Triples with Bitwise AND Equal To Zero

lcpy gen -n 982   # by problem number
lcpy gen -s triples_with_bitwise_and_equal_to_zero   # by problem name

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

Input: nums = [0,0,0]
Output: 27

from collections import Counter


class Solution:
    # Time: O(n^2 + n * d) where d is the number of distinct pair AND values
    # Space: O(d)
    def count_triplets(self, nums: list[int]) -> int:
        pair_counts: Counter[int] = Counter()
        for a in nums:
            for b in nums:
                pair_counts[a & b] += 1

        total = 0
        for x in nums:
            for pair_and, count in pair_counts.items():
                if pair_and & x == 0:
                    total += count
        return total