#include<bits/stdc++.h>
#define pii pair<int,int>
#define LL long long
#define mp make_pair
#define pb push_back
using namespace std;
const int N=1e5+50;
int n,dat,sz[N],anss=1e9;LL ans;
vector<pii>v[N];
void dfs(int x,int ff){
    sz[x]=1;int mx=0;
    for(int i=0,y,z;i<v[x].size();i++){
        y=v[x][i].first;z=v[x][i].second;
        if(y==ff)continue;
        // v[y].erase(find(v[y].begin(),v[y].end(),mp(x,z)));
        dfs(y,x);sz[x]+=sz[y];if(sz[y]*2==n)anss=z;mx=max(mx,sz[y]);
        ans+=2ll*z*min(sz[y],n-sz[y]);
    }
    mx=max(mx,n-sz[x]);
    if(mx*2<n)for(int i=0;i<v[x].size();i++)anss=min(anss,v[x][i].second);
}
int main(){
    scanf("%d",&n);
    for(int i=1,x,y,z;i<n;i++){
        scanf("%d%d%d",&x,&y,&z);
        v[x].pb(mp(y,z)),v[y].pb(mp(x,z));
    }
    dfs(1,0);cout<<ans-anss;
    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<bits/stdc++.h>
#define pii pair<int,int>
#define LL long long
#define mp make_pair
#define pb push_back
using namespace std;
const int N=1e5+50;
int n,dat,sz[N],anss=1e9;LL ans;
vector<pii>v[N];
void dfs(int x,int ff){
    sz[x]=1;int mx=0;
    for(int i=0,y,z;i<v[x].size();i++){
        y=v[x][i].first;z=v[x][i].second;
        if(y==ff)continue;
        // v[y].erase(find(v[y].begin(),v[y].end(),mp(x,z)));
        dfs(y,x);sz[x]+=sz[y];if(sz[y]*2==n)anss=z;mx=max(mx,sz[y]);
        ans+=2ll*z*min(sz[y],n-sz[y]);
    }
    mx=max(mx,n-sz[x]);
    if(mx*2<n)for(int i=0;i<v[x].size();i++)anss=min(anss,v[x][i].second);
}
int main(){
    scanf("%d",&n);
    for(int i=1,x,y,z;i<n;i++){
        scanf("%d%d%d",&x,&y,&z);
        v[x].pb(mp(y,z)),v[y].pb(mp(x,z));
    }
    dfs(1,0);cout<<ans-anss;
    return 0;
}
```