Block Rearrangement Challenge

Byteasar bought his son Bytie a set of blocks numbered from \(1\) to \(n\) and arranged them in a row in a certain order. Bytie's goal is to rearrange the blocks so that they are in natural order, from the smallest number to the largest.

The only moves allowed are:

• Move \(a\): Take the last block and put it at the very beginning.
• Move \(b\): Take the third block and put it at the very beginning.

Your task is to determine whether a given arrangement can be sorted using these moves, and if so, provide the sequence of moves.

If the blocks are already sorted, output 0 moves. If no sequence of moves can sort the blocks, output NO.

inputFormat

The input consists of two lines:

1. The first line contains a positive integer \(n\) representing the number of blocks.
2. The second line contains \(n\) space-separated integers representing the current order of the blocks.

outputFormat

If the blocks can be rearranged into natural order \(1, 2, \dots, n\) using the allowed moves, output the following:

1. On the first line, output YES.
2. On the second line, output an integer \(m\) representing the number of moves.
3. On the third line, output a string of length \(m\) consisting of characters a and b which denote the sequence of moves performed (in order from first to last move).

If the blocks cannot be sorted using the allowed moves, output a single line containing NO.

sample

3
1 2 3

YES
0