#include "factories.h"
#include <bits/stdc++.h>
using namespace std;
const int ms = 5e5 + 20;
const long long inf = 1e18L + 20;
const int st = 20;
vector<pair<int, int>> adj[ms];
vector<pair<int, long long>> vch[ms];
long long de[ms];
int ti[ms];
int to[ms];
int f[ms];
long long dp[ms][2];
int par[ms][st];
int tz;
void dfs1(int u, int pr) {
ti[u] = ++tz;
for (auto x: adj[u]) {
int v = x.first;
int w = x.second;
if (v != pr) {
par[v][0] = u;
de[v] = de[u] + w;
dfs1(v, u);
}
}
to[u] = ++tz;
}
bool cmp(int u, int v) {
return ti[u] < ti[v];
}
bool anc(int u, int v) {
return ti[u] < ti[v] && to[v] < to[u];
}
int lca(int u, int v) {
if (anc(u, v)) {
return u;
}
if (anc(v, u)) {
return v;
}
for (int i = st - 1; i >= 0; i--) {
if (!anc(par[u][i], v)) {
u = par[u][i];
}
}
return par[u][0];
}
void Init(int N, int A[], int B[], int D[]) {
for (int i = 0; i < N - 1; i++) {
int u = A[i];
int v = B[i];
u++;
v++;
int w = D[i];
adj[u].push_back({v, w});
adj[v].push_back({u, w});
}
for (int i = 1; i <= N; i++) {
f[i] = -1;
}
par[1][0] = 1;
dfs1(1, -1);
for (int k = 1; k < st; k++) {
for (int i = 1; i <= N; i++) {
par[i][k] = par[par[i][k - 1]][k - 1];
}
}
}
void dfs2(int u) {
dp[u][0] = inf;
dp[u][1] = inf;
if (f[u] != -1) {
dp[u][f[u]] = 0;
}
for (auto x: vch[u]) {
int v = x.first;
long long w = x.second;
dfs2(v);
dp[u][0] = min(dp[u][0], dp[v][0] + w);
dp[u][1] = min(dp[u][1], dp[v][1] + w);
}
}
long long Query(int S, int X[], int T, int Y[]) {
vector<int> q;
for (int i = 0; i < S; i++) {
int u = X[i];
u++;
f[u] = 0;
q.push_back(u);
}
for (int i = 0; i < T; i++) {
int u = Y[i];
u++;
f[u] = 1;
q.push_back(u);
}
int sz = q.size();
sort(q.begin(), q.end(), cmp);
for (int i = 0; i < sz - 1; i++) {
q.push_back(lca(q[i], q[i + 1]));
}
sort(q.begin(), q.end(), cmp);
q.erase(unique(q.begin(), q.end()), q.end());
sz = q.size();
int root = q[0];
vector<int> p = {root};
for (int i = 1; i < sz; i++) {
int v = q[i];
while (!anc(p.back(), v)) {
p.pop_back();
}
int u = p.back();
vch[u].push_back({v, de[v] - de[u]});
p.push_back(v);
}
dfs2(root);
long long res = inf;
for (auto u: q) {
res = min(res, dp[u][0] + dp[u][1]);
vch[u].clear();
f[u] = -1;
}
return res;
}
