In this problem, a n × m rectangular matrix a is called increasing if, for each row of i, when go from left to right, the values strictly increase (that is, a_{i,1}<a_{i,2}<...<a_{i,m}) and for each column j, when go from top to bottom, the values strictly increase (that is, a_{1,j}<a_{2,j}<...<a_{n,j}).

In a given matrix of non-negative integers, it is necessary to replace each value of 0 with some positive integer so that the resulting matrix is increasing and the sum of its elements is maximum, or find that it is impossible.

It is guaranteed that in a given value matrix all values of 0 are contained only in internal cells (that is, not in the first or last row and not in the first or last column).

Input

The first line contains integers n and m (3 ≤ n, m ≤ 500) — the number of rows and columns in the given matrix a.

The following lines contain m each of non-negative integers — the values in the corresponding row of the given matrix: a_{i,1}, a_{i,2}, ..., a_{i,m} (0 ≤ a_{i,j} ≤ 8000).

It is guaranteed that for all a_{i,j}=0, 1 < i < n and 1 < j < m are true.

Output

If it is possible to replace all zeros with positive numbers so that the matrix is increasing, print the maximum possible sum of matrix elements. Otherwise, print -1.

Examples

Input


4 5
1 3 5 6 7
3 0 7 0 9
5 0 0 0 10
8 9 10 11 12


Output


144


Input


3 3
1 2 3
2 0 4
4 5 6


Output


30


Input


3 3
1 2 3
3 0 4
4 5 6


Output


-1


Input


3 3
1 2 3
2 3 4
3 4 2


Output


-1

Note

In the first example, the resulting matrix is as follows: 
    
    
      
    1 3 5 6 7  
    3 6 7 8 9  
    5 7 8 9 10  
    8 9 10 11 12  
    

In the second example, the value 3 must be put in the middle cell.

In the third example, the desired resultant matrix does not exist.

/**
 * @author egaeus
 * @mail sebegaeusprogram@gmail.com
 * @veredict Accepted
 * @url <https://codeforces.com/problemset/problem/1231/C>
 * @category implementation
 * @date 30/09/2019
 **/

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

import static java.lang.Integer.parseInt;

public class CF1231C {
    public static void main(String args[]) throws Throwable {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        for (String ln; (ln = in.readLine()) != null; ) {
            StringTokenizer st = new StringTokenizer(ln);
            int N = parseInt(st.nextToken()), M = parseInt(st.nextToken());
            int[][] T = new int[N][M];
            int[][] TT = new int[M][N];
            for (int i = 0; i < N; i++) {
                st = new StringTokenizer(in.readLine());
                for (int j = 0; j < M; j++) {
                    T[i][j] = parseInt(st.nextToken());
                    TT[j][i] = T[i][j];
                }
            }
            boolean ws = true;
            for (int i = N - 1; i >= 0 && ws; i--)
                for (int j = M - 1; j >= 0 && ws; j--)
                    if (T[i][j] == 0) {
                        int[] R = getRange(i, j, T);
                        int[] RT = getRange(j, i, TT);
                        int v = -1;
                        for (int k = R[0]; k <= R[1]; k++)
                            if (k >= RT[0] && k <= RT[1])
                                v = k;
                        if (v > 0)
                            T[i][j] = TT[j][i] = v;
                        else
                            ws = false;
                    }
            int sum = -1;
            //for(int[]a:T) System.out.println(Arrays.toString(a));
            if (check(T) && ws) {
                sum = 0;
                for (int i = 0; i < N; i++)
                    for (int j = 0; j < M; j++)
                        sum += T[i][j];
            }
            System.out.println(sum);
        }
    }

    static int[] getRange(int I, int J, int[][] T) {
        int R[] = new int[2];
        for (int j = 0; j <= J; j++)
            if (T[I][j] == 0)
                R[0]++;
            else R[0] = T[I][j];
        for (int j = T[I].length - 1; j >= J; j--)
            if (T[I][j] == 0)
                R[1]--;
            else R[1] = T[I][j];
        return R;
    }

    static boolean check(int[][] T) {
        for (int i = 0; i < T.length; i++)
            for (int j = 0; j < T[i].length; j++)
                if ((i > 0 && T[i - 1][j] >= T[i][j]) || (j > 0 && T[i][j - 1] >= T[i][j]))
                    return false;
        return true;
    }
}
