1207_B. Square Filling
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} 
```python
#!/usr/bin/python3
import pdb

n, m = map(int, input().split(" "))
matrix = []
for i in range(n):
	matrix.append(list(map(int, input().split(" "))))

def check_pos(matrix, x, y):
	if x + 1 >= len(matrix):
		return False
	if y + 1 >= len(matrix[0]):
		return False
	if matrix[x][y] == 0 or matrix[x+1][y] == 0 or matrix[x][y+1] == 0 or matrix[x+1][y+1] == 0:
		return False
	matrix[x][y] = 2;
	matrix[x+1][y+1] = 2
	matrix[x+1][y] = 2
	matrix[x][y+1] = 2
	return True

one_exists = False
result = []
for i in range(n):
	for j in range(m):
		if matrix[i][j] == 1:
			one_exists = True
		if check_pos(matrix, i, j):
			result.append((i+1, j+1))

if not one_exists:
	print("0")
	exit()

for i in range(n):
	for j in range(m):
		if matrix[i][j] == 1:
			print("-1")
			exit()
print(len(result))
for x, y in result:
	print("%d %d" % (x, y))
	

```