Largest Triangle Perimeter

You are given an integer \(n\) and an array of \(n\) integers representing the heights of mountains. Your task is to determine the largest possible perimeter of a triangle that can be formed by choosing any three mountains as its vertices. A triangle is valid if it satisfies the triangle inequality, i.e., for sides \(a\), \(b\), and \(c\) (with \(a \ge b \ge c\)), the following condition holds:

\(a < b + c\)

If no valid triangle can be formed, output \(0\).

inputFormat

The input is given via standard input (stdin) and consists of two parts:

1. The first line contains an integer \(n\) (\(3 \le n \le 10^5\)), the number of mountains.
2. The second line contains \(n\) space-separated integers representing the heights of the mountains.

outputFormat

Output a single integer to standard output (stdout), which is the largest perimeter of a valid triangle that can be formed. If no valid triangle exists, output \(0\).

5
2 1 2 4 5

11