2015 AIME I Problem 7

In the diagram below, A B C D is a square. Point E is the midpoint of \overline{A D}. Points F and G lie on \overline{C E}, and H and J lie on \overline{A B} and \overline{B C}, respectively, so that F G H J is a square. Points K and L lie on \overline{G H}, and M and N lie on \overline{A D} and \overline{A B}, respectively, so that K L M N is a square. The area of K L M N is 99 . Find the area of F G H J.