K-th K

AtCoder

IDagc008_d

Time2000ms

Memory256MB

Difficulty—

You are given an integer sequence $x$ of length $N$. Determine if there exists an integer sequence $a$ that satisfies all of the following conditions, and if it exists, construct an instance of $a$. * $a$ is $N^2$ in length, containing $N$ copies of each of the integers $1$, $2$, $...$, $N$. * For each $1 ≤ i ≤ N$, the $i$\-th occurrence of the integer $i$ from the left in $a$ is the $x_i$\-th element of $a$ from the left. ## Constraints * $1 ≤ N ≤ 500$ * $1 ≤ x_i ≤ N^2$ * All $x_i$ are distinct. ## Input The input is given from Standard Input in the following format: $N$ $x_1$ $x_2$ $...$ $x_N$ [samples]

Samples

Input #1

3
1 5 9

Output #1

Yes
1 1 1 2 2 2 3 3 3

For example, the second occurrence of the integer $2$ from the left in $a$ in the output is the fifth element of $a$ from the left. Similarly, the condition is satisfied for the integers $1$ and $3$.

Input #2

2
4 1

Output #2

No

API Response (JSON)

{
  "problem": {
    "name": "K-th K",
    "description": {
      "content": "You are given an integer sequence $x$ of length $N$. Determine if there exists an integer sequence $a$ that satisfies all of the following conditions, and if it exists, construct an instance of $a$. ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc008_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given an integer sequence $x$ of length $N$. Determine if there exists an integer sequence $a$ that satisfies all of the following conditions, and if it exists, construct an instance of $a$.\n\n...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments