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>
#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
//#include "boost/multiprecision/cpp_int.hpp"
//typedef boost::multiprecision::cpp_int LL;
typedef long double dd;
#define i_7 (ll)(1E9+7)
//#define i_7 998244353
#define i_5 i_7-2

ll mod(ll a){
    ll c=a%i_7;
    if(c>=0)return c;
    return c+i_7;
}
typedef pair<ll,ll> l_l;
typedef pair<dd,dd> d_d;
ll inf=(ll)1E16;
#define rep(i,l,r) for(ll i=l;i<=r;i++)
#define pb push_back
ll max(ll a,ll b){if(a<b)return b;else return a;}
ll min(ll a,ll b){if(a>b)return b;else return a;}
void Max(ll &pos,ll val){pos=max(pos,val);}//Max(dp[n],dp[n-1]);
void Min(ll &pos,ll val){pos=min(pos,val);}
void Add(ll &pos,ll val){pos=mod(pos+val);}
dd EPS=1E-9;
#define fastio ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define fi first
#define se second
#define endl "\n"
#define SORT(v) sort(v.begin(),v.end())
#define ERASE(v) v.erase(unique(v.begin(),v.end()),v.end())
#define POSL(v,x) (lower_bound(v.begin(),v.end(),x)-v.begin())
#define POSU(v,x) (upper_bound(v.begin(),v.end(),x)-v.begin())
//template<class T>void max(T a,T b){if(a<b)return b;else return a;}
//template<class T>void min(T a,T b){if(a>b)return b;else return a;}
//template<class T>bool Max(T&a, T b){if(a < b){a = b;return 1;}return 0;}
//template<class T>bool Min(T&a, T b){if(a > b){a = b;return 1;}return 0;}

//////////////////////////



#define MAX_V 200000//調節！！！！！！！！！！！！！！！！！！！！！！！！
struct edge{ll to,cost;};
ll d[MAX_V];//頂点sからの最短距離
ll V;//頂点数！！！！！！！！！！！！！！！！！！！！！！！！！！！！！！！！
vector<edge>G[MAX_V];
void dijkstra(ll s){
    priority_queue<l_l,vector<l_l>,greater<l_l>> que;//firstは最短距離、secondは頂点の番号
    fill(d,d+V+1,inf);//頂点番号は0~V-1でも1~Vでもお好きな方で
    d[s]=0;
    que.push(l_l(0,s));
    while(!que.empty()){
        //greater<l_l>なのでfirstが小さい順に取り出せる！
        l_l p=que.top();que.pop();
        ll v=p.second;
        if(d[v]<p.first)continue;
        for(ll i=0;i<G[v].size();i++){
            edge e=G[v][i];
            if(d[e.to]>d[v]+e.cost){
                d[e.to]=d[v]+e.cost;
                que.push(l_l(d[e.to],e.to));
            }
        }
    }
}
////////////////////////////////////////


int main(){fastio
    ll n;cin>>n;V=n;
    vector<l_l>v[n+1];
    rep(i,1,n-1){
        ll a,b,c;cin>>a>>b>>c;
        G[a].pb({b,c});
        G[b].pb({a,c});
    }
    ll q,k;cin>>q>>k;
    dijkstra(k);
    while(q--){
        ll a,b;cin>>a>>b;
        cout<<d[a]+d[b]<<endl;
    }

    
    return 0;
}