#include "roads.h"
#include <bits/stdc++.h>
using namespace std;
const int N = 1e5 + 5;
const long long INF = 1ll << 60;
long long dp[N][2];
int X, p[N];
set<array<int, 2>> adj[N];
vector<int> rec, val[N];
unordered_set<int> S;
bitset<N> enb, mark;
struct segment_tree {
vector<int> sum, cnt;
int n = 0;
void init(int _n) {
n = _n;
sum.assign(4 * n, 0);
cnt.assign(4 * n, 0);
}
long long get(int x) {
if (x < 0) return -INF;
int l = 0, r = n, v = 1, s = 0;
while (r - l > 1) {
int m = l + r >> 1;
v <<= 1;
if (cnt[v] >= x) r = m;
else x -= cnt[v], s += sum[v], v |= 1, l = m;
}
return s;
}
void add(int id, int x, int l, int r, int v = 1) {
if (l + 1 == r) {
sum[v] += x;
cnt[v]++;
return;
}
int m = l + r >> 1;
if (id < m) add(id, x, l, m, v << 1);
else add(id, x, m, r, v << 1 | 1);
sum[v] = sum[v << 1] + sum[v << 1 | 1];
cnt[v] = cnt[v << 1] + cnt[v << 1 | 1];
}
} SEG[N];
void dfs(int v, int p) {
if (enb[v]) return void(dp[v][0] = dp[v][1] = 0);
rec.push_back(v);
mark[v] = true;
long long dif = 0, ans = 0, mx = 0;
vector<long long> V;
V.reserve(adj[v].size());
for (auto P: adj[v]) {
int u = P[0], w = P[1];
if (u == p) continue;
dfs(u, v);
dif += dp[u][0];
if (w + dp[u][1] > dp[u][0]) V.push_back(w + dp[u][1] - dp[u][0]);
}
sort(V.rbegin(), V.rend());
dp[v][0] = dp[v][1] = 0;
for (int i = 0; i <= X && i <= V.size(); i++) {
if (i) ans += V[i - 1];
//dp[v][0] = SEG[v].get(X - i) + ans
//dp[v][1] = SEG[v].get(X - i - 1) + ans
mx = max(mx, ans);
if (i + 1 == X) dp[v][1] = mx + dif;
}
if (V.size() + 1 < X) dp[v][1] = mx + dif;
dp[v][0] = mx + dif;
}
vector<long long> minimum_closure_costs(int n, vector<int> U, vector<int> V, vector<int> W) {
long long all = 0;
for (int i = 0; i < U.size(); i++) {
adj[U[i]].insert({V[i], W[i]});
adj[V[i]].insert({U[i], W[i]});
val[U[i]].push_back(W[i]);
val[V[i]].push_back(W[i]);
all += W[i];
}
for (int i = 0; i < n; i++) sort(val[i].begin(), val[i].end()), SEG[i].init(val[i].size());
iota(p, p + n, 0), sort(p, p + n, [&](const int x, const int y) {return adj[x].size() < adj[y].size();});
for (int i = 0; i < n; i++) S.insert(i);
vector<long long> re(n);
re[0] = all;
for (int i = 1, ptr = 0; i < n; i++) {
X = i;
for (;ptr < n && adj[p[ptr]].size() <= i; ptr++) {
int v = p[ptr];
array<int, 2> P;
for (auto it = adj[v].begin(); it != adj[v].end(); it = adj[v].upper_bound(P)) {
P = *it;
if (enb[P[0]]) {
all -= P[1];
adj[v].erase(it);
adj[P[0]].erase({v, P[1]});
SEG[v].add(lower_bound(val[v].begin(), val[v].end(), P[1]) - val[v].begin(), P[1], 0, val[v].size(), 1); //at loc P[1] and v
}
}
enb[v] = true;
S.erase(v);
}
long long ans = 0;
for (auto v: S) if (!mark[v]) {
dfs(v, v);
ans += dp[v][0];
}
for (auto v: rec) mark[v] = 0;
rec.clear();
re[i] = all - ans;
}
return re;
}
