Given an integer array nums, find the maximum possible bitwise OR of a subset of nums and return the number of different non-empty subsets that have this maximum bitwise OR.
An array a is a subset of an array b if a can be obtained from b by deleting some (possibly zero) elements of b. Two subsets are considered different if the indices of the elements chosen are different.
The bitwise OR of an array a is equal to a[0] OR a[1] OR ... OR a[a.length - 1] (0-indexed).
Example 1:
Input: nums = [3,1]
Output: 2
Explanation: The maximum possible bitwise OR of a subset is 3. The subsets with OR equal to 3 are [3] and [3,1], so the answer is 2.
Example 2:
Input: nums = [2,2,2]
Output: 7
Explanation: The maximum possible bitwise OR is 2. Every non-empty subset has OR = 2. There are 2^3 - 1 = 7 non-empty subsets.
Example 3:
Input: nums = [3,2,1,5]
Output: 6
Explanation: The maximum possible bitwise OR of a subset is 7. There are 6 subsets with bitwise OR of 7.
1 <= nums.length <= 161 <= nums[i] <= 10^5