⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⢰⠀⠀⠠⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⠀⠀⠸⠀⠀⠘⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⢀⣠⣴⣶⣿⠿⠿⠿⢿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⠀⠀⠀⡆⠀⠀⠀⠀⠀⡇⡠⠄⠤⠤⢤⡄⠀⠀⣧⣼⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣄⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣇⡠⠔⠉⠀⢀⠤⠊⠁⠀⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⣇⡠⠒⠉⠀⢀⠤⠊⠁⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⢀⡠⠒⠁⠀⢀⠤⠊⠁⠀⠀⣠⢔⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠤⠛⠁⠀⢀⠤⠚⠁⠀⠀⢀⠴⣪⣤⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⢸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠁⠀⢀⡤⠚⠁⠀⠀⢀⡤⣊⢕⢞⣶⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⢸⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢀⡀⠀⠀⠀⣀⣀⣀⠀ ⠀⠀⠤⠚⠁⠀⠀⢀⡠⢚⢥⡮⠛⢁⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⢔⣩⡺⠓⠁⠀⢠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣯⣤⣤⣤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠔⡫⣶⠕⠉⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⣻⣿⣿⠟⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠝⠋⠀⠀⠀⠀⣀⢄⣾⡟⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡄⠀⠀⢀⡤⣚⠕⣾⡟⠀⠀⠀⠀⠀⠙⠛⠻⠿⣷⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡿⣋⣤⣶⣶⡿⠿⣿⣯⣝⠛⠿⣷⣦⡤⠄⠀⠀⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡯⠦⢔⡩⡪⠛⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⠇⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠟⠋⠁⢀⣤⣤⡀⠙⢿⣧⡀⠈⠛⢿⣧⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢷⣔⠝⠋⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⢺⣿⣿⡿⠀⠀⢻⣧⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡁⠀⠀⢀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠉⠁⠀⠈⠙⢿⣦⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢸⣿⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣕⣄⢔⣵⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⢀⣴⣶⡄⠈⢿⣇⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠈⣄⢔⠝⠁⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠸⣿⣿⡿⠀⢸⣿⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⢀⣠⣾⡿⠃⠀⠀⠀⠀⠀⠈⣿⡇⠀⠉⠉⠉⠉⠉⠉⠉ ⠀⠀⢸⠀⡟⠁⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣶⣶⣾⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠀⢟⢦⣠⢖⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⡇⢸⢀⢔⠕⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣤⣤⣀⣀⣤⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⢠⡎ ⠀⠀⠀⡇⢸⠗⠁⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⢠⠏⠀ ⠀⠀⠀⢣⢸⡣⡀⡠⢊⡜⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠿⠟⠛⠿⠿⠿⣷⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⠀⠀⠀⠀⢀⠎⠀⠀ ⠀⠀⠀⢸⠀⡏⣩⣶⠟⠁⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣷⣦⡀⠀⠀⠀⢀⠎⠀⠀⠀ ⠀⠀⠀⠸⠀⣿⠗⠁⠀⢀⣤⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠁⠈⠙⢿⣦⣄⢀⠎⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⢷⣄⢀⢔⣿⡿⠃⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢿⣷⣄⠀⠀⠀⠀⠙⢻⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⢸⠚⣡⣿⠟⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⠁⠀⠉⠻⢿⣦⣄⡀⢠⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢇⠀⣴⣿⠋⠀⠀⠀⠀⠀⣰⣿⠟⠿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⡿⠟⢻⣧⠀⠀⠀⠀⠀⠀⢉⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠨⢭⣭⡛⠿⣅⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠈⠙⠻⢿⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⣤⣴⣶⣶⣿⡿⣿⠛⠋⠁⠀⠀⠈⢿⣇⠀⠀⠀⠀⣴⡿⢋⠎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⢸⡒⠒⠒⠒⠒⠋⠑⠒⠂⠀⢀⡀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀