#include <bits/stdc++.h>
#include "factories.h"
using namespace std;
const int MAX = 5e5+10, LOG = 22;
const long long int INF = 1e18;
vector<int> g[MAX], p[MAX];
vector<int> rList;
int troidProf[MAX], troidPai[MAX], sub[MAX];
long long int troidDist[LOG][MAX], mnDist[MAX];
bool isTroid[MAX], active[MAX];
void CalcSub(int v, int pai)
{
sub[v] = 1;
for(int i=0;i<g[v].size();i++)
{
int prox = g[v][i];
if(prox == pai || isTroid[prox]) continue;
CalcSub(prox,v);
sub[v] += sub[prox];
}
return;
}
int FindTroid(int v, int pai, int sz)
{
for(int i=0;i<g[v].size();i++)
{
int prox = g[v][i];
if( prox == pai || isTroid[prox] ) continue;
if( sub[prox] > sz/2 ) return FindTroid(prox,v,sz);
}
return v;
}
void CalcDist(int v, int pai, int prof)
{
for(int i=0;i<g[v].size();i++)
{
int prox = g[v][i], peso = p[v][i];
if(prox == pai || isTroid[prox]) continue;
troidDist[prof][prox] = troidDist[prof][v] + peso;
CalcDist(prox,v,prof);
}
return;
}
void Decompose(int v, int prof, int ultTroid)
{
CalcSub(v,v);
int troid = FindTroid(v,v,sub[v]);
isTroid[troid] = 1;
troidProf[troid] = prof;
troidPai[troid] = ultTroid;
CalcDist(troid,troid,prof);
for(int i=0;i<g[troid].size();i++)
{
int prox = g[troid][i];
if(isTroid[prox]) continue;
Decompose(prox,prof+1,troid);
}
return;
}
void Init(int N, int A[], int B[], int D[])
{
for(int i=0;i<N-1;i++)
{
g[ A[i] ].push_back( B[i] ); g[ B[i] ].push_back( A[i] );
p[ A[i] ].push_back( D[i] ); p[ B[i] ].push_back( D[i] );
}
for(int i=0;i<N;i++) mnDist[i] = INF;
Decompose(0,0,-1);
return;
}
long long int Query(int S, int X[], int T, int Y[])
{
long long int resp = INF;
for(int i=0;i<S;i++)
{
int v = X[i], troid = v;
while(troid != -1)
{
mnDist[troid] = min( mnDist[troid] , troidDist[ troidProf[troid] ][v] );
rList.push_back(troid);
troid = troidPai[troid];
}
}
for(int i=0;i<T;i++)
{
int v = Y[i], troid = v;
while(troid != -1)
{
resp = min( resp , mnDist[troid] + troidDist[ troidProf[troid] ][v] );
troid = troidPai[troid];
}
}
for(int i=0;i<rList.size();i++) mnDist[rList[i]] = INF;
rList.clear();
return resp;
}
