⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣠⡄⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⢈⣭⣿⠆⢀⣠⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡘⠆⢠⣸⡿⢿⣭⣶⡿⢛⣡⣶⣾⣿⡄⠀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⢀⡀⣀⣴⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢾⠿⣋⣥⣾⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣷⣌⢦⡀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣿⢟⣵⠋⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣦⢻⣦⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣳⣾⣿⣷⠞⣱⣿⣿⡄⠀⣿⡿⣩⠉⠻⣿⣿⣿⣿⣇⠉⠻⢿⣿⣿⣿⣏⢻⣧⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⣼⣿⣿⢋⣾⣿⣿⣷⣿⠾⣫⠞⠁⠀⠀⠈⢻⣿⣿⣿⡀⠀⠀⠙⢿⣿⣿⡎⢿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⠀⣹⠟⡿⢡⠟⣻⣿⡿⢋⣥⠞⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇⠠⡀⠀⠀⠈⠻⣿⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣼⢋⡾⢡⣿⣿⣿⡏⡄⠛⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠈⢿⡇⠀⢿⣦⡀⠀⠀⠙⠷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡿⢡⣿⣿⣿⣿⣷⢱⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⢠⠸⡇⠀⠸⣿⣿⣆⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢡⡿⣿⣿⣿⣿⣿⣆⢦⠀⠀⠀⠀⣠⣴⣿⡿⢉⡴⠋⣤⡆⣷⡄⣿⣿⠏⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⢀⣴⣿⣶⣄⠀⠀⠀⠀⠀⠴⠀⠘⠁⢿⣿⣌⢿⣿⣿⣿⣿⣦⣀⡀⠀⠘⠿⠿⣋⡴⣻⠞⢁⣿⠀⣿⡇⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⢀⣴⣽⣿⣿⣿⣿⣿⣷⣶⣶⣶⡄⠀⠠⠀⠑⠛⠛⠳⢿⣿⣿⣿⣿⣿⣿⣦⣀⣐⣚⣫⣾⣥⣶⣿⠇⠀⣿⠃⣿⢡⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣦⣄⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠉⠉⠋⠉⣥⣴⠀⢀⡟⠀⡇⢿⡆⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠲⣶⣤⣤⣄⣀⣹⣿
⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣿⣷⣦⡐⢶⣶⣶⣶⣶⣶⣦⣤⣤⣴⣾⣇⣀⢿⡌⣷⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⡇⠀
⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⡈⡻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠈⢿⣿⣿⣦⣄⠩⣭⣭⣵⣒⣒⣲⣿⣿⣿⣿⠸⠡⣿⡆⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢧⢳⡙⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠙⠛⠛⠿⠿⠶⢦⣭⣭⣟⣛⣛⣛⣛⠟⢠⣦⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠉⠀