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)

pub fn main() {
    use std::io::Read;
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();
    let mut iter = buf.split_whitespace();
    
    let n: usize = iter.next().unwrap().parse().unwrap();
    let mut graph: Vec<Vec<(usize, u64)>> = vec![vec![];n];
    for _ in 0..n-1 {
        let a: usize = iter.next().unwrap().parse::<usize>().unwrap() - 1;
        let b: usize = iter.next().unwrap().parse::<usize>().unwrap() - 1;
        let c: u64 = iter.next().unwrap().parse().unwrap();
        graph[a].push((b, c));
        graph[b].push((a, c));
    }

    let q: usize = iter.next().unwrap().parse().unwrap();
    let k: usize = iter.next().unwrap().parse::<usize>().unwrap() - 1;
    
    
    // k -> i
    let mut costs: Vec<Option<u64>> = vec![None;n];
    costs[k] = Some(0);

    for _ in 0..q {
        let x: usize = iter.next().unwrap().parse::<usize>().unwrap() - 1;
        let y: usize = iter.next().unwrap().parse::<usize>().unwrap() - 1;
        let s = len(&graph, &mut costs, k, x, std::usize::MAX);
        let t = len(&graph, &mut costs, k, y, std::usize::MAX);
        println!("{}", s.unwrap() + t.unwrap());
    }
}

fn len(graph: &[Vec<(usize,u64)>], costs: &mut [Option<u64>], k: usize, cur: usize, pre: usize) -> Option<u64> {
    if let Some(v) = costs[cur] {
      return Some(v);
    }

    let mut ret: Option<u64> = None;
    for &(v, cost) in &graph[cur] {
        if pre == v {continue;}
        if let Some(rest) = len(graph,costs,k,v,cur) {
            if let Some(rr) = ret {
                ret = Some(std::cmp::min(rr, cost + rest));
            } else {
                ret = Some(cost + rest);
            }
        }
    }
    costs[cur] = ret;
    ret
}