Problem:
Score : 600 points

Problem Statement

We have a tree with N vertices numbered 1 to N.
The i-th edge in this tree connects Vertex a_i and Vertex b_i.

Consider painting each of these edges white or black. There are 2^{N-1} such ways to paint the edges. Among them, how many satisfy all of the following M restrictions?

The i-th (1 \leq i \leq M) restriction is represented by two integers u_i and v_i, which mean that the path connecting Vertex u_i and Vertex v_i must contain at least one edge painted black.

Constraints

2 \leq N \leq 50

1 \leq a_i,b_i \leq N

The graph given in input is a tree.

1 \leq M \leq \min(20,\frac{N(N-1)}{2})

1 \leq u_i < v_i \leq N

If i \not= j, either u_i \not=u_j or v_i\not=v_j

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
a_1 b_1
:
a_{N-1} b_{N-1}
M
u_1 v_1
:
u_M v_M

Output

Print the number of ways to paint the edges that satisfy all of the M conditions.

Sample Input 1

3
1 2
2 3
1
1 3

Sample Output 1

3

The tree in this input is shown below:

All of the M restrictions will be satisfied if Edge 1 and 2 are respectively painted (white, black), (black, white), or (black, black), so the answer is 3.

Sample Input 2

2
1 2
1
1 2

Sample Output 2

1

The tree in this input is shown below:

All of the M restrictions will be satisfied only if Edge 1 is painted black, so the answer is 1.

Sample Input 3

5
1 2
3 2
3 4
5 3
3
1 3
2 4
2 5

Sample Output 3

9

The tree in this input is shown below:

Sample Input 4

8
1 2
2 3
4 3
2 5
6 3
6 7
8 6
5
2 7
3 5
1 6
2 8
7 8

Sample Output 4

62

The tree in this input is shown below:

Solution in C++14 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <functional>
#include <algorithm>
#include <iostream>
#include <iomanip>
#include <cstring>
#include <string>
#include <vector>
#include <random>
#include <bitset>
#include <queue>
#include <cmath>
#include <stack>
#include <set>
#include <map>
typedef long long ll;
using namespace std;
const ll MOD = 1000000007LL;

int edge[50][50];
vector <int> st[50];

bool dfs(int cur, int par, int goal, int idx) {
    if (cur == goal) return true;

    for (int i = 0; i < 50; i++) {
        if (i == par) continue;
        if (edge[cur][i] != -1) {
            bool ret = dfs(i, cur, goal, idx);
            if (ret) {
                st[edge[cur][i]].push_back(idx);
                return true;
            }
        }
    }

    return false;
}

int main() {
    cin.sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);

    int n;
    cin >> n;
    fill(edge[0], edge[n], -1);
    for (int i = 0; i < n - 1; i++) {
        int a, b;
        cin >> a >> b;
        a--; b--;
        edge[a][b] = i;
        edge[b][a] = i;
    }

    int m;
    cin >> m;
    for (int i = 0; i < m; i++) {
        int u, v;
        cin >> u >> v;
        u--; v--;
        dfs(u, -1, v, i);
    }

    int dp[n][1 << m];
    fill(dp[0], dp[n], 0);
    dp[0][0] = 1;

    for (int i = 0; i < n - 1; i++) {
        // i番目の辺まで見たときに、

        int mask = 0;
        for (int j : st[i]) mask += (1 << j);

        for (int j = 0; j < (1 << m); j++) {
            dp[i + 1][j] += dp[i][j];
            dp[i + 1][j | mask] += dp[i][j];
        }
    }

    cout << dp[n - 1][(1 << m) - 1] << '\n';
    return 0;
}