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
input = sys.stdin.buffer.readline
sys.setrecursionlimit(10 ** 7)

N = int(input())
edge = [[] for _ in range(N + 1)]
for _ in range(N - 1):
    x, y = map(int, input().split())
    edge[x].append(y)
    edge[y].append(x)
M = int(input())
AB = tuple(tuple(map(int, input().split())) for _ in range(M))


parent = [-1] * (N + 1)
node = [1]
while node:
    s = node.pop()
    for t in edge[s]:
        if t == parent[s]:
            continue
        parent[t] = s
        node.append(t)

pair = [-1] * M
for i, (a, b) in enumerate(AB):
    pa = set()
    pb = set()
    while a != 1:
        pa.add(a - 1)
        a = parent[a]
    while b != 1:
        pb.add(b - 1)
        b = parent[b]
    pair[i] = pa ^ pb

ans = pow(2, N - 1)

whole = set(range(1, N))
for bit in range(1, 1 << M):
    popcnt = 0
    inter = set()
    for i in range(M):
        if (bit >> i) & 1:
            popcnt += 1
            inter |= pair[i]
    x = N - len(inter) - 1
    if popcnt % 2 == 1:
        ans -= 2 ** x
    else:
        ans += 2 ** x

print(ans)