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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
#define pb push_back
#define mp make_pair
#define int long long
#define inf 1000000007
#define LINF 1000000000000000007LL
#define ll long long
using namespace std;
int ct[1145140];
int dist[55][55];
vector<int> nex[55];
vector<int> pth[55][55];
bool col[1145140][55];
void nuri( int bi, int s, int t ){
	col[bi][s] = true;
	col[bi][t] = true;
	for(int i=0;i<pth[s][t].size();i++){
		col[bi][ pth[s][t][i] ] = true;
	}
}
signed main(){
	int n;
	cin>>n;
	vector<int> aa(n),bb(n);
	for(int i=0;i<n-1;i++){
		cin>>aa[i]>>bb[i];
		nex[aa[i]].pb(bb[i]);
		nex[bb[i]].pb(aa[i]);
	}
	for(int i=1;i<=n;i++){
		for(int j=1;j<=n;j++){
			if( i!=j ) dist[i][j] = LINF;
		}
	}
	for(int i=1;i<=n;i++){
		for(int j=0;j<nex[i].size();j++){
			dist[i][nex[i][j]] = 1;
		}
	}
	for(int k=1;k<=n;k++){
		for(int i=1;i<=n;i++){
			for(int j=1;j<=n;j++){
				dist[i][j] = min( dist[i][j], dist[i][k] + dist[k][j] );
			}
		}
	}
	for(int i=1;i<=n;i++){
		for(int j=1;j<=n;j++){
			for(int k=0;k<n-1;k++){
				if( dist[i][j] == dist[i][aa[k]] + dist[aa[k]][j] ){
					if( dist[i][j] == dist[i][bb[k]] + dist[bb[k]][j]){
						pth[i][j].pb(k);
					}
				}
			}
		}
	}
	int m;
	cin>>m;
	vector<int> u(m),v(m);
	for(int i=0;i<m;i++){
		cin>>u[i]>>v[i];
	}
	ct[0] = 1<<(n-1);
	for(int bi = 1; bi < (1<<m); bi ++ ){
		int mb = -1;
		int prv = bi;
		for(int i=0;i<m;i++){
			if( ( bi >> i ) % 2 == 1 ){
				mb = i;
				prv -= (1<<mb);
				break;
			}
		}
		for(int i=0;i<n-1;i++){
			col[bi][i] = col[prv][i];
		}
		nuri( bi, u[mb], v[mb] );
		int arb = 0;
		for(int i=0;i<n-1;i++){
			if( !col[bi][i] ) arb ++;
		}
		ct[bi] = 1LL<<arb;
	}
	/* for(int i=0;i<(1<<m);i++){
		cout<<ct[i]<<endl;
	} */
	int ans = 0;
	for(int i=0;i<(1<<m);i++){
		int bc = 0;
		for(int j=0;j<m;j++){
			if( (i>>j) % 2 ) bc ++;
		}
		if( bc%2 == 0 ){
			ans += ct[i];
		}
		else{
			ans -= ct[i];
		}
	}
	cout<<ans<<endl;
	return 0;
}