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.Text;
using System.Linq;

class Program
{
    long[,] dist = new long[100000 + 1, 100000 + 1];
    long[] distK = new long[100000 + 1];
    void solve()
    {
        string[] str;
        int N = int.Parse(Console.ReadLine());

        //long[,] dist = new long[N + 1, N + 1];
        //long[] distK = new long[N + 1];

        for (int i = 0; i < N - 1; ++i)
        {
            str = Console.ReadLine().Split(' ');
            int a = int.Parse(str[0]);
            int b = int.Parse(str[1]);
            long c = long.Parse(str[2]);
            dist[a, b] = c;
            dist[b, a] = c;
        }

        str = Console.ReadLine().Split(' ');
        int Q = int.Parse(str[0]);
        int K = int.Parse(str[1]);

        Queue<int> que = new Queue<int>();
        que.Enqueue(K);

        while (que.Count > 0)
        {
            int t = que.Dequeue();
            for (int i = 1; i < N + 1; ++i)
            {
                if (i == t) continue;

                if (dist[i, t] != 0)
                {
                    if (distK[i] == 0) {
                        que.Enqueue(i);
                        distK[i] = distK[t] + dist[i, t];
                    }
                }
            }
        }

        for (int i = 0; i < Q; ++i)
        {
            str = Console.ReadLine().Split(' ');
            int x = int.Parse(str[0]);
            int y = int.Parse(str[1]);

            Console.WriteLine(distK[x] + distK[y]);
        }
    }

    public static int Main()
    {
        bool loop = false;
#if ES_DEBUG
        loop = true;
#endif
        do
        {
            new Program().solve();
        } while (loop);
        return 0;
    }
}