Furry Cumming Emojis & Text

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠛⠉⠙⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⣀⣀⣀⣀⣿⣥⣶⣾⣿⣷⣦⣤⣤⣤⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣠⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⢟⡿⠀⠺⠶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾⠁⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⣿⣿⣿⣏⣻⣿⣿⣿⣿⣇⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡟⢿⣿⣿⣿⢿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣠⣼⣿⣿⣿⣿⣿⣿⣿⣯⣐⣿⣿⠿⠛⣿⠀⠙⢿⣿⡞⠻⠿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢳⣶⢠⣾⠟⠀⠀⠀⣾⡏⣷⣧⢊⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠷⠈⠛⢷⠄⠀⠀⠀⠙⠈⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⠋⠿⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⣷⠀⣴⣶⡖⠚⠛⠛⣟⢛⣻⣷⠀⠀⢸⣿⣿⣿⣿⣿⡿⠃⠀⢰⡿⢿⣻⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣏⠀⢿⡗⠘⠛⢛⡻⠠⠄⢸⣿⠦⢀⣼⣿⣿⡿⢿⣿⣷⣄⠀⠈⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣓⠒⠒⠒⠓⠒⠒⠚⣻⡴⣿⣿⣿⡟⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣬⣿⣿⣿⡷⣤⣤⣤⡴⠶⠛⠁⠀⣿⣿⣭⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⡬⠟⣿⡿⠯⢬⣙⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢨⡥⠖⣋⣹⣟⣛⠒⠶⠶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠚⠋⣡⢹⣿⢩⡉⠉⠉⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢻⣿⢀⡏⠰⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠻⢿⣿⣶⡾⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⡿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣧⡀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠲⠶⠾⠿⠟⠛⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠠⢤⣾⣷⠞⠋⢿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠓⠒⠒⠒⠢⣿⠋⠀⠀⠀⠈⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⣤⡾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣥⣤⣤⣼⣿⣧⣤⣤⣤⠾⣧⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⢸⣃⢁⣰⣯⡾⠋⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠸⣿⡿⠉⠀⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⢷⡀⠄⠀⠀⠀⠀⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⡟⠿⠿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠀⠀⠀⠀⡿⢉⣼⠟⠉⠀⠀⠠⣠⡴⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⡟⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠄⠀⠀⠛⢦⡀⠀⠀⠀⢹⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟ ⠘⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⣼⡿⠋⠁⠀⢀⣦⡷⠟⠉⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⠃⠀⠀⠀⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⢶⣄⠀⠀⠀⠙⢦⣀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⠿⠿⠿⠿⢻⡇ ⠀⢿⣵⠀⠆⠀⠀⢠⣄⡀⡀⠀⠀⢀⣀⣤⠞⢋⣁⣠⡤⠶⠛⠋⠁⠀⠀⢠⢀⣴⠞⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡟⠀⠀⠀⢀⡇⣾⣿⣿⣿⣿⣿⣿⡿⣅⣠⠀⠀⠉⠛⠶⣤⣀⠀⠙⠳⣤⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁ ⠀⠸⣯⠟⠛⠒⠒⠶⠾⠷⠟⠒⠚⠛⠛⠛⢫⠍⠁⠀⠀⠀⠀⠀⠀⢀⣸⠾⠋⠁⣠⣿⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⡇⠀⠀⠀⣼⢠⣿⣿⣿⣿⣿⣿⡟⡑⠈⠛⢦⣀⠀⠀⠀⠀⠉⠛⠶⢤⣌⣙⡳⢤⣀⡀⢀⢀⡀⡀⢀⢀⣀⢀⠤⠠⠂⣲⠇⠀ ⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠁⠀⠀⢀⣨⡶⠛⠁⢀⣤⣼⡿⠋⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣸⠀⠀⠀⢠⡇⣼⣿⣿⣿⣿⡿⠋⠳⣾⠠⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠈⠉⣽⠛⠛⠻⠿⠷⠶⠦⠤⠶⠶⠞⠛⢛⡟⠀⠀ ⠀⠀⠀⢷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠀⠀⣀⣤⠾⠋⠁⠀⠀⡀⣿⡾⠋⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠂⠀⠀⡟⠀⠀⠀⠀⣰⣿⣿⣿⠟⠋⠀⠀⠀⠈⠻⣦⡀⠀⠀⠈⠙⢶⣄⠀⡀⠀⠀⠀⣠⢿⠐⠀⠀⠀⠀⠀⠀⡐⠀⠀⡀⣀⡾⠁⠀⠀ ⠀⠀⠀⠘⣷⣲⣦⣬⣤⣀⣀⣀⣀⣄⣠⣿⠼⠖⠛⠉⠀⠀⠀⠀⣤⣥⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠻⣿⣿⣿⣿⡿⠀⠀⠀⡇⠀⠀⠀⢠⣿⣿⡿⠃⢀⡴⠃⠀⠀⠀⠀⠈⠻⣦⡁⠄⠀⠀⠈⠛⢦⣄⡀⠀⣀⢺⠴⠀⠀⠀⠠⠀⠐⠀⠀⠀⠑⣽⠃⠀⠀⠀ ⠀⠀⠀⠀⢹⡏⠉⠉⠉⠉⠉⠉⠉⠁⠀⣿⠀⠀⠀⠀⠀⠠⢤⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡄⢻⣿⣿⣿⡇⠀⠀⢰⡇⠀⠀⣾⣿⣿⠏⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠉⠉⠙⠳⢦⣿⣐⡀⠀⠀⠀⢀⣀⣀⣠⣤⣾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢽⡀⠀⠀⠀⢀⣵⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠙⠛⠏⠇⠀⢀⣾⠁⠀⣸⣿⡿⠋⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⣀⠀⠀⠀⠀⠀⢀⡟⠉⠉⠙⠛⠛⠛⠛⢛⠛⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⠾⢧⣄⣀⣀⡠⠶⠀⣘⣇⣭⢿⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡀⠐⠲⠦⢿⣯⡄⠀⣿⠟⠙⠳⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠂⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⣐⠈⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣇⡀⠈⠉⠉⠉⠉⢉⣁⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠈⠻⣼⡇⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣀⡀⠀⢀⠀⠰⢆⣀⣰⣾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣮⣭⣉⣉⣭⣽⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⢰⡏⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠙⢷⣦⣴⣿⣴⡾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠷⠀⠈⣽⡏⠁⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⣸⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠘⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⢸⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⢋⠀⣸⠁⠈⢙⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠓⣿⠒⠋⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⣿⣿⡿⠿⢿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡂⢰⠿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣩⠟⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⢟⣀⣀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣄⣀⣀⣀⣀⣀⣀⣠⣼⡿⠷⠚⠛⠛⠳⠶⢿⣷⣄⡀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣳⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣏⣷⡿⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡻⣡⣷⠟⡀⢼⣷⠧⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯⣽⣿⡓⢄⡐⠠⣀⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⢇⡘⢄⠒⣥⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⢯⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⣾⣿⣯⣟⡲⣬⣜⣮⣙⡾⢿⣿⣟⡿⣛⠷⣦⣄⡤⢔⣶⣶⣟⡾⣍⢯⣙⣧⢽⣯⡇⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠼⣗⣮⣾⣿⡿⠿⢿⣟⣟⣻⡽⣏⡿⣟⡿⣏⣷⢫⡟⣶⣹⢻⣿⣿⣻⣾⣽⣾⣟⣿⠞⢫⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠇⣀⣼⣿⣿⣁⣀⢀⣼⠿⣼⣳⡽⣯⢿⣹⣷⣻⡼⣣⣟⡲⣭⠳⡽⣿⣯⣷⣿⠟⡻⠁⠚⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⣴⣿⣷⡀⠉⢠⣾⣏⡿⣫⢷⣻⣽⣟⡿⣾⢟⣽⣻⣬⢳⣧⢻⡵⣏⣿⣿⣣⢋⢄⣠⢐⣨⡭⠇⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡵⠟⣿⡿⠹⣿⣶⣿⣷⢞⣽⢯⡿⣷⣿⡽⣿⣻⣿⣷⣟⣾⠿⣜⣣⣞⡧⣿⢿⣷⣩⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣤⣼⣯⣅⣤⣼⣿⣧⣶⢿⣿⣿⣼⣿⣧⣿⣾⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣵⣿⣷⣿⣿⣿⣿⣿⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⡟⣯⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡝⠻⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣃⢘⡀⡛⡘⢃⢃⡘⣀⠛⡘⠛⣃⠘⠛⡇⢿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⡿⣿⣿⣿⢏⣧⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣩⣿⣸⠘⡛⡇⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡔⢠⠂⢡⠐⣁⢂⠰⠀⡌⠄⡡⢀⠜⡐⠰⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡜⣿⣻⣽⣾⣧⢓⢃⠐⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠆⡂⢅⠢⢈⠄⢂⠄⢃⠐⠰⢀⠂⠔⡀⢃⡣⢿⢿⣿⣿⣿⣿⣾⢿⣿⣿⣿⣿⣿⣾⢰⣛⢣⢭⡾⠈⠻⣿⣷⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡓⠓⠌⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡱⠈⡄⠢⢁⠌⠂⡌⠄⢊⠐⠤⢈⡐⠄⢂⠁⠾⣿⣿⣿⣿⣷⣿⣿⡿⣯⣿⣿⣿⣿⣇⠌⠣⠎⠬⠢⣢⠀⠀⣼⣟⣫⠋⣻⣿⣿⣿⣿⡿⢿⣿⣦⠽⡂⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⡠⠑⡠⠑⡈⠄⢃⠰⢈⡐⠌⡐⠄⡐⡈⠤⢈⠴⡙⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣾⢿⣧⡐⢀⠂⠄⢀⠂⠁⣹⡖⡍⣦⣿⣿⣿⣿⣽⢣⢁⡀⠉⡄⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡅⢊⠤⠑⡈⢌⡐⢂⠂⠔⡐⠠⢊⠐⠠⠌⣀⠢⠘⢌⠻⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⢆⡈⠉⠣⢌⡐⣀⠌⠰⡉⢁⠙⣻⣿⣿⣿⡿⢃⠇⢤⣴⣡⢀⢃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠌⡐⠂⠥⡈⠤⠐⢂⢉⠰⢀⠃⢄⠊⡁⢂⠄⠂⠍⠢⠑⠢⠝⡿⡝⣿⣿⣿⣿⡿⢻⣯⣞⢢⠁⠠⠡⡤⡑⠣⡐⢀⣲⣿⣿⣿⡟⠔⠡⡈⠄⣻⡛⢦⡟⢳⡶⠓⡆⠀⣰⠆ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠎⡐⡉⠰⠐⣂⠉⡄⢊⠐⡈⠔⠂⠤⢁⠂⠌⠌⡐⠡⢈⠤⠁⢅⠰⢼⣿⣽⣾⣙⣧⢞⡽⣷⣾⣄⡐⢠⢐⣡⣴⣿⣿⣿⠏⣛⠿⠿⠐⡠⠑⡨⢉⠍⡋⠉⠁⠀⣇⣠⡓⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢣⠐⡡⢁⠣⢀⠎⡐⠨⠄⡡⢘⠈⠔⢂⠉⡰⠈⠤⠑⣀⠂⣁⢂⣄⣾⠿⡿⠽⠿⠿⣿⣿⠷⢓⠚⡉⠛⠻⣟⢛⣹⣟⠯⠊⡄⠂⡔⠡⠄⢃⠔⡁⠆⡇⠀⠀⠀⠉⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣂⠱⣀⠃⡌⠢⡐⠌⡁⠆⣁⠢⢉⠰⢈⠰⢀⠱⢈⠡⡀⡲⠚⣹⣿⡯⠟⠋⠍⡐⠠⠀⠄⡐⠂⠡⠀⠄⡁⠈⢯⣢⢀⠂⠥⠐⠡⠄⡑⡈⠆⡰⢈⠔⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⡠⢡⠐⡌⡐⠡⢄⠃⡌⠰⡀⠆⣁⠒⡈⠔⣈⠰⢈⢢⢊⠔⣫⢻⡽⡱⣈⢂⠡⠐⠀⠀⠀⠀⢈⠐⢀⠀⠠⠁⠈⢷⠢⠜⣨⣭⡭⣗⡔⡁⢢⠁⠆⡌⠄⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠡⢂⠥⡐⠌⡡⢂⠜⠠⡑⢠⠑⡠⠂⠥⠘⡀⠆⣡⢃⢏⣺⢋⡷⢗⡱⠨⡆⡑⢂⠐⢈⠀⢂⠀⠄⠠⠀⠄⡐⠈⠨⡷⣾⣽⡟⣡⡗⣞⡤⢁⠎⡰⣈⠜⣠⠤⠴⢦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠣⢌⠂⡔⢡⠂⡅⢊⡁⢆⠡⢂⠅⡱⢈⠡⢂⡑⡆⣎⠟⡁⣮⣼⢳⠂⢁⠘⠢⢆⡈⠢⡘⠤⠘⡀⢂⠈⡐⠀⠌⡀⢿⢾⣿⡟⣟⡼⣸⡘⠆⣊⠥⠞⠋⠉⠀⣿⡯⣧⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡱⢈⠒⢌⡐⢢⠘⢄⠒⡨⢐⠡⢌⠰⢈⠢⢡⢰⢰⡸⢂⢡⢣⣇⡟⠀⠀⠌⠑⠢⢌⡑⢢⡘⠤⢁⠂⡐⠀⠡⢀⡁⢾⡻⢞⣿⣯⡷⡣⣳⠟⠁⠠⢀⠂⠌⡐⠤⢿⣿⡦⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢅⠊⡌⢢⠘⢄⠊⡄⢣⠐⡡⢊⠰⡈⠆⡑⠢⢼⢸⡇⢢⢸⣽⢲⡀⠄⠀⠀⢈⠐⢠⢉⣾⡴⢃⢎⡐⠠⢁⠂⠄⠠⠸⡿⠭⢒⠭⡍⣱⡟⢀⠡⠂⢤⣜⣤⣣⣯⢗⡾⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢆⡱⢈⠆⡉⢆⠱⡈⠆⡱⢀⠃⢆⠱⡈⠔⡡⢊⢸⢁⠂⣯⢾⡙⢦⠐⡈⠠⢀⠌⡰⢎⡧⢻⣌⠒⡌⡑⢢⠈⠤⠁⠄⣧⠹⡡⡞⢠⡋⠄⢂⠡⢎⡿⡄⠀⠉⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢢⠐⡡⢊⠔⡈⢆⠱⡈⠔⡡⢊⠔⣂⠱⠘⠤⠡⡼⣼⠘⡧⢾⡝⣪⢣⢔⡡⢎⡜⡱⢎⡜⣣⢯⡘⠤⡑⠠⠑⠂⡁⠂⢸⡆⢷⢡⡟⠀⠌⣂⠱⣺⡰⡇⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣙⣂⠃⠴⡁⢎⠰⡈⢆⠱⡈⠔⡡⢊⠰⣈⠱⡈⠥⡇⡇⡎⢵⣣⢻⢖⣍⢲⡘⢦⡘⡱⢊⠜⡤⣛⣧⠱⠠⡁⠌⠐⡀⠐⠀⣳⢠⡗⢀⡘⠠⢢⣙⢇⠇⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢤⢶⡲⣖⠾⣹⢏⣟⡻⣭⢳⢯⣟⣿⡧⡓⢌⠢⡑⢌⠢⡑⢌⠰⣁⠒⡄⢣⠘⡐⠇⢷⣻⡌⢶⢣⠞⣣⡧⡙⠦⡑⠃⡌⢸⢐⢣⢾⣝⣧⠐⡈⠐⡀⠄⠁⠘⡏⢠⠂⠄⡡⢓⡾⢸⠌⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⢫⣏⡳⣬⢏⣶⣳⣞⣻⢷⣻⣞⣷⣯⣿⣻⣾⠟⡡⢋⠄⢣⠘⡄⢣⠘⡄⠣⢄⠣⡘⢄⠣⡘⠼⡸⡵⢧⢊⡯⢞⡡⠞⠃⠆⠡⠂⠌⠄⠊⡜⡧⢿⣞⣆⠄⠡⢐⠠⠈⠄⢻⣃⠌⠰⢡⢯⠇⡇⡌⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢯⣛⣮⣷⣾⠽⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⡖⢒⠩⣐⠡⢊⠆⡱⢈⠆⡱⢈⠱⡈⢆⠱⡈⢆⡑⢢⢣⠹⣟⡆⢺⡗⣸⢡⠍⠢⢁⠂⠌⡈⠂⢄⢹⢏⣿⡼⣆⢁⠂⡐⠈⡄⢃⣯⠰⣡⢋⡞⢸⠰⡐⡇⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⣰⢯⡷⣯⣿⡿⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠢⡑⡄⠣⢌⠢⡑⢌⠢⡑⢌⠢⡑⢌⠢⡑⢢⠘⡄⠦⠱⡙⣽⡄⢿⡥⠳⣌⠱⡀⠌⡐⠠⢉⠀⡂⢯⣚⢿⡼⣆⠱⡀⢡⠘⡠⢺⡱⣌⡿⢡⢃⠣⡐⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⢯⣿⣽⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠣⡔⢡⠃⡌⢒⢡⠊⡔⢡⠊⡔⢡⠊⡔⢡⠢⡑⣘⠢⣑⠺⢸⢜⡈⢳⡝⢦⡑⠬⡐⠄⢃⠄⠒⡈⠄⣏⡞⣽⣭⢧⠰⡁⢎⡐⢣⠓⣼⢃⠎⣌⠱⡀⠇⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⣼⣯⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠱⡈⢆⠱⡈⢆⢡⠊⡔⢡⠊⡔⢡⠊⡔⠡⢆⠱⣀⠣⢄⠃⢸⢚⢄⠈⢿⡢⡝⢢⠑⡌⢢⠈⢂⠑⡈⠜⣮⢵⣻⣎⠳⡌⢆⡍⢦⢹⠃⡬⠘⡄⢣⠘⡄⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⢸⣿⣽⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠣⡘⢄⡣⠜⣀⣂⣥⣬⣤⣅⣚⡠⠧⣌⠱⣈⠒⡄⠣⢌⢲⢸⢚⡈⠄⢸⡷⣉⠆⡱⠈⠄⠈⠀⠄⠐⡈⠜⡖⡧⡿⣧⣙⠶⣘⣦⢃⠜⣐⠣⡘⢄⠣⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠖⣫⡵⣞⢻⣝⣫⣞⣵⡺⣜⣯⣻⡽⣶⢮⣒⠭⣐⡉⡦⢝⡾⠆⢇⠂⣼⠳⢡⠘⢠⠁⠂⡁⠠⠀⠐⠠⢌⠹⡖⡟⢘⠻⠮⠵⢃⠎⡜⢠⠃⡜⡠⢃⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡻⣧⢷⣯⣿⣾⠿⠽⠾⠿⠿⣷⣿⣽⣾⣯⣿⣷⣌⡥⠚⢅⢊⠜⠤⢢⡿⣁⠃⢌⠀⠆⠡⠐⠀⠂⠁⠎⡄⢃⢜⡇⢸⠊⡍⢍⠣⡑⢌⠢⡑⠬⡐⢡⠂⠀⠀⠀⠀⠀⠀⠀ ⡃⠀⠀⠀⢿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⡿⣻⣍⢦⣟⢦⡜⡇⢿⡝⡻⣿⣿⣿⣿⣿⣷⡄⢨⡘⡼⣦⡿⣧⢏⠸⣨⡜⢆⠃⠆⠀⢀⠃⠆⡝⢮⢸⠁⡏⣞⢱⡘⣆⢳⡘⣆⡳⢦⠳⢮⠃⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠘⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡿⢻⠱⢳⠹⡜⢧⡜⢦⠳⡝⣮⢿⡵⢻⠛⣿⣿⣿⣿⣿⣶⡷⣾⠏⡟⢦⠋⡞⢱⠸⠈⠞⠀⡄⠈⡜⠶⡝⡏⡾⢸⠹⡌⢧⠹⡌⢧⠹⣬⠹⣬⠛⡎⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⣿⣽⣿⣿⣦⣤⣀⡀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⠿⠫⠄⠥⢃⠆⡱⢈⠆⡘⡤⢗⣩⠖⠋⢀⠂⡱⢈⠿⣿⣿⣿⣿⠿⢋⠔⡈⢎⠱⣈⠆⢡⠉⡐⢀⠀⠆⡐⢢⢳⠁⡇⡎⠱⠌⠦⠑⠈⠂⠓⠂⣁⣀⠁⡈⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣾⣿⣽⣻⣽⢿⣿⣿⣿⢿⣟⣿⣿⣿⣿⠟⠁⠀⡧⢉⠆⡥⢊⠔⣡⠞⣪⠔⠋⠀⠀⢀⠂⠰⣀⢃⢎⡹⣿⠻⠏⡜⠠⢊⡴⢊⠱⡀⠎⠐⠠⠐⠠⠈⡔⢡⠣⣍⢰⡇⡖⣄⣢⣄⣩⢉⡔⠢⠑⠂⠆⠣⠘⠄⠀⠀⠀⠀⠀⠀⠀ ⡁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⣇⠣⡘⠤⢃⡜⢡⡾⠃⠀⠀⠀⠀⡀⠈⢡⠀⢎⠦⣑⢩⡥⢗⡚⠱⡉⠔⡁⠂⠔⠈⠠⠁⡐⠠⢑⡈⢆⡱⢼⣸⢠⣀⠄⡠⣐⠐⡒⢒⠒⡒⢒⠒⣂⠒⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠣⣘⢐⠏⣰⠃⠀⠀⠀⡀⠀⠀⠠⢁⠂⡘⢌⣶⡷⢋⠜⢂⠈⠁⠐⡀⠀⢁⠂⠈⡐⠠⢄⡑⢢⠘⡤⢣⢷⠇⡎⡔⢨⠔⠤⠓⡌⢢⠑⡌⢂⠳⢠⠃⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡱⢀⡏⢰⢃⠆⠠⢈⠐⡀⠠⠈⠐⡀⢂⢱⣾⠋⡔⠡⢈⠠⠀⠀⠀⠀⠐⠀⠠⠁⠄⡡⢂⠜⣠⢋⠴⣋⣾⡀⡇⡜⢠⠊⡔⢣⠘⡄⢣⠘⠤⡉⢆⠱⡀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠩⠄⠀⡏⡼⡈⢅⠂⡐⠠⠀⡀⠂⠐⣨⡾⢡⠃⡌⠐⡀⠀⠀⡀⠄⠠⠁⠂⢁⠈⡐⢐⠠⠒⠠⡍⢎⡵⣊⣇⢱⡘⢄⠣⡘⢄⠣⡘⠤⡉⢆⠱⡈⢆⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣒⢺⠀⡇⡷⡁⢎⡐⠠⢀⠁⡀⠠⠁⣼⡥⢃⠜⣀⠡⠀⡌⠐⡄⠌⡄⠃⠌⡀⢂⠰⢈⠆⡁⢣⠜⣌⢲⡱⢺⠈⡜⡄⢣⠘⡄⢣⠘⠤⡑⠌⣆⠑⡢⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⡄⢺⠀⡇⡷⡉⢆⡘⠄⢂⠐⠠⠐⠠⣿⠰⣁⠢⢀⠜⡐⠄⡃⠔⠡⡘⠨⡐⠠⢁⠒⡨⢠⠑⠢⢍⢆⢣⡝⡭⡇⢳⢈⠆⡱⢈⠆⡉⢆⠱⡈⠤⢃⡑⡂⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⡌⡡⠇⢹⡸⡑⣎⠰⣁⠂⠌⠠⠉⢄⢻⡔⡡⢒⢈⡐⠌⡰⠈⠌⡡⠐⠡⠐⡁⠂⠌⡐⠠⢉⠒⠌⡌⢆⢳⢂⢷⠸⢌⠢⡑⢌⠢⡑⢌⢢⣁⢃⡒⠤⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠑⠚⠈⢷⡽⡤⢓⡄⢣⠘⠤⣉⠢⣹⣖⡱⢌⠢⢌⠰⠠⢑⠨⢐⠡⣁⠒⡠⢉⠔⣀⠃⡰⢈⠒⡌⣘⠢⢭⢸⠀⠃⠂⠑⠈⠂⠑⠈⠂⠐⠂⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣝⡧⡘⢦⣉⠲⣄⠳⣐⢻⣜⢎⡕⣊⠦⡑⡈⢆⠡⠒⠤⠑⡠⢂⠒⠠⢃⡐⡀⠎⠰⣈⠞⠬⡘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡙⢆⢆⡓⢌⠲⢡⢎⠻⢾⣴⢡⡒⢥⢊⡄⢣⠉⡔⠡⠒⡈⠌⡁⢂⠠⠐⠈⠂⠔⣊⠱⡂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠜⡢⠜⣌⢃⠣⣌⢣⡙⠷⣗⠍⣆⠣⢜⠢⡑⢌⠢⡑⡐⠄⡡⢀⠀⠄⠈⠄⡡⢂⠱⡁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢿⣦⡙⡰⢊⡱⢄⠲⣈⠕⡸⢮⣄⢋⠆⣣⠙⡌⠦⡑⠰⡈⠔⡀⠂⠌⠐⡠⠑⡌⢆⡁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⢋⣥⣴⣶⣦⣍⠻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣴⡟⡿⡿⣻⠿⠻⢷⡜⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⡿⣿⢿⡏⠁⠉⠠⠀⢇⢹⣿ ⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠸⢇⡟⠀⠁⢠⣦⣌⠚⣦⣦⢻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄ ⠀⠀⣬⣑⠟⠁⣰⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠄⣾⣿⣿⣿⣦⠸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢰⣿⣿⡛⢿⣿⣆⠹⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢃⣐⣛⡚⠿⣿⣧⣄⢻⣿⣧⠙⣿ ⣿⣿⣿⣿⠿⢛⣛⢛⣛⣡⣾⣿⣿⣿⣿⣷⣮⡙⢿⣦⠹⣿⣷⠘ ⣿⣿⡿⢡⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠁⠐⠚⠻⣿⠀ ⣿⡟⣰⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢸⣿⣿⣿ ⣿⢠⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿ ⣿⢸⣿⣿⣿⣿⣿⣿⢡⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿ ⣿⠀⠻⢿⣿⣿⣿⣿⣌⠛⠚⠋⡀⠿⣿⠿⠿⠛⠋⠅⠀⣿⣿⣿ ⣿⠀⠀⠀⠀⠈⠉⠉⠁⠀⣧⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⣿

⠀⠀⠀⠀⠀⢠⠃⠀⢸⠀⢸⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⡴⠋⡆⠀⢸⠀ ⠀⠀⠀⠀⠀⣼⠀⠀⡈⠀⠸⡆⠀⠀⠀⠙⠳⣦⣀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⣠⠞⠋⠉⠉⠉⠉⠉⠉⠉⠉⢉⡿⠋⠀⢀⣧⠀⢘⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⣇⠀⠀⠀⠀⠀⠀⠉⠛⠛⠆⠀⠀⠀⢀⣀⠤⠚⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⣼⢹⠀⠘⠀ ⠀⠀⠀⠀⠠⡇⠀⠀⣇⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢻⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⣰⠃⢸⠀⠀⡀ ⠀⠀⠀⠀⠀⡇⠀⠀⠸⡀⠀⠘⡾⠷⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⢎⣤⠀⠐⠲⢶⣒⠋⠁⠀⠀⠀⣀⢞⡁⠀⢸⠀⠀⡇ ⠀⠀⠀⠀⠀⢳⠀⠀⠀⢳⡀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⠉⢁⡜⠀⠀⢀⣀⠀⠉⠒⠲⢤⡼⠗⡟⠁⠀⢸⠀⠀⠇ ⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢱⠤⠤⠝⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠉⠁⠀⠔⠋⠉⠉⠙⣦⢀⠔⠋⠀⢸⠀⠀⠀⡟⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣀⡀⠀⣀⣀⡤⢴⣿⠁⠀⠀⠀⣼⡤⣶⡾⠁⢠⠇⠀ ⠀⠀⠀⠀⠀⠀⣤⣬⣳⣄⠀⠀⠙⠢⠀⢴⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢁⣤⠶⠛⠁⠀⠀⠐⠋⢀⡴⠟⣁⡴⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢧⠀⠉⠒⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣢⡀⠀⠀⠀⠀⢀⠆⣠⠾⠋⠁⢀⣀⣀⣀⠀⠀⠈⠉⠀⠉⠁⣨⠟⠃⠀ ⠀⠀⠀⠀⠀⠀⢠⣈⡳⣄⣀⣀⡀⠀⠀⠤⠤⠤⠤⠤⠤⢬⣿⣧⠀⣀⣀⣀⣸⣿⣥⡶⠾⠛⠛⠉⠉⠉⠀⠀⠑⠒⠠⠴⣾⡷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠉⠉⠀⠀⠀⢙⡟⠃⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⣀⠴⠚⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠳⢄⣀⣀⣀⡴⠋⠀⠀⠀⠀⠀⣠⠟⠀⢀⣴⠾⣯⣁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⢤⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⣯⣀⣀⣀⣠⣤⣴⢶⣛⡇⠀⢈⡽⢡⣀⠀⠉⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⠉⠀⠀⠀⠠⡵⠦⠄⠀⠀⢹⣶⣤⣤⡤⠖⠋⠙⡆⠀⠀⠀⠀⡇⠀⠈⠀⠀⣉⠝⠁⠙⢿⡓⠲⠿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⢲⡤⠗⠢⠄⠀⠀⠀⠉⠀⠱⡀⠀⠀⠀⠁⠀⠀⠀⡴⠃⠀⠀⠀⠈⣀⡠⠤⠤⢤⠽⠶⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⣀⣀⣠⠴⠊⠁⠀⠀⣠⠴⠯⠥⠤⠤⢴⡾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠿⠟⠛⠙⠓⠲⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠖⠋⠁⠀⠀⢀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠬⠷⠶⣤⡶⠶⠶⠶⢦⣄⡀⠙⢿⣿⣿⣷⣶⣿⡿⣿⣧⠶⠚⠛⠛⠓⢾⣍⠙⠒⢦⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⣾⠁⠀⠀⠀⠀⠀⠈⠛⢦⣀⠉⠙⠛⢉⣭⠞⢫⠃⠀⠀⠀⠀⢀⠇⠙⣦⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⢶⡦⣤⡀⠀⠀⠀⠀⠀⠈⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⣠⡞⠁⢠⠏⠀⠀⠀⠀⠀⡎⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠈⢳⡀⠙⠳⣄⠀⠀⠀⢀⡼⡇⣠⠖⠊⠙⠲⣶⠆⠀⠀⠀⠈⠻⠏⠀⢀⠎⠀⠀⠀⠀⠀⡼⠀⠀⠀⢸⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠛⢷⡄⠀⠈⢧⣀⡴⠋⣴⡿⠁⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⣸⠁⠹⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡾⢁⣤⣠⠏⠀⠀⠀⠀⠀⣠⠴⠛⠛⠲⣄⣀⡀⠀⢰⠁⠀⠀⠀⠀⡰⠁⠀⠀⠀⣴⠋⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡟⠀⢀⡇⢹⣖⡶⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⠋⠁⢠⠇⠀⠀⢀⣼⠟⠓⠒⠒⠦⣼⡃⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣿⢃⣠⣴⣶⣶⣿⣛⢯⣹⣾⠁⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣻⣾⣿⣞⣯⣷⣽⣾⣿⣁⣀⣠⢤⡶⣶⠿⣻⣶⣟⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣟⣯⣿⣶⣯⣿⣿⣿⡁⠀⣴⠿⣟⣿⣟⣿⣻⢷⢯⣞⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢒⣖⣲⡶⢶⡖⣶⣒⢶⡲⣞⣫⠭⣭⣭⣽⣭⣯⣽⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠿⠿⠿⣌⠿⢿⣿⣿⣿⣿⡾⣽⢯⣟⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣛⢧⣛⢧⣛⡶⣹⣎⢷⣝⡮⣟⢷⡾⣹⢯⡟⠉⠉⠛⢿⣿⣿⣯⣟⣿⣫⣽⡿⣃⣔⣬⣿⣷⣯⣿⣿⣿⣿⣽⣻⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⡾⣭⡟⣾⣹⢗⣾⣫⢾⡽⣽⢾⡽⢯⡟⠀⠀⠀⢀⢈⣿⣿⣿⣿⣿⠿⢻⣷⣼⣿⣿⣟⣿⣟⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣿⣷⣯⣟⡾⣽⣳⢿⡽⣾⡽⡟⠀⠀⢀⣰⠞⠟⠙⢻⣷⣿⣸⣷⣾⣟⣺⣽⣟⣻⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⣯⣿⣽⣳⢿⠃⠀⠀⢀⠀⢠⣤⣦⣄⣇⠉⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣉⠉⠉⠻⠀⠀⠠⢀⣾⢿⠋⢁⣿⣿⠀⠀⠀⠀⣿⣧⠙⢿⣹⣏⢠⣛⠟⠁⠀⠀⢀⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣓⣈⣰⣦⣤⣀⣼⠋⠀⠀⢭⣽⣿⡇⠀⣀⣀⣿⣿⡇⡸⣿⣿⡤⠉⠒⠤⣀⠀⠠⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠏⠀⠛⣞⣧⣾⠍⠢⣀⠀⠈⠻⠟⣇⢉⣡⡶⣭⠯⡀⠐⠛⠙⢇⠀⠐⢲⠏⠀⠀⠈⠲⠞⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢀⠄⠂⢸⠛⠁⣠⣲⡆⢔⠾⠋⠀⠈⠢⣉⠀⢀⣀⣈⡆⠀⠀⢸⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠤⣌⡁⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠀⠀⣜⣩⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣛⡉⠀⠀⠓⢄⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡹⠋⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠚⣿⣶⠦⣄⣀⡀⠘⠿⠽⠶⢾⣷⣀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⡀⣀⣀⣠⡿⠍⣛⠻⡿⠿⣟⣲⣶⣶⡶⠿⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠛⢻⠿⠻⢿⣿⣷⣿⣶⣆⠬⡯⣑⣿⣿⣿⣿⣹⣍⣧⣾⠈⠉⠉⠒⠒⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠁⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠐⠒⠠⣔⠁⠀⠉⣿⣿⣿⢛⡖⠾⠿⢿⡿⠿⣾⠟⠁⠀⠀⠀⠀⠀⠸⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡅⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⠘⢿⣿⠇⠈⠁⠒⠺⣤⣢⡼⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠹⡄⠐⠒⠠⠤⠀⣀⠀⠀⠀⠀⠈⣏⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠘⣆⠀⠀⠀⠀⠀⠉⠑⠢⡀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠈⢣⡀⠠⢄⣀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠧⣀⣀⠀⢀⡤⠋⠀⠀⠀⠀⠈⢁⠒⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⣠⢾⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣻⡿⠏⠀⠀⠀⠐⠢⠄⢀⡀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠖⠋⣁⡼⣇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡎⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡔⠍⠀⠀⠈⠢⣀⠀⠀⠀⡰⢠⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡴⠋⠁⠁⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢧⠄⠂⡄⠀⠀⠀⠀⠁⠢⢴⣁⡼⠀⠀⠀⠈⠑⠂⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣀⠤⠖⠉⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢠⠀⠀⠀⠑⠤⡀⠀⠀⡐⠁⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢆⠀⠀⠀⠀⠀⢑⠞⠤⣠⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡠⠤⢤⢤⠴⠃⠀⡀⠔⠊⠀⠠⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠣⡀⠀⠀⡤⠃⠠⣼⠃⢳⠈⠉⠉⣍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⡜⢸⢀⡔⠉⠀⢀⡠⢔⠊⠉⠻⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⡀⠀⠀⠈⠑⠺⠤⣴⠟⠃⠀⠸⡆⠐⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢀⠃⢸⡃⣇⠀⡰⠟⠂⠁⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠈⠺⠦⣄⣠⠤⠴⠊⠉⠀⠀⠀⡼⠁⠀⠐⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⢸⠀⢸⣇⠞⠉⠀⠀⠀⠀⢀⡠⠐⠀⠈⢣⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣁⠀⠈⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢀⠀⠀⠰⠀⢸⠹⡄⠀⠀⢀⡠⠒⠁⠀⠀⠀⡠⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠈⠉⠓⠦⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⠀⠀⠀⣆⣼⡆⢙⣤⡐⠁⠀⠀⠀⡠⠔⠉⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⠁⠉⠢⢄⡀⠀⠀⠀⠀⠈⠉⠁⠐⠒⠒⠒⠒⠒⠚⠓⠀⠈⠉⠀⠀⢧⠀⠘⢷⣀⡠⠔⠉⠀⠀⠀⠀⢀⠠⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⡱⠁⠀⠀⠀⠀⠈⠁⠒⠠⠤⢀⣀⣀⢀⠀⡀⢀⢀⡀⠀⠀⣀⡠⠔⠒⠂⠙⣆⠀⠀⠙⣦⠀⠀⠀⢀⠄⠊⠁⠀⠀⡀⠘⣄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢡⠊⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⡄⠀⠹⡄⠀⠀⠀⠳⡄⠐⠁⠀⠀⢀⠔⠉⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⡔⠁⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠹⡄⠀⠀⠀⠈⢷⣀⡠⠚⠁⠀⠀⢀⠄⠢⡀⠣⣀⠀⠀⠀⢀⣀⣤⣤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⠎⠀⠀⠀⠀⠀⠀⠀⠀⢰⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣹⡄⠀⠀⠀⠀⠀⠀⠀⡇⡆⠀⠀⢳⠀⠀⠀⠀⠈⠙⢵⠀⠀⢀⠕⢁⠖⡠⠁⠀⠉⡖⠚⠉⠩⢿⡟⣿⣭⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡘⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡎⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⢣⠀⠀⠀⠀⠀⠀⠀⢹⠸⡀⠀⠐⢇⠀⠀⠀⠀⠀⠀⠑⢶⡁⠀⢸⡔⠁⠀⢠⠃⢁⠀⠀⠀⠒⣿⡽⣶⢾⣿⣷⣄⠀ ⠀⠀⠀⠀⠀⠀⢰⠇⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⠇⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠸⠀⡇⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠘⢿⣦⣾⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⢸⣿⣷⣿⡿⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⢎⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡌⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠄⠀⠀⠀⠀⡇⢸⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠹⣴⠀⠀⡜⠀⠀⢘⣲⣄⣀⣈⣸⠿⢿⣯⣿⣽⣞⣿ ⠀⠀⠀⠀⠀⠀⠀⢣⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⡸⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡸⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠈⡇⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠓⣜⠂⠀⣴⣿⣿⣷⣾⣯⣿⣦⠈⠉⠛⠻⠞⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡇⢜⡀⠤⣀⠀⠀⠀⠀⠀⠀⠀⡇⢓⠨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣇⠀⠀⠀⠀⠀⠀⠀⠈⡆⢥⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠓⢦⢿⣿⣿⣾⣷⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠈⠑⠀⠦⠤⠄⠀⠀⠀⠀⣇⣽⠀⠀⠄⠀⠀⠀⠀⠀⠀⠒⠈⢸⠂⡏⠀⠠⠀⠀⠀⠀⠐⠀⠇⢸⠄⣀⣀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⣶⠤⠤⠤⠤⠤⠶⠖⠛⠉⠲⠤⣄⣀⣀⣀⢀⣀⣀⣤⣤⣼⣿⣧⣈⠉⠐⠒⠂⠀⠀⠀⢸⡻⠦⠤⣤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡀⠀⢠⣀⣤⠴⠖⠛⠋⠉⠉⠉⣩⡥⠬⠥⣬⣉⣹⡏⠉⠉⠉⠉⠉⠉⠒⠒⠒⠚⠿⠥⢤⣀⡀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡗⠚⠉⣀⠠⠤⠒⠒⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠉⠉⠉⠁⠉⠁⠀⠀⠀⠒⠤⢩⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠉⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠘⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢸⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢨⡇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢈⡰⢯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⢀⣸⣄⠇⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢸⢧⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠔⠁⠊⠁⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⣠⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⡤⠖⠋⠁⠀⠀⠠⢀⡿⠉⠙⠢⠤⠀⣉⠒⠤⣀⠀⠀⠀⠀⠀⠀⡿⢸⡀⠀⠀⠀⠀⠀⡀⠠⢖⠍⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠓⠋⠀⠀⠀⡀⠤⠀⠂⣠⠞⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⢠⠇⣈⣇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⡄⠹⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠀⠀⠀⠀⠀⠈⢀⠀⠠⠐⡴⢡⠂⠁⠂⠤⣤⣀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⡼⠀⣼⢹⡀⠀⠀⠀⠀⢀⡠⠤⠏⠁⠀⠀⠀⠀⠀⣰⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⡀⠁⠀⠂⠀⠄⡜⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠲⡄⠤⠀⢠⡼⠁⢀⡟⠀⣧⠐⠒⠒⠽⠋⠁⠀⠀⠀⠀⡠⠤⠎⠁⠁⠀⠸⡀⠀⠀⠀⡀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠁⢀⠂⡸⠀⠀⠈⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢀⡾⠁⣾⣸⠁⠀⡟⡆⠀⠀⡠⠖⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢀⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⢤⣀⢠⣃⣀⢀⡞⢁⡼⠛⠃⠀⣱⠁⢻⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⡇⠀⠀⡠⠋⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣎⣠⡶⠗⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠠⠈⢰⡇⠉⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⢁⠂⠀⢀⡟⠠⠞⠀⠠⡄⣱⠃⠀⠈⣇⣀⣀⡤⠆⠂⠂⠂⠂⠒⠉⠁⠁⠀⠀⠀⡇⢀⠎⠀⠀⠀⠀⠀⠁⠀⢠⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢚⣷⡾⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠠⠈⠀⠄⢸⣇⠀⠀⠀⠀⠁⠂⠠⢀⠀⠀⠀⠎⠀⢀⡞⠀⠠⠀⠂⣽⣻⠃⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠚⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⢾⣿⠇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠄⠐⠀⠠⢸⠁⠑⠤⢀⣀⠀⠀⠀⠀⠀⠀⠉⠀⢀⡏⠀⠐⠀⣡⢾⡟⠁⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⣀⡤⠔⠋⠉⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠃⣯⢾⠀⢀⣴⡟⠀⠀⠀⠀⡀⠈⠀⠄⠀⠂⠈⢀⢸⠀⠀⠀⠀⠀⠀⠁⠑⠢⣀⡀⠀⢠⠟⠀⣈⣤⠞⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢳⠐⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⠀⣷⣿⣴⣟⡿⠁⠀⠀⣀⣁⠀⠀⠐⠀⡈⠀⢁⠀⣼⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣎⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⢀⣀⣀⡀⠤⠂⠁⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠃⠀⠀⠉⢁⣼⡿⢶⣞⡿⣿⣿⡏⠀⠈⡀⠐⠀⢈⠀⣼⢹⠦⠀⠁⠂⠤⣀⠀⠀⠀⠀⠀⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣏⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⣸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡞⠀⠀⠀⠀⠞⠛⠛⠉⢁⣿⡿⣿⠁⣀⡐⢂⠄⢈⡆⢠⠇⣼⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⣀⡤⠄⠊⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣼⡟⠁⢃⣤⣿⣷⠋⠐⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡒⠋⠉⠉⠉⠁⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⢋⣿⢁⣴⣾⣿⣿⣟⣠⠟⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢀⡀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠘⣯⣼⣿⠟⣿⣿⠟⠁⣸⠁⠒⠠⢀⡀⠀⠠⠈⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡧⠖⠒⠒⠁⠉⠁⠀⠀⢻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⠀⣴⡇⠀⢰⠀⠀⠀⢀⠀⡜⠀⠀⠹⡏⢁⣴⠛⠁⠀⢠⠇⠀⠀⠀⠀⠀⠜⠁⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⢹⣒⣒⠶⠶⢦⡤⠝⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⠞⢠⡁⠀⢷⠀⠀⢀⠎⠸⠀⠀⠀⢀⣴⠋⠁⠀⠀⢀⠏⠈⠉⠀⠀⢀⣀⠀⠤⠐⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠸⡇⠀⠈⠆⢀⠇⠀⠁⠀⣼⢠⡞⡁⠀⠀⠀⢀⠏⠀⠀⠀⠚⠛⠂⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⠀⠀⢀⣀⣀⣀⣀⠠⠄⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⡄⠀⠈⠚⠂⠀⠀⣴⣿⡎⠀⠀⠀⠀⠀⡞⠀⠀⠐⠒⠐⠀⠀⠀⠀⠈⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⢀⠀⠀⠤⠄⠒⠂⠨⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠢⢤⣀⡀⢳⢀⣀⣠⠤⠤⠤⠤⠬⡇⠒⠈⠉⠀⠀⠀⠀⠀⠀⢀⠀⠘⣆⢀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠤⠂⠈⠙⠁⡀⠄⢂⠐⡀⠆⠐⣻⠀⠀⢀⡀⠄⠐⠂⠉⢀⣀⣀⣠⣼⣦⣤⣂⠐⠐⡈⠐⢂⠁⠒⠠⢁⠂⠌⢉⠑⢦⠀⣠⠤⠴⠾⢲⠶⠶⠤⠤⢤⣀⣀⠒⠀⠤⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⠤⣌⣌⣠⠁⡐⠈⠄⢂⠐⡈⠄⣹⡖⠀⣀⣠⣦⣶⣿⣿⣭⣽⣶⣷⣽⣶⣬⣭⡳⣥⠀⠡⠀⠌⠠⢁⠂⠌⡀⠂⠌⢀⣾⣥⣶⣶⣿⣿⢿⡿⣿⣿⣿⣿⣮⣽⣿⣶⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠌⠐⡀⢂⠐⠠⢈⣷⣿⣿⣿⣟⡿⣽⣻⣿⣟⡷⣯⣟⣿⣿⣟⣿⣿⠇⠠⢁⠈⡐⠠⠈⠄⠠⢁⠂⣼⣿⣯⣷⣻⣿⣽⢯⣟⣷⣿⣟⣾⣽⣻⣟⡿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣌⡐⢀⠂⡈⠐⡀⠻⣿⣿⣿⣾⣿⣿⣽⣯⣿⣟⣷⣿⣾⣿⣿⣿⡿⠀⡁⠂⡐⠠⠁⠌⠠⠁⠂⠄⡈⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣷⣿⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠃⠐⠤⠀⠙⠛⠿⠿⣿⣿⣿⣿⠿⠿⠟⠛⢋⠉⡀⠄⢂⠐⠠⠐⠠⠁⠌⠠⠁⠌⠠⠐⡀⠈⠉⠛⠛⠟⠻⠟⠟⠻⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠐⠒⠂⠂⠂⠑⠀⠃⠈⠀⠃⠈⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⡆⠰⠀⢢⡄⠙⣦⠐⣀⣢⠙⢿⣆⠰⢀⠂⠀⠀⢹⣿⣷⡀⠀⠀⠀⢀⣠⠞⢋⠐⡄⠂⢆⠒⡐⢂⠒⡐⢂⠒⡐⢂⠒⡐⢂⠒⡐⠢⠐⢢⠐⡐⠂⠔⢂⠢⠐⢢⠐⢢⠐⢢⠐⠢⢐⠢⢐⠢⠐⠢⠐⠰⡀⠆⢢⠐⠰⡀⠆⡐⠂⠔⡠⠂⠔⡠⠂⠔⠠⢂⠔⠠⠂⠔⡠⠂⠔⠠⠂⠔⡀⠢⠐⡀⠢⠐⣀⠂⠄⡐⠠⢀⠂⠄⠠⠀⠄⠠⠀ ⣿⠃⠀⠀⠀⠈⠁⣸⠃⠀⠀⠀⢀⣿⡁⠀⠀⠀⠀⢸⣿⣿⣿⣦⡤⠞⡉⢂⡉⠄⢃⡐⢉⠰⡈⠔⡁⢊⠰⢁⢊⠐⣁⠢⠑⢂⡘⠠⡁⢡⠂⡐⠠⢁⠌⣀⠂⢡⠂⠌⢠⠘⠠⢈⠒⡀⠒⡀⠢⠑⠠⢉⠐⡐⠈⢄⠈⢂⡐⠐⡀⢃⠐⡠⢁⠒⠠⢁⠊⡐⠂⠌⡀⢃⠂⠄⡁⠊⠄⡁⠒⠠⢁⠂⠄⡁⠂⠄⢂⠐⠠⠁⢂⠐⠠⠁⠂⠌⢀⠁ ⡇⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢀⣾⣿⠁⠀⠀⠀⠀⢸⣿⣿⠟⢋⠐⠠⠑⠂⢌⢈⠂⠌⡐⢂⡐⢂⠡⢂⠒⡈⠄⠌⡀⢂⢁⠂⠄⠡⢀⠃⣰⠞⣁⣦⣦⠀⠌⠠⠐⡈⠄⠂⡁⢂⠐⠠⠁⠄⠡⢈⠐⡀⠂⠄⡁⠂⠌⠠⢀⠡⠐⡀⢂⠐⠠⢈⠐⡀⠂⠄⡁⢂⠐⠠⢈⠐⠠⢁⠂⠄⡁⠂⠄⡈⠐⠠⠁⠌⠠⠈⡐⢀⠂⠈⠄⢈⠐⠀⠂⠀ ⠁⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⣾⣟⡻⣷⡀⠀⠀⢀⣾⠟⠁⠌⡄⢊⢁⠊⣁⠂⢂⠌⢂⢁⠂⡐⠠⢁⠂⡐⢀⢊⠐⣀⠂⠂⠌⠠⢁⢢⠞⣁⣾⡿⢻⡿⣇⠀⠁⠂⠐⠠⠁⠠⠀⠌⠀⠡⠈⠐⠀⡐⠀⢁⠠⠐⠈⢀⠂⠂⠄⠡⠐⠠⢈⠐⡀⢂⠠⠁⢂⠐⠠⠈⡐⠠⠈⠄⠂⡈⠠⢀⠁⠂⠄⡁⠂⡁⠌⠠⢁⠀⠂⡈⠐⠈⡀⠄⡈⠄⠁ ⡇⠀⠀⠀⢀⡞⠀⠀⠀⠀⣸⢯⡝⣳⣭⡗⣾⣆⣼⡃⠌⠠⢃⠐⠄⢂⠰⠀⡌⠄⠌⡀⠂⠌⠠⢁⠂⡐⠠⢁⠂⢂⠄⢂⠡⠀⠡⣰⢋⢰⣿⡟⠀⣾⣷⠹⣆⠐⢠⡁⠄⡀⠁⠄⠀⢈⠀⠀⠁⢀⠀⠐⡀⢀⡴⠊⡀⠌⠐⠈⠄⠁⠐⠀⠠⠐⠀⢀⠂⠠⠐⠀⡁⠠⠐⠀⠂⠐⡀⠁⠠⠈⠐⡀⠄⠂⠄⠐⠠⠀⠌⡀⠐⢈⠠⠀⠄⠠⠐⠀ ⣿⣆⠀⢠⣼⣧⡀⠀⠀⢀⣿⣷⣮⡕⣮⡽⠟⠻⠃⠄⡈⠐⠠⢈⠐⡀⢂⠡⠀⠌⠐⠠⠁⠌⠐⡀⠐⠀⡐⠀⠨⡀⠌⢂⡐⠈⣴⠃⢤⣿⡏⠠⢡⣿⠈⢦⡹⡞⡹⠕⠚⢉⣙⣒⢦⣤⡄⠀⠀⠀⠀⣠⠴⠋⠀⡀⠄⠀⠄⠂⠀⠈⠀⠀⠀⡀⠐⠀⠀⡀⠄⠀⠀⠄⠀⡈⠀⠐⠀⠈⡀⠄⠁⡀⠀⢂⠈⠀⠂⠁⠠⠀⢈⠀⠠⠈⢀⠐⠀⠂ ⣿⣿⣴⣿⣿⣿⡿⢀⣶⣿⣿⣿⣿⣿⣿⣁⠀⠂⣁⣰⣤⣥⣂⡁⠠⠐⠀⠠⠈⠀⠌⠀⠌⠀⠂⠠⠈⠄⡀⠈⠄⠐⡈⠄⢠⢡⠏⢠⡿⡿⢀⠡⢸⣧⣬⣾⣉⠭⠉⠓⠻⣤⣖⣋⣙⡓⠲⢤⣀⠀⠚⢁⣀⣦⣦⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠀⠂⠁⠀⠁⠀⠂⢀⠀⠁⡀⠠⠈⠀ ⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠛⠉⠀⠀⠈⢹⡶⠞⡿⠀⠀⠂⠀⠈⠀⠀⠀⠁⠈⠀⠀⠄⠀⠱⣄⠊⡀⡘⠠⢸⣷⠃⣄⡶⢋⠴⢸⡏⠁⠀⠀⠀⡴⡃⠀⠊⡙⡶⣝⣲⣼⠷⢾⠋⣭⡟⣹⡇⠀⠀⠀⠀⢀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠈⠀⠀⠐⠀⠀⠐⠀⠀⠐⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠐⠂⢀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣴⣤⣁⣼⣸⡼⠋⡠⠋⠀⣺⠁⠀⠀⠀⢸⡟⠀⠀⠀⢸⡗⠊⠙⠓⣶⢲⣿⠟⠀⣿⣇⠤⠊⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣤⠶⠚⠛⠁⠀⠀⠠⠄⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣰⣴⣾⣉⡠⠚⡠⠀⠄⡇⠀⠀⠀⠀⢤⠀⠀⠀⠀⢸⠁⠀⠨⢐⣿⣼⠃⠠⢸⣿⠘⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣐⠢⢤⡀⠀⠀⣀⣠⡴⠿⠟⠛⣫⡟⠀⢀⡇⠊⠀⣯⠀⠀⠀⣰⠃⠀⠀⠀⣰⣯⠀⠀⣀⠘⣿⣧⡐⢠⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡿⢃⠐⡼⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡹⣍⠁⠀⠀⢁⣀⣲⣿⠀⢠⠞⡀⢀⣿⣿⡄⠀⣰⡇⠀⣠⣶⣿⣿⣗⢀⣾⣿⠀⢸⣧⠹⣯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⢋⠐⡄⣺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠦⡄⢀⡤⠟⠺⣿⣠⠏⢠⢃⣾⣿⣿⣧⢰⣿⣇⡼⠿⣿⣿⣿⣿⣼⢿⣿⡀⠀⢻⣷⡾⠿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⡀⠂⢅⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣞⠋⠀⠀⠀⢻⣏⣤⣾⣿⣿⣿⡿⢿⣿⠁⠉⠀⠀⠛⣿⣿⣿⣿⣿⠸⣷⢀⣦⣿⣉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠠⢁⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣊⡡⡙⠲⣄⡀⣼⣿⣿⣿⣿⣿⠋⠀⢸⡏⠀⠀⠀⠀⠀⣸⠛⠉⠁⢿⣯⣿⡾⢻⣍⡿⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠥⠴⠶⠛⠚⢓⡛⠻⣿⣿⣽⣓⡶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡛⣲⠟⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⠰⠒⠒⠒⠦⠴⡁⠀⠀⠀⢸⣿⣿⡇⡿⠬⣭⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠐⠒⠒⠋⠉⠠⠴⢀⢺⣿⣿⣿⣿⣿⣾⣿⣦⣀⠀⠀⣖⡀⠂⡐⠠⠤⠤⣼⣗⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠛⠷⠖⣶⣇⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⣸⣿⢻⣳⣁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⠈⠑⢾⡉⠁⠀⠈⠉⠁⠒⠺⠂⠳⢌⡐⢄⣀⠀⠀⠀⠀⠀⠀⣞⣁⣈⣄⣀⣬⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣿⠏⣼⢃⡽⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⢩⡱⡄⠀⠀⠀⠀⢉⠉⠻⢧⣼⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠯⡔⠻⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠂⣉⠥⠉⠉⠒⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠘⠆⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⣶⣾⣿⣿⡯⠭⠭⠭⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣠⣤⣶⣿⣿⣶⢼⡀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣑⣸⡿⣟⣭⣦⣧⣦⣍⠻⣄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠉⠉⢓⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠿⠒⠼⠆⠀⠀⠀⠀⠀⢀⡠⢴⠖⠀⠀⣀⢀⠀⡀⠀⠀⠀⠀⣀⠔⠡⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠟⠀⣴⣾⠛⠿⣿⡟⠉⠀⠀⠉⠉⠉⠛⠛⢿⡿⢿⠟⢡⣾⣿⣿⣿⣿⣿⣿⣿⣷⣢⣤⣀⣀⠀⢀⣀⠤⠒⠡⠠⠙⠋⠤⠄⠀⠠⠾⠥⢀⣠⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢏⠛⠲⢤⣀ ⠀⠀⠀⠀⠀⠀⠀⠰⢯⣌⡙⠛⠿⣿⠠⣿⣿⡟⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣿⣿⡿⠋⠀⠀⠈⠺⠷⠽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠯⣁⠀⠈⠉⠉⠉⠛⠻⢿⣻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⡆⣾⣿⣿⣿⣶⣽⣼⡙⠻⢿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣴⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠄⠛⠀⠀⠀⠀⠀⠀⠀⠉⠛⣷⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡸⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⡀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⢡⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⠀⠀⠸⣽⣭⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣧⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠎⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠋⠀⠀⠀⠀⠁⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣇⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠳⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⡀⠀⡠⠄⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⢷⣆⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡪⣍⡞⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠓⠊⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇⠀⣸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣖⡏⢈⠐⣈⠙⠦⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡐⠒⢡⡀⠀⠀⠀⠄⠂⠄⡙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡆⢀⠦⡕⣄⢦⣍⣀⠤⡴⡞⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⠈⣼⢳⡘⠁⠀⠈⠈⠥⠀⠦⠣⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⡾⢀⠚⡜⠄⠀⠀⠀⠀⠁⠀⠘⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⡖⠒⠒⠒⠉⠉⠉⠋⠛⠭⣉⠛⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠆⠀⠘⡌⡄⠀⠀⠀⠀⠀⠀⠰⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡘⡀⠀⠘⡈⡄⠀⠀⠀⠀⠀⠀⠠⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⢀⠈⡄⠒⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠐⠒⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡐⡐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢺⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢤⠤⢄⣀⡀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠤⣈⠙⠓⠠⢄⡀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠒⠤⢀⠁⠂⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⡀⠂⢀⠀⠀⠀⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⡘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠁⠀⢀⣳⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠃⠉⠀⠀⠉⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⣿⢦⡄⠀⢠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠰⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⢳⡈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠒⠒⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣂⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣆⡋⢱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⠜⠉⠀⠈⠉⠁⠒⠒⠒⠒⠒⠒⠒⠋⠉⠉⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠉⠑⠂⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠒⠒⠒⠒⠒⠒⠤⢄⣀⣀⠀⠀⠀⠀⠀⡀⣀⣀⡠⠤⠔⠒⠋⠉⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⣤⣶⣷⣶⣿⠁⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣆⣼⡏⢠⣦⡈⢿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠘⠛⢻⣧⡈⠛⣀⣿⡀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡏⠀⠈⣷⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣀⠀⠀⠀⠀⠀⣀⡤⠶⣿⣿⠿⠤⣤⣴⣿⠀⠀⠀⢀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⠙⠻⣿⣿⣷⣶⣿⠥⡄⠀⠀⠀⠀⠀⠀⠈⠙⢷⡶⠆⠘⠟⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠉⠀⠈⠙⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣧⠘⠟⠙⣿⠁⠀⠀⠐⢀⡀⢤⡀⢤⡀⢢⡘⢦⡄⠀⠀⠀⢰⡂⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠈⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢽⣷⠆⢀⡿⠀⠀⠀⣶⠀⠹⡌⣷⠀⣿⣄⣿⡈⣿⡶⢳⡤⢸⣧⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣶⡄⠿⠠⣇⢸⡄⣿⡀⠀⢻⣿⡶⢿⣌⣻⣇⣿⣿⢈⡇⢸⣏⠳⣄⠀⠀⠀⠀⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⡀⠋⠁⢀⣼⢿⡎⣷⣘⣧⠀⠀⠙⠸⣾⡟⠛⣿⠃⢸⢿⣇⠘⣿⠳⣬⣟⣶⣤⠀⠈⠻⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠳⣾⣀⣼⠿⣌⣷⣼⣧⣽⡆⠀⠀⠀⠈⠁⠀⢉⣀⡜⣸⡏⠀⣿⡆⠀⠈⠁⠀⠀⠀⠀⠈⠙⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⠋⣽⡄⣿⠛⡃⡀⠙⠃⠀⣠⣶⣦⠀⢠⡿⠏⢀⣿⣀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⣾⣄⣿⣧⡹⣆⠀⠸⣧⣀⣀⣈⣛⣃⡴⠟⠁⣠⣿⣿⡏⣰⣿⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣾⠟⢁⠀⠀⠉⢷⡙⣦⡀⠀⠈⠉⠉⠉⠉⠶⠤⠞⢻⣿⣿⣷⣿⣿⡇⠀⠀⣀⣀⣀⠀⠀⠀⠀⣠⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣇⠀⡏⣰⢂⣀⠠⡟⠺⢇⣰⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠘⢿⣿⣿⣿⣿⣿⣶⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠓⠛⠈⠛⠉⠀⠘⠆⢸⣿⡇⠀⠀⠀⠀⠀⠀⠲⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⡿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⣾⣿⣿⣄⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⠏⠀⠀⠛⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡿⣿⣦⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⡰⠃⠀⠀⠈⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⡋⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡀⠀⣼⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠸⠟⠻⠿⠇⠀⠀⠀⠀⢀⡴⠃⢀⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡛⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⣠⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣷⣦⣭⣀⣀⣀⡀⣸⣃⣀⣠⣴⣶⣶⣿⣿⣿⣿⣯⣀⣀⠀⠀⣠⣾⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠌⠉⠉⠁⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⠀ ⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡫⠀⠴⠚⡠⠤⠤⠤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⡿⠿⠿⠿⠿⢿⣿⠿⠿⠿⡿⠟⠛⠀ ⠀⠀⣰⡾⠿⡟⠻⣷⣿⢻⣷⣀⣀⣀⣀⢀⣉⡀⣀⣉⠀⠀⢀⣀⣀⣉⣀⣀⡀⣀⣀⣀⡀⠀⢀⣼⡟⢻⡷⠀⠀⢀⣴⠿⢿⡿⣿⠟⠿⣦⡀ ⠀⠀⣿⣅⠘⠿⣷⣿⡉⠀⣙⣿⣉⣉⠻⣟⠛⣿⡟⢙⣿⠀⣿⠋⢉⠙⢋⠙⢻⣿⣉⡉⠻⣿⠟⠋⠁⢸⡇⠀⣴⡿⢃⣴⡿⣿⡿⠿⢀⣿⠇ ⠀⠀⣸⡿⢷⡦⠈⣿⡇⠈⢿⡟⠉⣥⠀⢹⣆⠘⠀⣾⠇⠀⣿⠀⢸⠂⢸⡇⢸⡟⢉⣅⠀⣇⠀⢿⠇⢸⡇⠀⢻⣧⡈⢿⣶⣿⣷⡶⠈⣿⠀ ⠀⠀⠻⣷⣤⣤⣾⠟⢿⣦⣴⣷⣦⣤⣤⣾⡿⠀⣼⡏⠀⠀⢿⣦⣾⣦⣾⣧⣼⣷⣤⣤⣤⣿⣷⣤⣤⣼⡏⠀⠀⠙⢷⣤⣽⣷⣤⣤⣾⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣠⣠⣶⣿⣷⣿⣿⣿⣷⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣾⣿⢿⣻⡽⣞⣳⡽⠚⠉⠉⠙⠛⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⢻⣟⣧⢿⣻⢿⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⣿⡿⠞⠛⠚⠫⣟⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠈⢻⡽⣆⠀⠀⣴⣷⡄⠀⠀⠀⠘⣿⡆⠀⠀⣀⣠⣤⡄ ⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⣿⠿⢷⡀⠘⠛⠃⠀⠠⠀⠀⣿⣅⣴⡶⠟⠋⢹⣿ ⠀⠀⢻⣿⡀⠀⠀⠀⢾⣿⡆⠀⢿⣴⣴⡇⠀⠀⠀⠀⠀⠀⢠⡟⠋⠁⠀⠀⠀⢸⣿ ⠀⠀⠈⢿⣇⠀⠀⠀⠈⠉⠥⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⣾⡏ ⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⠁⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⠀⠀⠀⠀⣹⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠐⢧⡀⠀⢀⣾⠟⠀⠀ ⠀⠀⢀⣰⣾⠟⠉⠀⠀⠉⠉⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⡟⠋⠀⠀⠀ ⣠⣶⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣿⡆⠀⠀⠀⠀ ⢻⣧⣄⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀ ⠀⠉⠛⠿⣷⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣦⡀⠀⢀⣀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢠⠖⠒⠲⢤⣀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⣀⣠⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣃⣀⣀⣀⣀⣈⡷⠦⠐⠒⠚⠻⡝⢲⣶⠞⡏⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠃⢴⠃⢀⡴⠚⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡤⠷⠿⠀⠀⠀⡴⠚⠲⡄⢰⠋⠉⠳⣄⠀⠀⠀⠀⢹⠀⠀⢠⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢧⠀⠀⠀⠀⠀⣷⡀⢀⡇⠘⢧⣀⢀⡿⠀⠀⠀⠀⠈⡇⢀⡞⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢧⠀⠀⣴⡾⢿⠻⢿⡄⠀⠀⡿⠿⡷⠲⣤⡀⠀⠀⠻⠊⠀⢀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠏⠀⠀⠈⠀⠘⣧⠘⣧⡀⠀⠀⠀⢹⡀⣨⣿⠀⠀⠀⣦⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠙⠒⢲⠄⠀⠀⠈⠉⠉⢠⣀⠀⠀⠈⠉⠉⠁⠀⠀⣀⣼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠿⠴⣆⠀⠀⢀⣀⣨⣿⣧⣀⣀⣠⣤⣀⣀⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠫⣿⠁⠛⠋⠁⠀⠀⢀⡤⣿⣤⡉⠛⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡏⠀⠀⠀⠀⢀⣠⣿⣿⡿⡶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣉⠳⣄⠀⣀⠴⠋⠁⠸⣯⣁⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡽⠆⠀⠈⠚⠁⠀⠀⠀⠀⣻⠋⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠔⠃⠀⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡤⠞⠁⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠋⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡼⠁⠀⠀⠀⠀⡸⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⡴⠋⠉⢻⠇⠀⠀⠀⠀⠀⠙⢦⣀⣀⣀⡤⠆⠸⡄⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⣠⢧⣀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⣷⡤⠶⠒⠒⠲⢤⡀⠀⠀ ⠘⣇⠀⣭⢉⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠳⣄⠀⣄⠀⢀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠙⣆⠀ ⠀⠀⠉⠉⠉⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢸⠟⡿⠤⣾⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆ ⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇ ⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡞⢿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀ ⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠸⣇⠏⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠓⠦⢤⣤⣤⣤⡴⠛⠤⣴⣤⣤⠤⠶⠚⠉⠙⠒⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⡔⠉⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠋⠉⠉⠓⡆⠀⠀ ⠀⣸⠁⠀⠀⠀⠙⢦⡀⢸⡉⠓⠲⣄⡀⢀⡞⠀⠀⠀⠀⣀⣽⡤⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠙⣦⠷⠄⠀⠀⠙⠞⠀⠀⠀⠀⠀⠒⠚⡏⠁ ⠀⡇⠀⠀⠀⠀⣀⣀⡚⠓⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⡇⠀⠀⠀⡎⠀⠀⠈⡆⠀⠀⠀⠀⠘⢄⣀⣀⡀⠀⠀⠀⣸⠁⠀ ⠀⠈⣇⠀⠐⡶⠖⣲⣶⡆⠀⠀⠀⠀⣶⣶⡒⠲⡒⠀⢀⡼⠁⠀⠀ ⠰⣖⠺⠧⢸⠁⠀⣿⣿⠇⠀⠀⠀⠀⣿⣿⠇⠀⡇⠀⠉⣩⠇⠀⠀ ⠀⠈⣳⠀⣨⢃⠀⠈⠉⠀⠒⠂⠀⠀⠈⠁⢀⠄⡡⠀⢼⡁⠀⠀⠀ ⠀⢰⣃⣈⣀⠁⠀⠀⠀⠦⠔⠓⠲⡲⠃⠀⠀⢈⣀⣀⣀⣹⡄⠀⠀ ⠀⠀⠀⠀⠀⠉⢳⠲⠤⢄⣀⣀⣀⣠⢶⠒⣏⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣳⠒⢲⠋⢱⠤⠧⠚⠋⠘⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠓⡆⠈⠒⠁⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣠⠴⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠈⢳⡄⠀⢀⡴⠛⣡⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⢦⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠞⠁⠀⠀⣧⠾⠋⠀⣰⣿⣿⣿⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⠁⠙⠻⢿⣧⠈⢷⡟⠛⢋⣩⣽⠿⠟⠛⢛⣛⣽⠇⠀⠀⠀⣸⣧⣤⡤⠴⠿⠟⠛⠋⠉⠉⢉⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⠸⣆⢀⣿⠞⠋⠁⢀⣤⠶⠛⠉⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⡷⠶⠂⢀⡽⠋⠀⢀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⢿⣿⣿⠏⠀⠀⣴⠟⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⢷⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠾⠯⠳⠶⣶⡶⠆⠀⠀⠀⠀⠀ ⠀⣼⠃⢹⣿⣿⣾⣿⣾⠃⠀⠀⢀⡾⢡⠖⠉⠉⠉⠉⠓⢬⣧⡀⣟⢦⣄⠀⠀⠀⠀⢀⡀⠀⡀⠀⣀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀ ⢠⡏⠀⢸⣿⣿⣿⣿⠁⠀⠀⢀⡾⠱⠕⠒⣉⣉⡉⠉⠉⠑⠻⠳⠿⠀⠈⢹⣷⣶⣤⣬⣿⣞⡟⢻⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠃⣀⡀⣧⠀⢹⡇⠀⠀⠀⣸⠃⠀⣠⡾⠋⠉⠙⢷⣄⠀⠀⠀⠀⠀⢠⡟⠀⠀⢙⣷⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡀⠸⣿⠻⠆⢸⡇⠀⠀⠀⡟⠀⣰⡟⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⣼⠁⠀⠀⢘⣿⠀⣾⠁⢸⠁⠀⠀⠀⠀⠀⢠⣿⡇⢀⡀ ⠘⣧⠀⠈⠻⠶⢼⡇⠀⠀⢸⡇⠀⣿⡄⠀⠀⠀⠀⢨⣿⢿⠀⠀⠀⠀⢿⠀⠀⠀⣿⣿⠀⡟⢀⡿⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⡇ ⠀⠈⢷⣦⡀⠀⣏⣇⠀⠀⢸⣇⠀⠀⠹⢦⣀⠀⠀⢸⣿⡾⠂⠀⠀⠀⠸⢦⣠⡠⠟⠋⠀⡿⣸⣇⣀⣀⠀⠀⠀⠀⠹⣿⡿⠋⠀ ⠀⠀⠀⠙⣿⡳⣽⡸⣀⣾⠾⠋⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⣀⣷⠏⠀⠈⢙⣻⣶⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⣾⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⠶⣦⢹⡇⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣋⣀⣀⣀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠛⢿⣿⣶⡿⠋⠈⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠛⣳⣄⠐⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠿⠥⢤⣀⠀⠀⠀⠀⠀⠀⣈⠲⣄⡀⠀⣀⣤⠞⠳⠤⢤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣄⡀⠀⠀⠀⠀⠙⠲⢦⣭⡭⠤⠤⠶⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⠆⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠖⠋⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣠⠶⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠒⡶⠂⠀⠀⠈⠉⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣠⣞⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢺⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠬⢽⣆⡉⠛⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⢤⠤⠤⠤⠶⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣤⠞⣣⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣆⣀⡀⠳⡄⠀⠀⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢧⠀⠀ ⠀⠀⢀⣤⠖⢋⣡⣾⣯⡀⠀⢀⣀⣤⡾⠗⠒⠚⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠓⠲⢤⡛⣎⠙⠲⣄⡀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠘⣇⠀ ⣠⡾⢋⣤⠾⠋⠁⠘⣯⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣉⡙⠷⠀⠀⠙⢶⣤⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡄⢹⠀ ⣿⣶⠟⠀⠀⠀⠀⠀⣈⣿⣦⣄⣀⣀⡀⠀⠀⢣⡀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠀⠀⠀⠀⠉⠓⠤⣄⡀⣰⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣧⢸⡇ ⠻⣿⣷⣶⣶⣶⣿⣟⣿⣿⣿⣿⠽⠛⠁⠀⠀⣀⠳⠄⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠶⠿⢰⣿ ⠀⠈⠉⠙⠛⠛⠛⠋⢉⡿⠋⠁⠀⠀⣠⠖⠋⡁⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋⣵⠋⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⣶⢦⢹ ⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⢠⠞⠁⢀⡞⠁⢠⠏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣾⠁⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠸⣿⡾⢸ ⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⣰⠏⠀⠀⢼⠆⠀⡟⠀⠀⠀⣀⣠⡴⠶⠂⠀⢀⣴⠾⠋⣠⣾⣿⢿⣿⣷⣦⡌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⠶⠂⠀⢠⣿ ⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⣸⠋⠀⠀⢠⡏⠀⠀⠃⣠⢴⣻⠟⠉⠀⠀⣀⣴⠟⠉⣠⡾⢋⣿⠀⠀⠀⠈⠙⢿⣆⠈⠻⣄⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⢀⣾⡏ ⠀⠀⠀⠀⠀⢸⡟⠀⠀⣰⡏⠀⠀⠀⡞⠀⠀⢰⠟⣡⠟⠁⠀⠀⣠⣾⠟⢁⣤⠞⠋⠀⣼⣿⣴⣶⣤⣤⡀⠀⠻⡆⠀⠈⢣⡀⠀⣠⠟⠉⠀⠀⠀⣠⠟⣹⠁ ⠀⠀⠀⠀⠀⠈⢷⠀⢠⡿⠀⠀⡄⠀⠇⠀⢰⣏⡼⠃⠀⢀⣤⣾⣿⠷⠚⠉⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣆⠀⢹⡀⠀⠈⢳⡼⠋⠀⠀⠀⣠⠾⠁⣰⠇⠀ ⠀⠀⠀⠀⠀⣀⠘⣆⢸⡇⠀⠀⡇⠀⠀⢰⣿⡿⠀⢀⣶⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠛⢿⠈⢿⣆⠈⢷⡀⠀⠀⢻⠀⠀⠀⠀⠁⢀⣴⠃⠀⠀ ⠀⠀⠀⠀⠀⠻⠯⢽⣾⣿⡀⠀⢱⠀⢀⣾⡿⠁⣠⢿⡉⠿⠭⢾⠇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣶⣦⠀⠘⣿⡀⠈⢷⡀⠀⢸⠀⠀⠀⢀⣠⠿⠵⣻⠇⠀ ⠀⠀⠀⠀⠀⠀⣠⡴⠛⢿⣷⡀⠈⣆⢸⡟⠁⢰⠋⠀⠙⣲⣶⣿⠶⣦⣤⣤⣀⡀⠠⣏⠮⣭⠿⠛⢿⡇⠀⠀⢻⡇⠀⠈⣷⡄⠘⡇⠀⠠⠛⢀⣠⡴⣋⣠⠀ ⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⢿⣷⣤⡈⢸⣧⢰⣏⣤⠴⠋⣿⣿⣿⣿⣿⣿⣿⣿⡟⠳⣽⡢⣤⣤⡴⠋⠀⠀⠀⣾⣧⠀⠀⢹⠀⢰⠇⠀⢀⣠⠾⠛⠛⢉⡟⠀ ⠀⠀⠀⡼⠋⠀⠀⠀⠀⢀⡟⠁⠈⠛⢮⣿⢿⡿⠉⠀⠀⠈⠻⣿⣿⣿⣿⡿⠛⠁⠀⠀⠙⠄⠀⠀⠀⠀⠀⠶⢿⣍⠀⠀⢸⠆⣼⣴⠞⠉⠀⣀⣤⣾⠟⠀⠀ ⠀⢀⣾⠤⢤⣴⠶⠆⠀⢸⢡⣤⣿⣷⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢻⣶⣦⠀⠀⠙⠿⣄⣼⠛⠵⠯⢄⣀⠈⠙⣛⣓⡾⠃⠀ ⠀⢨⣤⡴⠋⠀⠀⠀⠀⢸⡈⠏⢿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠃⣨⣿⣿⡆⠀⢹⣧⡀⠈⠛⢟⠉⠛⢿⡟⠋⠀⠀⠀ ⠀⠈⠛⢧⣄⡀⠀⠀⠀⠈⣧⣀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠉⠉⣀⣰⣿⢣⣿⠀⠀⠀⠙⣦⣀⢳⡄⠀⠀⠀ ⠀⠀⠀⠀⠉⠛⢦⣔⡒⠂⠘⣷⠚⠋⣤⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⢸⣿⣿⢯⣿⠏⠀⠀⠀⠀⠘⣿⣄⢷⠀⠀⠀ ⠀⠀⠀⠀⠀⠺⢯⣥⣀⠀⠀⠈⠳⣄⣴⣄⠀⠀⠀⠀⠀⠈⠻⣿⡿⠛⠛⠛⣿⡿⠃⠀⠀⠀⠀⠀⠙⠟⠁⠀⢠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⠘⢿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⢦⣌⡻⣍⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⡿⠛⣄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡟⠀⠀⠘⣿⡷⣄⠀⠀⢀⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠴⠺⣿⠟⠛⠯⠤⣄⣀⠀⠈⢷⢮⣷⣀⡾⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣟⠛⠳⣶⠤⣴⣶⠶⠶⡾⠟⠛⠉⠁⠀⠀⣸⣿⣄⠀⠀⠀⠀⠉⠙⠲⢼⠄⠉⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠛⠹⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣳⣄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⢶⣾⠉⠉⠀⢘⠀⠈⢿⣶⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠹⢿⠿⣛⣿⣿⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡤⠞⣫⠵⣒⣿⠟⠁⠀⠀⠸⡇⠉⢙⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢀⠿⠛⠉⠀⠀⠈⣽⣳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⠋⠀⠺⠗⠋⠉⠄⠒⣶⠀⢀⣀⡼⣖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠁⠉⠳⢦⡀⠀⠀⠀⠀⠀ ⠀⢸⠃⠀⠀⠀⢀⠀⠈⠁⢩⠗⠒⠉⠁⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣭⣳⣄⠀⠀⠀ ⠀⢸⠆⠀⠀⠀⠀⠀⢀⣠⣎⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⡙⢿⣧⡀⠀ ⠀⢸⠀⠀⢀⡠⠤⢐⣫⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⠀⠂⣿⡇⠀ ⠀⢸⡠⠜⣋⣤⡴⠀⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠈⣷⡀⢸⡇⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣤⢤⣤⡤⣤⢤⣤⢤⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣭⣟⣶⢿⣭⣟⣾⣻⣞⣶⣷⣾⠗⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠿⠿⠿⠚⠁⢀⠬⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⠲⣡⠣⢤⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠠⢤⡐⢎⡱⣉⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠣⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡊⢖⢪⠴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡽⣦⡀⠀⠀⠀⠀⠀⠀⣄⠀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣮⣑⠍⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣷⣻⡄⠀⠀⠀⠀⠀⢻⡿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡠⠠⠄⢤⠠⠄⠤⡀⠄⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⣝⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⣾⣳⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠂⡍⢆⠁⠀⠠⡁⠇⠉⠂⠑⠈⠁⠈⠀⠀⠈⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠁⠀⠀⠀⠠⢁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣯⣷⣯⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠐⠀⠀⠁⠈⠀⠀⢀⠀⠀⠀⢀⠀⡀⠠⠀⠠⠀⢀⠠⠀⠀⠀⡀⢂⠀⠄⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠠⠁⠂⠀⠀⠀⠀⠀⠀⣿⣯⣭⣉⡑⠋⠟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢏⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⡀⠀⡈⠀⠀⡈⠀⡆⢀⢁⠸⢀⠁⠀⠆⡁⠆⡇⠰⢀⡈⠰⠀⠆⠀⠀⠀⣹⣿⡇⠀⠀⠀⠀⠆⢁⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠈⠀⠀⠀⡆⠠⢈⠀⠂⡄⠡⠀⢠⠗⠈⠀⠀⠁⠀⠠⢀⠂⠄⢂⠀⡀⠀⠀⡃⠀⠁⡀⠃⠀⠂⢀⠀⠀⣿⣿⠀⠀⠀⠀⠐⡈⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣯⣷⢿⣲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠡⢀⠀⠀⠀⠀⠀⠀⡳⠀⠂⠀⠁⠄⠐⡀⢰⣶⠀⡀⠀⠐⣈⣐⣀⣈⡠⢄⣤⣠⢁⣀⣿⠀⠀⠄⠡⠀⢁⠂⠄⢠⢹⡇⠀⠀⠀⠀⢂⠐⠀⠀⠀⠀⠀⠀⢀⢻⣿⣿⣿⣿⣿⣯⣿⢯⣷⢫⡗⣆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣾⠀⠀⠀⠀⠀⠀⠁⢂⠀⠀⠀⠀⠠⠀⢝⣣⠀⠁⠄⠈⠀⢀⡛⣫⣤⠵⠼⠖⠶⣶⣾⣿⣿⣿⡟⠐⠚⠛⠚⠒⠒⠘⠀⠠⠀⡤⣤⡘⡬⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⡸⠌⣿⣿⣿⣿⣿⣿⣿⣟⡾⣭⡻⣼⡱⢆⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠂⠌⡀⠀⠀⠀⠱⣊⠶⡩⢡⢶⠂⠀⣀⠁⣀⣠⠄⠀⠀⡰⣿⣿⣿⣿⣿⣧⣘⣀⣀⣀⣚⡛⣥⢠⠀⠡⠐⡹⡇⠀⣦⠀⠀⠀⠡⠈⠀⠀⠀⠀⠀⠀⢰⡙⡖⢸⣿⣿⣿⣿⣿⣿⣯⣟⡷⣝⢶⡹⢎⡕⣂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠐⠠⠐⡀⠀⠀⠀⣍⢞⡁⠶⡌⠀⠂⢸⣷⡮⣭⡥⣤⣷⣿⣋⢤⣶⣿⣿⣿⣿⣿⣿⣿⣯⡣⣳⢠⠀⠁⢂⢡⠇⠸⠿⣛⣠⣤⣀⠀⠀⠀⠀⣀⣤⢦⠰⡱⣙⢆⠻⣿⣿⣿⣿⣿⣿⣯⣟⢾⣣⢟⠮⣜⢢⢃⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠡⠀⠄⠀⢀⠈⠶⣩⠘⠄⡁⠄⠘⣿⣴⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⣛⣃⣤⣤⣥⣤⣤⣤⣤⣴⣶⣯⣭⣛⡻⠦⣍⡛⢽⠎⠄⠠⠑⠮⣌⠳⣌⠛⢿⣿⣿⣿⣷⣯⢷⣹⢎⡷⣘⠦⣉⠖⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠁⠈⠀⣠⣾⡆⠙⢦⡋⠀⡔⠀⠀⢻⣿⣿⣿⣿⣿⠟⠛⢿⠩⠭⠿⠖⠂⠔⣮⠹⣄⠻⠿⠿⢿⡿⡿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣶⣾⣤⣤⣥⣄⡀⢍⣈⠳⠌⠝⡢⢌⡙⠛⠯⠟⠏⠓⠋⠒⠭⠲⠡⢎⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣷⣤⣤⣀⢠⣤⣴⣾⣿⣿⣿⡀⡑⠂⠡⡐⠀⢰⠘⣿⣿⣿⣿⣧⠀⢠⣠⣤⣶⣶⣦⠀⢈⣀⣥⣠⡶⠀⡖⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣻⣿⣶⣶⣶⣶⣶⣶⣿⢿⣛⢿⣹⢲⡑⢦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣞⡷⣯⢳⡻⣿⣿⣿⣿⣿⡇⢟⠆⠡⡐⠁⠀⢷⣈⠻⢿⣿⣿⣧⣞⣩⣥⣍⣉⣦⣶⣿⣿⣿⠟⣀⢞⡱⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⢟⡮⣇⢧⡙⢦⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⡿⣽⣳⡻⣞⢿⣿⣿⣿⣷⢸⣇⠂⢡⠃⠀⡞⣌⠳⣆⠍⠛⢿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣄⠲⣍⠞⢠⠀⠀⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣾⡱⣏⠶⡙⠦⣉⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⢎⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⡷⣯⢷⣌⠻⡻⣿⣿⡿⣼⣿⣄⠡⠌⠀⢚⡬⠳⠘⣂⠀⠀⠀⠉⠛⠛⠛⠋⢁⣼⡀⠊⠓⠜⢠⣿⢀⡆⠄⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣋⣭⣿⣿⣿⣿⣿⣿⣿⣿⡽⣧⢻⡜⢧⡹⢄⡄⠀ ⠀⠀⠀⠀⠀⠠⡌⠐⠮⠼⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⢟⠣⡞⢥⠘⡳⣏⡾⣛⡬⢞⢿⡇⣿⣿⣿⣦⣌⠀⢰⡶⣞⡿⣽⠘⣦⣀⠀⠀⠀⣠⡾⢩⣿⣇⠸⠿⠃⣽⣿⣻⢧⠐⡹⣏⣛⣿⣿⣿⣿⣿⣿⣿⠿⠿⢛⠫⠅⠀⠐⢎⡲⢍⡻⣿⣿⣿⣿⣿⣿⣯⣿⢳⣏⡞⣧⠓⠌⠀⠀ ⠀⠀⠀⢀⠰⢃⢸⣿⣿⣿⣿⣿⣿⣶⣶⣦⣭⡛⢋⢥⠲⣍⠳⡜⠃⠀⠈⢷⡹⣇⢯⡝⣦⠁⣿⣿⣿⣿⣿⣿⣦⣴⣯⣭⣭⣕⣋⣛⡛⠿⣻⡷⠃⣋⣥⣶⣾⣿⣿⣿⣶⣶⣯⣃⠐⠲⠐⠆⠮⠙⠣⠓⠂⠒⣈⣁⠡⠀⠀⠀⠀⠀⠈⠘⠰⢊⡍⣛⠻⠿⠿⣿⣽⣟⠾⠉⠀⠀⠀⠀⠀ ⠀⠀⡀⢎⢡⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠨⢳⣌⠓⠁⠀⠀⠀⠀⠳⣎⣳⢚⡅⠘⡫⢩⢻⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡲⡐⠶⣭⢳⣝⡛⢠⠲⣌⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡒⠍⡲⢡⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⡘⢄⢣⢒⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠓⢁⣥⣶⣿⣿⠏⠾⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠻⣛⠍⡀⠤⣉⠙⢿⣿⣔⠈⢲⣏⠞⢀⢥⠳⣜⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠣⠎⡅⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⡰⢆⡭⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣄⢀⣀⣀⣄⣀⣀⡀⠰⡿⡏⡀⣧⣓⢸⢧⠄⢻⣿⡆⣸⡎⠁⡎⣎⠳⣌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡠⢀⠀⠀⢀⠌⣲⠹⡜⡜⠁⠀⣀⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣻⣿⡿⠿⠟⢛⣕⣯⠽⣾⣎⡢⢉⡈⡉⡀⠘⠻⢣⡷⡞⢠⠱⣎⠳⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲⠢⠁⣤⣬⣥⣶⣶⣶⣶⣿⣿⣿⠿⢛⣩⣤⠾⠟⠓⣒⣀⣀⣄⡀⠀⠀⠀⠀⠀⠀⢠⣺⢫⡟⣴⢆⢾⣿⡇⢇⠔⠀⠀⠀⠀⠈⠃⣌⠳⣌⠳⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⢟⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠡⣚⣩⣥⣶⡎⢸⡻⡵⣏⡿⠼⠃⣁⣠⣶⣦⡤⡰⣱⣳⣟⣼⢯⢮⣟⡾⢁⠎⠀⠀⠀⠀⠀⠀⠀⢎⡳⣌⠃⠀⠀⠀⠀⠀⣀⣤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢍⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣾⣿⣿⣿⣿⣿⣿⠿⠿⠆⣛⣩⠭⢖⣚⠻⠛⢿⣿⣿⡱⣵⢷⣟⣾⢫⢯⣟⣼⠃⠄⠀⠀⠀⠀⠀⠀⠀⢀⢮⢱⣒⠀⠀⠀⠀⣨⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⠀⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢆⡹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠶⠎⣉⣉⣉⡶⣾⢿⡀⡶⠇⣸⣿⢇⢷⣏⣿⣾⢇⣏⡿⣾⠇⠎⣀⡀⡀⠀⠀⠀⠀⠀⢈⡎⣱⢎⡁⠀⣰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢀⠀⠆⠀⠀⠀⠀ ⠀⠀⢀⠐⠈⡀⠐⡀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠣⢝⡻⣿⣿⣿⣿⣿⣿⣯⣁⣭⣵⣾⣷⣿⣿⣿⣿⣿⣿⢼⠭⢛⣁⢠⣶⣿⣏⣞⢿⣼⣿⢏⣾⣿⣽⠏⠌⣼⣿⣿⣮⠲⣄⠀⠀⠀⢧⡚⣥⠚⣠⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢀⠐⠈⡀⠌⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠂⢀⠡⠀⢂⠈⡐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣦⣜⠨⢙⠿⢿⣿⣿⣿⣿⠿⠿⠿⣿⡛⣋⣭⣭⡽⢖⡲⠦⠙⣉⣼⣿⡿⡼⣏⢧⣿⣏⣾⣿⣿⢃⠌⣼⣿⣿⣿⡟⣼⣿⣦⠀⡘⢦⡙⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢀⠐⠠⠈⡐⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠀⡐⢈⠀⠂⠄⡁⢂⠐⠠⢀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣦⣉⠒⠶⡬⢭⣙⠳⠶⠿⠟⡴⢫⡝⠍⠒⣉⣴⣾⣿⣿⣿⣿⢣⢳⣭⣾⢟⣾⣿⣿⢃⠎⣼⣿⣿⣿⣭⡱⢛⡺⠏⢠⡙⢂⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠠⠈⠄⡁⠄⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠌⠐⠠⠐⠠⢈⠐⡀⠂⠄⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣄⠀⢀⡤⢂⣤⠴⣒⣶⣶⣶⣾⣿⠿⢿⣛⣛⣯⣵⡆⣮⣿⣿⡏⣸⣿⣿⠇⠊⣼⣛⠿⠿⣿⣿⣿⣷⣮⡢⡄⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢁⠂⠄⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡐⢀⠂⠄⡁⠂⠄⠡⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢛⣴⣿⣿⣿⣿⣿⣿⡇⡾⣧⡻⢏⠛⣛⢡⣿⣿⡟⢠⣿⣿⠏⠈⣼⣿⣿⣿⣶⣔⣦⡉⢻⡿⢃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡐⢀⠡⠈⠄⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡻⣿⣿⣿⣿⣿⣿⡇⣿⠽⢋⣠⣴⣶⣦⣍⠻⠃⣿⣿⠏⠀⣠⣶⣶⣬⣝⠻⣿⣿⣷⡌⢇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠡⢈⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠹⣿⣿⣿⣿⡇⢋⣴⣟⣵⣟⣿⡻⣿⣷⣆⠩⠥⡐⣰⣿⣿⣛⢿⣿⣷⠙⣿⣿⣿⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⣷⣶⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⢿⡟⢁⡄⣼⡟⣎⣿⣯⣿⣿⣿⣿⣿⣧⢓⣼⣿⣯⢾⣻⣼⡇⡝⠃⣿⣿⣿⣿⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡸⠿⠟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠀⣿⡆⢻⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⠎⣠⣿⣿⣿⣿⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⠛⣄⠫⢿⣿⠿⣿⣿⣿⣿⣿⣿⠳⢻⠿⡿⠟⢛⠉⢀⣴⡟⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣻⢶⣦⣭⣄⡀⣁⣉⣉⡁⠭⠤⠮⠤⢌⣂⣴⣟⠫⣾⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢮⡓⢆⡄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣾⡅⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠛⢽⣻⢾⡽⢠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢮⢧⡙⠦⡜⡰⠡⠀ ⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠃⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⡉⠛⡝⢻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣝⡛⠆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡮⣏⠶⣩⠓⡬⣁⢃⠀ ⠀⣦⡂⢤⢀⠀⢀⡔⣴⣿⣿⣿⣿⣿⡏⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡢⣄⡈⢧⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣞⢥⡛⡴⣉⠖⡰⣈⠀ ⠀⣿⣿⣷⣦⣤⣥⣾⣿⣿⣿⣿⣿⣿⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣕⠄⠹⡮⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣕⡪⢝⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡶⣻⣜⣣⢝⡲⢡⢎⡱⠂⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⠮⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣭⣭⣛⣛⠻⠿⠿⣟⣞⡷⣳⢞⡜⢮⣑⢣⡎⠑⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡛⠮⠝⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣭⣅⣛⡘⠧⠎⠓⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣟⣯⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣷⣶⣶⣦⣌⢩⣙⠋⠭⢭⣟⣛⣻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠄⡾⡽⣞⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣿⣿⣿⣿⣿⣿⣷⣝⢯⡖⣄⡠⢙⠛⢯⣽⣞⣙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀ ⠀⣟⣿⣿⣿⣿⣿⣿⡿⢋⡞⢰⣻⡽⣽⢾⡽⣞⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣧⡹⣧⢻⣤⡙⠲⡝⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⣏⣷⣿⣿⣿⣿⠏⣰⠏⠀⣿⢇⣿⣹⣏⢿⣹⢿⣷⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢷⣇⢿⣱⠈⢷⡹⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⣟⡾⣽⠊⠩⡔⠊⠁⠀⠀⠈⠳⣙⢷⢯⡿⣝⣟⡾⣽⢾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢧⣏⠿⣤⠘⢮⣝⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⢯⣳⠃⠀⠁⠀⠀⠀⠐⠀⠂⢀⠈⠛⢯⡿⣽⢾⡽⣯⣟⣾⣳⢯⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠀⣿⡽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠿⣜⡳⣤⠈⠳⣭⡻⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⣏⠗⠀⢀⢀⡀⠄⠁⡀⠂⢈⠀⠠⠀⠀⠙⠯⣿⣽⣳⣞⣧⣟⡿⣾⣽⣳⢯⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⡿⣼⣳⠀⢷⣛⡷⡽⣞⢿⣻⢿⡿⣿⢿⣿⣻⢟⣞⢯⡳⣝⢮⡻⣤⠈⠻⣮⣕⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠞⠀⡐⠈⠤⠐⡌⠱⠰⣑⠢⡌⢤⣁⡈⠄⡀⠈⠓⢿⣞⣧⣟⣾⣳⢯⣟⡿⣾⢽⣳⢯⣟⣿⣻⢿⡿⣿⣿⢿⡿⣿⢿⣻⢯⣟⣧⢿⣝⣾⠳⠃⠀⠘⢭⣷⣻⢽⣺⣭⠷⣯⠽⣾⡱⢯⢾⡹⣞⡵⣫⢞⡵⣫⢗⡦⡈⢿⣳⢭⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⡐⠠⠉⠄⢃⠌⡡⢃⠆⡓⡜⢢⢒⡍⢞⡱⣒⠦⣄⡈⠓⢿⣞⣽⣻⢾⡽⣽⢯⣯⣟⣾⣳⢯⡿⣽⣳⢯⣿⣹⢯⣟⣭⢷⡾⣭⣟⡾⠝⠁⠀⡐⠀⠀⠑⢯⣟⣶⣫⣟⡼⣛⡶⣻⢭⡳⣝⢮⡳⣝⡮⣝⣧⣻⢾⠽⠂⠉⠳⣽⢲⡝⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠄⠡⢈⠰⢈⠰⢁⠎⡰⠑⣌⠣⠎⡘⠌⡑⠈⠡⠀⢉⠈⠀⠈⠙⠿⣿⣽⣟⡾⣵⣞⣳⣽⣻⣼⣳⣭⡟⣶⢯⣛⣮⣟⡾⣽⡳⠋⠁⢀⠀⠂⠄⠁⠂⠄⠀⠈⠓⠳⣭⣟⡧⣟⡵⣯⠽⣞⡧⣟⠮⠷⠙⠊⠉⠀⠀⠀⢀⠀⠈⠓⢞⡭⣓⠦⡝⣛⠿⢿⣿⣿⣿⣷⣟⣻⣿⣿⣿⠀ ⠀⠀⠌⡐⢀⠂⠌⡰⢈⠢⣁⠣⡐⠦⢱⡐⢲⡐⣒⡒⠲⣄⢎⡤⣡⠤⣀⡠⢉⠛⠿⠷⣿⣳⣞⣷⣳⣟⣶⣻⡽⣾⡽⠾⠝⢊⡁⣄⠤⣄⠦⣜⡰⢆⡖⣒⠲⣜⠲⣒⠦⡤⢄⡌⣉⡉⣌⡉⢤⣀⠤⣀⠄⡠⢀⡀⠂⠀⠁⡀⠀⢀⠀⠀⠀⠙⢎⡱⢎⡍⢳⠪⡝⣭⢛⣟⡺⢶⣛⡿⠀ ⠀⠀⢂⠐⠠⢈⡐⠄⡡⠒⡠⢃⠜⡨⠅⢎⡅⡚⢤⣉⠳⣌⠲⡜⣰⡙⢦⣙⠣⠝⠒⠐⠀⠀⢉⡈⣁⣉⣈⢡⡉⢤⡐⣆⢎⢧⡹⣌⠳⣌⠳⣌⠳⣍⠶⣩⠳⣌⠳⣍⠶⣙⠼⣘⢥⡹⢤⠛⣆⢣⠞⣡⠞⡡⢇⡜⡡⢆⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠜⣡⠓⡜⢤⢋⠴⡙⢦⠳⡜⠀ ⠀⠀⢂⠈⡐⠠⠐⡠⠁⢆⡑⠌⢢⠑⣘⠢⢌⡱⢢⢌⡓⣌⠳⣌⠱⡘⢦⡁⢢⠌⣤⠒⣎⡹⢆⡝⡒⠦⣍⠶⡙⢦⡙⢦⢋⢦⢓⡬⢳⣌⠳⣌⠳⣜⢪⠥⢳⢌⡳⢜⡸⢌⠧⣩⠦⣱⢊⠳⣌⠲⣉⠦⡙⡔⢣⢌⡱⢌⢊⠔⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠦⣉⠲⣉⢆⠳⡌⠀ ⠀⠀⠂⠐⠀⠁⠂⠀⠉⠀⠐⠈⠂⠑⠂⠑⠊⠐⠁⠒⠈⠂⠓⠈⠃⠙⠂⠙⠂⠙⠀⠛⠀⠓⠈⠒⠉⠓⠈⠒⠙⠂⠙⠂⠋⠂⠋⠐⠃⠈⠓⠈⠓⠈⠒⠉⠃⠊⠒⠉⠒⠉⠒⠁⠚⠀⠋⠒⠈⠓⠈⠒⠑⠈⠁⠒⠐⠈⠂⠈⠑⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠊⠐⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⢠⡀⠸⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡁⢰⣋⡇⠀⡿⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣏⠉⠛⠳⢤⣟⠀⢧⠀⠀⣀⣤⣠⣤⣄⣀⠀⠀⢷⠀⠀⠈⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡔⠃⣀⠘⢆⣀⠀⠀⠉⠀⠘⠚⠉⠀⠀⢀⡀⠀⢸⠇⣀⢸⡀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠙⡾⠟⣷⠂⠉⠀⠀⠀⠀⠀⠀⠀⢶⢚⣹⠃⢠⡏⠀⡏⠹⠃⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⠇⣰⠀⠀⠀⠠⠶⠳⣦⠀⠀⠀⠘⠲⠃⢠⠟⠁⠀⡏⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡟⠷⠟⠁⠀⠀⣴⡆⠀⢸⡇⠀⠀⢠⣄⡴⠏⠀⡀⢰⠇⠀⠀⠀⠀⠀⠀⢠⡾⠚⠋⠉⠉⢳⡀⠀⠀⠀⠀⠀ ⠀⢹⡌⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢧⡐⠶⠄⠀⠀⠻⣃⡀⠸⡷⠀⠀⠀⠹⣆⠀⢀⡿⡏⠀⠀⠀⠀⠀⠀⣠⡾⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⢷⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠙⠦⣤⣀⡀⠀⠘⠿⠇⠀⣤⠴⣶⣞⣁⣠⣾⡀⠀⠀⣤⣠⣴⠶⢾⣁⣧⠀⠀⠀⠈⢧⡤⠖⠚⠦⣄⡀⠀ ⠀⠀⠘⡇⠀⠀⠈⠻⣷⡀⠀⠀⣠⢾⡉⢉⡍⠙⠳⣶⢟⣯⣭⠿⠷⣤⡀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠚⠻⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠙⣦ ⠀⠀⠀⢹⡀⠀⠀⠀⢿⣧⠀⠀⢧⣸⡀⠘⣇⣴⠀⠀⢘⠛⠛⠀⣰⠊⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⣄⣄⡓⣶⠏ ⠀⠀⠀⠀⣧⠀⠀⠀⠈⣿⣆⣠⣤⣭⡭⠿⣹⣿⡋⠉⠛⠓⠒⠴⠃⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⠈⠙⠛⠁⠀ ⠀⠀⠀⠀⠈⠳⣄⠀⠀⠸⣿⠉⠀⠈⢻⠞⠙⡾⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⣀⣀⣀⣀⣀⣀⣬⠷⠶⠤⢤⣤⣄⣀⣀⣤⣄⡀⣰⠤⢽⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢿⣧⠀⠀⠘⠷⠾⠷⣼⣅⣀⣀⠀⠀⠀⠀⠀⠀⠸⡅⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡈⡿⣄⣀⣀⣀⣀⣀⣈⣳⣍⠉⠉⠛⢿⡛⢦⡼⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠻⠶⠿⠿⠷⠷⠿⠿⠾⠶⠶⠶⠶⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠘⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣀⢤⣤⣤⣤⠤⠤⠤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⣉⣭⠾⢿⣿⣝⠛⠻⣿⣻⡿⠋⣩⣵⡓⠿⣽⣪⢍⠉⠑⠋⠹⣷⣌⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣮⣭⣭⡶⣦⣄⣀⡠⠊⡶⠋⣩⢋⣴⣿⣻⣽⣷⣤⣉⣿⣴⣿⣟⣿⢿⣆⠈⠙⠶⣝⠦⡀⠤⣀⠀⠉⠓⠢⣍⡢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣯⣿⣿⣾⣿⠟⠁⠀⠀⣴⡷⠿⢏⣡⣾⣿⠞⢻⠏⠀⢈⣉⠟⠺⣍⠛⢧⡀⠀⠈⠛⢽⣦⠀⠙⠢⣄⠀⠘⠿⣦⣑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣿⣿⣿⠋⠀⠀⠀⣼⢋⣤⡴⣋⣤⢮⣍⠁⠇⣈⠋⢅⠘⡄⠀⠈⢦⡙⠳⡄⠀⠀⠀⠙⢷⡤⣄⡐⢿⣀⠀⠸⡝⠳⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢴⣾⢏⢯⡽⠓⠀⠀⠀⣼⠷⠛⡵⣸⠟⠁⠀⠀⠃⣴⠋⢀⡈⠹⣸⠀⠀⠀⠙⢆⠙⣆⠀⠀⠀⠀⠙⢆⠉⠑⠉⠳⣄⠹⡄⠈⢻⣆⠀⠀⠀⠀⠀⣀⣠⣤⢴⠖⣲⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣿⣧⣴⣾⣯⣾⡿⠁⠀⠀⠀⢸⠋⢀⠂⣰⠏⠀⠀⠀⠀⡞⡜⠀⢀⡇⠀⣿⡆⠀⠀⠀⠈⢳⠘⢦⠀⠀⠀⠀⠈⢣⡀⠙⠦⣄⣙⣿⡄⠀⠎⢳⡄⣠⣶⡿⠿⣏⡽⢂⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⣿⣝⡳⢮⡳⣟⣻⡞⠀⠀⠀⠀⢠⠇⢠⠃⣰⠏⠀⠀⠀⠀⢰⠃⠇⠀⢘⡆⠀⠘⣧⠀⠀⠀⠀⠀⢳⡈⣇⠀⢀⠀⠀⠑⠱⣀⢰⣿⣟⠛⣿⣶⣅⣢⣿⡿⢏⣜⣳⣼⢰⣾⣿⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢝⣯⠷⣹⣮⠟⠀⠀⠀⠀⢠⡏⢀⡞⢠⡿⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⣇⠀⠀⠹⡄⠀⠀⠀⠀⠀⢣⠈⡆⠈⡆⠀⠀⠀⢙⣿⣟⣯⣷⡸⣿⣿⣿⣿⣿⡿⣿⣿⡟⡾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣽⢋⠎⠀⠀⠀⢠⡿⠀⡎⡇⢸⠀⠇⠀⠀⠀⢸⠁⠀⠀⢠⠀⢻⠀⠀⠀⢣⠀⠀⠀⠀⡀⠈⡇⠸⡀⠸⡄⠀⠀⠈⠙⣿⣷⣧⡗⢹⣿⣿⣿⡿⣷⡿⢻⣌⢳⡹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⡿⢁⠌⠀⡀⠀⢀⣾⠇⢰⠁⢹⡞⠀⣧⠀⠀⢀⡏⠀⠀⠀⣼⠀⢸⣇⠰⠰⡸⡄⠴⠒⠂⠱⠀⢹⠀⢣⠀⢛⡄⠀⠀⢀⠈⢿⣿⣯⡄⡿⣿⣿⣷⣧⣝⢣⠞⡱⢎⡽⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⠟⠀⡼⣰⠞⠀⠀⣸⡏⢠⡞⠀⣄⣇⠀⢸⠀⠀⠸⡏⠐⠀⠷⡿⠀⢸⡿⡆⠰⢥⡇⠠⣄⠀⢆⠀⠸⡆⢺⡆⠈⠘⡄⠀⠈⢦⡈⠻⣿⣿⣱⣏⣿⣿⣿⣿⣿⡺⠷⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⢷⡛⢬⡟⢩⣾⢋⠀⢰⢱⠃⠀⠀⠀⣿⠀⠀⡇⠀⢻⢻⠀⠘⢢⡀⠀⡇⠀⣠⣤⠇⡖⢸⣧⢿⠀⠀⢿⡀⠈⠣⢸⡄⠀⡇⠀⢻⠀⡆⠑⠀⠀⠘⢎⠦⠙⢿⢟⣻⣿⣟⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣵⡿⡷⠁⣠⡏⠁⠀⠀⠀⣸⡇⠀⢀⡇⠀⡯⠸⡄⠁⠀⠘⢦⣧⡏⠹⠸⠘⠀⣿⠙⡾⡁⠀⠸⣇⠀⠀⠀⣇⠀⢻⠀⠸⡇⣿⣄⠀⠀⠀⠈⢆⠀⡈⠻⣿⣟⣿⣿⣟⢿⣿⣿⢿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⠟⠌⠀⣠⣻⠃⠀⠀⠀⢀⡿⡆⠀⢸⡇⠀⡇⠀⢧⠀⡇⠀⠈⡇⠀⠀⡆⠀⣸⠃⡖⡿⣱⠀⠀⣿⡀⠀⠀⠸⡀⢸⠀⠀⢳⠹⢿⣆⠀⠀⠀⠈⢮⢎⣢⡈⠓⠶⣽⣿⡝⢿⣿⣯⡶⣩⠟⡽⣿⣶⣲⡤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡋⠁⠀⢰⡽⡷⠀⠀⠀⠀⣾⢃⡇⠀⣿⡇⢸⣇⡟⠈⣆⢡⠀⡀⢸⣰⠀⢇⠀⡏⢰⠃⠸⣧⢇⠀⢫⢧⠀⠀⠀⢧⣺⠀⠀⢸⡀⠀⠻⣧⡀⠀⠀⠀⢏⢻⡝⣿⣶⣶⣿⣿⣿⣿⣿⣷⣧⣻⡜⣿⣿⣿⣿⣷⣮⣝⣢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠋⠀⣄⢴⡿⢠⡇⠀⠀⠀⢸⣿⠀⡇⠀⣧⡇⢸⣿⢅⡀⠘⡞⡄⠇⠀⢟⠀⠸⣼⢡⠏⠀⠀⠹⣞⡄⢸⣟⡆⠀⠀⠈⣾⠀⠀⠀⡇⠀⠀⠈⢳⡀⠀⠀⠈⣦⣻⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣳⢿⣿⣷⢿⡾⣷⢯⣛⢯⡷⣗⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⢡⡠⠔⠋⠘⢿⠄⣼⠃⠀⠀⠀⣯⡟⠀⣷⠀⣿⡀⢸⡏⠀⠙⠆⢹⢣⠸⡀⠘⡄⠀⣟⣾⠤⠴⠒⠒⠻⡄⢸⠙⣾⡄⠀⠀⣿⠀⡄⠀⣷⠀⠀⠀⢸⢿⣄⠀⠀⢹⢿⣽⣿⣿⣿⣯⣟⠯⣏⡟⣾⣻⡿⢿⡾⠿⠿⠞⠓⠛⠓⠚⠋⠛⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠎⠓⠉⠁⠀⠀⠀⢀⡏⣸⣿⠀⠀⠀⢰⢻⣏⣴⣯⣇⣿⣿⣿⣯⣖⢦⣄⠈⡼⣧⢣⠀⡹⡄⢿⠃⠀⠀⠀⠀⠀⠹⡸⡇⠘⣷⡀⢸⡇⢰⡇⠀⣿⣷⡀⠀⠈⡎⢿⣆⠀⠸⣆⡙⢿⣛⠿⣍⠉⠋⠛⠿⣝⢏⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣞⡏⢸⡆⠀⠀⡾⣿⣷⣿⡿⢿⡟⠁⣾⢿⣿⣿⡟⡟⠁⠘⡮⡆⠀⢸⣼⡀⠴⢒⣉⣽⣭⣥⣽⣧⣦⣬⣧⣸⡇⡎⢹⠀⢹⠈⠻⣄⠀⠸⡜⣿⡆⠀⡿⣷⣤⣈⠑⠮⠳⢤⡠⣉⡓⠷⢽⣢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡼⢠⠜⡇⠀⢠⠟⣿⣷⣿⣧⠀⠃⠀⠿⢿⢿⣻⣿⠂⠀⠀⠘⢟⢆⢸⣯⠱⠶⠿⠻⠏⢩⣿⣿⣻⠿⣿⣾⣥⣿⡀⠈⡇⢸⣆⠀⠈⣷⡄⠹⡵⡻⡄⡗⠨⣿⠛⢿⠶⠶⣤⣽⣾⣿⣟⡒⠚⠿⠵⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⠁⡜⢸⢳⠀⠀⢸⣿⣿⢻⠟⡆⠀⠀⠐⣾⡛⢿⡿⠀⠀⠀⠀⠀⠀⠙⠻⡀⠀⠀⠀⠀⠿⣟⣟⣙⣿⣟⢺⣿⡏⠁⢀⣷⠸⢿⣆⠀⢸⣿⣦⡀⠱⡿⡇⡀⢻⡄⢸⡇⡆⠀⠀⠘⣷⣌⠱⣦⣠⣤⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠘⢠⠃⢸⠀⠀⣿⡇⢿⡼⡄⢷⠀⠀⠀⠈⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡘⠿⣛⣷⠟⠉⢨⠇⠀⡜⠻⣆⡀⢻⡆⢸⣿⡏⠙⠳⢍⡙⢷⣹⣧⢸⣧⠸⡄⠀⠈⢺⣯⣢⡙⠿⣶⣉⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡼⠀⣠⠃⠀⢸⡇⠈⣿⣧⠸⢧⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠚⠉⠀⠀⢸⣸⡼⠀⠀⢻⡇⠈⢻⣸⢻⣇⠀⠀⠈⢷⡄⣿⣿⣼⣿⡄⠱⡀⠀⠀⢹⣇⠻⡶⢌⣳⣽⣢⢄⣤⣴⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⡲⠁⣰⠃⠀⠀⢸⡿⡐⣿⠚⣧⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣿⠁⠀⢀⣿⣇⠀⠈⡇⠸⣿⡄⠀⢸⡌⣇⢹⡾⢿⣿⣷⢀⣵⡀⠀⣴⡟⣆⢹⣎⡟⠂⣈⠋⠠⠤⢮⣴⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠒⠷⣢⣴⢃⠔⡇⠀⠀⠀⣿⠁⢹⣧⢛⡘⣷⣼⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠃⠀⠀⣾⡏⢹⠀⠀⡄⢃⡏⣷⠀⢸⣷⠘⣾⢻⣘⣿⡿⠋⢿⡵⣺⠏⡇⠘⣄⢻⣇⠀⠀⠀⠉⣐⠶⢆⣰⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⡴⠛⠁⠀⡇⠀⠀⢰⡏⢀⡾⣟⣦⢩⣿⡷⡹⡎⢦⠀⠀⠀⠀⠀⠀⣠⡤⠤⠤⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⢀⡠⣺⣿⠇⠈⡇⢠⠁⢸⡇⢻⣧⢸⡿⡇⡏⠈⣿⣿⠁⠰⣸⡴⣱⢠⣃⣀⣘⣀⣿⣦⣀⠀⠀⠀⠐⢾⣷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⠀⠀⠀⠀⡇⠀⠀⢸⣇⣾⠞⣯⢹⡢⡿⣟⠄⣷⠀⡗⣄⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠈⢹⡇⠀⠀⠀⢀⡀⠀⠀⣰⣿⡏⠠⣺⣴⣿⣿⠀⠀⢳⠀⡔⣾⢣⠈⡟⣾⠃⣇⡇⠀⠘⠋⠀⣰⠟⢀⣧⠘⠀⠰⠶⢞⡉⣿⢆⠙⢢⡈⢢⡈⢈⣩⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠕⠂⠀⠀⣇⠀⠰⣼⠏⠀⡼⢿⠀⣷⡇⣿⠀⢹⡼⢳⡏⣗⢦⡀⠀⠀⠳⢄⣀⣀⣀⡠⠋⠀⠀⠀⠀⠀⢳⣤⣴⠏⡼⠁⢘⢿⠛⣿⣿⠀⠀⢸⠞⢰⠃⢸⡄⢸⢇⠀⡟⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠢⠖⠤⣤⣭⢿⡮⡅⠀⢳⠠⢤⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠤⢀⠀⠸⡀⠠⡏⠀⠀⠉⠙⣇⠸⣷⢿⡆⢨⣷⠞⣯⣿⢈⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢖⣾⡿⠟⠮⣹⣃⠔⠛⠒⢧⠈⢺⠀⠀⠁⠀⠁⠀⣞⣟⡟⠃⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠢⣄⠈⠙⢷⡝⠹⡀⣸⣶⣶⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠂⢧⠀⡇⠀⠀⠀⠀⠘⣼⠇⠘⢳⡼⢁⡾⢺⣿⢬⣻⣭⣝⣗⣤⣀⣠⣤⣶⣞⢋⠡⡐⣺⠟⠉⠵⣶⣿⣅⡀⠀⠀⠀⠃⢸⡄⠀⠠⠤⠒⠒⣹⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠱⣄⡈⠳⣦⠤⣽⣾⣠⣿⡏⢉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠦⢄⡀⠈⢾⢧⠀⠀⠀⠀⠀⠘⠖⠂⠀⠁⢇⠁⠋⠙⢷⣽⣧⣼⣿⣿⣿⣿⣿⣿⣿⣯⢠⢿⠏⠀⠈⠛⠣⣄⠈⠉⠀⠠⠄⠀⠉⠃⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠤⣀⡀⠀⠀⢠⣶⠣⢀⡀⢱⡉⠳⣞⠿⣆⢋⡙⠿⣼⡠⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⡤⢀⡀⠀⣈⠉⠘⢿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⡑⢶⣖⠪⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠾⠤⠤⢤⡶⣶⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠉⠉⣙⠦⠱⣦⣌⢳⠈⠁⠈⢷⡌⢳⢶⣌⠛⣧⢹⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⢎⣉⣀⠄⠀⠈⠣⠀⠀⠀⠀⡀⡠⡜⡆⠀⠆⡇⠢⣌⢢⠘⣷⣮⣿⣿⣿⣿⣿⣿⣿⣿⣳⣦⡄⣲⡴⣋⣤⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣠⠴⢀⠀⠉⠒⠰⣶⠾⣦⣀⡀⠘⢍⠙⠆⠀⠀⠀⠛⡾⡿⢿⣿⢧⣼⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⡤⠀⠀⣠⡞⠁⠀⡼⡱⢡⠇⢰⠀⠐⣷⡀⠸⡿⣵⢿⢿⡦⣀⠉⠻⢿⣿⣯⣝⣿⣿⣷⣯⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡔⠣⠤⡤⢭⠭⠉⠉⣹⣮⡻⠋⠛⠛⠚⠂⠀⠀⠀⠀⠀⣧⣿⢩⡽⣿⣾⣿⢿⣎⡳⣄⣀⣠⣤⣄⣀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠉⠀⠀⠀⢀⠀⢠⡜⢱⠃⣸⡀⣿⢀⣧⣿⣧⡀⢳⠀⣻⡀⢻⡄⠀⠀⠒⠩⠍⡛⠛⠛⠛⠋⠩⣖⡻⠀⢀⡞⠀⠀⠀⡈⢀⠀⠀⠀⠀⠀⠠⠔⠁⠤⠤⣒⠟⠁⣀⠤⣺⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢦⢀⠈⣙⡿⣎⠽⣿⣮⡏⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣦⠀⠀⠀⠀⣠⠾⠔⣿⢾⡧⣾⠛⢇⣿⡟⠻⡿⠛⡿⠮⣧⡁⣧⠀⢹⣆⠀⠀⠀⠐⠒⠒⡒⢺⣿⢟⣿⡇⣠⢳⠃⢰⡀⠀⢧⡎⢰⣆⡐⢦⣬⡹⠶⠶⢋⣩⠉⠉⠁⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢵⠉⣿⣶⣌⠐⡸⣿⣿⣇⠧⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠻⡧⡀⠐⠋⠁⠀⠀⠉⠋⡘⠁⠀⠸⣯⣼⣶⣃⡀⣠⢤⠹⣷⣻⣷⡘⢯⠑⠂⠀⠀⠀⠀⢴⣽⣥⡿⢿⣰⣵⡟⠀⢰⡇⢠⣿⣷⡾⢟⠛⢹⣷⣤⡀⡴⠋⠀⣤⠖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⣿⣷⡟⣳⢦⡉⡙⢛⢣⡟⣿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⢙⣧⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⣾⢧⡼⠙⡍⠿⢟⣧⣽⢻⣿⣿⣾⣇⠀⠀⠀⠀⢀⡾⢛⠫⢘⡐⣸⡿⢁⣴⣿⣀⣿⣿⡿⣝⡠⢭⠮⠿⠟⠌⢠⠾⢊⡡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣠⠙⠻⢷⣔⣾⣳⣶⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⣸⢀⠈⢁⠖⠋⠀⠀⠀⠀⢀⡠⠚⢁⠘⣧⠔⠁⠀⠈⣱⢾⣿⣿⣿⣿⣿⣿⣶⣤⣄⣾⣚⣦⣥⣦⣿⣾⣿⣿⣿⣿⣟⠘⠻⣮⠛⡇⠈⢢⣴⡯⠔⠁⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠙⣴⣙⢦⡀⠐⠹⣿⠈⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢀⡤⠊⠁⠘⠓⠁⠀⠀⠀⠀⠐⠊⣁⣤⣼⣶⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⢻⣿⡇⢻⣿⣿⠟⢻⣫⢏⢏⣝⠳⣿⢶⡹⣎⣽⡿⣶⣮⠗⢀⠟⡤⠞⠉⣠⣴⣾⣛⡟⣳⢦⣤⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢻⣷⣯⣕⡆⠹⣴⡿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣶⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡛⣾⣷⣤⡛⠾⣿⠟⠀⠼⣿⣛⣮⣼⠧⠿⣟⣿⣭⣿⣿⣏⠉⠉⠁⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣾⣷⣿⣷⣦⣄⠀⠀⠀⠙⠣⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠛⠝⢳⣿⠁⢹⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⢛⣛⣿⣓⡢⣄⡀⡠⣔⣤⣶⣿⣿⣿⣿⣿⣿⣿⣏⠟⣿⠻⣥⠻⡟⣷⣿⣶⣿⣿⣿⣟⣿⣿⣶⣤⡭⠭⣭⣭⡶⠿⢻⡻⣿⡽⣋⣵⣷⡻⣦⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⣷⣦⡀⠀⠀⠀⠑⠢⢄⣀⡀⠀⠀⠀⣀⡀⠸⢮⠏⢶⣀⠀⠹⡤⠃⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠝⠢⣄⠀⡠⢍⣙⠇⠈⢝⡿⣯⡻⣿⡙⠿⣛⢿⣙⡛⣿⣿⠁⢣⡐⠩⣿⣷⣿⣿⣿⣿⣟⣿⣷⣿⣣⣽⣷⣬⣽⡿⣞⣻⡵⣾⢛⣷⡻⢞⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣄⠀⠀⠀⠀⠀⠈⠙⠻⢄⣀⠀⢀⠀⠘⣷⣄⠀⠀⠀⢹⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠯⠟⠛⠛⢻⢈⣰⡇⠀⠀⠀⠈⠑⢋⣙⣛⠛⠉⠩⠙⠓⢻⡷⣮⣄⣠⣁⠸⣿⣿⣿⣿⣿⣯⣿⣿⣿⣩⣽⣭⣭⣻⡯⣝⣣⠽⣬⠷⣎⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⢀⣼⡿⣗⣄⠀⠊⠠⣠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣟⣿⣦⣀⡀⢠⣒⣲⠞⠁⠀⠀⠀⠀⠀⢞⣄⠀⠀⠀⠀⠀⣴⠗⢉⡤⠖⣣⠽⠛⢋⡟⠛⠛⠛⠻⣿⡿⣿⣼⣟⣿⣻⣼⡿⣼⣽⣻⣵⡻⣵⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⡩⠷⢴⠖⠯⣄⠀⠈⠛⣷⣯⢟⣯⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡎⠋⠀⠙⣿⡷⢀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠈ ⠀⠀⠀⠀⢀⣀⣤⣤⣔⣿⣿⣿⣿⣿⣿⠛⠊⠉⢹⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠘⣏⠉⠙⢒⣾⠁⡰⠁⢀⠞⠁⡠⠊⡩⣠⣶⠄⠀⣸⣧⡏⠙⠃⠤⡼⢋⣻⣽⣷⣻⣼⣶⣻⣽⣿⣿⡿⠛⠉⠀⠀⢀⡠⠞⢲⢴⣇⠀⠀⠀⠙⢦⣠⢼⣧⢏⣿⣷⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⡄⠹⣧⡾⠟⢡⣇⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏⠀⠀⠀ ⠀⠀⣤⣾⢿⣿⣻⢿⣿⣿⣿⣟⣾⡱⢺⣗⠦⢄⡎⠉⣙⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⣎⡇⠀⡇⠀⡘⠀⢰⠁⠀⢻⣷⣿⡿⢠⠏⣸⡇⠀⠀⡜⠁⣶⠛⠫⢿⣏⡉⣿⢿⣿⣷⠏⠀⠀⠀⠀⠀⢸⣏⣠⡎⠀⠈⠻⣢⡤⠤⠤⢗⠀⢻⣎⡼⣿⣞⢿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠱⢰⠏⠁⠀⣠⡟⠀⠀⠀⠀⠀⢀⣼⣟⣽⢻⡄⠀⠀⠀ ⡞⢿⡹⢞⣛⣾⡽⠿⢾⣷⣻⣿⡜⣷⣃⡼⢏⡁⠈⣦⣈⣦⠄⠀⠀⠀⠀⠀⢀⡼⠞⠀⠀⣿⠁⠀⡱⠀⠡⠀⢲⠀⠀⠈⠉⢁⠔⢋⣰⠋⠀⠀⡰⠃⣴⠃⣠⠖⢉⣭⣿⣿⣻⣿⣿⣅⠀⠀⠀⠀⢶⡭⢱⠛⠈⠲⢄⣀⡠⢵⡄⠀⠈⢟⣲⣷⣮⣽⡿⢮⣿⣿⣽⣿⣿⣷⣻⢦⡀⠀⢀⡤⠖⠒⡚⡄⠀⢀⠎⠀⣲⣴⠏⠀⠀⠀⠀⣠⠾⣋⡖⡿⢱⢋⠇⠀⠀⠀ ⠚⠓⠉⠉⠀⠀⠀⠀⠀⠀⠉⠛⠿⣼⡿⢤⣴⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⢿⡿⣷⣖⡦⣽⡀⢀⠁⠂⠀⠀⣨⠓⠤⢄⣰⣃⣴⠟⠁⠀⣠⡊⢊⠕⢁⣴⠁⣰⣿⢫⡷⢿⣛⢿⡟⣾⣳⣄⣄⡀⠈⢧⣼⣄⣀⣀⣈⣣⡀⠀⠫⡙⢳⣍⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣯⣷⡞⠀⠀⠀⣼⣿⡤⣯⠖⣟⢲⠃⠀⢀⣠⢖⡻⣉⠞⣥⢿⣵⠃⣸⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣹⣻⣿⣿⡿⢛⢧⣹⣿⢭⣿⣿⡿⠟⣸⣿⣿⣿⣻⣷⡦⣄⠀⠀⢠⠃⠀⢀⣜⢁⡼⠣⠄⡀⣔⡕⡱⠃⠀⡜⠁⢰⡏⠋⠣⢏⡷⣹⢞⡽⣾⣿⣿⣿⣿⣾⣿⣷⣶⣿⣍⠁⠀⠙⡶⠶⡏⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣶⡟⣻⡷⠃⠀⣿⣞⣥⣶⢻⢣⡚⠴⣡⣾⣷⣿⠇⣰⣿⣛⢿⣶⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⡿⢳⠴⣋⣾⣿⢓⣾⣼⢯⡱⡜⣤⣿⣿⣿⡇⠉⠓⠦⡑⠦⣁⠀⠀⡞⢀⣾⠇⠀⠀⡞⢉⡼⠁⠀⢰⡅⠀⣿⣿⢀⢳⢫⡜⢣⣿⡿⣿⡿⣿⣿⣷⣞⡽⢿⣿⣿⣿⣿⡉⠋⢯⠀⣿⣿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⡇⠀⡄⣽⠟⢉⠤⣲⣾⣿⣟⡧⢺⣍⣦⣽⣾⣿⣧⡿⢃⣴⣟⢧⣛⠾⣜⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡽⣩⢏⣽⣩⢣⣻⣿⣯⢖⡹⡵⢪⡝⣧⠀⢹⠀⠀⠀⠈⠓⢌⡑⢼⡇⣾⠝⠀⠀⡸⠀⣼⠃⠀⠀⢸⠀⢸⣿⣿⡈⠧⠛⠀⣺⣿⣽⡟⠹⢻⣿⢻⣟⣿⣭⣛⢷⣭⣯⣽⣦⣈⣷⣾⣿⣿⣿⣽⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠘⡔⣷⣸⣤⣥⢶⣶⣟⣻⣉⣛⣯⡿⠟⠛⢿⣿⣟⣾⠟⢁⣼⣿⣽⣮⣝⡻⣼⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣿⣷⢭⣻⣿⣳⡿⣾⣿⣿⣏⡞⣭⠳⣼⣿⣇⠀⢧⠀⠀⠀⠀⠀⠈⠺⡷⣿⡀⠀⠀⡇⢠⣿⠀⠀⠀⢯⠁⢸⣟⣾⣟⣦⡀⢠⢻⣯⡿⡰⣉⠆⣿⢈⡻⡝⣿⣿⢎⡽⣮⣽⢿⣿⡽⢿⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣾⣿⡽⠠⢠⣿⣯⢻⣿⣋⣙⣷⣄⠀⠀⠈⣻⣋⣴⠟⠿⣯⣟⡿⣽⡷⠋⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣷⣿⣬⣿⣿⣿⣿⣿⣿⣷⣎⣿⣿⣿⣿⣷⣛⣧⣀⠀⠀⠀⢀⣀⡨⠮⠿⢢⡀⢧⠸⣟⠀⠀⠀⢹⠀⢸⣿⢾⣿⡽⣹⢞⠦⣻⣿⡵⣩⠖⣼⣏⢶⡙⣾⡟⣮⣽⣿⣿⡯⠋⠙⠳⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠿⠟⠋⢱⡿⢏⠀⠀⡟⠁⠀⣠⢿⠽⠻⣿⠋⣩⠰⡄⠫⠦⣲⣾⣿⠿⣶⡤⣀⠀⠙⠻⣋⣴⣾⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⡿⠟⠛⠉⠺⠬⠛⠉⠉⠁⠀⠄⠀⠀⠀⠈⠘⣶⣿⣕⢢⣀⠈⣇⣸⣿⣟⣾⣿⣵⣫⣗⡹⣿⣯⢇⡻⢬⡟⣮⣹⣿⣹⣾⡿⠛⠁⠄⡈⢁⠂⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠧⠈⢧⡘⢀⠴⠺⡵⢋⠬⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠛⠶⢭⣭⣼⣿⡁⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢽⣛⡉⠑⠾⣿⣛⡽⣯⡉⢷⣟⡾⣽⣻⢧⣯⡝⡶⣻⣶⣿⣷⡿⠋⠐⠀⠃⠄⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠠⢿⡏⠀⠈⣽⣣⣦⣤⣤⣬⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⡸⠉⠛⢿⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠘⠓⠿⣿⣷⣯⣟⡾⣿⣕⣻⣿⡿⠋⠀⣀⠤⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣬⣷⣴⣤⣶⣷⣶⣾⣯⡹⣹⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⠾⣿⣿⡿⠟⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣧⡙⠿⣯⣽⣿⣿⣿⣿⢻⣿⣿⣿⣷⣿⣿⣿⣠⣤⣤⣤⠀⠀⢠⠀⠀⠀⠀⠀⠀⢇⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⡿⣿⡿⣳⢻⠈⢢⡀⠉⠛⠿⣿⣿⣿⣿⣿⣿⡁⢀⣠⡇⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣀⣤⣤⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠲⣤⠀⠀⠀⠀⠀⠀⣈⣿⣾⣿⣿⠁⡎⢸⠀⠰⢍⡢⢄⠀⠈⠑⢍⡈⢉⠉⠉⣩⠏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢽⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⠱⢨⣦⠟⠀⢰⣿⣿⠃⠘⠢⣀⠀⠀⠂⠀⢀⠀⣤⣔⣒⣊⣩⣯⣿⣿⣿⡟⠀⣧⠸⡀⠐⠂⠉⠆⡈⠓⠢⠄⠉⠲⣶⣾⡯⠤⢾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⣉⣉⠀⠀⠀⠀⠣⠤⠤⠤⠠⠀⠈⢛⢯⣿⣿⣿⣿⣿⡟⠙⡌⢻⢳⣵⣤⣤⡀⠀⠈⠑⢤⣤⣄⡀⣀⣀⣀⡤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀

⠀⠈⠀⠈⠁⠀⠉⠙⠒⠶⢤⣤⣤⣀⣀⣤⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⢴⠆⢰⠃⠀⠀⠀⠀⠀⢷⠦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀ ⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠛⣻⠛⠉⠁⠀⠀⢸⢀⡏⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠈⠙⠛⠓⠢⠤⣤⣀⡘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⣀⣀⢠⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣠⡾⠃⠀⠀⠀⠀⢀⡏⢸⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀ ⠈⢙⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣠⡞⣻⣃⣠⡤⠤⠒⠒⠛⠁⣼⠀⠀⠀⠀⠀⠀⠀⣼⡛⠓⠒⠦⢤⣄⡀⠀⠀⠀⠈⢻⣝⠳⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⡿⠛⣹⠋⠀⠀⠀⠀⠀⠀⣠⠞⡇⠀⠀⠀⠀⠀⠀⣼⠉⢧⠀⠀⠀⠀⠀⠈⠉⠙⠲⠦⣄⠹⣆⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢋⣿⠏⢀⡴⠁⠀⠀⠀⠀⠀⣹⡾⠋⠀⡇⠀⠀⠀⠀⠀⣸⠃⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣧⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀ ⠀⠀⠀⠀⢀⣀⣤⠴⠻⣉⠀⠀⠚⠁⣠⠞⢁⣀⣀⣤⣤⣤⠾⠽⡀⠀⠀⢹⠀⠀⠀⠀⢠⠇⠀⠀⣠⡋⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡖⠒⠒⠋⠉⠁⠸⣦⣄⣙⣳⣦⣤⣴⣷⣾⣿⣿⣿⣿⣿⣿⣶⣤⠞⠀⠀⢸⡀⠀⠀⢰⣿⠀⠀⠺⣏⣤⣤⣽⣿⣿⣶⣶⣤⣀⡀⠀⠀⠀⢳⡀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠒⠒⣦⣤⠤⢤⣽⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⠟⠛⠻⣿⣇⠀⠀⠀⣇⠀⠀⢸⠇⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣧⡤⠚⠉⢙⣻⡶⠶⣤⣄⠀⡤⠀⠀ ⠀⣠⠞⣽⠁⣀⣀⣴⣾⣿⣿⣿⣿⠟⠉⠀⠀⠘⢯⠉⢷⣄⣴⡿⠏⠁⠀⠀⢸⡄⠀⢸⠀⠀⠘⡿⣿⡀⠀⢀⡿⢿⣿⠿⣯⡛⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠹⣷⣄⠀⡀ ⣰⠃⣸⠁⠀⠀⠀⠀⠀⠘⠻⣿⣿⠀⠀⠀⠀⠀⠀⠙⠒⠚⠉⠀⠀⠀⠀⠀⠀⢳⠀⢸⠀⠀⠀⠃⠹⣿⣲⣛⣳⠾⠁⠀⠈⠙⢶⣄⠈⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠙⠷⣿ ⠃⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⡸⠛⠂⢀⡠⢤⣶⣾⠿⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⢧⢸⡄⠀⠐⠤⠤⢤⣤⣍⣀⡀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠁⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⡟ ⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠘⠁⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⢳⣷⠀⠀⠀⠀⠈⠉⠉⠙⢿⢿⡖⠦⢤⣀⣀⠘⢫⠇⠉⠓⠦⣄⡀⠻⣤⡀⠀⠀⠀⠀⠀⡇ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⣴⣶⣶⡄⠀⠀⠀⠀⠀⢿⡏⠉⠲⠖⠒⠒⠒⢶⠄⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣤⡀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠉⠓⠦⣽⣦⡀⠀⠀⣸⠀ ⢠⣇⠀⠀⠀⠀⠀⠀⣰⡏⠀⣤⣿⡙⣿⣷⠄⠀⠀⠀⠀⠈⠳⣄⠀⠀⣀⣠⡶⠟⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⢀⣘⣿⢿⣟⡀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⠇⠀ ⠘⣿⡀⠀⠀⠀⠀⢀⣿⡷⠀⠙⡟⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠸⠿⠟⣠⠏⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀ ⠀⠸⣇⠀⠀⠀⠀⢸⢸⡇⠀⠿⠷⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠃⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀ ⠀⠀⢹⡄⠀⠀⠀⡏⠀⢇⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣞⣫⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀ ⠀⠀⠀⢻⡄⠀⠀⡇⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⣿⣿⣷⣶⣦⣤⣤⣤⣀⣠⣴⣶⣾⠏⠀⠀⠀⠀⠀⠈⢉⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡄⠀⢻⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⠙⣆⠘⡆⠀⡀⠹⡄⠀⠀⠀⠀⠀⠀⢠⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠐⠀⠀⣀⡴⣚⣡⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠞⠁⠀⠈⠳⣽⡞⠀⠀⢙⣦⡀⠀⠀⠀⠀⠈⢧⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⠟⣫⠞⠁⠀⠀⠀⢀⣀⡏⠀⠀⠀⠀⢀⡤⠞⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰ ⣤⠞⠁⠀⠀⠀⠀⣰⠏⠳⣄⡔⠋⠀⠛⣦⡀⠀⠀⠀⠈⣿⣿⣟⣰⣿⣿⣿⣿⣿⡵⠚⠁⠀⢀⣠⠔⠒⠈⡿⠀⠀⠀⣠⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃ ⠁⠀⠀⠀⣀⡤⣾⠏⠀⡴⠋⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠘⣿⣿⣉⣠⣿⣿⠏⠀⠀⠀⠀⡰⠋⠀⠀⠀⢰⡇⠀⢀⡼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀ ⠛⠛⠋⢉⡏⠠⡟⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣻⡳⢤⣀⠈⠉⠋⠉⠿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⡇⢠⠟⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠖⣋⡀⠀⠀ ⠀⠀⢀⡿⡼⠀⡇⡸⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠀⠀⠀⠉⠓⠦⣄⣀⠠⠄⠀⣀⣀⣠⠤⠴⠚⠋⣡⠞⠁⣧⡟⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠁⠀⠀⠀⠀⢀⣀⠉⠓ ⠀⠀⢸⢣⠃⠀⣷⠇⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠈⠒⢦⣀⠀⠀⠀⠉⠉⢿⡉⠉⠁⠀⠀⠀⢠⡾⠃⠀⠀⠻⠇⡿⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀ ⠀⠀⢸⠀⠀⠀⢿⠀⠀⠀⡼⠋⠐⠂⣠⣤⣄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠰⣶⡆⠀⠀ ⠀⠀⢘⠀⠀⠀⢸⠀⠀⢸⠱⣶⠆⠠⣾⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡄⠀⣾⠁⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠗⠀⠀⠀⠀⡀⠀ ⠀⠀⠈⡀⠀⠀⢸⡆⢠⡟⢀⣤⣄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠄⠀⠀⠀⠋⣭⠀ ⠀⠀⠀⠑⠀⠀⠀⢧⢸⠁⠈⠛⣯⣄⣛⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⢀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠏⠁⠹⠿⣧⠀⣰⠋⠁⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⡇⢻⢠⣯⠀⠀⠈⢂⢻⡐⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⢰⡗⠀⠀⣼⣁⣾⢸⡇⠀⠀⢀⣼⢨⡇⢀⣾⡴⠿⣯⠀⠀ ⠀⣴⠿⢛⡿⣦⡘⣧⡀⠀⡼⣳⡟⢸⣇⠀⢠⣈⠍⣹⣿⣾⠙⠀⢢⠹⣧⠀ ⠀⣿⠀⠀⠸⡮⢻⣎⠻⢷⡿⠋⠀⠀⠙⠳⢾⣿⠞⠁⣿⠁⠀⠀⠸⠃⣿⠀ ⢠⣿⡄⠀⠀⢸⠸⣏⠀⢀⣴⣾⡿⣿⣦⣤⣦⣤⣄⠀⢹⡆⠀⠀⠀⡆⣿⠄ ⠀⢿⣏⠁⠀⢸⣣⣿⢀⣿⠋⠀⠀⠀⠉⠉⠉⠉⠻⣷⠀⢿⡄⢀⡞⣠⡟⠀ ⠀⠐⢿⣯⣀⡾⠛⢃⣼⡏⠀⠀⠀⠀⠀⠈⡆⠀⠀⢿⣧⠸⠿⣿⠾⠋⠀⠀ ⠀⠀⠀⠈⠉⢣⣶⡿⠛⠀⠀⠀⠀⠀⠀⠀⠉⢶⣤⡈⢻⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡽⢿⠁⢰⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣶⣦⣄⡀⠀⠀⠀⠰⣿⣏⣤⣞⣀⣼⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢿⣦⣄⣤⣴⡾⠛⠉⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠠⠀⠤⢀⡠⠀⠀⠀⠀⠠⠤⠄⠠⠀⠠⠀⠀⠀⣐⣀⠠⠤⠤⠀⠀⠀⡀⠄⠀⠂⠰⠄⠠⣀⣀⠢⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠙⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡤⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠈⠻⡾⣽⢶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⡿⠛⠉⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠹⣧⢟⡾⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡿⣞⡽⣫⢟⣦⣤⣤⣴⣶⣿⡿⠉⠉⠉⠉⠙⠋⠩⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠛⠛⠛⠛⠻⣿⢧⡀⠀⠀⠀⠀⠀⢀⣿⢣⡟⣵⣫⢟⣻⣵⡯⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣅⠀⠀⠀⠀⠀⠀⢸⠛⠛⠛⠛⠛⠛ ⠀⠀⠀⠀⠀⣿⢯⣻⢦⣴⣀⣀⣶⠾⣭⣳⡿⠼⠙⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⡀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣎⡷⣎⢷⣹⢮⣿⣡⣥⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣄⡀⠀⢠⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⡼⣹⢮⣷⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⡄⢀⣎⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣷⣯⣿⣿⣿⠿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⠿⠛⠛⢎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢹⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⡿⡿⠁⠀⠀⠀⣀⣀⣀⣠⠤⠤⠞⢣⠀⠸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⠀⠀⠀⠀⠋⠑⠒⠒⠒⠒⠒⠊⠉⠉⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢰⣶⠒⢲⣶⣶⣶⣶⣾⣷⣿⣷⣿⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⢾⣿⣿⣷⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡓⠲⢶⣶⣶⣶⣶⣶⣶⣶⡖⣤⡤⠀⠀⠀⠀ ⢸⣧⠀⠀⢈⣿⣿⣟⢿⡿⣿⣿⡋⢙⣿⣷⣌⢿⣿⣿⣿⣿⣿⣟⣚⣿⣿⣿⣁⡀⠙⠃⠀⢸⣿⣷⡬⣟⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⠇⠀⠀⠀⠉⢛⣿⣿⣿⣿⡇⠖⠁⠀⠀⠀⠀ ⢸⣿⣷⣿⣿⣿⣿⡏⠀⠀⣹⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣄⣀⡀⠰⣪⣿⣿⣿⡍⡻⣿⣿⣿⣿⣽⣿⣿⣿⣿⣀⠀⠀⠀⣴⣿⣿⣿⣿⣻⣿⡤⠅⠀⠀⠀⠀ ⢸⣿⣿⠻⣟⣿⣿⣿⢛⣿⣿⠿⣿⣿⣿⡟⣷⣷⡄⠀⠙⠓⠯⠿⠿⣛⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⡶⡘⡎⢿⣿⢽⡾⣿⣿⣿⣿⣿⡶⠾⣿⣿⣿⣿⣿⠉⢈⣿⣾⣾⣶⡄⠀ ⢸⣿⣿⠀⢿⣿⣿⣿⣿⣷⠟⢛⣛⡻⣭⣿⣻⡳⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣽⣇⠀⠀⣿⣾⢸⣿⣿⣿⣿⣿⣷⣰⣿⣿⣿⣿⣿⡻⠟⢛⣿⢿⣟⢿⣦ ⢸⣿⣭⡀⢠⣽⣿⣿⣯⣏⣎⣠⣬⣝⡚⠻⣌⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⡄⠀⡽⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⢀⣿⣷⣌⢿⣷⠻ ⢸⣿⣿⡇⣿⣿⡟⣿⣿⣿⣏⣶⣶⣮⠷⠶⠛⠋⠉⠉⠛⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠾⠼⠿⢟⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⣼⣟⣽⣍⢻⣿⣃ ⢸⣿⣿⣿⠻⣿⣿⡏⣷⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣰⢏⣾⣻⢿⣇⢻⣿ ⢸⣿⣿⣿⣼⣿⣿⣿⢡⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢫⡿⣳⣿⣧⢿⡌⣿ ⢸⣿⣿⣿⣿⣿⣻⠿⠚⠋⠉⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣧⡿⣱⠟⡜⣿⣸⣇⢻ ⢸⣿⡿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢫⣧⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡽⡏⢼⣧⣿⣿⣿⢸ ⢰⣿⣯⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣯⠟⠸⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡴⣀⠋⣿⢻⡇⢸ ⢸⣽⢆⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⣁⣜⠥⢴⡾⠿⡄⠀⡀⠰⣤⣏⣧⠀⠀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡘⠝⣿⢸⡇⣾ ⢸⣿⣿⣗⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣖⣋⡡⠴⠚⠉⠀⠀⠹⣄⠸⡄⢻⠷⣝⣟⠷⢦⣀⢀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠁⡟⢀⣿ ⢸⣿⣿⣿⣷⣿⣽⣖⣦⣤⣤⣤⡤⠀⣀⣴⣿⣋⣭⣿⣿⠉⢤⣤⣤⡀⢲⡄⠀⣰⠙⢦⣻⣼⠀⠈⠙⣶⠲⢮⣽⣷⣼⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⣜⡏ ⢸⣿⣿⡻⣯⣷⣶⠂⠈⠉⠙⢳⣶⣶⣿⣿⣻⣿⣿⣿⣿⣽⣿⣶⣄⣸⡦⡀⢰⡏⠀⠀⠙⢿⣶⠂⠈⣟⣳⣶⣷⣿⣬⣿⣟⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣌⢌⣾ ⢸⣿⣿⣷⣾⣿⣾⠏⠙⠻⠶⢦⣽⣿⣿⣿⡏⠁⠘⢿⢿⡟⠛⠛⢿⡛⠃⠙⡼⠁⠀⠀⠀⢈⣻⣶⣿⣿⣷⣾⣿⣿⣹⣿⣿⣿⣿⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿ ⢸⡿⢻⠛⡻⠋⠀⠀⠀⠀⠀⢀⡾⠁⣿⢹⣿⡀⠀⠈⠻⣄⣀⡤⢾⣟⢛⣛⣷⣤⠀⠀⠀⠀⠀⡟⠉⠀⠈⢁⣹⠋⠀⠈⣿⣿⣽⣿⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣇⠃⡼⠁⡀⠀⠀⠀⠠⢠⣾⠁⠀⢸⠸⣿⣿⣷⣶⠿⠛⠉⠀⠈⠛⣿⠟⠛⠻⢦⣄⡀⠀⠀⠛⠷⣤⣤⠟⠁⠀⠀⣴⠿⠟⠋⠁⠉⠻⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀ ⢸⣿⣼⣵⡞⠁⠀⠀⠀⠀⣾⠇⠀⠀⣼⠀⠘⠛⠛⠁⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠈⠉⠓⠦⣄⡀⠈⠹⣿⣶⣶⣾⣿⡆⠀⠀⠀⢸⡀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣽⣿⣿ ⢸⣿⡿⣽⠁⠀⠀⠀⣠⣞⣩⣤⡄⠀⢹⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠶⢤⡀⠀⠀⠀⠀⠀⠀⠉⢳⠶⣤⣘⠳⠟⠿⠇⠄⠀⠀⠘⠃⠀⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⢸⣿⣿⣝⣿⡶⣶⠿⠛⠋⠉⠩⠀⠀⢸⠀⠀⠐⠗⠀⣀⣀⣀⠴⢋⣀⣀⣀⣀⡈⠲⣄⠀⠀⠀⠀⠀⠘⠀⠀⠸⠛⠶⢤⣄⡀⠀⠀⢀⠀⣸⡏⡟⠛⠿⢷⣶⣦⣠⠀⠀⠀⠀⢙⣮ ⢸⣿⣿⣿⡟⡾⠃⠀⠀⣀⣀⣴⣿⠷⠾⣄⡀⠀⠀⠀⠈⠹⣄⣸⣿⣿⣿⣿⣿⣿⣷⠀⢙⡦⣄⣠⠴⠁⠀⠀⠀⠀⠀⠀⡞⠙⠓⠦⡾⢀⣿⡷⣇⠀⠀⠀⠈⠙⡿⢿⣷⣤⡀⣬⣿ ⢸⣿⡿⣿⢱⠁⣠⡾⠉⠉⠉⠉⠁⠀⠀⣇⢷⡄⠀⠀⠀⠀⢻⣯⣿⣿⡿⣿⢿⣿⣿⣠⣾⡤⣤⠏⠀⠀⠀⠀⠀⠀⠀⣾⢧⠀⠀⢰⠃⣸⠟⠀⠹⣷⣄⠀⢰⡾⠃⠀⠈⢙⣇⡟⣿ ⢸⣯⠀⣿⢸⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠸⣤⡇⠀⠀⠀⠀⠈⣿⣿⠿⢺⡿⠶⢿⣿⣿⣿⣷⠏⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠳⠤⠬⠞⠁⠘⣧⡀⠈⢻⣷⡌⠀⠀⠀⠀⠈⣿⡇⠙ ⣼⠛⢾⢿⢸⣏⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⣿⢻⣄⠈⢁⣴⣦⣹⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⡀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠙⢿⣆⠀⠀⢀⣷⡟⠀⠈ ⠹⣤⡌⣶⣬⠞⠙⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣧⡀⠀⠀⠀⠘⢧⣙⣒⣛⣛⡼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡳⢤⣀⣀⠀⠀⠀⠀⠈⢷⡄⠀⢰⠹⠀⣠⣟⣟⣶⡆⡲ ⠀⠘⠻⣿⣿⡀⠀⠀⠈⠙⠲⢄⣰⡀⠀⣀⡴⠋⠁⠙⢦⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠋⢀⣽⣿⡟⠉⠀⢀⣠⡤⠤⠶⠴⠾⠛⠛⢻⣭⣟⠗ ⠀⢀⡔⠙⣷⣿⣒⣦⣄⠀⠀⠀⣻⣿⡞⠋⢴⣄⣀⠀⠈⣿⣄⡀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠟⣻⠃⢀⡴⠋⢸⣿⡴⣠⣴⢟⣥⡄⠀⠀⠀⠀⠀⠀⠀⢻⠈⠐ ⢰⡟⠁⠀⢈⣿⣿⡟⣼⡦⣤⣔⣿⣿⣝⣦⡈⢿⣿⣿⣿⠟⠿⢷⣦⣄⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⡾⠛⠋⡥⢂⣴⠓⠀⠉⠀⠀⠸⣿⣿⣿⠃⡟⣰⠇⠀⠀⠀⠀⠀⠀⠈⠘⡂⢰ ⢸⣷⣶⣾⣷⣿⢿⡧⣽⣿⣿⠯⠿⠿⠿⠿⠿⠶⣽⣿⣿⣆⠀⣀⣳⣿⣿⣯⣽⣿⣿⣿⠿⠟⠉⠀⢀⡴⠊⣤⡞⠁⠀⠀⠀⠀⠀⠀⠿⣿⣯⣠⠾⡏⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠀ ⢸⣿⣿⣿⣿⣿⡿⣿⣿⣥⣤⣤⣤⣀⣀⡀⠀⠀⠀⠈⢹⠻⢌⣿⣿⣿⣬⠷⠿⠛⠉⠀⠀⢀⣠⠞⠉⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣼⡃⠀⠀⠀⠀⠀⠀⠠⠤⢺⠀⠀ ⢸⢿⣞⣋⠟⣡⡟⠁⠀⣆⣀⢠⣀⣈⣙⠛⠶⣶⣖⡒⠚⠛⠛⠛⠿⣿⣆⠀⠀⠀⢀⣀⠒⠋⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣰⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⢠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠀⢠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢦⡀⠛⣿⠁⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡏⠀⢸⣿⠛⣑⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡆⠓⡆⠛⣶⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⣦⠑⠺⣾⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⣾⠛⡖⠃⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡆⠓⡄⢹⡆⠀⠉⣷⠀⠀⠀⠀⠀⠀⠈⠹⠯⠁⠀⠀⠀⠀⠀⠀⢰⡾⠁⠀⣾⠉⣾⠁⢲⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⢹⠈⢹⡇⠀⡿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇⢀⣿⣏⣹⠉⣺⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠈⣿⣀⣹⠀⠙⠛⠃⠘⠛⢣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡟⠛⠃⠘⠛⠃⢸⣀⣸⣗⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠶⠞⠛⠛⠛⠛⠳⠶⣆⡿⠀⠀⠀⠀⢀⣀⣤⠀⠙⣷⠀⠀⠀⠀⠀⠀⢰⡾⠏⠀⣀⣠⡀⠀⠀⠀⢸⣿⣰⠶⠟⠛⠛⠛⠛⠷⠶⣀⠀⠀⠀⠀ ⠀⠀⣤⠾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠸⠿⠿⠀⠀⣉⣷⠀⠀⠀⠀⠀⣾⢭⠀⠀⠿⠿⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡄⠀⠀ ⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠀⠀⠀⠀⢀⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡇⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡟⠛⠀⠀⠀⠀⠀⠀⠘⠛⢳⣴⣶⣤⣤⣤⡔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠸⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⣀⠀⢠⡿⠇ ⠀⠺⣧⡀⢠⣀⠀⠀⣀⣟⠛⠛⣧⣄⡀⠀⠀⣸⡇⠀⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣷⣾⡇⠀⢀⣠⣼⣿⣿⣿⣟⣀⣀⣀⣶⣁⢰⡾⠗⠀ ⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀

⠰⠀⢆⠐⡂⢌⢧⣙⢎⡳⡝⡾⣭⢟⡽⢯⡿⣽⢿⣻⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⢿⣻⢿⡽ ⢘⠡⣘⠀⡅⢸⢎⢮⡝⣳⣝⡳⣭⢯⣟⣯⢿⣽⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠻⠿⠿⠁⠀⢹⢿⢟⣻⣭⣭⣭⢭⣉⣛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣟⣿⣟⣿⣯⡟ ⠸⡀⢜⡀⠆⣩⢞⣣⢞⡵⣎⢷⢯⣷⢻⣞⣯⣷⣟⣿⣽⣷⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⠀⢠⣠⣯⣷⣿⣟⣵⣾⢿⡿⢋⣭⢬⡒⠩⠻⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⣾⣿⣳⣟ ⢸⠀⢎⡄⠃⢴⢫⣞⡹⣞⣭⣟⡾⣽⢯⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⠥⠀⠀⠀⡴⣻⣿⡻⣿⣫⢾⣟⣿⢯⣽⣿⣷⠃⣷⣱⡂⢊⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢯ ⣘⠂⠼⣀⠃⡜⣳⢎⡷⣹⢶⣏⡿⣽⣻⣾⣟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣽⡀⠀⣪⣷⣷⣿⣿⣏⣦⣿⡿⣥⢞⡵⣛⢄⣿⣻⣧⣮⢃⢊⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣻⣯ ⣘⠂⡹⡄⢃⠸⣧⢻⡼⣝⣧⢿⣽⢯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡐⣿⡿⣿⠁⢰⣷⡿⣯⣽⡟⣼⣿⡟⡿⢨⡿⠟⣱⣿⡿⣯⡏⣾⣯⠇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽ ⢬⡁⠲⣅⠊⡜⣧⢻⡼⣛⣾⣻⣞⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠳⣿⣏⡇⡀⢸⣿⣿⣿⠽⠁⠏⣿⣿⡇⠍⠤⣞⣛⡋⢃⣻⡗⣿⠆⢊⠇⣹⣿⣿⣿⣿⣿⣿⣿⣾⣿⢿ ⢢⠅⡹⡔⠂⢼⡳⣏⢷⣻⣞⡷⣯⣷⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⣿⡇⠀⠀⢻⡝⡑⡌⢆⢡⢷⣳⡆⠀⢀⣄⣊⣿⣜⠄⠇⠹⡆⠾⡀⢧⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿ ⡘⠆⣱⢹⠈⢲⡽⣚⣯⢷⣫⣟⣷⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢯⢹⣿⣽⠀⠠⠈⠪⡐⢤⣜⣿⣺⣯⢫⠟⣷⣛⣿⣿⡿⠋⠀⠑⠀⡃⠄⠸⣾⣿⣿⣿⣿⣿⣿⣷⣿⢿ ⢸⡁⢲⣍⢂⢩⡷⣻⡼⢯⣷⣻⢾⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣾⣼⣿⡼⡎⠱⠀⣶⠌⢀⣭⣘⡟⣞⠯⣿⣷⣿⣿⣿⣽⡲⡌⠀⠀⠜⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿ ⢢⠅⣚⢬⢂⢸⣳⢳⣽⣻⢾⣽⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡾⣿⣿⡾⡗⢭⠱⡀⢱⣿⠼⠟⠳⠌⠺⣗⢷⣺⣿⣭⣽⣻⣿⠃⠀⡀⠀⣵⣿⣟⣿⡿⠿⣿⣿⣿⣯⣿⣾ ⡘⠆⡸⢎⠤⢸⡭⣟⡶⢯⣟⡾⣽⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢨⠷⡎⡼⣗⠄⠘⠀⠀⠈⣫⣶⣶⣶⣦⣀⣼⣦⣽⣿⣿⣯⡩⣵⠰⢺⢿⢹⣿⣿⣿⣏⣿⠇⣿⣿⣿⣟⣷⣿ ⢱⠂⣱⢚⡄⢸⣳⢽⣳⢾⣽⣳⡿⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡔⠃⣗⢽⡀⠀⠀⣠⣴⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⢻⠀⠈⡘⢈⣿⣿⣿⣿⣿⣴⣿⣿⣿⢿⣟⣿ ⢌⡃⢬⢳⡀⢺⡝⣾⢭⡷⢯⡷⣿⢯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡳⠆⠀⣓⡔⣾⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠇⡀⠁⣌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣿ ⠸⡄⢊⠷⡐⢨⡟⣾⣹⢞⣯⢿⣽⣻⣷⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡻⣾⣿⣿⣿⣿⣯⣏⣿⣿⣿⣿⣟⢿⢿⣿⣿⣿⣧⢥⣒⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣽⣻ ⠸⡄⢙⢮⢁⠲⣝⡧⣏⣟⢾⣛⡾⣽⣾⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⡿⣹⣿⣿⣟⣿⡿⡿⣟⢾⣿⡽⣻⢿⡎⣼⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣟⣯⣿ ⢱⠂⢜⢎⠢⢘⡧⣟⣞⡮⣟⣽⢻⡷⣯⢿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⡿⣷⣿⣣⣟⣿⣴⣟⣮⣻⣻⣽⣜⣕⠅⣻⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣾⣽⡾⣟⣾ ⢨⠃⡘⢮⠡⢈⠗⠉⠈⠑⠻⡼⣏⡿⣽⢯⣿⣻⣯⣷⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣧⣿⣾⣿⣿⣷⣿⡿⡿⣟⡿⣇⢩⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣻⡾⣿⣯⠗⠉⠉⠘ ⢨⠃⡘⢧⡘⠠⢂⠀⠀⠀⠰⢙⣷⢻⣭⣟⣾⣳⣟⣾⣽⣾⢿⣿⢿⣿⣿⣷⣿⢿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣯⡽⣯⣖⢺⢩⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣻⣾⢿⡽⣷⢯⡄⠀⠀⠀ ⢨⠃⢸⡡⠒⢀⠃⠀⠀⠀⠈⠉⠈⠙⠀⠋⠒⠙⠊⠓⠙⠚⠋⠛⠋⠛⠛⣣⣾⣿⣿⡿⠿⣿⣿⣿⡿⢿⣷⣟⢿⣛⢨⣃⢸⣿⣿⣿⠃⠻⠛⠟⠛⠯⠻⠝⠯⠛⠿⠹⠋⠎⠀⠀⠈ ⢌⡃⠤⡓⡍⢀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⣴⢛⠿⠿⠿⠛⠛⠻⠿⠯⣽⣗⢿⣮⡱⣿⣿⢃⠼⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣀⠢⡝⡄⠀⠂⠀⣠⣶⣿⣾⣥⡭⣽⡖⢄⢤⣤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠑⢞⢻⡆⠱⣽⡄⢿⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⡿⣟⣾⣶⣦⡲⣿⣿⣿⣟⡻⡝⠂⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠐⠈⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠣⢠⢏⠶⢁⢯⡓⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣻⢼⡻⣼⢳⣏⣟⢾⣷⣺⢿⡵⣆⡀⠀⠤⣴⣄⠀⠀⠀⡀⠀⠀⢀⣀⠀⠄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⠈⡶⢡⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠳⠝⠶⠋⡬⣈⠻⢼⡳⡟⠾⠹⠟⢿⣋⠦⣉⢳⣦⣴⡲⢤⣠⣿⣶⣾⣾⣶⣤⣤⣀⣸⣵⣢⣄⠀⠀⠀⠀⠀⠀⠀⠈⣷⡘⣧⢞⡆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⡀⢀⠳⠀⠄⠀⠀⠀⠀⢀⣢⣿⣶⣶⣾⣅⡡⢶⡿⠿⡍⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣤⣀⠀⠀⠀⠀⠀⠳⣝⢮⣏⡇⣿⣿⡿⠂⠀⢀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀ ⠐⠆⡀⢏⠀⠃⣀⣄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⡣⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⢀⠀⠀⠈⠷⡾⣽⢹⣿⢇⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶ ⢘⡁⠐⢈⣤⣿⠏⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣡⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⡿⣵⢯⣸⡏⣺⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⠂⣴⣿⣿⣿⣆⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⢿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⡀⠀⠙⣷⡋⡷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢈⣾⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣉⢸⣿⡿⣟⠦⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⡇⠀⠰⣯⠇⢃⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠚⠿⢿⡿⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣏⡷⡁⡸⡅⣋⣡⠦⣇⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⡇⢠⣶⣟⡇⣾⣛⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣠⡴⣶⣶⣷⣾⣶⣦⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣇⣿⣿⣿⡝⡆⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡷⡏⣤⡻⣞⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣦⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⢿⡱⢛⢯⢳⡙⢂⡘⣏⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⢯⣻⠱⣿⢿⣞⣿⡸⣯⡟⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣯⣾⣿⣯⣎⡻⣿⣿⣿⣿⣿⣿⣿⣿⡶⣬⢅⠀⣦⣆⢫⠥⠘⣿⣻⣿⣿⣻⣿⣽⣯⣟⣷⣯⢿⡝⠧⠁⠀⣿⣰⣫⣻⣇⣜⣿⡿⠞⠠⢻⣝⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣷⢿⣖⢯⡐⣬⣛⡆⣿⡁⠈⠳⢯⢷⣻⢷⣻⢾⡽⢾⠙⠊⠁⠀⠀⠀⣿⣶⣵⣵⣙⣮⣧⣴⣒⢷⢽⣮⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣟⠿⠿⠿⣻⢟⠾⠣⠃⠘⢿⣞⠰⡌⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣻⣿⣿⣲⣯⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⣀⠀⠉⠈⠀⠀⠀⠀⠘⠻⡄⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣿⣿⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⣿⣿⣷⣶⠄⠀⠀⠀⠀⠀⠑⠐⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⡀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢎⢝⡼⢫⡿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠟⠁⣌⠻⠄⠀⠉⠻⠿⠿⠛⠉⡁⠠⢄⠣⡘⠤⢉⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠨⠆⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡟⠀⠱⡈⢣⠁⠀⠀⠀⠀⠀⠀⠂⠄⠁⠂⠄⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠤⢊⡐⢀⠂⢀⡔⢢⠂⠄⠈⠻⣛⢿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⠁⠀⠁⡐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡤⣶⡶⣖⣎⣡⠤⠀⠀⠀⠀⠄⠃⠤⠐⠀⠀⠢⡙⠤⡉⠂⠄⠀⠐⣿⣿⠿⣻⣿⣿⣿⣿⣿⣿⣿ ⠟⠁⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣄⣤⣴⣾⣻⣿⣽⣿⣲⣶⣿⣶⡟⣿⣿⣾⣯⣿⣆⣀⠀⠈⠀⠐⠀⠈⠀⠀⢁⠒⠀⡁⠂⠀⠀⠙⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣯⣞⣿⣷⣿⣿⣿⣿⣿⢾⣿⣽⣷⣿⣿⣿⣳⢿⡯⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣶⣶⣶⣿⣭⣿⣿⣿ ⠀⠀⡐⠀⠀⠀⠀⠀⣀⣺⣭⣿⢿⣻⣽⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡽⣻⣿⣷⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⡜⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣽⣻⣷⣻⣿⣿⣿ ⠀⠐⠀⠀⠀⠀⢐⣺⣏⣷⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣽⣿⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡻⢗⣿⣿⣿ ⠀⠀⠀⠀⣠⠾⣿⣻⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣾⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣻⣼⣿⣿⣿ ⠀⠀⢀⣒⣾⣿⣳⣿⣾⣶⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣿⣿⣽⣻⢿⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢝⣺⣯⣟

🐺🐾🐶🐕🐕‍🦺

🐅🐾🐆🦁🐯 🐈

🦊🐾

🦝🐾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣶⣤⣔⣶⡶⣦⣤⣠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⡏⠉⣴⣿⢿⢿⣿⢷⣶⣍⡻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡶⢤⣴⣿⠟⠀⢁⡞⠛⡟⢣⠐⢳⡀⠈⢻⣯⡺⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣇⣾⣟⠎⠀⢠⡞⠀⡀⢀⠆⠀⠀⣧⠀⡀⠹⡳⣦⣿⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡸⣻⣟⡟⠀⠀⢸⠁⢀⢧⢸⡾⡀⠶⣿⡿⣳⣅⣼⢻⠙⢿⡶⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠞⠉⡿⢡⢡⠀⠀⣿⠀⣿⣯⣭⣹⢝⡊⢸⠚⢻⠝⢺⣗⢆⣸⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⢳⣮⣣⣤⣄⡟⣇⡿⣻⡿⣿⠉⠻⣜⠐⠿⣛⡻⠿⠿⠵⡳⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡿⢻⢡⡿⣼⡃⢡⠈⣴⠈⠒⠋⠀⠀⠐⠀⠀⠀⠌⡟⡦⣌⡉⠻⡉⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠃⢹⣾⠀⢹⣷⡜⣷⣿⣧⠀⠀⢴⠞⠛⣿⠀⢀⢧⡜⡟⠀⠉⠓⢄⡀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⢸⢹⡆⢸⣿⡛⡷⣝⣽⠳⢦⣌⡓⠀⣢⠔⡡⢻⡋⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠑⠢⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣼⢇⡼⠿⣿⣿⡿⣿⡄⠀⠀⢹⢉⡰⠛⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠙⢶⡀⠀⠀⠀⠙⠢⡀⠀ ⠀⠀⠀⠀⠀⢏⣞⠝⠀⠀⠸⣿⣿⡺⣮⣤⢀⣘⠓⠶⣶⡔⢶⣖⢤⡤⠤⠤⠠⣖⢲⣦⡤⠽⢦⡀⠀⠀⠀⠘⣆ ⠀⠀⠀⢀⢴⣾⡾⠀⠀⠀⢀⠚⣿⣷⡈⠻⣆⡈⠁⢁⣈⣇⠘⣿⣄⠀⠀⠀⠀⢸⠈⡿⡇⠀⠀⠉⠀⠀⠀⠀⢸ ⠀⠀⠀⡎⣫⠟⡇⠀⠀⠀⠘⠀⠈⠻⣿⣶⣾⣽⣲⣗⠋⢻⣦⣿⠀⠀⠀⠀⠀⢠⣤⣆⡧⠤⠤⠄⠤⠐⠒⠂⠁ ⠀⠀⢀⢾⢯⡎⠀⠀⠀⠀⠀⣴⠁⠀⠀⠉⠙⢟⠻⠿⣿⣼⡟⣬⠂⣧⠴⠐⠂⠚⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⡼⢣⣿⡖⠒⠂⠀⠒⡳⠀⠀⠀⠀⠀⠈⠑⠚⠓⣟⣉⣳⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡧⢺⢻⣿⣿⣓⣲⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠫⣆⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡻⡅⠊⣶⡇⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⡿⡾⠈⡇⠀⠀⠀⢸⢇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣴⡀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⣝⠿⣐⡏⠀⠀⠀⣼⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠱⡄⠀⡟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⣿⣿⣯⠀⠀⠀⡟⡇⠀⠀⠀⠀⠀⣀⣀⡀⠤⠬⢆⡿⣄⣃⡈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣿⠀⠀⠀⢱⣷⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠘⠁⢸⠧⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠯⣆⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣳⠟⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡾⢇⠀⠀⠉⠓⠲⠤⠤⠤⠤⠤⠤⠤⠲⢲⣻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠏⠀⡸⠓⢵⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⠛⢀⡞⠁⠀⠀⡞⠉⠉⠉⠁⡖⠀⠈⠹⡍⠉⠈⠙⣞⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡴⡟⠉⠀⡾⠀⠀⠀⡸⠀⠀⠀⠀⢠⠇⠀⠀⠀⡇⠀⠀⠀⠘⡜⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡽⠀⠀⡰⠁⠀⠀⢰⠃⠀⠀⠀⠀⣼⠄⠀⠀⠀⢱⡄⠀⠀⠀⠹⣄⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢨⣿⣄⠀⣴⠃⠀⠀⢀⡏⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⢸⣳⠀⠀⠀⠀⠙⣦⢝⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⢿⣿⣥⣀⡀⠀⡼⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⡟⢇⠀⢀⠀⣀⣌⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⠟⠙⢻⣿⣶⣿⣿⣷⣶⣤⣀⣰⡿⣿⣶⣶⣦⣤⣼⣾⠿⠛⠛⠋⠉⠉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢧⠉⠙⠁⠈⠉⠛⠛⠚⠛⢀⡇⠉⢯⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⠀⠀⠀⠀⢀⢴⠅⡀⣄⠀⠀⠀⢸⡄⠀⠀⠀⠀ ⢸⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⠈⠐⢄⠀⠀⡸⣹⠾⢰⠁⠀⠙⢆⠘⣼⣧⠀⠀⠀⠀ ⠈⡆⠀⠲⣄⠀⠉⠒⠤⣀⠀⡜⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⠀⢱⡞⠀⠀⢠⠃⢠⡇⠀⠒⢧⣏⣿⡄⠀⠀⠀ ⠀⢿⡀⠀⠈⢧⠀⠀⠀⠀⢉⣱⡦⢍⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⢿⠁⠀⣰⠟⠀⠸⣇⠀⢀⠟⠁⠉⢣⠀⠀⠀ ⠀⠁⢳⠀⠀⠀⠳⢀⡠⠖⠉⠀⣀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡼⠁⡞⠀⣸⣫⡤⠀⠤⠏⢀⠎⠀⠀⡇⢸⡀⠀⠀ ⠀⠀⠀⢣⠀⠀⢐⡯⠤⣶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⡇⠀⣠⠃⢡⠀⠀⠲⣾⣀⣀⢠⡇⠀⣇⠀⠀ ⠀⠀⡀⠈⢧⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢳⡐⠁⠀⠹⠆⠀⢸⠓⠒⣿⢸⠁⠀⢹⠀⠀ ⠀⠀⢰⠀⠈⣆⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠉⠲⣤⣄⠀⠠⣸⠀⠀⣿⠀⠀⠀⠸⡇⠀ ⠀⠀⠀⡆⠁⢘⠟⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⣿⡀⠀⡏⠀⠀⠀⠀⣧⠀ ⠀⠀⠀⠸⣄⠎⠀⠀⠀⠀⠀⠀⠐⢶⠄⠀⠀⠀⢀⡴⢊⡤⠞⠁⢀⣤⣴⣶⠶⠶⣤⣄⡀⠀⠀⠘⣟⠓⠀⡇⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⢠⣇⠀⠀⠉⠀⢀⣀⣀⡀⢀⣀⣤⡴⠾⠛⠛⠁⠀⠀⣾⠟⣉⣁⣤⣀⣀⡉⠙⢧⠀⠀⠀⠘⡆⠀⢧⡀⠀⠀⠀⣯⡆ ⠀⠀⠀⠀⣹⣿⡿⠓⠲⣾⡍⠉⢸⣿⣯⡉⠀⠀⠀⠀⠀⠀⣾⣽⣿⡿⢿⣿⣿⣿⣿⣿⢿⡖⠐⠒⠂⠠⢤⣀⡱⣆⠀⢈⡟⠀ ⠀⠀⠀⠀⢹⡁⠀⠀⢠⠛⣷⡰⡟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠁⡞⠋⠀⢿⡟⠻⣿⡿⣣⠎⠀⠀⠀⠀⠀⠀⠀⠉⠉⢙⡻⠀⠀ ⠀⠀⠀⠀⠀⣧⠀⠀⣾⠀⠈⠿⣿⣾⣼⡇⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⠬⢷⣾⡩⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠻⣧⡀⠹⡄⠀⠀⢈⡙⢋⠇⢀⠀⠀⠀⠀⠀⣸⠿⠁⠛⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡷⠗⡶⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣧⡑⢻⣤⠖⢉⠔⣡⣴⠏⠀⠀⠀⣀⠜⠁⠀⠀⠀⠀⢀⡤⠔⠒⠀⠉⠀⠀⠀⠀⠀⣈⣴⠏⠀⣼⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⢳⠻⡶⠋⢀⣴⣿⣿⣿⣿⣤⡀⢀⠖⠁⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡾⠋⠀⠀⠀ ⠀⠀⠀⠀⢰⡶⠚⠷⡇⠀⢿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠠⡾⠁⠀⠀⠀⠀⠀⣀⠄⣀⠴⠛⠃⣰⠟⠁⢈⠟⠀⠀ ⠀⠀⠀⠀⠀⢱⣄⠀⢹⡀⠈⠻⢿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⣀⠤⠒⢙⡷⠊⠁⢀⣤⡾⠁⢀⡴⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣙⣯⠀⢣⡀⢀⣀⣀⣀⡀⠀⠀⠀⠀⣀⠤⢊⡤⠊⢀⡤⠒⠉⢀⡤⠒⠁⠀⠀⠤⢖⡏⠀⣰⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⣏⠀⠀⠙⣿⡛⣿⡏⣻⣿⡷⠖⠒⠒⠊⣡⠴⠊⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠠⠮⠤⠴⢯⠆⠀⣽⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠿⣿⡀⠀⠘⠻⣷⠚⠋⠁⠀⢀⣠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠴⠧⢴⣞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣄⣹⣽⠂⠀⠀⠀⠀⠙⡿⠭⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⢀⣤⣿⠋⠀⠀ ⠀⠀⠀⠀⠀⢸⣆⠈⠙⢧⠀⠀⠐⡖⠒⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠧⠤⡀⠀ ⠀⠀⠀⠀⠀⠚⢿⠇⢠⠠⠱⡑⠄⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⠿⠿⡏⠁⠀⠈⡿⠀⠀⠀⣀⡤⠞⠛⠉⠁⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠛⠻⠿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠉⠳⣄⠀⢸⠀⠀⠀⢸⡧⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⢀⣠⠶⢿⣿⡿⠟⠋⠉⠻⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠉⠉⠈⠣⡀⠀⠀⠀⠀⠀⠈⠳⡇⠀⠀⠀⣀⣠⠤⠤⠤⠤⣄⣀⣀⣀⣠⡖⠋⠀⠀⡠⠋⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⢤⠎⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⣶⣦⣤⣤⣤⣤⣶⣶⣶⠿⠟⠛⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⣀⣀⡀⠀⣿⡿⠿⠟⠛ ⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⢀⡔⠉⠁⠀⠀⢸⠁⠀⠀⠀⠀ ⠈⠻⣿⣿⣿⣿⣿⣷⣶⣶⣶⡶⠁⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢠⠎⠀⠀⠀⠀⢀⡏⣠⠴⠒⠀⠉ ⠀⠀⠙⢿⣿⣿⣿⣿⢿⣿⠿⠒⠊⠉⠁⠀⠀⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡏⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⣿⣿⣿⣿⠇⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠴ ⣄⠀⠀⠀⠈⢿⣿⣿⠃⠀⢀⡴⠋⠉⠉⠉⠙⢦⠀⠀⠀⠸⡀⠀⠀⠀⣠⠴⠀⠀⡀⠀⠀⠙⢄⠀⠀⠘⣆⡠⢾⡏⠀⠀⠀⠀⢀⡔⠀⠀ ⠸⠉⠓⠦⡀⢸⣿⡏⠀⢠⠋⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢀⠃⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠛⢿⡂⢸⡇⠀⠀⢀⡴⠃⠀⠀⠀ ⠀⠤⣄⠀⠘⡞⣿⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠖⠁⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⣇⠀⡠⠋⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠘⢳⡏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⢐⣻⣦⣤⣤⣤⣀⣠⢀⡀⠀⠀⠀⠀⡇⢸⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠛⢦⠀⢸⠀⠀⠘⠷⢤⡤⢄⣀⣀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠃⠀⠀⠉⠉⠛⠻⢷⣤⡀⠀⠀⢱⠞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣞⣴⠏⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡟⢁⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠒⠤⠄⣀⣀⠀⠀⠀⠀⣠⡿⢠⠏⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⢖⣉⠴⠋⠈⠻⡄⠀⡰⠊⠉⠑⢦⣼⣷⣿⣿⣿⣿⣶⣄⠀⣀⣠⡤⣄⠀⠀⠀⠀⠀⠀⠉⠑⠒⠚⠋⠀⡎⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠀⠀⠀⠀⢘⣏⠀⠀⠀⠀⠀⠙⢿⡿⠭⣍⣻⠟⠿⠿⣿⣿⣿⠶⠷⠤⢀⡀⠀⠀⠀⠀⠀⠀⠈⡿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠀⠀⠀⣤⠃⣸⠀⣀⣀⣀⣀⠀⠉⢆⠀⠀⠈⢉⡵⠖⠋⠁⠀⠀⠀⠀⠀⠈⢣⠀⠀⣠⠴⠒⠒⠛⠲⢄⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀ ⠀⠀⠀⠠⢺⡥⠿⡟⠉⠀⠀⠀⠈⠳⣄⣈⣧⡔⠊⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⡼⠒⢹⠃⠀⣀⡀⠀⡤⠀⠙⠢⣤⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠒⣾⠏⠀⠀⠁⠀⠀⠀⣀⠀⠀⠉⠀⠈⠉⠲⣄⠀⠀⠀⠀⠀⠀⢀⡔⠀⣼⠀⡠⠚⢷⡋⠀⠙⢾⡥⢤⡀⠀⠈⢿⣿⣷⠀⠀⠀⠀ ⠀⠀⢠⡇⠀⠀⠀⣀⣦⡴⠋⠀⠙⠢⣄⣀⣀⡀⠀⠀⠙⢦⡀⠀⠠⠔⠉⢀⣼⠉⢠⡇⠀⠀⢳⡀⠀⠈⡆⠀⢱⠀⠀⠘⣿⣿⣷⡀⠀⠀ ⠀⠀⣸⠿⠀⠀⡜⠁⠀⢣⠀⠀⠀⠀⠘⡇⠀⠙⣆⠀⠀⠀⢳⠀⠀⠀⠀⣸⣿⡄⣯⠀⠀⠶⠊⠉⠉⠙⠓⠀⢸⡁⠀⠀⢻⣿⣿⣷⡀⠀ ⢀⣴⠃⠀⠀⢀⣧⠀⠀⠀⢳⡄⠀⠀⠀⡆⠀⠀⠘⡄⠀⠀⠀⠣⣤⠴⠚⠁⠘⠿⣿⣿⡇⠀⠄⠀⣀⣄⠀⢀⡼⠁⠀⠀⢸⣿⣿⣿⣿⣆ ⠈⣿⡆⠀⢀⠏⠉⢣⣄⣀⡜⠉⠉⠀⠈⠉⠒⠤⣞⠁⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠈⢻⣟⣒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢠⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣆⠀⢸⡇⣼⡇⣠⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣦⣸⣿⣿⣷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠳⢾⣷⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⣿⣿⡄⠀⠀⢀⣤⣴⣒⣿⣿⣿⠛⠳⠿⠟⣅⣤⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡄⠀⣿⠉⣩⣟⡃⠀⠀⠀⠀⠀⠀⣾⣿⣁⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣶⣾⡟⠻⢿⣷⡀⠙⢿⣿⠋⢀⣶⠀⢀⡀⢀⣤⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⠃⠀⠈⠉⢳⣀⠈⢙⣿⣟⣛⣶⣏⣡⠿⣟⣻⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣶⠀⠀⢀⣀⣽⡟⠋⢻⡏⠛⣋⣇⣈⠋⠉⠀⠀⠈⠻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⡄⢀⣠⣴⠋⠁⠀⠀⠘⢳⡉⠛⠋⢠⠖⠃⠀⣀⡲⢼⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⡉⠉⠉⠉⣹⢷⣶⣄⠀⠻⣶⡶⠋⣤⣶⣻⢽⣏⢿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣠⠀⡾⢁⣾⢡⡟⣷⠀⠀⠀⣰⠁⡿⣏⠳⣽⡳⣌⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡀⠀⠘⠁⠀⣳⠟⠀⠀⠠⣿⠀⢳⡜⢶⣤⡴⠶⠓⠒⠲⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣠⠞⠁⠀⠀⠀⠀⠹⣆⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆⠀⠀⣀⡀⠀⠀⠀⢰⢠⡀⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣷⣄⠀⣀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢠⡇⠘⠶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣠⣴⣶⣶⣶⣾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣦⣀⣀⣸⣇⠀⠀⠀⠀⠀⠀⣸⣻⡇⠀⣾⠁⠀⠀⠙⠻⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠁⠹⢤⡀⠀⠀⢀⣰⠟⠀⠀⣴⠇⠀⠀⠀⠀⠀⢈⣿⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠉⠉⣽⠋⠁⠀⠀⣰⠏⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣷⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⢀⣸⠁⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⢸⣻⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⡇⠀⠀⣤⠀⠀⠀⢸⣵⠀⠀⣠⠾⡟⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠘⢿⣿⣟⢹⣿⣿⡏⢹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢸⡇⠀⠀⣿⡄⠀⠀⠈⢿⣦⠈⠁⠀⣷⠀⠀⠀⠀⠀⠀⠀⠹⣾⢷⡄⢼⣿⣿⠀⣿⣿⣷⠀⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⣇⠀⠀⠘⠃⠀⠀⠀⢸⡝⢦⡀⠀⣻⡆⠀⠀⠀⠀⠀⠀⠀⠘⡾⡇⣸⢿⣛⣿⣿⣿⣷⣄⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⢀⡼⠃⠀⠁⢰⣶⣿⣿⣿⡿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣤⣤⡤⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢹⣧⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠈⢷⣤⣀⣀⡤⠞⠁⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠙⣤⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠸⡟⣧⠀⠀⠀⠀⠀⡄⣿⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣤⣤⣤⣀⡀⠠⣤⣀⡈⠻⢿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠙⢽⠓⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠁⠘⢧⡀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣏⠉⠉⠉⠁⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⡛⠿⣿⣦⣄⡸⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⢳⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⡭⣤⡀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠈⠛⣍⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠘⣎⠳⠷⢾⡇⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠛⠉⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢹⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠹⣤⣀⣸⠇⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣗⠦⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣟⣒⠄⢀⣳⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠃⠛⠁⠁⣦⣈⣉⣛⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠸⣟⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢧⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⣿⣿⣿⣿⣿⣦⣌⠉⠋⠀⠀⢀⠀⠘⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠳⢤⣀⡀⠀⣀⣀⣽⠯⠟⠛⠛⠛⠛⠛⠿⣾⡀⠀⠀⠀⣌⢧⠀⠈⢂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠘⢮⢳⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⠙⣆⠀⠀⠀⠀⠀⣾⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠈⢿⡻⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠘⣆⡎⠀⠙⣇⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠻⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣀⠶⠤⢄⣀⣀⣿⡇⠀⠀⠘⢧⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡆⠀⠀⠀⢸⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⣾⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠸⠏⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⡀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣧⠀⠸⡄⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣿⡆⢰⣿⣀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⣿⣷⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⡤⠤⣤⣀⣀⣠⣴⣶⣤⠤⢤⡀⠀⠀ ⠀⠀⣇⠀⠀⠀⠀⢸⣿⣿⣿⣶⣾⣷⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠉⠉⠛⠿⣿⡟⠀⠀ ⠖⣺⣀⠀⣤⠀⠀⠀⠀⠀⣤⠀⣐⣟⡒⠂ ⠩⢿⡏⢉⣆⠀⠀⠛⠂⠀⢠⣋⠙⡿⠍⠀ ⠀⠀⠛⡏⣸⣶⣤⠤⢤⣶⣮⢈⡟⠁⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀ ⠀⠀⠀⠸⣦⡀⠀⣸⡀⠀⣠⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠒⢒⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⢀⣀⣀⣀⡀⠀⠀⢧⠀⠀⠀⠀⠀⡴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣰⠿⠒⠋⠉⠉⠀⠀⠀⠈⠉⠓⠾⢄⣀⠀⠀⢠⡇⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣩⠏⠉⠒⢒⣲⡤⠤⣀⣀⠀⠀⠀⠀⠀⠈⠑⢤⡘⡄⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⠀⠀⠀⠀⢰⠾⣣⠴⠚⠉⠉⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣔⡿⡍⡇ ⠀⠀⠀⠀⠀⢸⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⢳⡀⠀⠀⠀⠀⠀⣀⡤⠞⠋⣡⠞⠉⠀⣇⡇ ⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠛⠓⠚⠉⠉⠉⠁⠀⣴⡟⠁⠀⠀⠀⣿⠁ ⠀⠀⠀⣼⣁⣠⡤⢴⠖⠒⠒⠦⠤⢴⣶⣢⠤⠤⠔⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡞⠀⠀⠀⠀⢰⢿⠀ ⠀⠀⠀⠉⠉⢙⣦⠞⠀⡠⠞⠉⢉⡷⡄⠉⢙⡶⠃⠀⠀⠀⢀⣠⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⡼⠀⠀⠀⠀⠀⡜⡞⠀ ⠀⠀⠀⣤⡖⠛⠀⠀⡜⠁⠀⡴⢋⣀⣹⣠⠋⠀⠀⠀⠀⣰⣿⠿⠛⠛⠿⣿⣷⣄⡀⠀⠀⠀⠀⠀⡼⢰⠃⠀⠀⠀⠀⡼⢱⠃⠀ ⠀⢀⣴⠛⠀⠀⠀⢼⠁⠀⣼⢁⣿⡬⣿⠃⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⣸⢃⡏⠀⠀⠀⢀⡜⢡⠏⠀⠀ ⠀⠸⡿⠀⠀⠀⠀⢻⡀⠀⠀⠀⠉⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠁⣀⡜⠁⡼⠀⠀⠀⡠⠋⣰⠋⠀⠀⠀ ⠀⠀⣧⠀⠀⠀⠀⠈⢳⣀⣙⣦⡤⠋⠀⠀⠀⠀⠀⠀⠀⣰⠄⠀⠀⠀⠀⠀⠀⢤⠀⣹⠌⢩⠏⢠⣇⣠⠴⠊⢀⡼⠁⠀⠀⠀⠀ ⠀⠀⠘⡆⢀⡴⠖⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⣾⣷⣿⣿⣿⣷⣦⡀⠀⢸⠀⠻⣾⠉⠀⠀⠀⠀⢀⣠⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡟⣥⠤⠦⠤⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠛⠿⣿⣿⣄⣸⠀⠈⠻⣇⠀⢀⣀⠤⠟⠓⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⡆⢧⡀⠀⠀⠀⠀⠀⠈⠙⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⣸⡍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢳⡄⠙⢦⡀⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢦⣀⣉⣷⡚⠉⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣦⣴⠚⢁⡾⠋⠉⠳⢤⣀⢀⣀⣀⣠⠔⠋⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⠁⢀⣺⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣷⡇⠀⡞⠀⠀⠀⠀⠀⡼⠋⠉⠁⠀⠀⣀⣀⠤⠴⠒⠊⠉⠉⠀⠀⠀⠀⠀⣼⣿⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢯⡛⢦⡀⠀⠀⠀⢀⡾⠥⠤⠔⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⣸⣹⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡿⠀⢹⣶⣶⣖⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡿⠿⠉⠉⠋⠀⠀⠉⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠹⢤⣀⣀⣀⣀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠙⠋⠩⠿⢿⣁⠀⠀⠀⠀⠀⠀ ⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠉⠑⠶⢤⣀⣀⣠⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣅⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀ ⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡀⠀⠀⠀⠀⠀⢀⡾⢷⡀⢰⡇⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠃⢸⠙⢆⠀⠀⠀⠀⢸⠁⠀⠙⢦⡇⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢠⠛⠀⢸⣷⡀⠀⠀⠸⡄⠀⢠⣼⣿⡀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⡇⠘⡄⠀⣸⠀⠹⣄⠀⠀⣿⣀⣾⡿⢿⣿⣿⣶⣶⣿⣷⣼⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⢿⠲⣄⡇⠐⠃⠀⣧⠀⠀⠙⣧⣤⣿⣿⢧⡇⢨⣿⡿⢛⣡⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⠀⠀⠘⡄⠈⢿⡓⠢⢤⣽⣷⣤⣶⣿⣿⣿⣿⣿⣠⣾⠿⠖⠛⠛⠻⠶⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡀⠀⠸⡁⠀⠀⢻⡄⠀⠀⠀⠈⢿⣿⣿⣿⠟⡋⠁⠀⢀⣠⣤⣴⣶⣶⣶⣼⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢱⡀⠀⠀⠻⣦⡀⠀⢀⣸⣿⠟⣱⠋⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠟⠻⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢹⠅⠀⠀⠘⣿⡿⣿⡿⣫⠞⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠈⠢⡀⠀⠀⠈⣻⣿⣷⠃⠀⣴⣿⣿⣿⣿⣿⣿⡿⣟⣭⡤⣤⣀⠀⠀⠀⠀⢄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠘⠖⠀⠀⣽⠃⠀⢰⣿⣿⣿⣿⣿⣿⡽⠟⠉⠀⠀⠀⠈⠙⢦⡀⢀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢳⣤⣀⢘⣷⣄⡀⠀⠀⠀⠀⠀⣿⣤⣤⣾⣿⣿⣿⣿⣿⣿⣁⣀⡤⠀⠀⠀⠀⠀⠀⣳⢸⣿⣶⣄⠀⠀⠈⠳⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡏⠛⠛⠯⣽⣇⠉⠑⠒⢲⡞⠉⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⣵⣿⣿⣿⣿⣷⣤⣀⣀⣸⣷⣤⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠹⣆⠀⠀⡞⠀⠀⠀⠀⠀⠀⠘⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⠀⠀⠀⠀⢤⣤⣿⣿⣿⡒⠶⠼⣷⣤⡇⠀⠀⠀⠀⠀⠀⠀⢸⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀ ⠀⠀⠀⢠⣶⡶⠿⠤⠶⠶⠉⣋⣉⣙⠋⠉⢿⡀⠀⠀⠀⠀⠀⢸⢘⣿⣿⣿⣿⣿⣿⣿⣝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⡀⠀ ⠀⠀⠀⠈⢻⡀⠀⠀⠀⢀⣀⣈⣉⣉⣍⠁⠀⠻⣷⢤⡀⠀⠀⠘⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠽⢻⠃⠀ ⠀⠀⠀⠀⠀⠹⢷⣦⣤⣤⣭⣍⠉⠀⠀⢀⣴⢖⣊⣛⣶⣤⠶⢺⡟⠳⠤⣉⠙⢿⡿⢿⣿⣿⣿⣿⣶⣌⠙⠿⢿⣿⡿⠛⠛⣁⡴⢷⠃⠀ ⠀⠀⠀⠀⠀⠀⠤⣾⠋⣩⡴⠶⠛⠒⢚⣿⢟⣩⡥⠤⠉⠉⠛⢶⡝⢦⡀⠈⠙⢦⣀⠀⠀⡉⠉⠉⠉⠙⠛⠒⠚⠉⠀⠀⠉⢁⡴⠃⠀⠀ ⠀⠀⠀⠀⠀⣠⢴⣷⠞⠁⣰⣿⠖⠋⠉⢀⣋⣤⣶⠶⠶⣤⣀⠀⠙⢦⣙⡂⠀⠀⠈⠹⣶⠈⠙⠂⠀⠀⠀⠀⠀⠦⣍⣑⣺⠟⠓⠤⡀⠀ ⠀⠀⣠⠔⠋⢀⡾⠁⣠⣾⡿⠁⠀⣠⣾⠿⠏⢠⣤⣄⡀⠰⣍⠉⠑⠲⠤⣍⣙⠲⠤⠀⠈⠷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣤⣀⠈⠂ ⢀⠜⠁⠀⠈⠙⠋⠹⢻⣿⡇⢀⡞⣿⣥⣶⡏⢻⡏⠙⠿⣷⣾⢧⣀⠀⠀⠀⣀⣉⣉⡉⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⠷⠂ ⠋⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⡞⠀⠋⢠⣿⡇⢸⣿⠀⠀⠈⠙⠲⣌⡑⠲⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣛⣿⣦⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠃⠀⠀⢸⡏⡇⠈⣿⠀⠀⠀⠀⠀⠀⠙⠲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠖⠊⠉⠀⠉⠻⡿⡿⣍⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⡾⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠙⢦⣧⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⡄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡀⠀⠈⠛⠲⠤⣄⣈⠙⠳⠤⣀⢀⣀⡤⠤⠶⠛⠁⢰⣷⢿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡟⠳⣄⠀⠀⠀⠀⠉⠙⠳⣤⠟⠉⠁⠀⠀⠀⠀⠰⢟⠁⣸⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⡇⠀⣨⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⣷⡀⠙⠳⣤⠤⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣻⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣹⣧⣸⡷⣌⠉⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⡿⢿⡏⢹⣄⣀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠳⢿⣿⡇⠈⠛⢧⡄⠀⠀⠀⠀⠀⠀⠐⠟⠛⠛⠿⢿⣿⣧⠀⠀⠀⢿⣿⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣀⣿⢷⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣉⣀⣀⠀⣀⡌⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠿⢧⣍⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢿⠋⣩⡍⢉⡿⠟⣡⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⢥⣄⡀⠀⢀⡾⢻⠀⠀⠀⠀⠀⠀⠸⠿⠷⠋⢁⣤⠞⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡇⠙⠻⠗⢚⡏⠀⠀⢠⠄⠀⠀⢀⣠⠴⠛⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡤⠤⠤⠤⠴⠚⠛⠋⠉⠉⠙⠛⠓⠲⠤⠤⠴⠞⠁⠀⠀⠀⣸⠃⣀⣴⠟⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠦⠤⠤⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠛⠙⠛⠶⠒⠋⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣆⠙⢯⡙⠒⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⡆⠀⠑⣄⠀⠀⠉⠓⠶⣤⣀⠀⠀⠀⠀⠀⣸⣆⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠤⠤⡶⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⢷⣛⣳⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠤⢴⡿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠘⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠸⡇⢤⣓⣮⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠗⠲⢶⢤⣄⠀⠀⠘⡇⠀⠀⠀⠀⠀⠐⡗⢲⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣷⡲⠶⠆⠀⠀⠀⠀⠀⠀⠀⣀⡾⣵⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠸⡆⠘⠿⣟⣩⡇⠀⠀⠀⠀⠀⠀⣧⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠤⠤⠤⠤⠤⠔⠛⠟⠋⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⣇⠀⠀⠁⢿⡆⠀⠀⠀⠀⠀⠀⢻⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⢀⣾⣇⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⣴⠟⠁⢹⡄⠀⠀⠀⠀⣼⠃⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⢸⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⡾⠃⠀⠀⢠⡇⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠘⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢀⡟⠁⠀⠀⠀⠸⡆⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⣿⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢿⡀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠸⡖⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⢳⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⡄⠀⣈⡇⠀⠀⠀⠀⠀⠀⠘⣧⡲⡆⢸⣳⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⡆⠀⢎⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠈⢻⠛⠚⠟⣁⠀⠀⠀⠀⠀⢀⣀⣈⣉⠉⢙⠋⣀⠀⠀⣀⣀⠀⠀⠀⠀⢉⡉⠉⠙⠉⢁⣀⠀⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣹⣿⣿⣫⢿⣿⣿⣿⣿⣿⠒⠒⠊⣿⣿⣹⣿⣹⣍⣿⣃⣀⣿⣻⢿⣿⣿⡿⣹⣿⣿⣿⣿⡏⣏⣽⣿⣻⣿⢿⣃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⢀⣀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠈⠁⢉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢒⣴⡶⣄⠀⡀⠀⠀⠙⠋⠉⠀⠀⠀⠀⠀⠀⣠⡶⣋⣯⡭⠉⠳⠤⠤⠤⠶⣽⣄⠀⣤⣤⣤⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡜⣀⣤⣤⡾⠁⣀⢙⣷⣄⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⣴⢯⠉⠉⠀⠀⠈⠛⠒⠒⠀⠀⠀⠀⠛⠉⠛⢧⣷⡆⠀⠀⠀⢀⡤⢄⠀⠀⠀⠀⢀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢁⢠⠟⠀⠀⠈⠻⣍⠻⣝⠦⡜⠂⠀⠀⠀⠀⢀⡞⠱⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢞⣀⣀⡀⢠⢖⣭⠟⠛⢳⣄⠀⠀⠈ ⡇⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠠⢯⡟⣀⣤⡤⠤⠔⠚⠦⡈⢳⡈⠣⣝⠆⢀⣴⠋⠀⢠⣤⣄⡀⠀⠀⣤⣤⡀⠀⢀⡄⠀⠀⠈⠉⠉⠁⣈⣩⣷⠞⠋⠁⠀⠀⠀⢹⡄⠀⠀ ⡇⠀⠀⠠⠀⠀⠙⡲⠄⠀⠀⠀⠀⢠⡟⠘⠛⠒⠲⠒⠀⠀⠀⠀⢀⣱⡄⠈⠓⠛⢒⠛⡛⠛⠛⠛⠛⠛⠒⠲⠤⠥⣌⡉⠙⠦⠀⢀⣳⢔⣻⠟⣫⠗⠒⠘⠁⠀⠀⠀⠀⢻⠀⠀ ⡇⠀⠀⠀⡀⠀⠻⢦⣀⣀⠀⠀⣀⣾⠁⠀⡴⠋⠁⠀⣀⣠⠶⠚⠉⠉⠁⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠖⠉⡰⠛⠁⠀⠀⠀⠚⠲⠶⠦⣄⠀⠀⠾⡇⠀ ⡇⠀⠀⠈⠀⠀⠀⠀⠈⠉⠙⢋⣹⡟⠀⠐⠂⣴⢋⢴⠉⠀⠀⠀⠀⣠⠞⢀⡼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠂⠀⠀⠀⢻⡁⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⠀⢳⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏⣏⡇⠀⣠⠞⢁⡿⠋⠀⠀⣀⠀⡰⠃⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠃⢀⡶⠀⠀⠀⠀⠙⠘⡄⠀⠀⠀⠀⠻⣽⠀⠀⠀⠀⠀⢸⡆ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣡⠞⠁⣴⠋⠀⠀⠀⣴⠁⡼⠁⣰⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢀⠀⠀⠀⠀⢠⡀⠘⢶⡄⠀⠀⠀⣈⣧⠀⠀⠀⠀⢸⡇ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠫⢀⡴⠁⠀⠀⠀⣼⠁⠈⠀⡰⠃⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡇⢸⠀⠀⠀⠀⠀⢳⡀⠀⠙⢦⠐⣆⢻⣿⠀⠀⠀⠀⢸⡇ ⡇⠀⠀⠀⠀⠀⠀⠀⠉⢁⡴⠋⠀⣠⡞⠁⡜⠀⠀⣠⡇⠀⠀⡰⢃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⡇⣧⡆⠀⠀⡀⠀⢋⢧⠀⠀⠈⠧⠍⢾⣄⠀⠀⠀⠀⡀⠃ ⡇⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢠⡞⡿⠀⣸⠃⠀⣴⠋⠀⠀⢰⠃⠀⠀⣇⠀⠄⠀⠀⠀⠀⠀⠀⠀⣄⣴⣿⠃⠀⠀⣿⢻⣧⠀⠀⢹⠀⠘⣾⡇⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⢠⠀ ⡇⠀⠀⠀⠀⡤⢀⡾⠁⢀⡾⠃⢸⠃⢠⡇⠀⣴⠃⠘⡀⢰⠏⢀⣤⡴⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠙⠓⢦⣹⢸⢻⡀⠀⠀⣧⠀⢹⢷⠀⠀⠀⠀⠀⠘⡝⣄⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⣴⣿⡾⢣⡿⠀⠀⡏⠀⣼⠁⣠⠃⢀⠠⣷⢿⠛⠉⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⢰⢰⠇⠀⠀⠀⠀⠀⠙⣦⡏⣧⠀⠀⢻⠀⢸⣾⡇⠀⠀⠀⠀⠀⣿⠙⠆⢠⠁⠀ ⡇⠀⠀⠀⣼⣿⠏⢠⣿⠁⠀⢸⡇⡼⡇⢀⡟⠈⠀⠀⠉⠛⠖⠀⠒⠒⠲⠾⣧⠀⠀⠀⠀⢀⣿⣿⠀⠀⣀⠤⠄⠀⠀⢿⣿⠹⡦⠀⢸⡆⠈⣿⡇⠀⠀⠀⠀⠀⢹⠀⠀⢹⠀⠁ ⡇⠀⢀⣾⣿⡏⠀⣿⣿⠀⠀⢸⣿⠃⢳⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠸⣷⣄⠀⠀⡿⣿⠃⠀⠈⠁⠀⠀⠀⠀⠈⣿⡀⢻⡀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠸⠀⠀⠸⡆⢀ ⡇⠀⢸⣏⣿⠀⠀⠉⡿⠀⠀⠘⢯⢰⡟⠿⣄⣀⣤⣶⡶⠶⠶⠶⢶⣦⣐⡆⠀⠀⠈⠳⠶⠇⠿⠀⠀⢈⣉⣱⣖⡢⠀⡀⠈⣷⠀⢷⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿ ⡇⠀⠈⣼⠁⠀⠀⣸⠁⠀⠀⠀⠀⢸⢠⣤⡿⢿⠿⠇⢀⣀⣀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠐⠀⠈⠑⠛⢛⣛⠛⠛⠻⠿⣶⣌⡶⡸⣾⢇⠀⠘⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⡇⠀⢰⠇⠀⠀⠀⡟⠀⠀⠀⢠⠀⡇⠈⠛⢧⣤⡷⡄⠦⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠡⢬⣟⣶⠶⠒⠺⣿⣿⣿⣯⣼⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⡇⠀⠘⠀⠀⠀⣸⠁⠀⠀⢀⡎⢸⡇⠀⠀⠐⠒⠚⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠒⠛⢁⣬⡿⢿⡆⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⣸⢃⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⡼⠀⠀⡼⠃⠀⠀⠀⣴⠀⠀⠀⠀⣾⣿ ⡇⠀⠀⠀⠀⢠⡇⠀⠀⢀⡇⣸⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⡼⠁⠀⠀⠀⢠⣇⠀⠀⠀⠀⣿⣿ ⡇⠀⠀⠀⢀⣼⠀⠀⠀⢸⢻⡿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠖⠒⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⡼⠁⠀⠀⠀⠀⠬⠀⠀⠀⠀⢠⣿⣿ ⡇⠀⠀⠀⣼⣿⡀⠀⠀⣸⣾⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⢼⣶⣶⣶⣶⣤⣉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢠⡞⠁⠀⠀⠀⠀⠀⠀⠐⢺⠀⠀⢸⣿⣿ ⡇⠀⠀⢀⣿⣿⡇⠀⣠⣿⣿⣽⢾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣄⣨⣿⣿⣿⣿⣿⣿⣿⣮⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⡾⢿⡟ ⡇⠀⠀⣼⡟⣿⡇⢠⣿⣿⢿⣿⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢠⠾⢁⡤⢁⡤⢠⠀⡀⠀⢀⠀⣀⢔⡾⠁⠀⣸⣱⠈⠃ ⡇⠀⢰⣿⠀⣧⣧⠈⠘⣾⣿⣿⡄⠈⢧⡀⠀⠀⣠⠶⠒⠶⣄⠀⢿⣿⡿⠋⠉⠛⠛⠉⠉⣿⠟⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠈⠀⠚⠀⢈⣉⠁⢠⠞⢉⡵⠛⠀⠀⣰⢟⡁⠀⠀ ⡇⠀⢘⡏⠀⢿⣿⠀⠀⣿⠋⢿⡁⠀⢸⣷⡀⠸⣅⠀⠀⠀⠌⠀⢸⣿⣀⠀⠀⠀⣀⣀⣴⠟⠀⠀⠀⠀⠀⢀⣴⠏⣱⠂⠀⠀⠀⠀⢀⠀⠁⢠⣬⡴⠋⠁⠀⣠⢧⢿⡄⠈⠙⠲ ⡇⠀⢸⡇⠀⠘⣿⣇⡃⣿⠀⢸⣧⠀⣼⢿⣿⣤⠈⠓⠒⠚⠀⠀⠀⠐⠒⠭⢭⡭⠒⠋⠈⠀⠀⠀⠀⢀⣴⠛⢡⡾⠁⠀⠀⠀⠄⠠⠐⠀⢠⣿⠋⡔⠀⠀⣰⢏⣿⣇⠀⠀⠀⠀ ⡇⠀⠈⡇⠀⠀⠘⣯⡄⢽⡄⢸⣿⠛⠃⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢀⡴⠋⢠⡼⣿⣷⠦⠖⣺⠟⡗⠀⠀⢀⣿⢳⡼⠃⠀⣰⢧⣿⠙⣧⠀⢀⣤⣄ ⡇⠀⠀⣧⣀⣤⣤⣼⣿⡈⣷⣾⠟⠁⠀⠀⠀⠀⠀⢙⣷⣤⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⡴⢋⣤⠞⠃⣰⡿⠃⠀⠤⢯⠋⠃⠀⢠⣿⣣⡟⠁⠀⣰⣯⡟⡇⠱⡙⣄⠀⠈⠉ ⡇⠀⠰⣽⡀⠀⠀⠀⠻⣿⣼⡝⠓⠦⣄⡀⣀⣀⣤⣾⣿⣿⣗⢀⣀⠀⠀⠀⠀⠠⠧⠴⠿⢷⣛⣉⠤⠴⢚⡟⠃⠀⠐⣿⡟⠀⠀⢀⣿⣷⣿⠅⠀⣰⣿⡇⣿⠁⠀⠙⢿⣄⣀⡀ ⡇⠀⠐⠚⠋⠀⠀⠀⠀⠙⠾⠷⠂⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣧⠉⠓⠶⠶⠶⠶⠖⠒⠉⠉⠉⠀⠀⠀⣼⠁⠀⠀⠀⠹⠛⠆⣰⣿⢿⣿⠏⢀⣾⣻⣻⣠⠿⠖⠊⠉⠉⠉⠉⠉ ⡇⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠨⣛⣿⠟⣿⣿⣿⣧⣴⣶⣄⣀⣤⣤⣤⣦⣤⣤⣤⣶⡞⡁⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⠏⣰⣾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡟⠀⢸⡀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⣠⠞⢡⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢰⡇⠀⠀⣇⠀⠀⠀⠈⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⣰⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠖⢚⣿⠞⠁⠀⢸⡄⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠈⣿⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⣾⣇⠀⠈⡆ ⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⡁⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⠀⠀⢀⣀⠤⠔⠛⠁⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⣰⠇⣿⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢸⡇⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠴⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⣠⠏⠀⢿⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠈⣇⠀⠀⠀⢮⡳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢠⣤⣤⣤⣤⠶⠛⠉⠀⠀⠀⠀⠀⡴⠋⠀⠀⣼⠀⠀⢻ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⡄⠀⠀⢸⡏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠾⠯⠶⢻⠂⠀⠀⠈⠉⠻⠦⣄⣀⠀⠀⠀⠀⡴⢋⣴⠆⠀⠀⣿⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠳⡄⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀⣀⠀⣀⡞⠀⠀⢀⣀⣀⣀⠀⠀⠉⠉⠛⣲⡾⠟⢹⠃⠀⠀⠀⣿⠀⠀⡟ ⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠹⡦⠤⠤⠿⠦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠈⠉⠁⠀⡤⠚⠋⠉⠀⠙⠻⣦⠀⣠⠞⠃⠀⠀⡿⠀⠀⠀⢸⠏⠀⢀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡽⠚⠁⠀⠀⠀⢠⡇⢀⣠⣄⡼⠀⠀⡾⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠤⠤⠤⠖⠒⠚⣩⣽⡿⠀⠀⠀⢀⣠⡾⠓⢉⣟⡾⠃⢀⡼⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣷⡶⠮⣷⣄⠀⠀⠀⠈⠙⠆⠀⠿⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋⠁⠀⠀⠀⠀⠈⠀⢀⣴⠟⢋⣠⣶⣋⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠈⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⡑⢄⠀⠀⠀⠀⠀⠀⠀⢰⠂⣠⣶⠟⠋⠀⠀⠀⠀⣀⣀⡀⠀⠀⠋⠉⠀⠉⠁⠀⠀⣠⡾⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣈⡻⣮⣧⠀⠀⠀⠀⠀⠀⣿⣾⣋⣀⣤⣴⣶⠿⠿⠟⠛⠛⠃⠀⠀⠷⢤⣄⣀⣀⣤⣞⣡⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠶⠭⠿⠶⠒⠒⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⣻⣿⣿⠦⠖⠒⠒⠒⠶⣿⣿⡛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⡿⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣏⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠉⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⢀⣤⡴⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠈⠳⣄⣀⡀⢀⣀⣠⠾⠁⠀⠀⠀⠀⠀⠀⣀⣾⠏⠀⠀⢠⣶⢿⣯⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⢉⣁⣀⣀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠈⠉⡏⠁⠀⠀⠀⠀⢀⣀⣠⣴⠾⡟⠁⠀⠒⢻⡟⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠈⠻⣄⡀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⣀⣤⡶⢿⠛⠛⠛⠛⠛⠛⢻⠁⠙⠲⠇⠀⠀⠴⢯⡤⠻⢶⣤⣄⣀⣈⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣥⡀⠀⠀⠀⠀⠸⡞⠛⠒⠂⠀⠀⠀⢯⣻⠶⣶⠶⠟⠋⠁⠀⠘⡆⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠈⠙⢮⡉⠉⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠲⢶⡶⠟⠲⠤⡄⠀⠀⠀⠈⠁⠀⠈⣆⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠈⠁⢀⣠⣤⠤⠶⠶⠦⢽⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⠀⠀⣀⣠⠞⠁⠀⠀⠀⠀⣀⣴⣞⣉⣀⣀⣀⣀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣥⡤⢤⣤⣤⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠀⠀⠀⢀⣠⠴⠛⠁⠀⠀⠈⠀⠀⣠⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣛⠛⠋⠉⠉⠀⠀⠈⠉⠛⠓⠶⠦⢤⣤⣀⣀⣀⣀⠀⠀⣀⣠⣴⣶⣾⠋⠁⢀⣀⣀⣀⡀⢠⣴⣞⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠦⠽⠗⢲⣤⣶⠶⠚⠛⠳⢶⣦⣄⡀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣧⡶⠟⠛⠉⠉⠙⠛⢶⣅⠉⠙⠓⠶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⢀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣄⠈⠙⠛⠻⠟⠛⢫⣵⠾⢋⠏⠀⠀⠀⠀⠀⠀⢠⡏⠙⣷⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⢀⣴⠟⠁⢀⡎⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⡛⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢀⣀⣀⠀⠀⣀⠀⠀⠀⠀⠈⢻⣧⣀⡾⠃⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⣀⠘⢷⡄⠀⠙⠳⣄⠀⠀⠀⠀⢀⡴⢻⡇⣠⠞⠋⠉⠉⠛⢯⡝⠀⠀⠀⠀⠀⠀⠙⡿⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⣿⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠙⠓⢾⣷⡀⠀⠀⠘⢷⠀⢀⡴⠋⢀⣼⡷⠋⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⢀⣿⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠀⠀⠀⢸⡾⠋⠀⠀⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣯⣤⣄⡀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⢀⣼⠋⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⢸⠓⢶⠋⢀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠹⣦⢤⡤⠀⠀⡾⠀⠀⠀⠀⢠⢄⣠⠇⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢸⠀⢸⣟⣹⡟⠀⠀⠀⠈⢁⡀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⡺⠁⠀⠀⠀⢀⣼⡟⠛⠉⠉⠛⠛⠦⣞⡁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡌⠀⠇⢁⠈⠓⢄⡀⠀⠀⣀⠔⠈⠀⠀⡜⠀⠀⠀⠀⠀⢤⡦⠊⡆⠀ ⠀⠀⠀⠃⠀⠀⠸⠀⠀⠀⠉⠑⠊⠀⠀⠠⠄⢊⠀⠀⠀⠀⠀⢀⠎⠀⢰⠃⢐ ⠀⠀⠀⡀⠀⡆⠀⡷⣄⠀⠀⠀⠀⠀⠀⡀⢀⡙⡀⠠⢤⡤⠒⠁⠀⣰⠁⠀⠘ ⠀⠀⠀⢇⠀⠘⣄⠰⣀⠀⠀⠀⠀⠀⠀⢰⠠⠤⢃⠠⠤⢄⠁⡲⠒⡏⠀⡄⢸ ⠀⠀⠀⠈⢄⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣀⡀⠤⣼⠋⠀⡠⢤⡦⢁⠆ ⠀⠀⠀⠘⢇⠓⠄⠀⠁⠁⠒⠢⢄⣄⠀⠀⠀⡀⣠⠖⠋⢀⣀⠀⠐⠊⠒⣳⠆ ⠀⠀⠀⠀⢮⠶⠤⠀⠀⠒⠒⠒⢒⡿⠦⠤⠤⢿⡓⠚⠉⢉⠀⠀⠁⢐⠾⠃⠀ ⠀⠀⠀⠀⠈⠑⣤⠄⠀⠀⢀⠀⠊⠣⠄⡀⠤⠃⠀⢀⣠⠎⣀⠶⢎⡁⠀⠀⠀ ⠀⠀⠀⠀⣤⠊⠀⢙⠄⠀⠘⣦⣀⡠⠴⢳⠒⠒⢸⠉⠂⠀⠪⠒⢤⠬⠆⠀⠀ ⠀⠀⠀⠀⠀⠉⢁⠖⠑⠂⠀⠈⠈⢆⡀⠀⠀⡠⠊⠀⢀⡡⠐⢒⡒⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠖⠒⠒⠂⠤⢄⣀⣀⡉⣁⣠⡄⢊⣁⡀⣠⡂⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡉⡹⠋⠉⠉⠑⢦⡙⠛⠟⣻⢟⠋⠁⠀⠸⠳⣈⠝⠀⠀⠀⠀ ⠐⣖⠦⡀⠀⠀⠈⡇⢀⠀⣀⡀⠀⠙⢦⡜⠁⠎⠀⠀⢀⠃⠀⡧⡀⠀⠀⠀⠀ ⠁⠚⠆⠈⢂⠴⢪⡗⠁⠀⠀⢣⡀⠀⠀⠀⡘⠀⠀⢀⠆⠀⢀⡇⢱⠀⠀⠀⠀ ⠀⠀⠀⢠⠋⠂⢪⡄⠀⠀⠊⠁⠈⢳⠂⠠⠀⠀⡶⠮⠤⢄⡎⠀⠀⡇⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⡍⠈⠉⠉⠉⡉⣈⣿⣿⣉⣭⡭⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢻⣦⣀⣀⣾⢿⡿⠉⠡⠎⠉⢙⣦⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢈⣇⠈⠻⣿⠛⠓⠚⠴⣾⡯⠭⣔⣪⣭⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠃⠈⢻⠂⠀⢸⢀⡀⠀⠀⠻⣿⡉⢳⣜⣯⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⡠⢿⣧⠁⢻⣦⣭⣽⣟⠦⢸⣷⣸⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣻⣷⣄⣹⡉⠉⢷⣿⣻⡟⠀⣸⣿⣿⣿⣾⣍⠉⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⢿⡄⠀⠀⠈⠉⠀⣿⣿⣿⡟⢻⡇⣭⡳⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⡸⡗⣄⠀⠀⢠⣀⣿⣿⣿⣿⣦⣹⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣳⣾⠿⠓⢲⣟⣲⢤⣿⠁⠀⠀⢸⣿⣶⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⡿⠛⠳⢼⣿⠾⢿⣿⡄⠀⠀⠘⡹⠇⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠋⠻⣿⣶⣦⡈⠉⠳⣼⠻⣷⣤⣄⣰⢿⣷⣶⣤⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠄⠀⠀⠈⠻⣷⠚⠋⠙⠣⢤⡙⠓⠻⣟⠛⠲⢧⣴⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠘⣆⢀⠀⠀⠀⠙⢦⡀⠈⢳⣤⣾⢠⡿⣻⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡀⠀⠀⢀⣼⣯⠀⠀⠀⠀⠀⠳⠦⣼⢿⠃⠈⠀⢹⣺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠶⠶⠛⣋⡼⢧⡀⠀⠀⢀⣀⡽⠿⠟⠦⠀⣀⣾⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣩⡟⠁⠀⣠⡷⠒⠚⠉⠉⠀⠀⢀⣤⠖⠉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⡼⠁⠀⠀⠀⠀⢀⡤⢺⡋⢸⡧⠞⠁⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣼⣁⠀⠀⣠⡴⠛⠉⢀⣼⣷⠚⢷⡀⣀⣤⠤⠒⠛⠋⠉⠀⠀⠀⠀⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⣛⣻⠿⠯⠽⣹⣧⠤⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⡭⠤⢤⣠⡾⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣀⠀⠀⠀⠀⠀⠀⠀⣸⢋⣁⣤⣾⢟⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠤⣄⣀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣽⣒⣶⣶⣶⣶⣾⡏⣩⣟⡟⠁⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠉⠑⣄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⣶⠭⣉⡤⠴⠂⠈⠉⠉⣽⡇⠁⠈⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡄⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠟⢁⣠⠞⠋⠀⠀⠀⠀⠀⠀⠉⣧⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⢀⡜⠁⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡞⠁⠤⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⡟⠲⣤⣀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠟⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠋⠳⢦⣀⣈⣻⣷⣄⣀⣀⣤⡾⠯⠤⠤⠤⡾⠃⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠈⠛⢦⡘⢦⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀ ⠀⢠⡏⠀⠀⢸⡀⠀⠀⠀⠀⡠⠶⡖⠉⣽⡟⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠈⢳⡀⠁⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀ ⠀⢸⡁⠀⠀⢸⠃⠀⠀⠀⠊⠀⠀⢀⣰⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢹⡀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⣄⠀⠀⠀⠀⠀⠙⢦⣀⡀⠀ ⠀⢸⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⢠⣿⡋⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠾⣍⣿⣷ ⠀⢸⣿⣶⠀⠀⣴⠀⠀⢀⣀⡶⠋⢸⠇⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⣤⣼⡿⠏⠈ ⠀⢸⣿⢻⣶⡀⠀⢀⣤⠿⠋⣄⣲⣇⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⣿⣷⠀⠀ ⠀⠀⢹⡞⡏⣿⡀⠀⠁⢀⣴⣿⣿⣫⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⣿⠿⠃⠀ ⠀⠀⠀⠻⣿⠘⣿⣀⣰⣫⠞⠁⠳⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣄⠀⠿⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⠁⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢶⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠐⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⠅⢰⠀⢠⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣧⣼⣪⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣄⣤⣠⣀⣄⣤⣠⣀⣄⣄⣀⣀⣁⣠⣀⣠⣀⣀⣀⣠⣀⣄⣤⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣥⣴⠿⠛⠋⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠉⠁⠀⠀⠀⠀⢰⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠂⡰⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⡀⠀⠐⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠦⣄⠀⠀⠀⢀⣠⠴⠚⢁⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢀⣠⡄⠀⠀⣶⠀⠀⠀⠀⠀ ⣿⣿⣿⣶⣤⣄⣀⡀⠒⠠⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⡟⢳⡘⢦⣤⠞⠉⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣠⡾⣻⡇⠀⠀⢻⡄⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠲⢤⣄⣉⡉⠐⠒⠠⠤⣤⣄⣀⣀⠀⠀⣠⠇⠀⠀⢳⡀⠙⢦⡅⠀⣠⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠇⢠⠿⣇⠀⠀⠈⠇⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣿⣿⡿⠛⠲⠶⣤⣄⣀⠈⠉⠉⠉⣀⣀⣠⠬⢧⣄⠀⠈⠙⠳⠿⢷⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⡿⣿⡆⠎⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⠟⢁⠀⠀⠀⢀⣀⣭⠿⠟⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠾⠋⢀⣿⠇⢀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠸⣿⡋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⣧⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠚⡇⠀⢹⡀⠀⠀⠀⠀⠀⢠ ⠿⠿⠿⠿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣷⠙⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡹⡆⠀⠀⠀⠀⠀⢠⣿⣿⠀⢠⡇⠀⢸⠃⠀⠀⢀⣀⣠⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⠀⠀⠀⠀⢠⠟⣸⠃⠀⢸⢀⣀⡾⠞⠛⣿⣿⡟⠋⠀ ⣀⣀⣀⣀⣀⣀⣀⣠⡄⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣰⡿⠀⠀⣴⣟⣉⣠⠄⣾⡟⠋⠀⠀⠀ ⠻⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢠⣾⣋⣠⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣴⢤⡄⠙⣹⠏⣸⣾⠁⠀⠀⠀⠀ ⣿⣿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠘⣳⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣼⡇⣴⢋⣴⣻⣃⣦⠀⠀⠀⠀ ⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⠞⠁⠀⣀⠀⠀⠀⡤⠤⢤⣀⠀⠀⢠⡿⢻⣿⣶⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟⣠⣿⡋⢈⠉⢠⡏⠀⠀⠀⡰ ⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠲⡿⠋⠀⠀⠀⠀⢿⡄⠀⠈⢷⠀⠈⢿⣦⣾⣿⣤⡟⣠⠀⠀⠀⠀⢀⣤⠤⠖⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢠⣿⣡⠛⣴⠋⠀⠀⠀⠀⠁ ⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣴⣾⣿⣤⡀⠘⡆⠀⠀⣷⣿⣿⣫⡶⠋⠀⠀⣠⠚⠁⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡥⠤⠾⠿⠀⠀⡀⠁⠠ ⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣾⡿⠋⣸⣿⣿⣝⣗⠃⠀⠀⣿⠀⠙⠋⠁⠀⠀⠀⡇⠀⠀⣀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⣠⣾⡀⠀⠀⠀⠀⠀⠀⢀ ⢳⡀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣼⣿⠁⢠⣿⣿⣿⣿⡏⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠷⠾⠿⠛⠉⠀⠀⢀⣠⣴⣾⣷⣄⠀⠀⠀⠀⠀⠀⠠⠟⠉⠁⣠⠆⠀⠀⠀⡠⠊ ⠀⠹⣄⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⢸⠀⢻⡏⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⣤⣶⣭⣄⡀ ⠀⠀⢹⡀⠀⢴⠞⠉⠓⠶⠆⠀⠀⠘⣦⢿⡇⠀⢸⣿⣿⠋⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠛⠋⠉⠉⠉⠙⠛⠛⠩⠞⠚⢀⣠⣴⠆⠀⠀⠀⠀⣠⡖⠁⠀⠀⣀⡴⠃ ⠀⠀⠀⠙⢦⡀⠳⢦⣤⣀⡀⠀⠀⠀⢹⣾⣧⠀⠈⠀⣸⠃⢀⣿⠃⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣴⠃⠀⠀⠀⠀⠾⠯⣤⠶⠖⠋⠁⣀⠄ ⠀⠀⠀⠀⠀⠙⠳⣄⠉⢛⣶⢦⡶⠞⢿⣿⣿⣄⣀⠘⣿⣼⠿⠋⠀⠀⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠙⠲⢤⣀⣀⣠⣤⡾⠿⡆⣠⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢳⡜⠓⡾⠛⠲⠈⡛⠋⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⡾⠛⠋⣩⡿⠋⣀⣴⡆⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡘⠓⣖⡂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⣩⣿⣋⣠⣴⣾⣛⠒⠋⠉⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠘⣏⣹⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠷⠶⠿⠿⠋⠁⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⣀⣈⣳⣦⣀⠀⠉⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣏⣀⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠖⠉⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢦⣤⣤⣤⣤⣤⣤⠤⠴⠖⢻⣿⣭⣵⠾⠯⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠋⠁⠀⠀⠀⠀⠉⠛⠲⢤ ⠀⠀⠀⠀⠰⠁⣠⣾⣁⡀⠀⠒⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣍⣭⡄⠉⠛⢶⣀⣀⣈⣳⣄⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⡏⠉⢻⡉⠉⠑⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣗⠒⠒⠚⠋⠉⢉⣥⡭⠬⠷⠒⠛⠉⠉⠉⠛⠒⠦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠚ ⠀⠀⠀⠀⠀⠀⠈⢷⡀⠻⣄⠈⠑⠲⠶⠦⠤⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦⣀⠀⠴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠈⠙⠶⢤⣀⣀⣀⡀⣁⠀⠀⣀⣀⢀⣀⡀⠀⠀⠀⡀⠀⢙⣷⠾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⠤⣄⣀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠤⢖⠚⠉⠁⣀⢀⣀⣉⡁⠀⠀⠀⠉⠓⠚⣃⣀⣴⣿⢷⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⣠⡾⠃⠀⠀⠀⠀

⣴⡟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠻⠿⣿⣿⣿⣿⣿⢦⠤⠀⠀⠀ ⣿⣧⣤⣴⣿⣿⠛⠛⣿⣧⣼⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠈⠀⣀⣿⣷⡾⢿⣿⣿⣿⢿⣿⣿⣿⠁⠀⠀⣠⣿⣿⣿⣿⡏⠀⠀⠀⠀ ⣿⣿⡿⣿⣿⣿⣶⣾⣿⣿⣿⣿⢿⣧⠈⠙⠻⠿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣆⡹⠿⣿⣿⣿⣿⣿⣷⣦⠴⣿⣿⣿⣿⠋⣻⣴⣤⣄⠀ ⣿⣿⠇⠻⣿⣿⣿⡿⡋⠙⣻⣿⠿⣟⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇⠀⢹⡟⢹⣿⣿⣿⣿⣶⣿⣿⣿⣿⠟⢋⡿⢿⣿⣷ ⣿⣿⡆⣴⣿⣿⣿⣿⢗⣒⣾⣉⣳⡬⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠘⠀⣾⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⣾⣿⣾⣿⣟ ⣿⣿⣿⠿⣿⣾⣿⣍⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠉⠙⠛⠋⠁⠀⠀⠀⣼⣿⣿⣷⣻⣿ ⣿⣿⣿⣾⣿⣿⣏⣱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢯⣿⣿⣇⣿ ⣿⣿⣿⣿⠿⠋⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⢏⣾⣿⣿⢸ ⣽⣿⣋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠞⢇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠌⢻⣿⣿⢸ ⣿⣿⡙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢋⡱⢏⣴⠾⢆⠀⠀⣦⣾⣆⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡎⠚⢿⡟⢸ ⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⣠⣤⣾⣿⠯⠐⠒⠉⡀⠀⢈⣦⠰⣼⠛⠿⣍⣓⣤⣄⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠐⢁⡿ ⣿⣿⣿⣿⣿⡿⠛⠛⠿⣥⣴⣾⣿⣷⣿⣿⣶⣾⣉⣲⣙⠀⡼⠀⠙⢿⣧⠄⢼⣯⣽⣿⣟⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡘⣷ ⣿⣿⣷⣿⣿⠟⠒⠒⠤⢽⣿⣿⣟⠉⠹⣿⡟⠛⠻⡟⠊⢣⠃⠀⠀⠀⣻⣶⣿⣿⣾⣿⣿⣿⣿⣿⣦⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿ ⣿⡿⢋⠟⠁⠀⠀⠀⢀⡞⠁⡟⣿⣦⣀⣘⣦⠴⠺⢿⣭⣽⣷⡀⠀⠀⠀⣏⡀⠀⣡⠏⠀⢀⣿⣿⠿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣧⣎⡴⠂⠀⠀⢀⡿⠀⠀⡇⠹⠿⠟⠋⠀⠀⠀⠀⣿⠀⠀⠉⠒⠤⣀⡀⠙⢻⣧⣤⣤⣾⡍⠀⠀⢀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢲⣶⣶ ⣿⣿⣿⣁⠀⠀⣠⣾⣥⡀⠈⡇⠀⠀⠀⠀⠀⠀⠀⡠⠿⠦⣀⠀⠀⠀⠀⠉⠳⠦⢌⣛⠛⠛⠀⠀⠀⠘⠀⣿⣦⣀⡀⠀⠀⠀⠀⠈⢿⣿ ⣿⣿⣿⣿⣲⠟⠉⠉⠀⣀⣀⡇⠀⠀⠀⠠⣤⠔⣫⣤⣤⣤⣄⡑⢦⡀⠀⠀⡀⠁⠀⠉⠙⠲⣦⣀⠀⡀⢠⣿⡏⠉⠛⠷⣶⣄⡀⠀⠀⣷ ⣿⣿⣿⢳⠃⣠⠴⠒⠾⠛⠉⢹⢦⡀⠀⠀⠈⣷⣿⣿⣿⣿⣿⣿⢀⣞⣑⡞⠁⠀⠀⠀⠀⣸⡇⠀⢹⠇⣾⠛⢷⣄⠀⢀⡼⠉⠛⢷⣼⣿ ⣿⣏⣹⣿⣼⡏⠀⠀⠀⠀⠀⠈⢦⡇⠀⠀⠀⢸⣿⡿⢿⠷⠿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢠⣿⠓⠦⠼⠞⠁⢧⡀⠙⣷⡌⠀⠀⠀⢸⡟⠙ ⣟⠛⠟⢻⣿⣗⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⣿⣧⣀⣴⡶⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠈⢷⡀⠈⢻⡆⠀⣠⣿⡁⢀ ⠘⢿⣼⣿⠁⠈⠒⠤⣀⢀⠀⠀⢀⡾⠓⣄⠀⠀⢈⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠗⣶⣤⡤⠀⠀⢓⣀⣀⣁⡴⠿⣿⣷⣾ ⠀⢀⠘⣿⣦⣤⣄⠀⠈⢹⣷⡞⢡⣀⡀⠈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⢻⠋⢀⠔⢹⣿⣄⣤⢞⣉⠀⠀⠀⠀⠀⠈⡏⠃ ⣾⡃⢀⡼⣿⣿⣿⣶⣶⣿⣿⡿⣄⡻⣿⣿⠋⠛⢷⣦⣀⣀⣀⣀⣤⣤⣶⠾⠛⣩⠔⣤⠋⠀⠀⠀⠘⣿⣿⠇⢫⡞⠀⠀⠀⠀⠀⠀⡁⠸ ⣿⣿⣿⣿⣿⣿⣿⡛⠋⠉⠉⠉⠉⠙⠛⢿⣧⢠⣾⣿⣿⣿⡿⠟⠋⠉⠀⡠⠞⣡⡞⠁⠀⠀⠀⠀⠀⠙⠛⠚⣹⠁⠀⠀⠀⠀⠀⠀⠄⠀ ⣿⢿⢟⠟⣽⠟⠉⣉⢉⣉⣙⡳⠦⣤⣤⠘⠒⠛⠻⣿⡍⠀⠀⢀⡀⠖⠉⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠘⢿⣿⣿⣿⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡿⠃⠀⠈⢿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⢿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⡋⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⣠⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣴⣾⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣹⣿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣷⣿⣿⣿⣿⣛⣿⣿⣿⣷⣶⣶⣦⣤⣴⣿⣿⣿⠿⠛⠛⢿⣿⣿⣿⣿⠟⣫⠟⠁⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣹⣿⣧⡀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⢹⣿⣿⣟⡿⠿⢿⣿⣷⣶⣄⡀⠀⠈⠉⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣠⡾⠉⢳⠹⣧⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⢿ ⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⢠⡿⣿⠀⠈⠙⠳⡄⠀⠉⠙⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠋⣤⠶⡟⠀⢿⡇⠀⠀⢸⣿⠘⢿⣿⣿⣿⣯ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠃⠘⠿⡛⠛⡟⠂⠀⠀⠀⠀⠙⢿⣿⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣟⣽⡿⠁⠀⠀⢠⡾⠁⠀⢸⡇⠀⠀⣼⡏⠀⠀⢻⣿⣿⣿ ⣿⣿⠿⣿⡆⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⢠⡌⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⢿⣿⣯⡿⣿⡇⠀⠀⠀⣸⠁⠀⠀⣼⠇⠀⢀⣿⠇⠀⠀⢸⣿⣿⣿ ⣿⡟⠀⢻⣿⡄⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⣾⠁⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡾⠃⣸⡿⠋⠀⣿⡇⠀⠀⣠⠏⠀⠀⢀⡏⠀⠀⣼⡟⠀⠀⠀⣿⣿⣿⣿ ⣿⡇⠀⢀⣹⣿⣆⡀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠈⢳⣄⣠⡾⠁⠀⣸⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠀⠀⠋⠀⠀⠀⣿⠳⠶⠾⠁⠀⠀⢀⣾⠁⠀⣼⡟⠀⠀⠀⠀⠻⢿⣿⣿ ⣿⡇⠀⠀⠈⠁⠈⠉⠉⠉⠛⠛⠓⠚⠛⠶⠦⠤⣄⣀⣀⣉⠀⠀⣰⠏⢸⡇⠀⠀⠀⣀⣀⣠⠴⠶⠚⠛⠛⠛⠛⠛⠓⠲⠿⢦⣀⡀⠀⠀⣠⣞⣁⣠⠼⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀ ⣿⣷⡀⠀⠀⠀⠀⠀⠰⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⠤⠸⣇⣴⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠺⠿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣧⡀⠀⠀⠀⠀⠀⢰⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⣤⡀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣬⣭⣂⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠁⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⠋⠙⢳⡄⠙⢦⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⠀⠀⠹⣄⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢹⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠀⠀⢠⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣸⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠙⠻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣄⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀ ⠉⠛⠛⠿⠿⠿⢿⣿⣿⣷⡉⠻⠦⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀ ⣦⡀⠀⠀⠀⠀⠀⠀⠙⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀ ⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠒⠒⠒⢒⣶⡒⠒⠒⠒⠒⠚⠋⠉⠉⠉⠉⠉⠓⠲⣤⣀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠸⣄⣠⠞⠋⠉⠉⠛⢯⣍⠉⠉⠉⠻⣿⣿⠿⠿⠿⣶⡄⠉⢙⡶⠚⠋⠁⠀⠀⠀⠀⠀⠀⢀⣤⠂⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣭⡁⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠙⠿⣮⣤⣀⣿⣧⡴⠎⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⢁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣞⢧⡀⣠⣄⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠈⠻⣿⠫⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⡷⠋⢹⡄⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠙⣦⠇⠀⠀⠀⠀⠀⠀⣤⣞⣡⡤⠴⠒⠒⠒⠒⠒⠀⠀⠀ ⠀⠀⠀⠀⠤⠴⠒⢶⠒⠒⠶⠤⣭⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⣸⠀⣤⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢹⡀⠀⠀⠀⠀⢠⡾⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠈⠉⠛⠦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⡈⠉⠳⢦⣀⠀⠀⠀⣀⡴⢀⣀⣾⠁⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢦⡀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⡄⢀⠈⠉⠉⠉⠁⠀⣘⡿⠃⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠟⡙⠛⠛⠛⠋⠁⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠁⠀⠀⠀⠀⠆⠀⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠈⡀⠰⠀⠀⠀⠀⠀⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠁⠄⢀⠀⠀⠀⢂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡄⠀⠀⠀⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠌⠀⣀⣀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠒⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢰⠀⠀ ⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠄⠀⡠⠚⠓⠦⣄⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⠤⠤⣀⠀⠐⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀ ⠀⠀⠀⠀⡐⠰⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀ ⠀⠀⠀⠀⠐⠠⡇⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀ ⠀⠀⠀⠀⠀⣀⣒⣾⠋⠉⢻⡆⠀⠀⠀⠀⠀⠀⠀⣤⡶⠚⠛⠶⣦⣤⡤⠄⠀⠀⠀⠀⠀⠐⠀⠀⠠⠊⠀⠀ ⠀⢀⠀⡀⠀⠀⠺⡇⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠇⠙⢿⡿⠭⠀⠀⠀⠀⠂⠉⠠⠀⠀⠀⠀ ⠀⠀⢀⠤⠀⠀⠀⠰⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀ ⠀⠀⠁⠀⠀⠀⠀⠀⠑⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⢀⠂⠀⠀⠀⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⢂⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠨⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⠀⢠⠀⠀⠠⠀⠀⠀⠁⢀⠰⠛⠀⠀⠀⠀⠀⠀⠀⠜⠙⠀⠀⠀⠀⠀⠠⠂⠀⠀⡀⠀⠀⠀⠀⡀⠆⠀⠀⠀ ⠀⠀⠢⠀⠄⠀⠀⠀⡀⠀⠄⠄⢀⣀⡀⣀⣀⠄⠂⢠⠃⠀⠀⠀⠐⠀⠀⠀⡄⠀⡔⡄⠀⢰⠄⠀⠈⠀⠀⠀ ⠀⠀⠀⠀⠄⠐⠀⠀⠁⠀⠀⠀⠀⠈⡟⠉⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠣⢺⠂⢰⠀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠃⠀⢀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠐⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠡⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠍⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⡀⠠⡠⠂⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⢠⠃⢳⡀⠀⠀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⢀⣼⡤⠴⠛⠒⠉⠽⠿⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢁⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠾⣷⣀⣀⡤⠖⠚⣻⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⢫⣶⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⠀⣠⠎⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣶⡄⠀⠀⠀⠀⠀⠀⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠰⣻⠁⠀⣸⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠁⠉⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣀⣴⡇⠤⠊⣸⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯⣿⣳⡀⠙⠀⠀⠀⠀⠀⣀⣤⣶⣀⣀⣀⠀⠀⠀⠠⣬⠴⠋⠀⠠⢾⡁⢠⢿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣠⣿⡿⠯⣀⠀⠀⠀⠀⠀⠀⠛⠛⢉⠽⠛⠛⠛⠛⠦⡀⠈⢶⡤⠤⠖⢊⣴⣻⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢿⠀⣯⠀⠀⠀⢹⡆⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢦⣿⢶⣾⠽⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠈⠂⠹⣷⡤⠖⠚⠁⠀⠀⢀⡤⠿⣿⠏⢀⣠⠤⠴⡖⠢⣄⣠⣼⠏⠀⠙⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⣨⠟⠒⠢⣤⠶⠾⠯⠷⢚⣥⠖⠉⠙⡆⠀⡟⢀⡿⣿⠀⠀⠀⢲⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠈⠉⠒⠒⠋⡟⠁⠀⠀⠚⠑⠊⠀⢸⡄⢸⡆⠀⠀⢈⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⡇⠀⣀⡾⠁⠀⠀⠀⠀ ⠀⠀⡴⠚⢓⣶⠤⢄⡀⢀⣀⣀⡤⠼⣷⣶⣶⠒⢺⡟⢣⡀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠞⠉⠀⠀⢀⣠⣤⠀ ⢀⣾⣿⠛⢺⠉⠢⡀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠳⣿⡀⠀⠙⠆⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⠞⠁⢠⡇⠀ ⠀⠯⣀⣱⠼⠷⠴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⡴⠁⠀⠀⢸⠀⠀ ⠀⠀⠈⢳⣄⡀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠑⠦⣄⣀⣀⣠⣴⠋⠀⣸⠁⠀⠀⠀⢸⡄⠀ ⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠉⠉⠉⠳⣄⠀⠀⠀⢀⡇⠀⣰⠃⠀⠀⠀⠀⣼⡇⠀ ⠀⠀⠀⠀⠀⠙⠲⠤⠶⠒⠒⠒⠒⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⡸⠛⠟⠁⠀⠀⠀⠐⠊⢀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢀⡾⠗⢲⡶⠢⢄⠀⠀⠀⠀⠀⣇⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⣾⡤⢤⡾⠤⣄⢀⡷⣄⠀⠀⠀⣯⡰⠃⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡗⠚⠳⠤⣬⠟⠦⣈⡆⠀⢰⡟⠁⠀⠀⠀⣀⣀⣤⡤⠖⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠦⢄⣀⠈⣳⣤⠟⠁⣰⢿⣳⣤⣀⣀⣀⡠⠴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡀⠀⠀⣉⡽⠷⠒⠋⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀ ⠀⢾⣻⠶⢆⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢾⡫⠥⢄⢳⠀ ⢠⣼⠀⠀⠀⠀⠑⠪⢝⣢⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠋⠁⠀⠀⠘⣼⡇ ⢸⠹⠀⠀⠀⠀⠀⠀⠀⠉⢻⣦⡤⣤⡤⢤⣤⣠⣽⡟⠁⠀⠀⠀⠀⠀⠀⠘⡇ ⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⢠⢀⠇ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣺⠀ ⠀⢸⡇⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀ ⠀⢇⠃⠀⠀⠀⠀⠀⣀⣥⠤⠤⠀⠀⠀⠀⢈⢡⣤⣄⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⢸⡞⠀⠀⠀⠀⠀⡼⢹⡟⣦⣴⣧⠀⠀⢀⣧⣤⢻⣿⢣⠀⠀⠀⠀⠀⢸⢧⠀ ⡄⡇⠀⠀⠀⠀⠀⡇⠈⠻⠿⢟⣿⠀⠀⢸⡿⠿⠿⠋⣸⠀⠀⠀⠀⠀⠀⣿⡀ ⣷⠀⠀⠀⠀⠀⠀⠙⢶⣶⡬⠟⠁⠀⠀⠀⠻⠦⢤⠴⠃⠀⠀⠀⢀⡀⠀⢸⡇ ⡇⢇⠀⠚⢷⡠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣺⠿⠿⠀⡏⡇ ⠙⢮⣷⣄⡀⠙⠷⣿⡷⣶⣦⣔⡜⠦⠆⢀⣤⠤⠖⣂⣩⣴⠾⠁⠀⢀⣜⡽⠃ ⠀⠀⠙⠺⢬⣑⡢⢤⣭⡗⠀⠉⠉⠉⠉⠉⠉⠉⢩⣿⣉⣀⣀⣤⣾⠽⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠊⠉⠀⠀⠀⠀⠀

⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀ ⠇⠑⡉⠢⢄⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⢉⠔⢡⠀⠀ ⠀⠀⠐⡀⠀⠭⠦⣄⡠⢼⡎⢆⠀⠀⢀⠠⠐⠉⠀⢀⠔⠁⠀⢸⠀⠀ ⡀⠀⠀⠱⡀⢇⠀⠀⠈⠁⠒⠉⠑⠊⠀⠀⠀⠀⢠⠊⠀⡠⠆⢸⠀⠀ ⡇⠰⠠⡀⠱⡀⣂⡀⠀⢀⠀⢀⠀⠀⠀⠀⠀⢰⢁⠠⠊⠀⡆⢸⠀⠀ ⢰⠰⡀⠙⠦⠍⣀⣀⢤⠊⠀⡣⣇⡀⠀⠀⠀⠈⠁⠀⠀⡰⠁⡎⠀⠀ ⠀⠷⠕⡢⡄⣠⡒⢆⠘⠒⠂⡏⠀⡰⣀⣠⠄⠀⢐⠔⠉⠀⠸⠀⠀⠀ ⠀⠸⡀⠈⠀⠙⢻⡿⠀⠀⠀⠑⣮⠞⠉⠀⠀⠀⠫⠒⠉⠈⢹⠀⠀⠀ ⠀⢠⠑⠀⡠⠮⠉⠩⠖⠤⣄⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⡰⠁⢀⡀⠀ ⠀⠀⢣⣀⠱⠂⣠⢄⡒⢙⡛⠀⢀⠞⠀⠀⠀⠀⠀⠀⠚⢈⡭⠁⢸⠀ ⠀⠀⠈⠂⠀⠷⣍⠦⠀⠉⠀⠒⠉⣀⠀⠀⠀⣀⣀⣠⠴⠓⡒⠩⠉⢰ ⠀⠀⠀⠀⠀⢀⣈⣵⡦⠐⠒⡎⠁⠀⠀⠀⠭⠐⠿⠑⠒⢅⠀⡠⠂⠆ ⠀⠀⠀⡖⠉⢟⠀⠀⢰⠤⠤⠂⠀⠀⠀⠀⠀⠠⠚⡲⢆⢜⠊⡀⠌⠀ ⠀⠀⠀⣹⠀⠀⠑⠴⢎⣨⣀⣀⣀⠀⠤⠤⠀⠒⠉⠐⢁⠼⠉⠀⠀⠀ ⠀⠀⠀⢇⠁⠀⠠⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠳⡀⠀⠡⠀⠀⢉⠍⠀⠀⣀⠤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠒⢄⡈⣉⡀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⢄⡢⡀⠀⠀⢀⠞⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⣼⢰⠱⡀⡠⠃⠀⢱⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢃⣮⡐⠋⠉⢻⢾⡾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢱⡜⡏⢡⣿⢄⠼⣷⠷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡀⠘⠂⠣⠀⠝⠛⣠⠞⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠀⠑⢢⠀⠀⠀⠀⣎⠀⠀⠀⠀⠀ ⠀⠀⢀⠖⢹⠀⠀⣀⣤⡧⣄⠀⠀⣹⡀⢠⣶⡦⡄ ⠀⢠⠃⠀⣴⡀⠸⣀⠈⢹⠈⣸⠉⠉⣧⠸⢂⠴⠊ ⢠⣌⠀⠀⠀⠟⡀⠈⡁⢁⠀⠏⠀⠀⢸⠃⠸⠀⠀ ⠘⡇⠀⠀⠀⠀⢣⠀⣇⢀⡿⠀⠀⠀⡌⣀⡇⠀⠀ ⠀⠸⡀⠀⠀⠀⠈⢇⢈⠅⠀⠀⠀⠰⠀⠀⠀⠀⠀ ⠀⠀⠙⢄⡀⠀⠀⠠⡏⠐⠤⠤⠐⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠂⡴⠁⠈⠒⠀⠤⠎⠱⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡜⠀⠀⠀⢠⠶⠒⠃⢀⢵⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡽⣄⡀⣴⣁⣀⣇⢀⡠⡂⠤⠰⢤⡀ ⠀⠀⠀⠰⣿⣶⡦⠼⠿⠛⠛⠛⠓⠒⠒⠒⠒⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⡷⣄⡀⠀⠀⠀⠀⠀⠀⢻⡀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣧⠈⠛⠦⣄⡀⠀⠀⠀⠀⠹⣆⠀⠀⠈⠙⠓⠦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣄⠀⠀⠀⠉⠙⠲⠶⢤⣀⣈⣷⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠒⠲⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠓⠒⠤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢤⣠⣶⡮⠤⢤⣤⣀⣈⡳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡄⡈⠉⠉⠛⠻⢯⣍⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⠀⠀⠙⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠛⣯⣤⠼⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠶⠋⠉⠁⠀⠀⢿⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣕⠒⠦⣀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠛⠁⣀⡤⠀⠀⠀⠀⠈⢳⣤⣈⡁⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢤⣜⣆⠀⢸⠆⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣡⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠶⢶⣡⡶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡓⠒⠲⠶⢤⣈⣻⡴⠉⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⢋⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠳⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⢹⡷⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⡜⠁⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡤⢾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⣀⠀⠀⠀ ⢸⢃⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣌⣉⣩⣽⣯⣤⣤⠤⠤⣴⠖⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠙⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄⠈⠓⢦⡀ ⣿⡞⠁⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⠈⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⢻ ⡟⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠉⠉⠉⠓⠲⣤⡀⠀⠀⠀⠀⠀⠉⠑⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⡾ ⡇⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠓⠦⢤⣝⣦⠀⠀⠀⠀⠀⠀⠀⠸⠔⢻⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡾⠁ ⣷⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠶⣌⣹⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠉⢹⣁⣀⣠⠴⢆⠀⠀⠀⠀⣴⠟⠁⠀ ⢻⡅⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣾⠉⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠻⣤⣴⠟⠁⠀⠀⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⣆⡀⠀⠀⠉⠓⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⢨⠷⡌⢿⡀⠀⠀⠀⠀ ⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣼⣿⣯⠀⠀⠀⠀⠀⢀⡙⢿⣿⣤⣤⣆⣶⡴⠋⠀⢹⣾⡇⠀⠀⠀⠀ ⠀⠀⠈⣧⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⢀⡀⠀⠙⢷⣷⡌⠉⠉⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠹⢦⡀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠈⢻⣄⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠈⢧⣹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣖⠀⠀⠀⠀⠀⠀⠈⡟⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠀⠙⢿⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⠠⠂⠙⠛⢦⣀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⣀⠀⢰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠳⢤⡀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⡿⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠉⠑⠲⣽⡓⠦⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣰⢃⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠈⠉⠛⠒⠤⣄⡀⠀⢠⡄⠀⠀⡇⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡈⣇⠀⣸⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣿⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⣠⠤⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⣀⠀⠀⢰⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠀⠀⠀⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⠀⠀⠉⠓⠻⢬⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠷⡄⠀⠀⠀⠀⠀⣠⠞⠉⣀⡠⠤⡶⠒⠊⠉⠁⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠒⢤⣄⣀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣶⣀⠀⢠⣾⠥⠒⠉⠁⠀⠀⣧⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⠙⣶⣄⡙⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⡶⣏⠁⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢿⠀⠀⠘⢷⣍⠻⠆⠀⠀⠀⠀⣀⠀ ⠀⠀⠀⢿⡇⠈⠛⠲⢤⣀⣀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣤⣄⣀⠀⣀⣠⣤⣼⣿⣼⣆⠀⠀⣴⠙⠷⣦⡀⠀⠀⠀⠘⣇ ⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠃⠀⠈⠙⠛⠶⣤⢤⣿ ⠀⠀⠀⠘⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⣿⣽⠛⠛⠛⠻⢿⣿⣿⣿⣷⡀⢀⣀⡶⠑⠸⡆⠀ ⠀⠀⠀⠀⢿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠉⢈⣁⠈⠃⠀⡞⠛⢦⠈⠻⣿⣿⣿⣿⠟⠁⠀⠀⣷⠀ ⠀⠀⠀⠀⢸⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⠀⠀⠘⣏⣀⠀⠀⠓⠒⠋⠀⠀⣿⠹⣿⣷⣤⣤⠀⠀⠛⠀ ⠀⠀⠀⠒⣿⠟⢻⣿⣿⣿⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠙⢧⣀⠀⠀⠀⢀⣠⡾⠋⣳⡏⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⣸⠏⠚⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⢹⣷⠁⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠉⢁⣠⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⠿⣤⢤⣀⣀⢀⠜⠋⠁⠀⠉⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢦⣤⣤⣀⣀⣀⣤⣤⣴⡾⠿⣿⣯⡀⢈⣹⡇⠀⠀⠀⠀⠀⠀ ⠀⢸⡁⢀⡇⠀⡇⠀⠙⣦⠀⠀⠀⠀⠀⠀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡉⠉⣩⣭⣿⣿⣠⣤⣄⠈⣿⠋⢸⡇⠀⠀⣀⡀⠀⠀ ⡀⠀⢻⡏⠉⠙⠓⠢⠴⠟⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠦⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢸⣿⠋⢻⣿⣿⣽⣿⡾⠁⠀⠈⠛⠶⠞⠋⠀⠀⠀ ⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣿⣛⣡⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠛⢁⠞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠓⠦⠤⠤⠶⠞⠛⠳⢦⣀⠀⠀⠀⢀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣘⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣈⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠟⠉⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⠟⠉⠻⡿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡿⠁⠀⠀⠀⢻⡌⠿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡶⠋⠀⠀⠀⠀⠀⣼⠇⠀⢨⠟⢿⣦⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡼⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢰⡏⣀⡘⣦⡙⢦⡀⠀⠻⣆⠀⠈⠉⠛⠳⢦⣭⣓⠦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⡏⡉⠻⣆⠀⠀⠀ ⠀⠀⣿⣤⠼⣟⢮⣻⠶⠛⢉⠉⠉⠙⣂⡀⠀⠠⠞⢛⣙⡳⠈⠧⠖⠋⠉⣉⣓⣶⡿⢡⠏⣠⡇⢀⠹⣧⠀⠀ ⠀⢀⡇⢻⣀⡴⠟⠁⠠⣊⡀⢠⠖⠋⠀⡀⠐⠋⠉⠉⢠⠀⢠⠀⠀⠈⠉⠉⢳⡟⠀⣸⣰⠃⣷⠹⡆⢹⣇⠀ ⠀⢾⣯⣽⡿⠤⢴⣿⠭⠁⢠⡯⢖⣋⡯⠵⢚⠁⠀⠀⢿⠀⡼⠀⢀⠀⠀⣀⣿⠀⠀⣿⠃⠀⠀⠀⣷⠀⣿⠀ ⠀⠸⣿⣚⠳⣤⠞⠁⠀⢀⣯⠴⣻⠃⣠⠔⢸⠀⢀⠀⠘⢦⡃⠀⡈⢳⣄⠀⠙⢦⣀⡟⠀⠀⠀⣠⠏⠀⣿⠀ ⠀⠀⢻⣿⡟⠁⠀⠀⠀⡾⠃⢰⣧⠞⠁⣤⡟⢀⡸⡄⠳⣄⠹⡄⠘⢦⢻⣦⡀⠀⠙⢦⡀⠠⠶⠋⢸⢄⣿⠀ ⠀⠀⣴⠋⠀⠀⠀⠀⡜⠀⣸⠞⠃⣠⣾⠏⡇⣸⠃⠙⣆⢹⣧⡙⣦⠀⠻⡏⣿⡖⢦⣄⡻⡦⣤⣖⢉⣾⠃⠀ ⣠⣞⣁⣠⡶⠂⠀⢠⠇⣴⠃⣠⠼⠋⠀⠀⣷⢋⡀⠀⠈⠳⣗⠝⣽⣥⡀⠀⠘⢱⡀⠳⡉⠳⠼⡿⣿⠁⠀⠀ ⠀⠉⠁⣼⠁⠀⠀⠘⣼⣿⣿⣷⣄⢀⡠⠚⢱⠛⢀⣴⣶⣶⣶⣤⣬⣃⣇⡀⠀⠀⢳⠀⢻⠀⠀⣿⣜⡆⠀⠀ ⠀⠀⢀⡏⠀⠀⠀⠀⡿⣿⣏⣿⣿⣿⠀⠀⠀⠹⣿⣿⣿⣿⣟⣿⠛⣿⡿⠀⠀⠀⢸⣇⡼⡄⢠⣿⣿⢷⠀⠀ ⠀⠀⢸⡇⣰⠃⠀⢠⠃⠈⡿⣿⣝⡏⠀⠀⠀⠐⠿⠉⢯⡻⠟⣸⣼⢿⡇⠀⡀⠀⢰⢳⡀⡯⣼⣿⢿⡏⠀⠀ ⠀⠀⢸⣷⢻⠀⢀⣿⡇⠀⠳⣀⣹⣷⠒⡦⡤⠀⠀⠈⠙⠛⠻⠟⠃⣸⢣⠀⡇⠀⠸⢸⠀⢃⣿⣿⢷⡇⠀⠀ ⠀⠀⠀⠃⢸⡀⠞⠉⡇⠀⣤⣟⣁⡈⠉⠳⠞⠀⠀⠀⢀⠀⠀⠀⣰⣿⡏⠀⡇⠀⠀⢸⢸⡟⣿⢻⠀⠁⠀⠀ ⠀⠀⠀⠀⠈⣧⠀⠀⢷⠀⢿⡀⠀⢉⡆⠀⠀⠀⠀⢠⡟⠀⣠⢾⣿⣿⠀⣼⠃⡆⠀⣟⡟⣱⠏⡾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣻⠀⡴⠚⣆⠈⢿⣗⢏⣀⣀⣀⣠⡴⠋⣠⣾⠛⢫⢥⠇⣰⠃⠘⠀⡼⣿⣷⣋⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠏⣼⠁⠀⠈⠀⠀⠈⡟⠉⠉⠉⣯⣥⡾⠟⠁⠀⣾⣟⡴⠃⠀⢀⣸⢣⣿⣯⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⣫⡾⢻⠀⠀⢠⠇⠀⠀⠳⡄⠀⠀⣷⣟⣦⠀⠀⣸⠟⠈⠀⠀⣠⡿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀ ⠀⠀⠐⠋⠁⠀⢸⠀⠀⡼⠀⢠⣶⡿⠟⣳⣶⡿⠿⢿⡀⢰⠃⢀⠀⠀⣰⣿⡵⠋⢉⣽⠿⣿⣯⡁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣆⢸⡇⣰⡿⠉⠀⠀⢫⡉⠙⢮⡓⠀⠎⣰⠋⠀⣰⢿⠃⠀⣠⡾⠁⠀⠀⢻⣿⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⣿⣭⣽⣳⣶⡤⢽⢦⣀⡙⣦⣴⠋⡇⢀⡏⢀⣤⡾⠋⠀⣤⣤⣾⣿⣶⣿⣿⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣻⣿⣷⡟⠀⠙⠻⢿⣍⠀⢷⢸⡷⠟⠉⠀⠀⠸⣯⣾⣿⣿⢿⣿⠽⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣮⣵⣿⡟⠀⠀⠀⠀⣶⠈⠃⠈⢿⣤⢦⠀⠀⠀⠀⠛⣿⣿⣿⣇⣿⣟⣻⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⢰⠟⡄⠀⠀⠀⢹⡌⡇⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠉⣿⡏⠀⠀⠤⣄⣀⣸⠀⡇⠀⠀⠀⢸⡇⣷⠀⠀⠀⠀⠀⠈⢿⣿⠿⠟⠻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⢻⣷⡄⠀⠀⠀⠀⠘⡇⢻⡁⠀⠀⢸⡇⡏⠉⠉⠉⠉⠀⠀⢘⣿⡆⠀⢰⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠋⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⡸⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⣰⠒⣶⠁⠀⠀⠀⠀⡜⣁⡠⠷⠒⠢⠤⣀⡀⡟⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣠⡾⣏⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠈⢧⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⡠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⡄⠀⠀⠀⠀⢀⣇⠀⣠⣆⡏⠁⢀⡀⠀⢩⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢀⡴⠊⠁⠀⢀⠔⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠃⠈⠛⠀⠀⠀⠀⣸⣀⠿⠒⠚⠁⠺⣁⡴⠀⢸⠀⠈⡆⠀⢰⠦⠀⠀⡤⢄⠀⠘⣧⠖⠉⠀⠀⠀⢠⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢠⡦⡀⠀⢧⣠⠇⠀⠰⠾⢁⣀⣆⣸⠄⠀⠹⡄⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⢀⠇⢠⣾⣿⣿⡄⠀⠀⠸⡇⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡄⡖⡞⢆⠀⠀⡎⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡿⢦⡀⠀⢀⡞⢀⣿⣿⡿⠛⡇⠀⠀⠀⢣⣀⡷⠀⠀⠀⠀⢀⣠⣤⣀⣀⡀⠀⠙⠳⠆⠀⢳⣼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠙⢲⡞⠀⢸⣿⡿⠁⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⠊⠀⠀⢸⣿⠃⡀⠹⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠁⢄⠈⠹⣿⣿⣿⣿⣿⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⣯⠀⠀⠀⠀⠈⢿⣦⠶⠫⠍⡒⠤⡀⠀⠀⠀⢰⠁⠀⠀⠈⠄⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⢧⣀⣈⠑⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⣀⠔⠊⠀⠀⠀⡠⠄⠓⢌⠡⣀⠀⢸⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠟⠀⠀⠀⠀⠘⡄⠀⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⣠⠞⠁⠀⠀⢀⡤⠊⠀⠀⠀⠀⠑⢌⠳⡜⠒⠒⠒⠒⠒⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢇⡀⠀⠀⠀⢀⡼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡰⠟⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢣⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠈⣁⣀⣠⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡝⠓⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠜⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⢀⣀⢀⡴⣺⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠈⠉⢑⠒⠦⢤⣄⣀⣀⣀⣀⡠⠤⠔⠊⠀⣀⡀⠤⠄⠤⠒⠉⢁⡟⠁⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⣆⠀⠀⠀⠀⢀⣀⢼⡀⠀⠀⠀⠀⠐⠀⡠⠀⠈⡿⠴⢁⡠⠤⠒⠉⠀⠀⠀⠀⠀⣠⠖⠁⠀⠸⠧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢧⠀⡴⠊⠁⠀⠀⠣⢄⠀⠀⠀⠀⠀⠃⢀⡴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⢠⣞⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢣⣌⡦⠀⠀⠀⠀⠀⠈⠉⠉⠒⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⢀⡴ ⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⣼⠂⠀⠀⢀⠔⠊⠀ ⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡵⠛⢟⠒⠚⠁⠀⢀⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠘⡄⠀⣤⣴⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⣿⣿⣿⣿

⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠶⠟⠛⠻⣦⡀⠀⠀ ⠀⠀⢸⡟⠈⣹⣷⣦⣭⣛⡳⠦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣞⣿⠾⣟⣉⣥⣤⣿⣷⠀⢿⣧⠀⠀ ⠀⠀⢸⢻⢸⠛⠉⠀⠈⠈⠙⠛⠿⣬⣝⡛⠿⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣟⣽⣟⣫⡷⠞⠋⠉⠀⠀⠈⠻⣧⠸⡿⡆⠀ ⠀⠀⣸⡜⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣽⡛⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⡇⣷⠀ ⠀⢸⣿⠗⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣟⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣿⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⡇⣿⠀ ⠀⢸⡇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⣷⣦⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⡀⢀⣼⢱⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀ ⠀⠘⡇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠶⠶⠶⠶⠶⠶⠾⠿⢿⣿⣿⣟⣋⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⣿⠀ ⠀⠀⣇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡏⠀ ⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣿⠁⠀ ⠀⠀⢨⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏⠀⠀ ⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⡇⠀⠀ ⠀⠀⠀⠀⣼⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣩⡿⠃⠀⠀ ⠀⠀⠀⣰⡟⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣴⣶⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠁⠀⠀⠀ ⠀⠀⢀⡿⢁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡅⠀⠀⠀⠀ ⠀⠀⣸⠃⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡿⠋⠀⠈⠹⣆⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⢻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀ ⠀⠀⡏⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢹⣿⣿⣷⣄⣀⣀⣼⣿⡄⠀⠀⠀⠀⠀⠀⣾⡀⠀⢀⣴⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⣿⡀⠀⠀ ⠀⢸⠡⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⢸⣿⣧⣨⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣏⣀⣿⣿⡿⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡸⣇⠀⠀ ⠀⣼⢐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡇⠀⠀⠻⣿⣿⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣿⠀⠀ ⠀⡇⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⣧⠀⠀⠀⠀⠉⠛⠛⣉⣴⣿⣿⠃⠀⠀⠀⠀⠈⣿⣿⠛⠛⠛⠛⠁⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀ ⢀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡠⠤⣤⠤⠖⣋⣽⣿⡟⠁⠀⠀⠀⠀⠀⠀⠹⣿⣷⣤⡀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠀ ⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠶⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⢸⢿⣿⠀ ⣸⡇⢻⣄⠀⠀⠀⣶⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣿⣿⣿⣿⡇⠀⠀⣿⢸⣿⠀ ⢼⣇⡀⢻⣆⠀⠀⠀⠈⠻⣿⣯⣙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⣩⣾⡿⠛⠛⠋⠀⠀⢀⡿⢸⣿⠆ ⠘⢿⣷⣀⣹⣦⣄⠀⠀⠀⠈⠻⢿⣷⣶⣬⣝⣛⠶⣤⣤⣀⡀⠀⠀⢤⣀⣶⣦⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠖⠛⠉⣡⣴⣿⡿⠋⠀⠀⠀⠀⠀⢀⡾⢃⣿⡿⠀ ⠀⠀⠙⢿⣯⡛⢿⣷⣦⣀⠀⠀⠀⠉⠻⢿⣯⣝⡛⠿⢿⣿⣿⣽⣟⣟⣿⣓⠉⠻⠿⡁⣦⣶⣶⣶⡾⠿⠿⠉⣉⣠⣤⣴⣶⣿⣿⠟⠋⠀⠀⠀⠀⠀⣀⣴⡏⣡⣾⡿⠁⠀ ⠀⠀⠀⠀⠉⠻⢷⣯⣛⠉⠛⠶⣤⣀⠀⠀⠈⠉⣛⠿⣶⡄⠈⠉⠉⠛⠛⠛⠛⠻⠿⠷⠶⠶⠶⠶⠶⠟⠛⠛⢛⣯⣿⠿⠛⠋⠀⠀⠀⠀⠀⣀⣴⣾⢟⣽⣾⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣶⣤⣍⡛⠶⣶⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣖⣀⢀⣀⣀⣠⣤⣶⠿⣋⣭⣶⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⠷⠶⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣭⣭⣭⣭⣭⠷⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡠⠋⠁⠚⢓⡳⢀⢾⠀⠀⠀⣸⢾⠉⢛⠌⠺⢄⡰⢀⡀⠀⠀⠀ ⠀⡇⡰⣤⠞⠁⡰⠁⢀⡓⢡⠋⣸⠀⠀⡀⠁⡏⢇⠀⠫⠂⠻⠉⢹⣃⠀⠀⠀ ⣤⣧⣆⠾⠣⢲⠃⣀⠴⡶⠛⠉⠀⡇⠀⣀⠀⡇⠀⢳⡒⠚⠒⠲⢅⡀⠰⠀⠀ ⠀⢰⠁⠑⢠⡿⠊⢁⠞⠠⢄⠀⠀⠸⡀⠑⠄⡇⠀⠀⠑⢦⡀⠀⠀⠙⢆⢁⠀ ⠀⢸⠀⡏⢺⣇⠔⠁⠀⠀⠀⠁⠀⢠⠱⡄⠀⢇⠀⠀⠀⠀⠙⠦⡀⠀⠀⠘⡀ ⡀⠘⡄⠂⠀⠁⢀⣠⣶⣶⣶⣦⡄⠀⠀⠈⢆⠘⡐⣤⣶⣶⣶⣤⣈⠑⠢⢀⡇ ⠈⠢⣧⠀⢰⡾⠛⠉⠉⣀⠀⠤⠀⠁⠀⠀⠀⠑⠶⡤⠤⢀⡀⠉⠙⢿⡖⠀⢸ ⠀⠀⠹⡄⢸⠈⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⢿ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢘ ⠋⢠⠇⠀⠀⡆⠀⠀⠀⠀⠀⠀⢀⣶⣧⣤⣶⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣣⣾ ⢠⣇⠀⠀⠀⢷⡀⠀⠀⠀⠀⠠⣿⣿⠟⠛⠛⢿⣿⡆⠀⠀⠀⠀⠀⠀⣼⣿⣿ ⠚⠛⠣⡀⠀⠸⣷⡀⠰⠀⠀⠀⢹⠀⠀⠀⠀⠀⠻⠰⠀⠀⠀⠀⢀⣼⡟⠛⡏ ⠀⠀⠠⠝⣆⠀⢻⣷⣤⡀⠐⠁⠜⢄⠈⠄⠀⠀⠆⠒⠠⢀⣠⡞⢋⡱⢀⡴⡁ ⠀⠀⠀⠀⠀⠑⢄⡩⡙⢿⣯⣶⣤⣀⡣⠤⠠⣞⣀⠄⣶⡿⠗⠚⠚⠛⠋⠁⠀

⠀⣆⣮⣪⠦⠑⠄⠉⠱⡯⠢⠠⢤⣤⢾⢣⠑⡄⠀ ⢠⣾⠎⣅⠒⣮⡀⠌⠁⠀⠀⠀⢈⠇⠰⠙⢹⢹⠀ ⠈⢟⠏⠀⡐⣫⢐⡌⡠⢨⡢⠢⣦⠑⢆⠠⢎⢼⠀ ⣔⣁⠄⢠⣠⡡⠊⡠⡁⠑⠷⢗⡈⢩⢓⠫⡷⠃⠀ ⠀⠈⠀⠘⢿⣷⡎⠘⣾⣿⡟⣳⡆⠀⡦⡄⣾⡇⠀ ⠀⠠⡁⡼⠈⡽⢤⠄⠈⠚⠒⢋⠃⠀⠈⢛⡟⡆⠀ ⠀⠀⢃⢀⡜⣍⠂⠀⢀⠄⣠⡟⢉⠆⣴⣙⡆⠀⠀ ⠀⢀⢌⠆⠀⠉⠒⠘⣵⠊⣠⠯⢂⣼⣿⣟⠀⠀⠀ ⠀⠈⠁⡄⡌⡴⠒⠶⡛⠄⢃⠀⡼⢋⠝⠻⣄⠀⠀ ⠀⠀⠀⠘⢿⣿⣶⡳⠬⣦⠻⢰⡴⠋⣤⣾⣾⣷⡀ ⠀⠀⠀⠀⢸⣿⡿⠁⠀⣆⠁⠓⡄⠀⠙⣿⣿⣭⡇ ⠀⠀⠀⠀⠸⣾⡅⠐⠂⡯⡄⠀⡧⠤⠄⠈⣏⠉⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠄⠐⠒⠒⠒⠒⠒⠒⠔⠦⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⣀⣀⣠⠴⠞⠋⠁⠀⠀⠀⢀⣠⠴⠖⠚⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠲⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡖⠛⠉⢉⡄⠘⠁⠀⠀⠀⣠⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠀⠀⠀⠓⠦⣄⠀⠐⠂⠭⢿⣳⡦⢤⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⢫⠟⢻⣻⣆⠀⠋⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠈⠙⠒⠲⢄⡀⠀⠉⠙⠛⠋⠁⠀⠄ ⠀⠀⠀⠀⠀⣼⢣⠟⠀⠀⢧⠹⣆⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠙⢆⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⢃⡏⠀⠀⠀⠈⢇⢹⡄⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⢠⡏⣼⠀⠀⠀⠀⠀⠈⠀⢷⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⠁⠋⠀⠀⠀⠀⠀⠀⠀⢸⠀⠱⣦⣀⣀⠀⠀⠀⠀⢀⣠⣶⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠻⣿⣦⣄⡀⠀⠀⠀⠀⣀⣀⣴⠖⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠈⡙⠻⠿⣶⣶⡿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢈⠛⠿⠿⣿⣶⣾⠿⠟⠋⠀⠁⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡿⣄⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠙⠒⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠀⠀⠀⠀⠈⠙⠶⠶⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⣠⣶⣶⣿⠿⠿⣿⣿⣿⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⡿⠿⢿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡟⠋⠁⠀⠀⠀⣈⡟⣩⡿⠋⠀⠉⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠀⠈⠙⠛⠛⠋⠀⠀⠀⠀⠉⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⡄⠀⠀⠀⠀⣠⠂⠈⡸⣿⣿⠀⠀⠀⣠⠖⠋⠁⠀⢸⡇⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠑⠀⠀⠀⡼⠃⢠⡄⠀⠸⣿⡄⣠⠞⠁⠀⠀⠀⠀⠘⠓⠒⠒⠒⠲⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⡼⠶⠒⠒⠒⠒⠒⠦⣤⣄⡀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡄⠀⣼⠁⠀⠈⠁⠀⠀⣬⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣾⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣛⡶⣄⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣧⢀⡟⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣼⠁⠀⠀⠀⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠚⠉⣭⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⣰⡟⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠶⢦⣤⣀⣀⣀⣀⣀⣀⣀⣤⣧⠀⠀⠀⣰⡿⢻⣿⠃⠀⠀⠀⠀⠀⠀⣠⠟⡵⢮⢻⡀⠀⣠⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠉⠀⠀⠉⠉⠉⠉⠀⠀⠙⢷⣀⣠⣿⣤⣿⠇⠀⠀⠀⠀⠀⠀⢰⡟⡼⠁⠈⢧⢻⡤⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢱⣿⠃⠄⠀⠀⠀⠀⠀⢠⡟⣴⠃⠀⠀⠈⣆⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⠶⠚⠉⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡇⠀⠀⠀⠀⠀⠀⢠⡾⢰⠃⠀⠀⠀⠀⠸⡜⣧⠀⠀⠀⠀⠀ ⠀⣠⡾⠋⠀⠀⠀⠀⣠⠞⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⣾⠃⠘⠀⠀⠀⠀⠀⠀⠁⢹⡀⠀⠀⠀⠀ ⢸⠋⠀⠀⠀⣀⡴⠋⠀⠀⠈⠻⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀ ⠘⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠷⣄⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣶⣶⣶⣶⠟⠛⠁⠀⠀⠀⠀⠀⠀⢀⣤⠔⠋⠁⠀⠙⠳⣤⣤⣤⡤⠞⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠶⠶⠖⠒⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠔⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⣄⠠⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀ ⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⢀⣀⣀⡤⠶⠒⠢⡀⠈⠻⢧⡐⢆⠀⠀⠀⠀⠀⠀⠀⠑ ⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡤⠶⠚⠉⠁⠀⠀⠀⠀⣈⣤⡄⠁⠳⣌⢷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣛⣒⣒⣠⡤⠤⠤⠶⢚⡻⠟⠁⠈⢦⠀⠈⢯⣣⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠙⢾⣦⣤⣀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠋⠀⠀⠀⠀⠈⢧⠀⠀⠻⣧⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣄⡀⠀⠉⠻⢿⣝⡒⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠙⣆⠀⠀⠀⠀ ⠀⣸⠁⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠹⣗⠶⢤⣀⣀⠉⠻⠿⣗⣛⠳⠶⠶⠶⠶⠶⠶⠖⣒⣶⠚⣻⣍⠁⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠘⣆⠀⠀⠘⣆⠀⠀⠀ ⠀⡏⠀⠀⠀⣿⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠳⣄⡠⣿⠟⠛⠒⠶⠾⠿⠯⠭⠶⣶⣲⣶⣿⣯⡿⠿⠗⠛⡆⠠⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⢸⣧⡀⠀⠙⡆⠀⠀ ⠀⡿⠀⠀⠀⢻⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠙⢿⡁⠀⢀⡤⠚⠀⠀⣀⣴⣿⣿⣏⠀⠀⠘⢿⠀⠀⠀⠘⣄⢇⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣷⠁⠀⠀⠸⡄⠀ ⢸⠃⠀⠀⠀⠸⣇⠈⢦⠀⠀⣄⠀⠀⠀⠀⣠⠤⠄⠻⣆⠀⠈⠳⣴⠏⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⡀⠀⠈⠀⠀⠀⠀⠹⣼⡀⡠⠀⡀⠀⢀⡴⠁⠀⠀⠀⢀⡄⢸⡄⠀⠀⠀⠱⠀ ⢸⠀⠀⠀⠀⠀⣿⡆⠈⢳⡀⠈⢶⣀⡤⠚⠁⠀⠀⠀⠈⠛⢦⡀⠙⣦⠀⣴⣿⣿⣿⣿⣧⣴⣄⠙⣿⠀⠀⠀⢀⠖⠀⣠⢻⣿⣡⠞⢳⡴⠋⠀⠀⢁⣤⠚⠉⠀⠀⣇⠀⠀⠀⠀⢇ ⡆⠀⠀⠀⠀⠀⢸⡿⠐⢄⡑⢆⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⢿⣿⢿⣇⣿⡉⠛⡿⠟⢀⣿⡐⠀⢠⠎⣰⡟⣠⠏⢿⠁⠀⠸⣧⡔⣀⠖⢹⡄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠨ ⡇⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠁⠑⢄⠀⠩⣖⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡻⣆⠈⠙⠻⠿⠶⠾⠛⢁⢧⣦⠋⣸⠋⡼⢁⠖⠘⡆⢀⠚⡏⠻⣄⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⡀⢳⣷⡀⠀⠀⠀⠀⠙⠦⣌⡙⠲⠤⣄⡀⠀⠀⠀⠀⠀⠹⣎⢣⡀⠀⠀⠀⠀⢀⣾⢯⠃⡴⠃⠼⡵⠋⠀⠀⣟⠀⠀⡇⠀⠈⠳⣄⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⠘⡟⢷⡀⠰⣄⠀⠀⠀⠈⠙⠒⠤⣤⣉⠑⠒⠦⢤⣄⣀⠈⠳⣽⣄⠀⠀⣔⡞⢈⠆⠘⠁⠀⠘⠁⠀⠀⠀⢸⡄⢠⡇⠀⠀⠀⠈⠳⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣦⠀⠀⠸⣇⢱⣨⢷⡄⠈⢳⣄⡈⠓⠦⣄⠀⠀⠀⠉⠉⠉⠑⠒⠒⠚⢲⢿⣿⣿⡟⡟⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣸⠁⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣇⠀⠀⠈⠀⠛⢾⣿⣦⠀⠻⡝⠶⣄⡈⠙⣲⣤⢀⠀⣀⡀⢀⡀⢠⣇⣟⣣⣿⠿⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠃⠀⠀⢰⡀⠀⠀⠸⡇⠀⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠘⢿⣿⠳⣄⠘⢦⡂⠙⠳⢤⣈⣙⠿⢿⣛⣛⣛⣫⣽⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠳⠇⠀⢀⣧⠀⠀⠀⢸⡄⠀⠀⠀ ⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠈⣿⠀⠈⠛⠦⣟⣦⣀⣴⣾⣿⣿⣷⣟⠛⠛⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡼⠓⡀⠀⠀ ⡄⠀⠀⠀⣆⢻⢧⡀⠀⠀⠀⠀⠘⣆⡀⠀⠀⠀⢹⣿⣿⡟⣿⣦⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠡⠀⠀ ⡇⠀⡀⠀⠸⡄⠈⠳⡄⠀⠀⠀⠀⢸⡷⣦⡀⠀⣸⣇⠈⠁⠻⠷⣶⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣼⠀⠀⠀⠐⡄ ⢷⠀⣧⠀⠀⠙⠀⠀⠙⢦⡀⠀⠀⠀⠷⢿⣿⡿⣿⠉⠙⠲⠦⠀⠀⠰⠧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣽⣿⣿⡟⢰⣿⣿⣽⣧⡀⠀⠀⠀⠀⠀⢸⠀⣸⡏⠀⠀⠀⠀⠈ ⣸⡆⢹⣆⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠈⢻⡅⠈⠙⠦⣄⠀⠀⠀⠀⠀⠈⠙⠓⠂⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣟⢿⠁⡟⠛⢚⡟⠯⣷⡀⠀⠀⠀⠀⣸⣰⠋⡇⠁⠀⠀⠀⠀ ⠁⡇⢸⠻⣆⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢄⡀⢳⡄⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠉⠁⠒⠒⢻⡀⠀⠀⢠⡿⠃⠀⣿⠀⠀⠀⠀⠀ ⠀⣿⡞⡄⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⢹⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡏⠈⣧⠀⠀⠀⠀⠀⠀⠀⣷⠀⢀⠞⠁⠀⢠⡏⠀⠀⠀⠀⠀ ⠀⢻⢹⢿⠀⠈⠳⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⡀⠚⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠮⣿⣧⠀⠈⠷⠀⠀⠀⠀⠀⠀⢸⣆⠈⠀⠀⢠⣿⣿⡏⠉⠉⠓⠀ ⣆⢸⡄⢻⣇⠀⠀⠙⢮⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠶⠬⠽⢦⣤⡤⠶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⢠⡘⠿⡄⡙⠖⣒⣾⢿⣿⡇⠀⠀⠀⠀ ⠉⠀⠧⠤⠟⠦⣄⠀⠀⠹⡄⠀⠀⢸⡀⠀⠀⠀⠀⠁⠒⠦⠤⠤⠤⠤⣴⠖⠛⠋⠉⠛⠦⠤⣱⣄⠀⠀⠀⠀⠀⠀⠀⢈⠻⣤⡐⢄⠀⠀⣾⢃⣴⡃⠃⢀⣿⡿⣿⣿⠃⠀⠀⠀⠀ ⢳⡄⠀⠀⠀⠀⠈⢳⡀⠀⢻⡀⠀⢸⢿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠈⠉⢝⠳⢶⡒⠒⠲⣒⣶⣕⣦⣽⡾⠵⢰⡇⡀⠻⣥⠴⠿⣿⠁⠙⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢸⡇⠀⢸⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣠⡤⠤⠤⣤⣀⠀⠈⢦⠈⠙⢦⡀⠈⠁⢿⣏⣷⡄⠀⡈⠀⠀⠀⣿⠀⠀⣸⢠⠀⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢸⡇⠀⡏⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠉⠉⠓⢮⡳⣄⠀⠉⠲⣄⠀⠈⠙⢷⡄⢰⠀⠘⣆⣿⡇⢠⣿⠇⢀⡟⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⠃⡼⠁⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠈⠢⡀⠀⠀⠙⠆⡀⠀⢻⣌⣆⠀⠹⣸⡇⣼⠏⢠⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡞⠁⠀⠀⠀⠀⠀⢳⡀⠀⠀⣸⢦⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⡈⠢⡀⠄⠀⠀⠀⠀⠘⣷⡀⠀⣁⣱⢃⡴⠋⠀⠀⠀⠀⠀⠀⠀

⣆⢸⣇⠈⢿⡆⠀⠀⠀⣇⠀⠸⣇⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠉⠙⠲⣄⣄⡀⠀⢀⡈⠙⠻⣿⡇⠀⣿⡎⠻⣾⣿⣇⠀ ⢻⡀⢿⠀⢸⣿⣄⠀⠀⢸⣆⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⠙⠲⣤⣤⠚⣏⠛⠓⠒⠒⠚⠩⠗⢶⣄⡀⠀⠀⠈⠙⢯⣦⣌⠻⢤⡀⠈⠛⢦⣿⡇⠀⢸⣿⣿⣆ ⠈⣧⠸⡇⠀⢿⣿⡇⢘⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⢠⡀⠀⠀⠢⠈⠳⣶⠖⠛⠛⠙⢶⣌⠳⢄⠀⠀⠐⠢⡀⠀⠈⠙⠶⣄⠀⠀⠀⠈⠻⣶⣄⠳⣤⡀⠀⢹⣷⠀⠸⣏⣽⣿ ⣀⣽⣦⣿⣄⣸⣿⣿⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⡏⣧⠀⠻⣄⠀⠀⠀⠀⠈⢻⣶⡄⠀⠘⢾⡳⣄⠹⣦⡀⠀⠈⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠈⠻⣷⣎⢿⣶⣄⠻⣤⠞⠋⠉⠙ ⣿⠈⢿⠹⣿⣿⡿⠃⠀⣠⠏⠀⠀⠀⠀⠀⢀⠀⣸⠀⣼⡆⠀⠙⣟⢦⣀⠀⠀⠀⠙⢮⣦⡀⠀⠻⣌⢳⣌⢻⣶⡀⠱⣄⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠈⠻⣿⢿⣼⠟⠁⠀⠀⠀⠀ ⣿⣦⣸⣀⣽⠏⠀⠀⢰⠏⠀⢀⠀⠀⣀⣰⠿⠄⣿⢀⡏⠹⡄⠀⠈⣳⡉⠳⣤⡀⣀⠈⠻⡽⣄⠸⣟⢧⡙⢀⣿⣬⣷⣧⣿⣦⣀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠈⠳⡤⢤⡀⠀⠀⠀⠀ ⣿⣿⡟⢿⡟⠀⠀⢠⡏⠀⠀⣏⣴⠿⠟⠃⠀⣇⣿⣸⠀⠀⠙⣄⠀⠹⣟⣦⣀⠙⡿⠿⢶⣽⣽⣆⠘⣇⣷⡿⠟⠛⠛⠛⠛⠛⢿⣿⣆⠀⠀⠈⢳⡄⠀⠀⠀⠀⠙⢮⠻⣄⠀⠀⠀ ⣿⢿⣇⡿⠁⠀⠀⡞⠀⠀⣼⠋⢀⡄⠀⢠⣔⣿⣿⠏⠀⠀⠀⠘⢷⣄⠈⠻⣎⠿⠷⠂⠀⠈⠻⣿⣿⣿⣯⣤⣤⣤⡀⠀⠀⠀⠀⠉⠻⣷⡀⠀⠀⠹⡄⠀⠀⠀⣄⠈⠃⠈⠳⠄⠀ ⢻⣾⣿⠃⠀⠀⢰⠇⠀⣾⡇⠀⢸⠀⠀⣸⢸⢹⣿⡆⠀⢠⡀⠀⠀⠉⠓⠒⠊⠛⠀⠀⠀⠀⠀⢱⢫⣿⠋⠁⣤⡍⢿⡆⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠻⡄⠀⠀⠘⣦⠀⠀⠀⠀⢤ ⠺⣿⡟⠀⠀⠀⣼⠀⠀⣼⠀⠀⡾⠀⠀⣿⣼⢸⢹⣷⠀⠈⠙⠓⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢾⣷⣿⡇⢀⣿⠀⠀⠀⠀⠀⠀⡀⢱⡀⠀⠀⠹⣦⠀⠀⠈⢧⠀⠀⠀⠀ ⣿⣿⠃⠀⠀⠰⡇⠀⠀⡇⠀⠀⡇⠀⣸⣏⡏⢸⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠈⡟⢦⣭⣭⣵⠟⠁⠀⠀⠀⢀⣤⢮⠄⠀⠳⡄⠀⠀⢻⣷⣄⠀⠘⢧⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⡇⠀⢠⡇⠀⣰⡇⢰⣧⡿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠿⠀⠀⠀⠀⠀⠹⡄⠀⠈⣿⣿⣷⣄⠘⡆⠀⠀ ⣿⠀⠀⠀⠀⢸⣇⠀⢸⠀⠀⣿⣇⡿⠛⠁⠀⣀⣶⣖⣊⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠞⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠸⣿⣿⣿⣷⣿⡀⠀ ⡿⠀⠀⠀⠀⠘⣿⠀⢻⠀⠀⣿⡿⢀⣠⣴⣿⠟⢋⣡⣤⣭⣽⡳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢿⣿⣿⣿⣿⣧⠀ ⢧⠀⠀⠀⠀⠀⠹⡄⢸⡀⠀⡿⣷⣾⣿⠏⠁⢴⠟⣁⢠⣿⡏⢻⡀⠙⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠸⣿⣿⣿⣿⣿⡄ ⣾⠀⠀⠀⠀⠀⠀⣇⠈⡇⠀⡇⢻⣿⠇⠀⠀⢸⡀⠿⣿⣿⡇⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⢻⣿⣿⣿⣿⡇ ⣿⠀⠀⠀⠠⡀⠀⠸⡆⢧⠀⡇⢸⣿⡄⠀⠀⠈⠻⠤⣤⣤⠴⠋⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⡜⣿⣿⣿⣿⣿ ⣿⠀⠀⠀⠃⣷⠀⠀⠙⠸⣷⣿⡆⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣰⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢷⣿⣿⣿⣿⣿ ⣿⡆⠀⠀⠀⠸⡇⠘⣇⠀⠈⠻⢿⡈⠻⣆⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢞⣽⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢸⣿⣿⣿⣿⣿ ⣿⣇⠀⠀⠀⠀⢻⡀⠹⡄⠀⠀⠀⣇⠀⠈⠀⠠⠶⠶⡞⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢞⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⣿⣿⣿⠏⢻ ⣿⣿⠀⣠⡀⠀⠀⢧⠀⢹⡄⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⢸ ⣿⣿⠀⣿⡇⠀⠀⣌⣧⠀⢻⣆⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸ ⣿⡞⣸⠁⢻⡀⠀⠸⣟⣆⠀⢻⣦⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣅⣉⣻⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⡎ ⣿⣿⣿⠀⢸⣧⠀⠀⠹⣾⢧⡈⢻⣷⣄⠀⠈⠳⣤⣀⣀⣀⣀⣠⠤⣤⡀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡳⡇ ⣿⣿⣿⢠⠘⣿⣧⡀⠀⢻⡗⢿⣆⡻⣿⡷⣤⡀⠀⠈⠉⠉⠉⠀⢀⡼⣋⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⢣⠇ ⣿⣏⣿⢸⡇⣿⡏⠳⣷⡌⢻⡀⠀⠉⠙⢿⣮⢿⡲⣴⣶⣤⣴⣾⡽⠞⠉⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢀⣾⣿⣿⣿⠟⠁⣸⢀ ⢿⣿⣿⢰⣿⢹⣧⡀⢻⠙⡶⣷⡄⠀⠀⠈⠻⣯⡳⣄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢠⣿⣿⣿⣿⠃⠀⣸⢿⠸ ⠀⠙⠿⣧⣯⣟⡿⡇⠘⡆⢹⣹⡿⣆⠀⠀⠀⠈⠻⣮⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⣰⣿⣿⣿⡿⠁⠀⢠⠇⣸⠃ ⠀⠀⠀⠘⠻⠾⢿⣿⣤⣽⣄⣷⡳⡜⢧⡀⠀⠀⠀⠈⠙⢾⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢾⣿⣿⣿⢿⠃⠀⠠⢾⠃⠁⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠿⢿⣦⡀⠀⠀⠀⠀⠀⠛⠻⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⢤⣀⣠⠞⠁⣠⣴⣿⠿⠟⢛⠠⣿⠇⢠⣾⡿⠀⡆⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣗⣦⣀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣷⣤⣤⣤⣀⣀⣀⣀⣀⣀⡀⣀⡀⠀⣀⣀⣠⣤⣴⣿⣿⠏⣁⡴⠊⢁⣠⡿⢶⡟⠉⠁⠀⡇⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣛⡲⠶⣦⣀⠀⠀⠀⠀⠉⠋⣙⡙⡛⠛⢿⣟⠛⠛⠿⠿⠿⣿⣿⣿⠻⣿⣿⡿⠋⠀⢁⡐⠚⠋⠉⡓⠸⠀⠀⠀⢀⡇⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠔⠓⠀⢙⡆⠀⠀⠀⠀⠀⣖⠀⠐⠒⠤⢹⡀⠀⠀⠀⠀⠀⠀ ⠳⣀⠀⢀⢔⡡⠄⠒⠂⠉⠀⠱⣄⠀⠀⠀⠀⠀⠀⠉⠁⢲⠤⣉⠢⡀⠀⠀⠀⠀ ⠀⠘⡧⣏⠁⠀⠀⠀⠇⠀⠀⠀⠈⠲⢄⡀⠀⠀⠀⠀⠀⡼⡀⠈⢯⡲⠀⠀⠠⡀ ⠀⠀⣇⠀⠉⠐⠒⠂⠚⠂⠀⠀⠀⠀⠀⠈⠙⣲⣶⣶⣿⣿⣷⣤⡧⠉⠓⠤⣄⣰ ⠀⠀⢹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠿⠿⠉⡩⡛⢿⣿⣤⣤⠏⢸⡀ ⠀⠀⢸⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⢸⡀⠀⠒⠊⠀⣏⣿⣥⡄⠀⠃ ⠀⠀⡜⠍⠛⠿⣿⣷⣶⣶⡄⠀⠀⠀⢸⡇⠀⠀⠀⠙⠂⠤⠒⢊⣴⡃⠀⠀⠀⠀ ⠀⡜⠳⢢⠠⣜⠁⠀⠉⠀⡀⠀⠀⠀⠀⠙⠒⠶⠤⠤⢶⡞⠛⠻⣄⢽⠀⠀⠀⠀ ⠀⢳⠁⠚⠂⠞⠀⠀⠀⠈⠛⠳⠄⠀⠀⠀⠀⠘⠀⣿⢻⣟⢿⡷⠁⠘⠒⠚⠁⠀ ⠀⠘⣧⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠷⢋⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢧⡀⠀⠀⠑⠒⠒⠊⠙⠢⢄⣀⡤⠂⠀⠀⠀⠀⠀⠈⠊⣷⠤⠤⠀⠀⠀ ⠀⠀⡰⠋⠻⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡺⠁⠀⠀⠀⠀⠀ ⢠⠞⠁⠀⠀⡇⠙⡶⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣣⡇⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣠⠖⠲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠖⢢⡀⠀⠀⠀⠀ ⠀⠀⣴⠋⢠⡆⢹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇⢰⡀⠹⣦⠀⠀⠀ ⠀⣼⡏⠀⠸⡇⠸⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠁⢸⠃⠀⢹⣧⠀⠀ ⢰⣿⡇⠀⠀⠁⠀⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⠀⠌⠀⠀⢸⣿⡄⠀ ⢸⣿⣿⣦⡀⠠⠀⢻⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⣴⣿⣿⡇⠀ ⠈⠿⣿⣿⣿⣤⣤⣤⡍⢩⣭⡍⠉⢩⣭⠓⢠⣤⣤⣤⣄⡀⠀⠀⣭⣭⣭⣍⡛⢿⢻⣯⠀⠀⢠⣿⣿⣿⠟⠀⠀ ⠀⠈⠙⢻⣿⡟⠛⠛⠃⢸⣿⡇⠀⢸⣿⠀⢸⣿⡟⠛⢻⣷⠀⠀⣿⡟⠛⢻⣿⡄⠈⣿⣇⠀⣿⡿⠛⠋⠀⠀⠀ ⠀⠀⠠⢸⣿⡃⠀⠀⠀⢸⣿⡇⠀⢸⣿⠀⢸⣿⡇⠀⢸⣿⠀⠀⣿⡇⠀⢸⣿⡇⠀⠸⣿⣼⣿⠁⠄⠀⠀⠀⠀ ⠐⠂⠀⢸⣿⡿⠿⠇⠀⢸⣿⡇⠀⢸⣿⠀⢸⣿⣷⣶⣿⠟⠀⠀⣿⣷⣶⣾⡟⠀⠀⠀⢻⣿⠇⠀⠀⠒⠂⠀⠀ ⢀⠔⠁⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⢸⣿⠀⢸⣿⡇⠘⣿⡇⠀⠀⣿⡏⠈⣿⣧⠀⠀⠀⢸⣿⠀⠀⠉⠢⡀⠀⠀ ⠀⠀⠀⢸⣿⠇⠀⠀⠀⠈⢿⣷⣤⣾⡿⠀⢸⣿⡇⠀⢻⣿⡀⠀⣿⡇⠀⢸⣿⡄⠀⠀⢸⣿⣿⣾⣤⢄⠀⠀⠀ ⠀⠀⠀⠈⠉⠀⣀⡀⢀⡀⠀⠉⠉⠉⠀⠀⠈⠉⠁⠀⠈⠉⠁⠀⠉⠁⠀⠀⠉⠁⠀⠀⠈⠉⢻⣿⣿⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⠀⠀ ⠀⠀⢀⣴⣶⡿⠿⣏⡹⠿⢿⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀ ⠀⠀⢸⣿⣿⢃⣾⣿⣿⣧⡸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀ ⠀⠀⠀⣩⣷⣿⣿⣿⣿⣿⣿⣮⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄ ⠀⠀⠀⢿⣿⣿⣿⢿⡿⣿⣿⣿⡿⠀⠀⢀⣾⣷⣼⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠛⣋⣀⡀⠀⠈⠙⠛⠁⣠⣤⣸⣿⡿⢹⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇ ⠀⠀⢀⣴⣿⣿⣿⣿⣷⣄⠀⠀⢀⣿⣿⡇⣩⣾⣷⣮⠰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠛⣻⣵⣿⣿⣿⣿⣷⣝⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡟⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⠿⠿⠋⠉⠉⠙⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠃⠀ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀ ⠀⠐⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀ ⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡾⠿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠀⠀⢸⠇⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡷⠶⡦⣄⠀⠀⠀⠀⠀⠀⠀⣾⠉⠙⢧⡀⢸⡄⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢠⡇⠘⢧⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⢿⣇⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢰⡞⠇⠀⢘⣷⡄⠀⠀⠀⠀⣷⠀⠀⠀⣤⣸⣿⡀⠀⠀⠀⠀⠀⠈⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⢸⠃⠻⣆⠀⠀⠀⢸⣇⠀⢰⣿⣿⣿⣷⣶⣶⣀⣤⣴⣶⣄⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠛⠶⣄⡀⠀⢸⠃⠀⢷⠀⠀⣿⠀⠀⠹⣷⡀⠀⢸⣿⣴⣿⢻⡇⢻⣿⣿⣿⣿⠿⠋⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⣿⠙⢦⣼⡆⠉⠉⠐⠀⣿⠀⠀⠀⠈⢿⣦⣿⣿⣿⢏⣿⠀⣠⣿⣿⠟⢁⣠⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠸⡄⠀⠹⣿⡛⠦⢤⣤⣿⣷⣤⣰⣶⣾⣿⣿⣿⣿⣼⣟⣠⣿⣿⠷⠿⠛⠻⠿⠷⠶⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⣶⠛⠀⠀⠈⢧⡀⠀⠈⠉⠉⠉⠻⣯⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⣀⣀⣀⣀⣀⣀⣙⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠈⣆⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⢹⣿⣿⣿⠟⣡⠖⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⣦⣀⡀⠀⠈⢻⣦⣀⣀⣀⣠⣼⣿⡿⢡⡾⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠙⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢈⣧⡄⠀⠀⠀⠸⣿⣿⣿⣿⣿⢋⡴⠋⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠈⢳⣀⠀⠀⠀⠀⠙⢷⣾⣿⢣⡟⠁⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣋⣉⡉⠃⠀⠀⠀⠀⠀⠀⠘⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠈⠂⠠⡄⢀⠀⠒⠛⣿⡟⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡿⢟⣯⡷⠛⠛⠉⠛⠳⢦⣄⠀⠀⠄⠈⠳⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠛⠉⠀⠀⢸⣯⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⣵⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⢷⣄⠰⣎⣀⠀⠀⠀⠈⠙⢦⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣷⡠⣀⠀⠘⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣴⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⢻⡄⣿⣿⣷⣶⡀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠾⠿⢯⣍⣛⢿⠉⠛⠒⠦⠤⣤⣤⠞⠋⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣀⣀⠀⠀⢋⣼⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⢽⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠈⠙⠿⣧⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠻⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣀⡀⠀⠀⠙⣧⡀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡘⣿⣿⣿⣿⣯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣾⣿⣯⣭⡛⠳⠶⣾⣿⣦⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣧⢻⣿⣿⣿⣿⣿⣮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀ ⠀⠀⠀⠀⢀⣠⣤⣴⣞⣉⣡⣤⣬⠛⠿⠛⠓⠲⠾⠛⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀ ⠀⠀⠀⠀⠸⣿⡟⠉⠉⠁⠀⠀⠀⠀⠙⠿⠿⠷⠶⠄⠀⠈⢧⡢⡀⠀⠀⠀⠀⠀⣼⠇⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢏⣰⣷⠀⠀ ⠀⠀⠀⠀⠀⠘⢧⣄⠀⠀⠀⠀⢤⣤⣤⣤⣴⠶⠶⠦⠀⠀⠀⠻⣝⡲⠤⠀⠀⠀⢀⣼⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣍⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⡴⠋⣱⢋⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣶⣖⣦⣤⣭⡀⠀⠀⠀⠀⣠⣶⠞⣛⣨⣙⣲⣶⡶⠶⠛⣟⠛⠒⢦⣄⡉⠉⣿⡻⢿⣿⣿⣿⣿⣿⣿⣷⣤⡉⠛⠻⣿⣿⣿⡿⠛⠚⢉⣀⡾⢷⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⡿⠛⢉⣡⣴⡶⠶⠶⠶⢿⣫⡿⢛⣉⣉⣉⡉⠉⠛⠷⣦⡙⣷⡀⠀⠈⠙⢶⣄⠀⠀⠀⠈⠉⠋⠙⠛⠛⠛⠿⠒⠶⠶⠋⠁⠀⠀⠉⠉⠁⣠⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢁⡼⣡⣶⠟⠁⣠⣦⣠⣴⠶⠟⢋⣴⠟⢉⣉⣉⣁⠀⠀⠀⠈⠻⣄⠙⢶⡄⠀⠀⠈⠓⠦⣤⡉⠲⠦⣄⠀⠀⠀⠀⠀⠀⠀⣀⠰⠦⢄⣀⣴⣾⣋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡤⠞⢻⣿⠟⠀⢀⣾⣿⠛⠁⠀⠀⣀⣤⣴⠾⠿⠛⠋⠛⢻⠷⢤⣤⣀⠙⠓⠦⢤⣄⡀⠀⠀⠀⠙⢮⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⢴⣟⠁⠈⠙⠢⣄⠀ ⠀⠀⠀⣤⠞⠉⠀⣰⡟⠁⢀⣴⣿⣿⠁⠀⠀⣴⣾⡿⠻⠗⢀⣤⣤⣄⡀⠈⢷⡄⠀⠉⠙⠒⠦⢤⣈⣙⠓⠶⠤⠄⠐⠻⢦⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠮⣟⣢⣄⡀⠈⠑ ⠀⣠⠞⠁⠀⠀⠚⠛⠒⢛⣿⣿⢹⡇⠀⢠⡿⣿⢃⣠⣴⡞⢻⣿⠛⠻⣿⣷⣦⣙⣦⡀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠒⠢⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣻⣦⠄ ⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣇⢀⡟⠀⡿⠋⣹⣿⣧⠸⣿⡇⠀⠀⠉⠳⢮⣄⡙⠶⣄⣀⡈⠉⠉⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠶⢶⢶⣾⣏⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣻⣾⠀⠀⠀⠀⣿⣿⣿⠀⣿⣇⠀⠀⠀⠀⠀⠈⠻⢦⣀⠉⠙⠛⠶⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠥⢤⣔⠶⣿⣟⠷⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠋⠀⠀⠀⠀⣿⢣⣿⠀⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠖⠋⠀⠀⠀⠀⠈⠻⡿⣿⢷⣌⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣟⠻⣍⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠚⢳⣄⠀⠉⠉⠓⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣠⠔⣪⠟⠋⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⠁⡠⠊⠁⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢈⡜⠁⠀⠀⡇⠀⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⠋⠀⠀⠀⢀⣠⡴⠃⡇⠀⠀⠹⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⢸⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⡌⠀⠒⠒⠚⠉⠉⠳⡀⠘⠀⠀⠀⡠⠢⠭⡑⠒⠤⣀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠈⠳⣄⠀⢸⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⢇⠀⠤⠒⠻⣿⣿⡆⠀⠀⠀⠀⠞⢷⣶⣶⠦⢤⡀⠀⠁⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠈⠳⣼⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⡸⠀⠈⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠲⠭⢄⣀⣠⣾⠃⠀⠀⠀⢈⡿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣠⠃⢀⠔⡏⠀⢯⡉⢉⡽⠃⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⠀⠀⠀⠀⣇⠘⢆⠀⠀⠀⠀⠀⢠⣿⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⢧⢀⠞⡟⠀⠀⠀⢇⠀⢀⣹⡁⠀⠀⠀⠀⠀⠀⣀⡠⠔⠊⠁⠀⠀⠀⠀⠀⢸⡄⠈⠣⡀⠀⠀⣠⠎⢸⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⢳⡀⠀⠀⠀⠙⠧⣀⣈⡵⣶⣶⠿⣷⠞⠋⠀⠀⠀⢀⣤⡄⠀⠀⠀⢀⡷⠀⠀⠙⣄⡴⠃⠀⢸⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣄⠀⠀⠀⠀⣼⠁⣴⠞⠁⣰⠃⠀⠀⠀⠀⠀⠈⠛⠃⠀⢀⡴⠿⣤⣤⠤⠖⠋⠀⠀⠀⢸⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠰⡻⡀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣷⣈⠋⠙⢚⣠⡶⠇⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⡍⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⠏⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡼⠷⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⢸⠀⠈⡆⠀⠀⠀⠀⠀⢀⠔⠁⠀⡰⠁⢀⠀⢻⡙⠳⢤⡀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠁⠀⠀⠀⢸⡄⠀⠘⣄⠀⢀⣠⠔⠁⠀⠀⢰⠃⠀⢸⢠⠀⢣⠀⠀⠉⠳⢤⡀⠀⠀⢸⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣤⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⡰⡿⣦⠟⠙⡄⠀⠀⢠⠃⠀⠀⠸⡈⡆⠈⡆⠀⠀⠀⠀⠉⠳⢤⣸⣿⣿ ⣿⣿⡇⠀⠀⠀⢀⡴⠛⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠁⣸⢹⠀⠀⠸⣄⢀⠏⠀⠀⠀⠀⢧⡇⠀⠀⠀⠀⠀⠀⡠⠂⠒⢿⣿⣿ ⣿⣿⡇⠀⠀⢠⡟⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⣿⣿ ⣿⣿⣇⣀⣀⣼⣀⣸⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣇⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣎⣀⣀⣀⣠⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀ ⢀⠀⠀⠀⠐⠒⠀⠀⠉⠀⢂⡤⠤⠄⠀⠐⠀⠈⠉⠁⠀⠀⣀⠄⡠ ⠀⠈⠕⠒⠀⠀⠀⠀⡠⠖⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠊⠀ ⠀⡠⠂⠀⠀⠀⣠⠟⠹⢟⣡⢤⣦⡤⠀⠤⣀⡀⣠⢾⠟⡕⠁⠀⠀ ⠛⠂⠀⠒⢲⣾⡿⠀⠐⣇⠈⠜⠛⠁⠀⠀⡊⠵⡛⣥⡾⠇⠀⠀⠀ ⠀⠀⠀⣀⣼⡋⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠈⠳⡝⠀⢐⠩⢉⠀⠀ ⠀⠀⠀⢿⡖⠋⠀⠀⠀⢀⡠⠜⠉⠁⠀⠀⢀⠔⠁⠀⠐⠃⠆⡴⠀ ⠀⠀⠀⠈⠺⡒⠠⠝⠋⠁⠀⣀⣀⢤⠔⡾⠁⠀⠲⠎⠀⠀⡸⡀⠀ ⠀⠀⠀⠀⠀⠑⠂⠒⠚⢿⣻⣿⠟⠃⡜⠀⠀⠀⠄⠽⠓⠰⢁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠀⠀⢀⠀⣤⡐⡖⠄⠤⠞⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⢃⡀⠀⠀⡀⢔⠇⠘⡏⢈⡱⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣀⢉⠤⠤⣾⡣⢤⣜⡀⢀⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡞⠂⠐⠗⠃⠋⠀⠠⠎⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣄⡀⠀⠀⠀ ⠀⠀⣤⡶⢶⣖⡶⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡿⠛⠉⢉⠉⠙⣿⡄⠀⠀ ⠀⠀⣿⢰⣌⣭⡽⠷⠶⢮⣭⣛⣲⢶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣻⡵⢞⣋⣥⠶⠶⠒⠿⣧⡀⢸⣿⡀⠀ ⠀⠀⡏⣾⡟⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣌⡙⠻⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⣿⣫⣷⠞⠋⠉⠀⠀⠀⠀⠀⠘⣧⠀⡟⡇⠀ ⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣌⡛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣿⣿⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⡇⢿⠀ ⠀⣿⡟⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢩⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣧⢸⠀ ⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⡿⣷⣶⠶⠶⠒⠒⠒⠲⠶⢶⣦⣤⣤⣴⣷⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾⠀ ⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠚⠛⠋⠉⠉⠉⠉⠉⠉⠑⠒⠛⠿⢿⣥⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢀⡿⠀ ⠀⠸⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀ ⠀⠀⢻⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⣿⠁⠀ ⠀⠀⢺⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢩⡇⠀⠀ ⠀⠀⠈⠻⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣣⣿⡇⠀⠀ ⠀⠀⠀⢰⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣼⠟⠁⠀⠀ ⠀⠀⠀⣿⢁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀ ⠀⠀⣸⠇⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⠶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀ ⠀⢠⡟⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⡿⠁⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠉⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⣆⠀⠀⠀ ⠀⣸⢳⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⢼⣿⣿⠿⣦⣄⣠⣾⣿⣧⠀⠀⠀⠀⠀⠀⣸⣇⣀⣀⣴⡿⢿⣿⣿⡏⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⢿⡀⠀⠀ ⠀⡏⢼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠸⣿⣷⣤⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣄⣴⣿⣿⠇⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡞⣧⠀⠀ ⢰⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠙⠿⣿⣿⣿⣿⠟⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣿⡄⠀ ⢸⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠁⠀⠀⠀⠀⠀⢻⣿⣍⠙⠛⠉⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀ ⣸⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⣿⣗⣒⠒⢚⣋⣡⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣦⣀⠀⢀⣤⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀ ⣿⠘⣇⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣤⠀⠀⠀⣼⢻⣿⠀ ⣿⠀⢻⡄⠀⠀⠰⠿⢿⣿⡶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢟⣿⣿⣿⣿⠀⠀⠀⣿⢸⣿⠀ ⣿⡄⠀⢻⣄⠀⠀⠀⠈⠻⣿⣶⣍⡙⠳⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⣡⣴⣿⠟⠉⠉⠀⠀⠀⢠⡟⣸⣿⠂ ⠙⢿⣦⡀⣹⣶⣄⡀⠀⠀⠈⠙⠿⣿⣷⣶⣬⣝⣛⣶⡤⣤⣤⣀⣀⣰⣄⣾⣷⣄⣀⣾⠀⠀⠀⠀⠀⣀⣀⣠⡤⠴⠞⠛⠋⢁⣠⣴⣾⣿⠟⠁⠀⠀⠀⠀⠀⣠⠟⢡⣿⡟⠀ ⠀⠀⠙⢿⣮⣟⠿⣟⠶⣤⣀⠀⠀⠈⠙⠻⢶⣬⣝⣛⠿⠿⢿⣶⣤⣬⣥⣄⣃⣉⣉⡀⠚⠻⠿⠿⠛⠛⣛⣛⣀⣤⣤⣶⣾⣿⣿⠟⠋⠁⠀⠀⠀⠀⢀⣤⡾⢏⣴⡿⠛⠀⠀ ⠀⠀⠀⠀⠈⠛⠷⣮⣗⣈⠙⠛⢦⣄⣀⠀⠀⢈⣍⣛⣿⡆⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢉⣽⠿⠿⠛⠉⠀⠀⠀⠀⠀⣀⣤⡾⢟⣫⣴⠿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣶⣦⣬⣉⣙⠳⠿⣭⣽⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣻⣥⣤⣄⣤⣤⣤⡶⠿⣛⣭⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣶⣶⣶⠶⠶⠞⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣺⣿⠿⣷⣦⡀⣄⠀⠀⠀⠀⢀⣤⣶⣿⣿⣷⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⢽⢿⣿⣷⡀⠀⢰⣿⠋⠁⠀⠈⠙⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠈⣧⠹⣿⡇⠀⣿⡇⠀⠀⠀⠀⢦⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢸⣿⠀⣿⡇⣸⣿⡄⠀⠀⠀⠀⠀⢣⠈⣿⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣹⣇⠀⠀⠀⠀⣸⡏⠀⣿⡇⣸⡿⠀⠀⠀⠀⠀⠀⣸⠀⢻⣿⠀⠀⢀⡖⣀⣤⣶⣶⡂⠀⠀⠀ ⠀⠀⣀⣀⣀⣄⡀⠀⠀⢸⣿⠉⠀⠀⠀⣴⣿⣤⢄⣿⡇⣿⡇⠀⠀⠀⠀⠀⣴⣿⣁⣼⣿⡀⢠⣿⣿⡿⠛⠙⢿⣷⣀⠀⠀ ⢀⣾⣿⣿⣿⣿⣿⣶⣄⠘⣿⡆⠀⠀⠀⢠⣾⢻⣾⣿⠁⢻⣷⠀⠀⠀⠀⠀⢉⡽⠙⣿⣿⡇⣿⡟⠛⠀⠀⢆⠀⢿⣿⡀⠀ ⣿⣿⠋⠀⠀⠲⢌⡛⢿⣧⡘⣿⣦⣄⣀⣿⣧⣾⣿⠃⠀⠹⣿⣗⡀⠀⢸⣶⡟⣠⣾⠏⢸⣿⡿⠀⠀⠀⠀⠘⣆⡈⣿⡇⠀ ⣿⡟⠀⠀⠀⠀⠹⣿⠄⢻⣿⡌⠛⠿⢿⣿⡿⠃⠀⠀⠀⠀⠈⠛⠿⣷⣾⣷⣾⠟⠁⠀⢸⡇⠁⠀⠀⠀⠀⢠⠏⡇⢻⡇⠀ ⢻⣷⠀⠀⠀⠀⠀⠹⡆⢸⣿⡷⠀⠀⠈⠋⢀⣠⣴⣶⣶⣤⡄⠀⠀⠀⠈⠉⠁⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⢠⡇⣿⡇⠀ ⣎⣿⣧⡀⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀⣠⣾⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠈⣿⣇⠀⠀⠀⠀⣀⣼⠃⣿⣷⠃ ⢿⣿⣟⡛⠂⠀⠀⠀⣿⠃⣿⡇⠀⢰⣿⣿⠋⠀⠀⠀⠀⠉⠉⠉⠉⠛⠉⠉⠛⢿⣿⣆⠀⠹⣿⣆⠀⠀⢀⣿⠏⢠⣿⠇⠀ ⠀⠻⣿⣦⣀⠀⠀⢀⣿⣴⣿⡇⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⣿⣿⡄⠀⢻⣿⣀⣠⣾⢃⣴⣿⠏⠀⠀ ⠀⠰⣿⣿⣧⣀⢀⣾⡿⠛⠟⢀⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⢸⣿⣿⡄⠸⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀ ⠀⠀⠈⠙⠿⢿⣿⣿⠁⢀⣤⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠀⠀⠈⠻⣿⣧⡀⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣷⣦⣄⠀⠘⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠙⠃⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⠛⢻⡇⠀⠀⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣴⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⣀⣤⡴⠂⠀⣠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠉⠻⣿⣿⣦⣀⣠⣤⣶⣾⣿⠿⠋⠁⢸⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⠀⠀⠀⢰⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⡉⠢⠄⣀⠱⡈⠁⠒⠀⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠡⡀⠀⠀⠈⠉⠀⠀⠐⠂⠄⡠⠀⣁⣂⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠉⠑⠃⠤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠽⠛⠑⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⡀⢣⠀⠀⠀⠀⠀ ⢀⣔⡥⠊⠀⠀⠘⠦⢄⠀⠀⠀⠀⠀⠀⠀⢮⠤⢔⣱⠚⠀⢄⠀⠀⠀⠀ ⠀⣜⠄⠀⠀⠀⠀⠀⢀⠽⢦⡄⣀⡀⠀⠀⡀⠑⠺⡊⠀⠀⠀⠁⢂⠤⡀ ⢐⢃⡴⠂⠀⠀⠀⠀⠀⠙⠂⠤⢶⢅⡀⠀⠐⠢⠄⡀⠀⠀⠀⠀⠀⢡⡸ ⠘⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠩⣹⡄⣀⠀⠀⠓⠐⠤⢤⢄⢀⠔⠁ ⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣷⡄⠈⢐⠦⣀⣀⡤⠓⣷⠀⠀ ⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠠⡈⢷⡄⠀⠀⠈⠀⠀ ⠀⠀⠀⠑⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡌⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠢⢄⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡜⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠀⢄⢀⢠⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠐⠀⠀⢠⡔⠉⡠⢚⡿⠉⠀⢀⢀⣴⡾⠉⠀⣠⣤⣴⢞⡿⠋⠀⣠⢄⡞⠁⠀⠀⢰⠇⠀⢸⡀⠘⢆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⢠⠏⣠⣾⢶⣟⣀⣀⣈⡴⠋⡾⠁⣠⡾⠋⡴⣳⠋⠀⣠⠜⠀⡜⠀⠀⠀⣠⡏⠀⠀⡀⠘⡄⠈⡆⠀⠀ ⠀⠀⠀⠀⠀⣸⠁⠀⠀⣸⡜⠀⠎⣴⠟⢡⠎⣠⠎⡠⠋⠉⣹⠓⢲⠿⢄⣼⣟⠁⠀⡴⠋⠀⣰⠃⠀⠀⣰⡟⠀⠀⢠⡇⠀⠸⡆⠸⡀⠀ ⠀⠀⠀⠀⢀⣷⡀⢀⢀⡟⠀⢠⠞⠁⢀⣎⣼⢃⠞⠀⠀⢠⠇⠀⠁⠀⣼⡟⠉⣩⠟⠉⠉⣍⡇⠀⠀⣰⡟⢀⠀⢠⣿⠀⠀⠀⣿⠀⡇⠀ ⠀⠀⠀⠀⢸⠉⣧⣀⣿⣳⣦⣾⣶⣶⣾⣿⣷⣿⣤⣀⡀⣼⣦⠂⢀⠎⡜⢀⣾⠃⠀⠀⠈⡾⠀⠀⢸⡿⢀⡞⢀⣾⡟⠀⠀⠀⣿⡆⡇⠀ ⠀⠀⠀⠀⠈⠀⢹⣆⣿⠛⠻⢿⣯⣙⣿⡿⠋⠛⠻⣿⣿⣿⣯⡀⠀⡜⣠⢿⠃⠀⠀⠀⣰⡇⠀⠀⣾⡿⣿⠀⣰⣿⠃⠀⠀⢀⡿⡇⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠈⠹⠟⠒⠦⠤⣀⡹⣌⣿⢻⣿⣴⣽⣧⡏⠀⠀⠀⡜⣿⠀⠀⣸⠋⢸⠋⣷⣿⠇⠀⠀⢀⡿⢱⠁⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⣀⢅⠀⠀⠀⠀⠈⠙⠻⠍⠈⡿⠁⣿⠁⠀⠀⡜⠀⡏⠀⢠⣿⣶⣧⣞⣀⡟⠀⠀⠀⡼⠁⡜⢠⠀⠀ ⣆⠀⠠⠀⣆⠀⠰⣿⠈⣯⠀⡄⡨⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⡄⣸⠀⠀⡜⣀⣼⡧⠶⣿⣻⡿⢯⠛⣻⣧⡄⠀⡰⠃⣰⠃⡜⠀⢀ ⠛⣆⠀⠀⢸⡀⠀⠘⡆⠈⢇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⢹⡶⢾⠟⠁⠘⡇⢠⡟⠯⣀⡼⠐⢋⣽⣿⠞⠁⣰⡟⣰⠃⠀⠎ ⠀⢟⣦⠀⠀⣷⣀⠀⠹⡄⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⣼⠀⠀⠀⡇⡌⠙⠒⢤⡀⠀⠉⢼⡟⢦⠞⣹⣵⠏⡴⠃⠀ ⢀⣘⠀⢓⣤⣍⠉⠳⢤⣘⢆⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠤⠀⠀⠸⣇⢳⡤⠊⠉⠒⢲⠿⡟⠁⣰⣿⡿⠋⠀⠀⠀ ⣾⠿⣧⢸⡏⢹⡇⢆⠀⠈⢉⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠞⠀⠀⠀⠀⠀⢠⣧⢞⣽⡟⠀⠀⠀⢀⣀ ⣿⠀⣿⣸⡇⣼⠇⠈⠇⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠋⢸⠀⠀⠀⠀⠀⠙ ⣿⠀⣿⣿⠁⣿⠀⠀⠀⠀⠀⠈⣧⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠸⡀⠀⠀⠀⠀⠀ ⡿⠀⠈⣿⢠⡿⠀⠀⠰⠤⠀⢀⡞⢏⣉⡩⣍⡉⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢇⠉⠒⠤⢤⣤⠄ ⠀⢀⡾⣿⠿⠃⠀⠀⡀⠀⠀⠘⡿⠋⢹⡇⠀⢯⠉⠉⠙⡟⠛⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡰⢻⡄⠀⠀⢸⠑⠒⠈⢉⡀⠀ ⣠⣾⠇⢸⡄⠀⣤⠀⢱⠀⠀⠀⠙⠒⠺⡇⠀⢸⠀⢠⠀⡇⠀⠀⢤⡈⠑⠒⠦⠶⣶⡀⠀⠀⠀⠀⢠⣿⠁⠈⡇⠀⠀⡜⠀⠀⠐⠁⠀⢀ ⠋⠉⡆⠀⢷⠀⠘⣄⠀⢇⠀⠀⠀⠀⢀⡇⠀⢸⠀⢸⠀⣇⡀⠀⠀⠈⠒⠶⢄⡀⠀⠙⠲⢄⣀⡰⠟⠼⠀⣰⢁⣠⠞⠁⣀⡠⠤⠒⠒⠛ ⠀⠀⡇⠀⠸⡆⠀⠈⢦⡈⡄⠀⢀⠀⢸⠀⠀⠰⠀⣾⠀⠀⢿⠀⠀⠐⣄⠀⠀⠉⠒⢤⣀⠀⠉⠳⢄⡀⠈⠉⠉⠀⠀⢸⡁⠀⠀⠀⠀⠀ ⡇⠀⡇⠀⠀⣧⠀⠀⠀⠙⢿⡴⣜⡆⢠⠀⠀⠀⢇⡟⠀⠀⢸⡄⠀⠀⠈⢆⠀⠀⠀⠈⢳⣍⡒⢤⣀⠈⠑⠢⢄⣀⠀⢠⣧⠀⠀⠀⠀⠀ ⠘⢀⣡⣤⣄⢼⠀⠀⠀⠀⠸⣿⣿⣼⣾⠀⡆⠀⢸⡇⠀⠀⢼⢷⡀⠀⠀⠈⢷⡀⠀⠀⠀⢹⡝⠦⣍⡛⠶⣤⣀⠈⠙⠺⣿⣷⣤⣶⠒⠒ ⣴⡟⢋⣾⠏⢸⠀⠀⠀⠀⡀⢻⣿⣿⣧⠀⠇⢠⢸⡇⡀⠀⠈⠀⠳⡄⠀⠀⠈⢻⣄⠀⠀⠀⣿⢦⡀⠙⠲⣄⣀⠉⠒⢤⣈⠈⠉⠙⢷⠤ ⠋⣠⡟⠁⠀⢸⠀⠀⠀⠀⢣⠈⣟⣿⣿⡆⠀⢈⣿⠀⡇⠀⠀⠀⠀⠙⢄⠀⠀⠀⠉⢃⣀⣀⣿⣤⣽⠾⠤⠬⠭⠷⠤⢀⡈⠙⠒⢤⣈⠀ ⣼⠟⠠⢤⣤⣼⣄⣀⠀⠀⠀⠻⣿⣟⣿⣿⡀⠘⣿⠀⡟⠀⣀⡠⠤⠀⠀⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⣀⣠⣽⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡤⣶⣿⣻⡤⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⠋⠀⠉⠀⠀⠀⠀⠀⠉⠛⠣⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⣀⠀⢀⡴⠞⠁⠀⣠⠀⠀⠶⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡠⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⢠⠎⠁⠀⠀⠈⣠⡾⠤⠴⣶⠞⢁⡴⣾⠋⠀⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠥⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣀⡤⠴⠚⣿⠁⢀⣴⠋⠁⠐⢋⡴⠋⠀⠀⢀⡟⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡀⢤⡶⠚⠉⠀⠀⠀⢠⡏⣰⠟⠁⠀⠀⢀⡞⠀⠀⠀⣰⣾⠁⠀⠈⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⡶⢶⠉⠀⠀⠀⠱⢤⣀⣀⣀⡴⣻⡿⠁⠀⠀⠀⢠⠏⠀⢠⣷⣿⡟⠛⣿⣇⠀⠀⠀⠙⢦⣠⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢳⠸⡇⠀⠀⢠⣶⡄⣠⣄⠀⣰⠋⠀⠀⠀⠀⢀⡏⠀⡴⠋⣡⠏⠀⣀⠈⠑⢶⣦⣄⠀⠀⠈⠳⢤⡙⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡄⢿⠀⠀⠈⠛⠁⠈⠁⣰⠋⠀⠀⠀⠀⢠⡞⠀⣼⣁⣼⣿⣿⣿⣿⣷⣄⠀⠙⢿⣿⣶⣤⣄⣰⣏⠳⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⢺⠇⠀⠻⣿⡟⠁⡴⣿⣿⡿⣯⠁⠀⠀⠈⠛⣿⣿⣯⢻⢦⡀⠙⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠚⠳⣦⡤⠄⢠⡀⠀⣀⣸⠀⠀⠀⠀⢰⡀⢸⠀⢀⢸⡏⠳⠤⣵⡘⠋⡰⣿⠀⠀⠀⠀⠀⣿⡿⣻⡿⠈⢿⣷⢸⡷⠀⢀⠀⠀ ⠀⠀⠀⢀⣤⣿⡻⠒⢿⣷⣏⣉⣿⠀⠀⠀⠀⠸⠃⢸⠀⡎⡟⡇⠀⠀⠀⠈⠉⠉⠛⢄⠀⠀⠀⠀⠈⠻⣉⠀⠀⠈⣿⠞⠁⢠⠎⠀⠀ ⠀⢴⣶⡟⠁⠈⠻⣄⣮⢿⣝⢻⣿⡄⠀⠀⠀⠀⠀⠈⡇⢱⡻⣷⠀⠀⠀⠀⡀⠀⠀⠀⠑⠀⣴⣶⣶⣦⠀⢳⠀⢀⡟⠀⢀⣏⠀⠀⠀ ⠐⠢⠤⣉⡙⠒⠒⠿⠿⠔⠿⣿⢿⢷⡀⠀⠀⠀⠀⠀⠹⡄⠳⠙⣆⠀⠀⠀⠙⣄⠀⠀⠀⠀⠈⠙⡟⠁⢀⠃⢀⡜⠀⢀⡞⢧⠀⡴⠀ ⠀⠀⠀⠁⠈⠹⢭⠉⠒⠂⠀⠙⠺⡧⠷⣄⠀⠀⠀⠀⠀⠉⠀⠀⡈⢦⡀⠀⠀⠈⢳⣶⣄⣠⣤⣤⣤⡴⠁⡰⠋⠀⠀⣸⠴⠿⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠞⠳⡄⠧⠴⠀⢰⠟⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠈⠲⣵⣤⣀⠀⠀⠙⢿⣿⣿⣿⡿⢀⡞⠁⠀⠀⠠⣝⡆⣠⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠦⣠⠏⠀⠀⣰⠃⠈⠳⣷⣄⠀⠀⠀⠀⠀⠙⣿⣝⠿⠲⢄⣀⠉⠉⠉⡱⠋⠀⠀⠀⠀⠀⠀⠹⡇⢻⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⣰⠃⠀⠀⠀⠈⢿⡳⡄⠀⠀⠀⢀⠘⡟⣆⡀⠀⠀⢀⣀⣸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⢿⡟⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⠿⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⢀⣺⡄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢸⠉⠀⠀⠀⠀⣰⠁⠀⠉⢛⠓⠒⠒⠒⠛⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⢀⡿⠏⠀⠙⢦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠐⢂⠄⠑⢄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠮⡏⢸⡟⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⡟⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢸⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣤⠖⠛⢉⡵⠁ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡠⠤⣒⡯⠟⠊⠉⠀⠀⡠⠊⠀⠀ ⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⣠⣴⠟⠋⣡⠔⠊⠁⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠀⠀⡀⠀⠀⠀⠈⣆⠀⠀⠀⣀⠔⣯⣠⣾⡵⠶⢤⣀⣠⠞⠋⢀⠔⠊⠀⢀⣀⣀⡀⠀⠀⡰⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠟⡄⠀⣇⠀⡤⠀⠀⠸⣤⡴⠛⠁⠀⣼⠋⠉⠀⠀⠉⣓⣮⣷⣾⣧⣐⣺⠝⠋⠁⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⡆⢇⠀⡿⣤⡃⠀⣤⠞⡽⠁⠀⠀⢰⠃⠀⢠⣦⠖⠋⠁⠉⠢⡙⠻⢦⡑⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣧⠘⡦⠃⠃⢨⠎⠀⡼⠁⠀⠀⠀⣾⠀⢀⠾⡍⠓⢦⣀⠀⠀⠈⢦⠀⠹⣦⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡤⢾⡇⠹⡀⣰⠃⠀⢰⠃⠀⠀⠀⡜⠹⡄⠀⢀⡇⠀⠀⠈⠳⡀⠀⠈⢇⠀⢹⣟⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣯⣶⠋⠹⣄⢿⠇⠀⠀⡞⠀⠀⠀⡼⠀⠀⡇⠀⢰⡇⢠⣠⣶⣶⣿⣶⣶⣺⡄⠀⣿⢰⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⡿⡽⠁⠀⡀⡞⡜⠀⠀⠀⡇⠀⠀⢰⠁⢀⣀⣧⠀⢸⢠⣾⣿⣿⡗⣏⢿⡟⢛⣇⣄⣿⡧⣇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡾⢸⠃⠀⡜⣰⣁⣇⣀⣀⣠⡧⡤⣴⣿⣉⡁⠀⡟⠀⡾⢸⣿⣿⣿⣷⢺⠀⢧⢰⢿⣹⣧⣡⠤⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣷⡏⠀⣼⠁⢻⠍⣯⠀⢀⣸⣿⡿⢽⣿⣿⢻⣷⡇⢀⠇⠀⠘⠮⣛⣋⠼⠀⢸⣼⣿⣿⢿⡓⢦⣼⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⢰⢻⠀⠈⡇⡟⣌⣻⣿⣿⡃⢺⣿⣿⡿⡻⡇⢸⣀⡠⠤⠀⠀⠀⠀⠀⢸⡇⣹⠇⠀⠙⢦⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⢸⢸⡀⠀⠹⣷⣹⡉⠙⢻⢇⠈⡇⠩⠑⢡⢋⡏⠀⠐⣣⡀⠀⠀⠀⠀⢸⠇⡟⣀⡀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⡀⠻⣼⠀⢇⠀⡰⢛⣏⠹⡄⠈⢏⢆⢃⠀⠀⢸⣸⠀⢀⣜⡻⠽⡄⠀⠀⢀⣿⢤⡀⣸⣿⢧⣀⡇⠀⣀⣀⣀⣀⣀⣀⠀⠀ ⡇⠀⠀⢻⣆⠘⡄⣷⣿⠋⠣⣙⢆⠈⢎⢾⡄⠀⣜⠇⠀⠸⣋⠤⠞⠁⣠⢖⣿⠷⣰⣽⠏⡇⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⡇⠀⠀⠀⠙⣄⠘⣝⣿⡀⠀⣼⡟⠳⢌⢧⣽⣦⣿⣤⣤⣤⣤⣤⠴⠚⣿⠮⡞⢀⡿⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠁⠀⠀⠀⠀⠈⠀⠈⢷⡑⠤⣏⣇⢀⣶⡿⠛⢾⠧⢼⡇⠀⠀⠀⠀⠀⡟⠀⣡⣿⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢀⡨⠿⣖⠛⠢⢌⣀⣸⡇⠀⠀⠀⠀⠀⢻⣺⠟⠁⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⢮⠥⠀⠈⠑⠠⠤⠮⠁⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⠏⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⢉⡤⠁⠀⠀⡀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢤⣖⣋⣧⡴⠤⠤⢴⣒⠾⠭⠁⠀⠀⠉⡀⠀⠀⠀⠀⠱⡀⢼⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠁⠀⢀⣠⢯⠇⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠳⡀⢱⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⣰⣇⠼⢤⠤⢞⠑⢦⠀⠀⠀⠀⠀⡤⠒⣶⠒⢣⠤⣧⡈⢿⡆⠀⠀⠀⠀⠀⣾⡷⡏⢸⠀ ⣆⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣠⡎⠈⢻⠀⠘⡄⢸⡀⢸⣀⣀⣀⣀⣀⡇⢠⡇⠀⡞⠀⣿⠓⣄⣳⣀⣀⣀⣐⣊⣁⣉⣁⣸⠀ ⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠲⠬⠧⢄⡗⠼⠙⠋⠉⠉⠉⠉⠉⠙⠾⠣⡞⠧⠼⠧⠔⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠀ ⠀⠀⢠⡀⡀⢠⣄⢀⡄⢠⣄⣠⣤⣤⡖⣀⣤⣄⠀⠀⢠⠀⠀⠀⣶⣄⣠⣤⣠⠀⣀⣀⣤⣀⣀⣤⣀⡀⢠⣤⣦⡤⡤⣄⠀⠀ ⠀⠀⠈⣿⣳⡏⣿⢛⣗⣾⣽⣼⡇⠀⠀⣿⣓⡟⠀⢠⣟⣷⡀⠀⠈⠀⡗⠋⢻⣠⣯⣿⣖⡋⣧⣔⡃⣱⠋⠀⠁⣚⠋⠁⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠈⣁⡀⠀⠈⣀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶⢶⣄⠀⠀ ⠀⠀⣿⢩⣛⣿⣯⣽⣒⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⣛⣩⡤⠤⣦⡀⢻⡆⠀ ⠀⠀⣇⣼⠋⠀⠀⠀⠀⠉⠛⠦⣌⡙⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠟⠋⠉⠀⠀⠀⠈⣧⢸⣷⠀ ⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣽⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⣻⠀ ⠀⢸⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣄⣀⣠⣤⣤⣤⣤⣀⣀⣀⣸⣽⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹⠇ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠒⠚⠛⠒⠒⠒⠛⠻⠿⣿⣭⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⠀ ⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡟⠀ ⠀⠀⣹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢾⠇⠀ ⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣾⠀⠀ ⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣽⠋⠀⠀ ⠀⠀⢰⡇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢉⣁⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡋⠀⠀⠀ ⠀⠀⡞⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡟⠉⠉⢳⡀⠀⠀⠀⠀⠀⢀⠴⠒⢿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⠀ ⠀⢸⢳⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠻⣿⡿⢧⣤⣤⣾⣷⡀⠀⠀⠀⠀⣿⣀⣀⡼⠿⣿⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀ ⠀⡞⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢿⣷⣾⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣷⣴⣿⡟⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡾⡆⠀ ⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠙⠛⠛⢛⣹⣿⠇⠀⠀⠀⠘⣿⡿⠿⠿⠛⠉⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀ ⢠⢇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡤⠤⠐⣚⣽⠿⠋⠀⠀⠀⠀⠀⠹⣿⣦⣀⠀⢀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀ ⢸⠈⣇⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⣠⣴⣶⡆⠀⠀⣿⣿⠀ ⢸⡇⠹⣄⠀⠈⠙⢿⣿⡲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣾⣿⡿⠿⠇⠀⠀⡇⣿⡇ ⠘⢷⣄⠙⣦⡀⠀⠀⠙⠻⣷⣮⣽⣓⣶⣤⣀⣀⣀⠀⣄⣠⣦⠀⣠⠄⠀⠀⠀⠀⢀⣀⣠⠤⠶⠒⢉⣤⣾⡿⠃⠀⠀⠀⢀⡼⢁⣿⠃ ⠀⠀⠙⢿⣿⣿⣷⢤⣀⠀⠈⠙⠻⢯⣿⣛⠿⠿⣯⣭⣼⣍⣊⣙⣉⠒⠲⠶⠟⢛⣻⣁⣤⣤⣶⣿⡿⠟⠉⠀⠀⠀⢀⣴⢟⣤⡿⠃⠀ ⠀⠀⠀⠀⠈⠛⠿⣦⣌⡙⠲⢤⣄⣀⡬⣽⣿⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⢡⣿⣟⠉⠁⠀⠀⢀⣠⣴⢞⣫⡷⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⢶⣭⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣓⣚⣛⣿⠽⠞⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⠀⠀⠀⠀⠀⠘⡏⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⡏⠑⢤⣀⠀⠀⠀⠘⢦⠀⠉⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⡄⠀⠈⠉⠒⠢⠤⢀⣳⣄⠀⠀⠀⠀⠉⠉⠑⠒⠒⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠐⠒⠠⢄⡀⠀⢀⠀⠀⠉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢟⠉⠙⠛⢶⣶⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠉⠛⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⣈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡨⠿⠖⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠔⠉⣀⠀⠀⠀⠘⣍⡓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢈⣆⠈⢣⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣧⡴⠋⠁⠀⠀⠀⠀⠈⠻⠷⢤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠒⠒⠠⠤⣽⡖⠁⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⢁⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣷⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⢈⠟⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀ ⠀⡎⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⢓⣶⡄⣀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠈⠻⢯⡇⠀⠀⠀⠀⠀⠀⠀⣌⠑⢤⡀⠀ ⢰⡷⠁⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠉⠁⠈⢉⡴⠋⠀⠀⠀⠀⠰⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠙⡆ ⢸⠃⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠒⠦⡀⠀⠀⠀⠈⠉⠲⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢰⠃ ⢸⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣉⠲⣿⣆⠀⠀⠀⠀⠀⠙⠹⣄⠤⠆⠀⠀⡀⠀⠀⠀⠀⡽⠃⠀ ⠸⡇⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⠗⠤⣀⠀⠀⠀⠀⠀⠀⠓⠒⠻⣍⠢⣀⣤⠞⠀⠀⠀ ⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠉⠒⠠⣄⡀⠀⠀⠀⠀⢀⡷⡌⣧⠀⠀⠀⠀ ⠀⠀⢸⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠇⠀⠀⠀⠀⢨⣿⡷⠶⠶⠿⠋⠀⠸⡿⠀⠀⠀⠀ ⠀⠀⠀⢧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⠀⠀⠐⢦⠀⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢧⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠱⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠳⣽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣆⠀⠀⠀⠀⠀⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡆⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠾⡷⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣸⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠑⠢⢄⠀⡄⠀⣼⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣷⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⡠⣒⡇⠀⠀⠀⠀⠀ ⠀⠀⣿⠻⢿⡕⣤⠤⣄⡴⠶⣶⠎⠀⣼⣋⡰⠿⠿⠀⠄⠀⠀⠀ ⠀⢸⣿⣦⠄⢱⠜⢉⡤⠊⠉⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀ ⢠⢿⣿⣥⡴⠁⢰⠫⠄⠠⢜⡄⣄⡀⠀⠀⠐⠊⢉⠴⠃⠀⠀⠀ ⡜⡈⡟⠿⠀⢠⠃⣨⠄⢤⡈⠉⠁⢨⠓⢶⢻⢿⠁⠀⠀⠀⠀⠀ ⢣⠹⢅⣀⠀⠸⢰⡃⠀⠐⣷⠀⠀⡇⠀⣼⢸⢸⠀⠀⠀⣾⣤⠄ ⠀⠳⣦⡿⣠⡷⠀⠑⠂⠘⠛⠀⠀⠑⠲⣍⢸⠗⠢⣄⠀⠙⠋⠀ ⠀⠀⣨⣊⡁⠀⠀⠀⠀⠀⠀⠀⠠⢶⣾⡷⢹⠖⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣨⣓⠀⠀⠀⠑⢄⠀⢀⠽⣀⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣦⣤⣀⣩⣶⠒⡂⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠤⠔⡨⠛⠻⠿⠿⠿⠟⠊⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⠊⠀⠀⠀⠀⠀⢀⢐⣔⠣⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠑⡀⠁⠢⡀⠀⠀⠀⢀⢴⠠⠐⠁⠀⠀⠀⠀⡁⠮⠀⠀⠤⢀⠀⠰⠀⠀⠀ ⠀⠀⢠⠀⠀⠈⠁⡂⠄⡁⠐⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠒⠲⢎⢢⠀⠀⠀ ⠀⠀⢨⠆⠀⠀⠀⠈⠀⠀⠑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀ ⡀⠀⠈⡜⢄⠀⠀⠀⠀⠀⠀⢀⣡⣀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠇⠀⠀ ⡊⠦⠀⠘⡢⡁⠀⠀⠀⡠⠚⠋⠉⠀⠙⠖⠔⡄⢠⠀⠀⡆⠀⠈⡇⠰⠀⠀⠀ ⠈⠲⣤⠀⠐⢌⢂⣀⠈⣤⡶⠿⢶⣦⡀⠀⠀⢡⡘⠑⠄⡱⡀⠀⠈⢆⠀⠀⠀ ⠱⢒⠉⡲⢒⡩⠀⠸⢿⢻⠀⠀⡖⠪⡷⠀⠀⠀⠀⠀⣀⣈⢉⡢⢄⣀⣐⠤⠀ ⡇⡦⣀⡕⠁⢀⡀⠀⠘⠎⠦⣀⠝⠁⡇⠀⠀⠀⠀⡾⠛⠛⠯⠀⠑⢇⠀⠀⠀ ⠑⢌⣒⢀⠔⡁⠀⠀⠀⠀⠀⠀⠀⠁⠳⠀⢀⣀⡀⢀⠀⠀⠀⠀⠈⢤⠀⠀⠀ ⠀⠀⠀⡇⡘⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠑⠶⢄⣠⡶⠁⢢⠀⠀⠀⡆⠀⠀ ⠀⣀⠤⠵⡇⡌⠀⠀⠄⠀⠀⠀⠈⢆⡀⠀⠀⠀⣠⣣⡤⠖⠎⣒⠠⢄⠃⠀⠀ ⡴⠂⠉⢁⡰⡇⠀⣘⠤⠀⠠⡀⡰⠄⠉⠣⡾⡁⡺⠏⠉⠐⠢⢄⠁⠀⠈⠢⠀ ⠀⠀⡔⢁⣀⠈⠄⣘⡄⠀⠀⠉⢀⠢⢀⠀⠈⠁⢩⣒⠒⠠⢀⡀⠀⠀⠀⠀⠁ ⠀⡈⠖⠠⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣒⢬⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠱⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢎⠀⠀⠀⠉⡆⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀ ⠀⠀⡌⠵⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠮⠹⠀⠀ ⠀⠀⠰⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⡁⠁⠀⡇⡄⠀ ⠀⠀⠆⠆⠀⠀⣠⠃⡀⢉⠉⠀⠘⢦⡀⠀⢠⢡⠀⠀ ⠀⠀⠘⡄⠀⠙⣠⣴⠃⣍⠞⡘⣰⣿⠉⠀⠠⠂⠀⠀ ⠀⢄⣸⠇⠀⠀⢿⡿⠀⠁⠀⠁⢿⡿⠀⠀⠀⢆⡠⠀ ⠰⢬⠂⠀⠀⠀⠀⠁⠠⣠⣄⠄⠈⠀⠀⠀⠀⠐⡥⠆ ⠀⠀⠀⠃⠄⡀⠀⠀⠢⣸⣃⠔⠀⠀⢀⠀⠐⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⢀⠒⢒⠒⠂⡄⠈⠁⠀⠀⠀⠀⠀ ⠀⠀⢶⠓⠂⠀⠀⠂⠀⡛⠦⠀⠐⠀⠀⠐⠂⡄⠀⠀ ⠀⠀⡌⠀⠀⠀⠀⠀⠐⠩⠄⠀⠀⠀⠀⠀⠀⠱⠀⠀

⠀⠀⠀⠀⠀⢠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⠐⢄⡀⠀⠢⡁⠂⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠣⠀⠀⠉⠀⠒⠂⠠⠤⢀⡀⠉⠁⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣍⠋⠲⠖⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⡠⢒⠉⠉⢆⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⡂⠄⠘⠀⠀⠀⠀⠀ ⠀⣬⠖⠁⠀⠀⠈⠛⠰⡁⠀⠀⠀⠀⠀⠀⢖⠒⠂⢵⠀⠀⠣⡀⠀⠀⠀ ⠀⣌⠔⠀⠀⠀⠀⠀⠈⡙⢣⣄⣀⣀⠀⠀⠀⠉⠲⢶⠀⠀⠀⠀⢑⠢⡀ ⢀⠂⡠⠀⠀⠀⠀⠀⠀⠐⠤⠤⠦⢁⠀⠀⠐⠦⡀⠀⠀⠀⠀⠀⠀⢣⢨ ⠘⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⣲⣄⠀⠀⠈⠡⠐⣀⡠⡀⠀⡨⠂ ⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡉⠂⠤⣀⠀⠀⠈⡮⣪⠀⠀ ⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠚⣿⠛⠉⠀⠙⠀⠀ ⠀⠀⠈⢄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⢢⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠢⢑⣄⡀⠀⠀⠀⠀⠀⠇⠀⣄⠌⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠁⠒⢄⢠⢠⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢄⣸⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠙⠳⠤⣀⡉⠒⠤⣀⠀⣀⣠⠤⠖⠋⣷⣶⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠟⠢⣀⠀⠀⠈⠉⠲⠞⠉⠀⠀⠀⠀⠘⣁⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡄⠰⣞⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣦⡙⢻⠃⠀⠀⠀⠀⠀⠀⣀⣀⣀⡸⣿⠟⣆⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠻⢿⡇⠈⠻⡄⠀⠀⠀⠀⠀⠚⠛⠛⠻⢿⡦⠀⠀⠿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣾⣟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠤⢤⣴⣦⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣆⣀⠀⠀⣠⢶⠀⠀⠀⠀⠘⠷⠾⠖⢋⡥⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠈⠀⡿⠙⠚⠓⡏⠀⢀⡄⠀⢀⡤⠔⠚⠁⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢶⣒⠒⠊⠉⠉⠀⠀⠀⠉⠉⠓⠒⠋⠁⠀⠀⣸⣅⢴⣟⣀⣠⡟⠀⠀⠀⠀⠀⠀⠀ ⣟⠳⡖⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣏⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⠹⡆⠈⠢⠀⠈⠑⠲⢤⣀⠀⠀⠀⣘⣇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠤⣴⠀⠀⠀⠀⠀⠀ ⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⢯⡽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣒⠾⠃⠀⠀⠀⠀⠀⠀ ⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⢤⣳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠀⠀⠀⠀⠀⠀⠀⢠⠗⠢⡤⢄⡀⠈⢧⠀⠀⠀⠀⢸⠷⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⢕⣂⠀⠀⠀⠀⢀⣠⣼⠝⢹⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢳⠈⠛⢷⡟⠀⠀⠀⠀⠸⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⣼⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠸⡀⠀⠈⢧⠀⠀⠀⠀⠀⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⢀⡼⠉⢧⠀⠀⠀⢠⠇⠀⠀⠈⢇⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣰⠋⠀⠀⣸⠀⠀⠀⡞⠀⠀⠀⠀⠈⣆⠀⠀⠀⢹⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⠇⠀⠀⠀⢹⡀⠀⠈⣇⠀⠀⠀⠀⠀⠘⡄⠀⠀⠘⣎⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢸⠀⠀⠀⠀⠀⢳⡀⠀⠹⡄⠀⠀⠀⠀⠀⢹⡀⠀⠀⢳⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⣀⣬⡇⠀⠀⠀⠀⠈⠷⣴⣤⣿⠀⠀⠀⠀⠀⠀⠳⣤⣀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣤⣼⣬⣭⣦⣤⣤⣀⣀⢶⣶⣦⡤⡤⣤⠀⣴⣶⣤⣤⣤⢴⣤⣤⣤⣶⢤⣤⣤⣤⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠁⠉⠉⠉⢉⠉⠉⠉⠁⠈⠉⠉⠉⠈⠉⠉⠉⠀⠁⠀⠀

⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢤⡀ ⠀⣧⡞⠓⠛⠱⢖⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠝⠒⠚⡎⣧ ⢰⢿⠀⠀⠀⠀⠀⠈⠑⢽⣦⠀⠀⠀⠀⠀⠀⢀⢼⡿⠋⠁⠀⠀⠀⠀⠸⢿ ⠘⠸⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠍⠙⠉⠙⠶⠾⠿⠁⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡎ ⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⠇ ⠀⡸⡍⠀⠀⠀⠀⠀⠐⢒⣋⡀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀ ⠀⢧⠁⠀⠀⠀⠀⣠⢾⣿⣁⣨⡄⠀⠀⢠⡊⢹⣿⣷⡄⠀⠀⠀⠀⠘⣷⡀ ⢸⡄⠀⠀⠀⠀⢰⡏⠘⢷⣿⡿⣿⠀⠀⢸⣿⣷⣾⠇⡇⠀⠀⠀⠀⠀⢱⡇ ⡀⡇⠀⠀⠀⠀⠈⠳⣤⢤⣔⡾⠋⠀⠀⠘⢷⣄⣀⡰⠃⠀⠀⠀⠀⠀⠈⣿ ⡇⢇⠀⠴⣦⢄⡀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡠⣴⣿⠆⢠⣿ ⠻⣬⣦⣀⠈⠻⢾⣵⣶⣤⣤⣠⣴⢄⢄⣀⣀⣠⠤⠐⣂⣭⠾⠋⠀⢀⢜⡾ ⠀⠈⠑⠿⣅⣢⠤⣉⣽⡮⠉⠉⠛⠛⠛⠛⠓⠒⢻⡟⠋⠁⣀⡤⣖⠽⠋⠀ ⠀⠀⠀⠀⠀⠉⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠓⠉⠀⠀⠀⠀

⠀⠀⠱⡀⠈⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⡠⠖⠉⠁⠀⠀⠀⠀⠀⠀⠉⠲⣎⣀⣀⣀⣀⡀⠀⠀⠀⠀⠹⡄⠀⠀⠀ ⠀⠀⠀⠹⡀⠀⠀⠈⠱⣤⣀⠀⠀⠀⠀⡰⠋⢰⢡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠉⠁⠀⠀⠀⠀⠀⠉⠒⢤⡀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⢣⠀⠀⠀⠀⠈⠮⡑⠢⢄⣘⠁⠀⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠉⠓⠒⠷⣒⠺⢦⡇⠀⠀⠀ ⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠈⠲⠄⠀⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⠇⠀⠀⠀ ⠀⠀⠀⠀⢸⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀ ⠀⠀⠀⠀⠸⡄⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀ ⠣⡀⠀⠀⠀⠱⡀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠶⢄⣀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⡎⠀⠀⠀ ⡑⠻⢦⣀⠀⠀⢿⢦⡈⠁⠀⠀⠀⠀⠀⣠⡴⠟⠋⠁⠀⠀⠀⠀⠘⢷⠢⣌⣆⠀⠐⡆⠀⠀⠀⡆⠀⠀⠀⠈⡇⠀⢰⠃⠀⠀⠀ ⠙⣦⣀⠀⠀⠀⠈⢆⠙⠢⣀⠀⠀⠀⠔⠁⠀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠹⡄⠀⡟⢦⠀⠀⢰⠀⠀⠀⠀⠘⣄⡸⠀⠀⠀⠀ ⠀⠈⠙⢿⣶⣄⠀⠀⠳⣄⣀⣀⣤⡀⢀⣴⣿⠿⠛⠛⠻⣿⣿⣦⡀⠀⠀⠀⠀⣧⡰⠁⠀⠑⠦⣀⠳⡀⠀⠀⠀⠈⢷⡀⠀⠀⠀ ⠳⣤⡴⠚⠓⢦⢤⡤⠒⠉⠀⠀⠘⣿⣿⠿⡏⠀⠀⠀⣤⠾⣜⣿⣳⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠛⠢⣀⠀⠀⠀⠑⢤⣀⡀ ⣰⠃⡰⠚⠒⡾⢉⡠⠖⠋⠀⠀⠈⠉⣿⠀⡇⠀⠀⠀⢇⡀⠈⢹⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣄⣠⡖⠈⣙⠲⡆⠀⠐⠛⠁ ⡇⠀⣅⡀⢰⣥⠊⠀⠀⠀⡀⠀⠀⠀⠘⢦⣙⣦⣀⣀⡴⠋⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠛⠛⠻⠯⠆⠀⠈⠳⣷⠀⠀⠀⠀ ⢣⡀⠣⣈⣉⠇⠀⣀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠲⠤⣼⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠓⢄⠈⡆⠀⠀⠀ ⠀⠙⠦⣄⣸⠀⡴⠁⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⣠⠤⣄⣀⣀⣀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠳⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠯⣠⡤⢄⠉⢣⢠⣶⠃⠙⢆⠀⠀⠀⠀⠀⢣⠀⠀⠀ ⠀⠀⠀⠀⠀⢇⢠⠃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣅⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⡮⠟⠁⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⡠⠤⠬⣾⠀⢠⠃⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⢀⣼⣁⣠⠤⠶⠾⢏⡉⠒⠢⢄⣀⡜⠀⠀⠀ ⠀⡔⣋⠤⠤⠤⠈⣇⢸⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⡀⠈⠙⢶⠤⠀⣤⠤⠖⢛⣿⡿⠯⠤⣀⣀⠀⠈⠑⠢⠀⠈⠑⢦⡀⠀ ⡼⠋⠁⠀⠀⢀⣠⠼⢾⡀⠀⠀⣾⠴⠊⠉⠉⠒⠤⣀⣠⠋⡆⠀⠀⠙⢶⡛⣆⠘⢧⠟⠀⠀⠀⠀⠈⠙⠲⢤⠀⠀⠀⠀⠀⠙⢆ ⠀⠀⠀⢀⡴⠉⠀⠀⠀⠱⣄⠀⠸⡄⠀⠀⠀⠀⠈⠉⠀⢀⣏⠀⠀⠀⠀⠈⠙⠒⠚⣲⣤⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡿⢀⡠⢤⡾⠀⠀⠈⠓⠢⠼⠀⠀⠀⠀⠀⠀⠰⠊⠀⠙⠲⠄⣀⠀⠀⠀⢀⣷⡤⠃⠀⠀⠉⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠏⠀⡞⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⢉⣡⡄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠉⠉⢠⠃⠀⠀⠈⠉⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠳⣄⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠧⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢰⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⢹⠰⡀⠀⠀⡃⠑⢾⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⡀⠀⡆⠇⠀⠛⣄⠀⣇⣰⡿⣧⣤⣤⣬⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⠀⠸⠐⣧⣈⢸⣄⢈⣷⣿⣿⢃⣿⣫⣴⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⡄⠐⡁⠈⢆⠈⠉⠻⣿⡿⡛⠉⣀⣤⣤⣤⣭⣿⡓⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠀⠐⡆⠈⢳⣶⣶⢯⠊⣠⣾⣿⣿⣿⣿⡍⠉⠳⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢆⠀⠑⠀⡀⠙⡿⠁⣾⣿⣿⣿⣿⠝⠒⠢⢄⠀⠀⠑⢤⡀⠀⠀⠀ ⠀⠀⠀⠐⣤⣈⣦⣀⣀⠀⢀⡧⢤⣿⣿⣿⣿⣀⠄⠀⠀⠀⣣⣷⣦⡀⠈⠢⡀⠀ ⠀⠀⠀⠀⢣⡈⠙⢣⡀⢨⠃⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣶⣶⣿⡆ ⠀⠀⢀⣐⣶⣛⠯⠖⠳⢼⠀⠀⠀⠀⡜⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠹⣁⠀⠀⣈⣩⠥⠀⠳⣦⠀⠀⣳⡿⢿⣿⣿⣿⣮⡻⢿⣿⣿⣿⣿⡫⣺⠀ ⠀⠀⠀⢈⣻⢛⡳⠤⠤⡾⣟⣒⠛⠯⡽⣍⠐⢌⡉⠙⠛⠛⠳⠬⠟⠋⠐⢊⠍⠀ ⠀⠀⡠⢐⡗⢁⡾⠋⣉⣬⠖⠒⠲⡤⠌⣂⠥⢀⡈⢣⡈⠀⠀⠀⠐⠪⢽⣋⠒⢄ ⡠⠊⠀⠛⠲⣿⡃⠜⡯⣴⢺⡛⠲⣵⢄⡀⠨⠁⠒⠒⠈⠀⠀⠀⠀⣀⣀⣉⡹⠂ ⠀⠀⠀⠀⠀⠘⡿⠀⢀⢿⢸⡇⠀⠀⠑⠪⡍⠒⠂⠀⠀⠀⠀⣠⠤⠐⠒⢾⡿⡂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢗⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡛⠛⢹⣿⠀⠀⠀⠀⠀⠀⡇⠀⠈⠋⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡿⠎⠀⠀⠀⠀⠀⠀⠻⠶⠶⠝⠋⠀⠀⠀⠀⣠⢤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠼⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⡆⠀⠀⠀⠀⢰⠛⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠍⣇⠶⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢲⠒⣲⡦⠼⠁⠀⢿⡀⠀⠀⠀⢸⡁⠀⡀⡙⠦⣄⣂⡶⠶⠿⠟⠛⠁⣠⡤⣦⣺⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣧⠀⠈⠀⠀⠈⠫⣤⠖⠒⠀⠀⠀⠀⠀⣴⣮⠹⢷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣒⡶⠋⠀⠀⠀⠀⠀⡿⡆⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⢽⣿⠀⣨⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⢹⣻⣿⣿⡇⠀⠀⣴⣿⡆⠘⠛⠹⡡⢀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠉⣉⢭⣶⡆⠀⠉⢻⡇⢀⠀⢠⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢳⡄⠀⠀⠀⠀⠠⡞⣩⢓⡞⠐⠒⠶⠚⠉⡅⣘⡐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠛⠷⣤⣆⠀⢁⠾⠁⢣⡇⠀⠀⠀⠀⠀⢜⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢑⠆⠀⠀⠀ ⠀⡖⣒⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⡀⠀⠀⠀ ⢸⣟⠉⠉⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡄⠀⠀⠀ ⠈⠓⢷⡄⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣧⠀⠀⠀ ⠀⠀⣴⡇⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⣞⠟⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⢸⡎⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀ ⢸⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢽⠀⠀⠀⠀ ⢸⡄⡰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠀⠀⡞⠀⠁⣿⠀⠀⠀⠀ ⠈⢧⠧⣱⡀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣸⠀⣰⠃⠀⠀⣿⠀⠀⠀⠀ ⠀⠘⣷⡈⠻⣄⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡇⢠⣧⡇⠀⠀⢽⠀⠀⠀⠀ ⠀⠀⠈⢣⡀⠈⠓⠶⣖⠂⠻⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢸⡷⠟⠸⡇⠀⠀⢻⣇⠀⠀⠀ ⠀⠀⠀⠀⠙⠶⢤⣴⣂⣒⣒⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠭⣭⡽⣇⠀⠀⡏⢷⡀⠘⣷⡀⠀⠀⠙⢳⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡤⣀⣀⠀⠀⠀⢀⣼⠇⠀⠰⡌⢳⡿⡄⠀⠀⢧⡱⡄⠀⠻⢶⣔⣾⠿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠚⠉⠻⠶⠼⠿⠛⠉⠉⠻⣍⣳⣴⣷⠗⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⣶⢄⠀⠀⠀⣀⡤⣶⠶⠒⠒⠒⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢱⡇⢸⠀⠙⢻⡉⣳⣭⠔⠒⠋⠉⠉⠉⠓⠺⢽⣢⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢠⣿⡇⠀⣢⢀⠶⣿⡏⠉⠺⡉⠑⠲⣒⠤⠤⢄⣐⠪⢝⢳⣄⠤⠒⣻⠛⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣣⡏⡏⠘⣤⡟⡵⠀⠙⠁⠀⠀⠈⢦⠀⠘⢏⠒⠤⣶⢋⣉⠉⠀⠀⢀⠇⢸⡌⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣻⠛⣿⢰⡇⡴⢫⢏⠄⠀⠀⠀⠀⠀⠀⠀⠓⠀⠈⠳⠀⠀⠙⢷⠒⢶⣰⡿⠁⣾⣵⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣹⢻⡀⡏⢘⠟⠁⢠⠎⠀⡇⡸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⢻⣶⡾⣓⣟⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⢵⠃⡜⢧⣫⠋⢀⣤⠏⢀⣼⢁⡧⢵⠀⢠⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡝⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣇⠏⡜⠀⡸⠁⢀⠞⡎⢠⠞⢻⡜⠀⠈⢦⠀⣇⡿⣄⠀⠀⠠⡀⠀⠘⣆⠀⠀⢆⠀⠹⡵⡽⣦⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡾⡼⠀⢰⠃⢠⠎⣼⣰⣏⠠⣼⣀⣀⡀⠈⢣⣸⣾⠈⠳⣄⠀⠱⡀⠀⠘⣆⠀⠘⣆⠀⠹⡹⡄⠈⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡾⢸⠁⢀⣯⠇⠀⣰⣿⠛⠻⣿⡿⣻⡽⢿⣢⣄⠳⣿⡆⢀⡈⠳⣄⡱⣄⣀⣘⣆⣀⣽⢶⣲⠷⢿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡇⢸⠀⢸⡏⠀⠀⢿⡿⠀⠀⢿⣏⣿⣿⣿⣯⣀⣉⣙⣿⡟⣻⣿⠿⠿⣽⣷⡤⣾⠯⣽⡿⣤⢤⡀⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⢠⣿⠀⠼⢸⠀⠀⢸⠱⢷⣤⣤⠝⠷⣾⣹⣯⠁⠀⠀⢧⣠⣿⣿⢲⢠⡟⢁⣿⣽⢀⣾⠙⠉⠁⠛⠄⠀⢱⡀⠀⠀⠀⠀ ⠀⠀⣀⣠⠞⠁⡞⠁⠀⠀⢸⡆⠀⠀⢧⠀⠀⠈⠉⠉⠙⠛⠁⠀⠀⠀⠸⢟⣯⢿⣟⡋⠀⣾⣷⣻⢻⢹⠀⠀⠀⠀⡆⠀⠀⡇⠀⠀⠀⠀ ⢐⣛⣉⣀⣤⢾⣱⠀⠀⠀⠀⢿⡀⠈⠲⣵⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⢻⡿⡅⠙⠿⢴⡂⠀⠀⣰⠃⠀⠀⢧⠀⠀⠀⠀ ⠈⠑⠒⢊⡿⡏⡇⢰⠀⠀⠀⠀⠳⡄⠀⠸⡈⠑⢆⠀⠀⠈⠻⡒⢒⣢⠄⠀⠀⠀⠀⢀⡼⠀⡟⢆⠀⠀⠙⠂⢀⡏⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⡼⢡⢿⠀⡼⠀⡇⠀⢰⡄⠘⡆⠀⢷⡀⠀⠱⣤⣤⣠⣽⡋⠀⢀⡴⠀⢀⣴⢻⠃⡤⢧⣜⡄⠀⠀⠀⡸⠀⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⢀⡼⠁⠈⢸⠀⡇⠀⢱⠀⢸⡇⠰⡄⠀⣯⣿⣖⢄⡀⠑⠤⠤⠟⠉⣉⡤⣶⣿⠇⠸⢰⠁⢸⣇⢣⠀⠀⢀⠇⠀⠀⠀⠀⠀⠠⠀⠀⠀ ⠔⠁⢀⣠⠀⢸⣀⣧⣴⣼⡇⢸⡇⠀⣷⡀⢸⣼⠈⢆⠈⠓⠶⠶⠒⠉⠹⠁⠉⡟⠀⠀⢸⠀⢸⢸⡀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⡤⠒⡻⢁⡴⣾⠋⠙⠿⣿⢧⢸⠁⠀⡿⡇⠀⣟⣧⣘⡀⠀⠀⠀⠀⢀⣀⣠⠴⢇⠀⡇⢸⠀⠈⠀⢳⡀⠈⠓⡄⠀⠀⠀⠀⠀⠘⠂⠀⠀ ⢀⣼⠁⢸⡇⠹⣷⡀⠀⢸⣿⢸⠀⢀⢇⡇⢠⠆⡇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⡄⢿⡀⠀⠀⢠⡀⠹⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢺⡎⠀⡎⢹⡄⠈⢿⣦⡸⠸⠀⠀⢸⣽⡇⡾⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⣇⠀⠀⠀⢧⠀⢻⣼⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀ ⣨⡇⢸⠀⠀⠙⢄⠀⠹⡇⠀⠀⠀⣾⡿⢰⣱⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠘⣇⠸⡏⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀ ⢸⡁⣇⠀⠀⠀⠈⠑⣾⠀⢠⠀⢀⡟⠁⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢨⡎⠁⠀⠀⢹⡾⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀ ⠀⡇⠘⡄⠀⠀⠀⢠⠃⠀⡸⠀⢰⡇⡸⣎⠀⠀⠀⠙⠲⢄⡀⠀⠀⠀⠀⡠⠒⠁⠀⢠⠏⢿⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⣜⠆⠀ ⠀⢳⠀⢸⡆⠀⠀⢺⠀⠀⡇⠀⢸⣁⠇⡇⠳⡀⠀⠀⠀⠀⠙⢦⠀⢠⠞⠀⠀⠀⣰⡻⠀⢸⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠆⠀ ⠀⠈⣇⡎⠙⡄⠀⢻⠀⢸⠁⠀⠐⣿⠀⡆⠀⢮⡢⣄⠀⠀⠀⠀⢳⠏⠀⠀⢠⠔⡵⠁⠀⢸⠀⡠⣾⠁⠀⠀⠀⠀⠀⠀⠀⡆⠀⣇⠹⡀ ⠀⠀⠸⣵⡀⠀⠀⢸⣆⢸⠀⠀⠀⣿⠀⢇⠀⠀⠙⠪⣕⡦⣄⣀⣎⣀⡠⢔⡧⠊⠀⠀⢀⠏⠀⡇⠿⣄⠀⠀⠀⠀⠀⠀⠀⣷⣼⢹⠀⠑ ⠀⠀⢠⣯⢳⠀⠀⠘⡽⡄⡇⠀⠸⡟⢦⡘⣆⠀⠀⠀⠀⠉⠀⠈⠉⠀⠈⠁⠀⠀⠀⠀⡜⠀⣼⣇⠀⠈⠳⣄⠀⠀⠀⠀⣺⡿⣿⢸⠀⠀ ⠀⢀⡞⣹⡞⡇⠀⠀⣿⠈⢣⠀⡆⢱⠈⠳⢌⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢁⠜⢹⠈⠷⣄⠀⠈⠉⠒⠒⠒⠉⢀⣸⢸⠀⠀ ⠀⠊⠔⢹⢻⠃⠀⠀⣿⣆⠈⠄⢻⣸⡀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣱⠟⢀⡾⠀⠀⠈⠙⠒⠤⢤⡤⠤⠒⣿⣿⡎⠀⠀ ⠀⠀⠀⢸⡌⣇⠀⠀⠘⡜⡤⡀⠈⣇⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢻⠇⡴⠋⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⢿⠃⠀⠀ ⠀⠀⠀⠘⡇⢸⣆⠀⠀⠘⣞⣆⠀⢸⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡞⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⢀⣴⢇⡏⠈⠀⠀⠀ ⠀⠀⠀⠀⢸⢸⢻⡆⠀⠀⠈⠻⢧⡀⢣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡯⠳⢄⡀⣀⢀⡤⠟⣿⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣼⠀⠀⠀⠀⠀⠀⠑⣜⣿⠤⠤⠤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠲⠼⣂⣀⠀⠀⡇⠀⠀⠉⠛⠉⠀⠀⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠋⠀⢣⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⢯⡇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣠⠔⣋⡴⠃⠀⠀⢀⡀⢀⣀⣠⣤⠴⠦⢤⣰⣄⠀⠰⣤⣀⡀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⡏⣇⠀ ⠀⣠⠖⣫⡴⠚⢿⠶⠤⠖⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠺⢧⡈⠓⢤⡀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠸⡄ ⣼⣵⠞⠁⠀⠀⠈⣳⣄⡀⠀⠀⠀⠠⡀⠀⠀⠀⢀⡤⠔⠒⠈⠉⠑⠒⠤⣀⠀⡝⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡄⣧ ⠘⢿⣶⣶⣶⣿⣿⣿⣿⠿⠋⠁⢀⡠⠑⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠃⢿ ⠀⠀⠀⠉⠉⠉⢠⠞⠁⠀⢠⠖⢉⠄⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⡞⠁⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢰⣿⣿ ⠀⠀⠀⠀⠀⣰⠃⠀⠀⡴⠃⠀⡾⠀⡼⠀⠀⢀⣀⡤⠄⠀⢀⡤⠖⣠⣿⣶⣶⣤⡈⢦⡀⠀⠀⠀⠀⠀⢀⣾⠤⠀⠉⣽ ⠀⠀⠀⠀⢀⡟⠀⠀⡼⠁⠀⢠⠃⠀⣇⡤⣾⠟⠁⠀⣀⡴⠋⣡⡶⢫⡏⠀⠀⠉⠻⣆⠈⢢⡀⠀⠀⢀⡾⠃⠀⠀⣰⡟ ⠀⠀⠀⠀⠸⡇⠀⣸⠃⢀⠀⡏⠀⣰⢋⠞⠁⢀⣠⣾⣯⠴⠚⠁⢀⣿⣿⣿⣷⣦⡀⠙⡆⠀⠱⣄⣠⠋⠀⠀⢀⠞⢱⠃ ⠀⠀⠀⠀⠀⢣⠀⡏⠀⢸⠀⠁⢰⣷⠋⢠⣴⣿⣿⡏⠀⠀⠀⠀⢸⣿⣿⡿⠿⡟⢿⡄⠹⡀⠀⠙⡇⠀⠀⠘⠁⣠⠋⠀ ⠀⠀⠀⠀⠛⠿⢷⣿⡀⠘⡀⢀⣿⠃⣠⢿⡛⠟⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣶⡄⠈⣿⠀⠱⡄⠀⡇⠀⠀⣠⠼⠓⡾⠀ ⠀⠀⠀⠀⣠⠔⠋⠙⣷⡀⠱⢸⡇⣸⠁⢀⣽⣿⣿⣿⣷⣶⣤⣄⣯⡓⠛⠉⡽⠁⠀⢸⡆⠀⢿⠆⢹⠀⠈⢁⣴⣮⢤⠆ ⠀⠀⢀⠜⠁⠀⠀⠀⡿⠛⠲⣜⣷⣿⠟⠁⠘⠿⣿⣿⣿⣿⠟⠀⠙⠏⠛⠉⠀⠀⠠⢿⠃⠀⢸⠀⣏⡤⠒⠉⢀⣤⠎⠀ ⠀⢠⡯⢤⡤⠤⠀⢸⣥⣼⣷⠀⠉⠁⠀⠀⠀⠀⠈⡏⠁⠀⠀⠀⠀⠀⠸⡖⢲⣶⡄⡀⠻⢇⣼⠫⠿⢤⣀⣙⣛⣓⠞⠀ ⠀⠰⣶⠋⠀⠀⠀⠸⡜⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠿⠿⠂⣸⣷⡄⠈⠩⣌⠙⢏⠁⠀⠀ ⠀⠀⠈⠑⠦⣀⠠⠀⢳⣦⠟⣀⠀⠀⠀⠀⠀⠀⣀⣶⣤⣀⠀⠀⠀⠀⠀⠀⣠⣶⡄⢰⣾⣿⣾⠇⠀⠀⠈⢷⣆⢧⠀⠀ ⠀⠀⠀⠀⠰⠾⣍⣀⠀⠙⢆⣩⡀⠀⠀⠀⠀⠻⢿⡟⠛⢻⣿⠇⠀⠀⠀⠀⠛⠛⠀⢸⣿⣿⡇⠀⠀⠀⠀⠈⡏⢿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⢿⣦⡀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⡿⠛⢙⣦⡀⠀⠀⢀⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⠿⣿⣁⠀⠀⢻⣿⣦⢀⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡛⠲⠤⠤⠤⠤⠶⠶⠛⠋⠁⠀⣸⣧⡀⠀⠈⠉⠒⠦⠧⠙⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠖⠋⣙⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣽⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡠⢴⣲⢭⡿⠃⠀⢠⡖⠠⢼⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠉⣯⠿⠟⠉⠛⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡴⠉⠰⠟⠚⠉⢰⡄⠀⣀⢵⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠻⠇⠙⠶⣄⠀⠀⠀⠀ ⠀⢸⠁⠀⠀⠀⠀⠀⡹⠂⠉⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢿⣦⠀⠀ ⠀⢸⠀⠀⠀⠀⠠⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠐⠹⣧⠀ ⠀⢸⡀⢚⣥⡄⢘⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⢲⡀⢹⠀

⠀⠀⠀⢀⠔⠉⠒⢤⣀⣀⣠⢄⣀⣠⠄⠒⠲⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⠉⠉⠉⠉⠀⠀⠀⠑⠋⠜⢀⠔⡆⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡿⠀⢀⡤⢄⢠⠒⢄⠀⠀⠘⡀⢀⠃⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⢡⡀⠀⣨⣦⡼⠈⢢⣼⣀⠀⠀⢃⠜⢀⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡃⠈⠁⠣⣸⡀⠀⠘⣄⣵⠀⠐⡤⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡏⡄⠀⠀⢰⣆⣀⣀⣀⠀⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⢧⠈⠁⠀⢰⣺⣦⡑⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⠝⢄⣀⠔⠉⢿⣙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡜⢸⠁⠀⠀⠀⠀⢸⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠤⠊⠀⡨⠀⠀⠀⠀⠀⡇⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠔⠁⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀ ⠘⢀⠄⠠⠇⠀⠀⠐⢄⡀⣀⠄⡇⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀ ⠰⠜⠢⠤⡀⠀⠀⠀⠀⠁⠀⠀⠘⡄⠀⠀⠀⢀⡗⠂⠁⠒⢄⠀ ⠀⠁⠁⠉⢇⠀⠀⠀⠀⢰⠀⠀⠀⠈⠷⣣⡧⠟⠀⠀⠀⠀⠈⡆ ⠀⠀⠀⠀⡸⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠃⠀⠀⠀⠀⣶⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠰⠀ ⠀⠀⠀⠀⡀⠀⠀⠀⢰⢸⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⢀⠔⠁⠀ ⠀⠀⠀⠀⠱⠄⣀⣀⡸⢆⣀⣀⠠⠜⠠⠤⠤⠐⠒⠉⠀⠀⠀⠀

🦱🧔🦣

⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡼⢣⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠸⡄⣢⡖⢒⠒⠢⢄⣦⠀⠀⠀⠀⢀⣠⠶⣢⠀⠀⠀ ⣾⡀⣴⠿⠚⠁⠀⠁⠀⠀⠇⠱⣀⠠⠔⡝⠁⠀⢹⡀⠀⠀ ⡾⡟⠢⢤⠤⠔⠀⢀⠀⢠⠀⠆⠁⠀⡜⠀⠀⠀⢸⠀⠀⠀ ⢃⠈⢰⠋⣀⡀⠲⢥⣲⣧⠊⢆⠀⠰⠀⠀⠀⢠⡿⠀⠀⠀ ⢠⡗⠁⢸⢸⡇⠀⠈⡽⣿⡍⠈⠆⠀⠀⢀⠴⠕⡇⠀⠀⠀ ⢸⡇⢀⣀⣖⠁⠀⢸⡀⢻⠿⠀⢼⡄⠈⠀⣠⠎⠀⠀⠀⠀ ⠀⠣⡇⠂⡀⣈⠆⠀⠀⡀⠀⠀⢰⠗⢖⡾⠁⠀⠀⠀⠀⠀ ⠀⠀⠈⠰⣽⠄⣀⠀⡔⢁⣀⣔⣩⠔⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣄⣀⣴⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⣄⣤⣤⣄⢤⣤⣤⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⡴⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⠿⠿⠛⠛⠛⠋⠉⠉⠉⠛⠛⠛⠛⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⣻⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⣀⣤⣄⢴⣖⣒⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣟⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⠟⠋⠀⠀⠀⣀⣤⣦⣿⣿⣿⣿⣿⣯⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠿⠿⠿⣿⣿⣷⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⣿⡿⠁⠀⠀⠀⣀⣶⣿⣿⡟⠯⠍⠋⢁⣀⣠⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣄⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣦⣤⣴⣿⣿⣟⣋⣡⣤⠴⠖⠋⢉⣽⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠧⡀ ⠀⠀⢠⣿⠟⠉⠁⠈⠉⠉⠙⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⢠⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠟⠛⠉⠀⢀⣀⣥⣴⣶⣶⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣷⣶⣦⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠂⠈⢉⠛⠿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠘⢿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠽⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣴⣿⣿⣄⠀⠀⠀⠀⠀⣀⣠⣴⠶⣿⣿⠋⠉⠉⠉⠙⢻⣿⡆⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⣿⡍⠛⠻⢷⣶⣶⣶⠟⢿⣿⠗⠀⠹⠃⡀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣴⣿⣿⣿⣿⠿⠿⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⡇⠀⠀⠀⢻⣽⣿⠀⠈⠛⠀⠀⠀⢹⠇⠀⠀⠀⠀⢶⣿⠇⠀⢀⣴⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⣀⡾⠀⠀⠀⠀⠀⢸⡿⠀⣠⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣦⠀⠀⢠⣿⢳⠀⠀⠀⠙⣿⣿⠁⢰⣿⡿⣻⡿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⡾⠿⠃⢸⣷⣀⠀⢀⣾⠃⢀⣿⣿⣻⣿⡿⡯⣻⣣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠻⠷⢾⣿⣿⣷⡿⠁⠀⢸⣿⣟⡿⣏⣿⣿⣿⣯⣿⣗⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣷⣄⠀⠀⠉⠛⠀⠀⠀⢸⣿⡇⠈⠉⠛⢧⣝⣟⣯⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⣄⡀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠉⠙⠯⣯⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶⣶⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠻⠯⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢰⠉⠑⠄⡎⠉⢱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢱⠀⠀⠀⠀⠀⠀⠣⣀⠈⠁⠜⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠘⠎⢀⡀ ⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⡐⡇⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⠐⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀ ⠀⠀⠀⠀⠀⠀⡖⠀⡔⠉⠀⡇⠀⠈⠁⠀⠀⠉⠉⠓⠤⠋⠀⠾⠀⢸⠀⠀⡇⠀⠠⠄⠀⠀⠀⠠⠎⠀⠀⠀ ⢠⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠓⢫⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⡅⠁⠁⠉⠁⠀⢀⠤⠒⠒⣲⣦⣈⠑⠄⠐⠊⣤⡤⢤⣀⠤⣀⠀⠀⠀⠀⠀⠐⠓⠦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠝⠀⠀⠀⠏⡀⠀⠀⠀⢰⡯⠃⢉⡏⢀⡴⠋⠁⠀⣿⡇⠀⠀⢹⠀⠀⠀⠀⠀⡤⠔⠋⠀⠀⠀⠀⠀ ⠀⠶⣉⠀⠀⠀⠀⠀⠀⠉⠒⠒⠚⠓⠉⠁⠀⠉⠂⠒⠒⠚⠉⠁⠉⠁⠀⠀⠀⠀⠙⠅⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⠤⠇⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢠⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⡄⠀⠀⠀ ⠀⠀⠀⠉⠒⠤⠀⠀⠀⠀⠀⠀⠘⡄⠬⠀⢣⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠒⠁⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠤⠤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠋⠉⠁⠀⠀⠀⢀⣰⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠁⠀⠀⠀⠀⠀⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⣀⡤⠤⠶⠖⠒⠒⠒⠒⠲⠦⢤⣀⣻⠀⠀⠀⠀⠀⠀⣾⠉⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣋⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠶⣄⡀⠀⠀⡟⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠈⢉⣉⣩⡷⠶⠶⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣀⣷⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄ ⠀⠀⠀⠀⠀⠀⠀⢠⡷⣿⢃⡴⠖⠋⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠳⠆⠀⠀⠀⠀⠀⠀⠀⠉⢿⡄⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢖⣿⡍⢹ ⠀⠀⠀⠀⠀⠀⠀⢸⣇⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠞⢋⣹⠞⠋⠁⢱⢸ ⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣀⣙⣷⣤⣀⡤⠴⠶⠶⠶⠞⠉⠀⣠⣶⠛⠁⠀⠀⠀⣸⡾ ⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠁⠀⠀⠀⠀⠀⡏⡇ ⠀⠀⠀⠀⢠⣏⣀⣀⡤⠴⢶⡖⠒⠒⠒⠲⠶⠶⢽⣷⣲⡶⠶⠶⠖⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡽⠁⠀⠀⠀⠀⠀⢰⣿⡇ ⠀⠀⠀⠀⠈⠉⠉⠉⢷⣄⡾⠁⢀⣤⠾⠋⠉⣻⣶⡀⠉⠉⢳⣶⠇⠀⠀⠀⠀⠀⢀⣠⣆⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣼⠃⠀⠀⠀⠀⠀⢀⡼⣻⠃ ⠀⠀⠀⠀⠀⣀⣠⣶⠏⠉⠀⢠⡟⠁⠀⢠⡾⠋⠈⣷⠀⣰⠟⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢸⡇⠀⠀⠀⠀⠀⠀⣼⢣⡏⠀ ⠀⠀⠀⠀⣸⡿⠃⠀⠀⠀⢰⡟⠀⠀⣰⠋⣰⡶⢶⣿⡾⠃⠀⠀⠀⠀⠀⢀⣾⠿⠉⠁⠀⠀⠈⠙⠻⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⣼⢁⡞⠀⠀⠀⠀⠀⠀⣼⢃⡼⠁⠀ ⠀⠀⢀⣼⣏⠁⠀⠀⠀⠀⣺⡇⠀⠠⠏⠀⣿⡷⠞⡿⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣦⡀⠀⠀⠀⣸⠇⣸⠃⠀⠀⠀⠀⣠⡞⢁⡼⠃⠀⠀ ⠀⠀⠸⢻⠃⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠉⠁⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⠀⣠⡞⠁⢰⠇⠀⠀⠀⢀⡶⠋⣠⡞⠁⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⢷⡄⠈⠻⣄⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢘⡇⠙⣫⡟⠁⡞⠀⢀⣠⠴⠋⠀⣰⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣧⠀⠀⠀⣀⣀⡤⠴⠿⠖⠒⠛⠋⠁⠀⠀⠀⠀⠀⢠⣄⠀⣀⣴⣞⣥⣴⣶⣶⣤⣀⠀⠀⠀⠈⣷⠀⢿⣷⡤⠿⠀⠈⠛⠚⠉⠁⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣦⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⠿⠛⠿⠿⣿⣿⣿⣿⣷⣄⠀⠀⣿⠀⠈⣽⣦⠀⠀⠀⠀⠀⠀⣠⣾⣋⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠋⡶⠖⠛⠓⠒⠶⠶⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣦⣠⠏⠀⠀⠈⠻⣦⣀⣀⣠⠴⠖⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⢀⣹⡍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣇⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⢀⣠⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢧⡀⠈⠙⠶⣄⣀⡤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢙⣶⡤⣤⣼⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⠛⢹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣶⣴⠋⠁⣰⠞⠉⠀⠉⠓⠶⣄⣀⢀⣀⣀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠶⠞⠉⠁⠀⢀⣈⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⡏⡇⠀⢰⡇⠀⠀⠀⠀⠀⠀⢨⡿⠋⠉⠉⠀⠀⠀⠀⣀⣀⣠⠤⠶⠖⠊⠉⠉⠉⠀⠀⠀⠀⠀⠀⣼⣹⡟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⡿⢷⣄⠈⠀⠀⠀⠀⠀⠀⣴⣏⣀⣀⣀⣀⡤⠶⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢰⢏⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⣤⡙⠷⣄⡀⠀⠀⣠⡾⠁⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣾⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣛⣀⣀⣾⣿⠿⠿⢥⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣨⡿⠷⠂⠀⠈⠉⠀⠀⠀⠈⠉⠳⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠻⢦⣀⣀⣀⣀⣀⣀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠉⠉⠐⠾⠛⢻⣯⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠐⠶⢤⣀⣀⠀⠀⠀⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡶⠆⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠉⠉⠓⠶⠶⣶⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀ ⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀ ⢸⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀

🐺💦❤️‍🔥

🐾😏🌶️

🐺🥵💋

🐱👅💋

🐾❤️‍🔥🍑

🦊👉👌🐺

🐺🍆👨‍❤️‍👨

🐰🐱🥵

🦊🍑👅

🐱‍👤😈💦

🧑‍🤝‍🧑➡️🐾

💪🐻🔞

🐶🫦🐱

🐾🍑💦

🦊🐺❤️‍🔥