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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <algorithm>
#include <cmath>
#include <deque>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <tuple>
#include <vector>
using namespace std;
typedef long long ll;
ll const INF = 1LL << 60;

vector<ll> search(ll x, vector<vector<pair<ll, ll>>> &g) {
  priority_queue<pair<ll, ll>> q;
  vector<ll> memo(g.size(), INF);
  memo[x] = 0;
  q.push({0, x});
  while (!q.empty()) {
    ll len = q.top().first;
    ll pos = q.top().second;
    q.pop();
    if (memo[pos] < len) continue;
    for (auto next : g[pos]) {
      ll next_len = memo[pos] + next.second;
      if (next_len < memo[next.first]) {
        memo[next.first] = next_len;
        q.push({next_len, next.first});
      }
    }
  }
  return memo;
}

int main() {
  ll N;
  cin >> N;
  vector<vector<pair<ll, ll>>> g(N);
  ll a, b, c;
  for (int i = 0; i < N - 1; i++) {
    cin >> a >> b >> c;
    a--, b--;
    g[a].emplace_back(b, c);
    g[b].emplace_back(a, c);
  }
  ll Q, K;
  cin >> Q >> K;
  K--;
  vector<ll> dist = search(K, g);
  ll x, y;
  for (int i = 0; i < Q; i++) {
    cin >> x >> y;
    x--, y--;
    cout << dist[x] + dist[y] << endl;
  }
}