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>
#include <iostream>
#include <cstring>
#include <algorithm>
#include <vector>
#define PB push_back
#define MP make_pair
#define PII pair<int,int>
#define FIR first
#define SEC second
#define ll long long
using namespace std;
template <class T>
inline void rd(T &x) {
	x=0; char c=getchar(); int f=1;
	while(!isdigit(c)) { if(c=='-') f=-1; c=getchar(); }
	while(isdigit(c)) x=x*10-'0'+c,c=getchar(); x*=f;
}
const int mod=1e9+7;
inline void Add(int &x,int y) { x+=y; if(x>=mod) x-=mod; }

const int N=310;
int a[N<<1],n;
int dp[N<<1][N<<1][N<<1];
int p[N<<1],m;
int vis[N<<1],vis2[N<<1];
int main() {
	rd(n);
	for(int i=1;i<=2*n;++i) rd(a[i]);
	int cnt=0;
	for(int i=1;i<2*n;i+=2) if(a[i]==-1||a[i+1]==-1) {
		if(a[i]!=-1) vis2[a[i]]=1;
		else if(a[i+1]!=-1) vis2[a[i+1]]=1;
		else cnt++;
	}
	else vis[a[i]]=vis[a[i+1]]=1;
	for(int i=1;i<=2*n;++i)
		if(!vis[i]) p[++m]=vis2[i];
//	for(int i=1;i<=m;++i) printf("%d ",p[i]); puts("");
	
	dp[m+1][0][0]=1;
	for(int i=m;i>=1;--i)
	for(int j=0;j<=m-i;++j)
	for(int k=0;k<=m-i;++k) if(dp[i+1][j][k]) {
		int v=dp[i+1][j][k];
		if(!p[i]&&k) Add(dp[i][j][k-1],1ll*v*k%mod);
		Add(dp[i][j-1][k],v);
		if(p[i]) Add(dp[i][j][k+1],v);
		else Add(dp[i][j+1][k],v);
	}
	int res=dp[1][0][0];
	for(int i=1;i<=cnt;++i) res=1ll*res*i%mod;
	printf("%d ",res);
	return 0;
}