Squared Subsequences

Let's call a sequence of integers *good* if the product of its elements can be represented as a difference of squares of two integers. More formally, a sequence $S_1, S_2, \ldots, S_K$ is *good* if it is possible to find two integers $p$ and $q$ such that $S_1 \cdot S_2 \cdot \ldots \cdot S_K = p^2 - q^2$. Chef has a sequence $A_1, A_2, \ldots, A_N$. He wants to find the number of contiguous su