Tree and Hamilton Path

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

inputFormat

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}

outputFormat

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

样例

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

132