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: Time Limit Exceeded)

import java.io.BufferedInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.util.Arrays;

public class Main {

	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		long[][] map = new long[N][N];
		for (int i = 0; i < map.length; i++) {
			Arrays.fill(map[i], Long.MAX_VALUE / 2);
		}
		for (int i = 0; i < N; i++) {
			map[i][i] = 0;
		}

		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;
		Point[] points = new Point[Q];
		for (int i = 0; i < points.length; i++) {
			points[i] = new Point(sc.nextInt() - 1, sc.nextInt() - 1);
		}

		for (int i = 0; i < N; i++) {
			for (int j = 0; j < N; j++) {
				for (int k = 0; k < N; k++) {
					map[j][k] = Math.min(map[j][k], map[j][i] + map[i][k]);
				}
			}
		}

		for (int i = 0; i < points.length; i++) {
			Point point = points[i];
			System.out.println(map[point.x][K] + map[K][point.y]);
		}
	}

	private static class Point {
		private int x;
		private int y;

		public Point(int x, int y) {
			super();
			this.x = x;
			this.y = y;
		}

		public int getX() {
			return x;
		}

		public int getY() {
			return y;
		}

		@Override
		public int hashCode() {
			final int prime = 31;
			int result = 1;
			result = prime * result + x;
			result = prime * result + y;
			return result;
		}

		@Override
		public boolean equals(Object obj) {
			if (this == obj)
				return true;
			if (obj == null)
				return false;
			if (getClass() != obj.getClass())
				return false;
			Point other = (Point) obj;
			if (x != other.x)
				return false;
			if (y != other.y)
				return false;
			return true;
		}

		@Override
		public String toString() {
			return "Point [x=" + x + ", y=" + y + "]";
		}
	}

	private static boolean isDebug = System.getProperty("sun.desktop") != null;

	private static void debug(Object... o) {
		if (isDebug) {
			System.err.println(Arrays.deepToString(o));
		}
	}

	public static class Scanner {
		private BufferedInputStream inputStream;

		public Scanner(InputStream in) {
			inputStream = new BufferedInputStream(in);
		}

		public int nextInt() throws IOException {
			int num = 0;

			int read = skip();
			do {
				num = num * 10 + (read - 0x30);
			} while ((read = inputStream.read()) > 0x20);

			return num;
		}

		public void fill(int[] a) throws IOException {
			for (int i = 0; i < a.length; i++) {
				a[i] = nextInt();
			}
		}

		public void fill(int[] a, int[] b) throws IOException {
			if (a.length != b.length) {
				throw new IllegalArgumentException();
			}

			for (int i = 0; i < a.length; i++) {
				a[i] = nextInt();
				b[i] = nextInt();
			}
		}

		public long nextLong() throws IOException {
			long num = 0;

			int read = skip();
			do {
				num = num * 10 + (read - 0x30);
			} while ((read = inputStream.read()) > 0x20);

			return num;
		}

		public void fill(long[] a) throws IOException {
			for (int i = 0; i < a.length; i++) {
				a[i] = nextLong();
			}
		}

		public void fill(long[] a, long[] b) throws IOException {
			if (a.length != b.length) {
				throw new IllegalArgumentException();
			}

			for (int i = 0; i < a.length; i++) {
				a[i] = nextLong();
				b[i] = nextLong();
			}
		}

		public long[] nextLong(int n) throws IOException {
			long[] array = new long[n];
			for (int i = 0; i < n; i++) {
				array[i] = nextLong();
			}

			return array;
		}

		public String next() throws IOException {
			StringBuilder builder = new StringBuilder();

			int read = skip();
			do {
				builder.append((char) read);
			} while ((read = inputStream.read()) > 0x20);

			return builder.toString();
		}

		private int skip() throws IOException {
			int read;
			while ((read = inputStream.read()) <= 0x20)
				;

			return read;
		}
	}
}