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.Collections.Generic;
using System.Linq;
using System.IO;
using static System.Console;
using Pair = System.Collections.Generic.KeyValuePair<int, int>;
//using System.Numerics;
//using static System.Math;

class Program
{
    static void Main()
    {
        SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
        new Program().solve();
        Out.Flush();
    }
    Scanner cin = new Scanner();
    readonly int[] dd = { 0, 1, 0, -1, 0 };
    readonly int mod = 1000000007;
    readonly string alfa = "abcdefghijklmnopqrstuvwxyz";
    readonly string ALFA = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";

    int N;
    void solve()
    {
        N = cin.nextint;
        G = Enumerable.Range(0, N).Select(i => new List<Edge>()).ToArray();
        for (int i = 0; i < N - 1; i++)
        {
            int a = cin.nextint - 1;
            int b = cin.nextint - 1;
            int c = cin.nextint;
            G[a].Add(new Edge(b, c));
            G[b].Add(new Edge(a, c));
        }
        int Q = cin.nextint;
        dijkstra(cin.nextint - 1);
        for (int i = 0; i < Q; i++)
        {
            WriteLine(D[cin.nextint - 1] + D[cin.nextint - 1]);
        }
    }

    // ref: http://abc070.contest.atcoder.jp/submissions/1505233
    struct Edge : IComparable<Edge>
    {
        public int to; public long cost;
        public Edge(int to, long cost)
        {
            this.to = to;
            this.cost = cost;
        }
        public int CompareTo(Edge e)
        {
            return cost.CompareTo(e.cost);
        }
    }
    List<Edge>[] G;
    //G = Enumerable.Range(0, N).Select(i => new List<Edge>()).ToArray();
    long[] D;
    const long inf = long.MaxValue / 3;
    void dijkstra(int s)
    {
        int n = G.Length;
        D = Enumerable.Repeat(inf, n).ToArray();
        var Q = new PriorityQueue<Edge>();//小さい順に取り出す
        D[s] = 0;
        Q.Enqueue(new Edge(s, D[s]));
        while (Q.Any())
        {
            var e = Q.Dequeue();
            var v = e.to;
            if (D[v] < -e.cost) continue;
            foreach (var gv in G[v])
            {
                if (D[gv.to] > D[v] + gv.cost)
                {
                    D[gv.to] = D[v] + gv.cost;
                    Q.Enqueue(new Edge(gv.to, -D[gv.to]));
                }
            }
        }
    }
    class PriorityQueue<T> where T : IComparable<T>
    {
        List<T> heap;
        int size;
        int Compare(T x, T y) { return y.CompareTo(x); }
        public PriorityQueue() { heap = new List<T>(); }
        public void Enqueue(T x)
        {
            heap.Add(x);
            int i = size++;

            while (i > 0)
            {
                int p = (i - 1) >> 1;

                if (Compare(heap[p], x) <= 0) break;

                heap[i] = heap[p];
                i = p;
            }
            heap[i] = x;
        }
        public T Dequeue()
        {
            T ret = heap[0];
            T x = heap[--size];

            int i = 0;
            while ((i << 1) + 1 < size)
            {
                int a = (i << 1) + 1;
                int b = (i << 1) + 2;

                if (b < size && Compare(heap[b], heap[a]) < 0)
                    a = b;
                if (Compare(heap[a], x) >= 0)
                    break;

                heap[i] = heap[a];
                i = a;
            }
            heap[i] = x;
            heap.RemoveAt(size);
            return ret;
        }
        public int Count { get { return size; } }

        public bool Any() { return size > 0; }

        public T Peek() { return heap[0]; }
    }
}

class Scanner
{
    string[] s; int i;
    char[] cs = new char[] { ' ' };
    public Scanner() { s = new string[0]; i = 0; }
    public string[] scan { get { return ReadLine().Split(); } }
    public int[] scanint { get { return Array.ConvertAll(scan, int.Parse); } }
    public long[] scanlong { get { return Array.ConvertAll(scan, long.Parse); } }
    public double[] scandouble { get { return Array.ConvertAll(scan, double.Parse); } }
    public string next
    {
        get
        {
            if (i < s.Length) return s[i++];
            string st = ReadLine();
            while (st == "") st = ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            i = 0;
            return next;
        }
    }
    public int nextint { get { return int.Parse(next); } }
    public long nextlong { get { return long.Parse(next); } }
    public double nextdouble { get { return double.Parse(next); } }
}