⠀⣠⣶⣿⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡎⢻⣽⢶⢀⠀⠀⠀
⢀⣵⣔⢺⡆⠀⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⢉⠆⡜⡱⡄⠀
⠀⠸⢈⡏⠀⠀⠀⢲⣮⣦⡀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠹⡀⠴⠟⠽⠄
⠀⠀⢸⠀⣇⣆⣦⠑⢈⠁⠵⠒⠒⢞⡁⠀⠀⠀⠀⡀⠀⠀⠓⠿⣟⠄
⠀⠀⣸⠄⠿⠘⠚⠉⠀⠀⠀⠁⠀⠀⠀⠉⠑⠂⠔⢓⠠⠞⠀⢀⠇⠀
⠀⠀⢸⡀⠀⠀⠀⠈⠒⢄⠀⠀⠀⠀⡐⢀⡇⠀⣀⣚⠀⢴⠀⡌⠀⠀
⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠹⠆⡀⠪⠂⣊⠤⠒⠊⠙⠲⡤⠋⠀⠀⠀
⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⡀⠓⠈⠀⠀⠀⠀⠒⢺⠃⠀♥

░░░░░▄▄░░░░▐█▄░░░░░
░░░░████▄▄▄█▌░░░░░░
░░░░▀████████░░░░░░
░░░░░░▀███▀▀░░░░░░░
░░░░░░░░╩═░░░░░░░░░

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣠⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢟⠮⢯⡳⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⠳⣱⢍⣯⡟⠀⠀⠀⠀⠀
⠠⠀⠠⠀⢨⡼⠉⡳⢦⣌⡀⠠⢰⢏⢜⡱⡹⢖⢯⡞⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣕⠀⠪⡢⢪⡙⢖⢫⠢⡣⢪⢊⠖⠥⣇⠀⠀⠀⠀⠁
⠀⢀⠀⠀⠀⢳⡄⠣⡊⠦⣣⢗⢕⢍⢎⢎⢜⡱⡑⢾⡄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠳⡌⡪⢘⡎⠦⡑⡕⣱⢇⡣⡪⣊⢺⠃⠀⠀⠀⠀
⡀⠀⠀⠐⠀⠀⠀⢧⠊⡔⣙⢓⡛⡝⡱⢅⢎⠪⣬⠋⠀⠀⠀⠀⠀
⠀⠀⠠⠀⠀⢀⠀⠈⠳⢔⣄⠕⢌⢌⣪⣢⠷⠋⠁⠀⠀⠀⠀⠀⠀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⣖⣋⠀⠚⠓⠦⠄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠘⠈⠁⠀⠀⠀⠀⠀

.................................⡐⢊⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠇⠀⢀⠂⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀
⠀⠀⠀⡸⠀⠀⠀⠰⠷⠀⡄⠀⠀⢤⠀⠾⠇⠀⠀⠀⠀⠣⡀⠀⠀
⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠁⠀⠀⠀⠈⠀⠀⢀⠀⠈⠢⠀
⡜⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣱
⢧⠁⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢰
⠠⠤⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡢⠤⠈
⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⠀
⠀⠀⠀⠀⠁⠢⠤⢰⣥⣘⣀⣀⣀⣀⣐⠼⠴⠥⠔⠪⢁⠤⠜⠁⠀

..............................,⡰⡫⣎⡻⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⡞⡼⡜⣕⢇⡔⡖⢦⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢪⢞⡜⡮⡪⡧⣫⢺⢕⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠄⠂⠉⠑⣗⠵⠝⠼⠕⡳⣱⡣⣳⠁⠀⠀⠀⠀
⠀⠀⠀⠀⡠⠊⠀⢀⣷⠃⠀⠀⠀⠀⠀⠀⠀⠈⠘⢇⠀⠀⠀⠀⠀
⠀⠀⢀⠌⠀⠀⠀⠀⠁⡐⢀⠢⠀⠀⢸⣾⠀⠀⠀⠀⢢⠀⠀⠀⠀
⠀⠀⠎⠀⢀⠀⡄⠀⠀⠑⠂⠊⠀⠀⠈⠁⠀⠀⠀⠀⠀⢆⠀⠀⠀
⠀⠘⠀⠀⠈⠒⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⠀⠀⠀⠀⠀⠀⡇⠀⠀
⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀
⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀
⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀
⠀⠀⠀⠀⠮⠶⠤⣀⡀⠀⠀⠀⠀⠀⠀⢀⢀⣠⢴⠊