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} 
n = input().split()
i = 0
ans = []
while int(n[0]) > i:
    str = input()
    if i == 0: x = [None]*int(n[0]); y = [None]*int(n[0])
    x[i] = str.split()
    y[i] = ['0']*int(n[1])
    i+=1
i=0
end = 1
while int(n[0]) > i:
    for j, item in enumerate(x[i]):
       if item == '0':
           continue
       if j+1<len(x[i]) and i+1<int(n[0]):
           if x[i+1][j+1]=='1' and x[i][j+1]=='1' and x[i+1][j]=='1':
               y[i+1][j+1] = y[i][j+1] = y[i+1][j] = y[i][j] = '1'
               ans.append([i,j])
    i+=1
i=0
while int(n[0]) > i:
    for j, item in enumerate(x[i]):
        if item != y[i][j]:
            print("-1")
            end = 0
            break
    if not end: break
    i+=1
i=0
if end:
    if not ans:
        print(0)
    else:
        print(len(ans))
        for item in ans:
            print("{one} {two}".format(one=int(item[0])+1,two=int(item[1])+1))