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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using static System.Console;
using static System.Math;

namespace CP
{
    class Atria
    {
        static long[,] graph;
        static bool[] vs;
        static long[] ans;
        static void Main(string[] args)
        {
            int n = int.Parse(ReadLine());
            graph = new long[n, n];
            for (int i = 0; i < n-1; i++)
            {
                long[] s = ReadLine().Split(' ').Select(long.Parse).ToArray();
                graph[s[0]-1, s[1]-1] = s[2];
                graph[s[1]-1, s[0]-1] = s[2];
            }
            int[] qk = ReadLine().Split(' ').Select(int.Parse).ToArray();
            //DFSによってKからの距離を計算する
            vs = new bool[n];
            vs[qk[1]-1] = true;
            ans = new long[n];
            ans[qk[1] - 1] = 0;
            Dfs(qk[1]-1,0);
            //答える部分
            for (int i = 0; i < qk[0]; i++)
            {
                int[] s = ReadLine().Split(' ').Select(int.Parse).ToArray();
                WriteLine(
                    ans[s[0]-1] + ans[s[1]-1]
                    );
            }

        }

        static void Dfs(int v,long tmp)
        {
            if (vs.Count(x => x == true) == vs.Count())
            {
                return;
            }

            for (int i = 0; i < vs.Count(); i++)
            {
                if (graph[v,i] > 0 && vs[i] == false)
                {
                    vs[i] = true;
                    ans[i] = graph[v, i] + tmp;
                    Dfs(i, ans[i]);
                    vs[i] = false;
                }
            }
            return;
        }
    }
}