\prod_{i=1}^n \prod_{j=i}^n gcd{a_i, a_{i+1}, ..., a_j}
= \prod_{i=1}^n gcd{a_i}gcd{a_i, a_{i+1}}...gcd{a_i, a_{i+1}, ..., a_n} ....current : O(n^2) 20%


1. gcd(a_{n-1})gcd(a_{n-1}, a_n) ? gcd(a_n)
2. gcd(a_{n-2})gcd(a_{n-2}, a_{n-1})gcd(a_{n-2}, a_{n-1}, a_n) ? gcd(a_{n-1})gcd(a_{n-1}, a_n)
3. gcd(a)gcd(a, b)gcd(a, b, c) ? gcd(b)gcd(b, c)
G. LHS =