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Triples with Bitwise AND Equal To Zero

Given an integer array nums, return the number of AND triples.

Given an integer array nums, return the number of AND triples.

An AND triple is a triple of indices (i, j, k) such that:

Triples with Bitwise AND Equal To Zero diagram

Example 1

Input: nums = [2,1,3]

Output: 12

Explanation: We could choose the following i, j, k triples: (i=0, j=0, k=1) : 2 & 2 & 1 (i=0, j=1, k=0) : 2 & 1 & 2 (i=0, j=1, k=1) : 2 & 1 & 1 (i=0, j=1, k=2) : 2 & 1 & 3 (i=0, j=2, k=1) : 2 & 3 & 1 (i=1, j=0, k=0) : 1 & 2 & 2 (i=1, j=0, k=1) : 1 & 2 & 1 (i=1, j=0, k=2) : 1 & 2 & 3 (i=1, j=1, k=0) : 1 & 1 & 2 (i=1, j=2, k=0) : 1 & 3 & 2 (i=2, j=0, k=1) : 3 & 2 & 1 (i=2, j=1, k=0) : 3 & 1 & 2

Example 2

Input: nums = [0,0,0]

Output: 27

Constraints

  • 1 <= nums.length <= 1000
  • 0 <= nums[i] < 216

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