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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Queue;

public class Main {
	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		Map<Integer, List<Hen>> map = new HashMap<Integer, List<Hen>>();
		for (int i = 0; i < n - 1; i++) {
			String[] sa = br.readLine().split(" ");
			Hen hen = new Hen();
			hen.a = Integer.parseInt(sa[0]);
			hen.b = Integer.parseInt(sa[1]);
			hen.c = Integer.parseInt(sa[2]);

			List<Hen> listA = map.get(hen.a);
			if (listA == null) {
				listA = new ArrayList<Hen>();
				map.put(hen.a, listA);
			}
			listA.add(hen);

			List<Hen> listB = map.get(hen.b);
			if (listB == null) {
				listB = new ArrayList<Hen>();
				map.put(hen.b, listB);
			}
			listB.add(hen);
		}

		String[] sa = br.readLine().split(" ");
		int q = Integer.parseInt(sa[0]);
		int k = Integer.parseInt(sa[1]);

		long[] d = new long[n + 1];
		Queue<Integer> que = new ArrayDeque<Integer>();
		que.add(k);
		while (!que.isEmpty()) {
			Integer cur = que.poll();
			List<Hen> list = map.get(cur);
			for (Hen o : list) {
				if (o.a == cur) {
					if (d[o.b] == 0 && o.b != k) {
						que.add(o.b);
						d[o.b] = d[o.a] + o.c; 
					}
				} else {
					if (d[o.a] == 0 && o.a != k) {
						que.add(o.a);
						d[o.a] = d[o.b] + o.c; 
					}
				}
			}
		}

		for (int i = 0; i < q; i++) {
			sa = br.readLine().split(" ");
			int x = Integer.parseInt(sa[0]);
			int y = Integer.parseInt(sa[1]);
			System.out.println(d[x] + d[y]);
		}
		br.close();
	}

	static class Hen {
		int a, b, c;
	}
}