Alice has an even number of N beads, and each bead has a number from 1 to N painted on it. She would like to make a necklace out of all the beads, with a special requirement: any two beads next to each other on the necklace must sum to a prime number. Alice needs your help to calculate how many ways it is possible to do so.

For example:
N = 4
There are two possible ways to build the necklace. Note that the last bead connects to the first bead.
1 2 3 4
1 4 3 2
Note: The necklace should be unique. For example: 1 2 3 4 is the same as 2 3 4 1 and 3 4 1 2 and 4 1 2 3


Reverse and Add Function
The reverse and add function starts with a number, reverses its digits, and adds the reverse to the original. If the sum is not a palindrome, repeat this procedure until it does.

Write a program that takes number and gives the resulting palindrome (if one exists). If it took more than 1,000 iterations (additions) or yield a palindrome that is greater than 4,294,967,295, assume that no palindrome exist for the given number.