⢀⣤⡴⠶⠦⠦⡀
⠒⠒⣤⣤⣤⡴⡴⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠶⠦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠈⠉⠛⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡾⠇⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠚⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⣿⣦⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠛⠃⠀⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣅⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠟⣁⠀⠀⠀⠀⠀⠀⠀⣷⢸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⠄⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⣿⣸⣿⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣿⣿⣿⣿⠇⡿⠀⠀⠀⠀⠀
⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣏⣿⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣯⡼⠁⠀⠀⠀⠀⠀
⠀⢻⡁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⠆⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢠⡟⠁⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀
⠀ ⠀⠸⣇⠸⣆⠀⠀⠀⠀⠀⠀⠻⡟⣦⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢠⡟⣿⣿⣦⣤⣤⣤⣤⡴⠞⠛⠉⠙⡇⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠙⢷⣘⢦⡀⠀⢀⣀⣀⣀⣹⣮⣷⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠉⣛⣋⣁⣀⣀⡀⠀⠀⠀⠀⢈⡟⠉⠉⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⠓⢶⣿⣿⡿⣻⣟⠛⣿⣿⣿⣯⡉⠉⠙⠛⠁⠀⣾⣋⢹⡟⢉⡁⣠⣤⣀⣈⣉⣉⣉⣉⡉⠉⠀⠀⠙⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣝⣫⣴⣿⣿⣿⣿⣇⣲⣶⡆⣤⣄⠙⡛⠛⠛⠻⠷⠟⣻⣿⣿⠛⠛⢿⡉⠁⠀⠀⠀⠀⠘⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣃⣴⣶⠄⣼⣳⡏⠈⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠻⢿⣇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠸⣧⣤⣤⣤⣄⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣶⠖⠶⠶⣦⣤⡀
⠀⠀ ⠀ ⠀&⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⣦⣤⣤⣤⡤⠤⠶⠶⣦⣤⣤⣤⡤⠞⠛⠿⠿⠶⠶⠶⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀