/*
:---:--:--::::::--:-:----:
::-:::. ::-:::
.* -===.. :---
.-+*##=-------====-: :--:
:+##=.* -= :=+- .-=:
.+++-. :- -=. .=+- .--.
.++=- + -= :*- :-.
+*+- :- -=. -*: :=:
#*: * -=. +- .=
=:%+ -: -=. +- --
-%: * -=. *: +.
:%-.. =. -=. # -:
:=# .. + -=. == -=
---+ . = -=. .# .+
-: == . = :------::------:.-=. % .=
:- == .=. ---:. :--#+. .% :-
= .* .+.. :=- :++ -+ =:
+ #. + -=: :*%-*: *
:= :# :=:= . :-----: =+-+ .+
* -* *=- . .- :::::::. :* .#+. +
:- -+ :#. --::-----: :* ++= .-
+ :*. *. .:::::*%: ++ +.-=. +
+ -#**----: .= -*. + -= =
* +.#=+: + . .=+: =. -=. =
= -+ :++: + .. .=+= .= -=. -
= %- :====-:. =. .:--===- * -=. -
+ +-- .:--==#==-:.= + -=. =
* + * =. : .= -=. =
+ = * + = -=. +
:- = .= =: = -=. .-
* + =: * * -=. +
:- .+ =- :- .+ -=. .+
* * := * := -= *
= :- =: .- .=: -=. =:
-: * .=- + .=- -= :-
=: -: --: :- :--: -=. .=
=:+ ----. * :---. -= .+
--=*----------------------=*+=--=+--=+*+------------------------------------------------%+:.
:: := +:- -- :.
.=. =.
-= -=
.=: .=.
.=: .+:
:-- :-:
-- -=.
:--. --:
:--: .--:
.-:-: ::--.
:----. .:----
.:::::::::-::::::--::::::::.
*/
// Hello this is Tyx2019's clone
#include "factories.h"
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define debug(x) cerr << #x << " is " << x << "\n"
#define hehe ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define rep(i, a, b) for (int i = a; i <= b; i++)
#define repb(i, a, b) for (int i = b; i >= a; i--)
#define pii pair<int, int>
#define linebreak cout << "---------------------------------------------------------\n"
#define f first
#define s second
#define pb push_back
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
// good luck
const ll MS = 5e5+5, mod = 1e9+9, INF = 3e18, blk = 400;
int parent[MS], depth[MS], s[MS], twok[MS][20];
ll dis[MS], m[MS];
vector<pii> adj[MS];
int dfs1(int x, int par, int dep) {
// returns size of subtree of x
s[x] = 1;
for (auto v : adj[x]) {
if (v.f == par) continue;
if (depth[v.f] != -1) continue;
s[x] += dfs1(v.f, x, dep);
}
return s[x];
}
int dfs2(int x, int par, int m) {
// return centroid of the subtree
for (auto v : adj[x]) {
if (v.f == par) continue;
if (depth[v.f] != -1) continue;
if (s[v.f] > m/2) return dfs2(v.f, x, m);
}
return x;
}
void build(int x, int par, int dep) {
int m = dfs1(x, par, dep);
int centroid = dfs2(x, par, m);
if (par == -1) par = centroid;
parent[centroid] = par;
depth[centroid] = dep;
for (auto v : adj[centroid]) {
if (depth[v.f] != -1) continue;
build(v.f, centroid, dep+1);
}
}
void init(int x, int par) {
for (int k = 0; k < 20; k++) {
if (twok[x][k] == -1) break;
twok[x][k+1] = twok[twok[x][k]][k];
}
for (auto v : adj[x]) {
if (v.f == par) continue;
twok[v.f][0] = x;
depth[v.f] = depth[x]+1;
dis[v.f] = dis[x]+v.s;
init(v.f, x);
}
}
int kpar(int x, int k) {
for (int j = 0; j < 20; j++) {
if (x == -1) break;
if (k&(1<<j)) x = twok[x][j];
}
return x;
}
int lca(int a, int b) {
if (depth[a] < depth[b]) swap(a, b);
a = kpar(a, depth[a]-depth[b]);
if (a == b) return a;
for (int k = 19; k >= 0; k--) {
if (twok[a][k] != twok[b][k]) {
a = twok[a][k]; b = twok[b][k];
}
}
return twok[a][0];
}
void Init(int n, int a[], int b[], int d[]) {
memset(depth, -1, sizeof(depth));
for (int i = 0; i < n-1; i++) {
adj[a[i]].pb({b[i], d[i]});
adj[b[i]].pb({a[i], d[i]});
}
build(0, -1, 0);
for (int i = 0; i < n; i++) if (depth[i] == 0) parent[i] = -1;
depth[0] = 0; dis[0] = 0; memset(twok, -1, sizeof(twok));
init(0, -1);
for (int i = 0; i < n; i++) m[i] = INF;
}
void update(int x) {
int u = x;
while (u != -1) {
m[u] = min(m[u], dis[u]+dis[x]-2*dis[lca(u,x)]);
u = parent[u];
}
}
void undo(int x) {
int u = x;
while (u != -1) {
m[u] = INF;
u = parent[u];
}
}
ll ask(int x) {
int u = x; ll res = INF;
while (u != -1) {
res = min(res, m[u]+dis[u]+dis[x]-2*dis[lca(u,x)]);
u = parent[u];
}
return res;
}
ll Query(int s, int x[], int t, int y[]) {
ll ans = INF;
if (2*s+t < 2*t+s) {
for (int i = 0; i < s; i++) update(x[i]);
for (int i = 0; i < t; i++) ans = min(ans, ask(y[i]));
for (int i = 0; i < s; i++) undo(x[i]);
}
else {
for (int i = 0; i < t; i++) update(y[i]);
for (int i = 0; i < s; i++) ans = min(ans, ask(x[i]));
for (int i = 0; i < t; i++) undo(y[i]);
}
return ans;
}
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