The Rotating Disk 

A neat puzzle consists of a circular track with n marbles numbered $1,\dots,n$. The marbles are arranged in a random order, and they can be moved around the track without altering their relative order. In one section of the track there is a rotating disk. The disk contains 4 marbles. The disk can be rotated by 180 degrees so that the inner order of the 4 marbles is reversed. Your mission, should you choose to accept it, is to write a program that will read the content of a puzzle and use the rotating disk to rearrange the marbles in natural order.

Input 

The following example will demonstrate a description of a puzzle and display of moves. The size of the track will vary from one data set to another.

Each data set will be a permutation of the integers $1,\dots,n$ on a single line.

Output 

In your output echo the initial track, followed by the rotations. Mark the four rotated disks by placing * as the boundary as shown below. You must not display moves around the whole track. In case there are no possiblity to put the disks in natural order, simply write the initial track and the statement: "It is not possible to rearrange these disks in natural order."

The outputs of two consecutive cases will be separated by a blank line.

Sample Input 

8 1 2 3 7 10 4 6 5 9
1 2 3 5 4
6 5 4 3 1 2

Sample Output: 

8 1 2 3 7 10 4 6 5 9
8 1 2 3 7 10 *9 5 6 4*
4 8 1 2 3 7 *6 5 9 10*
4 *3 2 1 8* 7 6 5 9 10
4 3 2 1 *5 6 7 8* 9 10
*1 2 3 4* 5 6 7 8 9 10

1 2 3 5 4
It is not possible to rearrange these disks in natural order.

6 5 4 3 1 2
*3 4 5 6* 1 2