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:
#!/usr/bin/env python3
import sys
input = sys.stdin.readline
 
n = int(input())
edge = [[] for _ in range(n)]
edge_dict = dict()
 
for i in range(n - 1):
    a, b = [int(item) - 1 for item in input().split()]
    edge[a].append(b)
    edge[b].append(a)
    if a > b:
        edge_dict[(b, a)] = i
    else:
        edge_dict[(a, b)] = i
 
m = int(input())
uv = []
for _ in range(m):
    uv.append([int(item) - 1 for item in input().split()])
 
def dfs(p, v, dest):
    if v == dest:
        return [v]
    if p != -1 and len(edge[v]) == 1:
        return False
    for nv in edge[v]:
        if nv == p:
            continue
        ret = dfs(v, nv, dest)
        if ret:
            return ret + [v]
    return False
 
# edge-bitset of each constraint
target_edge = [0] * m
for i, (u, v) in enumerate(uv):
    ret = dfs(-1, u, v)
    for uu, vv in zip(ret, ret[1:]):
        if uu > vv:
            uu, vv = vv, uu
        if (uu, vv) in edge_dict:
            target_edge[i] |= (1 << edge_dict[(uu, vv)])

# edge-bitset of each set of constraints
edgest = [0] * 2**m
for i in range(1, 2**m):
    lsb = i & (-i)
    edgest[i] = edgest[i ^ lsb] | target_edge[lsb.bit_length() - 1]
 
# dp[set of constraints]
dp = [0] * 2**m
dp[0] = 1 << (n - 1)
ans = dp[0]
for i in range(1, 2**m):
    lsb = i & (-i)
    n_edgest = edgest[i]
    p_edgest = edgest[i ^ lsb]
    limit_num = bin(n_edgest ^ p_edgest).count("1")
    dp[i] = dp[i ^ lsb] >> limit_num
    if bin(i).count("1") % 2 == 0:
        ans += dp[i]
    else:
        ans -= dp[i]
print(ans)