'''
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 with the 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. There are 2 subsets with a bitwise OR of 3:
- [3]
- [3,1]
Example 2:

Input: nums = [2,2,2]
Output: 7
Explanation: All non-empty subsets of [2,2,2] have a bitwise OR of 2. There are 23 - 1 = 7 total 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 a bitwise OR of 7:
- [3,5]
- [3,1,5]
- [3,2,5]
- [3,2,1,5]
- [2,5]
- [2,1,5]
 

Constraints:

1 <= nums.length <= 16
1 <= nums[i] <= 105
'''
import unittest

from typing import *

class Solution:
    res = 0
    def countMaxOrSubsets(self, nums: List[int]) -> int:
        target = 0
        for n in nums:
            target |= n

        def dfs(i, value):
            if value == target:
                self.res += 2 ** (len(nums) - i)
                return
            if i >= len(nums):
                return
            dfs(i + 1, value)
            dfs(i + 1, value | nums[i])

        dfs(0, 0)
        return self.res



class TestSolution(unittest.TestCase):

    def test_case(self):
        examples = (
            (([3,2,1,5],),6),
        )
        for first, second in examples:
            self.assert_function(first, second)

    def assert_function(self, first, second):
        self.assertEqual(Solution().countMaxOrSubsets(*first), second,
                         msg="first: {}; second: {}".format(first, second))


unittest.main()
