human
Can you provide a Python program to find the number of triples of indices (i, j, k) such that: given the following:
Solve in Python:
Given an array of integers A, find the number of triples of indices (i, j, k) such that:

0 <= i < A.length
0 <= j < A.length
0 <= k < A.length
A[i] & A[j] & A[k] == 0, where & represents the bitwise-AND operator.

 
Example 1:
Input: [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 <= A.length <= 1000
0 <= A[i] < 2^16
assistant
#Here is Python program to find the number of triples of indices (i, j, k) such that:
.

class Solution:
    def countTriplets(self, A: List[int]) -> int:
        combo = collections.Counter(x&y for x in A for y in A)
        return sum(combo[k] for z in A for k in combo if z&k == 0)