Rinnosuke wants to type a paragraph $S$ that contains only the first $m$ characters in the alphabet. 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 a string $S$.
### Output
- Print the minimum tiredness.
### Constraints
- $1 \le n \le 10^5$.
- $1 \le m \le 20$.
### Example
Input:
```
6 3
aacabc
```
Output:
```
5
```
Note: She arranges the keyboard like this `bac`.
