Problem Description

Given an array of positive integers, count the number of triples (i, j, k) where i < j < k and A[i] × A[j] = A[k]. These are called "lucky triples" because the product of two earlier elements equals a later element.

Input Format

First line contains n (array size). Second line contains n space-separated positive integers.

Output Format

Number of lucky triples in the array.

Constraints

• 3 ≤ n ≤ 1000

• 1 ≤ A[i] ≤ 1000

• Indices must satisfy i < j < k

• Count all valid triples

• Handle duplicate values correctly

Sample Input/Output

Explanation

Lucky triples: (0,1,2) where A[0]×A[1] = 2×3 = 6 = A[2], and (1,3,4) where A[1]×A[3] = 3×4 = 12 = A[4]. Total: 2 triples.