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: Runtime Error)

import java.util.*;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);

		int n = sc.nextInt();
		Dijkstra dj = new Dijkstra(n);

		for (int k = 0; k < n - 1; k++) {
			int i, j;
			i = sc.nextInt();
			j = sc.nextInt();

			dj.setE(i, j, sc.nextInt());
		}

		int q = sc.nextInt();
		int k = sc.nextInt();

		dj.dijkstra(k);
		long D[] = new long[n+1];
		for (int i = 0; i <= n; i++) {
			D[i] = dj.D[i];
		}

		for (int i = 0; i < q; i++) {
			System.out.println(dj.D[sc.nextInt()] + D[sc.nextInt()]);
		}

	}

	static class Dijkstra {
		DijList[] e;
		boolean[] S;
		long D[];
		int n;
		int s;

		Dijkstra(int n) {
			this.n = n;
			e = new DijList[n+1];
			S = new boolean[n+1];
			D = new long[n+1];
			for (int i = 0; i <= n; i++) {
				e[i] = new DijList(i, 0);
			}
		}

		void setE(int i, int j, int e) {
			this.e[i].setNext(new DijList(j, e));
			this.e[j].setNext(new DijList(i, e));
		}

		void dijkstra (int s) {
			this.s = s;
			for (int i = 1; i <= n; i++) {
				D[i] = Long.MAX_VALUE;
				S[i] = false;
			}
			D[s] = 0;
			for (int i = 1; i <= n; i++) {
				long min = Long.MAX_VALUE;
				int k = 0;
				for (int j = 1; j <= n; j++) {
					if (!S[j] && D[j] < min) {
						min = D[j];
						k = j;
					}
				}
				S[k] = true;
				DijList conec = e[k];
				DijList jud;
				for (int j = 1; j <= n; j++) {
					jud = conec.get(j);
					if (jud == null) continue;
					conec = jud;
					long temp = conec.w;
					if (temp != -1 && !S[j]) {
						long temp2 = D[k] + temp;
						D[j] = D[j] < temp2 ? D[j] : temp2;
					}
				}
			}
		}
	}

	static class DijList {
		DijList next;
		DijList back;
		int n;
		long w;

		public DijList(int n, long w) {
			this.n = n;
			this.w = w;
		}

		public void setNext(DijList next) {
			if (this.next == null) {
			       	this.next = next;
				next.back = this;
			} else {
				if (next.n > this.n) {
					this.next.setNext(next);
				} else {
					this.back.next = next;
					next.back = this.back;
					next.next = this;
					this.back = next;
				}	
			}
		}

		public DijList get(int n) {
			if (this.n == n) return this;
			if (this.next == null) return null;
			return this.next.get(n);
		}
	}
}