Given an integer array nums, you can rearrange its elements in any arbitrary order.

Let prefix be an array containing the prefix sums of nums, where prefix[i] equals the sum of all elements from nums[0] through nums[i] for each index i.

The score of the rearranged array is defined as the total number of strictly positive values in the array prefix.

Return the maximum score achievable after optimally rearranging nums.

Constraints:

• $1 \leq$ nums.length $\leq 10^5$

• $-10^6 \leq$ nums[i] $\leq 10^6$

Input: nums = [4, 1, 7]-List[int]
Output: 3-int
Explanation: Arrange the elements as [4, 1, 7]. The prefix sums are 4, 5, and 12, all of which are strictly positive, giving a maximum score of 3.

Input: nums = [5, -2, -6, 3, 1]-List[int]
Output: 5-int
Explanation: Arrange the elements as [5, 3, 1, -2, -6]. The prefix sums are 5, 8, 9, 7, and 1, so all five prefix sums are strictly positive.

Input: nums = [-1, -4, 2, -3]-List[int]
Output: 2-int
Explanation: Arrange the elements as [2, -1, -3, -4]. The prefix sums are 2, 1, -2, and -6, so the first two are strictly positive, giving a maximum score of 2.

Input: nums = [0, 0, 0, 0]-List[int]
Output: 0-int
Explanation: Every prefix sum is 0 regardless of the arrangement, and 0 is not strictly positive, so the score is 0.

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.