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
n = int(input())
ls = [list(map(lambda x:int(x)-1, input().split())) for i in range(n-1)]
m = int(input())
cond = [list(map(lambda x:int(x)-1, input().split())) for i in range(m)]
ans=0
graph = [[0]*(n) for _ in range(n)]



for i in range(n-1):
    graph[ls[i][0]][ls[i][1]]+=1<<i
    graph[ls[i][1]][ls[i][0]]+=1<<i

eset = []

for cns in cond:
    d=deque()
    d.append([cns[0], 0])
    while d:
        s, es = d.pop()
        for i in range(n):
            if graph[s][i] and not es&graph[s][i]:
                es2 = es|graph[s][i]
                if i == cns[1]:
                    eset.append(es2)
                    break
                d.append([i, es2])

for i in range(1<<m):
    mask=0
    for j in range(m):
        if i&1<<j:
            mask|=eset[j]
    white=bin(mask).count('1')
    if bin(i).count('1')%2:
        ans-=1<<(n-1-white)
    else:
        ans+=1<<(n-1-white)

print(ans)