#include "factories.h"
#include <iostream>
#include <vector>
#include <algorithm>
#include <queue>
using namespace std;
const long long inf = 1'000'000'000'000'000;
struct idt
{
int y;
long long dist;
bool const operator<(const idt &oth) const
{
return dist>oth.dist;
}
};
int n,idx;
vector<int> nxt,top,sz,cen,active;
vector<idt> G;
priority_queue<idt> Q[500005];
vector<vector<pair<int,long long>>> up;
void add_edge(int x,int y,int dist)
{
idx++;
G[idx]={y,dist};
nxt[idx]=top[x];
top[x]=idx;
}
int Size(int x,int tata)
{
sz[x]=1;
for(int i=top[x];i;i=nxt[i])
{
int y=G[i].y;
if(y==tata || cen[y])
continue;
sz[x]+=Size(y,x);
}
return sz[x];
}
int centroid(int x,int size,int tata)
{
for(int i=top[x];i;i=nxt[i])
{
int y=G[i].y;
if(y==tata || cen[y])
continue;
if(2*sz[y]>size)
return centroid(y,size,x);
}
return x;
}
void dfs(int x,int c,int tata,long long d)
{
up[x].emplace_back(c,d);
for(int i=top[x];i;i=nxt[i])
{
auto [y,dist]=G[i];
if(y==tata || cen[y])
continue;
dfs(y,c,x,d+dist);
}
}
void decompose(int x,int tata)
{
int c=centroid(x,Size(x,tata),tata);
for(int i=top[c];i;i=nxt[i])
{
auto [y,dist]=G[i];
if(y==c || cen[y])
continue;
dfs(y,c,c,dist);
}
cen[c]=1;
for(int i=top[c];i;i=nxt[i])
{
int y=G[i].y;
if(y==c || cen[y])
continue;
decompose(y,c);
}
}
void Init(int N,int A[],int B[],int D[])
{
n=N;
G=vector<idt>(2*n+1);
nxt=vector<int>(2*n+1);
top=cen=sz=active=vector<int>(n+1);
up=vector<vector<pair<int,long long>>>(n+1);
for(int i=1;i<=n-1;i++)
{
add_edge(A[i-1]+1,B[i-1]+1,D[i-1]);
add_edge(B[i-1]+1,A[i-1]+1,D[i-1]);
}
decompose(1,0);
}
long long dist_to_active(int c)
{
long long ans=inf;
while(!Q[c].empty())
{
auto [x,d]=Q[c].top();
if(active[x])
return d;
Q[c].pop();
}
return ans;
}
void upd(int x)
{
Q[x].emplace(x,0);
for(auto [c,dist]:up[x])
Q[c].emplace(x,dist);
}
long long que(int x)
{
long long ans=inf;
for(auto [c,dist]:up[x])
{
ans=min(ans,dist+dist_to_active(c));
}
return ans;
}
long long Query(int S,int X[],int T,int Y[])
{
long long ans=inf;
for(int i=1;i<=S;i++)
{
upd(X[i-1]+1);
active[X[i-1]+1]=1;
}
for(int i=1;i<=T;i++)
{
ans=min(ans,que(Y[i-1]+1));
}
for(int i=1;i<=S;i++)
{
active[X[i-1]+1]=0;
}
return ans;
}
