Cuisine Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡤
⠀⢀⣀⡀⡀⢙⠁⠀⠄⣀⡀⠀⠀⠀⢰⡁⣷⠘⢆⠀⠀⠮⠀⠀⠀⠀⠀⣤⣿⣮⡟⠀⠀⠀⠀⢀⣠⣄
⠀⠉⠉⠁⠐⠋⠓⠀⠐⠓⠒⠋⠀⠀⠈⣇⠈⣀⡜⠀⠀⠐⠒⢐⠀⠀⠘⠿⣽⠟⠀⠀⠀⠀⠀⠺⠷⠟
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠄
⠀⠀⢞⠉⠀⠀⠀⠀⢀⠀⡠⡄⠀⠀⢀⡰⡖⠃⡄⠀⠘⠚⠿⠟⠃⠀⠀⢀⡁⠀⢤⡀⠀⠰⠷⣾⠿⠄
⠀⠀⠀⢠⠆⠀⠀⢠⠐⠐⢋⠀⠀⠀⢈⠁⠄⠊⠀⠀⠀⠀⠀⠀⣠⠄⠰⠋⣐⣂⠀⠁⠀⠀⠐⠈
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⠄⠀⠀⢈⠁⠶⠄⡀⠀⠀⠐⠲⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠉⠉⢳⡄
⠀⠀⠀⠰⣦⣤⠀⠰⠁⠀⠀⠀⠚⠀⠈⠁⠀⠀⠁⠀⢠⣤⣀⣤⡄⠀⠀⠘⢀⣀⠀⠀⠀⠀⠀⠀⠚⠉⠁
⠀⠀⠀⠈⠛⠋⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⣤⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠆⠀⠀⠀⢠⠐⣀⡤⠀⠀⠀⡀⢠⠀⠀⢀⣤⣤⣤⣀
⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⡀⡀⣤⡈⠀⠠⠤⠴⠊⠁⠀⠀⠤⠄⢀⡀⠀⠀⠘⠄⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣷⠇⠀⠐⠒⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠈⠀⠀⠈⢀⡇⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠲⡀⠀⠀⠀⠐⠀⠀⡀⣂⢢⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠈⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠙⠿⠞
⠀⠀⠀⠓⠄⠀⠀⠀⣀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⡀⠀⠀⡀⠰⡆⠀⠀⠀⠀⣀⠀⠀⣀
⠀⢦⣤⣤⣤⡴⠀⠐⠿⣽⣦⠿⠀⠀⡀⠊⠑⢀⠀⠀⠉⠁⠀⠉⠡⠀⠰⢁⢶⠦⣔⢢⡀⠾⢏⡽⠃
⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠉⠉
⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠰⡆
⠀⠀⠈⠉⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠒⠶⠀⠀⠀⠘⢻⡙⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠻⣀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠴⠿⠄⠀⠀⠀⠀⢦⣤⡤⠟⠁
⠀⠀⠀⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠠⠁⣠⡆⠀⠠⠄⠂⠴⠈⠀⠀⣀⣿⣄⡑⠀⠀⠀⢀⠀⢢⠀⠀⠀⠀⠀⠛⠃⠈⠀⢠⡤⡤⢤⡄
⠀⠀⠀⠈⠂⠀⠀⠀⢀⣀⠀⠀⠀⠤⠟⠽⠑⠷⠀⠀⢀⡘⢑⡎⠀⠀⠘⠋⣤⠀⠆⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠒⠒⠂
⠀⠀⠂⣀⡀⠀⠀⠀⠀⠉⡄⠀⠀⢀⣠⡴⠶⠂⠀⠀⠀⠀⡀⠒⠀⠀⠀⠒⠒⠂⠤⠀⠀⠘⠃⠀⢴⢓⡄
⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⣀⠀⠿⠁⠀⢀⣶⡤⠼⠶⠁⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⢿⣿⡿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣾⣶⣷⣶⣷⣶⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣠⣈⣡⡘⠋⠀⠀⠀⠀⠀⢀⡀⠄⢀⡀⠴⠁⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠈⠑⠀⠐⠈⠀⠀⠀⠈⣅⣀⠄
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⡠⠃⠀⠀⢀⠀⠀⠀⠀⠀⠁⡀⠐⠁⠀⡀⢀⠀⠀⠁⠀⠠⠀⠀⠠⠀⠊⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡂⠠⢐⠡⠂⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠋⢉⠡⡉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠂⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⡆⢠⠋⠀⠀⠀⠀⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢋⠀⠂⠀⠐⠖⠀⠀⠀⠈⠂⠁⠀⠀⠀⠀⠀⠊⠀⠀⠀⠁
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠁⠀⠀⢀
⠀⠀⠀⠐⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠑⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠈⠁
⠰⢄⠰⠄⠤⠂⠀⢀⡤⠠⠀⠆⠆⠰⠀⠀⠀⠀⠜⠢⢀⡠⠄⠤⠄⢠⡤⠀⠰⠄⠠⠀⠀⡠⠄⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠰⠂⠸⠀⠀⠀⠀⠀⠀⠠⠤⠥⠀⠐⠀⣈⢐⠂⠀⠀⠃⠠⠄⠆⢀⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠙⠂⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⡀⠀⠀⠐⠒⠀⠀⠈⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠠⠄⠀⠂⠀⠀⠀⠠⢉⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠
⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⢉⠁⠀⠂
⠇⠀⠈⠀⠑⠦⠠⠄⠀⠈⡄⠀⢀⠤⠆⠀⠈⣆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠁⠀⠒⠀⠀⠸⡀⠀⡇⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⢀⠠⠥⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠈⠒⠈⠀⠄⠀⠀⠀⡈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⠀⡀⠀⢠⡴⠋⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠬⢉⠡⡐
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠭⠕⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠴⠄
⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠈⠁⠀⢠⣰⡀⠀⠀⠀⠠⠀⢀⠀⠀⢀
⠀⠀⠀⠂⠐⢊⠢⠀⠀⠀⠀⠀⣈⠀⠤⣴⠁⠀⠀⠀⠀⠁⡜⠀⠀⠐⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠂⠀⠂⠀⠀⠐⠂⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢀⣠⣤⣤⣀
⠀⠀⠀⠀⠐⣀⣴⣿⣿⠏⠀⠀⠀⠈⠋⡀⠀⠡⠁⡀⠀⠤⠀⠔⠀⢀⠀⠀⡀⡀⠁⢀⠄⠀⠀⢼⠿⠟⠻⠿⠿⣷⡀
⠀⡀⠀⣠⣾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠂⠀⢀⡀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠘⠟⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠐⠆⠉⠛⠁⠉⢀⣀⡀⠀⠀⠀⠂⠀⠀⠀⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⣜⣠⡖⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⡐⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣐⢎⠗⣼⣷⡱⡀
⠀⠀⠉⣠⡆⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⡿⢷⣮⠡⠊⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⢯⣠⣴⣾⠫
⠀⠀⠀⡆⢀⠀⠀⠀⢀⡴⠖⣢⡶⢶⡄⠀⠘⠀⠀⠀⠸⢛⠿⠟⠀⠀⢀⠂⣵⠁⠀⡱⢍⠀⠀⠀⠀⠀⠈
⠀⠄⠀⠀⠀⢰⠀⢠⡿⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠁⠀⠇⠀⠐⠀⢀⠀⠀⢶⡷⣷⠆
⠀⡄⠰⠔⡀⠀⠀⢸⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣈⠫⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⠨⣥⠀⠙⣃⠀⠐⠀⠀⠀⠀⠐⠈⠁⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠶⢰⣋⠰⠿⠀⠺⠽⡀⠀⡀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡦⠁⣤⠠⢞⡇⠠⡇⠀⡀⠀⠀⠀⠀⢤⢆⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⡇⢸⠅⣐⡋⢈⠧⠀⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠄⠐⠀⠂⠒⠸⢎⣀⡚⣠⢀⠀⠀⠀⠈⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⢀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢙⣫⣑⠂⢦⡀⠀⠀⠀⢠⣴⣶⣤⣤⣤⠒⠀⠀⠉⠙⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⣙⣤⠤⢤⡃⠀⠐⠿⣿⣿⣿⣿⣿⡓
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡅⡋⢈⡂⡁⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠈⠐⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡋⡷⡹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠠⢄⡀⠀⠹⣿⣋⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘
⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠈⠉⠀⠀⣀⣄⠀⢀
⠀⠀⠀⠀⠘⢷⣤⣄⣀⠀⣀⣠⠜⠁⠀⠀⠀⢀⠀⠘⣄⠀⠤⠂⠀⡅⠀⠀⠄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠤⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣠
⠀⠰⠁⠀⠀⠀⠀⠉⠈⣆⠈⠁⡎⠀⠂⠀⠑⡄⠀⠀⠠⠁⡠⠖⢄⠠⠕⠌⠀⠀⠀⠀⠀⠃⠠⠀⡠⠂⠀⠂⠁⠀⢅⢜⠀⢀⠄⠒⣄⢤
⠀⠀⠀⡀⠀⠤⠀⢐⠊⢮⡀⠀⠳⡀⠈⠆⢄⠀⡆⠀⢇⣀⡠⢀⠔⠀⠀⠀⠠⠀⠀⢀⠀⡀⢀⠊⠀⠀⠈⡰⠁⢠⣤⡉⠀⠓⠒⠂⠌⠉
⠀⠀⠐⡲⠤⠁⠀⡀⢈⠠⠃⠀⠀⠑⠢⣈⠠⡑⠘⠀⡀⢒⢝⣱⠀⠀⠀⢠⢁⣄⡀⡈⠀⠃⠂⠀⠀⢀⠜⢡⠀⠀⠀⠀⠄
⠀⢰⡀⠐⢒⠂⠀⠀⣠⠄⡒⢢⢂⠒⠠⣀⠀⠁⢀⣾⠅⠘⡮⡞⠀⠀⢢⡐⠁⠀⠰⠀⠀⢈⠐⢄⠔⠁⠀⠀⠏⠑⠒⠂⠀⠀⠀⠈⠁⢄
⠀⠀⠁⠀⠘⠀⠠⠊⠄⠄⢀⢁⠂⣬⠤⣂⡗⠀⠈⠁⢀⠀⢹⠃⠀⠈⠙⠥⢀⣀⢾⡢⠄⠈⠀⠁⠠⢁⠂⠀⠑⠒⠊⠀⡄⡘⠂⡄⠀⠈
⠀⠀⡏⠙⡆⠀⢡⠬⢉⠭⠆⠤⠔⠊⣉⡴⠀⢸⠉⠉⠑⢢⠈⠁⠀⡀⠀⢀⠀⠂⠀⠀⠀⠀⣀⣀⣀⠁⠐⠗⠀⠐⠀⠀⠀⠀⠐⡀⠠
⠀⠀⡷⢀⠘⢄⠀⠐⠒⠒⠒⠒⠋⠉⠀⠀⠀⡌⠀⠀⠀⡷⠀⢀⠠⠀⠠⡊⠘⠀⠀⢠⣾⣿⣻⣟⣙⣷⠀⢠⠀⠀⢠⡀⠀⣰⠃⢀⠋
⠀⠀⢧⠐⠂⡸⠀⠀⠀⢖⠒⠂⠠⠤⠐⠲⠂⠙⠀⠒⠊⠀⠀⠀⠈⠃⠀⠀⠀⠀⠠⡀⢀⠿⠁⠀⠀⠀⢃⠐⢀⡀⠐⠀⠀⠈⠉⠁
⠀⠀⠈⠉⠉⢁⠔⣄⡀⣄⠉⠀⠒⠒⠈⠁⠀⠀⣀⢒⣂⠀⠀⡠⢀⡀⠀⠒⡲⢲⠀⢡⠀⠀⠀⡙⠅⠨⠀⢀⡀⢇⠀⠀⣠⠈⠣⠈⠀⡆
⠀⢌⡀⠅⠀⠂⠀⠈⠀⠈⠀⠀⠀⠊⠖⣂⡎⠧⠓⢃⠜⣠⡄⢰⠀⣀⣀⡀⠁⠁⠀⠀⠐⠂⠀⠐⠀⠁⠰⠀⠀⠉⠀⢐⠁⠀⡠⠋⠑⠕
⠀⠀⠀⠀⠌⠀⠀⠄⠠⠀⢸⠆⠈⢉⡀⢁⠀⠄⠂⢁⠬⠐⡁⢀⡮⠞⠁⠀⠀⠀⠈⡄⠀⠋⠀⢠⠦⠄⠰⠢⠄⣤⠀⢇⡀⠼⡀
⠀⠀⠀⡈⠠⢄⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⢔⠄⠰⠗⠚⠓⠉⠀⣠⠾⠆⠀⠀⠠⡠⠁⠀⠀⠃⠌⠀⠁⠉⠀⠃⠀⠱⠀⠐⠊⢁⠔⠂
⠀⢰⡀⠁⠀⠠⠒⠀⠀⠀⣐⣥⡌⠁⠄⠀⣀⣀⣤⡄⣸⣆⠀⠀⠲⠉⢀⠳⠒⠀⠠⠲⠀⢀⠠⠀⠁⠀⠠⠀⠀⠀⠴⠀⠀⠀⡄⢀
⠀⠀⠉⢀⡄⢢⠞⠁⠀⠀⠀⠘⢄⠁⠀⠜⠉⠀⠀⠠⠀⠚⠛⠂⠠⢒⠁⡀⠀⠀⡀⠀⡀⠸⠂⠀⢀⣀⣀⣀⣀⠤⠶⡀⠀⢀⠁⠀⠘⡆
⠀⢐⠁⠖⠀⠠⠀⢈⠀⣀⢀⣀⠀⠀⠌⠀⠀⠀⠀⠠⠀⠠⠀⠒⠄⠀⠑⠁⠅⡀⠤⠊⠁⠀⢀⢀⠀⠀⠀⠀⠀⠂⠈⠐⢂⠈⢤⣀⠠
⠀⠈⡄⠀⢀⠤⠂⠀⡊⡴⠀⡄⠡⡀⠐⠀⠀⠐⠒⠛⠠⠁⠀⠀⢰⠀⠠⠀⠤⠃⠔⠐⠄⠰⠯⢀⡀⠀⠀⣀⠔⠆⠀⠙⠗⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⢱⠈⠈⣀⠀⠄⢰⠁⠂⠒⠀⠐⠀⠀⠀⠄⣼⠀⢠⠀⠀⠀⠀⠀⠀⠀⡠⠖⠂⠀⠒⠺⡀⡀⢀⠱⠀⠀⠀⠀⡀
⠀⢠⠄⠅⠋⢇⢸⡄⠈⠒⣊⡀⠀⠠⣁⢠⢔⠁⠐⠀⠀⠙⠀⠀⠱⠀⠐⠈⣉⠀⠀⠠⠒⠉⠀⠀⢀⠔⠂⠁⢁⡟⠁⠀⠀⢺⣿⡤⠐
⠀⠀⢀⠀⣂⢀⠠⠄⠀⠈⡤⠌⠂⠀⠀⠈⠈⡄⠀⠢⠁⢀⡠⠴⠁⠀⠀⡀⠀⢠⠂⠣⣀⡀⢐⣢⠄⣀⣀⡠⠎⡐⠇
⠀⠀⠨⠀⠀⠠⠀⠀⠀⠀⠀⠀⠆⡀⠔⠀⠀⠀⢀⡠⢤⣄⠀⠠⢀⠀⢀⠊⠐⠠⠑⠂⠀⠀⠀⠑⠊⠈⠁⠒⠉⠀⠰⠅⠀⠀⠈⠀⠰⡀
⠀⠀⠀⠁⠀⠀⠀⠄⠀⡀⢆⠀⠀⠁⠀⢔⠒⡂⢹⠀⠀⡜⠂⠀⠌⠀⢀⠀⠀⢀⠄⠀⠀⢰⢩⠇⠔⢉⠆⠆⠙⠄⠀⠀⠀⢠⡠⡀⡀
⠀⠘⠜⠀⠀⣀⠀⠀⠀⠈⣉⠀⠀⡀⢀⠀⠋⠀⠘⠤⠤⠧⠀⠠⠀⣠⡀⠁⠈⠋⠀⢠⡀⠀⠀⠀⠈⠁⠀⠀⠁⠀⢰⠉⠀⠒⠀⠀⠐⣺
⠀⠀⡴⡝⠃⣴⠓⠀⡠⡈⢂⠄⠂⠀⠀⡅⠀⢀⠄⠂⣀⣂⡄⠀⠀⢀⠠⠠⠆⠀⠀⠀⠠⠀⠐⢢⠴⣶⣖⠀⠐⠀⠀⢣⠄⣀⣀⣀⡐⠃
⠀⠀⣧⠤⠙⠀⠀⡄⠀⠀⢀⠀⠀⣀⠔⣁⠀⡂⡰⠋⠀⠤⠈⠂⠤⠤⠄⠊⠀⠠⠂⠀⠀⡀⡀⠜⠀⠀⠢⡀⠀⠀⠀⠄⠀⠀⠀⠀⡀⢰
⠀⠀⠀⠑⠒⠒⠒⠁⠀⠀⠀⠈⠀⠀⠀⠁⠀⠋⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⡀
⠀⠀⢠⢴⡧⠖⠚⡛⣷⠀⠀⠀⢀⠌⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢣⠀⢀⠔⣄⠀⢠⣄⣀⡀⠀⠀⣤⢤⡤
⠀⠀⢸⡄⠁⢁⡀⠤⠸⡆⠀⠘⠀⠀⠀⠀⠀⠀⠱⠑⡀⠀⢀⠔⠲⡒⡀⠀⠀⡆⢹⠀⢇⠀⢸⠀⢘⠿⢿⠂⠀⠀⡆⠀⡆
⠀⠀⠀⡧⠠⠀⢒⣂⠁⣳⠀⠰⣄⠀⠀⠀⠀⠀⢀⡴⠁⡠⠃⢄⡄⠈⢶⡀⠀⢁⠸⡆⠀⡕⡅⠀⢀⢳⠁⠀⠀⢀⠇⠀⢇
⠀⠀⠀⢳⡈⠭⢄⡐⠦⠝⠀⠀⠀⠍⠹⠹⠉⠍⡇⠀⣰⢁⣀⡈⠀⠀⣀⢳⠀⠈⢸⠃⠀⠀⡇⠀⠈⢠⠀⠀⢠⡋⠀⠀⠘⢷
⠀⠀⠀⠈⠊⠀⠒⠂⠁⠁⠀⠀⠀⠺⠈⠙⠛⠋⠇⠀⠈⠉⠉⠉⠉⠉⣉⣁⣀⣀⣀⣋⣀⣉⣁⣀⣈⣁⠀⠀⢠⠀⣉⡀⠈⠈
⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈⠒⢲⣲⡒⠒⠒⢒⣖⡖⠒⠒⠒⠁⠀⢸⡀⣊⣈⣀⢀
⠀⠀⠀⡔⣡⠔⠂⠁⠐⢌⠢⡀⠀⠀⠀⢀⡔⢈⠉⠈⠉⠒⢄⠀⠀⠀⠸⠘⠉⣠⠖⠒⢦⡉⠙⣮⠀⠀⠀⠀⠨⣀⡀⠀⢀⡰
⠀⠀⠈⠘⠔⠒⡄⣀⢀⣀⢡⠡⠀⠀⠐⠑⠁⡎⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⣿⣶⢠⣴⡇⠀⣿⠀⢀⠄⠀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⢀⢸⡀⢀⠇⡣⠿⢝⡜⠠⠀⡤⣦⣤⣤⡄⠐⠒⠒⠒⠒⠚⠢⡄⢰⢀⠀⠈⡷⠒⡏⠁⠀⠿⠀⠸⠼⡆⣷⠲⢷⢸⢈⢼⢃
⠀⠀⠀⠢⠋⠅⣀⣈⡒⢛⠔⢁⣀⡈⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠁⠀⠈⠈⠉⢀⠀⠀⠀⠈⠉⠈⠀⠐⠒⠒⠒⠒⠒⠒⠒⠊⠁
⠀⠀⠀⢸⡸⠁⠐⠀⠀⠀⠠⣟⣒⡨⡆⠀⢀⠔⡒⡒⠒⠈⢕⠌⣇⠀⠀⡏⠀⠤⠀⠐⠃⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠌⠃⠹⠁⠀⣤⠰⠀⠃⠆⠃⣀⠴⡍⠀⠀⢳⠛⠉⣽⣟⡇⠀⠀⢹⠓⣛⡛⣛⠛⡛⢛⢛⠻⣻
⠀⠀⠀⢀⣀⣀⢀⡀⠀⠀⠙⠦⠦⠄⠀⠀⠘⠵⣲⣖⡆⠽⠚⠉⠀⠀⠀⢸⡴⣶⠏⢹⠇⠀⠀⢧⠘⣅⠗⠟⠹⡇⠟⠾⢀⢿
⠀⠀⢰⠧⠤⠄⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠛⠀⠀⠀⠂⠁⠀⠈⠈⠀⠀⠀⠀⠁⠘
⠀⠀⢈⡺⠡⠀⠘⡂⠀⠀⢰⢑⡠⠤⠤⠤⠴⠥⠯⠮⠬⠤⠤⠤⠤⡄⡏⡇⠀⢀⠤⠐⣑⣒⣑⡒⠠⠤⣀⡀⠀⠀⢀⣀⡀
⠀⠀⠘⡔⢄⣀⠰⡱⠀⠀⢸⢸⣈⣉⣉⠉⠉⠉⠋⢹⠉⠉⠉⣉⣉⣁⡇⡇⠀⢨⠢⠉⡇⠆⠀⡂⢉⠢⣤⠛⡂⢠⠇⠀⠘⡆
⠀⠀⠀⠈⠑⣲⠉⠀⠀⠀⢸⢰⠒⠒⡆⡇⠀⠀⡀⢸⠀⠀⢸⢰⠀⠀⡆⡇⠀⢸⡤⣀⡃⠂⠀⠃⡈⠴⠙⢄⡀⠀⢙⠉⠉⡅
⠀⠀⠀⠀⠰⠾⠄⠀⠀⠀⠸⡸⠀⠀⡇⠇⠀⠀⣅⡸⠀⠀⠸⡸⠀⠀⠇⠇⠀⠀⠘⠚⠩⠉⠍⠃⠊⠁⠀⠀⠀⠈⢤⣀⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠄⠀⠀⠀⣀⣀⡀⣀⡠⢜⠵⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠠⢄⡢⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠁⠁⠑⠋⠭⠝⠋⠁⠀⠀⠀⢀⠔⡩⠢⠀⠰⠉⠀⠠⢆⠀⠀⠀⠀⠀⠀⠹⣿⣧⠎⠉⠀⠀⠀⠀⠀⠀⡔⢮⣹⠖⢤⡀
⠀⠸⡡⡁⠁⠁⠀⠀⠀⡇⠀⠀⠀⠈⠰⡁⢣⡄⠈⠂⠒⡡⡸⠀⠀⠀⠀⣠⡤⢦⣽⣦⢦⣤⡀⠀⠀⠀⠀⢸⡠⠤⠒⣊⡩⠇
⠀⠀⡱⠕⣂⣀⢀⡠⢮⡀⠀⠀⢄⠘⠂⠘⠒⠃⠀⠀⠁⠚⢁⠄⢠⡤⠼⠿⠿⠿⠿⠿⠿⠿⠷⠤⢤⠀⠀⡗⠐⣋⡉⠥⠔⠃
⠀⠀⠈⠁⠀⠉⠀⠀⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉

⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢠⣖⡀⠢⢗⣦⣀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢠⡀⠀⠀⠀⢀⠀⢀⠀⠀⢠
⠀⠠⢌⡘⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺⣡⣮⣿⢶⡇⠀⠀⠀⡀⠀⢀⣉⠿⠇⠁⠘⠀⠀⠀⠀⢀⠈⠀⡄
⠀⠀⠘⠀⠂⠀⠰⠔⠁⠀⠀⠀⠀⠀⢠⡆⡆⠀⠀⠀⠸⠤⠞⠁⠀⠀⠀⠘⠓⡚⢁⣀⠠⠄⢂⠀⠰⠣⡀⠀⠀⠀⡀⠀⣀
⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣉⢸⠗⠤⠔⠂⠁⣰⠳⡀
⠀⠐⡀⠠⠀⠀⠈⠢⠤⠄⣤⣤⡄⠍⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⣅⠄⠀⠀⠈⢴⣰⠂⠀⡀⠀⠈
⠀⠃⢀⠰⠦⠀⠀⠀⠀⠀⠁⠀⠤⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⠖⠚⠉⠉⠀⠀⠘⠟
⠐⠀⠀⠃⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠲⠆
⠀⠀⢀⠀⠀⠀⢀⠄⡄⠓⣴⡄⠀⠀⠀⢀⠠⢠⠀⠀⣠⢠⡀⠠⠠⠀⠠⢀⢠⢀⠄⠀⠀⠀⠀⠀⣠⠄⠀⠀⢠⡀⠀⢀⡀
⠀⠁⠀⠀⠀⠀⠀⡌⡿⣿⣿⡧⠀⠀⠀⠀⠀⠉⠉⠈⠉⠉⠁⠀⠈⠁⠈⠁⠉⠉⠀⠀⠀⠀⠀⠀⣄⠀⠑⠆⠈⠉⠉⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠈⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⣤⣖⡢⠐⠋⠀⠀⢤
⠀⠀⠘⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣴⡽⠟⠿⠑⠺⠫⠈⠂⠀⠠⠒
⠀⠀⠠⡀⠀⠁⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⠀⡀⢀⠠⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⣀⡀⢠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠀⠀⠐⠀⠉⢉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⣩⡭⢎⠉⠿⠀⠀⠠⠒⠀⠀⠀⠸⠣⠀⠀⠀⠀⣀⠀⠀⠈
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢒⡯⢉⣶⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠬⡤⠦⠠⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠦⣄⣰⠋⣳
⠀⠀⠀⣠⣻⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣀⡠⠶⣇⣠⣇⠀⠀⠀⠀⠀⠀⢀⠤⠤⣀⣀⠴⠒⠲⡄
⢀⡴⣧⠬⣧⠀⠀⠑⠤⣀⡀⠀⡀⠀⠀⢸⣧⢇⣴⣉⣷⢭⡟⢳⠀⠀⠀⠀⠀⢇⠀⠀⣠⠤⠤⣄⠀⢧⡀
⠛⠛⡇⠀⠈⠑⢦⣀⣀⣀⣈⣹⣡⠀⠀⢸⡛⠳⠧⠤⢼⠏⠀⠈⡇⠀⠀⠀⠀⢀⡷⠠⡇⠀⠀⢘⡆⠀⠙⣆
⠀⠀⠙⢦⣀⠀⠀⠈⠉⠙⢳⡴⡆⠀⠀⠀⢧⠀⠉⢠⠏⠈⠀⠀⢹⡀⠀⠀⢰⠋⠀⠀⠑⠦⠤⠊⠀⠀⠀⡼
⠀⠀⠀⠀⠈⠙⠒⠒⠒⠒⠚⢶⠃⠀⠀⠀⠀⠳⣴⠃⠀⠀⠁⠀⠀⢧⠀⠀⠸⢄⣀⡠⠴⠒⠒⠦⢤⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢀⠀⠒⠀⠀⣸⠂
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⠀⠀⠀⠀⣀⡀⠈⢦⡀⠀⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⣌⡅⠉⠁⠀⠀⠀⠀⠀⠈⠓⣿⠀⠀⠈⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⣆⡄⢴⢉⣆
⠀⠀⠀⣀⣀⣸⣻⣀⣀⣀⡀⠀⠀⠀⠀⢀⣴⣁⣣⣄⠀⢰⡇⡆⠀⠀⢀⣴⠆⠀⢀⣄⣱⡏⣹⡾⣻⡈⢯⠆
⠀⠾⡭⠭⠭⠤⠤⠴⠶⢶⠟⠀⠀⠀⠀⡸⠖⠒⠒⠪⣀⠈⡇⢣⡞⠓⢿⠁⠀⠀⠘⠒⣦⡉⠣⡇⡟⢳⠈⣣⡀
⠀⠀⢧⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⡖⠓⢿⡦⠞⠀⠀⠀⠀⠹⡛⠛⠒⠛⠓⠛⠋⣹⠁
⠀⠀⢸⡄⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡼⠶⢿⡦⠜⠁⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣇⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢸⠀⠀⢀⡴⠦⣿⣤⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⣀⣀⢀⡇
⠀⠀⠀⠸⠤⠤⠤⠤⠼⠀⠀⠀⠀⠀⢸⣄⣀⣸⣄⡀⣈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⠶⠤⢄⣀
⠀⠀⣠⠿⢛⠻⠯⣹⠯⣽⣦⣄⡀⠀⠀⠀⠁⠀⣠⠴⠒⠒⣶⠦⣄⡀⠀⠀⠀⠀⠀⣻⠴⣄⣀⡄⠈⠙⠲⣄
⠀⣰⠁⠀⠀⠰⠀⠈⠳⡟⢮⡦⣝⡆⠀⠀⠀⡞⠥⠈⠃⠓⡀⠚⣠⠽⡄⠀⠀⠀⠀⣿⠳⡄⠈⡙⠲⢆⡀⡀⠱
⠀⠘⢄⠀⠠⠀⠀⠀⠠⠜⡌⢻⣷⣽⠀⠀⠀⢹⠲⣶⠶⠾⢷⣶⠶⢶⣟⠀⠀⠀⠀⣿⠵⢃⣴⣚⣿⣶⣝⡦⠴
⠀⠀⠀⠙⠢⣄⡀⠁⢀⠀⢹⣼⢼⠇⠀⠀⠀⢻⣍⣭⠭⢿⣭⡬⠭⠭⣾⠀⠀⠀⠀⡧⣄⢸⣝⠾⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⣨⡧⠋⠀⠀⠀⠀⠀⠳⠤⣄⣀⣈⣹⠦⠴⠃⠀⠀⠀⠀⠧⠚⠉
⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣾⣛⡲⣄
⠀⠀⠀⠀⣰⠞⠩⠍⠩⠉⠭⠙⢦⡀⠀⠀⠀⠀⢀⣴⣒⣚⣓⣒⣦⠀⠀⠀⠀⠀⠀⢀⡇⢸⡇⠀⠀⠀⠀⠀⢀⡴⢛⣭⢽⡇⡷⣋⣙⣮⣷
⠀⠀⠀⢸⣧⣬⣥⣬⣤⣬⣤⣥⣤⡷⠀⠀⠀⠀⢸⣭⣭⣭⣭⣭⣭⡇⠀⠀⠀⠀⠀⣼⠛⠛⢷⠀⠀⠀⠀⢀⡟⣴⣫⣄⢸⡟⣿⠷⣛⡭⡄
⠀⠀⠀⢘⡷⠶⠶⠴⠶⠦⠴⠶⠶⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⡏⠙⡆⢸⡇⠀⠀⠀⢸⠰⡇⠳⡞⢹⡤⢖⣋⢹⡇⡇
⠀⠀⠀⠀⣿⠛⢿⡛⠉⠉⢛⡿⢻⠇⠀⠀⠀⠀⠀⢸⡄⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣿⠛⠁⢸⠀⠀⠀⠀⠘⣇⢳⡸⣿⠆⣂⡛⢛⡼⢡⠇
⠀⠀⠀⠀⠈⠛⠛⠛⢦⡾⠛⠛⠉⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⡀⠀⠀⠀⠀⠘⠦⣙⠒⠾⠭⠟⣋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁
⠀⠀⠀⠀⠀⣤⢦⡞⢳⡶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⡶⣤⡀
⠀⠀⠀⢠⣿⣹⣌⣧⣼⣡⣏⣿⡄⠀⠀⠀⠀⠀⠀⠀⠨⠇⠟⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠍⠉⠛⠲⣄⠀⠀⠀⠀⠀⠀⣰⠏⠀⠂⠙⠮⣷
⠀⠀⠀⠘⡇⠈⠉⠉⠉⠉⠁⢸⠇⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⣿⠶⣄⠀⠀⠀⢺⣥⠤⣅⣤⢥⣨⠤⣬⡇⠀⠀⠀⠀⢰⠇⠈⠀⡁⠈⣰⠋
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣧⠴⠃⠀⠀⠀⠀⢹⡀⢸⠀⠀⡟⢠⡏⠀⠀⠀⠀⢀⡞⢳⣅⣤⠴⠛⠁
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢰⡒⠚⠛⠒⠒⠒⠚⠓⠒⡶⠀⠀⠀⠀⠀⣧⠘⡇⢸⡇⣼⠁⠀⠀⠀⣟⠋⡶⠋
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠛⠁⢀⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀⠀⠀⠀⠀⣠⠟⠓⢶⠚⢧⡀
⠀⠀⠀⠀⠀⡴⠖⠛⠁⠘⢦⡀⠀⠀⠀⠀⣠⠶⠒⢲⡴⠒⠲⡴⠖⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣄⣹⡄⠀⠀⠰⣟⣛⣛⣛⣛⣛⡷
⠀⠀⠀⠀⣾⠛⠛⠛⠋⠛⠛⢳⠀⠀⠀⢠⣏⣀⣀⣈⣁⣀⣀⣁⣀⣀⣀⣷⠀⠀⠀⠀⠀⠀⢀⡴⢯⣀⠀⠉⡧⠀⠀⠀⠸⣄⣤⠶⢋⣽
⠀⠀⠀⠀⢿⠉⢻⡏⠙⡟⠉⡿⠀⠀⠀⢸⣿⠯⠼⣿⠬⠖⠦⠴⣿⠽⢛⣿⠂⠀⠀⠀⢀⡤⢿⡄⠀⠈⠓⢶⠃⠀⠀⠀⠀⢿⡤⠖⢻⠇
⠀⠀⠀⠀⠘⡇⢸⡇⢸⡇⢸⠃⠀⠀⠀⠘⢯⣽⣓⣛⣛⣛⣛⣛⣛⣛⣯⠿⠀⠀⢠⡖⠛⣆⠀⠙⢦⡀⣠⠞⠀⠀⠀⠀⠀⠘⡷⠚⡿
⠀⠀⠀⠀⠀⠻⠤⠧⠼⠧⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠙⠓⠞⠶⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠹⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠲⡟⠷⢶⠀⠀⠀⠀⢀⡴⢶⡀⠀⡴⠶⣄⠀⠀⠀⠀⢰⣟⣚⣳⢀⡼⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⢫⢟⡷⢤⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⢹⡾⢻⣳⣟⡦⠀⠀⢠⠟⠀⣦⠙⣾⠁⣦⠙⣦⠀⠀⠀⠀⡇⠀⡇⢈⡿⠛⣟⠀⠀⠀⠀⠀⠀⣠⠞⣱⢋⡞⠀⠀⢹⡄
⠀⠀⠀⠀⢀⡴⠋⠀⠀⢸⠟⠚⣧⠟⠀⠀⠀⢸⠀⢰⠏⠀⣿⢠⠏⠀⣸⠀⠀⠀⣠⠇⠀⢷⡏⠁⠀⠈⣷⠀⠀⢀⡴⢚⡵⢾⡵⠋⠀⠀⢀⡞
⠀⠀⠀⢴⠋⠀⠀⢀⡴⠋⣠⠞⠁⠀⠀⠀⠀⠈⢷⡘⢃⡴⢿⡌⠃⡰⠋⠀⠀⠀⡏⠀⠀⠈⡇⠀⠀⠀⣿⠀⠀⠘⣟⡽⠞⠉⠀⠀⢀⡴⠋
⠀⠀⠀⠈⠳⣤⡴⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠙⠚⠁⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠉⢷⣀⣀⣠⡴⠋
⠀⠀⠀⠀⠀⠈⠓⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠚⠛⠒⠒⠒⠋⠀⠀⠀⠀⠀⠈⠉⠁

⡿⢿⠿⠿⡿⢿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣛⣛⣻⣿⣟⣻⣿⣻⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠐⠘⠀⠀⠀⠀⠐⠒⠒⠈⠉⠉⠁⠒⠒⠒⠀⠀⠒⠒⠢⠤⣀
⠀⠀⠀⢀⡂⠐⠰⠀⠀⣠⠠⠾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⡀
⠀⠄⠈⠉⠀⠂⢄⣀⠐⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣖⠒⢰⠤⡄⡀⠀⠀⠈⢀
⠀⠈⠦⣌⠋⠀⠶⠴⠶⠂⠘⠟⠀⠀⡁⢀⠈⡄⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⠃⠲⠶⢀⢠⡄⠀⢀⡄
⠀⠀⠑⢝⠢⡀⠠⡀⠀⠠⢁⠂⠒⢠⢂⣊⣩⠁⠀⠀⢀⣠⡄⠀⢐⠀⠐⢰⠲⣍⣈⣀⣀⠀⠀⠈⠀⠀⢠⠇⠀⠊⡇⠀⢙
⠀⠀⠈⠛⢷⣤⣀⣁⡈⢁⢛⣶⠴⡯⠝⠒⠉⠀⠀⠀⡙⠀⢠⢒⠋⠄⢆⣀⢈⣑⡇⠁⠀⣀⠀⠀⠀⢀⠊⣠⠎⢀⡇⠀⢨
⠀⠀⠀⠠⠀⠀⠁⠉⠀⠠⠈⠀⠀⠀⠠⠄⠀⠀⠀⠀⡁⢸⡡⢼⠀⠀⠀⠀⡈⠁⠂⠀⢀⡀⠀⣠⡔⢁⡌⠀⣠⠞⠀⠀⠔
⠀⠀⠀⠀⠀⡤⢠⣔⠒⣀⢶⣆⣀⠠⠀⠀⠀⠀⠀⠀⠈⢺⠱⣏⠀⠀⠀⠀⠀⠀⠀⣀⣠⣦⠞⠉⠔⣟⣤⠖⠁⠀⣀⠂
⠀⠀⠀⠀⢤⡀⠀⠀⠉⠛⢷⠞⠐⣊⣄⡀⠀⠁⠀⠘⣀⠸⡔⠋⢁⠐⠒⠒⢒⡈⢩⠏⠋⠥⢈⠄⡤⠁⠴⠖⠋⣨
⠀⠀⠀⠀⠀⠁⠀⠀⠐⠠⡄⠹⡤⢠⣶⠅⠀⠀⠀⠀⠙⠉⣧⡀⠑⠤⠤⠖⠉⠀⣀⡴⣊⠀⠀⠀⠠⠄⠀⠄⠀⠀⠀⡀⡀⢀
⠀⠀⠀⠈⠃⠀⢀⡀⠀⠀⠀⠀⣧⠈⣶⠈⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠶⠶⡖⢺⡁⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠
⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⣄⠈⢆⢅⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠈⠉⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⢨
⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠁⠀⢈⡈⠳⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠣⠤⠦⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠃

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⢠⣤⣤⣤⡄⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣴⣶⣶⣶⣶⣶⣶⣶⣶⣆
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⢻⣿⣿⡇⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⣿⡇⠀⣀⢸⣇⡀⠀⣿⡇⣿⣿⣿⢻⣿⣿⣻⣿⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⡟⢿⢻⣿⢸⣿⣿⡇⠀⠀⣸⣿⣿⣿⣧⠀⠀⠀⣿⡇⠀⣿⣿⣿⡇⠀⣿⡇⣿⣿⡟⠀⢿⡇⠈⣿⣿⡇
⠀⠀⠀⠀⢸⣿⠀⢠⣤⣤⣤⡀⢸⣿⠀⣿⣿⣷⣿⣾⣿⣼⣿⣿⡇⠀⣰⣿⣿⣿⣿⣿⣷⡀⠀⣿⡇⠀⠙⢻⡟⠃⠀⣿⡇⣿⣿⣧⣤⣿⣧⣼⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣶⣶⣶⣶⣶⣶⣾⣿⠀⣿⣶⣶⣶⣶⣶⣶⣶⣿⡇⣰⣿⣿⣿⣿⣿⣿⣿⣷⡀⣿⣷⣶⣶⣾⣷⣶⣶⣿⡇⢿⣷⣶⣶⣶⣶⣶⣶⣾⡇
⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢤⠤⡤⠤⠤⠤⠀⠀⠀⣄⣠⣠⣄⣄⣤
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣇⢠⣷⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢦⣭⣭⣬⣥⣭⣭⡤
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠆⠛⠀⠀⠀⠀⠀⣶⠶⠶⠶⠶⢶⡶⡆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⢦⡀⠀⠀⠀⢀⣀⣐⣀⡀⠀⣰⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣠⡇⠀⠀⠀⠀⠿⠷⠾⠀⠠⠿⠿⠿⠆⠀⠀⠀⠶⠂⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠶⠶⠾⠿⠇
⠀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⣩⣭⣭⣭⣭⣭⣭⣭⣭⡍
⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⣿⣿⣿⣛⣛⣛⣿⣿⣿⡇⣿⡷⠷⠾⠶⠾⠶⠷⣿⡇⣿⡇⠀⣠⣤⣤⣄⠀⢽⡇⣿⡇⠀⠴⠶⠶⠦⠀⢸⡏
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡏⠋⢻⣋⣟⠙⠋⣿⡇⣿⣧⣤⣤⣤⣤⣤⣤⣼⡇⣿⡟⠛⣛⣛⣛⣛⠛⢻⡯
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇⠀⣿⣿⣿⠀⠀⣿⡇⣿⡇⠀⣤⣤⣤⣄⠀⢹⡇⣿⡷⠶⠶⠾⠿⠶⠶⢾⡯
⠀⡁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣧⣴⣾⣿⣷⣦⣤⣿⡇⣿⣧⣤⣤⣤⣤⣤⣤⣼⡇⣿⣇⣀⣛⣛⣛⣋⣀⣸⡧
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⢂⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠁⠀⠀⢀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣄⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠙⠒⠒⠋⠀⠀⠀⠀⢠
⠀⠑⢀⡀⠈⠐⠠⠀⠀⠀⢐⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⢀
⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢀⠁
⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣍⣴⠋⠙⣆⡞⠉⢹⡄⡏⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠘⠲⠞⠁⠙⠲⠚⠁⠳⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⣰⣇⢰⠋⡂⣶⡃⣞⢹⡀⣿⠢⡎⢱⢸⢰⢰⢦⡆⣞⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠈⠀⠉⠀⠀⠁⠈⠉⠀⠀⠀⠈⠁⠀⠉⠀⠀⠁⠈⠁
⠀⢀⢀
⠀⠰⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠠⠀⠀⠀⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⠀⠀⠀⠂⠤⡀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠋⠁⠀⠈⠙⣆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠋⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠂⠀⠀⠀⢀⠠⠊⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⡗⠐⠂⢲⠀⠄⢨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠸⢇⠸⠟⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⠀⠀⠐⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⠛⠠⡘⠳⠀⠒⡦⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣹⡀⡀⠀⠀⠀⠆⠀⣆⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠
⠀⠀⠀⠈⣶⡦⣤⣤⣤⣤⣄⣀⣀⣀⣀⣄⣤⣤⣤⣤⣶⠁⠀⠀⠀⠀⠀⠈⠙⠛⠒⠓⠻⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠰⣿⣷⣿⡿⢽⣿⣿⣯⣿⣿⠷⢾⣿⣷⠾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⢸⠂⢉⡛⢛⠓⡻⠿⡿⠿⠿⣿⣏⣀⣦⣜⣭⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⢸⣿⣭⠟⠾⠃⠐⠊⠙⠁⠉⠉⠉⠉⠉⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡁
⠀⠀⠀⠈⠙⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⣥⠨⠟




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠀⢠⠞⠃⠀⠀⠀⠔⠂
⠀⠀⠀⠀⠀⠀⣼⠀⣀⣀⣀⠳⠶⢶⠤⣤⡤⣀⢄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡀⢲⡀⠀⢀⡄⢰⠃⠐⢄
⠀⠀⠀⠀⢠⠛⣼⣯⣢⡿⢥⠑⢀⠙⠾⠟⣓⡛⠐⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⠁⠈⠨⠟⢮⠁⣨⠠⠴⠚⣦⢤⠁
⠀⠀⠀⠀⠀⠀⣿⠃⠜⢲⡈⣥⠤⢤⡴⠎⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣆⡘⠲⠒⠲⠋⠃⠀⡆⢰⣅⠀⠂⡴⠃
⠀⠀⠀⠀⠀⠀⠻⣄⡤⠤⠀⠻⢆⣠⠗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣾⣆⣀⠀⢸⣷⡷⣌⣉⣾⣿⣠⣼⢀⣰
⠀⠀⠀⠀⠀⠀⠀⣟⠀⠐⢃⣴⠞⠀⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⣧⠈⢻⣏⣢⣄⡹⢷⠀⢸⣿⣤⣠⣟⠸⡏
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡈⢙⢷⠾⠓⣾⣠⣽⣿⣦⣭⣵⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡳⠶⠶⠞⢁⠞⢬⠭⠫⠤⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡀⠀⠀⠀⠀⠆⠀⠄⠀⠀⠀⢀⠀⠢⠀⠀⠀⠀⠀⠌⠁⠀⠀⠈⠂⠤⠀⡖⡂⢆⡔⣀⠀⠀⠀⠀⢀
⠀⠀⡀⠀⡐⢂⠀⠀⠀⠠⠁⠄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠪⠄⠀⡀⡆⠐⢀⠴⢀⠀⠀⠀⠀⠐⠁
⠀⢀⠐⠂⠀⡀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉
⠀⠀⢐⠁⡄⠔⢒⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠑⠀⢠⠀⡶⠡⣤⡔
⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡶⠀⠠⡧⠟⠄⡆
⠀⠀⠡⡄⠀⠐⠂⠀⠀⠀⠀⢉⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈
⠀⠘⠁⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠈⠈⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐
⠀⠠⠀⠉⠘⠶⠆⠉⠐⠄⠀⠄⠀⠀⠐⠀⡡⡈⠟⣰⡆⠀⠦⠀⠀⠁⣀⡀⢠⣴⡀⠀⠀⠀⠉⠀⠀⠐⢀⠀⠀⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠈⠀⠀⠀⠂⠀⠀⢺⣆⣬⠗⣢⡁⠢⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⢸⠇⠠⠀⠀⠀⠀⠀⠀⠀⢠⡴⠂⠀⠀⠏⠁⠙⠜⠅

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠿⠿⢹⣿⠃⡇⢀⠀⠀⠀⠀⠢⠀⠀⡀⠀⠀⡀⠀⠀⠁⠀⠀⢀⠀⠈⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠂⠀⠀⠀⠑⠾⢿⣶⢾⡫⣔⠣⠙⠀⠀⠀⢀⣀⠀⠈⠀⠀⠐⠀⠀⠀⡆⠂⠄⠀⠀⠀⠈⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠊⠁⠀⠀⠀⠀⠀⡁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠆⠀⠀⠀⠄⠰⠴⡠⢦⡈⠰⠄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢠⠈⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠉⠀⠀⠙⠉⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⢁⠀⠁⠀⠀⠄⠀⠈⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠐⢀⢀⠘⣀⣤⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠨⠈⡙⡉⢉⠞⠀⠀⠠⢄⡄⣤⡀⠀⠀⠀⠈⠀⡀⠀⢀⢄⠠⣠⣤⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣁⠀⠀⠀⠀⠈⠐⡈⢶⡅⠈⠀⠀⠀⠀⠀⠀⣴⣛⢣⣶⢻⣇⠖⣦⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⢀⡉⣤⡀
⠀⠀⠀⢀⣰⣿⣾⣿⣿⣭⢧⣤⣤⡄⠀⠀⠀⠱⠄⠼⠄⠀⠀⠀⢀⠀⢰⡿⢻⣟⡷⣿⣿⣈⣏⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⢀⣀⢽⠀⠁
⠀⠀⠀⠘⢽⡷⣿⣟⣿⢿⣿⣿⡋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣿⣯⣿⣮⣹⡋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠻⠾⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠈⡀⢀⠀⡄⠂⠀⠀⠀⠀⠀⠀⢠⠀⢼⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⣿⣿⠇⠀⠠⣾⣿⣿⠀⠂
⠀⠀⠀⠀⡈⠀⠋⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⣿⣿⣿⣿⡟⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⣿⡇⠀⠀⠀⠈⢿⡟
⠀⠀⠄⡀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⣿⣿⡿⠠⡡⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠘⣧⠘⣧⡀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠚⠀⠀⢻⣿⠃⢀⠠⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⣻⡄⠙⠿⣦⣀
⠀⠀⠀⠀⠀⡧⠀⠀⠈⠑⠄⠀⠠⠐⠀⠀⠀⠀⠈⠗⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⡟
⠀⠀⠀⠀⠀⠇⢀⣤⣄⠀⠁⠀⠐⠠⠄⢀⠐⠓⠀⠂⠀⡈⠀⠀⠀⠀⠂⠈⣠⡀⠀⠀⠙⠧⠀⠀⠛⠃⠀⢀⣿⡿
⠀⠀⠀⠀⢰⢀⣿⣿⣟⠀⠀⠀⠠⢠⡀⠀⠀⠀⠀⠘⢂⡠⠀⠠⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⠀⢀⡄⠀⠀⠀⠀⠀⡀⠄⠀⠈⢻⡗⠂⢠⣤⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠌⠄⠀⠀⠀⠀⡈⠀⠀⠀⠀⠘⠓⠚⢿⣿
⠄⠀⠀⠀⠀⠀⢠⠚⠉⠁⠄⠀⠀⠀⠀⠂⡠⠀⠀⠄⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠙⠃
⠀⠰⠤⠐⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠁⠀⠻⠏
⠀⠠⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠂
⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⣠⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⠀⠈⠓⠀⠉⠟⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀⠀⠈⡌⢿⣦⣐⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣾⣿⡿⣦⣤⠀⠀⠀⠀⠑⢦⡈⠻⢿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⠀⠀⠈⣿⡷⣼⡟⠀⠄⠀⠀⠀⠱⣄⠈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡻⣶⡤⡿⣿⡟⠎⠉⢾⣷⣠⡀⠀⠀⠘⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣿⡿⠷⠶⣴⡌⠠⣅⠀⠀⠀⢹⣿⣿⡆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⣿⡆⠀⠀⠀⠋⠹⠶⢋⣀⣤⣤⡈⢳⠀⢉⣷⢧⡶⣺⣹⡿⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⣀⣴⣿⣷⣿⣆⡿⣦⡹⠿⣿⣧⢹⡿⠾⠛⠁⢀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⡀⠀⠀⠘⠀⠀⠀⠾⠟⠉⣸⠛⠛⠋⢰⣽⣯⠈⠋⠙⠋⠀⠀⠀⠀⠈⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢠⣴⢆⡄⠘⠁⠀⠀⠀⠈⣿⡿⠀⠀⠀⢀⣀⡦⣀⣴⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡙⢦⡀⠀⠀⠟⣀⡀⠀⠀⠀⢀⡼⠛⠠⣄⠢⢴⣿⣿⣧⡿⡟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣷⠀⠀⠐⣌⠻⢶⣤⣀⣘⠁⠀⠀⢀⣀⣨⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠸⣷⡀⠀⠉⠙⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠒⠚⠉⠛⠉⠙⠛⠉⠳⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠃⠀⠀⠀⣀⠀⢀⣤⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠘⠲⡀
⠀⠀⠀⠀⠀⠀⠀⡤⠃⠀⠀⣀⡴⠚⠉⠉⠉⠀⠀⠀⠈⠉⠋⠙⢦⣤⣄⡀⠀⢀⣧⡀
⠀⠀⠀⠀⠀⢀⡴⣇⣀⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠻⡀⢹⡀
⠀⠀⠀⠀⠀⢸⢀⡞⠁⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⢳⡀
⠀⠀⠀⠀⢠⠏⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡞⠁
⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣆⠀⢀⡰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⢀⡤⣤⣤⣤⡶⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⢸⣿⣿⣟⣻⡇⠀⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⣸⠛⠛⠓⠚⣇⣀⣠⠤⣶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡾⠶⠭⣦⡀⢀⣜⣉⣠⡤⠴⢿⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⢠⡇⠀⠀⠀⣹⠋⠀⠀⠀⠀⠀⠘⡇⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢠⣼⣀⡤⠖⠚⣇⣸⡀⠀⠀⠀⠀⠀⢹⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⡟⠀⠀⠀⠉⣩⡿⡄⠀⠀⠀⠀⠘⡇⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠘⣇⡀⠀⠀⠀⣇⠀⠀⠀⠀⣤⣶⣅⠀⠀⠀⠀⠀⢹⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⢹⡖⠒⣛⣶⠒⠲⡖⣇⣀⣸⠷⢶⣶⣶⢤⣈⣇⡴⢻⢷
⠀⠀⠀⠀⡴⠒⠒⣲⡾⣭⣿⣿⠽⠋⠙⠤⠴⠃⠀⠉⠁⠀⢯⠀⣸⡇⠈⢿⡷⣿⠾⣷⡒⠒⠒⢦
⠀⠀⠀⣸⠃⣠⠞⠁⢠⣾⣷⣛⣦⡤⢖⣦⠀⠀⣠⣤⣄⠀⢈⣭⣭⣤⠖⢋⣴⡿⠓⡆⠙⢢⡀⠈⢧
⠀⠀⣰⠃⠀⢻⡀⠀⠘⢯⡙⠻⢭⣛⣛⣛⠓⠛⠓⠛⢋⣉⣉⣠⡤⠴⠚⣩⣾⣳⠋⠁⠀⣰⠃⠀⠘⣆
⠀⢠⠇⠀⠀⠀⠙⠲⢤⣀⡉⠓⠶⠤⣬⣉⣉⣉⣉⣉⣉⣉⣥⠤⠴⠒⠋⠁⠀⣉⣠⠴⠚⠁⠀⠀⠀⠸⡆
⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠲⠶⠤⠤⠤⠤⠤⠤⠤⠴⠶⠒⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠀⠀⠀⠠⠖⡡⠐⠒⠒⠠⡙⢦⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄
⠀⠀⠀⠀⠀⠀⡠⢂⠥⢂⠈⠌⢁⠠⠤⢀⠀⠀⠀⡀⠀⠀⠈⠂⢃⠀⢀⡀⢞⠃⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⡠⡪⢚⠕⠈⠀⠐⢊⡔⠂⠀⢨⡇⠢⠀⠀⠐⠄⠀⡀⠈⠀⠀⠹⡄⢣⠁⠀⠳⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢀⠌⠔⠔⠑⠀⠀⠀⡀⠈⠂⢊⠔⠋⠈⠓⠀⠀⠈⢆⠀⠡⠀⠀⠀⠀⠰⠀⠃⠳⡘⣆⣄⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂
⠀⠀⡌⠀⠀⠀⠀⠀⠁⠀⠙⢄⡉⠀⠀⠀⠆⠀⠆⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⢣⠀⠀⠈⠀⠁⠀⠀⠀⠒
⠀⠀⠀⢁⠀⣤⠀⠛⣀⡀⠀⠀⠉⠀⠀⠀⠁⠀⠈⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡀⠙⠀⠘⠉⢼⣻⡆⠀⠀⠈⠀⠀⠀⠀⠈⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢴⢼⠰⠔⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⡀⠂⠀⠀⠀⠀⠀⢠⣻⠛⠀⠀⠀⠀⠀⠀⠒⢄⠀⡄⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⠀⠈
⠀⠀⢀⡀⠀⠄⠀⠀⠀⠈⠠⡄⠀⠇⣞⠄⠀⠂⠁⠀⠁⠐⢀⠀⠂⠐⠀⠆⠱⠠⠈⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠘⠀⠀⠀⠀⢄
⠀⠀⡜⠱⠀⢄⠀⠀⠀⠀⠀⠠⠖⠚⣿⢲⡦⢀⡄⢀⠄⠠⢂⠀⠀⠀⠀⡄⠃⠀⡀⠀⠀⠂⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠠
⠀⠀⡇⠀⠈⠀⠁⠀⡀⠀⠀⠀⠀⠀⠉⢋⠉⠅⢀⠠⢊⠔⠁⠀⠀⠀⠀⢟⠀⠰⡇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡄⠀⠀⡈
⠀⠀⠐⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⢒⣀⠠⠐⠈⠀⠀⢀⡀⠀⡀⠀⢀⣀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠌
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⢿⠀⠇⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⢉⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠇⠀⡆⠀⢀⠈⠀⠀⢈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠐⠢⢤⠂⠐⢄⠀⠀⠀⠇⠄⠀⠀⠂⠃⠀⠘⠂⠃⠀⠛⠀⠀⠇⠀⠀⠀⠀⠀⢀⡤⣤⢤⡤⠄⣲⠶⡄⣀
⠀⠀⠀⠀⠀⢀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⢀⠆⠀⠀⠀⠀⠀⠐⠐⠠⠒⠀⠔⠂⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⡀⠀⠀⠀⠈⠢⢬⣎⡢⠄
⠀⠀⢀⠄⠢⠎⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠈⠈⠄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⠀⠀⣠⠎⠀⢢
⠀⠀⠠⠀⠀⡄⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⢢⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡇⠀⢣⠀⠀⠀⠀⠀⠙⠲⣄⢸⡇
⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⠤⠄⠀⠀⠀⠀⠀⢠⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠑⠊⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⢂⡵⢶⠒⢦⠀⠀⠀⠈⢹
⠀⠀⠀⠀⠀⡂⢡⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠰⠦⢴⣒⣐⠀⡠⠶⠆⠀⠄⠀⠀⡐⡀⣄⣘⠶⢞⡴⠀⠑⡄⠀⣠⠇
⠀⠀⠀⠀⠀⠘⠉⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡜⣯⠍⠄⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⠺⠀⠀⠏⠀⠀⠀⠈⡁⠀⠀⠀⡼⠜⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⢀⢼⠀⠀⠀⠀⠀⠀⢰⠄⠉⡄⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⢄⠞⠁
⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠛⠄⠀⢌⠀⠀⠀⠀⠀⠀⢸⠀⠀⡁⡼⠇⠀⠀⢀⡠⠒⠉⣀⠤⠀⠀⠀⠀⠀⠉⠀⠀⠚⠛⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠔⠒⠒⠶⠤⢀⠀⠄⠀⠀⠀⠀⠀⢸⠀⡏⠁⡇⠀⠠⠚⠁⠀⢀⠄⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⠃⢀⠈⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠺⠄⡰⠃⡀⠰⠅⠒⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢤⡐⠓⠒⠓⠒⠓⠒⠒⠒⠢⢤⣶⡄⠀⠀⠀⢀⣤⡴⢲⠖⢢⣄
⠀⠀⠀⢀⣴⠞⠋⢉⠉⠛⢦⡀⠀⠀⠀⠀⠀⠈⠀⠀⠛⠒⠚⠒⠚⠛⠓⠉⠁⠀⠀⠀⠀⠀⢀⡾⣠⣤⣼⣄⣤⣼⢳⠀⠀⠀⠀⠀⢰⠨⠤⠤⢼⡀
⠀⠀⠀⣾⠁⠀⠀⣀⡀⠀⠈⠿⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⡞⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠟⠀⠒⡒⠚⣣⡀
⠀⠀⠀⣟⠁⠀⢰⠋⠙⠂⠂⣸⠃⠀⠀⠀⠀⠀⣰⡟⠀⠁⠀⠀⢀⢄⡀⣸⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠉⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠘⢦⣀⡉⡄⣀⣠⡴⠋⠀⠀⢠⣀⡆⠀⣿⡅⠀⣾⠙⡶⠻⠼⠋⢹⣿⡃⣠⡏⢰⡟⡇⣾⣹⡀⠀⠀⠀⠰⠄⠀⠀⠀⢀⣇⣀⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⣀⣤⠞⣿⡀⠀⠘⠳⠔⠛⠚⠁⠀⠀⠀⠈⠁⠉⠉⠛⠉⠀⠉⢉⢽⠇⠀⠀⣠⠶⣦⡀⠀⠀⠘⠛⠋⢥⢈⡭⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡋⠀⠄⠊⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠒⠀⢀⠀⠈⠋⠀⢀⡾⢥⣬⣏⣝⣷⡄⠀⣀⣴⠟⠀⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣐⡡⢀⠁⡆⣿⡄⠀⠀⠀⠀⢀⣀⠤⠔⠒⠀⢐⠒⠤⣀⠀⠀⠄⠀⠀⣿⠄⣺⢲⠓⡇⢁⡟⠀⠉⠉⠉⠉⠉⠉⠁
⠀⠀⣠⠶⠛⠛⠛⠛⠓⢦⠀⠘⠿⢻⣄⢀⠢⢀⡇⠀⢀⡤⠚⠉⠀⠀⠴⠀⠀⠀⠉⣢⡈⠡⠀⠐⠢⡀⠙⠶⣍⣹⢙⣳⠟
⠀⠀⡯⢏⠉⠉⣢⠀⠀⢸⠀⠀⠀⠀⠙⠳⠾⠛⠀⡴⠉⠀⠀⠀⠀⠀⠀⡐⣈⠀⠂⠀⢌⠀⠀⠀⠀⠈⠢⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠈⠓⠚⠛⢶⠖⣾⠋⠀⠀⠀⠀⠀⠀⠀⢀⡞⢠⡦⠀⠀⠀⠀⠀⠀⡀⠁⠀⠁⠐⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣴⣲⣶⣾⣷⣰⣶⣶⡄
⠀⠀⠀⠀⠀⠀⣼⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠘⠀⠻⠀⠀⠀⠀⠀⠹⡛⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠨⡇⠆
⠀⠀⠀⠀⠀⠀⠳⠛⠾⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠄⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⢀⡠⠤⠤⣄⠤⡤⢤⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠲⠒⢈⡶⠤⢴⡄⢰⠋⠁⠀⠀⠀⠀⠀⠈⡃⠀⠀⠀⠀⠧⠤⠤⠤⠤⠤⠤⠼⠂
⠀⠀⠀⠀⢀⠎⠁⢰⢏⠤⠂⠑⠀⢸⠆⠀⠀⡆⠀⠀⠀⠉⠢⠤⠄⢀⣀⡜⠙⠀⠸⡁⢙⠀⠀⢀⡄⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠘⣄⠐⠬⢀⡀⠠⠊⣠⠞⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⢈⡃⠀⠀⠀⡇⠀⠀⠀⡄⠀⠀⠀⠀⡼⠀⠀⠀⡀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠈⠑⠒⠶⠶⠚⠋⠁⠀⠀⠀⠀⠀⢠⣤⢴⠶⣀⣲⠶⣤⣼⣄⠀⠀⠀⡧⠀⠀⡠⠇⠀⠀⠀⡴⠁⠀⠀⠀⠀⢿⠀⠀⠆⠀⢀⡿⢶⡆
⠀⠀⠀⠀⠀⣤⠤⢤⠤⠤⠤⡄⠀⠀⠀⠀⠀⠀⠈⠓⢧⠤⠭⠥⢴⣎⡓⢋⠁⠀⠀⣤⠤⠚⠀⠀⠀⢀⠜⠁⠀⠀⢲⠀⠀⠸⡄⠀⠂⠀⢠⣧⠟⠁
⠀⠀⠀⠀⠀⢷⠋⠉⠉⠙⢲⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⢩⠀⡀⠀⠀⠤⠀⠀⢀⡀⠞⠁⠀⠀⠀⣴⠀⠀⠀⠀⢇⠀⠥⠀⢸
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠈⡇⠀⠀⠀⣀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠀⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⠒⠒⠒⠃
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣧⠀⠀⠀⣧⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⡀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⣤⠤⢤⣤⣤⣤
⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⡸⠀⠀⠀⢸⠀⠀⢰⠃⠀⢺⣯⣭⣭⣝⣳⠀⠀⠀⠀⠰⣽⣿⣿⣯⡿⠀⠀⠀⢠⢻⣷⠀⠀⠀⠀⠀⠀⠈⠉⠛⢛⠉⠉
⠀⠀⠀⠀⠀⠈⠲⠶⠦⠤⠞⠁⠀⠀⠀⠈⠈⠉⠉⠀⠀⢠⠇⠀⠀⠀⣇⣠⣤⣄⠀⠀⠘⢼⣿⡿⠀⠀⠀⠀⠘⠾⠟⠀⠀⠀⠀⠀⠀⢠⠴⠚⡚⠒⢄
⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠀⠀⣀⡀⣹⣇⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣿⣫⠄⠠⢑⡊⡇
⠀⠀⠀⣔⣒⣒⣚⣛⣒⣒⣒⣆⣀⣀⣀⣠⡤⣤⡄⠀⢸⣇⠀⠀⠀⠀⢨⡿⠋⠀⠀⠀⠀⠀⠀⠀⣠⡔⣊⣉⣀⣀⣀⣉⣑⣦⡀⠀⠘⠰⠷⠶⠶⠶⠥⠗
⠀⠀⠀⣇⣭⣄⣬⣡⣤⣄⣤⡟⠉⠁⠓⠛⠉⠉⠁⠀⠀⠛⢷⣦⣤⣴⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢫⣿⣭⣭⣥⣭⣭⣭⣭⣭⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣯⣭⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠛⠉⣹⣿⠿⠋⠉⠀⠘⢦⣴⣿⣿⣿⣿⡛⠉⠛⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⣤⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠙⣿⣭⡀⠁⠀⠀⡠⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⣿⣿⣿⣿⠗⠀⠰⠟⣋⣉⡁⠀⠀⢯⣤⣾⣶⣷⣾⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠘⣿⣿⡿⣿⠆⠀⠘⠻⠛⠋⠀⠀⠀⢻⢫⡟⠻⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⣀⠂⣁⠀⠀⣸⣿⠀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠋⣠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣾⡿⢿⣧⣤⣶⣿⣿⡆⢙⢉⡀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⢀⡇⠀⠙⠿⣾⣿⣿⣿⣿⣿⣿⡻⣭⡽⠁⠀⠀⠀⠀⠀⢀⠜⣿⣿⣿⣿⢿⣿⣿⣿⡀⠀⠀⠀⠀⢸⡀⡷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⡜⡇⣠⢀⣴⣯⣥⣉⠛⢿⣿⣿⣧⡀⠀⠀⢀⣀⣠⣤⠖⠁⠀⣿⡿⠛⠁⣼⡟⠋⢻⠱⡀⠀⠀⢀⢸⢣⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢶⣂⢼⣿⠇⣇⣿⣿⣿⣿⣿⣿⡷⢈⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢸⣧⣰⣶⣿⠀⣠⣾⣇⠹⠀⠀⣼⣼⠈⣿⡧⣐⡾
⠀⠀⠀⠀⠀⠀⠀⠘⢿⠄⢻⡆⢸⣿⣿⣿⣿⣿⣿⣿⠿⠛⠻⢿⠿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣶⠃⢠⢧⡇⢸⡏⢀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡌⣿⡾⣷⣼⣿⠏⠈⢹⣿⣿⣾⣿⣶⣦⣤⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⡴⠛⣻⡿⠿⣿⣿⣿⣿⡆⢸⣾⠁⣾⢿⣿⢡
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡾⣿⡻⣿⣏⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠁⠀⠀⣀⣤⣴⣿⣵⠶⠋⠁⠀⠠⣴⠿⣿⣿⣿⣾⡿⣰⢛⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣜⣷⣿⠿⢻⣿⠟⠿⢿⣿⡿⣿⠟⢻⣿⣧⡀⢀⣠⡴⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⣼⣣⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⢻⣷⣿⣿⣦⣶⣦⣬⣼⠏⠀⠀⢻⣿⣿⢫⣡⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠟⣡⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⠻⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢐⣿⡿⢛⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣿⣿⣿⢏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡙⢶⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣞⢛⣉⠀⠈⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣗⠁⠀⢉⡟⣳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣽⠗⣺⣿⣄⠹⣷⣀⠀⠀⠀⠀⠀⢈⡉⠀⠀⠉⠁⠀⢠⣴⠟⣡⣾⣗⠺⣯⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⢯⣍⣶⣦⣝⣻⣦⣬⣄⡀⠀⠀⣀⣠⣤⣴⣞⣯⣶⡶⣩⣽⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠙⣻⢶⣿⣯⣿⣿⠿⠿⣿⣿⠿⠟⣿⣿⣿⣿⡶⣟⠿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠫⠽⢿⣆⢠⣤⣧⡄⣰⣿⠯⠉⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣋⣙⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣟⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣭⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠋⠉⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡓⠂⠀⠀⠀⠚⡉⠂⠀⠀⠉⠉⢉⢩⡅⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠿⠆⠀⠀⠸⠿⠃⠀⠀⠀⠀⢱⡆⠃⣀⠔⢸⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣈⢴⠊⠀⠐⠋⠉⢉⠍⣠⠞
⠀⠀⠀⡀⣤⠀⠀⠀⠀⠀⠀⢧⠀⢤⠤⠤⢀⡠⠄⠀⠀⠀⡀⠡⡼⢶⠶⠿⠭⠄⠒⠈⠁
⠀⠇⠀⠄⠋⠓⣦⢤⡀⠀⣠⣤⣷⡄⠻⠉⠹⠁⠀⠀⢀⡔⣀⣴⣿⣷⣤⣤⣀⡀
⠀⡄⠀⠀⠓⠀⡌⠀⢰⣾⣿⣿⡏⢹⡄⠒⠃⠀⣠⣴⡫⢕⡫⡾⠃⣿⣿⣿⣿⣿⣿⣷⣶⣄
⠀⠈⢦⡀⠈⠠⢁⣴⣿⣿⣿⣿⣿⣿⣿⣶⢖⣋⠉⡀⠀⠁⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠄⠊⠙⠻⣿⣿⣿⣿⣿⣿⣿⣍⠽⠳⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣾⣿⣿⣿⣿⣿⣿⣦⣙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⣿⣿⣿⣷⡄
⡀⠀⠀⠀⠀⡇⠀⠀⣠⠶⠟⠋⠨⠟⠛⠛⠛⠛⠛⠛⠛⠳⣬⣙⠿⠿⢿⡿⠟⠛⢷⣽⣿⣿⠟⠋⠉⠙⢄
⡇⠀⠀⠀⢠⢂⠴⠋⠀⢀⠤⠤⣀⣈⣀⣤⡀⡠⣤⣠⣤⣾⣿⣿⣷⣿⠛⠀⠀⠀⠀⠈⠉⠉⠀⠂⠀⠀⠀⠙⠢⢄
⠱⠤⠤⠄⠊⠁⠀⠀⠀⢸⣿⣿⣿⠿⣿⠿⡿⢿⣿⣟⣿⣟⡁⠉⠉⠙⢼⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣭⣿⢿⣿⣽⣿⣿⣿⣿⣟⣳⣆⠀⠀⢀⠊⠐⠤⠐⠀⠂⠉⠀⠉⠒⠤⡀
⠀⠀⠀⠀⠀⢄⠀⠀⢼⠛⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡿⠿⠁⢈⡡⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠉⠐⠒⠦⠤⠭⠭⠉⠭⠭⠽⠯⠥⠜⠂⠲⠛⠁

⠀⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⡆⢰⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⠀⢰⠖⠒⠒⠒⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠖⢷
⠀⡇⠀⠀⠀⠀⠀⣤⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸
⠀⡇⠀⢀⣀⣀⣀⣿⡦⠴⣦⣤⣀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⡤⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢸
⠀⡇⠀⢠⣿⣿⣿⣧⡄⢾⣿⠟⠟⠁⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⢠⣤⣼⡏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⢸
⠀⡇⠀⠀⠀⣽⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⢀⣸⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸
⠀⡇⠀⠀⠺⠟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⢀⡴⢻⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⢀⣨⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⢸
⠀⡇⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⣰⠋⢰⡟⢻⣿⢿⡀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⡿⠿⠏⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⡆⠀⠀⠀⠀⠻⣿⣿⠃⠀⠀⠀⠀⡇⢸⠂⠀⡴⠁⠀⠉⠀⠀⣿⠁⢧⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⢠⣄⣤⣼⣿⢋⡿⠁⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢀⡾⠁⠀⠀⠀⠀⠀⡙⠀⠘⡆⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⢩⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠐⠻⠿⠷⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⠃⠀⠀⠀⠀⠀⠀⠹⣀⠀⣇⠀⠀⠀⠀⠀⣸⡇⢸⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣿⠀⠀⠀⠀⠀⢿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛






⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣛⣭⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠻⣿⣿⡿⠿⠿⢟⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢀⣀⡀⡀⠈⠛⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⠀⢻⠿⡤⠀⠀⠀⠟⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣑⡒⠊⢀⡀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⡓⠀⠉⠀⠀⢀⣤⠂⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⢶⠿⣿⣧⣀⣀⣠⣴⠟⠁⢀⠀⢸⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢿⡇⠙⣿⡍⠁⢀⡄⠀⠀⡎⠀⠈⣏⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠟⠀⠀⢀⠀⠀⠀⠀⡀⠸⠇⠀⠈⣧⣤⠈⠀⠀⢸⠃⠀⠀⣿⠀⠀⠉⠓⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡁⠀⠀⠀⠀⠀⠉⠀⠺⠁⠀⣾⠠⠞⣿⣿⠢⡀⠀⡌⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠋⠑⣄⠀⠀⠰⠀⠀⠀⡄⠀⠀⠐⠀⠀⢿⡄⢀⣿⣷⡀⠀⢰⠃⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠼⠃⠀⢀⠀⢠⡇⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⡇⠀⡎⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢹⠂⠀⠈⠀⢸⠃⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⢰⠃⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠈⠘⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠇⣄⠉⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡟⠀⠀⠀⡜⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣞⡼⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠃⠀⠀⡼⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠀⠀⡰⠁⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠰⠁⠀⠀⠀⠀⣧⠀⣀⣀⣤⣤⣄⡀⢻⡀
⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⡏⢠⣿⣿⣿⣿⡋⣁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⣀⣠⡼⠟⣿⠀⠀⠀⢰⡿⠀⠀⠀⠀⠸⠟⢠⡴⢀⣠⡄⠀⠀⢸⡇⠈⣿⣿⣿⡟⣼⡿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣛⣉⣀⣀⣀⣿⠀⢀⠀⠈⠁⠀⠀⠀⠀⠀⠰⣿⣅⡉⠁⠀⠀⠀⡼⠧⠤⠬⠷⢤⡾⠿⠦⠴⠷⠶⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢧⣀⡈⠓⠶⠶⠶⠶⠒⠀⠀⠀⠊⣉⣁⡤⣤⠤⠊⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠷⠿⠿⠿⠿⠛⠛⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠠⠆⠀⠀⠠⠤⢄⣔⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠄⣀⡴⢶
⠀⠀⠀⠀⠀⠈⠀⠀⠸⠃⠒⠓⠚⠂⠀⠀⠀⠀⠀⠀⢐⠣⢰⡁⠀⠀⠀⠀⠀⠀⢀⣤⠒⠘⠃⠰⠉⣁⡼⠶⠒⢁⢅⡴⡋
⠀⣴⣢⣴⡀⠀⣤⣲⣼⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢚⢀⡒⠈⡓⠀⠀⠀⠀⢀⠊⣶⣄⡤⣚⡛⠋⢀⣆⡄⣤⣚⣡⢼⠏
⠘⠠⠴⠓⠐⠒⠀⠒⠋⠒⠒⠂⡬⠄⠃⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠳⣌⠛⠻⠴⣇⣼⡥⠖⣪⠯⠥⠚⢁⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⠬⢤⣬⣭⠤⠤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠
⠀⠀⢀⣴⢶⣀⡔⠉⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⡸⢁
⠀⠀⠀⢹⡟⠁⡄⢁⠀⠉⠑⡄⠀⠀⠀⠀⠀⣀⠀⢰⡦⣴⣉⡉⡳⠛⡅⠀⢀⡀⠀⠀⠀⠀⠀⡼⠙⠓⠚⠃⢆
⠀⠀⠀⢾⣓⣒⣒⣲⣖⣓⣒⣷⠆⠀⠀⠘⣁⢹⡽⣛⡛⠀⠀⢈⢷⠱⠟⣾⣞⡐⠀⠀⠀⠀⠀⢧⢤⠤⠤⢤⡿
⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⢰⣹⣕⣸⡫⢓⢲⣬⢵⡛⠊⢑⣥⢟⡇⠀⠀⠀⠀⠀⢸⡉⠉⠉⠉⠁
⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠘⡟⠮⣍⣉⣙⣄⠁⠀⣩⣟⣫⠴⣺⠃⠀⠀⠀⠀⠀⠀⡅⠀⠀⣀
⠀⠀⠀⠀⠙⣶⠤⠴⠤⢶⠏⠀⠀⠀⠀⠀⠈⠲⢤⣌⣉⣙⢦⡴⣋⣩⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠈⠉⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠴⠤⠇
⠀⠀⡠⠖⡍⠙⠉⣻⣷⠏⣠⡻⣋⣵⠀⠀⠀⠀⠀⠉⠓⣤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢰⠁⣠⣓⣶⠟⠉⡄⣬⠉⠐⡏⠀⠀⠀⠀⠀⠀⢰⠋⠁⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠚⠓⠢⡀
⠀⣿⡜⡻⣯⣏⠀⢮⣀⡨⠀⢠⣿⠀⠀⠀⠀⠀⠀⡞⡞⠲⠖⠒⢺⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⢙
⠀⣟⠮⣿⣷⣮⣶⣶⣶⣶⣿⠿⢻⠀⠀⠀⠀⠀⠀⡇⢧⠀⠀⠀⡸⢸⠀⠀⠀⢀⡀⡔⢉⡉⠉⠉⠉⠉⠉⠉⠙⠁⠈⢣⡀
⠀⠙⣷⠤⣀⣉⡉⠉⠉⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠑⠤⢽⣶⡯⠤⠊⠀⠀⠀⠀⠁⢂⢰⣿⣶⡦⠀⠀⠀⠀⢀⡅⠀⠐
⠀⠀⠈⠙⠲⠤⣤⣤⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣤⣷⠄⠀⠀⠀⠀⠀⠀⠈⠲⠤⠤⠦⠤⠤⠤⠤⠤⠤⠖⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠒⠶⠋⠙⠚⠉⠙⠚⠋⠙⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣀⣠⠦⠤⠴⠞⠲⠶⠛⢦⣄⣠⢤⡀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⢀⣤⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠲⣄⡀⢀⣸⠷⣄
⠀⠀⠀⠀⠀⠀⢀⡤⢿⣀⣰⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢧⡀⢹⡄
⠀⠀⠀⠀⠀⠀⢸⠃⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠹⡄
⠀⠀⠀⠀⠀⢀⡟⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡦⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣴⠃
⠀⠀⠀⠀⠀⠸⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠧⣤⣀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣴⣤⣴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢸⡾⣿⣿⠿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⠀⠀⣼⢿⣿⣿⣯⡽⡇⠀⠀⠀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣟⠲⠾⡀⠀⠀⠀⣰⠷⠖⠛⠉⣩⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⢹⠋⠙⠓⠻⢦⢀⡾⠧⠶⠶⠒⠋⠉⢿⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⡿⠀⠀⠀⠀⢸⢸⡀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢠⣼⣇⣠⠴⠖⠛⢻⢸⡇⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢸⠇⠀⠀⠀⠈⢋⣩⣇⡀⠀⠀⠀⠀⠀⠸⡆⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢈⣉⣼⠃⠀⠀⠀⠀⠀⠀⢷⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⣸⣇⣀⣀⣀⣀⣼⠋⠉⢳⣄⠀⢀⣀⡀⠀⠸⡆⢀⣤⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣰⣇⣨⣭⡽⣏⠀⠈⣿⠙⠦⠤⠞⠉⣩⠟⠻⢯⠛⢶⣷⣞⢁⡟⢳⡀
⠀⠀⠀⠀⢠⡟⠉⠛⣉⡿⠿⣶⠿⣿⡖⠋⠀⠙⠒⠚⠃⠀⠀⠀⠀⠀⢻⣄⣀⡼⠀⠀⢹⠞⢻⣟⠻⢿⣝⠉⠉⠙⢧
⠀⠀⠀⢀⡞⠀⣠⠞⠁⠀⣴⣾⣿⣉⣧⣤⠴⢛⣧⠀⠀⣠⣤⣤⣄⠀⠀⣠⣴⢤⣤⠟⢋⣠⣿⠟⢒⡆⠈⠳⡄⠀⠘⣇
⠀⠀⠀⡾⠁⠀⢿⡀⠀⠀⠻⣍⠛⠯⣝⣓⡛⠻⠿⠶⠾⠿⠒⠚⠛⠛⠛⢁⣀⣠⡤⠖⢋⣴⡛⣶⠋⠁⠀⢀⡿⠀⠀⠸⣆
⠀⠀⣼⠁⠀⠀⠀⠛⢦⣄⡀⠈⠓⠦⣤⣉⣉⠛⠛⠓⠒⠒⠒⠒⠛⠛⠛⢉⣉⣤⠴⠞⠋⠀⠙⠛⠀⣠⡴⠛⠀⠀⠀⠀⠹⡄
⠀⣰⠃⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠦⣤⣌⣉⣉⣛⠛⠛⠓⠚⠛⠛⠛⠉⠉⣁⣀⣀⣠⣤⠴⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⢻⡀
⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷

⠀⠀⠀⠀⠈⠀⢀⠀⠀⢀⠀⠀⠀⢀⡍⠑⢖⠓⢀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠈⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⠜⠁
⠐⠄⡈⠒⠀⠐⠂⡁⠀⠀⠀⠀⠀⠀⠁⠉⢀⡙⢌⡁⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢄⠆
⠀⠀⠰⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⣀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠄⠀⠄⠒⠂
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⢀⠄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⣀⠀⠀⠀⠀⠀⠀⡠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣠⣤⡖
⠀⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⣠⢠⡾⣞⣷⢠⠃⠀⠀⠀⠀⠁⡉⢀⠀⠐⠀⡎⠉⢲⠀⠈⡓
⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠃⠀⠀⡽⠐⠑⠡⠋⢈⠆⠀⠀⠀⠀⠀⠀⠄⠀⠀⡄⠓⠒⠚⠁⢀⠁
⠀⡀⠐⢠⠀⠀⢀⡂⣀⠤⠂⠀⠀⠈⡀⠀⠀⠀⡘⢸⠀⠀⠀⠠⡴⠀⠀⠀⢀⣤⣄⠀⣀⡤⠖⠁⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠆⠀⢀⢠⠟⠁⠂⠀⣁⡀⠀⠀⠀⠀⠀⠀⢀⠑⠂⠀⠁⠀⠑
⠀⠀⡄⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⠔⢬⡀⠤⠂⠉⠀⢀⣀⣀⡀⠀⠀⠀⠙⠀⠻⡄⠀⢀⡄
⢀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡈⠀⠀⠀⠈⠉⠂⠄⠀⠀⠀⢣⡐⠉
⠈⠃⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⢀⡀⠢⠀⢀⠀⠀⠠⠄⠀⡀⠁⡀⠌⠀⠀⠀⠀⠀⠈⠂⡀⠐⠀⠀⠪⢠⠀⠐
⠀⠀⠀⠀⠀⠀⠒⠊⠀⠀⠀⠀⠀⠈⠑⠀⠀⠄⠀⠀⠀⠀⠘⢀⠀⠀⠐⠀⡈⠐⠀⠀⠄⠀⠈⡄⠰⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠄⠀⠀⠐⣤⠀⠀⠆⠀⠀⠈⢢⠈⡇⠀⠀⠀⡅⠀⠀⠘⠀⠀⠀⢀⠀⠀⠀⠀⠀⡁⠀⡅⠀⠀⠀⠨⠃
⠀⠀⠀⠐⠋⠀⠀⠀⠂⠈⠁⠄⠀⠱⡀⠀⠀⠀⡇⠀⠀⠀⢃⠀⠀⡓⠂⠀⠀⠀⠀⠁⠀⠀⠐⠀⢰⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡙⠓⢄⢀⡇⠀⠀⠁⠨⢆⠐⢀⠀⠐⠀⠠⠀⠀⠀⠄⠀⠤⠁⠀⠀⠠
⠀⠀⠀⠰⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠄⠀⠀⠱⠤⡈⠀⠀⠀⠂⢀⣀⠴⠊
⠁⣀⡀⣠⣶⣿⣧⣴⣾⡟⠀⠀⠀⠀⢀⡀⠋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⡄⠀⢠⠀⠀⠀⠀⠀⠀⠠
⣈⣿⣿⣍⣟⣿⣿⣿⣯⣷⣤⠤⠄⠒⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡲
⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣛⠆⠀⠀⠀⠄⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠟⠛⢻⢿⣿⣿⠂⠃⠀⠙⠋⠀⠀⠀⠀⠀⠈⠂⠈⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠘
⠀⠀⠀⠛⡙⠉⠀⠀⠀⠀⠀⠀⠠⠔⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⣀⡤⠄⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠀⠐⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠄⢄⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠇⠡⢃⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⡀⠀⡀⠂⠄⣁⠁⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠠⠂⢄⣀⢌⢂⠀⠀⠈⠐⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠠⡀⢜⣀⠜⡘⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⢀⠀⠈⠀⠂⠈⠀⢀⠀⠤⠄⠀⠀⠠⡄⠀⠀⢀⡀⢀⣀⠀⢀⣀⠀⣀⠀⠀⡀
⠀⠀⠀⠀⠰⠉⢈⠲⠂⢠⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⢀⣀⣀⣀⠠⠄⡤⠀⠰⢆⠀⡝⠅⠝⠃⡨⠑⣠⠉⢂⡔⢑⡠⠉⠄⠔⢡⢈⠕⠄
⠀⠀⠀⠀⠀⠙⡃⠤⠆⢁⣆⠔⠙⡀⠜⢣⢀⠛⡌⠘⠣⠀⠛⠄⡌⠡⣀⠂⢑⣴⠀⠱⠦⠤⠑⠒⠚⠃⠈⠁⠀⠉⠀⠈⠈⠈⠁⠀⠉⠀⠘⢃⠌
⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⠈⠉⠀⠙⠂⠐⠓⠀⠘⠃⠀⠛⠐⠈⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠐⠠⠤⠤⠤⠤⠤⠤⠄⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⢀⣀⠈⠉⠭⠉⠒⠃⠈




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠈⠉⠉⠉⠉⠉⠐⠒⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⢀⣤⡶⠾⠛⠛⠉⠉⠉⠙⠛⠛⠷⢶⣤⣄⡀⠀⠀⠈⠲⣄
⠀⠀⢠⢀⡄⣠⣠⡀⠀⠀⠀⠀⢀⡔⠁⠀⠀⣠⣾⣟⠥⠒⠈⠉⠁⠒⢤⡀⡰⠉⠉⠓⣄⠀⠉⠻⢷⣄⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⢀⢄
⠀⠀⢸⣾⣿⣿⢻⡇⠀⠀⠀⢠⠊⠀⠀⢀⣾⢫⠊⠀⠀⠀⠀⠪⠕⠘⠓⢹⣧⠀⠀⠀⢨⠗⠲⣦⡴⠋⠙⣆⠀⠀⠈⠣⡀⠀⠀⠀⠀⢸⠀⠑⡄
⠀⠀⢸⣧⣿⣿⣾⡇⠀⠀⢠⠃⠀⠀⣰⡟⡱⠁⠀⠀⠀⠀⠰⠆⠀⠆⢰⡆⡟⠀⠀⠀⠈⢦⣁⣎⣣⣌⣰⠽⣷⡄⠀⠀⠱⡀⠀⠀⠀⢸⠀⠀⠸⡀
⠀⠀⠘⣿⢿⠿⣿⠃⠀⢀⠃⠀⠀⢰⡟⢠⠃⠀⠀⠀⠀⠀⠀⠀⢰⡲⠀⢀⠃⠀⣀⡀⣀⠀⣃⠤⠈⣧⠶⣀⣠⢿⡄⠀⠀⠱⠀⠀⠀⢸⠀⠀⢀
⠀⠀⠀⠈⢲⡖⠁⠀⠀⡎⠀⠀⢀⡿⠁⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢉⡉⢡⣒⡄⢍⠙⠶⡴⣿⡯⠟⠀⠀⢿⡄⠀⠀⠇⠀⠀⢸⠀⠀⡸
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠇⠀⠀⢸⡇⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⡳⠞⢔⡣⠈⠒⢁⠼⢄⣩⠧⠀⢀⡀⠘⣷⠀⠀⢸⠀⠀⢸⢀⠜
⠀⠀⠀⠀⢸⡇⠀⠀⢰⠀⠀⠀⣼⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢣⠃⢞⡆⣀⡰⠽⠃⠀⠀⠀⠀⠀⠀⠘⡄⣿⡀⠀⠈⠀⠀⢸⡏
⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⠀⢿⢀⠎⠀⠀⠀⠀⠀⠀⡀⠔⠊⠀⢔⡲⠣⠗⠭⡼⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣿⡇⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⢸⢰⠀⠀⠀⡇⠀⠀⡼⠋⠀⠀⠀⠀⢠⠔⠉⠀⠀⡴⠒⠲⢤⡀⠪⢵⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣿⠀⠀⢸⠀⠀⢈⣿
⠀⠀⠀⠀⢸⢸⠀⠀⠀⢡⠀⠀⠑⣾⣄⣀⡀⢠⠃⢠⣊⠉⢆⠙⢅⠠⠀⠛⡄⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢫⡟⠀⠀⡆⠀⠀⠸⢨
⠀⠀⠀⠀⢸⠸⠀⠀⠀⠀⢇⢰⠒⠛⠀⡇⠈⠁⠀⡆⠀⠐⡎⣰⠫⢿⠒⠛⢁⢴⠦⢕⠢⢤⡀⠀⠀⠀⠀⢀⠞⢠⡿⠀⠀⡸⠀⠀⠀⡆⢸
⠀⠀⠀⠀⢸⠀⡆⠀⠀⠀⠈⢎⠒⠢⣀⣼⡀⠀⠀⣇⠄⢸⠃⡌⠀⠬⡆⠀⢂⢏⠔⣹⡤⡖⠸⡂⠤⠤⠔⠉⣰⡟⠁⠀⡰⠁⠀⠀⠀⡇⢸
⠀⠄⠀⠀⢸⠀⡇⠀⠀⠀⠀⠈⠣⡀⠀⠈⢿⣦⡀⠈⠋⠁⠀⠹⡀⣴⠀⢀⡤⠹⢏⠐⡤⠬⡷⡝⠀⠀⣠⡾⠋⠀⢀⠔⠁⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⢸⠀⢡⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠈⠻⣦⣄⡀⠀⠀⠈⠁⠀⢺⡈⢆⣲⠇⠈⠑⢉⣠⣴⠟⠋⠀⢀⡤⠋⠀⠀⠀⠀⠀⠀⡄⢸
⠀⠂⠀⠀⠈⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠉⠛⠷⢶⣤⣤⣄⣀⣑⣶⣥⣴⠶⠞⠛⠉⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠉
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠒⠒⠒⠒⠂⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠄⡠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠁⠀⠈⠑⢄
⠀⠀⠀⠀⠂⠀⢸⠁⠀⠀⠀⣧⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⢈⠇⠐
⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡉⠀⠘⠃⠈⠁⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢋⠙⠳⣄⠀⠀⠀⠀⠀⠀⣴⠟⢉⠙⠳⣄
⠀⠀⠜⣃⡀⢀⠤⣄⢑⣄⣀⣀⣀⣀⡊⢀⠤⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⣿⠐⢺⠺⡁⠸⠀⠀⠀⠀⠀⠠⠇⠐⢪⠮⡁⠿
⠀⠀⠀⠉⠁⠹⢤⠜⠈⠉⠉⠉⠉⠉⠁⠸⠤⠜⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠠
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⢠⠄⠀⠀⢀⠀⡄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢸⡀⠀⠀⠀⠀⠘
⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠁
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠈⡠⠤⠦⠤⢦⡬⠤⠤⠤⠄⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠠⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣠
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠛⠉⠉⠉⠉⠉⠋⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣷⡄⠀⠀⠾⠂⠀⠀⠀⠛⠆⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⢀⡀⠀⢀⢄⣀⠀⠀⢧⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢛⣻⣿⡀⠀⠀⠀⠉⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⣣⡙⠃⠀⠀⢰⠀⠘⠲⠼⠀⠀⠀⠀⢸⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⠙⣧⠀⠀⠈⠙⠦⣀⣀⣀⣀⠴⠀⠀⡟⠀⠀⠀⢹⡃
⠀⠀⠀⠀⠀⠀⠀⠚⠃⣤⣀⠉⣻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢀⣸⣯⢳
⠀⠀⠀⠀⠀⠀⠀⡴⠯⣀⣨⠟⠃⡏⠙⢦⣄⣀⡈⢀⣓⣃⡤⢾⣅⠀⠀⠀⠁⣽⢛⠿⣀⡴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢉⣀⡂⠇⠀⠀⣼⠋⡏⠉⢫⠀⠱⠸⣏⢦⡀⠀⠘⣌⠷⢂⣩⠟
⠀⠀⠀⠀⠀⠀⠀⣰⠯⢻⢩⢉⡟⣧⢀⣼⠃⠀⠃⠀⠘⡀⣄⢤⡹⣆⡛⣤⠀⢸⠀⡎
⠀⠀⠀⠀⠀⠀⢰⡇⡇⠘⢸⢸⡇⡎⢹⡃⠀⠀⢞⢢⣠⠁⠟⢌⡇⠙⢟⠁⠀⡸⠀⡇
⠀⠀⠀⠀⠀⢠⡏⡇⣧⠀⢸⢸⡇⠃⣨⡧⠀⢠⠈⡇⠁⠀⢀⣘⡵⠁⠈⡇⢠⠃⠀⢹
⠀⠀⠀⠀⠀⣸⡃⡇⢹⣧⢐⣨⡷⠟⢫⡀⠀⣸⣅⡇⢠⠞⠉⣡⣤⣤⡼⠱⡾⠀⠀⡼
⠀⠀⠀⠀⠀⣿⡇⡇⠀⢹⠻⣿⡄⠀⠀⣿⡛⢫⠟⢠⢻⢳⢻⣽⠀⠳⣄⢀⡠⠄⠰⠳⢤⡄⡀
⠀⠀⠀⠀⠀⣿⠁⠇⠈⢸⢀⠀⢷⡄⠀⠘⠷⠋⠀⣾⢸⢸⣹⡇⠀⠀⢠⠋⠐⠒⠀⣀⣠⠤⠈⣶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⣿⠷⢿⣦⣼⣬⣀⣆⣻⣄⠀⠀⠀⣸⣃⣸⣴⣿⣡⣤⣶⠾⡎⠁⠐⠁⠀⠀⠀⣠⠏⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠉⠉⠉⠙⠛⢧⣀⣴⣯⣿⣿⣿⣿⣿⣿⣿⣄⠈⠒⠤⠤⠤⠔⠚⢁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠃
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠤⠴⠶⢦⣤⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠻⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⠻⣆⠉⠻⣿⣿⣿⣿⣿⣿⣿⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣤⣤⣤⣤⣤⣤⣼⣿⣀⡀⠀⠀⠈⢷⡀⢿⢀⣩⣿⣿⠋⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠉⠛⢦⡀⠀⠀⢳⣾⣿⣿⣿⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠻⣄⣴⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣿⣿⡿⢫⣉⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠘⠿⣿⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣠⣶⣶⣤⣀⣤⣶⣶⣄⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠿⠿⠟⢛⣛⣛⣛⠛⠻⠿⢿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠟⣋⣥⣶⣶⣿⣿⣿⣿⣿⣭⣍⣛⠛⠶⣦⣍⡛⠿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⠿⣫⣴⡿⣻⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣦⣍⣙⢷⣤⡙⢿⣷⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣡⣾⣿⣿⣿⣿⠿⠛⠉⠁⢀⠀⠀⡀⠀⢀⠀⠈⠙⠻⢿⣿⣿⣾⣿⣦⡙⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⢏⣼⣿⣿⣿⡿⠛⠁⠀⢠⣆⠀⣿⠇⠰⠻⠀⠞⣾⢀⡤⠄⠀⠈⠻⣿⣿⡿⠿⢆⣙⣉⢠⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢃⣾⣿⣿⣿⠟⠀⠀⢤⣳⠈⠋⠁⠀⠀⢀⡠⠔⡀⠀⠈⠓⠃⢀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣧⢹⡇⣴⣶⣾⡿
⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⣾⣿⣿⣿⠏⠀⣘⣷⠄⠁⠀⣀⠀⠀⠚⠓⣈⣉⣤⣤⣶⣶⢿⣿⠛⣿⢁⣿⢸⣿⣿⣿⣟⢿⣇⠀⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⣾⣿⡿⢸⣿⣿⣿⡏⠀⠀⠈⠃⠀⣀⣀⣤⣴⣶⡾⣿⣿⠿⣿⣿⠉⣿⡆⠹⡇⢻⠸⣿⡼⣿⣿⣿⡏⢻⣿⠘⣷⢹⣿⣄
⠀⠀⠀⠀⠀⠀⢹⣿⡇⠿⠿⠛⣛⣠⣤⣴⣶⢿⡿⢿⡟⣿⡏⣋⢸⡇⢹⡇⣸⣿⡄⣿⠇⢦⠻⢸⣆⢻⡇⢹⣿⣿⣿⣻⣿⡇⠋⣾⣿⣿⣷⣄
⠀⠀⠀⠀⠀⢀⠀⣥⣶⣶⣿⣿⣿⠛⣿⡇⢹⡀⣿⢸⡇⠸⢰⣿⡶⣷⢘⣦⠉⣤⣅⢻⣶⡘⣷⣬⣿⣷⣷⣼⠿⠟⣛⡉⢩⣴⣦⠻⠿⠟⠛⠋
⠀⠀⠀⠀⠀⠘⠀⣿⣿⣿⣿⢻⣿⡆⢹⡇⢸⡇⣿⡀⣇⢸⣇⢹⣄⣹⣌⣛⣴⣿⣿⣿⣿⠿⠟⠛⠋⠉⠀⢰⣾⣿⣿⡇⣸⣿⡿⠃
⠀⠀⣤⣶⣶⣿⡆⢿⣿⣿⣿⣿⣿⡇⣎⢻⡸⣇⣹⣧⣹⣾⣿⣷⣿⡿⠿⠟⠛⠉⠉⠀⠀⠀⡀⡀⠀⠀⠀⣿⣿⣿⣿⠃⣿⣿
⠀⠀⠈⠻⣿⣿⣷⠠⣿⣿⣿⣿⣿⡧⢹⣾⣿⣿⠿⠿⠛⠛⠉⢁⣀⠠⣤⠤⠀⠀⠉⠀⠀⡀⠳⠏⠀⠀⣼⣿⣿⣿⡏⣸⣿⣿⡆
⠀⠀⠀⠀⠈⣿⣿⣧⠹⣿⣿⠿⠟⠛⣉⡉⠁⠀⠀⢠⣶⣠⠀⠀⠒⠊⠁⠀⠀⠀⣤⡀⠻⠟⠂⠀⢀⣼⣿⣿⣿⡟⣰⣿⡟⠉
⠀⠀⠀⠀⢰⣿⣿⣿⢠⣴⣶⣆⢻⣿⣿⣿⣷⣄⡀⠀⠉⠃⠸⣥⠇⢰⣆⠘⣿⠄⠘⠉⠀⠀⢀⣴⣿⣿⣿⣿⠏⣴⣿⣿⡄
⠀⠀⠀⠀⠾⠿⠛⠛⠈⠛⠻⢿⣷⡙⢿⣿⣿⣟⡿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⠟⣡⣾⡿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢶⣝⠻⣿⣿⣿⣿⣿⣿⣯⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⢟⣡⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⢭⡛⠲⣭⣛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣋⣥⣶⣿⡿⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⠦⢭⣉⡓⠶⠦⣬⣭⣭⠭⠤⢴⣶⣚⣭⡿⠿⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠛⠛⢿⣿⡿⠛⠛⠻⠿⠋

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


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠔⠒⠒⠒⠤⠤⠤⢤⣤⣤⣤⠤⠔⠒⠒⠚⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠖⠊⠉⠉⠉⠉⠉⠉⠉⢉⡉⠉⠉⠉⠉⠉⠉⠉⠑⠺⢧⣄
⠀⠀⠀⠀⠐⠀⢠⠞⡝⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢣⠹⡄
⠀⠀⠂⠀⠀⠀⡎⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⢷⠀⡇⠀⠀⢈⠎⠀⠀⠀⠀⢨⢀⠀⡁⡁⠀⣁⠀⠁⠀⠡⠀⠑⠀⢸⠀⠏⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢸⣠⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠁⠀⠃⠀⠀⠀⢸⢰
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠰⣿⣶⣿⢰⣷⢰⣷⢰⣶⣀⣾⡆⣶⣦⣠⣾⡆⢿⣶⣾⠆⢸⣼
⠀⠀⠀⠀⠀⠀⠀⡏⡇⠰⠿⠛⠁⠈⠻⠾⠟⠸⠟⠛⠻⠇⠻⠟⠛⠿⠇⠿⠟⠁⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠇⡇⠀⠄⡀⢤⠀⠄⠀⠀⠠⠄⠀⡠⠄⠠⠄⠀⠤⠀⠄⠀⢤⠀⢸⠋⡆
⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⡀⠀⠁⠀⠀⠀⠀⠐⠰⠀⠆⠄⠀⠢⠰⠄⠀⡀⠠⠊⠀⢸⠀⢇
⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡼⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⢢⣱⡀⠀⠘⠂⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣎⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠈⠻⡢⠤⠤⠤⠤⠤⢤⣤⣤⣬⣥⠤⠤⠤⠤⠤⠤⠤⠤⢔⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠴⠲⠒⠚⠉⠉⠉⠉⠛⠓⠒⠒⠒⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⢠⡄⠠⠄⠉⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠁⢀⠀⢀⠀⠀⡀⠀⡀⠈⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠿⠇⠿⠇⠺⠿⠻⠿⠀⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⣠⣤⠀⠠⡄⠀⠀⣤⠀⢠⣤⡀⠈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣿⣿⠿⠿⠟⠛⠛⡛⠉⠉⠉⠉⣉⠉⠉⠉⠉⣍⠉⠉⠉⠉⣉⠉⠉⠙⠛⠛⠛⠻⠿⠿⣿⣿⣶⣶⣤⣄⡀
⠀⠀⣀⣴⣾⡿⠿⠛⠉⠉⠀⢀⣶⣄⠀⠀⣼⣿⣦⡀⢀⣼⣿⣷⡄⢀⣾⣿⣷⡀⢀⣼⣿⣷⡀⠀⣠⣾⣦⠀⠀⠀⣠⣄⠉⠉⠛⠿⢿⣷⣦⡀
⢀⣾⣿⠟⢡⣄⡀⠀⣼⣶⣄⣾⣿⢿⣷⣼⣿⠋⠻⣿⣾⡿⠁⠙⣿⣿⡟⠈⢻⣿⣿⠟⠉⢿⣷⣾⡿⠛⣿⣧⣠⣾⡿⣿⣆⠀⢀⣤⣦⠈⠻⣿⣧
⣾⣿⣁⠀⣾⣿⢿⣶⣿⣛⣿⣿⣧⣤⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣾⣿⣿⣶⣶⣾⣿⣿⣯⣄⣹⣿⣾⡿⠻⣿⣆⠀⣨⣿
⣿⣿⣿⣿⣿⣥⣴⣿⣿⡿⠿⠛⠋⣹⠉⣹⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⢿⣍⠛⠛⠿⢿⣿⣶⣤⣽⣿⣿⣿⣿
⠹⣿⣿⣿⡿⠟⠋⠉⢀⡀⠀⣶⡆⠙⢷⣿⣿⣿⣿⠐⠿⠿⠿⠿⠿⠿⠇⠀⠸⠿⠿⠿⠿⠿⠷⠸⣿⣿⣿⣶⠟⠠⣶⠆⢀⡀⠉⠛⠿⣿⣿⣿⣿
⠀⠹⣿⣏⠀⢠⣦⠀⠙⠛⠀⠀⣤⡔⢛⣿⣿⣿⣿⠀⠀⣴⣶⣦⠀⢸⣧⠀⣿⠀⢠⣶⣶⡄⠀⠀⣿⣿⣿⣟⠳⣦⡀⠀⠙⠛⠀⣴⡄⢀⣽⣿⠏
⠀⠀⠈⠻⣿⣦⣅⡀⠀⠺⠷⠈⠋⣱⣿⡿⢿⣿⡏⠀⠀⠙⠛⠁⠀⢸⣿⢸⣿⠀⠀⠙⠛⠁⠀⠀⣿⣿⡿⢿⣷⣍⠁⠺⠷⠀⢀⣠⣴⣿⠟⠁
⠀⠀⠀⠀⠈⠙⠿⣿⣷⣦⣤⣀⣻⣿⣿⡟⡧⢻⡇⠀⠀⠀⠀⠀⠀⣸⡟⠀⣿⡄⠀⠀⠀⠀⠀⠀⣿⢿⡟⣾⣿⣟⣀⣤⣴⣾⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣷⣀⣸⣇⠀⠀⣤⣤⣤⣾⣿⣷⣶⣿⣿⣦⣤⣤⡄⠀⢀⣿⣀⣰⣿⣿⡿⠿⠛⠋⠉
⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⡈⠻⠿⣿⣿⣤⣴⣿⣿⣿⣿⡿⠋⠉⠻⢿⣿⣿⣿⣿⡄⣼⣿⡿⠿⠋⢁⣀⣀⠀⣀⣀⠀⣀⣀⣀⣀⡀
⠀⠀⠸⣿⠇⠀⢿⡿⠀⠸⣿⠇⠀⠺⣿⠆⠀⠘⣿⣿⣍⠛⠛⠋⠁⢠⣶⣶⣶⡄⠉⠛⠛⠉⣰⣿⡟⠀⠀⢰⣿⡿⢿⣿⡿⢿⣿⡿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⠀⣠⣾⣿⣷⡿⠟⣠⣿⡟⢠⣿⠃⣿⣿
⠀⠀⠀⠀⣴⣿⣿⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣤⣤⣤⣀⣠⣴⣿⠟⠁⠀⢀⣼⣿⠟⠁⠀⢀⣴⣿⠋⢠⣿⡇⢸⣿⡇
⠀⠀⠀⠀⢻⣿⡌⢿⣍⠻⣿⣿⣶⣤⣄⣀⣀⣀⣀⣀⣿⣿⣀⣀⣤⣴⣿⣿⣿⡿⠿⠋⠁⠀⣠⣴⡿⠋⠀⠀⢀⣴⣿⡿⠁⣰⣿⣿⢃⣿⣿
⠀⠀⠀⠀⠈⢿⣿⡄⠻⣷⣌⠛⢿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉⠁⣀⣠⣴⡶⠟⠋⠁⠀⢀⣠⣶⣿⡿⠋⣠⣾⡟⣽⢏⣾⣿⠇
⠀⠀⠀⠀⠀⠈⢿⣿⣄⠈⠻⣿⣦⣌⡙⠛⠷⠶⠶⣶⣶⣶⣶⣶⣶⠶⠶⠿⠛⠛⠉⠁⠀⢀⣠⣤⣶⣿⣿⠟⠉⣠⣾⡿⢫⣾⢋⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⡀⠈⠙⠻⢿⣷⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⣿⣿⠿⠛⠉⣀⣴⣾⡿⢋⣴⡟⣡⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄⠢⣀⠀⠈⠉⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠉⣀⣤⣶⣿⠿⠛⣁⣴⡿⣫⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣬⡳⢦⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣴⣶⣿⡿⠿⠛⢋⣡⣴⡾⢟⣡⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣭⣛⠶⢦⣤⣄⣉⣉⣉⡉⠉⢉⣉⣉⣉⣁⣤⣤⣶⠾⢟⣋⣥⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣶⣦⣭⣭⣙⣛⣛⣛⣛⣛⣛⣋⣩⣭⣥⣶⣾⣿⡿⠟⠋⠁

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

⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⢀⣴⠊⠙⠁⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⡴⠆⠀⠐⠃⠀⠀⠐⠚⠂⡀⢀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⣀
⠀⠀⡘⠁⠀⣠⣄⠀⠈⠓⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠐⠂⠀⣀⠀⠀⠀⠀⠐⡻⠁⠀⢰⡀⠠⠟⠂⠀⠀⢠⣄⠉⠁
⠀⠀⠇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡦⠋⠀⠀⣀⠠⠁⠀⢾⠦⠐⠉⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⡇⠀⠀⠀⠀⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠛⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠰⠦⠀⠀⢀⡤
⠀⠀⠻⠄⠀⢀⡀⠀⠈⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⢤⣄
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠘⠁⠘⠃⠀⢀⣤⢤⡄⠀⣤⣤⣤⣤⣀⣰⣏⡼⢀⠀⠀⣠⢤⠀⠀⠀⠘⠺⢇⡀⠀⣉⠠⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢡⣾⠇⢈⣋⠀⣨⢍⢩⣿⢭⡄⣾⣰⢒⠛⢮⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠸⠿⢠⣿⢸⣾⣧⣸⣾⣿⣞⠱⠧⠻⠄⢺⣆⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⣠⠿⣏⠟⠙⠳⢋⣈⣥⡿⢷⣋⣉⣱⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠁⠀⠀⠘⠿⠿⠛⠋⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢀⠀⣀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠠⢤⡀⠀⠀⠀⠀⠀⠀⣠⢇⣈⣉⠠⠄⣄⠀⠂⠀⣀
⠀⠀⠀⠚⢱⡄⠘⠁⠀⢀⣠⡀⠀⠘⠿⠀⠀⠀⠀⢀⠠⠞⠁⠠⡶⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⣿⠞⣉⠀⠀⠤⠀⠀⣀⠀⠁
⠀⠀⢸⣇⠀⠀⣀⠀⣤⡄⠁⢠⣤⣄⠠⢢⠆⠀⢠⡇⠐⠂⠀⠀⠀⠘⠀⠈⠉⠀⠙⠂⠀⠀⠀⣾⣶⡿⢷⠛⣛⠛⠛⠻⣄⣠⡗
⠀⠀⣾⣿⣿⣦⣦⣤⣠⣤⣄⣀⣀⣤⠴⠏⠀⠀⡰⠀⠈⠉⠀⠀⠀⠄⠰⣆⠀⠂⠀⠀⠀⠀⠀⣿⠋⢠⣄⠈⠋⠀⠠⣤⠀⠙⢆
⠀⠀⠙⣾⣶⣤⠆⠈⠉⢉⠀⣀⣰⣿⣧⡾⠀⠀⠈⠀⠀⠁⠈⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⡆⢀
⠀⠀⠈⣛⡛⠛⠉⠙⠛⠛⣻⡏⠉⠁⣀⣀⡤⠀⠀⠀⠀⠲⠀⠀⠀⠀⠘⠀⠈⠁⠠⠒⠂⠀⠀⣷⠉⢀⡀⠀⠀⠙⠀⢀⠀⡆
⠀⠀⢘⡹⠋⢹⣗⠛⠛⡿⢓⡖⠚⠛⠙⣋⡀⠀⠀⠀⠀⣀⠀⠠⠔⠒⠀⠂⠀⠀⢀⡀⠀⠀⠀⠘⡆⠈⠋⠀⠤⠀⠀⠀⠁
⠀⠀⢾⡿⣻⡗⢶⢤⡶⠶⠶⠶⠚⢋⣍⠡⢠⠀⠀⠀⠀⠀⣄⠀⠀⠀⣶⡆⠀⠀⠈⠁⣰⠂⠀⠀⠈⠲⠄⣀⡀⠐⠖⡠⠖
⠀⠀⠀⠛⠻⠷⠦⠍⢁⣀⣠⠤⠤⠤⠽⠚⠁⠀⠀⠀⠀⢤⠀⢤⠄⠀⠀⠀⠀⠤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡀⠄⠀⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢌⡔⠊⣠⣶⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⠏⠀⢘⡕⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠈⠲
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠘⠁⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠐⡄⠀⠀⠀⠰⠀⡠⠄⡠⠐⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⣰⠃⣠⠈⢢⠀⠀⠀⢲⠀⠠⣅⠀⠀⣠⢃⠠⠄⠒⠒⠈⠁⠀⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠐⠀⢈⢹⣧⠀⠀⠀⠂⡼⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠠⠄⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣀⠀⠀⠀⠀⠀⡠⠞⠀⠀⠔⡒⢆⡉⢰⡄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠠⠂⠈⡀⠀⢠⠒⠖⠠⠤⢤⠠⣄⢀⡈⣙⣋⡉⠉⠀⠀⠀⣀⠰⠇⡾⠟⠣⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠓⠶⠤⠴⠄⠤⠄⠥⠠⠃⠀⠀⣀⡤⢎⣀⣀⣀⣀⡀⣀⣀⣀⡀⣀⣈⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠘⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡪⠥⠠⢍⡹⠯⠸⣁⡆⢺⡟⠳⠿⣿⡉⠶⢂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢻⣮⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⢤⡤⠶⠚⠛⠛⠉⠙⠚⠾⠭⠶⣶⣿⣽⣣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠘⣿⣇⣃⡀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⠀⣤⣀⣀⣀⣀⡀⠠⠄⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢩⠈⠀⠀⠋⣨⠁⢃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡸⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠈⡆⢰⠉⢤⠌⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠘⡀⠘⡁⢡⠌⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⡜⢡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠣⢄⡉⢳⠀⠑⠊⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⡠⠊⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠈⠐⠣⢀⡀⠀⠀⡐⠤⠀⠠⢄⡀⠔⢊⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠄⡀⠈⢹⢂⣍⠈⠁⠀⠈⡖⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠒⠼⠀⠛⢃⠀⢠⡄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢐⡀⠀⠀⠀⠀⠀⠘⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡒⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠄⠠⠐⣄⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠰⠴⠂⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡰⢁⠀⠀⠀⠀⠀⠀⠒⢺⠞⠀⠀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠁⠉⠿⠀⠐⠒⠒⠒⠒⠂⠀⠘⠒⠒⠾⠿⠽⠧⠤⠤⠤⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠁⣸⣿⣿⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠁⣠⣴⣿⣿⣿⡿⣡⣾⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣤⣾⣿⣿⣿⣿⣿⣥⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠛⠛⠛⠛⠿⠟⠟⠙⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡿⠋⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡷⠶⢦⠀⠠⢴⠶⠒⠒⠀⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠊⠃⠀⠀⠐⠆⠈⠁⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡅⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣭⠁⠀⣀⡀⠄⠀⠀⠀⣠⡿⣸⠃⠀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣾⣷⡈⠿⠿⠟⠀⠀⠀⣠⡼⠋⠜⠁⠀⢀⡆⠙⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠋⠁⠀⠙⣿⣷⠀⠀⠀⠀⣠⣾⣟⡥⠊⠀⠀⢀⡞⠀⠀⠀⠈⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡟⠐⠛⢯⡾⠋⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣠⣾⣿⡿⣆⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠶⣤⠾⠗⠈⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⠁⠸⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢂⣨⡷⠞⢿⠲⠬⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠉⣩⢷⡂⠈⣦⠀⠀⠉⡳⣦⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣠⠾⢻⣧⡼⠃⠀⢴⣿⠈⢳⣤⡀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣿⣉⣤⣤⡶⠾⢻⠀⠀⠙⠛⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⢍⠁⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠈⠂⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠰⠦⠈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣶⣷⣿⣧⡀⠀⣤⣧⣽⣿⣏⠐⢾⡉⣶⠄⡀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠶⠶⠶⠶⠶⠶⠶⠶⠗⠒⠾⠾⠿⠿⠿⠷⠿⠿⠿⠿⠿⠟⠻⠾⠛⠛⠒⠃⢘⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⡤⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠾⠶⠶⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠐⣶⣾⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⢝⡉⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠮⢤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢰⠃
⠀⠀⠀⠀⣀⠤⠒⢠⠉⠉⠉⠉⠐⠒⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠚⣆⠒⠄⡖⢲⣄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡇⠀⣿⣀
⠀⢀⡴⢈⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⡙⢦⠀⠀⠀⠀⢀⣶⡦⣀⡭⣶⠀⣿⢸⢉⣇⣽⠉⣯⠉⣹⠀⠀⠀⠀⠀⠀⡠⠒⠉⠁⠀⢸⡀⣠⠏⠉⠉⠲⣄
⢀⡮⠄⠄⠀⠀⡄⠐⠀⢀⡀⠀⠀⠀⠀⠀⠀⢡⠀⣧⠀⠀⠀⠘⢦⠑⣿⠊⢹⠀⡾⢼⡌⡍⢹⢠⡿⣄⡏⢹⠖⣆⠀⠀⠀⣧⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣸⠆
⠸⡇⠒⠀⠙⠀⢀⠀⠤⠀⠀⠠⠁⠀⠀⠤⠀⠀⠂⣾⡀⠀⠀⠀⠈⢣⠘⡇⢸⡆⡇⢀⡇⡇⢸⢸⠉⢸⡇⣯⡴⠁⠀⠀⠀⠳⡍⣓⠒⠶⠶⠶⠶⠶⠖⠒⢋⡹
⠀⠙⠦⣅⡘⠁⠀⠠⠀⠴⠀⠀⠄⠐⠂⠀⢀⣩⠞⠁⢈⡆⠀⠀⠀⢰⡷⣧⣤⣧⡥⣬⣇⡥⣼⣼⣦⣯⣧⣿⡄⠀⠀⠀⠀⠀⣇⠀⠉⠁⠒⠒⡲⠒⠞⠉⢈⠇
⢣⠔⠖⠄⠉⡉⠓⣒⡒⠒⠒⠒⠒⣒⣊⡉⢩⣤⣤⢿⡉⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢩⠀⠀⠀⠀⠸⡀⠸⡀⠀⢸
⠈⢦⡳⡶⠮⠗⠊⠙⠙⢒⠞⠢⠴⠣⣈⢋⡩⣞⡡⢊⡼⡄⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠑⠄⠙⢄⡜
⠀⡚⠿⣒⠶⠬⠭⠤⠔⠊⠀⠀⠀⠉⢉⣉⣉⠥⠔⢻⡠⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⣀⠴⠃⢠⠎⡇
⠀⠱⣄⣀⠈⣉⠕⠛⠀⠀⠈⠉⠉⠉⠉⠀⠈⣓⡦⢬⠇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⡜⠉⠀⠀⠀⣇⢰⠇
⠀⠀⠀⠙⠚⠓⠤⠤⠤⠤⠤⠤⠤⠤⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠛⠒⠒⠒⠒⠒⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⠤⠤⠤⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠤⠄⠐⠀⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠒⠒⠒⠒⠂⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⢀⣀⣀⡀⠸
⠀⠀⠀⢀⡠⠔⢚⣉⡥⡴⠒⢺⣏⣩⠯⠤⠔⠒⠤⡉⠈⢆⠀⠀⠀⠠⠐⠁⠀⠀⠀⠄⠒⠒⠒⠤⠀⠀⠀⠈⠱⢦⡀⠀⠀⠀⠀⠀⠀⢂⡠⠢⣀⡠⠤⣀⡇
⠀⢠⣊⠥⣶⠋⣹⠤⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⠖⠃⠀⠀⡀⠀⠀⢀⠀⠀⠐⠂⠬⠭⠉⠒⠁⠀⠀⠀⠀⢀⠙⡄⠀⠀⠀⠀⠀⢀⣇⡤⠀⠀⠤⢨
⢠⠛⠓⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣢⠞⠀⠀⠀⠀⣇⣁⡀⡀⠀⠁⠀⠁⠀⠀⡀⠀⠄⠀⠀⣂⡈⠀⣠⡇⠀⠀⠀⠀⠀⡜⠘⠑⠀⠀⠀⠚⢣
⠘⠢⠄⢇⠀⠀⠀⠀⠀⠀⠀⢀⣒⣀⡭⠤⠖⠊⠁⠀⠀⠀⠀⠀⠈⢄⠀⠐⠤⠗⠉⠲⣄⣀⠴⠊⠢⣤⠜⠁⠈⢊⡵⠁⠀⠀⠀⠀⡼⠱⠁⠀⠀⠀⠀⠄⠠⠱⡀
⠀⠀⠀⠀⠈⠁⠐⠒⠊⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠠⠤⠄⢀⣀⣀⣀⣀⡠⠤⠔⠚⠉⠀⠀⠀⠀⠀⢸⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠐⠀⠀⠈⠁⠀⠀⢠⠃
⠀⠀⠀⠀⣀⠀⠤⠀⠐⠒⠒⠂⠠⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢠⠠⢠⠃
⠀⢠⠂⡡⠔⠒⡂⠨⠍⢈⣉⠉⠀⣒⠒⠪⡑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠸⢀⠀⠇⠸⠈⢸
⠀⢸⡛⠤⠄⣀⣀⣐⠂⣀⣀⣈⣂⠠⠥⠴⣛⣯⢩⣳⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠂⠉⠀⠀⠀⠀⠀⠀⠉⠒⠢⢀⠀⠀⠀⠀⠀⠀⢀⠏⠄⠀⠀⠀⠀⠘⠈⢆
⠀⠀⡟⠓⠶⠤⠤⠤⠤⠤⠤⠤⢰⠒⠲⠟⠋⣇⡠⢻⠀⠀⠀⢀⡀⠀⠈⠁⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⠀⠀⠀⡞⠀⠀⠴⠀⠀⠀⠂⠀⠘⣆
⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠧⠔⠃⠀⠀⢨⣉⣀⣠⢠⣀⡄⣀⢀⡀⡄⠠⠤⠤⣤⣤⡤⣖⣲⣶⣶⣶⣾⠀⠀⢰⡇⠀⠀⠀⠀⠀⠐⠀⢠⠀⠸
⠀⠀⠄⠓⢤⣀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠯⢐⠒⠤⡀⠀⠀⠐⡛⡯⢜⣛⣭⣴⡟⢉⣤⣢⡀⢂⣠⣌⣯⣥⣩⡭⠍⣋⣉⣩⠀⠀⠘⡇⢃
⠀⡁⠀⠀⠀⠈⠉⠛⠧⠒⠛⠫⠍⠃⠀⠀⠀⣈⠇⢈⡇⠀⠀⢉⢉⠉⠛⣦⣀⡠⣠⢚⣁⣀⣉⣀⣠⡒⢄⢀⡠⣲⣉⣁⣸⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⢁⡴
⠀⠈⠒⠂⠥⠤⠄⢀⣀⣀⣒⣒⣀⣀⣀⡩⠭⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠨⠆⣀⠄⡆⡀⠀⠀⠀⠀⠀⠀⠘⠀⠉⢦
⠀⠀⠀⢘⡀⡘⠠⡴⡀⡀⡛⠀⡄⠀⠀⠀⠀⡀⣀⣀⣠⢿⣀⣠⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠
⠀⠀⠀⣀⠤⠆⠀⡀⠹⢠⠓⢰⠇⠀⠀⡀⠀⠀⠙⠋⠁⠈⠙⠋⢛⣾⣅⡀⠀⠀⠒⠄⣀⣀⡀⣀⢀⣀⡀⠔⠛⠀⠀⠈⠤⣀⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠙⠅⠐⡳⠀⠉⢡⠖⠘⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⢹⣿⡇⠀⢶⣀⠆⢠⠤⢤⠤⣤⠤⣤⠀⣤⡄⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠠⠄⡘⢷⠸⠝⠖⡁⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠙⠷⢾⣤⣴⣄⣤⣄⡼⠶⠛
⠀⠀⠀⠀⠀⠁⠐⠀⠠⠀⠁⠁⠀⠀⠀⠳⠀⠀⣤⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣦⣹⣦⡀⣠⣠⣿⣿⣿⡟⠀⠀⠀⡀⠙⣀⢤⣈⠀⠀⠀⢸⠀⠀⠀⠀⠠⠤⠄⠐⣀
⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣯⣿⣿⠿⠿⠁⠀⠀⠀⠃⠀⠀⠁⢠⡎⠀⠀⡼⠀⠀⡄⠀⠀⠀⠀⠀⠉⢳⡄
⠀⠀⠀⠀⠀⡰⠊⠉⠿⣦⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠦⠦⠔⠁⠀⣰⠁⠀⠀⣇⠀⠀⠀⠀⠀⢀⣀⣹
⠀⠀⠀⠀⠀⡏⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⣼⠀⠀⠀⠀⠀⣤⡄⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠰⢾⡇⠀⠀⠀⠈⠲⣶⣤⣴⣶⣾⠿⠃
⠀⠀⠀⠀⠀⡇⠀⠀⢐⣿⠀⠀⠀⠀⠀⠈⠴⠄⠀⠀⠀⠀⠘⢿⣿⣿⣿⠾⣠⡿⠀⠀⠀⠀⠀⠀⣠⡗⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⢰⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠤⠴⠚⠋⠀⠀⠀⠀⠇⠀⣼⡿⠁⠀⢀⠀⠀⠀⠉⠁⠀⠀⠐⢦⡀
⠀⠀⠀⠀⠀⠘⡆⠀⢸⡃⠀⠀⢀⠀⠀⠀⠀⠀⢀⢨⡆⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠐⣈⣿
⠀⠀⠀⠀⠀⠀⠧⠀⣸⠀⠀⠈⢤⣆⠀⢸⠀⢀⣼⣼⠃⢀⠄⠰⣼⣻⣸⣧⣴⣦⣄⠀⠀⠄⢠⡟⠀⠀⠈⠻⣦⡀⠀⠀⠄⠀⣤⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⡛⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⡔⠒⠉⠒⢣⠋⠁⠀⠹⢻⣇⠀⠀⠈⢷⠀⠀⠀⠀⠈⠛⠻⠾⠟⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⣸⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠃⠃⠀⠀⠀⠈⡇⠀⠀⠀⠀⢀⠀⠀⠣⡀⠀⠀⠀⠀⢀⡀⣀⣿⠟⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠂⠀⠀⠀⢐⡿⠀⠀⠀⠉⠲⠦⣤⣴⡾⠿⠟⠉⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣤⡄⣠⡾⢇⡀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⣶⣶⣶⣞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣷⣦⠀⠀⢀⡏⠀⠀⠀⠀⠀⣨⡛⠓⠉⠇⢸⠅⡀⠄
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠷⠀⠀⢻⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⢐⣢⣾⡿⠃
⠀⠀⠀⠀⠀⠈⠁⠙⠿⠿⠛⠛⠛⠓⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠁⠈⠀⠀⠀⠁⠁⠀⠀⠁⠀⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠛⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡸⣿⠃⠀⠀⠀⠡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡘⡼⠋⠀⠀⠀⠀⠀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣤⣩⣟⠁⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣿⣿⣿⣟⢯⣉⢀⠀⣀⠀⠀⡤⡤⢼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣓⣉⣙⣓⣛⣛⣛⣋⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⡟⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣸⡿⢀⣀⣦⣄⣠⡀⢶⢆⡈⢿⣿⣿⣿⠿⠟⢩
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⢼⣿⣿⣿⣿⡿⠶⣾⣿⣿⣾⠋⠁⠀⠀⠀⠸⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠻⠻⣯⣿⣿⣿⢏⣉⡛⠛⠋⠀⠀⠸⣿⡟⠽⠉⠁⠐⣬⡿⠃⡟⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠻⣿⣿⣿⣦⠈⠻⠷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⣠⠇⠀⠀⠀⡇⠀⠀⠆⠀⠀⡆
⠀⠀⠀⠀⠀⢀⠈⡇⢰⠁⠀⠀⠀⠀⠃⠀⠀⠀⠈⠛⠛⢻⡆⠀⠀⠀⣿⣿⣿⣿⣶⣭⣶⣼⣿⣾⣿⣅⠀⠀⠀⠀⣇⠀⡸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⡇⢸⠀⠀⠀⠀⣇⣎⠀⠀⠀⠀⠈⠘⢾⡇⠀⠀⠀⠋⢸⣿⠛⠿⢿⣿⡿⢿⢿⡿⠃⠀⠀⠀⠀⠹⣦⡄⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠘⡄⠁⣸⠀⠀⠀⠀⠘⢿⠀⠀⠀⠀⠺⠦⣌⣣⠀⠀⠀⠀⠀⠀⠪⢛⡶⣦⠤⢔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⣠⡴
⠀⠀⠀⠀⠀⠀⠙⣷⠸⠂⠀⠀⠀⠀⢸⡆⠀⠀⠀⡤⢀⣈⠛⢦⣤⣀⠀⠀⠀⠀⠀⠈⠉⠁⢼⠒⠂⠀⠐⠒⠂⠀⠂⠀⢸⡆⠀⠛⠐
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠤⠴⠺⠆⢀⣄⢰⣿⣛⡈⠿⠿⢿⣿⣷⠢⢀⡀⠀⠀⢀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢀⣠⣶⡿⠿⠋⠘⢿⡿⠙⢳⣿⡶⠿⢿⣿⣶⣭⣙⣛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀
⠀⠀⠀⠀⠀⠒⠚⠋⢀⣀⣤⣴⡿⠛⠁⠀⠀⠀⠀⠈⡳⣶⣤⣴⡶⢷⣿⠀⠉⠛⠛⠿⠿⠿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⢸⣷⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠟⠋⠉⠁⠀⠀⢠⣴⣶⣶⣿⣿⣿⣋⠙⢿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⡀⠈⠙⠷⠤⠀⠀⠀⢀⣠⣼⣿⢀⡁⣠⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⣻⠽⠛⠉⠉⠁⠀⠀⠻⢿⡿⠈⠙⠛⠛⠻⠿⣿⣿⣿⣶⡄⠀⠀⠀⠈⠉⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣟⡵⠊⠁⠀⠀⠀⢀⣠⣴⣶⣿⡌⠣⣤⣤⣤⣤⣀⣀⠀⠀⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠁⠀⠀⠀⢀⣠⣶⣿⣿⠟⠛⠋⠁⠀⠘⠿⣿⣿⣿⣿⣿⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣶⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠁

⣿⣿⣿⣿⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⡿⠿⣿⡿⠿⠿⠷⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⠀⠈⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢬⣄⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⡠⠋⠀⠀⡄⡀⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⡑⠀⠀⠀⠠⠀⠀⠁⠊⠉⠛⠳⠶⢶⣦⠤⢤⡀⠀⢒⠍⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⠁⠀⠀⢀⠐⠁⠈⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠠⠀⠀⠌⢂⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠁⠀⠀⠀⠀⠁⠀⠀⢀⠄⠄⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢡⠀⠀⠀⠡⡐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⡳⠀⠀⠀⠔⢃⠀⠀⠀⠀⠀⠐⠗⠂⠀⠀⠀⠠⠸⢂⠅⠀⠀⢸⣀⠖⢄⠀⠐⣬⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠑⢢⠀⠀⠀⡀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡘⠀⠀⡠⠖⠁⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⣀⠀⠘⢄⠀⠀⠈⠂⠘⡀⠀⠀⠀⠀⡏⠉⠀⠀⠈⠉⡀⠀⠀⠀⠀⡐⠀⠀⠁⠀⢀⠅⠀⠀⣀⢄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⠌⠀⠑⢄⠀⠁⠢⡀⠀⠀⠐⠄⠀⠀⠀⠐⠤⠄⢀⢠⠔⠀⠀⠀⠀⡐⠀⠀⠀⡠⠀⠁⢀⠄⠁⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠡⡀⠀⢈⠖⠈⠢⡀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣀⠂⢤⠊⠀⢀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡲⢁⠔⠈⠀⠈⠢⡀⠁⠀⡤⠠⠠⠄⡄⠀⠁⡠⠊⠀⠑⢄⠀⠤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢁⠀⠀⠀⠀⠀⠀⠁⠈⡇⠀⠀⠀⢽⠁⠈⠀⠀⠀⠀⠀⠑⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢀⠀⠀⠀⠀⠀⠃⠐⠐⠨⠊⠀⡶⠦⢀⡀⣠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢰⣦⠐⠀⠒⠀⠂⠎⠀⢦⣑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠠⠐⠈⠁⠀⠀⠀⠀⠀⠀⢻⡄⠁⠸⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠠⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠄⠀⠱⣖⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⣴⠀⢶⡄⠀⢸⡆⠀⠠⠹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⠒⠈⠙⠀⠉⠙⠠⡀⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠊⠉⠉⠛⠈⠀⠈⠠⠀⠀⠀⠈⢄⠀⣿⣧⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠒⠠⠀⣀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢻⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠉⠡⡀⠀⠀⠀⠈⠁⠐⡄⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⠀⢸⡗⠀⠈⠑⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠈⠺⢦⣀⠀⠀⡠⠊⠀⠀⠀⣂⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⣠⡀⢀⣬⠏⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⢀⡀⠉⠙⠓⠤⠤⠀⣠⣄⠁⠀⣄⣀⢀⣀⣠⣄⣀⡠⠤⠶⠛⠋⠉⠁⡀⠠⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠉

⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀
⠀⠀⡆⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠠⢄⠀⠀⠀⢀⠀⠈⠄⠀⠀⠀⠀⠀⢀⠁⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠉⠆
⠀⠀⠀⠈⠙⠤⠄⢠⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠄⠀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠡⠂⠀⠀⠀⠀⣔⠃⠋⠓⡄⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠈⠁⠀⠠⠀⠂⣀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⡀⢀⢈⠉⠈⠀⠀⠀⠀⡌⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡄
⠀⠀⡀⠀⠀⠀⠀⠈⠂⡀⠀⠂⡀⠈⠁⠁⠄⠀⡁⠀⢀⠠⡄⢀⠈⠀⠀⠠⠄⡀⣀⢀⠀⣼⣇⢄⠀⠀⠀⠈⠀⠀⢀⡀⠠⠲⠀⢀⡀⢀⠀⠀⠐⠁⢁
⠀⢰⡀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡘⠀⠀⠁⠐⢁⡄⠀⡀⠈⠑⡽⠋⠉⠀⠀⠀⠀⠀⠀⠀⠁⠈⣤⡠⡤⣤⡴⡀⠈⢤⡀⠔⢀⠠
⠀⠀⣦⣄⡠⠆⠀⠒⠁⠉⠀⠀⠀⠀⠡⠄⠠⡁⠀⠀⠁⠀⠀⠀⢀⠌⠀⠀⢨⡕⠀⠀⡀⢠⠀⠀⠀⠠⠀⠀⠠⠀⠦⠄⠘⣄⢋⠀⠤⠂⠀⠀⠀⠀⠆
⠀⠀⠀⡀⠂⠀⠀⢀⡀⠀⠀⠤⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠐⠀⠄⠀⠀⢀⠀⠀⠀⣀⠁⠀⠀⠀⠀⠠⠄⡀⠀⠀⢘⠀⠀⠀⠀⠀⡊⠀⠀⠀⠀⠰
⠀⠀⠀⠈⠀⠀⠀⠀⠀⡌⠡⠒⢈⠀⠂⠀⠀⠀⠀⠐⠀⢀⣀⠈⠀⠀⠣⠊⠁⠆⠀⠀⠀⡀⠀⠀⠀⠔⠁⠀⠀⠀⠰⠀⠅⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠂⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠁⣀⣀⣀⣀⣄⣄⣀⣀⣀⠀⠀⠀⠈⠁⠀⠀⠠⠄⠀⠊⢀⡐⠊⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⢠⣶⣿⣿⣿⠛⢛⡛⡻⡟⣿⣿⣿⣶⡄⠀⠁⠀⠉⠀⠠⠸⡈⣈⠀⠀⠀⠀⠀⠡⠀⠀⠀⠠⡐⠂⠠⠁⠀⠀⠀⠀⠀⠑⠄
⠀⠘⡒⠐⠈⠀⠀⢀⠀⢀⣿⢛⡟⣿⢻⡛⢛⣿⢛⡛⠻⠟⠟⢻⣿⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠃⢀⠀⣂⢀⣀⣀⣀⠀⠀⡀⡂
⠀⠀⢡⠀⡄⠀⠀⠀⠀⠘⣿⢨⠁⢹⡜⣿⢸⣿⢈⡁⡇⠀⠀⡆⣿⠃⠀⠀⠀⠀⠐⠁⠀⠀⠀⠄⡂⠀⠀⡁⠀⠁⠀⠀⠇⠀⠍⠛⠋⠀⠛⠀⠐⠈⠁
⠀⠀⠀⠆⠃⠀⠀⢀⠀⠀⠹⣼⣼⣮⣭⣿⣼⣿⣼⣧⣡⣬⣤⣴⠏⠀⠀⠀⠀⠰⠀⠀⠀⡐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠈⠠⠀⠐⠀⠀⠀⠉⠛⠛⠛⠻⠛⠛⠛⠛⠛⠉⠀⠀⠀⠂⠀⠀⡀⠀⠠⠄⠁⠀⠀⠀⠀⠈⠀⠀⠀⢐
⠀⠀⢅⠀⠀⠀⠂⠀⠒⠠⠀⠀⢠⠐⢀⠀⠀⠠⢀⠀⠠⡀⠀⠀⠀⠀⠄⠀⠀⠠⡈⠀⡀⠔⠀⠄⠀⠀⣀⣀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⢉⠀⠸⠀⣕⠐⠘⠂⠀⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠐⢀⠗⠁⠀⠀⠉⠄⠀⠀⠂⠈⠂⠀⣈⠀⠀⠀⠀⢙
⠀⠀⠀⠀⢀⠀⠁⠈⠀⠀⠀⡀⠀⠐⢀⠀⠀⠘⠕⠀⡀⠀⠀⢘⡂⠀⠀⠆⠀⠀⣀⠀⠀⠀⢱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⢀⠅⠀⠀⠀⠀⠀⠀⠑⠂⠀⠘⠀⠰⣀⣀⠬⠃⢈⠀⠀⠀⠘⠀⠀⠀⠀⠀⠆⠀⠁⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠐⠬⠄⠀⠀⠠⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⡄⠀⠀⠀⠀⠀⠀⢀⠰⠸⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠁⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠢⠀⠀⠀⠀⠒⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⣀
⠀⠖⠃⢀⠄⢀⠀⠒⠑⢀⠀⠀⠠⠀⠀⠀⠃⠁⠦⠀⠐⠀⠅⠀⢸⠀⠁⠈⠀⠂⠀⠐⠀⢴⣊⠖⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⠀⠀⠀⢈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠂⠠⠤⠆⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⠀⠀⠀⠠
⠀⠀⡀⠀⠀⠀⢀⠀⠀⠨⠂⠀⠀⠠⠊⠀⠀⢄⠀⠀⢀⡈⠀⠂⢰⣀⡠⡰⠱⢡⠄⠀⠀⠀⠀⡆⠀⠠⠀⠠⠀⠁⠒⠈⠀⠤⠀⠀⠀⠀⣠⠀⢀⠠
⠀⠈⠀⠀⠀⠄⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠁⠀⠀⠠⢇⡀⠀⢸⢆⡀⠄⢠⠀⠀⠀⠀⠀⠀⠀⡤⠠⠀⠀⠀⠀⠀⠲⠆⠀⠀⠀⠀⠀⠀⠐
⠀⠢⠀⠠⠄⠂⠁⠀⠀⡀⠀⠀⡠⠔⠊⠁⠁⠀⠀⠈⠍⠀⡄⠀⠀⠈⠚⠚⠁⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠰⠀⠀⠀⡄⠀⠀⡀⠀⠀⡄⠀⠄
⠀⠀⠀⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠑⠂⢀⠉⠀⠐⠀⠄⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠁⠀⠠⠤⠄⠀⠁⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠓⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⣠⣿⣦⣶⣀⣀⡄⠀⠀⠀⠀⣠⣞⣓⣻⠉⢙⣓⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣦⣤⡀
⠀⠀⠹⣶⣾⣿⣿⠿⠿⠿⢿⣿⣦⡆⠀⠀⣿⢏⣭⡍⣿⢏⣭⣍⢾⡇⠀⢀⣤⣠⣄⠀⠀⠐⠆⠾⠹⠭⠧⠖⠃
⠀⢀⣀⣼⣿⣿⣶⣶⣶⣴⣶⣾⣿⣧⣀⠀⢿⡘⠿⣣⠿⢇⠻⢟⣼⠇⠐⠿⠟⠙⠿⠗⠀⢤⣰⣤⣀⣠⡴⢦⣄
⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠂⠀⠙⣿⢟⣺⣺⢿⡟⠁⣤⣤⣤⣤⡀⠀⠀⣰⣿⣴⣏⣿⢳⣜⣷⣽⡄
⠀⠀⠰⠿⠿⠿⠟⠛⠛⠿⠿⠿⠏⠉⠁⠀⠀⠀⢻⣐⣒⣒⡸⠀⢸⡏⠁⠈⢹⡇⠀⢀⡽⠿⣿⣿⣿⣿⣿⠿⢟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠰⠶⠶⠀⠀⠀⣩⣅⠀⠀⢸⠁⠀⠀⠈⡇⢀⣿⣧⣿⣸⢈⣆⣱⡆⣷⣸⣿⡀
⠀⠀⠀⠀⠀⢀⣤⣰⠻⣿⠀⠀⠀⠀⢩⣋⡊⠂⠀⠀⠘⣷⣅⠀⠈⠀⠀⠀⠀⠁⠠⣟⡿⣿⣿⣿⣿⣿⣿⣿⡟⣯⠆
⠀⠀⠀⠀⢀⣿⣿⣿⣿⢹⡄⣠⣤⡀⢀⣒⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⢡⠙⠾⣇⣾⢩⡏⣱⣅⡷⠟⢁⠐
⠀⣼⣶⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⠇⠸⠿⠀⢀⠲⡙⢷⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠁⠄⠈⠙⠻⠗⠛⢉⠠⠘
⠀⣿⣿⡄⢸⣿⣿⣿⣿⣿⣇⣿⡟⠀⠀⣀⣄⠀⠳⠉⠂⠀⠀⠀⠀⢻⣦⣴⣶⣄⠀⠀⠀⠀⠐⠠⠀⠂⠈
⠀⠈⠛⠿⠿⣿⣿⣿⣿⣿⠉⠁⠀⠀⢄⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⣝⢻⣆⡀⠀⠀⠀⠀⡤⢴⣶⣶⡤⡄
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣄⣀⠀⠻⢿⣌⣉⣼⣿⣿⣷⣆⠀⢰⣿⣿⣷⣿⣿⣷
⠀⠀⠀⠀⠀⢹⣿⣏⣿⠁⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⡆⠀⠘⣿⡿⢋⣥⣾⣿⡿⠀⠈⢿⣿⣿⣿⣿⠟
⠀⠀⢠⣴⣶⣾⡿⢻⣿⣶⣶⣤⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠣⣄⡤⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣭⡥⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⢰⣿⣿⣿⡆⠀⣁⣘⢶⠃⣰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢸⣿⡝⣿⡇⠀⠺⡩⠡⠂⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢠⡖⡶⣄⡶⣖⠂⠀⣀⣀⣀⣀⠀⠀⠀⠈⠁⠁⠀⠀⠀⢠⣀⡄⠀⠀⣴⣾⠳⢻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠓⠃⠙⠀⠓⠂⠀⠨⠭⠭⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠻⠿⠶⠾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⣾⡏⢀⡇⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⢃⡞⠁⠀⠀⠈⠁
⠀⠀⠀⣤⠀⠀⠀⠀⢠⠀⠀⠀⠀⠉⠻⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂⢤⡄⢀⣀⡀⠶⠆
⠀⠀⠀⢸⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠠⣤⠀⢤⡄⠉⢠⡤
⠀⠀⠀⠀⠃⠀⠀⠐⠁⠀⠀⠀⠀⠰⠦⠤⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠇
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢻⣷⣤⡀⠀⠀⠀⠀⠀⣠⣶⡟⠁⠀⠀⠀⠉⠉⠓⠀⠀⠀⠀⠀⢸⣿⣶⣿⡇
⠀⠀⠀⠀⠸⢿⡿⠏⠀⠀⠀⠙⠿⠇⠀⠙⠟⠀⠀⠿⠛⠀⠀⠀⠀⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠁
⠀⠀⠀⠀⠀⢸⡟⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠸⠇⠈⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⡀⡀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠻⠋⠙⠟⠁⠀⠈⠛⠁⠘⠛⠀⠀⠀⠀⠀⠆⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠁
⠀⠀⠀⠈⠁⠀⠀⣀⡀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠉⠀⢠⣤⣤⣤⠀⠀⣴⣦⣤⣄
⠀⠀⢠⣀⣀⡀⠀⠙⠛⠛⠁⠀⢲⠶⣶⠆⠀⠀⠀⠈⠀⠀⠀⢸⡋⠈⢻⠀⠀⠉⣭⣍⠉
⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠰⠶⠶⠀⠀⠀⢀⠀⠀⠀⠀⠈⣷⣶⡿⠀⠀⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠛⠋⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣦⡄⠀⠀⣀⠀⠀⣤⣀⡄⠀⠀⠀⢀⡂⠀⠀⢀⠐⠲⠂⠀⠀⠀⠀⠀⠀⣦⡦
⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣀⣀⣀⣛⢦⣀⣬⠶⣴⠚⠛⢯⡁⣈⠀⠀⠀⡀⠘⣆⠀⣉⣻⣿⣿⣿⣿⣿⡖
⠈⠻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⠛⠉⠉⠉⠙⢿⣍⣢⣤⠬⠷⢶⡛⠉⠃⠀⠀⠀⠀⠀⠙⠀⣒⣶⠿⢿⠿⠛⠉⠁
⠀⠀⠈⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠘⢿⣁⣈⣳⣤⡴⠛⠞⠀⡀⠀⠉⠀⠀⠀⠀⣭⡀⠀⠀⣀⡀⣀⠤
⠀⠀⠀⠀⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢈⠁⠈⠁⠀⠀⠀⠀⢀⣿⠉⠉⠀⠀⠀⠑⠀⠀⢠⡄⠀⠀⠀⠀⠀⢸⣷⠀⢀⣿⢳⡟⢁⣰⣶⣧⣄⢀
⠀⠀⠀⠀⢸⣿⣿⣿⠟⠂⠀⠀⠀⠀⠀⠈⠋⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⡤⢿⠇⠀⠀⠀⠀⠀⢸⣿⡇⠘⣿⣸⠃⣿⣿⣿⣿⣿⡆⣷⡀
⠀⠀⠀⠀⠸⠿⠿⠿⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠹⣿⣧⡙⢿⣿⣿⡿⣡⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢯⣻⣤⣤⠄⠀⠙⠛⠲⠟⠻⠇⢻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠀⠤⠔⠀⣠⡀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠐⠂⠀⠂⠀⠀⣹⣷⣀⣠⣤⣶⡶⠶⠶⠶⠾⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⢴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸⡎⠻⡆⠀⠀⠀⢀⠔⠂⠀⠀⠀⠀⠀⠀⠀⣴⢛⡴⢦⡄⠀⠀⠀⠀⠀⠉
⠀⢀⣄⣤⣄⠀⡄⢠⢀⡄⠀⠘⠠⠤⠤⠀⡀⠀⠀⠀⢸⡇⢸⣷⠀⠛⡄⠀⠐⠉⠂⠀⠀⠀⠀⠀⠀⣀⢚⡷⣭⢟⡷⠁⠀⠀⠀⠀⠀⢀⡤⠖⣦
⠀⠀⠀⠁⠈⠀⠱⠜⠘⠃⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠈⣟⠀⠠⠀⣰⠃⠀⠀⠂⠘⠓⠀⠂⠀⠀⠀⠣⠾⣡⡿⠋⠀⠀⠀⠀⠀⠀⠀⠸⣏⡰⠟
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁⠀⠀⠀⠀⠀⠈⠚⠃
⠀⠀⠀⣠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⣠⣀⣤⣀⠀⠀⠀⠀⠀⢤⠀⠊⠁⠀⠀⠀⠀⢀⡀⣀⣀⣄
⠀⠀⠀⢩⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡠⢤⡀⠀⠀⠀⢀⡐⠿⠈⠁⣰⠀⠀⠀⠉⠛⠿⠟⠉⠀⠀⠀⠈⢀⡤⠈⠑⢴⣆⠀⠀⠀⠿⠿⣿⡿⠛⠂
⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢀⡐⠅⠰⠟⠀⠀⠀⠀⠀⠈⠛⢀⡠⠞⠁⠀⠀⠀⠂⠀⠀⠀⠀⢄⡀⠀⣰⠾⠁⠶⠆⠀⠉⠀⠀⠀⠀⠰⠎⠁
⠀⠀⠀⢠⣄⡉⠀⠀⠀⠀⠈⠃⠀⠲⠶⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠁⠀⠠⠴⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠨⠟⠛⠢⡄⠀⠀⠀⡀⠉⠰⢶⡄⠀⠀⠀⠀⠐⠞⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⢲⡆⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣆
⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⢠⡞⠠⠀⠀⠀⠀⣰⠀⠀⠙⠧⠈⠀⠄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⡴⠖⠛
⠀⠀⠀⠀⠀⣽⣟⢟⠀⠀⠈⠁⠀⢠⣄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠾⠶⠾⠿⠃⠀⠀⠀⠀⠀⡞⣶
⠀⠀⠀⠀⠀⠈⠙⠉
⠀⠀⠀⡀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣦⠀⠀⠀⠀⠀⢀⠀⢂⠀⢂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠐⠛⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⡇⠀⠀⠀⠄⠘⢀⢨⠖⠉⠀⠰⠀⠀⠈⠀⠀⠃⠀⠀⠐⡛⠛⠛⠛⢋⣙⡦
⠀⠀⡀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠄⠀⠠⡦⠀⠀⠀⠀⠠⠦⠀⠤⠶⠤⠃⠀⠈⠛⠃⠛⠋⠀⠀⠀⠀⠘⠀⠓⠀⠠⠤⠄⠀⠀⠀⠉⠢⠄⠀⢊⠉
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡄⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⠀⠂⠀⠨⠿⠀⠀⠀⠀⠀⠀⠆⠀⢀⠀⠀⠀⠀⠰⠀⠛⡟⠁⠀⠀⠀⠀⠤
⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⣰⠇⣸⡄⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠵⡄⠀⠢⠤⠀⠀⠈⠄⠀⠀⣀⢊⡀⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠴⠌⠀⠀⠀⢹⠿⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⣸⠇
⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⣠⣴⡶⢶⣶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⢠⣤⡀⠀⠀⠠⡀⠀⠿⠀⠀⠀⠀⠀⠀⣀⣤⣀⣠⠀⣤
⠀⢣⣤⣄⡀⣀⣠⣤⠆⠀⠀⠿⣧⣰⣦⣬⣯⠀⠀⠀⠀⠞⠙⠆⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⡶⢁⢴⣷⠧⣴⠒⢤⡀⢾⣯⣍⣹⠇
⠀⠀⠙⠛⠛⠛⠛⠋⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠘⢶⣤⣤⡤⠞⠀⠀⠀⠀⠀⡄⠀⠁⠀⠀⠀⠀⠄⠈⣼⣃⣠⠿⠦⠚⠁⠀⠀⠈⠉

⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⢺⡆
⠀⠀⠀⠈⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡤⢤⡤⠀⠀⠀⠀⠘⠿⣿⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠻⡆⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢠⡀⠀⠀⠀⠀⠐⠀⠈⠁⠀⠀⠀⠀⠀⠀⠻⠧⠀⠀⠀⠀⠰⢀⡴⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⢱⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠃⠀⠀⠄⠀⠀⠀⠻⠶⠶⠶⠟⠁
⠀⠀⠀⠀⣀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠘⠀⠰⠀⠀⡑⠀⠀⠀⠀⠀⢀⣤⡀⠐⠀⠀⠀⠠⣦⡍⠓⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠴⢷⡆
⠀⠀⠀⠚⢁⡴⠾⢃⠀⠀⠐⠓⠒⠂⠀⠐⠀⠀⠀⢰⣧⣿⡿⡶⡄⠀⠀⠀⠀⠀⣼⠀⣉⡿⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠶⠊⠛⠒⠛⠁⠀⠁
⠀⠀⠈⠒⠀⠑⠤⠘⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠰⠦⠏⠰⠆⠱⠟⠂⠀⠀⢀⣁⠉⢀⡏⠀⠀⠀⠀⠈⠋⣤⡤⠸⠷⠀⠀⠀⠑⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠃⠤⠴⠦⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠠⣶⠄⠀⠀⢀⣀⡀
⠀⠀⠈⠁⣤⣤⡀⠀⠀⠀⢠⠀⠀⠀⢷⠀⠀⠀⠀⣠⣶⡾⠛⠋⠁⠠⠀⠀⠂⠀⠐⣄⡉⠁⠀⠀⠀⠀⠉⠉⡉⠀⠰⠀⠀⠀⠀⠈⠠⠀⠘⣽⢀⡿
⠀⠀⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢉⡿⠏⠀⠀⠀⢲⣶⣤⣤⣷⡬⠃⠀⠀⠀⠀⢀⠦⠀⠀⠠
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠈⠀⠀⠀⠀⠐⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠠⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⡿⣿⣿⡿⢿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣆⣥⣤⣿⣄⣴⣇⣄⣷⣬⣴⣾⣁⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠂⡬⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠙⠀⠀⣰⣦⣄⡀⠀⠀⢀⡤⠶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣦⡀⠿⣧⣶⣼⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡈⠙⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⡄⠸⣿⢇⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠁⠀⢋⢈⠀⣿⣿⣿⠿⠁⠿⢿⣿⣿⡿⠟⠋⠀⠀⣹⠀⣟⣛⡃
⠀⠀⠀⠀⠠⣤⣴⣶⣶⠀⣂⣀⣉⡸⡗⢶⣿⣶⣶⣶⣶⣶⠒⠀⠀⣁⠀⠀⠀⠀⠉⠀⢹⣿
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⢈⣍⣭⣭⣭⣭⣡⣤⣭⣭⡁⠀⠀⠀⠐⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⡆⢘⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡧⠀⠀⠇⠸⠀⡆

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣾⣿⣻⣻⣟⣻⣿⣿⣿⣟⣟⣻⣿⣿⣿⣻⣿⣻⣿⣿⣿⣿⣻⣿⣻⣻⣿⣧
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣯⣿⣭⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⣿⣟⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣻⣿⣻⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣯⣿⣿⣯⣿⣿⣿⣯⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣻⣿⣿⣿⣟⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣯⣭⣭⣭⣭⣭⣭⢭⣭⣭⢭⣭⣭⣭⠭⣭⡭⡭⢭⣭⣭⣭⣭⣭⣭⣽⣿
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⢹⣿⡜⡈⢸⢘⢹⡧⢹⣸⣿⡇⣧⡳⣿⡏⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⣧⣷⣾⣼⣿⠴⣾⣿⣿⣧⢧⡵⣿⡿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡘⠁⡇⡇⡇⠱⡇⣓⣿⠀⣿⡘⢸⢸⢺⡞⣼⡿
⠀⠀⠀⠀⠀⠀⣴⣿⠿⠿⠿⠿⠿⠧⠷⠥⠧⠷⠵⠭⠯⠶⠭⠷⠼⠬⠼⠿⠿⠿⠿⠿⢿⣷
⠀⠀⠀⠀⠀⠀⢻⣿⣖⣖⣶⣖⣶⣶⣷⣶⣶⣶⣲⣶⣶⣷⣶⣶⣖⣶⣖⣶⣲⣶⣶⣶⣾⡿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣯⣿⣿⣿⣭⣽⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣻⣿⣿⣛⣿⣛⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣛⣿⣟⣿⣷
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣽⣯⣽⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣽⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣟⣛⣟⣻⣿⣟⣿⣻⣟⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⢀⣀
⠀⠀⢀⠠⠤⠄⠀⠀⠀⠀⣀⣠⡾⠋⠥⣯⣜⣿⣿⣿⣿⣿⣿⣓⣽⠡⠑⠢⣦⣄⡀
⠀⠀⠠⠀⠠⠄⠀⢀⡴⠿⡍⠀⢱⣿⡆⠩⢱⣾⣻⣛⣛⣏⡿⡎⠥⠱⣿⠂⠀⢩⡿⠲⣄
⠀⠀⠠⠀⠰⢆⡴⣫⠤⣞⡁⠤⠜⠛⠀⠀⢈⣐⠋⠏⠹⠏⣃⢄⠀⠀⠈⠓⠤⢌⡓⠦⣍⠳⣄
⠀⠀⠠⠐⢰⣯⠞⣡⡀⢀⣥⠀⠀⠀⠀⠀⡳⣿⣧⠀⠀⣼⡾⢛⡀⠀⠀⠀⠀⣬⡅⠀⣤⡳⣬⣆
⠀⠀⠰⠀⣿⣏⡦⡉⣶⡦⣿⢷⡗⠀⠀⠸⣿⣿⣿⡆⢀⣿⣵⡿⠟⠀⠀⠸⣇⣿⢷⣷⢉⢴⣾⣿
⠀⠀⠐⠀⣿⡏⠐⣻⣼⣿⠿⠋⠀⠀⠀⢰⣒⣬⣻⡁⢈⣝⣣⣲⡶⠀⠀⠀⠙⠺⣼⣿⣾⣂⢸⣿
⠀⠀⠐⠒⣿⣯⣰⡿⠞⠁⠀⠐⢀⡂⠂⠰⢀⢯⣻⣧⣼⣟⡽⢂⠐⠘⣀⣃⡂⠀⠈⠛⢿⣆⣽⣿
⠀⠀⠐⠂⣿⣯⣿⣵⣢⣶⣾⣿⣿⣿⣿⣦⡀⢀⣿⣿⣿⣿⣆⢀⣴⣿⣿⣿⣿⣿⣶⣴⣮⣿⣿⣾
⠀⠀⠘⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡏⢩⣿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⠁⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⣽⣧⣼⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⡀⡀
⠀⠀⠈⢁⣿⡧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⣷⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡂
⠀⠀⠈⢸⣟⡃⠡⡻⣿⣿⣿⣿⣿⠿⣿⡟⣰⢻⣿⣿⣿⣿⣟⣧⢙⣯⡿⢿⣿⣿⣿⣿⡟⡈⠀⣹⣯
⠀⠀⠀⢈⢉⣁⢀⠘⠉⠋⣭⣥⣤⣶⣿⣇⢣⣿⣿⣿⣿⣿⣿⡎⣌⣿⣷⣦⣤⣭⠍⠉⠁⡀⡀⠈⠙
⠀⠀⠀⢸⣿⡁⣨⣤⣀⡀⢸⣶⣷⠱⡿⠀⢸⣿⣿⣿⣿⣿⣿⡇⡀⢸⡞⢸⡷⡖⠀⣔⣤⣦⣀⣾⡟
⠀⠀⠀⠈⢿⣿⣯⣽⣟⣷⣤⣄⡁⣹⠀⠈⣦⣛⢛⣙⢫⡙⢛⣵⠇⠀⣿⣈⣠⣶⣶⣻⣯⣽⣿⠿⠁
⠀⠀⠀⠀⢈⡁⠻⣟⢫⣽⣿⣿⣻⣿⡁⣀⠩⠉⡄⢉⡌⠀⡌⢩⢠⢈⣿⣿⣿⣿⣿⡝⣻⠟⠁
⠀⠀⠀⡀⢀⡁⠀⠈⣎⣿⣿⣿⣿⡽⠷⠣⣃⡾⣠⣘⣣⣤⡱⣈⡎⠳⠳⣿⣿⣿⣿⣧⠁
⠀⠀⢀⠀⢀⡄⠀⢠⡿⣿⣿⣿⠶⡗⡎⠻⠁⠿⠁⠈⠃⠀⢻⠀⠟⢹⢻⢶⣾⣿⢷⡿⡇
⠀⠀⢀⠀⢀⡄⠀⢸⣿⣿⢻⣿⣶⡶⢶⠞⡦⠲⡤⠰⠖⢲⠖⢶⠓⠾⠶⣾⣿⡟⣷⣿⡿
⠀⠀⢀⡀⢠⡄⠀⢨⣾⣿⣼⣯⡻⠿⣼⣄⡴⣤⠧⡰⠧⠼⠦⢾⣠⢧⡿⡟⣽⣧⣿⣿⡇
⠀⠀⢠⠄⢠⡄⠀⠘⣿⢻⣏⢙⡟⠻⠐⡆⠰⡄⢲⠀⠄⡞⢀⠆⠠⠃⠞⠹⡏⡀⣿⣿⠏
⠀⠀⠠⠄⢠⡄⠀⠀⠘⢿⡧⡈⢀⣤⣤⡀⠀⠀⣠⣠⣆⣄⠀⠀⢠⣠⢤⣀⢈⣼⡿⠃⠀⠀⠀⠀⠀⡀
⠀⠀⠠⠄⢠⡄⠀⠀⠀⠀⠙⢮⣻⡶⠲⣜⡀⢠⣌⣷⢾⣧⡤⢀⣣⡞⢳⣜⡵⠋⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠭⠙⠦⠙⠩⠮⠋⠴⠋⠽⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢀⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠉⠉⠁⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⣀⣤⣶⡶⣶⣶⣤⣔⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠁⠀⠀⠀⣀⣽⠻⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠆⠰⢰⡿⠁⠀⠀⢀⣤⠾⠁⠀⠀⠀⢹⣧⠀⠐⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⠋⠀⢠⡿⠓⠘⠁⠑⠀⠀⠀⠀⠀⠂⠠⢀⢹⡆⠀⠑⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⠀⢸⡇⡰⠁⢠⣤⡄⠀⠀⠀⣤⣤⠀⠀⠘⡇⠀⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢆⡁⠀⠀⠀⠁⡗⠀⠀⠘⠛⠀⠀⠀⠀⠛⠋⠀⠀⢸⡇⠁⠀⠀⠀⢻⠗⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢅⠀⠀⠀⡀⠀⠀⠠⠴⡀⠀⠀⠀⠰⠖⠒⠢⠀⠀⠀⠀⠸⠄⠂⠀⠀⠀⠂⠀⢀⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠑⢄⠈⠐⠄⠀⠀⠐⡀⠀⠀⠀⠳⠖⠃⠀⠀⠀⠔⠀⠀⠀⠠⠂⠀⠔⠁⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠑⠄⡠⠋⠀⠐⢌⠂⠄⣀⠀⠀⢀⠀⠐⠀⡠⠐⠁⠙⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠀⠀⠀⠀⠁⠀⠂⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⡀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⢀⣀⠠⠐⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠀⠀⠀⠉⠠⡀⠀⠈⠆⠀⠄⠀⠈⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠐⢤⡀⠀⠁⠢⠀⠠⠀⠐⠀⢀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢬⠀⠀⠈⣷⠀⠀⠀⠀⢀⠂⠀⢀⣀⡥⠖⣀⠄⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⡐⠚⠛⠿⠿⠒⠌⠀⣤⠂⠠⣄⣹⣇⠀⠀⠀⢀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠐⠀⠀⢀⠀⠀⠀⠈⠞⡁⢰⣤⣿⣿⣏⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⡉⠆⠀⠀⠀⠀⠀⠈⡄⠔⠂⠀⠉⠀⠀⠀⠀⠀⠀⢑⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠌⠀⢠⡴⣶⡶⢆⠀⡀⠀⠀⠀⠃⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⡄⢁⠀⠐⠂⠠⠾⠚⠉⠀⠀⠞⠛⠛⠁⠀⢀⠀⠀⡠⠀⠈

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

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

⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢴⣶⣿⣿⠿⠓⠀⠀⠀⠀⠈⠃⠀⠀⠀⠔⠚⢳⡶⣤⡄⠀⠀⠐⢦⠀⠀⠀⠀⠘⠁⠀⠚⠁⠀⠚⠁⠐⠂
⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⠇⠀⠀⠀⢸⠀⠀⢸⡷⣶⠿⡶⢾⡷⢶⡒⠿⠆⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣰⣤⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⢀⣤⡶⠿⠿⠶⠄⠀⠀⠀⠀⠀⠀⠘⠿⣟⣦⣴⣶⡶⣾⡇⠈⠒⠂⠘
⠀⠀⠀⠠⠀⠀⠀⠀⠠⣠⠀⠀⠀⠀⣶⠟⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠁⠀⠀⡀⠀⠀⠀⠆
⠀⢠⡄⣀⠐⠀⠀⠀⠖⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠃⡈⠀⡄⣆
⠀⠈⠙⠛⠇⡵⠚⠁⠀⠀⢀⣴⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢠⢄⡄⠀⠀⠒⠀⠀⠀⠈⠀⠀⡴⠀⢀⠓⠋⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠐⡘⠁⠀⢀⣶⡟⢁⠀⠀⠀⠀⠀⡆⠀⢸⢰⠀⡇
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠾⠿⢽⡷⢶⠀⠀⠀⠈⢢⡄⠈⠿⢧⠘⠁⠀⠀⠀⠀⠀⠀⢨⠘⢰⠁
⠀⠀⠀⠀⠖⡀⠠⡠⡄⡀⡠⠚⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠐⢃⠔⠀⠱⡈⠅⠀⠀⠀⠀⠀⢀⠀⠤⣦⣄⠀⠀⠀⠀⠀⢠⡇⠀⡴⠶⠟⠿⠇⠐⠲⠀⠉⠀⠀⡇⢸⠇
⠀⠀⠀⠀⠀⠈⠀⠀⢀⡀⠀⠀⠀⠀⢠⣼⣿⣾⣞⣦⣠⣶⣄⠀⠀⢀⠜⠁⠀⠧⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⣐⠶⣿⣯⣳⢦⡀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠖⠉⠐⠀⠀⠘⠀⠀⠀⠀⠈⣹⠀⢀⡷⢶⣤⠿⡀
⠀⠀⠀⢀⣀⠀⠙⠻⣦⠙⠋⠘⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢠⠁⣰⠏⠀⠀⠉⠈⠉⠒⠁
⠀⢰⠃⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡴⣶⠟⠀⠀⠀⠀⠁⢰⠏⠀⠀⠀⢠
⠀⢸⠀⠀⣤⠃⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠋⠁⠀⠀⠀⠀⠀⠒⠋⠀⠀⠀⠀⢈⢠⠡⠀⡀
⠀⢸⠀⠀⠚⡅⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⠛⠁⠀⠀⠀⠀⠀⠀⠐⣶⡷⠀⠀⠀⠀⠂⠄⠸⣶⡀
⠀⠸⠀⠀⣷⠄⠀⠀⠀⠀⢀⢤⣄⣠⣀⢀⣀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣤⡀⡀⡀⠀⠐⠄⠀⠀⠀⠀⠀⣿⠆
⠀⠀⠂⢠⣷⠦⠀⠠⢎⠉⠼⠿⠰⠶⠹⠿⠯⠾⠢⠀⠀⠠⠀⠀⠀⠀⠀⠀⠘⡧⠤⠠⠡⠱⠡⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⡀⠐⠀⡀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠉⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠭⠁⠠⠤⠄⠍⠦⠀⠁⠀⠀⠘⠉⢱⠒⠂⠀⠀⠐⠂⠀⠀⠀⠀⢀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⣀⣀⡄⠸⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡃⠀⠀⠙⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠚
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠒⢚⠀⠀⠀⠀⠠⢄
⠀⠀⢸⠉⠉⠉⢉⡉⣉⠉⠉⠉⠉⢉⢀⣀⠀⠀⡀⢀⡐⢲⠀⠀⠀⠀⠀⠀⠀⢠⠄⠰⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢸⠀⢠⠊⠁⠀⠀⠉⠢⡀⢰⠁⠀⠈⡆⢌⠀⠀⢘⢘⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉
⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⢱⠈⠓⠤⠐⠁⠘⢂⡐⠊⢸⠀⠀⠈⠀⠁⠀⠀⢸⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠙⠂
⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⢸⢰⠋⠀⠙⡆⠜⠁⠈⢱⢸⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀
⠀⠀⢸⠀⠘⢆⡀⠀⠀⠀⡠⠃⠈⠢⠄⠴⠁⠐⠤⠤⠚⢸⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠘⠤⠤⠤⠬⠭⠬⠭⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢐⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⡠⠄⠀⠒⠂⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⠀⠀⢻⠁
⠀⠀⠀⠀⡀⠀⠀⢃⠀⠀⠀⠀⡇⢹⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⢀⠅⠀⠀⠲⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⢸
⠀⠀⠀⠀⠃⠀⠀⠘⠀⠀⠀⣼⢁⡜⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⡒⠒⠲⢌⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢘⠀⠀⢘
⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠰⠁⡀⠈⠂⡀⠄⠀⢱⡀⠀⠀⣠⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⡇⠈⠈
⠀⠀⠀⢸⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠑⠄⠀⠀⢘⡀⢃⠀⠀⠠⠀⠀⢠⡇⠀⡎⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⢀⠄⠀⠀⠀⠣⣀⠀⠀⡄⢊⠀⠔⠀⠀⢇⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡆
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢀⠀⠁⠀⠀⡠⠒⠢⡈⠑⠉⠈⠂⠁⠀⠀⠀⠈⠓⠲⠔⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠀⠒⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠈⠂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠀⠀⠀⡄⠀⠀⡁⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠂⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⡆⠀⠀⢁⠀⠀⠀⢀⠄⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠃⠀⠐⠀⠀⠀⠤⠠⠠⠀⠀⠀⠈⠢⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠁⠀⠀⠃

⠀⠀⠀⠆⡀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢀⡠⠐⡠⠆⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⣄⡆⣦⡤⠼⠞⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢀⠟⠁⠀⠠⢂⡘⡄⠀⡘⠀⠀⠀⢠⡖⠒⠒⠛⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠘⠁⠀⠚⠀⠀⠀⠀⠈⠙⠖⠀⠀⠃⠀⠀⠀⠁⠀⠀⠂⠀⢀
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠠⠐⡤⠀⠀⠸⠃⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠸⠀⠀⠀⠀⠀⠀⢀⣀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⢀⡐⠂⠀⠀⠀⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠸⠀⠀⠙⠀⠀⠀⠀⠀⠀⡀⢤⡁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠠⠤⠀⠀⠀⠀⠸
⠀⠀⠔⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠓⢎⡩⣄⠀⠀⠑⢌⠀⢡⠀⠀⠠⠈⠂⠀⠀⠀⢀⠀⠘⡀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠘⠨⠗⡀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠃⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉

⢀⠄⠀⠋⠀⠁⠐⠀⠀⠀⠠⣴⡄⠐⡤⣧⠄⠀⠀⠀⠀⠀⣄
⠀⠀⠔⠋⠽⣟⠐⠀⠀⠀⠀⠍⠉⢰⠛⠧⠀⠀⠀⢀⠄⠈⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⢀
⠀⠀⠀⠈⢰⠁⠀⠀⠀⠀⠀⢰⠀⠰⢀⠀⠀⠀⠀⠀⠀⠄⠤⠀⠠⡐⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠈⠚⢻⠋
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢂⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠁⠀⠀⠀⠀⠀⠀⠈⠐⠂⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⡀⠀⠀⠀⢀⢖⠃⠒⠒⢤⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⣄
⠀⠈⠀⡀⣠⠤⠤⣀⡄⠀⠀⠀⠄⠠⡂⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢣⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⠠⠁⢠⠀⢰⠀⠠
⠀⠃⠀⠀⠀⠀⠀⠐⠀⠀⠀⠣⢀⡐⠀⠂⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠐⠈⠀⠀⠀⠈⠂

⢀⣀
⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⣴⣦⡄
⠀⠀⡀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡿⠟⠁⠀⠀⢀
⠀⠀⡇⠀⡆⠀⡆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⡮⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢳⡄
⠀⠀⠃⠀⡇⠀⠁⠀⢠⠦⠤⠤⠤⠤⠤⠤⠤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⡀⠀⠀⠀⠀⠂⠀⠠⢉⠁
⠀⠀⠈⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

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

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

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣤⡀⠀⠀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⣿⣷⠆⢻⡉⢻⡥⢤⡄
⠀⠀⠀⠀⠀⢀⣀⣠⣿⠂⠚⢹⢈⡟⠚⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣏⣸⡗⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣤⣶⣦⣼⡦
⠀⠀⠀⠀⠐⢉⡏⠉⢻⣰⣾⡏⣢⣽⠆⢰⣋⣭⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣿⣿⣹⣿⡈⢇
⠀⠀⠀⣀⠀⢿⣿⣿⡿⠟⣻⣟⡽⢋⡄⢺⡿⢿⣿⣿⣿⣿⣿⡿⣿⠻⠛⡻⢽⣿⣿⡿⠟⠻⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⡿⠃⡜⠂
⠀⠐⢲⣿⣶⣾⣿⡏⣠⠺⠟⢋⣠⣾⣧⣾⠀⣼⡇⢀⣤⡉⠓⠉⠀⠸⠷⠁⠀⠈⠁⠀⠒⠦⠌⢻⣿⣿⣿⣿⣾⣿⣿⣿⣦⣿⣿⣟⠛
⠀⠊⣋⣿⣿⣿⣿⣿⣿⡶⠾⢋⣵⡏⣩⣿⣄⡟⠠⠐⠂⠀⠀⠠⢀⡐⠖⢀⠄⠀⠀⣀⡀⣆⡐⣀⢻⣿⣿⣿⣿⣿⠙⣿⣿⣿⡟⣼⠇
⠀⠐⠌⢛⡛⣿⣯⣶⣾⣷⣶⠟⣫⡾⣿⡿⣿⢀⣤⣶⣾⣶⣶⣤⣄⠀⠄⠀⢾⣿⣿⣿⣿⣿⣿⣿⣌⣿⡿⣿⣿⣿⣇⣩⣴⣿⡅
⠀⠤⠴⠚⣋⣽⣼⠟⠑⣷⣦⣶⣿⡀⠈⣿⢻⣿⣿⣿⣛⣿⣿⣿⣿⠀⢀⠰⠸⣿⣟⠛⠛⠛⢿⣿⡿⢸⣧⣿⣯⣿⢻⡿⣿⣿⠇
⠀⠀⠑⠛⠋⡿⠁⣤⡾⢛⣥⣋⣵⣿⣆⣸⢮⣽⣿⣥⣤⣴⣿⣿⠇⣠⣼⣤⡀⠻⠿⣿⣿⣿⣿⣿⢇⠸⣿⣿⣿⡟⣹⣿⡎⢿
⠀⠀⠀⠀⢀⣇⡠⢥⣾⣿⣿⣿⣿⣿⣿⣿⡙⠿⠿⠿⡿⠉⠀⠀⣸⣿⣿⣿⣿⣦⡀⠀⠀⢙⡯⠁⠀⢰⣿⣿⣿⡇⣽⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠳⣌⠁⠚⠁⢠⡄⠘⠛⠋⢻⠉⠙⠋⠁⠀⠴⠀⠈⠁⠠⠞⢿⡿⢿⣿⣿⣿⣧⡈
⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⢿⣿⠀⠘⠂⠁⠀⠀⠁⢠⠐⢃⣉⣡⣬⣟⠦⡀⠀⠀⠀⠀⠀⠀⣾⣇⡼⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣿⣿⢿⡾⣿⣿⣿⣿⣿⠃⠀⠀⠀⢀⢀⣠⣮⣶⠛⠂⠋⠘⣛⣷⠿⠲⠂⠤⡀⠀⠀⣿⣿⢿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⢀⣴⢟⣵⣿⣷⣾⣧⡿⢿⠿⣷⠀⡑⠒⠺⠉⠁⠀⠘⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⡰⢰⣿⡟⠿⣿⣿⣇⢸⡀⣠⣀
⠀⠀⠀⢀⣴⣛⣵⣿⣿⣿⣿⣿⣿⣜⢢⣶⣿⣧⡑⠦⢤⡤⢄⡀⡀⣀⣶⠶⢮⣵⣀⠀⣠⡒⠰⠊⢁⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⡄
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣾⠟⣿⣿⣿⣿⣿⣿⣿⣷⣴⣤⣀⣈⣉⣯⣽⣴⣿⣷⣾⣯⣄⣀⣡⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⡟⢏
⠀⠀⠀⠀⣿⢀⣾⣿⡟⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋
⠀⠀⠀⢰⠏⣼⣿⣿⠇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢼⣿⣿⣿⣿⣿⣿⠟⠛⠿⠿⣿⠂⢠⡔⣩⣾⣿⡈⣿⣿⣿⣧⠀⢸⣿⣦⢦⣄
⠀⠀⠀⢼⣄⣿⣿⡏⢷⣄⡘⣧⣻⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⢿⠃⠀⠀⠈⢠⡏⢠⣻⠞⣽⢿⣿⣷⣿⣿⣿⣿⡤⢸⣿⣿⣦⣈⣙⣤
⠀⠀⠀⠸⣯⣟⣿⣿⣼⣿⣿⣼⣿⣿⣿⣿⣿⣛⣻⠿⣿⡀⢿⣿⣿⣿⠃⠀⠀⠀⠔⠉⠀⢸⡏⢸⣧⡾⢿⣿⣿⣿⣿⣿⡵⢸⣿⣿⣿⣿⡿⣙
⠀⠀⠀⠀⠘⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⢌⣷⡈⢿⡿⡂⠀⠀⠀⠀⠊⠁⠀⠘⣇⢈⣿⡀⣿⣿⣿⣿⣋⣼⢧⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⢀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣦⣌⣸⣷⠀⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣷⣦⣤⣿⣿⠟⢣⣾⣿⣿⣿⣿⡸⣿⠁
⠀⠀⠀⣾⢩⣤⣾⣿⣿⣿⣝⣻⣿⣿⣿⣿⣟⣿⣿⣿⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⣿⠀⠀⡘⠁⢈⣍⣻⣿⣭⣤⣤⣤⡄⠈⣿⣿⣿⣷⡇
⠀⠀⠀⢿⣮⣻⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣮⣁⣾⡿⠻⠆⡇⠀⠀⠀⠀⠀⣼⠇⠀⠀⠁⠀⠈⠛⢿⣯⣛⠿⣿⣿⡏⠀⢻⣿⣿⡿⠃
⠀⠀⠀⠈⢻⣿⣷⣬⢉⣿⣯⡙⢿⣿⣿⣿⣿⣿⡿⣿⣻⣏⣙⣚⠃⠀⠀⢀⣀⣼⡿⠀⠀⡶⠆⢀⡄⠀⠀⣀⣙⣷⣝⢿⣇⠀⣈⣭⠇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⢻⣿⣆⠹⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⠿⣆⠉⢛⠿⣿⡷⠀⣠⠶⠛⢉⣶⣿⣿⣟⡻⣿⣿⣿⣿⣿⣿⣽⠃
⠀⠀⠀⠀⠘⢿⣿⡌⢻⣷⠀⠻⣿⣶⡟⡛⠻⣿⣿⣿⠿⠟⠋⣠⣶⣿⠀⠈⠳⠶⠟⠠⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⣙⠻⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠈⢻⡇⠀⠹⠀⠀⠉⠹⠿⢿⣷⣿⣿⣿⣄⣴⣿⣿⢧⡟⠀⠈⢁⣄⠀⠀⠘⠛⢱⣿⣿⣿⣿⣿⣿⣿⠟⠛⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡾⣻⣶⣭⣿⣿⣿⣿⣿⣿⣯⡞⠀⠀⠀⠨⠵⠂⣠⢰⣦⣼⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⣾⣿⣿⣿⣿⣿⣹⣿⡿⢿⣧⣄⣱⣾⣙⣲⣞⣙⣿⡶⠋⠉⢿⡻⣿⣿⣿⣿⡻⣦⣸⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠾⠿⠟⠃⠀⠀⠀⠉⠉⠈⠙⠋⠉⠉⠉⠁⠀⠀⠀⠀⠉⠈⠉⢿⣯⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣽⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣻⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⣿⡿⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣛⣿⣟⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⡘⠀⠤⢤⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⠀⠀⠈⠘⠛⠛⠿⠿⠯⠂⠀⠁⠀⣤
⠀⠀⠀⢦⠀⠀⠀⡀⡀⠀⠀⡄⠀⠀⠘⠆⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣚⠓⠒⠀⠐⠂⠒⠂⠀⠖⠒⠶⠒⠚⠋
⠀⠀⠀⠈⠃⠀⠀⠀⠣⠀⠀⠑⠀⠂⠀⠸⠇⠀⠀⠇⠀⠀⠀⠀⠀⢠
⠂⠀⠀⠀⠀⠀⣺⡀⠀⢀⠀⢠⠄⠘⠀⠀⣜⠁⠄⠀⠀⠀⠀⠀⠀⠀⡀
⢨⠆⠀⠀⡀⢁⣈⠃⣀⣰⠀⠀⠘⠃⢀⣀⡉⣀⠀⠄⠄⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⢰⡆⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠐⠀⠢⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠘⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣷
⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⣸
⠀⠳⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⢿
⠀⠈⠀⠀⠀⠀⠀⠀⠀⡌⠒⠒⠒⠒⠛⠓⠒⠂⠀⠀⠴⠶⠶⠒⠒⠠⠶⠶⠶⣦⠤⢤⠀⠀⠀⠀⠀⠀⠀⠠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⡠⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⢠⣤⡄⠀⢀⡀⠀⠠⢈⠁⠀⠐⠂⠂⠀⠤⠀⠀⠐⡀⠀⠀⠀⠀⢀⡇
⠀⠀⢋⠁⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⡀⠀⠀⠀⠀⠋⠈⠀⠀⠀⠀⠐⡇
⠀⠀⠈⢠⣄⣀⣀⣀⡀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠠⠄⠒⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠘⠋⠀⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣶⣿⣇⣤
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠐⠂⠈⠁⠙⠟⠿⠿⠀⠀⠘
⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⣄⣤⣀⣀⡀⠀⠀⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣄⣻⣳⠀⠀⠀⠀⠀⠀⠀⠚⠉⡹⢻⣿⣧⣿⣿⣷⣦⠼⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⢀⣨⣠⣾⣿⣿⣿⣫⠔⠛⠿⠆⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢀⣴⣶⣶⣷⣄⢾⣿⣿⣿⣿⣿⣿⣷⡀⠄⠀⠀⠀⠁⠀⠈⠛⠻⣿⡿⠋⠀⠀⠀⠀⣤⣄⣄⣀⠀⢁
⠀⠀⢸⡳⣿⣟⢻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠙⠻⠾⣽⣛⣻⠿⣿⠷⢿⣿⣿⣿⣿⣿⣧⣶⡦⡀⠀⠀⠀⠈⠉⠁⠀⠀⣀⣤⣴⣾⣟⣻⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠷⠿⠿⠥⠤⢼⣭⣯⣷⣭⣶⠤⠀⠴⠷⠾⠿⠟⠛⠛⠉⠉⠉
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⣿⣻⣟⣛⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡏⠰⠅⡆⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣛⡛⠢⢍⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢘⠗⣸⢀⠀⠣⢠⢠⢸⡀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠻⠦⡉⠁⠀⠀⠈⠀⡊⡈⡇⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣮⠑⡄⢀⠀⠀⠀⠀⠀⠐⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢾⠀⠁⠒⡡⠂⠀⠀⠀⠀⠀⢀⠁⣁⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⣢⡀⠀⣿⣻⢰⠍⡦⠂⠀⠀⠀⣀⣴⣶⣾⠿⠛⠃⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢠⡿⡄⣶⢾⣿⠹⡄⠘⣾⣆⠈⢁⣠⠴⠚⣽⡿⠋⠀⠀⠀⠀⢀⣞⡟⢉⡽⢧⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠽⠓⣺⣦⣧⡿⣿⡀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣭⠾⣥⠤⢚⣷⡀
⠀⠀⠀⠀⠀⢀⣿⣷⠸⣿⠿⢷⠘⣄⣱⢳⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⣿⢞⡽⡖⢉⢞⣷⡀
⠀⠀⠀⠀⠀⠸⣿⡟⢐⣾⣯⡘⠣⣻⣿⣏⡆⠘⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⣀⣯⢟⡿⣯⠔⢻⡄⢊⡿⣧
⠀⠀⠀⠀⠀⠀⠙⢧⣿⣿⠛⠀⠀⢹⣟⢻⣧⠀⠀⠀⠈⠀⠀⠀⢺⠀⠀⠘⢫⣹⡲⣧⡷⣂⡠⢷⣊⠀⣻⣀
⠀⠀⣠⣶⢿⣿⠛⣷⡺⣿⣦⣠⢄⡀⠈⡈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢋⣾⣟⣥⡤⠼⢃⠀⠁⠸⠧⡄
⠀⢸⣲⠏⣨⣍⢡⠟⠛⢙⡺⣽⣿⢽⣦⣻⣿⣴⡆⠀⠀⠀⠀⠀⠀⠀⠠⠀⠏⠆⠈⠘⢻⣧⡴⠚⠑⢻⣅⡠⠴⠿⡀
⠀⠸⡟⣷⡰⢆⣜⣛⠷⣶⣖⣿⣿⠿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣀⣀⠀⠙⣯⡗⣦⠁⠀⢹⡆⠀⠐⠛⢀⣀⣀
⠀⠀⠙⠺⠷⠾⠿⠛⠋⠉⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣶⠶⠤⢿⣽⣧⠤⠤⣿⡁⢸⣻⡏⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠉⠛⠲⢧⣸⠯⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⣟⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⣾⣿⡿⠿⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠇⠀⠀⠀⢀⣠⣴⣶⣶⣿⣯⢉⣾⣿⣿⣿⣿⠶⠌⣤⠁⠴⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⣶⠏⠈⠙⣻⣿⢶⡷⠹⣿⠿⠻⠛⠉⠀⢰⡤⣴⠀⣤⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⣾⣷⣖⠆⠀⠔⠋⠄⠘⠛⠄⠈⠀⠀⠀⠀⠀⠀⠰⠿⣶⣄⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡍⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⣠⣼⡟⠙⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢹⢿⠀⢀⣠⠀⠀⡀⠠⠀⡀⢰⣄⠀⠀⣤⣄⠀⢿⣿⣿⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳⠾⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣷⠀⠙⠋⠀⠈⠉⠀⠀⠈⠹⠿⠿⡄⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⢀⣤⣠⣴⡾⣷⣦⠀⠀⣿⠀⣰⣶⡶⣶⣄⡀⠀⠀⠀⠀⠐⡇⠀⢈⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢀⣠⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣼⣿⣷⣿⣿⡥⢉⣤⠀⠀⣿⠇⣠⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⢷⠀⠸⣿⣿⣿⣿⣿⣿⣿⠃⠀⡀⠀⢸⣷⢼⣷⣿⣾⣿⣿⠄⣤⡟⠸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠻⠿⣿⣿⣿⠏⠀⣸⣿⡄⠀⢳⣿⣩⣿⠿⠛⠁⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠇⠁⠀⠀⡄⠀⠀⠈⠛⠀⠘⣿⣿⡟⡆⠘⠋⠁⠀⢀⡄⠄⠐⢿⣶⣶⢲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣶⠠⠀⠀⠀⠀⠀⢠⠀⢸⡐⣿⣿⡿⣸⠀⢠⡄⢂⠠⠤⠂⡌⢸⣿⣿⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣼⢷⣶⣥⣈⣉⠀⠃⠀⠀⠛⠋⡈⠛⠋⠀⠈⠛⢈⣋⣠⣵⣶⣿⡿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡿⠆⡛⠘⣏⡛⣽⡇⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣝⢷⣻⣿⡗⢿⣟⣹⡿⡀⠻⠟⠓⠚⠆⠒⠉⠛⠳⠒⠞⠻⠿⣿⠃⠀⠿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣟⢴⣿⡶⠀⠘⣡⠀⠀⠃⠀⠀⠀⠤⠤⡧⠤⢤⠓⠗⣺⡇⠂⢰⣄⣄⣉⣀⠉⠙⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡋⠀⠉⢁⣀⠈⠛⠀⠀⣀⠁⠒⠲⢶⢷⣶⢷⡾⡶⠟⢫⡀⠂⣸⣿⣿⣿⣿⣿⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠉⠁⠀⠋⠠⠸⡄⠀⠀⠀⠐⠗⠀⣠⣦⡠⣜⣷⡌⠁⠀⣰⣿⣿⣿⣿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢃⠴⠄⣀⣶⣄⠀⠀⠀⢼⣿⡿⠿⠀⠀⠀⣀⣴⡿⣿⡿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠉⠈⠙⠷⣶⣤⣿⣷⣣⣴⣴⣶⣿⣿⣄⠙⢿⣾⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⢠⠀⣿⣛⠘⠻⣻⣾⡿⣿⢿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⢀⡾⢸⣿⠇⠀⠀⠈⢻⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⣤⣠⣿⣄⠀⠀⢠⠒⠛⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣁⣈⡃⡰⠈⠒⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠉⠀⠀⣀⣤⡚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⣀⡤⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⣀⣀⣏⣁⡀⠀⠀⠀⠀⠀⢸⠻⡇⠀⠀⠀⠀⠀⢀⣠⠤⣤⣿⣯⣕⢦
⠀⠀⠀⡜⠁⠈⠀⠁⠈⠀⢹⡄⠀⠀⠀⣴⠓⠒⠒⠚⢳⠀⠀⠀⠀⠀⡾⠤⢧⠀⠀⠀⠀⡰⢫⠖⠋⡇⣯⣶⠾⡛⠁
⠀⠀⠀⣿⠭⢭⡩⠭⣩⠭⢽⡇⠀⠀⠀⠈⡏⠉⠉⠉⡏⠀⠀⠀⠀⢸⠓⢦⢸⡆⠀⠀⢰⡇⡟⢯⠗⣇⠭⡒⢻⢹
⠀⠀⠀⢹⡒⣖⠚⠛⢒⡶⣺⠁⠀⠀⠀⠀⣧⠀⠀⢸⠃⠀⠀⠀⠀⠘⡗⠋⢸⠁⠀⠀⠈⣇⢧⡺⡧⣀⡛⢋⠞⡼
⠀⠀⠀⠀⠉⠉⠑⠶⠋⠉⠁⠀⠀⠀⠀⠀⢸⣀⣀⣼⠀⠀⠀⠀⠀⢰⣃⣀⣸⡄⠀⠀⠀⠈⠳⢝⣚⣓⣛⡥⠞
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡀
⠀⠀⠀⣤⢻⠹⡇⡟⡽⣦⡀⠀⠀⠀⠀⠀⠀⣯⣯⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠦⢤⡀⠀⠀⠀⠀⠀⢀⡴⠫⠙⣝⣧
⠀⠀⠀⣏⠉⠛⠛⠛⠉⢹⠇⠀⠀⠀⠀⢰⠒⠒⠒⠒⣦⢤⠀⠀⠀⢾⣁⣀⣀⣀⣀⣈⡳⠀⠀⠀⠀⡞⠐⠀⠀⢂⡟
⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢸⡀⠀⠀⢀⡧⠞⠀⠀⠀⠈⢧⠸⡇⢀⡇⣸⠁⠀⠀⢀⡴⢳⣬⡤⠖⠉
⠀⠀⠀⠘⣇⣀⣀⣀⣠⡇⠀⠀⠀⠸⣏⣉⣉⣉⣉⣉⣉⡹⠃⠀⠀⠀⠸⣄⣧⣸⣠⠇⠀⠀⠘⢯⡵⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⣞⣙⣦
⠀⠀⠀⠀⣀⠤⠔⠛⢆⠀⠀⠀⠀⢀⣠⠤⣄⡤⢤⣠⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⢠⣏⢳⡄⠀⠀⣸⢥⣤⣿⣤⣷
⠀⠀⠀⢰⠛⠒⠒⠒⠚⢣⠀⠀⠀⣞⣀⣀⣈⣀⣀⣁⣀⣀⣹⡀⠀⠀⠀⠀⢀⡴⢇⡈⠉⡧⠀⠀⠈⣏⣩⠽⢛⡏
⠀⠀⠀⢸⡉⢻⠉⣻⠉⡟⠀⠀⠘⣿⡳⢾⣷⠞⠳⣞⡷⢞⣿⡇⠀⠀⢀⡤⠾⣄⠀⠙⢲⡇⠀⠀⠀⢹⡴⢚⡽
⠀⠀⠀⠀⣧⢸⡀⡟⢰⠃⠀⠀⠀⠓⠻⠯⠭⠭⠭⠭⠽⠿⠚⠀⠀⠸⣍⣳⡀⢈⣧⡤⠚⠀⠀⠀⠀⠀⢿⢩⠇
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡤⡶⣤⣄⠀⠀⠀⢀⡤⣄⠀⣠⢄⠀⠀⠀⠀⣤⣤⣤⡄⡸⢧⡀⠀⠀⠀⠀⠀⠀⢠⢾⢶⣄⡀
⠀⠀⠀⠀⠀⣠⠞⠙⡶⢳⣶⣳⠄⠀⢠⠎⢠⡈⢾⠁⣌⢳⡀⠀⠀⢸⠁⢹⢘⡗⢺⡃⠀⠀⠀⠀⢀⡴⣳⣫⠏⠀⢹⡆
⠀⠀⠀⣠⠞⠁⠀⢠⠏⢙⡷⠃⠀⠀⢸⡀⣞⠀⣸⢰⠃⢠⠇⠀⠀⡼⠀⠸⡏⠀⠀⢹⠀⠀⢠⣞⣽⣺⠖⠁⠀⢀⡞
⠀⠀⠐⢧⡀⢀⡴⢋⡴⠋⠀⠀⠀⠀⠀⠳⣄⡔⠙⢦⡰⠋⠀⠀⠀⡇⠀⠀⡇⠀⠀⢸⠀⠀⠘⢷⡋⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠙⢯⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠧⠤⠤⠼⠀⠀⠀⠀⠑⠒⠚⠁

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

⠀⠀⠀⠀⠀⠀⣠⣄⣤⣀⣀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡟⠀⠀⠀⠀⠀⢼⢑⡢⡰⡄⠀⠀⠀⠀⢰⠿⡎⠋⡾⣷⠀⠀⠀⠀⠀⢛⡟⢻⠛
⠀⠀⠀⠀⠀⠀⠸⠿⣛⠿⠇⠀⠀⠀⠀⠀⣮⣿⣿⣷⡆⠀⠀⠀⠀⠀⣿⠙⠸⢿⡏⠀⠀⠀⠀⠀⣻⣏⣹⣋⠄
⠀⠀⠀⠀⠀⠀⠰⡿⠂⡾⠇⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠘⠃⠄⡄⡄⡿⠀⠀⠀⠀⠰⣾⢍⡸⣷⡇
⠀⠀⠀⠀⠀⠀⠀⣥⣶⣤⠅⠀⠀⠀⠀⠀⠈⠥⠁⠝⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠛⠈⠑⠛

⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⣀⢠⣄⠀⠀⠀⠀⢀⣤⠀⡀⠀⠀⢀⣠⣤⡄⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀
⠀⠀⠀⠀⠀⠀⢀⣷⣾⣴⡀⠀⠀⢹⣿⣿⣦⣴⢴⣦⣾⣿⣿⡅⠀⠀⢸⢻⡿⢅⠀⠀⠀⠀⠀⠀⣞⡙⢋⣷
⠀⠀⠀⠀⠀⠀⣼⠿⠈⢿⣦⠀⠀⠀⠀⠙⣼⠿⠘⢿⡞⠀⠀⠀⠀⠀⡼⢾⣟⠻⡄⠀⠀⠀⠀⠀⡿⠥⡬⢿
⠀⠀⠀⠀⠀⠀⡥⢼⣤⡵⠾⠀⠀⠀⠀⠀⠸⣧⣬⣽⠁⠀⠀⠀⠀⠀⢰⣟⢛⡷⠀⠀⠀⠀⠀⠀⣿⡓⢓⣻
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠘⠛⠑⠋⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠰⣦⣿⣠⡆⠀⠀⠀⠀⠀⢠⣴⣢⣤⠀⠀⠀⠀⠀⠀⠠⣄⣆⡤⠀⠀⠀⠀⠀⠀⣄⣠⣦⣠
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠛⠁⠀⠀⠀⠀⡿⣿⢹⡿⡆⠀⠀⠀⠀⠀⢨⣼⡤⣭⠀⠀⠀⠀⠀⠀⣉⡙⢟⣉
⠀⠀⠀⠀⠀⠀⠀⢉⣭⡍⠀⠀⠀⠀⠀⠀⣟⣛⢘⣛⣇⠀⠀⠀⠀⠀⢸⣶⠱⡘⠀⠀⠀⠀⠀⠀⢿⠃⠸⣿
⠀⠀⠀⠀⠀⠀⣴⠁⠉⠨⢽⠀⠀⠀⠀⠸⣆⡋⡇⣓⡼⠀⠀⠀⠀⠀⢸⡧⠤⣿⠀⠀⠀⠀⠀⠀⢣⣀⣀⡼
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠤⠶⠒⠊⠉⠉⠀⠀⠀⠀⠈⠉⠉⠐⠒⠦⢤⡀⠀⠀⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⠔⠋⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⠀⠀⠀⠒⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠙⠃⠐⠀⠀⠐⠄⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠰⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠂⠀⠀⠀⠀⢀⠀⡀⢀⡈⠀⠀⢀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⡰⠊⢁⡈⠙⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣤⣤⣤⣤⣴⠶⠦⠶⠶⠶⣶⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⢁⠔⡚⠛⡳⣦⡓⠺⠃⠁⣿⢈⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⠛⠛⠛⠛⠒⢦⣤⢤⣀⡤⠤⢤⣀⣠⠴⠋⢉⣩⠟⢿⣶⡄⠀⠀⡆⣠⠆⠃⡖⠛⠉⠄⠈⡇⢉⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠸⢿⣧⡀⠀⠀⠀⠀⠀⠀⢳⣤⡄⠛⣦⢀⡤⠤⠖⠚⠉⠀⢀⣼⡿⠛⠀⠀⠀⡸⠃⠆⠳⡤⢶⡎⡰⣧⡀
⠀⠀⠀⠀⠀⣀⣴⣾⣄⠙⠿⣦⣄⠀⣞⠛⠛⠛⠁⠉⠙⠷⠛⢧⡀⠀⢀⣠⣴⠟⠋⡠⠀⣀⣀⣀⠀⠀⠀⠚⢀⡤⠛⢼⡌⣷⠠
⠀⠀⠀⠀⢸⣿⣏⠀⠀⠑⠀⡈⠙⠻⢿⣦⣤⣀⣀⣀⣀⣠⣤⣴⠾⠟⠛⠉⣀⢴⠀⡰⠋⠐⡔⢈⢳⡄⠀⣀⡨⠓⣤⠺⢃⠏
⠀⠀⠀⠀⠀⡘⠿⣷⣄⠀⠀⡤⠶⠦⠄⠀⠀⠉⠉⠉⠉⠁⠀⠀⢀⣴⣶⠟⢁⠌⠀⡃⢾⡇⠀⣿⠂⡷⠋⢁⡀⠀⢤⡀⠁
⠀⠀⠀⠀⠀⠈⠠⠈⠛⠷⣦⣷⣀⡀⠀⠀⠀⠀⠁⢀⣈⣷⣴⠾⠛⠋⡀⠔⠀⠀⠀⠰⢴⣤⡧⣬⡜⠁⢾⡁⠈⣿⢸⡇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠿⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⣹⠟⣧⢈⠙⠃⢩⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠀⠀⠀⠀⠒⠂⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠐⢻⣽⠇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠁⠉⠠⠘⡡⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡨⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢉⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡒⢒⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⡇⢸⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⢀⡔⠊⡽⠒⠊⠉⠉⠉⠉⠈⢇⡸⠁⠈⠉⠉⠉⠙⠓⢪⡉⠲⡄
⠀⠀⠀⠈⣗⡲⠭⠶⠶⣦⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⡶⠶⠭⢔⣺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣩⠉⠒⠦⡀
⠀⠀⠀⠀⢇⠈⠉⠐⠒⠒⠒⠀⠠⠤⠤⠤⠤⠤⠀⠒⠒⠒⠒⠉⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠦⠀⠈⠣⡀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁⢠⠀⠀⠀⠰⠆⠘⡆
⠀⠀⠀⠀⠸⡆⠀⠀⠀⢀⡾⢷⡀⠀⠀⠀⠀⢀⣼⢿⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠴⠀⢀⠀⠀⠖⠀⠀⠀⢸⣄
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠛⠁⠈⠛⣠⣤⣤⣄⠘⠁⠀⠙⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢦⣀⠀⠀⠈⠁⣀⣀⡀⠈⠁⣸⡀⡷⣄
⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠋⢇⠐⠃⠀⠉⠙⠏⠁⠀⠤⠈⠉⠉⣀⠔⣁⠈⢣
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠹⣿⣠⠞⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡉⠒⠦⠤⠤⠤⠤⠤⠴⠒⢒⠉⠀⣀⠀⠀⢨⠂
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡔⠓⠒⢄⠀⣀⣀⣀⣀⣈⣦⣀⠀⠀⠈⠁⣀⣀⣀⠓⠀⠀⠈⠀⢀⣀⡠⢴⠋
⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣉⣥⡴⠞⠉⠑⢎⣉⣉⡛⣒⡲⠤⢉⠳⣮⣍⠉⣁⠀⠀⠀⠈⠉⠉⠉⡉⠁⠀⠀⡎
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣵⠞⠋⣀⡴⠶⠚⠛⠛⠛⠛⠛⠷⢦⡭⣙⠛⠚⢌⡖⠂⠙⠂⠀⠀⠀⠘⠋⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⠁⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⡳⣄⠈⣇⠀⠀⠀⢄⠀⡄⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣨⣾⠃⠀⠀⠀⠐⠲⠄⠀⠀⠀⠶⠢⠀⠀⠀⠈⠎⢶⡝⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠘⠤⣀⣀⠀⠀⠀⠀⠀⢸⣹⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠹⣧⣀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣀⣴⡴⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠓⠲⠶⠶⠶⠶⠶⠶⠖⠚⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠐⠂⠉⠉⠁⠀⠀⠀⠐⠒⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⣀⣀⣀⡠⠶⠾⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣥⣤⣤⣤⣴⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠁⠁⠍⠻⡇⠀⠀⠀⠀⠀⢀⠤⢤⣀⡀⠀⠉⠹⢦⡀⠀⠀⠈⠂⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⣀⠀⠀⠀⠀⠉⠳⢦⣄⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡇⠀⡀⠐⠉⠛⠛⠳⠆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⡸⠁⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣠⠶⠛⠁⠀⠀⠹⢦⣀⣀⡀⠀⠀⠀⢀⣀⣀⣠⣤⣴⠶⠾⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⢀⣤⠄⠀⠠⠴⣤
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠠⠟
⠀⠀⠀⠀⠀⠸⠿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠶⠋⢀⡀⠀⠀⠀⢩⡿
⠀⠀⢠⣀⠀⠀⠀⠀⠉⠛⠲⢿⣆⣻⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠰⠤⠀⠀⠈⠁⠀⣀⠼⠀⠀⠀⡞⠀⠀⢀⣿⠀⠀⠀⠀⣸⡅
⠀⠀⠼⢿⣗⡦⣄⣀⣀⡀⠀⣤⣀⣠⣭⣥⡿⠋⠁⠀⠀⠀⠀⠀⠤⢄⡀⠀⠉⠀⠀⠀⣀⣠⠴⠒⠉⠁⠀⢠⠾⠇⢣⣤⢀⠔⠀⠀⠀⠀⢀⡿
⠀⠰⣤⣄⣀⠀⠉⠈⠛⠃⢀⣿⠀⠀⠘⠁⠀⠀⠀⠀⠐⠒⠲⠤⠀⠀⠀⠀⣀⡀⠐⠊⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠰⠁⠿⠀⠀⠀⢀⣠⡏
⠀⠀⠈⠙⠛⠛⠤⠶⣶⡄⠸⠃⠀⠀⠀⢀⣀⡀⠉⠉⠀⠀⠀⢀⡤⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣷⢀⢀⡴⠚⠀⠀⠀⠀⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⢞⡘⠇⠀⠀⠀⢀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠤⠀⠐⠒⢤⣀⡀⠀⠀⠀⠀⠀⠈⢂⣾⡿⠉⠁⠀⠀⢛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣚⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡀⠀⠀⠀⠈⠹⢿⣤⣤⡶⠶⠋
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⣿⣿⣶⣦⣴⡂⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣆⠀⠀⠀⠙⠻⢿⣾⣽⣛⠳⢦⣄⣀⠠⠔⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⣠⠴⠒⠲⠒⠦⣄
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠉⠛⠻⡷⢶⣏⠉⢠⣄⠴⠒⠛⠁⠀⠀⠀⡠⠂⠂⢬⣀⠀⠀⠀⠀⢈⡶⣄
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠴⠛⠋⣿⠿⣶⡉⠀⠘⣇
⠀⠀⠀⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⡄⠀⠀⠀⠙⣾⠟⠀⠀⢠⡏
⠀⠀⠀⠀⠉⠻⠿⣶⣶⣀⣐⠲⣶⣶⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠁⠠⢄⣀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠹⣇⠀⠀⠀⠀⠘⢤⣠⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠷⠶⠿⠓⠂

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⠄⠀⠀⠰⠄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠐⠀⠒⠂⠉⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⠼⠄⣀⡀⠀⠀⣤⣀⣀⣀⣀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁⠀⠀⠄⠀⡄⠀⡠⠈⠑⢢⡘⠿⠿⡿⠟⠛⠿⠖
⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠠⠀⠒⢘⠄⠀⠀⠤⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴
⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠁⣀⡰⠉⠢⡀⠀⠀⠀⠀⠀⠀⢎⢹⠄⣀⠤⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⡜⠁⠈⠀⠄⠀⠀⠀⠠⠤⠒⠉⠀⠀⠀⠂⠀⣎⠙⠼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁
⠀⠀⠀⢰⠁⠀⠀⠀⠀⡀⠀⠀⡀⠀⡀⠀⠈⠀⡔⠐⢦⢈⣧⢾⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁
⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢀⠜⠀⢀⡤⠋⠁⠀⠈⠙⠒⠒⠒⠒⠚⠉⠉
⠀⠀⠀⠀⠉⠻⣅⠉⠂⠤⠒⠁⠀⠀⠉⣉⠥⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠀⠒⠒⠈⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿