Count Subsets With Even XOR II

Count the number of triplets (i, j, k) with i < j < k from an integer array such that the XOR of the three elements has an even number of set bits. The array can be large, so use combinatorial counting rather than brute-force enumeration.

Examples
Input: [1,2,3]
Output: 1
Hints

Count Subsets With Even XOR II

Count the number of triplets `(i, j, k)` with `i < j < k` from an integer array such that the XOR of the three elements has an even number of set bits. The array can be large, so use combinatorial counting rather than brute-force enumeration.