An array of elements can be rotated to the right by taking the last element and moving it to the front. For example, rotating to the right once results in .

An array is considered *rotational* if it can be rotated some number of times to the right, where , and result in the original array. For example, the array is considered *rotational*.

One *modification* of an array consists of increasing or decreasing an element's value by . Given an array , can you determine the **minimum** number of **modifications** needed in order to convert an array to a *rotational* array?

#### Input Specification

The first line will contain the integer , the number of elements.

The second line will contain integers, , the elements of the array.

#### Output Specification

Output the **minimum** number of modifications needed to convert to a *rotational* array.

#### Subtasks

For 3/15 of the points, .

For an additional 5/15 of the points, .

#### Sample Input

```
4
1 2 2 2
```

#### Sample Output

`1`

#### Explanation For Sample

We can increase the first element's value to , which transforms it into a *rotational* array. This is exactly one modification.

## Comments