Triplets Summing to Zero

You are given an array of integers. Your task is to find the number of unique triplets \((i, j, k)\) that satisfy the conditions:

\(0 \le i < j < k < n\) and \(nums[i] + nums[j] + nums[k] = 0\).

Note that a triplet is considered unique based on the values, not the indices, and duplicate triplets should not be counted more than once.

Example:

Input: nums = [-1, 0, 1, 2, -1, -4]
Output: 2
Explanation: The two unique triplets are [-1, -1, 2] and [-1, 0, 1].

Solve this problem using an efficient algorithm (for example by sorting the array and using the two pointers technique).

inputFormat

The first line of input contains a single integer \(n\) representing the number of elements in the array.

The second line contains \(n\) space-separated integers representing the array \(nums\).

If \(n = 0\), the second line may be empty.

outputFormat

Output a single integer representing the number of unique triplets \((i, j, k)\) such that \(nums[i] + nums[j] + nums[k] = 0\).

## sample

6
-1 0 1 2 -1 -4

2

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