⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⡿⠋⠀⠀⠀⠈⢄⠀⠀⣄⢀⣾⡿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⠿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⢸⣿⡿⠳⠃⠀⠀⠀⠀⠀⡄⢠⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢋⣿⣿⠉⠃⠀⠀⠀⠀⠐⠺⢷⣿⣿⣥⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⣼⣿⡏⠀⠀⠀⠀⢰⠿⠀⣼⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢸⣿⣿⠁⠃⠀⠀⠀⠸⠁⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣾⣿⡏⠀⠀⠀⠀⠀⠀⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣠⣄⣀⣀⡀⠀⢰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⠶⠛⠋⠛⠛⠀⠀⠈⠉⠉⠛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠘⣷⠀⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣄⣀⣀⣀⣤⣶⣿⡿⠇⠀⠹⣧⢹⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡾⢷⠀⠀ ⠀⠀⠀⢀⡆⢰⡿⠀⠀⠀⠠⠤⣄⠀⠀⠀⣠⠶⠟⠉⠀⠀⠀⠀⠀⠀⠉⢧⡀⠀⠀⠀⣿⠀⠀⠀⠀⣿⢸⠀⠀ ⠀⠀⠀⠋⢁⣿⠅⠀⠀⠀⢀⠀⠘⢯⣷⣾⣃⣀⣹⣯⣭⣭⣯⣭⣝⣓⣐⡀⢷⡀⠈⣿⣷⣼⠀⠀⡆⡯⡿⠀⠀ ⠀⠀⠀⠀⢸⡇⠃⠀⠀⠀⢨⣷⡄⠈⣿⡦⠤⠤⠤⠼⠷⠾⠤⠤⠤⠤⠤⢼⣿⠇⢀⡿⠁⠀⠀⢠⣷⡷⣟⣿⣶ ⠀⠀⢀⠀⣾⠁⠀⠀⠀⠀⢸⣿⢿⠀⢹⠙⢧⣀⠀⠒⠒⠒⠒⠒⠒⢀⣤⠞⠃⠀⣽⠇⠀⠀⠀⠘⣿⣟⠻⣿⠋ ⠀⠠⠚⢰⡏⠀⠀⠀⠀⠀⢸⣿⠈⠀⠀⠀⠀⠉⠙⠓⠒⠶⠶⠒⢛⣡⠄⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⣼⢸⡏⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡿⢶⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠛⠉⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠐ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⣌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⣄⣀⣠⣄⣄⣄⣀⣠⡿⣸⠁⠀ ⠀⠀⠀⢠⡿⠓⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠤⠤⠤⠤⠤⠤⠤⠤⠤⠾⠏⠀⠀ ⠀⠀⠀⣿⢁⡄⠀⠀⠀⠀⢘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⡟⢸⡇⢠⢴⣶⣶⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡆⠀⡇⢸⣧⣿⢀⣿⡟⡆⣿⣿⡙⣆⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡇⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⠐⣷⢿⣻⣿⠾⠏⠀⠈⢾⣿⣿⡙⢦⡀⠀⠀⠀⢠⠀⠻⠄⢀⣿⡶⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣯⣿⣿⠀⠀⠀⠀⠈⣿⣿⣿⣦⡙⣦⣄⡛⠛⠛⠛⢛⣛⣵⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠀⣿⣧⠀⠀⠀⠀⠙⢮⡳⣍⠙⠓⢮⣽⣉⣙⣋⣹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣟⠀⠀⠀⠀⠈⠳⣬⣛⠶⢤⣽⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⢀⠀⠀⠀⠘⠛⠻⠶⠧⠼⠬⠯⢽⣿⣿⣮⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡺⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣎⠻⣿⡗⠶⠒⢦⡄⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣠⡮⣭⣭⣭⡤⠴⢶⣛⡿⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀