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 Go (1.6) (judge verdict: Time Limit Exceeded)

package main

import "fmt"

func main() {
  var n,a,b,c,q,k,x,y,v,max int
  fmt.Scan(&n)
  mp := make(map[int][]int)
  md := make(map[int][]int)
  for i := 1; i < n; i++ {
    fmt.Scan(&a,&b,&c)
    mp[a] = append(mp[a],b)
    md[a] = append(md[a],c)
    mp[b] = append(mp[b],a)
    md[b] = append(md[b],c)
  }
  fmt.Scan(&q,&k)
  dist := make([]int,n+1)
  max = n*1000000000
  for i := 0; i < n+1; i++ {
    dist[i] = max
  }
  dist[k] = 0
  l := []int{k}
  for {
    v = l[0]
    for i := 0; i < len(mp[v]); i++ {
      b = mp[v][i]
      c = md[v][i]
      if dist[b] == max {
        l = append(l,b)
      }
      if dist[b] > dist[v] + c {
        dist[b] = dist[v] + c
      }
    }
    l = l[1:]
    if len(l) == 0 {
      break
    }
  }
  for i := 0; i < q; i++ {
    fmt.Scan(&x,&y)
    fmt.Println(dist[x]+dist[y])
  }
}