⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠤⠤⠤⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠒⠠⠤⠤⠤⠤⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⢀⡀⠤⠄⠒⠒⠂⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢀⣨⠭⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⠉⠁⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠐⠉⠀⠀⠀⠈⢡⠀⠀⠀⠀⠀⠀⣰⠈⠁⠀⠈⠙⠦⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⠒⠒⠒⠒⢒⣒⡒⠒⠲⠷⣤⣀⣀⣀⣀⣡⠤⠴⠖⠒⠒⠒⠒⠲⠤⣼⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⡠⠊⢩⣭⡓⠦⣄⣿⠁⠀⠀⣿⠀⡤⠶⣖⡚⠣⡀⠀⠀⠀⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠑⠦⠿⠿⠷⠶⠚⣿⠀⠀⠀⢹⠀⠳⠼⠟⠓⠉⠉⠀⠀⢠⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣤⣤⣤⣤⣤⣤⣤⡤⠶⠶⠃⠀⠀⠀⠈⠓⠒⠲⠤⠤⠤⠤⠤⠤⠼⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠒⠚⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠈⠧⣤⠤⢄⠀⠀⠀⠀⠴⣦⠜⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣠⣤⣤⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢽⠂⠁⠀⠀⠀⠀⣠⠴⠁⣠⣾⠋⢸⡇⠉⡿⠶⣶⢶⣄⠉⠒⠢⢄⠀⠀⠀⠀⠨⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⣽⢂⠤⠀⠀⢠⠊⠀⢀⣾⣏⣿⣀⣸⣇⣀⡇⠀⣿⢸⢙⣧⡄⠀⡇⠀⠀⠀⣌⡻⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠜⣿⣸⠉⠀⠈⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⠃⢰⠀⡉⢡⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡧⢊⠠⡆⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⢠⠏⠀⠳⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣕⢊⢸⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⠐⠲⢭⢟⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⣀⡤⠖⠒⡟⠁⢯⠉⠉⡇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⡇⢀⣖⣟⠩⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⠤⠖⠋⠉⠉⠁⠀⠀⠀⠀⢇⠀⢜⣇⠀⢹⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣂⢴⣿⠄⠀⣿⠉⠓⠲⣤⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣢⠩⣮⢹⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢸⠬⡿⠞⡠⢂⡟⠀⠀⠀⠀⠉⠳⢤⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡵⣼⣾⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢸⣞⠵⢪⡠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢎⣿⡀⢀⠀⠀⠈⠿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⢸⠀⠀⠈⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⡰⠒⠂⡠⠤⠀⢰⡀⡄⡁⡀⠄⠀⠀⡶⣾⠚⠁⠀⠀⠀⠀⠈⠉⠛⠒⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡃⣄⠇⡀⢇⢸⠀⠰⢀⠸⢀⣓⣧⣹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⠮⢧⣚⣼⣼⣔⣡⣈⣴⡿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀