Title Description

$\text{Byteasar}$ bought his son $\text{Bytie}$ a set of blocks numbered from to and arranged them in a row in a certain order. $\text{Bytie}$'s goal is to rearrange the blocks so that they are ordered naturally, from the smallest number to the largest. However, the only moves $\text{Bytie}$ is allowed to make are: putting the last block at the very beginning (move $a$), and putting the third block at the very beginning (move $b$). Help $\text{Bytie}$ by writing a program that tells whether a given arrangement of blocks can be properly reordered, and tells the right sequence of moves if it is.

Input format

In the first line of the standard input there is a single integer $N$. In the second line there are integers from the range to , separated by single spaces. No number appears twice, and thus they represent the initial arrangement of the blocks. .

Output format

Sample

4 
1 3 2 4

4 
3a 2b 2a 2b

7 
1 3 2 4 5 6 7

NIE DA SIE

3 
1 2 3

0

Data scope and agreement

For $100\%$ of the data:$1\le N\le 2000,m\le N^2$.