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(dead_code)]
fn is_whitespace(c: &char) -> bool {
    c.is_whitespace()
}

#[allow(dead_code)]
fn is_eol(c: &char) -> bool {
    ['\r', '\n'].contains(c)
}

#[allow(unused_macros)]
macro_rules! input {
    ($var:ident, $($r:tt)*) => {
        input_inner!{$var, $($r)*}
    };

    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        #[allow(unused_mut, unused_variables, bare_trait_objects)]
        let mut next = move |f: &Fn(&char)->bool| -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|f(&c))
                .take_while(|c|!f(&c))
                .collect()
        };
        input_inner!{next, $($r)*};
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; eol ]) => {
        $next(&is_eol).split(' ').map(|x| x.parse::<$t>().unwrap()).collect::<Vec<_>>()
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, bytes) => {
        read_value!($next, String).into_bytes()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, parser) => {
        $next
    };

    ($next:expr, $t:ty) => {
        $next(&is_whitespace).parse::<$t>().expect("Parse error")
    };
}

#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::{BinaryHeap, HashMap};

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

#[allow(dead_code)]
type Graph = Vec<Vec<Edge>>;
#[allow(dead_code)]
const M: usize = 1e9 as usize + 7;

fn dfs(pos: usize, par: usize, to: usize, graph: &Graph, edges: &mut Vec<usize>) -> bool {
    if to == pos {
        return true;
    }
    for next in &graph[pos] {
        if next.to == par {
            continue;
        }
        let res = dfs(next.to, pos, to, graph, edges);
        if res {
            edges.push(next.id);
            return true;
        }
    }
    false
}

fn main() {
    input! {
        n: usize,
        edges: [(usize1, usize1); n - 1],
        m: usize,
        consts: [(usize1, usize1); m],
    }

    let mut graph = vec![vec![]; n];
    for (i, &(f, t)) in edges.iter().enumerate() {
        graph[f].push(Edge {
            from: f,
            to: t,
            id: i,
        });
        graph[t].push(Edge {
            from: t,
            to: f,
            id: i,
        });
    }

    let mut edge_set = vec![];

    for &(u, v) in &consts {
        let mut edges = vec![];
        dfs(u, u, v, &graph, &mut edges);
        let mut set = 0;
        for e in edges {
            set |= 1 << e;
        }
        edge_set.push(set);
    }

    let mut ans = 0i64;

    for i in 0..1 << m {
        let mut set = 0usize;
        for j in 0..m {
            if i >> j & 1 == 1 {
                set |= edge_set[j];
            }
        }
        let bits = set.count_ones();
        let cnt = 1usize << (n as u32 - 1 - bits);
        if (i as usize).count_ones() % 2 == 0 {
            ans += cnt as i64;
        } else {
            ans -= cnt as i64;
        }
    }

    println!("{}", ans);
}