#include <bits/stdc++.h>
#define DEBUG 0
using namespace std;
const int MX = 5e5 + 10;
const long long INF = 1e18 + 7;
int sz[MX];
vector <pair <int, int>> adj[MX];
bool visited[MX];
int ancestor[MX];
int depth[MX], parent[MX][22];
long long dist[MX];
long long ans[MX];
void preprocess_lca(int u, int p) {
for(auto [v, w] : adj[u]) {
if(v == p) {
continue;
}
depth[v] = depth[u] + 1;
dist[v] = dist[u] + w;
parent[v][0] = u;
preprocess_lca(v, u);
}
}
int find_size(int u, int p) {
for(auto [v, w] : adj[u]) {
if(v == p or visited[v]) {
continue;
}
sz[u] += find_size(v, u);
}
return ++sz[u];
}
int find_centroid(int u, int p, int n) {
for(auto [v, w] : adj[u]) {
if(v == p or visited[v]) {
continue;
}
if(sz[v] > n / 2) {
return find_centroid(v, u, n);
}
}
return u;
}
void build_centroid(int u, int p) {
int c = find_centroid(u, -1, find_size(u, -1));
ancestor[c] = p;
visited[c] = true;
for(auto [v, w] : adj[c]) {
if(visited[v] == false) {
build_centroid(v, c);
}
}
}
int lca(int u, int v) {
if(depth[u] < depth[v]) {
swap(u, v);
}
for(int i = 21; i >= 0; i--) {
if(depth[parent[u][i]] >= depth[v]) {
u = parent[u][i];
}
}
for(int i = 21; i >= 0; i--) {
if(parent[u][i] != parent[v][i]) {
u = parent[u][i];
v = parent[v][i];
}
}
return (u != v ? parent[u][0] : u);
}
long long get_dist(int u, int v) {
int l = lca(u, v);
return dist[u] + dist[v] - 2 * dist[l];
}
void Init(int N, int A[], int B[], int D[]) {
for(int i = 0; i < N - 1; i++) {
A[i]++, B[i]++;
adj[A[i]].emplace_back(B[i], D[i]);
adj[B[i]].emplace_back(A[i], D[i]);
}
depth[0] = -1;
preprocess_lca(1, -1);
build_centroid(1, -1);
for(int j = 1; j < 22; j++) {
for(int i = 1; i <= N; i++) {
parent[i][j] = parent[parent[i][j - 1]][j - 1];
}
}
for(int i = 1; i <= N; i++) {
ans[i] = INF;
}
}
void reset(int u) {
int a = u;
while(a != -1) {
ans[a] = INF;
a = ancestor[a];
}
}
void update(int u) {
int a = u;
while(a != -1) {
ans[a] = min(ans[a], get_dist(a, u));
a = ancestor[a];
}
}
long long query(int u) {
int a = u;
long long res = INF;
while(a != -1) {
res = min(res, ans[a] + get_dist(a, u));
a = ancestor[a];
}
return res;
}
long long Query(int S, int X[], int T, int Y[]) {
for(int i = 0; i < S; i++) {
update(X[i] + 1);
}
long long res = INF;
for(int i = 0; i < T; i++) {
res = min(res, query(Y[i] + 1));
}
for(int i = 0; i < S; i++) {
reset(X[i] + 1);
}
return res;
}
