Let $a_1, a_2, a_3, \ldots$ be a G.P. such that $a_1 < 0$, $a_1 + a_2 = 4$ and $a_3 a_4 = 16$. If $\sum\limits_{i=1}^{\infty} a_i^2 = 4A$, then $A$ is equal to