Squares A B C D and E F G H have a common center and \overline{A B} \| \overline{E F}. The area of A B C D is 2016 , and the area of E F G H is a smaller positive integer. Square I J K L is constructed so that each of its vertices lies on a side of A B C D and each vertex of E F G H lies on a side of I J K L. Find the difference between the largest and smallest possible integer values for the area of I J K L.