#include <iostream>
#include <cstdio>
#define int long long
using namespace std;
const int N = 1e5 + 5;
int mx[N], siz[N], n, head[N], tot, ans, mxsiz = 0x3f3f3f3f;
struct node{int to, nex, val;}a[N << 1];
inline int read()
{
	int x = 0, f = 1; char ch = getchar();
	while(ch < '0' || ch > '9') {if(ch == '-') f = -1; ch = getchar();}
	while(ch >= '0' && ch <= '9') {x = (x << 3) + (x << 1) + (ch ^ 48); ch = getchar();}
	return x * f;
}
void add(int x, int y, int z) {a[++ tot].to = y; a[tot].nex = head[x]; head[x] = tot; a[tot].val = z;}
void dfs(int x, int fa)
{
	siz[x] = 1;
	for(int i = head[x]; i; i = a[i].nex)
	{
		int y = a[i].to; if(y == fa) continue;
		dfs(y, x); siz[x] += siz[y];
		mx[x] = max(mx[x], siz[y]);
		ans += 2 * a[i].val * min(siz[y], n - siz[y]);
	}
	mx[x] = max(mx[x], n - siz[x]);
	mxsiz = min(mxsiz, mx[x]);
}
void work()
{
	n = read();
	for(int i = 1, x, y, z; i <= n - 1; i ++)
	{
		x = read(); y = read(); z = read();
		add(x, y, z); add(y, x, z);
	}
	dfs(1, 0); int g1 = 0, g2 = 0;
	for(int i = 1; i <= n; i ++)
	{
		if(mx[i] != mxsiz) continue;
		if(!g1) g1 = i; else g2 = i;
	}
	int em = 0x3f3f3f3f;
	for(int i = head[g1]; i; i = a[i].nex)
	{
		int y = a[i].to;
		if(g2 && y != g2) continue;
		em = min(em, a[i].val);
	}
	cout << ans - em << endl;
}
signed main() {return work(), 0;}

### Prompt

Create a solution in CPP for 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 <iostream>
#include <cstdio>
#define int long long
using namespace std;
const int N = 1e5 + 5;
int mx[N], siz[N], n, head[N], tot, ans, mxsiz = 0x3f3f3f3f;
struct node{int to, nex, val;}a[N << 1];
inline int read()
{
	int x = 0, f = 1; char ch = getchar();
	while(ch < '0' || ch > '9') {if(ch == '-') f = -1; ch = getchar();}
	while(ch >= '0' && ch <= '9') {x = (x << 3) + (x << 1) + (ch ^ 48); ch = getchar();}
	return x * f;
}
void add(int x, int y, int z) {a[++ tot].to = y; a[tot].nex = head[x]; head[x] = tot; a[tot].val = z;}
void dfs(int x, int fa)
{
	siz[x] = 1;
	for(int i = head[x]; i; i = a[i].nex)
	{
		int y = a[i].to; if(y == fa) continue;
		dfs(y, x); siz[x] += siz[y];
		mx[x] = max(mx[x], siz[y]);
		ans += 2 * a[i].val * min(siz[y], n - siz[y]);
	}
	mx[x] = max(mx[x], n - siz[x]);
	mxsiz = min(mxsiz, mx[x]);
}
void work()
{
	n = read();
	for(int i = 1, x, y, z; i <= n - 1; i ++)
	{
		x = read(); y = read(); z = read();
		add(x, y, z); add(y, x, z);
	}
	dfs(1, 0); int g1 = 0, g2 = 0;
	for(int i = 1; i <= n; i ++)
	{
		if(mx[i] != mxsiz) continue;
		if(!g1) g1 = i; else g2 = i;
	}
	int em = 0x3f3f3f3f;
	for(int i = head[g1]; i; i = a[i].nex)
	{
		int y = a[i].to;
		if(g2 && y != g2) continue;
		em = min(em, a[i].val);
	}
	cout << ans - em << endl;
}
signed main() {return work(), 0;}

```