⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠶⠶⠶⢶⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡿⠟⣻⡟⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠠⠟⠁⣸⡏⠀⠀⠀⠀⠀⠀⣀⣄⣀⣠⣤⡤⢤⡤⣤⣄⣀⣀⣸⣿⣿⣿⣄⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⠀⠀⢀⡄⣿⣇⣤⡿⠛⠛⠛⠛⠉⠈⠋⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠿⣿⣦⣤⣽⣤⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⢀⣘⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠉⢦⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⣀⣼⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠈⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⢰⢲⣶⡖⠒⠒⠒⠊⠓⠒⣦⣄⣀⣤⡀⠀⠀⠀⠀⠀⣧⠴⠋⠀⠀⠀⠀⠀
⠀⠀⢀⣀⣸⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⡇⡏⢣⠤⡟⢹⡏⣧⠀⠀⠀⠀⣀⣸⠁⡇⢹⠟⣏⠙⢶⣤⡀⢠⠇⠀⠀⠀⠀⠀⠀⠀
⠀⡔⠋⠀⠸⠟⠑⡄⠸⡆⠀⠀⣀⡤⠖⡎⠉⢸⡀⠀⣿⣇⣸⣤⣇⡈⠀⣸⡞⡇⠀⢠⣧⣇⣀⣧⣟⣀⣸⡀⣸⠀⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⣹⠀⠹⡤⠞⠁⠀⠀⡇⠀⠀⢳⣆⣿⡏⣽⣿⣿⣿⣿⠛⠻⢷⢀⡾⠟⣿⣿⣿⣿⣿⢻⣧⡇⠐⡾⣆⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡀⠀⠀⠀⠀⢀⡟⠀⠀⢷⠀⠀⠀⠀⡃⠀⠀⠀⠹⣿⠀⢛⣻⣿⣿⣿⠀⠀⢸⠟⠀⠀⣿⣿⡿⣿⠀⡟⡿⠁⢸⡟⢿⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠙⢦⣄⣤⠖⠋⠀⠀⠀⣸⢰⠀⠀⠀⢱⠀⠀⠀⠠⣿⠀⠈⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⢸⡇⡇⠀⢸⡇⠀⠙⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢿⡀⠀⠀⠘⡆⠀⠀⡆⢸⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢺⣿⠁⢠⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⡇⠀⠀⠀⢿⠀⠀⢸⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⡿⢀⢢⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡇⢦⠀⠀⠈⣇⠀⠘⣧⣷⣄⣀⠀⠀⢿⠛⠲⡦⠀⣀⣠⡤⢾⠟⠀⢰⠇⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⡀⠀⠠⠈⠷⡄⠸⣿⣞⠙⠛⢿⣗⡒⢲⣾⢿⣍⡀⠀⣿⡀⠀⡏⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠉⣿⡀⣠⣶⣷⣿⣶⣿⣿⣦⡀⠀⠈⣿⣼⣷⡀⢹⣿⣶⣿⣧⣾⣸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣦⣰⡏⢳⠀⢳⣿⣽⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⡋⠳⡀⠀⠀⠀⠀⠀⣠⣿⠿⠿⠃⠈⢿⣿⣿⣿⡟⢪⠻⣧⣼⣆⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⠖⠛⠛⠛⠛⡇⠀⠹⢦⣴⣤⡀⢰⣿⣧⣀⣀⣀⣀⣀⢿⣿⢿⣿⣿⣟⣛⣻⣿⣷⢸⣿⣿⣿⡟⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣉⣉⠀⠀⠀⠃⠀⠀⣰⣿⣿⣿⣾⣏⠈⠛⠛⠛⠉⠉⢸⣿⣿⣛⣛⣿⣿⢟⣩⣽⠿⣿⣭⢿⣧⠈⣿⡆⠀⠀⣀⣤⣤⣠⠤⠤⢤⢤⡀⠀⠀
⠻⣭⢤⡄⠠⠖⠀⠀⣰⣿⣿⣿⣿⡿⠛⢷⣄⠀⠀⠀⠀⢸⣿⡋⣩⣽⣿⣻⡽⠟⠁⠀⠸⣿⡀⣿⡀⡟⣿⡶⠿⣿⣿⣿⣿⣦⠀⢘⢯⡁⠀⠀
⠀⠹⠭⠴⠶⣦⣴⠾⣿⠛⣾⣿⡿⠁⠀⠈⢻⣷⣄⠀⠀⣿⣿⣶⣿⣿⡏⠉⠀⠀⠀⠀⠀⣿⡇⣸⡇⠁⢹⣿⡀⠹⣿⣿⣿⣿⣷⡀⡰⠿⣦⠀
⠀⠀⠀⠀⠰⣿⣿⠆⢁⣴⣿⡟⠁⠀⠀⠀⠀⢿⣿⣷⣿⣿⠿⠋⣡⣿⣿⣠⣤⣤⣤⣤⣶⡿⣧⢿⡇⠀⢸⣿⡇⠠⠌⣿⣿⣽⣿⠧⣽⣦⣼⠇
⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⢻⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡏⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠈⡇⠀⢸⣇⠀⣾⢻⣿⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣴⣄⠀⠀⢀⣼⠋⢹⣿⡄⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⡁⠘⣿⣅⠋⠉⣽⣷⣶⠿⠛⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⣴⠟⠁⠀⣸⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠛⣿⣀⣶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣯⡁⠀⢀⣀⣿⢿⠀⠀⠀⠀⠀⠀⢸⡇⢀⣀⢿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠂⠈⠻⢦⣬⠉⣿⡿⠷⢶⣤⣄⣀⣠⣼⣿⡋⠁⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢿⠶⠶⠶⠶⠶⠷⠿⠿⠷⠶⠦⠴⠾⠿⠿⠿⠿⠶⢶⢿⢿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀