#include <bits/stdc++.h>
#include "factories.h"
#define ll long long
#define pb push_back
#define eb emplace_back
#define pu push
#define ins insert
#define fi first
#define se second
#define all(a) a.begin(),a.end()
#define bruh ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define fu(x,a,b) for (auto x=a;x<=b;x++)
#define fd(x,a,b) for (auto x=a;x>=b;x--)
using namespace std;
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
//mt19937 mt(chrono::steady_clock::now().time_since_epoch().count());
/*
Competitive Programming notes that I need to study & fix my dumbass self:
1. Coding:
- Always be sure to check the memory of arrays (maybe use vectors), for loops
- Always try to maximize the memory if possible, even if you are going for subtasks
- Do not exploit #define int long long, it will kill you
2. Stress:
- Always try generating big testcases and try if they run
3. Time management:
- Don't overcommit or undercommit, always spend a certain amount of time to think a problem, don't just look at it and say I'm fucked
- Do not spend too much time coding brute-force solutions, they should be easily-codable solutions that don't take up too much time
Time management schedule:
Offline / LAH days (4 problems - 3h):
15' thinking of solution / idea
1. no idea: skip
2. yes idea: continue thinking for <= 15'
+ implementing: <= 20'
+ brute-force: <= 5'
+ test generator: <= 5'
I hate offline because I am dumb
*/
typedef pair<ll, ll> ii;
const int N = 5e5+5;
const int M = 20;
const int mod = 1e9+7;
const int inf = 2e9;
using cd = complex<double>;
const long double PI = acos(-1);
int power(int a,int b) {ll x = 1;if (a >= mod) a%=mod; while (b) {if (b & 1) x = x*a % mod;a = a*a % mod;b>>=1;}return x;}
int n, q;
vector<ii> adj[N];
vector<ii> vt[N];
ll up[N][M], h[N], d[N], par[N], tin[N], tout[N], timer = 0;
ll dp[N];
ll sum = 0, ans = inf, root_h = 0;
ll sz[N], mns[N], mnt[N];
bool checks[N], checkt[N];
void reset()
{
timer = 0;
for (ll i = 1; i <= n; i++) adj[i].clear(), vt[i].clear(), dp[i] = 0;
}
void predfs(ll u, ll p)
{
tin[u] = ++timer;
up[u][0] = par[u] = p;
for (ll i = 1; i < M; i++) up[u][i] = up[up[u][i-1]][i-1];
for (auto i : adj[u])
{
ll v = i.fi, w = i.se;
if (v == p) continue;
h[v] = h[u] + 1;
d[v] = d[u] + w;
predfs(v, u);
}
tout[u] = timer;
}
ll lca(ll u, ll v)
{
if (h[u] < h[v]) swap(u,v);
ll diff = h[u] - h[v];
for (ll i = 0; i < M; i++) if (diff>>i & 1) u = up[u][i];
if (u == v) return u;
for (ll i = M-1; i >= 0; i--) if (up[u][i] != up[v][i]) u = up[u][i], v = up[v][i];
return up[u][0];
}
ll dist_anc(ll u, ll v)
{
return d[u] + d[v] - 2ll * d[lca(u,v)];
}
bool cmp(ll u, ll v)
{
return tin[u] < tin[v];
}
bool insub(ll u, ll v)
{
return tin[u] >= tin[v] && tin[u] <= tout[v];
}
void dfs(ll u, ll p)
{
if (checks[u]) mns[u] = 0;
if (checkt[u]) mnt[u] = 0;
for (auto i : vt[u])
{
ll v = i.fi, w = i.se;
dfs(v,u);
mns[u] = min(mns[u], mns[v] + w), mnt[u] = min(mnt[u], mnt[v] + w);
}
ans = min(ans, mns[u] + mnt[u]);
}
void Init(int N, int A[], int B[], int D[])
{
n = N;
for (ll i = 1; i < n; i++)
{
A[i]++, B[i]++;
adj[A[i]].pb({B[i], D[i]}); adj[B[i]].pb({A[i], D[i]});
}
for (ll i = 1; i <= n; i++) mns[i] = mnt[i] = inf;
predfs(1, 0);
}
vector<ll> nodes;
stack<ll> st;
ll Query(int S, int X[], int T, int Y[])
{
ans = inf, sum = 0;
ll s, t;
s = S, t = T;
for (ll j = 0; j < s; j++)
{
ll x = X[j];
++x;
checks[x] = 1;
nodes.pb(x);
}
for (ll j = 0; j < t; j++)
{
ll x = Y[j];
++x;
checkt[x] = 1;
nodes.pb(x);
}
sort(all(nodes), cmp);
// for (auto j : nodes) cout<<j<<" ";
// cout<<endl;
ll m = nodes.size();
for (ll j = 0; j < m-1; j++) nodes.pb(lca(nodes[j], nodes[j+1]));
sort(all(nodes)); nodes.erase(unique(all(nodes)), nodes.end());
sort(all(nodes), cmp);
// for (auto j : nodes) cout<<j<<" ";
// cout<<endl;
while (!st.empty()) st.pop();
st.push(nodes[0]);
for (ll j = 1; j < nodes.size(); j++)
{
while (!st.empty() && !insub(nodes[j], st.top())) st.pop();
if (!st.empty()) vt[st.top()].pb({nodes[j], dist_anc(st.top(), nodes[j])});
st.push(nodes[j]);
}
// for (auto x : nodes) cout<<x<<" ";
// cout<<endl;
// cout<<sum<<endl;
// pdfs(nodes[0], 0);
dfs(nodes[0], 0);
for (auto x : nodes) vt[x].clear(), checks[x] = checkt[x] = sz[x] = 0, mns[x] = mnt[x] = inf;
nodes.clear();
return ans;
}
// void solve()
// {
// cin>>n>>q;
// reset();
// for (int i = 1; i < n; i++)
// {
// int u,v,w; cin>>u>>v>>w;
// ++u, ++v;
// adj[u].pb({v, w}); adj[v].pb({u, w});
// }
// for (int i = 1; i <= n; i++) mns[i] = mnt[i] = inf;
// predfs(1, 0);
// // cout<<lca(1, 3);
// for (int i = 0; i < q; i++)
// {
// // cout<<endl;
// }
// }
/*
Go through the mistakes you usually make and revise your code, for god's sake...
*/
// signed main()
// {
// bruh
// //freopen("input.inp","r",stdin);
// //freopen("output.inp","w",stdout);
// int t = 1;
// // cin>>t;
// while (t--)
// {
// solve();
// }
// }
