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: Accepted)

#include <set>
#include <map>
#include <queue>
#include <ctime>
#include <cmath>
#include <cstdio>
#include <bitset>
#include <vector>
#include <cstring>
#include <cassert>
#include <iostream>
#include <algorithm>
using namespace std;
typedef double db;
typedef long long ll;
typedef long double ld;
typedef vector<int> vi;
typedef pair<int,int> pa;
typedef unsigned int uint;
typedef unsigned long long ull;
#define w1 first
#define ls (x<<1)
#define w2 second
#define ins insert
#define rs (x<<1|1) 
#define mp make_pair
#define pb push_back
#define mid ((l+r)>>1)
#define sqr(x) ((x)*(x))
#define cle(x) ((x).clear())
#define lowbit(x) ((x)&(-x))
#define SZ(x) (int((x).size()))
#define ms(x,y) memset(x,y,sizeof (x))
#define rep(i,a,b) for(int (i)=(a);(i)<=(b);(i)++)
#define rep2(i,a,b) for(int (i)=(a);(i)<(b);(i)++)
#define per(i,a,b) for(int (i)=(a);(i)>=(b);(i)--)
#define Rep(p,x) for(int (p)=head[(x)];(p);(p)=nxt[(p)]) 
#define Rep2(p,x) for(int (p)=cur[(x)];(p);(p)=nxt[(p)])
template<class T>inline void read(T&num){
	num=0;T f=1;char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
	while(ch>='0'&&ch<='9')num=num*10+ch-'0',ch=getchar();
	num*=f;
}
inline int getgcd(int x,int y){if(!x)return y;return getgcd(y%x,x);}
inline int power(int x,int k,int p){int res=1;for(;k;k>>=1,x=(ll)x*x%p)if(k&1)res=(ll)res*x%p;return res;}
const double pi=acos(-1);	
inline void judge(){
	freopen("input.txt","r",stdin);
} 
//********************************head*************************************
const int maxn=1e5+5;
ll ans;
int n,tot,flag,G;
int head[maxn],des[maxn<<1],nxt[maxn<<1],val[maxn<<1];
int f[maxn],sz[maxn];
void adde(int x,int y,int z){
	des[++tot]=y;val[tot]=z;nxt[tot]=head[x];head[x]=tot;
}
void dfs(int x,int fa){
	sz[x]=1;
	Rep(p,x)if(des[p]!=fa){
		dfs(des[p],x);
		ans+=2ll*min(sz[des[p]],n-sz[des[p]])*val[p];
		if(sz[des[p]]*2==n)ans-=val[p],flag=1;
		sz[x]+=sz[des[p]];
		f[x]=max(f[x],sz[des[p]]);
	}
	f[x]=max(f[x],n-sz[x]);
	if(f[x]<f[G])G=x;
}
int main(){
	read(n);
	rep(i,1,n-1){
		int x,y,z;
		read(x);read(y);read(z);
		adde(x,y,z);adde(y,x,z);
	}
	f[0]=n;
	dfs(1,0);
	if(!flag){
		int mini=1e9;
		Rep(p,G)mini=min(mini,val[p]);
		ans-=mini;
	}
	cout<<ans<<endl;
	return 0;
}