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 sys
n, m = [int(i) for i in input().split()]
data = []
for _ in range(n):
    data.append([int(i) for i in input().split()])


ans = []

for h in range(n-1):   
    for i in range(m-1):
        
        if data[h][i] >= 1:
            if data[h][i+1] * data[h+1][i] * data[h+1][i+1] == 0:
                if data[h][i] == 1:
                    print(-1)
                    sys.exit()
            else:
                ans.append(str(h+1) + ' ' + str(i+1))
                for q in range(4):
                    data[h+(q%2)][i + q//2] = 2

for i in range(n-1):
    if data[i][-1] >= 1:
        if data[i][-2] * data[i+1][-1] * data[i+1][-2] == 0:
            if data[i][-1] == 1:
                print(-1)
                sys.exit()
        else:
            ans.append(str(i+1) + ' ' + str(m-1))
            for q in range(4):
                data[i + q//2][-1 - q%2] = 2

for i in range(m-1):
    if data[-1][i] >= 1:
        if data[-2][i] * data[-1][i+1] * data[-2][i+1] == 0:
            if data[-1][i] == 1:
                print(-1)
                sys.exit()
        else:
            ans.append(str(n-1) + ' ' + str(i+1))
            for q in range(4):
                data[-1 - q//2][i + q%2] = 2

if data[-1][-1] == 1:
    if data[-1][-2] * data[-2][-1] * data[-2][-2] == 0:
        print(-1)
        sys.exit()
    else:
        ans.append(str(n-1) + ' ' + str(m-1))


print(len(ans))
print('\n'.join(ans))


