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::io::*;
use std::str::FromStr;
use std::collections::BinaryHeap;

struct Graph {
    node: usize,
    directed: bool,
    graph: Vec<Vec<(usize, i64)>>,
}

impl Graph {
    fn new(n: usize, flag: bool) -> Graph {
        Graph { node: n, directed: flag, graph: vec![vec![]; n] }
    }

    fn add_edge(&mut self, start_node: usize, end_node: usize, cost: i64) -> () {
        self.graph[start_node].push((end_node, cost));
        if !self.directed { self.graph[end_node].push((start_node, cost)); }
    }
    fn dijkstra(&self, start_node: usize) -> Vec<i64> {
        let mut dist = vec![std::i64::MAX; self.node];
        dist[start_node] = 0;

        let mut queue: BinaryHeap<(i64, usize)> = BinaryHeap::new();
        queue.push((0, start_node));

        while !queue.is_empty() {
            let (min_dist, idx) = queue.pop().unwrap();
            if dist[idx] < -min_dist {
                continue;
            }
            for &(to, weight) in &self.graph[idx] {
                let cost_cand = dist[idx] + weight;
                if dist[to] > cost_cand {
                    dist[to] = cost_cand;
                    queue.push((-cost_cand, to));
                }
            }
        }
        dist
    }
}

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char) 
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

fn main() {
    let n: usize = read();

    let mut g = Graph::new(n+1, false);
    for _ in 0..n-1 {
        let a: usize = read();
        let b: usize = read();
        let c: i64 = read();
        g.add_edge(a, b, c);
    }

    let q: usize = read();
    let k: usize = read();

    let v = g.dijkstra(k);
    for _ in 0..q {
        let x: usize = read();
        let y: usize = read();
        let ans = v[x] + v[y];
        println!("{}", ans);
    }
}