#include <bits/stdc++.h>
#include "factories.h"
using namespace std;
const long long INF = 1000000000000000;
struct heavy_light_decomposition{
vector<int> p, sz, in, next;
vector<long long> d;
heavy_light_decomposition(){
}
heavy_light_decomposition(vector<int> &p, vector<vector<int>> &c, vector<long long> &d): p(p), d(d){
int N = p.size();
sz = vector<int>(N, 1);
dfs1(c);
in = vector<int>(N);
next = vector<int>(N, 0);
int t = 0;
dfs2(c, t);
}
void dfs1(vector<vector<int>> &c, int v = 0){
for (int &w : c[v]){
dfs1(c, w);
sz[v] += sz[w];
if (sz[w] > sz[c[v][0]]){
swap(w, c[v][0]);
}
}
}
void dfs2(vector<vector<int>> &c, int &t, int v = 0){
in[v] = t;
t++;
for (int w : c[v]){
if (w == c[v][0]){
next[w] = next[v];
} else {
next[w] = w;
}
dfs2(c, t, w);
}
}
int lca(int u, int v){
while (true){
if (in[u] > in[v]){
swap(u, v);
}
if (next[u] == next[v]){
return u;
}
v = p[next[v]];
}
}
long long dist(int u, int v){
return d[u] + d[v] - 2 * d[lca(u, v)];
}
};
heavy_light_decomposition HLD;
void Init(int N, int A[], int B[], int D[]){
vector<vector<pair<int, int>>> E(N);
for (int i = 0; i < N - 1; i++){
E[A[i]].push_back(make_pair(D[i], B[i]));
E[B[i]].push_back(make_pair(D[i], A[i]));
}
vector<int> p(N, -1);
vector<vector<int>> c(N);
vector<long long> d(N, 0);
queue<int> Q;
Q.push(0);
while (!Q.empty()){
int v = Q.front();
Q.pop();
for (auto P : E[v]){
int w = P.second;
if (w != p[v]){
p[w] = v;
c[v].push_back(w);
d[w] = d[v] + P.first;
Q.push(w);
}
}
}
HLD = heavy_light_decomposition(p, c, d);
}
long long Query(int S, int X[], int T, int Y[]){
long long ans = INF;
for (int i = 0; i < S; i++){
for (int j = 0; j < T; j++){
ans = min(ans, HLD.dist(X[i], Y[j]));
}
}
return ans;
}
