#pragma GCC optimize("O2")
#include <bits/stdc++.h>
#include "factories.h"
#ifdef DEBUG
#include "debug.hpp"
#endif
using namespace std;
#define all(c) (c).begin(), (c).end()
#define traverse(c, it) for(auto it = (c).begin(); it != (c).end(); it++)
#define rep(i, N) for(int i = 0; i < (N); i++)
#define rep1(i, N) for(int i = 1; i <= (N); i++)
#define rep2(i, s, e) for(int i = (s); i <= (e); i++)
#define rep3(i, s, e, d) for(int i = (s); (d) >= 0 ? i <= (e) : i >= (e); i += (d))
#define pb push_back
#ifdef DEBUG
#define debug(x...) {dbg::depth++; string dbg_vals = dbg::to_string(x); dbg::depth--; dbg::fprint(__func__, __LINE__, #x, dbg_vals);}
#define light_debug(x) {dbg::light = 1; dbg::dout << __func__ << ":" << __LINE__ << " " << #x << " = " << x << endl; dbg::light = 0;}
#else
#define debug(x...)
#define light_debug(x)
#endif
template<typename T>
inline T& ckmin(T& a, T b){ return a = a > b ? b : a; }
template<typename T>
inline T& ckmax(T& a, T b){ return a = a < b ? b : a; }
using ll = long long;
using pii = pair<int, int>;
using vi = vector<int>;
struct custom_hash {
inline static uint64_t splitmix64(uint64_t x) {
// http://xorshift.di.unimi.it/splitmix64.c
x += 0x9e3779b97f4a7c15;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return x ^ (x >> 31);
}
inline size_t operator()(uint64_t x) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
return splitmix64(x + FIXED_RANDOM);
}
};
class CentroidDecomposition{
vi size, par, done;
int get_size(int v, int p, vector<vector<pii>>& adj){
size[v] = 1;
for(auto e : adj[v]){
int u = e.first;
if(!done[u] && u != p) size[v] += get_size(u, v, adj);
}
return size[v];
}
int get_centroid(int v, int p, int sz, vector<vector<pii>>& adj){
for(auto e : adj[v]){
int u = e.first;
if(!done[u] && u != p && size[u] > sz / 2) return get_centroid(u, v, sz, adj);
}
return v;
}
void build(int v, int p, vector<vector<pii>>& adj){
get_size(v, p, adj);
int c = get_centroid(v, p, size[v], adj);
par[c] = p;
done[c] = 1;
for(auto u : adj[c])
if(!done[u.first]) build(u.first, c, adj);
}
public:
void operator()(vector<vector<pii>>& adj){
int n = adj.size();
done.resize(n), size.resize(n), par.resize(n);
build(0, -1, adj);
}
inline int operator [](int i) const {
return par[i];
}
};
class TreeDist{
int n;
vector<ll> dist;
vi tour, in_time, inv_in;
vector<vi> RMQ;
void dfs(int v, ll dis, int p, vector<vector<pii>>& adj){
dist[v] = dis;
in_time[v] = tour.size();
tour.pb(in_time[v]);
for(auto u : adj[v])
if(u.first != p)
dfs(u.first, dis + u.second, v, adj), tour.pb(in_time[v]);
}
inline int rmq(int l, int r) const {
int k = __lg(r - l);
return min(RMQ[l][k], RMQ[r - (1 << k)][k]);
}
public:
void operator()(vector<vector<pii>>& adj){
n = adj.size();
dist.resize(n), in_time.resize(n);
tour.reserve(n << 1);
dfs(0, 0, 0, adj);
int m = tour.size();
inv_in.resize(m);
rep(i, n)
inv_in[in_time[i]] = i;
RMQ = vector<vi>(m, vi(__lg(m + 1) + 1, m));
rep(i, m) RMQ[i][0] = tour[i];
rep1(k, __lg(m))
rep(i, m){
RMQ[i][k] = RMQ[i][k - 1];
if(i + (1 << (k - 1)) < m)
ckmin(RMQ[i][k], RMQ[i + (1 << (k - 1))][k - 1]);
}
}
inline int lca(int u, int v) const {
if(in_time[u] > in_time[v]) swap(u, v);
return inv_in[rmq(in_time[u], in_time[v] + 1)];
}
inline ll distance(int u, int v) const {
return dist[u] + dist[v] - 2 * dist[lca(u, v)];
}
};
const ll INF = 1LL << 60;
int N;
vector<vector<pii>> adj;
CentroidDecomposition decomp;
TreeDist paths;
vector<ll> nearest;
vi upd;
void Init(int _N, int A[], int B[], int D[]) {
#ifdef DEBUG
freopen("debug", "w", stderr);
#endif
N = _N;
adj.resize(N), nearest.resize(N);
fill(all(nearest), INF);
rep(i, N - 1)
adj[A[i]].pb({B[i], D[i]}), adj[B[i]].pb({A[i], D[i]});
decomp(adj);
paths(adj);
}
long long Query(int S, int X[], int T, int Y[]) {
auto update = [&](int v){
for(int v_ = v; ~v; v = decomp[v])
ckmin(nearest[v], paths.distance(v_, v)), upd.pb(v);
};
auto query = [&](int v){
ll a = INF;
for(int v_ = v; ~v; v = decomp[v])
ckmin(a, nearest[v] + paths.distance(v_, v));
return a;
};
ll ans = INF;
rep(i, S) update(X[i]);
rep(i, T) ckmin(ans, query(Y[i]));
for(int i : upd)
nearest[i] = INF;
upd.clear();
return ans;
}
