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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.HashMap;

public class Main
{
  public static long d[] = new long[123456];
  public static HashMap<Integer, ArrayList<Integer>> h = new HashMap<>();
  public static HashMap<Integer, ArrayList<Long>> hd = new HashMap<>();

  public static void main(String[] args) throws IOException
  {
    BufferedReader r = new BufferedReader(new InputStreamReader(System.in), 1);

    int n = Integer.parseInt(r.readLine());


    for(int i = 0; i <= n; i++)
    {
      h.put(i, new ArrayList<Integer>());
      hd.put(i, new ArrayList<Long>());
    }

    for(int i = 0; i < n - 1; i++)
    {
      String s = r.readLine();
      String sl[] = s.split(" ");
      int a = Integer.parseInt(sl[0]);
      int b = Integer.parseInt(sl[1]);
      long c = Long.parseLong(sl[2]);

      h.get(a).add(b);
      h.get(b).add(a);
      hd.get(a).add(c);
      hd.get(b).add(c);
    }

    String s = r.readLine();
    String sl[] = s.split(" ");
    int q = Integer.parseInt(sl[0]);
    int k = Integer.parseInt(sl[1]);

    search(k, 999999, 0);
    
    for(int i = 0; i < q; i++)
    {
      s = r.readLine();
      sl = s.split(" ");
      int x = Integer.parseInt(sl[0]);
      int y = Integer.parseInt(sl[1]);
      System.out.println(d[x] + d[y]);
    }

  }

  public static void search(int src, int proh, long offset)
  {
    ArrayList<Integer> a = h.get(src);
    ArrayList<Long> ad = hd.get(src);
    d[src] = offset;
    int an = a.size();
    for(int i = 0; i < an; i++)
    {
      int z = a.get(i);
      if(z == proh)
      {
        continue;
      }
      long v = ad.get(i);
      search(z, src, offset + v);
    }
  }

}