⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢈⣁⣦⣤⣤⣤⣤⣤⣈⡁⠢⠤⠂⣀⣀⣀⣀⣀⣀⠐⠦⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⣴⡾⠯⠽⠀⠀⠀⠀⠯⠭⡵⣶⣴⡶⡯⠭⠭⠭⠭⡿⢷⣦⡈⢡⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢰⡾⡿⠊⠁⢀⡀⡐⠒⠒⠒⢢⠈⡓⢳⡏⠁⠀⠀⠀⠀⠈⠹⡸⣷⠀⠇⢀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠂⣸⣏⡉⠁⠀⠘⠛⠉⠁⠀⠀⠀⠈⠉⠛⠻⠧⡏⠙⠂⠀⠉⠉⠉⠉⠛⣦⣤⡄⠡⣀⠀⠀ ⠀⠀⠀⠀⠀⢠⠒⡉⣠⣿⠼⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⢮⡷⢤⡀⢀⡀⠀⠀⠀⠀⠀⠼⣿⣤⡄⠱⡀ ⠀⠀⠀⢀⡴⠃⣠⢿⠉⠟⠀⠀⠀⠀⠀⢀⡰⠶⠉⠁⣀⣀⣀⡦⠴⡦⠦⢼⣹⣟⣀⡴⠤⠤⢤⠴⠶⡶⣌⣳⡆⠀ ⠀⠀⢀⠎⢰⡾⣏⠍⠀⠀⠀⠀⠀⠐⠒⠦⠅⣟⠛⠛⠫⣷⣿⣿⠿⢷⣆⠈⢹⡟⠉⠁⣸⣿⣷⣿⣻⣷⣋⣹⡇⠀ ⠀⢀⠎⣐⣿⠧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢦⣤⠿⢯⡿⠶⠾⡿⢴⡞⠓⠒⠒⠛⠛⠛⠛⠛⣻⣽⠏⢁⠆ ⢀⠎⢠⣿⢹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⠇⠀⠀⣀⠀⠀⠀⣀⠀⣰⡶⠏⢀⠔⠁⠀ ⠈⢰⡾⡏⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢘⢻⣧⠈⡆⠀⠀ ⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⣤⠘⠆⠀ ⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢶⢶⣶⡶⡶⠶⢶⣦⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⡷⣿⡆⢸⠀ ⠀⠸⢷⡷⡆⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠈⠉⠉⡻⣷⣶⣶⣾⣆⣀⣘⣉⣉⣛⣛⣛⣛⣉⣉⣝⣆⣷⡾⠿⠁⡸⠀ ⠈⠆⠘⣷⣳⠀⡀⠀⠀⠀⠀⠘⢮⣙⡛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⢿⣿⣭⣭⣭⣽⣿⣿⣻⣏⣹⡿⠇⠐⠊⠀⠀ ⠀⠈⢆⠉⠿⢶⣯⣵⣄⣀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣉⣉⣻⣿⣽⡿⠏⣉⣁⠰⠃⠀⠀⠀ ⠀⠀⠀⠁⠒⠤⡀⠹⠷⣾⣡⣤⡦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢴⣤⣷⡶⠎⢉⣁⠤⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠐⠦⠄⠠⡀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⣀⠤⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀