⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣫⣯⡌⣡⣾⣿⡗⠀⢀⣾⣽⣿⣿⢿⢏⣿⡇⡇⢀⢸⣼⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣹⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⣿⣿⣿⣿⣷⣿⠟⢠⣾⣾⣿⣿⡿⣿⣾⣾⢻⡇⡇⡞⢘⣿⠈⢷⣀⡄⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣟⣽⣿⣿⣿⣯⣾⣾⣿⣿⣿⣋⣰⣿⣿⠇⠘⣿⡇⡏⠸⡟⠀⠈⢧⣷⢸⣆⠀⢠⠀⠀⠀⢸⣠⠀⠀⠀⠸⡇⠙⣿⣿⣿⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣿⣿⡿⣯⣿⣿⣾⠿⣿⡿⡋⠉⢻⣿⣽⣄⡀⣿⣿⣿⣿⢇⣀⣀⣈⣿⡏⣿⣿⣸⢰⡆⠀⢸⢸⣀⠀⠀⡄⣿⡀⣿⣿⢳⣿⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢋⣿⡿⣿⣿⣿⡿⠃⠈⠙⠲⣿⣿⣿⣿⣿⡉⠁⢹⣸⢸⣿⠋⠉⠉⠙⠛⣷⣿⣿⣿⢸⢳⣇⢸⢸⢻⢀⣴⣿⣧⢷⣿⣼⡆⠉⠓⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣷⣿⣿⠃⠐⣷⣄⠈⢿⣿⡟⢻⣿⠇⠀⠘⢻⡀⣿⣒⣶⣶⣤⣄⣸⣿⡏⣿⢸⣸⣻⣾⣸⢸⣿⣿⣿⣿⣦⣿⣿⣿⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢾⣿⠀⠀⠈⠛⠿⠗⠲⢤⣤⡋⠀⠀⠀⠀⠀⢨⡿⠟⢻⣿⡿⡿⢿⣅⣹⢸⣿⣿⣿⣿⣾⣿⣷⣿⣟⣿⣿⠻⡟⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣶⣬⣛⡛⠁⣀⣠⠌⣿⣿⣿⣿⣿⠟⣿⣻⢸⣷⣿⡏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⠭⠿⠋⠀⠀⠘⣿⣿⣿⡿⠀⣼⣫⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⢁⣼⣿⣿⣿⢻⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢳⣿⣷⡀⠀⠀⠀⠀⠀⠀⠰⣤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⣿⣿⠿⠘⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣻⣯⣿⠟⠁⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⣿⣿⣇⠀⠀⠙⠳⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡿⣆⠀⠀⠒⠦⣤⣈⠉⠛⠶⠤⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⢹⡇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢾⡇⢹⣆⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⣀⣴⠿⢋⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⢸⡇⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠉⠀⠀⢸⠟⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⣶⡟⠡⣤⡀⢸⡇⠈⣧⠈⠻⣶⠤⠤⠤⠶⠶⠛⠉⠁⠀⠀⠀⠀⠀⡟⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⠟⠁⠀⢀⣴⠟⠀⠀⢻⣆⢸⡇⠀⡗⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢸⡷⠟⠀⢹⣧⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⡴⠶⠾⠛⢉⡽⠋⠀⢀⣠⣤⡾⠃⠀⠀⠀⠀⠉⠛⠳⣤⣅⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣡⡴⠟⠁⠀⠀⠈⣿⡀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠛⣁⣤⠴⠖⠛⠋⠀⠀⢠⠏⣹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣿⢀⣀⣤⣤⠴⠶⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⠀⠙⠳⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠘⣛⣲⣶⣶⣶⡖⠀⠀⠘⠃⣿⣇⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣷⣾⣿⣿⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡝⣦⣙⢧⡀⠀⠀⠉⠉⠳⢶⣶⣤⣄⣀⣀