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: Runtime Error)

#require 'prime'
#require 'openssl'
MOD=10**9+7;  cnt=0; sum=0; prev=nil; can=true; h=Hash.new(0)
def gs() gets.chomp end
def gi() gets.chomp.to_i end
def gsmi() gets.chomp.split.map(&:to_i) end

def ar2(s1,s2,de=nil) Array.new(s1){Array.new(s2,de)} end
def ar3(s1,s2,s3,de=nil) Array.new(s1){Array.new(s2){Array.new(s3,de)}} end

def desc(ar) ar.sort!{|x,y| y<=>x} end
def min(a,b) a<=b ? a : b end
def max(a,b) a>=b ? a : b end
def sum(ar) ar.inject(:+).to_i end
def ceil(a,b) (a.to_f/b).ceil end

def C(a,b) b==0||a==b ? 1 : (b=a-b if a/2<b;(a-b+1..a).inject(:*)/(1..b).inject(:*)) end
def rui(ar) s=[0]; ar.size.times{|i| s<<s[-1]+ar[i]}; s end
def rev_rui(ar) s=[0]; ar.size.times.reverse_each{|i| s<<s[-1]+ar[i]}; s end

def puts_yesno(b) puts(b ? 'Yes' : 'No') end
def putsend(s) puts s; exit end
def pu(h) begin; require './../nemi_lib/debug.rb'; puts_val(h); rescue LoadError; end; end
########### ( ˘ω˘ )ｽﾔｧ… ###########
# Tree
class Tree
  attr_accessor :edges

  def initialize(ar,n,*option)
    @ar = ar
    @edges = build_edges(@ar,n)
  end

  def build_edges(ar,n)
    edges = Array.new(n){[]}
    ar.size.times do |i|
      edges[ar[i][0]-1] << [ar[i][1],ar[i][2]]
      edges[ar[i][1]-1] << [ar[i][0],ar[i][2]]
    end
    edges
  end

  def route(st, en, stack=[], current=nil) 
    # 外から呼ぶときはcurrentに値がない
    current = st if current.nil?

    stack << current
    # 見つかった
    return stack if current==en

    nears = @edges[current-1].map{|i|i[0]}
    nears.each do |i|
      # 同じ辺は探索しない
      next if stack.include?(i)

      ans = route(st,en,stack,i)
      # 見つかってたら返す
      return ans if ans[-1]==en
    end
    # 見つからない
    stack.pop
    stack
  end
end

n=gi
abc=(n-1).times.map{gsmi}

tree=Tree.new(abc,n)
ans=[]

q,k=gsmi
dist=Array.new(n,10**15)
dist[k-1]=0
def calc_dist(k,tree,dist)
  i=k-1
  to=tree.edges[i]
  d_base = dist[i]
  check=[]
  to.each do |j,d|
    d1=d_base+d
    if dist[j-1]>d1
      dist[j-1]=d1
      check<<j
    end
  end
  check.each do |j|
    calc_dist(j,tree,dist)
  end
end
calc_dist(k,tree,dist)


q.times do |qq|
  x,y=gsmi
  ans<< dist[x-1]+dist[y-1]
end
puts ans