⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣀⣀⣠⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣝⡛⠛⠿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⣿⡿⠉⠀⢣⠀⠈⠙⠿⣿⡛⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⠿⠒⠛⠉⠀⠀⠀⢸⡆⠀⠀⠀⠘⢧⠘⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡫⠕⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠟⠒⠉⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⡷⠖⠃⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣽⢯⡟⠙⠁⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⡟⠉⠃⠀⠀⢄⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣧⣇⠈⠀⠀⠀⣀⡤⠴⠶⣎⣉⡙⠻⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠈⢦⠀⠀⠀⠘⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⣿⣿⣾⣦⣤⠴⠊⠀⠀⠀⠀⠀⠀⠈⣝⣧⡝⢿⣿⣿⣿⠀⡀⠀⠀⠀⠈⣦⢀⠀⠀⢹⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣾⠟⠋⠳⣄⠀⠀⠀⣈⢳⣼⠟⠈⠪⣻⣿⣿⣼⣿⠀⠀⠀⠀⠘⡆⠀⠀⠀⣷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠘⣶⠤⢵⠾⠋⠀⠀⠀⠀⠈⠻⣿⣿⣿⡀⠀⠀⠀⠀⢹⢀⠀⠀⢹⣇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⠀⢻⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⡇⠀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣇⠀⠀⠀⠀⠈⡇⠀⠀⠀⣿⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢰⠁⣴⡗⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣿⡿⠋⠀⠀⠀⠀⠀⠀⢠⣯⠞⠙⢆⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣐⣒⣒⠶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⣼⡟⠁⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠈⢦⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠭⠋⠉⠫⠽⣺⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣦⣼⠋⠀⠀⠀⠀⢀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠈⠳⡀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡶⣵⣞⠉⢮⣷⢄⣀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠔⣩⠞⠁⣸⡿⣄⣀⣈⣵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀
⠀⣀⣀⣀⡀⠤⡶⠷⡞⢁⣠⡾⠋⠈⠒⠲⠚⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢤⡈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀
⠸⣿⢶⢾⣍⣉⣆⠀⣉⣉⣉⣀⣀⣤⠤⠤⠄⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠓⠮⣷⣤⡀⠀⠀⠀⠀⣀⡤⠞⣀⡀⠀
⠘⠂⠬⠫⠽⣖⣒⣒⣂⡤⠬⠭⠤⠀⠀⠒⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢉⣀⡀⠤⠤⠘⠃