⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢷⢸⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣼⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠚⠁⠉⠉⠈⠑⠲⢤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡴⠋⠀⠀⡴⠋⠁⠀⠀⠀⠈⠓⢦⠈⢳⣄⠀⠀⠀⠀
⠀⠀⠀⢀⡾⠁⠀⠀⠀⠁⣠⣦⠀⠀⠀⣠⢤⠈⠁⠀⠹⡆⠀⠀⠀
⠀⠀⠀⢸⠇⠀⠀⡤⣤⢤⠛⠛⠀⢀⠀⠻⠟⣡⣀⡀⠀⣿⠀⠀⠀
⠀⠀⠀⢸⠀⠀⠈⠁⠉⠈⠀⠀⠓⢻⡞⠀⠀⠉⠙⠛⠀⣿⠀⠀⠀
⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀
⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⣀⡤⠤⣄⡀⠀⠀⠀⣴⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠁⣠⢶⣚⡉⠁⠀⠀⢹⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠸⠂⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣤⣶⣦⣄⠀⠀⠀⠀⢀⣤⣶⣤⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⣶⣦⣴⣿⣿⣿⣿⣿⡄⠀⠀⠀
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⠀⠀⣴⣿⠿⣿⣿⣿⣿⡿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀
⠀⣾⡿⠁⠀⠀⠀⣠⡄⠀⠀⠀⢀⣌⠉⠙⠛⠉⠉⠀⢻⣿⡄⠀
⢸⣿⠁⠀⠀⠀⣴⣶⣦⠀⠀⠀⣤⣯⣄⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀
⢸⣿⠀⣴⣶⣶⡿⠿⠟⠀⣀⠀⠿⣿⣯⣤⣤⣄⠀⠀⠀⣿⣿⠀⠀
⠸⣿⡄⠙⠿⠟⠃⠀⠘⠿⣿⡟⠀⠀⠻⢿⡿⠟⠀⠀⢠⣿⡇⠀⠀
⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀
⠀⠀⠈⠉⣷⡆⠀⣤⣤⡀⢀⣤⣤⡄⠀⣀⠀⠀⣼⣟⣉⡀⠀⠀⠀
⠀⠀⠀⠀⠙⣿⣷⢾⡟⣿⡟⠿⣶⣶⠿⠛⠁⣠⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠻⣿⣷⣿⣧⣿⣤⣤⣤⣴⣾⠿⠿⠿⠛⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⣁⢴⣾⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀
⠀⠀⠀⣠⠴⠊⠴⣾⣿⣿⣿⣿⣿⢿⣿⣿⠿⣿⢿⣿⡏⠲⣄⠀⠀
⠀⠀⠸⣇⡀⣀⢴⣿⣿⣿⣿⢷⣟⣬⣽⣯⣜⣷⣈⣿⣇⠀⢸⣷⠀
⠀⠀⠀⠀⠁⠀⢸⣿⢟⢻⣿⡿⠗⠋⠀⠀⠉⠙⠛⣻⡇⠉⠉⠁⠀
⠀⠀⠀⠀⠀⠀⣸⣿⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣤⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⣿⡿⠋⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠀⠙⠧⠤⠴⢿⣿⣿⣿⣿⣿⠛⠁⠋⠁⠀⠀⠀⠀

⠀⠀⠀⢠⠀⣄⠠⠤⠤⠤⠤⠤⣀⠔⡄⠀⠀⠀⠀⠀
⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀
⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀
⢀⠃⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⠀⠘⡄⠀⠀
⢸⠀⠀⠀⠀⠀⠸⣭⠂⠀⠀⢮⡵⠀⠀⠀⠀⡇⠀⠀
⠀⡆⠀⠐⠘⠀⠂⠀⠀⠊⠂⢀⣀⣈⣃⣀⣰⣁⠀⠀
⠀⠈⡆⢀⢀⣤⣤⣤⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠇⠀
⠀⠀⡇⠠⠊⠛⠄⠴⢡⠤⣤⡇⠀⠀⠀⠀⠀⢠⠀⠀
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠙⠓⠃⠀⠀⠀⠀⠀⠘⠀⠀

⠀⠀⠀⠀⠀ ⣀⣀⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⡾⠛⢻⣿⣿⣿⣿⠁⠀⠀⠉⢂⠀⠀⠀⠀
⠀⠀⠀⣿⣄⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⢨⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢨⠀⠀⠀⠀
⠀⠀⠀⡻⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀
⠀⠀⠀⠀⡄⠰⡶⠀⠀⠀⠀⠀⢶⠆⢀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⢑⡲⠤⢤⣤⣤⠤⠖⡆⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠤⠤⢄⡠⣀⠤⠤⠈⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⡞⠹⣦⠰⡞⠙⣆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢴⠀⠀⣿⠐⡇⠀⢻⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡸⣄⠀⣿⣨⡇⠀⣟⡀⠀⠀⠀⠀⠀
⠀⠀⢠⡶⠚⠉⢁⡀⠀⠀⠀⠀⠀⡈⠉⠙⠲⣤⡀⠀
⢀⡶⠋⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠈⠻⡄
⣾⠁⠀⠀⠈⠀⣠⣂⡄⠀⠀⠀⣔⣢⠀⠈⠀⠀⠀⢹
⡇⠀⠀⢠⣠⣠⡌⠓⠁⠀⡀⠀⠙⠊⡄⢀⣀⠀⠀⢸
⢷⡀⠀⠈⠁⠁⠀⠀⠈⠓⡓⠂⠀⠀⠉⠈⠁⠀⠀⡼
⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⢾⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢸⠀⠀
⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠊⠁⠀
⠀⠀⠀⠘⣇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠀⠀⠀
⠀⠀⠀⠀⢿⣼⠉⠉⠙⠛⠛⠛⠛⠉⢹⣁⠟