Contest Duration: - (local time) (110 minutes) Back to Home
F - Permutation and Minimum /

Time Limit: 3 sec / Memory Limit: 1024 MB

### 問題文

すぬけ君は，A_i = -1 であるような i それぞれに対して，A_i1 以上 2N の整数で置き換えて，{A_i}1, 2, ..., 2N の並び替えになるようにします． そして，長さ N の数列 B_1, B_2, ..., B_N を，B_i = min(A_{2i-1}, A_{2i}) として求めます．

### 制約

• 1 \leq N \leq 300
• A_i = -1 あるいは 1 \leq A_i \leq 2N
• A_i \neq -1, A_j \neq -1 ならば A_i \neq A_j (i \neq j)

### 入力

N
A_1 A_2 ... A_{2N}


### 入力例 1

3
1 -1 -1 3 6 -1


### 出力例 1

5


{A_i}1, 2, ..., 2N の並び替えにする方法は 6 通りありますが，そのそれぞれに対して {B_i} は次のようになります：

• (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)

よって，異なる B_1, B_2, B_35 個あります．

### 入力例 2

4
7 1 8 3 5 2 6 4


### 出力例 2

1


### 入力例 3

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


### 出力例 3

9540576


### 入力例 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


### 出力例 4

374984201


Score : 1600 points

### Problem Statement

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}


### Output

Print the number of different sequences that B_1, B_2, ..., B_N can be, modulo 10^9 + 7.

### Sample Input 1

3
1 -1 -1 3 6 -1


### Sample 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.

### Sample Input 2

4
7 1 8 3 5 2 6 4


### Sample Output 2

1


### Sample Input 3

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


### Sample Output 3

9540576


### Sample 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


### Sample Output 4

374984201