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.Linq;
using System.Diagnostics;
using System.Collections.Generic;
class P
{
    static void Main()
    {
        int n = int.Parse(Console.ReadLine());

        List<edge>[] edges = Enumerable.Repeat(0, n).Select(_ => new List<edge>()).ToArray();
        for (int i = 0; i < n - 1; i++)
        {
            int[] abc = Console.ReadLine().Split().Select(int.Parse).ToArray();
            edges[abc[0] - 1].Add(new edge(abc[1] - 1, abc[2]));
            edges[abc[1] - 1].Add(new edge(abc[0] - 1, abc[2]));
        }
        int[] qk = Console.ReadLine().Split().Select(int.Parse).ToArray();
        long[] totalCost = Enumerable.Repeat(long.MaxValue, n).ToArray();
        totalCost[qk[1] - 1] = 0;
        Queue<int> queue = new Queue<int>();
        queue.Enqueue(qk[1] - 1);
        while (queue.Count != 0)
        {
            int ind = queue.Dequeue();
            List<edge> list = edges[ind];
            for (int i = 0; i < list.Count; i++)
            {
                if (totalCost[list[i].to] > totalCost[ind])
                {
                    totalCost[list[i].to] = totalCost[ind] + list[i].cost;
                    queue.Enqueue(list[i].to);
                }
            }
        }
        for (int i = 0; i < qk[0]; i++)
        {
            int[] ab = Console.ReadLine().Split().Select(int.Parse).ToArray();
            Console.WriteLine(totalCost[ab[0] - 1] + totalCost[ab[1] - 1]);
        }
    }
}
struct edge
{
    public int to;
    public long cost;
    public edge(int to, long cost)
    {
        this.to = to;
        this.cost = cost;
    }
}