⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢹⠅⠈⠀⠐⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠑⡇⡄⢄⠀⠀⠀⠀⠉⢖⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣆⠳⠀⠂⠀⠀⠀⠀⠀⠀⠀ ⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⠈⠱⣄⣘⢂⠒⠂⠂⠀⠀⠀⠑⠂⠀⠄⣀⣀⣀⠀⠠⠤⠤⠄⠀⣀⡀⠀⠀⠀⠀⠀⡀⠀⠈⡁⠀⡄⠈⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠈⠻⣮⣁⠀⠀⢀⡠⠤⠔⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠲⠐⣈⣏⡤⠐⠀⠀⠁⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡀⠁⠀⠀⠈⡱⠗⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠔⣡⣴⠯⠊⠀⠀⢀⠦⢰⢀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣅⠀⡀⠔⠉⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢮⡜⠀⠀⠀⠀⠈⠉⠀⠀⢏⠐⡄⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡸⠊⠀⠀⠔⠁⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⢸⠆⠈⢰⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡔⠀⢠⠎⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠸⢀⠀⠁⠈⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠔⡠⠟⠀⣰⠇⠀⢀⢼⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠓⡄⠀⠀⠀⣯⠀⠀⠀⠘⡜⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⢂⠔⠜⠀⡰⡏⠀⢠⢊⠎⠀⡾⠀⣌⡇⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⠀⣷⠀⠐⡄⠀⠀⠀⠀⠈⢦⠀⠀⣿⠀⠀⠀⠀⢡⠘⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⢁⠎⠰⠂⠤⣹⠀⢠⠇⡜⠀⡸⠇⢰⡏⠀⠀⠈⡇⠀⠀⠀⠀⢀⢿⠀⠀⠀⡸⡰⡸⡄⠀⢱⡀⠀⠀⠀⠀⠈⢣⡀⣿⠀⠀⠀⠀⠈⡄⠸⡀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⢢⠆⠀⡇⠀⠀⡆⠈⠙⢺⠃⠤⣱⠀⣷⠀⢰⠀⡀⢰⠀⠀⠀⠀⣸⢸⠀⠀⠀⣧⢣⠁⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⣳⣟⠀⠀⠀⠀⠀⠃⠀⢃⠀⠀⠀⠀⠀
⠀⠀⠀⣼⡏⠀⢠⠌⢀⠐⠒⢠⠄⣸⢀⠀⢰⠈⠃⠀⠸⠂⠧⠬⠀⠀⢀⡰⣇⡘⠀⠀⣰⣣⠃⢠⡇⠀⠀⢹⠀⠀⠀⠀⠀⠀⢧⢻⠀⠀⠀⠀⠀⠉⠀⣸⡀⠀⠀⠀⠀
⠀⠀⢠⠱⠀⠀⢸⡀⢸⠀⡄⢸⢸⣷⠀⡏⡏⣿⢀⢃⠐⢰⠀⢤⠤⠤⠤⢱⢀⡈⢉⣹⣽⣋⠁⡈⡇⠀⠀⢘⠀⠀ ⣘⣍⡄⠀⠀⠈⠀ ⠤⡇⠀⠀⠀⠀
⠀⠀⡘⡀⠀⠀⠈⡁⣸⠀⣧⣿⣼⢘⣸⣇⡇⡇⠂⠘⡀⡈⠀⠸⠀⡠⠁⠃⡘⣠⣾⣿⠋⡇⡰⢰⡃⠀⠀⢸⠀⠀⠀⠀⠀⠀⡆⡇⢣⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀
⠀⠀⣇⠁⠀⠀⠀⣷⡟⣆⡟⢘⣿⣦⡟⣿⣷⡇⠀⠀⣇⣇⣶⠇⡴⡡⡞⢀⡿⢋⣼⠇⢀⡰⢁⡇⡇⠀⠀⡾⠀⠀⠀⠀⠀⢰⠃⡇⢸⠀⠀⠀⠀⠠⠀⠀⣷⠀⠀⠀⠀
⠀⠀⢳⠀⠀⠀⠀⡏⠁⠘⣷⠩⣿⣯⣿⣾⣛⣇⠀⢸⢌⡟⢻⡜⠚⣴⠴⣏⣴⠮⣜⣠⠌⢠⢫⣾⠀⠀⢰⢙⠀⠀⠀⠀⠀⡄⡀⡇⢸⠀⠀⠀⢀⡆⠀⢰⠐⡀⠀⠀⠀
⠀⠀⠸⡀⠀⠀⠀⠁⠀⠀⠘⠆⡏⢿⡻⣿⠡⠉⠀⠋⡆⠀⠀⠰⣾⣦⣽⡓⠋⠐⠏⢲⠔⠍⠞⡼⠀⠀⡈⡎⠀⠀⠀⠀⢰⠁⣷⠁⣼⠀⠀⢀⣾⠀⠀⡎⠇⢧⠀⠀⠀
⠀⠀⠀⢃⠀⠀⢸⡄⠀⠀⠀⠀⡇⢤⣽⠋⡸⠀⠀⠀⠀⠀⠀⠀⠘⣧⣼⣿⣿⣶⣦⣬⣁⠀⢜⠃⠀⢰⢱⠁⠀⠀⠀⠀⡆⢰⡉⠀⡟⠀⢀⡞⠈⠀⠘⠀⠘⡈⣆⠀⠀
⠀⠀⠀⠀⠡⠀⠘⠁⠀⡄⠀⢰⠃⠀⢀⠴⠃⡇⠀⠀⠀⠀⠀⠀⠀⢿⡻⠿⢷⣿⡿⢪⡿⠯⡾⠀⢀⡆⡌⠀⠀⠀⠀⡜⠀⣸⠃⢰⢑⠀⡾⠀⡅⢠⣇⠀⠀⢣⠈⣄⠀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢃⠀⢸⡀⠰⠡⡀⠀⡇⠀⠀⠀⠀⠀⠀⠐⠷⣿⣖⣚⡊⠑⠋⠁⡔⠃⠀⡘⢰⠁⠀⠀⠀⡰⠀⠀⡍⠀⡎⢸⣾⠁⠀⣧⡏⠏⢂