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: Time Limit Exceeded)

INF = 1.0/0
N = gets.to_i
G = Array.new(N + 1){[]}
D = Array.new(N + 1){Array.new(N + 1)}
(N - 1).times do
  a, b, c = gets.split.map(&:to_i)
  G[a] << b; G[b] << a
  D[a][b] = D[b][a] = c
end
Q, K = gets.split.map(&:to_i)

class PriorityQueue
  def initialize
    @q = [nil]
  end

  def bubble_up(i)
    pi = i / 2
    return if i <= 1 || @q[pi] >= @q[i]
    @q[i], @q[pi] = @q[pi], @q[i]
    bubble_up(pi)
  end

  def add(e)
    @q << e
    bubble_up(@q.size - 1)
  end

  def bubble_down(i)
    ci = i * 2
    return if ci > @q.size - 1
    ci += 1 if ci != @q.size - 1 && @q[ci] < @q[ci + 1]
    return if @q[i] >= @q[ci]
    @q[i], @q[ci] = @q[ci], @q[i]
    bubble_down(ci)
  end

  def pop
    @q[1], @q[-1] = @q[-1], @q[1]
    ret = @q.pop
    bubble_down(1)
    ret
  end
end

class Node
  attr_reader :id, :c
  def initialize(id, c)
    @id, @c = id, c
  end

  def < other
    @c < other.c
  end

  def >= other
    @c >= other.c
  end
end

def dijkstra(s)
  d = Array.new(N + 1, INF)
  d[s] = 0
  q = PriorityQueue.new
  (1 .. N).each{|i| q.add(Node.new(i, d[i]))}
  while n = q.pop
    G[n.id].each do |i|
      d1 = d[n.id] + D[n.id][i]
      if d[i] > d1
        d[i] = d1
        q.add(Node.new(i, d1))
      end
    end
  end
  d
end

d = dijkstra(K)
Q.times do
  x, y = gets.split.map(&:to_i)
  puts d[x] + d[y]
end