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 java.util.Scanner

object Main {
  def main(args: Array[String]): Unit = println(solve(new Scanner(System.in)))

  def solve(in: String): String = solve(new Scanner(in))

  def solve(sc: Scanner): String = {
    val N = sc.nextInt
    val A = Array.fill(N)(sc.nextInt)
    val As = A.zipWithIndex.map { case (a, i) => a - (i + 1) }.sorted

    println(As.mkString(","))
    if (N % 2 == 1) {
      val b = As(N / 2)
      As.map(_ - b).sum.toString
    } else {
      val b1 = As(N / 2 - 1)
      val b2 = As(N / 2)
      val b3 = (b2 + b1) / 2
      Array(
        As.map(a => (a - b1).abs).sum,
        As.map(a => (a - b2).abs).sum,
        As.map(a => (a - b3).abs).sum
      ).min.toString
    }
  }
}