#include <bits/stdc++.h>
#include "factories.h"
using namespace std;
#define pii pair<int,long long>
#define F first
#define S second
#define pb push_back
bool jafoi[500005];
vector<pii> adj[500005] , vt[500005];
int n , pai[500005] , lca[22][500005] , depth[500005] , st[500005] , t= 0 , ed[500005] ;
long long dist[500005] , dp[2][500005];
int op[1000000];
int pointer = 0;
void pre_dfs(int x , int y){
pai[x] = y;
st[x] = ++t;
for(int j = 0 ; j < adj[x].size() ; j++){
pii u = adj[x][j];
if(u.first == y) continue;
dist[u.first] = dist[x] + u.second;
depth[u.first] = depth[x] + 1;
pre_dfs(u.first, x);
}
ed[x] = t;
}
int query_lca(int x , int y){
if(depth[x] > depth[y]) swap(x,y);
for(int j = 21 ; j >= 0 ; j--){
long long u = depth[y] - (1<<j);
if(u >= depth[x]){
y = lca[j][y];
}
}
if(x == y) return x;
for(int j = 21 ; j >= 0 ; j--){
if(lca[j][x] != lca[j][y] && lca[j][x] != -1){
x = lca[j][x] , y = lca[j][y];
}
}
return pai[x];
}
void Init(int N, int A[], int B[], int D[]){
n = N;
for(int i = 0 ; i < N - 1 ; i++){
adj[A[i]].pb(pii(B[i] , D[i]));
adj[B[i]].pb(pii(A[i] , D[i]));
}
depth[0] = 0 , dist[0] = 0;
pre_dfs(0 , - 1 );
pai[0] = -1;
for(int i = 0 ; i < N ; i++){
lca[0][i] = pai[i];
}
for(int j = 1 ; j < 22 ; j++){
for(int i = 0 ; i < N ; i++){
lca[j][i] = lca[j-1][lca[j-1][i]];
}
}
}
bool cmp(int a , int b){
return st[a] < st[b];
}
long long ansz = 0;
void solve(int x , int y){
for(int j = 0 ; j < vt[x].size() ; j++){
pii u = vt[x][j];
if(u.F == y) continue;
solve(u.F, x);
ansz = min(ansz , min(dp[0][x] + dp[1][u.F] + u.S , dp[1][x] + dp[0][u.F] + u.S));
dp[0][x] = min(dp[0][x] , dp[0][u.F] + u.S);
dp[1][x] = min(dp[1][x] , dp[1][u.F] + u.S);
}
return ;
}
long long Query(int S , int X[] , int T , int Y[]){
pointer = 0;
for(int i = 0 ; i < S ;i ++){
if(!jafoi[X[i]]){
op[pointer++] = X[i];
jafoi[X[i]] = 1;
}
}
for(int i = 0 ; i < T ;i ++){
if(!jafoi[Y[i]]){
op[pointer++] = Y[i];
jafoi[Y[i]] = 1;
}
}
sort(op , op + pointer , cmp);
int Z = (pointer)- 1;
for(int i = 0 ; i < Z ; i++){
int L = query_lca(op[i] , op[i+1]);
if(!jafoi[L]){
op[pointer++] = L;
jafoi[L] = 1;
}
}
sort(op , op + pointer , cmp);
stack<int> w;
int root = 0;
for(int i = 0 ; i < pointer ; i++){
dp[0][op[i]] = 1000000000000000LL;
dp[1][op[i]] = 1000000000000000LL;
if(w.empty()) w.push(op[i]) , root = op[i];
else{
while(w.size() && !(st[w.top()] <= st[op[i]] && st[op[i]] <= ed[w.top()])){
w.pop();
}
long long u =dist[op[i]] - dist[w.top()];
vt[op[i]].push_back(pii(w.top() , u));
vt[w.top()].push_back(pii(op[i] , u));
w.push(op[i]);
}
}
for(int i = 0 ; i < S ; i++) dp[0][X[i]] = 0;
for(int i = 0 ; i < T ; i++) dp[1][Y[i]] = 0;
ansz = 1000000000000000LL;
solve(root , root);
for(int i = 0 ; i < pointer; i++){
vt[op[i]].clear();
jafoi[op[i]] = false;
}
return ansz;
}
