Description

A ring is composed of n (even number) circles as shown in diagram. Put natural numbers 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 <= 16)

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.

You are to write a program that completes above process.

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 2

解题思路：用回溯法按照深度优先的顺序在遍历解答树，暴力枚举输入的n个数中相加可能是素数的数放入数组中标记，再用一个数组判断这个数字是否用过（即出现过），需注意的是最后一个数要与第一个数的和要也为素数。

程序代码链接：http://paste.ubuntu.com/11953276/