⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣿⣿⣷⣦⣀⢀⠀⡀⢀⣀⢀⠀⠀⣀⡀⠀⠀⠀⠀⢀⢀⢀⡀⠀⠀⠀⠀⠀⣀⢀⣀⣀⠀⡀⢀⡀⢀⣀⣀⡀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣾⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⡉⠈⢹⣿⡆⠺⣻⣷⣥⢹⣿⡿⣿⡿⣿⣾⣟⡓⠺⠲⢺⣿⣿⠂⠹⡻⣿⣷⡷⡻⠛⢛⢛⡯⣯⣷⡍⠉⠙⣿⣿⣿⡟⠛⠛⢛⡿⡿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢸⢿⣗⡆⠀⣼⣿⠃⠀⠱⡟⣟⣾⡫⠉⠀⠀⣿⣿⣿⠀⠀⠀⠈⠨⣿⡗⠀⢆⣭⣿⡇⠂⠀⠀⠀⠈⠘⢿⡶⠀⠀⠀⣻⣿⡇⠀⠀⠀⠈⢞⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣾⣿⠅⠑⣻⣿⣿⡥⠀⠀⠀⠀⠀⠀⠠⢻⣽⣿⣿⣾⣿⣦⣀⣘⠉⠙⠊⠀⠀⠀⠀⢿⣿⣿⣇⠀⠀⠀⠀⠈⠲⠁⠘⣿⣿⡇⡄⠀⢀⢠⡦⠄⠈⠂⠀⠀⢀⣿⣿⣧⠀⠀⠀⡰⡣⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⢠⠤⡰⣶⣿⣻⣿⣿⣿⣶⢠⢮⣿⣿⣿⣧⣠⡤⣤⠶⠲⠖⠈⠙⠹⢻⢿⣿⣿⣵⣯⡆⠀⠀⠀⠀⠀⠀⢹⣿⣿⡖⠀⠀⠀⠀⠀⠀⢰⣴⣿⢽⣿⣷⣾⣾⣿⠇⠂⠀⠀⠀⡠⣸⣿⣿⣯⣦⣶⣶⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⣟⠏⠓⠙⠽⣿⣿⣹⣿⣿⣾⠋⠀⠀⢰⠀⠀⠀⠀⠈⢺⣿⡝⠝⣿⡏⣍⠀⠀⠀⠀⠀⣼⢿⣻⠅⠀⠀⠀⠀⠀⠀⠀⢠⣻⣿⡇⠈⠉⠀⠊⣧⠃⠀⠀⠀⠛⠊⢿⣿⣯⠋⢟⢿⣿⣷⣕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⣿⠅⠀⠀⠀⠀⠀⠀⠈⢻⣷⣻⡄⠀⠀⢨⣯⢄⠀⠀⠀⢸⣿⡇⠀⠰⣾⣿⠦⠀⠀⠀⠀⢻⣿⣾⠂⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣲⠆⠀⠠⣽⣿⡇⠀⠀⠘⢟⢿⣿⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⣿⣿⣅⡀⢸⣿⣿⣆⠀⠀⣸⣿⡆⢠⣪⣿⡷⠄⠀⠀⠀⢐⣺⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣧⡂⣀⣀⢠⣄⣾⣿⣿⠇⠀⣾⣿⣿⣅⡀⠀⠀⠀⠺⢿⡿⠪⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⡿⠿⠧⠤⠄⠀⠀⠀⠀⠀⠤⠴⢿⢿⢿⣽⣮⣴⢿⠿⠻⠻⣷⡾⣿⡿⠟⠛⠁⠀⠀⠀⡠⠴⠳⠋⠛⠛⠿⠷⡤⡀⠀⠀⣀⠬⠾⠏⠟⠞⠙⠋⠋⠛⠻⠻⣿⢗⢰⠿⠟⠯⠣⠹⠆⠤⠀⠀⠀⣩⢿⢊⣸⣷⣄⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠀⠀⠀⢹⣟⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⢷⣦⣄⡀⠀
⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀