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: Wrong Answer)


import java.util.*;

public class Main {
    static Map<Integer, List<Path>> map;
    static int n;
    static int[] memo;
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        n = sc.nextInt();
        map = new HashMap<>();
        memo = new int[n+1];
        for (int i = 0; i < n - 1; i++) {
            int a = sc.nextInt();
            int b = sc.nextInt();
            int c = sc.nextInt();
            List<Path> tmp = map.get(a);
            if(tmp != null) {
                tmp.add(new Path(b, c));
            }
            else {
                List<Path> tmp1 = new ArrayList<>();
                tmp1.add(new Path(b, c));
                map.put(a, tmp1);
            }
            tmp = map.get(b);
            if(tmp != null) {
                tmp.add(new Path(a, c));
            }
            else {
                List<Path> tmp1 = new ArrayList<>();
                tmp1.add(new Path(a, c));
                map.put(b, tmp1);
            }
        }
        int Q = sc.nextInt();
        int k = sc.nextInt();
        Deque<Integer> q = new ArrayDeque<>();
        q.add(k);
        while (!q.isEmpty()) {
            int c = q.poll();
            for(Path next : map.get(c)){
                if(memo[next.a] != 0) {
                    continue;
                }
                memo[next.a] = memo[c] + next.b;
                q.add(next.a);
            }
        }
        for (int i = 0; i < Q; i++) {
            int a = sc.nextInt();
            int b = sc.nextInt();
            System.out.println(memo[a] + memo[b]);
        }
    }

    static class Path{
        int a;
        int b;

        public Path(int a, int b) {
            this.a = a;
            this.b = b;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Path path = (Path) o;
            return a == path.a &&
                    b == path.b;
        }

        @Override
        public int hashCode() {
            return Objects.hash(a, b);
        }
    }
}