#include <bits/stdc++.h>

using namespace std;

#ifdef _DEBUG
#include "debug.h"
#else
#define debug(...) 42
#endif

int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int n;
  cin >> n;
  vector<vector<int>> g(n);
  vector<int> x(n - 1), y(n - 1), w(n - 1);
  for (int i = 0; i < n - 1; i++) {
    cin >> x[i] >> y[i] >> w[i];
    --x[i]; --y[i];
    g[x[i]].push_back(i);
    g[y[i]].push_back(i);
  }
  vector<int> pv(n);
  vector<int> pe(n);
  vector<int> dist(n);
  auto Bfs = [&](int start) {
    ranges::fill(dist, -1);
    pv[start] = -1;
    pe[start] = -1;
    dist[start] = 0;
    vector<int> que(1, start);
    for (int b = 0; b < n; b++) {
      int v = que[b];
      for (int id : g[v]) {
        int u = x[id] ^ y[id] ^ v;
        if (dist[u] != -1) {
          continue;
        }
        dist[u] = dist[v] + w[id];
        pv[u] = v;
        pe[u] = id;
        que.push_back(u);
      }
    }
  };
  vector<int> diam;
  {
    Bfs(0);
    int far = ranges::max_element(dist) - dist.begin();
    Bfs(far);
    int v = ranges::max_element(dist) - dist.begin();
    diam.push_back(v);
    while (v != far) {
      v = pv[v];
      diam.push_back(v);
    }
    ranges::reverse(diam);
  }
  const int D = diam.size();
  vector<int> pos(D);
  for (int i = 0; i < D; i++) {
    pos[i] = dist[diam[i]];
  }

  vector<int> down(n);
  vector<int> best(n);
  function<void(int, int, int)> Dfs = [&](int v, int p, int p2) {
    vector<int> downs;
    for (int id : g[v]) {
      int u = x[id] ^ y[id] ^ v;
      if (u == p || u == p2) {
        continue;
      }
      Dfs(u, v, -1);
      downs.push_back(down[u]);
      down[v] = max(down[v], w[id] + down[u]);
      best[v] = max(best[v], best[u]);
    }
    if (downs.size() < 2) {
      int sum = accumulate(downs.begin(), downs.end(), 0);
      best[v] = max(best[v], sum);
    } else {
      int i = ranges::max_element(downs) - downs.begin();
      swap(downs[i], downs[0]);
      int second = *max_element(downs.begin() + 1, downs.end());
      best[v] = max(best[v], downs[i] + second);
    }
  };
  for (int i = 1; i < D - 1; i++) {
    Dfs(diam[i], diam[i - 1], diam[i + 1]);
  }
  int ans = pos.back() + *ranges::max_element(best);
  vector<int> pref(D + 1);
  for (int i = 0; i < D; i++) {
    pref[i + 1] = max(pref[i], down[diam[i]] + pos[i]);
  }
  for (int i = D - 1; i >= 0; i--) {
    int lenR = down[diam[i]] + (pos.back() - pos[i]);
    int lenL = pref[i];
    ans = max(ans, lenL + lenR);
  }
  int total = accumulate(w.begin(), w.end(), 0);
  cout << 2 * total - ans << '\n';
  return 0;
}