JBMO-SL 2002 Problem 12

Let $ABCD$ be a convex quadrilateral with $AB=AD$ and $BC=CD$ . On the sides $AB,BC,CD,DA$ we consider points $K,L,L_1,K_1$ such that quadrilateral $KLL_1K_1$ is rectangle. Then consider rectangles $MNPQ$ inscribed in the triangle $BLK$ , where $M\in KB,N\in BL,P,Q\in LK$ and $M_1N_1P_1Q_1$ inscribed in triangle $DK_1L_1$ where $P_1$ and $Q_1$ are situated on the $L_1K_1$ , $M$ on the $DK_1$ and $N_1$ on the $DL_1$ . Let $S,S_1,S_2,S_3$ be the areas of the $ABCD,KLL_1K_1,MNPQ,M_1N_1P_1Q_1$ respectively. Find the maximum possible value of the expression: $\frac{S_1+S_2+S_3}{S}$