The Ancient Tengu language consists of $m$ different characters, the $i^{th}$ character is denoted as $i$. Rinnosuke wants to type a paragraph $S$ of length $n$ in Acient Tengu language. Marisa wants to build a custom keyboard for him with $m$ keys arranged in a row.
The position of each character $c$ in the keyboard is denoted by $p_c$, and the tiredness of typing a paragraph $s$ of $n$ characters is given by the formula:
$$\sum_{i=1}^{n - 1} |p_{s_{i + 1}} - p_{s_i}|$$
Marisa wants to minimize the tiredness for Rinnosuke. Please help her determine the minimum tiredness!
### Input
- The first line contains 2 integers $n$ and $m$.
- The second line contains $n$ integers, denoting the paragraph $S$.
### Output
- On the first line, print the minimum tiredness.
- On the second line, print the order of the characters on the keyboard.
### Constraints
- $1 \le n \le 10^5$.
- $1 \le m \le 50$.
### Example
Input:
```
6 3
1 1 3 1 2 3
```
Output:
```
5
2 1 3
```
### Scoring
- All test cases are scored equally.
- Consider the jury's answer as $Y$ and your answer as $X$.
- If $X$ is less than or equal to $Y$, you receive a score of $100\%$ for test case.
- If $1 < \frac{X}{Y} \le 2$, your score for the test case is calculated as $(\frac{2X - Y}{X})^2\times 100 \%$.
- If $\frac{X}{Y} > 2$, you receive a score of $0\%$ for the test case.
