#include "factories.h"
#include <bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define mp make_pair
#define eb emplace_back
#define pb push_back
#pragma GCC optimize("O3")
#pragma GCC optimize("Ofast")
typedef long long LL;
typedef long double LD;
typedef pair<int,int> pii;
const int logn=19;
const int MAXN=500000;
int par[logn+3][MAXN+5]={},depth[MAXN+5]={},n;
LL jarak[MAXN+5]={};
vector <pii> node[MAXN+5];
inline void inisLCA(int now,int _par,int _depth,LL _jarak){
depth[now]=_depth;
jarak[now]=_jarak;
par[0][now]=_par;
for(auto v:node[now])
{
if(v.fi==_par)
continue;
inisLCA(v.fi,now,_depth+1,_jarak+v.se);
}
}
inline void inisLCA(){
inisLCA(1,0,0,0);
for(int j=1;j<logn;++j)
for(int i=1;i<=n;++i)
par[j][i]=par[j-1][par[j-1][i]];
}
inline int LCA(int u,int v){
if(depth[u]>depth[v])
swap(u,v);
int beda=depth[v]-depth[u],lsone;
while(beda)
{
lsone=beda&-beda;
v=par[__builtin_popcount(lsone-1)][v];
beda^=lsone;
}
if(u==v)
return u;
for(int i=logn-1;i>=0;--i)
{
if(par[i][u]!=par[i][v])
u=par[i][u],v=par[i][v];
}
return par[0][u];
}
inline LL dist(int u,int v){
return jarak[u]+jarak[v]-(jarak[LCA(u,v)]<<1);
}
int parCtr[MAXN+5]={},subtree[MAXN+5]={};
int hitungSubtree(int now,int tadi){
assert(parCtr[now]==-1);
subtree[now]=1;
for(auto v:node[now])
{
if(v.fi==tadi||parCtr[v.fi]!=-1)
continue;
subtree[now]+=hitungSubtree(v.fi,now);
}
return subtree[now];
}
void buatCtr(int now,int tadi){
assert(parCtr[now]==-1);
int target=hitungSubtree(now,-1)>>1;
int pilihan=-1,skipAja=tadi;
bool lanjut=true;
while(lanjut)
{
lanjut=false;
for(auto v:node[now])
{
if(v.fi==skipAja||parCtr[v.fi]!=-1)
continue;
if(subtree[v.fi]>target)
{
lanjut=true;
pilihan=v.fi;
}
}
if(lanjut)
{
skipAja=now;
now=pilihan;
}
}
parCtr[now]=tadi;
for(auto v:node[now])
{
if(parCtr[v.fi]==-1)
buatCtr(v.fi,now);
}
}
vector <LL> distPar[MAXN+5];
inline void distancePar(){
for(int i=1;i<=n;i++)
for(int j=i;j;j=parCtr[j])
distPar[i].pb(dist(i,j));
}
inline void buatCtr(){
memset(parCtr,-1,sizeof(parCtr));
buatCtr(1,0);
distancePar();
}
void Init(int N,int A[],int B[],int D[]){
n=N;
for(int i=0;i<N-1;++i)
{
++A[i];++B[i];
node[A[i]].eb(B[i],D[i]);
node[B[i]].eb(A[i],D[i]);
}
inisLCA();
memset(parCtr,-1,sizeof(parCtr));
buatCtr();
}
int lastReset[MAXN+5]={},kejadian=0;
LL registered[MAXN+5];
const LL INF=1000000000000000;
inline void ngeFix(int pos){
if(lastReset[pos]!=kejadian)
{
registered[pos]=INF;
lastReset[pos]=kejadian;
}
}
inline void update(int pos){
for(int i=0,now=pos;now;i++,now=parCtr[now])
{
ngeFix(now);
registered[now]=min(registered[now],distPar[pos][i]);
}
}
inline LL Query(int pos){
LL ret=INF;
for(int i=0,now=pos;now;i++,now=parCtr[now])
{
ngeFix(now);
ret=min(ret,registered[now]+distPar[pos][i]);
}
return ret;
}
LL Query(int S,int X[],int T,int Y[]){
for(int i=0;i<S;++i) ++X[i];
for(int i=0;i<T;++i) ++Y[i];
++kejadian;
for(int i=0;i<S;++i)
update(X[i]);
LL ret=INF;
for(int i=0;i<T;++i)
ret=min(ret,Query(Y[i]));
return ret;
}
