#include<bits/stdc++.h>
using namespace std;
const int N=1e5+10;
typedef long long ll;
int gi() {
    int x=0,o=1;char ch=getchar();
    while((ch<'0'||ch>'9')&&ch!='-') ch=getchar();
    if(ch=='-') o=-1,ch=getchar();
    while(ch>='0'&&ch<='9') x=x*10+ch-'0',ch=getchar();
    return x*o;
}
struct edge {
    int to,w,nxt;
} e[N<<1];
int tot=1,h[N];
void adde(int u,int v,int w) {
    e[++tot]=(edge){v,w,h[u]};h[u]=tot;
    e[++tot]=(edge){u,w,h[v]};h[v]=tot;
}
ll ans=0;
int n,fl=0,sz[N],f[N],mn=1e9;
void dfs(int u,int fa,int w) {
    sz[u]=1;
    for(int i=h[u];i;i=e[i].nxt) {
        int v=e[i].to; if(v==fa) continue;
        dfs(v,u,e[i].w),sz[u]+=sz[v],f[u]=max(f[u],sz[v]);
    }
    f[u]=max(f[u],n-sz[u]);
    ans+=2ll*w*min(sz[u],n-sz[u]);
    if(sz[u]*2==n) ans-=w,fl=1;
    if(f[u]<=n/2) for(int i=h[u];i;i=e[i].nxt) mn=min(mn,e[i].w);
}
int main() {
    cin>>n;
    for(int i=1,u,v,w;i<n;i++) u=gi(),v=gi(),w=gi(),adde(u,v,w);
    dfs(1,0,0);
    if(!fl) ans-=mn;
    printf("%lld\n",ans);
    return 0;
}

### Prompt

In cpp, your task is to solve 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>
using namespace std;
const int N=1e5+10;
typedef long long ll;
int gi() {
    int x=0,o=1;char ch=getchar();
    while((ch<'0'||ch>'9')&&ch!='-') ch=getchar();
    if(ch=='-') o=-1,ch=getchar();
    while(ch>='0'&&ch<='9') x=x*10+ch-'0',ch=getchar();
    return x*o;
}
struct edge {
    int to,w,nxt;
} e[N<<1];
int tot=1,h[N];
void adde(int u,int v,int w) {
    e[++tot]=(edge){v,w,h[u]};h[u]=tot;
    e[++tot]=(edge){u,w,h[v]};h[v]=tot;
}
ll ans=0;
int n,fl=0,sz[N],f[N],mn=1e9;
void dfs(int u,int fa,int w) {
    sz[u]=1;
    for(int i=h[u];i;i=e[i].nxt) {
        int v=e[i].to; if(v==fa) continue;
        dfs(v,u,e[i].w),sz[u]+=sz[v],f[u]=max(f[u],sz[v]);
    }
    f[u]=max(f[u],n-sz[u]);
    ans+=2ll*w*min(sz[u],n-sz[u]);
    if(sz[u]*2==n) ans-=w,fl=1;
    if(f[u]<=n/2) for(int i=h[u];i;i=e[i].nxt) mn=min(mn,e[i].w);
}
int main() {
    cin>>n;
    for(int i=1,u,v,w;i<n;i++) u=gi(),v=gi(),w=gi(),adde(u,v,w);
    dfs(1,0,0);
    if(!fl) ans-=mn;
    printf("%lld\n",ans);
    return 0;
}

```