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;
#[allow(unused_imports)]
use proconio::marker::{Bytes, Chars};
#[allow(unused_imports)]
use std::cmp::{min, max};
use std::collections::VecDeque;

fn main() {
	input! {
		n: usize,
		abc: [(usize, usize, usize); n-1],
		q: usize,
		k: usize,
		xy: [(usize, usize); q],
	}

	let inf = 9999999999999999999usize;

	let mut node: Vec<Vec<(usize, usize)>> = vec![vec![]; n];
	for i in 0..n-1 {
		node[abc[i].0-1].push((abc[i].1-1, abc[i].2));
		node[abc[i].1-1].push((abc[i].0-1, abc[i].2));
	}

	let mut m: Vec<usize> = vec![inf; n];
	let mut que = VecDeque::new();

	m[k-1] = 0;
	que.push_back(k-1);
	while que.len() > 0 {
		let tmp = que.pop_front().unwrap();
		for i in 0..node[tmp].len() {
			if m[node[tmp][i].0] != inf {
				continue;
			}
			m[node[tmp][i].0] = m[tmp] + node[tmp][i].1;
			que.push_back(node[tmp][i].0);
		}
	}

	for i in 0..q {
		println!("{}", m[xy[i].0-1] + m[xy[i].1-1]);
	}
}