#include <bits/stdc++.h>
#include "roads.h"
using namespace std;
typedef long long ll;
vector<ll> minimum_closure_costs(int n, vector<int> Uedges, vector<int> Vedges, vector<int> Wedges) {
const ll inf = (ll) 1e18 + 7;
assert((int) Uedges.size() == n - 1);
assert((int) Vedges.size() == n - 1);
assert((int) Wedges.size() == n - 1);
vector<vector<pair<int, int>>> g(n), ginit;
vector<vector<int>> vertsWithDeg(n);
vector<int> deg(n, 0);
vector<multiset<ll>> extras(n);
vector<ll> dp_take(n), dp_not(n);
vector<bool> good(n, 1);
int maxDeg;
vector<int> sub(n), value(n, 0), parrent(n, -1);
for (int i = 0; i < n - 1; i++) {
g[Uedges[i]].push_back({Vedges[i], Wedges[i]});
g[Vedges[i]].push_back({Uedges[i], Wedges[i]});
}
ginit = g;
for (int i = 0; i < n; i++) {
deg[i] = (int) g[i].size();
vertsWithDeg[deg[i]].push_back(i);
}
for (int root = 0; root < n; root++) {
sort(g[root].begin(), g[root].end(), [&] (pair<int, int> a, pair<int, int> b) {
return deg[a.first] > deg[b.first];});
}
function<void(int, int)> build = [&] (int a, int p) {
parrent[a] = p;
deg[a] = (int) g[a].size();
sub[a] = 1;
vector<pair<int, int>> kids;
for (auto &it : g[a]) {
int b = it.first;
if (b == p) continue;
value[b] = it.second;
kids.push_back(it);
build(b, a);
sub[a] += sub[b];
}
g[a] = kids;
};
function<void(int)> dfs = [&] (int a) {
assert(deg[a] > maxDeg);
dp_not[a] = dp_take[a] = +inf;
vector<ll> T;
ll sum = 0;
for (auto &it : g[a]) {
if (deg[it.first] <= maxDeg) break;
int b = it.first;
ll cost = it.second;
dfs(b);
sum += dp_not[b];
T.push_back(dp_take[b] - dp_not[b]);
}
sort(T.begin(), T.end());
int P = 0;
auto it = extras[a].begin();
for (int d = 0; d <= maxDeg; d++) {
dp_not[a] = min(dp_not[a], sum + value[a]);
if (d + 1 <= maxDeg) {
dp_take[a] = min(dp_take[a], sum);
}
if (d == (int) T.size() + (int) extras[a].size()) break;
if (P < (int) T.size() && it != extras[a].end()) {
if (T[P] < *it) {
sum += T[P++];
} else {
sum += *it;
it++;
}
} else {
if (P < (int) T.size()) {
sum += T[P++];
}
if (it != extras[a].end()) {
sum += *it;
it++;
}
}
}
};
build(0, -1);
vector<ll> print(n, 0);
set<int> goods;
for (int i = 0; i < n; i++) {
goods.insert(i);
}
ll pay = 0;
for (maxDeg = 0; maxDeg < n; maxDeg++) {
for (auto &v : vertsWithDeg[maxDeg]) {
good[v] = 0;
goods.erase(v);
for (auto &it : ginit[v]) {
int b = it.first, cost = it.second;
if (good[b] == 0) {
pay -= cost;
continue;
}
extras[b].insert(-cost);
pay += cost;
}
}
ll sum = pay;
for (auto &root : goods) {
if (parrent[root] == -1 || deg[parrent[root]] <= maxDeg) {
dfs(root);
sum += dp_not[root] - value[root];
}
}
print[maxDeg] = sum;
}
return print;
}
