Problem Statement

You are given an integer sequence $Y=(Y_1,Y_2,\ldots,Y_N)$ of length $N$ where each element is between $1$ and $N$ inclusive.

Determine whether there exists an $N \times N$ integer matrix $A=(A_{i,j})$ $(1\le i , j \le N)$ that satisfies all of the following conditions, and if it exists, find one such matrix.

• $1\le A_{i,j} \le N$ $(1\le i \le N, 1\le j\le N)$
• $A_{i,j}=A_{j,i}$ $(1\le i\le N, 1\le j\le N)$
• $A_{i,j_1}\neq A_{i,j_2}$ $(1\le i\le N, 1\le j_1 < j_2 \le N)$
• $A_{i,Y_i}=1$ $(1\le i\le N)$

You are given $T$ test cases; solve each of them.

Constraints

• $1\le T\le 5000$
• $1\le N \le 500$
• The sum of $N^2$ over all test cases is at most $500^2$.
• $1\le Y_i\le N$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

T
\text{case}_1
\text{case}_2
\vdots
\text{case}_T

Each test case is given in the following format:

N
Y_1 Y_2 \ldots Y_N

Output

Output the answers for each test case in order, separated by newlines.

For each test case, if there does not exist an $A$ that satisfies all conditions, print No.

Otherwise, print $A$ that satisfies all conditions in the following format:

Yes
A_{1,1} A_{1,2} \ldots A_{1,N}
A_{2,1} A_{2,2} \ldots A_{2,N}
\vdots
A_{N,1} A_{N,2} \ldots A_{N,N}

If there are multiple $A$ that satisfy all conditions, any of them will be accepted.