Permutation and Minimum

AtCoder

IDagc030_f

Time3000ms

Memory256MB

Difficulty—

There is a sequence of length $2N$: $A_1, A_2, ..., A_{2N}$. Each $A_i$ is either $-1$ or an integer between $1$ and $2N$ (inclusive). Any integer other than $-1$ appears at most once in ${A_i}$. For each $i$ such that $A_i = -1$, Snuke replaces $A_i$ with an integer between $1$ and $2N$ (inclusive), so that ${A_i}$ will be a permutation of $1, 2, ..., 2N$. Then, he finds a sequence of length $N$, $B_1, B_2, ..., B_N$, as $B_i = min(A_{2i-1}, A_{2i})$. Find the number of different sequences that $B_1, B_2, ..., B_N$ can be, modulo $10^9 + 7$. ## Constraints * $1 \leq N \leq 300$ * $A_i = -1$ or $1 \leq A_i \leq 2N$. * If $A_i \neq -1, A_j \neq -1$, then $A_i \neq A_j$. ($i \neq j$) ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $...$ $A_{2N}$ [samples]

Samples

Input #1

3
1 -1 -1 3 6 -1

Output #1

5

There are six ways to make ${A_i}$ a permutation of $1, 2, ..., 2N$; for each of them, ${B_i}$ would be as follows:

*   $(A_1, A_2, A_3, A_4, A_5, A_6) = (1, 2, 4, 3, 6, 5)$: $(B_1, B_2, B_3) = (1, 3, 5)$
*   $(A_1, A_2, A_3, A_4, A_5, A_6) = (1, 2, 5, 3, 6, 4)$: $(B_1, B_2, B_3) = (1, 3, 4)$
*   $(A_1, A_2, A_3, A_4, A_5, A_6) = (1, 4, 2, 3, 6, 5)$: $(B_1, B_2, B_3) = (1, 2, 5)$
*   $(A_1, A_2, A_3, A_4, A_5, A_6) = (1, 4, 5, 3, 6, 2)$: $(B_1, B_2, B_3) = (1, 3, 2)$
*   $(A_1, A_2, A_3, A_4, A_5, A_6) = (1, 5, 2, 3, 6, 4)$: $(B_1, B_2, B_3) = (1, 2, 4)$
*   $(A_1, A_2, A_3, A_4, A_5, A_6) = (1, 5, 4, 3, 6, 2)$: $(B_1, B_2, B_3) = (1, 3, 2)$

Thus, there are five different sequences that $B_1, B_2, B_3$ can be.

Input #2

4
7 1 8 3 5 2 6 4

Output #2

Input #3

10
7 -1 -1 -1 -1 -1 -1 6 14 12 13 -1 15 -1 -1 -1 -1 20 -1 -1

Output #3

Input #4

20
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 6 -1 -1 -1 -1 -1 7 -1 -1 -1 -1 -1 -1 -1 -1 -1 34 -1 -1 -1 -1 31 -1 -1 -1 -1 -1 -1 -1 -1

Output #4

374984201

API Response (JSON)

{
  "problem": {
    "name": "Permutation and Minimum",
    "description": {
      "content": "There is a sequence of length $2N$: $A_1, A_2, ..., A_{2N}$. Each $A_i$ is either $-1$ or an integer between $1$ and $2N$ (inclusive). Any integer other than $-1$ appears at most once in ${A_i}$. For ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc030_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a sequence of length $2N$: $A_1, A_2, ..., A_{2N}$. Each $A_i$ is either $-1$ or an integer between $1$ and $2N$ (inclusive). Any integer other than $-1$ appears at most once in ${A_i}$.\nFor ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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