Duck Emojis & Symbols

⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡄⢠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠉⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠘⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⣠⣤⡄⠀⠠⣀⠖⢨⣬⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠁⣤⣤⠀⠀⠀⠀⢠⣶⡄⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣹⣿⣿⠟⠻⢿⣭⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠘⢋⣿⠃⡰⠂⠒⢌⠹⠇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⠾⠛⠛⠙⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⢀⠀⠀⠤⠊⠀⢀⠤⠒⠉⠉⠁⠺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡵⣶⣝⠻⠛⣋⣡⣴⣾⣛⣻⣆⣼⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⡇⠀⢄⠀⠀⠀⢁⡠⢤⡒⠀⠢⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡈⠈⠑⢍⢢⠛⠁⠀⢴⣇⣀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢻⣿⣟⣿⣟⡫⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠵⠥⣂⣀⣊⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣏⣭⣽⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⠀⠠⠥⢄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⡙⠦⣄⣀⣀⣤⣾⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠑⠤⠀⠀⠠⡤⠃⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡧⠀⢀⣤⠶⠛⠿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⠤⠒⠃⠠⡀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣴⠏⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡠⠖⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇⡀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠕⠋⣂⠀⠀⠀⢀⠬⡀⢀⠀⢀⢀⡄
⠀⠀⠀⠀⣤⠐⠒⠒⢋⡻⣿⣿⣿⣷⡿⠋⠁⠈⠉⢉⣩⣿⡁⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠉⠻⢤⠤⠼⠖⠂⠁⠀⠉⠁⢈⡡⠃
⠀⠀⠀⠀⠈⠉⠉⢴⣂⠀⠉⠛⠛⠻⠿⠶⠶⠶⠛⠻⠷⠀⡠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠐⠒⠀⠀⠐⠒⠈⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠤⠀⠀⠀⠀⠀⠀⠠⠤⠐⠊
⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠘⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡈⠀⠀⡀⠀⠉⠲⡄
⠀⠀⠀⠀⠀⠀⣠⠞⠀⢣⡀⠈⠁⠀⠀⠀⢹
⠀⠀⠀⢠⢒⣩⣤⠴⠶⠥⣄⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠈⠋⠁⠀⠀⠀⡐⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡍⢶⠉⢦
⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⣀⣀⡀⠤⠤⠤⠤⠄⠀⢀⣄⣠⣀⠜⠀⠀⢀⡞⢻
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⢀⡴⠁⣠⠞⢳⠂⠀⠀⠈⣠⠃
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠠⢤⣀⠴⠃⠀⠀⠀⠴⡟
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠁⠀⠀⠈⣉⠟⠀⠀⠀⠀⢰⠎
⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣇⠘⢄⠀⠀⠀⠀⠐⡊⠀⠤⠔⠊⠀⠀⣩⠟⠀⠀⠀⣀⠜⠁
⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠈⠲⢤⣀⣀⣀⣒⣊⣀⣠⣴⣊⣀⣈⠽⠃⠀⠀⢀⠌⠁
⠀⠀⠀⠀⠀⠀⠑⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠠⠤⡄⢠⠄⢀⣀⣀⣀⣀⣀⠤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠜⠁⡎⠀⠀⡸⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⣁⣠⠤⠞⠀⣀⠤⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⡉⣀⣀⠜

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠶⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢳⡀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠑⠄⡀⠉⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡀⠄⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠈⠓⠤⠤⣤⣤⣀⣤⡤⠄⠄⠒⠛⢒⡸⢇⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠈⠁⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠓⠒⠒⠒⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⠄⠁⣈⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⠀⠀⠀⠀⠠⠃⡼⠁⠀⠊⠈⠀⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡰⣌⠢⠐⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠈⠳⡄⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡈⠁⠀⠀⠀⠀⠀⠀⠙⠾⣶⢤⣀⡀⠀⠀⠀⠤⢄⣀⡀⠀⠀⠉⣫⠉⠉⠁⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠒⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠔⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠓⠒⠒⠒⠒⠒⠲⡖⠚⡋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠳⡀⠀⠀⠀⠀⢱⠀⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠎⠁⠀⠀⠀⠀⠀⢀⡴⠊⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠠⠄⠀⠀⠀⠀⠀⢀⠤⠚⠉⠁⠀⠀⠆⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠀⠴⠓⠢⠔⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣻⣉⠙⠋⣻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠛⠛⠉⠀⠈⠛⠛⠫⠭⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣌⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣐⣀⠠⠴⠶⠖⠒⠒⠠⠀⠀⠀⠿⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠠⠴⠓⠚⣉⣡⣄⡀⣀⡤⣀⣀⣤⣀⣤⢈⣠⣾⣿⣿⠅
⠀⠀⠀⠀⠀⢀⠀⠒⠈⡭⢭⣚⣷⣿⣿⣿⡿⣿⣿⣿⣿⣟⣿⣿⣿⣿⢿⣿⣽⣷⢟⠕
⢀⣤⣤⣶⣿⣿⣿⣷⣦⣭⣵⣿⣻⣿⣿⡿⢿⣦⣝⠻⣿⣿⣿⠿⡿⠟⠋⢀⣚⡍⠉⠈
⠉⠉⠉⣩⡿⣻⣿⣿⣿⣿⣿⣿⣿⣎⡻⣿⣿⣽⠿⢧⢴⣴⢘⠁⠦⢚⡉⠋⠀⠁
⠀⠴⠚⣁⣴⣿⣿⣟⣻⣟⣙⡉⠉⠩⠛⣋⠡⡴⣂⣉⡦⠐⠈
⠀⣰⣾⣿⠿⠻⠍⣉⠛⣀⣷⡄⠀⠈⠗⠂⠉⠽⠏⠙⠂⠁
⠀⠀⠰⠀⠀⠊⠀⠀⠀⠉⠉⠉⠉⠒⠀⠄⠤⢠⣶⣇⣛⣳⣏⠅⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠳⠎⣿⡄⣐⣠⠴⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠷⠶⠖⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⢉⠉⠛⠿⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠛⠀⠀⠙⠻⠷⢄⡈⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⣼⣿⣟⣁⠀⠀⠀⠀⠀⠀⠙⢶⣝⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣿⢟⡿⣻⣿⡿⢿⠿⣿⣷⣿⣿⣿⣥⣤⣀⣠⣠⡴⣶⣶⣄⣹⣟⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⠶⠟⣛⠩⣫⠄⠀⠀⢈⡀⠀⠸⠾⠃⠾⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⡻⢷⣄⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠰⢶⣶⢶⣶⣶⠶⣶⠷⣯⣥⣶⣟⣒⣋⡤⣵⣦⣤⣴⡄⢀⠈⠀⠀⠚⣁⠀⠀⠀⠀⠘⠉⠟⣻⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣷⣞⠠⣀⠉⠂
⢤⣤⣀⠀⠀⠀⠠⣤⣽⣷⣯⣄⠺⣿⣿⣿⣯⣭⣭⣥⠴⠶⣶⣾⡋⠀⠀⠀⠀⢀⣤⣞⣥⢄⡾⠂⠀⠀⠀⠀⠀⠀⠋⣽⣶⠛⠹⢏⣹⡿⠿⣿⣿⡄⠀⠉⠉
⠈⠹⢿⣿⣿⣉⡉⣉⣹⣿⣿⣿⢳⣀⠻⣿⣿⠿⠿⢿⣿⣿⣿⣿⣷⡶⣦⡞⢀⣾⡿⠋⣠⠀⠀⣰⣧⠀⠀⠉⠀⢢⣧⡿⠋⠀⠀⠸⠃⢁⡼⡟⣿⣷
⠀⠀⠀⠛⢬⣅⡀⠈⠛⠛⠛⢿⣿⣿⣷⡄⢉⣲⣦⣿⣿⣿⣛⣋⣡⠾⠟⠣⣾⣿⡴⠞⣿⣤⠚⠋⠁⣀⠐⣀⣤⣾⡟⠀⠀⠀⠀⠀⠰⢚⣷⡇⣻⣿
⠀⠀⠀⠀⠀⠉⠛⠛⠒⠒⠶⠶⠾⠿⠛⠛⠻⢿⣿⣿⣿⡟⠋⠙⠉⣻⣶⣶⣿⠆⠀⢸⣯⣁⣈⢀⠾⠗⠈⠟⠋⠉⠀⠀⠀⠀⠐⢀⡰⠏⢿⡽⠛⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣧⣾⠻⢶⣶⣄⣈⣿⢫⡟⣿⡿⡟⢿⣿⣿⣿⣿⣿⣶⠿⠟⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⢃⣡⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⣤⣿⣫⣥⡥⣀⣴⠖⣠⢉⣼⠏⠻⠋⠀⠀⠀⠴⠃⠀⠀⠀⠀⠀⠀⠀⢀⡤⡴⢲⣧⣿⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⣿⣾⣿⣿⣿⣿⣟⣃⡀⠀⠀⠀⠀⠀⠄⠀⠀⣪⣤⣰⡆⡀⣐⣉⣼⣷⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣷⣾⣾⣽⣷⣤⣽⣿⣿⣿⣿⠿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⣧⣿⡛⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡸⡇⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣗⢙⣿⣿⣭⡽⠶⣤⡤⠦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠤⢄⣉⠙⠛⠿⠿⠲⠶⠦⠄
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣍⣮⣭⣤⣬⣭⣯⣴⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠚⠋⠒⠲⠆⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠈⠉⠁⠀⠁⠀⠀⣀⣤⡀⠀⢐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠓⢀⣀⣀⡀⢀⣤⡤⠤⠌⠁⠀⠰⣶⣤⣤⣤⠀⣠⠌⠁⠀⢀⣀⣀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠛⠟⠁⠀⠈⣅⠀⠉⠉⠢⡐⢦⣐⠲⠤⢝⠊⣉⣙⣥⣶⡟⢋⣩⣽⣿⣶⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣾⣧⠂⠀⠀⠦⠠⠶⠆⠂⠀⠐⠛⠂⠉⢀⡁⠈⠁⠉⠀⠉⠹⢿⣻⡵⠞⠛⠉⠉⠉⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⡐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣀⡀⡓⣀⣤⡀⠀⠀⠀⢀⣰⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠈⠛⠀⠐⠲⠟⠓⠒⠲⣶⣴⠶⠂⢒⣓⣒⣒⠒⠓⠒⠛⠛⠛⠿⠋⠭⢿⡝⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠠⠀⠀⠀⠈⠉⠉⠁⠀⠀⡀⠀⠀⠀⠀⠀⣀⣖⠀⠘⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄⣀⠉⠀⢀⡀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠒⠂⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⠛⠓⠀⠉⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣏⣿⣿⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡿⠷⠤⠶⠦⠴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠿⠿⠿⠟⠛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣀⣠⣤⣤⣶⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⣄⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡻⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢎⢿⣿⣿⣿⣇
⠀⢀⠀⠐⠶⣶⠶⠦⠤⠤⠴⠖⠒⠋⠉⠀⠴⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⢀⣀⣙⣷⣶⣮⣽⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⣿⣿⣿⣿⠂
⠐⢾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⢠⠄⣀⡀⠀⠀⠀⠀⠀⠀⣀⡤⠪⣾⣿⣿⣿⣿⡿
⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣷⣭⣓⡲⢶⣤⣤⣤⣤⣀⣀⣈⣁⣤⣯⣤⣦⣴⠾⠖⠉⠀⢈⣵⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠉⠻⢿⡻⠿⠿⠿⠿⠿⠿⠿⠷⠶⠭⠝⠛⠛⠛⠿⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠐⢽⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣫⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⣄⠀⠀⠀⠀⢀⣀⡤⠤⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⢦⡤⠴⠃⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠀⠀⠀⠁⠶⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁⠀⠀⠀⠀⠈⠁⡐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠀⠀⠀⠀⡂

⠀⠀⠀⠀⠀⠀⡠⠔⠋⠉⠉⠉⠑⠒⠒⠶⢶⡄
⠀⠀⠀⠀⢀⠎⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⣾⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⣰⠟⠉⣷⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⢠⡏⢾⡇⠘⣉⡧⠤⠴⢶⡶⣄⠈⠀⠀⠀⠀⠀⢁
⠀⡰⣣⠋⠀⡰⠚⠁⠀⠀⠀⣸⠀⠈⠀⠀⠀⠀⠀⠀⡜
⡜⢐⣩⠴⠋⠀⠀⠀⠀⢀⡤⠃⠀⠂⠀⠀⠀⠀⠀⠸⠃
⠉⠉⠀⠀⠀⠀⠀⠀⣰⠋⠀⠈⠀⠁⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⠤⣀⣀⣀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠛⠓⠤⣄⡀
⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⢀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⣀
⠀⠀⠀⠀⢸⠁⠀⠀⠀⡜⡀⠀⠃⠢⠈⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⢤⣀⡀
⠀⠀⠀⠀⢸⠀⠘⠈⠀⠁⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠓⠒⠶⠦⠤⣄⣀⠀⣀⣠⢠⣤
⠀⠀⠀⠀⢸⠄⢁⠄⠀⠘⠀⠀⠈⠀⢀⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠳⢦⣰⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣹⣿⠿⠋
⠀⠀⠀⠀⠸⡤⣙⡄⠀⡀⠂⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢳⡈⢦⡀⠀⣀⣀⠀⠀⠀⠀⠀⠉⠐⠂⢀⡄⠀⢲⡿⠋
⠀⠀⠀⠀⠀⠱⣄⠀⠄⢀⠠⠌⠃⠀⠢⡀⠀⢀⠀⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠓⢤⣉⠉⠉⠉⠀⢠⠚⢉⠀⢀⡀⠈⢰⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠐⠂⡀⠠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠒⠂⠈⠙⠛⡃⠔⠋⠀⠐⠉⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣖⠂⠁⣀⠀⠠⠐⠀⢄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⢠⣀⠂⣀⠀⢀⡠⠖⣯⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⠷⣤⣒⢀⠂⢁⠀⠂⠀⠀⢶⠀⠐⢆⠀⠀⠀⠶⣄⠀⠀⢘⠡⣄⠀⠉⣀⡨⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠿⠾⢤⣶⣖⣀⣀⠀⠀⠤⠀⠈⠀⢬⣷⣤⣬⡤⠿⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⢹⣿⢿⣶⡶⢤⡴⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣼⠏⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⣤⣤⡤⢔⣻⣿⣱⣟⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⣽⣾⣿⣯⣷⣾⣿⣿⡿⢷⣽⠇⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣥⣾⣿⣿⣯⣽⣿⡿⠟⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠟⠛⠛⠷⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⣠⣤⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠈⠓⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠉⣿⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣬⣿⣦⡀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⡶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⢿⣤⠶⠾⠛⠋⠉⠉⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⢀⣀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⣠⠖⠋⠉⠁⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠈⣳⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀
⠀⢀⠀⠀⠀⠀⣀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣠⣾⣆⣀⣀⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠒⢤⡀
⠀⠈⠛⠒⠚⠛⠉⠛⠚⢿⣄⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠳⡄⠀⠀⠀⠙⡌⢆
⠀⠀⠤⣤⣤⣤⡴⠖⠶⠶⠻⣦⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣴⡋⠀⠀⣸⠀⠀⠀⠀⣱⠈
⠀⠀⠀⠀⠀⠀⠒⠒⠚⠉⠙⠾⣿⣷⠶⠛⠻⢦⣤⣤⣤⠤⠲⢦⣤⣤⣤⣤⡴⠞⠛⠛⠛⠛⠉⢀⡤⠞⠁⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠔⠚⠉⠀⠀⠀⠀⢀⡰⠋⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠔⠒⠚⠉⠁⠀⣀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠒⠒⠂⠉⠉⠁⠀⠀⠀⠀⣀⣠⠤⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣿⣷⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣻⣿⣯⠻
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣅⠑⠆
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠈⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣼⣿⣿⣭⣟⣩⣷⣶⣆
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⠀⢀⣠⣤⣶⣶⣿⠿⠛⠛⠉⢉⢉⣉⣭⣽⣽⣿⣿⣿⣿⣿⣿⣿⡌⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠟⠋⣁⣀⣀⣀⣀⣤⣆⣨⣤⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢾⣿⣛⣉⣤⠤⠤⠤⣭⣿⣿⣿⣿⣿⣿⠿⣿⣛⣩⣥⣴⣾⡟⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣴⣿⣿⡿⣿⡟⣽⣿⣶⣦⣤⣤⣯⣿⣥⣤⣀⣱⡈⢻⠿⠛⠉⠀⠀⣼⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣈⣭⣽⣶⣿⣿⢁⣿⡉⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠋⠀⠀⢀⣀⣤⣶⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⣿⣸⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⡿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠉⠻⠿⣿⣦⣄⡀⠀⠀⠀⢀⣠⡶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣸⡄⣄⢠⣥⡀⠉⠉⠛⣿⠟⣿⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣜⡓⠿⢁⣿⣸⣿⣵⡆⣇⣆⡭⢀⠏⠸⠀⡆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣇⣿⣿⣿⣾⣿⣽⡿⠿⠳⢿⣿⡿⠟⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠚⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠷⠿⢿⣿⣷⣶⣶⣦⣶⣾⣯⣿⣷⣶⣝⠷⣦⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠚⠛⠉⠉⠛⠛⠋⠉⠹⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠒⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⡀⠀⠀⣠⠀⠀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠘⢡⡀⠀⠉⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⡠⠒⣋⣡⣤⣴⡮⠥⣄⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠳⠚⠋⠉⠀⠀⠀⣠⠈⠁⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢦⣀⠖⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠹⠀⢸⣀⡄
⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠘⢢⡀⠀⠀⠀⢀⣀⣤⠤⠤⠒⠒⠒⠒⠒⠀⠀⢀⡴⠦⢴⡦⠜⠁⠀⠀⢀⠞⢁⡇
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⠀⡰⠛⢉⡇⠀⠀⠀⠁⣠⡎
⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠤⢤⢀⡠⠎⠀⠀⠀⠀⠤⢾
⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠀⠀⠐⠒⢋⡟⠀⠀⠀⠀⠀⢠⡴⠃
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢤⠀⠀⠀⠀⠀⢀⣀⡴⠂⠀⠀⣀⡴⠀⢀⠠⠖⡟⠀⠀⠀⠀⠀⣰⠊
⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠈⠓⠀⠀⠀⠀⢀⣠⠞⠀⠈⠉⣡⠀⠀⠤⢴⠏⠀⠀⠀⠀⡤⠚⠁
⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠬⠭⢤⣤⡤⠾⠭⠤⠤⠴⠒⠁⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠦⠤⠤⡤⠂⡤⢀⣀⡀⠀⠀⢀⣀⣀⣠⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠇⢰⠇⠀⠀⢹⢩⠏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠊⠉⠀⢠⠞⠀⠀⠀⡎⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠒⠒⠚⠛⢁⡠⠴⠒⠉⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠮⠤⡤⠤⠴⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢰⡷⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢰⡛⠛⠉⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⠤⣼⠃⠀⠀⠀⠀⠀⠀⣞⠁⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠤⠤⠴⠖⠋⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢀⡴⠖⠛⠛⠲⠶⠤⠤⠤⠶⢦⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠤⡀⢀⣀⣼⠀⠀⠀⡾⠀⠀⠀⠐⠗⠀⡀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⣀⣀⣀⣠⠾⠁⠀⠀⣰⠃⠀⠀⠀⣀⣀⠘⠜
⠀⠀⠀⠀⠈⠒⠁⣀⡀⠀⠀⠹⣄⠀⠀⠀⠈⠳⠦⣤⣤⣤⡤⠶⠛⠁⠀⠀⠀⡰⠃⠀⠀⠀⠈⠧⠼
⠀⠀⠀⠀⠀⠀⠸⣄⠝⠀⡠⠄⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠑⢒⠤⠐⠒⠒⠒⠠⡄
⠀⠀⠀⠀⠀⠀⠠⠒⠒⠚⠢⠄⠀⠀⠉⠓⠶⠤⣤⣄⣀⣀⣤⣤⠴⠞⠋



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⠴⠖⠛⠻⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠿⠋⣀⡤⠤⢤⣄⠈⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⡾⡆⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢧⡀⠀⠘⠷⠃⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⢠⣤⣀⣀⣀⣠⡖⠋⢁⣄⠀⠀⠳⢤⣀⣀⡀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠈⠧⣄⡈⠉⠉⠀⠀⠘⠋⠀⠀⠀⠀⢀⣠⠽⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⣧
⠀⠀⠀⠀⠀⠀⠀⣹⠛⠓⠒⠶⠤⣤⣤⣤⡶⣾⠉⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣸⣿⣼⠹
⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠖⠚⠋⠉⠉⠁⢀⡟⠀⠀⠀⢾⠀⠀⣀⣀⣠⣤⣤⡴⠶⠾⣿⣿⡿⠋⣿⠃⠀⣇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⡼⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠉⠩⠴⠃⠁⠀⢀⡟⣿⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠈⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠑⠀⣀⠄⣀⠤⠒⠋⠉⠁⠀⠀⠀⠉⣽⣟⣂⠛⠻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠭⠋⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⡀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⣰⠃⣸⠃
⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⢧⡀⠰⣄⡀⠙⠶⣤⣴⣄⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋⠁⢀⣠⠞⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⠈⠻⣦⣌⡙⠓⠶⣤⣄⣈⡙⠛⠲⠦⢤⣤⣤⣴⠶⠛⠋⠁⢀⣠⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠦⠍⠙⠛⠓⠒⠒⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠒⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠈⠀⠀⠀⠉⠓⢄
⠀⠀⠀⠀⠀⠀⠀⡠⠂⠕⡀⠀⠚⠀⠀⠀⠈⡇
⠀⠀⠀⢀⠤⠒⣋⣀⣤⣆⣁⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠘⠖⠛⠉⠁⠀⢀⠌⠁⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⢤⠔⢦
⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢸⡤⡄
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠱⢄⣀⡠⠤⠖⠒⠊⠉⠉⠉⠀⠀⠀⢀⠜⠓⣺⣷⡅⠀⠀⠠⠋⡰⠁
⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⣀⠈⢁⡴⠁⠀⠀⠀⣺⠃
⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⠀⠬⠽⢷⠉⠀⠀⠀⠀⣉⠝
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠀⠀⠀⠀⣀⡤⠀⠉⢁⡠⠀⠀⡠⢴⠃⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠘⣄⠘⠂⠀⠀⠀⢈⡡⠂⠀⠈⣩⠄⠠⠤⡶⠁⠀⠀⢀⠴⠊
⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠙⠒⠠⠤⠀⠷⠤⠤⠾⠏⠠⠤⠒⠊⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠠⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⢲⠈⡗⠒⠠⣤⢤⠤⠤⠔⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠃⣠⠃⠀⠀⡇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠤⠤⠤⠔⢁⣠⠤⠊⢘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣁⣀⡤⠤⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣶⣦⣀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⢿⣿⣿⣿⣷⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢴⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠉⠀⠀⠀⠀⠈⠉⢑⡿⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⡀⠴⣶⣤⣯⣙⣛⠿⢿⣦⡄⣸⣿⣶⣲⣾⣧⣤⣴⣤⣄⡀⣿⣿⠁⠀⠀⠀⠀⠀⡰⠒⠻⠧⣄⣀⣑⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⣉⠉⣻⣿⣿⣿⣷⣮⣿⣿⡛⠛⠉⠉⠉⠛⠓⠾⢼⣿⣿⡄⠀⠀⢰⣶⣶⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠁⢚⣿⣿⣿⣿⣷⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠈⠳⢭⣳⡆⢾⣿⣿⣇
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⢿⣿⡇⠀⢸⠀⠉⠻⠿⠿⠿⠿⣿⣿⣿⣯⣴⣄⠀⠀⠀⠀⠀⠀⢻⣍⡈⣻⡈⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⠀⠘⣶⡀⠀⠀⠀⠀⠀⠀⠈⠛⠃⢿⣷⣤⣀⣀⠀⠀⢀⣾⣿⣷⣿⣿⣿⣿⡄
⠀⠀⠈⠙⠓⠂⠲⠄⠀⠤⠄⣀⣀⡀⠀⠀⠀⠑⠀⠈⠳⣦⡀⠀⠀⠀⠀⠈⠳⠀⠘⣯⡙⣽⣿⣿⣳⣾⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠛⢻⠶⢤⣤⣄⣀⣈⣉⣠⣤⣤⣶⠿⠿⠿⠿⠿⠿⠿⠟⠻⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠲⠦⠄⠀⠀⠀⠀⠀⠌⠉⠉⢉⠉⠉⠀⠀⠀⠂⠀⡀⠠⠁⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠄⠉⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠈⡀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡒⠀⢀⣀⣀⡀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠛⠛⠛⢿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠋⢠⣤⡄⠀⠀⠀⠸⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢰⣞⡇⠀⠀⠉⠀⠀⠀⠀⠀⠤⣿⣿⡀
⠀⠀⠀⠀⠀⣀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⡇
⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠉⠛⠉⠉⠀⠀⠀⠀⠙⠪⣧⠀⠀⠀⠀⠀⠀⠀⢼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⣸⣿⡿⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⡶⠶⠶⠶⠶⢶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⢰⣿⡿⣽⢁⠀⣀⣠⣴⣶⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⢀⣾⣿⣿⣯⡷⠟⠛⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣿⠀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠸⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⢋⣼⣿⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⠾⠿⠛⣁⣴⣿⢿⡿⠀⠀⠀⠀⠀⠀⠈⢙⢶⣤⣄
⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠚⠉⢀⣠⣴⣾⠟⢉⣵⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠷⣿⣿⣿
⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠲⠟⠛⠋⣁⣤⣶⠿⢻⣿⠀⠀⠀⠀⠀⠀⢀⣤⡴⢶⢿⣿⣤
⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⢀⣾⣿⣿⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⠿⠿⠋⣀⣴⣿⡿⠀⠀⠀⠀⠀⢀⣤⣾⣿⠿⠟⠉⠉
⠀⠀⠀⡀⣿⣿⡀⠀⠀⠀⣾⣿⣿⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⣀⣠⣶⠿⠛⣡⡿⠁⠀⠀⣠⣴⡿⢛⠉⠉
⠀⠀⠀⠀⢸⣿⣿⣿⠈⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣶⣾⠟⠋⠉⠀⣀⠔⠋⠀⢀⣠⣾⠟⠉⠈
⠀⠀⠀⠀⠰⡻⣿⣿⣷⣥⣿⣿⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⣁⣰⣶⡷⠟⠉
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⣶⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⢉⣠⣴⣾⣿⣷⡾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣷⣤⣄⣀⣀⡀⠐⠖⠛⣋⣉⣠⣤⣶⣿⠿⠿⠟⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠒⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠳⡀⠀⠿⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⡤
⠐⠥⢀⣀⣀⣀⣀⣀⠀⠠⠤⠤⢔⣇
⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠉⠁⠈⠙⠁⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠉⠓⠒⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢄⡀⠀⠀⠀⠀⠀⡠⢲⠀⠀⡠⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢀⠀⠀⠐⠀⠋⠀⠀⠀⠀⠤⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⢄⡠⠀⠀⠰⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠙⢦⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡉⠂⠀⠀⠀⠀⠀⠑⠦⣦⣄⡀⠀⠀⠀⠀⢀⣀⠀⠀⠉⢻⡒⠒⠁⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠒⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⡍⠉⠉⠉⠉⢫⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠈⠀⠀⠀⠀⡨⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣉⠀⠀⠀⠀⠀⠀⡠⠔⠛⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡤⠬⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠶⠀⠀⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠉⠀⠀⢀⡀⢀⡄⠀⠀⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠾⠛⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⣴⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣟⠙⠛⠋⠛⢉⠈⠋⡙⠋⣹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠿⢣⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⢦⣠⣤⣤⣤⣤⣤⣤⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⢈⡿⠃⠊⠙⣷⠆⠲⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⢀⡟⠀⠀⢀⡀⠀⢀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠀⠀⠀⠀⠀⣸⡃⠀⠀⠀⠀⠀⠀⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠛⣆⠀⠀⠀⠄⠹⠒⠀⠰⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣤⣴⡄⣄⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣀⣠⢀⠂⠀⢩⣄⠐⡿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣁⠙⢶⡈⠀⠙⢾⣷⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢘⠀⢀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠠⠀⣀⣀⣈⠁⢩⢘⠡⢦⢀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠎⠈⠀⠃⠈⠀⠀⠀⠨⠿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡄⠀⠀⣀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⡠⢰⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠩⢡⡜⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠛⢁⣼⠻⣛⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣍⣿⣍⠀⠀⢀⡀⠀⠀⠀⠀⠀⠤⠀⠈⠀⠊⠉⡀⢈⠄⣁⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣣⣌⣧⣤⠀⠀⠀⢠⠼⠀⠀⠀⠠⢐⡛⢃⣭⣾⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣄⣶⣦⣽⣾⣿⣖⣶⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠈⠉⠉⠉⠉⢹⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣄⠀⠀⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⢧⡁⠀⠀⠀⠀⢀⣴⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣍⣡⣿⣿⠛⢁⣼⣿⣷⣆⣀⣠⣴⡿⣿⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⣽⣿⡷⣾⣿⣿⡿⠿⣻⣿⣿⡿⢿⣿⣤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠛⢿⣶⣯⣿⡿⢁⣤⣿⡿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠙⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣰⠉⠞⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⡔⠓⣆⠀⠀⡏⠀⢠⠋⠉⢦⠀⠀⣠⠞⠳⡄⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⢸⠁⠀⠘⣄⠀⡇⠀⢸⠀⠀⠘⠀⠀⠃⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠈⡇⠀⠀⠈⠲⣽⣀⡠⠤⢄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠈⠳⣀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⣀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣰⠶⣴⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡌⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⠦⢄⣀⣀⣀⣠⠤⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠄⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡁⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⠀⠀⠀⠀⠀⠀⢀⡠⠃⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠊⠉⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠦⠤⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠤⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠁⠉⢀⠁⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⡎⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠤⠤⠀⠤⠤⠜⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠲⠤⢤⠴⠖⠡⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸⡤⠀⡠⢄⠀⠀⢁⡂⢀⡀⠀⠀⣀⠀⠊⠀⢀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⢤⠠⠀⠀⠀⠀⡄⠀⢬⠖⠀⣀⢀⠤⠤⠌⠍⠀⠈⢳⡆⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⠔⠉
⠀⠀⠀⠀⠀⠰⠐⠘⠐⠀⠀⡈⠀⢰⡀⡈⠉⠅⠀⠐⡆⠈⠃⠐⠐⠀⠀⢠⠆⠀⠀⠈⢙⣶⡦⠶⢤⡶⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠁⠲⠖⠲⠚⠄⠀⠀⠉⢠⣤⣤⠔⠋⠀⠀⠀⠑⠤⠴⢊⠀⠀⠀⠀⠀⠘⣌⣄⣀⠈⠻⢦⣤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣠⢄⡄⢀⡀
⠀⠀⠀⠀⠀⢀⠀⣎⠛⢟⣻⣦⣄⡀⠀⠀⠀⠀⠀⠀⣬⡻⣵⣺⡭⣞⣻⡥⢶⣶⣄
⠀⠀⠀⠈⠛⠉⠉⠛⠛⠛⠿⠿⣯⣭⣳⣶⢤⣴⣾⣧⣿⣿⣾⡪⠯⣕⣲⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠒⠲⠂⠀⠐⣶⣄⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣭⣯⣭⣭⣙⣛⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢿⣻⣽⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠇

⠀⠀⠀⠀⠀⠀⡠⠒⠉⠉⠙⠲⢄
⠀⠀⠀⠀⣀⠜⠀⢠⣦⠀⠀⠀⠀⢳⡀
⢖⡒⠋⠉⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠉⠉⠉⠉⠈⠓⠲⠤⢄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⡏
⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⢸⡇⠀⠀⠀⣀⣀⣠⡤⠴⠖⠒⠚⠛⠛⠛⠛⠛⠒⠦⢤⣀
⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠓⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀
⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠒⢲⡆
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠠⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⠴⠚⠋⠁⣀⡴⠋⣗
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠒⠦⠤⠽⠶⠤⣄⣀⣉⠓⠲⢦⣤⠤⠤⠖⠃⢀⣀⡤⠴⠚⢁⣠⠞
⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠈⠉⠉⢉⡀⠤⠴⠒⠉⢀⣠⠞
⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠙⠲⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⢛⡗⢲⠶⡤⠤⠤⠤⠤⠶⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡸⠸⣄⠈⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡿⢟⡀⡴⠒⠚⣡⠇⢣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠛⣕⣚⣭⣡⢠⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣩⠞⢿⡼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠾⠟⠛⠛⠷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⣴⡆⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠻⠃⠀⠀⢀⡴⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠉⠓⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⢸⡇⠀⢀⣀⣠⣤⣤⡶⠶⠶⠶⠶⠿⣷⠄⠀⠀⠀⠀⠀⠘⣿⡿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠘⠷⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⣀⣠⠤⠤⠶⠾⣷⠀⠀⠀⠀⠀⠀⠐⣇⡀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠚⠉⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⣠⡀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⠠⣀
⠀⠠⣤⣀⣀⣤⢦⣄⣿⡄⠀⠀⠀⠀⠀⠈⠛⠶⠞⠛⠳⢶⣶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠀⠀⠀⠙⢢⠀⡀
⠀⠀⠀⠉⠀⠀⢀⣀⣈⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠑⠀⠀⠀⠀⢣⠹
⠀⠀⠉⠛⠛⠛⣉⣀⡤⠤⣬⣳⣦⣀⣠⣦⣀⡀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣀⣤⠶⣤⣴⡿⠗⠀⣀⠔⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠉⠙⠛⠋⠉⠀⠉⠛⠛⠛⠋⠉⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⠀⠀⡴⠃⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠤⠀⠒⠒⠉⠁⠀⠀⠀⠀⠀⣀⡴⠊⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠒⠋⠁⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⠤⠤⠤⠒⠒⠂⠉⠉⠀⠀⠀⢀⣀⠤⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠣⣤⡀⠀⠈⠿⠿⠟⠋⣁⡀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⡿⠁⠆⠀⠀⠀⠀⠐⢫⣶⡀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡤⠀⢀⠖⠛⠒⢶⡆⠀⠘⠿⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣠⣾⣋⣄⣐⠨⢷⠀⠙⣆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⠀⠻⣦⣀⠀⢈⣁⣸⠇⠀⠘⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⣄⣈⣉⣉⣉⠉⠀⢀⡀⣀⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠛⠛⠋⠉⠉⠙⠋⠉⠈⠙⠿⢿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠏⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⢹⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⠏⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⢿⣟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⡺⠏⠁⠀⠀⠀⢸⡏⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣨⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣴⢿⣧⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠈⠛⡷⣶⠦⣦⣦⣤⣴⡶⠾⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢴⠃⠸⣦⠀⠀⠀⠀⢠⡼⠃⠘⡄⢀
⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣖⣊⣁⣐⡋⠚⢙⣂⣑⣤⣤⣴⣀⣂⣉⠃⢹⣀⣀⣁⣦⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠐⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⢲⣄⣀⡀⢰⣆⢰⢰⢀⣀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠓⠛⠃⠚⠙⠛⠚⠚⠚⢳⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠛⠛⠛⠛⠛⠻⠶⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠈⠛⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠷⠶⠶⠶⠶⠦⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠺⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠷⣄⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢀⡴⠞⠛⠛⠻⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣴⠏⠀⠀⢴⣶⣤⡀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⣠⣤⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢠⡟⠀⣀⠀⢀⣿⣿⣿⡄⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣰⣿⣿⡁⠀⢀⠀⢸⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠸⣇⠀⢻⣿⣿⣿⣿⣿⠁⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⣿⣿⣾⣿⠃⢸⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠻⣄⠀⠛⠿⠿⠟⠁⢀⡼⠃⠀⢀⣀⣤⣄⣀⡀⠀⠈⢷⡀⠘⢿⣿⣿⡿⠋⠀⣼⠇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠙⠷⣤⣄⣀⣤⡴⠟⢁⣤⠞⠋⠁⠀⠀⠉⠙⠷⣤⡈⠻⣦⣀⡀⠀⣀⣠⡾⠋⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠉⠙⠛⠉⠁⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⣰⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⡇⠀⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠙⢯⣝⠶⣤⣄⣀⣀⣀⣀⣤⣤⠶⣋⡵⠋⠀⠀⠀⠀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠙⠳⣤⣌⣉⣉⣉⣉⣠⣴⠞⠉⠀⠀⠀⢀⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠿⠶⢤⣤⣄⣈⣉⣉⣉⣉⣁⣀⣀⣤⣤⡴⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠶⠛⠛⠛⠛⠙⣿⠏⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⣷⠞⠛⠛⠳⠶⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀
⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⣰⠏⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠹⣆
⢠⡟⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⢻
⣾⠁⠀⠀⠀⠀⠀⢀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠘
⣿⠀⠀⠀⣀⣤⡶⠛⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠛⢦⣄⡀
⠙⠻⠶⠛⠉⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠈⠙⠳⠶⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⢦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣸⠏⠉⠉⠉⠉⠉⠉⠙⣯⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠇⠸⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣛⣥⣴⡄⣶⢦⣝⣦⡀⠀⠀⠀⠀⠀⣴⣟⣥⣶⢠⣦⣌⡻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⢿⣤⣼⡁⣿⣀⣽⣷⣿⠀⠀⠀⠀⣾⣿⣏⣀⣿⠈⣧⣬⡿⣾⡷

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠿⠿⠿⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠉⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠸⣿⡿⠀⠀⠀⢀⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠙⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⡧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣈⣿⣦⡀⠀⠀⠀⠀⠀⠀⠸⣷⣄⣀⣀⣤⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⢰⣇⣀⣠⣤⡶⠶⠿⠛⠛⠛⠛⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠹⣯⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⣀⣤⠤⠶⠖⠒⢺⣇⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠚⠉⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⡄⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠂⠤⣀
⠀⠠⣄⣀⣀⣀⣤⣤⣘⣷⡀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠾⠛⠷⣦⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠙⢢⡀⡀
⠀⠀⠈⠉⠉⠁⠀⠈⣉⠉⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠉⢢⠀⠀⠀⠀⢱⠘
⠀⠀⠐⠲⠶⠶⠞⠋⠉⣉⣉⣙⢷⣄⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣠⣴⣿⠅⠀⢀⡼⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠙⠛⠿⠟⠛⠉⠙⠻⠶⠶⠶⠖⠋⠛⠶⠶⠶⠶⠶⠛⠉⠉⠉⠉⠉⢀⣠⠔⠋⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠖⠚⠉⠀⠀⠀⠀⠀⢀⡴⠋⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠚⠉⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠴⠒⠚⠉⠉⠀⠀⣀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠒⠒⠒⠋⠉⠉⠀⠀⠀⠀⠀⢀⣀⡠⠤⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⢄⣸⢃⡌⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠛⠂⠉⠀⠁⠀⠀⠈⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠖⠀⠀⠀⠀⡴⠖⠶⢤⡀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⠓⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠢⢴⣾⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⣠⠞⠉⠈⠉⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣤⡀⠀⠀⠀⢠⡏⠀⠀⣀⣀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⣠⣄⣀⣠⠶⠛⠁⠀⠀⠀⠹⡄⠀⠀⢸⡇⠀⣾⣻⣿⣷⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢧⡀⠙⠦⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠈⠉⠺⢿⣿⣿⣯⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠙⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠙⢲⣤⣀⣀⠀⢀⣀⡤⠘⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣢⠁⣸⡭⠟⠋⠉⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠘⡙⠚⣉⡠⠴⠚⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠛⠊
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠈⠳⢦⣄⡀⠀⠀⠀⠀⠀⣀⣠⣶⡴⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠉⠉⠛⠛⠛⠛⠋⠉⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠽⢦⣄⣀⡀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠤⠄⠀⢦⣀⡠⠖⢋⡡⠚⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠁⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⠀⠀⠀⢀⡴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⡴⠋⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢎⠀⠀⠀⠀⠈⢀⠜⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠴⠚⠁⠀⡜⠀⠀⠀⠀⡰⠁⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠊⠀⠀⠀⠀⠊⠀⢀⠏
⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⠄⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠐⢊⡽⠃⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⢠⡏⠀⠀⠀⠀⣀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⡀⠀⠀⢀⣀⣀⡤⠴⠚⠉⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠈⠳⢄⣀⡀⠀⠀⠙⠓⠒⠛⠛⠦⣄⣠⡤⠖⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠴⠒⠛⠲⣤⣀⣀⣀⣠⡤⠖⠛⠲⠦⠤⠴⠔⠋⠉⠁⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠊⠓⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⠤⠤⢄⣀⠀⠠⠄⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠈⠁⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠐⠦⣀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⣀⣤⠐⠒⠲⠀⠒⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠁⠀⠀⠀⠉⠀⠒⠂⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⣀⠠⠐⠒⠤⠄⠀⠤⠄⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠁⠀⠀⠀⠁⠀⠈⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢠⣷⠀⢀⠄⠀⢤⡀⠀⢀⣶⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡠⠃⠀⠀⠀⠀⢄⠈⠉⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠁⣀⠤⠐⠐⠂⠄⣀⠈⢀⡀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠈⠻⢥⣀⠀⠀⠐⠀⠀⢠⣬⠝⠁⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠉⠪⠥⠦⠤⠒⠉⠀⠀⢀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠲⠶⠦⠤⠤⠤⠴⠶⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢃⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⣁⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠙⣖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⠂⠀⠀⠈⠑⠦⣤⣀⡀⢀⣀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⡰⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠃⢀⣏⣀⣀⣀⣀⡠⠤⠖⠞⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏⠀⡌⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠇⠂⠆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣖⣈⠁⠀⠀⠈⠉⢆⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⡠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠒⠒⠒⠾⠂⠀⠀⠀⠀⠁⠈⠉⠉⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⢿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣐⢶⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣴⠟⢹⡇⠀⠀⠀⢀⣠⣤⡶⠶⠿⠿⠿⠷⣽⣷⡝⢿⡻⢦⣄
⠀⠀⠀⠀⠀⠀⢸⠇⠀⣼⣷⡀⢀⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡧
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠟⠈⣷⡏⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⢠⣾⣋⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠳⠉⢧⠀⠀⡿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⢻⣿⣦⡀⠀⢀⠀⠀⢸⠆⠀⠷⢌⡉⠉⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠘⣷⠉⠛⠷⠟⠀⠀⣿⠀⠀⠀⠀⠉⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣧⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⡴⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⣀⣀⣠⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⢿⡶⠾⠛⠛⠛⠛⠛⠛⠛⠛⢷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣶⢶⣄⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢡⡾⠛⠁⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢲⣦⠖⠋⠉⢹⣦⣤⣄⡀⠀⠀⠀⠀⣠⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠋⠉⠀⢸⡟⠀⠀⠀⠀⠉⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣠⠔⢒⣩⣿⣄⣀⣀⣀⣿⣦⣠⣀⣤⣤⣤⣤⣀⣀⣀⣀⣠⣴⡟⠁⠀⠀⠀⠀⣀⣴⣿⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠰⠚⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐


⠀⠀⡄⡄⡄⢀⢶⡀⢠⢦⠀⣰⡄⠀⡄⠀⠠⣆⠀⣄⡄⢀⣦⠀⠀⠀⢰⢄⠀⢰⢦⠀⡴⡄⠀⡆⠀⢠⠀⠀⡆⠀⢠⢦
⠀⠀⢇⣇⡇⠸⣼⠃⢸⡸⠀⢿⠇⠀⡇⠀⠎⣿⠀⡟⡇⢸⡿⠀⠀⠀⢸⡼⠀⢸⡼⠀⢇⠇⠀⣷⠃⢸⠀⠀⡇⠀⠘⣤
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣵⣭⣴⣭⣿⣵⣯⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⢶⡶⢛⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⢠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠞⠑⠟⠛⠋⠉⠉⠉⠛⠛⠶⣤⣀⠀⠀⣿⡀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣰⠟⣧⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡶⢦⣄⠀⠀⠀⢀⣼⠏⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣾⣿⡄⠀⢠⠞⡡⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡙⠛⢛⣡⡇⠀⣿⠀⠀⠀⠀⢀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠞⠋⠀⠀⠀⢿⡀⠀⢷⡶⠟⢋⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢶⣶⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠶⠶⢶⣶⠂⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠶⠿⣶⣶⣦⣄⣸⡿⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⢉⡿⠃⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⢀⣀⡀⠀⣠⣤⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠘⣿⡉⠛⢿⡌⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠘⢷⡀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣶⣄⠀⠀⠀⠀⢀⣤⣤⣾⠉⠙⠲⢤⡖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⡇
⠀⠀⠀⠀⠀⠀⠻⣇⠉⠀⠀⠀⠀⢿⡀⠀⠉⠑⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⣼⣇
⠀⠀⠀⠀⠀⠀⠶⣶⣾⣷⣤⣀⣀⣀⣀⣈⣿⣶⣤⣤⣤⣤⣴⣤⡤⠤⠤⠴⠿⣧⣤⣤⣴⣿⣦⣍⡲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠈⠼⣀⣄⠀⠀⠈⠐⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢰⡓⠀⠀⡄⢐
⠰⡶⠇⠀⠧⣄⢜⡆⠉⠰⡃⢰⣦⡶⠀⠀⠀⠀⣀⠠⣀⠄⢄⣀⠄⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⠛⢀⠜⢻⠂⠀⢰⣀⣀⡀⡘⠳⡴⠾⠊⠱⢷
⢾⡓⠀⠀⠐⣻⡾⠁⠀⠈⢇⢀⣿⡠⠒⠚⠒⠀⠁⠀⠀⠀⠰⠀⠰⠃⠀⣁⣀⣀⢀⣀⡀⣀⣀⣈⠀⠠⡀⠀⠀⣤⠀⠹⠀⢸⣄⡔⠋⠀⠀⠈⢛⡃⢻⠇⢀⠀⢸
⣐⣿⡀⡀⣸⠓⣧⠀⠀⠀⣼⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣶⠁⢨⣭⣩⣭⣉⣭⣭⣭⡅⢉⣾⠀⠀⠀⣿⠀⠀⠀⢸⣯⣥⠀⠀⠀⠈⠹⡝⢻⠀⠀⠀⢸
⣷⠀⠙⡍⠀⠀⡇⠀⠀⠀⢸⣀⡀⠂⢠⢀⠆⠄⠲⠀⠀⠂⠀⠀⣶⡾⢷⣤⣄⣲⣗⣲⣛⣂⣤⣴⡾⢿⣶⣀⡤⣿⠀⠀⠀⢸⣿⣖⣇⡠⢀⣀⣘⣪⣺⠀⠀⠀⢸
⣿⠀⢀⡴⣆⠀⢃⢸⣾⡇⠠⠀⠈⡇⢸⠠⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠛⠉⠙⠛⠛⠙⠛⠉⠀⠀⠂⠀⠐⠈⡀⠀⠀⣸⢿⣿⠟⢯⣿⢿⣉⣿⣇
⡦⢀⣾⠁⢸⣄⠈⠛⠛⠛⠊⠛⠋⠱⠬⠦⠇⠀⠐⢬⠖⠂⠤⠄⢠⠤⠀⠀⠀⠀⢀⠀⠀⠀⠈⢹⠥⠠⠖⠊⠑⠲⣍⢓⣿⢁⣷⣧⣠⣀⣿⣾⠿⣿⣿⣦⣤⣴⣾
⠀⣾⡃⠀⠀⢻⡆⠀⠀⡠⠖⠲⢄⠀⣴⠖⠀⠶⡶⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠥⡞⠀⠀⠀⠀⠀⠀⠈⣮⠀⣿⠁⣿⣿⣿⣿⠿⡿⠿⢿⣿⣿⣿⣿
⢠⡿⠁⠀⠀⠙⣷⡀⠀⡁⠄⠠⢈⡆⢊⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠒⠒⠒⠂⠂⠀⢁⠃⢱⠀⡀⠀⣠⡄⢀⡼⡁⡟⠀⠻⣿⣿⡿⣿⣶⣷⣤⣼⣿⣳⣾⡿
⠀⠉⠓⠂⠐⠛⠁⠀⠂⠀⠀⠀⠀⡈⠄⡇⠙⠀⠀⠀⠀⠀⡅⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⣘⣖⠳⠞⠉⠓⠋⠄⠌⣇⠀⠀⠀⠈⠑⢿⣿⣿⣿⣿⣿⣻⣻⣷
⡀⠠⡞⠁⡁⠐⢰⣈⡄⡄⠀⠀⠀⣱⡄⠇⠀⠀⠀⡆⠀⠈⢀⠀⠀⢀⠖⠒⠒⠒⠀⢰⢁⡴⠋⠉⠉⠉⠉⠉⠙⠋⠉⠙⢹⡆⢀⡀⠀⠀⢸⣯⣿⣿⡉⠙⢿⣿⣧
⠃⣴⠣⣴⢓⣏⣘⢃⡁⠼⡄⢀⠀⠁⠰⡘⠀⡆⠀⣥⣀⣀⠄⠐⠀⢸⠀⠀⠀⠀⠠⠘⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⣸⣳⣼⣥⣤⣶⣾⣿⣿⣿⣿⣶⣿⣿⣽
⠀⢸⡏⣿⢭⡃⠨⠁⠬⡳⠛⠓⠚⢦⣤⡏⢉⣿⣿⣷⣉⠡⣤⠃⡈⢤⡄⠀⠀⠀⢤⣄⡏⠀⠀⣠⣤⣤⠀⠀⡀⠀⢸⣿⣷⣏⠫⣿⣻⣿⣿⣳⢛⡿⠛⠻⠿⠛⠋
⠀⢈⣓⠻⣚⡑⠀⠀⣀⣠⡆⠴⢀⠀⢸⣿⣾⣿⣿⣿⡹⠷⣤⣴⣿⡆⠀⠀⠀⠀⠄⡈⢧⠀⣴⠁⠀⣾⡀⢰⣇⠀⢸⢚⣼⣿⣷⡟⠿⠶⠟⣳⣿⣷⣀⣀⣴⣦⣤
⠀⠾⠉⠉⠁⢿⠄⠀⠄⠦⠷⢞⢀⠆⠀⠘⣿⣿⡿⠃⠀⠆⢸⢿⣿⠀⠀⢀⠀⠀⢰⠃⠈⠒⠚⠃⠀⢻⣷⣶⣿⢓⣶⣿⣿⣿⣿⠿⠋⡤⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⠀⠴⠀⡎⠁⠀⣄⢸⠤⠚⠉⠈⠀⠀⠄⠽⠿⠤⠀⠀⠀⡤⠇⢠⡐⠼⠐⡂⠀⠀⠀⠐⠂⠀⠐⠺⣿⣿⡉⠁⠀⠀⠁⠀⠀⠀⠀⢠⣟⣿⣿⣿⡋⠀⠤⣈⣽
⠀⣼⠀⠀⠀⣮⠈⡯⠈⠀⠂⠀⠀⠀⡦⠀⠀⠀⠀⠀⠀⢀⣾⣃⠗⢈⣉⠑⠆⠘⣆⠀⠀⠀⠀⣀⠀⠀⣿⣭⢧⠀⠀⣀⣀⣀⠀⠀⣠⣿⠋⠀⠉⠉⠉⠀⠢⠀⠙
⢀⠟⠀⠀⠀⠫⡀⠀⠁⠈⠉⠙⠳⢦⠈⠀⣠⠶⢶⠦⠀⠊⢸⣽⡄⢤⣥⠀⣠⠀⠈⠁⠀⠋⠉⠙⡄⢀⠹⣿⠃⠀⣼⣽⣿⣿⣧⠀⣿⣿⣿⠃
⠈⣆⡀⠀⢀⣠⠋⠳⠄⠀⡀⠀⠀⠀⡇⢂⢁⢀⡰⠈⠄⡂⠸⠋⢧⣘⢛⣃⠂⠀⠀⠀⣀⠀⠀⢠⢁⡎⡆⢻⡄⣆⢻⣼⣿⣼⣿⠀⣻⣿⣿⣿⣿⠷⠀⠀⠀⢀⣰
⠃⡈⠓⠓⠋⠁⠀⠐⠒⠛⠁⠒⠒⠉⠉⠋⠋⠀⠀⠀⠉⠃⠀⠀⠀⠑⠛⠁⠀⠀⠈⠛⠉⠀⠀⠈⠃⣿⣿⣟⡛⢻⢿⢻⣿⣿⣿⣿⣿⡋⣻⣿⣿⣾⣿⣷⣾⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠖⠛⠉⠁⠰⠞⠛⠛⠿⠶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡶
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠠⣤⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢀⣾⠟⣿⠀⠀⠀⠀⠀⠀⣼⣆
⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠿⠿⠏⠀⢀⣀⣠⡴⠚⠁⠈⠙⠛⠛⠛⠋⠉⢳
⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡀⠀⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠠⡏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣁⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠁
⠀⠀⠀⠀⠀⠙⣿⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⢯⡉⠛⠓⠶⠒⢶⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠉⢷⣴⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⡻⣦⡀⠸⡆⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠦⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⣠⡟⠦⡙⠻⠧⠤⢀⡇⠀⣀⣀⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠁⠒⠒⢋⡴⣫⠟⠁⠀⢸⡟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠳⠿⢦⣤⣀⠀⠀⠈⠁⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠞⡿⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢉⠛⢀⣠⠶⠚⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡴⠊⠉⣿⠏⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⣧
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⠀⢀⣀⣤⠞⠁⠀⣿⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⣿⠀⠀⠀⠀⢈⣉⣉⣳⡦
⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠺⠯⣉⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⡀
⠀⠀⡤⠆⠋⠉⠁⠀⠀⠈⠳⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠙⠒⠦⠤⠤⠤⠀⣀⣀⠀⠈⠙⠶⢤⣤⣀⣀⣀⠀⠀⠀⠀⣀⡄⠀⣀⡄⠀⠀⢀⣀⣤⣾⣫⡼⠷⠖⠛⠁⠀⠀⢀⣀⣀⠤⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠢⠤⠤⠬⠭⠬⠭⢝⣛⣉⣙⠛⠋⠤⠭⠿⠿⢭⡥⠤⠤⠤⠐⠒⠂⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠈⠉⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣈⣉⣉⣉⡉⠛⠛⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡗⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣾⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣼⣿⣿⣿⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⢀⡀⠊⣴⣿⣟⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠿⣿⣿⣿⣿⣵⣆⠀⠀⠀⠀⢠⠎⠉⠀⢰⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⣹⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣸⣯⣽⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠁⠛⠿⣍⣿⣿⣿⡶⠁⠀⠀⠀⢸⣿⣿⣿⣿⠿⠀⠀⠀⠀⢸⣷⡀
⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠃⠀⠀⠀⢠⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢿⣇
⠀⠀⠀⣠⠀⠀⣿⡇⠀⠀⠀⠀⣀⣹⣮⣴⣶⣶⣦⡤⠀⠀⠀⠀⠄⢀⣸⡿⠃⠀⠀⠀⢠⣿⣿⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⣿⠀⠀⣿⠁⠀⠀⠀⠉⠀⠀⠉⠉⠉⠙⠻⢡⣿⣷⣤⠀⠈⠉⠉⠀⠀⠀⠀⠀⢟⡛⣿⣿⠝⠀⠀⠀⠀⠀⠀⢰⡄⠀⢿⡇
⠀⠀⠀⣿⡀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣯⠀⠀⠀⠀⢀⠐⠻⣕⡿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⢹⡇⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⡟⠀⠀⠀⠀⠈⠙⢦⣀⠙⢾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠁
⠀⠀⠀⠘⣷⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⡀⠀⠀⠀⠀⠀⠙⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠹⠛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣀⣀⡀⠀⠀⠀⣀⣠⣤⣤⣤⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠿⠛⠿⠿⠿⠿⠗⠀⠀⠈⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠒⢦⣍⣀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⢶⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢄⠀⠀⢤⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣉⠻⠷⣤⣀⠙⢷⣄⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠍⠛⠳⠾⠿⢦⣄⡹⡄⠀⠀⣠⡶⣾⣛⡛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠒⠒⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠉⠑⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⠄⠤⣄⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢊⠐⠆⢸⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⣀⡴⠛⠥⣀⠀⠀⠀⠀⠐⠒⠁⠀⠀⠀⠀⠀⠀⢷
⠀⣀⡤⠖⠛⠁⠀⠀⠀⠀⠉⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠿⣅⣀⣀⣀⣀⣀⣠⣤⠤⠤⢤⣇⡀⠀⠀⠀⢀⡠⠞⠀⠀⠀⢸
⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⡏⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠂⠤⠤⠄⠀⠀⠠⠤⠤⠄⠒⠊⣹⣃⡤⠴⠒⠚⠛⠉⠉⠙⠓⠒⠶⠤⣄⣀
⠀⠀⠀⠀⠀⠀⢰⠋⠒⠒⠂⠄⠀⠀⠀⠠⠔⠒⠒⢋⠜⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣄
⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⡀
⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⣠⠴⠲⣄
⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠤⢤⡄⢉⣷⡖⠚⠋⠁⠀⠀⢸
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡍⠒⢤⡀
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠤⠄⣀⣀⠀⠀⠀⢸⠀⠀⠙⠆
⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⠍⠀⠀⠀⠘⣰
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠣⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠃⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠉⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢒⣠⠤⠄⠒⠉⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠒⠒⠒⠒⠒⠒⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢶⣊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠦⣤⣤⣀⣀⣀⣀⣑⣄⠀⠀⠀⢰⣀⣀⣤⡤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠠⠤⡏⠙⣦⠤⠤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡇⠀⢀⡇⠀⢹⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠉⠙⠛⠇⠀⢸⣇⣤⡼⠀⠀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠆⠀⠀⠀⣀⠔⠊⠉⠀⠁⠀⠘⠂⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠉⠓⠺⣆⣀⣤⣄⠀⣠⠞⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣥⣤⣼⣿⣥⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣀⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠒⠒⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠢⡄⠀⢀⣄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠄⡈⠋⠀⠀⠀⠀⠀⢀
⢀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘
⠀⠉⠐⠒⠒⠶⠶⠦⠤⠭⠬⠘⠣⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢄⡀⠀⠀⠀⠀⠀⡠⣄⠀⢀⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⠀⠃⠀⠀⠀⠨⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⣀⠄⠀⠀⠈⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠌⠁⠀⠀⠀⠀⠈⠓⠷⠤⣄⣀⠀⠀⠀⠤⠀⣀⡈⠹⠉⠉⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠒⠤⠤⠤⠤⢤⠔⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠣⠀⠀⠀⠀⠇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠉⠀⠀⠀⠀⢀⠤⠎⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠀⡠⠊⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠇⠈⠓⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠋⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⣀⣤⣤⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⠬⢿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⢝⢿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣀⣀⣀⣠⠤⠖⢊⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣀⢲⣤⣭⣲⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠈⠡⢄⣀⠀⠀⠀⠀⠀⢀⡤⢊⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣾⣵⣒⠶⢶⣶⣦⣤⣤⣤⣾⣶⡦⠾⠛⠉⠀⠠⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠫⣉⠉⠉⠙⠉⠉⠉⠁⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡹⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⢤⡀⠀⠀⢀⣀⡠⠤⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⡎⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠃⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠙⠂⠤⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⢰⠀⠀⠀⠀⠀⠀⠀⠎⠸⢀⡠⠄⢸
⠀⠀⠀⠀⠀⢀⠄⣀⢀⠠⡜⡰⠋⠁⠀⠀⠐⢄⠀⠀⠀⠾⢷⡉⠠⠴⢧⡀⠀⡀⠤⠀⣀⠠⠄⡀
⠀⠀⠀⠀⠀⢸⢘⢲⡆⠃⡇⡇⠀⠀⠀⠀⢠⠎⠉⢹⡄⠀⠘⠹⢄⠀⣌⣧⣼⠿⠛⠒⠒⠲⢬⡙⢦⡀⡀
⠀⠀⣠⣤⣤⣸⠆⠰⣖⣐⠵⠁⠀⠀⠀⠀⠱⡄⠀⠁⡰⠀⠀⠀⠾⢤⡠⠩⠔⠈⠈⠁⠢⡀⠀⠙⢄⠙⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠠⠛⠁
⠀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠸⣿⣿⣿⡟⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠒⢣⠤⢀⡀⠀⠀⠀⡔⠈⠀⠀⠀⠙⡆
⠀⠀⠻⡟⠋⠁⠀⠈⢣⠀⠀⠀⡠⠶⠙⠁⠀⡸⠃⠐⠠⢄⠀⠃⠀⠀⡜⠀⠀⢸⡀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠘⢢⡀⠀⠀⠀⠣⣠⠎⠀⠀⠀⠀⠀⠀⠢⢄⡀⠀⠑⠄⢠⡊⠀⠀⠀⠀⠀⠀⢹⣿⠁
⠀⠀⠀⠀⠀⠈⠒⠀⠠⠤⢡⣀⢄⢀⡤⠤⠤⠠⠄⡰⢌⡋⠐⠚⠿⠃⠀⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠛⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠇
⠀⠀⠀⠀⠀⠀⠀⡔⠒⡀⠀⢀⡀⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⡀⢄⢰⡀⢣⡴⢉⣁⣠⠇⠀⠀⠀⣀⢤⣤⣤⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢁⡈⠛⣁⣀⡀⠫⡀⠀⠀⠀⢠⠚⠟⠂⡹⠻⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡠⠆⠀⢀
⠀⠀⠀⢠⠞⠉⠹⡆⠑⢄⠉⠢⠼⠀⠀⠀⣇⠸⢿⠜⠙⠃⡹⠀⠀⠀⠀⠀⡀⠀⠈⠀⣠⠎⠁⠢⡀
⠀⠀⠀⠁⠀⠀⠀⠙⠒⣁⠀⠀⠀⠀⠀⠀⠘⢧⣞⣀⣸⠟⠁⠀⠀⠀⠀⠀⠈⠁⠐⠉⠁⠀⠄
⠀⠀⠀⡤⣄⠀⠀⢠⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠻⣿⣇⣀⠼⠿⡇⠀⠀⠀⠀⡠⠤⢤⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡠⠔⠊⢉⠇
⠀⠀⠀⠀⢘⠀⠀⠀⠀⢹⠂⠉⠉⠙⢧⡀⣸⠃⠀⠀⠀⢫⠀⠉⠁⣐⠒⠀⠠⢧⠐⠈⠀⣶⠆⢀⠜
⠀⠀⠀⠀⠘⠦⣀⣀⣰⠟⠀⢀⠤⣀⣀⢯⠀⠀⠀⠀⠀⠀⠑⠤⣀⠛⡁⣀⡤⢺⠒⢦⠤⠔⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠱⠏⠸⠗⠀⠺⠋⠛⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠁⡌⡲⠘⠗⠋⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢤⡤⣄⣀⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⠀⠄⠀⠀⢠⣿⣿⡟⠷⣤⣀⣠⣤⠀⠀⢀⠀⠀⠒⠒⢠⡀
⠀⠀⠀⠀⠀⠀⢰⡿⣷⠖⣦⡤⡀⠀⠀⢸⠙⣻⣿⣷⣾⣿⣿⠏⠀⠜⠁⠀⠀⠐⡁⠠⣈⠶⣄
⠀⠀⠀⠀⠀⠀⣿⢧⠀⠀⠉⠀⠷⠋⣆⠼⣾⣃⣈⣻⡿⠟⠁⠀⠸⡄⠀⠀⠀⠀⠰⠞⠁⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠹⣭⡗⣤⣾⢻⡇⠀⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⡶⢶⠖⠒⠶⢳⡤⠀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢷⡄⠀⠀⠀⠀⠀⢀⣀⣤⣴⣷⣿⣶⣝⣿⣟⢻⣷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⣼⡇⠀⠀⣠⣶⠟⠛⠉⠁⠀⠀⠀⠀⠉⠉⠙⠂⠙⠂⠙⢷⣄
⠀⠀⠀⠀⠀⠀⢰⡏⠀⢰⡟⢻⣄⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠡⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠁⠀⢻⣅⠀⠀⠀⠀⠀⢀⣤⣶⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⡙⢷⡀⠀⠀⢰⣿⣧⣴⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⠀⠉⠀⢹⡄⠀⢘⠻⣿⣿⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠈⣿⢿⣦⣀⠀⣠⠀⠀⢸⡇⠀⠘⠳⢤⣀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣇⠈⠛⠻⠇⠀⢀⣿⠁⠀⠀⠀⠀⠙⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⠾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠈⣿⡟⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⢿⣧⢀⣠⣴⣶⣶⣿⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠉⠉⠀⠀⠀⠀⠀⠀⠈⠙⠛⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠟⢿⣦⣤⢶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣰⠟⠉⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢲⣶⠞⠉⠉⢙⣧⣤⣤⣀⠀⠀⠀⠀⠀⣠⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⡇⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠉⠀⠈⣿⠂⠀⠀⠀⠀⠉⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣛⣷⡀⠀⠀⠀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣠⡾⠟⠁⠀⠀⠀⠀⢀⣰⣿⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣡⡶⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠷⠶⠶⠶⠶⠶⠾⠿⠟⠛⠛⠋⠁