#include "factories.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
//#define int long long
#define pii pair<ll, ll>
#define fi first
#define se second
#define MAX_N 500000
#define MAX_Q 100000
#define MAX_SUM_ST 1000000
#define MAX_VALUE 1000000000
const ll MAXN = 5e5 + 5, inf = 1e18, mod = 1e9 + 7, block = 320, lim = 20;
static int N, Q;
static int A[MAX_N], B[MAX_N], D[MAX_N];
static int S[MAX_N];
static int T[MAX_N];
static int X[MAX_SUM_ST];
static int Y[MAX_SUM_ST];
static int Qx[MAX_N];
static int Qy[MAX_N];
int in[2 * MAXN], out[2 * MAXN], timedfs, h[MAXN], lg[MAXN];
pii st[2 * MAXN][lim + 1];
int n;
vector <pii> adj[MAXN], mini_adj[MAXN];
ll dist[MAXN];
void predfs(int u, int par) {
in[u] = out[u] = ++timedfs;
st[timedfs][0] = make_pair(h[u], u);
for (auto [v, w] : adj[u]) {
if (v == par) continue;
dist[v] = dist[u] + w;
h[v] = h[u] + 1;
predfs(v, u);
st[++timedfs][0] = make_pair(h[u], u);
}
out[u] = timedfs;
}
void build() {
predfs(0, -1);
for (int i = 2; i <= timedfs; i++) lg[i] = lg[i / 2] + 1;
for (int i = 1; i <= lim; i++) {
for (int j = 1; j + (1 << i) - 1 <= timedfs; j++) {
st[j][i] = min(st[j][i - 1], st[j + (1 << (i - 1))][i - 1]);
}
}
}
int lca(int u, int v) {
int l = in[u], r = in[v];
if (l > r) swap(l, r);
int k = lg[r - l + 1];
return min(st[l][k], st[r - (1 << k) + 1][k]).se;
}
ll distance(int u, int v) {
return dist[u] + dist[v] - 2 * dist[lca(u, v)];
}
bool cmp(int a, int b) {
return in[a] < in[b];
}
void Init(int N, int A[], int B[], int D[]) {
n = N;
for (int i = 0; i < n - 1; i++) {
adj[A[i]].emplace_back(B[i], D[i]);
adj[B[i]].emplace_back(A[i], D[i]);
}
build();
}
bool check(int x, int y) {
return in[x] <= in[y] && out[y] <= out[x];
}
ll length[MAXN];
ll minn = inf;
vector <int> comp;
vector <int> val1, val2;
int ownX[MAXN], ownY[MAXN];
void dijk(int id) {
for (int i = 0; i < (int)comp.size(); i++) length[comp[i]] = inf;
priority_queue <pii, vector <pii>, greater <pii> > q;
if (!id) {
for (int i = 0; i < (int)val1.size(); i++) {
length[val1[i]] = 0;
q.push({0, val1[i]});
}
}
else {
for (int i = 0; i < (int)val2.size(); i++) {
length[val2[i]] = 0;
q.push({0, val2[i]});
}
}
while(q.size()) {
auto [c, u] = q.top();
q.pop();
if (c != length[u]) continue;
for (auto [v, w] : mini_adj[u]) {
if (length[v] > length[u] + w) {
length[v] = length[u] + w;
if ((!id && ownY[v]) || (id && ownX[v])) minn = min(minn, length[v]);
q.push({length[v], v});
}
}
}
}
void reset() {
comp.clear();
val1.clear();
val2.clear();
minn = inf;
}
long long Query(int S, int X[], int T, int Y[]) {
reset();
for (int i = 0; i < S; i++) {
comp.push_back(X[i]);
val1.push_back(X[i]);
ownX[X[i]]++;
}
for (int i = 0; i < T; i++) {
comp.push_back(Y[i]);
val2.push_back(Y[i]);
ownY[Y[i]]++;
}
sort(comp.begin(), comp.end(), cmp);
int sz = comp.size();
for (int i = 0; i < sz - 1; i++) {
comp.push_back(lca(comp[i], comp[i + 1]));
}
sort(comp.begin(), comp.end(), cmp);
comp.erase(unique(comp.begin(), comp.end()), comp.end());
sz = comp.size();
stack <int> st;
st.push(comp[0]);
for (int i = 1; i < sz; i++) {
while(!st.empty() && !check(st.top(), comp[i])) st.pop();
if (st.size()) {
mini_adj[st.top()].emplace_back(comp[i], distance(comp[i], st.top()));
mini_adj[comp[i]].emplace_back(st.top(), distance(comp[i], st.top()));
}
st.push(comp[i]);
}
dijk(0);
dijk(1);
sz = comp.size();
for (int i = 0; i < sz; i++) mini_adj[comp[i]].clear();
for (int i = 0; i < S; i++) ownX[X[i]]--;
for (int i = 0; i < T; i++) ownY[Y[i]]--;
return minn;
}
