_{This problem is a programming version of Problem 55 from projecteuler.net}

If we take , reverse and add, , which is palindromic.

Not all numbers produce palindromes so quickly. For example,

That is, took three iterations to arrive at a palindrome.

Although no one has proved it yet, it is thought that some numbers, like , never produce a palindrome. A number that never forms a palindrome through the reverse and add process is called a Lychrel number. Due to the theoretical nature of these numbers, and for the purpose of this problem, we shall assume that a number is Lychrel until proven otherwise. In addition you are given that for every number below , it will either
(i) become a palindrome in less than iterations, or,
(ii) no one, with all the computing power that exists, has managed so far to map it to a palindrome.

Now we see that a lot of numbers converge to the same palindrome, for example all converge to 121, a total of 18 numbers.

Note: For this problem we have assumed palindrome numbers like to be non-lychrel in iteration.

Given , find the palindrome to which maximum numbers converge. Print the palindrome and the count.