#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
#define ff first
#define ss second
#define pb push_back
#define all(a) (a).begin(), (a).end()
#define replr(i, a, b) for (int i = int(a); i <= int(b); ++i)
#define reprl(i, a, b) for (int i = int(a); i >= int(b); --i)
#define rep(i, n) for (int i = 0; i < int(n); ++i)
#define mkp(a, b) make_pair(a, b)
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> PII;
typedef vector<int> VI;
typedef vector<PII> VPI;
typedef vector<VI> VVI;
typedef vector<VVI> VVVI;
typedef vector<VPI> VVPI;
typedef pair<ll, ll> PLL;
typedef vector<ll> VL;
typedef vector<PLL> VPL;
typedef vector<VL> VVL;
typedef vector<VVL> VVVL;
typedef vector<VPL> VVPL;
template<class T> T setmax(T& a, T b) {if (a < b) return a = b; return a;}
template<class T> T setmin(T& a, T b) {if (a < b) return a; return a = b;}
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
template<class T>
using indset = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
#include "roads.h"
namespace TEST1 {
bool check(int n, VI U, VI V, VI W) {
for (int x : U) if (x) return false;
return true;
}
VL solve(int n, VI U, VI V, VI W) {
sort(all(W));
VL ans{0};
for (int x : W) ans.pb(ans.back() + x);
reverse(all(ans));
return ans;
}
};
namespace TEST2 {
bool check(int n, VI U, VI V, VI W) {
rep(i, n-1) if (U[i] != i) return false;
rep(i, n-1) if (V[i] != i+1) return false;
return true;
}
VL solve(int n, VI U, VI V, VI W) {
n--;
ll sum = 0;
for (int x : W) sum += 1ll*x;
VL dp(n);
rep(i, n) {
setmax(dp[i], 1ll*W[i]);
if (i >= 1) setmax(dp[i], dp[i-1]);
if (i >= 2) setmax(dp[i], dp[i-2] + W[i]);
}
VL ans;
ans.pb(sum);
ans.pb(sum - dp[n-1]);
while (ans.size() <= n) ans.pb(0);
return ans;
}
};
namespace TEST3 {
VL dpa, dpb;
VVPI gp;
int k;
void dfs(int u = 0, int p = -1) {
for (auto[v, w] : gp[u]) if (v != p) dfs(v, u);
ll asum = 0;
VL diff;
for (auto[v, w] : gp[u]) if (v != p) {
asum += dpa[v]+w;
diff.pb(dpb[v] - (dpa[v]+w));
}
sort(all(diff));
dpa[u] = dpb[u] = asum;
for (int i = 0; i < k && i < diff.size(); i++) if (diff[i] < 0) dpa[u] += diff[i];
for (int i = 0; i < k-1 && i < diff.size(); i++) if (diff[i] < 0) dpb[u] += diff[i];
}
VL solve(int n, VI U, VI V, VI W) {
gp = VVPI(n);
rep(i, n-1) {
int u = U[i];
int v = V[i];
int w = W[i];
gp[u].pb({v, w});
gp[v].pb({u, w});
}
dpa = dpb = VL(n);
VL ans;
for (k = 0; k < n; k++) {
dfs();
ans.pb(dpa[0]);
}
return ans;
}
};
VL minimum_closure_costs(int n, VI U, VI V, VI W) {
if (TEST1::check(n, U, V, W)) return TEST1::solve(n, U, V, W);
if (TEST2::check(n, U, V, W)) return TEST2::solve(n, U, V, W);
return TEST3::solve(n, U, V, W);
}
