⠀⠀⠀⠀⠀⠀⠀⢀⢀⠎⠀⠀⠀⡆⢠⠀⠀⠀⡜⡀⠀⠰⠁⠀⠀⠀⠀⢀⠎⢀⠜⡌⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠊⡰⠹⠀⠀⠀⣼⠀ ⠀⠀⠀⠀⠀⠀⡠⠁⡌⠀⠀⠀⢰⠀⡆⠀⠀⡸⢠⠁⢠⠃⠀⠀⠀⠀⢠⡎⢠⠊⠀⡇⠇⡆⠀⠀⠀⡌⠀⠀⢠⠇⡰⠁⡆⠀⠀⡸⠸⠀ ⠀⠀⠀⠀⠀⢠⠁⡘⠀⠀⠀⠀⢸⠀⡇⠀⠀⡇⠂⢠⡏⠀⠀⠀⠀⡰⢹⢀⠋⠀⠀⣷⠀⣇⠄⠀⢠⠃⠀⢀⡟⡰⠁⢠⠃⠀⡰⠁⡇⡘ ⠀⠀⠀⠀⠀⠇⢀⠇⠀⠀⠀⠀⢸⡆⡇⠀⠀⠀⠀⡎⢷⠀⠀⠀⢰⠁⡆⡌⠀⠀⠀⢃⡇⡟⡈⠀⢸⡆⠀⣸⡳⠁⠀⡎⠀⡰⠁⡸⣰⠃ ⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⡾⠰⣳⡀⠀⡀⢸⠀⣸⠀⠀⢀⠧⠤⠇⠁⠐⠂⠤⠬⠿⣽⢵⡀⢸⢣⠀⡿⡃⠀⣜⢎⡔⠁⣰⢟⠏⠀ ⠀⠀⠀⢰⠀⢰⢹⠀⡇⠀⠀⣼⢸⣇⠙⢕⣤⣇⢸⠒⣿⡀⠀⢸⠀⠀⠘⡆⠀⣀⣀⣀⣀⣈⠦⠵⣼⠮⠧⣸⣒⣾⣿⣏⣀⠚⠁⡸⠀⠀ ⢆⠀⡇⢸⠀⡌⠈⡄⡇⡆⢀⢿⣾⣻⣎⠩⠤⠼⢼⠒⠺⣣⣧⢸⠉⠉⠉⠉⠁⢀⣀⣀⠤⠤⠤⠶⠈⠀⠀⠈⠲⢄⠀⠀⠀⠉⢡⠃⠀⠀ ⠈⢆⢰⢸⡆⣇⡠⢧⣧⣇⡸⢹⠃⠀⠈⠑⠀⠀⠈⠃⠀⠀⠙⢟⣀⠤⣴⣲⣭⣽⣶⣶⣶⣶⣶⣖⡲⠦⠤⣀⡀⠈⠂⠀⠀⠀⡎⠀⠀⠀ ⡱⢀⡱⣻⡞⢥⢀⠈⢾⢿⡇⠁⠀⠀⠀⠀⠀⠀⢀⣀⠤⢐⣪⣵⣶⣿⣿⡆⢸⣿⣿⡀⠀⠀⠀⠈⠙⠓⠦⣀⠀⠁⠀⠀⠀⢰⠃⠀⠀⠀ ⣎⠳⡆⠉⠑⠐⠁⠑⠢⢅⠀⠀⢀⣀⣀⣈⣒⣦⣭⡶⠾⣿⣿⣿⣿⣿⣿⠀⣽⣿⣿⠇⠀⠀⠀⠀⢀⣀⠤⠤⠵⠂⠀⠀⡴⡙⠀⠀⠀⠀ ⠈⠁⢌⠀⠀⠀⠀⠠⠤⠤⢭⣤⣤⣴⣾⠿⣿⣯⡁⠀⠀⠼⠿⠿⠿⠿⠛⣰⢲⣿⡿⠀⢀⠤⠒⠉⢁⠀⠀⠀⠀⠀⢀⠜⠀⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⣁⣀⣭⣯⡿⠟⠛⠉⠀⠀⠹⣿⣿⣯⡿⣿⡞⢷⣾⡿⣫⣿⣿⣿⠕⠊⠀⠠⠔⠊⠁⠀⠀⠀⠀⡠⠋⠀⣼⠀⠀⠀⠀⠀ ⠢⡠⠤⢐⡒⠛⢛⡻⣝⣤⡀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣶⣶⣷⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⡠⠊⠸⠀⠀⠀⠀⠀ ⠀⠈⠑⢄⡈⠐⠤⡐⠉⠙⡻⡷⣶⣠⣤⡤⠄⠀⣠⣤⣬⣻⡯⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢀⠜⠀⠀⡀⠀⠀⠀⠀⠀ ⠀⠐⢄⠀⠈⠓⠤⡀⠐⢄⠈⠁⠃⠘⠉⠉⠉⠉⠉⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠸⡀⠀⢠⣿⠀⠀⠀⠀⠀ ⢦⡀⠀⠈⠢⣀⠀⠀⠑⠢⢌⡒⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠙⡄⠀⢡⠀⠘⡇⡄⠀⠀⠀⠀ ⠀⠙⠦⡀⠀⠀⠑⠄⡀⠀⠀⠚⢕⡢⣄⠈⠁⠒⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡜⣣⠀⠀⢃⠀⢇⠃⠀⠀⠀⠀ ⠀⠀⠀⠈⠢⡀⠀⠀⠈⠢⡀⠀⠀⠈⠲⢭⡲⢄⡀⠀⠀⠁⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⡜⠀⡏⡆⠀⠸⠀⠸⡸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠈⠢⡀⠀⠀⠀⠙⢷⣍⠢⡀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⢀⡠⠔⡇⠀⡜⠀⠀⡇⢱⠀⠀⠆⠀⢇⢃⠀⠀⠀ ⢆⠀⠀⠠⡀⠀⠀⠠⡑⢄⡀⠀⠈⠢⠀⠀⠀⠀⠙⢯⡪⡓⢄⠀⠀⠀⠢⣀⠤⠒⠈⠁⠀⣠⠁⡜⠀⠀⠀⢇⠘⡄⠀⠀⠀⠘⡌⡄⠀⠀ ⠀⠑⢄⡀⠈⠢⠀⠀⠈⠢⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠢⡑⣄⠔⠋⠀⠀⠀⠀⢀⠎⡜⠀⠁⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⢱⠰⡀⠀ ⠑⢄⠀⠈⠒⢄⡀⠀⠀⠀⠐⢄⠑⢌⠢⡀⠀⠀⠀⣀⠤⢀⣣⡨⠋⠀⠀⠀⠀⢀⠔⢁⣴⠃⠀⡇⠀⠀⠀⠈⡇⢱⠀⠀⠀⠀⠀⢇⠡⠀ ⠤⠤⠵⠤⠤⢀⣈⣒⢄⡀⠀⠀⠁⠈⢢⠑⢄⠴⠊⠀⠀⢀⠜⠁⠀⠀⢀⠤⠊⠁⢠⠎⡜⠀⠀⢰⠀⠀⠀⠀⢹⣼⠀⠀⠀⠀⠀⠘⡄⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠒⠒⠒⠓⠁⠀⢀⣀⣤⠊⠀⠀⡠⠒⠁⠀⠀⣰⠃⢰⠃⠀⠀⢸⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠱⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⣂⣵⢊⣁⡴⠁⢀⡰⠋⠀⠀⠀⠀⣰⣿⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠱