982 - Triples with Bitwise AND Equal To Zero\.

Hard

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

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

• 0 <= i < nums.length

• 0 <= j < nums.length

• 0 <= k < nums.length

• nums[i] & nums[j] & nums[k] == 0, where & represents the bitwise-AND operator.

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

• <code>0 <= numsi< 2¹⁶</code>