#include "factories.h"
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <vector>
#include <algorithm>
#include <cmath>
#include <cstring>
#include <cassert>
#include <string>
#include <set>
#include <map>
#include <random>
#include <bitset>
#include <string>
#include <unordered_set>
#include <unordered_map>
#include <deque>
#include <queue>
#define rep(i, n) for (int i = 0; i < (n); i++)
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
using namespace std;
using ll = long long;
using ul = unsigned long long;
using ld = long double;
const int N = 500001, L = 19;
vector<pair<ll, ll>> g[N];
int tin[N], tout[N], ct, up[L][N], th[N], par[N], st[N], li[N * 2];
ll h[N], d1[N], d2[N], inf = 1e16;
void dfs(int v, int p) {
up[0][v] = p;
tin[v] = ++ct;
for (auto &u : g[v])
if (u.first != p) {
h[u.first] = h[v] + u.second;
th[u.first] = th[v] + 1;
dfs(u.first, v);
}
tout[v] = ++ct;
}
int isp(int u, int v) {
return tin[u] <= tin[v] && tout[v] <= tout[u];
}
int lca(int u, int v) {
if (isp(u, v))
return u;
for (int i = L - 1; i >= 0; i--)
if (!isp(up[i][u], v))
u = up[i][u];
return up[0][u];
}
void Init(int n, int a[], int b[], int d[]) {
rep(i, n - 1) {
g[a[i]].push_back({b[i], d[i]});
g[b[i]].push_back({a[i], d[i]});
}
dfs(0, 0);
rep(i, L - 1)
rep(j, n)
up[i + 1][j] = up[i][up[i][j]];
rep(i, n)
d1[i] = d2[i] = inf;
}
long long Query(int s, int x[], int t, int y[]) {
int lp = 0;
rep(i, s) {
li[lp++] = x[i];
d1[x[i]] = 0;
}
rep(i, t) {
li[lp++] = y[i];
d2[y[i]] = 0;
}
sort(li, li + lp, [](int v1, int v2) {return tin[v1] < tin[v2];});
int k = lp;
rep(i, k - 1)
li[lp++] = lca(li[i], li[i + 1]);
sort(li, li + lp, [](int v1, int v2) {return tin[v1] < tin[v2];});
lp = unique(li, li + lp) - li;
int sp = 0;
rep(j, lp) {
int i = li[j];
if (sp == 0)
st[sp++] = i;
else {
while (tout[st[sp - 1]] < tout[i])
sp--;
par[i] = st[sp - 1];
st[sp++] = i;
}
}
ll ans = inf;
for (int i = lp - 1; i > 0; i--) {
ll v = li[i], cd = h[v] - h[par[v]];
d1[v] += cd;
d2[v] += cd;
ans = min(ans, min(d1[v] + d2[par[v]], d2[v] + d1[par[v]]));
d1[par[v]] = min(d1[par[v]], d1[v]);
d2[par[v]] = min(d2[par[v]], d2[v]);
}
rep(i, lp)
d1[li[i]] = d2[li[i]] = inf;
return ans;
}
