#include "factories.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int N = 5e5+10;
const ll INF = 1e18;
int n;
vector< pair<int,int> > g[N];
int par[N][19]; ll lev[N], dep[N];
void lcadfs(int u, int f, ll l, int d) {
lev[u] = l;
dep[u] = d;
par[u][0] = f;
for(auto it : g[u]) if(it.first != f)
lcadfs(it.first, u, l + it.second, d + 1);
}
int lca(int u, int v) {
if(dep[u] > dep[v]) swap(u,v);
for(int j = 18; j >= 0; j--)
if(dep[v] - (1<<j) >= dep[u])
v = par[v][j];
if(u == v) return u;
for(int j = 18; j >= 0; j--)
if(par[u][j] != par[v][j])
u = par[u][j], v = par[v][j];
return par[u][0];
}
ll dist(int u, int v) {
// cout << " dist " << u << "," << v << " = " << lev[u] << " + " << lev[v] << " - " << lev[lca(u,v)] << "*2 but lca was " << lca(u,v) << "\n";
return lev[u] + lev[v] - 2ll*lev[lca(u,v)];
}
int Deleted[N], sub[N], head[N];
int subdfs(int u, int f) {
sub[u] = 1;
for(auto it : g[u]) if(it.first != f && !Deleted[it.first])
sub[u] += subdfs(it.first, u);
return sub[u];
}
int get_centroid(int u, int f, int lim) {
for(auto it : g[u]) if(it.first != f && !Deleted[it.first])
if(2 * sub[it.first] > lim) return get_centroid(it.first, u, lim);
return u;
}
void decompose(int s, int dad) {
subdfs(s,-1);
int u = get_centroid(s, -1, sub[s]);
head[u] = dad;
Deleted[u] = 1;
for(auto it : g[u]) if(!Deleted[it.first])
decompose(it.first, u);
}
ll mnDist[N]; int deNode[N];
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({B[i], D[i]});
g[B[i]].push_back({A[i], D[i]});
}
memset(par,-1,sizeof par);
lcadfs(0,-1,0,0);
for(int j = 1; j < 19; j++)
for(int i = 0; i < n; i++)
if(par[i][j-1] + 1)
par[i][j] = par[par[i][j-1]][j-1];
decompose(0,-1);
for(int i = 0; i < n; i++)
mnDist[i] = INF, deNode[i] = -1;
}
void add(int u) {
for(int p = u; p + 1; p = head[p]) {
int d = dist(u, p);
if(d < mnDist[p]) mnDist[p] = d, deNode[p] = u;
}
}
void remove(int u) {
for(int p = u; p + 1; p = head[p])
mnDist[p] = INF, deNode[p] = -1;
}
ll get(int u) {
ll ret = INF;
for(int p = u; p + 1; p = head[p]) if(deNode[p] + 1)
ret = min(ret, dist(u, deNode[p]));
return ret;
}
long long Query(int S, int X[], int T, int Y[]) {
for(int i = 0; i < S; i++) add(X[i]);
ll ret = INF;
for(int i = 0; i < T; i++)
ret = min(ret, get(Y[i]));
for(int i = 0; i < S; i++) remove(X[i]);
return ret;
}
