Kawaií Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢸⡶⠀⣷⢰⣤⡼⣸⡆⣷⡷⠀⠀⠀⠀⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠉⠉⠉⠙⠃⣴⢸⡆
⠀⠀⠀⠘⠙⠘⠙⠛⠋⠁⠋⠛⠋⠃⠀⠀⠀⠀⠀⠀⠁⠀⢀⡀⠀⢀⠀⠀⠀⠀⡀⠀⠄⠀⠠⠀⠀⠀⠀⠀⣠⢰⡶⠀⠀⠀⢻⠀⡇
⠀⠀⠀⠀⡆⢠⡀⣄⣠⠄⢰⣤⢠⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠁⠈⠀⠠⠀⠀⠀⠀⠑⠀⠀⠀⢀⠿⠠⠿⠇⠀⠀⣾⢰⠇
⠀⠀⠀⠠⣬⠟⣧⡟⢬⡷⢸⢻⣼⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⡀⠀⠀⠀⠀⠀⢀⠐⠀⠈⠀⠉⠂⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠶⠶⠠⠆⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠃⠀⠀⡀⠀⠀⠀⠀⠁⠀⣀⠀⠀⠠
⠀⠀⠀⢀⡴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠠⠄⠀⠀⠀⠈⢷⠀⠀⢠
⠀⠀⠀⠀⠀⠈⠃⠀⠠⠀⠁⠀⠀⠠⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠠⠈⠉⠁⠄⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⠛⠿⠿⠿⠛⠋⠁⠀⠀⠀⠙⠛⠻⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠂⠀⠀⠀⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠄⠀⠀⠀⠀⢻⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠒⠀⠀⠰⠀⠈⠄⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⡇⠀⠀⠈⠀⠀⠀⠀⢰⣿⣶⣶⣶⠀⠀⢀⠀⠀⠀⠀⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡏⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⣀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣠⠤⢄⡀
⠀⠀⣀⠀⠈⠁⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⡀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⡄⠀⠠⠀⠀⠀⡀⠉⠀⢀⠁
⠀⠀⠁⠀⠀⠀⠀⠀⡄⢀⣄⡀⠀⠀⢀⠊⠹⢀⠀⠀⣀⠃⠉⠙⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⢄⠀⠁⠀⠘⠀⠘⠀⢀⠀⠀⠘⠀⢀
⠀⢠⠀⣤⡄⠀⢰⣦⠈⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⡀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠰⠆⢠⣴⠄⠈⢠⣴⠄⠀⠙
⠀⠀⠀⠉⠁⠀⠀⠁⢰⠀⠀⣠⡄⠆⠀⠀⠀⣴⡀⡀⢠⡆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠿⠂⠀⠸⠇⠂⠀⠀⠀⠀⠀⠐⠀⠉⠀⠀⠀⠉⠀⠂
⠀⠀⠃⠀⠀⠀⠀⠀⢈⠀⠀⠉⢁⠀⠀⠀⠁⠈⠀⠀⠈⠡⠀⠀⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠁⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠁⠀⠈⡁⣈⠂
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡀⠰⠀⠀⠄⠁⡤⠠⠀⠀⠀⠀⡀⠂⢀⠀⠀⡐⠈⡐⠀⠀⠁⠙⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠄⠀⠂⠀⠆⠀⠀⢠⢄⠀⠀⠀⠀⠀⠀⠒⠀⣄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠒⠃⠀⠈⠒⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣠⡄⠀⠀⣠⣄⠀⠀⠀⠀⠈⠉⡀⠀⠀⠀⠀⠀⢠⡀⠛⠁⠀⠘⠋⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀
⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠙⠁⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢀⠸⡷⠀⠀⢾⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠈⠉⠀⠀⠉⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⠈⠐⠀⠀⠀⠀⠀⢀⠀⠀⢈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⢈⢁⠀⣁⣀
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠒⠀⠀⠈⢀⡀⠀⢠⣦⢀⡄⠀⢀⡄⠀⡀⠀⠀⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⢠⠃⡀⠀⠀⢀⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠃⠀⠀⠉⠈⠁⠀⠈⠁⠈⠋⠀⠘⠣⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠀⠠⣧⠀⠐⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⢀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠠⠤⠄⠀⠀⠀⠠⠄⠐⢚⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⢸⢈⠀⠀⠀⠀⠀⠀⠀⠈⢫⠀⠀⠀⠀⠀⠸⠶⣶⣤⣤⣤⣤⣴⡶⠾⠂⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂
⠀⠀⠀⠀⢠⣄⣀⣀⡀⣀⣀⣀⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣄⣀⣀⣀⣤⣤⣴
⠀⠀⠀⠀⠀⠉⠉⠙⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣀⣤⣦⣄⡀⠀⠀⠀⢀⣴⡶⣶⣄
⠀⠀⠀⣰⣿⣻⣿⣆⠀⠀⢠⣿⣯⣿⣿⣆⠀⢰⣿⣿⣾⣿⣷⠀⠀⠀⣿⣿⣷⣿⣿⡇⠀⢀⣴⡾⣶⣦⠀⠀⠀⢠⣾⣟⣿⣷⡀
⠀⠀⠀⢻⣿⣟⣿⠟⠀⠀⠘⢿⣿⣹⡿⠏⠀⠀⠻⠿⠼⠿⠋⠀⠀⠀⠹⠿⠧⠿⠟⠁⠀⢸⣿⣿⢿⣿⠇⠀⠀⢻⣿⡟⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⣤⠾⠁
⠀⣠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡄
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠛⠓⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠚⠛⠛⠃

⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣟⣀⣀⣠⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⡀⠀⠀⠀⠌⣠⡄⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⣷⠀⠀⠠⠠⣿⡏
⠀⠀⠀⠀⡀⠒⠐⠁⠉⠒⠐⠂⡀⠀⠀⠀⠀⠐⠈⠿⠀⠀⠐⠀⠟⢀⠀⠀⠀⠀⠀⠀⠰⠂⢢⣶⠌⠁⠉⠰⡀⠀⠀⠀⠀⠀⢀⠰⠛⠉⠒⠒⠀⠄⢶⡄
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠙⠁⠀⠀⠀⠀⢂⠀⠀⠀⢠⠀⠀⠀⠀⠀⠒⠀⠀⠀⠲⡀
⠀⠀⠈⠀⠀⠀⠀⠄⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠄⠀⠀⠠⢤⠀⠀⠀⠆⠀⠀⠀⠐⢂⡀⠄
⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠂⠄⠀⠀⠀⠘⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢘⣦⠠⣤⣤⣤⣤⣤⠔⣮⡂⠀⠀⠀⠈⠀⠤⡤⠈⠈⡰⠅⠐⠀⠀⠀⠀⠀⠈⠐⠠⠤⠀⠁⠀⠐⠚⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⢀⢀⠠⠀⠈⠙⠛⠛⠁⠀⡌⣀⠀⠀⠀⠀⡠⠀⠀⢄⣀⠤⠀⠀⢀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⢀⡠⠔⠀⠀⠀⠀⠀⠀⠀⠠⣠
⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⠀⠀⠀⠻⠆⠀⢀⠀⡀⠀⠀⠀⠀⠾⠀⠀⠈⠟⠀⠀⠄⠀⣆⠀⢠⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⢬⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⣀⣀⠤⠦⠤⠆⢸⠦⠤⠤⢄⣀⡤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢅⡐⠁⢀⣀⠀⠀⠀⠐⠈⠀⠀⠀⠀⣀⠀⠑⣀⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠓⠠⠍⠁⠐⠛⠛⠛⠛⠛⠛⠛⠛⠓⠀⠩⠥⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠂⠀⠀⢠⡿⣆⠀⠀⠀⠀⢀⡾⣆⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⢡⠀⠀⠀⠀⠀⠀⠀⠋⠀⠘⢠⣤⣤⣄⠛⠀⠈⠁⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠤⠘⡆⠠⠜⠂⠓⠀⢠⣄⠀⠀⠀⠀⠀⢸⣿⠿⣿⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⢠⠂⠁⠡⢡⠀⠀⠰⡀⠀⠀⠀⣠⠃⠀⢈⠇⠔⠂⢄⠀⠻⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠔⠋⢃⠀⠀⢡⠀⠀⠀⠏⠀⠀⡼⠬⡀⠀⡘⢀⠤⠐⠂⠉⠉⠉⠉⠁⠘⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠘⡀⠈⡄⠀⠈⡇⠀⠀⠀⠀⢀⠀⠀⠃⠰⠋⠀⠀⠄⠐⢀⠀⢀⠈⠀⠀⠀⠀⠄⠑⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢁⠀⠁⠀⠀⠁⠀⠀⠀⠀⠈⠀⡘⢠⠃⠀⠀⠀⠀⢀⣤⡀⠀⠀⢀⣤⡁⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠪⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠹⠀⠀⠀⠀⠀⠹⠿⢃⣤⣄⠘⠿⠃⠀⠀⠀⠀⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠉⠒⠰⠤⠤⠦⠄⠒⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠸⡛⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠦⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⠦⠀⠀⠀⠰⠛⠳⠄⠀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⣾⡆⠀⠀⠀⠀⢐⠃⡈⠀⠀⠀⠀⠀⠀⠀⣀⠠⠴⠶⠖⠒⠚⠋⠉⠀⢀⣸⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⣸⠁⠉⠰⠤⠤⠤⠒⠈⠤⠫⠡⠤⠀⣤⠤⠄⠒⠂⠈⢁⡜⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡤⢤⠤⠠⠤⣤⡤⠤⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣼⡃⠀⢀⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠉⠂⠄⡀⠀⢀⠀⠱⠦⠤⠐⠂⠈⠉⠁⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⢀⣀⣀⣀⣀⠠⠔⠁⠀⠑⠢⠤⠀⣀⣀⣀⠁⠀⠀⠀⠀⣀⣀⣀⠠⠤⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠒⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡴⠋⠀⠀⠀⠀⠀⠀⠀⡠⠤⠐⡄⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣁⡿⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⠀⡠⠴⠘⡄⠀⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⠀⠀⡠⠔⠉⢎⢇⠀⠀⢃⢰⠀⠀⢃⡘⠀⠉⡲⡰⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⡇⠀⠀⠀⠘⡄⠀⡜⠛⡄⠀⠘⣬⠀⠀⢸⠁⠀⢠⠵⣁⠀⢠⠁
⠀⠀⠀⡠⢒⠔⠚⠛⠉⠉⠙⣀⠏⠉⠉⠙⠓⠻⡒⢷⠀⢡⠀⠀⢸⠀⠀⡆⠀⠀⡌⠀⡌⢠⠃
⠀⠀⠀⡿⢖⡛⣲⠦⠴⠶⠶⠤⠶⠶⠶⠴⣖⢚⡂⢽⠇⠀⡆⠀⢸⠀⠀⠇⠀⢠⠁⢰⢁⡆
⠀⠀⠀⢰⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⡘⢾⡀⡃⠀⢸⠀⢰⠀⠀⢸⢀⡴⠊⠇
⠀⠀⠀⠈⡄⠀⠀⢠⠿⡄⠀⠀⠀⢀⡾⣆⠀⠀⠀⣇⠀⠈⠉⠒⠚⠀⠘⠒⠒⠉⠁⠀⢸
⠀⠀⠀⠀⡇⠀⠀⠉⠀⠉⣴⣶⣦⡉⠀⠉⠀⠀⢸⠻⠀⠰⠋⠛⠆⠀⠀⠀⠞⠙⠆⠀⡆
⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⢿⡟⣻⠁⠀⠀⠀⠀⠸⠘⡂⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠉⠁⢠⢄⣀⠠⠤⢧⣀⣇⣀⢀⡀⠀⠻⠟⠀⠀⠀⠀⣸⢀⡀⣀⣀⠤⠤⢀⣀⣀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡜⠉⠑⡜⣖⠋⣤⡬⠉⠒⡛⠩⢍⡛⠿⠿⠿⠷⢶⠾⠓⠬⢉⣤⣬⢟⡨⠒⠚⠉⠆
⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢇⠀⡠⠊⠉⢠⠉⠭⢉⡐⢒⡂⢓⡚⠓⠒⠒⢛⠑⠛⣺⠋⣉⠉⣁⠈⠉⠲⡀⢀⠜
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠀⠀⠈⠓⠀⠰⢀⡐⠃⠉⠀⣾⡐⠂⠛⠐⠂⠀⠀⠀⠀⠀⠘⡁
⠀⠀⠀⠀⠀⠀⠓⠢⠤⠤⠀⠀⠀⠼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠘⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣴⠀⠀⢿⠉⠉⠁⠀⠀⢰⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⡴⠋⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢿⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠠⡃⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣠⣤⣿⠀⠀⣿⣄⣄⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠰⣇⠀⠀⠀⠀⠀⢻⡀⠀⣠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠁⠀⠀⠉⠉⠉⠁⠀⠀⠀⠉⠉⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣀⣀⣀⠈⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠐⠛⣀⣉⠙⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣴⠋⠀⠀⠙⠶⣄⡀⠙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⣀⠴⠞⠋⠀⠉⢳⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠙⣦⠀⠘⠷⠶⠒⠛⠛⠛⠛⠒⠶⠶⠋⢀⡴⠋⠁⠀⠀⠀⠀⠀⠘⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠙⡀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⡾⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢇⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⡸⠁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠘⣀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⣠⠃⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠃⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⣿⣭⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⠆⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠻⢿⡿⠃⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⡴⠞⠳⢶⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢤⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠉⠉⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠈⠉⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢤⣤⣤⡤⠛⠂⠠⣤⣤⠄⠒⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣞⣧⣽⣏⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡡⠒⠒⢤⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⢸⠀⠀⠀⠀⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⢢⠀⠀⠀⣤⢸⣀⣀⣀⣀⣇⣘⠀⠀⠀⡰⠒⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⢀⡠⢗⡢⠍⠓⠂⠐⠒⠒⠒⠂⠒⠋⠵⢖⡧⣀⠀⠀⠀⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⢀⡔⡡⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢕⣄⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣾⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⢠⣤⣤⡄⠀⠀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⢯⠉⠁⡩⠀⠰⡉⠋⢈⠆⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⡎⢙⠄⠀⠀⠀⡄⠀⠀⡄⠀⠀⠀⢰⠉⡆⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⢀⡤⠊⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⢤⡀
⠀⠀⠀⠀⠀⢎⠀⢀⠃⠀⠀⣀⣠⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡀⠀⠀⠀⠀⠀⡆⠀⡱
⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠺⠊⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⡜⠀⢼⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⡇⠀⢣
⠀⠀⠀⠀⡸⠀⠀⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣷⠀⠈⢇
⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠏⠀⠀⢸
⠀⠀⠀⠀⡆⠀⠀⠇⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠀⠀⢸
⠀⠀⠀⠀⡇⠀⠀⢲⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⢱⠀⠀⠘⡄⠀⠀⠀⠈⠒⠒⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠒⠒⠁⠀⠀⠀⠀⠀⡌⠀⠀⡎
⠀⠀⠀⠀⠀⠳⣀⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⣀⠞
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⣉⠭⢍⡙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡜⠁⠀⠀⠈⡆⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⠀⢘⡀⡇⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠁⠀⠈⣆⣀⠠⠼⣃⢓⣒⣒⣒⣒⡓⢚⡤⠄⣀⣸⠁⠀⠈⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⠀⠀⠀⢀⡤⢚⠭⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠫⣗⢄⡀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢠⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⣦⣶⠴⡀⠀⢀⣦⣶⢤⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠸⣌⠁⣀⠇⠀⠸⡈⠁⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣴⠉⡦⠀⠀⠀⠠⡄⠀⢠⠄⠀⠀⠀⢰⠋⢳⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠈⠚⠁⠀⠀⠀⠀⠓⠶⠊⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⡠⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠢⣀
⠀⠀⠀⠀⠀⢰⠋⠀⢸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢳
⠀⠀⠀⠀⠀⠈⡇⠀⡸⠀⠀⣔⠿⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡄⠀⠀⠀⠀⠘⡀⠀⡟
⠀⠀⠀⠀⠀⢀⡇⠀⡇⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⣇
⠀⠀⠀⠀⠀⡜⠀⠀⠇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠘⡄
⠀⠀⠀⠀⢰⠀⠀⢰⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⢰
⠀⠀⠀⠀⡎⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⡂
⠀⠀⠀⠀⡇⠀⠀⠈⡀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇
⠀⠀⠀⠀⢰⠀⠀⠀⡇⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⢸⠀⠀⢰
⠀⠀⠀⠀⠈⡆⠀⠀⠸⡀⠀⠀⠀⠈⠉⠒⠒⠂⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠐⠒⠊⠁⠀⠀⠀⠀⠀⠀⡆⠀⠀⡎
⠀⠀⠀⠀⠀⠘⢆⡀⠀⠑⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠄⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠶⠀⠀⠀⠀⠶⠶



⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀
⠀⠀⠀⠩⠍⠠⠿⡄⠘⠟⠀⠀⠀⢨⡍⠀⠻⣦⠘⢿⠄⡾⢷⠰⡶⠆⢴⣤⠀⠀⠀⠠⠜⠀⠿⡿⠸⠿⠇
⠀⠀⠀⠀⡀⠀⣠⡀⠠⠠⠀⡄⡀⢀⠀⠀⠔⡀⢠⣶⠂⢰⡆⢀⣴⣄⣠⣄⠀⢰⡄⠀⣴⠀⠴⣦⢀⣀
⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⢀⣄⠁⢈⣁⠀⣀⣀⢀⡁⠀⠈⠁⢀⡀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠠⡄⠈⠉
⠀⠀⠀⠈⠛⠀⠈⠁⠈⠂⠀⠀⠃⠙⠋⠀⠙⠛⠘⠛⠂⠀⠓⠈⠛⠂⠘⠛⠀⠒⠂⠈⠂⠀⠀⠃⠀⠂
⠀⠀⠀⠰⡆⠰⠶⠆⢶⡶⠀⣿⠗⠘⠷⠠⡄⣤⠠⣶⠀⡤⡿⠀⢾⠄⠻⢦⠀⠠⡆⢠⣥⠀⣰⡄⢸⣭⡇
⠀⠀⠀⣶⣶⠀⣀⡀⠀⠂⠀⠲⠂⡀⢀⡀⢦⡄⠀⣤⠀⣤⣄⠀⠀⠀⠀⡀⠀⣴⠀⠀⠀⠀⣠⡄⠀⣶
⠀⠀⠀⢉⠉⠀⠁⡀⢨⣇⠀⠀⠀⠉⣉⠁⣀⡀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠁⠀⠈⠀⠈⠀⠀⠉⠉⠀⠉
⠀⠀⠀⠘⠃⠀⠻⠃⠘⠁⠀⠀⠀⠀⠀⠀⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠠⠀⣀⠀⠤⠤⠀⠠⠀⢀⣄⠀⣀⡀⢀⣄⠀⠀⠀⠀⠴⠀⢠⡀⠀⠀⠀⠀⣤⠀⡄⡄⢀⠤
⠀⠀⠀⠉⡀⠀⠀⠀⢉⡉⠀⢀⠀⣀⠁⠀⣀⡀⢀⣀⠀⢑⡀⠐⣀⡁⢈⡁⠀⣀⡀⢀⣉⠀⣀⣁⠀⠉
⠀⠀⠀⠘⠃⠈⠺⠃⠬⠴⠀⠠⠀⠘⠸⠰⡯⠿⢾⢩⡇⠸⠇⠀⣭⠄⠸⠿⠀⣬⡄⠨⡭⠀⣯⣧
⠀⠀⠀⢘⣃⠀⠰⠀⣰⣶⠀⣾⠆⠤⠴⠄⣴⡖⢴⣤⡄⢠⡄⠰⣶⠆⢀⡀⠐⣶⡆⢀⣰⡆⠶⣄⢰⣿⡆
⠀⠀⠀⣬⣭⠀⣤⡄⠠⠍⠀⣠⠀⠀⡄⢀⣈⣄⠀⠠⠀⠀⣤⠀⠄⠀⢤⡤⢀⣀⠀⠀⠁⠀⠀⠀⢠⣭⡀
⠀⠀⠀⣛⣛⠀⣛⠃⣀⣀⠈⡛⠃⠐⠓⠘⠋⠛⢘⣛⠃⡚⠁⠘⠛⠃⠀⣀⠀⠙⠀⢙⠋⠀⠘⢁⠘⠛⠃
⠀⠀⠀⠿⠿⠀⣿⠀⠿⠿⠻⢿⠗⠶⢶⠶⠿⠟⢸⣿⠄⠳⣤⠀⠿⡆⢾⡿⠀⣤⡄⠸⢾⠀⠴⠋
⠀⠀⠀⢦⡀⠰⣶⡆
⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠄⠀⠁⠈⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⣆⣠⢰⢀⡄⣄⢠⡀⡀⡠⢀⣀⢀⡀⣠⢠⣀⡆⣄⢠⢀⡀⡀⡀⠀⢠⡀⡄⣀⢀⡀⡀⣠⢀⣀⡀
⠀⠀⠀⠉⠁⠈⢉⠀⠉⡉⠀⠉⠁⢈⢉⠀⠈⠁⢈⣭⠁⠩⡅⢈⣉⡁⢈⣍⠀⠭⠁⠈⠭⠀⣩⡅⢈⣭⡁
⠀⠀⠀⠈⠁⠀⠘⠀⠀⠁⠀⠈⠀⠈⠋⠀⠀⠀⠐⠛⠀⠀⠀⠀⠙⠀⠘⠛⠀⠐⠀⠀⠂⠀⠃⠊⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠤⠖⠒⠒⢚⢸⠒⠒⠒⠤⠤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠌⠠⠤⢄⣀⣀⣀⣀⣀⣀⣀⡤⠤⠈⢄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠀⠀⠀⢠⣦⠀⠀⠀⠀⢀⣦⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠂⠀⠀⠀⠀⠀⠀⠋⠈⠃⣠⣤⡀⠛⠈⠃⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⡆⠠⠘⠘⠀⢀⣄⠀⠀⠀⠀⠸⣿⠿⡿⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠐⠈⠀⢈⡄⠀⠘⡀⠀⠀⢠⠄⠀⢈⠠⠀⠂⡄⠙⠒⠁⠀⡀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢂⠀⡈⠈⠀⠀⢰⡀⠀⠘⠀⠀⠞⠃⠀⣠⠁⡐⠈⠀⠀⢀⠀⠀⠈⠁⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠈⡇⠀⠀⠀⠀⠀⡈⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡂⠘⠀⠀⠀⠀⠀⠀⠐⠀⡁⠞⠀⠀⠀⠀⢾⡷⠀⠀⠰⣿⠆⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠐⠦⠠⢀⣠⠀⠠⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⣅⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠆⠀⠀⠀⠖⠲⠄⢠⡀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⡀⠘⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣰⣷⠀⠀⠀⠀⣘⢀⡈⠀⠀⠐⠒⠂⢀⡠⠶⠖⠒⠂⠉⠉⠁⡀⢼⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⠟⠀⠀⠀⠀⠗⠀⠈⠂⠒⠒⠉⠀⠘⠀⠒⠀⠐⠒⠈⠉⠀⠠⡎⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢐⠃⠉⠍⠭⠍⠙⠛⠛⠛⠍⡉⠉⢉⠉⠉⠉⠩⠾⠄⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⢀⠌⠀⢄⡀⠀⠀⠁⠂⠀⠀⠀⠉⠈⠀⠀⠀⢀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠶⠶⠶⠶⣦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠻⣷⣄⠀⠀⠀⠀⠈⢻⣦⠀⠉⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣧⡀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠘⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠈⠻⣦⡀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠸⣷⠈⠣⡄
⠀⠀⠀⠀⠀⠀⠀⡼⠻⣷⡀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⢻⡆⠀⠘⢦
⠀⠀⠀⠀⠀⠀⣸⠁⠀⠘⣿⡄⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⢸⣷⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠘⣿⡀⠀⣀⣠⡤⠿⠶⠖⠒⠒⠺⠿⠤⢤⣄⣀⣀⣿⠀⠀⠀⠀⠀⣿⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠈⢳⠤⠤⠴⠞⠛⠉⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠉⠙⠓⠒⠒⠒⠛⠛⣹
⠀⠀⠀⠀⠀⠀⠀⠸⣅⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠲⣤⣤⣤⡶⠂⠀⠀⠈⠁⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢭⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠓⠓⠛⠚⠛⠛⠚⠛⠉⠉⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢠⠄⢠⡀
⠀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠈⡀⠀⠀⠀⠰⢀⡀⢀⠀⠠⠀⢀
⠀⠀⢀⠀⠀⢀⡘⠄⠒⠂⠄⠀⠃⠀⠐⠀⠐⠀⠀⠀⠛⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⠀⣠⠀⠆⣀⡀⠀⠆
⠀⠁⠘⠋⠀⠈⠃⡄⠀⢀⡠⠀⠀⠀⣠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠶⠄⠀⠀⠀⠀⠀⠌⠛⠀⠀⠙⠁
⠀⠐⠀⠀⠀⠀⠀⠁⠀⠙⡁⠀⠀⠀⠈⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⠀⠂⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠈⠈⠰⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⠀⠀⠀⠄⠀⠀⣀⠈⠀⠀⠀⠈⠠⠁⡀⠀⠀⡀⠀⠀⠀⠀⠂⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡄⠀⠀⣠⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠄⠛⠀⠀⠛⠄⠀⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠂⣀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠀⣀⡀⠀⣀⡀
⠀⠀⠀⠛⠀⠀⠛⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣄⢀⡀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠉⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁⠉⠁⠀⠉⠘⠃⠀⠓⠄⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠠⠀⠁⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⡧⠀⠰⡧⠀⠀⠀⠀⠀⠀⣴⡄⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠒⠶⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⢀⣠⡤⠶⠚⠛⠉⠉⠉⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢹⡄
⠠⣞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⢻⡀
⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠙⢦⡀⠀⠘⡇
⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠚⠻⢶⣤⣀⠀⠀⠀⠙⢦⡀⣿⠀⠀⣀⣤⣶
⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⢦⣬⣿⣿⡶⢛⣩⠴⠛
⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⢋⣡⡶⢿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠶⠶⣤⣤⣤⠴⠶⠶⠛⢛⡽⠟⣡⡴⠛⠁⠙⢦⡙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⡾⠋⠀⠀⠀⠀⠀⠹⣦⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⣠⡴⠶⠞⠛⠛⠛⠶⢦⣤⡀⣧⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣿
⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣀⣿⠶⠶⠛⠳⠶⢦⣄⠀⠀⠀⠀⣀⣤⠴⠶⠶⠶⠶⢦⣄⣸⡇⢀⣿⠶⠛⠛⠛⠛⠶⢦⣀
⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠳⣆⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⢸⠇⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⣿⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣿⠀⠀⠀⠀⠈⠳⣤⣤⣤⠞⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣤⣀⠀⠀⡷⠀⣠⡶⠒⠲⢦⡄⠀⠀⠀⠀⠀⠀⠀⣠⡶⠚⠛⢶⣄⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠙⣦⣀⣀⣀⡴⠋⠉⠀⢀⡇⢰⡏⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⢹⡆⠀⠀⢸
⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢠⡄⠀⠈⠉⠉⠉⠀⠀⠀⠀⣸⠃⠈⠀⠀⠀⠀⢀⣤⣥⣤⣤⣤⣤⣤⣬⣤⡀⠀⠀⠀⠀⠁⠀⠀⢸
⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣄⣠⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠈⣷⣶⣶⣶⣶⣶⣶⣶⣾⠃⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⣄⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠙⠳⣤⣄⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠛⠶⠶⠦⠴⠶⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣀⣀⣠⡴⢦⣄⣀⣀⣠⣤⠶⠛⠁
⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣀⣄⣤⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⠔⠁⠀⠀⠀⠀⠀⠀⠀⡖⠒⠰⠀⡅⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⠼⠀⠀⠀⠀⠀⣀⢀⠤⠒⢣⠀⠖⠃⢱⠀⡤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠀⠀⠀⢰⠉⠀⢣⣃⠀⠀⢂⠇⠀⠈⣴⠀⠀⠸⡐⠉⠒⡄
⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⡇⢰⢤⣤⣤⣀⣧⣀⡏⠈⡄⠀⠘⣦⠀⢀⠇⠀⢠⠛⢢⠀⡰
⠀⠀⠀⣏⣐⣅⣀⠀⣀⠀⠑⠂⠀⡀⠀⣀⣨⣂⣹⡀⢰⠀⠀⢻⠀⢸⠀⠀⠸⠀⡌⢰⠁
⠀⠀⠀⠏⠘⠀⠊⠩⠭⠭⠭⠭⠭⠭⠍⠓⠐⠂⢩⣡⠘⡀⠀⠘⠀⡈⠀⠀⡇⢀⡠⡇
⠀⠀⠀⢀⠀⠀⠀⢠⡄⠀⠀⠀⠀⣠⡀⠀⠀⠀⡆⠉⠢⠧⣀⣇⡀⣇⣀⠠⠖⠊⢀⠁
⠀⠀⠀⠘⠀⠀⠠⠏⠹⢆⣀⣀⡰⠋⠻⠀⠀⢠⠧⠀⢠⠶⢤⠀⠀⠀⢠⠴⢤⠀⢰
⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⢿⡇⠀⠀⠀⠀⢨⠸⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⡌
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠛⠚⠀⣀⠀⢀⣀⡆⠀⡆⠀⠀⠀⠘⣿⠇⠀⠀⠀⢀⠃⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠠⠊⠒⡝⡤⠖⣈⣙⠫⠵⠾⣒⠒⠶⣶⣶⠶⠤⣼⡷⣙⣛⣋⣀⡶⡘⠅⠝⠢
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀⠀⢀⠜⠋⢩⠉⣚⠓⠠⠧⠐⠮⠳⠦⠤⠶⠫⠶⢶⠒⢚⠛⣉⠉⠒⢤⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⠛⠀⠀⠘⠃⠈⠤⠈⠱⠐⠃⢨⡁⠆⠸⠂⠎⠀⠁⠀⠀⠀⢹⠁
⠀⠀⠀⠀⠀⠘⠢⠤⠤⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠀⠀⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⢠⣾⣿⣿⠋⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⡿
⣿⣿⣿⣿⡀⠀⠀⣠⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⡿⠿⠛⠉⠁
⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣤⣄⡀
⠈⠻⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣶⣤⣄
⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣤⣄⣀⣀⣀⣤⣶⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⣿⣿⠿⠟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣀⠛⠟⢀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠿⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠚⠛⠓⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠛⠛⠒⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠚⠛⠛⠒⠦⣄⡀
⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⢰⠃⠀⢀⣀⡀⠀⠀⠀⠀⢀⣀⡀⠀⠘⣆⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⢸⠁⠀⣀⢤⣤⣄⠀⠀⠀⣠⢤⣤⣀⠀⠈⡇⠀⠀⡏⠀⣰⠉⢙⣿⣷⠀⠀⣼⠉⢹⣿⣦⠀⢹⠀⠀⢸⠁⠀⢀⣈⣉⡳⠄⠀⡰⣪⢭⣦⣀⠀⠈⡇
⠀⠀⠀⢸⠀⢰⣇⣀⡿⢿⡇⠀⢸⣅⣠⡿⢿⡆⠀⡇⠀⠀⡇⠀⠹⣿⣿⣧⡟⠀⠀⠻⣿⣿⣤⠏⠀⢸⠀⠀⢸⠀⢰⣏⠀⣿⢿⡆⠀⢸⣇⣠⡿⢿⡆⠀⡇
⠀⠀⠀⠘⣇⠀⠻⠿⡿⠞⠁⠀⠈⠻⢿⠷⠞⠀⣸⠁⠀⠀⢹⡀⠀⠀⠉⠁⢀⣀⣀⣀⠈⠉⠁⠀⢀⡟⠀⠀⠈⣇⠈⢿⣿⣷⡼⠃⣀⡈⠻⢿⡷⠞⠀⣰⠃
⠀⠀⠀⠀⠘⢦⡀⠀⠀⢀⣀⣀⣀⠴⠀⠀⢀⡴⠃⠀⠀⠀⠀⠱⣄⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⣠⠞⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠛⠉⠙⠃⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠙⠢⢤⣀⡀⠀⢀⣀⡤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠀⠀⣀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⡀⠀⢀⣀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠉⠀⠉⠉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠁⠈⠉⠙⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠉⠀⠉⠉⠓⠢⣄
⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⡰⠋⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⣸⠁⢨⠖⢶⣶⣜⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⢀⡏⠀⡠⢶⣦⣄⠀⠀⠀⣠⠴⣶⣤⠀⢹⡄
⠀⠀⠀⢸⠀⠀⣄⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠀⠀⡇⠀⢿⣤⣼⡛⣿⠀⠠⣀⠀⣀⡴⠂⠀⢸⠀⠀⢸⠀⢸⣄⣠⡟⢻⡄⠀⠀⣧⣀⣼⠻⡇⠀⡇
⠀⠀⠀⢸⡀⠀⠈⠁⠒⠉⠁⠀⠉⠒⠊⠁⠀⠀⢀⡇⠀⠀⣇⠀⠈⠛⠛⠛⠁⠀⠀⠀⠉⠁⠀⠀⠀⣸⠀⠀⢸⡀⠈⠻⠿⠷⠋⠀⠀⠀⠙⠿⠿⠞⠁⢀⡇
⠀⠀⠀⠀⢧⠀⠀⠀⠀⡀⠀⠀⠀⣠⠄⠀⠀⠀⡼⠀⠀⠀⠸⡄⠀⠀⠀⠀⡤⠖⠒⠲⠄⠀⠀⠀⢠⠇⠀⠀⠀⢣⠀⠀⠀⠀⢰⣶⣤⣴⣦⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠳⣄⠀⠀⠉⠉⠋⠉⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠳⣄⠀⠀⠈⠻⣿⠟⠁⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣤⣤⡤⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⣤⣤⠤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⢤⣤⡤⠤⠖⠋⠁



⣿⣿⡿⠿⣿⠿⢿⣿⡿⡿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣷⣮⣾⣷⣶⣿⣶⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⡆⠄⠀⠀⠀⠀⠀⠀⣖⠀⠀⠀⠀⢠⣤⣀⣀⣀⣀⣀⣤⡤⠀⠀⠀⠈⠁⠂⠀⠀⠀⠀⠀⠀⡨
⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀⡈⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⣀⣀⣀⣠⡄
⠀⠀⠀⠀⠉⠉⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⣠⣤⡀⠀⠀⢠⣴⢶⣄⠀⠀⠀⣠⣶⢶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⢠⣿⣿⣿⡇⠀⠀⣾⣿⣿⣿⡆⠀⣿⣿⢿⣿⡇⠀⠀⣿⣿⠿⣿⡗⠀⣰⣿⣿⣷⡄⠀⠀⣾⣿⣿⣿⡄
⠀⠀⠀⠛⠓⠛⠁⠀⠀⠙⠛⠚⠋⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠀⠀⠘⠿⠿⠿⠃⠀⠀⠻⠿⠽⠿⠁
⠀⠀⠀⠀⠀⠀⠳⠤⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⢀⡴
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣥⣤⣤⣤⣤⣤⣤
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠳⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⠀⡖⠒⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠔⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢈⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⡇⠀⣇⣀⠀⠀⢈⠀⠀⠀⢸⠀⠀⠀⢰⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠇⠀⢧⣤⡄⠀⢠⣤⡄⠀⠸⣤⣤⠀⠈⢦⣠⠞


⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⡤⠤⣈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢂⡡⠤⡈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠙⢢⡈⠳⠤⠤⠴⠦⠤⠤⠔⢉⠔⠊⠁⠀⠀⠰⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⡄⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⢀⠃⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠐⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⡞⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠐⢿⠇⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠀⢶⡶⠀⡀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠈⠳⡊⢑⡞⠁⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⣀⣀⠴⠀⣀⡀⠠⠂

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠈⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡰⢄⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠒⠒⠆⠀⠀⠀⠀⠀⠀⠘⡞⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⠔⠚⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⢐⡉⠐⠒⠒⠒⠒⠒⢈⡰⠀⠀⠀⠀⠀⡠⠘⣜⡖⠢⡀
⠀⠀⠀⠀⠀⡇⠀⠂⠀⠀⠂⠀⡆⠀⠀⠀⠀⡀⢬⠒⠀⠀⠀⠀⠀⠪⠀⡀⠀⠀⠀⠀⠀⠉⠀⡈⠉⠉⢩⠀⠈⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠈⡂
⠀⠀⠀⠀⢈⢀⢤⠀⣀⠀⡀⡀⢘⡄⠀⠀⢸⠒⠈⠦⠤⠤⠤⠤⠴⠁⠒⣺⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠸⣉⠀⣁⣈⣀⣉⠁⣉⠂
⠀⠀⠀⠀⠀⠈⡜⠚⠉⠉⠂⡹⠉⠀⠀⠀⠈⡄⠀⠀⡀⠀⠀⠀⠀⠀⢀⠓⡌⡂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⢱⠂⣀⠀⢂⠃⠀⠀⠀⠀⠀⠘⢄⡈⠁⠀⠀⠈⠁⡠⠮⠭⠐⠁⠀⠀⠀⠨⠄⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⢣⡀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⡰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠣⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣄⣤⠀⠀⠀⠀⠈⠀⠒⠒⠂⠈⠀⠀⠀⠀⠀⠀⠀⢇⣀⣀⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⢀⠔⠓⢄⡀⠀⠀⠀⠀⢸⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠘⠤⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠰⠿⠖
⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠠⠂⠈⠁⠀⢱⠀⠀⠀⠀⠀⢐⠃⠐⠒⠒⠐⠂⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⡠⠄⠠⢄
⠀⠀⠀⠀⢳⠄⠀⢀⠀⡄⡲⣼⠀⠀⠀⠀⠀⡐⠀⠃⠀⠀⠀⠀⠈⠁⢂⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠋⡸⠁⠀⠀⠀⠀⠑
⠀⠀⠀⠀⢨⠀⣀⠀⠒⢀⠀⠸⡌⡆⠀⠀⢠⠔⠀⠀⡀⠀⠀⠀⠀⠀⠦⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠇⡍⠆⠀⠀⠀⡠⠊⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡏⠔⠃⠀⠀⠅⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⡰⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠦⢂⠌⠀⠀⠈⠀⣀⢀⠄⠄⠀⠒⠐⢆⢀⣄⢀⠇
⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠈⢲⠀⠐⠑⠠⠤⠔⠒⠲⠂⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⢐⠉⠁⠀⠀⠀⠈⠪⢄⣉⠀⠁⠀⠀⠈⠀⠀⢀⠍
⠀⠀⠀⠀⠀⠀⡜⠂⠀⢪⠀⠀⠀⠀⠀⠀⠀⠈⢄⡀⠀⠀⠀⠀⣀⠰⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡠⠇⢘⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠁⠚⠓⠊

⠀⠀⠀⠀⢀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐⣢
⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠈⠀⠀⠉⠀⠀⠀⠀⠀⡐⠃⠠⠤⠤⠀⠂⡄⠀⠀⠀⢀⠱⣣⠄⡀
⠀⠀⠀⢀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠜⠀⠀⠀⠀⠰⠀⡀⠀⠀⠀⠈⠁⠄⠀⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠴⣂⠤⠀⠠⡀⠀⠀⠈⠀⠈⠒⠀⠀⠐⠁⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠡⠀⠉⠤⠍⠀⠜
⠀⠀⠀⠀⠈⡄⠐⠀⠼⠀⠀⠀⠀⠡⡀⠐⠀⠀⠐⠀⣔⡀⠔⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠈⠀⡄
⠀⠀⠀⠀⠀⠱⡀⠰⠀⠀⠀⠀⠀⠀⠈⠐⡄⢀⠔⠁⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠠⠤⠄⠤⠄
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡂⠁⠀⠈⠠⡀⠀⠀⠉⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠁⠐⠐⠐⠀⡃⠀⠀⠀⠀⠀⠀⠀⡀⢀⠠⠀⠀⢄
⠀⠀⠀⠘⠀⠐⣀⠢⠑⡄⠀⠀⠀⢈⠈⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠐⠅⠁⠀⠀⠀⠀⠂
⠀⠀⠀⠠⠀⠀⠀⠀⢠⠃⠄⠀⠐⠀⠀⠐⠀⠀⠂⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠁⠀⠀⢀⠁⠀⠀⠀⠈⢢⠀⠒⠠⠤⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠈⠪⠀⠁⠂⠀⠐⠀⠁⡰
⠀⠀⠀⠀⠀⢉⢈⠁⠀⠀⠀⠀⠀⠀⠢⠄⠀⠠⠀⠐⠀⠀⠀⠀⠂⠄⠀⠀⠐
⠀⠀⠀⠀⠀⠍⠄⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⠤⠤⢤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠻⣿⣥⠀⠀⠀⠀⠀⠀⠈⢻⣯⡉⠙⠓⠶⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠋⠁⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠈⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠻⢿⣦⡀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⢹⣿⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⢿⣇⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠻⣷⡄⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠘⣿⡄⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠙⣿⣄⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⢹⣷⣀⣀⣀⣀⣀⣸⣿⣀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠸⣿⣄⣤⠴⠖⠛⠋⠉⠉⠉⠀⠀⠀⠉⠉⠉⠙⠛⠓⠲⠦⠾⣧⣀⣀⣀⠀⠀⢸⣿⣀⣤⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠓⠖⠚⠋⠉⠁⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠉⠉⠉⠉⠉⠉⠁⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠐⢦⣀⣀⣀⣤⠖⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡛⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠦⢤⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠤⠖⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡀⠀⢀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⠀⠀⡀
⠀⠀⠀⣿⡁⣾⣾⣶⠟⡿⣼⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⢸⡇⢿
⠀⠀⠀⢀⠀⠀⠀⢀⠀⡀⡀⠀⠀⢠⣤⣤⣤⣤⣤⣤⡄⠀⠐⠀⠀⠀⠐⠀⠈⠀⠈⠄⠀⠀⠀⢸⡎⣯⡀⠀⠀⡇⣾
⠀⠀⠀⣘⣦⣇⣿⣘⣆⣿⣧⡇⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠉⠆⠀⡨⠇⠃
⠀⠀⠀⠈⠁⠈⠁⠈⠁⠁⠉⠁⠀⠀⠉⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⡀⠀⠀⠀⠀⠀⡀⠀⠈⠈⠐⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠶⠆⠶⠀⣀⠀⠀⢀⣀⡘⠻⠿⠃⠀⣀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠴⠚⡀⠀⠀⢀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠒⠀⠀⢀⡈⡇⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⢺⣿⠂⠀⠀⠀⠀⠀⠀⣴⣶⣶⣦⡄⠀⠀⠀⠀⠀⢠⣶⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⣠⣶⣿⠿⠛⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⠳⢦⡀
⣼⣿⣿⣏⠀⠀⠀⣹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡁⠀⠀⢈⣿
⣿⣿⣿⣿⣶⣤⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣦⣴⣾⣿
⠘⢿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣶⣶⣶⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠒⠲⠤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⡀⠀⠀⠀⠈⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠆⠐⠀⠀⠉⠀⣤⣀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⠀⡔⣀⠀⠀⠱⠆⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⡀⠼⡆⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⢀⡀⠀⠀⠀⠀⣀⡉⣀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡨⠀⠀⠀⠃⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢃⣀⣒⡀⠐⣿⣧⣿⣤⡆⠀⠀⠀⠀⠀⠀⠻⣅⠀⣠⠀⣸⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⠀⢀⣠⣾⣿⢿⣿⣿⣿⠾⠟⠛⠻⢿⣧⣸⡆⢀⠀⠘⠀⠀⢿⣞⣹⡇⣽⣯⡌⠀⣄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣫⠁⠈⠉⣀⢨⣿⠁⠀⠀⠀⠀⠀⠀⠙⠻⣿⡦⠀⠀⠀⠀⣿⡿⠃⠙⢿⣧⣄⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠈⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡴⡄⠀⠀⠀⢿⠀⠀⠀⠀⠙⠿⣧⠀⠀⠀⢨⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢢⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠻⣷⣆⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⣷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⣾⢧⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⣨⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠦⠄⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠙⠺⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣎⣆⣀⢢⣀⡿⠃⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⣴⣿⣿⣦⣈⣀⣀⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⡤⠲⣒⡺⠟⠋⠉⠻⠯⠗⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢴⡶⠍⠑⠈⠹⠛⢛⣀⠂⠂⠘⡂⠀⠀⠈⠀⠀⠀⡀⠍⠉⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠁⠤⣾⡉⠀⡅⠀⡀⠁⢉⡽⠝⠀⠀⠈⠻⣮⣶⣤⣄⢄⠀⠀⠀⠀⠉⠹⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠗⠀⠀⠉⠅⢸⠆⠀⡗⠀⡀⠀⣬⠁⠀⠀⠐⠁⠀⢈⡯⣿⣿⠟⠇⠀⠀⠀⠀⠘⣾⣷
⠀⠀⠀⢠⢀⣦⣴⣯⣀⡀⠀⢠⡰⠂⣺⡂⠀⠁⠀⣡⠀⠂⠘⠇⢙⠀⠀⡀⠸⠇⡿⠂⠀⠀⠀⠠⠂⠀⡈⠟⣿⣇
⠀⠀⠀⠘⢾⣿⣿⣿⣿⣿⠿⣿⡻⣼⣿⠂⢠⣄⣤⡿⠀⠀⠀⠠⢨⣆⠀⣀⢀⠀⠁⠀⠀⠀⢼⠄⠀⠈⢀⣴⢿⡿
⠀⠀⠀⠀⢾⠻⣿⣟⠉⠈⣿⣿⣷⣯⣽⣧⣘⣜⠉⢻⣦⣤⡀⢠⢀⣿⢬⣾⣿⣿⡇⠂⠒⢨⣿⠀⠀⢀⣬⠏⣸⡇
⠀⠀⠀⠀⠸⣾⣿⣷⣦⣎⣠⡿⠟⠉⣿⣿⣿⣥⠄⡀⡹⠉⠻⠟⣿⣿⣿⣿⣿⣿⣷⠀⢰⡿⢋⠀⢠⣾⢯⣠⣿⠁
⠀⠀⠀⠀⠀⠈⠻⣿⣿⠿⠟⠀⢀⣴⣿⣷⣼⣿⣿⣶⠁⠀⡔⠀⠀⣿⠉⠉⠋⠛⣻⠛⠋⢀⠠⣆⣿⣯⣶⣿⡟
⠀⠀⠀⠀⠀⢤⣄⣼⠟⢀⡠⠎⢉⣿⣿⣩⣴⣿⡽⠟⠯⢠⠁⠀⠁⡼⡆⠀⠀⠀⡇⠀⠈⡀⠻⣫⣿⣾⣿⣿⣧
⠀⠀⠀⠀⢀⣀⡀⡀⢴⣷⣿⢭⠾⠛⠛⠋⠉⠁⠀⠀⠀⢎⡀⣘⠀⣺⠇⠀⠀⠀⠃⢀⢀⣣⠀⣵⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠙⡟⣣⡄⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⠀⣿⠀⠀⠀⠀⣵⣆⣼⣿⡿⠋⠻⡿⣾⡝⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠠⠍⠐⠒⠒⠒⠀⠄⢀⣀⡀⠀⢀⣤⣤⣫⣻⡿⢁⠤⣀⣀⣠⣿⣿⣿⣿⠧⣶⣶⣻⣯⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠋⠒⠓⠋⠁⠀⠀⠛⠺⠆⠒⠒⠛⠉⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣴⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣧⣿⣾⠿⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣃⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢽⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣤⣶⠓⠀⠀⠀⠀⠀⠠⠀⠠⠐⢺⡿⢟⡿⢿⣿⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠁⠀⠀⠀⢸⠍⠿⠷⣦⣶⣤⠀⠀⠀⠀⠰⢤⢻⣧⣥⡶⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣤⡑⠐⠀⣤⡝⢫⣍⣗⠵⣚⣿⣿⣿⡆⠀⠀⠀⠂⠀⣀
⠀⠀⠀⠀⣶⣶⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⢹⣿⣿⣿⣿⠇⢀⣹⣯⣟⡋⣀⣿⣯⢭⡩⢻⣿⣧⠀⠠⠔⠂⠀⡲⣬⡀
⠀⠀⠀⠀⢨⣵⣯⣩⠝⠀⠀⠀⠀⠀⠀⠘⢿⢆⣉⢻⣿⣷⣻⣤⣿⣯⣿⣿⣿⡿⢿⣾⡟⢻⣿⠿⠄⢀⣦⢠⡀⠨⣩⠳
⠀⠀⠀⠀⠀⢻⣿⣿⣄⣠⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⣴⣿⣟⠳⡿⣷⢦⡀⠉⠐⠙⡜⢿⠟
⠀⠀⠀⠀⠀⠀⠘⠿⣿⣷⣶⣶⣾⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡮⢕⠻⣷⡤⣰⢀⡆⠣⠸⡸⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⡅⠈⣿⣿⡿⣄⠀⠀⠙⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⢿⡟⢿⣿⣼⣿⣿⠋⣧⡿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣻⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣣⣽⣸⣿⣿⣿⢹⣿⠀⠅⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣯⣻⢿⣿⣻⣿⡙⣷⣿⣿⣿⣹⣇⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⢻⣿⣿⣾⣿⣿⣿⢸⣿⣿⡉⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣻⣿⣿⣿⣿⣿⢣⡏⠈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡏⣉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡟⡿⠿⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣠⣀⣄⣄⢀⡀⠀⠀⣲⡀⠀⠀⠀⠲⡤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠈⠉⠀⠀⢠⣄⠀⠙⠂⢀⠈⠀⠁⣉⠋⣷⡆⠀⠀⣬⠖⠠⣇⠀⠈⡲⠄⡉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⣄⠀⠀⣀⠀⠀⠄⣆⢬⡼⠓⠀⢠⣰⡧⣀⣀⣻⣇⡀⠀⠀⠀⢀⠉⢀⠙⣄⠈⠉⡒⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡻⠀⣧⡄⡈⣥⢾⣜⡓⢉⣁⡀⠀⡀⠈⠁⠀⠀⠀⠈⢛⣁⠐⠤⠤⢀⡉⠁⠳⢽⡄⠀⡇⠀⠀⣷⣼
⠀⠀⠀⠀⠀⠀⠀⢰⡈⢳⣶⣿⣦⣿⠿⢋⠁⡠⢈⣨⠍⣁⠐⠦⠀⠀⠀⠀⠀⠈⢥⡆⢀⠀⠨⡇⠢⣀⠀⣿⠢⣅⠀⠀⠹⣿⠀⢀⡄
⠀⠀⠀⢀⠀⠀⠀⠎⠀⣠⣿⡏⢱⢋⣴⠥⠐⠀⠀⠀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢀⡆⣷⢀⠈⠀⢹⠆⢺⣷⡀⢣⢹⣦⠞⢹⡆
⠀⠀⠀⢸⡄⠀⡄⠀⣸⠿⣸⠷⣿⠁⣀⢂⡂⣔⣬⣰⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⢿⠓⠾⢬⣤⡈⢧⡑⣼⢠⣿⣦⣿⠁
⠀⠀⠈⡀⢧⣠⠓⣤⣿⢟⡟⣸⡿⠬⠋⠣⠑⠈⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣳⠌⢳⣄⠸⡋⠙⢫⣷⣼⠁⢸⣿⠁⢰
⠀⢢⠀⢧⠸⣧⠑⣾⢧⡾⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠙⣿⡗⢾⣿⣊⣋⠄
⠀⠈⣧⢨⠃⠸⣿⣣⡾⢛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠶⣄⣿⣧⠸⣿⠈⣯⠆
⠀⠀⠘⣷⣀⠀⢻⣿⡡⣺⣻⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣌⢻⣿⠀⣿⣇⡳⠂
⢦⡀⢰⡛⣿⣦⣾⣯⣠⣿⢫⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣍⠹⣿⠳⣿⣧⣟⠁
⠈⢷⡌⡾⠰⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣱⣿⣧⣿⣿⠃
⠀⠈⢷⡸⡇⢸⣿⣿⠁⣀⡀⠀⣤⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⢹⣿⣿⣿⠇
⠀⠀⠘⣿⠷⣸⣿⣿⠘⡿⠛⡸⡯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣤⠀⠈⠣⣼⣿⣿⣿⣆
⠠⣼⡇⣹⣯⢸⣿⣿⡏⠀⠐⣮⣿⢅⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⢷⣫⣴⣶⣼⣿⣿⡇⢸
⠀⢨⣟⡵⢻⣿⣿⣿⣇⠀⢐⡫⢷⢝⡂⠀⢄⣧⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢭⣷⡋⠡⣼⣿⣿⡇⢸
⠀⠀⢻⣫⠌⢻⣿⣿⣿⡆⠀⢩⠽⣝⣃⣨⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣗⡂⢀⣿⣿⣿⡃⣾⠀⢸⠁
⠀⠀⠈⠧⣞⢄⢹⣿⣿⣿⣄⠈⠬⣯⢲⣵⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠬⢽⣿⠒⣾⣿⣿⣿⣶⠃⠀⠅
⠀⠀⠀⠀⠻⢎⢔⣿⣿⣿⣿⣦⠨⣧⣾⣿⢓⣂⣤⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣯⣄⠀⡄⠀⢀⣦⣄⢺⣿⣃⣼⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠈⢏⣿⣿⣿⣿⣿⣷⣾⣿⠻⠛⢻⣟⣿⣿⣤⣤⠀⠀⠀⢀⠀⠀⠐⡩⣻⣽⠇⡇⣇⡼⣻⠏⡽⢷⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠿⠿⣿⣿⣷⣬⣧⣼⣽⣽⣿⣿⣀⠀⣈⣄⣄⣀⣈⡴⠖⠓⣚⡛⠛⣿⣾⣾⣿⣿⣿⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠷⣤⣀⡀⢹⣿⣟⠁⠀⠀⠀⡀⢀⠌⠋⠙⠻⣧⡊⠁⢀⣅⠚⢻⣛⣠⣿⣿⣿⣿⣿⠋⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣽⠿⢿⣯⣭⣭⠾⢿⣤⣀⢀⠠⠊⢀⣱⡤⢶⣿⠖⡛⠛⠋⠛⠛⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⣿⣿⣧⣼⣾⣾⠾⠷⣦⠾⡉⠐⢣⡏⠀⠀⠀⣈⡥⠖⠚⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣁⣀⣙⣇⣀⣜⣁⣀⣈⣠⣎⣈⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⠭⣟⡛⣛⣛⡛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⣤
⢸⢛⠀⠀⠀⠲⣀⠀⢀⠀⠀⠀⠀⠀⣐⠀⠀⢰⠆⠤⢦⣤⣤⣄⣀⣀
⢸⢸⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⢀⣀⡆⠸⠃⠀⢀⠙⠚⡻⢯⡙⠲⠨⣧⠈⣠⡂⠀⠀⠀⠀⠀⢠⡆
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡿⣿⡇⠸⠇⠀⠀⡤⢤⠁⢸⡟⠙⠙⠿⣷⠊⠁⠀⠀⠀⠀⠀⣼⡁⢀⡇
⢸⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠀⠁⡹⡇⢰⠀⠀⢀⠀⠀⠀⢿⢿⠀⠒⢰⡘⢷⠀⠀⠀⠀⣶⣷⡿⠀⣩⡇
⢸⣿⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣠⣠⣤⣿⡇⢸⡇⠀⠷⠄⠀⠀⣾⣿⠷⡄⠠⣉⣻⣆⣤⡰⣆⣿⣿⠁⠀⣿⣇
⢸⣿⣦⣄⠀⠀⠀⠀⢨⡄⠀⠀⠈⠙⢛⣾⡇⢸⡁⠀⢐⣶⡄⠀⢹⣿⠠⠆⠀⠉⢹⣿⣿⠷⣿⡿⡟⡇⠀⢼⣤
⢸⣿⡿⣿⠨⠀⠄⠀⣼⢇⠀⠀⠀⠀⢠⢿⡧⢸⠆⢠⠤⠹⠇⠀⣾⣿⠃⣤⡀⠀⢸⣯⣟⡿⣛⠀⠷⠁⣴⣿⣿
⢸⣿⠀⢈⡁⠀⠀⢠⣃⡘⡀⡀⠀⠀⠀⠈⣇⢸⣷⣟⣾⣶⢀⠀⢿⣿⣶⣿⣿⣿⣿⣏⣿⡇⠉⠀⢐⣻⣿⣽⣿
⢸⣿⣴⣬⣿⡀⠀⠾⠟⠽⢷⡇⠀⠀⠀⠀⣿⢸⡿⣿⣿⡁⠀⣲⢾⣯⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⡽⣿⣿⣿⣿
⢸⣿⣿⣿⡃⢀⣦⣀⣀⣀⣼⡇⡄⣤⣴⡴⡿⢸⡇⠐⣇⣟⠀⠉⣿⡏⠙⠛⠋⠛⢹⡟⠙⣸⠟⠛⠿⡿⣿⣿⣿
⢸⣿⡿⣛⣿⣿⣇⠀⠄⠀⢻⡇⠰⣮⠔⣯⡇⢸⡇⢀⣿⣿⠦⠀⢿⠓⠂⠀⠀⠀⢸⡆⠀⢸⠄⠀⠀⠀⠼⢿⣿
⢸⣿⣿⣥⣾⣿⠛⠀⠀⠈⢻⣿⠷⣴⣾⣿⡿⢸⣿⣗⣯⣉⣁⡤⠯⠥⠤⠤⠤⠄⠘⠗⠒⠒⠒⠛⠓⠀⠈⠉⠁
⠘⠿⠿⠿⠿⠛⠂⠒⠒⠒⠛⠛⠋⠉⠉⠉⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣠⠚⠉⠉⠲⡌⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⠃⠀⠀⠀⠀⢹⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⢲⡀⠀⠀⠀⣷⢸⡆⠀⠀⠀⠀⣼⢀⡇⠀⠀⠀⢀⡖⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⣧⡠⠤⣒⣛⣊⠩⠭⠭⠭⠭⠍⢙⣓⣒⠤⢄⣼⠀⠀⠀⠀⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⠴⣊⠵⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠪⢝⡢⡀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⡰⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣦⡀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠏⠀⠀⠀⠀⠀⠀⠀⢠⣠⣦⣄⠀⠀⠀⣄⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠃⢘⡆⠀⢰⠛⠟⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠊⠀⠀⠀⠓⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⢀⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢿⣀⡼⠀⠀⠀⠀⢸⡀⠀⢠⠇⠀⠀⠀⠀⢸⣀⡼⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠳⢄⡀
⠀⠀⠀⠀⠀⠀⡜⠁⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⣠⣒⠾⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡆⠀⠀⠀⠀⠀⢸⡀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠈⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⡜⠀⠐⡇⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠘⡄
⠀⠀⠀⠀⠀⡸⠀⠀⢠⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⣿⠀⠀⠸⡀
⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡏⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰
⠀⠀⠀⠀⠸⡄⠀⠀⠈⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⡜
⠀⠀⠀⠀⠀⡇⠀⠀⠈⣇⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠹⡀⠀⠀⠸⡄⠀⠀⠀⠀⠈⠉⠛⠒⠒⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠊⠉⠈⠉⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠊⠉⠒⠊⠉

⠀⠀⠀⠀⢀⣤⣶⣆⣤⠶⠂⠀⠐⠂⡒⠀⢀⣠⠤⠆⠤⠤
⠀⠀⠀⠀⢸⣿⣿⣿⣦⣤⣪⡷⢾⢿⣥⣿⣦⠹⣿⣦⢀⠀⠃⠀⠰⢿⡀⡀⠄⠀⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⣤⣤⣤⣀⣠
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣻⠿⣻⣧⣶⣿⣿⣿⣿⣷⠒⠀⠌⡉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠉⢹⣋⣙
⠀⠀⠀⠀⢸⣿⣿⣟⣣⡿⢿⣿⡏⠉⠐⠘⡟⠛⠟⠁⠉⠻⠷⡶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⣿⣿⣻⢟⡿⣶⡆⣀⣉⡉⠉⠋⠠⠀⠀⠊⠒⡖⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⣿⣿⣿⣯⣼⣦⣽⣿⣿⣢⠌⠀⢀⣄⠀⠀⢘⡁⢀⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⢸⣿⣿⠀⢝⣯⣶⣬⣿⡿⣿⣶⣶⣿⣿⣿⣷⣌⣟⠻⢿⡀⠀⢠⣄⣄⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣼⡀⢀⡅⠀⠻⠤⠨
⠀⠀⠀⠀⢸⣿⣿⣿⣶⣿⣿⣿⣿⣄⡸⠿⣿⠟⢻⡌⠛⠁⡈⢘⢿⠏⣄⠀⠈⠉⠩⠭⠉⠁⠀⠀⠀⠀⠀⠀⢀⡷⣆⢈⡉
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⣻⣟⣽⣷⡤⠀⣎⣁⡀⣀⣄⠀⠀⠈⠊⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣃⣛⡘⡇
⠀⠀⠀⠀⢸⣿⣿⡛⣿⣿⣿⣿⣿⣼⠉⡡⣇⡤⢁⠀⠛⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⢰⣠⣿⣿⣿⡆⢘⠿⠟⠾⢿⣧⣶⣶⣰⣖
⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣿⠟⢷⠓⡶⠏⠀⠃⢠⠄⠀⠀⠂⢀⣶⣦⣽⣷⣶⣶⣤⣤⣽⣿⣉⣀⠀⠁⣿⣀⠀⢴⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⠻⣿⡿⠿⠽⢶⣄⠈⠤⠀⣀⣶⣤⣯⣿⣦⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣦⣬⣿⣾⣼⣿⣷⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣠⣿⣿⣴⡖⠀⣠⠁⢀⣠⡉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡛⣿⣿⡛⠛⠛⢻⡟⠛⢛⣛⣛
⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⣯⣄⣷⣷⣶⣿⣿⣿⣿⣿⣶⣾⣿⡿⠿⡿⢿⣟⣿⠟⠛⠻⣿⢿⣽⡿⠛⠛⠛⠛⠛⠛⢹⡟⢉⣉⣉⢉
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⣉⣉⣙⣛⡛⣋⣀⣀⣀⣉⡉⢁⣀⢀⡇⠀⠉⠁⠀⠀⠀⣾⠠⣿⢣⡀⠀⠀⠐⠂⠀⢸⡧⠽⠛⠋
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡯⠿⠋⠉⣻⡟⢻⢿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠃⣠⡶⣦⣤⣤⣼⣧⣤⣤⣤⣤
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣏⣡⣴⡶⠟⠋⣉⣵⡦⠻⠿⠿⠛⠛⠉⠙⠻⢻⣿⣿⡿⣟⡛⢻⠛⣻⣿⣾⡛⣟⠛⠛⣿⣿⣿⣷⣿⣿⣭⣿
⢀⣀⣀⣀⣸⣿⣿⠿⢿⣿⣯⣥⣤⣴⣾⣿⣿⣿⣿⣯⣆⣀⣀⣠⣤⣴⣿⣿⣋⡙⠫⣝⣳⣿⡻⢿⠿⠁⢧⠈⠹⠿⠿⠏⠛⠛⡻⠿⠟
⠀⠉⠻⢿⣿⣿⣿⣶⣾⣿⣿⣿⣿⠏⠒⠉⠓⠀⠁⠉⠉⠫⠖⡿⠿⠾⠟⠋⠈⠀⠐⠋⠉⠉⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠈⠻⢿⣿⠋⠉⠛⠛⠛⠒

⠀⠀⢠⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢰⠀⠀⠀⡀⠀⠀⣿⠀⠀⠀⠀⠆⠘⠃⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢀⣇⠀⠀⣿⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠂⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠈⠁⠈⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⣀⣠⣦⡀⠀⢀⠀⠀⠀⠈⠉⠀⡀⠀⠀⠀⠄⡀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠈⠙⢉⡟⠁⠀⠀⠀⠀⢤⠀⠀⠀⣷⠀⠀⠀⠀⠁⠀⠀⠀⠂
⠀⢰⣤⣠⠀⠀⠀⠄⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⢀⣿⡄⠀⢰⣿⡇⠀⠀⢠⠀⠀⠀⣀⣂
⠀⠀⠁⠀⠀⠀⠀⠀⠐⠿⠂⠀⠀⠀⢰⠛⡚⣅⠀⠀⠀⠀⢸⣿⡯⠀⠀⡞⠃⠀⠀⣿⣧⠀⠀⠈⠉
⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸⣿⣿⣧⣤⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠻⠉
⠀⠀⠀⠀⢀⠀⠀⠀⠁⢶⣀⠀⠀⠀⠀⠹⡿⡛⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠄⠈⢆⡀⠀⠀⠐⢍⣣⡀⠀⠻⠿⠿⢷⣿⣽⠄⠀⠘⠀⠶⠀⠀⠀⠄⡠⠀⠀⠢⣄⣠⡆⠉
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠉⠁⠀⠀⣀
⠀⠀⠀⠐⠀⠀⠀⠀⠖⠛⠇⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠁⠀⢈⣴⠛⣹⣤⠀⠀⠀⣠⠖⢀⠠⠀⠀⠀⠀⠀⠀⠀⢠⡩⠘⠁
⠀⠀⢠⠀⠀⠀⠀⠀⢼⣦⡄⠀⠀⠀⠀⠈⢹⡿⣿⡇⠀⠀⢀⣒⣀⡀⠏⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠛⠀⠀⢰⠶⠶⠆⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠠⠄⠀⠀⠀⠀⠀⠶⠦⠄⠀⠀⠀⣅
⠀⠀⠀⠀⠰⣛⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠛⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠋⠉⠉⠀⠀⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢤⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⢤⠀⢀⣠⡴⠖⠛⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⢤⡄⠀⢸⠇
⠀⠀⠀⠀⠀⠀⢀⡴⠖⠒⠚⠛⠛⠛⠒⠲⠦⢤⣀⡴⠋⠁⠀⠀⠸⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠲⣄⣸⠃⠀⣾
⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢹⠀⣰⠇
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣠⠏
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠛⠲⡶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃
⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢧⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠘⠋⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠻⣷⣤⡶⠀⠀⢸⣥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠹⠟⠁⠀⠀⠚⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠉⠛⣦⠀⠀⠀⠀⠀⠀⠸⣯⡇⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠳⣶⣿⠇⠀⠀⠘⠇⠀⠀⠀⠀⠦⠤⠞⠛⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠛⠲⣄⠀⠀⠀⠀⠀⠀⠈⠙⢳⠶⠤⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢀⡴⠾⠆⠀⠀⠀⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠈⣧⠤⢤⡀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠈⣳⣤⡀⠀⠀⠀⠀⠁⠀⠀⠹⡞⠓⠀⠀⠀⠀⠐⠶⠦⣄⠀⠀⠀⠀⣀⠀⠀⣂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢸⠀⠀⢹⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠹⢤⣀⣀⡀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠸⡇⠀⢸⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⣤⠴⠛⠙⠶⠖⠛⢦⣀⠀⠀⠀⠀⠀⠀⢀⣜⠙⣆⠀⠀⡇⠀⢸⠀⠀⠿⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣛⣃⠀⠀⠀⠀⠈⣳⣼⣆⣀⣿⣀⣯⣤⣀⣀⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠋⠉⠀⠀⠉⠀⠉

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

⠀⠀⠂
⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⣄⣠⣤⡤⠠⠀⠀⠠⠤⠄⢀⣀⣀⣤
⠀⠀⠀⠀⠀⠀⢶⣶⣆⡀⠐⣦⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣄⣠⣶⡾⠋⠁⢀⣠⢖⣤⣶⣶⣶⣿⣿⣿⡷⣦⣄⡀⠀⠀⠀⢀⣠⣠⢤
⠀⠀⠀⠀⠀⠐⣚⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⡄⠁⢀⣴⣾⣿⣿⡿⠃⠀⠀⣠⣼⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⢿⣿⣦⠀⢸⣿⣿⣿⣿⣶⡖
⠀⠀⠀⠀⠀⠤⣬⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⠁⠀⠘⣹⣾⣿⣿⠃⡠⠀⠀⠘⣿⣿⣿⣿⡿⣿⣿⣿⣿⠻⣿⡄⠈⢻⡗⠄⠈⢻⣿⣿⣿⠞
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠟⡃⠀⠀⠀⠈⠗⢰⣀⠀⠀⠻⢿⡗⡼⡕⠀⠀⣠⣾⣿⣿⣿⣤⣬⣿⣧⣤⣴⣿⣗⠀⢸⣧⡀⠀⠀⠹⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡄⠀⠀⠀⠀⠀⡄⠈⠁⠀⠀⡐⣻⠃⢹⣃⠄⠈⣛⢛⣩⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⠁⢸⡿⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⣿⠿⢾⠀⠀⢠⡞⠰⣺⣿⢰⡄⠀⠀⠀⡟⠀⠈⠉⠀⢀⣼⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⡀⣺⡇⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⢿⣿⠃⠀⠀⡄⠐⢠⣾⣯⣾⡦⠀⡀⣤⡳⠀⠀⠃⢀⣸⣿⣿⢻⣿⣿⣼⣿⣽⣽⣬⣿⡟⣿⣧⣽⠁⢤⣿⡷⠀⠰⠄
⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⢴⠁⣴⣿⣿⡿⡭⠁⠀⠀⠀⠉⠀⡀⠀⢨⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠋⢸⣿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⣿⠷⠀⠀⠀⠀⢘⣿⣿⣿⣂⠀⠀⠀⠀⠀⠠⠃⠀⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡟⣿⡆⢻⡿⢠⣄⠀⠁
⠀⠀⠀⠀⠀⠀⢴⣉⠃⠀⠀⠀⢀⠀⠁⣹⣯⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣇⣾⡿⢸⣿⠀⢀⣾⣯⡌⣡⡀
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠀⠩⣶⣿⣶⠀⠀⠀⠀⣤⠀⠀⣸⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡏⢀⣼⣿⣿⠣⢬⠁
⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⠀⠂⢰⡃⠀⠿⣿⡿⡀⠀⠀⣸⣧⢀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣷⣿⠁⢺⣿⣿⡿⡃⡠
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠰⢀⠘⡃⠠⠜⢟⣰⡧⡀⢀⣿⣿⡠⢃⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⢾⣿⠛⣛⣰⣿⣿⣿⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠫⠁⠀⠿⣹⡇⠉⠁⣿⣿⡄⢿⣿⡿⣿⣿⣽⣿⢾⣿⠇⣿⣿⡁⢩⣿⡿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣄⡤⠀⠰⢂⡠⣯⢇⠀⠀⢰⣿⣷⢸⣿⣧⣿⣿⣿⣿⢹⣿⢾⣿⡏⢉⣾⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠴⠦⢠⡁⠈⠠⠤⣸⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠋⢰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣅⣤⢀⠀⠀⠀⣇⠈⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⢿⢹⣿⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢹⡿⣷⣼⣆⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠈⠛⠻⣿⣿⣿⠈⢿⣿⡏⢿⣿⣿⣿⣿⣿⡿⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⡅⣿⣿⣿⡎⣿⣿⣿⣿⠿⣃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⢻⣿⣿⣿⡜⠻⣿⢿⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢻⣿⠻⣿⣿⣿⣿⣿⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⢽⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⡿⠛⠿⢿⡿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢼⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠠⠁⣀⣠⣂⠀⡤⠃⠀⠀⠀⠤⠀⠀⠀⠤⠀⠀⠀⢀⠈⢸⡆⠀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡰⠃⠄⠀⠁⠀⠁⠏⠀⠀⡤⠂⣠⠾⠅⠀⠀⠊⠭⠋⠀⣈⠉⠛⢤⡀⣧⡀⠀⠘⣿⢃
⠀⠀⠀⠀⠀⠀⠀⢠⢦⡟⠀⢁⠞⠁⠀⣢⠎⠀⣂⣴⡤⠊⠁⠀⠈⠈⠁⠀⠀⠀⣸⣿⣿⡧⠀⠙⢿⡄⠑⢀⣿⡈⣞
⠀⠀⠀⠀⠀⠀⡰⠃⡿⠀⢸⠃⣠⡶⢋⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣷⡄⠘⠀⠉⣷⣾⣿⣧⡿⡄
⠀⠀⠀⠀⠀⣰⠁⢰⡇⠀⣿⣟⠁⣰⣿⠡⠄⠀⠀⠀⠀⠀⠀⠒⠠⠤⣭⡽⠦⠤⡿⣿⣿⣿⣧⠀⠀⠀⣌⣿⣿⣿⡇⠘⡄⠀⡀
⠀⠀⠀⠀⢠⣿⠀⢸⣧⣰⡿⠈⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿⢦⡀⠀⠀⣿⣿⣿⡇⠀⢸⣠⠃
⠀⠀⠀⠀⠘⣿⠀⠀⣿⣿⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣾⣿⣿⣿⡇⢀⡾⠁
⠀⠀⠀⠀⠀⢻⡄⠀⣿⣿⣿⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣷⣼⠁⠀⢸⡆
⠀⠀⠀⠀⠀⠘⣧⠀⣿⣿⣿⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣇⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠘⣦⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢠⣿⣿⣿⣿⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢇⣾⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⡀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡄⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⢠⠃⠀⡊⣉⣷⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣧⣧⠀⢀⠀⠀⠀⠀⠀⢈⣽⡇⠀⣿⠀⠀⣄⡟⣠⣶⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠛⠻⠿⡿⠶⡷⠶⠶⣤⣬⣾⣿⣸⣿⣶⡶⠿⡿⣿⠟⠋⠉⢙⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠿⣧⣤⣤⣴⣷⣤⣧⣦⣀⠠⠬⣿⣿⠛⡲⣗⡂⢠⢠⣿⠀⠀⠒⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣨⣿⣾⣿⠁⠀⠀⠴⠿⠿⢭⣭⡭⠀⠼⠿⠷⠦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠼⠶⠒⠾⠖⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⡶⣤⣠⡾⠋⣾⡷⠶⢶⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠶⠿⠛⠿⢷⡀⠹⠃⠸⠃⢀⡾⠿⠛⠻⠷⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣭⡿⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠲⠿⢿⣭⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⡀
⠀⠀⠀⠀⠀⣼⣷⡀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⣰⣿⡀
⠀⠀⠀⠀⠀⣿⠙⢷⣄⡀⠀⢀⣾⠋⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠈⢿⣄⠀⠀⣀⣴⠟⢹⡇
⠀⠀⠀⠀⠀⣿⢀⡼⠉⢛⡿⣿⠁⠀⠀⡇⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡷⠀⠀⠀⢻⡿⡟⠋⠳⣄⢸⡇
⠀⠀⠀⠀⠀⢻⣏⠀⢠⠞⢰⠃⠀⠀⠘⠧⠶⠛⣇⢀⡴⠚⢹⡄⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡟⠳⢤⠀⡸⠉⠻⠃⠀⠀⠀⠈⣧⠙⣆⠀⢈⣿⠁
⠀⠀⠀⠀⠀⠀⢻⣦⡟⢀⡏⠀⠀⠀⠀⠀⡠⠶⠚⠛⠒⢦⡀⠳⣄⣿⡀⢠⠖⠀⠀⢀⡠⠞⢁⡴⠚⠛⠓⠲⣄⠀⠀⠀⠀⠀⢸⡆⠸⣦⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⠗⠋⠀⠀⠀⡞⢁⣴⣿⣿⣷⣄⠙⡆⠈⠙⢣⣏⣤⣶⠾⠋⠀⢰⠋⣠⣾⣿⣿⣶⡈⢳⡀⠀⠀⠀⠐⢧⣼⠟⠁
⠀⠀⠀⠀⠀⠀⢀⣴⣯⣥⡄⠀⠀⠀⢸⡇⢸⣿⣿⣋⣿⣿⠆⣿⠀⠀⠈⠻⠁⠀⠀⠀⠀⣿⠀⣿⣿⣙⣿⣿⡷⠀⡇⠀⠀⠀⠰⣦⣽⣷⡄
⠀⠀⠀⠀⠀⠀⠈⠉⣹⡟⠀⠀⠀⠀⠈⢧⠈⠿⣿⣿⡿⠏⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠹⢿⣿⣿⠿⠃⡼⠁⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣤⠀⠀⠀⠀⠀⠑⠦⢤⣤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣤⡤⠴⠚⠁⠀⠀⠀⠀⢳⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⡇⣠⡆⠀⠀⣦⠀⡀⠈⣯⢿⣶⠲⠦⢤⣤⣤⣤⣀⣀⣤⣤⣤⡤⠴⠒⣾⣽⠇⠀⠀⣠⠀⠀⢰⣄⢸⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢧⡀⢠⡟⠧⠽⠄⠘⢦⡘⠤⠔⠋⡡⢦⣀⠀⢀⡴⢦⡈⠙⠢⠼⣡⠏⠠⠾⠴⠟⣷⠀⣸⠏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠋⠀⢶⡀⠀⠀⠀⠙⠲⠤⣼⣁⣀⠈⠉⠉⣀⣀⣱⡤⠶⠊⠁⠀⠀⠀⣴⠀⠘⠚⠁⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠓⠚⠓⠦⣄⠀⡤⠶⠶⠤⣤⣉⣉⣉⣉⣉⣠⣤⡤⠤⢤⡀⢀⡤⠖⠛⠒⠂⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢧⡀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣠⡤⢤⡀⠀⠀⠀⠀⠀⠀⠙⠷⣤⠇⠀⠀⠀⠀⠀⣸⠉⣳⠞⠁⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣍⠳⢤⡠⠳⡄⠀⠀⠀⠀⠀⠠⢤⣯⡀⠀⠀⠀⠀⠀⠘⢾⣁⣀⠀⠀⠀⠀⠀⢠⠞⢧⣠⠿⣍⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠧⢽⢀⡴⠦⡀⠙⢆⠀⠀⠀⠀⠀⣤⡤⠇⠀⠀⠀⠀⠀⠀⣞⠉⣀⠀⠀⠀⠀⢀⡏⠀⡴⠶⣄⣌⢻⣉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⣿⠘⠦⠴⠃⠀⠀⠙⢶⣀⣷⣴⡇⢀⣄⠀⣀⡀⠀⠀⢀⠈⠉⣿⣴⣷⠼⠷⠞⠀⠈⢧⣤⠾⣈⢻⣿⠇
⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠶⠶⠶⣦⣤⣤⣤⣤⡽⠟⠛⠿⠾⠛⠿⠟⠻⠾⠿⠟⠿⠿⠿⠟⢿⣤⣤⣤⣤⣤⠶⠶⠶⠾⠿⠿⠶⠶⠶⠶⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⢀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠸⠀⢀⡄⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⢮⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠉⢣⡄⠀⠀⠀⣤⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⡀
⠀⢀⠀⠈⠁⠠⠂⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⢀⣀⡴⡼⠁⠀⡠⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⠀⠀⠀⠀⢀⠊⢹⣷⠻⡆⠸⣴⠏⠠⠔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄
⠀⠀⠀⠀⡄⠰⠏⠀⠀⡀⠀⠀⠀⢀⠀⠀⣿⢷⣿⣿⣱⢿⣾⢷⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁
⠀⠀⠆⠀⠀⠀⠂⠀⠀⠁⠀⠀⢀⠈⠀⠀⡹⣾⣿⡿⠁⣾⢃⠌⣰⠀⠀⠀⢠⡜⠁⠀⠀⠀⠀⢀⡀
⠀⢸⣀⡆⠀⡀⠀⠀⠀⢀⠤⡀⠀⠑⠀⠀⠁⢿⣿⡇⢠⠛⡏⣴⠿⠒⠀⣴⠁⠀⠄⢠⠈⠀⠀⠈⠙
⠀⠐⠀⠀⠈⠇⠀⢀⠔⣋⡀⠄⠁⠷⠛⢷⡉⠷⣼⣷⡶⢻⣠⡿⣢⠴⠆⠀⠀⠀⢶⠂⠀⠀⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠖⠈⣩⠖⠈⠀⠀⠀⠀⠀⠀⠚⠳⣦⣴⡬⠛⠛⠿⣵⠄⠀⠀⠛⠓⠚⣁⡴⠆⠰⢤⠤⠄
⠀⠰⡄⢰⠀⡔⠁⠀⠐⣦⡠⡄⠀⠀⠀⠀⠐⠉⣙⡕⠊⠉⠑⣖⠓⣞⡤⡶⠐⣊⠁
⠀⠀⠄⡌⡀⠀⠀⠀⠀⠈⠻⣶⣃⡀⠀⠀⠀⠀⡿⠀⠴⠀⠛⠹⡆⣉⢷⡄⢀⢈⠙⠢⣀⠀⠀⠀⣠⠄⠶⠀⡄⠀⠀⠀⠄
⠀⠰⡎⢀⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠇⠀⠀⢀⡝⠳⡄⠰⠟⠀⢿⣸⠎⠷⠆⢘⣋⡄⢹⠗⠂⠉⠐⠖⠒⠈⠀⢠⠾⠂
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠰⠀⠉⠒⣰⣷⡶⠟⠊⣠⣔⣻⣧⢈⣁⣙⣧⠳⣄⢦⣄⠠⠀⠉⣸⢇⣀⡀
⠀⢰⠆⡄⠷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣆⣼⠆⣠⣤⡀⢠⠞⢢⣴⢇⣼⠿⠿⡄⣉⡻⣹⡆⠈⠴⣉⣦⡰⠞⠁⠀⠈⢉⠆
⠀⢨⡂⡇⠘⢇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⡧⠴⠇⠀⠳⢶⣢⣶⣶⣿⣷⠄⣀⠿⢿⠙⢦⣛⡶⡘⠗⣤⠸⣄⠀⠰⠆⠈
⠀⢠⠍⠀⠀⠈⠷⢀⠀⠀⠀⠀⠀⠈⢉⠅⡲⣓⢛⠶⠹⠃⠌⢹⡄⣀⠙⠶⡫⠄⠰⢇⠠⡏⢳⠚⣤⠀⠙⢿⡓⠳⣄
⠀⢠⠀⣆⠐⠀⣄⠀⠙⠙⠢⠄⣠⣖⣁⡴⢉⠋⡽⢛⢄⣼⢳⣷⡾⠙⠥⠀⡿⣤⡚⠁⠀⠿⠀⠃⢻⡉⠩⣈⠣⢤⣁
⠀⠈⠀⠉⠠⡀⠈⠀⠀⢀⠀⠉⠉⣠⠞⣴⠋⣼⠳⠟⣘⡣⠙⠁⢀⡐⠂⠤⠭⢙⣡⡴⠂⠀⠀⠙⢮⣹⠶⠺⢿⠂⣉⠓⡀
⠀⠀⢀⠀⠰⠁⠀⠀⠴⣿⠀⠀⠀⠀⠘⠀⠢⠙⠒⠎⠁⠴⠣⠾⣦⡀⠀⠀⠀⠈⠳⠶⢞⡉⣤⡄⡀⠈⢷⡒⠦⠀⢉⡜
⠀⠀⠈⠂⠀⠀⠀⠀⢠⣄⠙⠆⣰⡆⠀⠂⠀⠀⠈⠀⠀⠀⢰⡞⢻⣿⡧⠀⠀⠀⠀⠀⠈⡡⠟⠐⣻⣿⡀⠘⢦⠁⠈⠓
⠀⠈⠀⢀⠄⢰⡆⠀⠰⣿⠀⠘⠉⠇⠀⠀⠀⠀⡄⠀⠀⠀⢠⡿⢇⣈⣿⣀⠀⠀⠀⠀⠀⢀⠀⠀⣿⠏⠿⣄⠈⠼
⠀⠀⠀⠈⢀⣈⠹⠀⡀⠁⣾⠀⠀⠃⠐⠀⠀⠀⠃⠀⠀⠀⢷⣄⣤⠙⣟⠻⡶⣦⣤⣄⣰⡁⠀⢸⣿⣿⠛⡇⢠⠀⠀⠀⡀
⠀⠀⡄⠀⠈⠟⠀⢠⡁⠢⠘⠄⠀⠀⠐⣦⠠⡀⠀⢀⠀⠀⠀⠀⢠⡁⣘⣇⠠⡏⡹⢏⡿⢻⢦⡏⠀⠀⠀⡀
⠀⠀⠁⢀⡈⠀⣀⣾⠑⠊⠀⠀⠀⠀⠈⠈⡠⡏⠀⠘⠀⠀⠀⠀⠀⣉⣹⠟⢻⡷⠇⠈⠱⡟⢬⣿⣶⠟⣿⣀
⠀⠀⠀⠸⠓⠁⠙⢉⠀⠀⠠⢦⠀⢠⡀⠄⠡⣁⠀⠀⠀⠀⠀⠀⠈⠉⠀⣤⣼⢁⢦⡀⠆⢻⡆⣿⠻⣿⣽⣯⣶⡖⠀⠠
⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠈⣇⠄⠻⢠⠀⢈⡇⠀⠐⠀⠀⠀⠀⠀⠀⠤⠜⣡⡜⠀⠈⠀⡌⢛⣦⡁⠈⠉⢻⡎⣠⠀⠇
⠀⠀⠀⠀⢳⡤⠤⣄⡈⠀⠀⠈⠀⡀⣦⠈⢀⣊⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⠁⠻⡄⠀⠀⠸⡇⠙⠻⣦⣡⣤⢹⡗⠀⡀
⠀⠠⠀⠀⠈⠃⠀⠈⠁⠀⠀⠀⠞⠉⢈⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠙⠄⠀⠀⣷⢀⡀⠟⣀⠀⠀⠀⠀⠁
⠀⢰⣤⠐⠒⣋⠟⣚⣡⡾⠲⣟⣵⠞⣍⣓⣶⣤⣼⡵⠦⠠⠀⢠⠀⠠⠄⠠⠤⠆⠤⠤⠔⠉⣉⣠⣾⠷⢦⠟⠷⣦⡄
⠀⢸⡟⠛⠛⠟⠛⠉⠏⠑⠛⠋⠉⠀⡁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠙⠋⠴⠁
⠀⠸⡇⣴⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⣀⣀⡀⢘⡀⢀⠐⠀⡀
⠀⢠⡀⡀⢀⠀⠀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠋⠁⠁⠀⠈⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠖⠀⠀⡌⠉⠛⠐⠓⠸⠗⠶⠂⠶⠲⠞⣿⣿⢷⣦⡄⠤⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢘⢀⣴⣄⠂⠀⠀⠀⠀⠠⢄⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠋⢀⠄⠈⠃⠀⠀⠳⡌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⢠⠀⢁⡦⣴⡦⢠⡌⠀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠐⠀⠀⠸⣇⠋⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠈⠧⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠘⢎⣦⣻⡀⣶⣶⢈⡷⠗
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⣀⣨⣾⠃⠀⠀⣠⡎⠀⠀⠀⢈⣿⣿⠋⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠂⠀⠀⠂⠀⢀⢰⣶⣭⣷⣷⣿⣶⣶⣾⣿⡿⠟⠻⣧⠀⢺⡿⠋⠀⠀⣠⣿⡿⠁⠃
⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⢰⣦⣨⠛⠉⢶⣯⡉⡍⠉⢻⡏⠀⠀⠀⠀⣿⠠⢀⡄⠃⡰⢿⣿⡿⢥⣼⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠾⡉⠀⠀⠀⣸⡾⠛⠀⠀⠀⠀⢻⡇⠀⠀⠈⡇⠀⠀⠀⠀⢻⡀⠀⠀⠐⠀⠀⠉⠛⠻⠿⠠⣟⡹⡄
⠀⠀⠀⠀⠀⢈⠁⣷⣄⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⣷⠴⠈⠘⠃⢤⡀⠀⠀⠸⢷⣿⠶⢣⡀⠀⠀⠀⠀⠀⠀⠈⠡⣾
⠀⠀⠀⠀⠀⠀⢷⣬⣿⣧⠀⠀⠀⠀⠀⣀⣀⠰⠶⠿⠶⢷⣶⣷⠾⠿⣤⠤⠤⢼⣷⣥⣭⣭⣵⡤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⡈⠉⣭⠉⠉⣩⠍⢈⣐⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠫⠶⠀⠀⠈⣡⠀⠁⠰⡄⠀⠲⠈⠉⠀⠀⡤⠈⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⡄⠐⠋⠀⠉⠲⠆⠀⠰⠆⠀⠰⠃⢠⡀⠀⣘⡋⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠁⠀⠀⠀⣀⣀⠚⠁⠀⠀⠀⠀⣀⣀⠀⠀⠈⠁⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⡷⠀⠀⠀⠀⢾⣿⣾⠆⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⣀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣴⣶⣶⣦⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠐⠠
⠀⠘⢄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠦⡔
⠀⠀⠀⠙⢦⡀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠈⢢
⠀⠀⠀⡠⠁⠈⠢⡙⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣂⣁⣀⣀⡀⠀⢃
⠀⠀⠀⠣⣀⡀⠀⠈⠢⡀⠀⠈⠉⠉⠁⠐⠒⠒⠒⠒⠒⠒⢒⡐⠶⠖⠒⠚⠋⠉⠉⠉⠀⠀⠀⠀⠀⡠⡇⠉⠉
⠀⠀⣤⠀⢇⠈⠑⠒⠒⠚⠓⢄⠀⠀⣀⡀⠤⠄⠒⠂⢉⢟⠂⢄⠀⠀⠀⠀⣀⠀⠠⠤⠄⠀⠒⠂⠉⢀⠧⣀
⠀⠀⠀⠉⠞⠉⡇⠈⠁⠀⠁⠉⠉⠉⠉⠀⠈⠈⠉⠈⠁⠈⠁⠀⠙⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢐⡇⠀⠀⠑⢄
⠀⠀⠀⠀⠑⢤⣁⡂⠀⠐⠒⠐⠀⠒⠀⢂⡀⢀⣀⣀⣀⣐⠐⠂⠀⠐⠒⠀⠀⠐⠀⠒⠂⠂⠐⣒⣥⣃⣀⣀⡀⣈⣂
⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠈⠙⠪⢄⡀⠀⠀⠀⠀⠀⠀⠉⠢⣀⣀⣀⡠⠤⠒⠒⠀⠀⠈⠁⠀⠸⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠔⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠠⠤⠄⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠤⠤⠒⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣶⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⢛⡻⢿⣿⠇⠀⠀⠀⠘⣿⣿⠿⠿⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣿⣿⣿⡿⠀⠀⠀⠀⠀⢿⣷⣿⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⠛⠀⠀⣄⣠⡄⠀⠈⠻⢿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⣉⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠉⠉⠐⠢⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⣄⡠⠊⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⢋⣬⠹⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣋⣴⣿⣿⣿⣿⣿⢟⣿⣯⣿⡿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣗⣿⣽⣿⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣁⣌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣿⠿⣿⣿⣿⣿⣿⣿⣿⣇⠐⢿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣒⣸⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⣿⣿⣿⣟⠋⡽⠋⠉⢻⣿⡿⠿⣿⡿⠛⣿⣿⣿⣿⣿⡟⣭⢹⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⣓⣽⣿⣿⣿⣿⣇⠀⠀⣼⡿⠁⠀⢈⡇⢀⣼⡷⠿⢿⣿⣿⣶⣾⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⠋⠈⠙⣿⣷⣾⣿⣷⣿⣿⠿⠿⠿⠋⢀⡴⢊⣽⣿⣿⡿⠿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⡿⣠⠴⠚⠙⠻⣿⣿⣿⣿⣿⣷⣶⡶⠋⠉⠉⠁⢿⣿⣿⣆⣣⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣧⣿⣿⣷⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢾⣾⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠿⣷⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⡠⠐⢄⠀⠀⠸⣧
⢀⣶⠟⠛⠛⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢀⠊⠀⠀⠀⠆⠀⠀⣿
⣾⠃⠀⠀⡀⢀⠈⠻⢷⡄⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡶⠶⠶⢶⠶⠶⠿⢤⣤⣁⠀⠀⠀⠀⢠⠀⠀⣿
⣿⠀⠀⢰⠀⠀⠑⢄⠈⠻⣦⡀⣀⣤⡶⠟⠋⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠘⠀⠀⣿
⣿⡀⠀⢸⠀⠀⠀⠀⠑⢀⣸⠟⠋⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆⠀⢰⡟
⢸⡇⠀⠈⡀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠘⠻⠿⠦⠀⠀⠘⣦⣾⠃
⠈⣿⡀⠀⢡⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢠⠀⡀⠀⡀⠀⠀⠈⢿⡀
⠀⠸⣧⠀⢀⡾⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠔⠁⠀⠀⠀⣠⣖⡊⠙⠓⢴⠁⠀⠀⠀⠘⣷⡀
⠀⠀⢻⡆⢸⠁⠀⢠⡿⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣠⡆⠀⢇⠀⠀⠀⠀⠸⣧
⠀⠀⠀⢿⣾⠀⠀⠈⠀⠀⢀⣱⢄⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡹⢿⣿⠿⠃⢀⡎⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠈⣿⠀⠀⠀⠐⠢⡞⣿⣿⣄⣠⡄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠠⠴⠊⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⡇⢿⣿⣿⡿⠃⢀⠇⠀⠀⠀⣀⡠⣤⣄⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠘⢦⣈⣁⣀⡠⠊⠀⠀⣀⠾⣷⣶⣿⠏⠀⠀⢠⠀⠀⠉⠑⠢⡀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠈⣧⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠘⢤⡀⢀⡴⠃⠈⠉⠉⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠈⠁⠀⠄⠀⠠⠂⠀⠀⣀⡤⠞⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣦⣤⣄⣀⣁⡀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⠶⠚⠋⠙⡄⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⡏⡙⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠸⣧⣀⡀⢀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡆⠀⠀⠈⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⡏⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣴⠟⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⣇⣴⠟⠁⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⡀⠀⠀⠀⢷⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡟⠋⠁⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠿⠛⠒⠒⣾⣤⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢰⣃⣀⣤⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⡀⠀⠀⣰⢋⠁⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣠⡿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠶⣿⣦⣤⣅⣀⣠⣤⣇⠀⠀⡄⠀⠠⠀⢀⣇⣀⣀⣤⣴⠾⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣛⣿⣶⣷⣶⣿⣾⣟⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠓⠦⠤⠖⠋⠙⢦⣀⠆⡰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣄⠈⠀⠀⠀⠀⠀⠀⠀⢀⡔⠩⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠙⠲⣦⡀⠀⠀⠀⣰⠏⠀⠀⠀⢉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⣠⠞⢳⡝⠲⣤⣼⠃⠀⠀⠀⠠⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠚⠒⠂⠘⠁⠀⠀⠙⠛⠛⢻⡀⠀⠀⠀⠀⠈⠛⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⢁⡀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠀⠀⠀⠀⠀⢠⡀⠀⢀⡴⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡤⠤⠤⣤⣤⣼⠳⣖⠋⠀⠀⠀⢠⠞⠁⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡁⠀⠀⠀⠀⠈⢹⡟⠛⠳⣤⣀⠀⠘⣷⠶⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠈⠛⣏⠁⠰⣞⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠃⠀⠀⠀⢰⣏⠀⠀⠀⠀⣀⠀⣾⣄⠀⠈⠙⠚⠦
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣤⡞⢻⣄⠀⡼⢻⣉⠛⠀⠸⣄⣠⡄
⠀⠀⠀⠀⣀⠀⣰⠏⠉⣿⢣⠾⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣰⠀⡜⣼⠛⠡⠚⣻⡗⣾⡓⠀⠀⠑
⠀⠀⠀⢀⠋⠉⠁⠀⢠⣿⡆⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠛⠀⣼⡉⠀⠀⠀⡙⠀⠈⠙⢆⠀⠤⣄⣀
⠀⠀⣀⣈⣣⡀⠀⠀⣺⣿⣥⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠝⠀⠀⠙⣇⣀⢄⠁⠀⠀⠀⠀⢻⡤⠞⠁
⢀⡴⠋⠀⠉⠻⢦⡾⢻⣯⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠒⢲⡶⠚⠑⡟
⠈⠻⣄⠀⠀⢠⡟⢁⡾⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⡤⠀⠀⠀⠐
⠀⣠⠟⠀⣴⢋⡴⠛⡁⢺⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡑⢾⣷⠂⢈⡁⠐
⠰⡏⠀⠀⣻⣸⡇⠈⠀⢈⡇⠀⣠⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣄⡀⣀⡹⡄⠈⠂⠈⠃
⠀⠙⢦⠄⠹⠏⠀⣀⣀⠀⣇⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠠⠤⠼⠀⠉⠻⣏⠛⢻⣄⡀
⠀⠀⠀⢀⡠⠖⠚⠁⠀⣬⠁⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⣀⠇⠀⠀⠛⠛⢧
⠀⠀⠐⢋⠀⠀⠀⠀⢀⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡐⠀⠀⠀⢀⣻⠆⠀⠀⢀⠠⠬⣄
⠀⣟⠉⠁⠐⣀⠀⢀⣼⠀⠀⣠⣎⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡁⠀⠀⠈⠉⠛⡞⢻⣶⡶⠋⠀⠀⣠⡿
⢀⡞⠁⠀⠀⠈⣳⣮⡟⠀⠘⡇⠈⠀⢀⡴⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⡄⠀⠀⠀⣸⠋⠈⢷⣄⠀⠘⣯
⠈⠳⠳⣄⡀⠛⠙⠏⠀⠀⣠⠇⠀⢀⣜⣳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⠜⡌⠀⠀⠀⠛⢦⠄⠚⠃
⠀⠀⠐⠈⣷⡐⠠⣦⣤⣞⢙⡆⠀⠀⠋⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢦⣤⠴⢦⣄⣼⠃
⠀⠀⠀⠀⠀⣀⡀⠀⡼⠀⠈⠑⠀⠀⠚⠉⢻⣄⠀⢀⣀⡀
⠀⠶⡤⠀⢀⡟⠈⠉⠁⠀⠀⠀⢀⡴⠒⠢⠼⠋⢱⠎⠀⠘⢧
⠀⠈⠐⠐⡺⣁⣀⡀⠀⠀⠀⢠⡈⠀⠀⠀⠀⠀⣨⠁⠀⠀⠀⠉⢱⠆
⠀⠀⠀⣼⠁⠀⠀⠉⠋⠰⢾⣅⠀⠀⠈⠑⢦⣠⣿⣀⣀⣀⣠⣤⣞⣀⢀⣠⡀⣦⠢
⠀⠀⠀⠈⠳⣄⠀⠀⠀⢀⣇⡞⠀⠀⠀⠀⠰⠿⣾⡋⠉⠉⠁⠀⠈⠙⡆
⠀⢀⠀⠀⠀⡟⠀⠀⠀⠛⠻⠤⣄⠀⠀⠈⠀⠀⠸⡇⠀⠀⠀⠀⢀⣼⠁
⠀⠈⠀⠀⠀⠈⠀⠀⠀⡇⠀⠀⠀⢠⠀⠀⠀⠀⠀⢳⡀⢀⣴⠟⠉⠁
⠀⠘⠀⠀⠀⠀⠀⠀⠘⠦⣤⠖⠢⢬⡷⠛⠓⢦⡴⠋⠉⠛⠁
⠀⠐

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⣴⣶⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣦⣾⣷⣤⣤⣤
⣠⡄⠈⠃⠉⠘⠁⣦⡄⠀⠀⠀⠀⠀⠀⠀⡸⠏⠀⠻⠙⠉⢧⠀⠀⠀⠀⠀⠀⠀⠸⢉⣤⡀⢀⣤⡙⠃⠀⠀⠀⠀⠀⠀⢻⡿⠋⠁⠀⠀⠈⠻⢿⣤
⢸⣏⠁⢐⣀⡀⢈⣹⠁⠀⠀⠀⠀⠀⠀⠠⣯⣁⣤⣤⣤⣄⣽⡆⠀⠀⠀⠀⠀⠀⠇⣾⠟⠃⠈⠻⣿⠸⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⣀⣀⠀⠀⢸⡟
⡀⠲⠂⠀⠉⠁⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣿⣿⣿⣾⠟⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠙⠛⠀⡠⠃⠀⠀⠀⠀⠀⠰⣿⣷⣀⠀⠈⠉⠀⣠⣾⠿
⢛⠀⣘⠀⠐⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣿⡿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣷⣶⣶⣿⠛⠃
⠘⣴⡇⢠⠄⡤⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠰⠯⠭⢭⢭⠽⡄⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⣶⢰⡆⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣧⠠⠃
⠈⠛⠆⣸⡀⣇⠰⠛⠃⠀⠀⠀⠀⠀⠀⠀⣾⢉⣻⣛⣼⡉⠷⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⢿⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⣿⢿⡿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢶⣆⢀⣶⠆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⠈⠁⠀⠉⠙⢿⠟⠀⠀⠀⠀⠀⢀⣠⣄⠀⣀⡀
⠀⢀⠀⠐⠒⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⣠⣤⣤⣤⣀⣈⠀⠀⠀⠀⠀⢠⠋⣸⣾⠿⠿⠿⣷⣄
⠣⠁⠀⠀⠀⠀⠀⠡⠇⠀⠀⠀⠀⠀⠀⣤⠆⠀⠀⠀⠀⠀⠰⣤⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢰⣿⢻⡟⠁⠠⠀⠀⠀⢻⡛⣷
⠠⠀⠀⢿⣿⠿⠀⢀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⢀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⣿⢩⠉⠀⠀⠀⠀⠀⠀⠀⠹⣏⠳⢄⠀⠀⠀⡀⠈⢛⡯
⠀⠑⠤⠀⣀⠠⡔⠁⠀⠀⠀⠀⠀⠸⢿⣿⣷⣄⠀⠀⠀⣠⣾⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠐⢂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡏⠉⠹⣷⣄⢿⣞
⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠈⣬⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⢀⣿⣜⡞
⢠⠂⠀⠀⠀⠀⠀⡓⡄⠀⠀⠀⠀⠀⠀⠀⢸⡿⢃⣴⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢘⠀⡄⣤⢚⠎⠀⠀⠀⠀⠀⠀⠐⢿⣿⣷⣤⣾⣿⣿⣿
⠈⠉⠺⠭⠶⠭⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠖⠲⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠓⠻⠆⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⠄⢀⣠⠎⠉⢷⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡰⡞⠈⠀⠀⠀⢀⠈⠵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢧⢱⠀⠒⠂⡀⠈⠀⢀⠉⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⡀⠈⠓⠂⠀⠀⠀⡀⠀⠉⠀⠙⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡀⠐⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⣀⣹⠀⠀⠀⠀⠀⡀⠤⠀⡂⠱⠌⡰
⠀⠀⠀⠀⢀⠔⠊⠒⠒⠀⢄⡀⠀⠰⠈⠈⠉⠀⠀⠀⠁⠀⠈⠈⠀⠉⠁⠠⠀⠀⠀⠀⠘⠰⠈
⠀⠀⠀⠔⠃⠈⠀⠀⠀⢀⠀⠀⠁⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡄⣆
⠀⠀⡎⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠡⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡔⠈⠠⠀⠀⠀⠑⢢
⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠨⠀⢀⡴⠒⠒⠒⠲⢄⡀⢠⠀⢸⠀⠀⠈⠀⠀⠀⠂⠀⡇
⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⢸⡧⠀⠀⣿⠆⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠘⡀⠀⣤⠀⠀⠀⠀⠹⠃⠀⡇⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠙⡒⠒⠠⠤⠤⠤⠴⢤⠂
⠀⠀⠀⢱⠀⠉⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸⠈⠲⠤⠤⠤⠴⠚⢡⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⣇⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠑⠒⠂⠤⠄⠒⠒⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⣀⣠⣤⡤⣖⡒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣠⡶⠆⠈⠉⠀⠀⠀⠉⢢⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠄⠒⠶⠼⣶⣤⣀⠠⠤⠘⠛⠛⠛⠳⠒⢦⣶⡼⣧⣘⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠁⠀⠸⠁⠀⠀⠀⠀⠐⠿⠷⠀⠀⠀⠙⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷
⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠴⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣀⡀⣠⣅⡞
⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⠀⠀⠀⠀⠘⢃⠀⠀⠀⠁⠀⠖⣀⣀⠀⢀⠴⠒⢶⣮⣷⠿⠇
⠀⠀⠀⠰⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠉⢉⡗⠁
⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣀⡞⠇
⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠈⣡⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠃
⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⣧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣿
⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⢘⣦⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠞⠋⠀⢻⡀
⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⢠⠷⣤⣀⣀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⡆⠸⠄⠀⠀⠀⠰⣷⠄
⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢿⠉⠉⠙⠳⠷⠒⢻⡆⠀⠀⠀⠀⠀⠀⢠⡇⠈⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⢳⡀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⣷⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢀⠟⢷⠀⠀⠀⠀⠀⠀⠻⣄⡀
⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⣠⣶⡟⠂⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⣿⠀⢾⡀⠀⠀⠀⠀⠀⠀⠈⢹⡄
⠀⠀⠀⠀⠹⠷⣤⡀⠀⠀⠀⠀⠀⠀⣽⡁⠀⠁⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠈⠓⢮⠛⠶⠦⠤⠤⣤⡤⠶⠾⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⠤⠴⣶⠛⠯⠙⠀⠀⠀⠀⠀⠀⠈⢻⣄⡀⠀⠀⠀⠀⣀⣼⣤⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠲⠟⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⢀⠲⡄⠀⠀⡠⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠉⠢⡜⢱⠀⠣⠤⠧⣤⠎⠙⢶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⣧⠈⢧⠀⠀⡴⠙⢄⣀⡎⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢫⢣⡀⠑⢌⡲⢤⣀⡼⠀⠀⣈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠳⣝⠢⢄⣉⠑⠚⢒⣚⡩⠥⢺⡤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣀⣠⣀⠀⠀⠀⠀⠉⠒⠂⠬⠝⠓⠚⠉⠉⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡠⢤⣀⠀⠀⠀⠀⡇⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠼⠶⠠⠤⡀⠀⠀⠀⠑⠐⠷⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⡇⠀⡘
⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠈⠳⠀⠀⣀⠄⠒⠒⠢⢄⠀⠀⠀⠀⠀⠀⡼⠀⢠⠃
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⡠⢾⠀⡰⠃
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡷⡖⡏⠀⢸⠀⡧⣂⠢⣄
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠘⣇⠀⢸⠀⠳⠽⠃⠈⡆
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠉⠉⠒⠚⠀⠀⠘⡆⠈⢧⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⢸⠤⠤⠵⢖⣋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⠲⠤⠄⠀⠀⠀⢸⠤⢄⣀⣋⣻⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⣠⡃⠀⠀⠀⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡦⠤⠤⠖⠚⡗⠒⢶⠒⠋⠀⠐⢲⡏⠣⣌⡉⠓⠚⠉⢉⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢀⡸⠁⠀⢸⡀⠀⠀⢀⡜⠙⢦⣀⠈⠉⠉⣉⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠙⠲⠖⠋⠀⠀⠀⠈⠉⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣴⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢀⣤⡆⠀⠰⣿⣿⣿⣿⣿⣶⣶⣶⣶⠂⠠⣤⣤⣄⣀⣀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡷⣄⡀⣥⠄⢿⣃⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡈⢿⣿⣉⣁⣸⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⡋⠃⣥⡀⢈⣭⠀⠀⡀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣟⠳⣤⠜⠀⠸⣿⠀⠠⣤⣴⣿⣿⡟⠋⠁⠈⣨⣿⣿⡿⣾⣿⡆⠸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣵⠀⠀⠀⠀⢀⣿⠀⢠⠜⠋⠉⠻⡟⠀⣠⣴⣿⠛⣿⡟⠻⢿⡟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⣸⣟⡳⠃⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣸⣶⣟⠻⠟⠁⠀⠁⢀⡈⣏⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠻⠇⠀⠀⣤⠀⠀⠀⢨⣿⠀⠀⣀⣀⣠⣤⣿⡟⠿⣏⡗⠀⣀⠀⠀⠛⢹⡀⢻
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠀⢠⣤⣤⡀⠀⠀⠀⢺⣿⠀⠈⣉⣽⣿⠋⠉⣡⣾⣿⣧⡅⠉⡀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠋⠛⠋⠂⠀⠀⣿⣿⠇⠈⣋⣘⡉⠠⠀⠙⣻⠉⠈⠀⠚⠅⢤⠇⠀⣷⢸
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣥⡜⠂⠀⠀⠀⠀⠀⣿⠘
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣴⣾⣿⣶⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣉⣹⣿⡿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠉⠉⢩⣷⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠘⠿⠿⢏⡙⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⢄⠀⢠⣾⣿⣿⣿⠋⢁⣤⣤⣾⣿⣿⣿⣿⣷⣶⣔⠄⣤⣦⣶⣿⣮⡑⠦⣼⢇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣌⣿⡇⠃⠘⠛⠛⠛⠛⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣀⣿⣼
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠛⣿⣷⣄⣤⡄⢠⣶⣶⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣹
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡸⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣀⣵
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⠊⠱⠟
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⡿⠟⡋⠁⠀⢀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠿⠟⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⠶⠛⠛⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⣀⡀⠀⠀⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣷⡿⢿⡓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⢨⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⢃⣀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⢼⡅⣺⣿⡀⣦⢿⣿⣿⣿⣿⣟⣿⣿⢉⣊⣿⣿⣦⣾⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⠚⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣿⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⡅⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⠉⣿⣿⣿⣿⠟⣻⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⢸⣿⣿⣿⠋⠀⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⠿⣠⣄⢻⣿⣟⠀⣠⣟⠻⠿⠯⣷⡀
⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠈⠁⠉⠥⠈⠉⠁⠉⠁⠙⠀⠀⠈⠉⠈⠉⠁⠁⠉⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠠⠀⣴⣶⣶⣶⡄⠉⠀⠀⠀⠀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⣰⡀⠻⠿⠿⠟⠃⠸⠂⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠘⢿⠟⠀⠀⠀⠰⠆⠀⠀⠘⠁⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣤⣾⣿⠟⠀⠃⠀⠈⠀⣠⣶⣶⣦⣄⠀⠀⠀⠀⠀⠻⣿⣷⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠉⢀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣄⠀⢰⠄⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠆⠀⠈⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠠⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠺⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠛⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⠟⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⡀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⡟⠀⠀⠀⠀⣠⡀⠘⠋⠀⣤⠀⠀⠀⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⠀⠀⠀⠺⣿⠗⠀⠀⢹⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣽⣿⣧⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠾⠿⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣭⣥⣤⣶⠾⠃⠀⠀⠀⠈⠻⠿⠋⠛⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣛⣛⣛⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⡌⠀⡀⠀⡥⠒⠉⠀⢀⡤⢲⠎⢀⠴⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⣟⠀⠀⠙⣆⠠⡇⡇⢀⡔⠁
⠀⠀⠀⠀⡀⠀⣸⠃⢀⠀⢰⠁⢀⣀⣰⣋⣠⣤⡴⠧⠒⠀⠀⢀⡠⠤⠒⣀⠀⠀⠐⠂⢀⡂⠄⠀⡀⠀⠀⣿⠀⠀⠀⠘⣿⣷⢷⣞⡀⠀⢀
⠀⢘⡐⢰⠃⡰⠃⢀⠈⡠⠃⠀⠘⠁⡝⠁⠀⢀⣄⠤⠀⢀⡴⣋⠀⠀⠀⠰⠋⣩⠟⠉⠉⠉⠉⠛⠧⣄⠀⢸⡇⠀⠀⠀⠸⣿⡾⡁⠀⣠⠋
⠀⢸⡇⣿⠞⠁⠶⢉⡼⠀⠀⣈⠀⡼⠁⣄⠐⣠⠃⣀⡶⠫⠤⠅⡦⠤⠖⢊⡉⠀⠀⠀⣰⣷⣶⣶⡊⠈⠳⣌⣇⠓⠠⣄⠈⣿⡇⢧⡴⠁
⢠⡞⣸⡏⠀⣀⡰⠋⠀⠀⣀⡵⠊⠁⣀⣭⣴⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⣿⣿⠃⠀⠀⡈⠻⣦⣀⠉⢠⣿⣧⠘⡇
⠏⢰⡿⠀⠀⣽⠁⢀⣴⠟⢉⣴⡶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡄⠈⠉⠐⠀⣹⣷⣿⣿⣿⣆⡿⣄
⠀⢸⡇⠀⢰⣿⡾⠋⠀⣰⣿⢋⣤⡁⠀⠀⠀⠀⠀⠀⠀⠐⠢⢀⣉⣉⣉⣙⣳⣤⣀⣘⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⡈⢹⣿⣿⣿⣿⠇⠙⣆
⠀⢸⡇⠀⣼⣿⠱⠆⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢲⣤⠤⠤⠤⠞⠋⠉⠁⠈⠉⠉⠛⠻⣿⣿⣿⡀⠀⠀⠀⠉⠹⣿⣿⣿⣿⠀⠀⠸
⠀⢸⣿⣰⣿⡏⢀⣶⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠋⠙⢶⣄⠀⠀⢠⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣿⣿⣿⣿⣿⡆⠀⣸
⠀⢸⣿⣿⣿⣿⡏⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣇⣰⡟
⠀⠈⣿⣿⣿⣿⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⡄⠀⣿⣿⣿⣿⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡀
⢷⣴⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇
⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇
⠀⢹⣿⣿⣿⣿⣿⣷⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠄⠀⣿⣿⣿⣿⣿⡇
⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⠍⢸⣿⣿⣿⣿⣿⣷
⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⡿⢣⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣃⡤⠾⡟⣻⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⢀⠀⠀⠀⠀⢀⡞⠀⠀⡇⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡼⣿⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢛⣻⣧⠀⢰⣯⠄⠀⠀⡞⣼⠃⣠⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣧⣤⣦⣤⣀⣀⠀⢀⢒⣻⣷⡒⣶⣻⣧⣤⣤⣿⣿⣾⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣿⣿⠟⠉⢹⣿⡏⣿⣿⡃⠀⠈⠉⠉⡿⡉⠉⡏⢹⠛⠛⠻⠷⠭⣽⣯⣷⣿⠿⣿⠟⠛⠛⡛⢻⡿⠁⠀⠀⠀⣠⣿⣿⠿⠛⠛⠛⠻⠿⠿
⠛⠉⠀⠀⠀⠀⢿⣷⣜⢿⣷⣦⣤⣤⣴⣷⣷⣶⣷⣾⣤⣀⠀⠶⠶⣿⣿⡛⢛⡛⣟⣋⡁⢰⡇⣼⣇⠀⠐⠒⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠉⠀⠀⣿⣷⣾⣿⡏⠀⠈⠉⣉⣽⣿⣿⣝⣋⣛⣏⡁⢀⣼⣷⢿⣿⣤⣤⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠶⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠛⣦⡀
⠀⠀⠀⣠⠞⠛⠛⠛⠛⠷⠶⣦⣄⣀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣄⠀⠀⠈⢻⣆
⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣄⠀⢿⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣶⣶⣶⣶⣶⣶⣤⣤
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣼⡇⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⢻⡆⠀⢀⣠⣶⠿⠟⠛⠋⠉⠉⠉⠉⠉⠉⠉⣿⡿
⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⢠⣆⠀⠀⣾⣿⡆⠀⠘⠁⠀⠀⠀⢀⣤⡶⠚⠂⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⡀⠈⠷⠀⠈⢿⣷⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠻⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠂⠐⢿⣷⣾⣿⣿⣿⣿⣀⣤⣶⡷⠀⠀⢠⣄⡀⠀⠀⢀⣠⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣬⣭⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠉⠻⣦⣾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣶⣤⣤⣤⣤⡤⢀⣠⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠉⣡⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣨⡆⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠻⣷⡀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠀⢻⣷⡀⠀⠀⠙⣿⣄⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢋⣿⡏⠀⠀⢻⣷⡄⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⣸⣿⠁⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⢠⣿⡏⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⣀⣴⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⣸⣿⣧⣴⣶⣶⣿⠆⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣄⣀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠛⠉⠀⠀⠀⢠⣶⣦⠀⠀⠀⣰⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⢸⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣦⣿⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⢱⡀⣀⣀⡀⠀⠠⢒⡒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⢒⠉⣑⠄⠀⠀⠉⠳⣄⠄⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣈⠄⢨⠀⠀⠀⠀⠀⠈⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣜⣧⠀⠀⠀⠈⠃⠀⠀⠀⣠⠴⡆⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠻⢿⠿⠃⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣄⠶⣀⣀⠀⠀⣀⣀⡤⠚⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⢄⣈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠃⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢷⠆⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣄⠀⠀⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠘⠃⠀⠀⠀⠀⠀⠀⠠⠄⠀⢰⠀⠀⠀⠀⠀⠀⠁⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡤⠃⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣀⢤⣶⢿⠄⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠉⠀⠀⠀⠀⠈⡇⠓⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡍⠑⠒⠲⠒⠠⠼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠉⠉⠉⢁⠴⠒⠈⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠢⠤⠤⠄⠼⠤⣄⣀⣀⣀⡠⠤⠤⠤⠤⠤⠐⠒⠚⠋⠁
⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣀⣀⠀⠐⠿⢛⠻⠓⣛⣠⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣶⡿⠃⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠁⠒⠆⢀⡀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⣠⣾⣿⣿⣿⣿⣿⣷⣆⠀⠀⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⢫⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣀⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠉⣡⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠲⠂⠀⠛⣿⠟⠋⠍⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣄⢀⡿⣷⣄⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠓⠈⠻⡿⠀⣠⡌⠉⣼⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⢠⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡄⠀⢀⠀⡈⠁⠀⠀⠀⠞⠻⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⣛⠛⠹⢄⠀⠀⠀⠆⢹⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠊⠁⣤⣶⣶⣦⣤⣴⣟⠀⢹⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⡀⠀⠀⣛⢷⡄⠀⠀⠀⠐⢶⡜⠷
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠿⣿⠀⠀⢀⠙⣿⣿⣿⣯⢽⠿⠁⠛⠟⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣦⡀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡯⠁⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⣿⡿⠁⠈⠓⠆⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠉⠉⠻⣀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠰⠖⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠈⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠜⠁⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⠔⠢⡀⠀⢀⠔⠉⠀⠀⠀⠉⠢⠤⠊⠉⠒⠨⠕⠢⡀
⠀⠀⠀⠀⠀⠘⢄⠀⠀⠇⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠉⠘⣀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠠⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢠⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠐⡆⡇
⠀⠀⠀⠀⠀⠀⠸⡸⡀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠑⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢎⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠔⠊⠁⠀⠆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠋⠑⠒⡄⠈⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⡒⠤⠤⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢀⠜⠀⠀⣆⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠂⠉⠀⠈⠑⠂⠤⠐⠂⠁⠀⠀⠀⠈




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿