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} 


if __name__ == "__main__":
    cords = [[0, 1], [1, 0], [1, 1]]
    def calc(a, i, j):
        is_ok = True
        for v in cords:
            if i + v[0]>=len(a):
                return None
            if j + v[1]>=len(a[0]):
                return None
            if a[i+v[0]][j+v[1]] != 1:
                is_ok = False
        if is_ok:

            return (i+1,j+1)
        return None
    m,n = [int(v) for v in input().split()]
    a = []
    b = []
    for i in range(0, m):
        row = input().split()
        a.append([int(v) for v in row])
        b.append([0 for _ in row])
    res = []
    for i in range(0,m):
        for j in range(0,n):
            val = calc(a, i, j)
            if a[i][j]==1 and val:
                res.append(val)
                for v in cords:
                    b[i + v[0]][j + v[1]]=1
                    b[i][j]=1
    if a==b:
        print(len(res))
        for k in res:
            print(k[0], k[1])
    else:
        print(-1)