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)

use std::collections::VecDeque;

fn main() {
    let mut sc = Scanner::new();
    let n: usize = sc.read();
    let mut graph: Vec<Vec<(usize, usize)>> = (0..n).map(|_| Vec::new()).collect();
    for _ in 0..(n - 1) {
        let a = sc.read::<usize>() - 1;
        let b = sc.read::<usize>() - 1;
        let c = sc.read::<usize>();
        graph[a].push((b, c));
        graph[b].push((a, c));
    }

    let q: usize = sc.read();
    let k: usize = sc.read::<usize>() - 1;

    let mut dist = vec![std::usize::MAX; n];
    dist[k] = 0;

    let mut queue = VecDeque::new();
    queue.push_back(k);
    while !queue.is_empty() {
        let v = queue.pop_front().unwrap();
        for e in &graph[v] {
            let (to, cost) = *e;
            if dist[to] <= dist[v] + cost { continue; }
            dist[to] = dist[v] + cost;
            queue.push_back(to);
        }
    }

    for _ in 0..q {
        let x = sc.read::<usize>() - 1;
        let y = sc.read::<usize>() - 1;
        println!("{}", dist[x] + dist[y]);
    }
}

struct Scanner {
    ptr: usize,
    length: usize,
    buf: Vec<u8>,
    small_cache: Vec<u8>,
}

impl Scanner {
    fn new() -> Scanner {
        Scanner { ptr: 0, length: 0, buf: vec![0; 1024], small_cache: vec![0; 1024] }
    }

    fn load(&mut self) {
        use std::io::Read;
        let mut s = std::io::stdin();
        self.length = s.read(&mut self.buf).unwrap();
    }

    fn byte(&mut self) -> u8 {
        if self.ptr >= self.length {
            self.ptr = 0;
            self.load();
            if self.length == 0 {
                self.buf[0] = b'\n';
                self.length = 1;
            }
        }

        self.ptr += 1;
        return self.buf[self.ptr - 1];
    }

    fn is_space(b: u8) -> bool { b == b'\n' || b == b'\r' || b == b'\t' || b == b' ' }

    fn read<T>(&mut self) -> T where T: std::str::FromStr, T::Err: std::fmt::Debug, {
        let mut b = self.byte();
        while Scanner::is_space(b) {
            b = self.byte();
        }

        for pos in 0..self.small_cache.len() {
            self.small_cache[pos] = b;
            b = self.byte();
            if Scanner::is_space(b) {
                return String::from_utf8_lossy(&self.small_cache[0..(pos + 1)]).parse().unwrap();
            }
        }

        let mut v = self.small_cache.clone();
        while !Scanner::is_space(b) {
            v.push(b);
            b = self.byte();
        }
        return String::from_utf8_lossy(&v).parse().unwrap();
    }
}