2588 - Count the Number of Beautiful Subarrays.

Medium

You are given a 0-indexed integer array nums. In one operation, you can:

• Choose two different indices i and j such that 0 <= i, j < nums.length.

• Choose a non-negative integer k such that the <code>k^th</code> bit ( 0-indexed ) in the binary representation of nums[i] and nums[j] is 1.

• Subtract <code>2^k</code> from nums[i] and nums[j].

A subarray is beautiful if it is possible to make all of its elements equal to 0 after applying the above operation any number of times.

Return the number of beautiful subarrays in the array nums.

A subarray is a contiguous non-empty sequence of elements within an array.

Example 1:

Input: nums = 4,3,1,2,4

Output: 2

Explanation: There are 2 beautiful subarrays in nums: 4,<ins>3,1,2</ins>,4 and <ins>4,3,1,2,4</ins>.

• We can make all elements in the subarray 3,1,2 equal to 0 in the following way:

• Choose <ins>3</ins>, 1, <ins>2</ins> and k = 1. Subtract 2¹ from both numbers. The subarray becomes 1, 1, 0.

• Choose <ins>1</ins>, <ins>1</ins>, 0 and k = 0. Subtract 2⁰ from both numbers. The subarray becomes 0, 0, 0.

• We can make all elements in the subarray 4,3,1,2,4 equal to 0 in the following way:

• Choose <ins>4</ins>, 3, 1, 2, <ins>4</ins> and k = 2. Subtract 2² from both numbers. The subarray becomes 0, 3, 1, 2, 0.

• Choose 0, <ins>3</ins>, <ins>1</ins>, 2, 0 and k = 0. Subtract 2⁰ from both numbers. The subarray becomes 0, 2, 0, 2, 0.

• Choose 0, <ins>2</ins>, 0, <ins>2</ins>, 0 and k = 1. Subtract 2¹ from both numbers. The subarray becomes 0, 0, 0, 0, 0.

Example 2:

Input: nums = 1,10,4

Output: 0

Explanation: There are no beautiful subarrays in nums.

Constraints:

• <code>1 <= nums.length <= 10⁵</code>

• <code>0 <= numsi<= 10⁶</code>