⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠾⣛⣛⡻⢿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠻⣟⡫⡭⣙⣻⣾⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢗⠱⠽⣾⣞⢑⡳⣮⠅⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣄⣤⣶⣿⣿⣿⣷⣿⣷⣿⣿⣿⡿⠿⣿⠦⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠘⣶⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⡿⣯⣿⣿⣿⣿⣿⣿⢟⣯⣾⣗⠀⢰⢿⣿⣿⣿⢟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣿⣿⣿⣮⡻⡛⢿⣯⠷⡿⣛⣡⣤⣶⠀⢹⣿⣿⡯⣻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠟⠁⣴⣿⣿⣿⣷⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⢻⣿⣿⣿⣿⣿⣿⡿⠋⠀⣠⣾⣿⡿⡿⣿⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣼⣿⡟⠸⣿⣿⣿⡿⠋⣁⣀⢀⣴⣿⡿⣅⠜⠁⣿⣟⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢽⣿⡟⢀⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣗⢣⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠨⣿⠀⠘⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⡄⠀⠘⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢰⣿⣇⠀⠀⢸⡿⠟⠱⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢨⣵⣤⣿⡿⣟⣿⣿⣯⣿⣟⣻⣛⡋⠧⣶⣿⣿⠀⠀⠀⢘⡡⣁⣀⡑⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠉⠙⢹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠃⠙⣷⠱⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡟⠀⠀⠻⣿⣿⣿⣿⣧⠀⠀⠀⠀⢰⠙⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡇⠀⠀⠀⠘⢿⣿⣿⣿⡀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⣴⣿⣷⣿⣷⠀⠀⠀⡌⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⠀⠀⠀⠀⢹⣿⣿⣿⡷⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠃⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⢦⣮⣽⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣌⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣽⣹⣦⣧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⢻⣤⣦⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⠌⠉⠋⠀⠀⠀⠀⠀⠀