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 popcnt(n):
    c = (n & 0x5555555555555555) + ((n>>1) & 0x5555555555555555)
    c = (c & 0x3333333333333333) + ((c>>2) & 0x3333333333333333)
    c = (c & 0x0f0f0f0f0f0f0f0f) + ((c>>4) & 0x0f0f0f0f0f0f0f0f)
    c = (c & 0x00ff00ff00ff00ff) + ((c>>8) & 0x00ff00ff00ff00ff)
    c = (c & 0x0000ffff0000ffff) + ((c>>16) & 0x0000ffff0000ffff)
    c = (c & 0x00000000ffffffff) + ((c>>32) & 0x00000000ffffffff)
    return c

def dfs(g,root,w):
    parent = [-1]*n
    enum = [-1]*n
    q = [root]
    while q:
        v = q.pop()
        for c,i in g[v]:
            if c != parent[v]:
                parent[c] = v
                enum[c] = i
                q.append(c)
    a = 0
    #print(parent,enum)
    while w != root:
        a |= 1<<enum[w]
        w = parent[w]
    return a
    

###################################
# coding: utf-8
# Your code here!
import sys
sys.setrecursionlimit(10**6)
readline = sys.stdin.readline
read = sys.stdin.read

#n,m = [int(i) for i in readline().split()]
#d = [int(i) for i in readline().split()]
MOD = 10**9+7

n = int(input())
g = [[] for _ in range(n)]
for i in range(n-1):
    a,b = [int(i)-1 for i in readline().split()]
    g[a].append((b,i))
    g[b].append((a,i))

m = int(input())

#使う要素のbitmask
res = [0]*m
for i in range(m):
    v,w = [int(i)-1 for i in readline().split()]
    res[i] = dfs(g,v,w)

ans = 1<<(n-1)
M = 1<<m
#print(res)
for mask in range(1,M):
    r = 0
    for j in range(m):
        if mask&(1<<j): r |= res[j]
    
    r = popcnt(r)
    c = popcnt(mask)
    if c%2:
        ans -= 1<<(n-1-r)
    else:
        ans += 1<<(n-1-r)

print(ans)