#include<cstdio>
#include<algorithm>
#include<cstring>
#define MN 100005
using namespace std;
int n,head[MN],f[MN],sz[MN],ans=0x3f3f3f3f,nans[MN],cnt,num;
struct edge{int to,next,w;}g[MN<<1];
long long res;
void dfs(int u,int fa){
	sz[u]=1;
	for(int i=head[u];i;i=g[i].next)if(g[i].to!=fa)dfs(g[i].to,u),sz[u]+=sz[g[i].to],f[u]=max(f[u],sz[g[i].to]);
	f[u]=max(f[u],n-sz[u]);ans=min(ans,f[u]);
	for(int i=head[u];i;i=g[i].next)if(g[i].to!=fa)res+=1ll*min(n-sz[g[i].to],sz[g[i].to])*2*g[i].w;
}
void ins(int u,int v,int w){g[++num].next=head[u];head[u]=num;g[num].to=v;g[num].w=w;}
int main(){
	scanf("%d",&n);int x,y,v;
	for(int i=1;i<n;i++)scanf("%d%d%d",&x,&y,&v),ins(x,y,v),ins(y,x,v);dfs(1,0);
	for(int i=1;i<=n;i++)if(f[i]==ans)nans[++cnt]=i;
	if(cnt==1){
		int tmp=0x3f3f3f3f;
		for(int i=head[nans[1]];i;i=g[i].next)tmp=min(tmp,g[i].w);
		res-=tmp;
	}else for(int i=head[nans[1]];i;i=g[i].next)if(f[g[i].to]==ans)res-=g[i].w;
	printf("%lld\n",res);
}
### Prompt

Construct a CPP code solution to the problem outlined:

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<cstdio>
#include<algorithm>
#include<cstring>
#define MN 100005
using namespace std;
int n,head[MN],f[MN],sz[MN],ans=0x3f3f3f3f,nans[MN],cnt,num;
struct edge{int to,next,w;}g[MN<<1];
long long res;
void dfs(int u,int fa){
	sz[u]=1;
	for(int i=head[u];i;i=g[i].next)if(g[i].to!=fa)dfs(g[i].to,u),sz[u]+=sz[g[i].to],f[u]=max(f[u],sz[g[i].to]);
	f[u]=max(f[u],n-sz[u]);ans=min(ans,f[u]);
	for(int i=head[u];i;i=g[i].next)if(g[i].to!=fa)res+=1ll*min(n-sz[g[i].to],sz[g[i].to])*2*g[i].w;
}
void ins(int u,int v,int w){g[++num].next=head[u];head[u]=num;g[num].to=v;g[num].w=w;}
int main(){
	scanf("%d",&n);int x,y,v;
	for(int i=1;i<n;i++)scanf("%d%d%d",&x,&y,&v),ins(x,y,v),ins(y,x,v);dfs(1,0);
	for(int i=1;i<=n;i++)if(f[i]==ans)nans[++cnt]=i;
	if(cnt==1){
		int tmp=0x3f3f3f3f;
		for(int i=head[nans[1]];i;i=g[i].next)tmp=min(tmp,g[i].w);
		res-=tmp;
	}else for(int i=head[nans[1]];i;i=g[i].next)if(f[g[i].to]==ans)res-=g[i].w;
	printf("%lld\n",res);
}
```