Problem:
Score : 1100 points

Problem Statement

There is a tree with N vertices, numbered 1 through N.
The i-th edge in this tree connects Vertices A_i and B_i and has a length of C_i.

Joisino created a complete graph with N vertices.
The length of the edge connecting Vertices u and v in this graph, is equal to the shortest distance between Vertices u and v in the tree above.

Joisino would like to know the length of the longest Hamiltonian path (see Notes) in this complete graph.
Find the length of that path.

Notes

A Hamiltonian path in a graph is a path in the graph that visits each vertex exactly once.

Constraints

2 \leq N \leq 10^5

1 \leq A_i < B_i \leq N

The given graph is a tree.

1 \leq C_i \leq 10^8

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 B_1 C_1
A_2 B_2 C_2
:
A_{N-1} B_{N-1} C_{N-1}

Output

Print the length of the longest Hamiltonian path in the complete graph created by Joisino.

Sample Input 1

5
1 2 5
3 4 7
2 3 3
2 5 2

Sample Output 1

38

The length of the Hamiltonian path 5 → 3 → 1 → 4 → 2 is 5+8+15+10=38. Since there is no Hamiltonian path with length 39 or greater in the graph, the answer is 38.

Sample Input 2

8
2 8 8
1 5 1
4 8 2
2 5 4
3 8 6
6 8 9
2 7 12

Sample Output 2

132

Solution in C++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <bits/stdc++.h>
using namespace std;
struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
#define FOR(i, begin, end) for(int i=(begin);i<(end);i++)
#define REP(i, n) FOR(i,0,n)
#define IFOR(i, begin, end) for(int i=(end)-1;i>=(begin);i--)
#define IREP(i, n) IFOR(i,0,n)
#define Sort(v) sort(v.begin(), v.end())
#define Reverse(v) reverse(v.begin(), v.end())
#define all(v) v.begin(),v.end()
#define SZ(v) ((int)v.size())
#define Lower_bound(v, x) distance(v.begin(), lower_bound(v.begin(), v.end(), x))
#define Upper_bound(v, x) distance(v.begin(), upper_bound(v.begin(), v.end(), x))
#define Max(a, b) a = max(a, b)
#define Min(a, b) a = min(a, b)
#define bit(n) (1LL<<(n))
#define Ans(f, y, n) if(f) cout << y << endl; else cout << n << endl;
#define debug(x) cout << #x << "=" << x << endl;
#define vdebug(v) cout << #v << "=" << endl; REP(i, v.size()){ cout << v[i] << ","; } cout << endl;
#define mdebug(m) cout << #m << "=" << endl; REP(i, m.size()){ REP(j, m[i].size()){ cout << m[i][j] << ","; } cout << endl;}
#define pb push_back
#define f first
#define s second
#define int long long
#define INF 1000000000000000000

using vec = vector<int>;
using mat = vector<vec>;
using Pii = pair<int, int>;
using PiP = pair<int, Pii>;
using PPi = pair<Pii, int>;
using bools = vector<bool>;
using pairs = vector<Pii>;

template<typename T> void readv(vector<T> &a){ REP(i, a.size()) cin >> a[i]; }
void readv_m1(vector<int> &a){ REP(i, a.size()){cin >> a[i]; a[i]--;} }

//int dx[4] = {1,0,-1,0};
//int dy[4] = {0,1,0,-1};

int mod = 1000000007;
//int mod = 998244353;
#define Add(x, y) x = (x + (y)) % mod
#define Mult(x, y) x = (x * (y)) % mod
#define AddMult(x, y, z) x = (x + (y) * (z)) % mod

struct edge{int to, cost;};

class Graph
{
public:
    int N;
    vector<vector<edge>> G;
    vec sz;

    Graph(int N): N(N){
        G = vector<vector<edge>>(N, vector<edge>(0));
        sz.resize(N);
    }

    void add_edge(int from, int to, int cost = 0){
        G[from].push_back(edge({to, cost}));
    }

    void add_edge2(int v1, int v2, int cost = 0){
        add_edge(v1, v2, cost);
        add_edge(v2, v1, cost);
    }

    void dfs(int v, int p = -1){
        sz[v] = 1;
        for(auto e: G[v]) if(e.to != p){
            dfs(e.to, v);
            sz[v] += sz[e.to];
        }
    }

    void calcans(int v, int &ans, bool &same, int p = -1, int c = -1){
        if(p != -1){
            int n1 = sz[v], n2 = N - n1;
            int n;
            if(n1 == n2){
                n = 2 * n1 - 1;
                same = true;
            }
            else n = 2 * min(n1, n2);
            ans += c * n;
        }
        for(auto e: G[v]) if(e.to != p) calcans(e.to, ans, same, v, e.cost);
    }

};


signed main(){

    int N; cin >> N;
    int A, B, C;
    Graph G(N);

    REP(i, N - 1){
        cin >> A >> B >> C;
        G.add_edge2(A - 1, B - 1, C);
    }
    int ans = 0;
    bool same = false;
    G.dfs(0);
    G.calcans(0, ans, same);
    assert(same);
    cout << ans << endl;

    return 0;
}