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)

macro_rules! scan {
    () => {
        {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            line.trim().to_string()
        }
    };
    (;;$n:expr) => {
        (0..$n).map(|_| scan!()).collect::<Vec<_>>()
    };
    ($t:ty) => {
        {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            line.trim().parse::<$t>().unwrap()
        }
    };
    ($($t:ty),*) => {
        {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            (
                $(iter.next().unwrap().parse::<$t>().unwrap(),)*
            )
        }
    };
    ($t:ty;;) => {
        {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            line.split_whitespace()
                .map(|t| t.parse::<$t>().unwrap())
                .collect::<Vec<_>>()
        }
    };
    ($t:ty;;$n:expr) => {
        (0..$n).map(|_| scan!($t;;)).collect::<Vec<_>>()
    };
    ($t:ty; $n:expr) => {
        (0..$n).map(|_|
                    scan!($t)
        ).collect::<Vec<_>>()
    };
    ($($t:ty),*; $n:expr) => {
        (0..$n).map(|_|
                    scan!($($t),*)
        ).collect::<Vec<_>>()
    };
}

struct Node {
    children: Vec<(usize, i64)>,
}

fn dfs(tree: &[Node], dists: &mut [i64], parent: usize) {
    for &(n, c) in tree[parent].children.iter() {
        if dists[n] == 1 << 60 {
            dists[n] = dists[parent] + c;
            dfs(tree, dists, n);
        }
    }
}

fn dists(tree: Vec<Node>, root: usize) -> Vec<i64> {
    let mut dists = vec![1 << 60; tree.len()];
    dists[root] = 0;
    dfs(&tree, &mut dists, root);

    dists
}
fn main() {
    let n = scan!(i64);
    let mut tree: Vec<Node> = (0..n).map(|_| Node { children: vec![] }).collect();

    for _ in 0..(n - 1) {
        let (a, b, c) = scan!(usize, usize, i64);
        tree[a - 1].children.push((b - 1, c));
        tree[b - 1].children.push((a - 1, c));
    }
    let (q, k) = scan!(i64, usize);
    let dists = dists(tree, k - 1);
    for _ in 0..q {
        let (x, y) = scan!(usize, usize);
        println!("{}", dists[x - 1] + dists[y - 1])
    }
}