Meteorology Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠿⠟⠛⠛⠛⠿⢿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⢋⣠⡤⠶⠚⠛⠓⠀⠀⠀⠈⠙⠻⣿⣦⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⢁⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠛⠛⠿⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣿⠏⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠿⠛⠛⠋⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣄⣀⠀⠀⣀⣠⣴⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⡀⠉⠛⠛⠒⠀⠀⢀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠟⠛⠉⠀⠉⠛⠻⠿⢿⣿⣿⠿⠿⠟⠛⠙⠻⠿⣿⣶⣶⣶⣶⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣆⠀⠀⠀⠀⠀⣠⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠹⣿⣆⠀⠀⠀⣰⣿⠛⣿⣦⠀⠀⠀⠀⠀⣤⠀⢶⣿⡶⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠘⣿⣆⠀⢰⣿⠇⠀⠘⣿⡇⠀⠀⠠⠿⢿⡀⠀⣿⠀⢀⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠘⣿⣆⠈⢿⣷⣤⣴⡿⠃⠀⠠⣦⡀⠀⡙⣦⣿⣴⡟⡁⢀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠉⠉⠉⠀⠀⠀⠨⡿⠋⠉⢉⣿⣿⢿⡉⠉⠙⢿⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⡀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⠟⠁⣿⠀⠙⣦⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠀⣠⣿⣦⠀⠿⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠠⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⣀⣤⣤⡀
⠀⠀⠀⠀⠸⣾⡿⠀⠀⠀⢀⠔⠈⠚⢿⠇⠀⠀⣀⣾⣶⣿⡷⠀⠀⠀⠤⠤⠬⢥⠀⠀⠀⠀⠙⠛⠛⠉
⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠘⠀⠀⠀⠀⠃⠀⠀⠛⠻⠻⠿⠟⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠰⣷⠀⠰⣷⠀⠀⠀⠚⠀⠈⠐⢄⠀⠀⢠⣾⣿⣷⣦⡀⠀⠀⢀⠔⠠⣀⠀⠀⠀⠀⢠⣤⣀⡀
⠀⠀⠀⠀⠀⠺⠇⠀⠀⠀⠀⠁⠄⠄⠠⠁⠀⠀⠈⠩⠩⠉⠍⠁⠀⠀⢇⡀⣀⠀⠱⠀⠀⠸⣿⣿⣿⣷⠆

⠀⠀⠀⠀⢠⠰⢠⠀⠀⠀⠀⣠⠂⠢⢄⠀⠀⠀⠀⣠⣶⣤⡀⠀⠀⠀⢀⠄⠢⢄⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢂⢀⢀⡓⠀⠀⠀⠄⠀⠀⠀⠅⠀⠀⠸⠿⠿⠿⠿⠂⠀⠀⠅⠀⠀⠀⠱⠀⠀⣠⣾⣿⣿⣽⠆
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠁⠈⠀⠀⠀⠀⠉⠈⠀⠁⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠈⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⣾⣀⠀⠀⠀⠀⢀⡀⣠⣄⡀⠀⠀⢰⣿⣿⣿⣦⡀⠀⠀⠀⡀⡠⢤⡀⠀⠀⠀⢀⣀⠤⣄
⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠠⠊⠀⠀⠙⠛⠀⠀⠈⠉⡍⢭⠉⠀⠀⠀⠊⠀⠈⠑⢪⠀⠀⢰⣿⣿⣿⣦⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⣴⡇⡀⡀⠀⠀⠀⡠⠤⣀⣿⡀⠀⠀⣴⣿⣷⣾⣷⠂⠀⠀⠠⢔⣒⡤⡀⠀⠀⠀⡠⢄⡤⡄
⠀⠀⠀⠀⠻⣷⡥⠀⠀⠀⠨⢁⠀⣀⣈⠍⠀⠀⠉⡍⠉⢩⠉⠀⠀⠠⠊⠠⠀⠈⠑⠀⠀⠀⠀⢸⡇

⠀⠀⠀⠀⠀⣬⡆⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⣀⣀⡀⠀⠀⠀⠄⣀⣀⡀
⠀⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⠀⢐⣿⠀⠀⠀⠀⠀⠀⣣⣆⠀⠀⠀⠀⠀⢘⡧⠤⠀⠀⠀⠀⢰⡏⠀⣉
⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠙⠚⠋

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣤⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠂⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠠⣂⠢⠀⠀⠀⠔⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠁⠀⠀⢀⡀⠒⠀⢄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠐⠀⠀⠀⠀⠀⠀⠈⠀⠑⡀⠀⠀⠀⠀⠈⠁⠒⠀⠀⡠⢁⠀⠁⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢸⡇⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢀⣀⣀⣀⣀⣀⣀⡀⠃
⠀⠀⠀⠀⠀⢠⢱⣯⣵⠁⠀⠂⣾⣭⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠆⠂⡄⢣
⠀⠀⠀⠀⠀⠀⠊⠙⠉⠂⠀⠑⠉⠋⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠃⢁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠒⢄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠉⠀⠀⢈⠀⠈⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⡀⠘⡀⠀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠌⡀⠀⠤⡀⠀⠈⠃⠀⠀⠀⠀⣄⣀⡠⠀⠀⠀⠀⡰⠋⠀⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠰⠁
⠀⠀⠀⠀⠱⡀⢀⠖⠁⠢⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡐⠈⠀⠈⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡀⠣⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠤⠱⠋⠉⠒⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠑⠄⢀⡀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⡉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⡁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⡊⠀⠀⠈⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠐⠀⠜⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣁⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠃
⠀⠀⠀⠀⠀⠄⠤⠌⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠔⠢⠤⠀⠀⢀⡴⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⢈⠄⡀⠀⡀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⣖⡒⣒⠦⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⡴⡙⣰
⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⢃⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣒⠚⣒⡫⠖⣒⡚⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠑⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠠⡀
⠀⠀⠀⠀⠀⠠⠀⠒⠃⠀⠀⠀⢈⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠐⠆⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠐⠃⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠐⠢⠄⠀⠀⢀⠔⠒⠃⠀⠀⢑⠀⠀⠀⠀⠀⠀⢀⠐⠠⠄⠀⠀⠀⠀⠀⠐⠛⠠⠀⠀⠀⠀⠀⢀⠐⠂⠤⠀⠀⠀⠀⠀⠐⠚⠢
⠀⠀⠀⠃⠀⠀⠀⠀⢰⠈⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠐⠒⠒⠒⠒⠒⠒⠈⠀⠀⠀⠀⠀⠀⠈⠉⡉⠉⠏⠁⡈⠁⠹⠁⠀⠀⠀⠀⠀⠀⠀⠠⠈⠼⠉⠱⠉⠸⡉⠉⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠐⠁⠈⠱

⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⢀⢻⣶⣷⣾⢁⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⢀⠠⢀⠀⠀⠀⠀⠀⠀⢀⣳⣾⣾⣁⠀⠀⠀⠀⢰⣿
⠀⠉⣹⣿⣿⢟⡉⠀⠀⠈⣿⣿⣄⠀⠀⠀⠀⢠⠂⠀⠀⠉⠠⢄⠀⠀⠀⠀⠘⠙⠻⠄⠀⠀⠀⠀⠈⠙⠦⣤
⠀⠀⠁⠐⠃⠈⠁⠀⠀⠀⠈⠛⠿⠗⠂⠀⠀⠈⠂⠀⠀⠀⠀⠊
⠀⠀⠀⣀⣠⣀⡀⠀⠀⠀⠀⠀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⣤⠀⡀
⠀⠀⡰⢸⣿⣿⠶⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⡠⠒⠢⡀⡀⠀⠀⠀⠀⣰⣦⡀⢿⡗⠀⠀⠀⠀⣾⣿⣇⠈
⠀⠈⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⢸⠀⠀⠀⠀⠈⢠⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠈⠘⠋⠉⠛⠈⠁
⠀⠀⢄⠠⡀⠄⠀⠀⠀⠀⠄⡠⢀⠤⠀⠀⠀⠀⢡⢀⢠⢀⢠⠀⠀⠀⠘⠺⠿⠋⠀⠀⠀⠀⠀⠀⠤⠆
⠀⠀⠀⡀⢠⠀⡀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⢠⢽⣿⣿⠥⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⠄⠄⡀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⢀⠄⠠⣁⠈⠂⠢⢀
⠀⠐⠀⠈⠉⠝⠂⠀⠀⠀⠀⠀⠉⠑⠦⠀⠀⢰⠁⠀⠀⠀⠑⢠⠀⠀⠀⠘⢻⠟⠀⠀⢠⠁⠀⠀⠀⠐⠂⡀⠠
⠀⠀⠰⠀⠆⠀⠀⠀⠀⠀⠐⠆⠶⠀⠀⠀⠀⠀⠀⢶⠀⢶⠀⠈⠀⠀⠀⠀⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⣹⣾⣾⣁⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⣠⣄⢸⡏⣠⣄⠀⠀⠤⠤⠤⠤⠤⠤⠄
⠀⠀⠀⠈⠛⠛⠆⠀⠀⠀⠀⠀⠛⠳⡤⠀⠀⢠⠂⠀⠀⠉⠱⢀⠀⠀⢈⣩⡵⢮⣝⡁⠀⠀⣫⠭⢝⣛⡭⠭⣇
⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠘⠀⠀⠙⠋⢸⣧⠙⠋⠀⠀⠒⠋⠓⠒⠊⠑⠒
⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠘⠃⠈⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣠⠄⢀⡄⠀⠀⠀⣀⠀⣤⣦⡀⠀⠀⠀⠀⠀⢤⣧⡤
⢠⣤⣤⣤⣤⡄⠁⠀⠀⠾⠷⠴⠿⠶⠿⠗⠀⠀⠀⣿⠀⠙⠛⠀⠀⠀⠀⠀⠀⠉⠏⠁⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠄⠀⠀⠀⠀⣰⣯⣠⣾⣀⣼⣇⠀⠀⢰⣿⡦⠀⠀⠀⠀⠀⢠⣾⣷⠀⠀⠀⠀⠀⠀⠀⢰⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠙⠷⠀⢀⣠⣤⠶⠶⢶⣤⣄⠀⠰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠟⠙⠛⠷⢶⣤⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠘⠶⠶⠆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣷⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠙⠉⠉⠉⠛⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⣼⣿⣿⣿⣿⣿⠿⠿⠛⠿⠿⢿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢀⣠⡞⠀⠀⠉⣛⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⣾⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠛⠋⠉⠙⠻⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠁⠀⠀⠈⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋⠉⠉⠉⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠀⠀⠈⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠟⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣄⣀⣀⣀⣀⣤⣤⣶⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠋⠉⢀⣠⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠈⠉⠛⠳⠶⢶⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠟⠛⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠉⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠘⠓⠓⢦⡀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠘⠓⠒⢦⡀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠘⠚⠒⢦⡀
⠀⠀⠀⠀⠀⡞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⢀⡞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢀⡞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡴⠃⠀⠀⠀⠈⢧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡴⠃⠀⠀⠀⠘⢦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⡄⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡷⠀⠀⢈⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠬⣷⡧⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠘⠆⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⠀⠉⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠅⠷


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡆⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣈⣂⡤⠶⢤⡉⠀⣀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠇⠀⣰⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠀⠈⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠈⠙⢆⠀⠀⢹⠈⠁⠀⠀⠀⠀⠀⣤⡀⣰⠊⠉⠙⢦⠠⠴⠂
⠀⠀⠀⠀⠀⠀⣀⣾⠀⠀⠀⠀⠀⠀⠈⠉⠉⠳⡄⠀⠀⠀⠀⠀⣀⣾⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⡌⠛⠂⠀⠀⠀⠀⠀⡀⣇⠀⠀⠀⢸⠇⣀⡀
⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⢠⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠉⠁⢈⠓⠶⠒⠋⣄
⠀⠀⠀⠀⠀⠳⢤⣠⣄⣀⣀⣀⣀⣀⣀⣄⡤⠔⠃⠀⠀⠀⠈⠳⣤⣄⣄⣀⣀⣀⣀⣀⣠⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠸⠇⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢘⠉⢵⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⡐⠀⠀⠀⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⢁⠔⠁⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠀⠀⠀⠀⢀⢠⠆⠸⠀⠀⠊⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠆⠐⠀⠀⡀
⠀⠀⡀⠀⠀⠂⠁⠀⡀⠰⠀⠀⠀⠀⠁⠈⠀⠀⠃⠀⠂⢀⠀⠈⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈
⠀⠀⢀⠀⠁⠀⠀⡀⠁⢀⠀⠁⠀⠀⠀⠀⠐⠂⠀⠀⠀⠈⠀⠐
⠀⠀⡀⠀⠀⠀⡄⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠁⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⢀⠤
⠀⠀⠀⢀⠊⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⠀⠆⠀⠀⠘⠀⠁⠀⡀⠀⠀⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠘⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠆⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⡙
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠄⠀⠀⠀⢀⡀⠀⠀⣀⠍⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠀⠀⠀⠃⠀⠀⠈⠠⠆⠈⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⠀⢰⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣠⠄
⠀⠀⢀⠀⡀⠤⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠐⠋⠀⠀⠀⠀⠀⠀⠰⠀⠀⠁
⠄⠐⢩⡉⡑⠤⠤⠤⠤⠑⡀⠀⠐⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⠂⢀⠀⠂
⠀⠀⢇⡀⢐⠀⠙⠃⠘⠚⢡⠀⠀⠀⠀⠀⠀⠐⠁⢀⠀⠀⠀⠘⠀⠀⠀⠀⢠⣋⠱⢢⣄⠁⠀⠀⠔⠃
⠀⠀⠀⠨⣥⣉⠥⠀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⡀⠀⠀⠀⠀⡞⠠⠤⠉⣀⠀⡃
⠀⠀⠀⠀⠃⡤⢀⠉⡁⠀⠀⠀⠀⠀⢀⠀⡬⠀⠀⠼⠀⠀⢐⠃⠀⠀⠀⠀⢠⠖⠁⠀⠉⠀⡠⠂
⠀⠀⠀⠀⠀⠀⣇⡩⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⠀⠈⠉⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢄⠀⠀⠀⠀⠀⡀⠀⡶⠀⢀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣦⡀
⠀⠀⠀⠀⠀⠀⡤⠴⠋⠉⠑⡄⠀⢧⡀⠀⠀⣀⠈⣴⣶⣦⠁⣀⠀⠀⠀⠠⠿⣽⡽⢷⠀⠀⢀⣤⣿⣿⣿⣼⣿⣷⣄
⠀⠀⠀⠀⣰⠊⠀⠀⠀⠀⠀⠙⢢⢀⡟⠀⠀⠉⢀⠻⠿⠟⡀⠉⠀⠀⠀⠀⠻⣽⡽⠛⠀⠀⠘⢿⡿⣿⣯⣿⢿⣿⠟
⠀⠀⠀⠀⠈⠒⠒⠒⠒⠒⠒⠒⠋⠀⠀⠀⠀⠀⠁⠀⠷⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⡏⡱⠄⠀⠀⠀⠀⢀⡔⠚⠁⠀⠈⢧⠀⠀⠀⠀⠀⣰⣄
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢀⡇⢪⡁⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⢰⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢈⡍⢩⡄⢠⡉⠀⠀⠀⠀⠀⠀⠸⣄⣀⠇⠀⠀⠀⠀⠉⠉⢉⠉⣉⠉⠉⠁⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠈⢡⡌⢠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣶⣄⠀⠀⠀⠀⠀⢰⢠⢠⢀⠀⠀⠀⠀⠀⣀⡀⠀⡀
⠀⠀⠀⠀⠠⠤⣼⣿⣿⣿⣏⣀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢸⠈⠀⠀⠀⣀⣶⣶⣶⣾⣁⣋⣹⠆
⠀⠀⠀⠀⠐⢲⣿⣿⣿⣿⡟⠃⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⠋⠉⠉⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠠⡀⠀⡇⠀⣠⠀⠀⠀⠀⠀⠀⠘⣛⣓⣒⣒⣛⡛⠁⠀⠀⠀⣠⠤⠊⠉⠙⢦⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⣀⠈⣴⣶⡦⠵⠊⠉⠓⡄⠀⠀⠈⠷⠶⠶⢶⠶⠀⠀⠀⢠⠊⠁⠀⠀⠀⠀⠈⢲⠀⠀⠀⣠⣶⣿⣆
⠀⠀⠀⠀⠀⣀⠹⠚⠁⠀⠀⠀⠀⠙⢦⠀⠀⠀⠉⡭⠭⠭⠁⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⠊⠀⠀⠀⣿⣾⡟⠋
⠀⠀⠀⠀⠈⠁⠘⠒⠒⠒⠒⠒⠒⠒⠋⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠰⡿⠀⢾⠇⠰⠿⠆⠀⠀⠀⠈⠉


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⣀⣰⣤⣦⣠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⣴⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣄⣀⣀⡀
⠀⠰⣾⢟⣽⣿⣟⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢿⣻⣺⣿⢿⡆⠀⠀⠀⠀⠀⠀⠀⢀⡨⣟⣻⣿⣿⣷⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⣻⣿⣻⣿⣿⣿⣼⡷⠂⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣞⠈⠁⠀⠀⠀⠈⠁⠀⠑⠀⠀⠀⠀⠀⠉⠉⠉⠻⠿⠛⠛⠛⠋⠉
⠀⠀⠿⣷⣿⣽⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠻⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⡀⣀⠤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠿⠂⠸⠗⠀⠿⠂
⠀⠀⠀⠁⠘⠁⠃
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠤⣄
⡖⠀⠈⠁⠉⠀⠉⠂⠀⠐⠀⠀⠀⠀⢀⣀⣾⣴⣤⣶⣶⣄⣤⣄⡀⢈⠀⠀⠀⠀⣴⣶⣾⣿⣿⣿⣿⣤⣶⣦⡀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠈⠱⠄⠀⢀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⠻⢿⡿⢿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⠠⠔
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠆⠰⠷⠀⠾⠆

⠀⠀⠀⣴⠳⡖⣣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⢽⠤⢵⣶⠥⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣳⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⣿⡷⠂
⠀⠀⠉⢾⣡⣆⡓⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣦⣤⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄
⠀⠀⢀⣀⣀⢸⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢸⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡇⢸
⠀⠀⠈⢸⡗⢸⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣋⡁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⡇⢸
⠀⠀⠀⠈⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢺⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣧⣼
⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡧
⣤⣤⣤⣤⣬⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣥⣤⣤
⣿⣿⣋⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢀⠀⠀⠈⠀⢀⠀⠀⠈⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠀⣿⣏⠀⠀⠀⠀⠀⠀⠀⡀⠉⡉⣙⠁
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠾⠲⠀⠀⠀⢀⠠⡄⠀⣀⣍⡈⣌⣙⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠒⢀⠠⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡄⡀⢩⢀⡉⠡
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠔⢁⡠⠏⣤⠠⡨⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡄⢠⢉⠈⡃⢄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⢈⢰⠏⠀⢄⡽⠯⢇⣠⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⣱⢈⡁⣍⣍⠛⡀
⠀⠀⠀⠀⠀⠀⡀⢀⣀⠤⠽⠡⢠⣤⠀⠀⠀⣀⡀⠀⠑⡴⢊⠰⠔⠀⢸⣮⣭⠄⡛⠛⠿⠻⠄⠒⠀⠐⠀⠒
⠀⠀⠀⠀⠀⠃⠐⠀⠀⠀⢀⡤⠙⠛⠓⠃⠰⠿⠗⢀⠧⠿⠯⢷⠐⠈⠀⠘⠛⠚⣇⣈⠔⠀⠒⠔⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠁⠀⠈⠉⠒⠊⠉⠐⢼⠀⠈⠠⡖⠊⠉⠀⠀⠀⠀⠀⠈⢰⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠳⠔⠲⠤⠠⣀⠠⠤⠤⠀⠁

⠀⣴⣶⣶⣶⣶⣶⣾⣶⣿⣶⣾⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣽⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣟⣿⣽⣻⣽⣿⣿⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣽⣿
⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣿⣷⢿⣷⣽⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣶⣿⢯⣿⢏⣼⣿⡿⣿⣷⣭⣹⣿⣿⡿⠟⡩⠿⣿⣿⣿⣽⣿⣾⣿⣾⣿⣿⣾⣿⣿⣷⣶⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⠀⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣮⣻⣿⣿⣿⣿⣿⣿⡻⣷⣿⣿⣽⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣯⡛⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⠤⠀⠂⠯⢩⡛⠂⠭⢥⣿⣉⣟⠛⠻⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣷⣿⣼⣿⣽⠩⠭⠤⠘⠛⠠⠈⣉⠂⠐⠀⠀⣤⢄⠒⠄⡀⠠⢀⠀⢙⡋⠠⠖⠦⠤⣼⣻⣿⣧⣾⡟⢀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⡿⣥⣾⣿⣧⠀⠀⠀⡠⠊⠀⣾⡇⠰⠀⠃⠀⠶⠘⠆⠀⠄⠐⠄⡀⠘⠃⠰⠇⢾⢠⡆⠿⣿⣿⣿⡇⢀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⡿⠋⡀⠸⣿⣿⡻⣄⣈⣠⠀⠀⠈⠀⡄⠀⠀⠀⠀⢄⠀⡀⠸⠀⢀⠄⠈⠀⠢⡄⠀⠀⠀⠈⠀⠉⠻⣿⢃⣼⣿⡄⣾⣿⣿⣿⣻⣿⣿⣿⣿
⢸⣿⣿⣿⣿⡏⠉⢁⣼⣟⡃⠈⢁⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠱⠀⠀⠰⢶⢶⠶⠶⢷⠆⠩⣿⣧⡶⢤⣦⣤⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣷⣿⣿⡇⠀⠜⢻⣿⣟⠂⠀⠐⡎⣀⡀⡥⢇⠀⠀⠀⠂⠀⠀⠆⠀⠀⠀⠈⠃⠀⣸⡇⠀⠀⢶⠄⠈⡟⣸⡗⠈⢹⣿⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⡇⠀⠠⣿⣿⡿⠰⡀⠈⠃⠿⠷⠄⠄⠀⠤⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡇⠀⠀⢫⡇⠀⣷⣸⡧⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠙⢹⡟⡟⠃⢀⠢⣿⣿⡑⠒⠧⠀⠀⡀⡀⢀⠂⢀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠃⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠑⠀⡈⠑⠃⢡⠐⠀⡆⠐⠀⠀⡀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠈⠉⠉⠙⠛⠛⠋⠛⠛⠛⣧⣴⣾⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠃⠡⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣼⣿⣿⣿⢿⣿⣿⣿⣿⣷⡬⠙⠿⠛⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⣙⣿⣿⣿⣿⣿⣟⠻⣿⡻⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠛⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠙⠛⠂
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣶⡿⢯⡿⢿⣿⠿⠛⠋
⡃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣁⠀⠞
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣤⠀⡄⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⠛⣿⢻⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢆⣤⡰⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⡻⠛⢟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢇⣿⣿⣿⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠸⠁⠀⠈⣇⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠻⠸⠟⠛⠻⠇⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣇⣠⣤⣄⣸⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⢄⡺⠟⠁⠀⠀⠀⠀⡠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣫⠟⡉
⠀⡀⢀⡀⠀⠀⠀⠀⣀⡼⠀⠀⠀⠎⠁⠈⠃⠀⢀⣠⠖⠈⠀⠁⠀⠀⠀⠀⠈⠂⠀⠀⣶⠀⠀⢀⣿⢨⡵⣿⡄⠉
⣼⣟⠽⢁⣿⡀⢀⡀⠹⠖⠙⠄⠀⠈⢿⠀⠀⠈⠀⠙⠀⠀⠀⢀⠔⠀⠀⠀⢀⡄⠀⠠⣟⡄⠀⣾⢟⠷⡖⢋⠙⡟⠋⣼⡀
⣿⠕⡇⣻⢙⣿⣿⠄⠀⠲⠁⠓⡆⠀⠊⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⠄⠸⠛⢥⠨⠖⢛⣌⠺⣾⠧⡘⠲⣬⣷
⠷⢪⣽⢑⣮⡿⠇⠘⠶⠊⠓⠧⣙⢶⣤⣤⣠⣆⡄⢼⡧⣀⣠⣤⣴⣴⣷⣶⢉⣃⢺⠞⣙⢰⡡⠂⠻⣌⠻⣹⣦⢤⡀⠘⢿
⢶⡁⢸⡙⣧⡶⠺⢤⡞⠓⣭⣇⠙⠻⣿⣿⣿⣿⣏⠹⠏⣿⣿⣿⢃⣿⣿⡿⠚⣍⡉⠩⣌⢫⠤⠀⣻⣈⠶⣿⢿⡄⠙⠳⢿
⠉⣱⢾⣟⡥⠐⠂⡖⢃⡀⠎⠋⠑⢦⣻⣿⢿⡿⡰⢺⡀⡜⢿⣻⠁⠸⣿⠄⠈⣉⡉⠳⣷⡞⠈⠉⠀⢹⠢⢌⡄⠀⠢
⣾⣉⣾⡟⠁⠲⡋⢀⡞⠀⡀⠸⣤⠀⠉⡿⣟⠁⠀⠂⡏⠀⢈⡕⠀⣴⠃⣂⣸⢉⣭⡑⢻⣷⡴⢿⡀⢈⡷⣄⡙⢆⣠⠈⢻
⠈⠩⠋⠀⣀⡤⠜⠉⠀⠀⠙⣆⣸⠚⠓⠃⠘⠂⠊⠙⠓⠂⠀⠁⠀⠀⠁⠀⠈⠈⠀⠘⢋⠄⠀⡈⠁⠋⠀⠀⠉⠻⣏⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠙⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠐⠋⠢⠄⠀⠢⠴⠆⠈⠛⠛



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⠦⣄⠀⠀⠀⣀⡤⠤⠶⠶⠶⠶⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⡁⠀⠀⠀⠀⠀⠙⣦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⣠⠞⠋⠉⠉⠉⠉⠓⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⡤⠤⢤⣀
⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠙⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⣠⣟
⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⠟⣽⠛⠛⠻⣴⣟
⠀⠀⠧⣄⣀⣀⣀⣀⣀⡤⠴⠋⠙⠦⠤⠤⠤⣴⡏⠈⠷⣦⢤⣄⣀⣀⣤⡴⣯⢟⡴⢿⠀⠀⢀⡯⣉⡇⢀⣤⡀
⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣶⣗⠙⣒⣶⣾⠊⣳⡾⠋⢳⠿⠀⢚⣒⡋⣛⣒⡋⣘⣓⣒⣋⢘⣓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⡜⢉⡿⢟⡜⠉⠉⣿⣭⢏⡶⡜⠯⣵⠟⠉⠳⡹⣄⡀⠈⠷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⣾⣇⣀⣀⣹⢆⡼⠷⢧⣄⢿⡀⠀⣠⣧⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣨⠿⣭⢁⢯⠀⠀⠀⡼⣀⢩⡭⣅⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⣣⢿⠎⢳⣶⡚⢱⡋⢧⠳⣭⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡯⣠⢳⡈⠛⠋⠘⠛⠋⠁⢸⣃⣰⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠙⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⢀⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣉⣥⣴⠂⠀⠀⣤⣦⣄⡀⠀⠀⠀⠀⠀⠀⢈⣦
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠐⠒⠂⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠈⠀⠀⠀⠀⢤⣤⣤⠖⠀⠀⠀⠀⠀⠀⠀⠰⣦⣀⣀⣿⣿⣷⣶⣦⡤⠀⠀⠀⣀⡉⢀⣀⣀⣀⣠⣴⠟⠛⠛⠛⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠛⣛⣫⣼⣿⣷⣴⣦⣤⣄⠽⠋⠀⠈⠉⠛⠿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠤⢤⡀
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠒⠶⠀⠀⠀⠀⠀⠀⢀⣾⢷⣶⣾⣿⣿⣿⣿⠿⠿⣿⣿⣥⡀
⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠀⠹⠿⡿⠏⠉⢠⡤⠒⠛⣛⣿⣿⡿⠆⠄
⠀⠀⠀⠀⢠⣄⣀⠀⠀⠬⠉⠀⠀⠈⢉⠛⠓⠶⠶⢆⠀⠐⠀⠀⠀⠈⠀⢀⣿⣿⣿⠿⠷⠶⠶⣶⠶⠚⠟⢶⣄
⣿⣧⣲⠴⢤⣄⠉⠉⠉⠀⠀⠀⠀⡀⠈⠷⢠⠄⠄⠀⠀⠈⣉⠀⠀⠐⡖⠀⠉⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠹⠯⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⣌⠙⠛⠛⠂⠀⠀⠀⠀⢠⣶⠶⠀⠀⠀⠀⠀⠀⠀⠂⢠⣾⣿⣿⣶⣤⠀⠀⠀⠀⢀⣤⣦⣄⡀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣦⣄
⠤⠀⠰⠆⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠄⠃⠀⠤⢀⣶⣾⣿⣿⣿⣿⣇⣠⣴⠆⠊⣳⣿⣿⣿⣿⣶⣦⣝⠓⣤⣄⣀⠉⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀
⠀⠀⣀⣀⡀⣭⣍⠛⠉⠁⠀⠀⠀⠒⡀⠀⢤⣴⣤⣮⣽⣿⣷⣶⣶⣾⡾⠛⣼⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣮⣍⠁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴
⠲⠦⠍⠉⠁⠛⠉⢁⡀⢶⣶⣮⣷⣾⣿⣿⣶⣾⣿⣿⣿⣭⣟⣟⣿⣿⣿⠛⣡⣽⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⡀⣀⣠⡴⠄⠺⠿⠿⠆⠀⠐⡛⠛⠛⠛⠛⠛⠻⣿⠛⠟⠛⠛⠏⠙⣿⣾⣶⣶⣶⣶⡤⢶⣶⣶⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⣿⡿⠿⠶
⠘⠉⢁⣀⣀⢠⣀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣿⠀⢹⣦⣠⣦⣶⠶⠂⣀⠀⠀⣬⣿⣿⣦⣤⣄⠉⢉⠛⠿⢿⣿⣿⣿⣭⣉⣉⣉⠉⠉⠁⠀⠀⠈⠙⠓

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠠⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣸⢿⡁⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄
⠀⣰⣄⡶⡟⠒⣤⣷⣤⡔⣧⣤⠠⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⣀⣀⠀⠀⠀⡇⠀⢰⣧⣾⣻⣦⢤⣀⠀⠀⢀⣞⢃⡀⢠⢀⣷⠀⡄
⠀⣥⠟⢈⡵⠦⣽⣿⣿⢷⠛⠗⠲⡘⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠀⠀⠀⠼⠿⣰⡆⢠⢶⣄⡏⢟⠹⡽⢆⠆⢿⣿⣿⠿⢁⣏⣻⡟⠚⣿⢰⣷
⠀⣴⢛⡆⠜⣄⡞⣙⣧⢴⡇⢀⣝⠃⠀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣆⠀⠀⠀⠀⠈⣍⣏⢱⡭⠐⡳⠈⠟⡦⢧⡘⣿⣏⢡⠄⠒⢄⣷⣋⢬⣏⠛⡇
⠀⢟⠌⢹⠷⡏⠼⠃⢸⣟⣿⣡⡜⠀⣼⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣛⣻⣿⣆⠀⠀⠀⠀⠱⣤⣆⡗⣤⠿⣌⢻⡛⢄⢛⠻⣿⠄⠋⢱⣀⢹⡅⣽⡙⣿⠁
⠠⠂⠠⡿⠶⠁⣹⠧⠟⠁⠈⢻⣀⡼⡟⠛⠿⢿⣄⠀⠀⠀⠀⠀⠀⣰⠧⠬⠯⠬⠬⠿⢦⣀⣀⣤⣤⣖⡿⢂⣽⡀⣷⣌⠳⣈⠛⢶⢷⡠⢹⠀⣩⠈⢶⠝⠢⢉⡃
⠀⠀⠀⣀⠃⠈⠓⢢⠃⠀⠠⢌⢿⡄⣀⣤⣬⡀⠝⣶⣶⣿⣶⣾⡿⠿⣶⣤⣤⣤⣤⣤⣤⣼⣿⣿⡿⣋⣍⠁⢈⠙⠇⢄⡉⠻⣤⣌⣸⣆⣤⡆⠜⠱⡦⢚⢀⠦⣁
⠀⠀⠰⠃⠀⠾⠴⠖⢲⡎⢱⠦⣘⢗⣻⣿⣿⠀⠀⣿⣭⣿⣿⡏⠄⠄⣿⣿⣿⠁⢸⡿⣿⣻⣿⣿⠟⣁⣸⣅⣸⣧⡀⡌⣏⡂⠨⠏⠁
⠀⠀⠀⠀⠀⠀⡘⠡⠊⡘⢃⠠⣈⠉⠛⠶⠾⠦⠉⠿⠾⠿⠿⠧⠠⠒⠛⠛⠿⠦⡼⣏⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠤⠴⠙⠥⠈⠷⢯⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈

⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠒⠒⠶⠦⣄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⣶⠞⠋⠉⠉⠛⠳⣤
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⠤⢤⣄
⡇⠀⠀⠀⠀⠀⢀⣤⠤⠤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⡇⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⡇⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟
⡇⠀⠀⣠⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣆
⡇⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄
⡇⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⡇⠀⠀⠻⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⠃
⡇⠀⠀⠀⠉⠉⠉⠉⠩⡍⠉⠉⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⡍⠉⠉⢩⡉⠉⠉⠉⠉⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠹⡄⠀⠰⡄⠀⠀⠀⢠⡀⠀⠀⠰⡄⠀⠀⢹⡀⠀⠀⢳⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⣀⠀⢱⡀⠀⢹⡀⠀⠀⠀⢳⠀⠀⠀⢹⡀⠀⠀⢳⡀⠀⠀⡥⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠜⠀⠀⢳⠀⠀⠳⠀⠀⠀⠈⢧⠀⠀⠀⠳⠀⠀⠀⢧⠀⠀⠣⠌
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢰⡉⡆⠀⠀⠈⣇⠀⠀⢠⠓⡄⠀⠈⢧
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠈⠀⠀⠀⠀⠘⣆⠀⠀⠙⠀⠀⠀⠘⡆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠢⡀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⡐⢢
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠀⠀⠀⠀⠀⠀⠀⡰⠢⡀⠀⠀⠀⠀⠈⠋
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚
⡇
⡇
⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀
⠠⠀⠀⠀⠘⠃⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠖⠀⠀⢀⣀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈
⠀⠀⠴⠆⠀⠀⢼⣇⠀⠐⠒⢄⡀⠀⠀⠀⠀⠶⠀⠀⠀⣀⠀⠀⠀⠀⠀⡐⡁⣒⠪⢂⠀⠊⠉⢂⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⢀⣌⠌⠡⣅⠈⠒⠠⠬⢁⡒⡄⠀⠀⠀⠀⡰⡿⠀⠀⠛⠀⠀⠇⡅⠛⢁⢀⠀⠑⠒⠠⡁⠢⠀⢰⢷⠀⠣⠉⢐⢄
⠀⠀⠀⠀⢸⠀⠘⠃⢸⠀⢀⣀⢀⣤⣁⣶⠀⠀⡤⠴⢸⠤⠷⢤⡀⠐⡍⠥⠃⠀⠘⢜⣈⠆⢈⠀⣲⡅⢠⠏⠈⠧⢀⠠⡠⣿
⠀⢠⡆⠀⠘⢘⡃⣘⢘⣴⡿⣿⣿⡿⠈⢿⣀⣀⡇⢠⣆⢀⣦⠀⣦⣠⡇⡼⣵⢠⢿⡆⢠⣊⠕⢉⠙⠗⣴⣶⢳⣶⡕⠈⢎⠪⡆⠀⢀
⢐⢕⣿⠄⠀⢠⡄⡤⠸⠁⡀⠀⡀⠀⢘⠀⠁⣈⡀⠀⠀⠀⠀⠀⣠⡀⡇⠉⢉⡤⡍⠁⠈⠀⡀⠻⠃⡀⠹⣈⣉⣸⠰⠄⠀⠤⢠⡐⢛⣳⡄
⠀⡺⣷⡁⢴⡠⠄⠷⠀⠀⠛⠐⠋⠀⣈⠀⡆⠛⠃⡔⠂⠃⠒⡄⠉⠁⡇⠀⢸⣁⡇⠀⡇⢸⣿⠀⢸⣿⢀⠿⠿⢿⠀⠠⣶⠀⣈⠀⣶⡄⡄
⠨⢚⠣⡂⢽⡇⣶⣺⠀⡆⠷⠰⠇⢸⣉⡇⠁⠀⢘⠠⠂⡅⠄⢠⠀⢰⡧⢀⣞⣒⣣⡀⡇⠼⠻⠆⠼⡻⠄⣿⣭⢿⠀⠀⠛⠀⣿⠀⡭⡄⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣷⣦⠀⣠⣴⣶⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣼⡿⢟⣛⣯⣭⣭⣽⣛⡱⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠟⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣠⣤⣤⣾⣿⣿⣿⣿⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣭⣭⣭⣝⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⢼⣿⣿⢟⣫⣽⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠻⠿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣮⡝⠛⠛⠛⠛⠛⠛⠛⠓
⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⠂⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⠂⠀⠀⠀⠀⢀⣶⣶⣶⣀⣀
⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⣿⣿⣿⣷⣶⡶⠀⠀⢀⣼⣿⣿⣿⣿⣇⣀⣀⡀⠀⠀⠚⠛⢻⣿⡿⠋⠀⠀⣠⣦
⠀⠀⠀⣰⣿⡿⠀⠀⠀⠈⠉⠉⣽⣿⠏⠀⠀⠀⠾⠿⠿⠿⢿⣿⣿⣿⠟⠁⠀⠀⠀⢀⣾⠟⠁⠀⠀⣼⣿⡟
⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⢀⡀⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⢀⣴⣿⡇⠀⠀⠀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⣼⠟⠁⠀⠀⣠⣾⡀⠀⠀⠀⠀⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣼⠋⠀⠀⠀⣼⣿⣿⠁⠀⠀⠀⠀⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠙⠿⠋




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣶⣦⣄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⠋⠉⠉⠉⠉⠉⠙⠻⢿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣼⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⣠⣾⣿⣿⠿⠿⠿⠿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠈⠻⣿⣷⡀
⠀⠀⢠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠹⣿⣷
⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆
⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿
⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⢀⣴⣿⡿⠁
⠀⠀⠀⠙⢿⣿⠆⠀⠀⠀⠀⠀⣠⣀⢸⣿⢀⣠⡀⠀⠀⠀⢰⣿⡧⠀⠀⠀⣼⣿⡏⠀⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠈⣛⣿⣿⣿⡋⠁⠀⠀⢀⣿⣿⠃⠀⠀⢰⣿⡿⠀⠀⠈⠉
⠀⠀⠀⠀⠻⢶⣾⣧⡶⠟⠀⠀⠺⠛⢹⣿⠙⠻⠇⠀⠀⢸⣿⠏⠀⠀⠀⠘⠛⠁
⠀⠀⠀⠀⣴⠾⢿⡟⢷⣦⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⢀⣾⣷⠀⠀⠀⣸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣤⣿⣤⣶⠆⠀⠀⠀⣼⣿⠇⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡿⣿⢿⣦⡄⠀⠀⢸⣿⡟⠀⠀⠀⠘⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣿⠀⠈⠁⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⣀⡀⢀⣀⡀⣀⣀⣠⠀⣀⣀⣤⣄⣀⣀⣀⣀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠪⠐⠁⠐⠫⠀⠀⢜⣻⠒⠋⡙⢣⣌⠻⡛⣿⣿⢦⡽⣿⣿⣿⣿⣿⣯⣿⢯⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢈⣤⡶⠒⡒⠲⡯⣌⣉⠘⣥⡘⢠⣝⣧⣹⣿⣼⣾⣇⣷⣼⣟⣿⣿⣿⣏⢠⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠤⢶⠟⠿⡛⠟⣀⣀⣬⣤⣶⣭⡈⣹⢷⡍⢈⠘⡿⣿⣧⣹⣿⣱⣿⣿⣿⡟⣷⡿⣷⣾⡏⡇
⠀⠀⠀⠀⠀⠀⣴⠿⠿⣾⡄⠀⢀⡴⠁⡞⠋⠁⠀⣫⡧⢄⣉⠻⢷⣤⢈⣳⡘⣿⣏⡜⢷⣾⣿⣯⣿⣷⣿⣿⣿⣿⣟⡇
⠀⠀⠀⢠⢈⣳⣾⢧⢛⡋⣁⠐⢛⡶⠚⠁⠀⠀⣰⣿⡷⢊⣭⠌⣁⡹⣧⣈⠙⠺⣯⡳⣾⣿⣯⣽⣻⣿⣿⣯⣳⣿⣿⡇
⠀⠀⠀⠀⠙⣿⠀⠀⠸⠁⠀⠀⣨⠀⣀⣠⡄⣉⡡⠶⢗⡾⠡⢤⠶⢷⢶⡽⣷⣧⣹⣇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣀⢵⠁⠀⢦⣤⠄⠚⠁⠖⠁⠀⢰⠋⠻⢓⠞⣷⠓⠢⣀⣭⣥⣌⡙⢿⣍⣿⡦⣿⣿⣿⣿⣿⣟⣿⡿⠿⠿⡇
⠀⠀⠀⠀⡉⢾⣖⠃⠐⠅⠀⠀⡀⠀⠀⠀⢿⡂⣤⡾⣏⣽⣄⠀⠀⠀⢥⣬⠟⡛⢿⡿⣧⣿⣿⣿⣿⣿⣿⣿⣽⢹⡿⠅
⠀⠀⠀⠀⡜⣽⣿⣰⣿⠂⡖⠄⠀⠀⠀⠰⣤⣿⠵⡴⠞⣐⣧⡤⣰⣯⡐⠯⢶⡌⢻⣿⣿⣿⣼⣿⣿⣿⣟⣿⣷⣟⢡⡖
⠀⠀⠀⠈⣡⠀⡧⢿⡿⡆⠀⠀⢄⠀⣄⠀⣨⡽⠿⢻⡟⡽⣿⠡⠑⠀⣹⡟⢦⣉⠛⢻⣿⣿⣿⣿⣿⣽⣿⣿⣿⡤⠟
⠀⠀⠀⠀⢸⡄⠁⣐⠲⠀⡀⠀⢀⣤⣭⣾⠍⣷⠶⠎⢑⢷⠻⣄⠀⠀⠉⠀⠀⠈⠳⣌⠻⣿⣼⣿⣿⣯⣾⣿⡟⠁
⠀⠀⢸⠀⣸⣧⠀⠩⠄⣰⡷⠰⡟⡏⢻⡿⣿⣧⠀⠀⠋⠈⠀⠛⠀⠀⠒⣀⣀⡀⡀⢻⣦⣽⣿⣿⣿⣯⣻⣿⠇
⠀⠀⠠⠀⣿⣿⡇⠀⠀⢘⢰⣼⣷⣄⠳⣦⡻⣥⣧⠀⠀⠀⠀⣦⣶⣪⣿⣿⣿⣿⣿⣆⡽⣿⣿⣿⣧⣿⣿⣿⠂
⠀⠀⢠⢸⣿⣿⣷⡂⡀⢘⣴⣟⣿⡾⡽⣸⣿⣧⡿⢈⡘⠀⣼⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡙⣿⣿⣿⣿⣿⣟
⠀⠀⠸⣼⣿⣿⣾⣷⣴⣝⣷⣾⣷⣿⣶⢙⠿⢿⣿⡏⢑⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣟⣿⣿⣿⡇
⠀⠀⢰⣿⣿⣿⣿⣿⡿⣿⡓⢸⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠛⢚⣿⣿⣿⣯⡁
⠀⠀⣸⣿⣿⣿⣾⣿⠹⣿⣿⣿⣿⣿⣿⣏⠻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣵⣿⣿⣿⣿⣅
⠀⠀⠘⢻⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣯⣿⡏⢻⣿⣿⠛⣉⠛⠛⢿⣿⣿⡷⢷⣿⢻⣟⡼⡷⣿⣿⣿⣿⣧⠐⠀⠀⢀
⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⠀⠈⠛⠛⠿⢿⣿⣿⠹⠋⠡⠞⠉⠑⠀⠀⢹⡏⠀⢹⣹⡊⣿⠇⠶⣿⣿⣿⣿⡿⠃⣀⣤⣿
⠀⠀⠀⠘⣿⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠤⡄⠀⠀⠚⣛⠋⢸⣇⠀⠀⠈⠉⠉⣳⣮⣹⣿⣿⣿⣿⡛⠇⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢔⣶⣾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠘⠂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠃⠀⠀⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣷⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣥⣼⡿⠟⢉⡰⢿⠻⠟⢆⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠊⠉⠀⠀⠀⠀⠀⠀⠈⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠠⠀⣄⣠⠄⠘⠀⠈⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⡀⠀⡀⠃⠀⠀⠀⠀⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣧⣠⣀⣤⣀⢀⣀⠀⠀⢀⣀⡀⢠⣀⣀⣀⡀
⠀⠀⠀⠀⢼⣿⠀⠀⠀⠀⠀⢸⣿⢯⣿⣿⣿⣿⣿⢿⣻⣷⣿⢟⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠉⠉⠉
⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⠸⠿⠾⠿⠿⠿⡟⢵⠿⠿⠿⢦⡿⠿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠷⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠊⢸⣷⣶⣦⣤⣤⣄⡶⣞⣷⠸⣷⣜⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡠⣀⠄⠀⠀⠀⢿⣿⡿⣿⢿⠁⡅⡿⢻⡆⢿⣯⢿⠿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⡅⡊⠊⠀⠀⠀⠀⠀⠛⠀⣡⣼⠀⠀⡆⣼⢣⡘⣿⡷⣀⢺⡏⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠂⣿⠁⠀⡄⣣⢇⣾⡧⢸⣿⠗⢸⡃⡄⠈⡛⠂⠀⡴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠈⠀⠁⠆⢋⠀⣿⡇⠘⡉⠒⠻⠿⢥⡆⠓⡤⠂⠐⢩⡷⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠂⠀⣼⣯⣇⢰⣿⣗⣱⣶⡆⢠⠎⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⢸⢠⡿⢻⡞⢟⡧⡝⠛⠄
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠐⠀⣿⣻⡇⡆⢘⠰⠛⠁⠿⠃⠀⠁⣼⠖
⠀⠀⠗⢆⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢀⣿⠾⠁⠀⠨⡊⠁⠊⠰⠀⠀⠀⠈
⠀⠀⠀⠏⠀⠀⠀⠉⣿⣷⣶⣶⣻⣵⣦⡤⢤⡤⠀⠀⠀⡂⢉⡴⠋⠘⠉⠀⠄⡀⠀⠀⢠⠀⠠⠀⠀⢀
⠀⠀⠀⠐⠀⠀⠀⠀⣿⣿⣿⠫⣾⣿⢃⠀⢈⡄⢀⡠⠎⡔⠈⠀⠀⠀⠄⠎⣠⣜⠳⣷⢸⣄⡄⠀⠀⠂
⠀⠀⠀⢸⠀⠀⠀⠀⠹⠺⢛⡄⢿⢿⡠⠜⠋⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⣿⣽⣷⣌⢻⣇⣵⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⣗⠋⠈⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠐⡫⠘⠁⢹⡄⢻⣿⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠅⠀⢠⠀⠀⠁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⢿⡀⢿⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⡁⠀⠁⢃⢘⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠈⠀⠀⣀⠔⠀⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⢀⠔⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘


⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠒⠀⠀⠀⠀⠀⡴⠃⠀⠀⡄⠀⠀⠀⢠⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠁
⠀⠀⠀⠀⡠⠀⠀⠀⠀⣠⣷⣤⠤⣤⣤⣶⣧⣰⣄⣀⡠⠔⠀⠀⠀⠀⠀⠀⠀⠒⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠔⡀
⠀⠀⢀⣾⡇⢠⠎⠀⠘⠛⠻⠁⠰⢿⣿⢿⣿⣯⠀⠀⠁⠠⠤⠀⣀⠀⠀⠀⠠⣤⡄⠀⠀⢀⠀⠀⠀⣀⠤⠂⠀⠀⠀⠁⠉⠛⡛⠉⠀⠀⠀⢀⠐⠄
⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠿⢟⣿⣶⣶⣶⡾⠋⠈⠉⠠⣄⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠀⠠⠀⠀⠀⠀⠰⡍⠓⠲⠶⠚⠁⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣵⡾⣿⣿⣿⣿⠿⣶⣤⣠⣠⠉⠙⠛⠁⠀⠀⡰⠀⢤⣤⡤⠤⠀⠳⣅⡀⠀⠀⢀⡈⠻⣶⣶⣾⡿⠃
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠈⠈⠁⠞⠔⠋⠁⠀⠑⢦⣌⣒⣭⣽⣇⠀⠀⢶⣄⣀⣀⣤⣮⣿⠛⣻⣟⣤⣿⣿⡿⠋⠀⣀⡄
⠀⠀⠀⠞⠀⢲⣄⣉⣂⠀⡀⠀⠈⠃⠄⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⣰⣶⢿⣿⠿⢛⣿⣿⣿⣷⡖⣹⣿⣟⡿⠋⠱⠁⠉⢀⣼⠟⢋⡀⠀⠀⠁
⠀⠀⠀⠀⠂⠁⣄⠀⠀⠀⠳⠆⠀⠐⠀⢠⡘⠉⠉⢉⠀⠀⡀⠀⠀⠈⢙⠁⠀⣴⡂⠊⢛⣿⡿⢋⣾⣯⣿⡟⠁⠀⠀⠀⠀⠈⢀⡔⠁⡰⠚⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢰⣆⠀⠰⣄⠀⠉⣓⡈⠁⢀⣌⢷⣤⢤⣶⡽⠂⡴⠛⡁⣰⣼⠟⣴⣿⡿⠟⠋⠀⠀⣴⡅⠀⠀⣰⣯⡀⠊⠀⠀⢀⠞⠁
⠀⠀⠘⣿⣷⣶⣆⣀⡴⠂⠀⠙⠛⠟⣹⣿⣿⣿⣿⣿⣿⣿⣷⣾⢫⡥⠀⠀⢀⢀⣰⣿⣧⡶⣠⢿⡃⠀⣠⣤⡾⢟⡖⠀⠀⢑⣏⠀⠀⠀⠀⠁⣠⠆
⠀⠀⠀⢋⡿⣯⠟⣵⠾⣠⡔⡡⢂⣼⣿⣿⠟⢻⣿⠿⣿⣿⣟⣽⣋⠠⢀⡴⢇⣭⣿⣿⢋⣴⡣⠈⣠⠊⠿⣩⣶⣿⡷⠀⢴⡿⠋⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠋⠀⢀⠞⢃⡿⠋⠀⢰⡾⣻⡿⠂⢠⡔⠂⠀⠀⠁⠭⠨⣻⡆⢈⣴⣿⣿⣿⣡⣿⣿⡿⡿⠛⠀⠘⠛⢻⠟⠂⠠⠍
⠀⠀⠀⠀⠀⣀⡰⠋⠐⠀⠀⠊⠀⠉⠀⠀⠀⢀⣊⠐⢛⣄⣤⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⣚⢞⣁⡀⠀⡐⠀⢠⡜⡁⠈⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠛⡀⠀⢠⡄⠀⠀⠀⠀⠀⣀⣾⣿⣷⣟⣴⣿⣿⣿⣯⣭⣿⣿⠟⣿⣿⣷⣖⣠⣥⣹⠞⡀⠈⠀⠀⠾⠻⠃⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⢀⠚⠿⠿⠁⠀⠀⠀⡠⠊⠁⠁⣰⣿⣿⣿⣿⣷⣽⣯⣼⣿⡿⠃⠾⢿⣿⢯⠿⢿⡿⣿⣿⣅⢠⠄⠀⠈⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠟⢻⣿⣷⣿⡿⣛⢿⣿⣿⣿⡟⣡⡞⣡⡯⠀⠈⠈⠉⠉⢱⣶⣴⣦⣿⣿⣿⣿⣷⣶⣶⣖⠃
⠀⠀⠀⢀⠂⠀⠀⢰⡇⠀⠀⠠⠀⠀⠀⠀⠠⡾⠿⢋⠜⠙⠁⣼⣿⣿⣏⣸⣿⡿⢈⣦⣾⣥⣤⣤⣴⡿⠟⣋⣩⣿⣿⣿⣿⣿⣿⣿⣯⣷⠀⠁
⠀⠀⠀⡤⠊⠀⠀⢼⣇⠀⠈⣆⢠⠀⠀⠀⠀⠀⠜⠃⠀⢀⣾⣾⣿⣿⣿⣿⣿⣧⣿⠛⡁⠾⢿⣿⣫⣵⣾⣿⣿⢟⣿⡛⣩⣷⣧⣍⣙⣷⣶⡄
⠀⠀⠀⠟⠀⠀⠀⣿⣟⠂⢼⡿⣿⡂⠀⠀⢀⡀⠀⠀⠀⢺⣿⣿⣭⣭⣽⣿⣿⡿⣡⠌⠑⠠⠘⠿⢻⣿⣿⣿⣁⣙⣻⣿⣿⣿⡏⠻⣿⣿⣟⣦
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣦⣸⣿⣿⡇⢰⡄⣾⡆⠀⠀⠰⠃⢾⣿⣿⣿⣿⣟⡿⠈⠁⣀⠄⠀⠀⠀⠀⠀⠸⢿⠿⣿⣿⣿⣦⣼⡰⣿⣿⣷⣿⠁
⠀⠀⠀⡀⠀⠠⢾⣿⣿⢿⣿⢫⣿⣇⣸⣟⣿⣟⠀⠀⣀⢀⣐⣫⣽⣭⣩⣭⣤⣉⠛⢁⣀⣀⡀⠀⠀⠀⢀⡘⡀⡟⠃⠉⠿⢁⠔⠙⠛⠋⣁⣀⣀
⠀⠀⠀⣿⣾⣿⣿⣿⣿⣾⣿⢟⣿⣻⡧⣿⣿⢾⣾⣿⣿⣿⠿⡟⣿⣿⠟⢻⠻⣻⣶⢃⣿⣧⠻⢶⣿⣧⣿⣿⣿⣿⣿⣧⣥⣧⣶⡷⠘⢿⣿⣿⣿⡆
⠀⠀⠀⣉⣍⣵⣾⡿⣧⣌⣵⢿⣿⣟⣡⣿⣿⣷⣙⣉⠁⣤⡤⠄⡀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠉⠉⠉⠉⠙⡇⠁⢹⡇⠉⠉⠀⠀⠈⠛⠛⠛⠁
⠀⠀⠀⡽⠿⠟⠿⡛⠒⠙⠛⠻⠉⠬⠽⠷⠼⠿⣦⣬⣅⡀⠀⠀⠐⠛⠛⠛⠛⠻⠿⠛⠓⠈⠀⠀⠒⠂⠀⠈⠀⣿⡀⢸⡇⠠⠀⢴⣤⡤⠤⢤⡤
⠀⠀⠀⣷⣴⣶⣶⣶⡶⣶⣦⣤⣴⣦⣤⢀⣀⠀⠀⠉⠉⠉⠋⠉⠒⠐⠒⢴⣤⣤⣤⣄⠀⠀⠀⠀⠀⠤⠤⠶⠖⠚⠷⠚⠻⢿⣿⣿⣿⡿⣿⣿⣷
⠀⠀⠀⡻⠓⠚⠉⠋⠀⠀⠈⠁⠐⠒⠛⠛⠛⠛⠻⠿⣶⣶⣶⣤⣶⣶⣾⣿⣿⣿⣿⣿⣷⣽⣿⣾⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠴⠿⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⢸⣿⣿⣹⣿⣿⣛⣿⣍⠉⣿⡏⣹⣿⣿⣿⣟⠉⢉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡉⠉⠙⣿⣿⣿⣍⠉⢛⡛⠛⠉⠉⠉⣛⣿⣹⣿⡇
⢸⣿⣿⣿⣿⡟⢸⡇⢸⡀⣿⣗⠸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣿⣿⣿⣿⢰⡿⡇⢀⠀⢿⣀⣿⣿⢿⣿⡇
⢸⣿⣿⣿⣿⣷⣿⣧⣾⣷⣾⣿⠀⢹⡟⠉⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠈⣿⠁⢸⠀⡇⢾⣤⢸⣿⣿⣿⢸⣿⡇
⢸⣿⣿⢿⣿⣿⣿⣿⡿⠻⡟⠉⠀⠈⠁⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠐⣷⠇⢿⣿⣿⣿⣿⢸⣿⡇
⢸⣿⣿⠸⢿⣿⣿⣿⡇⠀⠇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⢻⢸⣿⡇
⢸⣿⣿⢸⣿⣏⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠐⠏⢸⣿⡇
⢸⣿⣿⢸⠛⣿⡏⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠈⣿⣿⠈⠐⠟⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⣿⣿⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢸⣿⡇
⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⢸⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⢸⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⣿⣿⠀⠀⠂⠀⠀⣤⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣴⢇⠀⡄⠀⠀⠀⢀⡀⠀⠀⠀⢷⠄⠰⠀⠀⠀⢸⣿⡇
⠀⣿⣿⠀⠃⠀⠀⠀⣿⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣸⠀⠃⠀⠀⠀⠀⡏⠀⠀⣸⣟⡆⠁⠀⠀⠴⠈⣿⡇
⢠⣿⣿⠀⠀⠀⠀⠀⣸⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⠀⡶⠀⠀⠀⠀⡇⠀⠀⢸⡿⠀⠀⠠⠈⠀⢠⣿⡇
⢸⣿⣿⠀⠀⠀⠀⠀⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣾⣿⣰⡁⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⡇
⠸⣿⡿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡇⠀⠀⠀⠀⡇⠀⠀⣿⠇⠀⠀⠀⠀⠀⢸⣿⡇
⢰⣿⡇⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠇⠀⠀⠀⢀⡇⠀⣀⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠈⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢻⠀⠀⠀⢀⠈⡇⠀⣾⠋⠀⠀⠀⠀⠀⠀⠸⣿⡇
⢰⣿⡇⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⢀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠘⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣿⣿⡄⠀⢀⢠⣿⣾⣿⣠⠀⡄⠀⣤⠀⠀⢀⣿⡇
⠀⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠏⠿⠟⠛⠚⠛⠛⠛⠛⠛⠛⠒⠛⠛⠛⠓⠚⠸⣿⡇
⢸⣿⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⢀⣠⡶⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡂⠀⣯⡰⢀⣠⣶⡿⠋⠁⠀⠀⠀⠀⢀⡤⠀⠀⠀⢬⢯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀
⠀⠀⢀⠀⠀⠠⣅⢀⠀⠼⠻⠣⠞⡿⢞⣏⠘⢋⠀⠀⠀⢀⡤⠐⠉⠊⠀⢶⠄⠀⣶⢻⣤⠀⠀⠠⡷⠀⠀⠀⣭⡠⢶⡅⣬⣧⢸
⢰⣦⠿⡆⣶⢬⡩⣼⣷⢾⠾⡖⠾⣇⠈⠙⠀⠁⠀⠒⠘⠿⠀⠀⠀⠀⣘⣿⢃⠐⠻⡾⢆⡀⠀⠒⣷⠗⡄⢸⣏⡷⢆⠘⡿⣼⣼
⢸⣿⡟⢿⡷⠚⠃⠞⢧⡏⣰⣟⡠⢻⣴⠻⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⣼⠘⡓⣺⡿⣬⠁⠘⢛⣿⢬⠑⢈⣿⡶⢛⠚⢷⣧⣰
⣸⣯⣷⡟⠖⠊⢱⡓⠻⣿⣿⣿⣥⣾⣿⣄⣷⣧⣿⣤⣦⣦⣄⣀⣄⡤⢟⣸⣝⣓⡀⡀⠀⢀⣌⠉⣍⣠⠺⡠⣭⣷⣿⣷⣼⣞⢸
⢸⣿⣿⡗⠞⣠⡞⠳⡶⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣳⣾⣿⣊⢽⠉⣯⡙⣝⣿⣟⠑⠫⣿⠒⢣⠒⡖⠸⣿⣿⣿⣿⣿⣿
⢸⣿⣿⠆⢴⠀⢰⣄⣻⡬⠇⠙⠙⣿⠈⠙⠛⠛⠁⠉⠈⠛⠛⠿⡏⠅⠺⠃⠠⠿⠉⣟⠹⡊⡁⠘⢵⠊⣰⠙⣬⡟⣿⠟⠉⠉⠻
⠀⢀⣙⡒⢉⡉⢠⠄⠀⠛⠒⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠘⠂⠉⠀⠀⠀⠀⠀⠙⠉⠀⠀⠂⠐⠲⠂

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣸⢿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢰⡀⣶⡿⠴⣀⣦⣀⡰⣂⣀⣾⠀⠀⠀⢤⣀⠀⠀⢠⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢨⣧⡽⣿⣄⣀⢀⠀⠀⠀⣘⠀⠀⢠⢐⣷⠀⡀
⠀⣫⡿⠐⡷⢄⣹⣿⣿⣷⠛⠟⢴⠸⣿⣻⡭⡾⣶⣖⣸⣩⠡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢀⢷⡀⡞⢿⠻⣽⣌⠤⣿⣤⣶⢿⢈⡗⢻⡞⠾⣿⠠⣷
⠀⣭⢗⡎⠰⣀⡝⡻⣏⠬⡇⢀⣲⢃⣿⠁⣷⡁⡿⠁⠢⠼⠲⡃⢤⣄⣤⣀⣰⣧⡀⣀⣤⣴⣤⢛⣑⡖⣋⣍⠐⠯⠑⠿⡬⣖⠘⣿⣏⢃⡌⠣⣍⣷⠲⢹⡟⠻⡆
⠀⡟⡈⢹⡦⡟⢱⠇⢹⣴⢿⣋⣽⢠⣵⢇⣸⡹⠖⡙⣖⠉⣿⣍⠘⣿⠏⢿⣃⠋⢿⣿⣷⢿⡟⣸⣯⣁⡌⣗⣠⣷⡔⢻⠷⢌⢛⠻⣿⡅⠊⢲⠈⢹⡉⣸⠺⡿⠃
⠠⠊⢀⣾⡤⠁⣻⠦⡞⠟⣢⠂⣵⡬⢂⠚⣻⡗⣋⠎⢁⢿⠀⣆⠙⢫⣧⠊⠡⠲⠉⢿⢵⡽⢧⡠⢒⠈⢿⢅⣷⠀⣯⡘⢧⠈⠷⣴⣧⣀⢽⠀⢋⠘⣤⡯⠰⣙⡇
⠀⠀⠀⢈⠃⠒⠷⢄⠙⣀⠀⠀⠈⠐⠋⠙⠁⣤⣌⣻⡇⠀⢳⣸⡟⠲⠈⠒⠒⠒⠀⠈⠀⠀⠀⠁⠈⠐⣋⠋⢈⠱⠗⣈⡑⢯⣀⣌⠸⠓⠴⠀⠸⠢⣮⠔⠀⣌⠁
⠀⠀⠠⠯⠐⠚⠠⠈⠑⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢹⡀⢹⣆⡀⡘⡟⠢⢩⡍⠉⠀⠀⠀⠀⠀⠀⠈⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠁⠈⠁

⣽⣷⣶⡇⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣉⣿⣶⣿⣿⠿⠛⠃⠉⠙⠐⠉⠀⠀⠈⢻⣿⡷⠀⢠⠀⠀⠀⢻⣿⣿⣿⣷⣿⣿⣿⡿⢾⣏⣹⣿⣿⣿⣯⣨⣿⣤
⣿⢿⣿⣆⣸⣶⡆⢹⣧⣿⣿⡟⢹⡟⢤⡿⣽⣿⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⡗⣄⢷⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠹⣿⠟⢻⣿
⣿⣶⣶⣿⡿⠻⣿⣿⣿⣿⣿⣿⣶⠀⢺⣅⢠⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣼⡀⢁⠀⠀⠈⢿⣿⣟⠁⠘⠿⢛⢃⣀⣀⠀⠀⠀⠈⣳⣿⢻
⣽⣟⠉⠛⠛⠀⠉⠁⠀⠈⠉⠀⢤⣷⣾⣇⢸⣿⠃⠀⠀⠁⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠈⠇⠘⡦⠀⠀⠸⣿⣾⣄⠀⢀⣤⣛⠉⢻⣿⣷⣶⣺⣿⣿⣿
⣿⡿⠷⠀⠀⠁⠁⠀⠀⠀⠀⠀⡾⢿⡏⣸⣿⣿⢠⡤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠤⢤⣇⣰⡀⣿⠀⠀⠈⠛⡝⢻⢿⣷⣤⣿⠳⠾⠷⠾⣿⣿⣿⣧⣾
⠿⣧⣴⣶⣦⣤⣤⣤⣀⠀⠀⣘⣧⣬⣿⣿⣿⡷⠀⠀⠉⠉⠐⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣙⣿⣟⣹⣿⡄⠀⠀⢹⣿⣿⣿⣿⠋⠀⠀⠀⠀⣾⣟⣿⣿⣿
⣿⣟⣿⣿⣿⣿⠉⣿⣿⣿⠠⣗⡟⢿⣤⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠿⠿⣷⣿⠀⢻⣻⡟⠃⠀⢰⣏⠻⠟⣹⠟⢣⣤⣤⡀⠀⠻⣿⣿⣿⠿
⣿⣿⡉⠟⠛⠿⣿⣿⣿⣿⣤⡿⣄⣼⣿⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠈⣻⣧⣀⢸⡟⡿⡀⠀⣴⣾⣻⣿⣿⡇⠀⠀⠙⢿⣧⣀
⠿⣿⡃⠀⠀⠀⣯⣬⣿⢟⡿⠻⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣧⡄⢿⣿⣿⠸⣷⣿⡷⢀⣿⣿⣿⣿⠿⢇⠀⠀⢴⣿⣿⡏
⣀⣼⣧⣀⠀⠀⠐⠂⡸⣹⣿⣿⣿⣿⡿⢳⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢤⡇⢸⣿⡿⠀⣿⢿⠅⠙⣹⣿⣅⣽⠀⠀⠀⠠⣾⣿⣿⣿
⣟⣻⣧⣜⣷⣶⣿⡟⢣⣼⡇⠸⣿⣿⣦⣿⣼⠀⠀⠀⠒⠒⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣠⣿⣿⢸⡇⠸⠇⣿⡆⢸⣇⠀⢄⣹⣟⠿⠿⠀⠀⢀⣤⣿⣿⣿⣿
⡟⠉⠻⣿⣿⣷⣛⣿⣏⡿⣷⠰⣿⣏⠒⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠃⡝⠛⢿⠃⡆⠀⣴⣿⣾⢿⡀⣿⣟⣿⣦⣤⣦⣴⣾⣿⣹⣿⣿⣏
⠀⠀⠀⠀⠀⠉⠉⢘⣿⠓⣿⠀⢋⣁⠠⣟⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣶⠆⠀⡇⡀⣿⣿⠙⣸⣿⣿⣤⣿⣿⣿⣽⠿⣿⣿⣉⣿⣿⣿
⠀⠀⠀⠀⠀⢲⠂⢸⡇⢸⡇⢈⣬⡏⣼⣿⣿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠀⢸⣿⣿⠀⢸⡏⣇⢹⡟⠀⠙⣿⣿⠿⣿⣿⠿⠿⠷⢿⢿⣅⣿⡟⠙
⣶⣤⣴⢶⣴⣯⣤⣼⠀⣸⠁⢿⣿⣿⣿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⢸⣿⡟⠀⣼⠁⢻⣿⡇⠀⠦⣼⣿⣾⣿⣿⣿⠀⠀⠀⠀⠟⢹⣷⣾
⣿⣿⠿⣿⣿⣽⣿⣻⡆⢿⣄⣈⡾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⠔⢺⣯⡿⠀⠀⠘⠻⠁⠐⠛⢠⣸⣿⠠⠀⠨⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⢀⠻⣿⣿
⣿⣿⣦⣾⣿⣷⣿⣿⣄⡀⢹⣿⣿⣿⣿⣿⡏⠸⠂⠀⠀⠀⠀⠀⠀⠀⢀⣿⡛⠀⢀⡀⠆⡀⠀⢿⠀⣾⠘⣇⣠⣦⢠⣿⠻⣿⣋⣿⡿⣿⠧⣠⣴⣿⣿⣿⣻
⡞⠁⢹⢻⡟⠛⠉⠘⠘⣇⠙⠍⡉⣸⢿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣤⣦⡜⠡⠀⠀⠀⡀⢒⣶⣷⡎⣸⣿⡷⠈⠉⠙⠿⣿⣿⣿⣏⣿⣿⣿⣷⣿⣿⣿⣽⣿⡿
⣿⣶⣾⠈⠀⠀⠀⠀⠀⠸⣿⣰⣷⣿⣾⠛⡇⠀⡀⠀⠀⠀⠐⢯⣹⣿⣦⠠⠀⠠⠌⣠⣾⣿⣏⣹⣿⢿⡇⠀⠀⠀⠀⠈⠛⠉⣿⣿⣿⣿⣿⣯⣯⣿⣿⣿⣿
⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠉⣿⡄⠀⠀⡇⠀⠀⠀⠀⠀⢻⡿⠋⢀⠀⠀⣴⣤⡿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣽⣿
⠷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠔⠛⠁⠀⠀⠁⠀⠀⠀⣶⣶⠞⠁⡀⠁⠀⣼⣍⠟⠀⠘⢽⣿⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⣿⣿⣉⣿⡟

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⣿⣧⣸⣀⣤⣘⣿⣸⣁⣹⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠶⠶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⡾⠋⠁⠀⠀⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⡶⠾⠿⠶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⣾⠋⠁⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠟⢻⡇⠀⠀⣴⣄⣿⣧⣴⡆⠀⠀⢀⣴⠟⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢸⡇⠀⠀⣤⣿⣿⣿⣧⡄⠀⠀⣿⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠟⠁⠀⠀⠉⠀⠿⠇⠈⠁⠀⠀⠙⠷⠶⠟⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⡄⡄⠀⠀⠄⣤⢠⠀⡄⢠⠀⠀⢄⠠⠀⡄⠀⠀⣀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈
⣿⣿⠿⠿⡿⢻⠿⡿⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢡⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠤⢀⠔⠉⠐⠄⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⡠⠁⠈⠔⡠⢂⠂⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠨⠂⠄⠀⡠⠠⠂⠀⠀⠠⠊⠀⠀⠀⢀⠔⡡⡀⠁⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⣀⠀⠀⠀⠀⢀⢀⠁⠈⠈⠈⠉⡠⠁
⠀⠀⠀⠀⠀⠀⠃⢠⠀⡠⠀⠴⠀⠀⠖⠀⠰⠂⢀⠄⠀⠀⡐⠁⢀⠟⠉⠐⠁⠀⠤⠂⠀⠀⠀⡄⣠
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⠠⠂⠠⠀⠰⠀⠀⠃⡔⢀⠊⠀⠀⠠⠮⠄⠀⢲⣂⠀⡰⠂⠀⢈⡀⠀⠚
⠀⠀⠀⠀⠀⠘⠀⠀⠀⡔⠀⢀⠀⢠⠀⠀⡰⠂⠀⠰⠇⠒⠒⠒⠒⠀⠀⠀⠄⠀⠊⠠⠆⠀⠈⡠⠀⠐
⠀⠀⠀⠀⠀⠀⡌⠀⠀⡄⠀⠉⠀⠃⡤⠀⢀⠀⠀⠀⠰⠂⠠⠊⠀⠀⢀⠔⠁⠀⠀⢀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠐⢀⠀⠰⠁⡄⠀⠀⠊⠀⠸⠁⢀⠔⠁⠀⢀⠔⠁⡰⠀⡀⠀⠊⠀⠀⠈⠀⠊
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⠘⠀⠈⠀⠠⠂⠀⠔⠁⠀⠀⠀⠀⢀⠀⠀⠈⠀⣀⠀⠋⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⢠⠇⠀⠀⠄⡠⠂⠀⡀⠈⠀⠀⠀⠋⢀⠀⠀⠈⠁⠀⠜
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⢠⣊⣀⡀⠀⠀⠀⠀⠊⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⡨⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠊⠁⠀⡔⠀⠀⠀⠀⡠⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠉⠛⢽⡦⢤
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⢺⡗⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⡀⠀⠙⠛⠛⠛⠀⠀⠀⠀⠀⢾⡛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣦⣄⣤⠤⡄⠀⠀⠀⠀⠤⠟⣺⣠⠙⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⢾⠀⣳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⣼⠗⠀⢠⡶⣻⣿⢹⣮⣿⣦⣀
⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡻⢾⣹⣇⣀⢡⣛⣬⢙⣛⣿⣷⣏⣑⣄
⠀⠀⠀⠠⣀⡀⠑⣺⡃⠄⠐⠠⠄⠀⢀⣄⣤⢟⠟⢫⣿⣿⣿⣻⡿⣿⣿⣿⣿⣿⣿⡿⢿⢀
⠀⠀⠀⠘⠟⠲⠒⠛⣷⡔⢲⡀⠀⠈⠁⣨⣿⣣⠖⣈⣿⣟⣙⣫⢿⣩⢿⣿⣿⣿⣧⣶⣿⣼⣧
⠀⠀⠀⠀⠈⣵⠛⠋⠽⢿⡁⠉⡛⠿⢃⣿⡿⣋⠀⢀⣼⠿⣿⣷⣾⣏⣿⣳⣿⣿⣿⣴⣿⢩⣵⣧
⠀⠀⠀⠀⠀⠘⣷⢤⣠⠜⣿⣿⣫⣴⣏⣿⢯⣟⣰⢿⣿⡶⠛⣻⡿⣿⣿⣿⣿⡟⣿⣏⣿⣾⣯⡟⡄
⠀⠀⠀⠀⠀⠀⠘⣷⣿⣾⡽⣟⣿⣿⣿⣯⡿⣾⡤⣼⣍⣷⣌⣧⣶⣴⣯⣾⣽⣛⣿⣍⣛⣤⣿⣟⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠸⢾⣟⣴⣿⢿⠿⣿⣿⣿⣿⣿⣽⡟⣻⢿⡷⢋⢛⣣⣾⣻⠟⣛⣟⣻⣿⣻⣩⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣯⣿⣿⣳⢬⡟⢷⣾⣛⣿⣿⣿⣿⣯⣼⡿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣭⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠿⣿⢿⣵⣿⣿⣿⣿⣏⣽⣿⣿⣿⣧⣤⣧⣄⣿⣇⠈⣼⠿⣿⠿⣛⣫⢿⣿⣿⢿⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣹⣷⣻⣍⣿⡾⣿⣿⣿⣿⣿⣯⣛⣿⣻⣿⣿⣿⣿⣿⣷⣿⣶⣿⣿⣼⣿⣿⣯⡄⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡿⣿⣿⢟⣿⣏⣽⢿⣻⣿⣿⣿⣿⣿⣿⣿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣻⣟⣩⣟⣛⣿⣟⣧⡾⣿⡿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣭⣿⣿⣿⣿⡤⠒⣛⣷⣫⣞⣿⣿⣯⠈⠛⠿⠟⠿⣿⣿⢿⢿⡙⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⠛⠁⠉⠿⣿⣿⣽⣧⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠉⠻⣯⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣴⣶⠉⠈⠀⠀⠀⠀⠀⠈⠻⢿⠟⠙⠻⠻⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠉⠾⠛⠃⠀⠀⢠⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠆

⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢐⢀⠄⠀⠀⠀⠀⠀⠀⡀⠢⠠⠀⠄
⠀⠠⠀⢀⠚⠀⠀⠐⠀⠀⠀⠀⠌⠢⠐⠁⠖⠀⠀⠀⠀⠀⠀⠄⠈⠋⠵⠀⡀⠀⠀⠀⢀⠀⠂⠑⠅⢀⡜⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠈⠀⠀⠀⠂⠀⠀⠀⢠⠂⠠⠀⡀⠀⠁⠀⠀⠀⠀⠄⠀⠈⠀⠂
⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠊⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠤⢀⠄⠀⠀⠀⠀⠀⠀⣠⡄⠨⠜⠀⠀⠀⠀⠠⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⠀⠀⡀
⠀⠰⢊⠀⡀⣈⠆⠀⠀⠀⠈⠀⠀⡄⠀⠠⠀⠀⠈⠀⠄⠄⠀⠀⠀⠀⠀⢀⠀⢀⠀⡀⠀⠀⠀⠠⠀⠀⠁⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠐



⠀⠀⠀⠁⠰⠀⠂⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠐⠀⠀⠀⠤⠐⠀⠀⠀⠠⠀⠂⠠⠄
⢀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⣀⠂⠀⠀⠐⠀⡐⠀⠀⡀⠂⠄⢂
⠈⠁⠉⠀⠀⠀⠀⠀⢀⠈⢁⠘⢀⠃⢈⠀⠀⠀⠉⠀⠖⠀⠘⠀⠀⠠⠄⠐⠀⡉⠀⠆⠁⠀⠐⠠⢄⠐⠈⠃⠠


⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣠⡬⠚⠀⢐⠀⠀⠀⠀⠀⠀⢠⣆⠥⠁⡀⠀⠀⠀⠀⠀⠂⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠐⠉⠈⠭⢍⡀⠀⠀⠀⠀⠀⠀⢠⠀⣄⠐⡲⠀⠀⠀⠀⠀⠂⠐⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁

⠀⠀⠀⠘⠿⢶⣶⣦⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠰⡶⠟⠛
⠀⠀⡤⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⡦⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠈⢒⣎⡳⡶⠆⠀⠀⠀⠀⢀⣀
⣿⠂⣄⠀⠈⣿⣿⣿⠀⠀⠀⡀⠀⢀⣠⣀⠀⠀⠀⢀⣤⠀⣥⣤⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉
⣿⠞⢿⣷⣿⣇⠀⠀⠀⠀⣼⣧⡼⠾⠟⠋⠐⠀⠀⣈⠉⡀⠘⢿⣿⣿⡦⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡄⠀⠀⠀⡀
⣿⣧⣼⣿⢿⡟⠀⠁⠒⠊⡙⢉⡀⠀⠀⠀⢄⡀⠀⠀⠈⠃⠀⠞⠉⠛⠿⣶⣤⠈⠁⠀⠀⠳⠆⠿⢟⡃⣀⠀⠻⢶⣤⣤⣈⣁⠀⠐⡇
⣿⣿⢯⡁⢈⣁⠲⡧⠚⢂⠁⠈⣩⠉⠁⠀⠠⢯⡁⠰⢦⣄⣀⠀⠀⠀⠀⠐⠐⠦⠤⠀⠀⠀⠀⠀⠀⠍⢿⣿⣷⣤⡙⡛⢿⣯⣤⠈⠁⠀⠁
⠉⠉⠙⣶⣟⣹⠋⢉⠃⢘⡀⠋⠁⣍⣀⡀⠑⠛⠃⠀⠙⠻⠿⣴⣖⡲⣦⣄⠀⠀⠀⣀⠀⢐⢶⣀⡀⠀⠀⠉⣏⠙⠛⠋⢻⣾⣷⡀⠀⠀⢴
⠀⠀⠀⣿⣽⣧⣴⡯⣼⣿⣿⣿⠻⡙⠟⡉⠀⠀⡄⠀⠀⠀⠀⠀⠈⠉⠙⢿⢤⣤⡄⠉⠐⠾⡷⠇⠀⠀⠀⠀⠻⠊⠴⠀⠿⣿⣿⣿⣿⣶⣾
⠀⣠⣸⣛⣈⡩⠁⠂⢽⡟⣿⢹⡿⠃⠀⠀⠀⣰⠁⠰⡄⠀⠈⠀⠈⠀⠀⠛⠈⡉⠲⢴⣦⠌⡘⠻⢿⣷⠀⢰⡀⠑⣤⠀⢤⣿⣿⣿⣿⣿⣿
⣷⣿⣿⣽⣿⣶⣾⣷⣾⠇⡃⠸⠀⠀⠀⠀⠠⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡿⠿⠦⣝⡳⣮⣄⠀⠀⢀⢸⣧⠀⠈⢳⡇⢹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢿⣇⣿⡏⠟⢸⠁⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠓⠀⡷⠸⠈⠁⠀⠘⡆⣿⣿⣿⠙⠻⡯⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡄⠀⠐⠀⠀⠈⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠈⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠀⠄⠀⠀⠀⠀⠚⠀⠀⠀⠃⠈⠀⠀⢒⡔⠫⢣⠀⠀⠀⠈⣡⠎⢱⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠥⢌⣧⠀⠐⠀⠀⠀⠀⣠⠞⢳⠀⠐⠂⣠⣞⠉⠙⢺⡁⠀⠀⣰⠏⠉⠑⢿
⠀⠀⠀⠀⠀⠀⡀⠁⢾⡥⢄⣀⣹⡄⢀⠀⢀⠁⢠⣎⣉⡙⣇⠈⣠⣔⠉⠙⡓⢿⠃⠀⠀⡽⢋⠙⡒⢞⠂⠀⠄
⠀⠀⠀⠀⠀⣀⠀⠠⣎⣄⣀⣀⢱⡀⠀⠄⠀⠀⣼⣁⣤⣘⣏⢀⣔⠉⠙⢓⠲⡼⠆⠀⢈⠗⠒⡒⠓⣼⠆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣔⣁⡂⠀⠈⠹⡁⠀⠄⡀⠰⠯⣤⣆⣈⣫⠁⠉⢹⠒⡶⠤⠵⠐⠀⠓⠒⡶⢤⠤⠬⠆⠰
⠀⠀⠀⠀⣀⣀⣈⣀⣀⣏⣹⣉⣉⣁⣀⣀⣁⣀⣀⣸⣼⣤⡤⠤⠤⠾⠴⠦⠤⢤⣤⣀⣀⣀⣇⣼⡤⠶⠤⣄⡀
⠀⠀⠀⠀⣿⠉⢉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⡠⠤⠄⠠⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣀⠉⣷
⠀⠀⠀⠀⣿⠀⠀⠉⠑⠒⠒⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠒⠤⣀⣀⠤⠤⠤⠒⠂⠀⠀⠀⠉⠉⠙⠒⠒⠒⠋⠀⠀⠀⠀⠀⠈⠑⠒⠒⠉⠉⠉⠁⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠤⠤⠤⠤⠒⠢⠄⣀⠀⠀⠀⠀⠐⠉⠉⠑⠢⢄⣀⣀⠤⠤⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⢹⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢋⠆⡀⠀⠆⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢻⡆⠀⣴⢟⣿⣴⣆⣄⢰⣦⣠⣙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠄⠁⠚⢿⣾⠃⠾⠋⢀⡅⠹⠟⡌⠋⠙⠻⢿⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠶⣮⣠⣴⡿⠁⠐⢠⡄⠋⠀⠀⠀⠱⠀⢐⠄⣰⠃⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡻⡀⠀⢿⣿⠟⠀⢛⠖⡞⠃⠀⠀⣠⠒⠴⣰⢯⣴⡧⠀⠀⣷⣀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⣠⡄⣼⡟⠉⣧⠰⠃⢂⢠⡀⢰⡀⣤⡿⣾⡇⠀⣿⠆⠀⠀⠸⣿⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⣠⣶⠋⠹⣿⠄⠀⢹⣥⢿⣥⡈⣕⠸⣽⠛⣇⣿⡇⠚⢻⡶⣶⣶⣾⡟⢛⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡟⡴⢾⡏⢸⡇⢸⣿⣀⣀⣘⣏⠘⡏⣏⢃⣼⡃⢰⣾⣿⣷⡶⠟⠛⠻⠉⠙⠻⣿⡃⣷⢀⣾
⠀⠀⠀⠀⠀⠀⢀⣴⡏⢹⡟⣁⣬⣿⡿⠿⢿⣥⣿⣯⣟⣷⣴⡿⠻⣌⣿⣧⣴⡿⠋⢉⠁⠀⣠⠴⠒⠀⠀⡈⢻⣌⢻⠹⣦⡀
⠀⠀⠀⠀⠀⢰⡏⠀⢀⣾⡾⢋⣥⠆⠀⠀⠀⠀⠤⠬⡉⣙⠻⢶⣤⣿⠾⠛⠋⠠⠒⠠⠆⠀⠀⣀⡀⠀⠀⠉⠂⡙⢿⣆⡉⡇
⠀⠀⠀⠰⠟⠿⣷⡶⠟⠉⣀⡈⠠⠄⠀⠈⠃⢀⠀⢀⠀⠉⠂⠀⢈⢛⠛⢷⣶⠶⠀⠠⢄⠄⠀⠉⠓⠢⠤⠀⠀⠉⠁⠉⠻⠟⠻⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠉⠉⠉⠙⠶⠖⠋⠉⠉⠙⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠛⠲⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣀⡀⣀⣀⡀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣐⡢⠀⠀⠀⠀⠀⠈⠏⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡖⠁⠀⠀⠀⠀⠀⠀⠀⠚⠓⠒⠭⠶⠖⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡯⠤⢀⣀⠀⢀⣀⣀⣠⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣔⣰⡠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠒⠒⠋⠉⠀⠀⠉⠳⣞⣡⣖⣠⠖⠳⢴⣠⢖⣰⣦⠾⠛⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣰⠃⠈⠁⠀⢀⡤⠚⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢰⠃⠀⠀⢀⡴⢋⠗⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠰⠿⠶⢞⡶⠂⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢠⡯⠴⠒⡾⠃⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣠⠖⠉⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⢞⡵⢋⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢠⣾⠗⠉⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀
⣟⣛⣻⣛⣟⣟⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣟⣻⣛

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠛⠛⠲⢤⡀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⠚⠉⠀⠀⠈⠙⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦
⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⠀⠹⡀⠀⢳⡀⠀⠀⠰⡄⠀⠀⢹⡀⠀⠈⢇⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⡢⠀⢱⡀⠀⢧⠀⠀⠀⠹⡀⠀⠀⢳⡀⠀⠘⣆⠀⢀⡒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢣⠀⠈⠥⡄⠀⠀⢳⡀⠀⠀⡡⡀⠀⠘⡆⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠑⠃⠀⠀⠀⢳⠀⠀⠓⠎⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⡀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⡰⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠃⠀⠀⠀⠀⠀⠀⠤⡄⠀⠀⠀⠀⠁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠃
⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠈⠉⠀⠀⠈⠉⠁⠀⠈⠉⠉⠀⠀⠉⢹⡗⠛⠏⢹⡇⢠⠖⢛⡏⢀⡴⢛⣿⠁⠚⣿⠛⠉⠀⠀⠈⠉⠁⠀⠀⠉⠉⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡉⣻⡄⢸⡇⢻⣛⢉⣠⠸⣟⠋⣁⡄⠀⣿
⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠙⠛⠛⠐⠘⠃⠀⠙⠛⠁⠂⠙⠛⠋⠐⠂⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⠿⠿⠿⠿⠷⠶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠿⠿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⣠⣶⠟⠛⠉⠉⠉⠉⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⣠⣾⠿⠷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠹⠟⠉⠉⠛⢿⣆
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠛⢷⡄⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⣠⣴⠿⠛⠁⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡶⠿⢟⣿⣶⠀⠀⠀⠀⢀⣤⣤⣤⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣀⣀⣐⣿⡅⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⣸⡏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⢻⣦⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣸⡏⠀⠀⠸⣿⣿⣦⣄⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⣀⣼⠿⣷⣿⠃⣀⣤⣄⠀⢀⣿⣿⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠻⣿⡿⠿⠶⠶⠶⠾⠟⠋⠁⠀⠈⠿⠾⠛⢹⡿⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠛⠛⠿⠷⠿⠿⠆⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⢀⣀⡀⢀⣿⠁⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣽⣿⣆⠀⠀⠀⢠⣿⠉⠻⣾⠏⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⣸⡏⠀⡀⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⢻⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣱⣿⡿⣷⣄⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣌⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠁⠀⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡆⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⢀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀⠀⠀⢸⣿⠃⠀⠀⠙⣉⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡷⠀⠀⠀⠀⢿⠏⠀⠀⠀⠀⠉⠛⠋

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠦⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠄⠀⠀⠀⠁⠀⠐⠀⠀⢀⠀⠀⠂⠀⠀⠠
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠤⢆⡑⠀⡴⠜⢃⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡧⢰⠸⣿⠒⠒⣶⠂⣄⣤⡖⡇⠀⡀⣄⠀⠓⢴⡚⢚⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠒⠚⠓⠛⠀⠀⠁⠒⠕⠊⠇⠀⠠⡅⠹⡤⠀⠀⡠⠞⠒⠓
⠀⠀⠀⠀⠀⠀⠂⠀⠈⠉⠀⠈⠟⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠴⠖⠒⢲⠀⠀⠀⢀⠆⠀⠈⠙⠒⡐⠈⠱⢲⡷⠄⠀⢢⣄⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⡀⢀⡀⠀⠠⢜⡁⠀⠀⠁⠀⠀⣀⠀⠀⣗⠀⠀⠁⠀⠀⠀⠓⠛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠶⠀⠈⢄⠀⠄⡀⡀⠀⠀⠀⡰⠁⠉⠀⠀⣀⡠⠴⠒⢉⢄⡂⢼⠤⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠁⠀⠀⠀⠀⠉⠒⠢⠅⠀⠀⠀⣇⣄⣠⠶⣻⢶⠦⢖⠋⠁⠀⣤⡁⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠄⠸⡍⠉⠒⠶⣄⠁⠂⣬⡇⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡇⠀⠀⠈⠢⠄⠀⠀⠙⠢⡈⠑⢤⣀⠀⠀⠙⠀⠀⠀⠀⠈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣉⣠⣤⡠⡼⠶⠂⠀⠈⠓⠦⣈⣉⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠠⠔⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⣠⠤⡤⠊⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠛⠁⠀⠀⠀⣀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠤⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣤⡀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠈⡄⢠⠂⠀⠀⠐⠀⠀⠁⣀⢐⠀⢠⣴⡆⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⡀⠈⢦⣱⡎⠀⠀⠀⠀⠀⠀⢀⢀⠉⠀⠚⠍⡅⠀⠀⠁⠀⠀⠠⠀⠳⣀⡞⠀⢀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠁⠀⠀⠀⠀⠆⡀⠐⠬⠽⢁⢱⣿⣵⠦⠀⠀⠀⠀⠀⠀⠀⠗⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠋⠉⠁⠐⠒⠒⠐⠚⠋⠀⠀⠁⠀⠀⣀⠀⡇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢠⠀⠀⠂⠀⠀⠀⢀⣀⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠊⠘⠛⢯⡁⠤⠀⠂⢀⡀⢣⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠹⠂⡀⢀⡴⠺⡅⠁⠀⢈⡼⠱⣠⠁⠂⣀⠔⠋⠀⠀⠀⠀⠠⡀⠀⠀⠒⠛⠛⠣⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠑⠄⠀⠀⠐⠀⠀⠠⢀⡘⡄⠀⢸⠁⠁⠉⠒⠉⠀⢠⡞⠉⠀⠀⠁⠀⠤⣀⠀⡀⣒⡈⠒⠦⠛⠲
⠀⠀⠀⠀⠀⠠⣤⣀⣠⣄⠠⢴⡰⢧⣦⠴⠀⠀⠀⠀⠀⠀⠁⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⠀⢉⠉⠉⡑⢦⣦⣆⣤⣠⣌
⠀⠀⠀⠀⠀⢠⣍⣉⣉⣡⣄⣴⡴⣠⢌⣅⠠⠀⠠⠀⠀⠀⠀⢴⡍⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠚⠛⠙⢧⣄⡀⣀⣈⡁⡂⡄⠀⠂
⠀⠀⠀⠀⢀⡈⢁⠉⡀⣙⣠⢄⡄⣀⠀⡈⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠁⠵⠦⠆⠶⠖⢖⡟⠓⢈⠉⠙⠢⡀
⠀⠀⠀⠀⠠⠒⠋⠚⠙⠻⠌⠉⠓⠉⠁⠈⠣⠀⠀⠈⠠⣀⠀⠘⠵⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠘⣤⣆⣤⢠⣦⡠⣠⡉⣷⠀⠂⠁⠁
⠀⠀⠀⠀⠉⠖⠓⠊⠶⢿⡡⣖⡴⣆⡰⢴⣦⠎⠀⠀⠀⠀⠉⠂⠄⠠⢀⠀⠀⠄⠄⠊⠁⠀⠀⠀⠀⠀⠠⢤⠠⢄⠠⢀⠈⡙⢻⠆⠀⠀⠁⡀
⠀⠀⠀⠀⠐⠐⢤⡆⠠⢠⠄⠀⢀⡀⢀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠠⠹⠂⠀⠐⠀⠤⢬⡐
⠀⠀⠀⠀⠀⠀⣸⡧⢀⠀⠀⠀⠘⣿⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢈⠘⠐⠒⠀⢀⢀⢀⠠⠀⠉⠲⠀⠄
⠀⠀⠀⠀⣀⡀⢄⣀⡀⠈⠀⠐⠲⠼⠁⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢈⠀⠘⠲⠁⠀⠈⠀⠀⠀⠲⠨⢀
⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⠀⠜⠐⠀⠀⢀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⢄⠀⢀⢀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠒⠚⠒⠺⠡⠟⠈⡀⠈⠐⠄⠀⠤⠈⠀⠈⠀⠀⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠂⢀⠀⠀⠀⠒⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠈⠄⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⠄⠀⢀⢀⡀⢀⠀⠆⠀⠀⠨⠁
⠀⠀⠀⠀⢀⠀⠈⠁⠘⠃⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡠⠀⠂⠀⢄⠀⠓⠐⡖⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠈⠀⠂⢀⢀⣀⡀⠀⠀⠂⢀⠇⠁⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠚⡀⠈⠀⣀⠀⡟⣾⢍⡍⢳⡤⣄⠀⠉⠓⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠊⠀⡀⡼⠁⢠⢷⣠⡆⣼⠀⠀⠐⡄⣤⣄⡀⠀⠢⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀
⠀⠀⠀⠀⠤⠀⠀⡄⠀⠀⠀⢀⠔⠀⢠⡞⠉⠃⠀⠀⠈⠽⠼⠾⠀⢁⢀⠀⠋⠨⠙⡀⡀⠀⠐⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢺⡌⠀⡠⣤⡤⡄⠀⠀⠂⠀⢀⠤⣀⠑⠤⠀⢐⠾⣽⡶⡄⣨
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⡁⠈⠀⠀⣧⣾⡶⠆⠀⠀⢠⣶⣉⣼⣿⣷⢄⣑⢼⣾⠿⠇⢥⠅⠀⠰⠀⠀⠀⢠⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠠⢄⠁⠧⠵⠧⠀⠂⠊⠃⠰⣼⠲⣿⠘⣿⠀⠀⠀⠀⠘⠀⠄⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⣠⠀⠀⠀⠉⠃⠀⠀⠉⢲⠤⠆⠔⠛⠉⠛⠆⣛⠠⠄⠁⠀⠉⠑⠄⠀⠀⠘⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠄⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⡀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠄⠀⠀⠀⡀⠈⠀⠉⠐⠆⠒⠊⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠠⠄⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠖
⠀⠀⠀⠀⠄⠄⠔⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠉⠂⠅⠂⠀⠀⠉⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡷⡄
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢚⡽⠋⠀⠀⠀⠀⠀⠀⡠⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢊⡹⠋⠉
⠀⠀⠀⣶⡇⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢀⠔⠁⠐⠻⠀⠀⠀⢀⣠⠔⠈⠐⠃⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⣦⠀⠀⠀⢸⡇⢀⣏⣵⣎⠙⠒
⣠⣧⣼⣯⡇⣦⠀⠀⠀⠐⢋⠁⠲⠀⠀⠀⠤⢤⠀⠁⠠⠔⠂⢿⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⢀⣾⣿⣈⣉⡙⠟⣶⠦⠦⢀⡄
⣻⣿⣿⢻⣷⣟⣰⣠⠔⢂⡉⠁⠄⣁⢀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⣧⠀⠀⢸⣭⠃⠀⠜⠛⡅⢙⣳⠀⣀⠸⣇⡀⠾⣷⣀
⢸⣿⠄⡘⣿⣿⣿⣿⠖⡃⠁⢉⠀⠈⠋⣀⡀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣵⠀⠀⢣⣈⠲⣄⡴⠂⡴⢦⣹⣏⠈⠳⡈⠻⣶⣼⣿
⢈⣹⠾⠇⣸⣿⡿⠏⢐⠁⠂⠊⠀⠊⠤⠘⣿⣿⣦⣿⣤⣀⣆⣄⠀⠀⠀⢀⣀⣀⣰⣆⣀⣜⣡⣁⠀⠷⠋⢁⠐⣩⠗⠛⠀⠀⠹⣷⠀⠀⠀⡀⠈⠹⣿
⢀⡅⠠⠆⢺⣁⣤⠴⠅⣤⠞⠀⠀⠀⠀⠢⣿⣿⢿⡿⢿⢿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠀⠀⠙⠺⣁⠈⢻⣡⡴⠚⣡⣀⢢⣍⡀⠀⠀⠙⠶⢶⣿
⢸⣧⠀⢢⠾⠋⢀⡤⢀⣤⡀⠀⣴⣟⠒⢄⡘⠿⣚⠓⢛⣟⣹⡿⠛⠉⠁⠀⠈⠉⠙⢿⡏⢀⠀⠋⠲⣶⡌⢆⣸⠧⠤⠊⠀⠳⣄⠙⠆⠀⠀⢄⠀⠀⠙
⠀⠀⠀⠉⡿⠋⠀⣀⠈⠀⡘⠳⣇⠘⡤⠀⠙⠛⠛⠚⢹⠉⣁⠴⣎⣹⣦⣄⡀⣀⣀⣀⠉⠀⠀⠔⠀⠤⣙⣾⣗⡴⢠⡄⠀⠐⣄⠉⠑⢆⡀⠈⠁⢤⣘
⠀⠀⢀⡾⠂⠈⠁⠧⣀⠼⠁⠀⢀⡓⠛⡆⣠⡀⡄⠀⠀⠈⠷⠾⠿⠴⠷⠾⠿⠿⠟⠅⠨⠤⠒⠀⡼⠦⣤⣹⠿⠆⠁⡷⡀⣠⠿⠇⠀⣌⣣⣴⠀⠀⢻
⠀⠠⠏⠀⢀⣠⡴⠶⢅⠀⠀⠀⠈⢳⣠⠓⢎⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠄⠀⢀⣀⠀⠃⠐⡄⠠⡀⠘⣧⡀⣤⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠁⠐⠊⠉⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⡤⠄⠚⠉⠠⠤⡀⠰⠤⠵⠄⠀⠿⠯⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈
⣿⠿⠿⠿⡿⠿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⣿⣿⣿⣟⣿⣿⣻⡿⣿

⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠛⣻⣿⣿⡿⠟⡿⠉⡀⠀⡀⠚⢢⡷⠀⠀⠀⠐⠀⢰⠳⠘⠀⠈⠀⠀⢠⠍⢉⡿⢻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿
⣿⣿⣿⣯⣹⣿⣿⣿⣿⣿⣿⡿⠟⠉⠑⢤⣗⢐⡧⠊⡄⡄⢀⡿⠃⠀⠀⢀⠀⠹⡀⠀⢶⠃⢀⣴⡍⠀⣀⠀⠀⠈⠻⣿⣿⣿⣷⣾⣿⣾⣿⡿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⠀⠀⢹⡎⠀⡀⣀⠀⢸⡗⠀⠀⢠⠋⠀⣠⣧⡤⢸⣦⣿⠟⠋⠀⠀⠀⠀⠀⠀⣬⠻⣿⣿⣿⣿⣿⣿⣧⣾
⣿⣦⣿⣿⣿⣿⣿⣿⣿⣃⠶⢀⡄⢈⡖⠀⠈⠃⢀⡟⠁⠀⢨⣿⠀⡆⠉⠁⠀⠀⣹⠁⢠⡏⠁⠀⠀⠀⠀⣰⠃⠀⢠⠇⠐⣙⣿⣯⣽⣿⣿⣿⣿
⣿⣿⣿⣿⡿⢷⣿⣿⠃⠀⠀⡤⠽⢤⣤⡀⠀⢈⡀⠀⠀⢀⣾⠟⣠⠁⠀⠀⠀⠀⡏⣰⡿⠀⠀⠀⠃⠀⡈⠁⠀⠀⣼⠚⠉⠁⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣦⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠉⠃⢼⡧⠀⠉⢁⣿⣶⡟⠀⠀⠀⠀⢀⡿⣿⡇⠠⠀⠀⠀⣸⠃⠂⣠⠞⣁⠀⠀⡴⠀⣿⣿⣿⡟⣼⣿
⣷⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠘⣟⡻⢓⠀⠀⠀⠀⣼⣿⡟⣧⠂⠀⠀⢠⣿⣤⠾⠷⠞⠿⠶⠸⣷⡛⢸⣿⣿⣿⡿⣿
⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢒⡢⡄⠀⠀⠀⢻⣄⠀⢿⣿⣿⣇⠀⠀⣼⣭⣿⠁⣻⣀⣀⡴⠟⠋⠁⠀⠀⠀⢀⠰⠀⠈⠣⣼⣿⣿⣿⣿⣿
⣿⣯⣽⣿⣿⣿⠀⢀⢀⠐⣄⠀⠀⠀⣀⣨⠶⠶⠚⠛⠛⠳⣼⣿⣿⣽⣦⣼⣿⣿⡁⢀⡿⣿⣷⡆⢠⣖⠀⠀⠀⢠⠏⠠⠄⠀⣀⠘⣿⣿⣿⣿⣿
⣿⣿⣿⣛⣿⣿⣆⡀⢿⣀⡼⠶⢛⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⣻⣿⣿⣿⣟⢙⣿⣿⠋⠀⠀⠀⠀⠀⠀⢶⠲⠾⠤⠀⣀⠀⠈⢩⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡏⠁⠀⠁⣀⠴⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⣿⣿⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⢀⠀⠀⠀⠀⣸⣿⣻⣿⣿⣿
⣿⣿⣿⣿⣟⢻⣧⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠉⠓⠂⢠⣿⣿⣿⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿
⣿⣯⣿⣿⣿⢿⣻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣿⣿⣽⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⢻⣿⣿⣿⣿
⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣿⣿⣿⣿⣿⣻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣷⣿⣿⣿⣿⡿⣶⣤⣄⣀⢠⣾⣿⣿⣿⣿⣻⣿⣯⣿⣿⣷⡀⢀⣀⣠⣴⣺⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠾⠿⠿⠿⠿⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡶⠿⠿⠿⠿⢷⣶⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⣀⣠⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠉⠙⠛⠿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⢀⣴⡾⠟⠛⠉⠉⠙⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣹⣧⣤⣤⣀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⢀⣴⡿⠛⠋⠉⠉⠛⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠉⠉⠉⠛⠿⣶⣄⠀⣀⣤⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠛⣷⣄
⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠛⠉⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣴⣶⣶⣶⣤⣄⠀⣿⡆
⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠛⢿⣾⡇
⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⢰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡃
⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⢿⣦
⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢻
⠀⠈⠙⠿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢉⣽⡟⠉⠉⠉⠉⣩⣿⠋⢿⣏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⢀⣼⣿⣥⣤⣬⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣃⣀⣀⣀⣀⣈⠉⠉⠉⢉⣿⠏⠉⠛⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⣶⣶⠶⠶⠶⠶⢶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⠛⢻⡿⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⢠⣾⣿⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣁⣀⣀⣀⣀⣉⠉⠉⠉⣩⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⣿⡏⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠋⠉⠉⠙⠓⢦⡀⠀⠀⠀⣠⠴⠶⠶⢤⡀⣠⠴⠚⠛⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⡀⠀⣀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⠖⠚⠁⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠈⠙⠋⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠲⣄⡀
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⣸⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⡄
⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠒⠚⠛⠉
⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠃
⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⢀⠀⠀⢀⣡⠞⠛⠓⠶⣾⠟⠁⠈⠙⠓⠶⠦⣤⣤⣤⣴⣶⠟⠛⠶⢦⣤⣤⠶⠞⠋
⠀⠀⠀⠀⠀⠙⠳⠶⠤⣤⡤⠶⠾⠛⠁⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢀⣀⠀⠀⠀⠀⠀⠀⠠⠀⠛⠛⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⡠⠂⠀⠴⠗⢚⡽⠃⠀⠀⠀⠀⠀⠀⠀⠠⣠⡾⠃⠀⠀⣠⠀⠀⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⢀⠜⠁⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⠴⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠁⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣥⡤⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⣀⠀⠀⠀⠀⠀⠀⠘⣩⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠖⠚⣹⠏⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⣰⠃⠀⠀⠀⣠⠾⠋⠀⠀⠀⢀⡔⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⣰⠃⠀⠀⣠⠾⠁⠀⠀⠀⠀⡠⠊⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⠉⠉⠉⠉⠉⠉⠁⠈⠁⠀⢰⣄⠀⠉⠉⠉⠉⠛⠛⠟⠛⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿
⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⣸⡇⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⡀⣿⣿⣾⡿⢠⣿⣿⣷⡀
⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⡟⡜⠉⢰⣿⣿⣿⣿⣷⣦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⢀⢀⣿⡏⣿⠖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣒⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢟⡔⢫⠆⢸⠟⡼⢋⣀⠀⣫⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣁⠀⣀⠈⠉⠉⠙⠛⢃⣴⠞⠀⠋⢀⣄⢞⣴⡿⠁⣽⣛⣴⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠘⠀⠂⠀⡀⠀⣠⠞⡱⠀⡰⠀⣾⣧⣾⡿⢳⠿⡿⠛⠁⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣄⠀⠐⠀⢀⡞⠁⠔⠀⠈⢀⣀⣿⠟⠋⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣶⣯⣻⣿⣿⣿⣿⣿⣿⣿⣷⣝⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣦⣀⠰⠊⠀⠀⠀⠀⠠⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙⠛⣋⢀⣽⣿
⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣯⡻⣿⣿⣿⣿⣿⣿⣿⠆⠁⠚⠳⠳
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣿⣿⣿⣿⣶⣽⡋⠉
⠁⠀⢐⣾⣿⠿⠋⠀⢘⣧⡄⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣀
⣷⣶⣦⣥⣤⣶⣶⠶⠊⢛⣿⣦⢀⡀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣶⣝⠻⢿⣿⣿⣿⣷⣶⡾⠷⠒⣀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠈⠉⠻⣿⣼⡟⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⣿⣿⣿⣶⣴⣮⡿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⠓⠦⢄⡀⠀⠀⠀⠀⠀⠉⠻⢯⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠉⠙⠛⠛⠂
⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠛⠂⠉⠓⠂⠀⢀⠀⠀⠠⢄⣀⠈⠉⠉⠉⠉⠛⠛⠻⠻⠿⢷⣦⣄⣀
⠀⠈⠛⠻⣿⣿⣿⣿⡿⠿⠟⠋⣩⣿⣿⣿⣿⣶⣶⣶⣶⣿⣷⣤⡀⠐⠲⠤⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣀
⠀⣆⠀⠀⠀⠉⠉⠀⠈⠀⠒⠻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣆⢀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣆⠐⠚⠋⠁
⣦⣿⠀⠀⠀⠀⠀⠀⠀⠲⠶⣶⣿⣿⣿⣿⣮⡳⢯⣛⢿⣷⣿⣿⣿⣿⣶⡌⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣧⣄⡀⢸
⣿⣿⣦⡀⠀⢠⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣷⣤⣍⠳⢮⡙⠻⢿⣿⣿⣿⣤⣿⣦⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⣎
⡿⣿⣿⣷⣦⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣶⣍⡺⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⢿⣿⠻⢿⡃⠙⢿⢿⣟⢮
⣿⣵⣏⣛⠿⣿⣷⣾⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⢿⣿⣿⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣦⣀⠀⠀⠀⠈⠓
⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠿⠆⢀⣤⣶⣀⠀⠀⠀⠀⣨⡑⢌⡛⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣷⣤⣉⠙⠛⠂
⣿⣿⣿⣿⣿⣛⠿⣿⣷⣦⣤⣶⣿⣿⣿⠁⣀⣤⣴⣾⣿⣿⡤⣌⡑⢦⣍⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠓⠲⠆⠀⠀⣀
⣿⣿⣿⡿⣿⣿⣿⣦⣭⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠉⠳⢼⣟⣶⡄⠙⠛⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠺⢿
⣿⣿⣿⣿⣄⣾⡽⣻⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠉⠻⢿⣶⣦⣴⣿⠻⢿⣿⣿⣿⣿⣿⣿⣦⣀
⣿⣿⣿⡿⢿⣿⣗⣿⡇⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠠⣴⡌⠛⠻⣷⣦⠀⠉⠛⠿⠟⠻⢿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣷⠦⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠉⠐⠠⠄⠈⠑⠠⢄⡀⡀⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⠀⠀⠀⠀⢸⣿⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠲⣦⠀⠀⠀⠀⠉⠂⣄⣄⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢴⡆⠀⠀⣽⣿⣿⡧⢼⣿⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣇⣸⣷⠀⢴⣿⣿⣿⣿⣿⣿⡆⢀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣄⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⠶⠶⠶⢤⣄⣀⠀⢠⡏⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢾⡀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠙⠳⢦⣄⣀⣀⠀⣀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⠦⣤⡀⠀⠈⠉⠉⠉⣩⡽⠋
⠀⠀⠀⠀⠀⠀⢀⣤⠶⠖⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⠴⠶⠛⠁
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠈⠛⢦⣤⣀⣀⣀⣀⣀⣀⡀⠀⠐⡾⣄⣸⣃⡴⢶⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⢁⡀⠀⣤⠴⢻⡛⢤⣤⠀⣀⠀⠀⠀⠀⣾⠀⠀⠀⠀⡈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠉⠀⢼⡆⠀⠉⢠⡏⠀⠀⠀⢸⠇⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⡤⠀⠀⠀⣼⠃⠀⠀⢠⡤⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢸⠇⠀⠀⢠⡏⠀⠸⠳⣤⣧⠜⠛⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⡿⠀⠀⠀⣼⠁⠀⠰⠞⢉⡏⠳⠶⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣯⣹⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⣏

⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⡁⣞⠙⢣⢰⠈⢻⠁⣰⢧⠀⣏⣱⢰⡆⠀⣞⣉⠀⠰⣏⠀⢹⡏⢰⣋⡳⣴⠋⠳⡔⣧⠞⢰⣋⡁
⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣄⣣⣤⣞⣸⣀⣸⣀⣏⣙⣆⣧⣼⣸⣧⣄⣧⣤⣀⣠⣤⣇⣸⣃⣘⣁⣣⣙⣤⣴⣁⣇⣳⣘⣅⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢈⠂⠀⠀⠀⠰⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡂⢐⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢍⢈⡕⢃⣀⠀⠀⢀⣄⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡴⠛⢆
⠀⠀⠀⠀⠀⠀⠀⠀⣔⠢⠏⣶⢲⢰⢁⠔⢲⠀⢟⠢⢌⢃⡋⢗⡈⣆⠁⠀⠀⠀⠀⠀⠀⢀⠤⠤⣼⣵⣇⠀⣼⢺⣇⠤⣄⠀⠀⠀⠀⠀⢰⡉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢔⣆⢤⠉⢂⣀⣋⠚⣌⡒⡈⢀⢐⠪⠗⠁⠀⠀⠀⠀⠀⠀⠀⠈⢢⣀⡈⠃⣈⣀⠁⠛⠀⣀⠜⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⡎⢪⢣⣜⠉⢱⢴⠱⡁⡇⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢫⣾⠥⠐⣅⣀⡅⠀⣭⣟⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣑⡑⠂⠦⡘⠏⡻⢒⢃⠈⡸⠔⣷⢤⡀⠀⠀⠀⠀⠀⠀⢠⡋⠀⣠⡆⡀⠁⡀⣤⡀⠈⢣⠀⠀⠀⠀⠀⠀⢀⠤⠤⡀
⠀⠀⠀⠀⣠⠄⡀⠀⠀⠰⣔⠓⡀⢐⢌⠢⠼⠈⠁⣥⠞⢸⢡⡶⡄⠬⣐⠄⠀⠀⠀⠀⠀⠀⠀⠉⠯⢺⡁⠀⡹⢭⡍⠀⠉⠀⠀⠀⠀⠀⠀⢠⡀⢀⡄
⠀⠀⠀⠀⠣⠠⠀⠀⠀⠮⠔⠦⠋⠁⠈⠒⡡⠃⢘⢩⠉⠁⠀⠀⠈⠁⠀⠀⠀⢜⠉⡂⠀⠀⠀⠀⠀⠀⠳⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣋⢈⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡉⠀⢑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠫⡲⠸⢊⠝⢀⠄⠀⠀⠀⠀⠀⠀⢎⠑⠈⣶⠒⡼⡈⠁⠀⠋⣳⣠⣀⣤⣀⡀
⠀⠀⠀⠀⠀⢀⢀⠤⡀⢇⡀⢀⣠⢇⠔⠢⠔⠢⠀⠀⠀⠀⠘⠩⣂⠆⢇⣀⡜⠐⣧⣀⡌⠲⡲⠝⠀⠀⠀⠀⠈⢤⡤⠀⠀⠡⠬⠂⠰⣋⡜⠀⠛⠀⠀⠜
⠀⠀⠀⠀⠀⣅⠀⠀⠃⠐⠀⡀⠑⠒⠃⣀⠀⡎⠀⠀⠀⠀⠀⠎⠭⠒⠎⣈⡺⠸⢎⣀⡶⠂⠭⠴⠀⠀⠀⠀⠀⢈⣤⡒⠲⠀⡰⠂⢢⠀⣠⢀⡈⣻⠚
⠀⠀⠀⠀⠀⠸⠤⠴⣄⠀⠒⠉⠒⠂⠰⡉⡲⡁⠀⠀⠀⠀⠀⢖⡀⠤⠏⢈⠵⢠⢭⠈⠷⠄⣀⠲⠀⠀⠀⠀⡄⠺⠄⠀⠉⣀⠙⠶⠊⠀⠒⠐⠒⣄
⠀⠀⠀⠀⠀⠀⡃⠱⠃⠀⠃⠢⠊⠁⢀⠉⠀⠸⣀⠀⠀⠀⢀⣔⠭⠆⡌⠙⢧⠠⡝⠉⠇⠬⢕⣢⠀⠀⠀⢜⣁⡀⣰⠀⡰⡠⠃⠀⢎⢱⠀⢀⠘⠉⣀
⠀⠀⠀⠀⠀⢔⠁⣀⠐⡆⢱⡄⠀⢎⠸⢅⠀⠤⠎⠀⠀⠀⠀⠀⠀⠖⢀⣔⠵⢠⢝⣢⠈⠆⠀⠀⢀⡤⠢⡀⠀⠈⠀⠀⠸⣤⡄⢠⣀⠎⠂⠛⠤⠤⠼
⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠣⡀⠀⡴⠃⠀⠀⠀⠀⣠⢀⠀⠀⠀⠀⠀⠀⠁⠀⠜⠀⠉⠀⠀⠀⠀⠘⠄⡀⠄⠀⠀⠀⠀⠀⠢⡀⢀⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔⠂⠀⠀⠀⠀⠀⠧⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣬⡁⣠⣤⠈⢷⣣⡀
⡆⠠⡀⠀⠀⠈⠀⠀⠀⠁⠀⠀⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢈⣿⡳⣜⢿⣎⢻⣷⣔⠽⢿⣄⢠
⠈⠢⣀⡐⠒⣋⠀⠀⠀⠀⠀⠀⢈⠐⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣶⣯⠛⡛⢎⢢⡹⣷⣝⢿⣯⣂⠻⣧
⠀⠀⠀⠈⠉⠀⠀⣤⡤⢤⠖⠀⠈⠑⠀⠀⠀⢀⠀⠀⠀⠀⣠⡀⢴⣶⣷⣝⡿⠋⠙⠳⠘⠀⠑⠙⠊⠉⠀⠙⠁
⠀⠀⠀⠐⠒⠒⠚⠁⠀⠀⠉⠓⠀⠀⢀⣀⣤⣼⣿⣶⠲⣿⣿⣿⣦⡹⠿⠻⠃⠀⠀⠀⣀⡀
⠀⣀⢀⠀⠀⢀⣀⡀⠀⠀⢀⣤⡰⣾⣷⡙⢿⣿⣿⣿⣷⡌⠣⠉⠈⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠈⣿⣿⣍⢿⣿⣿⣿⣿⣧⡻⣿⣮⣿⣿⡦⠻⣿⣿⣇⡈⠒⠐⠠⠤⠔⠀⠀⠐⠒⠈⠀⢀⠀⠀⣤⣀⠰⣝⢷⣗⠄
⠀⠀⠈⢿⣿⣦⠻⠟⠹⣿⣿⣿⣮⣿⣿⣿⣆⢲⣾⣿⣿⣿⣿⣿⡻⣷⣿⣿⣶⣦⡺⣿⣿⣟⢦⡻⣿⣷⡳⠌⠢⡉⠳
⠀⠀⠈⢲⣝⢿⣷⣿⣧⡹⣿⣿⣿⣷⣝⢿⣿⣷⡙⢿⣿⣿⣿⣿⣿⣮⡿⣿⣿⣿⡛⣈⣿⣿⣷⣕⢮⢿⣿⣦⡢⠈
⠀⠠⡙⣝⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿⣿⣷⣿⣿⣷⡼⣿⣿⣿⣿⣿⣿⣿⣾⢿⣿⣿⣮⡻⣛⣿⣿⣯⣷⣝⠿⡿⡄
⠀⡝⢮⠺⣿⣿⣿⣿⣿⣏⠉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣄⢭⣝⣛⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣷⡝⠞
⠀⠈⣿⣿⣟⢿⣿⣿⣿⣿⣷⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⣿⣿⣼⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⡿⣦
⠀⠠⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⢆⣻⣿⣿⣿⣿⣿⣿⣿⣄⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⠿⢯⡘⠌⠢
⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣯⡻⡿⠟⡛⢮⢠⣧⠳⡀
⠀⠐⢠⡎⡙⡟⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⡛⢯⡻⢷⢰⡆⣿⠀⣸⣿⣀⡈
⠀⠀⢐⢯⣿⢰⣿⣸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⣿⣿⣿⣷⣿⣿⣿⡿⣿⣿⡏⣤⠁⡆⣼⣿⣿⢃⣼⣿⡇⠙
⠀⠀⠂⣼⣿⣵⣿⣏⠷⠈⠻⠿⠟⠍⠛⠟⠗⠙⠛⠉⠊⢛⠋⠛⣛⠛⠻⠿⠮⠙⠐⣿⢘⣷⣸⣿⣿⣿⣿⣿⣷⡄
⢠⣾⣷⣿⣿⣿⣿⣿⣶⣶⣦⣤⣾⣿⣶⣦⣶⣿⣷⣦⣔⢻⠿⣿⣿⣿⣷⣶⣶⣦⢸⣿⣿⣿⣿⣿⣾⣧⣿⣿⣿⣶⣦
⠀⠉⠋⠁⠀⢀⣈⣀⣉⣉⣋⣉⣉⣉⡙⠛⠋⠉⠉⠤⣤⠤⠀⠀⢤⣁⠤⠭⢙⣐⣿⣿⣿⣝⣿⣿⣿⣭⣽⢿⣿⣶⣍
⠀⠐⠀⠂⠢⠀⠐⠀⠀⠈⠓⠐⠒⠶⠒⠀⠀⠀⠃⠙⠛⠉⠛⠋⠁⠀⣀⣠⣬⣴⠼⠗⠒⠛⠛⠛⠛⠋⠛⠻⠿⠛⠫
⠀⠮⠙⠛⠻⠿⠿⠛⠛⠛⠛⠛⠓⠒⠒⠛⣀⡘⢛⣡⣛⠛⣻⡓⠁⠀⠀⠀⣀⣀⣠⣤⣤⡶⡶⠶⢶⠿⠛⢿⣶⠦⣜
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣠⣄⣒⣟⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣟⣛⣋⣉⣉⣉⣁⣀⣀⣀⣠⣀⣀⣀⣀⣈⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⠀⢄⣰⡀⠀⠌⠛⡀⠀⣄⠐⣀⠘⢦⡀⣦⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠈⠀⣠⣦⣶⣆⠀⠀⠀⠐⠀⠲⠞⠀⠀⢠⡄⠓⠿⢴⠰⣤⠙⠦⣵⠀⠀⢈⣺⣧⡾⢦⡄
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣷⣰⣿⣿⣿⣿⣿⣦⣄⠠⠀⠀⠀⢀⠀⠀⠀⠡⠘⠓⠒⠻⢿⣗⡀⡘⠧⠀⠉⠛⣿⡇⡀⢳⡀⢀⡸
⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠛⠭⠄⠈⠐⠦⣄⣠⣿⠋⡁⠀⠳⣼⠃⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣶⡄⠀⠀⣢⠀⠀⠀⠀⢀⠀⠀⠀⢙⢦⡀⠀⢻⣿⡆⠱⣄⠀⣿⡄⡄⠀⡆
⠀⠀⠀⠀⠀⣠⣴⣷⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠈⡁⡄⢀⣀⠐⠈⠉⠂⠖⠈⠉⠉⠛⣿⣷⡀⣿⡀⠸⣷⠁⣼⡄
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣪⣈⣙⣀⣛⣀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣯⠙⢷⣄⣿⣧⣿⡤⠆
⠀⠀⠀⢐⣿⣿⣿⠿⠋⠡⡽⣯⣭⡛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢉⠉⠉⠉⡷⠶⣦⣤⣴⣿⣿⣏⢹⣿⣿⠁⠀⣿⣿⣿⣿⠥
⠀⠀⠀⠀⣿⡟⠁⠀⠀⠀⠀⢨⢻⣿⡄⠀⡸⣹⣻⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⠇⠐⢊⣁⣴⡟⠁⠀⠈⠉⠉⠛⣿⣿⡆⠸⢻⣿⣿⠇
⠀⠀⠀⣠⣏⣀⣤⣲⡄⣠⣤⣼⣿⣿⣿⡆⣸⣿⠋⠌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣌⢆⣐⣢⠀⣂⣀⣳⡄⠰⣄⣿⣹⣿⠀⡞⢿⡃
⠀⠀⠀⠈⠉⠁⠐⠛⣟⣛⠛⠛⠟⠛⠉⠀⠁⠁⠃⠈⠘⠚⢋⣠⣽⣍⣭⣿⣭⣤⣤⣤⣥⣤⣈⣁⠀⠀⠀⠙⣶⣄⣼⣿⡏⠙⣤⣃
⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿⣿⠿⡃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣠⣶⣿⣿⡿⠛⠃⠀⠹⠏⠁
⠀⠀⠀⠀⠀⢠⣴⣦⣶⣉⣀⣤⣄⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣶⣶⣶⣶⣶⣶⣤⣤⣿⣿⣿⠿⠟⢋⡟⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⡭⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⢉⠁⡙⡛⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣦⣤⡄⠀⠀⠀⠐⣦⠀⠀⣶⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⢌⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣿⠿⠿⠇⠀⠰⣦⡀⠘⠃⠐⠇⢠⠞⠁⠀⠀⠀⠀⢀⣤⣾⣿⣷⣶⡕⠐⠀⠀⠀⠀⠀⠀⠋⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠛⣠⣾⣿⣻⣦⠀⠴⠶⠒⠂⠀⠻⠿⠿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⢸⣿⣿⡿⢛⣿⡇⣀⣀⠀⠀⠀⠀⠁⢀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠖⡀⠂
⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⢀⡀⠘⢿⣿⣷⡿⠟⠁⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠲⠀⠀⠀⡄⠀⣠⣴⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠘⢷⣔⠀⠀⠀⠀⠀⠐⠋⠁⢠⡆⠀⢠⡄⠀⣷⠀⠀⠀⠀⠀⠀⠐⠴⢤⡀⠀⠀⠨⠁⠀⠀⠈⠀⠀⠙⠿⠿⠟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⡍⠠⠀⠀⠛⠀⠀⣾⠇⠀⠘⠃⠀⢀⣰⣶⡠⠀⠉⣠⣽⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⣀⡀⠀⠀⠰⠿⠿⠿⠂⠀⠸⠿⠿⠟⠃⠀⠀⢀⣠⣤⣾⡋⠀⠈⠳⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣙⣛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣤⣤⣄⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⣠⣼⣧⣶⣶⣈⠂⠄⠀⠀⣤⡀⠀⠀⠁⠈⣸⠃⠀⠀⢀⣀⣴⣤⣀⠀⠀⠀⣠⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣠⠎
⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⣿⠇⠀⠀⠀⠈⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡄⠀⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡟⡆⠀⠀⡐⢣⠀⠀⢸⡿⠻⠿⢻⠿⠟⠛⠿⠀⠈⢙⡟⢛⠛⠛⡛⠛⢛⡛⢛⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣆⠀⠉⠁⠀⢠⠥⠈⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⠀⢀⡈⠀⡉⠀⢾⣤⠀⠈⠀⠉⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⢠⡈⢁⠃⠀⠀⠀⠀⢀⡸⠀⠀⢰⣿⣇⢸⡗⠘⠁⠀⠾⠁⠀⠋⠰⠋⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⣿⣿⢿⣿⣿⣿⣿⣿⠀⠉⠁⠀⠀⠄⠆⠀⠄⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄
⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠃⠀⠀⠀⢀⣡⣞⣉⡑⠐⠂⠀⠀⠀⠀⣀⡤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠾⠓⠀⠀⠰⠶⠄⠀⠘⠟⠁⠀⢠⣿⣿⣿⣿⣿⡟⠌⠁⠀⠀⣠⣾⣧⣶⣶⣌⠁⠄⠀⣀⣀⣤⣼⣿⣿⣿⢷⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡀⠀⠀⠀⢶⠆⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⠿⠓⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⢀⣀⠤⢤⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠍⠉⡉⠉⣉⡉⠉⢉⠉⣡
⠀⠀⠀⠀⠀⠀⠈⣵⣛⠃⠀⠀⠀⠀⠀⠒⣾⣷⠖⠂⠀⠀⠀⠀⢀⣁⣶⣦⣤⣄⠀⣠⣤⠤⠴⠃⠀⠀⠀⠋⠀⠘⠁⠀⠛⠁⠀⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢹⠿⠀⠀⠀⠀⠀⠀⠐⠁⠈⠃⠀⠀⠀⠀⠀⠿⣿⣿⠿⠿⠟⠀⠘⠛⠛⠩⠍⠂⠀⠀⠰⣾⡆⠰⠃⠴⠂⠀⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠂

⢿⡿⠛⣿⡗⣻⣟⣿⡿⣯⣼⡏⠻⠟⠿⣻⣿⡿⠎⣁⢀⠤⠀⢩⣠⠄⣀⢀⠛⡄⠄⠋⠀⠤⠄⠂⠀⠀⠀⠐⠀⠀⠀⠀⡐⠤⠊⠇⠴⢇⢂⡑⣀⢄⣀
⣿⣿⣳⣻⣿⣿⣿⣿⠏⣿⣻⣤⠀⣀⣀⣭⡿⡃⣈⠉⠀⠀⠁⠀⠀⢈⡈⠉⠔⠙⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠂⠈⢀⡂⢀⢠⡡⠘⣴⣉⠜⠁
⣼⣷⣾⣿⣿⣿⣿⣿⢺⣶⣏⢺⡟⣿⣶⣿⣶⠃⠀⠀⠀⠀⢂⡀⠊⠁⠂⢀⠠⠐⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠁⠀⣀⡓⠎⣼⣆
⡿⢾⣿⣧⣼⣿⣿⣧⣾⣿⣿⣼⣷⣾⣟⣿⡿⠀⠀⠁⠀⡴⠏⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⠀⠀⠈⢞⡃
⡀⢸⣿⣯⠝⡿⠟⠘⠋⣘⣇⠀⠉⠛⣻⡟⢷⠀⠀⡠⠋⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⡁⣯⣯⣱⣎⣻⣤⣴⠊⣛⣻⣿⢿⣿⣹⣉⠅⣠⠉⠁⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⠀⢀⣿⠁⠀⣀
⠉⣻⣙⣻⣿⣿⣿⡿⠐⢿⣿⡟⣿⡛⣿⡟⡰⠆⠀⠀⣠⠊⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢰⣿⡍⠸⠴⠄⠤⠍
⢨⣿⣯⢹⣾⣿⢿⠿⠖⣹⣿⡆⢹⣯⣷⠂⠄⠀⣀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠘⠋⢁⠠⡿⢼⠆
⣸⣾⡇⢨⣿⣿⢿⣶⠈⣿⣿⠀⢨⣿⣿⡇⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠺⡇⡀
⢩⣿⣀⢾⣻⣿⣿⠿⠰⣿⣿⠉⢱⣿⣿⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣟⡏⢰⡄⡀
⢈⣿⢃⡤⣿⣿⣿⡂⢀⣹⡿⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⢼⣿⣥⣭⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣇⠂⠀⠀⠁
⣾⡟⢀⡄⣽⣏⣿⡃⢸⣷⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣿⣿⠀⢻⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⡩⡇⠀⣧
⣿⣛⠐⠀⢻⣿⣩⠅⣸⣿⡅⠀⢸⣍⠁⡀⠀⠀⠀⠀⠀⢁⣠⡄⠸⣿⠃⢀⠈⣟⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇⠀⡿
⣿⡏⠀⠀⢸⣿⡿⠁⣿⡃⠃⠀⠈⢿⣖⣿⣿⠁⠀⠀⠀⠘⠛⠙⠘⠊⠃⠀⠀⣿⡀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠇⠀⠷⠆
⡿⠷⠄⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠝⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠓


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠐

⠀⠀⢀⡀
⡀⠀⠼⠡⠀⠀⠀⠀⠀⣀
⡏⣠⣟⠃⠤⣠⠆⠀⢠⣟⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢀
⠨⣿⢄⣀⡈⠧⣥⠀⢸⡛⢀⣀⣸⡃⠀⣀⠀⡿⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⢰⣦⡍⢠⡤⠛⠀⠸⢀⣀⢚⣿⠄⣰⣧⣾⡧⠰⣿⣴⠀⠀⣠⠀⠀⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⡿⢷⣶⠒⠠⠤⠶⠀⢀⣬⡍⠠⣷⡆⢼⣿⡟⠙⠂⣹⣯⢄⣰⠏⣀⠀⡌⢀⡀⠀⣰⠆⢀⠀⠀⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⡄⢀⡀⡀⣠
⣷⣌⣙⣟⣓⠶⠂⡆⢸⡟⢀⠐⣿⢨⢽⡟⢇⠛⣃⡀⣹⣿⡿⠟⢣⣴⣧⣾⡅⢠⡿⠷⣿⣴⣶⢿⠀⣄⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣀⣰⣾⣇⣼⢳⣿⣏⣷
⠀⠀⠀⠈⠉⠁⠁⠀⠘⠳⣯⡉⠅⣀⡝⠷⠈⣈⡭⠁⠬⣿⣷⡤⠁⢽⣿⠯⣉⣿⡉⡀⢿⣿⣿⢆⣻⣿⣿⢴⣾⡆⡀⠀⢀⢀⣤⣷⣷⣿⣿⣿⣿⣿⣿⣜⣿⣯⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⣾⠻⢂⣀⣀⡀⠀⠘⢿⡯⠀⠄⠲⣿⡖⠀⣺⡗⠂⠐⢿⡟⡐⠘⣿⠄⠜⣿⣛⣷⣾⣿⣿⠿⠿⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠨⣭⣉⣀⣤⣄⣸⣿⡶⠀⠴⢿⢄⡉⠼⣿⣎⣛⣸⣏⠠⠤⢻⣏⡈⢹⣧⣻⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⠶⣿⣔⣀⣙⣿⣼⣰⣿⣆⣶⣭⡿⠧⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⣿⣿⣿⣿⡿⠋⠀⠀⣿⠘⡄⠀⢰⠏⡇⣰⠀⣠⠒⠋⡡⠋⠀⠀⠀⠀⠀⣨⠊⠀⠀⠀⠠⠔⠐⠀⠙⣶⡀⢿⡌
⣿⣿⣿⡟⠀⠀⠀⠀⣿⠀⠘⡀⣸⣶⡾⠛⠑⢀⠜⠉⠀⠀⠀⠘⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠻⣎⢿
⣿⣿⣿⠁⠀⠀⠀⠀⢹⢶⠀⠺⡿⢟⠁⠀⣰⠁⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣿⣿⠏⠀⠀⢀⣠⣴⣿⠀⠀⢀⣇⠈⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠸⣏
⣿⡏⣤⣶⣶⠟⠛⣿⣿⡄⢰⠇⡎⢀⠔⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠐⡟
⡿⠀⠉⠁⠀⠐⠒⠙⢿⣦⠋⠈⢃⡔⠚⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠃
⢁⣰⡆⠀⠀⠀⠀⠀⠀⣿⠳⣶⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⢷⣅
⣾⡏⠀⠀⠀⠀⠀⠀⠐⣿⠀⠈⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿
⠉⠉⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⡾⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠤⡀⠀⠀⠀⠀⢠⢤⠀⠈⢇⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠲⡀⠀⠀⠀⢾⠛⠺⣷⠄⣼⣟
⠐⠀⠀⠀⠀⠘⣄⣀⡋⡠⠹⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢹⣿⠋⠀⠀⢷⣤
⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢸⡏⢱⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⢸⡇⠸⠀⠀⢨⣿
⠀⠀⠀⠀⠀⠀⢸⡇⢰⠀⠀⢸⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⣏⠁⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⢨⣇⢸⡄⠀⠘⠙⠀⠀⠀⠀⢰⣤⣴⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠛⠉
⠀⠀⠀⠀⠀⠀⣈⣋⡸⠃⠀⠀⠀⠀⣄⣠⣾⠛⣁⠌⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⢀⠀⢠⣴⡆⣏⡗⣿⠶⠃⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⣻⣿⠀⣴⡆⢸⣫⡇⡣⡟⠁⠘⠋⠙
⠀⠀⢰⠄⠀⠀⣾⣿⠀⢛⡅⢸⢫⡇⠃
⢀⣠⣼⡏⠀⠀⠙⡯⠀⢽⡇⢸⠁
⠉⠀⣿⡇⠀⠓⢾⡿⠓⣽⠇
⠀⠀⣩⡇⠀⠀⢨⣇⠀⠉
⡴⠊⣿⡇⠀⠀⣿⡇
⣤⣾⢟⡇
⠿⢇⣹⡗
⣴⣿⠿⠇