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# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using static System.Console;
using static System.Math;

namespace AtTest.ABC_152
{
    class F
    {
        static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(OpenStandardOutput()) { AutoFlush = false };
            SetOut(sw);

            Method(args);

            Out.Flush();
        }

        static void Method(string[] args)
        {
            int n = ReadInt();
            List<int>[] graph = new List<int>[n];
            for (int i = 0; i < n; i++) graph[i] = new List<int>();
            for(int i = 0; i < n - 1; i++)
            {
                int[] ab = ReadInts();
                int a = ab[0] - 1;
                int b = ab[1] - 1;
                graph[a].Add(b);
                graph[b].Add(a);
            }
            int m = ReadInt();
            List<int>[] paths = new List<int>[m];
            for (int i = 0; i < m; i++)
            {
                int[] uv = ReadInts();
                int u = uv[0] - 1;
                int v = uv[1] - 1;
                int[] costs = new int[n];
                for (int j = 0; j < n; j++) costs[j] = int.MaxValue / 2;
                Queue<int[]> que = new Queue<int[]>();
                que.Enqueue(new int[2] { u, 0 });
                while (que.Count > 0)
                {
                    int[] val = que.Dequeue();
                    int now = val[0];
                    int cost = val[1];
                    if (cost >= costs[now]) continue;

                    costs[now] = cost;
                    for(int j = 0; j < graph[now].Count; j++)
                    {
                        int to = graph[now][j];
                        que.Enqueue(new int[2] { to, cost + 1 });
                    }
                }
                paths[i] = new List<int>();
                int tmp = v;
                while (tmp != u)
                {
                    paths[i].Add(tmp);
                    for(int j = 0; j < graph[tmp].Count; j++)
                    {
                        int to = graph[tmp][j];
                        if (costs[to] < costs[tmp])
                        {
                            tmp = to;
                            break;
                        }
                    }
                }
                paths[i].Add(u);
            }

            long[] pows = new long[56];
            pows[0] = 1;
            for (int i = 1; i < 56; i++)
            {
                pows[i] = pows[i - 1] * 2;
            }
            long res = 0;
            int all = 1 << m;
            for (int i = 0; i < all; i++)
            {
                int select = 0;
                var hashSet = new HashSet<int>();
                for (int j = 0; j < m; j++)
                {
                    if ((i & (1 << j)) == 0) continue;

                    select++;
                    for (int k = 1; k < paths[j].Count; k++)
                    {
                        hashSet.Add(paths[j][k] * 100 + paths[j][k - 1]);
                        hashSet.Add(paths[j][k - 1] * 100 + paths[j][k]);
                    }
                }
                if (select % 2 == 0)
                {
                    res += pows[n - 1 - hashSet.Count/2];
                }
                else
                {
                    res -= pows[n - 1 - hashSet.Count / 2];
                }
            }
            WriteLine(res);
        }

        private static string Read() { return ReadLine(); }
        private static char[] ReadChars() { return Array.ConvertAll(Read().Split(), a => a[0]); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
    }
}