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:
N = int(input())
from collections import defaultdict
G = defaultdict(list)
EdaNum = {}
Ki = [[float('inf')]*(N+1) for i in range(N+1)]
for i in range(N-1):
    a,b = map(int,input().split())
    G[a].append(b)
    G[b].append(a)
    EdaNum[(min(a,b),max(a,b))] = i
    Ki[a][b] = 1
    Ki[b][a] = 1

Next = [[-1]*(N+1) for i in range(N+1)]
for i in range(1,N+1):
    for j in range(1,N+1):
        Next[i][j] = j

        
for k in range(1,N+1):
    for i in range(1,N+1):
        for j in range(1,N+1):
            if Ki[i][k] + Ki[k][j] < Ki[i][j]:
                Ki[i][j] = Ki[i][k] + Ki[k][j]
                Next[i][j] = Next[i][k]

M = int(input())
MM = [set() for i in range(M)]
#print(EdaNum)
#print(Next)
for i in range(M):
    u,v = map(int,input().split())
    now = u
    while now != v:
        nex = Next[now][v]
        MM[i].add(EdaNum[(min(now,nex),max(now,nex))])
        now = nex
        
#print(MM)
import itertools
zero1 = [0,1]
ans = 0

for i in itertools.product(zero1,repeat = M):
    #print(ans)
    count = 0
    root = set()
    for j in range(M):
        if i[j] == 0:
            count += 1
        else:
            root |= MM[j]
    #print(i,len(root),count)
    if (M-count)%2 ==0:
        ans += pow(2,N-1-len(root))
    else:
        ans -= pow(2,N-1-len(root))
        
print(ans)