⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣶⣿⣿⣀⠀⠀⠀⢀⣤⣤⣤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠯⢤⢤⣼⠟⠁⠀⠀⠀⠈⢻⣶⣶⣶⣯⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢐⡿⢻⣿⡿⠃⠀⣀⣀⣤⣤⣄⣀⠙⣿⡛⠛⠻⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠥⠌⠿⠷⠚⠉⠉⠉⡏⠀⠉⠉⠛⠿⠟⠀⠊⢷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠆⠀⠀⠀⠘⠿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀ ⠀⢀⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⣞⢿⠀⠀ ⠀⣿⣿⡧⠤⠚⡒⠒⠤⢄⣀⠀⠀⠀⠀⢿⠀⠀⠀⢀⣀⠤⠔⠒⢒⠒⠢⣽⣿⣿⠀⠀ ⠀⢿⢋⣴⣶⣾⣶⣶⣤⣄⡀⠉⠒⣄⠀⢸⠀⣠⠚⠁⣀⣤⣶⣶⣾⣶⣶⣬⣹⣿⠄⠀ ⠀⣼⣿⠁⢻⠇⠀⠀⠉⠙⠻⢷⣦⠀⣵⢸⣾⡇⣰⡿⠟⠉⠉⠀⠀⠈⡿⡎⢻⣧⠀⠀ ⠀⣿⡇⠇⡟⡇⠀⠀⠀⠀⠀⠀⠹⡇⢻⡷⡷⡀⡟⠀⠀⠀⠀⠀⠀⢠⣧⡇⢸⢻⠀⠀ ⠀⣿⡟⠂⣿⡷⢀⠀⠀⠀⠀⠀⢀⠃⣤⠇⣷⣇⢧⠀⠀⠀⠀⠀⠀⢘⣿⠃⢸⢸⠀⠀ ⠀⣿⣧⠀⣿⡏⠋⢁⡀⠀⠀⢀⡼⢀⣸⣶⢹⣼⡘⡄⠀⠀⠔⠀⠀⠈⣿⣴⢸⣸⡄⠀ ⢰⣏⣿⡄⣿⡇⠀⠀⠁⢀⣾⡿⠁⣸⢿⣿⡆⢧⣧⡙⡄⠀⠀⠀⠀⢠⣿⡿⣸⣿⢸⡄ ⣿⢹⣽⣷⣿⣧⣀⠀⢀⣾⠟⢀⣴⠛⠜⡷⣇⠢⠳⣽⢘⢄⠀⠀⠀⣸⣿⣴⣿⡉⢸⡇ ⣿⡅⢳⡻⠿⣿⣿⡿⠟⠃⣰⡾⠁⠃⠀⢻⡿⠀⠀⠙⣾⡈⠙⠻⢿⣿⠿⢛⣷⠋⠈⡇ ⢻⡇⠀⠙⠷⣤⣤⣤⠤⠛⠃⢳⢀⠄⠀⢸⠀⠀⠀⣰⠀⠙⠳⢶⣤⣤⡧⠞⠃⠀⢸⠃ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠻⠀⠀⢸⠀⠀⡴⠁⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠈⠂⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄ ⢸⠁⠀⠀⠀⠀⠀⠀⠀⣴⡾⠖⠂⠁⠀⠀⠀⠀⠀⠁⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⣙⡇ ⣾⣷⡀⠀⠀⠀⠀⢀⡾⠋⣀⣤⣶⣾⣶⠶⠶⣶⣥⣄⠀⠀⠱⡄⠀⠀⠀⠀⠀⣰⣿⡇ ⢹⣿⣧⡀⠀⠀⠀⡸⢀⣾⣽⣯⡶⣹⣶⣿⣿⣽⣿⡻⣷⣄⠰⣵⠀⠀⠀⠀⣰⣿⣿⠇ ⠈⣿⣿⣧⢀⠀⠠⡿⣼⡟⢻⣿⡿⣿⣷⣿⣿⢾⣯⣟⣿⣏⡆⢹⠀⠀⠀⢠⣿⣿⡏⠀ ⠀⠈⣿⣿⣿⡀⠀⣷⣿⣷⣿⣿⣻⣽⣿⣿⣿⣻⣿⡿⡃⣿⡇⢸⠀⢀⡀⣾⣿⣿⠇⠀ ⠀⠀⢹⣿⡿⣇⠀⢱⠸⣿⣿⣝⣾⣿⡽⣷⣿⣞⣿⢿⣿⣿⠇⡟⡂⠜⠛⣿⣿⠏⠀⠀ ⠀⠀⠀⡟⢷⡼⡜⢸⡄⡈⠻⣿⣿⣿⣭⣽⣾⣿⣶⣿⠟⠁⢀⡇⠀⣀⢠⣿⠋⠀⠀⠀ ⠀⠀⡸⠀⠈⢷⣵⡀⡇⠀⠀⠀⣾⢭⣛⣛⡿⠿⣯⣄⢀⠀⢸⣯⢀⣽⡟⢾⠀⠀⠀⠀ ⠀⢠⠃⠀⠀⠈⢿⣧⣰⡀⣼⣾⣻⣿⡿⣿⣿⣿⣿⣷⣾⠀⣾⣰⣽⡟⠑⢻⡄⠀⠀⠀ ⠀⢸⣶⣶⣶⣶⣶⣿⣿⣷⣿⢽⣯⡾⠛⠛⠻⣯⣟⡟⣿⣴⣿⣿⣋⣸⡃⢸⡇⠀⠀⠀ ⠀⠈⠉⠉⠉⠉⠉⠁⠉⢻⣿⣾⣿⡄⠀⠀⠀⢈⣿⣧⣿⣿⠿⠴⠼⢿⠷⣼⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣶⣶⣴⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀