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:
#!python3

class Node:
    
    def __init__(self, num):
        self.num = num
        self.depth = 0
        self.parent = (None, None)


LI = lambda: list(map(int, input().split()))

# input
N = int(input())
AB = [LI() for _ in range(N - 1)]
M = int(input())
UV = [LI() for _ in range(M)]

# params
links = [[] for _ in range(N)]
nodes = [Node(i) for i in range(N)]
w = []
p2 = [2 ** i for i in range(51)]


def create_links():
    for i in range(N - 1):
        a, b = AB[i][0] - 1, AB[i][1] - 1
        links[a].append((b, i))
        links[b].append((a, i))


def create_tree(v, p=-1):
    for u, i in links[v]:
        if u == p:
            continue
        nodes[u].parent = (nodes[v], i)
        nodes[u].depth = nodes[v].depth + 1
        create_tree(u, v)


def between_links(s, t):
    x = nodes[s]
    y = nodes[t]
    if x.depth > y.depth:
        x, y = y, x
    s = set()
    while x.depth < y.depth:
        y, i = y.parent
        s.add(i)
    while x is not y:
        x, i = x.parent
        y, j = y.parent
        s.add(i)
        s.add(j)
    return s


def create_between_links():
    for u, v in UV:
        s = between_links(u - 1, v - 1)
        w.append(s)


def main():
    create_links()
    create_tree(0)
    create_between_links()
    
    ans = 0
    n = p2[M]
    for i in range(n):
        f = 0
        s = set()
        for j in range(M):
            if i >> j & 1:
                f += 1
                s |= w[j]
        v = p2[N - 1 - len(s)]
        if f % 2 == 0:
            ans += v
        else:
            ans -= v
    print(ans)

    
if __name__ == "__main__":
    main()