CF1207B.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 $2 \times 2$, and replace every element in the chosen submatrix with $1$. In other words, you choose two integers $x$ and $y$ such that $1 \le x \lt n$ and $1 \le y \lt m$, 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.

给你两个矩阵 $A$ 和 $B$。每个矩阵恰好包含 $n$ 行和 $m$ 列。矩阵 $A$ 的每个元素为 $0$ 或 $1$；矩阵 $B$ 的每个元素初始均为 $0$。

你可以对矩阵 $B$ 执行若干次操作。每次操作中，你选择 $B$ 的任意一个大小为 $2 \times 2$ 的子矩阵，并将该子矩阵中的每个元素都置为 $1$。换言之，你选择两个整数 $x$ 和 $y$，满足 $1 \le x \lt n$ 且 $1 \le y \lt m$，然后将 $B_{x, y}$、$B_{x, y + 1}$、$B_{x + 1, y}$ 和 $B_{x + 1, y + 1}$ 均设为 $1$。

你的目标是使矩阵 $B$ 等于矩阵 $A$。当且仅当矩阵 $A$ 的每个元素均等于矩阵 $B$ 中对应位置的元素时，称两个矩阵 $A$ 和 $B$ 相等。

能否使这两个矩阵相等？若可以，请给出一个操作序列，使得 $B$ 变为 $A$。注意：你无需最小化操作次数。

The 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 $1$.

第一行包含两个整数 $n$ 和 $m$（$2 \le n, m \le 50$）。

接下来是 $n$ 行，每行包含 $m$ 个整数。第 $i$ 行中的第 $j$ 个整数为 $A_{i, j}$。每个整数均为 $0$ 或 $1$。

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 $0 \le k \le 2500$ should hold.

如果无法使 $B$ 等于 $A$，则输出一个整数 $-1$。

否则，请输出任意一个将 $B$ 变换为 $A$ 的操作序列，格式如下：第一行输出一个整数 $k$ —— 操作的次数；随后 $k$ 行，每行包含两个整数 $x$ 和 $y$，表示对应的操作（即将 $B_{x, y}$、$B_{x, y + 1}$、$B_{x + 1, y}$ 和 $B_{x + 1, y + 1}$ 均设为 $1$）。需满足条件 $0 \le k \le 2500$。

The sequence of operations in the first example:

$\begin{matrix} 0 & 0 & 0 & & 1 & 1 & 0 & & 1 & 1 & 1 & & 1 & 1 & 1 \\ 0 & 0 & 0 & \rightarrow & 1 & 1 & 0 & \rightarrow & 1 & 1 & 1 & \rightarrow & 1 & 1 & 1 \\ 0 & 0 & 0 & & 0 & 0 & 0 & & 0 & 0 & 0 & & 0 & 1 & 1 \end{matrix}$

第一个示例中的操作序列：

$\begin{matrix} 0 & 0 & 0 & & 1 & 1 & 0 & & 1 & 1 & 1 & & 1 & 1 & 1 \\ 0 & 0 & 0 & \rightarrow & 1 & 1 & 0 & \rightarrow & 1 & 1 & 1 & \rightarrow & 1 & 1 & 1 \\ 0 & 0 & 0 & & 0 & 0 & 0 & & 0 & 0 & 0 & & 0 & 1 & 1 \end{matrix}$