Liam, Mia, and Noah competed in a 100-meter dash. Liam announced his finishing time to Mia and Noah, but Mia and Noah kept their times private. Mia said, "I didn't run the fastest among us." Noah said, "I didn't run the slowest among us." Assuming they all finished with different times (where a lower time means faster), what is the ranking from fastest to slowest?