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: Accepted)

#![allow(non_snake_case)]
use proconio::input;
// use std::collections::HashMap;

fn sadness(As: &[i64], N: usize, b: i64) -> i64 {
    let mut ans: i64 = 0;

    for i in 0..N {
        let pInd = (i + 1) as i64;
        ans += (As[i] - (b + pInd)).abs()
    }

    return ans;
}

fn main() {
    input! {
        N: usize,
        As: [i64; N],
    }

    // 答えを見た
    // 平均かと思っていたけど中央値だった…

    let mut Bs: Vec<i64> = As.iter()
        .enumerate()
        .map(|(ind, a)| a - ind as i64 - 1)
        .collect();
    Bs.sort();

    if N % 2 == 0 {
        let b1 = Bs[N / 2 - 1];
        let b2 = Bs[N / 2];
        let ans1 = sadness(As.as_slice(), N, b1);
        let ans2 = sadness(As.as_slice(), N, b2);

        let ans = std::cmp::min(ans1, ans2);
        println!("{}", ans);
    } else {
        let b = Bs[(N - 1) / 2];
        let ans = sadness(As.as_slice(), N, b);
        println!("{}", ans);
    };



}