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)

/*Coded by::
    **Avinash Tiwary**
    **BE/10298/2015**
    **Production Engineer**
    **Producing <code>**
*/
#include<bits/stdc++.h>
#define buf ios_base::sync_with_stdio (0), cin.tie (0)
typedef long long ll;
typedef double dob;
#define MAX 1300009
#define M 1000000007
#define INF 5e17
using namespace std;
typedef vector<ll> V;
typedef queue<ll > Q;
typedef stack<ll> S;
typedef pair<ll,ll> P;
#define mp make_pair
#define mt make_tuple
#define pb push_back
bool desc(ll i, ll j) { return i > j; }
ll power(ll x,ll n)
{   if(n==0||x==0) return 1;
    else if(n%2 == 0) return power((x*x)%M,n/2);
    else return (x*power((x*x)%M,(n-1)/2))%M;
}
ll fac[MAX],not_prime[MAX],ar[MAX],dp[MAX],vis[MAX];
string s[MAX];
void fact(){
    fac[0]=1;
    for(ll i=1;i<=1000009;i++) fac[i]=(i*fac[i-1])%M;
}
void sieve(){
    not_prime[1]=1; not_prime[0]=1;
    for(ll p=2;p*p<=MAX;p++){
        if(!not_prime[p]){
            for(ll i=p*2;i<=MAX;i+=p) not_prime[i]=1;
        }
    }
}
vector<list<pair<ll,ll> > > g(MAX);
int main(){
    //buf; 
    //sieve(); 
    //fact();
    ll i,j,test,ans,a,b,c,d,n,z,m,p,k,flag; string sk; 
    cin>>n;
    for(i=1;i<n;i++){
        cin>>a>>b>>c;
        g[a].pb({b,c}); g[b].pb({a,c});
    }
    cin>>m>>k;
    queue<ll> qu;
    qu.push(k);
    while(!qu.empty()){
        ll cur=qu.front();
        qu.pop();
        vis[cur]=1;
        for(auto it=g[cur].begin();it!=g[cur].end();it++){
            if(!vis[it->first]){
                qu.push(it->first); dp[it->first]=dp[cur]+it->second;
            }
        }
    }
    while(m--){
        cin>>a>>b;
        cout<<dp[a]+dp[b]<<endl;
    }
    return 0;
}