Directed Tree

AtCoder

IDarc121_e

Time2000ms

Memory256MB

Difficulty—

Given is a directed tree with $N$ vertices numbered $1$ through $N$. Vertex $1$ is the root of the tree. For each integer $i$ such that $2 \leq i \leq N$, there is a directed edge from Vertex $p_i$ to $i$. Let $a$ be the permutation of $(1, \ldots, N)$, and $a_i$ be the $i$\-th element of $a$. Among the $N!$ sequences that can be $a$, find the number of sequences that satisfy the following condition, modulo $998244353$. * Condition: For every integer $i$ such that $1 \leq i \leq N$, Vertex $i$ is unreachable from Vertex $a_i$ by traversing **one or more** edges. ## Constraints * All values in input are integers. * $1 \leq N \leq 2000$ * $1 \leq p_i < i$ ## Input Input is given from Standard Input in the following format: $N$ $p_{2}$ $\cdots$ $p_N$ [samples]

Samples

Input #1

4
1 1 3

Output #1

Input #2

30
1 1 3 1 5 1 1 1 8 9 7 3 11 11 15 14 4 10 11 12 1 10 13 11 7 23 8 12 18

Output #2

746746186

*   Remember to print the count modulo $998244353$.

API Response (JSON)

{
  "problem": {
    "name": "Directed Tree",
    "description": {
      "content": "Given is a directed tree with $N$ vertices numbered $1$ through $N$. Vertex $1$ is the root of the tree. For each integer $i$ such that $2 \\leq i \\leq N$, there is a directed edge from Vertex $p_i$ to",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc121_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given is a directed tree with $N$ vertices numbered $1$ through $N$.\nVertex $1$ is the root of the tree. For each integer $i$ such that $2 \\leq i \\leq N$, there is a directed edge from Vertex $p_i$ to...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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