#ifndef CPL_TEMPLATE
#define CPL_TEMPLATE
/*
Normie's Template v2.5
Changes:
Added warning against using pragmas on USACO.
*/
// Standard library in one include.
#include <bits/stdc++.h>
using namespace std;
// ordered_set library.
// #include <ext/pb_ds/assoc_container.hpp>
// #include <ext/pb_ds/tree_policy.hpp>
// using namespace __gnu_pbds;
// #define ordered_set(el) tree<el,null_type,less<el>,rb_tree_tag,tree_order_statistics_node_update>
// AtCoder library. (Comment out these two lines if you're not submitting in AtCoder.) (Or if you want to use it in other judges, run expander.py first.)
//#include <atcoder/all>
//using namespace atcoder;
//Pragmas (Comment out these three lines if you're submitting in szkopul or USACO.)
// #pragma comment(linker, "/stack:200000000")
// #pragma GCC optimize("Ofast,unroll-loops,tree-vectorize")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,tune=native")
//File I/O.
#define FILE_IN "cseq.inp"
#define FILE_OUT "cseq.out"
#define ofile freopen(FILE_IN,"r",stdin);freopen(FILE_OUT,"w",stdout)
//Fast I/O.
#define fio ios::sync_with_stdio(0);cin.tie(0)
#define nfio cin.tie(0)
#define endl "\n"
//Order checking.
#define ord(a,b,c) ((a>=b)and(b>=c))
//min/max redefines, so i dont have to resolve annoying compile errors.
#define min(a,b) (((a)<(b))?(a):(b))
#define max(a,b) (((a)>(b))?(a):(b))
// Fast min/max assigns to use with AVX.
// Requires g++ 9.2.0.
// template<typename T>
// __attribute__((always_inline)) void chkmin(T& a, const T& b) {
// a=(a<b)?a:b;
// }
// template<typename T>
// __attribute__((always_inline)) void chkmax(T& a, const T& b) {
// a=(a>b)?a:b;
// }
//Constants.
#define MOD (ll(998244353))
#define MAX 300001
#define mag 320
const long double PI=3.14159265358979;
//Pairs and 3-pairs.
#define p1 first
#define p2 second.first
#define p3 second.second
#define fi first
#define se second
#define pii(element_type) pair<element_type,element_type>
#define piii(element_type) pair<element_type,pii(element_type)>
//Quick power of 2.
#define pow2(x) (ll(1)<<x)
//Short for-loops.
#define ff(i,__,___) for(int i=__;i<=___;i++)
#define rr(i,__,___) for(int i=__;i>=___;i--)
//Typedefs.
#define bi BigInt
typedef long long ll;
typedef long double ld;
typedef short sh;
// Binpow and stuff
ll BOW(ll a, ll x, ll p)
{
if (!x) return 1;
ll res=BOW(a,x/2,p);
res*=res;
res%=p;
if (x%2) res*=a;
return res%p;
}
ll INV(ll a, ll p)
{
return BOW(a,p-2,p);
}
//---------END-------//
#endif
#include "roads.h"
vector<pii(ll)> gt[100001];
pii(ll) par[100001];
vector<pii(ll)> val[100001];
ll las[100001];
ll why[100001];
ll n,m,i,j,k,t,t1,u,v,a,b;
int dfs(int x) {
// cout<<"dfs "<<x<<endl;
vector<int> ch;
for (auto g : gt[x]) if (g.fi-par[x].fi) {
par[g.fi]={x,g.se};
ch.push_back(dfs(g.fi));
}
sort(ch.begin(), ch.end(), [](int a, int b){
return (val[a].size()>val[b].size());
});
int u=ch.size();
if (u==0) {
val[x]={{par[x].se,1e14+7}};
las[x]=1;
why[x]=x;
// cout<<"val "<<x<<endl;
// for (auto g : val[x]) cout<<g.fi<<','<<g.se<<' '; cout<<endl;
return x;
}
else {
for (int i=0;i<max(val[ch[0]].size(),gt[x].size());i++) {
// cout<<"u "<<u<<endl;
while(u && i>=val[ch[u-1]].size()) u--;
if (u==1 && i>=las[ch[0]] && i>=gt[x].size()) break;
// cout<<"calc "<<x<<' '<<i<<endl;
if (i==0) {
// cout<<"c0 "<<u<<endl;
for (int j=1;j<u;j++) val[ch[0]][0].fi+=val[ch[j]][0].fi;
val[ch[0]][0].fi+=par[x].se;
}
else if (i<gt[x].size()) {
ll a = 0;
priority_queue<ll,vector<ll>,greater<ll>> pq;
for (int j=0;j<u;j++) {a+=val[ch[j]][i].fi; pq.push(val[ch[j]][i].se);}
for (int j=u;j<ch.size();j++) {
a+=par[why[ch[j]]].se;
pq.push(-par[why[ch[j]]].se);
}
for (int j=0;j<i-1;j++) if (pq.size() && pq.top()<0) {
a+=pq.top();
pq.pop();
}
pii(ll) sus;
sus.se=a;
if (pq.size() && pq.top()<0) {
a+=pq.top();
pq.pop();
}
a+=par[x].se;
sus.fi=a;
sus.se-=sus.fi;
if (val[ch[0]].size()>i) val[ch[0]][i]=sus; else val[ch[0]].push_back(sus);
}
else {
val[ch[0]][i].fi+=min(0,val[ch[0]][i].se);
val[ch[0]][i].se=0;
for (int j=1;j<u;j++) {
val[ch[0]][i].fi+=val[ch[j]][i].fi;
val[ch[0]][i].fi+=min(0,val[ch[j]][i].se);
}
}
}
las[ch[0]]=gt[x].size();
why[ch[0]]=x;
// cout<<"val "<<x<<endl;
// for (auto g : val[ch[0]]) cout<<g.fi<<','<<g.se<<' '; cout<<endl;
return ch[0];
}
}
vector<ll> minimum_closure_costs(int N, vector<int> U,
vector<int> V,
vector<int> W) {
n=N;
for (i=0;i<n-1;i++) {
gt[U[i]+1].push_back({V[i]+1,W[i]});
gt[V[i]+1].push_back({U[i]+1,W[i]});
}
gt[1].push_back({0,0});
int t = dfs(1);
vector<ll> res;
for (i=0;i<n;i++) if (i<val[t].size()) res.push_back(val[t][i].fi+min(0,val[t][i].se));
else res.push_back(0);
return res;
}
// a;
