⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠦⣿⡫⠊⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣴⠟⣡⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣠⡿⠀⣰⠃⠀⠀⢀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠰⡀⢠⡍⠛⢷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢡⢳⠑⢠⡏⠀⠀⠀⠘⡆⢰⡀⠀⠀⢎⢧⡀⠀⢠⡀⢱⠀⣱⢀⡑⣞⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢣⡎⠀⠀⣾⡇⠀⠀⠀⠀⣧⢨⡇⠀⠰⠻⡌⣷⡘⢇⢧⠈⡇⠁⣇⠙⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡟⢱⠁⡀⢰⣹⡇⢰⢢⢰⠀⢸⡜⣾⡈⢦⠀⠀⠘⣷⡀⢸⡆⣿⠀⢸⣄⢾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⣷⣹⢰⡇⣸⠟⡇⢸⣼⡆⣧⠀⢻⣿⣳⡈⠳⣄⠀⠸⣷⠘⣧⣿⠀⢸⠘⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⣇⢿⢸⡇⣿⠀⢿⡜⣿⢻⣽⣦⠈⢿⣧⠻⣶⣌⠻⣦⡳⡇⣿⣿⠀⢸⡗⣼⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⢿⣿⠸⣧⣿⢀⣀⣻⣿⣆⠛⠿⣷⣷⣿⣆⠈⠑⣯⢖⣽⡿⣿⣿⠀⣿⣇⣯⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⣏⣧⣇⢿⣿⡟⣿⣿⢿⡟⠇⠀⠀⠀⠉⠙⣫⣿⣿⣿⡷⣿⣿⡏⣰⠁⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣼⡬⣭⣿⣜⣿⠋⠙⠛⠛⠃⠀⠀⠀⠀⠀⠀⠈⠻⣫⣻⠣⠞⡿⣰⠃⣰⢧⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢍⠙⢱⣿⣵⡟⣿⠹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢫⣾⡟⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣷⢟⣿⢿⡵⠛⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣽⣯⢿⠩⢷⣿⣷⢸⢩⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⢁⡾⠁⣼⢮⡟⢫⡏⠳⡀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣰⡟⢯⣤⡓⡟⢿⡝⠻⢷⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣬⣤⠴⡇⢱⣇⣀⣀⣀⠈⠢⣀⠀⠀⠈⠉⠉⠁⠀⠀⢀⡠⠞⠻⡇⠀⣿⣿⠷⣪⣷⣤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠁⠀⣷⢪⠋⡩⠂⠉⠭⠽⢬⣵⢤⡀⠀⠀⣀⠤⢲⣭⠀⠀⠀⠉⡰⣹⣿⠀⢸⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⢯⡏⠀⠀⢫⠁⠀⠀⠀⠀⠀⢳⢿⣿⣶⣬⢅⣩⢤⣶⣟⢳⣧⠀⠀⢰⢱⠙⣿⠀⠀⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣼⠋⣆⠀⢸⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣼⣻⣎⣿⣿⣧⣻⢦⠄⡇⣇⠀⢿⡆⡇⢏⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣄⣀⣀⣀⣠⣹⢯⣠⣿⣾⣿⣿⣶⣶⣶⣿⣿⣿⣿⣟⣿⣇⢿⣿⣿⢎⢿⣫⡞⠁⢸⡞⣿⠀⠸⣷⣧⠸⣸⣹⣥⣀⣀⣀⡀