Given an integer array nums indexed starting at $0$, determine the total number of distinct quadruplets of indices (a, b, c, d) that satisfy the following conditions:

• nums[a] + nums[b] + nums[c] == nums[d]

• $0 \le a < b < c < d <$ nums.length

Constraints:

• $4 \le$ nums.length $\le 50$

• $1 \le$ nums[i] $\le 100$

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