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: Accepted)

import scala.io.StdIn

object Main extends App {

  def solv(pd: Long) = aind.foldLeft(0L)((acc, ai) => acc + scala.math.abs(ai._1 - (pd + ai._2 + 1)))

  val n = StdIn.readLine().toInt
  val a = StdIn.readLine().split(" ").map(_.toLong)
  val aind = a.zipWithIndex

  //val r = aind.map( ai => scala.math.abs(ai._1 - (ai._2 + 1)))
  val r = aind.map(ai => ai._1 - (ai._2 + 1))
  //println(r.mkString(" "))
  //val ds = r.distinct.sorted
  val ds = r.sorted
  //println(ds.mkString(" "))
  val c = ds.length
  val r1 = if (c % 2 == 0) {
    //println("s1 :" + solv(ds(c / 2 - 1)))
    //println("s2 :" + solv(ds(c / 2)))

    scala.math.min(solv(ds(c / 2 - 1)), solv(ds(c / 2)))
  } else {
    solv(ds(c / 2))
  }


  println(r1)

  //val mina = for(d <- ind) yield solv(pd)

  //println(mina.toList.mkString(" "))

  //println(mina.min)

}