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:
#F - Tree and constraints
import itertools
from collections import defaultdict
N = int(input())
G = [[] for i in range(N+1)]
edge = defaultdict(int)
for i in range(N-1):
    a, b = map(int, input().split())
    edge[(min(a, b), max(a, b))] = i+1
    G[a].append(b)
    G[b].append(a)
M = int(input())
que = [tuple(map(int, input().split())) for i in range(M)]
Data = [set([]) for i in range(M)]


def dfs(node):
    visited[node] = True
    for child in G[node]:
        if visited[child] == False:
            parent[child] = node
            dfs(child)


for i in range(M):
    s, g = que[i]
    visited = [False for i in range(N+1)]
    parent = [-1 for i in range(N+1)]
    dfs(s)
    now = g
    while parent[now] > 0:
        number = edge[(min(now, parent[now]), max(now, parent[now]))]
        Data[i].add(number)
        now = parent[now]
ans = 2**(N-1)
seq = [i for i in range(M)]
for i in range(1, M+1):
    # Mこからi+1こを選ぶ
    S = 0
    subset = set([])
    for v in itertools.combinations(seq, i):
        subset.clear()
        for x in v:
            subset = subset | Data[x]
        S += 2**(N-1-len(subset))
    ans -= (-1)**((i-1) % 2)*S
print(ans)