⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀
⠀⠀⢻⠋⢑⠒⠂⠢⠤⠤⠤⠤⠤⠤⠨⢐⡰⣶⠮⣿⢦⠖⠒⠺⡙⠛⢿⣛⠒⠤⢍⠉⠉⠑⠿⢶⡒⠒⠋⠑⠒⠈⠈⠉⠉⠉⡩⢳⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠑⢄⠑⠡⡀⠀⠀⠀⠀⢀⡤⠒⠉⠉⡠⠊⡠⠁⠀⠀⠀⢳⡀⠀⠉⠳⣢⡀⠁⠠⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⣀⠴⢉⠔⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢙⠴⠈⠁⠂⣤⠔⠁⠀⠀⢠⠊⠀⡔⡘⠀⠀⠀⠀⠀⢳⠀⠀⠀⠈⢧⡄⠀⠐⠄⠀⠀⠈⠢⠀⢠⠔⠈⢀⢴⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⠃⠀⢑⣔⠔⠁⠀⠀⠀⡰⠁⠀⠐⢠⠃⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠩⣆⠀⠘⠄⢄⠀⠀⠐⠄⠃⠰⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠀⠀⢀⣾⠊⠀⠀⠀⠀⡸⠁⠀⢀⠃⣸⠀⠀⠀⠀⠀⠀⠀⢨⠀⢰⠀⠀⠀⢹⣦⠀⠠⠈⡄⠀⠀⠈⢂⢇⠢⡀⠈⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠂⠀⠀⢠⠃⠀⠀⡼⠀⢋⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⡇⠀⠀⠀⡿⡄⠀⠀⠻⡄⠀⠀⠀⢾⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡾⠁⠀⡌⠀⠀⠀⡎⠀⠀⠀⡇⢀⡀⠀⠀⠀⠀⠀⠀⠸⡇⠇⠀⢱⡀⠘⡄⢰⢱⡀⠀⡏⢳⡀⠀⠀⠀⠗⠈⠻⡃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠰⠁⠀⠰⠀⠀⠀⠀⠁⠀⠀⢸⠇⢘⣇⡄⠀⠀⠀⠀⠀⠀⡇⢸⠀⢂⠱⠀⠐⡀⠀⢇⢀⠇⠨⠑⡀⠀⠀⠘⡄⠀⣇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠆⡈⠀⠄⠀⠀⠀⠀⠀⠀⢠⡇⢻⢨⢹⣇⠀⠀⠀⠀⠀⠀⡄⠈⠀⢰⠘⣇⠀⢷⠀⣸⡾⠀⠀⡆⠰⡀⠀⠀⠰⠀⢹⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡸⢠⠃⠀⠀⠀⠰⠀⠀⠀⠀⣼⢂⢨⢳⠀⢿⠰⠀⠀⠀⠀⢂⡇⠀⡄⢸⠀⠸⣆⠈⣶⡝⢇⠀⠀⢃⠀⠰⡀⠀⠀⢆⠈⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠃⣼⠀⠀⠀⠀⠐⠀⠀⠀⠀⣿⡇⠸⡸⡀⢸⡇⠣⠀⠀⠀⢸⡇⠀⠀⡈⠀⠀⠙⡄⢛⠀⢸⠀⠀⢸⠀⠀⡕⡀⠀⠈⡀⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢘⣬⠁⠀⢳⡅⠈⢻⡀⠀⠀⠀⠾⡇⠀⠄⡇⠀⠀⣐⣣⠈⡂⠀⡀⠀⠘⠀⠀⠘⢾⠄⠀⠰⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⡇⠀⠀⢸⣩⣀⣤⠬⡷⠤⠈⢷⡀⠀⢀⢃⠃⠀⡿⢋⣴⣾⣿⣿⣿⣿⣦⣅⠀⠀⠀⠀⢠⠸⠌⠢⠀⠱⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⠀⠀⠀⡇⡜⠀⣇⣼⣿⣿⣿⣿⠿⢦⡀⠀⢳⣄⡸⠘⠀⢰⡇⢡⣿⣿⣿⣿⣷⣀⣧⣽⠃⠀⠀⠀⢈⠀⡇⠁⢱⡄⠣⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⡇⠀⠀⢀⢰⠀⢟⠁⣿⣿⢿⣿⣓⢾⡃⠀⠀⠙⠃⠀⠀⠀⠀⠀⢻⡀⠊⠉⠈⣸⠁⡋⠀⠀⠀⠀⢰⠀⣧⠸⠀⠙⢄⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡏⢠⠀⢸⠀⣇⠸⣈⠙⢇⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⠶⠁⢀⠀⡄⢰⠀⠀⢸⡄⠹⡆⠀⠀⢉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢐⢃⠘⡀⠘⠀⠹⡄⢿⠀⠈⠢⢤⡤⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢠⠁⢸⢰⠀⢸⡇⠠⢳⡀⠀⠀⡂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠂⠈⡀⠃⠀⡇⠀⢻⣌⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡡⡏⠀⡌⢸⠀⢸⡇⠰⠀⣷⠀⠀⠐⡀⠀⠀⠀
⠀⠀⠀⠀⡀⠅⠄⢡⠈⡀⢡⠀⠐⠻⣮⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣴⡇⠀⡇⡆⠀⣾⡇⢸⠈⡞⡇⠀⠀⠅⠀⠀⠀
⠀⠀⠀⠀⠨⠀⡇⠀⣧⠑⡸⡄⠀⠀⣿⡦⡉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣤⠊⢸⡇⠸⢠⠃⢀⣿⡇⢸⠀⢱⠘⡄⠀⠈⡆⠀⠀
⠀⠀⠀⡸⠃⠀⢰⢠⢿⡳⡔⢧⠀⠸⣿⡇⠈⣶⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡾⢛⡇⠀⢸⡧⢣⡿⠀⡼⣿⡇⢸⡄⠈⡗⡈⢆⠀⠩⠀⠀
⠀⠀⢠⠁⠀⠀⢸⡟⠀⣷⠘⢮⡢⡀⢻⣇⠀⣿⡇⠀⢹⢳⡆⠠⢄⣀⠀⣀⠄⠊⠁⢸⡇⠈⣷⠀⣸⡇⣞⠃⡜⢰⡏⠀⣾⢳⠀⠠⠘⢾⡁⢄⠙⡄
⠀⢀⠆⠀⢀⠂⡼⠁⠀⣾⡆⠀⠹⡻⢴⣿⣀⣟⡇⠀⢸⣚⣷⣤⣤⣤⣬⣤⣴⣶⣶⣿⡇⠀⢿⠀⣽⡽⠉⠔⠀⣾⡸⢀⡿⠸⣧⠀⢃⠈⢣⠀⠠⡀
⠀⠌⠀⢀⠂⣸⠃⢀⡰⠧⠿⠄⠀⠓⠀⠼⣿⣿⣧⣴⣾⣿⡿⠿⢿⣿⣿⣿⡿⠿⠿⠛⠿⣷⣾⣦⡿⢡⠎⠀⣸⣿⠃⣼⡇⠀⢻⣇⠈⡄⠈⢆⠀