Three Permutations

AtCoder

IDabc214_g

Time2000ms

Memory256MB

Difficulty—

Given are permutations of $(1, \dots, N)$: $p = (p_1, \dots, p_N)$ and $q = (q_1, \dots, q_N)$. Find the number, modulo $(10^9 + 7)$, of permutations $r = (r_1, \dots, r_N)$ of $(1, \dots, N)$ such that $r_i \neq p_i$ and $r_i \neq q_i$ for every $i$ $(1 \leq i \leq N)$. ## Constraints * $1 \leq N \leq 3000$ * $1 \leq p_i, q_i \leq N$ * $p_i \neq p_j \, (i \neq j)$ * $q_i \neq q_j \, (i \neq j)$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $p_1$ $\ldots$ $p_N$ $q_1$ $\ldots$ $q_N$ [samples]

Samples

Input #1

4
1 2 3 4
2 1 4 3

Output #1

4

There are four valid permutations: $(3, 4, 1, 2)$, $(3, 4, 2, 1)$, $(4, 3, 1, 2)$, and $(4, 3, 2, 1)$.

Input #2

3
1 2 3
2 1 3

Output #2

0

The answer may be $0$.

Input #3

20
2 3 15 19 10 7 5 6 14 13 20 4 18 9 17 8 12 11 16 1
8 12 4 13 19 3 10 16 11 9 1 2 17 6 5 18 7 14 20 15

Output #3

803776944

Be sure to print the count modulo $(10^9 + 7)$.

API Response (JSON)

{
  "problem": {
    "name": "Three Permutations",
    "description": {
      "content": "Given are permutations of $(1, \\dots, N)$: $p = (p_1, \\dots, p_N)$ and $q = (q_1, \\dots, q_N)$. Find the number, modulo $(10^9 + 7)$, of permutations $r = (r_1, \\dots, r_N)$ of $(1, \\dots, N)$ such th",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc214_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given are permutations of $(1, \\dots, N)$: $p = (p_1, \\dots, p_N)$ and $q = (q_1, \\dots, q_N)$.\nFind the number, modulo $(10^9 + 7)$, of permutations $r = (r_1, \\dots, r_N)$ of $(1, \\dots, N)$ such th...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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