Given an array \(A\) of \(N\) integers.

Find the count of subarrays whose product of elements is a perfect cube.

Input Format:

• First line contains an integer \(N\).
• Next line contains \(N\) space-separated integers denoting the array elements.

Output Format:

Print the number of subarrays whose product of elements is a perfect cube.

Constraints:

\(1 \le N \le 10^5 \\ 1 \le A[i] \le 10^2\)