The pair sum of a pair $(a, b)$ is defined as $a + b$. The maximum pair sum is the largest sum among a given set of pairs.

Given an integer array nums of an even length n, group the elements of nums into $\frac{n}{2}$ pairs such that:

• Every element in nums belongs to exactly $1$ pair.

• The maximum pair sum among all formed pairs is minimized.

Return the minimized maximum pair sum.

Constraints:

• n $==$ nums.length

• $2 \leq$ n $\leq 10^5$

• n is even.

• $1 \leq$ nums[i] $\leq 10^5$

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.