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: Accepted)

use std::cmp::Ordering;
use std::collections::BinaryHeap;
const INF: i64 = std::i64::MAX;

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()
}

#[derive(PartialEq, Debug)]
struct MinInt {
    value: i64,
}

impl Eq for MinInt {}

impl PartialOrd for MinInt {
    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
        other.value.partial_cmp(&self.value)
    }
}

impl Ord for MinInt {
    fn cmp(&self, other: &MinInt) -> Ordering {
        other.value.cmp(&self.value)
    }
}

fn make_pair(x: i64, y: usize) -> (MinInt, usize) {
    (MinInt { value: x }, y)
}

#[derive(Debug, Clone)]
struct Edge {
    to: usize,
    cost: i64,
}

fn solve(edges: &Vec<Vec<Edge>>, start_idx: usize, num_apexes: usize) -> Vec<i64> {
    let mut d = vec![INF; num_apexes];
    d[start_idx] = 0;
    let mut que = BinaryHeap::new();
    que.push(make_pair(0, start_idx));

    while let Some((u, v)) = que.pop() {
        if d[v] < u.value {
            continue;
        }
        for e in &edges[v] {
            if d[e.to] > d[v] + e.cost {
                d[e.to] = d[v] + e.cost;
                que.push(make_pair(d[e.to], e.to));
            }
        }
    }
    // println!("{:?}", d);
    d
}

fn main() {
    let n = read::<usize>();
    let mut edges: Vec<Vec<Edge>> = vec![Vec::new(); n];
    for i in 0..n - 1 {
        let v = read_vec::<usize>();
        let (a, b, c) = (v[0] - 1, v[1] - 1, v[2] as i64);
        edges[a].push(Edge { to: b, cost: c });
        edges[b].push(Edge { to: a, cost: c });
    }
    let v = read_vec::<usize>();
    let (q, k) = (v[0], v[1] - 1);

    let d = solve(&edges, k, n);
    for i in 0..q {
        let v = read_vec::<usize>();
        let (x, y) = (v[0] - 1, v[1] - 1);
        println!("{}", d[x] + d[y]);
    }
}