#pragma GCC optimize("Ofast")
#pragma GCC optimize("O3,unroll-loops")
#include <bits/stdc++.h>
using namespace std;
#define f0r(i, n) for (auto i = 0; i < (n); ++i)
#define fnr(i, n, k) for (auto i = (n); i < (k); ++i)
#define all(v) (v).begin(), (v).end()
#define pb push_back
#define F first
#define S second
#define ctn(x) cout << x << '\n'
#define forl(a, l) for (auto a : l)
#define ctl(l) for (auto &a : (l)) cout << a << ' '; cout << endl;
#define lb(v, x) (lower_bound(all(v), x) - begin(v))
#define ub(v, x) (upper_bound(all(v), x) - begin(v))
#define pq priority_queue
template <class T>
using V = vector<T>;
using ll = long long;
using vi = V<int>;
using vl = V<ll>;
using pi = pair<int, int>;
using ti = tuple<int, int, int>;
using Adj = V<V<pi>>;
using vvi = V<vi>;
#include "factories.h"
const ll MX = 1e17;
Adj G;
struct centroid {
vi sz;
V<bool> rem;
V<V<pi>> ancs;
V<vl> close;
centroid() {}
centroid(int n): sz(n), rem(n), ancs(n), close(n, vl(2, MX)) {
build();
}
int get_sz(int v, int p = -1) {
sz[v] = 1;
for (auto &[c, w]: G[v]) if (!rem[c] && c != p) sz[v] += get_sz(c, v);
return sz[v];
}
int get_centroid(int v, int n, int p = -1) {
for (auto &[c, w]: G[v])
if (!rem[c] && c != p && sz[c] > n/2) return get_centroid(c, n, v);
return v;
}
void calc_dists(int ce, int v, int p, ll d) {
ancs[v].pb({ce, d});
for (auto &[c, w]: G[v]) if (!rem[c] && c != p)
calc_dists(ce, c, v, d+w);
}
void build(int v = 0) {
int ce = get_centroid(v, get_sz(v));
for (auto &[c, w]: G[ce]) if (!rem[c]) calc_dists(ce, c, ce, w);
rem[ce] = true;
for (auto &[c, w]: G[ce]) if (!rem[c]) build(c);
}
ll upd(int v, bool typ) {
close[v][typ] = 0;
ll ans = close[v][!typ];
for (auto &[p, d]: ancs[v]) {
close[p][typ] = min(close[p][typ], (ll)d);
ans = min(ans, close[p][typ] + close[p][!typ]);
}
return ans;
}
void reset(int v) {
close[v][0] = close[v][1] = MX;
for (auto &[p, d]: ancs[v]) close[p][0] = close[p][1] = MX;
}
};
centroid cen;
void Init(int N, int A[], int B[], int D[]) {
G = Adj(N);
f0r(i, N-1) {
G[A[i]].pb({B[i], D[i]});
G[B[i]].pb({A[i], D[i]});
}
cen = centroid(N);
}
ll Query(int S, int X[], int T, int Y[]) {
ll ans = MX;
f0r(i, S) cen.upd(X[i], 0);
f0r(i, T) {
int u = Y[i];
ans = min(ans, cen.close[u][0]);
for (auto &[p, d]: cen.ancs[u]) {
ans = min(ans, cen.close[p][0] + d);
}
//ans = min(ans, cen.upd(Y[i], 1));
}
f0r(i, S) cen.reset(X[i]);
//f0r(i, T) cen.reset(Y[i]);
return ans;
}
