⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⣓⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢁⡤⠞⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⢀⡴⠋⠳⢭⣾⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡴⢇⡴⡟⠋⠥⠄⣘⣿⠉⠀⠀⠉⠉⠓⠒⠢⢤⣤⣤⠤⠖⠒⠚⠉⠉⣀⠭⣿⡟⠀⠀⠀⠀⠀
⠀⠀⢠⠿⠚⠛⠲⣄⢠⣤⡀⠀⠀⢀⡾⡞⣿⣤⢴⠯⠍⣉⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢻⣯⠀⠀⠀⢀⣴⡏⠁⢠⣿⡇⠀⠀⠀⠀⠀
⠀⠀⡞⠀⠀⢀⣀⠸⡜⡇⠉⠢⣠⡾⡾⢀⡏⠈⠁⠀⠈⠁⠀⠸⡀⠀⠀⠀⠀⢲⡀⡀⠀⠈⠉⠳⣦⣖⡋⠈⢽⣦⡟⢸⡇⠀⠀⠀⠀⠀
⠀⠀⣇⢸⣿⣿⣿⠇⢧⣷⠀⠀⢘⣾⠀⣸⠁⠀⢰⠃⠀⠀⡀⢀⣷⡀⡇⠀⠀⢸⡙⣷⢀⡀⠀⠀⠘⠦⠠⠶⣤⣟⣤⣾⡇⠀⠀⠀⠀⠀
⠀⠀⢹⡀⠉⠙⠁⠀⣼⠯⠀⠀⣿⠃⣶⡇⠀⠀⡞⠀⠀⠀⡇⠘⡇⠱⢧⣠⠀⢸⣇⠹⠀⢣⠀⠀⠀⢿⠼⣿⡟⠉⣸⢻⡇⠀⠀⠀⠀⠀
⠀⠀⠀⣷⣄⣀⣀⡼⡟⠀⢀⡖⡟⣸⡏⠀⠀⢀⣇⣀⠤⢾⡗⢺⢧⠀⠀⠘⡄⣄⡿⣶⣄⣸⡀⠀⠀⠘⡆⠀⢳⣠⠇⢸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⣿⠀⠀⢠⠇⣇⡴⢻⣼⡷⢻⠀⡇⠀⢸⣿⣇⡤⠼⢹⣸⠘⣆⡄⠀⣻⣿⣧⣜⣧⡈⣷⣄⠀⠀⣹⠀⠀⢿⠀⢸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⣿⠀⠀⠘⣼⢻⠞⡹⠉⢱⢾⢀⣇⠀⢸⣈⣉⣤⣬⣷⡉⠀⠈⠋⠉⠁⣸⠟⠛⢿⣿⣯⣏⠀⡇⡿⡀⣤⡸⡇⢸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⣿⠀⠀⠀⠃⢸⡀⡇⢀⣾⠸⣿⡈⢧⢸⣟⣉⠀⠀⠈⠉⠀⠀⠀⠀⠀⣿⠰⠇⣠⡿⢘⣿⣧⣻⠁⡇⢸⡷⡇⢸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⣿⠀⠀⠀⠀⢀⣿⡷⡏⣿⠀⣿⣇⠈⢿⣿⢯⡁⠀⠀⠀⠀⠀⠸⠀⠀⠙⠁⠸⢷⣀⠈⣟⢸⣿⠀⣧⢸⠀⠁⢸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⣿⠀⠀⠀⢀⡞⠀⠀⢷⣿⣇⠋⢿⠀⠀⢻⡗⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢺⠋⠿⡿⣴⠛⢿⡄⣰⢾⡇⠀⠀⠀⠀⠀
⠀⠀⠀⣿⠀⠀⠀⠈⠣⣄⠀⠘⣿⡘⠀⠈⠀⠀⠀⢻⡀⠃⠀⠀⠈⠉⠑⠂⠀⠀⠀⠀⠀⣠⠞⠀⠀⣧⡘⠀⡾⠊⠁⢸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⣳⠌⣟⣯⠀⠀⠀⣀⡤⠚⠛⠛⠲⣄⣀⡀⠀⣀⣀⣠⡴⣶⣿⠿⡇⠀⣤⣇⠟⠀⠻⣄⠀⢸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⣿⠀⣠⠖⠉⠀⣰⠃⡴⠋⠘⢦⡀⡴⢧⠀⢀⣤⣤⣤⣏⢻⣯⠽⡿⢛⣿⣾⢁⠙⠓⣿⢀⣿⠻⡄⠀⢀⡼⠂⢸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⣿⠞⠁⠀⠀⠀⢯⣀⡇⠀⠀⠀⡿⠁⠈⡽⠉⠀⠀⠀⠈⠛⠿⣤⣷⡾⠟⣡⠏⠀⢠⠷⠛⡇⣠⠞⠀⢿⡀⠉⢺⡇⠀⠀⠀⠀⠀
⠀⠀⠀⣿⠀⠀⠠⣖⠚⠉⠉⡇⠀⠀⠀⣧⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢀⡏⠀⠀⠀⠀⠀⢻⣧⡀⠀⣠⠇⠀⢸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⣿⠀⠀⠀⠈⠹⡆⣠⡇⠀⠀⠀⡇⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠞⠁⠀⠀⠀⠀⠀⣸⠍⣹⣾⠓⠲⢄⢸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠙⢻⢳⣦⣤⣀⣟⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⡟⡿⠋⠹⣆⡟⠉⢸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀