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)

#
# 優先度つきキュー + ダイクストラ
# ダイクストラなので負の辺は不可
#
class PriorityQueue
  def initialize
    @q = []
    @h = {}
  end

  # push obj unless already contained
  def push_ex(obj, cost)
    return if @h.key?(obj)
    i = (0...@q.size).bsearch{|i| @q[i][1] > cost} || @q.size
    @q.insert(i, [obj, cost])
    @h[obj] = true
  end

  def pop
    return nil if @q.empty?
    obj = @q.shift[0]
    @h.delete(obj)
    return obj
  end

  # ルート計算あり
  # - Node number starts from 1
  def self.dijkstra(edges, start, goal)
    best = Array.new(edges.size+1){ [Float::INFINITY, nil] }
    best[start] = [0, [start]]
    q = PriorityQueue.new
    q.push_ex([start, [start]], 0)
    while (item = q.pop)
      a, route = *item
      edges[a].each do |b, cost|
        new_cost = best[a][0] + cost
        #p a: a, route: route, b: b, cost: cost, best: best[b][0], new_cost: new_cost
        if new_cost < best[b][0]
          best[b] = [new_cost, route+[b]]
          q.push_ex([b, route+[b]], new_cost)
        end
      end
    end
    return best[goal]
  end
end

N = gets.to_i
EDGES = Hash.new{|h, k| h[k] = [] }
(N-1).times{ a,b,c = gets.split.map(&:to_i); EDGES[a] << [b, c]; EDGES[b] << [a, c] }
Q, K, *rest = $stdin.read.split.map(&:to_i)
QUERIES = rest.each_slice(2).to_a

dists = Array.new(N+1)
for k in 1..N
  dists[k], _ = PriorityQueue.dijkstra(EDGES, K, k)
end

QUERIES.each do |x, y|
  p dists[x] + dists[y]
end