Given an array of $n$ integers $a_1, a_2, \dots, a_n$. In each step, you can increase or decrease any element by 1.Find the minimum number of steps required to transform the array into a strictly increasing sequence.
### Input
- The first line contains a positive integer $n$.
- The second line contains $n$ positive integers $a_1, a_2, \dots, a_n$.
### Output
- Print the minimum number of steps required.
### Constraints
- $1 \le n \le 100000$.
- $1 \le a_1, a_2, \dots, a_n \le 10^9$.
### Example
Input
```
6
6 5 4 3 1 2
```
Output
```
18
```