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} 
A1 = [[1, 1, 1],
      [1, 1, 1],
      [0, 1, 1]]

A2 = [[1, 0, 1],
      [1, 0, 1],
      [0, 0, 0]]

A3 = [[0, 0],
      [0, 0],
      [0, 0]]


def get_steps(a):
    n = len(a)
    m = len(a[0])

    steps = []

    for i in range(n):
        for j in range(m):
            if a[i][j] == 1:
                bottom_right = get_bottom_right(a, i, j)
                if bottom_right:
                    steps.append((i, j))
                elif not get_bottom_left(a, i, j) | get_top_right(a, i, j) | get_top_left(a, i, j):
                    return -1

    return steps


def get_top_left(a, i, j):
    if i - 1 < 0 or j - 1 < 0:
        return False
    return a[i][j - 1] & a[i - 1][j - 1] & a[i - 1][j]


def get_top_right(a, i, j):
    if i - 1 < 0 or j + 1 >= len(a[0]):
        return False
    return a[i][j + 1] & a[i - 1][j + 1] & a[i - 1][j]


def get_bottom_left(a, i, j):
    if j - 1 < 0 or i + 1 >= len(a):
        return False
    return a[i][j - 1] & a[i + 1][j - 1] & a[i + 1][j]


def get_bottom_right(a, i, j):
    if i + 1 >= len(a) or j + 1 >= len(a[0]):
        return False
    return a[i][j + 1] & a[i + 1][j + 1] & a[i + 1][j]


if __name__ == '__main__':
    n, m = map(int, input().split())

    A = []

    for i in range(n):
        A.append(list(map(int, input().split())))

    x = get_steps(A)
    if x == -1:
        print(x)
    else:
        print(len(x))
        for i, j in x:
            print(i + 1, j + 1)
