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: Accepted)

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

namespace Program
{
    public class ABC070D
    {
        static class Console_
        {
            private static Queue<string> param = new Queue<string>();
            public static int NextInt() => int.Parse(NextString());
            public static long NextLong() => long.Parse(NextString());
            public static string NextString()
            {
                if (param.Count == 0) foreach (var item in Console.ReadLine().Split(' ')) param.Enqueue(item);
                return param.Dequeue();
            }
        }
        static public void Main(string[] args)
        {
            var N = Console_.NextInt();
            var next = new List<Tuple<int, int>>[N];
            for (int i = 0; i < N; ++i)
            {
                next[i] = new List<Tuple<int, int>>();
            }
            for (int i = 0; i < N - 1; ++i)
            {
                var a = Console_.NextInt();
                var b = Console_.NextInt();
                var c = Console_.NextInt();
                next[a - 1].Add(Tuple.Create(b - 1, c));
                next[b - 1].Add(Tuple.Create(a - 1, c));
            }

            var Q = Console_.NextInt();
            var K = Console_.NextInt() - 1;

            var kpath = new long[N];
            var done = new bool[N];
            var queue = new Queue<int>();
            queue.Enqueue(K);
            done[K] = true;
            while (queue.Count != 0)
            {
                var item = queue.Dequeue();
                foreach (var item2 in next[item])
                {
                    if (!done[item2.Item1])
                    {
                        done[item2.Item1] = true;
                        queue.Enqueue(item2.Item1);
                        kpath[item2.Item1] = kpath[item] + item2.Item2;
                    }
                }
            }

            for (int i = 0; i < Q; ++i)
            {
                var x = Console_.NextInt() - 1;
                var y = Console_.NextInt() - 1;
                Console.WriteLine(kpath[x] + kpath[y]);
            }
        }
    }
}