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: Wrong Answer)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static System.Math;
using MethodImplAttribute = System.Runtime.CompilerServices.MethodImplAttribute;
using MethodImplOptions = System.Runtime.CompilerServices.MethodImplOptions;
public static class P
{
    static long[][] masks;
    public static void Main()
    {
        int n = int.Parse(Console.ReadLine());

        masks = Enumerable.Repeat(0, n).Select(_ => new long[n]).ToArray();
        for (int i = 0; i < n - 1; i++)
        {
            var st = Console.ReadLine().Split().Select(x => int.Parse(x) - 1).ToArray();
            masks[st[0]][st[1]] = 1 << i;
            masks[st[1]][st[0]] = 1 << i;
        }

        for (int i = 0; i < n; i++)
            for (int j = 0; j < n; j++)
                for (int k = 0; k < n; k++)
                    if (masks[j][k] == 0 && masks[j][i] != 0 && masks[i][k] != 0)
                    {
                        masks[j][k] = masks[j][i] ^ masks[i][k];
                    }

        int m = int.Parse(Console.ReadLine());
        var restrictions = Enumerable.Repeat(0, m).Select(_ => Console.ReadLine().Split().Select(x => int.Parse(x) - 1).ToArray()).ToArray();
        long res = 0;
        for (int i = 0; i < (1 << m); i++)
        {
            long bit = 0;
            int popcnt = 0;
            for (int j = 0; j < m; j++)
                if ((i >> j & 1) == 1)
                {
                    bit |= masks[restrictions[j][0]][restrictions[j][1]];
                    popcnt++;
                }
            res += ((popcnt & 1) != 0 ? -1 : 1) * (1L << ((n - 1) - PopCount(bit)));
        }
        Console.WriteLine(res);
    }

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    static int PopCount(long n)
    {
        n = n - ((n >> 1) & 0x55555555);
        n = (n & 0x33333333) + ((n >> 2) & 0x33333333);
        return (int)(((n + (n >> 4) & 0xF0F0F0F) * 0x1010101) >> 24);
    }
}