You are given an integer array nums representing possible side lengths. Your task is to count the number of unique triplets (i, j, k) with i < j < k that can be chosen from the array to form the sides of a valid triangle.
A triangle is considered valid if the sum of the lengths of any two sides is strictly greater than the length of the third side.
Input Format:
The first line of input contains an integer 'N', the size of the array.
The second line contains 'N' space-separated non-negative integers, representing the elements of the nums array.
Output Format:
Print a single integer representing the total number of valid triangle triplets.
Note:
The condition for three sides a, b, and c to form a triangle is a + b > c, a + c > b, and b + c > a.