Find the median of <code>nums</code> after sorting it (if the length is even, we can select any number from the two in the middle). Let’s call it <code>m</code>.

Try the smallest palindromic number that is larger than or equal to <code>m</code> (if any) and the largest palindromic number that is smaller than or equal to <code>m</code> (if any). These two values are the candidate palindromic numbers for values of all indices.

We can use math constructions to construct the two palindromic numbers in <code>O(log(m) / 2)</code> time or we can do it using brute-force by starting from m and checking smaller and larger values in <code>O(sqrt(10^log(m)))</code>.

It is also possible to just generate all palindromic numbers using recursion in <code>O(sqrt(10⁹log(10⁹))</code>.