Mouse Peter is passionate about playing the piano. He chooses increasingly longer and more demanding pieces to play which he then practices for hours. Of special importance when successfully playing a piece is an impeccable fingering.

For the sake of simplicity we will consider a piece that consist only of one note at a time and that can be played with just the right hand. Only the white keys of the keyboard are used. These white keys are enumerated from left to right from 1 to 50 (7 octaves).

We define a 'fingering' as follows: Beside each note, Peter indicates with which finger he plays that note by writing down a number from the set ${1,2,3,4,5}$.

- Thumb
- Index finger
- Middle Finger
- Ring finger
- Little finger

Now, Peter would like to find the most elegant fingering for his piece. A fingering is considered elegant if it can be played with as little movements of the hand as possible. In order to determine a fingering's elegance, he uses following simple method:

A note earns one point of elegance in the following cases:

- The note is the first one of the piece.
- Or the difference between the numbers of the current and the previous note is equal to the difference between the numbers of the current and previous finger. Mathematically: For keys $k_i$ and $k_{i+1}$ fingers $f_i$ and $f_{i+1}$ the following equation must hold: $k_i - k_{i+1} = f_i - f_{i+1}$. Intuitively this means that Peter can place his hand such that there is one finger per key while playing the $i$-th and $i+1$-th note.

In all other cases the note earns no point of elegance.

Find a fingering which maximizes the points of elegance.

The input consists of two lines. The first line contains an integer $N$, the number of notes in the piece. The second line contains $N$ integers $k_i$ ($1 \leq t_i \leq 50$), the keys for notes of the piece.

The output should contain two lines. In the first line, output the optimal number of points of elegance. In the second line, output $N$ numbers $f_i$ ($1 \leq f_i \leq 5$), separated by spaces, which describe an optimal fingering. If multiple solutions exist, output any of them.

- For test cases worth 40% of all points, it holds that $1 \le N \le 10$.
- For test cases worth 60% of all points, it holds that $1 \le N \le 1\,000$.
- For test cases worth 100% of all points, it holds that $1 \le N \le 1\,000\,000$.

Input | Output | |

27 5 6 7 8 9 9 10 10 10 10 9 10 10 10 10 9 8 8 8 8 7 7 6 6 6 6 5 |
25 1 2 3 4 5 5 5 5 5 5 4 5 5 5 5 4 3 3 3 3 2 2 1 1 1 1 1 |

Input | Output | |

28 5 8 5 3 5 8 8 8 10 9 8 7 8 9 5 8 5 3 1 5 5 6 10 9 8 7 6 5 |
22 1 4 1 1 3 2 2 2 4 3 2 1 2 3 1 4 1 3 1 5 5 1 5 4 3 2 1 1 |

1) The notation C'=3 stands for the note number of the middle C. It simply helps you if you want to play the song yourself, but is not relevant for the task itself.