⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠁⠈⠳⠋⠉⢙⡆⠀⠀⠀⠸⣏⠀⠈⠉⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠣⣀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠬⣝⠺⠄⢀⣤⠖⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠈⠙⢦⣠⣾⣿⣁⣀⣀⠀⠀⢀⣠⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣁⣀⣘⠦⣠⡿⠒⠒⠒⠒⠒⠒⠒⠲⠲⢤⣄⣀⡤⠴⠖⠚⢻⣿⠏⠀⠀⠈⠉⠉⣿⣿⡧⣤⣤⣴⠖⠚⠋⠉⠉⠉⠙⠳⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⣛⣙⠒⠦⣤⣌⡁⠀⠀⠀⠀⠀⠀⠿⠟⠛⠉⠀⠈⠉⠓⠲⢤⣀⠀⠀⠀⠈⠻⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⣿⡇⠀⠀⢀⣠⡴⠶⠲⠖⠲⡏⣿⣿⣿⣷⣶⣦⣍⣉⠛⠻⠶⠦⢤⣀⣀⣀⣀⣀⠀⠀⠀⣀⡮⠞⢻⠀⠀⠀⠀⢻⣦⠀⠀ ⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠐⢹⣄⡤⠚⠋⠁⠀⠀⢀⢀⢠⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣬⣭⣭⣉⠙⠳⡏⠁⠀⠀⢸⠀⠀⠀⠀⠀⢻⡆⠀ ⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⡠⣸⢿⡀⢀⣤⣶⣯⠽⠟⠻⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢿⠀ ⠀⠀⠀⢰⠏⠀⠀⠀⠈⠀⠀⢰⠃⢈⣿⣿⣋⢁⣠⣀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⡇ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣼⣀⡿⠃⠀⢩⣿⣿⣿⣷⠀⢸⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣧⠆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⠘⢷⣿⣿⠟⠀⢸⠀⣿⣿⣿⣶⣿⣿⣛⣿⣿⣿⣿⣿⣿⡿⠟⣛⣛⣛⣿⣿⠋⠀⢀⣤⡾⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⢰⡇⠀⠀⠀⠀⠀⣀⣀⡀⣤⣸⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣇⡇⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⢰⠇ ⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⡏⡸⡇⠀⠀⠠⢄⠨⠉⠛⠿⣷⣍⠻⣌⣻⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣸⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀ ⠀⠀⠀⠈⢧⠀⠀⠀⠀⢀⣿⡇⢻⡄⠀⠈⠉⠈⠓⠀⠀⠙⣿⡿⢻⣿⣿⢷⣯⣭⣟⣛⡿⠿⠾⣿⣿⣿⣿⣿⣿⠏⡇⢀⣠⠼⢃⣴⣿⣿⣶⠄⣀⣤⠟⠀⠀ ⠀⠀⠀⠀⠀⠻⣦⠀⠀⠈⠛⠒⠲⣿⣄⡀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣆⣬⣿⣿⣿⠉⠙⣷⣶⣶⣶⣦⣤⣤⡤⠞⡟⠛⣷⠀⠸⣿⣿⣿⡟⠉⠉⠀⠀⠀⠀ ⠀⠀⢀⣤⠤⣤⢬⣳⡄⠀⠀⠀⠀⠀⠉⣍⡳⣄⠀⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠃⠀⢸⡃⠈⠙⠛⡿⠚⣿⠃⢘⣁⣤⡟⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣤⠿⠉⠀⠹⠄⠈⡇⠀⠀⠀⠀⠀⠀⠀⠹⢽⠓⠾⠷⣤⣤⣤⣤⣬⠿⠟⠉⠀⠀⠀⢠⡟⠀⠀⠐⢭⡟⠙⣄⣄⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⢀⡄⠀⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠮⠟⠁⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠓⣗⣀⣾⠷⠴⠞⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀