⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⣧⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡎⢱⠀⠀⡟⠁⠈⡇⠀⠀⢰⠀⠀⠀⠋⠀⡇⠀⠙⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⠃⠘⡆⠀⣇⠀⠀⡇⠙⢆⡼⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠃⠀⠓⠒⠃⠀⢠⠏⠓⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠋⡏⠁⡇⣠⡏⠈⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠇⠀⠀⠉⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠉⠀⠀⠀
⢸⡞⢧⠀⠀⡏⠓⡆⠀⣆⠀⣸⠉⡅⠀⠀⡏⠳⡄⠀⢸⠀⢠⠀⠀⠀⠀⠀⠀⠀
⠀⣇⠀⠈⠓⡟⠒⠋⠀⠀⠉⡏⠀⢸⠀⠀⠑⠴⠃⠀⠀⠧⠼⠃⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠀⠀⠛⠀⠀⠀⠀⠀⠋⠀⠀⢁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⡀⠀⣰⠀⠀⢸⢉⣁⡀⠀⠀⣿⡀⠀⠀⠀⢧⣸⠀⣠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠉⠁⠇⠀⠘⠦⠤⠆⠀⠟⠀⠃⠀⠀⠀⠈⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀

⠀⡇⠀⠀⠀⡏⠉⢳⠀⠀⡴⠲⣄⡤⠖⢶⠂⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡏⠀⠀⠀⡇⣀⡤⡆⠀⣧⣴⣃⠀⠀⠘⡆⠀⢀⡇⠉⣇⠀⠀⠀⡆⠀⠀⠀⠀
⠀⠹⣄⡤⠬⠧⠴⢿⠀⠀⣇⣀⡴⠃⠀⠘⠀⠀⢸⡀⣳⡇⠉⠉⢹⠒⠒⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀
⠀⢺⠒⠒⡆⠀⠀⡴⠢⠀⢸⡆⢳⠀⠀⡏⠀⠤⢤⡄⡄⢀⠀⣅⠀⠤⠤⡄⠀⠀
⠀⠸⠤⠤⠞⠀⠸⢄⣀⠀⢸⠗⠋⠀⡏⠀⠀⡤⠏⠀⡧⢼⠀⢸⠀⠀⠀⡇⠀⠀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠉⠉⠁⠋⠀⠇⠈⠃⠀⠯⠤⠄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠉⠙⡆⠀⠀⡇⠀⡆⠀⠀⡤⣿⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠓⠉⠁⠀⠈⠙⠋⠀⠀⠀⠏⠁⡇⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⡄⠀⠀⠀⠁⠀⠀⡇⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠑⡀⡇⢰⣆⠀⢸⠀⢸⡗⠦⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⠧⡀⠀⡇⢇⠀⡃⢸⣀⡟⠀⠀⢸⠀⢻⡀⠀⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⡇⠀⠘⡇⢇⡇⠀⠀⢸⠀⠀⠀⠻⠀⠀⠀⠀⠀
⠀⠘⡏⠁⠉⠉⠙⡧⡀⠀⠞⠀⣠⠀⠇⠀⠻⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢻⡆⠀⠀⠀⢠⠋⠧⡴⢃⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀
⠀⠀⠀⢿⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⢀⠂⠈⠀⠀
⠀⠀⠀⠀⠇⡔⠃⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⡇⠀⡀⠄⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠸⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣆⠀⠀⠀⢠⠀⠀⡧⠤⠤⠀⠀⡄⠀⠀⠀⠰⡇⠙⡆⡆⠀⡏⡴⣆⠀
⠀⠀⠀⢀⠏⡇⠀⠀⡇⠀⠀⡧⠤⠄⠀⡸⠳⡀⠀⠀⠀⣧⠴⠃⡇⡇⣿⠒⠛⠀
⠀⠀⢬⡟⠒⢻⠂⠯⠤⠆⠸⠀⠀⠀⢀⠗⠊⢳⡀⠀⠀⠃⠀⠀⠋⠀⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀
⠀⠀⠐⣧⠀⠀⣴⡀⠀⠀⣄⣀⡤⠀⠀⢠⡦⠤⠤⠄⠀⠀⠀⠀
⠀⠀⠀⢹⢳⡞⠀⡇⠀⠀⡇⣀⡀⠀⠀⠀⣇⣀⣀⡤⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠀⠁⠀⠃⠀⠀⢧⠀⣀⡤⠄⠀⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡏⠉⠉⠀⠀⡇⠀⢰⠀⠀⢫⠉⠉⡆⠀⡖⠦⡄⠀⠀
⠀⠀⠀⠉⠉⣉⡇⠐⡗⠚⢧⡀⠀⢧⡀⡜⠀⢸⠤⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠉⠉⠁⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀

⠀⠀⢀⡞⠁⠀⠀⠈⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⢠⡀⠀⠦⡄
⠀⡴⠃⠀⠀⠀⠀⢠⢼⠀⡆⠀⠀⠀⠀⠀⠀⠈⣇⡀⠀⡇⠀⠀⢳⡀⠀⠳
⠀⡇⠀⠀⠀⠀⢀⡏⢸⡼⠀⠀⠀⢰⠀⡆⠀⠀⠀⢧⣸⠀⠀⠀⠀⠙⡆⠀⠹⡄
⠀⣇⠀⠀⠀⡖⠃⢀⣞⣠⠤⠄⠀⠀⠀⠁⠀⣄⣀⣑⣇⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠈⢧⡀⠀⠹⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⣇⣀⠴⠊⠉⠀⣇
⠀⠀⠀⠺⣇⠀⡇⠹⢯⣩⠇⠀⠀⢀⣀⡀⠀⠀⠀⣏⠉⠛⠉⡇⠀⠀⠀⣰⠃⠀
⠀⠀⠀⠀⠀⠓⡧⢤⡀⠀⣤⡇⠀⠘⠒⠃⠀⠀⠸⡅⠀⠀⠤⡧⠤⢤⡼⠁
⠀⠀⠀⠀⠀⠀⠓⣆⣀⣉⣁⡖⠃⠀⠲⣄⣀⣀⣚⣒⡟⠉
⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⡇⢧⣠⡄⠀⡆⢸⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⢀⡇⠀⡇⠉⣩⠁⠀⢳⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⡏⠀⣸⣀⣀⡇⠀⠀⠀⡇⠀⠀⠀⠀⢧⠀
⠀⠀⠀⠀⡼⠁⠀⠀⠀⣸⠁⠀⠀⠓⠒⠃⠀⠀⠀⠘⠂⠀⠀⠀⠀