# Prime Ring Problem

Time Limit: 10 Seconds Memory Limit: 32768 KB

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 8

## Sample 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 2Submit

Source: Asia 1996, Shanghai (Mainland China)