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Number of Unique XOR Triplets I

You are given an integer array nums of length n, where nums is a permutation of the numbers in the range [1, n].

You are given an integer array nums of length n, where nums is a permutation of the numbers in the range [1, n].

A XOR triplet is defined as the XOR of three elements nums[i] XOR nums[j] XOR nums[k] where i <= j <= k.

Return the number of unique XOR triplet values from all possible triplets (i, j, k).

Number of Unique XOR Triplets I diagram

Example 1

Input: nums = [1,2]

Output: 2

Explanation: The possible XOR triplet values are: The unique XOR values are {1, 2} , so the output is 2.

Example 2

Input: nums = [3,1,2]

Output: 4

Explanation: The possible XOR triplet values include: The unique XOR values are {0, 1, 2, 3} , so the output is 4.

Constraints

  • 1 <= n == nums.length <= 10^5
  • 1 <= nums[i] <= n
  • nums is a permutation of integers from 1 to n.

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