Coastline Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⠤⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⠇⣀⣠⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⢀⠰⠂⠀⠀⠀⠀⣀⡏⠀⠁⠀⠀⠙⠀⠄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡐⠻
⠀⠠⠦⠀⠀⡀⠀⠁⠀⠻⠃⠀⠀⠀⠆⠀⠀⠈⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠧⠀⠀⠀⢀⠤
⠀⠐⠂⠀⠀⢠⡀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠔⠂⠀⢀⠁⠀⠀⠀⡤⢃⡀⠂
⠀⠀⣧⠀⠒⡌⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡋⠁⠀⠸⠀⠀⠀⡜⢙
⠀⠀⡃⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡜
⠀⠀⢰⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⢰⠀⢠⣁⣀⣠⣤⡀
⢀⣀⢘⡆⣀⣀⢰⡿⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠂⠘⠘⠋⠉⣉⠉⠉⠁
⢀⢞⣄⣿⣫⢉⢸⣇⠀⠀⠀⢀⡀⠈⠉⠉⠀⠀⠀⠀⠠⠄⢈⣠⠀⠀⠀⠀⠀⠐⡂
⡏⣾⣿⣿⣿⣾⣿⡏⢸⡦⣀⡀⠀⠐⠀⠐⠸⠶⠶⠤⣤⣼⣿⣿⣶⣦⡐⠾⠶⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣧⣯⣥⣼⣿⣿⣿⠇⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠛⠉⠛⠋⠀⢠⣯⠁⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣐
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠐
⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀
⠀⠀⠀⠹⣝⠳⢰⣄⠀⠀⢀⠚⠉⣀⠐⠂
⠀⠀⠀⠀⠈⠦⣄⠈⢳⡀⢀⣀⠉
⠀⠀⠀⠀⠐⠂⠛⠢⣀⢠⡎⠀⠀⠄⠄⠓⠦⣤⡀
⠀⠄⠒⠛⠤⠶⠒⣲⣽⣿⣃⣈⡈⠒⠦⠀⠀⠈⠁
⠀⠀⠀⠀⢠⠎⠀⢿⣿⡍⢻⣿⣿⠀⠀⠀⠁⠄
⠀⠀⠀⠀⡄⢴⡟⠁⠁⡜⠀⠹⣿⡄⠀⠉⠢⣰
⠀⠀⠀⢀⠏⡟⠁⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⢐⠀⠀⡁
⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢛⡿⠿⣿⠂⢰⣤⡆⠀⠀⠀⠀⠀⢐⠀⠡⠄⠁⠀⠀⣰⣋⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⣬⠁⠸⠀⠀⠹⠛⠃⣤⣐⡶⢎⣯⣿⣮⣻⣽⠃⠀⣾⣱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂⠛⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣀⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⡀⢀⠀⠀⠀⣀⡀⢀⣀⠀⣀⣀⡀⢀⠀⠀⠀⢀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠶⠶⣿⣿⣶⡬⡽⠿⠿⢿⣛⡛⣻⣾⣿⣿⠶⢶⣶⣶⣆⣬⣍⣥⣤⣭⣭⣭⣥⢭⣭⣽⣿⣿⣷⣦⡚⢫⣭⣭⣿⣭⣿⣭⣿⣿⣷⣾⣿⣿⣿⣯⣭
⠠⠭⢷⣶⣶⣾⡿⠿⢿⣻⣿⣿⣿⢿⣿⣿⢓⣻⣿⣿⣟⣛⣫⣭⣿⢿⣿⡾⠿⣿⣿⣾⣽⣿⣿⢿⡿⣿⡿⠿⠛⠛⣩⣿⡿⢟⠻⠟⠛⠋⠛⢩⠶
⣒⣀⣉⠿⢭⡍⠥⠬⠯⠍⠛⠻⠿⠏⣉⢙⣿⣿⣯⠿⠷⢿⠗⠒⠊⢉⠤⡭⠛⠋⠈⠉⠙⠛⠷⠆⢀⠉⠉⠀⠘⠈⣭⠈⠉⠁⠀⠀⠀⠙
⣤⡀⠁⠀⠀⠀⠈⠉⠉⠉⢓⣂⣀⡀⠘⠛⠛⠓⠒⠀⣀⡀⠀⠐⠂⠀⠀⠀⠒⠒⠒⠀⡀⠀⠀⠈⠉⠁⠤⠠⠠⢀⣠⠤⠤⠀⠠⠤
⠉⠁⠀⠀⠀⠀⠐⠂⠤⠀⠉⠉⠉⠙⠃⠀⠀⠀⢀⡤⣉⢁⠀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠐⠲⠟⠿⠛⠋⠀⠠⠁⢀⣠⡶⠟⠉
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⣷⣤⣤⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣿⣿⣿⣿⣶⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠀⣠⣴⣶
⠉⠉⠁⠀⢸⣿⣷⠄⠀⠀⠐⠀⡀⠀⠀⣀⣄⠀⠈⠛⠲⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⡀⠀⠀⠀⠺⠶⠀⢀⣄⣀⠀⠀⠈⣻⡿⠟
⠰⢷⡦⠄⠀⠶⠄⠀⠀⢤⣾⣦⣀⡀⠸⠿⠟⠀⠈⠀⠀⢀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣽⣄⠀⠈⠁⠀⠀⠀⠀⠉⠙⠛⠉⠭⢀⣤⣀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠺⠷⠦⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠠⠀⠀⠂
⠀⠀⠀⠀⠬⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⢀⠂⠀⢀⣶⣾⡏⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡀⠈⠂⢤⣀⣀
⠀⠀⠀⠁⠀⠀⠈⠈⠁⠆⠀⠀⠀⡀⠀⠠⠀⠻⠟⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡉⡁⠐⣧⠄⠁⢐⡤⠂⠈
⠀⠀⠀⠀⠀⠘⠘⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠟⠀⠀⠔⠬⠉⣹⠒⢁⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠴⠂⣠⣄⠉⠂⠀⠀⠀⠈⠈⢟⠢⠄
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣄⣶⣶⡀⠀⠀⠀⠀⠀⠥⠈
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⡁⠈⠉⠛⠁
⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⢰⣀⡐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠑⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠉⠉⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠨⠉⠁⠀⠁
⠀⢀⠃⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠁⠀⠤⠀⠀⠀⠀⠠⠄⠁
⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠠⠗⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀
⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠤⣄
⠀⠐⠀⠀⠀⠀⢀⣀⠀⢀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠒
⠴⠶⠤⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⢀⠀⠀⠀⠀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠒
⣤⣤⣤⣤⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣿⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣛⣛⣛⣂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡷⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣤⣭⣭⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢘⡻⢿⣿⡿⢛⣛⡛⢿⣿⣿⠟⣛⣿⣿⣿⢇⣿⣿⣿⣿⣿⠿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⣾⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⠏⣼⣿⣿⣿⣿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⠿⠻⢿⣿⣿⠿⢻⣿⣿⣿⢋⣼⣿⣿⣿⣿⣿⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⣿⣿⣷⣶⣶⣿⣿⡿⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣭⣭⣭⣭⡙⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⢛⣩⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢋⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⠀⢀⠤⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠢⠤⠤⠄⠀⠄⣀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠈⠀⠐⠢⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄
⠀⠀⠀⠀⠠⢄⣒⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⢄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠐⠠⠀⠀⠀⠤⢀⠤⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣽⣯⣮⣯⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣯⣿⣿⣿⣿⣿⣯

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⠂⠤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢮⣀⣀⡉⠁⢠⡀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡚⠛⠀⠈⢉⣽⢿⣿⣤⣭⠿⠗⠚⠁
⠀⠀⠀⠀⠀⣀⠀⠈⠛⢟⠛⠿⠻⠃⠈⠀⡰⣦⣍⣍⣁⣢
⠀⠀⢠⡿⢾⣻⡿⠒⣺⣃⣀⣀⣢⠀⣀⠀⠸⢯⣤⣤⣤⣈⠆
⠀⠀⠈⠙⠉⠉⠁⠀⠀⠀⢠⣼⠃⠰⣤⣄⣴⣤⠀⠤⡆⠚⠢⣄
⠀⠀⠀⠀⢤⣀⡈⠙⢦⣄⠈⠁⠘⠛⠛⠋⠈⣿⠿⣦⣿⣿⣦⠤⠃
⠀⠀⠀⠳⠶⠞⠿⠿⣧⢼⠆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⢀⢠⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢀⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡉⣀⣴⡿⠋⠉⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⠀⠀⠀⠀⠀⠋⢀⣾⠁⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠰⢛⡷⢁⣤⣶⡶⠀⠀⣴⡽⢀⣷⠊⢤
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠐⠄⠈⢉⠐⠒⢄⡀⢀⣰⡃⣤⣰⣈⣵⠾⠋⢠⠞⠁⠋⣠⠀⢀⣸⣷⠞⢻⣧
⠀⠀⠀⠀⠀⠀⠀⣠⢟⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠟⣡⣼⠾⠃⡤⠀⢸⣿⡆⠛⠉⠁⠰⣦⣿⣦
⠀⠀⠒⠒⠚⠛⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠐⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠀⠃⠀⠀⠀⠀⠐⢶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⢠⠀⠀⣀⣦
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣶⣄⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠻⢿⣿⣿⣿⣮⡷⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠄⠀⠀⠀⠉⠉⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠲⡄⢠⡔⢈⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠄⠀⠀⢀⠆⠀⠀⠀⠀⢀⣀⡤⠐⢳⡆⡀⢁⣄⡀⡀⠂⠠⠀⠀⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠄⡀⠈⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠁⠃⠘⠀⠀⠀⠀⠂⠀⡆⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⢤⠀⠀⠄⠐⠐⢄⡀⡩⠀⠀⠀⠠⡄⠀⡰⡆⢂⠊⠀⢲⣿⡂⡈⢻⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⢃⠀⠀⠀⠠⢀⡌⢻⡇⠶⠐⠆⠀⠤⠬⢼⢬⣥⠄⠀⠈⠈⠉⠁⠁⠘⣳⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⠋⠶⠀⠀⠁⠀⠀⢹⠢⠄⣀⣦⡖⠀⠀⠈⠉⠀⠘⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠸⠀⠀⠘⢹⠛
⠀⠀⠀⠀⠀⣠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠈⠀⢀
⢠⡄⠀⢀⡾⢛⡁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡄⠀⠀⣀⣼⠀⢀⢀⣧⡀⡀⠀⠠⣀⣶⡀⢀
⠀⠀⠀⠈⠀⠘⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⡇⠰⡿⡇⠀⣌⣙⡟⠓⠛⠛⢋⣩⡁⣰⣀⡯⣟⣻⣿
⠀⠀⠀⠀⠀⢀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣈⠉⠀⠀⠀⠀⢀⠉⠀⠋⠉⠥⠐⠂⠀⢈⣙⠃⠁⠐⠦⠍⠉⣋
⠀⠀⠀⠀⠠⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠁⠀⠀⠉⠙⠂⠒⠲⠌

⠀⠀⠀⠀⡀
⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒
⠄⠀⠀⠀⠐⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠄⠠⣠⠄

⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣀⡴⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡠⠂⠀⠄⠀⠺⠀⠀⠄⠀⠀⠀⠀⠀⠰⢀
⠀⠀⠀⢀⠐⠃⠀⠀⠈⠀⠀⠆⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠁
⠀⠀⢣⡌⠀⠀⠀⠀⠀⠀⢰⠀⠀⣀⠀⠀⣼⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡏⠀⠺⠟⠀⣴⣿⣿⠃⠀⠀⣤⣦
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢩⣁⡠⠀⢸⣏⠀⠀⠀⠀⠀⠠⢶⠀⠀⠀⠀⢤⡄
⠀⠀⠀⡧⠀⠀⠀⠐⠆⠚⠠⢀⠀⢻⠀⠛⣾⢿⣷⠦⣄⣀⠄⠀⠘⣳⣶⣶⠂⠀⠀⠀⠙⠟⠿⡟⠁⢀
⠀⠀⢰⠁⢣⠀⠀⢀⣴⠃⢀⠀⠀⠀⠀⠈⠀⠈⠀⢻⡿⠯⡖⠀⢘⠏⠈⠏⠁⠀⠀⠄⠀⢀⡄⠀⢰⣾⡦
⠀⢀⠘⠀⠘⠄⠀⠘⢙⡁⠈⠀⠀⠀⠀⠀⠀⠀⡄⠀⢰⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠋⡅⠀⢠⠀⠁
⠀⠀⠀⠈⠀⢣⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢘⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠂⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⡰⠇⠰⠚⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠐⠒⠒
⠀⠀⠀⠀⠀⠀⠇⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣶⣶⠶⢶⣶⣦⣤⣤⣤⣤⡤⣤⣤⣤⣤⣶⣶⠶⠋⠁
⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⡿⢿⢿⣿⠋⠈⠛⠝⠛⠉⢉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠐⢠⠔⠀⠀⠀⣤⣶⣿⣿⣿⠿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠆⠘⠀⠙⠓⠟⢉⣙⣛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠦⠤
⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠲⠤⠄⠠⠀⠀⠀⠀⠈⠓⠣⣖⡀
⠀⠀⠀⠦⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠐
⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠐⠚⠂⠐⠂⠀⠀⠀⠀⠀⠀⠉⠁⠂⠀⠀⠀⠈⠁⠀⠀⢀⣤⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣲⣦⣀⣀⣀⣀⣀⣀⣀⣀⣘⣃⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣠⣴⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⢲⠀⠃⢀⣿⡃⣿⠊⠁⡲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⠟⠀⡇⠀⠀⢸⠀⢸⢱⢸⢋⡶⢞⣀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠊⠀⠀⡇⠀⣷⢸⠀⠘⢊⡾⡩⢊⠥⢊⠝⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⠆⠱⡐⣄⢆⢁⠀⡯⡸⠀⣰⣏⡤⠭⠵⣊⣥⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡘⡘⡄⠱⡀⠙⢶⠀⠘⢭⡶⣋⣠⣒⣒⠬⣛⠒⠜⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠑⢌⠺⢦⠇⠀⠈⢏⣄⡾⠓⡓⠉⡉⠉⣁⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⢅⠢⢁⣆⠈⠫⢵⣠⣿⢒⣛⠚⠻⠐⠠⠬⠈⠤⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣕⡂⠬⣀⠉⣩⠓⣦⣟⣁⠉⠒⠓⡔⠮⠴⠦⢄⡒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠢⠭⠬⠋⠉⣩⡟⢀⠇⠑⡄⢖⠨⠰⠶⠦⠬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠂⠊⢡⡿⠇⢸⠀⡖⢌⠒⠭⠒⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⠃⠐⢈⠢⣡⠀⠑⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡜⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠙⠛⠶⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠛⠛⠛⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣿⠀⢿⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣿⠀⠘⣇⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⣿⠀⠀⢻⡀⢻⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣿⠀⠀⠸⡇⠈⢧⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣿⠀⠀⠀⣧⠀⠸⡆⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⢻⠈⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⢸⡇⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠈⡇⠀⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⣧⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡏⠀⠀⠀⣿⠀⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠇⠀⠀⠀⣿⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⡆⣿⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⡇⣿⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣀⣀⣠⠄⠀⢀⣀⣧⣿⣿⠴⠶⠶⢤⣤⣀⣀⠀⠀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣻⣯⠭⢷⣶⣾⣿⠯⠽⠶⠿⠚⠛⠛⠛⠉⠉⠉⣉⣹⣿⣿⣿⣿⡿⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡥⠶⠒⠋⠉⠁⠀⣀⣀⣀⣀⣤⣤⣤⣶⣶⣾⣿⣿⣿⠿⠟⠛⠉⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣶⣶⣶⣾⣿⣿⣿⡿⠿⠿⠿⠿⠛⠛⠛⠋⠉⠉⠉⠀⣀⣀⣀⣤⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠉⠉⠉⠉⠉⢀⣀⣀⣀⣀⣀⣤⣤⣤⠤⠴⠶⠶⠒⠚⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉


⣀⣀⣀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⡗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢸⡇⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠈⠃⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠀⠀⠀⠀⢀⡼⣃⣴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠇⢀⠀⠀⣠⣾⠿⠋⠁⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⢠⡟⣠⡾⠋⠁⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡾⠋⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⡟⣹⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣼⡟⢀⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢋⠜⡿⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⡼⠁⠈⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⡼⠁⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⡾⠁⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⢀⡾⠁⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⢀⡾⠁⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢟⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠛⢉⣴⡿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠁⠀⠀⠀⠉⠁⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢠⡀⣰⠏⠀⠀⠀⠀⠀⢀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⣀⣴⣋⣡⡤⠀⠀⠀⢀⣀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠘⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿
⠀⠀⠀⣠⣾⣿⣿⣿⡷⠶⠶⠚⠛⣹⠿⣷⣶⣶⣦⣤⣤⣤⣤⣴⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠁
⠀⠀⠚⠛⠋⠡⠤⠤⢤⣤⣤⣤⣾⣥⣤⣤⡤⠤⠤⢶⠒⠒⡆⢿⣋⠛⠒⠒⠒⠀⠀⠠⠤⠤⠤⢤⣤⣴⣶⣾⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⡹⠯⠛⠻⣷⣦⣤⣅⣈⣁⠘⠳⠦⠬⢥⣤⣀⣀⣀⣀⣀⣐⠺⠗⠀⣀⡵⠀⠀⡈⠉⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢰⡟⠋⡉⠙⠛⠿⣿⣟⡛⠛⠲⠶⢶⣶⣶⣶⣶⣶⣶⣖⣚⣋⣉⣠⣤⠞⠀⠤⢒⣋⣭⣤⠶⠶⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠈⠻⣿⣦⣄⡀⠋⢀⡀⠈⠹⣿⢿⣿⣿⣛⣛⣉⣁⣤⣴⠾⠛⠉⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠀⠀⠀⠀⠈⠙⠿⣯⣍⣉⣀⣠⣴⠟⠀⠉⠙⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⡸⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢦⠀⠀⢄⠀⠀⡇⠀⡇⠀⡇⠀⢰⠀⠀⡞⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠐⣆⠈⢆⠀⠸⡀⠀⡇⠀⡇⢀⡇⠀⡇⠀⡼⠀⢠⠂⠀⡠⠋
⠀⠀⠀⠀⠠⡀⠀⠀⣄⠈⢣⡀⠈⢆⠘⡆⠀⢇⠀⢧⠀⡇⢸⠀⢸⠀⣰⠁⣰⠃⢀⡜⠁⢀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠢⣄⠈⠣⡀⠑⣄⠈⢆⠘⡄⠸⡀⢸⠀⡇⣸⠀⡇⢠⠃⡰⠃⣠⠊⢀⠔⠁⢀⡴⠊
⠀⢀⡀⠀⠀⠤⡀⠈⠳⢄⠈⢢⡈⢢⡈⢧⠹⡀⢇⢸⠀⡇⡇⢸⢀⠏⡰⠁⡴⢁⡴⠋⣀⠔⠉⢀⡤⠂
⠀⠀⠉⠒⠤⣀⠈⠑⢤⡀⠑⢤⡙⢦⠑⣌⢧⠱⠘⠈⠀⠁⠃⠃⠞⡰⢡⠎⡠⠋⡠⠞⢁⡤⠚⠁⣀⠤⠒⠉
⠀⠀⠠⠤⣀⡀⠉⠒⠤⣈⠓⢤⡙⠦⡑⠈⣠⠔⠚⠉⠉⠉⠉⠑⠲⢄⡁⠊⡴⢊⡤⠚⣁⡤⠖⠋⢁⣀⡤⠄
⠤⢤⣀⣀⠀⠉⠙⠒⠤⢄⣙⠲⢬⠃⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠘⡡⠖⣋⡡⠤⠒⠊⢉⣀⣀⠤⠤
⠀⢀⣀⣀⣉⠉⠑⠒⠒⠤⠬⢍⠃⢰⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⢐⡩⠥⠴⠒⠚⠉⠉⢀⣀⣀⡀
⠀⠀⠀⠀⠉⠉⠉⢉⣉⣑⣒⣲⣤⣿⣤⣤⣤⣿⣿⣿⣾⣶⣷⣴⣶⣤⣶⣦⣼⣿⣒⣒⡚⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⠀⢰⣿⡄⠀⠀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⣿⣿⣶⠶⠿⠿⠿⠶⣾⣿⣿⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡾⠛⣁⣤⣴⣶⣶⣶⣦⣤⡉⠙⢶⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣠⡿⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⢿⣀⣀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣤⣶⣿⣿⣿⣤⣽⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⣀⣛⣛⣛⣂⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠶⠾⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣉⣉⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⠍⠉⠉⠉⠁




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣯⣭⣭⣽⣯⣬⣽⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣯⣿⣿⣭⣿⣯⣯⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢾⣟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢸⡏⢹⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⢸⡇⣰⠌⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⢸⡏⠁⠨⠶⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣾⠇⠀⠀⢸⡇⠀⠀⢐⣨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⢠⣿⠀⠀⠀⢸⣿⢶⣞⣯⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢸⣿⠀⠀⠀⢸⡇⢻⡅⠞⠃⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⢸⣿⡀⠀⠀⢸⡇⠀⢂⣠⣤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢸⣿⠁⠀⠀⢸⣗⡀⠈⣿⡯⠖⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⡇⠀⠀⠈⡶⣒⣈⠄⠀⠈⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠸⣟⢿⡄⠀⢸⣯⣀⣤⠀⠺⡿⠂⠁⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⠄⠀⠀⠀⠀⠀⠀⣿⢘⣷⡀⢸⣿⣫⣥⡀⠀⠸⠀⠀⠀⠀⠀⢀⣱⡀⢀⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠡⠀⠀⠀⠀⠀⠀⠠⠈⢿⣿⣷⣸⣿⣿⣿⡁⠀⠀⣡⣤⣶⠾⠛⠋⠙⠉⠉⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⣀⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⡷⠶⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠐⢒⣖⠠⣤⢠⣿⣿⣤⣶⠾⠿⠟⠛⠛⠛⠛⠉⠉⡉⠉⢻⣿⠀⠀⠀⠀⢀⡀⣀⣀⣀⡀⠀⠀⢀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⢿⠾⠶⠶⠶⠶⠶⠶⠷⠾⣿⠿⠿⠿⠿⠿⠶⠶⠷⠟⠿⠿⡟⠿⠷⠶⢶⡶⠶⣿⠷⣦⠔⠃
⠀⠀⠀⠀⠀⠠⠤⢤⣤⣵⣤⠈⠛⠛⠉⠉⠉⠉⠉⠙⠛⠛⠛⠋⠛⠒⠒⠀⠀⠙⠛⠋⠀⠀⠛⠛⠓⠈⠛⠛⠛⠾⠟⠛⢋⣷⣤⣤⣤⡤⢀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣼⣷⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⡤⠤⠤⠴⠶⡾⠿⠯⠥⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠲⠬⠉⠙⠛⠖⢛⣻⣿⣟⣙⠛⢻⣯⣭⣄⣉⡙⢛⣯⣭⣥⣭⣭⣥⠶⠾⠟⠛⠛⠛⠛⠒⠶⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢉⡙⣛⣉⣉⣉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣄⣘⡛⠻⠿⢿⣿⣛⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠉⢉⣉⠁⠀⠤⠖⠒⠒⠛⠒⠚⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢤⣤⣤⣶⣶⣶⣾⣻⣂⣀⣀⣀⠀⠄⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⢄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠛⠉⠉⠉⠉⠉⠉⠥⠤⣤⡀⠉⠑⠓⠲⣶⢶⣶⣶⡶⣶⣶⣶⣦⠐⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣴⠖⢛⣩⠤⠀⠀⠐⠀⠐⠛⠛⠛⠛⠛⠛⠉⠁⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠈⠉⣀⡀⢀⣀⠈⠃⣀⡉⠀⠀⠀⠀⠒⠒⠂⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⣤⠀⣤⣴⣦⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⢀⣤⢽⣷⣿⡾⢚⣉⣀⣀⠈⠈⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⢾⣶⣾⣿⣿⣿⣭⣏⡛⠉⠉⡙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡴⢛⡟⣡⡞⡟⠲⡅⠈⠻⢷⡆⢤⢤⠀⠀⠀⠀⠀⢠⣄⣀⣀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⣼⣿⡇⢱⣀⢻⣦⠀⠀⠙⠀⠡⠀⠀⢀⣤⢺⣷⣿⠍⠠⣍⠁⢀⣲⣿⣴⣮⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⡼⣼⠘⣿⣧⠈⡙⢿⡟⢷⡀⡀⠀⠀⠇⠀⢀⡾⠫⠺⡿⣷⣀⠘⢰⣿⢣⣾⢻⣅⠤⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⢹⡇⠀⠀⠐⢿⡁⠀⠁⠀⠀⠀⠀⢸⠉⠁⠀⠿⢷⣽⠄⡘⠃⠘⠃⠰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡄⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣉⢉⣉⣀⢄⡀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣄⡀⠀⠀⠀⠀⠈⠙⠦⣀⠀⠀⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣒⣂⣦⠀⣠⠒⣄⢲⠒⢖⣒⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠈⠓⢦⡀⠈⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣟⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⡀⠀⠀⠀⠈⠲⣄⠈⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⠄⡀⠀⠈⠻⣶⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⡇⠀⢂⠀⠠⠄⢀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢳⣕⡄⠀⠀⠈⣛⡀
⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⠤⢼⣆⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡵⡀⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠂⠶⠚⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠂

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⢸⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⣿⣿⣿⣇⢀⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣸⣿⣿⣟⣛⣉⣭⣤⣄⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⠾⠟⠛⠛⣛⠒⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠿⠿⠿⠿⠟⠛⠉⠀⠒⠒⠒⠉




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣬⣍⣤⣬⣽⣏⣴⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠉⠉⠉⠙⣆⠀⠀⠀⠀⠀⠀⣠⡤⣤⡤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⣄⠀⠀⢀⡄⠈⠙⣆⠀⠀⣠⡼⠁⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⠀⠈⠃⢀⡞⠀⢀⣠⠏⠀⢰⡇⢀⠐⣆⠀⣠⠖⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⡀⢀⡀⠀⣀⡟⠁⠀⠀⠀⠙⢾⡀⠘⠂⠀⠀⣰⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠋⠉⣿⢹⡏⠉⡇⠀⠀⠀⠀⠀⢸⠓⢶⡖⣶⠞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⣀⣀⠀⣿⢸⡇⠀⡇⠀⠀⠀⠀⠤⠞⠀⢸⡇⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠉⠀⠀⠀⢀⣠⠤⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⡇⠀⠀⠀⠀⢀⣀⣀⠀⠀⢸⡇⣿⠀⠀⢀⡴⠒⠛⠳⢦⡀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣦⡀⠀⣿⠀⡇⠀⠀⣀⡴⠋⠁⢉⠳⣄⣸⠇⣿⡤⠶⠋⢠⡀⠀⠀⠀⠳⠾⣄⠈⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢸⠁⢻⡀⢿⣤⣧⣤⣾⣥⣤⣴⣤⣿⣤⣤⣽⣦⣿⣤⣤⣤⣤⣷⣤⣾⣤⣤⣤⣼⣧⣤⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⡿⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⡇⠀⣀⣽⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠈⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣲⣄⢰⡇⠘⠛⢶⣀⣠⣄⢸⡏⠁⠀⠀⠀⣀⣠⡽⣷⠀⠀⠀⠀⡼⠋⠁⠀⣄⠀⣰⠃⠈⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠀⢸⡇⠀⠀⢸⠋⠀⠈⠛⢁⣠⠴⠖⠋⠉⢀⡴⠃⠀⠀⠀⠈⠃⠀⠀⠀⠙⠀⠃⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠘⡇⢠⣴⡚⠀⣀⡤⠞⠋⠀⢶⣤⣀⡴⠋⠀⠀⠀⠀⠀⣠⠖⠚⠒⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⣄⠀⡇⠀⠀⣿⠚⠩⣄⡀⠀⣀⡼⠃⠉⠀⠀⠀⠀⢠⠴⠞⠁⠀⠀⢀⡄⠙⠲⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠀⣿⠀⠀⡏⠀⣀⡿⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠳⠀⠾⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢸⡄⠠⡟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠀⡀⠀⠂⢀⢆⠀⢂⠀⠀⠐⠀⠠⡐⠀⠖⢠⠂⠠⠀⠄⣀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠘⠀⠁⠀⠀⠈⠈⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠁⠂⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⠚⠛⠛⠛⠛⠛⠛⠛⠛⠳⠶⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠒⠚⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠙⠲⡄⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠠⣇⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠙⠓⢒⣀⣀⣠⠋⠉⠁⠀⢦⡀⢸⡇⢀⣤⠴⠀⠀⠀⠈⢷⡀
⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⢀⣤⣤⣤⣌⣿⣿⣷⣿⣥⣤⣤⣀⠀⠀⠈⢷⡀
⠀⣾⠁⠀⠀⠀⣄⠀⣠⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣲⣶⠶⣿⣿⣿⣿⣽⣿⣿⣦⡀⠀⠀⠀⠀⠈⣧
⢰⡇⠰⠶⠶⢦⣸⣷⣿⣿⣥⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠒⠒⠒⠒⠒⠲⠤⣀⢀⣾⢟⣾⣯⣿⣿⣮⣿⣍⠃⠀⠀⠀⠀⠀⢹
⣾⠀⠀⣺⠟⣛⣿⣿⣿⣿⣟⠲⢦⡀⠀⠀⠀⠀⡤⠚⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠙⢣⣼⠏⣿⣿⠻⣷⠈⠻⡀⢀⠘⠀⠀⠀⠈
⣿⠀⠀⠁⣼⣿⣾⣿⣿⣿⣟⠳⣄⠀⡠⠖⠚⠛⠓⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⢱⣿⣧⢀⡹⣴⣾⣿⣿⣆⡀
⣿⠀⠀⠀⢏⣼⡿⠉⢿⠈⢻⣤⣤⠟⠀⠀⠀⠀⠀⠀⠈⢳⣄⣠⠤⠤⢤⣄⡀⠀⠀⠀⠂⠀⠘⠀⣿⣧⡀⠀⠀⠙⢿⠋⠁
⣿⠀⠀⠀⢼⣿⠧⠄⠸⡷⠫⠇⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣷⡆⠀⠀⠀⠙⢢⡀⠀⠀⠀⠀⠀⣿⡇⠙⣄⠀⠀⠸⡆⠀⢀⣤⣾⣿
⢿⡀⠀⠀⣸⣿⠀⠀⠀⣧⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⡾⣿⣿⢿⡁⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⣀⣿⣧⣀⡈⠃⠀⠀⣿⣾⣿⣿⡿⣿
⠸⣿⣿⣿⣿⣿⣄⠠⡶⠿⠿⠿⠛⣿⣿⣿⣿⡿⢻⣿⡁⠁⣿⠀⠁⠀⠀⠀⠀⠀⠀⠁⣠⣶⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⡿⣿
⠀⢿⣿⣿⣿⡯⣿⣿⣷⠋⢹⣴⣾⡏⠀⡆⢸⣦⡄⢹⣿⣄⣿⢀⣀⣀⣀⣀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⣿⣻⣿⣿⡿
⠀⠈⣿⡿⣿⠷⡿⠿⣿⣷⣾⣿⠿⣷⣶⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠘⣿⠛⠿⠟⠋⠉⠉⠉⠛⠿⠟⠛⠛⠿⠛⠉⠉⠉⠙⠛⠿⠛⠙⠻⠟⠋⠉⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠈⢷⣀⡀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣛⣋⣉⣉⣠⣤⣬⣯⣵⣦⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣼⣻⠟
⠀⠀⠀⠀⠀⠀⠈⠻⣏⣩⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⡿⣽⣾⣿⣿⣿⣿⢿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣲⣾⣿⣖⡂⠀⠠⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⠉⣷⠀⠙⠆⠹⠛⠉⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡽⡿⠯⠁⠀⠀⠀⠀⢂⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⣀⣀⢸⣤⣠⢼⣶⣷⣦⣖⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣦⠶⠴⠾⠷⢾⢿⠿⢿⠿⢿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣉⠉⠁⠐⠀⠀⠀⠀⠄⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣠⣤⡤⠶⠋⢉⠀⠀⠀⠐⢞⠉
⠀⠀⠀⠠⠄⠠⠤⠤⠐⠒⠒⠛⠛⠛⠉⠋⠉⠉⠉⠁⠀⠀⠀⠁⠀⠀⠀⢀⣀⣀⣨⡿⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⠒⠒⠚⣛⡛⠛⡛⠛⠑⠒⠚⠉⠉⠉⠉⢀⣀⠴⠃⠀⠀⠀⠀⠤⠊
⠀⠀⠀⠀⢀⣒⣒⣒⣒⡋⠩⠭⠶⠖⠛⠛⠉⠋⠛⠋⢉⣛⡛⠷⠒⠒⠒⡒⠞⠋⠙⠃⠾⠆⢀⠒⠈⠀⠀⣢
⠀⠉⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠤⠤⠔⠒⠒⠉⠁⠀⠈⠁⠀⢀⠴⠂⠁⠀⠀⠀⠀⠀⢀⣀⡈⣷⡞⠾⣅⡀
⠀⠀⠀⠀⠀⠠⠄⠠⠀⣀⣀⣤⠤⠖⠋⠁⣀⡤⠔⠒⠈⠁⠀⠀⠁⠠⠀⠀⠀⠠⢨⠖⢳⠛⠲⠿⠀⠴⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠲⠦⠤⠤⠤⠤⢴⡶⢀⣀⣀⡏⠉⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢦⡀⢀⣧⣀⣤⣤⣶⣾⣿⣿⠇
⠀⠀⠠⠄⡀⠀⠀⠀⠐⢶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣯⠀⠀⠀⠀⠀⠀⢄⠀⢀⣀⡀
⠀⠠⠌⠀⣀⣛⣒⣶⣤⣤⣽⣟⣿⣿⣽⣿⠿⣿⣿⢿⣿⣿⣟⣫⣭⣥⣶⣿⣿⣿⣿⣶⣄⠀⠀⠤⠤⠬⠭
⠀⢀⣬⣭⣍⣉⣙⣿⣷⣶⣾⣿⣿⣿⣿⡳⠾⣿⣯⣭⣭⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣯⣭⡤⠤⠄⠒⠒
⠉⠉⣍⣉⣛⣋⠋⠛⠦⣤⣀⣨⡍⠉⢿⣿⣏⣉⢾⣿⣿⠗⠛⠛⠀⠀⠀⠛⣟⣛⣻⣿⣇
⠀⠀⠀⠀⠉⠀⠀⠙⠓⠲⠦⠤⠤⠀⣀⣀⣀⠒⠒⢺⣿⠂⠀⠈⣉⡉⠉⠭⠤⠴⠒⣀⣀⡀⠉⣉⣉⡉⠑⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠉⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⢶⣿⣶⣤⣤⣀⣾⣿⣿⡷⣁⣤⣴⣒⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣭⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛⠛⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠟⡩⠿⠛⣩⣿⣿⡿⠋⠘⣷⠈⠛⢿⣿⣿⣿⣿⣟⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⢀⣾⣿⣿⡿⠁⠀⠀⣿⡆⠀⠀⠻⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃⠀⠀⠀⢻⣷⠀⠀⠀⠙⣏⢻⣿⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⢻⠀⠀⠀⠀⢸⣿⡃⠀⠀⠀⠈⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⡇⠀⠀⠀⠀⢘⣿⣧⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠿⣄⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠇

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢆⡀⠠⠠⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠠⠄⠄⡠⡀⠀⡴⠤⠶⠚⠂
⠀⠀⡠⣄⣄⠀⠒⠀⠒⣷⣉⡀⣠⣀⢀⠈⠂⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣴⡀⣘⣷⠄⠲⠶⢠⡆⣴⠄⠀⠰⠄
⠀⠀⢰⣿⠏⠀⡀⠠⣿⠾⡏⠻⣭⠇⠰⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡼⣶⠟⠻⢻⢿⢧⡔⠂⠀⠁⠀⠂⠁⠄
⠀⠀⡿⠚⠀⠐⠌⠀⠀⠀⣿⠂⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡠⠶⡾⠁⢈⣷⡓⡿⠂⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠐⡄⠀⠀⠺⠿⠦⠖⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠃⠀⢀⠃⠀⢈⡿⠂⠟⠅⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣠⣤⢤⠂⠀⠐⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠀⣈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢨⡀⠀⠀⠀⠀⠀⢀⠀⣀⡀
⠀⠀⠀⠀⠀⡔⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠒⣶⡧⠀⢷⠤⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠖⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢂⠰⠀⠀⠀⠀⢀⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢉⡍

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡤⢤⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣶⡀⣰⡿⠉⢠⣽⠿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⣋⣴⣾⣷⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠘⢷⢿⡅⢠⡿⡛⠀⢈⣙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣷⡿⠛⢻⣿⣿⣗⣶⣶⣏⢾⡷⠶⠋⠀⠀⠀⠀⠀⣠⣤⣴⣶⠖⠀⠀⢀⣬⡶⢶⡌⢀⡠⣄⡀⠄⣠⣀⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢋⡴⠖⢒⣛⣿⣿⣿⣯⣿⡭⢀⠀⠀⠀⠀⠀⠰⠚⠚⠉⠋⡵⠀⠀⠘⠋⣿⠀⢨⣿⡈⠓⠄⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣠⡎⢿⣿⣿⣿⣿⣿⣿⠿⣆⠉⠒⠄⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠠⠃⠀⢸⠈⢷⠀⠀⠀⠀⠀⠀⠀⡰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣵⠛⠁⣿⠋⡿⠉⢿⡇⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠘⢀⡄⠀⠀⠰⠀⡜⠀⠈⢇⠀⠀⣠⠀⠀⠀⣷⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⢰⣿⡴⠁⠀⠈⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⢨⡇⠀⠀⠘⡀⠀⠁⠈⠀⢸⠃⠡⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡮⠃⠀⠀⠀⠘⠛⠁⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣧⠀⢘⠀⠃⡞⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠸⠀⢰⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⣼
⠀⠀⠀⠀⡄⠀⣶⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢿⡀⠀⡏⠀⠀⠤
⠀⠀⠀⡠⣏⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⠖⡾⢳⡦⠴⣶⣟⣇⠠⡇
⠀⠐⣴⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣊⢚⣉⢊⠰⢓⣣⠔⢪⣉⣼⣷⢸⣇⡀
⢀⣈⣹⣯⣿⣷⣷⣦⠄⣀⠀⠀⣀⡀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡷⠚⠑⠣⣏⡉⠄⠛⢅⡒⢂⣰⣾⣿⣿⣿⣷⣆⡤⠄
⠀⢨⣽⣷⣿⣟⣿⣟⣗⣺⣿⣿⣿⣿⣷⣄⡄⢠⡏⠏⠇⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣷⣾⣖⣬⣥⣬⣤⣞⣋⣭⣿⣿⣷⣿⣿⣿⣿⣿⡶⠖⠂
⠀⢸⣿⣿⡟⠀⠈⠉⠩⣤⣿⣿⣿⣟⣿⡏⠀⢸⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠉⢛⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣁⣙⢛⣷⡈⠷⣦
⠀⣀⣿⠟⠤⡴⣶⣶⣾⡿⢿⠉⠽⢿⠣⠀⠀⠸⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠤⠰⠶⠌⣩⣿⣿⣿⣿⠿⢿⣟⢋⣿⣿⠿⠽⠿⠿⠿⠙⣷⠀⠐⢦
⣀⡵⠋⠀⠀⠀⠐⠚⠋⠤⣗⠐⠀⠠⡶⠈⠁⢸⢀⡇⡧⠀⠀⠀⠀⢀⣀⣀⣠⡴⢴⠖⣛⣛⣛⡿⢶⣶⣶⡍⣉⠁⠀⠀⠀⠀⠀⠀⠀⠛⠳
⠈⠁⠀⠀⠀⠀⠀⠒⠂⠐⠒⠘⠃⠔⠦⠤⠀⢸⢾⠇⡇⠀⠀⠉⠉⠉⠁⠈⠛⠛⠛⠻⠛⠻⠿⠭⠞⠛⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣟⣩⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡴⠌⢅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⢁⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⣄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠑⠢⣼⣆⣀⣀⣀⠀⠀⠀⠀⠀⣄⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠉⠒⠤⢀⠀⠀⠁⠲⠢⠬⣦⡀⠘⠆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠐⠀⠑⠐⠒⠓⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⣱⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⣠⠴⠖⠛⠉⣉⣉⣉⣉⣙⣛⡲⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣈⣦⠖⠋
⠀⠀⠀⠀⠀⠉⠀⠀⠔⠚⠉⣉⡠⠤⠤⠤⠬⠭⣽⣓⡻⠽⣟⣓⡶⠶⠶⠶⠶⠶⠛⣋⣩⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠪⠭⢭⣙⣛⣛⣋⣉⣡⠤⠔⠂


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣦⠀⢴⡄⢸⣇⢀⣶⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣹⡷⠿⠛⠛⠛⠛⠻⢶⣿⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣦⣬⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣤⡾⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⠛⠻⠷⣦⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣅⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⢀⣴⠟⠛⠛⠷⣦⡀⠀⣼⣏⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣿⣿⡿⠁⠀⠀⠀⠀⠈⣿⣾⣏⠙⠻⠦
⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣛
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⢀⣴⣄⠀⠀⠀⢀⣴⣄⠀⠀⠀⢀⣴⣄⠀⠀⠀⢀⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠹⣷⠀⢠⡿⠁⠹⣷⠀⢰⡿⠁⠹⣧⠀⢰⡟⠁⠹⣧⠀⢰⡟⠁⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣴⠟⠀⠘⢷⣤⣴⠟⠀⠘⢷⣤⣴⠟⠀⠘⢷⣤⣴⠟⠀⠘⢷⣤⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⢿⣆⠀⢀⣾⠟⢿⣆⠀⢀⣾⠛⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⣠⡿⠀⠸⣧⣀⣠⡿⠀⠸⣧⣀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠈⠛⠉⠀⠀⠀⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⢘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠠⡄⠀⠀⠀⠀⡏⠀⠀⢠⡆⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖
⠀⠀⠀⠀⠀⠈⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢻⡄⠀⠀⠀⡇⠀⠀⣾⠁⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠘⢦⡀⠈⢧⡀⢀⡀⢳⡀⢶⠀⡇⠺⢰⠇⡔⠀⡴⠃⠀⠀⣠⠞⠃⠀⢀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⡀⠀⠀⠙⢦⡀⡑⣄⠱⡄⢣⠸⠀⡇⠆⡌⡼⢁⡞⢠⠜⣠⠞⠁⢀⡠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠢⡙⠢⡈⠣⡀⠀⢀⡀⠇⡀⠈⣠⠋⠔⡡⠊⢁⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳⢦⣤⣀⠀⢬⡑⠬⡂⠀⠠⠂⣠⠤⠄⠢⠄⡁⠐⠄⢀⡠⠖⣉⠤⠒⢀⣠⡤⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠶⠶⠦⣤⣤⣀⣀⣀⠀⠈⢉⡒⠈⠑⢈⠟⢠⠊⠀⠀⠀⠀⠀⠈⠳⡔⢅⠀⠪⠄⠒⠊⠁⢀⣀⣠⡀⣀⣀⣀⣴⠖⠶⠤⠤⠤⠶⠶⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠈⠉⠉⠉⠑⠒⠒⠤⠌⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⢃⠈⠂⠀⠐⠒⠊⠉⢉⡝⠒⠛⠁⠈⠉
⠠⡤⠶⠒⠒⠒⠚⠋⠉⠀⠀⠀⠉⠉⠳⢄⣀⡉⠉⠉⠀⠐⠀⢇⠀⠀⠀⠀⠀⠀⢀⣀⡧⠬⠥⠤⠬⠭⣱⠖⠋⢀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⠤⣄⣠⠤⠸⠓⠒⠒⠒⠒⠚⠉⠁⠀⠀⠀⢀⣠⠼⠃⣀⠖⠋⠀⠀⠈⠉⢁⣠⠤⠤⠀⠀⠒⠀⠉
⠀⠀⠀⠀⠀⠐⠂⠁⠁⠐⢦⡀⣀⡀⠀⠀⠀⠤⡀⠀⡀⢠⣳⣖⡒⠒⠠⠤⠤⠤⠤⠤⣴⠞⠉⢉⡀⠐⠬⠈⠀⠴⡆⡀⠾⣉⣉⠁
⠀⠀⢀⣄⠀⣤⠄⢤⠄⠀⣠⠀⠤⠤⠬⠭⠥⠴⠦⠤⠤⠤⠴⠶⠿⠖⠂⠀⠀⠀⣤⠼⢃⢰⣀⠉⡤⡀⣀⠠⠀⣠⠔⢁⡽⠄⠈⢫⣉⣙⡤⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢠⡼⣃⣤⠾⠷⡼⠖⠛⠶⢅⣀⣀⣀⣜⣠⣤⣅⣐⣀⣈⣉⣄⣁⢇⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡖⠒⣒⠲⠤⠶⠻⢛⣛⣋⢀⣤⣄⠤⠤⠤⠤⠤⠶⠤⠭⠭⠁⠀⠀⠀⠉⠉⠁⠀⠀⠉⠉⠁
⠀⠀⠀⠀⣀⣴⠶⠒⠒⠚⠛⠚⠛⠛⠒⣾⣉⡉⠀⠀⠀⠈⣡⣤⣵⣐⠒⣒⣒⣃⡀⠀⠀⠀⠀⠀⠤⠤⠤⠤⡤⠤⠤⠔⠀⠀⠦⠤⠤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡀
⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠉⠉⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢠⣶⣶⣶⣾⣷⣤⣤⣴⣶⣶⣤⣀⣈⣡⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⠿⣿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠉⠉⠉⠙⠛⠛⠛⠿⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡿⠿⢿⠷⠄⣴⣿⣿⣿⣿⣷⠶⣦⠀⠀⣴⣾⡿⢿⣿⢦⠄⠀⠀⢀⣤⣶⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣦⢠⢸⡤⠄⠉⠀⡏⠀⠉⠀⠀⢸⠀⠀⢀⣅⣄⣀⣇⣀⠀⠀⠀⠀⡏⡏⠀⢹⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠾⠾⠛⠁⠓⠲⠿⠒⠛⠒⠒⣾⣤⣤⣼⣿⣿⣿⣿⣿⣤⣤⣤⢀⣷⣧⣤⣼⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⣀⣤⣶⣤⣀⠀⠀⠀⠀⣠⣶⡀⠀⠀⠀⢀⣠⡤⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠿⡿⠿⠿⣿⣷⡄⢺⠟⣿⠛⠛⠛⣿⠻⡆⠠⠾⠿⠿⠿⠷⠐⠚⠛⠛⡟⠒⠚⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣷⣶⣶⣷⣾⡆⢸⣀⣿⠀⠀⠀⣇⣀⡇⠀⣀⣀⢀⣀⡀⠀⠀⠀⠀⡇⠐⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠋⠀⠘⠛⠋⠀⠀⠀⠛⠛⠃⠀⠤⠦⠤⠤⠆⠀⠀⠀⠀⠧⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣶⣄⡀⢠⠴⠶⠟⠛⠷⠶⢤⠀⠀⠀⣴⣿⣿⣦⡀⠀⠀⣴⣾⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⠀⠉⡇⢈⢸⡇⠀⠀⠀⠀⠂⠀⠐⠀⠀⠉⠉⡟⠉⠉⢹⠉⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⠀⠈⡇⠈⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⣷⣤⣤⣾⣏⠄⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠃⠀⠈⠀⠘⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠛⠛⠛⠛⠁⠀⠀⠀⠈⠉⠉
⣿⣿⡟⠻⣿⡏⢹⠛⡏⣿⡏⡍⢙⠹⣿⡏⡋⠉⢹⣿⠋⡟⠙⠹⣿⡏⡋⠛⠩⣿⣿⠋⢙⠉⣿⢩⠉⡟⢹⡏⡏⠙⠙⠙⠉⣽⢹⣿⣿
⣿⣿⣷⣶⣾⣷⣾⣾⣿⣿⣷⣶⣿⣶⣿⣿⣷⣾⣿⠛⠓⠟⠛⠖⢻⡟⠛⢻⡖⠻⣷⣶⣿⣶⣿⣿⣷⣶⣾⣿⣷⣾⣷⣶⣶⣾⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠀⠀⢠⢠⡀⣀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠢⡾⠁⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⢀⡐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠠⣴⡶⡀⠙⡄⠂
⠀⠀⠀⠀⠀⠀⠊⠁⠀⠷⠏⠀⠁⠀⠀⢀⣨⣴⢙⣿⡿⣿⣟⣿⣾⢿⣿⡇⠀⠑⠳⠽⠇⢲⡿⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠙⢯⠠⠑⢶⣶⣬⠭⣤⣥⣭⣤⣼⣿⣿⣣⣬⣛⢿⣿⣇⣐⣀⣖⣚⣿⣷⣾⣷⣿⣿⣦⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠶⣛⣽⣒⣶⣿⣿⣿⣿⣿⣿⣿⡿⣿⡭⢙⣮⣡⣌⣿⣿⣿⣿⡯⠿⢿⣏⡷⠝⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠉⠁⠀⠈⠉⠋⠉⠋⠉⠚⠋⠉⠙⠛⠋⠋⠉⠁⠉⠈⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣾⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⣩⣽⣿⣿⣿⣭⣕⠀⠀⢐⣶⣷⣶⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣹⡟⠘⣽⠀⠀⠉⢧⠀⣹⡿⠁⠈⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠉⠐⡀⠀⠀⠀⠃⠀⠰⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣆⣤⡀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⡄⠀⠊⡿⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣩⠿⡿⢻⠍⠉⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣀⣿⣀⢼⣤⢄⡠⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⡘⢳⣤⢀⣆⣶⣶⣼⣟⣻⣮⠋⣽⣿⣿⢿⣿⣿⣾⣯⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣤⣶⣶⡶⠷⠾⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⢿⣷⣿⣿⣿⣿⣿⣿⣯⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠚⠒⠂⠒⠂⠀⠤⣄⠀⠈⣉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠶⠶⠒⠂⠁⠀⠀⣀⣠⠤⠶⠇⠀⠐⠀⢀⣀⣤⠤⠖⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣐⣒⣲⣦⣤⣤⣤⣤⣤⣀⣤⣤⣀⣴⣶⣶⡴⠟⠛⠋⠁⢠⠄⠀⠀⠀⠀⠥⠐⠤⠤
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⣤⠬⠴⠶⠖⠚⠛⠛⠛⠋⠍⠉⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢙⣿⡷⠰⡄⠀⠀⠰
⠀⠀⠀⠀⠀⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⡤⢀⢀⣐⣒⠖⠒⠿⠿⠿⠛⠋⠁⠀⢰⠇⠀⠀⠀⡀⠄⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⠿⠛⠛⢉⣉⣉⣁⣀⣠⣄⣀⣀⣠⣀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠞⣫⠀⠀⠀⠀⠀⢀⡤⠚⠉
⠀⠀⠀⠀⠤⠄⠀⠙⠓⠒⠒⠒⠛⣋⣉⣩⣤⡶⠾⠟⠿⠛⠛⠉⠙⠋⠿⠙⠉⠉⠙⢛⣛⡿⠿⠶⢖⠾⠒⢚⣛⠯⠭⠛⠙⠲⠴⢿⡡⠄⠐⠒⠉⠁⠀⠀⠙⡀
⠀⠐⠂⠐⠂⠒⠚⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠖⢒⠛⠩⠽⠛⠋⠩⠐⠂⢈⣠⠄⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣄⣤⢦⣼⠲⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠉⠉⠉⠉⣁⡠⠀⠀⠀⠀⠀⠀⢀⣀⠤⠀⡐⢾⠉⠀⠀⠀⠀⠀⡀⠀⠀⡠⠚⣄⢶⡤⡤⠘⣻⠗⠚⠛⡛⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠤⠄⣀⣀⣀⣠⣤⣤⠶⠞⠋⠀⠀⢀⣠⣤⠶⠒⠉⠉⠀⠐⠁⠀⠀⠤⠀⠄⠀⠠⠀⠀⠠⠎⣸⠞⠛⣾⠉⠒⠾⠿⠀⢰⡶⠟⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠭⠈⠉⠁⠀⠀⠀⠀⠀⠐⠐
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣻⣻⣛⣻⣻⣛⣛⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣭⣯⣭⣿⣿⣭⣽⣯⣭⣽⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣤⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣌⢻⣿⡟⣰⣿⣿⡇⠀⠀⠀⣠⣶⣿⢿⣿⣿⡿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣿⣿⣿⣿⣴⣿⡟⠋⠀⠀⠀⠀⠻⠟⣿⣎⢻⣯⣴⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠛⠛⣛⠻⠛⢵⠀⠀⠀⠀⠀⠀⢠⠻⣿⡿⢿⣿⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠟⠀⠀⢠⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⡆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⣄⠀⢸⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⠀⠀⠀⠀⠠⠴⠞⠀⠀⢸⡇⠀⠘⠃⠀⠀⠀⠀⢀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⣤⣦⣬⡙⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣠⣶⣿⣷⣄⠀⠀⣸⣇⠀⣀⣠⣾⡟⣿⣿⣿⣿⣮⣁⡸⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⣶⡀⠀⠸⠿⠃⠀⠀⠰⠿⠿⠙⠟⠐⠿⠿⠆⠻⠟⠸⠿⠿⠿⠷⠘⠿⠃⠿⠿⠿⠿⠘⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢸⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⣸⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣴⣶⣶⣌⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⡇⣿⠛⠉⢴⣿⣿⣿⣟⢋⣭⣴⣶⣶⣶⣶⣦⡍⠻⣿⣿⣿⣿⣿⢋⣭⣴⣿⣿⣿⡿⢻⣷⣬⣝⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⡇⣿⣿⣿⡆⢉⣵⣦⡙⢸⣿⣿⡿⠟⣋⣩⣤⡶⢠⣿⣿⣿⣿⡇⠛⠛⠛⠛⠈⠛⠃⠛⠛⠛⠛⠂⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⠇⣿⣿⣿⡿⠟⣉⡵⢶⣿⣿⡿⠟⣰⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣉⣀⠶⡿⢛⣥⣶⣿⣿⣷⡀⣌⣋⣴⣾⣿⣿⣿⣿⣿⢋⣴⣾⣿⣷⣦⡙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡇⢻⣿⣿⠀⣾⣿⡉⠻⡿⠟⣋⣴⣿⣿⣿⣿⣿⣿⡟⣡⣶⣾⡿⢿⣿⠏⣽⣷⣶⣌⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣷⢸⣿⣿⢸⡿⠟⣁⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣉⣉⣉⣉⣈⣉⣀⣉⣉⣉⣉⣠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠈⠿⠟⠰⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠃
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠂
⠠⠄⠠⡁⠀⢀⠀⠀⠀⠀⢀
⠀⠠⠂⢐⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⣘⡫⢵⠀⡠
⠀⠀⠀⠘⡀⠀⠀⠀⠀⠈⠸⠁⣨⢊⡅⠐⢠⢄
⠁⠀⠀⠀⢃⠀⠀⠀⠀⠀⠠⠀⡅⢸⠗⠀⠄⠀⠀⣠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠐⠿⢾⡿⢙⡊
⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⢈⠀⠀⠀⠀⠐⠛⡛⣹⠍⢲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠋⠈⠒
⠀⠀⠀⢀⠑⣾⠀⠀⠀⠠
⠀⠀⠀⡃⠰⠋⠀⠀⠀⡾⠁⠀⠀⢠
⠀⠀⠀⠒⠀⢈⠀⠀⠸⠄⠀⠀⠀⠀⠁⠀⠎
⠀⠀⠀⠀⠀⢸⡁⠀⡚
⠀⠀⠀⠀⠀⠐⠂⠀⠁
⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⠀⠀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⢑⠀⠐⠒⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠐⠂⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠄⠀⠀⠀⢀⣀⣀⣀⢀⡀⠀⠀⢠⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠿⢿⠉⠁
⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣶⣵⣶⣤⣿⣵⣿⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣄⣠⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠇⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⣀⣰⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋
⠀⢀⣤⠷⠉⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠈⠉⠀⠀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠆⠀⠊
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠠⢘⢅
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡾⠛⠉⠉⠉⠉⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠤⣾⣏⣠⣤⣤⡄⠀⠀⠀⣀⠹⣷⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩⣽⣿⣷⣾⣿⣷⣶⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⡿⠟⠶⠶⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠺⠿⠿⠿⠿⠿⣿⡟⠛⠛⠛⠻⠿⠿⠿⠿⢿⣿⠿⠟⠉⠉⠉⠉⠛⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣷⣄⠀⠀⠀⠀⠀⠀⣠⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠶⠦⠴⠶⠿⠟⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⠀⠀⠀⠉⠉⠉⠙⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡂⠀⢐⣾⠂⠀⠀⠀⠀⢀⠀⠀⠠⠆⠀⢀⣼⣻⡀⠟⣃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣿⣿⣷⣼⣯⣿⣷⣶⣼⣦⣤⣶⣶⣴⣧⣴⣶⣿⣿⣿⣷⣶⣿⣿⣿⣤⣤⣤⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠀⠁⠈⠉⠉⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣀⣠⠊⠙⢂⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⣤⣤⣀⣀⣀⡀⠈⠉⠉⠀⠀⠈⠀⠀⠀⠀⠠⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⣉⣉⣉⣷⣶⣄⣀⠀⠀⠀⠀⠴⠀⠀⠠⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⢻⣿⣿⣿⣶⡶⢤⡤⠤⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣼⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠚⠿⠿⠿⠿⠟⠷


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠛⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠤⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠤⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠠⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡃⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡤⠤⠤⠓⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠀⠀⠀⠀⠀⠀⠰⣀⣀⣤⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠄⡷⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢼⠁⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⠀⠀⠀⠀⢸⠁⠀⢀⣀⣠⠤⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⣠⡤⠴⡟⠛⠉⠉⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢾⠉⠁⠀⠀⢰⠇⠀⠀⠀⠀⡁⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⠀⠀⠀⠆⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⡾⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣀⣤⠔⠛⢲⠏⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣆⡠⠤⠔⢺⠉⠉⣀⣡⣥⡛⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠁⠒⠉⠹⡀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⣚⣨⣤⣾⣿⣿⡿⠻⣿⣿⣿⡿⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠈⣛⢛⠛⢛⣻⣭⢛⣻⣷⠆⣟⣿⡍⢻⣿⣿⡟⠳⢶⣶⣷⣶⣋⣀
⠀⠀⠀⠈⠉⠀⠀⣄⣉⣉⣼⠯⣬⣿⣿⣞⣛⣯⣴⣾⣿⣿⠛⢋⣭⣶⠉⠨⣽⣋⣉⠛⠿⡿⠷⠾⢿⣿⡏⠁⠤
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠴⠶⠀⠽⠯⠍⠀⠐⠊⣉⣉⣁⡒⠁⠴⣟⡏⠀⠘⢶⣼⣷⠤⠒⠲⣿⣷⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠛⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒

⠀⣀⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⠀⣀⠀⠀⣀⣀⣀⡀⢀⣀⣀⠀⠀⠀⠀⢀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⡀
⣒⣒⣿⡷⠾⡿⢿⢿⣿⣛⣛⣿⣿⣿⣖⣖⣒⣲⣦⣭⣭⣤⣭⣭⣷⡾⢯⣭⣿⣿⣿⣶⣛⣫⣭⣿⣭⣽⣽⣿⣿⣖⣿⡿⢿⣯⣭
⠐⢶⣶⣾⣿⣟⢻⣻⣿⣿⣿⣿⣿⣿⣫⣽⣭⣿⣯⣽⠶⢿⣻⠿⣟⣻⡿⣿⣿⣿⣿⠿⠟⣿⣟⠛⣉⣭⢿⣟⡻⠙⠋⢉⡉⠩⠶
⠷⠶⠌⠋⠒⠐⢒⣻⣮⣉⠙⠛⠐⣬⣽⣿⠛⠛⠛⠛⠉⣁⠐⠒⠂⣉⡁⠀⠀⠉⠙⠃⡤⠀⠀⠀⠁⠒⠂
⠶⠄⠀⠀⠀⠀⡀⠀⠀⠤⠶⠶⡄⠀⠀⠀⠀⠀⠶⠄⠀⠀⠀⠀⠀⠀⠈⠡⠄⠀⠀⠀⠀⠀⣀⣀⣀⡔
⣀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⠐⠁⠂⠖⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈
⣧⣀⣀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⣿⣷⣶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢀⣄⣤
⠉⠋⠉⠉⣿⣷⡤⠀⠀⠀⢠⠀⠀⣀⣀⠀⠘⠓⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⡀⢀⡀⠀⠀⠐⠶⠄⢀⣄⣀⠀⠀⢹⡿⠿
⠸⠷⠶⠀⠰⠇⠀⠀⠴⣷⣦⣀⠀⠿⠟⠀⠈⠀⠀⡀⠀⢠⠄⢀⡀⠀⠀⠀⠀⠈⠉⣽⣄⠀⠉⠀⠀⠀⠀⠉⠉⠉⠩⠅⣠⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠂⠀⠀⠐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⠰⠤⣆⡈⣐⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠠⠆⡈⠐⢀⠀⠈⠠⢀⠀⠀⠀⠣⠄⠀⠛⠂⠀⠀⢀⠀⠀⠉⠀⠈⠀⡦⠤
⠀⠀⠀⠀⠀⠈⠀⠐⠛⠉⠾⣝⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢧⣦⢴⠠⠄⠈⠉⠂⢄⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠤⠢⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠀⠀⠀⠀⠀⢀⠒⠐⠂⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠠⠤⠀⢀⠀⠀⠚⠓⠀⠀⠐⠂
⠀⠐⠛⠲⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⢤⣶⡀⠀⠡
⣄⠀⠀⠀⠀⢀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠈⠈⠕⠀⠁
⣿⣯⢠⠀⣀⢾⣧⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢤⠤
⣿⣷⠟⠀⠛⠻⣿⣯⣿⣿⡔⠀⠂⠠⠾⠃⠠⠊
⠀⠈⠀⠀⢂⡀⢸⣿⣿⣿⣿⣿⠦⣠⠂
⣆⣄⣠⡄⠀⠀⠈⠛⠟⢭⡟⢿⠀⣷
⠀⠈⠉⠃⠀⠀⠀⠀⠀⠀⠈⠐⣼⣿⣦⡀
⠀⠀⠒⠒⠒⠀⠀⠀⠓⠒⠂⠀⠀⠉⠨⢇
⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠀⠀⠀⠀⠈⠛⢀⣀
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠤⠤⠄⣠⠤⠤⠤⠤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠀⣀⣤⡟⠛⠛⢶⡀⠀⠀⠀⠸⣄⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣀⣾⠁⠀⠀⠀⠀⠀⢻⠀⠴⠞⠁⠙⠳⢤⣤⣬⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠂⠀⠖⠳⠶⠶⠋⠀⠀⠀⠀⢀⡞⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢶⣶⣤⡄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠖⢛⠲⣼⠑⣞⡿⢭⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣤⡞⢉⣽⡷⢻⢟⡵⡆⢸⡏⠉⠳⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢻⣿⣾⠘⡟⠋⠀⣾⣼⢠⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣾⣘⡇⠀⠀⠹⡏⡼⠓⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⠃⢸⡇⠀⠀⠀⡼⠃⠀⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠶⠾⠇⠀⠀⠾⠷⠶⠶⠾⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣌⠻⠈⠋⠘⢃⣴⠄⠀⠀⠀⠀⣿⠉⣉⣉⣉⡉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢀⣾⠛⠛⢻⣆⠰⠶⠀⠀⠀⠀⣿⠀⣈⣉⣉⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠘⠃⠀⠀⠀⠛⠀⠛⠃⠀⠀⠀⣿⠀⣉⣉⣉⠁⢸⡇⠀⢠⡄⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣿⣛⠛⢷⣤⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⣿⠀⢉⣉⣉⠀⢸⡟⠛⠛⠛⠛⠛⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⡄⠙⣷⣴⠟⠉⣠⡶⠿⠟⠛⠀⣿⠀⢉⣉⣉⠀⢸⡇⠘⠗⠀⠺⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠿⢿⡿⠛⢿⣤⣾⣋⠁⠀⠀⠀⠀⣿⠀⠙⠉⠙⠁⢸⡇⠰⠗⠀⠺⠆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢏⣤⣤⣶⣾⣧⣤⣾⣏⡉⠙⠻⣦⡀⠀⠀⣿⠀⠙⠛⠛⠁⢸⡇⠰⠖⠀⠶⠆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠉⢁⣾⢻⣿⣿⠀⢹⡟⠷⣦⡘⣷⠀⠀⣿⠀⠙⠛⠛⠁⢸⡇⠰⠶⠀⠶⠆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣾⠃⣾⠃⢿⡇⢸⡇⠀⠈⢻⣿⠀⠀⣿⠀⠙⠛⠛⠁⢸⡇⠰⠶⠀⠶⠆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢠⣿⢀⣿⣵⠟⠁⠀⢀⣀⣉⣀⣀⣿⠀⠚⠛⠛⠀⢸⡇⠰⠶⠀⠶⠆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢸⡇⠸⠛⠁⠀⠀⠀⣿⠉⣉⣉⠉⣿⠀⠚⠛⠛⠂⢸⡇⠰⠶⠀⠶⠆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⢬⡥⠀⣿⠀⠺⠿⠿⠂⢸⡇⠰⠦⠀⠴⠆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⢸⣇⠀⠘⣿⠀⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣸⣿⣴⣤⣿⣦⣤⣴⣤⣤⣠⣤⣴⣤⣤⣠⣤⣴⣤⣤⣠⣤⣶⣤⣤⣠⣤⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣌⣉⣥⣤⣤⣌⣉⣥⣤⣤⣍⣉⣥⣤⣤⣍⣉⣥⣤⣤⣍⣉⣤⣤⣤⣍⣉⣥⣤⣤⣍⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣍⣉⣡⣤⣤⣍⣉⣥⣤⣤⣍⣉⣥⣤⣤⣉⣉⣥⣤⣤⣍⣉⣥⣤⣤⣉⣉⣥⣤⣤⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠉⠉⠁⠀⠀⠉⠉⠉⠀⠈⠉⠉⠁⠀⠈⠉⠉⠁⠀⠈⠉⠉⠁⠀⠈⠉⠁




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⣰⣷⣿⣯⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⢿⢿⣲⣄⣿⣿⣿⣿⣿⠿⠛⠙⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣯⣴⣶⣶⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠈⠉⠁⠉⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⣿⣿⣿⣿⣿⡈⠠⢤⣄⡀⣠⣶⠟⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⠁⢰⣿⠟⠉⡟⠿⣿⣄⣤⣽⣿⣿⣿⣿⣝⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⣼⡏⠀⠀⡇⠸⢿⡟⢉⣿⣿⣿⣿⣿⡛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠈⠀⠀⠠⡇⠀⢸⠃⣼⠟⡜⣿⠇⠙⢷
⠀⠀⢤⣤⡀⠀⡀⡀⢀⡠⢀⣠⢘⠀⠀⠀⠩⡢⠀⣀⢸⣄⣀⣤⣀⡀⡜⠀⠈
⠀⠀⠛⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠂⠈⠈⠙⠉⠉⡼⠉⠉⠉⢉⠞⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠋⢱⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣢⣠⣬⣿⣷⣶⣾⣿⣯⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉
⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⡿⠿⣿⡏⠿⠤⣤⠴⣤⣤⣶⣶⣖⣲⣶⣶⣾⣷⡶⢶⡶⠄⠌⠀⠀⠀⠀⠀⡉⠀⠀⣶
⠀⠀⠀⠀⠰⣾⣻⣿⣿⣿⣿⡟⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣗⠛⠛⣿⠀⠂⠀⠠⠤⠋⠉⠀⠌⠉
⣀⣀⣀⣀⣀⣹⣿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣓⠛⠿⢿⡋⠉⠙⠉⠀⠰⣶⡖⡀⡀⠊⠉⡀
⠿⢛⣻⣿⡏⢡⣾⣿⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⡿⠖⢚⢳⡶⠀⠐⠰⡾⠛⠉⠃⠀⠀⠈⠁
⣤⣼⣿⣩⣿⣶⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢒⡛⣻⣞⣷⠤⠀⠐⢿⢄⣘⠁⠀⣠⠄⠀⠀⠀⠌
⠀⠈⠉⠛⠛⠉⠉⠉⠉⠉⠙⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠈⢛⡉⠁⠀⠐⠛⠙⣿⡇⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⡀⠀⠀⠀⠀⢄⣴⣤⡀⠀⠀⠀⠈⠳⠂⠀⠀⠀⠀⠉⠀⠀⠉⠀⢀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠹⠿⠷⠶⠀⣠⡄⠀⡠⠯⠫⠎⠻⢂⣤⣦⣤⠐⠿⠟⠶⠀⠁⠀⠀⠀⠀⠠⠤⠀⠀⠠
⠀⠀⠀⠀⠄⠀⠈⠀⠀⠈⠛⠻⢷⣦⣄⣀⣴⡶⣦⣉⣡⡘⠀⠀⠀⠀⠀⠈⠉⠋⠉⡉⠛⠂⠀⠠⠄⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠉⠁⠈⠉⠉⠃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠠⠤⠤⠤⡤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣄⣾⣿⣿⣇⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠒⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⣀⡀
⠀⠀⠀⠀⠿⠛⡿⠿⠿⠿⠿⠟⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠺⠀⠐⠉⠘⠛⣿⣿⣿⡟⠙⠁⠀⠠⠀⠀⠀⠀⠀⠀⡹⠯⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠒⠒⠂⠐⠀⠂⠀⠀⠀⠀⠒⠀⠒
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⡀⠘⠀⢠⠔⢊⡩⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⠀⠐⠀⢱⣀⡟⠀⠞⠀⠀⠀⢀⠀⠀⠀⠀⢀⠄⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠠⠃⠀⠀⠀⠀⣀⣤⠰⠎⢁⡀⢿⠡⠄⢰⠷⠆⠠⠐⠆⠁⠂⡤⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠑⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠈⠃⠀⣧⠀⠠⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⣙⠀⠤⠀⠀⠤⠀⠣⡒⢄⠔⣱⠂⠀⠀⠄⠰⠂⠀⡰⣲⠐⡘⠁⢀⢺⣿⡇⢀⠙⣆⣄⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠘⠛⡆⢠⠀⠀⠀⣄⣀⠝⣺⡔⢦⠴⠦⠄⠠⢤⣭⢼⢞⣃⣠⠂⠂⠘⠘⠉⠁⢈⠑⠛⢾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠄⠀⠀⠀⠀⡁⠘⠿⡇⣤⠄⠀⠀⠀⠀⠀⢻⢆⡁⠀⢠⣠⠆⠀⠀⠀⠛⠀⠈⠿⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡇⠀⠀⠀⠄⠀⠀⠀⢸⠀⠀⢈⡟⢿⡖⠀⠆⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠳⣾⡁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⣠⣾⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠇⠀⠰⠀⠀⠀⢀⠁
⠠⠞⠀⠀⣼⠯⢭⡆⠀⡀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⢰⠀⠀⢠⣄⣿⡀⣠⣀⣼⣦⣆⡄⠀⠀⣦⣾⣷⣀⣤
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣄⣠⣾⠓⠒⠾⢿⠀⢠⡌⣘⡋⠛⠛⠛⠛⠉⣤⡀⠰⢄⡼⠾⢉⣻⡝
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣈⠉⠁⠀⠀⠀⠀⠄⠀⠂⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠐⠀⠀⠀⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂

⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠁
⠂⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠁⠐⠒⠒⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠀⠀⠀⠀⢰⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠤⠄⠠⢤⡄
⣤⣤⣤⣤⣤⣦⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣷⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣁⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠂⠀⠐⢲⣦⡀⢀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⠀⣀⣀⣤⡖⠂⠀⠑⣲⣆⣀⢀⣀⣀⣀⡀
⠀⠀⣯⣉⣉⣛⠛⠿⡿⠿⢛⣛⣛⣛⣻⣯⣟⣻⣛⣯⣿⡷⠀⢠⣯⣉⣉⣛⠛⠿⡿⠿⣛⣟⣛⣛⣻⣭⣟⣛⣻⣽⣿⡇
⠀⠀⣭⣭⣭⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢠⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠛⠛⠋⠉⠉⠉⢛⠛⠛⠛⠙⠛⢛⡉⠛⠛⠛⠛⠛⠃⠀⠈⠛⠛⠉⠉⠉⠙⣟⠛⠛⠋⠉⠉⢙⠉⠛⠛⠙⠛⠛⠃
⠀⠀⠀⠀⠀⣦⠀⣠⣾⠀⠀⠀⠀⠀⢸⣇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣠⣿⠀⠀⠀⠀⠀⣿⣄⢰⡇
⠀⠀⠀⠀⠀⣹⡞⣫⣾⣇⠠⠤⢤⡀⢸⣯⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢞⣡⣿⣄⠤⠤⣤⡄⢿⣯⣻⣧
⠀⠀⠀⢀⠔⢻⣾⣿⠧⠀⢴⡶⠾⠯⠤⢿⣿⣿⠳⣄⠀⠀⠀⠀⠀⡠⠞⣿⣾⡿⠅⠀⠤⡴⠯⠭⠌⢿⣿⣏⠳⣄
⠀⠀⠖⠁⣴⣿⡿⠁⠀⠀⠀⠠⠤⠤⠾⠯⣿⣿⣷⡎⠳⡄⠀⠠⠊⢠⣶⣿⡿⠁⠀⠀⠀⠀⠀⠀⠻⢯⣿⣿⣷⡌⢳⡄
⠀⠀⣴⣿⡿⣿⡉⠉⠉⣉⢉⡉⢉⢉⠉⣉⣛⣻⣿⣿⣇⡈⠀⠀⣶⣿⣟⣟⡉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣛⣻⣿⣿⣧⡁
⠀⠀⣿⣟⣼⠩⠤⠤⠄⠀⢀⣀⣀⣀⣀⡈⣈⣸⣿⣿⣿⣷⠀⠀⣿⢏⡾⠥⢤⡤⠤⠄⢀⣀⡀⣤⡀⠀⣤⣼⡿⣿⣿⡇
⠀⠀⣟⡾⣉⣀⣀⣀⣀⠀⠀⠐⠀⠀⢀⣤⣄⡍⢭⣿⣿⡿⠀⠠⢏⡟⠁⣀⡀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣤⠭⢭⣽⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠃⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠏⠀⠉⠙⢻⣿⣿⣿⡏⠙⠟⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣷⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠿⠽⠿⠛⠿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣸⠟⣿⡿⠋⠘⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠾⠃⠀⠀⠀⠀⠀⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣬⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣏⠉⠉⢀⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣧⣬⣜⣓⠤⡦⠶⠶⠤⣄⣚⣶⠈⠹⠹
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⡤⠈⠙⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠄⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠰⠌⠡⠈⠁⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠃⠀⠀⠀⡀⠤⠖⠀⠩⡯⡄⢰⠦⠄⠌⠄⠐⠠⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠐⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⡀⢀⡈⠀⣸⡀⠠⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⣇⠙⠀⠀⠂⠈⢨⢲⢑⣁⣀⠀⠀⠡⢠⢪⠀⠀⡀⠌⠿⠗⠠⠨⣗⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠘⠡⣿⢄⡁⠀⠀⠈⠉⢹⣘⠋⢁⣀⡄⠀⠀⠴⠀⢸⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⡿⠻⠆⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⢀
⢀⡄⠀⢠⡾⠛⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠠⠀⠀⣀⠀⠀⠀⣸⠀⠀⢠⣅⠀⠁⠀⣀⣴⡀
⠀⠀⠀⠈⠀⠂⠀⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢀⡿⠀⢼⢷⠀⡄⢛⠟⠲⠿⠛⠛⣝⢀⠆⡽⠽⢻⡾
⠀⠀⠀⠀⢀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠠

⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⣷⢂⠀⠀⣠⣠⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⢿⢷⣾⣦⡀⠀⣸⣿⡤⠄⢠⣿⣿⣏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⠀⠀⠠⢾⣿⣿⠳⣄⣨⣿⣷⣤⣾⠋⠉⠀⢀⣤⣶⣀⣀⣰⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣷⣶⣾⣿⣯⣀⣾⣿⣿⣿⣿⣾⡿⢿⣶⣶⣿⣿⣿⣿⣿⣿⣿⠇⢀⣠⣶⡶⠖
⠀⠀⠲⢶⣶⣵⣄⡀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣤⣽⣿⣭⣴⣿⣿⣿⣟⣄⡀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⣀⣉⣙⣻⢿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠃
⠀⣴⡾⠟⠋⠉⠋⠙⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣶⢿⣿⣹⠿⠟⣻⣿⣿⣿⣿⡿⣿⣿⣧⣤⣄⣀
⠀⠁⠀⣀⣤⡴⣶⠿⢛⣿⣿⢻⣿⠟⠻⣿⣿⣿⣿⠀⢹⠀⠀⢈⣿⣾⣿⡿⠛⢻⣿⣍⢻⣮⣝⠋⠛⠋⠻⢿⡆⠀⠀⠀⡀⡀⠀⢠⡄
⠀⠀⢠⣿⠻⠃⠈⠀⣸⣿⡯⠉⢿⡀⠀⠈⢿⡿⠓⠀⢸⡄⠀⢸⣿⠇⠈⠀⠀⢿⣿⡿⠀⠙⢿⣦⠀⠀⠀⠈⠁⠀⠀⢐⢌⠂⢀⢹⣧
⠀⠀⠈⠁⠀⠀⠀⠀⢘⣿⡝⠀⠸⣧⠀⠀⠈⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣷⣅⠠⢨⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⣰⡟⠿⠀⠀⠀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⢙⠿⡐⡅⡿⡔⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⢸⣛⣿⣇⡟⣿⣀⠀⠀⠀⠀⠠⠭⠥⠱⡐⡸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⢸⣿⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⣙⡾⢿⣿⣿⣷⣫⠀⠀⠀⠀⠈⠭⠤⠄⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣷⣤⣤⣼⣿⣤⣤⣾⣟⠁⠀⠀⠀⠀⠀⠀⠈⢩⣭⢿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⠦⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⢀⠐⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡉⢉⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⠸⡇⠉⢠⡇⢀⡄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣮⡛⣦⣿⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠛⠄⠁⠀⠀⠀⣫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣶⣿⣷⣿⢿⡻⠇⠀⠀⠀⠀⠀⡀⠀⠂⠃⠘⣱⣲⣥⠀⠀⠘⠁⠀⠀⠀⠒⠀⠘⠁
⠀⠀⠀⠀⠀⠀⡀⠠⢀⠠⡀⠀⠀⠀⠀⠀⢸⣿⣿⢩⡿⢸⡜⡗⠀⠀⠀⢀⠰⠂⠁⠀⠀⠀⠞⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠡⠁⠃⠀⡀⠀⠀⠉⠁⠘⠁⠋⠁⠀⠀⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣤⡶⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠈⠋⠠⡄⠐⠀⡀⠁⢿⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⣿⣿⢻⣇⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣒⣒⠈⠂⠘⢼⢷⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢠⣄⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣻⣿⣿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢛⣒⣂⠐⢌⢃⠇⡄⠀⠀⠀⠀⠀⠀⢤⣿⣿⣾⣿⣿⣄⡤⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡷⠾⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠭⠿⠥⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⡿⠝⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡻⠗⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡏⠀⠀⠀⣀⣀⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠙⢈⣤⣶⣿⣿⣿⣿⣟⢿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣦⣄⣧⣿⣽⡟⢛⣶⣿⣿⠿⠿⣛⣻⣭⠛⠂⣹⡙⠙⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⡿⢛⣛⣻⣧⡘⣯⣽⣿⣿⣶⣿⢿⣶⣾⣯⠴⣛⡀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⢨⠟⠙⠉⣏⣬⣾⣾⣿⣽⣿⢿⣜⣿⣿⣿⣿⣿⣏⣻⣫⣿⣿⣿⣿⣿⣶⣦⡤
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⢏⣿⣿⣿⣿⣼⣿⣞⢿⣽⢿⣿⣿⣿⣯⣽⡏⡿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡝⣾⣿⣿⣿⡛⣿⣿⣷⣫⣿⣸⢉⢿⢻⣿⣿⡇⠇⠛⠛⣿⠿
⠀⠀⠀⠀⠀⢠⣿⣿⣿⠍⢏⢹⣿⣿⢿⢿⡳⣿⣿⡿⣟⢹⣇⠀⠁⢸⢿⣿⣿⡳⠀⠀⠈
⠀⠀⠀⠀⠀⢸⠃⠁⠈⠀⠀⣿⣿⣿⣆⠙⠁⢻⣿⡓⠦⠀⣿⠀⠀⠀⠈⠋⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⡜⢎⠁⠀⠸⣿⡷⠤⠀⣿⣧⣾⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⣀⣘⣡⢾⣿⢿⡧⠉⠟⢿⡙⢿⣟⠛⠋⠓⠦⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣖⣒⣛⡻⠋⠐⠋⠹⢼⡇⣀⣀⣀⡣⢀⠋⠙⣂⡐⠦⢬⡛⢶⡽⢷⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⣀⣤⣀⡀⠀⠉⢉⣉⠉⠉⠉⠿⠿⠿⠯⡽⠷⡶⣸⡯⣁⡈⣍⠁⠨⠽⢿⢋⣙⣷⣽⡿⠿⠛⠛⠛⠋⠉⠉⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣀⣤⠶⠶⠒⠒⠂⠀⠀⠉⠉⣿⡇⢀⡄⣼⣿⢀⡆⣠⠆⠠⠤⢤⣵⣒⣛⣛⣛⢛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣿⠁⣼⢡⢇⣇⣼⢞⡕⣆⡀⠒⠒⠒⣶⣿⣿⣷⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣬⠍⢀⡞⣸⡄⡴⢮⡘⢷⣿⣦⣄⣀⣈⣿⣟⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠊⠉⠀⣨⠟⠋⠋⠀⠘⠳⠑⠃⠙⠂⠈⠙⠛⠛⠻⠽⠿⠿⠟⠛⠛⠉⠁

⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇
⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⡇⠀⠀⠀⠀⠀⠀⠠⠀⠠⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀⡀⣀⡠⠄⠠⠄⠀⠀⠀⠀⠀⠒⠈⠐
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠈⠁⠂
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠂⠄⢀⡀⠀⢀⠀⡆⠀⠀⠀⠂⠀⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠐⠀⠀⠀⡀⠀⣤⠠⠀⢀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⣦⣄⡄⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢡⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⡇⠀⠀⡀⠀⠀⠀⠀⢰⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣳⡤⡀⠀⣿⠀⠀⢻⣦⢀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⡆⢃⠈⠲⣿⡀⠀⢸⠋⠀⠑⣦⣠⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢢⣿⡀⠀⡔⠀⠀⠀⠈⣽⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠃⠀⠀⠀⠈⠸⣯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⣿⣸⡰⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣿⠿⠇⠀⠀⠀⠀⠀⠀⣿⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⣬⠆⠀⠀⠀⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠃⠀⠀⠀⠀⠀⠀⡤⠌⠀⠄⠙
⠀⠀⠀⠀⠀⠀⣘⡁⠀⠀⠀⠀⣈⣺⣿⣇⡠⠀⠀⠀⠀⠀⠀⣿⣇⢸⠀⠀⠀⠀⠐⣢⡄
⠀⠀⠀⠀⠀⣰⡿⠁⡠⠀⠀⠀⠈⠹⣿⣥⣬⡟⢋⣠⡁⣀⠀⣹⣿⣄⠀⢀⣡⣴⣾⠏
⠀⠀⠀⠀⠠⠟⠹⠋⠀⠈⠀⠉⠉⠛⣿⣿⣿⡇⠀⠀⠀⠀⣀⣽⣫⣤⣾⣿⣿⣿⡏⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣇⣀⣿⣇⣠⣴⣶⣿⣿⢿⠟⣛⡈⢀⠙⢠⣞
⣶⣶⣶⣤⡐⠄⣀⠀⢀⡀⠀⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠿⣟⣻⣤⣼⡇⣼⣿⡄⣾⣄⠀⠀⠀⠀⢀
⠿⠿⠿⠍⠁⠀⠠⣤⣈⡛⠲⢦⣽⣿⣿⣯⣿⣿⣭⣾⣿⣿⣷⣤⣶⣿⣿⣿⣿⡆⢻⠁⠀⣿⣿⡿⢿⣾⣿⣜⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣦⡈⠙⠛⠛⠿⣭⡭⠉⠁⠀⠀⠈⠙⠂⠈⠉⠀⠀⠀⠀⠀⢻⣿⡟⠀⠸⣭⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⡿⢿⠿⣦⡀⠠⠄⠀⠀⠀⢀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣦⣭⣽⢄⠀⠀⠠⠾⠯⠟⠻⠻⣇
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⣿⠿⢿⡷⠛⠉⠀⣤⠘⣄⠤⣤⣥⣀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠘⠓⠋⠁⢀⡴⠋⠀⠀⢠⡈⠽⡄⣿⡆⠙⢻⠋⢾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠌⣠⠉⢿⣿⡄⠀⠘⢺⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⡐⠀⣿⠀⢸⣿⡇
⣀⣀⣀⣤⣤⣤⣤⣤⣠⠏⠀⢠⣤⣀⣠⡌⢁⣄⠸⢤⣠⢿⡇⠀⣀⣠⣀⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣀⣀⣀⣀⣀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⠀⠚⠛⢋⡲⠈⠈⠓⠿⠿⠆⢻⡇⠀⠀⠈⠉⠀⠉⠉⠉⠉⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠁⠀⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⣀⣀⡀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠒⠠⠤⠤⠀⣤⡀⠀⠀⠀⢀⡐⠈⠉⠉⠀⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⢀⠀⢉⣁⡛⠓⠤⢤⠤⠀⠀⣠⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⠲⠦⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠛⠛⠷⠶
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢀⣠⠐⠂
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠐⠀⢙⣀⣐⣀⣀⡀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣷⣶⣾⠖
⠀⠀⠀⠀⠀⠸⣷⣶⣦⣤⢠⡀⠀⣀⣾⣿⢿⣿⠿
⠀⠀⡀⣀⣤⣤⣤⡘⢿⣿⣿⣿⣾⣿⣿⣣⢿⣿⣱⣾⣿⣿⣿⣦⣤
⠀⠸⢟⣿⣿⡿⣿⣷⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡏⠉
⠀⠀⠀⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⠻⠛⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠈⠹⢳⢫⣟⡿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠙⣴⣆⢀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣄⣶⣶⠀⣀⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣘⣿⣿⣿⣿⣿⣿⣤⣀⣀⣤⣾⡄⠀⠰⢶⣯⣵⣾⣿⣿⡀⠀⠹⣶⣾⢀⢀⣼⣖⡒⠄⠀⠰⣷⣦⣤⣤⡄
⠀⠀⠀⠀⠀⢠⣤⡤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣄⣿⣿⣿⣷⣧⣼⣿⣿⣴⣶⣿⣿⣷⣿⣿⣤⣤⡀
⠀⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⢠⣀⡄⢷⣾⠾⡅⠀⠀⠀⠀⠀⠀⠀⢚⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠠⡇⠀⠀⠀⠄⠀⠀⢀⠎⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢠⠋⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⡠⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢴⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⠤
⠀⠀⠀⢀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣦⣤⣇⣀⠄⠀⠀⢀⣼⣿⡿⠀⠀⢀⣀⠄⠄⠐⢻⣿⣿⢑⣾⠄⠀⠒
⠀⠀⠀⠀⠀⠒⠀⠒⠂⠀⠭⣖⣊⡭⠽⢟⣿⣹⣿⣿⣷⣶⣾⣿⣛⣁⠀⡁⠤⠠⢖⠒⢀⣈⣻⠃⠘⡁⠀⠀⠒⠀⠤⠄⠁
⠀⠀⠀⠀⡀⠬⠢⠴⠒⠤⠤⢽⣿⣿⣿⣷⣲⣶⣦⡤⠤⡤⠤⢤⣄⣀⣀⣈⣨⣑⣮⣧⣿⣶⡿⠤⠀⢱⠀⠌⠉⠡⠤⠤
⠀⠉⠁⠭⠿⠶⠶⠶⣤⣤⣬⡍⠉⠙⠛⠻⠿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⠑⠢⠄⢸⣄⣀⣀⠀⠤⠀⣀
⠀⠀⠀⠐⠚⠉⠓⠀⠀⠘⠛⠩⠟⠓⠂⠐⠓⠐⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠛⠢⠴⠐⠒⠒⠉⠳⠀⢠⣀⣀⣤⡄⠤⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⣿⣿⠿⠿⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣾⣷⣿⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⢦⡓⣆⢀⡤⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠀⠀⣀⢣
⠀⠀⠈⣄⠀⠀⢷⠀⠀⠄⠀⠀⣠⠂⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠊⠁⠒⢠⡻⠴⢰⡂⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⡐⠁
⡀⢐⠀⠘⡆⠀⢸⠀⠀⠐⠀⡜⠁⠀⠀⠀⠀⡛⢼⠄⠀⠓⠀⢀⢠⠔⠀⠁⡙⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡅
⡁⠌⠄⠀⠸⡀⠈⣷⢤⣠⡎⠁⠀⠀⠀⠀⠀⠘⢿⠂⠀⠈⠁⣄⠀⠀⠘⠀⠁⠀⠒⠆⠀⢄⠀⠀⠀⠂⠐⢠⠘⠀⠉⠳⢤⡄⠠
⢘⠇⢰⠊⠀⢗⡀⠉⠀⣞⠀⠀⢈⡡⠖⠒⠉⠉⢻⡄⠀⠀⠀⠈⠂⠀⠀⠀⢹⡃⠐⠚⠚⠈⣴⢞⠠⣦⡲⠂⣤⣶⡶⣴⣿⣿⣾
⡮⡀⠻⢄⡀⠈⢧⡄⢠⠋⢀⠔⠉⠁⠀⠀⠀⢀⠠⠣⠀⠀⠀⠀⡀⠀⠀⠃⠼⣽⠉⣉⡯⢠⠉⠉⠁⠉⠡⣾⣿⣿⣿⡿⣿⣿⣿
⡇⡃⡀⠀⠒⣷⠀⠸⠚⠠⢇⠀⠀⢀⡠⠌⠺⡋⡀⠠⠀⠤⠄⠀⠁⠀⠀⠀⠀⢸⠀⠀⠁⠀⠦⠀⠀⠀⠀⠀⠊⡌⠃⠀⠈⡇
⣧⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⢉⠁⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡀⠀⠐⠄⠀⠀⠐⠀⠹⣏⠤⠂⡞⠤
⣼⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠠⠀⠀⠈⠀⠀⡀⠁⡀⠀⠀⠀⠐⠄⠀⠀⢸⢰⠆⡀⡅⠀⠀⠀⠀⠂⠔⠀⠀⡀⠀⢀⡅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡗⠙⠋⠃⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠋⠙⢛⡛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠶⠖⠲⠒⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠶⠒⠒⠒⠒⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⠃
⠠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠠⠷⠛⣦⣠⣶⠦⠀⠀⡠⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⡤⠤⢤⣄
⢶⡿⢿⣿⢿⣿⣷⣂⡀⣀⡀⢈⣲⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⡿⡬⠨⠡⠁⠊⠑⢤⡀
⢀⡇⢠⣽⢸⣿⣏⣻⡿⠉⣽⣏⠉⠀⠀⠀⡞⠳⠀⠀⣿⣿⣿⡏⢺⠳⣾⠛⡛⣲⡚⠟
⠀⠠⠜⠲⣾⡟⠉⠉⢂⠀⠄⠡⣶⣄⣠⡤⣿⣟⣳⣤⣼⣿⣿⢄⠸⣿⣿⡴⡇⢡⡷⠖⠀⡀
⠀⠄⢀⣔⠉⠁⠀⠐⠙⣛⣀⡤⢾⡡⠀⠀⠀⢈⡉⠙⠻⠾⠡⠀⠛⠀⠉⢀⣯⡀⠀⠀⠓⢈⡇
⠀⠀⣡⣯⠀⢀⡤⡾⠿⢿⣏⠁⣄⠀⡤⡤⢾⡏⠋⠁⠀⠒⠛⢶⣄⡀⠀⠊⠁⢑⡶⠀⢀⠀⠼⠑⠄
⠀⢨⡿⠀⠀⣀⠛⠀⣄⠀⣉⠉⠀⠔⡑⠂⠀⠀⠀⠀⣀⣤⡤⠾⠛⢀⣠⡶⠔⠛⠃⢴⡁⢌⠀⢀⣀⣦⠄⣀
⠀⠈⠀⠀⠸⣁⣀⠰⠛⠁⠈⠋⠀⢀⣤⠤⠤⠆⠀⠉⠟⠉⠀⢀⣤⠾⡏⠀⢀⡤⠀⠊⠁⠀⠀⠘⠃⠉⠀⠀⠀⠄
⠀⠀⠀⣄⡾⠋⠉⠁⢲⠚⠓⠒⠲⠟⡟⠙⠃⠀⠀⠀⠀⠈⡆⠉⠀⠀⣛⠓⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⡀
⠀⠀⠀⠋⠀⠀⠠⠄⡁⢀⢠⡀⠠⠀⠧⣀⠀⠄⠀⠀⠀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠⠀⠀⡶⠖⠁⣀⠟⠛⠫⣄⠌⠢
⠀⠀⠠⢤⠀⠀⠀⠀⠀⠀⠀⠘⢤⠀⠀⠉⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⠉⢀⡜⠐⠋⠉⠀⠈⠷⠚⠉⠀⠀⠈
⠀⠀⢀⣤⣽⡃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠠⣤⠢⡀
⠀⠘⠁⡀⠀⣹⠋⠀⠉⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠉⠙⠗⠀⠚
⠀⠀⠀⠀⠘⠛⠐⠤⢀⠀⢁⠰⠿⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠉⠂⠀⠀⠀⠀⠀⢀⣠⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⢷⡉⠁⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠉⠐⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⢸⡇⠀⠀⢠⡄⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴
⠀⠀⠀⠀⠀⠈⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠘⣆⠀⠀⠀⢸⡇⠀⠀⡿⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⢆⠀⠈⠳⡀⠀⠀⠘⣆⠀⡄⢸⡇⡆⢰⠇⡤⠀⣠⠋⠀⠀⢀⡴⠆⠀⠀⢀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠑⢄⠀⠙⢆⠘⣆⠘⡄⡇⢸⠀⠃⡏⡼⢁⡴⢁⡔⢀⡴⠋⠀⢀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⢠⡑⢌⠠⠣⡈⠂⠁⠀⢸⠀⠀⠐⢡⠎⡠⢋⠔⠋⢀⡠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⡀⠀⠀⢉⠲⢌⠢⠀⠀⢈⠀⠂⣁⣈⣈⠀⠐⢁⠈⠀⢁⡤⠞⢉⡠⠀⠀⣀⣠⠴⠖
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠈⠉⠙⠲⠤⣉⠂⠈⢂⠔⢁⠔⠉⠀⠀⠀⠈⠐⢄⠠⡒⠁⠐⢊⠁⠤⠒⠉⠁⠀⠀⠀⠀⠀⢀⣠⣄⣀⡀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠓⠒⠶⠦⠬⠅⣀⣀⡀⠂⢠⠇⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠈⣀⠀⠤⠴⠖⣒⠿⠥⠖⠛⠓⠋⠀⠀⠉⠉⠉⠁⠀⠈⠉⠁
⠀⣀⣀⣀⣀⣄⣤⠴⠒⠒⠒⠒⠒⠶⢤⡀⠀⠀⠒⠀⠀⠀⠉⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣀⣀⣀⡒⢀⣠⠼⠃
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⢤⡀⠀⠀⠈⠀⢣⣀⣤⡤⣄⣀⡤⠴⠚⠉⠁⠉⠉⠀⢠⡞⠁⣀⠴⠀⠐⠂⠖⠂⠀⠀⠀⠀⠀⢠⡄⠠⠄
⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠙⠒⠪⣉⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠚⢉⠰⠲⠁⠀⣀⠀⢀⡤⠴⠚⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠒⠂⠠⠤⠄⢈⡓⠁⠐⠀⠓⠻⣲⣭⣀⠉⠉⠉⠉⠉⢩⠟⢁⠀⠀⠀⠀⠉⠀⠀⠈⠓⡂⢬⠖⠲⣤⠤⢤
⠀⠀⠐⠒⠀⠛⠃⠈⠃⠀⠐⠂⠈⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⣰⡟⠉⡴⡀⢴⣐⣋⡂⠆⠀⠀⠐⢉⠀⠞⠁⠀⠐⠳⠶⠎⠡⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠚⣁⣀⣜⣫⡶⠛⠉⠙⠋⠁⠉⠉⠳⠶⠶⠶⠦⠖⠛⠒⠲⠶⠶⠶⠶⠶⠧⠿⢦
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡠⠤⠴⠶⠶⠚⠭⠭⠍⠭⠟⠉⠉⢰⡄⠒⠐⠒⠒⠊⠉⠐⠒⠊⠉⠉⠉⠁⠁
⠀⠀⠀⠀⠰⠾⠋⠉⠉⠁⠀⠀⠀⠀⠉⠹⠦⢤⠀⠀⠀⠀⠐⠶⠞⠺⠭⠥⠥⠄⠠⠀⠀⠀⠀⠀⠀⠘⠛⠓⠒⠒⠒⠛⠋⠀⠀⠙⠛⠛⠛

⠀⠤⣤⡄⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⢤⡀⠤⣤⠀⠤⢤⠤⠤⣤⣤⣤⣤⣀⠠⣤⡤⣤⣤⣤⣤⡤⣤⣤⢤⣤⣤⣤⣤
⠉⣝⣛⣋⣻⣿⣭⣽⣿⣿⣿⣿⣿⣯⣽⡿⢿⣿⣷⡶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣶⣾⣿⣿⠿⢿⣿⣿⣿⣿⡿⠿⠿⣒
⣈⣹⢛⡛⣛⣛⣲⣞⠿⢿⣿⡟⠛⢷⣿⣿⣿⣿⣿⡭⠽⠟⣉⡻⠿⠛⠛⠻⠿⣯⠉⠙⠛⠀⠰⠒⡋⠛⠒⠂⠀⠀⠆⠉⠉
⣉⠉⠁⠀⠀⠀⠒⠚⠓⢂⣀⡀⠘⠛⠛⠃⠀⢀⠀⠀⠒⠀⠀⠁⠒⠢⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⡀
⠉⠁⠀⠀⠀⠐⠂⠆⠈⠉⠉⠉⠀⠀⠀⠀⠤⣩⣁⣀⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠒⠒⠚⠀⠀⠀⠀⠠
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣷⣶⣄⣠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠀⠀⠀⠀⣀
⠻⠿⠛⠛⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠁⠀⠀⠰⣷⣿
⢰⣦⣄⠈⣹⡉⠁⠀⣠⣤⡁⠀⢸⣿⠇⠀⠀⠀⠉⠁⢀⡀⠀⠀⠀⠀⠀⠉⠛⢓⣆⡈⠐⠂⠀⠀⠀⠐⠛⠿⠒⡆⢀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠺⠷⠄⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠊⣀⠤⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⡀⠀⠀⣀⡀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠂⡀⠀⡠⠃⠀⢆⡁⠀⠈⠈⠉⡟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⠐⢆⠀⠉⠉⠋⠙⣗⣛⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⠠⠁⠀⠀⠀⠘⠀⠀⠀⠚⠋⠉⠉⡉⠉⠀⠙⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⠀⠂⣀⠀⡄⣀⠔⠶⠬⠬⠧⠤⠧⣄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠂⠙⠈⠁⠙⣚⠢⠄⠀⠀⡄⠀⠆⠋⠄⢠⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡉⠀⠀⠈⠁⠀⠈⠀⠀⢀⡗⠀⠂⠀⠟⠓⠚⠓⠛⢢⡄⠄⠀⢈⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢊⠀⠀⠑⠀⢐⡄⡂⠡⠀⠀⠠⠀⣃⡂⠐⡆⠀⢃⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠂⢀⡀⠐⠀⠀⠀⠀⡀⠤⠀⠦⠄⡇⠀⡗⠈⠀⠐⠐⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠉⠉⠀⠀⠀⠀⢀⠀⠀⠤⠠⠧
⠀⠀⣠⣶⡾⢿⡿⠿⠿⣶⣦⡀
⠀⠀⢿⣿⣻⣟⣿⣟⣟⣿⣿⠇
⠀⠀⠀⠈⠉⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠤⣴⠀⠀⠈⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⣤⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡂⢶⡀⢀⠀⠰⠀⠥⡿⢈⠋⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⡅⢀⣤⡀⡆⠀⠈⠰⡿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡤⠀⠈⠙⠇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⠁⠀⠀⠀⠀⣰⠀⠄⠀⣤⠀⡀
⠠⠤⠤⢤⣤⣄⣤⣤⣄⣀⣤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠺⠣⡤⢿⡇⣩⠿⡆⠐⠟⢃⣸⢻
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠘⡀⢳⡀⠹⠞⢸⠠
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠂
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠉


⠀⡀⡀⡀⣀⣀⣀⡀⢀⣀⠀⢀⢀⡀⡀⣀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⢀⡀⠀⠀⠀⡀⡀⠀⣀⠀⡀
⣿⣿⢛⠿⢛⠛⢿⢟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠄⠛⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠁⡀⢀⣀⢠⣀⠠
⠀⠀⠀⠀⠈⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢀⡀⢘⠂
⠀⠈⠄⠠⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⢀⡀⣀⠠⠤⠐⠒⠒⠒⠦⠤⣀
⠀⠀⠀⠀⠀⠀⣀⡀⣠⣔⣀⡂⠐⢀⠰⠤⠀⠚⠛⠉⢁⡐⠢⡀⠀⠀⣀⠤⠶⠒⠙⠒⠚⠓⠒⠲⠤⠤⣀
⠀⠀⠄⠂⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠉⠁⠀⠀⢁⣀⠥⠤⣁⣉⡐⠒⠲⠀⡀⣀⡠⠤⠄⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⢀⣀⡠⠤⠤⠑⠐⠒⠚⠃⠀⠈⠑⣄⣀⠤⠉⠁⠠⢍⡀⠀⠀⠀⠀⠀⠈
⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⢀⣀⡀⠠⠄⠀⣀⡀⡀⣈⡆⡴⠒⠉⠉⠀⢄⠀⠀⠀⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠠⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠈⢦⡠⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⢠⣤⡀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⢿⠞⣋⣩⡽⣿⡷⡂⣄⣤⠀⠀⠀⠀⠀⠀⡤⡀
⠀⠀⠀⠀⠀⢰⣻⣧⡾⢻⠿⠛⠛⢬⡙⣿⣷⣞⠿⣿⡦⢤⣤⠴⣉⢻⣷⣤⡄⣤
⠀⠀⠀⠐⠀⠊⠉⠉⡂⢸⣄⣤⣴⣿⣿⣈⣿⣿⣦⢿⣿⣾⣿⣿⣿⣿⣿⣭⣻⣿⣷⠦⡄
⠀⢀⣾⡶⢯⢻⣤⠉⠋⣿⢿⣿⣿⣿⣿⣿⠻⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠻⣶⣿⣄
⠀⣯⣿⡞⢱⣼⣿⣶⠼⢻⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣟⢡⡀
⣸⣻⣯⣘⣿⡻⠿⢛⠘⡿⣇⢹⡿⠿⣿⣿⣧⣸⣿⣿⣾⣿⣿⣿⡝⠟⣿⣿⣿⣿⣿⣿⣿⣌⢿⠳⡀
⣿⣿⣿⣿⡞⢻⡼⣿⣇⠦⠚⡈⣧⠀⠀⠀⠹⡟⣿⣿⢻⣿⣿⣿⣷⡀⠈⣿⡿⣿⣿⢽⣿⣿⣆⢲⣷
⣥⣿⣿⣷⡵⣼⣇⢸⠀⠀⠀⠐⠸⣆⠀⠀⠀⣿⣿⣿⣾⣿⣿⣿⣿⡇⠀⠹⡟⣯⢹⡘⠙⣿⣿⣇⢻⣧
⠸⢫⢿⣸⣿⡇⣹⡎⢧⠀⠀⠀⠀⣘⣆⠀⠀⣧⣼⣿⣿⣿⣟⢿⣿⣷⠀⡀⠘⢤⠀⠹⢀⣸⣷⣽⣄⣿⡇
⠀⣾⣿⣿⠙⣷⣿⢿⡞⢧⠀⠀⠀⠈⠈⣷⣴⣿⣿⣿⣿⣿⡇⢸⣿⣿⠆⠀⠀⠈⠗⠀⡸⠓⢿⣿⢿⠸⣿
⠀⠘⡱⣿⣷⣞⣿⣹⣿⣦⡱⣤⣀⣀⣤⣼⣾⣿⣿⣿⣼⣿⣗⠀⢯⣿⡆⠀⠀⠀⠀⠀⢱⠀⠘⣿⠺⡄⢻
⠀⠀⠹⣿⣿⣿⣄⣱⣶⡎⠻⣧⣍⣻⣿⣿⣿⣿⣿⡿⣿⢻⣟⠁⠘⡿⡇⠀⠀⠀⠀⠀⠀⢤⡀⢿⣣⣧⣸
⠀⠀⠀⠘⢬⣿⣿⣿⣦⣌⣻⡛⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡇⢸⡷⠆⠀⠀⠀⠀⠀⠀⡟⠋⣿⡟⣿⣿
⠀⠀⠀⠀⠀⠙⢯⣙⣿⣿⣿⣿⠋⠉⠁⠈⠉⢻⣿⣿⣿⣟⢄⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠷⣶⣿⣗⣸⠻
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣶⣖⠂⠀⠀⠀⠉⣿⣿⣿⣿⡇⠀⡼⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢉⣿⡿⠀⠀⠀⠀⣀⣿⣏⣿⢿⡇⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠁⠉⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠒⠀⣹⣿⣧⣯⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢤⣿⣿⣿⡿⠝⠀⢀⣀⡠⠂⠀⠠⠂⠀⢠⣜⠻⠟⣷⣶⢁⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡠⣾⣿⣿⡿⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠐⣿⣿⣧⣄⠛⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠐⠠⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠾⣻⠗⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡧⣷⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡹⡄⢉⠻⢶⣦⠄⠀⢀⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡉⠀⠀⠀⠀⠐⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣠⣶⢀⣾⡞⣠⠋⢠⣆⢄⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡇
⠀⠀⠀⢀⠀⢸⣿⡇⣼⣿⢱⠏⣴⣿⣿⣿⣵⣿⣾⣷⣞⡤⠄⠀⠀⠀⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⠇⠀⠀⠘⢷⡀⣆⢀⡀
⠀⠀⡀⢸⠀⣿⢻⣳⣿⠇⢏⣾⢿⢿⡻⢙⠙⣻⣿⣿⡖⠂⠀⠀⠀⠀⣻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡷⠀⠀⠀⠹⢆⠀⠘⢼⣇⣾⡀
⠀⠀⣘⣮⡇⠻⢈⡡⠳⢬⣿⣾⣶⣿⣿⣿⣿⡻⢿⡿⠍⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠿⠁⠀⠀⠈⢥⣒⣶⡄⠀⢸⡷⣜⡆
⠀⠀⠈⣮⠲⡊⣤⡰⣝⠲⣬⡛⠿⠿⣿⡻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣐⣒⣊⠀⠀⠈⡿⡁
⠀⠀⠁⠀⢧⣟⢾⣿⣮⡳⢄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠚⣛⣃⠀⠀⠈
⠀⠀⠀⠀⠘⢟⢆⠻⢧⠉⠀⠀⢀⣀⣀⣤⢖⣤⣄⣠⡄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡄⢀⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡞⠭⢩⠿⠅⣙⣻⣟⡿⣿⣿⡿⣖⣢⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠙⠓⠺⠿⣿⣿⢿⣷⢶⣦⣶⣌⣭⣿⣖⡂⠀⠀⠀⠉⠛⠿⣿⠃⠀⠻⣿⣿⠿⠋⢀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠙⠛⠋⠊⠻⠛⠗⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⡏⢀⣠⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢁⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⢄⠘⡄⢆⢰⠀⡇⠀⡀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⠀⢹⣿⠀⢸⣦⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⢠⣷⣷⣆⣦
⠀⠀⠀⡀⠐⣌⢦⢹⡸⣜⡆⡇⢰⠇⡠⠀⠀⠀⠀⠸⣷⣬⣿⣿⣧⣼⣿⠀⣼⣿⡟⢰⣆⠀⠀⠀⠀⢹⠟⠁⠀⣀⣄⠀⠀⠀⠀⠀⠘⣻⣿⣟⣿⡦⡀⡄
⠀⠀⠀⢌⡳⣌⢳⣷⣷⣿⣧⡇⣾⣼⠃⡠⠂⠀⠀⢠⣈⠉⠙⠻⣿⣿⡇⢠⣿⡿⣡⣿⠏⡀⠀⠀⠰⠁⢠⣶⠸⣿⣿⢟⣤⠀⠀⠀⠀⠚⣿⣿⡏⢹⣿⣧⡄
⠀⠀⠀⠤⣍⣲⢵⣿⣿⣿⣿⣷⣿⣣⢞⣡⠖⠁⠀⠸⢿⣿⣶⣶⣷⣾⢿⣿⣯⣴⡿⣣⣾⡷⠀⠀⢰⣿⡎⢻⣧⣿⣷⡾⢋⣴⣆⠀⠀⠀⢹⣿⣷⡈⠛⣿⣇
⠀⠀⠈⣙⣒⣻⠿⣿⣿⣿⣿⣿⣿⣿⡫⠔⠒⠁⠀⢰⣶⣦⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⣾⣌⢿⣿⣤⣿⣿⣿⣶⣿⠿⠋⡀⠀⠀⠀⢻⣿⣧⠀⢻⣿⡇
⠀⠀⣉⣉⣩⣭⠭⣽⣿⡿⠛⠋⠛⠛⠛⠉⠉⠀⠀⠀⠉⣛⣛⣋⣭⣴⡿⣿⣿⠀⠈⠁⠀⠀⢈⠿⣿⣦⣽⣿⣿⣿⣿⣥⣤⣴⣾⣷⠀⠀⠀⠀⢙⣿⣋⡤⣿⡷
⠀⠀⠀⠀⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣛⣭⣾⡿⠋⠀⢠⡀⠀⠀⢻⣷⣌⠙⣿⣿⣿⣿⣿⠛⠛⠛⢛⣡⠀⠀⠀⠀⠀⠺⣧⢼⣿⠅
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⣼⣿⣦⡄⠀⣭⣛⣻⣿⣿⣿⣿⣿⡿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⢠⡅
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⣿⣾⡥⠈⠛⠿⠿⠟⠁⠙⢿⣿⣷⡶⠆
⠀⠀⠀⠀⢀⡔⡆⠲⣶⣶⣶⣦⡀⠀⠀⠀⠀⣀⣠⣤⣄⣤⢠⣤⡀⢀⠀⠀⠀⠀⠸⠿⠷⡾⣿⢃⡄
⠀⠀⢀⣴⣿⠆⠘⠀⢽⣿⣷⣶⣤⠄⠀⠀⠀⠹⣿⣿⣿⣽⣫⡿⣷⢽⣾⣧⡆⠀⠈⣉⣛⣻⣣⣿⣴⢂⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀⣸⠀⡆⡄⡠
⠀⠀⡰⠫⢣⣞⢄⢡⠀⠠⢭⣫⢟⣿⡀⠀⠀⠀⠀⠉⠛⠿⣿⢿⣵⢏⡼⢿⡟⣿⠀⠀⠴⢿⣾⣾⣣⡟⣴⠀⠀⠀⠀⠠⡈⢦⣢⣆⣶⣿⣾⡸⡱⢃⡔⠁⡀
⠀⠀⠀⢁⠏⣾⢧⠀⠱⡈⠭⠾⣿⣾⣝⠂⠀⠀⠀⠀⠀⠀⠀⠉⠘⢻⠷⣿⡷⢛⣼⠃⠀⠉⠽⠿⣿⣾⡷⠀⠀⠀⠀⠢⣌⡳⣽⣿⣿⣿⣿⣿⡵⣫⠴⢋
⠀⠀⠀⠀⠁⠘⣾⠀⣴⠐⢀⠉⣽⣿⣿⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠚⠋⠀⠀⠀⠀⠀⠀⠉⠀⠑⠀⠀⠀⠀⠐⠢⠭⢾⣿⣿⣿⣿⣿⣿⣓⣋⣁⡀
⠀⠀⠀⠀⠀⠀⢸⢠⣿⡎⣴⣐⠄⡛⡿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣷⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣟⠳⠦⠤⠄
⠀⠀⠀⠀⠀⠀⠘⠀⠸⠣⠃⢿⣿⣕⢶⣽⣖⡀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠈⠓⠌⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠂⠛⠛⠓⠀⢠⡶⠿⠿⠿⠋⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⠛⠿⠻⠿⠟⠙⠦

⠀⠀⠀⠀⠀⡃⠀⠀⡠⢶⠀⢰⠐⠆⣀
⡀⠀⠀⠠⠊⠐⠋⠀⠁⠀⠇⠀⠀⠀⠈⠓
⠀⠲⡌⠀⠐⠀⠀⡨⠀⣀⠀⣴⠋
⠀⠀⠀⠀⠂⠀⠙⠇⠈⠋⣰⡿⠟⠁⢠⡾⠂⠀⠀⢀⡀⠀⠀⢀
⠈⠁⣦⡀⠀⠠⢴⢤⡀⢾⠡⣼⣷⡥⣈⣁⠀⠰⣤⣬⠁⡀⠐⠾⢷⡆
⠀⢰⡀⡄⠁⣠⡟⢀⠀⠀⠀⠁⢠⠘⠿⠻⠂⡸⠉⠛⠀⠀⠀⢠⡄⠀⠾⡆
⡀⠀⠤⢡⠀⠀⡂⠀⠀⠀⠀⠀⢸⠀⢸⠀⢰⠀⠀⠀⠀⠀⠀⠀⠂⠠
⠀⠀⠀⠀⠂⠀⡄⠀⠀⠀⠀⢀⠼⠀⠚⠐⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠐⠒
⠀⠀⠀⠀⢀⢐⠁⠀⠀⠂⠀⣀⣠⣤⣤⣴⣶⣶⣶⣷⣷⠶⠶⢶⣶⠶⠶⠶⠶⠶⠟⠋⠁
⠄⠄⠂⠆⣼⠈⠀⣀⣴⣶⣿⡿⠿⠟⠋⠉⠙⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠃⠙⠛⠫⢽⠛⡀
⡀⠈⠉⠁⠀⡁⠐⠀⠠⢤⣀⢀⠀⠉⠙⠠⣤⣀
⠀⠀⠴⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠉⠀⠐
⠀⠀⠀⠲⠄⠀⠀⠀⠀⠋⠁⠋⠀⢀⡀⠀⠈⠉⠁⠀⢀⣅⡀⠀⠶⠄⠀⠀⠀⢀⠀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⢠⠀⠇⢠⠄⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⢀⡴⠲⡄⣠⠖⢦⡀⣰⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣡⠖⠛⣿⣟⢦⡁⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⠉⣠⢤⡉⢉⡴⣄⠉⣡⢤⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⢴⡇⠀⠀⢀⠝⣿⣿⠰⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠙⠋⠀⠈⠛⠁⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡘⣧⠀⣶⣟⡿⢭⡿⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⡌⢛⠶⠶⢶⠛⣄⠙⠃⠀⠀⠀⠀⠀⠀⠀⢰⠏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠃⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⢁⣠⠴⠖⠶⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠶⢬⡷⠺⣏⣀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⢲⡶⠾⣆⣠⣾⣉⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⡴⡏⠈⡇⠹⡍⠓⠺⠇⢀⣀⣀⠀⠀⣰⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡴⠋⠀⢻⡀⣧⠀⠹⡄⠀⠀⠀⠻⣍⠓⣤⡇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⢻⠀⠀⢹⡀⠀⢠⣖⣛⣻⣏⢹⡗⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⣇⠀⠈⣩⠟⣹⢋⣯⠙⣏⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢿⠀⡼⠁⢰⡷⠚⠈⢧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣀⣀⣀⣼⣾⠁⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣛⣻⣭⣿⣭⣭⣭⣭⣭⡛⣛⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⢀⣠⣄⠀⢀⣤⣀⠀⣠⣦⣠⣾⣿⣧⣚⣫⣶⣎⣙⣱⣾⣙⣛⣵⣮⣙⣫⣶⣝⣳⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢉⣤⠉⠉⣡⣌⠉⠉⣤⡉⠉⢉⣄⠉⠉⣡⣌⠉⠉⣤⡉⠉⢉⣄⠉⠉⣡⣌⠉⠉⣤⡉⠉⢉⣄⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⣉⠛⠛⢉⡉⠛⠛⣉⠙⠛⠋⣉⠛⠛⢉⡉⠛⠛⣉⠙⠛⠋⣈⠛⠛⢉⡉⠛⠛⣉⠙⠛⠋⣈⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣚⣙⣓⣒⣋⣙⣲⣚⣋⣓⣖⣚⣙⣓⣒⣋⣙⣲⣚⣋⣓⣖⣚⣙⣓⣒⣋⣙⣲⣚⣋⣓⣖⣚⣙⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠘⠙⠰⡀⠄⠀⡴