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)

#![allow(unused_parens)]
#![allow(unused_imports)]
#![allow(non_upper_case_globals)]



#[allow(unused_macros)]
macro_rules! invec {
    ( $ t : ty ) => {{
        let mut s = String::new();
        match std::io::stdin().read_line(&mut s) {
            Ok(0) => Vec::<$t>::new(),
            Ok(n) => s
                .trim()
                .split_whitespace()
                .map(|s| s.parse::<$t>().unwrap())
                .collect::<Vec<$t>>(),
            Err(_) => Vec::<$t>::new(),
        }
    }};
}

#[allow(unused_macros)]
macro_rules! get {
      ($t:ty) => {
          {
              let mut line: String = String::new();
              std::io::stdin().read_line(&mut line).unwrap();
              line.trim().parse::<$t>().unwrap()
          }
      };
      ($($t:ty),*) => {
          {
              let mut line: String = String::new();
              std::io::stdin().read_line(&mut line).unwrap();
              let mut iter = line.split_whitespace();
              (
                  $(iter.next().unwrap().parse::<$t>().unwrap(),)*
              )
          }
      };
      ($t:ty; $n:expr) => {
          (0..$n).map(|_|
              get!($t)
          ).collect::<Vec<_>>()
      };
      ($($t:ty),*; $n:expr) => {
          (0..$n).map(|_|
              get!($($t),*)
          ).collect::<Vec<_>>()
      };
      ($t:ty ;;) => {
          {
              let mut line: String = String::new();
              std::io::stdin().read_line(&mut line).unwrap();
              line.split_whitespace()
                  .map(|t| t.parse::<$t>().unwrap())
                  .collect::<Vec<_>>()
          }
      };
      ($t:ty ;; $n:expr) => {
          (0..$n).map(|_| get!($t ;;)).collect::<Vec<_>>()
      };
}

#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let mut s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($next:expr, [$t:tt]) => {
        {
            let len = read_value!($next, usize);
            (0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
        }
    };
    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}


 
#[cfg(debug_assertions)]
macro_rules! mydbg {
    //($arg:expr) => (dbg!($arg))
    //($arg:expr) => (println!("{:?}",$arg));
      ($($a:expr),*) => {
          eprintln!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
      }
}
 
 
#[cfg(not(debug_assertions))]
macro_rules! mydbg {
    ($($arg:expr),*) => {};
}



use std::cmp;
use std::collections::HashMap;


#[allow(dead_code)]
static INF_I64 :i64 = 9223372036854775807;
#[allow(dead_code)]
static INF_I32 : i32 = 2147483647;
#[allow(dead_code)]
static INF_USIZE : usize = 18446744073709551615;



fn main() {

    input! { 
       n: usize,
       a:[usize;n],
    }

    let mut ans = 1000000000000000;

    let mut b = vec![0;n];
    let mut s = 0_i64;
    for i in 0..n{
        s += a[i] as i64 - i as i64;
    }
    if s > 0 {
        let c = s as usize / n;
        s = 0;
        for i in 0..n{
            s += (a[i] as i64 - (i as i64 + c as i64)).abs();
        }
        let mut s2 = 0;
        for i in 0..n{
            s2 += (a[i] as i64 - (i as i64 + c as i64) +1 ).abs();
        }
        let mut s3 = 0;
        for i in 0..n{
            s3 += (a[i] as i64 - (i as i64 + c as i64) -1 ).abs();
        }

        
        ans = std::cmp::min(ans,s2);
        ans = std::cmp::min(ans,s);
        ans = std::cmp::min(ans,s3);

    }
    else {
        let c = s.abs() as usize / n;
        s = 0;
        for i in 0..n{
            s += (a[i] as i64 - (i as i64 - c as i64)).abs();
        }
        let mut s2 = 0;
        for i in 0..n{
            s2 += (a[i] as i64 - (i as i64 - c as i64) +1 ).abs();
        }
        let mut s3 = 0;
        for i in 0..n{
            s3 += (a[i] as i64 - (i as i64 - c as i64) -1 ).abs();
        }

        ans = std::cmp::min(ans,s2);
        ans = std::cmp::min(ans,s);
        ans = std::cmp::min(ans,s3);

    }

    
    
    println!("{}",ans);


}