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 proconio::input;
use proconio::marker::Usize1;
use std::collections::BinaryHeap;
use std::cmp::Reverse;
fn main() {
    input! {
        n: usize,
        es: [(Usize1, Usize1, usize); n-1],
        q: usize, k: Usize1,
        qs: [(Usize1, Usize1); q]
    };
    let mut edges: Vec<Vec<(usize, usize)>> = vec![Vec::new(); n];
    for (a,b,c) in es {
        edges[a].push((b,c));
        edges[b].push((a,c));
    }
    let inf = std::usize::MAX;
    let mut d = vec![inf; n];
    let mut heap = BinaryHeap::new();
    d[k] = 0;
    heap.push(Reverse((0, k)));
    while  !heap.is_empty() {
        let (dist, i) = heap.pop().unwrap().0;
        if d[i] < dist {
            continue;
        } else {
        for &(j, w) in &edges[i] {
            if d[j] > d[i] + w {
                d[j] = d[i] + w;
                heap.push(Reverse((d[j], j)));
            } else {}
        }}
    }
    for (x,y) in qs {
        println!("{}", d[x]+d[y]);
    }
}