⠀⠀⠀⠀⠀⠀⠀⢠⠋⣇⣀⣀⠀⠀⠀⠀⠀⣠⠤⡀⠀⠀⠒⡄⠀⠀⠀⢀⣀⡴⠋⣇⡀⠀⡠⣠⠤⣤⠄⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠰⣆⣉⣲⠀⠀⠀⠀⣠⠤⣄⠀⠀
⠀⠀⠀⠀⠀⢀⠤⠚⠀⠉⣠⣼⡠⢄⠀⠀⠀⣇⠀⠗⣦⢸⠀⡇⠀⠀⠀⠧⣠⠀⠀⣀⠈⡷⡇⢸⠦⠛⠂⠀⠘⡌⠳⠖⠉⣩⠇⠀⠀⠀⠀⢀⡤⠤⢄⡀⠀⠀⠀⡇⠀⡸⠀
⠀⠀⠀⠀⠀⠙⢒⡾⠇⠀⣉⠉⠀⡎⠀⠀⠀⠘⠤⠔⠁⢸⠀⡇⠀⠀⠀⢰⠃⢀⣾⠏⡰⠁⠘⠼⠀⠀⠀⠀⢀⡞⠀⡔⠉⢀⡀⠀⠀⠀⠀⠧⠤⢤⡄⠈⡆⠀⠀⡇⢠⠇⠀
⠀⠀⠀⠀⠀⢰⠋⠶⠆⠀⢈⣤⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⢠⠃⠀⠀⠀⠘⠤⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠉⠉⣉⡽⠂⠀⠀⠀⠀⢀⠜⢁⡰⠁⠀⠀⢑⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠣⠤⠤⠔⠋⠈⠓⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠒⠉⠀⠀⠀⠀⢯⡵⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠒⠒⠒⠂⠠⠶⠤⠤⣄⣀⡀⠀⠀⠀⠀⣀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠒⠊⢘⢀⣠⣴⡚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⡀⡇⠐⠒⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢸⠟⠋⠉⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠃⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠙⠢⢄⡞⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⠤⡴⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⣰⣤⣀⣀⣼⠇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡴⠋⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠑⠤⠤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⢦⣄⣴⠏⠈⠉⠉⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠉⠁⠀⠀⠀⣸⠀⠀⢀⡾⡇⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣇⠀⠀⠀⠀⠀⡏⢱⡤⢤⠀⠀⠀
⠀⠀⠀⠀⠀⢎⠈⠉⢀⠃⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢠⡞⠀⡇⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠣⠤⠤⠊⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢀⡀⠀⣾⡇⣠⡾⠀⠀⣇⣷⠀⠀⠀⠀⠀⢸⡇⠻⡴⣤⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣸⡇⢰⢻⡟⡿⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⢘⡇⠀⠹⣆⢹⠘⣇⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⠤⠤⠄⡼⠢⡀⠀⣿⠀⠀⠀⠀⠀⠀⢿⡇⡟⠘⣿⠁⠀⠀⠀⠀⢣⠙⢦⣴⢦⣄⡼⠇⠀⠀⠘⢾⠀⠘⣆⢠⠀⠀⠀⠈⣷⠀⠀⢘⣇⣀⡰⠁⠧⠄⠐⠠⢄
⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠐⡞⢻⡄⠀⠀⣾⠀⠀⢸⣷⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⣿⠀⠀⣼⠃⠀⡇⠀⠀⠀⠀⠀⡨⠂⠀
⠀⠀⠀⠀⠈⠑⠢⠤⣀⣀⠀⣰⠃⠀⢷⣄⠀⣿⠀⠀⠀⡏⠀⠀⢀⣀⣰⣤⠤⣀⡀⠀⠀⠀⠀⠀⠀⢀⡤⠴⣦⣤⣄⡀⠀⢸⡇⠀⠀⠀⣿⣠⣼⠋⠀⠀⠘⣆⣠⠴⠚⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠋⠀⠀⢠⠄⢹⣇⣿⠀⠀⠀⣿⠀⠨⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠀⣼⡇⠀⠀⢀⡏⠀⠀⡆⠈⠣⠀⠀⣱⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⡄⠚⠉⠀⠈⠙⢿⡀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⡀⢀⠇⠀⠘⣇⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⣠⣶⣶⠶⠒⠒⠒⠶⢦⣤⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢸⠇⠀⣠⡞⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⣷⠸⠀⠀⠀⢿⡀⠠⡀⠙⢦⡀⠀⠀⠀⠀⢿⡿⠁⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⢀⣾⣵⡆⠀⡖⠀⣿⠀⠀⠀⣠⣴⠞⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠘⣇⠀⠀⠀⠘⢧⡀⠙⢷⣬⣽⣶⡂⠀⠀⠀⠙⠦⠀⠀⠀⠀⠒⠁⠀⠀⠀⣀⣩⣿⣿⡇⣸⠇⣸⠇⠀⢀⣼⠃⣾⡆⡟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢻⣦⠀⠀⠀⠈⠿⣦⣀⢻⣿⣿⣿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⣷⣿⣷⣯⠿⠋⠀⢠⣿⣿⠞⢻⠟⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣿⢧⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠋⠀⠀⠀⢀⣾⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⣇⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠟⠁⠀⠀⠀⠀⣼⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠙⠛⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠛⠁⠀⠀⠀⢀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠘⣆⠀⠉⠉⠉⠉⠉⠉⠀⠀⣠⠃⠀⠀⠀⠀⠀⠘⣦⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣠⠃⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⢠⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠹⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⢠⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀
⠀⠀⠀⠀⠀⠀⠐⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⠃⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠂