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

rel = Array.new(n+1){Array.new(n+1,false)}
(n-1).times do |i|
    a,b = gets.split.map(&:to_i)
    rel[a][b] = rel[b][a] = i
end

m = gets.to_i
pre = Hash.new
pas = []
m.times do 
    u,v = gets.split.map(&:to_i)
    sta = [u]
    while now = sta.pop
        rel[now].each_with_index do |e,i|
            next if !e
            pre[i] = [now,e]
            sta << i
            if i == v
                sta.clear
                break
            end
        end
    end

    pas << []
    while v != u
        pas.last << pre[v][1]
        v = pre[v][0]
    end
end

s0 = "0" * m
ans = 0
(2 ** (n-1)).times do |i|
    i = (s0 + i.to_s(2)).reverse

    j = false
    pas.each do |arr|
        j = false
        arr.each do |e|
            if i[e] == "1"
                j = true
                break
            end
        end

        break if !j
    end
    ans += 1 if j
end

puts ans