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 aij.

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 aij (1 ≤ aij ≤ 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).

Examples

Input

2 2 2
2 4
6 8


Output

4


Input

1 2 7
6 7


Output

-1
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

public class B {

    public static void main(String[] args) throws IOException {
        ReaderB.init(System.in);
        int n = ReaderB.nextInt();
        int m = ReaderB.nextInt();
        int d = ReaderB.nextInt();

        int[] elements = new int[n*m];
        int[] diffFromSmallest = new int[n*m];
        int[] diffPrefix = new int[n*m];

        for (int i = 0; i < elements.length; i++) elements[i] = ReaderB.nextInt();

        Arrays.sort(elements);
        int smallest = elements[0];

        for (int i = 0; i < elements.length; i++) {
            diffFromSmallest[i] = elements[i] - smallest;
            if (diffFromSmallest[i] % d != 0){
                System.out.println(-1);
                return;
            }

            diffFromSmallest[i] /= d;
            diffPrefix[i] = diffFromSmallest[i];
            if (i != 0) diffPrefix[i] += diffPrefix[i - 1];
        }
        int ans = Integer.MAX_VALUE;
        for (int i = 0; i < diffPrefix.length; i++) {
            int steps = diffFromSmallest[i]*(2*i - n*m + 1) + (diffPrefix[diffPrefix.length - 1] - 2*diffPrefix[i] + diffFromSmallest[i]);
            if (steps < ans) ans = steps;
        }

        System.out.println(ans);
    }
}

/**
 * Reader class based on the article at "https://www.cpe.ku.ac.th/~jim/java-io.html"
 */
class ReaderB {
    private static BufferedReader reader;
    private static StringTokenizer tokenizer;

    static void init(InputStream inputStream) {
        reader = new BufferedReader(new InputStreamReader(inputStream));
        tokenizer = new StringTokenizer("");
    }

    private static String next() throws IOException {
        String read;
        while (!tokenizer.hasMoreTokens()) {
            read = reader.readLine();
            if (read == null || read.equals(""))
                return "-1";
            tokenizer = new StringTokenizer(read);
        }

        return tokenizer.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

//    static long nextLong() throws IOException {
//        return Long.parseLong(next());
//    }
//
//    //    Get a whole line.
//    static String line() throws IOException {
//        return reader.readLine();
//    }
//
//    static double nextDouble() throws IOException {
//        return Double.parseDouble(next());
//    }
}

