A window was broken at the school. Four students were at the scene of the crime, but only two of them tell the truth, while the other two lie. Here are their statements:

Joey: "Lizzy is a liar."
Bobby: "Janey and I are the truthful ones."
Janey: "It wasn't me."
Lizzy: "I did it."

Mr. Smith tells the principal which students are telling the truth. With that information, the principal takes the culprit to her office.

Who broke the window?