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:
import sys
from collections import defaultdict
readline = sys.stdin.readline
N, = map(int, readline().split())
def con(ll,E):
    r = 0
    for u, v in zip(ll,ll[1:]):
        u, v = sorted([u,v])
        r += 1<<E[(u,v)]
    return r

def process():
    G = [[] for _ in range(N+1)]
    E = dict()
    for i in range(N-1):
        a, b = sorted(map(int, readline().split()))
        G[a].append(b)
        G[b].append(a)
        E[(a,b)] = i

    M, = map(int, readline().split())
    qes = dict()
    for _ in range(M):
        u, v = sorted(map(int, readline().split()))
        if u not in qes:
            qes[u] = list()
        qes[u].append(v)
    dep = []
    for i in qes:
        ms = qes[i]
        path = []
        stack = [i]
        vs = set([i])
        while stack:
            v = stack.pop()
            if v > 0:
                vs.add(v)
#                parent = path[-1]
                path.append(v)
                for u in G[v]:
                    if u in vs:
                        continue
                    if u in ms:
                        dep.append(con(path+[u],E))
                    stack += [-v, u]
            else:
                path.pop()
    r = 0
    for i in range(1,2**M):
        t = 0
        ns = 0
#        lns = 
        for j in range(M):
            if i % 2:
                ns = ns | dep[j]
                t += 1
            i = i>>1
        xx = (1 if t%2 else -1)*2**(N-1-bin(ns).count("1"))
        r += xx
    print(2**(N-1)-r)
if __name__ == '__main__':
    process()