Namori Grundy

AtCoder

IDarc079_d

Time2000ms

Memory256MB

Difficulty—

There is a directed graph with $N$ vertices and $N$ edges. The vertices are numbered $1, 2, ..., N$. The graph has the following $N$ edges: $(p_1, 1), (p_2, 2), ..., (p_N, N)$, and the graph is weakly connected. Here, an edge from Vertex $u$ to Vertex $v$ is denoted by $(u, v)$, and a weakly connected graph is a graph which would be connected if each edge was bidirectional. We would like to assign a value to each of the vertices in this graph so that the following conditions are satisfied. Here, $a_i$ is the value assigned to Vertex $i$. * Each $a_i$ is a non-negative integer. * For each edge $(i, j)$, $a_i \neq a_j$ holds. * For each $i$ and each integer $x(0 ≤ x < a_i)$, there exists a vertex $j$ such that the edge $(i, j)$ exists and $x = a_j$ holds. Determine whether there exists such an assignment. ## Constraints * $2 ≤ N ≤ 200$ $000$ * $1 ≤ p_i ≤ N$ * $p_i \neq i$ * The graph is weakly connected. ## Input Input is given from Standard Input in the following format: $N$ $p_1$ $p_2$ ... $p_N$ [samples]

Samples

Input #1

4
2 3 4 1

Output #1

POSSIBLE

The assignment is possible: {$a_i$} = {$0, 1, 0, 1$} or {$a_i$} $=$ {$1, 0, 1, 0$}.

Input #2

3
2 3 1

Output #2

IMPOSSIBLE

Input #3

4
2 3 1 1

Output #3

POSSIBLE

The assignment is possible: {$a_i$} $=$ {$2, 0, 1, 0$}.

Input #4

6
4 5 6 5 6 4

Output #4

IMPOSSIBLE

API Response (JSON)

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  "problem": {
    "name": "Namori Grundy",
    "description": {
      "content": "There is a directed graph with $N$ vertices and $N$ edges. The vertices are numbered $1, 2, ..., N$. The graph has the following $N$ edges: $(p_1, 1), (p_2, 2), ..., (p_N, N)$, and the graph is weakly",
      "description_type": "Markdown"
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    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
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    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc079_d"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a directed graph with $N$ vertices and $N$ edges. The vertices are numbered $1, 2, ..., N$.\nThe graph has the following $N$ edges: $(p_1, 1), (p_2, 2), ..., (p_N, N)$, and the graph is weakly...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments