⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣀⣀⣠⣾⣿⠟⠋⣡⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠖⠉⠀⠀⠘⢿⣿⣿⣿⣄⢠⣾⣿⣿⣻⡇⠀⠀⠀⢺⣏⠉⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡠⠐⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⡎⠀⠀⠀⢀⣀⣛⣿⠷⣧⠀⣾⡿⠁⠈⠳⠗⠀⠀⠀⢸⡏⠀⠀⣿⣿⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⣿⡇⠀⠀⠀⠠⠂⠀⠀⢸⡧⠤⠤⠿⠿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⢼⢹⠈⣿⣷⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⣄⡀⠀⠀⠀⢀⣴⣾⣿⠇⠀⠀⠀⠀⠀⠀⡈⢸⠈⠆⣿⣿⡇⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⢻⢿⣷⣤⣴⡿⠛⢚⣿⠀⠀⠀⠀⠀⠀⠀⢇⢸⠃⠀⣿⣿⡇⣿⣶⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⣴⣶⠟⠉⠙⠿⠿⠟⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣾⣬⣿⣷⣯⣭⡟⣧⣤⡠⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⣀⣀⣀⣀⠀⠀⠀⡠⠄⠐⠂⠢⡀⠀⠀⠀⣼⠛⢛⣿⢿⣷⣶⣷⢸⣿⣧⣵⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡑⠚⠛⢀⣤⣦⠊⠀⠀⡤⠠⠀⠘⢆⠀⠀⠉⠀⠀⢽⣈⠒⢿⣝⢲⡿⠿⣸⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡽⠷⠂⡉⠛⠛⠀⠀⠀⠀⠐⠀⠂⢈⣂⠀⢀⠀⠀⠀⠉⣛⠦⣌⢛⣸⡏⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠃⠀⠀⣶⣶⠀⠈⠀⢠⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⢢⠛⡼⢿⠀⠐⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⢨⠀⠀⠙⠿⣿⣦⣠⣿⡮⠉⠛⢦⡀⠀⠀⠀⠀⠀⠁⠧⠠⠀⠀⢱⠈⢰⢀⠀⡅⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠉⢡⣿⡇⡀⠈⠉⠀⠀⣿⣄⣘⣿⣦⠀⠤⡴⠰⠁⠀⡰⣄⠀⠨⠐⠀⢘⠐⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⠀⠀⢰⣿⣿⣜⠀⢀⣀⣀⣴⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⡀⣱⡎⠻⡶⠓⠈⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠙⠆⠀⠻⣿⡏⣿⣇⠈⠛⠿⢿⣿⣿⣿⠿⠿⠛⢃⡀⠘⣿⣿⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢰⢠⣿⣿⣿⣿⣷⣄⡀⠀⠙⠉⠀⠀⠀⠀⠈⣿⣦⡈⢻⢟⡀⢀⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣄⠀⠀⢹⣿⠈⠻⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣿⣿⡇⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠂⣿⡏⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢹⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⣿⡇⠀⠀⠀⠀⠈⢡⠀⠀⠀⠀⠊⠀⠀⣿⣇⣼⡧⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⣿⣷⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⢸⣿⣿⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣋⢧⣿⣿⠀⢀⡠⠄⠒⠈⠁⠀⠀⠀⠀⠀⣾⣿⡏⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⢀⣶⡿⠟⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢣⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀