⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣕⡒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡽⣻⣦⡀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⢯⣟⣳⣽⣻⣦⡀⠀⠳⡄⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠓⢶⡶⠶⣶⣞⣯⢟⣞⣯⢞⣷⣿⣿⣿⣷⣶⣶⣾⣿⣿⠟⡻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⢦⣄⠉⠙⠺⢞⣿⣿⡿⠏⠹⡍⣿⣿⣿⣿⣿⣷⣷⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣻⢞⡷⣦⡀⣸⣿⡟⠘⢀⣃⣴⣿⣿⡿⠋⠉⠛⣟⡛⢤⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⢻⣼⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⢿⣾⡞⣏⡠⠔⠢⢤⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⡼⣣⣿⣿⡿⠟⠉⣿⢉⡿⠛⠳⣄⠉⢧⡀⠀⢠⡾⢋⡿⠉⣀⣀⠀⠀⠙⡄⠀
⠀⠀⠀⣤⣤⠤⠶⠿⠼⣯⣾⣿⣿⣟⠀⠰⣾⣇⢸⡦⣤⣴⡛⡇⠀⡇⢀⣯⢁⢾⠀⠈⠀⠈⠁⠀⠀⡇⠀
⠀⠀⠀⠀⢀⣻⠿⠛⢚⣉⣉⣠⠀⠀⠀⠀⠀⠙⠢⠷⠽⠿⠿⠇⠊⠀⠸⣼⠸⢸⠀⠀⢀⡀⠀⠀⢠⠃⠀
⠀⣀⣴⣮⣽⢶⡶⣿⢻⣽⠟⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⡯⠴⠻⠖⠊⠉⠉⠉⠹⠀⠀⠀
⠈⠉⠀⠙⣯⡟⣼⡷⠋⠁⢀⣤⢶⣻⠋⠀⠀⠀⠀⠀⠐⠊⠁⠀⠀⠉⠚⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀
⠀⠀⠀⠀⣿⡽⠋⣀⡴⣞⠻⣘⣼⠃⢀⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠤⠤⠔⠒⠁⠀⠀⠀⠀
⠀⠀⠀⣰⣫⢶⣿⣭⡓⡌⠓⣼⠃⣠⢿⣿⣯⡉⠓⢶⣶⣶⣶⣶⡟⠁⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⠋⠀⠀⢳⡌⢿⣬⢱⡏⣰⢿⡀⠙⢿⣿⣦⠠⡈⠙⠻⠟⣇⠀⠀⠙⠿⠿⣿⣷⣶⣤⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣏⠤⢻⣿⡼⢃⠾⡇⡱⡀⢻⣿⣷⡐⡀⠀⠀⠈⠦⣀⠀⠀⠀⠀⠀⠙⣿⠟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡟⢠⠉⠟⡁⠎⣼⡇⠈⠣⠀⣿⣿⡇⡅⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣤⣼⠵⠶⠮⠴⠵⢶⡞⣈⠆⠀⣰⣿⣿⠇⡃⠀⠀⠀⣀⡠⢤⣖⣛⢞⣹⣍⣯⣟⣋⣀⣀⠀
⠀⠀⠀⠀⠀⠈⢯⠉⠓⠲⢶⣴⣫⠽⠀⠀⠐⢿⣿⠏⡘⠀⣠⠖⠉⠁⠀⠀⠀⠛⢻⣭⡾⠴⣦⣵⠚⠉⠀
⠀⠀⠀⠀⠀⠀⢸⠀⣁⡶⠟⠉⠀⠀⠀⡀⠀⡠⠙⠊⣠⠞⠁⠀⠀⢀⠀⠀⠀⠀⠁⠙⢧⣋⢖⣩⣙⣳⣤
⠀⠀⠀⠀⠀⢀⣮⠞⠉⠀⠀⠀⠀⠀⠀⢷⠀⠇⠀⢰⠃⠀⠀⠀⠀⠈⠑⠶⣄⠀⠀⠀⠈⡟⢏⠁⠀⠀⠀
⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⡃⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⡴⠃⠘⡆⠀⠀⠀
⠀⠀⠀⢀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡣⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⡇⠀⠀⠀