Given a 0-indexed integer array `nums`, return the number of distinct quadruplets `(a, b, c, d)` such that:

- `nums[a] + nums[b] + nums[c] == nums[d]`, and
- `a < b < c < d`

Example 1:

    Input: nums = [1,2,3,6]
    Output: 1
    Explanation: The only quadruplet that satisfies the requirement is (0, 1, 2, 3) because 1 + 2 + 3 == 6.

Example 2:

    Input: nums = [3,3,6,4,5]
    Output: 0
    Explanation: There are no such quadruplets in [3,3,6,4,5].

Example 3:

    Input: nums = [1,1,1,3,5]
    Output: 4
    Explanation: The 4 quadruplets that satisfy the requirement are:
    - (0, 1, 2, 3): 1 + 1 + 1 == 3
    - (0, 1, 3, 4): 1 + 1 + 3 == 5
    - (0, 2, 3, 4): 1 + 1 + 3 == 5
    - (1, 2, 3, 4): 1 + 1 + 3 == 5

Constraints:

- `4 <= nums.length <= 50`
- `1 <= nums[i] <= 100`