Divide Players Into Teams of Equal Skill

lcpy gen -n 2491   # by problem number
lcpy gen -s divide_players_into_teams_of_equal_skill   # by problem name

Input: skill = [3,2,5,1,3,4]
Output: 22
Explanation:
Divide the players into the following teams: (1, 5), (2, 4), (3, 3), where each team has a total skill of 6.
The sum of the chemistry of all the teams is: 1 * 5 + 2 * 4 + 3 * 3 = 5 + 8 + 9 = 22.

Input: skill = [3,4]
Output: 12
Explanation:
The two players form a team with a total skill of 7.
The chemistry of the team is 3 * 4 = 12.

Input: skill = [1,1,2,3]
Output: -1
Explanation:
There is no way to divide the players into teams such that the total skill of each team is equal.

from collections import Counter


class Solution:
    # Time: O(n log n)
    # Space: O(n)
    def divide_players(self, skill: list[int]) -> int:
        n = len(skill)
        total = sum(skill)
        target, rem = divmod(total, n // 2)
        if rem:
            return -1
        counts = Counter(skill)
        chemistry = 0
        for val in sorted(counts):
            need = target - val
            if need < val:
                break
            if need == val:
                if counts[val] % 2:
                    return -1
                chemistry += val * val * (counts[val] // 2)
            elif counts[need] != counts[val]:
                return -1
            else:
                chemistry += val * need * counts[val]
        return chemistry