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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

n=gets.to_i
g=Array.new(n){[]}
(n-1).times{|i|
	a,b=gets.split.map &:to_i
	a-=1
	b-=1
	g[a]<<[b,i]
	g[b]<<[a,i]
}
m=gets.to_i
mask=Array.new(1<<m){0}
def collect(g,u,v,p)
	return 0 if u==v
	for t,i in g[u]
		next if t==p
		s=collect(g,t,v,u)
		return s|(1<<i) if s
	end
	nil
end
m.times{|j|
	u,v=gets.split.map &:to_i
	u-=1
	v-=1
	mask[1<<j]=collect(g,u,v,nil)
}
ans=1<<(n-1)
def popcount(n)
	s=0
	64.times{|i|s+=n[i]}
	s
end
(1...1<<m).each{|s|
	d=s&-s
	mask[s]=mask[s^d]|mask[d]
	if popcount(s)%2==0
		ans+=1<<(n-1-popcount(mask[s]))
	else
		ans-=1<<(n-1-popcount(mask[s]))
	end
}
puts ans