Inverse of Rows and Columns

给你一个$n \times m$的$01$矩阵，你可以对整行或整列进行取反操作。问是否有一个操作方案，使得最后得到的矩阵，按照$a_{1,1},a_{1,2},\cdots a_{1,m},\cdots a_{2,1},\cdots,a_{n,m}$形成一个有序的排列。 输出格式： 如果没有，仅输出一行$NO$。 如果有，第一行输出$YES$；第二行输出长度为$n$的$01$字符串，第$i$个字符为$1$代表对第$i$行进行取反操作；第二行输出长度为$m$的$01$字符串，第$i$个字符为$1$代表对第$i$列进行取反操作。如有多种方案，输出任一方案即可。

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.

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) $ .

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.

2 2
1 1
0 1

YES
00
10

3 4
0 0 0 1
0 0 0 0
1 1 1 1

YES
010
0000

3 3
0 0 0
1 0 1
1 1 0

NO