Score : $1100$ points

Problem Statement

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.

Notes

A Hamiltonian path in a graph is a path in the graph that visits each vertex exactly once.

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.

5
1 2 5
3 4 7
2 3 3
2 5 2

38

The length of the Hamiltonian path $5$ → $3$ → $1$ → $4$ → $2$ is $5+8+15+10=38$. Since there is no Hamiltonian path with length $39$ or greater in the graph, the answer is $38$.

8
2 8 8
1 5 1
4 8 2
2 5 4
3 8 6
6 8 9
2 7 12

132