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.*;
import java.math.BigInteger;
import java.nio.Buffer;
import java.sql.BatchUpdateException;
import java.util.*;
import java.util.stream.Stream;
import java.util.Vector;

import static java.lang.Math.*;

import java.util.*;
public class icpc
{
    public static void main(String[] args)throws IOException
    {

        Reader in = new Reader();
        int n = in.nextInt();
        int m = in.nextInt();
        int d = in.nextInt();
        int[] A = new int[n*m];

        for(int i=0;i<A.length;i++)
            A[i] = in.nextInt();

        int mod = A[0] % d;
        boolean flag = true;
        for(int i=1;i<A.length;i++)
        {
            if(A[i] % d != mod)
            {
                flag = false;
                break;
            }
        }
        if(flag)
        {
            Arrays.sort(A);
            int k = A.length;
            int med = A[k/2];
            long moves = 0L;
            for(int i=0;i<k;i++)
            {
                moves += Math.abs(med - A[i])/d;
            }
            System.out.println(moves);
        }
        else
            System.out.println(-1);
    }
}class Solver
{
    public void solve(long[] A,Game[] B)
    {
    }
}
class Point implements Comparable<Point>
{
    int x;
    int y;
    Point(int a ,int b)
    {
        this.x = a;
        this.y = b;
    }
    public int compareTo(Point ob)
    {
        if(ob.x < this.x)
            return 1;
        else if(ob.x > this.x)
            return -1;
        else
            return 0;
    }
}
class MergeSort
{
    // Merges two subarrays of arr[].
    // First subarray is arr[l..m]
    // Second subarray is arr[m+1..r]
    void merge(int arr[], int l, int m, int r)
    {
        // Find sizes of two subarrays to be merged
        int n1 = m - l + 1;
        int n2 = r - m;

        /* Create temp arrays */
        int L[] = new int [n1];
        int R[] = new int [n2];

        /*Copy data to temp arrays*/
        for (int i=0; i<n1; ++i)
            L[i] = arr[l + i];
        for (int j=0; j<n2; ++j)
            R[j] = arr[m + 1+ j];


        /* Merge the temp arrays */

        // Initial indexes of first and second subarrays
        int i = 0, j = 0;

        // Initial index of merged subarry array
        int k = l;
        while (i < n1 && j < n2)
        {
            if (L[i] <= R[j])
            {
                arr[k] = L[i];
                i++;
            }
            else
            {
                arr[k] = R[j];
                j++;
            }
            k++;
        }

        /* Copy remaining elements of L[] if any */
        while (i < n1)
        {
            arr[k] = L[i];
            i++;
            k++;
        }

        /* Copy remaining elements of R[] if any */
        while (j < n2)
        {
            arr[k] = R[j];
            j++;
            k++;
        }
    }

    // Main function that sorts arr[l..r] using
    // merge()
    void sort(int arr[], int l, int r)
    {
        if (l < r)
        {
            // Find the middle point
            int m = (l+r)/2;

            // Sort first and second halves
            sort(arr, l, m);
            sort(arr , m+1, r);

            // Merge the sorted halves
            merge(arr, l, m, r);
        }
    }
}
class Node
{
    int[] A;
    int moves;
    Node(int[] B,int c)
    {
        this.A = new int[B.length];
        A = B.clone();
        this.moves = c;
    }
    @Override
    public boolean equals(Object ob)
    {
        if(ob == null)
            return false;
        if(!(ob instanceof Node))
            return false;
        if(ob == this)
            return true;
        Node obj = (Node)ob;
        boolean flag = true;
        for(int i=0;i<obj.A.length;i++)
        {
            if(this.A[i] != obj.A[i])
                flag = false;
        }
        return (flag & (obj.moves == this.moves));
    }
    @Override
    public int hashCode()
    {
        return (int)this.A.length;
    }
}
class Reader
{
    final private int BUFFER_SIZE = 1 << 16;
    private DataInputStream din;
    private byte[] buffer;
    private int bufferPointer, bytesRead;

    public Reader()
    {
        din = new DataInputStream(System.in);
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }

    public Reader(String file_name) throws IOException
    {
        din = new DataInputStream(new FileInputStream(file_name));
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }

    public String readLine() throws IOException
    {
        byte[] buf = new byte[64]; // line length
        int cnt = 0, c;
        while ((c = read()) != -1)
        {
            if (c == '\n')
                break;
            buf[cnt++] = (byte) c;
        }
        return new String(buf, 0, cnt);
    }

    public int nextInt() throws IOException
    {
        int ret = 0;
        byte c = read();
        while (c <= ' ')
            c = read();
        boolean neg = (c == '-');
        if (neg)
            c = read();
        do
        {
            ret = ret * 10 + c - '0';
        }  while ((c = read()) >= '0' && c <= '9');

        if (neg)
            return -ret;
        return ret;
    }

    public long nextLong() throws IOException
    {
        long ret = 0;
        byte c = read();
        while (c <= ' ')
            c = read();
        boolean neg = (c == '-');
        if (neg)
            c = read();
        do {
            ret = ret * 10 + c - '0';
        }
        while ((c = read()) >= '0' && c <= '9');
        if (neg)
            return -ret;
        return ret;
    }

    public double nextDouble() throws IOException
    {
        double ret = 0, div = 1;
        byte c = read();
        while (c <= ' ')
            c = read();
        boolean neg = (c == '-');
        if (neg)
            c = read();

        do {
            ret = ret * 10 + c - '0';
        }
        while ((c = read()) >= '0' && c <= '9');

        if (c == '.')
        {
            while ((c = read()) >= '0' && c <= '9')
            {
                ret += (c - '0') / (div *= 10);
            }
        }

        if (neg)
            return -ret;
        return ret;
    }

    private void fillBuffer() throws IOException
    {
        bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
        if (bytesRead == -1)
            buffer[0] = -1;
    }

    private byte read() throws IOException
    {
        if (bufferPointer == bytesRead)
            fillBuffer();
        return buffer[bufferPointer++];
    }

    public void close() throws IOException
    {
        if (din == null)
            return;
        din.close();
    }
}
class Game
{
    int last;
    int diff;
    boolean flag;
    Game(int a,int b,boolean z)
    {
        this.last = a;
        this.diff = b;
        this.flag = z;
    }
}
class Play implements Comparable<Play>
{
    int x;
    int y;
    Play(int a,int b)
    {
        this.x = a;
        this.y = b;
    }
    @Override
    public int compareTo(Play ob)
    {
        if(this.x < ob.x)
            return -1;
        return 1;
    }
}