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 Ruby (2.3.3) (judge verdict: Accepted)

N = gets.to_i
abcs = (N - 1).times.map { gets.split.map(&:to_i) }
Q, K = gets.split.map(&:to_i)
xys = Q.times.map { gets.split.map(&:to_i) }

graph = Array.new(N) { [] }
abcs.each do |(a, b, c)|
  a -= 1
  b -= 1
  graph[a].push([b, c])
  graph[b].push([a, c])
end

def dijkstra(s, graph)
  d_list = Array.new(graph.size, 1 << 60)
  d_list[s] = 0
  queue = [[s, 0]]
  while !queue.empty?
    v, d = queue.shift
    next if d > d_list[v]
    graph[v].each do |(u, c)|
      if d_list[u] > d_list[v] + c
        d_list[u] = d_list[v] + c
        queue.push([u, d_list[u]])
      end
    end
  end
  d_list
end

d_list = dijkstra(K - 1, graph)
xys.each do |(x, y)|
  x -= 1
  y -= 1
  ans = d_list[x] + d_list[y]
  puts ans
end