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-csc 3.5.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Diagnostics;
using System.IO;
using System.Text;
using System.Linq;
using System.Collections.Generic;
using System.Text.RegularExpressions;
using System.Runtime.InteropServices;

class Program
{
    const string Yes = "Yes";
    const string No = "No";
    const long Mod = 1000000007;
    const char White = '.';
    const char Black = '#';

    static void Main(string[] args) {
#if DEBUG
        MyDebugger.Test(process, "../TextFile1.txt");
#else
        object ret = process(new StreamReader(Console.OpenStandardInput()));
        Console.WriteLine(ret);
#endif
    }

    static object process(TextReader input) {
        var n = int.Parse(input.ReadLine());
        var ab = new Dictionary<int, List<int>>();
        var cc = new int[n][];
        for(int i=0; i<n; i++) {
            ab[i] = new List<int>();
            cc[i] = new int[n];
        }

        for(int i=0; i<n-1; i++) {
            var spl = input.ReadLine().Split(' ');
            var a = int.Parse(spl[0]) - 1;
            var b = int.Parse(spl[1]) - 1;
            var c = int.Parse(spl[2]);

            ab[a].Add(b);
            ab[b].Add(a);
            cc[a][b] = c;
            cc[b][a] = c;
        }

        var splx = input.ReadLine().Split(' ');
        var q = int.Parse(splx[0]);
        var k = int.Parse(splx[1]) - 1;

        var box = new long[n];
        Search(n, ab, cc, k, -1, box);

        var sb = new StringBuilder();
        for(int i=0; i<q; i++) {
            var spl = input.ReadLine().Split(' ');
            var x = int.Parse(spl[0]) - 1;
            var y = int.Parse(spl[1]) - 1;

            sb.AppendLine((box[x] + box[y]).ToString());
        }

        return sb;
    }

    static void Search(int n, Dictionary<int, List<int>> ab, int[][] cc, int p, int from, long[] box) {
        //Debug.WriteLine(x);

        if(from != -1) {
            box[p] = box[from] + cc[from][p];
        }

        //次の再帰
        foreach (var to in ab[p]) {
            if (to == from) continue;
            Search(n, ab, cc, to, p, box);
        }
    }

    static int[] ToIntArray(string strs, int n) {
        var ret = new int[n];
        var spl = strs.Split(' ');
        for (int i = 0; i < n; i++)
            ret[i] = int.Parse(spl[i]);
        return ret;
    }
}