#include"factories.h"
#include<bits/stdc++.h>
using namespace std;
#define ii pair<int,int>
#define il pair<int,long long>
#define fi first
#define se second
const int MAXN=1e6+5;
const long long INF=1e18;
int dt[MAXN],L[MAXN],R[MAXN],tag[MAXN],tdfs=0,nn;
long long dis[MAXN],dp[MAXN][2],ans;
vector<ii> ds[MAXN];
vector<il> sd[MAXN];
ii sp[MAXN][21];
bool ck[MAXN];
bool comp(int a,int b) { return L[a]<L[b]; }
int getlog(long long n) { return 63-__builtin_clzll(n); }
void minimize(long long& a,long long b)
{
if(a>b) a=b;
}
void dfs(int i,int pre)
{
L[i]=R[i]=++tdfs,sp[tdfs][0]={dt[i],i};
for(auto v:ds[i]) if(v.fi!=pre)
{
dis[v.fi]=dis[i]+v.se,dt[v.fi]=dt[i]+1;
dfs(v.fi,i);
R[i]=++tdfs,sp[tdfs][0]={dt[i],i};
}
}
int lca(int a,int b)
{
int l=min(L[a],L[b]),r=max(R[a],R[b]),lg=getlog(r-l+1);
return min(sp[l][lg],sp[r-(1<<lg)+1][lg]).se;
}
void dfsus(int i,int pre)
{
for(auto v:sd[i]) if(v.fi!=pre)
{
dfsus(v.fi,i);
minimize(dp[i][0],dp[v.fi][0]+v.se);
minimize(dp[i][1],dp[v.fi][1]+v.se);
}
minimize(ans,dp[i][0]+dp[i][1]);
}
void Init(int n,int A[],int B[],int D[])
{
nn=n;
for(int i=0;i<n-1;i++) ds[A[i]].push_back({B[i],D[i]}),ds[B[i]].push_back({A[i],D[i]});
dfs(0,0);
for(int j=1;(1<<j)<=tdfs;j++) for(int i=1;i<=tdfs-(1<<j)+1;i++) sp[i][j]=min(sp[i][j-1],sp[i+(1<<(j-1))][j-1]);
}
long long Query(int s,int X[],int t,int Y[])
{
ans=INF;
vector<int> vi;
for(int i=0;i<s;i++) vi.push_back(X[i]);
for(int i=0;i<t;i++) vi.push_back(Y[i]);
sort(vi.begin(),vi.end(),comp);
int sz=vi.size();
for(int i=0;i<sz-1;i++) vi.push_back(lca(vi[i],vi[i+1]));
sort(vi.begin(),vi.end(),comp);
vi.erase(unique(vi.begin(),vi.end()),vi.end());
stack<int> st;
for(auto v:vi)
{
while(!st.empty()&&!(L[st.top()]<=L[v]&&R[v]<=R[st.top()])) st.pop();
if(!st.empty()) sd[st.top()].push_back({v,dis[v]-dis[st.top()]});
dp[v][0]=dp[v][1]=INF,st.push(v);
}
for(int i=0;i<s;i++) dp[X[i]][0]=0;
for(int i=0;i<t;i++) dp[Y[i]][1]=0;
dfsus(vi[0],vi[0]);
for(auto v:vi) sd[v].clear();
return ans;
}
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