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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using static Input;

public class Prog
{
    private const int INF = 1000000007;
    private const long INFINITY = 100000000000007;
    public static void Main()
    {
        int N = NextInt();
        Node[] node = new Node[N];
        for (int i = 0; i < N; i++) node[i] = new Node(i);
        int[] a = new int[N - 1];
        int[] b = new int[N - 1];
        long[] c = new long[N - 1];
        for (int i = 0; i < N - 1; i++)
        {
            int A = NextInt() - 1;
            int B = NextInt() - 1;
            int C = NextInt();
            Edge e = new Edge();
            e.to = B;
            e.cost = C;
            node[A].relate.Add(e);
            e = new Edge();
            e.to = A;
            e.cost = C;
            node[B].relate.Add(e);
        }
        int Q = NextInt();
        int K = NextInt() - 1;
        Stack<Node> stack = new Stack<Node>();
        stack.Push(node[K]);
        while (stack.Count() != 0)
        {
            Node now = stack.Pop();
            now.visit = true;
            foreach (var e in now.relate)
            {
                if (!node[e.to].visit)
                {
                    node[e.to].cost = now.cost + e.cost;
                    stack.Push(node[e.to]);
                }
            }
        }
        for(int i = 0;i < Q; i++)
        {
            Console.WriteLine(node[NextInt()-1].cost + node[NextInt() - 1].cost);
        }
    }
}
public class Node
{
    public List<Edge> relate = new List<Edge>();
    public int name = 0;
    public bool visit = false;
    public long cost = 0;
    public Node(int name) { this.name = name; }
}
public class Edge
{
    public int to;
    public long cost;
}
public class Input
{
    private static Queue<string> q = new Queue<string>();
    private static void Confirm() { if (q.Count == 0) foreach (var s in Console.ReadLine().Split(' ')) q.Enqueue(s); }
    public static int NextInt() { Confirm(); return int.Parse(q.Dequeue()); }
    public static long NextLong() { Confirm(); return long.Parse(q.Dequeue()); }
    public static string NextString() { Confirm(); return q.Dequeue(); }
    public static double NextDouble() { Confirm(); return double.Parse(q.Dequeue()); }
    public static int[] LineInt() { return Console.ReadLine().Split(' ').Select(int.Parse).ToArray(); }
    public static long[] LineLong() { return Console.ReadLine().Split(' ').Select(long.Parse).ToArray(); }
    public static string[] LineString() { return Console.ReadLine().Split(' ').ToArray(); }
    public static double[] LineDouble() { return Console.ReadLine().Split(' ').Select(double.Parse).ToArray(); }
}