B. Square Fillingtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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 \times 2, and replace every element in the chosen submatrix with 1. In other words, you choose two integers x and y such that 1 \le x < n and 1 \le 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.InputThe first line contains two integers n and m (2 \le n, m \le 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.OutputIf 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 \le k \le 2500 should hold.ExamplesInput
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
NoteThe sequence of operations in the first example: \begin{matrix} 0 & 0 & 0 & & 1 & 1 & 0 & & 1 & 1 & 1 & & 1 & 1 & 1 \\ 0 & 0 & 0 & \rightarrow & 1 & 1 & 0 & \rightarrow & 1 & 1 & 1 & \rightarrow & 1 & 1 & 1 \\ 0 & 0 & 0 & & 0 & 0 & 0 & & 0 & 0 & 0 & & 0 & 1 & 1 \end{matrix} 
3 3
1 1 1
1 1 1
0 1 1

3 1 1 1 2 2 2 
['constructive algorithms', 'greedy', 'implementation', '*1200']