Coprime Subarrays

The *beauty* of an array $A$ of length $N$ is defined as follows. Let $S$ be a set of pairs of integers satisfying the following conditions: - Each element $(x, y)$ of $S$ should satisfy $1 \leq x \leq y \leq N$. - For each $(x, y) \in S$, $\gcd(A_x, A_{x+1}, A_{x+2}, \ldots, A_y) = 1$ should hold. That is, the GCD of the subarray of $A$ from index $x$ to index $y$ (inclusive) should be $1$. -