Question 7
Squares $ABCD$ and $EFGH$ have a common center and $\overline{AB} \parallel \overline{EF}.$ The area of $ABCD$ is $2016,$ and the area of $EFGH$ is a smaller positive integer. Square $IJKL$ is constructed so that each of its vertices lies on a side of $ABCD$ and each vertex of $EFGH$ lies on a side of $IJKL.$ Find the difference between the largest and smallest possible integer values for the area of $IJKL.$