#include "factories.h"
#include <iostream>
#include <queue>
#include <cassert>
#include <set>
#include <vector>
#include <algorithm>
#include <stack>
using namespace std;
typedef pair<int, int> P;
typedef pair<long long, long long> P2;
#define rep(i, n) for (int i=0; i<(n); i++)
#define all(x) x.begin(), x.end()
#define uniq(x) x.erase(unique(all(x)), x.end())
#define index(x, y) (int)(lower_bound(all(x), y) - x.begin())
#define pb push_back
#define _1 first
#define _2 second
#define INF (1LL<<60)
int N;
vector<P> G[500000];
int R[500000];
long long W[500000];
int IN[500000], OUT[500000];
int rev[500000];
vector<int> T;
vector<int> T2;
int pos[500000];
int sparseL[20][1000000], sparseR[20][1000000];
void dfs(int x, int p, int r, long long w) {
IN[x] = T.size();
rev[IN[x]] = x;
T.pb(x);
pos[x] = T2.size();
T2.pb(IN[x]);
R[x] = r, W[x] = w;
for (P pp : G[x]) if (pp._1 != p) {
dfs(pp._1, x, r+1, w+pp._2);
T2.pb(IN[x]);
}
OUT[x] = (int)T.size()-1;
}
inline int rmq_min(int l, int r) {
int k = 31-__builtin_clz(r-l+1);
return min(sparseL[k][l], sparseR[k][r]);
}
inline int lca(int x, int y) {
if (x == y) return x;
if (pos[x] > pos[y]) swap(x, y);
return rev[rmq_min(pos[x], pos[y])];
}
void Init(int NN, int A[], int B[], int D[]) {
N = NN;
rep(i, N-1) {
G[A[i]].pb(P(B[i], D[i]));
G[B[i]].pb(P(A[i], D[i]));
}
dfs(0, -1, 0, 0);
rep(i, T2.size()) sparseL[0][i] = sparseR[0][i] = T2[i];
rep(k, 19) rep(i, T2.size()) {
sparseL[k+1][i] = sparseL[k][i];
sparseR[k+1][i] = sparseR[k][i];
if (i+(1<<k) < T2.size()) sparseL[k+1][i] = min(sparseL[k+1][i], sparseL[k][i+(1<<k)]);
if (i-(1<<k) >= 0) sparseR[k+1][i] = min(sparseR[k+1][i], sparseR[k][i-(1<<k)]);
}
}
long long D[500000];
bool isS[500000], isT[500000];
vector<int> G2[500000];
long long ans;
P2 dfs(int x) {
P2 m = P2(isS[x]?0:INF, isT[x]?0:INF);
for (int t : G2[x]) {
long long w = W[t]-W[x];
P2 p = dfs(t);
m._1 = min(m._1, p._1+w);
m._2 = min(m._2, p._2+w);
}
ans = min(ans, m._1+m._2);
return m;
}
long long Query(int S, int X[], int T, int Y[]) {
vector<int> ps;
rep(i, S) ps.pb(IN[X[i]]);
rep(i, T) ps.pb(IN[Y[i]]);
sort(all(ps)); uniq(ps);
vector<int> new_ps(ps);
rep(i, (int)ps.size()-1) {
int v = lca(rev[ps[i]], rev[ps[i+1]]);
if (v != rev[ps[i]] && v != rev[ps[i+1]]) new_ps.pb(IN[v]);
}
swap(new_ps, ps);
sort(all(ps)); uniq(ps);
stack<int> st;
for (int &p : ps) p = rev[p];
for (int v : ps) {
D[v] = INF;
while (!st.empty() && !(IN[st.top()] <= IN[v] && IN[v] <= OUT[st.top()])) st.pop();
if (!st.empty()) {
int p = st.top();
G2[p].pb(v);
}
st.push(v);
}
rep(i, S) isS[X[i]] = true;
rep(i, T) isT[Y[i]] = true;
ans = INF;
dfs(ps[0]);
rep(i, S) isS[X[i]] = false;
rep(i, T) isT[Y[i]] = false;
for (int v : ps) G2[v].clear();
//for (int v : ps) G2[v].clear(), G2[v].shrink_to_fit();
return ans;
}
