⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠋⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⣘⣶⢤⣶⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢠⢎⣼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⣠⣧⣾⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⠿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡗⢿⣿⣿⣿⣿⠏⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢇⣠⣿⣿⣿⣿⣿⣿⢿⣷⣿⣿⣿⣿⠼⠟⠁⢘⣻⢿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠞⣾⣿⣾⡏⢹⣿⡿⡄⠙⣾⠿⠿⠛⠀⠀⢀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣰⢏⣴⣿⣿⣿⡷⢸⣿⡇⠘⢾⡁⠀⠀⠀⠀⢤⣍⠛⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡴⣧⣾⣿⣿⣿⣿⣷⣿⣿⡇⠀⢸⠈⠁⠀⠀⠀⠼⠋⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡤⣞⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⡀⢸⠀⠀⠀⠶⠶⡶⢀⣼⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀
⠀⢀⡤⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣾⣅⡀⠀⠀⠀⣠⣿⣿⣿⣿⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⣴⣽⣿⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⠠⠘⣿⡹⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠊⣱⠿⣻⠏⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠐⠀⠸⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡜⢡⡞⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣹⣖⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⡏⠀⠀⣠⠖⣋⣉⣉⣙⣛⡟⠛⠒⠺⣿⡉⠉⠀⠀⠉⠉⠉⠀⠀⠙⠛⠻⠿⠿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡏⠀⠀⢰⢡⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣶⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⡟⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣧⣄⣠⠤⠤⠤⠤⢶⣦⣄⠀⠀⠀⢠⠤⡄⠀⠀⣽⠀⠈⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⣹⠁⠉⠙⠒⠶⢦⣄⡠⠤⠝⠳⣄⠀⠀⠀⠀⠀⢀⡟⡀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠱⠀⢰⡇⡇⠀⠀⠀⠀⢻⣦⡀⠀⡘⠀⢰⠃⠀⠀⠀⠀⠐⢤⠏⠙⠷⣦⡀⠹⣦⡀⠀⠀⣠⡾⡞⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣷⣷⡇⠀⠀⠀⠀⢸⣿⣿⣦⣧⠀⡏⢀⢀⠴⠋⠁⠀⠀⠀⠀⠀⠈⠻⣷⡿⣿⣿⣾⣿⢤⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⠟⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⡇⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣾⣿⣿⢾⠿⠿⠿⢷⣶⣶⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⡇⠀⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡝⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋⠀⠈⣆⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⡀⠀⠻⡆⠀⠀⠀⢸⡏⠻⣿⣿⣿⣿⣿⣦⣤⣀⣀⣀⣠⣤⣶⣿⠟⠋⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢧⠀⢠⢹⠀⠀⠀⢸⠇⠀⠹⣿⣿⠹⣿⡟⠉⠉⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠳⢼⠈⣇⠀⠀⢸⠀⠀⠀⢻⡿⠀⠸⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⢸⠀⢸⡀⠀⣸⠀⠀⢀⠞⠁⠀⢀⡏⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣦⠀⠀⠀⠀⠀⠀
⣿⣆⠀⠀⢸⠃⡆⡇⠀⡿⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠈⢳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⡑⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣄⡀⠘⠀⣷⡄⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⠄⠀⡇⠁⠀⢸⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀