It girl Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⣀⣤⣖⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⣿⣿⣿⣿⣿⣿⣷⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣿⣌⣿⣯⣟⣹⣬⣿⣷⣿⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣿⣿⣿⣿⠿⠛⠻⠻⠿⠿⠿⠿⣿⣿⣿⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣦⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡧⢶⣶⣦⣀⣀⣠⣶⣶⣖⣀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣈⣻⣿⣿⡏⣒⡀⣿⣿⣿⣿⣿⣿⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡹⠟⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⠦⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⡇⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⠀⣅⠀⡌⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⣍⣁⠲⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣆⠀⠀⠀⠈⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢰⣿⣿⣦⣀⠀⣰⣟⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠋⠉⠉⠭⢉⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠉⢻⠟⠋⠉⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⢀⠀⠈⠙⠻⢋⠁⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣀⣀⣀⠠⠂⠹⡆⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢤⡀⠀⠀⠁⠂⢀⠀⠀⠁⠀⢤⣤⣀⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣴⣾⣿⡟⠁⠀⠀⠀⠹⡄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⠀⠀⠀⠄⠀⠀⠉⠻⣿⣦⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢰⣿⣿⠟⠀⠀⠀⢀⠀⠀⠘⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⡀⠀⠀⠀⠀⣈⣻⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⠂⠀⠀⢀⠌⠀⢄⠠⢀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠚⠉⣡⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠏⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠄⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠈⠁⠀⠠⠶⢈⣠⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠔⠁⠀⠀⠐⠀⠀⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠠⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠉⠁⠈⠉⠙⠣⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⠀⣦⣤⡤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠠⢄⣀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠂⠊⠁⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠁⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠀⠀⠀⢿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠁⠀⠀⢀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡄⠀⠀⠈⢿⣿⣿⣿
⡟⠛⠉⠁⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠉⠛⠻
⣷⣤⣄⣀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠠⠤⠤⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⡻⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠛⠋⠛⠛⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡃⠀⠀⢀⣀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣦⠀⣴⣶⣶⠚⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⡿⠟⠀⠛⠿⠋⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣾⣿⣿⣆⠀⠉⠁⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣿⣿⣿⣿⣿⣇⣀⣀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢋⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢀⣠⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠋⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠃⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⢄⣤⣄⣀⣀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⢏⣾⣿⣿⡋⠛⠛⠛⠛⠛⠛⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⢋⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣀⣿⣦⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⣤⡶⠾⠛⠛⠁⠀⠀⠀⠴⣾⠿⠋⢻⡆⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⡴⠋⠁⠀⠀⠀⣀⣀⣀⠀⢀⠤⠾⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠶⣶⣶⣶⣿⠿⠋⠀⠀⠀⡀⠀⢆⠀⠀⢸⣧⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡹⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⡹⠋⠁⠀⠀⠀⠀⠀⡆⠀⠀⠁⠂⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢷⡹⣿⣿⣿⣿⣿⣿⣿⠶⣤⣀⣇⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⣀⣤⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣎⢷⡘⢿⣿⡿⣿⣿⣿⣧⠀⠀⠙⣆⠀⠀⠀⡠⠎⠀⣀⣴⠾⣛⠏⢸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡝⣮⢻⣌⢯⠻⡜⢿⣿⣿⣷⡀⠀⠀⠉⠁⠉⠀⠀⠀⠈⠉⠉⠀⠀⢸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣎⢳⣝⢦⡂⠙⣎⠫⣿⡟⢿⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣯⡿⣝⡳⠈⢧⡐⠙⢎⠛⢦⡀⠉⠁⠐⠀⠀⠀⣶⣾⣿⣿⡿⣿⡜⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣹⡿⢿⢯⣟⣦⡄⠫⠢⡀⠁⠀⢝⠦⡀⠀⠀⠀⠀⢿⣿⣿⢿⠀⢹⡇⢣⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠋⠙⣃⡤⠶⠛⠻⣮⡃⠀⠀⠀⠀⠀⠑⢌⠀⠀⠀⠀⠸⣿⣿⡀⠀⠀⢷⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢨⡴⠛⠁⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⢻⣿⡇⠀⠀⠈⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠋⠀⠀⡀⣀⣠⣤⢀⣼⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⢻⣷⡀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⣀⣀⣤⠴⣫⣿⠿⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠈⢿⣧⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⡤⠖⠚⣛⣭⣽⠶⠟⠉⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠈⢿⣇
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠡⠐⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠸⣷⣤⡹⡀
⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⣿⣿⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠳⠄⠀⠀⣠⠄⢾⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⢊⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⣀⡀⠀⠀⠈⠉⠙⠆⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣿⠂
⠀⠀⠀⣿⠁⠀⠀⠀⠀⠆⠀⠀⠀⢨⡏⠁⠀⠀⢀⣀⡀⠀⠀⠐⠀⢹⡷⠶⢦⡾⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⣿⣿⠇⠀⠀⢠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⢀⡶⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⡀⠄⠒⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢠⠉⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⣞⠀⠀⣀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⢠⡀⠀⠀⠀⠘⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠋⠀⠀⠀⠀⠼⠁⠈⠙⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⢀⡱⠀⠀⠀⡄⠀⠀⠛⠋⠛⠻⢿⣿⣦⠀⠀⠀⢰⣿⠟⠋⠉⠉⠙⠁⠀⠀⠀⠀⠀⢀⠻⢤⣀⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⡶⠶⠶⠶⣤⠈⠉⠀⠀⠀⠈⠁⣤⠶⠶⠶⣦⡄⠀⡆⠀⢠⡄⢲⣶⣿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⣠⡔⢢⣦⠀⠀⠁⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠈⣤⠀⢣⡄⢘⠇⠈⠁⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⢐⡦⠤⠀⠁⡤⢀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢨⣶⣄⡀⠀⠀⠀⢀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠒⠀⠈⠀⠐⠢⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⣺⠁⠀⠹⣶⣾⠟⠉⠀⠁⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⢤⡊⠀⠀⠀⠀⠀⢀⣤⡄⢀⡌⠁⣦⣔⡆⠀⠀⠀⠀⠀⠀⠀⠲⢤⡴⠂⠀⠀⠀⠀⠀⠀⡘⢯⠏⠰⠏⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣢⣄⣀⣠⠾⠟⢻⣏⠙⠦⢩⡍⠀⣀⠀⠀⠀⠀⠀⢀⣠⣀⣤⣄⡀⠀⠀⠀⠀⣰⡟⠀⠀⠖⠂⠀⠀⠀⠀⢹⣆⣤⣠⣤
⠀⠀⠀⠀⠀⠀⢠⠜⠉⠉⠁⠈⠉⠀⠀⠀⠈⡼⠆⢠⠜⠁⠀⠙⣷⡄⠀⠀⠘⠿⣿⣿⣿⣿⠟⠀⠀⣀⢰⣦⠀⠀⢹⠄⠀⠀⠀⠀⠀⠠⡟⠉⠙⠉⠀⢀⡀⠂
⠀⠀⠀⠀⡠⠀⠀⣀⠰⠆⠀⠀⠀⢀⡄⠀⠀⠀⠉⣸⠀⠠⠲⠤⠛⣿⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⢺⣟⡀⠁⠀⠀⡼⠀⠀⠀⠀⠀⠀⢸⣦⡀⣀⢀⠀⠈
⠀⠀⠀⠈⣠⡜⠋⠀⠀⠀⠀⠀⠠⣿⣧⡀⠀⠀⠀⠘⢦⣤⡶⣧⢰⡟⠛⠓⠶⠶⠶⠶⠶⠶⠶⠶⠛⠻⠃⠂⣠⣟⡀⠀⠀⠀⠀⠀⠀⣸⠇⢈⠋
⠀⠀⠀⠉⡴⣙⠦⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀⣀⣠⡾⠇⢠⠜⠓⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⡀⠘⢤⠆⣝⠋⠀⠀⠀⠀⠀⠀⢰⣯⡔⠁
⠀⠀⠀⠀⠀⠛⢦⣤⣤⠀⠐⠒⠋⠁⠀⠀⠀⠀⠈⠻⠋⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢹⡆⠀⠀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠉⠉⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠰⠦⠶⠆⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣶⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣨⡇⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠋
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣀⣼⣿⣿⠟⠁
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠟⠁
⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣶⣶⣶⣶⣿⣿⠿⠛⠉
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣶⡿⠙⢿⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣛⣠⠶⣤⡉⢻⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣏⣿⣿⣏⣑⣺⣿⣾⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⣷⣦⣀⣀⣀⣀⣼⡿⠿⠿⠿⠿⠷⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣽⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⡶⢞⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡷⢦⡄⠀⠀⠿⠛⣩⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣿⣿⡄⠀⠀⠸⠿⠿⠛⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠉⢀⠛⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠚⢂⠉⠀⠀⠀⠀⠀⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣾⣿⣿⣿⡄⢰⣿⣶⣶⡤⠀⠀⢀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⡾⣿⣿⣿⣿⣿⣷⡈⠷⠶⠂⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣤⣶⣾⡟⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⠀⣸⣿⣿⣿⣿⣿⢿⣿⣿⣿⡹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠿⠁⣼⣿⣿⣿⣿⣿⠈⠛⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠃⢀⣴⢿⣿⣿⣿⣿⣿⠆⠀⢀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠋⣠⣿⣷⠟⢩⣾⣿⡟⠻⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣿⣷⣸⣿⡿⢁⣾⣿⣿⠏⠀⠀⠀⠀⢀⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠏⣠⣾⣿⣯⠍⠁⠀⠀⠀⠀⢼⠀⠀⠀⠈⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⢿⣿⣷⢿⡟⢹⣿⣵⣴⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⣸⡿⣿⣿⣷⣿⣿⣿⣿⣯⣿⣟⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⡿⢋⣴⣿⣧⡿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣠⢼⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⠟⣡⣾⣣⣿⣏⣼⣿⣿⣿⣿⣕⢄⢠⠀⣀⣠⣞⣵⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣯⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⣾⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⣷⣽⣭⣿⣿⣿⣿⣿⣏⣿⣇⣾⣿⡝⣿⣿⣿⣿⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢻⣿⣿⡏⠸⣿⡿⡿⢿⣿⠿⠿⢿⣿⣿⡿⢻⠛⠿⡟⠠⣿⣿⣿⣿⣷⣿⡌⠻⣿⡜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠤⠀⠀⠀⠐⢂⣿⠿⣿⣿⣿⣿⠛⠀⠸⡧⠸⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠘⢡⡿⡿⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠙⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠋⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⢠⣶⣿⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢠⣿⣿⣷⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠉⢿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⡋⠁⠀⠀⠀⠀⠀⠀⠀⢰⢹⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⣿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣦⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⢀⡠⠼⠋⠃⠀⠀⠀⠈⠛⠲⣌⡲⢄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠀⠓⢤⡐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⢀⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⣠⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠁⠀⠘⠁⠚⠻⢿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠙⣴⠀⠀⠀⠄⠀⠀⠀⢀⣀⢀⣀⣘⣤⣠⡀⠀⠀⠉⠛⠳⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠺⣦⡰⠀⡇⠀⠀⠀⠀⠀⠠⠀⡀⠙⠛⠿⢿⣿⣿⢭⡢⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⣆⡇⠀⡴⠂⠀⡀⠀⠀⠁⠲⢶⣤⡞⠁⠁⠀⠨⠖⠒⠲⡀⠀⣀⣤⠶⠦⣤⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⢰⠃⡼⡰⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣇⣀⣈⡟⠋⠑⣼⣿⡛⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡠⣇⠃⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⣠⠎⠁⠉⠻⠀⠀⠀⠈⣤⢟
⠀⠀⠀⠀⠀⠰⡄⢂⠀⠀⢀⠀⠀⢳⠀⠂⠀⠀⠁⠀⠀⠀⠀⠸⣄⠀⣀⠴⠚⠑⠄⠀⠀⠤⠀⠀⠀⠀⡰⠇
⠀⠀⠀⠀⠀⠀⡈⢢⣤⣄⣀⢱⣷⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠊⠀⢠
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠻⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢹⡆⢸⡧⡀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠈⠑⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣿⠟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⢤⣸⡏⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⡀⢁⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣤⠞⠀⠢⠀⠈⠀⠀⠀⠀⠐⡒⠂⢸⡇⢁⡄⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢧⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢱⣄⡀⠹⣏⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢳⡀⠀⠀⣶⠀⠀⠀⠀⠀⢆⡈⢉⡿⠟⠀⡠⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠑⢿⣥⠀⠘⡏⠀⠀⠀⠀⠀⠨⣷⣾⢁⣤⣾⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⡺⣿⡀⣼⡇⠀⠀⠀⠀⠀⠀⣈⠉⠛⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠙⠛⠉⠊⠀⠀⠀⠀⢀⠀⠀⡌⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠐⡇⠀⠈⢆⠀⠀⣎⡰⢠⡢⢠⡇⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⣆⠀⣿⢁⡿⠁⠸⢁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⢁⠼⠁⢠⠇⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢀⢳⡅⠀⢸⠀⠀⢴⡄⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠓⣀⢸⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⣀⣀⠀⠀⢠⠄⠐⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠑⠢⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠄⠀⠀⠒⠀⠀⣤⣴⠚⠋⠉⠁⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠛⠳⠤⠄⠀⠀⠀⠀⠀⠀⣠⣤⡤⠤⠤⠄⠀⢐⣶⣤⣌⣀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⣠⣴⣞⣍⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⠿⠹⠟⢿⣿⣛⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣦⣆⣸⡀⢸⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠠⠂⠀⠀⢀⣠⣾⢿⣿⣿⣿⠁⠙⠳⢤⣍⣉⠜⠙⠇⠀⠀⠀⠀⠀⠀⢀⠟⣟⣷⣿⠍⢹⣿⣟⡇⢸⣿⣿⣿⣿⣧⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣠⡶⣿⡿⠋⢸⣿⣿⠿⡇⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠻⠷⠶⠞⠋⣸⠁⢸⣿⡇⢿⣿⣿⡆⠀⠄
⠀⠀⠀⠠⠀⢠⡾⠋⣐⡍⠁⠀⢸⣿⣿⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⠀⢸⣿⡇⣸⣿⣿⣿⡄
⠀⠀⠀⠂⢠⠏⠀⡸⡟⠀⠀⠀⡾⣿⣟⡆⢠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠘⢰⢿⡄⣼⡟⢰⣼⣿⣿⡟⣷⠀⢠
⠀⠀⠀⠀⢸⠀⣼⡙⠀⠀⠀⣸⡇⢹⣿⡇⠀⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡌⣸⡇⣿⠇⠀⣼⣿⠘⣿⠘⣇⠈
⠀⠀⠀⠀⠀⣦⠏⠀⠀⠀⠀⣻⡇⢸⣿⣷⠀⠀⢹⢦⡀⠀⠀⠀⠐⠲⣶⣧⡀⢓⡤⠀⠀⠀⠀⢀⡆⢰⢠⣿⣿⡟⠀⠀⣿⡿⠀⢹⡇⣿
⠀⠀⠀⠀⡄⢹⠁⠀⠀⠀⢀⣿⡇⠘⣿⣿⠀⠀⠘⢿⣿⣦⡀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⣠⣴⡿⢠⣯⣿⣿⡿⠁⡀⠀⢻⠇⠀⢸⡇⣸
⠀⠀⠀⠀⣴⠀⠃⠀⠀⠀⢸⣿⡇⠀⢹⣇⠀⠀⠀⢸⣿⣿⣿⠓⢤⡀⠀⠀⠀⠀⣀⡴⠚⠁⣼⡇⣬⣿⣿⡿⠀⢸⠃⡸⠀⠀⠀⢸⣷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣇⠀⢈⣿⠀⠀⠀⢸⣿⣿⣿⠀⠀⠙⠳⠶⠖⠋⠁⠀⠀⠀⣿⡇⣯⣼⣿⡇⠀⡞⢠⡇⠀⢸⢀⣼⡇
⠀⠀⠀⠀⠄⠀⡼⠂⠀⠀⢸⢿⣿⠀⢸⡇⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⣿⣿⣇⠀⠁⣾⠁⣤⣏⢸⣿⡇
⠀⠀⠀⠀⢀⣄⠀⢠⠀⢨⢸⣿⣿⠀⣤⠁⠀⠀⢠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣏⠀⣼⡇⢠⡿⣭⣿⣿
⠀⠀⣠⠖⠛⠁⠻⣿⡄⠸⣼⣿⡇⠀⡇⠀⠀⠀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣿⣿⣿⡟⢺⡿⢀⡟⣡⣿⣿⠇
⠀⡞⠁⠀⠀⠀⡸⠻⣷⣄⣿⣿⠃⢰⡇⢰⠀⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⠁⣾⣱⣿⣿⠿⠦⡄
⠐⠀⠀⠀⣠⠈⠀⠀⢻⣿⣿⡟⠀⣼⢀⠀⣼⣿⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠸⠛⣿⣴⣿⣿⣿⣿⠀⠀⠘⣦
⠀⠀⠀⠈⠀⠀⠀⠀⢸⣿⠟⠀⣰⡧⢋⣼⠟⠁⠰⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢋⡠⠀⠀⠀⢸⡇⣸⣿⣿⣿⣿⠀⢀⠄⠊⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⣠⣿⡶⠟⠁⠀⠀⠀⠀⠉⠛⠒⠢⠤⠄⣠⣤⠤⠴⠒⢋⠤⠂⠁⠀⠀⠀⠀⢸⣧⣾⣿⣿⡿⠋⢲⠁⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣸⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣧⠀⢸⠇⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⠀⣎⠀⠀⢨⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣽⣿⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠈⠁⠈⠉⠑⣽⣇⢹⣿⣿⣿⠿⠛⠁⠀⠀⢈⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣄⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⣹⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡾⣱⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⡽⣿⣷⡹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣱⣿⣿⣿⣾⣿⡇⣿⣿⣿⣯⢿⣿⣿⣿⣿⡝⣿⣿⣿⣿⣷⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⣿⣿⣿⣿⣿⢈⣷⣿⣿⣿⢻⣮⣿⣿⣿⣿⣿⣌⢿⣿⣿⣿⡎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⢻⡟⠉⢻⣿⢿⣿⣇⠻⣿⣿⣿⣆⠉⠻⣦⡻⣿⣿⣧⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢸⣿⣿⣿⢈⣴⣶⣤⠙⠈⠛⠿⠧⠀⠉⠉⢩⣴⣶⣄⡙⣿⣿⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡿⠋⢻⡇⠸⣯⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⡿⠀⣿⠉⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣧⠀⠘⠇⠀⠘⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠶⠟⠁⠀⠋⠀⣰⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣶⣦⡀⠈⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠈⠀⣰⣶⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡏⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⣧⢿⣿⣿⣿⣿⣿⣶⣦⣤⠤⠤⢤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⢹⡇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢸⣿⣿⣿⣿⡿⢿⡉⠈⢑⠶⡉⠀⢹⠏⢻⣿⣿⣿⣿⣿⣿⢸⣿⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢸⡿⣿⣿⡿⠁⠀⠑⠒⠋⠀⠙⠒⠋⠀⠀⢻⣿⣿⣿⣿⣿⢨⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠞⣡⡿⣳⣿⡿⠁⠀⠆⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣿⣿⣿⣿⡿⣸⡿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⢯⣭⡾⣟⣿⣍⠒⡾⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⣁⣤⣿⣟⣩⡵⠟⠱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡏⢙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⢃⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠓⠦⢤⣤⣀⣀⣀⣀⣀⣀⣠⣤⡤⠴⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⣤⣤⣤⣭⣭⣥⣤⣤⠴⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠇⠀⡆⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠀⠀⠇⠀⢨⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠀⢸⡀⠀⣸⡀⢘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡍⣉⣩⡇⠀⢫⣥⡤⢽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣾⣿⣽⠃⠀⢿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⡿⠋⠀⠀⠈⠿⠿⠿⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⢿⣿⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣾⣽⠿⣿⣿⣶⣿⣿⣛⣿⣴⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠁⠀⠀⠈⠙⠻⢿⣿⣿⣿⡿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣼⣿⡙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣤⣤⠀⠀⠴⠖⠃⠀⠀⠀⢹⣿⣿⣿⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢠⠀⠀⠀⠐⠊⠁⠀⠀⢸⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣿⣿⣿⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢡⣾⣿⣷⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⢙⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⣷⣿⠧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣹⣷⣏⠻⣯⣵⣽⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠟⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⡄⠀⠀⠀⠈⢀⢻⣿⢁⡴⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡻⣾⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⢤⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⣨⡿⠙⣆⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢃⠀⢿⣦⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠘⡆⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣾⣶⣾⣷⣶⣤⣤⣀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠟⠁⠀⠙⠿⠿⢿⡯⠻⠿⢿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢻⣿⠁⣾⣿⠆⠀⠀⠀⠀⢺⣿⠆⠀⣿⡏⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣬⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⢠⣿⣷⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢹⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⣿⣷⠙⢿⣿⣿⣿⣷⡶⠶⠶⢶⣾⣿⣿⣿⡻⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠈⠙⢧⠀⠹⠋⠉⢯⡀⠤⢤⣴⠕⠁⠈⠻⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡣⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⡽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠐⡀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢠⣀⡈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠈⠛⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠋⡛⠒⠢⠤⠤⡤⠤⠤⠤⠤⠶⠒⠚⠙⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⡤⣤⣧⣤⣤⣤⡤⣶⠖⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⠀⠀⣿⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⢸⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠉⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠰⢋⣵⣶⣶⣄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣭⣶⣶⣦⡀⠀⣿⣿⣿⣿⠈⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠈⠻⠿⠟⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠤⠚⠛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢰⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣥⣴⣶⣶⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⣰⣦⣭⣛⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠻⣿⣦⡀⠀⠀⠀⢀⣾⣿⣿⡆⣠⣾⣿⡿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡟⢋⣥⣤⣴⣶⣶⣿⣿⣿⣿⣿⣶⣶⣴⣾⣿⣿⠟⣵⣿⣿⡟⣡⣾⣿⣶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠛⢋⣥⣶⣯⣾⣿⣿⡟⢠⣿⣿⣿⣿⣠⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣦⣌⠻⣿⣿⡿⢏⣉⣤⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠿⠋⣠⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⡛⠻⢿⣿⣿⣿⣿⣷⣌⢻⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⣋⣉⣭⣥⣤⣴⣶⣾⠻⠿⠿⡿⢿⠟⣩⣤⣌⡀
⠀⠀⠀⠀⠀⣠⣿⣿⣷⣦⣉⠻⣿⣿⣿⣿⣦⣹⣿⣉⣍⣉⣩⣭⣭⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⢂⣠⣾⠿⣿⣿⣿⠆⡀
⠀⠀⠀⠀⠐⠻⠿⣿⣿⣿⣿⣷⣌⡙⢿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣛⣉⣉⣉⣥⣤⣘⣻⣵⣾⣿⣿⡏⣸⣿⣿⡿⢠⣿⣆
⠀⠀⢠⣾⣿⣶⣤⣄⡉⠻⢿⣿⣿⣿⣦⡙⣿⠿⣯⣉⣉⣙⣛⣛⣋⣭⣴⣾⣿⣿⣿⣿⡿⠿⠿⣟⣻⣿⣿⡿⠛⢁⣿⣿⣿⠃⣾⣿⣿
⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣦⣙⠻⡿⢋⢿⣿⣿⠟⠻⣿⣿⣿⣿⣟⢿⣿⣿⣟⠋⢭⣷⣶⣶⣶⣿⣿⣯⣡⣤⣶⣿⣿⣿⠏⣸⣿⣿⠇
⢀⣩⣍⣉⣉⣉⣛⣿⣿⣿⢿⣿⣿⣿⢸⣿⣿⣷⢿⣿⣿⠙⣿⣿⣿⣦⠻⣿⣿⣧⡀⠀⠀⠀⠈⠉⠉⠙⠻⣿⣿⣿⠟⢁⣼⣿⣿⡿
⣿⣿⠿⠛⣛⣋⣩⠟⣹⠃⣾⣿⣿⣿⠈⣿⣿⣿⣇⣿⣿⡆⢻⣿⣿⣿⣧⠙⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣠⣝⠻⠦⢿⣿⠿⠟⠁
⢉⣠⣶⣿⣿⣿⢋⣾⣿⠀⣿⣿⣿⣿⠀⣿⣿⠛⣿⣿⣿⣷⠈⢿⣿⣿⣿⣧⠹⣿⡿⠷⠀⠀⠀⠀⠐⠦⠀⠉⠁
⣿⣿⣿⣿⠟⣱⣿⣿⡿⢰⣿⣿⣿⡟⣰⣿⣿⡄⢹⣿⣿⣿⣧⠈⣿⡿⠿⠛
⣿⣿⠟⢡⣾⣿⣿⣿⢃⣾⣿⣿⠟⣶⣿⣿⣿⣧⠈⠿⠿⠛⠋
⠟⢀⣴⣿⣿⣿⠟⣡⣾⣿⣿⡿⠀⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⣾⣿⣿⣿⣿⣦⣈⠻⠿⣿⣷⣤⡀⠹⡑⠺⢦⡤⠤⣀⠀⠘⠢⡀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⣦⣌⠙⢿⣿⣶⣬⡢⠄⡈⠒⠤⡑⠲⣄⠈⠢⡀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠈⢻⣿⢧⠀⠈⠂⢄⠈⠁⠀⠉⠀⠘⠂⠀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⢿⣻⣿⡻⣿⢿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠱⡄⠀⡋⠉⠲⡄⠀⠑⠦⣤⣄⣀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠸⣿⣧⣿⣷⣯⣿⣿⣿⣿⣿⣿⣧⣿⣧⣿⢿⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⠢⡀⠈⠖⠀⠀⠀⠀⡇⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⡿⢮⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠢⡀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠈⢢⡀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠰⢿⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠮⠻⢿⣿⣮⣿⢯⠁⠀⠀⠀⠀⠀⣀⡤⠶⠾⠟⠛⠛⠃⢠⣠⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡭⠗⠻⢿⣿⣇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⡀⠀⠀⠈⢋⠁⡇⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⢀⠀⢀⠙⠓⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠿⠋⠀⠀⠀⠈⠣⣀⠈⠀⠀⠀⠀⠈⢢⠄⠀⠀⢀⣀⣀⡀⠀⠀⠑⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣄⡒⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠟⢷⡄⠀⠀⠀⠀⠸⡀⠀⡆⠀⢀⠈⠉⠑⠒⠤⠤⠵⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡖⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢁⣱⠀⠀⠹⣆⠸⡀⠀⠀⠳⣀⣧⠀⢸⠀⠀⠀⠀⠀⠀⡆⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡽⣷⣮⣆⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠓⢈⠆⠀⠀⠸⡆⠡⠸⠀⠀⠙⢼⡆⢸⠀⠀⠀⠀⠀⢰⠃⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠚⣏⠀⠀⠀⠀⢻⠀⢃⢂⠀⠀⠈⢳⣿⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⠀⠀⠀⠈⠓⠲⠤⠤⣄⣀⣀⣀⣀⣀⡴⣿⣷⡀⠀⠀⠀⢣⠈⢆⠣⡀⠀⠀⢻⡀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠙⣿⣿⣦⠀⠀⠀⠀⠈⠀⠈⠀⢢⡀⠳⣄⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠀⠙⢿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡈⠈⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠈⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠑⠦⣈⠛⠿⣿⣦⡤⠤⠤⠀⠀⠀⠤⠒⢁⡔⠁⠀⠀⠹⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠁⢲⣕⠄⣀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⣏⣀⡠⣤⣦⣤⣉⣑⠛⠿⣿⣦⣀⢀⡀⠤⠄⠒⠁⠀⠀⠀⠀⠀⠘⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣤⡿⠃⠑⠤⡱⣤⣀⠀⠀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢈⣉⣉⣛⢶⣭⣉⠉⠀⠛⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣷⡄⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠘⢄⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡠⠤⠒⠛⠐⠂⠐⠒⠢⡉⠢⣄⠢⢄⠈⠻⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡄⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠈⠛⢦⡑⠢⣈⠉⠻⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠙⢶⡄⠉⠢⢌⠻⣿⣿⣿⣷⢦⣄⠀⠀⠠⣀⠀⠸⢿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠙⠳⣄⡀⠑⠬⣹⣿⣿⣶⣭⠻⢶⣄⡀⠉⠢⠌⢹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣄⠀⢄⡀⠀⠃⠀⠀⠀⠀⠈⠻⢦⡀⠈⠃⢽⣿⣿⣿⣶⡌⠛⠶⣤⣀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⡉⢆⠃⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠈⠙⠿⣿⣿⣦⣀⡀⠉⠓⠦⣄⡙⢿⣆⡀⠀⠀⠀⠀⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠘⢦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠘⠿⣿⣿⣷⣄⠀⠀⠈⠉⠙⢻⣷⣄⠀⠀⣼⣿⡿⢦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⣒⣟⡻⢟⣿⣷⣶⣦⣿⣷⣦⣀⠀⠀⠀⠀⠀⣀⣀⣀⣄⣀⣀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣄⠒⠚⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⣉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⢉⣿⣿⣿⢟⣫⣷⡿⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠤⠤⠤⢶⣺⣿⣿⣿⠿⢋⡼⣫⠞⠁⣿⣦⣤⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⠿⠛⠉⠀⣠⣾⠟⣡⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠑⠀⠉⠉
⠀⢀⠔⠒⠚⠛⠛⠛⠛⠋⠉⠉⣁⣤⡤⠴⠾⠟⢛⣰⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢿⣛⡥⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⡿⠛⠛⠋⠁⡠⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢉⠉⠭⠔⠈⠁⠀⠀⢀⣀⣠⣶⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡿⠿⠛⠉⠉⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠒⠒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣞⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠂⠾⣥⢸⡏⠁⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣷⣄⠈⢿⢀⣷⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠈⣽⡿⣄⠀⠀⠀⠀⠀⠀⣠⠏⢹⠀⠀⢀⡟⠸⡆⢸⠛⢌⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣸⠻⣧⠀⠀⠀⠀⣀⡠⠞⠁⢀⡾⣂⡼⠞⠁⢠⣇⡞⢳⡈⠀⠀⢰⡜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣼⠀⢠⡇⠀⠳⡴⢁⠀⠉⠁⢀⣤⡀⠈⠁⠀⢠⣴⠤⠏⢩⡗⡄⢹⡄⠀⣸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡟⢧⡈⣇⠀⠀⠳⣙⠀⠀⠀⠀⠛⠁⠀⠀⣀⠈⠉⠀⠀⣸⡵⠃⠸⠧⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠙⢦⡀⠀⠀⠀⠉⠁⠀⣀⡴⠋⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡖⠆⢤⡀⠈⠁⠒⠒⠒⠂⠉⠁⠀⣀⣀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠘⢦⠀⠀⠀⠀⠀⢀⡼⠁⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢦⡀⠈⠓⢤⡀⠀⣠⠊⠀⣠⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠉⠓⠦⢄⠈⠉⢣⡠⠞⠁⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠘⢷⣤⡠⠇⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⢦⣀⣄⡀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠉⠉⣿⠚⢹⡇⠉⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡏⠀⠈⡇⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢸⡇⠀⢠⡧⠄⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠺⣇⠀⢸⠃⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡴⢞⠱⣿⠞⠫⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠚⠁⢀⣾⣀⣀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣦⠄⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⠤⠞⠉⠉⠁⠉⠈⠉⢓⣦⣐⣖⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣈⣙⣄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤
⠀⠀⠀⠀⠀⠀⢠⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠈⣃⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅
⠀⠀⠀⠀⢀⠔⠉⢩⡁⠀⠀⠀⠀⠀⠀⠀⠰⠂⠰⠋⢶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠋⡆
⠀⠀⠀⠀⠈⢀⠰⡀⢣⡆⠀⠀⠄⠀⠁⢀⡀⣀⣐⣄⡀⠀⠉⠛⠿⠄⠀⠀⣀⣀⣀⠆⠰
⠀⠀⠀⠀⠀⠙⢷⣵⣸⡃⠀⣀⠀⠐⠂⡈⠙⠛⢿⣿⠯⢵⡀⠀⠀⠀⠀⠉⠉⠉⢙⠃
⠀⠀⠀⠀⠀⠐⠊⠙⢿⠃⡜⢁⣰⢀⠀⠀⠙⠳⡎⠀⠀⠀⠋⠉⠣⠀⠶⣾⡟⢲⣧⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢁⣿⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠞⠒⢾⠁⠀⠙⣛⡆⠀⠁
⠀⠀⠀⠀⢠⠠⠀⠀⣀⢐⢹⠙⠀⠀⠀⠀⠀⠀⠹⡄⢀⡠⠖⠡⠀⠀⠈⠀⠀⠀⡭⠃
⠀⠀⠀⠀⢀⠑⠦⢤⣌⣿⠾⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⣤⠴⠎⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⢢⡀⠀⠀⠀⠀⠀⠀⣤⠀⠄⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡾⠑⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⢹⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠙⠒⢦⡟⢀⠀⡀⠀⠀⡌⠀⠀⠀⠀⠀⢠⣌⠔⢁⠂⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣼⡞⠁⠑⢄⠀⠀⠀⠀⢈⡁⠸⣏⠔⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠹⡄⠀⢸⡀⠀⠀⠀⢠⡟⢶⣼⠇⢀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣅⠈⠲⣷⡀⢸⠇⠀⠀⠀⠈⣿⣾⢁⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣝⣿⣥⣾⡀⠀⠀⠀⠀⡨⢉⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣬⣭⡀⠣⡀⠀⠀⡌⡀⡆⢹⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠈⠗⠄⠸⡆⢸⡟⣰⠇⣼⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠰⢠⠀⠛⠈⣷⡟⢠⢧⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⢠⣷⡀⢸⠀⠰⣇⠟
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣈⣱⣼⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣛⣛⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣿⣿⣿⣿⣻⣿⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠒⡩⠖⣈⣑⢼⡃⠓⠐⡢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⢀⠞⢁⠜⢑⡠⢹⡇⠠⢄⠨⣦⡱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⢠⢀⠎⢠⠎⠉⠉⠉⠛⢣⠀⠐⠄⠘⡷⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⢃⠎⢠⠋⠀⠀⠀⠀⠀⠈⡆⡀⠈⣆⢡⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢠⠃⡎⢠⣇⣀⠀⠀⠀⠀⣀⣀⣱⡈⢢⡘⡜⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠇⡜⢠⢿⣾⣿⠅⠀⠀⡀⢩⣿⣶⡷⡀⠑⢹⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡼⣠⠃⠈⠛⠛⠀⠀⠀⠁⠈⠛⠛⠀⢹⣦⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⡗⠿⢦⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡯⠎⢘⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡟⠀⠀⠈⢧⡀⠀⢤⠤⠤⢤⠄⠀⢠⠞⠀⢀⠀⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠙⢦⡈⠑⠒⠁⣀⢴⢹⠀⡂⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⣟⠒⠒⠚⡇⢸⢸⠀⠇⣰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⠀⠀⣰⠇⡀⠀⠀⢣⣘⠘⠀⠀⠈⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡴⠤⠖⠚⠛⢿⡧⣀⡀⢀⡠⢎⠝⠉⠉⠑⠒⠧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⠒⠁⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⡘⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣀⣠⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⢹⡇⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠸⠁⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠙⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⡇⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠜⠸⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠇⠳⠤⠤⠼

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠄⠒⠀⠀⠀⠀⠒⢄
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠁⠀⠀⠀⡀⡀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⡇⣴⠴⠀⠗⡺⢠⠔⠁⢸⡆⠀⠀⠀⠀⠀⡆⢀⠔⠀⡰⠟⢿⢄⠀⢄⠀⢁
⠀⠀⠀⠀⠀⠀⠀⣷⡋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢀⣇⣠⢒⡉⠀⠀⠀⠀⣓⠢⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠤⠀⠀⠀⠠⠆⠀⠆⠀⠀⠀⠰⠉⢆⠀⠈⠷⠀⠀⠀⠰⠎⠀⠀⡉⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠒⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡱⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢠⠀⢀⠀⠀⠀⠀⠀⠀⠒⠅⠤⠚⠁⠑⠤⢀⣀⣀⡠⠔⠁⠈⠢⠤⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⠒⡎⠀⠀⢑⠒⡄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡐⣁⠀⠀⠀⠀⠀⠀⠇⠡⡀
⠀⠀⠀⠀⠀⠀⠀⡜⠉⡇⠀⠀⠀⠀⠀⠀⢀⠀⠇⠀⠀⠀⠀⢰⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⢠⠁⢸⠁⠀⠀⠀⠀⠀⠀⠸⡆⠈⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⡘⠀⣺⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡆⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⠁⢠⢻⠄⠀⠀⠤⠀⠀⠀⢰⡧⠆⢨⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠈⠑⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠁⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠉⠉⠁⠈⠁⠀⠀⠀⠀⠀⠰⣁⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠙⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠪⠵⠀⠒⠐⠀⠪⠕⠂⠀⠀⠀⠀⠀⠀⠀⠒⠭⠂⠐⠐⠀⠲⠕⠂
⠀⠀⠀⠀⠀⠀⠀⠰⠀⢤⠤⠄⠊⠉⠀⠤⣤⠀⠆⠀⠀⠀⠀⠀⠲⠠⡤⠄⠊⠈⠂⠤⣤⠠⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⢀⡀⠀⢀⠄⠀⠰⢤⠀⠔⠃⠀⠀⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⢀⡀⠀⠤⣬⠝⢫⣴⠊⢉⢰⠀⠴⠒⠚⠍⣤⠄⠀⠝⠀⠀⠠⠄⠀⠀⢤⣦
⠀⠀⠀⠀⠀⠀⢀⡾⠃⡤⠄⠀⠀⠐⠂⠠⠉⠨⠀⠀⠀⠀⢬⠴⠀⠄⠘⠈⠏⢨⡁⠀⠐⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⢀⣴⠶⠷⠐⠀⡖⠒⣆⠴⠀⠉⠊⠚⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢜⢢⡄⠀⠀⠀⠀⠀⣿⠷⡄
⠀⠀⠀⠰⠏⠀⡤⢤⡀⠀⣁⡴⢉⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⢀⠀⠘⠐⣀⣀⠀⠄⢀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⡿⠀⠀⣐⠀⠀⠂⠨⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠩⡄⢍⣷⡁⢾⠉⠀⠃
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠸⠃⣰⠋⠹⢏⣤⣒⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠅⣸⠀⢀⣌⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢋⠅⢠⣀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⡁⡟⢴⡄⠛⠅
⠀⠀⠀⢀⣀⠀⡀⢠⡞⢶⣇⣴⣵⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⢸⠻⡎⢷⠂
⠀⠀⠀⠀⡀⠀⣠⡏⣵⣙⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠣⣾⠀⠀⣸
⠀⠀⠀⠀⠳⣴⣿⣶⣝⣿⣿⣿⠿⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠁⠀⢀⠀⠀⠐⠀⣠⡊⠈⠓⠚⠃
⠀⠀⠀⠀⣠⣿⣿⣾⡿⢿⠟⠁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⢺⡄⠰⢆⠀⢠⡜⠃
⠀⠀⢀⡄⣙⡿⠛⣩⣛⠿⠆⠀⠲⡀⠑⡀⠀⢀⡀⢠⠀⡀⠀⠀⠀⠠⡀⠉⠡⣁⠈⠁⢞⡁⠠
⠀⠀⠐⡻⠋⠐⡹⣵⠿⠇⠀⠀⠀⣅⣤⢈⣀⠄⠉⢀⡀⣀⡀⣀⡘⠀⠀⢳⡀⠈⠽⠯⡁⠁⢦⠰⡿⠈
⠀⠀⠈⣄⢨⠙⣠⣿⣠⡆⠀⠀⠀⠸⠓⠸⠋⣢⢀⡁⡀⠉⠁⠀⠈⠉⠒⠈⢤⠠⠀⠈⢳⡤⠈⠇⠄
⠀⢀⣀⡀⠠⣼⠋⢉⣉⡀⠀⠀⠀⠀⠀⣰⣞⡻⠯⠉⠀⠒⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⡄⠀⠁
⠀⠈⠄⣠⠹⡏⡇⢸⢶⡧⠀⢀⠀⢰⡷⡿⢿⡅⠢⠀⠀⠀⠀⠀⣤⠀⠠⢠⡂⡀⠀⠀⠀⠀⢀⢠⡶⢀
⠀⠀⢠⠃⠀⣱⣿⣶⣻⣿⣄⡏⣄⢾⣿⠇⠈⡠⢀⠀⠀⠀⠀⡀⠀⠁⡰⠁⠈⠀⠂⠀⠀⠀⠠⠎⠀⠀⠀⣠
⠀⠀⠰⠆⠀⠒⠒⢒⣾⣩⡏⠀⠿⠓⠋⢀⠈⠀⠈⠁⠀⢀⠈⣀⠀⡗⠁⡈⠁⡀⢀⣨⣀⣶⡅⠡⠆⣤⠊⣉⠅
⠀⠀⠀⠓⠀⡀⢀⣿⣰⢿⠫⡆⡀⣑⡴⠈⢠⡄⢤⡥⠀⢬⣤⡴⢸⣧⡀⠀⢒⢻⣄⣠⡹⣽⠾⣱⢦⣼⣇⡀
⠀⠀⡃⠘⠃⣤⢤⡈⠋⠸⡟⠗⠃⢘⢣⣌⣿⣉⢳⣶⣖⣆⡽⡃⠾⠀⣝⠶⣯⣤⣼⠚⠏⢹⡳⣴⣿⣿⡘⠳
⠀⠀⢃⣐⢤⡍⠀⠀⠀⠐⡇⡦⠐⠺⠺⠙⠟⠹⠛⠉⢉⠁⠀⠉⠉⠋⠛⠷⢭⣦⡿⠀⠀⠀⠀⠎⢼⠋⣃
⠀⠄⠀⠿⠛⢿⠀⠀⠀⢀⣹⣄⠀⠀⠈⢀⠈⠤⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠀⠀⢀⣌⠈⣰⠓⢽⠂
⠀⡂⠀⢠⠐⡎⢃⠀⣰⣾⡛⠋⠃⠀⠀⠀⠁⠀⠤⠀⠠⢀⠀⠀⠁⠀⠀⠀⠛⠿⣴⣆⡄⠟⠛⣇⣹⠉⠫⠁
⠀⠀⠀⠤⠄⠼⠈⣦⠋⠨⡅⠀⡄⠀⠀⠀⣰⣳⢘⡞⢓⣞⢻⡦⠄⠀⠀⡀⠘⡄⠸⣿⡗⣼⠋⢀⣛⠠
⠀⡆⠀⠀⠻⠶⠓⠚⢂⣠⢦⠀⠤⡐⠉⣡⠺⠷⢭⠞⠛⠟⠫⡔⠻⢊⣿⣲⣞⣹⣅⣾⡱⢦⢮⣟⠉
⠀⡄⠀⠀⢀⠠⡌⠉⣂⣋⢈⠀⡘⠛⠀⠩⠋⢙⠷⠉⠀⠀⠠⠷⠷⠟⠶⠿⡯⡏⠉⢶⠆⠀⠈
⠀⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠋⠁⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⣠⣤⣤⣤⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠄⠀⠀⠀⠀⠀⠀⣾⣿⣯⡩⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠐⠘⠋⠉⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣸⣿⣿⣥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠾⠯⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣀⣀⣀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣧⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⡀⠀⠀⠠⠙⠙⠶⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣯⣯⢽⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣻⣆⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣿⣿⣿⣦⣥⣌⣟⣽⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡿⣿⣿⣗⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⣍⣿⣿⣿⣏⣍⡝⠿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣽⣿⣿⣿⡻⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡻⣿⣿⣿⣭⣻⡤⢪⡝⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣽⣾⣿⣼⣿⡟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣷⣾⣶⣶⣷⣯⣷⡀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠈⠻⣿⣧⣿⡠⢜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣿⣿⣿⣿⣿⡿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢿⣿⢱⡎⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⡻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠶⣿⠿⡽⢻⣧⣀
⠀⠀⠀⠀⠀⠠⠶⠖⠛⠛⠒⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢪⣷⣿⣿⣿⣿⣿⣿⢿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿⡿⣿⡘⣿⡉⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢻⣿⣿⣿⢨⣛⢿⣹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣟⠅⣿⡿⢏⠺⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢟⣿⣿⣧⣩⠟⢽⣿⣽⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⢷⣿⣷⡆⠄⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣴⠻⣿⣏⢿⣷⣾⣻⣹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠘⠷⣾⣿⣿⡟⢾⣳⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣧⢿⣿⡟⢻⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣟⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⣇⣠⡝⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣭⣽⣷⡌⣿⣿⡈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⣿⣾⣿⣯⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡻⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⡀
⠀⠀⠀⠈⠃⠂⠀⡀⠀⢀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⡢⠀⠀⢂⣤⠔⠛⠛⠁
⠀⠀⠀⠀⢒⣌⡳⣾⣄⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⠀⠀⡄
⠀⠀⠀⠀⠈⢉⣿⣿⣷⣮⣶⠁⠂⠀⠀⠈⠀⠀⠀⠀⠀⠐⠊⠀⠑⠀⣀⠄⠀⠀⠀⠀⠀⠈⡠⣦⡀⠶⡤⠄
⠀⠀⠀⠀⠀⠰⢻⠛⢳⡦⣿⢀⡀⢈⢤⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠘⠉⠀⠀⠀⠀⠀⠐⠚⠁⣄⡁⠀⢀
⠀⠀⠀⠀⠀⠀⢈⣹⣭⣽⣆⠄⠀⠀⠎⠠⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠂⠀⠀⠀⠀⠀⣠⣤⠀⠰⠷⠅⠊⠐
⠀⠀⠀⠀⠐⠀⠀⠙⢿⣧⣟⡊⠀⢲⡔⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⠀⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠩⣶⠥⠀⢉⣯⠐⡀⠀⠀⠀⠀⠐⢠⢁⡔⠀⠀⠀⠀⠐⠀⠀⠈⠀⡼⢂⠐⠀⠀⠀⠂⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠈⠽⠃⠐⠀⠀⡆⠀⠀⠈⠀⠉⢀⠀⠀⠀⠀⠀⢀⡀⠌⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠈⠑⣤⣤⡤⠤⠤⠂⠁⠀⠄⡘⣀⡃⢼⠆⠈⠑⢏⠁⠂⠠⡬⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠠⡄⠀⠀⠀⠀⠓⠒⠀⢀⡠⠀⠋⢰⣋⣠⣉⡁⠘⢄⠠⣀⠀⠀⢀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠀⠀⢀⠔⠊⠁⠀⠀⠀⠁⡠⢉⡃⢴⡄⠈⢃⠀⠑⠢⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⣛⡚⢛⢹⡇⠀⠀⠡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠲⡿⠥⣈⠛⠏⠩⠀⢠⠎⠀⠀⣤⡀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠚⠷⢶⠒⠘⠆⠘⠀⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡤⠤⠤⠔⢛⣂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠆⠀⢱⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⠀⠀⠀⠀⠘⢠⡟⠲⣄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⡤⠀⠀⢹⡀⠀⠻⠇⢠⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡤⠀⠀⠸⡆⠀⠐⡀⠀⠂⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇⠀⠀⠀⡇⠀⠀⢸⣥⠀⠀⣿⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠄⠀⠠⠤⠀⠠⠄⠶⠂⠾⢀⠇⠀⠀⠸⡇⠀⠀⠈⡷⠀⠀⢻⠀⠠⠄⠺⠇⠠⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⡀⢀⣰⡆⠀⠀⡠⠟⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡡⠁⠀⠀⢠⠀⢆⠀⠀⠀⠀⣀⡄⠈⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠐⠀⡁⠂⠔⠁⠁⡂⠀⠂⠉⠁
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⢢⠀⠀⠀⠀⠀⠀⠊⠀⠀⠆⠀⠀⠀⠄⠘⠀⠈⠡⠀⠋⠀⡀⠀⠀⠄⠄
⠀⠄⠀⠀⠀⣠⠀⠀⠀⣀⠈⠁⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠚⠀⠀⢀⡀⠀⠀⠄⠀⠀⠀⠀⢀⡀⠀⠀⣤
⠀⢀⠀⠀⠀⠐⠁⠀⠈⣿⠀⢠⡄⠀⠈⠁⠁⠒⠈⠉⠃⠄⡈⠡⠀⠠⠤⠀⠊⠑⠦⠀⠀⠀⢠⣄⠀⢸⡏⠀⠀⠑
⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⣀⡀⠶⢶⠀⠀⠀⠀⠈⠀⠐⠀⠁⠀⠁⠀⠀⢰⠶⠆⣀⡀⠹
⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠇
⠀⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡍⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠑⠛⡇⠀⠀⠀⢀⣀⠠⠀⠀⠀⠀⠀⠐⠶⣦⣤⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⠀⠈⣿⡤⠔⠀⣈⠁⠀⠀⠀⠀⠀⠆⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠠⢶⣾⣯⠙⠿⠿⠒⠢⢤⣤⣽⣿⣿⣾⣛⣿⡦⢀⣼⣿⡆⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣶⣂⠈⢀⣩⣿⣿⣿⣿⣿⡍⠙⢿⣿⣿⣿⣇⡔⠀⢀⠠⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⡟⢻⣿⣿⣿⠏⠀⢀⣾⣿⣿⣿⣿⣿⡟⢛⠤⣀⣄⣈⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣅⣈⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⠻⠿⠟⠀⠀⠘⢿⣿⣿⣿⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠪⠻⣧⠠⠀⠀⠀⠠⢆⣈⣿⣿⣿⣷⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡹⠄⠀⡜⢢⠀⠀⠀⠙⠻⢩⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠄⠀⠘⠁⠀⠀⠀⣀⣴⣶⣾⣿⣿⣿⡃⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠠⠾⣿⣿⣿⣿⠀⠁⠘⣷⣶⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣀⣠⣿⣿⡿⠇⠀⠰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢸⣿⣿⣿⠿⠿⣿⣿⣿⣿⠁⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠙⡄⠀⠿⣷⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⣿⣿⡏⡂⠀⠀⠈⠻⢇⡀⠘⢀⡿⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⡏⠢⣄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠑⢤⣼⠇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⡳⣄⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢊⣿⣿⣿⠷⢶⣦⣀⠀⠀⠀⠀⠀⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢱⡇⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠁⣇⣾⠟⠋⠁⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⢢⡙⢷⣄⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠙⢷⡄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠻⢾⡿⠿⢿⣿⣟⢿⣿⣿⣿⡟⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠳⢍⠙⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⣶⡶⣢⢖⠴⣒⡢⠶⠀⣆⡴⣠⣴⡄⠰⣄⠰⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣿⢿⣾⠋⣠⣿⡿⠿⠷⠄⠀⠀⠉⠉⢀⣀⡘⢷⣽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⠃⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣆⠙⢿⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣪⡿⢁⣰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣦⣽⣂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣷⢮⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⠀⠀⢟⣿⣿⣿⣏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣫⣿⣫⣿⣿⣯⣭⣿⣿⣷⡀⠀⠀⠺⢛⣋⡁⠀⠀⠀⡾⢻⣿⣯⢻⡄
⠀⠀⠀⠀⠀⠀⣰⢟⣵⡟⣵⣿⣿⣿⣿⣟⡿⠛⢿⣧⠀⠀⠠⠛⠟⠹⠃⠀⠀⠃⣦⢻⣿⡀⣷
⠀⠀⠀⠀⠀⡼⣱⠟⣡⣾⣿⣿⣿⣿⣿⡛⠁⢀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡼⣿⡇⢸⡆
⠀⠀⠀⠀⠈⠘⣡⡾⢫⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠇⣿⠃⢸⠃
⠀⠀⠀⠀⡠⢺⠏⣠⣿⡿⡿⣿⡏⢿⣿⣿⣿⣿⣿⡿⠖⠀⠀⠀⠀⠀⠀⢸⣿⢸⣧⠀⡿⠀⠈
⠀⠀⠀⠀⠀⢸⣾⣿⡿⡽⣹⡟⡆⣯⡻⣿⣿⣿⣿⡶⠶⠶⠆⠀⠀⠀⣠⣿⡏⡆⢿⣆⠇
⠀⠀⠀⠀⠀⠀⣿⣿⣽⢣⡿⢀⠇⣧⣿⣮⣻⣿⣿⡿⠛⠃⠀⠀⡠⠀⣿⣿⢣⠇⠈⢿⡗⠂
⠀⠀⠀⠀⠀⠀⣽⣿⢧⣿⠃⠸⠀⣿⢹⣿⣿⣿⣽⣷⣀⣀⣴⡞⠀⠀⣿⠏⡼⠀⠀⡌⠳⡀
⠀⠀⠀⠀⠀⢰⣿⡟⢸⣿⢰⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣠⠏⣰⠃⠀⢀⠹⣆
⠀⠀⠀⠀⢆⠘⠏⠁⠀⣿⢼⡆⠀⡘⣿⣟⣿⣿⣿⣿⣿⠏⠀⠀⣰⠃⡴⠃⠀⢀⢸⣆⠙⣷⡀
⠀⠀⠀⠀⢸⡁⠀⣾⢀⠘⣏⠻⡄⠑⠘⣿⣿⣿⣿⣿⠏⠀⠀⠀⡇⣼⣵⠀⣞⢸⡄⠻⣆⢈⠻⣄
⠀⠀⠀⠀⢨⣷⣆⡘⢿⣦⣨⡀⠙⣦⣄⠹⣿⣿⣿⣆⠀⠀⠀⠀⣧⢻⣿⡄⢿⣌⢿⣄⠈⠀⠀⠹⡄
⠀⠀⠀⠀⠪⢿⣿⣿⣦⡙⠿⣿⣦⡀⠉⠻⢾⣿⡏⢿⠀⠀⠀⠀⠈⢯⣿⣿⣌⠻⣦⡻⣷⣾⣤⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠲⠄⠉⠉⠀⠀⠀⠈⠳⢿⠀⠀⠀⠀⠀⠀⠙⠷⢝⠧⣈⠻⢮⡛⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠉⠳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠖⠚⠋⠉⠉⠉⠉⠉⠙⠒⠲⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⠋⢂⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⠃⠀⠀⠢⡀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡄⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡆⠀⠀⠀⡎⠀⠀⠀⠀⠑⠢⡀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢡⠀⠀⢠⠀⠀⠀⠀⠀⣀⠀⠀⠁⠂⠀⠀⠀⠑⢤⣀⠀⠀⠀⠱⡄⠀⠀⢠⠁⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢆⠀⠘⢀⠄⠀⣀⣀⡀⢱⠄⠀⠀⠀⠀⠀⠀⠎⢀⣀⣉⠀⠲⠘⢦⠀⡨⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠸⠃⠦⢨⠀⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠇⠀⣧⠃⢄⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢆⡀⢣⡀⠀⠑⠼⠿⣧⠾⠃⠀⠀⠀⣤⠀⠀⠀⠙⢧⣼⠿⠇⠂⠀⢀⡍⠀⠘⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠈⠷⡈⠀⠂⠆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠘⠀⣀⠞⠁⠀⠠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢀⣬⠷⠦⡄⣀⠀⠈⠒⠀⠤⠀⠀⠀⠀⠀⠀⣀⠀⠴⠞⢅⡀⠀⠀⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⡴⠋⠀⠀⠀⠀⠈⠈⠳⣀⠀⠀⠀⠀⠀⠀⠚⢀⡝⠀⠀⠀⠀⠉⢧⡀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠤⠔⠋⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⢣
⠀⠀⠀⠀⠀⠀⢀⡴⣋⣀⡠⢶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣤⣀⡳⣄⡀
⠀⠀⠀⠀⠀⠘⠉⠉⠉⠁⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⡇
⣤⠤⢤⣤⣤⣤⣤⠤⠤⢼⠁⠀⠀⠀⠀⠀⠀⠈⢦⠤⠤⠄⠀⠠⠤⠤⠄⠀⠀⠀⠀⠠⠤⠴⠀⠀⠀⠀⠀⠀⢹⣤⣠⣤⣤⣤⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡤⠤⠤⠤⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⢳⠄⠀⠀⠒⠂⠀⠀⠀⠀⠀⠐⠀⠚⢃⠀⠀⠀⠀⠀⠀⠇⠀⠒⠒⠂
⠀⠀⠀⠀⠀⠘⡟⠃⠀⠀⠀⠀⠈⢦⠀⠀⠀⠄⠀⠠⢜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣠⠀⠀⠐⢆⠁
⠀⠀⠀⠀⠀⠙⣟⡁⠀⠀⠀⠀⠀⠀⠳⣤⣁⡔⠉⠰⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠈⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⢫⠐⠀⠀⢁⠾⡙⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡴⠀⡄⢰⡙⡄⠓
⠀⠀⠀⠀⠀⠙⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣈⡡⠶⠇⡀⡩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⠈⡗⠆
⠀⠀⠀⠀⠀⠈⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂⠃
⠀⠀⠀⠀⠀⠈⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢈⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢈⣯⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠒⠒⠒⠂⠚⠤⢄
⠀⠀⠀⠀⠀⢠⣧⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⣈⣄⠀⠓⠢⠤⠄⣀⣀⣀⡀⠕
⠀⠀⠀⠀⠀⠠⣧⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠸⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠰⠷⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⠋⠛⠉⠛⠉⠁⠀⠤⠀⠀⠒⠚⠉⠛⠛⠯⠭⠭⠉⠙⠛⠋⠥⠀⠂⠤⠶⠒⠋⠻⡖⢀⠳⠲⠶⠶⠶⠶⠾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣿⡿⢿⣿⣿⡟⠿⣿⡿⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⠞⠁⠀⠀⠙⠻⣿⣷⣦⣍⣙⡒⠾⢭⣤⣈⡙⠲⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣝⡢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⠋⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣬⣍⣙⠓⠲⢮⣭⣳⢮⣷⣵⡝⣿⣿⣿⣿⣿⣿⣿⣿⣦⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠚⠭⢷⣒⣶⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣟⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠛⠓⠂⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣶⠈⠀⠹⣿⣿⣿⣿⣿⢧⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠰⠿⠋⢁⠀⣀⣀⣀⡀⢀⡠⠤⠒⠉⠁⠙⣿⣿⣿⣿⣧⡐⢀⣿⣿⣿⣿⣿⣷⡁⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢰⡶⠿⠗⠀⣠⠊⠉⠀⠉⠻⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠸⡟⠘⣿⡞⣿⣾⣿⣿⣿⣿⣿⣿⣷⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣷⠬⢄⣀⢠⣀⡇⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣀⡼⡟⢺⢋⠳⡀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⠀⠀⢃⠀⡇⠀⠙⠢⢄⣀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣆⠀⠈⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢰⡇⡿⣸⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣷⢠⠉⠉⠑⡄⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⡇⠁⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣏⠄⠀⠀⠈⢆⢈⡤⠴⠒⠊⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⡟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠘⡟⣦⠀⠀⠀⠀⠡⡄⠐⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡏⢿⣿⣿⣿⣿⡟⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢱⠘⣷⡀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⣠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠇⢸⠻⣿⣿⡿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡇⠈⢿⣄⠀⠀⠀⠀⠈⠂⠀⠒⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⠀⠈⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠁⠀⠀⠄⠒⠀⠀⠈⠃⠐
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠈⠀⢀⢀⣀⠈⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠄⠀⢸⠞⠉⢆⠀⠀⠀⢀⠉⠀⢀⠘⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⡀⢀⠈⠙⠖⡋⠘⠂⠂⠀⠚⢂⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠄⠉⠐⡀⠚⡅⠛⠐⠧⡤⠀⢶⠀⠆⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠸⠖⠌⠀⠸⠧⡇⠀⡀⠠⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢀⠷⡀⡁⠞⠀⠀⠀⠀⢀⠀⠆⠀⠐⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠐⡄⠀⡐⠂⠄⠈⠙⢱⠾⠶⣁⠀⠀⠒⣈⠦⡲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠀⠀⠘⠛⠲⣄⢸⡆⢠⡄⣵⢀⡔⠋⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⠀⠀⠈⠀⠀⠀⠀⠄⢸⠀⠀⠀⠀⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠸⠀⠠⠀⠀⠀⠀⢀⠊⠘⡁⡀⠀⠀⢀⣸⠀⠂⠀⠀⠀⠀⠀⣀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⠸⠷⠈⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣠⠞⠀⠀⠀⢱⠈⠑⠔⠀⡆⢥⡀⠀⠀⠀⠻⣄⠀⠀⡾⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠙⢄⠁⠀⠀⠀⠄⠀⠀⠀⠀⠁⢀⢧⠀⠀⠀⠀⠈⠀⠀⠙⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠟⠴⡆⣿⢳⡄⠧⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢸⢀⣬⠀⠀⠀⢿⠠⠃⢰⠀⢀⠀⠀⠀⠐⠶⠄⠀⠠⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⣁⠛⢢⡀⠀⠸⣧⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣍⡄⠀⠳⠀⠀⡿⣇⢰⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣧⡟⢰⡗⠀⣰⠇⣇⣿⠀⢀⣀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⠁⠀⠀⠈⠀⢀⣤⡠⠞⡩⠀⡞⠀⡐⠛⣠⣿⠟⠀⠸⣁⠉⣠⡀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠂⠂⠀⠴⠦⡈⠀⠄⠀⠊⢀⣼⠁⠐⣇⠀⢼⡸⣟⡄⠁⠀⠀⢨⣄⠠⠀⠀⢤⡀
⠀⡀⠀⠀⠀⠀⠀⠘⣃⡀⠀⢄⡑⠆⠀⠑⠲⡆⠰⠶⠋⠉⠃⢰⡿⠄⠀⠓⠿⠄⠒⠀⡴⠕⠘⠧⠀⣀⠀⠀⠀⢀⡀
⠀⠅⠀⠀⠀⡠⠄⠀⠈⠀⠘⠉⣔⠊⡇⠀⠀⠱⠀⢢⡀⠁⠸⠸⠫⢶⡀⢢⣴⠲⠶⢏⡁⠀⠈⠦⠘⠋⡈⢰⠐⠊
⠀⠂⠀⠀⠀⠀⠤⠀⠀⠠⠀⠀⠈⡠⠇⣘⠂⢀⡲⡦⢄⢠⡴⢐⠁⢺⠀⣠⠀⠀⠐⢀⠱⠀⠁⠀⠆⠀⠐⢣⣄⠀⡁
⠀⠀⠀⠀⠀⠀⠘⡂⠀⠘⠑⠄⠘⣠⠠⣀⡼⠏⠀⠀⠀⡈⢤⢀⣀⠈⠻⠑⡀⢠⠀⢀⠠⠃⠂⠉⠤⡷⠄⠀⠀⠈⠉
⠀⠃⠀⠀⠀⠈⠒⠓⠖⣠⡄⠐⠀⡠⠏⠈⠀⠚⠀⠀⠀⠈⠠⠠⠈⡼⠀⢈⠲⢈⡕⠠⠆⠠⡄⠹⠏⠀⠉⠁⠠⠐⠐⠒
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠃⠀⠘⠂⠀⠀⠀⠀⠀⠚⠒⠈⠁⠀⠁⠀⠉
⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⢔⢶⣪⣧⣵⣥⣭⣏⣜⡰⠢⣄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣐⣤⣲⡽⠞⠛⠉⣽⣿⣿⣿⡟⣿⣿⡉⠙⠳⢭⣗⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⡋⠁⠀⠀⠀⢸⣟⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠈⠙⢿⣶⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠨⡑⠦⣄⣀⠈⢿⣿⣿⣿⣿⣟⣹⠃⠀⢀⣀⡤⢖⡫⠒⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠴⢂⢌⣉⡛⠛⠿⠿⠿⠿⠗⠒⢋⡩⡵⢮⠋⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠜⠙⠑⢰⠐⠺⡙⠌⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠤⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠶⠶⠲⠒⠶⠤⣤⣀
⠀⠀⠀⠀⠀⠀⡠⠔⠋⠉⠀⠀⢀⣀⣀⣀⣀⠀⠉⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠁⠀⠀⣀⠀⠀⣀⡀⠀⠀⠀⠈⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⢷⣶⣶⣶⣶⡯⠶⢤⡀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢷⣶⣶⣶⣶⡶⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⠼⣿⣿⣿⡿⠁⠀⠀⠁⠀⠀⠈⡄⠀⠀⠀⠆⠀⠀⠈⠀⠀⠌⣿⣿⣿⣿⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⡀⠀⠀⢀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠠⠦⠤⠐⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡄⠀⠀⠀⠄⢀⣀⠄⠀⠀⠀⠀⡴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⢀⣀⣀⣀⠀⠤⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠈⠙⠢


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠚⠛⠛⠛⠛⠛⠛⠳⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⢰⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⢀⡞⠁⢀⠄⢀⠆⠀⠀⠀⠀⠀⠀⢠⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⣠⡴⠶⠶⠶⠶⠶⣤⣀
⠀⠀⠀⠀⣰⠋⠀⢠⠏⢀⠏⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠⡾⠅⠒⠂⠀⠀⠀⠀⠀⠉⠳⢦⡀
⠀⠀⠀⢰⠇⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠘⣦⠈⠑⠦⣄⣀⠀⠀⠀⠀⠀⣿⡤⣴⠋⣠⠤⠔⠒⠂⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠿⠴⠶⢶⠾⣶⣾⣤⡤⣤⣄⣀⣀⣀⣀⣀⣷⣴⡾⣿⡦⡀⠀⠉⠙⠒⠶⠦⠤⣿⣤⣘⡟⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠸⣆⠹⢿⣿⡶⢿⠏⢸⡅⠉⠹⣿⣿⣿⣧⣾⢃⠗⠀⠀⠀⠀⠀⠀⢠⠁⠀⣽⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⡝⠲⠤⡤⠖⠏⠀⠠⠻⣄⡀⠙⠻⠿⠟⣫⡛⠀⠀⠀⠀⠀⠀⠀⠘⣷⠛⠁⠀⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⡖⠀⠀⠀⠈⠉⠓⡶⠒⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⡄⠀⡇⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⢠⡀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⡇⠀⡇⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢰⠁⢀⠇⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⡀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⡌⠀⡼⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣈⣉⡻⠟⡟⣻⠛⠻⠭⣥⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⠀⠰⠁⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣆⠀⠀⠀⢈⡁⠀⡠⣀⣴⠢⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⡄⢠⠁⢀⠁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠉⢸⠁⠑⠒⠁⠈⠋⠀⢨⠈⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⢣⢸⠀⠸⡀⢳
⠀⠀⠀⡆⢀⠀⠀⢀⠠⢔⡪⠷⢤⡏⠀⠀⠀⠀⠀⠀⠀⠸⣦⡤⢞⢣⡀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠘⠿⣾⣆⠀⠙⢦⣵⣤⣄
⠔⢀⠍⠑⠀⢑⠨⠐⠊⠁⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠈⠓⢬⣒⠤⣀⣀⡤⠂⠴⣀⠖⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠚⠛⠉
⠐⢔⠠⡂⠀⠁⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠈⠙⠒⠺⡀⠈⠀⠩⢜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠈⠁⠂⠥⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣀
⠀⠀⠀⠀⠀⠀⠀⠰⠯⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣄⣀⣤⣤⣤⠦⣤⣄⣀⣀⣠⡴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠨⣀⡇⡿⠠⠐⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠺⢀⠛⠂⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡎⠀⠀⣰⠠⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣁⡀⠁⠒⠺⠓⢲⠎

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣦⡭⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⢀⠾⠒⠑⠀⠙⠳⣦⡀
⣿⣿⣿⣿⢟⣏⣴⣿⣿⣿⣿⣿⣿⣆⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢐⣴⡟⠃⠀⠀⠀⠀⠀⠙⣏⡠
⣿⣿⣿⡿⣻⣽⢿⡿⣿⣿⣿⣿⣿⣃⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⣬⠼⣠⠀⡀⠀⠀⠀⠀⢠⣿⢰
⣿⣿⣿⣿⡿⣿⣟⣿⣿⣿⣿⠟⣻⣿⣿⣽⣿⣿⣿⣿⠀⠀⠀⠀⠁⡂⢘⣔⢀⡀⠀⢀⣤⠊⢜⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠁⠀⠀⠌⠘⠈⠀⡯⠥
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠥⢌
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠅⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⠀⠸⠀⠂⠐⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⢀⠀⠐⠀⠀⢠⢀⠀⠀⠀⠀⠁
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡿⢿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣏⣰⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⣿⣿⣌⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⢡⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡿⣿⣿⣿⣿⣷⡹⣿⣿⣾⣿⣿⣆⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⣿⣿⣿⣿⣿⡿⣿⣸⣿⣿⣿⣧⢻⣿⣿⣿⣿⣷⡙⣿⣿⣿⣿⣿⡌⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣸⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⢻⣷⣻⣿⣿⡿⢿⣷⡌⢿⣿⣿⣿⣧⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⢹⡟⠁⠘⣿⡟⣿⣿⣇⠙⢿⣿⣿⣷⡄⠙⠻⣦⡹⣿⣿⣿⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣿⣿⣿⣿⢀⣤⣶⣦⡈⠃⠈⠻⠿⠧⠀⠀⠉⠉⣤⣶⣦⣄⠙⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡿⠛⣿⠁⠸⣯⣬⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣼⡟⠀⣿⠋⠻⣇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡁⠀⢻⠂⠀⠹⣭⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⢭⣭⡿⠁⠀⡟⠀⠀⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⣿⣦⣄⣀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣠⣤⣤⣾⣿⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣿⡏⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣉⣉⡹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⣿⡿⣿⣿⣿⡿⠋⢧⠀⠀⡸⠛⣄⠀⢠⠇⠈⢻⣿⣿⣿⣿⣿⣿⡇⣿⡏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⣾⣇⣿⣿⡿⠁⠀⠀⠙⠋⠁⠀⠈⠛⠁⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠖⣋⣴⡟⣸⣿⣿⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣈⣿⣿⣿⣏⣿⢡⣿⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠾⣯⣥⡾⢟⣿⣍⠓⢶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡉⣁⣼⣿⣟⣈⣵⠟⢃⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡿⠉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⡇⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⠛⠳⠶⠶⠤⣤⣤⣤⣤⠤⠶⠶⠶⠚⢛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⡶⠦⢤⡤⢤⡤⠴⢶⠶⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠇⠀⡆⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢸⠀⠀⢸⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠒⠒⢛⠆⠀⣟⣑⢊⣙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣯⣼⡟⣿⠀⠀⣼⣿⣯⣭⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡟⠀⠀⠹⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠙⠋⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄⣀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⡄⢸⠁⠀⢀⣀⡀⠀⠀⠀⠀⠀⠁⠂⠑⠈
⠀⠀⠀⠀⠱⢵⣰⣄⣀⡀⢐⣁⣹⠀⢀⣀⣴⣰⠵⠅⠀⠀⠀⠀⠀⠀⠁⠘⠀⡔⠁⠀⠈⡆⠀⠀⢀⠄⢸⠀⠀⡄⡠⡀
⠀⠀⠐⠀⠀⡐⠥⡝⢹⠃⠆⢀⠀⠦⢻⠝⡥⠕⡀⠀⠐⠀⠀⠀⡀⠁⠀⠐⠎⡢⠀⠀⡰⠀⠀⠀⠸⠺⠂⠸⠇⠀⡀⠄
⠀⠀⠀⠀⡧⠀⠀⠈⠒⢻⠀⠼⡀⢸⠓⠊⠀⠀⠂⡅⠀⠀⠀⠘⢀⠀⠀⠀⣯⣆⢡⠎⠀⠀⣀⠀⣰⠺⠀⠀⠁⠀⡃⢄⣀⣀
⠀⠀⠀⠀⠈⢶⠮⢒⡤⠊⢂⠛⢃⠈⠣⡔⠢⢶⠎⠀⠀⠀⠀⠀⠀⠀⠰⠀⣉⡁⠰⠀⠀⠀⠡⡀⠉⠀⠀⢀⢀⠀⠑⠉⢀⠌
⠀⠀⠀⠀⠀⠀⠒⠊⠁⠀⠀⠐⠂⠀⠀⠉⠒⠊⠀⠀⠀⠀⠀⠈⢄⠘⠀⢠⠍⡡⠃⠀⠀⠀⠀⠱⡀⢠⠚⢳⡖⣛⠆⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠊⠀⠀⠀⠀⠀⠀⠀⠑⠀⠊⠉⠀⠁⢠⠊
⠀⠀⠀⠀⣠⠥⠺⢤⡐⣀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣴⠀⣀⠀⠀⠀⠀⠑⠂⠐⠊
⠀⠀⠀⣻⠁⣒⡥⠒⠛⢠⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⢀⠺⣤⠚⢵⣼⡆
⠀⠀⠀⠋⠍⠁⠈⠀⠐⢸⠀⠀⠀⠰⠄⠀⠀⣀⣀⡀⠀⠀⠶⠀⠀⠀⡄⠘⣜⠀⡜⣀⠅⡂⠀⠀⡐⠄⢡⠤⢤⣊⡠
⠀⠀⠀⠀⠚⠀⠀⠀⠃⡘⠀⠀⠀⠦⠀⡔⢉⠄⠂⢌⠑⡄⠠⠆⠀⠀⢃⠀⠈⠉⠉⠁⡐⠀⠀⠀⠀⠀⢠⣘⣣⠀⠃
⠀⠀⠀⠈⠢⠄⢉⠠⠊⠀⠀⠀⠀⠀⠚⠂⠒⠀⠀⠐⠂⠚⠒⠀⠀⠀⠀⠑⠤⠤⠐⠊⠀⠀⠀⠀⠀⠀⠀⠐⠄⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠸⠶⣤⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⢷⠃⡏⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⣸⣧⠀⢢⠄⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⢦⠀⠁⣤⠀⠀⣤⣠⠄⠀⠰⠬⠀⠀⠄⠀⢙⡿
⠀⠀⠀⠀⠀⠀⠀⠉⢻⠄⡟⠀⠀⠀⡄⠀⠀⠀⠀⠠⡄⢛⠂⠘⠴⢆⠙⠆⡀⠀⠁⠀⠀⠀⠇⠀⠀⠘⡄⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⡀⠀⠀⠀⠀⠘⠀⡒⠙⠂⠀⠀⠀⠄⠠⡙⠛⠀⠀⠀⠀⠀⠀⠐⡀⠀⠰⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡌⠀⠀⠀⠀⠀⠀⠆⠡⠀⠀⡄⠘⠀⠄⡀⠀⠻⣨⠆⠀⠴⠀⠀⠀⠀⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⠁⢀⡄⠀⠀⢂⠀⠀⠀⠁⠂⡀⠀⢈⠆⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⣘⡣⠀⠠⣅⠀⠒⠀⠂⢰⡫⠀⠀⢈⡅⠌⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠠⢂⠈⠁⢀⠀⠑⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠀⠀⠀⠈⠀⠈⠀⠄⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠀⠀⠟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠅⠀⠀⠄⠀⠂⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⣩⠀⠀⡄⠀⡀⠀⠞⠀⠀⠰⠀⠀⠁⠀⠂⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠒⠀⠀⠰⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡇⠀⠀⠀⠀⠀⠆⠀⠀⠀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠠⠠⠀⠀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⢀⠀⠀⠀⠀⠴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣈⠀⠶⠚⠚⠀⡂⠀⠘
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠲⠆⠀⠀⡘⠁⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠁⠋⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠊⢠⠁⠀⠀⠀⠀⠂⠀⠀⠐⠰⠄⠀⠀⠀⡀⠄⠀⠀⠈⠀⠀⢀⡠⠁⠂⠀⠀⠀⢰⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠄⠀⠀⡠⠀⠀⠀⠀⠂⠠⠈⠁⠀⠀⠠⠄⠀⠀⠀⠀⠀⠙⠃⡄
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⢄⡀⠀⡐⠀⠀⠄⣀⠴⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁
⠀⠀⠀⠀⡠⠀⠤⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡘⠀⢀⠈⠘⠧⣄⠀⠘⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠐⢀⡽⣀⠀⠀⠀⠀⣠⡴⠂⣀⠄⠁⠀⢩⠄⢀⡀⠁⠄⠀⠈⠰⣄⡈⢷⡄⠀⠀⠀⣰⠠⢀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⢠⣦⠀⠀⠀⣿⠠⡈⢿⣄⡀⠤⠀⠀⠀⠁⠀⠀⠀⠒⣤⠋⠁⠨⣇⠀⠀⠠⠔⠋⠀⠈⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢃⠀⠀⢹⡀⠈⠀⣈⡗⢂⠀⠀⠀⠀⠀⠀⠠⡀⠒⠖⠀⢸⠇⢀⣴⠎⠁⠀⠀⠀⣀
⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡶⠀⠀⠃⢀⣀⡬⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠑⣀⡔⠋⣁⠐⠀⠀⠀⠀⠀⠀⠁
⠀⡘⠀⠀⠀⠰⠁⠀⠀⠀⠀⡘⠀⠀⠁⢐⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢚⠣⠀⠴⠫⠄
⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠄⠒⠂⠀⠀⠀⠂⠀⢀⠀⣀⠀⠀⠂⠢⠀⠀⠀⠠⠀⢀⠀⠀⠀⢀⠀⠀⠈⠀⣀
⠀⢨⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠀⠂⡃⠀⠀⠀⠀⠀⢀⡅⠂⡱⠀⠄⠀⠀⠐⠑⠀⠀⢀⡀⠈⠑
⠀⢉⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠈⠀⣀⠀⠀⠀⠀⠀⠀⠲⠁⠈⠀⠠⠉⢀⠀⠀⠸⠀⠀⠀⠁
⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠲⠶⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢒⡀⠀⠀⠀⠀⠀⠉⠀⠈⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠐⣛⣛⣀⣀⣀⣀⣀⣀⣀⣀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠨⣿⠟⡟⣿⡟⡟⣿⡟⢿⣿⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠍⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢨⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡒⠙⡿⡟⣿⡿⡟⣿⢻⡏⢹⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣘⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢘⡂⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢘⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤⠴⣭⣭⠻⢥⣈⣛⠤⠬⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠤⠆⠀⠠⠦⠦⠁⠀⠤⠤⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣷⣯⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣫⡿⢛⣫⣽⡿⠋⠙⢿⣿⣯⡻⢿⣿⣿⡝⣿⣿⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢳⣿⣾⠟⠛⠉⠀⠀⠀⠀⠉⠻⣿⣦⡻⣿⣿⡌⢿⡇⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⢹⣿⣿⠘⣷⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⠉⡇⠀⣀⣠⣤⣤⡄⠀⠀⠤⣤⣤⣿⡀⢻⣿⡇⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡄⢧⠀⣠⣄⣀⡀⠀⠀⠀⠀⢀⣀⣼⣧⠀⠙⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢻⣿⣷⣬⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠘⠉⢹⣷⡀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⣿⣿⡿⣿⣇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⣿⣿⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣟⠀⣿⣿⡇⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡃⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⢹⣿⣿⣿⣿⣿⣦⡀⠀⠈⠉⣭⠁⠀⢀⣼⣿⣿⣿⡇⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⡆⢄⣀⣀⣀⡴⣺⣿⣿⣿⣿⣧⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠃⣰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠉⠁⢀⣿⣿⣿⣿⣿⣿⡀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⣴⣿⣿⣿⣿⢻⣿⣿⣿⠁⠀⠀⠀⠀⢸⣿⣿⡏⣿⡇⣿⣧⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⣼⣿⡿⢿⡿⢃⣾⡿⠟⠁⠀⠀⠀⠀⠀⣼⣿⣿⡇⠸⡇⠹⣿⣧⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠘⠃⠀⡼⠁⢋⣾⠿⠷⠻⢥⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢻⡀⠙⠿⣷⡀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠈⠙⠒⠒⠶⠖⠒⠒⣿⣿⣿⣇⠀⠀⢧⠀⠀⠈⢷⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡏⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡄⠀⠈⢷⡀⠀⠈⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡌⢿⣿⡄⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠙⢿⣆⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⢻⡆⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠶⠶⠶⣦⣀⣠⠴⠶⠶⠶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠉⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣠⡀⢀⡤⠖⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⣠⠟⠹⣶⠋⠀⠀⠀⠻⣄⠀⢀⠀⠀⢠⡴⢰⣾⣇⡼⢧
⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⢰⡄⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⡧⢠⣌⠳⠖⠋⠁⠀⠀⣦
⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⢠⠟⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣿⠏⢀⡀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢠⠟⠀⠀⠀⢹⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣿⣧⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⣇⠸⡀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⣤⣤⣀⡀⠀⠘⠛⡇⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⢷⣿⡄⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠈⠙⠿⠁⠀⠀⢀⠇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡄⢻⣆⠀⠀⠀⠀⠰⣤⡀⢀⣠⡄⠀⠀⠀⠀⢠⣾⣿⡆⠀⠀⠀⠀⠀⢳⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠙⢷⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⣀⠀⢠⣀⠀⢉⡻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⣙⣳⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⣾⣇⠀⠀⢿⣷⣤⣽⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡟⠉⠉⠛⢳⡶⠤⠶⠚⠛⠉⠀⠀⠘⣏⠀⠴⠤⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣤⣀⣀⣼⣧⣀⣀⣀⣀⣀⣀⠤⠚⠉⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⣿⠃⠀⠀⣿⡉⣹⠏⠉⠉⠉⠉⢁⣀⠀⣼⠿⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣼⠏⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⢰⡏⢉⣿⣿⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⣼⢋⡴⠲⡄⠀⠀⣠⠖⠲⡄⠀⠀⠀⠉⠊⢹⡟⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⠃⠈⠳⠞⠃⠀⠀⠛⣤⠾⠁⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠲⣄⠀⠘⢷⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⣼⠋⢙⡆⠀⠀⠀⠀⠀⠀⠘⢧⡴⠇⠀⠀⠀⢳⡀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣀⡀⠀⠀⠙⠓⠋⠀⠀⠀⢠⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡅⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠳⣆⡸⠃⠀⠀⠀⠀⢀⣀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⢀⡷⠀⠀⢀⣼⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢴⣶⠀⠀⠀⠀⠀⠀⣤⠶⣄⠀⠉⠉⠀⠀⠀⠺⣅⣿
⠀⠀⠀⠀⠀⠀⢸⡿⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⠿⠀⠀⠀⠀⠀⠀⢀⣀⢼⡇
⠀⠀⠀⠀⠀⢠⡟⠀⠙⣿⡽⣟⠓⣂⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣶⠾⣿⠛⠊⢳
⠀⠀⠀⠀⢠⡎⠀⠀⢰⡟⠀⡏⠀⠀⠀⠀⠈⠘⡿⢻⡄⠈⠉⠉⠉⠛⠛⢻⣿⠹⠉⢻⠀⢹⠀⠀⠘⡆
⠀⠀⠀⠀⠘⢧⣄⡀⠸⡇⠀⠁⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⢸⡏⠀⢃⢸⡇⠈⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣤⣀⣀⣀⠀⠀⠀⠀⠹⠀⠇⠀⠀⠀⠀⠀⠀⠘⠁⠆⠀⠀⠀⣀⣠⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠿⠛⠿⠶⠶⠶⠶⠾⠿⣶⣶⣶⣶⣶⣶⣶⠶⠾⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢀⡀⣠⡀⢻⣄⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠙⠁⠀⠈⣻⠃⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⣺⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣄⣀⣀⡜⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⢀⣨⠟⠛⠷⣤⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣅⣀⣀⢀⣀⣈⣉⣉⣬⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠉⠉

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⠿⣿⠿⠿⡿⠿⠿⢏⠹⠿⢿⡿⠿⠿⠿⣿⣿⣿⣿⡟⣻⣛⠛⠛⠛⣛⡛⣛⢻⣿⣿⠛⠛⠛⠿⠿⠟⢻⠛⠛⠻⣿
⣿⣷⣿⣶⣶⣷⣾⣶⣾⣶⣾⣶⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠿⣷⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⣿⢻⣿⣾⣿⡿⣿⡇
⠀⢠⣶⠶⣤⣤⣄⣚⣟⣛⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣭⣄⠀⠀⣿⣶⠿⣿⡻⢶⣿⡇
⠀⣻⣿⣿⢏⢭⣟⢻⡿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⣟⡀⠀⣿⣽⣷⣯⣷⡯⣽⡇
⠀⠀⢈⡅⡷⣉⣯⣿⣿⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⣷⣿⣿⡇
⠀⣠⣾⣿⠌⠀⠉⠉⠛⠻⠿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠉⠀⠀⣿⣿⣿⣟⣿⣿⣿⡇
⢾⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘




⠀⠀⠀⢀⡀⣠⣄⣠⣄⢀⡀
⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⠀⣰⣦⠀⢀⣶⡄⠀⣰⣦
⢀⣼⣿⣿⣿⢿⣟⣿⣯⣭⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠙⠋⠀⠈⠙⠁⠀⠉⠋
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆
⢻⣿⣿⣿⣿⣽⣿⣿⣿⣽⣿⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠶⣶⠟⣿⡟⢿⣿⣛⣶⡶⣶⣤
⠰⣿⣿⣯⣿⣿⣿⡛⣽⣽⠿⣻⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⢯⣭⣭⣭⣿⣿⣿⣿⣿⣿
⠀⠀⠛⠛⠈⢹⣿⠍⣿⣿⣷⣼⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣟⣿⣛⣻⣟⣻⣟⣛⣿⣛⣿⣻⣿
⠀⠀⠀⠀⠀⠿⠿⠿⠟⢿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⡟⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⡉⠁
⠀⠀⠀⠀⠀⠠⠠⠤⠀⠐⠛⠗⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠋⠙⠃



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢠⠤⠄⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣀⠶⢧⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣤⡀⠘⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢵⠶⣴⣿⣷⡴⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠋⠛⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠⠀⠠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡔⠀⠀⢸⣶⣞⢬⣷⣶⣾⠠⠀⡐⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⢿⣡⠄⡀⢠⣼⣏⣷⣝⣿⣤⠀⡀⢤⣹⢿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⠁⠀⠉⢲⣾⠟⣿⡟⢻⣶⠊⠁⠀⣽⣾⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⢻⡇⠀⠀⠘⡇⠄⠈⠀⢄⠏⠀⠀⠀⡿⠋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣉⠂⠃⠀⠀⠀⠘⡂⢈⠀⡊⠀⠀⠀⠀⠃⢊⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠰⢁⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠋⠁⠀⠀⡀⢀⠀⢈⢋⡃⠀⠀⢀⡀⠀⠀⠉⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡄⠀⠀⠀⠀⠿⡀⡄⢬⡁⣩⢄⡄⣸⠃⠀⠀⠀⠠⡤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢜⡴⠛⠁⠀⠠⣤⡐⠂⠄⠮⢮⣟⣧⠾⢆⡠⠚⣠⣤⠀⠀⠙⠳⣜⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠁⢀⡘⠃⠚⠉⡄⢶⡀⡀⢴⡶⣿⡷⣶⢄⡀⣱⠖⡌⠙⠀⠋⣀⠁⠉⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⠒⢲⠏⠀⠐⢶⣆⠀⠘⣧⠀⢠⠴⠻⠳⢄⠀⢸⡟⠄⢀⣶⠦⠀⠈⢶⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣯⣀⠀⠈⠋⠁⣀⣩⣱⢂⡗⢰⡀⣰⢐⣇⢳⡩⣁⡀⠙⠁⠀⢀⣨⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠋⡩⠛⠻⢂⣶⣀⣷⡏⠘⠋⠚⠷⠟⠎⠛⠈⣷⣆⣘⣆⠚⠛⠫⡈⠣⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠐⠂⠂⠓⠁⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠙⠂⠂⠒⠈⠒


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠆⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢰⠀⠀⣤⠀⢀⠀⠀⢰⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠔⠀⠁⠒⠣⠀⠓⠀⠉⠘⠁⠘⠚⠀⠀⠈⠉⢨⠀⠃⠀⠈⠁⠓⡃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠔⠒⠒⠉⠉⢉⣏⠉⣩⡉⣉⣉⣉⠉⠉⠑⠒⠒⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⢋⠉⢠⡶⠂⢰⣞⠘⣷⣿⠂⠀⠈⢧⠁⣿⢘⣷⣰⡟⢰⡆⣴⡆⢈⠉⠓⠢⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠁⣄⠐⢧⣇⡀⠻⠄⠀⠙⠛⠉⠈⠀⠀⠀⠀⠀⠀⠈⠍⠘⠛⠛⠛⠻⠇⡞⠀⡼⠀⢠⡙⠻⣦⣀
⠀⠀⠀⠀⠀⠀⢀⡴⠛⢡⡀⠀⠀⠯⠻⠞⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠡⢾⠋⢡⠟⣀⠙⠳⣄
⠀⠀⠀⠀⢀⠔⠃⣀⢳⣄⠻⠄⠀⠀⣀⣶⣧⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠋⠀⢹⡤⣇⡀⠓⢄
⠀⠀⠀⠠⠟⣠⡄⠙⣷⠈⠁⠒⢴⣾⣿⣿⣿⣷⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⢱⡏⠉⠰⠘⠇
⠀⠀⠀⠁⠀⠁⡙⠗⠀⠀⢤⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⠋⠀⠀⠀⠅
⠀⠀⠀⡀⠀⠀⠀⣀⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⣄
⠀⠀⠈⡇⠀⠀⠸⣇⡰⠖⠑⣶⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡴⠒⠉⠲⣆⡴⠀⠀⢐⡇
⠀⠀⠰⡇⠀⠀⠀⢸⣧⠶⠖⠋⢹⣿⣿⡿⠿⡿⢿⣿⡿⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⢿⣿⠿⣿⠿⢿⣿⡿⢿⣿⣿⣿⣧⡴⠶⠚⠉⠀⠀⠀⢸⡇
⠀⠀⢠⡇⠀⠀⠀⢸⣇⣀⣠⡴⢿⣿⣿⡇⠸⠟⢠⣿⡇⢸⣿⣿⣿⣿⣏⡀⢻⣿⡏⢠⣿⣿⣷⣿⡇⠸⠛⣿⣿⣿⣿⣿⡏⠀⣀⡴⠟⠀⠀⠀⢸⡇
⠀⠀⠀⠋⠀⠀⠀⢸⡿⠋⠁⣠⣾⣿⣿⡇⢸⡿⠀⣹⡇⠸⣿⡿⢻⠟⣼⣧⠀⢿⣇⠈⢿⣿⣿⣿⡇⢰⣦⠈⢻⣿⣿⣿⡿⠛⠉⢀⡤⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣷⡶⠟⠋⢸⣿⣿⣷⣶⣷⣿⣿⣷⣶⣷⣶⣿⣶⣿⣿⣶⣾⣿⣿⣶⣾⣿⣿⣷⣾⣿⣷⣶⣿⣿⣿⣧⡴⠚⠋⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣤⠞⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⡤⠖⠋⡀⠀⠀⠀⠃
⠀⠀⠀⡀⠀⠀⠀⢸⠟⠉⢀⣠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢱⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⣀⡴⠀⠀⠀⠀⡄
⠀⠀⠀⡇⠀⠀⠀⢸⣷⠾⠛⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠞⠋⠁⠀⠀⠀⠀⢠⡇
⠀⠀⠀⡇⠀⠀⠀⢸⣇⣠⣤⠞⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣴⠞⠋⠀⠀⠀⢸⡇
⠀⠀⠀⡇⠀⠀⠀⢸⡟⠉⢀⣠⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡟⢁⣀⣤⠶⠀⠀⠀⢸⡇
⠀⠀⠀⠇⠀⠀⠀⣾⡿⠛⠋⢁⣼⢟⣽⣯⣽⢯⣭⣽⢿⣭⣯⣯⣽⣯⣭⣽⣯⣭⣿⣭⣭⣭⣯⣭⣿⣭⣽⣯⣽⢟⣯⢻⡿⠛⠉⠀⣀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⣼⣇⣤⡶⠟⢡⠊⠀⠹⣿⡆⣿⣿⣠⡿⠀⣿⣇⣬⣿⡇⠈⣿⡇⠛⠸⣿⡇⠙⢸⣿⣧⡎⠛⠀⠁⢸⣷⡴⠶⠛⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⣀⡴⠃⠀⠀⠀⠹⣿⠃⢻⡿⠁⠀⣿⡏⠈⣿⡇⠀⣿⡇⠀⢐⣿⡇⠀⢸⣿⡏⢃⣤⠀⠀⢸⡏⢀⣠⡴⠊⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠉⣀⡄⠀⠀⠀⠀⠁⠀⠈⠁⠀⠈⠉⠉⠈⠉⠉⠈⠉⠉⠀⠈⠉⠁⠀⠈⠉⠉⠉⠁⠀⠀⠘⡿⠋⠁⢀⣤⠀⠀⠀⠀⡇
⠀⠀⠠⡇⠀⠀⠀⢸⣧⡶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡠⠀⠀⠀⠄⢠⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠶⠟⠋⠁⠀⠀⠀⢰⡇
⠀⠀⠀⡇⠀⠀⠀⢸⡇⢀⣠⡴⠃⠀⠀⠀⠀⠀⠀⠀⠐⠻⠆⠸⠄⠴⢧⠏⠷⠽⠿⠞⠀⠿⠞⠿⠀⠀⠀⠀⠀⠀⠀⢀⣏⣀⣠⡴⠆⠀⠀⠀⢸⡇
⠀⠀⠀⡇⠀⠀⠀⢿⡟⠋⠉⣀⠄⠀⠀⢀⡀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠋⠁⢀⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠇⠀⠀⠀⣾⣧⣶⠾⠋⠀⠀⠀⠈⠿⠸⠚⠸⠶⠇⠏⠄⠙⠞⠯⠃⠘⠆⠟⠟⠠⠗⠻⠶⠑⠊⠿⢸⣅⠀⠀⢸⣷⠶⠛⠉⢀⠂⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⣼⣇⣠⣴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⣀⣤⠾⠃⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⢹⡏⠉⣠⡶⠀⠀⠀⠀⠀⠀⠀⣤⠒⣀⣀⣠⣤⡀⣄⠀⡐⠠⢦⣀⠀⠐⠒⠒⠀⠤⠀⠀⠀⠀⠀⢈⡟⢉⣀⣠⡖⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡟⠉⢀⡄⠀⠀⠀⠀⢀⡀⢀⣾⠋⠉⠛⠛⠿⢿⣷⣷⣤⣢⡀⢭⠑⠚⢷⣶⣌⡇⠀⡀⣀⡀⠛⠛⠛⠋⣡⡆⠀⠀⠀⠀⡀
⠀⠀⠀⣷⠀⠀⠀⠀⠈⠳⣶⡋⢀⡌⠀⡖⠒⣾⣷⣄⠙⠷⣄⣿⠴⢟⠛⠉⠀⠈⢉⠉⠀⠁⠉⠂⠛⠋⠀⢠⡟⢤⣈⠛⠛⣿⡿⠋⠀⠀⠀⠀⢰⡇
⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠶⠟⠶⠛⠛⠛⠻⠶⠶⠾⣧⣬⣿⡥⠾⠿⠿⣟⡿⠷⢶⣦⣴⣶⠶⠛⠻⠶⠟⠛⠛⠋⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠉⠶⠶⣦⣤⣤⣤⣤⣤⡀⠀⡀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠛⠛⠃⠀⠀⢀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⡶⠶⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡧⠰⢽⢾⡇⠊⠏⠈⠿⠇⠹⠄⡧⢾⡄⠀⢿⣀⠜⠇⠇⠱⠙⠆⠹⠰⣦⣶⢶⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠟⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛

⣿⣿⠟⠋
⣟⣀
⣿⣿⡷
⣿⣁⡀
⣿⣿⡿⠄
⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⠀⣠⣾⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣾⣿⣿⣤⡀
⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣼⣿⣄⣀⣀⣤⣾⣿⣿⣁⣠⣤⣠⣤⣤⣤⣄⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⡐⠐⢶⠄⠦⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⠈⠡⡗⢤⢳⠄⣤⣱⠉⢨⠕⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠃⢹⣲⠇⠊⠀⠀⣼⣷⣦⣚⣙⡁⠀⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢧⡖⣸⣤⡾⠎⠀⠀⠀⠙⢯⣟⡟⣷⣿⣜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢉⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠝⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠰⠀⠨⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠒⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢺⣿⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⠈⠉⠁⣶⠆⠀⠀⣶⡆⠁⢸⣼⣏⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠠⢀⠄⠛⠳⣤⠴⡋⠗⢀⣼⡿⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢹⠗⡄⠇⠀⠀⠘⠀⠀⠁⠀⠘⢿⣷⣜⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠁⡄⢸⠀⠀⠀⠀⠀⢰⠀⡄⣎⣿⣧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣏⠀⢄⠀⣸⠀⠀⠀⠀⠀⠸⡁⠀⠏⣿⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⠎⢈⠁⠀⠄⠀⠀⢀⠀⠉⠀⢲⣿⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡔⠛⠃⠀⠂⠀⠀⠐⠀⠄⠀⠀⠘⣯⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠣⢀⣀⣀⣀⠀⠠⠤⠔⠓⠒⠒⠐⠒⠂⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠱⡄⠀⢀⣠⠄⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣿⡇⣼⣿⡯⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣴⢿⣷⣿⣷⣏⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠋⠁⠈⠙⢿⣿⣎⢻⣟⠎⠛⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠁⠀⠀⢀⠀⠈⢿⣿⣇⠙⠂⠀⠰⣌⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣦⣤⣾⣿⣿⡇⡰⠤⣉⠻⢆⠀⠀⣄⣈⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠏⠀⠿⠿⡋⠜⠀⠀⠀⠉⠒⢦⡄⠘⣮⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣚⡀⠀⠀⠀⠀⠀⠐⠊⠀⢠⣘⣿⣦⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢤⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠀⠀⠀⠀⠀⣀⡤⠀⡼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⣤⣤⠖⠚⠋⠁⠀⢰⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠙⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣀⠐⠙⢢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣷⣦⣠⣾⣿⣿⣶⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡏⡰⢋⣿⡿⢿⣿⣿⣧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⣿⣿⣿⣿⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠿⣿⡿⣿⣿⣿⡿⠻⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡀⠀⠀⠛⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣿⣆⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢾⡿⡿⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⡀⠀⠀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠚⡿⢰⡤⣦⠸⡓⠄⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠂⠈⠀⠀⠀⣀⣀⡐⢾⠦⢴⣅⠀⣄⠙⢿⠰⣸⠞⢁⡀⢠⣷⠴⣿⠖⣀⣀⠀⠤⠀⠁⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠣⢠⡤⠐⠚⠐⠊⣕⣤⣔⡀⠈⠁⠻⡄⢻⡷⣹⠃⡼⠋⡁⠀⢲⣤⣔⡍⠂⠐⠒⢠⣤⠼⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠖⠂⠶⠄⠀⠈⠑⠂⠛⣮⠿⢷⣾⣿⠈⣹⣿⣶⠿⣭⠟⠂⠒⠉⠀⠠⠶⠂⠚⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠨⠖⣺⡿⣿⡄⣿⢿⣯⡒⢄⠀⠀⠀⠀⡀⠀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢠⡘⢀⣴⠂⠀⠀⠀⠀⡽⢠⢹⣷⡿⠥⠹⡄⠀⠀⠀⠀⣾⣀⠘⣤⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢈⡻⠁⠁⠄⠀⠀⠀⠁⠀⡾⢻⢻⠆⠀⠃⠀⠀⢀⠌⠁⠹⡇⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣧⣠⠤⢀⠀⡀⠘⡇⠀⡀⠀⠀⠙⣠⠘⠀⠁⠀⡀⠨⠃⠀⡀⢠⠠⣤⣠⣿⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⡻⡧⠘⣾⡣⠒⠄⣀⠐⠀⠉⢲⣀⢤⡭⡥⢆⣴⠉⠁⠰⠀⠀⠕⢦⡻⠊⠰⣿⣙⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢻⣗⠡⠈⠈⣡⠀⣀⠂⠐⠀⠀⠀⢠⡎⢻⠛⡄⠀⠀⢀⠐⠐⢃⠀⢀⡉⠈⡰⢱⡷⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⡈⢹⣶⠳⠄⠨⢦⠙⣇⣰⢠⠌⡑⢳⢤⠟⢦⡔⢀⡀⣤⢰⣀⡎⣴⢮⠠⠞⣳⡟⢁⡄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠿⠶⣌⡓⢼⣦⡀⠀⢿⡻⣾⠓⠙⠋⠀⠀⠀⠈⠻⠗⢻⡾⣻⠆⢀⣀⣦⠘⣣⡴⠿⠧⠞
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠈⠀⠈⠩⡈⢁⠙⠳⣌⣛⠻⠆⢃⡤⣾⣋⣲⠦⣀⠋⠟⢙⣡⠴⠛⠁⠉⡄⠁⠐⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠂⠀⠌⢀⡀⠠⢙⣧⠴⣿⣷⣾⣷⣿⣾⣿⡶⣴⣟⠁⠀⠀⠀⠀⠐⠀⠀⠀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠐⠀⠚⠓⠒⠀⣀⣀⣦⣶⡿⠞⠛⢻⣿⣿⡀⣿⣿⣿⠛⠓⢿⣷⣴⣀⣀⣀⡒⠘⠓⠀⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣴⠾⠛⠛⠛⠛⠛⠛⡻⠛⢷⣄⡀⠀⢍⢻⣿⣽⢻⠀⢀⣠⣴⠟⠛⠛⠛⠛⠛⠛⠛⠻⣶⣄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠛⠉⠁⠀⠐⠂⠀⠂⡸⠁⠈⠅⣸⡿⢯⣴⡿⣿⡻⣦⣽⢿⣯⡠⠍⠀⢳⡐⠀⠀⠂⠀⠉⠉⠙⠛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣮⡀⡤⠀⠠⠘⠛⠆⠛⢁⠜⣡⣾⠋⣀⡞⠳⠾⣿⡷⠶⢹⣎⠈⢻⣦⡁⢀⠙⠢⠚⠃⠠⠀⠠⡄⣬⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠄⣠⠂⢀⠀⢰⡟⠮⠀⠸⠁⠀⠞⠛⢛⠂⠊⠙⠀⢹⠞⣷⠘⣤⠀⢦⡀⠤⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠀⠀⠀⣿⡄⢃⣠⠀⠀⠀⠀⣲⡁⠀⠀⠀⢠⣜⠃⣿⡀⠀⠀⢸⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢷⣤⣭⠭⢤⠀⠆⣿⠃⠀⣤⠼⢭⣥⣾⠟⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠾⠟⠛⠛⠀⠀⠀⠁⠀⠘⠛⠛⠿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣼⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⣿⣿⢟⠛⣿⡿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣞⣩⣷⣶⣦⣴⣶⣶⣦⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣶⣦⣤⣤⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣾⣿⣿⣿⠿⠿⠛⢛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡿⠿⠛⠉⠁⢀⣀⣠⣾⣦⣴⣦⣬⣿⣉⣉⣓⣤⠈⠙⠛⠿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⠿⠋⠁⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣷⣶⣄⠀⠈⠙⠿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡦⠄⠈⠻⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣤⣴⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠈⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠀⠀⡠⠃⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠒⠀⠀⠀⠹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⣶⣿⣧⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠁⠀⠀⠹⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣤⣾⠄⠀⢹⣿⣧
⠀⠀⠀⠀⠀⠀⣾⣿⡇⢀⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⠀⠈⣿⣿⡅
⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⣠⣤⣄⡀⠈⢻⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⠃⢻⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⣿⣿⣿⡇⠀⠀⣾⣧⣿⣿⣿⡆⠀⣾⣿⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⡙⣻⣿⣿⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⠀⢻⠂⠲⣿⣿⣿⣧⠀⠀⢻⣿⣿⣿⣿⠇⠀⢼⣿⣿⡀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⡇⠘⣿⣿⣿⣿⣿⠛⡤⢆⣀⣠⣿⣿⣞⢿⣆⣀⠀⠈⠉⠉⠁⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣷⠀⢻⣿⣿⣿⣿⣿⣧⣀⣿⣿⣿⣿⣿⣷⡙⠿⣶⣾⣷⣾⣿⡿⠟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣅⠀⠉⢙⣿⠃⣰⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣽⣤⣶⣿⣡⣴⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡄⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣶⣄⡈⠙⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣿⣿⣿⣿⣿⣟⣠⣴⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠿⠿⠿⠟⠋⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠠⠁