⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡏⠉⢠⣄⣉⠒⢄⠀⠀⠀⠀⠀⢀⡴⠟⠛⠉⠀⠀⠀⢀⣀⠤⠤⠒⠒⠒⠒⠉⠒⠒⠒⠒⠤⠤⣀⡀⠀⠈⠉⠓⠄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠠⣄⠀⠀ ⠀⡴⣇⢀⡤⠚⠋⠉⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠩⣳⣦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣞⣁⣤⡾⠀⠀⢸⡀⠀ ⠀⡇⢸⠎⠐⢦⠄⢀⣀⠔⢱⠀⠀⠀⠀⠀⣠⠖⠉⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣶⣄⠀⠀⠀⢠⠋⠀⠀⠀⠈⡑⢆⡞⢹⡀ ⢰⠳⣾⠀⢠⢇⡞⠁⠀⢀⠎⠀⠀⠀⡠⢊⠀⠀⢀⣂⠠⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⠀⢮⠙⠦⠤⣐⢪⡀⠈⢧⢸⣄ ⠈⠧⣷⣠⣯⠎⠀⣠⠞⠁⠀⠀⢠⠞⡠⣊⣤⠾⠛⠛⠓⠛⠷⣯⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣲⣯⣽⣿⣿⣿⣿⣿⣷⡌⠢⣀⠀⠈⢦⣻⡀⢸⢁⡾ ⠀⠀⠀⠉⠓⠤⠚⠁⠀⠀⠀⣰⢃⣼⡻⠋⠀⠀⠀⠀⣀⣀⠀⠈⠻⣎⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣿⠏⠁⠀⠀⠁⠉⠻⠿⣿⣿⣿⣆⠈⠳⢄⢠⢓⡽⠾⠊⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢸⡟⠁⠀⠀⠀⠀⣞⣿⣿⣷⠀⠀⠙⣧⠄⠀⠀⠀⠀⠀⠀⠀⡴⠋⠃⣾⣿⣦⠀⠀⠀⠀⠀⠺⣿⣿⣿⣆⠀⠀⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⡾⠀⢀⣀⡤⠤⠒⠛⠛⠛⠛⠒⠒⠒⠽⠷⠀⠀⠀⠀⠀⠀⣼⡷⠾⣯⣯⣭⣿⣿⣿⣶⣶⣶⣤⣼⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢀⡗⠋⠉⠀⠀⠀⠀⠒⠒⠒⠒⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠠⠤⠤⠤⠤⠤⣤⡤⠤⠤⠤⠤⢄⣀⣀⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢀⣀⠠⠀⣀⣀⣠⣤⣤⣴⣶⢶⠶⠻⣿⣿⡟⡟⠉⢿⣿⣿⡟⡟⠛⠿⣿⣿⢿⠗⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⣯⣶⣾⡿⠿⣿⡽⠏⠉⠙⢿⣿⠈⠀⠀⠙⣿⠟⠀⠀⠀⠙⡿⠃⠀⠀⠈⠻⣿⠈⠀⠀⠀⢹⡿⠼⠻⣿⡿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣿⣿⢹⠀⠀⠸⡇⠀⠀⠀⠀⣇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣸⠃⠀⠀⠈⠇⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡞⢹⣯⢿⣇⠀⠀⢿⣄⣀⣀⣀⣹⣤⣤⣤⣴⣾⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣷⣶⣤⣤⣤⣿⣄⣀⣀⣊⣸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠉⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣯⠏⠀⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⡷⠃⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⡿⠋⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣯⣟⡿⢶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣶⠾⣟⡯⠗⠉⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢏⡙⠈⠀⠉⠛⠲⣿⣭⣭⣭⣍⣉⣉⣉⣭⣭⣭⣴⠶⠛⠉⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠉⠙⠛⠛⠛⠻⠛⠛⠛⠉⠀⢀⣠⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⠤⠤⢤⣤⣤⡤⢤⠴⠶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀