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: Accepted)

N = gets.to_i
G = Array.new(N + 1){[]}
(N - 1).times{|i| a, b = gets.split.map(&:to_i); G[a] << [b, i]; G[b] << [a, i]}
M = gets.to_i
UVs = M.times.map{gets.split.map(&:to_i)}

def dfs(s, g)
  st = [[s, nil]]
  d = []; d[s] = true
  while !st.empty?
    u, _ = st.last
    return st.map(&:last).compact.inject(0){|s, i| s + (1<<i)} if u == g
    if t = G[u].find{|v, _| d[v].nil?}
      d[t[0]] = true
      st << t
    else
      st.pop
    end
  end
end

as = UVs.map{|u, v| dfs(u, v)}
res = (1 .. M).inject(0) do |r, n|
  val = as.combination(n).inject(0) do |v, a|
    b = a.inject(:|).to_s(2).count('1')
    v + (1 << (N - 1 - b))
  end
  n.odd? ? r + val : r - val
end
puts (1 << (N - 1)) - res