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 <bits/stdc++.h>
using namespace std;
using ull = uint64_t;
using ll = int64_t;
using ld = long double;

const int N = 328;
using Arr = array<array<ll, N>, N>;
const int MOD = int(1e9 + 7);

const int M = N * 2;

int a[M];
int ac;

int w[M];

void ad(ll& x, ll y) {
    x = (x + y) % MOD;
}

int main() {
#ifdef BZ
    freopen("input.txt", "r", stdin);
#endif
    ios_base::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr); cout.setf(ios::fixed); cout.precision(20);

    int n;
    cin >> n;

    int free = 0;

    int one = 0;

    for (int i = 1; i <= n; ++i) {
        int x, y;
        cin >> x >> y;
        if (x > y) {
            swap(x, y);
        }

        if (x != -1 && y != -1) {
            w[x] = w[y] = 1;
        }

        if (x == -1 && y != -1) {
            ++a[y];
            w[y] = 2;
            ++one;
        }

        if (y == -1) {
            ++free;
        }

    }

    int m = 2 * n;

    for (int i = m; i > 0; --i) {
        a[i] += a[i + 1];
    }

    Arr f{};
    f[0][0] = 1;

    for (int i = 2 * n; i >= 1; --i) {
        if (w[i] == 1) {
            continue;
        }

        Arr g{};

        if (w[i] == 0) {
            for (int j = 0; j <= n; ++j) {
                for (int k = 0; k <= one; ++k) {
                    if (k) {
                        ad(g[j][k - 1], f[j][k] * k);
                    }

                    if (j) {
                        ad(g[j - 1][k], f[j][k]);   
                    }

                    ad(g[j + 1][k], f[j][k]);
                }
            }
        } else {
            for (int j = 0; j <= n; ++j) {
                for (int k = 0; k <= one; ++k) {
                    if (j) {
                        ad(g[j - 1][k], f[j][k]);
                    }

                    ad(g[j][k + 1], f[j][k]);
                }
            }
        }

        f = g;
    }

    ll ans = f[0][0];
    for (int i = 1; i <= free; ++i) {
        ans = ans * i % MOD;
    }

    cout << ans << "\n";
}