Polo the Penguin and Matrix

2000ms

262144K

Description:

Little penguin Polo has an n × m matrix, consisting of integers. Let's index the matrix rows from 1 to n from top to bottom and let's index the columns from 1 to m from left to right. Let's represent the matrix element on the intersection of row i and column j as a_ij.

In one move the penguin can add or subtract number d from some matrix element. Find the minimum number of moves needed to make all matrix elements equal. If the described plan is impossible to carry out, say so.

Input:

The first line contains three integers n, m and d (1 ≤ n, m ≤ 100, 1 ≤ d ≤ 10⁴) — the matrix sizes and the d parameter. Next n lines contain the matrix: the j-th integer in the i-th row is the matrix element a_ij (1 ≤ a_ij ≤ 10⁴).

Output:

In a single line print a single integer — the minimum number of moves the penguin needs to make all matrix elements equal. If that is impossible, print "-1" (without the quotes).

Sample Input:

2 2 2
2 4
6 8

Sample Output:

Sample Input:

1 2 7
6 7

Sample Output:

-1

Informação

Provedor Codeforces

Código CF289B