You are given an array of length \(N\). You are required to count the number of \((i, j)\) pairs where \(1⩽i<j⩽N\) such that the difference of the array elements on that indices is equal to the sum of the square of their indices.

That is the count of the number of pairs of \((i, j)\) such that it satisfies this equation (\(A[j] - A[i] = i^2 + j^2\)).

Input format

The first line contains the length of the array \(N\). (\(1⩽N⩽10^5\))
The second line contains \(N\) integers representing array elements. (\(1⩽A[i]⩽10^{12}\))

Output format

Print the number of pairs that satisfy the provided condition.