#include "factories.h"
#include <bits/stdc++.h>
using namespace std;
#define X first
#define Y second
#define mp make_pair
#define pb push_back
typedef long long ll;
typedef pair <int, int> pii;
typedef pair <int, pii> pip;
typedef pair <pii, int> ppi;
typedef pair <ll, ll> pll;
const int INF=0x3f3f3f3f;
const ll MAX=(ll)INF*INF;
const int MAXN=5e5+5;
const int LOG=20;
int n;
ll dist[MAXN];
int par[LOG][MAXN], dep[MAXN];
vector <pii> ls[MAXN];
ll da[MAXN], db[MAXN];
void dfs(int node, int rod, ll d) {
par[0][node]=rod;
dist[node]=d;
dep[node]=dep[rod]+1;
// printf("node: %d, dist: %lld, dep: %d, par: %d\n", node, dist[node], dep[node], rod);
for (pii sus:ls[node]) if (sus.X!=rod) dfs(sus.X, node, d+sus.Y);
}
void build() {
for (int i=1; i<LOG; ++i) {
for (int j=0; j<n; ++j) {
par[i][j]=par[i-1][par[i-1][j]];
}
}
}
int lca(int x, int y) {
if (dep[x]<dep[y]) swap(x, y);
for (int i=LOG-1; i>=0; --i) {
if (dep[x]-(1<<i)>=dep[y]) x=par[i][x];
}
if (x==y) return x;
for (int i=LOG-1; i>=0; --i) {
if (par[i][x]!=par[i][y]) x=par[i][x], y=par[i][y];
}
return par[0][x];
}
void rek(int node) {
for (pii sus:ls[node]) {
if (sus.X!=par[0][node]) {
rek(sus.X);
da[node]=min(da[node], da[sus.X]+sus.Y);
db[node]=min(db[node], db[sus.X]+sus.Y);
}
}
}
void Init(int N, int A[], int B[], int D[]) {
n=N;
for (int i=0; i<n-1; ++i) {
ls[A[i]].pb(mp(B[i], D[i]));
ls[B[i]].pb(mp(A[i], D[i]));
}
dfs(0, 0, 0);
build();
}
long long Query(int S, int x[], int T, int y[]) {
ll sol=MAX;
if (S<=10 && T<=10) {
for (int i=0; i<S; ++i) {
for (int j=0; j<T; ++j) {
int lc=lca(x[i], y[j]);
// printf("x: %d, y: %d, lc: %d == %lld\n", x[i], y[j], lc);
sol=min(sol, dist[x[i]]+dist[y[j]]-dist[lc]-dist[lc]);
}
}
return sol;
}
for (int i=0; i<n; ++i) da[i]=db[i]=MAX;
for (int i=0; i<S; ++i) da[x[i]]=0;
for (int i=0; i<T; ++i) db[y[i]]=0;
rek(0);
for (int i=0; i<n; ++i) sol=min(sol, da[i]+db[i]);
return sol;
}
