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.Generic;
using System.Collections;
using System.Collections.Specialized;
using System.Linq;
using System.Text;
using System.IO;
using System.Reflection;
using static System.Math;
using System.Numerics;
static class Program{
	const int mod=(int)1e9+7;
	static List<Tuple<int,int>>[] li;
	static bool[] b;
	static int[] hn;
	static void Main(){
		Sc sc=new Sc();
		var s=sc.Ia;
		int n=s[0],m=n-1;
		li=new List<Tuple<int,int>>[n+1];
		var c=new long[n+1];
		hn=new int[n];
		for(int i=1;i<=n;i++){
			li[i]=new List<Tuple<int,int>>();
			c[i]=long.MaxValue;
		}
		for(int i=0;i<m;i++){
			var e=sc.Ia;
			li[e[0]].Add(Tuple.Create(e[1],i));
			li[e[1]].Add(Tuple.Create(e[0],i));
		}
		int q=sc.I;
		for(int i = 0;i<q;i++) {
			var e=sc.Ia;
			b=new bool[n+1];
			Fu(e[0],e[1],i);
		}
		long ans=1<<(n-1);
		int r=1<<q;
		for(int i = 1;i<r;i++) {
			int d=bits(i)&1,p=0;
			for(int j = 0;j<m;j++) {
				if((hn[j]&i)!=0){p++;}
			}
			if(d==0){ans+=1<<(n-p-1);}
			else{ans-=1<<(n-p-1);}
		}
		Console.WriteLine("{0}",ans);
	}
	static int bits(long bits){
		bits=(bits&0x55555555)+(bits>>1&0x55555555);
		bits=(bits&0x33333333)+(bits>>2&0x33333333);
		bits=(bits&0x0f0f0f0f)+(bits>>4&0x0f0f0f0f);
		bits=(bits&0x00ff00ff)+(bits>>8&0x00ff00ff);
		return (int)((bits&0x0000ffff)+(bits>>16&0x0000ffff));
	}
	static bool Fu(int a,int g,int m){
		b[a]=true;
		var bo=false;
		if(a==g){bo=true;}
		for(int i=0;i<li[a].Count&&!bo;i++){
			if(!b[li[a][i].Item1]){
				bo=Fu(li[a][i].Item1,g,m);
				if(bo){hn[li[a][i].Item2]|=1<<m;}
			}
		}
		return bo;
	}
}
public class Sc{
	public int I{get{return int.Parse(Console.ReadLine());}}
	public long L{get{return long.Parse(Console.ReadLine());}}
	public double D{get{return double.Parse(Console.ReadLine());}}
	public string S{get{return Console.ReadLine();}}
	public int[] Ia{get{return Array.ConvertAll(Console.ReadLine().Split(),int.Parse);}}
	public long[] La{get{return Array.ConvertAll(Console.ReadLine().Split(),long.Parse);}}
	public double[] Da{get{return Array.ConvertAll(Console.ReadLine().Split(),double.Parse);}}
	public string[] Sa{get{return Console.ReadLine().Split();}}
	public object[] Oa{get{return Console.ReadLine().Split();}}
	public int[] Ia2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),int.Parse);}}
	public int[] Ia3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),int.Parse);}
	public int[] Ia3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),int.Parse);}
	public long[] La2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),long.Parse);}}
	public long[] La3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),long.Parse);}
	public long[] La3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),long.Parse);}
	public T[] Arr<T>(int n,Func<T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f();}return a;}
	public T[] Arr<T>(int n,Func<int,T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i);}return a;}
	public T[] Arr<T>(int n,Func<string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(Console.ReadLine().Split());}return a;}
	public T[] Arr<T>(int n,Func<int,string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i,Console.ReadLine().Split());}return a;}
}