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:
from copy import copy
def dfs(x,v,s):
    for y,i in tree[x]:
        if parent[x] != y:
            parent[y] = x
            s.add(i)
            dfs(y,v,s)
            s.remove(i)
    if x == v:
        cons.append(s.copy())
    

N = int(input())
tree = [[] for _ in range(N+1)]
for i in range(N-1):
    a,b = map(int,input().split())
    tree[a].append((b,i))
    tree[b].append((a,i))
M = int(input())
uv = []
cons = []
for i in range(M):
    u,v =  map(int,input().split())
    uv.append((u,v))
    parent = [-1]*(N+1)
    dfs(u,v,set())
bit = [0]*(N-1)
for i in range(N):
    for j in range(M):
        if i in cons[j]:
            bit[i] += 1 << j
dp = [0]*(1 << M)
dp[0] = 1
for i in range(N-1):
    for j in range(1 << M)[::-1]:
        dp[j|bit[i]] += dp[j]
print(dp[-1])