/*
* Written by
* ______ _ _ ______ ____ ____ ____ ____
* |_ _|| |_| ||_ _||_ || __ || __ |/ _/
* | | | _ | | | / / || |||| ||| |__
* | | | | | | | | | |_ ||__||||__||\__ \
* |__| |_| |_| |__| |___||____||____|/____/
*/
#include <bits/stdc++.h>
using namespace std;
#define nmax 500050
#define ll long long
#define ii pair<int, int>
const int N = 1 << 20;
const ll inf = 1LL << 50;
template<class T>
struct RMQ
{
int n;
T inf;
T val[N << 1];
RMQ(T __inf): inf(__inf) {}
void init(const vector<T>& v)
{
int sz = v.size();
for(int i = 0; i < sz; ++i) val[i + N] = v[i];
for(int i = sz; i < N; ++i) val[i + N] = inf;
for(int i = N - 1; i > 0; --i) val[i] = min(val[i<<1], val[i<<1|1]);
}
void modify(int p, T v)
{
for(val[p += N] = v; p > 1; p >>= 1)
val[p >> 1] = min(val[p], val[p ^ 1]);
}
T get(int l, int r)
{
T ans = inf;
for(l += N, r += N; l < r; l >>= 1, r >>= 1) {
if(l & 1) ans = min(ans, val[l++]);
if(r & 1) ans = min(ans, val[--r]);
}
return ans;
}
};
int n, p[nmax], lv[nmax], sz[nmax], r[nmax];
ll depth[nmax], ans[nmax];
RMQ<ii> rmq(ii(INT_MAX, 0));
vector<ii> adj[nmax], lca_tbl;
vector<int> el;
void euler_tour(int u = 0, int p = -1, ll D = 0)
{
depth[u] = D;
lv[u] = el.size();
el.push_back(u);
for(auto [C, v]: adj[u]) {
if(v == p) continue;
euler_tour(v, u, D + C);
el.push_back(u);
}
}
inline int lca(int u, int v)
{
if(lv[u] > lv[v]) swap(u, v);
return rmq.get(lv[u], lv[v] + 1).second;
}
inline ll dist(int u, int v)
{
return depth[u] + depth[v] - 2 * depth[lca(u, v)];
}
int dfs(int u, int p = -1)
{
sz[u] = 1;
for(auto [C, v]: adj[u]) if(v != p && !r[v]) sz[u] += dfs(v, u);
return sz[u];
}
int get_centroid(int m, int u, int p = -1)
{
for(auto [C, v]: adj[u])
if(v != p && !r[v] && 2 * sz[v] > m) return get_centroid(m, v, u);
return u;
}
int centroid(int u = 0)
{
u = get_centroid(dfs(u), u);
r[u] = 1;
p[u] = -1;
for(auto [C, v]: adj[u]) {
if(!r[v]) p[centroid(v)] = u;
}
return u;
}
void Init(int N, int A[], int B[], int D[])
{
n = N;
for(int i = 0; i < n - 1; ++i) {
adj[A[i]].push_back(ii(D[i], B[i]));
adj[B[i]].push_back(ii(D[i], A[i]));
}
euler_tour();
for(int i: el)
lca_tbl.push_back(ii(lv[i], i));
rmq.init(lca_tbl);
centroid();
fill(ans, ans + 1 + n, inf);
}
template<bool undo>
inline void update(int x)
{
for(int u = x; u != -1; u = p[u]) {
if(undo) ans[u] = inf;
else ans[u] = min(ans[u], dist(u, x));
}
}
inline ll get(int x)
{
ll res = inf;
for(int u = x; u != -1; u = p[u])
res = min(res, ans[u] + dist(u, x));
return res;
}
ll Query(int S, int X[], int T, int Y[])
{
ll res = inf;
for(int i = 0; i < S; ++i)
update<0>(X[i]);
for(int i = 0; i < T; ++i)
res = min(res, get(Y[i]));
for(int i = 0; i < S; ++i)
update<1>(X[i]);
return res;
}
