#include"factories.h"
#include <bits/stdc++.h>
#define ll long long
#define ull unsigned ll
#define pb push_back
#define pa pair<int, int>
#define pall pair<ll, int>
#define fi first
#define se second
#define TASK "test"
#define Size(x) (int) x.size()
#define all(x) x.begin(), x.end()
using namespace std;
template<typename T1, typename T2> bool mini (T1 &a, T2 b) {if(a > b) a = b; else return 0; return 1;}
template<typename T1, typename T2> bool maxi (T1 &a, T2 b) {if(a < b) a = b; else return 0; return 1;}
const int MOD = 1e9 + 7;
const int LOG = 19;
const int maxn = 5e5 + 7;
const ll oo = 1e18 + 69;
int n, q, mark[maxn], A[maxn], B[maxn], D[maxn], X[maxn], Y[maxn], S, T, st[maxn], en[maxn], timer = 0, cur;
vector<pa> g[maxn];
ll dp[maxn][2], f[maxn], ans;
vector<int> node;
bool cmp(int i, int j) {
return st[i] < st[j];
}
struct LCA {
int p[LOG][maxn], dep[maxn];
void dfs(int u, int par) {
for(auto e:g[u]) {
int v = e.fi, w = e.se;
if(v == par) continue;
dep[v] = dep[u] + 1;
p[0][v] = u;
dfs(v, u);
}
}
void init() {
memset(p, -1, sizeof p);
dep[0] = 0;
dfs(0, 0);
for(int i = 1; i < LOG; i++) {
for(int u = 0; u < n; u++) p[i][u] = p[i - 1][p[i - 1][u]];
}
}
int get_lca(int u, int v) {
if(dep[u] < dep[v]) swap(u, v);
int k = dep[u] - dep[v];
for(int i = 0; i < LOG; i++)
if((k >> i) & 1) u = p[i][u];
if(u == v) return u;
for(int i = LOG - 1; i >= 0; i--)
if(p[i][u] != p[i][v]) {
u = p[i][u];
v = p[i][v];
}
return p[0][u];
}
} lca;
void dfs(int u, int par) {
st[u] = ++timer;
for(auto e:g[u]) {
int v = e.fi, w = e.se;
if(v == par) continue;
f[v] = f[u] + w;
dfs(v, u);
}
en[u] = timer;
}
void dfs2(int u) {
if(mark[u] == 1) dp[u][0] = 0;
if(mark[u] == 2) dp[u][1] = 0;
if(mark[u] == 3) {
dp[u][0] = 0;
dp[u][1] = 0;
}
mark[u] = 0;
cur++;
while(cur < Size(node)) {
int v = node[cur];
if(st[u] <= st[v] && st[v] <= en[u]) {
dfs2(v);
mini(ans, dp[u][0] + dp[v][1] + f[v] - f[u]);
mini(ans, dp[u][1] + dp[v][0] + f[v] - f[u]);
mini(dp[u][0], dp[v][0] + f[v] - f[u]);
mini(dp[u][1], dp[v][1] + f[v] - f[u]);
} else break;
}
}
void Init(int N, int A[], int B[], int D[]){
n = N;
for(int i = 0; i < n - 1; i++) {
g[A[i]].pb({B[i], D[i]});
g[B[i]].pb({A[i], D[i]});
}
for(int i = 0; i < n; i++)
for(int j = 0; j < 2; j++) dp[i][j] = oo;
dfs(0, 0);
lca.init();
}
long long Query(int S, int X[], int T, int Y[]){
for(int i = 0; i < S; i++) {
node.pb(X[i]);
mark[X[i]] = 1;
}
for(int i = 0; i < T; i++) {
node.pb(Y[i]);
if(mark[Y[i]] == 1) mark[Y[i]] = 3;
else if(mark[Y[i]] == 0) mark[Y[i]] = 2;
}
sort(all(node), cmp);
for(int i = 1; i < S + T; i++) {
int par = lca.get_lca(node[i], node[i - 1]);
if(!mark[par]) {
mark[par] = 4;
node.pb(par);
}
}
if(!mark[0]) {
mark[0] = 4;
node.pb(0);
}
sort(all(node), cmp);
cur = 0;
ans = oo;
dfs2(0);
for(auto i:node) {
mark[i] = 0;
dp[i][0] = dp[i][1] = oo;
}
node.clear();
return ans;
}
