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)

#![allow(unused_imports)]
#![allow(non_snake_case)]
use std::cmp::*;
use std::collections::*;
use std::io::Write;

#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), std::io::stderr());
            writeln!(err, "{} = {:?}", e, $e).unwrap()
        })*
    };
}

#[derive(Clone)]
struct Edge {
    to: usize,
    idx: usize,
}

fn dfs(
    cur: usize,
    parent: usize,
    goal: usize,
    edges: &Vec<Vec<Edge>>,
    throughed: &mut Vec<usize>,
) -> bool {
    if cur == goal {
        return true;
    }
    for &Edge { to, idx } in edges[cur].iter() {
        if to == parent {
            continue;
        }
        if dfs(to, cur, goal, edges, throughed) {
            throughed.push(idx);
            return true;
        }
    }
    false
}

fn main() {
    let n = read::<usize>();
    let mut edges = vec![vec![]; n];
    for i in 0..n - 1 {
        let v = read_vec::<usize>();
        let (a, b) = (v[0] - 1, v[1] - 1);
        edges[a].push(Edge { to: b, idx: i });
        edges[b].push(Edge { to: a, idx: i });
    }

    let m = read::<usize>();
    let mut constraints = vec![];
    for _ in 0..m {
        let v = read_vec::<usize>();
        let (u, v) = (v[0] - 1, v[1] - 1);
        constraints.push((u, v));
    }

    let mut disallowed = vec![0i64; m];

    for i in 0..m {
        let mut throughed = vec![];
        let (u, v) = constraints[i];
        dfs(u, n + 1, v, &edges, &mut throughed);
        for idx in throughed {
            disallowed[i] |= 1 << idx;
        }
    }

    let mut ans = 0i64;
    for state in 0..1 << m {
        let mut flags = 0i64;

        for j in 0..m {
            if state >> j & 1 == 1 {
                flags |= disallowed[j];
            }
        }

        if (state as u64).count_ones() % 2 == 0 {
            ans += 1 << (n as u32 - 1 - flags.count_ones());
        } else {
            ans -= 1 << (n as u32 - 1 - flags.count_ones());
        }
    }
    println!("{}", ans);
}

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}