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)

//ヘッダー
#include<bits/stdc++.h>
using namespace std;

//型定義
typedef long long ll;

//定数
const ll INF=1e+18;
const int MOD=1e+9+7;

//REPマクロ
#define REP(i,n) for(ll i=0;i<(ll)(n);i++)
#define REPD(i,n) for(ll i=n-1;i>=0;i--)
#define REP2(i,a,b) for(ll i=a;i<(ll)(b);i++)
#define REPD2(i,a,b) for(ll i=a;i>(ll)(b);i--)

//vectorの扱い
#define ALL(x) (x).begin(),(x).end() //sortなどの引数省略
#define SIZE(x) ((ll)(x).size()) //size
#define MAX(x) *max_element(ALL(x)) //最大値
#define MIN(x) *min_element(ALL(x)) //最小値

//グローバル変数


//ライブラリ挿入


int main(){
    int N;
    cin >> N;
    int a,b;
    ll c;
    vector<vector<pair<int,ll>>> G(N);
    REP(i,N-1){
        cin >> a >> b >>c;
        a--;
        b--;
        G[a].push_back(make_pair(b,c));
        G[b].push_back(make_pair(a,c));
    }
    int Q,K;
    cin >> Q >> K;

    vector<int> x(Q),y(Q);
    int tmp1,tmp2;
    REP(i,Q){
        cin >> tmp1>>tmp2;
        x[i]=tmp1-1;
        y[i]=tmp2-1;
    }

    //ダイクストラ O(ElogV)
    // データ構造
    vector<ll> dist(N, INF); // 全頂点を「未訪問」に初期化
    priority_queue<int> que;

    // 初期条件 (頂点 0 を初期ノードとする)
    dist[K-1] = 0;
    que.push(K-1); // 0 を橙色頂点にする

    // 開始 (キューが空になるまで探索を行う)
    while (!que.empty()) {
        int v = que.top(); // 優先度キューから先頭頂点を取り出す
        que.pop();

        // v から辿れる頂点をすべて調べる
        for (auto itr=G[v].begin();itr!=G[v].end();itr++) {
            // 新たな頂点 nv について距離が短いなら更新
            int nv=itr->first;
            ll cost =itr->second;
            if(dist[v]+cost<dist[nv]){
                dist[nv] = dist[v] + cost;
                que.push(nv);
            }
        }
    }

    
    
    REP(i,Q){
        cout << dist[x[i]]+dist[y[i]] << endl;
    }
    
}