#include <cstdio>
#include <cstring>
#include <algorithm>
#define fo(i,a,b) for(int i=a;i<=b;i++)
#define fd(i,a,b) for(int i=a;i>=b;i--)
#define rep(i,a) for(int i=lst[a];i;i=nxt[i])
using namespace std;

typedef long long ll;

const int N=1e5+5;

int t[N<<1],v[N<<1],nxt[N<<1],lst[N],l;
void add(int x,int y,int z) {
	t[++l]=y;v[l]=z;nxt[l]=lst[x];lst[x]=l;
}

int n,x,y,z,rt,size[N];
ll dist[N];

void get_size(int x,int y) {
	size[x]=1;
	rep(i,x) if (t[i]!=y) get_size(t[i],x),size[x]+=size[t[i]];
}

void find_root(int x,int y) {
	bool pd=1;
	rep(i,x) 
		if (t[i]!=y) {
			find_root(t[i],x);
			if (size[t[i]]>n/2) pd=0;
		}
	if (n-size[x]>n/2) pd=0;
	if (pd) rt=x;
}

void dfs(int x,int y) {
	rep(i,x)
		if (t[i]!=y) {
			dist[t[i]]=dist[x]+v[i];
			dfs(t[i],x);
		}
}

int main() {
	scanf("%d",&n);
	fo(i,1,n-1) {
		scanf("%d%d%d",&x,&y,&z);
		add(x,y,z);add(y,x,z); 
	}
	if (n==2) {
		printf("%d\n",z);
		return 0;
	}
	get_size(1,0);find_root(1,0);dfs(rt,0);
	ll ans=0;
	fo(i,1,n) ans+=dist[i];
	ans=ans*2;
	int mn=0x7fffffff;
	rep(i,rt) {
		if (size[t[i]]==(n+1)/2) {mn=v[i];break;}
		mn=min(mn,v[i]);
	}
	printf("%lld\n",ans-mn);
}
### 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 <cstdio>
#include <cstring>
#include <algorithm>
#define fo(i,a,b) for(int i=a;i<=b;i++)
#define fd(i,a,b) for(int i=a;i>=b;i--)
#define rep(i,a) for(int i=lst[a];i;i=nxt[i])
using namespace std;

typedef long long ll;

const int N=1e5+5;

int t[N<<1],v[N<<1],nxt[N<<1],lst[N],l;
void add(int x,int y,int z) {
	t[++l]=y;v[l]=z;nxt[l]=lst[x];lst[x]=l;
}

int n,x,y,z,rt,size[N];
ll dist[N];

void get_size(int x,int y) {
	size[x]=1;
	rep(i,x) if (t[i]!=y) get_size(t[i],x),size[x]+=size[t[i]];
}

void find_root(int x,int y) {
	bool pd=1;
	rep(i,x) 
		if (t[i]!=y) {
			find_root(t[i],x);
			if (size[t[i]]>n/2) pd=0;
		}
	if (n-size[x]>n/2) pd=0;
	if (pd) rt=x;
}

void dfs(int x,int y) {
	rep(i,x)
		if (t[i]!=y) {
			dist[t[i]]=dist[x]+v[i];
			dfs(t[i],x);
		}
}

int main() {
	scanf("%d",&n);
	fo(i,1,n-1) {
		scanf("%d%d%d",&x,&y,&z);
		add(x,y,z);add(y,x,z); 
	}
	if (n==2) {
		printf("%d\n",z);
		return 0;
	}
	get_size(1,0);find_root(1,0);dfs(rt,0);
	ll ans=0;
	fo(i,1,n) ans+=dist[i];
	ans=ans*2;
	int mn=0x7fffffff;
	rep(i,rt) {
		if (size[t[i]]==(n+1)/2) {mn=v[i];break;}
		mn=min(mn,v[i]);
	}
	printf("%lld\n",ans-mn);
}
```