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())

es = []
adj = [[] for _ in range(N)]
e_index = dict()
for i in range(N-1):
    a, b = map(int, input().split())
    a -= 1
    b -= 1
    es.append((a, b))
    es.append((b, a))
    adj[a].append(b)
    adj[b].append(a)
    e_index[(a, b)] = i
    e_index[(b, a)] = i

M = int(input())
uvs = [tuple(map(int, input().split())) for _ in range(M)]

edges = [0] * (N - 1)
for i, (u, v) in enumerate(uvs):
    u -= 1
    v -= 1
    parent = [-1] * N
    stack = [u]
    while stack:
        node = stack.pop()
        if node == v:
            break

        for next_node in adj[node]:
            if parent[node] != next_node:
                parent[next_node] = node
                stack.append(next_node)
             
    node = v
    while node != u:
        next_node = parent[node]
        index = e_index[(node, next_node)]
        edges[index] |= 1 << i
        node = next_node

dp = [0] * (1 << M)
dp[0] = 1
for e in edges:
    for i in range((1 << M) - 1, -1, -1):
        dp[i | e] += dp[i]

print(dp[-1])