This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <iostream>
#include <vector>
#include <algorithm>
#include <set>
typedef long long ll;
using namespace std;
const int maxn = 2e5 + 5;
const int inf = 2e9 + 5;
vector<vector<vector<ll> > > dp(maxn, vector<vector<ll> >(2, vector<ll>(2, -inf)));
vector<vector<pair<int, int> > > g(maxn);
void upd(ll& a, const ll& b) { a = max(a, b); }
void dfs(int u, int p, int w)
{
vector<vector<ll> > dp2(3, vector<ll>(2, -inf)); // pocet hran ktore idu nadol, mam uz zly podstrom?
dp2[0][0] = 0;
for (const pair<int, int>& v : g[u])
{
if (v.first == p) continue;
dfs(v.first, u, v.second);
vector<vector<ll> > dpnw(3, vector<ll>(2, -inf));
for (int i = 0; i < 3; i++)
{
// nepride zly podstrom
for (int j = 0; j < 2; j++)
{
upd(dpnw[i][j], dp2[i][j] + max(dp[v.first][0][0], dp[v.first][1][0])); // nepridam novu hranu, ani zly vrchol
if (i < 2 && (j == 0 || i > 0)) // nemozem pridat novu hranu ak sme uz mali zly podstrom ktory nie je napojeny
upd(dpnw[i + 1][j], dp2[i][j] + dp[v.first][0][0] + v.second); // pridam novu hranu
}
// pride novy zly podstrom
if (i < 2) upd(dpnw[i + 1][1], dp2[i][0] + dp[v.first][0][1] + v.second);
}
upd(dpnw[0][1], dp2[0][0] + dp[v.first][0][1]);
dp2 = dpnw;
}
upd(dp[u][0][0], dp2[0][0]); // nie som stred, nemam zly vrchol
upd(dp[u][0][1], dp2[0][1]); // nie som stred, mam zly vrchol
upd(dp[u][0][1], dp2[2][0]); // som stred, dve hrany nadol, nemam zly vrchol
upd(dp[u][0][1], dp2[2][1]); // som stred, dve hrany nadol, mam zly vrchol
if (p > -1) upd(dp[u][1][0], dp2[1][0] + w); // som stred, jedna hrana nadol, nemam zly vrchol
if (p > -1) upd(dp[u][1][1], dp2[1][1] + w); // som stred, jedna hrana nadol, mam zly vrchol
}
int main()
{
ios::sync_with_stdio(false);
cin.tie(0);
int n;
cin >> n;
for (int i = 0; i < n - 1; i++)
{
int a, b, c;
cin >> a >> b >> c;
g[--a].push_back({ --b, c });
g[b].push_back({ a, c });
}
dfs(0, -1, -1);
cout << max(dp[0][0][0], dp[0][0][1]) << "\n";
return 0;
}
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