2007 AIME II Problem 3

Square ABCD has side length 13, and points E and F are exterior to the square such that BE=DF=5 and AE=CF=12. Find EF^{2}.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.