Prime Ring Problem

描述
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.


输入
n (0 < n < 20).
输出
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.
样例
样例输入 #1
6
8
样例输出 #1
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
来源
Asia 1996, Shanghai (Mainland China)
HDOJ-1016
题目来源:HDOJ-1016
时间限制:2000 MS
内存限制:32768 KB
Java 类名:Main
64 位整数占位符:%I64d