⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠑⡔⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠉⠢⣀⠸⡎⠉⣦⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⣄⠀⠀⠀⠀⠀⠈⠢⢄⠈⠣⠽⠀⣸⣠⡤⡏⠀⣳⠀⠀⠀⠘⠢⡙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠑⡄⠀⢪⠞⢫⠁⡷⠖⣟⣇⠀⠀⠀⠀⠱⡌⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢸⠚⢁⣠⡾⢖⡗⠚⠋⢹⡄⠀⠀⠀⠀⠇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣾⣿⣿⣷⣶⣦⣄⡀⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢠⠀⠈⢦⠉⠹⠀⠈⠇⠀⠀⠘⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣹⣿⣿⣿⣿⣿⣿⡀⠀⣇⠘⡄⠀⠈⠳⣄⣀⠀⠀⢠⣄⣴⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⢆⠈⠂⠀⠀⠀⠀⢱⣴⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢺⣇⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠑⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡿⠃⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⣿⠋⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠋⠑⢄⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠸⠇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣭⣾⣼⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠀⠀⠀⠈⢧⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣄⣿⡿⠁⠠⢫⢏⣈⣿⡿⢹⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⠀⠘⣇⠀⠀⠀⠘⢇⠀⠀⠀⡿⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⡡⢬⠻⠁⠀⠀⠈⠁⢸⢿⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⢈⣲⣄⡀⠀⠈⠀⠀⢸⡄⠘⢆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣰⠁⠀⣤⠀⠀⣶⠀⠀⠀⢈⡆⢠⡿⣿⡿⡿⣿⣿⣿⣿⣭⣤⣀⣀⢀⡴⠛⠉⠀⠀⢨⠁⠀⠀⠀⠀⠁⣠⡞⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⢸⠀⠀⠉⠀⠀⠀⠀⣤⡶⠾⠓⠋⣼⡿⠱⣿⢸⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣸⠶⠴⣮⡅⠀⢀⡤⢦⠀⠀⠀⠘⠁⢀⡼⣣⣿⡿⠟⠉⡼⠋⡿⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⣰⠃⠀⠀⢀⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⢻⡇⠀⠀⢠⠖⠒⡡⠔⢺⠀⠀⠀⠀⢠⠯⣾⣿⣿⠀⠀⡸⠀⠀⡇⠀⠀⠀⠀⠀⡴⠃⢠⡆⠀⣰⠃⠀⠀⢀⣿⣧⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣾⡇⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠘⢭⡤⠤⠖⠋⠀⠀⠀⡀⠋⢀⡜⡉⡇⠀⠀⠁⠀⠀⡇⠀⠀⠀⣠⡞⠁⠀⢸⣥⠞⠁⠀⠀⠀⣾⡿⠉⢉⣽⣿⠟
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⠇⢱⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⢀⣠⣴⣿⠀⣠⢎⠜⡇⡇⠀⠀⡀⠀⡼⠁⠤⠶⠛⠉⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠈⠀⣠⣿⠟⠁⠀
⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀?