⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⡿⢡⣿⣿⣿⣿⣿⣿⣶⡻⣷⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⣿⣿⣿⣿⡇⢿⢻⣿⣿⣿⣧⠱⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣼⣿⡇⣿⣿⡟⢿⢿⡈⠈⢿⣿⣿⣿⡆⠑⣿⣿⣿⣿⡟⢿⣇⢻⣿⢡⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⠸⣿⢿⢸⡄⢱⣄⠈⢻⣿⣿⣷⣠⡈⢿⣿⣿⣿⣼⣿⢼⣿⡀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣿⣿⣧⡜⣿⣇⠹⡦⠄⢇⢸⣿⣦⣘⣷⣦⣽⣿⣿⣶⣿⢿⣤⣿⡟⢸⠁⠇⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⣿⣿⡇⢹⣿⠀⠄⠀⠈⠚⠙⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠉⠛⢦⡏⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡎⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣿⣿⣿⣿⡈⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⡀⠀⠀⠈⠁⠈⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠉⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢠⠸⣿⣏⢿⠣⠸⡇⠀⠀⠘⠁⠀⣼⣿⣿⣿⣿⣿⣿⣆⠀⠁⠀⠀⢀⣴⢀⣿⡿⣃⡀⠀⠀⠀⢠⠴⣶⡒⠺⠟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢰⣼⡇⢻⣿⡌⢧⡑⣼⣦⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣶⡿⢃⢾⣿⣷⠀⠀⡌⠀⠀⠈⣆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⣿⣷⠀⠛⣎⠢⡙⢿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠉⠉⠛⠻⠿⣿⣿⣟⣴⠇⡼⢩⠇⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⡀⠐⠈⢷⡀⠈⣿⣿⣿⠁⠀⠰⠀⠗⠘⢸⠀⠀⡆⠀⠈⣿⡟⣡⠞⠁⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢣⠀⢲⡄⠀⠀⠀⠙⢿⣷⣤⠀⡀⠘⠇⠸⠀⠀⠀⢠⡄⠟⠀⠁⠀⠀⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠙⠆⠈⠳⠠⡀⠈⠿⠀⣿⣿⣶⣶⣾⡇⠀⣾⠃⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠂⠀⠀⢠⡄⠈⠙⠻⠿⠛⠀⠀⠀⣴⢀⣤⣾⣠⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠁⠀⠀⣶⣤⣾⣶⣾⣿⠀⢿⣿⣿⣿⣿⠀⣸⣷⣿⣿⣿⣿⡷⠀⡆⢹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠀⠀⢀⣬⣿⣿⣿⣿⣿⣇⠸⣿⣿⡿⠃⣰⣿⣿⣿⣿⣿⣿⡇⠘⠇⢸⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣆⠻⡿⠃⣴⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⡿⢷⣴⠾⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠻⣿⣿⡿⠿⠛⠉⠀⠈⠀⠀⠀⠈⠙⠻⠿⣿⣿⡟⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀