DMOPC '17 Contest 4 P3 - Third Place

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Points: 7 (partial)
Time limit: 1.0s
Memory limit: 256M

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Ada, Assembly, Awk, Brain****, C, C#, C++, COBOL, CommonLisp, D, Dart, F#, Forth, Fortran, Go, Groovy, Haskell, Intercal, Java, JS, Kotlin, Lisp, Lua, Nim, ObjC, OCaml, Octave, Pascal, Perl, PHP, Pike, Prolog, Python, Racket, Ruby, Rust, Scala, Scheme, Sed, Swift, TCL, Text, Turing, VB, Zig

Roger, Jessica, and Victor held an impromptu math contest, where Roger promptly got third place (what did you expect?). The third place prize was the second-longest path in a weighted tree with N nodes. However, when he went to collect his prize, he felt as though he had been scammed. Thus, he hires you to write a program to print the length of this path so that he may file a formal complaint to the contest organizers.

Constraints

For all subtasks, 1 \le a_i, b_i \le N and 1 \le c_i \le 10^5.

Subtask 1 [20%]

3 \le N \le 1\,000

Subtask 2 [80%]

3 \le N \le 100\,000

Input Specification

The first line of input will contain N.
The next N-1 lines of input will contain 3 space-separated integers, a_i\ b_i\ c_i, indicating there exists an edge of weight c_i between nodes a_i and b_i.

Output Specification

A single integer, the length of the second-longest path in the tree.

Sample Input 1

4
1 2 1
1 3 1
1 4 1

Sample Output 1

2

Sample Input 2

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

Sample Output 2

3

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