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.Scanner;

public class Main {

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

	public void run() {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		long INF = 10000000000L;
		long g[][] = new long[n][n];
		for(int i=0; i<n; i++) {
			for(int j=0; j<n; j++) {
				g[i][j]=INF;
			}
		}
		for(int i=0; i<n-1; i++) {
			int a=sc.nextInt(); a--;
			int b=sc.nextInt(); b--;
			long c=sc.nextLong();
			g[a][b]=c;
			g[b][a]=c;
		}

		long d[] = new long[n];
		boolean used[] = new boolean[n];
		int q = sc.nextInt();
		int k = sc.nextInt(); k--;
		for(int i=0; i<n; i++) {
			d[i]=INF;
		}
		d[k]=0;


		while(true){
			long minv = INF;
			int u = -1;
			for(int i=0; i<n; i++) {
				if(used[i]) continue;
				if(d[i] == INF) continue;
				if(d[i] < minv) {
					minv = d[i];
					u = i;
				}
			}
			if(u == -1) break;
			used[u]=true;
			for(int i=0; i<n; i++) {
				if(used[i]) continue;
				if(g[u][i] == INF)continue;
				if(d[i] > d[u] + g[u][i]) {
					d[i] = d[u] + g[u][i];
				}
			}
		}

		for(int i=0; i<q; i++) {
			int x = sc.nextInt(); x--;
			int y = sc.nextInt(); y--;
			System.out.println(d[x] + d[y]);
		}
		sc.close();
	}

}