Cute rose Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠌⠀⠀⠐⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀
⠀⠘⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⡀
⠀⠀⠀⠀⠑⢤⡀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⣀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣀⡀⠀⠁⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠐
⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠖⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⢀⡀⠀⠐⠂
⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠈⠈⢉⠀⠀⠉⠀⠀⠐⠀⠀⠘⠀⠀⠀⠀⠀⠀⠠⢤⠄⡀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠐⠀⠀⠀⠤⠀⠈⠁⠀⠐⡠⠀⠀⠑⠔⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠄⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⢀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠊⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣨⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⣀⠀⠠⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⢠⡤⠤⠐⠒⠈⢆⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠁⠀⠡⠊⠀⡠⠚⠁⠀⠀⠀⠀⠀⠈⢣⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⢀⠁⠀⡐⠀⠀⠀⠀⠐⠂⠀⠀⠢⡀⠱⠀⠀⠑⢤
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢸⠀⠀⠀⠄⠀⠀⠀⠀⠠⢌⠀⠀⢸⠀⡇⠀⠀⠈⡇⠀⢀
⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⢀⠶⠀⠀⠠⣤⡀⠈⢠⠁⠀⠀⢀⠇⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠐⣀⢧⠀⠙⠀⠀⠀⠀⠐⠀⢀⠆⠀⠀⠀⠌⠀⠀⡌⠀⢀
⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⢸⠀⢠⡃⠀⠁⠀⠀⠀⠀⢀⡄⠀⣸⠇⠀⠀⠀⢀⠤⠚⠄⠀⠨
⠀⠀⠀⠀⠀⠑⢀⠀⠱⡀⠀⠀⢠⠀⠀⢝⣃⠀⠀⠀⠀⠀⠈⠒⣊⠁⢀⡸⠂⠈⠀⠀⠀⠘
⠀⠀⠀⠐⣄⠀⠀⠀⠀⠈⡲⣄⠀⠑⠤⣈⣃⣈⠁⠀⠀⠀⠀⠈⠑⠒⠉⠁⠀⠀⠀⠀⠀⡧⣀⠄
⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠠⠈⠢⡀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠑⠄⣀⣀⠀⠀⠡⡀⠈⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠒⠀⠀⠀⠀⣀⡠⠤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢀⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⠤⠤⠀⠀⠈⠁⠀⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⠀⠤⠀⠃⠀⠀⠀⠄



⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡤⠀⣰⣀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⢠⣴⠁⣇⢰⣿⣥⣖⠒⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⣿⠀⠀⣼⠟⣤⣘⡆⣷⠀⠈⠙⢾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠃⠀⢹⡤⣼⠟⠃⣿⠷⢦⣄⣸⣭⡅⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠘⠇⡠⠁⠀⠀⢀⠎⠀⠀⠃⠀⠱⣌⢃⢹⠀⣾⢿⠿⣶⣤⣬⡀⠐⡅⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣏⠀⣿⠛⠻⠶⠶⠶⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡤⠊⠒⠚⠛⠛⠿⠷⠶⢶⡒⠦⣄⡁⠙⢤⠃⠀⢸⣷⣤⣠⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢀⣠⠶⠖⠚⠛⠛⠒⠒⡂⠘⢦⡈⢻⡄⠀⠀⡀⢸⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠉⡥⢒⣻⣭⣭⣉⠳⢦⣉⠑⢦⠉⢼⢃⡐⠶⢄⠚⠷⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⡏⠀⡆⢸⢱⡏⣒⣭⣴⠟⠛⠶⣿⠀⡾⠀⠼⢰⠋⠲⢴⣩⢦⣀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠔⠐⠁⠈⠰⡇⣰⠀⢱⣤⢸⠧⢿⢸⡹⣙⡴⠁⡧⠸⡇⣠⠇⠈⠃⠀⢀⡹⠈⢽⡏⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢻⡘⣷⡦⣀⠉⠠⠷⢆⣠⠞⣸⠏⠀⠃⢘⣿⠯⠀⢣⠘⣓⣖⢒⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⣤⣥⣌⣉⢀⠉⣀⡵⠛⠁⠀⠁⠀⠀⠀⡼⠿⣦⣤⣀⠢⣿⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢣⡍⠉⠀⠀⠀⢠⠀⠀⢀⣾⣠⣤⡾⠳⣝⣶⣋⠓⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡎⠉⠇⠀⠀⢠⠟⡀⠀⢼⣿⢻⣿⣁⡴⣾⠿⢷⡄⠁⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠈⠀⣿⠆⣿⢃⡴⠿⢋⢪⡵⣸⠏⣷⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣀⣉⡈⢧⣰⣾⢾⣟⣁⡾⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠙⡘⠟⠿⠓⠤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠶⠞⠹⠓

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣧⢸⣏⣛⣟⣋⣋⣝⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢠⣆⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡃⠈⠸⢛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡏⣉⣦⣰⠀⠀⠀⢀⠀⠀⠀⠀⠠⠄⠀⠀⠀⢻⣇⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣏⣿⠀⠀⠀⣃⠀⠀⠠⠀⠀⠀⣤⠀⠀⢈⡝⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠺⡄⢲⡟⠁⠀⠀⠀⣠⠀⠀⣿⠀⢀⡃⠀⠀⠀⠀⠀⠀⢠⣴⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠹⣾⡏⢠⢧⠀⣸⡏⢀⣰⡏⣠⣾⢃⠞⡿⣿⡟⣡⠴⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣬⣶⡹⣆⢸⠀⣹⣿⣿⣿⠏⢴⣿⣿⡿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠒⠄⣀⠀⠉⠈⠉⣿⣿⣷⡜⣿⢿⡿⠛⠋⠁⠀⡰⠟⠿⣤⢤⣀⣀⠔⢢⣀⣠⡀
⠀⠀⠀⠀⠀⠶⠶⠶⠖⣿⣿⡿⣿⠿⢿⣿⣿⡇⢈⣿⡤⢠⣠⣶⣧⡀⠀⢀⠀⠀⠙⢣⡀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠂⠀⣠⡾⠋⠀⠀⠀⢀⡝⠁⠈⡝⠋⠁⠰⠋⢁⣠⣼⠟⠛⠻⠶⢶⣦⣼⣧⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⠋⢤⠀⠀⠀⠄⠁⠀⠈⠀⠀⣀⠀⢠⡴⠛⣩⠵⣱⣟⣥⣿⣙⡁⠀⠻⣧⣾⣇⠀⠀⠀⠀⡄⠀⠀⠂
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⣀⠀⢀⡀⢦⣤⠟⢿⠀⣼⡀⣸⣇⢼⢳⣷⠿⣯⠋⠰⢤⣶⠏⢹⣿⡄⠀⠀⠀⢣
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⡿⠶⣦⣿⣼⡇⠀⠈⣷⣿⢿⡇⣿⣸⣻⣿⢱⠛⠔⠀⠠⠁⠀⢰⡉⣿⡄⠀⠘⣼⢀
⠀⠀⠀⠀⠀⢳⣀⠀⡆⠀⢀⣀⣠⡿⠉⠛⡁⠀⠀⢸⣏⠸⣧⠨⣻⡽⠄⠙⠁⠀⠀⣆⠀⠀⠜⠁⠻⣿⣤⣿⣷⠋
⠀⠀⠀⠀⠀⠪⢽⣿⡇⢰⣯⡟⠉⠀⠀⡰⠟⠂⠀⢸⡇⠑⣄⣆⡀⠀⡀⣿⠟⠀⠈⠁⠀⡼⠀⠀⢰⣿⣿⣿⣿⣤⣤⣄⠀⡶
⠀⠀⠀⠐⠛⠓⢋⣉⣽⣬⡟⠃⠀⢀⠀⠳⠦⣄⠀⠻⣷⡄⠀⣥⠉⠓⠶⢧⣀⠀⠀⠀⣼⡇⢠⣄⣾⣯⠟⠉⠀⠀⠀⢹⡿⠁
⠀⢀⠐⠆⠈⢠⢿⡿⡇⠈⠳⣄⠀⠀⠀⠀⠀⠘⢧⡀⠈⠻⣦⣸⡷⠶⠶⠖⠛⠷⣦⣤⣿⠃⣸⣿⣿⣿⠄⠠⣤⣴⡤⠞⠁
⠀⠈⠁⠀⠀⠴⣿⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣆⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⣿⣿⠞⠋⠀⠀⠀⠀⠀⣸⠟⠀⠀⠀⠀⠀⢀⡤⢠⡤
⠀⠀⠀⠀⠀⠰⡂⢰⣀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠷⠶⣶⣦⣴⣶⣶⣶⡶⠾⣿⠇⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⢀⣠⠘⣧⡄
⠀⠀⠀⠀⠀⠀⣿⠟⢁⣀⣄⠀⣤⣤⣤⡀⠀⢠⡞⠁⠀⠀⠀⠀⠈⠉⠋⠈⠙⠿⣶⣦⣅⢀⣀⣀⣠⡴⠋⠀⠀⢀⣀⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠁⠄⠛⠡⠒⢀⠠⣶⣭⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠉⠉⠉⠉⠙⠛⢷⣶⠾⣭⠅⢶⡶⠒⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠒⠚⠷⢖⣸⣿⠟⢸⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⢸⣿⡆⠈⢢⠀⠁⡀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀⠀⢼⣟⣯⣽⣿⣿⣿⠂⠶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣠⣾⣿⠃⠀⠀⠁⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠠⠉⠓⣄⡀⠲⠦⣹⣦⣼⣿⣿⣿⢿⡈⣿⣄⠀⠀⠈⠓⠤⡀⢀⣴⠀⣠⡀⠀⣠⡴⣪⣕⣠⣉⣀⡀⠀⠀⠀⠀⠀⠑⠤⣦⡀
⠀⠀⠀⠀⠀⡤⡜⠉⠋⠀⠰⠋⠀⣠⣰⣿⣿⣿⡈⣷⣿⣿⠗⢀⣀⡀⠀⢀⡞⠁⢰⢿⣿⣻⢿⡟⢉⣻⠄⢵⡏
⠀⠀⠀⣠⡞⣰⠁⠴⠖⠘⠁⠄⢈⣿⣿⣿⣿⡛⠋⠉⢻⡟⠀⣠⢤⠖⠊⣿⣷⣦⠀⣾⣿⠻⢦⠙⢦⡀⠀⠀⢠⠔⢛⣱⣴⢿⠷⡶⠖⢤⡀
⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠏⢸⡿⠀⠀⠀⠙⡷⠶⠞⠁⢰⡉⢿⣷⡖⠉⣿⡀⠈⡇⠀⠙⣦⠴⣿⣿⣿⣋⡀⢠⠆⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⣿⡄⠉⠁⣶⡀⠀⠀⠀⠀⠀⠀⡿⣇⠀⠻⡇⠈⠙⢿⢆⡀⠀⠀⠈⢦⡀⡉⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠉⠀⠀⠸⢇⡈⠑⢶⡦⠀⠀⠀⣷⣈⠀⠀⠀⠀⢀⠘⡈⣿⠀⠀⠀⡘⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⣿⠷⠶⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠁⣿⡇⠀⠀⠀⡁⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢳⣾⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠤⣀⠐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠐⠀⢀⠀⠀⠀⡤⠀⢀⡠⠌⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⡘⠀⠀⠰⠀⠀⠠⠒⠈⠁⠀⠀⠀⢀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠈⡴⣶⠅⠀⢀⠀⡀⠀⡀⢄⠐⠀⢀⠀⠀⠀⠁⠤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠐⡇⢈⠆⠀⠸⠀⡱⡀⠃⣰⢆⠀⠌⠀⠅⠀⠀⠀⡀⠠⠀⠈⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡶⠇⠀⢧⠱⡀⠹⣄⣁⡀⣿⣄⠲⣤⡀⠈⠐⠃⠀⠀⠀⠓⠲⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠉⢳⣷⠀⠀⠈⠳⠷⣄⠹⡋⠟⠓⠻⢧⡄⠷⣤⣆⣴⡀⢀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡔⡇⠙⡷⣤⡀⠀⠀⠈⠳⢽⣠⣤⣤⠠⠉⣀⡀⡀⣉⣹⣿⠇⠀⠀⠀⠀⢀⡄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⢽⣷⡆⠀⢸⣧⢙⠲⣤⡶⣄⠀⠙⠻⢤⣀⠐⠤⠀⠀⠀⣀⣠⣤⣜⡗⠀⠀⡾⠃⠀⠈⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⣻⡞⣻⣇⠀⠀⢻⣼⠇⠀⢀⠛⠲⠶⢦⣀⣈⠙⠢⢤⣄⣀⣿⣿⡏⠁⠀⠀⠈⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⡿⠂⠘⣹⣄⠀⠀⠙⢧⣤⣾⣤⣦⣀⡀⠀⠁⠀⠈⠯⠷⡟⣿⣉⠀⠀⠀⠠⠀⠀⠀⡼⠃⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡴⠯⣤⢀⠀⠺⠿⡷⣦⣤⣄⣉⠲⢶⣖⠨⢉⠉⠉⠉⠉⠁⠉⠁⠉⠀⠀⢀⣀⣰⠦⣀⢨⣃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡀⠀⠘⢿⣶⣀⠀⡁⡼⣸⣿⣿⣷⣦⣬⡙⡆⠀⢁⢐⢒⢶⣤⣤⣤⣐⣚⣵⡿⠁⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢱⢤⣄⠀⣿⠛⢛⠛⢶⡇⣸⣿⣿⣿⣿⡇⢠⠀⠘⢸⠋⣾⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⢿⣸⢽⣷⡬⣤⠀⠀⠌⣷⣟⣿⠏⣼⢹⣇⠘⣆⡤⠟⠋⣡⠤⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⣿⣾⣿⣿⡌⢳⠀⠀⣿⣿⠣⢂⣻⡭⠿⠆⢹⣄⡈⠁⠀⣰⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⠁⣄⣦⣄⢿⣿⠖⠋⠀⠀⢀⣴⣟⣿⣹⣶⣋⠟⠞
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⢿⣿⡿⣿⣿⣿⣷⣬⣽⣾⡀⠃⠀⣠⠀⠀⣼⡿⢽⢻⣿⣿⠏
⠀⠀⠐⠛⠻⠁⠤⠍⠙⠶⠛⠚⠉⢁⣴⣿⣿⣿⡿⣿⣿⣿⡷⠶⣤⣿⠻⢿⢿⣿⣾⣿⠟⠁
⠀⠀⠀⠀⠀⢀⣀⣦⣤⣤⣤⡤⠴⠿⠛⠉⢠⡟⠀⡸⠋⠉⠙⠛⠛⠿⢶⡿⣿⢻⣟⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠻⡜⣇⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣮⣯⡣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⢾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡀⢀⣀⣀⠄⠀⢀⣀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡸⠀⠁⠀⠀⠀⠠⡌⢰⣄⠀⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠀⠀⠀⠈⠑⠀⢰⢀⠀⠁⡌⠶⢋⣧⣇⠀⠉⠀⠀⠃⠠
⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⢡⠀⠀⠄⠀⠸⡆⠀⠘⠇⠘⠇⠀⢀⣀⣤⢠⠀⠠⠀⠀⠑⠆⠀⡀⠀⠀⠀⠀⠀⠀⠄
⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⡇⠀⠙⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠁⢀⠠⠔⠂
⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠴⠀⠀⠁⢀⣀⠀⠀⠀⠀⠐⣊⠠⠊⠄⠀⠀⠀⡠⠀⠄
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠉⡠⢒⠁⠊⠁⠀⠘⠃⠀⠦⠠⠄
⠀⠀⠀⠈⠢⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠂⠀⠀⠀⠰⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⡠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠙⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡀⡠⢀⠠⠤⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⠤⠤⠴⠶⠒⠛⠋⠉⠉⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⣠⡶⠚⠛⠛⠶⣤⣀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⡀⠀⢈⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⣯⣄⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣯⡁⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⢀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⡀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⣾⠃⠀⠀⠀⠀⢀⣴⠞⠛⠉⠛⠛⣶⣄⣀⢀⣀⣤⣤⣤⣤⣤⣼⡃⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⣴⠞⠉⠉⠉⠛⠿⣤⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⣾⠟⠛⠓⢶⣄⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠘⣷⡀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⢿⡆⠀⠀⠀⢹⡆⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠙⠶⣤⣤⠿⠃⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⠿⣦⣀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⢰⡏⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⣿⠀⠀⠉⠛⠳⢶⣤⣀⠀⣼⠛⠶⣤⣤⣤⣤⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⣿⢤⡴⠞⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣤⣄⣿⡀⠀⠀⠀⠀⠀⠀⠉⠛⣿⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣄⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠛⠁⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠶⣤⣄⣀⣀⣤⠞⠋⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⡀⠀⠀⠀⢀⣀⣠⣤⠾⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠈⠉⣿⠟⠛⠙⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣻⢻⡄⠀⠀⠀⢰⡟⠀⠀⠀⠀⠈⠙⠳⢦⣤⣤⣤⠶⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢡⡏⢸⡇⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣸⠃⢸⡇⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⢸⡇⢀⣾⠏⠀⠀⣀⣤⡤⠶⠖⠒⠛⠛⠛⣛⣛⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢸⡆⢸⢇⣾⣏⡴⠞⠋⠉⢀⣀⣤⣤⠶⠶⠟⠛⠉⣉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠘⣇⣼⣿⢟⣩⣤⠶⠞⠛⠉⠉⠀⠀⠀⢀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣿⣿⣿⣋⣁⣀⣀⣀⣠⣤⣤⠴⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠋


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠴⠶⠶⠶⣶⣦⣄⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠚⢛⣛⣿⣷⣶⣦⣿⣿⣯⣍⣉⣀⣒⣙⣋⣩⣥⡴⠶⢦⢤⣭⣭⠽⠿⠛⠛⠛⣻⣿⣿⣿⣿⣿⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇⢸⠉⠉⠐⠒⠒⠢⠤⠀⠉⠉⠉⠉⣉⡽⢿⣿⢿⣷⣶⠞⠋⠀⠀⠀⠀⠀⣀⣀⣤⡶⠛⠉⠁⠀⠀⢈⣿⣦
⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠤⣤⣹⡄⠙⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⠔⠁⣜⡥⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⣀⣤⣾⣿⠏
⠀⠀⠀⢠⣾⡿⠛⠉⠀⠀⠀⠘⢯⣽⣶⠤⠤⠷⢄⠀⠀⠀⠀⠀⠀⢀⡞⡑⠁⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⡀⢀⣠⣶⠟⠋⠐⠿⣥⡀
⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⢸⡄⠀⠀⠀⠀⢀⡟⢠⠃⠀⣼⠟⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠉⠛⢻⣿⡿⢛⡇⠀⣴⣿⠃
⠀⠀⠘⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣀⣨⠇⢀⣤⣤⣄⣼⡇⡜⠀⡞⠉⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢠⣿⣉⣠⣿⣃⣰⣿
⠀⠀⠀⠈⠉⠙⣿⣿⣶⣤⣀⡀⠀⠀⠀⠞⠛⠁⠀⠀⠀⠀⠉⠻⣿⣧⠃⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⣿⣟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠻⢾⣿⣿⣥⣠⣤⣀⠀⠐⠊⠉⠑⢦⡀⠀⠀⠈⢻⣶⡏⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢸⠇⣿⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠹⣿⣆⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⢠⡏⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⣈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⠃⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡟⠀⠘⠿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⠿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⢁⣴⡆⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⣀⡀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠎⣰⣿⣿⣿⠃⡾
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠤⠤⢾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⣴⣿⣿⣿⠃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⠒⣺⣿⣿⣧⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⣠⣾⣿⣿⠟⢡⣾⣁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⢸⣿⣿⡀⠀⠈⠳⣿⡛⠛⠛⠂⠀⠀⠀⠀⠀⠲⠶⠶⣦⣀⣸⣿⣿⣿⠿⠟⠓⠚⠿⢿⣛⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣷⣤⡀⠀⠀⠙⠳⠶⣤⣤⣄⣤⣴⣶⡶⠶⣒⣚⣯⣴⠟⠋⠁⠀⠀⣀⣠⣤⣤⣉⣻⡆⠀⣤⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠛⠛⠛⠛⠿⠿⠶⠶⠶⠞⠉⢀⣠⣾⡿⠾⣷⠏⠉⠉⠉⣀⣀⣀⣠⡴⠊⠁⠀⠀⠀⠉⠁⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⣿⣿⣿⣿⡗⠒⠒⠶⠶⣶⡿⠟⠋⠁⢀⣼⣿⣷⣄⣀⡴⠋⣉⣩⣥⣤⣤⣀⣴⣦⣌⡛⢻⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⢀⣀⣤⠶⠛⠉⠀⢀⣠⣴⣿⣿⣿⣿⡿⠉⠀⠸⠛⠉⠉⠉⠙⠻⢿⣟⠛⠛⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣁⣴⣾⣿⡿⠶⠶⠶⠶⣛⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⣠⣶⠶⢤⣤⣄⣀⣀⣀⣭⣽⠿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠛⢿⣿⣁⣀⣀⣤⣾⣿⡿⠿⠻⣿⣿⠿⣶⣶⣶⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠛⠋⠉⠀⠀⠀⣸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠃

⠀⠀⠀⠀⠀⢀⡤⠚⠉⠁⠀⠀⠀⠀⠀⠔⣈⡴⠚⠁⠀⠀⠙⠶⣄⡀⡠⠤⠄⠀⠤⠤⢤⣀⠑⢄
⠀⠀⠀⢀⡴⠋⠀⠀⢀⣀⣀⣀⣀⢄⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⠀⠀⠀⠀⠀⠀⠉⠺⣧⠀⠀⠉⠐⢄
⠀⠀⢠⠊⠀⠀⠀⡴⠁⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠈⠑
⠀⢠⠃⠀⠀⠀⢰⠃⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠈⠉⠓⢲⡀⠈⢣⡀⠀⠀⠀⠀⠀⠀⢳
⠀⡄⠀⢀⠴⠂⡞⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⡼⠁⠄⠀⢠⡀⣀⡀⠀⠀⢧⠀⠈⣇⠀⠀⠀⠀⠀⠀⠘⡇
⣰⠴⠊⠁⠀⢸⠀⠀⠀⠀⡏⠀⠀⠁⠀⠀⢀⠞⠠⠁⠀⢀⣀⣀⡀⢈⠳⡀⠘⠇⠀⢸⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⢿⠀⠀⠀⢠⡇⠀⡇⠀⠀⠀⡜⠀⢀⠀⠀⠈⡀⠒⠂⡀⢣⡁⢰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⡇⠀⢱⡀⠀⠀⠀⠀⡀⢸⠀⢀⡀⠀⠱⠕⠛⣙⠇⠀⠀⢸⡆⠀⠀⠀⠀⠀⠇⠀⠀⢀⡜
⠀⠀⠀⢀⠀⠀⢧⠀⠀⠀⢡⠠⠁⠹⣄⡀⠀⠀⢹⡓⢅⠀⠀⠀⠀⠠⠈⠋⠀⠀⠀⡼⢳⠀⠀⠀⠀⡜⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢦⠀⠀⠀⠈⠑⠠⢯⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡘⢠⠃⠘⡷⠀⠀⡴⡅⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠐⡄⠀⢰⢄⡀⠀⠀⠀⠈⠀⠂⠀⠀⠠⠄⠀⣰⢡⠋⣠⠞⠀⢀⠎⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠘⢆⢸⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠟⣡⠞⠁⢀⠔⠁⣠⠎⢰
⢀⠀⠀⠀⠀⠀⠀⠑⠦⢤⡀⠀⠠⡈⢳⠃⠀⠀⠀⠉⠐⠂⠂⠒⢒⡊⠁⠀⠕⠁⡠⢖⠏⣠⠾⠁⠀⢸
⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠐⢜⠤⣬⣔⣒⣒⣒⠠⠔⠊⠁⠀⢂⠤⠒⠁⢔⠁⠈⠁⠂⠀⠀⠸
⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠳⢄⠳⣀⣤⢀⡤⠤⠐⠂⠁⠀⡠⠀⠴⠁⠀⠀⠀⠀⠀⢀⠃⠀⡠
⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠙⠻⠧⢄⡀⠀⠀⠄⠀⠈⠀⠁⠀⢀⣀⣄⠀⠀⠀⠌⡠⠊
⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣤⣤⣤⠤⠴⠒⠉⠉⠀⠤⠤⠐⠂⠉⠁⣀⠀⠠⠴⠛⠉⠀⠀⠀⠀⠀⢠
⠤⣀⠀⠀⠀⠀⠉⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠉⠓⠂⠠⠤⠤⠤⢤⠚⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠦⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠉⠓⠂⠤⠄⠐⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⢲⠤⠤⠔⠚⠁
⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⣀⡴
⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡲⠦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠁⠀⠀⠀⠀⢀⡤⠖⠊⠁
⠀⡁⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⢀⣀⡀⠀⠀⠈⠀⠐⠒⢐⡀⠁⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠔⠁⠀⠀⡠⠶⠒⠋⠉⠉⠀⠱⡄⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠀⠉⠈⠁⡠⠃⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣖⠒⠠⢄⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢰⠁⠀⢠⠋⠀⠀⠀⠀⠀⠖⠒⠒⠒⠢⣄⠈⢆⠀⠀⠉⠢⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⡙⠀⠀⠆⢐⠁⠀⡠⠊⠄⠀⣀⠐⠠⡀⠈⡇⠘⡄⠀⠀⠀⢹⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀⠈⣆⠀⠀⣀⡄⠀⠍⠉⠀⠰⢀⠇⢠⠁⠀⠀⠀⢸⠁⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠎⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠠⣴⠋⡁⠁⠀⠛⢲⡧⠀⠀⡞⠀⠀⠀⠀⡸⠀⠀⢀⡬⢀
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠸⠀⠀⠀⠀⠐⣄⠀⠀⣄⡟⢇⠀⠈⠀⠀⠀⠀⠀⠉⢀⠀⣼⠀⠀⠀⠀⠜⠁⠀⠀⡜⠀⠀⡇
⠀⠀⠀⠀⠀⠶⡀⠀⠀⢠⠀⠀⠀⠀⠀⡟⠀⢠⡏⢁⠀⠀⢀⠀⠀⠀⠀⢀⡔⡡⠊⡾⠀⠀⡠⠂⠀⣀⠴⠊⢦⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⢢⡀⠀⠀⠀⡇⠀⠀⢈⣷⠢⠀⠀⠉⠀⠒⠒⠈⠥⠒⢉⡀⠄⣸⠔⠒⠉⠀⠀⠀⢰⠀⠀⠈
⠀⠀⠀⠀⢆⠀⠀⠀⠑⠄⡀⠑⢦⡀⠀⠘⢄⡀⠈⠻⡉⠒⠒⠒⠂⠀⠀⢀⠰⢊⣡⠔⠚⠇⠀⠀⠀⠀⠀⠀⢸⠀⢀⠜
⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠉⢆⠙⢦⠀⠀⠈⠓⠒⠒⠲⠔⠒⠂⠀⠐⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⢸⠔⠃
⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢣⠀⠑⢄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠒⠒⠀⠀⡠⠊⡀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠈⠳⠤⡄⣀⣀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠐⠦⡀⠀⠀⠁⠉⠉⠁⠀⠀⠀⠀⣀⡤⠔⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀⣀⠔⢋⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⡀⠀⠀⠀⠈⠓⠦⢄⣀⣀⣄⡀⠠⠀⠙⠒⠒⠂⠈⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⣀⣀⠀⠀⡀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⠉⠁⠀⠀⠁⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠁⡀⠈⠳⡄
⠀⠀⠀⠀⠀⢀⡀⣀⣤⠀⡄⣤⣀⡀⠚⠀⠀⠸⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠦⢄⡽⠀⠀⠀⢂⣀⡀⠀⠀⠠⠀⣂⡑⠢⢄⡀
⠀⠀⠀⠀⠀⠀⢒⠀⠈⠐⣦⣀⣀⠀⠀⠀⠈⢫⠀⢠⠞⠉⠀⠉⠒⠒⣖⠁⣠⠀⠀⠀⣽⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠥⠀⠀⠀⠀⠙⢚⣧⠄⠀⢙⠀⠹⡀⢰⠁⢀⠖⢊⠤⠛⢁⣤⠞⢀⣸⠀⠤⣀⠙⢦⡀⠒⠠⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⣠⣄⠚⠋⠀⠀⣠⠊⠀⢰⠁⠈⠳⢮⣀⠈⢀⣴⠟⠁⣠⠔⢏⠀⠀⡘⠀⠀⠙⢶⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⢰⡇⠀⠀⠀⡇⠢⠀⠀⠈⠓⣿⠁⠀⢀⡇⠀⠘⡄⢇⠘⢦⡀⠀⢸⡀⠀⠰⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⡼⣇⠀⠰⡐⡇⠀⠀⠀⠀⢰⠃⠀⠀⣨⠃⠀⢠⣇⡸⠂⢰⠇⢀⡾⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠸⣇⠈⠓⣆⠙⢿⣦⡀⠀⠀⠌⠀⠀⠉⢀⣠⡼⠟⠋⠀⣀⡿⠰⠋⢱⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢻⡄⠀⠘⢦⡄⠙⠻⢶⣤⣀⠀⠀⣰⠏⠁⠀⠰⢲⠛⠁⡴⠋⠀⠈⠀⠀⠀⢰⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠹⣄⠀⠀⠙⢦⡘⣷⡘⠒⢤⡄⠀⠈⠙⠿⡇⣀⣤⣤⣤⡼⢀⡈⢀⡀⠀⠀⠀⢠⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠛⢀⠀⠀⣠⠼⠛⠳⠶⠾⠛⠛⠉⣙⣉⠭⠐⠀⣠⠞⠋⢁⡶⢤⡠⢀⡾⠧⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⡠⠀⠀⠀⠀⢸⠁⠀⠘⢬⣐⠛⠋⠉⠉⠁⢀⣀⣠⠾⠋⠀⢀⡞⠁⠀⢠⠟⠀⠀⠀⡀⣀⣈⡁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠤⣄⣀⡀⠀⠁⠀⠀⠀⠉⠛⠿⠶⠶⠾⠛⠋⠁⠀⠀⡴⠋⠀⠀⠔⢁⣤⡴⠖⠛⠉⠁⢀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠂⠁⠀⠀⠢⡄⣀⣤⠤⠶⠒⠒⠒⠉⠀⠀⠀⣄⡄⠀⠀⠀⠘⢢⣤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢶⠒⠚⠉⠳⣄⠀⠀⠀⠀⠩⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠤⠔⠲⠤⢄⣀⣀⡤⠛⠀⢾⠀⠀⠀⠀⠈⢳⣆⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁⠀⠀⠻⣀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⡞⠉⠹⢆⣄⠀⠀⠀⠀⠈⠓⠤⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠠⠁⡠⠛⠀⠉⠙⠓⠶⠲⠆⠴⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⠟⢣⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢂⠘⡆⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⣿⢀⢔⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⡒⢄⠀⠙⣾⡿⠃⠀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠈⣿⢿⣢⣥⢤⣭⣗⠋⢹⣎⠑⣉⣭⣽⣿⠂
⠀⠀⠀⠀⠀⠀⠀⣰⠏⣁⢀⡤⠄⣹⢧⡀⠉⢳⡙⣻⡛⠁
⠀⠀⠀⠀⠀⣀⣰⢏⣎⢹⡁⠞⣺⡎⢱⠙⠀⢸⡆⠀⠹⡆
⠀⠀⠀⠀⠘⣯⠒⠋⠀⠉⠿⣠⣿⠃⡼⢀⣧⣼⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠘⢣⣀⠠⠾⠖⠒⠁⣸⢀⡎⣠⡎⢠⠴⡏
⠀⠀⠀⠀⠀⠀⡞⠉⠛⠲⣶⠶⠾⠥⠚⢀⡿⠒⠚⡴⢃⣴⣧
⠀⠀⠀⠀⢀⡤⢣⡀⠀⠘⠳⠶⢠⡖⠛⠉⠀⢀⡾⢡⢋⣾⣿⡆
⠀⠀⠀⢠⣿⣿⣷⣕⡤⣀⡀⢤⣊⣀⠠⠄⠒⠚⠃⡏⢸⣿⣿⡇⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠈⠉⠉⠉⢀⣴⣦⠲⣾⣯⢍⣩⣭⣄⡁⢸⣿⣿⠃⣪⣽⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢸⣿⡇⠈⣳⠿⠋⠉⠉⠉⠓⠾⢤⣬⣽⡿⠋
⠀⠐⢶⣿⣭⣭⣉⡉⠓⠂⢨⡾⠛⠛⠛⠒⠲⢦⣄⣀⣀⠀⠀⠘⣄⠀⠀⠀⠀⠀⣀⣠⡄
⠀⠀⠈⠻⣿⣿⣿⣿⣷⡆⣿⠁⣀⡴⠋⢉⣐⣤⣼⢿⣏⠙⢦⡀⠈⠑⡄⠀⡠⢊⣵⣿⡇
⠀⠀⠀⠀⠀⠉⠛⠻⢻⠿⣿⠊⣼⢡⢖⣿⣿⣽⣎⢻⢻⡆⠀⠹⣆⠳⣟⠈⢠⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⡰⠁⢰⣯⠀⣿⠸⣿⣫⢟⡽⢹⡾⢸⡇⠀⠀⣿⠀⢹⠀⠚⠛⠋⠀⠀⠀⠀⠀⢀⡔⠛⢒⠗⣤
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠸⡏⠷⣿⠱⠿⣓⣋⣤⠟⣰⠻⡷⠤⠚⡏⠀⢸⡇⠤⠄⣲⣦⣤⣰⣠⠖⠚⠛⠿⠭⣭⡖
⠀⠀⠀⠀⠀⢀⠸⣷⠄⠐⣇⠀⠘⠧⣤⠼⠓⣠⡿⠁⢰⡇⢀⡜⠀⢀⣾⢠⣾⣿⣿⠟⣱⡏⣿⡖⠓⠻⣷⠶⠞⣞⠛⠀⢒⣢⣶⡶
⠀⠀⠠⣶⣯⣥⣤⡻⡄⠀⠈⠻⣶⠴⠖⠒⠛⢉⣠⠴⣋⡴⠋⠀⣴⣿⠏⠿⠿⢿⣁⠸⣿⣟⢛⣶⣤⠼⢒⡭⢶⢸⠇⣾⡿⠿⠋
⠀⠀⠀⠈⠙⠻⠿⡿⠟⠢⠀⠀⢙⡻⠶⣶⣿⡛⠛⠋⠁⠀⠀⣠⢿⣫⣦⡶⣤⡀⠈⠳⣄⠈⠓⣉⣋⡉⢥⡀⣌⣁⣄⣈⣉⠒⢤⡀
⠀⠀⠀⠀⠀⣠⠞⣡⣤⣶⣆⠀⣻⡄⠀⠀⠙⣿⠿⠶⠒⠚⣫⣷⡘⢿⣿⣿⣿⣿⣿⣦⡈⢷⡀⠻⣿⣿⣦⡱⡘⢿⣿⣿⣿⣿⣶⣿⣄
⠀⠀⠀⠀⣰⣥⣾⣿⣿⠟⢹⢸⣿⡟⠶⠤⢴⠇⠀⠀⢰⣸⣿⡟⠀⠈⠛⢿⣿⣿⣿⣿⣿⣾⣷⡀⠈⠛⠻⠿⠧⠀⠉⠙⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠛⠛⠋⠉⠀⠀⠈⢾⠟⠀⠀⠀⠀⠀⠀⠀⠸⠟⠋⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡛⣵⣶⠒⠶⢦⡀⢀⡔⠊⠀⠀⠀⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⠉⠉⠓⠂⠠⣄⣀⣴⠒⠺⠤⣈⣉⡛⢻⣮⣿⣏⣀⢀⣆⠀⠀⢀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡔⠀⠀⠀⠀⠈⠹⠟⠀⠀⣀⠀⠈⣙⢳⣿⣿⠿⣿⠏⠙⠇⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡍⠀⠀⠀⡔⠁⠀⣤⡠⢤⣻⣟⣽⣻⣧⣻⣿⣆⢨⣿⢀⡄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⡀⠀⠀⣇⠀⢠⣿⡇⠈⢿⠋⣉⡿⠿⠟⠚⣻⣾⡷⢿⡇⡀⠀⠀⠀⣷⠶⠒⠒⠈⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⢛⣻⣿⣿⣿⠀⠰⣿⣷⠀⣬⣾⣿⣧⣄⠀⢀⠙⠋⠀⠈⠻⣽⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠻⠛⠛⢫⣿⡆⢰⣿⡟⣧⠀⠈⠛⣿⣷⣿⣿⡗⠀⠀⠀⠀⢹⡇⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⢰⣉⣤⠆⠀⠀⠀⠰⣽⣷⢸⣿⣳⣿⣷⡄⠀⠀⠈⠙⢿⣧⡀⠀⠀⠀⢸⢇⣾⣷⡷⠦⠄⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⣆⠘⣦⡀⠈⣿⣄⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠈⠛⢿⣦⣄⡾⠋⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡩⢷⡾⢿⣿⣿⣿⣧⣄⠀⠀⠀⢻⣿⣿⣿⣻⣿⣿⣷⣎⠉⠓⠂⠀⠠⠤⣿⣿⠀⠀⠀⠀⠀⠐⢾⡏⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠙⠓⠈⠛⠿⢿⣿⡁⣦⠀⠀⠘⢻⣿⣿⣮⣿⡿⠃⠀⠀⠀⠀⣠⣾⣿⠁⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠠⠐⠀⠀⠀⠻⣿⣧⣄⣄⣀⣀⣁⣠⣼⣿⣿⣶⣶⣶⣶⣿⡿⠃⠀⠀⠀⠀⠀⣠⣴⣯⠤⡀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡏⢠⣶⣆⠀⠀⣠⠴⠿⠿⠿⣷⣶⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⣿⣿⡿⠿⣏⣡⠈⠙⠻⣿⣿⣿⣦⣿⡼⠷⢾⣅⠀⠈⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⡙⢃⣀⣀⡀⠙⠃⠀⠀⠀⠉⠛⣿⠛⠛⠂⢄⠙⣶⡄⠈⢹⠿⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⣿⣿⠟⠛⠿⠛⠉⠹⣿⣿⣦⣤⣄⣤⡖⠻⠆⠀⠀⢀⡥⣄⠹⣆⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⡟⠁⡠⠀⠀⠀⠀⢠⡟⠙⠫⡝⢿⡁⠀⢀⠌⠙⠃⠈⠀⠸⡷⢾⣧⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸⡇⠀⠀⠀⢀⣼⣡⣴⡶⢄⠘⣿⢀⣸⡀⠀⠀⠀⠀⠘⠇⠀⠈⠛⠳⠖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⢹⡟⢹⡇⣸⣆⠁⣼⣿⣁⡘⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⡾⠻⣿⣿⠚⠋⣉⣡⣤⡐⠂⠸⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡄⠤⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢀⠁⢀⣿⣉⣀⠻⠿⣿⣿⣿⣒⣄⠀⠀⠉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⣤⠾⢃⣤⠶⠋⠉⠉⠐⠒⠊⠑⠀⠀⠀⠀⠀⠀⠀⣼⠁⣆⡴⠋⠀⠀⠀⠀⢰⣤⣉⡈⠉⠃⠀⠀⠀⠀⣈⠶
⠀⠀⠀⠀⠀⠀⢘⠆⢀⣶⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠇⢸⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⣶⣟⡿⠁
⠀⠀⠀⠀⠀⣼⡇⣸⣿⣿⣀⣄⠀⢀⠀⠀⢀⣤⠖⠒⠂⠐⠶⢧⡀⢹⡆⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡽⠋
⠀⠀⠀⠀⠀⣿⢀⣽⠿⣿⠿⠋⠉⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠟⠋⢛⣁⣉⡀
⠀⠀⠀⠀⠀⢿⡆⠀⠀⣠⣴⣶⣿⣷⣦⣄⣤⡀⢰⣠⠄⠤⠂⣰⢿⡏⢠⡾⠃⠀⣀⠀⠀⠀⢠⣤⣀⣈⠀⠀⠀⠈⠉⠉⠀⠀⢠⣀
⠀⠀⠀⠀⢀⣾⢃⣀⠈⠉⠘⠛⠛⠿⠻⠿⠛⠁⢈⣠⣄⡠⠞⢁⡟⢀⣿⠖⠛⠋⠉⣁⠐⠛⠃⠀⠉⠻⠷⣦⡀⠀⠀⠀⠀⠀⠀⠉⠒⢠⡀
⠀⠀⠀⠀⠛⠁⠉⠉⠙⠛⠛⠳⢠⣤⠤⣤⠶⠞⠋⠉⠁⢀⣠⠞⢡⠞⠁⠀⠀⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⠀⣶⡀⠀⠀⠀⠉⣿⣿⡷⣲⠂⡀⠀⠀⠀⠀⠀⠀⠀⠲⢦⣄⠀⠀⠀⠀⢘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⡞⠋⠁⠀⠀⠀⢸⣧⣠⠞⠻⣿⡿⣀⣀⡄⠀⣠⠀⠀⠀⠀⠉⠳⠄⠀⠀⢈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣠⠾⢁⡜⠀⠀⠀⠀⠀⠀⠀⠟⠙⣆⠀⠉⠚⠉⠻⢗⣷⡶⠀⣆⢀⡤⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣯⠁⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⠷⣤⡀⠀⢈⣁⠀⠈⠁⣀⣀⣠⣶⠛⠛⠋⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⣠⠴⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠏⠉⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠋⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣧⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⠶⢒⣁⡤⢌⠁⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠎⠁⠀⣠⡞⡹⠒⡉⡜⣰⡶⡬⡖⢄⡱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢠⡞⠁⡀⠳⢤⡅⣫⡹⡎⠵⠟⢠⡗⠛⠒⠒⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠚⣆⠀⠈⠑⣤⣀⠞⡇⠀⠐⣴⢁⠜⠥⠲⠤⠠⡶⣋⠄⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⣒⣫⡟⠀⠀⠈⡧⠀⡞⢿⡅⠀⠈⠓⠒⢌⠣⣄⢀⡠⠴⠚⠉⠀⠀⣴⠒⠺⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⢐⣸⡲⡆⢹⠀⠀⠸⡄⠺⣇⣸⢣⠀⠀⠹⡀⠀⣠⠟⠁⠠⠄⢤⣀⣤⠞⠉⣲⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡞⢎⡗⢲⢁⡸⢻⠀⠀⣼⠠⣏⣉⣾⡆⠀⠀⠙⠯⣀⡀⣀⣄⣠⡞⠀⠀⠀⠀⣧⠤⠖⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡷⡇⢀⡥⠇⠋⠀⡆⢀⠚⢣⣀⠀⠀⢳⡙⠒⠒⢾⠀⠀⠹⠀⠀⠀⠉⠂⠀⣀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢹⠈⠉⠹⠤⠄⠴⠇⠀⠀⡼⠁⠀⠀⠀⡧⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢀⣴⣿⣶⣶⣶⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠘⢦⣄⡀⠴⣉⠀⡸⢀⠴⠂⠀⢀⣤⣊⠁⠀⠀⠀⢈⣷⣿⣭⣭⣲⡶⣿⣭⣷⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢀⣈⡇⠀⠀⠉⠉⠉⢠⣤⣤⣴⣿⣏⡿⢷⣤⢀⣾⣿⣛⣿⣼⣿⣇⣷⡈⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⢍⠋⠀⠒⡦⢴⣿⣿⣽⣿⣿⢿⣿⣿⣿⣿⣷⣿⣿⡿⠿⢻⣿⣏⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⠼⢀⣿⢿⣾⣿⡿⠃⠀⠀⠉⠛⠻⠁⠀⠀⠀⠀⠘⣿⣿⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠐⠒⠀⠀⣀⡀⠀⠄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⡤⠤⠔⠒⠂⢣⡀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠐⠂⠀⢀⠊⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠱⡄⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⢀⠃⠀⠰⠁⠀⠀⠀⠀⠒⠂⠀⠒⢄⠘⡄⠀⠈⠢⡄
⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⢨⠀⠀⠁⢨⠀⠀⠀⠀⠀⠌⡐⠀⠀⠁⠡⠀⠀⠀⢱⠀⠀⡀
⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡶⠃⠄⢠⣄⣄⠀⠀⡆⠀⠀⠀⡸⠀⠀⠰
⠀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⢄⠀⠀⣀⡶⠀⠙⠀⠀⠀⠀⠐⠃⠀⡼⠀⠀⠀⠰⠁⠀⢠⠃
⠀⠀⠀⠀⠰⠀⠀⠀⡀⠀⠀⠀⢸⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⡷⠀⠀⠀⠀⠀⠔⠣⠀⠀⡇
⠀⠀⠀⠀⠀⠑⢀⠀⠰⡀⠀⠀⢸⠀⠀⢉⣗⠀⠠⠤⠀⠒⠀⠕⢒⡉⠀⣠⠗⠂⠁⠀⠀⢀
⠀⠀⠀⠠⣀⠀⠀⠁⠀⢈⡲⣄⠀⠑⠄⣀⠛⠀⠈⣉⡀⠀⠀⠈⠩⠐⠊⡙⠀⠀⠀⠀⠀⢸⣀⡠
⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠡⡈⠢⡀⠀⠀⠈⠈⠁⠠⠀⠀⠀⡀⠀⢀⠐⠀⠀⠀⠀⠀⠀⢸⠋
⠀⠀⠀⠀⠀⠑⢄⣀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⣀⠠⢴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠘⠲⣄⠀⠀⠀⠀⠀⠁⠠⡀⠀⠀⠀⠀⡠⠖⠋⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠑⠢⠤⢤⡤⠄⠀⠈⠁⠒⠀⠁⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⣀⡀⠀⠊⠀⠀⠀⠠⠄⠀⠀⠐

⠀⠀⠀⠀⠀⠀⢀⡀⠄⠒⡒⠒⢄
⠀⠀⠀⢠⠒⡉⢀⠠⠈⠀⠄⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⠄⠀⠂⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣲⣤
⠀⠀⠀⠰⠀⠂⠀⠀⠠⠀⡔⢤⠀⢸⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠀⢇⠀⠉⢀⡄
⠀⠀⠀⠀⢃⠀⠰⠁⠢⠔⠀⠀⠣⠴⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠠⠀⠀⠈⠉⢉⠃⠈⠢
⠀⠀⠀⠀⠀⢄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⢀⡤⡆⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⢔⠞⡟⠁⡧⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢀⠜⢡⠂⡜⠀⠀⢣⡈⠑⠲⣑⣄⡠⡀⢀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⢀⣠⠃⠀⡇⠀⡁⠀⠀⠀⠑⡄⠀⠈⣦⡱⠁⡯⠷⡔⠚⡢⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠐⠂⢫⠀⠸⢆⠀⢇⠀⠱⡀⠀⠀⢀⣇⣀⡠⣗⣌⠉⠵⢄⠘⡖
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠦⠁⡶⠗⡢⡀⡨⠬⡁⡲⢯⢁⠴⢅⡠⢄⢀⢥⡠⠵⢤⢤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢒⠖⢱⠢⠤⠩⡇⠀⢨⠀⠀⡅⠀⠠⠀⢠⢁⠜⡚⠈⠉⠉⠉⠁⠒⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠈⡄⠸⡀⠰⠀⠈⡄⠀⡇⠀⡈⢀⠜⠁⠀⠀⢀⠄⡔⠓⠄⡀⠁⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠰⠀⠀⣀⣰⣀⠗⠤⣇⠀⠇⠀⠁⠀⠃⡎⠀⠀⡀⢫⠛⠉⠀⠈⢑⠇⠂⢀⠀⢰
⠀⠀⠀⠀⠀⠀⡎⠀⠀⠛⠁⠈⠇⠀⠁⠀⠀⢸⠀⠐⠀⠀⠘⠀⢧⢤⡠⢄⠀⠉⠒⡀⠈⠁⠀⣀⠇⠉⠎
⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⢀⣄⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠱⣀⠈⠢⠒⠐⠄⠔⠑⠊⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠂⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⠤⠤⠤⠄⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠖⣒⣒⣶⣛⣉⠙⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢏⡵⢛⣻⡿⣭⣻⢥⣍⣿⠲⣦⣄⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⣶⠋⣾⣾⣱⠿⣿⣫⠴⢛⣵⡿⢞⡵⣽⣠⠟⣲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢿⣷⣿⣿⠛⢷⣟⠛⢚⣫⠵⠚⠁⣼⡿⢁⡞⠁⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠦⣳⣌⡛⢧⣤⣼⣛⡉⠀⠀⠀⢰⡏⠀⡎⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⢷⣌⡙⠿⣦⡀⠀⠀⠉⠓⠶⢤⣼⣤⣼⠃⢀⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠈⢿⣿⣦⡈⠻⣧⡀⠀⠀⠀⠀⠈⣿⣿⠀⣾⡥⠤⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣬⡇⡀⠉⠳⢌⣻⣄⠀⠀⣄⣠⡿⢃⡞⠁⢠⣞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠘⢿⣿⡠⡀⠀⠀⠙⠻⣿⣿⣿⠿⠗⠋⢀⡴⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⢤⡈⠻⠿⣿⣷⣦⣴⡖⠛⠉⣀⣼⣷⣾⣿⣿⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠉⠙⢻⣿⣿⣿⣿⠿⣿⡿⠻⣮⡿⣿⣿⣦⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣿⣯⣭⣽⣶⣦⣄⠀⣿⡟⢹⡿⠋⠀⣿⡇⠀⠈⢻⡘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣽⣿⣿⣿⣿⣿⣿⣿⣷⣞⠁⠈⠃⠀⠀⣿⡇⠀⠀⠀⠻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⢿⣿⣿⣿⣿⡻⣿⣿⣷⠀⠀⠀⢸⣽⡗⠀⠀⣀⣀⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⢰⣿⠀⣴⣿⣿⣿⣿⣷⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡻⣿⣿⣿⣿⣿⣇⠀⠀⠀⢸⣿⢴⡿⣟⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠬⠽⠛⠉⠈⢻⣦⠀⠀⣿⣯⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⢀⣿⠉⠀⠙⢮⣙⡛⠿⣿⡿⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⡟⠀⠀⠀⠀⠀⠉⠉⠉⠙⠚⠛⠾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠘⠃⠁⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⢀⠈⠁⣀⡄⠀⠤⣌⡉⠐⠀⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⢾⡏⢠⠾⢡⣀⣾⣶⣼⣿⢴⣆⢸⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠡⠸⠷⣟⡛⠋⠁⣿⣿⠻⣆⣿⠟⣱⣎⠀⠀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠐⠠⠀⢠⣀⠀⠀⠀⠀⠉⠠⣄⣰⡌⠉⠈⠙⠿⠿⠾⣯⣴⣟⣿⠟⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠸⠿⣶⣤⣿⣿⡀⠀⠀⠀⠳⢆⢠⣭⠛⠒⠶⠿⣿⣷⣶⣿⣿⣿⡿⠃⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣝⠻⠿⣿⣷⣦⠀⠀⠈⢿⣿⣿⣿⣿⣶⡶⣭⣿⣿⡿⣋⣠⣤⢤⣴⡞⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⢲⣤⣿⣿⣶⣴⣶⡶⠶⣽⣿⣿⣿⣶⣾⣿⣿⠿⢿⣟⡷⠘⠿⡷⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠙⠃⠛⠩⠿⠟⠀⠀⠛⡿⠿⠟⠻⣿⣿⣿⣆⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣦⡄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⢠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠄⡀⠀⠀⠀⠀⠀⠀⣠⣷⣦⣀⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⠿⣶⣄⠀⠀⠀⠀⠰⢋⣼⡇⣿⣿⣯⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠻⡿⠟⠛⢲⣆⠀⡀⠀⢸⣿⢻⣿⢿⣷⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣤⣼⣓⣤⣭⣾⣿⣷⣄⠸⣿⢺⣿⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠉⡿⢃⠋⠈⢷⣼⠆⠀⠀⣠⣴⠀⠀⣰⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠀⠊⠀⠀⡾⠃⠀⣠⣾⣿⠿⠧⣰⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⡔⢀⣾⣿⣿⣟⠁⣇⣼⠿⠃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⣿⣿⣿⣇⣠⣠⣿⡿⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠟⠻⠿⠿⣿⣿⣷⡳⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠰⣾⣿⣟⣿⡆⠫⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⠏⠉⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⡆⠈⠯⠒⠀⠂⠀⠀⠠⠀⠀⠀⠔⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣥⡼⢠⠀⠀⠀⡸⠈⢤⡀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠉⡀⠀⠠⠇⠀⠸⡗⠀⠀⠀⣀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⠀⢰⠀⠀⠐⠰⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠁⠀⠁⢓⡄⠀⠈⠀⠀⠠⠁⡀
⠀⠀⠀⠀⡀⠀⠀⠈⠉⠀⡠⡲⠋⢠⣀⠐⠀⠆⢠⣶⣦⡀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⣰⠷⠂⠁⠀⠀⠑⠀⠙⢦
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠁⠀⠃⠉⠛⠿⠛⠂⠀⠀⠀⠀⣰⠁⠀⠀⠀⠃⢾⠀⠀⠀⠀⡀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠰⡧⠆⠀⠀⠑⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⠀⠀⠀⢀⣄⣄⠀⠀⠀⠈⠄⠀⡀⠀⠀⡄⣀⠒⠘⠂⠠⠴
⠀⠀⠀⠀⠀⠠⡀⡀⠀⠀⠈⠀⠀⠐⣺⣿⣿⠁⠀⠀⠀⢀⠖⠀⠀⠀⠁⠈⠀⠊⠈
⠀⠀⠀⠀⠀⠀⢄⣉⠽⠛⡦⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠈⢀⣀⣠⡤⠤⢀⡀⠀⢰⠹⠉
⠀⠀⠀⠤⠶⠛⠛⠁⠀⠀⡿⠀⠀⠂⠀⠀⠀⠀⠀⠐⠂⡴⠋⠑⣤⡂⠚⠀⠐⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠙⢄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠑

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠚⠉⠙⠀⠀⠀⠛⠛⠛⠓⠲⠢⠠⣀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠒⠐⢤⣀⠈⠙⠻⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⡟⠀⠀⠀⠀⢠⣏⢠⠆⠂⢀⠒⠀⠉⠀⠁⠀⣘⣮⠛⣭⠉⠙⠲⢄⠀⠀⠀⢑⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠾⠻⠹⠀⠀⠀⠀⠀⢨⠃⢻⣤⣾⣦⣤⣴⡀⠀⠃⠀⠙⢻⡆⠉⢲⣄⡀⠀⠁⠠⡀⠀⠆⠀⠐⠁⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠀⠀⢰⠀⣄⠀⠀⢸⡀⠈⡙⠻⢿⢯⣬⡙⠳⠀⣡⣹⣆⣷⠀⣸⡿⠃⠀⠀⠀⡵⠀⠀⢀⣤⣬⡀⣄⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣿⡆⠀⣿⣧⠀⠈⠀⠀⠀⠈⠛⠶⣿⡿⡏⠘⠋⠸⣿⣧⠀⠀⠀⠘⢇⠀⠀⣻⢿⣿⣿⣯⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⣿⡟⠀⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠄⠀⢿⣿⡷⠀⠀⢀⣞⡃⢠⡿⠒⠃⠘⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠄⡉⠙⠲⣶⠖⠈⡠⠀⠀⣾⠻⢣⣿⡇⠀⠀⠀⠻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⠃⠄⠐⠀⠙⣿⣿⣿⣶⣤⢤⣤⣤⣤⡤⠄⠀⢀⣴⡊⣠⡔⠋⠀⢀⣿⡟⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⠉⠉⠛⠛⠚⠛⠋⠁⠀⠀⠀⠀⠈⢠⡟⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠄⢀⡀⠀⠀⢀⣀⣴⡿⠀⠀⢠⣿⠟⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢗⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣷⣤⡶⠟⠁⠀⢠⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⠈⢣⣀⡀⠀⢀⣤⣤⣤⣤⣤⠤⡤⠤⠤⠖⠒⠐⠉⠁⠀⠀⠀⠀⠀⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⡟⣉⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠁⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠈



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣠⣴⡶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣄⣀⣀⠠⣶⣶⣄⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠾⣶⣽⣶⣤
⠀⠀⠀⢀⣴⠟⣿⣿⣿⣿⣾⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⡞⣻⣿⣾⠃⣿⣽⣿⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠿⣾⡄
⠀⠀⠀⢼⣩⣶⣮⣭⢿⣟⣶⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣻⡾⣶⣿⣯⣿⣏⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⢿⣿⣽⣿⠻⠿⠿⣧⣿⣧⡄
⠀⠀⠀⠈⢻⣿⣿⡧⢿⣾⣿⢟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣽⣝⣿⣿⣿⣿⣻⣷⢟⠡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡿⠛⠿⣿⣿⣿⣿⣿⣾⣿⠟⠃
⠀⠀⠀⠀⠹⣿⣉⣷⠾⣿⠷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⣿⣿⠍⣽⡿⠿⠘⠷⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠐⡿⢬⣿⠋⢩⢻⣧
⠀⠀⠀⠀⢠⡟⣮⠏⠉⠉⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠁⠀⠈⠸⣏
⠀⠀⠀⠀⠸⠛⠁⠀⠀⠀⢀⣖⣢⣾⡾⣧⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣻⣟⣹⣒⢾⣵⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣤⣶⣶⡤⣤⡀⠀⠀⠀⠀⠀⠠⠦⣻⡿⡻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣟⣩⣟⠁⠀⠀⠀⠀⠀⢀⣸⣿⣿⡹⡾⣩⣖⡮⣧⡀⠀⠀⠀⠀⠀⠀⠟⠛⠉⠀⠀⠀⢀⣤⣤⠤⡀
⠀⠀⠀⠀⢠⡶⣘⣛⣶⣦⠀⠀⠀⠸⠋⠈⠃⠀⠀⠀⠀⠀⢀⣠⢸⡿⣷⣿⣏⡿⣮⣬⣿⣛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡿⣽⣾⣷⡻⡶⢀⡀
⠀⠀⠀⣼⣧⡷⣾⠏⡶⢋⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣯⣽⣜⣿⣾⣿⣬⣿⣶⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣯⣻⣷⣻⣿⣷⣽⣿⡏
⠀⠀⠈⣿⣹⡇⣾⣿⣿⣯⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣩⡋⢽⣿⣯⣽⣿⡏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡞⢿⣾⢏⣫⣿⡏
⠀⠀⠀⣾⣿⣿⣟⣛⡿⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡾⠃⠀⠈⠉⠈⠳⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡅⣺⢿⣿⡿⢛⣟⡽⣧
⠀⠀⠀⠈⢻⠿⡿⠟⠛⢭⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠞⠉⠀⠀⠀⠀⠈⠛⠻⠆
⠀⠀⠀⠀⢸⠇⠁⠀⠀⠀⠙⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⣍⣾⣗⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠾⣎⡷⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣿⣿⣿⣿⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣟⣿⣟⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢿⡿⠦⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠫⣿⡞⠂⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡵⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠼⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣔⠛⠻⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣤⡰⣶⣖⣦⡀
⠀⠀⠀⠀⣠⣬⣿⣿⡿⢺⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⣵⣷⣶⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣛⡿⣿⣷⣲⣦⡀
⠀⠀⠀⣰⣤⢛⣻⣿⣾⣟⡿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣻⣫⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣳⣿⣿⠵⢷⠿⣿⣯⣿⠇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣶⣞⣫⣯⡿⣻
⠀⠀⠀⠉⠉⢉⡝⣛⣛⠛⡛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠛⢉⣟⠻⣿⣶⣾⣿⡿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠗⢿⣷⣾⣍⣛⣻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣴⠟⠉⠉⠉⠁⠻⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⡼⠟⠉⠉⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⡶⣋⣙⠲⠒⠒⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠙⢀⡠⡶⣫⠞⠛⠳⣶⣤⢸⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠒⢶⡟⠀⣠⣿⣸⠟⢉⣉⡛⣆⢸⡌⣿⡀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢈⣧⠀⡇⠸⣯⣰⣧⣚⡷⢋⡼⣱⢻⡇⢠⠷⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⢸⠏⠻⣧⠀⠙⠿⣽⡿⢚⡭⠞⣁⣼⣵⡏⠀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠦⢼⡇⠀⠈⠳⢾⡛⠛⠛⣿⠛⠋⠉⠁⣸⠁⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣄⠀⠈⢳⣄⠀⠀⠀⠙⣆⣀⣯⡀⠀⠀⣠⡿⠖⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠉⠳⣤⡀⠀⣿⠁⠈⠉⢛⣻⠏⠀⢀⣠⡴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⢤⣄⣀⣉⣻⡿⠶⠶⣾⣏⣥⣤⠶⠋⢁⣀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠤⣄⣀⠉⠉⠁⢀⣶⡀⠘⣇⠀⠀⣰⠋⣧⠚⢓⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⢄⡸⡟⣄⢀⡜⣯⢷⠀⣿⠀⣾⠁⢦⡇⢁⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⣊⢳⡅⢹⡿⢣⡟⢺⢀⡿⠀⣟⠜⢋⣤⣟⣥⡤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣳⣸⣧⡏⣠⠋⣼⡷⠚⢻⣟⣶⣿⣶⠷⠶⢞⣻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⣤⣄⠙⢿⡯⠞⠁⣰⠟⠀⢰⠃⢿⡍⢳⡉⠙⠚⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⡞⢷⣭⠾⡽⠃⠀⠀⢷⢀⣼⠋⠀⠀⠘⣧⠼⣯⢪⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠥⠗⠋⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠈⢻⣩⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⢹⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣟⣷⢆⣭⣭⣭⣶⣶⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣾⣿⡿⠟⣛⣿⢸⣏⢸⣿⡛⣻⡛⣻⣟⣛⣿⣛⠻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠁⣿⣿⣿⣸⣿⣌⢿⣿⣦⠻⣿⡏⠛⢶⡝⢿⣎⢙⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⢻⣿⡀⢿⣿⣿⣦⠹⣿⣧⡙⢿⣿⣦⢿⡎⢿⡏⢿⣷⡜⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢨⣆⢻⣿⣦⣙⠻⣿⣷⣜⢿⣷⡝⢮⣝⡚⣿⢸⣿⠸⣿⣿⠘⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠸⣿⣿⣿⣿⣿⣷⣬⣙⠿⣷⣿⣿⣦⡙⢿⣷⣾⣿⠗⣸⣿⠆⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢦⣌⡛⠿⣿⣿⣿⣿⣿⡓⢦⣄⣙⣿⣿⣦⡙⢿⣥⣾⣿⣿⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡌⢿⣿⣷⣦⣍⡛⠿⣿⣿⣷⣬⣙⠻⠿⣿⣿⣦⡹⣿⣿⢇⣾⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⠛⠻⣶⣬⣿⣿⣿⡈⣿⣿⣿⣿⣿⣷⣦⣍⡛⠿⣿⣿⣶⣦⣬⣝⣻⣍⣫⣾⣛⣋⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣝⠻⢿⣿⣿⡿⠿⠿⠟⠛⢋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢂⣀⣤⣤⣶⣶⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠻⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⠟⣉⣴⣾⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣤⣶⣦⣌⠻⢁⣿⣿⣿⣿⣿⣿⣿⡟⢡⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⢋⣠⣈⠻⢿⣿⣿⣿⣿⠏⣴⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠖⢈⣉⡛⠋⣸⡛⠛⠛⢛⣛⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠉⢠⣶⣾⣿⣿⠟⠀⣿⣿⠀⠙⢿⣿⣿⣦⣄⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⡾⠁⠀⠀⠘⣿⣿⡿⠁⠀⠀⣿⠃⠀⠀⠀⠈⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠉⠀⠀⠀⠀⣿⡟⠀⠀⢠⠞⠁⠀⠰⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⠀⠀⣿⣶⣤⣄⡀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⠀⠀⠘⣿⣿⣿⣿⣷⣄⠀⠀⣿⣤⠄⠀⠀⢀⣴⠟⠁⢀⣴⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿⣆⠀⠀⠹⣿⣿⣿⣿⣿⡆⠀⣿⠁⢀⣠⣶⣛⣁⣀⣤⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠛⠻⣧⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠹⣿⣿⣿⣿⠃⣼⣷⠾⠛⠉⠉⠉⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣶⣤⡀⠀⠀⠙⢷⡄⠀⠀⢠⣾⣿⠀⠀⠀⠀⢸⡟⠋⣽⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠟⠟⠛⠛⠉⠁
⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣤⣬⣿⣦⠀⠀⢻⣿⠀⠀⠀⠀⣾⣃⡾⢋⡀
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠙⢷⣄⠸⣿⠀⠀⠀⢠⣿⡿⠟⠉
⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢻⣦⣿⡆⠀⢠⡿⠋
⠴⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠁⣠⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣀⠠⠤⠄⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡉⠉⠀⢀⣀⣀⣤⡤⠽⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠛⠋⠡⣤⢶⣛⢉⣡⣴⣻⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠉⠉⡟⠋⠑⠨⠴⡀
⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⢣⣀⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡏⠙⠒⠲⠤⣤⣀
⠀⠀⠀⡠⠖⠋⠁⠠⢔⣮⡅⠻⢼⣽⣿⣿⡶⠦⣤⣠⣇⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⣇⣭⣵⠦⣄⠀⠈⠙⠲⢄
⠀⠀⠈⠀⠀⢠⣴⣿⣛⣻⣥⡴⠶⠛⠛⢛⣻⣿⣷⡿⣯⣿⣓⣲⡦⢤⣼⣀⣀⠀⠀⡷⠟⠛⠉⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠈⠦⣀⠈⠉⠉⠙⠳⠀⠀⢠⣶⣿⣯⠭⠶⠶⢒⣻⠿⣋⣉⣽⠿⠛⠷⠿⠿⠽⠇⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠈⠙⠒⠦⢤⣄⣀⣀⠀⠉⠁⠀⠀⠀⠀⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠓⠒⠒⠲⠶⠶⠶⠤⠤⠶⠶⠶⠒⠒⠒⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠖⠲⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠚⣻⡿⠛⢉⣤⠤⢤⣤⣉⠙⠓⢶⡶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⣠⣾⠋⣴⠞⡟⢠⠞⢛⣷⢈⣷⣀⠀⢹⡌⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇⠀⣇⣿⢸⡇⣼⣿⣾⣴⣯⠾⣿⡏⠉⣷⣼⣧⡀⠈⣿⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⣰⠟⣧⠙⣿⣆⠹⣿⣌⡙⠳⠶⢤⣿⣷⠋⣸⠇⢸⡇⢠⣟⣠⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣠⡾⠁⠠⣽⡄⠘⠷⣼⣿⣦⣿⠀⢉⣛⣀⣤⡼⠿⠛⣁⡴⠋⢀⣾⠋⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠲⢬⣻⣶⣦⡈⠙⠿⣿⣭⣉⣉⣩⣤⡤⠶⠛⣿⢁⣴⢿⡇⣀⣤⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠙⠲⢿⣿⣮⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠛⢁⣾⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠙⠻⠿⠿⢿⣦⣀⠀⢀⣠⣴⣞⣋⣥⠴⠶⠿⢯⣄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣀⣠⣤⣄⠀⠀⠈⠙⠻⠿⣿⣿⠭⠥⠐⠀⠀⠀⣠⡿⠀⠀⠀⠀⢠⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣼⠛⠶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣀⣤⠾⢋⠀⢀⣠⣶⠿⢋⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠈⠘⠹⣉⡿⢿⠛⣿⣿⢻⣯⣄⢀⣾⡶⠛⠁⠀⢠⡎⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⠶⢦⣤⣴⣤⣀⠀⡀⠈⠛⠶⠶⣾⠋⢷⠈⠀⡿⠘⠏⢀⡼⠟⠁⠀⣿⠀⣷⠟⠀⠠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠢⣄⠀⡍⢉⠳⣿⣦⣀⠀⠀⠀⠀⠘⡇⢸⠇⠀⣰⠟⠀⠀⢠⠀⢸⣴⣏⡤⠂⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⣈⣳⣿⡀⣧⠸⡄⠙⢷⡀⠀⠀⠀⣇⣿⠀⢰⡏⠀⠀⡄⠘⣆⡼⠋⠁⢀⠀⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡆⠀⢀⣀⣙⣿⣄⣧⢘⡈⡇⠀⠀⠀⣿⡏⠀⣾⠀⡆⠀⣧⢀⣿⠥⠖⠚⠁⢈⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⢀⣀⣀⣬⠿⢾⣧⣇⣀⡀⠀⣿⡇⠀⢹⡄⠸⡄⣸⠟⢀⣀⡤⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⠀⠤⠤⠖⣻⣯⣍⣉⠳⣿⡇⠀⠀⢷⣀⣿⠛⠛⠉⠁⠀⠐⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⣀⣀⣀⣪⡽⠃⠀⠈⠳⣌⡇⠀⢀⣸⡿⠓⠖⠒⠚⠁⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⣿⣧⡴⠛⣟⠿⣓⠒⠂⢀⡼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠈⠓⠶⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠷

⠀⠀⠀⠀⠂⠀⠀⠉⠉⠀⢠⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠉⠉⠀⢠⡄⠀⠀⠉⠉
⠐⠄⠄⠀⠀⠀⠀⠀⠀⡤⠔⢇⠀⠀⠘⠀⠀⠀⠀⠀⠐⠄⠄⠀⠀⠀⠀⠀⠀⡤⠔⣇⠀⠀⠘
⠀⠀⠀⠀⣄⠐⠂⠀⠀⠓⠲⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠐⠂⠀⠀⠓⠲⠎⠀⢀
⠒⠀⠀⠀⠈⠙⠂⠀⠀⢀⠄⠀⠀⠄⠈⠉⠁⠀⠀⠀⠒⠀⠀⠀⠈⠙⠂⠀⠀⢀⠄⠀⠀⠄⠈⠉⠁
⠀⠀⠀⠘⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠖⠋⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠖⠋⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠘⠄⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠈⠄⠀⣀⠆
⠂⠀⢐⠘⠙⢢⠄⠀⠀⠈⠀⣀⠀⠀⠀⠀⡀⠰⠙⢢⠆⠀⢘⠘⠉⢢⠀⠀⠀⠈⠀⣀⠀⠀⠀⠀⡀⠰⠙
⠀⠀⠈⠓⠒⠉⠀⢠⡄⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠙⠒⠉⠀⢠⡄⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣤⣴⠆⠀⠉⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⠆⠀⠉⠀⠀⠀⢠
⠀⠀⠀⠀⠢⠀⠀⠉⠉⠀⢠⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠉⠉⠀⢠⡀⠀⠀⠉⠉
⠐⠄⢄⠀⠀⠀⠀⠀⠀⡬⠔⣃⠀⠀⠘⠀⠀⠀⠀⠀⠐⠄⠄⠀⠀⠀⠀⠀⠈⡭⠔⣂⠀⠀⠘
⠀⠀⠀⠀⣄⠐⠂⠀⠀⠓⠲⠆⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣄⠐⠂⠀⠀⠓⠲⠊⠀⢀⠀⠄
⠒⠀⠀⠀⠈⠙⠂⠀⠀⢀⠄⠀⠀⠀⠈⠉⠁⠀⠀⠀⠒⠀⠀⠀⠈⠙⠂⠀⠀⢀⠄⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠖⠊⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠖⠋⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠈⠄⠀⢀⠆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⡀⠀⠀⠈⠄⠀⢀⠆
⠀⠀⢈⠘⠙⢢⠀⠀⠀⠈⠀⣀⠀⠀⠀⠀⡀⠰⠙⢀⠄⠀⢐⠘⠉⢢⠀⠀⠀⠈⠀⣀⠀⠀⠀⠀⡀⠰⠙
⠀⠀⠈⠑⠒⠉⠀⢠⡄⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠙⠒⠉⠀⢠⡄⠀⠀⣿⡄
⠀⠀⠀⠀⠀⡀⢠⣤⣴⠆⠀⠉⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣤⣴⠆⠀⠉⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠶⢒⡒⣛⣛⢋⠉⣉⠙⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠉⣶⣶⣴⣦⢸⣿⠃⢹⡇⠘⢾⡟⢠⡟⠉⠉⠉⢛⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠋⠁⢸⡄⣟⠁⠛⠹⠆⠉⠓⢀⣁⣑⣛⣁⣸⣇⣀⣀⣀⣙⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀⠀⠛⣻⠂⢀⣸⣧⣤⠤⠶⠶⠚⠛⠉⠉⠉⠉⠉⠉⠉⡁⠀⠀⠀⠀⠉⠉⢁⣀⣴⠊⠀⢀⠴
⠀⠀⠀⠀⠀⠀⢰⢸⡇⢴⠀⢰⣧⠖⠋⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⢺⡇⠀⠀⠀⣿⡷⢲⣒⡶⣶⣻⠛⢆⣿⠀⣀⢸⣯
⠀⠀⠀⠀⢀⣀⣸⣸⣇⣿⠀⠈⠁⠀⠀⡶⣶⠲⡖⢲⢺⣿⣿⡇⠸⣮⢿⠀⠀⠀⠛⢀⡘⠟⠀⠈⠛⠀⠀⠁⠀⣿⢸⣿⢀⣶⣆
⠀⢀⡞⠩⠁⣀⡈⣉⣁⠉⠍⠙⢦⡀⠀⠯⡏⠐⡷⢾⠀⠿⠛⠇⠀⠁⣀⠀⣀⠀⢀⣼⡅⠀⢾⡆⠀⠰⣿⡆⠀⣿⡜⠋⠀⠈⠀⣀⡀
⠀⠀⡇⣤⣤⣴⢶⢠⡶⣄⣶⣦⢈⡇⠀⠀⠀⢀⠀⣤⠀⠀⠀⠀⢷⢴⠻⠔⣇⠀⣼⠽⡇⠀⣟⢳⡀⢀⣯⡿⣄⠙⢁⢠⣿⣆⡆⠘⠁
⠀⠀⢻⣇⠻⠿⢾⣼⠧⠿⠃⣿⣼⠃⠀⠀⢀⣸⣿⣿⣽⣃⠀⠀⠘⠄⠑⣒⠋⠘⠳⠛⠃⢸⣯⢈⣧⠸⠷⠿⠛⠀⠈⢳⣻⠯⠂
⠀⢠⠼⢯⣔⣆⣈⣩⣄⣀⣺⠴⠛⠑⣆⢏⣉⣩⣿⣧⠤⢼⡇⠈⣏⣧⣼⣹⠀⠀⢠⢒⠤⢠⡬⠉⡁⠀⣀⣀⠀⢀⡤⠠⡁⠀⢴⣤⠄
⠀⢸⠈⣀⠀⣠⡀⣰⣦⠀⣠⡀⢠⣄⢹⠈⡇⠀⣿⡇⠀⣸⠀⢺⡿⣿⣿⠿⡿⠀⠜⠬⠗⠠⠽⠖⠁⢸⡁⠈⠳⠏⠀⢀⡇⣀⠈⠁
⠀⠘⡟⢹⣾⠇⣿⣿⢸⣸⡏⢧⣾⠘⡾⠃⣇⠀⣿⣷⣀⡏⠀⠘⣷⠀⢐⢿⡇⠰⠀⠀⣠⡴⠲⣄⠀⠘⠧⣄⠀⠀⢀⡼⠁⣿⣿⠟
⠀⠀⣧⣠⢉⠠⡙⠇⡀⣙⣂⢬⡗⢔⡿⠀⢈⡅⢠⡀⢀⣀⡀⠀⠻⠼⠿⠾⠃⠀⢀⣠⡟⠀⠀⢸⣇⡤⢄⠀⠉⢷⡟⠁⠀⠈⣁⡀
⠀⠀⠛⠬⣏⣙⣙⣋⣹⡥⠽⠖⠚⠉⠀⠀⠘⢦⣾⣷⣯⡴⠃⢀⣤⢀⣀⠀⢀⣰⣋⠸⡇⠀⠀⢸⡏⠀⢸⡇⠀⠸⣅⠀⢠⠞⠁⠀⠉
⣀⠞⢦⡄⣀⠀⣀⣤⡤⡄⠀⡀⠀⢿⡷⠀⡏⠉⣿⠀⣿⠁⢹⣾⣿⣿⠟⣰⠏⠀⠉⣷⢳⣀⣠⣾⡞⠋⠉⢳⡄⠀⢸⡆⡏
⢨⡶⠼⠆⢹⡽⠛⠛⠉⠃⣸⣽⢠⣏⣷⠀⢻⠀⢿⢀⡯⠀⣼⢸⣿⢹⠇⣿⠀⠀⠀⣿⡏⠉⣷⣼⠁⠀⠀⢸⠇⢀⡾⠁⢹⣄⣀⣠⠼
⢠⣄⡄⠀⠀⠀⠴⣿⡆⠀⠧⠿⢀⠌⡄⠀⠘⠲⠺⠞⠓⠒⠋⠘⠛⠚⠀⠘⠦⣤⠞⣿⠀⠀⣿⡿⢄⣀⣠⠟⠀⠀⠀⠀⡾⠉⢠⣤⣤
⠚⢶⠛⠠⠴⣱⠴⢋⡀⣰⣆⢻⡿⠀⡗⣠⡀⠀⠀⠀⣀⢤⡎⣳⣀⠀⠀⠀⠀⢩⠀⡻⣄⣠⠏⡀⠘⢋⡴⠊⠉⠑⢦⠀⢇⠀⠮⣿⠿
⠴⠆⢀⣀⡉⠋⠀⠈⠙⠾⠋⠁⠀⢀⣔⣛⣓⣄⠀⢴⡙⠦⠟⠗⣚⣳⠀⠤⠀⠀⠄⢃⠘⠉⠠⠁⠌⢸⠀⠀⠀⠀⠈⡇⠈⡆⢀⣁
⠀⠀⣿⠁⡭⠉⠉⣉⣷⡆⠀⠀⢠⡗⠢⠗⡒⢚⡇⢸⣸⣿⢻⢫⣿⠇⠀⡿⡄⠀⠀⠱⣄⢀⢀⠊⠀⠸⣄⠀⠀⣀⡾⠁⣠⠇⠺⠿⠂
⠀⠀⣿⣀⣠⣴⠞⠛⣩⡿⡵⠀⢪⣤⣑⣭⣤⡭⣼⠀⠛⠛⠛⠛⠋⡤⠀⠛⠳⠤⡀⠀⠸⡶⠁⠀⠀⣠⠟⠛⠉⠁⣤⡀⠁⣤⣤⡄
⠀⠀⠈⠙⣯⣄⡴⢞⡥⠚⣁⢀⠈⢿⣿⣿⣶⣧⠏⢀⢀⣴⡄⠀⢺⡁⠀⠀⠀⠀⣈⠇⢰⣧⠀⠀⠀⡇⠀⣴⣶⠀⠉⢁⡄⠘⠋
⠀⠀⠀⠸⣯⠵⠚⠉⠀⠠⣻⣟⠄⠀⠀⠀⠀⠀⠀⢹⠾⡿⣿⠃⠀⠹⡟⡟⣿⣿⣿⠀⠸⠁⠀⠀⠀⢸⠀⠈⠈⢀⣽⡁⡷⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣀⣀⣧⣿⣟⣛⣛⣀⣀⣀⣀⣀⣴⣃⣀⣀⣀⣈⣉⣉⣃⣀⣀⣀⣀
⣿⣿⠛⡿⢛⠻⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣦⣤⡀
⠀⠀⠀⠀⠀⣠⡦⠞⢻⠃⠀⠀⠀⠀⠀⠀⠀⢰⣏⠳⣍⡽⣿⠀⠀⠀⠀⠀⠀⠀⣰⠚⡔⠿⠷⣨⠓⣦⠀⠀⠀⠀⠀⣰⣇⣸⣮⣁⣩⣿⠷⡶
⠀⠀⠀⠀⣜⠜⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢨⠏⠀⠀⢳⠸⡄⠀⠀⠀⠀⠀⠀⠷⣤⡙⠶⣩⠕⠚⠁⠀⠀⠀⠀⠀⢹⠀⠙⠺⢥⣺⠏⠀⡇
⠀⠀⠀⠀⠘⠦⣄⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⣘⡼⠁⠀⠀⠀⠀⠀⠀⠀⠱⣕⠀⠁⣀⡼⠀⠀⠀⠀⠀⠀⠈⢧⣀⠀⠀⠙⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⣠⠤⠒⢐⣒⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢤⠒⢲⡀⠀⠀⠀⠀⠀⣠⢴⣯⣭⣍⡓⠢⡄⠀⠀⠀⠀⠀⠀⢀⡴⢦⣖⣓⢦
⠀⠀⢸⣅⠀⢺⠟⠛⣷⡈⢧⠀⠀⠀⠀⠀⠀⣘⣥⡞⣩⠿⡆⣼⢩⡇⠀⠀⢀⡞⠡⣏⣶⠖⡟⢯⠙⣷⣄⠀⠀⠀⢠⡞⠉⡤⣞⠯⠏⣬⡓⣆
⠀⠀⢸⡈⢧⡈⠓⣖⣋⠗⢀⣷⠀⠀⠀⢠⠊⢺⣤⣵⣤⣤⠿⡻⢸⠃⠀⠀⠘⢦⠘⣍⠫⣝⠿⣫⣢⠏⣸⠆⠀⠀⠈⢧⢧⠹⠈⠥⣄⢋⣇⣸
⠀⠀⠀⠙⢤⡙⠀⠈⣉⡽⠋⠀⠀⠀⠀⠈⠙⢦⣐⠤⣤⠶⣚⡵⠋⠀⠀⠀⠀⠈⠹⣌⠓⠶⠚⢉⣇⠞⠁⠀⠀⠀⠀⠀⢯⠓⠚⢛⡋⢈⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⣠⠤⢤⣔⠒⠲⡄⠀⠀⠀⠀⠀⠀⣠⠤⣴⣒⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠔⠒⣦⣄
⠀⠀⠀⣰⢃⡴⡯⠬⣝⢳⡗⢄⠀⠀⠀⠀⡴⠃⡼⣿⣻⠝⡎⢹⡄⠀⠀⠀⢀⡴⠋⣉⣷⡾⢿⣺⣟⠙⡆⠀⠀⠀⢀⡞⡱⣚⣺⡫⡉⣿⠳⣄
⠀⠀⣾⠀⡿⣌⣧⡼⢎⣿⠇⢸⠄⠀⠀⢰⡇⠀⡀⠈⠁⠴⠻⡄⣻⠀⠀⠀⠀⠳⣸⡟⡏⠓⠒⣺⢿⠇⢻⠀⠀⠀⡼⡷⠉⡧⣤⣨⠟⣮⢳⣈⡇
⠀⠀⠹⣄⢻⠬⠿⣛⣫⠾⡶⠋⠀⠀⠀⠨⡟⠳⣌⠓⠖⢂⡠⠃⣸⠃⠀⠀⠀⠸⡍⠓⠬⠶⡍⠒⠋⢛⡏⠀⠀⠀⠙⢿⢦⡙⢶⣶⡚⢁⡾⣯
⠀⠀⠀⠈⠉⠳⣄⣀⣤⠞⠁⠀⠀⠀⠀⠀⠙⠶⠬⠿⠿⣉⡤⠶⠃⠀⠀⠀⠀⠀⠙⠦⠤⠖⠳⠤⠞⠉⠀⠀⠀⠀⠀⠘⣆⣩⣭⠽⠯⠭⣤⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠
⠀⠀⠀⠀⢀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠄⠀⠀⠀⠀⠀⠀⣾⠈⠀⠀⢀⡄⠃
⠀⠀⡰⠎⠉⣠⠀⠈⣤⠆⠂⠂⡄⠀⠀⠀⠀⢀⡤⢂⠀⠐⠲⡄⠀⠀⠀⢸⢾⠆⢁⣠⣿⠃⠀⠀⠆⡀
⠀⠀⣱⢀⣀⠀⣒⣠⢴⠀⠀⠈⣻⣄⠀⠀⠅⠘⣰⠂⡈⠁⡄⣌⠠⡆⣀⠈⢏⣼⣿⡟⡃⠂⣀⣴⠉⠈⠉⠒
⠀⠀⠉⠡⠀⠴⠆⠀⠛⢁⡦⠄⢈⡺⣷⠀⡃⢀⠐⠂⢿⠿⠁⠁⡔⣈⠀⠓⠊⠉⠉⠁⠀⢰⣿⣿⠀⢧⠀⢁
⠀⠀⠀⠀⠀⠀⠀⢠⢔⣣⣴⠞⣋⡵⣃⡀⠛⢀⢠⠀⠢⠄⠠⡈⢰⠉⠿⣧⠉⠠⡄⠀⠀⠘⠛⢁⡐⠀⢳⠃
⠀⠀⠀⠀⠀⠀⠠⠐⠋⠁⠒⠋⠁⠀⠳⣣⠀⠈⠠⠰⢌⠴⠫⠖⠊⠰⣦⠈⠳⣄⠈⠆⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠅⠀⠀⠑⠙⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⠀⠉⢀⠀⢾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⢀⠀⠁⢀⣠⠄⠀⢠⣄⣉⡁⠰⠘⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⡆⠠⣶⣿⠀⣴⡎⣁⣀⣶⣦⣘⣿⣧⣴⡀⢸⣦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⠀⢎⠰⣦⡴⠾⠿⠟⠋⢽⣿⣿⣷⣘⣿⡾⢋⡴⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠆⠈⠀⢡⡝⠳⠢⠐⢴⣿⣿⣷⣾⡟⣋⣴⣻⣿⡆⠀⠶⠊⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣀⠀⠀⣾⣶⡀⠀⠀⠀⠠⡄⠀⠳⠤⣿⣄⣀⣀⣤⣩⣭⣙⢹⣿⣿⣵⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣆⣀⠀⠀⠀⠙⠳⣝⣷⣆⢉⣉⡛⠛⠿⢿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣌⠙⠻⢿⣿⣿⡆⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⠿⢶⣾⣿⣿⣟⣫⣴⣶⠶⣶⣿⠉⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⢲⣤⣾⣿⣿⣶⣤⣾⣷⠶⢮⡿⣿⣿⣿⣶⣿⣿⣿⣿⠿⢿⣿⢳⠀⠻⣿⣶⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠻⠏⠹⠏⢽⣿⠟⠁⠀⠚⢻⣿⣽⠿⠻⣿⣿⣿⢻⡀⠀⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠦⠒⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⠻⢿⣿⣷⣄⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⡀⠀⢀⣿⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣅⠁⠠⠀⠀⠀⠀⠀⠀⠀⣠⣴⡟⣿⣦⣾⣿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡛⢿⣶⡆⠀⠀⠀⠀⠀⠟⣡⣼⡇⣿⣿⣿⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠹⣿⠿⠟⠛⢶⣆⠀⠀⠈⠆⣿⣿⢻⣿⣿⣿⡷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣤⣈⡲⢦⣄⣓⣿⣷⣿⣄⠀⢿⣿⢸⣿⣶⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠟⠻⣿⠏⡻⠛⠲⡜⢻⡈⠉⠁⠀⢀⣀⠀⠀⢀⣠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⡰⠁⠀⢀⣿⠏⠀⠀⣠⣶⣿⣿⡀⢀⣾⣍⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠸⠋⣀⣀⣴⣿⡿⢋⡉⣳⣾⡯⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡶⠁⣸⣿⣿⣿⢿⡀⢸⣤⣿⠛⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⢸⣿⣿⣿⣷⢠⣤⣼⣿⠿⠶⢦⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣸⠿⢻⡿⢿⣿⣿⣿⣿⣷⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⡌⣤⣶⣷⡶⢶⣮⣽⡛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⢸⢿⣛⡾⠿⡃⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣣⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢽⡓⣆
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⡖⠒⢲⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠉⢻
⠀⠀⠀⠀⠀⠀⡠⠟⢤⡀⢹⠀⡜⠀⡸⠙⢆⠀⠀⠀⠀⢠⣄⠤⠖⠢⡀⠀⠀⠀⠀⠀⠀⣧⠈⠓⢾
⠀⠀⠀⠀⠀⢠⠃⢀⣀⠱⣜⣴⣁⠔⠁⣠⠎⢧⠀⠀⠀⠈⢦⢀⠀⢠⠇⠀⠀⠀⠀⠀⠀⡟⠓⢦⣸
⠀⠀⠀⠀⠀⠸⡎⠁⢀⡽⠋⣿⠯⣐⣉⡠⠤⢺⠀⠀⠀⠀⠀⣳⣾⣎⠀⠀⠀⠀⠀⠀⠀⢰⣄⡀⠙
⠀⠀⠀⠀⠀⠀⠳⣀⠎⠀⠀⡇⢆⠀⠀⠀⣠⠃⠀⠀⠀⢠⡋⠙⠀⢨⢷⠀⠀⠀⠀⠀⠀⢠⠀⠙⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣄⣧⣀⣱⠶⠚⠁⠀⠀⠀⠀⡟⠋⠠⡦⠀⣀⡇⠀⠀⠀⠀⠀⢸⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢹⠀⠀⠀⠀⠀⠀⠀⠀⡷⠆⢀⣄⠀⠉⡇⠀⠀⠀⠀⠀⢸⣤⡀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠀⣀⠐⠶⡇⠀⠀⠀⠀⠀⠸⠀⠙⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠀⢀⣀⡀⠀⠀⠀⠀⢻⣁⠀⡉⢀⣼⠁⠀⠀⠀⠀⠀⠸⠶⣄⡀⠱
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⢾⣶⣖⣉⣠⡼⠀⠀⠀⠀⠈⠫⢤⣫⡴⠃⠀⠀⠀⠀⠀⠀⠀⣆⡀⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⣹⠛⡷⢄⡀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠷⡄⠀⠀⠀⠀⠀⠀⠀⡇⠙⠢⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢹⠀⡄⠀⠙⠂⠀⠀⠀⠀⠀⢀⡇⣀⠤⠼⠀⠀⠀⠀⠀⠀⠀⢸⠦⣄⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⣤⠤⠼⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠘⡡
⠀⠀⠀⠀⠀⠀⠀⠘⣧⣴⢶⡆⠀⢠⠀⠀⠀⠀⠀⠀⠀⠻⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠩⡄⢤⠊⠀⠀⢀⡀⢰⡇⢀⠊⠀⠀⠀⠀⢠⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡘⣿⠁⠧⣀⣿⣠⣼⣠⣾⣵⣹⣿⠋⠔⠛⠋
⠀⠀⠀⠀⠀⠠⠀⠐⠾⠲⢶⣿⣜⢮⣤⣿⡿⠟⠁⣻⣿⢋⠉⠁⠀⡀
⠀⠀⠀⠠⠶⠶⢾⣶⡶⡶⢾⣿⣿⠈⣿⡥⣀⣤⣎⠀⠀⠁⠙⢯⠀⠉⢻
⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠜⠁⠨⠉⠀⠂⢡⣤⡞⣋⡙⣓⡶⠾⣇⢀⡘
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣀⣴⠀⣾⢁⡔⣱⣿⣾⣷⠆⣀⣹⠻⣷⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠁⡳⢤⣽⣼⡇⠀⣷⣿⡾⢽⣽⣿⣧⠻⠄⠈⠋⢠⡏⣧⠀⠀⡔⡀
⠀⠀⠀⠀⢧⣀⡂⢀⣤⡴⠋⠉⣄⠀⢸⡏⠳⠈⠿⠃⣈⡀⠀⡤⠀⡈⠁⢻⣷⣾⡟
⠀⠀⠀⢤⡼⠟⣇⣻⠯⠀⠀⢮⣉⠀⢼⣇⠐⡗⠦⣤⣟⠁⠀⠀⣰⠁⣀⣾⣿⠟⠛⠛⢲⡼⠁
⠀⠀⠄⠀⣴⡿⡏⠛⢄⠀⠀⠀⠈⢣⡀⠙⢦⣸⡶⠶⠜⠳⢦⣠⣿⢸⣿⣿⡅⠠⣤⣤⠜⠁
⠀⠁⠀⠀⠾⠁⠁⡀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠉⠀⠀⣀⠀⢀⣹⡟⠋⠀⠀⠀⢀⡿⠁⠀⠀⠀⢠⠀⠖
⠀⠀⠀⠀⢰⡼⠚⠁⠀⣀⣀⠀⠀⣠⠞⠉⠉⠙⠻⠿⠛⢿⣭⣛⠄⠀⠀⢀⡠⠊⠀⠀⠀⡠⠖⠊⠛
⠀⠀⠀⠀⠈⠀⠚⠉⢀⢩⣽⣷⣶⣯⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠓⠋⠙⠛⠷⣶⢶⡋⢵⡤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠚⠛⠣⠿⣏⣸⣿⣶⣄⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣿⠆⠑⠀⠡
⠀⠀⠀⠀⠀⠄⠈⢀⣀⢦⣘⣿⣿⣿⠟⣯⠈⠉⠢⣄⠀⢀⡀⠀⠀⠀⣀⢀⠛⠻⠀⠀⠀⠀⠀⢄⢣⡀
⠀⠀⠀⢀⡠⠒⠋⠀⠞⢉⣩⣿⣿⣏⣷⣿⡷⠀⢀⠀⢀⠞⠁⢿⣷⣿⣟⢛⠏⢩⡏⠀⠀⠀⠀⠀⠀⠁
⠀⠀⣰⠃⠄⠐⠃⠁⠀⢸⣿⣿⢿⡉⠉⠹⣁⠐⣒⠀⣹⣷⡆⢼⡏⠳⡝⢦⡀⢀⣴⣈⡵⠞⠛⠖⠒⢄
⠀⠀⠉⠀⠀⠀⠀⠀⠀⣾⣿⡁⠾⢁⡀⠀⠈⠉⠁⢸⡆⠹⣯⠀⢿⣄⠁⠀⠙⠎⠛⠻⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠁⠀⠾⡁⠢⣤⠀⠀⢰⣌⠀⠀⠀⢀⠋⡷⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⡓⡂⠀⠀⠸⠃⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈

⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠒⠤⢀⠀⠀⠀⠀⠀⣀⣴⣎⣩⣶⣦⡀⠀⠀⠀⠀⠀⣀⢆⠁⠀⡌⢆⠀⠀⠀⠀⠀⡠⣶⣬⣿⣷⣴⣿⡐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡎⠀⠀⠀⠀⠂⠁⠀⠀⠉⠛⣿⣿⡄⠀⠀⠀⢰⠌⡁⣈⢁⠡⠄⠇⠀⠀⠀⢠⣴⣿⣿⡁⠀⢀⣹⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡘⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢸⡿⠃⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣸⣿⣟⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠈⠉⠉⠙⠓⠍⣁⠀⠠⠁⠀⠀⠀⠀⠐⠤⣄⡀⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠭⠹⠿⠋⠍⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠔⠒⠒⠤
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⡀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⢴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠀⣀⡔⠀⠀⠀⠀⠀⠀⠈⠢⠊⡀⠤⠈⡄⠀⠀⠀⠠⠆⠀⠉⠿⠛⠁⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⢸⠷⣽⣿⣛⣛⣛⣫⠭⠇⠀⠀⠀⠀⠀⢄⠀⠠⢄⢁⠄⠀⠁⠀⠀⠀⢸⠓⠲⠶⠤⣤⣀⣀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠦⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠠⢀⡈⠃⠀⢃⡦⠂⠀⠀⠀⠀⠘⠉⠙⠛⠒⠶⠶⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠉⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠤⠐⠀⠈⠀⠀⠈⠐⠄⠀⠀⠀⠀⡼⢿⡟⠁⢹⡟⠻⣷⠀⠀⠀⠀⠀⣰⣾⣿⣛⣻⣷⣶⡀⠀⠀⠀⠀⠀⠀⢸⠃⢠⠞⠙⢢⠈⣷
⠀⠀⠀⠀⠘⠠⠶⠀⠀⡤⠀⠀⠰⠊⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⢀⠈⠙⠛⠛⠛⠛⠉⢃⠀⠀⠀⠀⠀⠀⠘⣄⠸⣦⣐⣁⣼⠇
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⡤⡠⢤⠀⠁⠀⠀⡠⠂⡍⠀⠀⠀⠀⠀⠀⠀⠘⡅⠠⠀⠀⠀⠀⠀⠈⡷⠆⠉⠉
⠀⠀⠀⠀⠀⠢⡀⠈⠀⠀⠀⠈⠕⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠈⠞⠀⠀⠀⠣⡀⠐⠢⠤⢤⣀⣤⠤⠴⠎⠁⡠⠀⠀⠀⠀⠀⡐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠸⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡌
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠆⠙⣿⣿⣿⣿⡿⠃⡓⠀⠀⠀⠀⠀⠀⢀⣀⣠⣠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠆⠀⠀⠀⠀⠀⣀⠐⠁⠑⠉⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢈⠻⣿⣋⠌⠀⠀⠀⠀⠀⢠⣾⣻⢻⣟⣞⣻⣿⢽⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⡶⡶⠀⠀⠀⢀⡴⠋⠉⠉⠉⠳⣄⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠸⣷⣷⣿⣿⣷⣯⣿⣿⣿⢿⠏⠀⠀⠀⠀⠀⠀⠀⣰⢶⠇⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠉⠉⠁⠉⠈⠁⠀⠀⠀⠀⠀⢣⡾⢅⡠⠷⡶⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢸⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠃⠸⠷⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠛

⠀⣀⢀⡀
⠀⡁⠀⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡏⠘⣯⡁⠂⠀⠄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠣⡀⠈⠙⠲⢤⣀⠐⡸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀⠀⠀⢱⣤⠀⢀⠀⠹⣿⣾⠇⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⢀⠤⠐⠀⣠⠃⢈⠤⠀⣀⣈⡀⠐⢿⡇⠀⠀⠀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠒⠒⠛⠂⠙⠱⢂⠋⠁⣡⠶⠋⠀⠈⢢⠀⠀⣩⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢸⠃⠀⠀⠀⠀⢨⣷⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠲⠤⠴⠤⠞⠃⠀⣼⠀⠀⠀⠀⠀⣸⠁⢸⣄⠈⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠚⣁⣀⣠⡤⠖⠋⠁⠀⢠⡧⢀⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠑⢦⣶⠖⠒⠶⠒⠒⠉⠓⠀⠀⢀⡴⠞⠋⠉⠉⠁⠀⢀⣀⣤⣴⣿⣿⣛⡳⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠉⠢⢤⡀⠀⠀⠀⣠⣶⡛⠁⠀⠀⣀⣀⣤⣴⣾⠿⢟⠭⠋⡙⡉⡍⢐⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢀⠀⠀⠀⠀⠉⠋⠛⠛⠛⠛⠟⡛⠚⡛⠟⠻⡏⢍⠁⠀⠈⠀⣾⣶⣾⣷⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠹⡶⣤⣄⣠⡄⠀⣀⠀⣀⢀⣄⣀⢡⣈⣠⣇⣴⣥⣼⣿⢷⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢧⢸⡆⠸⡏⠉⣻⠉⢿⠉⢻⡋⢻⠛⢻⠍⢉⡇⢠⣯⢸⣿⣭⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⡄⣷⠀⣷⠀⢹⡀⢿⠀⣼⠀⢸⠁⣸⠀⣸⡇⣸⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠰⣸⡆⢻⠂⠸⣇⢼⠣⣸⡅⢸⠆⣿⢈⣿⣹⣿⣿⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠸⣿⣟⣹⣧⠀⣏⣾⡇⣿⣧⣿⢐⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡿⣿⣻⣲⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡼⣿⣿⣷⣿⡟⣿⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣧⣤⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣷⣿⣿⣷⣿⣿⣷⣿⣏⣿⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡷⠿⡏⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣏⠿⠿⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠻⠟⠻⠿⠻⠛⠛⠛⠛⠛⠋⠛⠉⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠃⢤⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠆⠀⠀⡀⠀⢄⠀⣀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣠⠀⣶⠉⠀⡀⠒⢉⠤⠂⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣠⠄⡴⠦⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠉⠈⠩⠘⠀⡀⢳⣀⢋⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⣼⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠴⢦⠀⣺⣦⣉⡯⠀⠀⠀⠀⠀⠁⠀⠀⠐⣄⠘⢧⡀⢀⠁⣀⣀⣠⠤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠠⡠⠋⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠔⠀⠀⠐⠤⣀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢀⣀⣦⠀⠀⠘⠒⡡⠁
⠀⠀⠀⠀⡄⠀⠀⠀⠀⡤⠄⠀⠀⠉⠁⠀⠀⠀⠀⠀⠙⠶⠀⢧⠀⠀⠀⠀⢘⣿⣿⡷⠂⢒⠁⡤⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠜⠀⠀⠁⠀⡤⡆⠀⠀⠀⠈⣄⠀⣠⠴⠂⣀⡼⠓⠀⠀⠀⠐⠩⠏⠀⠀⠈⠉⢴⣷⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠛⠁⠀⠀⠈⠀⠘⢷⠤⠖⠈⠁⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠘⣿⣿⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠂⡄⠀⠀⠀⠀⡛⠄⢠⡀⣀⡀⠀⠀⠀⠀⠁⠀⠐⠉⠀⠹⣦⣌⠢⠀⠀⠐⢄⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠁⠀⠠⣈⣠⡁⠀⠫⠁⠀⢀⠀⠀⠀⠈⣉⡉⣙⠷⢦⡀⠠⠈⡉⠂⢲⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠹⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢠⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⣿⣿⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠈⣤⡄⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀⢀⣴⡄⠀⠀⠀⠀⠀⣀
⠖⠠⠀⠀⠀⠀⠀⠀⣿⠁⠀⡀⠄⠀⣤⢠⡀⠀⠀⠀⠉⠁⠀⢀⣤⣤⣾⠟⠃⠄⡀⠀⠀⡀⢰⠏⠛⠉⠀⠀⠀⣼⣾⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠟⠛⠇⠀⠉⠀⢠⠃⠟⠁⠀⠀⠆⠀⠀⢰⡇⠀⠀⠙⣧⠀⠀⠉⠓⠘⠏⠀⠀⠀⠀⠀⠀⢰⣏⣠⣶⣿
⢺⡏⠀⠀⠀⠀⠀⠀⣾⣷⣶⣶⣆⢸⣶⣦⡀⢀⠀⠀⠀⠀⠈⠁⠀⡀⢀⣍⠀⠀⠀⠀⡹⠀⣤⠶⠀⠀⠀⠀⣿⢻⡟
⠘⠁⠀⠀⠀⠀⣠⢾⡿⠛⠋⠁⢙⣿⣭⣥⣿⡿⠿⢷⡀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⢻⡿⠇⠀⠀⠀⠀⠀⠻⠘⠃
⠀⠀⠀⠀⢀⣀⡛⠚⠃⠀⠀⠀⠈⠉⢨⣿⠁⠀⠀⠀⢹⠀⠀⠀⠀⠸⠟⠃⠀⠀⠀⠀⠘⠟⣀⣤⣶⣶⣦⣴⣄⡀⣦
⢀⡄⠀⠀⢀⣇⣿⠛⠂⠀⠀⠀⠀⣿⣿⢻⠀⠀⠀⠀⢸⣠⣤⣼⣷⣷⣶⡄⠀⠀⠀⠀⠀⣇⠝⠛⠿⣿⣿⣿⣿⣿⣿⣦⡀

⠀⠀⢀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠈⡃⢄⠀⠸⣧⠯⠃⠀⠀⢀⣀⣐⠀⠉⠁⠀⠀⠐⠀⠠⢀⠀⠀⠐⠻⡟⠂⠀⠀⠀⠀⠐
⠀⠐⢤⠃⠀⢀⠔⡅⠀⠀⠐⣋⠤⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⢀⣀⣂⣀⠀⣴⠆⠾⠇
⠀⠀⠀⢀⠔⢁⠢⡇⠀⠀⠀⠀⢀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠽⠒⠅
⠀⢀⡔⠁⢌⢢⢳⡇⠀⢹⡃⠀⣸⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠈⠀⠤⠑⡄⠀⠀⠀⠀⣤⡞⠀⠹⠆⠬
⠀⠫⣉⠉⠚⢦⣻⠁⠀⡈⠳⠎⢸⣀⠄⡟⢃⡠⢧⣀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡠⠒⠀⠋⠀⠑⢲⠊
⠀⠀⠈⠉⠓⠒⠛⠀⠀⡷⠴⢶⣺⢅⡜⠀⠀⠹⢪⠋⣹⠒⠶⠤⢤⠴⠶⡊⠟⣄⠴⠄⠈⠁⠲⠉⠀⢠⠄
⠀⠀⢀⣀⣀⡀⢀⣀⠀⠫⠻⣷⣮⡟⢠⢒⡒⢄⠀⠉⠀⠃⠰⠢⠌⠦⠆⠈⠃⠈⠀⠀⠀⢀⡈⠀⠀⠈⠂
⠀⠀⠙⢄⠀⢠⡋⠶⠥⡀⠀⠀⣀⠀⢧⡇⠈⢪⡄⣰⠞⠉⢢⠀⠀⢤⠀⠀⢰⠠⠂⠀⡠⢊⢁⠝⠑⠒
⠀⠀⣀⠀⠑⢼⢢⣔⠀⠉⠳⣄⣈⣯⠚⠿⣄⠌⣷⡟⠀⣀⠎⠀⠒⠈⣁⣠⠤⠒⠂⠀⠀⠁⠃⠔
⠀⡰⢤⡂⠐⣢⠉⠈⢳⡉⣉⠽⡏⠉⡑⠲⢬⡟⢙⣶⣚⣉⠙⢧⠀⣸⠑⠀⡗⠀⢀⠀⠀⡠⠀⠀⠀⠠⡀
⠀⠰⠔⠄⢀⡽⡄⠀⠀⠻⠴⡞⠁⠀⢦⠀⢠⠀⢀⡀⢀⡰⠀⠀⠀⢇⢀⡔⠱⢄⡜⠀⢠⠁⠀⠀⠀⠀⠄
⠀⠀⢀⣀⣸⢀⠇⢀⠀⠀⠀⢹⠀⠀⡆⠀⢸⠀⠀⠀⢠⠀⠀⠀⠀⡨⠉⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢠
⠀⠀⢘⢒⠢⡿⠤⠒⡃⠀⠀⢸⠀⠀⡇⠀⢸⠀⠃⠀⡆⠀⠀⠀⠴⡇⠀⠀⠀⢠⡼⠤⢀⡆⠄⠤⠒⠁
⠀⢀⣸⠂⠈⠑⠎⢸⠀⠀⢿⡛⣏⠀⠉⠉⠉⠘⠒⠒⠃⠀⢠⡤⠐⠀⠤⠶⠂⠀⠀⠀⠙⠂
⠀⠘⠤⣑⣦⣤⣔⡃⠴⠀⡰⠉⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡇⠃⡰⡟⣭⣕⡄⢯⡟⠀⠀⠀⢀⣸⠙⣳⠆
⠀⠀⠀⠈⣒⣒⡉⠀⠀⠀⠀⠀⠴⡀⠀⠀⠢⡁⢀⡀⢀⣀⢧⣆⠘⠷⢝⠿⠃⢀⠀⠂⠀⡠⠢⡀⢙
⠀⠀⢠⠊⡉⢳⣹⣀⠠⠰⣷⠄⠣⡁⠠⠀⢠⣌⠀⠲⠟⠉⠀⠉⠑⠒⠀⠀⠀⠀⠀⠀⢀⡫⠒⣠⠏
⠀⠀⠈⠦⣑⣊⣁⣀⠤⠒⠉⠀⠀⠈⠢⠘⠋⠈⠀⠈⠀⠈⠀⢠⡀⢢⠘⢑⡀⠀⠀⠀⢏⣋⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠁⠊⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠉⠁⠉⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⡀⠀⠀⢀⡾⠉⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠉⠙⠳⣦
⠀⠀⠀⠀⠀⠀⠀⣠⡞⠋⠀⠀⠀⠀⠉⠓⢤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣴⠟⠛⢳⠶⠶⠛⠛⠛⢧⠀⠀⠀⢷⠀⠑⢦⡀
⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⢀⡴⠋⠉⠉⠓⠀⢀⣧⡴⠶⢦⡀⠀⠀⠀⠀⠈⠃⠠⣄⠘⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣠⠟⣁⠀⣴⠚⠃⠀⠐⣦⠐⠢⣄⡀⠘⣷⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⢰⠃⠀⣿⠀⠻⣦⡀⠘⣷⠿⣇⠀⡈⠻⣦⡜⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠉⠳⡇⠀⡸⢀⣼⠀⠀⡿⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠿⠸⣍⠛⠳⠶⢦⣤⣚⠁⠠⠞⢁⣀⡤
⠀⠀⠀⠀⠀⢀⡤⠶⠒⠚⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⡀⠀⠀⠙⣧⢀⣤⣤⡴⠶⠖⠂⠙⠉⠉⠀⠀⢄
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠦⣄⣀⣸⠀⠀⠀⠈⠣⠀⠀⠀⣠⡾⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠉⠁⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠐⠒⠶⠶⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈⢻⡶⠶⠞⠛⠛⠛⠛⠋⠁⠀⢠⠴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠴⠟



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

⠀⠄⠀⡀
⠀⠀⠘⢮⢳⡔⠢⡀
⠀⠀⠀⠈⠱⢿⣆⠀⢳⣄
⠀⠀⠀⠀⠀⢀⠙⢄⡀⣻⡆
⠀⠀⠀⠀⠀⠀⢳⣴⣿⡿⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⣀⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣾⠇⠀⢰⣾⢶⣄⣼⠧⠀⠖⡆⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⢿⣇⠀⠀⣸⡇⢀⣻⣏⠀⢀⣄⠳⡆⠀⠀⣠⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣶⠶⠞⠃⠀⠀⢽⣆⠐⣿⠇⠀⠀⠉⢙⣿⣿⡆⠘⣆⣆⡟⢀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⢀⣽⣿⣿⣿⣧⣠⡴⠟⠛⠿⢿⣿⠀⢹⣿⣥⠾⠷⠾⣶⠀⣽⠂⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⠀⠀⠀⢄⡽⠟⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠻⣄⢾⣿⡁⠀⠀⠀⣿⠸⡟⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢴⡾⠁⠀⠀⠀⣠⣷⣤⡤⣶⡢⣴⣆⠀⠈⠻⣿⣿⡄⠀⠀⢳⡄⢻⡇⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢻⡟⠀⠈⠁⣹⣟⠿⣿⠏⡿⠂⠃⠁⠃⠈⠈⠻⣤⣀⡙⢿⣿⣷⠀⢻⡇⡞⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⢤⣜⠯⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⡟⠛⠸⣿⡇⢘⠉⢗⡼⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠇⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠜⢉⡍
⠀⠀⠀⠀⠀⠴⠂⠒⠒⠛⠓⠈⠃⠶⢦⣤⣶⣾⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⣉⣩⣷⣤⡀⠀⡀⢀⠀⠀⠀⣀⠤⠖
⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠦⠄⠆⠈⡼⠛⠀⠙⣿⣏⣹⣿⣷⣄
⠀⠀⣠⣷⣾⡶⠶⠶⠶⠦⣤⣀⣰⢁⣠⣶⣆⠁⠀⠀⠀⠀⢿⣿⠀⠙⠿⣿⡄
⠠⠄⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⡿⠛⢿⣏⣿⠂⠀⠀⠀⠀⠸⣿⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠁⠀⠀⢉⡿⢤⠤⠀⠀⠀⠀⣿⡇⠀⠀⠀⠙⢧⡄
⠀⠀⠀⠀⠀⠀⠐⠀⡀⣀⢠⣤⠿⠿⢠⠂⣀⣀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠁⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠙⠿⠿⠂⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠠⣯⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣶⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⢀⣀⡀⠀⢾⣿⣿⣿⡟
⣾⣿⣷⠄⠀⠀⠲⢀⠀⠀⠉⡀⠀⠁⠀⠀⠛⢿⣿⣿⠀⠀⠑⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⠟⠃⠀⠀⠀⠐⡂⠀⠐⠛⠀⠀⢿⡿⠟⠋
⣀⣀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠤⠄⠀⠀⠀⠀⠀⠀⠀⠄⠂
⠿⠋⢀⣦⡈⢿⡏
⣟⡷⢸⣿⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠛⠁⠈⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴
⣶⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿
⡟⢻⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣿⢿⣿⠑⣻
⣷⣾⠏⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⣴⡶⢶⣦⣀⣀
⣶⣿⣿⣿⢿⣯⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣴⣶⣦⡀
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣯⣿⣷⠀⠈⠹⠿⠛⢁⡄⣀
⣿⣿⣿⣿⣦⣈⣷⣿⡞⣿⣿⣧⡀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⣂⠄⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠐
⢿⣿⣿⣻⣿⣿⣿⣿⣧⣻⣿⣿⡇⠀⠊⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⠑⠂⡄⢀⠆⠀⣸⣿⣿⣿⣿⣿⣿⣇⡀⡀⠀⠻⡿⢿⠿⠁⠀⠀⠀⠀⠀⠀⠠⢾

⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢀⡞⠻⣟⢛⡻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⢟⡛⣻⠟⢳⡀
⠀⠀⠀⠀⣼⠁⠀⠈⢷⣽⣿⣿⣏⡻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢟⣹⣿⣿⣿⡾⠁⠀⠀⣧
⠀⠀⠀⢀⡇⠀⠀⠀⠀⠹⣧⢹⣿⣿⡷⣝⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣻⢾⣿⣿⡏⣵⠏⠀⠀⠀⠀⢸⡀
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠠⡘⢷⡻⣿⣿⣶⣟⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⡷⣿⣾⣿⣿⢟⡾⢃⠎⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠐⡈⢷⣸⣿⣿⢿⣿⣷⣯⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣵⣿⣟⡿⣿⣿⣇⡾⠁⠂⠄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢣⠘⣿⢿⣟⣾⣿⣿⣿⣿⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣿⣿⣿⣿⣷⣻⡿⣾⠃⡌⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠄⢃⢹⣆⣿⣿⣿⣿⣿⡧⡽⠚⢻⢖⣐⢖⣨⣆⣰⣁⡲⣊⠲⡟⠓⢭⢾⣿⣿⣿⣯⣿⣴⡏⡘⢠⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⡘⡈⡌⣿⢷⣿⠟⢹⠃⣶⣇⣾⡿⣼⣟⣾⠟⣰⣌⠻⣷⣻⣷⢿⣷⣸⣶⠘⡏⠻⣿⣾⣿⢡⢁⠃⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠰⠱⢹⣿⢊⣽⢺⣿⢸⣿⣻⣿⣱⡿⠿⢗⣴⣿⣿⢷⡙⠷⣿⣞⣿⣿⣿⡇⣿⡇⣯⡑⣿⡜⡆⠆⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⢡⣣⢏⣵⢸⣿⢸⡟⢾⣓⣛⣭⠿⠶⠀⣿⣿⠟⠻⣿⣷⠀⠖⠯⣭⣛⣚⡷⢻⡇⣿⡇⣮⡹⡜⡜⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⢺⡏⣼⣿⡟⣫⠴⣺⣿⣿⠛⢶⣫⣭⣗⢾⡇⣸⣇⢸⡷⣺⣭⣝⣶⢛⣿⣿⣟⠦⣽⢻⣿⣵⢹⡇⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢻⢱⣽⢏⡿⣱⣿⣿⣿⣿⡿⠿⠟⠿⣿⣷⣷⢸⡇⣾⣾⣿⠿⠛⠿⢿⣿⡿⣿⣿⣬⢷⡹⣯⡎⡟⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢉⣻⣿⣾⣿⠧⠖⠚⠉⠉⠈⠀⠀⠀⠀⠙⢿⡞⢳⡿⠋⠀⠀⠀⠀⠀⠉⠋⠓⠶⠼⢿⣷⣿⣟⡙⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣠⣟⠡⠠⠒⠐⠀⠀⣀⣠⣤⣤⣀⣀⣀⣀⣬⣽⣿⣿⣯⣥⣀⣀⣀⣀⣤⣤⣄⣀⠀⠀⠀⠐⠀⢈⣻⣄⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⣀⣤⣾⣿⣿⣿⣿⡟⣫⢿⣿⣫⣾⣿⢿⡿⣿⣷⣝⢿⡻⣽⢻⣿⣿⣿⣿⣶⣤⣀⠀⠀⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⣿⣿⣿⣿⡿⣫⢟⣽⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣯⡳⣝⢿⣿⣿⣿⣿⢻⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⡿⣱⢫⣾⠟⠋⠙⠛⠋⢹⣯⣽⡏⠛⠛⠋⠙⠻⣷⡹⣎⢿⣿⣿⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⣾⣿⣯⡿⣿⢱⢏⡞⠁⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠈⢳⡹⡄⣿⣿⣽⣿⣷⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣿⣿⣷⣿⣿⡷⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⣹⣟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⢾⣿⣿⣾⣿⣿⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣮⠻⣿⣯⢹⡟⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀⢻⡏⣽⣿⠟⣽⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⢿⣿⣷⣌⢡⠾⣀⡀⠀⠀⠀⢀⣀⠴⡋⢀⡾⢷⡀⢙⠦⣀⡀⠀⠀⠀⢀⣀⠷⡌⣡⣾⣿⡿⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣥⣉⣽⡿⣤⣃⠹⠉⠽⠉⠍⢀⣠⢴⡿⣣⣘⢿⡦⣄⡀⠉⠉⠭⠉⠏⣈⣤⠿⣯⣉⣬⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠈⠉⠉⠛⠒⠛⠛⢉⣵⠛⣵⡟⢻⣦⠛⣦⡉⠛⠛⠒⠛⠋⠉⠁⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠤⠤⠤⠶⣺⣭⣞⣣⣦⢡⡌⣴⣜⣷⣭⣗⠶⠤⠤⠴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣾⣯⣵⣻⣾⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡰⢄⠈⠀⠀⢀⠀⠀⠅⠑⢶⣦⣄⣀⠀⠀⠀⠀⠀⠈⠀⠀⠰⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⣁⣀⡴⠖⢾⡟⠀⢀⠀⠀⢀⢀⡄
⠀⠀⠀⠃⠦⠈⢱⠚⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠶⠈⠡⠈⢲⣶⠄⣠⠠⣤⡀⢠⡤⣀⣀⣀⢀⠄⣀⣤⠀⠄⠰⡶⠒⠄⠉⠏⠁⢀⠀⠀⠀⠈⠀⠐⠲⠖⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠀⠛⠀⠀⠀⠈⠟⠁⠁⠀⠙⠁⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣈⠻⣤⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣀⡸⠟⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠁⠀⠀⠊⠀⠈⠓⠖⠒⡀⠤⢤⠀⠀⢀⣀⠀⠀⢌⡀⢀⠀⠀⣠⠶⠤⡤⢀⠀⠰⠛⠀⠸⠁⠉⠉⠀⠅⠀⠀⠀⠈⠁⠀⠀⡏⡆
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠤⠀⠠⡖⢆⠀⠰⣴⡄⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠶⠈⠀⠀⠀⠃⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⣀⠈⠀⠀⠈⠀⠀⠀⢱⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠽⠁⠀⠀⠀⠁⠀⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠘⢶⡄⠀⠀⢀⣀⠀⢀⡈⠰⠆⠀⠀⠀⠁
⠀⠀⢤⣴⠾⠶⠶⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠀⠀⠘⣛⢂⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢺⠂⠄⠈⠁⡀⠈⠈⠒⢀⣀⠀⠰⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣤⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠁⠈⡀⠀⠀⠈⠁⠀⠀⠆⠁⠀⠐⠦⡈⠉⢠⠀⠀⠀⠉
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁⠀⠀⠀⢀⡰⠒⠇⠀⠰⠂⠀⡀⠀⢀⠀⠈⡧⢀⠀⠀⣀⠈⠉⠁⠀⠀⠀⣃⡦⠀⢀⠇⠐⠀⠀⠀⠺⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠈⠋⠀⠀⠀⠀⣀⣷⣄⢈⡧⠀⣧⠈⡷⡀⢨⣦⣀⠀⠀⠀⣠⡝⠀⠀⠀⠀⢀⠤⠈⠀⢠⡦⠀⢀⠀⠘⠛⠅
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⢀⠊⠀⠀⠀⠀⠀⠀⠒⠈⠀⠐⠣⡾⢀⡨⠉⡍⢛⡍⣯⠉⡍⡈⢺⠀⠀⠁⠛⠀⠀⠀⠘⡐⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⣇⡘⡄⢀⢁⠉⡍⣀⢠⢀⡁⣸⠀⠀⠀⣀⡀⠀⢀⠟⠀⠀⠀⠰⠆⠘⠇⡀⢀⠀⡀⠌
⠀⠀⠀⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣘⣋⡶⣀⠏⡇⠀⢿⡜⠙⠇⠘⢿⣟⠃⢙⠛⡆⠀⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠆⣁⠘⠀⠀⡀
⠀⠀⢀⠀⠀⠀⠀⠀⠉⠀⠸⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡟⠘⠃⢀⠻⠃⢀⠓⠀⠘⠀⠐⠎⠁⠆⠉⠰⡧⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⣀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢆⠂⠀⠀⡀⠀⠘⠋⠀⢀⠘⠁⠀⠘⠁⠀⠀⠖⠀⠛⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⢢⣶⠱⠀⢿⠎⠀⣀⢠
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢘⢥⠀⡛⠩⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣣⣾⠃⠀⠀⠀⠸⢛⠄⠀⠀⠶⠃⠚⠛⢠⣤⣿⠂⠁
⠀⠀⠀⠀⡀⠀⠄⠀⢀⠀⠀⠀⡠⣤⠀⠀⠀⠀⠘⣞⠀⣟⠢⠤⡉⣀⠒⠀⠀⠀⣀⠤⠤⠤⠐⠒⠀⠀⣈⠔⠀⡀⠀⠀⠀⠀⠀⠀⠚⠠⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠇⠀⠘⠛⠁⠀⠀⠀⡀⠀⠉⠀⢨⠙⠲⢤⣄⣀⣀⡀⠀⠀⠀⢀⡀⠠⠄⠒⠋⣀⠄⠨⢁⣀⠀⠀⠀⠀⢀⣀⠂
⠀⠀⠀⢠⣊⣅⡰⢄⡀⠀⠂⠀⠀⠀⠀⠀⠀⠛⢋⠉⠉⠀⠑⠢⠤⠄⢈⣉⣉⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⢀⠀⠀⠉⠀⡀⠀⠀⠀⠄⠀⡄⠠
⠀⠀⠀⠘⠉⠞⠀⠙⢍⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠠⠄⠀⣰⣆⠀⡀⠀⠀⠀⠀⠠⠊⠀⠰⣤⠶⢎⡛⣠⣀⢠⡄⠀⠀⢈⠀⠈⠱⠀⠀⠠⡄⢸⠀⡇⢀⠆
⠀⠀⢠⡄⠀⠀⠀⠀⠀⠘⠌⡆⠀⠀⠈⠀⠀⠀⠀⢹⠀⠀⠀⠘⠳⠦⠴⠁⣁⣀⣴⣄⠀⠐⠀⠀⢬⣻⢨⣻⣯⢹⣶⢃⡢⠀⠠⠀⠁⢨⠀⠀⠀⡇⢸⠀⣇⢸
⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠾⠿⡧⣥⢿⣼⡇⠀⠐⠐⠒⠐⠀⠀⠀⠁⠈⠀⠁⠈
⠀⠀⠀⠀⠠⠤⠀⠛⠠⠤⠤⠀⠀⠈⠑⣄⡀⠐⠀⠉⠁⠀⠁⠘⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠁⢻⠶⠜⠃⠀⠰⣤⠖⡩⡀⠀⢴⣤⠀⠀⠠⠈⠓
⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢑⠑⡇⠀⠀⠁⣀⠀⢀⡤
⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠉⠀⠀⠀⠀⠾⢗⠀⠀⢤⡀⠀⠀⠀⠀⠄⡀⢸⣦⠀⠀⠈⠀⠀⡅⠀⠀⢀⠀⠑⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠙⠛⠉⠀⠒⠀⠀⠀⠄⠀⠀⠀⠀⠈⠙⠀⠀⠀⡐⠿⠁⠈⠋⠀⠀⠠⠀⠰⠀⠀⠀⠈⠀⠀⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠄⠀⠀⠠⠠⠄⠤⠀⠄⠀⠠⠀⠴⠤⠀⠐⠀⠀⠙⠿⠂⠀⠀⠀⠀⠀⠀⠀⢂⡟⠁⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⠁⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠠⠊⠀⠉⠀⠀⠼⠃⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠄⢀⠔⠈⠒⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡔⠀⠀⡄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡌⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐
⠀⠀⠀⢀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠘⠢⣀⠀⠸⠑⠈⡀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠣
⠀⠀⢀⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣤⣧⡈⠂⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢸⣿⣿⣹⣿⣿⣿⣷⣶⣦⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠉⠂⠄⠀⠀⠤⠤⠤⠀⠀⠀⠀⠀⡘
⠀⠀⠈⢿⣿⣿⣿⣛⣿⣿⣟⢻⣿⣷⠤⢤⣄⡀⠀⠀⢀⣼⠋⣿⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠈⠙⢦⣀⣾⠃⠀⡿⠁⠈⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢿⣿⢀⡶⠛⠻⣷⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠢⠀⠀⠄⡀⠀⠀⠀⠀⠈⣿⡏⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿
⠀⠐⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠸⣿⣿⣹⣿⣿⣍⣿⣿⣯⣼⣿⣿⡇
⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⢻⣷⣴⡀⠀⢀⡾⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠁⠸⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡁⢠⣤⠤⠀⠙⢿⣷⣀⣾⠀⠀⠀⠈⠙⠛⠿⠿⠟⠛⠋⠁
⠀⠀⠀⠀⢠⡀⡀⠀⠀⠀⠀⠀⠆⠀⠀⠁⢀⣿⣧⠀⠀⢀⣀⣙⣿⣿⣦⡀
⠀⠀⡠⠂⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⢾⣿⠛⠛⠛⠛⠛⠛⠿⣿⣿⣿⣷⡀
⠀⠰⠁⢀⠠⠀⠤⠤⡄⠐⠈⠀⣀⠠⠒⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠀⠀⡀⠀⠀⠀⠢⠀⠀⠀⡀
⠀⠀⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣿⣿⣿⠂⠀⠁⠀⠀⢦⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⣿⣦⣠⡄⠀⠠⠆⣴⣿⣼⣴⢸⡮⠶⣹⢧⡄⢱⡎⠁⠘⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣅⡀⠀⠀⠀⢿⡟⠛⠃⠀⠀⢠⣿⣿⡧⡫⡁⠱⠖⣿⣿⣿⣿⡧⢠⡆⠀⠈⢿⣷⡖
⠀⠀⠀⠀⢀⣠⣄⠀⣀⠘⢿⡇⠀⠀⣀⣨⠇⠀⠻⣷⣄⠀⠻⣇⠑⢤⡙⠲⠾⣿⣿⣿⡿⠁⣼⠋⠁⣴⣿⡽⠁
⠀⢀⣠⡚⠉⠉⠿⣷⣼⣛⣚⣛⠖⠀⣬⣿⣧⡀⠀⠈⠻⡷⢤⡈⠛⣦⣈⣛⣒⣶⣿⢋⣠⡾⠋⠀⢸⠿⠞
⠀⠈⠓⢮⣿⣿⣿⣿⠋⠉⠛⢫⣩⣿⠿⣿⣿⣷⡀⠀⠀⢹⣦⣄⣀⣬⣍⣉⣉⣉⣩⠟⠉⢀⣠⣤⣶⣦
⠀⠀⠀⠀⠈⠉⠋⠁⠀⠀⠀⠋⠉⠠⢼⣃⣻⣿⣿⣶⡞⠉⠉⠛⠻⠟⠿⣿⣿⢿⡔⣶⣾⣿⣿⣿⣧⠄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⡿⣿⣧⡀⠀⣀⠀⣀⠀⡀⢰⣿⣅⠙⢿⡈⠏⠈⠻⣦⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣽⣠⣇⣽⠏⠀⠀⠈⢿⣿⣿⣾⣿⣿⣿⡆⠀⠀⠀⠀⠑⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠈⠻⣍⣿⣿⣿⢿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠆⠀⠀⠀⠀⠒⠈⠁⠀⠀⠀⠀⡖⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠈⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠄⠀⠈⠈⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⣀⡀⠀⠀⠀⠈⣦⣤⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠉⢯⠼⠊⠀⠀⠠⡄⠀⠄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⢠⡹⠀⠀⢭⡶⣄⠀⢠⣿⣿⣤⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠿⠀⡟⠀⠀⠀⠀⠀⠀⢈⠈⠁⠀⠈⠉⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡇⢈⠩⢽⠙⣿⠉⠓⠂⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠾⠞⢱⡇⠀⡄⠀⠒⠄⠁⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡾⠀⠀⠀⠘⢣⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠒⠒⠀⣀⡁⢘⡄⢀⠀⡀⠀⢈⣧⢯⣤⡾⠃⠠
⠀⠀⠀⠀⢈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠕⠳⡶⠾⡞⠀⠁⠀⠐⠃⡄⠑⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠉⠛⠌⠓⠋⠀⠀⠀⠈⢤⡄⠀⠈
⠀⠀⠀⢀⡞⠀⠂⠀⠀⢸⡀⠀⠀⢀⠀⠎⠈⠓⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠁⡀⠀⠀⠀⠀⠀⠀⡀⣀⠁⠀⠀⢀⠂
⠀⠀⠀⠈⠇⠜⣆⠀⠀⠀⣇⠀⠀⡄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡀⢀⣦⣤⣴⡀⠀⠀⠀⠀⣀⠀⠄⠀⣠⡴⠂⠀⠀⠀⠀⠀⠀⢨⡐
⠀⠀⠀⠀⠘⠀⢘⣧⠀⠀⢸⡆⠐⠁⠀⠀⠀⠀⢰⣤⣴⡂⡰⠀⠀⠀⠀⠀⠁⠈⠻⣿⣿⣷⠀⠀⠀⠀⠉⠈⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⢀⣀⣀⣀⣀⣤⠤⠾⠃⠀⢠⠷⠆⠀⢀⣼⣿⣿⣿⡾⠀⠀⠀⠀⠀⠂⢀⠀⠈⠋⠈⠒⠦⠀⠀⠐⠂⢻⣖⠤⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠛⢿⠿⠇⠀⠀⠀⠈⠉⠒⠀⠀⠄⠀⠤⣄⠀⠀⠀⠀⠀⠀⠙⣇⠀⡏⠻⠷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠀⠒⠠⢀⠀⠠⠈⠂⠀⠠⠀⠤⡞⠠⠀⠊⠛⠐⢁⢀⣀⠕⠂⠀⠀⠀⠀⠀⠘⣀⠀⠀⠀⠀⠉⠉⠓⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠓⣶⡀⠠⠐⠀⠘⣇⠘⠳⢄⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⠙⠓⠂⢂⡀⠈⢰⠛⡖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠁⠘⠀⠉⠈⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠈⠉
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠚⠋⠉⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠶⠒⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⢀⣀⣀⣤⡤⠴⠖⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠲⢤
⣶⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠁⠀⠀⠀⠘⡇
⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠆⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⢿
⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠄⠂⠀⠉⠀⠀⠀⣠⠀⠀⠀⢻⠀⠀⠀⠀⠀⢀⡾⠿⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠄⠐⠂⠀⠀⠁⠀⠀⠀⢀⡀⠠⠄⠒⠚⠁⠀⠀⠀⠀⠀⠘⡇⠀⠀⢠⣤⠏⠀⠀⠀⠀⠀⠀⡠⠀⢠⡞
⠀⠸⡇⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⣀⢀⠄⠀⠄⠐⠂⠀⠉⠀⠀⠀⢀⢠⠠⠀⠀⠉⠁⠀⠀⠀⢳⠀⣀⡿⡿⠀⠀⠀⠀⠀⢀⣼⠇⠔⣹⠃
⠀⠀⢷⠀⠀⠀⠀⠀⠀⠐⠒⠂⠈⠁⠀⠀⠀⠀⢀⠀⠀⠤⠄⠒⠀⠁⠀⠀⠀⢀⣀⠠⠔⠒⠀⠀⠀⠘⣶⣿⠁⠀⠀⠀⠀⠀⣠⠿⠃⣠⠞⠁
⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠉⠀⠀⠀⡀⠀⠠⠄⠐⠐⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⢠⠀⠀⡐⠀⠈⠁⠀⢙⡟
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⠀⠒⠂⠉⠁⠀⠀⠀⠀⢀⡀⠤⠐⠒⠈⠁⠀⢀⣀⠀⣷⡀⡇⠿⣿⠀⡰⠁⠀⠀⢀⣠⢿⠇
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠠⠤⠐⠒⠈⠁⠀⠀⠀⠀⢀⡀⠤⠔⠒⠀⠈⠀⠀⡇⠹⣇⠀⡇⢠⠁⠀⢀⠔⡽⢣⠏
⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠐⠒⠀⠉⠁⠀⠀⢀⡀⠀⠤⠀⠄⠀⠒⠈⠉⠀⠀⢀⣀⠠⠤⠖⠚⠉⡇⠀⠀⠀⢡⠃⠀⠀⠁⢀⣰⣯⣴
⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣀⠀⠤⠀⠀⠀⠉⠀⠀⠀⣀⣀⣴⢀⡇⢀⠀⠀⠎⠀⠀⠀⠀⠉⢁⡼⠁
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢀⡀⠠⠤⠀⠒⠀⠈⠀⠀⠀⠀⠀⢀⡀⠤⠄⠒⠂⠀⠀⠀⠀⡿⣿⠇⢸⠀⠈⠀⡴⢁⠀⠀⢠⠞
⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠤⠀⠒⠂⠀⠀⠀⠀⢀⣀⠀⠀⠀⠐⠂⠉⡇⠉⢸⡞⢀⠀⣞⣴⠋⠀⣰⢋⡴
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⡀⠄⠀⠐⠒⠈⠉⠀⠀⠀⠀⣀⡀⠤⠄⢹⡀⠀⠃⠄⠼⠋⠁⠀⠀⢟⡿⠁
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠐⠂⠘⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠂⠀⠀⠈⠁⠀⠀⠀⠀⠈⠳⡄⠸⠀⠀⠀⢀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠠⠤⠀⠐⠒⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢀⣠⣿⢃⡖⠒⠋⠉⣧
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢀⠀⠀⠠⠤⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠉⠈⢸⣧⡜⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠐⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡟⡾⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⠇⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⡤⠤⠤⠶⠖⠒⠒⠒⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠶⠒⠒⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⣤⠤⠴⠖⠚⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢡⢠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⡖⢸⠇⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢾⠅⢊⡼⠋⢠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠆⡜⠀⠀⠀⣷⠐⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠒⠲⠶⣒⠒⠢⣄⡁⠀⠀⠆⠃⠀⠀⠀⢹⢀⣴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠉⠉⣩⠋⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠻⣄⠀⣇⣀⠀⢀⡠⠞⣉⠤⠒⠉⠁
⠀⠀⠀⠀⠀⠠⡤⠒⠂⠈⠉⠈⠈⠉⠒⢦⣀⡔⠁⠀⢠⠞⠁⡠⠄⠚⠛⠈⠀⠀⠀⠀⠀⠸⡀⠀⠹⡐⢤⡤⣤⡤⣄⣀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⢄⡀⠀⠀⣏⠀⠀⠀⠈⠀⢈⠀⠀⠔⡀⠀⡲⡄⠈⠐⡄⠀⢣⠀⠀⢱⠺⠤⣀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⢈⣳⠖⠙⡆⠀⠀⠈⢄⢯⠑⢼⡘⢀⣀⠴⡇⠀⡠⡁⠀⡸⠀⠀⢀⠀⠀⠈⠑⢄⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡜⠓⠦⣀⠔⠉⠀⠀⠀⢳⠀⠀⠀⠈⡂⠳⡀⠈⠉⠒⠰⠖⠁⢰⢀⠞⠁⠀⠀⢸⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠤⡞⠀⢀⡠⠄⠒⠸⡄⠀⠀⠰⠁⠀⠈⢆⠔⠁⠀⠀⠀⠀⡇⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⢹⡠⠋⠀⠀⠀⠀⠈⠢⡀⢠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣀⡠⠔⡴⠛⠀⠀⠀⠀⠀⠀⡿⠒⠒⠒⠒⠒⢦
⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⢒⣾⢃⣀⠀⠀⠀⠀⢀⣤⣚⡛⠃⠀⠀⢠⢈⣀⡀⠠⠠⠚⠉⡰⠋⠀⠀⠀⠀⠀⠀⠀⣸⠃⢀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠉⠉⠉⠉⢱⠀⠀⠀⠋⠀⠀⠉⠲⣄⡀⠀⠀⠀⠀⠀⣀⡤⠚⠀⠀⠀⠀⠀⠀⠀⣠⠞⠓⠺⢥⣀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠠⠤⠤⠤⠤⡆⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⠈⠉⠥⠾⣯⣀⣀⠀⢀⣀⣀⠤⠖⣻⡃⠀⠀⠀⠀⠈⢣⡞⠁
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠈⠉⠁⠀⠀⠀⡴⠃⠈⠑⠂⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣤⠔⠒⠉⢉⠟⡏⠒⠢⠤⡤⠤⠤⣤⡒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⣠⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣰⠋⠀⠸⡀⠀⠀⠁⠀⠀⡏⠉⠓⠲⠤⣀⣀⣀⣀⣠⠴⠚⠁⠀⠈⠙⠦⣄⣀⣀⣀⣀⣀⣀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠁⠀⠀⢀⡟⢦⣀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⠞⠀⠀⠈⠙⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⣀⠠⠔⠚⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⣠⣚⢢⠀⠀⠀⠀⠀⣷⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⢧⠀⠀⠀⠀⢀⠼⣁⣪⠉⠀⠀⠀⠀⠶⠿⣿⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠻⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⡛⢄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣵⠃⠀⠀⠀⠀⠀⠀⣠⣜⠣⠙⠋⠀⠀⠠⠒⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡙⡅⠀⠀⠀⠀⠀⠀⠀⠛⠁⠙⠁⠀⠀⠀⠐⠄⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠀⠀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣱⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡧⠄⠀⠀⠀⠀⡠⠢⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠈⠈⠃⠀⠀⠀⠀⠀⠀⠈⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡂⣣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠠⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠢⣀⡀⠀⠀⠠⢄⠚⠈⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣄⠀⠈⠒⡤⠂⢄⠀⠀⠀⠀⠀⠀⣶⢑⣈⡄⠛⠁⠀⠀⠀⠀⣥⠐⠺⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠉⠢⡀⠀⢄⣀⣴⠀⠀⠀⢴⡙⣄⣨⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⢙⣄⠀⠀⠀⠑⢶⡑⣤⡥⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⢠⣾⠉⠨⠿⠁⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⣰⣿⣿⣷⣄⠀⢠⣶⡷⡉⠀⠀⠀⠀⡊⠀⢐⠀⠀⠀⠀⠤⣾⠇⠀⠙⠁
⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⣠⣾⣿⣿⣿⠿⠋⠉⠢⡀⠀⠈⢆⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⣼⡟⠀⢀⣴⣿⣿⡿⠟⠁⠀⠀⣀⣤⣾⣷⣦⣤⠇
⠀⠀⠀⠀⠀⣸⡟⠀⣴⣿⣿⠟⠋⠀⢀⣠⣴⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⢰⠟⣠⣾⡿⠛⢁⣠⣴⣾⡿⠟⠛⠉
⠀⠀⠀⢠⢏⣼⠟⣋⣤⡶⠟⠛⠉
⠀⠀⢀⣿⡿⠷⠛⠉
⠀⠀⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡠⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢅⢽⣴⣤⣲⣄⣌⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡶⣿⣭⣟⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⣴⠈⠓⠄⢌⠙⣷⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠂⠐⠠⡆⢘⠁⠁⠈⠺⣅⡱⢤⢀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⣉⣸⣇⠘⢔⠆⠂⠀⢡⢀⡞⠸⠱⢿⢀⣖⣂⣲⡴⠂⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠻⢿⣧⡘⢦⣈⠀⠁⢷⡼⠋⠄⠀⠀⣀⣿⢿⣿⣿⣿⠷⣾⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠛⠛⡉⠀⠰⠚⢫⣠⡴⠶⢄⡛⠃⠀⠈⠛⢯⣈⠛⠭⠒⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣈⠀⡔⠂⣤⡀⠄⢈⣿⣗⣠⣀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠀⠒⠛⠉⠀⠤⠘⠉⠿⠭⠖⠀⠀⠀⠶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠤⣶⡿⠂⠉⣀⠒⠂⠀⣰⣁⣴⣤⡾⢿⣥⠥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠟⣷⣤⡤⣤⣶⣾⢷⡩⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠀⠷⣟⠛⠀⠐⠛⣿⣷⡾⢷⠂⣦⡠⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠳⢤⡾⡇⢸⠈⣧⣼⣍⣉⠄
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⣿⣿⣽⣯⣁⡀⠂⠀⠀⠀⠀⠻⣇⠀⡄⢸⣿⢳⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠢⣉⠉⠑⠲⠤⣠⣄⡄⠹⣆⠱⠀⣿⣾⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠦⣄⠉⠳⢶⣽⡤⠀⢸⣩⡄⣁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⠀⠙⣿⣜⣿⣿⡿⠋⣉⣿⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⢤⣽⣾⣧⠛⠘⡯⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢹⢿⡅⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠎⣧⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⢀⠠⠄⠀⢠⢄⡀⡚⠑⠀⠂⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠠⣀⡀
⠀⣂⠳⣠⡴⢯⡁⠀⣈⠆⠀⢙⡤⠞⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⠃⠴⠙⡌⠄⢉⠁⠉⢳⠆⠀⡆
⡠⠊⠀⠀⢀⠝⠻⠀⠀⠠⣀⠇⣷⢴⠈⡡⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠊⢀⡈⣣⠀⢸⠀⢸⡄⣈⡿⢗⡔⠊
⠣⠀⠖⠣⡈⢑⣔⡌⡈⢂⢐⡶⠙⠢⠤⠃⠀⠀⣠⠄⠰⠒⣒⡲⠂⠤⢄⠀⠉⣟⡴⠈⠁⠁⠋⠁⠉⠉⠉
⠀⠀⠀⠀⠈⠁⠀⠉⠒⠊⠁⠀⠀⠀⠀⠀⠀⠘⠂⠬⠄⣋⣉⣉⣑⡍⠴⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀
⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠉⠢⡀⠀⠀⠀⠀⠘⠀⣐⠀⠀⣀⠀⢀⣇⠜⠁⠀⠀⠀⠀⠀⠀⠠⠎⠀⠀⢠⠒⡋⢂
⠀⠀⠀⢀⡀⠣⡀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠔⠀⠀⠆⠈⠀⢎⡀
⠀⠀⠀⠀⡓⢄⡈⠢⠄⣀⢀⣀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠂⠠⠄⣀⠀⠀⠀⠀⠀⢆⠠⠀⠀⠀⠤⠜⡀⠁
⠀⠀⠀⠀⠘⢄⡈⠀⠂⠠⠀⡴⠊⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⡀⠀⠠⠖⠉⠀⠀⠉⠰⠆⠀⠀⠙⠠⠠⣠⠶⠊⣑⡢
⠀⠀⠀⠀⠀⡸⠈⠗⠒⠒⠉⠀⠀⠀⠀⠀⣀⣈⠓⢆⠀⠀⠀⠀⠁⠀⠲⠄⠀⠂⠀⠀⡸⠀⠀⠀⠀⠐⠂⠑⠂⠐⡄
⠀⠀⠀⠀⢠⠃⡌⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⡀⠛⠶⠄⣀⣀⠤⣄⠀⢸⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⢠⠃⡘⠀⠀⠀⠀⠀⠀⠣⢄⡂⣄⣀⣀⠬⠄⣀⡀⣀⠐⠉⠂⢈⡄⠈⠁⠀⠀⢀⡠⠴⠲⠶⢤⡀⠀⠀⠀⠂
⠀⠀⠀⠁⠴⠁⠀⠀⠀⠀⠀⠀⠑⠤⣈⡀⢀⡅⠀⠀⣇⡀⢀⡁⢀⠜⠚⠀⠀⠀⢀⠞⠁⠀⢀⣀⡀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⡀⠉⠀⠀⠀⠀⠀⠀⡟⢀⣀⠔⢁⣄⢹⠃⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣦⠀⠢⡀⠀⠀⠀⠀⠀⢧⡀⢸⡀⡨⠶⠚⠠⣀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠐⠂⠛⢍⢂⠀⢱⡄⠀⡃⠀⠀⠀⠀⠀⠀⠑⠯⣙⣦⡤⠴⠞⢁
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣒⠈⠁⠀⠀⠑⡀⠀⢀⣦⠴⠋⠉⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠱⡀
⠀⠀⠀⠀⠑⡒⠠⠤⠀⠑⠄⠑⠠⣀⡠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠘⢆
⠀⠀⠀⡏⠀⣈⣒⡖⠊⠤⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠪⢈⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⡿⠗⠀⠀⠀⠴⣭⠪⡵⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢶⡴⠓⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠀⠀⠀⠀⠀⢘⢸⡰⠭⣵⢉⠄
⠀⠀⠀⢀⣀⣤⣤⣴⣶⣤⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣰⣡⣤⣬⣄⠀⠀⠀⠀⠀⢰⣿⠁⣉⣿⠏⠀⠀⠀⠀⠀⠈⠦⣙⣙⡥⠜
⠀⠀⣴⣿⣿⣿⠿⡿⣛⣹⡄⠀⠀⠀⢸⠀⠀⠀⠀⢀⢼⠿⠿⠿⡿⠻⠤⠀⠀⠀⠀⣺⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⣶⣷⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⢂⠂⢠⠀⠁⢇⠁⠀⢀⣴⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠢⠤⠼⠼⠌⠀⠀⠀⠛⠿⣿⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣦⢀⣀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢠⣴⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠫⠬⠯⠥⡞⠉⢃⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢈⠖⠀⠒⠄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⡈
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢢⠀⠀⠀⡼⠉⡇⠀⠀⠘⠢⠤⠤⠤⠤⠗⠋
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠑⠚
⠀⠀⠀⠀⠀⢹⡢⣞⣢⢯⠇⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⡚⢳⣤⡀
⠀⠀⠀⠀⠀⠀⣷⢾⣉⡾⠀⠀⠀⠀⢠⠞⠡⢀⠀⠈⠀⡀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡞⠙⣦⡴⠛⢏⣠⠟⢦⡀
⠀⠀⠀⠀⠀⠀⠸⣞⣭⠇⠀⠀⠀⠀⠇⠨⢠⢰⣿⠿⣦⠀⠠⠀⠃⠀⠀⠀⠀⠀⠀⣠⣴⠚⢣⣠⠽⢏⢉⡷⣖⢋⣱⣶⠋⣱
⠀⠀⠀⠀⠀⠀⠀⢫⡟⠀⠀⠀⠀⠀⡇⢁⠀⢘⠦⠤⠊⠈⠀⠀⡇⠀⠀⠀⠀⠀⣾⢀⡸⢶⠋⣹⣴⠚⢻⣤⠞⢻⣀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢳⣆⣀⠂⠄⠂⠐⢀⣀⣾⠃⠀⠀⠀⠀⠀⠙⣯⣠⠼⢻⣁⡼⢿⡉⣹⣶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠶⠷⠶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⣴⠚⢹⣤⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠠⡀
⠀⢀⠢⠀⠀⠀⠀⠀⢀⠀⠐⠄⠀⠀⠀⠀⠀⠀⢈⣩⠿⠿⢿⣅⠁⠀⠀⠈⠀⠀⠀⣿⠈⠀⠀⣀⠂⡠⠀⠂
⠀⠀⠀⠈⠦⠀⠀⠀⠈⢂⣈⡄⠀⠀⠀⠀⠀⠀⡿⠁⠀⡀⢖⡀⡀⠀⠐⣄⠀⠀⢀⢸⠇⣤⠐⠋⠁
⠀⠀⠀⠀⠀⢉⢠⣠⠞⠉⠉⠁⠀⠀⠀⠀⠀⡀⠀⠸⠋⠉⣿⠅⠈⡾⣄⣸⠆⠀⢸⠉⢀⢑⡆
⠀⠀⠀⠀⠈⠀⠎⠁⠀⡀⠀⠀⠀⣀⣠⠄⠀⠃⠀⠀⡁⠘⠶⠤⡾⠱⠋⣹⠆⢀⡦⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠀⢀⣴⣿⣿⠀⠀⠀⠘⢷⡟⢶⣶⡾⠁⣰⣾⠏⠀⠏⠀⠀⠀⠀⠀⠈⢲
⠀⠀⠀⠐⠁⠂⠀⠠⠄⠀⠀⢾⡿⢛⠙⠓⢀⣄⠀⠀⠙⢦⣈⡁⣀⣉⣁⡤⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠶⠟⠡⠎⠈⠀⠀⡄⢠⣄⣀⣀⣨⠀⠘⠿⣥⡤⠠⢲⡀⠀⠀⠀⠀⢱⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠰⠀⠀⠉⠉⠈⠙⢳⡀⠀⠀⠀⠂⢈⠁⠦⡄⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠁⠀⠀⠀⠀⠀⠠⢊⣠⠖⠋⠀⠀⠀⠙⢦⣀⠀⠀⠤⠤⠤⠤⠤⢤⣀⡈⠢⡀
⠀⠀⠀⠀⢠⠞⠁⠀⠀⢀⣀⠀⠀⢀⣀⣡⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠉⠓⢮⣆⠀⠈⠉⠒⢄
⠀⠀⠀⡴⠁⠀⠀⠀⡜⠁⠀⠉⠉⢉⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠓⢤
⠀⠀⡜⠀⠀⠀⠀⣸⠁⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠛⠒⠦⢤⡀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠰⠀⠀⠀⡠⢢⠇⠀⠀⠀⢠⠏⠀⠀⢀⠀⠀⠤⠄⡴⢋⡀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⣠⠔⠋⠀⡞⠀⠀⠀⠀⡏⠀⠀⠄⠀⠀⠀⢀⠎⡠⠁⠀⠉⠉⠁⠐⠒⢄⠀⠘⡆⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠚⠉⠀⠀⠀⢠⡇⠀⠀⠀⢸⠇⠀⡀⠀⠀⠀⢀⠎⠀⠁⠀⠀⡰⠒⣒⡢⠐⢄⠆⠀⡏⡀⠀⡇⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢸⠀⠀⣇⠀⠀⠀⠌⠀⠀⠆⠀⠈⠠⠁⠀⡈⢆⣸⢦⢠⠁⠁⠀⡇⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠘⡄⠀⡸⢆⠀⠀⠀⠀⠰⣀⠗⠀⠤⠀⠀⠊⠉⢈⣰⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⠃⠀⠀⢀⠞⠁
⠀⠀⠀⢀⠀⠀⠘⡇⠀⠀⠀⢃⠰⠀⠈⠦⢤⡀⠀⢀⡮⠑⢄⠀⠀⠀⠠⠐⠀⠀⠀⠀⡄⢰⠇⣇⠰⠀⠀⠀⡞⠀⢀⡴⠋
⠀⠀⠠⠀⠀⠀⠀⠹⡄⠀⠀⠀⢦⠀⠀⠀⠀⠈⠑⠺⠤⣀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠰⠀⡎⠀⢹⠃⠀⢀⠞⣄⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠈⡄⠀⢐⠧⡀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠄⠀⢀⢃⠜⢀⡴⠃⠀⡠⠋⢠⠏
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠘⢆⠰⡄⠈⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⢃⡴⠋⠀⣠⠎⠀⣠⠋⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⣄⠀⠀⠀⡈⢳⢣⠀⠀⠀⠈⠐⠒⠤⠤⠤⠔⣒⠉⠔⠠⠊⢀⠤⡺⠃⡠⠾⠁⠀⢸
⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠐⡘⣆⣑⣀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⣀⠤⠂⢁⢈⠁⠨⠁⠀⠀⠀⢸
⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠈⠢⡈⠫⡉⠉⡉⠁⣀⣀⠠⠐⠂⠈⠀⠠⢂⠔⠁⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠈⠳⢼⣟⡉⠉⠈⠀⠀⠀⡠⠔⡀⠐⠉⠀⠀⠀⠀⠀⠀⠀⡌⠀⡠⠂
⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠈⢉⣉⡤⠤⠔⠂⠀⠀⣀⡀⠤⠔⠒⠈⠁⠀⣀⡼⠔⠉⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⡠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠉⠒⠤⣀⡀⠀⠀⠀⠈⠉⠓⢲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠫⣀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⢀⣀⠤⠐⠈⠉⠉⠓⠒⠢⠤⣀⣀⠀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠈⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠉⠁⠀⠀⠀⠀⢀
⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⠒⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠚⠁⠀⠀⠀⠀⠀⣠⡴⠒⠉
⣟⣿⣿⣿⣿⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣻⣻⣿⣿⣛⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡶⠚⢙⡉⡉⢹⣄⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡰⠀⣼⢹⠓⢶⡏⢖⣹⠇⡻⢿⡆⠀⣎⡈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⣏⠀⠐⢿⣞⣆⡀⢻⣈⣭⢎⣵⣿⣶⣤⠼⠋⡸⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠲⢬⣦⡀⣿⡟⢀⣽⣷⣻⠕⠉⣼⢋⠤⠄⣤⡜⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠓⠲⣼⣿⣾⣿⡞⢩⡉⠁⠤⢚⠝⠁⠀⢰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⣀⣤⣤⣄⣀⡴⠉⠁⠀⠀⣠⣿⡅⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠋⠁⠀⠛⡻⣿⣧⣤⣆⣀⣴⠟⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠋⠙⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢻⣄⡀⠀⠀⠀⠀⠁⠀⠀⠹⡧⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡘⢦⢄⠀⠀⠀⠀⠀⢠⡄⢀⠄⢠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⢻⡦⡀⠀⠀⠀⠀⠁⠋⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢤⠀⠀⡀⠁⣧⠀⣾⠀⠁⠀⡔⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠁⣀⡟⠀⡇⠀⢀⠀⡀⠀⠠⣇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠘⠅⠀⠁⣀⠯⠄⢀⣤⡼⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⢦⣽⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣠⣶⠒⠐⣇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠚⠋⠐⠄⠀⠘⣄⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⡀⠀⠀⠴⠄⠘⠲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣿⠃⠈⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⢾



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢘⠀⠒⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠤⠀⠀⡄⠀⠈⠃⠀⠀⠀⠙⠁⠀⠀⠀⠹⠁⠀⠀⠀⣀⡀
⠀⠐⠀⠀⠀⢰⡄⢦⠀⣰⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠀⣦⡀⢸⠃⠈⢳⣿⡖⠃⠐⡆⢠⣆⢀⡆⠐⡆⢠⣆⠀⠀⢰⡀⢠⡆⢸⠃⠀⣦⡀⢀⡄⢀⡀⢀⣤⠀⡴
⠀⠀⡴⣿⡖⠃⠀⠀⢸⡿⣇⠀⠀⠈⢺⣷⠋⠀⠀⠈⣾⣷⠒⠢⠀⠙⢺⣷⠁⠀⡠⣿⣶⠋⠀⠀⠙⣲⣿⠞⠁
⠀⠀⠓⣿⡇⠀⠀⣰⠏⠀⠘⢦⠀⠀⢸⣿⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⢸⣿⡇⠀⠓⢸⡿⡄⠀⠀⢠⣿⣿⡇⠈
⠀⠀⠀⣿⡇⠀⠀⠁⠀⠀⠀⠈⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⣸⢃⡗⠀⠀⠀⣿⣿
⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣘⣿⡀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⢀
⠀⠀⠀⠸⢿⡿⣿⠶⠄⠀⠀⠀⠀⢰⣾⣿⣦⠶⠍⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⡄
⠀⠀⠀⠀⢸⡗⣧⠀⠀⠀⠀⠀⠀⠸⣿⣟⠿⣄⠀⠅⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⢀⣠⡀⠀⢀⡗
⠀⠀⠀⠀⣸⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡟⠀⠀⠀⢠⡀⠀⠀⢰⡄⠀⠙⣇⡘⠿⣿⣿⡾⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⣿⢷⡀⠸⣿⡷⢀⢰⡌⢻⣷⣿⣿⣶⣦⠈⠁⠀⣠⠄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢿⣿⣶⣿⡟⣶⣾⣾⣿⣿⣧⣹⣯⣤⡶⠟⠁
⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣿⣿⡷⣶⣷⣾⡟⣿⢸⣿⣿⣷
⠀⠀⢠⣧⣀⣀⡀⠀⢀⣀⣀⣸⣧⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡾⣷⣿⣿⣿⡇⣿⢸⣿⣿⣿⣇
⠀⠀⢸⣿⠈⠁⠀⠀⠀⠀⠉⣿⣿⡄⠀⠀⠀⠀⠀⠀⣻⡿⢿⣿⣿⣿⣷⣿⣿⣿⣿⠇⠿⠛⢿⡟⣿⠛
⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠘⢿⠟⠃⠀⠀⠀⠀⣠⡾⠋⠀⣾⠇⠁⢿⠿⣿⣿⣿⣿⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡿⣿⠀⠀⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⠶⠶⠶⢶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠸⣉⢸⠒⠇⣗⠸⣁⢸⢯⠀⣇⢸⠌⣣⠨⡇⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡖⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠧⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠓⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣇⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡞⠋⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣼⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠧⠤⠤⠀⠀⠠⠤⠤⠄⠀⠠⠤⠤⠄⣾⣿⣿⣿⡛⠛⢻⣿⣿⡿⠃⢀⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡀⠀⢻⡿⠁⢀⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣆⣠⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠟⠛⠋⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⢶⡴⠃⡿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢿⠃⠈⢀⡆⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⡏⠀⡀⢠⢀⣾⡥⠠⣿⠃
⢀⣀⡀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⡀⠀⠈⠉⠛⡒⠦⣤⡀⠀⢰⠃⢀⡔⣴⣱⢣⣾⣿⡗⣰⣯
⠈⢯⡉⠙⠻⠌⣙⢦⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⣦⣿⣷⠿⠾⠷⣿⣿⣶⣍⠳⡏⢀⣾⣿⣿⣷⣿⣿⣿⠆⣠⠏
⠀⢠⡿⠄⠉⠲⣿⣷⣅⣌⢿⠳⣄⡤⠶⠶⠞⠉⠉⠉⢹⣷⣾⣿⣯⣦⣤⣄⣀⠀⠀⠀⠀⠻⣷⣽⢋⢉⢀⠈⠉⠉⠛⢧⡞⠁
⠀⢈⣧⡀⠀⠀⢌⠻⣿⣿⣆⣴⡿⠀⠀⠀⠀⡀⢄⣰⣶⣿⠿⠋⠉⠀⠀⠀⠈⠛⢧⠀⠀⠀⠈⢿⡛⠛⠻⢮⣮⢔⡀⠀⠙⣆
⠀⠀⢻⡁⠀⠀⢄⠳⡹⣿⣿⣿⠇⠀⠀⠒⢬⣮⣿⣿⡿⢁⣤⣶⠦⠶⢦⣄⠀⢀⠈⢳⣠⠠⣱⣾⣿⠶⠶⠶⠾⠿⣖⠅⠀⠈⢳⡀
⠀⠀⢠⣷⣄⠀⢌⢳⣙⣿⠿⡟⠀⢀⠀⣠⠖⢛⣻⠟⢠⡿⠋⠀⢀⠀⠀⢹⠧⢿⣾⣦⠹⣧⣿⣿⡇⠀⠀⠀⠀⣼⣷⡮⡂⠀⠀⠙⣦
⠀⠀⠀⠹⣄⠀⠈⣷⠋⣵⣾⠃⡀⣦⠞⠁⣠⡿⠃⠀⡼⠁⠀⢀⡌⢻⣇⢸⣧⣀⠈⢻⡇⢻⣿⣿⣿⣧⣶⡀⠀⢹⡿⡫⢂⡡⠖⠉⣾
⠀⠀⠀⠀⠈⠳⡞⠁⠀⣨⣿⢀⣧⡏⢀⣸⣿⠃⠀⣼⠁⠀⢠⠈⠱⣾⣿⣿⣿⣿⡇⠈⣷⠈⣿⣿⣿⣿⣿⠁⠀⠈⡟⣱⣟⠃⠀⠀⣿
⠀⠀⠀⠀⠀⣸⠁⠀⢀⣿⣿⠀⣿⠁⢀⣺⣿⠀⣸⠹⣤⣿⣤⠶⠶⢿⣻⣿⣿⠟⣠⣾⡇⡄⣿⣿⣿⣿⠋⠀⠀⠀⣿⣿⣿⣒⣀⠀⢹
⠀⠀⠀⢀⣼⠁⠀⠐⠾⣿⣿⡄⣿⠀⠀⠺⣿⡄⠸⣄⢀⡤⠶⠶⢚⣿⣿⠟⣁⢴⣻⣿⣿⣿⢿⣿⣿⣿⠦⠀⠀⢀⣿⣿⣟⡒⠦⠀⠈
⠀⠀⠀⠀⠹⡄⠀⠀⠀⣲⣾⡷⢾⡇⠀⠀⡞⠙⢦⣈⡉⠙⠲⠖⠒⠉⠀⣈⣥⠽⣟⣿⣿⡇⣿⣿⣿⡋⠁⠀⠀⣼⣿⡍⣓⠪⠁⠀⢰
⠀⠀⠀⠀⠀⢳⡀⠀⠀⢠⠏⢼⣿⣷⠀⠀⠳⢤⣀⠉⠉⠉⠉⠛⣉⣉⣭⢵⠶⣿⣿⣿⣿⣿⡿⠓⠂⠀⠐⣤⣾⣷⡮⠉⠸⡯⠀⠀⡾
⠀⠀⠀⠀⠀⢀⣷⡔⢵⡏⠀⢽⣿⣿⣆⡀⠀⠉⠹⣿⣿⣿⠍⠉⠉⠀⠀⠀⠈⣺⣿⣿⡿⠛⠀⠀⢀⣴⣿⣿⣿⣿⠇⠀⠀⢹⣀⡼⠁
⠀⠀⠀⠀⠀⢸⠀⣿⣾⡇⠀⠩⠛⠉⣙⣻⣷⣄⠀⠨⢝⣿⣦⡀⠀⠀⠀⠀⠈⣿⣿⠟⠀⠀⠀⣰⣿⣿⣿⣿⣿⠯⠁⠀⠀⢸⡏
⠀⠀⠀⠀⠀⢸⠀⢘⣿⡇⠀⠀⠀⠀⠀⠈⠛⢛⣛⣦⣔⣭⣿⣿⣷⣶⣶⣶⣾⣿⣧⡤⠶⠒⠋⣹⣿⣿⣿⣿⣿⠯⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⠀⠈⢾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠟⣹⠟⡿⠋⠟⢩⠁⠁⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡯⣝⠂⠀⠀⢸
⠀⠀⠀⠀⠀⠈⣇⠀⠈⠾⡿⣆⡆⠀⠀⠀⠀⠀⠀⠈⠀⠘⠁⠀⠁⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⢿⡳⢭⠓⠍⠈⠙⠦⣀⢸
⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⢛⡳⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣶⣿⣿⣿⠿⡙⠎⠓⠈⠀⠀⠀⠀⠀⣀⡬⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠁⣐⡭⠴⠞⠛⢲⡤⢤⣤⣤⡶⣾⡻⣿⠿⠛⠻⠝⠎⠃⠑⠈⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢾⣤⠞⠁⠀⠀⠀⠀⢸⣁⠈⡟⡿⣽⣿⣿⣌⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠰⢱⣿⣿⣿⢉⣹⠶⠦⠤⠤⠴⠖⠚⠛⠛⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣾⣿⢏⣈⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⢣⣌⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠔⠊⠀⠀⠈⠁⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠖⠋⠉⠀⠀⠀⠀⠀⢀⣀⠀⣀⣀⡀⠀⠈⠑⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡴⠚⠉⣹⠃⠀⠀⠀⢰⠛⠉⠉⠁⠉⠁⠀⠈⠉⠉⣉⠉⠙⡆⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⢀⠞⠁⠀⣀⣏⣀⠀⠀⢠⠃⠀⠀⡄⠀⢠⠔⢒⣴⠾⡉⠈⣇⠀⡷⠦⠤⣽⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣠⠔⠋⠀⡠⠚⠉⠉⠉⠉⢩⠃⠀⠀⠸⡇⡰⠁⠰⡿⠁⠀⢹⠀⢹⠀⢻⡀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠙⡀⠈⠉⠀⠀⡰⠊⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣷⠛⣄⠀⣇⣰⡤⣋⣠⠞⠳⣼⠙⠦⣀⠀⠀⠈⠂⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⡜⠀⠀⠀⠀⢀⠆⣴⣾⠿⠷⣄⠀⠀⠸⡄⠘⡆⡿⠱⠛⣡⢾⠀⠀⠈⢣⠀⠈⠑⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⡼⠀⠀⠀⠀⠀⢸⣾⠋⠁⠀⠀⠈⠳⡀⠀⢧⠴⠿⣗⣓⠉⢁⣼⠀⠀⠀⢸⡀⠀⢠⡀⠀⠀⢀⡏⡀
⠀⠀⠀⠀⠀⠀⠠⡏⠀⠀⢰⠃⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠹⡄⢸⡀⠀⠀⠈⠉⠁⢸⡄⠀⠀⢀⡇⠀⣸⠀⠀⠀⣼⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⣿⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢳⠸⡇⠀⢀⣀⠤⠖⠋⠀⣀⠔⠛⢤⣰⠃⠀⠀⢠⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠈⠳⣄⠀⠀⠀⠀⢼⣇⠀⠀⠀⠀⠀⠀⠀⠘⢰⣧⣾⣭⠤⠤⠤⠴⣾⠁⠀⠀⠀⠙⡄⠀⢠⠞⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠘⢦⡀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠘⣴⡯⠖⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠳⡄⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠓⠦⣽⣆⠀⠀⠀⠙⢷⣄⠀⠀⣰⠏⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠙⣧⣀⠀⠀⠀⠙⣿⠷⠿⠦⠶⠶⠖⠋⠉⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣠⠤⠴⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠈⠉⠙⠛⠛⠓⠚⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢀⡴⠋⣀⡤⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣤⣀⣀⣀⣠⣤⠤⠔⠒⠁⠀⠀⠀⣠⠋⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⢀⣠⢞⡡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⢀⣀⠤⠖⠋⠉⠛⠓⠒⠚⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠟⠛⠛⠳⣴⠚⠛⠛⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⣴⣿⣫⢾⣶⣤⠞⠛⣿⣷⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠶⠟⣿⣿⣇⢀⠿⢿⣿⡈⡰⠟⡆⢀⣾⡟⠀⠉⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠹⣿⡿⣿⣦⡀⠉⢿⠀⣀⣼⠿⢿⠀⠀⢀⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠓⠒⠒⢺⡇⠀⠙⣷⣠⣴⠟⠋⠁⠀⠘⣇⣴⡿⠿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⢀⡾⠁⠀⢀⣾⠋⠀⠀⠀⢀⣤⠞⠛⡏⠀⠀⠀⠙⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⠀⠀⠀⣼⠁⠀⠀⣼⠃⠀⠀⢠⡾⠋⠀⠀⠀⣷⠀⠀⢀⣠⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⢹⡀⠀⠀⢻⡀⠀⢠⠏⠀⠀⠀⠀⠀⡿⣶⡾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠙⢿⣿⣦⡀⠑⢤⣀⠀⠳⣄⡜⠀⠀⠀⢀⣠⠞⠁⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠻⣶⣝⠻⠿⠷⣶⠾⠿⠻⣿⣷⣶⣛⠋⠉⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠈⠻⣧⠀⠀⠀⠀⠀⠀⠙⣿⠛⠛⠻⠷⠶⢶⣶⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⢹⡇⠀⠀⣀⣤⣾⡇⣻⡆⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⢸⠇⣰⠟⠉⠀⢻⣧⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣙⠓⠒⢇⢠⡏⠀⠀⠀⣼⡟⠀⣷
⠀⠀⠀⠀⣠⣶⡟⠛⠉⠉⠙⠳⣄⠈⢷⡇⠀⢀⣰⠟⣡⡤⣿⣶⠂
⠀⠀⠀⠈⠉⠙⢿⣦⡀⠀⠀⠀⠈⠳⣬⣟⠛⠛⢡⡞⠁⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠤⠤⠴⠚⠁⠘⢆⠀⢸⡇⠀⠈⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⠤⣵⣄⢁⣠⢶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⣠⠞⠹⡅⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣀⣠⣴⡾⠋⠀⠀⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠈⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⡀⠑⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠸⠀⠘⠀⠐⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⢈⢩⡙⠘⠒⠁⠀⠀⠆⠈⠀⠀⠁⠁⠢⡀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠘⣄⠢⡑⠀⠀⢠⠀⠀⠀⠂⠈⠀⠀⡆⠀⠀⠈⢆⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠈⠑⠀⠩⡥⠀⠀⠀⠀⠁⢈⠀⠀⠸⡀⠀⠀⠀⢣⠀⠡⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣁⣨⠀⠀⢄⢡⠀⠀⢕⢄⣇⠀⣁⠀⠄⠑⣇⠠⠀⠀⠀⢀⠂⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡠⢀⠔⠼⠢⠠⠀⠊⠀⢣⠀⠀⠦⢻⢀⢀⠠⠌⠦⠧⢀⠀⠀⠀⠀⠀⡠⠜⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠈⢲⠒⣦⣀⠀⠒⠐⣬⠡⡆⢤⡾⢠⣌⣒⣐⣒⠶⡊⠭⠩⠉⣁⣠⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠑⠒⠒⠳⠤⠤⠜⠋⠉⠉⠀⠀⠈⠉⠉⠁⠀⠀⠀⠈⠠⠀⢀⡀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⢂⠀⠁⠀⠀⠐⠀⡰⠂⠀⢀⣀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠤⢀⡀⡑⢄⠀⠀⠈⠹⠀⠀⠀⠀⡏⠁⠀⠀⢀
⠀⡎⠀⢴⡁⠉⠉⠉⢇⣀⣀⠀⠀⡁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠰⠁⠈⠀⠈⠀⠀⡀⠉⡀⠀⢀⡀⠁⢠⠀⠀⣠
⠀⠈⠒⠤⠤⣀⡴⠀⠀⠀⠀⠉⠉⠉⠒⠀⠀⠰⠤⠄⠀⠀⠠⡚⠀⠀⠠⢀⠁⡀⠉⠁⢠⠀⠀⠈⠐⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠧⢄⣀⠴⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢳⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠈⠉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠚⠛⠛⠛⠛⠛⠶⣾⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠀⠀⠀⠀⠁⠀⠀⠀⢀⡠⡀⠑⠀⠀⠀⠀⠀⠰⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠔⢈⡐⠄⠅⠀⠀⠀⢀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠐⠀⠀⠀⠀⠀⢀⠰⡉⠙⠂⠈⠗⠁⡠⠄⠀⠀⢲⠶⣤⣑⠀⢂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢨⠀⠀⠀⣀⠤⣰⠁⢄⠄⠑⠄⠗⠚⠉⠀⠀⠀⠀⣸⠀⠀⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠠⠃⠀⠀⡜⠁⢀⢜⠧⢠⢸⠐⢊⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢆⠀⠈⠁⣠⠎⠁⠀⢀⡀⠀⠈⠀⠀⣠⡟
⠀⢠⡴⢒⠒⠶⠶⠴⠋⠁⠀⢢⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋
⠠⡏⠈⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠹⣦⡀⠁⠉⠙⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣠⡴⠞⠋
⠀⠀⢨⡇⠀⠀⠈⠂⡑⠁⠀⠀⠀⣿⠙⠓⠲⠶⠶⠶⠚⠋⠉
⠀⠀⠈⢷⡀⠀⠀⠀⡄⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠉⠛⢶⡄⢇⡘⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠶⠴⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣄⣾⣿⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣦⠀⠀⠀⣠⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⣻⣟⣿⣷⡀⣼⣿⣿⣿⣿⡿⠀⠀⠀⣠⣴⣶⣦⣼⣿⣻⣿⣝⠛⣡⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣫⣾⣿⢿⣿⢹⣄⢿⣟⣿⣿⣿⣿⣷⠀⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡽⣿⣿⣯⣿⣿⣬⡻⠟⠋⢙⡿⢫⣶⣶⣿⣿⣷⣾⣿⢿⣿⣿⣿⣿⣿⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⢿⡟⣿⣿⡿⣿⡇⠀⢀⠀⢠⣾⣿⣿⣻⣿⣿⢿⣿⣾⣿⣯⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⡿⣛⣠⣠⣤⣤⡘⢿⣿⣿⣿⣿⣯⣾⣿⡿⣟⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠙⠛⠛⣩⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣯⢻⣿⣿⣽⣿⡿⣿⣿⣿⣿⣻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣄⠀⠀⣾⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣷⣿⣀⠉⣿⣿⣿⣽⣿⣿⣿⣿⣋⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⢰⣿⣿⣿⣿⣿⣿⣷⠲⣿⣿⣿⣻⣿⣿⣷⡀⠉⢏⠉⢛⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⢿⣷⢘⣻⣟⠋⠁
⠀⠀⠀⠀⢀⣠⣴⣾⡿⣿⣌⣽⣷⡜⣿⣿⣿⣿⣿⣿⣿⣾⡿⣷⣿⣿⣿⣿⣿⣿⣿⣽⣿⢸⣿⣿⣿⣶⡄
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⡈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢿⣿⣿⡿⠈⢿⣿⣟⣿⣿⡆
⠀⠀⠀⠘⠿⠿⠿⠿⠛⠁⠘⣿⣿⣿⠇⠀⠘⢿⣿⣿⣿⣿⣽⣿⣿⣿⠟⠁⠀⠈⢿⠏⠀⠀⠀⠙⠛⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠏⠀⠀⠀⠈⠙⠋⠉⠀⠀⠈⠉⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠷⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⠀⠀⠀⠀⠀⠰⠄⠀⠀⢀⣀⡀⠀⠀⠀⠀⣄⣠⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⠀⠀⠀⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣤⡴⢶⣶⣶⣤⡀⠀⠀⠀⠘⡇⠀⠀⠀⠀⣠⣴⠶⠛⠛⠛⠂⠀⠀⢀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠀⠀⠀⠈⠙⢿⣧⡀⠀⠀⠹⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⢀⡾⠁⠀⠀⢀⣤⣶⣶⣶⣶⣦⣄⡀
⠀⠀⠉⠀⠀⠀⠀⠀⠉⠁⣀⣴⠾⠟⠛⠻⠷⣦⣄⠀⠀⠀⠘⢷⡀⠀⠀⣸⠁⠀⢀⣴⠟⠋⠁⠀⠀⠀⠈⠉⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠋⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠘⣇⠀⠁⠇⠀⢠⠞⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠳⡀⠀⠸⡀⠀⠀⠀⠊⠀⢀⣴⡾⠿⠿⠿⢷⣦⣀⠀⠀⠀⠀⠀⠀⣀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠿⠷⠶⣤⡀⠀⠘⠄⠀⠃⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠐⠂⠀⠀⠉⠲⠄⠀⠀⠀⣼⣾⣀⠞⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⣰⣶⡀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠴⠚⠉⠙⠛⢿⣦⠂⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠈⠃⠀⠀⠀⡼⠁⠀⠀⠀⠀⣠⣿⠟⠉⠀⠀⠉⠀⠀⠀⠸⠧⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠹⣧⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠐⠀⠀⠀⠸⠁⢠⣤⠀⠀⢰⡿⠁⠀⠀⠀⢠⣶⠶⠆⠀⠀⠀⠀⠈⠁⠈⠙⣷⡀⠀⠀⠀⠀⢹⡆⠀⢠⣿⣿⡄⠀⠀⠆
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣿⠁⠀⠀⠀⢠⡟⠁⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⢇⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣼⠁⠀⠀⠀⣿⠀⠀⠀⢀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡀⡟⠀⠀⠀⠀⡇⠀⠀⠀⠼⡿⠆⠀⠀⠸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⠀⠀⢀⡀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠁⠀⠀⠀⠀⠁⠀⠀⣠⡄⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠟⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠁⠀⠀⠀⠈⠢⣄⠈⠉⠓⠲⢄⡀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠙⢦⡴⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢄⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⣀⣀⠀⠀⠀⠀⠀⡟⠓⠢⠤⣄⣀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⣠⠖⠒⠛⠉⠉⠉⠉⠉⠉⢹⠀⠀⠈⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢚⠇⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⣧
⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠉⠒⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠹⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠁⠀⠈⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠞⠢⣉⠒⠲⠤⠄⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠤⡀⠀⠀⠀⠀⢀⡞⠀⠀⠈⠙⠲⠤⣤⣀⣀⣀⣀⣤⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⡤⠞⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⣀⣀⠀⠀⠀⠀⣀⣤⣤⣴⣤⣤⣶⣶⣶⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣨⣤⣽⣶⣴⣾⣿⣿⣿⣿⣯⣿⣏⠙⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⡀⠀⣼⣿⣿⠿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢻⡇⢿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢅⢸⣿⠀⠀⠀⣰⣾⣿⢟⡿⠛⣿⣿⣿⣿⡿⠿⢿⣿⣿⣼⣿⢏⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⢰⣿⣿⣷⣿⡵⠿⠟⠉⠻⣇⣉⣴⢸⣿⣿⢹⡏⣾⣿⣿⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⡀⢇⠀⢠⣧⠈⠉⠻⣄⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⢎⣼⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⢀⣠⡴⣿⣿⣼⣄⣾⣿⣷⣄⠀⠘⢷⣦⣄⡀⠀⠀⠀⣀⣀⣤⢻⣿⣿⠿⠻⠿⢟⣽⣿⣿⣿⡿
⠀⠀⠀⠸⡀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣄⡀⠘⢻⣿⣿⣶⣾⣿⡿⣱⡿⠋⠁⠀⠀⢀⣾⣿⣿⣿⡿⠁
⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠈⠙⠿⠿⠿⣿⣿⣦⣀⠙⡻⢿⣿⣿⡟⠁⠀⢀⣀⣤⣶⣿⣿⣿⣿⡿
⠀⠀⠀⠀⢿⣿⣶⣤⣄⣀⣀⣀⠀⣀⠀⠈⣉⣫⡽⠟⠛⠛⠛⠿⠷⣶⣾⠿⠿⢿⣿⣿⣿⣿⣿⣁⣀
⠀⠀⠀⢀⣤⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⣿⡏⠀⠀⠀⣀⣠⣴⣶⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⣿⣿⣿⡿⠿⡿⠦⣀⠀⠀⠀⠀⠀⠈⠙⠾⣿⣿⣿⣿⣿⣿⣟⣛⣫⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂
⠀⠀⠀⠉⠁⠀⣠⣶⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣭⣿⣭⣭⣽⡿⠿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣷⣄⢀⣠⣴⣾⣿⠿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⢠⠿⠛⠛⠻⠿⠿⡿⠿⠿⠛⠁⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣿⡿⠋⠁⠛⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠂⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢯⢣⠈⢻⣄⠀⣀⡠⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⢁⡀⠀⠣⡑⣄⠹⡏⠀⠀⠀⠀⠀⠀⡴⣺⣛⠻⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⠁⠀⠈⠁⠀⠀⠈⠪⡵⠁⠀⠀⠀⠀⠀⠈⠘⢐⡠⡁⠀⢠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣧⡀⠋⠀⠀⡤⠀⠀⠙⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠽⢑⣫⣷⠶⠮⡙⢦
⠀⠀⠀⠀⠀⠀⣀⣀⠨⣧⠈⢗⡄⠀⡀⠀⠀⡶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⡠⡤⡀⡀⡼⡄
⠀⠀⠀⠀⠰⢍⠀⠀⠀⠈⢷⣀⠪⣒⣏⠔⠊⠀⠀⠀⠀⠀⠀⡀⠠⠠⢀⠀⠀⣄⣀⣀⠀⠓⣬⡥⠞⠋⡠
⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⢀⠟⠓⠉⠀⠀⢀⠔⠈⠀⠀⠀⠈⠀⠘⠛⠖⠀⠄⠠⠄⣀⣀⣀⣀⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⢈⢀⠔⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢀⣀⡥⣐⣂⠄⠶⢦⡀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢁⠀⠀⠀⠀⠀⣀⠄⠂
⠀⠀⠀⠀⠰⠚⠉⠃⠀⠀⠀⡀⢀⠀⢷⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⡠⠂⠀⠀⢠⠖⠭⣀
⠀⠀⠀⠀⠀⣀⠠⠼⠖⠒⠈⢁⠀⠀⢸⡆⠀⠀⠀⠑⢄⠀⠀⠀⡠⠊⠀⠀⠀⡠⠁⠀⠀⠀⠉⠒⢤
⠀⠀⠀⠀⠀⢁⠀⢀⣡⠠⠤⠘⣆⠀⠩⣦⠀⠀⠀⠀⠀⠁⠲⠊⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⢀⠛
⠀⠀⠀⠀⠀⠈⠯⠀⠠⠖⠉⠓⠁⢀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠂⠌
⠀⠀⠀⠀⠀⢀⣀⠀⠄⠐⠀⠈⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠠⠁⡌
⠀⠀⠀⠀⠀⠀⠈⡀⢀⡀⠄⠄⠄⠂⠈⠂⢻⠀⠀⠀⠀⠀⠀⠀⠀⢠⣅⠀⠀⠀⠀⠀⠠⠁⠌
⠀⠀⠀⠀⠀⠀⠀⠏⠁⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⣀⡰⢁⠊
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡔⢛⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⣀⣀⠠⠄⠒⠁⠀⠀⠀⠀⠆⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⣽⢚⣛⡓⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢹⣧⠀⢿⠬⠞⢡⠛⣿⣿⡒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠈⢿⣷⣤⣥⠖⠁⢠⡿⠃⣷⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠷⢦⣝⢿⡛⠛⠲⣿⠒⠒⢿⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠈⠳⣷⡀⠀⠸⡆⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢹⡇⠀⣰⠃⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣦⣤⣼⣿⣾⣧⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠉⠀⢀⣼⠿⣿⠏⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣤⣄⡀⠀⠀⠀⢾⠁⠀⢸⡇⠀⠀⠀⠁⠀⣀⣀⣀⣀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣼⡇⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣟⣿⣿⣿⣿⣆⠀⠀⠀⣾⠇⠀⣼⣿⣿⣿⣿⣵⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⠀⣠⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡄⠀⢠⣯⠞⠉⠉⠛⠛⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠈⠹⡄⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⡿⠿⠿⠛⠛⠛⠻⢷⣦⣤⣀
⠀⢰⣿⠟⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣶⣄
⠀⢸⣿⠀⠈⠻⢿⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⡀
⠀⢸⣿⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⡀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⣤⣤⡶⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣿
⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⢸⣿⠃⠀⠀⠀⠀⣤⣴⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠛⠋⠁
⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁
⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⢹⣿⣧⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋
⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠿⠿⣦⣄⠀⢻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋
⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠿⠉
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣶⣶⣶⣶⣶⡿⠿⠿⠛⢻⣿⠇⠀⣴⣷⣶⣶⣦⣤⣤⣤⣤⣶⡾⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⣼⣿⠀⠀⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠹⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣿⣿⠀⠀⠀⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣛⠛⠛⠛⠿⢿⣿⣶⣿⡿⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠟⠛⠛⠉⠉⠉⠉⠉⠉⠛⠛⠁⣶⣆⣀⠀⠀⠀⣻⡇⠀⠀⢸⣿⣅
⠀⠀⠀⠀⣠⣾⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣆⣼⡟⠀⠀⢰⡿⠻⢿⣷⣄
⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠙⢿⣆⡀⣰⡿⠁⠀⠀⠙⢿⣷⣄
⠀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠛⠛⠛⢿⣦⠀⠀⠹⣿⣏⡀⠀⠀⠀⠀⠀⠘⢿⣦⡀
⣰⣿⠃⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⡀⠀⠀⠀⣿⡇⠀⢰⣶⡄⠈⣿⡇⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠈⢻⣿⡄
⣿⡿⠀⠀⠀⠀⢀⣾⡿⠋⠁⠀⠀⠙⣿⡆⠀⠀⢿⣇⡀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠹⣿⣄
⣿⡇⠀⠀⠀⠀⣾⡟⠀⠀⣾⣿⠀⠀⣿⣷⠀⠀⠈⠻⢿⣶⣶⣿⠟⠃⢠⣆⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠸⣿⣆
⣿⣧⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⣠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢷⡄⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠘⢿⣄
⢹⣿⠀⠀⠀⠀⠀⠙⠻⣷⣶⣴⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡞⠋⠀⠀⠈⠁⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠘⢿⣄
⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆
⠀⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠿⠿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆
⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠈⠛⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠁⠀⠀⠀⠀⠀⣰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠷⣶⣦⣤⣀⣀⣀⣀⣀⣀⣤⣴⣶⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣸⡏⠀⠉⢻⣿⠟⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣇⣀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⡀⠀⢻⣿⣿⡁⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠋⢹⣧⡀⠀⠙⠻⢿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠛⠻⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⣠⣿⠿⢿⣦⣀⣀⠀⠀⢀⣀⣀⣠⣤⣤⣄⣀⣀⠀⠀⠙⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⢀⣿⡏⠀⠀⠙⠛⠻⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠿⣷⣦⡀⠈⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⣀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠟⠁
⣶⣶⣤⣴⣶⣦⣤⣶⣶⣶⣶⣶⣦⣶⣶⣶⣤⣾⣿⣿⣿⣷⣶⣦⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣤⣤⣤⣤⣴⣶⣶⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⣴⣦⣤⣤⣶⣶⣶⣦⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣗⢿⡂⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡄⠀⠀⠓⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⠆⣠⡶⠛⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣰⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢃⠀⠀⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⣜⣿⣿⣿⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡈⠳⠘⣯⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⡼⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠈⠛⠀⣰⠃⢾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⡀⢀⣀⣀⣾⣿⣿⣿⣿⣶⣧⡀⠠⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣟⣿⣿⢿⡿⣿⣭⣻⣽⡿⣿⣷⡀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣧⣏⢿⣽⣿⢿⣾⣿⣿⣷⠀⢈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣜⢿⣿⣿⣷⠿⣟⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⣠⣤⣄⡀⠙⠦⠀⠀⡰⠹⣿⣷⣭⣿⣿⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣰⣿⣟⣿⣿⣮⡻⣿⣿⣦⡀⠀⡐⣥⣴⣉⠿⠻⠿⠿⣿⡿⣟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢟⣾⣿⣿⣿⣿⢻⣻⣿⣎⣿⣿⣿⡧⠞⠋⠁⠀⠀⣠⣀⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⢆⣿⡟⣼⣿⣿⣯⣭⣻⢗⣽⣿⣿⣿⣿⣿⣧⠀⣄⠀⠀⢀⠻⣿⣧⠈⠉⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣯⣭⢹⣿⣏⣿⣿⡻⡾⠻⠷⣋⡿⢿⣾⣿⡿⣼⢛⣀⡘⠲⠶⠋⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣟⣿⣏⣿⢏⣿⣿⣿⣯⣴⡶⣼⣿⣟⣵⣿⣹⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣮⢹⣷⣽⡮⣙⣻⣯⣭⣾⣿⣿⣿⡿⠓⠿⢿⣿⡿⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣻⣿⣿⣿⣾⠿⣿⣇⣟⣿⣿⣿⣿⣯⣖⣾⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⢿⣿⡿⠿⠛⠁⠀⢸⣿⣿⣿⠆⠀⠘⢿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄⠀⠀⠀⠀⠀⠰⢄⡀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠲⠂⠀⠀⠀⠀⠀⣠⠏⡐⠶⠃⠀⠀⠀⢀⡐⠂⠀⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠰⠊⠁⠀⠀⠀⢀⣞⠉⠳⠞⠀⠀⠀⠀⠀⠀⠀⠡⡌⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢬⡂⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢦⡵⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢖⠸⠃⠀⠀⠀⠀⠀⠀⠀⣾⠤⣌⠆⠀⠀⠀⢰⠁⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢥⠊⠀⠀⢔⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣤⠂⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⡔⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⢠⡏⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⢩⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢢⣀⡀⠀⠀⠀⢤⡐⠀⠁⡘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⡀⠀⠈⠢⡤⠀⢄⠀⠀⠀⠀⠀⠀⠠⣎⢂⢈⡰⠂⠁⠀⠀⠀⠀⢈⡤⠂⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⡐⠉⢆⠀⠀⢄⡀⣠⠀⠀⠀⠀⡖⢢⠀⣩⠜⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡐⠀⠀⠀⠑⡄⠀⠀⠀⠑⢤⡈⢆⢙⡸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡠⠒⠣⣰⣁⠁⠑⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡐⠁⠀⠀⡠⠊⠈⠢⡀⠀⠀⡠⣅⡜⠉⠀⠀⠀⢀⠊⠈⠲⠀⠀⠀⠀⢀⣠⢉⠀⠐⠗⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠃⡜⠀⠀⢀⠔⠁⠀⠀⢀⠜⠓⢄⠑⠉⠈⢢⠀⠀⠀⠀⠢⠄⠘⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⢀⠃⡜⠀⠀⡰⠃⠀⠀⡠⠖⠁⠀⠀⠀⣁⠦⢀⡀⠡
⠀⠀⠀⠀⠀⠀⡌⠌⠀⡠⠊⠀⢀⠤⠊⠀⠀⢀⠠⠒⠉⠀⣀⠠⠘⠋
⠀⠀⠀⠀⠀⡐⠌⢀⠔⠁⡠⠐⠁⢀⡠⠐⠈⣀⠠⠐⠊⠉
⠀⠀⠀⠀⢰⠏⡠⢃⠴⠊⡀⠄⢂⠡⠔⠒⠉
⠀⠀⠀⢠⣏⣨⢔⣡⠔⠍⠒⠉
⠀⠀⢠⡿⠟⠛⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⡄⠤⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⠀⢛⡿⣾⡿⠚⣤⠀⠈⠛⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣰⡤⣤⣶⣿⣷⣌⡓⠉⠽⠀⣇⠀⡌⠻⣄⠀⠙⠳⡤⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣿⣿⣿⣿⠟⠉⢋⣻⡟⠁⢰⣿⠀⠸⣄⣭⣢⡄⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⠉⠻⣿⡟⠀⠀⢼⠏⠀⢠⠂⣿⣿⠀⢹⣿⡿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡜⣧⠀⠘⢁⠀⢀⠀⠀⣠⠉⠤⠰⣿⣇⠈⡟⠀⣰⠇⠀⡀
⠀⠀⠀⠀⠀⣴⣶⣾⣝⠗⠻⢿⣿⣽⣧⡄⠀⢂⣀⡄⡂⠀⠀⠀⢈⣿⣿⡄⠀⣰⣿⣿⣀⠹⡄
⠀⠀⠀⠀⠀⠀⠉⠛⢿⣣⠀⠀⢻⣿⣿⠃⠀⠸⣧⠁⣄⡀⡀⢀⣸⣿⡟⢠⣏⣿⣿⣿⡿⠂⠁⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠘⣿⡿⠀⠀⠀⠈⠓⠿⢿⣿⣿⣿⠟⢠⣿⣿⣿⣿⡟⣤⣵⡤⠶⠦⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠘⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢫⣦⣾⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⠛⠛⣛⣿⣽⣿⣶⣶⣤⣄⣄⠀⠐⡾⢻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢽⣞⡿⠉⠀⣸⣿⡿⠃⠀⠀⢣⣀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⠴⠤⠤⠴⣻⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠠⠯⣶⢖⣬⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠦⠄⡀⠀⠀⡇⠀⠐⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⠑⠲⣤⡀⢈⠂⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡾⢃⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⠋⠉⠉⠉⠙⠛⠛⠋⠉⠉⠉⠙⣿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀
⠀⠀⠀⠀⠀⢠⣶⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣷⣄
⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄
⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀
⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣶⣄⡀⠀⠀⠀⠀⢀⣠⣾⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡄
⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠋⠉⠉⠀⠈⠉⠉⠛⠛⠋⠉⠁⠀⠉⠙⠛⠛⠳⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇
⠀⠀⢠⣿⣿⡄⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢠⣿⣿⡀
⠀⢀⣿⣿⠛⣷⣀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⣠⡞⠙⣿⣷⡀
⠀⣼⣿⡇⠀⠀⠙⠻⠷⠟⠛⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠙⠻⠶⠟⠋⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⢀⣴⠟⠉⢉⣠⣴⣮⣽⣿⣦⡀⠀⠀⣀⣴⣿⣭⣷⣤⣄⠈⠉⠻⣦⡀⠀⠀⠀⠀⠀⢠⣿⣟
⠀⢰⣿⡟⠁⠀⠀⢽⡒⣶⣿⡏⠀⠐⠋⠿⠿⠿⠧⠀⢸⣿⠩⠟⣿⠁⢨⣿⡿⠿⠏⠑⠄⠀⣿⣿⡶⣒⡶⠀⠀⠈⢻⣿⡆
⠀⠸⣿⣧⣤⣄⣀⣺⣽⣿⡇⠹⣄⠀⠀⠀⠤⠦⠀⢀⣼⠃⠀⠀⠹⣆⠀⠀⠴⠴⠄⠀⠀⡰⠃⣿⣿⣉⣀⣠⣤⣤⣼⣿⠇
⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣧⠀⠈⠳⠄⡀⠀⣠⠴⠞⠁⠀⠀⠀⠀⠙⠳⢤⣄⠀⣠⡴⠊⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⣴⣇⣀⠀⠀⠀⠀⣀⡼⢦⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣿⠟⢿⣧⠀⠀⢠⣤⠶⠋⠀⠀⠉⠛⠶⠶⠛⠉⠀⠀⠙⠶⣤⣄⠀⠀⣾⡿⠻⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣾⣿⡀⠀⠀⠀⠀⡆⠀⠤⢤⣤⣶⣤⣤⡤⠤⠀⢰⠀⠀⠀⠀⢰⣿⣷⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠸⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⠛⢿⣷⣤⣀
⠀⠀⠀⠀⢀⣀⣀⣀⣠⣴⣾⡿⠟⠋⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠙⠻⢿⣷⣦⣤⣀⣀⣀⡀
⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣴⣿⣿⠿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣠⣾⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣦⣄⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⣤⠔⡛⠙⣲⣶⣤⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣿⠯⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⣮⣿⢿⡁⢿⣟⡏⢈⠙⣆⢧⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣟⣿⣾⡛⣋⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡤⣤⣴⢡⠏⣾⡏⢶⣭⣁⡛⢛⣓⡤⣿⠋⡞
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⢿⣿⣿⣿⣿⣯⡿⣿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢝⣬⠶⠿⢧⣌⣻⠌⢻⣭⣽⣭⡁⢀⠼⠇⡱⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠧⠿⢩⣟⣻⢌⣉⡛⢿⠆⣽⡶⠿⣛⣯⠒⢭⣽⣷⢽⣢⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠻⣿⣿⣿⣿⣿⣿⣽⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠼⣟⢫⡿⣹⣦⣨⠩⣭⣭⢭⡰⡺⣦⣝⡎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡿⣽⠟⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡝⢸⡷⣣⡇⣿⣰⡬⣙⠷⣿⡟⠒⠘⠣⢼
⠀⠀⠀⠀⠀⠀⠀⢠⡴⠖⠉⠀⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⠒⠊⠁⠑⢬⡻⢧⠅⠈⠓⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣳⣄⣤⢀⣤⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⣷⢠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⡿⣼⣿⣻⣷⡿⣸⣛⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⣿⣿⣽⣯⡾⠋⣽⣷⣿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⣿⣿⣋⣿⣿⣷⣻⣿⣿⡿⣻⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠻⡾⣽⣿⣟⣻⣽⡿⢴⣟⠋⣿⡀⣧
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣟⡿⣹⣿⣿⣿⣏⣿⣿⣾⣿⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠰⢷⣤⣈⠻⠷⠿⣶⣶⣿⣵⡏⢻⣜
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⣿⣿⣿⣿⢹⣿⣿⢿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡸⠷⢬⣭⣿⣿⣭⣥⣴⠟⢁⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⢻⡿⢿⣿⣜⣋⡶⣫⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢶⣒⣨⠉⣿⣿⣧⣭⠍⠹⢯⣵⣺⠉⣭⣀⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣞⣻⢿⣿⣾⣿⣿⣿⣼⣋⡺⠿⠿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠷⠶⠎⡍⢹⣟⡛⠋⡉⢡⡆⠙⢻⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⣠⠿⠿⠛⠁⣦⣻⣷⣺⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢀⣴⣿⣿⠟⠋⠁⠀⠰⣿⡿⣱⣧⣝⠻⣷⣤⢺⡇⠀⠀⠀⠉⠛⠿⣿
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢿⣿⠹⠏⠻⠿⠿⢿⣯⠉⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⣿⣷⣿⡟⠁⠀⠈⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣾⡿⠋⠀⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠟⣋⣀⣀⡀⠿⠿⠛⠛⠿⢿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢋⣾⣿⡿⢋⣥⣶⣿⣿⣿⣷⣦⣌⣉⠻⢿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⣼⣿⡿⠁⣾⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣦⡙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡇⢿⣿⠃⣾⣿⣿⣿⡿⠋⠁⢴⣾⣿⣿⣿⣎⠳⠈⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣶⣤⡙⠃⠸⣿⢰⣿⣿⣿⠋⣠⣶⣶⣶⣶⡌⢻⣿⣿⡆⠀⠈⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠁⣾⠇⠹⣇⢿⣿⡏⣸⣿⠋⢹⣿⣿⡟⢸⣿⣿⢉⣿⡄⢸⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠃⣸⣿⡆⠀⠙⠪⠻⣇⠸⣷⣀⡘⠛⠋⢠⣿⣿⠃⣸⣿⣧⠀⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡟⢀⣿⣿⣷⠠⣤⣜⠳⣦⣄⠨⠽⣧⣤⣾⠿⠛⣡⣾⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣧⠹⣿⣷⡜⢿⣿⣶⣶⣶⣶⣾⣿⣿⣿⡿⠋⣠⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣷⣌⠻⣿⣌⠻⣿⣿⣿⣿⣿⣿⡿⠋⠀⠚⠛⠛⢛⠋⢉⣥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣷⡀⢻⣿⣿⣿⣿⣿⣷⣦⣌⣀⡈⠉⠛⠛⠋⣁⡀⢰⣿⣿⣿⣿⠟⣠⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣄⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣿⣿⡿⢛⣡⣾⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣤⡀⠈⠉⠻⢿⣿⣿⠿⠿⠛⠋⠥⠞⣛⣋⣥⣶⣿⣿⣿⣿⣿⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⣶⡜⢿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠉⠙⠻⠿⠿⠿⠟⠋⠁
⠀⠀⠀⠀⣀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⣿⡈⠻⣷⡄⠀⠀⠀⠀⠀⠀⢀⣿⡏
⠀⣠⣴⣾⡿⠟⠛⠛⠛⠛⠻⢶⣄⠀⠀⠀⠀⣿⣧⠀⢹⣇⠀⠀⠀⠀⠀⠀⣼⡟
⠘⠛⠿⣿⣿⣶⣶⣶⣶⣶⣶⣦⣌⡃⠀⠀⠀⢿⣿⣧⠀⡟⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠦⣄⠈⢿⣿⡇⠃⠀⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠀⠈⠙⢦⣌⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡾⠟⠛⢛⣲⣄⠈⠷⣄⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠉⢀⣠⣶⣿⣿⡟⠀⠀⠘⢧⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⠋⣰⣿⡆⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣶⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠈⢷⡀⢀⣿⠃⠀⠀⠀⠀⠀⠀⣸⠇⢠⣿⣿⠃⠀⠀⠀⡴⠟⠛⠉⠉⠉⠉⠛⢻⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⢷⣸⣿⠀⠀⠀⠀⠀⠀⠀⢸⢀⣿⣿⡟⠀⠀⠀⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠋⣠⠶⠛⠀⠈⠻⢿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⢁⣤⣤⣀⡀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣠⡾⠉⢠⣾⣷⣤⣉⠉⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⣴⠋⠀⠀⠀⢿⣿⣿⣿⣷⣦⣀⣹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⢀⡾⠁⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡧