Snuke has an integer sequence $A$ of length $N$.

He will freely choose an integer $b$. Here, he will get sad if $A_i$ and $b+i$ are far from each other. More specifically, the _sadness_ of Snuke is calculated as follows:

-   $abs(A_1 - (b+1)) + abs(A_2 - (b+2)) + ... + abs(A_N - (b+N))$

Here, $abs(x)$ is a function that returns the absolute value of $x$.

Find the minimum possible sadness of Snuke.

Input is given from Standard Input in the following format:

```
$N$
$A_1$ $A_2$ $...$ $A_N$
```

Print the minimum possible sadness of Snuke.

-   $1 \leq N \leq 2 \times 10^5$
-   $1 \leq A_i \leq 10^9$
-   All values in input are integers.

2

If we choose b=0, the sadness of Snuke would be abs(2−(0+1))+abs(2−(0+2))+abs(3−(0+3))+abs(5−(0+4))+abs(5−(0+5))=2. Any choice of b does not make the sadness of Snuke less than 2, so the answer is 2.