1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
#include <bits/stdc++.h>
using namespace std;

typedef long long LL;
typedef long double LD;
typedef pair<int, int> PII;
typedef pair<LL, LL> PLL;

#define all(x) (x).begin(), (x).end()
#define sz(x) (int)(x).size()

template<typename _T> inline void _DBG(const char *s, _T x) { cerr << s << " = " << x << "\n"; }
template<typename _T, typename... args> void _DBG(const char *s, _T x, args... a) { while(*s != ',') cerr << *s++; cerr << " = " << x << ','; _DBG(s + 1, a...); }

#ifdef LOCAL
#define _upgrade ios_base::sync_with_stdio(0);
#define DBG(...) _DBG(#__VA_ARGS__, __VA_ARGS__)
#else
#define _upgrade ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define DBG(...) (__VA_ARGS__)
#define cerr if(0) cout
#endif

// ********************** CODE ********************** //

const int N = 2e5 + 7;
const int P = 250;
const LL INF = 1e18;

mt19937 rng(1998);

int n;
LL dp[N][4];
LL dp_aux[2][2 * P][2];
vector<pair<int, int>> G[N];

void dfs(int v, int f = -1)
{
    vector<pair<int, int>> children;
    for (auto [u, c]: G[v])
    {
        if (u != f)
        {
            dfs(u, v);
            children.push_back({u, c});
        }
    }

    for (int j = 0; j < 4; j++)
        dp[v][j] = -INF;

    for (int t = 0; t < 6; t++)
    {
        shuffle(all(children), rng);

        for (int j = 0; j < 2 * P; j++)
            for (int k = 0; k < 2; k++)
                dp_aux[0][j][k] = dp_aux[1][j][k] = -INF;

        dp_aux[0][P][0] = 0;

        for (int i = 1; i <= sz(children); i++)
        {
            auto [u, c] = children[i - 1];
            for (int j = max(0, P - i - 1); j < min(2 * P, P + i + 2); j++)
            {
                for (int k = 0; k < 2; k++)
                {
                    dp_aux[i & 1][j][k] = max(-INF, dp_aux[(i - 1) & 1][j][k] + max(dp[u][0], dp[u][3] + c));
                    dp_aux[i & 1][j][k] = max(dp_aux[i & 1][j][k], dp_aux[(i - 1) & 1][j][k ^ 1] + dp[u][1] + c);
                    if (j > 0)
                    {
                        dp_aux[i & 1][j][k] = max(dp_aux[i & 1][j][k], dp_aux[(i - 1) & 1][j - 1][k] + dp[u][2] + c);
                    }
                    if (j + 1 < 2 * P)
                    {
                        dp_aux[i & 1][j][k] = max(dp_aux[i & 1][j][k], dp_aux[(i - 1) & 1][j + 1][k] + dp[u][0] + c);    
                    }
                }
            }
        }

        dp[v][0] = max(dp[v][0], dp_aux[sz(children) & 1][P][0]);
        dp[v][2] = max(dp[v][2], dp_aux[sz(children) & 1][P][1]);
        dp[v][1] = max(dp[v][1], dp_aux[sz(children) & 1][P - 1][0]);
        dp[v][3] = max(dp[v][3], dp_aux[sz(children) & 1][P + 1][0]);   
    }
}

int main()
{
    _upgrade
    
    cin >> n;
    for (int i = 1; i < n; i++)
    {
        int a, b, c;
        cin >> a >> b >> c;
        G[a].push_back({b, c});
        G[b].push_back({a, c});
    }

    dfs(1);

    cout << dp[1][0] << "\n";

    return 0;
}