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;
using System.Collections.Generic;
using System.Collections.ObjectModel;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

public sealed class Edge
{
    public int U { get; }
    public int V { get; }
    public long Cost { get; }

    public Edge(int u, int v, long cost)
    {
        U = u;
        V = v;
        Cost = cost;
    }
}

public sealed partial class Program
{
    void DfsCore(int u, IReadOnlyList<IReadOnlyList<Edge>> graph, long cost, bool[] done, long[] dist)
    {
        done[u] = true;
        dist[u] = cost;

        foreach (var e in graph[u])
        {
            if (done[e.V]) continue;

            DfsCore(e.V, graph, cost + e.Cost, done, dist);
        }
    }

    long[] Dfs(IReadOnlyList<IReadOnlyList<Edge>> graph, int u)
    {
        var dist = graph.Count.MakeArray(_ => long.MaxValue);
        DfsCore(u, graph, 0L, new bool[graph.Count], dist);
        return dist;
    }

    public void EntryPoint()
    {
        var a = scanner;
        var n = a.N();
        var es = (n - 1).MakeArray(_ => new Edge(a.N() - 1, a.N() - 1, a.L()));
        var q = a.N();
        var k = a.N() - 1;

        var graph = n.MakeArray(_ => new List<Edge>());
        foreach (var e in es)
        {
            graph[e.U].Add(e);
            graph[e.V].Add(new Edge(e.V, e.U, e.Cost));
        }

        var dist = Dfs(graph, k);

        for (var i = 0; i < q; i++)
        {
            var x = a.N() - 1;
            var y = a.N() - 1;
            WriteLine(dist[x] + dist[y]);
        }
    }
}

#region Custom Library
public static class TemplateExtension
{
    public static X[] MakeArray<X>(this int count, Func<int, X> func)
    {
        var xs = new X[count];
        for (var i = 0; i < count; i++)
        {
            xs[i] = func(i);
        }
        return xs;
    }

    public static int[] Range(this int count, int start = 0)
    {
        return count.MakeArray(i => i + start);
    }

    public static string Intercalate<X>(this IEnumerable<X> @this, string separator)
    {
        return string.Join(separator, @this);
    }

    public static void ForEach<X>(this IEnumerable<X> @this, Action<X, int> action)
    {
        var list = @this as IReadOnlyList<X>;
        if (list != null)
        {
            var count = list.Count;
            for (var i = 0; i < count; i++)
            {
                action(list[i], i);
            }
        }
        else
        {
            var i = 0;
            foreach (var x in @this)
            {
                action(x, i);
                i++;
            }
        }
    }
}

public sealed class Scanner
{
    readonly TextReader reader;

    /// <summary>
    /// Reads next word separated by spaces.
    /// </summary>
    public string Word()
    {
        var sb = default(StringBuilder);
        var firstChar = default(char);
        var count = 0;

        while (true)
        {
            var r = reader.Read();

            if (r == '\r')
            {
                if (reader.Peek() == '\n') reader.Read();
                break;
            }
            else if (r == -1 || r == ' ' || r == '\n')
            {
                break;
            }
            else
            {
                var c = (char)r;

                switch (count)
                {
                    case 0:
                        firstChar = c;
                        count = 1;
                        break;
                    case 1:
                        sb = new StringBuilder();
                        sb.Append(firstChar).Append(c);
                        count = 2;
                        break;
                    default:
                        sb.Append(c);
                        break;
                }
            }
        }

        switch (count)
        {
            case 0:
                return "";
            case 1:
                return firstChar.ToString();
            default:
                return sb.ToString();
        }
    }

    /// <summary>
    /// Reads next word as <see cref="int"/>.
    /// </summary>
    public int N()
    {
        return int.Parse(Word());
    }

    /// <summary>
    /// Reads next word as <see cref="long"/>.
    /// </summary>
    public long L()
    {
        return long.Parse(Word());
    }

    /// <summary>
    /// Reads next word as <see cref="double"/>.
    /// </summary>
    public double F()
    {
        return double.Parse(Word());
    }

    public int[] Ns(int count)
    {
        return count.MakeArray(_ => N());
    }

    public long[] Ls(int count)
    {
        return count.MakeArray(_ => L());
    }

    public double[] Fs(int count)
    {
        return count.MakeArray(_ => F());
    }

    /// <summary>
    /// Reads next line and splits it by spaces.
    /// </summary>
    public X[] Words<X>(Func<string, X> func)
    {
        return reader.ReadLine().Split(' ').Select(func).ToArray();
    }

    public Scanner(TextReader reader)
    {
        this.reader = reader;
    }
}

public partial class Program
{
    readonly TextReader input;
    readonly TextWriter output;
    readonly Scanner scanner;

    void WriteLine(int value)
    {
        output.WriteLine(value);
    }

    void WriteLine(long value)
    {
        output.WriteLine(value);
    }

    void WriteLine(double value)
    {
        output.WriteLine(value);
    }

    void WriteLine(char value)
    {
        output.WriteLine(value);
    }

    void WriteLine(string value)
    {
        output.WriteLine(value);
    }

    public Program(TextReader input, TextWriter output)
    {
        this.input = input;
        this.output = output;
        scanner = new Scanner(input);
    }

    public static void Main(string[] args)
    {
#if DEBUG
        using (var writer = new VainZero.IO.DebugTextWriter(Console.Out))
#else
        var writer = Console.Out;
#endif
        {
            new Program(Console.In, writer).EntryPoint();
        }
    }
}
#endregion