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:
import sys
from collections import defaultdict as dd
from itertools import combinations as combi
input = sys.stdin.readline
N = int(input())
el = []
e = dd(list)
for _ in range(N - 1):
  u, v = map(int, input().split())
  e[u].append(v)
  e[v].append(u)
  if u > v: u, v = v, u
  el.append((u, v))

vis = []
def dfs(s, t):
  global vis
  vis.append(s)
  if s == t:
    res = list(vis)
    vis.remove(s)
    return res
  res = []
  for x in e[s]:
    if x in vis: continue
    tt = dfs(x, t)
    if len(tt):
      res = tt
      break
  vis.remove(s)
  return res


M = int(input())
table = [[0] * (N - 1) for _ in range(M)]
for i in range(M):
  u, v = map(int, input().split())
  p = dfs(u, v)
  #print(p, i, vis)
  for j in range(len(p) - 1):
    for k in range(N - 1):
      x = p[j]
      y = p[j + 1]
      if x > y: x, y = y, x
      #print(el[k], x, y, i)
      if el[k] == (x, y):
        table[i][k] = 1
        break
revtable = [0] * (N - 1)
for i in range(N - 1):
  for j in range(M):
    if table[j][i]: revtable[i] += pow(2, j)

dp = [0] * pow(2, M)
dp[0] = 1
#print(revtable)
#print(table)
for i in range(N - 1):
  for j in range(pow(2, M) - 1, -1, -1):
    dp[revtable[i] | j] += dp[j]
print(dp[-1])