#include <bits/stdc++.h>
#include "factories.h"
using namespace std;
#define mkp make_pair
const int MAXN = 5 * 100100, MAXLN = 20;
const long long LINF = 0x3f3f3f3f3f3f3f3f;
int n, sz[MAXN], cdp[MAXN], lvl[MAXN];
long long aux[MAXN];
bool rmd[MAXN], flg[MAXN];
vector<pair<int, int>> g[MAXN];
long long dist[MAXN][MAXLN];
void szdfs(int v, int p = -1)
{
sz[v] = 1;
for(const auto&[w, u] : g[v])
if(u != p && !rmd[u])
szdfs(u, v), sz[v] += sz[u];
}
int getCentroid(int v, int p = -1, int rt = -1)
{
if(rt == -1)
rt = v;
for(const auto&[w, u] : g[v])
if(u != p && !rmd[u] && sz[u] > sz[rt] / 2)
return getCentroid(u, v, rt);
return v;
}
void distdfs(int v, int lvl, long long d = 0, int p = -1)
{
dist[v][lvl] = d;
for(const auto&[w, u] : g[v])
if(u != p && !rmd[u])
distdfs(u, lvl, d + w, v);
}
void cd(int v, int cp = -1, int x = 0)
{
szdfs(v);
int c = getCentroid(v);
lvl[c] = x;
distdfs(c, x);
cdp[c] = cp, rmd[c] = true;
for(const auto&[w, u] : g[c])
if(!rmd[u])
cd(u, c, x + 1);
}
void Init(int N, int A[], int B[], int D[])
{
n = N;
for(int i = 0; i < n - 1; ++i)
g[A[i]].push_back(mkp(D[i], B[i])), g[B[i]].push_back(mkp(D[i], A[i]));
for(int i = 0; i < n; ++i)
aux[i] = LINF;
cd(0);
}
long long Query(int S, int X[], int T, int Y[])
{
long long ans = LINF;
vector<int> s;
for(int i = 0, cur; i < S; ++i)
{
cur = X[i];
while(cur != -1)
{
if(!flg[cur])
s.push_back(cur), flg[cur] = true;
aux[cur] = min(aux[cur], dist[X[i]][lvl[cur]]), cur = cdp[cur];
}
}
for(int i = 0, cur; i < T; ++i)
{
cur = Y[i];
while(cur != -1)
ans = min(ans, aux[cur] + dist[Y[i]][lvl[cur]]), cur = cdp[cur];
}
for(const int& x : s)
aux[x] = LINF, flg[x] = false;
return ans;
}
