⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⣺⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠶⠄ ⠠⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣤⣞⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠑⠢⡄⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⢴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣝⠀⠉⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⢄⠴⠁⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣤⣄⠀⠀⠀⠀⠀⠀⣸⣿⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣠⣾⣿⠛⠋⠻⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣠⣾⡿⠟⠻⣿⣦⣀⠀⠀⠀⣰⣿⠿⠋⠛⢿⣷⣄⡀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⣴⣿⠟⠀⠀⠀⠀⠈⣿⣷⣤⣄⣀⣠⣤⣶⣿⠿⠿⠻⣿⣶⣾⣿⠋⠀⠀⠀⠈⠻⣿⣦⣤⣴⣿⣯⣤⣤⠀⠀⠘⣿⣷⠄⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠘⠿⠇⠀⠙⠉⠀⠀⠀⠀⡄⠀⠈⠙⠛⠛⠿⠿⠛⠁⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⢙⠋⠍⡏⢫⢭⠙⡍⠀⠀⠀⠈⠉⠰⢀⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⢶⣶⠄⠀⠀⠀⠀⠙⠻⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠓⠃⢠⣠⠀⢠⣀⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⡅⠀⠀⠀⠀⠀⠀⠸⣄⠆⢡⣸⠈⣄⠆⠀⠀⠀⠀⠀⠀⢘⠛⣠⣤⣾⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⢋⣀⡀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⠐⠿⠿⠋⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⢀⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⣦⠀⢾⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡿⠀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣷⣄⠉⠉⠀⢰⣿⣶⣶⣶⣆⣀⣠⣄⠀⢰⣶⣶⣶⡀⠀⢍⣀⠀⠀⠀⢰⣶⣶⣦⠀⢠⣤⣀⣠⣶⣶⣶⣿⡷⠀⠈⠉⢁⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠿⣿⣶⣤⣄⠈⠙⠛⠙⠛⠿⢛⠋⠀⠀⠀⠀⠀⣀⣠⣾⡿⣿⣦⣀⡀⠀⠀⠀⠀⠘⠛⣿⣿⠛⣹⣿⠉⢠⣴⣶⣾⡿⠿⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣧⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⢰⢨⠀⠀⠀⠀⠀⢼⣿⣿⣏⣀⣼⣿⣿⡿⠀⠀⠀⠀⠀⠀⢻⣿⣦⣿⡇⠀⠈⠉⠉⠁⠀⣠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡙⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⠿⠻⣿⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣥⣭⣤⣤⣤⣤⣀⣀⡀⣈⣀⣁⣀⣀⢀⣀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠈⠉⠉⠹⣿⣆⠀⠀⠀⢀⣀⣀⣀⣘⣀⣙⣀⣀⣀⣀⣤⣤⣤⣤⣬⣤⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠋⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⣿⣷⣀⣠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣀⣼⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉⠋⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀