Suppose you are given an array of strings, words, and each element in the array has a length of two. You need to return the length of the longest palindrome that can be made by concatenating some elements from words. If no palindrome can be made, return 0.

A palindrome is a sequence of characters that reads the same forward and backward.

Constraints:

• $1 \leq$ words.length $\leq 1000$
• words[i].length $= 2$
• Each word can be used at most once.
• words should only consist of lowercase English letters.

The solution to the problem involves concatenating strings to form a palindrome. We need to track which strings to combine in order to produce the longest palindrome. For example, the strings “ab” and “ba” can be concatenated to form the palindrome “abba”. Similarly, the strings “xy” and “yx” can be concatenated to form the palindrome “xyyx”. If we insert this palindrome in the middle of the first palindrome, we get “abxyyxba”, which is also a palindrome.

Let’s break the problem into two cases.

Case 1: A word is not a palindrome

Consider that a word is not a palindrome. For example, “ab” is not a palindrome. To include it in a palindromic sequence, we must pair it with its reverse, “ba”. Together, they will be part of the possible palindrome.

Note that when a word such as “ab” appears multiple times in an input array, the maximum number of times it can be used in a palindrome is the minimum of its occurrences and the occurrences of its reverse. For example, if “ab” appears 10 times, and “ba” appears seven times, we can only use a maximum of seven occurrences of both words in a palindrome.

To understand this better, let’s look at the illustration below:

Case 2: A word is a palindrome

When a word is a palindrome, there are two possibilities to consider:

• If the word appears an even number of times, it can be placed in the middle or on the sides of the potential palindrome.

• If the word appears an odd number of times, its even occurrences can be used as in step 1, and the single odd occurrence can be placed in the middle of the potential palindrome. A word that appears in the middle of a palindrome is called a central word.

It’s important to note that every word in a palindrome, except for the central word, has a pair. Without a central word, there will be an even number of words that concatenate to make a palindrome. With a central word, the number of words will be odd. Since there can be only one central word, there will be only one palindrome word that occurs an odd number of times in the final palindrome.

Consider the following two examples:

• There are two occurrences of “aa”, four occurrences of “xx”, and three occurrences of “cc”. All these words can be included in the final palindrome, making a total of $2 + 4 + 3 = 9$ ...