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: Runtime Error)

#include <iostream>
#include <vector>
#include <deque>
#include <algorithm>
#include <numeric>
#include <string>
#include <cstring>
#include <list>
#include <unordered_set>
#include <tuple>
#include <cmath>
#include <limits>
#include <type_traits>
#include <iomanip>
#include <map>
#include <unordered_map>
#include <queue>
#include <stack>
#include <set>
#include <bitset>
#include <regex>
#include <random>
#include<bits/stdc++.h>

using namespace std;

typedef long long ll;
#define rep(i,n)for(ll i=0;i<n;++i)
#define exout(x) printf("%.10f\n", x)
const double pi = acos(-1.0);
const ll MOD = 1000000007;
const ll INF = 1e18;
const ll MAX_N = 201010;

//最大公約数
ll gcd(ll x, ll y) {
	return y ? gcd(y, x % y) : x;
}

ll lcm(ll x, ll y) {
	if (x == 0 || y == 0)return 0;
	return (x / gcd(x, y) * y);
}

ll dx[4] = { 0,0,-1,1 };
ll dy[4] = { -1,1,0,0 };
ll ans[110][110];
bool flag[2][110];
using edge = struct { ll to;ll cost; };
vector<edge>tree[101010];
ll depth[101010];

void dfs(ll v, ll p, ll d) {
	depth[v] = d;
	for (auto &nv : tree[v]) {
		if (nv.to == p)continue;
		dfs(nv.to, v, d + nv.cost);
	}
}

//long longしか使わない
//素数は1より大きい
//lower_boundは指定したkey以上の要素の一番左のイテレータをかえす
//upper_boundは指定したkeyより大きい要素の一番左のイテレータをかえす
int main() {
	ll n;
	cin >> n;
	rep(i, n) {
		ll a, b, c;
		cin >> a >> b >> c;
		a--, b--;
		tree[a].push_back({ b,c });
		tree[b].push_back({ a,c });
	}
	ll q, k;
	cin >> q >> k;
	k--;
	dfs(k, -1, 0);
	rep(i, q) {
		ll x, y;
		cin >> x >> y;
		x--, y--;
		cout << depth[x] + depth[y] << endl;
	}
	return 0;
}