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Given an array of integers nums, find the number of triples 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

 

Note:

  1. 1 <= nums.length <= 1000
  2. 0 <= nums[i] < 216

class Solution { public int countTriplets(int[] nums) { } }