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:
def dfs(tree, v, tv, p, es):
    if v == tv:
        return True
    for e in tree[v]:
        if e[0] == p:
            continue
        if dfs(tree, e[0], tv, v, es):
            es.append(e[1])
            return True
    return False

def main():
    n = int(input())
    tree = [[] for i in range(n)]
    for i in range(n-1):
        a, b = map(int, input().split())
        a -= 1
        b -= 1
        tree[a].append((b, i))
        tree[b].append((a, i))
    m = int(input())
    eset = [0]*m
    for i in range(m):
        u, v = map(int, input().split())
        es = []
        dfs(tree, u-1, v-1, -1, es)
        for e in es:
            eset[i] |= 1 << e

    ans = 0
    for i in range(1 << m):
        mask = 0
        for j in range(m):
            if i >> j & 1:
                mask |= eset[j]
        white = bin(mask).count('1')
        now = 1 << (n-1-white)
        if bin(i).count('1') % 2 == 0:
            ans += now
        else:
            ans -= now
    print(ans)


main()