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 itertools import combinations 
from collections import defaultdict
input = sys.stdin.readline
N = int(input())
ab = [list(map(int,input().split())) for i in range(N-1)]
M = int(input())
uv = [list(map(int,input().split())) for i in range(M)]

g = defaultdict(list)
pathnum = {}
for n,(a,b) in enumerate(ab):
    g[a].append(b)
    g[b].append(a)
    a,b = sorted([a,b])
    pathnum[(a,b)] = n

def eulerTour(g,s):
    n = len(g)
    dq = [s]
    ls = [-1]*(n+1)
    rs = [-1]*(n+1)
    vtour = []
    etour = []
    depth = [-1]*(n+1)
    parent = [False]*(n+1)
    visited = [False]*(n+1)
    def dfs(v,d):
        depth[v] = d
        visited[v] = True
        ls[v] = len(vtour)
        vtour.append(v)
        etour.append(v)
        for nv in g[v]:
            if not visited[nv]:
                parent[nv] = v
                dfs(nv,d+1)
        rs[v] = len(vtour)
        etour.append(-v)
        vtour.append(parent[v])
    dfs(s,0)
    return ls,rs,etour,vtour,parent,depth

ls,rs,etour,vtour,parent,depth = eulerTour(g,1)
paths = []
depthind = [depth[v] for v in vtour]

for u,v in uv:
    l,r = ls[u],ls[v]
    l,r = (l,r) if l < r else (r,l)
    lcaind = depthind[l:r].index(min(depthind[l:r]))
    lca = vtour[l+lcaind]
    lpath = []
    x = u
    while x != lca:
        lpath.append(pathnum[tuple(sorted((x,parent[x])))])
        x = parent[x]
    rpath = []
    x = v
    while x != lca:
        rpath.append(pathnum[tuple(sorted((x,parent[x])))])
        x = parent[x]
    path = set(lpath + rpath)
    h = sum([1<<i for i in path])
    paths.append(h)
    
ans = 2**(N-1)

memo = {1<<i:paths[i] for i in range(M)}
memo[0] = 0
for i in range(1,M+1):
    for vs in combinations(list(range(M)),i):
        sign = i % 2
        h = sum([1<<i for i in vs])
        ph = h ^ (1<<vs[-1])
        sect = memo[ph] | paths[vs[-1]]
        memo[h] = sect
        num = N-1 - str(bin(sect)).count('1')
        ans += (-1)**sign * (2**num)

print(ans)