⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⡶⠶⠾⠿⠿⠿⣶⣤⣄⣴⡞⠋⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢀⣠⡶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣦⣀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠤⠀⠒⠒⢺⣷⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⡛⠛⠷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠊⠀⠀⢀⣠⡴⠟⠛⠋⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠀⠀⠀⣠⡟⠉⠀⠀⠀⠀⣠⡶⠀⢰⡟⠀⠀⠀⠀⢰⣦⠀⠀⣄⠀⠀⢀⡀⠀⢀⣦⡀⠀⠀⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⢀⣼⠋⠀⠀⠀⠀⢀⡼⠃⠀⠀⣿⠁⠀⠀⠀⠀⠀⣿⡄⠀⢻⣇⠀⠈⣿⡀⠀⣿⠀⠀⠀⣿⠘⣷⡉⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⡿⠁⠀⠀⠀⠀⢠⡞⠁⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠻⡆⠀⠘⣧⠀⢻⡆⠀⠀⢿⡄⢹⣧⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡿⠁⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠙⢦⡀⠘⣦⢸⡇⠀⠀⢸⡇⠀⢻⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⡇⠀⠀⠀⣴⡆⠀⣧⣤⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠙⢦⡈⢿⣇⠀⠀⠸⣧⠀⠘⣿⣿⣧⣤⣀⣀⣀⣀⡀⠀⠀
⠀⠈⣇⠀⠀⠀⣿⠀⠀⣧⣿⠀⠀⠀⠀⠀⠹⢷⣤⣀⠀⠀⠀⠀⣤⣙⣷⣄⣀⣀⣀⣒⣸⣿⣀⣀⠀⣿⣄⢰⣿⣏⠉⠉⠛⠛⠻⠿⠿⣷⡄
⠀⠀⠻⣦⡀⠀⣿⠖⠒⠛⣿⡖⠒⠒⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⢹⡏⠉⠋⠀⢿⠉⢻⣿⣿⣿⣿⣿⣶⣤⣤⣤⣿⠃
⠀⠀⠀⠈⠙⢶⣿⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⠀⠀⣿⣿⣤⡉⠛⢿⣶⣿⠉⠁⠀
⠀⠀⠀⠀⠀⠈⣿⢤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣶⣷⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣶⣶⣼⣿⣶⠿⠀⢸⠀⣰⡟⠀⠙⢿⣦⣀⣹⣿⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡇⠀⠩⣿⣿⠿⠿⢿⣶⣛⣿⣿⣭⣿⠆⠀⠀⠀⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣟⠀⢸⣿⡟⠁⠀⠀⠀⠘⠛⠛⠉⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡇⠀⠘⣿⡟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⢻⡟⠛⠃⢸⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣖⣶⠀⠀⠀⣇⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⣾⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⣾⣿⢀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢿⡄⠀⢰⣿⠀⠈⠙⠦⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠞⠛⢿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⣷⡀⢸⣿⠀⠀⠀⠀⠀⢸⡿⠙⠛⠛⠻⣿⣷⣶⣶⣿⡟⢻⡿⠀⠀⠀⠘⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣾⣿⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⣧⡿⠁⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⣿⣿⡏⠈⠿⣿⣿⣇⠀⠀⠀⣰⡟⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⢀⣨⣽⣿⡇⠀⠀⠈⡟⠙⠷⣦⣴⡟⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⡟⠉⠁⢸⣷⣶⣶⣶⡇⠀⢀⣼⣿⣶⣶⢶⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣷⡄⠀⢸⣿⠀⠀⢹⣧⣶⡿⠛⠉⠀⠀⠀⠙⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠈⠛⢷⣼⣿⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢃⣼⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⣆⡀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣾⠏⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣷⣶⣿⠿⠛⠛⠿⢷⣶⣴⣦⣤⣶⣶⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀