Problem:
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

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<cstdio>
using namespace std;
#define N 605
#define mod 1000000007
int dp[N][N][N],c1,n,is[N],a,b;
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		scanf("%d%d",&a,&b);
		if(a>b)a^=b^=a^=b;
		if(b==-1)c1++;
		else if(a==-1)is[n*2-b+1]=1;
		else is[n*2-a+1]=is[n*2-b+1]=2;
	}
	dp[0][0][0]=1;
	for(int i=1;i<=n*2;i++)
	for(int j=0;j<=i&&j<=n;j++)
	for(int k=0;k<=i;k++)
	if(dp[i-1][j][k])
	{
		if(is[i]==2)dp[i][j][k]=dp[i-1][j][k];
		else if(is[i]==1){dp[i][j+1][k]=(dp[i-1][j][k]+dp[i][j+1][k])%mod;if(k)dp[i][j][k-1]=(dp[i][j][k-1]+dp[i-1][j][k])%mod;}
		else
		{
			if(k)dp[i][j][k-1]=(dp[i][j][k-1]+dp[i-1][j][k])%mod;
			if(j)dp[i][j-1][k]=(dp[i][j-1][k]+1ll*dp[i-1][j][k]*j)%mod;
			dp[i][j][k+1]=(dp[i][j][k+1]+dp[i-1][j][k])%mod;
		}
	}
	int as=dp[n*2][0][0];
	for(int i=1;i<=c1;i++)as=1ll*as*i%mod;
	printf("%d\n",as);
}