Counting Triangle Triplets

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.

Print a single integer representing the total number of valid triangle triplets.

The condition for three sides a, b, and c to form a triangle is a + b > c, a + c > b, and b + c > a.

Sample Input 1:

4
2 2 3 4

Sample Output 1:

3

Explanation for Sample 1:

First, sort the array: `{2, 2, 3, 4}`. We find triplets `(a, b, c)` where `a + b > c`.
1.  Fix `c = 4` (the last element). We need pairs `(a, b)` from `{2, 2, 3}`.
    - The pairs `{2, 3}` (from index 0 and 2) works since `2+3 > 4`.
    - The pairs `{2, 3}` (from index 1 and 2) works since `2+3 > 4`.
2.  Fix `c = 3` (the element at index 2). We need pairs `(a, b)` from `{2, 2}`.
    - The pair `{2, 2}` works since `2+2 > 3`.
The total count of valid combinations is 3.

Sample Input 2:

3
1 2 10

Sample Output 2:

0

Explanation for Sample 2:

The only triplet is `{1, 2, 10}`. Since `1 + 2` is not greater than `10`, no valid triangle can be formed.

Expected Time Complexity:

The expected time complexity is O(N^2).

Constraints:

1 <= N <= 1000
0 <= nums[i] <= 1000

Time limit: 1 sec