AT_arc208_d [ARC208D] Symmetric Matrix

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.

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 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.

### Sample Explanation 1 Consider the first test case. It can be verified that the $ A $ in the sample output satisfies all conditions. Other than this, for example, the following $ A $ will also be accepted: ``` 1 3 2 3 2 1 2 1 3 ``` ### 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.