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
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
#include <bits/stdc++.h>

using namespace std;

#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define reunique(v) v.resize(std::unique(v.begin(), v.end()) - v.begin())
#define sz(v) ((int)(v).size())

#define vec1d(x) vector<x>
#define vec2d(x) vector<vec1d(x)>
#define vec3d(x) vector<vec2d(x)>
#define vec4d(x) vector<vec3d(x)>

#define ivec1d(x, n, v) vec1d(x)(n, v)
#define ivec2d(x, n, m, v) vec2d(x)(n, ivec1d(x, m, v))
#define ivec3d(x, n, m, k, v) vec3d(x)(n, ivec2d(x, m, k, v))
#define ivec4d(x, n, m, k, l, v) vec4d(x)(n, ivec3d(x, m, k, l, v))

#ifdef LOCAL
#include "pretty_print.h"
#define dbg(...) cerr << "[" << #__VA_ARGS__ << "]: ", debug_out(__VA_ARGS__)
#else
#define dbg(...) 42
#endif

#define nl "\n"

typedef long double ld;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> pii;

template <typename T> T sqr(T x) { return x * x; }
template <typename T> T abs(T x) { return x < 0? -x : x; }
template <typename T> T gcd(T a, T b) { return b? gcd(b, a % b) : a; }
template <typename T> bool chmin(T &x, const T& y) { if (x > y) { x = y; return true; } return false; }
template <typename T> bool chmax(T &x, const T& y) { if (x < y) { x = y; return true; } return false; }

auto random_address = [] { char *p = new char; delete p; return (uint64_t) p; };
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count() * (random_address() | 1));
mt19937_64 rngll(chrono::steady_clock::now().time_since_epoch().count() * (random_address() | 1));


int main(int /* argc */, const char** /* argv */)
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
#ifdef LOCAL
    assert(freopen("i.txt", "r", stdin));
    assert(freopen("o.txt", "w", stdout));
#endif

    int n;
    cin >> n;
    vec2d(pii) e(n);
    for (int i = 1; i < n; ++i) {
        int u, v, w;
        cin >> u >> v >> w;
        --u;
        --v;
        e[u].push_back({v, w});
        e[v].push_back({u, w});
    }

    const ll UNDEF = -1e+18;
    auto f = ivec2d(ll, n, 4, UNDEF);
    auto g = ivec3d(ll, 2, n + n + 42, 2, UNDEF);

    function<void(int, int)> dfs = [&](int x, int p) {
        for (auto& [y, w] : e[x]) {
            if (y == p) {
                continue;
            }
            dfs(y, x);
        }

        int idx = 0;
        int offset = n + 21;
        int left = offset;
        int right = offset;
        g[0][offset][0] = 0;

        ll limit = -1e+16;

        for (auto& [y, w] : e[x]) {
            if (y == p) {
                continue;
            }
            auto v = ivec1d(ll, 4, UNDEF);
            auto& inp = g[idx];
            auto& out = g[1 - idx];

            v[0] = f[y][0];
            for (int i = 0; i < 4; ++i) {
                if (f[y][i] == UNDEF) {
                    continue;
                }
                chmax(v[(i + 1) % 4], f[y][i] + w);
            }

            for (int b = left; b <= right; ++b) {
                for (int p = 0; p < 2; ++p) {
                    if (inp[b][p] == UNDEF) {
                        continue;
                    }

                    chmax(out[b + 1][p], inp[b][p] + v[3]);
                    chmax(out[b - 1][p], inp[b][p] + v[1]);
                    chmax(out[b][1 - p], inp[b][p] + v[2]);
                    chmax(out[b][p], inp[b][p] + v[0]);
                    inp[b][p] = UNDEF;
                }
            }

            for (;;) {
                bool ok = false;
                for (int p = 0; p < 2 && !ok; ++p) {
                    if (out[left - 1][p] > limit) {
                        ok = true;
                        break;
                    }
                }
                if (!ok) {
                    break;
                }
                --left;
            }

            for (;;) {
                bool ok = false;
                for (int p = 0; p < 2 && !ok; ++p) {
                    if (out[right + 1][p] > limit) {
                        ok = true;
                        break;
                    }
                }
                if (!ok) {
                    break;
                }
                ++right;
            }
            // dbg(left, right, right - left, sz(e[x]));

            idx ^= 1;
        }

        auto& out = g[idx];
        f[x][0] = out[offset][0];
        f[x][1] = out[offset - 1][0];
        f[x][2] = out[offset][1];
        f[x][3] = out[offset + 1][0];
        for (int i = 0; i < 4; ++i) {
            if (f[x][i] < limit) {
                f[x][i] = UNDEF;
            }
        }
        for (int b = left; b <= right; ++b) {
            for (int p = 0; p < 2; ++p) {
                for (int x = 0; x < 4; ++x) {
                    out[b][p] = UNDEF;
                }
            }
        }
    };

    dfs(0, -1);
    cout << f[0][0] << nl;

#ifdef LOCAL
    cerr << "Time execute: " << clock() / (double)CLOCKS_PER_SEC << " sec" << endl;
#endif
    return 0;
}