Problem Statement

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.

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 $10^6$.

Input

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

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.