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)

class Edge
  attr_accessor :s, :e, :c, :z
#  attr_writer :c
  def initialize(s,e,z)
    @s = s
    @e = e
    @c = 0
    @z = z
  end
end

class Graph
  def initialize(graph)    #hはHash
#    @vs = vs    #Array:頂点（要素は Vertex）
    @es = {}    #Hash:枝（Vertex=>Array）:Arrayの要素はEdge
    graph.each do |hash|
      unless @es.has_key?(hash[:s])
        @es[hash[:s]] = []
      end
      @es[hash[:s]] << Edge.new(hash[:s],hash[:e],hash[:z])
    end
  end

  def get_edges(v)
    @es[v]    #頂点vからのすべての枝（Array）を返す
  end

  #goalを見つければtrue, 見つけられなければfalseを返す
  def find(start, goal)
    dfs(start, goal, [], 0, 0)
  end

  def dfs(v, goal, visited, score, point)
#    puts %(v:#{v},g:#{goal},v:#{visited})
    score += point
#    puts %(score:#{score})
    vis = Marshal.load(Marshal.dump(visited))

    if v == goal
#      puts "ごーる"
      return score
    end

    unless (edges = get_edges(v))
#      puts "はじっこ"
#      p edges = get_edges(v)
#      puts %(v:#{v},g:#{goal},v:#{visited})
      if v == goal
#        puts "ごーる"
        return score
      else
        return false
      end
    end
#    return score unless (edges = get_edges(v))
#    if edges.all? {|edge| visited.include?(edge.e)}
#      return score if v == goal
#      puts "loop"
#      return "loop"
#    end

#    p edges.all?{|edge| visited.include?(edge.e)}
#    puts %(visited:#{visited})
#    edges.each do |edge|
#      puts %(visited.include?(#{edge.e}):#{visited.include?(edge.e)})
#    end
    if visited.size - visited.uniq.size > 0
#      puts "loop"
      return "loop"
    end
#    edges.each do |edge|
#      if visited.include?(edge.e)
#        return score if v == goal
#        puts "loop"
#        return "loop"
#      end
#    end

#    return "loop" if get_edges(v) - (visited)
#    return score if v == goal
    vis << v
#    puts %(vis:#{vis})
#    gets
#    puts %(edge : #{edges})
    edges.each {|edge|
#      puts %(v:#{v},g:#{goal},v:#{vis})
#      puts %(v_before:#{vis})
#      puts %(edge.e: #{edge.e})
      ret = dfs(edge.e,goal,vis,score,edge.z)
      if ret != "loop"
#        puts "goal score #{ret}"
#        puts %(v_after:#{vis})
        $score << ret
#        return true
      else
        $score << false
      end
    }
#    false
    false
  end
end

n = gets.chomp.to_i
graph = []
(n-1).times do
  input = gets.chomp.split.map(&:to_i)
  graph << {:s => input[0], :e => input[1], :z => input[2]}
  graph << {:s => input[1], :e => input[0], :z => input[2]}
end
#p graph

q,k = gets.chomp.split(" ").map(&:to_i)
query = []
q.times do
  input = gets.chomp.split.map(&:to_i)
  query << {:s => input[0], :e => input[1]}
end


g = Graph.new(graph)
query.each do |task|
  $score = []
  g.find(task[:s],k)
  # p $score
#  if $score.include?("loop")
#    puts "inf"
#  else
    $score.delete(false)
    ans = $score.min
#  end
#  puts ""
  $score = []
  g.find(k,task[:e])
#  p $score
#  if $score.include?("loop")
#    puts "inf"
#  else
    $score.delete(false)
    ans += $score.min
#  end
  puts ans
#  puts ""
end