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 Rust (1.42.0) (judge verdict: Accepted)

struct DFS {
    g: Vec<Vec<(usize, usize)>>,
    set: Vec<Vec<usize>>,
}

impl DFS {
    fn new(n: usize) -> DFS {
        DFS {
            g: vec![vec![]; n],
            set: vec![vec![0; n]; n],
        }
    }

    fn search(&mut self, r: usize, u: usize, p: usize, s: usize) {
        self.set[r][u] = s;
        for (v, t) in self.g[u].clone() {
            if v != p {
                self.search(r, v, u, s | t);
            }
        }
    }
}

fn main() {
    let n: usize = {
        let mut buf = String::new();
        std::io::stdin().read_line(&mut buf).unwrap();
        buf.trim_end().parse().unwrap()
    };
    let mut dfs = DFS::new(n);
    for i in 0..(n - 1) {
        let [a, b]: [usize; 2] = {
            let mut buf = String::new();
            std::io::stdin().read_line(&mut buf).unwrap();
            let mut iter = buf.split_whitespace();
            [
                iter.next().unwrap().parse::<usize>().unwrap() - 1,
                iter.next().unwrap().parse::<usize>().unwrap() - 1,
            ]
        };
        dfs.g[a].push((b, 1 << i));
        dfs.g[b].push((a, 1 << i));
    }
    for i in 0..n {
        dfs.search(i, i, !0, 0);
    }
    let m: usize = {
        let mut buf = String::new();
        std::io::stdin().read_line(&mut buf).unwrap();
        buf.trim_end().parse().unwrap()
    };
    let mut set: Vec<usize> = Vec::with_capacity(m);
    for _ in 0..m {
        let [u, v]: [usize; 2] = {
            let mut buf = String::new();
            std::io::stdin().read_line(&mut buf).unwrap();
            let mut iter = buf.split_whitespace();
            [
                iter.next().unwrap().parse::<usize>().unwrap() - 1,
                iter.next().unwrap().parse::<usize>().unwrap() - 1,
            ]
        };
        set.push(dfs.set[u][v]);
    }

    let mut ans = 1usize << (n - 1);
    for i in 1usize..(1 << m) {
        let mut sum = 0;
        for j in 0..m {
            if i & (1 << j) > 0 {
                sum |= set[j];
            }
        }
        let res = 1 << (n - 1 - sum.count_ones() as usize);
        if i.count_ones() % 2 == 1 {
            ans -= res;
        } else {
            ans += res;
        }
    }
    println!("{}", ans);
}