You are given an integer array nums of length n.

You need to distribute all elements of nums into two arrays, arr1 and arr2, using the following process:

1. Append nums[0] to arr1.

2. Append nums[1] to arr2.

3. For each subsequent element nums[i] from index $i = 2$ to $n - 1$:

   • Let greaterCount(arr, val) be the number of elements in arr that are strictly greater than val.

   • If greaterCount(arr1, nums[i]) > greaterCount(arr2, nums[i]), append nums[i] to arr1.

   • If greaterCount(arr1, nums[i]) < greaterCount(arr2, nums[i]), append nums[i] to arr2.

   • If greaterCount(arr1, nums[i]) == greaterCount(arr2, nums[i]), append nums[i] to the array with the smaller length. If both arrays have the same length, append nums[i] to arr1.

Return the array formed by concatenating arr1 and arr2.

Constraints:

• $3 \leq n \leq 10^5$

• $1 \leq$ nums[i] $\leq 10^9$

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.