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)

// AGC030F.cpp
#include <bits/stdc++.h>

using namespace std;

const int MAX_N = 330, mod = 1e9 + 7;

int n, ai[MAX_N << 1], dp[MAX_N << 1][MAX_N][MAX_N], both_nexist, single_exist, seq[MAX_N << 1], m;
bool vis[MAX_N << 1], pending[MAX_N << 1];

int main()
{
    scanf("%d", &n);
    for (int i = 1; i <= n << 1; i++)
        scanf("%d", &ai[i]);
    for (int i = 1; i <= n << 1; i += 2)
    {
        if (ai[i] > 0 && ai[i + 1] > 0)
            vis[ai[i]] = vis[ai[i + 1]] = true;
        else if (ai[i] < 0 && ai[i + 1] < 0)
            both_nexist++;
        else
            single_exist++, pending[max(ai[i], ai[i + 1])] = true;
    }
    for (int i = (n << 1); i >= 1; i--)
        if (!vis[i])
            seq[++m] = i;
    dp[0][0][0] = 1;
    for (int i = 1; i <= m; i++)
        for (int j = 0; j <= both_nexist + single_exist; j++)
            for (int k = 0; k <= single_exist; k++)
            {
                if (!pending[seq[i]])
                {
                    dp[i][j + 1][k] = (0LL + dp[i][j + 1][k] + dp[i - 1][j][k]) % mod;
                    if (j > 0)
                        dp[i][j - 1][k] = (0LL + dp[i][j - 1][k] + dp[i - 1][j][k]) % mod;
                    if (k > 0)
                        dp[i][j][k - 1] = (0LL + dp[i][j][k - 1] + 1LL * k * dp[i - 1][j][k] % mod) % mod;
                }
                else
                {
                    dp[i][j][k + 1] = (0LL + dp[i][j][k + 1] + dp[i - 1][j][k]) % mod;
                    if (j > 0)
                        dp[i][j - 1][k] = (0LL + dp[i][j - 1][k] + dp[i - 1][j][k]) % mod;
                }
            }
    int ans = dp[m][0][0];
    for (int i = 1; i <= both_nexist; i++)
        ans = 1LL * ans * i % mod;
    printf("%d\n", ans);
    return 0;
}