Jog Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣀⠈⣿⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⢶⢆⠀⠀⠀⠀⠀⠀⠈⡃⠀⠀⠈⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠘⠶⣿⡃⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢳⡆⠀⠀⠀⠀⠀⠀⠒⣚⡡⠊⠀⠀⡅⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⢢⠶⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢰⡅⠀⠀⠤⢀⣀⡠⠴⠚
⠀⠀⠀⠀⠀⠀⢀⢜⡀⠀⡔⠂⠀⠀⠀⠀⠀⠀⠀⢀⣈⡗⠠⠀⠭⠤⠀⣀⣀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠺⠏⠋⠙⠁⠐⠂⠀⠀⠀⠀⠀⠀⣩⣥⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣀⡁⢀⠀⠀⠀⠀⠘⠋⡇⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⠀⢀⣈⠤⠀⢀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠂⠀⠀⠀⠠⠊⠀⡀⠃⢄⠀⠀⠀⠀⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢈⠀⠀⠤⠀⡒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠆⠌⠠⠤⠄⣀⠀⠀⡀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠀⠀⠊⠁⠀⠀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⡦⠁⠀⠀⠂⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠇⠀⠀⠀⣠⣊⠁⠀⠀⠈⠀⡀⣀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠄⠀⠀⠀⠘⠄⠀⠀⠀⠀⢰⠡⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡆⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢶⡒⠀⠀⠐⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠁⠀⢱
⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⡒⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣤⡆⠁⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡶⣅⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠊⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣎⠉⠉⠁⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠒⠚⠳⠖⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠚⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠈⠙⠛⠉⡌⠛⠛⠋⠀⠀⠉⠛⠛⠿⠿⠿⠿⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⡇⢀⣤⠀⠀⠀⠠⠦⠄⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⢉⠙⣿⣿⣿⣿⠃⠀⠘⢿⣿⣿⣿⣇
⠀⠀⠀⠀⢁⠀⣼⡆⠀⠀⠐⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠂⣿⣿⣿⡟⠀⠀⠀⠀⠉⠛⠛⠛⠛
⠀⠀⠀⠀⠈⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⠟
⠀⠀⠀⠀⠀⠘⢄⠈⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠈⠣⡀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡄⢀⠀⠀⠀⠠⢤⡾⠟⢁⠚⠒⠛⠀⠒⢤⡀⠀⣀
⠀⠀⠀⠀⠀⢀⢄⠒⠱⣄⠀⠀⠀⠀⠀⠀⢀⠜⢃⡠⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠓⠢⢄
⠀⠀⠀⠀⠀⢏⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠈⣀⠌⠁⢀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡄⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠑⠤⡀⠀⠀⢀⡐⠁⢀⠔⠠⠊⢀⣴⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⠢⠔⠀⠀⢶⡀⢀⣤⣾⡿⠃⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠶⠟⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⠐⠈⠀⠀⠀⠘⣿⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠈⠀⠀⠀⠀⣀⣀⣀⣀⣤⣬⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣴⣾⣿⣿⠻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣾⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⣿⣿⠏⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⢁⣿⣿⣧⣶⣾⣿⣶⣶⣶⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⠁⠀⣿⣿⣿⣿⠘⠿⠿⣛⣋⣭⣭⣭⣭⣉⣛⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠉⠙⢣⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⠒⠚⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠂⠉⠉⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⣻⠿⠒⠒⠈⠉⠉⠉⠉⠀⠀⠀⢀⣔⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣥⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⣾⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⢤⡏⣿⡀⠀⠀⠀⠀⠀⠀⠀⠙⡦⣀⠀⠀⢛⢤⡀⠀⠀⠀⠑⢦⣀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢱⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠉⠒⣉⢜⣛⠢⣄⠀⠀⠈⢫⠑⠢⢄⣀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢣⠪⠇⠀⠀⠀⠀⠀⠀⠀⡰⠁⠘⢉⠐⠁⠀⢂⠀⠙⢢⢄⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢔⡄⠀⠀⠀⡠⠞⠁⠀⠀⠂⠀⠀⠀⢘⠀⠀⡄⠀⠀⠀⠀⠙⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠑⣭⣷⣶⣶⣄⠳⣄⠀⠀⠀⢀⠀⠀⠀⣨⠀⠀⠓⠂⠉⣹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢸⣿⢛⣝⢻⣿⡷⠼⠆⠀⠀⠒⠘⠉⠉⠁⠀⠀⠀⣰⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡀⠸⣿⣷⣥⣾⣿⠇⠀⠀⠠⠒⢧⢄⡀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠢⣈⠛⠛⢛⠁⠀⠀⠀⠀⠀⠈⠓⢤⣉⣉⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠦⢄⣀⠀⠀⢀⣀⣀⣠⠬⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⡔⠒⠒⢋⠏⠀⠈⠑⠺⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢇⠀⡰⠃⠀⠀⠀⠀⠀⢀⠏⠉⠒⠒⠒⠒⠒⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡀⢄⠀⠘⢆⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠖⠋⠀⠀⠀⠀⠁⠈⠁⠂⠄⡧⠠⠤⠤⠔⠊⠀⠀⠀⠘⣌⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⡀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠸⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⡀⠀⠀⢻⣿⣿⣿⡏⢰⣶⣤⣤⣤⣤⣿⣿⠏⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠁⢠⠐⠤⣀⢾⣿⣿⡟⢠⣿⣿⣿⣿⠿⠟⠛⠛⠉⠉⡆⠀⡞
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⣆⠀⠀⠀⠻⣏⣰⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⡷⢺⠁⣀⣤⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠈⢉⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣇⣴⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⣿⡿⢿⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠙⠿⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢦⣄⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠙⠎⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣤⣿⣿⣷⣤⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣛⠋⡹⠿⣿⡿⠋⠴⣧⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠻⣷⣶⣦⡄⣽⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡟⠐⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠿⠿⠟⠻⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⣶⣆⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⣿⣿⣷⣄⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠙⢿⣿⣷⣄⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠀⠀⠈⠙⢿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣯⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠁⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠸⣿⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣠⣶⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠛⠛⠋
⠀⠀⠀⢶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉


⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣶⣶⣤⣤⣤⣄⣤⣤⣴⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⠻⠿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠿⠿⣿⣿⡿⠋⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣟⠀⠀⠈⠋⠀⠀⠀⠀⠀⠰⣿⠆⠠⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀
⠀⠀⠀⠀⠠⢀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⠂⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⢿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣬⡛⠿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⣿⡟⠁⢰⣤⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣦⣝⠻⢿⣿⣿⣿⣿⣦
⠀⢀⣿⠁⠀⠸⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠟⢿⣶⡍⢿⣿⣿⣿⡆
⠀⢸⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿⣿⡄⢿⣿⣿⣇
⠀⢸⡇⠀⠐⢠⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣷⠘⣿⣿⣿⡀
⠀⢸⡇⠀⠀⠁⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⠿⠋⠀⠀⠀⠀⠀⢿⣿⡆⢻⣿⣿⣧
⠡⠾⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠸⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⣿⣿⠟⠋⢁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⡶⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣿⡟⠀⣸⣿⣿⣿⣿⣷⣄⣠⣴⣦⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠀⣰⣿⠇⠀⠀⠀⠀⠈⠿⠟⠛⠛⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⠛⠀⢠⣿⣿⣿⡿⠀⠻⠿⠛⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣴⣿⡟⠀⠀⠀⢠⣿⣄⣠⣤⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣴⣶⣤⣤⣿⣿⠻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠋⠛⠛⠛⠁⠀⣤⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠏⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣤⣤⣤⣀⣬⣿⡅⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⢠⠃⡇⠀⢀⣠⣄⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⠀⢧⡼⠀⠳⡴⠁⠀⠹⠴⢣⢸⠈⠳⡄⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡟⢦⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠸⡾⠯⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⣀⣹⡄⠉⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠄⠸⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⣠⣀⣀⣀⣀⠴⠒⠉⠀⠀⠀⠀⣨⠋⠀⠀⠀⠀⠀⠺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠠⠁⠀⠀⢀⠤⢬⡂⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡔⠛⡆⠀⠀⣏⠀⠀⢻⠀⡀⣴⡇⠀⣀⣀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡷⢠⠃⠀⠀⣿⠀⣠⠏⢀⡏⠀⢱⠏⣅⡈⡇⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠘⠶⠋⠖⠉⠀⠈⠉⠁⣠⣾⣧⠀⠀⠀⣋⣴⠃⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠢⢄⣀⠀⠀⢀⣀⣤⣾⠿⠛⣻⠀⠀⠀⢀⡨⠧⢮⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠈⢿⣿⣿⡿⣿⠃⠀⣰⠏⠀⣠⠞⣿⠴⠲⡒⠒⢪⡕⠊⠑⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣄⣀⠈⠳⢤⡀⠻⢧⣤⡥⠴⠛⠁⠀⡰⠃⠀⠱⡀⢀⠇⢠⠏⢀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣛⡖⢁⠀⡇⠀⠀⠉⠓⠲⠶⠶⣶⠶⠚⠉⠀⢀⡤⠖⠋⠉⠀⠈⠲⡞⠁⢰⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣉⡷⢊⡈⠣⣀⠀⠀⠀⡤⢤⠞⠁⠀⠀⠀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠘⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠉⠙⢦⣈⣉⣓⣋⡷⠃⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣁⣀⣀⣀⣀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢯⡉⠉⠛⠋⠁⠀⠀⠀⠀⠈⣙⡿⠀⠀⠀⠀⢠⣴⣦⣶⣢⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢉⡭⢷⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⢀⣯⠴⢤⡀⠀⠉⡳⡕⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡼⠙⠺⠦⠚⠉⠈⠒⠶⢾⡀⠀⠀⠀⣠⠏⢀⠿⢢⣳⠴⣃⠆⠔⠁⣸⠏
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⠤⢾⡙⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⠴⢾⡉⠒⣣⠔⠋⠁⠀⠈⠉⠒⠉
⠀⠀⠀⠀⠀⠀⠰⡋⠙⠒⠒⠮⢽⣒⠬⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠈⠙⠮⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣒⣒⣒⣚⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠂⠉⠉⠉⠁⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢞⠁⠀⠀⠀⠀⢀⡀⢤⡀⠀⠀⠈⠂⠠⢄⠀⠀⠀⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠄⠀⠐⠖⢋⠉⠈⠑⠂⠀⠀⠀⠀⠑⣶⠋⠁⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢒⢶⠦⢸⡀⢸⠀⠀⠀⠀⠀⠀⠟⠂⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣋⢀⡠⡄⠀⡄⠸⡀⢀⣤⠄⠒⠊⡐⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠈⠁⠘⠊⠀⠀⠉⠐⠊⠂⠀⢠⡇⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⣠⠀⠀⠀⠀⠀⠀⡈⠁⠒⠁⠀⠀⠁⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⠤⡄⠘⢄⠀⠨⠭⠹⠦⠤⠃⠠⠁⠀⠐⠀⠀⡄⠘⠤⠤⠌⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠡⣴⣃⠓⢄⠀⠑⠤⡀⠀⠢⢂⡔⠁⠀⠀⠀⠙
⠀⠀⠀⠀⠀⢠⠄⠠⢤⠤⠤⠤⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠐⠆⣉⠔⠂⠀⠀⠀⠈⠁⠈⡟⣇
⠀⠀⠀⠀⠀⠘⠤⡀⡶⢗⠒⠒⠒⠚⣧⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢂⢂⠀⢀⡠⠄⢒⣟⠼⠋⠀⠀⢸⠀⠤⠬⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⠨⣓⠊⡉⠑⢬⡑⠄⡀⠀⠀⠀⠀⠀⠀⠈⠂⠒⠀⢇⢠⡁⠀⣔⠖⠒⠤⠄⠀⠀⠈⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠠⢑⠠⣀⣷⡮⣑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠁⠀⡈⠀⠀⠀⠀⠀⡠⠔⠀⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢘⠢⣝⡣⢌⠓⢌⠂⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠣⣀⠀⠀⠀⠀⠱⠂⠀⠀⣌⣚⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠆⠇⠈⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⡌⠁⠉⢓⠀⠀⠀⠀⠑⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⡄⠀⠀⠀⠀⠀⠀⠀⠀⢱⠜⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⡇⠀⠀⠀⠀⠀⠀⢀⠔⠁⡀⢴⣿⣆⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠁⠀⠀⠀⠀⢀⠔⠡⠒⠀⠀⠀⠫⡈⢂⠀⠀⠀⠤⢸⣌⠙⠑⡆⠀⠲⢀⡠⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠄⠣⡀⠀⠀⠀⠀⠙⢌⠢⠔⠉⢉⡏⠩⠷⠺⠟⠟⠓⠦⠤⠤⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠸⡛⠂⠄⡀⠀⠰⡺⣀⡇⠀⠀⠀⠀⠀⠀⠡⠌⠀⠈⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡄⢴⠈⡞⠳⣤⡋⢛⡖⢷⡯⢀⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠄⠠⠤⠸⠷⢃⠖⠐⠀⠀⠀⠈⠓⢧⣁⣉⠛⣟
⠀⠀⠀⠀⠀⠀⡠⠴⠶⠀⠙⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢢
⠀⠀⡠⠖⠒⠲⠦⠴⠶⠤⠧⠤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⢀⡅⠠⣤⣄⡁
⠀⠀⠉⠉⠁⠀⠐⠒⠒⠂⠀⠠⠤⠤⠄⠱⠬⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⣑⣄⡀⠀⠘⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠠⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣷⣦⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠉⠁⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⣼⣿⣿⣿⣿⠟⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡠⢂⢸⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⣿⣿⠻⠟⠃⠀⠄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⠈⠁⠀⠀⠙⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣿⣿⠃⠀⠀⠀⠘⠟⠒⠀⠀⠀⣄⠔⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠛⠀⠀⠀⠈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⠀⢀⣀⠂⠀⠀⡠⠀⠘⠀⠀⠀⠀⠀⠀⠴⠕⠈⠈⠟⠦⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠂⠁⠀⠀⣿⡗⠠⢀⡁⠀⠀⠀⠀⠠⠂⠁⠀⠀⢀⠀⢀⠇⠈⠀⠈⠙⢒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⢀⡀⠀⣐⠏⠸⣀⠀⢸⠛⠐⡀⠀⠆⠀⠔⠲⠁⠀⠒⠁⠀⠀⠈⠐⠂⠀⡀⠂⠀⠀⠀⠀⠀⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢒⠀⠀⠀⢰⠾⠋⠀⠀⠑⠤⠜⠀⠂⠀⠀⠐⠀⠈⠀⢑⠤⢄⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⡄⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⠡⠀⠀⠇⠀⢀⠅⠀⠀⠀⠀⠀⡠⠊⠀⡄⠀⢀⠔⢉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠃⠀⠀⢰⡸⠀⠀⠀⠀⠀⠀⣀⠔⠁⢠⠀⠀⣱⠖⢉⠶⠥⣀⠀⠀⠀⠀⡔⠀⡄⠀⠠⠐⠁⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠰⡀⠀⣼⡅⠀⠀⠀⠀⠀⠠⠁⠄⠀⠀⠄⠔⠁⡀⢳⠀⠀⠀⠀⠉⢁⠊⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢨⢄⠀⠀⠉⠀⠒⠀⠴⠁⠀⠈⢄⠀⠀⡠⠊⣡⠟⠓⠂⠄⣤⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣠⢦⣤⢀⡀⠀⠀⡘⠀⠀⠀⠀⠀⠑⠊⠀⠀⠁⠀⠀⠀⠀⠀⠒⠃⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠈⠉⠁⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⠀⠃⡀⠀⡀⠀⠀⠀⠈⠰⠀⠄⢀⠀⠀⢀⠂⠀⠀⠈⠰⠂⠤⠄⠀⠀⠀⠀⠀⡀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢐⠦⠈⠐⠂⠌⠀⠂⠀⡄⠀⠀⠀⠈⠑⠢⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⠀⠀⢀⠌⠉⠁⠀⠒⠒⠚⠒⠀⡤⠀⠀⢠⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠺⢅⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⣈⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠁
⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠆
⠀⠀⠀⠀⠀⠠⠂⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢀⠼⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠷⠾
⠀⠀⠀⠀⠠⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠱⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⣀⠀⠁⢄
⠀⠀⠀⡠⠁⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⡠⡀⠐⣠⢦⣴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠒⠤⠵
⠀⢠⣒⣅⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡅⠀⠀⠐
⠔⠄⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠢⢄⣀⡐⡄
⠀⠁⢱⣀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⣀⣀⣀⣍⣳⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡠⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⡩⢸⠋⡁⠖⣻⣤⠴⣶⣶⣶⠀⣀⠄⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢏⡸⣽⣀⣼⡇⢈⡭⠆⣚⣉⢈⢛⢯⡥⢂⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡮⢀⣿⠷⣻⣿⣿⣿⣾⣶⣿⣾⣿⣿⣿⣯⣴⢋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢋⢼⣷⣾⣿⣿⡿⠟⠛⠛⠛⠻⠛⣙⣛⢿⣭⣿⣗⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⣿⢗⣷⡿⠛⢁⣴⡿⠿⠆⠀⠀⠘⠛⠻⡇⢻⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⣿⣾⣾⡇⠀⠚⡡⠒⠢⠀⠀⠀⠠⢒⠢⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠛⢿⡟⠀⠀⠀⢸⡿⠀⠀⠀⠀⢿⠇⠀⣯⠔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠈⠙⠀⠁⠀⠀⠀⡀⠀⠀⢀⣀⣠⠂⠀⠀⠘⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⣠⣄⠀⠀⠋⠹⣶⣀⣀⢀⣀⡶⠋⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⡬⢽⣿⣷⣄⣀⠀⠉⠉⠭⠍⠛⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠛⡆⠀⠀⠀⠹⠋⠙⣿⠓⠶⠤⢤⠴⠞⠭⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⣄⣀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠋⠀⠀⠀⠈⠓⡆⠀⢠⠄⡤⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠜⠁⠀⠘⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡄⣰⠛⠦⠼⢆⣷⠒⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠘⠃⢄⠀⠀⠀⠀⢀⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⠊⠑⠤⣀⡀⢀⣨⣿⣤⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢐⣇⡎⠀⠀⠀⢰⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠀⠀⠀⠀⠀⢸⡐⠀⠀⠀⠀⠀⠀⠀⠀⠠⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠁⣿⣤⣀⡀⢀⣈⣭⣶⡿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢉⠷⠤⣏⣸⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⢀⣄⣇⡀⠀⠙⢿⣿⣿⠿⠋⠈⢻⣿⠶⢼⠁⠀⢀⣠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠠⠦⣼⠋⠉⠉⠦⠤⠞⠀⠀⠀⠀⠀⠁⠀⣏⣤⡶⠛⡡⠊⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠊⠀⡽⠁⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⣾⠃⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠩⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⡶⡿⢟⣛⣻⣟⣛⡻⠿⣿⣷⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣟⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣧⣬⣽⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢅⣈⣢⡀⢿⣿⣿⣿⣿⣿⠟⠋⠉⠁⣀⡈⠛⠛⠙⠋⠉⠉⠉⠻⣿⣿⣿⠀⠀⢠⢊⡀⠅
⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡀⠀⢺⣿⣿⣿⡿⠁⢀⠀⠀⠾⠛⠋⠀⠀⠀⠀⠀⠀⣠⣄⠹⣿⣿⠀⠀⠀⢠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠐⠒⠁⠀⠀⠘⣿⣿⣿⠁⠀⠀⣱⠖⠋⠑⢢⡀⠀⠀⠀⠀⠀⣀⣈⠀⢿⣿⠀⠀⠀⠀⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⡇⣀⣀⣀⡠⡷⠀⠀⠀⠀⠾⠤⣬⡗⢸⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣼⣿⣿⠀⠀⠀⢫⡉⠁⠈⡠⠃⠀⠀⠀⠀⠈⠒⠊⠀⢸⣇⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠛⠛⠃⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢸⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣄⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣠⠗⠀⠀⠀⠀⣼⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⣰⣿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠉⢹⡄⠀⠀⠀⢀⣾⣷⣻⡄⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⣏⡻⣿⣿⠁⠀⠀⣠⠎⠀⠀⣰⡋⡳⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡆⠀⠀⠀⠀⠉⠋⠀⣠⠞⠁⠀⠀⢸⠁⣨⣇⡐⢹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣲⠟⠛⠧⢭⡽⢤⣀⠀⠀⢀⣠⢾⡁⠀⠀⠀⠀⢸⠆⣈⠈⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡼⠁⠀⠀⠀⣼⠁⠀⠉⠉⠹⠩⠰⣮⢷⣄⣀⣠⣖⡡⠞⠁
⣞⣒⡖⠦⠤⢤⣀⣀⠀⢀⠶⠋⠀⠳⡄⠀⠀⢰⠇⠀⠀⠀⠀⠀⠇⠀⡇⠀⠈⠉⠉⠁
⠀⠈⠉⠉⠒⠒⠤⠤⢬⡏⠀⠀⠀⣠⠵⣤⣠⣟⡀⠀⠀⠀⢀⣤⣴⣤⣷⣤⣴⡶⠶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⢺⠤⣧⣽⠒⠒⢤⡬⣉⣟⡑⠋⢩⣟⣹⣩⡟⠉⠉⠙⢦⡶⠟⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡞⡁⢡⣴⡹⣆⠀⣴⠚⢧⡀⠀⠉⠲⣼⣍⣉⡿⠃⠀⠀⠀⢸⣧⣄⣹⡇
⠀⠀⠀⠀⠀⠀⡴⢋⠎⠀⡽⠋⢣⡘⢚⡿⢦⠴⠛⠓⠦⣤⣈⣻⣿⣷⣦⣀⣄⣤⣟⠀⢩⣿⠃
⠀⠀⠀⠀⠀⣾⣕⣁⡼⠋⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡟⢿⣷⣦⣽⣷⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⣴⣃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⣉⡙⠛⠉⢉⠝⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠲⠶⠶⠤⣭⣭⣰⣚⡧
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⡘⠀⠀⠀⠀⠠
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢴⠄⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠈⢭⠀⠄⠀⠀⠀⠀⠈⠀⠑⠀⠀⠀⢆⢀⠒
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⠴⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⢈⠀⠀⠀⠈⠀⠈⠠⡤⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⢠⠝⠐⠀⠁⠀⢀⠀⠒⢠⡀⠀⠀⢀⠀⡲⠀⠀⢀⠄⠀⠀⢐⡀⠈⠀⠀⠀⠀⠀⠀⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡄⠀⠀⠀⠀⠀⠀⢠⡡⠎⠀⠚⠁⠀⠀⠀⠀⣰⠁⠀⠠⡀⠁⠆⠀⠀⠀⠀⠀⠀⠙⢠⠖⠀⡘⣠⠀⠀⠀⠀⠀⠀⡜⠫⠀⠙⡄
⠀⠀⠀⠀⠀⠀⢀⡤⠠⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠖⠠⠤⠀⠀⢀⡀⠀⢳⠀⠠⡄⠈⠉⠁⠀⠐⠀⠀⠀⢀⣸⠁⢠⡄⠀⡁⠀⠀⠀⢀⡀⣀⡏⠀⢀⠘
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠄⡸⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠉⠐⠠⡀⠀⠀⠀⠀⢀⡤⠛⣦⢒⡱⣆⠀⠀⢀⣴⡋⠀⠈⠻⠆⠛⡄
⠀⠀⠀⠀⡀⠖⡆⠀⠀⠀⡄⠲⢀⠁⠀⠀⠀⠀⠖⠀⠀⡄⠃⠀⠀⠀⠀⡄⠀⠀⠑⠢⠀⠉⠒⠀⠀⡴⠛⣤⠆⠈⠉⡟⣹⠀⢠⠎⢠⡟⠁⠀⠀⢀⠂⡇
⠀⠀⠀⠀⠀⠀⢰⠂⠈⠱⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠣⠀⡀⣠⠆⠘⣄⠀⠀⠀⠀⠀⠐⠤⢄⣵⠁⠞⣿⠀⠀⡘⡎⠁⠀⠈⡀⢸⣇⠀⠀⠀⠿⠉⡇
⠀⠀⢠⡄⠂⠀⢀⠀⠀⠀⡇⠀⠀⢠⠦⡔⠀⢀⠀⢀⣀⠠⠜⠹⣴⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢠⡞⠉⠉⠒⢻⡁⠄⠀⠀⣗⢘⡌⠉⡀⠏⠈⠀⡁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠀⠡⣀⠹⠂⠀⠌⢈⠀⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⠊⠀⠀⠀⠀⠀⠈⢂⠐⠋⠙⣎⠀⠀⠸⡄⠐⠤⠆
⠀⠀⠀⠀⠀⠀⡸⠀⠀⠜⢀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⡖⠳⡤⠰⡖⠒⠟⠀⠀⢠⠛⢦⠀⠀⢱⡀
⠀⠀⠀⣠⡆⠉⢀⠀⠂⠀⠀⠓⠄⠀⠒⢢⠁⠀⠀⠀⠀⠀⠀⠠⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⡴⠀⠀⠸⠀⠺⠀⣠⠏⠀⢈⢦⠀⠀⡇
⠀⠀⣷⡁⡚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⡜⠀⠀⠀⠀⢆⢀⣴⠃⠑⠲⠁⠘⣆⠀⠴⡄
⠀⠀⠈⢣⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⣌⠀⠀⠀⠀⠀⠈⢃⠉⢵⠲⡀⠀⠀⠙⣆⠐⠿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠩⠄⠀⠀⠀⠀⠀⠈⠔⠋⠙⠁⠀⠀⠀⠈⠣⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠈⠙⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠄⠰⡐⢀⠈⠀⠁⡀⢡⢆⡐⠳⢣⡦
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠈⠀⠀⠀⠀⠢⠐⠈⠃⠁⠀⠀⠃⠀⠁⠀⠈⠀⢨⠀⠠
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀⠀⠈⠀⠀⢘⠀⡠⠄⠲⠴⡁⠀⠁⠀⠱⢤⠤⡠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠌⠢⠀⠀⠀⠞⠀⠁⠀⢠⡜⡀⠁⠀⠀⠀⢩⡜⣶⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⠀⠛⠃⠀⢃⠀⠀⠀⠘⡣⠀⠀⠠⡀⠀⠈⡡⠻⢖⡄⠀⠀⠤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠠⠵⠀⠀⠘⠀⠀⠁⠒⠂⠊⠀⠀⠀⠒⠈⠁⠈⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠉⡊⠀⠀⠄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠃⠀⠀⠇⢀⠠⠒⠢⡀⠀⠀⠠⠄⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⢤⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠈⠓⠢⠤⠄⣀⣀⠀⠀⡀⠀⣀⢠⡄⠂⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⢀⠀⠀⠑⢄⠀⠀⠒⢬⡨⠩⡁⠀⡘⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠰⠊⠆⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠲⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢠⠄⠤⠐⢃⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⣤⠈⠄
⠀⠀⠀⢔⠐⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⡱⠀⠀⢠⣿⣿⠿⠛⠉⣇⠸⡀
⠀⠀⠀⣀⣽⣿⠦⡁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠸⠱⠀⠀⠘⣿⣇⠀⠀⠀⡇⠀⠈⡄
⠀⠀⢠⣿⣿⡁⠀⠈⠢⡬⠒⢄⠀⠀⠀⠀⠀⠀⡄⢣⠀⠀⠈⢻⣷⡖⠈⢳⠐⢄⡁
⠀⠀⠀⠙⢿⣥⣀⣀⠠⠧⡄⠀⠵⢄⠀⠀⠀⠀⠡⠘⠁⠀⠀⠀⡜⠁⠈⠁⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⢸⣄⠔⠁⠀⠀⠀⠈⠢⡀⠀⠀⠙⠢⠄⠐⠘⡀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠔⠁⠐⡀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠐⡀⢀⠤⠒⠐⠇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⢈⠦⠀⠀⠀⠀⠀⠘⡳⠀⠂⠀⠒
⠀⠀⠀⠀⠀⠀⠃⠂⠈⠉⠢⡀⠀⠀⢀⡠⠄⠂⠁⠀⢡⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠎⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⡘⠀⠀⠀⢀⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⡌⠀⠀⡠⠊⠉⢄⠀⠀⠃⠀⢀⠁⠀⡠⠂⠁⠈⠢⣀⠀⠘
⠀⠀⠀⠀⠀⠀⠰⠢⠄⠀⠀⡘⠀⢀⠎⠀⠀⠀⠀⠡⠀⠀⠀⠈⢀⠊⠀⠀⠀⠀⠀⠈⠢⡀⠆
⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⡰⢀⠔⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⡆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠱⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠰⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠂⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠐⠦


⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⣿⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⡠⠀⢈⣧⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠰⠀⣠⠋⠈⠷⣄⠀⠀⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⢠⡎⠉⠑⠦⡀⠀⢀⣿⠀⠐⠃⠀⠉⠀⠁⣠⠟⠷⣤⣀⠀⠀⠉⠒⠢⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⢸⡇⠀⣠⠔⠈⠉⢱
⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠛⠂⢸⡇⠀⠀⠀⠀⠀⠁⣼⠏⠀⠀⠈⣹⣿⣿⣷⣦⣄⣀⣀⡉⠉⠐⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⢸⡇⠐⠛⠒⠒⠒⠊
⠀⠀⠀⠀⠀⣠⠤⠤⢤⡄⠀⠀⢸⡇⠀⠀⠀⠀⠀⣼⠏⠀⣄⠀⠀⠛⠋⠁⠀⠀⠈⠉⠉⠛⠛⠛⠛⠓⠶⢦⣤⣤⣄⠀⠀⢁⢸⡇⠀⠀⣠⡤⠤⠤⣄
⠀⠀⠀⠀⠀⠧⡠⠶⠋⠀⠀⠀⢸⡇⠀⠀⠀⠀⣸⠇⠀⠀⠈⣳⡶⠛⠛⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⣄⠈⣼⡇⠀⠀⠈⠙⠶⢄⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⢠⡿⠀⠀⠉⣹⠏⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠓⣶⡁⢹⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⢸⡇⠀⠀⠀⣿⢀⣀⣀⣠⣤⣤⠶⣿⠃⠀⠀⠀⠀⠀⠀⢻⠖⠶⣤⣼⠃⠈⣿⠛⢲⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡄⠀⣿⠀⠀⠀⠀⢻⡋⠉⠉⠀⠈⠉⢠⡟⠀⠀⠀⠀⣶⠀⠀⠈⠲⠤⠔⠋⠀⠀⣿⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣠⣿⠀⠀⠀⠀⠀⠛⠦⣄⣀⣠⠴⠋⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢟⠉⠉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡈⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣿⠋⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠟⠋⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣧⢼⣗⢙⠆⠀⠀⠀⠀⠀⠀⢀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢁⠀⢠⠀⢿⡄⠀⠀⠀⠀⠀⢠⣿⣿⣿⣦⣭⣿⠀⠀⠀⠀⠀⠀⣠⠞⠁⢿⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣏⣠⣌⣀⣈⠀⠘⣧⠀⠀⠀⠀⢀⣟⠈⠿⣿⣿⣿⠃⠀⠀⠀⠀⢀⡾⠋⠀⠀⢸⡇⣾⠉⢙⡷⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⢻⡄⠀⠀⠀⠀⠉⠙⠛⠻⢿⡏⠀⠀⠀⢀⣴⠋⢀⠂⠀⢀⣸⠛⠛⠶⣿⠀⢀⡿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠖⣛⣭⣷⣶⣦⣤⣤⣬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠉⠙⠛⠛⠛⠾⣷⠀⢠⣴⡿⣠⡞⠁⣸⠇
⠀⠀⠀⠀⣠⡤⠞⠛⠒⠛⠉⣠⡶⠋⠉⠀⠀⠀⠉⣇⣀⣀⣙⣧⣀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡛⠁⠀⠀⠀⠀⠀⠀⠀⢘⡦⠀⠘⠁⢈⠿⠛⠁
⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡯⠌⣹⠛⠶⠶⠤⠴⠶⠻⢋⡉⣻⣆⠀⠀⠀⠀⠀⠀⣠⠞⢁⣴⠟⠀⠈
⠀⠀⠸⢦⡜⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠏⠀⠀⢀⠀⠀⠀⢘⣿⣷⡾⢿⣦⣤⣤⣤⣶⣛⣡⠶⠋
⠀⠀⠀⠸⣧⣤⡞⠀⣴⠷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠰⣦⠀⣤⡀⠀⠀⣿⠀⠀⠈⠉⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠘⢷⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠸⠀⣤⣾⠋⢀⣾⠏⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⢤⣤⣀⣀⡀⠉⠉⠀⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡾⢋⡽⣷⡀⠀⠀⠀⠀⠀⣿⣻⠶⣤⣤⣀⣀⣉⠉⠉⠛⠛⠋⠁⠀⣿
⠀⠀⠀⠀⠀⢀⣴⠟⣡⠞⠀⣸⣧⠀⠀⠀⠀⠀⣿⣅⠀⠀⠀⠉⠉⠙⠛⠛⠷⠶⢦⣤⣰⡟
⠀⠀⠀⠀⣠⡾⢃⡜⢁⣤⣾⣇⠾⣧⠀⠀⣴⠿⠋⢿⣄⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣠⡿⠁
⠀⠀⢀⣼⠏⣠⠋⠀⢺⣿⠏⢿⡀⠹⣦⣴⣿⣧⡀⢀⣹⠷⣾⣅⣀⠀⠀⠀⠀⠙⣻⣿⡆
⠀⣠⡿⢁⡞⢹⡄⢠⡾⠉⠀⠈⢿⣄⣈⡴⠟⠁⠛⠋⠁⠀⠀⠈⠙⠛⠶⣦⡶⠿⢿⣯⣟⠳⢶⣤⡀
⣼⣏⣰⢋⣀⣰⠿⠋⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⠀⢨⡿
⠈⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣏⣉⣾⣯⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⠁⠀⠉⠉⠿⠻⠃⠈⠉⣉⠿⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣤⣭⣏⣉⣛⡒⠒⠶⠒⢴⡧⣤⣤⣀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠿⠷⠾⠶⣶⣤⣯⣬⣿⠆
⣾⣶⣶⣷⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣿⣿⣶⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣷⣾⣷⣶⣾⣷⣶⣶⣶⣾
⣿⣿⣿⡇⠀⠉⠈⠀⠈⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⠋⠉⠉⠱⠚⠋⠉⠉⠙⠒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠈⠑⠲⢄⡀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⢋⡤⢤⠀⠀⡤⠄⠀⠀⠙⢦⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡐⢁⠢⣀⢠⢎⡈⠋⠘⠀⠀⠀⠀⠀⠐⠒⡄⠀⠀⢳⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⢲⣜⣠⠈⠃⢸⠈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢧⢀⡜⠁⢧⠀⠀⠀⠈⣆⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠳⣄⠀⠀⠈⠢⢄⣀⡠⠞⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣀⣀⠀⠀⠀⣀⣀⡤⠔⠊⠀⠀⠀⠀⠀⠠⠋⠙⠈⠱⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⠬⠏⠉⡯⣅⣀⣀⣀⠀⠀⠀⠀⠀⢠⠊⢀⠀⢁⠄⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠀⠀⡎⠉⠉⠀⠀⠀⠘⢦⠳⡀⠀⠀⢀⠍⠈⠁⠉⠒⢄⡀⠀⠀⠣⡀⠫⣩⠤⠖⠁
⠀⠀⠀⠀⠀⠀⢠⠃⠀⢀⣀⣠⠃⠀⢀⣀⡀⠀⠀⠀⠑⢌⢂⠀⠌⠀⠀⠀⠀⡆⠀⢈⣢⡀⠀⡈⠀⡎
⠀⠀⠀⠀⠀⠀⡌⠀⠀⡜⠀⠸⠒⠋⠉⠈⡆⠀⠀⠀⠀⠈⠢⠊⠀⠀⠀⠀⠀⠘⡎⠉⠳⣄⠜⠁⠸
⠀⠀⠀⠀⠀⠀⠇⠀⡰⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠈⠀⢠⠇
⠀⠀⠀⡠⠄⠐⠁⠘⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣖⠢⠞
⠀⠀⢸⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠒⠒⠂⠀⠉⠁⡠⠦
⠀⠀⠀⠓⢄⡄⣘⣠⠋⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⢠⠎⠀⡄⠀⠰
⠀⠀⠀⠀⡀⠬⢌⠁⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣊⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠃⢀⠃
⠀⠀⠠⠪⠊⡔⠀⢱⠀⠀⠀⠀⠀⠀⠀⡝⠓⠒⠦⠤⠤⠤⠤⠤⡖⠒⠚⠉⠀⠀⠈⠙⠒⠤⣄⣀⣠⠋⢸⠀⠀⠀⡔
⠀⡰⡱⠁⠀⠈⢡⠎⠒⠤⣀⠀⠀⡤⠊⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⠀⠀⡐⠀⠀⠀⢀⣀
⠐⢰⠁⠀⠀⠀⡼⠤⡄⠀⠀⠈⠐⡇⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠠⢠⣃⠔⠊⡍⠀⢀⠈⠲
⣆⠃⢣⠀⠀⡼⠁⠀⠈⠓⣄⠀⠀⠸⡄⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠞⠁⠀⠀⠀⠁
⢿⡀⠀⣩⠟⠀⠀⠀⠀⠀⠈⠓⢄⠀⠱⡄⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⠔⠈⠀⠀⠀⠀⣀⠤⠊
⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠊⠉⠢⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⠁⠀⣀⡠⠤⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠈⠉⠉⠉⠉⠉⠐⠢⣤⣠⠔⠒⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⣀⣠⣤⣤⣤⣤⣤⣀⡀⠀⠹⣷⡄⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣥⣾⠿⠛⠋⠉⠉⠉⠉⠉⠙⠻⢷⡄⠹⣿⡀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠋⣠⠴⠆⠙⠋⠀⠶⠄⢀⣀⡀⢀⠷⢧⡀⠏⠲⣄⡀⠀⠀⠙⠶⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡎⣀⣤⡀⠀⠀⠴⠦⡄⠀⠀⢹⣸⠀⠀⠇⢸⠀⠀⠈⠉⠐⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⣦⡄⠀⠀⢶⡆⠀⠀⠀⠘⠧⣄⣤⠃⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠉⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠑⠢⠀⣀⣤⠀⠀⠀⠀⠀⢸⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠸⡂⠃⠁⡰⠀⠀⠀⠀⠀⡮⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠬⣉⠉⠀⠀⠀⣀⡤⠊⢡⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠘⣛⠀⠀⠀⠈⡶⢴⠶⠚⠁⠀⠀⡟⠉⠉⠀⠰⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠊⠙⠤⠀⠠⠔⠙⠀⠀⠀⠀⠀⠸⠀⢀⡀⠀⠀⠀⠀⠑⢄
⠀⡀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⡅⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⢠⡏⠁⠀⠀⠀⠙⠢⡀⠀⠈⢣⡀
⡎⠁⠈⠁⣼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡏⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠡
⠀⠂⠀⣴⣿⠁⠈⠉⠒⠠⣄⣀⠀⠀⠀⢀⡠⠖⠁⠈⠲⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢣
⠀⠀⠀⠈⠉⠑⠤⣀⡀⠀⠀⠈⠁⠐⠃⠉⠀⠀⢀⡠⠊⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⠤⠤⠤⠤⠔⠊⠁⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⠿⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⠀⠀⢀⣀⣀⣀⣀⢀⡀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⢀⠴⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⢳⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠈⠳⣄⠀⠀⠀⣀⡠⠚⠁⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢷⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⢀⡔⠁⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡎⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⣿⡟⠉⠁⢲⣄⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⡄⠀⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠘⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡣⣸⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣠⣾⡿⠛⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢠⡏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢫⡀⠀⣨⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⢏⣠⢞⡫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣡⡴⢋⠕⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⣯⣊⣁⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠻⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠞⠁⠀⠀⠀⠈⢳⡄⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠻⡴⠋⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⡠⠄⠒⠈⠁⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⣀⡀⡀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠼⠅⡀⠤⠤⠐⠂⠉⢀⠠⠀⠐⠘⠉⠉⠉⠉⠁⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⡁⠤⠀⠀⠀⠀⠀⠀⠒⠒⠒⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠁⠀⠀⠀⢠⠀⢄⣀⣤⠴⠚⢋⡥⠂⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠛⣦⠀⠀⣌⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣀⣀⣀⣤⡤⠶⠟⠋⠉⠀⢀⡴⠚⠁⠀⡠⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢬⠉⠢⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡰⠀⠀⢸⠗⠀⢀⠜⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⠀⠀⠀⠀⡐⠉⠑⠀⠀⠀⠀⡈⠉⠆⠀⡿⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢸⠀⠀⠀⠀⠙⠄⠔⠀⠀⠀⠀⠣⠠⠂⢀⡇⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⢹⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠉⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⡟⢠⠤⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡄⠀⠀⠀⠀⠀⠀⠟⠛⠋⠉⠁⠀⠀⡰⠀⠅⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⣈⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠉⠓⠿⣦⣤⣀⣀⣀⣀⣀⣀⠤⠤⣎⠀⠀⣠⠃⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠾⡈⢳⡴⠚⠳⢄⡀⠀⠙⠦⠤⠤⠤⠴⡉⠢⠒⣧⠀⠀⣀⣀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⢀⣸⠋⠀⠀⠀⠀⢙⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⣀⠀⠀⠀⠀⠀⡓⠀⣀⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠻⣄⠀⠀⠀⠀⣿⠙⠛⠟⠿⠿⠿⠿⣁⡀⢋⡷⠶⠤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢉⡀⠀⠘⢦⡀⣠⠞⠁⠀⠀⣠⣀⣀⣀⣀⣤⣶⣟⣀⠀⠀⠀⠀⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⣄⡴⠞⠻⡋⠀⢀⡴⠞⠁⠉⠉⠉⠁⠀⠀⠈⠉⣹⠿⣆⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⢀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣀⣀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠀⠤⠀⠠⠀⠀⠄⠄⠄⠀⠆⠄⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠂⠀⠀⠂⠔⠀⠦⠐

⢠⣴⣶⣆⠀⣶⣶⣦⠀⠀⠀⠀⣀⣠⣶⣶⣶⣦⣀⠀⠀⠀⠀⢀⣴⣾⣿⣷⣦⡀⠀⠀⠀⠀⠀⢠⠊⢶
⠲⣿⣿⣿⠰⣿⣿⣿⠆⠀⠀⠘⠛⠻⠿⠿⠛⡿⠛⠃⠀⠀⢀⢾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠶⠶⠶⠆⢸⠷⠶⠖
⠀⠈⠛⠉⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠈⠲⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢤⣀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡄
⠀⣠⠄⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠈⠉⠁⠈⡆⠀⠀⠀⠀⡁⠀⠀⠀⠀⢁
⢤⣧⠀⣴⢮⣥⠲⣆⠀⠀⠀⠀⠀⣆⣀⠀⢀⣰⡆⠀⠀⠀⠀⢇⠈⠀⠛⠀⠁⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙
⠀⠀⠠⠯⠄⠀⠠⠽⠄⠀⠀⠀⠀⠏⠁⠀⠈⠹⠇⠀⠀⠀⠀⠈⠲⠼⠶⠣⠚⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠸


⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠺⡟⠂⠁
⠀⠀⠀⠀⢹⠁⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⠾⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⢷⠀⠀⠀⠀⠀⠒⡆⠀⠀⢣
⠐⢖⡀⠤⠊⢁⠀⠒⡆⠀⠀⠀⠈⣖⢒⡫⠵⠛⠃⠀⠀⠀⠀⠀⠀⠀⣼⠁⠰⠀⠀⠀⠀⠀⣾⠁⠀⠘⠋⠃
⠀⠀⠀⠀⠙⠁⠒⠉⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠈⠀⠀⠀⠀⠀⠀⠉⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢤⡀⢀⠀⣠⠄⠐
⠀⠀⠀⢀⣻⣃⣀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡷⠚⠁⠀⠀⠀⠀⠀⢼⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡗⠁
⠀⠀⠀⣼⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⡀⠀⠀⠀⠀⠀⠀⣀⢨⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠨⡟⠁⠀⠀⠀⠀⠀⠀⠀⢰⠃⠸⠁⠀⠀⠀⠀⠀⠀⢽⠽⠿⠿⠿⠻⡆⠀⠀⠀⠀⠀⠀⡏⣇
⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠈⠁⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠖⠛⠉⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠘⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠉⠁⠙⠆⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⢀⣠⠞⠙⠛⠓⢦⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⢠⠆⠀⢀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠈⠙⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠀⠀⠀⠀⣸⣀⡴⢋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠛⠛⠳⢤⠞⡹⢯⡀⣾⠀⠀⠀⠀⠀⠀⠀⠸⡇⣀⣀⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⢀⡴⠶⢦⠏⠀⠀⣙⣿⡀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠈⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣇⠀⠀⢀⠋⠀⠀⠣⣀⠀⠀⠙⢦⣷⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⣿⠀⠀⢸⡤⠤⢄⣠⠏⣿⠲⣄⣀⣿⠁⠀⠀⠀⠀⠀⡀⠀⠑⣤⣤⣤⣄⣀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣿⠀⠀⣼⠀⠀⠀⣟⢰⣷⢀⡼⠛⢿⡆⠀⠀⠀⠀⠰⠀⠀⢠⡇⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⣿⠀⠀⢾⠀⠀⠀⠈⠉⠉⢁⣀⣀⣿⠀⠀⠀⠀⠀⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠘⠷⠤⠤⠶⡖⠊⠉⠀⢀⣏⣀⣤⣤⣄⣀⣃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢈⡟⠉⠁⠀⠈⠉⠉⠙⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢸⣷⡆⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠛⠛⠓⠒⠶⠶⠶⠖⢃⠀⠀⠀⠈⣯⣷⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢈⡟⠀⠀⠀⠀⠀⠀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠱⡄⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣼⠃⠀⠀⠀⠀⠀⢀⡏⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⢷⠀⠀⠀⠀⡀⠀⠈⣇⠀⢰⡃⠀⢀⡀⠀⠀⢀⣾⡴⠶⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣼⡧⣴⠚⠛⠙⢺⣏⣁⣀⡼⠉⠑⠛⠤⣄⣠⡟⠀⠀⠀⢸
⠀⠀⢀⣤⢤⣀⣀⠀⢀⣀⣠⡤⠶⠶⠾⠧⠘⣦⡶⠛⠉⠉⠀⠀⠀⠀⠀⠀⢠⡾⠁⢻⡄⠀⠀⣸
⠀⠀⢸⠃⢸⠀⣼⠁⢹⣏⣀⣠⢄⣀⣠⡴⠟⠁⠀⠀⠀⢀⣀⣀⡠⠤⠤⠴⠋⠀⠀⢸⠇⠀⠀⡏
⠀⠀⢸⣧⡏⠀⢸⠗⠉⢩⢿⡇⣾⠉⠁⣀⣠⠤⢖⡖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢧
⠀⠀⢸⢿⢁⡜⠁⠀⠀⢸⣾⠃⢈⠓⡏⠁⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢸⡆
⠀⠀⢸⣾⡟⠀⠀⠀⠀⢸⣿⠀⣾⣻⠁⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠸⡇
⠀⠀⠀⠙⠁⠀⠀⠀⠀⠘⡿⢠⣿⡗⠤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣯⣤⠼⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠈⣧⣄⣀⣀⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡓⠒⠦⣤⣀⣉⣉⣲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠒⠋⠈⢉⣀⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣴⡾⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠒⠲⠶⠶⣄⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⡀⣀⡀⠀⠀⠀⠀⠤⣤⣭⣵⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣟⠻⡟⠷⣤⠄⠀⠀⠀⢀⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡂⠉⣄⡟⠀⠸⣖⠶⠤⠠⠤⣼⡭
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣀⡀⠀⠀⠘⢹⡿⠿⠿⢋⣶⣶⣀⡀
⠀⠻⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⢻⣿⣿⣿⣷⣶⡶⠋
⣠⣴⣿⠿⣟⢦⣤⣤⣤⣤⣄⣴⣤⡤⠤⣤⣰⣟⣁⣴⣟⣋⡏⠉⠉
⢠⣿⣟⣛⠻⢧⠙⠸⠦⠤⠤⠬⠿⢿⣿⡟⠛⠋⠉⠉⠁⠀⠙⢦⡀
⠈⠉⢻⣽⣿⣧⣀⣀⣀⣀⣀⣀⣀⣤⣷⣽⣆⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠈⠉⢰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠛⢷⡲⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠙⢦⣄⣀⣠⡤⠶⠚⠛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀
⠀⠀⠀⠀⢰⢤⡀⠀⠀⢠⡴⠛⠁⠀⠀⣠⠴⢤⣤⣀⣀⣀⣀⣀⣀⣀⣤⠄⠀⠀⡇⠀⠀⠀⠀⠀⢀⣠⣤⠐⠛⢻⡇
⠀⠀⠀⠀⠈⢯⣿⢤⣀⡼⡇⢀⣠⡴⠛⠁⠀⠀⠀⠈⠉⠉⠉⠀⠀⠉⢣⠀⠀⠀⢳⡀⠀⢀⡠⠖⠋⠀⢹⠛⠳⣾⣿
⠀⠀⠀⠀⠀⠈⢿⣷⣄⣀⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢰⡿⠚⠉⠀⢀⣠⠴⠚⠃⠀⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡈⢁⣠⠴⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠈⠉⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣢⠤⢀⣠⡤⠟⢉⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⢠⠆⠹⡅⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣸⣦⡀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⡄⢉⢲⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠑⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠤⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠠⠴⠤⢤⣄⠒⡉⠄⠀⠀⠀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⠁⠐⢌⠢⢠⣄⢼⠣⡉⠄⠀⠀⠀⠀⡠⠃⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠐⠈⠀⢱⡈⠁⢠⢤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠸⣅⡠⠄⠀⣃⠈⢻⡀⠀⠀⠙⠓⠢⢄⡀⠀⠀⠀⡇⠠⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠃⠀⠣⠀⠙⠂⡴⠁⠀⡠⠠⠌⡁⠒⡼⠧⣅⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⣀⠀⠀⠀⠀⡠⠊⠀⠀⠘⢧⡀⢀⠴⠋⠀⠀⠀⠈⠑⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠰⢋⠀⠀⢦⡀⡀⠄⠋
⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣿⠛⠐⠠⡀⠀⠈⠀⠐⠉
⠀⠀⠀⠀⢀⣮⠊⠀⠵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠐⠃⠀⠀⠁⠀⢀⡔⠁
⠀⠀⣀⡶⠋⣀⠸⣁⠀⠈⠠⠄⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠡⠀⠀⡀⠀⠀⠑⣤⡀
⢀⠀⠛⠀⡀⡥⠙⢍⡠⢔⠀⠀⠀⠉⠂⢄⠀⠀⠀⣠⠂⢂⠀⠠⡑⢵⡌⠢⠔⠉⠀⠙⢦⡀
⠙⠒⠂⠉⠀⠀⠀⠀⠀⠀⠑⢀⠀⠀⠀⠀⠱⣄⠎⠀⠀⠈⠑⢄⠈⢢⠝⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢱⢇⡀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⣀⠴⠁⠀⠉⠲⣄⡀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣀⣀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠐⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⢀⠺⠤⠴⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠅⠀⣈⡀⡉⠀⡰⠀⠀⠈⢦
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠩⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠐⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠄⠀⣀⠠⠀⠀⢠⠦⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⣴⠀⠀⠀⡤⣈⠤⣤⠂⠉⠉⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⢀⠀⠀⢅⠀⡀⠼⢆⣀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⠀⠈⠀⠀⠐⠉⠀⠀⠀⠈⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⡄⢄⡀⠀⠀⠀⠀⠈⠀⠀⠀⠁⢠⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠶⠉⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠘⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⠀⡀⢀⠀⠠⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠰⣤⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⡰⣀⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣦⣦⠰⢤⠓⠆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠋⡦⡀⠀⠀⠀⠉⢻⠀⠀⢀⢣⠀⠀⠀⠀⠀⠀⢀⢀⠄⠒⠺⢥⠀⠀⢀⢐⣇⣄⠀⢠⡌
⠀⠀⢀⡠⠀⠀⠀⠄⠀⠀⠀⠀⠁⣤⣀⢰⢀⠁⠱⣄⠀⠀⠀⢰⠀⠀⢠⠀⢆⢰⡖⠀⠉⠁⠀⠐⠀⠀⠀⠀⠈⠀⠉⠉⠛⠀⠑⠁⠃
⠀⢀⡏⠁⠀⠀⢇⣰⣶⡤⡎⢨⡟⢻⠀⠀⠉⠀⠀⢈⠀⠀⢀⠆⠀⠀⠈⠀⠘⡷⠐⠃
⠀⠀⠣⡀⠀⠀⠄⢰⣾⢷⣡⡸⣆⠀⠀⠀⠀⠀⠀⠀⢣⠀⢸⠀⠀⠀⠀⠐⣜⣃⢀⣷⡆⣿⠏⡐⢢⣖⠆
⠀⣀⣤⣤⣤⣾⣿⣶⣶⣾⣿⣿⣿⣷⣄⣀⠀⠀⢀⣀⣼⣿⣿⣆⠠⠒⣒⡾⠛⠭⠀⠠⣑⣄⣀⠀⠉⠁⡑⠀⠀⠀⢀⣄⣀
⠈⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣬⣤⣴⠀⣷⣤⣿⣿⣿⣿⣿⣶⣶⣾⣿⣶⡾⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠂⠲⠀⠀⠐⠰⠐⠐⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠂⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡽⡥⢤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠈⣀⣾⡑⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠻⠀⡔⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠗⠟⡠⠐⠉⢁⣀⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠱⢆⡅⠀⠀⢐⡁⢊⣉⡴⠒⠐⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⣁⢺⡏⠀⠀⠘⠁⠀⡨⣧⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠑⠊⠀⠁⠀⠐⠐⠉⠀⠀⠈⠑⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⠉⢀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢤⠠⡀⠤⠤⠚⠟⠉⠉⠀⠈⠀⡄⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠈⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢎⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⠀⣠⡀⠀⠀⠀⢀⠳⣄⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢰⣿⢠⡅⣠⠈⠲⠄⠄⢸⠀⠈⠉⠐⠒⠈⠀⢀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠘⠿⠘⠂⠀⠀⠀⠀⠀⠀⠉⢂⡀⠀⢀⠀⠠⠒⠲⡦⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⡆⠀⠀⠀⠈⢌⢆⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠈⠁⠀⡷⠷⠘⠲⠉⠢⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⠈⠸⢢⡀⠀⠀⠀⠙⠃⠀⢀⠱⠀⠀⣀⡀⠀⠤⠀⠖⠈⠉⠒⠄⡀⠠⢴⣷⠦⣀⠰⠂⢀
⠀⣠⠔⠀⠒⡒⠒⠒⠄⢄⣺⣂⡗⠂⠧⢄⡀⠑⠄⠀⠀⠠⠀⠀⠰⡀⣳⡜⣣⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠁
⠀⢏⠀⠀⠀⠑⢘⣿⣹⠁⣿⠃⠻⡀⠀⠀⠀⠑⢦⢢⠀⠃⠀⠀⠀⣇⣰⡍⢠⣀⣀⣤⣄⣀⣀⡀
⠀⠀⠂⣀⣤⣥⣜⣻⣷⣷⣿⣧⣀⠈⠀⠀⠀⠀⢘⣮⣼⣄⠀⣀⣀⣬⡷⠶⠒⠻⢍⠋⠳⠶⠿⢪
⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⡟⠛⠚⠚⠋⡀⠉⡆⢈⣾⣶⣶⣤⣤⣤⣤⣤⣤⣼⣿⣶⠄
⠀⠈⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⣒⠦⡀⠀⠀⠀⡴⣩⣶⣾⣷⣶⣍⢦⠀⠀⠀⢀⠴⣒⠦⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⣴⣾⣿⣿⣷⢸⠄⠀⢸⢰⣿⣿⣿⣿⣿⣿⡆⡇⠀⠠⡇⣾⣿⣿⣷⣦⡙⢄
⠀⠀⠀⠀⠀⠀⣠⢎⣴⣿⡷⢉⡩⠭⠔⠋⠀⠀⠸⡘⣿⣿⣿⣿⣿⣿⢃⠇⠀⠀⠙⠢⠭⢍⡉⢾⣿⣦⡱⣄
⠀⠀⠀⠀⠀⡴⣡⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⣣⢻⣿⣿⣿⣿⡟⣼⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣌⢦
⠀⠀⠀⠀⡼⣰⣿⣿⣿⣿⢁⣓⠢⠔⣪⣭⣭⣭⣉⡱⣶⣬⣛⣛⣥⡶⢎⣉⣭⣭⣭⣕⠢⠔⣚⡈⣿⣿⣿⣿⣆⢧
⠀⠀⠀⠀⡇⣿⣿⣿⣟⣡⣿⣿⣿⣶⢿⣿⣿⣿⣿⣿⣦⣭⣽⣯⣭⣴⣿⣿⣿⣿⣿⡿⣶⣿⣿⣿⣌⣻⣿⣿⣿⢸
⠀⠀⠀⠀⣇⠿⢿⣿⣿⣿⣿⣿⣿⣿⣦⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣴⣿⣿⣿⣿⣿⣿⣿⡿⠿⣸
⠀⠀⠀⠀⠈⠉⠓⠪⠭⣙⣛⣛⣛⣋⣍⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣩⣙⣛⣛⣛⣋⠭⠕⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⢦⣙⣛⣛⣛⣫⣿⣿⣝⣛⣛⣛⣋⡴⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⣿⣿⡿⢟⣭⣼⣧⣭⡻⢿⣿⣿⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢹⡟⣱⣿⣿⣿⣿⣿⣿⣎⢻⡏⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣼⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠸⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣾⣿⣿⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⣴⣿⡿⠃⠀⢰⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⣾⣿⣿⠟⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣅⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠛⠯⠉⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢠⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⡿⠿⠛⠋⠉⠻⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠛⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠟⠋

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠷⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣈⠛⠛⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠹⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣷⣄⠀⠀⣠⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢀⣶⠆⠀⠀⠀⠀⠀⠈⠋⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⢉⣿⣿⣿⣿⣿⣿⣶⣾⣿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢀⣼⡟⠀⠀⠀⠀⣾⣧⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⠀⣸⣿⣿⣿⡿⠀⠹⠿⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣦⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠓⢶⣤⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣍⡙⠻⣿⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣼⡿⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠁⣸⣿⣿⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣀⣴⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁⠀⣿⣿⡏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠟⠁⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣲⣶⣄
⠀⠀⠀⠀⠀⡰⣽⣽⣿⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣾⣿⣽⡵⡀
⠀⠀⠀⣰⣿⡶⢿⠚⢻⣿⣿⣿⣞⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣾⣿⣿⣿⠛⢻⠷⣾⣷
⠀⠀⠀⡇⢰⠁⢸⠀⢸⣿⣿⣿⣿⣽⣄⠤⠤⠴⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠦⠤⠤⢄⣼⣽⣿⣿⣿⣿⠀⢸⠀⢡⠀⡇
⠀⠀⠀⡇⠈⡆⠸⡀⠀⣿⣿⡟⣧⣤⣴⣶⣶⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣶⣶⣶⣤⣤⡟⣿⣿⡇⠀⡘⠀⡆⠀⡇
⠀⠀⢸⣽⠀⣇⠀⣇⠀⢹⣿⣷⡻⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⡿⣳⣿⣿⠁⢀⡇⢀⠇⢸⣽
⠀⠀⠀⠛⡆⠸⡀⠸⡀⠈⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⡏⠀⡸⠀⡸⠀⡞⠃
⠀⠀⠀⠀⠘⣤⣷⣶⣧⣻⣞⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣾⣳⣷⣶⣧⡜
⠀⠀⠀⠀⠀⠘⠿⡿⣿⣷⣝⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣟⣵⣿⡿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⣄⣠⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣿⣿⣿⣿⣿⠿⠿⢿⡿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠿⠟⠛⣩⣤⣴⣶⣶⣶⣶⣶⣶⣦⣽⣿⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣟⣽⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⡟
⠀⠀⠀⠀⠀⣠⠶⠦⣀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡅⠀⠀⠀⠀⢀⡠⠶⢦⡀
⠀⠀⠀⠀⠀⠳⠤⠤⠬⠷⠄⢘⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠴⠯⠤⠤⠼⠃
⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠈⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣾⡿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠈⣷⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠸⣁⠤⠔⠉⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⢀⣤⠶⠒⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⢸⡆⠀⠀⠈⠑⠤⣄⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢠⠖⠛⠶⡄⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡀⠀⠀⣿⠀⣀⣀⣠⣤⣤⠲⡗⠀⠀⠀⠀⠀⠀⢿⠶⢦⣤⡏⠀⣿⠛⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⠀⠀⠹⡏⠉⠉⠀⠈⠁⣴⠃⠀⠀⠀⠀⠀⠀⠈⠢⠤⠚⠀⠀⢸⡇⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣿⣿⣿⡄⠀⠀⠙⠶⢤⣤⠴⠚⠁⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢸⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠩⠀⠠⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣌⣈⣠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣀⣤⠟⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢀⣶⣿⣯⡓⢦⡀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⢀⡟⢻⣿⣿⣿⡟⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⢠⠞⠳⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠘⠓⠒⠺⢿⣿⠁⠀⠀⠀⣰⠞⠁⠀⠀⢀⡴⠺⠤⣴⠁⠈⡧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⣤⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢸⡀⠀⣠⣾⢀⡼⠀⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣰⠞⠛⢿⣁⣀⣹⣷⣀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⠁⣈⠱⠚⠁
⠀⠀⠀⠀⠠⠖⣀⣲⡴⠶⠦⣴⠏⢀⡇⠀⠀⣼⡍⢹⣿⢩⡟⠛⠶⠶⠶⠶⠞⠛⣿⢻⣦⠀⠀⠀⠀⠀⣀⡼⠋⣠⠞⠂
⠀⠀⠀⠀⡇⠀⢼⣁⡄⠀⠀⠀⠀⡀⠉⠛⠲⣿⠀⣾⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⡿⣶⣤⣤⣴⣾⣭⠴⠋⠁
⠀⠀⠀⠸⠁⠀⣸⠁⣀⠄⢀⡴⠻⢝⠳⣤⣴⣿⡴⣿⣣⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠈⠉⠉⠉
⠀⠀⠀⠇⠀⠀⢹⡖⠁⢠⠏⠀⠀⠈⠀⠉⢤⣝⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠰⠀⠀⠀⢸⡀⣠⡟⠀⠀⠀⠀⠀⠀⢿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠐⢆⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢸⣾⡯⠛⠛⠛⠶⠶⢦⣤⣤⣀⣀⠀⠀⣼⠃
⠀⠀⠀⠈⢑⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢻⡟
⠀⠀⠀⣴⠟⣡⠎⢠⣷⣦⣀⠀⠀⠀⢻⢷⡟⠎⠻⣦⣤⡀⠀⠀⠀⠐⠒⠶⢶⣏
⠀⢠⡾⢋⡼⢇⠀⣠⠟⠁⠘⣿⡀⢸⣷⠟⠳⠶⠚⠁⠉⠙⠳⢦⣤⣄⣤⣶⣿⣻⠦⣤⣀
⣴⡟⡰⠋⢀⣼⠾⠋⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠙⢳⡆⢉⣷
⠉⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣉⣸⣿⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢏⣀⣈⠉⠛⠛⠃⠀⠀⣹⠛⠷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣦⣭⣭⣭⣁⣛⣓⠒⠾⠤⠤⢤⣌⣷⡄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣙⣛⡛⠛⠿⢷⣶⣶⣾⣇⡀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣤⣄⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣤⣀⣶⣿⣿⣷⣦⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⡿⠛⢉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣟⣻⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣤⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣀⣙⣦⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠟⠿⠟⠛⠋⠁⠈⠻⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠈⢧⣀⡤⠞⠋⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠶⢷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠏⠀⣠⡤⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⣤⣌⠙⢿⣿⣿⠃⠀⠀⠀⠀⠀⢀⣿⡉⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⠀⠀⣼⣿⡟⠀⠈⠻⠦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⠈⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⡀⠀⠀⣿⡿⠁⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢉⡽⠂⢸⣿⡁⠀⠘⣯⠙⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⠻⠟⠁⠀⠰⠎⣿⠀⠀⠈⠳⠤⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠗⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠛⠻⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠶⠾⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⢶⡷⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⣤⡶⠟⠉⠀⠀⠀⠀⢠⡿⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⢹⡾⠛⢻⣆
⠀⠀⠀⠀⣠⡶⠛⠉⠀⠉⠁⠀⠀⠀⣀⣴⣶⣤⣾⡁⠀⠀⠙⢿⣷⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⣀⣀⣤⡶⠟⢹⡇⠀⠳⣶⡟⠀⢀⡴⠛⣷
⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⢰⡟⠋⠁⠀⠀⢉⣿⠛⠒⠀⠀⠉⠻⢶⣭⣭⣙⣿⣿⠿⠛⠛⠻⣯⡀⠀⠀⣨⡿⠀⠀⠈⠙⠶⣏⠀⣠⡿
⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⡄⠀⢈⣿⣦⡾⠋⠀⠀⠀⣠⣄⣀⣽⠿⠋
⠀⠀⠀⠀⠈⠻⣦⡆⠀⢠⣄⣠⡾⠃⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⠟⠁⠉⠀⠀⠀⢀⡾⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠻⠶⠾⠛⠋⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠻⠶⣶⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣠⡾⠛⣷⣄⠀⠀⠀⢸⣿⠛⠶⢶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⢀⣴⠏⣠⠚⠀⢹⣧⡀⠀⠀⢿⡄⠀⠀⠀⠈⠉⠙⠛⠷⣶⣦⣤⣄⣀⠀⠀⠀⣰⡏
⠀⠀⢀⣴⠟⣡⠞⢁⡀⢠⡿⠉⠙⢷⣄⢨⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⡿⢿⣶⡟
⠀⣰⠟⢁⣴⢁⡴⣇⢹⣟⠀⠀⠀⠀⠉⠻⠷⣬⡙⠷⣦⣤⣀⡀⠀⠀⠀⠀⣰⡏⠀⠀⠙⣷
⣾⣋⡴⠋⠀⣮⣥⡼⠋⠙⢷⣄⠀⠀⠀⠀⠀⠈⠙⣷⡾⠉⠉⠛⠛⠷⠶⢶⣿⠀⠀⠀⠀⢸⡇
⠈⠛⠷⠶⠟⠋⠁⠀⠀⠀⠀⠙⠷⣦⣀⣀⣀⣤⡾⠋⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠙⠻⢶⣤⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡛⠦⣀⠀⠀⢏⣤⠟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⡙⠲⢄⣉⡾⠾⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⣉⠳⢤⡀⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣬⡿⠁
⣶⣶⣶⣿⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶
⣿⣿⣿⡏⠀⠉⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣶⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⠏⠀⣁⣀⡀⣨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⠉⠁⠀⠈⠋⠁⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⡄⠀⠀⠀⠠⢽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⢿⠈⠙⣶⣤⣤⣀⣭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣾⡿⠿⠟⠒⠋⠀⢤⣼⡆⣆⠈⠻⣿⡿⣿⣿⣷⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠟⢻⣿⠁⠀⠀⣤⣤⣤⣶⠄⠈⠉⢙⡦⣷⠟⠁⠀⠉⠻⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣭⡴⠶⣾⠿⣿⣷⣤⣄⣤⣤⣶⠏⠀⠀⠀⢠⣽⡀⠀⠀⠀⠈⠉⠀⣶⣤⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⢻⡟⢰⣾⣅⡀⢨⣻⣷⣬⣽⡿⠁⠀⠀⠀⠀⠤⢼⡇⠀⠀⠀⠀⠂⠀⡟⢡⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣴⣿⢡⡸⣷⣬⣭⣷⣾⣿⠟⢿⣄⠀⠀⠀⠀⠐⠂⣸⠇⠘⢦⣤⣀⣀⣴⡇⠀⠈⠻⣆⢄⣞⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡇⠈⣿⠀⠉⠁⠀⠻⣟⠀⠀⠙⢷⣶⣦⣴⣶⣾⡏⠀⠀⠠⣭⣿⣿⣿⣷⣄⠀⠀⢻⡾⠖⣛⢽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⣧⣼⡿⠀⠀⠀⠀⠀⢙⣦⣀⠀⠀⠀⢀⣉⣉⣭⣿⣿⣾⣻⣿⣿⡟⢻⣿⣿⣿⣶⡿⣡⢿⡔⣚⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢿⡿⠁⠀⠀⠀⠀⠀⠘⣯⠉⠛⠲⣄⡀⢤⣄⣀⣽⣿⣿⣷⣽⡿⠀⠀⠻⣿⡟⢰⣷⠟⣠⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢸⠁⠀⠀⠀⠀⠀⠀⢀⡉⢳⣄⠀⠀⠙⣦⠈⠻⣿⡝⣿⣿⠋⠀⠀⠀⠀⢹⣇⣿⣴⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡞⢦⡀⠀⠀⠀⠀⠀⢸⣿⣾⣿⣷⣬⡳⣼⣷⣤⣼⡇⣿⠃⠀⠀⠀⠀⠀⠀⠙⠿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⢹⣆⠀⠀⢀⣴⣿⢖⣤⠀⠘⢿⣿⣒⠯⡝⠿⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⠃⠀⢠⣿⣿⣧⠻⠿⠛⠛⠲⠮⣭⣛⢦⣜⠷⣮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⣙⣷⣭⡳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠘⠀⠀⠀⠀⠐⠂⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣶⣿⣿⣿⣦⣤⣄⣀⣄⡠⢆⠀⠀⠖⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⠛⠉⠥⠀⠀⠉⠁⠉⠁⢄⠘⢻⣶⣾⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠉⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢀⡤⣦⡀⠀⠀⠀⣠⣄⠁⠈⣿⠏⠀⠀⠀⠀⢀⠀⡐⠁⠀⠀⠀⠀⡀⢀⣀⠀⠠⢀⡀
⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⢀⢸⡄⠀⠀⠛⠁⠀⠀⠈⠱⠿⠃⢰⡏⠀⠀⠀⢀⠊⢀⡼⠀⠀⢀⠼⠿⠿⠉⠉⠛⠚⠿⠞⠛⣷⣦⣀
⠀⠀⠀⠀⢀⠀⠄⠀⠀⠁⠈⠀⠁⠀⠀⠀⣄⣀⣀⣤⠀⠀⠀⠈⠠⠁⠀⠀⢸⣠⣿⣧⣦⣴⠏⠀⡠⣤⡄⠀⠀⠀⠈⠃⠀⠻⠿⣷⠂
⠀⠀⠀⠀⢹⠀⠀⠀⠈⠀⠀⠀⠈⠢⠀⠀⠙⠋⠙⠃⠀⠀⠔⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠻⠀⠀⠸⠟⠀⠀⠀⢠⣿⠂⢀⣆
⠀⠀⠀⠀⠸⠀⠀⠀⠰⠀⠀⣀⠀⠀⠚⠉⠗⠀⠀⠛⠉⢀⠂⠀⠀⠀⠀⠀⠀⡠⠘⣷⣶⣆⠀⠀⠀⠀⣤⡀⠀⡀⠁⠀⢸⠟
⠀⠀⠀⠀⠀⠀⠐⠎⠀⠈⠈⠁⠀⢀⠁⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠠⠀⠀⠐⡀⠁⣸⡿⠿⠷⣀⡀⠀⠉⠻⠟⠁⠀⣀⣾⣆⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠈⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠢⠀⠀⢀⡅⠀⠏⠀⠀⠈⠉⠉⠀⠐⠒⠶⠞⠛⠿⠟⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠐⠄⠀⠹⢻⡀⠀⢃⣰⣿⠷⠄⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣈⠁⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⢡⠚⠙⢣⠀⠈⡘⢿⠀⠀⠀⠐⡴⢠⠂⠀⠀⠀⠀⠀⠛⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⣇⣰⡋⠀⠀⢡⠀⠀⠀⠀⠀⠁⡰⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠰⠖⠤⢄⡀⠀⠀⠀⢀⣠⡄⠱⣄⣀⠌⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠢⢀
⠀⠀⠀⠀⠀⠐⠉⠀⠁⠀⠀⠀⠀⣸⠴⠒⠲⢾⣿⣿⡿⡏⢘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⡿⢿⣿⣿⣄⡼⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠔⢒⣶⠀⢀⠠⠂⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠐⠆⠀⠀⠀⡀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠐⡖⠊⢭⠋⠁⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠸⡀⠱⢿⠀⠀⠀⠀⠀⠐⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⢠⡀⠀⠑⠦⢠⠄⠀⡇⠀⠀⠀⠀⠀⡠⠄⠀⠀⡄⠀⠀⠙⢄⡊⠃⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢰⠀⠀⡁⠀⠀⠀⠀⠀⠀⠈⠳⢄⠁⢳⣀⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⡼⢇⣀⡀⠔⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡔⠀⢀
⠀⠀⠀⠀⠳⠀⠘⣤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣈⢯⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡘⠇⠀⢠⠷⡄
⠀⠀⢀⠙⠻⠳⠟⠿⠙⠃⠐⠀⠀⠀⠀⠶⠀⠠⠀⢀⠋⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠉⠉⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⡀⣀⠀⠀⠀⠀⠀⠀⠘⠄⠠⠔⠃⢀⡀⠀⡀⠀⠀⠠⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠀⢑⡀⠀⠀⠀⠀⠄⠡⡀
⠀⠀⠀⠚⠀⠀⠄⠤⠤⠀⠀⠁⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠁⠀⠀⠚⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⢓⡍⢀⣒⣀⡀⠀⠀⠀⠀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⢤⠀⠀⠀⣠⠞⠑⠋⢀⣈⠀⢉⡤⡄⠀⠀⠀⠀⠘⠋⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠇⠀⢀⠔⠉⣬⣱⡇⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠃⠀⠀⠁⠠⢤⠽⠛⢷⣟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⢀⡆⠀⠀⠀⠀⠀⢶⣤⡤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠟⠀⢀⡤⠴⢶⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡶⠶⠖⠚⠋⠉⠁⡀⠈⠻⣶⣤⣀⡀⣀⠴⢶⡞⢻⡇⠀⣰⣿⡛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣯⡭⠳⣄⠀⠀⢀⡴⠚⠿⢦⠀⠀⠈⠉⠻⣯⠀⠀⣧⣴⣿⣿⣧⠈⣿⡉⠛⠶⣄⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⡞⣩⡄⠀⡼⠛⠲⠋⠀⠀⠀⠀⠳⢤⣀⡀⣠⣿⡆⠀⡟⠸⣗⢷⠘⣿⡍⣧⡀⠀⠘⣧⠀⠀⠸⣹⡆⠀⠀⠀⣠⠟⠹⣏⡽⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣏⣾⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠃⠇⠀⡇⡸⢟⣿⠀⣽⣿⠛⣿⣦⠀⢈⣇⣀⠀⠀⢀⣠⢶⣿⣏⠀⠳⣧⠰⢺⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡾⠁⠀⡆⣰⣷⠀⢸⠇⢀⣿⢸⣇⣻⡟⣷⡌⠋⠈⠋⠘⠉⠁⢸⣎⣽⢇⠴⠏⡭⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⣤⡴⠿⣯⠻⡆⠀⢸⡿⠛⡿⣦⠏⠀⣸⠏⢘⡿⢹⡇⠘⢷⡀⠀⠀⣀⣠⡤⠶⠋
⠀⠀⠀⡀⠀⠀⠀⣀⣀⣤⡴⠛⠙⣧⠀⠀⠘⣯⠁⠀⠀⠈⠳⠌⢠⣿⡇⣀⡽⠃⠀⡴⢋⣴⠟⠁⢸⡇⠀⠀⠉⠛⠉⠁
⠀⠀⠘⣟⠛⠿⢛⡛⢻⣷⡂⠀⣴⢿⡄⠀⠀⠹⣷⡀⠀⠀⢀⣴⣟⣠⣭⣵⡶⠶⣿⣿⣿⣥⣄⣠⣼⠇
⠀⠀⠀⠈⠓⠶⢾⡷⡾⠟⣿⠟⠁⠀⢻⡄⠀⠀⠈⠻⣦⣴⣟⣥⣾⣷⣿⠿⠟⠛⠋⠉⠉⠉⠉⠉⠉⠉⠓⠲⠄⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢧⡀⠀⠀⠀⠳⣤⡄⡄⡴⠦⠜⠉⠀⠀⠀⣠⣤⣦⣠⣤⣤⣤⣤⣤⣄⣀⣤⡦⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠬⠀⠘⠁⠀⠀⠀⢀⡴⠊⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣹⠟⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⢀⣠⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢀⣀⣀⣀⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠞⠉⠁⢈⡿⡻⣻⠟⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣈⣘⣱⣥⡤⠴⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠶⠛⠉⠁

⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢐⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⣮⠁⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠊⠈⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠛⢀⡻⠐⠂⠀⣀⢿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠖⠛⠉⠉⠓⠫⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡼⠦⠔⢻⡀⢀⠂⡖⠋⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡚⠁⢠⠀⠀⠀⠀⠀⠀⡔⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠇⠀⢀⣄⡠⠃
⠀⠀⠀⠀⠀⠀⢠⠔⠁⠀⢑⣄⡎⠀⠀⠀⠀⠀⠀⢳⠀⠀⠈⣧⠀⠀⠀⠀⢀⡞⠙⡆⠔⠈⠀⠀⠙⠒⠬⠾⠤⣀
⠀⠀⠀⠀⠀⠀⡟⠀⢸⠉⠉⠀⣇⠀⠀⠀⠀⠀⠀⡴⠢⡎⠀⠘⠷⠖⠒⠒⢋⣠⠖⠀⠈⠆⠀⠀⠀⠀⠀⢠⠂⠀⡆⠀⡠⠿⢆
⠀⠀⠀⠀⠀⠀⡇⠀⡆⠀⠀⢸⣈⣤⠤⠤⣤⣀⢘⠇⠀⠙⠦⡤⠤⠤⠐⠊⠁⠀⠢⡀⢸⡀⡀⠀⠀⠀⠀⢸⠀⡀⢱⡠⠁⡠⠊
⠀⠀⠀⠀⢀⠠⡃⢰⠀⠀⠀⢠⠗⢀⠀⠀⡑⢺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠛⠉⠍⢐⠠⢄⡠⠞⡇⠀⠈⢀⠜⠁
⠀⠀⠀⠀⠸⣷⡡⠊⠀⠀⠀⣾⠀⢀⠀⠐⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⢙⡞⠀⠀⠘⠦⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠁⠀⢀⡾⡀⠀⠀⠀⠀⠠⣤⡄⢀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⣸⠁⠙⣄⠀⠀⢐⡞⠃⡺⢄⣑⠦⡀⠀⡀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢰⠃⠀⠀⠸⡄⣐⡡⠶⢮⡀⠀⢸⠓⠚⠯⡉⠑⢲⡤⠤⠄⢶⠚⠁
⠀⠀⠀⠀⠀⠀⣀⣤⠴⠾⠛⠂⠀⠀⢠⠋⢆⠀⠀⠀⢫⡉⠀⠀⠀⠈⠉⠳⢤⣀⠀⢀⡴⠁⢱⡀⠀⢸
⠀⢀⡀⣄⠶⣏⠁⠀⠱⡀⠀⢀⣀⠴⠃⠀⠈⢢⡀⠠⠊⠱⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⡇⠀⠀⢣
⠐⣻⣆⠈⢣⠼⣆⢀⠤⠗⠊⠁⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⡽⣀⢠⠔⡶⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⡨⢄
⠀⢹⣿⠆⣼⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠐⢯⣰⠁⢠⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠘⡦⢴⢒⡆
⠀⠘⢻⣇⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠾⢀⣼⠋
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠞⠁