Curly line symbol Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣄⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠉⠙⣿⡆⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⣿⡇⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣠⡾⠛⠛⢶⣄
⣤⡄⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠸⣿⡀
⠹⣿⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣾⡟⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⢠⣿⣷⡀
⠀⠘⢿⣦⡀⠀⠀⠀⣿⡇⠀⢀⣾⡟⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⢿⠟⣧
⠀⠀⠀⠙⢿⣦⣤⣀⣿⣧⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⢰⡟⠀⠀⠀⠀⠘⠁⣾⠀⢹
⠀⠀⠀⠀⠀⠈⠙⠛⠛⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⣼⠃⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣰⡟⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⢧⣤⣀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⣀⣀⣀⣀⣤⣶⠿⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠁⠀⠈⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⢶⣶⣶⠶⠟⠋⠁

⠀⠀⠒⠲⢄⡀⠀⠀⠀⢀⡤⠖⠒⠒⠲⣄⠀⠀⠀⠀⢀⡴⠒⠒⠒⠦⣄⠀⠀⠀⠀⣀⡴⠒⠒⠒⠦⣀
⠀⠀⣀⡀⠀⠙⠒⠒⠚⠉⠀⣀⣀⣀⡀⠀⠙⠒⠒⠚⠉⠀⣀⣀⣀⡀⠈⠙⠒⠒⠚⠁⠀⣀⣀⣀⠀⠈⠙⠒
⠀⠀⠀⠉⠳⢤⣀⣀⣀⡴⠚⠉⠀⠀⠉⠳⢤⣀⣀⣀⡴⠋⠁⠀⠀⠉⠲⣄⣀⣀⣠⠴⠋⠁⠀⠈⠙⠢⣄⣀
⠀⠀⠲⠦⣄⠀⠀⠁⠀⠀⣠⠴⠖⠲⢤⣀⠀⠀⠁⠀⠀⣠⠴⠖⠶⢤⡀⠀⠀⠁⠀⢀⡠⠴⠒⠶⢤⡀
⠀⠀⡀⠀⠈⠓⠶⠶⠖⠋⠁⠀⣀⡀⠀⠈⠓⠶⠶⠖⠋⠀⠀⣀⡀⠀⠉⠓⠶⠶⠖⠋⠀⠀⣀⠀⠀⠙⠒⠶
⠀⠀⠉⠙⠢⣄⡀⠀⢀⣠⠖⠋⠉⠉⠙⠦⣄⡀⠀⣀⣠⠞⠉⠉⠉⠙⢦⣀⠀⠀⣀⡤⠚⠉⠉⠉⠓⢦⣀
⠀⠀⠤⣤⡀⠀⠉⠉⠉⠀⢀⡤⠤⠤⣄⡀⠈⠉⠉⠉⠀⣀⡤⠤⠤⣄⡀⠈⠉⠉⠁⠀⣠⡤⠤⠤⣄⠀⠈⠉
⠀⠀⠀⠀⠉⠲⠤⠤⠤⠞⠁⠀⠀⠀⠀⠙⠲⠤⠤⠴⠚⠁⠀⠀⠀⠀⠙⠶⠤⠤⠴⠚⠁⠀⠀⠀⠈⠙⠦⠤
⠀⠀⠙⠓⢦⡀⠀⠀⠀⣀⡴⠚⠉⠙⠓⢤⡀⠀⠀⠀⣠⠴⠚⠉⠙⠲⢤⡀⠀⠀⠀⣠⠖⠛⠉⠙⠲⣄⡀
⠀⠀⣤⣀⠀⠈⠙⠛⠋⠁⢀⣀⣤⣤⣀⠀⠉⠛⠛⠋⠁⢀⣠⣤⣄⣀⠀⠉⠛⠛⠉⠁⢀⣠⣤⣄⡀⠀⠉⠛
⠀⠀⠀⠈⠙⠦⣄⣀⣠⠴⠋⠀⠀⠀⠈⠓⠦⣄⣀⣤⠖⠋⠀⠀⠀⠈⠓⢤⣄⣀⡤⠞⠉⠀⠀⠀⠈⠳⢤⣀
⠀⠀⠒⠲⣄⡀⠀⠀⠀⢀⡤⠖⠒⠒⠦⣄⠀⠀⠀⠀⢀⡤⠖⠒⠒⠦⣄⠀⠀⠀⠀⢀⡴⠒⠒⠒⠦⣀
⠀⠀⣀⡀⠀⠙⠒⠒⠚⠉⠀⢀⣀⣀⡀⠈⠙⠒⠒⠚⠉⠀⣀⣀⣀⡀⠈⠛⠒⠒⠚⠉⢀⣀⣀⣀⡀⠈⠓⠲
⠀⠀⠀⠉⠳⢤⣀⣀⣀⡤⠚⠉⠀⠈⠉⠳⣄⣀⣀⣀⡴⠊⠉⠀⠈⠙⠢⣤⣀⣀⣠⠤⠉⠉⠀⠉⠙⠶⣄⣀
⠀⠀⠶⠤⣀⠀⠈⠉⠀⠀⣠⠴⠶⠶⢤⣀⠀⠈⠉⠀⠀⣠⠴⠶⠶⢤⡀⠀⠈⠉⠀⢀⣠⠴⠶⠦⢤⡀⠀⠈
⠀⠀⠀⠀⠈⠓⠶⠤⠶⠊⠁⠀⢀⠀⠀⠈⠓⠶⠤⠖⠋⠁⠀⢀⠀⠀⠉⠓⠦⠴⠖⠋⠀⠀⠀⠀⠀⠙⠲⠦
⠀⠀⠉⠙⠢⣄⡀⠀⢀⣠⠖⠋⠉⠉⠙⠦⣀⠀⠀⢀⣠⠞⠉⠉⠉⠓⢦⣀⠀⠀⢀⡤⠞⠉⠉⠉⠓⢦⣀
⠀⠀⠤⣄⡀⠀⠉⠉⠉⠀⢀⡤⠤⠤⣄⡀⠈⠉⠉⠉⠀⣀⡤⠤⠤⣄⠀⠈⠉⠉⠉⠀⣀⡤⠤⢤⣄⠀⠈⠉
⠀⠀⠀⠀⠙⠲⠤⠤⠤⠞⠉⠀⠀⠀⠀⠙⠲⠤⡤⠤⠞⠁⠀⠀⠀⠀⠙⠦⠤⠤⠴⠚⠁⠀⠀⠀⠈⠑⠦⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠛⠛⠉⠉⠛⠓⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠛⠓⠶⣄⡀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀⢸⡄
⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢸⡇
⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⣇⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⣼
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠙⠦⣤⣀⣠⠴⠋⠀⠀⠀⠀⠀⣰⠇
⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠒⠒⠚⠋⠁
⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⠤⣤⣤⣤⣤⣤⣤⡤⠤⠶⠒⠋⠉


⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠓⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⢰⠀⠰⠀⠄⡄⢰⠂⡰⡀⣔⡂⠀⠀⣔⠀⠀⢔⠀⢰⠀⡆⡆⡔⠐⡄⣤⠂⡆
⣤⣤⣤⣤⣤⣤⣬⣤⣴⣤⣧⣧⣼⣤⣥⣥⣤⣬⣴⣤⣥⣤⣤⣤⣥⣬⣤⣥⣧⣥⣤⣥⣭⣧⣧⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣉⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠢⠒⠂⠔⠒⠔⠒⠔⠒⠄⠒⠠⠒⠢⠒⠢⠒⠀⠀⠀⠀⠒⠀⠒⠒⠂⠐⠒⠂⠐⠒⠂⠐⠒⠂⠐⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠠

⠀⠀⠀⠄⣀⠤⠤⣀⠤⠤⣀⠤⠤⣀⡠⠤⣀⡠⠤⡀⠀⠀⠀⠀⠤⣀⡠⠤⣀⡠⠤⢀⡠⠤⢀⡀⠤⢄⣀⠤⢄⡀
⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⣀⡀⠀⡀⡀⠀⡀⡀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⢀⡀⠀⢀⡀⠀⠀⡀⠀⢀

⠀⠀⠀⡀⣀⠀⣀⠀⣀⠀⣀⠀⣀⢀⡀⢀⡀⢀⡀⢀⠀⠀⠀⠀⣀⠀⢀⣀⠀⢀⣀⠀⠀⣀⠀⠀⣀⡀⠀⣀⡀
⠀⠀⠀⠈⠀⠉⠀⠉⠀⠉⠀⠉⠀⠁⠈⠁⠈⠁⠈⠁⠀⠀⠀⠀⠀⠉⠁⠀⠉⠁⠀⠈⠁⠀⠈⠁⠀⠈⠉⠀⠈⠁
⠀⠀⠀⠈⠀⠈⠀⠉⠀⠉⠀⠉⠀⠁⠈⠁⠈⠁⠈⠁


⠀⠀⠀⠂⠤⠂⠒⠤⠂⠐⠤⠒⠑⠤⠔⠐⠢⠔⠀⠢⠀⠀⠀⠀⠐⠒⠐⠂⠒⠐⠂⠒⠀⠒⠐⠂⠒⠐⠂⠐⠂⠂
⠀⠀⠀⠂⠄⠂⠀⠤⠀⠀⠄⠀⠐⠀⠐⠐⠀⠐

⠀⠀⠀⠢⠔⠢⠔⠢⠔⠒⠤⠒⠤⠒⠤⠒⠢⠖⠢⠔⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠀⠂⠀⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂

⠀⠀⠐⠤⠢⠔⠤⠒⠤⠢⠔⠤⠲⠔⠢⠔⠤⠢⠔⠆⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂
⠀⠀⠀⠄⠂⠐⠠⠂⠄⠢⠔⠤⠂⠔⠢⠐⠤⠢⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠉⡤⣀⢤⣍⠱⢤⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠀⣨⢱⡇⠀⠀⠑⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡄⡾⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢀⠠⣹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢻⠘⡀⣡⢋⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠛⠑⠀⠉⠻⣦⡀⠀⠀⠀⠰⠁⠸⣔⢌⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢼⣿⣆⠈⠈⠂⠀⠀⠀⢀⠁⠃⢓⣹⣴⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢀⠀⢸⣿⡆⠠⣄⣀⣤⠄⠀⠁⠀⠀⢇⠁⢳⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠐⢌⡻⣽⡦⢽⣷⠀⠌⠋⠁⠀⠀⠀⠀⠀⢺⡎⠐⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠑⢿⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠐⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡘⣇⠀⠸⡿⡳⠀⠠⠀⠀⠀⠀⢀⢼⡇⢠⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⣾⡆⠀⢻⡄⠀⠀⠀⠀⠀⠀⢀⡾⠃⠠⣸⠁
⠀⠀⠀⠀⠀⠀⢀⣴⣆⡀⢀⠀⢤⣀⠀⠀⠀⢀⣼⡇⠊⢻⡄⠀⠙⢦⣀⠀⠀⠀⠀⠞⠁⣰⡿⠃
⠀⠀⠀⠀⠀⠀⡾⠉⠁⠀⠀⠑⢢⢿⣿⡿⠿⠋⢸⡇⣇⠈⢇⠀⠀⠀⠉⠛⠲⠤⠶⠾⠛⠉
⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠈⠒⠞⣍⣷⣄⠐⠼⢠⡏⠀⡞
⠀⠀⠀⠀⠀⠀⠆⠀⢄⣌⠛⠶⣄⡘⠦⡙⠉⣭⣴⠞⠁⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠰⣽⡆⠀⠀⠉⠑⠛⠒⠤⠶⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⢀⢄⡜
⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⠀⣀⣠⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⣾⣿⠛⠙⢿⣿⡄⠀⢀⣼⣿⠟⠛⠛⠻⣿⣿⡿⠟⠛⠛⠛⠛⠻⢿⣷⣦⣀⣴⣿⡿⠟⠛⠙⠛⠻⣿⣷⣄
⠀⠀⠀⠀⠀⣿⣷⣄⣀⣼⣿⡇⠀⢸⣿⠇⠀⣴⣦⠀⠘⣿⣷⠀⠀⣠⣶⣶⣤⡀⠉⠻⣿⣿⠋⠀⣠⣶⣶⣦⡀⠈⢻⣿⡆
⠀⠀⠀⠀⠀⠈⣿⣿⠿⠿⣿⣇⠀⠸⣿⣧⡀⠈⠁⠀⣰⣿⡏⠀⣼⣿⠏⠙⣿⣷⠀⢠⣿⣟⠀⢸⣿⡏⠉⣿⣿⠀⠈⣿⣷
⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⢻⣿⣆⠀⠙⠿⣿⣶⣶⣿⡿⠋⠀⣰⣿⣿⡇⠀⢻⣿⡄⠀⠻⣿⣿⣿⠟⠁⢀⣿⡿⠀⢠⣿⣏⣀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠙⢿⣷⣤⣀⠀⠉⠉⠀⣀⣤⣾⣿⠛⢿⣷⡀⠈⢻⣿⣦⣀⠀⠀⠀⣀⣴⣿⡿⠁⠀⠺⡿⠿⠟⠛⠻⠿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⢹⣿⡿⣿⣿⣿⣿⡿⠟⠿⣿⣿⣿⣿⣿⣄⠀⠉⠻⠿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⢀⣀⣤⣤⣤⡀⠈⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣮⣿⣷⣄⠀⠙⢿⣷⣤⣄⣀⣀⣀⣀⣽⣿⣿⣦⣄⣀⣀⡀⣀⣀⣠⣄⠀⠀⢠⣶⣿⠿⠛⠛⢻⣿⡆⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣧⣄⠀⠉⠛⠿⠿⠿⠿⠿⠛⠉⠉⣙⣿⣿⠿⠿⠿⢿⣿⡟⠀⢰⣿⡟⠁⢀⣤⣶⣾⡿⠃⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣶⣤⣤⣀⣀⣀⣤⣤⣶⣿⡿⠟⠁⠀⠀⠀⢸⣿⡇⠀⣿⣿⠀⠀⣿⣿⠋⠉⠀⣠⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⢀⣼⣿⡇⠀⢻⣿⡄⠀⠻⣿⣶⣾⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⢿⣷⡀⠈⢻⣿⣦⣀⠀⠉⠉⠉⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⢨⣿⣷⣄⠀⠙⠻⢿⣿⣿⣷⣦⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⢀⣿⡿⠛⣿⣷⣦⣄⣀⡀⠀⣹⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⢸⣿⡇⠀⣿⣿⠛⣿⣿⣿⣿⡿⠛⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠸⣿⣇⠀⢻⣿⣾⡿⠛⠉⢀⣀⣀⣀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⢻⣿⣄⢠⣿⡟⠁⢠⣾⣿⠿⠿⠿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠹⣿⣿⣿⠁⢠⣿⡟⠁⢀⣤⡀⠈⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⠀⣿⣿⠀⠘⣿⣧⠀⠈⠛⠁⢀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣾⣿⣇⠀⠙⢿⣷⣦⣤⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣏⠉⠙⣿⣷⣄⠀⠉⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⠀⠈⠛⢿⣿⣶⣶⣤⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣠⣄⣀⠀⢹⣿⡟⠋⠙⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣧⣀⣠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠟⠛⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠛⠉⣁⣄⠀⠀⠀⠀⣠⡄⠀⠀⣀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⣠⡄⢠⣾⠟⢩⣤⠀⠀⠀⠸⣷⠀⠈⢿⡆⠀⠀⠹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⣼⡟⢀⣿⠃⠀⣿⠃⣸⡿⠀⣸⡟⠀⢀⣿⠇⠀⣼⡇⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢀⣾⠟⢀⣾⠟⠀⠀⣿⡄⢿⣇⠀⠹⣷⠀⠀⢿⣆⠀⢿⣇⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠙⢁⣤⡌⠁⣰⡆⢠⣿⠀⣸⣿⣀⣰⣿⣀⣠⣾⣏⣀⣼⡿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⢀⣴⡿⠋⣠⣾⠟⢁⡘⠋⠀⢻⣿⡿⠛⠛⠛⠉⠉⠙⠛⠛⠛⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⢸⡏⠀⠰⣿⠁⠀⢸⣏⠀⠀⢼⣿⡄⠀⠀⠀⠀⠀⠸⠿⠛⠃⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⣠⣿⠃⠀⣼⡿⠀⢠⣾⠇⠀⣠⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⢸⣿⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⣿⡇⠀⢨⣿⠀⠀⣼⡇⠀⢀⣿⣇⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡁⠀⢸⣟⠀⠀⣿⡇⠀⢸⣿⠀⠀⢸⣟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣤⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇⠀⢈⣿⠀⠀⢹⡷⠀⠈⣿⡆⠀⢘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⣼⡟⠀⢠⣿⠃⠀⢸⡟⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠸⣿⡀⠀⢻⣇⠀⠘⣿⡄⠀⠸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⢰⣿⠀⠀⣾⡏⠀⢠⣿⠁⠀⢰⡿⠙⢿⣶⣦⣤⣤⣀⣀⣀⣀⣠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠸⣿⡄⠀⢻⣧⠀⠘⣿⡄⠀⠸⣿⡄⣼⡏⠀⠉⠉⠙⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⢀⣿⡇⠀⣰⣿⠀⢀⣼⡇⠀⢀⣿⣇⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠀⠀⠉⠙⠻⢿⣿⣶⣤⣤⣤⣴⣾⣿⡿⠿⠛⠛⠻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠈⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧
⠀⠀⠀⠀⢀⣀⣠⣤⣴⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆
⠀⣠⣶⣿⡿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣦⣤⣀
⣾⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣷⣦
⣿⣿⡀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇
⠸⣿⣧⠀⠀⠀⠀⣰⣿⡿⠛⠋⠁⠈⠙⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇
⠀⢻⣿⡆⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟
⠀⠀⣿⣿⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠈⠉⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⢸⣿⡇⣀⣀⠀⠀⢀⣀⠀⠀⠀⠈⠻⣿⣷⣤⣤⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠻⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠙⠛⠻⠟⠉⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡄
⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿
⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢀⣼⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿
⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠁
⠀⠀⠀⠈⠻⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣤⣶⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣷⣤⣀⣀⣠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⢠⣦⡙⠻⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣶⣤⡄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⣿⣛⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠀⠈⠁⢀⠶⠂⠀⠀⠀⠀⠀⠀⠀⢸⣫⡆⢐⢮⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠺⠂⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣤⣄⠁⠀⣠⡄⠀⠀⠀⠀⠀⣀⣤⣠⡋⠈⢩⣤⣶⣦⠄⠀⠀⠀⠀⠀⠐⠛⠢⣤⡤⠒⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠉⠁⠀⠀⠈⠁⠀⠀⠀⠀⠈⠛⠚⢈⡶⠭⢶⣁⠉⠀⠀⠀⠀⠀⠀⠀⣔⡶⠊⠉⠈⠐⡶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⣠⡄⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⢼⡝⠂⠙⠾⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣺⡃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣠⢀⡘⠓⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣀⠁⡀⠀⣤⠀⠀⠀⠀⠀⠀⠰⣖⡴⠈⠪⠞⢱⢰⣲⠂
⠀⠀⠀⠀⠀⠀⠐⠷⡵⠄⡦⢱⡎⣥⢀⡴⣠⡀⠀⠀⠀⠀⠀⠀⠬⣖⣭⡲⠅⠀⠀⠀⠀⠀⠀⠀⠀⣓⠊⢑⡊⢰⠉⠐⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⠇⠻⡂⠀⠘⠈⠀⠀⠀⠀⠀⡀⠶⠀⠔⠙⠂⠀⠶⠀⠀⠀⠀⠀⠀⣠⣖⢭⠃⣨⡁⢹⣱⣲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠑⠀⠠⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢔⡮⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢦⣧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢋⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡡
⠀⠀⠀⠀⠀⠀⠀⠈⣷⠇⡰⠲⠔⢦⢸⣷⠂⠀⠀⠀⠀⠀⠛⣨⣄⠀⠭⢀⣸⡀⠓⠀⠀⠀⠀⠀⠘⣂⣅⡀⠸⠇⣀⣦⡘⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠺⣁⠀⠀⣁⡶⠈⠁⠀⠀⠀⠀⠀⢈⡀⢈⡹⣿⢎⠀⣀⡁⠀⠀⠀⠀⠀⠀⡀⢈⣉⠾⠦⣉⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠰⢿⡇⠳⢞⠦⠆⢰⠯⡄⠀⠀⠀⠀⠀⡤⢘⠇⢀⣖⠀⢸⠑⡴⠀⠀⠀⠀⠀⠠⠌⠋⠁⢸⡆⠉⠏⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⠓⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠰⣦⠀⠀⢺⣇⠀⠀⡰⠆⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠛⣤⢘⣇⡤⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣳⣆⠀⡐⡿⠁
⠀⠀⠀⠀⠰⠾⠾⠒⡒⣇⣪⡓⠓⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⣄⣟⢆⢸⢃⣤⡼⠞⠃
⠀⠀⠀⠀⠀⠀⣐⡶⠋⢐⣇⠙⢦⡄⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⣈⣨⡭⠝⡿⡗⠤⣶⣴⡄
⠀⠀⠀⠀⠀⠐⠋⠂⠀⢐⡗⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠛⠉⠁⣺⡇⠈⢶⣀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⠀⠈⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠜⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⢀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠
⠀⠀⠀⠀⠀⠀⢬⢵⠷⣛⠀⠀⠀⠀⠀⠀⠀⠠⡄⣆⡄⠀⠀⠀⠀⠀⠀⣀⡇⠀⢠⡥⠀⣀⠜⠄
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠒⡺⡿⡖⠀⠀⠀⠀⢀⠀⠀⡘⠣⣀⣀⡔⠓⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠼⠉⠉⠉⢉⡽⠯⣉⠉⠋⠉⠙
⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠰⡆⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⠋⢀⡆⠘⢣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣥⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠑⠀⢨⣇⠀⠈
⠀⠀⠀⠀⠀⢀⣄⠀⠀⠘⠉⡴⢰⡈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲

⣿⣟⣛⣟⣛⣻⣛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠌⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠳⣦⣄⠀⣿⠀⣠⣴⠞⠃⠀⠀⠀⣰⢤⡹⣽⢃⣤⡆⠈⠀⠀⠀⠀⠀⠀⠶⠀⠰⠇
⠀⠀⠀⠀⠀⠰⣶⠆⠀⠀⠀⠀⠀⠀⠂⠀⢉⣓⢾⣞⡉⠀⢐⠀⠀⠀⠀⢈⣛⣻⣿⣟⣋⡁⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠠⡷
⠀⠀⢂⠨⠀⠀⠀⠀⠀⠀⡐⠀⠀⢀⣤⠾⠋⠁⣾⠀⠙⠻⢦⡀⠀⠀⠀⠻⠞⢱⣻⡜⠾⠇⠀⠀⠀⠀⠀⠀⢐⡴⠀⠰⡄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠤⣤⢠⣬⣼⣥⡤⢤⡤⠀⠀⠀⠀⠠⠄⠈⠀⠉⠀⠄⠠⠀⠀⠀⢀⡀⢀⢀⠀⠄⠀⢀⠀⠀⠀⠀⢀⠀⠀⠻⡦⠀⣴⠦⠄
⠀⠀⠘⢣⣿⣯⣝⣿⣿⡜⠁⠀⠀⠀⠀⠂⠀⠀⣤⡀⠀⠐⠀⠀⠀⠀⠀⠀⢀⡉⠀⢉⡤⠀⠀⠀⠀⠀⠘⠶⠖⠀⠀⠀⠉
⠀⠀⢰⣮⢟⣿⣽⣿⡿⢴⡆⠀⠀⠀⠀⠂⠀⠈⠉⠀⠀⠐⠀⠀⠀⠀⢠⡄⠡⢔⠀⠤⠀⢠⠀⠀⠀⠀⠀⠀⣰⠄⢀⡀⠘⠛⢧
⠀⠀⠉⠉⠀⠡⣭⡍⠀⠉⠉⠀⠀⠀⠀⠈⠁⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⡿
⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠃⠭⠘⢠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⡄⢓⣿⢿⢠⡄⣠⡄
⠀⠀⠀⠀⠠⣀⣀⣀⠀⠀⠀⠀⠀⠀⢬⠑⢣⣄⣻⣠⡄⠪⡥⠀⠀⠀⠀⠀⠠⠠⠡⠀⠀⠀⠀⠀⠀⠀⢩⢻⡶⣍⣹⣩⡶⣟⣯⠁
⠀⠀⠀⠀⠠⠘⠛⠣⠀⠀⠀⠀⠀⠀⠴⢄⡠⠜⢻⠳⢆⡠⠦⠀⠀⠀⠀⠀⠀⠡⠡⠌⠀⠀⠀⠀⠀⠀⠰⣰⣥⠞⣿⠳⣮⣇⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠡⠆⡀⢭⢀⠰⠮⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠫⠆⡹⣿⢾⠱⠏⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠾⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⠍
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣰⠛⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢳
⠀⠰⣶⢫⠧⣩⠉⣏⠴⡜⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⠢⣤⣾⢾⣆⣤⠴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢙⡛⢴⢽⣿⡯⡦⢚⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣧⣽⣻⣯⣿⠋⠀⠀⠀⠀⠀⡀
⠀⢀⣮⣱⡄⠾⠭⠗⣀⢟⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣫⠷⢾⣹⡷⢿⣑⣄
⠀⠀⠉⠉⠁⢏⣒⡟⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣹⠁
⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⢹⣿⠁⠀⠀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣶⣄⢸⣿⢀⣴⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠋⠀⠀⠀⣀⠀⠀⠀⠀⠰⣿⡀⠀⠀⣠⣴⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣄⠀⠀⢸⣿⠀⠀⠀⢴⡆⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⣿⡇⠀⣸⣿⠁⢈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⣨⣿⣆⡀⠀⣿⡇⠀⠀⠀⢠⣤⠀⠀⠀⢸⣿⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⣸⣿⣴⡾⠟⠛⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠋⠙⠿⣷⣿⣧⠀⠀⠀⠀⠀⣤⡀⠀⢸⣿⠀⠀⣰⡶⠀⠀⠀⢀⣠⣶⡿⠿⠿⢷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠿⠿⠿⢿⣦⣄⡀⠀⠙⣿⣄⢸⣿⠀⣰⡿⠁⣀⣤⣾⠿⠋⠁⠀⠀⠀⠀⠀⠉⠛⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠉⠀⠀⠀⠀⠀⠈⠙⠻⣷⣦⣜⣿⣾⣿⣴⣿⣷⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⢀⣀⣤⣤⣭⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⠶⠀⠰⠆⠀⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠛⠃⠈⠉⠉⢉⣩⣿⢿⣿⣿⣿⡿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠋⢁⣾⠟⣿⡿⣿⡄⠉⠛⢿⣶⣄⡀⠀⠀⠀⠀⢀⣠⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣶⣶⣶⡿⠟⠉⠀⠀⢠⣾⠏⠀⣿⡇⠘⢿⣆⠀⠀⠈⠙⠻⢷⣶⣶⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣴⣾⠟⣿⡿⠁⠀⠀⠀⠀⠘⠋⠀⠀⣿⡇⠀⠈⠉⣀⠀⠀⠀⠀⠀⢹⣿⠿⣷⣦⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠉⣿⡏⠀⢠⣿⠃⠀⠀⠀⠀⠸⠃⠀⠀⠀⣿⡇⠀⠀⠈⠛⠀⠀⠀⠀⠀⢸⣿⡄⠀⠉⢿⣏⠉⣹⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣶⡾⠟⠀⠀⢸⣿⠀⠀⠀⠀⠰⠆⠀⠀⠀⣰⣿⣧⡀⠀⠀⠀⠺⠇⠀⠀⠀⠀⣿⡇⠀⠀⠈⠛⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣿⡿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⣿⡇⠈⠻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⣿⣇⡀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⡴⢊⡶⡄⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢧⡘⠛⢁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢉⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡋⠀⠀⡄⠀⠀⠀⢀⣀⣤⣤⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⠛⠛⠉⠙⠛⠻⠿⣶⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠛⠉⠁⠀⠀⠀⠉⠉⠻⢿⣦⡀
⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⡀⡀⠂⡀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⣠⣤⣶⣶⣤⣀⠀⠀⠀⠈⢻⣇
⠀⠀⢠⣿⠃⠀⠀⠀⣠⣾⠟⠛⠛⠻⢿⣦⡀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠐⢀⠛⠄⠀⠰⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⢠⣾⠟⠉⢀⣀⠉⢿⣧⠀⠀⠀⠸⣿⡀
⠀⠀⢸⣿⠀⠀⠀⢠⣿⠁⣴⣶⣶⡄⠀⢹⣷⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⣀⣼⡟⠁⠀⠀⠀⠀⠀⠀⣿⡇⠀⢰⣿⣿⡷⢸⣿⠀⠀⠀⢰⣿⠁
⠀⠀⠘⣿⡄⠀⠀⠀⢿⣦⣙⣻⣿⠇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠈⠻⢿⣶⠟⠃⠀⠀⠀⣼⡟
⠀⠀⠀⠹⣷⡄⠀⠀⠀⠉⠛⠛⠁⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⣴⣿⡁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⢀⣠⣾⠏
⠀⠀⠀⠀⠘⠿⣶⣤⣀⡀⠀⢀⣀⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢀⣾⡟⠁⠀⠀⠀⠀⢩⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣶⣶⣶⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⣾⠏⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⣿⣵⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⡦⡀⠉⠀⠀⠀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠁⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠛⠉⠉⠉⠙⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢿⣿⠀⠀⣀⣤⣤⣄⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠢⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⣾⡇⠀⣴⠋⢠⣦⡌⣷⠀⠀⡷
⠀⠀⠀⠀⠀⢠⠋⠀⣀⢀⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢰⣿⠃⢀⣿⠃⠀⢻⡄⠘⠻⠟⠁⠀⣼⠃
⠀⠀⠀⠀⠀⢸⠀⠾⣱⣦⠙⡆⠀⠀⠀⠹⣄⠀⠀⠀⣿⠏⠀⣸⡿⠀⠀⠀⠙⠶⣤⣤⠴⠟⠁
⠀⠀⠀⠀⠀⠈⠶⣄⣉⣁⠴⠁⠀⠀⠀⠀⠈⢦⠀⣸⡿⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⠃⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣷⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⠿⠿⢻⣿⣿⣿⣟⠛⠛⠛⠻⠿⢿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠟⠋⠉⠀⠀⢀⣾⡿⠉⠻⣿⣦⡀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠟⠉⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠈⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠙⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⠀⢀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆
⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧
⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣤⣹⣿⡆
⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣠⣴⣶⣿⣿⠿⠿⠿⣿⣷⣦⠀⠀⠈⢿⣿⠀⠀⣰⣾⡿⠟⠛⠉⠉⠉⠛⠁⣿⣷
⢠⣿⡏⣠⣴⣶⣾⣿⣿⣿⣶⣶⣤⣄⠀⠀⠀⢸⣿⠃⠀⢠⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠸⣿⡇⠀⠈⠉⠀⢀⣀⣀⣀⣀⣀⡀⢹⣿
⣸⣿⠉⠻⠛⠉⠀⠀⠀⠀⠈⠉⠛⠛⠁⠀⠀⢸⣿⠀⠀⠀⠉⣀⣤⣶⣶⣿⣿⡿⢿⣿⣿⣷⣶⣦⣄⠀⣿⣿⠀⣠⣶⣿⡿⠿⠛⠛⠛⠻⠿⣿⣿
⣿⣿⠀⢀⣠⣤⣶⣶⣾⣿⣿⣷⣶⣶⣤⣀⠀⢸⣿⠀⢀⣴⣿⡿⠛⠋⠁⢹⣿⠀⠀⠀⠀⠀⠉⠛⢿⣷⣾⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣿⣿⣶⣿⠿⠛⠉⠁⠀⠀⠀⠀⠉⠉⠛⢿⣿⣾⣿⣴⣿⡟⠁⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉
⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡿⠋⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⣠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠒⣤⠾⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠾⠛⠋⠉⢁⣀⠘⠻⠿⢒⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠞⢁⣴⡞⣲⣤⣀⠀⢬⡙⠳⣦⣀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⣴⣿⠷⠛⠛⠻⣿⣿⣦⡙⢦⡨⣻⣞⣄⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡟⠾⡟⠁⠀⠀⠀⠀⠈⣿⣿⣿⣷⣷⢹⣿⣼⣆⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇⣿⣇⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⡿⡀
⠀⠀⣀⡤⠶⠶⠶⢿⣿⣶⣤⡀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⣫⣿⣿⣿⣿⣿⡟⢰⣿⣿⠃⡼⡱⣡⣄⡀⢀⠄
⠀⠈⢀⡠⠴⠞⠛⠛⠻⠿⠿⣿⣷⣤⡈⠉⠁⠒⢒⣖⣛⣛⣫⣭⣶⣿⡿⣿⣿⣿⠿⢋⣴⠟⠞⣡⠞⢟⣴⣿⢟⡵⢋⢄
⠀⠀⠀⠀⢐⣚⣛⣛⣛⣛⣓⣶⣬⣙⠻⢷⣦⣀⠠⢬⣭⣭⣭⣍⠁⢒⣛⣯⡭⠶⠞⠋⠁⠀⣀⣤⣶⠿⣛⣵⢟⣪⠖⠁
⠀⠀⠀⠀⠀⠀⠐⢒⣒⣒⣲⣿⣿⣿⣻⠦⣌⡙⠻⢶⣦⣍⡛⠿⣿⣦⣄⡀⠀⠀⠀⠒⠉⠍⠭⠴⢒⣋⡭⠖⠋
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠿⢿⣿⣿⣶⠦⠤⠈⠉⠛⠻⠶⢮⣭⣽⣛⣛⡒⠒⠒⠒⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣿⠃⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠙⠻⣶⣦⣤⣀⣀⣤⣤⣶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠚⠉⠉⠉⠉⠙⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⡼⠀⢄⠈⣦⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢁⠰⣄⠀⠀⠀⢀⡠⠞⡁⣄⠈⠙⢁⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠉⠉⠉⠁⠐⠀⠑⠈⠙⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠐⡉⢀⠙⠦⣀⣀⣀⡠⠔⠋⠓⢤⣀⣀⣠⠔⠋⠑⠦⠤⠤⠤⠜
⠀⠀⠀⠤⠤⠤⠒⠉⣠⡀⠙⠲⠤⠤⠤⠒⠁⠈⠒⠤⠤⠤⠤⠒⠀⠑⠒⠶⠶⠒⠋⠈⠓⠒⠒⠂⢀⡀
⠀⠀⠀⠀⠒⠒⠒⠉⠀⠙⠒⠤⠤⠤⠐⠀⠈⠲⢤⣀⣀⣀⣀⠀⠀⠠⣀⣀⠀⢀⣀⡤⠂⠤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠶⠶⠒⠁⠀⠑⠢⠤⣄⣀⣀⠤⠂⠐⠢⢬⣭⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠖⠊⠀⠈⠒⠤⢤⣄⣀⡤⠄⠀⠐⠢⠤⠔⠂

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⢿⣧⡀
⠀⠀⠀⠀⠀⣼⡿⠁⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠈⢻⣷⡀
⠀⠀⠀⠀⣾⡿⠁⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠃⠀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⣰⣿⣷⡄⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣹⣿⠀⠀⢀⣼⡿⠁⠹⣿⣆⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠹⣿⣦⣀⠀⠀⣀⣴⣿⠇⠀⢀⣾⡟⠁⠀⠀⠘⢿⣦⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠈⠛⠻⠿⠿⠟⠋⠁⠀⢠⣿⠟⠀⠀⠀⠀⠀⠈⢿⣧⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠈⠛⢿⣷⣶⣤⣴⣶⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⣀⡀⠀⠀⢀⣀⣤⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠐⠂⠤⠄⠀⠠⠤⠐⠒⠀⠀⠐⠒⠠⠤⠀⠀⠤⠀⠒⠀⠀⠀⠐⠂⠤⠀⠀⠠⠄⠐⠂
⠀⠀⠀⠀⠐⢄⠀⡠⠒⠢⡀⢀⠔⠒⢄⠀⡠⠒⢄⠀⢀⠐⠢⡀⢀⡔⠒⢄⠀⡠⠂⠢⡀⢀⠔⠒⢄⠀⡠⠂
⠀⠀⠀⠀⠀⣀⠉⠀⠀⠀⡈⠅⡀⠀⠀⠉⢀⡠⢀⠉⠀⠀⠀⣈⠥⡀⠀⠀⠉⠀⡠⢄⠈⠁⠀⠀⢀⠉
⠀⠀⠀⠀⠀⡀⠉⠒⠒⠉⡀⠀⠈⠑⠒⢊⢁⠀⠀⠈⠒⠒⡈⠀⠀⠀⠁⠒⠂⠁⠀⠀⠈⢐⠒⠊
⠀⠀⠀⠀⠀⠀⠑⠒⠒⠁⠀⠈⠐⠒⠊⠁⠀⠉⠒⠒⠈⠀⠀⠑⠒⠒⠁⠀⠈⠐⠒⠂⠁⠀⠉⠒⠒⠈
⠀⠀⠀⠀⠉⠐⠠⠄⠄⠒⠈⠉⠐⠢⠄⠤⠐⠈⠉⠑⠂⠄⠠⠐⠊⠉⠁⠂⠤⠠⠔⠂⠉⠁⠒⠠⠠⠄⠂⠉
⠀⠀⠀⠀⠀⠀⠒⠂⠤⠀⠠⠄⠒⠂⠀⠀⠒⠠⠄⠀⠠⠄⠒⠀⠀⠐⠒⠠⠄⠀⠠⠐⠒⠀⠀⠐⠂⠤
⠀⠀⠀⠀⠀⠀⠐⠒⠀⠤⠤⠀⠤⠤⠄⠐⠂⠀⠀⠀⠒⠂⠠⠄⠄⠠⠀⠤⠀⠒⠀⠀⠀⠀⠒⠀⠤⠤
⠀⠀⠀⠀⠐⠢⡀⠀⢀⠔⠂⠒⢄⠀⠀⡠⠒⠐⠢⡀⠀⢀⠔⠀⠢⡀⠀⠀⡠⠂⠐⢄⠀⠀⢠⠐⠀⠢⡀
⠀⠀⠀⠀⢀⠀⠈⠁⠁⠀⣀⡀⠀⠁⠉⠀⢀⣀⠀⠈⠈⠁⢀⣀⡀⠈⠁⠉⠀⣀⣀⠀⠉⠈⠀⢀⣀⡀⠈⠁
⠀⠀⠀⠀⠈⠹⣄⠀⢠⠞⠁⠙⢦⡀⢀⡴⠋⠈⠳⡄⠀⣠⠏⠁⠙⣆⠀⢀⡜⠉⠈⢳⡀⠀⣰⠋⠈⠹⣄
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⢠⡀⠀⢀⡤⣄⠀⠀⣠⢤⡀⠀⢠⠤⣄⠀⠀⡤⢤⠀⠀⣠⢤⡄⠀⢀⡤⣄⠀⠀⣠⢤⡀⠀⢀⡄
⠀⠀⠀⠀⠀⠹⠤⠞⠀⠈⠧⠼⠁⠀⠳⠤⠏⠀⠘⠦⠞⠁⠈⠳⠴⠃⠀⠉⠤⠉⠀⠘⠷⠼⠃⠀⠻⡴⠟

⠀⠀⠀⠀⠀⠙⠦⣤⡤⠞⠉⠙⢦⣤⡴⠋⠉⠳⢤⣤⠖⠋⠙⠲⣤⡤⠞⠉⠙⢦⣤⡴⠋⠉⠳⢤⣤⠴⠋

⠀⠀⠀⠀⠀⠙⠓⠦⣤⣀⣠⡤⠖⠛⠉⠙⠓⠦⣄⣀⣠⠴⠚⠋⠉⠙⠲⢤⣄⣀⣤⠴⠚⠋⠉⠛⠲⢤⣄

⠀⠀⠀⠀⠀⠛⠓⠶⢤⣀⣀⣀⡤⠴⠚⠛⠛⠛⠲⠦⣄⣀⣀⣠⠤⠖⠛⠛⠛⠓⠦⢤⣀⣀⣀⡤⠶⠚⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣴⣿⣿⣿⣿⡇⠈⢻⣦⣤⣤⣤⣄⣀⣀⣀⣀
⠀⠀⢀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢹⣿⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀
⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡐⢿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣉⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣻⣧⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣛⣻⣭⣷⣾⠿⣫⣿⣿⣿⣿⣿⣿⡟⣿⣿
⠳⠾⠛⠓⠮⣝⣛⠿⢿⣿⣿⣿⣿⣿⣿⣽⣿⣛⣻⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣟⣿⣭⣵⣶⣿⣿⣿⣿⡿⢿⣛⡭⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⠿⠿⠟⠚⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠘⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠲⢤⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⡀⠐⠈⠉⠛⠓⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢰⣿⡆⠀⠀⠀⢂⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢨⠀⣾⣷⠀⠀⠀⠂⠀⠀⠀⠀⠈⠳⡄
⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠹⡄
⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣄⠀⡘⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠁⠢⣀⠀⠀⠈⠀⠀⠀⠀⠀⠸⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣦⣤⣀⣀⠀⠀⠀⠀⣀⣀⣴⣶⡿⠳⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠈⠁⠚⠲⠦⣄⠀⠀⠀⠀⠘⠋⠉⠉⠙⠟⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠀⠀⠠⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠛⠛⢿⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠆⠀⠀⠈⠙⠦⠆⠀⠀⠀⠀⠈⠙⠛⠃⠀⠀⠈⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢀⠃
⠀⠀⠀⠀⠀⠀⡰⠊⠐⣆⠀⠀⠀⠀⡆⠀⠀⡎
⠀⠀⠀⠀⠀⢀⠉⠀⠀⡎⠀⠀⠀⠸⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠈⡃⠀⡀⢦⣀⡀⣠⡃⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠁⠀⠀⡜
⣀⣀⣀⣀⣀⣀⣀⣀⣉⣒⣤⣤⣤⣄⣊⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣙⣿⣡⠄⢄⢸⣇⡤⠀⠀⠀⡆⣶⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠑⢄⠀⢹⡏⢀⡴⠃⢀⡿⠯⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⡆⠀⢰⠈⠀⣤⠑⢼⡷⢋⣄⠀⠈⡆⠀⢰⢀⡴⠋
⠀⠀⠀⠀⠀⠀⢤⣠⠀⡄⠠⠤⠷⢇⠀⢸⠀⠘⣿⠇⣸⣇⠸⡿⠀⠀⡇⢀⡼⠯⠤⠄
⠀⠀⠀⠀⠀⠀⢘⣛⣷⣇⢀⣀⣀⣠⣵⣾⠀⠀⡠⠊⢸⡏⠳⣄⠀⢀⣷⣋⣀⣀⣀⡀⠀⢀⡔⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠁⠀⠀⠀⠀⠀⡱⢎⠀⢠⢾⣧⡀⢈⡵⢏⠀⠀⠀⣀⠀⠐⠚⡻⣟⠻⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣄⠈⠳⣄⠺⠿⠗⣠⠞⠁⢀⡝⢇⢸⣇⡽⠫⡀⠀⠑⢄⠻⠿⠛⣠⠊⠀⡨
⠀⠀⠀⠀⠀⠰⠶⠾⡷⠶⠾⡷⠶⢾⠷⠶⢶⡷⠶⢶⣿⣿⠶⠶⣾⠷⠶⢾⡷⠶⢾⡶⠶⢾⡶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⡊⠀⡠⠋⣤⣶⣦⠑⢄⠀⢉⡶⣋⢸⡇⢱⣞⠁⢀⡴⠋⢴⣾⡦⠙⢦⡀⠙
⠀⠀⠀⠀⢀⣀⣦⣽⣮⡤⠀⠀⠉⠀⠀⢀⡵⢋⡀⠈⢻⡷⠃⠀⡱⢎⠀⠀⠀⠀⠀⢀⡀⠉
⠀⠀⠀⠀⠀⠀⠋⠜⠁⠀⠈⠉⠉⢉⡽⣿⠀⠀⠙⢦⣸⣇⡠⠊⠀⠀⡟⢏⠉⠉⠉⠀⢹⢿⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⡿⡏⠀⢹⠀⠀⣾⡆⢹⡏⢰⣿⡄⠀⡇⠀⣷⢖⠒⠂⠘⠀⠋⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠇⠀⠘⡀⠀⠙⣡⢾⡗⣄⠛⠀⠀⠇⠀⠸⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣲⣾⠁⢠⠞⠁⣸⣇⠀⠑⢄⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠿⠸⠀⠀⠀⠚⢹⡇⠑⠐⢋⣿⣍⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣶⣶⣤⣀⣀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣷⣶⣤⣀⣀⠀⠀⣀⣀⣤⣶⣾⣿⣿⣷⣶⣤⣄⣀⠀⠀⢀⣀⣤⣶⣶⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣤⣀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠿⣿⣶⣶⣿⠿⠟⠋⠉⠉⠉⠉⠙⠻⠿⣿⣶⣶⣿⠿⠟⠋⠉⠉⠉⠉⠙⠻⠿⣿⣶⣶⣾⠿⠟⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⢿⣶⣶⣤⣴⣶⣾⡿⠟⠛⠛⠛⠛⠻⢿⣶⣶⣦⣴⣶⣶⡿⠟⠛⠛⠛⠛⠻⢿⣷⣶⣦⣤⣶⣶⡿⠿⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⢿⣶⣤⣤⣤⣤⣤⣴⣶⡿⠿⠿⠿⠿⢿⣶⣦⣤⣤⣤⣤⣴⣶⡿⠿⠿⠿⠿⢿⣷⣦⣤⣤⣤⣤⣤⣶⡿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣷⣶⣤⣄⣀⣀⣀⣀⣠⣴⣶⣾⣿⣿⣷⣶⣤⣄⣀⣀⣀⣀⣠⣤⣶⣶⣿⣿⣷⣶⣦⣄⣀⣀⣀⣀⣠⣤⣶⣾⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠟⠛⠋⠁

⠀⠀⠀⠀⢀⠀⢀⣤⠀⢠⠶⡀⠀⢀⣤⠀⠀⢀⠀⢀⡀⠀⢀⣤⡀
⠀⠀⠀⠀⠈⢧⣸⠋⣇⣸⠀⠳⣤⠏⠘⣇⢠⡟⣇⣿⠹⢦⠏⠀⢻⡄⢠⠞⢦⡀⢀⡴⢦⣄⢀⡴⠋
⠀⠀⠀⠀⠀⠈⠉⠀⠘⠋⠀⠀⠀⠀⠀⠈⠋⠀⠹⡟⠀⠀⠀⠀⠀⠙⠋⠀⠀⠙⠋⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠹⢦⡼⠻⣄⣰⣆⣠⡿⣤⡾⣦⡾⠻⠶⢷⣤⠟⢷⡴⢷⣤⠶⢶⣄⣠⠞⠷⠶⠋⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠚⠁⠙⣆⣀⣠⡤⣄⣀⣀⠴⠒⠶⡤⠶⠶⣤⠖⠛⢷⡤⠖⠳⢦⣤⡤⣤⣀⣀⡤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⣠⡤⢤⣄
⠀⠀⠛⠛⢷⡀⠀⣠⠖⠳⣦⡀⢀⣴⠏⠁⠻⣄⣀⣠⠴⠋⠉⠹⣆⠀⢀⣴⠏⠁⠙⠶⠶⠋⠁⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠙⠟⠋⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠛⠛⠶⣤⣤⣤⠶⠟⠛⠛⠳⢦⣤⣤⣤⠶⠛⠛⠛⠶⣦⣤⣤⡴⠞⠛⠛⠛⠶⣤⣤⣤⠶⠟⠛⠛⠳⢦⣤⣤⣴⠾⠛⠛⠛⠶⣤⣤


⠀⠀⠀⠀⠀⠛⠛⠶⢤⣤⣤⠴⠚⠛⠛⠳⠦⣤⣤⡤⠖⠛⠛⠛⠲⢤⣤⣤⠴⠞⠛⠛⠓⠶⣤⣤⡤⠶⠚⠛⠛⠳⠦⣤⣤⡤⠖⠛⠛⠛⠲⢤⣤


⠀⠀⠀⠀⠀⠉⠑⠢⢤⣀⡤⠔⠚⠉⠉⠒⠦⢤⣄⠤⠖⠊⠉⠑⠒⠤⣄⡤⠤⠒⠉⠉⠓⠢⢤⣠⡤⠔⠊⠉⠉⠒⠤⢤⣠⠤⠖⠊⠉⠑⠲⠤⣄


⠀⠀⠀⠀⠀⠛⠳⢦⣤⣤⣤⡴⠾⠛⠛⠶⢦⣤⣤⣤⠶⠞⠛⠳⠶⣤⣤⣤⣴⠶⠛⠛⠷⢦⣤⣤⣤⡴⠞⠛⠛⠶⣦⣤⣤⣤⠶⠞⠛⠳⠶⣤⣤


⠀⠀⠀⠀⠀⠛⠒⠦⣤⣀⣤⡴⠖⠛⠓⠲⢤⣄⣀⣤⠶⠚⠛⠓⠶⣤⣀⣠⡤⠖⠚⠛⠲⠦⣤⣀⣤⠴⠖⠛⠛⠲⢤⣄⣠⣤⠶⠚⠛⠓⠶⣤⣀


⠀⠀⠀⠀⠀⠚⠒⠦⣄⣀⣠⠴⠒⠚⠓⠲⠤⣀⣀⡤⠴⠚⠛⠒⠦⢤⣀⣀⠤⠖⠚⠓⠒⠦⣄⣀⣠⠴⠒⠛⠓⠲⠤⣀⣀⡤⠔⠒⠛⠒⠦⢤⣀


⠀⠀⠀⠀⠀⠛⠶⣦⣄⣀⣠⣴⠶⠞⠳⠶⣤⣀⣀⣠⡴⠶⠓⠶⢦⣤⣀⣀⣤⠶⠞⠓⠶⣦⣄⣀⣠⣴⠶⠟⠷⠶⣤⣀⣀⣤⡴⠶⠛⠶⢦⣤⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠒⠲⢤⣄⣀⣀⡤⠶⠒⠒⠶⣤⣀⣀⣠⠴⠖⠒⠲⠦⣄⣀⣀⣤⠶⠒⠒⠶⢤⣄⣀⣠⡤⠶⠒⠒⠶⣤⣀⣀⣠⠴⠖⠒⠲⢦⣄⣀


⠀⠀⠀⠀⠀⠒⠒⠤⣀⣀⣀⡤⠖⠒⠒⠢⢄⣀⣀⣀⠤⠒⠒⠒⠦⣄⣀⣀⡠⠔⠒⠒⠲⢤⣀⣀⣀⡤⠖⠒⠒⠢⢄⣀⣀⣠⠴⠒⠒⠒⠤⣄⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣿⡇⠀⠀⢸⣿⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡃⠀⠙⢿⡇⠀⠀⢸⡿⠋⠀⢘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⢻⣷⡄⠀⠈⠃⠀⠀⠘⠁⠀⢠⣾⠟⠀⠀⠀⢀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⣿⠟⠉⠻⣿⡄⠀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⢠⣿⠟⠉⠻⣿⠀⣀⣤⣤⣀
⠀⠀⠀⠀⣼⡿⠋⠙⠻⢿⣿⣧⠀⠀⠹⣿⡄⠀⠀⠀⠈⢿⣧⡀⠀⠀⢀⣼⡿⠁⠀⠀⠀⢠⣿⠏⠀⠀⣼⣿⡿⠟⠋⠙⢿⣧
⠀⠀⠀⠀⠹⣷⣤⡀⠀⠀⠈⠛⠦⠀⠀⠹⣷⡄⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⢠⣿⠏⠀⠀⠴⠛⠁⠀⠀⢀⣤⣾⠏
⠀⠀⠀⠀⠀⠈⣹⣿⣷⣦⣄⠀⠀⠀⠀⠀⠹⣷⣄⡀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⢀⣠⣾⠏⠀⠀⠀⠀⠀⣠⣴⣾⣿⣏⠁
⠀⠀⠀⠀⠀⣼⡿⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣶⣤⣿⡇⠀⠀⢸⣿⣤⣶⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢿⣇
⠀⠀⠀⠀⠀⠸⣿⣦⣤⣤⣤⣶⣶⣶⣶⣶⣦⣀⠀⠀⠈⠙⠻⡇⠀⠀⢸⠟⠋⠁⠀⠀⣀⣴⣶⣶⣶⣶⣶⣤⣤⣤⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠻⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⣄
⠀⠀⠀⠀⠀⢠⣶⡿⠿⠿⠿⣶⣶⣶⣶⣶⡿⠛⠉⠀⠀⢀⣠⡆⠀⠀⢰⣄⡀⠀⠀⠉⠛⢿⣶⣶⣶⣶⣶⠿⠿⠿⢿⣶⡄
⠀⠀⠀⠀⠀⢺⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⣿⡇⠀⠀⢸⣿⠿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡗
⠀⠀⠀⠀⠀⠈⢻⣿⣿⡿⠟⠀⠀⠀⠀⠀⢰⣿⠟⠋⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠙⠻⣿⡄⠀⠀⠀⠀⠀⠻⢿⣿⣿⡟⠁
⠀⠀⠀⠀⢠⣾⠿⠋⠁⠀⠀⣀⡄⠀⠀⢠⣿⠇⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠸⣿⡄⠀⠀⢤⣀⠀⠀⠈⠙⠿⣷⡄
⠀⠀⠀⠀⢿⣇⡀⢀⣠⣴⣿⡿⠀⠀⢠⣿⠏⠀⠀⠀⠀⣴⡿⠃⠀⠀⠘⢿⣦⠀⠀⠀⠀⠹⣿⡄⠀⠀⢿⣷⣦⣄⡀⢀⣼⡿
⠀⠀⠀⠀⠈⠛⠿⠿⠛⠉⣿⣇⠀⣠⣿⠏⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠹⣿⣄⠀⣨⣿⠉⠛⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠋⠀⠀⠀⣰⣿⠋⠀⠀⡀⠀⠀⢀⠀⠀⠹⣿⣆⠀⠀⠀⠙⠻⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡁⠀⢀⣼⡇⠀⠀⢸⣧⡀⠀⢘⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣶⡿⣿⡇⠀⠀⢸⣿⢿⣶⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣾⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣤⣒⣀⠍⣍⠏⢫⠉⣉⠙⢢⡾⠛⢒⡀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢐⡏⠡⠠⠈⠃⢈⠒⠉⢄⡰⡘⠏⠀⠢⠈⢒⡨⠏⠀⢀⠯⢲⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠮⠃⠁⣃⠀⠁⠀⢠⠊⠑⣀⠀⢐⠀⠥⠀⠤⠀⢰⡧⡀⠀⢹⠂⠀⡠⠝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⡀⢻⢀⠆⠀⡀⢇⠋⠈⢠⠌⠀⠁⢢⠔⣬⠙⣨⢥⠘⣮⡀⠎⠐⠖⠐⠀⠄⢉⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⡤⠀⠀⠀⡰⠆⣀⠒⡠⡯⣔⡡⠖⠤⠐⢆⠃⢠⠀⡎⣙⡃⢰⠋⡇⠂⠀⢛⠈⡀⠈⢬⡡⢜⣀
⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠠⠀⣄⠁⠂⣺⡑⠺⠁⠓⢩⡄⣒⢒⠲⢍⠂⠰⢡⠧⠉⠉⠁⢽⡘⣀⠉⡤⡈⠠⠈⠠⠴⠀⣡
⠀⠀⠀⠀⠀⠀⡰⠛⢛⢣⡉⢊⡡⠜⠓⠛⠋⠁⣟⠛⠀⠆⠀⠍⢈⠀⠀⢙⡤⠂⠈⠀⠲⠔⢨⡓⠌⠠⠀⠜⢤⠉⠠⠀⠏⠀⠃
⠀⠀⠀⠀⠀⢠⠝⠃⠈⠀⠀⠀⠉⠑⠶⡇⢁⠀⠇⠀⠀⢠⣀⢀⢚⣃⣴⣾⣄⡚⢀⠅⠢⢠⡔⡟⠐⡀⢻⠮⠔⠛⠋⠐⠀⠲⢌⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣈⠗⡤⠗⠊⠈⠁⠀⠀⠰⠀⠀⠈⠉⠘⠀⢴⡑⠳⣪⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⡄⠀⠀⠀⢸⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢇⠀⠀⠀⡔⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢬⡦⣤⣞⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁

⣿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⠀⠀⠈⢣⣸⠁⠀⠀⣠⠴⠶⢦⡀⠀⣼⠖⠁
⠀⠀⠀⠀⠀⠀⢰⠏⠰⠶⠶⣭⡳⣄⠀⠀⠛⠀⠀⡴⣳⠋⠙⠋⡇⠀⠀⣠⣾⡟⡆
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠹⠞⢦⠀⠀⠀⢠⠇⡏⠀⠀⢀⠇⠀⢰⠇⢀⡼⠁⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠈⢇⠀⠀⢸⠀⠀⠀⢀⠞⠀⠀⣾⡴⠋⠀⢠⠿⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⡀⠀⠘⡆⠀⠸⡇⠀⢠⠏⠀⠀⠀⠉⠀⠀⠀⢀⣠⠤⣴⣒⡶⣤
⠀⠀⠀⠀⠀⠀⣠⠤⣤⣀⠀⠀⠈⠙⠳⣤⣹⠀⠀⢧⢠⡏⠀⡤⡄⠀⠀⠀⣠⠞⡩⠞⠋⠉⠉⠉⢸⠇
⠀⠀⠀⠀⠀⠀⠙⠳⠶⠾⠷⠀⠀⠀⠀⠈⠛⠀⠀⠘⣾⡇⠀⣧⠇⠀⠀⣰⠃⠚⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠘⢿⣦⠘⠀⠀⠉⠀⠀⢰⠃⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⣠⠶⣋⡭⠵⠖⠀⠀⠈⠉⠓⢦⣄⠙⠀⠀⠀⠀⠀⢀⡏⠀⠀⣀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⣼⢡⡟⠁⠀⠀⠀⠀⢀⣠⡴⠞⢛⣛⡀⠀⠀⠀⠀⠀⣸⣀⡴⠚⠉⠀⠀⣀
⠀⠀⠀⠀⠀⠙⢮⣥⣀⣠⣤⠴⠞⠋⠁⠀⣼⣛⣛⣋⣳⣄⠀⠀⠀⠟⠁⠀⠀⣠⣖⣉⣉⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣛⣙⣻⣛⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡀⣀⣜⣿⣟⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢦⣿⡴⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡂
⠀⠀⠀⣽⢿⣿⡈⢹⠋⣸⣿⢿⡅⠀⠀⠀⢻⣿⣶⣨⣿⣅⣰⣿⣿⠂⠀⠀⠀⢳⣾⣄⠀⣿⢀⣠⣷⡚⠀⠀⠀⠈⡿⣷⣆⢉⣏⢁⣶⡿⡟
⠀⠀⠀⠰⣏⣁⣹⣿⣿⣁⣉⡷⠀⠀⠀⠀⠀⣈⣙⣿⣿⣿⣏⣉⠀⠀⠀⠀⠀⣍⠀⣈⣽⣿⣯⡁⢀⣉⠀⠀⠀⠀⠀⣍⣈⣿⣩⣏⣀⡅
⠀⠀⠀⠽⣿⣿⢁⣼⣄⢸⣿⡾⠅⠀⠀⠀⡼⣿⠿⢙⣿⣍⠹⢿⢿⠄⠀⠀⠀⠼⢿⠉⠀⣿⠀⢙⡿⠧⠀⠀⠀⠠⢿⡟⠏⣀⣇⡀⠿⣷⠧
⠀⠀⠀⠀⠁⠈⠩⢾⠮⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠛⣿⠓⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠆

⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆
⠀⠀⠀⢤⡀⣦⠙⢾⠞⢡⣆⣠⠄⠀⠀⠀⣴⡆⢿⠶⣿⡴⣿⢀⣦⠄⠀⠀⠠⣤⣴⠀⢙⣿⠋⢀⣆⣤⠀⠀⠀⠠⣤⣄⠀⣸⣿⡁⢀⣤⣤
⠀⠀⠀⢠⠽⠛⣦⠞⢦⡞⠻⢥⠀⠀⠀⠀⣉⡽⠿⢦⣿⡤⠿⢯⣉⠁⠀⠀⠀⠹⠛⣷⢯⣿⡽⡾⠛⠏⠀⠀⠀⠀⠙⠛⡿⣬⣯⡼⢿⠛⠁
⠀⠀⠀⠘⣳⣶⠛⢶⠞⢳⣶⡚⠀⠀⠀⠀⣍⣹⣶⠚⣿⠙⣶⣟⣉⡀⠀⠀⠀⣰⣤⡿⣟⣿⣻⢷⣴⣆⠀⠀⠀⠀⣠⣼⢷⢛⣟⢳⢿⣤⡄
⠀⠀⠀⠉⠁⠟⡤⢾⠶⡌⠇⠉⠁⠀⠀⠀⠛⠃⣾⠞⣿⠳⢿⠈⠟⠁⠀⠀⠈⠛⠛⠀⣠⣿⣄⠀⠋⠛⠀⠀⠀⠈⠉⠉⠀⢩⣿⡁⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣠⣶⢷⣦⡀⠀⠀⢀⣴⣦
⠀⠀⣠⠀⠀⡰⠒⠲⢤⣀⣠⡾⠋⠀⠹⣧⡀⠀⢀⣠⣤⣿⣷⡤⠀⠀⠀⣴⣾⣿⣤⣴⣶⣾⠿⠋⠁⠀⠘⣿⣄⣴⠟⠁⠹⣆⠀⠀⠀⠀⠈⠙⠓⢦⣄
⠀⠀⣿⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠻⠿⠛⠋⣡⣾⠟⠁⠀⠀⠀⠀⠉⠻⡯⠉⠁⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣠⣴⢶⣤⡀⠀⠀⢀⣴⠶⠶⢶⣼⡇
⠀⠀⢹⣆⠀⣠⣤⣤⡀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⡿⣯⣥⣀⡀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⢻⣿⡏⠀⠀⠙⣷⠀⠀⠘⢷⣤⣴⠾⠻⣷⡀
⠀⠀⠀⠻⣶⣿⣀⣼⠇⠀⠀⠀⠘⢧⡀⠀⠀⢶⣄⠀⠀⠀⠀⠀⠙⠿⠆⠈⠉⠛⠷⣤⡀⠀⠀⠀⢸⡏⠀⠀⠻⣿⠟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇
⠀⠀⠀⠀⠈⢿⣍⠁⠰⢦⣤⣤⡄⠈⢳⡄⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠈⢷⡀⠀⠀⠀⠀⢀⣄⣼⠟⠀⠀⣰⣾⠿⠿⢿⣶⡟
⠀⠀⠀⠀⠀⠈⠛⠿⠶⠾⣿⡟⠀⠀⠀⣿⠀⠀⠀⠀⠙⢷⣤⣀⠀⢤⣤⡀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠈⠻⢦⡀⠀⠀⠾⠿⢿⣤⠀⠀⠻⣿⣶⡶⠟⠋⢿⣆
⠀⠀⠀⠀⢀⣠⠴⠀⠀⠰⠟⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠈⠛⠿⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠹⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡀⠀⢸⣿
⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠿⠿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⣠⣿⠇
⠀⠀⠀⢸⣇⣤⣄⡀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣃⡀
⠀⠀⠀⣼⣿⣍⣹⡿⠀⠀⠀⠀⠀⠙⣷⡄⠀⣠⣶⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠉⠉⠻⣦⡀⠀⠀⢀⣨⡿⢿⡄⠀⠀⠀⠀⠀⠈⠻⠛⠛⠋⠉
⠀⠀⠀⢻⣆⠀⠁⠀⠀⠀⠀⠀⠀⢲⣼⣿⣾⡟⠁⠀⠀⠀⠈⠳⣄⣴⡋⣻⡆⠀⢰⡟⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠙⠷⣦⣤⣤⣀⣀⠀⠀⠀⠹⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣍⠉⠀⣠⡿⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠉⠉⠉⠙⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⣦⡀⠀⠀⠀⠀⠀⣀⣤⣶⡗⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⠀⠀⠀⣠⠴⠂⠀⠀⠹⣧⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⠙⠉⣽⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⣾⣷⡀⠀⠀⠀⠀⠀⠀⢀⣾⣁⣄⡀⠀⠀⠀⢹⣇⣴⡟
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣾⠏⠀⠀⠀⠀⢀⣼⠟⠈⠛⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⢿⠇⠸⣧⠀⠀⠀⠀⠀⢀⣼⣟⠉⠉⢻⡆⠀⢸⣾⣿⠏
⠀⠀⢠⣾⠟⠛⠋⠉⠙⠛⠉⠉⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⣀⡀⠀⠀⠶⠛⣻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⢀⣿⠀⠀⣼⡏⠙⠷⠶⠟⠀⠀⠈⠛⠋
⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠁⠀⠀⣾⠋⠀⠀⠀⠀⣼⡟⣿⡇⠀⠀⢶⣶⣦⠀⠀⢀⡸⣿⣸⡏⠀⠀⢿⡇⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠘⣷⣄⡀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠋⠀⠀⠀⠀⠀⢿⣤⣦⡀⠀⢸⡿⠀⠘⠁⠀⣴⠟⠹⠇⠀⠀⠈⠻⣿⣿⠃⠀⠀⠈⠻⣦⣤⣤⣴⠾⠟⠛⠛⢿⡄
⠀⠀⠀⠈⠙⠛⠿⠶⠿⠟⠛⠋⠁⢀⡀⠀⠀⠀⠀⠀⠀⢠⡿⠟⠁⠀⣾⡇⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠉⠉⠀⢀⣴⠶⢶⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣺⣿⠃⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⣠⡤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⣤⡿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠻⠆⠀⠀⠀⢿⣀⣤⣾⣆⠀⠀⠀⠀⢿⣧⡀⠀⠀⠀⠀⢸⡏⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣼⢷⣄⣼⡿⠁⠀⠀⠀⠀⠀⠈⠛⠁⠈⢿⡄⢶⡄⠀⠀⠹⣿⣦⣀⠀⠀⠘⣧⡀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠙⠛⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⣘⣿⣿⡇⠀⠀⠀⠀⠙⠻⠿⢷⣶⣾⠿⢿⣯⣀⣀⠀⠀⠀⣀⠀⠰⣿⣿⣷⣶⣶⣶⠾⠛⠁
⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⣀⣀⣤⣼⠿⣿⠀⢠⣤⣄⡀⠈⠛⢿⡇⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋⠉⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠁⠀⠀⠃⠀⠀⢿⠿⣥⣀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣦⣤⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⠋

⣿⣿⡿⠿⣿⠟⢿⠿⡿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣾⣶⣷⣶⣿⣶⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠒⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁⠀⡉⠝⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⢀⠔⠈⠀⢀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠲⠀⠀⡠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⡠⠊
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠃
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⡿⠟⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠋⠁⠀⢹⣿⣿⠟⠉⠀⠀⠀⢳⡄
⠀⠀⠀⠂⠀⠀⠀⠀⡀⠔⠀⠙⠀⠀⢀⠀⠨⠟⠁⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⢀⡔⠈⠀⠀⢀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠁⢀⣴⣿⠀⢀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⢰⠔⠛⠛⢿⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠀⠀⠀⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⣹⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣶⣶⠿⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠃⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⢀⡤⠶⣦
⠀⠀⠀⠀⠀⣐⠉⢉⢙⠳⠀⠀⠀⠀⢀⣴⠟⢳⡄⡄⠀⠀⠀⠀⡐⠀⠨⣍⠳⠀⠀⠀⣾⠋⠰⡄⣄⠀⠀⠀⠀⠀⠀⣯⡮⠝⠂
⠀⠀⢀⣠⣾⣿⡀⠈⠀⠀⠀⠀⠀⣠⣿⣿⣄⠈⠀⠀⠀⠀⠀⢀⣧⡔⠀⠀⠀⠀⠀⢀⣿⣆⠀⠀⠛⠀⠀⠀⠀⠀⣴⣿
⠀⠐⠉⠙⠛⠛⠻⠶⠀⠀⠀⠀⠊⠉⠉⠉⠙⠓⠂⠀⠀⠀⠀⠚⠛⠛⠆⠀⠀⠀⠀⠚⠛⠛⠓⠲⠄⠀⠀⠀⠐⠛⠛⠛⠓⠂


⠀⠀⠀⠀⢠⡶⢻⣷⡆⠀⠀⠀⠀⠀⢀⡤⣴⣦⣀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢤⡀⠀⠀⠀⠀⢀⣤⡤⣄⠀⠀⠀⠀⠀⢠⢖⣚⠲
⠀⠀⠀⢠⣟⣿⠈⠋⠁⠀⠀⠀⠀⣰⡏⣾⠙⠛⠛⠀⠀⠀⠀⣠⣾⡇⠠⠙⠂⠛⠀⠀⠀⣰⣿⡇⣄⣸⠇⠀⠀⠀⠀⣳⠯⠍⠁
⠀⠀⠴⠫⠾⠿⠧⡀⠀⠀⠀⠠⠾⢿⣿⣌⡳⠄⠀⠀⠠⠴⠿⠿⢿⣧⣀⠀⠀⠀⠀⠴⠾⠿⠿⢷⣄⡀⠀⠀⠀⣠⣾⣿⣄⡀


⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⢠⢏⡴⠞⠿⣶⣤⠀⠀⠀⠀⣠⣾⣿⣿⡿⠇⠀⠀⠀⢠⢞⣽⣶⣶⣤⡀⠀⠀⠀⣠⢖⣻⣭⣽⣛⢦⠀⠀⠀⡠⣐⣤⣤⣄
⠀⠈⣿⣼⠛⠓⠘⠛⠀⠀⠀⠀⣿⢣⠒⠒⠊⠁⠀⠀⠀⢧⣿⣿⣿⠿⠝⠀⠀⠀⢰⣷⡟⠉⠉⠿⠛⠀⠀⠀⣼⣼⣿⡿⠛⠟
⠀⠀⠻⣜⢄⠀⠀⠀⠀⠀⠀⠀⠹⣮⡦⣀⣀⠀⠀⠀⠀⠡⣻⣿⣿⣤⡤⠀⠀⠀⠈⢻⣷⣄⣀⠀⡀⠀⠀⠀⠹⣿⣿⣧⣤⡶⠄
⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣒⡁⠀⠀⠀⠀⢀⡠⠤
⠀⠀⠀⠀⡰⣡⣦⡤⠀⠀⠀⠀⠀⠠⣱⡃⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⢶⣦⠀⠀⠀⠀⠀⢠⣾⣾⣿⠛⠃⠀⠀⣰⣫⣾⡿⡖
⠀⠀⢀⣼⣿⣿⣿⣇⡀⠀⠀⠀⢀⣾⣿⣿⣧⣀⠀⠀⠀⠀⢠⣾⣿⣇⠀⠁⠀⠀⠀⢀⣴⣿⣿⣿⡁⠀⠀⠀⢠⣿⣿⣇⡀
⠀⠐⠛⠛⠛⠋⠉⠉⠉⠀⠀⠐⠛⠛⠋⠉⠉⠉⠀⠀⠀⠚⠛⠛⠉⠉⠁⠀⠀⠀⠐⠛⠛⠋⠉⠉⠁⠀⠀⠐⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁⠈⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⢻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠏⠀⠀⠀⠀⠀⠀⠹⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀
⠀⠀⠀⠀⠀⢠⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄
⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄
⠀⠀⠀⢀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀
⠀⠀⢀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀
⠀⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧
⠀⣸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇
⢀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⢸⣿
⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⣼⣿
⠸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⢀⣿⣿
⠀⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠏⠀⢀⣾⣿⡟
⠀⠈⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⢀⣾⣿⡿⠁
⠀⠀⠀⠻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡿⠟⠁⠀⣠⣿⣿⠟
⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣾⣿⣿⡿⠟⠋⠀⠀⣠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠛⠿⠛⠛⠛⠉⠁⠀⢀⣠⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣷⣦⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⣴⣾⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠉⠁

⠀⣠⣴⠾⠛⠛⠷⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠛⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⠛⠛⠷⣦⣄
⠺⠋⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⣀⣠⣄⣀⠀⠀⠀⠈⠻⢦⣤⣤⣤⡴⠟⠉⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠉⠻⣦⣤⣤⣤⡴⠛⠁⠀⠀⠀⣀⣠⣄⣀
⢀⣴⠟⠋⠉⠉⠉⠻⢦⣄⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀⣴⠟⠋⠉⠉⠙⠻⣦⣀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣠⣴⠟⠋⠉⠉⠙⠻⣦
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⣠⣴⠶⠶⣦⣄⡀⠀⠀⠉⠛⠶⠶⠶⠟⠋⠀⠀⢀⣠⣴⠶⠶⣦⣄⠀⠀⠀⠙⠻⠶⠶⠶⠛⠉⠀⠀⢀⣠⣴⠶⠶⣦⣄
⢴⠟⠋⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⣀⠀⣀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⡀⠀⣀⣠⡶⠟⠁
⠀⣠⡶⠟⠛⠛⠻⢶⣄⠀⠀⠀⠉⠙⠛⠋⠉⠀⠀⠀⣠⡶⠟⠛⠛⠻⢶⣄⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⣠⡶⠟⠛⠛⠻⢶⣄
⠚⠋⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣤⣤⡶⠟⠁






⠀⢀⡴⠚⠋⠉⠛⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠶⠦⣄
⠀⠁⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠀⣀⣤⣤⣄⣀⠀⠀⠀⠙⠷⣦⣤⡤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⣀⣀⣀⣠⡴⠟⠁⠀⠀⠀⢀⡀
⠀⠴⠋⠁⠀⠀⠈⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠈⠉⠙⠉⠁⠀⠀⢀⣠⡶⠛⠉⠉⠙⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⢀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⣠⠴⠖⠶⠶⣤⣀⠀⠀⠈⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣤⣴⡶⠟⠁⠀⠀⢀⣠⣤⣤⣄⡀
⠀⠊⠁⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠀⠀⠀⠀⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠉⠂
⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠙⠻⣦⣄⣀⣀⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⢀⣤⡾⠋
⠀⢀⠴⠛⠉⠉⠙⠳⣦⣀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠙⠛⠾⠟⠛⠉⠀⠀⢀⣤⠶⠖⠒⠲⢤⡀
⠀⠁⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣦⡶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⣀⣀⣤⡾⠛⠁
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢠⡀

⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⡀⠀⠀⢸⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⢛⡍⠁⠀⠉⠻⠻⢿⣶⣦⣄
⠀⠀⠁⠠⠀⠘⢀⣀⣉⠁⠀⠀⠀⠀⣁⠤⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⣒⣂⠀⠀⡶⡒⠊⠩⢔⣣⣄⡀⡀⠀⠈⢑⠀⠀⠀⠈
⠀⠀⠀⠀⢀⣄⣿⡏⠉⠉⠀⠒⠖⠊⠁⠐⠂⠀⢦⡴⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠖⡉⠥⠒⢒⣒⡺⡂⠀⠀⠀⠉⠻⣟⢮⠒⡀⠀⠈⠔⠀⢀
⠀⠐⠒⠚⡳⠛⠹⢿⢦⡀⡀⠀⠀⠠⡄⠀⢀⡠⣠⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠈⠀⠑⠆⠀⠀⢠⠀⠈⠈⢧⢑⣀⠀⠀⠀⠡⠚
⠀⠀⠀⠈⠀⢀⠀⠀⠁⠀⢨⠀⠀⠘⠂⠈⠁⠘⣯⠠⠀⠀⠀⠀⠀⠀⢀⢇⠀⠀⠀⣀⠁⡀⠀⠀⠀⠀⢀⠀⠀⠸⢀⠆⠀⢀⡰⠂⠀⠐⠒
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠐⠂⠀⠀⠀⠀⠣⡂⠀⠀⠙⠂⠀⠉⠉⠉⢭⠄⠀⠀⠔⠋⣠⠄⠀⠁⡔⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢀⠀⣀⣀⣀⣠⣤⡤⠤⠶⣛⠵⠂⣠⠞⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠴⠒⢋⣡⡴⠚⠁⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡤⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠌⢛⠩⠅⣀⣀⠀⢡⡎⠀⠐⠠⢤⠤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢈⠔⠉⠀⠠⣤⣤⠍⢡⣌⣉⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⢄⠀⠀⠀⢠⣤⠿⠋⠀⠀⠈⢳⡄⠀⡈⠄⠀⠐⠖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⢦⡜⢾⣦⡈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠀⠀⡼⢃⡠⠏⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⠲⢝⣛⠷⢦⣤⣀⣀⢀⡄⢀⣂⣀⡤⢔⡒⠍⠐⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠀⠀⡀⠀⠈⣐⣂⠉⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⠶⡄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⣙⠻⠀⠟⢋⡽⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢰⣋⠳⠿⠸⠷⠊⣹⢀⣤⡀
⠀⠀⠀⠀⣀⠀⡏⢹⢀⣠⡖⠮⣷⠀⣾⠵⢲⣄⡀⡏⢹⠀⣀⠀⠀⠀⠀⢠⠶⢤⡇⢸⢠⠬⣕⣦⢠⣖⡫⢤⢸⡀⣧⡴⢦
⠀⠀⠀⠘⢏⡙⠃⢸⣸⠀⡟⠲⣤⠀⣠⠖⢻⠀⣇⡇⠘⢋⡹⠇⠀⠀⠀⣈⡷⠄⠀⢿⡞⢠⣄⡉⠈⣉⣤⠘⣯⠇⠀⠴⣏⡀
⠀⠀⠀⣴⠚⣡⠴⣦⡉⠀⢧⣄⣸⠀⣇⣠⠼⠀⠉⣴⠦⣌⠓⣦⠀⠀⠘⠥⠴⣚⡽⠆⠀⠸⡤⠿⠘⢧⡼⠀⠀⠾⣝⡲⠤⠽
⠀⠀⠀⠈⠉⠱⣏⣡⠖⠛⠲⣌⡙⠀⢋⣡⠖⠛⠲⣌⣹⠎⠉⠁⠀⠀⣞⠳⣄⢧⡀⢾⣉⡗⠀⠀⠀⠀⠐⣏⣹⠆⣠⢇⡴⢛⡆
⠀⠀⠀⣠⢤⣘⢧⣉⠓⠶⠚⣉⣤⠀⣤⣉⠓⠶⠚⣉⡼⣃⡤⣄⠀⢀⡬⠷⠈⠛⣋⠀⢩⣤⠀⠀⠀⠀⢠⣬⠁⢈⠓⠋⠰⠯⣄
⠀⠀⠀⠙⢦⣌⠙⢋⣡⠀⡟⠁⢸⠀⡇⠈⢹⠀⣌⡙⠋⢡⡴⠋⠀⠘⠲⢲⠂⡾⡽⠀⠷⠼⠃⡴⠶⡄⠻⠤⠇⠸⡽⡆⢲⠲⠚
⠀⠀⠀⠰⣏⡤⡆⢸⢹⣀⡷⠞⣉⠀⣉⠓⢾⣀⡏⡇⢰⢦⣹⠆⠀⠀⠀⠻⠴⢃⣙⣒⣲⠂⣤⠙⠞⢡⡄⢲⣒⣚⣁⠳⡼⠃
⠀⠀⠀⠀⠀⠀⢧⡼⠀⠉⢓⣫⠽⠀⠿⣝⡚⠉⠀⢧⡼⠀⠀⠀⠀⠀⠀⠀⠀⢯⣥⣤⠀⡈⢯⡳⠴⣫⠏⠀⢠⣬⣭⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⡤⢶⠀⡶⢤⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡼⠳⣄⣳⢰⣃⡴⠳⣌⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡶⢼⠉⣧⠶⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣙⠾⠹⢚⣩⠇
⠀⠀⠀⠀⠀⢠⡶⣴⢋⣇⣠⢽⣶⠀⣶⡯⣅⣸⡝⣧⢶⡄⠀⠀⠀⠀⠀⠀⡴⣄⢠⣄⠰⣟⠻⢿⢰⠿⢚⡽⠀⣀⢠⡤⡄
⠀⠀⠀⠀⢠⡴⢛⣀⡸⡿⣸⠓⢮⠀⡵⠚⣇⢻⠇⣀⡛⢦⡄⠀⠀⠀⠀⡴⠇⣿⣿⢸⣀⡬⠟⣂⢀⡚⠯⣄⣸⢹⣿⡆⠷⣄
⠀⠀⠀⠀⣀⠉⣹⣛⣋⣤⡻⣄⢸⠀⡇⣠⠞⣠⣘⣛⣯⠉⣁⠀⠀⢀⡴⢋⣤⣬⠋⠘⣩⡖⠋⢹⢸⡏⠓⣮⡙⠈⢫⣤⣌⡓⣦
⠀⠀⠀⣘⣏⢳⣧⡹⣄⣀⣙⣮⡻⠀⢟⣡⣊⣀⣠⠏⣼⡾⣹⣃⠀⠀⠉⢹⣋⡵⣶⢰⠦⣝⠲⢾⢸⠷⢚⡥⢶⢰⡶⢍⣳⡍⠁
⠀⠀⠘⠯⡭⢠⣭⢄⡬⠭⠭⣭⠅⠀⡨⣭⠭⠭⢥⡠⣭⡄⢭⠽⠃⠀⠀⣠⢤⣀⣿⢸⣀⡤⠟⣂⢀⡚⠯⣄⣸⢸⣇⣠⣥
⠀⠀⠀⠸⠥⠋⣯⠾⣤⣠⢞⡵⢻⠀⡟⢮⡳⣄⣤⠷⣽⠙⢮⠇⠀⢠⡶⢼⣶⣬⠋⠘⣭⡖⠋⢹⢸⡍⠓⣮⡝⠈⢫⣴⣾⠖⡦
⠀⠀⠀⠀⢠⣖⠾⠿⢖⡀⢿⠀⣸⠀⣇⠀⡿⢀⡲⡾⠷⢲⡄⠀⠀⠀⠉⣗⡈⣱⣶⢰⠦⣝⡲⢾⢸⠷⢚⡥⢶⢰⣶⡍⣐⡏⠁
⠀⠀⠀⠀⠀⢩⣟⣤⢸⡿⣼⣋⣥⠀⣬⣙⣧⢿⡇⣤⣻⡍⠀⠀⠀⠀⠀⠉⣇⣹⠻⠼⢀⡤⠟⣂⢀⡘⠧⣄⠸⣼⢿⣇⡏⠁
⠀⠀⠀⠀⠀⠀⠉⠘⠷⠇⢠⢟⣫⠀⣝⡻⡄⠸⠶⠃⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⢒⡿⠟⠘⠻⣷⡋⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠶⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠖⠛⠞⠛⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠁⡠⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⢿⣧⡙⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣮⣽⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠙⠂⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⠤⠤⣄⣤⣀⣀⡀
⠀⠀⠀⠀⠀⢶⣏⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠢⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠙⢍⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠉⢦⡀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣉⡑⠲⣄⡀⠀⢰⢛⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠙⢶⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⢛⣷⣿⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠸⡏⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⡇⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⣎⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠺⣛⠒⠒⠲⠤⣄⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⣆⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢹⡄⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⣰⠃⢙⡦⣄⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢷⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⡴⠁⢀⡞⠀⠈⠣⡀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⡞⠁⣠⠿⠤⢤⣀⠀⠙⢦⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⡴⠃⠀⠀⠀⠀⠉⠲⢄⣻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠖⠒⢶⠦⠤⢤⣠⣏⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⠉⠑⠦⣄⡀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠤⣍⡲⢼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣞⣀⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡆
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⠀⡀⠀⠀⠀⠘⠀⠃⠀⠀⠀⢀⠀⢔⡄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⢀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣭⡛⠀⢀⠀⠀⠅⠀⠀⢚⣥⠒
⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠊⡄
⠀⠀⠀⠀⠤⠀⢀⠄⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⠁⠐⠀⠢⠄⡀⢁⣄
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠈⠤⠛⠀⠀⠈⠀⠠⠔⠀⠳⠠⢁⡠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⡀⡇⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠜⠋⠡⠄⢀⠀⠀⠀⠀⠂
⠀⠀⢀⣢⣀⠀⠀⠀⢀⢰⡀⠀⠀⠀⣀⣐⠄⠂⠀⠀⠀⠀⠠⠠⢤⡂⠆⠂⠈⠁⢠⠀⠀⠀⠋⠐⠤⠤⢣⠄
⠀⠀⠀⠀⠉⠐⣰⠄⣀⠈⣀⠰⣂⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠁⢠⡀⠀⢾⡀⣰⠶⠂⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠘⠓⢒⣉⠡⢴⣄⠀⠰⠦⠄
⠀⠀⠀⠀⣀⠠⠻⠀⠉⡀⠁⠰⠏⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠂⠀⠠⠶⠋⠀⣷⠀⠈⠁⠀⣆
⠀⠀⠀⠍⠁⠀⠀⠀⠈⠏⠁⠀⠀⠀⠉⠹⠄⠀⠀⠀⠀⠀⠀⠀⢪⠔⠃⠆⢠⠀⠀⠀⠃⠀⣀⠰⠰⠎⣟⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⢠⡔⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠠⣌⣰⠄⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠀⠉⠘⣿⡋⡠⣀⡤⣐⠂⠑
⠀⠀⠀⠀⠀⠀⠀⠄⣠⣤⣮⣤⣶⣾⣿⣾⣾⣿⣿⣷⣿⡿⠗⠂⠐⠆⠠
⠀⠀⠀⡀⢀⠐⠀⠙⠯⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣤⡤⠀⣀
⠀⠀⠀⣄⣾⣥⣤⣠⠤⢄⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣭⡉⠁⠰
⢀⠄⠀⠁⠀⠀⠹⣟⠁⠈⠻⠶⠌⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠟⢻⣿⣤⡶⢦⢀
⠣⣦⣶⣦⣌⣷⣝⣮⣻⣦⣸⣿⣿⣄⢀⠀⠹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠞⠉⣹⣷⣎⡉⠒
⠉⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⠞⢻⡄⠈
⠀⠉⠲⢦⣄⢄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢻⣿⣿⣿⣯⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡊
⠀⠰⣄⢦⣹⡿⣋⠉⠉⢙⠿⠛⠛⢿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣷⣕⢤⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⣾⣿⣯⣾⣣⠄
⠀⠀⢻⣿⣿⣿⣮⣷⣼⣦⣝⣦⣷⣤⣘⠿⢿⣿⣿⣿⣿⡻⣿⣿⣿⣷⣌⠓⠿⣿⣿⣷⣶⣿⣿⣦⣴⣾⣿⣿⣿⣿⣿⡟
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢄⣬⡲⣍⣈⠙⠿⣿⣮⣝⡿⣿⣿⣿⣶⣤⣬⣩⣩⣿⣿⣿⣯⣽⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣮⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠟⠛⣛⣛⣛⣛⣛⡛⠋
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣶⣟⣿⣽⣿⣶⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⠛⠃⠀⠀⠀⠀⠘⠛⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⣤⣾⣿⣿⣿⣿⣷⣤⠀⢹⣿⣿⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿
⠀⠀⠀⣠⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣄⠀⠀⠀⣿⣿⣿⡿⠃⣀⣿⣿⣿⣿⣿⣿⣿⣿⣀⠘⢿⣿⣿
⠀⠀⠀⠙⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠋⠀⠀⠀⣿⣿⣿⣷⡄⠉⣿⣿⣿⣿⣿⣿⣿⣿⠉⢠⣾⣿⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣤⡄⠀⠀⠀⠀⢠⣤⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠛⢿⣿⣿⣿⣿⡿⠛⠀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿


⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⢸⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚
⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇
⠀⠀⠀⢽⡄⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠈⠛⠂⠀⠀⠀⠀⠀⠐⠒

⠙⢢⠀⠀⠀⢠⠞⠙⢦⠀⠀⠀⢠⠞⠙⢦⠀⠀⠀⢠⠞⠙⢦⠀⠀⠀⢠⠞⠙⢦⠀⠀⠀⢠⠞⠙⢦⠀⠀⠀⢠⠞⠙⢦
⠀⠈⢧⠀⢠⠏⠀⠀⠈⢧⠀⢠⠏⠀⠀⠈⢧⠀⢠⠏⠀⠀⠈⢧⠀⣠⠏⠀⠀⠈⢧⠀⣠⠏⠀⠀⠈⢧⠀⣠⠏⠀⠀⠈⢧
⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈
⣤⡀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⣠⣤⡀
⠀⠹⡄⠀⠀⣼⠁⠀⠹⡄⠀⠀⣼⠁⠀⠹⡄⠀⠀⡼⠁⠀⢹⡄⠀⠀⡼⠁⠀⢹⡄⠀⠀⡼⠁⠀⢹⡀⠀⠀⡼⠁⠀⢻⡀
⠀⠀⠹⢤⠴⠃⠀⠀⠀⠹⢤⠴⠁⠀⠀⠀⠱⢤⠴⠁⠀⠀⠀⠳⢤⠼⠁⠀⠀⠀⠳⢤⠼⠁⠀⠀⠀⠳⢤⠼⠁⠀⠀⠀⠱

⠒⢆⠀⠀⠀⢀⠔⠓⢆⠀⠀⠀⢀⡖⠓⣆⠀⠀⠀⢀⡖⠓⣆⠀⠀⠀⢀⡖⠓⣆⠀⠀⠀⢀⡖⠓⣆⠀⠀⠀⢀⡖⠓⣆
⠀⠘⣇⠀⢀⡞⠀⠀⠘⣆⠀⢀⡞⠀⠀⠘⣆⠀⢀⡞⠀⠀⠘⣆⠀⢀⡞⠀⠀⠘⣆⠀⢀⡟⠀⠀⠘⣆⠀⢀⡎⠀⠀⠘⣆
⠀⠀⠈⠛⠋⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠈
⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀
⠈⢳⡀⠀⠀⣰⠋⠈⢳⡀⠀⠀⣰⠋⠈⢳⡀⠀⠀⣰⠋⠈⢳⡀⠀⠀⣰⠋⠈⢳⡀⠀⠀⣰⠋⠈⢳⡀⠀⠀⣰⠋⠈⢳⡀
⠀⠀⠳⣄⡴⠃⠀⠀⠀⠳⣄⡴⠃⠀⠀⠀⠳⣄⡴⠃⠀⠀⠀⠳⣄⡴⠃⠀⠀⠀⠳⣄⡴⠃⠀⠀⠀⠳⣄⡴⠃⠀⠀⠀⠳

⠢⣄⠀⠀⠀⢀⡴⠲⣄⠀⠀⠀⢀⡴⠲⣄⠀⠀⠀⢀⡴⠲⣄⠀⠀⠀⢀⡴⠲⣄⠀⠀⠀⢀⡴⠲⣄⠀⠀⠀⢀⡴⠲⣄
⠀⠘⣆⠀⢀⡞⠀⠀⠘⣆⠀⢀⡞⠀⠀⠘⣆⠀⢀⡞⠀⠀⠘⣆⠀⢀⡞⠀⠀⠘⣆⠀⢀⡞⠀⠀⠸⣆⠀⢀⡞⠀⠀⠸⡆
⠀⠀⠘⠒⠚⠀⠀⠀⠀⠘⠒⠚⠀⠀⠀⠀⠘⠒⠚⠀⠀⠀⠀⠘⠒⠚⠀⠀⠀⠀⠘⠒⠚⠀⠀⠀⠀⠘⠒⠚⠀⠀⠀⠀⠙
⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀
⠉⢳⡀⠀⠀⢠⠏⠉⢳⡀⠀⠀⢰⠏⠉⢣⡀⠀⠀⣰⠋⠉⢳⠀⠀⠀⣰⠋⠉⢣⠀⠀⠀⣰⠋⠉⢧⠀⠀⠀⣰⠋⠉⢧
⠀⠀⢷⣀⣠⠏⠀⠀⠀⢧⣀⣠⠏⠀⠀⠈⢧⣀⣠⠏⠀⠀⠀⢧⣀⣠⠏⠀⠀⠈⢧⣀⣠⠇⠀⠀⠈⢧⣀⣰⠃⠀⠀⠈⢧
⣶⣶⠶⠿⠷⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶

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

⣀⣀⣀⠀⡀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠻⣦⣻⣟⣴⠟⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⣦⡀⢀⡈⢻⡟⢁⡀⢀⣴⣶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢿⣿⣿⣧⢸⡇⢸⡇⢸⡇⣼⣿⣿⡿⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡀⠀⠀⠀⢀⣈⣉⣻⣿⣇⢸⡇⣸⣿⣟⣉⣁⡀⠀⠀⠀⢀⣴⣿⣿
⠘⢿⣿⣿⣷⡄⢸⣆⠀⠀⢿⣿⣿⡇⣀⡀⣶⣤⡉⠉⠉⠉⠻⣿⣿⠟⠉⠉⠉⢉⣠⣶⢀⣀⠸⣿⣿⡿⠀⠀⣰⡇⢠⣾⣿⣿⡿
⠀⠈⠻⣿⣿⣿⣮⣿⡀⣴⣄⡻⣿⣰⡿⠁⢸⣿⣿⣶⠀⢀⠀⢸⡇⠀⡀⠀⣶⣿⣿⡇⠈⢿⣆⣿⢟⣠⣦⢀⣿⣵⣿⣿⣿⠟⠁
⠀⠀⠀⢠⣴⡶⠿⠛⠿⣦⣍⡛⢿⡟⠀⠀⠘⠻⣿⣿⣀⣿⠁⢸⡇⠈⣿⡀⣿⣿⠟⠃⠀⠀⢻⡿⢛⣩⣴⠿⠛⠿⢶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠛⠷⣦⣝⣻⣾⣿⣀⠀⠰⢶⣮⣿⣿⡏⠀⢸⡇⠀⢹⣿⣿⣵⡶⠆⠀⣀⣿⣷⣟⣫⣴⠾⠛
⠀⠀⠀⢀⣴⣾⣿⣿⣷⢿⣿⠟⠉⠉⠛⠷⣦⣄⡀⠈⠹⣷⡀⢸⡇⢀⣾⠏⠁⢀⣠⣴⠾⠛⠉⠉⠻⣿⡿⣾⣿⣿⣷⣦⡀
⠀⠀⠐⠛⠛⠻⠿⠟⢡⣾⠃⠀⠀⠀⢶⣄⠀⠙⠻⢶⣤⡘⣷⣼⣧⣾⢃⣤⡶⠟⠋⠁⣠⡶⠀⠀⠀⠘⣷⡌⠻⠿⠟⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⣴⣾⣿⣷⣦⣽⣷⣤⣤⣤⣭⣿⣿⣿⣿⣿⣿⣭⣤⣤⣤⣾⣯⣴⣾⣿⣷⣦⣌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⠙⠻⠿⠟⢋⣽⠟⠉⠉⢉⣭⡿⣿⣿⣿⣿⢿⣭⡉⠉⠉⠻⣯⡙⠻⠿⠟⠋⣩⡀
⠀⠀⠐⢶⣶⣾⣿⣷⣌⢻⣆⠀⠀⠀⠛⠁⣀⣴⡾⠛⠉⣰⡟⢹⡏⢻⣆⠉⠛⢷⣦⣄⠈⠛⠀⠀⠀⣰⡟⣡⣾⣿⣷⣶⡶⠂
⠀⠀⠀⠀⠙⠻⠿⠿⠟⣿⣿⣷⣤⣤⣶⠟⠋⢁⣀⣠⣼⡟⠀⢸⡇⠀⢻⣧⣄⣀⡈⠙⠻⣶⣤⣤⣾⣿⣿⠻⠿⠿⠟⠋
⠀⠀⠀⢀⣀⡀⠀⠶⠟⣋⣵⡾⢻⡿⠀⠀⠘⠛⣫⣿⣿⣧⠀⢸⡇⠀⣼⣿⣿⣝⠛⠃⠀⠀⢿⡟⢷⣮⣙⠻⠦⠀⢀⣀⡀
⠀⠀⠀⢈⣙⣛⣿⣶⡿⣋⣥⡶⣿⣷⡀⠀⢰⣾⣿⣿⠀⢿⠄⢸⡇⠠⡿⠀⣿⣿⣷⡆⠀⢀⣾⣿⢶⣬⣙⢿⣶⣿⣛⣋⣁
⠀⢠⣾⣿⣿⡿⢫⣿⠀⠙⢁⣾⣿⠘⣷⡄⣸⣿⡿⠛⠀⠀⠀⣸⣇⠀⠀⠀⠛⢿⣿⣇⢠⣾⠃⣿⣷⡈⠋⠀⣿⡝⢿⣿⣿⣷⡄
⠰⠿⠿⠿⠟⠁⠸⠃⠀⠀⣿⣿⣿⡇⠀⠀⠛⢉⣤⣤⣤⣤⣾⢿⡿⣷⣤⣤⣤⣤⡉⠛⠀⠀⢸⣿⣿⣿⠀⠀⠘⠇⠈⠻⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠋⠀⠀⠀⠀⢀⣠⣤⣾⢿⡗⢸⡇⢸⡿⣷⣤⣄⡀⠀⠀⠀⠀⠙⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣿⣿⣿⡟⢸⡏⢸⡇⢸⡇⢻⣿⣿⣿⡀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠿⠛⠋⠀⠀⣠⣾⣷⣄⠀⠀⠙⠛⠿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⢋⣾⣷⡙⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⠒⠚⣋⣩⡭⠤⠒⢒⣂⣠⣥⣬⡻⢿⣿⣿⣿⣿⣿⣿⡿⢟⣥⣬⣄⣐⡒⠒⠤⢭⣍⣙⠓⠒⠶⢤⣤⣀⣀
⠀⠀⠀⠀⢠⣶⣿⣿⡏⠁⠀⠀⠀⢿⣿⣅⠀⠀⠺⠿⣿⣿⣿⣿⣿⣷⣶⣯⣭⣭⣭⣶⣾⣿⣿⣿⣿⣿⠿⠗⠀⠀⣨⣿⡿⠀⠀⠀⠈⢹⣿⣿⣶⡄
⠀⠀⠀⠀⠈⠛⠿⣿⣿⣶⣤⣄⣀⡀⠈⠉⠙⠛⠒⠶⠦⠤⠭⠭⠭⣭⣉⣉⣉⣉⣉⣉⣭⡭⠭⠭⠤⠴⠶⠒⠛⠋⠉⠁⢀⣀⣠⣤⣶⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⠷⠶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⠶⠾⠿⠿⠟⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣌⢹⡆⣿⢩⣤⣀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⢦⣄⠀⠀⠀⠻⣄⠈⠻⠇⠛⠋⣠⡟⠀⠀⠀⠀⡼⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠹⣆⠀⠀⠀⠈⠙⢦⠀⣴⠛⠁⠀⠀⠀⢀⡾⠁⣼⠃
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠙⣆⠀⢰⡖⢦⣽⠀⣿⡴⠲⣆⠀⢀⡾⠁⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀
⠀⣾⡛⠙⠛⢶⡄⢰⡟⢦⡀⠀⠀⠀⠘⣧⠀⠘⣆⠘⠳⣄⠉⠀⠋⢀⡴⠇⢀⡞⢁⡼⠁⠀⠀⠀⣠⢶⣄⠀⣴⠟⠉⠉⣿⡟
⠀⠙⢷⣄⣀⣈⡳⠾⡇⠸⡇⠀⣴⢦⡀⠘⢧⠀⠘⣦⠀⠈⢳⡄⣴⠋⠀⢀⡞⢀⡾⢁⡴⠶⡄⠀⡿⠀⣿⡶⢋⣠⣤⡾⠟
⠀⠀⠀⠙⢋⣭⠿⠶⠀⠀⠻⣄⣻⠀⢹⡆⠈⢧⣀⣸⡁⠀⢸⡇⣿⠀⠀⣸⢠⡞⠀⢸⡇⢠⣏⡴⠇⠀⠀⢾⣯⡀
⠀⠀⠀⠀⠾⢦⣤⡴⠞⠛⢳⣦⡉⠀⠘⣇⠀⠀⠉⢳⡳⡄⢸⡇⣿⠀⡼⣳⠋⠀⢀⣾⠀⠈⢩⡴⠛⠛⠲⠦⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⢁⣠⡤⠶⢬⣛⠶⣤⡀⢳⡹⣼⡇⣿⣼⡷⢃⣤⠶⣋⡥⠦⣤⣈⠉⢻⡄
⠀⠀⠀⣀⣀⣀⣀⣀⣈⣙⣛⣋⣁⣀⣀⠀⠉⠛⠶⣝⡳⢷⣹⡇⠿⡽⠟⣩⠴⠚⠉⠀⢀⣀⣈⣉⣉⣀⣀⣀⣀⣀⣄⣤⣄
⠀⠀⠺⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣙⣿⣿⣿⣿⣿⣛⣂⠉⠀⠀⢀⣻⣿⣿⣿⣭⣽⣭⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣽⠟
⠀⠀⠀⠈⠉⠉⠉⠉⠉⣉⣉⡉⠉⠉⠁⠀⠀⢀⣤⠖⣫⢵⡆⡀⣤⢤⣍⡳⢦⣄⡀⠀⠀⣀⣤⠦⢤⣄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠉⠛⢶⣄⣠⡴⢞⡭⠖⠋⢁⣞⣼⡇⣿⣜⣦⠙⠳⢮⡉⠓⠛⠉⠀⣀⡼⠇⠀⣀⣀⡀
⠀⠀⠀⠀⠸⣟⠛⠳⢦⣈⣹⡶⠀⠈⣵⠞⠉⠀⠀⢠⢏⡞⢸⡇⣿⠘⣎⢧⠀⠀⢹⡆⠀⣘⣿⢥⡤⠖⠋⠉⢨⡟

⠀⠀⠀⠀⠀⠈⢙⣦⠀⠈⣠⠖⣷⠀⣿⠀⠀⠀⡴⠋⡞⠀⢸⡇⣿⠀⠘⣾⢧⡄⠀⣷⠀⣿⠙⣧⠀⣀⡲⣿⡉⣀
⠀⢀⣴⠞⠛⠚⢋⣥⡄⠀⡟⠀⢿⣀⣿⠀⢀⡼⠁⣼⠃⢀⡼⠇⢿⡀⠀⢿⡀⠹⣆⠸⣄⣸⡆⢹⡄⢹⡟⢻⣍⠉⠛⢶⣄
⠀⣸⣇⠀⢀⣸⠏⢸⡇⢠⡿⠀⠀⠉⠁⢀⡾⠁⡼⣡⠶⠋⢀⠀⢀⠙⠶⣄⠹⡄⠹⣆⠈⠉⠀⠘⢧⣰⡇⠀⠙⢶⣄⣠⣿
⠀⠉⠉⠛⠋⠁⠀⠀⠙⠟⠀⠀⠀⠀⢀⡞⢁⡾⣹⣃⣀⡴⢻⡇⣿⠳⣄⣸⣇⠹⡄⠙⣆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⡞⠀⠈⠉⢉⡴⠟⠁⠙⢷⡈⠉⠉⠀⠹⣆⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠟⠀⠀⢠⡶⠋⠀⣠⡄⣶⣄⠙⢳⣄⠀⠀⠹⢶⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠶⠋⣽⠇⢯⡈⠷⠾⠟⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡾⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠇⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣶⡀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣝⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠙⠳⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠂⠹⡀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⣰⠃⠀⠁⠀⠳⡀⠀⠀⠀⡰⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠼⠀⠀⠀⠀⠀⡴⠁⡐⠀⠀⠀⠀⠹⣄⠀⠀⠳⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢀⠄⢄⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠃⠀⠀⢀⡴⠋⠀⠀⢀⠂⠀⠀⠀⠀⢠⠀⠀⠙⢦⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠙⡆⠀⠀⠀⣠⠞⠀⠀⠀⠀⠘⣀⢀⡐⠀⢠⠊⢦⠀⠀⠀⠳⣄⠀⠀⠀⡸⠳⡀
⠀⠀⠀⠀⠀⢀⠷⠀⠀⠙⠒⠁⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⢦⡀⠀⠳⠴⠃
⠀⠀⠀⠀⠀⠘⠴⠃⠀⠀⠀⢀⡼⠁⠀⠀⣠⣴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠞⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡉⠙⠳⣄⠀⢻⡀⠀⠀⢠⡀⠀⠁
⠀⠀⠀⢠⠋⡀⠀⠀⠀⢰⠃⠀⠀⢀⣴⣿⠛⠙⣿⣿⣦⡀⠀⠀⠀⠀⢠⣾⠟⠙⢿⣿⣷⣄⠈⠀⠀⢳⠀⠀⡜⢣
⠀⠀⠀⠀⠉⠀⠀⠀⢠⡏⠀⠀⠀⡜⣿⣿⣤⣤⣿⣿⣿⢣⠀⠀⠀⢀⢿⣿⣦⣠⣾⣿⣿⡏⡆⠀⠀⠘⡇⠀⠓⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠀⠀⢇⠹⣿⣼⣿⣿⣿⠇⡼⠀⠀⠀⠘⡘⢿⣭⣿⣿⣿⡿⢁⡇⠀⠀⠀⣷
⠀⠀⠀⠀⠠⠆⠀⢀⣿⠀⠀⢀⠤⠼⢆⡈⠛⠛⠋⢁⡴⠃⠀⠀⠀⠀⠱⣄⠙⠛⠛⠉⣀⠾⠤⢤⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⢠⠞⢸⡄⠀⠠⠊⠉⢢⠉⠑⠒⠚⠉⠀⠀⠀⠰⠔⠀⠀⠈⠉⠒⠒⠋⢡⠊⠈⠑⡄⠀⡏⢳⡀⠀⠀⣜⠄
⠀⠀⠀⠀⠀⠀⢸⡀⢀⣧⠀⠘⠄⡠⠜⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣄⠀⠀⠀⠀⠀⠀⠘⠤⠀⠴⠁⣸⣃⣠⠇
⠀⠀⠀⠀⠀⠀⠀⢸⠋⠈⢧⡀⠀⠀⠐⠀⢢⠀⠀⠀⠀⠀⢺⠿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠁
⠀⠀⠀⠀⠀⠀⢀⠎⢳⡀⠀⠱⢤⡀⠈⠒⠁⠀⠀⠀⠄⠠⠈⠙⠒⠋⠀⡀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣠⠻⣄
⠀⠀⠀⠀⠀⠀⡎⠀⠀⢱⠀⠀⠀⠙⠲⢤⣄⣀⡀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠖⠋⢿⠀⠀⠀⠀⣇⠀⣸
⠀⠀⠀⠀⠀⠀⠙⠦⠴⠋⠀⠀⠀⠀⠀⠀⢸⠉⢹⠋⠛⠓⠒⠒⠒⠛⠛⠋⠉⠉⠀⠸⣄⣀⡞⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋

⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢠⣤⠴⠖⠛⠉⠉⠉⠉⠛⠶⢤⣤⣤⣤⠤⠖⠛⠉⠉⠉⠉⠛⠲⠤⣤⣤⣤⠤⠶⠛⠉⠉⠉⠉⠛⠲⠦⣤⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⢤⣤⣀
⠀⠀⠀⠀⠀⠀⢠⠤⠶⠋⠁⠀⠀⠀⠀⠉⠓⠶⢤⣤⡤⠶⠛⠁⠀⠀⠀⠀⠈⠛⠶⢤⣤⡤⠶⠛⠉⠀⠀⠀⠀⠈⠛⠶⠤⡄

⠀⠀⠀⠀⠀⠀⠐⠲⢤⡀⠀⠀⠀⠀⢀⡴⠖⠒⠲⢦⣀⠀⠀⠀⠀⢀⣤⠖⠒⠒⠦⣄⠀⠀⠀⠀⠀⣠⠶⠒⠒⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠶⠞⠋⠀⠀⠀⠀⠀⠉⠳⠶⠶⠖⠋⠀⠀⠀⠀⠀⠈⠓⠶⠶⠶⠛⠁⠀⠀⠀⠀⠈⠙⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠙⢦⡀⠀⠀⠀⣰⠞⠉⠉⠛⢦⡀⠀⠀⢀⡴⠛⠉⠉⠳⣆⠀⠀⠀⢀⡴⠋⠉⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠙⠓⠒⠛⠁⠀⠀⠀⠀⠀⠙⠒⠒⠋⠀⠀⠀⠀⠀⠈⠛⠒⠒⠋⠀⠀⠀⠀⠀⠈⠓⠂
⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⢀⣠⣀⡀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠉⢷⣀⠀⢀⣴⠋⠀⠀⠙⢦⡀⠀⢀⡼⠋⠀⠈⠹⣆⡀⠀⣠⠞⠁⠀⠈⠳⣄⠀⠀⣠⠟⠁⠀⠙⢷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠈⠉⠋⠁⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠦⣄⠀⠀⠀⠀⢀⡤⠤⣄⠀⠀⠀⠀⣠⡤⢤⣄⠀⠀⠀⠀⣠⠤⢤⡀⠀⠀⠀⠀⣠⠤⢤⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠈⠳⣄⣀⡴⠋⠀⠀⠈⢷⣀⣀⡴⠃⠀⠀⠘⢦⣀⣀⡾⠁⠀⠀⠙⢦⣀⣠⠞⠁⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣷⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⢛⡡⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⣠⡾⠿⠟⠛⠉⠀⡠⢚⣩⣤⣀⡀⠀⠀⢀⣈⠛⠿⣿⣿⣿⡿⠋⠉⠛⢿⣿⣿⣦⡀
⠀⠀⠀⠀⡀⠀⠁⠐⠒⠂⠀⠀⣸⣿⠟⣩⣶⣤⡤⠄⠀⠀⠈⠿⢶⣿⣿⣿⡅⠀⠀⠀⢸⣿⣿⣿⣿⣄
⠀⠀⠀⠀⣶⣾⣭⡶⠒⠂⠀⠀⠙⠏⣾⣿⣿⣯⣹⣶⡶⠤⣴⣤⣤⣽⣿⣿⣿⣦⣤⣶⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⢰⣿⣿⠿⠀⠴⣤⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠟⠉⠀⠲⢦⣄⣾⣷⡤⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠐⠲⣦⣾⣿⣿⣿⣿⡵⡀⠀⠈⠛⢿⣿⡿⢿⣻⣯⣽⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢠⣉⠻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣷⣬⡻⣿⠿⠿⠟⠿⢿⣿⣿⣷⣶⣔⣿⣶⣤⣂⣀⠌⠋⠉⠉⠏⢭⣭⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣽⣶⣿⣿⣿⣷⣶⣬⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠭⠽⢿⣿⠿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠈⢿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣭⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠁
⠀⠀⠉⠉⠉⠙⠻⢷⠾⠟⠿⠿⠿⣿⣿⣿⣿⣿⣷⣮⣽⣟⣻⣿⣿⣿⣟⣛⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠷
⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣳⣮⣝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⠟⢀⡀
⠀⠀⠀⠀⠘⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣵⠾⠋⠉⠁
⠀⠀⠀⠀⠐⠒⠒⠶⠦⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉

⣿⣆⠀⠀⠀⠀⢰⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⡄⠀⠀⢰⣿⣿⣿⣧⠀⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⣠
⣿⠟⠀⠀⠀⠀⠘⠿⣿⠿⠃⠀⠀⠀⠀⠈⠉⠀⠀⠀⠘⠿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⢠⣾⡆⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣠⠀⠀⠰⣿⣷⠀⠀⠀⠀⡀⠀⠀⠀⠀⣴⣿⡄⠀⠀⠀⠀⠀⣰⣿⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣾⣷
⠀⢠⣾⣿⡆⠀⠀⠈⠀⠀⠀⢀⣼⣷⡀⠀⠀⠸⣿⣿⡗⠀⠀⠀⢠⣾⣿⣿⣷⠀⠀⠀⠀⢠⣿⣷⠀⠀⠀⢻⣿⣿⠇
⠀⠘⠻⠿⠋⠀⠀⠀⠀⠀⢰⣿⣿⣿⣧⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⢿⣿⣿⠿⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠘⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀
⡄⠀⠀⠀⢰⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣿⣇⠀⠀⠀⣠⣾⣿⡆⠀⠀⠀⠀⡀⠀⠀⢀
⠟⠀⠀⠀⠀⠉⠁⠀⠀⢠⣶⡀⠀⠀⠀⠀⢀⣾⣷⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⣾⣿⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣧⠀⠀⠀⠀⠀⠉⠉⠀⠀⣠⣾⣧⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠋⠀⠀⠀⠈⠁
⠀⠀⢀⣴⡄⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿
⠀⠀⣾⣿⣷⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣧
⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⢀⣼⣿⡄⠀⠀⠀⠀⠀⢠⣾⣿⣿⣇⠀⠀⠀⠀⣠⣆⠀⠀⢾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⠇⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⠀⠀⠀⠘⠿⠿⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢱⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡈⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠋⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣶⡾⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⢿⣿⣿⣿⠿⠿⣷
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠋⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢲⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢬⡥⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢬⣙⣋⡥⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠐⠠⠀⠑⠢⢬⡥⠔⠊⢀⠀⠂⠀⠀⠀⠀⠀⢀⢠⠊
⠀⠀⠀⠀⠀⠀⠂⠤⠜⡳⢄⡄⡆⢀⢀⠀⠀⠀⠀⠰⠀⢸⠁⠀⠆⠀⠀⠀⠀⠀⡀⢠⢠⡬⢞⠣⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡨⠜⣳⠶⣸⡀⠀⡐⠀⠀⠀⠈⠀⠀⠀⠀⢒⠀⢀⣧⠶⣎⠃⢍⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠠⠒⠉⢉⠲⢄⡁⠄⢈⡢⠔⡀⠠⢈⡤⠒⡉⠉⠒⠄⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠑⠂⠁⠂⠀⣊⠀⠁⠀⠁⠐⠀⠐⠈⠐⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠄⡀⠄⠀⢄⢀⠀⢀⠀⡩⠀⠠⢀⠠⣄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠐⠤⣀⣈⠤⠊⡁⠂⢈⠔⠪⡁⠐⢈⠑⠦⣁⣀⠤⠂⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⢠⡹⠶⢻⠁⢀⠥⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠈⡏⠶⢏⡔⡊⠄
⠀⠀⠀⠀⠀⠀⠄⠒⢢⡴⡚⠃⠃⠀⠀⠀⠀⠀⠀⠰⠐⢀⡀⠂⠆⠀⠀⠀⠀⠁⠀⠸⠘⢑⢮⡔⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠁⠀⠀⠀⠀⠀⠰⠀⠁⡠⠔⢚⡓⠢⢄⠀⠂⠄⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢚⣩⣍⡓⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢚⡓⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠸⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⠹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠁⠀⠀⠀⠀⠹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣶⣤⣤⣄⣀⣠⣤⣤⣴⣶⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠟⠛⠛⠋⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⢀⠰⣦⡄
⠀⠀⠀⠀⠀⠀⣠⣤⡄⣶⣿⣦⣰⠿⣿⣇⣿⣼⣷⡜⣷⡸⣷⣄
⠀⠀⠀⠀⠀⢤⡦⠾⢧⣿⣿⣿⣿⠴⣶⣾⣿⣿⣿⣷⣿⣗⣿⣿⣷⡀⣀
⠀⠀⠀⠀⠀⢀⣤⣰⣦⡉⠈⢠⣄⣄⠻⣿⣿⣿⣿⣿⡿⡿⡻⣿⣿⣷⣿⣷⡄
⠀⠀⠀⢀⣠⣿⣿⣿⣿⣇⣿⢸⣿⣿⣷⣿⣿⣿⣿⠋⠀⠀⠙⠘⠉⢛⡻⡿⣡⡀
⣤⣶⡾⢟⣿⣿⣿⡿⣫⣾⢯⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⢷⠁⠙⠻
⣴⣶⡾⠿⣛⣫⣵⡾⠟⠋⠉⢰⣮⡛⣓⠻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠚⠀⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠐⠒⠚⠛⠋⢉⣀⡤⠂⣠⣿⣾⣿⣷⣿⣿⣾⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⢊⣡⣔
⠶⠶⠶⠾⠛⣋⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⢿⣿⣷⣄⠀⠀⠀⠠⠤⠤⠤⠶⠶⠖⠛⢉⣡⡴⠾⠛⣉⡠
⠶⠶⠾⠿⠿⠿⢛⣻⣭⠷⢿⣛⣭⠿⠟⢉⠀⣄⣿⣦⡻⣿⣿⣿⣦⣤⣄⣀⣀⡀⠀⠀⣀⠨⠭⠄⠒⠮⠽⠖⣛
⠲⠶⠦⠤⠤⣤⣤⣤⣤⣭⣭⣤⣤⡶⠞⣡⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣶⣶⣶⠤⢤⣤⡴⠶⠖⣀⣨⣤⣤
⠛⠛⠛⠒⠒⠒⠶⠶⠶⠿⠭⠽⠶⠾⠿⠿⢿⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡒⠒⠒⠒⠒⠒⢒⣒⡒
⠈⠙⠒⠒⡶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⣛⣛⣛⣛⣛⣛⣯⣭⣭⡭⠭⢭⣭⣿⣿⣷⣶⣶⡶⠖⠂
⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠭⠭⠭⠭⠭⠵⢶⣶⣒⣶⣾⣿⣿⠿⠿⠛⠛⠋⠉

⠀⠀⠀⠐⢦⣀⣠⠖⠶⣄⣠⠖⠲⣄⣠⠖⠲⣄⣠⠖⠲⣄⣠⠖⠲⣄⣠⠖⠲⣄⣠⡴⠲⣄⣀⡴⠂
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁
⠀⠀⠀⠐⢦⡀⣠⠖⢦⡀⣠⠔⠦⣀⣠⠔⠦⣀⣀⠴⠢⣀⣀⠴⠢⣄⣀⠴⠲⣄⢀⡴⠲⣄⣀⡴⠂
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⠁
⠀⠀⠀⠀⢄⠀⢀⠤⢄⠀⢀⠤⢄⠀⢀⠤⢄⠀⢀⠤⠤⡀⠀⡠⠤⡀⠀⡠⠤⡀⠀⡠⠤⡀⠀⡠
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠁⠀⠀⠉⠁⠀⠀⠉⠁⠀⠀⠈⠉⠀⠀⠈⠉⠀⠀⠈⠉⠀⠀⠈⠉
⠀⠀⠀⠠⢤⡀⠀⢀⣠⠤⣤⡀⠀⢀⣠⠤⣤⡀⠀⢀⣠⠤⣄⡀⠀⢀⣤⠤⣄⡀⠀⢀⣤⠤⣄⡀
⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠉⠛⠉⠀⠀⠀⠉⠛⠉⠀⠀⠀⠉⠛⠉⠀⠀⠀⠉⠛⠉⠀⠀⠈⠙⠃
⠀⠀⠀⠠⣄⡀⠀⠀⣀⣤⣄⡀⠀⠀⣀⣤⣀⠀⠀⠀⣠⣤⣀⠀⠀⠀⣠⣤⣀⠀⠀⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠉⠓⠋⠁⠀⠀⠉⠒⠋⠁⠀⠀⠙⠒⠋⠀⠀⠀⠙⠒⠋⠀⠀⠈⠙⠚⠉⠀⠀⠈⠙⠂
⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠑⠒⠒⠁⠀⠈⠑⠒⠒⠁⠀⠈⠑⠒⠊⠁⠀⠈⠐⠒⠊⠁⠀⠈⠒⠒⠊⠀⠀⠈⠒
⠀⠀⠀⢀⡀⠀⢀⣀⠀⠀⣀⡀⠀⠀⣀⡀⠀⢀⣀⠀⠀⣀⡀⠀⢀⣀⠀⠀⢀⣀⠀⠀⣀⡀⠀⢀⡀
⠀⠀⠀⠀⠙⠶⠋⠉⠳⠞⠋⠙⠶⠞⠉⠙⠶⠋⠉⠳⠞⠉⠙⠶⠋⠉⠳⠶⠋⠙⠳⠞⠉⠙⠶⠋
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠑⠤⠊⠉⠳⠴⠋⠙⠦⠞⠉⠑⠴⠋⠉⠢⠔⠉⠙⠦⠚⠉⠳⠴⠋⠙⠦⠞⠉⠑⠤⠊⠁

⠀⠀⠀⠀⠳⠤⠔⠉⠢⠠⠊⠑⠄⠔⠉⠢⠤⠊⠙⠦⠴⠋⠑⠄⠔⠉⠢⠠⠊⠑⠤⠔⠉⠢⠤⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠒⠲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠷⣤⡀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⣠⠴⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⣏⠀⠀⠙⠳⣄⡀⡇⠀⠀⡇⣠⠴⠋⠁⠀⣈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠓⢲⠀⠀⠀⠙⠦⣄⠀⠀⠙⠃⠀⠀⠋⠁⠀⣀⡴⠚⠁⠀⠀⢰⠚⠋⡏
⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⡇⠀⢸⡆⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⣰⠋⠈⠛⠦⣄⡀⠀⡇⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⣀⡤⠞⠉⠈⢧⡀
⠀⠀⠀⠀⠘⠳⢤⡀⠀⠀⠈⠙⠲⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠷⠚⠉⠀⠀⢀⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⠀⠀⠀⢷⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣸⠇⠀⠀⠀⠀⣀⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠋⠀⠀⢀⠀⠀⠈⠓⠦⣄⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⣀⡤⠞⠋⠀⠀⢀⠀⠀⠈⠛⠦⣄⡀
⠀⠀⠀⠀⠀⣴⠞⠋⠁⠀⢀⣠⠴⠚⠉⠛⠦⣄⡀⠀⠈⠙⠲⣄⣀⡇⠀⠀⡇⣠⡴⠚⠉⠀⠀⣀⡤⠞⠉⠙⠲⢤⣀⠀⠀⠉⠓⢦⡄
⠀⠀⠀⠀⠀⠈⢧⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⠀⠀⠉⠃⠀⠀⠋⠁⠀⢀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣦⠄⠀⠀⠀⠀⢤⣞⠉
⠀⠀⠀⠀⠀⠀⡴⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠀⠀⡀⠀⠀⡀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⡄
⠀⠀⠀⠀⠀⢾⣁⠀⠀⠉⠛⠦⢄⡀⠀⢀⣠⠖⠋⠁⠀⢀⣠⠴⠛⡇⠀⠀⡟⠲⢤⡀⠀⠀⠉⠓⢦⣀⠀⢀⣠⠴⠞⠋⠁⠀⣀⣹⠆
⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠉⠛⠉⠀⠀⢀⣤⠖⠋⠀⠀⠀⡇⠀⠀⡇⠀⠀⠉⠳⢦⣀⠀⠀⠈⠙⠉⠁⠀⣀⡤⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠀⠀⠀⠀⣴⠞⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠈⠙⢶⡄⠀⠀⠀⠈⠛⢦⣄
⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⣠⡄⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣤⡀⠀⠀⠈⠙⠲⢤⡀
⠀⠀⠀⠀⠈⢳⡀⠀⢀⡤⠖⠋⠁⡇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠉⠓⢦⣀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠹⠞⠉⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⢀⣠⠞⠃⠀⠀⠳⢦⣀⠀⠀⠀⠀⠀⠀⣷⠀⠀⡇⠀⠀⠀⠈⠙⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣀⣸⠀⠀⠀⢀⣠⠖⠋⠀⠀⡀⠀⠀⡀⠀⠈⠓⢦⣀⠀⠀⠀⢹⣀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠀⠀⠠⡖⠋⠀⢀⣠⠴⠛⡇⠀⠀⡟⠳⢤⡀⠀⠈⠓⡦⠀⠀⠈⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⠶⠋⠁⠀⠐⡇⠀⠀⡇⠀⠀⠉⠳⢤⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⡇⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣠⡗

⡀⠰⣰⠀⠃⠃⠐⠄⠀⣉⠀⡌⠁⠐⠂⠠⠂⠸⡸⠰⣉⠀⢁⠀⠐⠀⠀⠤⠀⢇⠅⢐⢙⠈⠂⠘⠊⠀⣡
⡠⡀⢀⠆⠰⠙⠀⡰⡄⢀⢄⠈⣥⢠⢱⢀⠛⠀⣤⠀⣀⠀⡰⠀⡜⢃⢀⢢⠀⡰⡀⢀⠅⢠⢉⠀⣎⠀⠄
⠄⠅⠈⠂⠈⡉⠀⠒⠃⠣⠜⠐⠤⠀⡁⠀⢉⠀⠤⠰⣁⠇⠑⡁⠁⢁⠈⠊⠀⠤⠂⠘⠜⠀⡁⠀⡰⠀⡜
⡰⠀⠜⡄⢘⡡⢰⠡⠀⠶⠀⢠⡀⢈⡱⢠⠉⡆⢰⠂⠀⠆⠀⢙⠀⡊⡆⡌⡂⠴⠀⡐⠂⠸⡰⠀⠂⠁⢈
⠃⠃⢁⠁⠀⢤⠈⢁⠀⠒⡀⠀⠂⠀⣠⠀⡤⠀⢈⡁⠈⡊⠀⣄⠀⢀⠀⢈⡀⠒⠁⠑⡂⠀⣤⠀⠜⠀⢆
⡜⡀⢆⡇⠨⠠⠀⠧⠂⡎⣱⢀⠳⠰⡀⠂⠠⠀⢈⡁⢐⠡⠘⠬⠀⠍⠀⣂⡡⢀⢳⠠⡱⠀⠠⠀⠑⠁⡄
⠁⠁⠀⡰⡀⠠⠄⠀⡄⠀⢀⠈⠈⠀⠀⡴⠀⢢⠀⢀⠀⢠⡀⢠⠄⠀⡠⠀⢠⠀⠁⡀⠀⡴⡀⡔⢃⠘⠜
⡄⠋⠀⠂⠃⠐⠔⠐⠜⠀⢆⡇⢰⠉⠀⠒⠀⠉⠀⣎⡃⠣⠆⠀⠄⠀⠠⠂⠑⠃⢘⡰⠀⡁⠁⠈⠁⣤
⡀⠉⡀⠀⣖⠀⠔⠄⢠⡀⠀⣤⠀⣩⠀⡘⠂⡊⡆⣀⠀⢀⡄⠰⠆⢠⠒⠀⡰⡀⢀⢄⢠⢙⠀⡰⠀⠤⠂
⡁⠘⢙⠀⢉⠀⠒⠁⠂⠅⠸⠠⠂⠥⠃⠑⠁⠈⠀⣉⠄⠇⠸⠈⠁⠈⠒⠀⠓⠃⠣⠜⢀⠁⠀⠂⠃⠰⡆
⡀⠀⡄⠀⣉⠀⡔⠀⢠⠀⠠⠄⠀⢆⠀⠚⡄⡐⠆⢀⡀⢠⠀⠘⠃⢠⢣⢀⠒⠀⣄⢠⠊⡆⠰⢂⠀⢈⡁
⠄⠸⡰⠀⡀⠀⠓⠁⠇⠇⠀⠀⠀⠉⠀⠉⠁⠂⠂⠨⠅⠠⠄⠈⠁⠈⠊⠈⠊⠸⠨⠀⠉⣁⠐⠊⠀⣆⡇
⠄⢀⠆⠸⡸⠀⡔⠆⠀⡄⢠⠚⡄⠜⡀⠔⠃⢠⡀⢀⡄⠀⢄⠀⡴⠀⢈⡄⡠⠂⢠⠄⠀⣉⠀⡌⠆⢀
⠜⠘⠜⠀⡄⠀⠓⠂⠐⠔⠈⠀⠀⠁⠁⠁⠀⠣⠄⠠⠔⠘⠬⠀⠒⠀⢀⠀⠁⠂⠐⠂⠀⢀⠀⠈⠁⢈⠂
⡄⢀⢆⠨⡸⠀⠐⠃⠀⣄⠀⢦⠀⠎⠃⢠⠆⠀⣤⠀⢤⠀⠴⠀⡴⠀⡌⡂⢀⠆⠀⠚⡀⣃⡃⡜⡃⠀⡀
⠄⠘⠘⠀⢀⠄⠈⠁⠀⠊⠈⠚⠀⠉⡁⠈⡁⠀⠒⠘⠤⠀⠒⠀⠒⠀⠈⡀⠈⠊⠀⠉⠁⢀⡀⠈⡀⢐⢡
⠆⠀⠊⠆⠘⠂⡔⢡⢀⢢⠀⠎⡆⢰⢱⢰⢱⢀⠓⠀⡴⠀⠎⠂⠠⠄⡎⡡⠠⠂⢠⠊⡆⢆⠄⢰⢡⠀⠁
⠂⠀⢉⠁⠐⡄⠈⠁⠈⠚⠀⠁⢁⡀⠁⡀⠁⡀⠉⠀⠒⠁⠁⠁⠐⠂⡈⠀⠘⠊⠀⠉⠀⣤⠀⢀⠁⠰⢣
⠞⠀⡎⡄⠑⠃⡎⡄⡜⡆⢠⢂⠨⠅⢘⡁⠐⢙⠀⢶⠀⢦⠀⠛⡀⢐⢱⠀⠞⠀⡐⠆⠨⠠⠀⣎⡆⠈⡁
⡍⠀⡈⠀⡰⡀⠈⡀⠈⣁⠐⠂⠀⠠⡀⢠⡀⠁⡄⠉⡀⠉⣀⠉⢀⢆⠀⣠⠉⢠⠑⠂⡀⢀⠆⢀⡄⠐⢡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⣦⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⠛⠿⣍⠉⠙⠛⠓⠶⢤⣍⡉⠉⠉⠉⠉⠛⠛⠓⠒⠶⠦⠤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⢡⡇⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢫⡞⠁⠀⢸⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠏⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣠⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣰⠏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⢀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⢠⠏⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⣠⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠛⠋⠁
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⣀⣠⣴⠖⠋⠁
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⣀⣀⡼⠷⠶⠚⠋⠉⢧⠘⣇
⠀⠀⠀⠀⢾⣁⣀⣀⣀⣀⣀⣠⡼⠻⠴⠶⠖⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⣇⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣽

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠉⠈⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣠⢀⣸⣇⡀⣄⣤⠆⠀⠀⠠⣼⡆⢹⡟⢁⣿⡤⠀⠀⠰⣤⣆⢶⣼⣇⡶⢠⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⠋⠙⣿⡍⠀⠀⠀⠀⣛⡋⣙⣿⣿⣟⢉⣛⡀⠀⠀⠨⣭⣿⣿⣿⣿⣭⡍
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⠻⠷⡾⠟⡶⣤⡀⠀⠀⠸⢿⡏⢹⣇⠉⣿⠏⠀⠀⢀⣴⡶⣻⡿⡿⣟⢲⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠐⠛⠏⠓⠈⠀⠀⠀⠀⠀⠀⠉⢼⡷⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣦⣀⠦⣽⠴⣀⣴⡶⠀⠀⠲⣤⣀⠀⣹⡁⠀⣠⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣝⣳⣾⣞⣛⠌⠀⠀⠀⠀⠀⠉⣛⣾⣶⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠛⡇⣿⢬⡛⣶⣦⠀⠀⣠⡶⠞⠉⢺⠒⠉⠷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⢀⣀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣤⠀⠘⡏⠀⣠⣄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣶⣷⡚⠉⠁
⠀⠚⠒⠂⠒⠂⠒⠒⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠋⠉⡇⠉⢻⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣉⠁⠀⠈⠉⠻⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⠴⢋⣥⡤⠴⠦⠀⠀⠀⠀⠀⢻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠻⣯⡞⣡⣾⢟⣥⣖⣯⣭⣭⠤⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠈⠀⢀⣼⣫⣾⣿⣷⣿⣿⣿⣿⣵⣾⡿⠋⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠃⣠⠂⡴⣢⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣴⣶⣿⣷⣦⣄⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡏⣼⢇⣾⣳⣿⣿⡿⠉⠀⠈⠛⠛⢿⣿⡿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣦⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠏⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠺⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⠁⠀⠉⠁⠀⠈⠋⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣾⣼⣄⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠸⣿⣿⡿⢀⡄⢠⠆⣰⠀⡠⢀⠄⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢻⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣧⣼⣿⣿⣿⢿⣿⣟⣿⣿⡟
⠀⠀⠀⢟⣫⡴⣋⣴⣏⣼⢏⣼⢃⡾⢀⡇⠀⠀⢰⣿⣸⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀
⠰⢮⣭⣭⣷⣾⣿⣿⣿⣿⣿⣣⡿⢡⡞⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠙⠿⣿⣿⣿⣿⣽⣿⣿⡿⣿⣿⣿⣯⣽⣿⣿⡿⠟⠉⢀⡴⣫⠎
⠀⠲⣭⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⠟⡀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠉⠛⠛⠿⠿⠿⠷⠿⠿⠛⠛⠋⠉⠀⢀⣠⣾⣿⣿⠋
⠀⠠⣈⠙⠻⠿⠿⠟⢛⣩⡴⢟⣡⢞⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⣀⣀⣠⣤⣤⠶⣚⣥⣶⣿⣿⣿⠟⠁⢀⡠
⠀⠠⣬⣙⣛⣛⣛⣛⣩⣥⡶⢋⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⠟⠁⢀⣴⣫⡖
⠀⢠⣀⡙⠛⠛⠛⢛⣉⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣀⣠⣤⣤⣤⣤⣀⡀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⢀⣠⣶⣿⣿⠋
⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠙⠿⠿⠿⠿⠿⠛⠛⢉⣁⣤⣴⣾⣿⣿⡿⠟⢁⡤⢂
⠀⠀⠀⠙⠶⣾⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢁⣴⣾⣿⣿⠿⠛⢋⣉⣤⣤⣤⣬⣍⣛⠿⣿⣷⣄⡐⠶⣶⣶⣾⣿⣿⣿⣿⣿⡿⠟⢋⣤⣾⣯⡾⠁
⠀⠀⠀⠀⠀⠨⣙⠛⠿⠿⠿⣿⠿⠿⠿⠛⢋⣡⣴⣾⣿⣿⠿⢋⣡⣴⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣾⣿⣿⣿⣷⣦⣬⣉⣉⣉⣉⣭⣤⣶⣾⣿⣿⠿⢋⡠
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣶⣶⣶⣶⣾⣿⣿⣿⠿⠟⢋⣡⣶⣿⡿⠿⠛⠉⢀⣠⣤⣶⣶⣦⣤⣌⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢋⡡⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠭⠭⠭⠤⠴⠶⠾⠟⢛⣉⡡⠄⢀⡠⠖⠛⠉⠉⠀⠀⠈⠉⠛⠿⣦⣄⠀⠈⠉⢉⣉⣉⣉⣉⠭⠤⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠒⠛⢋⠝⠉⠙⠳⡒⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢔⠯⠋⠁⠀⠀⠀⡠⠋⠀⠀⠀⠀⠘⢆⠀⠉⠛⢗⠤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⡫⠚⠁⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠉⠪⡑⢄
⠀⠀⠀⠀⠀⢀⡔⢡⠎⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢦⠑⢄
⠀⠀⠀⠀⣠⣎⡔⠁⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠱⡄⠳⡀
⠀⠀⠀⢰⢣⡜⢄⡠⠤⡀⢀⡀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢸⡏⠱⡄
⠀⠀⠀⢨⠎⢡⠀⠴⢂⢈⣁⡘⠤⠔⡛⠲⣀⡠⠔⠢⢄⢀⡠⠤⢄⠀⣀⠼⡦⣀⠖⠑⠒⢁⡉⢁⠸⡌⠘
⠀⠀⠀⠘⠠⠤⠤⠤⢉⡀⠈⢰⠄⢢⠳⠆⣤⠰⠆⠰⢀⡌⠲⠠⠆⣩⠠⠆⡧⠄⡄⠊⠁⠇⠀⠈⠁⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⢄⡸⢀⣀⣋⣀⣀⣀⣈⢋⣀⣀⣀⠛⠀⠀⠇⢀⡤⠔⠊⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠉⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣤⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣹⣫⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠘⢦⣸⣇⡴⠁⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣰⡀⡄⢠⠀⠘⠻⡇⠀⠀⢹⡏⠀⠀⣸⠟⠃⠀⡄⢠⢀⣆⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣛⣱⠿⣌⣇⠀⠀⢸⣦⣦⢼⣧⡤⣴⡃⠀⠀⣸⣡⠾⣎⣙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠖⠚⠛⠲⣴⡟⠛⢇⢸⡇⡼⠓⢿⡤⠖⠛⠓⠲⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⡴⣻⠈⠓⢮⣿⣾⡵⠚⢉⡟⣆⠀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠉⠉⢯⣹⢉⡩⢟⣿⣿⡻⢍⣉⣏⠟⠉⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⢤⣤⠴⢻⡧⣤⡎⢸⡇⢳⡤⢾⠟⠦⣤⡤⠴⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣍⡻⣶⢋⡟⠀⠀⢱⠯⠽⢾⡿⠭⠵⡏⠀⠀⢻⠙⣶⢞⣩⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠹⠡⠇⠘⠀⢠⣴⡇⠀⠀⣸⣇⠀⠀⢹⣦⡄⠀⠃⠸⠌⠏⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⢀⠞⢹⡍⢣⡀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣻⡝⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⣏⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⡠⡰⣀⣤⡀⡀
⠀⠀⠀⠀⢀⣀⣠⣤⡀⠘⠶⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠤⢈⢣⠀⠀⠀⠀⢉⠸⣇⠦⠃⣙⡚⠉⠉⣀⡀
⠀⠀⠀⠞⠉⠀⠈⠀⠩⠛⠀⠒⠒⠒⠀⠀⣀⣀⣀⡀⠜⠑⠀⠄⣀⣉⡒⠥⠃⠀⠀⠀⢀⠈⠀⠈⠛⠛⠡⡞⠿⠀⠥⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠉⠓⠂⠀⠀⠀⠙⠶⠤⠴⠚

⠀⠀⠀⠀⠀⠀⢰⣄⡀⠀⠀⣀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠄
⠀⠀⠀⠀⠀⠀⠘⠿⢁⠔⢋⣭⣝⠊⡀⠀⣀⢤⣀⣲⣶⠖⣊⠕⠂⠀⠀⠒⠄⠀⠀⠀⡀⢀⡤⢤⡄⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠤⠤⠔⠁⠀⠻⣀⣈⡔⠀⠀⠙⠳⠯⠵⠖⠊⠀⠀⠀⠀⠠⠄⠂⠀⠀⠀⠳⠾⠦⠤⠶⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣨⣭⣔⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠉⠛⢿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠚⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠰⠢⠀⢎⠘⠿⢷⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⢐⠂⠀⠀⠀⠀⠬⠳⡄⡀⡼⠁⠙⣀⣠
⠀⠀⣀⠠⢀⡲⠖⠚⠋⠉⣈⣡⠤⠖⠒⣒⣈⠭⠍⣉⠉⠁⠇⢘⡇⣈⣋⣒⡓⠒⠢⠬⣅⠈⠉⠉⠒⠠⠔⠂⠀⠤⣀
⠐⠉⢀⡔⠁⠀⠀⠠⠂⣹⠋⠀⢰⡞⠉⠁⠀⢆⠀⠀⠐⠈⠀⣁⡐⢤⣀⡀⢭⠙⣷⣅⠈⠛⢶⣔⠀⠀⠀⠀⠑⣦⡀⠈⠐⠤⡀
⠀⠀⠸⡤⠀⠀⠀⠀⠄⣻⡀⠀⠐⠳⣄⡀⠀⠀⠁⠲⢤⡄⠠⠈⠉⠋⠒⠀⠊⣠⡟⢹⠀⠀⠨⡹⡄⠀⠀⠀⠪⡊⡇⠀⠀⠀⠈
⠀⠀⠀⠈⠲⠤⡀⡀⠄⠀⠙⢮⡢⣀⣀⠈⠑⢓⠰⠶⠷⣶⣶⠻⠿⣿⠾⠟⠥⠒⢊⡁⠤⡚⣠⠞⠀⡀⡠⣐⡼⠊
⠀⠀⠐⠄⡀⠀⠀⠀⠘⠒⠦⠤⠤⣀⣀⡀⠀⠚⠚⠯⠼⢷⣶⠶⠧⣴⠤⢤⠬⠝⠑⠒⢈⣁⣄⠤⠦⠖⠋⠁⢀⡠
⠀⠀⠀⠀⠀⠉⠁⠒⠂⠀⠠⠤⠄⠀⠀⠉⠉⠉⠙⠒⠛⠛⠛⠉⠉⠒⠛⠒⠒⠊⢉⠁⠁⠠⠤⠀⠐⢒⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠒⠀⠀⠈⠁