#include<iostream>
#include<cstdio>
#define LL long long
using namespace std;
int n,tot,x,y,z,g=2e9,root1,root2,t=2e9;
LL ans;
const int N=100010;
int head[N],to[N<<1],nt[N<<1],len[N<<1],siz[N],mx[N];
void add(int f,int t,int d)
{
	to[++tot]=t;len[tot]=d;nt[tot]=head[f];head[f]=tot;
}
void dfs(int x,int fa)
{
	siz[x]=1;
	for(int i=head[x];i;i=nt[i])
		if(to[i]!=fa)
		{
			dfs(to[i],x);siz[x]+=siz[to[i]];
			mx[x]=max(mx[x],siz[to[i]]);
			ans+=2*(LL)min(siz[to[i]],n-siz[to[i]])*len[i];
		}
	mx[x]=max(mx[x],n-siz[x]);
}
int main()
{
	cin>>n;
	for(int i=1;i<n;++i)
	{
		scanf("%d%d%d",&x,&y,&z);
		add(x,y,z);add(y,x,z);
	}
	dfs(1,0);
	for(int i=1;i<=n;++i)g=min(g,mx[i]);
	for(int i=1;i<=n;++i)
		if(mx[i]==g){if(!root1)root1=i;else root2=i;}		
	for(int i=head[root1];i;i=nt[i])
		if(!root2||to[i]==root2)t=min(t,len[i]);
	cout<<ans-t;
	return 0;
}
### Prompt

Please formulate a Cpp solution to the following problem:

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.

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.

Examples

Input

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


Output

38


Input

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


Output

132

### Response

```cpp
#include<iostream>
#include<cstdio>
#define LL long long
using namespace std;
int n,tot,x,y,z,g=2e9,root1,root2,t=2e9;
LL ans;
const int N=100010;
int head[N],to[N<<1],nt[N<<1],len[N<<1],siz[N],mx[N];
void add(int f,int t,int d)
{
	to[++tot]=t;len[tot]=d;nt[tot]=head[f];head[f]=tot;
}
void dfs(int x,int fa)
{
	siz[x]=1;
	for(int i=head[x];i;i=nt[i])
		if(to[i]!=fa)
		{
			dfs(to[i],x);siz[x]+=siz[to[i]];
			mx[x]=max(mx[x],siz[to[i]]);
			ans+=2*(LL)min(siz[to[i]],n-siz[to[i]])*len[i];
		}
	mx[x]=max(mx[x],n-siz[x]);
}
int main()
{
	cin>>n;
	for(int i=1;i<n;++i)
	{
		scanf("%d%d%d",&x,&y,&z);
		add(x,y,z);add(y,x,z);
	}
	dfs(1,0);
	for(int i=1;i<=n;++i)g=min(g,mx[i]);
	for(int i=1;i<=n;++i)
		if(mx[i]==g){if(!root1)root1=i;else root2=i;}		
	for(int i=head[root1];i;i=nt[i])
		if(!root2||to[i]==root2)t=min(t,len[i]);
	cout<<ans-t;
	return 0;
}
```