⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠈⠋⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⢦⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⡿⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⣷⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⡧⢕⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣿⣿⡄⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⠏⠃⠈⠉⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠐⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⣴⣴⣴⣄⣿⣿⣇⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣦⣤⣤⠌⣻⣦⣤⡀⢀⣤⡠⢔⡀⢀⣀⣉⢻⢿⣿⠇⠀⠀⠀
⠀⠀⠀⠀⢿⣿⠋⡟⠙⠛⠚⠘⠋⢉⠁⠈⠙⠋⠃⠿⠟⠛⠩⠹⣿⡿⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⡎⡐⠙⠓⠚⠉⠠⣾⡆⠀⢰⠀⠒⠒⠒⠂⡀⢺⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⡁⠀⠀⠀⡤⠔⡎⠂⠀⠈⡖⣀⡀⠀⠀⠨⠄⢿⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠈⣷⣿⣧⣠⡖⠁⠀⣿⣧⣀⣀⣠⣷⠀⠉⢦⣤⣤⣷⡗⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⣸⠉⠛⢿⣶⣄⡨⠻⢿⣿⣿⣅⣄⣶⣾⠿⠛⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⢿⣦⠀⠀⠈⠻⢍⠙⠉⠋⠋⠉⡿⠋⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠞⣦⠀⢬⢧⣄⣀⡁⠉⣀⣠⡽⠁⠀⡼⠅⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣄⡉⠛⠛⠛⠛⠛⠋⠀⢠⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠈⠀⠀⢀⢀⣤⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⠼⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡿⡱⡿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⡟⠟⠛⠁⠄⠂⠀⠓⠋⢟⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⠜⢖⣁⣀⣀⡀⠀⢀⣐⢠⣴⣟⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣷⣛⠿⠻⠉⠯⣉⠠⠹⠚⠺⠿⢿⣟⣿⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⢐⣿⣿⡿⡿⣿⣷⠆⠀⠐⠀⠀⠀⠀⢠⣼⣶⣿⣿⣿⣿⣿⡶⠀⠀⠀⠀
⠀⠀⠀⠘⣿⡟⠻⣋⢉⣉⠁⣀⢀⣄⣠⣄⡀⠀⣉⣉⣙⠻⢻⣿⣿⡷⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣾⡏⠑⠓⠉⢉⣾⣿⣿⣿⣯⠑⠚⠓⢛⣾⣼⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⢹⣿⡿⠻⠠⢤⣔⣼⣿⣿⣾⣿⣿⣲⣄⠀⠘⠻⣿⣿⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣿⣧⠀⣀⠟⠃⠡⣿⠿⠞⠽⣿⠈⠛⣶⣀⣇⣿⡿⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢹⣿⣾⣯⠃⢠⣴⣦⠀⠀⣠⣴⣦⡀⠘⣿⡷⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣾⡇⢠⡿⡿⠻⠁⢠⠸⠻⢿⢷⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⣿⡇⠊⣠⣤⣤⣤⣤⣶⣦⣤⣀⠃⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⣧⣬⡶⠀⠀⠀⠀⠀⠀⠸⣿⣦⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⡛⢟⢶⣶⣽⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⣴⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀