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 2

Source:

**Asia 1996, Shanghai (Mainland China)**
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