#include "factories.h"
#include "bits/stdc++.h"
using namespace std;
#define int long long
const int MOD = 1e9 + 7;
mt19937_64 rng((int)std::chrono::steady_clock::now().time_since_epoch().count());
int rnd(int x, int y) {
int u = uniform_int_distribution<int>(x, y)(rng); return u;
}
void Init(int32_t N, int32_t A[], int32_t B[], int32_t D[]);
long long Query(int32_t S, int32_t X[], int32_t T, int32_t Y[]);
const int MAXN = 500003;
vector<pair<int, int> > adj[MAXN];
pair<int, signed> st[20][2*MAXN];
int tin[MAXN], tout[MAXN], cur = 0;
int dep[MAXN];
int l[MAXN], r[MAXN];
vector<int> e;
void dfs(int node, int prv, int ohno) {
tin[node] = ++cur;
dep[node] = ohno;
e.push_back(node);
for(auto x: adj[node]) {
if(x.first != prv) {
dfs(x.first, node, ohno + x.second);
e.push_back(node);
}
}
tout[node] = ++cur;
}
int lca_dep(int x, int y) {
int m1 = min(l[x], l[y]), m2 = max(r[x], r[y]);
int k = 32 - __builtin_clz(m2 - m1 + 1) - 1;
return min(st[k][m1], st[k][m2 - (1<<k) + 1]).first;
}
int dist(int x, int y) {
return dep[x] + dep[y] - 2 * lca_dep(x, y);
}
int lca_idx(int x, int y) {
int m1 = min(l[x], l[y]), m2 = max(r[x], r[y]);
int k = 32 - __builtin_clz(m2 - m1 + 1) - 1;
return min(st[k][m1], st[k][m2 - (1<<k) + 1]).second;
}
int miS[MAXN], miT[MAXN];
void Init(int32_t N, int32_t A[], int32_t B[], int32_t D[]) {
for(int i=0; i<N; i++) {
miS[i] = miT[i] = 1e18;
}
for(int i=0; i<N-1; i++) {
adj[A[i]].push_back({B[i], D[i]});
adj[B[i]].push_back({A[i], D[i]});
}
dfs(0, -1, 0);
for(int i=0; i<e.size(); i++) {
r[e[i]] = i;
}
for(int i=e.size()-1; i>=0; i--) {
l[e[i]] = i;
}
for(int i=0; i<e.size(); i++) st[0][i] = {dep[e[i]], e[i]};
for(int i=1; i<20; i++) {
for(int j=0; j<e.size(); j++) {
if(j + (1<<i) - 1 < e.size()) {
st[i][j] = min(st[i-1][j], st[i-1][j + (1<<(i-1))]);
}
}
}
}
bool dfs_order(int a, int b) {
return tin[a] < tin[b];
}
vector<int> adj2[MAXN];
char grp[MAXN];
int dpf(int node, int prv) {
int ans = 1e18;
for(int x: adj2[node]) {
if(x != prv) {
ans = min(ans, dpf(x, node));
miS[node] = min(miS[node], miS[x]);
miT[node] = min(miT[node], miT[x]);
}
}
if(grp[node] == 'S') {
miS[node] = dep[node];
}
else if(grp[node] == 'T') {
miT[node] = dep[node];
}
ans = min(ans, miS[node] + miT[node] - 2 * dep[node]);
return ans;
}
long long Query(int32_t S, int32_t X[], int32_t T, int32_t Y[]) {
vector<int> v;
for(int i=0; i<S; i++) {
v.push_back(X[i]);
grp[X[i]] = 'S';
}
for(int i=0; i<T; i++) {
v.push_back(Y[i]);
grp[Y[i]] = 'T';
}
sort(v.begin(), v.end(), dfs_order);
unordered_map<int, int> here;
for(int x: v) here[x] = 1;
int V = v.size();
for(int i=1; i<V; i++) {
int lol = lca_idx(v[i], v[i-1]);
if(!here[lol]) {
here[lol] = 1;
v.push_back(lol);
grp[lol] = 'L';
}
}
sort(v.begin(), v.end(), dfs_order);
stack<int> st;
for(int x: v) {
adj2[x].clear();
miS[x] = miT[x] = 1e18;
}
int rt;
for(int x: v) {
while(st.size() && !(tin[st.top()] < tin[x] && tout[x] < tout[st.top()])) {
st.pop();
}
if(st.size()) {
adj2[st.top()].push_back(x);
}
else {
rt = x;
}
st.push(x);
}
return dpf(rt, -1);
}
