Counting Valid Triangle Triplets

Given an array of positive integers representing side lengths, your task is to count the number of triplets (i, j, k) that can form a triangle. A triplet can form a triangle if and only if for sorted sides (a \le b \le c), the triangle inequality (a + b > c) holds. In other words, you need to find the number of triplets such that (a+b>c) (in (\LaTeX): ($a+b>c$)).

The input will be given through standard input, and the result should be printed to standard output as a single integer representing the count of valid triangle triplets.

inputFormat

The input starts with an integer (n) denoting the number of elements in the array, followed by (n) space-separated positive integers that represent the side lengths.

outputFormat

Output a single integer to standard output which is the total number of triplets that can form a triangle.## sample

4
2 2 3 4

3