/*
IN THE NAME OF GOD
*/
#include <bits/stdc++.h>
#include "factories.h"
// #pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
using namespace std;
typedef long long ll;
typedef pair<ll, ll> pll;
typedef pair<int, int> pii;
typedef long double ld;
#define F first
#define S second
#define Mp make_pair
#define pb push_back
#define pf push_front
#define size(x) ((ll)x.size())
#define all(x) (x).begin(),(x).end()
#define kill(x) cout << x << '\n', exit(0);
#define fuck(x) cout << "(" << #x << " , " << x << ")" << endl
#define endl '\n'
const int N = 5e5+23, lg = 19;
ll Mod = 1e9+7; //998244353;
inline ll MOD(ll a, ll mod=Mod) {a%=mod; (a<0)&&(a+=mod); return a;}
inline ll poww(ll a, ll b, ll mod=Mod) {
ll ans = 1;
a=MOD(a, mod);
while (b) {
if (b & 1) ans = MOD(ans*a, mod);
b >>= 1;
a = MOD(a*a, mod);
}
return ans;
}
int n, tin[N], tout[N], tim, par[lg][N], h[N], mark[N];
ll wh[N], dp[2][N];
vector<pll> adj[N];
vector<int> tree[N];
void init(int v, int p) {
par[0][v] = p, tin[v] = ++tim;
for(int i=1; i<lg; i++) par[i][v] = par[i-1][par[i-1][v]];
for(auto u : adj[v]) {
if(u.F == p) continue;
h[u.F] = h[v] + 1, wh[u.F] = wh[v] + u.S;
init(u.F, v);
}
tout[v] = tim+1;
}
int getPar(int v, int dist) {
for(int i=0; i<lg; i++) if((dist>>i)%2 == 1) v=par[i][v];
return v;
}
int LCA(int v, int u) {
if(h[v] > h[u]) swap(v, u);
u = getPar(u, h[u]-h[v]);
if(v == u) return v;
for(int i=lg-1; i>=0; i--) {
if(par[i][v] != par[i][u]) v=par[i][v], u=par[i][u];
}
return par[0][v];
}
void Init(int _n, int _a[], int _b[], int _d[]) {
n=_n;
for(int i=0; i<n-1; i++) {
_a[i] ++, _b[i] ++;
adj[_a[i]].pb({_b[i], _d[i]}); adj[_b[i]].pb({_a[i], _d[i]});
}
init(1, 0);
}
bool cmp(int i, int j) {
return (tin[i]<tin[j] ? true : false);
}
ll ans = 1e18;
void dfs(int v, int p=0) {
dp[0][v]=dp[1][v]=1e18;
if(mark[v]==1) dp[0][v]=0;
if(mark[v]==2) dp[1][v]=0;
for(auto u : tree[v]) {
dfs(u);
dp[0][v]=min(dp[0][v], dp[0][u]+wh[u]-wh[v]);
dp[1][v]=min(dp[1][v], dp[1][u]+wh[u]-wh[v]);
}
ans = min(ans, dp[0][v]+dp[1][v]);
}
ll Query(int s, int V[], int t, int U[]) {
//return 2;
vector<int> vec;
for(int i=0;i<s;i++) {
V[i]++; mark[V[i]] = 1; vec.pb(V[i]);
}
for(int i=0;i<t;i++) {
U[i]++; mark[U[i]] = 2; vec.pb(U[i]);
}
sort(all(vec), cmp);
int ttt = size(vec);
for(int i=0; i<ttt-1; i++) vec.pb(LCA(vec[i],vec[i+1]));
sort(all(vec));
vec.resize(unique(all(vec)) - vec.begin());
sort(all(vec), cmp);
vector<int> st; st.pb(vec[0]);
//for(auto it : vec) fuck(it);
for(int i=1; i<size(vec); i++) {
while(tout[st.back()]<=tin[vec[i]]) st.pop_back();
tree[st.back()].pb(vec[i]);
st.pb(vec[i]);
}
//fuck("here");
ans = 1e18;
dfs(st[0]);
for(auto it : vec) {
tree[it].clear();
mark[it] = 0;
}
return ans;
}
