⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠛⠛⢿⣿⣦⠀⠀⣐⣤⣤⣶⣴⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣶⣿⡟⠁⠀⠀⠉⠛⠿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⠃⠀⠀⠀⠀⠻⣿⣿⣿⠿⠟⠛⠉⠉⠙⣿⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠉⠉⠉⢉⣿⣿⡅⠀⠀⢠⣤⣤⣤⣹⣿⣇⠀⠀⠀⠀⠀⠀⠸⣿⡇⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⠀⢀⢠⣿⡟⣩⣿⣿⠿⣿⣿⣶⣤⣤⣤⣤⣤⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣧⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠢⠻⣿⣿⡏⠀⠀⠀⠉⢻⣿⡟⠋⠛⠛⢿⣿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣾⣤⣤⣾⣾⣿⡅⠀⠀⠀⢠⣼⣿⣷⣆⠀⠀⢈⣻⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡠⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠉⢻⣿⣦⣤⣤⣾⣿⣯⣾⡟⠀⢀⢹⣿⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⢺⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣏⠋⠉⠁⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢊⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣴⣶⣿⠟⢻⣿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠉⠉⠉⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀
⣴⣶⣶⣷⣿⣿⣷⣶⣶⣤⣄⣀⠰⠟⠉⠉⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⠀⠀⠀⠀⣠⣤⣼⣿⣷⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠸⣿⣧⣼⣿⠿⠛⢿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠶⣶⣄⠀⠀⠀⠀⠀⠀⠿⣿⡿⠀⠀⠀⠀⠀⠉⠉⢩⣿⡿⠉⠉⠉⠙⠁
⠀⠀⣀⣤⣶⣿⣿⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣮⣬⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⡃⠀⠀⠀⠀⠀
⠀⢀⣾⡿⠋⠉⠙⣿⣧⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⠿⢿⣶⡦⠀⠀
⠀⠘⣿⣧⠀⠀⠀⠀⠙⠀⠀⠀⠈⠿⠿⠿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⣿⣿⡃⠀⠀⠀⠀⠀⠀
⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣈⠙⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⡿⣿⣦⣄⡀⠀⠀⠀⠀
⠀⠀⠀⠈⠙⢿⣿⣶⠀⠀⠀⢀⣴⣿⠟⠛⠻⠁⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠋⠀⠈⠙⠻⠿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣽⣿⡏⠀⠀⠀⠸⣿⣇⠀⣀⣠⣤⡄⢸⣿⣿⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⠟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⣿⣿⡀⠀⠀⠀⠙⠿⣿⠿⠟⠋⢡⣿⡿⠉⢻⣿⣿⣿⣿⣿⣿⠟⠛⣿⣿⣿⣿⣿⣿⣰⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⡀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠃⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠈⣻⣿⠛⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣷⣶⣶⣶⣿⡿⠟⢻⣿⣧⣀⠀⠀⣰⡚⢶⡀⢠⣠⣶⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠹⣿⣿⠿⣷⣾⣿⣿⡿⠿⢟⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣶⠿⣷⣴⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⠿⠿⣿⣿⣿⣿⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣾⡿⢻⣿⣛⠲⠶⣶⣍⢿⣿⣿⢠⣮⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣿⡏⢩⡿⣤⣈⠉⠲⣷⣟⢿⣧⠹⣧⠹⡿⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⢘⢸⡇⠀⠉⣷⣄⠈⢄⣸⣿⡆⢻⣧⠈⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣏⣈⣌⢻⡄⠀⣍⡙⣦⡂⢻⣿⠀⢸⣿⣧⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣄⠻⣄⠹⣦⡀⠙⢾⣿⣮⣿⡤⣼⣿⣽⣇⠸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠙⣦⠹⣯⠯⣿⡷⢤⣽⣿⣿⡏⢻⣿⡿⠻⣆⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣽⣿⡟⣉⣉⠷⣌⢧⠀⠈⣭⣿⣿⣿⡇⢸⢻⣇⠀⣿⡼⣿⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡛⢿⡗⠈⠛⠳⡀⠀⠛⠚⠨⣽⡎⣾⣿⣴⣿⣧⢿⡆⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣱⣿⣿⡿⡟⣿⣼⣷⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢳⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⢹⡜⣿⣿⡄⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣿⢸⣿⣦⣀⠀⠀⠀⣀⣼⣿⣿⡿⢻⣿⣧⠀⢷⠹⣿⣧⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣷⠟⠉⢠⡍⣿⣶⣿⣧⣼⣿⠟⠓⠛⣿⣿⣧⠈⢧⠙⣿⣣⡀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⣿⣿⠃⠀⠀⣾⡿⣡⣿⢯⣹⣿⠵⠖⠒⠶⣿⣿⣿⣧⠈⠆⠹⣯⡱⡄⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢰⣷⡇⠀⠀⠀⢀⣴⣿⣿⡾⠋⠀⠀⠀⡀⠀⠹⣿⣿⣿⡆⠀⠀⠘⣧⠘⢦⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣿⣿⠁⠀⣠⣶⢟⣽⢫⡟⠀⠀⠀⠀⠀⠘⡆⠀⣿⣿⣿⣿⣷⡀⢲⡌⢧⡈⠳⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⣾⣯⣭⣴⡿⠋⢹⣿⣿⣿⠃⠀⠀⠀⠀⠀⢠⣷⣾⣿⣿⣿⣿⣷⡳⡀⠻⣮⠻⣦⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢡⣾⣻⣿⣿⡏⠀⠀⢸⣾⢃⣟⠀⠀⠀⠀⢀⣠⣿⡿⢋⣿⢿⣿⣿⣿⣷⡙⢦⣸⣷⡌⠻⣿⡘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣡⣿⣵⡏⠙⣿⡇⠀⠀⠸⣇⣼⠏⢀⣠⠴⣺⢽⣿⡟⠋⢉⣿⢸⣿⣿⣿⣿⣷⡌⢳⡄⠙⣦⣿⣿⣦⣝⢦⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣾⣿⣿⣿⣇⠀⠉⠁⠀⠀⠀⣿⠳⠛⢉⢴⣾⢿⣿⠛⠀⢀⣞⡿⣼⣿⣿⣿⣿⣿⣿⡀⢻⣦⠘⣷⣝⢟⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀
⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢟⣽⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢹⣯⣠⠾⠋⢡⡾⠁⠀⠀⣼⣿⡇⢺⣿⣿⣿⣿⣿⣿⣷⡀⠙⣷⣌⢻⣷⡌⢿⣷⣍⠛⠶⣄⠀⠀⠀
⠀⢻⣦⡀⠀⠀⠀⠀⠀⣀⡤⠞⢋⣴⡿⣻⣿⣿⣿⡐⣿⣷⠀⠀⠀⠀⠸⣷⣍⠻⣶⣿⠁⠀⠀⣸⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⢿⣷⣿⣿⣿⣿⣿⣦⠀⠈⢳⡄⠀
⠀⠀⠙⠛⠿⠷⠞⠛⠋⠁⣠⣾⠟⢉⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⠏⡀⠀⢰⣷⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣄⠸⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃⣴⣿⣿⣿⣿⡿⡋⠙⣿⣿⣷⡀⠀⠀⠀⠀⣻⡟⣿⡆⣷⢀⣼⣽⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⢹⣿⣿⣯⠻⣿⣿⣿⣟⣦⣿⠀
⠀⠀⠀⠀⠀⠀⠀⣰⡿⢋⣴⣾⣿⣿⣿⣿⣿⣇⢧⡀⠈⢻⣿⣿⣄⠀⠀⣠⡟⠀⠸⣿⣾⣿⣿⣿⣿⣿⣿⣧⢹⣟⣿⣿⡏⣿⣿⣿⣿⡇⠘⡏⣿⣿⣿⡄⠹⣿⣿⣿⡾⣿⠀
⠀⠀⠀⠀⠀⠀⣰⡿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣷⣿⣶⠢⢻⣟⣝⣷⡾⣋⠀⠀⠀⠙⢿⣿⡘⢿⣿⣿⣿⣿⣾⣿⣿⡏⣇⣿⣿⣿⣿⡇⠀⣿⢿⣿⢿⢱⠀⢻⣿⣿⣿⡹⡄
⠀⠀⠀⠀⢀⣾⣯⣼⡟⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⠛⠁⠀⠀⠀⠀⠈⣿⣷⣰⣿⣿⣿⣿⢻⣿⡿⠀⢸⣿⣿⣿⣿⡇⠀⣷⣾⣿⣿⢸⠀⠈⣿⣿⣿⡇⡇
⠀⠀⠀⢀⡞⣹⣿⣿⢠⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣷⢿⣿⡄⠀⠀⠀⢀⣀⣀⣀⣤⢿⣿⣿⣿⣿⡿⢃⡾⢻⣧⣠⣿⢿⡿⣿⣿⡇⠀⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⣿⠁
⠀⠀⠀⢸⠁⣿⣿⡟⢸⣿⢸⢻⡏⣿⣿⣿⣿⣿⣿⡇⢻⡿⣦⣿⣷⣶⣶⣮⣭⣭⣽⣶⣿⣿⣿⣿⣿⠛⢻⡿⣦⣄⠿⣿⡡⠞⢡⣿⣿⠁⣼⣿⣿⣿⢧⠇⠀⠀⣿⣿⡿⠁⠀
⠀⠀⠀⠸⣆⣿⣿⡇⠈⣿⡼⡼⣷⢻⣿⣧⠹⣿⣿⣷⡀⢑⣾⡿⠛⠿⠟⣿⡿⢛⣿⣿⣿⣿⣿⣟⢩⡆⠀⣻⣦⢝⣷⣬⡻⣦⠉⣽⠇⣰⣿⢿⣿⠏⡜⠀⠀⣸⣿⠏⠀⠀⠀
⠀⠀⠀⠀⠙⢿⣿⣷⠀⠙⢿⡳⡹⣎⠻⢿⡷⢌⠓⠋⣩⣾⠟⠃⣀⡴⠊⢁⣴⣾⠅⢀⡿⢋⣼⣿⣾⡇⠀⣷⢿⣯⣿⣿⣿⣿⣷⠃⣴⡿⢣⣿⢏⡼⠁⠀⣴⣿⠟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠙⠦⢌⠁⠀⣀⣀⣤⡞⠋⢁⡴⠞⠉⢀⣴⠞⠁⠁⣴⡟⠁⣸⣿⣿⣿⣧⢰⣿⡿⣿⣿⣿⣿⠟⣡⣾⣟⣱⣿⣣⠾⠤⠴⠿⠛⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣆⢀⣀⣤⣴⡾⠿⠛⠉⣁⡤⠞⠋⣀⣤⡾⠛⠁⠠⢡⡾⠋⠀⢰⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⢟⣡⣾⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣏⡉⠀⢀⡠⠶⣻⠍⣀⣴⣾⡿⠋⠀⠀⣠⣾⡟⠁⠘⢀⣿⣷⣿⣿⣿⣿⣾⠿⣟⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣍⡛⠛⢵⣾⣿⣿⣿⣿⠟⠉⠀⣠⣴⣿⣿⠏⠀⠀⢰⣿⠏⣻⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⠟⠁⣀⣴⣾⣿⣿⡿⠋⠀⠀⣴⣿⠏⣼⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡿⠟⢁⣠⣾⣿⣿⣿⣿⡟⠁⢀⣤⣾⣿⣯⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀