⠀⠀⣠⡶⢶⣦⠀⠀⠀⣠⡶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⡟⠀⠀⢹⣧⠀⣸⠏⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⠁⠀⠀⠀⢿⣴⡿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢿⡆⠀⠀⠀⠈⣿⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀
⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠀⠀⠀⣀⣀⣀⣀⣀⣾⠋⠉⠹⣇⠀⠀⠀⠀
⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣶⠞⠋⠉⠀⠈⠉⠃⠀⠀⢠⡟⠀⠀⠀⠀
⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀
⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀
⢿⡇⠸⣿⠀⠀⠀⠀⠀⠀⣴⣆⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠸⣧⡀⠀⠀⢀⣶⣶⡆⠀⠈⠁⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣸⡇
⠀⠙⠻⣦⣄⣀⣀⣈⣁⣀⣤⠾⠋⠀⠀⠀⠀⠀⣀⣠⣴⡶⢿⡿⠿⠶⣶⠶⠟⠀
⠀⠀⢠⡟⠉⢙⣿⠛⠋⠉⠁⠀⠀⣀⣠⣴⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⢿⣤⣘⣿⡀⠀⠀⢀⣴⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠛⠉⠀⠀⠀⠀⠀

⠀⠀⣠⡶⢶⣦⠀⠀⠀⣠⡶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⡟⠀⠀⢹⣧⠀⣸⠏⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⠁⠀⠀⠀⢿⣴⡿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢿⡆⠀⠀⠀⠈⣿⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀
⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠀⠀⠀⣀⣀⣀⣀⣀⣾⠋⠉⠹⣇⠀⠀⠀⠀
⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣶⠞⠋⠉⠀⠈⠉⠃⠀⠀⢠⡟⠀⠀⠀⠀
⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀
⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀
⢿⡇⠸⣿⠀⠀⠀⠀⠀⠀⣴⣆⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠸⣧⡀⠀⠀⢀⣶⣶⡆⠀⠈⠁⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣸⡇
⠀⠙⠻⣦⣄⣀⣀⣈⣁⣀⣤⠾⠋⠀⠀⠀⠀⠀⣀⣠⣴⡶⢿⡿⠿⠶⣶⠶⠟⠀
⠀⠀⢠⡟⠉⢙⣿⠛⠋⠉⠁⠀⠀⣀⣠⣴⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⢿⣤⣘⣿⡀⠀⠀⢀⣴⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣠⡶⢶⣦⠀⠀⠀⣠⡶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⡟⠀⠀⢹⣧⠀⣸⠏⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⠁⠀⠀⠀⢿⣴⡿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢿⡆⠀⠀⠀⠈⣿⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀
⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠀⠀⠀⣀⣀⣀⣀⣀⣾⠋⠉⠹⣇⠀⠀⠀⠀
⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣶⠞⠋⠉⠀⠈⠉⠃⠀⠀⢠⡟⠀⠀⠀⠀
⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀
⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀
⢿⡇⠸⣿⠀⠀⠀⠀⠀⠀⣴⣆⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠸⣧⡀⠀⠀⢀⣶⣶⡆⠀⠈⠁⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣸⡇
⠀⠙⠻⣦⣄⣀⣀⣈⣁⣀⣤⠾⠋⠀⠀⠀⠀⠀⣀⣠⣴⡶⢿⡿⠿⠶⣶⠶⠟⠀
⠀⠀⢠⡟⠉⢙⣿⠛⠋⠉⠁⠀⠀⣀⣠⣴⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⢿⣤⣘⣿⡀⠀⠀⢀⣴⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀