Prime Ring Problem

     A ring is compose of n circles as shown in diagram. Put natural number 1, 2, ..., n into each circle separately, and the sum of numbers in two adjacent circles should be a prime.    Note: the number of first circle should always be 1.Input    n (0 < n < 20).Output    The output format is shown as sample below. Each row represents a series of circle numbers in the ring beginning from 1 clockwisely and anticlockwisely. The order of numbers must satisfy the above requirements. Print solutions in lexicographical order.    You are to write a program that completes above process.    Print a blank line after each case.Sample Input    6    8Sample Output    Case 1:    1 4 3 2 5 6    1 6 5 2 3 4    Case 2:    1 2 3 8 5 6 7 4    1 2 5 8 3 4 7 6    1 4 7 6 5 8 3 2    1 6 7 4 3 8 5 2