The pair sum of a pair `(a,b)` is equal to `a + b`. The maximum pair sum is the largest pair sum in a list of pairs.

- For example, if we have pairs `(1,5)`, `(2,3)`, and `(4,4)`, the maximum pair sum would be `max(1+5, 2+3, 4+4) = max(6, 5, 8) = 8`.

Given an array `nums` of even length `n`, pair up the elements of `nums` into `n / 2` pairs such that:

- Each element of `nums` is in exactly one pair, and
- The maximum pair sum is minimized.

Return the minimized maximum pair sum after optimally pairing up the elements.

Example 1:

    Input: nums = [3,5,2,3]

    Output: 7

    Explanation: The elements can be paired up into pairs (3,3) and (5,2).

    The maximum pair sum is max(3+3, 5+2) = max(6, 7) = 7.

Example 2:

    Input: nums = [3,5,4,2,4,6]

    Output: 8

    Explanation: The elements can be paired up into pairs (3,5), (4,4), and (6,2).

    The maximum pair sum is max(3+5, 4+4, 6+2) = max(8, 8, 8) = 8.

Constraints:

- `n == nums.length`
- `2 <= n <= 105`
- `n` is even.
- `1 <= nums[i] <= 105`