⠀⠀⠀⡠⠂⢀⡆⠀⠀⢕⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⣀⠠⠄⣀⣀⡀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⡀⢰⢸⠡⢄⠀⠀⠈⠈⠑⠒⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄⣀⣀⡀⢀⡀⠂⠠⠀⠱⢡⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠜⡜⢿⡄⣯⠁⠗⡤⣢⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠢⠐⠢⣄⠀⠀⠀⠀⠀⠈⠁⠀⠉⠑⠄⠀⢀⠨⣢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠄⠊⠑⢌⢸⠏⣆⣌⠾⠍⠛⠒⠋⠓⠞⠒⠶⠤⠤⠔⠄⣑⡁⠒⠒⠒⠐⠒⠒⠄⣀⠀⠀⠀⠀⠀⠀⠈⡡⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⡲⠀⠀⡀⡻⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠠⡀⠀⡈⢮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠰⠉⠉⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠱⡀⠁⠀⠱⠀⢰⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠷⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣠⡴⠖⠚⠉⠁⠀⠀⠑⠤⠐⢄⢠⡀⡩⡡⣐⡤⣧⠈⢀⠪⠀⠈⡏⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠠⠐⠀⣩⣴⡾⠖⠂⠀⢀⣀⣀⠀⠀⠀⠀⠀⠢⡕⠄⢇⠈⣦⡢⢠⠆⠀⠀⢠⢠⠰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡎⠀⠀⠀⠀⢠⠀⠐⠚⠋⠙⠴⣾⠟⢋⠀⠊⠀⠀⠀⠀⠀⠀⠈⠋⠐⢌⡀⢉⢂⢎⠃⠀⠀⠀⢿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢲⠨⡗⢏⡌⡆⠀⠀⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠇⠂⡝⢸⡌⠃⠀⢤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠘⠀⠸⠳⢠⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠍⠆⢠⡁⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠧⡀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⡌⠀⠈⢀⡇⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢱⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢹⠀⠀⡘⠅⡆⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡄⠀⣀⡖⠀⠀⣂⠨⠁⠀⠁⠀⠀⠀⠀⠀⠀⢀⡰⠃⠀⠀⢸⠀⠀⡟⡀⡿⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢀⠀⠀⠀⢸⠀⠈⠀⠷⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⢀⠂⣀⣀⣀⡀⣈⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢋⣀⠤⠤⠒⠂⠂⢈⠋⠉⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⢀⣠⡶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠚⠁⠃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠀⠀⠀⠐⠒⠣⡀⠛⠊⠶⠒⠞⢳⠒⠒⠒