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.util.Scanner;
import java.util.ArrayList;
import java.util.Arrays;

class Main {
    int N, Q, K;
    int[] x, y;
    ArrayList<Cost>[] list;
    long[] fromK;
    void solve(){
        Scanner in = new Scanner(System.in);
        N = in.nextInt();
        list = new ArrayList[N];
        fromK = new long[N];
        for(int i = 0; i < N; i++){
            list[i] = new ArrayList<>();
        }
        for(int i = 0; i < N - 1; i++){
            int a = in.nextInt() - 1, b = in.nextInt() - 1, c = in.nextInt();
            list[a].add(new Cost(b, c));
            list[b].add(new Cost(a, c));
        }
        Q = in.nextInt(); K = in.nextInt() - 1;
        x = new int[Q]; y = new int[Q];
        for(int i =0; i < Q; i++){
            x[i] = in.nextInt() - 1;
            y[i] = in.nextInt() - 1;
        }
        in.close();
        dfs(K, -1, 0);
        for(int i = 0; i < Q; i++){
            System.out.println(fromK[x[i]] + fromK[y[i]]);
        }
    }

    void dfs(int pos, int parent, long cost){
        fromK[pos] = cost;
        for(Cost c : list[pos]){
            if(c.to == parent){
                continue;
            }
            dfs(c.to, pos, cost + c.cost);
        }
    }
    public static void main(String[] args) {
        new Main().solve();
    }
}

class Cost{
    int to;
    int cost;
    Cost(int t, int c){
        to = t; cost = c;
    }
}