⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠸⣿⣇⣀⣀⣀⡀⠈⠉⠉⠉⢹⣿⠀⠀⠀⣸⡿⣀⠀⣿⡧⢍⣿⢩⣿⢉⣸⡇⠀⣿⡟⠀⠀⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠂⠀⠀⣶⡆⢸⣿⠀⠀⠚⣋⣀⣘⣃⣛⡃⢸⣿⣸⡟⢀⣸⡇⢀⣿⢧⡈⠙⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⢨⣭⠿⠇⠉⣿⡇⣀⣀⣿⣇⣈⣉⡀⠀⠀⣤⣤⠀⠘⠛⠃⡼⢁⡟⠙⣦⢸⣧⡼⠃⠈⣿⠀⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠉⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⡤⠤⠼⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⢤⣤⠀⠠⠤⣤⡄⠀⣶⡄⠀⠀
⠀⠀⣠⠶⠋⢉⣀⣠⣶⣶⣾⠿⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣶⡖⠛⠋⠘⣿⡇⠀⠀
⡴⠋⣠⡴⠚⢉⣀⣴⣿⣧⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⢨⣭⠭⠭⢤⣭⡀⠀⠀
⣠⠚⠁⠀⠸⠟⠛⠛⡏⠁⠀⠀⠀⠀⠀⠀⠙⠳⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠂⠘⠿⠤⠤⠴⠿⠃⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⣲⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠤⣀⣀⣀⣀⠀⠀⢀⣠⠞⠀⠀⠘⢄⠉⠉⠉⠛⠛⠒⠶⠶⠤⠤⣤⣀⣀⣀⣀⡠⠤⠤⠤⠴⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁⠒⠤⢄⣀⡀⠀⠀⠀⣠⠎⠀⠈⢆⠀⠀⠀⠀⣠⡤⢤⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢸⡄⠀⠀⠸⣧⡀⣀⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢀⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⡴⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠫⣀⣨⠇⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⠀⢸⣇⠞⠀⠀⠀⠀⠀⠙⣄⠀⢰⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠹⣷⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⠀⠀⠘⣿⣿⣿⣿⣿⣷⣶⡶⠆⠙⢾⠀⢀⣤⠔⠋⠀⠀⠀⠀⠀⠀⢻⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⣧⠀⠀⣿⣿⣿⡇⢀⣿⣿⣿⣦⠀⠾⠚⠫⣽⣄⣴⣶⣿⠻⣿⣿⣷⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀
⣇⠀⠀⠀⠀⠈⣧⡀⣏⠀⠀⠈⠉⠉⠉⠙⢻⠀⠀⠀⠀⠀⢿⣿⣿⡧⠤⠿⠿⣿⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⣆⠀⠀⠀⠀⡏⠙⠿⠳⠀⠀⢀⠀⠠⠔⠋⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⣠⠃⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⠳⣄⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠉⠉⠑⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠞⠀⡌⠓⢦⣘⡷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣎⠴⠊⢀⣔⡃⠀⠁⠀⠉⠓⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⠀⠀⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠑⠢⠤⠤⠤⠧⣦⣦⣔⠣⣤⠊⠀⠹⣿⠭⠻⣒⠶⣶⡦⢤⡤⡤⠤⢤⡤⠤⠤⢶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣌⡑⢤⡀⠘⢶⡒⠂⢈⡠⠖⠋⠀⠑⢒⣩⣧⢀⣤⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀