#include "factories.h"
#include <bits/stdc++.h>
using namespace std;
#define int long long
#define fi first
#define se second
#define cmin(a, b) a = min(a, b)
const int inf = 1e18;
const signed LOG=18;
signed n;
vector<pair<signed, signed>> adj[500005];
unordered_map<signed, unordered_map<signed, int>> dists;
signed sz[500005], par[500005];
bool centro[500005];
void dfs(signed u, signed p) {
sz[u]=1;
for (auto [v, w]: adj[u]) if (v!=p && !centro[v]) {
dfs(v, u);
sz[u]+=sz[v];
}
}
signed centroid(signed u, signed p, signed obj) {
for (auto [v, w]: adj[u]) if (v!=p && !centro[v]) {
if (sz[v]*2>=obj) return centroid(v, u, obj);
}
return u;
}
void calc(signed u, signed p, int d, signed c) {
dists[c][u]=d;
for (auto [v, w]: adj[u]) if (v!=p && !centro[v]) {
calc(v, u, d+w, c);
}
}
signed decompose(signed u, signed p) {
if (centro[u]) return u;
dfs(u, u);
signed c=centroid(u, u, sz[u]); centro[c]=1;
par[c]=p; calc(c, c, 0, c);
for (auto [v, w]: adj[c]) if (!centro[v]) {
decompose(v, c);
}
return c;
}
int distres[500005];
void update(signed u, signed changing) {
if (u==-1) return;
cmin(distres[u], dists[u][changing]);
update(par[u], changing);
}
void reset(signed u, signed changing) {
if (u==-1) return;
distres[u]=inf;
reset(par[u], changing);
}
int query(signed u, signed changing) {
if (u==-1) return inf;
return min(distres[u]+dists[u][changing], query(par[u], changing));
}
void Init(signed N, signed A[], signed B[], signed D[]) {
n=N;
for (int i=0; i<n-1; i++) {
adj[A[i]].push_back({B[i], D[i]});
adj[B[i]].push_back({A[i], D[i]});
distres[i]=inf, centro[i]=0;
}
distres[n-1]=inf, centro[n-1]=0;
decompose(0, -1);
}
int Query(signed S, signed X[], signed T, signed Y[]) {
int ans=inf;
for (int i=0; i<S; i++) update(X[i], X[i]);
for (int i=0; i<T; i++) cmin(ans, query(Y[i], Y[i]));
for (int i=0; i<S; i++) reset(X[i], X[i]);
return ans;
}
