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 collections import deque
from collections import Counter
N=int(input())
E=[set() for _ in range(N)]
for i in range(N-1):
    a,b=map(lambda x:int(x)-1,input().split())
    E[a].add((b,i))
    E[b].add((a,i))
M=int(input())
P=[tuple(map(lambda x:int(x)-1,input().split())) for _ in range(M)]

pc=[set() for _ in range(M)] #各制約で使用する辺の集合

def bfs(S,G,p):
    q=deque([S])
    parent=[(-1,-1)]*N
    while q:
        n=q.popleft()
        for to,i in E[n]:
            if parent[to][0]!=-1:
                continue
            parent[to]=(n,i)
            if to==G:
                break
            q.append(to)
    n=G
    while n!=S:
        n,i=parent[n]
        pc[p].add(i)

for i,p in enumerate(P):
    bfs(p[0],p[1],i)

ans=0
for i in range(1<<M):
    whiteset=set()
    sign=1
    for j in range(M):
        if i>>j&1:
            whiteset|=pc[j]
            sign*=-1
    ans+=sign*(1<<(N-1-len(whiteset)))

print(ans)