#define _CRT_SECURE_NO_WARNINGS
#include <bits/stdc++.h>
//#include "temp.cpp"
#include <cstdio>
using namespace std;
#ifndef ONLINE_JUDGE
#define dbg(x) cerr << #x <<" "; print(x); cerr << endl;
#else
#define dbg(x)
#endif
#define sz(x) (int((x).size()))
#define len(x) (int)x.length()
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define clr(x) (x).clear()
#define uniq(x) x.resize(unique(all(x)) - x.begin());
#define pb push_back
#define popf pop_front
#define popb pop_back
#define ld long double
#define ll long long
void print(long long t) {cerr << t;}
void print(int t) {cerr << t;}
void print(string t) {cerr << t;}
void print(char t) {cerr << t;}
void print(double t) {cerr << t;}
void print(unsigned long long t) {cerr << t;}
void print(long double t) {cerr << t;}
template <class T, class V> void print(pair <T, V> p);
template <class T> void print(vector <T> v);
template <class T> void print(set <T> v);
template <class T, class V> void print(map <T, V> v);
template <class T> void print(multiset <T> v);
template <class T> void print(T v[],T n) {cerr << "["; for(int i = 0; i < n; i++) {cerr << v[i] << " ";} cerr << "]";}
template <class T, class V> void print(pair <T, V> p) {cerr << "{"; print(p.first); cerr << ","; print(p.second); cerr << "}";}
template <class T> void print(vector <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]";}
template <class T> void print(deque <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]";}
template <class T> void print(set <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]";}
template <class T> void print(multiset <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]";}
template <class T, class V> void print(map <T, V> v) {cerr << "[ "; for (auto i : v) {print(i); cerr << " ";} cerr << "]";}
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
#define nl '\n'
// for random generations
mt19937 myrand(chrono::steady_clock::now().time_since_epoch().count());
// mt19937 myrand(131);
// for grid problems
int dx[8] = {-1,0,1,0,1,-1,1,-1};
int dy[8] = {0,1,0,-1,1,1,-1,-1};
// lowest / (1 << 17) >= 1e5 / (1 << 18) >= 2e5 / (1 << 21) >= 1e6
void fastIO() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr); cout.tie(nullptr);
}
// file in/out
void setIO(string str = "") {
fastIO();
if (str != "") {
freopen((str + ".in").c_str(), "r", stdin);
freopen((str + ".out").c_str(), "w", stdout);
}
}
// Indexed Set
template <class T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
const int N = 2e5 + 10;
vector<int> d[N];
vector<pair<int, int>> adj[N], adj2[N];
int n, deg[N], can[N];
long long sub;
bool active[N], vis[N];
vector<int> curr;
void dfs(int node, int parent) {
vis[node] = true;
for(auto i: adj2[node]) {
if(i.first == parent) continue;
dfs(i.first, node);
if(can[node] && can[i.first]) {
can[node]--, can[i.first]--;
sub++;
}
}
}
vector<long long> minimum_closure_costs(int N, vector<int> U, vector<int> V, vector<int> W) {
n = N;
for(int i = 0; i < n - 1; i++) {
adj[U[i]].emplace_back(V[i], W[i]);
adj[V[i]].emplace_back(U[i], W[i]);
deg[U[i]]++, deg[V[i]]++;
}
for(int i = 0; i < n; i++) {
d[deg[i]].push_back(i);
}
vector<long long> ans(n, 0);
for(int i = n - 2; i >= 0; i--) {
if(d[i + 1].empty()) continue;
for(auto j: d[i + 1]) {
active[j] = true;
curr.push_back(j);
}
for(auto j: d[i + 1]) {
for(auto k: adj[j]) {
if(active[k.first]) {
adj2[k.first].emplace_back(j, k.second);
adj2[j].emplace_back(k.first, k.second);
}
}
}
for(auto j: curr) {
can[j] = deg[j] - i;
ans[i] += can[j];
vis[j] = false;
}
sub = 0;
for(auto j: curr) {
if(!vis[j]) {
dfs(j, -1);
}
}
ans[i] -= sub;
}
return ans;
}
