Bouncing Lights

Being in the CodeChef College Chapter team, Chef thought of putting up a problem about palindromes. But he is unable to create a solution for it and asks for your help. You will be given a string $s$. You have to find the longest palindrome which can be formed by elimination of consecutive letters from between. i.e. you need to delete characters from index $i$ to $j$ where $j \geq i$, $i \