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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace AtCoder
{
    class Program
    {
        private const int MODULO = 1000000007;
        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }

        class Solver
        {
            private readonly long[] costs;
            public Solver(int N, int K, int[][] paths)
            {
                var q = new Queue<int>();
                costs = Enumerable.Repeat(long.MaxValue, N).ToArray();
                costs[K] = 0;
                q.Enqueue(K);
                while (q.Count > 0)
                {
                    int i = q.Dequeue();
                    for (int j = 0; j < N; ++j)
                    {
                        if (paths[i][j] < int.MaxValue && costs[j] > costs[i] + paths[i][j])
                        {
                            costs[j] = costs[i] + paths[i][j];
                            q.Enqueue(j);
                        }
                    }
                }
            }
            public IEnumerable<long> Solve(int Q, Tuple<int, int>[] queries)
            {
                var answers = new long[Q];
                for (int i = 0; i < Q; ++i)
                {
                    int x = queries[i].Item1;
                    int y = queries[i].Item2;
                    answers[i] = costs[x] + costs[y];
                }
                return answers;
            }
        }
        static void Main(string[] args)
        {
            int N = ReadInt();
            var paths = new int[N][];
            for (int i = 0; i < N; ++i) { paths[i] = Enumerable.Repeat(int.MaxValue, N).ToArray(); }
            for (int i = 0; i < N - 1; ++i)
            {
                int[] v2 = ReadInts();
                int a = v2[0] - 1;
                int b = v2[1] - 1;
                int c = v2[2];
                paths[a][b] = c;
                paths[b][a] = c;
            }
            int[] v1 = ReadInts();
            int Q = v1[0];
            int K = v1[1] - 1;
            var queries = new Tuple<int, int>[Q];
            for (int i = 0; i < Q; ++i)
            {
                int[] v2 = ReadInts();
                queries[i] = new Tuple<int, int>(v2[0] - 1, v2[1] - 1);
            }
            foreach (var ans in new Solver(N, K, paths).Solve(Q, queries))
            {
                Console.WriteLine(ans);
            }
        }
    }
}