⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣟⣀⣤⣀⣀⠀⠁⠉⠉⠉⠓⠲⠶⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠁⢈⣁⡀⠀⠉⠛⠉⠙⠲⣆⣀⣤⣀⣀⠀⠈⠉⠙⠒⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⠃⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠉⠳⣦⣤⣤⣄⠀⠀⠉⠳⢤⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠏⠀⠀⠀⠀⠻⣤⠀⠀⠀⠀⠀⢀⣀⣎⠀⠀⠀⠀⠀⠈⠀⠀⠘⠳⢤⣄⡀⠀⠙⠳⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⡆⠀⠀⢀⠀⠀⠀⠘⢦⡀⠀⠀⠀⣸⡿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⠀⠀⠘⢷⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⣼⡇⠀⠰⡄⠀⠁⠀⠀⠀⠀⠈⠉⠉⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⣄⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣤⣄⢰⡇⠛⠓⠂⡽⠖⠛⠻⣭⣁⣾⠀⢰⣶⠀⣀⣙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠩⠛⠻⠿⠯⢵⣏⣙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠰⠛⣇⣠⡿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠉⠉⠪⣻⣶⡆⠀⠀⠀⠀⠀⠀⣀⣿⡿⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠄⣾⣯⠉⠉⠉⠙⠓⠒⠲⠶⠦⣄⡀⢠⣼⣀⣀⠀⠀⠀⠀⠀⠉⠙⠶⣆⡀⠀⢶⣾⠿⣿⣇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡟⠘⢧⡀⠀⠀⠀⠀⠀⠀⢠⡿⣩⠿⡇⠀⠈⠉⠛⠓⠶⢤⣤⣀⠀⣸⡟⣿⣿⣵⠦⣽⡟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⡇⠀⠀⣹⣶⣤⣀⣀⣠⠶⠛⠛⠉⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⠋⠉⠀⠀⢰⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡇⣸⣇⠀⠉⠉⠉⠈⠛⠷⢦⣤⣤⣄⣀⣀⡀⠙⢶⣄⣀⣀⣀⣠⣴⣿⡿⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⣿⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠓⠻⠿⠿⣿⢁⡾⠁⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀
⠀⠀⢠⣤⣤⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡜⣷⡀⠀⣀⣤⠴⠖⣲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⡟⠀⠀⠀⠀⠀⠀⢠⡏⣿⠀⠀⠀
⠀⠀⢻⡇⠀⠈⣷⠀⠀⠀⣠⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⣿⠸⣇⠘⢿⣿⡓⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⣼⠁⢺⡆⠀⠀
⠀⠀⣈⡷⠷⠖⠛⣿⡆⢸⡏⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⣧⢿⡇⠀⠈⠛⠶⣤⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡴⣿⣿⠁⠀⠀⠀⠀⠀⠀⢠⠇⠀⢸⣇⠀⠀
⢠⡾⠉⠀⢀⣤⡤⣬⣿⣮⡇⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⢷⡄⠀⠀⠀⠀⠉⠉⣻⣷⠀⠈⠉⠙⣿⡏⠁⣶⣿⠏⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠈⣹⠀⠀
⣿⡀⠠⠞⠋⠁⠀⠀⠙⢻⡟⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠯⠿⣦⣴⠴⢾⣿⡟⠉⠁⠈⠁⠀⢨⣿⡷⣿⣿⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢀⣴⠟⠀⠀
⢻⣇⠀⠀⣀⣤⠤⠤⢤⣤⣿⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠘⣇⠻⣦⣀⣀⣠⠴⣻⠞⠁⠉⣿⣷⡀⠀⠀⠀⣀⣉⣠⠴⠞⠉⠀⠀⠀⠀
⠀⣷⠀⠀⠀⠀⠀⠀⣠⣨⣽⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠙⠲⢬⣳⡮⠭⠭⠷⠚⠁⠀⠀⠀⠈⣽⡷⠶⠾⣏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢿⣀⣠⡤⠖⠚⠉⠉⠉⠉⣿⠏⢹⡀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢱⡟⠲⢤⣀⠀⠀⠀⠀⠉⠁⠂⠀⠀⠀⠀⠀⠀⣠⠏⠈⠀⠀⠜⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⢿⠁⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⣧⠀⠀⠀⠀⠀⠀⣴⠋⠀⢸⡇⠀⠀⣀⠉⠓⠂⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠈⢾⣧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣧⣀⣀⣀⣀⡤⠶⠞⣹⣧⠀⠸⡄⠀⠀⠀⣠⡿⠁⠀⠀⢸⡇⠀⠀⠀⠉⠐⠲⠤⠤⠀⠉⠉⠀⠀⠀⠀⠁⣿⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣷⡀⠀⣀⣀⢐⠒⡰⠿⣿⠀⠀⢻⡀⠀⢰⣏⠀⠀⠀⢄⠀⢷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠹⢿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢻⡇⠀⢨⠛⡼⣾⡇⣪⣿⡄⠀⠀⢳⣴⣟⠉⠻⣤⡀⠀⠳⣼⡆⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢀⠀⠀⠀⠐⠘⣿⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠸⡷⠀⡶⠛⠛⠛⠀⣰⣿⡇⠀⢀⠋⢽⢻⣄⠀⠈⠻⣆⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠻⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢿⢤⣈⣠⣤⠶⠞⠋⣽⣷⠀⠉⠀⢸⠀⠘⣷⠀⠀⢽⣇⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡿⣿⠀⠀⠀⡾⠀⠀⢸⣆⠀⣨⣿⡶⠋⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⣠⣤⣾⠏⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢸⠁⢻⡷⠀⢰⡇⢠⠾⠀⣫⡾⠋⠉⠀⠀⠘⢦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠓⠒⠒⠚⠋⠉⢻⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⠀⠀⣷⠀⡾⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⣾⠀⠀⠀⠑⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢰⡇⣀⡴⣿⢶⣁⣰⠾⠋⠀⠀⠀⠀⠀⠀⠀⢉⡿⠒⠀⠀⠀⠈⠉⠓⠦⣤⣀⡀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠛⠒⠒⠒⠚⠋⠉⠀⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠠⠦⠤⠄⠉⠉⠓⠂⠀⠀⠀⢹⡆⠀⠀⠀⣀⠀⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠒⠒⠒⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠓⠒⠒⠒⠛⠚⠛⠓⠂⠀⠀⠀