⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠖⠛⠉⠁⠀⠀⠀⠀⢸⣷⠃⠀⠀⠀⠉⠓⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠐⢾⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡴⠛⠁⠀⠀⠀⠀⠀⡇⡀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⠀⠀⢀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠰⡇⡇⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠠⡀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣳⡂⢤⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⣄⠀⠀⠀⠀⠀⠀⠘⣎⣆⠀⢠⡀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠈⠇⠀⠀
⠀⠀⠀⢀⣴⣿⣽⣯⣿⣿⣿⣿⣿⡇⢀⡆⠀⠀⠀⠀⠀⡀⠀⣿⢸⡻⣦⡀⠀⠀⠀⠀⠀⠸⡾⡆⠀⠳⡄⠀⡄⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀
⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⠁⠀⠀⢠⠀⠀⡇⢀⣿⡌⣇⠙⣷⣄⡀⠀⠀⠀⠀⠹⣷⠀⠀⢹⡀⢸⡀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀
⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠀⠀⠀⣿⠀⢸⠇⢸⡿⠹⣹⣀⡀⡙⣟⠙⠓⠲⠶⢤⣿⡇⠀⠀⢳⠸⡇⠀⠀⠀⠀⠈⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀
⣶⣶⣿⣿⠉⠀⡏⠀⢉⠉⠉⠙⡏⠀⣿⠀⠀⠀⣿⠀⣸⢀⡿⠁⠀⣹⣿⠁⠙⠈⢿⠿⣶⢤⣀⠈⣿⣦⠀⠈⣧⣧⠀⣄⠀⠀⠀⠈⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⠛⠉⡇⠀⢰⠃⠀⡜⠀⠀⢀⡇⠀⣿⡄⠀⠀⢸⡄⣿⠞⠁⣀⣼⠟⠁⠁⠀⠀⠀⠀⠈⠉⠛⠻⠿⠾⠷⣄⠸⣿⣧⢻⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢰⠃⠀⡸⠀⠈⠀⠀⠀⣸⡇⢰⣿⣷⠀⠀⢸⣇⢻⠐⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣸⠹⣿⠀⠀⠀⠀⣿⠟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⣸⠀⠰⡅⠀⠁⠀⠀⠀⠈⠳⢬⣿⣿⣦⠀⢸⡟⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⣀⣀⣀⣠⣤⣿⠂⢹⠄⠀⠀⢰⡏⢠⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢣⠀⠙⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠆⢸⠁⠙⣇⡀⢠⣄⣀⡀⠀⠀⠀⣀⡀⠀⠛⠉⠙⣻⣿⣟⣋⡉⠀⠀⢸⠀⠀⠀⣼⠁⢸⡘⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣯⣭⣥⣀⠒⠼⠉⠉⠐⠒⠂⠨⠍⠛⠻⠿⢿⠓⠀⠀⣾⠀⢀⣰⠃⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡯⠛⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣴⢾⠋⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠻⠿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢷⠀⠀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡞⣿⡇⡏⠀⠀⠀⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣷⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠉⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠋⢰⣿⣷⡇⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠒⢄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢱⠀⡟⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⢀⣤⣤⣴⡶⠯⠅⢀⡆⠀⠀⠀⠀⢀⣾⣿⣿⣿⠀⠀⠀⢸⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⠎⠰⠁⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠉⠁⣠⠄⠀⠤⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠀⠀⠀⢸⣧⢹⠀⠀⠀⠀⠀⠀⠀⠀
⠊⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡇⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⢸⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣎⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⡇⠘⣿⣿⣦⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⣾⣿⠘⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠹⣿⣿⣿⣿⣿⡷⣦⡀⠀⣀⣤⠞⠁⠀⠀⠀⠀⠸⡿⣿⣿⢸⠁⠀⠀⠀⣿⡏⠀⠈⠳⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠻⣿⠃⡟⠀⠀⠀⣼⡟⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀
⣤⣤⣀⠴⠒⠋⠙⠛⠻⠿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⢹⡾⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣷⡀⠀⢹⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣠⠞⠓⣶⣦⠤⠤⠤⠤⢤⠤⢤⠤⣄⣀
⡟⡀⠀⠁⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⠘⠿⣦⣄⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢃⡤⠞⢁⡠⠐⢹⣿⡆⠀⠀⡰⠃⠀⠄⠀⠀⠀
⠁⠀⠀⠀⢀⠠⠤⠤⠀⢴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠈⠻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣵⠫⠔⠊⠁⠀⠀⠈⣿⣷⢠⠎⠀⠀⠊⠀⠀⠀⠀
⠀⠀⠀⢀⡦⠤⠂⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣄⠀⠀⠀⠀⠀⠙⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠂⠁⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠛⢦⡀⠀⠀⠀⠀⠀⠹⡈⠲⡀⠀⠀⡠⠊⠁⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠄⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡀⠀⠈⠒⢤⡀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡄⠀⠀⢀⠊⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠑⠢⢀⡀⠈⠑⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⢁⠤⠤⠤⠤⠤⠤⠀⢀⠀⠀⠀⠀⠀⠀
⡇⠀⢠⠁⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠐⠢⢀⠀⠉⠒⠦⢄⡀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⠀⠀⠀⠀
⠁⢀⠃⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⡀⠀⠀⠀⠀⠀⠉⠒⠄⠀⠀⠉⠀⠒⠒⠉⠀⠀⠀⢄⣀⣀⣠⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀
⡀⡌⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠁⢰⡅⠀⠀⢹⡀⢠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠣⡀
⡿⠀⠀⠀⠀⡠⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢵⣄⠀⢧⠈⡄⠀⠀⠠⠂⠀⠀⢀⠀⠀⠂⠉
⠃⡀⠀⣴⣾⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡘⢦⠼⣄⠘⡄⢀⠀⠈⠁⠀⠀⢸⠀
⠀⠀⡜⠈⣿⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⠧⡽⠳⣧⢸⠀⠀⠀⢀⣠⠀⠀
⡄⡸⠀⠀⠹⡄⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠘⢾⠀⠀⢸⠀⠸⠀⠐
⣇⠇⠀⠀⠀⠱⡌⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢸⡆⠀⣼⠀⡀⠀⠀
⣿⡄⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⣇⣷⠃⢀⠁⠀⠀
⣿⣿⣦⡀⠀⠀⠀⠘⢦⡄⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⢘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠈⠁⠀⡘⠀⠀⠀
⣿⣿⣿⣿⣄⠀⠀⠀⠀⠈⠳⠤⣄⣠⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢈⡿⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⡇⠀⠀⠀