⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⠿⢛⣟⣉⣀⣀⠀⠀⠀⠀⣘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠰⠛⢉⣩⣽⣿⣓⠀⢀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠘⠿⣿⣿⣿⠏⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠉⠉⣿⢻⣿⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⠐⠺⠈⣿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠻⣞⣻⡏⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡶⠚⠃⠀⠀⠀⠀⠀⠀⠀⣀⣐⣥⣼⣿⣿⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠇⠀⠀⢾⡄⠀⠀⠀⠀⠀⠈⠁⠀⠐⠚⣻⠏⣉⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣿⠏⠀⠀⠀⠀⠙⢦⣤⣀⠀⡀⠀⠀⠀⠀⠐⣻⡾⢁⡆⣨⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢹⣾⣇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢶⣿⣿⣦⠶⢾⣿⣁⣾⣴⡿⠀⣹⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠤⠖⠋⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣿⡇⠀⠀⠀⠈⠉⠉⠀⢀⣴⠿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠴⠒⠉⠉⠁⢀⠉⠢⠶⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠐⠋⢁⣾⣿⠿⡆⠀⠀⠀⠀⠀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⣀⡀⣀⣀⡴⠞⢻⣷⡀⠀⠀⠀⠀⠀⣴⣿⣿⠃⠀⢹⡀⠀⠀⠀⠀⢹⡗⠲⢄⡀⠀⠀⠀⠀⠀ ⠀⢰⠇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣇⠙⠉⠁⠀⠀⢲⣿⣷⠀⠀⠀⠀⠀⣽⣿⠃⠀⠀⠀⢧⠀⠀⠀⠀⠀⣿⡀⠀⠙⢦⠀⠀⠀⠀ ⠀⡞⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⢀⠀⡀⢿⣿⡏⠻⠶⣤⣼⣿⡏⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠸⣇⠀⠀⠀⢷⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⢸⠀⠘⢾⣿⣿⠀⠀⢸⣿⣿⠃⠀⠀⠀⡀⠀⢹⡀⠀⠀⠀⠀⢻⡄⠀⠀⢀⣇⠀⠀ ⢸⠁⠀⠀⠀⠀⠐⢤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻⠀⠀⢸⣿⣿⠀⠀⣾⣿⡟⠀⠀⢀⡜⠁⠀⠋⡇⠀⠀⠀⠀⠀⢳⠀⠀⠁⢹⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢸⣧⣿⠀⢰⣧⣽⠃⠀⢠⠎⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠈⣧⠀⠀⢸⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⣿⢠⣾⣿⡏⠀⣠⠏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⣇⠀⢸⠀⠀ ⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⣿⣷⣴⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⡆⠈⣇⠀ ⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠟⣻⡋⠙⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠘⡄