You are given two matrices A and B. Each matrix contains exactly n rows and m columns. Each element of A is either 0 or 1; each element of B is initially 0.

You may perform some operations with matrix B. During each operation, you choose any submatrix of B having size 2 × 2, and replace every element in the chosen submatrix with 1. In other words, you choose two integers x and y such that 1 ≤ x < n and 1 ≤ y < m, and then set B_{x, y}, B_{x, y + 1}, B_{x + 1, y} and B_{x + 1, y + 1} to 1.

Your goal is to make matrix B equal to matrix A. Two matrices A and B are equal if and only if every element of matrix A is equal to the corresponding element of matrix B.

Is it possible to make these matrices equal? If it is, you have to come up with a sequence of operations that makes B equal to A. Note that you don't have to minimize the number of operations.

Input

The first line contains two integers n and m (2 ≤ n, m ≤ 50).

Then n lines follow, each containing m integers. The j-th integer in the i-th line is A_{i, j}. Each integer is either 0 or 1.

Output

If it is impossible to make B equal to A, print one integer -1.

Otherwise, print any sequence of operations that transforms B into A in the following format: the first line should contain one integer k — the number of operations, and then k lines should follow, each line containing two integers x and y for the corresponding operation (set B_{x, y}, B_{x, y + 1}, B_{x + 1, y} and B_{x + 1, y + 1} to 1). The condition 0 ≤ k ≤ 2500 should hold.

Examples

Input


3 3
1 1 1
1 1 1
0 1 1


Output


3
1 1
1 2
2 2


Input


3 3
1 0 1
1 0 1
0 0 0


Output


-1


Input


3 2
0 0
0 0
0 0


Output


0

Note

The sequence of operations in the first example:

\begin{matrix} 0 & 0 & 0 & & 1 & 1 & 0 & & 1 & 1 & 1 & & 1 & 1 & 1 \\\ 0 & 0 & 0 & → & 1 & 1 & 0 & → & 1 & 1 & 1 & → & 1 & 1 & 1 \\\ 0 & 0 & 0 & & 0 & 0 & 0 & & 0 & 0 & 0 & & 0 & 1 & 1 \end{matrix} 
import java.util.*;

public class Main {

    public static void main (String[] args) {
        int Actions = 0;
        Scanner Input = new Scanner (System.in);
        int n = Input.nextInt(), m = Input.nextInt();
        int Matrix[][] = new int [n][m];
        int Answer[][] = new int [n][m];
        int Flag[][] = new int [n][m];
        for (int i=0; i<n; i++) {
            for (int j=0; j<m; j++) {
                Matrix[i][j] = Input.nextInt();
                Answer[i][j] = 0;
                Flag[i][j] = 0;
            }
        }
        for (int i=0; i<n-1; i++) {
            for(int j=0; j<m-1; j++) {
                if(Matrix[i][j] == 1 && Matrix[i+1][j] == 1 && Matrix[i][j+1] == 1 && Matrix[i+1][j+1] == 1) {
                    Actions++;
                    Answer[i][j]=1;
                    Flag[i][j]=1;
                    Flag[i+1][j]=1;
                    Flag[i][j+1]=1;
                    Flag[i+1][j+1]=1;
                }
            }
        }
        for (int i=0; i<n; i++) {
            for (int j=0; j<m; j++) {
                if(Matrix[i][j] != Flag[i][j]) {
                    System.out.println(-1);
                    System.exit(0);
                }
            }
        }
        System.out.println(Actions);
        if (Actions!=0) {
            for (int i = 0; i < n - 1; i++) {
                for (int j = 0; j < m - 1; j++) {
                    if (Answer[i][j] == 1) System.out.println((i + 1) + " " + (j + 1));
                }
            }
        }
    }

}

// Never Give up