Potential Attack Vector

Problem Preview

"Design an algorithm to detect potential attack vectors within a network. An attack vector in an array of keys is defined as a trio of indices (i, j, x) where keys[i] and keys[j] are both divisible by x. Given an array of integers keys, count the total number of possible attack vectors. For example, valid attack vectors for keys = [7, 2, 4] include: (0, 1) and keys[1] = 2 are both divisible by 1 (0, 2) and keys[0] = 7 and keys[2] = 4 are both divisible by 1 (2, 2) and keys[2] = 4 are both divisible by 4 (0, 2) and keys[2] = 4 are both divisible by 2 And others. Given a network of n keys and a 2-d array queries of dimensions * 2, each query provides an inclusive range [x <= queries[i][0] and x <= queries[i][1]]. Report an array of exactly q integers where the ith element of the array is the answer to the ith query."