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_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}
#[allow(unused_macros)]
macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};
    ($iter:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
    ($iter:expr, mut $var:ident $($r:tt)*) => {
        let mut $var = $iter.next().unwrap().parse::<usize>().unwrap();
        input_inner!{$iter $($r)*}
    };
    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
    ($iter:expr, $var:ident $($r:tt)*) => {
        let $var = $iter.next().unwrap().parse::<usize>().unwrap();
        input_inner!{$iter $($r)*}
    };
}
#[allow(unused_macros)]
macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };
    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };
    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };
    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };
    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().unwrap()
    };
}
#[allow(unused_macros)]
macro_rules! outbuf {
    ($var:ident) => {
        use std::io::{stdout, BufWriter, Write};
        let stdout = stdout();
        let mut $var = BufWriter::new(stdout.lock());
    };
}
use std::cell::RefCell;
fn main() {
    input! {n, ab: [(usize1, usize1); n-1], m, uv: [(usize1, usize1); m]};
    // outbuf! {out};
    let mut ans = 0;
    let mut graph = vec![vec![]; n];
    for (i, &(a, b)) in ab.iter().enumerate() {
        graph[a].push((b, i));
        graph[b].push((a, i));
    }
    let dfs = |u: usize, v: usize| {
        let path = RefCell::new(vec![]);
        let visited = RefCell::new(vec![false; n]);
        visited.borrow_mut()[u] = true;
        struct DFS<'s> {
            f: &'s Fn(&DFS, usize) -> bool,
        };
        {
            let dfs_ = DFS {
                f: &|dfsf, x| {
                    if x == v {
                        return true;
                    }
                    for &(y, i) in &graph[x] {
                        if !visited.borrow()[y] {
                            visited.borrow_mut()[y] = true;
                            if (dfsf.f)(dfsf, y) {
                                path.borrow_mut().push(i);
                                return true;
                            }
                        }
                    }
                    false
                },
            };
            (dfs_.f)(&dfs_, u);
        }
        path.into_inner()
            .into_iter()
            .map(|x| 1 << x)
            .fold(0, |acc, x| acc | x)
    };
    let e = uv.into_iter().map(|(u, v)| dfs(u, v)).collect::<Vec<_>>();
    for i in 0..(1 << m) {
        let mut mask: usize = 0;
        let mut k = i;
        for &b in &e {
            if k % 2 == 1 {
                mask |= b;
            }
            k >>= 1;
        }
        let p = 1isize << (n - 1 - mask.count_ones() as usize);
        let pm = if (i as usize).count_ones() as usize % 2 == 1 {-1} else {1};
        ans += p * pm
    }
    println!("{}", ans);
}