// #pragma GCC optimize("Ofast,unroll-loops")
// #pragma comment(linker, "/stack:200000000")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,fma")
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include "factories.h"
using namespace std;
using namespace __gnu_pbds;
typedef int ll;
typedef long double ld;
typedef pair <ll, ll> pll;
#ifdef SINA
#define dbg(...) __f(#__VA_ARGS__, __VA_ARGS__)
template <typename Arg1> void __f(const char* name, Arg1&& arg1) { cout << name << " : " << arg1 << std::endl; }
template <typename Arg1, typename... Args> void __f (const char* names, Arg1&& arg1, Args&&... args) {
const char* comma = strchr(names + 1, ',');cout.write(names, comma - names) << " : " << arg1<<" | ";__f(comma+1, args...); }
#define dbg2(x, j, n) cout<< #x << " : "; output((j), (n), x, 1); cout.flush();
#else
#define dbg(...) 0
#define dbg2(x, j, n) 0
#endif
#define SZ(x) ((ll)((x).size()))
#define File(s, t) freopen(s ".txt", "r", stdin); freopen(t ".txt", "w", stdout);
#define input(j, n, a) for (int _i = (j); _i < (n)+(j); _i++) cin>> a[_i];
#define output(j, n, a, t) for (int _i = (j); _i < (n)+(j); _i++) cout<< a[_i] << (((t) && _i != (n)+(j)-1)? ' ' : '\n');
#define kill(x) return cout<< (x) << endl, 0
#define cl const ll
#define fr first
#define sc second
#define lc (v << 1)
#define rc (lc | 1)
#define mid ((l + r) >> 1)
#define All(x) (x).begin(), (x).end()
const long long inf = sizeof(long long) == 4 ? (1e9 + 10) : (3e18), mod = 1e9 + 7, MOD = 998244353;
template <class A,class B> ostream& operator << (ostream& out,const pair<A,B>&a){return out<<'('<<a.first<<", "<<a.second<<')';}
template <class A> ostream& operator << (ostream& out, const vector<A> &a) {
out<< '['; for (int i = -1; ++i < int(a.size());) out<< a[i] << (i + 1 < int(a.size()) ? ", " : ""); return out<<']'; }
template <class T, typename _t = less <T> > using Tree = tree <T, null_type, _t, rb_tree_tag, tree_order_statistics_node_update>;
cl N = 5e5 + 7, lg = 20;
ll sz [N], cen [N][lg], wcen [N], n, cur1, cur2;
long long dist [N][lg], rn [N];
vector <pll> adj [N];
bool hide [N];
ll plant (cl &v, cl &pr = -1) {
sz[v] = 1;
for (auto &u : adj[v]) if (!hide[u.fr] && u.fr != pr) sz[v] += plant(u.fr, v);
return sz[v];
}
inline ll find_centroid (ll v, cl &_n, ll pr = -1) {
for (ll i = 0; i < SZ(adj[v]); i++) {
ll &u = adj[v][i].fr;
if (sz[u] << 1 > _n && !hide[u] && u != pr) pr = v, v = u, i = -1;
}
return v;
}
void dfs (cl &v, cl &pr) {
cen[v][cur2] = cur1;
for (auto &u : adj[v]) if (!hide[u.fr] && u.fr != pr) dist[u.fr][cur2] = dist[v][cur2] + u.sc, dfs(u.fr, v);
}
void centroid_decomposition (ll v = 0, cl &lev = 0) {
v = find_centroid(v, plant(v)); cur1 = v; cur2 = lev;
wcen[v] = lev;
cen[v][lev] = v;
for (auto &u : adj[v]) if (!hide[u.fr]) dist[u.fr][lev] = u.sc, dfs(u.fr, v);
hide[v] = 1;
for (auto &u : adj[v]) if (!hide[u.fr]) centroid_decomposition(u.fr, lev + 1);
}
void Init (ll N, ll A[], ll B[], ll D[]) {
memset(rn, 61, sizeof rn);
n = N;
for (ll i = 0; i < n - 1; i++) adj[A[i]].push_back({B[i], D[i]}), adj[B[i]].push_back({A[i], D[i]});
centroid_decomposition();
}
long long Query (ll S, ll X[], ll T, ll Y[]) {
long long ans = inf;
for (ll i = 0, u; i < S; i++) {
u = X[i];
for (ll v = u, lev = wcen[v]; ~lev; lev--) {
v = cen[v][lev];
rn[v] = min(rn[v], dist[u][lev]);
}
}
for (ll i = 0, u; i < T; i++) {
u = Y[i];
for (ll v = u, lev = wcen[v]; ~lev; lev--) {
v = cen[v][lev];
ans = min(ans, rn[v] + dist[u][lev]);
}
}
for (ll i = 0; i < S; i++) for (ll v = X[i], lev = wcen[v]; ~lev; lev--) {
v = cen[v][lev];
rn[v] = inf;
}
return ans;
}
