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.

Examples

Input

5
1 2 1
1 3 1
2 4 1
3 5 1
3 1
2 4
2 3
4 5


Output

3
2
4


Input

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


Output

5
14
22


Input

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


Output

17000000000
import java.util.Scanner;
import java.util.Vector;

public class Main {
    final  static int max=1000010;
    static class Pair{
        int  f ;
        long s;
        Pair(int a,long b){
            f=a;
            s=b;
        }
    }

    static Vector<Pair> edge[]= new Vector[max * 2];
    static long res[]=new long[max*2];

    public static void main(String[] args) {
        Scanner in=new Scanner(System.in);
        int cases=in.nextInt();
        while(--cases!=0) {
            int a = in.nextInt();
            int b = in.nextInt();
            int c = in.nextInt();

            if(edge[a]==null)
                edge[a]=new Vector<>();
            edge[a].add(new Pair(b, c));

            if(edge[b]==null)
                edge[b]=new Vector<>();
            edge[b].add(new Pair(a, c));

        }

        int n=in.nextInt(),k=in.nextInt();
        DFS(k,0);
        while (n--!=0){
            int  f=in.nextInt();
            int  t=in.nextInt();

            System.out.println(res[f]+res[t]);
        }

    }

    static boolean visited[]=new boolean[max*2];
    private static void DFS(int k, long e) {
        visited[k]=true;
        for(int i=0;i<edge[k].size();i++)
        {
            if(!visited[edge[k].get(i).f])
            {
               res[edge[k].get(i).f]=e+edge[k].get(i).s;
               DFS(edge[k].get(i).f,e+edge[k].get(i).s);
            }

        }
    }
}
