2016-10-11

21:18:45

HDU 1016

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

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