⠀ ⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣶⡏⠀⠀⠈⠉⠙⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⢶⡶⣦⣤⡀⠀⣠⣤⠶⠎⠉⠉⠀⠀⢮⣷⡆⠀⠀⠀
⠀⠀⠀⢀⣼⢻⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠤⠶⠛⠛⠛⠛⢻⣿⡻⣜⢧⡻⣝⡞⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⢠⢂⡿⣀⠀⠀
⠀⠀⠀⢸⣇⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣸⣿⢳⡝⣮⣳⣝⡾⡼⣭⣻⣇⢀⠀⠀⠀⠀⠀⠀⠰⡨⠔⣿⠀⠀
⠀⠀⠀⢸⡧⣹⠀⠀⠀⠀⠀⠀⢀⡠⠔⠈⠉⠀⠀⠀⠀⣿⢮⡳⣝⣶⣟⡻⣿⣷⡟⣟⡻⣟⣧⡄⠀⢠⣤⣤⣤⣷⡜⣿⠀⠀
⠀⠀⠀⠘⢳⣬⠇⠀⢀⠠⠖⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣳⡝⣞⠾⣿⣽⣷⢫⡞⣵⢻⡼⣽⣿⣿⣿⡹⣎⢷⣫⢟⣦⠀⠀
⠀⠀⠀⢠⡿⠈⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣷⣽⣮⣿⢷⣿⣯⣷⡹⣎⣷⣿⣯⡿⣏⢿⣷⡹⣎⢷⢫⣿⠀⠀
⠀⠀⠀⡇⠀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠾⠿⠏⠁⠘⠿⠿⠿⠾⣿⣿⢿⣾⢳⡝⣮⢏⣷⣿⠀⠀
⠀⠀⣿⡃⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣷⣮⢳⡝⣮⣿⡟⢼⡇⠀
⠀⠀⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣿⣷⣿⡓⠋⢳⣸⡇⠀
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡇⠀
⣀⣀⣿⣀⣀⣀⣀⡀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⢐⣀⣀⣀⣀⣷⣇⣀
⠉⠉⣿⡍⠉⠉⡍⠁⠀⠀⠀⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠈⡉⠍⠉⠉⣿⠉⠉
⠀⠀⣀⣇⡴⠶⠆⠀⠀⠀⢀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⣶⢿⡟⣦⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⡀⠀⠀⠀⢶⠶⢆⣿⣀⠀⠀
⠘⠛⠋⢹⣇⠀⣀⣤⣤⠀⡀⠀⠀⠈⠀⢀⣀⣀⡀⠀⠀⠉⠛⠚⠉⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢈⠆⣤⣄⣀⠀⣸⡏⠉⠛⠃
⠀⠀⠀⢠⡾⠷⣏⠁⠀⠀⠈⠁⠀⢡⡶⠾⠉⠉⠹⢶⡀⠀⠀⠀⠀⠀⢠⡶⠉⠉⠹⠶⢦⡀⠈⠁⠀⡀⠎⣍⠶⢧⡀⠀⠀⠀
⠀⠀⠈⠋⠁⠀⠘⠳⣀⣀⠀⠀⣸⠏⠁⠀⠀⠀⠀⢈⣿⠀⠀⠀⠀⢸⡏⠁⠀⠀⠀⠀⠈⠿⡀⠀⣀⡠⠞⠋⠀⠈⠛⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣤⠟⠀⠀⠀⠀⠀⣠⣾⡟⠀⠀⠀⠀⠘⢯⡇⡄⠀⠀⠀⠀⠀⢿⡖⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⣟⣿⠉⢉⣉⣉⣉⣉⡉⠉⢻⡞⡄⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣌⠦⡠⠤⣴⣾⢛⠄⠚⠀⠀⠀⠀⠘⠒⢾⠫⣷⡀⠤⠤⢼⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢻⠿⠻⠏⢡⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠉⠻⠟⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠰⣿⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⠀⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⢸⣿⣐⣦⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠙⠀⣀⠀⢀⡘⠉⠀⠀⠀⠀⠀⢰⣿⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⠂⣿⢂⡆⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠈⣜⣿⡂⠆⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⠶⠶⠴⠶⠾⠛⠃⠛⠻⠴⠶⠶⠶⠴⠞⠃⠀⠀⠀