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())
ab = {i: [] for i in range(n)}
for j in range(n - 1):
    a, b = [int(i) - 1 for i in input().split()]
    ab[a].append((b, j))
    ab[b].append((a, j))


def dfs(a, b, d=[], c=-1):
    if a == b:
        return d
    for i in ab[a]:
        if i[0] == c:
            continue
        e = dfs(i[0], b, d + [i[1]], a)
        if len(e) != 0:
            return set(e)
    return set()


m = int(input())
ms = []
for _ in range(m):
    u, p = [int(i) - 1 for i in input().split()]
    ms.append(dfs(u, p))

ans = 0
for i in range(1 << m):
    k = 0
    a = set()
    for j in range(m):
        if (i >> j) & 1 == 1:
            k += 1
            a |= ms[j]
    if k % 2 == 1:
        ans += 2 ** (n - 1 - len(a))
    elif k != 0:
        ans -= 2 ** (n - 1 - len(a))
            
print(2**(n-1)-ans)