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())
g=[[]for i in range(n)]
for i in range(n-1):
    a,b=map(int,input().split())
    g[a-1].append((b-1,i))
    g[b-1].append((a-1,i))

def path(i,goal,mam=-1):
    if len(g[i][0])==1 and g[0]==mam:
        return 0
    else:
        for j,idx in g[i]:
            if j==mam:
                continue
            if j==goal:
                return 1<<idx
            p=path(j,goal,i)
            if p>0:
                return p | (1<<idx)
        return 0

m=int(input())
ps=[]
for _ in range(m):
    a,b=map(int,input().split())
    ps.append(path(a-1,b-1))

dp=[0]*(1<<m)
dp[0]=1
for i in range(n-1):
    newdp=[0]*(1<<m)
    hit=0
    for j,p in enumerate(ps):
        a=p & (1<<i)
        if p & (1<<i):
            hit+=1<<j
    for j in range(1<<m):
        newdp[j|hit]+=dp[j]
    for j in range(1<<m):
        dp[j]+=newdp[j]
print(dp[-1])