AT_arc199_a [ARC199A] Flip Row or Col 2

You are given an $ N\times N $ matrix $ A=(A_{i,j})\ (1\leq i,j\leq N) $ and integer sequences of length $ N $ : $ R=(R_1,R_2,\ldots,R_N), C=(C_1,C_2,\ldots,C_N) $ . Each element of $ A $ is $ 0 $ or $ 1 $ , and each element of $ R,C $ is at least $ 0 $ and less than $ \frac{N}{4} $ . You can freely choose a pair of strings $ X,Y $ of length $ N $ consisting of `0` and `1`. Based on the chosen strings $ X,Y $ , perform the following operations: - First, for each $ i=1,2,\ldots,N $ , do the following. Let $ X_i $ be the $ i $ -th character of $ X $ : - If $ X_i $ is `0`, do nothing. - If $ X_i $ is `1`, flip all elements in the $ i $ -th row of $ A $ . That is, for each $ j=1,2,\ldots,N $ , replace $ A_{i,j} $ with $ 1-A_{i,j} $ . - Next, for each $ j=1,2,\ldots,N $ , do the following. Let $ Y_j $ be the $ j $ -th character of $ Y $ : - If $ Y_j $ is `0`, do nothing. - If $ Y_j $ is `1`, flip all elements in the $ j $ -th column of $ A $ . That is, for each $ i=1,2,\ldots,N $ , replace $ A_{i,j} $ with $ 1-A_{i,j} $ . Determine whether it is possible to choose $ X,Y $ cleverly so that the matrix $ A $ after the operations satisfies the following conditions, and if possible, output one such pair. - For each $ i=1,2,\ldots,N $ , the sum of elements in the $ i $ -th row of $ A $ , $ \displaystyle \sum_{j=1}^N A_{i,j} $ , is $ R_i $ . - For each $ j=1,2,\ldots,N $ , the sum of elements in the $ j $ -th column of $ A $ , $ \displaystyle \sum_{i=1}^N A_{i,j} $ , is $ C_j $ . You are given $ T $ test cases, so answer each of them.

The input is given from Standard Input in the following format: > $ T $ $ \textrm{case}_1 $ $ \textrm{case}_2 $ $ \vdots $ $ \textrm{case}_T $ Each test case is given in the following format: > $ N $ $ A_{1,1}A_{1,2}\dots A_{1,N} $ $ A_{2,1}A_{2,2}\dots A_{2,N} $ $ \vdots $ $ A_{N,1}A_{N,2}\dots A_{N,N} $ $ R_1 $ $ R_2 $ $ \ldots $ $ R_N $ $ C_1 $ $ C_2 $ $ \ldots $ $ C_N $

Output your solutions for $ \textrm{case}_1,\textrm{case}_2,\ldots,\textrm{case}_T $ in order in the following format: If there is no pair $ X,Y $ that satisfies the conditions, output `No`. If there exists such a pair, output: > Yes $ X $ $ Y $ If there are multiple solutions, any of them will be considered correct.

### Sample Explanation 1 For the first test case, $ A=\begin{pmatrix}1&0 \\ 0&1\end{pmatrix} $ . Consider the case where $ X,Y $ are `01` and `10`, respectively. The operations are performed as follows: - $ X_1 $ is `0`, so do nothing. - $ X_2 $ is `1`, so flip the elements in the $ 2 $ nd row of $ A $ , resulting in $ A=\begin{pmatrix}1&0 \\ 1&0\end{pmatrix} $ . - $ Y_1 $ is `1`, so flip the elements in the $ 1 $ st column of $ A $ , resulting in $ A=\begin{pmatrix}0&0 \\ 0&0\end{pmatrix} $ . - $ Y_2 $ is `0`, so do nothing. Therefore, the matrix $ A $ after the operations is $ A=\begin{pmatrix}0&0 \\ 0&0\end{pmatrix} $ . The sum of elements in the $ 1 $ st row, the sum of elements in the $ 2 $ nd row, the sum of elements in the $ 1 $ st column, and the sum of elements in the $ 2 $ nd column are all $ 0 $ , so the conditions are satisfied. It would also be correct to output: ``` Yes 10 01 ``` ### Constraints - $ 1\leq T\leq 10^5 $ - $ 1\leq N\leq 1000 $ - $ A_{i,j} \in\lbrace 0,1\rbrace $ - $ 0\leq R_i,C_j\lt \frac{N}{4} $ - $ T,N,R_i,C_j $ are integers. - The sum of $ N^2 $ over all test cases in one input file is at most $ 10^6 $ .