⠀⠀⣀⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⠤⡀⢠⠋⠑⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⠁⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠎⠀⠀⠀⠈⠄⠀⠀⠀⠀⢲⣿⣴⣿⣴⠄⢀⣀⠀⠀⣀⠀⢀⡀⠀⠀⠀⢰⠋⢀⠀⠀⢸⠈⡄⢰⠛⠀⠀⠀⢀⡤⣤⣄⠑⠒⠁⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠓⠊⠀⠀⠀⡀⣴⡾⡿⠈⠛⠃⢺⡞⠿⠀⣘⡿⢶⣿⣷⢄⢀⡀⠜⣄⠈⠉⠀⠁⠀⠈⠪⣆⠀⠀⠀⡏⠀⡀⢈⡇⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡄⠀⠀⠀⠀⠀⠀⠎⠀⠉⠀⠀⡠⠒⢰⠛⡗⠈⠿⠚⠛⣸⠙⢀⡀⡆⠈⠢⣈⣱⣦⣴⠶⠶⢖⣶⠾⠷⠦⣄⣡⣠⣶⣿⠀⠀⠀⠀⡰⣀⡤⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢱⡆⡄⠀⠀⠀⡜⠈⠀⠁⢢⠐⠁⠀⢠⡞⠁⠀⠀⠀⠀⠘⡄⠀⢠⣥⡖⠋⢡⣾⣿⣶⡄⣼⣿⡏⣶⣤⣤⠀⢸⡟⣿⣿⣷⣶⣶⡟⠋⠀⠀⠛⠈⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠳⣄⢄⠀⠊⠀⠀⠀⠀⠀⠉⢶⡂⢡⣦⢠⣴⠀⣰⣶⣤⣠⡿⠋⢁⣀⣀⡎⣋⣛⣿⡿⠿⣿⣃⢿⣿⢿⣿⣮⠇⣿⠟⣹⣿⣿⣶⣖⠀⠀⠀⠀⢀⠝⠈⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣦⠈⠙⠶⢼⣿⣼⣷⣿⣶⣄⣀⡙⢺⣯⣶⣿⣿⠻⢿⣿⠋⣧⡾⠋⠀⢀⣙⣿⣿⣯⣁⡰⣿⠿⡟⢛⣷⡮⠍⠁⠘⠚⣛⣯⣿⠟⠈⠻⢟⠉⠉⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⢾⣥⠀⠀⠀⠀⢹⢿⠙⢿⡏⠉⠉⠁⠀⠀⠘⢙⠴⠋⢀⣠⣿⣿⠋⠩⠊⠉⠀⢠⡿⡟⢻⣿⣶⣾⣿⠿⢟⡋⡀⡀⡘⣶⣶⣤⡠⣄⣣⡟⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣄⣀⡠⠴⠊⠁⠀⡰⠋⠛⣿⣶⡄⢃⠀⢒⠀⠀⠀⠑⠦⠄⠉⢛⠻⠛⢫⡞⣼⣿⠹⣮⣽⣿⣷⣄⣀⣀⡷⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠋⠿⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢺⣷⣿⡟⠀⠀⠙⣏⠁⠀⠉⠉⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⣽⠋⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠿⠃⢀⠖⠉⠁⡄⡴⠹⣷⡀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣤⣀⠀⠣⡰⠘⣷⣤⠊⠀⠀⠀⠀⢀⣾⣧⣶⣶⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⢿⣯⡛⠿⠒⠊⠁⠉⠘⣎⠳⣄⣀⣿⣆⡸⣿⣿⣿⣏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠇⠀⠀⠀⠀⠀⠀⢸⡀⠈⢿⣿⣿⡷⠉⠹⠿⠉⡀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⢙⣽⣿⣦⠀⢀⡀⢿⣿⠧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢿⡆⢠⣿⣯⣮⠁⢠⣮⠟⢾⡧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⡷⢆⠀⠀⠀⠀⣼⢷⢃⠩⠇⠌⣷⠊⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣤⡀⠀⣷⣿⣷⠾⠀⠀⠀⢀⡟⢻⡁⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢋⣻⣿⡀⠀⠙⣄⠈⣾⠇⠀⣠⠞⠀⢸⡇⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⠛⢻⣽⣆⣴⣿⣿⠗⠒⠭⢁⠀⢀⣿⡇⠀⢠⣿⣿⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠙⠿⠏⠀⠀⠀⠀⣡⣾⣿⡇⠀⠘⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣿⠮⠋⠁⠀⠀⠀⡀⠀⠀⠹⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠐⠒⡂⠄⣀⣀⡾⠜⢧⣤⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠘⠤⣤⡄⣠⡀⠘⠟⠇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⠐⢄⠀⣠⢀⡟⠛⠁⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⣶⡞⢿⣴⣿⣿⡋⠀⠀⠀⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠸⠿⠄⠈⠀⠀⢀⣤⠞⠁⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⣀⡤⠴⠞⠉⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀.