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;

class Progaram
{
    static int N;
    static int K;
    static bool[,] graph;
    static long[,] dis;
    static long[] disfk;

    static void Dfs(int v, int b, long d, bool[] visited)
    {
        d += dis[v, b];
        disfk[v] = d;
        visited[v] = true;
        for (var i = 0; N > i; i++)
        {
            if (graph[v, i] == false) continue;
            if (visited[i]) continue;
            Dfs(i, v, d, visited);
        }
    }

    static void Main(string[] args)
    {
        N = int.Parse(Console.ReadLine());
        graph = new bool[N, N];
        dis = new long[N, N];
        disfk = new long[N];
        for (var i = 0; N - 1 > i; i++)
        {
            var l = Console.ReadLine().Split(' ');
            var a = int.Parse(l[0]) - 1; var b = int.Parse(l[1]) - 1; var c = long.Parse(l[2]);
            graph[a, b] = true;
            graph[b, a] = true;
            dis[a, b] = c;
            dis[b, a] = c;
        }

        var line = Console.ReadLine().Split(' ')
            .Select(x => int.Parse(x)).ToArray();
        var q = line[0]; K = line[1] - 1;
        var visited = new bool[N];
        Dfs(K, K, 0L, visited);
        var ans = new List<long>();
        for (var i = 0; q > i; i++)
        {
            var l = Console.ReadLine().Split(' ')
                .Select(x => int.Parse(x)).ToArray();
            var s = l[0] - 1; var y = l[1] - 1;
            ans.Add(disfk[s] + disfk[y]);
        }

        foreach (var i in ans)
        {
            Console.WriteLine(i);
        }
    }
}