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: Accepted)

use std::io;

fn read_line() -> String {
    let mut s: String = String::new();
    io::stdin().read_line(&mut s).unwrap();
    return s.trim().to_string();
}

fn read_nums() -> Vec<i32> {
    return read_line().split(' ').map(|x| x.parse::<i32>().unwrap()).collect();
}

fn read_num() -> i32 {
    return read_line().parse::<i32>().unwrap();
}

fn calc(a: &Vec<i32>, b: i64) -> i64 {
    let mut res: i64 = 0;
    for (i, &aa) in a.iter().enumerate() {
        res += ((aa as i64) - (b + i as i64)).abs();
    }
    return res;
}

fn main() {
    let _n = read_num();
    let a = read_nums();

    let mut low: i64 = -2000000000;
    let mut high: i64 = 2000000000;

    for _ in 0..100 {
        let diff = high - low;
        let m1: i64 = low + diff / 3;
        let m2: i64 = low + diff * 2 / 3;

        let v1 = calc(&a, m1);
        let v2 = calc(&a, m2);

        // println!("{} {} : {} {} : {} {}", low, high, m1, m2, v1, v2);

        if v1 > v2 {
            low = m1 + 1;
        } else if v1 < v2 {
            high = m2 - 1;
        } else {
            if low + 1 == high {
                break;
            } else {
                low = m1;
                high = m2;
            }
        }
    }

    println!("{}", std::cmp::min(calc(&a, low), calc(&a, high)));
}