⣿⣿⡟⠁⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣿
⣿⣿⡇⠄⠄⠄⠐⠄⠄⠄⠄⠄⠄⠄⠠⣿
⣿⣿⡇⠄⢀⡀⠠⠃⡐⡀⠠⣶⠄⠄⢀⣿
⣿⣿⣶⠄⠰⣤⣕⣿⣾⡇⠄⢛⠃⠄⢈⣿
⣿⣿⣿⡇⢀⣻⠟⣻⣿⡇⠄⠧⠄⢀⣾
⣿⣿⣿⣟⢸⣻⣭⡙⢄⢀⠄⠄⠄⠈⢹⣯
⣿⣿⣿⣭⣿⣿⣿⣧⢸⠄⠄⠄⠄⠄⠈⢸
⣿⣿⣿⣼⣿⣿⣿⣽⠘⡄⠄⠄⠄⠄⢀⠸
⡿⣿⣳⣿⣿⣿⣿⣿⠄⠓⠦⠤⠤⠤⠼⢸
⡹⣧⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⢇⣓⣾
⡞⣸⣿⣿⢏⣼⣶⣶⣶⣶⣤⣶⡤⠐⣿
⣯⣽⣛⠅⣾⣿⣿⣿⣿⣿⡽⣿⣧⡸⢿
⣿⣿⣿⡷⠹⠛⠉⠁⠄⠄⠄⠄⠄⠄⠐⠛⠻
⣿⣿⣿⠃⠄⠄⠄⠄⠄⣠⣤⣤⣤⡄⢤⣤⣤⣤⡘
⣿⣿⡟⠄⠄⣀⣤⣶⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⡎
⣿⡏⠄⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿
⣿⡏⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⣿⣿⡟
⣿⡠⠜⣿⣿⣿⣿⣟⡛⠿⠿⠿⠿⠟⠃⠾⠿⢟⡋
⣿⣧⣄⠙⢿⣿⣿⣿⣿⣿⣷⣦⡀⢰⣾⣿⣿⡿⢣⠁

⠀⠀⠀⠀⡴⠋⢹⡏⠙⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⠏⠀⠀⠘⠀⠀⠀⠹⣄⠀⠀
⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢧⣀⡠⠤⠞⠙⠢⣄⠀⣇⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⡅⠀⠀⠀⠀⠀⠈⠩⡇⠀⠀
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢸⠀
⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢹⠀
⠀⠀⠀⠀⠀⠀⢸⡟⠆⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⣀⠀⡇⢧⠀⠀⠀⠀⠀⢸⡄⢀⡤⠤⡄⠀⠀⠀
⠀⡴⠋⠀⠀⠀⠙⡿⡸⡄⠀⠀⠀⠀⠐⣏⠀⠀⠀⠀⠙⡄⠀
⡜⠀⠀⠀⠀⠀⠀⣧⡃⢇⠀⠀⠀⠀⠀⠉⡆⠀⠀⠀⠀⠘⡆
⠹⡀⠀⠀⠀⠀⠀⠉⠳⠘⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⡠

⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⡟⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⡇⢣⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡧⣄⣀⣰⣀⣀⣣⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⣠⠤⠒⠒⠲⠶⡀⠀⠀⠀⠀⠀⣀⣇⡤⣤⡀⠀
⡇⠀⠀⠀⠀⠀⠀⠈⣇⠀⡔⠋⠁⠀⠀⠀⢸⠀
⡇⠀⠀⠀⠀⠀⠀⠀⣇⡏⠀⠀⠀⠀⠀⠀⠀⡇
⡇⠀⠀⠀⠀⠀⠀⡰⡝⠀⠀⠀⠀⠀⠀⢀⡇⠀
⠈⠓⠒⠐⠒⠉⠁⠛⢄⡀⠀⠀⠀⡴⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣮⣝⠿⠿⠿⣻⡟
⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠉⠀
⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⠉⠁⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠻⢿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⠻⠿⠟⠋⠑⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣌⠁⠾⠁⢠⣿⣿⣧⣶⣿⠟⠋⠉⠀⠀⠀⠈⠉⠛⠉⠙⠻⢿⣦⣄⠀⠀⠀⠀
⢻⣿⣿⣿⣿⣿⣿⣿⡽⠋⠀⠀⢀⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀
⠀⠀⠀⠀⢨⣿⡿⠋⠀⠀⠀⠀⢸⣿⣿⡟⠀⡄⠀⠀⠀⠀⢀⣶⣤⠈⢿⣧⠀⠀
⠀⠀⢀⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠘⣇⠀⢀⡾⠀⣿⣿⣿⠀⠘⣿⡇⠀
⣀⣴⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⠉⠁⠀⠙⠛⠁⠀⠀⢿⣿⡀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣪⠆⢇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁
⠉⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⣡⢾⠏⢰⠈⢧⠀⠀⠀⠀⠀⠀⢸⡇⠀
⠀⢰⣿⠟⠓⠤⣀⣀⡀⠤⠴⠂⠉⠠⢘⠕⠁⠰⠀⠡⡀⠳⡄⠀⠀⠀⠀⠸⣧⠀
⢠⣿⠏⠀⠀⠀⠀⠀⢀⣀⠤⠒⠭⠊⠁⠀⠀⠀⢃⠀⠑⢄⠈⠢⣀⠀⠀⠀⢈⣿
⣯⡟⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠉⠀⠀⠛⣶⣶⡿⠟

⠀⠀⠀⠀⠀⢀⡴⢹⠙⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣸⠀⠘⠀⢸⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⡧⢤⣤⣤⠴⢻⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀
⠀⠀⣀⠤⢄⣰⠀⠀⠀⠀⣸⠂⠉⠲⡄⠀
⠈⣹⠁⠀⠀⠈⣧⠀⠀⠘⠊⠀⠀⠐⢺⠂
⠐⢻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠒
⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢱⠋⠀
⠀⠀⠈⠻⠦⠴⡤⠒⠈⠀⠒⠒⠚⠧⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀