⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣏⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⡇⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣰⣧⠀⠀⠀⠀⠀⢀⣇⣀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣀⣸⡀⠀⠀⠀⠀⠀⣴⣦⠀
⠈⣿⣾⠇⠀⠀⠀⠀⠈⡟⠛⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⢻⠁⠀⠀⠀⠀⠠⣷⣾⠃
⠀⡿⠿⠀⠀⠀⠀⠀⠀⣇⠶⡄⡇⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⣠⠚⢡⠃⠀⠘⡌⠓⢄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⢠⣶⣼⠀⠀⠀⠀⠀⠀⡿⢿⠀
⠀⣧⣴⠀⠀⠀⠀⠀⠀⡇⠓⠃⡇⠀⠀⠀⣰⣿⡄⠀⠀⢠⡏⠀⡰⠃⠀⠀⠀⠘⢆⠀⠱⡄⠀⠀⢠⣞⣆⠀⠀⠀⢸⠘⠚⢻⠀⠀⠀⠀⠀⠀⣧⣼⠀
⠀⡿⠿⠀⠀⠀⠀⠀⢀⣇⣀⣀⣇⢀⡠⢚⡝⠉⢯⡢⣄⢈⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⡱⣀⠔⡿⠉⠹⡑⢄⡀⣸⣀⣀⣸⡀⠀⠀⠀⠀⠀⡿⢿⠀
⢀⣇⣠⡀⠀⠀⡄⠀⠘⠿⠿⠿⠟⡌⠀⡏⠀⠀⠀⢡⠈⣿⣖⣒⣛⣒⣒⣒⣒⣒⣛⣒⣲⣿⠃⠈⠀⠀⠀⢹⠀⢱⢻⠿⠿⠿⡏⠀⠀⠀⠀⢀⣇⣸⡀
⠀⣏⣹⠁⢠⡾⢷⣄⠀⣀⣴⣄⡄⡸⠾⠿⠿⠿⠿⢿⢷⣷⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣟⠿⠿⠿⠿⠿⠿⠿⢏⢸⢠⣦⣀⡇⣠⡾⢷⡄⠀⢋⣉⠁
⠀⡿⢿⠀⣸⠿⡿⢿⠀⣸⣙⣿⠁⡏⠉⠉⠉⠉⠉⠉⠉⢹⠾⠗⠛⠻⠛⠗⠻⠿⠾⠗⠷⡏⠉⠉⠉⠉⠉⠉⠉⢹⢸⣳⣿⡟⡇⣿⠿⠿⣷⠀⠻⠿⠀
⢠⣧⣤⣄⣼⣾⣿⢸⠀⢸⠛⠛⡀⡇⠀⢀⣴⣶⣤⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣠⡾⣦⡀⠀⢸⢸⠘⠛⠃⡇⡷⣿⣷⢻⢠⣦⣴⡄
⠈⠉⠉⣿⠛⢛⠛⠛⣛⠓⠒⡚⠓⡇⠀⠟⠁⠀⠘⡇⠀⢸⢀⣴⣤⡀⣠⣶⣄⡀⣤⣦⡀⡇⠀⢸⠉⠀⠀⢹⠀⢸⠚⢓⠒⠛⢛⠛⠛⣛⠛⣿⠉⠉⡇
⠀⣴⣦⣿⠀⣟⡇⢸⣿⠀⣾⣿⠀⡇⠀⠀⠀⠀⠀⡇⠀⢸⢸⠂⠈⡏⡟⠀⢻⢹⠁⠉⡏⡇⠀⢸⠀⠀⠀⢸⠀⢸⠀⣟⣿⠀⣟⡇⢸⣻⠃⣿⣴⣦⡇
⠀⠿⠼⠿⠤⠤⠤⠤⠤⠤⠤⠤⠤⠧⠤⠤⠤⠤⠤⠧⠤⠼⠼⠤⠤⠧⠧⠤⠼⠼⠤⠤⠷⠧⠤⠼⠤⠤⠤⠼⠤⠼⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠧⠼⠇