⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢀⠠⠂⠈⢀⠄⠁⢀⡴⠋⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠑⣄⠉⠲⢄⡀⠀⠀⠹⣿⣄⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⢠⠁⠀⠀⡔⠁⣠⡶⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⡇⠀⢀⠀⠈⢳⣀⠀⠌⠲⣀⠀⠘⣿⣆⢹⣿⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⡏⠀⠀⠀⣧⡾⠋⠀⠀⠀⢠⠂⣿⠀⠀⠀⠀⢠⠀⠀⢠⡇⠀⠀⠀⠀⣿⡇⠀⣼⠀⠀⡄⠹⣦⠈⢄⠀⠑⣄⠘⣿⡞⣿⣿⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⡇⠀⢀⡾⠋⣰⠀⢠⠃⠀⡾⠀⣿⠀⠀⠀⠀⢸⠀⠀⢸⣿⠀⠀⠀⢀⣿⠃⢰⡇⠀⢸⠁⢰⠘⢷⡄⢆⠀⠸⡆⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⠀⠄⢀⡇⡴⠏⠀⠀⡇⠀⡎⠀⣸⣧⠃⣿⣤⠀⢰⠀⣿⠀⠀⢸⣿⠀⠀⠀⢸⡿⢠⡿⠁⠀⣾⠀⢸⢰⠈⣿⣼⠀⠀⣿⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡇⡜⣠⡟⠈⠀⠀⠀⣸⡇⢀⡇⢰⣿⡹⢸⠀⢯⣇⢸⢠⣿⠀⠀⣼⣿⠀⠀⠀⣿⣧⣿⠇⠀⣼⡇⢀⣾⣸⠀⣿⡿⣦⠀⣿⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡻⣰⡟⠀⠀⠀⡠⠀⣿⡇⣸⢠⡿⢸⢇⠇⠀⠸⣿⢸⢸⣿⡅⠀⡇⣿⠀⠀⢰⣿⣿⡏⠀⣴⡿⢀⡜⣾⠇⡄⣻⡇⠘⢷⣿⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢐⣱⣿⠀⠀⡆⣰⡇⢰⣿⠥⣿⣾⠧⢾⣾⣤⡤⢄⣹⣯⣿⡏⡇⢠⠇⣿⠀⠀⣿⣿⠏⢀⣜⡿⢁⠎⢀⢿⠀⡇⣿⡇⠀⢨⡿⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⡟⡎⠀⣼⢱⣿⡇⢸⡏⢀⣿⠇⠀⣼⠁⠀⣀⡀⠉⠛⣿⡧⣿⢸⢰⡿⠀⣸⢟⣏⡴⢯⡾⡿⠛⠋⢹⠋⠉⢻⣿⡇⠀⣼⠃⠀⢠⣿⡇⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡿⢸⠀⣸⢧⣿⣿⡇⣼⣇⣾⡏⢠⡶⡟⡟⢿⣷⣶⣭⡑⠜⡇⢸⣸⢸⡇⢠⢋⣮⠟⢡⡮⢞⣒⣤⣤⣤⣤⣀⢸⣿⡇⢸⠏⠀⢀⣟⣿⣇⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⣾⠁⡾⢠⣿⣿⣿⣿⣇⣿⣯⡿⣧⢸⠁⠀⣷⣾⣿⣿⡿⠈⠂⠈⢸⡏⢸⢡⣧⠟⠁⡴⢫⢿⠉⣿⣿⣿⠀⠀⢹⢾⡿⢠⡟⠀⢀⣞⣾⣿⢸⣿⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠇⠀⣇⣾⣿⣿⠇⣿⣿⣿⢻⣧⢻⡀⠀⠀⢻⣿⣿⡹⠃⠀⠀⠀⠈⠁⣼⠊⠀⠀⠊⠀⠀⠘⣿⣿⡿⡟⠀⠀⠈⢸⢡⠟⠀⣰⣿⡿⣿⠃⣾⡏⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠀⢠⣹⣽⣿⡟⠀⣿⠙⣿⣯⠙⣧⣧⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠂⠀⠀⠀⣾⣫⣴⣾⣿⣿⣱⠏⡰⣿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡟⠃⠘⡄⠀⢿⡀⠈⢿⣷⡌⢟⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⢻⣿⠏⠀⢰⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⠁⠀⠀⠱⠀⢸⡇⠀⠐⡝⢿⣮⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣹⣿⣿⣿⣿⢏⣼⡇⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠈⣧⠐⡄⠱⡀⢫⠻⣆⠀⡄⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢒⠀⠀⠼⢻⣿⣿⢳⣿⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣧⢇⠱⡄⠻⡄⢧⡀⠀⢀⠸⣷⠀⠀⠀⠀⠄⢀⠀⠀⡀⠠⠀⠀⠀⡰⡅⡸⠀⢀⣰⣿⣿⡟⣾⡿⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⠣⣿⣆⠻⣦⣻⣦⣼⡀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⡇⣇⣴⣿⣿⣿⣿⣸⡏⣧⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣿⣿⣿⡿⠀⣼⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡄⣿⣿⣿⡟⢹⣿⡟⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⢹⡿⣿⠃⢠⣿⣤⣈⠑⠤⣀⠀⠀⢀⡠⠔⢊⣥⡟⣿⡇⢹⣽⠏⢀⣿⠟⠀⡜⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠱⡌⠀⣼⢿⣿⣿⣿⣶⣦⣭⣭⣥⣶⣾⡿⡿⡇⣿⡇⠀⡇⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⢰⣿⣼⣿⣿⠋⠛⠛⣿⣿⡟⠉⠀⣸⣜⢷⣏⣷⠀⠘⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣀⣀⣹⣿⡆⠀⢻⣿⠃⢠⡿⠟⠟⠁⠈⠙⠃⠤⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠙⡄⠀⠀⠀⠀⠀⢠⠊⠙⠛⠒⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡌⠀⠀⠀⠀⠀⠈⠉⠉⣳⠀⠀⠀⠀⠀⡾⠿⠦⠄⠀⠀⠀⠀⠀⠘⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠔⠒⠀⣸⣿⣿⣷⢰⠀⠀⠀⠀⠀⢠⣾⡽⠀⢀⠀⡆⠀⣇⣀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣆⠉⠁⠀⠒⠢⠤⠀⢀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠔⠂⠉⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⠸⠀⠀⠀⠀⠀⢨⡿⣄⠀⢸⠀⣇⡠⠜⠻⣿⡆⠀⠀⠀⠀⢸⠸⣸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⡀⠀⠀⠀
⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⣤⠂⠀⠀⠀⠀⠀⢸⠇⠀⠀⢾⠀⡟⠀⠀⠀⣿⡇⠀⠀⠀⠀⠸⡀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀
⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠘⠛⠛⠁⠁⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠈⠤⠇⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠳⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢳⠄
⠐⡅⠀⢀⣤⡀⠂⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠤⠤⣀⢀⢴⠉⠀⠀⠀⢠⢠⢠⢠⠀⠀⠀⢀⠹⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢠⠁⣾⣿⡆⡀⠈⣿
⡇⡇⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀⠀⠀⠀⠈⠉⠁⢀⣙⡆⠀⠀⢸⢱⢸⠊⠀⠀⠀⠁⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⠈⠸⣿⣿⣿⢇⠀⣿