Given an array \(A\) of \(N\) elements, a prime number \(P\) and an integer \(K\). It is guaranteed all the elements in the array are distinct.

Find the number of pairs of indices \((i,j)\) such that \((1 \le i < j \le N)\) and \((A[i] + A[j]) \times (A[i]^2 + A[j]^2)) \equiv K \ \text{mod} \ P\) 

Note: 1 based indexing is followed.

Input format

• The first line contains 3 space-separated integers \(N, P, K\).
• The second line contains \(N\) space-separated integers denoting the array \(A\).

Output format

Print the number of pairs of indices which satisfy the given condition in a new line.

Constraints

\(2 \le N \le 10^5 \\ 0 \le K, A[i]\le P - 1 \\ 2 \le P \le 10^5\)