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 (1.15.1) (judge verdict: Wrong Answer)

use std::io::{self, BufRead};
use std::cmp::min;

fn main() {
  let stdin = io::stdin();
  let mut lines = stdin.lock().lines();
  let _: usize = lines.next().unwrap().unwrap().parse().unwrap();
  let xs: Vec<i32> = lines.next().unwrap().unwrap().split(' ').map(|x| x.parse().unwrap()).collect();
  let a: i32 = xs.iter().enumerate().map(|(i, x)| x - i as i32).min().unwrap();
  let mut ds: Vec<i32> = xs.iter().enumerate().map(|(i, x)| x - i as i32 - a).collect();
  ds.sort();
  let mut ans: i32 = ds.iter().sum();
  let mut sum: i32 = ans;
  let mut b: i32 = ds[0];
  let mut i: usize = 0;
  while i < ds.len() {
    if b == ds[i] {
      i += 1;
    } else {
      sum = sum - (ds.len() - i) as i32 * (ds[i] - b) + i as i32 * (ds[i] - b);
      ans = min(ans, sum);
      b = ds[i];
    }
  }
  println!("{}", ans);
}