#include <bits/stdc++.h>
#include <factories.h>
/*#pragma comment(linker, "/stack:200000000")
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")*/
#pragma GCC optimize("O2")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("avx,avx2,sse,sse2,fma")
using namespace std;
using ll = long long int;
#define F first
#define S second
#define pb push_back
#define lc v<<1
#define rc v<<1|1
#define fast_io ios::sync_with_stdio(false);cin.tie(nullptr);cout.tie(nullptr);
const int N=5e5+10,LN=20,M=2e2+10,SQ=250,inf=1e9;
const ll INF=1e18;
const int MOD=1000000007 /*998244353*/;
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
using pll=pair<ll,ll>;
using pii=pair<int,int>;
#define ordered_set tree<ll, null_type,less<ll>, rb_tree_tag,tree_order_statistics_node_update>
ll pow(ll x, ll y, ll mod){
ll ans=1;
while (y != 0) {
if (y & 1) ans = ans * x % mod;
y >>= 1;
x = x * x % mod;
}
return ans;
}
ll n,h[N],H[N],p[LN][N],st[N],t,q,mp[N],di[N];
vector<pll> adj[N];
vector<ll> z;
stack<ll> s;
queue<ll> pq;
bool iq[N];
void dfs(ll v, ll P=0){
p[0][v]=P;
st[v]=++t;
for(auto [u,w] : adj[v]){
if(u!=P) H[u]=H[v]+1,h[u]=h[v]+w,dfs(u,v);
}
}
bool cmp(ll a, ll b){
return st[a]<st[b];
}
ll LCA(ll v, ll u){
if(H[u]<H[v]) swap(v,u);
for(ll i=LN; i--;){
if(H[p[i][u]]>=H[v]) u=p[i][u];
}
if(v==u) return v;
for(ll i=LN; i--;){
if(p[i][u]!=p[i][v]) u=p[i][u],v=p[i][v];
}
return p[0][v];
}
ll dist(ll v, ll u){
ll z=LCA(v,u);
return h[v]+h[u]-2*h[z];
}
void Init(int n, int A[], int B[], int D[]){
fast_io;
cin >> n;
memset(di,63,sizeof di);
memset(mp,-1,sizeof mp);
for(ll i=0; i<n-1; i++){
ll v=A[i],u=B[i],w=D[i];
v++;
u++;
adj[v].pb({u,w});
adj[u].pb({v,w});
}
dfs(H[1]=1);
for(ll i=1; i<LN; i++)
for(ll j=1; j<=n; j++)
p[i][j]=p[i-1][p[i-1][j]];
}
ll Query(int S, int X[], int T, int Y[]){
ll x=S,y=T,ans=INF;
z.clear();
while(!s.empty()) s.pop();
for(ll i=0; i<x; i++){
ll P=X[i];
P++;
z.pb(P);
mp[P]=0;
}
for(ll i=0; i<y; i++){
ll P=Y[i];
P++;
z.pb(P);
mp[P]=1;
}
sort(z.begin(),z.end(),cmp);
for(ll i=0; i<x+y-1; i++) z.pb(LCA(z[i],z[i+1]));
z.pb(LCA(z[0],z[x+y-1]));
sort(z.begin(),z.end(),cmp);
z.resize(unique(z.begin(),z.end())-z.begin());
s.push(z[0]);
if(!mp[z[0]]) di[z[0]]=0,pq.push(z[0]),iq[z[0]]=1;
adj[z[0]].clear();
for(ll i=1; i<z.size(); i++){
adj[z[i]].clear();
while(LCA(z[i],s.top())!=s.top()) s.pop();
ll d=dist(s.top(),z[i]);
adj[s.top()].pb({z[i],d});
adj[z[i]].pb({s.top(),d});
s.push(z[i]);
if(!mp[z[i]]) di[z[i]]=0,iq[z[i]]=1,pq.push(z[i]);
}
while(!pq.empty()){
auto v=pq.front();
pq.pop();
if(mp[v]==1) ans=min(ans,di[v]);
iq[v]=0;
for(auto [u,w] : adj[v]){
if(di[v]+w<di[u]){
di[u]=di[v]+w;
if(!iq[u]) pq.push(u);
}
}
}
for(ll i : z){
mp[i]=-1;
di[i]=di[0];
}
return ans;
}
