// Recodando pra lembrar virtual tree
#include "factories.h"
#include <bits/stdc++.h>
using namespace std;
constexpr int maxn = 5e5+10, logn = 21;
constexpr long long inf = 0x3f3f3f3f3f3f3f3f;
vector<pair<int,long long>> g[maxn];
int in[maxn], pai[logn][maxn], profundidade[maxn], t, n;
long long depth[maxn];
void dfs(int u) {
in[u] = ++t;
for(auto [v, w] : g[u]) {
if(v == pai[0][u]) continue;
pai[0][v] = u;
profundidade[v] = profundidade[u] + 1;
depth[v] = depth[u] + w;
dfs(v);
}
}
void build_binary_lifting() {
for(int l = 1; l < logn; l++)
for(int i = 1; i <= n; i++)
pai[l][i] = pai[l-1][pai[l-1][i]];
}
int LCA(int a, int b) {
if(profundidade[a] < profundidade[b])
swap(a, b);
for(int l = logn-1; l >= 0; l--)
if(profundidade[a] - (1<<l) >= profundidade[b])
a = pai[l][a];
if(a == b) return a;
for(int l = logn-1; l >= 0; l--)
if(pai[l][a] != pai[l][b])
a = pai[l][a], b = pai[l][b];
return pai[0][a];
}
vector<pair<int, long long>> vt[maxn];
void get_vt(vector<int>& v) {
sort(v.begin(), v.end(), [](const int& a, const int& b) { return in[a] < in[b]; });
int sz = (int)v.size();
for(int i = 1; i < sz; i++)
v.push_back(LCA(v[i], v[i-1]));
sort(v.begin(), v.end(), [](const int& a, const int& b) { return in[a] < in[b]; });
v.erase(unique(v.begin(), v.end()), v.end());
for(int x : v)
vt[x].clear();
for(int i = 1; i < (int)(v.size()); i++) {
int lca = LCA(v[i], v[i-1]);
long long d = depth[v[i]] - depth[lca];
vt[v[i]].push_back({lca, d});
vt[lca].push_back({v[i], d});
}
}
void Init(int32_t N, int32_t A[], int32_t B[], int32_t D[]) {
n = N;
for(int i = 0; i < n-1; i++) {
A[i]++, B[i]++;
g[A[i]].push_back({B[i], D[i]}), g[B[i]].push_back({A[i], D[i]});
}
profundidade[1] = 1;
depth[1] = 1;
dfs(1);
build_binary_lifting();
}
long long dd[maxn];
bool mark[maxn];
long long dijkstra(const vector<int>& tudo, const vector<int>& X, const vector<int>& Y) {
static priority_queue<pair<long long,int>, vector<pair<long long,int>>, greater<pair<long long,int>>> q;
for(int x : tudo)
dd[x] = inf, mark[x] = 0;
for(int x : Y)
dd[x] = 0, q.push({0, x});
while(q.size()) {
int u = q.top().second;
q.pop();
if(mark[u]) continue;
mark[u] = 1;
for(auto [v, w] : vt[u])
if(dd[v] > dd[u] + w)
dd[v] = dd[u] + w, q.push({dd[v], v});
}
long long ans = inf;
for(int x : X)
ans = min(ans, dd[x]);
return ans;
}
long long Query(int32_t S, int32_t X[], int32_t T, int32_t Y[]) {
vector<int> v, x, y;
for(int i = 0; i < S; i++)
v.push_back(X[i]+1), x.push_back(X[i]+1);
for(int i = 0; i < T; i++)
v.push_back(Y[i]+1), y.push_back(Y[i]+1);
get_vt(v);
return dijkstra(v, x, y);
}
