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} 
temp = input().split()
n = int(temp[0])
m = int(temp [1])
A = []

for i in range (n):
    A.append (input().split())

out = []
t = 0
# FLAG = 0

for i in range (n):
    for j in range (m):

        if A[i][j] == '1':

            #FLAG = 1

            F1 = 1
            if i == n - 1 or j == m - 1:
                pass
            else:
                if A[i][j] == '1' and A[i + 1][j + 1] == '1' and A[i + 1][j] == '1' and A[i][j + 1] == '1':
                    out.append(str(i+1) + ' ' + str(j+1))
                    t += 1
                    F1 = 0

            F2 = 1
            if i == 0 or j == m-1:
                pass
            else:
                if A[i - 1][j] == '1' and A[i - 1][j + 1] == '1' and A[i][j] == '1' and A[i][j + 1] == '1':
                    F2 = 0

            F3 = 1
            if j == 0 or i == n-1:
                pass
            else:
                if A[i+1][j-1] == '1' and A[i + 1][j] == '1' and A[i][j-1] == '1' and A[i][j] == '1':
                    F3 = 0

            F4 = 1
            if j == 0 or i == 0:
                pass
            else:
                if A[i][j-1] == '1' and A[i][j] == '1' and A[i-1][j-1] == '1' and A[i-1][j] == '1':
                    F4 = 0

            FLAG = min (F1, F2, F3, F4)
            if FLAG:
                print ('-1')
                exit()

# if FLAG:
#     print ('-1')
# else:

print (t)
for el in out:
    print (el)

