⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠻⢯⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⢿⠷⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⢧⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⡆⠰⠀⠀⠀⠀⠀⢸⠀⠀⡏⢧⠈⣧⡀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢚⠁⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⢸⠀⠀⡇⠈⢇⢱⠱⣄⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣀⣠⠤⣒⣩⢴⠏⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⢸⠀⢠⠇⠀⠘⣼⢀⡬⠷⡂⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠉⠀⠀⡎⠀⠀⠀⠀⠀⠀⢸⠀⢰⢁⡇⠀⠀⠀⠀⠀⢸⠀⢸⠀⢀⡴⣿⠁⠀⠀⠘⢦⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⡀⠀⢰⠀⠀⡤⠬⡦⠾⢼⡟⡄⠀⠀⠀⠀⡸⡄⡇⠴⠊⠀⣿⠀⠀⠀⠀⠀⠙⢮⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡇⠀⠈⡇⠀⠀⢠⣇⡇⠀⢷⢹⡀⠀⠀⠀⡇⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡞⢇⠀⠀⢣⠀⠀⢸⠸⡇⠐⠚⢾⠱⡄⠀⠸⠃⠁⠀⠀⠀⠀⠀⡀⠀⣠⣤⣤⣴⣮⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡇⢸⢆⠀⠈⡆⠀⢸⠀⣷⣾⢿⠿⣖⠝⢦⡀⡇⠀⠀⠀⠀⠀⢞⣵⠿⠋⠉⠁⠀⠈⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢿⡄⠀⠸⡄⢸⣀⣿⠀⣌⠀⢻⣷⡄⠙⠃⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⢿⣄⢤⠘⣄⣧⠻⣧⢹⣿⣎⣀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡼⣧⠈⠃⡵⣜⠋⢻⣧⣩⡟⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢧⢣⡀⡟⡜⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡸⡄⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢇⡇⢱⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠖⠊⠁⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢠⠃⣇⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⠋⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⢸⡀⠸⡀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠃⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢸⢦⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⣏⢧⠀⠀⠀
⠀⡠⣀⡀⠀⡇⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠈⠑⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣇⣀⣀⠀⢀⡔⡇⠀⠀⢸⡀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠘⡄⠳⡀⠀
⡞⠁⠀⣈⠙⢢⠀⠈⠉⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠉⡗⠒⠤⢤⣤⡤⢤⡴⠚⠉⠁⠀⠀⠀⠀⠉⠛⠳⢾⠀⠀⠈⡇⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⢳⡀⠱⡀
⡆⠘⠉⠁⠉⠚⡄⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢉⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠘
⡆⠀⠒⠊⠉⠑⢺⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢱⠀⠠⠶⠒⠒⠒⡆⠀⠀⢸⡖⠢⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⢱⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠘⣆⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀
⠘⡄⠀⠀⣀⡤⠴⠳⡄⠀⠉⡣⠀⠙⢆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠘⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠘⢆⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀
⠀⢰⡀⠀⠃⠀⠀⠀⠿⠀⢰⠃⠀⠀⠈⢧⠤⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡎⠀⠸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠈⢧⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠙⠢⢄⡀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠈⡆⠈⢢⡀⠀⡇⠀⠀⠀⠀⢰⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠈⡆⠀⡀⠳⡀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠉⢷⣦⡴⠁⠀⠀⠀⠀⠀⢸⠹⡀⠀⢳⡀⡇⠀⠀⠀⠀⡎⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⢱⠀⡇⠀⠘⢆⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢇⠉⠀⠀⠀⠀⠀⠀⢠⠇⠀⡇⠀⠀⠙⡇⠀⠀⠀⡸⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡇⢇⠀⠀⠈⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⢠⠃⠀⠀⣹⠀⠀⠀⡇⠀⠀⠰⠃⠀⠀⠀⠞⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢱⢸⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀