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 (1.42.0) (judge verdict: Accepted)

use std::io::Read;
use std::collections::VecDeque;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();

    let answer = solve(&buf);

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

fn solve(input: &str) -> String {
    let mut iterator = input.split_whitespace();

    let n: usize = iterator.next().unwrap().parse().unwrap();
    let mut graph: Vec<Vec<(usize, usize)>> = vec![vec![]; n];
    for _ in 0..(n - 1) {
        let ai: usize = iterator.next().unwrap().parse().unwrap();
        let bi: usize = iterator.next().unwrap().parse().unwrap();
        let ci: usize = iterator.next().unwrap().parse().unwrap();
        let ai = ai - 1;
        let bi = bi - 1;
        graph[ai].push((bi, ci));
        graph[bi].push((ai, ci));
    }

    let q: usize = iterator.next().unwrap().parse().unwrap();
    let k: usize = iterator.next().unwrap().parse().unwrap();
    let k = k - 1;

    const INF: usize = std::usize::MAX;
    let mut costs: Vec<usize> = vec![INF; n];
    costs[k] = 0;
    let mut queue = VecDeque::new();
    queue.push_back((k, 0_usize));
    while let Some((u, cost)) = queue.pop_front() {
        for &(v, c) in &graph[u] {
            if costs[v] != INF {
                continue;
            }
            costs[v] = cost + c;
            queue.push_back((v, costs[v]));
        }
    }

    let mut result = String::new();
    for _ in 0..q {
        let x1: usize = iterator.next().unwrap().parse().unwrap();
        let y1: usize = iterator.next().unwrap().parse().unwrap();
        let x1 = x1 - 1;
        let y1 = y1 - 1;
        result.push_str(&format!("{}\n", costs[x1] + costs[y1]));
    }
    result.trim().to_string()
}