A matrix of size \(M \times N\) where \(M\) and \(N\) are integers that denote the number of rows and columns of the matrix respectively. The matrix contains integer elements only. You are given an integer \(P\).

Write a program to determine the number of submatrices of this matrix such that the sum of all the elements of a submatrix is divisible by \(P\).

Input format

First line: \(M\), \(N\), and \(P\)
Next \(M\) lines: \(N\)

Output format

Print the number of submatrices such that the sum of all the elements in those submatrices is divisible by P.

Constraints

\(1 ≤ Element \; in \; each \; cell ≤ 200\)

\(1 ≤ M, N, P ≤ 200\)