⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡰⢁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡜⠀⡌⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⡘⠀⢸⠁⠀⠀⠀⠀⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⡰⣽⠀⠀⠀⡇⠀⡎⠀⠀⠀⠀⢰⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⡰⠏⡼⠀⠀⠀⢇⠀⡇⠀⠀⠀⠀⡗⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⠋⠀⢀⡤⠀⠀⠀⠀⢀⣴⣁⢀⣩⠀⡇⠀⠘⡄⢱⠀⠀⣀⣸⠁⠸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⠃⠀⡠⢫⠃⠀⠀⠀⠄⣸⠃⠀⠀⢸⢐⡇⠀⠀⠘⢎⢇⠀⠀⡎⠉⠉⡗⠢⢤⣀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀
⠀⠀⠀⣰⠃⣠⠊⠀⡎⠀⠀⠀⢨⠀⡏⠀⠀⠀⠈⡎⢸⠀⠀⠀⠀⠙⠀⡇⡇⠀⠀⢳⠀⡄⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀
⠀⠀⡴⡡⠚⠁⠀⢰⠃⠀⣷⠀⠘⣼⣅⡀⣀⣀⣻⢽⣇⢿⣦⡀⠀⠀⠀⢧⣟⣢⠀⠈⡆⡟⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀
⣠⠞⠋⠀⠀⠀⠀⢸⠀⢸⡏⣇⠀⣿⣾⠿⠛⠙⣿⣿⣇⠈⠳⠑⠲⢄⣀⣯⣧⣽⣦⣤⣘⡇⠘⣄⢸⠀⠀⠀⠀⣰⠀⠀⠀⡞⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⢿⣆⠻⡹⣆⢸⣿⣿⣻⡇⠀⠀⠀⠀⠀⠉⠙⠁⡀⢛⣿⣿⣿⣷⣬⢾⠀⠀⠀⣰⡟⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠈⢻⣦⣧⠀⠸⣟⠧⢮⠇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣫⠇⡎⠀⠀⣰⣿⡇⠀⠀⢰⠁⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⠀⠀⠀⢿⠙⠂⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣑⠒⣊⡽⠋⣰⠁⠀⣰⠏⣾⠃⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡀⠀⠀⠸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⣼⠇⠀⠈⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⣴⡿⠁⠀⠀⠀⠀⢀⡿⡇⠀⠀⠀⠀⠀⡆⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⡜⣆⠸⡀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡷⠋⢸⡅⠀⠀⠀⢀⣖⣾⠀⡇⠀⠀⠀⠀⠀⣧⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢣⢻⣣⣳⠀⠀⢙⡗⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⣿⠇⠀⠀⢀⣟⣾⡟⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⣧⠀⠀⠀⢸⠁⡇⢹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠋⡟⠀⠀⢀⣞⠞⣿⡇⠀⠀⠀⠀⠀⠀⠀⡏⡇⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⡆⠀⢰⠯⠀⡇⢸⣿⣿⣷⣤⣀⣀⣀⣠⡤⠒⠚⠉⠁⠀⠀⠀⠂⡯⠀⢀⢾⠏⢂⣿⡇⠀⠀⠀⠀⠀⠀⠀⢁⢃⢡⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⣝⣶⣟⣀⡀⣇⠈⣿⢻⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⠀⠀⣧⣠⣿⡧⣄⠘⡏⡇⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⡤⢹⠀⢻⣸⣿⡓⠈⣿⢻⣿⠟⡄⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⡅⠘⡆⢧⡇⠀⠀⠀⠀⠀⠀⠀⢸⡈⡟⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢡⢿⠋⠙⠃⠈⡇⠈⣿⣿⡧⠤⢛⡯⣊⣤⠇⠀⠀⠀⠀⠰⢛⣿⣿⠻⠏⠁⠀⠙⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⡇⢣⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢹⠀⠀⢴⠐⠻⡉⠉⠀⠀⣰⠛⠉⠀⠈⠁⠀⠀⠀⣠⠞⡹⠋⢻⠀⠀⠀⢀⡀⠈⠻⡄⠀⣆⠀⠀⠀⠀⠀⢇⠸⣽⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢸⢀⣠⣿⡇⠀⢧⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⡴⠊⠀⡰⠁⠀⡇⠂⠀⠀⠀⠀⠀⠀⠙⣷⣿⠀⠀⠀⠀⠀⢸⠈⢟⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢰⣿⡿⠋⠀⠀⠀⢳⣀⡎⠀⠀⠀⠀⠀⣠⠊⠀⠤⣲⠁⠀⢰⢁⣀⠀⣀⣴⣷⣤⡀⠀⠉⢿⡇⠀⠀⠀⠀⠘⡆⠸⣇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣿⣏⠀⠀⠀⠀⠀⠀⣹⡉⣷⣀⣀⢤⠟⠁⠀⠀⣰⠁⠀⢠⣷⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⢌⣷⠀⠀⠀⠀⠀⡇⠀⢿⡠⠀