UVa 524 Prime ring Problem: Number theory &dfs

524-prime Ring Problem

Time limit:3.000 seconds

http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=465

A ring are composed of n (even number) circles as shown in diagram. Put natural numbers to each circle separately, and the sum of numbers in two adjacent circles be a should E.

Note: the number of the circle should always is 1.

Input

N (0 < n <= 16)

Output

The output format is shown as sample below. Each row represents a series of the circle numbers into the ring beginning from 1 clockwisely and anticlockwisely. The order of numbers must satisfy the above requirements.

You are 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 The 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