Problem: 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.

Examples

Input

3
1 2
2 3
1
1 3


Output

3


Input

2
1 2
1
1 2


Output

1


Input

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


Output

9


Input

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


Output

62

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
typedef long long ll;
using namespace std;
ll n,d[100][100],a[50],m;
void init()
{
	for(ll i=0;i<=n;i++)
	{
		for(ll j=0;j<=n;j++)d[i][j]=(1ll<<60);
		d[i][i]=0;
	}
}
int main()
{
	scanf("%lld",&n);
	ll i,j,k,u,v;
	init();
	for(i=1;i<n;i++)
	{
		scanf("%lld%lld",&u,&v);
		d[u][v]=d[v][u]=(1ll<<(i-1));
	}
	for(k=1;k<=n;k++)for(i=1;i<=n;i++)for(j=1;j<=n;j++)
	d[i][j]=min(d[i][j],d[i][k]+d[k][j]);
	scanf("%lld",&m);
	for(i=0;i<m;i++)
	{
		scanf("%lld%lld",&u,&v);
		a[i]=d[u][v];
	}
	ll ans=0;
	for(j=0;j<(1ll<<m);j++)
	{
		ll base=0,cnt=0;
		for(k=0;k<m;k++)
		{
			if((j>>k)&1)base|=a[k],cnt++;
		}
		ll num=__builtin_popcountll(base);
		if(cnt&1)ans-=(1ll<<(n-1-num));
		else ans+=(1ll<<(n-1-num));
	}
	printf("%lld\n",ans);
}