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} 
dim = input().split()
n = int(dim[0])
m = int(dim[1])
A = []
for i in range(0,n):
    A.append(list(map(int, input().split())))

B = [[0 for i in range(m)] for j in range(n)]

def poscheck(A,n,m):
    for i in range(0,n):
        for j in range(0,m):
            if A[i][j] == 1:
                num = 0
                coords = [(i-1,j-1),(i,j-1),(i-1,j),(i+1,j),(i,j+1),(i+2,j),(i,j+2),(i+2,j+2)]
                for k in range(0,8):
                    try:
                        if A[coords[k][0]][coords[k][1]] == 1:
                            num += 1
                    except:
                        pass
                if num < 3:
                    return False
    return True

if A == B:
    print(0)

#elif poscheck(A,n,m) == False:
 #   print(-1)

else:
    instr = []
    for i in range(0,n):
        for j in range(0,m):
            if A[i][j] == 1:
                num = 0
                coords = [(i+1,j),(i,j+1),(i+1,j+1)]
                for k in range(0,3):
                    try:
                        if A[coords[k][0]][coords[k][1]] == 1:
                            num += 1
                    except:
                        pass
                if num == 3:
                    instr.append([i+1,j+1])
                    
    for coord in instr:
        ccoord = coord.copy()
        ccoord[0] -= 1
        ccoord[1] -= 1
        
        B[ccoord[0]][ccoord[1]] = 1
        B[ccoord[0]][ccoord[1]+1] = 1
        B[ccoord[0]+1][ccoord[1]] = 1
        B[ccoord[0]+1][ccoord[1]+1] = 1

    if A == B:
        print(len(instr))
        for coord in instr:
            print(coord[0],coord[1])

    else:
        print(-1)
