You are given an integer array nums of length n, which is a permutation of the integers from $1$ to n.

You can select any three indices i, j, and k ($0 \leq i, j, k < n$), where the indices are not necessarily distinct, and calculate the bitwise XOR sum nums[i] ^ nums[j] ^ nums[k].

Return the total number of unique XOR values that can be formed across all possible triplets.

Constraints:

• $1 \leq$ n $==$ nums.length $\leq 10^5$

• $1 \leq$ nums[i] $\leq$ n

• nums is a permutation of integers from $1$ to n.

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.