CF1157G.Inverse of Rows and Columns

You are given a binary matrix $a$ of size $n \times m$. A binary matrix is a matrix where each element is either $0$ or $1$.

You may perform some (possibly zero) operations with this matrix. During each operation you can inverse the row of this matrix or a column of this matrix. Formally, inverting a row is changing all values in this row to the opposite ($0$ to $1$, $1$ to $0$). Inverting a column is changing all values in this column to the opposite.

Your task is to sort the initial matrix by some sequence of such operations. The matrix is considered sorted if the array $[a_{1, 1}, a_{1, 2}, \dots, a_{1, m}, a_{2, 1}, a_{2, 2}, \dots, a_{2, m}, \dots, a_{n, m - 1}, a_{n, m}]$ is sorted in non-descending order.

给你一个大小为 $n \times m$ 的二进制矩阵 $a$。二进制矩阵是指其中每个元素均为 $0$ 或 $1$ 的矩阵。

你可以对该矩阵执行若干次（可能为零次）操作。每次操作可选择翻转该矩阵的一行或一列。形式上，翻转一行是指将该行中所有元素取反（即 $0$ 变为 $1$，$1$ 变为 $0$）；翻转一列是指将该列中所有元素取反。

你的任务是通过若干次上述操作，将初始矩阵变为“已排序”状态。当数组

$$[a_{1, 1}, a_{1, 2}, \dots, a_{1, m}, a_{2, 1}, a_{2, 2}, \dots, a_{2, m}, \dots, a_{n, m - 1}, a_{n, m}]$$

按非降序排列时，称该矩阵为已排序。

The first line of the input contains two integers $n$ and $m$ ($1 \le n, m \le 200$) — the number of rows and the number of columns in the matrix.

The next $n$ lines contain $m$ integers each. The $j$-th element in the $i$-th line is $a_{i, j}$ ($0 \le a_{i, j} \le 1$) — the element of $a$ at position $(i, j)$.

输入的第一行包含两个整数 $n$ 和 $m$（$1 \le n, m \le 200$）—— 分别表示矩阵的行数和列数。

接下来的 $n$ 行，每行包含 $m$ 个整数。第 $i$ 行的第 $j$ 个元素为 $a_{i, j}$（$0 \le a_{i, j} \le 1$）—— 即矩阵 $a$ 在位置 $(i, j)$ 处的元素。

If it is impossible to obtain a sorted matrix, print "NO" in the first line.

Otherwise print "YES" in the first line. In the second line print a string $r$ of length $n$. The $i$-th character $r_i$ of this string should be '1' if the $i$-th row of the matrix is inverted and '0' otherwise. In the third line print a string $c$ of length $m$. The $j$-th character $c_j$ of this string should be '1' if the $j$-th column of the matrix is inverted and '0' otherwise. If there are multiple answers, you can print any.

如果无法得到一个有序矩阵，则在第一行输出 "NO"。

否则，在第一行输出 "YES"；在第二行输出一个长度为 $n$ 的字符串 $r$，其中第 $i$ 个字符 $r_i$ 为 '1' 表示矩阵的第 $i$ 行被翻转，为 '0' 表示未翻转；在第三行输出一个长度为 $m$ 的字符串 $c$，其中第 $j$ 个字符 $c_j$ 为 '1' 表示矩阵的第 $j$ 列被翻转，为 '0' 表示未翻转。若存在多个可行解，输出任意一个即可。