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)

#![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,
        mut As: [i64; N],
    }

    // Naive
    // let mut ans: i64 = i64::MAX;
    // for b in -1000..1001 {
    //     let sad = sadness(As.as_slice(), N, b);
    //     ans = std::cmp::min(ans, sad);
    // }

    // なんとなくAsの平均近辺にしたい気がするのは
    // なんでなんだぜ
    let avg: i64 = As.iter().sum::<i64>() as i64 / (N as i64);
    let mut ans: i64 = std::i64::MAX;
    for b in (avg - 10)..(avg + 11) {
        let sad = sadness(As.as_slice(), N, b);
        ans = std::cmp::min(ans, sad);
    }

    println!("{}", ans);
}