/* Bismillahir Rahmanir Rahim */
#include <bits/stdc++.h>
#include "factories.h"
using namespace std;
typedef pair <int, int> pii;
const int N = 500005;
const long long oo = 1e18;
vector < vector <pii>> g(N);
vector < int > e[N];
long long mn[N], dis[N];
long long pre[N][25], idx[N];
int n, anc[N], sub[N], vis[N];
void dfs(int at, int par){
pre[at][++idx[at]] = dis[at];
sub[at] = 1;
for(auto u : g[at]){
if(vis[u.first] || u.first == par) continue;
dis[u.first] = dis[at] + u.second;
dfs(u.first, at);
sub[at] += sub[u.first];
}
}
void decompose(int at, int par, int tot){
int cen = 0, mx = -1;
for(auto u : g[at]){
if(vis[u.first] || sub[u.first] > sub[at]) continue;
if(sub[u.first] > mx){
cen = u.first;
mx = sub[cen];
}
}
if(mx <= tot / 2){
if(par){
anc[at] = par;
}
tot = 0;
vis[at] = 1;
dis[at] = 0;
dfs(at, at);
for(auto u : g[at]){
if(!vis[u.first]){
decompose(u.first, at, sub[u.first]);
}
}
}
else decompose(cen, par, tot);
}
long long Query(int S, int X[], int T, int Y[]){
int cur, from, j;
for(int i = 0; i < S; ++i){
cur = X[i] + 1, from = X[i] + 1, j = 1;
for(j = idx[from]; j; --j){
mn[cur] = min(mn[cur], pre[from][j]);
cur = anc[cur];
}
}
long long ret = oo;
for(int i = 0; i < T; ++i){
cur = Y[i] + 1, from = Y[i] + 1, j = 1;
for(j = idx[from]; j; --j){
ret = min(ret, pre[from][j] + mn[cur]);
cur = anc[cur];
}
}
for(int i = 0; i < S; ++i){
cur = X[i] + 1;
while(cur) mn[cur] = oo, cur = anc[cur];
}
return ret;
}
void Init(int N, int A[], int B[], int D[]){
n = N;
for(int i = 0; i < N - 1; ++i){
g[A[i] + 1].push_back({B[i] + 1, D[i]});
g[B[i] + 1].push_back({A[i] + 1, D[i]});
}
memset(idx, -1, sizeof(idx));
dfs(1, 0);
decompose(1, 0, sub[1]);
for(int i = 1; i <= n; ++i) mn[i] = oo;
}
