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: Memory Limit Exceeded)


import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		try (Scanner sc = new Scanner(System.in)) {
			int n = sc.nextInt();
			int[][] map = new int[n][n];
			for (int i = 0; i < n; i++) {
				for (int j = 0; j < n; j++) {
					map[i][j] = (i == j) ? 0 : -1;
				}
			}

			for (int i = 0; i < n - 1; i++) {
				int a = sc.nextInt() - 1;
				int b = sc.nextInt() - 1;
				int c = sc.nextInt();
				map[a][b] = c;
				map[b][a] = c;
			}

			int q = sc.nextInt();
			int k = sc.nextInt() - 1;
			long[] distance = new long[n];
			dijkstra(map, k, distance);

			for (int i = 0; i < q; i++) {
				int x = sc.nextInt() - 1;
				int y = sc.nextInt() - 1;
				System.out.println(distance[x] + distance[y]);
			}
		}
	}

	public static void dijkstra(int[][] map, int src, long[] distance) {
		int nTown = distance.length;
		boolean[] fixed = new boolean[nTown];
		for (int i = 0; i < nTown; i++) {
			distance[i] = Long.MAX_VALUE;
			fixed[i] = false;
		}
		distance[src] = 0;
		while (true) {
			int marked = minIndex(distance, fixed);
			if (marked < 0)
				return;
			if (distance[marked] == Integer.MAX_VALUE)
				return;
			fixed[marked] = true;
			for (int j = 0; j < nTown; j++) {
				if (map[marked][j] > 0 && !fixed[j]) {
					long newDistance = distance[marked] + map[marked][j];
					if (newDistance < distance[j])
						distance[j] = newDistance;
				}
			}
		}
	}

	static int minIndex(long[] distance, boolean[] fixed) {
		int idx = 0;
		for (; idx < fixed.length; idx++)
			if (!fixed[idx])
				break;
		if (idx == fixed.length)
			return -1;
		for (int i = idx + 1; i < fixed.length; i++)
			if (!fixed[i] && distance[i] < distance[idx])
				idx = i;
		return idx;
	}
}