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.Text;
    using System.Collections.Generic;
    using static System.Math;
    using System.Linq;
    using static System.Array;
    
    namespace ConsoleApp2
    {
    class Program
    {
        static long H;
        static long W;
        static String[] map;
        static void Main(string[] args)
        {
            var N = long.Parse(Console.ReadLine());
            //

            var map = new long[N + 1, N + 1];
            for (int i = 1; i <= N; i++)
            {
                for (int j = 1; j <= N; j++)
                {
                    if(i == j)
                    {
                        map[i, j] = 0;
                    }
                    else
                    {
                        map[i, j] = (long)Pow(10,12);
                    }
                }
            }

            for (int  i = 1;  i < N;  i++)
            {
                var ABC = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
                var A = ABC[0];
                var B = ABC[1];
                var C = ABC[2];
                map[A, B] = C;
                map[B,A] = C;
            }

            for (int k = 1; k <= N; k++)
            {
                for (int i = 1; i <= N; i++)
                {
                    for (int j = 1; j <= N; j++)
                    {
                        map[i, j] = Min(map[i, j], map[i, k] + map[k, j]);
                    }
                }
            }

            var QK = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
            var Q = QK[0];
            var K = QK[1];
            for (int i = 0; i < Q; i++)
            {
                var XY = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
                var X = XY[0];
                var Y = XY[1];

                Console.WriteLine(map[X,K]+map[K,Y]);
            }

            
            
        }
    }

}