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.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.rmi.server.ExportException;
import java.util.*;

public class Main {
    public static void main(String[] args) throws Exception {
        Main m = new Main();
        m.solve();
    }
    private void solve() throws Exception {
        FastScan scan = new FastScan(System.in);
        int N = scan.scanInt();
        List<List<Path>> graph = new ArrayList(N);
        for (int i = 0; i < N; i++) {
            graph.add(new ArrayList<>());
        }
        for (int i = 0; i < N - 1; i++) {
            int a = scan.scanInt()-1;
            int b = scan.scanInt()-1;
            long c = scan.scanLong();
            graph.get(a).add(new Path(b, c));
            graph.get(b).add(new Path(a, c));
        }
        int Q = scan.scanInt();
        int K = scan.scanInt()-1;
        Queue<Integer> queue = new ArrayDeque<>();
        long[] distances = new long[N];
        boolean[] visited = new boolean[N];
        queue.add(K);
        while(!queue.isEmpty()) {
            int current = queue.poll();
            visited[current] = true;
            for (Path p : graph.get(current)) {
                if (visited[p.to]) {
                    continue;
                }
                distances[p.to] = distances[current] + p.cost;
                queue.add(p.to);
            }
        }
        for (int i = 0; i < Q; i++) {
            int from = scan.scanInt() - 1;
            int to = scan.scanInt() - 1;
            System.out.println(distances[from] + distances[to]);
        }
    }

    class Path {
        int to;
        long cost;
        Path(int to, long cost) {
            this.to = to;
            this.cost = cost;
        }
    }
    class FastScan {
        BufferedReader br;
        StringTokenizer st;
        FastScan(InputStream is) {
            InputStreamReader isr = new InputStreamReader(is);
            this.br = new BufferedReader(isr);
        }
        String next() throws IOException {
            while (this.st == null || !this.st.hasMoreTokens()) {
                this.st = new StringTokenizer(br.readLine().trim());
            }
            return st.nextToken();
        }
        long scanLong() throws IOException {
            return Long.parseLong(this.next());
        }
        int scanInt() throws IOException {
            return Integer.parseInt(this.next());
        }
        double scanDouble() throws IOException {
            return Double.parseDouble(this.next());
        }
        char scanCharacter() throws IOException {
            return this.next().charAt(0);
        }
        String nextLine() throws IOException {
            return br.readLine().trim();
        }
    }
}