Problem:
Score : 300 points

Problem Statement

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.

Constraints

1 \leq N \leq 2 \times 10^5

1 \leq A_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the minimum possible sadness of Snuke.

Sample Input 1

5
2 2 3 5 5

Sample Output 1

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.

Sample Input 2

9
1 2 3 4 5 6 7 8 9

Sample Output 2

0

Sample Input 3

6
6 5 4 3 2 1

Sample Output 3

18

Sample Input 4

7
1 1 1 1 2 3 4

Sample Output 4

6

Solution in Rust (1.42.0) (judge verdict: Wrong Answer)

use proconio::input;
 
fn main() {
  input! {
    n: usize,
    mut vals: [isize;n]
  }
  
  let mut total = 0;
  for i in 1..=n {
    vals[i-1] = vals[i-1] - (i as isize);
    total += vals[i-1];
  }
  
  let v = total / (n as isize);
  let mut min = isize::max_value();
  for v in [v-1, v, v+1].into_iter() {
    let mut temp = 0;
    for i in 0..n {
      temp += (vals[i] - v).abs();
    }
    min = std::cmp::min(min, temp);
  }
  
  println!("{}", min);
}