容斥

#include <iostream>
#include <bitset>
#include <vector>
#include <cstring>

using namespace std;

#define DEBUG 0

#define MAXN 18

typedef long long LL;

struct GRAPH {
    vector<vector<int> > s;
    void ClearEdges() {
        for (auto& i : s)
            i.resize(0);
    }
    void Init(int n) {
        ClearEdges();
        s.resize(n+1);
    }
    void AddUndi(int u, int v) {
        s[u].push_back(v);
        s[v].push_back(u);
    }
};

GRAPH g, G;
bitset<MAXN> ban;
int n;
LL f[MAXN][MAXN];
bool vis[MAXN];
void dfs(int u) {
    vis[u] = true;
    for (int i = 0; i < n; ++i) {
        f[u][i] = ban[i] ? 0 : 1;
    }
    for (int v : g.s[u]) {
        if (vis[v]) continue;
        dfs(v);
        for (int i = 0; i < n; ++i) {
            if (ban[i]) continue;
            LL res = 0;
            for (int j : G.s[i]) {
                if (ban[j]) continue;
                res += f[v][j];
            }
            f[u][i] *= res;
        }
    }
}
int main() {
    int m;
    cin >> n >> m;
    g.Init(n);
    G.Init(n);

    while (m--) {
        int u, v;
        cin >> u >> v;
        --u;
        --v;
        G.AddUndi(u, v);
    }
    m = n-1;
    while (m--) {
        int u, v;
        cin >> u >> v;
        --u;
        --v;
        g.AddUndi(u, v);
    }
    LL ans = 0;
    for (int s = 0, maxs = 1 << n; s < maxs; ++s) {
        memset(vis, 0, n * sizeof(bool));
        ban = s;
        dfs(0);
        LL now = 0;
        for (int j = 0; j < n; ++j) {
            now += f[0][j];
        }
        if (ban.count() & 1)
            ans -= now;
        else
            ans += now;
#if DEBUG
        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < n; ++j) {
                cout << f[i][j] << ' ';
            }
            cout << endl;
        }
        cout << endl;
#endif
    }
    cout << ans << endl;

    return 0;
}

#include <cstdio>
#include <vector>

using namespace std;

#define MAXN 21

typedef long long LL;

const int p = 1000000007;

template <typename T>
T Sub(T x, int p) {
    return x < 0 ? x + p : x;
}

template <typename T>
void SubMod(T& x, int p) {
    if (x < 0)
        x += p;
}

template <typename T>
void AddMod(T& x, int p) {
    if (x >= p)
        x -= p;
}

//x < p
//p must be prime
template <typename T>
T Inv(T x, int p) {
    return 1 == x ? 1 : (LL)(p - p / x) * Inv(p % x, p) % p;
}

//simple
struct MATRIX {
    const static int maxr = MAXN, maxc = MAXN;
    int row, col;
    int s[maxr][maxc];

    void clear() {
        for (int i = 0; i < row; ++i)
            for (int j = 0; j < col; ++j)
                s[i][j] = 0;
    }

    //O(n^3)
    int det_laplacian() {
        int ans = 1;
        for (int i = 0; i < row && ans; ++i) {
            if (0 == s[i][i]) return 0;
            int invi = Inv(s[i][i], p);
            for (int k = i + 1; k < row; ++k) {
                if (0 == s[k][i]) continue;
                int d = (LL)s[k][i] * invi % p;
                for (int j = i; j < col; ++j) {
                    s[k][j] = (s[k][j] - (LL)s[i][j] * d) % p;
                }
            }
            ans = (LL)ans * s[i][i] % p;
        }
        return Sub(ans, p);
    }
};

int main() {
    int n;
    static vector<pair<int, int> > es[MAXN];
    static MATRIX ma;

    scanf("%d", &n);
    --n;
    ma.row = ma.col = n;
    for (int i = 0; i < n; ++i) {
        int m;
        scanf("%d", &m);
        while (m--) {
            int u, v;
            scanf("%d%d", &u, &v);
            --u;
            --v;
            es[i].emplace_back(u, v);
        }
    }
    int ans = 0;
    for (int s = 0, maxs = 1 << n; s < maxs; ++s) {
        ma.clear();
        for (int i = 0; i < n; ++i) {
            if (0 == (s & (1 << i))) {
                for (auto e : es[i]) {
                    --ma.s[e.first][e.second];
                    --ma.s[e.second][e.first];
                    ++ma.s[e.first][e.first];
                    ++ma.s[e.second][e.second];
                }
            }
        }
        int t = ma.det_laplacian();
        if (__builtin_popcount(s) & 1) {
            SubMod(ans -= t, p);
        } else {
            AddMod(ans += t, p);
        }
    }
    printf("%d\n", ans);

    return 0;
}