Zoonosis Emojis & Symbols

⠉⠸⣿⣿⠿⠂⠀⡄⠀⣴⠂⠀⠀⠈⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠐⠾⣿⣿⡇
⠦⣴⣿⠃⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⠀⠀⠀⠀⠀⠀⠂⣸⠃⡈⠀⠀⠀⠀⠀⠀⠘⣿⣦
⠶⠟⠁⢀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⠀⢐⠀⠀⠠⠈⠀⠀⠀⠁⠀⠀⢠⡟⡀⠁⠀⠀⠀⡀⠈⠀⠀⠈⠻
⠀⠀⠀⠰⠒⠀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠉⢀⡀⠀⠀⢰⣿⠃⠀⠀⣀
⠀⠢⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠤⠀⣤⡀⠀⠈⠀⠀⠁⠀⣿⠏⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂
⠉⠉⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢢⠘⠀⠈⠸⠧⠐⢀⠈⠐⠂⠁⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡠⠤⠒
⠛⢛⠓⠒⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠢⠀⠘⡙⠁⠀⣀⠘⠛⠘⢠⢋⠃⠀⢀⡀⢀⡀⠀⠀⢀⠈⠋⠀⠀⠀⠀⠀⡀⠀⠒
⠐⡛⠊⡁⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠁⠀⢀⣡⣅⢂⡉⠁⢀⡘⣣⣌⡀⠀⠀⠓⡄⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠠⠄⠀⡈
⠾⠗⠋⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠪⣠⠅⢢⢤⣄⠕⠈⠀⠀⠀⠀⡠⠁⠩⡄⠀⠀⠀⠀⠀⢀⣀⣀⠀⠑⠈
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠁⠉⠈⠉⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⢷⠀⠘⠁
⠠⢀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⣴⠶⠶⠶⠶⣦⣄⠀⠀⠶⠀⠀⢣⠀⠀⠀⢀⠞⠀⠀⠀⠀⠈⠛⠋
⠂⠐⢁⠀⣀⢠⡄⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠠⠀⠀⣼⠏⣥⣄⠁⠈⣀⣤⠹⣧⠀⠀⠀⠀⠀⠁⠠⠄⠉⠀⠀⠀⠀⠀⠀⠂⠀⡄⠁
⠀⢀⠙⠇⠖⠘⠃⢌⠂⣀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⣿⣄⡈⠉⠀⠐⠉⢁⣠⣿⠀⠀⠀⠀⡠⠈⠀⠈⠁⢄⠀⠀⠀⠀⠀⢰⠀⡇
⣴⣥⠁⢀⣀⠀⣤⡀⠿⢙⠀⠀⠀⠀⠓⠒⠃⠀⠀⠀⠐⠿⢿⣿⠇⠉⠉⠸⣿⡿⠿⠂⠀⠀⡸⠁⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠸⠀⡇⠀⢠
⢐⣊⡰⠂⠉⠀⠈⡀⠢⣬⠄⠀⠉⠀⠐⠀⢀⠈⠀⠀⠀⠀⠘⣿⣦⠴⠦⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢁
⠈⠋⢁⠨⡀⠣⢜⡉⠵⠈⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⢀⡀⠀⠈⠻⠶⠾⠟⠁⠀⠀⠔⢈⠔⠄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠐⠓⠒⠀⠁
⠀⠀⠀⠘⠓⠈⠐⠛⠀⠀⠆⠀⠀⠀⠀⡇⢨⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠪⠕
⠀⠐⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠘⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠁⡄⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠆⠀⠘⠀⠐⠠⠀⠘⠀⠀⠀⠔⠐⠂⠦⢀⡀⠀⠀⠀⠀⢀
⠀⡃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢴⠂⠀⠀⢀⠤⡴⠤⢤⣄⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠊⠀⡀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠠⠤⣧⠠⠤⠐⠀⡁⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈
⠀⠀⡀⠀⠀⠀⠒⠀⠀⠈⠢⡀⠀⠠⠊⠀⠀⠀⠀⠀⠐⢦⣤⠤⠴⢒⠠⠊⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠈⠉⠢⣀⠀⠀⠔⠀⣐⡀⠀⠀⠀⠀⠀⠀⠘⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠀⠁
⠶⢶⣤⡀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢸⡆⠀⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⣀⠀⠀⢀⣴⡶
⠀⣀⣌⠻⣦⠀⠘⠃⠀⠹⢄⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡹⠀⢀⠀⠉⠉⢁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣡⡀
⠐⠋⠉⣠⣿⠀⠀⠀⠀⠀⠈⡐⠐⡈⠀⠀⠠⠀⠀⡄⠈⢰⠀⠀⠀⠀⠀⠀⠈⠈⠀⢠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⣿⣄⠉⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠂⠁⠀⠀⠀⠀⣠⣤⡀⠀⣰⡶⣶⡄⠀⣶⡆⣤⡄⠀⠀⠀⠀⠀⠈⠐⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⣠⣴⣾⠀⢸⣿⠙⣿⡄⣿⡇⢸⣿⢰⣿⣿⣿⠇⣰⡿⢻⣷⠀⠀⠀⠀⠀⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠉⢸⣿⠀⡈⢿⣦⣿⠃⠘⠿⠿⠃⠸⠏⠸⣿⠀⣿⣇⣼⡟⢰⣿⠻⠇⢀⡀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠰⣯⠙⢦⡀⠀⠸⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⢴⣬⣿⠇⣴⣿⢿⠆⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠐⢦⡀⠈⠳⣄⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⣾⣟⠛⠁⣴⣶⣦⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠜⠀⠀⠠⣞⠳⣄⠙⢶⣴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣶⣤⣿⠀⠁⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠌⠀⠀⣠⣤⣌⡙⢿⣝⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠀⠁⠀⠀⠈⠀⠐⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢀⣠⡴⢺⡄⠀⠀⠡
⠀⠀⠀⠈⠀⠀⠀⠻⢦⣈⡙⣶⠈⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠐⣯⣡⡴⠛⠁⠀⠀⠀⢁
⠀⠀⠠⠀⠀⢀⣙⣳⣦⣌⡉⠁⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠶⣖⣺⠿⠋⠀⠀⠀⠄
⠀⠀⠆⠀⠀⠠⣭⣽⣯⣍⡉⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠐⢋⣁⣤⣞⡁⠀⠀⠰
⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⣰⣶⣶⣷⣶⣶⠀⣴⣶⣿⣶⣦⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠁⠀⠀⠀⡆
⠀⠈⠀⠤⣶⣶⣤⣤⣀⣀⣀⣠⣀⡀⠀⠀⡄⠀⠀⠀⢀⠀⢸⣿⣿⣿⡏⣿⣰⢿⣿⣿⣿⡿⣇⠀⢀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣀⣿⣃⡼⢻⣿⣿⡇⠿⠟⣸⣿⣿⣿⣧⠹⢆⣿⣇⠀⠀⠀⢸⡇⠀⠠⣤⣀⣴⣶⣄⢀⣠⣴⡟
⠀⠀⠀⠀⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠃⠀⠀⣿⣿⣿⡇⢸⣿⢿⡇⠀⠀⠿⣿⠿⣿⠿⢀⣾⣿⣿⣆⠀⠀⢸⠁⠀⠀⠙⠻⢿⣿⣿⣿⣿⣋⡀
⠀⠸⠀⠀⠀⠀⢹⢘⡀⠀⠈⢹⠉⢿⠂⠀⠐⡀⠀⠉⣿⡏⠀⢸⣿⢸⡇⠀⠀⠀⣿⠀⣿⠀⠀⠼⣿⣿⠈⠀⢀⡿⠀⠀⠀⠀⠀⠀⠈⠙⠛⠙⠛⠁⠀⠀⠇
⠀⠀⠆⠀⠀⠀⠘⠘⠃⠀⠀⠊⠀⠘⠀⠀⠀⠱⡀⠀⡇⡇⠀⢸⡿⢸⡇⠀⠀⠀⣿⠀⣿⠀⠀⠀⡇⡇⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢠⡿⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⣶⣦⣤⣾⠿⠃⠀⠀⠀⠀⠀⠂
⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⠃⠀⠀⠀⠀⠀⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠹⣿⣿⠂⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠠⣶⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⢤⣤⣀⣀⣀⣀⣤⣤⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣇⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⢨⣿⣿⣧⡀⠀⠀⠀⠀⠀⢰⣤⣦⠀⠀⠀⠀⠉⠉⠁⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢀⣿⣿⣿⣿⡆⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⣼⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⠀⣀⡀⠀⠀⠀⠢⠜⣻⠿⠿⢿⠃⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⢸⣿⣿⣿⡿⠃⠀⠀⠀⠀⠉⢙⣿⣧⣴⣶⣶⣄⠀⠀⠈⣿⣿⣷⣄⣀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⢿⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⡏⡯⢸⡿⠀⠀⠀⠘⠿⣿⡿⣿⡏⠀⠀⠀⠀⠀⠀⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠄⡀⠀⠀⠀⠀⠀⡏⠀⡷⠁⠠⠀⠀⠀⠀⠀⣀⡿⠀⣸⠆⠀⠀⢀⡠⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠄⢀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢴⣶⣶⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡀⠀⠿⠇⠀⣸⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⢴⣶⣶⣶⣶⡆⠀⠀⠀⠀⠉⢁⣴⣶⣶⣄⠉⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇⣰⣿⣿⣿⣿⣦⣽⣿⣿⣯⣴⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣿⣿⠟⣛⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣾⣿⣿⢟⣵⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢀⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠸⡿⢿⣿⣿⣿⣿⣿⣿⣡⣶⡎⣿⣿⣿⢰⣿⣿⣆⠀⠀⢰⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⢻⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣧⢸⣿⣿⡿⠀⠀⢸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⡎⠻⠟⠁⠀⠀⠈⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⣿⣿⡏⣾⣷⣿⣿⢿⣿⣿⣿⣿⢫⣶⣶⡝⣿⠁⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢿⣿⣿⣿⣮⣙⠿⣿⡇⣹⣿⣿⡇⢾⣿⣿⡧⠀⠀⠀⣴⣿⣿⣿⣿⣷⡀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⡘⢿⡿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⢿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣭⣿⣿⣿⣏⠻⠿⠛⠋⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠟⠛⠋⠉⠛⠻⠿⠿⠿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣄⢀⣠⣴⣶⣿⣿⣿⣷⣦⣄⣀⣴⣶⣤⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡷⠊⠄⠡⣸⢹⣿⣿⡿⢟⡿⠿⠿⠿⠋⢀⣈⣉⣛⣶⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠉⠀⢀⣠⢶⠥⡄⠈⠀⠀⠉⠉⠀⠀⡠⡺⠉⣀⣀⣀⡧⢃⢬⡹⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⣿⢁⡀⢀⠔⠁⠘⠷⠖⢡⠚⡕⠦⣀⣀⠀⠫⣦⣔⠉⢠⡪⣉⠹⠞⠟⢤⣁⠀⢈⠓⣄
⠀⠀⠀⠀⠀⠀⣴⣿⠋⠰⢙⣓⣶⣥⣤⣤⣤⣄⡀⠀⠣⣀⣀⡀⠀⡈⠗⡄⠀⠀⠘⣛⣷⣤⣤⣤⣤⣌⣳⡀⠀⢈⢇
⠀⠀⠀⠀⠀⠀⡿⠁⣠⣾⣿⣿⡿⢿⠿⠉⠙⠛⠻⢿⣦⣄⡉⠉⣑⣢⠛⣁⣤⣶⠿⠟⠛⠹⠿⠿⠿⣿⢿⣷⣌⣠⡼⣦⣄
⠀⠀⠀⠀⠀⢠⠃⣴⣿⣿⣟⡕⠋⠀⠀⠁⠁⠀⠀⠀⠀⠙⠻⠿⣶⣾⠿⠛⠉⠀⠀⠀⠀⠀⠁⠀⠈⠑⢟⢿⣿⣿⡄⢹⣿⣆
⠀⠀⠀⠀⣠⣾⢰⣿⣿⠉⠀⢀⠔⢒⣩⣉⣉⣉⣒⠂⠤⢄⣀⣄⣤⣄⡀⣀⠠⠤⢒⣂⣉⣛⣋⠉⠒⢤⠀⠈⢿⣿⣿⠈⣿⣿
⠀⠀⠀⠀⣿⣯⢸⣿⣿⡄⠀⢸⡀⢻⣿⣿⣿⣿⡿⠿⠿⠷⣖⣻⣿⣿⣟⡲⠿⠿⠿⣿⣿⣿⣿⠗⢀⣤⣇⠀⢸⣿⣿⠀⣿⠟
⠀⠀⠀⠀⢻⣿⠈⣿⣿⡟⡄⠀⠙⠒⠬⠥⠤⠤⠄⠒⠊⠉⠀⣠⣶⣦⡄⠈⠉⠒⡒⢤⠤⠴⠶⠞⠛⢹⡙⠱⣼⣿⡟⢠⠃
⠀⠀⠀⠀⠀⠙⣧⣈⢿⣿⣮⣀⠀⣠⢄⠐⡰⠀⠀⣀⣤⣶⣿⠿⠛⠛⢿⣷⠖⠉⣉⠌⣹⠀⠀⠀⠠⢘⡄⠀⣿⠟⠀⣾
⠀⠀⠀⠀⠀⠀⠻⢧⠟⢏⠻⢿⣿⡇⠒⠑⢶⣾⣿⠿⠛⠋⣡⣤⠄⢏⣑⣀⣀⣠⠴⣾⣷⣶⣶⣶⣾⣿⢀⢀⠃⢀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣷⣌⠓⠤⣈⠫⣦⡀⠀⢀⠠⠱⡀⠘⡟⠜⡇⠀⠈⠉⠀⠀⠠⣞⡭⠧⠀⠀⢠⣧⣵⡯⣠⣿⣟⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⣃⠇⠈⠺⢵⣖⣜⣊⠀⢞⣁⡡⠃⢀⣀⡀⢀⣶⠤⣀⢤⠠⡀⠀⠀⢈⡥⠊⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠶⢤⣀⠀⣴⣶⢶⣤⡀⠀⠀⠀⢧⡌⠍⠁⠀⠉⢀⡠⢚⣀⣤⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠷⠺⣤⣬⣯⣀⣀⣀⣀⣉⣁⣶⣾⣿⣷⣾⣿⠟⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⠟⠁⠙⠿⣽⣿⡿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠠⣾⣿⣿⣧⡀⠀⢀⣀⣀⣀⣀⣀⡀⠀⢀⣼⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣦⠀⠀⠀⠈⠁⠈⠛⣡⣾⣿⣿⣿⣿⣿⣿⣿⣷⣌⠛⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⢫⡝⣿⣿⣿⣿⠿⢛⣡⣾⣿⣿⣿⣿⣿⠸⣿⠏⣙⠻⣿⣿⣿⠟⣋⢹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣌⣛⣃⣼⣿⣧⣚⣛⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⣿⣿⣏⣤⣻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⡟⣋⣙⣋⣴⣬⠙⢻⣿⢻⣿⠟⣿⡟⠋⣵⣦⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣄⠻⠿⣿⣟⢱⣿⣌⣉⣌⣉⣀⣉⣡⣿⡎⣻⣿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠉⠉⢿⣿⣿⣿⣿⣄⠿⠟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⣀⣀⣤⣶⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠒⢶⣶
⠀⠀⠀⠀⠀⠀⠰⣀⣤⣶⣾⣿⣷⣶⣤⢤⣴⡟⠁⠀⠀⠀⠀⠀⠊⣀⡀⠀⠀⠳⣄⠀⠀⠀⠀⣀⣴⣿⡿⠇⠁⡌⠁
⠀⠀⠀⠀⠀⢀⣀⢈⣿⡟⢿⣿⠛⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⣠⣏⣷⣶⣦⣾⣿⡿⠟⠁⠀⠂
⠀⠀⠀⠀⠀⢾⣿⠄⢿⣇⣴⣿⣾⣿⢟⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣻⣿⣿⣿⣿⣿⣿⣧⣤⣄
⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣧⢸⣿⠿⠿⠏⠂⠀⠀⡄⠀⠀⠀⣠⠀⠀⠈⠛⠿⢿⣷⣾⣻⣿⣿⣿⠿⠛⠉
⠀⠀⠀⣀⣀⣀⣀⣀⣀⡈⠓⠚⠁⠀⠀⠀⠀⠀⠀⢻⡄⣧⣐⣇⡀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣉⣀⣀⣠⣤⣄⣀⣀⡀
⠀⠙⠻⢿⣿⠟⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀⣀⣀⣀⣟⣿⣿⣿⣄⣀⣀⣀⣤⣴⣶⣿⣿⣿⣿⡿⣿⣿⣿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠚⠙⠋⠩⠝⣼⠿⠿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⠏⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡠
⠀⢀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠿⣍⠉⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢀⡄
⢀⣿⠀⣷⠀⡎⠀⠀⠀⣦⠀⠹⣾⡇⠀⠀⠀⠁⠘⠡⢙⠣⣿⡿⠋⠋⠀⠀⠀⡼⠀⠀⠀⣄⠀⣴⡇⠀⡄⣴⣿⡀
⠸⣿⢰⣏⣤⡇⣘⣠⠀⠘⣷⣴⣿⣷⣤⠠⣄⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⢀⣧⣿⣀⣴⣿⠀⢿⣹⣦⣿⣿⣿⣿⡷
⠀⢻⣤⣿⢹⣧⣽⡏⠀⠀⢿⣯⣽⣿⣿⣶⡿⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢼⣿⣿⣿⣿⡟⠀⠈⣛⣿⣿⣿⣿⣿⠁
⠀⢀⣿⣭⣼⣿⣿⡁⠀⠀⠀⠀⠀⠀⠈⠀⠀⡠⠶⣿⣤⣴⣿⣿⣿⡿⢦⣀⠀⠈⠉⠉⠉⠉⠀⠀⠉⠛⠛⠛⠋⠉
⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣰⣤⣿⣿⢛⣻⣿⣿⣿⣻⣶⣤⣾⣷⢳⡄⠀⠀⠀⠀⣴⢶⣞⡶⣶⣄
⠀⠀⢀⣤⡀⣿⠛⢿⣿⣾⡀⠀⠀⠀⢀⡼⣿⠛⣿⣿⣯⠙⡏⢹⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⣾⡿⠟⠞⡷⢻⣿⡆
⠀⠀⠘⢿⣿⣿⣦⣿⣿⣿⣇⠀⠀⠀⢸⡇⣻⣿⣝⣓⣽⣶⣷⣾⣿⣿⣿⣿⣿⣿⣾⠂⠀⠀⢿⡧⢼⣿⣿⠧⣿⡇
⠀⠀⠸⣿⣉⣭⣯⣿⣭⣿⡿⠀⠀⠀⠻⠿⢻⢿⡉⡿⣶⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⠁⠀⠀⠘⣷⣶⡧⣿⣾⡿⠁
⠀⠀⠀⠉⠛⠀⠿⠺⠟⠋⠀⠀⠀⠀⠀⢴⣶⣿⣥⣶⣿⠯⠘⢿⣿⣻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢛⡟⠹⡽⣿⣰⣖⣼⡿⣿⠟⣻⠛⢁⣴⢾⣖⡒⣶⣿⣷⣄
⠀⠀⠀⠀⠀⢠⣿⠀⣦⠴⢶⣴⣠⣷⠀⠀⠈⠛⠛⢗⢤⡩⡏⠉⠈⠋⠅⠀⣠⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠸⣿⣼⡿⣦⣾⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⡉⠈⠙⠛⠛⣋⣭⣿⣿⡇
⠀⠀⠀⠀⠀⠘⣿⣿⣧⣴⣾⣿⣿⣟⠀⠀⠀⠀⠀⠀⢠⣴⣾⣷⣤⡀⠀⠀⠈⠋⠛⠛⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠘⠻⠿⣿⣾⣿⠿⠿⠛⠁⠴⠶⢦⣠⣾⣿⠋⠹⢿⣿⡿⣆⡶⠗⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠄
⠀⠀⠰⣄⡀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠠⣿⣻⠟⢛⡟⡼⣿⠟⢳⣿⣇⡀⠀⠀⠀⢠⡇⢀⡄⠀⠀⢀⡟⠀⣷⡀
⠀⠀⢰⣆⣿⣶⣾⣿⣶⣿⣟⡀⠀⠀⠀⠐⣿⣦⣅⠙⢠⡴⢻⣤⣈⣿⣿⣿⡷⠀⠀⠀⣼⣧⠈⢠⣶⢶⣾⣿⣀⣿⡇
⠀⠀⣺⣿⣿⣿⣯⣿⣿⣿⣿⡇⠀⠀⣀⣴⠋⢱⠺⢿⣯⡽⣻⣭⣿⣿⣿⣿⣧⣀⠈⠀⢹⣿⣷⣿⡷⢼⣿⣿⣿⣿⠁
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢻⣿⡆⠀⢷⢶⣽⣿⢿⣛⣿⣿⡿⠀⣼⡿⠀⠀⠸⣿⣿⣏⣵⣾⣿⣿⣿⡿
⠀⣠⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣆⠀⠈⠻⣿⣄⠀⠑⢭⣿⣾⡭⠾⠃⢀⣴⠟⠀⠀⠀⢀⣽⣿⣷⣝⣿⣿⣿⣿⣥⣤
⠀⠙⠛⠛⠿⠿⠿⣿⠿⠟⠛⠉⠉⠀⠀⠀⠙⠛⠷⠤⣤⣤⣤⡤⠤⠖⠛⠁⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⡿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⣿⣦⣰⣤⣞⣠⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠙⠿⢿⣿⣿⣿⡿⠛⠁⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠙⠻⡿⠁⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⢰⡆⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠙⠃⣀⣽⣿⣁
⠀⠀⠀⢠⡀⠀⠀⠀⠀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣤⣾⣿⣄⣤⡟⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡆
⠀⠀⢠⣿⣷⠀⠀⣤⣾⣿⡏⢰⣶⠀⠀⠀⠀⠘⢷⣶⣾⠟⣿⣿⣿⣭⣿⣧⣤⡶⠊⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⡧
⠀⠀⠈⣿⣿⣿⣶⣿⣿⣿⣧⣾⣧⠀⠀⠀⠀⣀⣠⣿⣿⣶⣿⡿⠉⢻⣿⡿⣿⣀⣀⠀⠀⠀⠀⢸⡇⣾⣿⣿⣿⠸⣿
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠉⠉⠙⠛⣿⣿⠛⣿⣿⣶⣿⣿⣿⡟⠉⠉⠁⠀⠀⠀⢸⡅⣿⣿⣿⣿⡇⣿
⠀⠀⠀⠀⠈⢙⠋⢋⠉⢻⠻⠋⠀⠀⠀⠀⠀⢠⠾⠿⢿⣷⣿⣿⣏⢉⣿⠿⠿⣦⠀⠀⠀⠀⠀⠈⠀⣿⣿⢿⣿⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠻⣿⡟⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢧⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠙⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⢀⡜⠀⢸⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠘⡇⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣴⡔⠋⠀⠀⠀⠀⠘⠃⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣥⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⢿⠛⠛⠛⢻⡿⡟⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉⠘⠙⠉⠛⠘⠙⠉⠃


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠂⠈⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠁⠐⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢸⠀⠀⠙⢻⣿⣿⣿⣿⣶⣤⣤⣶⣶⣶⣤⡑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⣄⠀⠀⣤⣶⣦⡀⠀⠀⢀⣤⣾⡏⠀⠀⠀⢸⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠻⣿⣶⣿⣿⣿⣿⣶⣾⣿⣿⠋⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣷⣶⣤⡄⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⢹⡌⡇⠀⠀⠉⢹⡏⠹⡿⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⢠⠧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠙⠇⠙⠟⠋⠀⣀⠠⠤⠤⠄⠠⠀⢀⠀⠀⠸⠇⣷⠀⠀⠀⠸⠃⠀⣿⠀⠀⠀⠀⢀⡤⠛
⠀⠀⠀⢠⠃⠀⠀⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠈⠄
⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⢀⡠⠖⠋⠁⡀⠀⣠⡆⠀⠀⠈
⠀⠀⡘⠀⠀⢀⣤⣄⠀⠀⢠⣶⣶⠀⠉⠲⢤⠄⠀⠀⠀⠀⢠⣾⣿⡆⠀⠀⠀⣴⣶⣦⠀⠀⠀⠀⠀⠀⠱⡤⠒⠉⠀⠀⠀⠀⣷⣠⣿⠇⠀⠀⠀⢀
⠀⢀⠁⠀⠀⠘⠿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠎⠀⠀⠀⠀⢀⣈⣛⣟⣁⣀⠀⢀⣙⣿⣛⡀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⣙⣿⠏⠀⠀⠀⠀⠈⡀
⠀⠘⠀⠀⠀⠀⠀⠸⣿⣿⣿⡏⠀⠀⠀⡘⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⣿⢀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢀⣠⣼⣿⣿⡆⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⠀⠀⠀⠁⠀⠀⠀⣴⡄⣸⢼⣿⣿⡇⣿⣾⢹⣿⣿⣿⡏⢷⠀⣴⡄⠀⠀⠀⢸⡀⠀⠈⠻⢿⣿⣿⣯
⠀⠀⠀⠀⠀⡄⠀⢸⣿⣿⣿⣿⣇⠀⠀⡀⠀⠀⣶⣿⣷⡎⢸⣿⣿⡇⠉⠁⣾⣿⣿⣿⣿⠈⣱⣿⣷⡀⠀⠀⢸⠃⠀⠀⠀⣾⣿⣿⣿⣧⡀
⠀⢠⠀⢠⠎⠀⢠⣿⣿⣿⣿⣿⣿⡆⠀⢀⠀⠀⠻⣿⡿⠃⢸⣿⢹⡇⠀⠀⠉⣿⠙⣿⠉⠰⢻⣿⣿⠓⠀⠀⣼⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⡄
⠀⠈⡀⠘⠦⣤⠼⠿⣿⡿⠿⣿⡿⠃⠀⠀⢆⠀⠀⡏⡇⠀⢸⣿⢸⡇⠀⠀⠀⣿⠀⣿⠀⠀⠘⣟⡏⠀⠀⣰⡏⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣤⠀⢀⠁
⠀⠀⠁⠀⠀⠀⠀⠘⠉⠀⠀⠀⠉⠁⣀⠤⠚⢆⠀⠃⠃⠀⠘⠋⠘⠃⠀⠀⠀⠛⠀⠛⠀⠀⠀⠋⠃⠀⣰⠟⠢⣄⠀⠀⠐⠿⠿⣿⣿⡿⠏⠁⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁⣠⣀⣤⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠐⡀⠀⠀⢀⡤⠖⠉⠀⠀⠀⠀⢸⣿⣿⡆⠀⠑⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢞⣁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⣀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⣴⠊⠁⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣷⠀⠀⣀⡀⠈⠙⠒⠒⠲⡶⠶⠒⠛⠉⠁⢠⣿⣯⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠃
⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣾⣿⣿⣦⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⣿⣿⣧⣀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⡟⢿⠀⠀⠀⠀⢀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⢿⠛⣿⠛⡇⢸⣿⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⡏⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⢸⠀⢸⣰⠃⠈⡇⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣟⠀⣹⡄⠀⢀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⡀⠚⠀⠸⠁⠀⠀⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢁⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣷⣄⠀⠀⣸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⡀⢸⣿⣿⣿⡀⢰⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⣿⡀⣿⣿⣿⡏⣇⠏⣾⣿⣿⣧⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡛⠁⣿⣿⡇⠈⠀⢹⣿⠇⠈⣿⣿⡧
⠀⢀⣤⣤⣶⣦⠀⣤⣤⣾⠆⠀⠀⠀⠀⢸⣿⠀⠀⣿⢿⠇⠀⠀⢸⡿⠀⠀⣿⣿⠀⣀⡀⠐⠻⣿⣿⣿⣿⣶⢀⣀
⠀⢈⣿⡛⣻⡘⠈⣟⠉⣟⠀⣼⡟⣟⢁⣸⣏⣀⣀⣿⣿⣀⣀⣀⣸⣇⣀⣀⣸⣇⣀⣻⣿⣤⣴⣙⡏⠉⢛⣿⡌⣿⠛⣷⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⣿⡿⡿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣷⣯⣶⣯⣶⣦⣯⣷⣿⣭⣼⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⡀⡀⡠⢠⣶⣾⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠙⠿⢿⣿⣿⣿⡿⠛⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠁⠀⠀⠀⠀⠙⠻⡟⠀⠀⠀⠀⠈⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⢠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⡀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠙⠀⣸⣿⣁
⠀⠀⠀⢠⡄⠀⠀⠀⣶⣦⠀⠀⠀⠀⠀⢀⣀⣸⡷⣿⣷⣿⣁⣀⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡄
⠀⠀⠀⣿⣿⣀⣰⣾⣿⡇⣸⡇⠀⠀⢀⣀⣹⣿⣿⡋⣻⣿⢿⣯⣀⡀⠀⠀⠀⠀⢸⡟⣿⣿⣿⢻⡇
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⣹⣧⣿⡿⢿⣿⣾⣯⡁⠀⠀⠀⠀⠀⢸⢣⣿⣿⣿⣸⡇
⠀⠀⠀⠀⠙⠻⠻⠛⢻⠿⠋⠀⠀⠀⠀⠈⠁⢸⡿⢿⡿⢿⡇⠀⠉⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⠇⠁
⠀⠀⠀⠀⠀⠈⠀⠁⠈⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⣿⠘⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣷⠂⠀⢀⠔⠁⠀⠀⠺⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠹⣿⣿⣿⣿⣿⣿⣿⡿⠛⠐⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⠻⠛⠛⠉⡿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⠃⠓

⠀⠀⠀⠀⠀⠀⣹⢃⣤⣀⣤⣀⣤⣀⣤⣰⡆⣠⣠⣄⠀⣿⢳⢨⢀⣄⢠⣄⢠⣄⣠⡄⣠⡄⣤⡀
⠀⠀⠀⠀⠀⠠⣯⠸⠿⠻⡾⠿⠿⠿⡼⠛⠇⠿⠻⡴⠀⢿⠼⠸⠨⡷⠺⡭⠸⠿⠬⡷⢯⠅⢽⠆

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⠀⢀⣀⠀⣀⣀⠀⢀⠀⠀⢀⣀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣷⠈⣿⠐⠿⣭⡀⡿⠭⢀⣟⣧⠐⠿⣭⡐⡯⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠘⠛⠈⠛⠋⠀⠛⠛⠘⠁⠙⠉⠛⠋⠀⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠄⠄⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠒⠤⠠⠄⠠⠔⠀⠀⠀⠈⠠⠔⠀⠀⠀⠀⠀⠄⠈⠁⣀⠂⠀⠀⠀⠀⡸⠀⢈⠃⠀⠀⠀⠁⠀⠚⠀⠂
⠀⠀⠀⠀⠀⠀⠠⠀⠂⠐⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠂⠐⠀⠀⡠⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⠀⠀⡰⠀⢀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠁⠀⡁⠀⠀⠀⠀⠚⠙⠂⠀⠀⠀⢀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠑⠃⠀⠀⠀⠀⠀⠠⡒⠢⠀⠁
⠀⠀⠀⠀⢀⡄⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⠀⠠⠄⠀⢀⠀⠀⠀⠠⠀⠄⠀⠀⠐⠀⠀⣄⡃⠀⠒⣁⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⢴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠒⠂⣀
⠀⠀⠀⠀⠀⠑⣀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⢠⠀⠀⠀⠀⠀⠘⠞⠀⠀⠀⠀⠀⠂⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⢠⠈⢰⡯⢗⠀⠀⡠⠂⠒⢒⠂⠀⠀⠀⠈⠉⠀⠀⠐⢂⠀⠀⠀⠂⠀⠈⠈⡣⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⢤⠀⠀⠀⠀⠴⠄⢀⠠⠄⠀⠀⠠⢰⢔⠤⣆⡄⠀⠀⠀⠀⠄⡄
⠀⠀⠀⠀⢰⢀⠀⠈⠀⠈⠀⠀⢠⠄⠀⠂⠙⠀⠀⠀⡔⢉⠠⠈⠀⠈⠀⠀⠓⠪⠄⠬⠝⠊⠀⠀⠀⠀⠀⠀⠍
⠀⠀⠀⠀⠰⡀⠀⠈⡀⠀⠀⠀⠐⠀⠀⠂⠁⠀⠀⠀⢢⡀⠀⢀⡀⠀⠀⠀⠖⣯⢉⣁⣤⢐⠀⠀⠐⣭⠉⢁⡀⡂
⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⡀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⣴⡦⢠⢫⡋⡄⠍⣙⢄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣰⠃⠈⠙⠓⠃⠃⠛⠀⠙⠘⠂⡀
⠀⠀⠀⠀⣴⡋⠉⠣⠈⠁⠀⢀⡠⠐⠒⠀⠀⠀⠀⠀⠀⠀⠁⣠⢄⡀
⠀⠀⠀⣼⣿⣇⠂⠀⡄⠀⡀⠁⠀⣴⣶⣦⣶⡎⠀⠀⠀⠀⡌⠁⣶⣿⣦
⠀⠀⠀⣿⣿⣿⣄⣀⡇⠀⠆⠀⣾⣿⣿⣿⣿⡇⠀⠀⠀⢸⠀⠈⣿⣿⣿⡇
⠀⠀⠀⢿⡿⠃⠀⣸⣗⡄⠇⠀⠾⣿⣿⣿⡿⠁⠀⠘⠀⠸⠀⠈⢽⣿⣿⡇
⠀⠀⠀⠘⣧⣀⣾⣿⣿⢱⡈⠄⠈⠉⠉⠟⠁⢀⡔⠁⠂⠀⢡⡀⠘⣿⣿⠇
⠀⠀⠀⠀⠈⢻⡿⣼⡇⣱⣋⣀⠀⠀⠂⠐⠊⠁⠀⠰⡄⢀⣾⣷⡤⠟⠁
⠀⠀⠀⠀⠀⠀⢻⣷⣇⠹⢭⠉⠀⠀⠀⠀⠀⠀⠰⠠⠔⢿⣿⠏
⠀⠀⠀⠀⠀⠀⠈⣿⣧⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣄⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣽⣟⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣮⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣷⣮⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣵⣿⣇⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⢻⣿⣷⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡇
⠀⠀⠀⠀⠀⠀⣿⣟⣛⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣰⡇
⠀⠀⠀⠀⠀⢠⣿⣟⣛⣋⡉⠁⠀⠀⠀⠀⠀⠀⠂⠀⠶⠦⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢸⣿⣋⣉⣈⣁⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠊⠀⢁⡡⣤⢍⣑⠢⡀
⠀⠀⠀⠀⠀⢸⣿⣯⠭⠴⠴⠄⠀⠀⠀⠀⠀⠀⠀⠈⣛⣒⠚⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠦⠀⡰⡹⠛⠽⠉⡛⢷⠈⢂
⠀⠀⠀⠀⠀⣿⡷⢶⡶⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣛⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢨⢾⠃⢘⠀⣥⡃⠆⣬⣲⣼⢰⣧⢸
⠀⠀⠀⠀⠀⣻⣿⣿⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⡳⠞⠀⣆⢃⡋⠾⠓⢟⡼⡍⡼
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠛⠛⠃⠀⠠⠄⠀⣤⣤⣀⣀⣬⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡀⠀⠈⠛⠭⣶⠦⠥⢊⠔
⠀⠀⠀⠀⠀⣿⡿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠤⠀⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠒⠀⠀⠉⠉⠉⠉⠉⠁⠀⠐⠒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠁⠀⠀⢀⣤⣄⠀⣠⣶⣦⡀⢰⣦⢠⡄⠀⠀⠀⠀⠉⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⢠⣴⣿⠀⢾⡏⢻⡇⢿⣇⣿⡇⣾⣿⣿⠇⣼⡟⣿⡆⢀⣀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⡠⠚⠀⠀⣀⣀⠀⠀⠀⣿⣠⡜⠿⠾⠃⠈⠛⠛⠀⠛⠘⠿⠀⣿⣴⡿⠁⣿⡛⢃⣤⡀⠀⠈⠢⡀
⠀⠀⠀⠀⢀⠔⠀⠀⡀⠈⢳⡌⢷⡀⠀⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠿⠿⣡⣾⣯⠛⣀⡀⠀⠑⢄
⠀⠀⠀⠠⠃⠀⢀⣤⡙⠳⣄⣙⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣄⣸⡟⠟⠀⠀⠀⠢
⠀⠀⡰⠁⠀⣀⣈⠳⢿⡶⠌⠁⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠒⠀⠐⠂⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⢀⣠⣤⡀⠀⠡⡀
⠀⠰⠁⠀⠀⢯⣍⡙⢦⠉⠀⠀⠀⠀⠀⠀⡠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⡀⠀⠀⠀⠀⠀⠀⢾⣋⡥⠞⠁⠀⠀⢱
⢀⠃⠀⢀⣙⣲⣬⣉⠉⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⣠⣤⡄⠀⠀⠀⣠⣄⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠶⣖⡾⠟⢃⠀⠀⢃
⠘⠀⠀⠰⠮⠿⠿⡍⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠻⣿⠏⠀⠀⠘⣿⡿⠃⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠘⣩⣤⣶⣭⡀⠀⠘
⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣿⢿⣿⣿⡿⢠⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢧
⡇⠉⣿⣿⣿⣷⣶⣶⣶⣶⣄⠀⠘⠀⠀⠀⣤⠀⣿⢸⣿⡟⣷⡾⣸⣿⣿⡇⢣⠀⣤⠀⠀⠀⢸⠀⠀⠀⠀⢀⣄⠀⠀⢀⣰⠆
⡇⠘⠛⢻⣿⣿⣿⣿⣿⣿⣿⠀⢠⠀⠀⣰⣾⡖⠉⢾⣿⡟⠉⢠⣿⣿⣿⣿⠈⡴⣿⣆⠀⠀⢸⠀⠀⠙⢷⣿⣿⣷⣶⡿⠋
⠃⠀⠀⠀⢿⢻⠉⠉⢻⠟⣿⠀⠀⠆⠀⠙⣿⡟⠀⣿⢸⣿⠀⠀⢸⡇⣿⡁⠈⣿⣿⡇⠀⠀⡾⠀⠀⠀⠀⠈⠙⠿⠟⠿⠟
⢠⠀⠀⠀⠚⠘⠀⠀⠘⠀⠘⠀⠀⠘⡄⠀⣿⡇⠀⣿⢸⡿⠀⠀⢸⡇⢿⠅⠀⢸⣿⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠆⠀⠀⠀⠀⠀⠀⠀⢲⣰⡇⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠰⣷⣶⣾⠟⠀⠀⠀⠀⠀⠆
⠀⠈⡀⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠀⠀⠀⠀⠀⠈⣿⣿⡁⠀⠀⠀⠀⡘
⠀⠀⠐⡄⠀⠀⠀⠀⠻⣿⣿⡀⠀⠀⠀⠀⠀⢀⢀⠉⠛⠒⠶⠶⠶⠶⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⡀⢰⣿⣿⣧⠀⠀⠀⡔
⠀⠀⠀⠘⢄⠀⠀⠀⠰⣿⣿⣿⡄⠀⠀⠀⠀⣹⣿⡇⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⢈⣀⣾⣿⣿⣿⠇⢀⠜
⠀⠀⠀⠀⠈⠢⡀⠀⢸⣿⣿⣿⡷⠀⠀⠀⠀⠛⢿⣿⣀⣤⣤⡀⠀⠀⢿⣿⣦⡀⢀⣾⣷⠀⠀⠀⠀⠈⠉⠀⠉⡠⠊
⠀⠀⠀⠀⠀⠀⠈⠢⡀⠈⠉⠉⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⢻⠇⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⢸⡏⡟⡿⢸⠿⠀⠀⠈⠻⣿⠿⣿⠁⠀⠀⠀⠀⢀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠨⠁⡱⠁⠘⠀⠀⠀⠀⢠⠿⠠⠾⠀⢀⡠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⢄⣀⣀⣀⣀⣀⣀⣀⣀⠄⠐⠂⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠠⢤⢠⣠⠀⣤⢠⣤⢠⠠⡤⢤⠀⣤⣤⢠⣤⣤⢠⣠⢠⡄⠄⢠⢤⠠⢤⣠⠤⢤⡤⠠⣤⡤⡄⢤⠤⡄⠤
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠀⠉⠈⠈⠘⠘⠉⠉⠀⠉⠉⠈⠀⠉⠈⠉⠈⠁⠁⠁⠘⠙⠈⠙⠀⠈⠃⠘⠉⠊⠁⠉⠊⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⢻⡿⢿⣿⣿⢃⠀⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠈⠃⠀⠀⠙⠀⠀⠀⠀⠈⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣅⣀⣠⣴⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡄⣰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⣿⡞⢽⣿⡟⡀⣠⡖⠀⠀⠀⠀⠀⠀⢀⣤⠁⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠆⠈⣿⠁⢸⣿⡇⠀⢹⣧⠀⠀⠀⠀⠀⠀⢸⡿⠿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⣿⡇⠀⠿⠀⠸⣿⠇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⠀⡄⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⠿⢿⡃⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⣀⠤⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁⠐⠢⢄⡀⠀⠀⣠⣤⣴⣿⡏⠁⠀⢀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠝⢻⠋⢹⠃⠀⠉⠁
⠀⠀⣤⣤⣦⣴⣤⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀
⠀⠀⠛⠋⠚⠋⠛⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠼⠧⠸
⠀⠀⠉⡟⢸⢹⠀⡏⡇⢸⣰⢢⡏⣧⢾⠑⢸⡋⠰⡏⠂⠀⡟⢳⢀⣿⠘⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠳⠐⣾⠃⡆⢸
⠀⠀⣼⡀⢸⣸⠈⡇⡇⡍⢹⡸⣇⡿⣄⣱⢸⣉⢀⣉⡆⠀⣇⣸⢸⠼⡆⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢹⠀⣿⠀⡟⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠉⠀⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠀⠁⠈

⠈⣇⠰⡀⢡⡊⠙⡆⢏⡕⠀⠃⠀⣿⠈⢢
⠀⠈⠀⠉⠈⠃⠀⠀⠃⠙⠀⠃⠀⠙⠀⠁
⢀⣤⣀⣀⣀⡀⠀⠀⣀⣤⣤⣀⠀⠀⠀⢀⣠⣄⣤⡀⠀⠀⣠⣀⠀⠀⢀⣤⠀⠀⢀⣠⣤⣄⡀⠀⠀⢀⣤⣤⣀⠀⢀⣤⣀⣀⣄⡀⠀⢀⣄⣠⡀
⠘⠀⠀⣠⡟⠁⢀⣾⠁⠀⠀⠙⣷⡀⢰⡟⠀⠀⠀⢻⣦⠀⢸⠻⣦⡀⠀⡇⠀⣰⡏⠀⠀⠈⢻⣆⠀⣿⡀⠀⠈⠀⠀⣸⠀⠀⠈⠁⠰⣯⡀⠀⠙
⠀⠀⣴⠟⠀⠀⢸⣧⠀⠀⠀⠀⣿⡇⢿⡇⠀⠀⠀⠀⣿⠀⢸⠇⠘⢷⣄⡇⠀⣿⡇⠀⠀⠀⠀⣿⠀⠈⠛⠿⣦⡀⠀⣿⠗⠒⠇⠀⠀⠉⠛⠷⣦
⢀⣾⣏⣀⣀⣴⠀⠻⣦⣀⣀⡴⠟⠀⠈⠿⣄⣀⣠⡼⠃⠀⣸⡆⠀⠀⠹⡇⠀⠘⢿⣄⣀⣠⡼⠃⠀⣧⣀⣀⡽⠃⢀⣿⣄⣀⣠⡆⠸⣧⣀⣀⡿

⠀⠀⠀⠀⠀⠐⠰⠀⠂⡆⠐⡄⠀⢤⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢲⠀⣶⠐⢦
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠁⠀⠈⠀⠀⠀⣀⠠⠄⠐⠒⠂⠉⠉⠉⢹⠉⠉⠉⠁⠐⠒⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠊⠃⠈⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢨⠀⠀⠶⣶⣿⣷⣶⣶⣄⣀⣀⣤⣤⣌⡑⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⣠⣾⡏⠀⠀⠀⢸⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⠢⡀
⠀⠀⠀⠀⠀⠀⡠⠊⠀⠸⣷⣦⣼⣿⣿⣿⣦⣤⣴⣾⣿⠟⠀⠀⠀⠀⢸⠀⠀⠈⠛⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣉⣀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢿⢹⡏⠙⠙⠻⢿⡿⢿⣧⠀⠀⠀⠀⠙⠄
⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⢿⡛⢿⣿⠟⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⣸⠀⡇⠀⠀⠀⣸⠇⢘⣏⠀⠀⠀⠀⠀⣀⣦
⠀⠀⢠⠏⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠄⠒⠀⠉⠉⠀⠈⠉⠀⠐⠂⠄⡈⠀⠁⠀⠀⠀⠉⠀⠀⠉⠀⠀⣠⡴⠚⠉⠀⠱
⠀⢠⠏⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⢀⡀⠀⠀⠡
⠀⡎⠀⠀⠀⠀⠀⠀⠀⢀⣤⣌⠓⢦⣄⠀⠔⠁⠀⠀⠀⢠⣴⣤⡀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠑⣄⣀⠤⠒⠉⠀⠀⢸⣆⢠⣿⡇⠀⠀⠀⠆
⢰⠀⠀⠀⣾⣿⣷⣶⣶⣿⡿⠟⠀⠀⠀⡟⠀⠀⠀⠀⠀⠹⣿⡿⠇⠀⠀⠐⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⢿⣿⡟⠀⠀⠀⠀⠰
⡀⠀⠀⠀⠀⠉⣿⣿⣿⣿⠆⠀⠀⠀⠸⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⢀⣶⣾⣿⣶⣦⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⣰⣾⣿
⡇⠀⠀⠀⠀⠀⠉⣿⣿⣿⡄⠀⠀⠀⡀⠀⠀⠀⣀⠀⣿⣽⣿⣿⡏⣯⣼⢻⣿⣿⣿⣿⣆⠀⣀⠀⠀⠀⠀⢿⠀⠀⠘⣿⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⡃⠀⠀⣸⣿⣅⠿⢻⣿⣿⡇⠿⠃⣿⣿⣿⣿⡇⠻⣈⣿⣃⠀⠀⠀⢸⠀⠀⠀⠀⣿⣿⣿⣿⡄
⡇⠀⢀⠜⠁⢠⣿⣿⣿⣿⣿⣧⠀⠀⠁⠀⠀⣿⣿⣿⠀⢸⡿⢿⡇⠀⠐⢿⣿⢿⣿⠿⢰⣿⣿⣿⡆⠀⠀⣿⠀⠀⠀⠰⣿⣿⣿⣿⣿⣄
⢁⠀⢏⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠘⠀⠀⢹⣿⡏⠀⢸⡇⢾⡇⠀⠀⢈⣿⢸⣿⠀⠀⢿⣿⡿⠀⠀⢰⡏⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿
⠘⠀⠈⠉⠉⠁⠽⠟⠉⠉⠛⠧⠀⠀⢀⣥⠀⢸⢿⠇⠀⢸⡇⢿⠇⠀⠀⠘⣿⠸⡿⠀⠀⠸⡯⡇⠀⢠⣿⡁⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⠗⠀⠸
⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠁⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠈⠓⠦⣀⠀⠉⠈⠛⠛⠉⠁⠀⢀⠃
⠀⠈⠄⠀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠀⣿⣾⣷⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠙⠲⣤⡀⠀⠀⠀⢀⡏
⠀⠀⠈⢄⣀⡤⠚⠉⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠉⠓⠶⢤⣄⣀⣀⣀⣀⣠⡤⠶⠛⢩⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣠⠏
⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣧⣀⣤⣶⣦⡀⠀⠀⠀⢸⠉⠁⠀⠀⠀⠀⢼⣿⣷⡀⠀⠀⣰⣶⡦⠀⠀⠀⠀⠀⠀⢀⠉
⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣴⣿⣿⣷⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣿⢿⡟⣿⣿⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡿⠁⠙⠀⠀⠀⣠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⣿⠈⡿⢸⠇⢸⡛⠆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⠛⢿⠃⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀⠀⠀⡏⠀⢡⠇⠀⠸⠇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠶⠇⠠⠺⠁⡀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠄⣀⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠒⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣐⣒⣀⣀⣀⣀⣸⣤⣤⣄⣐⣒⣒⣈⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠟⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠖⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠙⠛⠛⠛⠲⠶⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣯⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣽⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣿⢸⠈⢹⠉⠉⣻⠛⠛⠛⡟⠛⠛⢿⠛⠛⢻⠛⠛⢻⠛⠛⢹⡏⠉⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠙⢾⣦⣼⣄⣀⣽⣀⣀⣠⣇⣀⣀⣼⣀⣀⣸⣀⣀⣸⣄⣀⣼⣄⣤⣧⠾⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠧⠤⢤⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣁⡠⠿⣆
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⣼⠷⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣼⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠁⠀⠀⠀⠀⠘⠛⠛⣶⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣷⠀⠀⠀⠀⣴⠟⠛⠃⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠶⠶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠘⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡏⠀⣼⠋⠉⠉⠉⡏⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣴⠟⠀⠀⢿⣤⣤⣤⣤⣿⣤⣤⣤⠾⠁
⠀⠀⠀⠀⢀⣤⠶⠶⢶⣤⣤⣭⣍⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⡴⠶⢶⣤⡀
⠀⠀⠀⠀⣟⠀⠀⠀⡼⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠛⠁⠈⢹⣧⠀⢀⡼⠛⢶⣄
⠀⠀⠀⠀⠙⢦⣄⣀⣳⡀⠀⠀⢀⣰⠟⢀⣀⠀⠀⣿⠁⠀⠀⠙⣳⣦⣀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠙⢦⣠⡾⠋⠳⣮⡀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⢛⣻⣷⠞⠋⠉⢻⡄⠹⣦⡀⢠⠞⠁⠀⠙⢷⣄⠀⠀⠀⢿⡀⠀⠀⣠⡾⠋⠀⠀⠀⠈⠻⢦⣄⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠈⢧⠀⠀⣠⠟⠀⠈⠻⣧⡀⠀⠀⠀⠀⢹⡇⠀⠀⠈⠛⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣀⣼⠷⠛⠁⠀⠀⠀⠀⠈⠻⢦⣀⣀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣄⡀
⠀⠀⠀⠀⠀⠀⢠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣶⣶⣶⣶⡶⠶⣶⣶⣶⣶⡆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⡿⠿⢰⣇⠸⠿⣿⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣇⣛⢻⡿⢛⣃⣿⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣿⣿⣘⣃⣸⣿⣿⣿⡇⠀⠀⣿⡴⠖⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣡⣴⣾⠉⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣧⡴⠶⠶⠶⠶⣿⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠘⠷⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠹⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠙⠳⠶⠶⠦⠴⢿⣿⣿⣿⡿⠟



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠪⢒⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠊⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠁⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⠀⠀⠐⠒⠶⣶⣄⡀⠀⠀⠀⠀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⢽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠉⠻⢷⡂⠤⠒⠋⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⢼⡇
⢀⡄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣃⢸⣦⡀⠀⠀⠀⠀⢀⡠⠛⠲⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⡈
⡟⠁⠀⠀⠘⡄⠀⠠⠄⠀⠀⠀⠀⣻⠀⠈⠳⡀⠀⢠⠔⠁⠀⠀⠀⠀⠙⢄⢀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠁
⢹⡄⠁⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢳⣤⣶⣷⣦⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠁
⠀⢹⡄⢰⣄⢤⣼⡄⠀⠀⠀⠀⠀⣸⣽⡄⠀⣀⢀⠆⡶⣄⡀⢐⡤⠀⣀⣀⣨⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠃⠀⠀⠀⠀⠀⣰⠄
⠀⠀⢻⣿⣷⡈⢿⣿⡆⠀⠀⠀⣠⡿⠻⠃⠚⠉⠉⠈⠐⠋⠻⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⠟⢋⣡⣤⣶⠄⠀⢀⣠⡴⠞⠋
⠀⠀⠀⢿⣿⣷⡈⢻⣿⡄⠈⠈⠍⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠉⠉⠣⠛⡄⠀⠀⠀⠀⠀⠘⣧⣴⣾⣿⣿⣿⡿⠷⠛⠉
⠀⠀⠀⠈⢿⣿⣷⣼⠛⡇⢀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢼⠇⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⢸⡉⠀⠀⠀⠠⡙⣶⣤⡀⠀⠀⠀⣀⣀⡀⣠⡴⠔⠋⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⡀⢢⣼⠿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⣿⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣠⡀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡱⠂⠈⠛⢿⣿⣤⣌⠻⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠀⠈⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠚⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢆⠀⠙⠻⣿⣧⣄⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠁⠀⠀⠀⣸⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠀⢀⢂⢀
⠀⠀⠀⠀⢺⢆⡀⠀⠀⠀⠀⣀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⠀⠈
⠀⠀⠀⠀⠀⠢⣍⣿⣷⣏⣍⣇⡴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠀⠈⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠻⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⣀⡤⠖⢒⣶⣾⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠘⠁⢀⠤⠚⣛⡛⢟⣟⣻⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⡄⠀⠀⠀⠁⡰⠟⢛⣿⣮⣭⣧⣤⣤⣝⡲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢰⢱⣤⣆⡴⢊⠔⢺⣿⣏⡙⣿⣿⣿⣿⣿⣿⢦⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠛⢿⡴⠁⠀⠀⢻⠀⠀⢹⣿⣿⣿⣿⣿⡇⡟⢶
⠀⠀⠀⠀⢀⣠⡤⠶⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡷⠺⠤⠈⠷⡦⠾⠆⠀⣠⣿⣿⣿⣿⣟⡏⢱⣾
⠀⢀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⣤⣤⠄⠀⠄⠀⠘⠻⣿⣿⣿⣿⡟⠀⣾⡟
⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⣉⢿⣿⣀⠀⢀⠀⠀⡀⠀⠈⠙⣿⣿⣷⡦⠉
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠆⠀⠀⠀⠀⠀⠀⠻⢆⣿⡿⠋⠉⠁⠉⠁⢀⠀⠀⠘⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢈⠳⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠈⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈
⠈⠳⣦⣌⡉⠙⠛⠛⠛⠛⠛⢉⡉⠤⠀⡾⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠀⡀⠀⠀⠀⠐⡆⠀⠀⠀⢹⡤⡤⠐⠁⠀⠀⠀⣆⡀⠀⠀⠀⢸⠤
⠀⠀⠈⠙⠒⠷⠠⠀⠠⠈⠄⠄⠚⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠄⠀⠀⠀⢀⣧⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣦⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠐⢶⠶⠆⠀⠠⠀⠀⠀⠀⠙⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠂⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⣶⡀
⠀⠀⠀⠀⢀⠤⢲⠉⠽⠍⢵⡒⡄⠀⠀⠀⠐⣼⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⢦⣵⣶⣾⡴⢛⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⣿⡿⠁
⠀⠀⠀⡰⢩⠊⠁⠀⠀⡠⢄⠀⠀⠀⠀⠀⠀⠘⣆⠘⢆⡀⠀⠀⠀⠀⠀⠀⣤⠭⣿⣿⡿⣟⣿⠭⠴⠀⠀⠀⠀⠀⠀⡠⣿⣟⡿⠁
⠀⠀⠐⠥⠃⠀⠀⢀⠔⡥⠃⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠉⣷⣀⠀⠀⠀⠀⠀⢒⡹⢿⣷⣿⢿⣑⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉
⠀⠀⠀⠀⠀⠀⣆⡱⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠙⠕⠆⠀⠀⠀⠀⠀⠙⠁⠃⣼⠘⠀⠉⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⢠⠔⣉⠉⢉⡙⠢⡀⠀⠀⠀⠀⠀⠀⠀⣱⠟⣻⡇⠉⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢽⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢄⡀
⠀⠀⢠⠃⣠⠘⠂⠋⠀⢦⢹⠀⠀⠀⠀⠀⠀⣴⢋⡶⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢊⣥⡶⢂⠇
⠀⠀⠸⡄⢁⣠⠈⠉⢁⡀⢸⠀⠀⠀⠀⠀⠀⣇⠎⢰⢀⣘⠂⡄⠀⠀⠀⠀⠀⠀⢿⠀⢸⡇⠁⠀⠀⠀⠀⠀⡰⢊⡵⣞⠽⠒⠉⠁
⠀⠀⠀⠑⢤⡀⠰⠃⣚⡴⠋⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⡗⠠⠀⠀⠀⠀⠀⠀⠈⠒⠿⠁⠀⠀⠀⠀⠀⠀⠳⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠹⠇⠀⠁

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠆
⠀⠀⠀⠰⣤⠞⠋⠉⠙⠺⡅⠀⠀⠀⠀⢠⣿⣿⣧⠀⡠⠔⠊⠙⠆⠀⠀⠀⠀⣾⡿⠘⢛⡛⣦⡀⠀⠀⠀⠀⣠⡀⣰⣶⣾⣶⣦⠄⠒
⠀⠀⠀⢸⠃⠀⠀⢀⡀⠆⣿⠉⠀⠀⠀⠀⣿⣿⣿⠎⠀⢀⡀⢤⠇⠀⠀⠀⢰⣿⠋⣾⣿⣿⢈⣏⠀⠀⠀⠀⠉⢹⣿⣿⢛⣿⢿⡆⣀⡀
⠀⠀⠀⠘⣆⠀⠀⠀⠰⢢⡏⠀⠀⠀⠀⠀⠙⠛⡇⠀⠀⠀⡠⠋⠀⠀⠀⠀⠈⠛⣾⣮⣭⣽⣿⠿⠀⠀⠀⠀⣤⠐⠲⣿⣿⣿⠞⠁⠈⠁
⠀⠀⠀⠀⠋⠙⢲⠖⠺⠁⠉⠀⠀⠀⠀⠀⠀⠀⠣⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⢩⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢀⠦⢄⡀
⠀⠀⠀⠀⢀⣵⣦⣀⣤⣤⣠⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠀⠀⠀⠀⠀⠀⢼⢋⣡⢤⠞⠀⡤⠷⣦⠀⠀⠀⠀⢠⢎⣀⠃⠨⡁⠠⠝⣆
⠀⠀⠀⢀⣿⣶⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣼⠾⣿⣿⣧⣤⠀⠀⠀⠀⠈⠉⠀⠀⣠⠎⠀⡠⠏⠀⠀⠀⠀⢸⠀⠠⡀⠖⠀⠀⠄⢸
⠀⠀⠀⠐⠻⣽⣿⡿⣿⣿⠿⡀⠀⠀⠀⠀⠀⠼⣷⠼⠿⣛⡿⠂⠀⠀⠀⠀⠀⠀⢴⠁⢀⠾⠁⠀⠀⠀⠀⠀⠘⣄⠃⠀⠃⣀⠰⢀⠏
⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠻⠛⠏⠁⠀⠀⠀⠀⠀⠀⠀⠘⠲⠚⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⠴⠚⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣛⣛⣛⣲⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠞⠻⢦⣤⣀⣉⣉⠉⠉⠉⠉⠉⠉⠉⣉⣉⣁⣬⠟⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⠶⣶⣤⣬⣭⣭⣉⣉⣉⣉⣉⣉⣉⣉⣩⣥⣤⣶⡾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⠀⢸⡇⢸⡏⢹⡏⢹⡏⢹⡏⢹⡏⠉⡏⠉⡇⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⣄⣸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⠀⡇⢀⣇⣠⣧⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡟⠙⠛⠛⠻⠿⠷⠾⠷⠾⠷⠾⠿⠿⠛⠛⠛⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⢷⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⡾⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣴⣦⣤⣤⣀⣀⣀⣀⣤⣤⣤⡄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⣤⣤⣤⣀⣀⣤⣤⣄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣉⣉⣉⣛⣛⡋⠉⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡇⠀⠀⠀⠀⠀⠀⢀⣴⠶⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠛⠿⢿⣶⣶⣤⣤⣤⣤⣤⣴⣶⣶⠿⠟⠛⢻⡇⠀⠀⠀⠀⢀⣴⣟⡱⠋⠀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠛⠻⡿⠷⠶⣦⡀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣷⣄⠀⠀⢰⡿⠃⠈⠹⣦⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⡀⣠⡇⠉⠛⢸⡇⠀⠀⢻⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⡇⠀⠸⣧⣀⣠⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⢿⣿⣷⣾⠟⠁⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠈⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢟⣛⡛⣟⠛⠙⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠉⣀⣿⣀⣀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣆⠀⠀⠀⠀⠀⠀⠀⢸⡴⠋⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠳⡇⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢠⠞⣧⠀⠀⢀⣀⡤⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠉⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⣠⠋⠀⠘⠚⠉⠉⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠈⠙⠲⢤⠞⠉⠉⠙⠣⡀⠀⠉⠳⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⡞
⣀⣀⣀⣀⣀⣀⣀⣀⣀⡈⣧⠀⠀⠀⠀⡰⣋⣞⠉⣱⣄⡀⢸⡄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⡼⠁
⠙⣄⠀⠈⠉⠉⠉⠀⠈⠉⠉⠀⠀⢠⡾⣽⠣⣼⠃⢌⣇⡜⡸⠀⢀⡤⠲⡈⠳⣄⠀⠀⠀⠀⠘⠧⠤⠤⢤⣤⣀⣀⣀
⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠒⠲⢧⡦⢴⠛⣬⣶⠁⡰⠛⢢⠰⢇⣠⠟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠈⢾⣠⣿⠏⠻⣅⣀⠼⣀⡠⠃⢱⠛⡆⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⣨⠆⠀⠀⢠⡇⠀⠀⠀⠀⠠⠁⠀⣼⠟⠁⠀⠀⠘⠷⣤⢼⠒⠒⡇⢀⠇⠀⠀⠀⠀⠀⠐⠛⠲⠤⣄⣀
⠀⢀⡠⠖⠋⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠈⠛⠳⠿⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡨⠽⠗
⠶⣉⡀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⣀⣤⠞⠉⠀⠀⠀⠀⠀⠀⣀⣤⣤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉
⠀⠀⠉⠙⠒⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⡛⢏⣙⡦⢵⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀
⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠉⢫⠈⣇⣸⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⡏⣧⣞⡁⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⣀⣀⣀⣈⣶⡄
⠀⠀⠀⣴⣁⣤⠤⠤⠶⠒⣶⠂⠀⠀⠀⡠⢿⡀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠉⠙⠲⢤⣀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣠⠔⠋⠀⠀⠙⠓⠒⠚⠋⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⠑⠢⢌⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡠⠞⠁⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡽⠃⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⢀⡴⠋⠸⡆

⠀⠀⠀⠀⣠⠴⠶⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⢠⠞⠁⠠⣾⠇⣀⡈⢦⠀⠀⠀⠀⠀⠀⠀⣠⣿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⢝⡧⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣀⣀⣿⣿⠁
⠀⠀⢸⠘⠛⡓⠀⠀⠙⠗⢸⠄⠀⠀⠀⠀⠀⠲⣿⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢨⡍⠈⠉⠉⣿⣿
⠀⠀⠘⣆⠸⠿⠀⠺⠿⢆⡞⠀⠀⠀⠀⠀⠒⠷⣶⣦⣼⠇⠀⠀⠀⠀⠀⠀⢀⠜⠛⠋⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⠶⠂⠀⠿⠿⠁
⠀⠀⠀⠈⠑⠶⠤⠴⠖⠉⠀⠀⠀⠀⠀⠐⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⣀⣀⣀
⠀⠀⢠⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⢸⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⢀⣼⣷⣏⢹⣶⣧⣀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠙⠋
⠀⠀⠀⠻⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠁⠀⢇⢡⡌⣱⠇⠈⠀⠀⠀⠀⠀⢸⣿⢿⡿
⠀⠀⠀⠀⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁


⠀⠀⢀⣴⣾⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣶⣣⡤⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⢀
⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣯⢞⡁⠀⠀⠀⠀⣄⣼⣿⣿⡤⣜⣿⣿⣇⡄
⠀⠀⠘⢿⣿⣿⣯⠛⠋⠀⠀⠀⠀⠀⠀⠀⢰⡏⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⢹⣿⣿⡟⠁⠈⠉⠙⣿⠃
⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢾⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢠⣴⣧⡀⠀⠀⠀⠀⠀⠀⠀⣄⣿⡟⣻⣥⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⡀⠀⠀⠀⠀⠀⣴⡶⠶⡶⠶⠶⢶⣦
⠀⠀⠀⠀⠈⠙⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣽⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠟⠁⠀⠀⠀⠀⠀⣿⣀⣂⣐⡒⠂⠸⠛
⠀⠀⠀⠿⠇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠍⠁⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣦⡶⠂⠀⠀⠀⠀⠙⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠉⠝⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠒⠛⠛⠉⠉⠉⠉⠉⠉⠉⠛⠓⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣴⣾⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣄⣀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⡿⠛⠓⠀⠀⠀⠀⠈⠉⠙⠛⠛⠂⠀⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠛⠛⠿⠛⢩⠤⠆⠀⠉⠁⣤⣶⣶⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⢄⠀⠀⢷
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡀⠠⠰⠆⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠄⢀⣿⣷⣶⠀⠄⢀⡀⠀⠀⠀⠀⠀⡂⠀⠘⣇
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣴⣾⣿⣿⣿⡄⠀⠀⡐⠁⠀⠀⠀⠔⠀⠀⠀⢹
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⡠⠊⠀⠀⠀⢀⠊⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠿⣿⣧⡀⠀⠰⠿⠟⠃⠀⢀⣾⣿⣿⣿⣿⣿⢯⡄⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⡆⠀⠀⠀⠀⡶⠿⠿⠛⠉⢙⠟⠋⠀⢳⡄⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡇⠠⢠⡔⠈⠁⠀⠀⠀⠈⢷⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⢶⡀⠈⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠙⠦⣄⣀⣀⣀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢁⢐⡄⠁⠀⠀⠀⠠⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠰⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠰⠉⠛⠿⠷⠂⠀⠀⠀⠰⠂⠀⠠⠀⠀⠒⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣀⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠴⢤⣀⣀⣀⣀⠀⠀⢀⣀⣀⣀⣠⠴⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠒⠀⡖⠒⠂⢲⡄⢰⡆⣶⠒⠒⢠⡖⠒⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠀⣟⣉⡁⠈⣧⡾⠀⣿⣉⣉⢸⡟⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠉⠁⠀⠈⠁⠀⠈⠉⠉⠀⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣦⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠉⠉⠙⠛⠛⠻⠿⢿⣿⣿⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠉⠻⣿⣦⣄⣠⣤⣤⣴⣶⣶⣶⣾⡿⠿⠿⠿⠟⠛⠻⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⠻⣿⣯⣍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣽⣿⣷⣄⡀⠀⠀⠀⠙⠻⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣟⡛⠛⠋⠉⠉⠉⠙⠻⣿⣶⣤⣀⠀⠀⠀⠉⠛⠿⣿⣷⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⣻⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠀⠈⠙⠻⣿⣷⣤⣀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣦⣄⣀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣷⣶⣶⣶⣶⣿⣿⠁
⠀⠀⠀⠀⠀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣦⣄⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢉⣿⠃
⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣶⣶⣤⣤⣤⣤⣤⣤⡾⠋
⠀⠀⠀⠀⣼⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠉⠉⠉⠉⠁
⠀⠀⠀⠀⣿⣿⡿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⣦⣄⣀⣠⣾⠟⣿⣿
⠀⠀⠀⠀⠘⣿⣧⡈⠙⠻⣿⣿⣶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣿⣿⣿⠟⠋⢠⣿⣿
⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠈⠉⠙⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠀⠀⣠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣷⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⣶⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠋⠉⠙⠛⠲⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠛⠛⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡾⠥⠤⠤⣀⡀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠏⠀⠀⠀⠀⠀⠉⠓⣄⠀⢀⡼⠁
⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡞
⢀⡴⢏⠉⠋⠉⠙⠓⠦⣄⠀⣷⣀⣀⣀⣀⣀⣤⡤⠤⠤⠶⠒⠚⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⣾⡇⠀⠑⢦⡀⠢⡀⠀⠈⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⣯⠱⡀⠀⠀⠙⢦⡈⠢⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠹⡄⠱⣄⠀⠄⣀⠙⠢⡘⢦⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠰⠐⠀⢀⡾⠁
⠀⠙⣆⠈⠣⣄⠀⠀⠀⠈⠢⡙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡴⠏
⠀⠀⠈⠛⢦⣀⠉⠒⠦⠤⠤⢾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠶⠴⠶⠚⠉⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠛⠉⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢀⣠⠴⠚⠋⠉⠁⢀⡠⠞⠋⣻⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⢀⣴⠋⠁⠀⠈⠁⡠⠖⠉⣠⠔⠋⠁⢀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠈⠛⠲⠶⠶⠒⠋⠁⠀⠀⠀⠀⣼⠃⠀⠀⣠⠔⠁⢀⡴⠊⠡⠀⠀⢀⢼
⠀⠀⠀⠀⣠⡞⠻⢭⣀⠀⠀⠀⠀⠉⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠦⣴⠋⠀⣀⠔⠁⠀⢀⣀⠤⠞⢁⡾
⠀⠀⢀⡾⠉⠙⠲⢤⣈⠉⠒⠤⣀⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠘⢧⣀⡉⠉⠉⠋⠉⣉⣉⣀⡤⠶⠋
⠀⠀⢸⣧⣀⠀⠀⠀⠈⠙⠲⢤⣀⠉⠒⠤⣄⡀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⢿⡈⠓⠦⢄⡀⠀⠀⠀⠈⠙⠲⢤⣀⣉⣳⠖⢻⡆
⠀⠀⠀⠈⠳⣄⠀⠀⠈⠉⠑⠒⠒⠒⠒⠚⠋⠉⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣿⣶⣶⣶⣶⣾⣯⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠠⠄⢠⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⡄⡅⢛⡄⠒⡘⡀⠬⢤⡛⢨⢠⡆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⣩⠐⠆⠀⠪⠇⡀⠀⢡⡁⠨⠕⠀⠰⠂⣍⠾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠈⠧⡁⢼⣀⠹⣐⣍⠠⡠⡼⠁⣠⣊⠏⣀⡧⢈⠼⠁⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠐⠃⡡⡑⣼⠷⠀⠺⣿⠀⢻⡏⠀⢿⠗⠀⠾⣧⢈⢈⠘⠂⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠦⠌⢳⡍⠀⢊⠛⠦⣬⣇⠀⢆⣳⡄⣸⣥⠴⠛⡑⠀⢩⡞⠡⠴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣊⢜⣧⣤⣤⣦⣀⡀⠙⣷⡄⢸⣿⠋⢀⣀⣴⣤⣤⣼⡣⣑⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠂⠐⠁⠀⠉⠛⢷⣿⣿⣿⣿⡾⠛⠉⠀⠈⢂⠐⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⣀⣄⣀⠀⠀⠀⢀⣿⣿⣿⣿⡀⠀⠀⠀⣀⣠⣀⣀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠔⠋⣉⡿⠿⠶⢿⣿⣿⣿⣿⡿⠶⠾⢿⣉⠙⠢⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢴⡇⠠⠞⠋⣉⡵⠟⢻⣯⣉⠙⡷⠄⢸⡦⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠳⡄⠀⣿⠙⠀⠀⣀⡿⠈⣻⠀⢠⠞⠉⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠑⠌⠙⡓⢦⠀⢠⠗⢠⠃⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⠀⠂⡆⢰⢰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⣘⣀⣁⣃⣘⣘⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⣀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢸⠉⢉⣉⣉⣉⣈⡀⠀⠀⠀⡴⠊⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢨⡇⠀⢀⠎⠈⠢⡀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠘⣀⠤⡄⠒⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⠤⠤⠤⠤⠤⠤⡇⢠⠊⠀⠀⢱⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢀⡇⠣⢀⣀⣀⣀⠠⠔⠊





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠈⢿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⣾⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠰⢶⣤⡀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣷
⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣦⢺⡟⣠⣾⠟⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢻⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⢠⣦⣭⣼⣷⡬⠄⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣶⣶⡶⢸⡿⠋⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⠾⠋⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣰⡿⠁⠀⠀⠀⣠⡶⠂⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠿⠛⠉⠙⠛⠃⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⡇⠀⠀⠀⠸⠋⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⠟⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣠⡾⢛⣃⣀⣴⡾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠠⣾⣿⠷⢬⣝⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣰⡶⢸⣯⡸⣷⡌⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣿⡇⠈⠉⠁⠘⣿⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠙⠗⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠙⠻⢶⠦⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣠⣤⠤⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠚⠁⠈⠓⠞⠘⠀⠀⠀⠉⠓⠲⠦⠄⢀⣠⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠱⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢦⣠⡄⠀⠀⡴⠙⣺⣿⣧⣘⣽⣦⡀⠉⠀⠒⢢⡀⠀⠀⠀⠀⠀⠀⠀⠙⢤
⠀⠀⠀⠀⠀⠀⠀⠈⢦⣉⢫⣁⢨⣚⣂⡝⠻⣿⣿⣻⣯⡃⢤⣶⡂⠠⠷⡠⢄⣘⣢⢤⠀⠀⠀⠀⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣿⠛⣿⡌⢹⠀⠀⢻⣿⡟⣿⢿⡏⢹⣿⡿⡿⣿⣦⣤⣤⣉⣙⡚⠲⢤⡀⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢹⡇⠈⠆⠀⠈⣿⠇⠸⠀⠆⠈⣿⡇⠇⣿⡟⢿⣿⣿⣟⢿⣶⣶⣔⡤⠀⢸⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⡇⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⢿⠇⠀⣿⠀⠸⣿⢻⣿⡸⢻⣿⣿⣿⣦⣄⠸⡝⠔⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢐⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⠀⠀⣿⡄⠀⢿⠀⣿⡟⠀⢿⣿⣿⣿⣿⣇⠻⡄⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢠⡏⡈⠀⠀⠀⠋⠀⠀⠀⠀⠀⡿⠀⠀⢻⠃⠀⠈⠀⢸⡇⠀⠈⣿⣿⣧⢿⣿⣷⣸⡆⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⠆⠡⠋⠙⠁⢀⡆⣄⠀⠀⠀⠀⠀⢀⣷⠁⠀⣼⠀⠀⠀⠃⢸⡇⠀⠀⢿⠃⢻⡘⣿⣿⣷⡅⠀⢿⣷⡀
⠀⠀⠀⠀⠀⠀⣠⡼⣳⣏⠐⠁⠀⠀⡀⠸⢿⠏⠀⠀⡼⢠⡇⢸⡏⠀⠀⠀⠀⠀⡀⠀⠠⣧⠀⠀⢸⠄⠀⡀⠘⣿⣿⣷⠀⠸⢷⠁
⠀⠀⠀⠠⠶⠋⣩⠽⠋⣁⠄⠀⢀⢄⡴⠿⠀⠀⠀⡼⠀⣸⡇⡼⢃⠀⢠⡆⠀⠀⡅⠀⢰⡇⠀⣄⣾⠀⢠⠇⠀⢿⣿⣿⠀⠀⢘⡷⡀
⠀⠀⠀⠀⠀⠉⠃⠀⠚⠓⠁⠀⣱⠟⠀⠀⡔⠀⡾⠃⢠⠋⣱⣧⢸⡄⣾⠀⠀⢰⢁⠀⠈⠀⣠⢧⡧⠀⡾⠀⠀⠸⣿⣿⡆⠀⠸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠊⣁⣠⣆⡼⣠⣾⠁⠀⠊⠀⣿⣷⣾⢣⡟⡴⠀⡿⠸⠀⠀⠐⠁⣿⠃⢸⣷⠀⠀⢰⣿⣿⡇⢠⠀⣷⡇
⠀⠀⠀⠀⠀⠀⢀⠴⠊⠑⠒⠋⠁⡰⠋⠀⠡⡧⠀⢀⠀⣴⣽⠋⠃⡞⠁⠁⢹⡇⠀⠀⠀⠀⣴⠏⠐⠁⢡⡄⠀⣾⣿⣿⠀⠀⡀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⡮⠂⠀⠀⣾⠓⢠⠂⠀⡼⠘⠀⠀⠁⠀⢠⡾⠁⠀⠀⠀⡰⠃⡴⠀⢀⣾⠃⠀⢹⣿⡿⢀⣾⡅⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⠶⠋⠀⠀⠀⠀⡞⠁⢀⠄⠀⠀⠀⠸⠃⠀⠀⠀⠘⡌⡼⠁⠀⢸⣿⢃⠄⣯⣿⠇⣸⣿⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⢀⠌⢀⡴⠋⠀⠀⠀⠀⡀⠀⠀⢀⡀⠎⡜⠁⣴⢰⣿⡇⣾⣰⣿⠋⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠄⠠⢊⠰⠋⠁⠀⠀⢀⡠⠊⢀⠰⠇⠘⠟⠀⠘⠁⣸⢽⠋⢰⢿⡿⠃⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠥⠚⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣰⣯⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⡔⡹⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠒⠒⠒⠒⠒⠒⠶⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⠀⠈⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⠿⠿⠿⠛⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡄⠀⠀⠀⠉⠁⠉⠹⣿⣿⣿⣿⣦⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠄⠀⠸⣿⣿⠏⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⡄⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⣠⣴⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠒⠂⠀⠀⠀⠀⢀⣀⢀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠈⠂⠀⠀⠤⠊⠀⠀⠁⢢⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠚⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢊⡀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠒⠙⡒⠠⠀⠀⠀⠀⠀⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠚⡇⠀⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢬⣀⡀⠀⠀⠀⠀⠀⠀⠀⢃⢀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠒⠒⠒⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠙⠂⣧⣤⡇⣿⣭⠐⢯⣃⠉⡟⠁⠀⣾⣹⢆⡾⡄⢸⢸⢧⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠃⠃⠀⠃⠓⠒⠈⠒⠋⠀⠃⠀⠀⠛⠀⠘⠉⠙⠘⠘⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣟⣻⡿⣿⠿⠿⠿⣿⡿⢿⣟⣻⢿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠶⢮⣭⣭⣭⣭⣭⣭⣭⣭⡵⠶⠛⠿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⡶⠛⠛⢶⡞⠉⠀⠈⠉⢉⣭⣭⣿⣿⡛⠉⠉⠉⣴⣶⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣼⣷⡀⠀⠀⠹⢦⣤⣤⣤⣴⣿⣿⣿⣿⣇⣀⣀⣤⣿⡿⣿⠟⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠁⠀⠻⢶⣄⣠⣶⣽⣶⡉⠁⢻⣿⣿⣿⡟⠉⠉⠀⣨⣽⣿⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢰⣀⠀⠀⠀⠀⣩⣛⣿⣿⣇⣠⣴⠿⠿⢿⣻⣿⣶⣤⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⣙⠻⠶⣦⣤⣿⣿⣿⣿⡟⠉⠀⠀⠀⢻⣿⣿⣿⠇⠀⠉⣉⣽⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣌⣉⡙⠛⠋⣄⣀⣠⣤⠶⠟⢛⣉⣀⣤⣶⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠉

⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠹⢿⣿⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠂⢱⠁⣸⠤⡀⠀⠀⠀⠀⠀⢠⣶⣬⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⣠⣤⡀
⠀⠀⠀⠀⠈⠸⣯⣽⣦⠀⠀⠀⠀⠀⠀⡀⠀⢈⠁⠁⠂⢁⡀⠁⠀⠀⠀⠀⠀⠀⢍⠻⣟⣎⠂⠀⠀⠀⠀⠀⠀⣙⣿⠟⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠈⠈⠻⠑⠄⠀⠀⠀⠀⠀⠚⠏⢠⡌⡄⢄⠈⠂⠀⠀⠀⠀⠀⠀⠀⠁⢹⣻⠀⠀⠀⠀⠀⠀⠀⠻⣿⢾⣿⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡄⠒⡘⣐⠠⠄⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠄⡄⠀⢄⣀⠨⠀⠀⠀⠀⠀⠀⢀⣴⣴⣤⡀
⠀⠀⠀⠀⡘⡈⢁⠐⢀⠐⠘⡀⠀⠀⠈⠷⢦⡄⠻⠀⠘⢋⠀⠀⠀⠀⠀⠀⠠⠀⠑⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠤⠐⠀⡐⠀⠄⠠⠀⠀⠀⠀⠀⣀⣴⠂⢸⡆⠈⠻⣤⠀⠀⠀⠨⠙⡏⠀⢀⠀⡠⢒⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠁⠆⠡⠰⠈⠁⠀⠀⠀⠀⠈⠉⠀⠀⠊⠃⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠘⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢸⣭⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⡾⠀⡠⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⣀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠰⡤⢄⡀
⠀⠀⠀⠀⢸⣻⣿⠉⢹⡦⠀⠀⠀⠀⠀⠐⢄⠀⠘⠀⠐⠃⠀⠀⠀⠀⠀⢠⡴⣿⡟⠁⢰⡿⠀⣰⠆⠀⠀⠀⢐⡌⠀⡨⢄⠀⠳
⠀⠀⠀⠀⠀⠻⣿⣶⣿⡻⣆⠀⠀⠀⢀⠄⠀⡁⠀⠀⠀⠠⣊⡥⠀⠀⢰⠟⠁⠈⠁⢀⣬⣿⡶⠇⠀⠀⠀⠀⢨⣄⢁⠪⠐⠄⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠼⣺⡯⠌⠀⠀⠀⠀⠋⠩⠙⢂⢠⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣤⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⢦⠅⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠰⠀⠸⠸⠁⠦⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠂⢠⣀⣠⠀⠀⠀⠀⠀⠀⢲⡶⣿⣻⡷⣴⠀⠀⠀⠀⠀⠀⠐⠉⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⡑⢚⠀⢀⠀⠀⡔
⠀⠀⠀⠀⢸⣶⣿⠿⣿⣦⡄⠀⠀⠀⠒⣿⣻⡽⡾⣿⣻⡷⠀⠀⠀⠀⠀⠀⢄⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⢲⠸⠢⠬⡄⢄⠈⠁
⠀⠀⠀⠀⠘⢿⣿⣀⣼⣿⠇⠀⠀⠀⠀⢹⣯⣿⣻⣯⣿⡁⠀⠀⠀⠀⠀⠀⠀⠑⠄⢀⣤⡀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠱⣉⣠⠂⡆
⠀⠀⠀⠈⠂⠘⠛⠻⠇⡀⠀⠀⠀⠀⠀⠈⠀⠉⠯⠀⠈⠉⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠨⠕⠀⠀⢤⢙⣮⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉⠈⠒⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⢰⡅⡤⡄⠀⠀⢀⠀⠀⠀⠄⠀⢐⠧⠀⢻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣴⠶⠀⠀⠀⠀⠀⠀⠀⡄⠀⣸⣿⢯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠐⠀⠀⠠⠀⠀⠀⠂⠐⠈⠀⠁⠀⠄⠀⠀⠈⠀⠀⡤⠟⠉⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢰⠃⠀⠐⠋⠀⠀⢀⠀⠀⠀⠀⢀⡉⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠈⠀⢠⡈⠀⠐⠆⠀⠀⢨⡇⡀⠀⠊⠀⢠⣺⡃⠀⠀⠀⣄⣁⣀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⠀⠀⠀⠸⠋⠢⠀⣀⠀⢠⠀⠉⠙⡀⢀⠀⠞⠙⠃⠀⢠⠞⠋⠁⠀⠈⠁⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠠⢆⢸⡀⠀⢀⡀⠀⠀⠀⣿⠀⠘⡇⠀⢷⡷⠧⠀⠑⠦⠔⠁⠃⠠⠀⠀⠀⢀⣰⠃⠣
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⢨⢣⠀⠐⢤⡀⠀⠀⠀⠀⠸⣇⠀⠀⢀⢐⠇⡄⠀⠀⠀⠀⠀⠈⡻⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⢸⠀⠀⠀⡀⠈⠂⠀⠀⠀⠀⣌⠛⡟⠉⠋⠀⠇⠀⠀⠀⠀⢀⣴⣇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡈⡄⢼⠃⠀⠘⠁⠁⡒⠀⠀⠀⠀⣧⣀⢨⠀⠀⢀⠘⣆⠦⣤⠶⢪⠆⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣠⣥⣀⣿⡇⣸⡀⠀⠀⠀⢠⡀⠈⠀⠀⠀⣿⣿⢸⠀⠀⣿⠀⠙⣦⣀⠀⠀⠑⠒⠚
⠀⠀⠀⠀⠀⠀⢰⣙⣄⠀⠀⠀⠀⠉⠉⠙⠻⠿⠉⠋⠉⠉⠛⠓⣿⡇⠀⠀⠀⣼⡃⠰⡇⠀⣴⣯⣿⣿⣂⣠⡿⠂⠀⠀⠇⠡⠀⠀⡆
⠀⠀⠀⠀⠀⣦⡀⠙⠿⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⢰⣎⣿⣧⠀⠇⠐⠀⠀⠀⠀⠉⠉⠑⢴⡶⢂⣃⣆⠀⢀⡱⣷⠄
⠀⠀⠀⠀⠀⠙⠯⠦⣄⢵⣤⣉⣛⠓⠒⠒⠀⣁⣦⣽⣐⠄⡀⠸⠟⠻⡀⣈⣟⠿⢡⠴⣶⣺⠤⠄⡀⠀⠀⠀⠀⠈⠉⠉⠚⠥⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠷⢿⣿⡷⣬⣈⣛⠻⣿⠟⣛⣓⣿⣁⡈⠓⢤⢞⠢⣌⠛⡿⢧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢾⣟⠉⢆⠀⣤⣬⠦⣤⡷⠀⠀⠀⠒⢬⡋⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠙⢦⣬⣧⣤⣀⣀⠀⢀⠞⡩⠀⠂⠀⠐⠋⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠛⠷⠷⢤⣀⣀⠈⠹⣽⣖⣠⡾⣦⣰⣶⣶⣶⣦⣀⣀⠀⢀⡌⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠶⢿⣧⣄⣸⠟⠈⠛⠉⠉⣿⣿⣀⣤⣴⣾⣷⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣻⣯⣽⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠚⠉⠳⣄⠀⠀⡴⠋⠀⠀⠀⡈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣰⠖⠓⢦⡀⢰⡇⣶⠛⡇⢸⠀⢸⠃⢸⠙⠳⠟⢹⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⢋⣉⠳⡄⢰⠃⡟⢙⡆⣧⢸⡇⣨⣉⠁⢸⠀⢸⠀⢸⡀⠀⡴⠾⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⣦⢸⡇⠯⠼⠃⡇⢸⠀⠉⠉⠀⣿⢸⡇⢧⡘⡆⢸⠀⢸⡄⠀⣙⠒⠛⢦⡿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠣⡞⣳⢸⠘⡇⠀⠀⢀⡇⢸⡆⠀⠀⢠⡇⠀⡇⠀⠉⠀⢼⠀⢈⡇⠸⣍⡹⠂⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠈⠁⢸⠀⣧⠀⠀⠈⣄⣠⠇⠀⠀⠀⠙⠚⠁⠀⠀⠀⠈⠓⠋⠀⠀⠉⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸



⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂


⡖⠒⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⠒
⠓⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⢠⠤⢄⠀⡀⢤⠤⠀⣠⠀⢠⠤⢄⢠⠀⠀⡠⠄⠀⢀⠠⠄⠠⡤⠄⡤⢄⡀⡠⠤⡀⢠⠀⡀⢠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⢸⠀⢈⠀⡇⠀⡂⢰⠄⡆⢸⠒⢣⢸⠀⠀⡗⠀⠀⠈⠑⠄⠀⡇⠀⡇⢺⠠⡇⠀⡸⢸⠻⡀⢸
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣷⣶⣶⣶⣶⣶⣾⣷⣷⣾⣾⣶⣿⣶⣶⣶⣷⣶⣶⣷⣶⣷⣶⣶⣾⣶⣷⣾⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠤⠤⠤⠤⢤⢤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⣀⣸⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠉⠉⠉⠉⠈⠹⢿⣇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠠⠤⠤⠤⠤⠶⠾⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠏⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡰⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⣀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⣇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠛⡌⠐⢲⡶⠲⠂⠒⠒⢒⣾⢻⠀⠀⠀⠀⠀⠀⠀⣧⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣄⡔⠺⣾⡟⢀⣦⣀⡸⠟⡀⣸⠀⠀⠀⠀⠀⠀⠀⣥⣿⡆⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⢈⣿⡋⢁⣼⡁⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⣽⣿⡇⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠘⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢀⣀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠓⠲⣶⠶⣾⠟⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠃⠀⠀⢤⣧⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢙⡆⠀⠀⣞⠉⣷⠀⠀⣚⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀⣀⣀⣠⣤⣬⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠈⠋⠁⣀⡀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⢸⡇⣼⣿⣿⣿⣿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡄⢀⠀⡤⠠⡄⠀⠀⣠⠒⢠⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠹⠉⠉⠉⠉⠉⠉⢸⠰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠼⠃⠀⠀⠢⠴⠃⠀⠀⠙⠶⠞⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣋⣸⡇⠀⠀⢨⣀⣵⠀⠀⠺⣤⡿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡈⠐⠀⠀⢠⣤⣤⣤⣤⣤⣶⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢰⡄⠀⠀⣔⠀⣆⠀⠂⢠⡁⣰⠄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⢹⠙⠛⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠙⠛⠃⠀⠀⠈⠛⠋⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⣀⣈⣀⣀⣼⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉⠁

⣷⠛⠛⣶⢶⡶⣶⠶⠶⣾⠶⢶⠶⠶⣾⠷⠶⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⢶⡶⡶⣾⢿⣿⣿⠾⠿⠷⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠀⠀⠀⠀⠀⠌⣉⡁⠠⣤⠀⢠⡊⠠⢖⠀⢼⠀⣉⣦⠀⣴⠀⢠⠀⢁⣐⠂⠰⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠁⢰⠒⡆⠺⠇⠸⠀⠑⣂⣀⠙⠀⠈⠆⠀⠈⠀⠈⠀⠉⠁⠀⠙⠠⠜⠀⠀⢈⣀⠋⠇⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⢀⣉⠤⠶⡊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣁⠶⠊
⠀⠀⠀⠀⠀⢀⠀⣀⢀⡰⠄⡀⠌⠉⢿⣓⣲⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡿⠂⠉⠀⠀⢢⡀⣀
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⢢⠕⠐⠢⢀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠈⠁⠀⠄⠿⣍⠤⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠐⢒⡱⠆⠠⣤⠷⣀⠜⠀⠀⠠⣀⠱⣆⠀⡰⠋⢘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⣀⠁⠀⠀⠐⠐⠃⡁⠀⠀⠘⣩⢿⢾⡛⣧⠀⠈⠙⠉⢃⠈⠀⠀⠀⠀⠄⠀⣇⠀⠀⠜⠁⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠒⠀⠀⠀⠘⠃⠋⠉⣁⠀⠀⠐⠈⠈⠀⠈⠉⠀⠀⠀⠀⠀⢰⡹⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠂⠠⠀⠆⠒⢈⡉⠆⠀⠀⠀⠘⠀⢠⠜⠇⡤⠠⠀⠄⠀⠀⡀⠀⣀⠉⠀⠀⠀⠀⠀⠁⠀⠀⣀⣀⣀⡀⣀⠬⡀⠙⣳⣄⣀
⠀⠀⠀⠀⠀⠲⠀⠠⠈⠩⢁⡰⣾⣷⣄⣤⣄⢠⡼⢧⡀⣀⣀⣀⣀⣰⣏⡀⡀⠀⣱⡄⡀⠀⠀⠀⢠⠔⢉⠠⣴⣟⡛⡆⠀⠁⠀⠀⠉⠀⠈⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠉⠡⠉⠀⠈⠉⠉⠘⡷⠀⠉⢯⣉⠉⠻⣭⠉⠍⠻⠀⠉⠣⠘⡆⢀⠜⢁⡄⠀⣎⣴⣿⠏⣷⣴⣤⣤⡤⢀⡀
⠀⠀⠀⠀⠀⠀⠐⣈⣥⣤⢴⠄⠀⠀⠀⠀⠀⠀⡇⠀⠀⢈⠇⠀⠀⠈⠀⢠⣸⠀⠀⠠⢤⢼⠏⢠⡋⣴⠚⣿⣃⣀⣨⠷⠾⠿⣋⠿⠆⢹⡀
⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠃⠀⠀⠀⠀⠀⢀⣰⠇⠀⠀⠀⠀⠀⣆⠀⡄⠀⢜⠦⠠⠴⢀⣼⣀⣹⣿⣿⡐⠪⠙⠛⣉⣛⡛⠈⠁⠄⢐⠟⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢋⠡⠀⣠⣠⣴⠿⢇⠐⠿⣶⣴⢤⡙⢻⡿⣷⡛⠋⠛⠲⠶⣶⣿⡗⠶⣶⣤⣤⣤⣖⣤⡰⠅⠊⣹⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠷⠂⠛⠛⠳⠆⠀⠤⠞⢺⠿⢦⡌⠁⠘⣓⠾⠛⠛⠁⠀⠀⠲⠀⠓⠲⠦⠤⣤⣤⣤⡤⠴⠶⠿⠿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠈⠹⡄⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠂⠀⠀⠴⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠘⠲⠐
⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀⡜⢲⠊⢱⠊
⠀⠀⠀⠀⠀⠰⢻⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠘⣿⡿⠀⠀⠀⣶⣤⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣼⠉⢹⠋⠙⠓
⠀⠀⠀⠀⠀⠀⠀⣷⣤⠀⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠂⠘⠋⠀⠀⠀⠀⠀⣶⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠘⠃⠀⠀⠀⠀⠐⣿⠗⠀⢀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣾⣿⣧⠀⠀⠀⠀⠛⠃⠀⠀⠀⣿⣿⣿⣿⣿⠉⠛⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⢠⠀⠀⠀⠀⠻⠂⠀⠠⣿⡷⠀⠀⠙⠛⠃⠀⠀⢼⣿⠀⠀⠀⢀⠀⣿⣿⡿⠿⠿⠀⠀⠀⠘⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⢀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠘⢿⠆⠀⠀⠀⠛⠀⠀⣾⣿⣿⠀⠐⠉⠀⠁⠀⢹⡋⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢠⣆⡀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣦⠀⠀⠈⠉⠃⠅⠀⠤⠤⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠒⢸⣿⡇⢸⣿⡇⠐⣿⡗⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⣶⣶⣶⣶⣤⣤⣤⣄⣤⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⣿⡇⢸⠀⠀⠐⠀⠀⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⢠⣬⣭⣤⣤⣭⣥⣤⣭⣥⣼⠀⠀⠀⢠⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣤⣤⣬⣭⣭⣭⣥⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠉⠉⠉⠉⠉⠛⢻⣶⣶⣿⣿⣿⣶⣾⣟⠋⠉⠉⠁⠀⢉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⢀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⣠⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣶⠄⠀⢠⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢁⣴⠟⣿⡿⢛⣛⣃⣛⣛⣛⣛⣛⣛⣃⣛⣛⡻⣿⡟⠳⣦⡈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠇⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠙⠿⠿⠿⠿⠟⣱⣷⣜⠿⠿⠿⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢠⣾⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣛⣛⣛⣛⡋⠁⠀⠀⢠⣿⢫⡍⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣄⢻⣿⣿⣿⢇⣤⡀⣰⣿⣿⢸⡇⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣦⣝⣛⣭⣾⡟⣱⣿⣿⣿⣬⣥⣾⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⡑⠆⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣬⣝⠒⠀⠀⣷⣤⣄⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣦⣄⣀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⡯⠭⠏⢙⢹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠃⠈⠻⣿⣿⣿⣿⣿⡏⣷⠚⣼⣿⣿⣿⣇⡿⡤⣸⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⢻⣿⣿⣷⣮⡘⢫⣛⠿⣋⣬⣤⣶⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣥⣿⣷⣿⣿⣿⣿⣿⣷⣦⣴⣶⣾⣾⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⣀⣀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⡿⠀⠉⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⡄⢀⡀⠨⠏⣠⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣯⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢿⣧⣿⣿⣾⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡋⠁⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣴⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⢟⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠋⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⠁⢩⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⠉⠀⠀⢻⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⠗⢺⣿⣿⣿⣿⣿⣿⠁

⠀⠀⠀⠀⠀⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠢⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢰⡇⠀⠀⠀⠀⠉⢳⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⡐⡇⠀⠀⠀⠀⠀⠞⠁
⠀⠀⠻⣤⡀⠈⠳⣶⣤⣈⠻⢿⣶⣤⡀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⡥⠀⠀⢀
⠀⠀⠀⠈⠙⠷⣾⣿⣿⣿⣷⣦⣉⣻⣟⠂⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣼⣷⣔⡁⠀⠀⠀⢀⡸
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣟⣋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣟⣿⠡⣓⣤⡻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢜⠁⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠
⣀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠒⠉⠁⢀⣤⠏⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢷⠀⢀⠀⠀⢀⠀⣀⣴⣿
⣿⣶⠦⠄⠀⠂⠀⠈⠀⠀⣀⡠⠴⠚⠋⠁⠀⠀⠀⠀⢠⣄⣀⣀⣀⣤⣆⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⢉⣻⣿⣿⡿⠃
⠙⠻⠶⣤⣤⠤⠤⠖⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠂⠄
⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠒⠐⠚⡆⠀⠀⠀⠀⠀⠀⢠⣾⣿⠞⠓⠂⠐
⠀⠀⠀⠉⢁⢤⠁⠀⠀⠀⠀⠀⠀⠘⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣟⡽⠁
⠀⠀⣾⡤⠴⠐⢦⠀⠀⠀⠀⠀⠀⠀⢻⡧⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⠀⡀⢸⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⣿⢳⡴⠀⠚⠇⠰⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠸⡇⢹⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⢹⣿⢀⣄⣄⣰⡶⠀⠀⠀⠀⠀⠀⢹⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⢸⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠻⣏⡭⠵⢿⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⣭⣿⡇⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣀⡠⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠶⠦⠴⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⠀⠀⠀⢀⡀⠀⠀⠀⠙⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠀⠀⠀⠺⣿⡿⠃⠀⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⢿⣷⡄⠀⠀⠀⠘⣷⠀⠀⠀⢸⣿⠇⠀⠀⠀⢻⣿⣧⠀⠀⠀⢀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⢀⣀⣤⣿⣶⣶⣶⣾⣿⣤⣀⠀⣰⡟⠁⠀⠀⠀⠀⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢀⣤⣾⡿⠿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠻⢶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡆⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣶⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⡶⢿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⡀⠀⠀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⠾⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⠿⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠸⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠷⣦⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣶⣿⡿⠛⠁⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠈⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣯⠀⠀⠀⠀⢀⣼⠏⠀⠉⠛⣿⣿⠿⠿⠿⣿⠛⠉⠀⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⢻⣿⣧⠀⠀⠀⢰⣿⡇⠀⠀⠀⢿⡄⠀⠀⠀⠙⣿⣷⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣼⣿⠁⠀⠀⢠⣾⣿⡆⠀⠀⠀⣼⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠛⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⠿

⠀⠀⠀⠀⠀⣀⡴⠖⡛⠉⠉⠉⠛⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⡼⠃⡴⠋⠁⣠⠄⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⢸⡇⠸⡇⠀⢸⡁⠀⠀⠈⠉⠳⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⢰⠚⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠘⢧⡀⠑⢤⡀⠙⣆⠀⠀⢀⡼⠁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⡟
⠀⠀⠀⠀⢀⡗⠀⠀⣷⠀⡟⠀⢠⠏⠀⠀⠉⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢰⠃
⠀⠀⠀⠀⣼⠀⠀⡼⠁⣸⠁⠀⠸⣄⠀⠀⠘⣦⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⡾
⠀⠀⠀⠀⣿⠀⢸⡇⠀⢻⣀⠀⠀⠈⠁⠀⢀⡼⠀⡿⠀⠀⣀⣀⣀⣀⣀⣀⣸⠇⠀⠀⠀⢧⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠘⣦⡀⠑⠦⡄⠉⠓⣄⠀⠀⠛⠉⣀⡼⠁⠀⣼⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠈⠙⠲⠤⠤⣄⠀⠈⡇⠀⠀⣾⠁⠀⠀⠀⣻⠦⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣇⠀⠀⠹⣄⠀⠀⠀⢿⣄⣀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠈⠳⠦⠤⠌⠛⠒⣃⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠁⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠤⠤⠤⠴⠖⠋⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢀⡴⠶⣦⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠒⠒⠒⠒⠒⠒⠒⠒⠒⢿⡀⠀⠘⢷⣤⠞⠀⠀⢰⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⠖⠛⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣭⣽⣿⣭⣽⣿⣭⣿⣿

⠀⡤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢦⡀⠀⡠⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⠦⡀⠀⣠⠴⠶⠶⠶⢶⣶⣶⡶⠶⠶⠶⠶⠶⠦⡄
⠀⡇⠀⢻⣽⠓⠒⠒⢳⡀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⢀⣀⡀⠤⢤⣖⡲⠭⠭⡽⠅⡇⠀⡇⠀⠀⡠⠖⡩⠖⠒⠚⠀⠀⠀⠀⠀⠀⡇
⠀⡇⣀⠯⠼⢄⡀⠀⠀⠀⠁⠄⡀⠀⠀⠀⡇⠀⡇⠀⠀⠀⣯⠒⠉⠉⣿⠀⠀⠀⠈⡜⠀⡇⠀⣇⠔⢋⡴⠊⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡇
⠐⣿⣁⣀⣀⣀⡧⠀⠀⠀⣀⣀⣀⣀⣀⣀⡇⠀⡇⠀⠀⠀⣫⠔⠚⠃⣿⡀⠀⠀⠀⣿⡆⡇⠀⣧⠔⠉⠀⠀⠀⠁⠈⠀⣁⣀⣀⣀⡀⣀⡇
⠀⣿⠀⠀⠀⠀⣷⠀⠀⢸⣒⠒⠒⠂⠤⠒⡇⠀⡇⠀⠒⠉⣾⠀⠀⠀⣿⠇⠀⠀⢀⣿⠆⡇⠀⡇⠀⢀⡀⠀⢀⠠⠔⠩⣗⠒⠂⠤⠤⠖⡇
⠀⣿⠀⠀⠀⠀⡟⢠⣒⠥⡚⠁⠀⠀⠀⢀⡇⠀⡇⠀⠀⢀⡥⠒⠁⠀⣿⠀⠀⠀⠀⣿⡆⡇⠀⡇⠀⠈⠀⠀⡨⢠⣖⡭⠖⠋⠀⠀⠀⠀⡇
⠀⣿⠒⠒⠒⠒⢃⡾⣒⡪⠕⡀⠀⣀⠔⠋⡇⠀⡇⠛⠉⠁⣞⠤⠤⠤⣿⣀⣀⣀⣀⡿⠁⡇⠀⡇⠀⣆⢰⠀⠣⡸⢕⣊⠥⣂⠀⢀⡴⠊⡇
⠀⣏⠓⠒⠒⠒⠋⠉⠓⠾⠭⠒⠋⠀⠀⢀⡇⠀⣇⠀⠀⠀⠀⠉⠉⠙⠒⠒⠒⠂⠤⠼⢁⡇⠀⣇⠀⠀⠀⠀⠀⠉⠓⢶⡭⠕⠊⠁⠀⢀⡇
⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⡞⠉⠉⢉⡩⠭⠭⠟⠛⠻⢭⡉⠉⠉⠙⡆⠀⡞⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡆⠀⡞⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡆
⠀⡇⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⡇⠀⡇⢀⡴⠚⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⡜⠉⠙⣆⠀⠀⠀⠀⠀⠀⡞⠉⠙⡆⡇
⠀⡇⢀⡇⠀⡴⢄⣼⠢⣼⠳⣄⠀⠈⡆⠀⡇⠀⡇⡞⠒⠒⠚⠤⣀⡀⠀⠀⠀⢀⣠⣄⡀⡇⠀⡇⠑⠤⠴⠃⠐⣲⢦⢤⢤⠀⠳⠤⠴⠃⡇
⠀⡇⠈⣇⡞⠀⣤⠀⠀⠀⢠⠈⠙⣆⡇⠀⡇⠀⣷⠁⠂⠀⠀⠀⠀⠈⠉⠉⠛⡇⠀⠀⢱⡇⠀⡇⡴⠋⠙⣆⢈⡉⠉⠈⢈⡀⡔⠋⠑⡄⡇
⠀⡇⠸⡉⠙⠚⠋⠉⠉⠉⠉⠛⡎⢉⡕⠀⡇⠀⡏⡆⠀⠄⠀⠀⠀⠀⠀⠀⢐⡇⠀⢠⠇⡇⠀⡇⡇⠀⠀⡏⠙⠉⠉⠉⠙⠁⡇⠀⠀⡇⡇
⠀⡇⠀⠈⢲⡀⠀⠀⠀⠀⠀⠀⡷⠋⠀⠀⡇⠀⡇⢱⡀⠀⠀⠀⠀⠀⠀⠀⢠⡧⠔⠁⠀⡇⠀⡇⣧⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⡇
⠀⡇⠀⠀⠀⠈⢳⠶⠤⠔⡖⠉⠀⠀⠀⠀⡇⠀⡇⠀⠉⠒⠤⠤⠤⠔⠒⠋⠁⠀⠀⠀⠀⡇⠀⡇⢸⣤⣤⠇⠀⠀⠀⠀⠀⠀⢿⣤⣤⠇⡇
⠀⠧⠀⠠⣶⣭⣽⣤⣤⣤⣼⣭⣵⣦⣤⡴⠃⠀⠣⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠃⠀⠳⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠐⠲⠤⠤⠤⠤⢤⠤⠤⠴⣶⢶⢾⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠸⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡽⠦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣾⣟⣲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠁⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠉⠉⠉⠛⣛⣿⢿⣿⠑⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⣙⡎⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠠⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⠿⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠹⠀⡆⡆⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣱⢳⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢼⣟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⡆⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠦⠴⠶⠞⠳⠻⠛⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡖⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠤⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇⢰⡆⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡼⠇⠸⣤⣄⣄⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣤⣤⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣮⠉⢧⠀⠀⡎⠘⢿⣿⠉⠉⢏⠉⠉⠉⠉⢩⠉⣴⣦⡶⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢀⣡⡀⣷⠀⣸⣿⡖⠀⢈⢄⠀⠀⠀⣸⢴⡿⠈⢅⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣿⡀⠉⠻⣿⡻⣿⡇⣠⢞⣺⣧⣤⡰⠣⠋⠁⡐⠕⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣄⠀⠈⠻⣾⣿⡿⠋⠁⠀⣨⡧⠁⠀⡰⠋⣴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣟⣷⠤⣠⣿⣿⣀⡠⣤⣾⢟⣷⣀⣠⣦⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠿⠿⠶⠾⠿⠛⠛⠛⠉


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

⠀⠀⠀⣀⠤⠤⠤⢄⠀⠀⠀⠀⢀⡤⠤⠤⢄⡀⠀⠀⠀⠀⣀⠤⠤⠤⣄⠀⠀⠀⠀⢀⠤⠤⠤⢄⡀
⠀⠀⠜⣁⠀⣀⠀⢀⠑⡄⠀⡰⠁⣴⡄⠄⠀⠈⢦⠀⢠⠎⠀⠀⠀⠀⠀⠱⡀⠀⡔⠁⠀⢠⣴⡆⠙⠆
⠀⢸⠀⡇⠀⠀⠀⣸⡂⠱⠀⡇⢘⡀⣃⢀⣶⣄⢘⠀⢸⢎⠉⠀⠀⠀⠁⡑⡇⠰⠀⠀⠀⠈⢙⠉⢁⢸
⠀⠈⢆⠑⠒⠒⠒⠚⣠⠃⠀⠱⡘⠀⠓⠀⠁⢀⡜⠀⠘⣄⠉⠀⠀⠀⠉⡰⠁⠀⢣⡀⠀⠀⠀⠃⢊⠇
⠀⠀⠀⠉⠒⠖⠒⠊⠁⠀⠀⠀⠈⠐⠂⠖⠒⠉⠀⠀⠀⠈⠑⠒⠀⠒⠊⠀⠀⠀⠀⠉⠒⠂⠖⠚⠁
⠀⠀⠀⡠⠤⠒⠢⢤⡀⠀⠀⠀⢀⠤⠐⠒⠤⣀⠀⠀⠀⢀⡠⠔⠂⠢⢄⠀⠀⠀⠀⣠⠤⠒⠢⠤⡀
⠀⢀⠎⠀⠀⢄⠢⡀⠘⡄⠀⡴⢁⣤⠀⠀⣠⡌⢣⠀⢠⠋⠀⠀⠀⣀⢤⡱⡄⠀⡞⣀⣦⣆⡀⠀⠈⢆
⠀⢸⠀⠈⠆⣠⡴⠢⠀⡸⠀⡇⢰⣷⠀⠀⣾⡆⢸⠀⢨⠀⠀⡐⠀⠑⠉⠀⡇⠰⡀⠺⠿⡟⢤⣤⡀⢸
⠀⠀⢣⡁⠁⠙⠃⠀⡢⠃⠀⠱⣜⠛⠁⠀⠛⢋⠎⠀⠈⢆⠋⠀⠀⠀⢀⡴⠁⠀⠣⡀⠀⠀⠈⠛⣡⠃
⠀⠀⠀⠈⠒⠒⠒⠋⠀⠀⠀⠀⠈⠑⠒⠒⠊⠁⠀⠀⠀⠀⠉⠒⠒⠒⠉⠀⠀⠀⠀⠈⠑⠒⠒⠊

⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠄⠀⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠁⠠⣀⡀⠀⠀⠀⠀⠻⣵⢀⠔⠠⡆
⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⠀⠀⣀⠤⠴⠷⠆⠈⠛⠿⣦⡀⠀⠀⠹⣾⡠⠀⠁
⠀⠙⠿⣤⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠙⢢⣄⠈⠓⠄⠀⠀⠹⣦⢀⡀
⠀⠀⠀⠀⠉⠛⢿⣷⣦⡄⠀⠀⠀⠀⠀⠀⣀⡼⠻⢖⠀⠉⠓⢦⣠⡾⢄⠀⢹⡿⣴⣄⠀⠀⠀⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⠄⠀⣀⢀⠀⢀⡿⠷⢄⡈⠙⠲⢄⣀⣹⣷⣀⠀⠀⠻⣟⣿⣿⣷⠀⠀⠉⠉⠙⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣾⣶⣿⣧⣀⡀⠉⠛⠶⣤⣼⣿⣿⣿⢦⣈⡀⠙⣏⣿⣿⡀⢀⡀⠀⠀⢦⡀⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⢶⣶⣿⣿⣿⣿⠃⠑⠮⡑⠀⣿⣿⣿⣦⣿⣿⣶⠀⠈⣿⣆⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠈⠀⣼⣿⣿⢟⠛⢻⣯⠀⠸⠛⢛⣻⣷⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠻⣿⣿⣦⣅⠠⣭⣓⣁⣀⣰⣿⣿⣿⣿⡿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣥⣛⠿⠿⢿⣧⣬⣿⣿⣿⣿⡿⠿⠗⠫⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢽⣛⠿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡑⠉⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠦⠤⠤⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⠂⢀⣰⣿⠟⢉⣭⡮⠿⠛⠁⣠⣤⡄⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢚⣥⣿⣿⠋⣠⣶⣿⠟⣠⣾⡿⠋⠀⣀⣴⡾⠛⠉⠀⠀⢠⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣥⣿⣿⣿⣥⣾⣿⣿⣿⣦⣽⣧⣤⣠⣾⣿⣧⣀⠀⢀⣴⣼⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⣋⣽⣟⣉⣡⣿⡏⣉⣹⣿⣯⣉⣽⣿⡟⣋⣿⣿⣷⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⣿⠿⠿⣿⡿⠿⠿⠿⠿⠿⠿⠛⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡿⢤⢤⣀⣀⣀⣀⣀⣀⣀⣠⡽⡇
⠀⠀⠀⠀⠀⠀⣀⠴⠚⠙⢧⡀⠻⣤⣀⣀⠀⠀⠀⠁⢈⣀⣀⡴⠃
⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠙⣆⡧⢀⣈⡉⠉⠉⠉⠉⠁⠀⣶⣛⣉⢉⣙⣦
⠀⠀⠀⢠⣶⠋⠙⢫⡳⡀⠀⠀⠘⡇⠀⠀⢩⢭⠉⢹⠀⠀⢸⡷⠤⠤⠤⠤⢾⣀
⠀⠀⠀⠇⡇⠀⣠⠤⣷⢹⠀⠀⠀⣷⠀⠀⠘⡫⠆⢸⠀⠀⢸⠀⠀⠀⠀⠀⠈⡇⠉⠓⠢⢄⡀
⠀⠀⠀⡇⢧⡠⠗⣶⣹⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⣾⠑⠒⠲⠶⠒⠊⡇⠀⠀⢀⠔⠉⡆
⠀⠀⠀⠘⢾⣤⣞⣡⡧⠏⠀⠀⠀⢸⠉⠒⠦⠤⠴⠚⠀⠀⢻⠀⠀⠀⠀⠀⠀⡇⡌⡀⡜⢰⠁⢩⣦
⠀⠀⠀⠀⠀⠈⢉⣈⣱⡦⠤⠤⠴⠚⠓⠤⣄⣀⣀⣀⡤⠔⢻⡄⣀⣀⢀⣀⣠⠏⠙⠓⠷⠞⠛⠛⠉⠑⠢⢄⡀
⠀⠀⡠⠤⢤⠴⢅⣀⡤⠟⠀⠀⠀⠀⠀⡴⠶⠶⣆⠀⠀⠀⠀⠉⠛⠛⠚⠛⠁⠀⢠⠤⠖⠢⠤⢤⡀⠀⠀⠀⠀⠁
⠀⠀⠑⠲⠦⠤⠤⠃⠀⠀⠀⡆⢉⠉⣹⡯⠭⢭⡿⠶⡉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠄⣤⡤⠤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠭⠭⠟⠁⠀⣎⠀⣀⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

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

⠸⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠅⠟⠃⠸⠘⠇⠇⠛⠘⠃⠀⠂⠚⠘⠉⠃⠛⠀⠘⠙⠃⠛⠀⠘⠓⠋⠛⠘⠛⠂⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠶⠶⠶⠒⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⢴⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣖⣀⣀⡀⣸⣿⣿⣿⣿⡿⠗⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⣆⣰⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠉⠉⠙⠁⠀⢨⣿⠅⣾⣏⠀⠀⠀⠐⠀⣠⠘⠀⠀⠀⠀⠀⠀⠈⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣇⣿⣾⣿⣿⣷⣦⡀⠀⠀⠈⢰⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠈⠋⠹⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⣀⣠⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢀⣼⣿⡿⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⣸⣿⣟⠹⠛⣿⠄⠀⢀⠀⠀⠀⠀⠀⢀⣼⢇⣿⠟⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣁
⠀⠀⢠⣾⣿⠋⠑⠀⢰⢡⢺⢿⣆⣱⠀⠀⠀⠀⠈⡟⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡉⠻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢹⠛⠛⠋⠁
⠀⠀⠘⠿⢿⣿⣴⣿⣿⣿⠄⣰⠾⣁⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⣠⣮⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⠿⡟⣂⡄
⠀⠀⠀⠀⠀⣿⣿⣿⠋⠀⠐⠟⠆⣠⠣⡀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢀⡙⢧⣀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢽⣿⣷⠘⣿⣶⣖⣾⣟⣀⡇⠠⣾⣧⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠐⡿⠤⡄⠉⠳⣄⠀⠀⠙⠋
⠀⠀⠀⠀⠀⢸⣿⡏⢿⡿⠟⠉⠉⢿⣿⡄⢀⣿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠛⠛⠛⢚⣻⢻⣿⣿⣷⣷⣷⣶⣷⣄⠀⠈⠛⣦⡀⡄
⠀⠀⠀⠘⠀⠀⢸⠉⢶⣬⣀⠀⠀⣀⠹⠁⠘⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⢀⣂⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⢠⠠⣿⣿⣿⣴⣧⣦
⠀⠀⠀⠀⠀⢸⡇⠀⡼⡇⢹⠖⢾⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⡑⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⣿⣿⣿⣯⣿⣻
⠀⠀⠀⠀⠀⠻⠷⠒⠛⢿⡇⢰⢿⣀⡀⠀⠀⣿⠀⠀⠤⠴⠶⠆⣸⣿⣿⠋⣘⣛⣻⣿⣿⣟⠃⣿⣿⣿⠋⡙⠛⠙⠟⠻⢿⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠻⠵⠒⠶⣿⡀⠄⠀⠀⠀⢠⣿⣿⣿⢰⣿⣿⣿⣿⡿⠛⠉⢹⣿⣿⡀⠐⣳⣶⣾⣶⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣤⠿⠷⠾⠷⠒⠂⣰⣿⣿⠯⠤⣤⣤⠾⠋⠙⠋⠀⢸⣿⡟⣇⠀⠀⠘⠛⠿⠿⠊⠀⠀⣉⡁⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠡⠤⠤⣄⣀⣀⣀⡀⠀⠀⠀⠚⠛⣿⣿⣿⣿⣀⣄⣀⣀⣀⣴⣾⣯⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⠻⢿⠛⣻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠒⠛⡓⠤⠀⠀⠀⠀⠈⠙⡛⠛⠛⢿⠿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣯⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠒⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠙⠛⠛⠉⠛⠛⠛⠛⠛⠉⠉
⠀⠀⢀⡄⣀⠀⠠⠀⠀⡄⠀⠀⠀⠀⢠⠤⠀⠀⠀⠀⠄⠠⠀⠀⠄⠀⠀⠀⠄⠀⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠄⠀⠤⠄


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠈⠀⠀⠀⠀⠃⠀⠀⠀⣀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⢀⢠⠇⠀⢀⣠⠖⠀⠀⠀⠀⠐⠁⠀⠀⢑⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⢣⣀⡭⢶⢾⠚⡶⢤⣞⠀⠀⠀⠀⠀⠀⠘⠦⠠⠰
⠀⠀⠀⠀⠀⠐⠂⠀⠀⢀⣈⡽⠋⣀⠀⠀⢠⠀⣠⠌⠉⢣⡤⠤⠒⠀⡠⠀⠀⠀⠀⠀⡅⠀⠀⡄⠀⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣸⡁⠀⣀⡀⠀⡈⠀⠀⢀⠀⠉⡇⠀⠀⠀⠁⠀⠀⠈⢢⣠⠵⠔⢶⣁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢼⡂⠘⠁⡀⠠⠖⠀⠂⠉⠁⢰⠗⠂⠀⠀⠀⠐⠢⢤⠟⢀⠀⠆⠀⠈⢫⣀⡀
⠀⠀⠀⠀⠐⠄⠀⠈⠁⢀⡼⠳⣀⡀⠠⠂⢠⠀⠑⠀⢲⠿⢄⠀⠀⠒⢂⠀⢒⡎⠀⡀⠁⠀⠁⠄⢈⣇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠉⢳⡤⣤⣈⣀⡤⠿⡏⠀⠘⠂⢀⠀⠀⠀⠨⢧⡀⠀⡄⠴⠈⠀⡰⢇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠠⠇⠈⡇⠀⠇⠀⠱⠀⡀⠀⠁⠀⠀⠀⠐⠈⡹⢦⠤⡦⠴⡋⠣
⠀⠀⠀⠀⠀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠈⠢⠀⠁⠈⠀⠁⠀⠈
⠀⠀⠀⠀⠊⠀⠀⠀⠀⣀⡴⠚⠒⠆⡀⠀⠈⠁⠀⠀⠀⠀⢃⠀⡄⠀⡇⠀⠀⡰⠀⠀⠀⠀⠀⠀⡀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⢥⠀⠀⠀⠀⠀⡀⠲⡤⠓⠛⠀⠛⠲⢷⣅⢀⠤⠴⠂⠀⡜⠁⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⢀⡀⠏⠀⠀⠀⢀⣀⠈⡞⠀⠐⠂⠀⠌⠀⠤⠈⢻⠀⠀⠀⠀⠐⠤⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⢀⡩⡇⠀⠠⠂⠐⠀⠀⠀⣀⢸⠃⠒⠂
⠀⠀⠀⠀⠀⠀⠘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠻⣆⠀⠀⢠⠀⠑⠀⢠⠯⠄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠟⢲⢤⣀⣀⣤⠝⢣⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠊⠀⠈⠀⡆⠀⠘⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢸⣿⠀⠀⢸⡇⠀⠀⣿⡇⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣸⣿⣀⣀⣸⣇⣀⣀⣿⣇⣀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡏⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⠾⠷⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⣀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣴⠟⠋⠉⠉⠉⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⠶⣶⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⣀⣀⣿⠀⠀⣿⣀⣀⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠉⠉⠉⠀⠀⠉⠉⠉⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠿⠶⠶⣶⠀⠀⣶⠶⠶⠿⠀⠀⠀⠀⠀⣿⣷⠀⠀⢀⣀⣀⣤⣤⣴⢾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡿⠛⠛⠋⠉⠉⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣿⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠀⣿⡀⢶⡄⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⢸⣧⠈⠻⣦⣤⣤⡀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⠟⠁⠀⠀⠙⢷⣤⣀⣀⣀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⣠⡀⠀⠀⠀⠀⠀⡄⠠⠀⠀⠀⠀⠀⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢧⢰⢻⡇⣾⣩⠆⣶⠙⡇⢰⢠⡎⠁⢐⣩⡆⢹⠋⢷⢠⠎⢱⡄⡖⠙⡆⢾⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠃⠘⠃⠙⠒⠂⠙⠒⠃⠘⠀⠓⠒⠙⠒⠃⠘⠂⠙⠈⠓⠚⠁⠃⠀⠃⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠠⣄⣀⡀⠀⢀⠀⢀⣴⢶⡚⠳⠀⢀⣀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠾⢶⣦⣽⠀⠈⠉⠙⠁⠂⠉⠁⢱⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠠⠐⢢⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠱⠀⠀⣸⢳⡖⠀⠀⠈⠠⠤⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠃⠀⠀⠀⠀⣠⠞⣁⠀⠀⠀⠀⠀⢀⠃⠀⠀⡿⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡤⢺⠁⠉⠙⠛⠁⠀⠀⢀⡎⠀⢠⠴⠃⠀⢉⠓⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⢠⠀⠛⠛⠟⠀⠀⠠⣀⠄⠀⠀⣸⠃⠀⠀⠀⠰⠋⠘
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡀⠀⠠⢟⡧⣀⣀⣀⠰⡄⠀⠀⠀⠀⠐⣾⠶⠴⠛⠈⣳⢄⡀⡄⣀⡠⠂
⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⡿⠇⠀⠀⢱⣌⣹⠋⠈⠙⠄⢰⣶⣄⣀⣅⠀⢀⣠⣴⢧⠀⠀⠈⠁
⠀⠀⠀⠠⢄⠀⠀⠀⠀⢀⠀⠀⠐⠤⡄⢶⠾⠛⠛⠀⠀⠀⠈⣟⠉⠉⢽⣛⣛⣯⡅⠀⢣⠁⣠
⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢻⣋⠙⠻⠿⢿⡄⠀⠈⠒⠁⠀⠀⡀
⠀⠀⠀⠤⠴⠂⠀⠀⠀⡠⠐⢢⣄⠀⣀⠀⠀⠀⠹⣀⠀⢠⠾⣿⢽⣯⡷⠄⠀⠀⠉⡄⠀⢠⣄⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠹⠀⠈⠀⠒⠒⢂⠀⠉⡁⠈⠀⠀⠀⡳⠳⠾⠛⠋⠀⠉⠀⠈⠀⠀⠈⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠁⠀⠀⠀⠀⠀⢀⡴⠀⡠⡗⠀⠀⢁⡀⠀⡄⠀⠀⠀⠀⠀⢀⠄⠀⠀⢠⡔⠊⠀⠀⡀
⠀⠀⠀⠠⠂⠀⠀⠀⠹⠿⠄⠀⠀⠀⠀⠀⠀⠜⠀⠀⡁⠁⠀⠀⠀⣠⡴⠀⠀⠀⠐⠂⠀⠀⠀⠀⠐⠁⠀⠠⡀
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠋⠔⠉⠀⢠⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⢿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣀⡷⠾⠛⢹⡄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⢇⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠖⠒⠚⠛⠛⠛⠛⠛⠛⠒⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⠲⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⢿
⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠫⣉⠀⠸⣄⠀⠀⠀⠈⠈⠉⠉⠉⠉⠉⠉⠀⠀⣀⠟
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⠳⡄⢸⠙⠛⠒⠒⠶⠦⠴⠤⠶⠶⠖⠚⠛⡃⣠⡤⠤⠤⢤⣄⡀
⠀⠀⠀⠀⣜⣀⣤⣀⡀⠀⠀⠀⠀⠹⣼⡇⠂⠤⢤⣄⣀⣀⣀⡀⠀⠀⠀⢰⣿⠧⠤⠤⠤⠤⠴⢿
⠀⠀⡴⡿⠋⠉⠙⢦⡹⣄⠀⠀⠀⠀⢹⡇⠀⠀⠀⡤⠤⡄⠀⣿⠀⠀⠀⢸⡿⠶⠤⠤⠤⠴⠶⣏⣀
⠀⡼⢰⡇⠀⠀⢀⣈⣧⠘⡆⠀⠀⠀⠀⡇⠀⠀⠀⠷⢮⡤⠀⣿⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠈⡏⠉⠓⠦⢤⣀
⠀⣇⢸⡇⠀⢾⣁⣈⢿⡄⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠉⠀⢸⠀⠀⠀⣿⠤⣀⣀⠀⠀⢀⣀⡤⡇⠀⠀⠀⠀⠈⣹⠦⡄
⠀⢹⡀⢧⠔⠋⢩⠿⣼⢡⡏⠀⠀⠀⠀⣧⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠉⠉⠉⠉⠁⠀⡧⠀⡀⠀⠀⡞⢁⡀⣿⡀
⠀⠀⠳⣜⡦⢴⣋⣴⣣⠞⠀⠀⠀⠀⠀⢿⠈⠙⠓⠶⠶⠶⠖⠋⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣇⢰⠁⡄⣸⠀⡏⠀⢀⣽⡆
⠀⠀⠀⠈⠉⠉⠉⠉⠳⢤⣀⣀⣀⣀⡤⠾⠦⣄⣀⠀⠀⠀⠀⠀⠀⣀⡤⣿⡀⠀⠀⠀⠀⠀⠀⢀⡟⠛⠲⢧⣿⣤⠽⠳⠾⠋⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠤⠒⠻⠉⢹⡄⠉⠉⠀⠀⠀⠀⠀⣉⣉⣉⡛⠛⠋⠉⠀⠀⠈⠳⣭⣓⣒⣒⣒⡪⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠄
⡞⠋⠉⡛⠛⠓⢦⡴⠒⠋⠀⠀⠀⢀⣀⣀⡀⡾⣒⣂⣉⣹⡆⠀⣀⣀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡖⠉⠉⠉⢹⠉⠓⢦⡀
⠉⠒⠲⠧⠤⠤⠼⠁⠀⠀⠀⢠⡎⠁⡸⠉⢉⡷⠦⠭⠭⣾⠖⠫⡁⢀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣤⣼⡤⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣙⣛⣛⡩⠇⠀⠀⡼⠁⠀⠀⣰⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡀⠀⠀⢀⣴⣾⣶⣦⡀⠀⠀⢰⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⠿⣿⣿⣿⡧⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⣼⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠟⠁⠀⢀⢀⢶⢟⡽⠃⠀⢸⣿⠿⠿⠿⠿⢟⠀⠀⢹⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⡀⠀⠙⠳⣄⣴⣿⡏⣪⠟⠀⠀⠀⠀⣿⠶⠂⠀⠀⣾⣧⠂⡼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⣿⣽⣿⣦⠀⠀⢹⣏⡙⢾⣇⣀⣀⣀⠀⠀⣿⣶⣶⣶⣿⣿⣿⠎
⠀⠀⠀⠀⠀⠀⠀⠊⠙⠋⠛⣿⣿⣿⡇⠀⠀⣿⣿⣄⠙⠳⣭⡉⠀⠀⢻⣿⣿⣿⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢶⣿⣿⣟⣁⣀⣼⣿⣿⣿⣷⡆⠘⣿⣷⡿⠿⣿⣿⣿⣿⣿⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢿⣿⣿⣿⠛⠺⣃⡌⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣏⣀⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠋⣹⠄
⠀⠀⠀⠀⣀⣤⡤⠤⣤⣄⣀⠸⠚⠉⠁⢀⣀
⠀⠀⣰⠋⠁⠀⠀⠀⠀⠀⠉⠓⢦⢠⣞⣉⣈⡷
⢠⠎⠁⠀⢀⡀⠀⠀⢠⣄⡀⠀⠀⢻⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡆
⡟⠀⠀⠀⢸⡏⠉⠉⠉⠀⠉⠛⠙⣾⠗⠛⠉⠀⠀⠀⠀⠉⣹⠶⠶⡄⠀⢻⠀⠀⠀⠀⢠⣄⢰⠃
⣇⠀⠀⣶⡼⠀⡤⠃⠁⠀⢠⣾⡄⢹⡄⠀⠀⠀⣀⡤⠴⠶⢧⣀⣠⠏⢀⣸⡆⠀⠀⣀⣸⠉⠋⠀⠀⠀⠀⠀⢀
⠹⡄⢀⣻⠀⠀⠀⠹⠆⠀⢀⡤⣄⢀⡇⠀⢀⡜⠁⠀⠀⠀⣀⠉⠀⠀⠀⢏⠁⠀⠀⡏⠋⠀⠀⠀⠀⣴⡀⢀⡞
⠀⠙⣏⠉⡀⠀⢰⠛⠒⠛⣉⣤⣾⣾⠀⣄⡀⠱⣄⠀⣠⢞⡁⢀⣀⣤⣄⠈⠀⠀⢀⡇⠀⠀⢀⣄⣰⠃⢳⠏
⠀⠀⣠⠋⠉⠓⠾⠷⠶⣿⢳⡿⢥⠏⠀⢳⠉⠃⠈⣧⣁⡊⠴⢈⡿⢤⣽⣇⠀⠀⠈⠁⠀⢠⠏⠘⠁
⠀⡼⠁⠀⠀⢀⣠⣤⡀⠈⠉⠀⠀⠀⠀⣨⠇⠀⢲⣛⣉⣿⠀⡼⠓⠋⠉⠉⠉⠉⠓⢦⠀⠉⠀⠀⠀⣠⡆
⢰⠃⠀⢀⡔⠋⠀⠀⠙⣆⠀⠀⠀⠀⢼⣁⣀⠀⠀⢯⠀⢈⡟⠀⡀⢠⡀⠠⣄⡀⠀⠈⢳⠀⠀⡤⠊⢱⣇⡤⠖
⢸⣤⠴⣾⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⣸⠁⠀⠘⢦⣸⢠⠞⠙⠒⡉⣤⢎⠉⡅⠀⢸⡆
⠸⣅⣀⡼⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠛⠚⠃⠀⢀⣿⣬⠄⠽⠦⠁⠰⠯⡔⠻⡟⢺⠛⠲⢤⡀
⠀⠈⠁⠀⠀⠀⠀⠀⠀⣰⠋⠙⠛⠒⠒⠒⠒⠒⠛⠉⠉⣧⠾⡀⣞⠳⠴⠚⠛⠉⡷⠛⢭⣀⣀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢀⡞⣇⠀⠀⠀⠀⢰⢻⡇⠉⣟⠲⠶⠶⠚⠛⠁⠀⢸⣸⠎⣷⠤⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢠⠎⠀⣿⠀⠀⠀⠀⣸⠚⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠳⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡞⠀⠀⢿⠀⠀⠀⠀⡏⠀⠀⣀⣧⣄⣀⡀⠀⠀⠀⢀⣀⡼⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣧⠀⠀⠸⡄⠀⠀⠀⡇⠀⡼⠁⠀⠀⠈⣉⣉⣉⠉⠉⠁⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⢸⡀⠀⠀⠹⣄⠀⠀⣷⠀⢧⠀⠀⣴⠋⠉⠉⠉⠙⠲⢤⡀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡋⣉⣉⣩⡇⠀⠀⢠⠟⠉⠉⣙⡆⣨⠷⠶⣿⠀⠀⠀⠀⠀⠀⠀⢹⠦⠤⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁

⠀⡤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢦⡀⠀⡠⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⠦⡀⠀⣠⠶⠶⠶⠶⢶⣶⣶⡶⠶⠶⠶⠶⠶⠦⡄
⠀⡇⠀⢻⣽⠛⠛⠛⢳⡀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⢀⣀⣠⠤⢤⣒⡲⡭⠭⣭⡅⡇⠀⡇⠀⠀⣠⠖⡩⠖⢒⠚⠀⠀⠀⠀⠀⠀⡇
⠠⡇⣀⠯⠼⢄⡀⠀⠀⠀⠁⠄⡀⠀⠀⠀⡇⠀⡇⠀⠀⠀⣿⠒⠉⠉⣿⠀⠀⠀⠈⣿⡅⡇⠀⣇⠔⢋⡤⠊⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡇
⠈⣷⣁⣀⣀⣀⡇⠀⠀⠀⣀⣀⣀⣀⣀⣠⡇⠀⡇⠀⠀⠀⣫⠖⠚⠃⣿⡀⠀⠀⠀⣿⠇⡇⠀⣧⠔⠉⠀⠀⠀⠁⠈⠀⣁⣀⣀⣀⡀⣀⡇
⠀⣿⠀⠀⠀⠀⡷⠀⠀⢰⣒⠒⠒⠂⠴⠒⡇⠀⡇⠀⠒⠉⣾⠀⠀⠀⣿⠇⠀⠀⢀⣿⠆⡇⠀⡇⠀⢀⡀⠀⠀⡠⠔⠩⣗⠒⠂⠤⠤⠒⡇
⠀⣿⠀⠀⠀⠀⡏⢠⣒⠭⡚⠁⠀⠀⠀⠀⡇⠀⡇⠀⠀⢀⡥⠒⠁⠀⣿⠀⠀⠀⠀⣿⡇⡇⠀⡇⠀⠈⠁⠀⡨⢠⣖⠭⠖⠋⠀⠀⠀⠀⡇
⠀⣿⠓⠒⠒⠒⣇⡾⣒⡫⢕⣂⠀⣀⠔⠋⡇⠀⡇⠛⠉⠁⣞⠤⠤⠤⣿⣀⣀⣀⣀⣿⡃⡇⠀⡇⠀⣆⣰⠀⠧⡸⢕⣊⠥⣂⠀⢀⡴⠊⡇
⠐⣏⠓⠒⠒⠒⠋⠉⠓⢾⠭⠒⠋⠀⠀⢀⡇⠀⣇⠀⠀⠀⠈⠉⠉⠙⠒⠒⠒⠒⠬⠼⢃⡇⠀⣇⠀⠀⠀⠀⠀⠉⠓⢶⡭⠔⠊⠁⠀⢀⡇
⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⡞⠉⠉⢉⡭⠭⠽⠟⠛⠻⢭⡉⠉⠉⠙⡆⠀⡞⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡆⠀⡞⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡆
⠀⡇⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⡇⠀⡇⢀⡴⠚⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⡜⠉⠙⣆⠀⠀⠀⠀⠀⠀⡞⠉⠙⡆⡇
⠀⡇⠀⡇⠀⡴⢄⣼⠣⣼⠳⣄⠀⠈⡆⠀⡇⠀⡇⡞⠒⠒⠚⠤⣄⡀⠀⠀⠀⢀⣠⣄⡀⡇⠀⡇⠑⠤⠴⠃⠐⣲⢦⢤⣤⠀⠳⠤⠴⠃⡇
⠀⡇⠈⣇⡞⠀⣤⠀⠀⠀⢠⠈⠙⣆⡇⠀⡇⠀⣷⠃⠂⠀⠀⢀⠀⠈⠉⠉⠛⡇⠀⠀⢱⡇⠀⡇⡴⠋⠙⣆⢈⡉⠉⠈⢈⡀⡔⠋⠑⡆⡇
⢀⡇⠸⡉⠙⠞⠋⠉⠉⠉⠙⠛⡞⢉⡕⠀⡇⠀⡏⡆⠠⠄⠀⠀⠀⠀⠀⠀⢐⡇⠀⢠⠇⡇⠀⡇⡇⠀⠀⡏⠙⠉⠉⠉⠙⠁⡇⠀⠀⡇⡇
⠀⡇⠀⠈⢲⡀⠀⠀⠀⠀⠀⠀⡷⠋⠀⠀⡇⠀⡇⢱⡀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠖⠁⠀⡇⠀⡇⣧⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⡇
⠘⡇⠀⠀⠀⠉⢳⠶⠤⠔⡖⠉⠀⠀⠀⠀⡇⠀⡇⠀⠉⠒⠦⠤⠤⠔⠒⠋⠁⠀⠀⠀⠀⡇⠀⡇⢹⣤⣤⠇⠀⠀⠀⠀⠀⠀⢿⣤⣤⠇⡇
⠀⠣⠀⠠⠖⢫⣽⣤⣤⣤⣼⣭⣵⣦⣤⡴⠃⠀⠣⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡴⠃⠀⠳⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣦⢤⢤⣴⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⢠⡼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣼⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠀⠁⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⣿⣿⠿⠿⠿⣼⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡷⢶⣦⢉⡉⡋⠉⠁⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠸⡧⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠈⠉⠓⢥⡀⠄⣪⣽⡄
⠀⠀⠀⠀⠀⠀⢸⣿⠶⠴⡶⢶⠒⣻⠂⠀⠀⠀⢀⣹⡥⡀⠀⠀⠹⡿⠿⠿⠿⢿⣶⣶⡶⢶⣤⣤⣇⡀⢸⠉⠙⠓⠒⢲⠀⠀⢱⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣀⠸⠀⠿⡂⠀⢠⣾⡿⠛⠿⣖⢄⠀⣠⣷⣄⠀⠀⠀⠀⠈⠉⠲⡄⠈⠙⣿⣿⡄⠀⠀⠀⢸⠀⠀⢸⢸⣿⣿⣇
⠀⠀⠀⠀⢀⣤⠟⢳⣯⡿⠯⢿⣄⣶⣛⣦⣼⣿⣦⣤⣤⣾⣿⣟⢋⣡⣾⡁⠀⢀⣹⣿⣿⣷⣷⣦⣶⣿⣿⠁⠀⠀⠀⢸⠀⠀⢸⣼⣿⣿⡟
⠀⠀⠀⠀⡿⢥⣀⣀⠈⠉⠉⠉⢡⣿⣤⣤⣠⡤⣼⣟⣭⢫⡉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⣽⢫⣿⡏⢸⠀⠀⠀⠀⢸⠀⠀⢸⣿⣿⣿⣷
⠀⠀⠀⠀⡇⠀⠀⠈⠉⠉⠉⠉⢹⣿⣿⡆⡇⠀⢸⡟⣸⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣿⡇⠸⠀⡀⠀⠀⢸⠀⠀⢸⡟⣿⣿⣿
⠀⠀⠀⠀⡇⠀⡏⠓⠒⠒⠒⠒⠚⣿⢛⣿⠻⠛⣿⡇⣿⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠻⣿⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⣿⣿⣿
⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⣠⣾⣛⠋⣘⣃⢨⡳⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣜⠂⠉⠉⠉⠀⠒⣦⡀⠀⠀⠀⠀⡇⣿⣿⣿
⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⣞⣿⣿⣿⣾⣿⣿⣗⠙⡘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠛⠛⠛⠒⠚⠋⢹⡇⠀⠀⠀⠀⡇⣿⣿⣿
⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠳⠤⠤⢤⣤⠤⠴⠚⡇⠀⠀⠀⠀⡇⣿⣿⣿
⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⡇⠀⢉⠉⠉⠉⢉⣉⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡉⠛⠒⠤⠶⠶⠶⠖⠙⢙⣆⡠⠤⢤⣧⣿⣿⣿
⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⡇⠀⠘⢒⡶⠻⣟⠛⠀⠀⣿⣝⡢⢤⣄⣀⣀⣀⣀⣀⡤⣿⣝⣲⠲⠤⠤⠤⠤⠒⣎⣭⡏⠀⠀⠀⠀⠈⠉⠙⠓⠲⠦⢤⣄⣀⡀
⠀⠀⠀⠀⣧⠀⠓⠤⠤⠤⢤⡇⠀⢰⡋⠀⠀⠈⣱⠆⠀⣿⣿⡿⠋⠓⠓⠒⠒⠒⠒⣋⣿⠀⠉⠉⠛⠒⠛⠋⠉⠁⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠽
⠀⠀⠀⠀⠙⠦⣄⣀⣀⣀⢀⡇⠀⢀⠙⢦⣤⠞⢁⠀⠀⢿⣿⡇⠒⠢⢤⠖⠂⠛⢿⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⡇⠀⠈⠙⠋⠛⠋⠋⠀⠀⣸⠿⣇⣀⡀⢸⣶⣶⣲⠷⡳⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣦⣤⣀⣀⠴⠊⠁⠀⠀⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣷⣶⣦⣤⣤⣴⣶⡆⢹⣿⠀⠀⠈⢉⡹⣻⡉⢈⠇⢱⣿⣄⣀⠀⠀⠀⠀⠀⠀⣀⡤⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⡤⠞⠉
⠀⠀⠀⢠⠶⠶⠖⠒⠒⠒⠒⠛⠉⠉⠉⠙⣿⣟⣛⣡⠴⠃⣴⣆⣢⠿⠿⣿⣏⣁⣠⣿⣽⠀⠉⠙⠛⠒⠒⠛⠋⠁⠀⣿⠉⠙⠻⠿⢿⣿⣿⣇⡤⠞⠉
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠄⠀⡄⠀⡈⠉⠛⠂⠀⠼⠈⠉⠉⠀⠘⠧⣄⣀⣀⠀⠀⢀⣀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣗⠺⢿⡶⠦⠛⠲⣎⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠸⡧⠤⠤⠶⠒⠒⠒⠒⠒⠚⠛⠋⠉⠉⢻⠀⠈⠳⠖⠚⠉⠁
⠀⠀⠀⠀⣧⡤⠤⠤⠤⠴⠶⠶⠒⠒⠒⠒⠛⠛⠋

⠀⠀⠀⣤⣶⣦⡀⠀⠀⠀⢰⣶⠟⣷⡆⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⠀⠀⠀⠆⠀⠆⠀⠀⠀⠀⣴⣖⣶⣢⡀
⠀⠀⠘⣇⠛⢉⠃⠀⠀⠀⠰⣾⡟⣻⡧⠀⠀⠀⠀⢿⣳⡟⠀⠀⠀⠀⠀⠸⣝⠅⠀⠀⠀⠀⣟⣙⣋⣹⡇⠀⠀⠀⣥⣭⣭⣭
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⢠⣼⣿⠇⠀⠀⠀⢴⣿⣿⣿⡆⠀⠀⠐⣿⣿⣟⢛⣛⠀⠀⢀⣴⣾⡿⠟⢢⠀⠀⠈⢻⢟⡻⡟⠃⠀⠀⠠⣞⣲⣋⣇⠂
⠀⠀⠰⣿⣿⠛⠀⠀⠀⠀⠹⣌⣉⣽⠃⠀⠀⠀⢾⣿⠟⠉⠁⠀⠀⠈⠦⣶⡤⠾⠋⠀⠀⠀⣼⠮⠷⣧⠀⠀⠀⢰⡿⠛⠩⠛⠃
⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠛⠀⠀⠀⠀⠁
⠀⠀⠀⣀⣠⣀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠠⡦⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣠⣶⡄⠀⠀⢀⠀⣀⡀⠀⠀⠀⠀⣰⢢⡄
⠀⠀⢰⡿⠓⠻⡇⠀⠀⠀⢸⣻⠏⠁⠀⠀⠀⠀⣸⡇⠀⢀⡀⣹⣿⣏⣀⠀⠀⢀⣼⠀⠀⠀⠀⣘⣲⣿⣷⡞⠀⠀⠘⠹⡏⠧
⠀⠀⠈⠳⠤⠴⠃⠀⢠⣶⡏⠀⠀⠀⠐⣿⣿⣿⠟⠀⠀⠐⠚⢿⣿⡿⠧⠀⠀⢸⣇⡀⠀⠀⠀⠨⠿⠿⢯⠁⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠁