Polo the Penguin and Matrix

- 给定一个 $n$ 行 $m$ 列的矩阵 $a_{i, j}$； - 每次操作可以使矩阵中任意一个元素增加或减少 $d$； - 求最小操作次数，使矩阵中所有元素相等；若无解则输出 `-1`； - $1 \leqslant n, m \leqslant 100$，$1 \leqslant a_{i, j}, d \leqslant 10^4$； - translated by [KHIN](/user/236807).

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.

The first line contains three integers $ n $ , $ m $ and $ d $ $ (1<=n,m<=100,1<=d<=10^{4}) $ — 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}<=10^{4}) $ .

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).

2 2 2
2 4
6 8

4

1 2 7
6 7

-1