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 = map(int, input().strip().split())
a = [[0 for i in range(m + 1)] for j in range(n + 1)]
for i in range(1, n + 1):
  a[i] = [0] + input().strip().split()
  a[i] = [int(x) for x in a[i]]


d = [[-1, -1], [-1, 1], [1, 1], [1, -1]]


def ok(x, y):
  return x >= 1 and x <= n and y >= 1 and y <= m


def f(x, y):
  for i, j in d:
    if ok(x + i, y + j) and ok(x + i, y) and ok(x, y + j):
      if a[x + i][y + j] == 1 and a[x + i][y] == 1 and a[x][y + j] == 1:
        return True
  return False


flag = True
ans = 0
b = [[] for i in range(n * m)]

for i in range(1, n + 1):
  for j in range(1, m + 1):
    if a[i][j] == 1:
      if f(i, j) == False:
        flag = False
        break
  if flag == False:
    break

if flag == False:
  print(-1)
  sys.exit(0)

for i in range(1, n):
  for j in range(1, m):
    if a[i][j] == 1:
      if ok(i + 1, j + 1) and a[i + 1][j + 1] == 1 and a[i][j + 1] == 1 and a[i + 1][j] == 1:
        ans += 1
        b[ans].append(i)
        b[ans].append(j)

print(ans)
for i in range(1, ans + 1):
  print(b[i][0], b[i][1])
