Symmetric Matrix

AtCoder

IDarc208_d

Time2000ms

Memory256MB

Difficulty—

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: $N$ $Y_1$ $Y_2$ $\ldots$ $Y_N$ [samples]

Samples

Input #1

Output #1

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

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

API Response (JSON)

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  "problem": {
    "name": "Symmetric Matrix",
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      "content": "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})",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
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    "sign": "arc208_d"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "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.\nDetermine whether there exists an $N \\times N$ integer matrix $A=(A_{i,j})...",
      "is_translate": false,
      "language": "English"
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