Maximum of GCDs

**Note the unusual time limit in this problem.** You are given an array $A$ of $N$ positive integers. The *power* of a subarray $A[L, R]$ $(1\le L\le R \le N)$ having size $(R-L+1)$ is defined as $\gcd(A_L, A_{(L+1)}, \ldots, A_R)$, where $\gcd$ denotes the [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor). Your task is to find the **maximum** *power* of a subar