⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠉⠉⠉⢢⠤⠤⡀⢀⣀⣀⠀⡠⠖⠋⠉⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠈⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠠⠄⡀⠀⠀⠀⢀⠄⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠹⠔⠒⠢⠇⠀⠀⠀⠀⠀⠀⠠⠤⡖⠁⠘⡄⠀⠀⠀⠀⣠⣃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠰⡄⠀⠀⠈⠁⠀⠙⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⡜⠂⠲⠀⠀⠀
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠀⠀⠘⠒⠂⡀
⠀⢀⡠⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⠂⠈⠆⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⡝
⢠⠋⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⣀⣀⡠⡂⠀⠀⠀⠠⡄⠀⠀⢀⡀⠀⢀⡰⠃⠀⠀⠀⠺⣅
⡇⠀⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡄⠀⠰⣀⡠⣀⠀⢀⣠⠎⠉⣹⣀⠀⠀⠀⠀⠀⣸
⡇⠀⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢷⠒⠂⠐⡎⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠁⠀⠉⢢⠀⢰⠊⠁
⠘⢤⡤⠀⠀⠀⠑⠂⠐⢆⠀⣄⣀⣀⠀⠀⡀⢀⡴⠀⠀⡧⣀⠜⠑⠂⢺⢳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜⠐⠃⠀⠀
⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢎⠀⠡⠀⠀⠱⡀⣠⠀⠀⡏⠈⢱⢲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀
⠀⠱⣄⡀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠉⢫⣁⢫⡳⢄⢣⠀⠀⠉⠀⠀⢰⠇⢀⠇⢾⡻⠖⢖⠁⠀⡀⡀⠀⢀⡼⠀⠀⠀⠀
⠀⠀⠀⠀⠸⡀⠀⠀⠀⠐⣄⣀⣀⡠⠎⠓⢯⡀⠀⢸⠀⠀⠀⠀⠀⣸⢁⠎⡴⡋⠀⠀⠀⡉⠉⠀⠈⡏⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠒⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⣿⢏⡾⠝⠓⠢⠤⠊⠈⠑⠒⠊⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⡠⠄⣀⣿⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡜⣉⢿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠸⡱⡻⡸⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⢄⡀⠀⢀⣀⣀⢇⠀⠀⠀⠉⠈⠀⡎⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⢤⡤⠀⢘⡆⠈⠋⣑⣽⣾⠌⠀⠀⠀⠀⠀⠀⠣⣸⣄⠀⢹⡅⠀⠔⠪⠿⢤⣤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠀⢀⣤⣖⣋⣁⣀⣋⣀⣀⠀⠒⠒⠄⠀⠀⠈⠈⠓⠦⢤⣀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⣄⣸⡟⠒⠒⠒⠒⠒⠚⠛⠀⠀⠀⠀⠀