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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define rep2(i, m, n) for(int i = (int)(m); i < (int)(n); i++)
#define rep_inv(i, n, m) for(int i = (int)(n); i > (int)(m); i--)
using namespace std;
using ll = long long;
using vl = vector<ll>;
using vc = vector<char>;
using vvl = vector<vl>;
using vvc = vector<vc>;
using pll = pair<ll, ll>;
using vpll = vector<pll>;

ll INF = (ll)pow(10, 16);

int main(){
  ll N;
  cin >> N;
  ll a, b, c;
  vector<vpll> abc(N + 1);
  rep(i, N - 1){
    cin >> a >> b >> c;
    abc[a].push_back(make_pair(b, c));
    abc[b].push_back(make_pair(a, c));
  }
  ll Q, K;
  cin >> Q >> K;
  vl x(Q), y(Q);
  rep(i, Q){
    cin >> x[i] >> y[i];
  }

  vl cost(N + 1, INF);
  cost[K] = 0;
  vl vis(N + 1, 0);
  priority_queue<pll, vpll, greater<pll> > cv;
  cv.push({0, K});

  while(!cv.empty()){
    ll v1 = cv.top().first, v2 = cv.top().second;
    cv.pop();

    if(vis[v2] == 1) continue;
    
    vis[v2] = 1;
    
    rep(i, abc[v2].size()){
      ll update = abc[v2][i].second + cost[v2];
      if(update < cost[abc[v2][i].first]) cost[abc[v2][i].first] = update;
      cv.push({cost[abc[v2][i].first], abc[v2][i].first});
    }
  }

  rep(i, Q){
    cout << cost[x[i]] + cost[y[i]] << endl;
  }
  
  return 0;
}