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 PYTHON3):

Solution:
from itertools import product as p
n=int(input())
s=[[]for i in range(n+1)]
for i in range(n-1):
    a,b=map(int,input().split())
    s[a].append([b,i])
    s[b].append([a,i])
m=int(input())
l=[]
for i in range(m):
    u,v=map(int,input().split())
    a=[[]for i in range(n+1)]
    a[u]=[]
    q=[u]
    while q:
        t=q.pop(0)
        d=0
        for i,j in s[t]:
            if a[i]==[]:
                a[i]=a[t]+[j]
                q.append(i)
                if i==v:
                    d=1
                    break
        if d==1:
            break
    l.append(a[v])
for i in range(m):l[i]=set(l[i])
s=[0]*(m+1)
for i in p([0,1],repeat=m):
    d=set([])
    if sum(i)!=0:
        for j in range(m):
            if i[j]:
                d|=l[j]
        s[sum(i)]+=pow(2,n-1-len(d))
l=0
for i in range(1,m+1):
    l+=((-1)**(i-1))*s[i]
print(pow(2,n-1)-l)