⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⣯⡿⣷⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣾⠏⠤⠖⢈⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣤⣍⣇⣹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠿⠿⢋⣠⣴⢞⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⠇⠀⠀⢀⣐⣶⣶⣶⣤⢄⠀⠀⠀⠀⢀⣠⠤⣀⣠⠴⠟⠃⣠⣾⣿⠍⣠⣾⡿⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⣿⣿⣾⣿⣿⣿⠟⣉⣬⣥⣿⣿⣿⣿⣄⣀⣀⣀⣉⣛⣛⡻⠷⠶⢾⣛⡥⠾⠟⢁⠞⣀⣼⡿⠟⠉⣠⡿⠋⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣷⣄⠀⠙⢋⡉⣀⣠⠶⢋⡴⣛⣏⣠⣶⣾⠋⣡⡞⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣺⣿⠟⠏⢸⣿⣿⣿⣍⠻⣿⣿⣿⣿⣿⣿⣿⡿⣧⣬⣙⠻⢷⣤⢀⣉⣭⣵⡶⠟⣛⣭⡿⠛⣿⢋⣰⣿⡷⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣏⡆⢠⣾⡇⠀⣿⣻⠇⢹⣿⣿⣿⣛⣿⣿⣷⠈⣿⠿⠶⣦⣝⡿⣍⠛⠛⠻⠿⠟⣛⡁⠐⢃⣾⣿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢼⣧⣿⣿⠀⠀⣈⣿⣧⠀⠙⣿⣿⣿⣿⣿⣿⣦⠙⡇⠀⠀⠙⠛⠛⠿⠶⢶⣶⣶⣿⠷⣲⡿⠛⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠓⣾⡏⢹⣿⠀⠘⣿⣿⣿⡆⢀⣽⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢯⣥⣶⣯⣶⣾⣷⣤⠴⣿⣿⣽⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣶⢦⣤⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡟⢀⣼⣿⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣭⣹⣿⣿⣿⡿⠿⡿⠉⢩⣿⣿⠂⠀⠀⠀⠀⠀⢀⣶⣷⠎⢩⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⡶⠟⢻⣿⣿⣿⣿⣿⡿⢋⣽⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠸⣿⣿⣯⣤⣴⣦⣴⣾⡄⠿⢟⣁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣀⣠⣿⣿⣿⣿⣿⡋⢁⣼⣿⣷⣿⣧⣾⣿⣿⣿⣇⠀⠙⢿⣦⡀⠘⡛⠿⢿⣌⠙⣿⠀⠀⠘⠿⠋⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣯⣘⢻⣿⣿⣿⡿⣿⡿⠟⠁⢿⣿⣿⣿⣿⡀⠀⠈⠙⠻⢷⣄⣀⣀⡴⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣶⣶⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⠀⠀⠀⢸⣻⣿⡿⢿⣿⠀⠀⠀⠀⠈⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠹⣿⣷⣿⣿⣿⣿⣿⡿⠦⣾⣿⣦⡀⠀⢸⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠈⡿⠀⠻⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⣼⣻⣿⣤⣿⣿⣿⣿⠷⣶⣾⣿⣿⣿⡄⠈⣿⣿⣿⣿⡿⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢀⣾⣿⣿⣿⣿⣿⡿⠋⠀⣄⣸⣿⣿⣿⣿⢿⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⢠⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⣾⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣴⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀