#include "roads.h"
#include <bits/stdc++.h>
#include <bits/extc++.h>
#define StarBurstStream ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define iter(a) a.begin(), a.end()
#define riter(a) a.rbegin(), a.rend()
#define lsort(a) sort(iter(a))
#define gsort(a) sort(riter(a))
#define pb(a) push_back(a)
#define eb(a) emplace_back(a)
#define pf(a) push_front(a)
#define ef(a) emplace_front(a)
#define pob pop_back()
#define pof pop_front()
#define mp(a, b) make_pair(a, b)
#define F first
#define S second
#define mt make_tuple
#define gt(t, i) get<i>(t)
#define tomax(a, b) ((a) = max((a), (b)))
#define tomin(a, b) ((a) = min((a), (b)))
#define topos(a) ((a) = (((a) % MOD + MOD) % MOD))
#define uni(a) a.resize(unique(iter(a)) - a.begin())
#define printv(a, b) {bool pvaspace=false; \
for(auto pva : a){ \
if(pvaspace) b << " "; pvaspace=true;\
b << pva;\
}\
b << "\n";}
using namespace std;
using namespace __gnu_pbds;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pdd = pair<ld, ld>;
using tiii = tuple<int, int, int>;
const ll MOD = 1000000007;
const ll MAX = 1LL << 60;
template<typename A, typename B>
ostream& operator<<(ostream& o, pair<A, B> p){
return o << '(' << p.F << ',' << p.S << ')';
}
ll ifloor(ll a, ll b){
if(b < 0) a *= -1, b *= -1;
if(a < 0) return (a - b + 1) / b;
else return a / b;
}
ll iceil(ll a, ll b){
if(b < 0) a *= -1, b *= -1;
if(a > 0) return (a + b - 1) / b;
else return a / b;
}
struct OwO;
ostream& operator<<(ostream& o, OwO& owo);
struct OwO{
multiset<ll> large, small;
ll sum = 0;
void insert(ll v){
if(!small.empty() && v < *small.rbegin()) small.insert(v), sum += v;
else large.insert(v);
}
void erase(ll v){
if(large.find(v) != large.end()){
large.erase(large.find(v));
return;
}
small.erase(small.find(v));
sum -= v;
}
ll query(int k){
while(small.size() < k && !large.empty()){
small.insert(*large.begin());
sum += *large.begin();
large.erase(large.begin());
}
while(small.size() > k){
large.insert(*small.rbegin());
sum -= *small.rbegin();
small.erase(prev(small.end()));
}
return sum;
}
};
ostream& operator<<(ostream& o, OwO& owo){
o << "s: ";
for(int i : owo.small) o << i << " ";
o << "l: ";
for(int i : owo.large) o << i << " ";
o << "sum: " << owo.sum;
return o;
}
int n;
vector<vector<pii>> g;
vector<vector<pii>> tg;
vector<ll> sum;
vector<OwO> owo;
vector<bool> ok;
vector<int> okv;
vector<bool> vst;
int k;
pll dfs(int now, int p, int w){
ll ts = sum[now];
vst[now] = true;
vector<ll> tmp;
for(pii i : g[now]){
if(i.F == p) continue;
pll t = dfs(i.F, now, i.S);
ts += t.S;
// cerr << "r " << now << ' ' << i.F << " " << t << " " << ts << "\n";
tmp.eb(min(0LL, t.F - t.S));
}
for(ll i : tmp) owo[now].insert(i);
ll ans1 = MAX, ans2 = MAX;
if(k != 0) ans1 = ts + owo[now].query(k - 1);
ans2 = ts + owo[now].query(k) + w;
// cerr << "dp " << now << " " << mp(ans1, ans2) << " " << sum[now] << " " << ts << " " << owo[now] << "\n";
for(ll i : tmp) owo[now].erase(i);
return mp(ans1, ans2);
}
ll solve(int K){
k = K;
ll ans = 0;
for(int i : okv){
if(vst[i]) continue;
ans += dfs(i, i, 0).S;
}
for(int i : okv) vst[i] = false;
return ans;
}
vector<ll> minimum_closure_costs(int N, vector<int> U, vector<int> V, vector<int> W){
n = N;
g.resize(n);
tg.resize(n);
sum.resize(n);
owo.resize(n);
ok.resize(n);
vst.resize(n);
for(int i = 0; i < n - 1; i++){
int u = U[i], v = V[i], w = W[i];
tg[u].eb(mp(v, w));
tg[v].eb(mp(u, w));
sum[u] += w;
sum[v] += w;
owo[u].insert(-w);
owo[v].insert(-w);
}
vector<vector<int>> deg(n + 1);
for(int i = 0; i < n; i++) deg[tg[i].size()].eb(i);
vector<ll> ans(n);
for(int i = n - 1; i >= 0; i--){
for(int j : deg[i + 1]){
ok[j] = true;
okv.eb(j);
for(pii v : tg[j]){
sum[v.F] -= v.S;
owo[v.F].erase(-v.S);
g[v.F].eb(mp(j, v.S));
}
}
// cerr << "test " << i << "\n";
// printv(okv, cerr);
// for(int j : okv){
// cerr << j << " " << sum[j] << " ";
// printv(g[j], cerr);
// }
ans[i] = solve(i);
}
return ans;
}
