Problem:
Score : 400 points

Problem Statement

You are given a tree with N vertices.

Here, a tree is a kind of graph, and more specifically, a connected undirected graph with N-1 edges, where N is the number of its vertices.

The i-th edge (1≤i≤N-1) connects Vertices a_i and b_i, and has a length of c_i.

You are also given Q queries and an integer K. In the j-th query (1≤j≤Q):

find the length of the shortest path from Vertex x_j and Vertex y_j via Vertex K.

Constraints

3≤N≤10^5

1≤a_i,b_i≤N (1≤i≤N-1)

1≤c_i≤10^9 (1≤i≤N-1)

The given graph is a tree.

1≤Q≤10^5

1≤K≤N

1≤x_j,y_j≤N (1≤j≤Q)

x_j≠y_j (1≤j≤Q)

x_j≠K,y_j≠K (1≤j≤Q)

Input

Input is given from Standard Input in the following format:

N
a_1 b_1 c_1
:
a_{N-1} b_{N-1} c_{N-1}
Q K
x_1 y_1
:
x_{Q} y_{Q}

Output

Print the responses to the queries in Q lines.

In the j-th line j(1≤j≤Q), print the response to the j-th query.

Sample Input 1

5
1 2 1
1 3 1
2 4 1
3 5 1
3 1
2 4
2 3
4 5

Sample Output 1

3
2
4

The shortest paths for the three queries are as follows:

Query 1: Vertex 2 → Vertex 1 → Vertex 2 → Vertex 4 : Length 1+1+1=3

Query 2: Vertex 2 → Vertex 1 → Vertex 3 : Length 1+1=2

Query 3: Vertex 4 → Vertex 2 → Vertex 1 → Vertex 3 → Vertex 5 : Length 1+1+1+1=4

Sample Input 2

7
1 2 1
1 3 3
1 4 5
1 5 7
1 6 9
1 7 11
3 2
1 3
4 5
6 7

Sample Output 2

5
14
22

The path for each query must pass Vertex K=2.

Sample Input 3

10
1 2 1000000000
2 3 1000000000
3 4 1000000000
4 5 1000000000
5 6 1000000000
6 7 1000000000
7 8 1000000000
8 9 1000000000
9 10 1000000000
1 1
9 10

Sample Output 3

17000000000

Solution in Rust (1.15.1) (judge verdict: Time Limit Exceeded)

use std::io::{BufRead, Write};
use std::io;
use std::collections::{HashMap, HashSet};
use std::usize;

// Each node is represented as an `usize`, for a shorter implementation.
#[derive(Copy, Clone, Debug)]
struct Edge {
    node: usize,
    cost: usize,
}

fn shortest_path(adjacency: &Vec<Vec<Edge>>, start: usize, goal: usize) -> Option<usize> {
    let mut visited: HashSet<usize> = HashSet::new();
    let mut path: HashMap<usize, (usize, usize)> = HashMap::new();
    let mut queue: Vec<usize> = vec![start];
    visited.insert(start);
    while let Some(x) = queue.pop() {
        if x == goal {
            let mut sum = 0;
            let mut current = x;
            while let Some(&(next, c)) = path.get(&current) {
                sum += c;
                current = next;
            }
            return Some(sum);
        }
        for y in &adjacency[x] {
            if visited.insert(y.node) {
                path.insert(y.node, (x, y.cost));
                queue.push(y.node);
            }
        }
    }
    None
}

fn solve<R: BufRead, W: Write>(mut input: R, mut output: W) {
    let mut s = String::new();
    input.read_line(&mut s).unwrap();
    let n: usize = s.trim().parse().unwrap();
    let mut adjacency = vec![Vec::<Edge>::new(); n];
    for _ in 0..n - 1 {
        s.clear();
        input.read_line(&mut s).unwrap();
        let (a, b, c): (usize, usize, usize) = {
            let mut split = s.split_whitespace();
            let a = split.next().unwrap().parse().unwrap();
            let b = split.next().unwrap().parse().unwrap();
            let c = split.next().unwrap().parse().unwrap();
            (a, b, c)
        };
        adjacency[b - 1].push(Edge {
            node: a - 1,
            cost: c,
        });
        adjacency[a - 1].push(Edge {
            node: b - 1,
            cost: c,
        });
    }
    s.clear();
    input.read_line(&mut s).unwrap();
    let (q, k): (usize, usize) = {
        let mut split = s.split_whitespace();
        let a = split.next().unwrap().parse().unwrap();
        let b = split.next().unwrap().parse().unwrap();
        (a, b)
    };
    for _ in 0..q {
        s.clear();
        input.read_line(&mut s).unwrap();
        let (x, y): (usize, usize) = {
            let mut split = s.split_whitespace();
            let a = split.next().unwrap().parse().unwrap();
            let b = split.next().unwrap().parse().unwrap();
            (a, b)
        };
        writeln!(
            output,
            "{}",
            shortest_path(&adjacency, x - 1, k - 1).unwrap() +
                shortest_path(&adjacency, k - 1, y - 1).unwrap()
        ).unwrap();
    }
}

fn main() {
    let stdin = io::stdin();
    let stdout = io::stdout();
    solve(stdin.lock(), stdout.lock());
}

#[cfg(test)]
mod tests {
    fn test(input: &str, output: &str) {
        let mut v: Vec<u8> = Vec::new();
        ::solve(input.as_bytes(), &mut v);
        assert_eq!(String::from_utf8(v).unwrap(), output);
    }

    #[test]
    fn case1() {
        test(
            "5
1 2 1
1 3 1
2 4 1
3 5 1
3 1
2 4
2 3
4 5\n",
            "3
2
4\n",
        );
    }
    #[test]
    fn case2() {
        test(
            "7
1 2 1
1 3 3
1 4 5
1 5 7
1 6 9
1 7 11
3 2
1 3
4 5
6 7\n",
            "5
14
22\n",
        );
    }
    #[test]
    fn case3() {
        test(
            "10
1 2 1000000000
2 3 1000000000
3 4 1000000000
4 5 1000000000
5 6 1000000000
6 7 1000000000
7 8 1000000000
8 9 1000000000
9 10 1000000000
1 1
9 10\n",
            "17000000000\n",
        );
    }
}