⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣲⣯⡉⠉⢉⠔⠁⠉⢉⠝⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢸⣿⣯⣿⡠⠃⠀⠀⡔⠁⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡊⠁⡛⣽⡓⡝⠀⠒⠒⡞⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⣠⠊⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⡀⠀
⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⡽⠁⢋⡎⢟⡿⠭⠟⠹⡖⠀⠀⠀⠀⠀⠀⢱⠀⠀⡼⠁⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⡼⠁⠀
⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⢀⠖⠉⠠⡾⠁⠀⠜⢧⠀⠈⠢⢀⠀⠱⠀⠀⠈⠳⡄⠀⢸⠀⡼⠁⠀⢀⠴⠊⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢼⠀⠀⠀⠙⠢⡤⠼⠋⠀⠀⠀⠀⠳⡀⢃⠀⠀⠀⡇⠀⢸⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀
⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⣀⣴⠘⠒⠃⠀⠀⠀⠀⢠⣤⡀⠘⠜⠀⠀⡜⠀⣠⠃⠀⣇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀
⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢸⠀⢇⠀⠉⠓⠒⠂⠒⠒⠉⠁⠀⠹⠀⠀⠀⠘⠁⠸⣿⠀⠀⢸⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀
⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡆⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀
⠀⠀⠀⠀⠸⡄⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀
⠀⠀⠀⠀⡴⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢙⠖⠢⠤⣀⠀⠀⠀⠀⠀⠀⢀⣀⠖⠁⠀⠀
⠀⠀⠀⠞⠁⣀⠴⠊⠉⠘⢆⡀⠀⠀⠀⠐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⡸⠀⠀⠀⠀⠉⢒⠤⣤⠤⠤⠄⣀⣀⠀⠀⠀
⠔⠊⠉⣩⠟⠉⡾⣿⣿⣿⡿⡏⠉⢲⣶⣶⣾⣧⣄⣀⣀⠀⠀⣀⣀⣠⠤⠖⠋⢀⡞⠀⡴⢁⣴⣽⣉⣷⣍⣿⣶⡄⠑⢦⡀⠀⠀⠉⠒⢄
⠀⠀⢀⣁⣀⣤⡧⢯⠿⠷⠷⠝⠀⠀⣿⣿⣿⣿⣿⣿⡇⠉⠀⠀⠀⠀⠀⠀⠀⢸⡠⠞⠀⠸⣿⡟⠟⢿⠿⢛⣿⠇⢀⡀⣀⣀⣀⣀⠀⠀
⠰⢿⣿⡿⠿⢿⣿⣦⣉⣒⣠⣤⣀⣀⣋⠈⠉⠛⣟⠛⠣⠤⠤⠤⠤⠔⠒⠒⡩⠯⠤⠤⣤⡤⢴⣯⠵⠶⠮⠭⢅⠀⠸⠿⠿⣟⣻⣿⠀⠀
⠀⠀⠁⠀⠀⠀⡹⠀⠒⠒⠒⠒⠚⠚⠻⡀⠀⠀⠈⢓⣤⠄⠀⠀⠀⠀⠤⠔⡇⠀⠀⢀⣿⣿⣿⣿⣿⡀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠀⠀⠀
⠀⠀⠀⠀⡞⠀⢇⣀⣀⣒⣛⣚⣃⣀⣀⢸⠰⣴⣤⣤⣤⣤⠀⠀⠀⠀⢀⠔⡗⡒⠒⠚⠛⠛⠛⠛⠛⠓⠒⠒⠚⠀⠀⠱⡄⠈⣣⡟⠲⡀
⠀⠀⠀⢸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠸⠈⠛⠋⠋⠋⠋⠀⠉⠑⠒⠁⠀⠃⢣⢧⢷⣦⢲⢪⣶⠐⠤⡝⠀⠀⠀⠀⠀⢹⡀⡤⣝⣶⠃
⠀⠀⠀⡎⠀⠀⢸⢿⣿⣿⡟⡿⠿⠿⢿⢰⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⣆⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢣⠀⠀⠀⠀
⠀⠀⠀⡇⠀⠀⢰⣶⣶⣿⣶⣶⣶⣶⣶⢸⣀⣀⣰⣿⣀⣀⣀⠀⠀⠀⢐⣀⣈⣉⣉⣉⣉⣙⠉⢹⠭⠭⣭⣭⡭⠤⠤⡆⠀⢸⠀⠀⠀⠀
⠀⠀⠀⡇⠀⠀⢸⣿⣿⣿⣟⣿⣿⣿⣿⠸⠤⠤⠤⠤⠤⠤⠼⢀⠀⠀⢐⠂⠀⠀⠀⠀⢐⣒⠀⢸⣉⣉⣿⢿⣿⣉⣉⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠀⠸⠭
