠶⠶⠚⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣤⣀⠀⡴⠋⢳⡀
⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠉⣻⠇⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀
⠀⠀⢀⠀⣴⣧⡟⠛⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣰⠶⠞⣉⣻⠶⣴⡟⣦⠀⠀⠀⠀⠀⠀⠀⠀⡰⠚⠛⠓⠦⠴⠖⠋⠀⠀⢹
⠀⣠⠟⣧⣤⣼⣇⠀⠀⠀⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣃⡟⣀⣾⣩⣹⡦⢦⡽⠋⣇⠀⠀⠀⠀⠀⠀⠰⣇⠀⠀⠀⢀⡤⠶⠦⣄⠀⠘⣆⡀
⠾⠷⢶⠋⠀⠀⠙⠷⣄⡀⠀⠀⠀⠉⠙⢳⡟⡇⠀⠀⠀⣾⠿⣾⣵⣏⣀⣈⣳⡞⠁⠀⢹⡆⠀⠀⠀⠀⠀⠀⠈⢳⠀⢰⡏⠀⠀⠀⠈⣇⠀⠈⠙⢦
⠀⠀⠘⢧⠀⠀⠀⠀⠈⠛⠷⢶⣶⣶⡖⠊⠙⠇⠀⠀⠀⠸⡆⠀⠀⡍⠉⢩⡟⢠⠀⠀⠀⢷⠀⠀⠀⠀⠀⢀⡴⠏⠀⠸⣇⠀⠀⠀⢀⠏⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⢙⡟⣻⠀⠀⠀⠀⠀⠹⡄⠀⠀⢠⠏⠀⠀⢀⠀⠀⠘⡇⠀⠀⠀⠀⡟⠀⠀⠀⠀⠈⠛⠒⠛⠉⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠶⠶⠶⠒⠋⢷⡿⠀⠀⠀⠀⠀⠀⠙⣦⣰⠏⠀⠀⠀⠈⠀⠀⠀⢹⡄⠀⠀⠀⢧⣀⠀⢀⣠⡤⠶⠶⠶⠤⣤⣀⣀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⢠⠀⠀⠀⠀⣷⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠄⠀⠈⠀⠀⠈⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠈⠳⣄⡀⠀⣀⣤⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢩⠗⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣼⡇⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣄⠀⡤⣠⡋⢳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡏⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢻⡄⠀⠀⠀⢀⡾⢀⡀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠙⣦⡼⠿⢧⣸⢷⡞⢳⡶⢦
⠀⠀⣀⣀⣠⣤⣤⣼⣵⣧⡤⠤⠤⠤⣄⠀⠀⠀⠀⠀⠀⣴⠿⠤⠦⠿⢶⠀⠀⢸⡇⢿⠀⢀⡀⠀⣠⣯⠟⠀⠀⠀⡶⠶⢼⣇⣠⡞⣿⢠⣷⡀⠹⣏
⠀⠰⢧⡤⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⠿⠀⠀⠀⠀⠀⢀⡿⠖⠒⠒⠒⠺⣄⠀⠀⡷⠘⢰⡏⠹⠻⣿⠁⠀⠀⠀⠀⠛⠛⣶⡌⠙⢶⡇⢸⠏⣷⠀⠘⣆⡀
⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠈⣷⠀⣡⠴⢮⣷⣄⣈⡿⠀⠀⠀⠀⠀⠀⣷⠿⠽⢤⣤⣽⣯⡴⠿⠗⠛⣿⠁
⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⣧⡀⠀⢹⡏⠉⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⡟⠛⠻⣟⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡴⢦⣼⣧⣴⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣏⠀⠂⠈⠹⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠒⠒⠒⠚⠛⠛⠒⠛
⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⣶⣿⠷⣼⣤⠾⠁
⠀⠀⠀⠀⠀⢀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠓⠲⠦⢤⣄⣀
⠀⠀⠀⢀⣾⣭⠿⢭⣝⡛⢻⣞⣛⣷⣀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣠⡤⠶⠶⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣰⡀⠀⠀⣤⠀⠉⠛⠦⣄
⠀⠀⣠⠞⠁⠀⠃⠀⠀⠉⠳⣍⢹⣟⠻⡍⠓⣦⠀⠀⠀⠀⠀⢀⡴⠋⠱⣤⠀⣄⠉⢂⡤⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⣯⣍⠉⠛⠺⢧⣀⢀⡀⠀⠈⠳⣄
⠀⠰⡇⠀⠀⠀⠀⠈⠃⠀⡀⠈⢳⡉⢳⡟⣳⠌⣧⠀⠀⠀⠀⣾⠀⠟⠀⠀⠀⢁⣠⠀⠀⠶⠂⢹⡆⠀⠀⠀⠀⠀⠠⣇⠚⢷⠀⠀⠆⠈⠙⠦⣄⡴⠄⠈⢷
⠀⠀⠻⣄⠁⠀⠰⠀⠀⠀⠀⠀⡤⢻⡌⠙⣏⡧⣿⠀⠀⠀⠀⠈⡿⠲⠶⠶⠶⠶⠶⢶⡶⠶⠶⢶⡇⠀⠀⠀⠀⠀⢸⣯⡵⠏⣠⠖⣋⢩⣽⡲⣌⣳⣤⠶⠚
⠀⠀⠀⠈⠳⢦⣀⠀⠀⠲⠀⠀⠀⠀⢳⢰⣏⣷⡏⠀⠀⠀⠀⢸⡟⠚⠛⢛⣳⣶⣚⣋⣙⠓⢒⣋⣽⠀⠀⠀⠀⠀⢸⡇⠀⠀⣏⢾⣹⣯⠷⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⠀⠃⠀⠸⡟⢉⡟⠀⠀⠀⠀⠀⠀⢻⡛⠛⠉⠉⠙⠻⢯⣍⠉⠉⢩⡇⠀⠀⠀⠀⠀⢸⠉⣳⣤⠿⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⣤⣤⣤⡼⠷⠖⠋⠀⠀⠀⠀⠀⠀⠺⠚⠉
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⣄
⠀⠀⠀⠀⢀⡤⠶⢒⠒⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠠⢻⡀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠈⣧
⠀⠀⠀⢰⢋⡀⢂⠌⢄⠂⠈⢧⠀⠀⠀⠀⠀⠠⣶⣒⣖⣻⣖⣖⣶⡄⠀⠀⠀⠀⠀⠀⣼⠂⣄⢀⡀⢠⢼⡀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⡼
⠀⠀⠀⢸⠄⠁⢇⣀⣠⠆⠁⣿⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢠⡄⣹⠀⠀⠀⠀⠀⠀⠀⠈⣏⠩⢋⠹⣺⠏⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⡴⠁
⠀⠀⠀⠈⢧⣠⠂⠌⠑⢂⡴⠃⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡔⡈⢆⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡴⠃
⠀⠀⠀⠀⠀⠉⠛⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⣺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀
⠀⠀⢀⡖⢋⠩⠅⠠⢀⡠⢉⢳⡄⠀⠀⠀⠀⠀⠀⢀⣼⣙⣲⣀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⣶⣏⣿⣽⣿⣿⢶⠄
⠀⠀⠀⢷⣡⢢⠋⢃⣞⠵⢆⡟⠁⠀⠀⠀⠀⠀⢸⡉⠤⢀⠤⢭⡇⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣂⣀⣐⣀⣧⠀⠀⠀⠀⠀⠀⣿⣿⢹⡏⡟⣯⡾⠃
⠀⠀⠀⠈⢧⡁⢫⠈⣬⣢⡟⠀⠀⠀⠀⠀⠀⠀⢼⣀⡀⣈⡆⢀⡿⠀⠀⠀⠀⠀⠀⢸⣭⣭⣉⣭⣭⣉⣭⡇⠀⠀⠀⠀⠀⠀⢿⠛⠺⠗⠛⢿⡇
⠀⠀⠀⠀⠈⢿⠛⣤⣩⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣉⣁⣈⠾⠁⠀⠀⠀⠀⠀⠐⠫⡍⠹⠭⠛⠍⠿⢉⡟⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠳⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠈⠧⠤⠤⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣦⠀⠀⠀⠀⠀⠀⢀⢤⣤⢖⣦⡴⣄⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⣀⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠛⠛⠉⠀⠀⠀⠀⠀⠀⡏⢸⣺⢼⠟⡇⠸⡆⠀⠀⠀⠀⢸⢯⠻⣿⣿⣳⡀
⠀⠀⢠⣖⠟⠙⠉⠉⠉⠙⠻⣦⡀⠀⠀⠀⠀⠀⠐⠈⣿⣿⡀⠃⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⣉⢺⣾⠇⠀⡇⠀⠀⠀⠀⢸⡆⠳⡹⣿⢷⣷⡄
⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⢶⠟⠯⠭⠭⠭⠍⢿⠂⠀⠀⠀⠀⠀⢸⠀⢘⣷⡞⢋⡇⠀⡇⠀⠀⠀⠀⢸⡇⠀⠙⣝⢿⣿⣷⡀
⠀⠸⣧⣀⣀⣀⣀⣀⡀⢀⢀⣀⣸⠇⠀⠀⠀⢸⣤⣀⣀⣀⢀⣀⣼⠀⠀⠀⠀⠀⠀⠸⡄⠈⣟⠱⢲⡇⢀⡇⠀⠀⠀⠀⢸⡇⠀⠀⠈⢪⢻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠈⡟⠻⠟⠿⠿⠛⡇⠀⠀⠀⠀⠀⠀⠀⢧⠀⣿⡾⢛⣇⣸⠁⠀⠀⠀⠀⠈⢧⣀⣀⣀⣀⣱⣻⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⢠⠖⠲⣄⡖⠛⢦⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠛⠳⡄
⠀⠀⠀⠀⢸⠀⠀⠘⡀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⣒⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢶⡦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⡇
⠀⠀⠀⠀⡟⠓⠐⠒⠑⠒⢛⡆⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢀⣴⡯⠒⠉⠉⠁⠑⢽⣷⡀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠠⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣿⡔⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⢸⠆⠀⠰⡇
⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⣀⣴⡯⠟⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠈⢦⣀⡴⠃
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠉⠻⠭⣉⢉⣩⠿⠛⠉⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏
⠀⠀⠀⠀⠈⠛⠚⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⣄⡀⢠⣶⣿⠛⠓⠒⠲⣶⣤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣣⡾⠟⠋⠉⠉⢀⠀⠁⠀⠴⠟⠛⠳⣿⣟⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⡴⠋⠀⠠⠀⠀⠄⠀⣸⡿⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠠⠀⢀⣴⠜⠋⠁⢀⠃⠀⢀⡼⠃⠀⡄⠀⠀⠀⡐⣠⣟⣴⣦⢡⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢠⡿⠋⠀⠀⠀⣴⣦⡴⠚⠀⠀⠀⣾⠗⡀⢰⣿⣿⡿⠋⠹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠶⣶⣶⣶⣶⡇⠀⣿⠃⠀⠀⠀⣸⠟⠉⠀⠀⠀⠀⢀⣿⣴⢇⣾⡿⢯⢀⠀⠀⣿⠿⠃⠁
⠀⠀⠀⠀⠀⠀⢠⡶⢾⣛⣻⣿⣿⣦⣽⣟⣷⠶⣤⣌⡙⠃⢼⣛⠤⣀⢀⠀⠋⢈⣂⠀⠀⠀⠀⣼⣿⣿⠟⠋⠀⠈⣿⣿⣆⣻⠂⣠
⠀⠀⠀⠀⠀⡀⠀⠸⢿⣿⡿⠿⢿⣿⣿⡿⠿⠿⣷⣯⡛⠷⣄⠙⢷⣌⡻⣄⠀⣼⣧⣶⣤⠖⠚⣿⠟⠁⠀⠀⠀⠀⣿⣿⣿⣿⣾⡏
⠀⠀⠀⠀⠀⣷⢰⣮⠝⡡⠶⠛⠋⠉⠉⠉⠙⠓⠀⠀⠀⠁⠈⠓⠄⠻⣿⡌⣶⣿⣿⣯⣅⡄⠀⢸⠀⣠⠀⠀⠀⠀⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⣿⣾⣿⣎⠀⣾⣾⣿⣷⣶⣌⠑⠒⠀⠤⠤⠄⠀⠤⡀⠀⠘⣷⠸⡟⣿⣿⣿⣶⠀⣸⣿⣧⣷⣦⣿⣰⠃⢸⡿⠃⠀⠈
⠀⠀⠀⠀⣧⢹⣯⣿⡟⠀⢻⣿⣿⣟⣽⣿⣿⣶⣶⡶⣾⠿⠷⢚⠾⣤⡀⢿⡇⣿⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠁⠀⣼⣇⢀⡔
⠀⠀⠀⠀⢹⡟⣿⣹⣿⡄⠀⠻⣿⣿⣿⠁⠈⢉⣍⣭⣴⣾⣿⣿⣷⣌⠁⢸⡇⣸⠘⣿⣿⣿⣿⣿⣿⣿⢟⡩⣂⢔⣽⣿⡷⠋
⠀⠀⠀⠀⠀⢿⡹⣏⢿⡿⡄⠀⠙⢮⣿⣷⢰⣿⣿⣿⣿⣿⣿⠟⠃⠻⠀⡼⠁⡿⢠⣿⣿⣿⣿⣿⣯⣶⣿⣾⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠈⢧⡹⣿⣷⡀⠀⠀⠀⢿⣿⣺⣿⣿⣿⣿⡎⠃⠀⠀⠀⠐⠀⣸⠃⠘⠿⢿⣿⣿⣿⣿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⢷⡌⢳⡘⢿⡿⠀⠀⠀⢸⣿⢿⣿⣿⠿⠁⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠙⡄⠈⡈⠻⣦⣀⠀⠀⡿⣜⢿⣌⠃⠀⠀⠀⠀⢄⣮⣿⠩
⠀⠀⠀⠀⠀⠀⠳⡀⠀⠈⠢⣀⠙⠻⠦⣤⡬⠓⢀⣠⠄⠀⣤⣶⣾⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠚⠟⠶⠶⠶⠶⠿⢋⠁⢀⠀⢊⣥⢬⣝⠿⣿⣿⣃⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡶⢤⣌⣐⣒⣒⣻⣭⣴⠃⡰⠋⠀⠀⠈⠳⣌⠺⡇⠀⠀⠀⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠭⠭⠭⠭⠭⠖⠋⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡮⠜⠁


⠀⠘⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⠀⠐⠒⠶⠖⠲⠆⠀⠀⠰⠒⠦⠶⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⢸⡍⣷⠀⠀⢀⡄⣶⣤⣠⣴⠀⣶⣄⡰⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣇⠀⠀⣽⠀⠀⠘⠃⠁⡉⡉⠀⢀⡀⠁⠀⠀⡆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠐⠋⢀⡇⠸⠀⡖⠀⠏⡖⡸⠂⣾⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠉⠀⠛⠀⠂⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠰⠒⠛
⠀⠀⠀⠀⠀⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡠⠒⡰⠄⢢⣎⣁⠀⠐⠚⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠶⠶⠒⣒⡒⠲⢤⡀⠀⡤⠀⠀⠀⠀⠀⠀⢀⣠⠖⠻⡄
⡟⠓⠺⣄⠀⢀⣇⣀⣹⡄⠀⢸⣄⠀⠀⠂⠀⠀⠀⠀⢸⣁⠀⠀⠀⠀⠀⢀⠀⠈⢑⡦⢷⡀⣌⠐⢣⡄⢀⣀⡰⠟⢫⣾⠟⠁
⠇⠀⠀⠀⠉⠉⠀⠀⠀⣹⢿⣧⡎⠀⠀⠀⠀⠀⠀⠀⢸⡂⡈⠀⠀⡐⢀⡀⣈⢀⣀⣤⣾⠁⠉⠀⠛⠓⢀⣤⠶⠛⠉
⢰⠀⠀⠀⠄⠀⠀⠀⡐⠉⠀⢧⠀⠀⢐⠀⠀⠀⠀⢴⠉⠻⠽⠿⣭⠿⣯⠽⠛⣛⡻⢟⡟⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀
⠸⠀⠀⠀⠀⠀⠀⠐⢀⣠⠴⠚⠀⠀⠀⠉⠉⠁⠀⠈⠲⢍⣀⣒⣐⣒⣀⡨⠭⠄⠒⠉⠀⠀⠰⠀⠀⠀⠀⠈⠀⠈⠁⡆⠀⠀⡀⠀⠀⠨⢆
⠀⠉⠙⠛⠛⠒⠚⠞⠋⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⢀⡀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⡼⠁⠀⠈⠀⠀⠱⢂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡨⠓⠀⠀⠀⡈⠓⢦⡀⠀⠀⠘⣆⠀⠀⠀⠀⣼⠃⠀⠀⠀⣤⣶⠶⣤⣤
⠀⠀⠀⡀⠀⢀⡄⠀⠀⠀⠀⠰⢄⣨⠁⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠈⠢⡀⠙⢆⠀⠀⠁⣆⠀⠀⠀⡇⠀⠀⠀⠀⠁⢀⠠⠐⡄
⠀⠀⠀⠀⠐⠳⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠤⠀⠀⠀⢀⠎⠀⠀⠐⠦⠀⠀⡀⢀⣨⡦⠠⠇⠀⢀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠈⠀⡁⢄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠄⠀⠀⢀⠀⣠⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡀⢂⣤⠾⠛⠁⠐⠃⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠄⡆
⠀⠀⠀⠀⠀⠀⠄⢙⣣⡄⠀⠀⠈⠀⠉⠀⠀⠀⠀⢸⣀⣴⠟⠋⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠘⠶⠤⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠘
⠀⢀⠄⠒⠢⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⡤⠒⠛⠛⠉⠉⠉⠓⠦⡀⠀⠀⠀⠀⡤⢀⢄⡀
⠀⡀⢰⠀⠀⢧⠀⠀⠀⠀⣠⣄⣴⣄⠐⢃⣀⡀⠀⠀⠀⢠⠏⠀⠀⠈⠀⠀⠀⠀⢀⣠⢼⠀⠀⠤⣜⠷⠻⣇⢱⠈⡁⠀⠀⠀⠐⠀⠀⠈⠠
⠀⠄⣸⠀⠀⢸⠀⠀⢠⣾⠏⡠⠊⠀⠀⠀⠀⠉⢶⠀⠀⡟⠀⠤⠀⠀⠀⣠⣤⣶⠿⢳⣻⡀⠀⠀⣿⠄⠀⠟⣸⣄⡿⠃
⠀⡇⣇⠀⠀⣼⠀⠀⢼⡫⠜⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠳⣤⡤⠶⠊⣙⢋⠽⣷⢦⣎⡥⢴⠋⠀⡋⠘⠚⠷⠛⢛⡇⠀⠀⠀⠀⠀⡀⠠⠤
⠀⢶⢸⠀⠀⡇⠀⠀⠀⠉⠓⠲⠤⠤⠤⠤⠤⠀⠠⠃⠀⠀⠈⣼⣄⣸⣭⣴⡶⠿⠋⠃⣱⠎⠀⠀⢸⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢀⠃⠀⠄
⠀⢸⡌⠀⢰⠇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⢀⣀⣈⣉⣀⠤⠒⠊⠁⠀⠀⠀⠀⠃⠀⠀⠠⠓⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠳⣤⠟⠀⠀⠀⠀⠀⠀⠁⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠂⠐⠚⠀⠀⠀⢀⠀⠐⡀
⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡶⠟⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⣠⡌⠢⡀
⠀⠀⠀⢸⠀⠀⠀⠐⠂⠀⠀⠐⠖⠒⠲⡤⠠⢤⡶⠀⠀⢀⠤⣠⠶⠶⠚⠋⠉⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡽⡆⢀⣬⡦
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠀⠀⠂⠀⠀⠁⢨⠀⠀⠀⠀⠀⣀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠘⠦⠂⣀⣒⠀⠉⠝⠃⠚⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣵⣤⣤⣤⣮⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⠤⣽⣋⣛⣛⣛⣛⣋⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿