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,m=[int(k) for k in input().split(" ")]
a=[]
for i in range(n):
    a+=[[int(k) for k in input().split(" ")]]

done=[[0 for j in range(m)] for i in range(n)]

res=[]

def isgood(i,j):
    global done
    global res
    for ot in ((i-1,j-1),(i+1,j+1),(i-1,j+1),(i+1,j-1)):
        ii,jj=ot
        if min(ii,jj)>=0 and ii<n and jj<m and a[ii][jj]:
            if a[i][j] and a[ii][j] and a[i][jj]:
                done[i][j]=1
                done[ii][jj]=1
                done[i][jj]=1
                done[ii][j]=1
                res+=[(min(i,ii),min(j,jj))]
                return True
    return False

isok=True
for i in range(n):
    for j in range(m):
        if a[i][j] and not done[i][j]:
            if not isgood(i,j):
                isok=False
                break
    if not isok:
        break

if isok:
    print(len(res))
    for j in res:
        print(j[0]+1,j[1]+1)
else:
    print(-1)