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:
def DFS(graph,root,parent):
  dist = [-1]*(n+1)
  dist[root] = 0
  stack = [root]
  while stack:
    x = stack.pop()
    for y in graph[x]:
      if dist[y] == -1:
        parent[y] = x
        dist[y] = dist[x]+1
        stack.append(y)
  return dist

#親のリスト、頂点v、kが与えられたときに「vのk個上の祖先」を見る
class Doubling:
  def __init__(self,graph,root):
    self.root = root
    n = len(graph)-1
    self.ancestor_ls = [[0]*(n+1)]
    self.distance = DFS(graph,root,self.ancestor_ls[0])
    self.bitn = n.bit_length()
    for i in range(1,self.bitn+1):
      ancestor_ls_app = [0]*(n+1)
      for j in range(1,n+1):
        ancestor_ls_app[j] = self.ancestor_ls[i-1][self.ancestor_ls[i-1][j]]
      self.ancestor_ls.append(ancestor_ls_app)
  
  def dist(self):
    return self.distance
  
  def parent(self):
    return self.ancestor_ls[0]

  def ancestor(self,v,depth):
    if depth == 0:
      return v
    if n<depth:
      return self.root
    ret = v
    for i in range(self.bitn):
      if depth&1<<i:
        ret = self.ancestor_ls[i][ret]
    return ret
  
  def LCA(self,u,v):
    if self.distance[u]<self.distance[v]:
      u,v = v,u
    dif = self.distance[u]-self.distance[v]
    w = self.ancestor(u,dif)
    if w == v:
      return v
    for i in range(self.bitn,-1,-1):
      if self.ancestor_ls[i][w] != self.ancestor_ls[i][v]:
        w,v = self.ancestor_ls[i][w],self.ancestor_ls[i][v]
    return self.ancestor_ls[0][v]

import sys
input = sys.stdin.readline
n = int(input())
ab = [list(map(int,input().split())) for i in range(n-1)]
graph = [[] for i in range(n+1)]
for a,b in ab:
  graph[a].append(b)
  graph[b].append(a)

sol = Doubling(graph,1)
pls = sol.parent()

m = int(input())
cons = [0 for i in range(m)]
for i in range(m):
  u,v = map(int,input().split())
  lca = sol.LCA(u,v)
  while u != lca:
    cons[i] |= 1<<u
    u = pls[u]
  while v != lca:
    cons[i] |= 1<<v
    v = pls[v]
ans = 0
for i in range(2**m):
  x = 0
  for j in range(m):
    if i & 1<<j:
      x |= cons[j]
  bcnt = 0
  for j in range(n+1):
    if x & 1<<j:
      bcnt += 1
  if bin(i).count("1")%2 == 1:
    ans -= 2**(n-1-bcnt)
  else:
    ans += 2**(n-1-bcnt)
print(ans)