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 Scala (2.11.7) (judge verdict: Time Limit Exceeded)

import java.util.Scanner
import scala.math.{abs, min}

object Main{
  def main(args: Array[String]): Unit = {
    val sc = new Scanner(System.in)
    val n = sc.nextInt
    val a = List.fill(n)(sc.nextInt)
    var b = List.empty[Int]
    (0 to a.size-1).foreach{ i =>
      b = b ::: List(a.apply(i)-(i+1))
    } 
    b = b.sorted
    val median = b.apply(n/2)
    var res = 0
    (0 to a.size-1).foreach{ i =>
      res = res + abs(a.apply(i)-(median+i+1))
    }
    println(res)
  }
}