⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⡀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀
⠀⠀⣆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢸⡇⠀⠀⠀⠀
⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⢸⣾⣇⣀⣀⣀⣀
⠀⠀⣿⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣷⣉⣉⣉⣉⣉
⣦⣶⣿⣦⠀⣸⠇⠀⠀⠀⠀⠀⢀⣠⣤⣼⡦⠀⠀⠀⠀⠀⢶⣿⣤⡀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉
⣿⣿⣿⡿⢠⣟⡆⠀⠀⠀⠸⣶⠟⠋⠁⠙⠃⠀⠀⠀⠀⠀⠛⠉⠉⠻⣷⣠⢀⠀⢠⢰⣞⣇⠀⠀⠀⠀
⣿⣿⣿⣧⣿⣿⣿⣼⡄⠀⣶⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⡟⠀⣿⢾⣿⣿⣆⠀⠀⠀
⠿⠿⣿⠿⠿⠏⢿⣿⣿⡶⣽⡿⠿⠀⠀⢀⣠⣤⣤⣤⣤⣄⡀⠀⠀⢰⣿⢿⣧⣾⣿⣿⡟⠉⠛⠉⠉⠉
⠀⠀⣿⠀⠀⢸⡏⢿⣿⣿⢿⡀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⣸⠯⣿⣿⣼⢹⡏⠉⠉⠉⠉
⠀⠀⣿⠀⠀⢸⡇⠈⣿⣟⣮⢷⡀⠀⠀⠸⣦⣀⠀⠀⢀⣠⡟⠁⠀⠀⣠⣯⠞⣱⣿⡏⢸⡇⠀⠀⠀⠀
⠀⠀⣿⠀⠀⢸⡇⠀⠀⠉⠈⢻⣿⣦⡀⠀⠀⠉⠛⠛⠋⠁⠀⠀⣀⡴⣿⠁⠀⠛⢻⡇⢸⡇⠀⠀⠀⠀
⠀⠀⣿⠀⠀⠸⠷⠶⠶⠶⠶⢾⣿⢿⣙⣷⢦⣄⣀⣀⣀⣤⢶⡿⣹⣿⡷⠶⠶⠶⠾⠇⠘⠷⠶⠶⠶⠶
⠀⠀⣿⠀⠀⢰⡶⠶⠶⠶⠶⠾⢿⣟⣿⣿⠓⠶⠭⠭⠵⠞⢻⣿⡿⠿⠷⠶⠶⠶⢶⡆⢠⡶⠶⠶⠶⠶
⠀⠀⣿⠀⠀⢸⣇⣀⣤⣤⠤⠶⠾⠟⢹⣿⠀⠀⠀⠀⠀⠀⣿⣿⠙⠳⠶⠦⣤⣄⣸⡇⢸⡇⠀⠀⠀⠀
⠀⠀⣿⠀⣠⠾⣿⣿⣇⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣹⣿⡿⢧⡀⠀⠀⠀
⠀⠀⣿⢰⠏⣴⣿⣿⣿⡆⠀⠀⠀⠀⠀⠹⣆⠳⣄⣠⡴⢖⡾⠁⠀⠀⠀⠀⠀⣰⣿⣿⣿⡌⢷⠤⠤⠤
⠀⠀⣿⣿⠀⡽⢣⣿⣿⣿⣆⠀⠀⠀⠀⠀⢹⡦⠶⠧⢤⡾⠁⠀⠀⠀⠀⠀⣴⣿⣿⣏⢷⣅⢸⡦⠤⠤
⠀⠀⣿⡇⠀⠀⢸⡇⣿⣿⣿⣷⣦⣄⣀⡀⠀⢻⡄⢀⣾⣁⣀⣀⣠⣤⣴⣾⣿⣿⡇⣿⠀⠉⠀⡇⠀⠀
⠀⠀⣿⡇⠀⠀⠈⠁⣿⣿⠋⠻⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⠿⠛⢹⣹⠁⠀⠀⠀⠀⣷⠀⠀
⠀⠀⣿⡇⠀⠀⠀⠀⢻⡟⠀⠀⠀⠙⠓⠒⠚⣿⠋⠉⢻⠷⠦⠾⠋⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣀⣠
⢀⣀⡟⢰⡀⠀⣤⣤⣸⡇⠀⠀⠀⠀⠀⠀⠀⣹⡏⣿⡙⣦⡀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⢀⣻⣤⣤
⣿⣿⡇⠀⢙⣷⠼⠿⣬⢽⣷⡀⠀⠀⠀⠀⢠⣿⡇⠈⠃⠈⠻⣄⠀⠀⠀⠀⢰⡇⠀⢠⣶⣧⠞⢉⡇⠀
⣿⣿⣇⠀⠘⢿⣍⣩⡍⢷⣿⡅⠀⠀⠀⠀⣼⢻⣇⣤⣄⢀⣠⣿⣶⣦⣄⣀⣸⣡⣴⠞⠋⠀⠀⢸⡇⠀
⣿⣿⣿⠀⠀⠀⠿⣭⣭⣉⣻⣷⠀⠀⠀⠀⢿⣼⠟⢁⡾⢿⡍⠈⢿⣿⣿⣽⣟⣉⠀⠀⠀⠀⠀⣼⣀⣀