Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

3
1 2
2 3
1
1 3

Sample Output 1

3

The tree in this input is shown below:

All of the M restrictions will be satisfied if Edge 1 and 2 are respectively painted (white, black), (black, white), or (black, black), so the answer is 3.

Sample Input 2

2
1 2
1
1 2

Sample Output 2

1

The tree in this input is shown below:

All of the M restrictions will be satisfied only if Edge 1 is painted black, so the answer is 1.

Sample Input 3

5
1 2
3 2
3 4
5 3
3
1 3
2 4
2 5

Sample Output 3

9

The tree in this input is shown below:

Sample Input 4

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

Sample Output 4

62

The tree in this input is shown below:

Solution in Julia (0.5.0) (judge verdict: Accepted)

const N=parse(Int,readline())
const U=Int[]
const V=Int[]
const G=[Int[] for _=1:N]
for i=1:N-1
	u,v=map(x->parse(Int,x),split(readline()))
	push!(U,u)
	push!(V,v)
	push!(G[u],v)
	push!(G[v],u)
end
const depth=zeros(Int,N)
const subtree=zeros(Int,N)
function dfs(u,p,d)
	depth[u]=d
	subtree[u]=2^u
	for v=G[u]
		if v!=p
			subtree[u]+=dfs(v,u,d+1)
		end
	end
	subtree[u]
end
dfs(1,0,0)
const M=parse(Int,readline())
const check=zeros(Int,N-1)
for i=1:M
	a,b=map(x->parse(Int,x),split(readline()))
	test=2^a+2^b
	for j=1:N-1
		w=depth[U[j]]<depth[V[j]] ? V[j] : U[j]
		x=test&subtree[w]
		if x!=test&&x!=0
			check[j]+=2^(i-1)
		end
	end
end
function main()
	ans=0
	for i=0:2^M-1
		cnt=N-1
		for j=1:N-1
			if (check[j]&i)!=0
				cnt-=1
			end
		end
		now=2^cnt
		parity=0
		for j=0:M-1
			if (i>>j)%2==1
				parity+=1
			end
		end
		ans+=parity%2==0 ? now : -now
	end
	println(ans)
end
main()