⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠈⠛⢷⣄⠀⠙⠷⡄⠀⠀⠀⠀⠀⠀⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠘⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠈⠙⢷⠄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀
⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠈⢷⣄⠀⢀⣀⣤⣤⡀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀
⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⢴⣷⣤⣤⣶⡿⣿⣿⠛⠋⠁⠀⠀⠀⠀⠘⣿⠀⠀⠀ ⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀
⣼⣿⣧⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⢷⣤⣀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀
⢿⠻⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢦⣤⣄⣀⢸⣧⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀
⢸⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀
⢸⡀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⢶⡿⠿⣿⠟⠛⠛⠛⠛⢿⣧⡀⠀⣿⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣷⡶⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢻⣷⡀⣿⡏⠀⠀ ⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀
⣄⣻⣾⣿⡇⠈⠛⢷⣤⣶⣤⣤⣤⣴⠷⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⢸⣿⣷⡿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠘⡆⠀⠀⠀⠀
⠈⠙⠛⢿⣿⡀⠀⠀⠉⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣤⣴⣶⠿⣿⡿⠁⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⣧⠀⠀⠀⠀
⣦⡀⠀⠈⠻⢿⣶⣤⣤⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡋⠀⠀⢀⣀⣠⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠀⠀⠀⠀
⠈⠻⣦⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⣿⣿⠟⠉⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⠀⠀⠀⠀
⠀⣤⡘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⣠⠶⠶⠺⠿⣶⡄⠀⠀⠀⢀⣠⣾⡿⠃⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀
⢸⣿⣿⡈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⠛⠋⠉⠀⠀⠀⠀⠀⠘⣿⣦⣠⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀
⣿⣿⣿⣷⡀⠙⢿⣦⣄⣀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀
⣿⣿⣿⡛⠿⢦⠀⠀⠉⠛⠻⠿⢷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢀⣿⣇⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀
⣿⠿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠑⢶⣿⣿⣷⣼⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢹⣿⡇⠀⢀⣠⣴⣿⣿⣿⡀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀
⠉⠀⠀⠹⣿⣿⣿⣿⣦⣀⠀⢷⡀⠈⠙⢻⣿⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⢿⣿⣧⡈⠙⠛⠛⠁⠀⠀⡼⠁⠀⠀⢻⣧⡙⢿⣿⣿⣿⣿⣿⡏⠀⢀⠀⠙⣿⣿⣿⣿⣿⢻⣿⣿⡿⠿⣷⣀⠀⢀⣰⡟⠀⠀⠀⠀⠀⠀