Skillet Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠒⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄
⡎⠀⠀⠀⠀⠀⠀⡀⠤⠠⠄⠐⠒⠀⠀⠤⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢔⠿⠜
⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⡀⠀⠠⠤⠄⠒⠀⠁⠀⠬⠃
⠀⠈⢦⡀
⠀⠀⠀⠙⠢⠄⣀⡀




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠤⠄⠀⠀⠤⠤⠤⠄⠀⠀⠀⠀⠀⣀⣤⣠⠴⠚⠛⠉⠁
⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⢭⡛⠁
⠀⠀⠀⢄⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠐⠦⣴⣀⣴⡿⡣⠂
⠀⠀⠀⠀⢻⣿⣿⣿⣥⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣾⣾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠙⢦⣁⡀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⢉⣽⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠦⢤⣤⣀⣠⣠⣀⣤⣶⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⢀⣠⣶⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⡀
⠀⠀⠀⣠⡿⢿⣿⣿⠿⠛⠉⠉
⠀⠀⡆⡇⠑⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠁⢇⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⢳⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣮⠾⣥⠀⢀
⠀⠀⠀⠀⠀⠙⠿⣷⣦⣄⣀⣀⣀⣀⣀⣤⣤⣾⡿⠟⠋⠉⠙⠛⠒⠦⢌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢤⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢄⣀⠠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠛⣻⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣽⣿⣟⣁⣤⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⣀⣤⡾⣯⣾⣿⣛⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⢾⣿⣯⣵⣿⣿⣿⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⣿⣿⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⡋⢡⠊⡀⠂⡠⣾⣿⡿⠉⣉⣉⠙⠏⢹⡉⠛⣉⣟⣻⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢈⠀⠀⡿⢃⣼⣿⣟⢀⣏⣁⣨⡇⣸⠋⣀⠙⣿⣧⢘⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣯⣿⣛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣥⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣄⣀⠀⢀⣠⣤⣶⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠡⠍⣿⣿⣶⣬⣙⠿⠟⠁
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⢋⡙⣷⡄
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣛⣋⣭⣭⣭⣭⣤⣤⣭⣭⣭⣭⣙⣛⠻⠿⣿⣿⣿⣿⣿⣶⣴⣿⣿
⠀⠀⠀⠙⣿⣿⣿⣿⣿⠟⣫⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣝⠻⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⢨⣙⠿⣿⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⠿⢋⡅
⠀⠀⠀⠀⠀⠙⢷⣦⣥⣙⡛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢛⣋⣬⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣷⣶⣶⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣶⣶⣾⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠠⠔⠚⠉
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣶⣾⡛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢤⣶⠴⠋⠉
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡄⠀⠀⣀⢀⠀⠀⠀⠀⡆⠀⣱⡆⡀
⠀⠀⠀⠐⣿⣿⣿⣿⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡻⣷⣿⣿⡵⠁
⠀⠀⠀⠀⠘⢿⡛⠟⠒⠚⠷⠶⠶⠤⠤⠤⠤⠤⠤⠴⣶⣶⣾⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠈⠙⠶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠛⠒⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠶⠛⠛⠛⠉⠉⠁
⠀⠀⠘⣶⣶⡖⠒⠚⠛⠛⠛⠛⠛⠒⠓⣶⣾⣿⣿⣿⣿⣿⣿⡷⠛⠉
⠀⠀⠀⠻⣿⣿⣆⣀⠀⠀⠀⠀⠀⠀⣰⣯⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⠷⠶⠶⠿⠿⠿⠿⠿⠿⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠄⣼⣿⣿⣿⣷⣤⣄
⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣶⣶⣶⠾⠿⠿⠛⠋
⠀⠀⠀⠀⠳⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣴⣾⣤⠶⠞⠛⠛⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠑⣜⢿⣿⡉⠙⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠐⢽⣷⣄⡀⠀⠀⠀⠀⠀⣴⣶⣾⣼⣿⣿⣿⣿⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⣠⣤⣶⠶⠶⠒⠒⠒⠒⠶⠶⠦⠀⠀⠀⢀⠀⠀⠀⣀⣠⣄⣤⠖⠛⠉⠉
⠀⠀⠀⠀⠀⠄⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⠒⠭⡙⠋
⠀⠀⠀⠀⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠃⠀⠐⠂⠂⠠⠄⠀⠠⣄⣀⣸⠀⡠⣼⣿⢠
⠀⠀⠀⠀⠘⢾⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣍⣻⣿⣿⣯⣶⠁
⠀⠀⠀⠀⠀⠘⢿⣿⠻⡟⠳⠶⠿⠷⠦⣤⡤⣤⣤⣤⣤⣤⣤⣤⠤⠴⣶⣶⣾⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢧⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠦⣤⣤⣀⣀⣤⣠⣰⣤⣴⣿⣿⣿⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⣛⣿⡛⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠺⠟⣉⠴⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⣀⠴⢊⣥⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⢀⡴⢚⣡⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⣠⠞⣉⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⠤⠶⠶⠶⠶⠶⠶⠶⠤⠤⣤⣤⣀⣀⡀⠀⠀⣀⣠⣴⠾⠋⠀⠀⢀⡾⢃⣴⠋
⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⣚⣛⣭⡭⠶⠶⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠲⠶⠭⣭⣛⣛⠿⢯⣄⡀⠀⠀⠀⣸⢃⣾⠁
⠀⠀⠀⢀⣠⡶⣛⣭⠶⠞⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⠦⣍⡳⢦⣤⡟⣸⡇
⠀⢀⣴⢟⣵⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣝⢷⣿
⢠⡟⣱⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠹⣆
⣿⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⣿⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⢿⣎⢷⡀⠀⠀⠀⠀⠀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⣠⠟⣰⡏
⢸⣿⣷⣝⢦⣀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣤⠞⣫⣾⣿⠁
⠀⢿⣌⠙⠷⣯⣛⠧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⣫⣵⠞⢋⣼⠃
⠀⠈⢻⣦⠀⠈⠙⠻⢶⣯⣝⣒⡦⠤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⠤⠶⣒⣛⣭⡴⠾⠛⠉⠀⢀⡾⠃
⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠉⠙⠛⠛⠷⠶⠾⣿⣭⣭⣭⣭⣭⣭⣭⣭⣽⣶⠶⠶⠟⠛⠋⠉⠁⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⠲⠤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠖⣋⣥⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⢶⣤⣭⣉⣉⣛⣛⠓⠒⠒⠒⠒⠚⢛⣉⣉⣉⣥⣴⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⣰⣏⠉⠲⣄
⠀⠀⠀⠀⠉⠢⣑⢤⡈⠑⢄
⠀⠀⠀⠀⠀⠀⠈⠳⣝⢦⡈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡝⢆⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⢣⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢤⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⢉⡩⠶⢲⠊⠉⠉⠉⠉⠉⠙⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠉⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⡀⠀⠀⣀⡤⠗⣒⠚⠛⠛⠓⠒⠒⠤⢄⡀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠆⣠⠚⣡⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⣠⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢰⠁⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣦⡊⠁⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡏⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡱⡀⢀⡠⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢫⠁⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⢮⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢕⢮⡑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠮⣇⣤⡈⠉⠒⠲⠤⠤⠤⠤⠤⠤⠤⠖⣚⡽⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⣄⣀⣀⣀⣀⡤⠤⠖⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠛⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠉⢀⣠⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠀⣠⣶⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠁⣀⣴⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠀⣠⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⠚⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠲⠶⢤⣤⣀⠀⠀⠀⠀⣠⡴⠟⠁⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣾⡋⠀⣠⣴⣿⠟⠁
⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢾⣿⠟⠁
⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠶⠞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳⠶⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⣿⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⢸⡇
⢻⡀⠀⠀⠀⠀⣠⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⡀⠀⠀⠀⠀⣸⠇
⠈⢷⡄⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⣴⠏
⠀⠀⠹⣶⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣴⡾⠁
⠀⠀⠀⠘⢿⣿⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⢟⣿⠟
⠀⠀⠀⠀⠀⠙⢷⣌⡙⠛⠷⢶⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⠶⠾⠛⠋⣁⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⣀⡀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⣀⣠⣴⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⢶⣦⣤⣤⣄⣀⣀⣀⣀⣀⣠⣤⣤⣤⡶⠶⠟⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢖⣫⢩⡶⢶⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠑⠈⠁⠀⢈⣉⣥⣾⠟
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⠶⠾⠛⠛⠛⠛⠛⠛⠛⠋⠉⠛⠛⠛⠛⠻⠶⢶⣦⣤⣀⡀⠀⠀⠀⠀⣀⣠⠴⠖⠋⠁⢀⣀⣠⣤⡴⠶⠿⠛⠋⠉
⠀⠀⢀⣠⣴⣾⣿⣭⣧⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⢭⣛⠷⣶⣟⠋⢉⣀⣤⣴⡶⠿⠛⠋⠉
⢀⣴⢟⣽⣿⣿⣿⠿⢒⣉⣥⣤⡶⠶⠶⠾⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠲⠶⢦⣄⡀⠈⢿⢜⣿⣿⡿⠛⠉
⣿⡇⢿⡿⢛⣩⠶⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⡟
⢻⡛⢦⣄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠟⢫⢦⡟
⠘⣯⢷⣿⣻⡶⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⠶⠟⠋⠉⠀⣠⢏⡾⠁
⠀⠹⣯⣻⢿⣿⣷⣾⣭⣝⣛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⣈⣥⠟⠁
⠀⠀⠈⠙⠿⢿⣽⣛⠿⢿⣒⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⡶⠶⠿⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⡿⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣾⠃⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠐⡇⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢀⣠⣤⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠶⠶⣤⣄⡀
⣼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⢿⣷⣤⣤⡶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳⠶⢦⣤⣤⣾⡿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟
⢸⡇⠈⠙⠛⠻⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠛⠛⠉⠁⣼⡷⠟⠉⠁
⠀⠻⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠿⠿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠋⠁⠀⠀⢀⣠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠋⠀⠀⠀⢀⣠⣶⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⣠⣴⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃⠀⠀⠀⢠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣴⣿⠏⠀⠀⠀⠀⣰⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣿⡿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⢿⣿⣶⣶⣾⣿⣏⡀
⠀⠀⠀⠀⠀⣠⣴⣿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⣷⣦⣄
⠀⠀⠀⢠⣾⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄
⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⡿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⢿⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⢸⣿⣿⣶⣄⣀⣤⣾⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣷⣄⣀⣤⣶⣿⣿⡇
⠀⠀⠀⠈⣿⣧⠉⠛⠿⣿⣿⣶⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣶⣿⡿⠿⠛⢉⣾⡿
⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠉⠉⠛⠛⠻⠿⠿⠿⢿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⡿⠿⠿⠿⠟⠛⠛⠉⠉⠀⠀⠀⢀⣾⡿⠁
⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣶⣶⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠚⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⣽⠚⣉⡷⣀⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁⠀⠀⢈⣩⠷⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠶⠶⠖⠒⠒⠒⠒⠒⠒⠒⠶⠶⠶⠤⣤⣄⣀⡀⠀⠀⠀⢀⣀⡤⠶⠋⠁⠀⢀⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡉⠛⠲⢿⣍⡁⠀⠀⢀⣤⠖⠋⠁
⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠿⠀⠀⠀⠈⠙⠶⣴⠋
⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣛⡇⠘⣧
⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠚⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠓⠶⠦⣤⣀⠀⠀⠀⠀⠀⠉⠀⠀⣸
⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠈⢿⡳⢤⣀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⣀⡴⢞⡿⠁
⠀⠀⠀⠀⠀⠈⠳⣄⠉⠙⠻⠦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⠟⠋⠁⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⠀⠉⠉⠙⠛⠛⠒⠒⠒⠶⠶⠶⠒⠒⠒⠛⠛⠋⠉⠉⠀⠀⠀⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠶⠦⠤⢤⣤⣤⣤⡤⠤⠶⠶⠒⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠈⠆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠱⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠚⠓⠒⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⣀⣠⠤⠤⠶⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⢿⢟⣛⣟⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⡄⣀⣸⣠⠄⡧⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⢹⣿⡟⣿⣿⣿⣿⡿⡃
⠀⠀⠀⠀⠀⠀⣰⠁⠀⢸⠀⠈⠉⠀⣸⣀⠀⠁⠀⡠⠒⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢸⣿⣶⣿⣿⢾⣿⣿⣿⣿⣟⣭⣾⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠒⠐⠘⠉⠉⠉⠀⠀⡠⠋⠀⣠⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣽⣿⣶⣶⣷⣿⣿⣿⣫⣾⣿⠟⠋
⠀⠀⠀⠀⠀⠀⢿⠑⠦⢀⣀⣀⣀⣀⣀⠤⠊⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣝⡿⣿⣿⣿⣿⣿⠿⣻⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⢀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⣶⣶⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠉


⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠚⠉⠉⠉⠉⠉⠉⠀⠉⠍⠢⣄⣀
⠀⢀⣀⡤⠤⠴⢞⣡⠔⠂⠀⣄⠀⡀⠈⠡⣠⠆⠀⡀⢀⡠⣀⠈⡇
⠀⣏⠀⠀⣠⡔⠋⠑⣤⠀⠀⢈⠿⣅⠠⠀⠀⠀⠠⠈⠁⣀⣠⢴⠇
⠀⠘⡶⠦⢤⣌⣳⣉⡀⢈⣂⣀⣀⡠⠴⠒⠛⣋⣉⣉⣉⡡⠴⠋⢀⣀⣤⣔⣪⣿⣯⣵⣖⡒⣒⢤⡀
⠀⠀⠈⠷⣤⣀⣀⣈⢉⣉⠉⣉⣁⡤⠴⠊⠉⠁⠀⠀⠀⠀⣀⡴⢿⣿⣿⣿⣿⣿⣿⡿⣛⣁⠛⣿⣎⢢
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⠤⣒⣯⣵⣶⢶⢟⣳⣦⣼⣷⣿⣾⣿⣿⡕⣿⣿⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠟⣷⠫⣝⣾⠿⢯⣭⡭⠿⠭⢿⣿⣿⣿⣟⣸⡿⢥⡾
⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣀⣞⢠⣿⡇⠀⣿⣿⡇⠀⠀⠀⢹⣿⡦⢀⣀⡠⠟⠁
⠀⢀⡴⣫⣶⣦⢰⣍⠒⠤⢤⣄⣀⣀⣀⣀⣈⣉⠁⠈⠉⠉⠉⠉⠉⠉⠛⠒⠒⠒⠛⠋⠉⠉
⠀⣾⣴⣿⣿⣿⠸⣿⣿⣿⠿⢃⣶⣶⣶⣶⣤⣍⣙⠢⣄
⠀⡇⣿⣿⣿⣿⣆⠠⣭⣀⠒⠛⠛⠛⠛⢛⣉⣭⣭⣶⢘⡆
⠀⣇⠹⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡿⠟⣛⣉⣥⣾⡇
⠀⢹⣦⣝⡛⠟⠃⣸⣿⣿⣿⣿⣿⠟⣫⠴⠋⠁⣠⠴⠛⠀⣀⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⢿⡄⠉⠛⠒⠬⢭⣭⣭⣭⣶⣿⣿⣤⠔⠋⠀⢀⡔⠋⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠊⠁⠀⠈⠓⠤⡀
⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⣿⣿⠿⠛⠁⠀⠀⢀⠊⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢾
⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⣡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⠓⠤⣀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠔⠒⠉⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠈⠉⠉⠉⠉⠉⠀⣀⣠⡤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⠐⠂⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⣀⣠⠴⠚⣹⣇⣤⣾⣤⣨⡏⠀⠀⠂⠲⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢠⡤⡀
⠀⠀⠀⣠⠊⡁⠀⣸⣿⣿⣿⣟⣿⡿⠟⣇⠀⣀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣐⣤⣤⣄⡀⠙⣩⡄
⠀⠀⡼⠁⠐⢻⠉⣿⡿⢋⣷⠶⠺⡟⢠⢿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢀⣴⣿⢯⠿⡁⠉⠻⣿⡍⣶⠆
⠀⢠⠁⠀⠠⢾⠞⠛⡏⠀⢹⡘⢐⣧⠄⠸⠂⢉⣡⣤⠾⠁⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⢀⣤⣿⣿⣿⠁⠀⠈⢳⣄⣿⣿⠈⢡⡀⡀
⠀⣬⠀⠀⠀⣸⡤⠀⢿⠂⢻⡇⠀⣽⠛⠛⣟⠯⠙⠋⠁⠀⣀⣤⡾⠟⠒⠛⠚⠻⠷⣶⣀⡸⣿⣿⣻⣦⣀⣀⣼⣽⣿⣿⠁⠀⠻⠑
⠀⣷⠀⠁⠀⠈⡇⠀⢠⡄⠀⢇⣼⡇⠀⠎⠁⠀⢀⣠⣴⡟⠉⡀⡶⠠⠶⠤⣾⠤⣴⠤⣍⠳⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢔⢀
⠀⠹⢤⡀⠀⠈⠋⠁⠈⠂⢀⣾⣽⠏⠀⠀⡰⣺⢉⣿⡏⠀⠲⢿⡧⠤⡦⠬⣷⣆⣼⣀⣸⣄⡛⢷⣾⣿⣿⠛⣋⢽⡿⠛⠳⣦⡀⡠⠘⢋⣠⡀
⠀⠀⠀⠈⠑⠲⠶⠦⠴⠞⠻⠚⠀⠀⠀⠀⢧⢿⣿⣿⡀⠀⠀⢴⡄⠀⡇⢀⣏⢉⣼⣿⣿⣿⣷⡇⠙⣿⣷⠓⢲⠙⣷⡀⣸⣿⡇⠀⠄⠊⠷⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣛⣿⣿⣦⠀⣸⡀⣀⡄⢃⣇⠀⡏⠻⣿⠁⢹⠋⠉⡇⠙⢶⣟⣾⣿⣿⣿⠟⠀⠀⠀⠀⠔⢃⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡼⣿⣿⣧⣌⠀⢈⣁⣬⣭⣬⣭⣭⣭⣡⣙⡃⠘⠷⠂⠀⣙⡟⠋⠁⠀⠀⠠⠐⣩⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣭⢿⣿⣿⣷⣿⢟⣻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⢿⡿⠀⡀⠄⢊⣡⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⢾⣿⣿⣽⢿⣿⣿⣿⣿⣿⢓⡀⡽⢘⣿⣿⠿⠋⢒⣡⣶⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⠻⡉⡀⠛⠛⣉⠥⠚⣿⣶⣥⣤⡾⠋⣠⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣻⣤⠖⠈⠀⠀⠀⠾⠛⣛⣭⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣌⢄⣀⠀⢀⣠⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⢦⡀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠄⡀⣀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⣰⣶⡄⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⢠⣿⣬⣿⣦⣧⠀⠀⠀⠀⠋⠀⠈⠐⠓⠒⠒⠉⠉⠁⠀⠀⢱⣄⡀
⠀⢲⡻⣷⣿⠀⠀⠀⢀⣀⣠⣿⠀⠀⠀⢸⣾⣇⣿⣼⣅⣿⡾⠀⠀⠴⢄⣀⣀⡀⠀⢀⣀⣀⣠⣴⡆⠀⣾⠇⠁
⠀⢻⣭⣻⣢⡦⢰⡲⣯⡳⣽⡏⠀⠀⣰⢾⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠈⠙⢿⣇⢸⡿⠿⠿⣿⣦⠸⡟
⠀⠀⠙⠻⣿⣷⣶⣿⣮⣽⠟⠀⠀⠀⠈⢢⡻⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢺⠹⣸⠀⠀⠀⢌⡏⢠⠇
⠀⠀⠀⠀⠈⠻⠿⠿⡿⠃⠀⠀⠀⠀⠀⠀⣼⣩⡭⡯⠍⣹⡄⠀⠀⠀⠀⠀⠈⠈⠢⠋⠀⠀⠀⠈⠀⠘
⠀⠀⠀⠀⠀⠀⠁⠐⡘⠀⢤⠀⠀⠀⠀⢰⠋⠛⠤⡷⠞⠋⢳⠀⠀⠀⢀⢾⢀⠀⠀⠀⠀⢀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠀⠀⠀⣧⠀⠀⠸⡧⠀⢠⡿⡟⣿⡄⠀⢠⡴⣻⣭⣵⡽⢿⣷⡆
⠀⠀⠀⠀⣀⡄⡰⠁⢀⢂⣤⣀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠘⠷⣷⠷⠃⠀⣵⡞⣿⣿⡟⣿⣯⠻⣿
⠀⠐⣿⣶⣌⣿⡇⠀⠀⣹⣏⣠⣶⡷⠀⠀⢀⠀⠀⠀⢆⡀⠀⠀⢀⢀⢀⠀⠀⠀⠀⢠⣁⣾⣿⣧⣿⣻⢄⡿
⠀⠀⠈⠉⠋⢻⣿⠀⢠⣿⠏⠙⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠋⠾⣼⣿⣷⣠⡀⠀⢸⡿⣽⣿⣿⣿⠏⣼⠁
⠀⠀⠀⠀⠀⠘⣿⠃⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⣉⣙⣛⡀⠀⠀⠤⢤⣴⡏⠀⠀⢠⡷⣱⡿⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠱⣥⣥⠇⠀⠀⠀⠀⠀⠀⠀⠀⠬⢭⣭⠄⠀⠀⠀⠀⢸⡇⠀⠀⠸⣟⣫⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣄⠀⣶⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠊⠁⣐⡂⠀⠀⠐⢒⢖⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢧⣈⢣⠒⡟⠘⣇⡖⡄⠀⠀⠀⠀⠀⠀⡜⠠⣀⠔⢂⠀⢈⣦⠴⠓⡄⠀⠳⣄⠀⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠌⢱⣠⡄⡂⢀⡸⢹⣠⡆⠀⠀⠀⠀⢰⡧⠀⠙⣦⡴⠚⡍⠀⢱⣤⠞⠣⡀⢈⠦⡄⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠾⠞⣹⡻⡁⣄⠙⢉⠘⡿⡄⠀⠀⠀⠸⢈⠀⠈⠉⢶⣀⠝⢿⡁⢈⣧⡔⠉⠣⡀⡨⠶⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⣧⣿⣿⣿⣯⠾⡍⢐⡀⢸⣦⠀⠀⠈⠃⣱⣀⠀⠋⠱⣄⡠⠓⣏⠀⢙⣦⠐⠉⠂⣠⢎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠿⠛⠋⠃⡀⠀⢻⠚⠓⠊⠘⠂⠀⠈⢿⢁⡃⢄⣀⣉⠃⠀⠬⠓⠉⢀⣠⠴⠋⠀⠈
⠀⠀⠀⠀⣠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠙⠁⠀⠀⠀⣶⢉⡓⣚⣹⠃⠀⠀⢐⠀⠀⠀⠁⠀⠀⢈⡉⢋⠉⠉⠉⠉⡉
⠀⠀⠀⠸⠉⠉⠉⠁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣴⣦⡃⠀⠀⠘⠀⢱⣦⡦⠘⠇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⡀
⠀⠀⠀⠀⣤⣤⣤⣴⠷⠤⣤⣀⣠⣤⣤⡄⢀⣀⠀⠀⠘⠝⠙⠀⠀⠀⠀⣪⡙⣷⡴⢐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⣡⠶⠺⣕⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣼⣿⣟⣦⢄⡒⣛⣸⠑⢦⣄⡐⢝⣀⡠⣄⡀⡈⠓⠀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢾⣧⠈⡀⠈⠹⣿⠘⣇⡀
⠀⠀⠀⠀⠀⠀⢀⡙⠏⠞⠃⠢⠀⡁⠰⡵⣸⡏⠀⣷⢟⠛⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⢋⠴⣊⣬⢿⡮⡅⠀⠀⠉⠀⢇⠄
⠀⠀⠀⠀⠀⠀⠠⠙⠲⠽⣟⡳⢀⣺⣡⣎⠉⠀⠀⢡⡼⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠿⠷⣾⢛⣼⡿⠉⠈⠱⡄⠀⠀⠀⠾⠸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⢻⡿⠺⢖⣤⡀⣠⣬⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⢁⣴⠾⣓⡯⠒⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠙⠮⣭⢱⣎⡀⠄⠚⠁⠀⠀⠀⠀⠀⣀⣤⠔⠋⣉⠠⢚⣩⠔⠛⢉⡴⠀⠀⠌⠀⠀⠀⠈⠀⠀⢀⠃⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⢀⣀⣤⣶⡷⠷⠒⢒⣩⡴⠞⠉⠀⠀⠀⢸⣿⣄⠀⠀⢶⣀⠂⠈⠐⠀⠁⠀⠎⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢿⣧⠀⣀⡤⠞⠋⠁⠀⠀⠀⠀⠀⢀⣾⣿⠓⠀⠀⠀⢹⣇⠀⠀⠀⣨⢀⣴⠇
⠀⠀⠀⠀⠀⣠⠖⠀⠂⠀⠀⠀⠀⠀⠂⠐⠂⠀⠀⠀⠀⢀⣀⣀⣰⣿⣯⣻⣿⡶⠦⣦⡄⠀⠄⠠⣀⣺⣟⣾⡿⢷⡄⠀⣀⣼⣟⢃⣠⠜⣡⠞⡟
⠀⠀⠀⠀⠀⠛⠃⠀⠀⠐⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠿⠿⠭⠿⣾⠿⠿⣭⣉⣉⣙⣙⠿⢿⣦⣭⣠⣡⡤⠶⣊⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠿⠿⢶⣭⠴⠖⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠶⣒⣂⣠⡶⠒⠀⣲⡞⢉⣠⣾⣿⠏⠉⠑⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣁⣤⣤⠾⠟⠋⢉⡵⠋⠀⣀⣴⡿⠾⠛⢉⡿⠋⣀⣤⣾⠟⠹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣁⠞⠁⠀⢀⣴⣿⠵⠖⢛⡿⣁⠄⢀⣠⣾⡴⠾⢋⣽⠁⠈⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠤⢖⡾⠛⠁⠀⢀⠶⢋⡨⢴⡾⠋⠉⠁⠀⣠⡿⠷⠞⠛⣿⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣴⠋⠀⠀⢀⡴⠟⠚⠉⣠⠏⣀⡠⠤⢒⡞⠁⡀⠀⢀⡜⠁⣰⡇⠀⢦⣀⡄⢀⣤⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣧⢖⡟⠁⠀⠈⣠⣾⣷⣾⣦⣤⣴⣏⣄⣀⣠⣴⣯⣴⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣿⣿⣧⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣛⣵⣯⣟⢻⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣟⣿⡿⠛⠋⠁⠀⠀⠈⠁⠈⠉⠙⠻⠿⢿⣿⡿⠟⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠈⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣴⠄⠈
⠀⠀⠀⠀⠸⣿⣴⣿⠃⠀⠀⠀⢀⡀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢄⣐⡭⠐⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⠼⠋⢀⣄⡄⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣀⣤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈



⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠵⠚⠉⠓⠢⣄⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⢀⣠⣤⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⠔⠁⠀⠀⠀⠀⠀⠀⠙⢦⠀⠹⣧⡀
⠀⠀⠀⠀⢀⡴⠋⡠⠒⠀⠐⠈⠍⣻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠘⣷
⠀⠀⠀⠀⣼⠁⡎⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡶⠦⣤⣤⣀⣠⣤⣤⣖⡯⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣿
⠀⠀⠀⢠⡿⠀⢧⠀⠀⠀⠀⢀⡴⠖⢒⢶⡄⠙⢢⡀⢀⡤⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣿
⠀⠀⠀⢸⣇⠡⠘⢆⠀⠀⠀⡞⠀⠊⠉⢳⣿⠀⠀⠳⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⠀⠀⣿⡀⢁⠘⢆⠀⠸⡇⡆⠀⢀⡞⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣼
⠀⠀⠀⠀⠸⣧⠀⠣⡈⢣⡀⠳⣝⣒⣋⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⡜⣿
⠀⠀⠀⠀⠀⠙⣧⠀⠈⠢⡱⣄⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠎⢰⡟
⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠈⠪⣳⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡠⠚⠁⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠈⠓⢌⡉⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢚⡡⠔⠉⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠈⠑⠒⠨⠵⣲⡶⠶⠶⠶⠶⠖⠖⠒⠒⠚⣉⡥⠔⠚⠁⠀⠀⢀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠉⠁⠁⠀⠀⠀⠀⣀⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠶⠶⠟⠛⠛⠛⠛⠉⠉



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

⠀⠀⢿⡂⡖⣴⡆⢴⡆⣿⡔
⠀⢀⣓⣃⣓⣙⣃⣛⣃⣛⣛⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⡤⣤⣤⣖⣲⣶⡀⠀⡈⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⣼⣧⣘⡆⠀⠠⠈⢷⡀⠀⠀⠻⡍⠛⠛⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠗⠶⣯⣀⠀⠉⢹⡞⠒⠲⠦⢷⣄⣀⣀⣘⣦⣼⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢾⣦⣀⠀⠀⢹⡏⠙⠷⣦⣷⡀⠀⠀⠀⠹⣄⠀⠉⠉⠛⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢼⠀⠉⠙⠓⠾⣧⡀⠀⠀⠙⣿⠲⠤⣦⣤⣿⣇⣼⢒⡤⣸⠃
⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣼⣆⠀⠀⢀⠀⢹⡟⠓⠶⢤⣼⣆⠀⠀⠀⠉⣾⡏⣾⣅⠁⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⡀⢄⠀⡀⢄⠈⠙⣿⠶⠦⣤⣘⣧⡀⠀⠀⠀⠹⡟⠛⠂⣰⣯⣾⣿⠃⠀⠀⠀⣟⡿⣤⡆
⠀⠀⠀⠀⠀⠀⠹⣼⣦⣶⣤⣀⡑⠀⢣⠀⠀⠈⢻⡷⢦⣀⠀⠀⢻⣀⣾⣿⠓⣹⠇⠀⠀⠀⣠⠈⢀⣿⡿⣴
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣶⣼⣧⣄⡀⠈⣇⠀⣩⣿⣶⣿⣿⡏⢋⣴⡟⠀⠀⠀⠈⠻⠟⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣬⠉⢪⡛⣼⣿⣿⣿⣿⣿⣿⣿⠛⢝⣛⣿⣃⣼⠗⠁⠀⠀⠀⠀⠐⠆⢰⣤⠀⠆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠿⠷⠿⣿⣦⣿⣾⣿⣿⣧⣤⡷⠟⠛⠉⠀⠀⠀⠀⣀⠈⢁⡳⠆⠠⠐⠂⠘⣨
⠀⠀⠀⠔⣂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡇⠀⠁⠠⠍⠰⠏
⠀⠀⠀⠀⠤⠤⠭⠦⡶⣤⣄⣤⣤⣄⣀⣀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣍⡳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠙⢒⠺⢿⣽⣿⠿⢿⡟⠿⢷⣤⣷⣤⣄⣀⡀⠀⠘⠻⠋⠈⠹⠇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠶⠀⠈⠙⠛⠛⠛⠛⠉⠉⠒⠒⠦⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⣩⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠵⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⢻⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡠⣄⡔⠁⠀⠀⠀⠀⠀⠀⠊⢀⣠⡤⠺⢛⠿⡀⠀⢸⠋⠁⢿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⠄⢀⡔⠉⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⣠⠞⣸⠁⠀⣾⠁⡅⠀⠉⣠⣤⡿⢋⡺⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠁⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⢲⠋⠀⠐⢁⣀⣤⣾⢟⣻⣯⠟⠹⠿⣿⣶⣄⣭⣖⣤⡄
⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠞⠀⠀⠁⠠⣤⣽⡛⠻⠷⠛⠛⠀⢀⣜⠀⠀⠀⠸⠁⠀⢡⢸⣷⡄
⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⣠⠆⠀⠀⠐⠚⠛⢛⡟⠃⠀⢠⠃⠀⠀⠽⠟⠂⠀⣾⣀⠀⢈⣿⣭⣿⠀⢀
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⡜⠁⡀⢠⠟⠁⠀⢠⡞⠀⠀⢰⠋⠀⠀⣶⠧⠀⠀⣰⠛⢲⣶⣟⠿⣿⣿⢀⡌
⠀⠀⠲⢭⣀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣦⡋⠀⠀⣸⣏⣀⣀⣤⣟⣀⡀⣠⠟⠀⢤⣾⡏⠀⢦⣾⣿⢽⣏⣧⣿⣿⢟⣯⣾⡇
⠀⠀⠀⠀⠈⠉⠓⠒⠦⠄⠠⠂⠀⠁⢄⣄⣉⣻⣉⠉⠉⠉⠟⠛⠟⣿⣿⠻⣙⣷⣬⣿⣦⣀⣉⣙⣿⣿⠛⣁⣴⠿⣩⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠁⠀⠀⠀⢀⡀⠈⠀⠀⠉⠛⠃⠚⠳⠦⠽⠿⠓⠛⠛⠋⢁⠀⠈⠉⢈⡥⠒⠛⠁⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠈⢄⠀⠈⠳⣤⡶⣶⠟⠉⠀⠀⠀⠀⠀⡀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⡠⠞⠁⠴⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠣⣄⠀⡟⡟⠓⠤⢀⠀⠀⠀⠀⠀⠁⠀⠀⡀⢀⣀⣀⣀⣀⣀⡤⠖⠋⠁⠀⣠⠴⠒⠉⠀⢠⡦⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠸⠛⠁⠀⠀⠀⠀⠀⠀⠛⠀⢀⡤
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠒⠠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⢤⣤⡑⣄⡐⠀⢤⣀⣌⣒⣒⣶⣶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠉⠁⠈⠈⠉⠉⠀⢿⠿⠟⠛⢛⣿⡿⢟⡫⢟⡿⠿⢉⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠡⠚⠁⠀⠁⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢶⢚⣫⣩⡩⠉⡉⣟⣒⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣋⣥⣾⣿⣼⣿⠟⢁⠲⢭⣒⡾⠭⣤⣭⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡵⡞⠿⢛⡁⣤⣠⡀⣄⡿⣇⠰⣮⣽⣛⣻⡶⠶⠌⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣵⡧⠛⣀⣤⡳⣝⢮⡳⣽⡻⣽⣿⡆⣌⠙⠿⢭⣽⣟⣓⡦⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡠⣤⡀⢾⣿⢿⣝⢮⡳⢝⡳⢽⣷⣿⣷⠺⢧⣤⠳⣶⠮⣭⣝⡂⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡻⣎⢿⡈⢿⣷⣽⡳⣯⣳⢭⣓⠋⣽⣛⡨⣿⣲⣦⠘⠛⠶⣭⡃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠘⢾⡷⣅⠀⢻⣶⣝⡳⢭⣓⣾⠀⡓⠾⣽⣳⢮⡟⠀⠀⢙⠮⢱⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠳⣝⠏⡀⢰⣝⠾⣝⡳⢾⣙⠢⣭⣛⢶⣉⡛⠶⡄⠀⣮⢃⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠐⡄⢠⠁⣝⢯⣳⢮⣝⠷⣏⣙⠶⣍⡿⠁⣙⠷⣦⡘⢃⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣼⣿⠁⣬⡳⣿⡳⣮⣻⡧⣝⡳⣮⣑⡇⣝⠷⡎⠁⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⠀⢹⣿⣮⣝⡳⣭⣓⢮⡻⣮⣿⢰⣝⠟⠀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢹⣿⡿⢠⣎⢿⣿⣮⣝⠦⣝⢷⣝⢦⡹⣧⠙⠀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⣸⣿⠁⡸⣿⣮⡻⣝⢮⡳⣌⢳⣝⣦⠻⠉⢀⣶⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢠⢧⠋⡰⣝⢮⡻⣿⠀⡠⠅⠈⠁⠀⠀⣀⣤⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢰⣎⠃⣰⣿⣜⢷⣹⠎⠀⠀⠀⠀⢀⢠⡆⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣴⡿⢃⣴⣝⣿⣿⠟⣁⠆⠀⢀⢠⡄⣿⢸⣧⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠺⡎⣷⠻⠞⠃⠀⣀⢠⡆⣿⢸⣷⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⢠⢠⡄⣤⣴⡇⣿⣸⣧⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⣼⣧⣿⡾⠿⠛⠉

⠀⡴⠟⠻⣦⣤⣤⡀
⣼⠀⠀⠀⠁⠀⠈⢻⣄⣀
⠻⣤⣤⣄⠀⠀⠀⠀⠈⠉⠛⠶⣤⡀
⠀⠀⠈⠻⠦⢦⣤⡀⠀⠀⠀⠀⠈⢙⡷⠶⠾⠿⠷⠶⠶⠶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡸⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⣠⠤⠤⠶⠶⠶⠶⠾⠿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⣉⣤⠤⠶⠶⠶⠒⠒⠲⠦⢄⣉⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢁⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣤⢾⡄⡀⠀⠀⠀⢀⡴⠋⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠙⢦⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⢿⡀⠀⠉⠀⠀⠀⣠⢏⡴⠉⠀⠀⠀⠤⠀⠂⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠈⣧⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠟⠁⠀⠀⠸⡇⠀⠀⠀⠀⣴⢣⠏⠀⠀⠀⣠⡤⠶⠶⢤⣀⠀⠀⠀⡴⠊⠉⠀⠀⠈⠉⠙⠢⡀⠀⠀⢸⡆⢿⠀⠀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣼⢣⠆⠀⠀⣴⠟⠁⠀⠀⠀⣠⠈⢳⠀⢸⡁⠀⣀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⡇⢸⡀⠐⢯⣄⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢸⡆⠀⢠⢇⠎⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⣠⠴⠃⠈⠧⣄⠈⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⡏⢸⠁⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⣿⠃⠀⠀⢸⣇⠀⡟⣸⠀⠀⡼⠁⠀⠀⠀⠁⠀⢠⠎⢁⡤⠶⢤⡀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠾⠃⠀⠀⠀⠀⣿⢰⠇⡇⠀⢰⠇⠀⠀⠀⠀⠀⠀⡏⠀⢸⠁⠀⠀⡿⠀⢹⠀⠀⠀⠀⠀⠀⢀⡟⠀⡼⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⢰⡇⠀⢸⡀⠀⠀⠀⠂⠀⠀⢧⠀⠘⠦⠤⠞⠁⢠⡆⠀⠀⠀⠀⠀⢀⡞⠀⡼⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠸⡇⠀⠈⣇⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⣠⠋⢀⡼⣱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⣧⠀⠀⠘⢦⣀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠸⡅⠀⠀⠀⣠⠞⠁⣠⠎⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠸⡄⠀⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠙⠓⠛⠋⠁⢀⡴⢁⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢦⣤⣉⣙⠒⠒⠶⠶⠶⠒⣒⣊⣩⣥⠴⠟⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣽⣿⣿⣿⣿⣿⣿⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣈⣄⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⡻⣧⣼⠇⠀⠀⠀⢀⡴⠋⠉⠙⢷⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⢛⡿⣿⡿⣿⡀⠀⠀⠀⠀⠀⣀⡤⠚⠃⠈⠳⣄⠀⠀⠀⠀⠀⠀⢀⣿⢇⣿⢿⠀⠀⠀⠀⣸⠃⣼⠛⢦⣀⣉⣉⡙⢷
⠀⠀⠀⠀⠀⢀⡶⢋⡵⠒⢉⣡⢾⣿⣧⠘⣷⠀⠀⠀⡰⠊⠀⠁⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⡾⡼⣸⡿⢸⡤⠀⠀⣰⠟⡴⠃⠀⠀⠉⠀⠈⡷⢸⡇
⠀⠀⠀⠀⠀⣿⠁⡼⠀⡔⢉⠔⣿⡏⡏⣇⠸⡇⠀⢰⣅⠀⠀⠀⠀⠀⠀⠀⠤⠴⣧⠀⠀⠀⢰⠇⡇⠹⠃⢿⡇⠀⢰⢣⡞⠀⠀⠀⠀⠀⢀⡼⢃⡞
⠀⠀⠀⠀⠀⣿⠀⢿⠘⡇⣿⢰⣳⢃⡇⡿⢀⡇⠀⢸⡀⠀⠐⠤⠀⠀⠀⠀⠀⣀⡟⠀⠀⠀⣼⢸⡀⠀⠀⣸⠁⠀⢸⡌⠳⠤⠶⣄⠀⠀⣸⢣⡏
⠀⠀⠀⠀⠀⠹⣧⡈⢧⢱⣿⣾⣫⢞⡴⢃⣼⠁⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢈⡽⠃⠀⠀⠀⡏⠸⠇⠀⢠⠇⠀⠀⠀⠙⠛⠲⡆⠈⠓⠚⠋⣼⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣮⣿⣿⣟⣛⣉⣤⠞⠁⠀⠀⠀⠀⠈⠳⡄⣰⠖⠚⠛⠉⠀⠀⠀⠀⠀⣧⣀⣀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⠤⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡇⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠈⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣷⡀⠀⠀⠀⠀⠀⠀⡾⠀⠘⠓⠒⢺⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⠀⠀⠀⠀⢰⠃⠀⣤⠀⠀⡼⠀⠀⠀⠀⢀⡴⡖⠉⠉⡇⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣘⣧⡴⠋⠉⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⢀⣧⣀⠀⡀⠀⢀⠇⠀⠀⢀⡾⠋⠀⢿⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⢠⠞⠉⠉⠉⠁⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣼⠁⠈⢉⣩⣤⡞⠀⠀⠀⡟⠃⠀⠀⠀⠀⠀⠀⠀⢹⣄⡴⠃
⠀⠀⠀⠀⠀⡾⠀⠀⢀⠀⢠⣄⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⢰⢟⡆⠀⠀⠀⠀⢠⡷⢤⣀⠀⠀⡜⠀⠀⠀⠈⣇⠀⠀⠆⠀⣄⠀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⢷⠀⠀⣾⠆⠘⠿⠀⠀⠀⣿⣿⠃⠀⠀⠀⢰⡟⢠⠃⠀⠀⠀⠀⣼⠀⠀⠠⢤⡾⠁⠀⠀⠀⠀⠙⢦⣀⡀⣀⣸⠟⠁
⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⡿⢿⢸⠀⠀⠀⠀⢠⡇⠀⠠⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⣀⣠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠹⣄⡀⣀⣤⣤⣴⣾⡿⠟⠀⠀⠀⠀⠀⣿⢸⡏⠀⠀⠀⠀⢸⠋⠂⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢞⣩⡤⡤⣄⡉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⣤⣀⠀⠀⢸⡀⣠⠏⠀⠀⠀⢀⣤⠶⠒⠶⣄⠀⠀⠀⣼⣳⠏⡁⢸⡵⣀⡹⣆⢹⡀
⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡇⠀⠈⢣⡉⢧⡀⠈⠛⠁⠀⠀⠀⡴⢋⡴⠛⠛⢦⢹⡆⠀⠀⣿⣿⢺⡽⣠⣄⠳⠆⣿⢸⡇
⠀⠀⠀⠀⢠⡞⠉⢠⡇⠀⠀⢹⡿⢦⡀⠀⠀⢠⡏⠀⠸⠁⠀⠀⠀⠃⠈⡇⠀⠀⠀⠀⣀⡼⢡⡿⠀⠀⠀⣸⠀⣧⠀⠀⢻⡜⢦⡀⠳⠞⢀⣴⢃⡼⠁
⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠘⠀⠈⢻⡀⠀⢼⠀⢠⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⡼⠋⡴⠋⠀⢀⡀⠀⠙⣦⠘⡆⠀⠀⠙⠶⣭⣙⣛⣩⡵⠞⠁
⠀⠀⠀⠀⠈⢻⣶⠀⢀⡴⠀⠀⢀⠀⣼⠁⠀⠘⣧⠘⣆⠀⠀⢸⣀⣠⡟⠁⠀⠀⢸⡃⠸⣇⣀⡴⠛⢷⡀⠀⣸⠀⡿⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠉⠛⠿⢧⣤⡤⠾⠞⠁⠀⠀⠀⠈⠳⠿⣦⣄⣼⣿⠉⠀⠀⠀⠀⠘⠷⣤⣬⣥⠴⠶⣌⠓⠚⢁⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⡀⠀⠤⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⡀⠀⠀⠀⢁⠀⠀⢲⡀⣀⣀⣤⠠⠤⣤⠀⠈⠓⠀⢈⠀⠀⠐⠦⣐⣳
⠀⠀⠀⠀⠀⡀⠀⠀⠊⠀⠀⠀⠈⠻⠃⠤⠀⠀⠉⢄⠀⠀⠀⠉⠠⡄⠀⠀⠀⢓⣴⣧⣄⡠⠄⠒⢀⣠⣼⣿⠂⠒⠀⢀
⠀⠀⠀⠀⠀⠀⠒⢆⡀⠈⣙⡑⠀⠀⠀⠠⡐⣀⡶⠀⠭⢶⣀⠘⠗⠒⡒⣆⠉⠀⠐⣶⣚⢍⣻⡍⠩⢍⣉⣿⠤⠈⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠴⠋⠁⠀⠀⠀⠉⠉⠑⢄⡀⠀⠀⠀⠐⢦⣀⡤⠄⠈⠳⢊⣩⠀⣿⠟⡟⢢⡴⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⡀⠀⠀⠀⠜⠲⣞⠙⠈⠁⠈⠒⣄⣀⣴⡿⠷⣄⡈⠠⠓⠁⠀⠀⠠⠄⠀⠤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⠀⠀⠀⠢⠀⠀⠀⢠⡵⢦⡖⠚⠉⢀⣿⣿⡀⠾⠋⠀⠀⠀⠀⠀⠀⠀⡈⣂⡠⠃⠛⠂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠙⠓⠶⠚⠛⠁⠠⡤⣄⡀⠀⢀⣉⠷⠖⡯⢉⠽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠆⠈⢀⠀⣏⡁⠈⠘⢆⣰⣧⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠙⠆⠀⠀⠀⠁⠀⠂⠰⠿⠋⠉⠀⡀⠀⠿⠟⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠰⢶⣳⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠄⠠⠀⠈⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢣⡞⠉⣩⣆⠈⠛⣿⣄⠀⠀⠀⠀⠀⠀⠓⢄⠀⣑⡈⣳⣤⣶⡛⠋⠁⠈⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⣨⠇⠀⠎⠛⠁⠀⠀⠀⠛⡆⢀⠀⡀⠀⠉⠻⣅⢠⣶⠟⣉⠙⡛⠛⠉⠈⢁⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣶⣄⣀⠀⠀⠉⠲⣄⠀⠀⢲⣄⣼⠦⠶⠃⠄⠀⣈⠀⠀⡀⠈⢉⡟⠉⠛⠉⠙⠋⠀⠐⠋
⠀⠀⠀⠰⠂⠀⠀⠀⠆⠀⢾⣿⢁⠹⣜⢦⠀⠀⠙⠶⣽⡮⠹⣿⣍⣷⠶⠶⠟⠿⠿⢷⣬⡤⠀⠁
⠀⠀⠀⠀⣨⠥⠀⠀⡤⠀⠈⢿⣟⣷⡜⢿⡇⠀⢀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠀⠀⠐
⠀⠀⠐⡤⠿⠔⠀⠀⢅⠀⠀⠸⣿⣿⣿⣛⣣⡄⠀⣀⠀⠀⠀⠀⠀⠀⠠⠄⡦⢀⡀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠡⣀⠀⠄⠀⠀⠀⢄⡀⠈⠻⠿⣿⠟⠁⠀⠁⠀⣀⠤⠀⠀⠀⣠⠠⢲⠇⢰⡆⢀⠀⠀⠀⠀⠀⠈⢶⡆
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠑⠚⠋⠁⠀⠀⠀⢠⠊⠀⠀⠀⠄⢀⠘⣠⣷⣤⣼⣿⣿⠀⠀⠀⠀⠘⠛⠠
⠀⠀⠀⠀⣀⠀⣈⡄⢦⣤⠀⢄⡀⠀⠀⠀⠀⣰⡤⠀⠀⠀⢀⣠⣾⣿⡿⣿⣿⣿⣿⣿⣷⡦
⠀⢀⠀⣀⡿⠟⣹⢧⣭⣶⣛⣳⠛⡆⠀⠀⠀⠋⢒⠘⠃⡀⣿⣿⣷⣿⡿⣟⠙⠙⠏⠙⠢⣅⣾⠁⠀⠀⠀⢀⠔
⠀⠘⣿⢿⠳⢞⢧⢺⣿⣟⠻⡿⣷⢤⣀⠀⠀⠐⠚⠒⠶⠚⠛⠛⣁⣈⠉⠻⡗⢲⠖⣢⣴⣯⣿⣦⠒⠆⠀⠁⠐⠶
⠀⠀⢰⣾⡖⣸⢋⡧⠌⠹⠇⢰⡜⣧⣌⣧⣄⠀⠀⠀⠀⠀⠀⢀⡿⠉⠀⠀⠀⠘⠓⠴⠼⠿⠟⠁⠀⠀⠀⠂
⠀⠀⠈⢛⣿⣽⡿⢶⠐⣆⡀⢈⡷⣼⠟⣿⣟⣆⠀⠀⢀⣄⣴⠰⣾⡆⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡤
⠀⠀⠀⠨⠙⢛⣛⣛⠁⣬⣿⣟⣿⣯⣯⣿⣿⠷⠂⠀⠀⠙⢿⠂⢩⠃⠈⠉⠉⠀⢧⣤⣡⣶⣿⣿⣧⣄⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⡀⠀⠀⠈⠁⢲⣍⢡⠀⡀⠀⠀⠿⢻⣧⣽⣷⢾⣤⡤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣾⡓⢸⠂⠀⠀⠀⠼⡦⠀⠁⠀⢀⡄⠈⣿⣿⣿⣸⣯⡐⠀⠀⠀⢠
⠀⠀⣀⠀⢀⡤⠴⠶⠚⠓⣒⠈⢉⠀⠀⠀⠀⠀⠸⣿⣷⠲⡤⣤⡤⠀⠁⠲⠂⠀⠀⠐⢃⡟⣿⣯⣿⣷⣷⡖⠀⡐⠀⡀
⠀⢠⣏⢳⣛⡅⠶⠾⠿⣷⡎⢠⠃⠀⠀⠀⠀⠀⠀⠈⠉⠙⠁⠤⠂⢉⡭⣿⣇⠀⠀⠀⠩⡰⠛⣿⣿⣿⣿⣷⣵⣤⡟
⠀⠀⣿⣿⢽⣷⣿⣾⣿⡟⠑⠁⠀⠀⡠⠞⠀⠀⠂⠘⠂⠀⡰⣯⣿⠿⠷⠛⠁⢀⠀⠀⠀⠠⠾⣛⠛⠿⢿⣛⠷⠚⠁
⠀⠀⠘⣿⣵⣿⣿⣿⣿⡿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋
⠀⠀⠀⠈⠐⠀⠒⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢷⠀⠀⠀⠀⠾⢥⣶⣴⠟⢿⣦⡀⠀⢀⠀⠀⠀⠀⢀⡤⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⡒⢉⣡⢤⡾⠀⠀⣴⣤⣀⠂⢤⡀⠀⢾⠿⣿⠟⠻⣷⣄⡀
⠀⠀⠀⠀⢠⠀⠀⠀⢀⡀⠀⠀⠀⣀⠤⢰⣏⢱⠍⠐⠋⠀⠀⢶⡶⢶⣿⢿⣦⣈⠿⠛⠳⢤⡀⠀⠀⠙⠳⢦⣄
⠀⠀⠀⠀⢤⣉⠂⠠⠊⠀⣠⠶⣯⣵⡿⠟⠋⠀⣀⠀⠄⠀⠀⢀⡀⠀⠀⠀⠀⠻⢿⣳⣦⡀⠙⠧⠀⠈⠀⠤⡉⠻⣿⣶⡆
⠀⠀⠀⠀⠠⢌⠲⢠⣰⡾⣱⣾⡽⠋⠀⠀⠀⢀⠀⠈⢰⣶⣾⣿⡷⠤⡀⠀⠀⠀⠀⠈⠙⠛⠦⠘⢦⠀⠀⣀⣀⡁⠠⠙
⠀⠀⠀⠀⠀⠀⠈⠒⠿⠾⠛⠁⠀⠀⠒⠂⢀⣷⣮⣓⣞⣟⣛⣻⣥⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⡆⠈⠻⠲⡛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣯⣒⠚⠛⠛⠛⠻⣿⣿⣿⣿⠟⠎⢀⠀⠀⠀⠀⡄⡠⠀⠀⠈⠓⠠⠄⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡟⣾⣿⣷⣷⡶⣞⣾⣶⣾⠗⡶⠁⠀⠀⢀⣻⣴⡌⠤⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠙⠛⠛⠿⠇⠒⠋

⢀⠀⠀⠀⢀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠚⠂
⠐⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠠⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠨⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠂⠀⠐⠀⠀⠀⠀⠀⠤⠤⠄
⠀⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠄
⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠁⠀⠀⠀⣀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀
⠀⣄⣤⠛⠁⢠⡴⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐
⢄⠀⠀⣁⠔⠀⠀⠀⠀⠀⠠⢄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠘⠢
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠂⠁⠂
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠅⠀⠄⠈⠈
⠀⠀⠀⠀⠅⠀⠸⠒⠀⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠐⠂⠀⠈⠀⠀⠀⠁⠀⠀⡀⠀⢀⣼⠉⡪⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡶⢇⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠀⡀⠀⠀⢄
⠀⠀⠉⠀⠀⠄⠀⠠⠀⠀⠁⠀⡰⠋⠑⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠤⠚⠁⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠁⠘⠀⢠⡀⠊⠀⠀⠀⠢⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢚⣭⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢸⣿⠂⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡁⠀⠀⠸⣿⠀⠀⣧⡈⠳⣄
⠀⠀⠀⠐⡄⢀⡤⠖⠉⠀⠈⠳⣄⡀⠀⠀⠀⠀⢀⣠⢞⡥⣸⡷⠀⠀⠀⢿⠀⣄⣿⣧⡄⠈⣳⡄
⠀⠀⠀⠀⠘⠾⡀⠀⠀⠀⠀⠀⠀⠙⣦⣀⣤⡴⠋⢠⢸⡇⣿⡇⠀⠀⣠⠀⢰⣯⣿⡟⢃⢞⠝⠁
⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢀⠀⡑⠈⢿⣧⠹⡄⢸⢸⡇⣿⡇⠀⠀⣿⠀⢸⠛⣃⢔⠕⠁
⠀⠀⠀⠀⠀⠀⣈⡆⠀⢐⠆⠰⡁⠘⣆⠈⡿⠛⠛⣆⢼⡇⢹⠀⠀⠀⡟⢀⣠⡾⠗⠁⠀⡆
⠀⠀⠀⠀⠀⢸⣿⣿⣦⡀⢳⡀⢹⣄⣸⠖⠃⠀⠀⠈⢆⠁⢸⠀⢀⣠⡶⢟⣋⠴⢒⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠙⠲⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⢧⣴⡾⠛⠉⠀⢘⠇⠀⠏⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡎⠀⢀⣸⠀⠀⢠⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⠤⢤⣤⣄⣀⣠⡤⠶⠒⠚⢛⣒⣚⠛⢧⠀⢧⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⣥⣤⣍⡉⠉⣤⣤⣄⠲⣶⣶⣶⣶⣶⣿⢃⣾⣿⡿⣋⣴⣿⢀⡟⣷⠇
⠀⠀⠀⠀⠀⠀⣼⠁⠾⣿⣶⣯⣽⣿⣦⡘⢿⣿⣷⣮⣿⣿⣿⡿⠃⣚⣻⣻⣿⣿⣿⣿⡿⢁⣿
⠀⠀⠀⠀⠀⠶⣿⠗⠲⠶⠤⣭⣛⠿⣿⣿⣌⡛⢋⣭⣭⣭⣍⠐⢋⣭⣭⣭⣭⡭⠀⢀⣴⡿⣿
⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠆⡖⢩⣛⠶⣌⡙⠻⠶⣦⣭⣭⣭⡴⠿⠟⣋⣉⣥⠴⠞⡻⢟⣼⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠙⢛⡲⠶⣾⣿⣑⠈⠉⠛⠒⠶⠶⠶⠖⠚⠋⠉⠉⠀⠰⠖⣋⡵⢛⡁⠦⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠀⠁⢀⠍⠙⠶⣤⣀⣀⠀⠀⠀⠀⣀⣀⣠⡤⠴⠛⠋⠇⠀⠢⠀⢁⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⠙⠛⠉⠉⣉⠁⠁⠀⢀⠠⠀⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠉⠁⠀⠉⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠴⠖⠒⠒⠒⠒⠒⠛⠋⠙⠛⡒⢤⡀
⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠠⠀⠀⠉⢀⠉⠓⠲⣄
⢀⡤⠴⠖⠚⠛⠉⣥⡴⠞⠉⠀⠀⠳⣄⢀⡔⠀⠀⠢⡴⠋⠀⠢⡀⢀⠴⠃⢄⠀⣼
⢸⠀⠀⠀⣡⣴⠛⠁⠈⢢⣤⠀⠀⠀⡨⠻⣄⠠⠖⠁⠀⠀⠀⠤⠈⠁⢀⣀⡤⢾⡇
⠈⣷⢤⣤⣀⡈⠙⢦⡚⠁⠈⠑⠄⠀⠀⠀⢈⣡⡤⠖⠒⠒⠒⠒⠚⠛⠉⣁⡴⠏⠀⠀⢀⣀⣠⠔⣫⣽⣭⣓⣒⠤⠤⠤⢄⡀
⠀⠈⢳⣄⣈⠉⠉⠛⠓⠶⠖⠲⠖⠒⠚⠛⠉⢀⣠⠴⠖⠒⠚⠛⠋⠉⠉⠁⠀⢀⡴⣻⣿⣷⣶⣿⣿⣿⣿⣿⣿⡿⠆⣿⣶⣌⠳⣄
⠀⠀⠀⠙⠛⠷⠴⠤⣴⣤⣤⣤⣀⡴⠴⠖⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣋⣘⣻⣿⣛⠿⠿⣛⣛⣿⣛⣡⣶⣶⡆⣹⣿⣷⣜⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠖⣫⣽⡶⢿⡿⠿⣟⣩⣿⣿⣜⣿⣿⣿⣿⣿⣿⣿⡷⢹⣿⣿⠏⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠻⠿⡗⠮⣍⣲⣟⣿⣯⣭⣭⠭⠽⣯⣼⣟⣛⣛⣛⣿⡿⣃⣿⣋⣥⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⡄⠀⡿⠀⣾⣿⠁⠀⢸⣿⣿⡄⠀⠀⠀⠀⢻⣿⣧⡉⠉⠉⠁⢠⡿⠃
⠀⠀⢀⡴⢒⣛⠛⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠶⠚⠳⠶⣿⣿⣥⣤⣼⣿⣿⣧⣀⣀⣀⣀⣼⣿⣿⠧⠶⠒⠚⠉
⠀⣴⢋⣾⣿⣿⣇⢸⣧⣄⣉⠓⠲⢶⠶⠶⠶⠶⠶⠶⠦⣤⣀⡀
⢸⢃⣾⣿⣿⣿⣇⠸⣿⣿⣿⣿⠿⠋⣰⣿⣿⣿⣿⣶⣶⣤⣉⣙⠶⣄
⣿⢸⣿⣿⣿⣿⣿⡄⠈⣉⣉⠁⠴⠾⠿⠿⠿⠿⠟⠛⠋⣉⣉⣩⣤⠘⣆
⣯⠘⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⠿⠟⠋⣠⣿
⢹⣆⠹⣿⣿⣿⣿⡟⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣡⠤⠶⠞⠻⣿⡏
⠀⣿⣷⣬⣉⡛⠋⠀⢸⣿⣿⣿⣿⣿⣿⡿⢛⣡⡖⠋⠁⠀⣠⡴⠞⠋⠀⣀⡤⠔⠒⠒⠦⠤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀
⠀⠸⣿⡀⠈⠙⠓⠲⠬⣭⣉⣉⣉⣭⣴⣾⣿⣿⣧⣠⠖⠋⠁⠀⢀⡴⠊⠁⠀⠀⠀⠀⠐⠀⠀⠉⠉⠉⠉⠉⠛⠉⠁⠀⠀⠉⠓⢄⡀
⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠟⠁⠀⠀⠀⢠⠞⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨
⠀⠀⠀⠀⠉⠓⠶⢤⣄⣀⣀⣀⣤⠴⠟⠛⠉⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣠⠖⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠖⠒⠋⠉⢀⡴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠈⠉⠓⠒⠚⠛⠉⠉⠀⠀⢀⢀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⡀⠀⠀⣠⡤⠴⠒⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣄⣸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠙⡄⠀⢠⠤⠜⠁
⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠸⡀⡏
⠀⠀⠀⠀⠀⠀⠈⢤⣈⣂⠜⢆⠀⢿⡇⢰⢁⢈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢸⡇⠸⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠧⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠎
⠀⠀⠀⠀⠀⠘⢠⡀⠀⠀⠀⢠⠇⠀⡜⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⢤
⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠸⡀⢰⠁⣀⠀⠀⢠⠎⠁⠀⠀⡔⠁⢨
⠀⠀⠀⢶⠒⠂⠤⢄⡀⠀⠀⠀⡇⡘⠀⠀⠀⠀⠋⠀⠀⠀⢀⡇⠀⣸⠤⠤⢒⡰⠖
⠀⠀⠀⢳⠀⠀⠘⠁⠘⢤⠀⠐⢳⣹⠀⠀⠉⠉⠉⢉⡩⠚⠁⢀⡴⠡⠔⠚⠉
⡠⠐⠈⠉⠁⠀⠀⠀⠤⠋⠁⠒⠀⠋⡰⠆⠠⠆⠀⠈⢀⠀⢠⠋⠀⠈⡱⡶⠤⠤⠤⠤⠤⠀⠀⠀⠒⠒⠚⠋⠉⠉⠉⠉⠉⠑⠒
⠑⡄⠀⠠⡄⠐⠦⡁⠀⠠⠐⠁⠀⢀⠆⠀⠀⠀⠀⠀⡠⠖⠁⡠⠖⠁⢠⠣⢀⣀⡀⡀⠀⠀⠤⠤⠀⢀⣀⣀⣀⣀⣀⣀⡀⠠⠔
⠀⢱⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠐⠒⠀⠀⠀⠚⠤⠁⠐⠈⠀⠀⠀⢀⠴⠋⠁
⠀⠀⠣⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠁
⣀⣀⣀⣀⣈⣁⣒⣢⣤⣤⣄⣀⣀⣀⣀⣀⣤⣤⣄⣒⣊⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⠛⠛⢦⡀⠀⠀⣀⣠⠤⠤⠖⠒⠛⠋⠉⠉⠉⠀⢀⡴⠶⠶⠶⣤⣄⣀⠀⠈⠉⠉⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⡟⠮⠉⠀⠀⠀⠀⡿⠉⠉⠉⢥⠤⣔⣘⣒⣦⣀⣀⣀⡴⠛⠛⠁⠀⠀⠀⠠⢼⡍⠛⢶⡄⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣩⡄⢹⣧⣀⣠⡤⠶⠞⠛⠓⠶⢤⡴⠟⠚⠛⠉⠉⠉⠉⠉⠁⢀⠀⠀⠠⠄⠀⠀⠀⠀⢀⠀⢸⡏⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⠆⠀⢴⣽⠟⠁⠀⠀⠀⠍⡉⠉⠁⠀⡩⠉⠉⠈⠡⡛⠛⠀⠀⠀⠀⠖⠠⠀⠀⠀⠀⣠⢊⣴⠏⢀⣀⡀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠳⣤⣈⣿⠃⢀⠀⠂⠒⠂⠀⠁⠀⡀⠋⠀⠈⠁⠀⠒⠒⠀⠀⠀⠤⠀⠀⠀⠐⢂⢔⠽⣩⡾⠷⠦⠾⢡⢈⡗⡐⡝
⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⢀⣡⠽⢿⣇⠀⠀⠈⠀⠀⠐⠂⠀⠒⠙⠀⠀⠀⠖⠀⠀⠙⠀⠠⠂⠀⢀⠀⠀⢀⢨⢀⡾⢋⡴⠀⠀⠀⠀⢸⢀⡴⠁
⠀⠀⠀⠀⠀⢰⡟⠀⠀⢠⠋⠀⠀⠀⢻⣥⡄⠑⠤⠤⠤⣀⠀⠺⠦⠀⠠⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠵⠃⢈⡇⠗⠈⠀⠤⣤⢤⣴⠏
⠀⠀⠀⠀⠀⣿⠇⠀⠀⢻⡔⠀⠀⠀⠐⣿⣿⣷⣄⡀⠀⠄⠀⠉⠑⢖⠒⠒⠲⠤⠤⠤⠠⠄⠤⠤⠔⠊⠁⣠⠞⠻⣄⣲⡷⢦⣼⡷⠛⠁
⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⡉⠓⠶⠶⢺⡿⠿⠉⠛⠻⡿⢶⠶⠶⠤⠤⣬⣀⡀⠀⠀⠂⢀⣀⠀⣤⣕⣤⠾⠋⢀⡠⢀⣨⠴⠛⠉
⠀⠀⠀⠀⠀⠘⢷⡀⠠⡀⠀⠀⠀⠀⠛⠶⣄⠠⠤⣞⣁⡾⠈⠉⢀⡀⠀⠈⠉⠛⠛⠋⠉⠉⠛⠟⠉⠀⣀⣡⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠷⣬⣀⡒⠒⠢⠤⠀⣈⣉⣉⣉⣉⢀⣀⣀⣀⣠⡤⠤⠤⠔⢒⣒⣠⣤⣴⠶⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⠶⠶⣤⣤⣤⣤⣤⣤⠴⠶⠶⠶⠒⠒⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣧⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⢿⡆⠀⠀⠀⠀⠀⠀⢸⡿⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢸⡇⠀⠀⠀⠀⠀⢠⣿⠃⣼⡏⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢸⡇⠀⠀⠀⠀⣰⡿⠁⣰⡟⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⣿⠃⠀⠀⣠⡾⠋⢀⣼⠟⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢀⣼⠏⠀⠀⣰⡟⠁⢠⣾⠋⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⣠⡾⠋⠀⠀⢰⡿⠀⢠⣿⠁⢠⣴⠟⠉⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠸⠏⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠻⣦⠀⢀⣤⡶⠀⢸⣧⠀⢸⣧⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⣰⡿⡋⠀⠀⠀⢿⣆⠀⢻⣆⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⢰⣿⠈⢻⣦⠀⠀⠈⠻⣦⡀⠻⣧⡀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠸⠇⠀⠀⠙⢷⡄⠀⠀⠙⠻⣦⡌⠿⣦⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀
⠀⠀⣀⣠⣤⣶⣶⣾⣿⣿⠿⠛⠛⠿⠿⠿⣿⣿⣿⠿⣛⣋⣉⣙⡛⠿⣿⣿⣿⣿⠿⣿⠟⣋⣭⣉⡛⢿⣿⣿⣶⣶⣦⣤⣀⡀
⣴⣿⣿⣿⣿⣿⣿⣿⡟⣡⣾⣿⣿⣷⣦⣷⡌⠛⣱⣿⣿⣿⣿⣿⣿⣷⣌⢻⡿⢡⣶⡆⣾⣿⣿⣿⣿⣆⢨⠹⣿⣿⣿⣿⣿⣿⣷⡆
⣌⠻⠿⣿⣿⣿⡟⣩⣅⢻⣿⣿⣿⣿⣿⣿⡃⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠧⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⠆⣿⣿⣿⣿⡿⠿⢛⡁
⣿⣿⣶⣶⣬⣍⣁⣛⡛⠻⠿⠿⠿⢿⣶⣬⡍⠘⠟⠛⣛⣋⣩⣭⣭⣤⣶⣶⣶⣾⣶⡌⢿⣿⡿⠿⠌⠿⠁⣚⣛⣉⣭⣤⣶⣾⣿⡇
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⡿⢛⣩⣭⣭⣭⣍⡛⢿⣿⡿⠃
⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣙⠳⣍⡛⢿⣿⣿⣶⣍
⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠓⠀⠙⠲⢬⡛⠿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢬⣙⠿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣝⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⢰⣿⣷⡀⠀⠀⣰⣿⣿⡀⠀⠀⣰⣿⣷⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⣉⡑⠶⢎⡛⡿⣣⣿⣧⣻⣿⣿⣣⣿⣧⡻⢿⣋⡶⢖⡈⣉⠀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⠀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⢀⣤⣀⣠⣄⡀⢀⣀⣀⡤⠤⠤⠀⣠⣀⢀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠖⠉⠀⠀⠀⣄⠀⠀⠀⣀⣙⣷⣥⠀⠤⠀⠀⠀⠀⢤⣈⠉⢩⣷⡀⠀⠁⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀⠀⠀⢤⡴⠶⠾⠓⠛⠉⠙⠻⣭⡀⠀⠀⠀⠐⠲⣠⣄⡈⠀⠀⡙⠳⢦⣼⠇⢠⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠉⠌⠠⣄⡀⠀⠀⠁⠀⠈⠰⢤⣄⡀⣀⣄⣰⣦⣽⣧⣤⡶⠿⠞⠛⠉⠳⢤⣤⣀⠠⠋⡻⡇⠀⠃⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠔⠐⠈⠁⠀⠀⠀⠀⠀⡀⠀⡙⣻⣧⣤⠶⠶⠿⠋⠙⢿⣉⡉⠉⠁⠀⠀⠘⠓⠦⣄⠀⢀⣀⠤⠽⠛⡿⠀⣴⠁⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠠⢌⣷⡤⣴⠖⠛⠋⠉⠁⠀⡹⢷⡄⠂⠤⡀⠀⠈⠙⠶⣄⣀⣤⣴⠶⠶⢛⣿⣿⣿⡔⠀⠉⢳⣼⠟⢷⣆⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠀⠀⠀⠀⠀⠙⠳⣄⣤⠶⠶⠛⠛⠉⠋⢤⣤⡞⠉⢹⡿⠋⡟⠁⡠⠞⠉⠀⠀⠀⠀⠉⠑⠀⠀⠀⠸
⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⢠⡽⢷⣤⡖⠛⢏⠛⠉⠀⠙⢶⡦⠄⠀⢀⣾⢺⣿⣥⡀⠈⠃⣀⡷⠖⠁⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⢀⠃⠰
⠀⠀⠀⠀⢈⢢⠤⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡄⠠⠠⣄⣤⣤⠾⠛⢷⣾⣿⠋⢫⣽⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⢀⠊⠠⠁
⠀⠀⠀⠐⠠⣆⢳⣀⣀⠀⠀⠀⠀⠀⠈⠓⠂⠀⠀⠀⢠⠴⠶⠿⠿⣟⡉⠀⠀⢀⣠⣿⣻⢿⡄⠼⠋⠀⠐⠪⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡠⠁
⠀⠀⠀⠀⠀⠸⡈⠉⠹⡷⣶⡶⠿⠿⠛⠓⠂⢀⣀⣀⠀⠀⠀⠀⠀⠉⠻⣶⡤⢾⡏⣉⢙⣿⠁⠀⠀⠀⠀⠀⠀⠁⠒⠠⡀⠀⠀⠀⠀⠀⡠⠊⢀⠔
⠀⠀⠀⠀⠀⠀⠉⠀⠒⢄⢀⠋⠀⠂⢠⡀⠑⡶⠃⠉⢹⡗⠤⢀⠼⢻⣭⡄⠁⣼⠀⡸⠋⠀⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⣠⣀⢸⣥⣤⠀⠡⠀⠙⣧⣤⣿⡿⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⢬⣇⡟⠉⠋⠀⠀⠀⠀⢻⣿⠿⠟⢥⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⡉⢉⠒⠒⠁⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠤⠠⠀⠄⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡴⠀⠀⡔⠀⠀⠢⠀⢀⠀⠀⠀⠀⠀⠀⢀⠈⣄⠀⠀⢠⠄⠁⠀⠀⠀⠀⠰⠒⠒⠀⠀⢹
⠀⠨⢰⣤⢠⡀⠀⠔⠐⣪⠟⠁⠀⠀⠓⠐⠀⠁⠀⠀⠀⠀⠀⠀⣠⡞⠛⠓⠋⠀⠀⠃⠀⠀⢶⠆⠀⠀⠀⠒⠁⢈⣁⢸
⠀⠀⠙⠁⠸⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠦⣴⡈⠈⠀⠀⠀⠀⡀⠀⠀⢀⣠⠐⡀⠀⠐⠀⠀⠀⠀⠤⠴
⠀⣤⡄⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢻⡇⣍⠂⠀⠀⠀⠀⠀⠀⠀⠄⠒⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢦⣄⣠⣄⣀⡀⠀⠀⠀⠂⢠⠀⡦⠤⡇⢰⡄⠀⠈⠛⠦⡤⠆⠀⠀⠀⠀⠀⣀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠉⠈⠑⠉⠻⠿⠃⠀⠠⠒⠐⠀⠦⠀⣇⣾⡧⠀⠀⠀⠀⠀⠀⣰⠂⡔⢁⠜⢠⠂⡠⠄
⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⡀⠀⠀⠀⠐⠚⠃⠸⠂⠸⣠⢿⡙⠁⠀⠢⠴⣶⣤⠀⠸⢿⡴⣁⡄⢀⠖⢀⠔⢀
⠀⠀⠘⣿⣓⡂⣿⢛⡏⢋⠗⠀⠀⠀⠈⠒⠀⠀⠀⠲⣾⣬⣧⣺⡏⠉⢀⣄⠀⠀⠀⠘⠋⠳⠆⠀⠈⠉⠚⠷⠶⣧⣴⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⣀⣀⡤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠐⠶⣻⣭⣥⣾⡿⠷⣤⣠⣤⣤⠶⠖⠒⠒⠟⠻⠓⠒⠒⢼⣾⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⢀⣤⣄⣀⣀⡠⠤⣤⣶⣚⣭⡭⠖⡰⠟⣃⣵⢖⣫⣤⣶⣾⣿⢁⣀⠤⢀⣐⣀⣀⣀⠀⠌⠉⠀⠰⠟
⠀⠀⠀⠀⠀⢀⡤⣶⣆⢀⣿⣉⣅⡄⢀⣘⣿⡏⠀⣴⣾⣟⣛⣻⣭⣥⢽⠶⠿⠟⢋⣵⣿⣿⣿⣿⣿⣳⣯⠴⠒⠉⠉
⠀⠀⠀⢀⢔⡵⢦⣟⡜⠢⣗⠵⣤⣤⡝⠋⢉⣺⣛⣻⣿⠻⠭⠤⢔⣀⡘⣤⡖⣿⣿⣿⣿⣟⣿⡿⠋⠁
⠀⠀⠀⡆⡾⢱⣬⣿⠀⣧⠘⣦⡴⢞⡑⠛⢋⠁⠀⡸⠉⢙⠒⣛⢛⢳⣬⡋⣸⣿⣿⣿⣿⣿⣿⠃
⠀⠀⢸⢀⣧⢿⢟⠦⢷⣾⠤⠥⢄⠪⠀⠀⡌⠀⢀⠳⡀⠉⠀⢃⢺⢀⡻⣧⣿⣿⣿⣻⣿⣿⡟
⠀⠀⠈⡞⢿⣿⠟⢠⢏⠌⡇⢠⣤⣬⣄⣀⡃⠰⣎⠀⡅⠀⡘⣄⢠⣨⡗⣹⣋⣿⣿⣿⣿⡿⠃
⠀⠀⠈⣇⡈⢯⣷⡏⣾⣤⡷⣿⠁⠐⠀⣈⠻⢦⣥⡦⣤⢤⡶⠼⠾⠋⣰⣷⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣤⡖⠢⡄⠀⠀⠀⠀⣰⠆⡆
⠀⠀⠀⡦⠙⢢⡻⣽⣿⣿⣿⡁⡼⠀⢆⡏⠀⢪⡻⠘⠿⣋⡵⠖⣠⡼⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⡇⣴⢃⡴⣆⡤⣤⣯⠊
⠀⠀⠀⣂⠀⠀⢱⠉⢻⣿⣷⠏⠀⣒⣎⡗⣄⠣⠧⠐⣋⡩⣴⣻⣿⣷⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⡸⠛⠇⠸⠅⠸⡋⡇
⠀⠀⠀⠈⢄⠀⠀⠑⢤⣉⠙⠷⠷⢛⣉⠥⡶⠲⠟⢿⣟⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠂⢢⢀⠀⠀⣀⣤⡄⠀⣀
⠀⠀⠀⠀⠈⠑⣀⡀⠀⡀⠈⡁⢨⠽⠃⠆⣡⣜⣶⣯⣼⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡀⠀⣁⣿⢜⡥⢄⡤⣴⢸⣯⠖
⠀⠀⠀⠀⠀⠀⠘⢧⣶⡇⡀⣇⡈⢁⡶⣷⣿⣿⣿⣷⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢈⡇⠉⣇⢸⡀⢼⡥⣏⢸⡿⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠷⠿⠿⠿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠢⡀⠀⠀⠀⠀⢠⠖⡀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡆⣦⢊⡯⢤⣡⠀⠘⠄⠀⠀⢠⠁⠀⠠
⠀⠀⠀⠀⠀⠀⢇⠈⠰⠄⢀⠀⠀⠀⢸⣿⣟⠔⠉⣁⠀⣚⠀⢱⢀⠄⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠠⡆⠐⢆⢀⠳⢀⡞⠁⠀⠉⢳⠀⣁⠀⠘⡃⠀⢃⠀⢀⠁⢐⣤⠔⣺⡟⠀⣿⠀⠀⠀⢀⡐⠁⢸⠀⢀
⠀⠀⠀⠀⡠⠶⢲⣙⡒⢮⣿⣀⢸⡇⠀⠀⢀⡟⠀⢁⠀⠐⣟⠀⠶⠔⠚⠉⣁⠠⢠⢿⣇⣠⣋⣳⣤⡤⢅⣀⡀⠲⠘⡁⡇
⠀⠀⢰⠈⡡⠏⡊⢱⡸⠒⠀⣽⢸⠃⠀⢠⣾⡿⣻⢻⣧⠀⠠⠄⠀⠀⢀⣠⣀⡴⢃⣿⠋⠋⠙⠋⢘⣷⢀⡀⣗⠀⡾⢸⠇
⠀⠀⡍⢀⡴⠲⣽⡘⠫⡷⣧⠘⡟⣀⣤⣿⡏⣸⢯⣾⡣⠤⢀⣀⣠⣴⡟⢉⢽⣷⡟⣻⣷⣀⡀⣠⡴⣷⡜⣇⣜⡟⠄⠚⠤⢀⡀
⠀⠀⢆⢇⠳⠠⡏⣮⡓⠉⢸⡀⣿⡏⡽⣿⡇⣹⣿⡟⢿⡾⢷⢟⠛⣿⠀⡾⢠⡿⢰⡿⣯⣍⣻⣧⣾⡵⢧⣷⣫⢐⡈⣨⠤⠤⡏
⠀⠀⠈⠉⠒⠘⡈⠲⢁⠀⢀⣷⣿⣷⣆⣿⣆⢸⣿⠇⣸⣁⣫⣨⣦⣵⣤⣷⣈⣷⣼⢁⡁⠚⣹⡿⠁⠀⠀⠈⠛⡇⠀⢀⢀⠐
⠀⠀⠠⣤⣤⣵⣎⠳⣄⢳⡾⢡⣶⣿⣿⣿⣿⣄⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣐⢿⣇⠀⠀⠀⠀⣰⡟⠀⣄⣾⣮⡟⣀
⠀⠀⠀⢡⢹⣗⣪⢟⣪⣻⡇⣿⠟⡭⢻⡟⢡⢦⣿⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⣾⣿⣷⣿⣇⣀⣠⡴⣻⠖⠚⠛⣿⠅⠒⠋
⠀⠀⠀⠈⢆⢿⣪⣯⡳⣽⠻⣮⠨⣵⠏⢐⣷⣿⣿⣿⣿⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣙⠿⣅⣸⠃⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠈⢆⠑⢵⣟⣽⠆⠻⣶⠆⣰⣿⣿⣿⡿⠋⣿⣾⡡⣷⣿⣿⣿⠋⡿⠿⠟⣿⠟⣙⣿⣿⣿⣷⢹⡇⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠈⢳⡄⠀⠙⢧⣸⡟⢠⣿⣿⣨⣿⠁⣼⣿⣿⣿⣶⣿⣿⡆⢰⣶⣶⣿⡿⢠⣯⣿⢟⢻⢏⣼⣧⡴⠛⠁
⠀⠠⠖⠒⠠⠒⠂⠛⠓⠮⣼⣿⠇⣼⣿⠏⢸⠇⢼⣿⠋⣤⡏⢰⣿⣻⠀⣾⡏⣽⠁⡇⢠⡿⠉⣿⣆⣿⢛⠁⠀⠀⢦⢠⡤⠖
⠀⠀⠑⠢⡄⠰⠛⣷⣦⡤⠼⣿⣧⣽⣷⣧⣴⢀⣿⢹⣦⣽⣿⣦⡄⣻⣄⣯⣦⣭⠀⣧⠘⣇⠸⠟⣼⠇⠀⠀⠀⠐⣻⡶⠃
⠀⠀⠀⠀⠀⠂⠬⢀⠘⣇⡴⠿⠆⠉⠋⣿⡏⢸⣿⢸⡇⠈⠻⠿⠛⢋⣩⣿⣿⣯⠀⣿⣻⣻⡳⣛⣁⣀⣀⠤⠶⠻⠄⠀⠂⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠫⡟⠓⠀⠀⢀⡾⠻⣧⠸⣣⣿⡇⠀⠀⠈⢯⣟⣿⣿⣿⡏⣸⡏⠹⣌⠙⢯⣄⣈⠉⠦⢀⡀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠄⠈⠀⣠⠽⣦⢀⣠⣿⠁⠀⠙⠛⢻⢣⣿⡄⠀⠀⠘⠻⣿⣿⣿⡴⢿⠀⢀⢮⡧⡎⠉⢲⢤⡈⢢⠀⠀⠋⠒⠒⠒⠂
⠀⠀⢀⠜⠁⠀⠀⠀⠉⣤⡒⡒⣒⣿⠦⠄⠠⠴⡷⣿⣺⣽⢦⡀⢀⠙⡭⡏⠉⢠⠼⣞⢮⠓⢷⣅⣨⠘⠸⠦⢀⡀
⠀⠀⠀⠀⠉⠈⠀⠀⢀⠞⡤⠛⡟⡹⠀⠀⠀⠀⠀⣿⠫⠔⠊⠉⠲⣯⣾⡁⠰⢾⠆⡉⡝⡇⠹⣈⡤⢀⣦⡌⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠐⠘⠡⡀⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡇⠈⡛⠁⠀⠑⢦⣉⡚⣃⣇⠜⠀⠀⠘⠦⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡋⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⢀⡼⠒⠒⠠⢩⣶⠘⠟⠒⠈⠤⠒⠀⠖⠆⡶⠂⠧⠖⠗⠴⠐⠀⠂⠆⠃⢠⣮⠡⠐⠒⠻⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠
⠀⠀⠀⠁⠈⠆⠀⠀⠀⠀⠀⠁⠶⠀⣀⡀⠀⠀⠀⢮⣧⠞⠀⢬⡷⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬
⠀⠠⠀⠠⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠐⣿⠆⠀⠐⢷⠖
⠀⠀⠈⠀⣿⠦⠀⠀⠀⢀⠄⠒⠇⡈⠃⠀⠀⠀⠀⠀⠛⠀⠀⠀⠚⢀⠀⠀⢀⣀⠀⠀⠀⣀⢠⣤⣤⡤
⠀⠀⠄⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠈⠀⡀⠀⠀⡄⣠⣄⠀⠀⠙⠀⠀⠁⠠
⠀⠀⠀⠀⠰⠀⠀⠀⣀⡀⠀⠀⠀⠤⠉⠰⠄⢂⠀⠈⠀⠀⠀⠸⠀⠂⠀⢰⠇⠋⢸⠀⠀⠀⠖⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠗⠀⠀⠐⠀⠀⠀⠀⠘⠀⠈⠄⠀⠀⠀⠄⠁⠀⢸⠁⠀⠘⠀⠀⠀⠀⠘⠷
⠀⠐⡾⠚⠀⠀⠓⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⢀
⠀⠈⠂⠠⠤⠄⠀⠈⠀⣰⠓⠀⠀⠀⠀⠀⠀⠚⠶⢷⠚⠃⢐⡄⠀⠀⠀⡸⠀⠀⠁⠀⠀⠀⢰⡷⠝⣇
⠀⢠⣄⡀⠀⠀⠀⠐⠟⠛⠖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⡠⠄⠀⡀⠤⡁⠀⠀⠈⠁
⠀⠀⣠⡷⠻⠃⠀⠀⠀⠠⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⠀⠀⡴⠔⠀⠀⢆⠀⠀⡄⠀⠀⠀⠀⠀⢠
⠀⠀⠁⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠁⠀⠀⠀⠈⠁⠀⢀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠰⠈⠃⠀⠀⠀⠂⢠⠀⠠⠀⠀⢀⣀⣴⣴⠀⠀⢰⣿⡀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀
⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⣤⠀⠀⠁⠀⣿⣿⣿⠀⠀⠸⣿⠃⠀⠀⠠⠀⠀⠉⠀⠀⠀⠀⠘⠀⡘
⠀⠀⠀⡡⠂⣢⢬⡳⡄⠀⠀⠸⠟⠀⠀⠀⠉⣷⣿⣿⡤⠀⠀⢻⠀⠀⠀⠀⠁⠀⠃⠀⠀⠀⠀⠀⠉
⠀⠀⣄⠣⠀⠠⠄⠂⠇⡖⠀⣈⣡⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠛⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠠
⠀⠀⠈⠀⠀⠀⠀⣀⠜⠀⠀⠈⠃⠀⠀⠀⠀⣿⣿⣽⠃⠀⠢⣤⠄⠀⠀⠁⠤⠤⣤⣄⠀⠀⠀⠤⠖
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢞⡿⢿⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⢀⡠⢖⡥⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣀⢔⡫⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⢤⣤⣒⣠⣤⠤⠤⢤⣀⣀⣀⣤⠞⠋⠀⡼⣡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣲⠭⠗⠒⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠑⠚⠭⢕⡢⣄⣰⢷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡴⡫⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⢿
⠀⠀⠀⠀⠀⠀⠀⡼⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⡇
⠀⠀⠀⠀⠀⠀⠀⢧⢇⠀⠀⠀⠀⢀⠠⠐⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣯⡣⣄⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣫⣾
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡉⠳⢽⣶⣤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⣔⣮⠵⠋⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠉⠛⠓⠿⠾⠯⢥⢴⣤⡤⠭⠵⠿⠒⠛⠉⠁⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⡠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣔⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠯⢭⣭⣽⣚⣚⣓⣪⣭⡭⠵⠖⠋⠁

⠀⢄
⠀⠀⠑⠦⣀
⣀⠀⠀⠀⠈⠉⠒⠀⢀
⣿⣷⣦⣄⣀⣤⡀⠀⠀⢱⣄
⠉⠛⠛⠛⢿⣯⠔⠀⠀⠀⠙⠛⢦⡀
⠀⠀⠀⠀⠀⢷⣾⠀⠀⢠⠀⠢⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢻⣿⢁⡀⠀⣱⠀⠙⣦⢄⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⣿⣿⡄⢠⡏⠀⣶⡏⠀⣿⠈⣇
⠀⠀⠀⠀⠀⢸⣿⡿⢀⣿⡁⢠⣿⣇⠀⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠈⠛⠿⠾⠿⣧⣾⣿⣿⡀⠙⣷⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠻⣍⠓⢆⣻⡀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡤⢀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣹⡇⠈⡇⠀⠀⠀⠀⠀⠠⠂⠀⠄⠀⠸⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠀⠀⠚⠛⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠅⠀⠀⠀⠙⠲⢌⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠙⢴⡠⠀⢰⠁⠈⠔⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣔⠠⠀⣀⣀⠛⠁⠀⠀⠦⠀⠸⡀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣼⣆⠀⢰⣶⣄⣀⢤⣤⣤⣦⣴⣥⣀⣀⣀⣤⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣷⣾⣿⣿⣮⡻⠛⠻⣷⡹⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠓⠒⠛⠛⠛⣛⣿⣿⣿⣿⣿⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠦⠤⣤⠤⠤⠤⠴⠾⠿⠛⠛⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⡿⠁
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⠟⠛⠋⠉⠉⠉⠉⠉⠉⠉⠛⠻⢿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⢀⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⡄
⠀⠀⠀⠀⠀⢘⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⢄⠀⢀⠠⣄⣄⣀⠀⠀⠀⠀⣀⣀⣤⣴⣴⣦⣶⣦⠀⠀⠀⠀⠀⠀⠀⢠⣴⠁⠀⠆
⠀⠀⠀⠀⠀⠀⢰⣿⡿⠟⠻⢖⠒⠂⢒⠚⠣⠿⣯⣿⡦⠄⠺⠟⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠸⣿⠷⣶⢾⣶⣤⡶⢶⣶⢶⣄⣀⣤⣶⣾⡿⠟
⠀⠀⠀⠀⠀⠀⣀⣿⣳⠟⠺⠗⠺⠒⢓⡚⠃⠭⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⣠⣿⣿⠏⣅⢻⡇⢸⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠒⠶⠶⠶⠶⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⡄⠀⠀⠀⠀⠀⡀⠾⣔⣱⣼⠏⣠⣿⡌⢀⣸⣻⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⣽⡿⠛⠁⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⠶⢿⣿⡿⠟⠛⠛⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣞⣵⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠄⣀⣀⣀⣀⣰⣧⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣮⠷⢼⣚⣊⠉⡀⠈⠁⣉⡹⣿⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠸⠛⢿⣿⣿⣧⣤⠤⣤⣤⣤⠤⣽⣾⡿⠻⠂
⠀⠀⠀⠀⠀⠀⢀⡤⣖⣯⠾⠋⠴⢒⣩⡭⢉⡉⠛⠛⠿⠿⠿⢿⣿⣿⠿⡿⠀⠀⠀⠀⠀⠀⠀⢤⣬⣿⣿⣿⣩⣮⣿⣿⣿⣠⣿⣿⠴⠄
⠀⠀⠀⠀⠀⠀⢿⣶⣥⡔⢀⡤⠖⢋⡥⠢⢋⡡⠖⠉⣠⠔⣂⠔⢋⣠⣼⡇⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠋⠙⠛⠉⠉⠈
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣽⣚⠻⠤⣴⣍⣠⣴⡯⠖⠈⡾⠗⣫⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⢉⢙⣻⣿⣿⣿⣿⣷⡄⠉⠐⣀⠄⠀⣪⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣺⠿⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠩⠭⠿⠷⡤⠤⠶⠋⠅⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠲⠶⠶⠶⢶⣶⠶⣤⡴⠖⠲⠤⣤⡤⠆⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠷⣶⣶⣶⣤⣤⣄⣀⣤⣴⣤⣴⡿⠿⠟⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠐⠒⠒⠠⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⣈⡡⠴⠒⠒⠀⠉⠉⠉⠉⠉⠉⠐⠢⢭⡒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢚⡩⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣊⠴⠊⠁⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⢦⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡥⠊⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠈⢇⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠘⡄⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡡⠊⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢞⡭⠞⠁⠀⠀⠀⠀⠒⠀⠤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠄⠀⣀⡀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⣩⠴⠚⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣸⢸⠁
⠀⠀⠀⠀⠀⠀⣠⢞⡡⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠖⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠠⠄⠀⠀⠀⢠⢃⠏
⠀⠀⠀⠀⢀⡼⣱⠋⠀⠀⠀⠀⠀⣀⣀⡐⠒⠀⠤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠚⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢡⠎
⠀⠀⠀⠀⣼⢱⠃⠀⠀⠀⠀⠰⠋⠡⣀⠉⢆⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⢀⡠⠖⡋⠔⡡⠂
⠀⠀⠀⠀⣟⢸⠀⠀⠀⠀⠀⢀⠘⠤⠜⢀⡌⠀⠀⠴⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠖⢊⣩⣴⡊⠐⠈
⠀⠀⠀⠀⠻⠸⡄⠀⠀⠀⠀⠀⠓⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⢖⣒⣒⣚⣒⣒⣒⣛⣛⣛⣋⣩⣭⣥⠤⠶⠒⠊⠙⠉⠀⠀⠀⠄
⠀⠀⠀⠀⡄⢣⡻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⣋⡥⠖⠋⣉⠡⠤⠄⠒⠒⠀⠉⠉⠉⠭⠔⠒⠂
⠀⠀⠀⠀⢰⡀⠑⢝⠲⣤⣀⠀⠀⠀⠀⠀⠀⢀⣀⡴⢞⣩⠴⠋⠁⠀⠈⠄⠐⠀⣀⣀⡀⠀⠀⠤⠤⠄⠀⠀⠂
⠀⠀⠀⠀⠀⠱⣄⠀⠉⠲⠬⣍⣛⣒⣒⣒⣚⣯⠵⠞⠉⠀⢀⣠⠤⠖⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠤⠤⠭⠭⠭⠁⠀⣀⡠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⠒⠒⠉⠁





⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠁⢒⠛⠦⣄⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⢰⠃⠀⠀⠀⠐⠈⠣⠀⠀⠀⠈⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⢀⣷⡀⢀⠀⠃⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠈⠉⢉⠐⠢⡀⠉⠛⣾⠳⣆⠈⣟⠙⢦⡀⠅⠀⠒⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⡀⠂⣨⣆⡀⠀⠐⠉⠀⠀⠟⢻⣉⡴⠶⠀⣀⠊⢠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢈⠁⠻⠋⠀⡀⠀⠀⠀⠰⠐⠃⠀⠁⠀⠶⠉⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠋⠈⠀⠀⢣⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣄⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠱⣄⠀⠀⠀⠀⠀⠀⠻⠓⠶⠚⠁⣄⡀⠈⠀⢀⠤⠛⠉⣼⢻⢶⡄
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡤⣘⡛⠃⢄⠀⠘⠃⠁⠄⠀⠰⢠⡄⡠⠺⠉⠋⡄⣀
⣾⣿⠈⠙⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⡟⠀⠀⢠⡟⢸⡿⠷⠤⠈⢳⠀⠀⠀⢈⠀⢰⡞⠁⠀⣀⣀⣴⡃
⢹⣿⡄⠀⠁⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡴⠋⠁⠀⠀⠀⢷⠘⠀⠀⢾⠁⢘⠃⠀⠀⠀⠀⠀⠛⢠⠄⠡⠙⠉⠁
⠀⠻⣷⣆⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠍⠋⠱⠢⠀⠀⠀⣿⢸⡀⠀⣸⡇⢰⡆⠰⠀⠀⠀⡄⠀⢸⡇
⠀⠀⠈⠻⣶⣄⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠉⠠⣤⣴⡶⣦⡈⠆⠀⠹⣌⠻⠿⠟⣡⡾⠤⢀⣀⡀⠀⣏⠀⢸⡇
⠀⠀⠀⠀⠈⠹⣷⣄⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠓⠀⠀⠀⠀⠀⡰⡟⢀⠐⠬⢱⠚⠀⠀⢈⣩⠵⣤⣀⠀⠀⠚⢤⡏⢉⣄⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣷⡌⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡬⠁⠀⠀⠂⠀⢸⣰⠀⣄⠹⠁⠀⠐⠎⣀⠀⠀⠈⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣆⠱⣄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠴⠀⡶⠀⡗⠀⠀⠀⠀⠀⠚⢻⠀⠃⠀⠀⠀⠴⣶⠀⠀⠀⣀⣀⠄⠀⠀⠀⢀⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠘⢳⣄⠀⠀⢀⢠⡙⢁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠘⢈⡤⠔⢴⣗⣀⣀⠙⡿⠋⠀⠀⠀⠠⠀⢴⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣴⣟⠙⢂⡀⠈⡆⠸⠂⠀⠀⠈⠀⠀⣀⡴⠢⣄⠀⠀⠀⠀⠀⠀⠰⠀⠀⠉⠀⠈⠁⠀⠀⠃⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠋⢹⣷⣾⣿⠶⢹⣿⣿⣾⣿⣖⠙⣿⢍⣐⣀⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡟⣩⠞⠻⠛⠋⢨⡌⠉⡅⠉⠛⢾⡀⢯⡷⠾⠿⣶⣤⣔⡠⢂⣀⣀⡀⣠⠼⠟⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠠⠈⠁⠀⣀⡀⠹⡆⠀⠀⠀⠀⡹⠻⠛⠳⣿⡷⢉⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢀⢀⣠⠔⢶⣾⢷⣄⠀⠈⠀⣄⣷⣦⣤⣀⡞⢠⣶⣷⣶⣦⡛⣶⣕⢀⠀⢺⢠⣴⡞⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣄⠀⠀⢀⣟⣉⡤⠾⣷⣧⣤⣄⠀⠀⠙⠉⠋⠻⠛⢧⠸⠏⠁⠀⣿⠃⢾⣿⣿⡷⣶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⢋⠉⢛⠉⠁⠀⠀⣯⠽⢿⢹⣷⠶⣧⣴⣤⣇⡀⢰⣿⣧⣤⣄⣿⣧⣾⣽⣿⣷⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⠀⠀⠀⠠⡶⠄⠤⣠⣤⣼⢿⣀⠀⣟⢿⣼⣄⣜⠀⠻⠿⠟⠛⣿⠿⠟⠻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⢀⡆⢀⠈⠀⠁⠨⠩⡀⢷⣿⣇⡼⠈⠛⠶⣶⠖⠛⠁⠀⠀⢠⣿⣿⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠈⠁⠉⠀⠀⠘⠀⢠⡅⢰⡇⢸⣧⠑⢀⣶⠏⣀⠀⠀⠀⠀⣸⠏⣽⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⣠⣴⡿⢟⠳⣮⣴⣾⠿⢄⣿⣷⢇⠀⢠⡟⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⠒⠤⡀⠲⢶⣿⣋⠀⠈⠲⣈⡉⠀⠀⣤⡟⠋⠾⠂⠀⣀⣽⠟⡕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠁⠒⠨⠍⣃⣀⠂⠬⠽⠿⠿⠩⠴⠶⠶⠺⠛⡋⠕⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⣄⡀⠈⠉⢉⣙⣂⣀⣶⡶⠾⠛⠋
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣁⣉⣏⣀⣍⣉⣭⣋⣭⣟⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣂⠈⡉⣱⠦⠤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄
⠀⠀⠀⠀⠀⠀⠀⡤⠜⠉⠉⠀⠉⠉⠓⢦⠀⠀⠀⠈⠳⣦⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡀⢺⣋⡵
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢠⡾⠁⠀⠀⡴⠋⠉⠉⠁⠂⠀⣴⠏⠉
⠀⠀⠀⠀⠀⠀⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠁⠀⠀⠸⡏⠀⠀⠀⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠱⠄⠀⠀⢐⣲⠆⣀⠀⣰⠶⠚⢹⠀⠀⠀⠀⠀⠀⣥⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣠⠴⣦⠴⠦⣬⡑⠚⠋⠉⠒⠮⡙⠍⢂⡀⢸⠀⠀⠀⠀⠀⠀⠈⠟⢌⣀⣀⣠⡾⠁
⠠⠚⣅⡀⠁⠀⠀⠈⢻⡄⠀⠀⠀⠀⠘⢆⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣴⠓⢄
⡂⢦⠏⡋⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⢣⡀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⡆⢱⡤⢤⡀
⣀⠚⠉⠃⠀⠀⠀⠀⠘⢿⣄⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠋⡷⠊⠙⠺⢿⠛⠙⠲
⠘⣇⠀⠀⠒⠤⠄⣠⠴⠦⠽⠀⠀⠀⠀⠀⠀⠀⣀⢤⡀⣏⡐⢲⣦⣄⡀⠀⠀⠀⣼⠀⢰⠃⠀⠀⠀⠀⠇
⠀⠈⠳⠤⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠵⢒⣿⣿⠴⠋⠀⠈⠹⣆⠀⠀⣿⠀⡜
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⡇⢠⠃⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⢀⣴⠾⢯⣍⠉⢧⡉⠒⢦⡀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⡇⠸⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⢀⡴⠋⠂⠀⠁⠳⠈⠀⠙⣆⠐⠿⣦⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣠⠋
⢠⡾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣬⣇⠀⠀⠙⠢⠤⢄⣠⣤⠴⠞⠁⠀⠀⠀⠙⠲⠤⣤⣀⣠⣇⠴⠃
⢸⠀⠛⡆⠀⠀⠀⠀⠖⢠⡊⠰⠤⣤⣼⠎⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⢀
⣿⠀⠀⠳⠦⣀⣰⠧⠬⠀⠀⢀⡎⢀⠇⡆⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠴⠃
⠹⣄⡇⠈⠲⢶⠶⣄⠀⠀⢀⢞⡔⠁⠀⡇⢳⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠊⠉⠉⠀⠴⠛⠁⠚⠋⠉⠉
⠀⠘⢧⠆⠀⠨⣄⠈⠙⢯⣴⣂⠀⢀⡞⢁⣸⠃⠀⠀⣀⡤⠴⠒⠋⠁⠀⠀⠀⢀⠀⢀⣶⠀⢦⡉⠉⠙⠒⠤
⠀⠀⠘⢧⣀⣀⣈⠓⠙⢓⣺⡿⣻⠋⡰⠋⠀⢠⣶⣉⣀⣠⣀⣠⣤⣤⡶⠴⠶⠾⠛⠛⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⢿⣿⣿⣦⡀⠀⠀⣈⠉⠓⠦⣄
⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⢈⢿⣿⣿⣷⣄⠀⠀⠀⠂⠈⠑⢄
⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⢀⠻⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⢰⣿⣿⠁⠀⠀⠀⠀⠈⢢⡈⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⡒⠲⡄
⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡆⠀⠐⠐⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠸⡄⠁⠀⣹
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠈⠐⠘⢦⣀⠀⠀⠀⠀⢀⣠⠏⠀⢰⣏
⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⢀⡤⣄⠀⠀⠀⢀⣿⣿⠀⡀⠀⠀⡠⠀⠀⠀⡀⠈⠈⠉⠓⠒⠚⡿⠀⠀⠀⠘⠈⠳⡄
⠀⠀⠀⠀⠈⣿⣿⡄⠀⢠⡏⡞⢢⢳⠀⠀⣸⣿⡏⢀⠇⠀⠀⣇⠀⣠⠀⣇⡤⠂⠀⠀⠀⣀⣽⠤⠤⣄⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠘⣿⣷⡀⠘⣇⢧⡼⡸⠀⣠⣿⡟⠀⡼⡠⠊⠀⣿⠞⣁⡴⠿⠒⠚⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠉⠉⣁⣴⣿⠟⢀⣠⠏⢁⡠⢚⣧⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠿⣟⠥⠒⢁⣮⣔⡫⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠒⠚⠋⠉⠁

⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⣀⡀⠀⠀⢰⡄⢀⣀⡀⠀⣠⣀⣀
⠀⠀⠀⠄⠈⠀⠀⠁⢠⡴⠊⠁⠀⠀⠀⠘⡇⠘⠿⠏⠈⠙⠜⠛⠃
⠀⠀⠀⠁⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⢠⠴⢀⣀⣀⡀⣠⡴⠚⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠁⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠓⠀⣀⡀⠈⠓⠛⠛⠛⠛⠙⠓⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠈⠉⠉⢩⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⢸⠀⠀⣀⠀⠀⢀⠀⠤⠀⣀⠀⠀⠀⠀⠀⠒⠲⠀⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠤⠤⠤⠚⠀⠀⠀⠀⢰⠁⠈⠉⠉⠙⡦⠀⠂⠀⠈⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡇⠀⠀⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡇⠀⢀⠬⠙⠀⠞⠀⠀⠀⠀⠀⠀⠀⡠⠮⢆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠢⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢀⠀⠀⢀⠀⠔⠀⠀⠀⠀⠀⠀⢀⠠⠠⠄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⡠⠖⢀⣀⠀⠀⠀⣤⣍⡋⣴⣲⠶⢚⣉⣥⣿⡟⣿⣶⣦⣄⣀
⠀⠀⠀⠀⠁⠀⢠⡼⠉⠀⠀⠀⠀⠀⢨⠈⠏⣼⣿⣿⡷⠚⠉⠁⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠠⡄
⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⣴⣒⣶⠟⣼⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⡤⢢⣀⢀⠀⠀⠉⠒⠏
⠀⢠⡀⠆⣂⣁⠀⠀⡀⣠⣾⣖⣿⣷⡽⢻⣿⣿⠁⠀⠀⠀⠀⡀⠀⣡⠤⣤⣿⣿⣿⠜⣹⣆
⠀⠀⠃⠀⠹⠃⠀⠼⠃⣼⠿⠞⠋⣡⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⢬⣡⣵⣿⣯⡿⠿⠯⠴⠟
⠀⠀⠀⠀⠀⠀⠤⠠⠀⠀⣠⣴⣿⣿⣿⣿⡿⠁⠀⠀⠀⡀⠀⠀⠀⢀⣤⣴⣿⠻⡛⠲⠐⡄
⠀⠀⠀⠀⠀⠀⠤⣤⣠⣄⢸⡿⠿⠛⠉⠁⠀⠀⠀⡄⠀⠐⠂⠀⠀⠀⠈⠛⠛⢷⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⣒⡒⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠫⠓⠋⠘⠋⣉⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡶⠶⠶⠶⠞⠛⠛⠒⠒⠲⠶⠶⠦⣤⣤⣄⣀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠋⠁⢀⣀⣤⣤⡶⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⣠⡴⣶⣿⣿⡉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠭⣟⠶⣶⡖⠛⢉⣠⣤⡴⠶⠛⠋⠉⠁
⠀⠀⠀⠀⣴⢟⣵⣿⣿⠿⢟⣋⣥⠴⠶⠶⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠶⠤⣄⠈⠻⢎⣿⣿⠟⠉⠁
⠀⠀⠀⢸⣿⡹⠟⠫⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣿⠃
⠀⠀⠀⠈⣇⢝⡶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠞⠋⣱⣰⠃
⠀⠀⠀⠀⠸⣎⢿⣾⣯⣿⣷⡶⠶⢦⣤⣤⣤⣤⣤⣤⣤⡶⠶⠶⠿⠛⠋⠉⠀⠀⠀⠜⣱⠏
⠀⠀⠀⠀⠀⠘⠻⢿⣟⣿⣿⣛⡫⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣭⣤⣄⣀⣀⣀⣀⣤⣤⣤⡴⠶⠖⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠛⠉⠉⠉⠉⠉⠙⠻⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⣶⣦⣄⣀⠀⣿⣿⣷⣾⣿⣿⠿⠿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄
⠀⠀⠀⠀⠀⣾⣿⠋⢀⣿⠉⠛⠻⢿⣿⣿⣿⡿⠛⠁⣀⣤⣤⣄⣈⠙⠻⢿⣿⣶⣄⠀⠀⠀⠀⠀⠘⢿⣿⣧⡀
⠀⠀⠀⠀⠀⢻⣿⣾⣏⡁⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⠿⠟⠛⠻⢿⣷⣦⡀⠙⠿⣿⣷⣄⠀⠀⠀⠀⠀⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣦⡀⣠⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡷⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠙⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣄⠀⠀⠀⠈⢻⣿⣷⡀
⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠹⣿⣿⣄
⠀⠀⠀⣠⣾⣿⡿⠛⠉⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣄⠀⠀⠀⠈⢿⣿⣷⡀
⠀⢀⣾⣿⡿⠉⠀⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡀⠀⠀⠀⠙⢿⣿⣦⡀
⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣄⠀⠀⠀⠀⠙⢿⣿⣦⡀
⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡀⠀⠀⠀⠀⠙⢿⣿⣦⡀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣄⠀⠀⠀⠀⠀⠻⣿⣿⣄
⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀⠀⠀⠀⠀⠈⢿⣿⣧⡀
⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣆⠀⠀⠀⠀⠀⠹⣿⣿⡄
⠀⠈⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡀⠀⠀⠀⠀⠙⣿⣿⡄
⠀⠀⠀⠙⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣄⠀⠀⠀⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣆⣠⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣄⡀⠀⠀⢀⣠⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣦⣄⣀⣀⣀⣀⣀⣠⣤⣶⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⡿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣉⠻⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⣍⡛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣋⣥⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶⣶⣤⣭⣭⣉⣉⣉⣉⣉⣭⣭⣥⣴⣶⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢞⣻⡟⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠀⢉⡩⢖⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⣠⠖⣩⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⢀⡴⣋⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠤⠤⠶⠶⠶⠦⠤⠤⢤⣤⣀⣀⡀⢀⣀⣤⠾⠋⠀⠀⣰⢋⡼⠋
⠀⠀⠀⠀⠀⣀⡤⢶⣚⣯⠭⠷⠒⠚⠛⠉⠉⠉⠉⠉⠉⠉⠉⠛⠓⠒⠿⠭⣟⣻⠦⣄⡀⠀⢠⢇⡾
⠀⠀⣠⡶⣻⡵⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢭⡳⣾⣸⠇
⢀⡾⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡻⡄
⡿⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢻
⣧⢻⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠢⢄⡀⠀⠀⠀⠀⠀⢀⡟⣼
⢻⣮⢧⡀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⣠⠞⣱⡏
⠸⣟⠳⣿⣶⣤⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡷⢞⡥⢞⡿
⠀⠹⣦⠈⠙⠳⢯⣷⣢⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⢴⣒⣭⠷⠞⠋⢠⡾⠁
⠀⠀⠘⢷⣄⠀⠀⠈⠉⠛⠛⠶⠿⠿⣿⣿⣿⣿⣿⣿⣭⣭⣭⠿⠶⠞⠛⠋⠉⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣀⡼⠋
⠀⠀⠀⠀⠀⠀⠙⠳⢦⣍⣓⠲⠦⠤⣤⣄⣀⣀⣀⣀⣀⣀⣤⡤⠤⠖⣚⣩⣵⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠚⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢀⡄⣠⢖⠀⠀⠠⠀⠄⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣇⠀⠀⠠⠴⠥⠤⣤⠎⢀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⠄⠿⢱⡧⠡⠀⠀⠀⠀⠀⣠⣾
⠀⠀⠀⠀⠀⠀⢠⣽⣧⡀⠀⠀⠀⠤⠶⠤⢤⣤⣎⠁⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⡄⠀⠄⠠⡎⠀⣡⣾⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠑⠥⡀⠀⠀⠀⠀⠀⠀⠈⠀⢠⢀⠰⣶⡐⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⢀⣾⣿⠐⡶⡲⠂⣀⢘⠉⠋⠀⢱⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠠⢦⠀⠀⠁⠀⠀⠀⠳⣄⠘⠻⣧⡆⣤⣤⢤⣦⣶⠀⠀⠀⠀⡀⠀⢔⡼⡿⢋⣾⠈⢆⡠⣘⣿⣿⡿⡛⠁⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⣽⠸⠟⠁⠀⠘⣻⢗⡍⢿⡟⠫⣿⠋⠀⠀⠀⠀⠷⠀⠞⠉⠐⠃⢙⠆⠘⠭⠋⠹⠉⢊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⡾⠜⢴⡉⡔⢁⠊⠛⠀⠀⠀⠀⠀⠂⠘⠂⢤⡤⢀⠀⠐⠒⠀⢀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣘⡍⠋⠀⢢⠠⠿⡶⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠁⠰⠒⠲⠴⠁


⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣀⣠⣶⣶⣤⣤⢴⣯⠶⢾⡿⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠐⠉⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣤⣶⣦⠶⠦⠼⠖⠶⢶⣶⣤⣄⡀⠀⠀⠀⠀⣀⡀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠈⠁⠂⠀⢐⣂⡝⠋⠉⠉⣉⠀⠀⠀⠀⠐⠀⠀⠀⠀⢹⠁⢀⠍⡀⣀⡉⡁⠀⠀⠀⠀⠈⠉⠋⠙⢻⣞⠻⠤⠈⡄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠒⠭⣛⠛⠂⠀⠀⠐⠗⠂⠀⠀⠘⡎⠔⠚⠉⠁⠈⠈⠀⠄⠀⠁⠀⠀⣰⠖⣻⣿⡏⢁⣠⠆
⠀⠀⠀⠀⢒⠒⠛⠲⠖⢶⢶⡷⠿⣟⣶⠦⠀⠀⢀⠀⠲⠊⠉⠀⠐⠶⠚⠛⠓⠀⠀⠀⠀⡀⠠⠖⢀⣐⢀⣐⡘⠠⠀⣄⠀⢀⡀⠀⠙⢻⣷⡆⠛
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠆⠀⠀⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣭⣤⠶⣤⡤⠐⠂⣤⣥⠞⣳⣿⣇⣀⠤⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠁⠀⠀⠀⠉⠉⠈⠉⠉⠉

⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⣀⣠⣤⣶⣶⣾⡿⠟⠛⠿⠿⠟⠻⡿⡿⣿⣷⣶⣶⣦⣤⣄⡀
⠀⠀⠀⣠⠊⠉⠟⢋⣿⠿⡿⠿⠿⠻⢻⣿⠉⠀⠀⠀⠀⠀⠀⣈⠥⠀⠒⠛⠉⠁⠀⡀⢀
⠀⠀⢸⣷⣿⣿⣳⣿⠋⡞⠁⣠⠆⣴⠎⢠⠆⣠⣂⠀⠤⠒⠈⠀⢀⣀⠠⠀⠀⠀⠀⠀⠀⣈⠁
⠀⠀⠀⠉⠛⢿⣿⣿⣶⣄⣼⣇⣪⣼⣶⣿⣿⣿⠟⠁⢀⡀⢰⢋⣄⠄⠀⠀⠀⠀⠀⠀⡰⠁⠀⣃⣆⡃⢂
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠉⠀⠼⣏⠁⡄⠀⠀⠀⠀⠀⠀⠰⢃⣄⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⣰⠀⠠⠀⡀⣰⠆⠁⠀⠑⠀⡴⠆⢉⡀⣤⣤⣀⣤⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠁⠀⢿⣀⠀⣨⡴⢷⡀⠁⢀⡤⠀⠀⠛⡛⠷⠾⣿⣿⣉⣀⣀⣠⣄⡀⠤⢶⣤⡀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣫⡍⢙⢻⡄⠀⠷⢡⣷⡟⢩⠧⢴⡖⢈⢁⠠⠔⠀⠂⢉⣫⣙⣷⣾⣿⣟⡋⣴⣴⠦⠓⢒⠼⠀⢠⡟⠿⢶⡄⠀⢦⡴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⡀⠀⠀⠙⣿⣷⣄⡈⠺⠿⠿⣿⠻⣜⠖⣬⡾⣿⣛⡯⣝⠻⣤⣅⠀⠒⠂⠂⣁⣠⣶⣏⡄⡈⠎⢀⣰⣿⡿⡾⠂⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠂⠀⠙⠫⢿⣓⣀⣁⢀⣀⣴⡙⠯⠾⠾⠾⠛⠋⠉⠉⣀⣠⣴⣶⣿⠏⠹⠚⠋⢁⣠⣴⡿⠧⠒⠋⣠⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣄⣀⣀⣉⣁⣀⣀⣤⢤⣴⢶⠾⠿⠿⠻⠛⠛⣉⣁⣠⣤⣤⣶⣶⠿⠟⠛⣉⣡⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⠘⠶⠤⠴⠶⠖⠒⠚⠛⠋⠙⣯⣉⣉⣡⣬⡤⠴⠒⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢠⡄⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣴⣤⠀⠀⠰⠀⠀⠂⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⡇⢈⣃⠸⣿⡿⠂⠀⣤⡀
⠀⠀⠀⠀⠀⠀⢴⣀⣿⠃⠈⠛⠻⢀⣀⡀⡀⠀⡀⠀⠈⣴⣿⣿⣦⠀⠀⠀⢠⠀⠂⠀⠀⠁⢰⡿⣀⡀⠈⠀⠀⢀⠄⠹⠄
⠀⠀⠀⠀⠀⠀⢚⣯⣟⣿⠶⢠⢇⣼⣾⣧⠀⠀⠀⠔⠂⣿⣿⣿⣿⠃⠀⠀⡀⠀⣢⡈⢱⠀⠈⢀⡓⠛⠿⠠⢾⡟⠀⢠⠀⠀⣠
⠀⠀⠀⠀⠀⠘⠈⡿⠛⠉⢀⡌⠸⣿⣿⣿⠃⣌⠀⠠⠀⠈⠉⠙⡅⠇⠀⠈⠉⠣⢦⠁⠀⠀⢆⡼⠑⣧⣤⢆⣀⠦⡌⠻⠂⠈⠙⡄
⠀⠀⠀⢠⡞⢰⣿⡷⠀⣹⣿⣿⠒⠀⠁⣠⠆⠙⣦⠀⠀⠙⠀⠀⢫⣤⠴⠂⠀⠀⠀⠀⢤⣀⠈⠁⣺⣿⣿⣿⣿⣷⡄⣰⣷⣄⠀⢕
⠀⠀⠀⠈⠀⣿⡿⢱⠈⣿⣿⣿⠇⠀⠀⠛⠀⢰⡄⠀⠻⣷⣠⣶⣤⠀⠀⡤⠀⠈⠀⠀⠀⠙⠋⠀⣿⣿⣿⣿⣿⣿⣷⠘⠛⠃⡀⠈
⠀⠀⠀⠀⠸⠟⠁⢈⡁⠙⠛⠁⠀⢵⠨⡀⡖⠂⠱⠀⢾⣿⣿⣿⣿⡇⠀⠆⠀⠀⠀⠀⠀⠀⠀⡖⠘⢿⣿⣿⣿⣿⡿⠀⠀⠘⠃⠐⡄
⠀⠀⠀⢻⠀⣿⣦⠹⣷⣆⣠⡀⠘⠚⠃⠁⠀⠶⠴⠶⠈⠻⠿⠿⠋⢡⣀⣠⡀⢈⡃⠀⠀⠀⢀⣴⣶⡇⠙⠿⠛⢋⣤⠘⡄⠀⠀⠀⢀⡀
⠀⠀⠀⠘⠃⠚⠿⠿⢾⣿⣋⠁⡴⢋⡙⢶⠳⠄⠀⣂⠀⣀⣀⡵⠖⢈⡉⢉⣀⡈⠑⠶⠄⢀⠀⠙⠛⠁⢠⣦⠀⠋⣀⣤⣠⣄⡀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⡿⠀⣿⣿⣿⠂⠧⣌⣠⣾⣏⣀⣴⢶⣄⠺⣿⠇⠀⢘⡻⢿⠿⠁⡸⡁⢠⢺⣷⡄⢠⣶⣿⣿⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣈⠙⠇⢀⣠⣤⡄⠀⠀⣟⠰⠆⣻⢠⡌⣠⣾⣿⣿⣿⣷⠆⡀⠑⢌⠉⢁⡀⠘⠻⠟⠋⢀⠀⠀⠙⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡵⣄⠈⠛⠿⠇⣀⠀⠈⠓⠚⢁⡼⠹⣿⣿⣿⣿⣿⡟⠀⠃⣀⡀⣴⣿⣿⢀⣤⡴⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣟⣲⢠⣄⣀⠀⠀⠀⢀⢠⠀⠀⠈⠙⢛⣫⣥⠀⢺⣻⣿⡷⢈⣭⣤⡄⢠⣼⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⢠⡰⢢⠉⠁⣤⣤⣤⠀⠛⠿⠿⠀⠀⠙⠋⢁⡈⠻⠻⠁⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⢃⠀⠀⠀⠘⣿⠁⠀⠠⠑⠠⠀⠆⠀⡇⠀⠈⢰⠀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⢠⣴⣤⣤⡀⠀⢰⡁⠇⠀⢀⢀⡀⠓⠄⠐⣡⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠻⣿⣿⣶⡄⠀⢀⣾⣿⣿⣿⣆⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠃⠀⠀⢿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢸⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠈⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⢣⡀⠀⠀⡰⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠒⠒⠛⠛⠉⠉⠉⠉⣉⡩⠝⠛⢉⡡⢤⣔⡀⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢹⠃⠀⠀⠘⣄⠀⠀⠙⣆⠀⣇⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⠀⣀⣀⣀⣀⣠⡤⠤⠒⣋⡩⠤⠒⠚⢛⣉⣉⢉⣉⡉⢠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⠸⣄⠀⠀⠀⠈⠳⡀⠀⢸⠀⠘⢦⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠺⡿⣭⣥⠴⠖⣂⡩⠤⠖⠚⡛⠋⠩⠉⠉⠁⠀⠀⠈⠀⠀⣀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠈⢣⠀⠀⠀⠀⢱⠀⡸⠀⠀⠀⠱⡀⡃⠀⠀⠀⠀⠀⠀⠀⠰⠿⡙⠂⠉⠙⠒⠲⠤⠤⠤⣤⣤⣀⣀⣁⣤⡭⠤⠴⠒⠉⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⢠⠇⠀⠀⢀⣜⡴⠁⠀⠀⠀⢀⣧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⠚⠁⠀⠀⠀⠋⠁⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠒⠒⢦⣀⣀⣠⡶⠶⠦⢤⣄⣀⠀⢀⡀⠀⠀⠈⠳⢤⣉⣙⡓⠒⠒⠒⠒⣚⣉⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠓⠲⢴⡞⠉⠉⠙⡟⠁⢀⡀⢀⣼⠁⠉⠈⠁⠉⣄⠀⣀⣀⣉⣹⣏⡻⢤⠤⠶⣆⠀⠀⠈⠁⠈⠉⠉⠉
⠀⠀⣀⣠⡤⠤⣶⣶⣾⠿⣧⣀⠀⠀⠉⠛⣦⣸⡷⣾⠁⢸⢋⡁⢙⠛⠛⠛⠛⢧⣠⠳⡈⠋⠡⣴⡿⡁⡙⠺⣏⣳⣶⣟⠒⠒⠶⢤⡀
⣰⠞⢉⡤⢶⡞⢏⣀⡅⠼⠏⠀⠀⡶⢶⣞⣻⣯⣀⣀⡠⠁⠞⢡⡉⠀⢠⡶⠦⣴⣧⠶⢿⠗⠀⠐⠁⠀⢀⣾⠈⡁⠀⡿⣿⡉⠳⡄⠈⢧
⢧⠀⠹⢄⣸⣄⡀⠻⣧⡀⣠⠤⠊⢰⡏⠉⠉⠛⢲⣊⠶⣌⡹⣍⣠⠤⠼⠧⣄⣀⣀⡤⠾⣄⣀⡔⠈⣳⠟⣛⢀⣢⢞⡵⢻⣇⡴⠋⢀⡼
⠈⠙⠦⣄⣈⢧⡙⠲⢬⣉⡛⠳⠶⠾⠿⣄⡀⠀⠈⠁⢀⣠⣿⡊⣀⠤⠤⣄⡈⢻⣁⣀⣴⣏⣈⣑⣠⠟⠒⣚⣫⠕⢋⣠⣞⣥⠤⠖⠋
⠀⠀⠀⠀⠉⠉⠙⠓⢦⣄⣉⣙⠓⠲⠶⠤⠭⢭⣭⣭⣭⣭⣤⣭⣭⣭⣭⣥⣬⣭⣭⣥⣤⠤⠭⠶⠖⣚⣋⣥⣴⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢬⣍⣉⢙⠓⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⠦⠤⠶⠶⠶⠶⠒⠒⢒⠋⣉⣩⠴⠊⠁

⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⠄⠀⠐⠒⠒⠒⠒⠒⠒⠒⠂⠀⠠⠤⠄⢀⣀
⠀⣀⠤⠒⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⣀⢒⡀⠀⠤⠤⠤⠭⠭⠉⠬⠷
⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣓⣦⠀⠖⣒⡢⠭⠇⠒⠈⠉⣀⣀⡠⠤⠤⠴⠶⠶⠶⠤⢤⣀⣀
⡗⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡆⢹⠀⠁⠀⣀⡤⠔⠒⠋⠉
⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡄⣨⡤⠒⠉
⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠴⠚⠁
⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠑⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠄⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠃⠀⣠⠀⣀⣀⠀⠀⠘⠀⠀⠨⠀⠊⠉⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡤⠀⠀⠀⠀⠔⠃⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⢴⡄
⠀⠀⠀⠀⠀⠀⠠⣀⢀⠀⠀⠀⠀⠀⠀⢀⣴⠁⠀⣀⠠⣤⣄⠀⠶⡄
⠀⠀⠀⠈⣇⣠⡉⡾⠛⢧⣦⡄⠀⠀⠀⠀⠀⣠⠀⠠⢀⢄⠀⠈⠛⡘⢷⣄⡀
⠀⠀⠀⠏⠛⠑⠀⠁⠀⠸⡏⢰⣤⣇⠁⢴⣦⢾⣾⠁⠀⠈⢁⣠⣀⡀⢀⠻⠿⡏⠑⠂⠀⠀⠓⠭⠒⠤⢀⡀
⠀⠀⢧⠀⡠⠀⠐⠀⠀⠀⢸⣛⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⠉⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⣮⢶⣄⠈⠙⠢
⠀⠀⠐⢄⡀⣀⣀⣠⢴⣾⣿⣿⣿⣿⣯⣿⣿⠛⠑⢷⠄⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⡆⠙⢎⠳⣽⠷⡆
⠀⠀⠀⠈⠛⠉⠸⠗⠛⠛⠻⠿⣿⣿⣿⡟⠁⠀⣸⣿⡖⠀⠀⢢⣠⠀⣞⠉⠁⢀⠀⢀⠚⠛⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⡏⠀⠀⢀⠀⠀⢀⠀⠚⢻⡄⠙⠃⠴⢛⡅⠝⠃⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⡀⠂⠀⠀⠀⣀⠁⠀⣀⠀⠐⠉⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄⠀⠀⠀⠀⠠⠤⢀⣀⡀
⠀⠀⠀⠀⣀⠄⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠐⠀⠀⠀⠀⠰⡄
⠀⢠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⢄⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇
⢀⡃⠀⠀⠀⠀⠀⠀⢀⡠⠤⠄⠐⠒⠒⠒⠒⠒⠠⠤⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠄⠤⠄⠐⠒⠂
⠘⡅⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⡠⣿⣧⠞
⠀⢡⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠖⠒⠉⣠⡳⠂
⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠈⠉⠒⠒⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠘⠿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋


⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠁

⡗⢺⣆⠧⠔⠀⠀⠀⢀⡜⡏⣿⠋⢀⡴⢾⣟⣭⣿⣿⣿⣧⠀⠀⠀⢹⣧⣄⠀⠉⢳⡄⠀⠀⡇⠀⡃⠀⣇⠀⡃
⠟⠊⠁⠀⠀⠀⠀⠀⠈⢷⣿⣯⣤⢻⠽⣴⣻⣮⣿⣿⣿⠏⠀⠀⠀⠀⠉⠙⠻⢿⣿⡇⠀⠀⢧⣄⢰⡀⠱⡀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠊⠓⠒⠚⠻⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠉⠁
⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀⣀⣤⣄⣀⠀⠀⠀⠀⣴⣶⣾⣭⣴⣟⠙⢫⡿⠀⠀⠈⠂
⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⡌⠃⠀⣴⣿⣥⠙⢦⣭⣏⡘⣆⠀⠀⠉⠻⠏⠿⠯⠽⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⣠⣾⣧⣿⣷⠀⠀⠀⠀⠀⢰⣿⣟⢿⣧⡄⢸⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⣀⡀⠀⠀⢀
⢠⡞⢹⣿⡯⢞⠛⠀⠀⠁⠀⠀⢸⣏⠛⠊⠉⠸⠿⠁⠀⠀⠀⢀⠠⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⣀⡿
⣇⢨⡴⠋⠂⠀⠀⠠⠁⠀⠀⢠⣟⢁⡀⣠⡼⠃⠀⠄⠀⣠⣬⣶⣤⡾⢳⡖⣠⣀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⢮⣾⠃⠀⠀⣾⡜⢻⡿⠉⠢⠀⠀⠀⢰⡟⠀⠿⠋⣼⣷⣶⣏⠽⣷⠄⠀⠀⠀⠀⢠⠏
⣠⣤⠖⣦⠠⣾⠇⡏⠀⠀⠐⢯⢕⡈⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠘⢻⣿⡏⠷⠴⣯⠘⢦⣀⠀⣰⠏⢀⣀⣤⣤
⢏⠁⠀⣀⣠⣡⡟⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⢢⡀⠀⠉⢯⣀⣘⣃⠛⢻⣯⣄⣘⠿⣷⡒⣨⣿⠋⢠⣾⡟⠛⠻
⡄⢀⢈⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⠈⠛⠯⣽⣏⣚⣷⣶⣿⡿⠟⠁⢠⣿⡅⣳⠆⢂
⣶⡿⣫⣿⠏⠀⠀⢆⠀⠘⡄⠀⢢⠀⢃⠘⡄⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⣿⣱⡀⣠⣼
⣸⣿⠟⠁⠀⠀⠀⢠⣡⠀⣇⡀⣸⡆⢨⡄⣱⠀⠀⠀⠰⡈⠿⣷⠶⣦⣄⣀⣀⣀⣀⣤⣤⡀⠀⠀⢿⣿⣆⣩⡌
⠋⠁⠀⣤⡀⠀⣶⡛⢿⣶⡉⡙⡋⠙⣋⣻⣿⠿⠇⠀⠀⠈⢷⣍⠓⢮⣭⣭⣭⠷⣶⣶⣈⣿⣦⠀⠈⣙⣛⣩⣵
⠀⠀⣴⣹⡿⠀⣻⣧⠀⠛⠿⠷⠲⠾⠛⠿⠃⠀⠀⠀⠀⠀⠀⠙⠳⣔⣏⠉⠈⠒⠈⠛⠻⣿⢿⣶⡄⡀⠈⠉⠉
⡼⠋⢉⣽⠁⣰⠋⠋⠈⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢇⠀⠀⠀⠀⠛⠀⣰⡏⣿⡄
⣤⡶⣼⡇⠀⣿⡒⠠⢀⠀⠇⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⡀⠀⠈⢳⡀⠀⢀⠐⣊⣼⣶⡿⠁⠀⠀⣴
⣸⢿⣿⠁⠀⠘⢿⣄⣉⣈⠻⢀⣄⣠⣠⡭⡴⠾⠋⠀⠀⢠⣶⡜⠺⢿⣷⡦⠀⠹⣗⣧⣌⣤⠾⠟⠀⠀⠰⠘⣿
⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⢉⡀⠀⠀⠀⠀⠀⢀⣇⠁⠀⠈⠁⠁⣝⣧⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠙
⠄⢠⠀⡄⠀⠀⠀⠀⠀⠀⠀⣖⣴⣾⡿⢻⣿⣿⣷⡶⣄⠈⠋⠙⢹⣄⡀⠔⢦⡾⠇⠀⠀⠀⡠⠂⡠⠀⡀⠀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣤⣶⡶⣿⠛⠉⠉⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠈⠁⠀⢰⠃⢠⠊⠁⠈⠑⠦⡈⠑⢄⡀
⢠⠖⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⢸⠀⡆⠀⠀⠀⠀⠀⠈⡆⠀⠙⢆
⡏⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢇⠂⠀⠀⠀⢀⠞⢀⠞⠓⣄⠑⡄
⢻⣄⠀⠀⠾⠷⠶⠦⠤⠤⠤⠤⠤⢤⣤⣤⣤⣤⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠈⠙⠲⠤⣤⠏⣠⠋⠀⠀⠈⢦⠘⣆
⢀⡟⠃⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢸⠉⠒⠢⠤⢍⣉⡐⠒⠒⠚⠀⠘⡄
⣾⠀⠀⠀⣼⠛⠛⠻⠶⠶⠶⠶⠶⠶⠤⠤⣤⣤⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⢆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠲⡀⢳
⠘⠷⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣄⣀⢄⠀⠀⠀⠀⠀⠀⠀⠱⡌⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⡦⢄⣀⠀⠀⠀⠀⠙⣄⠳⣄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠀⠀⠀⠀⠀⠈⢣⡘⢦⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠙⢦⡙⠦⣀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢾⣦⣤⣀⣀⠙⢦⡈⠓⠦⣄⡜⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠷⢿⣷⣤⣀⣠⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⣷⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⡿⢁⣼⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣯⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠟⣽⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣣⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢪⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠣⢯⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡃⠄⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣤⣶⣶⣶⣮⣽⣿⣿⣿⣿⣿⣯⣭⣭⣝⣛⣘⠷⣀
⠀⠀⠀⠀⠀⠀⡀⣔⡮⠟⢚⠉⠭⠁⡄⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣦⡀
⠀⠀⠀⠀⢀⢮⣾⣫⠀⣠⠸⢀⣈⠁⢁⣛⠫⠭⠭⠭⠭⠭⠽⠿⠟⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⢀⣿⣿⣟⣡⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⠏⢻⣳
⠀⠀⠀⠀⠸⣟⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣔⣿
⠀⠀⠀⠀⠀⠹⣿⣿⣶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⣿⣾⠇
⠀⠀⠀⠀⠀⠀⠈⢾⣿⣿⣾⣯⣶⣴⣠⣤⡀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣶⣾⣽⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⢿⣟⡿⣻⣿⣿⠿⠿⡿⡿⣻⣿⣿⣿⣿⣟⣿⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣾⣷⣿⣿⣴⡾⠿⢶⣿⣻⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣤⣶⣦⣤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⢸⣂⡠⠚⠛⠛⠠⢷⣶⣶⣾⣛⣀⣀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡷⢤⣄⣻⠟⠧⣤⣄⡀⠀⠁⠁⠀⠂⠀⠉⠀⠀⠀⠀⠈⢍⡛⠻⡿⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢄⠐⠻⢤⡀⠀⠀⠠⠍⠛⠳⠆⣀⡤⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠑⠓⣁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠁⠀⢐⣟⣀⣠⡄⠀⠉⠀⠂⠠⠀⡀⠀⠀⠉⠑⠢⠤⠀⠀⠀⠀⠀⠐⠄⠀⡀⠀⠀⠘⠛⠿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⠀⠀⢰⡏⠉⠉⡓⠛⡾⢧⣤⡄⠀⠀⠙⠃⠲⠦⢀⠀⠀⠀⠀⠐⠂⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣏⡇⠛⠋⠀⡈⠱⠤⠀⠰⠮⠀⠰⠟⠉⠙⠋⠓⡦⠀⠀⠀⠀⠉⠂⠠⢤⣀⡀⠀⠈⢑⠤⠆⠠⠄⠠⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣩⡄⠈⠁⣜⠣⠈⠀⠀⠀⠘⠛⠓⠯⣅⣤⣠⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⢀⡰⢛⡭⡴⡥⠀⠀⠀⡣⢄⠈⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⢱⢾⡴⠂⣼⡋⠀⠘⠻⠒⠤⢒⣀⣄⠠⠀⠈⠉⠑⠲⠆⣠⣤⣀⣠⣴⠒⣂⣩⣶⠶⠚⡩⢖⡥⣪⣞⡀⠁⠸⣀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢘⣿⠷⠶⠙⢿⣤⣖⡦⠤⠀⠀⠀⠁⠘⠲⣟⢓⠤⠴⠊⠙⠛⢿⢿⣟⠉⠐⢊⠴⣣⢞⠕⡩⢊⡹⢻⣵⣿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣿⢿⣿⣦⡤⠁⠋⢉⣰⣶⣦⣬⡷⠢⠀⠀⠀⠀⠀⠀⠀⠘⠉⡡⢀⣈⠁⠔⠱⡳⢋⠔⣉⣴⣿⣿⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡏⣿⢦⡟⢿⣿⣶⣶⣿⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⡰⠋⠀⢀⡡⢔⡁⣢⣮⡾⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⢿⣇⣧⡖⣳⣿⡿⠏⠊⠠⠀⠠⡀⠀⢀⣀⠀⡀⠀⠀⠀⠀⡴⠀⠈⡰⢀⣔⣩⣶⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠿⢻⣧⣿⣿⣿⣿⣿⡇⠐⠆⠀⠈⠂⠀⠀⠀⢁⣸⣀⣀⣀⣄⣴⣷⣤⣤⠴⠛⠛⠉⠁⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡃⠀⡤⢶⠔⣀⣤⣶⣿⣿⠿⠿⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠦⠀⠀⠈⠒⠐⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣻⣿⡿⠿⠟⠋⠁⠿⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠤⠀⠙⠀⠀⠀⠀⡠⠀⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡠⠄⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⣖⣈⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣁⣲⠄⠀⠀⢀⡀
⠀⠀⠀⠀⣿⠈⠉⠙⠛⠛⠛⠛⠛⡛⠛⠛⣛⣋⣉⠩⣿⠀⢠⠚⣁⠨⠆
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠓⡏⢠⢁⠎⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢀⡀
⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣨⡀⢸⣧⢋⡈⠰⠶⠤⡔⠊⠉⠑⠚⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠶⠀⠀⠀⢀⡤⠀⠀⠀⠀⣻⣾⣏⣀⡀⠠⠤⠰⡀⠀⠀⠀⠠⣀⠀⣀⠄⠀⠀⠀⡆
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢠⣚⠝⢡⠆⠰⢄⡀⠒⢄⡎⠀⠀⠀⠀⠀⢈⡝⠁⠀⠀⠀⢀⡕
⠀⠀⠀⠀⠀⢸⡀⠀⠰⠆⠀⠀⠀⠀⠀⢠⠟⢁⠔⠁⠇⠀⠃⠉⠢⢄⣗⠦⣤⠤⣢⢭⢭⢺⢳⣤⠢⠴⢊⡴
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢾⣿⠀⠀⠀⠐⠓⢪⠀⠀⠀⢰⠀⡄⠀⠀⠀⠉⠑⠒⢘⠧⣓⠵⠇⠘⡇⠈⠈⠁
⠀⠀⠀⠀⠀⠀⡕⢄⡀⠀⠀⠀⠀⠀⠀⠀⢈⣦⠀⠀⠀⠦⠁⠀⠀⠀⠀⠀⢠⠃⠀⠀⠑⡄⢀⢳
⠀⠀⠀⠀⠀⠀⠈⠢⢌⣀⣁⣀⣀⣀⣀⣀⡡⠔⠓⠤⣀⠀⠀⠀⠀⢀⡠⠒⠁⠀⠀⠀⠀⣄⡞⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉





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

⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠠⠄⠀⠀⢀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⠄⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢰⠎⠄⠂⣠⣦⡀⠠⠀⠀⢀⠀⠀⠀⠀⠂⢠⣤⢴⠵⡀
⠀⠘⣄⠀⠄⠀⡿⠀⠀⠀⠀⠠⡀⠀⠀⠀⡊⠀⠀⠀⢄⠙⠮⣙⠒⠂⠀⠀⠀⠀⠈⠐⢺⠋⠑⠀⠑⠂⠀⠒⠉⠀⠀⠀⠀⣤⣲⡭⣆⣼⣽⣄
⠀⠀⠈⠓⠺⠀⠘⠆⠀⠀⣀⡴⠃⠀⠀⠀⣧⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠈⠃⠻⠜⡰⢡⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⡀
⠀⠀⠀⠘⠠⠟⠄⠐⢂⣠⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠤⠬⣳⡤
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠈⠄⠀⠀⢠⠀⡜⢀⡴⠒⠀⣄⠀⠀⠀⢰⠀⠃⣀⣸⢼⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡠⠩⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠒⠈⢠⠀⠐⠄⢠⠈⠀⠀⠀⠈⠦⡴⠒⠁⠈⠣⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⢰⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⢸⡄⣀⠂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠉⠓⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠉⠁⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣄⠀⢀⢭⠘⠶
⠀⠻⠶⠄⠀⠁⠒⠦⢄⣀⠀⠠⠀⠀⠀⠀⢀⣀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠑⢀⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠉⠓⠒⠂⠀⠀⠰⢄⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⣤⡤⣦⡤⠄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠖⠤⢺⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠐⠒⠛⠃⠈⠀⠀⠀⠀⠤⠀⠠⠜⠀⠃

⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠈⡄⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣥⣖⢦⡀⠠⠄⡂⣤⡇⠂⠀⠀⠀⠀⢀⡠⠄⠂⠀⠀⠀⠀⡠
⠀⠐⠄⠑⡀⠐⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠀⠀⠀⡿⣹⠃⠀⠀⢀⠴⠋⠀⠠⡔⠀⠀⠀⠈⠁⠠⠂⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠒⡈⠆⠐⡀⠀⠛⢠⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⠁⠁⠃⠀⠀⠐⡀⠀⠀⠀⠀⠀⡠⠴⠁⠄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠘⠈⠆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢧⡀⣀⠀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠀⠃⠀⠀⠀⡄⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠂⣀⠉⠩⠬⠭⠉⠁⣀⠂⠀⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⡀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡑⠤⡀
⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢉⠁⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠈⠐⢌⠢⡀
⠀⠀⠀⠀⠀⡠⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⡑⠄
⠀⠀⠀⠀⡐⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠄⠤⠀⣀⠀⠀⠡⠉⠀⠀⠒⠂⠀⠀⠀⠐⠌⢂
⠀⠀⠀⡐⢀⠃⠀⠀⠀⠀⠀⠀⠀⣀⠔⠒⠐⠤⠁⠀⠀⠠⠠⠀⠤⠄⠀⠠⣀⠀⠀⡀⠐⠀⠐⡀⠀⠀⠀⠀⠘⠄⠄
⠀⠀⢀⠁⠂⠀⠀⠀⠀⠀⠀⡠⠎⠀⠀⠣⠀⠂⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠢⠔⠀⠠⠀⠓⠀⠀⠀⠀⠀⠀⠈
⠀⠀⡈⠠⠀⠀⠀⠀⠄⠀⠐⠁⠀⠀⠁⠠⡐⢆⡀⠖⠠⢀⡀⠀⡀⠀⠀⠀⢀⠐⠒⠒⠒⠓⠒⠠⠄⠀⡀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⢄⠈⠢⢄⠀⠁⢐⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠁⡇⠀⠀⠀⠀⠰⠇⠀⠀⠀⣌⢀⡠⠄⢂⡑⠀⣀⠀⠀⠀⠀⡤⠃⠀⠃⠀⠔⠐⠀⠀⠀⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠖⠉⠀⢀⠐⠉⠀⠀⠈⡻⢁⠄⠊⠀⠐⠀⠀⡄⠀⢂⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢈⠀⠀⠀⠀⡨⠄⠀⠀⢈⠀⠀⠀⠀⠉⠀⠀⢀⠀⠀⠀⠈⠢
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⠴⠊⠀⠀⠉⠁⠢⢴⡀⠊⠀⠀⠀⠔⠁⠐⠀⢁⠄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠌⠀⠀⠀⠱⠀⢀⢀⡀⠘⠢⠤⠄⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⡄⠀⠀⠄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⢄⠠⡀⠀⠀⠀⠀⠀⠁⠈⠌⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡈⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠤

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

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠀⠈⠁⠒⠂⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣄
⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⡀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⡎⠀⠀⠀⠀⠀⠀⡀⠠⠤⠀⠒⠒⠂⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢺⢧⠋
⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣀⣀⡀⠠⠄⠤⠀⠂⠈⠁⠠⠟⠁
⠀⠈⢦⡀
⠀⠀⠀⠙⠢⠤⣀⣀
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶