// In the name of the God
#include "factories.h"
#include <bits/stdc++.h>
#define ll long long
// #define int long long
#define pb push_back
#define F first
#define S second
#define mp make_pair
#define pii pair <int, int>
#define smin(x, y) (x) = min((x), (y))
#define smax(x, y) (x) = max((x), (y))
#define all(x) (x).begin(), (x).end()
using namespace std;
const ll inf = (1e9+7)*(1e9+7);
const ll mod = 998244353;
const ll maxn = 5e5+5;
ll n, sz[maxn];
ll mn[maxn];
bool mark[maxn];
vector <pair <ll, ll> > adj[maxn];
vector <pair <ll, ll> > c[maxn];
void dfs1(ll v, ll p) {
sz[v] = 1;
for (pair <ll, ll> e : adj[v]) {
ll u = e.F;
if (!mark[u] and u != p) {
dfs1(u, v); sz[v] += sz[u];
}
}
}
ll dfs2(ll v, ll s, ll p) {
for (pair <ll, ll> e : adj[v]) {
ll u = e.F;
if (!mark[u] and u != p and sz[u] > s/2) return dfs2(u, s, v);
}
return v;
}
void dfs3(ll v, ll h, ll p, ll b) {
c[v].pb(mp(b, h));
for (pair <ll, ll> e : adj[v]) {
ll u = e.F;
if (!mark[u] and u != p) dfs3(u, h+e.S, v, b);
}
}
void cd(ll v) {
dfs1(v, v);
v = dfs2(v, sz[v], v);
dfs3(v, 0, v, v);
mark[v] = 1;
for (pair <ll, ll> e : adj[v]) {
ll u = e.F;
if (!mark[u]) cd(u);
}
}
void Init(int N, int A[], int B[], int D[]) {
n = N;
for (ll i = 0; i < n-1; i++) {
adj[A[i]].pb(mp(B[i], D[i]));
adj[B[i]].pb(mp(A[i], D[i]));
}
cd(0);
fill(mn, mn+n, inf);
}
ll Query(int S, int X[], int T, int Y[]) {
ll ans = inf;
for (ll i = 0; i < S; i++) {
ll v = X[i];
for (pair <ll, ll> p : c[v]) smin(mn[p.F], p.S);
}
for (ll i = 0; i < T; i++) {
ll v = Y[i];
for (pair <ll, ll> p : c[v]) smin(ans, mn[p.F]+p.S);
}
for (ll i = 0; i < S; i++) {
ll v = X[i];
for (pair <ll, ll> p : c[v]) mn[p.F] = inf;
}
return ans;
}
