#include<bits/stdc++.h>
#define ll long long
#define inf 1000000000
#define N 100009
using namespace std;

int n,rt,tot=1,fst[N],pnt[N<<1],len[N<<1],nxt[N<<1],sz[N]; ll ans;
void add(int x,int y,int z){
	pnt[++tot]=y; len[tot]=z; nxt[tot]=fst[x]; fst[x]=tot;
}
void dfs(int x,int p){
	int i,y,tmp=0; sz[x]=1;
	for (i=fst[x]; i; i=nxt[i]) if (i^p^1){
		y=pnt[i]; dfs(y,i);
		sz[x]+=sz[y]; tmp=max(tmp,sz[y]);
	}
	ans+=2ll*len[p]*min(sz[x],n-sz[x]);
	if (!rt && max(tmp,n-sz[x])<=(n>>1)) rt=x;
}
int main(){
	scanf("%d",&n);
	int i,x,y,z;
	for (i=1; i<n; i++){
		scanf("%d%d%d",&x,&y,&z);
		add(x,y,z); add(y,x,z);
	}
	dfs(1,0);
	ans=0; dfs(rt,0);
	for (i=fst[rt]; i; i=nxt[i]){
		x=pnt[i];
		if ((sz[x]<<1)==n) break;
	}
	if (i) ans-=len[i];
	else{
		for (i=fst[rt],x=inf; i; i=nxt[i]) x=min(x,len[i]);
		ans-=x;
	}
	printf("%lld\n",ans);
	return 0;
}

### Prompt

Your challenge is to write 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<bits/stdc++.h>
#define ll long long
#define inf 1000000000
#define N 100009
using namespace std;

int n,rt,tot=1,fst[N],pnt[N<<1],len[N<<1],nxt[N<<1],sz[N]; ll ans;
void add(int x,int y,int z){
	pnt[++tot]=y; len[tot]=z; nxt[tot]=fst[x]; fst[x]=tot;
}
void dfs(int x,int p){
	int i,y,tmp=0; sz[x]=1;
	for (i=fst[x]; i; i=nxt[i]) if (i^p^1){
		y=pnt[i]; dfs(y,i);
		sz[x]+=sz[y]; tmp=max(tmp,sz[y]);
	}
	ans+=2ll*len[p]*min(sz[x],n-sz[x]);
	if (!rt && max(tmp,n-sz[x])<=(n>>1)) rt=x;
}
int main(){
	scanf("%d",&n);
	int i,x,y,z;
	for (i=1; i<n; i++){
		scanf("%d%d%d",&x,&y,&z);
		add(x,y,z); add(y,x,z);
	}
	dfs(1,0);
	ans=0; dfs(rt,0);
	for (i=fst[rt]; i; i=nxt[i]){
		x=pnt[i];
		if ((sz[x]<<1)==n) break;
	}
	if (i) ans-=len[i];
	else{
		for (i=fst[rt],x=inf; i; i=nxt[i]) x=min(x,len[i]);
		ans-=x;
	}
	printf("%lld\n",ans);
	return 0;
}

```