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

public class Main {
    int n;
    ArrayList<Edge>[] es;
    int q, k;
    int[] xs, ys;

    public static void main(String[] args) {
        Main m = new Main();
        m.read();
        m.solve();
    }

    private void read() {
        Scanner sc = new Scanner(System.in);
        n = sc.nextInt();
        es = new ArrayList[n];
        for (int i = 0; i < n; i++)
            es[i] = new ArrayList<>();
        for (int i = 1; i < n; i++) {
            int a = sc.nextInt()-1;
            int b = sc.nextInt()-1;
            long c = sc.nextLong();
            es[a].add(new Edge(a, b, c));
            es[b].add(new Edge(b, a, c));
        }
        q = sc.nextInt(); k = sc.nextInt()-1;
        xs = new int[q]; ys = new int[q];
        for (int i = 0; i < q; i++) {
            xs[i] = sc.nextInt() - 1;
            ys[i] = sc.nextInt() - 1;
        }
    }

    private void solve() {
        long[] ret = new long[n];
        Arrays.fill(ret, Long.MAX_VALUE);
        boolean[] used = new boolean[n];
        dfs(k, 0L, used, ret);
        long d1, d2;
        for (int i = 0; i < q; i++) {
            d1 = ret[xs[i]]; d2 = ret[ys[i]];
            System.out.println(d1+d2);
        }
    }


    private void dfs(int cur, long cost, boolean[] used, long[] path) {
        if (used[cur])
            return;
        used[cur] = true;
        path[cur] = cost;
        for (Edge e: es[cur]) {
            if (!used[e.b]) {
                dfs(e.b, cost + e.c, used, path);
            }
        }
    }

    private class Edge {
        int a, b;
        long c;
        Edge(int a, int b, long c) {
            this.a = a;
            this.b = b;
            this.c = c;
        }
    }
}