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>
using namespace std;

typedef long long ll;
typedef pair<ll, ll> Pll;

constexpr ll INF = 1e15;

int main() {
    int N; cin >> N;
    vector<vector<Pll>> graph(N+1);
    for (int i = 0; i < N-1; i++) {
        int a, b, c; cin >> a >> b >> c;
        graph[a].push_back(Pll(b, c));
        graph[b].push_back(Pll(a, c));
    }
    int Q, K; cin >> Q >> K;
    vector<ll> cost(N+1, INF);
    vector<bool> searched(N+1, false);
    cost[K] = 0;
    priority_queue<Pll> pq;
    pq.push(Pll(0, K));
    while (!pq.empty()) {
        Pll x = pq.top(); pq.pop();
        ll c = x.first, f = x.second;
        if (searched[f]) continue;
        searched[f] = true;
        for (auto y : graph[f]) {
            if (y.second + c < cost[y.first]) {
                pq.push(Pll(y.second + c, y.first));
                cost[y.first] = c + y.second;
            }
        }
    }
    while (Q--) {
        int x, y; cin >> x >> y;
        cout << cost[x] + cost[y] << endl;
    }
}