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 Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)

import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Scanner;

public class Main {

    private static class Edge {
        int from;
        int to;
        long cost;

        private Edge(int from, int to, long cost) {
            this.from = from;
            this.to = to;
            this.cost = cost;
        }
    }

    public static long dijkstra(Map<Integer, List<Edge>> allEdges, int start, int end, int nodeNum) {
        long[] d = new long[nodeNum + 1];
        Arrays.fill(d, -1);
        PriorityQueue<Edge> heap = new PriorityQueue<>(Comparator.comparingLong(a -> d[a.from] + a.cost));
        d[start] = 0;
        List<Edge> edges = allEdges.get(start);
        heap.addAll(edges);
        while (d[end] < 0) {
            Edge nearest = heap.poll();
            if (d[nearest.to] >= 0) {
                continue;
            }
            d[nearest.to] = d[nearest.from] + nearest.cost;
            if (!allEdges.containsKey(nearest.to)) {
                continue;
            }
            edges = allEdges.get(nearest.to);
            for (int i = 0; i < edges.size(); i++) {
                Edge edge = edges.get(i);
                if (d[edge.to] < 0) {
                    heap.add(edge);
                }
            }
        }
        return d[end];
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] a = new int[n - 1];
        int[] b = new int[n - 1];
        long[] c = new long[n - 1];
        Map<Integer, List<Edge>> map = new HashMap<>();
        for (int i = 1; i <= n; i++) {
            map.put(i, new ArrayList<>());
        }
        for (int i = 0; i < n - 1; i++) {
            a[i] = sc.nextInt();
            b[i] = sc.nextInt();
            c[i] = sc.nextLong();
            List<Edge> l1 = map.get(a[i]);
            l1.add(new Edge(a[i], b[i], c[i]));
            map.put(a[i], l1);
            List<Edge> l2 = map.get(b[i]);
            l2.add(new Edge(b[i], a[i], c[i]));
            map.put(b[i], l2);
        }
        int q = sc.nextInt();
        int k = sc.nextInt();
        int[] x = new int[q];
        int[] y = new int[q];
        for (int i = 0; i < q; i++) {
            x[i] = sc.nextInt();
            y[i] = sc.nextInt();
        }
        long[] d = new long[n + 1];
        for (int i = 1; i <= n; i++) {
            d[i] = dijkstra(map, k, i, n);
        }
        for (int i = 0; i < q; i++) {
            System.out.println(d[x[i]] + d[y[i]]);
        }
    }

}