### Prime Ring Problem

Time Limit: 2000 ms
Memory Limit: 65535 KiB

#### Problem Description

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.

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.

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

#### Hint

#### Source

Asia 1996, Shanghai (Mainland China)