#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#pragma GCC optimize("O3,unroll-loops")
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define all(v) v.begin(), v.end()
#define pb push_back
#define ss second
#define ff first
#define vt vector
using namespace std;
using namespace __gnu_pbds;
typedef long long ll;
typedef pair<int, int> pii;
typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;
const ll inf = 1e16;
const int mod = 1e9+7;
const int maxn = 5e5 + 1;
#include "factories.h"
int dp[maxn], up[maxn][20], sz[maxn], cup[maxn];
ll p[maxn], dst[maxn], tc[maxn][20];
vt<pii> g[maxn];
vt<int> rst;
bool first;
void dfs(int v){
sz[v] = 1;
for(auto i : g[v]){
if(i.ff != up[v][0]){
up[i.ff][0] = v;
dp[i.ff] = dp[v] + 1;
p[i.ff] = p[v] + i.ss;
dfs(i.ff);
sz[v] += sz[i.ff];
}
}
}
int cd(int v, int m){
for(auto i : g[v]){
if(sz[i.ff] > m / 2){
sz[v] = m - sz[i.ff];
return cd(i.ff, m);
}
}
sz[v] = -1;
for(auto i : g[v]){
if(sz[i.ff] != -1){
cup[cd(i.ff, sz[i.ff])] = v;
}
}
return v;
}
void dist(int x, int y, ll& q){
if(dp[x] > dp[y])swap(x, y);
int a = x, b = y;
for(int j = 19; j >= 0; j--){
if(((dp[b] - dp[a]) >> j) & 1){
b = up[b][j];
}
}
if(a == b){
q = p[x] - p[a] + p[y] - p[a];
return;
}
for(int j = 19; j >= 0; j--){
if(up[b][j] != up[a][j]){
a = up[a][j], b = up[b][j];
}
}
a = up[a][0];
q = p[x] - p[a] + p[y] - p[a];
}
void Init(int n, int a[], int b[], int d[]) {
for(int i = 0; i < n - 1; i++){
g[a[i]].pb({b[i], d[i]});
g[b[i]].pb({a[i], d[i]});
}
dfs(0);
for(int j = 1; j < 20; j++){
for(int i = 0; i < n; i++)up[i][j] = up[up[i][j - 1]][j - 1];
}
cup[cd(0, n)] = -1;
for(int i = 0; i < n; i++){
dst[i] = inf;
for(int j = 0, puc = i; puc != -1; j++){
dist(i, puc, tc[i][j]);
puc = cup[puc];
}
}
}
long long Query(int s, int x[], int t, int y[]) {
ll ret = inf;
for(int i = 0; i < s; i++){
int go = x[i];
for(int j = 0; j < 20 && go != -1; j++){
if(dst[go] == inf)rst.pb(go);
dst[go] = min(dst[go], tc[x[i]][j]);
go = cup[go];
}
}
for(int i = 0; i < t; i++){
int go = y[i];
for(int j = 0; j < 20 && go != -1; j++){
ret = min(ret, dst[go] + tc[y[i]][j]);
go = cup[go];
}
}
for(auto i : rst)dst[i] = inf;
rst.clear();
return ret;
}
