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)

fn get_line() -> String {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().to_string()
}

fn reads<T>() -> Vec<T>
    where
        T: std::str::FromStr,
        <T as std::str::FromStr>::Err: std::fmt::Debug {
    get_line().split(' ').map(|x| x.parse().unwrap()).collect()
}

fn readln<T>() -> T
    where
        T: std::str::FromStr,
        <T as std::str::FromStr>::Err: std::fmt::Debug {
    get_line().parse().unwrap()
}

use std::collections::BinaryHeap;
use std::cmp::Ordering;

#[derive(Clone, Copy, Eq, PartialEq)]
struct E {
    d: u64,
    v: usize,
}

impl Ord for E {
    fn cmp(&self, other: &Self) -> Ordering {
        other.d.cmp(&self.d)
    }
}

impl PartialOrd for E {
    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
        Some(self.cmp(other))
    }
}

fn main() {
    let inf = std::u64::MAX;

    let n = readln();

    let mut es = vec![vec![]; n];

    for _ in 0..(n - 1) {
        let abc: Vec<usize> = reads();
        es[abc[0] - 1].push((abc[1] - 1, abc[2] as u64));
        es[abc[1] - 1].push((abc[0] - 1, abc[2] as u64));
    }

    let qk: Vec<usize> = reads();
    let mut ds = vec![inf; n];
    let mut q = BinaryHeap::new();
    ds[qk[1] - 1] = 0;
    q.push(E{d: 0, v: qk[1] - 1});

    while let Some(e) = q.pop() {
        if e.d > ds[e.v] {
            continue;
        }

        for &(d, w) in &es[e.v] {
            if ds[d] > ds[e.v] + w {
                ds[d] = ds[e.v] + w;
                q.push(E{d: ds[d], v: d});
            }
        }
    }

    for _ in 0..qk[0] {
        let xy: Vec<usize> = reads();

        println!("{}", ds[xy[0] - 1] + ds[xy[1] - 1]);
    }
}