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

$1 ≤ Element \; in \; each \; cell ≤ 200$

$1 ≤ M, N, P ≤ 200$