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: Runtime Error)

#[allow(unused_macros)]
macro_rules! parse_line {
    ( $t:ty ) => (
        {
            let mut line = String::new();
            ::std::io::stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            iter.next().unwrap().parse::<$t>().unwrap()
        }
    );

    ( $( $t:ty), +) => (
        {
            let mut line = String::new();
            ::std::io::stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            ( $(iter.next().unwrap().parse::<$t>().unwrap()),* )
        }
    );
}

#[allow(unused_macros)]
macro_rules! read_line {
    () => (
        {
            let mut line = String::new();
            ::std::io::stdin().read_line(&mut line).unwrap();
            line.pop();
            line
        }
    )
}

#[allow(unused_macros)]
macro_rules! parse_vec {
    ( $t:ty ) => (
        {
            let mut line = String::new();
            ::std::io::stdin().read_line(&mut line).unwrap();
            let iter = line.split_whitespace();
            iter.map(|v| v.parse::<$t>().unwrap()).collect::<Vec<_>>()
        }
    )
}

use std::collections::HashMap;

fn dfs(table: &HashMap<usize, Vec<(usize, usize)>>, dists: &mut Vec<usize>, p: usize, d: usize) {
    dists[p] = d;

    if !table.contains_key(&p) { return }

    for &(b, c) in table.get(&p).unwrap().iter() {
        if dists[b] < std::usize::MAX { continue }

        dfs(table, dists, b, d+c);
    }
}

fn solve(abc: Vec<(usize, usize, usize)>, k:usize, xy: Vec<(usize, usize)>) -> Vec<usize> {

    let mut table = HashMap::new();

    for (a,b,c) in abc {
        {
            let x = table.entry(a).or_insert(vec![]);
            x.push((b, c));
        }

        {
            let x = table.entry(b).or_insert(vec![]);
            x.push((a, c));
        }

    }

    let mut dists = vec![std::usize::MAX; 100001];

    dfs(&table, &mut dists, k, 0);

    xy.iter().map(|&(x, y)| dists[x] + dists[y]).collect()
}

fn main() {
    let n = parse_line!(usize);
    let abc = (0..n).map(|_| parse_line!(usize, usize, usize)).collect();

    let (q, k) = parse_line!(usize, usize);
    let xy = (0..q).map(|_| parse_line!(usize, usize)).collect();

    for i in solve(abc, k, xy).iter() {
        println!("{}", i);
    }
}

#[test]
fn solve_test() {
    assert_eq!(solve(vec![(1,2,1),
                          (1,3,1),
                          (2,4,1),
                          (3,5,1)], 1,
                     vec![(2,4),
                          (2,3),
                          (4,5)]), vec![3,2,4]);

    assert_eq!(solve(vec![(1,2,1),
                          (1,3,3),
                          (1,4,5),
                          (1,5,7),
                          (1,6,9),
                          (1,7,11)],
                     2,
                     vec![(1,3),
                          (4,5),
                          (6,7)]), vec![5,14,22]);

    assert_eq!(solve(vec![(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,
                     vec![(9, 10)]), vec![17000000000]);
}