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 (1.15.1) (judge verdict: Accepted)

use std::io::{stdin, Read};

macro_rules! parse {
    ($it: ident) => {
        $it.next().unwrap().parse().unwrap()
    };
    ($it: ident,2) => {
        (parse!($it), parse!($it))
    };
    ($it: ident,3) => {
        (parse!($it), parse!($it), parse!($it))
    };
    ($it: ident,4) => {
        (parse!($it), parse!($it), parse!($it), parse!($it))
    };
    ($it: ident, $n: expr) => {
        (&mut $it).take($n).map(|e| e.parse().unwrap()).collect();
    };
}

fn solve(s: &str) {
    let mut it = s.split_whitespace();
    let n: usize = parse!(it);
    let mut g: Vec<Vec<usize>> = vec![vec![]; n];
    let mut e = std::collections::HashMap::new();
    for i in 0..(n - 1) {
        let (a, b): (usize, usize) = parse!(it, 2);
        g[a - 1].push(b - 1);
        g[b - 1].push(a - 1);
        e.insert((a - 1, b - 1), i);
        e.insert((b - 1, a - 1), i);
    }
    let m: usize = parse!(it);
    let get_path = |i: usize, j: usize| -> usize {
        let mut stack = vec![(i, 0)];
        let mut seen = vec![false; n];
        while let Some((u, mut path)) = stack.pop() {
            for &v in &g[u] {
                if !seen[v] {
                    seen[v] = true;
                    let path = path | 1 << e[&(u, v)];
                    if v == j {
                        return path;
                    }
                    stack.push((v, path));
                }
            }
        }
        unreachable!()
    };

    let mut paths = vec![];
    for _ in 0..m {
        let (a, b): (usize, usize) = parse!(it, 2);
        paths.push(get_path(a - 1, b - 1));
    }

    let mut whites = 0i64;
    for i in 1usize..(1 << m) {
        let positive = i.count_ones() % 2 == 1;
        let mut path = 0;
        for j in 0..m {
            if (i >> j) & 1 == 1 {
                path |= paths[j];
            }
        }
        whites += 2usize.pow((n - 1 - path.count_ones() as usize) as u32) as i64
            * if positive { 1 } else { -1 };
    }
    println!("{}", 2usize.pow((n - 1) as u32) - (whites as usize));
}

fn main() {
    let mut s = String::new();
    stdin().read_to_string(&mut s).unwrap();
    solve(&s);
}

#[cfg(test)]
mod tests {
    use super::*;
    #[test]
    fn test_input() {
        let s = "
        5
        1 2
        3 2
        3 4
        5 3
        3
        1 3
        2 4
        2 5
        ";
        solve(s);
    }
}