Description

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A ring is composed of n (even number) circles as shown in diagram. Put natural numbers $1, 2, \dots, n$ 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 <= 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/