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: Wrong Answer)

import scala.io.{StdIn => in}
import scala.collection.{mutable => mu}

object Main extends App {
  val n = in.readInt
  val a = in.readLine.split(" ").map(_.toInt)

  val map = mu.HashMap.empty[Int, Int]
  val maxCnt = (0 until n)./:(0) { (acc, i) =>
    val c = a(i) - (i+1)
    val v = map.getOrElse(c, 0) + 1
    map(c) = v
    if(acc < v) v else acc
  }

  val b = map.filter(_._2 == maxCnt).minBy(_._1.abs)._1.toLong

  val ans = a./:(0L, 1L){ case ((acc, idx), ai) =>
    (acc + (ai - (b + idx)).abs, idx + 1L)
  }._1

  println(ans)
}