We define an $n \times n$ matrix $A$ as a Latin square if and only if every row and every column is a permutation of $1 \sim n$.

You are given an $R \times C$ submatrix at the top-left corner of a matrix $A$, i.e., $A_{i,j}$ ($1 \le i \le R, 1 \le j \le C$). Determine whether it is possible to fill in the remaining positions such that the matrix becomes a Latin square.

Input

The input is read from the file latin.in.

There are multiple test cases. The first line contains an integer $T$, representing the number of test cases.

For each test case, the first line contains three integers $n, R, C$, representing the matrix size and the size of the known submatrix.

The next $R$ lines each contain $C$ integers, where the $j$-th number in the $i$-th line represents $A_{i,j}$.

Output

The output is written to the file latin.out.

For each test case, output "Yes" or "No" on the first line, indicating whether a valid Latin square can be found.

If a valid Latin square can be found, output $n$ lines, each containing $n$ numbers, representing a valid Latin square. If there are multiple valid solutions, any one of them is acceptable.

Examples

Input 1

3
2 1 1
1
3 2 2
1 2
2 1
5 2 3
1 2 3
4 3 2

Output 1

Yes
1 2
2 1
No
Yes
1 2 3 4 5
4 3 2 5 1
2 4 5 1 3
3 5 1 2 4
5 1 4 3 2

Note

In the first example, for the second test case, it can be observed from the first two rows that $A_{1,3} = A_{2,3} = 3$, so no valid Latin square exists.

For the third test case, the output is a valid Latin square, and its top-left corner matches the input matrix. Another valid solution is:

$$ \begin{bmatrix} 1 & 2 & 3 & 5 & 4 \\ 4 & 3 & 2 & 1 & 5 \\ 3 & 5 & 1 & 4 & 2 \\ 2 & 4 & 5 & 3 & 1 \\ 5 & 1 & 4 & 2 & 3 \end{bmatrix} $$

Examples

Input 2

See the provided files latin/latin2.in and latin/latin2.ans. This example satisfies the constraints for test cases $6 \sim 7$.

Input 3

See the provided files latin/latin3.in and latin/latin3.ans. This example satisfies the constraints for test cases $11 \sim 12$.

Constraints

For all data, it is guaranteed that $1 \le T \le 10$, $1 \le n \le 500$, $1 \le R, C \le n$, and $1 \le A_{i,j} \le n$. It is also guaranteed that the input submatrix does not contain two identical numbers in any row or column.

The details are as follows:

Special Property A: Guaranteed $R = 1$. Special Property B: Guaranteed $C = n$. Special Property C: Guaranteed $R, C \le \frac{n}{2}$.