Arrangement

AtCoder

IDdwacon6th_prelims_d

Time2525ms

Memory256MB

Difficulty—

Niwango has $N$ cards, numbered $1,2,\ldots,N$. He will now arrange these cards in a row. Niwango wants to know if there is a way to arrange the cards while satisfying all the $N$ conditions below. To help him, determine whether such a way exists. If the answer is yes, also find the lexicographically smallest such arrangement. * To the immediate right of Card $1$ (if any) is NOT Card $a_1$. * To the immediate right of Card $2$ (if any) is NOT Card $a_2$. * $\vdots$ * To the immediate right of Card $N$ (if any) is NOT Card $a_N$. ## Constraints * $2 \leq N \leq 10^{5}$ * $1 \leq a_i \leq N$ * $a_i \neq i$ ## Input Input is given from Standard Input in the following format: $N$ $a_1$ $a_2$ $\ldots$ $a_N$ [samples]

Samples

Input #1

4
2 3 4 1

Output #1

1 3 2 4

*   The arrangement $(1,2,3,4)$ is lexicographically smaller than $(1,3,2,4)$, but is invalid, since it violates the condition "to the immediate right of Card $1$ is not Card $2$."

Input #2

2
2 1

Output #2

\-1

*   If no arrangements satisfy the conditions, print `-1`.

Input #3

13
2 3 4 5 6 7 8 9 10 11 12 13 12

Output #3

1 3 2 4 6 5 7 9 8 10 12 11 13

API Response (JSON)

{
  "problem": {
    "name": "Arrangement",
    "description": {
      "content": "Niwango has $N$ cards, numbered $1,2,\\ldots,N$. He will now arrange these cards in a row. Niwango wants to know if there is a way to arrange the cards while satisfying all the $N$ conditions below. To",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2525,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "dwacon6th_prelims_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Niwango has $N$ cards, numbered $1,2,\\ldots,N$. He will now arrange these cards in a row.\nNiwango wants to know if there is a way to arrange the cards while satisfying all the $N$ conditions below. To...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments