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::collections::HashMap;
fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

fn read_vec2<T: std::str::FromStr>(n: u32) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}
fn main(){
    let n = read::<i32>();
    let mut v = read_vec::<i32>();
    let mut sub = v.clone();
    sub.sort();
    sub.dedup();
    let div = v.iter().enumerate().map(|x| (x.1 - (x.0 as i32)-1)).collect::<Vec<i32>>();
    let hash = div.iter().fold(HashMap::new(),|mut map,x| {
        let y  =map.get(&x).map(|i| i+1).unwrap_or(1);
        map.insert(x,y);
        map
    });
    let next = hash.clone();
    let checker = hash.iter().fold(0,|ans,(x,y)| *y);
    let b = if hash.into_iter().all(|(x,y)| y == checker){
        next.into_iter().fold(100000000000000,|ans,(x,y)| if ans > (*x).abs(){
            (*x).abs()
        }else {
            ans
        })
    } else{
        next.into_iter()
        .fold((0,0),|ans,(x,y)| if y > ans.1{
                (*x,y)
            }else {
                ans
        }).0
    };
    let ans = v.iter().enumerate().fold(0,|x,y| (x + (y.1 - (y.0 as i32)-1 - b).abs()));
    println!("{:?}",ans);
}